Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (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: | \(6.26027151847\) |
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 | 165.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.165 |
Dual form | 784.2.x.h.765.1 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.707107 | + | 0.707107i | ||||
\(3\) | −0.500000 | − | 1.86603i | −0.288675 | − | 1.07735i | −0.946112 | − | 0.323840i | \(-0.895026\pi\) |
0.657437 | − | 0.753510i | \(-0.271641\pi\) | |||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | −0.866025 | + | 3.23205i | −0.387298 | + | 1.44542i | 0.447214 | + | 0.894427i | \(0.352416\pi\) |
−0.834512 | + | 0.550990i | \(0.814250\pi\) | |||||||
\(6\) | 1.36603 | − | 2.36603i | 0.557678 | − | 0.965926i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | −0.633975 | + | 0.366025i | −0.211325 | + | 0.122008i | ||||
\(10\) | −4.09808 | + | 2.36603i | −1.29593 | + | 0.748203i | ||||
\(11\) | −4.23205 | + | 1.13397i | −1.27601 | + | 0.341906i | −0.832331 | − | 0.554279i | \(-0.812994\pi\) |
−0.443680 | + | 0.896185i | \(0.646327\pi\) | |||||||
\(12\) | 3.73205 | − | 1.00000i | 1.07735 | − | 0.288675i | ||||
\(13\) | −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 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −0.232051 | + | 0.401924i | −0.0562806 | + | 0.0974808i | −0.892793 | − | 0.450467i | \(-0.851257\pi\) |
0.836512 | + | 0.547948i | \(0.184591\pi\) | |||||||
\(18\) | −1.00000 | − | 0.267949i | −0.235702 | − | 0.0631562i | ||||
\(19\) | −4.23205 | − | 1.13397i | −0.970899 | − | 0.260152i | −0.261692 | − | 0.965152i | \(-0.584280\pi\) |
−0.709207 | + | 0.705000i | \(0.750947\pi\) | |||||||
\(20\) | −6.46410 | − | 1.73205i | −1.44542 | − | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.36603 | − | 3.09808i | −1.14404 | − | 0.660512i | ||||
\(23\) | 2.13397 | − | 1.23205i | 0.444964 | − | 0.256900i | −0.260737 | − | 0.965410i | \(-0.583965\pi\) |
0.705701 | + | 0.708510i | \(0.250632\pi\) | |||||||
\(24\) | 4.73205 | + | 2.73205i | 0.965926 | + | 0.557678i | ||||
\(25\) | −5.36603 | − | 3.09808i | −1.07321 | − | 0.619615i | ||||
\(26\) | −0.535898 | −0.105098 | ||||||||
\(27\) | −3.09808 | − | 3.09808i | −0.596225 | − | 0.596225i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.73205 | + | 3.73205i | −0.693024 | + | 0.693024i | −0.962896 | − | 0.269872i | \(-0.913019\pi\) |
0.269872 | + | 0.962896i | \(0.413019\pi\) | |||||||
\(30\) | 6.46410 | + | 6.46410i | 1.18018 | + | 1.18018i | ||||
\(31\) | 0.133975 | − | 0.232051i | 0.0240625 | − | 0.0416776i | −0.853743 | − | 0.520694i | \(-0.825673\pi\) |
0.877806 | + | 0.479016i | \(0.159007\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.707107 | − | 0.707107i | ||||
\(33\) | 4.23205 | + | 7.33013i | 0.736705 | + | 1.27601i | ||||
\(34\) | −0.633975 | + | 0.169873i | −0.108726 | + | 0.0291330i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.732051 | − | 1.26795i | −0.122008 | − | 0.211325i | ||||
\(37\) | −2.86603 | + | 10.6962i | −0.471172 | + | 1.75844i | 0.164399 | + | 0.986394i | \(0.447432\pi\) |
−0.635571 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(38\) | −3.09808 | − | 5.36603i | −0.502574 | − | 0.870484i | ||||
\(39\) | 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 | \(0.754440\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.464102 | − | 0.464102i | −0.0707748 | − | 0.0707748i | 0.670833 | − | 0.741608i | \(-0.265937\pi\) |
−0.741608 | + | 0.670833i | \(0.765937\pi\) | |||||||
\(44\) | −2.26795 | − | 8.46410i | −0.341906 | − | 1.27601i | ||||
\(45\) | −0.633975 | − | 2.36603i | −0.0945074 | − | 0.352706i | ||||
\(46\) | 3.36603 | + | 0.901924i | 0.496293 | + | 0.132981i | ||||
\(47\) | 3.86603 | + | 6.69615i | 0.563918 | + | 0.976734i | 0.997149 | + | 0.0754516i | \(0.0240398\pi\) |
−0.433232 | + | 0.901283i | \(0.642627\pi\) | |||||||
\(48\) | 2.00000 | + | 7.46410i | 0.288675 | + | 1.07735i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.26795 | − | 8.46410i | −0.320736 | − | 1.19700i | ||||
\(51\) | 0.866025 | + | 0.232051i | 0.121268 | + | 0.0324936i | ||||
\(52\) | −0.535898 | − | 0.535898i | −0.0743157 | − | 0.0743157i | ||||
\(53\) | 11.0622 | − | 2.96410i | 1.51951 | − | 0.407151i | 0.599927 | − | 0.800054i | \(-0.295196\pi\) |
0.919580 | + | 0.392904i | \(0.128529\pi\) | |||||||
\(54\) | − | 6.19615i | − | 0.843190i | ||||||
\(55\) | − | 14.6603i | − | 1.97679i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.46410i | 1.12110i | ||||||||
\(58\) | −7.46410 | −0.980085 | ||||||||
\(59\) | 9.96410 | − | 2.66987i | 1.29722 | − | 0.347588i | 0.456819 | − | 0.889560i | \(-0.348989\pi\) |
0.840397 | + | 0.541972i | \(0.182322\pi\) | |||||||
\(60\) | 12.9282i | 1.66902i | ||||||||
\(61\) | −0.133975 | − | 0.0358984i | −0.0171537 | − | 0.00459632i | 0.250232 | − | 0.968186i | \(-0.419493\pi\) |
−0.267386 | + | 0.963590i | \(0.586160\pi\) | |||||||
\(62\) | 0.366025 | − | 0.0980762i | 0.0464853 | − | 0.0124557i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | −0.633975 | − | 1.09808i | −0.0786349 | − | 0.136200i | ||||
\(66\) | −3.09808 | + | 11.5622i | −0.381347 | + | 1.42321i | ||||
\(67\) | 1.96410 | + | 7.33013i | 0.239953 | + | 0.895518i | 0.975853 | + | 0.218427i | \(0.0700927\pi\) |
−0.735900 | + | 0.677090i | \(0.763241\pi\) | |||||||
\(68\) | −0.803848 | − | 0.464102i | −0.0974808 | − | 0.0562806i | ||||
\(69\) | −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 | \(-0.146055\pi\) | |||||||
\(72\) | 0.535898 | − | 2.00000i | 0.0631562 | − | 0.235702i | ||||
\(73\) | −2.76795 | − | 1.59808i | −0.323964 | − | 0.187041i | 0.329194 | − | 0.944262i | \(-0.393223\pi\) |
−0.653158 | + | 0.757222i | \(0.726556\pi\) | |||||||
\(74\) | −13.5622 | + | 7.83013i | −1.57657 | + | 0.910234i | ||||
\(75\) | −3.09808 | + | 11.5622i | −0.357735 | + | 1.33509i | ||||
\(76\) | 2.26795 | − | 8.46410i | 0.260152 | − | 0.970899i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 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 | \(0.845159\pi\) | |||||||
\(80\) | 3.46410 | − | 12.9282i | 0.387298 | − | 1.44542i | ||||
\(81\) | −5.33013 | + | 9.23205i | −0.592236 | + | 1.02578i | ||||
\(82\) | −8.92820 | + | 8.92820i | −0.985955 | + | 0.985955i | ||||
\(83\) | −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 | ||||
\(86\) | − | 0.928203i | − | 0.100091i | ||||||
\(87\) | 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 | 0 | ||||||||
\(92\) | 2.46410 | + | 4.26795i | 0.256900 | + | 0.444964i | ||||
\(93\) | −0.500000 | − | 0.133975i | −0.0518476 | − | 0.0138925i | ||||
\(94\) | −2.83013 | + | 10.5622i | −0.291905 | + | 1.08941i | ||||
\(95\) | 7.33013 | − | 12.6962i | 0.752055 | − | 1.30260i | ||||
\(96\) | −5.46410 | + | 9.46410i | −0.557678 | + | 0.965926i | ||||
\(97\) | −10.9282 | −1.10959 | −0.554795 | − | 0.831987i | \(-0.687203\pi\) | ||||
−0.554795 | + | 0.831987i | \(0.687203\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.26795 | − | 2.26795i | 0.227937 | − | 0.227937i | ||||
\(100\) | 6.19615 | − | 10.7321i | 0.619615 | − | 1.07321i | ||||
\(101\) | 7.06218 | − | 1.89230i | 0.702713 | − | 0.188291i | 0.110268 | − | 0.993902i | \(-0.464829\pi\) |
0.592445 | + | 0.805611i | \(0.298163\pi\) | |||||||
\(102\) | 0.633975 | + | 1.09808i | 0.0627728 | + | 0.108726i | ||||
\(103\) | 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 | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.0263 | + | 8.09808i | 1.36235 | + | 0.786555i | ||||
\(107\) | −0.232051 | + | 0.866025i | −0.0224332 | + | 0.0837218i | −0.976235 | − | 0.216715i | \(-0.930466\pi\) |
0.953802 | + | 0.300437i | \(0.0971324\pi\) | |||||||
\(108\) | 6.19615 | − | 6.19615i | 0.596225 | − | 0.596225i | ||||
\(109\) | −3.86603 | − | 14.4282i | −0.370298 | − | 1.38197i | −0.860095 | − | 0.510134i | \(-0.829596\pi\) |
0.489797 | − | 0.871837i | \(-0.337071\pi\) | |||||||
\(110\) | 14.6603 | − | 14.6603i | 1.39780 | − | 1.39780i | ||||
\(111\) | 21.3923 | 2.03047 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.46410 | 0.514019 | 0.257010 | − | 0.966409i | \(-0.417263\pi\) | ||||
0.257010 | + | 0.966409i | \(0.417263\pi\) | |||||||
\(114\) | −8.46410 | + | 8.46410i | −0.792736 | + | 0.792736i | ||||
\(115\) | 2.13397 | + | 7.96410i | 0.198994 | + | 0.742656i | ||||
\(116\) | −7.46410 | − | 7.46410i | −0.693024 | − | 0.693024i | ||||
\(117\) | 0.0717968 | − | 0.267949i | 0.00663761 | − | 0.0247719i | ||||
\(118\) | 12.6340 | + | 7.29423i | 1.16305 | + | 0.671488i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12.9282 | + | 12.9282i | −1.18018 | + | 1.18018i | ||||
\(121\) | 7.09808 | − | 4.09808i | 0.645280 | − | 0.372552i | ||||
\(122\) | −0.0980762 | − | 0.169873i | −0.00887940 | − | 0.0153796i | ||||
\(123\) | 16.6603 | − | 4.46410i | 1.50220 | − | 0.402514i | ||||
\(124\) | 0.464102 | + | 0.267949i | 0.0416776 | + | 0.0240625i | ||||
\(125\) | 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 | \(0.464110\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.707107 | − | 0.707107i | ||||
\(129\) | −0.633975 | + | 1.09808i | −0.0558184 | + | 0.0966802i | ||||
\(130\) | 0.464102 | − | 1.73205i | 0.0407044 | − | 0.151911i | ||||
\(131\) | 8.96410 | + | 2.40192i | 0.783197 | + | 0.209857i | 0.628194 | − | 0.778057i | \(-0.283794\pi\) |
0.155003 | + | 0.987914i | \(0.450461\pi\) | |||||||
\(132\) | −14.6603 | + | 8.46410i | −1.27601 | + | 0.736705i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.36603 | + | 9.29423i | −0.463554 | + | 0.802899i | ||||
\(135\) | 12.6962 | − | 7.33013i | 1.09271 | − | 0.630877i | ||||
\(136\) | −0.339746 | − | 1.26795i | −0.0291330 | − | 0.108726i | ||||
\(137\) | 11.7679 | + | 6.79423i | 1.00540 | + | 0.580470i | 0.909843 | − | 0.414953i | \(-0.136202\pi\) |
0.0955611 | + | 0.995424i | \(0.469535\pi\) | |||||||
\(138\) | − | 6.73205i | − | 0.573070i | ||||||
\(139\) | −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 | ||||
\(142\) | 7.46410 | − | 7.46410i | 0.626373 | − | 0.626373i | ||||
\(143\) | 0.830127 | − | 1.43782i | 0.0694187 | − | 0.120237i | ||||
\(144\) | 2.53590 | − | 1.46410i | 0.211325 | − | 0.122008i | ||||
\(145\) | −8.83013 | − | 15.2942i | −0.733302 | − | 1.27012i | ||||
\(146\) | −1.16987 | − | 4.36603i | −0.0968194 | − | 0.361335i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −21.3923 | − | 5.73205i | −1.75844 | − | 0.471172i | ||||
\(149\) | −2.40192 | + | 8.96410i | −0.196773 | + | 0.734368i | 0.795027 | + | 0.606573i | \(0.207456\pi\) |
−0.991801 | + | 0.127794i | \(0.959210\pi\) | |||||||
\(150\) | −14.6603 | + | 8.46410i | −1.19700 | + | 0.691091i | ||||
\(151\) | 8.13397 | + | 4.69615i | 0.661933 | + | 0.382167i | 0.793013 | − | 0.609204i | \(-0.208511\pi\) |
−0.131080 | + | 0.991372i | \(0.541844\pi\) | |||||||
\(152\) | 10.7321 | − | 6.19615i | 0.870484 | − | 0.502574i | ||||
\(153\) | − | 0.339746i | − | 0.0274668i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.633975 | + | 0.633975i | 0.0509221 | + | 0.0509221i | ||||
\(156\) | −0.732051 | + | 1.26795i | −0.0586110 | + | 0.101517i | ||||
\(157\) | −4.25833 | − | 15.8923i | −0.339852 | − | 1.26834i | −0.898513 | − | 0.438948i | \(-0.855351\pi\) |
0.558661 | − | 0.829396i | \(-0.311315\pi\) | |||||||
\(158\) | 0.241670 | − | 0.901924i | 0.0192262 | − | 0.0717532i | ||||
\(159\) | −11.0622 | − | 19.1603i | −0.877288 | − | 1.51951i | ||||
\(160\) | 16.3923 | − | 9.46410i | 1.29593 | − | 0.748203i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −14.5622 | + | 3.90192i | −1.14411 | + | 0.306564i | ||||
\(163\) | −0.232051 | − | 0.0621778i | −0.0181756 | − | 0.00487014i | 0.249720 | − | 0.968318i | \(-0.419661\pi\) |
−0.267895 | + | 0.963448i | \(0.586328\pi\) | |||||||
\(164\) | −17.8564 | −1.39435 | ||||||||
\(165\) | −27.3564 | + | 7.33013i | −2.12969 | + | 0.570650i | ||||
\(166\) | −16.9282 | −1.31388 | ||||||||
\(167\) | 5.85641i | 0.453182i | 0.973990 | + | 0.226591i | \(0.0727581\pi\) | ||||
−0.973990 | + | 0.226591i | \(0.927242\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8564i | 0.988954i | ||||||||
\(170\) | − | 2.19615i | − | 0.168437i | ||||||
\(171\) | 3.09808 | − | 0.830127i | 0.236916 | − | 0.0634814i | ||||
\(172\) | 0.928203 | − | 0.928203i | 0.0707748 | − | 0.0707748i | ||||
\(173\) | 4.59808 | + | 1.23205i | 0.349585 | + | 0.0936711i | 0.429339 | − | 0.903144i | \(-0.358747\pi\) |
−0.0797535 | + | 0.996815i | \(0.525413\pi\) | |||||||
\(174\) | 3.73205 | + | 13.9282i | 0.282926 | + | 1.05589i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 16.9282 | − | 4.53590i | 1.27601 | − | 0.341906i | ||||
\(177\) | −9.96410 | − | 17.2583i | −0.748948 | − | 1.29722i | ||||
\(178\) | 7.09808 | + | 1.90192i | 0.532023 | + | 0.142555i | ||||
\(179\) | 2.03590 | + | 7.59808i | 0.152170 | + | 0.567907i | 0.999331 | + | 0.0365704i | \(0.0116433\pi\) |
−0.847161 | + | 0.531336i | \(0.821690\pi\) | |||||||
\(180\) | 4.73205 | − | 1.26795i | 0.352706 | − | 0.0945074i | ||||
\(181\) | 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 | ||||||||
\(184\) | −1.80385 | + | 6.73205i | −0.132981 | + | 0.496293i | ||||
\(185\) | −32.0885 | − | 18.5263i | −2.35919 | − | 1.36208i | ||||
\(186\) | −0.366025 | − | 0.633975i | −0.0268383 | − | 0.0464853i | ||||
\(187\) | 0.526279 | − | 1.96410i | 0.0384854 | − | 0.143629i | ||||
\(188\) | −13.3923 | + | 7.73205i | −0.976734 | + | 0.563918i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | \(0.731893\pi\) | |||||||
\(192\) | −14.9282 | + | 4.00000i | −1.07735 | + | 0.288675i | ||||
\(193\) | 11.5000 | − | 19.9186i | 0.827788 | − | 1.43377i | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) |
0.899770 | − | 0.436365i | \(-0.143734\pi\) | |||||||
\(194\) | −10.9282 | − | 10.9282i | −0.784599 | − | 0.784599i | ||||
\(195\) | −1.73205 | + | 1.73205i | −0.124035 | + | 0.124035i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.660254 | + | 0.660254i | 0.0470412 | + | 0.0470412i | 0.730236 | − | 0.683195i | \(-0.239410\pi\) |
−0.683195 | + | 0.730236i | \(0.739410\pi\) | |||||||
\(198\) | 4.53590 | 0.322352 | ||||||||
\(199\) | 1.66987 | + | 0.964102i | 0.118374 | + | 0.0683434i | 0.558018 | − | 0.829829i | \(-0.311562\pi\) |
−0.439644 | + | 0.898172i | \(0.644895\pi\) | |||||||
\(200\) | 16.9282 | − | 4.53590i | 1.19700 | − | 0.320736i | ||||
\(201\) | 12.6962 | − | 7.33013i | 0.895518 | − | 0.517027i | ||||
\(202\) | 8.95448 | + | 5.16987i | 0.630035 | + | 0.363751i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.464102 | + | 1.73205i | −0.0324936 | + | 0.121268i | ||||
\(205\) | −28.8564 | − | 7.73205i | −2.01542 | − | 0.540030i | ||||
\(206\) | 0.633975 | + | 0.169873i | 0.0441711 | + | 0.0118356i | ||||
\(207\) | −0.901924 | + | 1.56218i | −0.0626880 | + | 0.108579i | ||||
\(208\) | 1.07180 | − | 1.07180i | 0.0743157 | − | 0.0743157i | ||||
\(209\) | 19.1962 | 1.32783 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.07180 | + | 2.07180i | −0.142628 | + | 0.142628i | −0.774816 | − | 0.632187i | \(-0.782157\pi\) |
0.632187 | + | 0.774816i | \(0.282157\pi\) | |||||||
\(212\) | 5.92820 | + | 22.1244i | 0.407151 | + | 1.51951i | ||||
\(213\) | −13.9282 | + | 3.73205i | −0.954345 | + | 0.255716i | ||||
\(214\) | −1.09808 | + | 0.633975i | −0.0750629 | + | 0.0433376i | ||||
\(215\) | 1.90192 | − | 1.09808i | 0.129710 | − | 0.0748882i | ||||
\(216\) | 12.3923 | 0.843190 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.5622 | − | 18.2942i | 0.715361 | − | 1.23904i | ||||
\(219\) | −1.59808 | + | 5.96410i | −0.107988 | + | 0.403017i | ||||
\(220\) | 29.3205 | 1.97679 | ||||||||
\(221\) | −0.0455173 | − | 0.169873i | −0.00306183 | − | 0.0114269i | ||||
\(222\) | 21.3923 | + | 21.3923i | 1.43576 | + | 1.43576i | ||||
\(223\) | 17.8564 | 1.19575 | 0.597877 | − | 0.801588i | \(-0.296011\pi\) | ||||
0.597877 | + | 0.801588i | \(0.296011\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.53590 | 0.302393 | ||||||||
\(226\) | 5.46410 | + | 5.46410i | 0.363467 | + | 0.363467i | ||||
\(227\) | 6.16025 | + | 22.9904i | 0.408870 | + | 1.52593i | 0.796804 | + | 0.604238i | \(0.206522\pi\) |
−0.387934 | + | 0.921687i | \(0.626811\pi\) | |||||||
\(228\) | −16.9282 | −1.12110 | ||||||||
\(229\) | −4.66987 | + | 17.4282i | −0.308594 | + | 1.15169i | 0.621213 | + | 0.783641i | \(0.286640\pi\) |
−0.929807 | + | 0.368047i | \(0.880027\pi\) | |||||||
\(230\) | −5.83013 | + | 10.0981i | −0.384427 | + | 0.665847i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 14.9282i | − | 0.980085i | ||||||
\(233\) | −9.69615 | + | 5.59808i | −0.635216 | + | 0.366742i | −0.782769 | − | 0.622312i | \(-0.786194\pi\) |
0.147553 | + | 0.989054i | \(0.452860\pi\) | |||||||
\(234\) | 0.339746 | − | 0.196152i | 0.0222099 | − | 0.0128229i | ||||
\(235\) | −24.9904 | + | 6.69615i | −1.63019 | + | 0.436809i | ||||
\(236\) | 5.33975 | + | 19.9282i | 0.347588 | + | 1.29722i | ||||
\(237\) | −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 | \(0.666720\pi\) | |||||||
\(240\) | −25.8564 | −1.66902 | ||||||||
\(241\) | 0.0358984 | − | 0.0621778i | 0.00231242 | − | 0.00400523i | −0.864867 | − | 0.502001i | \(-0.832597\pi\) |
0.867179 | + | 0.497996i | \(0.165931\pi\) | |||||||
\(242\) | 11.1962 | + | 3.00000i | 0.719716 | + | 0.192847i | ||||
\(243\) | 7.19615 | + | 1.92820i | 0.461633 | + | 0.123694i | ||||
\(244\) | 0.0717968 | − | 0.267949i | 0.00459632 | − | 0.0171537i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 21.1244 | + | 12.1962i | 1.34684 | + | 0.777598i | ||||
\(247\) | 1.43782 | − | 0.830127i | 0.0914864 | − | 0.0528197i | ||||
\(248\) | 0.196152 | + | 0.732051i | 0.0124557 | + | 0.0464853i | ||||
\(249\) | 20.0263 | + | 11.5622i | 1.26911 | + | 0.732723i | ||||
\(250\) | 5.66025 | 0.357986 | ||||||||
\(251\) | −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 | ||||
\(254\) | 2.53590 | + | 2.53590i | 0.159116 | + | 0.159116i | ||||
\(255\) | −1.50000 | + | 2.59808i | −0.0939336 | + | 0.162698i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 0.696152 | + | 1.20577i | 0.0434248 | + | 0.0752140i | 0.886921 | − | 0.461921i | \(-0.152840\pi\) |
−0.843496 | + | 0.537135i | \(0.819506\pi\) | |||||||
\(258\) | −1.73205 | + | 0.464102i | −0.107833 | + | 0.0288937i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.19615 | − | 1.26795i | 0.136200 | − | 0.0786349i | ||||
\(261\) | 1.00000 | − | 3.73205i | 0.0618984 | − | 0.231008i | ||||
\(262\) | 6.56218 | + | 11.3660i | 0.405413 | + | 0.702195i | ||||
\(263\) | −21.9904 | − | 12.6962i | −1.35598 | − | 0.782878i | −0.366905 | − | 0.930258i | \(-0.619583\pi\) |
−0.989080 | + | 0.147380i | \(0.952916\pi\) | |||||||
\(264\) | −23.1244 | − | 6.19615i | −1.42321 | − | 0.381347i | ||||
\(265\) | 38.3205i | 2.35401i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.09808 | − | 7.09808i | −0.434395 | − | 0.434395i | ||||
\(268\) | −14.6603 | + | 3.92820i | −0.895518 | + | 0.239953i | ||||
\(269\) | 5.79423 | + | 21.6244i | 0.353280 | + | 1.31846i | 0.882635 | + | 0.470059i | \(0.155768\pi\) |
−0.529354 | + | 0.848401i | \(0.677566\pi\) | |||||||
\(270\) | 20.0263 | + | 5.36603i | 1.21876 | + | 0.326566i | ||||
\(271\) | −6.06218 | − | 10.5000i | −0.368251 | − | 0.637830i | 0.621041 | − | 0.783778i | \(-0.286710\pi\) |
−0.989292 | + | 0.145948i | \(0.953377\pi\) | |||||||
\(272\) | 0.928203 | − | 1.60770i | 0.0562806 | − | 0.0974808i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.97372 | + | 18.5622i | 0.300473 | + | 1.12138i | ||||
\(275\) | 26.2224 | + | 7.02628i | 1.58127 | + | 0.423701i | ||||
\(276\) | 6.73205 | − | 6.73205i | 0.405222 | − | 0.405222i | ||||
\(277\) | −16.7942 | + | 4.50000i | −1.00907 | + | 0.270379i | −0.725240 | − | 0.688496i | \(-0.758271\pi\) |
−0.283828 | + | 0.958875i | \(0.591604\pi\) | |||||||
\(278\) | − | 3.85641i | − | 0.231292i | ||||||
\(279\) | 0.196152i | 0.0117433i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.9282i | − | 0.771232i | −0.922659 | − | 0.385616i | \(-0.873989\pi\) | ||
0.922659 | − | 0.385616i | \(-0.126011\pi\) | |||||||
\(282\) | 21.1244 | 1.25794 | ||||||||
\(283\) | −16.8923 | + | 4.52628i | −1.00414 | + | 0.269059i | −0.723180 | − | 0.690659i | \(-0.757320\pi\) |
−0.280963 | + | 0.959719i | \(0.590654\pi\) | |||||||
\(284\) | 14.9282 | 0.885826 | ||||||||
\(285\) | −27.3564 | − | 7.33013i | −1.62045 | − | 0.434199i | ||||
\(286\) | 2.26795 | − | 0.607695i | 0.134107 | − | 0.0359338i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.00000 | + | 1.07180i | 0.235702 | + | 0.0631562i | ||||
\(289\) | 8.39230 | + | 14.5359i | 0.493665 | + | 0.855053i | ||||
\(290\) | 6.46410 | − | 24.1244i | 0.379585 | − | 1.41663i | ||||
\(291\) | 5.46410 | + | 20.3923i | 0.320311 | + | 1.19542i | ||||
\(292\) | 3.19615 | − | 5.53590i | 0.187041 | − | 0.323964i | ||||
\(293\) | −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 | ||||||||
\(296\) | −15.6603 | − | 27.1244i | −0.910234 | − | 1.57657i | ||||
\(297\) | 16.6244 | + | 9.59808i | 0.964643 | + | 0.556937i | ||||
\(298\) | −11.3660 | + | 6.56218i | −0.658416 | + | 0.380137i | ||||
\(299\) | −0.241670 | + | 0.901924i | −0.0139761 | + | 0.0521596i | ||||
\(300\) | −23.1244 | − | 6.19615i | −1.33509 | − | 0.357735i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.43782 | + | 12.8301i | 0.197824 | + | 0.738291i | ||||
\(303\) | −7.06218 | − | 12.2321i | −0.405712 | − | 0.702713i | ||||
\(304\) | 16.9282 | + | 4.53590i | 0.970899 | + | 0.260152i | ||||
\(305\) | 0.232051 | − | 0.401924i | 0.0132872 | − | 0.0230141i | ||||
\(306\) | 0.339746 | − | 0.339746i | 0.0194220 | − | 0.0194220i | ||||
\(307\) | −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 | ||||
\(310\) | 1.26795i | 0.0720147i | ||||||||
\(311\) | −0.401924 | − | 0.232051i | −0.0227910 | − | 0.0131584i | 0.488561 | − | 0.872530i | \(-0.337522\pi\) |
−0.511352 | + | 0.859371i | \(0.670855\pi\) | |||||||
\(312\) | −2.00000 | + | 0.535898i | −0.113228 | + | 0.0303393i | ||||
\(313\) | 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 | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.14359 | − | 0.660254i | 0.0643322 | − | 0.0371422i | ||||
\(317\) | 11.7942 | + | 3.16025i | 0.662430 | + | 0.177498i | 0.574342 | − | 0.818615i | \(-0.305258\pi\) |
0.0880875 | + | 0.996113i | \(0.471924\pi\) | |||||||
\(318\) | 8.09808 | − | 30.2224i | 0.454118 | − | 1.69479i | ||||
\(319\) | 11.5622 | − | 20.0263i | 0.647358 | − | 1.12126i | ||||
\(320\) | 25.8564 | + | 6.92820i | 1.44542 | + | 0.387298i | ||||
\(321\) | 1.73205 | 0.0966736 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.43782 | − | 1.43782i | 0.0800026 | − | 0.0800026i | ||||
\(324\) | −18.4641 | − | 10.6603i | −1.02578 | − | 0.592236i | ||||
\(325\) | 2.26795 | − | 0.607695i | 0.125803 | − | 0.0337089i | ||||
\(326\) | −0.169873 | − | 0.294229i | −0.00940839 | − | 0.0162958i | ||||
\(327\) | −24.9904 | + | 14.4282i | −1.38197 | + | 0.797881i | ||||
\(328\) | −17.8564 | − | 17.8564i | −0.985955 | − | 0.985955i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −34.6865 | − | 20.0263i | −1.90943 | − | 1.10241i | ||||
\(331\) | 4.62436 | − | 17.2583i | 0.254178 | − | 0.948604i | −0.714369 | − | 0.699770i | \(-0.753286\pi\) |
0.968546 | − | 0.248834i | \(-0.0800474\pi\) | |||||||
\(332\) | −16.9282 | − | 16.9282i | −0.929056 | − | 0.929056i | ||||
\(333\) | −2.09808 | − | 7.83013i | −0.114974 | − | 0.429088i | ||||
\(334\) | −5.85641 | + | 5.85641i | −0.320448 | + | 0.320448i | ||||
\(335\) | −25.3923 | −1.38733 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.8564 | −1.84428 | −0.922138 | − | 0.386861i | \(-0.873559\pi\) | ||||
−0.922138 | + | 0.386861i | \(0.873559\pi\) | |||||||
\(338\) | −12.8564 | + | 12.8564i | −0.699296 | + | 0.699296i | ||||
\(339\) | −2.73205 | − | 10.1962i | −0.148385 | − | 0.553779i | ||||
\(340\) | 2.19615 | − | 2.19615i | 0.119103 | − | 0.119103i | ||||
\(341\) | −0.303848 | + | 1.13397i | −0.0164543 | + | 0.0614082i | ||||
\(342\) | 3.92820 | + | 2.26795i | 0.212413 | + | 0.122637i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.85641 | 0.100091 | ||||||||
\(345\) | 13.7942 | − | 7.96410i | 0.742656 | − | 0.428773i | ||||
\(346\) | 3.36603 | + | 5.83013i | 0.180959 | + | 0.313430i | ||||
\(347\) | −16.6962 | + | 4.47372i | −0.896296 | + | 0.240162i | −0.677425 | − | 0.735592i | \(-0.736904\pi\) |
−0.218871 | + | 0.975754i | \(0.570238\pi\) | |||||||
\(348\) | −10.1962 | + | 17.6603i | −0.546571 | + | 0.946689i | ||||
\(349\) | 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 | ||||||||
\(352\) | 21.4641 | + | 12.3923i | 1.14404 | + | 0.660512i | ||||
\(353\) | 6.89230 | − | 11.9378i | 0.366840 | − | 0.635386i | −0.622229 | − | 0.782835i | \(-0.713773\pi\) |
0.989070 | + | 0.147449i | \(0.0471062\pi\) | |||||||
\(354\) | 7.29423 | − | 27.2224i | 0.387684 | − | 1.44686i | ||||
\(355\) | 24.1244 | + | 6.46410i | 1.28039 | + | 0.343079i | ||||
\(356\) | 5.19615 | + | 9.00000i | 0.275396 | + | 0.476999i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.56218 | + | 9.63397i | −0.293970 | + | 0.509171i | ||||
\(359\) | −2.13397 | + | 1.23205i | −0.112627 | + | 0.0650252i | −0.555255 | − | 0.831680i | \(-0.687379\pi\) |
0.442628 | + | 0.896705i | \(0.354046\pi\) | |||||||
\(360\) | 6.00000 | + | 3.46410i | 0.316228 | + | 0.182574i | ||||
\(361\) | 0.169873 | + | 0.0980762i | 0.00894068 | + | 0.00516191i | ||||
\(362\) | 14.7846i | 0.777062i | ||||||||
\(363\) | −11.1962 | − | 11.1962i | −0.587646 | − | 0.587646i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.56218 | − | 7.56218i | 0.395822 | − | 0.395822i | ||||
\(366\) | −0.267949 | + | 0.267949i | −0.0140059 | + | 0.0140059i | ||||
\(367\) | −9.06218 | + | 15.6962i | −0.473042 | + | 0.819332i | −0.999524 | − | 0.0308537i | \(-0.990177\pi\) |
0.526482 | + | 0.850186i | \(0.323511\pi\) | |||||||
\(368\) | −8.53590 | + | 4.92820i | −0.444964 | + | 0.256900i | ||||
\(369\) | −3.26795 | − | 5.66025i | −0.170123 | − | 0.294661i | ||||
\(370\) | −13.5622 | − | 50.6147i | −0.705064 | − | 2.63133i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.267949 | − | 1.00000i | 0.0138925 | − | 0.0518476i | ||||
\(373\) | −0.866025 | + | 3.23205i | −0.0448411 | + | 0.167349i | −0.984715 | − | 0.174171i | \(-0.944275\pi\) |
0.939874 | + | 0.341521i | \(0.110942\pi\) | |||||||
\(374\) | 2.49038 | − | 1.43782i | 0.128775 | − | 0.0743480i | ||||
\(375\) | −6.69615 | − | 3.86603i | −0.345788 | − | 0.199641i | ||||
\(376\) | −21.1244 | − | 5.66025i | −1.08941 | − | 0.291905i | ||||
\(377\) | − | 2.00000i | − | 0.103005i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.1244 | − | 24.1244i | −1.23918 | − | 1.23918i | −0.960335 | − | 0.278850i | \(-0.910047\pi\) |
−0.278850 | − | 0.960335i | \(-0.589953\pi\) | |||||||
\(380\) | 25.3923 | + | 14.6603i | 1.30260 | + | 0.752055i | ||||
\(381\) | −1.26795 | − | 4.73205i | −0.0649590 | − | 0.242430i | ||||
\(382\) | −3.16987 | + | 11.8301i | −0.162185 | + | 0.605282i | ||||
\(383\) | −7.40192 | − | 12.8205i | −0.378221 | − | 0.655097i | 0.612583 | − | 0.790406i | \(-0.290131\pi\) |
−0.990803 | + | 0.135309i | \(0.956797\pi\) | |||||||
\(384\) | −18.9282 | − | 10.9282i | −0.965926 | − | 0.557678i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 31.4186 | − | 8.41858i | 1.59916 | − | 0.428495i | ||||
\(387\) | 0.464102 | + | 0.124356i | 0.0235916 | + | 0.00632135i | ||||
\(388\) | − | 21.8564i | − | 1.10959i | ||||||
\(389\) | −19.9904 | + | 5.35641i | −1.01355 | + | 0.271581i | −0.727113 | − | 0.686518i | \(-0.759138\pi\) |
−0.286440 | + | 0.958098i | \(0.592472\pi\) | |||||||
\(390\) | −3.46410 | −0.175412 | ||||||||
\(391\) | 1.14359i | 0.0578340i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 17.9282i | − | 0.904358i | ||||||
\(394\) | 1.32051i | 0.0665262i | ||||||||
\(395\) | 2.13397 | − | 0.571797i | 0.107372 | − | 0.0287702i | ||||
\(396\) | 4.53590 | + | 4.53590i | 0.227937 | + | 0.227937i | ||||
\(397\) | −5.13397 | − | 1.37564i | −0.257667 | − | 0.0690416i | 0.127673 | − | 0.991816i | \(-0.459249\pi\) |
−0.385340 | + | 0.922775i | \(0.625916\pi\) | |||||||
\(398\) | 0.705771 | + | 2.63397i | 0.0353771 | + | 0.132029i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 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 | \(0.711137\pi\) | |||||||
\(402\) | 20.0263 | + | 5.36603i | 0.998820 | + | 0.267633i | ||||
\(403\) | 0.0262794 | + | 0.0980762i | 0.00130907 | + | 0.00488552i | ||||
\(404\) | 3.78461 | + | 14.1244i | 0.188291 | + | 0.702713i | ||||
\(405\) | −25.2224 | − | 25.2224i | −1.25331 | − | 1.25331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 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 | \(0.597981\pi\) | |||||||
\(410\) | −21.1244 | − | 36.5885i | −1.04326 | − | 1.80698i | ||||
\(411\) | 6.79423 | − | 25.3564i | 0.335135 | − | 1.25074i | ||||
\(412\) | 0.464102 | + | 0.803848i | 0.0228646 | + | 0.0396027i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.46410 | + | 0.660254i | −0.121104 | + | 0.0324497i | ||||
\(415\) | −20.0263 | − | 34.6865i | −0.983051 | − | 1.70269i | ||||
\(416\) | 2.14359 | 0.105098 | ||||||||
\(417\) | −2.63397 | + | 4.56218i | −0.128986 | + | 0.223411i | ||||
\(418\) | 19.1962 | + | 19.1962i | 0.938915 | + | 0.938915i | ||||
\(419\) | 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 | 0.463843 | − | 0.885918i | \(-0.346470\pi\) |
−0.885918 | + | 0.463843i | \(0.846470\pi\) | |||||||
\(422\) | −4.14359 | −0.201707 | ||||||||
\(423\) | −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 | 0 | ||||||||
\(428\) | −1.73205 | − | 0.464102i | −0.0837218 | − | 0.0224332i | ||||
\(429\) | −3.09808 | − | 0.830127i | −0.149577 | − | 0.0400789i | ||||
\(430\) | 3.00000 | + | 0.803848i | 0.144673 | + | 0.0387650i | ||||
\(431\) | −6.66987 | + | 11.5526i | −0.321276 | + | 0.556467i | −0.980752 | − | 0.195259i | \(-0.937445\pi\) |
0.659475 | + | 0.751726i | \(0.270779\pi\) | |||||||
\(432\) | 12.3923 | + | 12.3923i | 0.596225 | + | 0.596225i | ||||
\(433\) | −29.1769 | −1.40215 | −0.701077 | − | 0.713086i | \(-0.747297\pi\) | ||||
−0.701077 | + | 0.713086i | \(0.747297\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −24.1244 | + | 24.1244i | −1.15667 | + | 1.15667i | ||||
\(436\) | 28.8564 | − | 7.73205i | 1.38197 | − | 0.370298i | ||||
\(437\) | −10.4282 | + | 2.79423i | −0.498849 | + | 0.133666i | ||||
\(438\) | −7.56218 | + | 4.36603i | −0.361335 | + | 0.208617i | ||||
\(439\) | 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 | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.124356 | − | 0.215390i | 0.00591500 | − | 0.0102451i | ||||
\(443\) | 3.42820 | − | 12.7942i | 0.162879 | − | 0.607872i | −0.835422 | − | 0.549608i | \(-0.814777\pi\) |
0.998301 | − | 0.0582637i | \(-0.0185564\pi\) | |||||||
\(444\) | 42.7846i | 2.03047i | ||||||||
\(445\) | 4.50000 | + | 16.7942i | 0.213320 | + | 0.796123i | ||||
\(446\) | 17.8564 | + | 17.8564i | 0.845525 | + | 0.845525i | ||||
\(447\) | 17.9282 | 0.847975 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.3205 | 0.534248 | 0.267124 | − | 0.963662i | \(-0.413927\pi\) | ||||
0.267124 | + | 0.963662i | \(0.413927\pi\) | |||||||
\(450\) | 4.53590 | + | 4.53590i | 0.213824 | + | 0.213824i | ||||
\(451\) | −10.1244 | − | 37.7846i | −0.476737 | − | 1.77921i | ||||
\(452\) | 10.9282i | 0.514019i | ||||||||
\(453\) | 4.69615 | − | 17.5263i | 0.220644 | − | 0.823456i | ||||
\(454\) | −16.8301 | + | 29.1506i | −0.789877 | + | 1.36811i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −16.9282 | − | 16.9282i | −0.792736 | − | 0.792736i | ||||
\(457\) | −25.2846 | + | 14.5981i | −1.18276 | + | 0.682869i | −0.956652 | − | 0.291232i | \(-0.905935\pi\) |
−0.226112 | + | 0.974101i | \(0.572601\pi\) | |||||||
\(458\) | −22.0981 | + | 12.7583i | −1.03258 | + | 0.596158i | ||||
\(459\) | 1.96410 | − | 0.526279i | 0.0916764 | − | 0.0245646i | ||||
\(460\) | −15.9282 | + | 4.26795i | −0.742656 | + | 0.198994i | ||||
\(461\) | −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 | \(0.255947\pi\) | |||||||
\(464\) | 14.9282 | − | 14.9282i | 0.693024 | − | 0.693024i | ||||
\(465\) | 0.866025 | − | 1.50000i | 0.0401610 | − | 0.0695608i | ||||
\(466\) | −15.2942 | − | 4.09808i | −0.708491 | − | 0.189840i | ||||
\(467\) | 0.0358984 | + | 0.00961894i | 0.00166118 | + | 0.000445112i | 0.259650 | − | 0.965703i | \(-0.416393\pi\) |
−0.257988 | + | 0.966148i | \(0.583060\pi\) | |||||||
\(468\) | 0.535898 | + | 0.143594i | 0.0247719 | + | 0.00663761i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −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 | ||||
\(474\) | −1.80385 | −0.0828535 | ||||||||
\(475\) | 19.1962 | + | 19.1962i | 0.880780 | + | 0.880780i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.92820 | + | 5.92820i | −0.271434 | + | 0.271434i | ||||
\(478\) | −15.4641 | − | 15.4641i | −0.707312 | − | 0.707312i | ||||
\(479\) | −7.79423 | + | 13.5000i | −0.356127 | + | 0.616831i | −0.987310 | − | 0.158803i | \(-0.949236\pi\) |
0.631183 | + | 0.775634i | \(0.282570\pi\) | |||||||
\(480\) | −25.8564 | − | 25.8564i | −1.18018 | − | 1.18018i | ||||
\(481\) | −2.09808 | − | 3.63397i | −0.0956640 | − | 0.165695i | ||||
\(482\) | 0.0980762 | − | 0.0262794i | 0.00446725 | − | 0.00119700i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.19615 | + | 14.1962i | 0.372552 | + | 0.645280i | ||||
\(485\) | 9.46410 | − | 35.3205i | 0.429743 | − | 1.60382i | ||||
\(486\) | 5.26795 | + | 9.12436i | 0.238959 | + | 0.413889i | ||||
\(487\) | 19.3301 | + | 11.1603i | 0.875932 | + | 0.505719i | 0.869315 | − | 0.494259i | \(-0.164560\pi\) |
0.00661681 | + | 0.999978i | \(0.497894\pi\) | |||||||
\(488\) | 0.339746 | − | 0.196152i | 0.0153796 | − | 0.00887940i | ||||
\(489\) | 0.464102i | 0.0209874i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.5885 | + | 27.5885i | 1.24505 | + | 1.24505i | 0.957880 | + | 0.287170i | \(0.0927145\pi\) |
0.287170 | + | 0.957880i | \(0.407286\pi\) | |||||||
\(492\) | 8.92820 | + | 33.3205i | 0.402514 | + | 1.50220i | ||||
\(493\) | −0.633975 | − | 2.36603i | −0.0285528 | − | 0.106560i | ||||
\(494\) | 2.26795 | + | 0.607695i | 0.102040 | + | 0.0273415i | ||||
\(495\) | 5.36603 | + | 9.29423i | 0.241185 | + | 0.417745i | ||||
\(496\) | −0.535898 | + | 0.928203i | −0.0240625 | + | 0.0416776i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.46410 | + | 31.5885i | 0.379285 | + | 1.41551i | ||||
\(499\) | −3.69615 | − | 0.990381i | −0.165463 | − | 0.0443355i | 0.175137 | − | 0.984544i | \(-0.443963\pi\) |
−0.340599 | + | 0.940209i | \(0.610630\pi\) | |||||||
\(500\) | 5.66025 | + | 5.66025i | 0.253134 | + | 0.253134i | ||||
\(501\) | 10.9282 | − | 2.92820i | 0.488236 | − | 0.130822i | ||||
\(502\) | − | 27.1769i | − | 1.21297i | ||||||
\(503\) | − | 4.14359i | − | 0.184754i | −0.995724 | − | 0.0923769i | \(-0.970554\pi\) | ||
0.995724 | − | 0.0923769i | \(-0.0294464\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.4641i | 1.08864i | ||||||||
\(506\) | −15.2679 | −0.678743 | ||||||||
\(507\) | 23.9904 | − | 6.42820i | 1.06545 | − | 0.285487i | ||||
\(508\) | 5.07180i | 0.225025i | ||||||||
\(509\) | 16.5263 | + | 4.42820i | 0.732514 | + | 0.196277i | 0.605749 | − | 0.795656i | \(-0.292874\pi\) |
0.126766 | + | 0.991933i | \(0.459540\pi\) | |||||||
\(510\) | −4.09808 | + | 1.09808i | −0.181466 | + | 0.0486236i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | 9.59808 | + | 16.6244i | 0.423765 | + | 0.733983i | ||||
\(514\) | −0.509619 | + | 1.90192i | −0.0224783 | + | 0.0838903i | ||||
\(515\) | 0.401924 | + | 1.50000i | 0.0177109 | + | 0.0660979i | ||||
\(516\) | −2.19615 | − | 1.26795i | −0.0966802 | − | 0.0558184i | ||||
\(517\) | −23.9545 | − | 23.9545i | −1.05352 | − | 1.05352i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 9.19615i | − | 0.403666i | ||||||
\(520\) | 3.46410 | + | 0.928203i | 0.151911 | + | 0.0407044i | ||||
\(521\) | 37.6244 | + | 21.7224i | 1.64835 | + | 0.951677i | 0.977727 | + | 0.209881i | \(0.0673078\pi\) |
0.670626 | + | 0.741796i | \(0.266026\pi\) | |||||||
\(522\) | 4.73205 | − | 2.73205i | 0.207116 | − | 0.119579i | ||||
\(523\) | −9.28461 | + | 34.6506i | −0.405988 | + | 1.51517i | 0.396239 | + | 0.918147i | \(0.370315\pi\) |
−0.802227 | + | 0.597019i | \(0.796352\pi\) | |||||||
\(524\) | −4.80385 | + | 17.9282i | −0.209857 | + | 0.783197i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.29423 | − | 34.6865i | −0.405248 | − | 1.51240i | ||||
\(527\) | 0.0621778 | + | 0.107695i | 0.00270851 | + | 0.00469127i | ||||
\(528\) | −16.9282 | − | 29.3205i | −0.736705 | − | 1.27601i | ||||
\(529\) | −8.46410 | + | 14.6603i | −0.368004 | + | 0.637402i | ||||
\(530\) | −38.3205 | + | 38.3205i | −1.66454 | + | 1.66454i | ||||
\(531\) | −5.33975 | + | 5.33975i | −0.231725 | + | 0.231725i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.39230 | − | 2.39230i | −0.103622 | − | 0.103622i | ||||
\(534\) | − | 14.1962i | − | 0.614328i | ||||||
\(535\) | −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 | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 14.6603 | + | 25.3923i | 0.630877 | + | 1.09271i | ||||
\(541\) | 21.5263 | + | 5.76795i | 0.925487 | + | 0.247984i | 0.689929 | − | 0.723877i | \(-0.257642\pi\) |
0.235558 | + | 0.971860i | \(0.424308\pi\) | |||||||
\(542\) | 4.43782 | − | 16.5622i | 0.190621 | − | 0.711406i | ||||
\(543\) | 10.0981 | − | 17.4904i | 0.433350 | − | 0.750584i | ||||
\(544\) | 2.53590 | − | 0.679492i | 0.108726 | − | 0.0291330i | ||||
\(545\) | 49.9808 | 2.14094 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.0526 | − | 15.0526i | 0.643601 | − | 0.643601i | −0.307838 | − | 0.951439i | \(-0.599605\pi\) |
0.951439 | + | 0.307838i | \(0.0996054\pi\) | |||||||
\(548\) | −13.5885 | + | 23.5359i | −0.580470 | + | 1.00540i | ||||
\(549\) | 0.0980762 | − | 0.0262794i | 0.00418579 | − | 0.00112158i | ||||
\(550\) | 19.1962 | + | 33.2487i | 0.818527 | + | 1.41773i | ||||
\(551\) | 20.0263 | − | 11.5622i | 0.853148 | − | 0.492565i | ||||
\(552\) | 13.4641 | 0.573070 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −21.2942 | − | 12.2942i | −0.904705 | − | 0.522332i | ||||
\(555\) | −18.5263 | + | 69.1410i | −0.786397 | + | 2.93487i | ||||
\(556\) | 3.85641 | − | 3.85641i | 0.163548 | − | 0.163548i | ||||
\(557\) | 1.40192 | + | 5.23205i | 0.0594014 | + | 0.221689i | 0.989245 | − | 0.146265i | \(-0.0467251\pi\) |
−0.929844 | + | 0.367954i | \(0.880058\pi\) | |||||||
\(558\) | −0.196152 | + | 0.196152i | −0.00830379 | + | 0.00830379i | ||||
\(559\) | 0.248711 | 0.0105194 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.92820 | −0.165849 | ||||||||
\(562\) | 12.9282 | − | 12.9282i | 0.545343 | − | 0.545343i | ||||
\(563\) | −11.4282 | − | 42.6506i | −0.481641 | − | 1.79751i | −0.594731 | − | 0.803925i | \(-0.702741\pi\) |
0.113089 | − | 0.993585i | \(-0.463925\pi\) | |||||||
\(564\) | 21.1244 | + | 21.1244i | 0.889496 | + | 0.889496i | ||||
\(565\) | −4.73205 | + | 17.6603i | −0.199079 | + | 0.742972i | ||||
\(566\) | −21.4186 | − | 12.3660i | −0.900290 | − | 0.519783i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.9282 | + | 14.9282i | 0.626373 | + | 0.626373i | ||||
\(569\) | 26.0885 | − | 15.0622i | 1.09369 | − | 0.631439i | 0.159130 | − | 0.987258i | \(-0.449131\pi\) |
0.934555 | + | 0.355818i | \(0.115798\pi\) | |||||||
\(570\) | −20.0263 | − | 34.6865i | −0.838809 | − | 1.45286i | ||||
\(571\) | 10.1603 | − | 2.72243i | 0.425193 | − | 0.113930i | −0.0398756 | − | 0.999205i | \(-0.512696\pi\) |
0.465069 | + | 0.885274i | \(0.346030\pi\) | |||||||
\(572\) | 2.87564 | + | 1.66025i | 0.120237 | + | 0.0694187i | ||||
\(573\) | 11.8301 | − | 11.8301i | 0.494211 | − | 0.494211i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −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 | \(0.428880\pi\) |
−0.955286 | + | 0.295682i | \(0.904453\pi\) | |||||||
\(578\) | −6.14359 | + | 22.9282i | −0.255540 | + | 0.953688i | ||||
\(579\) | −42.9186 | − | 11.5000i | −1.78364 | − | 0.477924i | ||||
\(580\) | 30.5885 | − | 17.6603i | 1.27012 | − | 0.733302i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −14.9282 | + | 25.8564i | −0.618794 | + | 1.07178i | ||||
\(583\) | −43.4545 | + | 25.0885i | −1.79970 | + | 1.03906i | ||||
\(584\) | 8.73205 | − | 2.33975i | 0.361335 | − | 0.0968194i | ||||
\(585\) | 0.803848 | + | 0.464102i | 0.0332350 | + | 0.0191882i | ||||
\(586\) | − | 11.8564i | − | 0.489784i | ||||||
\(587\) | −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 | ||||
\(590\) | −34.5167 | + | 34.5167i | −1.42103 | + | 1.42103i | ||||
\(591\) | 0.901924 | − | 1.56218i | 0.0371002 | − | 0.0642594i | ||||
\(592\) | 11.4641 | − | 42.7846i | 0.471172 | − | 1.75844i | ||||
\(593\) | 4.69615 | + | 8.13397i | 0.192848 | + | 0.334022i | 0.946193 | − | 0.323603i | \(-0.104894\pi\) |
−0.753345 | + | 0.657625i | \(0.771561\pi\) | |||||||
\(594\) | 7.02628 | + | 26.2224i | 0.288292 | + | 1.07592i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.9282 | − | 4.80385i | −0.734368 | − | 0.196773i | ||||
\(597\) | 0.964102 | − | 3.59808i | 0.0394581 | − | 0.147259i | ||||
\(598\) | −1.14359 | + | 0.660254i | −0.0467650 | + | 0.0269998i | ||||
\(599\) | 25.3301 | + | 14.6244i | 1.03496 | + | 0.597535i | 0.918402 | − | 0.395649i | \(-0.129480\pi\) |
0.116559 | + | 0.993184i | \(0.462814\pi\) | |||||||
\(600\) | −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 | 0 | ||||||||
\(603\) | −3.92820 | − | 3.92820i | −0.159969 | − | 0.159969i | ||||
\(604\) | −9.39230 | + | 16.2679i | −0.382167 | + | 0.661933i | ||||
\(605\) | 7.09808 | + | 26.4904i | 0.288578 | + | 1.07699i | ||||
\(606\) | 5.16987 | − | 19.2942i | 0.210012 | − | 0.783774i | ||||
\(607\) | −10.5263 | − | 18.2321i | −0.427249 | − | 0.740016i | 0.569379 | − | 0.822075i | \(-0.307184\pi\) |
−0.996627 | + | 0.0820591i | \(0.973850\pi\) | |||||||
\(608\) | 12.3923 | + | 21.4641i | 0.502574 | + | 0.870484i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.633975 | − | 0.169873i | 0.0256689 | − | 0.00687796i | ||||
\(611\) | −2.83013 | − | 0.758330i | −0.114495 | − | 0.0306788i | ||||
\(612\) | 0.679492 | 0.0274668 | ||||||||
\(613\) | 21.5263 | − | 5.76795i | 0.869438 | − | 0.232965i | 0.203593 | − | 0.979056i | \(-0.434738\pi\) |
0.665845 | + | 0.746090i | \(0.268071\pi\) | |||||||
\(614\) | −18.0000 | −0.726421 | ||||||||
\(615\) | 57.7128i | 2.32721i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.46410i | − | 0.300493i | −0.988649 | − | 0.150247i | \(-0.951993\pi\) | ||
0.988649 | − | 0.150247i | \(-0.0480068\pi\) | |||||||
\(618\) | − | 1.26795i | − | 0.0510044i | ||||||
\(619\) | −25.8923 | + | 6.93782i | −1.04070 | + | 0.278855i | −0.738403 | − | 0.674359i | \(-0.764420\pi\) |
−0.302296 | + | 0.953214i | \(0.597753\pi\) | |||||||
\(620\) | −1.26795 | + | 1.26795i | −0.0509221 | + | 0.0509221i | ||||
\(621\) | −10.4282 | − | 2.79423i | −0.418469 | − | 0.112129i | ||||
\(622\) | −0.169873 | − | 0.633975i | −0.00681129 | − | 0.0254201i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.53590 | − | 1.46410i | −0.101517 | − | 0.0586110i | ||||
\(625\) | −8.79423 | − | 15.2321i | −0.351769 | − | 0.609282i | ||||
\(626\) | 13.0981 | + | 3.50962i | 0.523504 | + | 0.140273i | ||||
\(627\) | −9.59808 | − | 35.8205i | −0.383310 | − | 1.43053i | ||||
\(628\) | 31.7846 | − | 8.51666i | 1.26834 | − | 0.339852i | ||||
\(629\) | −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 | \(0.895165\pi\) | |||||||
\(632\) | 1.80385 | + | 0.483340i | 0.0717532 | + | 0.0192262i | ||||
\(633\) | 4.90192 | + | 2.83013i | 0.194834 | + | 0.112487i | ||||
\(634\) | 8.63397 | + | 14.9545i | 0.342899 | + | 0.593918i | ||||
\(635\) | −2.19615 | + | 8.19615i | −0.0871517 | + | 0.325254i | ||||
\(636\) | 38.3205 | − | 22.1244i | 1.51951 | − | 0.877288i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 31.5885 | − | 8.46410i | 1.25060 | − | 0.335097i | ||||
\(639\) | 2.73205 | + | 4.73205i | 0.108078 | + | 0.187197i | ||||
\(640\) | 18.9282 | + | 32.7846i | 0.748203 | + | 1.29593i | ||||
\(641\) | 19.4282 | − | 33.6506i | 0.767368 | − | 1.32912i | −0.171618 | − | 0.985164i | \(-0.554899\pi\) |
0.938986 | − | 0.343957i | \(-0.111767\pi\) | |||||||
\(642\) | 1.73205 | + | 1.73205i | 0.0683586 | + | 0.0683586i | ||||
\(643\) | −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 | ||||
\(646\) | 2.87564 | 0.113141 | ||||||||
\(647\) | −29.1340 | − | 16.8205i | −1.14537 | − | 0.661282i | −0.197619 | − | 0.980279i | \(-0.563321\pi\) |
−0.947756 | + | 0.318997i | \(0.896654\pi\) | |||||||
\(648\) | −7.80385 | − | 29.1244i | −0.306564 | − | 1.14411i | ||||
\(649\) | −39.1410 | + | 22.5981i | −1.53642 | + | 0.887052i | ||||
\(650\) | 2.87564 | + | 1.66025i | 0.112792 | + | 0.0651205i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.124356 | − | 0.464102i | 0.00487014 | − | 0.0181756i | ||||
\(653\) | 20.7224 | + | 5.55256i | 0.810931 | + | 0.217288i | 0.640378 | − | 0.768060i | \(-0.278778\pi\) |
0.170554 | + | 0.985348i | \(0.445444\pi\) | |||||||
\(654\) | −39.4186 | − | 10.5622i | −1.54139 | − | 0.413014i | ||||
\(655\) | −15.5263 | + | 26.8923i | −0.606662 | + | 1.05077i | ||||
\(656\) | − | 35.7128i | − | 1.39435i | ||||||
\(657\) | 2.33975 | 0.0912822 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.85641 | + | 8.85641i | −0.344997 | + | 0.344997i | −0.858242 | − | 0.513245i | \(-0.828443\pi\) |
0.513245 | + | 0.858242i | \(0.328443\pi\) | |||||||
\(660\) | −14.6603 | − | 54.7128i | −0.570650 | − | 2.12969i | ||||
\(661\) | 18.0622 | − | 4.83975i | 0.702537 | − | 0.188244i | 0.110170 | − | 0.993913i | \(-0.464860\pi\) |
0.592367 | + | 0.805668i | \(0.298194\pi\) | |||||||
\(662\) | 21.8827 | − | 12.6340i | 0.850495 | − | 0.491033i | ||||
\(663\) | −0.294229 | + | 0.169873i | −0.0114269 | + | 0.00659732i | ||||
\(664\) | − | 33.8564i | − | 1.31388i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.73205 | − | 9.92820i | 0.222112 | − | 0.384710i | ||||
\(667\) | −3.36603 | + | 12.5622i | −0.130333 | + | 0.486409i | ||||
\(668\) | −11.7128 | −0.453182 | ||||||||
\(669\) | −8.92820 | − | 33.3205i | −0.345184 | − | 1.28825i | ||||
\(670\) | −25.3923 | − | 25.3923i | −0.980990 | − | 0.980990i | ||||
\(671\) | 0.607695 | 0.0234598 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.784610 | −0.0302445 | −0.0151222 | − | 0.999886i | \(-0.504814\pi\) | ||||
−0.0151222 | + | 0.999886i | \(0.504814\pi\) | |||||||
\(674\) | −33.8564 | − | 33.8564i | −1.30410 | − | 1.30410i | ||||
\(675\) | 7.02628 | + | 26.2224i | 0.270442 | + | 1.00930i | ||||
\(676\) | −25.7128 | −0.988954 | ||||||||
\(677\) | 13.2776 | − | 49.5526i | 0.510298 | − | 1.90446i | 0.0930654 | − | 0.995660i | \(-0.470333\pi\) |
0.417233 | − | 0.908800i | \(-0.363000\pi\) | |||||||
\(678\) | 7.46410 | − | 12.9282i | 0.286657 | − | 0.496505i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.39230 | 0.168437 | ||||||||
\(681\) | 39.8205 | − | 22.9904i | 1.52593 | − | 0.880993i | ||||
\(682\) | −1.43782 | + | 0.830127i | −0.0550571 | + | 0.0317872i | ||||
\(683\) | −43.2128 | + | 11.5788i | −1.65349 | + | 0.443052i | −0.960588 | − | 0.277977i | \(-0.910336\pi\) |
−0.692905 | + | 0.721029i | \(0.743669\pi\) | |||||||
\(684\) | 1.66025 | + | 6.19615i | 0.0634814 | + | 0.236916i | ||||
\(685\) | −32.1506 | + | 32.1506i | −1.22841 | + | 1.22841i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.8564 | 1.32985 | ||||||||
\(688\) | 1.85641 | + | 1.85641i | 0.0707748 | + | 0.0707748i | ||||
\(689\) | −2.16987 | + | 3.75833i | −0.0826656 | + | 0.143181i | ||||
\(690\) | 21.7583 | + | 5.83013i | 0.828325 | + | 0.221949i | ||||
\(691\) | 11.1603 | + | 2.99038i | 0.424556 | + | 0.113759i | 0.464770 | − | 0.885432i | \(-0.346137\pi\) |
−0.0402135 | + | 0.999191i | \(0.512804\pi\) | |||||||
\(692\) | −2.46410 | + | 9.19615i | −0.0936711 | + | 0.349585i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.1699 | − | 12.2224i | −0.803597 | − | 0.463957i | ||||
\(695\) | 7.90192 | − | 4.56218i | 0.299737 | − | 0.173053i | ||||
\(696\) | −27.8564 | + | 7.46410i | −1.05589 | + | 0.282926i | ||||
\(697\) | −3.58846 | − | 2.07180i | −0.135923 | − | 0.0784749i | ||||
\(698\) | 36.2487 | 1.37203 | ||||||||
\(699\) | 15.2942 | + | 15.2942i | 0.578481 | + | 0.578481i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.39230 | − | 7.39230i | 0.279204 | − | 0.279204i | −0.553588 | − | 0.832791i | \(-0.686742\pi\) |
0.832791 | + | 0.553588i | \(0.186742\pi\) | |||||||
\(702\) | 1.66025 | + | 1.66025i | 0.0626623 | + | 0.0626623i | ||||
\(703\) | 24.2583 | − | 42.0167i | 0.914920 | − | 1.58469i | ||||
\(704\) | 9.07180 | + | 33.8564i | 0.341906 | + | 1.27601i | ||||
\(705\) | 24.9904 | + | 43.2846i | 0.941192 | + | 1.63019i | ||||
\(706\) | 18.8301 | − | 5.04552i | 0.708681 | − | 0.189891i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 34.5167 | − | 19.9282i | 1.29722 | − | 0.748948i | ||||
\(709\) | 2.34936 | − | 8.76795i | 0.0882323 | − | 0.329287i | −0.907674 | − | 0.419675i | \(-0.862144\pi\) |
0.995907 | + | 0.0903879i | \(0.0288107\pi\) | |||||||
\(710\) | 17.6603 | + | 30.5885i | 0.662778 | + | 1.14796i | ||||
\(711\) | 0.418584 | + | 0.241670i | 0.0156981 | + | 0.00906332i | ||||
\(712\) | −3.80385 | + | 14.1962i | −0.142555 | + | 0.532023i | ||||
\(713\) | − | 0.660254i | − | 0.0247267i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.92820 | + | 3.92820i | 0.146906 | + | 0.146906i | ||||
\(716\) | −15.1962 | + | 4.07180i | −0.567907 | + | 0.152170i | ||||
\(717\) | 7.73205 | + | 28.8564i | 0.288759 | + | 1.07766i | ||||
\(718\) | −3.36603 | − | 0.901924i | −0.125619 | − | 0.0336595i | ||||
\(719\) | 15.7942 | + | 27.3564i | 0.589025 | + | 1.02022i | 0.994360 | + | 0.106054i | \(0.0338215\pi\) |
−0.405335 | + | 0.914168i | \(0.632845\pi\) | |||||||
\(720\) | 2.53590 | + | 9.46410i | 0.0945074 | + | 0.352706i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.0717968 | + | 0.267949i | 0.00267200 | + | 0.00997204i | ||||
\(723\) | −0.133975 | − | 0.0358984i | −0.00498257 | − | 0.00133508i | ||||
\(724\) | −14.7846 | + | 14.7846i | −0.549466 | + | 0.549466i | ||||
\(725\) | 31.5885 | − | 8.46410i | 1.17317 | − | 0.314349i | ||||
\(726\) | − | 22.3923i | − | 0.831056i | ||||||
\(727\) | − | 6.67949i | − | 0.247729i | −0.992299 | − | 0.123864i | \(-0.960471\pi\) | ||
0.992299 | − | 0.123864i | \(-0.0395288\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.5885i | 0.651424i | ||||||||
\(730\) | 15.1244 | 0.559778 | ||||||||
\(731\) | 0.294229 | − | 0.0788383i | 0.0108824 | − | 0.00291594i | ||||
\(732\) | −0.535898 | −0.0198074 | ||||||||
\(733\) | 45.1865 | + | 12.1077i | 1.66900 | + | 0.447208i | 0.964842 | − | 0.262832i | \(-0.0846566\pi\) |
0.704161 | + | 0.710040i | \(0.251323\pi\) | |||||||
\(734\) | −24.7583 | + | 6.63397i | −0.913847 | + | 0.244864i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.4641 | − | 3.60770i | −0.496293 | − | 0.132981i | ||||
\(737\) | −16.6244 | − | 28.7942i | −0.612366 | − | 1.06065i | ||||
\(738\) | 2.39230 | − | 8.92820i | 0.0880620 | − | 0.328652i | ||||
\(739\) | −13.4808 | − | 50.3109i | −0.495898 | − | 1.85072i | −0.524942 | − | 0.851138i | \(-0.675913\pi\) |
0.0290444 | − | 0.999578i | \(-0.490754\pi\) | |||||||
\(740\) | 37.0526 | − | 64.1769i | 1.36208 | − | 2.35919i | ||||
\(741\) | −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 | \(0.848830\pi\) | |||||||
\(744\) | 1.26795 | − | 0.732051i | 0.0464853 | − | 0.0268383i | ||||
\(745\) | −26.8923 | − | 15.5263i | −0.985258 | − | 0.568839i | ||||
\(746\) | −4.09808 | + | 2.36603i | −0.150041 | + | 0.0866263i | ||||
\(747\) | 2.26795 | − | 8.46410i | 0.0829799 | − | 0.309685i | ||||
\(748\) | 3.92820 | + | 1.05256i | 0.143629 | + | 0.0384854i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −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 | \(0.682225\pi\) | |||||||
\(752\) | −15.4641 | − | 26.7846i | −0.563918 | − | 0.976734i | ||||
\(753\) | −18.5622 | + | 32.1506i | −0.676443 | + | 1.17163i | ||||
\(754\) | 2.00000 | − | 2.00000i | 0.0728357 | − | 0.0728357i | ||||
\(755\) | −22.2224 | + | 22.2224i | −0.808757 | + | 0.808757i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.33975 | − | 1.33975i | −0.0486939 | − | 0.0486939i | 0.682341 | − | 0.731034i | \(-0.260962\pi\) |
−0.731034 | + | 0.682341i | \(0.760962\pi\) | |||||||
\(758\) | − | 48.2487i | − | 1.75247i | ||||||
\(759\) | 18.0622 | + | 10.4282i | 0.655616 | + | 0.378520i | ||||
\(760\) | 10.7321 | + | 40.0526i | 0.389292 | + | 1.45286i | ||||
\(761\) | −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 | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −15.0000 | + | 8.66025i | −0.542681 | + | 0.313317i | ||||
\(765\) | 1.09808 | + | 0.294229i | 0.0397010 | + | 0.0106379i | ||||
\(766\) | 5.41858 | − | 20.2224i | 0.195781 | − | 0.730666i | ||||
\(767\) | −1.95448 | + | 3.38526i | −0.0705723 | + | 0.122235i | ||||
\(768\) | −8.00000 | − | 29.8564i | −0.288675 | − | 1.07735i | ||||
\(769\) | 17.8564 | 0.643918 | 0.321959 | − | 0.946754i | \(-0.395659\pi\) | ||||
0.321959 | + | 0.946754i | \(0.395659\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.90192 | − | 1.90192i | 0.0684961 | − | 0.0684961i | ||||
\(772\) | 39.8372 | + | 23.0000i | 1.43377 | + | 0.827788i | ||||
\(773\) | 15.0622 | − | 4.03590i | 0.541749 | − | 0.145161i | 0.0224406 | − | 0.999748i | \(-0.492856\pi\) |
0.519308 | + | 0.854587i | \(0.326190\pi\) | |||||||
\(774\) | 0.339746 | + | 0.588457i | 0.0122119 | + | 0.0211517i | ||||
\(775\) | −1.43782 | + | 0.830127i | −0.0516481 | + | 0.0298190i | ||||
\(776\) | 21.8564 | − | 21.8564i | 0.784599 | − | 0.784599i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.3468 | − | 14.6340i | −0.908726 | − | 0.524653i | ||||
\(779\) | 10.1244 | − | 37.7846i | 0.362743 | − | 1.35377i | ||||
\(780\) | −3.46410 | − | 3.46410i | −0.124035 | − | 0.124035i | ||||
\(781\) | 8.46410 | + | 31.5885i | 0.302869 | + | 1.13032i | ||||
\(782\) | −1.14359 | + | 1.14359i | −0.0408948 | + | 0.0408948i | ||||
\(783\) | 23.1244 | 0.826397 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 55.0526 | 1.96491 | ||||||||
\(786\) | 17.9282 | − | 17.9282i | 0.639478 | − | 0.639478i | ||||
\(787\) | −4.16025 | − | 15.5263i | −0.148297 | − | 0.553452i | −0.999586 | − | 0.0287557i | \(-0.990846\pi\) |
0.851289 | − | 0.524696i | \(-0.175821\pi\) | |||||||
\(788\) | −1.32051 | + | 1.32051i | −0.0470412 | + | 0.0470412i | ||||
\(789\) | −12.6962 | + | 47.3827i | −0.451995 | + | 1.68687i | ||||
\(790\) | 2.70577 | + | 1.56218i | 0.0962670 | + | 0.0555798i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.07180i | 0.322352i | ||||||||
\(793\) | 0.0455173 | − | 0.0262794i | 0.00161637 | − | 0.000933210i | ||||
\(794\) | −3.75833 | − | 6.50962i | −0.133378 | − | 0.231018i | ||||
\(795\) | 71.5070 | − | 19.1603i | 2.53609 | − | 0.679544i | ||||
\(796\) | −1.92820 | + | 3.33975i | −0.0683434 | + | 0.118374i | ||||
\(797\) | 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 | ||||||||
\(800\) | 9.07180 | + | 33.8564i | 0.320736 | + | 1.19700i | ||||
\(801\) | −1.90192 | + | 3.29423i | −0.0672012 | + | 0.116396i | ||||
\(802\) | −5.49038 | + | 20.4904i | −0.193872 | + | 0.723541i | ||||
\(803\) | 13.5263 | + | 3.62436i | 0.477332 | + | 0.127901i | ||||
\(804\) | 14.6603 | + | 25.3923i | 0.517027 | + | 0.895518i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −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 | 0.200628 | − | 0.979668i | \(-0.435702\pi\) |
−0.748103 | + | 0.663583i | \(0.769035\pi\) | |||||||
\(810\) | − | 50.4449i | − | 1.77245i | ||||||
\(811\) | 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 | ||||
\(814\) | 48.5167 | − | 48.5167i | 1.70051 | − | 1.70051i | ||||
\(815\) | 0.401924 | − | 0.696152i | 0.0140788 | − | 0.0243852i | ||||
\(816\) | −3.46410 | − | 0.928203i | −0.121268 | − | 0.0324936i | ||||
\(817\) | 1.43782 | + | 2.49038i | 0.0503030 | + | 0.0871274i | ||||
\(818\) | 3.16987 | + | 11.8301i | 0.110832 | + | 0.413631i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.4641 | − | 57.7128i | 0.540030 | − | 2.01542i | ||||
\(821\) | −4.59808 | + | 17.1603i | −0.160474 | + | 0.598897i | 0.838100 | + | 0.545516i | \(0.183666\pi\) |
−0.998574 | + | 0.0533808i | \(0.983000\pi\) | |||||||
\(822\) | 32.1506 | − | 18.5622i | 1.12138 | − | 0.647430i | ||||
\(823\) | −27.0622 | − | 15.6244i | −0.943328 | − | 0.544631i | −0.0523262 | − | 0.998630i | \(-0.516664\pi\) |
−0.891002 | + | 0.453999i | \(0.849997\pi\) | |||||||
\(824\) | −0.339746 | + | 1.26795i | −0.0118356 | + | 0.0441711i | ||||
\(825\) | − | 52.4449i | − | 1.82590i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.7846 | + | 37.7846i | 1.31390 | + | 1.31390i | 0.918516 | + | 0.395383i | \(0.129388\pi\) |
0.395383 | + | 0.918516i | \(0.370612\pi\) | |||||||
\(828\) | −3.12436 | − | 1.80385i | −0.108579 | − | 0.0626880i | ||||
\(829\) | −9.06218 | − | 33.8205i | −0.314742 | − | 1.17463i | −0.924229 | − | 0.381838i | \(-0.875291\pi\) |
0.609487 | − | 0.792796i | \(-0.291376\pi\) | |||||||
\(830\) | 14.6603 | − | 54.7128i | 0.508865 | − | 1.89911i | ||||
\(831\) | 16.7942 | + | 29.0885i | 0.582585 | + | 1.00907i | ||||
\(832\) | 2.14359 | + | 2.14359i | 0.0743157 | + | 0.0743157i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.19615 | + | 1.92820i | −0.249182 | + | 0.0667682i | ||||
\(835\) | −18.9282 | − | 5.07180i | −0.655037 | − | 0.175517i | ||||
\(836\) | 38.3923i | 1.32783i | ||||||||
\(837\) | −1.13397 | + | 0.303848i | −0.0391959 | + | 0.0105025i | ||||
\(838\) | 38.0000 | 1.31269 | ||||||||
\(839\) | − | 37.7128i | − | 1.30199i | −0.759082 | − | 0.650995i | \(-0.774352\pi\) | ||
0.759082 | − | 0.650995i | \(-0.225648\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.14359i | 0.0394343i | ||||||||
\(842\) | − | 17.3205i | − | 0.596904i | ||||||
\(843\) | −24.1244 | + | 6.46410i | −0.830887 | + | 0.222635i | ||||
\(844\) | −4.14359 | − | 4.14359i | −0.142628 | − | 0.142628i | ||||
\(845\) | −41.5526 | − | 11.1340i | −1.42945 | − | 0.383020i | ||||
\(846\) | −2.07180 | − | 7.73205i | −0.0712298 | − | 0.265833i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −44.2487 | + | 11.8564i | −1.51951 | + | 0.407151i | ||||
\(849\) | 16.8923 | + | 29.2583i | 0.579742 | + | 1.00414i | ||||
\(850\) | 3.92820 | + | 1.05256i | 0.134736 | + | 0.0361025i | ||||
\(851\) | 7.06218 | + | 26.3564i | 0.242088 | + | 0.903486i | ||||
\(852\) | −7.46410 | − | 27.8564i | −0.255716 | − | 0.954345i | ||||
\(853\) | 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 | ||||||||
\(856\) | −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 | \(0.610553\pi\) | |||||||
\(858\) | −2.26795 | − | 3.92820i | −0.0774265 | − | 0.134107i | ||||
\(859\) | 10.6244 | − | 39.6506i | 0.362498 | − | 1.35286i | −0.508282 | − | 0.861191i | \(-0.669719\pi\) |
0.870781 | − | 0.491672i | \(-0.163614\pi\) | |||||||
\(860\) | 2.19615 | + | 3.80385i | 0.0748882 | + | 0.129710i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −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 | \(0.749253\pi\) | |||||||
\(864\) | 24.7846i | 0.843190i | ||||||||
\(865\) | −7.96410 | + | 13.7942i | −0.270788 | + | 0.469018i | ||||
\(866\) | −29.1769 | − | 29.1769i | −0.991472 | − | 0.991472i | ||||
\(867\) | 22.9282 | − | 22.9282i | 0.778683 | − | 0.778683i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.04552 | + | 2.04552i | 0.0693894 | + | 0.0693894i | ||||
\(870\) | −48.2487 | −1.63578 | ||||||||
\(871\) | −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 | 0 | ||||||||
\(876\) | −11.9282 | − | 3.19615i | −0.403017 | − | 0.107988i | ||||
\(877\) | −28.1865 | − | 7.55256i | −0.951792 | − | 0.255032i | −0.250669 | − | 0.968073i | \(-0.580651\pi\) |
−0.701122 | + | 0.713041i | \(0.747317\pi\) | |||||||
\(878\) | 19.7583 | + | 5.29423i | 0.666811 | + | 0.178672i | ||||
\(879\) | −8.09808 | + | 14.0263i | −0.273141 | + | 0.473095i | ||||
\(880\) | 58.6410i | 1.97679i | ||||||||
\(881\) | −50.0000 | −1.68454 | −0.842271 | − | 0.539054i | \(-0.818782\pi\) | ||||
−0.842271 | + | 0.539054i | \(0.818782\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.00000 | + | 5.00000i | −0.168263 | + | 0.168263i | −0.786216 | − | 0.617952i | \(-0.787963\pi\) |
0.617952 | + | 0.786216i | \(0.287963\pi\) | |||||||
\(884\) | 0.339746 | − | 0.0910347i | 0.0114269 | − | 0.00306183i | ||||
\(885\) | 64.4090 | − | 17.2583i | 2.16508 | − | 0.580132i | ||||
\(886\) | 16.2224 | − | 9.36603i | 0.545003 | − | 0.314658i | ||||
\(887\) | −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 | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.2942 | + | 21.2942i | −0.412103 | + | 0.713784i | ||||
\(891\) | 12.0885 | − | 45.1147i | 0.404979 | − | 1.51140i | ||||
\(892\) | 35.7128i | 1.19575i | ||||||||
\(893\) | −8.76795 | − | 32.7224i | −0.293408 | − | 1.09501i | ||||
\(894\) | 17.9282 | + | 17.9282i | 0.599609 | + | 0.599609i | ||||
\(895\) | −26.3205 | −0.879798 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.80385 | 0.0602287 | ||||||||
\(898\) | 11.3205 | + | 11.3205i | 0.377770 | + | 0.377770i | ||||
\(899\) | 0.366025 | + | 1.36603i | 0.0122076 | + | 0.0455595i | ||||
\(900\) | 9.07180i | 0.302393i | ||||||||
\(901\) | −1.37564 | + | 5.13397i | −0.0458294 | + | 0.171037i | ||||
\(902\) | 27.6603 | − | 47.9090i | 0.920986 | − | 1.59519i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.9282 | + | 10.9282i | −0.363467 | + | 0.363467i | ||||
\(905\) | −30.2942 | + | 17.4904i | −1.00701 | + | 0.581400i | ||||
\(906\) | 22.2224 | − | 12.8301i | 0.738291 | − | 0.426252i | ||||
\(907\) | −10.1603 | + | 2.72243i | −0.337366 | + | 0.0903969i | −0.423525 | − | 0.905885i | \(-0.639207\pi\) |
0.0861591 | + | 0.996281i | \(0.472541\pi\) | |||||||
\(908\) | −45.9808 | + | 12.3205i | −1.52593 | + | 0.408870i | ||||
\(909\) | −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 | \(0.649498\pi\) | |||||||
\(912\) | − | 33.8564i | − | 1.12110i | ||||||
\(913\) | 26.2224 | − | 45.4186i | 0.867836 | − | 1.50314i | ||||
\(914\) | −39.8827 | − | 10.6865i | −1.31920 | − | 0.353479i | ||||
\(915\) | −0.866025 | − | 0.232051i | −0.0286299 | − | 0.00767136i | ||||
\(916\) | −34.8564 | − | 9.33975i | −1.15169 | − | 0.308594i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.49038 | + | 1.43782i | 0.0821948 | + | 0.0474552i | ||||
\(919\) | −14.1340 | + | 8.16025i | −0.466237 | + | 0.269182i | −0.714663 | − | 0.699469i | \(-0.753420\pi\) |
0.248426 | + | 0.968651i | \(0.420087\pi\) | |||||||
\(920\) | −20.1962 | − | 11.6603i | −0.665847 | − | 0.384427i | ||||
\(921\) | 21.2942 | + | 12.2942i | 0.701669 | + | 0.405109i | ||||
\(922\) | −2.67949 | −0.0882444 | ||||||||
\(923\) | 2.00000 | + | 2.00000i | 0.0658308 | + | 0.0658308i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.5167 | − | 48.5167i | 1.59522 | − | 1.59522i | ||||
\(926\) | 29.8564 | + | 29.8564i | 0.981142 | + | 0.981142i | ||||
\(927\) | −0.169873 | + | 0.294229i | −0.00557936 | + | 0.00966374i | ||||
\(928\) | 29.8564 | 0.980085 | ||||||||
\(929\) | −20.0167 | − | 34.6699i | −0.656725 | − | 1.13748i | −0.981458 | − | 0.191676i | \(-0.938608\pi\) |
0.324733 | − | 0.945806i | \(-0.394726\pi\) | |||||||
\(930\) | 2.36603 | − | 0.633975i | 0.0775850 | − | 0.0207888i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11.1962 | − | 19.3923i | −0.366742 | − | 0.635216i | ||||
\(933\) | −0.232051 | + | 0.866025i | −0.00759700 | + | 0.0283524i | ||||
\(934\) | 0.0262794 | + | 0.0455173i | 0.000859890 | + | 0.00148937i | ||||
\(935\) | 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 | \(-0.247353\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.0981 | − | 13.0981i | −0.427440 | − | 0.427440i | ||||
\(940\) | −13.3923 | − | 49.9808i | −0.436809 | − | 1.63019i | ||||
\(941\) | 4.47372 | + | 16.6962i | 0.145839 | + | 0.544279i | 0.999717 | + | 0.0238050i | \(0.00757808\pi\) |
−0.853877 | + | 0.520474i | \(0.825755\pi\) | |||||||
\(942\) | −43.4186 | − | 11.6340i | −1.41465 | − | 0.379055i | ||||
\(943\) | 11.0000 | + | 19.0526i | 0.358209 | + | 0.620437i | ||||
\(944\) | −39.8564 | + | 10.6795i | −1.29722 | + | 0.347588i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.05256 | + | 3.92820i | 0.0342216 | + | 0.127717i | ||||
\(947\) | −39.5526 | − | 10.5981i | −1.28529 | − | 0.344391i | −0.449418 | − | 0.893322i | \(-0.648368\pi\) |
−0.835868 | + | 0.548931i | \(0.815035\pi\) | |||||||
\(948\) | −1.80385 | − | 1.80385i | −0.0585862 | − | 0.0585862i | ||||
\(949\) | 1.16987 | − | 0.313467i | 0.0379757 | − | 0.0101756i | ||||
\(950\) | 38.3923i | 1.24561i | ||||||||
\(951\) | − | 23.5885i | − | 0.764908i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 23.4641i | − | 0.760077i | −0.924971 | − | 0.380038i | \(-0.875911\pi\) | ||
0.924971 | − | 0.380038i | \(-0.124089\pi\) | |||||||
\(954\) | −11.8564 | −0.383865 | ||||||||
\(955\) | −27.9904 | + | 7.50000i | −0.905747 | + | 0.242694i | ||||
\(956\) | − | 30.9282i | − | 1.00029i | ||||||
\(957\) | −43.1506 | − | 11.5622i | −1.39486 | − | 0.373752i | ||||
\(958\) | −21.2942 | + | 5.70577i | −0.687985 | + | 0.184345i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 51.7128i | − | 1.66902i | ||||||
\(961\) | 15.4641 | + | 26.7846i | 0.498842 | + | 0.864020i | ||||
\(962\) | 1.53590 | − | 5.73205i | 0.0495194 | − | 0.184809i | ||||
\(963\) | −0.169873 | − | 0.633975i | −0.00547408 | − | 0.0204295i | ||||
\(964\) | 0.124356 | + | 0.0717968i | 0.00400523 | + | 0.00231242i | ||||
\(965\) | 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 | \(0.939492\pi\) | |||||||
\(968\) | −6.00000 | + | 22.3923i | −0.192847 | + | 0.719716i | ||||
\(969\) | −3.40192 | − | 1.96410i | −0.109286 | − | 0.0630960i | ||||
\(970\) | 44.7846 | − | 25.8564i | 1.43795 | − | 0.830199i | ||||
\(971\) | −13.4090 | + | 50.0429i | −0.430314 | + | 1.60595i | 0.321723 | + | 0.946834i | \(0.395738\pi\) |
−0.752037 | + | 0.659121i | \(0.770929\pi\) | |||||||
\(972\) | −3.85641 | + | 14.3923i | −0.123694 | + | 0.461633i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.16987 | + | 30.4904i | 0.261780 | + | 0.976975i | ||||
\(975\) | −2.26795 | − | 3.92820i | −0.0726325 | − | 0.125803i | ||||
\(976\) | 0.535898 | + | 0.143594i | 0.0171537 | + | 0.00459632i | ||||
\(977\) | 22.4282 | − | 38.8468i | 0.717542 | − | 1.24282i | −0.244429 | − | 0.969667i | \(-0.578601\pi\) |
0.961971 | − | 0.273152i | \(-0.0880661\pi\) | |||||||
\(978\) | −0.464102 | + | 0.464102i | −0.0148403 | + | 0.0148403i | ||||
\(979\) | −16.0981 | + | 16.0981i | −0.514497 | + | 0.514497i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.73205 | + | 7.73205i | 0.246865 | + | 0.246865i | ||||
\(982\) | 55.1769i | 1.76077i | ||||||||
\(983\) | −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 | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.66025 | + | 2.87564i | 0.0528197 | + | 0.0914864i | ||||
\(989\) | −1.56218 | − | 0.418584i | −0.0496744 | − | 0.0133102i | ||||
\(990\) | −3.92820 | + | 14.6603i | −0.124846 | + | 0.465933i | ||||
\(991\) | 19.7942 | − | 34.2846i | 0.628784 | − | 1.08909i | −0.359012 | − | 0.933333i | \(-0.616886\pi\) |
0.987796 | − | 0.155753i | \(-0.0497805\pi\) | |||||||
\(992\) | −1.46410 | + | 0.392305i | −0.0464853 | + | 0.0124557i | ||||
\(993\) | −34.5167 | −1.09535 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.56218 | + | 4.56218i | −0.144631 | + | 0.144631i | ||||
\(996\) | −23.1244 | + | 40.0526i | −0.732723 | + | 1.26911i | ||||
\(997\) | −5.59808 | + | 1.50000i | −0.177293 | + | 0.0475055i | −0.346373 | − | 0.938097i | \(-0.612587\pi\) |
0.169080 | + | 0.985602i | \(0.445920\pi\) | |||||||
\(998\) | −2.70577 | − | 4.68653i | −0.0856497 | − | 0.148350i | ||||
\(999\) | 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 | 784.2.x.h.165.1 | 4 | ||
7.2 | even | 3 | 784.2.x.a.373.1 | 4 | |||
7.3 | odd | 6 | 784.2.m.e.197.1 | 4 | |||
7.4 | even | 3 | 784.2.m.d.197.1 | 4 | |||
7.5 | odd | 6 | 112.2.w.a.37.1 | ✓ | 4 | ||
7.6 | odd | 2 | 112.2.w.b.53.1 | yes | 4 | ||
16.13 | even | 4 | 784.2.x.a.557.1 | 4 | |||
28.19 | even | 6 | 448.2.ba.b.177.1 | 4 | |||
28.27 | even | 2 | 448.2.ba.a.305.1 | 4 | |||
56.5 | odd | 6 | 896.2.ba.d.737.1 | 4 | |||
56.13 | odd | 2 | 896.2.ba.b.865.1 | 4 | |||
56.19 | even | 6 | 896.2.ba.a.737.1 | 4 | |||
56.27 | even | 2 | 896.2.ba.c.865.1 | 4 | |||
112.5 | odd | 12 | 896.2.ba.b.289.1 | 4 | |||
112.13 | odd | 4 | 112.2.w.a.109.1 | yes | 4 | ||
112.19 | even | 12 | 448.2.ba.a.401.1 | 4 | |||
112.27 | even | 4 | 896.2.ba.a.417.1 | 4 | |||
112.45 | odd | 12 | 784.2.m.e.589.1 | 4 | |||
112.61 | odd | 12 | 112.2.w.b.93.1 | yes | 4 | ||
112.69 | odd | 4 | 896.2.ba.d.417.1 | 4 | |||
112.75 | even | 12 | 896.2.ba.c.289.1 | 4 | |||
112.83 | even | 4 | 448.2.ba.b.81.1 | 4 | |||
112.93 | even | 12 | inner | 784.2.x.h.765.1 | 4 | ||
112.109 | even | 12 | 784.2.m.d.589.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.a.37.1 | ✓ | 4 | 7.5 | odd | 6 | ||
112.2.w.a.109.1 | yes | 4 | 112.13 | odd | 4 | ||
112.2.w.b.53.1 | yes | 4 | 7.6 | odd | 2 | ||
112.2.w.b.93.1 | yes | 4 | 112.61 | odd | 12 | ||
448.2.ba.a.305.1 | 4 | 28.27 | even | 2 | |||
448.2.ba.a.401.1 | 4 | 112.19 | even | 12 | |||
448.2.ba.b.81.1 | 4 | 112.83 | even | 4 | |||
448.2.ba.b.177.1 | 4 | 28.19 | even | 6 | |||
784.2.m.d.197.1 | 4 | 7.4 | even | 3 | |||
784.2.m.d.589.1 | 4 | 112.109 | even | 12 | |||
784.2.m.e.197.1 | 4 | 7.3 | odd | 6 | |||
784.2.m.e.589.1 | 4 | 112.45 | odd | 12 | |||
784.2.x.a.373.1 | 4 | 7.2 | even | 3 | |||
784.2.x.a.557.1 | 4 | 16.13 | even | 4 | |||
784.2.x.h.165.1 | 4 | 1.1 | even | 1 | trivial | ||
784.2.x.h.765.1 | 4 | 112.93 | even | 12 | inner | ||
896.2.ba.a.417.1 | 4 | 112.27 | even | 4 | |||
896.2.ba.a.737.1 | 4 | 56.19 | even | 6 | |||
896.2.ba.b.289.1 | 4 | 112.5 | odd | 12 | |||
896.2.ba.b.865.1 | 4 | 56.13 | odd | 2 | |||
896.2.ba.c.289.1 | 4 | 112.75 | even | 12 | |||
896.2.ba.c.865.1 | 4 | 56.27 | even | 2 | |||
896.2.ba.d.417.1 | 4 | 112.69 | odd | 4 | |||
896.2.ba.d.737.1 | 4 | 56.5 | odd | 6 |