Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3100,3,Mod(1549,3100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3100.1549");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3100.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(84.4688819517\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.256992219136.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 105x^{4} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 124) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1549.1 | ||
Root | \(-2.26020 + 2.26020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3100.1549 |
Dual form | 3100.3.f.b.1549.2 |
$q$-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 \(\left(\mathbb{Z}/3100\mathbb{Z}\right)^\times\).
\(n\) | \(1551\) | \(1801\) | \(2977\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −4.52040 | −1.50680 | −0.753399 | − | 0.657563i | \(-0.771587\pi\) | ||||
−0.753399 | + | 0.657563i | \(0.771587\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.21699i | − | 0.459570i | −0.973241 | − | 0.229785i | \(-0.926198\pi\) | ||
0.973241 | − | 0.229785i | \(-0.0738023\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 11.4340 | 1.27044 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 8.05991i | − | 0.732719i | −0.930473 | − | 0.366359i | \(-0.880604\pi\) | ||
0.930473 | − | 0.366359i | \(-0.119396\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.5230 | 1.19407 | 0.597037 | − | 0.802214i | \(-0.296345\pi\) | ||||
0.597037 | + | 0.802214i | \(0.296345\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.5446 | 1.50263 | 0.751313 | − | 0.659946i | \(-0.229421\pi\) | ||||
0.751313 | + | 0.659946i | \(0.229421\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 15.6510 | 0.823735 | 0.411868 | − | 0.911244i | \(-0.364877\pi\) | ||||
0.411868 | + | 0.911244i | \(0.364877\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.5421i | 0.692480i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.5829 | 1.02534 | 0.512671 | − | 0.858585i | \(-0.328656\pi\) | ||||
0.512671 | + | 0.858585i | \(0.328656\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11.0026 | −0.407502 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 38.7218i | − | 1.33523i | −0.744505 | − | 0.667617i | \(-0.767314\pi\) | ||
0.744505 | − | 0.667617i | \(-0.232686\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.56602 | + | 30.6619i | 0.147291 | + | 0.989093i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 36.4340i | 1.10406i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.94265 | 0.0795311 | 0.0397655 | − | 0.999209i | \(-0.487339\pi\) | ||||
0.0397655 | + | 0.999209i | \(0.487339\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −70.1699 | −1.79923 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.51893 | 0.158998 | 0.0794992 | − | 0.996835i | \(-0.474668\pi\) | ||||
0.0794992 | + | 0.996835i | \(0.474668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.52040 | −0.105125 | −0.0525627 | − | 0.998618i | \(-0.516739\pi\) | ||||
−0.0525627 | + | 0.998618i | \(0.516739\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 72.1699i | 1.53553i | 0.640732 | + | 0.767765i | \(0.278631\pi\) | ||||
−0.640732 | + | 0.767765i | \(0.721369\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 38.6510 | 0.788795 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −115.472 | −2.26415 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 71.3455 | 1.34614 | 0.673070 | − | 0.739578i | \(-0.264975\pi\) | ||||
0.673070 | + | 0.739578i | \(0.264975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −70.7486 | −1.24120 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −42.9529 | −0.728016 | −0.364008 | − | 0.931396i | \(-0.618592\pi\) | ||||
−0.364008 | + | 0.931396i | \(0.618592\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 83.9258i | − | 1.37583i | −0.725790 | − | 0.687916i | \(-0.758526\pi\) | ||
0.725790 | − | 0.687916i | \(-0.241474\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 36.7830i | − | 0.583857i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 82.8680i | 1.23684i | 0.785850 | + | 0.618418i | \(0.212226\pi\) | ||||
−0.785850 | + | 0.618418i | \(0.787774\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −106.604 | −1.54498 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −74.2549 | −1.04584 | −0.522922 | − | 0.852381i | \(-0.675158\pi\) | ||||
−0.522922 | + | 0.852381i | \(0.675158\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.11726 | 0.0700994 | 0.0350497 | − | 0.999386i | \(-0.488841\pi\) | ||||
0.0350497 | + | 0.999386i | \(0.488841\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −25.9287 | −0.336736 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.23109i | − | 0.104191i | −0.998642 | − | 0.0520955i | \(-0.983410\pi\) | ||
0.998642 | − | 0.0520955i | \(-0.0165900\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −53.1699 | −0.656419 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 103.585 | 1.24801 | 0.624007 | − | 0.781419i | \(-0.285504\pi\) | ||||
0.624007 | + | 0.781419i | \(0.285504\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 175.038i | 2.01193i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 114.759i | 1.28943i | 0.764425 | + | 0.644713i | \(0.223023\pi\) | ||||
−0.764425 | + | 0.644713i | \(0.776977\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 49.9372i | − | 0.548760i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.6402 | − | 138.604i | −0.221938 | − | 1.49036i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 21.8209i | − | 0.224957i | −0.993654 | − | 0.112479i | \(-0.964121\pi\) | ||
0.993654 | − | 0.112479i | \(-0.0358790\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 92.1568i | − | 0.930877i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −121.387 | −1.20185 | −0.600925 | − | 0.799305i | \(-0.705201\pi\) | ||||
−0.600925 | + | 0.799305i | \(0.705201\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 145.387i | 1.41152i | 0.708449 | + | 0.705762i | \(0.249395\pi\) | ||||
−0.708449 | + | 0.705762i | \(0.750605\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 119.651i | − | 1.11823i | −0.829089 | − | 0.559117i | \(-0.811140\pi\) | ||
0.829089 | − | 0.559117i | \(-0.188860\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 59.9908 | 0.550374 | 0.275187 | − | 0.961391i | \(-0.411260\pi\) | ||||
0.275187 | + | 0.961391i | \(0.411260\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.3019 | −0.119837 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 66.8587i | − | 0.591670i | −0.955239 | − | 0.295835i | \(-0.904402\pi\) | ||
0.955239 | − | 0.295835i | \(-0.0955979\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 177.489 | 1.51700 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 82.1768i | − | 0.690562i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 56.0379 | 0.463123 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −29.4682 | −0.239579 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −31.4716 | −0.247808 | −0.123904 | − | 0.992294i | \(-0.539541\pi\) | ||||
−0.123904 | + | 0.992294i | \(0.539541\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 20.4340 | 0.158403 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −93.1320 | −0.710932 | −0.355466 | − | 0.934689i | \(-0.615678\pi\) | ||||
−0.355466 | + | 0.934689i | \(0.615678\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 50.3490i | − | 0.378564i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −45.5880 | −0.332759 | −0.166379 | − | 0.986062i | \(-0.553208\pi\) | ||||
−0.166379 | + | 0.986062i | \(0.553208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 224.613i | 1.61592i | 0.589236 | + | 0.807961i | \(0.299429\pi\) | ||||
−0.589236 | + | 0.807961i | \(0.700571\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 326.237i | − | 2.31373i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 125.114i | − | 0.874920i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −174.718 | −1.18856 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 247.548 | 1.66139 | 0.830697 | − | 0.556725i | \(-0.187942\pi\) | ||||
0.830697 | + | 0.556725i | \(0.187942\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.88873i | − | 0.0522433i | −0.999659 | − | 0.0261216i | \(-0.991684\pi\) | ||
0.999659 | − | 0.0261216i | \(-0.00831572\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 292.077 | 1.90900 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 204.689i | 1.30375i | 0.758326 | + | 0.651875i | \(0.226017\pi\) | ||||
−0.758326 | + | 0.651875i | \(0.773983\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −322.510 | −2.02836 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 75.8659i | − | 0.471216i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 148.179i | 0.909074i | 0.890728 | + | 0.454537i | \(0.150195\pi\) | ||||
−0.890728 | + | 0.454537i | \(0.849805\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −69.5965 | −0.416746 | −0.208373 | − | 0.978049i | \(-0.566817\pi\) | ||||
−0.208373 | + | 0.978049i | \(0.566817\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 71.9621 | 0.425811 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 178.953 | 1.04651 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 114.340i | 0.660924i | 0.943819 | + | 0.330462i | \(0.107205\pi\) | ||||
−0.943819 | + | 0.330462i | \(0.892795\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 194.164 | 1.09697 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 80.7703i | 0.451231i | 0.974216 | + | 0.225615i | \(0.0724392\pi\) | ||||
−0.974216 | + | 0.225615i | \(0.927561\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.32667i | 0.0183794i | 0.999958 | + | 0.00918970i | \(0.00292521\pi\) | ||||
−0.999958 | + | 0.00918970i | \(0.997075\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 379.378i | 2.07310i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 205.887i | − | 1.10100i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 35.3951i | 0.187276i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −95.5568 | −0.500297 | −0.250149 | − | 0.968207i | \(-0.580480\pi\) | ||||
−0.250149 | + | 0.968207i | \(0.580480\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 77.5568i | − | 0.401849i | −0.979607 | − | 0.200924i | \(-0.935605\pi\) | ||
0.979607 | − | 0.200924i | \(-0.0643945\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 305.638 | 1.55146 | 0.775731 | − | 0.631064i | \(-0.217381\pi\) | ||||
0.775731 | + | 0.631064i | \(0.217381\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 181.158i | − | 0.910343i | −0.890404 | − | 0.455171i | \(-0.849578\pi\) | ||
0.890404 | − | 0.455171i | \(-0.150422\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 374.596i | − | 1.86366i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −124.568 | −0.613634 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 269.646 | 1.30264 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 126.145i | − | 0.603567i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 68.0092 | 0.322319 | 0.161159 | − | 0.986928i | \(-0.448477\pi\) | ||||
0.161159 | + | 0.986928i | \(0.448477\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 335.661 | 1.57587 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 98.6390 | − | 14.6888i | 0.454558 | − | 0.0676905i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.1320 | −0.105626 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 396.528 | 1.79425 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −263.293 | −1.18069 | −0.590344 | − | 0.807152i | \(-0.701008\pi\) | ||||
−0.590344 | + | 0.807152i | \(0.701008\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 164.416i | 0.724298i | 0.932120 | + | 0.362149i | \(0.117957\pi\) | ||||
−0.932120 | + | 0.362149i | \(0.882043\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 298.559i | 1.30375i | 0.758326 | + | 0.651876i | \(0.226018\pi\) | ||||
−0.758326 | + | 0.651876i | \(0.773982\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 117.208 | 0.507393 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 65.3112i | − | 0.280305i | −0.990130 | − | 0.140153i | \(-0.955241\pi\) | ||
0.990130 | − | 0.140153i | \(-0.0447593\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 37.2078i | 0.156995i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 192.202i | − | 0.804194i | −0.915597 | − | 0.402097i | \(-0.868281\pi\) | ||
0.915597 | − | 0.402097i | \(-0.131719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 38.5506i | 0.159961i | 0.996796 | + | 0.0799805i | \(0.0254858\pi\) | ||||
−0.996796 | + | 0.0799805i | \(0.974514\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 339.372 | 1.39659 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 242.949 | 0.983601 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −468.246 | −1.88050 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 139.281i | 0.554904i | 0.960739 | + | 0.277452i | \(0.0894900\pi\) | ||||
−0.960739 | + | 0.277452i | \(0.910510\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 190.076i | − | 0.751287i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 273.217i | 1.06310i | 0.847027 | + | 0.531551i | \(0.178390\pi\) | ||||
−0.847027 | + | 0.531551i | \(0.821610\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 9.46648i | − | 0.0365501i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 442.744i | − | 1.69634i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 388.287 | 1.47638 | 0.738188 | − | 0.674595i | \(-0.235682\pi\) | ||||
0.738188 | + | 0.674595i | \(0.235682\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 518.755i | − | 1.94290i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 192.374i | 0.715144i | 0.933886 | + | 0.357572i | \(0.116395\pi\) | ||||
−0.933886 | + | 0.357572i | \(0.883605\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 276.299i | − | 1.01955i | −0.860306 | − | 0.509777i | \(-0.829728\pi\) | ||
0.860306 | − | 0.509777i | \(-0.170272\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 225.736i | 0.826872i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 220.731 | 0.796864 | 0.398432 | − | 0.917198i | \(-0.369554\pi\) | ||||
0.398432 | + | 0.917198i | \(0.369554\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 52.2078 | + | 350.587i | 0.187125 | + | 1.25659i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 287.293 | 1.02239 | 0.511197 | − | 0.859464i | \(-0.329202\pi\) | ||||
0.511197 | + | 0.859464i | \(0.329202\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 24.2641i | − | 0.0857388i | −0.999081 | − | 0.0428694i | \(-0.986350\pi\) | ||
0.999081 | − | 0.0428694i | \(-0.0136499\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 20.9713i | − | 0.0730709i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 363.528 | 1.25788 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 98.6390i | 0.338966i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 187.359i | − | 0.639451i | −0.947510 | − | 0.319726i | \(-0.896409\pi\) | ||
0.947510 | − | 0.319726i | \(-0.103591\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 88.6796i | 0.298585i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 366.076 | 1.22433 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.5421i | 0.0483125i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 548.717 | 1.81095 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 491.123i | − | 1.59975i | −0.600168 | − | 0.799874i | \(-0.704899\pi\) | ||
0.600168 | − | 0.799874i | \(-0.295101\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 657.206i | − | 2.12688i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.19756 | 0.0134970 | 0.00674848 | − | 0.999977i | \(-0.497852\pi\) | ||||
0.00674848 | + | 0.999977i | \(0.497852\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 309.816 | 0.989828 | 0.494914 | − | 0.868942i | \(-0.335200\pi\) | ||||
0.494914 | + | 0.868942i | \(0.335200\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 196.859i | − | 0.621006i | −0.950572 | − | 0.310503i | \(-0.899503\pi\) | ||
0.950572 | − | 0.310503i | \(-0.100497\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −312.094 | −0.978352 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 540.870i | 1.68495i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 399.798 | 1.23777 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −271.182 | −0.829303 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 232.170 | 0.705684 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 495.152i | − | 1.49593i | −0.663739 | − | 0.747964i | \(-0.731031\pi\) | ||
0.663739 | − | 0.747964i | \(-0.268969\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 33.6462 | 0.101040 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −271.608 | −0.805958 | −0.402979 | − | 0.915209i | \(-0.632025\pi\) | ||||
−0.402979 | + | 0.915209i | \(0.632025\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 302.228i | 0.891528i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 247.132 | − | 36.8017i | 0.724727 | − | 0.107923i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 281.972i | − | 0.822077i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 300.562 | 0.866174 | 0.433087 | − | 0.901352i | \(-0.357424\pi\) | ||||
0.433087 | + | 0.901352i | \(0.357424\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 617.472 | 1.76926 | 0.884630 | − | 0.466293i | \(-0.154411\pi\) | ||||
0.884630 | + | 0.466293i | \(0.154411\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −170.792 | −0.486588 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −449.652 | −1.27380 | −0.636901 | − | 0.770946i | \(-0.719784\pi\) | ||||
−0.636901 | + | 0.770946i | \(0.719784\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 371.472i | 1.04054i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 294.312 | 0.819811 | 0.409906 | − | 0.912128i | \(-0.365562\pi\) | ||||
0.409906 | + | 0.912128i | \(0.365562\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −116.047 | −0.321460 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −253.313 | −0.697833 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 59.7044 | 0.162682 | 0.0813411 | − | 0.996686i | \(-0.474080\pi\) | ||||
0.0813411 | + | 0.996686i | \(0.474080\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 74.5374 | 0.201998 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 229.518i | − | 0.618646i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 149.727i | 0.401412i | 0.979652 | + | 0.200706i | \(0.0643236\pi\) | ||||
−0.979652 | + | 0.200706i | \(0.935676\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 601.077i | − | 1.59437i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −221.284 | −0.583862 | −0.291931 | − | 0.956439i | \(-0.594298\pi\) | ||||
−0.291931 | + | 0.956439i | \(0.594298\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 142.264 | 0.373397 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 186.275 | 0.486359 | 0.243179 | − | 0.969981i | \(-0.421810\pi\) | ||||
0.243179 | + | 0.969981i | \(0.421810\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −51.6861 | −0.133556 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 140.174i | 0.360344i | 0.983635 | + | 0.180172i | \(0.0576655\pi\) | ||||
−0.983635 | + | 0.180172i | \(0.942335\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 602.416 | 1.54070 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 420.994 | 1.07123 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 106.085i | 0.267217i | 0.991034 | + | 0.133608i | \(0.0426564\pi\) | ||||
−0.991034 | + | 0.133608i | \(0.957344\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 227.598i | 0.570420i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 97.9543i | − | 0.244275i | −0.992513 | − | 0.122138i | \(-0.961025\pi\) | ||
0.992513 | − | 0.122138i | \(-0.0389749\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 70.8781 | + | 475.963i | 0.175876 | + | 1.18105i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 23.7175i | − | 0.0582739i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 11.7289i | − | 0.0286771i | −0.999897 | − | 0.0143386i | \(-0.995436\pi\) | ||
0.999897 | − | 0.0143386i | \(-0.00456426\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 206.076 | 0.501401 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 138.179i | 0.334574i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1015.34i | − | 2.43487i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.74514 | −0.0137116 | −0.00685578 | − | 0.999976i | \(-0.502182\pi\) | ||||
−0.00685578 | + | 0.999976i | \(0.502182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.8209 | 0.0850852 | 0.0425426 | − | 0.999095i | \(-0.486454\pi\) | ||||
0.0425426 | + | 0.999095i | \(0.486454\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 825.189i | 1.95080i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −269.988 | −0.632291 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 565.563i | 1.31833i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 216.170 | 0.501554 | 0.250777 | − | 0.968045i | \(-0.419314\pi\) | ||||
0.250777 | + | 0.968045i | \(0.419314\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 274.847 | 0.634750 | 0.317375 | − | 0.948300i | \(-0.397199\pi\) | ||||
0.317375 | + | 0.948300i | \(0.397199\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 369.095 | 0.844610 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −549.463 | −1.25162 | −0.625812 | − | 0.779974i | \(-0.715232\pi\) | ||||
−0.625812 | + | 0.779974i | \(0.715232\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.934 | 1.00212 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 151.669i | − | 0.342369i | −0.985239 | − | 0.171184i | \(-0.945241\pi\) | ||
0.985239 | − | 0.171184i | \(-0.0547594\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1119.01 | −2.50339 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 345.854i | 0.770277i | 0.922859 | + | 0.385138i | \(0.125846\pi\) | ||||
−0.922859 | + | 0.385138i | \(0.874154\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 52.5420i | − | 0.116501i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 35.6602i | 0.0787201i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −707.060 | −1.54718 | −0.773589 | − | 0.633688i | \(-0.781540\pi\) | ||||
−0.773589 | + | 0.633688i | \(0.781540\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −281.056 | −0.612323 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 860.967i | 1.86761i | 0.357787 | + | 0.933803i | \(0.383531\pi\) | ||||
−0.357787 | + | 0.933803i | \(0.616469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −336.471 | −0.726719 | −0.363360 | − | 0.931649i | \(-0.618370\pi\) | ||||
−0.363360 | + | 0.931649i | \(0.618370\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 429.727i | − | 0.920186i | −0.887871 | − | 0.460093i | \(-0.847816\pi\) | ||
0.887871 | − | 0.460093i | \(-0.152184\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 266.585 | 0.568412 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 925.275i | − | 1.96449i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 36.4340i | 0.0770274i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 815.763 | 1.71019 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −232.652 | −0.485703 | −0.242852 | − | 0.970063i | \(-0.578083\pi\) | ||||
−0.242852 | + | 0.970063i | \(0.578083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 45.6786 | 0.0949660 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 342.944i | 0.710028i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 293.955 | 0.603604 | 0.301802 | − | 0.953371i | \(-0.402412\pi\) | ||||
0.301802 | + | 0.953371i | \(0.402412\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 669.828i | − | 1.36979i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 554.348i | 1.12902i | 0.825427 | + | 0.564509i | \(0.190934\pi\) | ||||
−0.825427 | + | 0.564509i | \(0.809066\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 989.134i | − | 2.00636i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 238.877i | 0.480638i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 49.4237i | 0.0990454i | 0.998773 | + | 0.0495227i | \(0.0157700\pi\) | ||||
−0.998773 | + | 0.0495227i | \(0.984230\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 314.604 | 0.627952 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 302.048i | − | 0.600493i | −0.953862 | − | 0.300247i | \(-0.902931\pi\) | ||
0.953862 | − | 0.300247i | \(-0.0970690\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −325.297 | −0.641612 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 904.593i | − | 1.77720i | −0.458687 | − | 0.888598i | \(-0.651680\pi\) | ||
0.458687 | − | 0.888598i | \(-0.348320\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 16.4622i | − | 0.0322156i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −172.201 | −0.335674 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 581.683 | 1.12511 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 516.861i | − | 0.995879i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 238.340 | 0.457466 | 0.228733 | − | 0.973489i | \(-0.426542\pi\) | ||||
0.228733 | + | 0.973489i | \(0.426542\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 328.027 | 0.627203 | 0.313601 | − | 0.949555i | \(-0.398464\pi\) | ||||
0.313601 | + | 0.949555i | \(0.398464\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 116.637 | + | 783.247i | 0.221323 | + | 1.48624i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.1515 | 0.0513260 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −491.123 | −0.924902 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 101.193 | 0.189856 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 365.114i | − | 0.679914i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 311.523i | − | 0.577965i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −842.067 | −1.55650 | −0.778250 | − | 0.627955i | \(-0.783892\pi\) | ||||
−0.778250 | + | 0.627955i | \(0.783892\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 15.0379i | − | 0.0276940i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 700.803i | 1.28118i | 0.767885 | + | 0.640588i | \(0.221309\pi\) | ||||
−0.767885 | + | 0.640588i | \(0.778691\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 959.606i | − | 1.74792i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 606.034i | − | 1.09988i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.4793 | −0.0478831 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.2274 | 0.0668355 | 0.0334178 | − | 0.999441i | \(-0.489361\pi\) | ||||
0.0334178 | + | 0.999441i | \(0.489361\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −70.1699 | −0.125528 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 930.693i | 1.65899i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 240.896i | 0.427879i | 0.976847 | + | 0.213939i | \(0.0686295\pi\) | ||||
−0.976847 | + | 0.213939i | \(0.931371\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 171.047i | 0.301670i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 129.301i | 0.227242i | 0.993524 | + | 0.113621i | \(0.0362450\pi\) | ||||
−0.993524 | + | 0.113621i | \(0.963755\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1092.40i | − | 1.91314i | −0.291499 | − | 0.956571i | \(-0.594154\pi\) | ||
0.291499 | − | 0.956571i | \(-0.405846\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 431.955 | 0.753847 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1052.62i | 1.82431i | 0.409850 | + | 0.912153i | \(0.365581\pi\) | ||||
−0.409850 | + | 0.912153i | \(0.634419\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 350.587i | 0.605505i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 333.232i | − | 0.573549i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 575.038i | − | 0.986343i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 625.906 | 1.06628 | 0.533140 | − | 0.846027i | \(-0.321012\pi\) | ||||
0.533140 | + | 0.846027i | \(0.321012\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 71.4626 | + | 479.888i | 0.121329 | + | 0.814751i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1381.60 | −2.33774 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 500.971i | − | 0.844808i | −0.906408 | − | 0.422404i | \(-0.861186\pi\) | ||
0.906408 | − | 0.422404i | \(-0.138814\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 818.907i | 1.37170i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −305.991 | −0.510836 | −0.255418 | − | 0.966831i | \(-0.582213\pi\) | ||||
−0.255418 | + | 0.966831i | \(0.582213\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 592.727i | − | 0.986235i | −0.869963 | − | 0.493117i | \(-0.835857\pi\) | ||
0.869963 | − | 0.493117i | \(-0.164143\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 947.511i | 1.57133i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 853.095i | 1.40543i | 0.711472 | + | 0.702714i | \(0.248029\pi\) | ||||
−0.711472 | + | 0.702714i | \(0.751971\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 563.095 | 0.924623 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1120.29i | 1.83354i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 129.856 | 0.211837 | 0.105919 | − | 0.994375i | \(-0.466222\pi\) | ||||
0.105919 | + | 0.994375i | \(0.466222\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 368.907i | − | 0.597904i | −0.954268 | − | 0.298952i | \(-0.903363\pi\) | ||
0.954268 | − | 0.298952i | \(-0.0966371\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 454.339i | 0.733989i | 0.930223 | + | 0.366995i | \(0.119613\pi\) | ||||
−0.930223 | + | 0.366995i | \(0.880387\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −259.472 | −0.417829 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 369.178 | 0.592581 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 570.227i | 0.909453i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 75.1689 | 0.119505 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 962.590i | 1.52550i | 0.646694 | + | 0.762749i | \(0.276151\pi\) | ||||
−0.646694 | + | 0.762749i | \(0.723849\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −307.429 | −0.485669 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 599.977 | 0.941880 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −849.029 | −1.32868 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 53.6434i | − | 0.0836870i | −0.999124 | − | 0.0418435i | \(-0.986677\pi\) | ||
0.999124 | − | 0.0418435i | \(-0.0133231\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 285.086 | 0.443368 | 0.221684 | − | 0.975119i | \(-0.428845\pi\) | ||||
0.221684 | + | 0.975119i | \(0.428845\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −997.134 | −1.54116 | −0.770582 | − | 0.637340i | \(-0.780035\pi\) | ||||
−0.770582 | + | 0.637340i | \(0.780035\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 346.197i | 0.533431i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −445.887 | + | 66.3994i | −0.684927 | + | 0.101996i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 205.660i | − | 0.314947i | −0.987523 | − | 0.157473i | \(-0.949665\pi\) | ||
0.987523 | − | 0.157473i | \(-0.0503348\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 58.5106 | 0.0890573 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1070.54 | −1.62449 | −0.812245 | − | 0.583316i | \(-0.801755\pi\) | ||||
−0.812245 | + | 0.583316i | \(0.801755\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −773.162 | −1.16968 | −0.584842 | − | 0.811147i | \(-0.698844\pi\) | ||||
−0.584842 | + | 0.811147i | \(0.698844\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1792.46 | −2.70357 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 913.171i | − | 1.36907i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1190.19 | 1.77906 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −676.434 | −1.00810 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1126.90 | −1.67445 | −0.837223 | − | 0.546862i | \(-0.815822\pi\) | ||||
−0.837223 | + | 0.546862i | \(0.815822\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −116.207 | −0.171650 | −0.0858250 | − | 0.996310i | \(-0.527353\pi\) | ||||
−0.0858250 | + | 0.996310i | \(0.527353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −70.1976 | −0.103384 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 743.223i | − | 1.09137i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1016.16i | − | 1.48779i | −0.668296 | − | 0.743895i | \(-0.732976\pi\) | ||
0.668296 | − | 0.743895i | \(-0.267024\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1349.60i | − | 1.96449i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1107.49 | 1.60739 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1008.84 | 1.45997 | 0.729986 | − | 0.683462i | \(-0.239527\pi\) | ||||
0.729986 | + | 0.683462i | \(0.239527\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −296.468 | −0.427803 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 166.524 | 0.238915 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 295.232i | 0.422364i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −594.632 | −0.848262 | −0.424131 | − | 0.905601i | \(-0.639420\pi\) | ||||
−0.424131 | + | 0.905601i | \(0.639420\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46.0553 | 0.0655126 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 390.500i | 0.552335i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 249.172i | − | 0.351442i | −0.984440 | − | 0.175721i | \(-0.943774\pi\) | ||
0.984440 | − | 0.175721i | \(-0.0562257\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 94.1141i | − | 0.132369i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 107.680 | + | 723.095i | 0.151024 | + | 1.01416i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 868.831i | 1.21176i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 667.700i | − | 0.928651i | −0.885665 | − | 0.464325i | \(-0.846297\pi\) | ||
0.885665 | − | 0.464325i | \(-0.153703\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 467.708 | 0.648694 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 174.264i | − | 0.241029i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 393.217i | 0.540876i | 0.962737 | + | 0.270438i | \(0.0871685\pi\) | ||||
−0.962737 | + | 0.270438i | \(0.912831\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1055.57 | −1.44797 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −115.472 | −0.157964 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 584.445i | 0.797333i | 0.917096 | + | 0.398667i | \(0.130527\pi\) | ||||
−0.917096 | + | 0.398667i | \(0.869473\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 667.908 | 0.906253 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 301.506i | 0.407992i | 0.978972 | + | 0.203996i | \(0.0653930\pi\) | ||||
−0.978972 | + | 0.203996i | \(0.934607\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1098.23 | −1.48209 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −988.819 | −1.33085 | −0.665423 | − | 0.746466i | \(-0.731749\pi\) | ||||
−0.665423 | + | 0.746466i | \(0.731749\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1184.39 | 1.58553 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −384.916 | −0.513907 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −315.708 | −0.420384 | −0.210192 | − | 0.977660i | \(-0.567409\pi\) | ||||
−0.210192 | + | 0.977660i | \(0.567409\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 629.605i | − | 0.836129i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −425.088 | −0.561543 | −0.280772 | − | 0.959775i | \(-0.590590\pi\) | ||||
−0.280772 | + | 0.959775i | \(0.590590\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 859.218i | 1.13204i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 148.234i | 0.194788i | 0.995246 | + | 0.0973941i | \(0.0310507\pi\) | ||||
−0.995246 | + | 0.0973941i | \(0.968949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 192.990i | − | 0.252935i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −666.756 | −0.869304 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 311.933 | 0.405635 | 0.202818 | − | 0.979217i | \(-0.434990\pi\) | ||||
0.202818 | + | 0.979217i | \(0.434990\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1235.05i | − | 1.60188i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 864.247 | 1.11804 | 0.559021 | − | 0.829153i | \(-0.311177\pi\) | ||||
0.559021 | + | 0.829153i | \(0.311177\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 42.7922i | 0.0550737i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 102.028 | 0.130973 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 598.487i | 0.766309i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 426.039i | 0.544111i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1348.53 | −1.71350 | −0.856751 | − | 0.515730i | \(-0.827521\pi\) | ||||
−0.856751 | + | 0.515730i | \(0.827521\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1755.21 | −2.22460 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −215.084 | −0.271914 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1302.78i | − | 1.64284i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 349.056 | 0.437962 | 0.218981 | − | 0.975729i | \(-0.429727\pi\) | ||||
0.218981 | + | 0.975729i | \(0.429727\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1843.55i | 2.30733i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1312.15i | 1.63814i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 41.2446i | − | 0.0513632i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 869.605i | − | 1.07758i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 285.974i | − | 0.353491i | −0.984257 | − | 0.176745i | \(-0.943443\pi\) | ||
0.984257 | − | 0.176745i | \(-0.0565569\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 165.775 | 0.204408 | 0.102204 | − | 0.994763i | \(-0.467411\pi\) | ||||
0.102204 | + | 0.994763i | \(0.467411\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1248.98i | 1.53626i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −70.7486 | −0.0865956 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 570.981i | − | 0.697168i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 424.496i | − | 0.517048i | −0.966005 | − | 0.258524i | \(-0.916764\pi\) | ||
0.966005 | − | 0.258524i | \(-0.0832360\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1338.93 | −1.62689 | −0.813445 | − | 0.581642i | \(-0.802410\pi\) | ||||
−0.813445 | + | 0.581642i | \(0.802410\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −699.125 | −0.845375 | −0.422688 | − | 0.906275i | \(-0.638913\pi\) | ||||
−0.422688 | + | 0.906275i | \(0.638913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1419.19i | − | 1.71193i | −0.517032 | − | 0.855966i | \(-0.672963\pi\) | ||
0.517032 | − | 0.855966i | \(-0.327037\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −997.793 | −1.20071 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 987.325 | 1.18526 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −50.2379 | − | 337.359i | −0.0600214 | − | 0.403058i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 411.114 | 0.490004 | 0.245002 | − | 0.969523i | \(-0.421211\pi\) | ||||
0.245002 | + | 0.969523i | \(0.421211\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −658.378 | −0.782851 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1298.68 | −1.54054 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 180.273i | − | 0.212837i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 109.683i | 0.129191i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 69.3961 | 0.0815465 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 683.171i | − | 0.800904i | −0.916318 | − | 0.400452i | \(-0.868853\pi\) | ||
0.916318 | − | 0.400452i | \(-0.131147\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 540.227i | 0.630370i | 0.949030 | + | 0.315185i | \(0.102067\pi\) | ||||
−0.949030 | + | 0.315185i | \(0.897933\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1137.82i | 1.32458i | 0.749246 | + | 0.662291i | \(0.230416\pi\) | ||||
−0.749246 | + | 0.662291i | \(0.769584\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 94.7988i | 0.110103i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 436.646 | 0.505963 | 0.252982 | − | 0.967471i | \(-0.418589\pi\) | ||||
0.252982 | + | 0.967471i | \(0.418589\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1643.29 | −1.89538 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −66.3418 | −0.0763427 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1286.36i | 1.47687i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 249.500i | − | 0.285796i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 73.7636i | − | 0.0841090i | −0.999115 | − | 0.0420545i | \(-0.986610\pi\) | ||
0.999115 | − | 0.0420545i | \(-0.0133903\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 846.938i | 0.963524i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 109.341i | 0.124110i | 0.998073 | + | 0.0620550i | \(0.0197654\pi\) | ||||
−0.998073 | + | 0.0620550i | \(0.980235\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1598.39 | −1.81018 | −0.905089 | − | 0.425221i | \(-0.860196\pi\) | ||||
−0.905089 | + | 0.425221i | \(0.860196\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1514.29i | 1.70721i | 0.520922 | + | 0.853604i | \(0.325588\pi\) | ||||
−0.520922 | + | 0.853604i | \(0.674412\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 101.244i | 0.113885i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 428.545i | 0.480970i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1129.53i | 1.26487i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1654.81 | −1.84482 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1187.28 | − | 176.804i | 1.32067 | − | 0.196668i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1822.49 | 2.02275 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 65.7359i | − | 0.0727973i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1501.96i | − | 1.65596i | −0.560757 | − | 0.827980i | \(-0.689490\pi\) | ||
0.560757 | − | 0.827980i | \(-0.310510\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1387.94 | −1.52688 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 426.662i | 0.468344i | 0.972195 | + | 0.234172i | \(0.0752379\pi\) | ||||
−0.972195 | + | 0.234172i | \(0.924762\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 834.886i | − | 0.914443i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 299.605i | 0.326723i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1692.49 | 1.84167 | 0.920834 | − | 0.389954i | \(-0.127509\pi\) | ||||
0.920834 | + | 0.389954i | \(0.127509\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2220.07i | 2.41050i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1152.65 | −1.24881 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1662.35i | 1.79326i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1196.29i | − | 1.28772i | −0.765144 | − | 0.643859i | \(-0.777332\pi\) | ||
0.765144 | − | 0.643859i | \(-0.222668\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 604.925 | 0.649759 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.9746 | −0.0203372 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1226.11i | 1.30855i | 0.756255 | + | 0.654277i | \(0.227027\pi\) | ||||
−0.756255 | + | 0.654277i | \(0.772973\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1400.49 | −1.49147 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 387.181i | − | 0.411457i | −0.978609 | − | 0.205728i | \(-0.934044\pi\) | ||
0.978609 | − | 0.205728i | \(-0.0659563\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 153.735 | 0.163028 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 385.636 | 0.407218 | 0.203609 | − | 0.979052i | \(-0.434733\pi\) | ||||
0.203609 | + | 0.979052i | \(0.434733\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 79.4350 | 0.0837039 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 889.880i | 0.935730i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −708.546 | −0.743490 | −0.371745 | − | 0.928335i | \(-0.621240\pi\) | ||||
−0.371745 | + | 0.928335i | \(0.621240\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1410.79 | 1.47418 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 146.656i | 0.152926i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −919.303 | + | 280.006i | −0.956611 | + | 0.291369i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 1368.09i | − | 1.42065i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 699.130 | 0.722988 | 0.361494 | − | 0.932374i | \(-0.382267\pi\) | ||||
0.361494 | + | 0.932374i | \(0.382267\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1807.25 | −1.86506 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 872.452 | 0.898509 | 0.449255 | − | 0.893404i | \(-0.351690\pi\) | ||||
0.449255 | + | 0.893404i | \(0.351690\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 722.579 | 0.742630 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 827.633i | 0.847116i | 0.905869 | + | 0.423558i | \(0.139219\pi\) | ||||
−0.905869 | + | 0.423558i | \(0.860781\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 924.946 | 0.944786 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 685.933 | 0.699219 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 265.857 | 0.270454 | 0.135227 | − | 0.990815i | \(-0.456824\pi\) | ||||
0.135227 | + | 0.990815i | \(0.456824\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1049.50 | −1.06332 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −106.604 | −0.107790 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1209.46i | − | 1.22045i | −0.792229 | − | 0.610223i | \(-0.791080\pi\) | ||
0.792229 | − | 0.610223i | \(-0.208920\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2238.28i | 2.25406i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 870.333i | − | 0.872951i | −0.899716 | − | 0.436476i | \(-0.856226\pi\) | ||
0.899716 | − | 0.436476i | \(-0.143774\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −32.3767 | −0.0324091 |
(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 | 3100.3.f.b.1549.1 | 8 | ||
5.2 | odd | 4 | 3100.3.d.b.1301.4 | 4 | |||
5.3 | odd | 4 | 124.3.c.b.61.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 3100.3.f.b.1549.8 | 8 | ||
15.8 | even | 4 | 1116.3.h.d.433.2 | 4 | |||
20.3 | even | 4 | 496.3.e.e.433.4 | 4 | |||
31.30 | odd | 2 | inner | 3100.3.f.b.1549.7 | 8 | ||
155.92 | even | 4 | 3100.3.d.b.1301.1 | 4 | |||
155.123 | even | 4 | 124.3.c.b.61.4 | yes | 4 | ||
155.154 | odd | 2 | inner | 3100.3.f.b.1549.2 | 8 | ||
465.278 | odd | 4 | 1116.3.h.d.433.1 | 4 | |||
620.123 | odd | 4 | 496.3.e.e.433.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.3.c.b.61.1 | ✓ | 4 | 5.3 | odd | 4 | ||
124.3.c.b.61.4 | yes | 4 | 155.123 | even | 4 | ||
496.3.e.e.433.1 | 4 | 620.123 | odd | 4 | |||
496.3.e.e.433.4 | 4 | 20.3 | even | 4 | |||
1116.3.h.d.433.1 | 4 | 465.278 | odd | 4 | |||
1116.3.h.d.433.2 | 4 | 15.8 | even | 4 | |||
3100.3.d.b.1301.1 | 4 | 155.92 | even | 4 | |||
3100.3.d.b.1301.4 | 4 | 5.2 | odd | 4 | |||
3100.3.f.b.1549.1 | 8 | 1.1 | even | 1 | trivial | ||
3100.3.f.b.1549.2 | 8 | 155.154 | odd | 2 | inner | ||
3100.3.f.b.1549.7 | 8 | 31.30 | odd | 2 | inner | ||
3100.3.f.b.1549.8 | 8 | 5.4 | even | 2 | inner |