Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,3,Mod(91,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("115.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.13352304014\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 34x^{4} + 50x^{3} + 690x^{2} - 600x + 4725 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.4 | ||
Root | \(0.396209 - 2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 115.91 |
Dual form | 115.3.d.a.91.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.500000 | −0.250000 | − | 0.968246i | \(-0.580431\pi\) | ||||
−0.250000 | + | 0.968246i | \(0.580431\pi\) | |||||||
\(3\) | 0.396209 | 0.132070 | 0.0660348 | − | 0.997817i | \(-0.478965\pi\) | ||||
0.0660348 | + | 0.997817i | \(0.478965\pi\) | |||||||
\(4\) | −3.00000 | −0.750000 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | −0.396209 | −0.0660348 | ||||||||
\(7\) | − | 8.16531i | − | 1.16647i | −0.812303 | − | 0.583236i | \(-0.801786\pi\) | ||
0.812303 | − | 0.583236i | \(-0.198214\pi\) | |||||||
\(8\) | 7.00000 | 0.875000 | ||||||||
\(9\) | −8.84302 | −0.982558 | ||||||||
\(10\) | − | 2.23607i | − | 0.223607i | ||||||
\(11\) | − | 18.9885i | − | 1.72622i | −0.505012 | − | 0.863112i | \(-0.668512\pi\) | ||
0.505012 | − | 0.863112i | \(-0.331488\pi\) | |||||||
\(12\) | −1.18863 | −0.0990522 | ||||||||
\(13\) | −18.6354 | −1.43350 | −0.716748 | − | 0.697333i | \(-0.754370\pi\) | ||||
−0.716748 | + | 0.697333i | \(0.754370\pi\) | |||||||
\(14\) | 8.16531i | 0.583236i | ||||||||
\(15\) | 0.885949i | 0.0590633i | ||||||||
\(16\) | 5.00000 | 0.312500 | ||||||||
\(17\) | 5.57206i | 0.327768i | 0.986480 | + | 0.163884i | \(0.0524023\pi\) | ||||
−0.986480 | + | 0.163884i | \(0.947598\pi\) | |||||||
\(18\) | 8.84302 | 0.491279 | ||||||||
\(19\) | − | 5.25110i | − | 0.276374i | −0.990406 | − | 0.138187i | \(-0.955873\pi\) | ||
0.990406 | − | 0.138187i | \(-0.0441274\pi\) | |||||||
\(20\) | − | 6.70820i | − | 0.335410i | ||||||
\(21\) | − | 3.23517i | − | 0.154056i | ||||||
\(22\) | 18.9885i | 0.863112i | ||||||||
\(23\) | −18.4468 | − | 13.7374i | −0.802035 | − | 0.597277i | ||||
\(24\) | 2.77346 | 0.115561 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 18.6354 | 0.716748 | ||||||||
\(27\) | −7.06956 | −0.261835 | ||||||||
\(28\) | 24.4959i | 0.874854i | ||||||||
\(29\) | 11.6227 | 0.400784 | 0.200392 | − | 0.979716i | \(-0.435778\pi\) | ||||
0.200392 | + | 0.979716i | \(0.435778\pi\) | |||||||
\(30\) | − | 0.885949i | − | 0.0295316i | ||||||
\(31\) | 49.5291 | 1.59771 | 0.798856 | − | 0.601523i | \(-0.205439\pi\) | ||||
0.798856 | + | 0.601523i | \(0.205439\pi\) | |||||||
\(32\) | −33.0000 | −1.03125 | ||||||||
\(33\) | − | 7.52339i | − | 0.227982i | ||||||
\(34\) | − | 5.57206i | − | 0.163884i | ||||||
\(35\) | 18.2582 | 0.521662 | ||||||||
\(36\) | 26.5291 | 0.736918 | ||||||||
\(37\) | 29.7470i | 0.803974i | 0.915645 | + | 0.401987i | \(0.131680\pi\) | ||||
−0.915645 | + | 0.401987i | \(0.868320\pi\) | |||||||
\(38\) | 5.25110i | 0.138187i | ||||||||
\(39\) | −7.38352 | −0.189321 | ||||||||
\(40\) | 15.6525i | 0.391312i | ||||||||
\(41\) | −10.4595 | −0.255110 | −0.127555 | − | 0.991832i | \(-0.540713\pi\) | ||||
−0.127555 | + | 0.991832i | \(0.540713\pi\) | |||||||
\(42\) | 3.23517i | 0.0770278i | ||||||||
\(43\) | 57.2218i | 1.33074i | 0.746514 | + | 0.665369i | \(0.231726\pi\) | ||||
−0.746514 | + | 0.665369i | \(0.768274\pi\) | |||||||
\(44\) | 56.9654i | 1.29467i | ||||||||
\(45\) | − | 19.7736i | − | 0.439413i | ||||||
\(46\) | 18.4468 | + | 13.7374i | 0.401018 | + | 0.298638i | ||||
\(47\) | −15.2709 | −0.324912 | −0.162456 | − | 0.986716i | \(-0.551942\pi\) | ||||
−0.162456 | + | 0.986716i | \(0.551942\pi\) | |||||||
\(48\) | 1.98104 | 0.0412717 | ||||||||
\(49\) | −17.6723 | −0.360658 | ||||||||
\(50\) | 5.00000 | 0.100000 | ||||||||
\(51\) | 2.20770i | 0.0432882i | ||||||||
\(52\) | 55.9063 | 1.07512 | ||||||||
\(53\) | − | 40.2492i | − | 0.759419i | −0.925106 | − | 0.379710i | \(-0.876024\pi\) | ||
0.925106 | − | 0.379710i | \(-0.123976\pi\) | |||||||
\(54\) | 7.06956 | 0.130918 | ||||||||
\(55\) | 42.4595 | 0.771991 | ||||||||
\(56\) | − | 57.1572i | − | 1.02066i | ||||||
\(57\) | − | 2.08053i | − | 0.0365005i | ||||||
\(58\) | −11.6227 | −0.200392 | ||||||||
\(59\) | −27.7872 | −0.470970 | −0.235485 | − | 0.971878i | \(-0.575668\pi\) | ||||
−0.235485 | + | 0.971878i | \(0.575668\pi\) | |||||||
\(60\) | − | 2.65785i | − | 0.0442975i | ||||||
\(61\) | − | 110.631i | − | 1.81362i | −0.421536 | − | 0.906812i | \(-0.638509\pi\) | ||
0.421536 | − | 0.906812i | \(-0.361491\pi\) | |||||||
\(62\) | −49.5291 | −0.798856 | ||||||||
\(63\) | 72.2060i | 1.14613i | ||||||||
\(64\) | 13.0000 | 0.203125 | ||||||||
\(65\) | − | 41.6701i | − | 0.641078i | ||||||
\(66\) | 7.52339i | 0.113991i | ||||||||
\(67\) | 35.0627i | 0.523324i | 0.965160 | + | 0.261662i | \(0.0842706\pi\) | ||||
−0.965160 | + | 0.261662i | \(0.915729\pi\) | |||||||
\(68\) | − | 16.7162i | − | 0.245826i | ||||||
\(69\) | −7.30879 | − | 5.44286i | −0.105924 | − | 0.0788821i | ||||
\(70\) | −18.2582 | −0.260831 | ||||||||
\(71\) | −70.4595 | −0.992387 | −0.496194 | − | 0.868212i | \(-0.665269\pi\) | ||||
−0.496194 | + | 0.868212i | \(0.665269\pi\) | |||||||
\(72\) | −61.9011 | −0.859738 | ||||||||
\(73\) | −0.377252 | −0.00516783 | −0.00258392 | − | 0.999997i | \(-0.500822\pi\) | ||||
−0.00258392 | + | 0.999997i | \(0.500822\pi\) | |||||||
\(74\) | − | 29.7470i | − | 0.401987i | ||||||
\(75\) | −1.98104 | −0.0264139 | ||||||||
\(76\) | 15.7533i | 0.207280i | ||||||||
\(77\) | −155.047 | −2.01359 | ||||||||
\(78\) | 7.38352 | 0.0946605 | ||||||||
\(79\) | − | 102.657i | − | 1.29946i | −0.760164 | − | 0.649731i | \(-0.774882\pi\) | ||
0.760164 | − | 0.649731i | \(-0.225118\pi\) | |||||||
\(80\) | 11.1803i | 0.139754i | ||||||||
\(81\) | 76.7861 | 0.947977 | ||||||||
\(82\) | 10.4595 | 0.127555 | ||||||||
\(83\) | − | 116.845i | − | 1.40777i | −0.710313 | − | 0.703886i | \(-0.751447\pi\) | ||
0.710313 | − | 0.703886i | \(-0.248553\pi\) | |||||||
\(84\) | 9.70550i | 0.115542i | ||||||||
\(85\) | −12.4595 | −0.146582 | ||||||||
\(86\) | − | 57.2218i | − | 0.665369i | ||||||
\(87\) | 4.60503 | 0.0529314 | ||||||||
\(88\) | − | 132.919i | − | 1.51045i | ||||||
\(89\) | − | 49.6338i | − | 0.557683i | −0.960337 | − | 0.278841i | \(-0.910050\pi\) | ||
0.960337 | − | 0.278841i | \(-0.0899504\pi\) | |||||||
\(90\) | 19.7736i | 0.219707i | ||||||||
\(91\) | 152.164i | 1.67213i | ||||||||
\(92\) | 55.3404 | + | 41.2121i | 0.601526 | + | 0.447958i | ||||
\(93\) | 19.6238 | 0.211009 | ||||||||
\(94\) | 15.2709 | 0.162456 | ||||||||
\(95\) | 11.7418 | 0.123598 | ||||||||
\(96\) | −13.0749 | −0.136197 | ||||||||
\(97\) | 69.6107i | 0.717636i | 0.933408 | + | 0.358818i | \(0.116820\pi\) | ||||
−0.933408 | + | 0.358818i | \(0.883180\pi\) | |||||||
\(98\) | 17.6723 | 0.180329 | ||||||||
\(99\) | 167.915i | 1.69611i | ||||||||
\(100\) | 15.0000 | 0.150000 | ||||||||
\(101\) | 146.919 | 1.45464 | 0.727322 | − | 0.686297i | \(-0.240765\pi\) | ||||
0.727322 | + | 0.686297i | \(0.240765\pi\) | |||||||
\(102\) | − | 2.20770i | − | 0.0216441i | ||||||
\(103\) | 120.016i | 1.16520i | 0.812759 | + | 0.582600i | \(0.197964\pi\) | ||||
−0.812759 | + | 0.582600i | \(0.802036\pi\) | |||||||
\(104\) | −130.448 | −1.25431 | ||||||||
\(105\) | 7.23405 | 0.0688957 | ||||||||
\(106\) | 40.2492i | 0.379710i | ||||||||
\(107\) | − | 191.386i | − | 1.78865i | −0.447415 | − | 0.894326i | \(-0.647655\pi\) | ||
0.447415 | − | 0.894326i | \(-0.352345\pi\) | |||||||
\(108\) | 21.2087 | 0.196377 | ||||||||
\(109\) | 134.741i | 1.23616i | 0.786115 | + | 0.618080i | \(0.212089\pi\) | ||||
−0.786115 | + | 0.618080i | \(0.787911\pi\) | |||||||
\(110\) | −42.4595 | −0.385995 | ||||||||
\(111\) | 11.7860i | 0.106180i | ||||||||
\(112\) | − | 40.8265i | − | 0.364523i | ||||||
\(113\) | − | 86.9688i | − | 0.769635i | −0.922993 | − | 0.384818i | \(-0.874264\pi\) | ||
0.922993 | − | 0.384818i | \(-0.125736\pi\) | |||||||
\(114\) | 2.08053i | 0.0182503i | ||||||||
\(115\) | 30.7177 | − | 41.2483i | 0.267110 | − | 0.358681i | ||||
\(116\) | −34.8682 | −0.300588 | ||||||||
\(117\) | 164.794 | 1.40849 | ||||||||
\(118\) | 27.7872 | 0.235485 | ||||||||
\(119\) | 45.4976 | 0.382332 | ||||||||
\(120\) | 6.20165i | 0.0516804i | ||||||||
\(121\) | −239.562 | −1.97985 | ||||||||
\(122\) | 110.631i | 0.906812i | ||||||||
\(123\) | −4.14414 | −0.0336922 | ||||||||
\(124\) | −148.587 | −1.19828 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | − | 72.2060i | − | 0.573063i | ||||||
\(127\) | 71.0835 | 0.559713 | 0.279856 | − | 0.960042i | \(-0.409713\pi\) | ||||
0.279856 | + | 0.960042i | \(0.409713\pi\) | |||||||
\(128\) | 119.000 | 0.929688 | ||||||||
\(129\) | 22.6718i | 0.175750i | ||||||||
\(130\) | 41.6701i | 0.320539i | ||||||||
\(131\) | 72.1391 | 0.550680 | 0.275340 | − | 0.961347i | \(-0.411210\pi\) | ||||
0.275340 | + | 0.961347i | \(0.411210\pi\) | |||||||
\(132\) | 22.5702i | 0.170986i | ||||||||
\(133\) | −42.8768 | −0.322382 | ||||||||
\(134\) | − | 35.0627i | − | 0.261662i | ||||||
\(135\) | − | 15.8080i | − | 0.117096i | ||||||
\(136\) | 39.0044i | 0.286797i | ||||||||
\(137\) | 56.1317i | 0.409721i | 0.978791 | + | 0.204860i | \(0.0656740\pi\) | ||||
−0.978791 | + | 0.204860i | \(0.934326\pi\) | |||||||
\(138\) | 7.30879 | + | 5.44286i | 0.0529622 | + | 0.0394410i | ||||
\(139\) | 266.091 | 1.91432 | 0.957161 | − | 0.289555i | \(-0.0935074\pi\) | ||||
0.957161 | + | 0.289555i | \(0.0935074\pi\) | |||||||
\(140\) | −54.7746 | −0.391247 | ||||||||
\(141\) | −6.05045 | −0.0429110 | ||||||||
\(142\) | 70.4595 | 0.496194 | ||||||||
\(143\) | 353.858i | 2.47453i | ||||||||
\(144\) | −44.2151 | −0.307049 | ||||||||
\(145\) | 25.9893i | 0.179236i | ||||||||
\(146\) | 0.377252 | 0.00258392 | ||||||||
\(147\) | −7.00190 | −0.0476320 | ||||||||
\(148\) | − | 89.2411i | − | 0.602980i | ||||||
\(149\) | − | 222.352i | − | 1.49230i | −0.665780 | − | 0.746148i | \(-0.731901\pi\) | ||
0.665780 | − | 0.746148i | \(-0.268099\pi\) | |||||||
\(150\) | 1.98104 | 0.0132070 | ||||||||
\(151\) | −194.788 | −1.28999 | −0.644995 | − | 0.764187i | \(-0.723141\pi\) | ||||
−0.644995 | + | 0.764187i | \(0.723141\pi\) | |||||||
\(152\) | − | 36.7577i | − | 0.241827i | ||||||
\(153\) | − | 49.2738i | − | 0.322051i | ||||||
\(154\) | 155.047 | 1.00680 | ||||||||
\(155\) | 110.750i | 0.714518i | ||||||||
\(156\) | 22.1506 | 0.141991 | ||||||||
\(157\) | − | 106.214i | − | 0.676520i | −0.941053 | − | 0.338260i | \(-0.890162\pi\) | ||
0.941053 | − | 0.338260i | \(-0.109838\pi\) | |||||||
\(158\) | 102.657i | 0.649731i | ||||||||
\(159\) | − | 15.9471i | − | 0.100296i | ||||||
\(160\) | − | 73.7902i | − | 0.461189i | ||||||
\(161\) | −112.170 | + | 150.624i | −0.696707 | + | 0.935552i | ||||
\(162\) | −76.7861 | −0.473989 | ||||||||
\(163\) | 39.9063 | 0.244824 | 0.122412 | − | 0.992479i | \(-0.460937\pi\) | ||||
0.122412 | + | 0.992479i | \(0.460937\pi\) | |||||||
\(164\) | 31.3785 | 0.191332 | ||||||||
\(165\) | 16.8228 | 0.101956 | ||||||||
\(166\) | 116.845i | 0.703886i | ||||||||
\(167\) | 79.7872 | 0.477768 | 0.238884 | − | 0.971048i | \(-0.423218\pi\) | ||||
0.238884 | + | 0.971048i | \(0.423218\pi\) | |||||||
\(168\) | − | 22.6462i | − | 0.134799i | ||||||
\(169\) | 178.279 | 1.05491 | ||||||||
\(170\) | 12.4595 | 0.0732912 | ||||||||
\(171\) | 46.4356i | 0.271553i | ||||||||
\(172\) | − | 171.665i | − | 0.998054i | ||||||
\(173\) | −298.323 | −1.72441 | −0.862205 | − | 0.506560i | \(-0.830917\pi\) | ||||
−0.862205 | + | 0.506560i | \(0.830917\pi\) | |||||||
\(174\) | −4.60503 | −0.0264657 | ||||||||
\(175\) | 40.8265i | 0.233295i | ||||||||
\(176\) | − | 94.9423i | − | 0.539445i | ||||||
\(177\) | −11.0095 | −0.0622008 | ||||||||
\(178\) | 49.6338i | 0.278841i | ||||||||
\(179\) | 48.1391 | 0.268934 | 0.134467 | − | 0.990918i | \(-0.457068\pi\) | ||||
0.134467 | + | 0.990918i | \(0.457068\pi\) | |||||||
\(180\) | 59.3208i | 0.329560i | ||||||||
\(181\) | 34.5224i | 0.190731i | 0.995442 | + | 0.0953657i | \(0.0304020\pi\) | ||||
−0.995442 | + | 0.0953657i | \(0.969598\pi\) | |||||||
\(182\) | − | 152.164i | − | 0.836066i | ||||||
\(183\) | − | 43.8330i | − | 0.239524i | ||||||
\(184\) | −129.128 | − | 96.1616i | −0.701781 | − | 0.522617i | ||||
\(185\) | −66.5164 | −0.359548 | ||||||||
\(186\) | −19.6238 | −0.105505 | ||||||||
\(187\) | 105.805 | 0.565801 | ||||||||
\(188\) | 45.8126 | 0.243684 | ||||||||
\(189\) | 57.7251i | 0.305424i | ||||||||
\(190\) | −11.7418 | −0.0617990 | ||||||||
\(191\) | 172.912i | 0.905299i | 0.891689 | + | 0.452650i | \(0.149521\pi\) | ||||
−0.891689 | + | 0.452650i | \(0.850479\pi\) | |||||||
\(192\) | 5.15071 | 0.0268266 | ||||||||
\(193\) | −114.255 | −0.591997 | −0.295998 | − | 0.955188i | \(-0.595652\pi\) | ||||
−0.295998 | + | 0.955188i | \(0.595652\pi\) | |||||||
\(194\) | − | 69.6107i | − | 0.358818i | ||||||
\(195\) | − | 16.5101i | − | 0.0846669i | ||||||
\(196\) | 53.0168 | 0.270494 | ||||||||
\(197\) | 139.191 | 0.706554 | 0.353277 | − | 0.935519i | \(-0.385067\pi\) | ||||
0.353277 | + | 0.935519i | \(0.385067\pi\) | |||||||
\(198\) | − | 167.915i | − | 0.848057i | ||||||
\(199\) | − | 245.347i | − | 1.23290i | −0.787395 | − | 0.616449i | \(-0.788571\pi\) | ||
0.787395 | − | 0.616449i | \(-0.211429\pi\) | |||||||
\(200\) | −35.0000 | −0.175000 | ||||||||
\(201\) | 13.8922i | 0.0691152i | ||||||||
\(202\) | −146.919 | −0.727322 | ||||||||
\(203\) | − | 94.9033i | − | 0.467504i | ||||||
\(204\) | − | 6.62309i | − | 0.0324661i | ||||||
\(205\) | − | 23.3881i | − | 0.114089i | ||||||
\(206\) | − | 120.016i | − | 0.582600i | ||||||
\(207\) | 163.125 | + | 121.480i | 0.788046 | + | 0.586859i | ||||
\(208\) | −93.1772 | −0.447967 | ||||||||
\(209\) | −99.7103 | −0.477083 | ||||||||
\(210\) | −7.23405 | −0.0344479 | ||||||||
\(211\) | −184.076 | −0.872399 | −0.436199 | − | 0.899850i | \(-0.643676\pi\) | ||||
−0.436199 | + | 0.899850i | \(0.643676\pi\) | |||||||
\(212\) | 120.748i | 0.569564i | ||||||||
\(213\) | −27.9167 | −0.131064 | ||||||||
\(214\) | 191.386i | 0.894326i | ||||||||
\(215\) | −127.952 | −0.595124 | ||||||||
\(216\) | −49.4869 | −0.229106 | ||||||||
\(217\) | − | 404.420i | − | 1.86369i | ||||||
\(218\) | − | 134.741i | − | 0.618080i | ||||||
\(219\) | −0.149470 | −0.000682513 | ||||||||
\(220\) | −127.378 | −0.578993 | ||||||||
\(221\) | − | 103.838i | − | 0.469854i | ||||||
\(222\) | − | 11.7860i | − | 0.0530902i | ||||||
\(223\) | −31.1064 | −0.139490 | −0.0697452 | − | 0.997565i | \(-0.522219\pi\) | ||||
−0.0697452 | + | 0.997565i | \(0.522219\pi\) | |||||||
\(224\) | 269.455i | 1.20292i | ||||||||
\(225\) | 44.2151 | 0.196512 | ||||||||
\(226\) | 86.9688i | 0.384818i | ||||||||
\(227\) | 192.411i | 0.847627i | 0.905750 | + | 0.423813i | \(0.139309\pi\) | ||||
−0.905750 | + | 0.423813i | \(0.860691\pi\) | |||||||
\(228\) | 6.24159i | 0.0273754i | ||||||||
\(229\) | − | 365.836i | − | 1.59754i | −0.601638 | − | 0.798769i | \(-0.705485\pi\) | ||
0.601638 | − | 0.798769i | \(-0.294515\pi\) | |||||||
\(230\) | −30.7177 | + | 41.2483i | −0.133555 | + | 0.179341i | ||||
\(231\) | −61.4308 | −0.265934 | ||||||||
\(232\) | 81.3592 | 0.350686 | ||||||||
\(233\) | 235.271 | 1.00975 | 0.504873 | − | 0.863194i | \(-0.331539\pi\) | ||||
0.504873 | + | 0.863194i | \(0.331539\pi\) | |||||||
\(234\) | −164.794 | −0.704246 | ||||||||
\(235\) | − | 34.1467i | − | 0.145305i | ||||||
\(236\) | 83.3617 | 0.353228 | ||||||||
\(237\) | − | 40.6738i | − | 0.171619i | ||||||
\(238\) | −45.4976 | −0.191166 | ||||||||
\(239\) | 178.278 | 0.745934 | 0.372967 | − | 0.927845i | \(-0.378340\pi\) | ||||
0.372967 | + | 0.927845i | \(0.378340\pi\) | |||||||
\(240\) | 4.42975i | 0.0184573i | ||||||||
\(241\) | − | 32.9156i | − | 0.136579i | −0.997666 | − | 0.0682896i | \(-0.978246\pi\) | ||
0.997666 | − | 0.0682896i | \(-0.0217542\pi\) | |||||||
\(242\) | 239.562 | 0.989925 | ||||||||
\(243\) | 94.0494 | 0.387034 | ||||||||
\(244\) | 331.893i | 1.36022i | ||||||||
\(245\) | − | 39.5164i | − | 0.161291i | ||||||
\(246\) | 4.14414 | 0.0168461 | ||||||||
\(247\) | 97.8565i | 0.396180i | ||||||||
\(248\) | 346.703 | 1.39800 | ||||||||
\(249\) | − | 46.2950i | − | 0.185924i | ||||||
\(250\) | 11.1803i | 0.0447214i | ||||||||
\(251\) | − | 193.339i | − | 0.770276i | −0.922859 | − | 0.385138i | \(-0.874154\pi\) | ||
0.922859 | − | 0.385138i | \(-0.125846\pi\) | |||||||
\(252\) | − | 216.618i | − | 0.859595i | ||||||
\(253\) | −260.851 | + | 350.277i | −1.03103 | + | 1.38449i | ||||
\(254\) | −71.0835 | −0.279856 | ||||||||
\(255\) | −4.93656 | −0.0193591 | ||||||||
\(256\) | −171.000 | −0.667969 | ||||||||
\(257\) | −88.0147 | −0.342470 | −0.171235 | − | 0.985230i | \(-0.554776\pi\) | ||||
−0.171235 | + | 0.985230i | \(0.554776\pi\) | |||||||
\(258\) | − | 22.6718i | − | 0.0878750i | ||||||
\(259\) | 242.894 | 0.937813 | ||||||||
\(260\) | 125.010i | 0.480809i | ||||||||
\(261\) | −102.780 | −0.393794 | ||||||||
\(262\) | −72.1391 | −0.275340 | ||||||||
\(263\) | − | 98.7568i | − | 0.375501i | −0.982217 | − | 0.187751i | \(-0.939880\pi\) | ||
0.982217 | − | 0.187751i | \(-0.0601197\pi\) | |||||||
\(264\) | − | 52.6638i | − | 0.199484i | ||||||
\(265\) | 90.0000 | 0.339623 | ||||||||
\(266\) | 42.8768 | 0.161191 | ||||||||
\(267\) | − | 19.6653i | − | 0.0736529i | ||||||
\(268\) | − | 105.188i | − | 0.392493i | ||||||
\(269\) | −337.903 | −1.25615 | −0.628073 | − | 0.778154i | \(-0.716156\pi\) | ||||
−0.628073 | + | 0.778154i | \(0.716156\pi\) | |||||||
\(270\) | 15.8080i | 0.0585482i | ||||||||
\(271\) | 150.086 | 0.553821 | 0.276911 | − | 0.960896i | \(-0.410689\pi\) | ||||
0.276911 | + | 0.960896i | \(0.410689\pi\) | |||||||
\(272\) | 27.8603i | 0.102428i | ||||||||
\(273\) | 60.2887i | 0.220838i | ||||||||
\(274\) | − | 56.1317i | − | 0.204860i | ||||||
\(275\) | 94.9423i | 0.345245i | ||||||||
\(276\) | 21.9264 | + | 16.3286i | 0.0794433 | + | 0.0591616i | ||||
\(277\) | −246.856 | −0.891177 | −0.445588 | − | 0.895238i | \(-0.647006\pi\) | ||||
−0.445588 | + | 0.895238i | \(0.647006\pi\) | |||||||
\(278\) | −266.091 | −0.957161 | ||||||||
\(279\) | −437.986 | −1.56984 | ||||||||
\(280\) | 127.807 | 0.456455 | ||||||||
\(281\) | 495.802i | 1.76442i | 0.470856 | + | 0.882210i | \(0.343945\pi\) | ||||
−0.470856 | + | 0.882210i | \(0.656055\pi\) | |||||||
\(282\) | 6.05045 | 0.0214555 | ||||||||
\(283\) | 191.002i | 0.674920i | 0.941340 | + | 0.337460i | \(0.109568\pi\) | ||||
−0.941340 | + | 0.337460i | \(0.890432\pi\) | |||||||
\(284\) | 211.378 | 0.744290 | ||||||||
\(285\) | 4.65221 | 0.0163235 | ||||||||
\(286\) | − | 353.858i | − | 1.23727i | ||||||
\(287\) | 85.4050i | 0.297578i | ||||||||
\(288\) | 291.820 | 1.01326 | ||||||||
\(289\) | 257.952 | 0.892568 | ||||||||
\(290\) | − | 25.9893i | − | 0.0896181i | ||||||
\(291\) | 27.5804i | 0.0947779i | ||||||||
\(292\) | 1.13176 | 0.00387588 | ||||||||
\(293\) | − | 302.569i | − | 1.03266i | −0.856391 | − | 0.516329i | \(-0.827298\pi\) | ||
0.856391 | − | 0.516329i | \(-0.172702\pi\) | |||||||
\(294\) | 7.00190 | 0.0238160 | ||||||||
\(295\) | − | 62.1342i | − | 0.210624i | ||||||
\(296\) | 208.229i | 0.703477i | ||||||||
\(297\) | 134.240i | 0.451987i | ||||||||
\(298\) | 222.352i | 0.746148i | ||||||||
\(299\) | 343.764 | + | 256.002i | 1.14971 | + | 0.856193i | ||||
\(300\) | 5.94313 | 0.0198104 | ||||||||
\(301\) | 467.233 | 1.55227 | ||||||||
\(302\) | 194.788 | 0.644995 | ||||||||
\(303\) | 58.2106 | 0.192114 | ||||||||
\(304\) | − | 26.2555i | − | 0.0863668i | ||||||
\(305\) | 247.378 | 0.811077 | ||||||||
\(306\) | 49.2738i | 0.161026i | ||||||||
\(307\) | 137.421 | 0.447626 | 0.223813 | − | 0.974632i | \(-0.428150\pi\) | ||||
0.223813 | + | 0.974632i | \(0.428150\pi\) | |||||||
\(308\) | 465.140 | 1.51019 | ||||||||
\(309\) | 47.5512i | 0.153887i | ||||||||
\(310\) | − | 110.750i | − | 0.357259i | ||||||
\(311\) | 106.051 | 0.340999 | 0.170500 | − | 0.985358i | \(-0.445462\pi\) | ||||
0.170500 | + | 0.985358i | \(0.445462\pi\) | |||||||
\(312\) | −51.6846 | −0.165656 | ||||||||
\(313\) | 376.278i | 1.20217i | 0.799187 | + | 0.601083i | \(0.205264\pi\) | ||||
−0.799187 | + | 0.601083i | \(0.794736\pi\) | |||||||
\(314\) | 106.214i | 0.338260i | ||||||||
\(315\) | −161.457 | −0.512563 | ||||||||
\(316\) | 307.972i | 0.974596i | ||||||||
\(317\) | −519.005 | −1.63724 | −0.818619 | − | 0.574337i | \(-0.805260\pi\) | ||||
−0.818619 | + | 0.574337i | \(0.805260\pi\) | |||||||
\(318\) | 15.9471i | 0.0501481i | ||||||||
\(319\) | − | 220.698i | − | 0.691844i | ||||||
\(320\) | 29.0689i | 0.0908403i | ||||||||
\(321\) | − | 75.8287i | − | 0.236227i | ||||||
\(322\) | 112.170 | − | 150.624i | 0.348353 | − | 0.467776i | ||||
\(323\) | 29.2594 | 0.0905865 | ||||||||
\(324\) | −230.358 | −0.710983 | ||||||||
\(325\) | 93.1772 | 0.286699 | ||||||||
\(326\) | −39.9063 | −0.122412 | ||||||||
\(327\) | 53.3857i | 0.163259i | ||||||||
\(328\) | −73.2165 | −0.223221 | ||||||||
\(329\) | 124.691i | 0.379001i | ||||||||
\(330\) | −16.8228 | −0.0509782 | ||||||||
\(331\) | −468.696 | −1.41600 | −0.707999 | − | 0.706213i | \(-0.750402\pi\) | ||||
−0.707999 | + | 0.706213i | \(0.750402\pi\) | |||||||
\(332\) | 350.535i | 1.05583i | ||||||||
\(333\) | − | 263.053i | − | 0.789950i | ||||||
\(334\) | −79.7872 | −0.238884 | ||||||||
\(335\) | −78.4026 | −0.234038 | ||||||||
\(336\) | − | 16.1758i | − | 0.0481423i | ||||||
\(337\) | 212.787i | 0.631416i | 0.948856 | + | 0.315708i | \(0.102242\pi\) | ||||
−0.948856 | + | 0.315708i | \(0.897758\pi\) | |||||||
\(338\) | −178.279 | −0.527454 | ||||||||
\(339\) | − | 34.4578i | − | 0.101645i | ||||||
\(340\) | 37.3785 | 0.109937 | ||||||||
\(341\) | − | 940.481i | − | 2.75801i | ||||||
\(342\) | − | 46.4356i | − | 0.135777i | ||||||
\(343\) | − | 255.801i | − | 0.745775i | ||||||
\(344\) | 400.552i | 1.16440i | ||||||||
\(345\) | 12.1706 | − | 16.3429i | 0.0352771 | − | 0.0473708i | ||||
\(346\) | 298.323 | 0.862205 | ||||||||
\(347\) | −300.161 | −0.865017 | −0.432508 | − | 0.901630i | \(-0.642371\pi\) | ||||
−0.432508 | + | 0.901630i | \(0.642371\pi\) | |||||||
\(348\) | −13.8151 | −0.0396986 | ||||||||
\(349\) | −54.4534 | −0.156027 | −0.0780134 | − | 0.996952i | \(-0.524858\pi\) | ||||
−0.0780134 | + | 0.996952i | \(0.524858\pi\) | |||||||
\(350\) | − | 40.8265i | − | 0.116647i | ||||||
\(351\) | 131.744 | 0.375340 | ||||||||
\(352\) | 626.619i | 1.78017i | ||||||||
\(353\) | −51.6964 | −0.146449 | −0.0732244 | − | 0.997315i | \(-0.523329\pi\) | ||||
−0.0732244 | + | 0.997315i | \(0.523329\pi\) | |||||||
\(354\) | 11.0095 | 0.0311004 | ||||||||
\(355\) | − | 157.552i | − | 0.443809i | ||||||
\(356\) | 148.901i | 0.418262i | ||||||||
\(357\) | 18.0265 | 0.0504945 | ||||||||
\(358\) | −48.1391 | −0.134467 | ||||||||
\(359\) | − | 277.495i | − | 0.772968i | −0.922296 | − | 0.386484i | \(-0.873690\pi\) | ||
0.922296 | − | 0.386484i | \(-0.126310\pi\) | |||||||
\(360\) | − | 138.415i | − | 0.384486i | ||||||
\(361\) | 333.426 | 0.923618 | ||||||||
\(362\) | − | 34.5224i | − | 0.0953657i | ||||||
\(363\) | −94.9165 | −0.261478 | ||||||||
\(364\) | − | 456.492i | − | 1.25410i | ||||||
\(365\) | − | 0.843561i | − | 0.00231113i | ||||||
\(366\) | 43.8330i | 0.119762i | ||||||||
\(367\) | 138.584i | 0.377612i | 0.982014 | + | 0.188806i | \(0.0604617\pi\) | ||||
−0.982014 | + | 0.188806i | \(0.939538\pi\) | |||||||
\(368\) | −92.2341 | − | 68.6868i | −0.250636 | − | 0.186649i | ||||
\(369\) | 92.4935 | 0.250660 | ||||||||
\(370\) | 66.5164 | 0.179774 | ||||||||
\(371\) | −328.647 | −0.885842 | ||||||||
\(372\) | −58.8715 | −0.158257 | ||||||||
\(373\) | − | 62.0247i | − | 0.166286i | −0.996538 | − | 0.0831431i | \(-0.973504\pi\) | ||
0.996538 | − | 0.0831431i | \(-0.0264958\pi\) | |||||||
\(374\) | −105.805 | −0.282901 | ||||||||
\(375\) | − | 4.42975i | − | 0.0118127i | ||||||
\(376\) | −106.896 | −0.284298 | ||||||||
\(377\) | −216.595 | −0.574522 | ||||||||
\(378\) | − | 57.7251i | − | 0.152712i | ||||||
\(379\) | 411.108i | 1.08472i | 0.840147 | + | 0.542358i | \(0.182469\pi\) | ||||
−0.840147 | + | 0.542358i | \(0.817531\pi\) | |||||||
\(380\) | −35.2254 | −0.0926985 | ||||||||
\(381\) | 28.1639 | 0.0739210 | ||||||||
\(382\) | − | 172.912i | − | 0.452650i | ||||||
\(383\) | − | 576.379i | − | 1.50490i | −0.658647 | − | 0.752452i | \(-0.728871\pi\) | ||
0.658647 | − | 0.752452i | \(-0.271129\pi\) | |||||||
\(384\) | 47.1488 | 0.122783 | ||||||||
\(385\) | − | 346.695i | − | 0.900506i | ||||||
\(386\) | 114.255 | 0.295998 | ||||||||
\(387\) | − | 506.013i | − | 1.30753i | ||||||
\(388\) | − | 208.832i | − | 0.538227i | ||||||
\(389\) | − | 233.138i | − | 0.599327i | −0.954045 | − | 0.299664i | \(-0.903126\pi\) | ||
0.954045 | − | 0.299664i | \(-0.0968744\pi\) | |||||||
\(390\) | 16.5101i | 0.0423335i | ||||||||
\(391\) | 76.5454 | − | 102.787i | 0.195768 | − | 0.262882i | ||||
\(392\) | −123.706 | −0.315576 | ||||||||
\(393\) | 28.5821 | 0.0727281 | ||||||||
\(394\) | −139.191 | −0.353277 | ||||||||
\(395\) | 229.549 | 0.581137 | ||||||||
\(396\) | − | 503.746i | − | 1.27209i | ||||||
\(397\) | −596.355 | −1.50215 | −0.751077 | − | 0.660215i | \(-0.770465\pi\) | ||||
−0.751077 | + | 0.660215i | \(0.770465\pi\) | |||||||
\(398\) | 245.347i | 0.616449i | ||||||||
\(399\) | −16.9882 | −0.0425769 | ||||||||
\(400\) | −25.0000 | −0.0625000 | ||||||||
\(401\) | 114.366i | 0.285201i | 0.989780 | + | 0.142600i | \(0.0455464\pi\) | ||||
−0.989780 | + | 0.142600i | \(0.954454\pi\) | |||||||
\(402\) | − | 13.8922i | − | 0.0345576i | ||||||
\(403\) | −922.996 | −2.29031 | ||||||||
\(404\) | −440.757 | −1.09098 | ||||||||
\(405\) | 171.699i | 0.423948i | ||||||||
\(406\) | 94.9033i | 0.233752i | ||||||||
\(407\) | 564.850 | 1.38784 | ||||||||
\(408\) | 15.4539i | 0.0378772i | ||||||||
\(409\) | 149.858 | 0.366401 | 0.183201 | − | 0.983076i | \(-0.441354\pi\) | ||||
0.183201 | + | 0.983076i | \(0.441354\pi\) | |||||||
\(410\) | 23.3881i | 0.0570443i | ||||||||
\(411\) | 22.2399i | 0.0541116i | ||||||||
\(412\) | − | 360.047i | − | 0.873900i | ||||||
\(413\) | 226.891i | 0.549374i | ||||||||
\(414\) | −163.125 | − | 121.480i | −0.394023 | − | 0.293429i | ||||
\(415\) | 261.273 | 0.629574 | ||||||||
\(416\) | 614.969 | 1.47829 | ||||||||
\(417\) | 105.427 | 0.252824 | ||||||||
\(418\) | 99.7103 | 0.238541 | ||||||||
\(419\) | 195.750i | 0.467184i | 0.972335 | + | 0.233592i | \(0.0750480\pi\) | ||||
−0.972335 | + | 0.233592i | \(0.924952\pi\) | |||||||
\(420\) | −21.7022 | −0.0516718 | ||||||||
\(421\) | − | 348.840i | − | 0.828599i | −0.910141 | − | 0.414299i | \(-0.864027\pi\) | ||
0.910141 | − | 0.414299i | \(-0.135973\pi\) | |||||||
\(422\) | 184.076 | 0.436199 | ||||||||
\(423\) | 135.041 | 0.319245 | ||||||||
\(424\) | − | 281.745i | − | 0.664492i | ||||||
\(425\) | − | 27.8603i | − | 0.0655536i | ||||||
\(426\) | 27.9167 | 0.0655321 | ||||||||
\(427\) | −903.336 | −2.11554 | ||||||||
\(428\) | 574.157i | 1.34149i | ||||||||
\(429\) | 140.202i | 0.326811i | ||||||||
\(430\) | 127.952 | 0.297562 | ||||||||
\(431\) | 293.133i | 0.680123i | 0.940403 | + | 0.340061i | \(0.110448\pi\) | ||||
−0.940403 | + | 0.340061i | \(0.889552\pi\) | |||||||
\(432\) | −35.3478 | −0.0818236 | ||||||||
\(433\) | 345.030i | 0.796835i | 0.917204 | + | 0.398418i | \(0.130440\pi\) | ||||
−0.917204 | + | 0.398418i | \(0.869560\pi\) | |||||||
\(434\) | 404.420i | 0.931843i | ||||||||
\(435\) | 10.2972i | 0.0236716i | ||||||||
\(436\) | − | 404.224i | − | 0.927120i | ||||||
\(437\) | −72.1363 | + | 96.8660i | −0.165072 | + | 0.221661i | ||||
\(438\) | 0.149470 | 0.000341257 | ||||||||
\(439\) | −570.096 | −1.29862 | −0.649312 | − | 0.760522i | \(-0.724943\pi\) | ||||
−0.649312 | + | 0.760522i | \(0.724943\pi\) | |||||||
\(440\) | 297.216 | 0.675492 | ||||||||
\(441\) | 156.276 | 0.354368 | ||||||||
\(442\) | 103.838i | 0.234927i | ||||||||
\(443\) | 146.539 | 0.330788 | 0.165394 | − | 0.986228i | \(-0.447110\pi\) | ||||
0.165394 | + | 0.986228i | \(0.447110\pi\) | |||||||
\(444\) | − | 35.3581i | − | 0.0796353i | ||||||
\(445\) | 110.984 | 0.249403 | ||||||||
\(446\) | 31.1064 | 0.0697452 | ||||||||
\(447\) | − | 88.0978i | − | 0.197087i | ||||||
\(448\) | − | 106.149i | − | 0.236940i | ||||||
\(449\) | 258.527 | 0.575783 | 0.287892 | − | 0.957663i | \(-0.407046\pi\) | ||||
0.287892 | + | 0.957663i | \(0.407046\pi\) | |||||||
\(450\) | −44.2151 | −0.0982558 | ||||||||
\(451\) | 198.610i | 0.440377i | ||||||||
\(452\) | 260.906i | 0.577226i | ||||||||
\(453\) | −77.1769 | −0.170368 | ||||||||
\(454\) | − | 192.411i | − | 0.423813i | ||||||
\(455\) | −340.249 | −0.747800 | ||||||||
\(456\) | − | 14.5637i | − | 0.0319380i | ||||||
\(457\) | 712.852i | 1.55985i | 0.625872 | + | 0.779926i | \(0.284743\pi\) | ||||
−0.625872 | + | 0.779926i | \(0.715257\pi\) | |||||||
\(458\) | 365.836i | 0.798769i | ||||||||
\(459\) | − | 39.3920i | − | 0.0858213i | ||||||
\(460\) | −92.1530 | + | 123.745i | −0.200333 | + | 0.269011i | ||||
\(461\) | 295.332 | 0.640634 | 0.320317 | − | 0.947310i | \(-0.396211\pi\) | ||||
0.320317 | + | 0.947310i | \(0.396211\pi\) | |||||||
\(462\) | 61.4308 | 0.132967 | ||||||||
\(463\) | 728.570 | 1.57358 | 0.786792 | − | 0.617218i | \(-0.211740\pi\) | ||||
0.786792 | + | 0.617218i | \(0.211740\pi\) | |||||||
\(464\) | 58.1137 | 0.125245 | ||||||||
\(465\) | 43.8802i | 0.0943661i | ||||||||
\(466\) | −235.271 | −0.504873 | ||||||||
\(467\) | − | 754.057i | − | 1.61468i | −0.590085 | − | 0.807341i | \(-0.700906\pi\) | ||
0.590085 | − | 0.807341i | \(-0.299094\pi\) | |||||||
\(468\) | −494.381 | −1.05637 | ||||||||
\(469\) | 286.298 | 0.610443 | ||||||||
\(470\) | 34.1467i | 0.0726526i | ||||||||
\(471\) | − | 42.0827i | − | 0.0893477i | ||||||
\(472\) | −194.511 | −0.412099 | ||||||||
\(473\) | 1086.55 | 2.29715 | ||||||||
\(474\) | 40.6738i | 0.0858097i | ||||||||
\(475\) | 26.2555i | 0.0552747i | ||||||||
\(476\) | −136.493 | −0.286749 | ||||||||
\(477\) | 355.925i | 0.746173i | ||||||||
\(478\) | −178.278 | −0.372967 | ||||||||
\(479\) | 129.310i | 0.269958i | 0.990848 | + | 0.134979i | \(0.0430967\pi\) | ||||
−0.990848 | + | 0.134979i | \(0.956903\pi\) | |||||||
\(480\) | − | 29.2363i | − | 0.0609090i | ||||||
\(481\) | − | 554.349i | − | 1.15249i | ||||||
\(482\) | 32.9156i | 0.0682896i | ||||||||
\(483\) | −44.4427 | + | 59.6785i | −0.0920138 | + | 0.123558i | ||||
\(484\) | 718.685 | 1.48489 | ||||||||
\(485\) | −155.654 | −0.320937 | ||||||||
\(486\) | −94.0494 | −0.193517 | ||||||||
\(487\) | 532.507 | 1.09344 | 0.546721 | − | 0.837315i | \(-0.315876\pi\) | ||||
0.546721 | + | 0.837315i | \(0.315876\pi\) | |||||||
\(488\) | − | 774.417i | − | 1.58692i | ||||||
\(489\) | 15.8112 | 0.0323338 | ||||||||
\(490\) | 39.5164i | 0.0806457i | ||||||||
\(491\) | 274.430 | 0.558922 | 0.279461 | − | 0.960157i | \(-0.409844\pi\) | ||||
0.279461 | + | 0.960157i | \(0.409844\pi\) | |||||||
\(492\) | 12.4324 | 0.0252692 | ||||||||
\(493\) | 64.7626i | 0.131364i | ||||||||
\(494\) | − | 97.8565i | − | 0.198090i | ||||||
\(495\) | −375.470 | −0.758526 | ||||||||
\(496\) | 247.645 | 0.499285 | ||||||||
\(497\) | 575.324i | 1.15759i | ||||||||
\(498\) | 46.2950i | 0.0929618i | ||||||||
\(499\) | 8.15135 | 0.0163354 | 0.00816769 | − | 0.999967i | \(-0.497400\pi\) | ||||
0.00816769 | + | 0.999967i | \(0.497400\pi\) | |||||||
\(500\) | 33.5410i | 0.0670820i | ||||||||
\(501\) | 31.6124 | 0.0630986 | ||||||||
\(502\) | 193.339i | 0.385138i | ||||||||
\(503\) | 202.082i | 0.401753i | 0.979617 | + | 0.200877i | \(0.0643790\pi\) | ||||
−0.979617 | + | 0.200877i | \(0.935621\pi\) | |||||||
\(504\) | 505.442i | 1.00286i | ||||||||
\(505\) | 328.521i | 0.650536i | ||||||||
\(506\) | 260.851 | − | 350.277i | 0.515517 | − | 0.692246i | ||||
\(507\) | 70.6359 | 0.139321 | ||||||||
\(508\) | −213.250 | −0.419784 | ||||||||
\(509\) | −640.462 | −1.25828 | −0.629138 | − | 0.777294i | \(-0.716592\pi\) | ||||
−0.629138 | + | 0.777294i | \(0.716592\pi\) | |||||||
\(510\) | 4.93656 | 0.00967953 | ||||||||
\(511\) | 3.08038i | 0.00602814i | ||||||||
\(512\) | −305.000 | −0.595703 | ||||||||
\(513\) | 37.1230i | 0.0723644i | ||||||||
\(514\) | 88.0147 | 0.171235 | ||||||||
\(515\) | −268.363 | −0.521093 | ||||||||
\(516\) | − | 68.0153i | − | 0.131813i | ||||||
\(517\) | 289.970i | 0.560871i | ||||||||
\(518\) | −242.894 | −0.468907 | ||||||||
\(519\) | −118.198 | −0.227742 | ||||||||
\(520\) | − | 291.691i | − | 0.560944i | ||||||
\(521\) | 471.404i | 0.904806i | 0.891814 | + | 0.452403i | \(0.149433\pi\) | ||||
−0.891814 | + | 0.452403i | \(0.850567\pi\) | |||||||
\(522\) | 102.780 | 0.196897 | ||||||||
\(523\) | 141.188i | 0.269958i | 0.990848 | + | 0.134979i | \(0.0430967\pi\) | ||||
−0.990848 | + | 0.134979i | \(0.956903\pi\) | |||||||
\(524\) | −216.417 | −0.413010 | ||||||||
\(525\) | 16.1758i | 0.0308111i | ||||||||
\(526\) | 98.7568i | 0.187751i | ||||||||
\(527\) | 275.979i | 0.523679i | ||||||||
\(528\) | − | 37.6170i | − | 0.0712443i | ||||||
\(529\) | 151.570 | + | 506.821i | 0.286521 | + | 0.958074i | ||||
\(530\) | −90.0000 | −0.169811 | ||||||||
\(531\) | 245.723 | 0.462755 | ||||||||
\(532\) | 128.631 | 0.241787 | ||||||||
\(533\) | 194.917 | 0.365699 | ||||||||
\(534\) | 19.6653i | 0.0368265i | ||||||||
\(535\) | 427.952 | 0.799910 | ||||||||
\(536\) | 245.439i | 0.457909i | ||||||||
\(537\) | 19.0731 | 0.0355179 | ||||||||
\(538\) | 337.903 | 0.628073 | ||||||||
\(539\) | 335.569i | 0.622577i | ||||||||
\(540\) | 47.4240i | 0.0878223i | ||||||||
\(541\) | 645.381 | 1.19294 | 0.596471 | − | 0.802635i | \(-0.296569\pi\) | ||||
0.596471 | + | 0.802635i | \(0.296569\pi\) | |||||||
\(542\) | −150.086 | −0.276911 | ||||||||
\(543\) | 13.6781i | 0.0251898i | ||||||||
\(544\) | − | 183.878i | − | 0.338011i | ||||||
\(545\) | −301.291 | −0.552827 | ||||||||
\(546\) | − | 60.2887i | − | 0.110419i | ||||||
\(547\) | 704.099 | 1.28720 | 0.643600 | − | 0.765362i | \(-0.277440\pi\) | ||||
0.643600 | + | 0.765362i | \(0.277440\pi\) | |||||||
\(548\) | − | 168.395i | − | 0.307290i | ||||||
\(549\) | 978.312i | 1.78199i | ||||||||
\(550\) | − | 94.9423i | − | 0.172622i | ||||||
\(551\) | − | 61.0322i | − | 0.110766i | ||||||
\(552\) | −51.1615 | − | 38.1000i | −0.0926839 | − | 0.0690218i | ||||
\(553\) | −838.230 | −1.51579 | ||||||||
\(554\) | 246.856 | 0.445588 | ||||||||
\(555\) | −26.3544 | −0.0474853 | ||||||||
\(556\) | −798.273 | −1.43574 | ||||||||
\(557\) | − | 377.571i | − | 0.677865i | −0.940811 | − | 0.338933i | \(-0.889934\pi\) | ||
0.940811 | − | 0.338933i | \(-0.110066\pi\) | |||||||
\(558\) | 437.986 | 0.784922 | ||||||||
\(559\) | − | 1066.35i | − | 1.90761i | ||||||
\(560\) | 91.2909 | 0.163020 | ||||||||
\(561\) | 41.9208 | 0.0747251 | ||||||||
\(562\) | − | 495.802i | − | 0.882210i | ||||||
\(563\) | − | 281.177i | − | 0.499426i | −0.968320 | − | 0.249713i | \(-0.919664\pi\) | ||
0.968320 | − | 0.249713i | \(-0.0803362\pi\) | |||||||
\(564\) | 18.1514 | 0.0321833 | ||||||||
\(565\) | 194.468 | 0.344191 | ||||||||
\(566\) | − | 191.002i | − | 0.337460i | ||||||
\(567\) | − | 626.983i | − | 1.10579i | ||||||
\(568\) | −493.216 | −0.868339 | ||||||||
\(569\) | − | 717.960i | − | 1.26179i | −0.775867 | − | 0.630897i | \(-0.782687\pi\) | ||
0.775867 | − | 0.630897i | \(-0.217313\pi\) | |||||||
\(570\) | −4.65221 | −0.00816177 | ||||||||
\(571\) | 828.411i | 1.45081i | 0.688324 | + | 0.725404i | \(0.258347\pi\) | ||||
−0.688324 | + | 0.725404i | \(0.741653\pi\) | |||||||
\(572\) | − | 1061.57i | − | 1.85590i | ||||||
\(573\) | 68.5093i | 0.119562i | ||||||||
\(574\) | − | 85.4050i | − | 0.148789i | ||||||
\(575\) | 92.2341 | + | 68.6868i | 0.160407 | + | 0.119455i | ||||
\(576\) | −114.959 | −0.199582 | ||||||||
\(577\) | 387.299 | 0.671228 | 0.335614 | − | 0.942000i | \(-0.391056\pi\) | ||||
0.335614 | + | 0.942000i | \(0.391056\pi\) | |||||||
\(578\) | −257.952 | −0.446284 | ||||||||
\(579\) | −45.2690 | −0.0781847 | ||||||||
\(580\) | − | 77.9678i | − | 0.134427i | ||||||
\(581\) | −954.075 | −1.64213 | ||||||||
\(582\) | − | 27.5804i | − | 0.0473889i | ||||||
\(583\) | −764.271 | −1.31093 | ||||||||
\(584\) | −2.64076 | −0.00452185 | ||||||||
\(585\) | 368.489i | 0.629897i | ||||||||
\(586\) | 302.569i | 0.516329i | ||||||||
\(587\) | 996.553 | 1.69770 | 0.848852 | − | 0.528630i | \(-0.177294\pi\) | ||||
0.848852 | + | 0.528630i | \(0.177294\pi\) | |||||||
\(588\) | 21.0057 | 0.0357240 | ||||||||
\(589\) | − | 260.082i | − | 0.441565i | ||||||
\(590\) | 62.1342i | 0.105312i | ||||||||
\(591\) | 55.1487 | 0.0933142 | ||||||||
\(592\) | 148.735i | 0.251242i | ||||||||
\(593\) | 524.228 | 0.884028 | 0.442014 | − | 0.897008i | \(-0.354264\pi\) | ||||
0.442014 | + | 0.897008i | \(0.354264\pi\) | |||||||
\(594\) | − | 134.240i | − | 0.225993i | ||||||
\(595\) | 101.736i | 0.170984i | ||||||||
\(596\) | 667.056i | 1.11922i | ||||||||
\(597\) | − | 97.2085i | − | 0.162828i | ||||||
\(598\) | −343.764 | − | 256.002i | −0.574857 | − | 0.428097i | ||||
\(599\) | −667.991 | −1.11518 | −0.557588 | − | 0.830118i | \(-0.688273\pi\) | ||||
−0.557588 | + | 0.830118i | \(0.688273\pi\) | |||||||
\(600\) | −13.8673 | −0.0231122 | ||||||||
\(601\) | −18.8858 | −0.0314240 | −0.0157120 | − | 0.999877i | \(-0.505001\pi\) | ||||
−0.0157120 | + | 0.999877i | \(0.505001\pi\) | |||||||
\(602\) | −467.233 | −0.776135 | ||||||||
\(603\) | − | 310.060i | − | 0.514196i | ||||||
\(604\) | 584.365 | 0.967492 | ||||||||
\(605\) | − | 535.676i | − | 0.885416i | ||||||
\(606\) | −58.2106 | −0.0960571 | ||||||||
\(607\) | −142.493 | −0.234750 | −0.117375 | − | 0.993088i | \(-0.537448\pi\) | ||||
−0.117375 | + | 0.993088i | \(0.537448\pi\) | |||||||
\(608\) | 173.286i | 0.285010i | ||||||||
\(609\) | − | 37.6015i | − | 0.0617430i | ||||||
\(610\) | −247.378 | −0.405539 | ||||||||
\(611\) | 284.579 | 0.465760 | ||||||||
\(612\) | 147.821i | 0.241538i | ||||||||
\(613\) | 787.223i | 1.28421i | 0.766615 | + | 0.642106i | \(0.221939\pi\) | ||||
−0.766615 | + | 0.642106i | \(0.778061\pi\) | |||||||
\(614\) | −137.421 | −0.223813 | ||||||||
\(615\) | − | 9.26659i | − | 0.0150676i | ||||||
\(616\) | −1085.33 | −1.76189 | ||||||||
\(617\) | − | 47.1461i | − | 0.0764119i | −0.999270 | − | 0.0382059i | \(-0.987836\pi\) | ||
0.999270 | − | 0.0382059i | \(-0.0121643\pi\) | |||||||
\(618\) | − | 47.5512i | − | 0.0769437i | ||||||
\(619\) | − | 738.262i | − | 1.19267i | −0.802736 | − | 0.596335i | \(-0.796623\pi\) | ||
0.802736 | − | 0.596335i | \(-0.203377\pi\) | |||||||
\(620\) | − | 332.251i | − | 0.535889i | ||||||
\(621\) | 130.411 | + | 97.1171i | 0.210001 | + | 0.156388i | ||||
\(622\) | −106.051 | −0.170500 | ||||||||
\(623\) | −405.275 | −0.650522 | ||||||||
\(624\) | −36.9176 | −0.0591628 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 376.278i | − | 0.601083i | ||||||
\(627\) | −39.5061 | −0.0630081 | ||||||||
\(628\) | 318.641i | 0.507390i | ||||||||
\(629\) | −165.752 | −0.263517 | ||||||||
\(630\) | 161.457 | 0.256282 | ||||||||
\(631\) | 692.184i | 1.09696i | 0.836163 | + | 0.548482i | \(0.184794\pi\) | ||||
−0.836163 | + | 0.548482i | \(0.815206\pi\) | |||||||
\(632\) | − | 718.602i | − | 1.13703i | ||||||
\(633\) | −72.9326 | −0.115217 | ||||||||
\(634\) | 519.005 | 0.818619 | ||||||||
\(635\) | 158.948i | 0.250311i | ||||||||
\(636\) | 47.8413i | 0.0752221i | ||||||||
\(637\) | 329.330 | 0.517002 | ||||||||
\(638\) | 220.698i | 0.345922i | ||||||||
\(639\) | 623.075 | 0.975078 | ||||||||
\(640\) | 266.092i | 0.415769i | ||||||||
\(641\) | − | 582.771i | − | 0.909159i | −0.890706 | − | 0.454580i | \(-0.849790\pi\) | ||
0.890706 | − | 0.454580i | \(-0.150210\pi\) | |||||||
\(642\) | 75.8287i | 0.118113i | ||||||||
\(643\) | − | 600.348i | − | 0.933668i | −0.884345 | − | 0.466834i | \(-0.845395\pi\) | ||
0.884345 | − | 0.466834i | \(-0.154605\pi\) | |||||||
\(644\) | 336.509 | − | 451.872i | 0.522530 | − | 0.701664i | ||||
\(645\) | −50.6956 | −0.0785978 | ||||||||
\(646\) | −29.2594 | −0.0452932 | ||||||||
\(647\) | −595.814 | −0.920886 | −0.460443 | − | 0.887689i | \(-0.652310\pi\) | ||||
−0.460443 | + | 0.887689i | \(0.652310\pi\) | |||||||
\(648\) | 537.503 | 0.829480 | ||||||||
\(649\) | 527.637i | 0.813000i | ||||||||
\(650\) | −93.1772 | −0.143350 | ||||||||
\(651\) | − | 160.235i | − | 0.246136i | ||||||
\(652\) | −119.719 | −0.183618 | ||||||||
\(653\) | 148.378 | 0.227225 | 0.113612 | − | 0.993525i | \(-0.463758\pi\) | ||||
0.113612 | + | 0.993525i | \(0.463758\pi\) | |||||||
\(654\) | − | 53.3857i | − | 0.0816295i | ||||||
\(655\) | 161.308i | 0.246272i | ||||||||
\(656\) | −52.2975 | −0.0797218 | ||||||||
\(657\) | 3.33605 | 0.00507769 | ||||||||
\(658\) | − | 124.691i | − | 0.189501i | ||||||
\(659\) | 94.1732i | 0.142903i | 0.997444 | + | 0.0714516i | \(0.0227632\pi\) | ||||
−0.997444 | + | 0.0714516i | \(0.977237\pi\) | |||||||
\(660\) | −50.4685 | −0.0764674 | ||||||||
\(661\) | − | 705.908i | − | 1.06794i | −0.845504 | − | 0.533970i | \(-0.820700\pi\) | ||
0.845504 | − | 0.533970i | \(-0.179300\pi\) | |||||||
\(662\) | 468.696 | 0.707999 | ||||||||
\(663\) | − | 41.1414i | − | 0.0620534i | ||||||
\(664\) | − | 817.915i | − | 1.23180i | ||||||
\(665\) | − | 95.8755i | − | 0.144174i | ||||||
\(666\) | 263.053i | 0.394975i | ||||||||
\(667\) | −214.403 | − | 159.666i | −0.321443 | − | 0.239379i | ||||
\(668\) | −239.362 | −0.358326 | ||||||||
\(669\) | −12.3246 | −0.0184224 | ||||||||
\(670\) | 78.4026 | 0.117019 | ||||||||
\(671\) | −2100.71 | −3.13072 | ||||||||
\(672\) | 106.760i | 0.158870i | ||||||||
\(673\) | 617.516 | 0.917558 | 0.458779 | − | 0.888550i | \(-0.348287\pi\) | ||||
0.458779 | + | 0.888550i | \(0.348287\pi\) | |||||||
\(674\) | − | 212.787i | − | 0.315708i | ||||||
\(675\) | 35.3478 | 0.0523671 | ||||||||
\(676\) | −534.838 | −0.791181 | ||||||||
\(677\) | 923.117i | 1.36354i | 0.731566 | + | 0.681771i | \(0.238790\pi\) | ||||
−0.731566 | + | 0.681771i | \(0.761210\pi\) | |||||||
\(678\) | 34.4578i | 0.0508227i | ||||||||
\(679\) | 568.393 | 0.837103 | ||||||||
\(680\) | −87.2165 | −0.128260 | ||||||||
\(681\) | 76.2350i | 0.111946i | ||||||||
\(682\) | 940.481i | 1.37900i | ||||||||
\(683\) | 440.495 | 0.644941 | 0.322471 | − | 0.946580i | \(-0.395487\pi\) | ||||
0.322471 | + | 0.946580i | \(0.395487\pi\) | |||||||
\(684\) | − | 139.307i | − | 0.203665i | ||||||
\(685\) | −125.514 | −0.183233 | ||||||||
\(686\) | 255.801i | 0.372887i | ||||||||
\(687\) | − | 144.947i | − | 0.210986i | ||||||
\(688\) | 286.109i | 0.415856i | ||||||||
\(689\) | 750.062i | 1.08862i | ||||||||
\(690\) | −12.1706 | + | 16.3429i | −0.0176386 | + | 0.0236854i | ||||
\(691\) | −934.136 | −1.35186 | −0.675930 | − | 0.736965i | \(-0.736258\pi\) | ||||
−0.675930 | + | 0.736965i | \(0.736258\pi\) | |||||||
\(692\) | 894.969 | 1.29331 | ||||||||
\(693\) | 1371.08 | 1.97847 | ||||||||
\(694\) | 300.161 | 0.432508 | ||||||||
\(695\) | 594.997i | 0.856111i | ||||||||
\(696\) | 32.2352 | 0.0463150 | ||||||||
\(697\) | − | 58.2809i | − | 0.0836168i | ||||||
\(698\) | 54.4534 | 0.0780134 | ||||||||
\(699\) | 93.2164 | 0.133357 | ||||||||
\(700\) | − | 122.480i | − | 0.174971i | ||||||
\(701\) | − | 462.313i | − | 0.659505i | −0.944067 | − | 0.329753i | \(-0.893035\pi\) | ||
0.944067 | − | 0.329753i | \(-0.106965\pi\) | |||||||
\(702\) | −131.744 | −0.187670 | ||||||||
\(703\) | 156.205 | 0.222197 | ||||||||
\(704\) | − | 246.850i | − | 0.350639i | ||||||
\(705\) | − | 13.5292i | − | 0.0191904i | ||||||
\(706\) | 51.6964 | 0.0732244 | ||||||||
\(707\) | − | 1199.64i | − | 1.69680i | ||||||
\(708\) | 33.0286 | 0.0466506 | ||||||||
\(709\) | 959.421i | 1.35320i | 0.736349 | + | 0.676601i | \(0.236548\pi\) | ||||
−0.736349 | + | 0.676601i | \(0.763452\pi\) | |||||||
\(710\) | 157.552i | 0.221905i | ||||||||
\(711\) | 907.802i | 1.27680i | ||||||||
\(712\) | − | 347.436i | − | 0.487972i | ||||||
\(713\) | −913.653 | − | 680.399i | −1.28142 | − | 0.954276i | ||||
\(714\) | −18.0265 | −0.0252472 | ||||||||
\(715\) | −791.251 | −1.10665 | ||||||||
\(716\) | −144.417 | −0.201700 | ||||||||
\(717\) | 70.6354 | 0.0985152 | ||||||||
\(718\) | 277.495i | 0.386484i | ||||||||
\(719\) | 195.959 | 0.272543 | 0.136272 | − | 0.990672i | \(-0.456488\pi\) | ||||
0.136272 | + | 0.990672i | \(0.456488\pi\) | |||||||
\(720\) | − | 98.8680i | − | 0.137317i | ||||||
\(721\) | 979.964 | 1.35917 | ||||||||
\(722\) | −333.426 | −0.461809 | ||||||||
\(723\) | − | 13.0414i | − | 0.0180379i | ||||||
\(724\) | − | 103.567i | − | 0.143049i | ||||||
\(725\) | −58.1137 | −0.0801569 | ||||||||
\(726\) | 94.9165 | 0.130739 | ||||||||
\(727\) | − | 959.462i | − | 1.31975i | −0.751373 | − | 0.659877i | \(-0.770608\pi\) | ||
0.751373 | − | 0.659877i | \(-0.229392\pi\) | |||||||
\(728\) | 1065.15i | 1.46312i | ||||||||
\(729\) | −653.812 | −0.896862 | ||||||||
\(730\) | 0.843561i | 0.00115556i | ||||||||
\(731\) | −318.843 | −0.436174 | ||||||||
\(732\) | 131.499i | 0.179643i | ||||||||
\(733\) | − | 1454.43i | − | 1.98421i | −0.125412 | − | 0.992105i | \(-0.540025\pi\) | ||
0.125412 | − | 0.992105i | \(-0.459975\pi\) | |||||||
\(734\) | − | 138.584i | − | 0.188806i | ||||||
\(735\) | − | 15.6567i | − | 0.0213017i | ||||||
\(736\) | 608.745 | + | 453.333i | 0.827099 | + | 0.615942i | ||||
\(737\) | 665.787 | 0.903375 | ||||||||
\(738\) | −92.4935 | −0.125330 | ||||||||
\(739\) | −430.714 | −0.582834 | −0.291417 | − | 0.956596i | \(-0.594127\pi\) | ||||
−0.291417 | + | 0.956596i | \(0.594127\pi\) | |||||||
\(740\) | 199.549 | 0.269661 | ||||||||
\(741\) | 38.7716i | 0.0523234i | ||||||||
\(742\) | 328.647 | 0.442921 | ||||||||
\(743\) | − | 331.646i | − | 0.446361i | −0.974777 | − | 0.223180i | \(-0.928356\pi\) | ||
0.974777 | − | 0.223180i | \(-0.0716439\pi\) | |||||||
\(744\) | 137.367 | 0.184633 | ||||||||
\(745\) | 497.194 | 0.667375 | ||||||||
\(746\) | 62.0247i | 0.0831431i | ||||||||
\(747\) | 1033.26i | 1.38322i | ||||||||
\(748\) | −317.414 | −0.424351 | ||||||||
\(749\) | −1562.72 | −2.08641 | ||||||||
\(750\) | 4.42975i | 0.00590633i | ||||||||
\(751\) | − | 55.4622i | − | 0.0738511i | −0.999318 | − | 0.0369256i | \(-0.988244\pi\) | ||
0.999318 | − | 0.0369256i | \(-0.0117564\pi\) | |||||||
\(752\) | −76.3544 | −0.101535 | ||||||||
\(753\) | − | 76.6027i | − | 0.101730i | ||||||
\(754\) | 216.595 | 0.287261 | ||||||||
\(755\) | − | 435.560i | − | 0.576901i | ||||||
\(756\) | − | 173.175i | − | 0.229068i | ||||||
\(757\) | − | 253.679i | − | 0.335111i | −0.985863 | − | 0.167556i | \(-0.946413\pi\) | ||
0.985863 | − | 0.167556i | \(-0.0535874\pi\) | |||||||
\(758\) | − | 411.108i | − | 0.542358i | ||||||
\(759\) | −103.352 | + | 138.783i | −0.136168 | + | 0.182849i | ||||
\(760\) | 82.1927 | 0.108148 | ||||||||
\(761\) | 474.238 | 0.623178 | 0.311589 | − | 0.950217i | \(-0.399139\pi\) | ||||
0.311589 | + | 0.950217i | \(0.399139\pi\) | |||||||
\(762\) | −28.1639 | −0.0369605 | ||||||||
\(763\) | 1100.21 | 1.44195 | ||||||||
\(764\) | − | 518.736i | − | 0.678974i | ||||||
\(765\) | 110.180 | 0.144026 | ||||||||
\(766\) | 576.379i | 0.752452i | ||||||||
\(767\) | 517.827 | 0.675133 | ||||||||
\(768\) | −67.7517 | −0.0882183 | ||||||||
\(769\) | 859.116i | 1.11719i | 0.829442 | + | 0.558593i | \(0.188659\pi\) | ||||
−0.829442 | + | 0.558593i | \(0.811341\pi\) | |||||||
\(770\) | 346.695i | 0.450253i | ||||||||
\(771\) | −34.8722 | −0.0452298 | ||||||||
\(772\) | 342.766 | 0.443997 | ||||||||
\(773\) | − | 1350.61i | − | 1.74724i | −0.486612 | − | 0.873618i | \(-0.661768\pi\) | ||
0.486612 | − | 0.873618i | \(-0.338232\pi\) | |||||||
\(774\) | 506.013i | 0.653764i | ||||||||
\(775\) | −247.645 | −0.319542 | ||||||||
\(776\) | 487.275i | 0.627932i | ||||||||
\(777\) | 96.2366 | 0.123857 | ||||||||
\(778\) | 233.138i | 0.299664i | ||||||||
\(779\) | 54.9239i | 0.0705056i | ||||||||
\(780\) | 49.5302i | 0.0635002i | ||||||||
\(781\) | 1337.92i | 1.71308i | ||||||||
\(782\) | −76.5454 | + | 102.787i | −0.0978841 | + | 0.131441i | ||||
\(783\) | −82.1677 | −0.104940 | ||||||||
\(784\) | −88.3613 | −0.112706 | ||||||||
\(785\) | 237.501 | 0.302549 | ||||||||
\(786\) | −28.5821 | −0.0363640 | ||||||||
\(787\) | − | 1010.62i | − | 1.28414i | −0.766644 | − | 0.642072i | \(-0.778075\pi\) | ||
0.766644 | − | 0.642072i | \(-0.221925\pi\) | |||||||
\(788\) | −417.573 | −0.529915 | ||||||||
\(789\) | − | 39.1283i | − | 0.0495923i | ||||||
\(790\) | −229.549 | −0.290568 | ||||||||
\(791\) | −710.127 | −0.897758 | ||||||||
\(792\) | 1175.41i | 1.48410i | ||||||||
\(793\) | 2061.66i | 2.59982i | ||||||||
\(794\) | 596.355 | 0.751077 | ||||||||
\(795\) | 35.6588 | 0.0448538 | ||||||||
\(796\) | 736.040i | 0.924674i | ||||||||
\(797\) | − | 1079.08i | − | 1.35393i | −0.736017 | − | 0.676963i | \(-0.763296\pi\) | ||
0.736017 | − | 0.676963i | \(-0.236704\pi\) | |||||||
\(798\) | 16.9882 | 0.0212884 | ||||||||
\(799\) | − | 85.0902i | − | 0.106496i | ||||||
\(800\) | 165.000 | 0.206250 | ||||||||
\(801\) | 438.912i | 0.547955i | ||||||||
\(802\) | − | 114.366i | − | 0.142600i | ||||||
\(803\) | 7.16343i | 0.00892084i | ||||||||
\(804\) | − | 41.6765i | − | 0.0518364i | ||||||
\(805\) | −336.805 | − | 250.819i | −0.418392 | − | 0.311577i | ||||
\(806\) | 922.996 | 1.14516 | ||||||||
\(807\) | −133.880 | −0.165899 | ||||||||
\(808\) | 1028.43 | 1.27281 | ||||||||
\(809\) | 577.335 | 0.713641 | 0.356820 | − | 0.934173i | \(-0.383861\pi\) | ||||
0.356820 | + | 0.934173i | \(0.383861\pi\) | |||||||
\(810\) | − | 171.699i | − | 0.211974i | ||||||
\(811\) | −655.395 | −0.808132 | −0.404066 | − | 0.914730i | \(-0.632403\pi\) | ||||
−0.404066 | + | 0.914730i | \(0.632403\pi\) | |||||||
\(812\) | 284.710i | 0.350628i | ||||||||
\(813\) | 59.4652 | 0.0731429 | ||||||||
\(814\) | −564.850 | −0.693919 | ||||||||
\(815\) | 89.2332i | 0.109489i | ||||||||
\(816\) | 11.0385i | 0.0135276i | ||||||||
\(817\) | 300.477 | 0.367781 | ||||||||
\(818\) | −149.858 | −0.183201 | ||||||||
\(819\) | − | 1345.59i | − | 1.64297i | ||||||
\(820\) | 70.1644i | 0.0855664i | ||||||||
\(821\) | 1117.23 | 1.36082 | 0.680410 | − | 0.732832i | \(-0.261802\pi\) | ||||
0.680410 | + | 0.732832i | \(0.261802\pi\) | |||||||
\(822\) | − | 22.2399i | − | 0.0270558i | ||||||
\(823\) | 331.810 | 0.403171 | 0.201586 | − | 0.979471i | \(-0.435391\pi\) | ||||
0.201586 | + | 0.979471i | \(0.435391\pi\) | |||||||
\(824\) | 840.109i | 1.01955i | ||||||||
\(825\) | 37.6170i | 0.0455963i | ||||||||
\(826\) | − | 226.891i | − | 0.274687i | ||||||
\(827\) | 158.794i | 0.192013i | 0.995381 | + | 0.0960063i | \(0.0306069\pi\) | ||||
−0.995381 | + | 0.0960063i | \(0.969393\pi\) | |||||||
\(828\) | −489.376 | − | 364.439i | −0.591034 | − | 0.440144i | ||||
\(829\) | 941.980 | 1.13629 | 0.568143 | − | 0.822930i | \(-0.307662\pi\) | ||||
0.568143 | + | 0.822930i | \(0.307662\pi\) | |||||||
\(830\) | −261.273 | −0.314787 | ||||||||
\(831\) | −97.8065 | −0.117697 | ||||||||
\(832\) | −242.261 | −0.291179 | ||||||||
\(833\) | − | 98.4708i | − | 0.118212i | ||||||
\(834\) | −105.427 | −0.126412 | ||||||||
\(835\) | 178.410i | 0.213664i | ||||||||
\(836\) | 299.131 | 0.357812 | ||||||||
\(837\) | −350.149 | −0.418338 | ||||||||
\(838\) | − | 195.750i | − | 0.233592i | ||||||
\(839\) | 817.388i | 0.974241i | 0.873335 | + | 0.487120i | \(0.161953\pi\) | ||||
−0.873335 | + | 0.487120i | \(0.838047\pi\) | |||||||
\(840\) | 50.6384 | 0.0602838 | ||||||||
\(841\) | −705.912 | −0.839372 | ||||||||
\(842\) | 348.840i | 0.414299i | ||||||||
\(843\) | 196.441i | 0.233026i | ||||||||
\(844\) | 552.228 | 0.654299 | ||||||||
\(845\) | 398.645i | 0.471769i | ||||||||
\(846\) | −135.041 | −0.159622 | ||||||||
\(847\) | 1956.10i | 2.30944i | ||||||||
\(848\) | − | 201.246i | − | 0.237319i | ||||||
\(849\) | 75.6768i | 0.0891364i | ||||||||
\(850\) | 27.8603i | 0.0327768i | ||||||||
\(851\) | 408.646 | − | 548.738i | 0.480195 | − | 0.644815i | ||||
\(852\) | 83.7500 | 0.0982981 | ||||||||
\(853\) | −251.633 | −0.294998 | −0.147499 | − | 0.989062i | \(-0.547122\pi\) | ||||
−0.147499 | + | 0.989062i | \(0.547122\pi\) | |||||||
\(854\) | 903.336 | 1.05777 | ||||||||
\(855\) | −103.833 | −0.121442 | ||||||||
\(856\) | − | 1339.70i | − | 1.56507i | ||||||
\(857\) | −264.475 | −0.308605 | −0.154303 | − | 0.988024i | \(-0.549313\pi\) | ||||
−0.154303 | + | 0.988024i | \(0.549313\pi\) | |||||||
\(858\) | − | 140.202i | − | 0.163405i | ||||||
\(859\) | 368.069 | 0.428485 | 0.214243 | − | 0.976780i | \(-0.431272\pi\) | ||||
0.214243 | + | 0.976780i | \(0.431272\pi\) | |||||||
\(860\) | 383.855 | 0.446343 | ||||||||
\(861\) | 33.8382i | 0.0393011i | ||||||||
\(862\) | − | 293.133i | − | 0.340061i | ||||||
\(863\) | −1521.94 | −1.76355 | −0.881775 | − | 0.471669i | \(-0.843652\pi\) | ||||
−0.881775 | + | 0.471669i | \(0.843652\pi\) | |||||||
\(864\) | 233.295 | 0.270018 | ||||||||
\(865\) | − | 667.070i | − | 0.771179i | ||||||
\(866\) | − | 345.030i | − | 0.398418i | ||||||
\(867\) | 102.203 | 0.117881 | ||||||||
\(868\) | 1213.26i | 1.39777i | ||||||||
\(869\) | −1949.31 | −2.24316 | ||||||||
\(870\) | − | 10.2972i | − | 0.0118358i | ||||||
\(871\) | − | 653.409i | − | 0.750183i | ||||||
\(872\) | 943.190i | 1.08164i | ||||||||
\(873\) | − | 615.569i | − | 0.705119i | ||||||
\(874\) | 72.1363 | − | 96.8660i | 0.0825358 | − | 0.110831i | ||||
\(875\) | −91.2909 | −0.104332 | ||||||||
\(876\) | 0.448411 | 0.000511885 | ||||||||
\(877\) | −1696.01 | −1.93388 | −0.966938 | − | 0.255011i | \(-0.917921\pi\) | ||||
−0.966938 | + | 0.255011i | \(0.917921\pi\) | |||||||
\(878\) | 570.096 | 0.649312 | ||||||||
\(879\) | − | 119.880i | − | 0.136383i | ||||||
\(880\) | 212.297 | 0.241247 | ||||||||
\(881\) | − | 258.150i | − | 0.293020i | −0.989209 | − | 0.146510i | \(-0.953196\pi\) | ||
0.989209 | − | 0.146510i | \(-0.0468040\pi\) | |||||||
\(882\) | −156.276 | −0.177184 | ||||||||
\(883\) | 1286.20 | 1.45663 | 0.728315 | − | 0.685243i | \(-0.240304\pi\) | ||||
0.728315 | + | 0.685243i | \(0.240304\pi\) | |||||||
\(884\) | 311.513i | 0.352390i | ||||||||
\(885\) | − | 24.6181i | − | 0.0278171i | ||||||
\(886\) | −146.539 | −0.165394 | ||||||||
\(887\) | 828.723 | 0.934299 | 0.467150 | − | 0.884178i | \(-0.345281\pi\) | ||||
0.467150 | + | 0.884178i | \(0.345281\pi\) | |||||||
\(888\) | 82.5022i | 0.0929079i | ||||||||
\(889\) | − | 580.419i | − | 0.652889i | ||||||
\(890\) | −110.984 | −0.124702 | ||||||||
\(891\) | − | 1458.05i | − | 1.63642i | ||||||
\(892\) | 93.3191 | 0.104618 | ||||||||
\(893\) | 80.1889i | 0.0897972i | ||||||||
\(894\) | 88.0978i | 0.0985434i | ||||||||
\(895\) | 107.642i | 0.120271i | ||||||||
\(896\) | − | 971.672i | − | 1.08445i | ||||||
\(897\) | 136.202 | + | 101.430i | 0.151842 | + | 0.113077i | ||||
\(898\) | −258.527 | −0.287892 | ||||||||
\(899\) | 575.664 | 0.640338 | ||||||||
\(900\) | −132.645 | −0.147384 | ||||||||
\(901\) | 224.271 | 0.248913 | ||||||||
\(902\) | − | 198.610i | − | 0.220188i | ||||||
\(903\) | 185.122 | 0.205008 | ||||||||
\(904\) | − | 608.781i | − | 0.673431i | ||||||
\(905\) | −77.1944 | −0.0852977 | ||||||||
\(906\) | 77.1769 | 0.0851842 | ||||||||
\(907\) | − | 973.777i | − | 1.07362i | −0.843702 | − | 0.536812i | \(-0.819629\pi\) | ||
0.843702 | − | 0.536812i | \(-0.180371\pi\) | |||||||
\(908\) | − | 577.234i | − | 0.635720i | ||||||
\(909\) | −1299.21 | −1.42927 | ||||||||
\(910\) | 340.249 | 0.373900 | ||||||||
\(911\) | − | 564.279i | − | 0.619406i | −0.950833 | − | 0.309703i | \(-0.899770\pi\) | ||
0.950833 | − | 0.309703i | \(-0.100230\pi\) | |||||||
\(912\) | − | 10.4027i | − | 0.0114064i | ||||||
\(913\) | −2218.71 | −2.43013 | ||||||||
\(914\) | − | 712.852i | − | 0.779926i | ||||||
\(915\) | 98.0135 | 0.107119 | ||||||||
\(916\) | 1097.51i | 1.19815i | ||||||||
\(917\) | − | 589.038i | − | 0.642353i | ||||||
\(918\) | 39.3920i | 0.0429107i | ||||||||
\(919\) | 119.220i | 0.129728i | 0.997894 | + | 0.0648638i | \(0.0206613\pi\) | ||||
−0.997894 | + | 0.0648638i | \(0.979339\pi\) | |||||||
\(920\) | 215.024 | − | 288.738i | 0.233721 | − | 0.313846i | ||||
\(921\) | 54.4474 | 0.0591177 | ||||||||
\(922\) | −295.332 | −0.320317 | ||||||||
\(923\) | 1313.04 | 1.42258 | ||||||||
\(924\) | 184.292 | 0.199451 | ||||||||
\(925\) | − | 148.735i | − | 0.160795i | ||||||
\(926\) | −728.570 | −0.786792 | ||||||||
\(927\) | − | 1061.30i | − | 1.14488i | ||||||
\(928\) | −383.551 | −0.413309 | ||||||||
\(929\) | −1117.77 | −1.20319 | −0.601596 | − | 0.798800i | \(-0.705468\pi\) | ||||
−0.601596 | + | 0.798800i | \(0.705468\pi\) | |||||||
\(930\) | − | 43.8802i | − | 0.0471831i | ||||||
\(931\) | 92.7988i | 0.0996765i | ||||||||
\(932\) | −705.813 | −0.757310 | ||||||||
\(933\) | 42.0182 | 0.0450356 | ||||||||
\(934\) | 754.057i | 0.807341i | ||||||||
\(935\) | 236.587i | 0.253034i | ||||||||
\(936\) | 1153.55 | 1.23243 | ||||||||
\(937\) | − | 226.429i | − | 0.241653i | −0.992674 | − | 0.120827i | \(-0.961445\pi\) | ||
0.992674 | − | 0.120827i | \(-0.0385545\pi\) | |||||||
\(938\) | −286.298 | −0.305222 | ||||||||
\(939\) | 149.085i | 0.158769i | ||||||||
\(940\) | 102.440i | 0.108979i | ||||||||
\(941\) | − | 523.829i | − | 0.556672i | −0.960484 | − | 0.278336i | \(-0.910217\pi\) | ||
0.960484 | − | 0.278336i | \(-0.0897829\pi\) | |||||||
\(942\) | 42.0827i | 0.0446738i | ||||||||
\(943\) | 192.944 | + | 143.686i | 0.204607 | + | 0.152371i | ||||
\(944\) | −138.936 | −0.147178 | ||||||||
\(945\) | −129.077 | −0.136590 | ||||||||
\(946\) | −1086.55 | −1.14858 | ||||||||
\(947\) | −978.726 | −1.03350 | −0.516751 | − | 0.856136i | \(-0.672859\pi\) | ||||
−0.516751 | + | 0.856136i | \(0.672859\pi\) | |||||||
\(948\) | 122.021i | 0.128714i | ||||||||
\(949\) | 7.03025 | 0.00740806 | ||||||||
\(950\) | − | 26.2555i | − | 0.0276374i | ||||||
\(951\) | −205.634 | −0.216229 | ||||||||
\(952\) | 318.483 | 0.334541 | ||||||||
\(953\) | 1859.65i | 1.95136i | 0.219192 | + | 0.975682i | \(0.429658\pi\) | ||||
−0.219192 | + | 0.975682i | \(0.570342\pi\) | |||||||
\(954\) | − | 355.925i | − | 0.373087i | ||||||
\(955\) | −386.643 | −0.404862 | ||||||||
\(956\) | −534.835 | −0.559451 | ||||||||
\(957\) | − | 87.4425i | − | 0.0913715i | ||||||
\(958\) | − | 129.310i | − | 0.134979i | ||||||
\(959\) | 458.333 | 0.477928 | ||||||||
\(960\) | 11.5173i | 0.0119972i | ||||||||
\(961\) | 1492.13 | 1.55268 | ||||||||
\(962\) | 554.349i | 0.576246i | ||||||||
\(963\) | 1692.43i | 1.75745i | ||||||||
\(964\) | 98.7467i | 0.102434i | ||||||||
\(965\) | − | 255.483i | − | 0.264749i | ||||||
\(966\) | 44.4427 | − | 59.6785i | 0.0460069 | − | 0.0617790i | ||||
\(967\) | 598.954 | 0.619394 | 0.309697 | − | 0.950835i | \(-0.399772\pi\) | ||||
0.309697 | + | 0.950835i | \(0.399772\pi\) | |||||||
\(968\) | −1676.93 | −1.73237 | ||||||||
\(969\) | 11.5928 | 0.0119637 | ||||||||
\(970\) | 155.654 | 0.160468 | ||||||||
\(971\) | 678.046i | 0.698296i | 0.937068 | + | 0.349148i | \(0.113529\pi\) | ||||
−0.937068 | + | 0.349148i | \(0.886471\pi\) | |||||||
\(972\) | −282.148 | −0.290276 | ||||||||
\(973\) | − | 2172.71i | − | 2.23300i | ||||||
\(974\) | −532.507 | −0.546721 | ||||||||
\(975\) | 36.9176 | 0.0378642 | ||||||||
\(976\) | − | 553.155i | − | 0.566757i | ||||||
\(977\) | 302.051i | 0.309161i | 0.987980 | + | 0.154581i | \(0.0494026\pi\) | ||||
−0.987980 | + | 0.154581i | \(0.950597\pi\) | |||||||
\(978\) | −15.8112 | −0.0161669 | ||||||||
\(979\) | −942.469 | −0.962685 | ||||||||
\(980\) | 118.549i | 0.120968i | ||||||||
\(981\) | − | 1191.52i | − | 1.21460i | ||||||
\(982\) | −274.430 | −0.279461 | ||||||||
\(983\) | − | 19.2099i | − | 0.0195421i | −0.999952 | − | 0.00977105i | \(-0.996890\pi\) | ||
0.999952 | − | 0.00977105i | \(-0.00311027\pi\) | |||||||
\(984\) | −29.0090 | −0.0294807 | ||||||||
\(985\) | 311.241i | 0.315980i | ||||||||
\(986\) | − | 64.7626i | − | 0.0656822i | ||||||
\(987\) | 49.4038i | 0.0500545i | ||||||||
\(988\) | − | 293.570i | − | 0.297135i | ||||||
\(989\) | 786.076 | − | 1055.56i | 0.794819 | − | 1.06730i | ||||
\(990\) | 375.470 | 0.379263 | ||||||||
\(991\) | 1291.94 | 1.30367 | 0.651837 | − | 0.758359i | \(-0.273999\pi\) | ||||
0.651837 | + | 0.758359i | \(0.273999\pi\) | |||||||
\(992\) | −1634.46 | −1.64764 | ||||||||
\(993\) | −185.701 | −0.187010 | ||||||||
\(994\) | − | 575.324i | − | 0.578796i | ||||||
\(995\) | 548.612 | 0.551369 | ||||||||
\(996\) | 138.885i | 0.139443i | ||||||||
\(997\) | −1343.41 | −1.34745 | −0.673727 | − | 0.738981i | \(-0.735307\pi\) | ||||
−0.673727 | + | 0.738981i | \(0.735307\pi\) | |||||||
\(998\) | −8.15135 | −0.00816769 | ||||||||
\(999\) | − | 210.298i | − | 0.210509i |
(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 | 115.3.d.a.91.4 | yes | 6 | |
3.2 | odd | 2 | 1035.3.g.a.91.1 | 6 | |||
4.3 | odd | 2 | 1840.3.k.a.321.4 | 6 | |||
5.2 | odd | 4 | 575.3.c.c.574.4 | 12 | |||
5.3 | odd | 4 | 575.3.c.c.574.9 | 12 | |||
5.4 | even | 2 | 575.3.d.e.551.4 | 6 | |||
23.22 | odd | 2 | inner | 115.3.d.a.91.3 | ✓ | 6 | |
69.68 | even | 2 | 1035.3.g.a.91.6 | 6 | |||
92.91 | even | 2 | 1840.3.k.a.321.3 | 6 | |||
115.22 | even | 4 | 575.3.c.c.574.3 | 12 | |||
115.68 | even | 4 | 575.3.c.c.574.10 | 12 | |||
115.114 | odd | 2 | 575.3.d.e.551.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.3.d.a.91.3 | ✓ | 6 | 23.22 | odd | 2 | inner | |
115.3.d.a.91.4 | yes | 6 | 1.1 | even | 1 | trivial | |
575.3.c.c.574.3 | 12 | 115.22 | even | 4 | |||
575.3.c.c.574.4 | 12 | 5.2 | odd | 4 | |||
575.3.c.c.574.9 | 12 | 5.3 | odd | 4 | |||
575.3.c.c.574.10 | 12 | 115.68 | even | 4 | |||
575.3.d.e.551.3 | 6 | 115.114 | odd | 2 | |||
575.3.d.e.551.4 | 6 | 5.4 | even | 2 | |||
1035.3.g.a.91.1 | 6 | 3.2 | odd | 2 | |||
1035.3.g.a.91.6 | 6 | 69.68 | even | 2 | |||
1840.3.k.a.321.3 | 6 | 92.91 | even | 2 | |||
1840.3.k.a.321.4 | 6 | 4.3 | odd | 2 |