Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(560,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.560");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.d (of order \(2\), degree \(1\), 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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 20x^{6} + 129x^{4} + 323x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 560.5 | ||
Root | \(1.21991i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 731.560 |
Dual form | 731.2.d.b.560.4 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 1.21991i | 0.704313i | 0.935941 | + | 0.352157i | \(0.114552\pi\) | ||||
−0.935941 | + | 0.352157i | \(0.885448\pi\) | |||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | − | 3.81798i | − | 1.70745i | −0.520724 | − | 0.853725i | \(-0.674338\pi\) | ||
0.520724 | − | 0.853725i | \(-0.325662\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.55222i | 1.72058i | 0.509808 | + | 0.860288i | \(0.329716\pi\) | ||||
−0.509808 | + | 0.860288i | \(0.670284\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.51183 | 0.503943 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.600184i | 0.180962i | 0.995898 | + | 0.0904812i | \(0.0288405\pi\) | ||||
−0.995898 | + | 0.0904812i | \(0.971160\pi\) | |||||||
\(12\) | − | 2.43981i | − | 0.704313i | ||||||
\(13\) | −3.14574 | −0.872472 | −0.436236 | − | 0.899832i | \(-0.643689\pi\) | ||||
−0.436236 | + | 0.899832i | \(0.643689\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.65757 | 1.20258 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −0.203767 | − | 4.11807i | −0.0494208 | − | 0.998778i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 7.63595i | 1.70745i | ||||||||
\(21\) | −5.55328 | −1.21182 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.06444i | 1.26452i | 0.774755 | + | 0.632261i | \(0.217873\pi\) | ||||
−0.774755 | + | 0.632261i | \(0.782127\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.57694 | −1.91539 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.50401i | 1.05925i | ||||||||
\(28\) | − | 9.10443i | − | 1.72058i | ||||||
\(29\) | 7.63595i | 1.41796i | 0.705228 | + | 0.708980i | \(0.250844\pi\) | ||||
−0.705228 | + | 0.708980i | \(0.749156\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.6759i | 1.91746i | 0.284324 | + | 0.958728i | \(0.408231\pi\) | ||||
−0.284324 | + | 0.958728i | \(0.591769\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.732168 | −0.127454 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 17.3803 | 2.93780 | ||||||||
\(36\) | −3.02366 | −0.503943 | ||||||||
\(37\) | 5.44471i | 0.895106i | 0.894258 | + | 0.447553i | \(0.147704\pi\) | ||||
−0.894258 | + | 0.447553i | \(0.852296\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 3.83751i | − | 0.614494i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.371145i | 0.0579632i | 0.999580 | + | 0.0289816i | \(0.00922641\pi\) | ||||
−0.999580 | + | 0.0289816i | \(0.990774\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | − | 1.20037i | − | 0.180962i | ||||||
\(45\) | − | 5.77212i | − | 0.860457i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.958550 | 0.139819 | 0.0699094 | − | 0.997553i | \(-0.477729\pi\) | ||||
0.0699094 | + | 0.997553i | \(0.477729\pi\) | |||||||
\(48\) | 4.87963i | 0.704313i | ||||||||
\(49\) | −13.7227 | −1.96038 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.02366 | − | 0.248577i | 0.703453 | − | 0.0348077i | ||||
\(52\) | 6.29149 | 0.872472 | ||||||||
\(53\) | 7.36608 | 1.01181 | 0.505905 | − | 0.862589i | \(-0.331159\pi\) | ||||
0.505905 | + | 0.862589i | \(0.331159\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.29149 | 0.308984 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.43981i | 0.323161i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.57694 | 0.856244 | 0.428122 | − | 0.903721i | \(-0.359175\pi\) | ||||
0.428122 | + | 0.903721i | \(0.359175\pi\) | |||||||
\(60\) | −9.31515 | −1.20258 | ||||||||
\(61\) | 6.23825i | 0.798726i | 0.916793 | + | 0.399363i | \(0.130769\pi\) | ||||
−0.916793 | + | 0.399363i | \(0.869231\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.88217i | 0.867072i | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 12.0104i | 1.48970i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.76413 | −1.07071 | −0.535354 | − | 0.844628i | \(-0.679822\pi\) | ||||
−0.535354 | + | 0.844628i | \(0.679822\pi\) | |||||||
\(68\) | 0.407535 | + | 8.23613i | 0.0494208 | + | 0.998778i | ||||
\(69\) | −7.39805 | −0.890620 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.47769i | − | 0.887439i | −0.896166 | − | 0.443720i | \(-0.853659\pi\) | ||
0.896166 | − | 0.443720i | \(-0.146341\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.86618i | 0.335461i | 0.985833 | + | 0.167731i | \(0.0536439\pi\) | ||||
−0.985833 | + | 0.167731i | \(0.946356\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 11.6830i | − | 1.34903i | ||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | −2.73217 | −0.311359 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.2475i | − | 1.37795i | −0.724787 | − | 0.688974i | \(-0.758062\pi\) | ||
0.724787 | − | 0.688974i | \(-0.241938\pi\) | |||||||
\(80\) | − | 15.2719i | − | 1.70745i | ||||||
\(81\) | −2.17889 | −0.242099 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.21085 | −0.571965 | −0.285983 | − | 0.958235i | \(-0.592320\pi\) | ||||
−0.285983 | + | 0.958235i | \(0.592320\pi\) | |||||||
\(84\) | 11.1066 | 1.21182 | ||||||||
\(85\) | −15.7227 | + | 0.777978i | −1.70536 | + | 0.0843836i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.31515 | −0.998688 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.4217 | 1.10470 | 0.552349 | − | 0.833613i | \(-0.313732\pi\) | ||||
0.552349 | + | 0.833613i | \(0.313732\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 14.3201i | − | 1.50116i | ||||||
\(92\) | − | 12.1289i | − | 1.26452i | ||||||
\(93\) | −13.0237 | −1.35049 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 7.63595i | − | 0.783432i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.57151i | 0.159563i | 0.996812 | + | 0.0797815i | \(0.0254223\pi\) | ||||
−0.996812 | + | 0.0797815i | \(0.974578\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.907375i | 0.0911947i | ||||||||
\(100\) | 19.1539 | 1.91539 | ||||||||
\(101\) | 5.73217 | 0.570372 | 0.285186 | − | 0.958472i | \(-0.407945\pi\) | ||||
0.285186 | + | 0.958472i | \(0.407945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.39578 | −0.827261 | −0.413630 | − | 0.910445i | \(-0.635739\pi\) | ||||
−0.413630 | + | 0.910445i | \(0.635739\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 21.2023i | 2.06913i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.86499i | 0.760337i | 0.924917 | + | 0.380169i | \(0.124134\pi\) | ||||
−0.924917 | + | 0.380169i | \(0.875866\pi\) | |||||||
\(108\) | − | 11.0080i | − | 1.05925i | ||||||
\(109\) | − | 12.2319i | − | 1.17160i | −0.810454 | − | 0.585802i | \(-0.800780\pi\) | ||
0.810454 | − | 0.585802i | \(-0.199220\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.64204 | −0.630435 | ||||||||
\(112\) | 18.2089i | 1.72058i | ||||||||
\(113\) | − | 16.3140i | − | 1.53469i | −0.641233 | − | 0.767347i | \(-0.721577\pi\) | ||
0.641233 | − | 0.767347i | \(-0.278423\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.1539 | 2.15911 | ||||||||
\(116\) | − | 15.2719i | − | 1.41796i | ||||||
\(117\) | −4.75583 | −0.439676 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.7463 | − | 0.927593i | 1.71847 | − | 0.0850323i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6398 | 0.967253 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.452762 | −0.0408242 | ||||||||
\(124\) | − | 21.3519i | − | 1.91746i | ||||||
\(125\) | 17.4746i | 1.56298i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.81281 | −0.515803 | −0.257902 | − | 0.966171i | \(-0.583031\pi\) | ||||
−0.257902 | + | 0.966171i | \(0.583031\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.21991i | 0.107407i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.9468i | 1.39328i | 0.717420 | + | 0.696641i | \(0.245323\pi\) | ||||
−0.717420 | + | 0.696641i | \(0.754677\pi\) | |||||||
\(132\) | 1.46434 | 0.127454 | ||||||||
\(133\) | 9.10443i | 0.789455i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 21.0142 | 1.80861 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.1539 | −1.63643 | −0.818213 | − | 0.574915i | \(-0.805035\pi\) | ||||
−0.818213 | + | 0.574915i | \(0.805035\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.53292i | 0.638934i | 0.947597 | + | 0.319467i | \(0.103504\pi\) | ||||
−0.947597 | + | 0.319467i | \(0.896496\pi\) | |||||||
\(140\) | −34.7605 | −2.93780 | ||||||||
\(141\) | 1.16934i | 0.0984763i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.88803i | − | 0.157885i | ||||||
\(144\) | 6.04731 | 0.503943 | ||||||||
\(145\) | 29.1539 | 2.42110 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 16.7404i | − | 1.38072i | ||||||
\(148\) | − | 10.8894i | − | 0.895106i | ||||||
\(149\) | 5.18493 | 0.424766 | 0.212383 | − | 0.977186i | \(-0.431878\pi\) | ||||
0.212383 | + | 0.977186i | \(0.431878\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.1539 | 1.23320 | 0.616602 | − | 0.787275i | \(-0.288509\pi\) | ||||
0.616602 | + | 0.787275i | \(0.288509\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.308061 | − | 6.22581i | −0.0249053 | − | 0.503327i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 40.7605 | 3.27396 | ||||||||
\(156\) | 7.67503i | 0.614494i | ||||||||
\(157\) | 19.4454 | 1.55191 | 0.775954 | − | 0.630789i | \(-0.217269\pi\) | ||||
0.775954 | + | 0.630789i | \(0.217269\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.98593i | 0.712631i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.6066 | −2.17571 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17.1277i | − | 1.34154i | −0.741664 | − | 0.670772i | \(-0.765963\pi\) | ||
0.741664 | − | 0.670772i | \(-0.234037\pi\) | |||||||
\(164\) | − | 0.742291i | − | 0.0579632i | ||||||
\(165\) | 2.79540i | 0.217622i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.06444i | 0.469280i | 0.972082 | + | 0.234640i | \(0.0753912\pi\) | ||||
−0.972082 | + | 0.234640i | \(0.924609\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.10429 | −0.238792 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.02366 | 0.231225 | ||||||||
\(172\) | −2.00000 | −0.152499 | ||||||||
\(173\) | − | 19.6774i | − | 1.49604i | −0.663675 | − | 0.748021i | \(-0.731004\pi\) | ||
0.663675 | − | 0.748021i | \(-0.268996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 43.5963i | − | 3.29557i | ||||||
\(176\) | 2.40074i | 0.180962i | ||||||||
\(177\) | 8.02325i | 0.603064i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.73217 | 0.204212 | 0.102106 | − | 0.994774i | \(-0.467442\pi\) | ||||
0.102106 | + | 0.994774i | \(0.467442\pi\) | |||||||
\(180\) | 11.5442i | 0.860457i | ||||||||
\(181\) | 21.1229i | 1.57005i | 0.619464 | + | 0.785025i | \(0.287350\pi\) | ||||
−0.619464 | + | 0.785025i | \(0.712650\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.61008 | −0.562553 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.7878 | 1.52835 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.47160 | − | 0.122298i | 0.180741 | − | 0.00894331i | ||||
\(188\) | −1.91710 | −0.139819 | ||||||||
\(189\) | −25.0554 | −1.82252 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.9689 | −1.44490 | −0.722451 | − | 0.691422i | \(-0.756984\pi\) | ||||
−0.722451 | + | 0.691422i | \(0.756984\pi\) | |||||||
\(192\) | − | 9.75925i | − | 0.704313i | ||||||
\(193\) | − | 24.7084i | − | 1.77855i | −0.457373 | − | 0.889275i | \(-0.651210\pi\) | ||
0.457373 | − | 0.889275i | \(-0.348790\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.6515 | −1.04922 | ||||||||
\(196\) | 27.4454 | 1.96038 | ||||||||
\(197\) | 16.2432i | 1.15728i | 0.815582 | + | 0.578641i | \(0.196417\pi\) | ||||
−0.815582 | + | 0.578641i | \(0.803583\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.88876i | 0.275667i | 0.990455 | + | 0.137833i | \(0.0440138\pi\) | ||||
−0.990455 | + | 0.137833i | \(0.955986\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 10.6914i | − | 0.754114i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −34.7605 | −2.43971 | ||||||||
\(204\) | −10.0473 | + | 0.497154i | −0.703453 | + | 0.0348077i | ||||
\(205\) | 1.41702 | 0.0989692 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.16839i | 0.637247i | ||||||||
\(208\) | −12.5830 | −0.872472 | ||||||||
\(209\) | 1.20037i | 0.0830312i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.13449i | − | 0.284630i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||
0.989821 | − | 0.142315i | \(-0.0454546\pi\) | |||||||
\(212\) | −14.7322 | −1.01181 | ||||||||
\(213\) | 9.12209 | 0.625035 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 3.81798i | − | 0.260384i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −48.5992 | −3.29913 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.49648 | −0.236270 | ||||||||
\(220\) | −4.58298 | −0.308984 | ||||||||
\(221\) | 0.641000 | + | 12.9544i | 0.0431183 | + | 0.871406i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.20859 | −0.281828 | −0.140914 | − | 0.990022i | \(-0.545004\pi\) | ||||
−0.140914 | + | 0.990022i | \(0.545004\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.4787 | −0.965246 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.5627i | 1.56391i | 0.623335 | + | 0.781955i | \(0.285777\pi\) | ||||
−0.623335 | + | 0.781955i | \(0.714223\pi\) | |||||||
\(228\) | − | 4.87963i | − | 0.323161i | ||||||
\(229\) | 4.18115 | 0.276298 | 0.138149 | − | 0.990411i | \(-0.455885\pi\) | ||||
0.138149 | + | 0.990411i | \(0.455885\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 3.33299i | − | 0.219295i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.0018i | − | 0.851778i | −0.904775 | − | 0.425889i | \(-0.859961\pi\) | ||
0.904775 | − | 0.425889i | \(-0.140039\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.65972i | − | 0.238734i | ||||||
\(236\) | −13.1539 | −0.856244 | ||||||||
\(237\) | 14.9408 | 0.970506 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.59247 | −0.555800 | −0.277900 | − | 0.960610i | \(-0.589638\pi\) | ||||
−0.277900 | + | 0.960610i | \(0.589638\pi\) | |||||||
\(240\) | 18.6303 | 1.20258 | ||||||||
\(241\) | − | 2.53818i | − | 0.163499i | −0.996653 | − | 0.0817494i | \(-0.973949\pi\) | ||
0.996653 | − | 0.0817494i | \(-0.0260507\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.8540i | 0.888733i | ||||||||
\(244\) | − | 12.4765i | − | 0.798726i | ||||||
\(245\) | 52.3929i | 3.34726i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.29149 | −0.400318 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 6.35675i | − | 0.402843i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.8707 | 1.00175 | 0.500874 | − | 0.865520i | \(-0.333012\pi\) | ||||
0.500874 | + | 0.865520i | \(0.333012\pi\) | |||||||
\(252\) | − | 13.7643i | − | 0.867072i | ||||||
\(253\) | −3.63978 | −0.228831 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.949061 | − | 19.1802i | −0.0594325 | − | 1.20111i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −7.15387 | −0.446246 | −0.223123 | − | 0.974790i | \(-0.571625\pi\) | ||||
−0.223123 | + | 0.974790i | \(0.571625\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.7855 | −1.54010 | ||||||||
\(260\) | − | 24.0207i | − | 1.48970i | ||||||
\(261\) | 11.5442i | 0.714571i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.338802 | 0.0208914 | 0.0104457 | − | 0.999945i | \(-0.496675\pi\) | ||||
0.0104457 | + | 0.999945i | \(0.496675\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 28.1235i | − | 1.72761i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.7135i | 0.778054i | ||||||||
\(268\) | 17.5283 | 1.07071 | ||||||||
\(269\) | − | 13.9294i | − | 0.849292i | −0.905359 | − | 0.424646i | \(-0.860399\pi\) | ||
0.905359 | − | 0.424646i | \(-0.139601\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.5911 | 1.49380 | 0.746902 | − | 0.664935i | \(-0.231541\pi\) | ||||
0.746902 | + | 0.664935i | \(0.231541\pi\) | |||||||
\(272\) | −0.815069 | − | 16.4723i | −0.0494208 | − | 0.998778i | ||||
\(273\) | 17.4692 | 1.05728 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 5.74792i | − | 0.346613i | ||||||
\(276\) | 14.7961 | 0.890620 | ||||||||
\(277\) | 5.21568i | 0.313380i | 0.987648 | + | 0.156690i | \(0.0500823\pi\) | ||||
−0.987648 | + | 0.156690i | \(0.949918\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.1402i | 0.966289i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.2523 | −0.611601 | −0.305801 | − | 0.952096i | \(-0.598924\pi\) | ||||
−0.305801 | + | 0.952096i | \(0.598924\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3749i | 0.913945i | 0.889481 | + | 0.456972i | \(0.151066\pi\) | ||||
−0.889481 | + | 0.456972i | \(0.848934\pi\) | |||||||
\(284\) | 14.9554i | 0.887439i | ||||||||
\(285\) | 9.31515 | 0.551782 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.68953 | −0.0997300 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9170 | + | 1.67825i | −0.995115 | + | 0.0987209i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.91710 | −0.112382 | ||||||||
\(292\) | − | 5.73237i | − | 0.335461i | ||||||
\(293\) | −4.22260 | −0.246687 | −0.123344 | − | 0.992364i | \(-0.539362\pi\) | ||||
−0.123344 | + | 0.992364i | \(0.539362\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 25.1106i | − | 1.46199i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.30342 | −0.191684 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 19.0772i | − | 1.10326i | ||||||
\(300\) | 23.3659i | 1.34903i | ||||||||
\(301\) | 4.55222i | 0.262385i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.99271i | 0.401721i | ||||||||
\(304\) | 8.00000 | 0.458831 | ||||||||
\(305\) | 23.8175 | 1.36379 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.91710 | −0.166488 | −0.0832438 | − | 0.996529i | \(-0.526528\pi\) | ||||
−0.0832438 | + | 0.996529i | \(0.526528\pi\) | |||||||
\(308\) | 5.46434 | 0.311359 | ||||||||
\(309\) | − | 10.2421i | − | 0.582651i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 18.9276i | − | 1.07329i | −0.843809 | − | 0.536644i | \(-0.819692\pi\) | ||
0.843809 | − | 0.536644i | \(-0.180308\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.57853i | − | 0.145747i | −0.997341 | − | 0.0728736i | \(-0.976783\pi\) | ||
0.997341 | − | 0.0728736i | \(-0.0232170\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26.2760 | 1.48048 | ||||||||
\(316\) | 24.4949i | 1.37795i | ||||||||
\(317\) | 3.97225i | 0.223104i | 0.993759 | + | 0.111552i | \(0.0355821\pi\) | ||||
−0.993759 | + | 0.111552i | \(0.964418\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.58298 | −0.256597 | ||||||||
\(320\) | 30.5438i | 1.70745i | ||||||||
\(321\) | −9.59455 | −0.535516 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.407535 | − | 8.23613i | −0.0226758 | − | 0.458271i | ||||
\(324\) | 4.35778 | 0.242099 | ||||||||
\(325\) | 30.1266 | 1.67112 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.9218 | 0.825176 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.36353i | 0.240569i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.20859 | 0.121395 | 0.0606975 | − | 0.998156i | \(-0.480668\pi\) | ||||
0.0606975 | + | 0.998156i | \(0.480668\pi\) | |||||||
\(332\) | 10.4217 | 0.571965 | ||||||||
\(333\) | 8.23147i | 0.451082i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.4612i | 1.82818i | ||||||||
\(336\) | −22.2131 | −1.21182 | ||||||||
\(337\) | − | 7.76196i | − | 0.422821i | −0.977397 | − | 0.211410i | \(-0.932194\pi\) | ||
0.977397 | − | 0.211410i | \(-0.0678057\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.9016 | 1.08090 | ||||||||
\(340\) | 31.4454 | − | 1.55596i | 1.70536 | − | 0.0843836i | ||||
\(341\) | −6.40753 | −0.346987 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 30.6031i | − | 1.65241i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 28.2456i | 1.52069i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.5332i | 0.565454i | 0.959200 | + | 0.282727i | \(0.0912391\pi\) | ||||
−0.959200 | + | 0.282727i | \(0.908761\pi\) | |||||||
\(348\) | 18.6303 | 0.998688 | ||||||||
\(349\) | 20.8745 | 1.11738 | 0.558692 | − | 0.829375i | \(-0.311303\pi\) | ||||
0.558692 | + | 0.829375i | \(0.311303\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 17.3142i | − | 0.924164i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.94302 | −0.103417 | −0.0517083 | − | 0.998662i | \(-0.516467\pi\) | ||||
−0.0517083 | + | 0.998662i | \(0.516467\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.5497 | −1.51526 | ||||||||
\(356\) | −20.8434 | −1.10470 | ||||||||
\(357\) | 1.13158 | + | 22.8688i | 0.0598894 | + | 1.21034i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.8175 | −0.782037 | −0.391018 | − | 0.920383i | \(-0.627877\pi\) | ||||
−0.391018 | + | 0.920383i | \(0.627877\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.9795i | 0.681249i | ||||||||
\(364\) | 28.6402i | 1.50116i | ||||||||
\(365\) | 10.9430 | 0.572784 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.8693i | 1.50696i | 0.657469 | + | 0.753482i | \(0.271627\pi\) | ||||
−0.657469 | + | 0.753482i | \(0.728373\pi\) | |||||||
\(368\) | 24.2577i | 1.26452i | ||||||||
\(369\) | 0.561108i | 0.0292101i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 33.5320i | 1.74090i | ||||||||
\(372\) | 26.0473 | 1.35049 | ||||||||
\(373\) | 20.1112 | 1.04132 | 0.520660 | − | 0.853764i | \(-0.325686\pi\) | ||||
0.520660 | + | 0.853764i | \(0.325686\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −21.3174 | −1.10083 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 24.0207i | − | 1.23713i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.8848i | 1.48371i | 0.670559 | + | 0.741857i | \(0.266055\pi\) | ||||
−0.670559 | + | 0.741857i | \(0.733945\pi\) | |||||||
\(380\) | 15.2719i | 0.783432i | ||||||||
\(381\) | − | 7.09108i | − | 0.363287i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.2368 | −1.18734 | −0.593672 | − | 0.804707i | \(-0.702322\pi\) | ||||
−0.593672 | + | 0.804707i | \(0.702322\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.4314i | 0.531631i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.51183 | 0.0768506 | ||||||||
\(388\) | − | 3.14303i | − | 0.159563i | ||||||
\(389\) | 32.0283 | 1.62390 | 0.811951 | − | 0.583726i | \(-0.198406\pi\) | ||||
0.811951 | + | 0.583726i | \(0.198406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.9738 | − | 1.23573i | 1.26298 | − | 0.0624937i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.4537 | −0.981308 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −46.7605 | −2.35278 | ||||||||
\(396\) | − | 1.81475i | − | 0.0911947i | ||||||
\(397\) | − | 3.56999i | − | 0.179173i | −0.995979 | − | 0.0895864i | \(-0.971445\pi\) | ||
0.995979 | − | 0.0895864i | \(-0.0285545\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.1066 | −0.556023 | ||||||||
\(400\) | −38.3077 | −1.91539 | ||||||||
\(401\) | − | 23.9338i | − | 1.19520i | −0.801795 | − | 0.597599i | \(-0.796122\pi\) | ||
0.801795 | − | 0.597599i | \(-0.203878\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 33.5838i | − | 1.67293i | ||||||
\(404\) | −11.4643 | −0.570372 | ||||||||
\(405\) | 8.31895i | 0.413372i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.26783 | −0.161980 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.8197 | 1.07892 | 0.539459 | − | 0.842012i | \(-0.318629\pi\) | ||||
0.539459 | + | 0.842012i | \(0.318629\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 23.3659i | − | 1.15256i | ||||||
\(412\) | 16.7916 | 0.827261 | ||||||||
\(413\) | 29.9396i | 1.47323i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.8949i | 0.976602i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.18946 | −0.450010 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 30.2164i | − | 1.47617i | −0.674709 | − | 0.738084i | \(-0.735731\pi\) | ||
0.674709 | − | 0.738084i | \(-0.264269\pi\) | |||||||
\(420\) | − | 42.4046i | − | 2.06913i | ||||||
\(421\) | −22.8745 | −1.11483 | −0.557417 | − | 0.830233i | \(-0.688207\pi\) | ||||
−0.557417 | + | 0.830233i | \(0.688207\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.44916 | 0.0704607 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.95147 | + | 39.4385i | 0.0946600 | + | 1.91305i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.3979 | −1.37427 | ||||||||
\(428\) | − | 15.7300i | − | 0.760337i | ||||||
\(429\) | 2.30321 | 0.111200 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 22.3077i | − | 1.07452i | −0.843416 | − | 0.537261i | \(-0.819459\pi\) | ||
0.843416 | − | 0.537261i | \(-0.180541\pi\) | |||||||
\(432\) | 22.0160i | 1.05925i | ||||||||
\(433\) | −33.6539 | −1.61731 | −0.808653 | − | 0.588286i | \(-0.799803\pi\) | ||||
−0.808653 | + | 0.588286i | \(0.799803\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 35.5650i | 1.70521i | ||||||||
\(436\) | 24.4638i | 1.17160i | ||||||||
\(437\) | 12.1289i | 0.580203i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 11.1340i | − | 0.531398i | −0.964056 | − | 0.265699i | \(-0.914397\pi\) | ||
0.964056 | − | 0.265699i | \(-0.0856027\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.7463 | −0.987921 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.4823 | 0.593051 | 0.296526 | − | 0.955025i | \(-0.404172\pi\) | ||||
0.296526 | + | 0.955025i | \(0.404172\pi\) | |||||||
\(444\) | 13.2841 | 0.630435 | ||||||||
\(445\) | − | 39.7898i | − | 1.88622i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.32513i | 0.299168i | ||||||||
\(448\) | − | 36.4177i | − | 1.72058i | ||||||
\(449\) | 14.6677i | 0.692213i | 0.938195 | + | 0.346107i | \(0.112496\pi\) | ||||
−0.938195 | + | 0.346107i | \(0.887504\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.222756 | −0.0104891 | ||||||||
\(452\) | 32.6280i | 1.53469i | ||||||||
\(453\) | 18.4863i | 0.868562i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −54.6738 | −2.56315 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.9171 | 1.02524 | 0.512619 | − | 0.858616i | \(-0.328675\pi\) | ||||
0.512619 | + | 0.858616i | \(0.328675\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.6659 | − | 1.12154i | 1.05795 | − | 0.0523488i | ||||
\(460\) | −46.3077 | −2.15911 | ||||||||
\(461\) | 29.6778 | 1.38223 | 0.691116 | − | 0.722744i | \(-0.257119\pi\) | ||||
0.691116 | + | 0.722744i | \(0.257119\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.7916 | −0.594474 | −0.297237 | − | 0.954804i | \(-0.596065\pi\) | ||||
−0.297237 | + | 0.954804i | \(0.596065\pi\) | |||||||
\(464\) | 30.5438i | 1.41796i | ||||||||
\(465\) | 49.7240i | 2.30590i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.6776 | −1.41959 | −0.709795 | − | 0.704408i | \(-0.751212\pi\) | ||||
−0.709795 | + | 0.704408i | \(0.751212\pi\) | |||||||
\(468\) | 9.51165 | 0.439676 | ||||||||
\(469\) | − | 39.8962i | − | 1.84224i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.7215i | 1.09303i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.600184i | 0.0275965i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.1539 | −0.878840 | ||||||||
\(476\) | −37.4927 | + | 1.85519i | −1.71847 | + | 0.0850323i | ||||
\(477\) | 11.1363 | 0.509894 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.45537i | 0.112189i | 0.998425 | + | 0.0560944i | \(0.0178648\pi\) | ||||
−0.998425 | + | 0.0560944i | \(0.982135\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 17.1277i | − | 0.780955i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 33.6775i | − | 1.53238i | ||||||
\(484\) | −21.2796 | −0.967253 | ||||||||
\(485\) | 6.00000 | 0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.0658i | 0.682698i | 0.939937 | + | 0.341349i | \(0.110884\pi\) | ||||
−0.939937 | + | 0.341349i | \(0.889116\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.8942 | 0.944867 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.8151 | 0.849112 | 0.424556 | − | 0.905402i | \(-0.360430\pi\) | ||||
0.424556 | + | 0.905402i | \(0.360430\pi\) | |||||||
\(492\) | 0.905525 | 0.0408242 | ||||||||
\(493\) | 31.4454 | − | 1.55596i | 1.41623 | − | 0.0700768i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.46434 | 0.155710 | ||||||||
\(496\) | 42.7038i | 1.91746i | ||||||||
\(497\) | 34.0401 | 1.52691 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 38.5693i | − | 1.72660i | −0.504692 | − | 0.863300i | \(-0.668394\pi\) | ||
0.504692 | − | 0.863300i | \(-0.331606\pi\) | |||||||
\(500\) | − | 34.9493i | − | 1.56298i | ||||||
\(501\) | −7.39805 | −0.330520 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 34.7910i | − | 1.55125i | −0.631192 | − | 0.775627i | \(-0.717434\pi\) | ||
0.631192 | − | 0.775627i | \(-0.282566\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 21.8853i | − | 0.973882i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 3.78695i | − | 0.168184i | ||||||
\(508\) | 11.6256 | 0.515803 | ||||||||
\(509\) | 43.3233 | 1.92027 | 0.960135 | − | 0.279536i | \(-0.0901807\pi\) | ||||
0.960135 | + | 0.279536i | \(0.0901807\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.0475 | −0.577187 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.0080i | 0.486016i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.0549i | 1.41251i | ||||||||
\(516\) | − | 2.43981i | − | 0.107407i | ||||||
\(517\) | 0.575306i | 0.0253019i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.0045 | 1.05368 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.06970i | 0.0468644i | 0.999725 | + | 0.0234322i | \(0.00745938\pi\) | ||||
−0.999725 | + | 0.0234322i | \(0.992541\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.9171 | −0.521098 | −0.260549 | − | 0.965461i | \(-0.583904\pi\) | ||||
−0.260549 | + | 0.965461i | \(0.583904\pi\) | |||||||
\(524\) | − | 31.8937i | − | 1.39328i | ||||||
\(525\) | 53.1834 | 2.32111 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 43.9643 | − | 2.17541i | 1.91511 | − | 0.0947623i | ||||
\(528\) | −2.92867 | −0.127454 | ||||||||
\(529\) | −13.7774 | −0.599017 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.94320 | 0.431498 | ||||||||
\(532\) | − | 18.2089i | − | 0.789455i | ||||||
\(533\) | − | 1.16753i | − | 0.0505713i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.0283 | 1.29824 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.33299i | 0.143829i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 8.23613i | − | 0.354755i | ||||||
\(540\) | −42.0283 | −1.80861 | ||||||||
\(541\) | 12.2319i | 0.525891i | 0.964811 | + | 0.262945i | \(0.0846939\pi\) | ||||
−0.964811 | + | 0.262945i | \(0.915306\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.7679 | −1.10581 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −46.7011 | −2.00046 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.8664i | − | 0.721155i | −0.932729 | − | 0.360577i | \(-0.882580\pi\) | ||
0.932729 | − | 0.360577i | \(-0.117420\pi\) | |||||||
\(548\) | 38.3077 | 1.63643 | ||||||||
\(549\) | 9.43116i | 0.402512i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.2719i | 0.650605i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 55.7531 | 2.37086 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 25.3592i | 1.07644i | ||||||||
\(556\) | − | 15.0658i | − | 0.638934i | ||||||
\(557\) | 4.97272 | 0.210701 | 0.105350 | − | 0.994435i | \(-0.466404\pi\) | ||||
0.105350 | + | 0.994435i | \(0.466404\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.14574 | −0.133051 | ||||||||
\(560\) | 69.5210 | 2.93780 | ||||||||
\(561\) | 0.149192 | + | 3.01512i | 0.00629889 | + | 0.127298i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.0283 | −1.22340 | −0.611699 | − | 0.791090i | \(-0.709514\pi\) | ||||
−0.611699 | + | 0.791090i | \(0.709514\pi\) | |||||||
\(564\) | − | 2.33868i | − | 0.0984763i | ||||||
\(565\) | −62.2865 | −2.62041 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 9.91878i | − | 0.416550i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.3234 | 0.516626 | 0.258313 | − | 0.966061i | \(-0.416833\pi\) | ||||
0.258313 | + | 0.966061i | \(0.416833\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 18.3867i | − | 0.769461i | −0.923029 | − | 0.384731i | \(-0.874294\pi\) | ||
0.923029 | − | 0.384731i | \(-0.125706\pi\) | |||||||
\(572\) | 3.77605i | 0.157885i | ||||||||
\(573\) | − | 24.3602i | − | 1.01766i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 58.0787i | − | 2.42205i | ||||||
\(576\) | −12.0946 | −0.503943 | ||||||||
\(577\) | −8.50008 | −0.353863 | −0.176931 | − | 0.984223i | \(-0.556617\pi\) | ||||
−0.176931 | + | 0.984223i | \(0.556617\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 30.1419 | 1.25266 | ||||||||
\(580\) | −58.3077 | −2.42110 | ||||||||
\(581\) | − | 23.7209i | − | 0.984110i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.42101i | 0.183099i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.1576i | 0.750725i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.8860 | 1.15098 | 0.575490 | − | 0.817809i | \(-0.304811\pi\) | ||||
0.575490 | + | 0.817809i | \(0.304811\pi\) | |||||||
\(588\) | 33.4808i | 1.38072i | ||||||||
\(589\) | 21.3519i | 0.879790i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.8152 | −0.815089 | ||||||||
\(592\) | 21.7789i | 0.895106i | ||||||||
\(593\) | 24.8151 | 1.01903 | 0.509516 | − | 0.860461i | \(-0.329824\pi\) | ||||
0.509516 | + | 0.860461i | \(0.329824\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.54153 | − | 71.5730i | −0.145188 | − | 2.93421i | ||||
\(596\) | −10.3699 | −0.424766 | ||||||||
\(597\) | −4.74392 | −0.194156 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 38.1383 | 1.55829 | 0.779145 | − | 0.626844i | \(-0.215653\pi\) | ||||
0.779145 | + | 0.626844i | \(0.215653\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.31090i | 0.339009i | 0.985529 | + | 0.169504i | \(0.0542167\pi\) | ||||
−0.985529 | + | 0.169504i | \(0.945783\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.2499 | −0.539576 | ||||||||
\(604\) | −30.3077 | −1.23320 | ||||||||
\(605\) | − | 40.6224i | − | 1.65154i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 17.2174i | − | 0.698833i | −0.936968 | − | 0.349417i | \(-0.886380\pi\) | ||
0.936968 | − | 0.349417i | \(-0.113620\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 42.4046i | − | 1.71832i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.01535 | −0.121988 | ||||||||
\(612\) | 0.616122 | + | 12.4516i | 0.0249053 | + | 0.503327i | ||||
\(613\) | −15.3057 | −0.618190 | −0.309095 | − | 0.951031i | \(-0.600026\pi\) | ||||
−0.309095 | + | 0.951031i | \(0.600026\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.72864i | 0.0697053i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.4348i | 1.58758i | 0.608190 | + | 0.793792i | \(0.291896\pi\) | ||||
−0.608190 | + | 0.793792i | \(0.708104\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 44.9157i | − | 1.80532i | −0.430358 | − | 0.902658i | \(-0.641613\pi\) | ||
0.430358 | − | 0.902658i | \(-0.358387\pi\) | |||||||
\(620\) | −81.5210 | −3.27396 | ||||||||
\(621\) | −33.3787 | −1.33944 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 47.4419i | 1.90072i | ||||||||
\(624\) | − | 15.3501i | − | 0.614494i | ||||||
\(625\) | 18.8330 | 0.753321 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.46434 | −0.0584800 | ||||||||
\(628\) | −38.8907 | −1.55191 | ||||||||
\(629\) | 22.4217 | − | 1.10945i | 0.894012 | − | 0.0442369i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.0283 | −1.43427 | −0.717133 | − | 0.696937i | \(-0.754546\pi\) | ||||
−0.717133 | + | 0.696937i | \(0.754546\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.04369 | 0.200469 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.1931i | 0.880708i | ||||||||
\(636\) | − | 17.9719i | − | 0.712631i | ||||||
\(637\) | 43.1680 | 1.71038 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 11.3050i | − | 0.447219i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.85626i | 0.310304i | 0.987891 | + | 0.155152i | \(0.0495867\pi\) | ||||
−0.987891 | + | 0.155152i | \(0.950413\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.51509i | 0.256930i | 0.991714 | + | 0.128465i | \(0.0410050\pi\) | ||||
−0.991714 | + | 0.128465i | \(0.958995\pi\) | |||||||
\(644\) | 55.2133 | 2.17571 | ||||||||
\(645\) | 4.65757 | 0.183392 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.4333 | 0.999885 | 0.499943 | − | 0.866059i | \(-0.333354\pi\) | ||||
0.499943 | + | 0.866059i | \(0.333354\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.94737i | 0.154948i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 59.2865i | − | 2.32362i | ||||||
\(652\) | 34.2554i | 1.34154i | ||||||||
\(653\) | 6.65372i | 0.260380i | 0.991489 | + | 0.130190i | \(0.0415588\pi\) | ||||
−0.991489 | + | 0.130190i | \(0.958441\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 60.8847 | 2.37896 | ||||||||
\(656\) | 1.48458i | 0.0579632i | ||||||||
\(657\) | 4.33318i | 0.169053i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.1281 | −0.472445 | −0.236222 | − | 0.971699i | \(-0.575909\pi\) | ||||
−0.236222 | + | 0.971699i | \(0.575909\pi\) | |||||||
\(660\) | − | 5.59080i | − | 0.217622i | ||||||
\(661\) | −6.68727 | −0.260105 | −0.130052 | − | 0.991507i | \(-0.541515\pi\) | ||||
−0.130052 | + | 0.991507i | \(0.541515\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.8031 | + | 0.781960i | −0.613743 | + | 0.0303688i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 34.7605 | 1.34795 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −46.3077 | −1.79304 | ||||||||
\(668\) | − | 12.1289i | − | 0.469280i | ||||||
\(669\) | − | 5.13408i | − | 0.198495i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.74410 | −0.144539 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 13.0099i | − | 0.501494i | −0.968053 | − | 0.250747i | \(-0.919324\pi\) | ||
0.968053 | − | 0.250747i | \(-0.0806762\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 52.7115i | − | 2.02887i | ||||||
\(676\) | 6.20859 | 0.238792 | ||||||||
\(677\) | 5.36588i | 0.206228i | 0.994670 | + | 0.103114i | \(0.0328806\pi\) | ||||
−0.994670 | + | 0.103114i | \(0.967119\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.15387 | −0.274540 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.7443 | −1.10148 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 10.9211i | − | 0.417884i | −0.977928 | − | 0.208942i | \(-0.932998\pi\) | ||
0.977928 | − | 0.208942i | \(-0.0670019\pi\) | |||||||
\(684\) | −6.04731 | −0.231225 | ||||||||
\(685\) | 73.1290i | 2.79412i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.10062i | 0.194601i | ||||||||
\(688\) | 4.00000 | 0.152499 | ||||||||
\(689\) | −23.1718 | −0.882776 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.4112i | 1.08081i | 0.841404 | + | 0.540406i | \(0.181729\pi\) | ||||
−0.841404 | + | 0.540406i | \(0.818271\pi\) | |||||||
\(692\) | 39.3547i | 1.49604i | ||||||||
\(693\) | −4.13057 | −0.156907 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.7605 | 1.09095 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.52840 | − | 0.0756273i | 0.0578923 | − | 0.00286459i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.8610 | 0.599919 | ||||||||
\(700\) | 87.1926i | 3.29557i | ||||||||
\(701\) | 5.27958 | 0.199407 | 0.0997036 | − | 0.995017i | \(-0.468211\pi\) | ||||
0.0997036 | + | 0.995017i | \(0.468211\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.8894i | 0.410703i | ||||||||
\(704\) | − | 4.80147i | − | 0.180962i | ||||||
\(705\) | 4.46451 | 0.168143 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26.0941i | 0.981369i | ||||||||
\(708\) | − | 16.0465i | − | 0.603064i | ||||||
\(709\) | 12.2630i | 0.460547i | 0.973126 | + | 0.230274i | \(0.0739621\pi\) | ||||
−0.973126 | + | 0.230274i | \(0.926038\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 18.5161i | − | 0.694406i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −64.7436 | −2.42467 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.20844 | −0.269580 | ||||||||
\(716\) | −5.46434 | −0.204212 | ||||||||
\(717\) | − | 10.4820i | − | 0.391458i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.86499i | 0.293315i | 0.989187 | + | 0.146657i | \(0.0468515\pi\) | ||||
−0.989187 | + | 0.146657i | \(0.953149\pi\) | |||||||
\(720\) | − | 23.0885i | − | 0.860457i | ||||||
\(721\) | − | 38.2194i | − | 1.42337i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.09635 | 0.115154 | ||||||||
\(724\) | − | 42.2457i | − | 1.57005i | ||||||
\(725\) | − | 73.1290i | − | 2.71594i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.8078 | 1.21677 | 0.608387 | − | 0.793640i | \(-0.291817\pi\) | ||||
0.608387 | + | 0.793640i | \(0.291817\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.4372 | −0.868046 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.203767 | − | 4.11807i | −0.00753660 | − | 0.152312i | ||||
\(732\) | 15.2202 | 0.562553 | ||||||||
\(733\) | 45.2651 | 1.67190 | 0.835952 | − | 0.548802i | \(-0.184916\pi\) | ||||
0.835952 | + | 0.548802i | \(0.184916\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −63.9144 | −2.35752 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 5.26009i | − | 0.193758i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.0992 | 0.812931 | 0.406465 | − | 0.913666i | \(-0.366761\pi\) | ||||
0.406465 | + | 0.913666i | \(0.366761\pi\) | |||||||
\(740\) | −41.5756 | −1.52835 | ||||||||
\(741\) | − | 7.67503i | − | 0.281949i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.9029i | 0.730168i | 0.930975 | + | 0.365084i | \(0.118960\pi\) | ||||
−0.930975 | + | 0.365084i | \(0.881040\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 19.7959i | − | 0.725267i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.87791 | −0.288238 | ||||||||
\(748\) | −4.94320 | + | 0.244596i | −0.180741 | + | 0.00894331i | ||||
\(749\) | −35.8031 | −1.30822 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.4728i | 1.87827i | 0.343551 | + | 0.939134i | \(0.388370\pi\) | ||||
−0.343551 | + | 0.939134i | \(0.611630\pi\) | |||||||
\(752\) | 3.83420 | 0.139819 | ||||||||
\(753\) | 19.3608i | 0.705545i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 57.8571i | − | 2.10564i | ||||||
\(756\) | 50.1109 | 1.82252 | ||||||||
\(757\) | 24.7087 | 0.898052 | 0.449026 | − | 0.893519i | \(-0.351771\pi\) | ||||
0.449026 | + | 0.893519i | \(0.351771\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 4.44019i | − | 0.161169i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.6895 | 0.713745 | 0.356873 | − | 0.934153i | \(-0.383843\pi\) | ||||
0.356873 | + | 0.934153i | \(0.383843\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 55.6823 | 2.01583 | ||||||||
\(764\) | 39.9379 | 1.44490 | ||||||||
\(765\) | −23.7700 | + | 1.17617i | −0.859406 | + | 0.0425245i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.6894 | −0.747049 | ||||||||
\(768\) | 19.5185i | 0.704313i | ||||||||
\(769\) | −9.91592 | −0.357577 | −0.178789 | − | 0.983888i | \(-0.557218\pi\) | ||||
−0.178789 | + | 0.983888i | \(0.557218\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 8.72705i | − | 0.314297i | ||||||
\(772\) | 49.4168i | 1.77855i | ||||||||
\(773\) | 9.07097 | 0.326260 | 0.163130 | − | 0.986605i | \(-0.447841\pi\) | ||||
0.163130 | + | 0.986605i | \(0.447841\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 102.243i | − | 3.67267i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 30.2360i | − | 1.08471i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.742291i | 0.0265953i | ||||||||
\(780\) | 29.3031 | 1.04922 | ||||||||
\(781\) | 4.48799 | 0.160593 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −42.0283 | −1.50197 | ||||||||
\(784\) | −54.8907 | −1.96038 | ||||||||
\(785\) | − | 74.2419i | − | 2.64981i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 18.1778i | − | 0.647967i | −0.946063 | − | 0.323983i | \(-0.894978\pi\) | ||
0.946063 | − | 0.323983i | \(-0.105022\pi\) | |||||||
\(788\) | − | 32.4865i | − | 1.15728i | ||||||
\(789\) | 0.413306i | 0.0147141i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 74.2649 | 2.64056 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 19.6239i | − | 0.696866i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 34.3081 | 1.21678 | ||||||||
\(796\) | − | 7.77752i | − | 0.275667i | ||||||
\(797\) | −8.35055 | −0.295792 | −0.147896 | − | 0.989003i | \(-0.547250\pi\) | ||||
−0.147896 | + | 0.989003i | \(0.547250\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.195321 | − | 3.94737i | −0.00690996 | − | 0.139648i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.7558 | 0.556705 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.72024 | −0.0607059 | ||||||||
\(804\) | 21.3828i | 0.754114i | ||||||||
\(805\) | 105.401i | 3.71491i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.9926 | 0.598168 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 12.1209i | − | 0.426149i | −0.977036 | − | 0.213074i | \(-0.931652\pi\) | ||
0.977036 | − | 0.213074i | \(-0.0683476\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.2126i | 0.534187i | 0.963671 | + | 0.267093i | \(0.0860632\pi\) | ||||
−0.963671 | + | 0.267093i | \(0.913937\pi\) | |||||||
\(812\) | 69.5210 | 2.43971 | ||||||||
\(813\) | 29.9988i | 1.05211i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −65.3931 | −2.29062 | ||||||||
\(816\) | 20.0946 | − | 0.994308i | 0.703453 | − | 0.0348077i | ||||
\(817\) | 2.00000 | 0.0699711 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 21.6495i | − | 0.756496i | ||||||
\(820\) | −2.83405 | −0.0989692 | ||||||||
\(821\) | 8.14866i | 0.284390i | 0.989839 | + | 0.142195i | \(0.0454160\pi\) | ||||
−0.989839 | + | 0.142195i | \(0.954584\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.8397i | 0.935572i | 0.883842 | + | 0.467786i | \(0.154948\pi\) | ||||
−0.883842 | + | 0.467786i | \(0.845052\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.01193 | 0.244124 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 30.8349i | − | 1.07223i | −0.844144 | − | 0.536117i | \(-0.819891\pi\) | ||
0.844144 | − | 0.536117i | \(-0.180109\pi\) | |||||||
\(828\) | − | 18.3368i | − | 0.637247i | ||||||
\(829\) | −17.4333 | −0.605483 | −0.302741 | − | 0.953073i | \(-0.597902\pi\) | ||||
−0.302741 | + | 0.953073i | \(0.597902\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.36264 | −0.220717 | ||||||||
\(832\) | 25.1660 | 0.872472 | ||||||||
\(833\) | 2.79623 | + | 56.5109i | 0.0968837 | + | 1.95799i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.1539 | 0.801273 | ||||||||
\(836\) | − | 2.40074i | − | 0.0830312i | ||||||
\(837\) | −58.7605 | −2.03106 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.1089i | 0.452571i | 0.974061 | + | 0.226285i | \(0.0726582\pi\) | ||||
−0.974061 | + | 0.226285i | \(0.927342\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.3077 | −1.01061 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 12.5068i | − | 0.430759i | ||||||
\(844\) | 8.26897i | 0.284630i | ||||||||
\(845\) | 11.8521i | 0.407725i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.4346i | 1.66423i | ||||||||
\(848\) | 29.4643 | 1.01181 | ||||||||
\(849\) | −18.7560 | −0.643703 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.0191 | −1.13188 | ||||||||
\(852\) | −18.2442 | −0.625035 | ||||||||
\(853\) | 26.8708i | 0.920038i | 0.887909 | + | 0.460019i | \(0.152157\pi\) | ||||
−0.887909 | + | 0.460019i | \(0.847843\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 11.5442i | − | 0.394805i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.1735i | 0.757433i | 0.925513 | + | 0.378717i | \(0.123634\pi\) | ||||
−0.925513 | + | 0.378717i | \(0.876366\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.0831 | −0.378149 | −0.189074 | − | 0.981963i | \(-0.560549\pi\) | ||||
−0.189074 | + | 0.981963i | \(0.560549\pi\) | |||||||
\(860\) | 7.63595i | 0.260384i | ||||||||
\(861\) | − | 2.06107i | − | 0.0702412i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.54724 | 0.324992 | 0.162496 | − | 0.986709i | \(-0.448046\pi\) | ||||
0.162496 | + | 0.986709i | \(0.448046\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −75.1276 | −2.55442 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.04731 | − | 20.6371i | −0.0695304 | − | 0.700873i | ||||
\(868\) | 97.1985 | 3.29913 | ||||||||
\(869\) | 7.35073 | 0.249357 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.5697 | 0.934164 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.37586i | 0.0804106i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −79.5483 | −2.68922 | ||||||||
\(876\) | 6.99295 | 0.236270 | ||||||||
\(877\) | 46.0603i | 1.55535i | 0.628669 | + | 0.777673i | \(0.283600\pi\) | ||||
−0.628669 | + | 0.777673i | \(0.716400\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 5.15118i | − | 0.173745i | ||||||
\(880\) | 9.16595 | 0.308984 | ||||||||
\(881\) | 6.30144i | 0.212301i | 0.994350 | + | 0.106150i | \(0.0338525\pi\) | ||||
−0.994350 | + | 0.106150i | \(0.966147\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.6621 | 1.53665 | 0.768326 | − | 0.640059i | \(-0.221090\pi\) | ||||
0.768326 | + | 0.640059i | \(0.221090\pi\) | |||||||
\(884\) | −1.28200 | − | 25.9088i | −0.0431183 | − | 0.871406i | ||||
\(885\) | 30.6326 | 1.02970 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 19.9830i | − | 0.670962i | −0.942047 | − | 0.335481i | \(-0.891101\pi\) | ||
0.942047 | − | 0.335481i | \(-0.108899\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 26.4612i | − | 0.887479i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1.30774i | − | 0.0438108i | ||||||
\(892\) | 8.41718 | 0.281828 | ||||||||
\(893\) | 1.91710 | 0.0641533 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 10.4314i | − | 0.348682i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.2724 | 0.777041 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −81.5210 | −2.71888 | ||||||||
\(900\) | 28.9574 | 0.965246 | ||||||||
\(901\) | −1.50097 | − | 30.3340i | −0.0500045 | − | 1.01057i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.55328 | −0.184802 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 80.6465 | 2.68078 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.60490i | 0.0864942i | 0.999064 | + | 0.0432471i | \(0.0137703\pi\) | ||||
−0.999064 | + | 0.0432471i | \(0.986230\pi\) | |||||||
\(908\) | − | 47.1253i | − | 1.56391i | ||||||
\(909\) | 8.66605 | 0.287435 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 6.96100i | − | 0.230628i | −0.993329 | − | 0.115314i | \(-0.963213\pi\) | ||
0.993329 | − | 0.115314i | \(-0.0367875\pi\) | |||||||
\(912\) | 9.75925i | 0.323161i | ||||||||
\(913\) | − | 3.12747i | − | 0.103504i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.0551i | 0.960532i | ||||||||
\(916\) | −8.36231 | −0.276298 | ||||||||
\(917\) | −72.5935 | −2.39725 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.8411 | −0.852421 | −0.426210 | − | 0.904624i | \(-0.640152\pi\) | ||||
−0.426210 | + | 0.904624i | \(0.640152\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 3.55859i | − | 0.117259i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.5229i | 0.774266i | ||||||||
\(924\) | 6.66598i | 0.219295i | ||||||||
\(925\) | − | 52.1437i | − | 1.71447i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.6930 | −0.416892 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 6.43558i | − | 0.211145i | −0.994412 | − | 0.105572i | \(-0.966333\pi\) | ||
0.994412 | − | 0.105572i | \(-0.0336674\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.4454 | −0.899485 | ||||||||
\(932\) | 26.0037i | 0.851778i | ||||||||
\(933\) | 23.0899 | 0.755931 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.466930 | − | 9.43650i | −0.0152703 | − | 0.308607i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.2796 | 1.15253 | 0.576266 | − | 0.817262i | \(-0.304509\pi\) | ||||
0.576266 | + | 0.817262i | \(0.304509\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.14557 | 0.102652 | ||||||||
\(940\) | 7.31944i | 0.238734i | ||||||||
\(941\) | − | 37.6416i | − | 1.22708i | −0.789663 | − | 0.613541i | \(-0.789745\pi\) | ||
0.789663 | − | 0.613541i | \(-0.210255\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.25079 | −0.0732957 | ||||||||
\(944\) | 26.3077 | 0.856244 | ||||||||
\(945\) | 95.6611i | 3.11185i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.8336i | 0.352045i | 0.984386 | + | 0.176023i | \(0.0563232\pi\) | ||||
−0.984386 | + | 0.176023i | \(0.943677\pi\) | |||||||
\(948\) | −29.8815 | −0.970506 | ||||||||
\(949\) | − | 9.01628i | − | 0.292681i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.84577 | −0.157135 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.88604 | 0.320240 | 0.160120 | − | 0.987098i | \(-0.448812\pi\) | ||||
0.160120 | + | 0.987098i | \(0.448812\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 76.2409i | 2.46710i | ||||||||
\(956\) | 17.1849 | 0.555800 | ||||||||
\(957\) | − | 5.59080i | − | 0.180725i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 87.1926i | − | 2.81560i | ||||||
\(960\) | −37.2606 | −1.20258 | ||||||||
\(961\) | −82.9759 | −2.67664 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.8905i | 0.383166i | ||||||||
\(964\) | 5.07637i | 0.163499i | ||||||||
\(965\) | −94.3361 | −3.03679 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.6942 | 1.40511 | 0.702556 | − | 0.711629i | \(-0.252042\pi\) | ||||
0.702556 | + | 0.711629i | \(0.252042\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.0473 | − | 0.497154i | 0.322766 | − | 0.0159709i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.9417 | 1.37806 | 0.689032 | − | 0.724731i | \(-0.258036\pi\) | ||||
0.689032 | + | 0.724731i | \(0.258036\pi\) | |||||||
\(972\) | − | 27.7080i | − | 0.888733i | ||||||
\(973\) | −34.2915 | −1.09933 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 36.7516i | 1.17699i | ||||||||
\(976\) | 24.9530i | 0.798726i | ||||||||
\(977\) | −39.2625 | −1.25612 | −0.628060 | − | 0.778165i | \(-0.716151\pi\) | ||||
−0.628060 | + | 0.778165i | \(0.716151\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.25494i | 0.199909i | ||||||||
\(980\) | − | 104.786i | − | 3.34726i | ||||||
\(981\) | − | 18.4925i | − | 0.590421i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 39.7473i | − | 1.26774i | −0.773439 | − | 0.633871i | \(-0.781465\pi\) | ||
0.773439 | − | 0.633871i | \(-0.218535\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 62.0163 | 1.97600 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.32309 | −0.169436 | ||||||||
\(988\) | 12.5830 | 0.400318 | ||||||||
\(989\) | 6.06444i | 0.192838i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 42.1560i | − | 1.33913i | −0.742754 | − | 0.669564i | \(-0.766481\pi\) | ||
0.742754 | − | 0.669564i | \(-0.233519\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.69427i | 0.0855001i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.8472 | 0.470687 | ||||||||
\(996\) | 12.7135i | 0.402843i | ||||||||
\(997\) | − | 47.2560i | − | 1.49661i | −0.663353 | − | 0.748306i | \(-0.730867\pi\) | ||
0.663353 | − | 0.748306i | \(-0.269133\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −29.9678 | −0.948138 |
(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 | 731.2.d.b.560.5 | yes | 8 | |
17.16 | even | 2 | inner | 731.2.d.b.560.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.d.b.560.4 | ✓ | 8 | 17.16 | even | 2 | inner | |
731.2.d.b.560.5 | yes | 8 | 1.1 | even | 1 | trivial |