Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(301,1500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1500, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.m (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.9775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 301.6 | ||
Character | \(\chi\) | \(=\) | 1500.301 |
Dual form | 1500.2.m.c.1201.6 |
$q$-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 \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.309017 | − | 0.951057i | 0.178411 | − | 0.549093i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.62675 | 1.74875 | 0.874373 | − | 0.485254i | \(-0.161273\pi\) | ||||
0.874373 | + | 0.485254i | \(0.161273\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00366 | − | 2.90883i | 1.20715 | − | 0.877045i | 0.212180 | − | 0.977231i | \(-0.431944\pi\) |
0.994969 | + | 0.100185i | \(0.0319435\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.04414 | + | 2.21170i | 0.844294 | + | 0.613415i | 0.923567 | − | 0.383438i | \(-0.125260\pi\) |
−0.0792730 | + | 0.996853i | \(0.525260\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.831378 | − | 2.55872i | −0.201639 | − | 0.620580i | −0.999835 | − | 0.0181824i | \(-0.994212\pi\) |
0.798196 | − | 0.602398i | \(-0.205788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.81426 | + | 5.58371i | 0.416219 | + | 1.28099i | 0.911156 | + | 0.412062i | \(0.135191\pi\) |
−0.494937 | + | 0.868929i | \(0.664809\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.42974 | − | 4.40030i | 0.311996 | − | 0.960224i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.40285 | + | 3.92540i | −1.12657 | + | 0.818502i | −0.985192 | − | 0.171453i | \(-0.945154\pi\) |
−0.141379 | + | 0.989955i | \(0.545154\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.809017 | + | 0.587785i | −0.155695 | + | 0.113119i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.370972 | − | 1.14173i | 0.0688878 | − | 0.212015i | −0.910686 | − | 0.413099i | \(-0.864446\pi\) |
0.979574 | + | 0.201084i | \(0.0644464\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.02048 | + | 3.14072i | 0.183284 | + | 0.564090i | 0.999915 | − | 0.0130708i | \(-0.00416068\pi\) |
−0.816631 | + | 0.577161i | \(0.804161\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.52926 | − | 4.70659i | −0.266210 | − | 0.819311i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.51873 | − | 1.10342i | −0.249677 | − | 0.181401i | 0.455907 | − | 0.890028i | \(-0.349315\pi\) |
−0.705584 | + | 0.708627i | \(0.749315\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.04414 | − | 2.21170i | 0.487453 | − | 0.354156i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.45366 | + | 1.78269i | 0.383198 | + | 0.278410i | 0.762663 | − | 0.646797i | \(-0.223892\pi\) |
−0.379464 | + | 0.925206i | \(0.623892\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.6626 | −1.62603 | −0.813014 | − | 0.582244i | \(-0.802175\pi\) | ||||
−0.813014 | + | 0.582244i | \(0.802175\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.0801015 | − | 0.246527i | 0.0116840 | − | 0.0359597i | −0.945045 | − | 0.326942i | \(-0.893982\pi\) |
0.956729 | + | 0.290982i | \(0.0939820\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.4068 | 2.05811 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.69040 | −0.376731 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.02731 | − | 9.31711i | 0.415833 | − | 1.27980i | −0.495670 | − | 0.868511i | \(-0.665078\pi\) |
0.911504 | − | 0.411292i | \(-0.134922\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.87106 | 0.777641 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.78643 | + | 5.65717i | 1.01371 | + | 0.736501i | 0.964983 | − | 0.262311i | \(-0.0844847\pi\) |
0.0487233 | + | 0.998812i | \(0.484485\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.07552 | + | 3.68758i | −0.649854 | + | 0.472147i | −0.863222 | − | 0.504825i | \(-0.831557\pi\) |
0.213367 | + | 0.976972i | \(0.431557\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.74312 | − | 2.71953i | −0.471589 | − | 0.342629i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.791247 | + | 2.43521i | 0.0966662 | + | 0.297508i | 0.987684 | − | 0.156460i | \(-0.0500082\pi\) |
−0.891018 | + | 0.453968i | \(0.850008\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.06370 | + | 6.35143i | 0.248441 | + | 0.764622i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.68143 | − | 8.25259i | 0.318227 | − | 0.979403i | −0.656178 | − | 0.754606i | \(-0.727828\pi\) |
0.974406 | − | 0.224797i | \(-0.0721718\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.94381 | + | 2.86534i | −0.461588 | + | 0.335363i | −0.794154 | − | 0.607717i | \(-0.792086\pi\) |
0.332566 | + | 0.943080i | \(0.392086\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.5239 | − | 13.4584i | 2.11100 | − | 1.53373i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.85443 | − | 11.8627i | 0.433657 | − | 1.33466i | −0.460800 | − | 0.887504i | \(-0.652437\pi\) |
0.894457 | − | 0.447155i | \(-0.147563\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.74724 | − | 8.45513i | −0.301549 | − | 0.928071i | −0.980943 | − | 0.194298i | \(-0.937757\pi\) |
0.679394 | − | 0.733774i | \(-0.262243\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.971218 | − | 0.705631i | −0.104125 | − | 0.0756516i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.7934 | + | 8.56841i | −1.25010 | + | 0.908249i | −0.998228 | − | 0.0595118i | \(-0.981046\pi\) |
−0.251870 | + | 0.967761i | \(0.581046\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.0845 | + | 10.2330i | 1.47646 | + | 1.07271i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.30235 | 0.342437 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.23202 | + | 3.79176i | −0.125092 | + | 0.384995i | −0.993918 | − | 0.110123i | \(-0.964875\pi\) |
0.868825 | + | 0.495119i | \(0.164875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.94880 | −0.497373 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.36896 | 0.932246 | 0.466123 | − | 0.884720i | \(-0.345650\pi\) | ||||
0.466123 | + | 0.884720i | \(0.345650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.22123 | − | 9.91391i | 0.317397 | − | 0.976847i | −0.657360 | − | 0.753577i | \(-0.728327\pi\) |
0.974757 | − | 0.223270i | \(-0.0716731\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.220683 | −0.0213342 | −0.0106671 | − | 0.999943i | \(-0.503396\pi\) | ||||
−0.0106671 | + | 0.999943i | \(0.503396\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.40941 | − | 3.93017i | −0.518127 | − | 0.376442i | 0.297771 | − | 0.954637i | \(-0.403757\pi\) |
−0.815898 | + | 0.578196i | \(0.803757\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.51873 | + | 1.10342i | −0.144151 | + | 0.104732i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.77355 | − | 5.64782i | −0.731274 | − | 0.531302i | 0.158692 | − | 0.987328i | \(-0.449272\pi\) |
−0.889966 | + | 0.456026i | \(0.849272\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.16276 | − | 3.57861i | −0.107497 | − | 0.330842i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.84658 | − | 11.8385i | −0.352615 | − | 1.08524i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.16882 | − | 12.8303i | 0.378984 | − | 1.16639i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.45366 | − | 1.78269i | 0.221239 | − | 0.160740i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9380 | + | 9.40003i | −1.14806 | + | 0.834118i | −0.988222 | − | 0.153025i | \(-0.951098\pi\) |
−0.159842 | + | 0.987143i | \(0.551098\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.29492 | + | 10.1407i | −0.290101 | + | 0.892840i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.80795 | − | 11.7197i | −0.332702 | − | 1.02395i | −0.967843 | − | 0.251556i | \(-0.919058\pi\) |
0.635140 | − | 0.772397i | \(-0.280942\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.39411 | + | 25.8344i | 0.727862 | + | 2.24013i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.60698 | + | 3.34717i | 0.393601 | + | 0.285968i | 0.766930 | − | 0.641731i | \(-0.221784\pi\) |
−0.373329 | + | 0.927699i | \(0.621784\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.5598 | − | 10.5783i | 1.23495 | − | 0.897242i | 0.237697 | − | 0.971339i | \(-0.423607\pi\) |
0.997251 | + | 0.0740969i | \(0.0236074\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.209709 | − | 0.152362i | −0.0176606 | − | 0.0128312i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.6212 | 1.55718 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.45195 | − | 13.7017i | 0.367190 | − | 1.13010i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.09001 | −0.0892972 | −0.0446486 | − | 0.999003i | \(-0.514217\pi\) | ||||
−0.0446486 | + | 0.999003i | \(0.514217\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3789 | 0.926004 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.831378 | + | 2.55872i | −0.0672129 | + | 0.206860i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.98415 | −0.317970 | −0.158985 | − | 0.987281i | \(-0.550822\pi\) | ||||
−0.158985 | + | 0.987281i | \(0.550822\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.92560 | − | 5.75829i | −0.628541 | − | 0.456662i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.9976 | + | 18.1618i | −1.97009 | + | 1.43135i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.6620 | − | 12.8322i | −1.38339 | − | 1.00509i | −0.996554 | − | 0.0829441i | \(-0.973568\pi\) |
−0.386837 | − | 0.922148i | \(-0.626432\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.78015 | − | 14.7118i | −0.369899 | − | 1.13843i | −0.946856 | − | 0.321658i | \(-0.895760\pi\) |
0.576957 | − | 0.816775i | \(-0.304240\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.357976 | + | 1.10174i | 0.0275366 | + | 0.0847490i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.81426 | − | 5.58371i | 0.138740 | − | 0.426997i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8911 | + | 10.0925i | −1.05612 | + | 0.767317i | −0.973367 | − | 0.229253i | \(-0.926372\pi\) |
−0.0827547 | + | 0.996570i | \(0.526372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.78643 | − | 5.65717i | 0.585264 | − | 0.425219i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.46392 | + | 13.7385i | −0.333649 | + | 1.02687i | 0.633734 | + | 0.773551i | \(0.281521\pi\) |
−0.967384 | + | 0.253316i | \(0.918479\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.83071 | + | 11.7897i | 0.284734 | + | 0.876322i | 0.986478 | + | 0.163893i | \(0.0524051\pi\) |
−0.701744 | + | 0.712429i | \(0.747595\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.93868 | + | 5.96664i | 0.143311 | + | 0.441066i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.7714 | − | 7.82590i | −0.787685 | − | 0.572287i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.74312 | + | 2.71953i | −0.272272 | + | 0.197817i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.33930 | + | 0.973056i | 0.0969081 | + | 0.0704078i | 0.635184 | − | 0.772361i | \(-0.280924\pi\) |
−0.538276 | + | 0.842769i | \(0.680924\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.3253 | 1.17512 | 0.587560 | − | 0.809181i | \(-0.300089\pi\) | ||||
0.587560 | + | 0.809181i | \(0.300089\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.21264 | + | 12.9652i | −0.300138 | + | 0.923730i | 0.681309 | + | 0.731996i | \(0.261411\pi\) |
−0.981447 | + | 0.191734i | \(0.938589\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.07817 | −0.430870 | −0.215435 | − | 0.976518i | \(-0.569117\pi\) | ||||
−0.215435 | + | 0.976518i | \(0.569117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.56053 | 0.180606 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.71639 | − | 5.28252i | 0.120467 | − | 0.370760i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.67829 | 0.464173 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.5057 | + | 17.0779i | 1.62593 | + | 1.18130i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8200 | + | 10.0408i | −0.951409 | + | 0.691239i | −0.951140 | − | 0.308761i | \(-0.900086\pi\) |
−0.000268984 | 1.00000i | \(0.500086\pi\) | ||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.02007 | − | 5.10038i | −0.481008 | − | 0.349472i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.72151 | + | 14.5313i | 0.320517 | + | 0.986450i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.50640 | + | 4.63622i | 0.101793 | + | 0.313287i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.12828 | − | 9.62787i | 0.210431 | − | 0.647640i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.634100 | + | 0.460700i | −0.0424624 | + | 0.0308508i | −0.608814 | − | 0.793313i | \(-0.708354\pi\) |
0.566352 | + | 0.824164i | \(0.308354\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.3755 | + | 14.0771i | −1.28600 | + | 0.934331i | −0.999716 | − | 0.0238153i | \(-0.992419\pi\) |
−0.286280 | + | 0.958146i | \(0.592419\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.71005 | + | 5.26299i | −0.113003 | + | 0.347788i | −0.991525 | − | 0.129914i | \(-0.958530\pi\) |
0.878522 | + | 0.477702i | \(0.158530\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.07551 | − | 21.7762i | −0.465535 | − | 1.43277i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.280508 | + | 0.863314i | 0.0183767 | + | 0.0565576i | 0.959824 | − | 0.280602i | \(-0.0905340\pi\) |
−0.941448 | + | 0.337159i | \(0.890534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.0910 | − | 7.33156i | −0.655482 | − | 0.476236i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.09227 | − | 6.60592i | 0.588130 | − | 0.427302i | −0.253516 | − | 0.967331i | \(-0.581587\pi\) |
0.841646 | + | 0.540030i | \(0.181587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.3840 | + | 11.9037i | 1.05539 | + | 0.766783i | 0.973229 | − | 0.229837i | \(-0.0738193\pi\) |
0.0821564 | + | 0.996619i | \(0.473819\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.82663 | + | 21.0102i | −0.434368 | + | 1.33685i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.89025 | −0.563397 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.6919 | −1.93725 | −0.968627 | − | 0.248520i | \(-0.920056\pi\) | ||||
−0.968627 | + | 0.248520i | \(0.920056\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.2129 | + | 31.4319i | −0.642077 | + | 1.97611i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.77543 | 0.297883 | 0.148941 | − | 0.988846i | \(-0.452413\pi\) | ||||
0.148941 | + | 0.988846i | \(0.452413\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.02676 | − | 5.10524i | −0.436622 | − | 0.317224i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.971218 | + | 0.705631i | −0.0601169 | + | 0.0436775i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.978638 | − | 0.711022i | −0.0603454 | − | 0.0438435i | 0.557204 | − | 0.830376i | \(-0.311874\pi\) |
−0.617549 | + | 0.786532i | \(0.711874\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.50468 | + | 13.8640i | 0.275682 | + | 0.848461i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.88763 | − | 24.2756i | −0.480917 | − | 1.48011i | −0.837808 | − | 0.545965i | \(-0.816163\pi\) |
0.356891 | − | 0.934146i | \(-0.383837\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.81499 | + | 5.58596i | −0.110253 | + | 0.339323i | −0.990927 | − | 0.134399i | \(-0.957090\pi\) |
0.880675 | + | 0.473722i | \(0.157090\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.0845 | − | 10.2330i | 0.852432 | − | 0.619328i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.96855 | − | 2.88332i | 0.238447 | − | 0.173242i | −0.462144 | − | 0.886805i | \(-0.652920\pi\) |
0.700591 | + | 0.713563i | \(0.252920\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.02048 | − | 3.14072i | 0.0610946 | − | 0.188030i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.400257 | − | 1.23186i | −0.0238773 | − | 0.0734868i | 0.938408 | − | 0.345530i | \(-0.112301\pi\) |
−0.962285 | + | 0.272043i | \(0.912301\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.34149 | + | 28.7501i | 0.555294 | + | 1.70902i | 0.695166 | + | 0.718849i | \(0.255331\pi\) |
−0.139873 | + | 0.990169i | \(0.544669\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.3525 | + | 8.24807i | 0.670116 | + | 0.486868i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.89744 | − | 5.73783i | 0.464555 | − | 0.337519i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.22546 | + | 2.34344i | 0.189080 | + | 0.137375i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.06831 | 0.471356 | 0.235678 | − | 0.971831i | \(-0.424269\pi\) | ||||
0.235678 | + | 0.971831i | \(0.424269\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.52926 | + | 4.70659i | −0.0887368 | + | 0.273104i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −25.1289 | −1.45324 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −49.3331 | −2.84351 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.89517 | − | 8.91041i | 0.166323 | − | 0.511890i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.7750 | −0.843255 | −0.421628 | − | 0.906769i | \(-0.638541\pi\) | ||||
−0.421628 | + | 0.906769i | \(0.638541\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.43328 | − | 6.12713i | −0.479752 | − | 0.348560i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.40552 | − | 5.38043i | 0.419929 | − | 0.305096i | −0.357680 | − | 0.933844i | \(-0.616432\pi\) |
0.777609 | + | 0.628748i | \(0.216432\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.7238 | + | 7.79128i | 0.606144 | + | 0.440389i | 0.848054 | − | 0.529909i | \(-0.177774\pi\) |
−0.241910 | + | 0.970299i | \(0.577774\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.244293 | − | 0.751858i | −0.0137209 | − | 0.0422286i | 0.943962 | − | 0.330055i | \(-0.107067\pi\) |
−0.957683 | + | 0.287827i | \(0.907067\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.83587 | − | 5.65021i | −0.102789 | − | 0.316351i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.0681947 | + | 0.209882i | −0.00380626 | + | 0.0117145i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.7788 | − | 9.28434i | 0.711032 | − | 0.516595i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.40941 | + | 3.93017i | −0.299141 | + | 0.217339i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.370610 | − | 1.14062i | 0.0204324 | − | 0.0628844i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.04253 | − | 3.20858i | −0.0573026 | − | 0.176359i | 0.918308 | − | 0.395866i | \(-0.129555\pi\) |
−0.975611 | + | 0.219506i | \(0.929555\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.580102 | + | 1.78537i | 0.0317894 | + | 0.0978376i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.6157 | + | 10.6189i | 0.796166 | + | 0.578449i | 0.909787 | − | 0.415076i | \(-0.136245\pi\) |
−0.113621 | + | 0.993524i | \(0.536245\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.77355 | + | 5.64782i | −0.422201 | + | 0.306747i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.2215 | + | 9.60597i | 0.715983 | + | 0.520192i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 34.2694 | 1.85037 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.943191 | + | 2.90284i | −0.0506332 | + | 0.155833i | −0.973176 | − | 0.230062i | \(-0.926107\pi\) |
0.922543 | + | 0.385895i | \(0.126107\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.628744 | −0.0336559 | −0.0168280 | − | 0.999858i | \(-0.505357\pi\) | ||||
−0.0168280 | + | 0.999858i | \(0.505357\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.76277 | −0.200842 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.83721 | − | 17.9651i | 0.310683 | − | 0.956184i | −0.666812 | − | 0.745226i | \(-0.732342\pi\) |
0.977495 | − | 0.210958i | \(-0.0676584\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.4478 | −0.658807 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.4087 | − | 17.0074i | −1.23546 | − | 0.897617i | −0.238176 | − | 0.971222i | \(-0.576550\pi\) |
−0.997287 | + | 0.0736053i | \(0.976550\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.5149 | + | 9.09264i | −0.658681 | + | 0.478560i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.9141 | − | 7.92957i | −0.572843 | − | 0.416195i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.66342 | − | 5.11949i | −0.0868299 | − | 0.267235i | 0.898209 | − | 0.439570i | \(-0.144869\pi\) |
−0.985038 | + | 0.172334i | \(0.944869\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.937217 | − | 2.88446i | −0.0487895 | − | 0.150159i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.0066 | − | 43.1079i | 0.727187 | − | 2.23805i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.89714 | + | 6.46415i | −0.460677 | + | 0.334701i | −0.793797 | − | 0.608183i | \(-0.791899\pi\) |
0.333120 | + | 0.942884i | \(0.391899\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.65447 | − | 2.65513i | 0.188215 | − | 0.136746i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.18405 | − | 6.72183i | 0.112187 | − | 0.345277i | −0.879163 | − | 0.476522i | \(-0.841897\pi\) |
0.991350 | + | 0.131245i | \(0.0418974\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.94189 | + | 15.2096i | 0.253181 | + | 0.779210i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.50346 | − | 7.70484i | −0.127921 | − | 0.393699i | 0.866501 | − | 0.499175i | \(-0.166363\pi\) |
−0.994422 | + | 0.105476i | \(0.966363\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.62621 | + | 6.26731i | 0.438495 | + | 0.318585i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.7325 | + | 19.4223i | −1.35539 | + | 0.984750i | −0.356669 | + | 0.934231i | \(0.616088\pi\) |
−0.998723 | + | 0.0505192i | \(0.983912\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.5358 | + | 10.5609i | 0.735107 | + | 0.534086i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.3228 | −0.621603 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.82155 | − | 11.7615i | 0.191798 | − | 0.590294i | −0.808201 | − | 0.588907i | \(-0.799559\pi\) |
0.999999 | − | 0.00138688i | \(-0.000441458\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 27.1639 | 1.35990 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.7983 | −0.738993 | −0.369496 | − | 0.929232i | \(-0.620470\pi\) | ||||
−0.369496 | + | 0.929232i | \(0.620470\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.83984 | + | 11.8178i | −0.191276 | + | 0.588687i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.29012 | −0.460494 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.1618 | + | 13.9219i | 0.947491 | + | 0.688392i | 0.950212 | − | 0.311604i | \(-0.100866\pi\) |
−0.00272132 | + | 0.999996i | \(0.500866\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.60698 | − | 3.34717i | 0.227246 | − | 0.165104i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.0258 | + | 26.1743i | 1.77272 | + | 1.28795i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.56136 | − | 17.1161i | −0.272341 | − | 0.838179i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.477059 | + | 1.46824i | 0.0233058 | + | 0.0717280i | 0.962033 | − | 0.272933i | \(-0.0879938\pi\) |
−0.938727 | + | 0.344661i | \(0.887994\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.43760 | + | 16.7352i | −0.265013 | + | 0.815625i | 0.726678 | + | 0.686978i | \(0.241063\pi\) |
−0.991691 | + | 0.128647i | \(0.958937\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.209709 | + | 0.152362i | −0.0101964 | + | 0.00740810i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.4832 | + | 17.0615i | −1.13643 | + | 0.825665i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.75426 | − | 17.7098i | 0.277818 | − | 0.855037i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.83527 | + | 14.8814i | 0.232907 | + | 0.716814i | 0.997392 | + | 0.0721724i | \(0.0229932\pi\) |
−0.764485 | + | 0.644641i | \(0.777007\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.0707586 | + | 0.217772i | 0.00340044 | + | 0.0104655i | 0.952742 | − | 0.303780i | \(-0.0982486\pi\) |
−0.949342 | + | 0.314245i | \(0.898249\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −31.7204 | − | 23.0462i | −1.51739 | − | 1.10245i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.7111 | + | 11.4147i | −0.749848 | + | 0.544796i | −0.895780 | − | 0.444498i | \(-0.853382\pi\) |
0.145932 | + | 0.989295i | \(0.453382\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.6553 | − | 8.46810i | −0.555016 | − | 0.403243i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.7980 | −0.608051 | −0.304026 | − | 0.952664i | \(-0.598331\pi\) | ||||
−0.304026 | + | 0.952664i | \(0.598331\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.336832 | + | 1.03666i | −0.0159316 | + | 0.0490325i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.1499 | −0.998124 | −0.499062 | − | 0.866566i | \(-0.666322\pi\) | ||||
−0.499062 | + | 0.866566i | \(0.666322\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.0092 | 0.706755 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.51628 | − | 10.8220i | 0.165209 | − | 0.508462i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.97118 | −0.419654 | −0.209827 | − | 0.977739i | \(-0.567290\pi\) | ||||
−0.209827 | + | 0.977739i | \(0.567290\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.17658 | + | 1.58137i | 0.101594 | + | 0.0738123i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.2764 | + | 16.1847i | −1.03751 | + | 0.753797i | −0.969799 | − | 0.243907i | \(-0.921571\pi\) |
−0.0677146 | + | 0.997705i | \(0.521571\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.7859 | − | 17.2815i | −1.10543 | − | 0.803140i | −0.123489 | − | 0.992346i | \(-0.539409\pi\) |
−0.981937 | + | 0.189206i | \(0.939409\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.09785 | + | 12.6119i | 0.189626 | + | 0.583609i | 0.999997 | − | 0.00230768i | \(-0.000734558\pi\) |
−0.810371 | + | 0.585917i | \(0.800735\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.66090 | + | 11.2671i | 0.169045 | + | 0.520266i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.23117 | + | 3.78915i | −0.0567293 | + | 0.174595i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −42.6893 | + | 31.0156i | −1.96286 | + | 1.42610i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.92560 | + | 5.75829i | −0.362888 | + | 0.263654i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.58057 | + | 17.1752i | −0.254983 | + | 0.784757i | 0.738850 | + | 0.673870i | \(0.235369\pi\) |
−0.993833 | + | 0.110887i | \(0.964631\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.18279 | − | 6.71793i | −0.0995266 | − | 0.306311i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.54824 | + | 29.3865i | 0.434460 | + | 1.33713i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.3725 | − | 8.26258i | −0.515336 | − | 0.374413i | 0.299508 | − | 0.954094i | \(-0.403177\pi\) |
−0.814844 | + | 0.579681i | \(0.803177\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.6620 | + | 12.8322i | −0.798701 | + | 0.580290i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.0310 | + | 16.0065i | 0.994247 | + | 0.722363i | 0.960847 | − | 0.277079i | \(-0.0893665\pi\) |
0.0334000 | + | 0.999442i | \(0.489366\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.22980 | −0.145463 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.4063 | − | 38.1827i | 0.556499 | − | 1.71273i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.17654 | −0.366032 | −0.183016 | − | 0.983110i | \(-0.558586\pi\) | ||||
−0.183016 | + | 0.983110i | \(0.558586\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.4689 | −0.691099 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.07311 | − | 9.45805i | 0.137023 | − | 0.421714i | −0.858876 | − | 0.512183i | \(-0.828837\pi\) |
0.995899 | + | 0.0904697i | \(0.0288368\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.15844 | 0.0514479 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.9758 | − | 10.1540i | −0.619464 | − | 0.450067i | 0.233270 | − | 0.972412i | \(-0.425057\pi\) |
−0.852734 | + | 0.522345i | \(0.825057\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.2470 | + | 13.2572i | −0.807200 | + | 0.586465i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.74979 | − | 3.45092i | −0.209708 | − | 0.152362i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.396406 | − | 1.22001i | −0.0174339 | − | 0.0536561i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.30593 | + | 16.3300i | 0.232905 | + | 0.716807i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.43786 | + | 10.5807i | −0.150615 | + | 0.463547i | −0.997690 | − | 0.0679269i | \(-0.978362\pi\) |
0.847075 | + | 0.531474i | \(0.178362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.03609 | − | 2.20585i | 0.132759 | − | 0.0964551i | −0.519424 | − | 0.854517i | \(-0.673853\pi\) |
0.652183 | + | 0.758062i | \(0.273853\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.18781 | − | 5.22225i | 0.313106 | − | 0.227485i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.67462 | − | 20.5424i | 0.290201 | − | 0.893146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.97415 | − | 9.15350i | −0.129067 | − | 0.397228i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.52653 | + | 10.8535i | 0.152751 | + | 0.470119i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.6867 | + | 8.49089i | 0.504318 | + | 0.366409i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 57.6799 | − | 41.9069i | 2.48445 | − | 1.80506i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.2752 | − | 11.0981i | −0.656731 | − | 0.477143i | 0.208826 | − | 0.977953i | \(-0.433036\pi\) |
−0.865557 | + | 0.500810i | \(0.833036\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.3964 | 0.531982 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.0479926 | − | 0.147706i | 0.00205201 | − | 0.00631545i | −0.950025 | − | 0.312173i | \(-0.898943\pi\) |
0.952077 | + | 0.305858i | \(0.0989431\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.27369 | 0.267755 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.04815 | 0.300261 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.8335 | − | 54.8858i | 0.758356 | − | 2.33398i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.0371 | −0.806626 | −0.403313 | − | 0.915062i | \(-0.632141\pi\) | ||||
−0.403313 | + | 0.915062i | \(0.632141\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.4584 | − | 23.5824i | −1.37285 | − | 0.997430i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.7714 | + | 7.82590i | −0.454770 | + | 0.330410i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.1369 | + | 18.2630i | 1.05939 | + | 0.769694i | 0.973976 | − | 0.226652i | \(-0.0727779\pi\) |
0.0854166 | + | 0.996345i | \(0.472778\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.42974 | + | 4.40030i | 0.0600436 | + | 0.184795i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.1573 | + | 37.4162i | 0.509659 | + | 1.56857i | 0.792794 | + | 0.609490i | \(0.208626\pi\) |
−0.283135 | + | 0.959080i | \(0.591374\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.78632 | − | 27.0415i | 0.367696 | − | 1.13165i | −0.580580 | − | 0.814203i | \(-0.697174\pi\) |
0.948276 | − | 0.317448i | \(-0.102826\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.33930 | − | 0.973056i | 0.0559499 | − | 0.0406500i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.1701 | − | 13.2014i | 0.756433 | − | 0.549581i | −0.141381 | − | 0.989955i | \(-0.545154\pi\) |
0.897814 | + | 0.440375i | \(0.145154\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.04479 | − | 15.5263i | 0.209654 | − | 0.645250i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.7108 | − | 39.1198i | −0.527332 | − | 1.62296i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.9815 | − | 46.1085i | −0.620472 | − | 1.90962i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.0114 | + | 9.45335i | 0.537039 | + | 0.390182i | 0.822984 | − | 0.568064i | \(-0.192308\pi\) |
−0.285945 | + | 0.958246i | \(0.592308\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.6854 | + | 11.3961i | −0.646307 | + | 0.469570i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.0288 | + | 8.01291i | 0.453665 | + | 0.329607i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.4648 | 0.840389 | 0.420194 | − | 0.907434i | \(-0.361962\pi\) | ||||
0.420194 | + | 0.907434i | \(0.361962\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.87826 | + | 5.78068i | −0.0768720 | + | 0.236588i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.5688 | 0.758699 | 0.379349 | − | 0.925253i | \(-0.376148\pi\) | ||||
0.379349 | + | 0.925253i | \(0.376148\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 47.2047 | 1.92552 | 0.962761 | − | 0.270355i | \(-0.0871409\pi\) | ||||
0.962761 | + | 0.270355i | \(0.0871409\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.791247 | − | 2.43521i | 0.0322221 | − | 0.0991693i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.0786576 | 0.00319261 | 0.00159631 | − | 0.999999i | \(-0.499492\pi\) | ||||
0.00159631 | + | 0.999999i | \(0.499492\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.49358 | − | 3.26478i | −0.182089 | − | 0.132295i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.789085 | − | 0.573304i | 0.0319230 | − | 0.0231934i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.29654 | − | 3.12162i | −0.173536 | − | 0.126081i | 0.497627 | − | 0.867391i | \(-0.334205\pi\) |
−0.671163 | + | 0.741310i | \(0.734205\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.40411 | + | 28.9429i | 0.378595 | + | 1.16520i | 0.941021 | + | 0.338349i | \(0.109868\pi\) |
−0.562426 | + | 0.826848i | \(0.690132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.77918 | − | 30.0972i | −0.393058 | − | 1.20971i | −0.930463 | − | 0.366385i | \(-0.880595\pi\) |
0.537405 | − | 0.843324i | \(-0.319405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.06370 | − | 6.35143i | 0.0828136 | − | 0.254874i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −54.5651 | + | 39.6439i | −2.18610 | + | 1.58830i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.5057 | − | 17.0779i | 0.938728 | − | 0.682026i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.56070 | + | 4.80335i | −0.0622293 | + | 0.191522i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.4722 | − | 32.2301i | −0.416891 | − | 1.28306i | −0.910548 | − | 0.413403i | \(-0.864340\pi\) |
0.493657 | − | 0.869657i | \(-0.335660\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.27877 | + | 16.2464i | 0.209812 | + | 0.645736i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43.8564 | + | 31.8635i | 1.73765 | + | 1.26248i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.02007 | + | 5.10038i | −0.277710 | + | 0.201768i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.6699 | + | 28.8219i | 1.56687 | + | 1.13840i | 0.930080 | + | 0.367358i | \(0.119737\pi\) |
0.636788 | + | 0.771039i | \(0.280263\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.2509 | −0.562000 | −0.281000 | − | 0.959708i | \(-0.590666\pi\) | ||||
−0.281000 | + | 0.959708i | \(0.590666\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.0820 | − | 40.2623i | 0.514307 | − | 1.58287i | −0.270233 | − | 0.962795i | \(-0.587101\pi\) |
0.784539 | − | 0.620079i | \(-0.212899\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 47.6300 | 1.86964 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.2791 | 0.598836 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.5328 | − | 44.7274i | 0.568713 | − | 1.75032i | −0.0879407 | − | 0.996126i | \(-0.528029\pi\) |
0.656654 | − | 0.754192i | \(-0.271971\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.87481 | 0.190185 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.05013 | + | 6.57531i | 0.352543 | + | 0.256138i | 0.749935 | − | 0.661511i | \(-0.230085\pi\) |
−0.397392 | + | 0.917649i | \(0.630085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.7102 | − | 27.3981i | 1.46676 | − | 1.06566i | 0.485218 | − | 0.874393i | \(-0.338740\pi\) |
0.981538 | − | 0.191268i | \(-0.0612599\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.18995 | − | 5.95035i | −0.318071 | − | 0.231092i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.47746 | + | 7.62483i | 0.0959276 | + | 0.295235i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.242204 | + | 0.745429i | 0.00936417 | + | 0.0288199i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.59412 | + | 29.5277i | −0.370377 | + | 1.13990i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.1110 | − | 8.07264i | 0.428299 | − | 0.311178i | −0.352669 | − | 0.935748i | \(-0.614726\pi\) |
0.780968 | + | 0.624570i | \(0.214726\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.7888 | + | 21.6428i | −1.14488 | + | 0.831801i | −0.987791 | − | 0.155784i | \(-0.950210\pi\) |
−0.157085 | + | 0.987585i | \(0.550210\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.70024 | + | 17.5435i | −0.218755 | + | 0.673259i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.40078 | + | 22.7772i | 0.283598 | + | 0.872826i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.29850 | − | 28.6179i | −0.355797 | − | 1.09503i | −0.955546 | − | 0.294843i | \(-0.904733\pi\) |
0.599748 | − | 0.800189i | \(-0.295267\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.47697 | + | 3.25271i | 0.170807 | + | 0.124098i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.8222 | − | 21.6671i | 1.13614 | − | 0.825451i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.76839 | + | 4.91752i | 0.257482 | + | 0.187071i | 0.709036 | − | 0.705172i | \(-0.249130\pi\) |
−0.451554 | + | 0.892244i | \(0.649130\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −22.8968 | −0.869779 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.52148 | − | 7.76033i | 0.0955080 | − | 0.293943i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.907742 | 0.0343340 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.42495 | −0.129359 | −0.0646794 | − | 0.997906i | \(-0.520602\pi\) | ||||
−0.0646794 | + | 0.997906i | \(0.520602\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.40581 | − | 10.4820i | 0.128453 | − | 0.395336i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 43.3478 | 1.63026 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.0330 | + | 29.0857i | 1.50347 | + | 1.09234i | 0.968973 | + | 0.247168i | \(0.0794998\pi\) |
0.534499 | + | 0.845169i | \(0.320500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.0910 | + | 7.33156i | −0.378443 | + | 0.274955i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.8421 | − | 12.9630i | −0.668191 | − | 0.485469i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.47294 | − | 10.6886i | −0.129699 | − | 0.399173i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.08148 | + | 24.8722i | 0.301388 | + | 0.927578i | 0.981000 | + | 0.194006i | \(0.0621481\pi\) |
−0.679612 | + | 0.733572i | \(0.737852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.9038 | − | 45.8692i | 0.555046 | − | 1.70826i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.3840 | − | 11.9037i | 0.609327 | − | 0.442702i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.0059 | − | 20.3475i | 1.03868 | − | 0.754647i | 0.0686545 | − | 0.997640i | \(-0.478129\pi\) |
0.970028 | + | 0.242994i | \(0.0781294\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.86463 | + | 27.2825i | 0.327870 | + | 1.00908i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.39704 | + | 16.6104i | 0.199344 | + | 0.613518i | 0.999898 | + | 0.0142577i | \(0.00453852\pi\) |
−0.800554 | + | 0.599260i | \(0.795461\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.2515 | + | 7.44814i | 0.377618 | + | 0.274356i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.2358 | + | 11.7960i | −0.597243 | + | 0.433922i | −0.844899 | − | 0.534926i | \(-0.820340\pi\) |
0.247656 | + | 0.968848i | \(0.420340\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.8724 | + | 12.9850i | 0.656557 | + | 0.477017i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.84644 | 0.214485 | 0.107243 | − | 0.994233i | \(-0.465798\pi\) | ||||
0.107243 | + | 0.994233i | \(0.465798\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.74724 | + | 8.45513i | −0.100516 | + | 0.309357i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.02104 | −0.0373081 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.7925 | −1.19662 | −0.598308 | − | 0.801266i | \(-0.704160\pi\) | ||||
−0.598308 | + | 0.801266i | \(0.704160\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.48431 | + | 29.1897i | −0.345627 | + | 1.06373i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.6371 | 0.822759 | 0.411379 | − | 0.911464i | \(-0.365047\pi\) | ||||
0.411379 | + | 0.911464i | \(0.365047\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 26.7376 | + | 19.4260i | 0.970513 | + | 0.705119i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.3923 | − | 21.3547i | 1.06547 | − | 0.774109i | 0.0903767 | − | 0.995908i | \(-0.471193\pi\) |
0.975092 | + | 0.221799i | \(0.0711929\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.0280 | − | 18.1839i | −0.906073 | − | 0.658301i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.1910 | + | 34.4425i | 0.404085 | + | 1.24365i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.51902 | + | 13.9081i | 0.162960 | + | 0.501539i | 0.998880 | − | 0.0473119i | \(-0.0150655\pi\) |
−0.835920 | + | 0.548851i | \(0.815065\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.47569 | − | 4.54170i | 0.0531456 | − | 0.163565i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.6953 | + | 17.9422i | −0.888229 | + | 0.645336i | −0.935416 | − | 0.353550i | \(-0.884975\pi\) |
0.0471864 | + | 0.998886i | \(0.484975\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.02676 | + | 5.10524i | −0.252084 | + | 0.183150i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.50245 | + | 16.9348i | −0.197146 | + | 0.606752i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.2699 | − | 40.8404i | −0.474833 | − | 1.46138i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.370972 | + | 1.14173i | 0.0132575 | + | 0.0408023i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.7644 | − | 28.8905i | −1.41745 | − | 1.02984i | −0.992186 | − | 0.124766i | \(-0.960182\pi\) |
−0.425262 | − | 0.905070i | \(-0.639818\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.978638 | + | 0.711022i | −0.0348404 | + | 0.0253130i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.9663 | − | 26.1310i | −1.27881 | − | 0.929112i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.6065 | −0.838290 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.7613 | + | 42.3529i | −0.487450 | + | 1.50022i | 0.340951 | + | 0.940081i | \(0.389251\pi\) |
−0.828401 | + | 0.560136i | \(0.810749\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.697388 | −0.0246718 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.5774 | 0.515069 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.45487 | + | 22.9437i | −0.263077 | + | 0.809667i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.5249 | −0.898519 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.5060 | + | 17.8046i | 0.861584 | + | 0.625978i | 0.928316 | − | 0.371793i | \(-0.121257\pi\) |
−0.0667312 | + | 0.997771i | \(0.521257\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.05382 | + | 3.67182i | −0.177464 | + | 0.128935i | −0.672971 | − | 0.739669i | \(-0.734982\pi\) |
0.495507 | + | 0.868604i | \(0.334982\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.75170 | + | 3.45231i | 0.166649 | + | 0.121078i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.3447 | − | 59.5367i | −0.676784 | − | 2.08293i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.37980 | − | 16.5573i | −0.187985 | − | 0.578559i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.95524 | + | 18.3284i | −0.207839 | + | 0.639664i | 0.791745 | + | 0.610851i | \(0.209173\pi\) |
−0.999585 | + | 0.0288127i | \(0.990827\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.11414 | − | 4.44218i | 0.213126 | − | 0.154845i | −0.476101 | − | 0.879391i | \(-0.657950\pi\) |
0.689227 | + | 0.724546i | \(0.257950\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.3821 | − | 18.4412i | 0.882621 | − | 0.641262i | −0.0513225 | − | 0.998682i | \(-0.516344\pi\) |
0.933944 | + | 0.357420i | \(0.116344\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.55625 | − | 26.3334i | 0.297171 | − | 0.914597i | −0.685313 | − | 0.728249i | \(-0.740335\pi\) |
0.982484 | − | 0.186349i | \(-0.0596654\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.51585 | − | 4.66531i | −0.0525843 | − | 0.161838i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.9775 | − | 36.8629i | −0.414996 | − | 1.27723i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.67165 | − | 1.94107i | −0.0923459 | − | 0.0670932i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.5642 | − | 22.2062i | 1.05519 | − | 0.766643i | 0.0819999 | − | 0.996632i | \(-0.473869\pi\) |
0.973193 | + | 0.229990i | \(0.0738693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.2956 | + | 16.1987i | 0.768812 | + | 0.558575i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.29526 | −0.0446110 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.2881 | − | 59.3626i | 0.662747 | − | 2.03972i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.2297 | 1.03748 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.5368 | 0.429756 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.2552 | + | 46.9508i | −0.522329 | + | 1.60756i | 0.247208 | + | 0.968962i | \(0.420487\pi\) |
−0.769537 | + | 0.638602i | \(0.779513\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.7692 | −0.538667 | −0.269333 | − | 0.963047i | \(-0.586803\pi\) | ||||
−0.269333 | + | 0.963047i | \(0.586803\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.60223 | − | 5.52335i | −0.259385 | − | 0.188454i | 0.450491 | − | 0.892781i | \(-0.351249\pi\) |
−0.709876 | + | 0.704327i | \(0.751249\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.3525 | − | 8.24807i | 0.386892 | − | 0.281093i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.4575 | + | 10.5040i | 0.492140 | + | 0.357560i | 0.806007 | − | 0.591907i | \(-0.201625\pi\) |
−0.313867 | + | 0.949467i | \(0.601625\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.01655 | − | 9.28400i | −0.102448 | − | 0.315301i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.0748 | − | 58.7061i | −0.647068 | − | 1.99147i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.97728 | + | 9.16312i | −0.100881 | + | 0.310481i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.22546 | − | 2.34344i | 0.109165 | − | 0.0793133i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.3238 | − | 10.4069i | 0.483681 | − | 0.351415i | −0.319068 | − | 0.947732i | \(-0.603370\pi\) |
0.802749 | + | 0.596317i | \(0.203370\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.49325 | − | 7.67342i | 0.0840951 | − | 0.258818i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.82007 | − | 30.2231i | −0.330847 | − | 1.01824i | −0.968732 | − | 0.248110i | \(-0.920191\pi\) |
0.637885 | − | 0.770131i | \(-0.279809\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.6950 | + | 32.9158i | 0.359916 | + | 1.10771i | 0.953104 | + | 0.302643i | \(0.0978689\pi\) |
−0.593188 | + | 0.805064i | \(0.702131\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.0735 | − | 16.7639i | −0.774732 | − | 0.562876i | 0.128661 | − | 0.991689i | \(-0.458932\pi\) |
−0.903393 | + | 0.428813i | \(0.858932\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −59.8610 | + | 43.4916i | −2.00767 | + | 1.45866i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.00366 | + | 2.90883i | 0.134128 | + | 0.0974495i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.52186 | 0.0509271 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.76524 | + | 23.8990i | −0.259274 | + | 0.797963i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.96444 | 0.132221 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.3567 | −0.878069 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.2448 | + | 46.9185i | −0.507314 | + | 1.56135i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.01754 | 0.233013 | 0.116507 | − | 0.993190i | \(-0.462830\pi\) | ||||
0.116507 | + | 0.993190i | \(0.462830\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.57965 | − | 5.50693i | −0.251401 | − | 0.182653i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.9145 | − | 12.2891i | 0.560403 | − | 0.407157i | −0.271203 | − | 0.962522i | \(-0.587422\pi\) |
0.831606 | + | 0.555365i | \(0.187422\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.5936 | − | 25.8602i | −1.17797 | − | 0.855849i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.6184 | − | 54.2240i | −0.581812 | − | 1.79063i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.4658 | + | 56.8320i | 0.609132 | + | 1.87471i | 0.465406 | + | 0.885097i | \(0.345908\pi\) |
0.143726 | + | 0.989618i | \(0.454092\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.56573 | + | 14.0519i | −0.150446 | + | 0.463025i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26.4149 | − | 19.1916i | 0.869458 | − | 0.631698i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.43328 | + | 6.12713i | −0.276985 | + | 0.201241i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.4320 | + | 38.2618i | −0.407881 | + | 1.25533i | 0.510585 | + | 0.859828i | \(0.329429\pi\) |
−0.918466 | + | 0.395501i | \(0.870571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.1376 | + | 80.4434i | 0.856626 | + | 2.63642i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.82866 | − | 8.70572i | −0.0926061 | − | 0.285012i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.9780 | + | 29.0457i | 1.30602 | + | 0.948881i | 0.999995 | − | 0.00314114i | \(-0.000999859\pi\) |
0.306028 | + | 0.952022i | \(0.401000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.7238 | − | 7.79128i | 0.349957 | − | 0.254259i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.0130 | − | 13.0872i | −0.587207 | − | 0.426631i | 0.254108 | − | 0.967176i | \(-0.418218\pi\) |
−0.841315 | + | 0.540545i | \(0.818218\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.2546 | −0.659579 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.0251 | + | 33.9316i | −0.358266 | + | 1.10263i | 0.595825 | + | 0.803114i | \(0.296825\pi\) |
−0.954091 | + | 0.299516i | \(0.903175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.3428 | −0.595433 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.790550 | −0.0256354 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.867341 | − | 2.66940i | 0.0280959 | − | 0.0864704i | −0.936025 | − | 0.351933i | \(-0.885525\pi\) |
0.964121 | + | 0.265462i | \(0.0855246\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.94099 | −0.192045 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.3153 | + | 15.4865i | 0.688308 | + | 0.500085i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.2568 | − | 11.8113i | 0.524413 | − | 0.381008i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.178536 | + | 0.129714i | 0.00575324 | + | 0.00417998i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.56243 | − | 10.9640i | −0.114560 | − | 0.352580i | 0.877295 | − | 0.479952i | \(-0.159346\pi\) |
−0.991855 | + | 0.127372i | \(0.959346\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.88107 | − | 15.0224i | −0.156803 | − | 0.482589i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.15578 | − | 22.0232i | 0.229640 | − | 0.706759i | −0.768148 | − | 0.640273i | \(-0.778821\pi\) |
0.997787 | − | 0.0664858i | \(-0.0211787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 67.3646 | − | 48.9433i | 2.15961 | − | 1.56905i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.68304 | + | 4.85551i | −0.213809 | + | 0.155342i | −0.689536 | − | 0.724252i | \(-0.742185\pi\) |
0.475726 | + | 0.879593i | \(0.342185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.2927 | + | 68.6100i | −0.712479 | + | 2.19278i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.06621 | + | 6.35914i | 0.0659690 | + | 0.203032i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.11506 | − | 18.8202i | −0.195040 | − | 0.600271i | −0.999976 | − | 0.00690994i | \(-0.997800\pi\) |
0.804936 | − | 0.593361i | \(-0.202200\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.970269 | − | 0.704941i | −0.0308840 | − | 0.0224385i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57.6083 | − | 41.8549i | 1.83184 | − | 1.33091i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.3036 | − | 12.5718i | −0.549666 | − | 0.399355i | 0.277997 | − | 0.960582i | \(-0.410330\pi\) |
−0.827662 | + | 0.561227i | \(0.810330\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.37370 | −0.107061 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.43350 | + | 16.7226i | −0.172081 | + | 0.529610i | −0.999488 | − | 0.0319923i | \(-0.989815\pi\) |
0.827407 | + | 0.561602i | \(0.189815\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.87725 | 0.0593935 |
(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 | 1500.2.m.c.301.6 | 24 | ||
5.2 | odd | 4 | 300.2.o.a.289.2 | yes | 24 | ||
5.3 | odd | 4 | 1500.2.o.c.949.6 | 24 | |||
5.4 | even | 2 | 1500.2.m.d.301.1 | 24 | |||
15.2 | even | 4 | 900.2.w.c.289.3 | 24 | |||
25.3 | odd | 20 | 7500.2.d.g.1249.13 | 24 | |||
25.4 | even | 10 | 7500.2.a.m.1.1 | 12 | |||
25.9 | even | 10 | 1500.2.m.d.1201.1 | 24 | |||
25.12 | odd | 20 | 1500.2.o.c.49.6 | 24 | |||
25.13 | odd | 20 | 300.2.o.a.109.2 | ✓ | 24 | ||
25.16 | even | 5 | inner | 1500.2.m.c.1201.6 | 24 | ||
25.21 | even | 5 | 7500.2.a.n.1.12 | 12 | |||
25.22 | odd | 20 | 7500.2.d.g.1249.12 | 24 | |||
75.38 | even | 20 | 900.2.w.c.109.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.109.2 | ✓ | 24 | 25.13 | odd | 20 | ||
300.2.o.a.289.2 | yes | 24 | 5.2 | odd | 4 | ||
900.2.w.c.109.3 | 24 | 75.38 | even | 20 | |||
900.2.w.c.289.3 | 24 | 15.2 | even | 4 | |||
1500.2.m.c.301.6 | 24 | 1.1 | even | 1 | trivial | ||
1500.2.m.c.1201.6 | 24 | 25.16 | even | 5 | inner | ||
1500.2.m.d.301.1 | 24 | 5.4 | even | 2 | |||
1500.2.m.d.1201.1 | 24 | 25.9 | even | 10 | |||
1500.2.o.c.49.6 | 24 | 25.12 | odd | 20 | |||
1500.2.o.c.949.6 | 24 | 5.3 | odd | 4 | |||
7500.2.a.m.1.1 | 12 | 25.4 | even | 10 | |||
7500.2.a.n.1.12 | 12 | 25.21 | even | 5 | |||
7500.2.d.g.1249.12 | 24 | 25.22 | odd | 20 | |||
7500.2.d.g.1249.13 | 24 | 25.3 | odd | 20 |