Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(289,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.ba (of order \(12\), degree \(4\), not 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: | \(7.15459602111\) |
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: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 737.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.737 |
Dual form | 896.2.ba.d.417.1 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 | 0 | ||||||||
\(3\) | 1.86603 | + | 0.500000i | 1.07735 | + | 0.288675i | 0.753510 | − | 0.657437i | \(-0.228359\pi\) |
0.323840 | + | 0.946112i | \(0.395026\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.23205 | − | 0.866025i | 1.44542 | − | 0.387298i | 0.550990 | − | 0.834512i | \(-0.314250\pi\) |
0.894427 | + | 0.447214i | \(0.147584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 2.00000i | 0.654654 | − | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.633975 | + | 0.366025i | 0.211325 | + | 0.122008i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.13397 | + | 4.23205i | −0.341906 | + | 1.27601i | 0.554279 | + | 0.832331i | \(0.312994\pi\) |
−0.896185 | + | 0.443680i | \(0.853673\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.267949 | + | 0.267949i | −0.0743157 | + | 0.0743157i | −0.743288 | − | 0.668972i | \(-0.766735\pi\) |
0.668972 | + | 0.743288i | \(0.266735\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.46410 | 1.66902 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.232051 | + | 0.401924i | 0.0562806 | + | 0.0974808i | 0.892793 | − | 0.450467i | \(-0.148743\pi\) |
−0.836512 | + | 0.547948i | \(0.815409\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.13397 | + | 4.23205i | 0.260152 | + | 0.970899i | 0.965152 | + | 0.261692i | \(0.0842803\pi\) |
−0.705000 | + | 0.709207i | \(0.749053\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.23205 | − | 2.86603i | 0.923509 | − | 0.625418i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.13397 | − | 1.23205i | −0.444964 | − | 0.256900i | 0.260737 | − | 0.965410i | \(-0.416035\pi\) |
−0.705701 | + | 0.708510i | \(0.749368\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.36603 | − | 3.09808i | 1.07321 | − | 0.619615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.09808 | − | 3.09808i | −0.596225 | − | 0.596225i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.73205 | − | 3.73205i | 0.693024 | − | 0.693024i | −0.269872 | − | 0.962896i | \(-0.586981\pi\) |
0.962896 | + | 0.269872i | \(0.0869813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.133975 | − | 0.232051i | −0.0240625 | − | 0.0416776i | 0.853743 | − | 0.520694i | \(-0.174327\pi\) |
−0.877806 | + | 0.479016i | \(0.840993\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.23205 | + | 7.33013i | −0.736705 | + | 1.27601i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.86603 | − | 7.96410i | 0.653478 | − | 1.34618i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.6962 | + | 2.86603i | −1.75844 | + | 0.471172i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.633975 | + | 0.366025i | −0.101517 | + | 0.0586110i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.92820i | − | 1.39435i | −0.716900 | − | 0.697176i | \(-0.754440\pi\) | ||
0.716900 | − | 0.697176i | \(-0.245560\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.464102 | + | 0.464102i | 0.0707748 | + | 0.0707748i | 0.741608 | − | 0.670833i | \(-0.234063\pi\) |
−0.670833 | + | 0.741608i | \(0.734063\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.36603 | + | 0.633975i | 0.352706 | + | 0.0945074i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.86603 | + | 6.69615i | −0.563918 | + | 0.976734i | 0.433232 | + | 0.901283i | \(0.357373\pi\) |
−0.997149 | + | 0.0754516i | \(0.975960\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.232051 | + | 0.866025i | 0.0324936 | + | 0.121268i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.96410 | − | 11.0622i | 0.407151 | − | 1.51951i | −0.392904 | − | 0.919580i | \(-0.628529\pi\) |
0.800054 | − | 0.599927i | \(-0.204804\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.6603i | 1.97679i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.46410i | 1.12110i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.66987 | + | 9.96410i | −0.347588 | + | 1.29722i | 0.541972 | + | 0.840397i | \(0.317678\pi\) |
−0.889560 | + | 0.456819i | \(0.848989\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0358984 | + | 0.133975i | 0.00459632 | + | 0.0171537i | 0.968186 | − | 0.250232i | \(-0.0805069\pi\) |
−0.963590 | + | 0.267386i | \(0.913840\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.83013 | − | 0.633975i | 0.230574 | − | 0.0798733i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.633975 | + | 1.09808i | −0.0786349 | + | 0.136200i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.33013 | + | 1.96410i | 0.895518 | + | 0.239953i | 0.677090 | − | 0.735900i | \(-0.263241\pi\) |
0.218427 | + | 0.975853i | \(0.429907\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.36603 | − | 3.36603i | −0.405222 | − | 0.405222i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.46410i | − | 0.885826i | −0.896565 | − | 0.442913i | \(-0.853945\pi\) | ||
0.896565 | − | 0.442913i | \(-0.146055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.76795 | + | 1.59808i | −0.323964 | + | 0.187041i | −0.653158 | − | 0.757222i | \(-0.726556\pi\) |
0.329194 | + | 0.944262i | \(0.393223\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.5622 | − | 3.09808i | 1.33509 | − | 0.357735i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.50000 | + | 9.59808i | 0.740744 | + | 1.09380i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.330127 | + | 0.571797i | −0.0371422 | + | 0.0643322i | −0.883999 | − | 0.467489i | \(-0.845159\pi\) |
0.846857 | + | 0.531821i | \(0.178492\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.33013 | − | 9.23205i | −0.592236 | − | 1.02578i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.46410 | + | 8.46410i | −0.929056 | + | 0.929056i | −0.997645 | − | 0.0685891i | \(-0.978150\pi\) |
0.0685891 | + | 0.997645i | \(0.478150\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.09808 | + | 1.09808i | 0.119103 | + | 0.119103i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.83013 | − | 5.09808i | 0.946689 | − | 0.546571i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.50000 | + | 2.59808i | 0.476999 | + | 0.275396i | 0.719165 | − | 0.694839i | \(-0.244525\pi\) |
−0.242166 | + | 0.970235i | \(0.577858\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0717968 | + | 1.00000i | 0.00752635 | + | 0.104828i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.133975 | − | 0.500000i | −0.0138925 | − | 0.0518476i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.33013 | + | 12.6962i | 0.752055 | + | 1.30260i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9282 | 1.10959 | 0.554795 | − | 0.831987i | \(-0.312797\pi\) | ||||
0.554795 | + | 0.831987i | \(0.312797\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.26795 | + | 2.26795i | −0.227937 | + | 0.227937i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.89230 | + | 7.06218i | −0.188291 | + | 0.702713i | 0.805611 | + | 0.592445i | \(0.201837\pi\) |
−0.993902 | + | 0.110268i | \(0.964829\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.401924 | + | 0.232051i | 0.0396027 | + | 0.0228646i | 0.519671 | − | 0.854367i | \(-0.326055\pi\) |
−0.480068 | + | 0.877231i | \(0.659388\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.1962 | − | 12.9282i | 1.09263 | − | 1.26166i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.866025 | + | 0.232051i | −0.0837218 | + | 0.0224332i | −0.300437 | − | 0.953802i | \(-0.597132\pi\) |
0.216715 | + | 0.976235i | \(0.430466\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.4282 | − | 3.86603i | −1.38197 | − | 0.370298i | −0.510134 | − | 0.860095i | \(-0.670404\pi\) |
−0.871837 | + | 0.489797i | \(0.837071\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.3923 | −2.03047 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.46410 | 0.514019 | 0.257010 | − | 0.966409i | \(-0.417263\pi\) | ||||
0.257010 | + | 0.966409i | \(0.417263\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.96410 | − | 2.13397i | −0.742656 | − | 0.198994i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.267949 | + | 0.0717968i | −0.0247719 | + | 0.00663761i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.20577 | + | 0.232051i | 0.110533 | + | 0.0212721i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.09808 | − | 4.09808i | −0.645280 | − | 0.372552i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.46410 | − | 16.6603i | 0.402514 | − | 1.50220i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.83013 | − | 2.83013i | 0.253134 | − | 0.253134i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.53590 | 0.225025 | 0.112512 | − | 0.993650i | \(-0.464110\pi\) | ||||
0.112512 | + | 0.993650i | \(0.464110\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.633975 | + | 1.09808i | 0.0558184 | + | 0.0966802i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.40192 | − | 8.96410i | −0.209857 | − | 0.783197i | −0.987914 | − | 0.155003i | \(-0.950461\pi\) |
0.778057 | − | 0.628194i | \(-0.216206\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.4282 | + | 5.06218i | 0.904240 | + | 0.438946i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.6962 | − | 7.33013i | −1.09271 | − | 0.630877i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.7679 | + | 6.79423i | −1.00540 | + | 0.580470i | −0.909843 | − | 0.414953i | \(-0.863798\pi\) |
−0.0955611 | + | 0.995424i | \(0.530465\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.92820 | − | 1.92820i | −0.163548 | − | 0.163548i | 0.620588 | − | 0.784136i | \(-0.286894\pi\) |
−0.784136 | + | 0.620588i | \(0.786894\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.5622 | + | 10.5622i | −0.889496 | + | 0.889496i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.830127 | − | 1.43782i | −0.0694187 | − | 0.120237i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.83013 | − | 15.2942i | 0.733302 | − | 1.27012i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.59808 | − | 13.4282i | 0.131807 | − | 1.10754i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.96410 | + | 2.40192i | −0.734368 | + | 0.196773i | −0.606573 | − | 0.795027i | \(-0.707456\pi\) |
−0.127794 | + | 0.991801i | \(0.540790\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.13397 | + | 4.69615i | −0.661933 | + | 0.382167i | −0.793013 | − | 0.609204i | \(-0.791489\pi\) |
0.131080 | + | 0.991372i | \(0.458156\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.339746i | 0.0274668i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.633975 | − | 0.633975i | −0.0509221 | − | 0.0509221i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.8923 | + | 4.25833i | 1.26834 | + | 0.339852i | 0.829396 | − | 0.558661i | \(-0.188685\pi\) |
0.438948 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.0622 | − | 19.1603i | 0.877288 | − | 1.51951i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.16025 | + | 2.13397i | −0.485496 | + | 0.168181i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.0621778 | − | 0.232051i | −0.00487014 | − | 0.0181756i | 0.963448 | − | 0.267895i | \(-0.0863282\pi\) |
−0.968318 | + | 0.249720i | \(0.919661\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.33013 | + | 27.3564i | −0.570650 | + | 2.12969i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.85641i | − | 0.453182i | −0.973990 | − | 0.226591i | \(-0.927242\pi\) | ||
0.973990 | − | 0.226591i | \(-0.0727581\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8564i | 0.988954i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.830127 | + | 3.09808i | −0.0634814 | + | 0.236916i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.23205 | − | 4.59808i | −0.0936711 | − | 0.349585i | 0.903144 | − | 0.429339i | \(-0.141253\pi\) |
−0.996815 | + | 0.0797535i | \(0.974587\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.09808 | − | 16.0981i | 0.234193 | − | 1.21690i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.96410 | + | 17.2583i | −0.748948 | + | 1.29722i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.59808 | + | 2.03590i | 0.567907 | + | 0.152170i | 0.531336 | − | 0.847161i | \(-0.321690\pi\) |
0.0365704 | + | 0.999331i | \(0.488357\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.39230 | + | 7.39230i | 0.549466 | + | 0.549466i | 0.926286 | − | 0.376821i | \(-0.122983\pi\) |
−0.376821 | + | 0.926286i | \(0.622983\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.267949i | 0.0198074i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −32.0885 | + | 18.5263i | −2.35919 | + | 1.36208i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.96410 | + | 0.526279i | −0.143629 | + | 0.0384854i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.5622 | + | 0.830127i | −0.841025 | + | 0.0603829i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.33013 | − | 7.50000i | 0.313317 | − | 0.542681i | −0.665761 | − | 0.746165i | \(-0.731893\pi\) |
0.979078 | + | 0.203484i | \(0.0652264\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.5000 | + | 19.9186i | 0.827788 | + | 1.43377i | 0.899770 | + | 0.436365i | \(0.143734\pi\) |
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.73205 | + | 1.73205i | −0.124035 | + | 0.124035i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.660254 | − | 0.660254i | −0.0470412 | − | 0.0470412i | 0.683195 | − | 0.730236i | \(-0.260590\pi\) |
−0.730236 | + | 0.683195i | \(0.760590\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.66987 | − | 0.964102i | 0.118374 | − | 0.0683434i | −0.439644 | − | 0.898172i | \(-0.644895\pi\) |
0.558018 | + | 0.829829i | \(0.311562\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.6962 | + | 7.33013i | 0.895518 | + | 0.517027i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.00000 | − | 13.9282i | −0.0701862 | − | 0.977568i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.73205 | − | 28.8564i | −0.540030 | − | 2.01542i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.901924 | − | 1.56218i | −0.0626880 | − | 0.108579i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −19.1962 | −1.32783 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.07180 | − | 2.07180i | 0.142628 | − | 0.142628i | −0.632187 | − | 0.774816i | \(-0.717843\pi\) |
0.774816 | + | 0.632187i | \(0.217843\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.73205 | − | 13.9282i | 0.255716 | − | 0.954345i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.90192 | + | 1.09808i | 0.129710 | + | 0.0748882i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.696152 | − | 0.133975i | −0.0472579 | − | 0.00909479i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.96410 | + | 1.59808i | −0.403017 | + | 0.107988i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.169873 | − | 0.0455173i | −0.0114269 | − | 0.00306183i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.8564 | −1.19575 | −0.597877 | − | 0.801588i | \(-0.703989\pi\) | ||||
−0.597877 | + | 0.801588i | \(0.703989\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.53590 | 0.302393 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.9904 | − | 6.16025i | −1.52593 | − | 0.408870i | −0.604238 | − | 0.796804i | \(-0.706522\pi\) |
−0.921687 | + | 0.387934i | \(0.873189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.4282 | − | 4.66987i | 1.15169 | − | 0.308594i | 0.368047 | − | 0.929807i | \(-0.380027\pi\) |
0.783641 | + | 0.621213i | \(0.213360\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.33013 | + | 21.1603i | 0.482287 | + | 1.39224i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.69615 | + | 5.59808i | 0.635216 | + | 0.366742i | 0.782769 | − | 0.622312i | \(-0.213806\pi\) |
−0.147553 | + | 0.989054i | \(0.547140\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.69615 | + | 24.9904i | −0.436809 | + | 1.63019i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.901924 | + | 0.901924i | −0.0585862 | + | 0.0585862i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.4641 | −1.00029 | −0.500145 | − | 0.865942i | \(-0.666720\pi\) | ||||
−0.500145 | + | 0.865942i | \(0.666720\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0358984 | − | 0.0621778i | −0.00231242 | − | 0.00400523i | 0.864867 | − | 0.502001i | \(-0.167403\pi\) |
−0.867179 | + | 0.497996i | \(0.834069\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.92820 | − | 7.19615i | −0.123694 | − | 0.461633i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.23205 | − | 21.5263i | −0.589814 | − | 1.37526i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.43782 | − | 0.830127i | −0.0914864 | − | 0.0528197i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −20.0263 | + | 11.5622i | −1.26911 | + | 0.732723i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.5885 | − | 13.5885i | −0.857696 | − | 0.857696i | 0.133370 | − | 0.991066i | \(-0.457420\pi\) |
−0.991066 | + | 0.133370i | \(0.957420\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.63397 | − | 7.63397i | 0.479944 | − | 0.479944i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.50000 | + | 2.59808i | 0.0939336 | + | 0.162698i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.696152 | + | 1.20577i | −0.0434248 | + | 0.0752140i | −0.886921 | − | 0.461921i | \(-0.847160\pi\) |
0.843496 | + | 0.537135i | \(0.180494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.7942 | + | 26.3564i | −0.794995 | + | 1.63771i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.73205 | − | 1.00000i | 0.231008 | − | 0.0618984i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.9904 | − | 12.6962i | 1.35598 | − | 0.782878i | 0.366905 | − | 0.930258i | \(-0.380417\pi\) |
0.989080 | + | 0.147380i | \(0.0470841\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 38.3205i | − | 2.35401i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.09808 | + | 7.09808i | 0.434395 | + | 0.434395i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.6244 | − | 5.79423i | −1.31846 | − | 0.353280i | −0.470059 | − | 0.882635i | \(-0.655768\pi\) |
−0.848401 | + | 0.529354i | \(0.822434\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.06218 | − | 10.5000i | 0.368251 | − | 0.637830i | −0.621041 | − | 0.783778i | \(-0.713290\pi\) |
0.989292 | + | 0.145948i | \(0.0466233\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.366025 | + | 1.90192i | −0.0221529 | + | 0.115110i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.02628 | + | 26.2224i | 0.423701 | + | 1.58127i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.50000 | + | 16.7942i | −0.270379 | + | 1.00907i | 0.688496 | + | 0.725240i | \(0.258271\pi\) |
−0.958875 | + | 0.283828i | \(0.908396\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 0.196152i | − | 0.0117433i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.9282i | − | 0.771232i | −0.922659 | − | 0.385616i | \(-0.873989\pi\) | ||
0.922659 | − | 0.385616i | \(-0.126011\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.52628 | − | 16.8923i | 0.269059 | − | 1.00414i | −0.690659 | − | 0.723180i | \(-0.742680\pi\) |
0.959719 | − | 0.280963i | \(-0.0906538\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.33013 | + | 27.3564i | 0.434199 | + | 1.62045i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.8564 | − | 15.4641i | −1.05403 | − | 0.912817i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.39230 | − | 14.5359i | 0.493665 | − | 0.855053i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.3923 | + | 5.46410i | 1.19542 | + | 0.320311i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.92820 | − | 5.92820i | −0.346329 | − | 0.346329i | 0.512411 | − | 0.858740i | \(-0.328752\pi\) |
−0.858740 | + | 0.512411i | \(0.828752\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.5167i | 2.00964i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.6244 | − | 9.59808i | 0.964643 | − | 0.556937i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.901924 | − | 0.241670i | 0.0521596 | − | 0.0139761i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.73205 | − | 0.124356i | 0.0998337 | − | 0.00716774i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.06218 | + | 12.2321i | −0.405712 | + | 0.702713i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.232051 | + | 0.401924i | 0.0132872 | + | 0.0230141i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.00000 | + | 9.00000i | −0.513657 | + | 0.513657i | −0.915645 | − | 0.401988i | \(-0.868319\pi\) |
0.401988 | + | 0.915645i | \(0.368319\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.633975 | + | 0.633975i | 0.0360656 | + | 0.0360656i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.401924 | + | 0.232051i | −0.0227910 | + | 0.0131584i | −0.511352 | − | 0.859371i | \(-0.670855\pi\) |
0.488561 | + | 0.872530i | \(0.337522\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.30385 | + | 4.79423i | 0.469361 | + | 0.270986i | 0.715972 | − | 0.698129i | \(-0.245984\pi\) |
−0.246611 | + | 0.969115i | \(0.579317\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.36603 | − | 3.63397i | 0.302341 | − | 0.204751i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.16025 | + | 11.7942i | 0.177498 | + | 0.662430i | 0.996113 | + | 0.0880875i | \(0.0280755\pi\) |
−0.818615 | + | 0.574342i | \(0.805258\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.5622 | + | 20.0263i | 0.647358 | + | 1.12126i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.73205 | −0.0966736 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.43782 | + | 1.43782i | −0.0800026 | + | 0.0800026i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.607695 | + | 2.26795i | −0.0337089 | + | 0.125803i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.9904 | − | 14.4282i | −1.38197 | − | 0.797881i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.69615 | + | 19.3301i | 0.369171 | + | 1.06570i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.2583 | − | 4.62436i | 0.948604 | − | 0.254178i | 0.248834 | − | 0.968546i | \(-0.419953\pi\) |
0.699770 | + | 0.714369i | \(0.253286\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.83013 | − | 2.09808i | −0.429088 | − | 0.114974i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.3923 | 1.38733 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.8564 | −1.84428 | −0.922138 | − | 0.386861i | \(-0.873559\pi\) | ||||
−0.922138 | + | 0.386861i | \(0.873559\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.1962 | + | 2.73205i | 0.553779 | + | 0.148385i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.13397 | − | 0.303848i | 0.0614082 | − | 0.0164543i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.7942 | − | 7.96410i | −0.742656 | − | 0.428773i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.47372 | + | 16.6962i | −0.240162 | + | 0.896296i | 0.735592 | + | 0.677425i | \(0.236904\pi\) |
−0.975754 | + | 0.218871i | \(0.929762\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.1244 | − | 18.1244i | 0.970175 | − | 0.970175i | −0.0293934 | − | 0.999568i | \(-0.509358\pi\) |
0.999568 | + | 0.0293934i | \(0.00935756\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.66025 | 0.0886178 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.89230 | − | 11.9378i | −0.366840 | − | 0.635386i | 0.622229 | − | 0.782835i | \(-0.286227\pi\) |
−0.989070 | + | 0.147449i | \(0.952894\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.46410 | − | 24.1244i | −0.343079 | − | 1.28039i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.13397 | + | 1.03590i | 0.112942 | + | 0.0548256i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.13397 | + | 1.23205i | 0.112627 | + | 0.0650252i | 0.555255 | − | 0.831680i | \(-0.312621\pi\) |
−0.442628 | + | 0.896705i | \(0.645954\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.169873 | + | 0.0980762i | −0.00894068 | + | 0.00516191i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.1962 | − | 11.1962i | −0.587646 | − | 0.587646i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.56218 | + | 7.56218i | −0.395822 | + | 0.395822i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.06218 | + | 15.6962i | 0.473042 | + | 0.819332i | 0.999524 | − | 0.0308537i | \(-0.00982261\pi\) |
−0.526482 | + | 0.850186i | \(0.676489\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.26795 | − | 5.66025i | 0.170123 | − | 0.294661i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.9904 | − | 25.0885i | −0.882097 | − | 1.30253i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.23205 | + | 0.866025i | −0.167349 | + | 0.0448411i | −0.341521 | − | 0.939874i | \(-0.610942\pi\) |
0.174171 | + | 0.984715i | \(0.444275\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.69615 | − | 3.86603i | 0.345788 | − | 0.199641i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.00000i | 0.103005i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.1244 | + | 24.1244i | 1.23918 | + | 1.23918i | 0.960335 | + | 0.278850i | \(0.0899533\pi\) |
0.278850 | + | 0.960335i | \(0.410047\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.73205 | + | 1.26795i | 0.242430 | + | 0.0649590i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.40192 | − | 12.8205i | 0.378221 | − | 0.655097i | −0.612583 | − | 0.790406i | \(-0.709869\pi\) |
0.990803 | + | 0.135309i | \(0.0432027\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 29.3205 | + | 25.3923i | 1.49431 | + | 1.29411i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.124356 | + | 0.464102i | 0.00632135 | + | 0.0235916i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.35641 | + | 19.9904i | −0.271581 | + | 1.01355i | 0.686518 | + | 0.727113i | \(0.259138\pi\) |
−0.958098 | + | 0.286440i | \(0.907528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.14359i | − | 0.0578340i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 17.9282i | − | 0.904358i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.571797 | + | 2.13397i | −0.0287702 | + | 0.107372i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.37564 | + | 5.13397i | 0.0690416 | + | 0.257667i | 0.991816 | − | 0.127673i | \(-0.0407509\pi\) |
−0.922775 | + | 0.385340i | \(0.874084\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.9282 | + | 14.6603i | 0.847470 | + | 0.733931i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.50000 | − | 12.9904i | 0.374532 | − | 0.648709i | −0.615725 | − | 0.787961i | \(-0.711137\pi\) |
0.990257 | + | 0.139253i | \(0.0444700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0980762 | + | 0.0262794i | 0.00488552 | + | 0.00130907i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −25.2224 | − | 25.2224i | −1.25331 | − | 1.25331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 48.5167i | − | 2.40488i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.50000 | − | 4.33013i | 0.370851 | − | 0.214111i | −0.302979 | − | 0.952997i | \(-0.597981\pi\) |
0.673830 | + | 0.738886i | \(0.264648\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.3564 | + | 6.79423i | −1.25074 | + | 0.335135i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.3038 | + | 22.5981i | 0.753053 | + | 1.11198i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.0263 | + | 34.6865i | −0.983051 | + | 1.70269i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.63397 | − | 4.56218i | −0.128986 | − | 0.223411i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.0000 | − | 19.0000i | 0.928211 | − | 0.928211i | −0.0693796 | − | 0.997590i | \(-0.522102\pi\) |
0.997590 | + | 0.0693796i | \(0.0221020\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.66025 | + | 8.66025i | 0.422075 | + | 0.422075i | 0.885918 | − | 0.463843i | \(-0.153530\pi\) |
−0.463843 | + | 0.885918i | \(0.653530\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.90192 | + | 2.83013i | −0.238340 | + | 0.137605i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.49038 | + | 1.43782i | 0.120801 | + | 0.0697446i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.330127 | + | 0.160254i | 0.0159760 | + | 0.00775524i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.830127 | − | 3.09808i | −0.0400789 | − | 0.149577i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.66987 | − | 11.5526i | −0.321276 | − | 0.556467i | 0.659475 | − | 0.751726i | \(-0.270779\pi\) |
−0.980752 | + | 0.195259i | \(0.937445\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.1769 | 1.40215 | 0.701077 | − | 0.713086i | \(-0.252703\pi\) | ||||
0.701077 | + | 0.713086i | \(0.252703\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.1244 | − | 24.1244i | 1.15667 | − | 1.15667i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.79423 | − | 10.4282i | 0.133666 | − | 0.498849i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5263 | + | 7.23205i | 0.597847 | + | 0.345167i | 0.768194 | − | 0.640217i | \(-0.221156\pi\) |
−0.170347 | + | 0.985384i | \(0.554489\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.90192 | − | 4.75833i | 0.0905678 | − | 0.226587i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.7942 | − | 3.42820i | 0.607872 | − | 0.162879i | 0.0582637 | − | 0.998301i | \(-0.481444\pi\) |
0.549608 | + | 0.835422i | \(0.314777\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.7942 | + | 4.50000i | 0.796123 | + | 0.213320i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.9282 | −0.847975 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.3205 | 0.534248 | 0.267124 | − | 0.963662i | \(-0.413927\pi\) | ||||
0.267124 | + | 0.963662i | \(0.413927\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.7846 | + | 10.1244i | 1.77921 | + | 0.476737i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.5263 | + | 4.69615i | −0.823456 | + | 0.220644i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.09808 | + | 3.16987i | 0.0514786 | + | 0.148606i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.2846 | + | 14.5981i | 1.18276 | + | 0.682869i | 0.956652 | − | 0.291232i | \(-0.0940652\pi\) |
0.226112 | + | 0.974101i | \(0.427399\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.526279 | − | 1.96410i | 0.0245646 | − | 0.0916764i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.33975 | + | 1.33975i | −0.0623982 | + | 0.0623982i | −0.737617 | − | 0.675219i | \(-0.764049\pi\) |
0.675219 | + | 0.737617i | \(0.264049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.8564 | 1.38754 | 0.693772 | − | 0.720194i | \(-0.255947\pi\) | ||||
0.693772 | + | 0.720194i | \(0.255947\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.866025 | − | 1.50000i | −0.0401610 | − | 0.0695608i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.00961894 | − | 0.0358984i | −0.000445112 | − | 0.00166118i | 0.965703 | − | 0.259650i | \(-0.0836070\pi\) |
−0.966148 | + | 0.257988i | \(0.916940\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.6244 | − | 11.2583i | 0.767641 | − | 0.519861i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 27.5263 | + | 15.8923i | 1.26834 | + | 0.732279i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.49038 | + | 1.43782i | −0.114508 | + | 0.0661111i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.1962 | + | 19.1962i | 0.880780 | + | 0.880780i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.92820 | − | 5.92820i | 0.271434 | − | 0.271434i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.79423 | + | 13.5000i | 0.356127 | + | 0.616831i | 0.987310 | − | 0.158803i | \(-0.0507636\pi\) |
−0.631183 | + | 0.775634i | \(0.717430\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.09808 | − | 3.63397i | 0.0956640 | − | 0.165695i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.5622 | + | 0.901924i | −0.571599 | + | 0.0410390i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 35.3205 | − | 9.46410i | 1.60382 | − | 0.429743i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.3301 | + | 11.1603i | −0.875932 | + | 0.505719i | −0.869315 | − | 0.494259i | \(-0.835440\pi\) |
−0.00661681 | + | 0.999978i | \(0.502106\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 0.464102i | − | 0.0209874i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.5885 | − | 27.5885i | −1.24505 | − | 1.24505i | −0.957880 | − | 0.287170i | \(-0.907286\pi\) |
−0.287170 | − | 0.957880i | \(-0.592714\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.36603 | + | 0.633975i | 0.106560 | + | 0.0285528i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.36603 | + | 9.29423i | −0.241185 | + | 0.417745i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.9282 | − | 12.9282i | −0.669621 | − | 0.579909i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.990381 | − | 3.69615i | −0.0443355 | − | 0.165463i | 0.940209 | − | 0.340599i | \(-0.110630\pi\) |
−0.984544 | + | 0.175137i | \(0.943963\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.92820 | − | 10.9282i | 0.130822 | − | 0.488236i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.14359i | 0.184754i | 0.995724 | + | 0.0923769i | \(0.0294464\pi\) | ||||
−0.995724 | + | 0.0923769i | \(0.970554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.4641i | 1.08864i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.42820 | + | 23.9904i | −0.285487 | + | 1.06545i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.42820 | − | 16.5263i | −0.196277 | − | 0.732514i | −0.991933 | − | 0.126766i | \(-0.959540\pi\) |
0.795656 | − | 0.605749i | \(-0.207126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.59808 | + | 8.30385i | −0.0706947 | + | 0.367341i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.59808 | − | 16.6244i | 0.423765 | − | 0.733983i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.50000 | + | 0.401924i | 0.0660979 | + | 0.0177109i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.9545 | − | 23.9545i | −1.05352 | − | 1.05352i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 9.19615i | − | 0.403666i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.6244 | − | 21.7224i | 1.64835 | − | 0.951677i | 0.670626 | − | 0.741796i | \(-0.266026\pi\) |
0.977727 | − | 0.209881i | \(-0.0673078\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.6506 | − | 9.28461i | 1.51517 | − | 0.405988i | 0.597019 | − | 0.802227i | \(-0.296352\pi\) |
0.918147 | + | 0.396239i | \(0.129685\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.8301 | − | 28.4904i | 0.603596 | − | 1.24342i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.0621778 | − | 0.107695i | 0.00270851 | − | 0.00469127i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.46410 | − | 14.6603i | −0.368004 | − | 0.637402i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.33975 | + | 5.33975i | −0.231725 | + | 0.231725i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.39230 | + | 2.39230i | 0.103622 | + | 0.103622i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.59808 | + | 1.50000i | −0.112325 | + | 0.0648507i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.1603 | + | 7.59808i | 0.567907 | + | 0.327881i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30.4545 | + | 3.62436i | 1.31177 | + | 0.156112i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.76795 | + | 21.5263i | 0.247984 | + | 0.925487i | 0.971860 | + | 0.235558i | \(0.0756917\pi\) |
−0.723877 | + | 0.689929i | \(0.757642\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.0981 | + | 17.4904i | 0.433350 | + | 0.750584i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −49.9808 | −2.14094 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.0526 | + | 15.0526i | −0.643601 | + | 0.643601i | −0.951439 | − | 0.307838i | \(-0.900395\pi\) |
0.307838 | + | 0.951439i | \(0.400395\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0262794 | + | 0.0980762i | −0.00112158 | + | 0.00418579i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.0263 | + | 11.5622i | 0.853148 | + | 0.492565i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.571797 | + | 1.65064i | 0.0243153 | + | 0.0701921i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −69.1410 | + | 18.5263i | −2.93487 | + | 0.786397i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.23205 | + | 1.40192i | 0.221689 | + | 0.0594014i | 0.367954 | − | 0.929844i | \(-0.380058\pi\) |
−0.146265 | + | 0.989245i | \(0.546725\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.248711 | −0.0105194 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.92820 | −0.165849 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 42.6506 | + | 11.4282i | 1.79751 | + | 0.481641i | 0.993585 | − | 0.113089i | \(-0.0360746\pi\) |
0.803925 | + | 0.594731i | \(0.202741\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.6603 | − | 4.73205i | 0.742972 | − | 0.199079i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −27.6962 | − | 5.33013i | −1.16313 | − | 0.223844i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.0885 | − | 15.0622i | −1.09369 | − | 0.631439i | −0.159130 | − | 0.987258i | \(-0.550869\pi\) |
−0.934555 | + | 0.355818i | \(0.884202\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.72243 | − | 10.1603i | 0.113930 | − | 0.425193i | −0.885274 | − | 0.465069i | \(-0.846030\pi\) |
0.999205 | + | 0.0398756i | \(0.0126962\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.8301 | − | 11.8301i | 0.494211 | − | 0.494211i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.2679 | −0.636717 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.6244 | + | 30.5263i | 0.733712 | + | 1.27083i | 0.955286 | + | 0.295682i | \(0.0955470\pi\) |
−0.221575 | + | 0.975143i | \(0.571120\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.5000 | + | 42.9186i | 0.477924 | + | 1.78364i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.26795 | + | 31.5885i | 0.0940904 | + | 1.31051i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.4545 | + | 25.0885i | 1.79970 | + | 1.03906i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.803848 | + | 0.464102i | −0.0332350 | + | 0.0191882i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.07180 | − | 8.07180i | −0.333159 | − | 0.333159i | 0.520626 | − | 0.853785i | \(-0.325699\pi\) |
−0.853785 | + | 0.520626i | \(0.825699\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.830127 | − | 0.830127i | 0.0342048 | − | 0.0342048i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.901924 | − | 1.56218i | −0.0371002 | − | 0.0642594i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.69615 | + | 8.13397i | −0.192848 | + | 0.334022i | −0.946193 | − | 0.323603i | \(-0.895106\pi\) |
0.753345 | + | 0.657625i | \(0.228439\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.09808 | − | 0.294229i | 0.168005 | − | 0.0120622i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.59808 | − | 0.964102i | 0.147259 | − | 0.0394581i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.3301 | + | 14.6244i | −1.03496 | + | 0.597535i | −0.918402 | − | 0.395649i | \(-0.870520\pi\) |
−0.116559 | + | 0.993184i | \(0.537186\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10.0000i | − | 0.407909i | −0.978980 | − | 0.203954i | \(-0.934621\pi\) | ||
0.978980 | − | 0.203954i | \(-0.0653794\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.92820 | + | 3.92820i | 0.159969 | + | 0.159969i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26.4904 | − | 7.09808i | −1.07699 | − | 0.288578i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.5263 | − | 18.2321i | 0.427249 | − | 0.740016i | −0.569379 | − | 0.822075i | \(-0.692816\pi\) |
0.996627 | + | 0.0820591i | \(0.0261496\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.09808 | − | 26.4904i | 0.206584 | − | 1.07344i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.758330 | − | 2.83013i | −0.0306788 | − | 0.114495i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.76795 | − | 21.5263i | 0.232965 | − | 0.869438i | −0.746090 | − | 0.665845i | \(-0.768071\pi\) |
0.979056 | − | 0.203593i | \(-0.0652621\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 57.7128i | − | 2.32721i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.46410i | − | 0.300493i | −0.988649 | − | 0.150247i | \(-0.951993\pi\) | ||
0.988649 | − | 0.150247i | \(-0.0480068\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.93782 | − | 25.8923i | 0.278855 | − | 1.04070i | −0.674359 | − | 0.738403i | \(-0.735580\pi\) |
0.953214 | − | 0.302296i | \(-0.0977532\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.79423 | + | 10.4282i | 0.112129 | + | 0.418469i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.9904 | − | 4.50000i | 0.520449 | − | 0.180289i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.79423 | + | 15.2321i | −0.351769 | + | 0.609282i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −35.8205 | − | 9.59808i | −1.43053 | − | 0.383310i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.63397 | − | 3.63397i | −0.144896 | − | 0.144896i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.2487i | 0.646851i | 0.946254 | + | 0.323425i | \(0.104835\pi\) | ||||
−0.946254 | + | 0.323425i | \(0.895165\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.90192 | − | 2.83013i | 0.194834 | − | 0.112487i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.19615 | − | 2.19615i | 0.325254 | − | 0.0871517i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.12436 | + | 1.58846i | 0.0841700 | + | 0.0629370i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.73205 | − | 4.73205i | 0.108078 | − | 0.187197i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.4282 | + | 33.6506i | 0.767368 | + | 1.32912i | 0.938986 | + | 0.343957i | \(0.111767\pi\) |
−0.171618 | + | 0.985164i | \(0.554899\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.3923 | + | 15.3923i | −0.607013 | + | 0.607013i | −0.942164 | − | 0.335151i | \(-0.891213\pi\) |
0.335151 | + | 0.942164i | \(0.391213\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.00000 | + | 3.00000i | 0.118125 | + | 0.118125i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.1340 | + | 16.8205i | −1.14537 | + | 0.661282i | −0.947756 | − | 0.318997i | \(-0.896654\pi\) |
−0.197619 | + | 0.980279i | \(0.563321\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.1410 | − | 22.5981i | −1.53642 | − | 0.887052i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.23205 | − | 0.598076i | −0.0482879 | − | 0.0234405i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.55256 | + | 20.7224i | 0.217288 | + | 0.810931i | 0.985348 | + | 0.170554i | \(0.0545556\pi\) |
−0.768060 | + | 0.640378i | \(0.778778\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.5263 | − | 26.8923i | −0.606662 | − | 1.05077i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.33975 | −0.0912822 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.85641 | − | 8.85641i | 0.344997 | − | 0.344997i | −0.513245 | − | 0.858242i | \(-0.671557\pi\) |
0.858242 | + | 0.513245i | \(0.171557\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.83975 | + | 18.0622i | −0.188244 | + | 0.702537i | 0.805668 | + | 0.592367i | \(0.201806\pi\) |
−0.993913 | + | 0.110170i | \(0.964860\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.294229 | − | 0.169873i | −0.0114269 | − | 0.00659732i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 38.0885 | + | 7.33013i | 1.47701 | + | 0.284250i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.5622 | + | 3.36603i | −0.486409 | + | 0.130333i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.3205 | − | 8.92820i | −1.28825 | − | 0.345184i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.607695 | −0.0234598 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.784610 | −0.0302445 | −0.0151222 | − | 0.999886i | \(-0.504814\pi\) | ||||
−0.0151222 | + | 0.999886i | \(0.504814\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −26.2224 | − | 7.02628i | −1.00930 | − | 0.270442i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −49.5526 | + | 13.2776i | −1.90446 | + | 0.510298i | −0.908800 | + | 0.417233i | \(0.863000\pi\) |
−0.995660 | + | 0.0930654i | \(0.970333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.9282 | − | 21.8564i | 0.726398 | − | 0.838772i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.8205 | − | 22.9904i | −1.52593 | − | 0.880993i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.5788 | + | 43.2128i | −0.443052 | + | 1.65349i | 0.277977 | + | 0.960588i | \(0.410336\pi\) |
−0.721029 | + | 0.692905i | \(0.756331\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.1506 | + | 32.1506i | −1.22841 | + | 1.22841i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.8564 | 1.32985 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.16987 | + | 3.75833i | 0.0826656 | + | 0.143181i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.99038 | − | 11.1603i | −0.113759 | − | 0.424556i | 0.885432 | − | 0.464770i | \(-0.153863\pi\) |
−0.999191 | + | 0.0402135i | \(0.987196\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.607695 | + | 8.46410i | 0.0230844 | + | 0.321525i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.90192 | − | 4.56218i | −0.299737 | − | 0.173053i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.58846 | − | 2.07180i | 0.135923 | − | 0.0784749i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.2942 | + | 15.2942i | 0.578481 | + | 0.578481i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.39230 | + | 7.39230i | −0.279204 | + | 0.279204i | −0.832791 | − | 0.553588i | \(-0.813258\pi\) |
0.553588 | + | 0.832791i | \(0.313258\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.2583 | − | 42.0167i | −0.914920 | − | 1.58469i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.9904 | + | 43.2846i | −0.941192 | + | 1.63019i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.8468 | + | 16.0167i | 0.407935 | + | 0.602369i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.76795 | − | 2.34936i | 0.329287 | − | 0.0882323i | −0.0903879 | − | 0.995907i | \(-0.528811\pi\) |
0.419675 | + | 0.907674i | \(0.362144\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.418584 | + | 0.241670i | −0.0156981 | + | 0.00906332i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.660254i | 0.0247267i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.92820 | − | 3.92820i | −0.146906 | − | 0.146906i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28.8564 | − | 7.73205i | −1.07766 | − | 0.288759i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.7942 | + | 27.3564i | −0.589025 | + | 1.02022i | 0.405335 | + | 0.914168i | \(0.367155\pi\) |
−0.994360 | + | 0.106054i | \(0.966178\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.16025 | − | 0.401924i | 0.0432101 | − | 0.0149684i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.0358984 | − | 0.133975i | −0.00133508 | − | 0.00498257i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.46410 | − | 31.5885i | 0.314349 | − | 1.17317i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.67949i | 0.247729i | 0.992299 | + | 0.123864i | \(0.0395288\pi\) | ||||
−0.992299 | + | 0.123864i | \(0.960471\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.5885i | 0.651424i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.0788383 | + | 0.294229i | −0.00291594 | + | 0.0108824i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.1077 | − | 45.1865i | −0.447208 | − | 1.66900i | −0.710040 | − | 0.704161i | \(-0.751323\pi\) |
0.262832 | − | 0.964842i | \(-0.415343\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.46410 | − | 44.7846i | −0.238432 | − | 1.65191i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.6244 | + | 28.7942i | −0.612366 | + | 1.06065i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −50.3109 | − | 13.4808i | −1.85072 | − | 0.495898i | −0.851138 | − | 0.524942i | \(-0.824087\pi\) |
−0.999578 | + | 0.0290444i | \(0.990754\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.26795 | − | 2.26795i | −0.0833152 | − | 0.0833152i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.9282i | 0.914527i | 0.889331 | + | 0.457264i | \(0.151170\pi\) | ||||
−0.889331 | + | 0.457264i | \(0.848830\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.8923 | + | 15.5263i | −0.985258 | + | 0.568839i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.46410 | + | 2.26795i | −0.309685 | + | 0.0829799i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.03590 | + | 2.13397i | −0.0378509 | + | 0.0779737i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5263 | − | 21.6962i | 0.457090 | − | 0.791704i | −0.541715 | − | 0.840562i | \(-0.682225\pi\) |
0.998806 | + | 0.0488582i | \(0.0155582\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.5622 | − | 32.1506i | −0.676443 | − | 1.17163i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.2224 | + | 22.2224i | −0.808757 | + | 0.808757i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.33975 | + | 1.33975i | 0.0486939 | + | 0.0486939i | 0.731034 | − | 0.682341i | \(-0.239038\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.0622 | − | 10.4282i | 0.655616 | − | 0.378520i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.2321 | − | 8.79423i | −0.552161 | − | 0.318791i | 0.197832 | − | 0.980236i | \(-0.436610\pi\) |
−0.749993 | + | 0.661445i | \(0.769943\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32.7224 | + | 22.1603i | −1.18463 | + | 0.802255i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.294229 | + | 1.09808i | 0.0106379 | + | 0.0397010i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.95448 | − | 3.38526i | −0.0705723 | − | 0.122235i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.8564 | −0.643918 | −0.321959 | − | 0.946754i | \(-0.604341\pi\) | ||||
−0.321959 | + | 0.946754i | \(0.604341\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.90192 | + | 1.90192i | −0.0684961 | + | 0.0684961i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.03590 | + | 15.0622i | −0.145161 | + | 0.541749i | 0.854587 | + | 0.519308i | \(0.173810\pi\) |
−0.999748 | + | 0.0224406i | \(0.992856\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.43782 | − | 0.830127i | −0.0516481 | − | 0.0298190i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −37.0526 | + | 42.7846i | −1.32925 | + | 1.53489i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37.7846 | − | 10.1244i | 1.35377 | − | 0.362743i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.5885 | + | 8.46410i | 1.13032 | + | 0.302869i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23.1244 | −0.826397 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 55.0526 | 1.96491 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5263 | + | 4.16025i | 0.553452 | + | 0.148297i | 0.524696 | − | 0.851289i | \(-0.324179\pi\) |
0.0287557 | + | 0.999586i | \(0.490846\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 47.3827 | − | 12.6962i | 1.68687 | − | 0.451995i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.46410 | − | 10.9282i | 0.336505 | − | 0.388562i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.0455173 | − | 0.0262794i | −0.00161637 | − | 0.000933210i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.1603 | − | 71.5070i | 0.679544 | − | 2.53609i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.6603 | − | 30.6603i | 1.08604 | − | 1.08604i | 0.0901101 | − | 0.995932i | \(-0.471278\pi\) |
0.995932 | − | 0.0901101i | \(-0.0287219\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.58846 | −0.126950 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.90192 | + | 3.29423i | 0.0672012 | + | 0.116396i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.62436 | − | 13.5263i | −0.127901 | − | 0.477332i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.0622 | + | 12.2321i | −0.636608 | + | 0.431123i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.4545 | − | 21.6244i | −1.31846 | − | 0.761213i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.5718 | − | 8.99038i | 0.547475 | − | 0.316085i | −0.200628 | − | 0.979668i | \(-0.564298\pi\) |
0.748103 | + | 0.663583i | \(0.230965\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.3205 | + | 10.3205i | 0.362402 | + | 0.362402i | 0.864697 | − | 0.502295i | \(-0.167511\pi\) |
−0.502295 | + | 0.864697i | \(0.667511\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.5622 | − | 16.5622i | 0.580861 | − | 0.580861i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.401924 | − | 0.696152i | −0.0140788 | − | 0.0243852i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.43782 | + | 2.49038i | −0.0503030 | + | 0.0871274i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.320508 | + | 0.660254i | −0.0111995 | + | 0.0230711i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.1603 | + | 4.59808i | −0.598897 | + | 0.160474i | −0.545516 | − | 0.838100i | \(-0.683666\pi\) |
−0.0533808 | + | 0.998574i | \(0.517000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.0622 | − | 15.6244i | 0.943328 | − | 0.544631i | 0.0523262 | − | 0.998630i | \(-0.483336\pi\) |
0.891002 | + | 0.453999i | \(0.150003\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 52.4449i | 1.82590i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.7846 | − | 37.7846i | −1.31390 | − | 1.31390i | −0.918516 | − | 0.395383i | \(-0.870612\pi\) |
−0.395383 | − | 0.918516i | \(-0.629388\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.8205 | + | 9.06218i | 1.17463 | + | 0.314742i | 0.792796 | − | 0.609487i | \(-0.208624\pi\) |
0.381838 | + | 0.924229i | \(0.375291\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.7942 | + | 29.0885i | −0.582585 | + | 1.00907i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.55256 | − | 2.00962i | 0.0884409 | − | 0.0696292i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.07180 | − | 18.9282i | −0.175517 | − | 0.655037i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.303848 | + | 1.13397i | −0.0105025 | + | 0.0391959i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.7128i | 1.30199i | 0.759082 | + | 0.650995i | \(0.225648\pi\) | ||||
−0.759082 | + | 0.650995i | \(0.774352\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.14359i | 0.0394343i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.46410 | − | 24.1244i | 0.222635 | − | 0.830887i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.1340 | + | 41.5526i | 0.383020 | + | 1.42945i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.4904 | + | 7.09808i | −0.704058 | + | 0.243893i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.8923 | − | 29.2583i | 0.579742 | − | 1.00414i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.3564 | + | 7.06218i | 0.903486 | + | 0.242088i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.1244 | + | 36.1244i | 1.23687 | + | 1.23687i | 0.961272 | + | 0.275603i | \(0.0888774\pi\) |
0.275603 | + | 0.961272i | \(0.411123\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.7321i | 0.367028i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.89230 | − | 5.13397i | 0.303755 | − | 0.175373i | −0.340373 | − | 0.940290i | \(-0.610553\pi\) |
0.644129 | + | 0.764917i | \(0.277220\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.6506 | + | 10.6244i | −1.35286 | + | 0.362498i | −0.861191 | − | 0.508282i | \(-0.830281\pi\) |
−0.491672 | + | 0.870781i | \(0.663614\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.5885 | − | 37.7846i | −0.872052 | − | 1.28770i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.66987 | − | 13.2846i | 0.261086 | − | 0.452213i | −0.705445 | − | 0.708765i | \(-0.749253\pi\) |
0.966531 | + | 0.256551i | \(0.0825862\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.96410 | − | 13.7942i | −0.270788 | − | 0.469018i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.9282 | − | 22.9282i | 0.778683 | − | 0.778683i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.04552 | − | 2.04552i | −0.0693894 | − | 0.0693894i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.49038 | + | 1.43782i | −0.0843833 | + | 0.0487187i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.92820 | + | 4.00000i | 0.234484 | + | 0.135379i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.758330 | − | 10.5622i | −0.0256362 | − | 0.357067i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.55256 | − | 28.1865i | −0.255032 | − | 0.951792i | −0.968073 | − | 0.250669i | \(-0.919349\pi\) |
0.713041 | − | 0.701122i | \(-0.247317\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.09808 | − | 14.0263i | −0.273141 | − | 0.473095i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.0000 | 1.68454 | 0.842271 | − | 0.539054i | \(-0.181218\pi\) | ||||
0.842271 | + | 0.539054i | \(0.181218\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.00000 | − | 5.00000i | 0.168263 | − | 0.168263i | −0.617952 | − | 0.786216i | \(-0.712037\pi\) |
0.786216 | + | 0.617952i | \(0.212037\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.2583 | + | 64.4090i | −0.580132 | + | 2.16508i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.7750 | − | 16.0359i | −0.932593 | − | 0.538433i | −0.0449622 | − | 0.998989i | \(-0.514317\pi\) |
−0.887631 | + | 0.460556i | \(0.847650\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.39230 | − | 5.07180i | 0.147313 | − | 0.170103i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 45.1147 | − | 12.0885i | 1.51140 | − | 0.404979i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.7224 | − | 8.76795i | −1.09501 | − | 0.293408i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.3205 | 0.879798 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.80385 | 0.0602287 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.36603 | − | 0.366025i | −0.0455595 | − | 0.0122076i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.13397 | − | 1.37564i | 0.171037 | − | 0.0458294i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.29423 | + | 0.633975i | 0.109625 | + | 0.0210974i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.2942 | + | 17.4904i | 1.00701 | + | 0.581400i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.72243 | + | 10.1603i | −0.0903969 | + | 0.337366i | −0.996281 | − | 0.0861591i | \(-0.972541\pi\) |
0.905885 | + | 0.423525i | \(0.139207\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.78461 | + | 3.78461i | −0.125528 | + | 0.125528i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.3205 | −0.905169 | −0.452584 | − | 0.891722i | \(-0.649498\pi\) | ||||
−0.452584 | + | 0.891722i | \(0.649498\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.2224 | − | 45.4186i | −0.867836 | − | 1.50314i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.232051 | + | 0.866025i | 0.00767136 | + | 0.0286299i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.0885 | − | 10.7224i | −0.729425 | − | 0.354086i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.1340 | + | 8.16025i | 0.466237 | + | 0.269182i | 0.714663 | − | 0.699469i | \(-0.246580\pi\) |
−0.248426 | + | 0.968651i | \(0.579913\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.2942 | + | 12.2942i | −0.701669 | + | 0.405109i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.00000 | + | 2.00000i | 0.0658308 | + | 0.0658308i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48.5167 | + | 48.5167i | −1.59522 | + | 1.59522i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.169873 | + | 0.294229i | 0.00557936 | + | 0.00966374i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.0167 | − | 34.6699i | 0.656725 | − | 1.13748i | −0.324733 | − | 0.945806i | \(-0.605274\pi\) |
0.981458 | − | 0.191676i | \(-0.0613922\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.1865 | − | 12.0885i | 0.923776 | − | 0.396183i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.866025 | + | 0.232051i | −0.0283524 | + | 0.00759700i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.89230 | + | 3.40192i | −0.192699 | + | 0.111255i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.9282i | 1.40240i | 0.712963 | + | 0.701202i | \(0.247353\pi\) | ||||
−0.712963 | + | 0.701202i | \(0.752647\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.0981 | + | 13.0981i | 0.427440 | + | 0.427440i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.6962 | − | 4.47372i | −0.544279 | − | 0.145839i | −0.0238050 | − | 0.999717i | \(-0.507578\pi\) |
−0.520474 | + | 0.853877i | \(0.674245\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.0000 | + | 19.0526i | −0.358209 | + | 0.620437i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −36.6506 | + | 12.6962i | −1.19225 | + | 0.413006i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.5981 | − | 39.5526i | −0.344391 | − | 1.28529i | −0.893322 | − | 0.449418i | \(-0.851632\pi\) |
0.548931 | − | 0.835868i | \(-0.315035\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.313467 | − | 1.16987i | 0.0101756 | − | 0.0379757i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.5885i | 0.764908i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 23.4641i | − | 0.760077i | −0.924971 | − | 0.380038i | \(-0.875911\pi\) | ||
0.924971 | − | 0.380038i | \(-0.124089\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.50000 | − | 27.9904i | 0.242694 | − | 0.905747i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.5622 | + | 43.1506i | 0.373752 | + | 1.39486i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.79423 | + | 35.3038i | −0.219397 | + | 1.14002i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4641 | − | 26.7846i | 0.498842 | − | 0.864020i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.633975 | − | 0.169873i | −0.0204295 | − | 0.00547408i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 54.4186 | + | 54.4186i | 1.75180 | + | 1.75180i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.7513i | 0.377896i | 0.981987 | + | 0.188948i | \(0.0605078\pi\) | ||||
−0.981987 | + | 0.188948i | \(0.939492\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.40192 | + | 1.96410i | −0.109286 | + | 0.0630960i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.0429 | − | 13.4090i | 1.60595 | − | 0.430314i | 0.659121 | − | 0.752037i | \(-0.270929\pi\) |
0.946834 | + | 0.321723i | \(0.104262\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.19615 | + | 0.516660i | −0.230698 | + | 0.0165634i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.26795 | + | 3.92820i | −0.0726325 | + | 0.125803i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.4282 | + | 38.8468i | 0.717542 | + | 1.24282i | 0.961971 | + | 0.273152i | \(0.0880661\pi\) |
−0.244429 | + | 0.969667i | \(0.578601\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.0981 | + | 16.0981i | −0.514497 | + | 0.514497i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.73205 | − | 7.73205i | −0.246865 | − | 0.246865i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.8660 | + | 10.8923i | −0.601733 | + | 0.347411i | −0.769723 | − | 0.638378i | \(-0.779606\pi\) |
0.167990 | + | 0.985789i | \(0.446272\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.70577 | − | 1.56218i | −0.0862130 | − | 0.0497751i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.83013 | + | 39.4186i | 0.0900839 | + | 1.25471i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.418584 | − | 1.56218i | −0.0133102 | − | 0.0496744i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.7942 | + | 34.2846i | 0.628784 | + | 1.08909i | 0.987796 | + | 0.155753i | \(0.0497805\pi\) |
−0.359012 | + | 0.933333i | \(0.616886\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.5167 | 1.09535 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.56218 | − | 4.56218i | 0.144631 | − | 0.144631i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.50000 | − | 5.59808i | 0.0475055 | − | 0.177293i | −0.938097 | − | 0.346373i | \(-0.887413\pi\) |
0.985602 | + | 0.169080i | \(0.0540797\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 896.2.ba.d.737.1 | 4 | ||
4.3 | odd | 2 | 896.2.ba.a.737.1 | 4 | |||
7.4 | even | 3 | 896.2.ba.b.865.1 | 4 | |||
8.3 | odd | 2 | 448.2.ba.b.177.1 | 4 | |||
8.5 | even | 2 | 112.2.w.a.37.1 | ✓ | 4 | ||
16.3 | odd | 4 | 896.2.ba.c.289.1 | 4 | |||
16.5 | even | 4 | 112.2.w.b.93.1 | yes | 4 | ||
16.11 | odd | 4 | 448.2.ba.a.401.1 | 4 | |||
16.13 | even | 4 | 896.2.ba.b.289.1 | 4 | |||
28.11 | odd | 6 | 896.2.ba.c.865.1 | 4 | |||
56.5 | odd | 6 | 784.2.m.d.197.1 | 4 | |||
56.11 | odd | 6 | 448.2.ba.a.305.1 | 4 | |||
56.13 | odd | 2 | 784.2.x.a.373.1 | 4 | |||
56.37 | even | 6 | 784.2.m.e.197.1 | 4 | |||
56.45 | odd | 6 | 784.2.x.h.165.1 | 4 | |||
56.53 | even | 6 | 112.2.w.b.53.1 | yes | 4 | ||
112.5 | odd | 12 | 784.2.m.d.589.1 | 4 | |||
112.11 | odd | 12 | 448.2.ba.b.81.1 | 4 | |||
112.37 | even | 12 | 784.2.m.e.589.1 | 4 | |||
112.53 | even | 12 | 112.2.w.a.109.1 | yes | 4 | ||
112.67 | odd | 12 | 896.2.ba.a.417.1 | 4 | |||
112.69 | odd | 4 | 784.2.x.h.765.1 | 4 | |||
112.101 | odd | 12 | 784.2.x.a.557.1 | 4 | |||
112.109 | even | 12 | inner | 896.2.ba.d.417.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.a.37.1 | ✓ | 4 | 8.5 | even | 2 | ||
112.2.w.a.109.1 | yes | 4 | 112.53 | even | 12 | ||
112.2.w.b.53.1 | yes | 4 | 56.53 | even | 6 | ||
112.2.w.b.93.1 | yes | 4 | 16.5 | even | 4 | ||
448.2.ba.a.305.1 | 4 | 56.11 | odd | 6 | |||
448.2.ba.a.401.1 | 4 | 16.11 | odd | 4 | |||
448.2.ba.b.81.1 | 4 | 112.11 | odd | 12 | |||
448.2.ba.b.177.1 | 4 | 8.3 | odd | 2 | |||
784.2.m.d.197.1 | 4 | 56.5 | odd | 6 | |||
784.2.m.d.589.1 | 4 | 112.5 | odd | 12 | |||
784.2.m.e.197.1 | 4 | 56.37 | even | 6 | |||
784.2.m.e.589.1 | 4 | 112.37 | even | 12 | |||
784.2.x.a.373.1 | 4 | 56.13 | odd | 2 | |||
784.2.x.a.557.1 | 4 | 112.101 | odd | 12 | |||
784.2.x.h.165.1 | 4 | 56.45 | odd | 6 | |||
784.2.x.h.765.1 | 4 | 112.69 | odd | 4 | |||
896.2.ba.a.417.1 | 4 | 112.67 | odd | 12 | |||
896.2.ba.a.737.1 | 4 | 4.3 | odd | 2 | |||
896.2.ba.b.289.1 | 4 | 16.13 | even | 4 | |||
896.2.ba.b.865.1 | 4 | 7.4 | even | 3 | |||
896.2.ba.c.289.1 | 4 | 16.3 | odd | 4 | |||
896.2.ba.c.865.1 | 4 | 28.11 | odd | 6 | |||
896.2.ba.d.417.1 | 4 | 112.109 | even | 12 | inner | ||
896.2.ba.d.737.1 | 4 | 1.1 | even | 1 | trivial |