Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(367,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.367");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.j (of order \(4\), degree \(2\), 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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 643.3 | ||
Character | \(\chi\) | \(=\) | 690.643 |
Dual form | 690.2.j.a.367.3 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.299475 | + | 2.21592i | −0.133929 | + | 0.990991i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.52616 | + | 3.52616i | 1.33276 | + | 1.33276i | 0.902888 | + | 0.429877i | \(0.141443\pi\) |
0.429877 | + | 0.902888i | \(0.358557\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −1.35513 | − | 1.77865i | −0.428531 | − | 0.562460i | ||||
\(11\) | − | 3.55731i | − | 1.07257i | −0.844037 | − | 0.536285i | \(-0.819827\pi\) | ||
0.844037 | − | 0.536285i | \(-0.180173\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | 1.85009 | + | 1.85009i | 0.513123 | + | 0.513123i | 0.915482 | − | 0.402359i | \(-0.131810\pi\) |
−0.402359 | + | 0.915482i | \(0.631810\pi\) | |||||||
\(14\) | −4.98675 | −1.33276 | ||||||||
\(15\) | −1.77865 | + | 1.35513i | −0.459247 | + | 0.349894i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.03324 | + | 2.03324i | 0.493132 | + | 0.493132i | 0.909292 | − | 0.416160i | \(-0.136624\pi\) |
−0.416160 | + | 0.909292i | \(0.636624\pi\) | |||||||
\(18\) | −0.707107 | − | 0.707107i | −0.166667 | − | 0.166667i | ||||
\(19\) | 4.34206 | 0.996136 | 0.498068 | − | 0.867138i | \(-0.334043\pi\) | ||||
0.498068 | + | 0.867138i | \(0.334043\pi\) | |||||||
\(20\) | 2.21592 | + | 0.299475i | 0.495495 | + | 0.0669646i | ||||
\(21\) | 4.98675i | 1.08820i | ||||||||
\(22\) | 2.51540 | + | 2.51540i | 0.536285 | + | 0.536285i | ||||
\(23\) | −4.50903 | − | 1.63360i | −0.940198 | − | 0.340629i | ||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −4.82063 | − | 1.32723i | −0.964126 | − | 0.265445i | ||||
\(26\) | −2.61642 | −0.513123 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 3.52616 | − | 3.52616i | 0.666382 | − | 0.666382i | ||||
\(29\) | − | 9.31080i | − | 1.72897i | −0.502656 | − | 0.864486i | \(-0.667644\pi\) | ||
0.502656 | − | 0.864486i | \(-0.332356\pi\) | |||||||
\(30\) | 0.299475 | − | 2.21592i | 0.0546763 | − | 0.404570i | ||||
\(31\) | −5.68459 | −1.02098 | −0.510491 | − | 0.859883i | \(-0.670536\pi\) | ||||
−0.510491 | + | 0.859883i | \(0.670536\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 2.51540 | − | 2.51540i | 0.437875 | − | 0.437875i | ||||
\(34\) | −2.87543 | −0.493132 | ||||||||
\(35\) | −8.86970 | + | 6.75771i | −1.49925 | + | 1.14226i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.97807 | + | 5.97807i | 0.982789 | + | 0.982789i | 0.999854 | − | 0.0170656i | \(-0.00543240\pi\) |
−0.0170656 | + | 0.999854i | \(0.505432\pi\) | |||||||
\(38\) | −3.07030 | + | 3.07030i | −0.498068 | + | 0.498068i | ||||
\(39\) | 2.61642i | 0.418963i | ||||||||
\(40\) | −1.77865 | + | 1.35513i | −0.281230 | + | 0.214265i | ||||
\(41\) | −0.173976 | −0.0271705 | −0.0135852 | − | 0.999908i | \(-0.504324\pi\) | ||||
−0.0135852 | + | 0.999908i | \(0.504324\pi\) | |||||||
\(42\) | −3.52616 | − | 3.52616i | −0.544099 | − | 0.544099i | ||||
\(43\) | −1.69950 | + | 1.69950i | −0.259172 | + | 0.259172i | −0.824717 | − | 0.565545i | \(-0.808666\pi\) |
0.565545 | + | 0.824717i | \(0.308666\pi\) | |||||||
\(44\) | −3.55731 | −0.536285 | ||||||||
\(45\) | −2.21592 | − | 0.299475i | −0.330330 | − | 0.0446430i | ||||
\(46\) | 4.34350 | − | 2.03324i | 0.640413 | − | 0.299784i | ||||
\(47\) | 4.77937 | − | 4.77937i | 0.697143 | − | 0.697143i | −0.266650 | − | 0.963793i | \(-0.585917\pi\) |
0.963793 | + | 0.266650i | \(0.0859168\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | 17.8676i | 2.55252i | ||||||||
\(50\) | 4.34719 | − | 2.47021i | 0.614786 | − | 0.349340i | ||||
\(51\) | 2.87543i | 0.402641i | ||||||||
\(52\) | 1.85009 | − | 1.85009i | 0.256561 | − | 0.256561i | ||||
\(53\) | −4.53693 | + | 4.53693i | −0.623195 | + | 0.623195i | −0.946347 | − | 0.323152i | \(-0.895257\pi\) |
0.323152 | + | 0.946347i | \(0.395257\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | 7.88272 | + | 1.06532i | 1.06291 | + | 0.143648i | ||||
\(56\) | 4.98675i | 0.666382i | ||||||||
\(57\) | 3.07030 | + | 3.07030i | 0.406671 | + | 0.406671i | ||||
\(58\) | 6.58373 | + | 6.58373i | 0.864486 | + | 0.864486i | ||||
\(59\) | 8.64060i | 1.12491i | 0.826828 | + | 0.562455i | \(0.190143\pi\) | ||||
−0.826828 | + | 0.562455i | \(0.809857\pi\) | |||||||
\(60\) | 1.35513 | + | 1.77865i | 0.174947 | + | 0.229623i | ||||
\(61\) | − | 5.58570i | − | 0.715175i | −0.933880 | − | 0.357588i | \(-0.883599\pi\) | ||
0.933880 | − | 0.357588i | \(-0.116401\pi\) | |||||||
\(62\) | 4.01961 | − | 4.01961i | 0.510491 | − | 0.510491i | ||||
\(63\) | −3.52616 | + | 3.52616i | −0.444255 | + | 0.444255i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −4.65372 | + | 3.54560i | −0.577222 | + | 0.439778i | ||||
\(66\) | 3.55731i | 0.437875i | ||||||||
\(67\) | −6.08730 | − | 6.08730i | −0.743682 | − | 0.743682i | 0.229602 | − | 0.973285i | \(-0.426257\pi\) |
−0.973285 | + | 0.229602i | \(0.926257\pi\) | |||||||
\(68\) | 2.03324 | − | 2.03324i | 0.246566 | − | 0.246566i | ||||
\(69\) | −2.03324 | − | 4.34350i | −0.244773 | − | 0.522895i | ||||
\(70\) | 1.49340 | − | 11.0502i | 0.178496 | − | 1.32076i | ||||
\(71\) | −10.0272 | −1.19001 | −0.595007 | − | 0.803720i | \(-0.702851\pi\) | ||||
−0.595007 | + | 0.803720i | \(0.702851\pi\) | |||||||
\(72\) | −0.707107 | + | 0.707107i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | −7.81740 | − | 7.81740i | −0.914957 | − | 0.914957i | 0.0816995 | − | 0.996657i | \(-0.473965\pi\) |
−0.996657 | + | 0.0816995i | \(0.973965\pi\) | |||||||
\(74\) | −8.45427 | −0.982789 | ||||||||
\(75\) | −2.47021 | − | 4.34719i | −0.285235 | − | 0.501970i | ||||
\(76\) | − | 4.34206i | − | 0.498068i | ||||||
\(77\) | 12.5437 | − | 12.5437i | 1.42948 | − | 1.42948i | ||||
\(78\) | −1.85009 | − | 1.85009i | −0.209482 | − | 0.209482i | ||||
\(79\) | 14.2774 | 1.60633 | 0.803165 | − | 0.595757i | \(-0.203148\pi\) | ||||
0.803165 | + | 0.595757i | \(0.203148\pi\) | |||||||
\(80\) | 0.299475 | − | 2.21592i | 0.0334823 | − | 0.247748i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0.123020 | − | 0.123020i | 0.0135852 | − | 0.0135852i | ||||
\(83\) | −4.22527 | + | 4.22527i | −0.463784 | + | 0.463784i | −0.899893 | − | 0.436110i | \(-0.856356\pi\) |
0.436110 | + | 0.899893i | \(0.356356\pi\) | |||||||
\(84\) | 4.98675 | 0.544099 | ||||||||
\(85\) | −5.11440 | + | 3.89659i | −0.554734 | + | 0.422645i | ||||
\(86\) | − | 2.40346i | − | 0.259172i | ||||||
\(87\) | 6.58373 | − | 6.58373i | 0.705850 | − | 0.705850i | ||||
\(88\) | 2.51540 | − | 2.51540i | 0.268142 | − | 0.268142i | ||||
\(89\) | −6.69008 | −0.709147 | −0.354574 | − | 0.935028i | \(-0.615374\pi\) | ||||
−0.354574 | + | 0.935028i | \(0.615374\pi\) | |||||||
\(90\) | 1.77865 | − | 1.35513i | 0.187487 | − | 0.142844i | ||||
\(91\) | 13.0474i | 1.36774i | ||||||||
\(92\) | −1.63360 | + | 4.50903i | −0.170315 | + | 0.470099i | ||||
\(93\) | −4.01961 | − | 4.01961i | −0.416814 | − | 0.416814i | ||||
\(94\) | 6.75905i | 0.697143i | ||||||||
\(95\) | −1.30034 | + | 9.62167i | −0.133412 | + | 0.987162i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −9.17535 | − | 9.17535i | −0.931616 | − | 0.931616i | 0.0661914 | − | 0.997807i | \(-0.478915\pi\) |
−0.997807 | + | 0.0661914i | \(0.978915\pi\) | |||||||
\(98\) | −12.6343 | − | 12.6343i | −1.27626 | − | 1.27626i | ||||
\(99\) | 3.55731 | 0.357523 | ||||||||
\(100\) | −1.32723 | + | 4.82063i | −0.132723 | + | 0.482063i | ||||
\(101\) | 17.0241 | 1.69396 | 0.846982 | − | 0.531622i | \(-0.178417\pi\) | ||||
0.846982 | + | 0.531622i | \(0.178417\pi\) | |||||||
\(102\) | −2.03324 | − | 2.03324i | −0.201320 | − | 0.201320i | ||||
\(103\) | 11.4713 | − | 11.4713i | 1.13030 | − | 1.13030i | 0.140170 | − | 0.990127i | \(-0.455235\pi\) |
0.990127 | − | 0.140170i | \(-0.0447651\pi\) | |||||||
\(104\) | 2.61642i | 0.256561i | ||||||||
\(105\) | −11.0502 | − | 1.49340i | −1.07839 | − | 0.145741i | ||||
\(106\) | − | 6.41619i | − | 0.623195i | ||||||
\(107\) | 2.64136 | + | 2.64136i | 0.255350 | + | 0.255350i | 0.823160 | − | 0.567810i | \(-0.192209\pi\) |
−0.567810 | + | 0.823160i | \(0.692209\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | −9.41859 | −0.902138 | −0.451069 | − | 0.892489i | \(-0.648957\pi\) | ||||
−0.451069 | + | 0.892489i | \(0.648957\pi\) | |||||||
\(110\) | −6.32723 | + | 4.82063i | −0.603277 | + | 0.459629i | ||||
\(111\) | 8.45427i | 0.802444i | ||||||||
\(112\) | −3.52616 | − | 3.52616i | −0.333191 | − | 0.333191i | ||||
\(113\) | −3.00726 | + | 3.00726i | −0.282899 | + | 0.282899i | −0.834264 | − | 0.551365i | \(-0.814107\pi\) |
0.551365 | + | 0.834264i | \(0.314107\pi\) | |||||||
\(114\) | −4.34206 | −0.406671 | ||||||||
\(115\) | 4.97027 | − | 9.50244i | 0.463480 | − | 0.886107i | ||||
\(116\) | −9.31080 | −0.864486 | ||||||||
\(117\) | −1.85009 | + | 1.85009i | −0.171041 | + | 0.171041i | ||||
\(118\) | −6.10983 | − | 6.10983i | −0.562455 | − | 0.562455i | ||||
\(119\) | 14.3390i | 1.31446i | ||||||||
\(120\) | −2.21592 | − | 0.299475i | −0.202285 | − | 0.0273382i | ||||
\(121\) | −1.65445 | −0.150405 | ||||||||
\(122\) | 3.94968 | + | 3.94968i | 0.357588 | + | 0.357588i | ||||
\(123\) | −0.123020 | − | 0.123020i | −0.0110923 | − | 0.0110923i | ||||
\(124\) | 5.68459i | 0.510491i | ||||||||
\(125\) | 4.38469 | − | 10.2847i | 0.392178 | − | 0.919889i | ||||
\(126\) | − | 4.98675i | − | 0.444255i | ||||||
\(127\) | 10.4069 | − | 10.4069i | 0.923466 | − | 0.923466i | −0.0738064 | − | 0.997273i | \(-0.523515\pi\) |
0.997273 | + | 0.0738064i | \(0.0235147\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −2.40346 | −0.211613 | ||||||||
\(130\) | 0.783553 | − | 5.79779i | 0.0687221 | − | 0.508500i | ||||
\(131\) | 14.0149 | 1.22449 | 0.612243 | − | 0.790670i | \(-0.290267\pi\) | ||||
0.612243 | + | 0.790670i | \(0.290267\pi\) | |||||||
\(132\) | −2.51540 | − | 2.51540i | −0.218937 | − | 0.218937i | ||||
\(133\) | 15.3108 | + | 15.3108i | 1.32762 | + | 1.32762i | ||||
\(134\) | 8.60874 | 0.743682 | ||||||||
\(135\) | −1.35513 | − | 1.77865i | −0.116631 | − | 0.153082i | ||||
\(136\) | 2.87543i | 0.246566i | ||||||||
\(137\) | 5.40475 | + | 5.40475i | 0.461759 | + | 0.461759i | 0.899232 | − | 0.437473i | \(-0.144126\pi\) |
−0.437473 | + | 0.899232i | \(0.644126\pi\) | |||||||
\(138\) | 4.50903 | + | 1.63360i | 0.383834 | + | 0.139061i | ||||
\(139\) | − | 16.9435i | − | 1.43713i | −0.695461 | − | 0.718564i | \(-0.744800\pi\) | ||
0.695461 | − | 0.718564i | \(-0.255200\pi\) | |||||||
\(140\) | 6.75771 | + | 8.86970i | 0.571131 | + | 0.749627i | ||||
\(141\) | 6.75905 | 0.569215 | ||||||||
\(142\) | 7.09033 | − | 7.09033i | 0.595007 | − | 0.595007i | ||||
\(143\) | 6.58135 | − | 6.58135i | 0.550360 | − | 0.550360i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 20.6320 | + | 2.78835i | 1.71340 | + | 0.231560i | ||||
\(146\) | 11.0555 | 0.914957 | ||||||||
\(147\) | −12.6343 | + | 12.6343i | −1.04206 | + | 1.04206i | ||||
\(148\) | 5.97807 | − | 5.97807i | 0.491394 | − | 0.491394i | ||||
\(149\) | −8.10858 | −0.664281 | −0.332140 | − | 0.943230i | \(-0.607771\pi\) | ||||
−0.332140 | + | 0.943230i | \(0.607771\pi\) | |||||||
\(150\) | 4.82063 | + | 1.32723i | 0.393603 | + | 0.108368i | ||||
\(151\) | −3.25889 | −0.265205 | −0.132602 | − | 0.991169i | \(-0.542333\pi\) | ||||
−0.132602 | + | 0.991169i | \(0.542333\pi\) | |||||||
\(152\) | 3.07030 | + | 3.07030i | 0.249034 | + | 0.249034i | ||||
\(153\) | −2.03324 | + | 2.03324i | −0.164377 | + | 0.164377i | ||||
\(154\) | 17.7394i | 1.42948i | ||||||||
\(155\) | 1.70239 | − | 12.5966i | 0.136739 | − | 1.01178i | ||||
\(156\) | 2.61642 | 0.209482 | ||||||||
\(157\) | 8.12046 | + | 8.12046i | 0.648083 | + | 0.648083i | 0.952530 | − | 0.304446i | \(-0.0984714\pi\) |
−0.304446 | + | 0.952530i | \(0.598471\pi\) | |||||||
\(158\) | −10.0956 | + | 10.0956i | −0.803165 | + | 0.803165i | ||||
\(159\) | −6.41619 | −0.508837 | ||||||||
\(160\) | 1.35513 | + | 1.77865i | 0.107133 | + | 0.140615i | ||||
\(161\) | −10.1392 | − | 21.6599i | −0.799083 | − | 1.70704i | ||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | 1.70018 | + | 1.70018i | 0.133169 | + | 0.133169i | 0.770549 | − | 0.637381i | \(-0.219982\pi\) |
−0.637381 | + | 0.770549i | \(0.719982\pi\) | |||||||
\(164\) | 0.173976i | 0.0135852i | ||||||||
\(165\) | 4.82063 | + | 6.32723i | 0.375286 | + | 0.492574i | ||||
\(166\) | − | 5.97544i | − | 0.463784i | ||||||
\(167\) | 14.8406 | − | 14.8406i | 1.14840 | − | 1.14840i | 0.161537 | − | 0.986867i | \(-0.448355\pi\) |
0.986867 | − | 0.161537i | \(-0.0516452\pi\) | |||||||
\(168\) | −3.52616 | + | 3.52616i | −0.272049 | + | 0.272049i | ||||
\(169\) | − | 6.15433i | − | 0.473410i | ||||||
\(170\) | 0.861118 | − | 6.37173i | 0.0660447 | − | 0.488689i | ||||
\(171\) | 4.34206i | 0.332045i | ||||||||
\(172\) | 1.69950 | + | 1.69950i | 0.129586 | + | 0.129586i | ||||
\(173\) | −3.36044 | − | 3.36044i | −0.255489 | − | 0.255489i | 0.567727 | − | 0.823217i | \(-0.307823\pi\) |
−0.823217 | + | 0.567727i | \(0.807823\pi\) | |||||||
\(174\) | 9.31080i | 0.705850i | ||||||||
\(175\) | −12.3183 | − | 21.6783i | −0.931177 | − | 1.63873i | ||||
\(176\) | 3.55731i | 0.268142i | ||||||||
\(177\) | −6.10983 | + | 6.10983i | −0.459243 | + | 0.459243i | ||||
\(178\) | 4.73060 | − | 4.73060i | 0.354574 | − | 0.354574i | ||||
\(179\) | 18.3275i | 1.36986i | 0.728607 | + | 0.684932i | \(0.240168\pi\) | ||||
−0.728607 | + | 0.684932i | \(0.759832\pi\) | |||||||
\(180\) | −0.299475 | + | 2.21592i | −0.0223215 | + | 0.165165i | ||||
\(181\) | 2.96040i | 0.220044i | 0.993929 | + | 0.110022i | \(0.0350922\pi\) | ||||
−0.993929 | + | 0.110022i | \(0.964908\pi\) | |||||||
\(182\) | −9.22594 | − | 9.22594i | −0.683872 | − | 0.683872i | ||||
\(183\) | 3.94968 | − | 3.94968i | 0.291969 | − | 0.291969i | ||||
\(184\) | −2.03324 | − | 4.34350i | −0.149892 | − | 0.320207i | ||||
\(185\) | −15.0372 | + | 11.4567i | −1.10556 | + | 0.842311i | ||||
\(186\) | 5.68459 | 0.416814 | ||||||||
\(187\) | 7.23285 | − | 7.23285i | 0.528918 | − | 0.528918i | ||||
\(188\) | −4.77937 | − | 4.77937i | −0.348572 | − | 0.348572i | ||||
\(189\) | −4.98675 | −0.362732 | ||||||||
\(190\) | −5.88407 | − | 7.72302i | −0.426875 | − | 0.560287i | ||||
\(191\) | − | 15.1230i | − | 1.09426i | −0.837048 | − | 0.547130i | \(-0.815720\pi\) | ||
0.837048 | − | 0.547130i | \(-0.184280\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | 7.54365 | + | 7.54365i | 0.543004 | + | 0.543004i | 0.924408 | − | 0.381404i | \(-0.124559\pi\) |
−0.381404 | + | 0.924408i | \(0.624559\pi\) | |||||||
\(194\) | 12.9759 | 0.931616 | ||||||||
\(195\) | −5.79779 | − | 0.783553i | −0.415189 | − | 0.0561114i | ||||
\(196\) | 17.8676 | 1.27626 | ||||||||
\(197\) | −4.44245 | + | 4.44245i | −0.316511 | + | 0.316511i | −0.847426 | − | 0.530914i | \(-0.821849\pi\) |
0.530914 | + | 0.847426i | \(0.321849\pi\) | |||||||
\(198\) | −2.51540 | + | 2.51540i | −0.178762 | + | 0.178762i | ||||
\(199\) | 3.49129 | 0.247491 | 0.123745 | − | 0.992314i | \(-0.460509\pi\) | ||||
0.123745 | + | 0.992314i | \(0.460509\pi\) | |||||||
\(200\) | −2.47021 | − | 4.34719i | −0.174670 | − | 0.307393i | ||||
\(201\) | − | 8.60874i | − | 0.607214i | ||||||
\(202\) | −12.0379 | + | 12.0379i | −0.846982 | + | 0.846982i | ||||
\(203\) | 32.8314 | − | 32.8314i | 2.30431 | − | 2.30431i | ||||
\(204\) | 2.87543 | 0.201320 | ||||||||
\(205\) | 0.0521014 | − | 0.385518i | 0.00363892 | − | 0.0269257i | ||||
\(206\) | 16.2228i | 1.13030i | ||||||||
\(207\) | 1.63360 | − | 4.50903i | 0.113543 | − | 0.313399i | ||||
\(208\) | −1.85009 | − | 1.85009i | −0.128281 | − | 0.128281i | ||||
\(209\) | − | 15.4460i | − | 1.06843i | ||||||
\(210\) | 8.86970 | − | 6.75771i | 0.612068 | − | 0.466326i | ||||
\(211\) | 12.0572 | 0.830050 | 0.415025 | − | 0.909810i | \(-0.363773\pi\) | ||||
0.415025 | + | 0.909810i | \(0.363773\pi\) | |||||||
\(212\) | 4.53693 | + | 4.53693i | 0.311597 | + | 0.311597i | ||||
\(213\) | −7.09033 | − | 7.09033i | −0.485821 | − | 0.485821i | ||||
\(214\) | −3.73545 | −0.255350 | ||||||||
\(215\) | −3.25701 | − | 4.27492i | −0.222126 | − | 0.291547i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −20.0448 | − | 20.0448i | −1.36073 | − | 1.36073i | ||||
\(218\) | 6.65995 | − | 6.65995i | 0.451069 | − | 0.451069i | ||||
\(219\) | − | 11.0555i | − | 0.747060i | ||||||
\(220\) | 1.06532 | − | 7.88272i | 0.0718241 | − | 0.531453i | ||||
\(221\) | 7.52334i | 0.506075i | ||||||||
\(222\) | −5.97807 | − | 5.97807i | −0.401222 | − | 0.401222i | ||||
\(223\) | −3.58953 | − | 3.58953i | −0.240373 | − | 0.240373i | 0.576631 | − | 0.817004i | \(-0.304367\pi\) |
−0.817004 | + | 0.576631i | \(0.804367\pi\) | |||||||
\(224\) | 4.98675 | 0.333191 | ||||||||
\(225\) | 1.32723 | − | 4.82063i | 0.0884817 | − | 0.321375i | ||||
\(226\) | − | 4.25290i | − | 0.282899i | ||||||
\(227\) | 9.88624 | + | 9.88624i | 0.656173 | + | 0.656173i | 0.954472 | − | 0.298300i | \(-0.0964195\pi\) |
−0.298300 | + | 0.954472i | \(0.596419\pi\) | |||||||
\(228\) | 3.07030 | − | 3.07030i | 0.203336 | − | 0.203336i | ||||
\(229\) | −8.77187 | −0.579661 | −0.289831 | − | 0.957078i | \(-0.593599\pi\) | ||||
−0.289831 | + | 0.957078i | \(0.593599\pi\) | |||||||
\(230\) | 3.20473 | + | 10.2338i | 0.211313 | + | 0.674794i | ||||
\(231\) | 17.7394 | 1.16717 | ||||||||
\(232\) | 6.58373 | − | 6.58373i | 0.432243 | − | 0.432243i | ||||
\(233\) | −6.20098 | − | 6.20098i | −0.406239 | − | 0.406239i | 0.474186 | − | 0.880425i | \(-0.342743\pi\) |
−0.880425 | + | 0.474186i | \(0.842743\pi\) | |||||||
\(234\) | − | 2.61642i | − | 0.171041i | ||||||
\(235\) | 9.15942 | + | 12.0220i | 0.597495 | + | 0.784230i | ||||
\(236\) | 8.64060 | 0.562455 | ||||||||
\(237\) | 10.0956 | + | 10.0956i | 0.655781 | + | 0.655781i | ||||
\(238\) | −10.1392 | − | 10.1392i | −0.657229 | − | 0.657229i | ||||
\(239\) | 1.95717i | 0.126599i | 0.997995 | + | 0.0632993i | \(0.0201623\pi\) | ||||
−0.997995 | + | 0.0632993i | \(0.979838\pi\) | |||||||
\(240\) | 1.77865 | − | 1.35513i | 0.114812 | − | 0.0874735i | ||||
\(241\) | 9.45390i | 0.608979i | 0.952516 | + | 0.304490i | \(0.0984859\pi\) | ||||
−0.952516 | + | 0.304490i | \(0.901514\pi\) | |||||||
\(242\) | 1.16987 | − | 1.16987i | 0.0752023 | − | 0.0752023i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | −5.58570 | −0.357588 | ||||||||
\(245\) | −39.5933 | − | 5.35091i | −2.52953 | − | 0.341857i | ||||
\(246\) | 0.173976 | 0.0110923 | ||||||||
\(247\) | 8.03320 | + | 8.03320i | 0.511141 | + | 0.511141i | ||||
\(248\) | −4.01961 | − | 4.01961i | −0.255246 | − | 0.255246i | ||||
\(249\) | −5.97544 | −0.378678 | ||||||||
\(250\) | 4.17192 | + | 10.3728i | 0.263856 | + | 0.656034i | ||||
\(251\) | 15.0794i | 0.951804i | 0.879498 | + | 0.475902i | \(0.157878\pi\) | ||||
−0.879498 | + | 0.475902i | \(0.842122\pi\) | |||||||
\(252\) | 3.52616 | + | 3.52616i | 0.222127 | + | 0.222127i | ||||
\(253\) | −5.81122 | + | 16.0400i | −0.365348 | + | 1.00843i | ||||
\(254\) | 14.7176i | 0.923466i | ||||||||
\(255\) | −6.37173 | − | 0.861118i | −0.399013 | − | 0.0539253i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.78800 | − | 1.78800i | 0.111532 | − | 0.111532i | −0.649138 | − | 0.760670i | \(-0.724870\pi\) |
0.760670 | + | 0.649138i | \(0.224870\pi\) | |||||||
\(258\) | 1.69950 | − | 1.69950i | 0.105806 | − | 0.105806i | ||||
\(259\) | 42.1593i | 2.61965i | ||||||||
\(260\) | 3.54560 | + | 4.65372i | 0.219889 | + | 0.288611i | ||||
\(261\) | 9.31080 | 0.576324 | ||||||||
\(262\) | −9.91002 | + | 9.91002i | −0.612243 | + | 0.612243i | ||||
\(263\) | 10.1360 | − | 10.1360i | 0.625011 | − | 0.625011i | −0.321798 | − | 0.946808i | \(-0.604287\pi\) |
0.946808 | + | 0.321798i | \(0.104287\pi\) | |||||||
\(264\) | 3.55731 | 0.218937 | ||||||||
\(265\) | −8.69479 | − | 11.4122i | −0.534117 | − | 0.701045i | ||||
\(266\) | −21.6527 | −1.32762 | ||||||||
\(267\) | −4.73060 | − | 4.73060i | −0.289508 | − | 0.289508i | ||||
\(268\) | −6.08730 | + | 6.08730i | −0.371841 | + | 0.371841i | ||||
\(269\) | − | 4.31486i | − | 0.263082i | −0.991311 | − | 0.131541i | \(-0.958008\pi\) | ||
0.991311 | − | 0.131541i | \(-0.0419925\pi\) | |||||||
\(270\) | 2.21592 | + | 0.299475i | 0.134857 | + | 0.0182254i | ||||
\(271\) | 12.2392 | 0.743481 | 0.371741 | − | 0.928337i | \(-0.378761\pi\) | ||||
0.371741 | + | 0.928337i | \(0.378761\pi\) | |||||||
\(272\) | −2.03324 | − | 2.03324i | −0.123283 | − | 0.123283i | ||||
\(273\) | −9.22594 | + | 9.22594i | −0.558379 | + | 0.558379i | ||||
\(274\) | −7.64346 | −0.461759 | ||||||||
\(275\) | −4.72135 | + | 17.1485i | −0.284708 | + | 1.03409i | ||||
\(276\) | −4.34350 | + | 2.03324i | −0.261448 | + | 0.122386i | ||||
\(277\) | −4.35452 | + | 4.35452i | −0.261638 | + | 0.261638i | −0.825719 | − | 0.564081i | \(-0.809230\pi\) |
0.564081 | + | 0.825719i | \(0.309230\pi\) | |||||||
\(278\) | 11.9809 | + | 11.9809i | 0.718564 | + | 0.718564i | ||||
\(279\) | − | 5.68459i | − | 0.340327i | ||||||
\(280\) | −11.0502 | − | 1.49340i | −0.660379 | − | 0.0892480i | ||||
\(281\) | − | 6.75477i | − | 0.402956i | −0.979493 | − | 0.201478i | \(-0.935426\pi\) | ||
0.979493 | − | 0.201478i | \(-0.0645744\pi\) | |||||||
\(282\) | −4.77937 | + | 4.77937i | −0.284608 | + | 0.284608i | ||||
\(283\) | 4.40365 | − | 4.40365i | 0.261770 | − | 0.261770i | −0.564003 | − | 0.825773i | \(-0.690739\pi\) |
0.825773 | + | 0.564003i | \(0.190739\pi\) | |||||||
\(284\) | 10.0272i | 0.595007i | ||||||||
\(285\) | −7.72302 | + | 5.88407i | −0.457472 | + | 0.348542i | ||||
\(286\) | 9.30743i | 0.550360i | ||||||||
\(287\) | −0.613468 | − | 0.613468i | −0.0362119 | − | 0.0362119i | ||||
\(288\) | 0.707107 | + | 0.707107i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 8.73191i | − | 0.513642i | ||||||
\(290\) | −16.5607 | + | 12.6174i | −0.972478 | + | 0.740918i | ||||
\(291\) | − | 12.9759i | − | 0.760661i | ||||||
\(292\) | −7.81740 | + | 7.81740i | −0.457479 | + | 0.457479i | ||||
\(293\) | 3.25957 | − | 3.25957i | 0.190426 | − | 0.190426i | −0.605454 | − | 0.795880i | \(-0.707008\pi\) |
0.795880 | + | 0.605454i | \(0.207008\pi\) | |||||||
\(294\) | − | 17.8676i | − | 1.04206i | ||||||
\(295\) | −19.1469 | − | 2.58764i | −1.11478 | − | 0.150658i | ||||
\(296\) | 8.45427i | 0.491394i | ||||||||
\(297\) | 2.51540 | + | 2.51540i | 0.145958 | + | 0.145958i | ||||
\(298\) | 5.73363 | − | 5.73363i | 0.332140 | − | 0.332140i | ||||
\(299\) | −5.31981 | − | 11.3644i | −0.307652 | − | 0.657222i | ||||
\(300\) | −4.34719 | + | 2.47021i | −0.250985 | + | 0.142618i | ||||
\(301\) | −11.9854 | −0.690829 | ||||||||
\(302\) | 2.30439 | − | 2.30439i | 0.132602 | − | 0.132602i | ||||
\(303\) | 12.0379 | + | 12.0379i | 0.691558 | + | 0.691558i | ||||
\(304\) | −4.34206 | −0.249034 | ||||||||
\(305\) | 12.3775 | + | 1.67277i | 0.708732 | + | 0.0957828i | ||||
\(306\) | − | 2.87543i | − | 0.164377i | ||||||
\(307\) | −19.9198 | + | 19.9198i | −1.13689 | + | 1.13689i | −0.147880 | + | 0.989005i | \(0.547245\pi\) |
−0.989005 | + | 0.147880i | \(0.952755\pi\) | |||||||
\(308\) | −12.5437 | − | 12.5437i | −0.714741 | − | 0.714741i | ||||
\(309\) | 16.2228 | 0.922884 | ||||||||
\(310\) | 7.70338 | + | 10.1109i | 0.437522 | + | 0.574262i | ||||
\(311\) | 6.46953 | 0.366853 | 0.183427 | − | 0.983033i | \(-0.441281\pi\) | ||||
0.183427 | + | 0.983033i | \(0.441281\pi\) | |||||||
\(312\) | −1.85009 | + | 1.85009i | −0.104741 | + | 0.104741i | ||||
\(313\) | −24.2861 | + | 24.2861i | −1.37273 | + | 1.37273i | −0.516358 | + | 0.856373i | \(0.672712\pi\) |
−0.856373 | + | 0.516358i | \(0.827288\pi\) | |||||||
\(314\) | −11.4841 | −0.648083 | ||||||||
\(315\) | −6.75771 | − | 8.86970i | −0.380754 | − | 0.499751i | ||||
\(316\) | − | 14.2774i | − | 0.803165i | ||||||
\(317\) | −5.81863 | + | 5.81863i | −0.326807 | + | 0.326807i | −0.851371 | − | 0.524564i | \(-0.824228\pi\) |
0.524564 | + | 0.851371i | \(0.324228\pi\) | |||||||
\(318\) | 4.53693 | − | 4.53693i | 0.254418 | − | 0.254418i | ||||
\(319\) | −33.1214 | −1.85444 | ||||||||
\(320\) | −2.21592 | − | 0.299475i | −0.123874 | − | 0.0167411i | ||||
\(321\) | 3.73545i | 0.208492i | ||||||||
\(322\) | 22.4854 | + | 8.14635i | 1.25306 | + | 0.453979i | ||||
\(323\) | 8.82843 | + | 8.82843i | 0.491227 | + | 0.491227i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | −6.46312 | − | 11.3741i | −0.358509 | − | 0.630921i | ||||
\(326\) | −2.40442 | −0.133169 | ||||||||
\(327\) | −6.65995 | − | 6.65995i | −0.368296 | − | 0.368296i | ||||
\(328\) | −0.123020 | − | 0.123020i | −0.00679262 | − | 0.00679262i | ||||
\(329\) | 33.7057 | 1.85826 | ||||||||
\(330\) | −7.88272 | − | 1.06532i | −0.433930 | − | 0.0586442i | ||||
\(331\) | −20.2812 | −1.11475 | −0.557377 | − | 0.830260i | \(-0.688192\pi\) | ||||
−0.557377 | + | 0.830260i | \(0.688192\pi\) | |||||||
\(332\) | 4.22527 | + | 4.22527i | 0.231892 | + | 0.231892i | ||||
\(333\) | −5.97807 | + | 5.97807i | −0.327596 | + | 0.327596i | ||||
\(334\) | 20.9878i | 1.14840i | ||||||||
\(335\) | 15.3120 | − | 11.6660i | 0.836583 | − | 0.637381i | ||||
\(336\) | − | 4.98675i | − | 0.272049i | ||||||
\(337\) | 8.75011 | + | 8.75011i | 0.476649 | + | 0.476649i | 0.904058 | − | 0.427409i | \(-0.140574\pi\) |
−0.427409 | + | 0.904058i | \(0.640574\pi\) | |||||||
\(338\) | 4.35177 | + | 4.35177i | 0.236705 | + | 0.236705i | ||||
\(339\) | −4.25290 | −0.230986 | ||||||||
\(340\) | 3.89659 | + | 5.11440i | 0.211322 | + | 0.277367i | ||||
\(341\) | 20.2218i | 1.09507i | ||||||||
\(342\) | −3.07030 | − | 3.07030i | −0.166023 | − | 0.166023i | ||||
\(343\) | −38.3211 | + | 38.3211i | −2.06914 | + | 2.06914i | ||||
\(344\) | −2.40346 | −0.129586 | ||||||||
\(345\) | 10.2338 | − | 3.20473i | 0.550967 | − | 0.172537i | ||||
\(346\) | 4.75237 | 0.255489 | ||||||||
\(347\) | 1.58819 | − | 1.58819i | 0.0852585 | − | 0.0852585i | −0.663191 | − | 0.748450i | \(-0.730798\pi\) |
0.748450 | + | 0.663191i | \(0.230798\pi\) | |||||||
\(348\) | −6.58373 | − | 6.58373i | −0.352925 | − | 0.352925i | ||||
\(349\) | − | 28.4591i | − | 1.52338i | −0.647941 | − | 0.761691i | \(-0.724369\pi\) | ||
0.647941 | − | 0.761691i | \(-0.275631\pi\) | |||||||
\(350\) | 24.0393 | + | 6.61854i | 1.28495 | + | 0.353776i | ||||
\(351\) | −2.61642 | −0.139654 | ||||||||
\(352\) | −2.51540 | − | 2.51540i | −0.134071 | − | 0.134071i | ||||
\(353\) | −11.0665 | − | 11.0665i | −0.589010 | − | 0.589010i | 0.348353 | − | 0.937363i | \(-0.386741\pi\) |
−0.937363 | + | 0.348353i | \(0.886741\pi\) | |||||||
\(354\) | − | 8.64060i | − | 0.459243i | ||||||
\(355\) | 3.00290 | − | 22.2196i | 0.159378 | − | 1.17929i | ||||
\(356\) | 6.69008i | 0.354574i | ||||||||
\(357\) | −10.1392 | + | 10.1392i | −0.536625 | + | 0.536625i | ||||
\(358\) | −12.9595 | − | 12.9595i | −0.684932 | − | 0.684932i | ||||
\(359\) | 14.1671 | 0.747711 | 0.373855 | − | 0.927487i | \(-0.378036\pi\) | ||||
0.373855 | + | 0.927487i | \(0.378036\pi\) | |||||||
\(360\) | −1.35513 | − | 1.77865i | −0.0714218 | − | 0.0937433i | ||||
\(361\) | −0.146530 | −0.00771209 | ||||||||
\(362\) | −2.09332 | − | 2.09332i | −0.110022 | − | 0.110022i | ||||
\(363\) | −1.16987 | − | 1.16987i | −0.0614024 | − | 0.0614024i | ||||
\(364\) | 13.0474 | 0.683872 | ||||||||
\(365\) | 19.6639 | − | 14.9816i | 1.02925 | − | 0.784175i | ||||
\(366\) | 5.58570i | 0.291969i | ||||||||
\(367\) | 4.28331 | + | 4.28331i | 0.223587 | + | 0.223587i | 0.810007 | − | 0.586420i | \(-0.199463\pi\) |
−0.586420 | + | 0.810007i | \(0.699463\pi\) | |||||||
\(368\) | 4.50903 | + | 1.63360i | 0.235049 | + | 0.0851573i | ||||
\(369\) | − | 0.173976i | − | 0.00905683i | ||||||
\(370\) | 2.53184 | − | 18.7340i | 0.131624 | − | 0.973935i | ||||
\(371\) | −31.9959 | −1.66114 | ||||||||
\(372\) | −4.01961 | + | 4.01961i | −0.208407 | + | 0.208407i | ||||
\(373\) | −15.9027 | + | 15.9027i | −0.823410 | + | 0.823410i | −0.986595 | − | 0.163185i | \(-0.947823\pi\) |
0.163185 | + | 0.986595i | \(0.447823\pi\) | |||||||
\(374\) | 10.2288i | 0.528918i | ||||||||
\(375\) | 10.3728 | − | 4.17192i | 0.535649 | − | 0.215437i | ||||
\(376\) | 6.75905 | 0.348572 | ||||||||
\(377\) | 17.2258 | − | 17.2258i | 0.887176 | − | 0.887176i | ||||
\(378\) | 3.52616 | − | 3.52616i | 0.181366 | − | 0.181366i | ||||
\(379\) | 26.3876 | 1.35544 | 0.677721 | − | 0.735319i | \(-0.262968\pi\) | ||||
0.677721 | + | 0.735319i | \(0.262968\pi\) | |||||||
\(380\) | 9.62167 | + | 1.30034i | 0.493581 | + | 0.0667058i | ||||
\(381\) | 14.7176 | 0.754007 | ||||||||
\(382\) | 10.6936 | + | 10.6936i | 0.547130 | + | 0.547130i | ||||
\(383\) | 15.7267 | − | 15.7267i | 0.803599 | − | 0.803599i | −0.180057 | − | 0.983656i | \(-0.557628\pi\) |
0.983656 | + | 0.180057i | \(0.0576282\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 24.0393 | + | 31.5523i | 1.22515 | + | 1.60805i | ||||
\(386\) | −10.6683 | −0.543004 | ||||||||
\(387\) | −1.69950 | − | 1.69950i | −0.0863906 | − | 0.0863906i | ||||
\(388\) | −9.17535 | + | 9.17535i | −0.465808 | + | 0.465808i | ||||
\(389\) | −30.2903 | −1.53578 | −0.767889 | − | 0.640583i | \(-0.778693\pi\) | ||||
−0.767889 | + | 0.640583i | \(0.778693\pi\) | |||||||
\(390\) | 4.65372 | − | 3.54560i | 0.235650 | − | 0.179539i | ||||
\(391\) | −5.84642 | − | 12.4894i | −0.295666 | − | 0.631617i | ||||
\(392\) | −12.6343 | + | 12.6343i | −0.638130 | + | 0.638130i | ||||
\(393\) | 9.91002 | + | 9.91002i | 0.499894 | + | 0.499894i | ||||
\(394\) | − | 6.28257i | − | 0.316511i | ||||||
\(395\) | −4.27571 | + | 31.6376i | −0.215134 | + | 1.59186i | ||||
\(396\) | − | 3.55731i | − | 0.178762i | ||||||
\(397\) | −22.4983 | + | 22.4983i | −1.12916 | + | 1.12916i | −0.138846 | + | 0.990314i | \(0.544339\pi\) |
−0.990314 | + | 0.138846i | \(0.955661\pi\) | |||||||
\(398\) | −2.46871 | + | 2.46871i | −0.123745 | + | 0.123745i | ||||
\(399\) | 21.6527i | 1.08399i | ||||||||
\(400\) | 4.82063 | + | 1.32723i | 0.241031 | + | 0.0663613i | ||||
\(401\) | 16.3195i | 0.814959i | 0.913214 | + | 0.407479i | \(0.133592\pi\) | ||||
−0.913214 | + | 0.407479i | \(0.866408\pi\) | |||||||
\(402\) | 6.08730 | + | 6.08730i | 0.303607 | + | 0.303607i | ||||
\(403\) | −10.5170 | − | 10.5170i | −0.523889 | − | 0.523889i | ||||
\(404\) | − | 17.0241i | − | 0.846982i | ||||||
\(405\) | 0.299475 | − | 2.21592i | 0.0148810 | − | 0.110110i | ||||
\(406\) | 46.4306i | 2.30431i | ||||||||
\(407\) | 21.2658 | − | 21.2658i | 1.05411 | − | 1.05411i | ||||
\(408\) | −2.03324 | + | 2.03324i | −0.100660 | + | 0.100660i | ||||
\(409\) | − | 37.8176i | − | 1.86996i | −0.354699 | − | 0.934981i | \(-0.615417\pi\) | ||
0.354699 | − | 0.934981i | \(-0.384583\pi\) | |||||||
\(410\) | 0.235761 | + | 0.309443i | 0.0116434 | + | 0.0152823i | ||||
\(411\) | 7.64346i | 0.377024i | ||||||||
\(412\) | −11.4713 | − | 11.4713i | −0.565149 | − | 0.565149i | ||||
\(413\) | −30.4682 | + | 30.4682i | −1.49924 | + | 1.49924i | ||||
\(414\) | 2.03324 | + | 4.34350i | 0.0999281 | + | 0.213471i | ||||
\(415\) | −8.09751 | − | 10.6282i | −0.397491 | − | 0.521720i | ||||
\(416\) | 2.61642 | 0.128281 | ||||||||
\(417\) | 11.9809 | − | 11.9809i | 0.586705 | − | 0.586705i | ||||
\(418\) | 10.9220 | + | 10.9220i | 0.534213 | + | 0.534213i | ||||
\(419\) | −39.5086 | −1.93012 | −0.965060 | − | 0.262030i | \(-0.915608\pi\) | ||||
−0.965060 | + | 0.262030i | \(0.915608\pi\) | |||||||
\(420\) | −1.49340 | + | 11.0502i | −0.0728707 | + | 0.539197i | ||||
\(421\) | − | 19.9633i | − | 0.972951i | −0.873694 | − | 0.486476i | \(-0.838282\pi\) | ||
0.873694 | − | 0.486476i | \(-0.161718\pi\) | |||||||
\(422\) | −8.52571 | + | 8.52571i | −0.415025 | + | 0.415025i | ||||
\(423\) | 4.77937 | + | 4.77937i | 0.232381 | + | 0.232381i | ||||
\(424\) | −6.41619 | −0.311597 | ||||||||
\(425\) | −7.10291 | − | 12.5000i | −0.344542 | − | 0.606341i | ||||
\(426\) | 10.0272 | 0.485821 | ||||||||
\(427\) | 19.6961 | − | 19.6961i | 0.953160 | − | 0.953160i | ||||
\(428\) | 2.64136 | − | 2.64136i | 0.127675 | − | 0.127675i | ||||
\(429\) | 9.30743 | 0.449367 | ||||||||
\(430\) | 5.32588 | + | 0.719775i | 0.256837 | + | 0.0347106i | ||||
\(431\) | − | 4.31840i | − | 0.208010i | −0.994577 | − | 0.104005i | \(-0.966834\pi\) | ||
0.994577 | − | 0.104005i | \(-0.0331658\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | 11.0514 | − | 11.0514i | 0.531096 | − | 0.531096i | −0.389802 | − | 0.920899i | \(-0.627457\pi\) |
0.920899 | + | 0.389802i | \(0.127457\pi\) | |||||||
\(434\) | 28.3476 | 1.36073 | ||||||||
\(435\) | 12.6174 | + | 16.5607i | 0.604957 | + | 0.794025i | ||||
\(436\) | 9.41859i | 0.451069i | ||||||||
\(437\) | −19.5785 | − | 7.09319i | −0.936565 | − | 0.339313i | ||||
\(438\) | 7.81740 | + | 7.81740i | 0.373530 | + | 0.373530i | ||||
\(439\) | 6.07173i | 0.289788i | 0.989447 | + | 0.144894i | \(0.0462841\pi\) | ||||
−0.989447 | + | 0.144894i | \(0.953716\pi\) | |||||||
\(440\) | 4.82063 | + | 6.32723i | 0.229815 | + | 0.301639i | ||||
\(441\) | −17.8676 | −0.850840 | ||||||||
\(442\) | −5.31981 | − | 5.31981i | −0.253037 | − | 0.253037i | ||||
\(443\) | 20.9363 | + | 20.9363i | 0.994714 | + | 0.994714i | 0.999986 | − | 0.00527186i | \(-0.00167809\pi\) |
−0.00527186 | + | 0.999986i | \(0.501678\pi\) | |||||||
\(444\) | 8.45427 | 0.401222 | ||||||||
\(445\) | 2.00351 | − | 14.8247i | 0.0949755 | − | 0.702758i | ||||
\(446\) | 5.07637 | 0.240373 | ||||||||
\(447\) | −5.73363 | − | 5.73363i | −0.271191 | − | 0.271191i | ||||
\(448\) | −3.52616 | + | 3.52616i | −0.166596 | + | 0.166596i | ||||
\(449\) | 40.0456i | 1.88987i | 0.327260 | + | 0.944934i | \(0.393875\pi\) | ||||
−0.327260 | + | 0.944934i | \(0.606125\pi\) | |||||||
\(450\) | 2.47021 | + | 4.34719i | 0.116447 | + | 0.204929i | ||||
\(451\) | 0.618887i | 0.0291422i | ||||||||
\(452\) | 3.00726 | + | 3.00726i | 0.141449 | + | 0.141449i | ||||
\(453\) | −2.30439 | − | 2.30439i | −0.108269 | − | 0.108269i | ||||
\(454\) | −13.9813 | −0.656173 | ||||||||
\(455\) | −28.9121 | − | 3.90738i | −1.35542 | − | 0.183181i | ||||
\(456\) | 4.34206i | 0.203336i | ||||||||
\(457\) | −1.02292 | − | 1.02292i | −0.0478501 | − | 0.0478501i | 0.682777 | − | 0.730627i | \(-0.260772\pi\) |
−0.730627 | + | 0.682777i | \(0.760772\pi\) | |||||||
\(458\) | 6.20265 | − | 6.20265i | 0.289831 | − | 0.289831i | ||||
\(459\) | −2.87543 | −0.134214 | ||||||||
\(460\) | −9.50244 | − | 4.97027i | −0.443054 | − | 0.231740i | ||||
\(461\) | −12.4686 | −0.580721 | −0.290360 | − | 0.956917i | \(-0.593775\pi\) | ||||
−0.290360 | + | 0.956917i | \(0.593775\pi\) | |||||||
\(462\) | −12.5437 | + | 12.5437i | −0.583584 | + | 0.583584i | ||||
\(463\) | 10.3193 | + | 10.3193i | 0.479577 | + | 0.479577i | 0.904996 | − | 0.425419i | \(-0.139873\pi\) |
−0.425419 | + | 0.904996i | \(0.639873\pi\) | |||||||
\(464\) | 9.31080i | 0.432243i | ||||||||
\(465\) | 10.1109 | − | 7.70338i | 0.468883 | − | 0.357236i | ||||
\(466\) | 8.76950 | 0.406239 | ||||||||
\(467\) | 17.3361 | + | 17.3361i | 0.802218 | + | 0.802218i | 0.983442 | − | 0.181224i | \(-0.0580060\pi\) |
−0.181224 | + | 0.983442i | \(0.558006\pi\) | |||||||
\(468\) | 1.85009 | + | 1.85009i | 0.0855205 | + | 0.0855205i | ||||
\(469\) | − | 42.9296i | − | 1.98231i | ||||||
\(470\) | −14.9775 | − | 2.02417i | −0.690863 | − | 0.0933678i | ||||
\(471\) | 11.4841i | 0.529158i | ||||||||
\(472\) | −6.10983 | + | 6.10983i | −0.281228 | + | 0.281228i | ||||
\(473\) | 6.04566 | + | 6.04566i | 0.277980 | + | 0.277980i | ||||
\(474\) | −14.2774 | −0.655781 | ||||||||
\(475\) | −20.9315 | − | 5.76289i | −0.960401 | − | 0.264420i | ||||
\(476\) | 14.3390 | 0.657229 | ||||||||
\(477\) | −4.53693 | − | 4.53693i | −0.207732 | − | 0.207732i | ||||
\(478\) | −1.38393 | − | 1.38393i | −0.0632993 | − | 0.0632993i | ||||
\(479\) | 26.2470 | 1.19926 | 0.599629 | − | 0.800278i | \(-0.295315\pi\) | ||||
0.599629 | + | 0.800278i | \(0.295315\pi\) | |||||||
\(480\) | −0.299475 | + | 2.21592i | −0.0136691 | + | 0.101143i | ||||
\(481\) | 22.1200i | 1.00858i | ||||||||
\(482\) | −6.68492 | − | 6.68492i | −0.304490 | − | 0.304490i | ||||
\(483\) | 8.14635 | − | 22.4854i | 0.370672 | − | 1.02312i | ||||
\(484\) | 1.65445i | 0.0752023i | ||||||||
\(485\) | 23.0797 | − | 17.5841i | 1.04799 | − | 0.798452i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 1.23197 | − | 1.23197i | 0.0558260 | − | 0.0558260i | −0.678643 | − | 0.734469i | \(-0.737431\pi\) |
0.734469 | + | 0.678643i | \(0.237431\pi\) | |||||||
\(488\) | 3.94968 | − | 3.94968i | 0.178794 | − | 0.178794i | ||||
\(489\) | 2.40442i | 0.108732i | ||||||||
\(490\) | 31.7804 | − | 24.2131i | 1.43569 | − | 1.09383i | ||||
\(491\) | 0.214208 | 0.00966705 | 0.00483353 | − | 0.999988i | \(-0.498461\pi\) | ||||
0.00483353 | + | 0.999988i | \(0.498461\pi\) | |||||||
\(492\) | −0.123020 | + | 0.123020i | −0.00554615 | + | 0.00554615i | ||||
\(493\) | 18.9311 | − | 18.9311i | 0.852612 | − | 0.852612i | ||||
\(494\) | −11.3607 | −0.511141 | ||||||||
\(495\) | −1.06532 | + | 7.88272i | −0.0478828 | + | 0.354302i | ||||
\(496\) | 5.68459 | 0.255246 | ||||||||
\(497\) | −35.3577 | − | 35.3577i | −1.58601 | − | 1.58601i | ||||
\(498\) | 4.22527 | − | 4.22527i | 0.189339 | − | 0.189339i | ||||
\(499\) | − | 2.91098i | − | 0.130313i | −0.997875 | − | 0.0651566i | \(-0.979245\pi\) | ||
0.997875 | − | 0.0651566i | \(-0.0207547\pi\) | |||||||
\(500\) | −10.2847 | − | 4.38469i | −0.459945 | − | 0.196089i | ||||
\(501\) | 20.9878 | 0.937668 | ||||||||
\(502\) | −10.6628 | − | 10.6628i | −0.475902 | − | 0.475902i | ||||
\(503\) | −11.2871 | + | 11.2871i | −0.503266 | + | 0.503266i | −0.912451 | − | 0.409185i | \(-0.865813\pi\) |
0.409185 | + | 0.912451i | \(0.365813\pi\) | |||||||
\(504\) | −4.98675 | −0.222127 | ||||||||
\(505\) | −5.09829 | + | 37.7242i | −0.226871 | + | 1.67870i | ||||
\(506\) | −7.23285 | − | 15.4512i | −0.321539 | − | 0.686888i | ||||
\(507\) | 4.35177 | − | 4.35177i | 0.193269 | − | 0.193269i | ||||
\(508\) | −10.4069 | − | 10.4069i | −0.461733 | − | 0.461733i | ||||
\(509\) | 0.259394i | 0.0114974i | 0.999983 | + | 0.00574871i | \(0.00182988\pi\) | ||||
−0.999983 | + | 0.00574871i | \(0.998170\pi\) | |||||||
\(510\) | 5.11440 | − | 3.89659i | 0.226469 | − | 0.172544i | ||||
\(511\) | − | 55.1309i | − | 2.43885i | ||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −3.07030 | + | 3.07030i | −0.135557 | + | 0.135557i | ||||
\(514\) | 2.52861i | 0.111532i | ||||||||
\(515\) | 21.9841 | + | 28.8548i | 0.968735 | + | 1.27149i | ||||
\(516\) | 2.40346i | 0.105806i | ||||||||
\(517\) | −17.0017 | − | 17.0017i | −0.747734 | − | 0.747734i | ||||
\(518\) | −29.8111 | − | 29.8111i | −1.30983 | − | 1.30983i | ||||
\(519\) | − | 4.75237i | − | 0.208606i | ||||||
\(520\) | −5.79779 | − | 0.783553i | −0.254250 | − | 0.0343611i | ||||
\(521\) | 19.5054i | 0.854545i | 0.904123 | + | 0.427273i | \(0.140526\pi\) | ||||
−0.904123 | + | 0.427273i | \(0.859474\pi\) | |||||||
\(522\) | −6.58373 | + | 6.58373i | −0.288162 | + | 0.288162i | ||||
\(523\) | −7.38191 | + | 7.38191i | −0.322788 | + | 0.322788i | −0.849836 | − | 0.527047i | \(-0.823299\pi\) |
0.527047 | + | 0.849836i | \(0.323299\pi\) | |||||||
\(524\) | − | 14.0149i | − | 0.612243i | ||||||
\(525\) | 6.61854 | − | 24.0393i | 0.288857 | − | 1.04916i | ||||
\(526\) | 14.3344i | 0.625011i | ||||||||
\(527\) | −11.5581 | − | 11.5581i | −0.503479 | − | 0.503479i | ||||
\(528\) | −2.51540 | + | 2.51540i | −0.109469 | + | 0.109469i | ||||
\(529\) | 17.6627 | + | 14.7319i | 0.767943 | + | 0.640518i | ||||
\(530\) | 14.2178 | + | 1.92148i | 0.617581 | + | 0.0834640i | ||||
\(531\) | −8.64060 | −0.374970 | ||||||||
\(532\) | 15.3108 | − | 15.3108i | 0.663808 | − | 0.663808i | ||||
\(533\) | −0.321872 | − | 0.321872i | −0.0139418 | − | 0.0139418i | ||||
\(534\) | 6.69008 | 0.289508 | ||||||||
\(535\) | −6.64407 | + | 5.06203i | −0.287248 | + | 0.218851i | ||||
\(536\) | − | 8.60874i | − | 0.371841i | ||||||
\(537\) | −12.9595 | + | 12.9595i | −0.559245 | + | 0.559245i | ||||
\(538\) | 3.05107 | + | 3.05107i | 0.131541 | + | 0.131541i | ||||
\(539\) | 63.5608 | 2.73776 | ||||||||
\(540\) | −1.77865 | + | 1.35513i | −0.0765411 | + | 0.0583157i | ||||
\(541\) | −30.9021 | −1.32858 | −0.664292 | − | 0.747473i | \(-0.731267\pi\) | ||||
−0.664292 | + | 0.747473i | \(0.731267\pi\) | |||||||
\(542\) | −8.65445 | + | 8.65445i | −0.371741 | + | 0.371741i | ||||
\(543\) | −2.09332 | + | 2.09332i | −0.0898328 | + | 0.0898328i | ||||
\(544\) | 2.87543 | 0.123283 | ||||||||
\(545\) | 2.82063 | − | 20.8709i | 0.120823 | − | 0.894010i | ||||
\(546\) | − | 13.0474i | − | 0.558379i | ||||||
\(547\) | 10.8020 | − | 10.8020i | 0.461862 | − | 0.461862i | −0.437403 | − | 0.899265i | \(-0.644102\pi\) |
0.899265 | + | 0.437403i | \(0.144102\pi\) | |||||||
\(548\) | 5.40475 | − | 5.40475i | 0.230879 | − | 0.230879i | ||||
\(549\) | 5.58570 | 0.238392 | ||||||||
\(550\) | −8.78730 | − | 15.4643i | −0.374692 | − | 0.659400i | ||||
\(551\) | − | 40.4281i | − | 1.72229i | ||||||
\(552\) | 1.63360 | − | 4.50903i | 0.0695307 | − | 0.191917i | ||||
\(553\) | 50.3443 | + | 50.3443i | 2.14086 | + | 2.14086i | ||||
\(554\) | − | 6.15822i | − | 0.261638i | ||||||
\(555\) | −18.7340 | − | 2.53184i | −0.795214 | − | 0.107471i | ||||
\(556\) | −16.9435 | −0.718564 | ||||||||
\(557\) | 15.6411 | + | 15.6411i | 0.662733 | + | 0.662733i | 0.956023 | − | 0.293291i | \(-0.0947503\pi\) |
−0.293291 | + | 0.956023i | \(0.594750\pi\) | |||||||
\(558\) | 4.01961 | + | 4.01961i | 0.170164 | + | 0.170164i | ||||
\(559\) | −6.28847 | −0.265974 | ||||||||
\(560\) | 8.86970 | − | 6.75771i | 0.374813 | − | 0.285565i | ||||
\(561\) | 10.2288 | 0.431860 | ||||||||
\(562\) | 4.77634 | + | 4.77634i | 0.201478 | + | 0.201478i | ||||
\(563\) | −7.40726 | + | 7.40726i | −0.312179 | + | 0.312179i | −0.845753 | − | 0.533574i | \(-0.820848\pi\) |
0.533574 | + | 0.845753i | \(0.320848\pi\) | |||||||
\(564\) | − | 6.75905i | − | 0.284608i | ||||||
\(565\) | −5.76325 | − | 7.56445i | −0.242462 | − | 0.318239i | ||||
\(566\) | 6.22770i | 0.261770i | ||||||||
\(567\) | −3.52616 | − | 3.52616i | −0.148085 | − | 0.148085i | ||||
\(568\) | −7.09033 | − | 7.09033i | −0.297504 | − | 0.297504i | ||||
\(569\) | −11.9076 | −0.499194 | −0.249597 | − | 0.968350i | \(-0.580298\pi\) | ||||
−0.249597 | + | 0.968350i | \(0.580298\pi\) | |||||||
\(570\) | 1.30034 | − | 9.62167i | 0.0544651 | − | 0.403007i | ||||
\(571\) | 22.4163i | 0.938092i | 0.883174 | + | 0.469046i | \(0.155402\pi\) | ||||
−0.883174 | + | 0.469046i | \(0.844598\pi\) | |||||||
\(572\) | −6.58135 | − | 6.58135i | −0.275180 | − | 0.275180i | ||||
\(573\) | 10.6936 | − | 10.6936i | 0.446730 | − | 0.446730i | ||||
\(574\) | 0.867575 | 0.0362119 | ||||||||
\(575\) | 19.5682 | + | 13.8595i | 0.816051 | + | 0.577980i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 4.75499 | − | 4.75499i | 0.197953 | − | 0.197953i | −0.601169 | − | 0.799122i | \(-0.705298\pi\) |
0.799122 | + | 0.601169i | \(0.205298\pi\) | |||||||
\(578\) | 6.17439 | + | 6.17439i | 0.256821 | + | 0.256821i | ||||
\(579\) | 10.6683i | 0.443361i | ||||||||
\(580\) | 2.78835 | − | 20.6320i | 0.115780 | − | 0.856698i | ||||
\(581\) | −29.7980 | −1.23623 | ||||||||
\(582\) | 9.17535 | + | 9.17535i | 0.380330 | + | 0.380330i | ||||
\(583\) | 16.1393 | + | 16.1393i | 0.668420 | + | 0.668420i | ||||
\(584\) | − | 11.0555i | − | 0.457479i | ||||||
\(585\) | −3.54560 | − | 4.65372i | −0.146593 | − | 0.192407i | ||||
\(586\) | 4.60973i | 0.190426i | ||||||||
\(587\) | 13.8586 | − | 13.8586i | 0.572004 | − | 0.572004i | −0.360684 | − | 0.932688i | \(-0.617457\pi\) |
0.932688 | + | 0.360684i | \(0.117457\pi\) | |||||||
\(588\) | 12.6343 | + | 12.6343i | 0.521031 | + | 0.521031i | ||||
\(589\) | −24.6828 | −1.01704 | ||||||||
\(590\) | 15.3686 | − | 11.7092i | 0.632717 | − | 0.482059i | ||||
\(591\) | −6.28257 | −0.258430 | ||||||||
\(592\) | −5.97807 | − | 5.97807i | −0.245697 | − | 0.245697i | ||||
\(593\) | 2.48988 | + | 2.48988i | 0.102247 | + | 0.102247i | 0.756380 | − | 0.654133i | \(-0.226966\pi\) |
−0.654133 | + | 0.756380i | \(0.726966\pi\) | |||||||
\(594\) | −3.55731 | −0.145958 | ||||||||
\(595\) | −31.7742 | − | 4.29418i | −1.30262 | − | 0.176044i | ||||
\(596\) | 8.10858i | 0.332140i | ||||||||
\(597\) | 2.46871 | + | 2.46871i | 0.101038 | + | 0.101038i | ||||
\(598\) | 11.7975 | + | 4.27419i | 0.482437 | + | 0.174785i | ||||
\(599\) | − | 18.3558i | − | 0.749997i | −0.927025 | − | 0.374999i | \(-0.877643\pi\) | ||
0.927025 | − | 0.374999i | \(-0.122357\pi\) | |||||||
\(600\) | 1.32723 | − | 4.82063i | 0.0541838 | − | 0.196801i | ||||
\(601\) | −11.3916 | −0.464672 | −0.232336 | − | 0.972636i | \(-0.574637\pi\) | ||||
−0.232336 | + | 0.972636i | \(0.574637\pi\) | |||||||
\(602\) | 8.47499 | − | 8.47499i | 0.345415 | − | 0.345415i | ||||
\(603\) | 6.08730 | − | 6.08730i | 0.247894 | − | 0.247894i | ||||
\(604\) | 3.25889i | 0.132602i | ||||||||
\(605\) | 0.495466 | − | 3.66614i | 0.0201436 | − | 0.149050i | ||||
\(606\) | −17.0241 | −0.691558 | ||||||||
\(607\) | −22.8486 | + | 22.8486i | −0.927398 | + | 0.927398i | −0.997537 | − | 0.0701391i | \(-0.977656\pi\) |
0.0701391 | + | 0.997537i | \(0.477656\pi\) | |||||||
\(608\) | 3.07030 | − | 3.07030i | 0.124517 | − | 0.124517i | ||||
\(609\) | 46.4306 | 1.88146 | ||||||||
\(610\) | −9.93503 | + | 7.56937i | −0.402257 | + | 0.306475i | ||||
\(611\) | 17.6846 | 0.715440 | ||||||||
\(612\) | 2.03324 | + | 2.03324i | 0.0821887 | + | 0.0821887i | ||||
\(613\) | 16.6871 | − | 16.6871i | 0.673985 | − | 0.673985i | −0.284647 | − | 0.958632i | \(-0.591876\pi\) |
0.958632 | + | 0.284647i | \(0.0918765\pi\) | |||||||
\(614\) | − | 28.1709i | − | 1.13689i | ||||||
\(615\) | 0.309443 | − | 0.235761i | 0.0124780 | − | 0.00950679i | ||||
\(616\) | 17.7394 | 0.714741 | ||||||||
\(617\) | −3.52666 | − | 3.52666i | −0.141978 | − | 0.141978i | 0.632545 | − | 0.774523i | \(-0.282010\pi\) |
−0.774523 | + | 0.632545i | \(0.782010\pi\) | |||||||
\(618\) | −11.4713 | + | 11.4713i | −0.461442 | + | 0.461442i | ||||
\(619\) | 13.6535 | 0.548781 | 0.274390 | − | 0.961618i | \(-0.411524\pi\) | ||||
0.274390 | + | 0.961618i | \(0.411524\pi\) | |||||||
\(620\) | −12.5966 | − | 1.70239i | −0.505892 | − | 0.0683696i | ||||
\(621\) | 4.34350 | − | 2.03324i | 0.174298 | − | 0.0815909i | ||||
\(622\) | −4.57465 | + | 4.57465i | −0.183427 | + | 0.183427i | ||||
\(623\) | −23.5903 | − | 23.5903i | −0.945126 | − | 0.945126i | ||||
\(624\) | − | 2.61642i | − | 0.104741i | ||||||
\(625\) | 21.4769 | + | 12.7961i | 0.859078 | + | 0.511845i | ||||
\(626\) | − | 34.3457i | − | 1.37273i | ||||||
\(627\) | 10.9220 | − | 10.9220i | 0.436183 | − | 0.436183i | ||||
\(628\) | 8.12046 | − | 8.12046i | 0.324042 | − | 0.324042i | ||||
\(629\) | 24.3097i | 0.969289i | ||||||||
\(630\) | 11.0502 | + | 1.49340i | 0.440252 | + | 0.0594987i | ||||
\(631\) | − | 3.15280i | − | 0.125511i | −0.998029 | − | 0.0627555i | \(-0.980011\pi\) | ||
0.998029 | − | 0.0627555i | \(-0.0199888\pi\) | |||||||
\(632\) | 10.0956 | + | 10.0956i | 0.401582 | + | 0.401582i | ||||
\(633\) | 8.52571 | + | 8.52571i | 0.338866 | + | 0.338866i | ||||
\(634\) | − | 8.22879i | − | 0.326807i | ||||||
\(635\) | 19.9444 | + | 26.1776i | 0.791468 | + | 1.03883i | ||||
\(636\) | 6.41619i | 0.254418i | ||||||||
\(637\) | −33.0568 | + | 33.0568i | −1.30976 | + | 1.30976i | ||||
\(638\) | 23.4204 | − | 23.4204i | 0.927222 | − | 0.927222i | ||||
\(639\) | − | 10.0272i | − | 0.396671i | ||||||
\(640\) | 1.77865 | − | 1.35513i | 0.0703075 | − | 0.0535664i | ||||
\(641\) | − | 47.5668i | − | 1.87878i | −0.342857 | − | 0.939388i | \(-0.611395\pi\) | ||
0.342857 | − | 0.939388i | \(-0.388605\pi\) | |||||||
\(642\) | −2.64136 | − | 2.64136i | −0.104246 | − | 0.104246i | ||||
\(643\) | −0.429808 | + | 0.429808i | −0.0169500 | + | 0.0169500i | −0.715531 | − | 0.698581i | \(-0.753815\pi\) |
0.698581 | + | 0.715531i | \(0.253815\pi\) | |||||||
\(644\) | −21.6599 | + | 10.1392i | −0.853520 | + | 0.399542i | ||||
\(645\) | 0.719775 | − | 5.32588i | 0.0283411 | − | 0.209706i | ||||
\(646\) | −12.4853 | −0.491227 | ||||||||
\(647\) | 27.5034 | − | 27.5034i | 1.08127 | − | 1.08127i | 0.0848805 | − | 0.996391i | \(-0.472949\pi\) |
0.996391 | − | 0.0848805i | \(-0.0270509\pi\) | |||||||
\(648\) | −0.707107 | − | 0.707107i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | 30.7373 | 1.20654 | ||||||||
\(650\) | 12.6128 | + | 3.47258i | 0.494715 | + | 0.136206i | ||||
\(651\) | − | 28.3476i | − | 1.11103i | ||||||
\(652\) | 1.70018 | − | 1.70018i | 0.0665843 | − | 0.0665843i | ||||
\(653\) | −24.3356 | − | 24.3356i | −0.952327 | − | 0.952327i | 0.0465870 | − | 0.998914i | \(-0.485166\pi\) |
−0.998914 | + | 0.0465870i | \(0.985166\pi\) | |||||||
\(654\) | 9.41859 | 0.368296 | ||||||||
\(655\) | −4.19710 | + | 31.0559i | −0.163994 | + | 1.21345i | ||||
\(656\) | 0.173976 | 0.00679262 | ||||||||
\(657\) | 7.81740 | − | 7.81740i | 0.304986 | − | 0.304986i | ||||
\(658\) | −23.8335 | + | 23.8335i | −0.929128 | + | 0.929128i | ||||
\(659\) | −24.4880 | −0.953918 | −0.476959 | − | 0.878926i | \(-0.658261\pi\) | ||||
−0.476959 | + | 0.878926i | \(0.658261\pi\) | |||||||
\(660\) | 6.32723 | − | 4.82063i | 0.246287 | − | 0.187643i | ||||
\(661\) | − | 5.54696i | − | 0.215752i | −0.994164 | − | 0.107876i | \(-0.965595\pi\) | ||
0.994164 | − | 0.107876i | \(-0.0344049\pi\) | |||||||
\(662\) | 14.3409 | − | 14.3409i | 0.557377 | − | 0.557377i | ||||
\(663\) | −5.31981 | + | 5.31981i | −0.206604 | + | 0.206604i | ||||
\(664\) | −5.97544 | −0.231892 | ||||||||
\(665\) | −38.5128 | + | 29.3424i | −1.49346 | + | 1.13785i | ||||
\(666\) | − | 8.45427i | − | 0.327596i | ||||||
\(667\) | −15.2101 | + | 41.9827i | −0.588939 | + | 1.62558i | ||||
\(668\) | −14.8406 | − | 14.8406i | −0.574202 | − | 0.574202i | ||||
\(669\) | − | 5.07637i | − | 0.196264i | ||||||
\(670\) | −2.57810 | + | 19.0763i | −0.0996007 | + | 0.736982i | ||||
\(671\) | −19.8701 | −0.767075 | ||||||||
\(672\) | 3.52616 | + | 3.52616i | 0.136025 | + | 0.136025i | ||||
\(673\) | 16.5963 | + | 16.5963i | 0.639741 | + | 0.639741i | 0.950491 | − | 0.310751i | \(-0.100580\pi\) |
−0.310751 | + | 0.950491i | \(0.600580\pi\) | |||||||
\(674\) | −12.3745 | −0.476649 | ||||||||
\(675\) | 4.34719 | − | 2.47021i | 0.167323 | − | 0.0950784i | ||||
\(676\) | −6.15433 | −0.236705 | ||||||||
\(677\) | 9.91246 | + | 9.91246i | 0.380967 | + | 0.380967i | 0.871450 | − | 0.490484i | \(-0.163180\pi\) |
−0.490484 | + | 0.871450i | \(0.663180\pi\) | |||||||
\(678\) | 3.00726 | − | 3.00726i | 0.115493 | − | 0.115493i | ||||
\(679\) | − | 64.7075i | − | 2.48325i | ||||||
\(680\) | −6.37173 | − | 0.861118i | −0.244345 | − | 0.0330224i | ||||
\(681\) | 13.9813i | 0.535763i | ||||||||
\(682\) | −14.2990 | − | 14.2990i | −0.547537 | − | 0.547537i | ||||
\(683\) | −21.1411 | − | 21.1411i | −0.808941 | − | 0.808941i | 0.175533 | − | 0.984474i | \(-0.443835\pi\) |
−0.984474 | + | 0.175533i | \(0.943835\pi\) | |||||||
\(684\) | 4.34206 | 0.166023 | ||||||||
\(685\) | −13.5951 | + | 10.3579i | −0.519441 | + | 0.395756i | ||||
\(686\) | − | 54.1942i | − | 2.06914i | ||||||
\(687\) | −6.20265 | − | 6.20265i | −0.236646 | − | 0.236646i | ||||
\(688\) | 1.69950 | − | 1.69950i | 0.0647929 | − | 0.0647929i | ||||
\(689\) | −16.7875 | −0.639551 | ||||||||
\(690\) | −4.97027 | + | 9.50244i | −0.189215 | + | 0.361752i | ||||
\(691\) | −5.79799 | −0.220566 | −0.110283 | − | 0.993900i | \(-0.535176\pi\) | ||||
−0.110283 | + | 0.993900i | \(0.535176\pi\) | |||||||
\(692\) | −3.36044 | + | 3.36044i | −0.127745 | + | 0.127745i | ||||
\(693\) | 12.5437 | + | 12.5437i | 0.476494 | + | 0.476494i | ||||
\(694\) | 2.24604i | 0.0852585i | ||||||||
\(695\) | 37.5454 | + | 5.07414i | 1.42418 | + | 0.192473i | ||||
\(696\) | 9.31080 | 0.352925 | ||||||||
\(697\) | −0.353734 | − | 0.353734i | −0.0133986 | − | 0.0133986i | ||||
\(698\) | 20.1236 | + | 20.1236i | 0.761691 | + | 0.761691i | ||||
\(699\) | − | 8.76950i | − | 0.331693i | ||||||
\(700\) | −21.6783 | + | 12.3183i | −0.819364 | + | 0.465588i | ||||
\(701\) | 8.81493i | 0.332935i | 0.986047 | + | 0.166468i | \(0.0532361\pi\) | ||||
−0.986047 | + | 0.166468i | \(0.946764\pi\) | |||||||
\(702\) | 1.85009 | − | 1.85009i | 0.0698272 | − | 0.0698272i | ||||
\(703\) | 25.9571 | + | 25.9571i | 0.978992 | + | 0.978992i | ||||
\(704\) | 3.55731 | 0.134071 | ||||||||
\(705\) | −2.02417 | + | 14.9775i | −0.0762345 | + | 0.564087i | ||||
\(706\) | 15.6504 | 0.589010 | ||||||||
\(707\) | 60.0298 | + | 60.0298i | 2.25765 | + | 2.25765i | ||||
\(708\) | 6.10983 | + | 6.10983i | 0.229621 | + | 0.229621i | ||||
\(709\) | 20.7494 | 0.779260 | 0.389630 | − | 0.920972i | \(-0.372603\pi\) | ||||
0.389630 | + | 0.920972i | \(0.372603\pi\) | |||||||
\(710\) | 13.5882 | + | 17.8350i | 0.509958 | + | 0.669335i | ||||
\(711\) | 14.2774i | 0.535443i | ||||||||
\(712\) | −4.73060 | − | 4.73060i | −0.177287 | − | 0.177287i | ||||
\(713\) | 25.6320 | + | 9.28635i | 0.959925 | + | 0.347776i | ||||
\(714\) | − | 14.3390i | − | 0.536625i | ||||||
\(715\) | 12.6128 | + | 16.5547i | 0.471692 | + | 0.619111i | ||||
\(716\) | 18.3275 | 0.684932 | ||||||||
\(717\) | −1.38393 | + | 1.38393i | −0.0516837 | + | 0.0516837i | ||||
\(718\) | −10.0176 | + | 10.0176i | −0.373855 | + | 0.373855i | ||||
\(719\) | − | 10.7490i | − | 0.400869i | −0.979707 | − | 0.200435i | \(-0.935765\pi\) | ||
0.979707 | − | 0.200435i | \(-0.0642354\pi\) | |||||||
\(720\) | 2.21592 | + | 0.299475i | 0.0825826 | + | 0.0111608i | ||||
\(721\) | 80.8991 | 3.01284 | ||||||||
\(722\) | 0.103612 | − | 0.103612i | 0.00385604 | − | 0.00385604i | ||||
\(723\) | −6.68492 | + | 6.68492i | −0.248615 | + | 0.248615i | ||||
\(724\) | 2.96040 | 0.110022 | ||||||||
\(725\) | −12.3575 | + | 44.8839i | −0.458947 | + | 1.66695i | ||||
\(726\) | 1.65445 | 0.0614024 | ||||||||
\(727\) | −4.60271 | − | 4.60271i | −0.170705 | − | 0.170705i | 0.616584 | − | 0.787289i | \(-0.288516\pi\) |
−0.787289 | + | 0.616584i | \(0.788516\pi\) | |||||||
\(728\) | −9.22594 | + | 9.22594i | −0.341936 | + | 0.341936i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −3.31083 | + | 24.4981i | −0.122539 | + | 0.906715i | ||||
\(731\) | −6.91098 | −0.255612 | ||||||||
\(732\) | −3.94968 | − | 3.94968i | −0.145985 | − | 0.145985i | ||||
\(733\) | 13.8564 | − | 13.8564i | 0.511796 | − | 0.511796i | −0.403280 | − | 0.915076i | \(-0.632130\pi\) |
0.915076 | + | 0.403280i | \(0.132130\pi\) | |||||||
\(734\) | −6.05752 | −0.223587 | ||||||||
\(735\) | −24.2131 | − | 31.7804i | −0.893112 | − | 1.17224i | ||||
\(736\) | −4.34350 | + | 2.03324i | −0.160103 | + | 0.0749461i | ||||
\(737\) | −21.6544 | + | 21.6544i | −0.797650 | + | 0.797650i | ||||
\(738\) | 0.123020 | + | 0.123020i | 0.00452842 | + | 0.00452842i | ||||
\(739\) | − | 8.74615i | − | 0.321732i | −0.986976 | − | 0.160866i | \(-0.948571\pi\) | ||
0.986976 | − | 0.160866i | \(-0.0514288\pi\) | |||||||
\(740\) | 11.4567 | + | 15.0372i | 0.421155 | + | 0.552779i | ||||
\(741\) | 11.3607i | 0.417344i | ||||||||
\(742\) | 22.6245 | − | 22.6245i | 0.830572 | − | 0.830572i | ||||
\(743\) | 17.1923 | − | 17.1923i | 0.630725 | − | 0.630725i | −0.317525 | − | 0.948250i | \(-0.602852\pi\) |
0.948250 | + | 0.317525i | \(0.102852\pi\) | |||||||
\(744\) | − | 5.68459i | − | 0.208407i | ||||||
\(745\) | 2.42831 | − | 17.9680i | 0.0889665 | − | 0.658296i | ||||
\(746\) | − | 22.4898i | − | 0.823410i | ||||||
\(747\) | −4.22527 | − | 4.22527i | −0.154595 | − | 0.154595i | ||||
\(748\) | −7.23285 | − | 7.23285i | −0.264459 | − | 0.264459i | ||||
\(749\) | 18.6277i | 0.680642i | ||||||||
\(750\) | −4.38469 | + | 10.2847i | −0.160106 | + | 0.375543i | ||||
\(751\) | − | 34.8556i | − | 1.27190i | −0.771731 | − | 0.635950i | \(-0.780609\pi\) | ||
0.771731 | − | 0.635950i | \(-0.219391\pi\) | |||||||
\(752\) | −4.77937 | + | 4.77937i | −0.174286 | + | 0.174286i | ||||
\(753\) | −10.6628 | + | 10.6628i | −0.388572 | + | 0.388572i | ||||
\(754\) | 24.3610i | 0.887176i | ||||||||
\(755\) | 0.975956 | − | 7.22146i | 0.0355187 | − | 0.262816i | ||||
\(756\) | 4.98675i | 0.181366i | ||||||||
\(757\) | −7.34710 | − | 7.34710i | −0.267035 | − | 0.267035i | 0.560869 | − | 0.827904i | \(-0.310467\pi\) |
−0.827904 | + | 0.560869i | \(0.810467\pi\) | |||||||
\(758\) | −18.6589 | + | 18.6589i | −0.677721 | + | 0.677721i | ||||
\(759\) | −15.4512 | + | 7.23285i | −0.560842 | + | 0.262536i | ||||
\(760\) | −7.72302 | + | 5.88407i | −0.280143 | + | 0.213438i | ||||
\(761\) | 29.4084 | 1.06605 | 0.533027 | − | 0.846098i | \(-0.321054\pi\) | ||||
0.533027 | + | 0.846098i | \(0.321054\pi\) | |||||||
\(762\) | −10.4069 | + | 10.4069i | −0.377003 | + | 0.377003i | ||||
\(763\) | −33.2115 | − | 33.2115i | −1.20234 | − | 1.20234i | ||||
\(764\) | −15.1230 | −0.547130 | ||||||||
\(765\) | −3.89659 | − | 5.11440i | −0.140882 | − | 0.184911i | ||||
\(766\) | 22.2410i | 0.803599i | ||||||||
\(767\) | −15.9859 | + | 15.9859i | −0.577217 | + | 0.577217i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −20.2771 | −0.731211 | −0.365606 | − | 0.930770i | \(-0.619138\pi\) | ||||
−0.365606 | + | 0.930770i | \(0.619138\pi\) | |||||||
\(770\) | −39.3092 | − | 5.31250i | −1.41660 | − | 0.191449i | ||||
\(771\) | 2.52861 | 0.0910656 | ||||||||
\(772\) | 7.54365 | − | 7.54365i | 0.271502 | − | 0.271502i | ||||
\(773\) | −5.35673 | + | 5.35673i | −0.192668 | + | 0.192668i | −0.796848 | − | 0.604180i | \(-0.793501\pi\) |
0.604180 | + | 0.796848i | \(0.293501\pi\) | |||||||
\(774\) | 2.40346 | 0.0863906 | ||||||||
\(775\) | 27.4033 | + | 7.54473i | 0.984355 | + | 0.271015i | ||||
\(776\) | − | 12.9759i | − | 0.465808i | ||||||
\(777\) | −29.8111 | + | 29.8111i | −1.06947 | + | 1.06947i | ||||
\(778\) | 21.4185 | − | 21.4185i | 0.767889 | − | 0.767889i | ||||
\(779\) | −0.755414 | −0.0270655 | ||||||||
\(780\) | −0.783553 | + | 5.79779i | −0.0280557 | + | 0.207594i | ||||
\(781\) | 35.6700i | 1.27637i | ||||||||
\(782\) | 12.9654 | + | 4.69730i | 0.463642 | + | 0.167975i | ||||
\(783\) | 6.58373 | + | 6.58373i | 0.235283 | + | 0.235283i | ||||
\(784\) | − | 17.8676i | − | 0.638130i | ||||||
\(785\) | −20.4262 | + | 15.5624i | −0.729042 | + | 0.555447i | ||||
\(786\) | −14.0149 | −0.499894 | ||||||||
\(787\) | 18.0980 | + | 18.0980i | 0.645124 | + | 0.645124i | 0.951811 | − | 0.306687i | \(-0.0992204\pi\) |
−0.306687 | + | 0.951811i | \(0.599220\pi\) | |||||||
\(788\) | 4.44245 | + | 4.44245i | 0.158256 | + | 0.158256i | ||||
\(789\) | 14.3344 | 0.510319 | ||||||||
\(790\) | −19.3477 | − | 25.3945i | −0.688362 | − | 0.903496i | ||||
\(791\) | −21.2082 | −0.754075 | ||||||||
\(792\) | 2.51540 | + | 2.51540i | 0.0893808 | + | 0.0893808i | ||||
\(793\) | 10.3340 | − | 10.3340i | 0.366973 | − | 0.366973i | ||||
\(794\) | − | 31.8175i | − | 1.12916i | ||||||
\(795\) | 1.92148 | − | 14.2178i | 0.0681480 | − | 0.504252i | ||||
\(796\) | − | 3.49129i | − | 0.123745i | ||||||
\(797\) | −17.4647 | − | 17.4647i | −0.618631 | − | 0.618631i | 0.326549 | − | 0.945180i | \(-0.394114\pi\) |
−0.945180 | + | 0.326549i | \(0.894114\pi\) | |||||||
\(798\) | −15.3108 | − | 15.3108i | −0.541997 | − | 0.541997i | ||||
\(799\) | 19.4352 | 0.687567 | ||||||||
\(800\) | −4.34719 | + | 2.47021i | −0.153696 | + | 0.0873351i | ||||
\(801\) | − | 6.69008i | − | 0.236382i | ||||||
\(802\) | −11.5397 | − | 11.5397i | −0.407479 | − | 0.407479i | ||||
\(803\) | −27.8089 | + | 27.8089i | −0.981355 | + | 0.981355i | ||||
\(804\) | −8.60874 | −0.303607 | ||||||||
\(805\) | 51.0331 | − | 15.9812i | 1.79868 | − | 0.563262i | ||||
\(806\) | 14.8733 | 0.523889 | ||||||||
\(807\) | 3.05107 | − | 3.05107i | 0.107403 | − | 0.107403i | ||||
\(808\) | 12.0379 | + | 12.0379i | 0.423491 | + | 0.423491i | ||||
\(809\) | − | 54.1167i | − | 1.90264i | −0.308203 | − | 0.951320i | \(-0.599728\pi\) | ||
0.308203 | − | 0.951320i | \(-0.400272\pi\) | |||||||
\(810\) | 1.35513 | + | 1.77865i | 0.0476145 | + | 0.0624956i | ||||
\(811\) | −18.5661 | −0.651945 | −0.325973 | − | 0.945379i | \(-0.605692\pi\) | ||||
−0.325973 | + | 0.945379i | \(0.605692\pi\) | |||||||
\(812\) | −32.8314 | − | 32.8314i | −1.15216 | − | 1.15216i | ||||
\(813\) | 8.65445 | + | 8.65445i | 0.303525 | + | 0.303525i | ||||
\(814\) | 30.0745i | 1.05411i | ||||||||
\(815\) | −4.27663 | + | 3.25831i | −0.149804 | + | 0.114134i | ||||
\(816\) | − | 2.87543i | − | 0.100660i | ||||||
\(817\) | −7.37934 | + | 7.37934i | −0.258170 | + | 0.258170i | ||||
\(818\) | 26.7411 | + | 26.7411i | 0.934981 | + | 0.934981i | ||||
\(819\) | −13.0474 | −0.455915 | ||||||||
\(820\) | −0.385518 | − | 0.0521014i | −0.0134629 | − | 0.00181946i | ||||
\(821\) | −32.5005 | −1.13428 | −0.567138 | − | 0.823622i | \(-0.691950\pi\) | ||||
−0.567138 | + | 0.823622i | \(0.691950\pi\) | |||||||
\(822\) | −5.40475 | − | 5.40475i | −0.188512 | − | 0.188512i | ||||
\(823\) | −29.6034 | − | 29.6034i | −1.03191 | − | 1.03191i | −0.999474 | − | 0.0324349i | \(-0.989674\pi\) |
−0.0324349 | − | 0.999474i | \(-0.510326\pi\) | |||||||
\(824\) | 16.2228 | 0.565149 | ||||||||
\(825\) | −15.4643 | + | 8.78730i | −0.538398 | + | 0.305935i | ||||
\(826\) | − | 43.0885i | − | 1.49924i | ||||||
\(827\) | 7.69751 | + | 7.69751i | 0.267669 | + | 0.267669i | 0.828160 | − | 0.560491i | \(-0.189388\pi\) |
−0.560491 | + | 0.828160i | \(0.689388\pi\) | |||||||
\(828\) | −4.50903 | − | 1.63360i | −0.156700 | − | 0.0567715i | ||||
\(829\) | 6.90960i | 0.239980i | 0.992775 | + | 0.119990i | \(0.0382863\pi\) | ||||
−0.992775 | + | 0.119990i | \(0.961714\pi\) | |||||||
\(830\) | 13.2411 | + | 1.78949i | 0.459605 | + | 0.0621142i | ||||
\(831\) | −6.15822 | −0.213626 | ||||||||
\(832\) | −1.85009 | + | 1.85009i | −0.0641404 | + | 0.0641404i | ||||
\(833\) | −36.3291 | + | 36.3291i | −1.25873 | + | 1.25873i | ||||
\(834\) | 16.9435i | 0.586705i | ||||||||
\(835\) | 28.4413 | + | 37.3301i | 0.984253 | + | 1.29186i | ||||
\(836\) | −15.4460 | −0.534213 | ||||||||
\(837\) | 4.01961 | − | 4.01961i | 0.138938 | − | 0.138938i | ||||
\(838\) | 27.9368 | − | 27.9368i | 0.965060 | − | 0.965060i | ||||
\(839\) | −42.5300 | −1.46830 | −0.734150 | − | 0.678988i | \(-0.762419\pi\) | ||||
−0.734150 | + | 0.678988i | \(0.762419\pi\) | |||||||
\(840\) | −6.75771 | − | 8.86970i | −0.233163 | − | 0.306034i | ||||
\(841\) | −57.6911 | −1.98935 | ||||||||
\(842\) | 14.1162 | + | 14.1162i | 0.486476 | + | 0.486476i | ||||
\(843\) | 4.77634 | − | 4.77634i | 0.164506 | − | 0.164506i | ||||
\(844\) | − | 12.0572i | − | 0.415025i | ||||||
\(845\) | 13.6375 | + | 1.84306i | 0.469145 | + | 0.0634033i | ||||
\(846\) | −6.75905 | −0.232381 | ||||||||
\(847\) | −5.83386 | − | 5.83386i | −0.200454 | − | 0.200454i | ||||
\(848\) | 4.53693 | − | 4.53693i | 0.155799 | − | 0.155799i | ||||
\(849\) | 6.22770 | 0.213734 | ||||||||
\(850\) | 13.8614 | + | 3.81634i | 0.475441 | + | 0.130899i | ||||
\(851\) | −17.1895 | − | 36.7211i | −0.589249 | − | 1.25878i | ||||
\(852\) | −7.09033 | + | 7.09033i | −0.242911 | + | 0.242911i | ||||
\(853\) | 7.05898 | + | 7.05898i | 0.241695 | + | 0.241695i | 0.817551 | − | 0.575856i | \(-0.195331\pi\) |
−0.575856 | + | 0.817551i | \(0.695331\pi\) | |||||||
\(854\) | 27.8545i | 0.953160i | ||||||||
\(855\) | −9.62167 | − | 1.30034i | −0.329054 | − | 0.0444706i | ||||
\(856\) | 3.73545i | 0.127675i | ||||||||
\(857\) | 21.3101 | − | 21.3101i | 0.727938 | − | 0.727938i | −0.242271 | − | 0.970209i | \(-0.577892\pi\) |
0.970209 | + | 0.242271i | \(0.0778922\pi\) | |||||||
\(858\) | −6.58135 | + | 6.58135i | −0.224683 | + | 0.224683i | ||||
\(859\) | − | 55.5976i | − | 1.89696i | −0.316831 | − | 0.948482i | \(-0.602619\pi\) | ||
0.316831 | − | 0.948482i | \(-0.397381\pi\) | |||||||
\(860\) | −4.27492 | + | 3.25701i | −0.145774 | + | 0.111063i | ||||
\(861\) | − | 0.867575i | − | 0.0295669i | ||||||
\(862\) | 3.05357 | + | 3.05357i | 0.104005 | + | 0.104005i | ||||
\(863\) | 5.17426 | + | 5.17426i | 0.176134 | + | 0.176134i | 0.789668 | − | 0.613534i | \(-0.210253\pi\) |
−0.613534 | + | 0.789668i | \(0.710253\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 8.45283 | − | 6.44010i | 0.287405 | − | 0.218970i | ||||
\(866\) | 15.6290i | 0.531096i | ||||||||
\(867\) | 6.17439 | − | 6.17439i | 0.209693 | − | 0.209693i | ||||
\(868\) | −20.0448 | + | 20.0448i | −0.680364 | + | 0.680364i | ||||
\(869\) | − | 50.7890i | − | 1.72290i | ||||||
\(870\) | −20.6320 | − | 2.78835i | −0.699491 | − | 0.0945339i | ||||
\(871\) | − | 22.5241i | − | 0.763201i | ||||||
\(872\) | −6.65995 | − | 6.65995i | −0.225534 | − | 0.225534i | ||||
\(873\) | 9.17535 | − | 9.17535i | 0.310539 | − | 0.310539i | ||||
\(874\) | 18.8597 | − | 8.82843i | 0.637939 | − | 0.298626i | ||||
\(875\) | 51.7266 | − | 20.8043i | 1.74868 | − | 0.703314i | ||||
\(876\) | −11.0555 | −0.373530 | ||||||||
\(877\) | 11.5091 | − | 11.5091i | 0.388636 | − | 0.388636i | −0.485564 | − | 0.874201i | \(-0.661386\pi\) |
0.874201 | + | 0.485564i | \(0.161386\pi\) | |||||||
\(878\) | −4.29336 | − | 4.29336i | −0.144894 | − | 0.144894i | ||||
\(879\) | 4.60973 | 0.155482 | ||||||||
\(880\) | −7.88272 | − | 1.06532i | −0.265727 | − | 0.0359121i | ||||
\(881\) | − | 34.1499i | − | 1.15054i | −0.817964 | − | 0.575269i | \(-0.804897\pi\) | ||
0.817964 | − | 0.575269i | \(-0.195103\pi\) | |||||||
\(882\) | 12.6343 | − | 12.6343i | 0.425420 | − | 0.425420i | ||||
\(883\) | −25.9591 | − | 25.9591i | −0.873592 | − | 0.873592i | 0.119270 | − | 0.992862i | \(-0.461945\pi\) |
−0.992862 | + | 0.119270i | \(0.961945\pi\) | |||||||
\(884\) | 7.52334 | 0.253037 | ||||||||
\(885\) | −11.7092 | − | 15.3686i | −0.393599 | − | 0.516611i | ||||
\(886\) | −29.6084 | −0.994714 | ||||||||
\(887\) | −6.71291 | + | 6.71291i | −0.225398 | + | 0.225398i | −0.810767 | − | 0.585369i | \(-0.800950\pi\) |
0.585369 | + | 0.810767i | \(0.300950\pi\) | |||||||
\(888\) | −5.97807 | + | 5.97807i | −0.200611 | + | 0.200611i | ||||
\(889\) | 73.3931 | 2.46153 | ||||||||
\(890\) | 9.06595 | + | 11.8993i | 0.303891 | + | 0.398867i | ||||
\(891\) | 3.55731i | 0.119174i | ||||||||
\(892\) | −3.58953 | + | 3.58953i | −0.120187 | + | 0.120187i | ||||
\(893\) | 20.7523 | − | 20.7523i | 0.694450 | − | 0.694450i | ||||
\(894\) | 8.10858 | 0.271191 | ||||||||
\(895\) | −40.6124 | − | 5.48863i | −1.35752 | − | 0.183465i | ||||
\(896\) | − | 4.98675i | − | 0.166596i | ||||||
\(897\) | 4.27419 | − | 11.7975i | 0.142711 | − | 0.393908i | ||||
\(898\) | −28.3165 | − | 28.3165i | −0.944934 | − | 0.944934i | ||||
\(899\) | 52.9281i | 1.76525i | ||||||||
\(900\) | −4.82063 | − | 1.32723i | −0.160688 | − | 0.0442409i | ||||
\(901\) | −18.4493 | −0.614635 | ||||||||
\(902\) | −0.437619 | − | 0.437619i | −0.0145711 | − | 0.0145711i | ||||
\(903\) | −8.47499 | − | 8.47499i | −0.282030 | − | 0.282030i | ||||
\(904\) | −4.25290 | −0.141449 | ||||||||
\(905\) | −6.56001 | − | 0.886563i | −0.218062 | − | 0.0294704i | ||||
\(906\) | 3.25889 | 0.108269 | ||||||||
\(907\) | −29.2217 | − | 29.2217i | −0.970290 | − | 0.970290i | 0.0292809 | − | 0.999571i | \(-0.490678\pi\) |
−0.999571 | + | 0.0292809i | \(0.990678\pi\) | |||||||
\(908\) | 9.88624 | − | 9.88624i | 0.328086 | − | 0.328086i | ||||
\(909\) | 17.0241i | 0.564655i | ||||||||
\(910\) | 23.2069 | − | 17.6810i | 0.769301 | − | 0.586121i | ||||
\(911\) | 28.2689i | 0.936592i | 0.883572 | + | 0.468296i | \(0.155132\pi\) | ||||
−0.883572 | + | 0.468296i | \(0.844868\pi\) | |||||||
\(912\) | −3.07030 | − | 3.07030i | −0.101668 | − | 0.101668i | ||||
\(913\) | 15.0306 | + | 15.0306i | 0.497440 | + | 0.497440i | ||||
\(914\) | 1.44662 | 0.0478501 | ||||||||
\(915\) | 7.56937 | + | 9.93503i | 0.250236 | + | 0.328442i | ||||
\(916\) | 8.77187i | 0.289831i | ||||||||
\(917\) | 49.4188 | + | 49.4188i | 1.63195 | + | 1.63195i | ||||
\(918\) | 2.03324 | − | 2.03324i | 0.0671068 | − | 0.0671068i | ||||
\(919\) | −23.2811 | −0.767973 | −0.383987 | − | 0.923339i | \(-0.625449\pi\) | ||||
−0.383987 | + | 0.923339i | \(0.625449\pi\) | |||||||
\(920\) | 10.2338 | − | 3.20473i | 0.337397 | − | 0.105657i | ||||
\(921\) | −28.1709 | −0.928263 | ||||||||
\(922\) | 8.81663 | − | 8.81663i | 0.290360 | − | 0.290360i | ||||
\(923\) | −18.5513 | − | 18.5513i | −0.610624 | − | 0.610624i | ||||
\(924\) | − | 17.7394i | − | 0.583584i | ||||||
\(925\) | −20.8838 | − | 36.7523i | −0.686656 | − | 1.20841i | ||||
\(926\) | −14.5937 | −0.479577 | ||||||||
\(927\) | 11.4713 | + | 11.4713i | 0.376766 | + | 0.376766i | ||||
\(928\) | −6.58373 | − | 6.58373i | −0.216122 | − | 0.216122i | ||||
\(929\) | 16.2226i | 0.532248i | 0.963939 | + | 0.266124i | \(0.0857430\pi\) | ||||
−0.963939 | + | 0.266124i | \(0.914257\pi\) | |||||||
\(930\) | −1.70239 | + | 12.5966i | −0.0558236 | + | 0.413059i | ||||
\(931\) | 77.5824i | 2.54266i | ||||||||
\(932\) | −6.20098 | + | 6.20098i | −0.203120 | + | 0.203120i | ||||
\(933\) | 4.57465 | + | 4.57465i | 0.149767 | + | 0.149767i | ||||
\(934\) | −24.5169 | −0.802218 | ||||||||
\(935\) | 13.8614 | + | 18.1935i | 0.453316 | + | 0.594991i | ||||
\(936\) | −2.61642 | −0.0855205 | ||||||||
\(937\) | 0.103737 | + | 0.103737i | 0.00338893 | + | 0.00338893i | 0.708799 | − | 0.705410i | \(-0.249237\pi\) |
−0.705410 | + | 0.708799i | \(0.749237\pi\) | |||||||
\(938\) | 30.3558 | + | 30.3558i | 0.991153 | + | 0.991153i | ||||
\(939\) | −34.3457 | −1.12083 | ||||||||
\(940\) | 12.0220 | − | 9.15942i | 0.392115 | − | 0.298747i | ||||
\(941\) | 54.1632i | 1.76567i | 0.469684 | + | 0.882835i | \(0.344368\pi\) | ||||
−0.469684 | + | 0.882835i | \(0.655632\pi\) | |||||||
\(942\) | −8.12046 | − | 8.12046i | −0.264579 | − | 0.264579i | ||||
\(943\) | 0.784463 | + | 0.284207i | 0.0255456 | + | 0.00925507i | ||||
\(944\) | − | 8.64060i | − | 0.281228i | ||||||
\(945\) | 1.49340 | − | 11.0502i | 0.0485804 | − | 0.359465i | ||||
\(946\) | −8.54985 | −0.277980 | ||||||||
\(947\) | −11.2599 | + | 11.2599i | −0.365899 | + | 0.365899i | −0.865979 | − | 0.500080i | \(-0.833304\pi\) |
0.500080 | + | 0.865979i | \(0.333304\pi\) | |||||||
\(948\) | 10.0956 | − | 10.0956i | 0.327891 | − | 0.327891i | ||||
\(949\) | − | 28.9258i | − | 0.938971i | ||||||
\(950\) | 18.8758 | − | 10.7258i | 0.612410 | − | 0.347991i | ||||
\(951\) | −8.22879 | −0.266837 | ||||||||
\(952\) | −10.1392 | + | 10.1392i | −0.328614 | + | 0.328614i | ||||
\(953\) | 3.20772 | − | 3.20772i | 0.103908 | − | 0.103908i | −0.653241 | − | 0.757150i | \(-0.726591\pi\) |
0.757150 | + | 0.653241i | \(0.226591\pi\) | |||||||
\(954\) | 6.41619 | 0.207732 | ||||||||
\(955\) | 33.5113 | + | 4.52895i | 1.08440 | + | 0.146553i | ||||
\(956\) | 1.95717 | 0.0632993 | ||||||||
\(957\) | −23.4204 | − | 23.4204i | −0.757073 | − | 0.757073i | ||||
\(958\) | −18.5595 | + | 18.5595i | −0.599629 | + | 0.599629i | ||||
\(959\) | 38.1160i | 1.23083i | ||||||||
\(960\) | −1.35513 | − | 1.77865i | −0.0437368 | − | 0.0574058i | ||||
\(961\) | 1.31454 | 0.0424045 | ||||||||
\(962\) | −15.6412 | − | 15.6412i | −0.504292 | − | 0.504292i | ||||
\(963\) | −2.64136 | + | 2.64136i | −0.0851166 | + | 0.0851166i | ||||
\(964\) | 9.45390 | 0.304490 | ||||||||
\(965\) | −18.9753 | + | 14.4570i | −0.610836 | + | 0.465388i | ||||
\(966\) | 10.1392 | + | 21.6599i | 0.326224 | + | 0.696896i | ||||
\(967\) | −23.7989 | + | 23.7989i | −0.765322 | + | 0.765322i | −0.977279 | − | 0.211957i | \(-0.932016\pi\) |
0.211957 | + | 0.977279i | \(0.432016\pi\) | |||||||
\(968\) | −1.16987 | − | 1.16987i | −0.0376012 | − | 0.0376012i | ||||
\(969\) | 12.4853i | 0.401085i | ||||||||
\(970\) | −3.88595 | + | 28.7536i | −0.124770 | + | 0.923223i | ||||
\(971\) | 54.9753i | 1.76424i | 0.471024 | + | 0.882121i | \(0.343885\pi\) | ||||
−0.471024 | + | 0.882121i | \(0.656115\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 59.7455 | − | 59.7455i | 1.91535 | − | 1.91535i | ||||
\(974\) | 1.74227i | 0.0558260i | ||||||||
\(975\) | 3.47258 | − | 12.6128i | 0.111212 | − | 0.403933i | ||||
\(976\) | 5.58570i | 0.178794i | ||||||||
\(977\) | −23.8400 | − | 23.8400i | −0.762708 | − | 0.762708i | 0.214103 | − | 0.976811i | \(-0.431317\pi\) |
−0.976811 | + | 0.214103i | \(0.931317\pi\) | |||||||
\(978\) | −1.70018 | − | 1.70018i | −0.0543658 | − | 0.0543658i | ||||
\(979\) | 23.7987i | 0.760609i | ||||||||
\(980\) | −5.35091 | + | 39.5933i | −0.170928 | + | 1.26476i | ||||
\(981\) | − | 9.41859i | − | 0.300713i | ||||||
\(982\) | −0.151468 | + | 0.151468i | −0.00483353 | + | 0.00483353i | ||||
\(983\) | −13.2747 | + | 13.2747i | −0.423397 | + | 0.423397i | −0.886372 | − | 0.462974i | \(-0.846782\pi\) |
0.462974 | + | 0.886372i | \(0.346782\pi\) | |||||||
\(984\) | − | 0.173976i | − | 0.00554615i | ||||||
\(985\) | −8.51372 | − | 11.1745i | −0.271270 | − | 0.356050i | ||||
\(986\) | 26.7726i | 0.852612i | ||||||||
\(987\) | 23.8335 | + | 23.8335i | 0.758629 | + | 0.758629i | ||||
\(988\) | 8.03320 | − | 8.03320i | 0.255570 | − | 0.255570i | ||||
\(989\) | 10.4394 | − | 4.88680i | 0.331954 | − | 0.155391i | ||||
\(990\) | −4.82063 | − | 6.32723i | −0.153210 | − | 0.201092i | ||||
\(991\) | 17.3508 | 0.551166 | 0.275583 | − | 0.961277i | \(-0.411129\pi\) | ||||
0.275583 | + | 0.961277i | \(0.411129\pi\) | |||||||
\(992\) | −4.01961 | + | 4.01961i | −0.127623 | + | 0.127623i | ||||
\(993\) | −14.3409 | − | 14.3409i | −0.455096 | − | 0.455096i | ||||
\(994\) | 50.0033 | 1.58601 | ||||||||
\(995\) | −1.04555 | + | 7.73643i | −0.0331462 | + | 0.245261i | ||||
\(996\) | 5.97544i | 0.189339i | ||||||||
\(997\) | 5.94309 | − | 5.94309i | 0.188220 | − | 0.188220i | −0.606706 | − | 0.794926i | \(-0.707510\pi\) |
0.794926 | + | 0.606706i | \(0.207510\pi\) | |||||||
\(998\) | 2.05837 | + | 2.05837i | 0.0651566 | + | 0.0651566i | ||||
\(999\) | −8.45427 | −0.267481 |
(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 | 690.2.j.a.643.3 | yes | 24 | |
5.2 | odd | 4 | inner | 690.2.j.a.367.4 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.j.a.643.4 | yes | 24 | |
115.22 | even | 4 | inner | 690.2.j.a.367.3 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.j.a.367.3 | ✓ | 24 | 115.22 | even | 4 | inner | |
690.2.j.a.367.4 | yes | 24 | 5.2 | odd | 4 | inner | |
690.2.j.a.643.3 | yes | 24 | 1.1 | even | 1 | trivial | |
690.2.j.a.643.4 | yes | 24 | 23.22 | odd | 2 | inner |