Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,2,Mod(37,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.w (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.894324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 112.109 |
Dual form | 112.2.w.a.37.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | + | 1.36603i | 0.258819 | + | 0.965926i | ||||
\(3\) | −1.86603 | + | 0.500000i | −1.07735 | + | 0.288675i | −0.753510 | − | 0.657437i | \(-0.771641\pi\) |
−0.323840 | + | 0.946112i | \(0.604974\pi\) | |||||||
\(4\) | −1.73205 | + | 1.00000i | −0.866025 | + | 0.500000i | ||||
\(5\) | −3.23205 | − | 0.866025i | −1.44542 | − | 0.387298i | −0.550990 | − | 0.834512i | \(-0.685750\pi\) |
−0.894427 | + | 0.447214i | \(0.852416\pi\) | |||||||
\(6\) | −1.36603 | − | 2.36603i | −0.557678 | − | 0.965926i | ||||
\(7\) | 1.73205 | + | 2.00000i | 0.654654 | + | 0.755929i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | 0.633975 | − | 0.366025i | 0.211325 | − | 0.122008i | ||||
\(10\) | − | 4.73205i | − | 1.49641i | ||||||
\(11\) | 1.13397 | + | 4.23205i | 0.341906 | + | 1.27601i | 0.896185 | + | 0.443680i | \(0.146327\pi\) |
−0.554279 | + | 0.832331i | \(0.687006\pi\) | |||||||
\(12\) | 2.73205 | − | 2.73205i | 0.788675 | − | 0.788675i | ||||
\(13\) | 0.267949 | + | 0.267949i | 0.0743157 | + | 0.0743157i | 0.743288 | − | 0.668972i | \(-0.233265\pi\) |
−0.668972 | + | 0.743288i | \(0.733265\pi\) | |||||||
\(14\) | −2.09808 | + | 3.09808i | −0.560734 | + | 0.827996i | ||||
\(15\) | 6.46410 | 1.66902 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 0.232051 | − | 0.401924i | 0.0562806 | − | 0.0974808i | −0.836512 | − | 0.547948i | \(-0.815409\pi\) |
0.892793 | + | 0.450467i | \(0.148743\pi\) | |||||||
\(18\) | 0.732051 | + | 0.732051i | 0.172546 | + | 0.172546i | ||||
\(19\) | −1.13397 | + | 4.23205i | −0.260152 | + | 0.970899i | 0.705000 | + | 0.709207i | \(0.250947\pi\) |
−0.965152 | + | 0.261692i | \(0.915720\pi\) | |||||||
\(20\) | 6.46410 | − | 1.73205i | 1.44542 | − | 0.387298i | ||||
\(21\) | −4.23205 | − | 2.86603i | −0.923509 | − | 0.625418i | ||||
\(22\) | −5.36603 | + | 3.09808i | −1.14404 | + | 0.660512i | ||||
\(23\) | −2.13397 | + | 1.23205i | −0.444964 | + | 0.256900i | −0.705701 | − | 0.708510i | \(-0.749368\pi\) |
0.260737 | + | 0.965410i | \(0.416035\pi\) | |||||||
\(24\) | 4.73205 | + | 2.73205i | 0.965926 | + | 0.557678i | ||||
\(25\) | 5.36603 | + | 3.09808i | 1.07321 | + | 0.619615i | ||||
\(26\) | −0.267949 | + | 0.464102i | −0.0525492 | + | 0.0910178i | ||||
\(27\) | 3.09808 | − | 3.09808i | 0.596225 | − | 0.596225i | ||||
\(28\) | −5.00000 | − | 1.73205i | −0.944911 | − | 0.327327i | ||||
\(29\) | −3.73205 | − | 3.73205i | −0.693024 | − | 0.693024i | 0.269872 | − | 0.962896i | \(-0.413019\pi\) |
−0.962896 | + | 0.269872i | \(0.913019\pi\) | |||||||
\(30\) | 2.36603 | + | 8.83013i | 0.431975 | + | 1.61215i | ||||
\(31\) | −0.133975 | + | 0.232051i | −0.0240625 | + | 0.0416776i | −0.877806 | − | 0.479016i | \(-0.840993\pi\) |
0.853743 | + | 0.520694i | \(0.174327\pi\) | |||||||
\(32\) | 5.46410 | + | 1.46410i | 0.965926 | + | 0.258819i | ||||
\(33\) | −4.23205 | − | 7.33013i | −0.736705 | − | 1.27601i | ||||
\(34\) | 0.633975 | + | 0.169873i | 0.108726 | + | 0.0291330i | ||||
\(35\) | −3.86603 | − | 7.96410i | −0.653478 | − | 1.34618i | ||||
\(36\) | −0.732051 | + | 1.26795i | −0.122008 | + | 0.211325i | ||||
\(37\) | 10.6962 | + | 2.86603i | 1.75844 | + | 0.471172i | 0.986394 | − | 0.164399i | \(-0.0525685\pi\) |
0.772043 | + | 0.635571i | \(0.219235\pi\) | |||||||
\(38\) | −6.19615 | −1.00515 | ||||||||
\(39\) | −0.633975 | − | 0.366025i | −0.101517 | − | 0.0586110i | ||||
\(40\) | 4.73205 | + | 8.19615i | 0.748203 | + | 1.29593i | ||||
\(41\) | 8.92820i | 1.39435i | 0.716900 | + | 0.697176i | \(0.245560\pi\) | ||||
−0.716900 | + | 0.697176i | \(0.754440\pi\) | |||||||
\(42\) | 2.36603 | − | 6.83013i | 0.365086 | − | 1.05391i | ||||
\(43\) | −0.464102 | + | 0.464102i | −0.0707748 | + | 0.0707748i | −0.741608 | − | 0.670833i | \(-0.765937\pi\) |
0.670833 | + | 0.741608i | \(0.265937\pi\) | |||||||
\(44\) | −6.19615 | − | 6.19615i | −0.934105 | − | 0.934105i | ||||
\(45\) | −2.36603 | + | 0.633975i | −0.352706 | + | 0.0945074i | ||||
\(46\) | −2.46410 | − | 2.46410i | −0.363312 | − | 0.363312i | ||||
\(47\) | −3.86603 | − | 6.69615i | −0.563918 | − | 0.976734i | −0.997149 | − | 0.0754516i | \(-0.975960\pi\) |
0.433232 | − | 0.901283i | \(-0.357373\pi\) | |||||||
\(48\) | −2.00000 | + | 7.46410i | −0.288675 | + | 1.07735i | ||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | −2.26795 | + | 8.46410i | −0.320736 | + | 1.19700i | ||||
\(51\) | −0.232051 | + | 0.866025i | −0.0324936 | + | 0.121268i | ||||
\(52\) | −0.732051 | − | 0.196152i | −0.101517 | − | 0.0272014i | ||||
\(53\) | −2.96410 | − | 11.0622i | −0.407151 | − | 1.51951i | −0.800054 | − | 0.599927i | \(-0.795196\pi\) |
0.392904 | − | 0.919580i | \(-0.371471\pi\) | |||||||
\(54\) | 5.36603 | + | 3.09808i | 0.730224 | + | 0.421595i | ||||
\(55\) | − | 14.6603i | − | 1.97679i | ||||||
\(56\) | 0.535898 | − | 7.46410i | 0.0716124 | − | 0.997433i | ||||
\(57\) | − | 8.46410i | − | 1.12110i | ||||||
\(58\) | 3.73205 | − | 6.46410i | 0.490042 | − | 0.848778i | ||||
\(59\) | 2.66987 | + | 9.96410i | 0.347588 | + | 1.29722i | 0.889560 | + | 0.456819i | \(0.151011\pi\) |
−0.541972 | + | 0.840397i | \(0.682322\pi\) | |||||||
\(60\) | −11.1962 | + | 6.46410i | −1.44542 | + | 0.834512i | ||||
\(61\) | −0.0358984 | + | 0.133975i | −0.00459632 | + | 0.0171537i | −0.968186 | − | 0.250232i | \(-0.919493\pi\) |
0.963590 | + | 0.267386i | \(0.0861598\pi\) | |||||||
\(62\) | −0.366025 | − | 0.0980762i | −0.0464853 | − | 0.0124557i | ||||
\(63\) | 1.83013 | + | 0.633975i | 0.230574 | + | 0.0798733i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −0.633975 | − | 1.09808i | −0.0786349 | − | 0.136200i | ||||
\(66\) | 8.46410 | − | 8.46410i | 1.04186 | − | 1.04186i | ||||
\(67\) | −7.33013 | + | 1.96410i | −0.895518 | + | 0.239953i | −0.677090 | − | 0.735900i | \(-0.736759\pi\) |
−0.218427 | + | 0.975853i | \(0.570093\pi\) | |||||||
\(68\) | 0.928203i | 0.112561i | ||||||||
\(69\) | 3.36603 | − | 3.36603i | 0.405222 | − | 0.405222i | ||||
\(70\) | 9.46410 | − | 8.19615i | 1.13118 | − | 0.979628i | ||||
\(71\) | 7.46410i | 0.885826i | 0.896565 | + | 0.442913i | \(0.146055\pi\) | ||||
−0.896565 | + | 0.442913i | \(0.853945\pi\) | |||||||
\(72\) | −2.00000 | − | 0.535898i | −0.235702 | − | 0.0631562i | ||||
\(73\) | −2.76795 | − | 1.59808i | −0.323964 | − | 0.187041i | 0.329194 | − | 0.944262i | \(-0.393223\pi\) |
−0.653158 | + | 0.757222i | \(0.726556\pi\) | |||||||
\(74\) | 15.6603i | 1.82047i | ||||||||
\(75\) | −11.5622 | − | 3.09808i | −1.33509 | − | 0.357735i | ||||
\(76\) | −2.26795 | − | 8.46410i | −0.260152 | − | 0.970899i | ||||
\(77\) | −6.50000 | + | 9.59808i | −0.740744 | + | 1.09380i | ||||
\(78\) | 0.267949 | − | 1.00000i | 0.0303393 | − | 0.113228i | ||||
\(79\) | −0.330127 | − | 0.571797i | −0.0371422 | − | 0.0643322i | 0.846857 | − | 0.531821i | \(-0.178492\pi\) |
−0.883999 | + | 0.467489i | \(0.845159\pi\) | |||||||
\(80\) | −9.46410 | + | 9.46410i | −1.05812 | + | 1.05812i | ||||
\(81\) | −5.33013 | + | 9.23205i | −0.592236 | + | 1.02578i | ||||
\(82\) | −12.1962 | + | 3.26795i | −1.34684 | + | 0.360885i | ||||
\(83\) | 8.46410 | + | 8.46410i | 0.929056 | + | 0.929056i | 0.997645 | − | 0.0685891i | \(-0.0218498\pi\) |
−0.0685891 | + | 0.997645i | \(0.521850\pi\) | |||||||
\(84\) | 10.1962 | + | 0.732051i | 1.11249 | + | 0.0798733i | ||||
\(85\) | −1.09808 | + | 1.09808i | −0.119103 | + | 0.119103i | ||||
\(86\) | −0.803848 | − | 0.464102i | −0.0866811 | − | 0.0500454i | ||||
\(87\) | 8.83013 | + | 5.09808i | 0.946689 | + | 0.546571i | ||||
\(88\) | 6.19615 | − | 10.7321i | 0.660512 | − | 1.14404i | ||||
\(89\) | 4.50000 | − | 2.59808i | 0.476999 | − | 0.275396i | −0.242166 | − | 0.970235i | \(-0.577858\pi\) |
0.719165 | + | 0.694839i | \(0.244525\pi\) | |||||||
\(90\) | −1.73205 | − | 3.00000i | −0.182574 | − | 0.316228i | ||||
\(91\) | −0.0717968 | + | 1.00000i | −0.00752635 | + | 0.104828i | ||||
\(92\) | 2.46410 | − | 4.26795i | 0.256900 | − | 0.444964i | ||||
\(93\) | 0.133975 | − | 0.500000i | 0.0138925 | − | 0.0518476i | ||||
\(94\) | 7.73205 | − | 7.73205i | 0.797500 | − | 0.797500i | ||||
\(95\) | 7.33013 | − | 12.6962i | 0.752055 | − | 1.30260i | ||||
\(96\) | −10.9282 | −1.11536 | ||||||||
\(97\) | 10.9282 | 1.10959 | 0.554795 | − | 0.831987i | \(-0.312797\pi\) | ||||
0.554795 | + | 0.831987i | \(0.312797\pi\) | |||||||
\(98\) | −9.83013 | + | 1.16987i | −0.992993 | + | 0.118175i | ||||
\(99\) | 2.26795 | + | 2.26795i | 0.227937 | + | 0.227937i | ||||
\(100\) | −12.3923 | −1.23923 | ||||||||
\(101\) | 1.89230 | + | 7.06218i | 0.188291 | + | 0.702713i | 0.993902 | + | 0.110268i | \(0.0351708\pi\) |
−0.805611 | + | 0.592445i | \(0.798163\pi\) | |||||||
\(102\) | −1.26795 | −0.125546 | ||||||||
\(103\) | 0.401924 | − | 0.232051i | 0.0396027 | − | 0.0228646i | −0.480068 | − | 0.877231i | \(-0.659388\pi\) |
0.519671 | + | 0.854367i | \(0.326055\pi\) | |||||||
\(104\) | − | 1.07180i | − | 0.105098i | ||||||
\(105\) | 11.1962 | + | 12.9282i | 1.09263 | + | 1.26166i | ||||
\(106\) | 14.0263 | − | 8.09808i | 1.36235 | − | 0.786555i | ||||
\(107\) | 0.866025 | + | 0.232051i | 0.0837218 | + | 0.0224332i | 0.300437 | − | 0.953802i | \(-0.402868\pi\) |
−0.216715 | + | 0.976235i | \(0.569534\pi\) | |||||||
\(108\) | −2.26795 | + | 8.46410i | −0.218234 | + | 0.814459i | ||||
\(109\) | 14.4282 | − | 3.86603i | 1.38197 | − | 0.370298i | 0.510134 | − | 0.860095i | \(-0.329596\pi\) |
0.871837 | + | 0.489797i | \(0.162929\pi\) | |||||||
\(110\) | 20.0263 | − | 5.36603i | 1.90943 | − | 0.511630i | ||||
\(111\) | −21.3923 | −2.03047 | ||||||||
\(112\) | 10.3923 | − | 2.00000i | 0.981981 | − | 0.188982i | ||||
\(113\) | 5.46410 | 0.514019 | 0.257010 | − | 0.966409i | \(-0.417263\pi\) | ||||
0.257010 | + | 0.966409i | \(0.417263\pi\) | |||||||
\(114\) | 11.5622 | − | 3.09808i | 1.08290 | − | 0.290161i | ||||
\(115\) | 7.96410 | − | 2.13397i | 0.742656 | − | 0.198994i | ||||
\(116\) | 10.1962 | + | 2.73205i | 0.946689 | + | 0.253665i | ||||
\(117\) | 0.267949 | + | 0.0717968i | 0.0247719 | + | 0.00663761i | ||||
\(118\) | −12.6340 | + | 7.29423i | −1.16305 | + | 0.671488i | ||||
\(119\) | 1.20577 | − | 0.232051i | 0.110533 | − | 0.0212721i | ||||
\(120\) | −12.9282 | − | 12.9282i | −1.18018 | − | 1.18018i | ||||
\(121\) | −7.09808 | + | 4.09808i | −0.645280 | + | 0.372552i | ||||
\(122\) | −0.196152 | −0.0177588 | ||||||||
\(123\) | −4.46410 | − | 16.6603i | −0.402514 | − | 1.50220i | ||||
\(124\) | − | 0.535898i | − | 0.0481251i | ||||||
\(125\) | −2.83013 | − | 2.83013i | −0.253134 | − | 0.253134i | ||||
\(126\) | −0.196152 | + | 2.73205i | −0.0174746 | + | 0.243390i | ||||
\(127\) | 2.53590 | 0.225025 | 0.112512 | − | 0.993650i | \(-0.464110\pi\) | ||||
0.112512 | + | 0.993650i | \(0.464110\pi\) | |||||||
\(128\) | −10.9282 | + | 2.92820i | −0.965926 | + | 0.258819i | ||||
\(129\) | 0.633975 | − | 1.09808i | 0.0558184 | − | 0.0966802i | ||||
\(130\) | 1.26795 | − | 1.26795i | 0.111207 | − | 0.111207i | ||||
\(131\) | 2.40192 | − | 8.96410i | 0.209857 | − | 0.783197i | −0.778057 | − | 0.628194i | \(-0.783794\pi\) |
0.987914 | − | 0.155003i | \(-0.0495388\pi\) | |||||||
\(132\) | 14.6603 | + | 8.46410i | 1.27601 | + | 0.736705i | ||||
\(133\) | −10.4282 | + | 5.06218i | −0.904240 | + | 0.438946i | ||||
\(134\) | −5.36603 | − | 9.29423i | −0.463554 | − | 0.802899i | ||||
\(135\) | −12.6962 | + | 7.33013i | −1.09271 | + | 0.630877i | ||||
\(136\) | −1.26795 | + | 0.339746i | −0.108726 | + | 0.0291330i | ||||
\(137\) | −11.7679 | − | 6.79423i | −1.00540 | − | 0.580470i | −0.0955611 | − | 0.995424i | \(-0.530465\pi\) |
−0.909843 | + | 0.414953i | \(0.863798\pi\) | |||||||
\(138\) | 5.83013 | + | 3.36603i | 0.496293 | + | 0.286535i | ||||
\(139\) | 1.92820 | − | 1.92820i | 0.163548 | − | 0.163548i | −0.620588 | − | 0.784136i | \(-0.713106\pi\) |
0.784136 | + | 0.620588i | \(0.213106\pi\) | |||||||
\(140\) | 14.6603 | + | 9.92820i | 1.23902 | + | 0.839086i | ||||
\(141\) | 10.5622 | + | 10.5622i | 0.889496 | + | 0.889496i | ||||
\(142\) | −10.1962 | + | 2.73205i | −0.855642 | + | 0.229269i | ||||
\(143\) | −0.830127 | + | 1.43782i | −0.0694187 | + | 0.120237i | ||||
\(144\) | − | 2.92820i | − | 0.244017i | ||||||
\(145\) | 8.83013 | + | 15.2942i | 0.733302 | + | 1.27012i | ||||
\(146\) | 1.16987 | − | 4.36603i | 0.0968194 | − | 0.361335i | ||||
\(147\) | −1.59808 | − | 13.4282i | −0.131807 | − | 1.10754i | ||||
\(148\) | −21.3923 | + | 5.73205i | −1.75844 | + | 0.471172i | ||||
\(149\) | 8.96410 | + | 2.40192i | 0.734368 | + | 0.196773i | 0.606573 | − | 0.795027i | \(-0.292544\pi\) |
0.127794 | + | 0.991801i | \(0.459210\pi\) | |||||||
\(150\) | − | 16.9282i | − | 1.38218i | ||||||
\(151\) | −8.13397 | − | 4.69615i | −0.661933 | − | 0.382167i | 0.131080 | − | 0.991372i | \(-0.458156\pi\) |
−0.793013 | + | 0.609204i | \(0.791489\pi\) | |||||||
\(152\) | 10.7321 | − | 6.19615i | 0.870484 | − | 0.502574i | ||||
\(153\) | − | 0.339746i | − | 0.0274668i | ||||||
\(154\) | −15.4904 | − | 5.36603i | −1.24825 | − | 0.432407i | ||||
\(155\) | 0.633975 | − | 0.633975i | 0.0509221 | − | 0.0509221i | ||||
\(156\) | 1.46410 | 0.117222 | ||||||||
\(157\) | −15.8923 | + | 4.25833i | −1.26834 | + | 0.339852i | −0.829396 | − | 0.558661i | \(-0.811315\pi\) |
−0.438948 | + | 0.898513i | \(0.644649\pi\) | |||||||
\(158\) | 0.660254 | − | 0.660254i | 0.0525270 | − | 0.0525270i | ||||
\(159\) | 11.0622 | + | 19.1603i | 0.877288 | + | 1.51951i | ||||
\(160\) | −16.3923 | − | 9.46410i | −1.29593 | − | 0.748203i | ||||
\(161\) | −6.16025 | − | 2.13397i | −0.485496 | − | 0.168181i | ||||
\(162\) | −14.5622 | − | 3.90192i | −1.14411 | − | 0.306564i | ||||
\(163\) | 0.0621778 | − | 0.232051i | 0.00487014 | − | 0.0181756i | −0.963448 | − | 0.267895i | \(-0.913672\pi\) |
0.968318 | + | 0.249720i | \(0.0803385\pi\) | |||||||
\(164\) | −8.92820 | − | 15.4641i | −0.697176 | − | 1.20754i | ||||
\(165\) | 7.33013 | + | 27.3564i | 0.570650 | + | 2.12969i | ||||
\(166\) | −8.46410 | + | 14.6603i | −0.656942 | + | 1.13786i | ||||
\(167\) | 5.85641i | 0.453182i | 0.973990 | + | 0.226591i | \(0.0727581\pi\) | ||||
−0.973990 | + | 0.226591i | \(0.927242\pi\) | |||||||
\(168\) | 2.73205 | + | 14.1962i | 0.210782 | + | 1.09526i | ||||
\(169\) | − | 12.8564i | − | 0.988954i | ||||||
\(170\) | −1.90192 | − | 1.09808i | −0.145871 | − | 0.0842186i | ||||
\(171\) | 0.830127 | + | 3.09808i | 0.0634814 | + | 0.236916i | ||||
\(172\) | 0.339746 | − | 1.26795i | 0.0259054 | − | 0.0966802i | ||||
\(173\) | 1.23205 | − | 4.59808i | 0.0936711 | − | 0.349585i | −0.903144 | − | 0.429339i | \(-0.858747\pi\) |
0.996815 | + | 0.0797535i | \(0.0254133\pi\) | |||||||
\(174\) | −3.73205 | + | 13.9282i | −0.282926 | + | 1.05589i | ||||
\(175\) | 3.09808 | + | 16.0981i | 0.234193 | + | 1.21690i | ||||
\(176\) | 16.9282 | + | 4.53590i | 1.27601 | + | 0.341906i | ||||
\(177\) | −9.96410 | − | 17.2583i | −0.748948 | − | 1.29722i | ||||
\(178\) | 5.19615 | + | 5.19615i | 0.389468 | + | 0.389468i | ||||
\(179\) | −7.59808 | + | 2.03590i | −0.567907 | + | 0.152170i | −0.531336 | − | 0.847161i | \(-0.678310\pi\) |
−0.0365704 | + | 0.999331i | \(0.511643\pi\) | |||||||
\(180\) | 3.46410 | − | 3.46410i | 0.258199 | − | 0.258199i | ||||
\(181\) | −7.39230 | + | 7.39230i | −0.549466 | + | 0.549466i | −0.926286 | − | 0.376821i | \(-0.877017\pi\) |
0.376821 | + | 0.926286i | \(0.377017\pi\) | |||||||
\(182\) | −1.39230 | + | 0.267949i | −0.103205 | + | 0.0198617i | ||||
\(183\) | − | 0.267949i | − | 0.0198074i | ||||||
\(184\) | 6.73205 | + | 1.80385i | 0.496293 | + | 0.132981i | ||||
\(185\) | −32.0885 | − | 18.5263i | −2.35919 | − | 1.36208i | ||||
\(186\) | 0.732051 | 0.0536766 | ||||||||
\(187\) | 1.96410 | + | 0.526279i | 0.143629 | + | 0.0384854i | ||||
\(188\) | 13.3923 | + | 7.73205i | 0.976734 | + | 0.563918i | ||||
\(189\) | 11.5622 | + | 0.830127i | 0.841025 | + | 0.0603829i | ||||
\(190\) | 20.0263 | + | 5.36603i | 1.45286 | + | 0.389292i | ||||
\(191\) | 4.33013 | + | 7.50000i | 0.313317 | + | 0.542681i | 0.979078 | − | 0.203484i | \(-0.0652264\pi\) |
−0.665761 | + | 0.746165i | \(0.731893\pi\) | |||||||
\(192\) | −4.00000 | − | 14.9282i | −0.288675 | − | 1.07735i | ||||
\(193\) | 11.5000 | − | 19.9186i | 0.827788 | − | 1.43377i | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) |
0.899770 | − | 0.436365i | \(-0.143734\pi\) | |||||||
\(194\) | 4.00000 | + | 14.9282i | 0.287183 | + | 1.07178i | ||||
\(195\) | 1.73205 | + | 1.73205i | 0.124035 | + | 0.124035i | ||||
\(196\) | −5.19615 | − | 13.0000i | −0.371154 | − | 0.928571i | ||||
\(197\) | 0.660254 | − | 0.660254i | 0.0470412 | − | 0.0470412i | −0.683195 | − | 0.730236i | \(-0.739410\pi\) |
0.730236 | + | 0.683195i | \(0.239410\pi\) | |||||||
\(198\) | −2.26795 | + | 3.92820i | −0.161176 | + | 0.279165i | ||||
\(199\) | 1.66987 | + | 0.964102i | 0.118374 | + | 0.0683434i | 0.558018 | − | 0.829829i | \(-0.311562\pi\) |
−0.439644 | + | 0.898172i | \(0.644895\pi\) | |||||||
\(200\) | −4.53590 | − | 16.9282i | −0.320736 | − | 1.19700i | ||||
\(201\) | 12.6962 | − | 7.33013i | 0.895518 | − | 0.517027i | ||||
\(202\) | −8.95448 | + | 5.16987i | −0.630035 | + | 0.363751i | ||||
\(203\) | 1.00000 | − | 13.9282i | 0.0701862 | − | 0.977568i | ||||
\(204\) | −0.464102 | − | 1.73205i | −0.0324936 | − | 0.121268i | ||||
\(205\) | 7.73205 | − | 28.8564i | 0.540030 | − | 2.01542i | ||||
\(206\) | 0.464102 | + | 0.464102i | 0.0323355 | + | 0.0323355i | ||||
\(207\) | −0.901924 | + | 1.56218i | −0.0626880 | + | 0.108579i | ||||
\(208\) | 1.46410 | − | 0.392305i | 0.101517 | − | 0.0272014i | ||||
\(209\) | −19.1962 | −1.32783 | ||||||||
\(210\) | −13.5622 | + | 20.0263i | −0.935879 | + | 1.38194i | ||||
\(211\) | −2.07180 | − | 2.07180i | −0.142628 | − | 0.142628i | 0.632187 | − | 0.774816i | \(-0.282157\pi\) |
−0.774816 | + | 0.632187i | \(0.782157\pi\) | |||||||
\(212\) | 16.1962 | + | 16.1962i | 1.11236 | + | 1.11236i | ||||
\(213\) | −3.73205 | − | 13.9282i | −0.255716 | − | 0.954345i | ||||
\(214\) | 1.26795i | 0.0866752i | ||||||||
\(215\) | 1.90192 | − | 1.09808i | 0.129710 | − | 0.0748882i | ||||
\(216\) | −12.3923 | −0.843190 | ||||||||
\(217\) | −0.696152 | + | 0.133975i | −0.0472579 | + | 0.00909479i | ||||
\(218\) | 10.5622 | + | 18.2942i | 0.715361 | + | 1.23904i | ||||
\(219\) | 5.96410 | + | 1.59808i | 0.403017 | + | 0.107988i | ||||
\(220\) | 14.6603 | + | 25.3923i | 0.988394 | + | 1.71195i | ||||
\(221\) | 0.169873 | − | 0.0455173i | 0.0114269 | − | 0.00306183i | ||||
\(222\) | −7.83013 | − | 29.2224i | −0.525524 | − | 1.96128i | ||||
\(223\) | −17.8564 | −1.19575 | −0.597877 | − | 0.801588i | \(-0.703989\pi\) | ||||
−0.597877 | + | 0.801588i | \(0.703989\pi\) | |||||||
\(224\) | 6.53590 | + | 13.4641i | 0.436698 | + | 0.899608i | ||||
\(225\) | 4.53590 | 0.302393 | ||||||||
\(226\) | 2.00000 | + | 7.46410i | 0.133038 | + | 0.496505i | ||||
\(227\) | 22.9904 | − | 6.16025i | 1.52593 | − | 0.408870i | 0.604238 | − | 0.796804i | \(-0.293478\pi\) |
0.921687 | + | 0.387934i | \(0.126811\pi\) | |||||||
\(228\) | 8.46410 | + | 14.6603i | 0.560549 | + | 0.970899i | ||||
\(229\) | −17.4282 | − | 4.66987i | −1.15169 | − | 0.308594i | −0.368047 | − | 0.929807i | \(-0.619973\pi\) |
−0.783641 | + | 0.621213i | \(0.786640\pi\) | |||||||
\(230\) | 5.83013 | + | 10.0981i | 0.384427 | + | 0.665847i | ||||
\(231\) | 7.33013 | − | 21.1603i | 0.482287 | − | 1.39224i | ||||
\(232\) | 14.9282i | 0.980085i | ||||||||
\(233\) | 9.69615 | − | 5.59808i | 0.635216 | − | 0.366742i | −0.147553 | − | 0.989054i | \(-0.547140\pi\) |
0.782769 | + | 0.622312i | \(0.213806\pi\) | |||||||
\(234\) | 0.392305i | 0.0256458i | ||||||||
\(235\) | 6.69615 | + | 24.9904i | 0.436809 | + | 1.63019i | ||||
\(236\) | −14.5885 | − | 14.5885i | −0.949628 | − | 0.949628i | ||||
\(237\) | 0.901924 | + | 0.901924i | 0.0585862 | + | 0.0585862i | ||||
\(238\) | 0.758330 | + | 1.56218i | 0.0491552 | + | 0.101261i | ||||
\(239\) | −15.4641 | −1.00029 | −0.500145 | − | 0.865942i | \(-0.666720\pi\) | ||||
−0.500145 | + | 0.865942i | \(0.666720\pi\) | |||||||
\(240\) | 12.9282 | − | 22.3923i | 0.834512 | − | 1.44542i | ||||
\(241\) | −0.0358984 | + | 0.0621778i | −0.00231242 | + | 0.00400523i | −0.867179 | − | 0.497996i | \(-0.834069\pi\) |
0.864867 | + | 0.502001i | \(0.167403\pi\) | |||||||
\(242\) | −8.19615 | − | 8.19615i | −0.526869 | − | 0.526869i | ||||
\(243\) | 1.92820 | − | 7.19615i | 0.123694 | − | 0.461633i | ||||
\(244\) | −0.0717968 | − | 0.267949i | −0.00459632 | − | 0.0171537i | ||||
\(245\) | 9.23205 | − | 21.5263i | 0.589814 | − | 1.37526i | ||||
\(246\) | 21.1244 | − | 12.1962i | 1.34684 | − | 0.777598i | ||||
\(247\) | −1.43782 | + | 0.830127i | −0.0914864 | + | 0.0528197i | ||||
\(248\) | 0.732051 | − | 0.196152i | 0.0464853 | − | 0.0124557i | ||||
\(249\) | −20.0263 | − | 11.5622i | −1.26911 | − | 0.732723i | ||||
\(250\) | 2.83013 | − | 4.90192i | 0.178993 | − | 0.310025i | ||||
\(251\) | 13.5885 | − | 13.5885i | 0.857696 | − | 0.857696i | −0.133370 | − | 0.991066i | \(-0.542580\pi\) |
0.991066 | + | 0.133370i | \(0.0425800\pi\) | |||||||
\(252\) | −3.80385 | + | 0.732051i | −0.239620 | + | 0.0461149i | ||||
\(253\) | −7.63397 | − | 7.63397i | −0.479944 | − | 0.479944i | ||||
\(254\) | 0.928203 | + | 3.46410i | 0.0582407 | + | 0.217357i | ||||
\(255\) | 1.50000 | − | 2.59808i | 0.0939336 | − | 0.162698i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −0.696152 | − | 1.20577i | −0.0434248 | − | 0.0752140i | 0.843496 | − | 0.537135i | \(-0.180494\pi\) |
−0.886921 | + | 0.461921i | \(0.847160\pi\) | |||||||
\(258\) | 1.73205 | + | 0.464102i | 0.107833 | + | 0.0288937i | ||||
\(259\) | 12.7942 | + | 26.3564i | 0.794995 | + | 1.63771i | ||||
\(260\) | 2.19615 | + | 1.26795i | 0.136200 | + | 0.0786349i | ||||
\(261\) | −3.73205 | − | 1.00000i | −0.231008 | − | 0.0618984i | ||||
\(262\) | 13.1244 | 0.810825 | ||||||||
\(263\) | 21.9904 | + | 12.6962i | 1.35598 | + | 0.782878i | 0.989080 | − | 0.147380i | \(-0.0470841\pi\) |
0.366905 | + | 0.930258i | \(0.380417\pi\) | |||||||
\(264\) | −6.19615 | + | 23.1244i | −0.381347 | + | 1.42321i | ||||
\(265\) | 38.3205i | 2.35401i | ||||||||
\(266\) | −10.7321 | − | 12.3923i | −0.658024 | − | 0.759821i | ||||
\(267\) | −7.09808 | + | 7.09808i | −0.434395 | + | 0.434395i | ||||
\(268\) | 10.7321 | − | 10.7321i | 0.655564 | − | 0.655564i | ||||
\(269\) | 21.6244 | − | 5.79423i | 1.31846 | − | 0.353280i | 0.470059 | − | 0.882635i | \(-0.344232\pi\) |
0.848401 | + | 0.529354i | \(0.177566\pi\) | |||||||
\(270\) | −14.6603 | − | 14.6603i | −0.892195 | − | 0.892195i | ||||
\(271\) | 6.06218 | + | 10.5000i | 0.368251 | + | 0.637830i | 0.989292 | − | 0.145948i | \(-0.0466233\pi\) |
−0.621041 | + | 0.783778i | \(0.713290\pi\) | |||||||
\(272\) | −0.928203 | − | 1.60770i | −0.0562806 | − | 0.0974808i | ||||
\(273\) | −0.366025 | − | 1.90192i | −0.0221529 | − | 0.115110i | ||||
\(274\) | 4.97372 | − | 18.5622i | 0.300473 | − | 1.12138i | ||||
\(275\) | −7.02628 | + | 26.2224i | −0.423701 | + | 1.58127i | ||||
\(276\) | −2.46410 | + | 9.19615i | −0.148321 | + | 0.553543i | ||||
\(277\) | 4.50000 | + | 16.7942i | 0.270379 | + | 1.00907i | 0.958875 | + | 0.283828i | \(0.0916044\pi\) |
−0.688496 | + | 0.725240i | \(0.741729\pi\) | |||||||
\(278\) | 3.33975 | + | 1.92820i | 0.200305 | + | 0.115646i | ||||
\(279\) | 0.196152i | 0.0117433i | ||||||||
\(280\) | −8.19615 | + | 23.6603i | −0.489814 | + | 1.41397i | ||||
\(281\) | 12.9282i | 0.771232i | 0.922659 | + | 0.385616i | \(0.126011\pi\) | ||||
−0.922659 | + | 0.385616i | \(0.873989\pi\) | |||||||
\(282\) | −10.5622 | + | 18.2942i | −0.628969 | + | 1.08941i | ||||
\(283\) | −4.52628 | − | 16.8923i | −0.269059 | − | 1.00414i | −0.959719 | − | 0.280963i | \(-0.909346\pi\) |
0.690659 | − | 0.723180i | \(-0.257320\pi\) | |||||||
\(284\) | −7.46410 | − | 12.9282i | −0.442913 | − | 0.767148i | ||||
\(285\) | −7.33013 | + | 27.3564i | −0.434199 | + | 1.62045i | ||||
\(286\) | −2.26795 | − | 0.607695i | −0.134107 | − | 0.0359338i | ||||
\(287\) | −17.8564 | + | 15.4641i | −1.05403 | + | 0.912817i | ||||
\(288\) | 4.00000 | − | 1.07180i | 0.235702 | − | 0.0631562i | ||||
\(289\) | 8.39230 | + | 14.5359i | 0.493665 | + | 0.855053i | ||||
\(290\) | −17.6603 | + | 17.6603i | −1.03705 | + | 1.03705i | ||||
\(291\) | −20.3923 | + | 5.46410i | −1.19542 | + | 0.320311i | ||||
\(292\) | 6.39230 | 0.374081 | ||||||||
\(293\) | 5.92820 | − | 5.92820i | 0.346329 | − | 0.346329i | −0.512411 | − | 0.858740i | \(-0.671248\pi\) |
0.858740 | + | 0.512411i | \(0.171248\pi\) | |||||||
\(294\) | 17.7583 | − | 7.09808i | 1.03569 | − | 0.413968i | ||||
\(295\) | − | 34.5167i | − | 2.00964i | ||||||
\(296\) | −15.6603 | − | 27.1244i | −0.910234 | − | 1.57657i | ||||
\(297\) | 16.6244 | + | 9.59808i | 0.964643 | + | 0.556937i | ||||
\(298\) | 13.1244i | 0.760274i | ||||||||
\(299\) | −0.901924 | − | 0.241670i | −0.0521596 | − | 0.0139761i | ||||
\(300\) | 23.1244 | − | 6.19615i | 1.33509 | − | 0.357735i | ||||
\(301\) | −1.73205 | − | 0.124356i | −0.0998337 | − | 0.00716774i | ||||
\(302\) | 3.43782 | − | 12.8301i | 0.197824 | − | 0.738291i | ||||
\(303\) | −7.06218 | − | 12.2321i | −0.405712 | − | 0.702713i | ||||
\(304\) | 12.3923 | + | 12.3923i | 0.710747 | + | 0.710747i | ||||
\(305\) | 0.232051 | − | 0.401924i | 0.0132872 | − | 0.0230141i | ||||
\(306\) | 0.464102 | − | 0.124356i | 0.0265309 | − | 0.00710894i | ||||
\(307\) | 9.00000 | + | 9.00000i | 0.513657 | + | 0.513657i | 0.915645 | − | 0.401988i | \(-0.131681\pi\) |
−0.401988 | + | 0.915645i | \(0.631681\pi\) | |||||||
\(308\) | 1.66025 | − | 23.1244i | 0.0946018 | − | 1.31763i | ||||
\(309\) | −0.633975 | + | 0.633975i | −0.0360656 | + | 0.0360656i | ||||
\(310\) | 1.09808 | + | 0.633975i | 0.0623665 | + | 0.0360073i | ||||
\(311\) | −0.401924 | − | 0.232051i | −0.0227910 | − | 0.0131584i | 0.488561 | − | 0.872530i | \(-0.337522\pi\) |
−0.511352 | + | 0.859371i | \(0.670855\pi\) | |||||||
\(312\) | 0.535898 | + | 2.00000i | 0.0303393 | + | 0.113228i | ||||
\(313\) | 8.30385 | − | 4.79423i | 0.469361 | − | 0.270986i | −0.246611 | − | 0.969115i | \(-0.579317\pi\) |
0.715972 | + | 0.698129i | \(0.245984\pi\) | |||||||
\(314\) | −11.6340 | − | 20.1506i | −0.656543 | − | 1.13717i | ||||
\(315\) | −5.36603 | − | 3.63397i | −0.302341 | − | 0.204751i | ||||
\(316\) | 1.14359 | + | 0.660254i | 0.0643322 | + | 0.0371422i | ||||
\(317\) | −3.16025 | + | 11.7942i | −0.177498 | + | 0.662430i | 0.818615 | + | 0.574342i | \(0.194742\pi\) |
−0.996113 | + | 0.0880875i | \(0.971924\pi\) | |||||||
\(318\) | −22.1244 | + | 22.1244i | −1.24067 | + | 1.24067i | ||||
\(319\) | 11.5622 | − | 20.0263i | 0.647358 | − | 1.12126i | ||||
\(320\) | 6.92820 | − | 25.8564i | 0.387298 | − | 1.44542i | ||||
\(321\) | −1.73205 | −0.0966736 | ||||||||
\(322\) | 0.660254 | − | 9.19615i | 0.0367945 | − | 0.512482i | ||||
\(323\) | 1.43782 | + | 1.43782i | 0.0800026 | + | 0.0800026i | ||||
\(324\) | − | 21.3205i | − | 1.18447i | ||||||
\(325\) | 0.607695 | + | 2.26795i | 0.0337089 | + | 0.125803i | ||||
\(326\) | 0.339746 | 0.0188168 | ||||||||
\(327\) | −24.9904 | + | 14.4282i | −1.38197 | + | 0.797881i | ||||
\(328\) | 17.8564 | − | 17.8564i | 0.985955 | − | 0.985955i | ||||
\(329\) | 6.69615 | − | 19.3301i | 0.369171 | − | 1.06570i | ||||
\(330\) | −34.6865 | + | 20.0263i | −1.90943 | + | 1.10241i | ||||
\(331\) | −17.2583 | − | 4.62436i | −0.948604 | − | 0.254178i | −0.248834 | − | 0.968546i | \(-0.580047\pi\) |
−0.699770 | + | 0.714369i | \(0.746714\pi\) | |||||||
\(332\) | −23.1244 | − | 6.19615i | −1.26911 | − | 0.340058i | ||||
\(333\) | 7.83013 | − | 2.09808i | 0.429088 | − | 0.114974i | ||||
\(334\) | −8.00000 | + | 2.14359i | −0.437741 | + | 0.117292i | ||||
\(335\) | 25.3923 | 1.38733 | ||||||||
\(336\) | −18.3923 | + | 8.92820i | −1.00338 | + | 0.487073i | ||||
\(337\) | −33.8564 | −1.84428 | −0.922138 | − | 0.386861i | \(-0.873559\pi\) | ||||
−0.922138 | + | 0.386861i | \(0.873559\pi\) | |||||||
\(338\) | 17.5622 | − | 4.70577i | 0.955257 | − | 0.255960i | ||||
\(339\) | −10.1962 | + | 2.73205i | −0.553779 | + | 0.148385i | ||||
\(340\) | 0.803848 | − | 3.00000i | 0.0435948 | − | 0.162698i | ||||
\(341\) | −1.13397 | − | 0.303848i | −0.0614082 | − | 0.0164543i | ||||
\(342\) | −3.92820 | + | 2.26795i | −0.212413 | + | 0.122637i | ||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | 1.85641 | 0.100091 | ||||||||
\(345\) | −13.7942 | + | 7.96410i | −0.742656 | + | 0.428773i | ||||
\(346\) | 6.73205 | 0.361917 | ||||||||
\(347\) | 4.47372 | + | 16.6962i | 0.240162 | + | 0.896296i | 0.975754 | + | 0.218871i | \(0.0702375\pi\) |
−0.735592 | + | 0.677425i | \(0.763096\pi\) | |||||||
\(348\) | −20.3923 | −1.09314 | ||||||||
\(349\) | −18.1244 | − | 18.1244i | −0.970175 | − | 0.970175i | 0.0293934 | − | 0.999568i | \(-0.490642\pi\) |
−0.999568 | + | 0.0293934i | \(0.990642\pi\) | |||||||
\(350\) | −20.8564 | + | 10.1244i | −1.11482 | + | 0.541170i | ||||
\(351\) | 1.66025 | 0.0886178 | ||||||||
\(352\) | 24.7846i | 1.32102i | ||||||||
\(353\) | −6.89230 | + | 11.9378i | −0.366840 | + | 0.635386i | −0.989070 | − | 0.147449i | \(-0.952894\pi\) |
0.622229 | + | 0.782835i | \(0.286227\pi\) | |||||||
\(354\) | 19.9282 | − | 19.9282i | 1.05917 | − | 1.05917i | ||||
\(355\) | 6.46410 | − | 24.1244i | 0.343079 | − | 1.28039i | ||||
\(356\) | −5.19615 | + | 9.00000i | −0.275396 | + | 0.476999i | ||||
\(357\) | −2.13397 | + | 1.03590i | −0.112942 | + | 0.0548256i | ||||
\(358\) | −5.56218 | − | 9.63397i | −0.293970 | − | 0.509171i | ||||
\(359\) | 2.13397 | − | 1.23205i | 0.112627 | − | 0.0650252i | −0.442628 | − | 0.896705i | \(-0.645954\pi\) |
0.555255 | + | 0.831680i | \(0.312621\pi\) | |||||||
\(360\) | 6.00000 | + | 3.46410i | 0.316228 | + | 0.182574i | ||||
\(361\) | −0.169873 | − | 0.0980762i | −0.00894068 | − | 0.00516191i | ||||
\(362\) | −12.8038 | − | 7.39230i | −0.672955 | − | 0.388531i | ||||
\(363\) | 11.1962 | − | 11.1962i | 0.587646 | − | 0.587646i | ||||
\(364\) | −0.875644 | − | 1.80385i | −0.0458962 | − | 0.0945473i | ||||
\(365\) | 7.56218 | + | 7.56218i | 0.395822 | + | 0.395822i | ||||
\(366\) | 0.366025 | − | 0.0980762i | 0.0191325 | − | 0.00512653i | ||||
\(367\) | 9.06218 | − | 15.6962i | 0.473042 | − | 0.819332i | −0.526482 | − | 0.850186i | \(-0.676489\pi\) |
0.999524 | + | 0.0308537i | \(0.00982261\pi\) | |||||||
\(368\) | 9.85641i | 0.513801i | ||||||||
\(369\) | 3.26795 | + | 5.66025i | 0.170123 | + | 0.294661i | ||||
\(370\) | 13.5622 | − | 50.6147i | 0.705064 | − | 2.63133i | ||||
\(371\) | 16.9904 | − | 25.0885i | 0.882097 | − | 1.30253i | ||||
\(372\) | 0.267949 | + | 1.00000i | 0.0138925 | + | 0.0518476i | ||||
\(373\) | 3.23205 | + | 0.866025i | 0.167349 | + | 0.0448411i | 0.341521 | − | 0.939874i | \(-0.389058\pi\) |
−0.174171 | + | 0.984715i | \(0.555725\pi\) | |||||||
\(374\) | 2.87564i | 0.148696i | ||||||||
\(375\) | 6.69615 | + | 3.86603i | 0.345788 | + | 0.199641i | ||||
\(376\) | −5.66025 | + | 21.1244i | −0.291905 | + | 1.08941i | ||||
\(377\) | − | 2.00000i | − | 0.103005i | ||||||
\(378\) | 3.09808 | + | 16.0981i | 0.159348 | + | 0.827996i | ||||
\(379\) | −24.1244 | + | 24.1244i | −1.23918 | + | 1.23918i | −0.278850 | + | 0.960335i | \(0.589953\pi\) |
−0.960335 | + | 0.278850i | \(0.910047\pi\) | |||||||
\(380\) | 29.3205i | 1.50411i | ||||||||
\(381\) | −4.73205 | + | 1.26795i | −0.242430 | + | 0.0649590i | ||||
\(382\) | −8.66025 | + | 8.66025i | −0.443097 | + | 0.443097i | ||||
\(383\) | 7.40192 | + | 12.8205i | 0.378221 | + | 0.655097i | 0.990803 | − | 0.135309i | \(-0.0432027\pi\) |
−0.612583 | + | 0.790406i | \(0.709869\pi\) | |||||||
\(384\) | 18.9282 | − | 10.9282i | 0.965926 | − | 0.557678i | ||||
\(385\) | 29.3205 | − | 25.3923i | 1.49431 | − | 1.29411i | ||||
\(386\) | 31.4186 | + | 8.41858i | 1.59916 | + | 0.428495i | ||||
\(387\) | −0.124356 | + | 0.464102i | −0.00632135 | + | 0.0235916i | ||||
\(388\) | −18.9282 | + | 10.9282i | −0.960934 | + | 0.554795i | ||||
\(389\) | 5.35641 | + | 19.9904i | 0.271581 | + | 1.01355i | 0.958098 | + | 0.286440i | \(0.0924717\pi\) |
−0.686518 | + | 0.727113i | \(0.740862\pi\) | |||||||
\(390\) | −1.73205 | + | 3.00000i | −0.0877058 | + | 0.151911i | ||||
\(391\) | 1.14359i | 0.0578340i | ||||||||
\(392\) | 15.8564 | − | 11.8564i | 0.800869 | − | 0.598839i | ||||
\(393\) | 17.9282i | 0.904358i | ||||||||
\(394\) | 1.14359 | + | 0.660254i | 0.0576134 | + | 0.0332631i | ||||
\(395\) | 0.571797 | + | 2.13397i | 0.0287702 | + | 0.107372i | ||||
\(396\) | −6.19615 | − | 1.66025i | −0.311368 | − | 0.0834309i | ||||
\(397\) | −1.37564 | + | 5.13397i | −0.0690416 | + | 0.257667i | −0.991816 | − | 0.127673i | \(-0.959249\pi\) |
0.922775 | + | 0.385340i | \(0.125916\pi\) | |||||||
\(398\) | −0.705771 | + | 2.63397i | −0.0353771 | + | 0.132029i | ||||
\(399\) | 16.9282 | − | 14.6603i | 0.847470 | − | 0.733931i | ||||
\(400\) | 21.4641 | − | 12.3923i | 1.07321 | − | 0.619615i | ||||
\(401\) | 7.50000 | + | 12.9904i | 0.374532 | + | 0.648709i | 0.990257 | − | 0.139253i | \(-0.0444700\pi\) |
−0.615725 | + | 0.787961i | \(0.711137\pi\) | |||||||
\(402\) | 14.6603 | + | 14.6603i | 0.731187 | + | 0.731187i | ||||
\(403\) | −0.0980762 | + | 0.0262794i | −0.00488552 | + | 0.00130907i | ||||
\(404\) | −10.3397 | − | 10.3397i | −0.514422 | − | 0.514422i | ||||
\(405\) | 25.2224 | − | 25.2224i | 1.25331 | − | 1.25331i | ||||
\(406\) | 19.3923 | − | 3.73205i | 0.962424 | − | 0.185219i | ||||
\(407\) | 48.5167i | 2.40488i | ||||||||
\(408\) | 2.19615 | − | 1.26795i | 0.108726 | − | 0.0627728i | ||||
\(409\) | 7.50000 | + | 4.33013i | 0.370851 | + | 0.214111i | 0.673830 | − | 0.738886i | \(-0.264648\pi\) |
−0.302979 | + | 0.952997i | \(0.597981\pi\) | |||||||
\(410\) | 42.2487 | 2.08652 | ||||||||
\(411\) | 25.3564 | + | 6.79423i | 1.25074 | + | 0.335135i | ||||
\(412\) | −0.464102 | + | 0.803848i | −0.0228646 | + | 0.0396027i | ||||
\(413\) | −15.3038 | + | 22.5981i | −0.753053 | + | 1.11198i | ||||
\(414\) | −2.46410 | − | 0.660254i | −0.121104 | − | 0.0324497i | ||||
\(415\) | −20.0263 | − | 34.6865i | −0.983051 | − | 1.70269i | ||||
\(416\) | 1.07180 | + | 1.85641i | 0.0525492 | + | 0.0910178i | ||||
\(417\) | −2.63397 | + | 4.56218i | −0.128986 | + | 0.223411i | ||||
\(418\) | −7.02628 | − | 26.2224i | −0.343667 | − | 1.28258i | ||||
\(419\) | −19.0000 | − | 19.0000i | −0.928211 | − | 0.928211i | 0.0693796 | − | 0.997590i | \(-0.477898\pi\) |
−0.997590 | + | 0.0693796i | \(0.977898\pi\) | |||||||
\(420\) | −32.3205 | − | 11.1962i | −1.57708 | − | 0.546316i | ||||
\(421\) | −8.66025 | + | 8.66025i | −0.422075 | + | 0.422075i | −0.885918 | − | 0.463843i | \(-0.846470\pi\) |
0.463843 | + | 0.885918i | \(0.346470\pi\) | |||||||
\(422\) | 2.07180 | − | 3.58846i | 0.100853 | − | 0.174683i | ||||
\(423\) | −4.90192 | − | 2.83013i | −0.238340 | − | 0.137605i | ||||
\(424\) | −16.1962 | + | 28.0526i | −0.786555 | + | 1.36235i | ||||
\(425\) | 2.49038 | − | 1.43782i | 0.120801 | − | 0.0697446i | ||||
\(426\) | 17.6603 | − | 10.1962i | 0.855642 | − | 0.494005i | ||||
\(427\) | −0.330127 | + | 0.160254i | −0.0159760 | + | 0.00775524i | ||||
\(428\) | −1.73205 | + | 0.464102i | −0.0837218 | + | 0.0224332i | ||||
\(429\) | 0.830127 | − | 3.09808i | 0.0400789 | − | 0.149577i | ||||
\(430\) | 2.19615 | + | 2.19615i | 0.105908 | + | 0.105908i | ||||
\(431\) | −6.66987 | + | 11.5526i | −0.321276 | + | 0.556467i | −0.980752 | − | 0.195259i | \(-0.937445\pi\) |
0.659475 | + | 0.751726i | \(0.270779\pi\) | |||||||
\(432\) | −4.53590 | − | 16.9282i | −0.218234 | − | 0.814459i | ||||
\(433\) | 29.1769 | 1.40215 | 0.701077 | − | 0.713086i | \(-0.252703\pi\) | ||||
0.701077 | + | 0.713086i | \(0.252703\pi\) | |||||||
\(434\) | −0.437822 | − | 0.901924i | −0.0210161 | − | 0.0432937i | ||||
\(435\) | −24.1244 | − | 24.1244i | −1.15667 | − | 1.15667i | ||||
\(436\) | −21.1244 | + | 21.1244i | −1.01167 | + | 1.01167i | ||||
\(437\) | −2.79423 | − | 10.4282i | −0.133666 | − | 0.498849i | ||||
\(438\) | 8.73205i | 0.417234i | ||||||||
\(439\) | 12.5263 | − | 7.23205i | 0.597847 | − | 0.345167i | −0.170347 | − | 0.985384i | \(-0.554489\pi\) |
0.768194 | + | 0.640217i | \(0.221156\pi\) | |||||||
\(440\) | −29.3205 | + | 29.3205i | −1.39780 | + | 1.39780i | ||||
\(441\) | 1.90192 | + | 4.75833i | 0.0905678 | + | 0.226587i | ||||
\(442\) | 0.124356 | + | 0.215390i | 0.00591500 | + | 0.0102451i | ||||
\(443\) | −12.7942 | − | 3.42820i | −0.607872 | − | 0.162879i | −0.0582637 | − | 0.998301i | \(-0.518556\pi\) |
−0.549608 | + | 0.835422i | \(0.685223\pi\) | |||||||
\(444\) | 37.0526 | − | 21.3923i | 1.75844 | − | 1.01523i | ||||
\(445\) | −16.7942 | + | 4.50000i | −0.796123 | + | 0.213320i | ||||
\(446\) | −6.53590 | − | 24.3923i | −0.309484 | − | 1.15501i | ||||
\(447\) | −17.9282 | −0.847975 | ||||||||
\(448\) | −16.0000 | + | 13.8564i | −0.755929 | + | 0.654654i | ||||
\(449\) | 11.3205 | 0.534248 | 0.267124 | − | 0.963662i | \(-0.413927\pi\) | ||||
0.267124 | + | 0.963662i | \(0.413927\pi\) | |||||||
\(450\) | 1.66025 | + | 6.19615i | 0.0782651 | + | 0.292089i | ||||
\(451\) | −37.7846 | + | 10.1244i | −1.77921 | + | 0.476737i | ||||
\(452\) | −9.46410 | + | 5.46410i | −0.445154 | + | 0.257010i | ||||
\(453\) | 17.5263 | + | 4.69615i | 0.823456 | + | 0.220644i | ||||
\(454\) | 16.8301 | + | 29.1506i | 0.789877 | + | 1.36811i | ||||
\(455\) | 1.09808 | − | 3.16987i | 0.0514786 | − | 0.148606i | ||||
\(456\) | −16.9282 | + | 16.9282i | −0.792736 | + | 0.792736i | ||||
\(457\) | 25.2846 | − | 14.5981i | 1.18276 | − | 0.682869i | 0.226112 | − | 0.974101i | \(-0.427399\pi\) |
0.956652 | + | 0.291232i | \(0.0940652\pi\) | |||||||
\(458\) | − | 25.5167i | − | 1.19232i | ||||||
\(459\) | −0.526279 | − | 1.96410i | −0.0245646 | − | 0.0916764i | ||||
\(460\) | −11.6603 | + | 11.6603i | −0.543662 | + | 0.543662i | ||||
\(461\) | 1.33975 | + | 1.33975i | 0.0623982 | + | 0.0623982i | 0.737617 | − | 0.675219i | \(-0.235951\pi\) |
−0.675219 | + | 0.737617i | \(0.735951\pi\) | |||||||
\(462\) | 31.5885 | + | 2.26795i | 1.46963 | + | 0.105515i | ||||
\(463\) | 29.8564 | 1.38754 | 0.693772 | − | 0.720194i | \(-0.255947\pi\) | ||||
0.693772 | + | 0.720194i | \(0.255947\pi\) | |||||||
\(464\) | −20.3923 | + | 5.46410i | −0.946689 | + | 0.253665i | ||||
\(465\) | −0.866025 | + | 1.50000i | −0.0401610 | + | 0.0695608i | ||||
\(466\) | 11.1962 | + | 11.1962i | 0.518652 | + | 0.518652i | ||||
\(467\) | 0.00961894 | − | 0.0358984i | 0.000445112 | − | 0.00166118i | −0.965703 | − | 0.259650i | \(-0.916393\pi\) |
0.966148 | + | 0.257988i | \(0.0830596\pi\) | |||||||
\(468\) | −0.535898 | + | 0.143594i | −0.0247719 | + | 0.00663761i | ||||
\(469\) | −16.6244 | − | 11.2583i | −0.767641 | − | 0.519861i | ||||
\(470\) | −31.6865 | + | 18.2942i | −1.46159 | + | 0.843850i | ||||
\(471\) | 27.5263 | − | 15.8923i | 1.26834 | − | 0.732279i | ||||
\(472\) | 14.5885 | − | 25.2679i | 0.671488 | − | 1.16305i | ||||
\(473\) | −2.49038 | − | 1.43782i | −0.114508 | − | 0.0661111i | ||||
\(474\) | −0.901924 | + | 1.56218i | −0.0414267 | + | 0.0717532i | ||||
\(475\) | −19.1962 | + | 19.1962i | −0.880780 | + | 0.880780i | ||||
\(476\) | −1.85641 | + | 1.60770i | −0.0850883 | + | 0.0736886i | ||||
\(477\) | −5.92820 | − | 5.92820i | −0.271434 | − | 0.271434i | ||||
\(478\) | −5.66025 | − | 21.1244i | −0.258894 | − | 0.966206i | ||||
\(479\) | 7.79423 | − | 13.5000i | 0.356127 | − | 0.616831i | −0.631183 | − | 0.775634i | \(-0.717430\pi\) |
0.987310 | + | 0.158803i | \(0.0507636\pi\) | |||||||
\(480\) | 35.3205 | + | 9.46410i | 1.61215 | + | 0.431975i | ||||
\(481\) | 2.09808 | + | 3.63397i | 0.0956640 | + | 0.165695i | ||||
\(482\) | −0.0980762 | − | 0.0262794i | −0.00446725 | − | 0.00119700i | ||||
\(483\) | 12.5622 | + | 0.901924i | 0.571599 | + | 0.0410390i | ||||
\(484\) | 8.19615 | − | 14.1962i | 0.372552 | − | 0.645280i | ||||
\(485\) | −35.3205 | − | 9.46410i | −1.60382 | − | 0.429743i | ||||
\(486\) | 10.5359 | 0.477918 | ||||||||
\(487\) | −19.3301 | − | 11.1603i | −0.875932 | − | 0.505719i | −0.00661681 | − | 0.999978i | \(-0.502106\pi\) |
−0.869315 | + | 0.494259i | \(0.835440\pi\) | |||||||
\(488\) | 0.339746 | − | 0.196152i | 0.0153796 | − | 0.00887940i | ||||
\(489\) | 0.464102i | 0.0209874i | ||||||||
\(490\) | 32.7846 | + | 4.73205i | 1.48106 | + | 0.213772i | ||||
\(491\) | 27.5885 | − | 27.5885i | 1.24505 | − | 1.24505i | 0.287170 | − | 0.957880i | \(-0.407286\pi\) |
0.957880 | − | 0.287170i | \(-0.0927145\pi\) | |||||||
\(492\) | 24.3923 | + | 24.3923i | 1.09969 | + | 1.09969i | ||||
\(493\) | −2.36603 | + | 0.633975i | −0.106560 | + | 0.0285528i | ||||
\(494\) | −1.66025 | − | 1.66025i | −0.0746984 | − | 0.0746984i | ||||
\(495\) | −5.36603 | − | 9.29423i | −0.241185 | − | 0.417745i | ||||
\(496\) | 0.535898 | + | 0.928203i | 0.0240625 | + | 0.0416776i | ||||
\(497\) | −14.9282 | + | 12.9282i | −0.669621 | + | 0.579909i | ||||
\(498\) | 8.46410 | − | 31.5885i | 0.379285 | − | 1.41551i | ||||
\(499\) | 0.990381 | − | 3.69615i | 0.0443355 | − | 0.165463i | −0.940209 | − | 0.340599i | \(-0.889370\pi\) |
0.984544 | + | 0.175137i | \(0.0560367\pi\) | |||||||
\(500\) | 7.73205 | + | 2.07180i | 0.345788 | + | 0.0926536i | ||||
\(501\) | −2.92820 | − | 10.9282i | −0.130822 | − | 0.488236i | ||||
\(502\) | 23.5359 | + | 13.5885i | 1.05046 | + | 0.606483i | ||||
\(503\) | − | 4.14359i | − | 0.184754i | −0.995724 | − | 0.0923769i | \(-0.970554\pi\) | ||
0.995724 | − | 0.0923769i | \(-0.0294464\pi\) | |||||||
\(504\) | −2.39230 | − | 4.92820i | −0.106562 | − | 0.219520i | ||||
\(505\) | − | 24.4641i | − | 1.08864i | ||||||
\(506\) | 7.63397 | − | 13.2224i | 0.339372 | − | 0.587809i | ||||
\(507\) | 6.42820 | + | 23.9904i | 0.285487 | + | 1.06545i | ||||
\(508\) | −4.39230 | + | 2.53590i | −0.194877 | + | 0.112512i | ||||
\(509\) | 4.42820 | − | 16.5263i | 0.196277 | − | 0.732514i | −0.795656 | − | 0.605749i | \(-0.792874\pi\) |
0.991933 | − | 0.126766i | \(-0.0404597\pi\) | |||||||
\(510\) | 4.09808 | + | 1.09808i | 0.181466 | + | 0.0486236i | ||||
\(511\) | −1.59808 | − | 8.30385i | −0.0706947 | − | 0.367341i | ||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | 9.59808 | + | 16.6244i | 0.423765 | + | 0.733983i | ||||
\(514\) | 1.39230 | − | 1.39230i | 0.0614119 | − | 0.0614119i | ||||
\(515\) | −1.50000 | + | 0.401924i | −0.0660979 | + | 0.0177109i | ||||
\(516\) | 2.53590i | 0.111637i | ||||||||
\(517\) | 23.9545 | − | 23.9545i | 1.05352 | − | 1.05352i | ||||
\(518\) | −31.3205 | + | 27.1244i | −1.37614 | + | 1.19178i | ||||
\(519\) | 9.19615i | 0.403666i | ||||||||
\(520\) | −0.928203 | + | 3.46410i | −0.0407044 | + | 0.151911i | ||||
\(521\) | 37.6244 | + | 21.7224i | 1.64835 | + | 0.951677i | 0.977727 | + | 0.209881i | \(0.0673078\pi\) |
0.670626 | + | 0.741796i | \(0.266026\pi\) | |||||||
\(522\) | − | 5.46410i | − | 0.239157i | ||||||
\(523\) | −34.6506 | − | 9.28461i | −1.51517 | − | 0.405988i | −0.597019 | − | 0.802227i | \(-0.703648\pi\) |
−0.918147 | + | 0.396239i | \(0.870315\pi\) | |||||||
\(524\) | 4.80385 | + | 17.9282i | 0.209857 | + | 0.783197i | ||||
\(525\) | −13.8301 | − | 28.4904i | −0.603596 | − | 1.24342i | ||||
\(526\) | −9.29423 | + | 34.6865i | −0.405248 | + | 1.51240i | ||||
\(527\) | 0.0621778 | + | 0.107695i | 0.00270851 | + | 0.00469127i | ||||
\(528\) | −33.8564 | −1.47341 | ||||||||
\(529\) | −8.46410 | + | 14.6603i | −0.368004 | + | 0.637402i | ||||
\(530\) | −52.3468 | + | 14.0263i | −2.27380 | + | 0.609263i | ||||
\(531\) | 5.33975 | + | 5.33975i | 0.231725 | + | 0.231725i | ||||
\(532\) | 13.0000 | − | 19.1962i | 0.563621 | − | 0.832259i | ||||
\(533\) | −2.39230 | + | 2.39230i | −0.103622 | + | 0.103622i | ||||
\(534\) | −12.2942 | − | 7.09808i | −0.532023 | − | 0.307164i | ||||
\(535\) | −2.59808 | − | 1.50000i | −0.112325 | − | 0.0648507i | ||||
\(536\) | 18.5885 | + | 10.7321i | 0.802899 | + | 0.463554i | ||||
\(537\) | 13.1603 | − | 7.59808i | 0.567907 | − | 0.327881i | ||||
\(538\) | 15.8301 | + | 27.4186i | 0.682485 | + | 1.18210i | ||||
\(539\) | −30.4545 | + | 3.62436i | −1.31177 | + | 0.156112i | ||||
\(540\) | 14.6603 | − | 25.3923i | 0.630877 | − | 1.09271i | ||||
\(541\) | −5.76795 | + | 21.5263i | −0.247984 | + | 0.925487i | 0.723877 | + | 0.689929i | \(0.242358\pi\) |
−0.971860 | + | 0.235558i | \(0.924308\pi\) | |||||||
\(542\) | −12.1244 | + | 12.1244i | −0.520786 | + | 0.520786i | ||||
\(543\) | 10.0981 | − | 17.4904i | 0.433350 | − | 0.750584i | ||||
\(544\) | 1.85641 | − | 1.85641i | 0.0795928 | − | 0.0795928i | ||||
\(545\) | −49.9808 | −2.14094 | ||||||||
\(546\) | 2.46410 | − | 1.19615i | 0.105454 | − | 0.0511906i | ||||
\(547\) | 15.0526 | + | 15.0526i | 0.643601 | + | 0.643601i | 0.951439 | − | 0.307838i | \(-0.0996054\pi\) |
−0.307838 | + | 0.951439i | \(0.599605\pi\) | |||||||
\(548\) | 27.1769 | 1.16094 | ||||||||
\(549\) | 0.0262794 | + | 0.0980762i | 0.00112158 | + | 0.00418579i | ||||
\(550\) | −38.3923 | −1.63705 | ||||||||
\(551\) | 20.0263 | − | 11.5622i | 0.853148 | − | 0.492565i | ||||
\(552\) | −13.4641 | −0.573070 | ||||||||
\(553\) | 0.571797 | − | 1.65064i | 0.0243153 | − | 0.0701921i | ||||
\(554\) | −21.2942 | + | 12.2942i | −0.904705 | + | 0.522332i | ||||
\(555\) | 69.1410 | + | 18.5263i | 2.93487 | + | 0.786397i | ||||
\(556\) | −1.41154 | + | 5.26795i | −0.0598627 | + | 0.223411i | ||||
\(557\) | −5.23205 | + | 1.40192i | −0.221689 | + | 0.0594014i | −0.367954 | − | 0.929844i | \(-0.619942\pi\) |
0.146265 | + | 0.989245i | \(0.453275\pi\) | |||||||
\(558\) | −0.267949 | + | 0.0717968i | −0.0113432 | + | 0.00303940i | ||||
\(559\) | −0.248711 | −0.0105194 | ||||||||
\(560\) | −35.3205 | − | 2.53590i | −1.49256 | − | 0.107161i | ||||
\(561\) | −3.92820 | −0.165849 | ||||||||
\(562\) | −17.6603 | + | 4.73205i | −0.744953 | + | 0.199610i | ||||
\(563\) | −42.6506 | + | 11.4282i | −1.79751 | + | 0.481641i | −0.993585 | − | 0.113089i | \(-0.963925\pi\) |
−0.803925 | + | 0.594731i | \(0.797259\pi\) | |||||||
\(564\) | −28.8564 | − | 7.73205i | −1.21507 | − | 0.325578i | ||||
\(565\) | −17.6603 | − | 4.73205i | −0.742972 | − | 0.199079i | ||||
\(566\) | 21.4186 | − | 12.3660i | 0.900290 | − | 0.519783i | ||||
\(567\) | −27.6962 | + | 5.33013i | −1.16313 | + | 0.223844i | ||||
\(568\) | 14.9282 | − | 14.9282i | 0.626373 | − | 0.626373i | ||||
\(569\) | −26.0885 | + | 15.0622i | −1.09369 | + | 0.631439i | −0.934555 | − | 0.355818i | \(-0.884202\pi\) |
−0.159130 | + | 0.987258i | \(0.550869\pi\) | |||||||
\(570\) | −40.0526 | −1.67762 | ||||||||
\(571\) | −2.72243 | − | 10.1603i | −0.113930 | − | 0.425193i | 0.885274 | − | 0.465069i | \(-0.153970\pi\) |
−0.999205 | + | 0.0398756i | \(0.987304\pi\) | |||||||
\(572\) | − | 3.32051i | − | 0.138837i | ||||||
\(573\) | −11.8301 | − | 11.8301i | −0.494211 | − | 0.494211i | ||||
\(574\) | −27.6603 | − | 18.7321i | −1.15452 | − | 0.781861i | ||||
\(575\) | −15.2679 | −0.636717 | ||||||||
\(576\) | 2.92820 | + | 5.07180i | 0.122008 | + | 0.211325i | ||||
\(577\) | 17.6244 | − | 30.5263i | 0.733712 | − | 1.27083i | −0.221575 | − | 0.975143i | \(-0.571120\pi\) |
0.955286 | − | 0.295682i | \(-0.0955470\pi\) | |||||||
\(578\) | −16.7846 | + | 16.7846i | −0.698148 | + | 0.698148i | ||||
\(579\) | −11.5000 | + | 42.9186i | −0.477924 | + | 1.78364i | ||||
\(580\) | −30.5885 | − | 17.6603i | −1.27012 | − | 0.733302i | ||||
\(581\) | −2.26795 | + | 31.5885i | −0.0940904 | + | 1.31051i | ||||
\(582\) | −14.9282 | − | 25.8564i | −0.618794 | − | 1.07178i | ||||
\(583\) | 43.4545 | − | 25.0885i | 1.79970 | − | 1.03906i | ||||
\(584\) | 2.33975 | + | 8.73205i | 0.0968194 | + | 0.361335i | ||||
\(585\) | −0.803848 | − | 0.464102i | −0.0332350 | − | 0.0191882i | ||||
\(586\) | 10.2679 | + | 5.92820i | 0.424165 | + | 0.244892i | ||||
\(587\) | 8.07180 | − | 8.07180i | 0.333159 | − | 0.333159i | −0.520626 | − | 0.853785i | \(-0.674301\pi\) |
0.853785 | + | 0.520626i | \(0.174301\pi\) | |||||||
\(588\) | 16.1962 | + | 21.6603i | 0.667918 | + | 0.893254i | ||||
\(589\) | −0.830127 | − | 0.830127i | −0.0342048 | − | 0.0342048i | ||||
\(590\) | 47.1506 | − | 12.6340i | 1.94116 | − | 0.520133i | ||||
\(591\) | −0.901924 | + | 1.56218i | −0.0371002 | + | 0.0642594i | ||||
\(592\) | 31.3205 | − | 31.3205i | 1.28726 | − | 1.28726i | ||||
\(593\) | −4.69615 | − | 8.13397i | −0.192848 | − | 0.334022i | 0.753345 | − | 0.657625i | \(-0.228439\pi\) |
−0.946193 | + | 0.323603i | \(0.895106\pi\) | |||||||
\(594\) | −7.02628 | + | 26.2224i | −0.288292 | + | 1.07592i | ||||
\(595\) | −4.09808 | − | 0.294229i | −0.168005 | − | 0.0120622i | ||||
\(596\) | −17.9282 | + | 4.80385i | −0.734368 | + | 0.196773i | ||||
\(597\) | −3.59808 | − | 0.964102i | −0.147259 | − | 0.0394581i | ||||
\(598\) | − | 1.32051i | − | 0.0539996i | ||||||
\(599\) | −25.3301 | − | 14.6244i | −1.03496 | − | 0.597535i | −0.116559 | − | 0.993184i | \(-0.537186\pi\) |
−0.918402 | + | 0.395649i | \(0.870520\pi\) | |||||||
\(600\) | 16.9282 | + | 29.3205i | 0.691091 | + | 1.19700i | ||||
\(601\) | 10.0000i | 0.407909i | 0.978980 | + | 0.203954i | \(0.0653794\pi\) | ||||
−0.978980 | + | 0.203954i | \(0.934621\pi\) | |||||||
\(602\) | −0.464102 | − | 2.41154i | −0.0189154 | − | 0.0982871i | ||||
\(603\) | −3.92820 | + | 3.92820i | −0.159969 | + | 0.159969i | ||||
\(604\) | 18.7846 | 0.764335 | ||||||||
\(605\) | 26.4904 | − | 7.09808i | 1.07699 | − | 0.288578i | ||||
\(606\) | 14.1244 | − | 14.1244i | 0.573763 | − | 0.573763i | ||||
\(607\) | 10.5263 | + | 18.2321i | 0.427249 | + | 0.740016i | 0.996627 | − | 0.0820591i | \(-0.0261496\pi\) |
−0.569379 | + | 0.822075i | \(0.692816\pi\) | |||||||
\(608\) | −12.3923 | + | 21.4641i | −0.502574 | + | 0.870484i | ||||
\(609\) | 5.09808 | + | 26.4904i | 0.206584 | + | 1.07344i | ||||
\(610\) | 0.633975 | + | 0.169873i | 0.0256689 | + | 0.00687796i | ||||
\(611\) | 0.758330 | − | 2.83013i | 0.0306788 | − | 0.114495i | ||||
\(612\) | 0.339746 | + | 0.588457i | 0.0137334 | + | 0.0237870i | ||||
\(613\) | −5.76795 | − | 21.5263i | −0.232965 | − | 0.869438i | −0.979056 | − | 0.203593i | \(-0.934738\pi\) |
0.746090 | − | 0.665845i | \(-0.231929\pi\) | |||||||
\(614\) | −9.00000 | + | 15.5885i | −0.363210 | + | 0.629099i | ||||
\(615\) | 57.7128i | 2.32721i | ||||||||
\(616\) | 32.1962 | − | 6.19615i | 1.29722 | − | 0.249650i | ||||
\(617\) | 7.46410i | 0.300493i | 0.988649 | + | 0.150247i | \(0.0480068\pi\) | ||||
−0.988649 | + | 0.150247i | \(0.951993\pi\) | |||||||
\(618\) | −1.09808 | − | 0.633975i | −0.0441711 | − | 0.0255022i | ||||
\(619\) | −6.93782 | − | 25.8923i | −0.278855 | − | 1.04070i | −0.953214 | − | 0.302296i | \(-0.902247\pi\) |
0.674359 | − | 0.738403i | \(-0.264420\pi\) | |||||||
\(620\) | −0.464102 | + | 1.73205i | −0.0186388 | + | 0.0695608i | ||||
\(621\) | −2.79423 | + | 10.4282i | −0.112129 | + | 0.418469i | ||||
\(622\) | 0.169873 | − | 0.633975i | 0.00681129 | − | 0.0254201i | ||||
\(623\) | 12.9904 | + | 4.50000i | 0.520449 | + | 0.180289i | ||||
\(624\) | −2.53590 | + | 1.46410i | −0.101517 | + | 0.0586110i | ||||
\(625\) | −8.79423 | − | 15.2321i | −0.351769 | − | 0.609282i | ||||
\(626\) | 9.58846 | + | 9.58846i | 0.383232 | + | 0.383232i | ||||
\(627\) | 35.8205 | − | 9.59808i | 1.43053 | − | 0.383310i | ||||
\(628\) | 23.2679 | − | 23.2679i | 0.928492 | − | 0.928492i | ||||
\(629\) | 3.63397 | − | 3.63397i | 0.144896 | − | 0.144896i | ||||
\(630\) | 3.00000 | − | 8.66025i | 0.119523 | − | 0.345033i | ||||
\(631\) | − | 16.2487i | − | 0.646851i | −0.946254 | − | 0.323425i | \(-0.895165\pi\) | ||
0.946254 | − | 0.323425i | \(-0.104835\pi\) | |||||||
\(632\) | −0.483340 | + | 1.80385i | −0.0192262 | + | 0.0717532i | ||||
\(633\) | 4.90192 | + | 2.83013i | 0.194834 | + | 0.112487i | ||||
\(634\) | −17.2679 | −0.685798 | ||||||||
\(635\) | −8.19615 | − | 2.19615i | −0.325254 | − | 0.0871517i | ||||
\(636\) | −38.3205 | − | 22.1244i | −1.51951 | − | 0.877288i | ||||
\(637\) | −2.12436 | + | 1.58846i | −0.0841700 | + | 0.0629370i | ||||
\(638\) | 31.5885 | + | 8.46410i | 1.25060 | + | 0.335097i | ||||
\(639\) | 2.73205 | + | 4.73205i | 0.108078 | + | 0.187197i | ||||
\(640\) | 37.8564 | 1.49641 | ||||||||
\(641\) | 19.4282 | − | 33.6506i | 0.767368 | − | 1.32912i | −0.171618 | − | 0.985164i | \(-0.554899\pi\) |
0.938986 | − | 0.343957i | \(-0.111767\pi\) | |||||||
\(642\) | −0.633975 | − | 2.36603i | −0.0250210 | − | 0.0933796i | ||||
\(643\) | 15.3923 | + | 15.3923i | 0.607013 | + | 0.607013i | 0.942164 | − | 0.335151i | \(-0.108787\pi\) |
−0.335151 | + | 0.942164i | \(0.608787\pi\) | |||||||
\(644\) | 12.8038 | − | 2.46410i | 0.504542 | − | 0.0970992i | ||||
\(645\) | −3.00000 | + | 3.00000i | −0.118125 | + | 0.118125i | ||||
\(646\) | −1.43782 | + | 2.49038i | −0.0565704 | + | 0.0979827i | ||||
\(647\) | −29.1340 | − | 16.8205i | −1.14537 | − | 0.661282i | −0.197619 | − | 0.980279i | \(-0.563321\pi\) |
−0.947756 | + | 0.318997i | \(0.896654\pi\) | |||||||
\(648\) | 29.1244 | − | 7.80385i | 1.14411 | − | 0.306564i | ||||
\(649\) | −39.1410 | + | 22.5981i | −1.53642 | + | 0.887052i | ||||
\(650\) | −2.87564 | + | 1.66025i | −0.112792 | + | 0.0651205i | ||||
\(651\) | 1.23205 | − | 0.598076i | 0.0482879 | − | 0.0234405i | ||||
\(652\) | 0.124356 | + | 0.464102i | 0.00487014 | + | 0.0181756i | ||||
\(653\) | −5.55256 | + | 20.7224i | −0.217288 | + | 0.810931i | 0.768060 | + | 0.640378i | \(0.221222\pi\) |
−0.985348 | + | 0.170554i | \(0.945444\pi\) | |||||||
\(654\) | −28.8564 | − | 28.8564i | −1.12837 | − | 1.12837i | ||||
\(655\) | −15.5263 | + | 26.8923i | −0.606662 | + | 1.05077i | ||||
\(656\) | 30.9282 | + | 17.8564i | 1.20754 | + | 0.697176i | ||||
\(657\) | −2.33975 | −0.0912822 | ||||||||
\(658\) | 28.8564 | + | 2.07180i | 1.12494 | + | 0.0807670i | ||||
\(659\) | −8.85641 | − | 8.85641i | −0.344997 | − | 0.344997i | 0.513245 | − | 0.858242i | \(-0.328443\pi\) |
−0.858242 | + | 0.513245i | \(0.828443\pi\) | |||||||
\(660\) | −40.0526 | − | 40.0526i | −1.55904 | − | 1.55904i | ||||
\(661\) | 4.83975 | + | 18.0622i | 0.188244 | + | 0.702537i | 0.993913 | + | 0.110170i | \(0.0351397\pi\) |
−0.805668 | + | 0.592367i | \(0.798194\pi\) | |||||||
\(662\) | − | 25.2679i | − | 0.982067i | ||||||
\(663\) | −0.294229 | + | 0.169873i | −0.0114269 | + | 0.00659732i | ||||
\(664\) | − | 33.8564i | − | 1.31388i | ||||||
\(665\) | 38.0885 | − | 7.33013i | 1.47701 | − | 0.284250i | ||||
\(666\) | 5.73205 | + | 9.92820i | 0.222112 | + | 0.384710i | ||||
\(667\) | 12.5622 | + | 3.36603i | 0.486409 | + | 0.130333i | ||||
\(668\) | −5.85641 | − | 10.1436i | −0.226591 | − | 0.392467i | ||||
\(669\) | 33.3205 | − | 8.92820i | 1.28825 | − | 0.345184i | ||||
\(670\) | 9.29423 | + | 34.6865i | 0.359067 | + | 1.34006i | ||||
\(671\) | −0.607695 | −0.0234598 | ||||||||
\(672\) | −18.9282 | − | 21.8564i | −0.730171 | − | 0.843129i | ||||
\(673\) | −0.784610 | −0.0302445 | −0.0151222 | − | 0.999886i | \(-0.504814\pi\) | ||||
−0.0151222 | + | 0.999886i | \(0.504814\pi\) | |||||||
\(674\) | −12.3923 | − | 46.2487i | −0.477334 | − | 1.78143i | ||||
\(675\) | 26.2224 | − | 7.02628i | 1.00930 | − | 0.270442i | ||||
\(676\) | 12.8564 | + | 22.2679i | 0.494477 | + | 0.856460i | ||||
\(677\) | 49.5526 | + | 13.2776i | 1.90446 | + | 0.510298i | 0.995660 | + | 0.0930654i | \(0.0296666\pi\) |
0.908800 | + | 0.417233i | \(0.137000\pi\) | |||||||
\(678\) | −7.46410 | − | 12.9282i | −0.286657 | − | 0.496505i | ||||
\(679\) | 18.9282 | + | 21.8564i | 0.726398 | + | 0.838772i | ||||
\(680\) | 4.39230 | 0.168437 | ||||||||
\(681\) | −39.8205 | + | 22.9904i | −1.52593 | + | 0.880993i | ||||
\(682\) | − | 1.66025i | − | 0.0635744i | ||||||
\(683\) | 11.5788 | + | 43.2128i | 0.443052 | + | 1.65349i | 0.721029 | + | 0.692905i | \(0.243669\pi\) |
−0.277977 | + | 0.960588i | \(0.589664\pi\) | |||||||
\(684\) | −4.53590 | − | 4.53590i | −0.173434 | − | 0.173434i | ||||
\(685\) | 32.1506 | + | 32.1506i | 1.22841 | + | 1.22841i | ||||
\(686\) | −19.3660 | − | 17.6340i | −0.739398 | − | 0.673268i | ||||
\(687\) | 34.8564 | 1.32985 | ||||||||
\(688\) | 0.679492 | + | 2.53590i | 0.0259054 | + | 0.0966802i | ||||
\(689\) | 2.16987 | − | 3.75833i | 0.0826656 | − | 0.143181i | ||||
\(690\) | −15.9282 | − | 15.9282i | −0.606376 | − | 0.606376i | ||||
\(691\) | 2.99038 | − | 11.1603i | 0.113759 | − | 0.424556i | −0.885432 | − | 0.464770i | \(-0.846137\pi\) |
0.999191 | + | 0.0402135i | \(0.0128038\pi\) | |||||||
\(692\) | 2.46410 | + | 9.19615i | 0.0936711 | + | 0.349585i | ||||
\(693\) | −0.607695 | + | 8.46410i | −0.0230844 | + | 0.321525i | ||||
\(694\) | −21.1699 | + | 12.2224i | −0.803597 | + | 0.463957i | ||||
\(695\) | −7.90192 | + | 4.56218i | −0.299737 | + | 0.173053i | ||||
\(696\) | −7.46410 | − | 27.8564i | −0.282926 | − | 1.05589i | ||||
\(697\) | 3.58846 | + | 2.07180i | 0.135923 | + | 0.0784749i | ||||
\(698\) | 18.1244 | − | 31.3923i | 0.686017 | − | 1.18822i | ||||
\(699\) | −15.2942 | + | 15.2942i | −0.578481 | + | 0.578481i | ||||
\(700\) | −21.4641 | − | 24.7846i | −0.811267 | − | 0.936770i | ||||
\(701\) | 7.39230 | + | 7.39230i | 0.279204 | + | 0.279204i | 0.832791 | − | 0.553588i | \(-0.186742\pi\) |
−0.553588 | + | 0.832791i | \(0.686742\pi\) | |||||||
\(702\) | 0.607695 | + | 2.26795i | 0.0229360 | + | 0.0855982i | ||||
\(703\) | −24.2583 | + | 42.0167i | −0.914920 | + | 1.58469i | ||||
\(704\) | −33.8564 | + | 9.07180i | −1.27601 | + | 0.341906i | ||||
\(705\) | −24.9904 | − | 43.2846i | −0.941192 | − | 1.63019i | ||||
\(706\) | −18.8301 | − | 5.04552i | −0.708681 | − | 0.189891i | ||||
\(707\) | −10.8468 | + | 16.0167i | −0.407935 | + | 0.602369i | ||||
\(708\) | 34.5167 | + | 19.9282i | 1.29722 | + | 0.748948i | ||||
\(709\) | −8.76795 | − | 2.34936i | −0.329287 | − | 0.0882323i | 0.0903879 | − | 0.995907i | \(-0.471189\pi\) |
−0.419675 | + | 0.907674i | \(0.637856\pi\) | |||||||
\(710\) | 35.3205 | 1.32556 | ||||||||
\(711\) | −0.418584 | − | 0.241670i | −0.0156981 | − | 0.00906332i | ||||
\(712\) | −14.1962 | − | 3.80385i | −0.532023 | − | 0.142555i | ||||
\(713\) | − | 0.660254i | − | 0.0247267i | ||||||
\(714\) | −2.19615 | − | 2.53590i | −0.0821889 | − | 0.0949036i | ||||
\(715\) | 3.92820 | − | 3.92820i | 0.146906 | − | 0.146906i | ||||
\(716\) | 11.1244 | − | 11.1244i | 0.415737 | − | 0.415737i | ||||
\(717\) | 28.8564 | − | 7.73205i | 1.07766 | − | 0.288759i | ||||
\(718\) | 2.46410 | + | 2.46410i | 0.0919595 | + | 0.0919595i | ||||
\(719\) | −15.7942 | − | 27.3564i | −0.589025 | − | 1.02022i | −0.994360 | − | 0.106054i | \(-0.966178\pi\) |
0.405335 | − | 0.914168i | \(-0.367155\pi\) | |||||||
\(720\) | −2.53590 | + | 9.46410i | −0.0945074 | + | 0.352706i | ||||
\(721\) | 1.16025 | + | 0.401924i | 0.0432101 | + | 0.0149684i | ||||
\(722\) | 0.0717968 | − | 0.267949i | 0.00267200 | − | 0.00997204i | ||||
\(723\) | 0.0358984 | − | 0.133975i | 0.00133508 | − | 0.00498257i | ||||
\(724\) | 5.41154 | − | 20.1962i | 0.201118 | − | 0.750584i | ||||
\(725\) | −8.46410 | − | 31.5885i | −0.314349 | − | 1.17317i | ||||
\(726\) | 19.3923 | + | 11.1962i | 0.719716 | + | 0.415528i | ||||
\(727\) | − | 6.67949i | − | 0.247729i | −0.992299 | − | 0.123864i | \(-0.960471\pi\) | ||
0.992299 | − | 0.123864i | \(-0.0395288\pi\) | |||||||
\(728\) | 2.14359 | − | 1.85641i | 0.0794469 | − | 0.0688030i | ||||
\(729\) | − | 17.5885i | − | 0.651424i | ||||||
\(730\) | −7.56218 | + | 13.0981i | −0.279889 | + | 0.484782i | ||||
\(731\) | 0.0788383 | + | 0.294229i | 0.00291594 | + | 0.0108824i | ||||
\(732\) | 0.267949 | + | 0.464102i | 0.00990369 | + | 0.0171537i | ||||
\(733\) | 12.1077 | − | 45.1865i | 0.447208 | − | 1.66900i | −0.262832 | − | 0.964842i | \(-0.584657\pi\) |
0.710040 | − | 0.704161i | \(-0.248677\pi\) | |||||||
\(734\) | 24.7583 | + | 6.63397i | 0.913847 | + | 0.244864i | ||||
\(735\) | −6.46410 | + | 44.7846i | −0.238432 | + | 1.65191i | ||||
\(736\) | −13.4641 | + | 3.60770i | −0.496293 | + | 0.132981i | ||||
\(737\) | −16.6244 | − | 28.7942i | −0.612366 | − | 1.06065i | ||||
\(738\) | −6.53590 | + | 6.53590i | −0.240590 | + | 0.240590i | ||||
\(739\) | 50.3109 | − | 13.4808i | 1.85072 | − | 0.495898i | 0.851138 | − | 0.524942i | \(-0.175913\pi\) |
0.999578 | + | 0.0290444i | \(0.00924642\pi\) | |||||||
\(740\) | 74.1051 | 2.72416 | ||||||||
\(741\) | 2.26795 | − | 2.26795i | 0.0833152 | − | 0.0833152i | ||||
\(742\) | 40.4904 | + | 14.0263i | 1.48645 | + | 0.514921i | ||||
\(743\) | − | 24.9282i | − | 0.914527i | −0.889331 | − | 0.457264i | \(-0.848830\pi\) | ||
0.889331 | − | 0.457264i | \(-0.151170\pi\) | |||||||
\(744\) | −1.26795 | + | 0.732051i | −0.0464853 | + | 0.0268383i | ||||
\(745\) | −26.8923 | − | 15.5263i | −0.985258 | − | 0.568839i | ||||
\(746\) | 4.73205i | 0.173253i | ||||||||
\(747\) | 8.46410 | + | 2.26795i | 0.309685 | + | 0.0829799i | ||||
\(748\) | −3.92820 | + | 1.05256i | −0.143629 | + | 0.0384854i | ||||
\(749\) | 1.03590 | + | 2.13397i | 0.0378509 | + | 0.0779737i | ||||
\(750\) | −2.83013 | + | 10.5622i | −0.103342 | + | 0.385676i | ||||
\(751\) | 12.5263 | + | 21.6962i | 0.457090 | + | 0.791704i | 0.998806 | − | 0.0488582i | \(-0.0155582\pi\) |
−0.541715 | + | 0.840562i | \(0.682225\pi\) | |||||||
\(752\) | −30.9282 | −1.12784 | ||||||||
\(753\) | −18.5622 | + | 32.1506i | −0.676443 | + | 1.17163i | ||||
\(754\) | 2.73205 | − | 0.732051i | 0.0994954 | − | 0.0266597i | ||||
\(755\) | 22.2224 | + | 22.2224i | 0.808757 | + | 0.808757i | ||||
\(756\) | −20.8564 | + | 10.1244i | −0.758540 | + | 0.368219i | ||||
\(757\) | −1.33975 | + | 1.33975i | −0.0486939 | + | 0.0486939i | −0.731034 | − | 0.682341i | \(-0.760962\pi\) |
0.682341 | + | 0.731034i | \(0.260962\pi\) | |||||||
\(758\) | −41.7846 | − | 24.1244i | −1.51769 | − | 0.876236i | ||||
\(759\) | 18.0622 | + | 10.4282i | 0.655616 | + | 0.378520i | ||||
\(760\) | −40.0526 | + | 10.7321i | −1.45286 | + | 0.389292i | ||||
\(761\) | −15.2321 | + | 8.79423i | −0.552161 | + | 0.318791i | −0.749993 | − | 0.661445i | \(-0.769943\pi\) |
0.197832 | + | 0.980236i | \(0.436610\pi\) | |||||||
\(762\) | −3.46410 | − | 6.00000i | −0.125491 | − | 0.217357i | ||||
\(763\) | 32.7224 | + | 22.1603i | 1.18463 | + | 0.802255i | ||||
\(764\) | −15.0000 | − | 8.66025i | −0.542681 | − | 0.313317i | ||||
\(765\) | −0.294229 | + | 1.09808i | −0.0106379 | + | 0.0397010i | ||||
\(766\) | −14.8038 | + | 14.8038i | −0.534885 | + | 0.534885i | ||||
\(767\) | −1.95448 | + | 3.38526i | −0.0705723 | + | 0.122235i | ||||
\(768\) | 21.8564 | + | 21.8564i | 0.788675 | + | 0.788675i | ||||
\(769\) | −17.8564 | −0.643918 | −0.321959 | − | 0.946754i | \(-0.604341\pi\) | ||||
−0.321959 | + | 0.946754i | \(0.604341\pi\) | |||||||
\(770\) | 45.4186 | + | 30.7583i | 1.63677 | + | 1.10845i | ||||
\(771\) | 1.90192 | + | 1.90192i | 0.0684961 | + | 0.0684961i | ||||
\(772\) | 46.0000i | 1.65558i | ||||||||
\(773\) | 4.03590 | + | 15.0622i | 0.145161 | + | 0.541749i | 0.999748 | + | 0.0224406i | \(0.00714368\pi\) |
−0.854587 | + | 0.519308i | \(0.826190\pi\) | |||||||
\(774\) | −0.679492 | −0.0244238 | ||||||||
\(775\) | −1.43782 | + | 0.830127i | −0.0516481 | + | 0.0298190i | ||||
\(776\) | −21.8564 | − | 21.8564i | −0.784599 | − | 0.784599i | ||||
\(777\) | −37.0526 | − | 42.7846i | −1.32925 | − | 1.53489i | ||||
\(778\) | −25.3468 | + | 14.6340i | −0.908726 | + | 0.524653i | ||||
\(779\) | −37.7846 | − | 10.1244i | −1.35377 | − | 0.362743i | ||||
\(780\) | −4.73205 | − | 1.26795i | −0.169435 | − | 0.0453999i | ||||
\(781\) | −31.5885 | + | 8.46410i | −1.13032 | + | 0.302869i | ||||
\(782\) | −1.56218 | + | 0.418584i | −0.0558634 | + | 0.0149685i | ||||
\(783\) | −23.1244 | −0.826397 | ||||||||
\(784\) | 22.0000 | + | 17.3205i | 0.785714 | + | 0.618590i | ||||
\(785\) | 55.0526 | 1.96491 | ||||||||
\(786\) | −24.4904 | + | 6.56218i | −0.873543 | + | 0.234065i | ||||
\(787\) | −15.5263 | + | 4.16025i | −0.553452 | + | 0.148297i | −0.524696 | − | 0.851289i | \(-0.675821\pi\) |
−0.0287557 | + | 0.999586i | \(0.509154\pi\) | |||||||
\(788\) | −0.483340 | + | 1.80385i | −0.0172183 | + | 0.0642594i | ||||
\(789\) | −47.3827 | − | 12.6962i | −1.68687 | − | 0.451995i | ||||
\(790\) | −2.70577 | + | 1.56218i | −0.0962670 | + | 0.0555798i | ||||
\(791\) | 9.46410 | + | 10.9282i | 0.336505 | + | 0.388562i | ||||
\(792\) | − | 9.07180i | − | 0.322352i | ||||||
\(793\) | −0.0455173 | + | 0.0262794i | −0.00161637 | + | 0.000933210i | ||||
\(794\) | −7.51666 | −0.266756 | ||||||||
\(795\) | −19.1603 | − | 71.5070i | −0.679544 | − | 2.53609i | ||||
\(796\) | −3.85641 | −0.136687 | ||||||||
\(797\) | −30.6603 | − | 30.6603i | −1.08604 | − | 1.08604i | −0.995932 | − | 0.0901101i | \(-0.971278\pi\) |
−0.0901101 | − | 0.995932i | \(-0.528722\pi\) | |||||||
\(798\) | 26.2224 | + | 17.7583i | 0.928264 | + | 0.628638i | ||||
\(799\) | −3.58846 | −0.126950 | ||||||||
\(800\) | 24.7846 | + | 24.7846i | 0.876268 | + | 0.876268i | ||||
\(801\) | 1.90192 | − | 3.29423i | 0.0672012 | − | 0.116396i | ||||
\(802\) | −15.0000 | + | 15.0000i | −0.529668 | + | 0.529668i | ||||
\(803\) | 3.62436 | − | 13.5263i | 0.127901 | − | 0.477332i | ||||
\(804\) | −14.6603 | + | 25.3923i | −0.517027 | + | 0.895518i | ||||
\(805\) | 18.0622 | + | 12.2321i | 0.636608 | + | 0.431123i | ||||
\(806\) | −0.0717968 | − | 0.124356i | −0.00252893 | − | 0.00438024i | ||||
\(807\) | −37.4545 | + | 21.6244i | −1.31846 | + | 0.761213i | ||||
\(808\) | 10.3397 | − | 17.9090i | 0.363751 | − | 0.630035i | ||||
\(809\) | 15.5718 | + | 8.99038i | 0.547475 | + | 0.316085i | 0.748103 | − | 0.663583i | \(-0.230965\pi\) |
−0.200628 | + | 0.979668i | \(0.564298\pi\) | |||||||
\(810\) | 43.6865 | + | 25.2224i | 1.53499 | + | 0.886226i | ||||
\(811\) | −10.3205 | + | 10.3205i | −0.362402 | + | 0.362402i | −0.864697 | − | 0.502295i | \(-0.832489\pi\) |
0.502295 | + | 0.864697i | \(0.332489\pi\) | |||||||
\(812\) | 12.1962 | + | 25.1244i | 0.428001 | + | 0.881692i | ||||
\(813\) | −16.5622 | − | 16.5622i | −0.580861 | − | 0.580861i | ||||
\(814\) | −66.2750 | + | 17.7583i | −2.32294 | + | 0.622429i | ||||
\(815\) | −0.401924 | + | 0.696152i | −0.0140788 | + | 0.0243852i | ||||
\(816\) | 2.53590 | + | 2.53590i | 0.0887742 | + | 0.0887742i | ||||
\(817\) | −1.43782 | − | 2.49038i | −0.0503030 | − | 0.0871274i | ||||
\(818\) | −3.16987 | + | 11.8301i | −0.110832 | + | 0.413631i | ||||
\(819\) | 0.320508 | + | 0.660254i | 0.0111995 | + | 0.0230711i | ||||
\(820\) | 15.4641 | + | 57.7128i | 0.540030 | + | 2.01542i | ||||
\(821\) | 17.1603 | + | 4.59808i | 0.598897 | + | 0.160474i | 0.545516 | − | 0.838100i | \(-0.316334\pi\) |
0.0533808 | + | 0.998574i | \(0.483000\pi\) | |||||||
\(822\) | 37.1244i | 1.29486i | ||||||||
\(823\) | 27.0622 | + | 15.6244i | 0.943328 | + | 0.544631i | 0.891002 | − | 0.453999i | \(-0.150003\pi\) |
0.0523262 | + | 0.998630i | \(0.483336\pi\) | |||||||
\(824\) | −1.26795 | − | 0.339746i | −0.0441711 | − | 0.0118356i | ||||
\(825\) | − | 52.4449i | − | 1.82590i | ||||||
\(826\) | −36.4711 | − | 12.6340i | −1.26899 | − | 0.439592i | ||||
\(827\) | 37.7846 | − | 37.7846i | 1.31390 | − | 1.31390i | 0.395383 | − | 0.918516i | \(-0.370612\pi\) |
0.918516 | − | 0.395383i | \(-0.129388\pi\) | |||||||
\(828\) | − | 3.60770i | − | 0.125376i | ||||||
\(829\) | −33.8205 | + | 9.06218i | −1.17463 | + | 0.314742i | −0.792796 | − | 0.609487i | \(-0.791376\pi\) |
−0.381838 | + | 0.924229i | \(0.624709\pi\) | |||||||
\(830\) | 40.0526 | − | 40.0526i | 1.39024 | − | 1.39024i | ||||
\(831\) | −16.7942 | − | 29.0885i | −0.582585 | − | 1.00907i | ||||
\(832\) | −2.14359 | + | 2.14359i | −0.0743157 | + | 0.0743157i | ||||
\(833\) | 2.55256 | + | 2.00962i | 0.0884409 | + | 0.0696292i | ||||
\(834\) | −7.19615 | − | 1.92820i | −0.249182 | − | 0.0667682i | ||||
\(835\) | 5.07180 | − | 18.9282i | 0.175517 | − | 0.655037i | ||||
\(836\) | 33.2487 | − | 19.1962i | 1.14993 | − | 0.663913i | ||||
\(837\) | 0.303848 | + | 1.13397i | 0.0105025 | + | 0.0391959i | ||||
\(838\) | 19.0000 | − | 32.9090i | 0.656344 | − | 1.13682i | ||||
\(839\) | − | 37.7128i | − | 1.30199i | −0.759082 | − | 0.650995i | \(-0.774352\pi\) | ||
0.759082 | − | 0.650995i | \(-0.225648\pi\) | |||||||
\(840\) | 3.46410 | − | 48.2487i | 0.119523 | − | 1.66474i | ||||
\(841\) | − | 1.14359i | − | 0.0394343i | ||||||
\(842\) | −15.0000 | − | 8.66025i | −0.516934 | − | 0.298452i | ||||
\(843\) | −6.46410 | − | 24.1244i | −0.222635 | − | 0.830887i | ||||
\(844\) | 5.66025 | + | 1.51666i | 0.194834 | + | 0.0522056i | ||||
\(845\) | −11.1340 | + | 41.5526i | −0.383020 | + | 1.42945i | ||||
\(846\) | 2.07180 | − | 7.73205i | 0.0712298 | − | 0.265833i | ||||
\(847\) | −20.4904 | − | 7.09808i | −0.704058 | − | 0.243893i | ||||
\(848\) | −44.2487 | − | 11.8564i | −1.51951 | − | 0.407151i | ||||
\(849\) | 16.8923 | + | 29.2583i | 0.579742 | + | 1.00414i | ||||
\(850\) | 2.87564 | + | 2.87564i | 0.0986338 | + | 0.0986338i | ||||
\(851\) | −26.3564 | + | 7.06218i | −0.903486 | + | 0.242088i | ||||
\(852\) | 20.3923 | + | 20.3923i | 0.698629 | + | 0.698629i | ||||
\(853\) | −36.1244 | + | 36.1244i | −1.23687 | + | 1.23687i | −0.275603 | + | 0.961272i | \(0.588877\pi\) |
−0.961272 | + | 0.275603i | \(0.911123\pi\) | |||||||
\(854\) | −0.339746 | − | 0.392305i | −0.0116259 | − | 0.0134244i | ||||
\(855\) | − | 10.7321i | − | 0.367028i | ||||||
\(856\) | −1.26795 | − | 2.19615i | −0.0433376 | − | 0.0750629i | ||||
\(857\) | 8.89230 | + | 5.13397i | 0.303755 | + | 0.175373i | 0.644129 | − | 0.764917i | \(-0.277220\pi\) |
−0.340373 | + | 0.940290i | \(0.610553\pi\) | |||||||
\(858\) | 4.53590 | 0.154853 | ||||||||
\(859\) | 39.6506 | + | 10.6244i | 1.35286 | + | 0.362498i | 0.861191 | − | 0.508282i | \(-0.169719\pi\) |
0.491672 | + | 0.870781i | \(0.336386\pi\) | |||||||
\(860\) | −2.19615 | + | 3.80385i | −0.0748882 | + | 0.129710i | ||||
\(861\) | 25.5885 | − | 37.7846i | 0.872052 | − | 1.28770i | ||||
\(862\) | −18.2224 | − | 4.88269i | −0.620658 | − | 0.166305i | ||||
\(863\) | 7.66987 | + | 13.2846i | 0.261086 | + | 0.452213i | 0.966531 | − | 0.256551i | \(-0.0825862\pi\) |
−0.705445 | + | 0.708765i | \(0.749253\pi\) | |||||||
\(864\) | 21.4641 | − | 12.3923i | 0.730224 | − | 0.421595i | ||||
\(865\) | −7.96410 | + | 13.7942i | −0.270788 | + | 0.469018i | ||||
\(866\) | 10.6795 | + | 39.8564i | 0.362904 | + | 1.35438i | ||||
\(867\) | −22.9282 | − | 22.9282i | −0.778683 | − | 0.778683i | ||||
\(868\) | 1.07180 | − | 0.928203i | 0.0363792 | − | 0.0315053i | ||||
\(869\) | 2.04552 | − | 2.04552i | 0.0693894 | − | 0.0693894i | ||||
\(870\) | 24.1244 | − | 41.7846i | 0.817892 | − | 1.41663i | ||||
\(871\) | −2.49038 | − | 1.43782i | −0.0843833 | − | 0.0487187i | ||||
\(872\) | −36.5885 | − | 21.1244i | −1.23904 | − | 0.715361i | ||||
\(873\) | 6.92820 | − | 4.00000i | 0.234484 | − | 0.135379i | ||||
\(874\) | 13.2224 | − | 7.63397i | 0.447255 | − | 0.258223i | ||||
\(875\) | 0.758330 | − | 10.5622i | 0.0256362 | − | 0.357067i | ||||
\(876\) | −11.9282 | + | 3.19615i | −0.403017 | + | 0.107988i | ||||
\(877\) | 7.55256 | − | 28.1865i | 0.255032 | − | 0.951792i | −0.713041 | − | 0.701122i | \(-0.752683\pi\) |
0.968073 | − | 0.250669i | \(-0.0806507\pi\) | |||||||
\(878\) | 14.4641 | + | 14.4641i | 0.488140 | + | 0.488140i | ||||
\(879\) | −8.09808 | + | 14.0263i | −0.273141 | + | 0.473095i | ||||
\(880\) | −50.7846 | − | 29.3205i | −1.71195 | − | 0.988394i | ||||
\(881\) | 50.0000 | 1.68454 | 0.842271 | − | 0.539054i | \(-0.181218\pi\) | ||||
0.842271 | + | 0.539054i | \(0.181218\pi\) | |||||||
\(882\) | −5.80385 | + | 4.33975i | −0.195426 | + | 0.146127i | ||||
\(883\) | −5.00000 | − | 5.00000i | −0.168263 | − | 0.168263i | 0.617952 | − | 0.786216i | \(-0.287963\pi\) |
−0.786216 | + | 0.617952i | \(0.787963\pi\) | |||||||
\(884\) | −0.248711 | + | 0.248711i | −0.00836507 | + | 0.00836507i | ||||
\(885\) | 17.2583 | + | 64.4090i | 0.580132 | + | 2.16508i | ||||
\(886\) | − | 18.7321i | − | 0.629316i | ||||||
\(887\) | −27.7750 | + | 16.0359i | −0.932593 | + | 0.538433i | −0.887631 | − | 0.460556i | \(-0.847650\pi\) |
−0.0449622 | + | 0.998989i | \(0.514317\pi\) | |||||||
\(888\) | 42.7846 | + | 42.7846i | 1.43576 | + | 1.43576i | ||||
\(889\) | 4.39230 | + | 5.07180i | 0.147313 | + | 0.170103i | ||||
\(890\) | −12.2942 | − | 21.2942i | −0.412103 | − | 0.713784i | ||||
\(891\) | −45.1147 | − | 12.0885i | −1.51140 | − | 0.404979i | ||||
\(892\) | 30.9282 | − | 17.8564i | 1.03555 | − | 0.597877i | ||||
\(893\) | 32.7224 | − | 8.76795i | 1.09501 | − | 0.293408i | ||||
\(894\) | −6.56218 | − | 24.4904i | −0.219472 | − | 0.819081i | ||||
\(895\) | 26.3205 | 0.879798 | ||||||||
\(896\) | −24.7846 | − | 16.7846i | −0.827996 | − | 0.560734i | ||||
\(897\) | 1.80385 | 0.0602287 | ||||||||
\(898\) | 4.14359 | + | 15.4641i | 0.138274 | + | 0.516044i | ||||
\(899\) | 1.36603 | − | 0.366025i | 0.0455595 | − | 0.0122076i | ||||
\(900\) | −7.85641 | + | 4.53590i | −0.261880 | + | 0.151197i | ||||
\(901\) | −5.13397 | − | 1.37564i | −0.171037 | − | 0.0458294i | ||||
\(902\) | −27.6603 | − | 47.9090i | −0.920986 | − | 1.59519i | ||||
\(903\) | 3.29423 | − | 0.633975i | 0.109625 | − | 0.0210974i | ||||
\(904\) | −10.9282 | − | 10.9282i | −0.363467 | − | 0.363467i | ||||
\(905\) | 30.2942 | − | 17.4904i | 1.00701 | − | 0.581400i | ||||
\(906\) | 25.6603i | 0.852505i | ||||||||
\(907\) | 2.72243 | + | 10.1603i | 0.0903969 | + | 0.337366i | 0.996281 | − | 0.0861591i | \(-0.0274593\pi\) |
−0.905885 | + | 0.423525i | \(0.860793\pi\) | |||||||
\(908\) | −33.6603 | + | 33.6603i | −1.11705 | + | 1.11705i | ||||
\(909\) | 3.78461 | + | 3.78461i | 0.125528 | + | 0.125528i | ||||
\(910\) | 4.73205 | + | 0.339746i | 0.156866 | + | 0.0112625i | ||||
\(911\) | −27.3205 | −0.905169 | −0.452584 | − | 0.891722i | \(-0.649498\pi\) | ||||
−0.452584 | + | 0.891722i | \(0.649498\pi\) | |||||||
\(912\) | −29.3205 | − | 16.9282i | −0.970899 | − | 0.560549i | ||||
\(913\) | −26.2224 | + | 45.4186i | −0.867836 | + | 1.50314i | ||||
\(914\) | 29.1962 | + | 29.1962i | 0.965723 | + | 0.965723i | ||||
\(915\) | −0.232051 | + | 0.866025i | −0.00767136 | + | 0.0286299i | ||||
\(916\) | 34.8564 | − | 9.33975i | 1.15169 | − | 0.308594i | ||||
\(917\) | 22.0885 | − | 10.7224i | 0.729425 | − | 0.354086i | ||||
\(918\) | 2.49038 | − | 1.43782i | 0.0821948 | − | 0.0474552i | ||||
\(919\) | 14.1340 | − | 8.16025i | 0.466237 | − | 0.269182i | −0.248426 | − | 0.968651i | \(-0.579913\pi\) |
0.714663 | + | 0.699469i | \(0.246580\pi\) | |||||||
\(920\) | −20.1962 | − | 11.6603i | −0.665847 | − | 0.384427i | ||||
\(921\) | −21.2942 | − | 12.2942i | −0.701669 | − | 0.405109i | ||||
\(922\) | −1.33975 | + | 2.32051i | −0.0441222 | + | 0.0764219i | ||||
\(923\) | −2.00000 | + | 2.00000i | −0.0658308 | + | 0.0658308i | ||||
\(924\) | 8.46410 | + | 43.9808i | 0.278449 | + | 1.44686i | ||||
\(925\) | 48.5167 | + | 48.5167i | 1.59522 | + | 1.59522i | ||||
\(926\) | 10.9282 | + | 40.7846i | 0.359123 | + | 1.34027i | ||||
\(927\) | 0.169873 | − | 0.294229i | 0.00557936 | − | 0.00966374i | ||||
\(928\) | −14.9282 | − | 25.8564i | −0.490042 | − | 0.848778i | ||||
\(929\) | 20.0167 | + | 34.6699i | 0.656725 | + | 1.13748i | 0.981458 | + | 0.191676i | \(0.0613922\pi\) |
−0.324733 | + | 0.945806i | \(0.605274\pi\) | |||||||
\(930\) | −2.36603 | − | 0.633975i | −0.0775850 | − | 0.0207888i | ||||
\(931\) | −28.1865 | − | 12.0885i | −0.923776 | − | 0.396183i | ||||
\(932\) | −11.1962 | + | 19.3923i | −0.366742 | + | 0.635216i | ||||
\(933\) | 0.866025 | + | 0.232051i | 0.0283524 | + | 0.00759700i | ||||
\(934\) | 0.0525589 | 0.00171978 | ||||||||
\(935\) | −5.89230 | − | 3.40192i | −0.192699 | − | 0.111255i | ||||
\(936\) | −0.392305 | − | 0.679492i | −0.0128229 | − | 0.0222099i | ||||
\(937\) | − | 42.9282i | − | 1.40240i | −0.712963 | − | 0.701202i | \(-0.752647\pi\) | ||
0.712963 | − | 0.701202i | \(-0.247353\pi\) | |||||||
\(938\) | 9.29423 | − | 26.8301i | 0.303467 | − | 0.876035i | ||||
\(939\) | −13.0981 | + | 13.0981i | −0.427440 | + | 0.427440i | ||||
\(940\) | −36.5885 | − | 36.5885i | −1.19338 | − | 1.19338i | ||||
\(941\) | 16.6962 | − | 4.47372i | 0.544279 | − | 0.145839i | 0.0238050 | − | 0.999717i | \(-0.492422\pi\) |
0.520474 | + | 0.853877i | \(0.325755\pi\) | |||||||
\(942\) | 31.7846 | + | 31.7846i | 1.03560 | + | 1.03560i | ||||
\(943\) | −11.0000 | − | 19.0526i | −0.358209 | − | 0.620437i | ||||
\(944\) | 39.8564 | + | 10.6795i | 1.29722 | + | 0.347588i | ||||
\(945\) | −36.6506 | − | 12.6962i | −1.19225 | − | 0.413006i | ||||
\(946\) | 1.05256 | − | 3.92820i | 0.0342216 | − | 0.127717i | ||||
\(947\) | 10.5981 | − | 39.5526i | 0.344391 | − | 1.28529i | −0.548931 | − | 0.835868i | \(-0.684965\pi\) |
0.893322 | − | 0.449418i | \(-0.148368\pi\) | |||||||
\(948\) | −2.46410 | − | 0.660254i | −0.0800303 | − | 0.0214441i | ||||
\(949\) | −0.313467 | − | 1.16987i | −0.0101756 | − | 0.0379757i | ||||
\(950\) | −33.2487 | − | 19.1962i | −1.07873 | − | 0.622805i | ||||
\(951\) | − | 23.5885i | − | 0.764908i | ||||||
\(952\) | −2.87564 | − | 1.94744i | −0.0932002 | − | 0.0631169i | ||||
\(953\) | 23.4641i | 0.760077i | 0.924971 | + | 0.380038i | \(0.124089\pi\) | ||||
−0.924971 | + | 0.380038i | \(0.875911\pi\) | |||||||
\(954\) | 5.92820 | − | 10.2679i | 0.191933 | − | 0.332437i | ||||
\(955\) | −7.50000 | − | 27.9904i | −0.242694 | − | 0.905747i | ||||
\(956\) | 26.7846 | − | 15.4641i | 0.866276 | − | 0.500145i | ||||
\(957\) | −11.5622 | + | 43.1506i | −0.373752 | + | 1.39486i | ||||
\(958\) | 21.2942 | + | 5.70577i | 0.687985 | + | 0.184345i | ||||
\(959\) | −6.79423 | − | 35.3038i | −0.219397 | − | 1.14002i | ||||
\(960\) | 51.7128i | 1.66902i | ||||||||
\(961\) | 15.4641 | + | 26.7846i | 0.498842 | + | 0.864020i | ||||
\(962\) | −4.19615 | + | 4.19615i | −0.135289 | + | 0.135289i | ||||
\(963\) | 0.633975 | − | 0.169873i | 0.0204295 | − | 0.00547408i | ||||
\(964\) | − | 0.143594i | − | 0.00462484i | ||||||
\(965\) | −54.4186 | + | 54.4186i | −1.75180 | + | 1.75180i | ||||
\(966\) | 3.36603 | + | 17.4904i | 0.108300 | + | 0.562744i | ||||
\(967\) | − | 11.7513i | − | 0.377896i | −0.981987 | − | 0.188948i | \(-0.939492\pi\) | ||
0.981987 | − | 0.188948i | \(-0.0605078\pi\) | |||||||
\(968\) | 22.3923 | + | 6.00000i | 0.719716 | + | 0.192847i | ||||
\(969\) | −3.40192 | − | 1.96410i | −0.109286 | − | 0.0630960i | ||||
\(970\) | − | 51.7128i | − | 1.66040i | ||||||
\(971\) | −50.0429 | − | 13.4090i | −1.60595 | − | 0.430314i | −0.659121 | − | 0.752037i | \(-0.729071\pi\) |
−0.946834 | + | 0.321723i | \(0.895738\pi\) | |||||||
\(972\) | 3.85641 | + | 14.3923i | 0.123694 | + | 0.461633i | ||||
\(973\) | 7.19615 | + | 0.516660i | 0.230698 | + | 0.0165634i | ||||
\(974\) | 8.16987 | − | 30.4904i | 0.261780 | − | 0.976975i | ||||
\(975\) | −2.26795 | − | 3.92820i | −0.0726325 | − | 0.125803i | ||||
\(976\) | 0.392305 | + | 0.392305i | 0.0125574 | + | 0.0125574i | ||||
\(977\) | 22.4282 | − | 38.8468i | 0.717542 | − | 1.24282i | −0.244429 | − | 0.969667i | \(-0.578601\pi\) |
0.961971 | − | 0.273152i | \(-0.0880661\pi\) | |||||||
\(978\) | −0.633975 | + | 0.169873i | −0.0202723 | + | 0.00543194i | ||||
\(979\) | 16.0981 | + | 16.0981i | 0.514497 | + | 0.514497i | ||||
\(980\) | 5.53590 | + | 46.5167i | 0.176838 | + | 1.48592i | ||||
\(981\) | 7.73205 | − | 7.73205i | 0.246865 | − | 0.246865i | ||||
\(982\) | 47.7846 | + | 27.5885i | 1.52487 | + | 0.880383i | ||||
\(983\) | −18.8660 | − | 10.8923i | −0.601733 | − | 0.347411i | 0.167990 | − | 0.985789i | \(-0.446272\pi\) |
−0.769723 | + | 0.638378i | \(0.779606\pi\) | |||||||
\(984\) | −24.3923 | + | 42.2487i | −0.777598 | + | 1.34684i | ||||
\(985\) | −2.70577 | + | 1.56218i | −0.0862130 | + | 0.0497751i | ||||
\(986\) | −1.73205 | − | 3.00000i | −0.0551597 | − | 0.0955395i | ||||
\(987\) | −2.83013 | + | 39.4186i | −0.0900839 | + | 1.25471i | ||||
\(988\) | 1.66025 | − | 2.87564i | 0.0528197 | − | 0.0914864i | ||||
\(989\) | 0.418584 | − | 1.56218i | 0.0133102 | − | 0.0496744i | ||||
\(990\) | 10.7321 | − | 10.7321i | 0.341087 | − | 0.341087i | ||||
\(991\) | 19.7942 | − | 34.2846i | 0.628784 | − | 1.08909i | −0.359012 | − | 0.933333i | \(-0.616886\pi\) |
0.987796 | − | 0.155753i | \(-0.0497805\pi\) | |||||||
\(992\) | −1.07180 | + | 1.07180i | −0.0340296 | + | 0.0340296i | ||||
\(993\) | 34.5167 | 1.09535 | ||||||||
\(994\) | −23.1244 | − | 15.6603i | −0.733460 | − | 0.496713i | ||||
\(995\) | −4.56218 | − | 4.56218i | −0.144631 | − | 0.144631i | ||||
\(996\) | 46.2487 | 1.46545 | ||||||||
\(997\) | −1.50000 | − | 5.59808i | −0.0475055 | − | 0.177293i | 0.938097 | − | 0.346373i | \(-0.112587\pi\) |
−0.985602 | + | 0.169080i | \(0.945920\pi\) | |||||||
\(998\) | 5.41154 | 0.171299 | ||||||||
\(999\) | 42.0167 | − | 24.2583i | 1.32935 | − | 0.767500i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 112.2.w.a.109.1 | yes | 4 | |
4.3 | odd | 2 | 448.2.ba.b.81.1 | 4 | |||
7.2 | even | 3 | 112.2.w.b.93.1 | yes | 4 | ||
7.3 | odd | 6 | 784.2.m.d.589.1 | 4 | |||
7.4 | even | 3 | 784.2.m.e.589.1 | 4 | |||
7.5 | odd | 6 | 784.2.x.h.765.1 | 4 | |||
7.6 | odd | 2 | 784.2.x.a.557.1 | 4 | |||
8.3 | odd | 2 | 896.2.ba.a.417.1 | 4 | |||
8.5 | even | 2 | 896.2.ba.d.417.1 | 4 | |||
16.3 | odd | 4 | 896.2.ba.c.865.1 | 4 | |||
16.5 | even | 4 | 112.2.w.b.53.1 | yes | 4 | ||
16.11 | odd | 4 | 448.2.ba.a.305.1 | 4 | |||
16.13 | even | 4 | 896.2.ba.b.865.1 | 4 | |||
28.23 | odd | 6 | 448.2.ba.a.401.1 | 4 | |||
56.37 | even | 6 | 896.2.ba.b.289.1 | 4 | |||
56.51 | odd | 6 | 896.2.ba.c.289.1 | 4 | |||
112.5 | odd | 12 | 784.2.x.a.373.1 | 4 | |||
112.37 | even | 12 | inner | 112.2.w.a.37.1 | ✓ | 4 | |
112.51 | odd | 12 | 896.2.ba.a.737.1 | 4 | |||
112.53 | even | 12 | 784.2.m.e.197.1 | 4 | |||
112.69 | odd | 4 | 784.2.x.h.165.1 | 4 | |||
112.93 | even | 12 | 896.2.ba.d.737.1 | 4 | |||
112.101 | odd | 12 | 784.2.m.d.197.1 | 4 | |||
112.107 | odd | 12 | 448.2.ba.b.177.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.a.37.1 | ✓ | 4 | 112.37 | even | 12 | inner | |
112.2.w.a.109.1 | yes | 4 | 1.1 | even | 1 | trivial | |
112.2.w.b.53.1 | yes | 4 | 16.5 | even | 4 | ||
112.2.w.b.93.1 | yes | 4 | 7.2 | even | 3 | ||
448.2.ba.a.305.1 | 4 | 16.11 | odd | 4 | |||
448.2.ba.a.401.1 | 4 | 28.23 | odd | 6 | |||
448.2.ba.b.81.1 | 4 | 4.3 | odd | 2 | |||
448.2.ba.b.177.1 | 4 | 112.107 | odd | 12 | |||
784.2.m.d.197.1 | 4 | 112.101 | odd | 12 | |||
784.2.m.d.589.1 | 4 | 7.3 | odd | 6 | |||
784.2.m.e.197.1 | 4 | 112.53 | even | 12 | |||
784.2.m.e.589.1 | 4 | 7.4 | even | 3 | |||
784.2.x.a.373.1 | 4 | 112.5 | odd | 12 | |||
784.2.x.a.557.1 | 4 | 7.6 | odd | 2 | |||
784.2.x.h.165.1 | 4 | 112.69 | odd | 4 | |||
784.2.x.h.765.1 | 4 | 7.5 | odd | 6 | |||
896.2.ba.a.417.1 | 4 | 8.3 | odd | 2 | |||
896.2.ba.a.737.1 | 4 | 112.51 | odd | 12 | |||
896.2.ba.b.289.1 | 4 | 56.37 | even | 6 | |||
896.2.ba.b.865.1 | 4 | 16.13 | even | 4 | |||
896.2.ba.c.289.1 | 4 | 56.51 | odd | 6 | |||
896.2.ba.c.865.1 | 4 | 16.3 | odd | 4 | |||
896.2.ba.d.417.1 | 4 | 8.5 | even | 2 | |||
896.2.ba.d.737.1 | 4 | 112.93 | even | 12 |