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 | 91.3 | ||
Root | \(0.396209 + 2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 115.91 |
Dual form | 115.3.d.a.91.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | \(0.198214\pi\) | ||||
−0.812303 | + | 0.583236i | \(0.801786\pi\) | |||||||
\(8\) | 7.00000 | 0.875000 | ||||||||
\(9\) | −8.84302 | −0.982558 | ||||||||
\(10\) | 2.23607i | 0.223607i | ||||||||
\(11\) | 18.9885i | 1.72622i | 0.505012 | + | 0.863112i | \(0.331488\pi\) | ||||
−0.505012 | + | 0.863112i | \(0.668512\pi\) | |||||||
\(12\) | −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 | \(-0.947598\pi\) | ||
0.986480 | − | 0.163884i | \(-0.0524023\pi\) | |||||||
\(18\) | 8.84302 | 0.491279 | ||||||||
\(19\) | 5.25110i | 0.276374i | 0.990406 | + | 0.138187i | \(0.0441274\pi\) | ||||
−0.990406 | + | 0.138187i | \(0.955873\pi\) | |||||||
\(20\) | 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 | \(-0.868320\pi\) | ||
0.915645 | − | 0.401987i | \(-0.131680\pi\) | |||||||
\(38\) | − | 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 | \(-0.768274\pi\) | ||
0.746514 | − | 0.665369i | \(-0.231726\pi\) | |||||||
\(44\) | − | 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 | \(0.123976\pi\) | ||||
−0.925106 | + | 0.379710i | \(0.876024\pi\) | |||||||
\(54\) | 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 | \(0.361491\pi\) | ||||
−0.421536 | + | 0.906812i | \(0.638509\pi\) | |||||||
\(62\) | −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 | \(-0.915729\pi\) | ||
0.965160 | − | 0.261662i | \(-0.0842706\pi\) | |||||||
\(68\) | 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 | \(0.225118\pi\) | ||||
−0.760164 | + | 0.649731i | \(0.774882\pi\) | |||||||
\(80\) | − | 11.1803i | − | 0.139754i | ||||||
\(81\) | 76.7861 | 0.947977 | ||||||||
\(82\) | 10.4595 | 0.127555 | ||||||||
\(83\) | 116.845i | 1.40777i | 0.710313 | + | 0.703886i | \(0.248553\pi\) | ||||
−0.710313 | + | 0.703886i | \(0.751447\pi\) | |||||||
\(84\) | − | 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 | \(0.0899504\pi\) | ||||
−0.960337 | + | 0.278841i | \(0.910050\pi\) | |||||||
\(90\) | − | 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 | \(-0.883180\pi\) | ||
0.933408 | − | 0.358818i | \(-0.116820\pi\) | |||||||
\(98\) | 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 | \(-0.802036\pi\) | ||
0.812759 | − | 0.582600i | \(-0.197964\pi\) | |||||||
\(104\) | −130.448 | −1.25431 | ||||||||
\(105\) | 7.23405 | 0.0688957 | ||||||||
\(106\) | − | 40.2492i | − | 0.379710i | ||||||
\(107\) | 191.386i | 1.78865i | 0.447415 | + | 0.894326i | \(0.352345\pi\) | ||||
−0.447415 | + | 0.894326i | \(0.647655\pi\) | |||||||
\(108\) | 21.2087 | 0.196377 | ||||||||
\(109\) | − | 134.741i | − | 1.23616i | −0.786115 | − | 0.618080i | \(-0.787911\pi\) | ||
0.786115 | − | 0.618080i | \(-0.212089\pi\) | |||||||
\(110\) | −42.4595 | −0.385995 | ||||||||
\(111\) | − | 11.7860i | − | 0.106180i | ||||||
\(112\) | 40.8265i | 0.364523i | ||||||||
\(113\) | 86.9688i | 0.769635i | 0.922993 | + | 0.384818i | \(0.125736\pi\) | ||||
−0.922993 | + | 0.384818i | \(0.874264\pi\) | |||||||
\(114\) | − | 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 | \(-0.934326\pi\) | ||
0.978791 | − | 0.204860i | \(-0.0656740\pi\) | |||||||
\(138\) | 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 | \(0.268099\pi\) | ||||
−0.665780 | + | 0.746148i | \(0.731901\pi\) | |||||||
\(150\) | 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 | \(0.109838\pi\) | ||||
−0.941053 | + | 0.338260i | \(0.890162\pi\) | |||||||
\(158\) | − | 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 | \(-0.969598\pi\) | ||
0.995442 | − | 0.0953657i | \(-0.0304020\pi\) | |||||||
\(182\) | 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 | \(-0.850479\pi\) | ||
0.891689 | − | 0.452650i | \(-0.149521\pi\) | |||||||
\(192\) | 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 | \(0.211429\pi\) | ||||
−0.787395 | + | 0.616449i | \(0.788571\pi\) | |||||||
\(200\) | −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 | \(-0.860691\pi\) | ||
0.905750 | − | 0.423813i | \(-0.139309\pi\) | |||||||
\(228\) | − | 6.24159i | − | 0.0273754i | ||||||
\(229\) | 365.836i | 1.59754i | 0.601638 | + | 0.798769i | \(0.294515\pi\) | ||||
−0.601638 | + | 0.798769i | \(0.705485\pi\) | |||||||
\(230\) | −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 | \(0.0217542\pi\) | ||||
−0.997666 | + | 0.0682896i | \(0.978246\pi\) | |||||||
\(242\) | 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 | \(0.125846\pi\) | ||||
−0.922859 | + | 0.385138i | \(0.874154\pi\) | |||||||
\(252\) | 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 | \(0.0601197\pi\) | ||||
−0.982217 | + | 0.187751i | \(0.939880\pi\) | |||||||
\(264\) | 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 | \(-0.656055\pi\) | ||
0.470856 | − | 0.882210i | \(-0.343945\pi\) | |||||||
\(282\) | 6.05045 | 0.0214555 | ||||||||
\(283\) | − | 191.002i | − | 0.674920i | −0.941340 | − | 0.337460i | \(-0.890432\pi\) | ||
0.941340 | − | 0.337460i | \(-0.109568\pi\) | |||||||
\(284\) | 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 | \(0.172702\pi\) | ||||
−0.856391 | + | 0.516329i | \(0.827298\pi\) | |||||||
\(294\) | 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 | \(-0.794736\pi\) | ||
0.799187 | − | 0.601083i | \(-0.205264\pi\) | |||||||
\(314\) | − | 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 | \(-0.897758\pi\) | ||
0.948856 | − | 0.315708i | \(-0.102242\pi\) | |||||||
\(338\) | −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 | \(0.126310\pi\) | ||||
−0.922296 | + | 0.386484i | \(0.873690\pi\) | |||||||
\(360\) | 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 | \(-0.939538\pi\) | ||
0.982014 | − | 0.188806i | \(-0.0604617\pi\) | |||||||
\(368\) | −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 | \(0.0264958\pi\) | ||||
−0.996538 | + | 0.0831431i | \(0.973504\pi\) | |||||||
\(374\) | −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 | \(-0.817531\pi\) | ||
0.840147 | − | 0.542358i | \(-0.182469\pi\) | |||||||
\(380\) | −35.2254 | −0.0926985 | ||||||||
\(381\) | 28.1639 | 0.0739210 | ||||||||
\(382\) | 172.912i | 0.452650i | ||||||||
\(383\) | 576.379i | 1.50490i | 0.658647 | + | 0.752452i | \(0.271129\pi\) | ||||
−0.658647 | + | 0.752452i | \(0.728871\pi\) | |||||||
\(384\) | 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 | \(0.0968744\pi\) | ||||
−0.954045 | + | 0.299664i | \(0.903126\pi\) | |||||||
\(390\) | − | 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 | \(-0.954454\pi\) | ||
0.989780 | − | 0.142600i | \(-0.0455464\pi\) | |||||||
\(402\) | 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 | \(-0.924952\pi\) | ||
0.972335 | − | 0.233592i | \(-0.0750480\pi\) | |||||||
\(420\) | −21.7022 | −0.0516718 | ||||||||
\(421\) | 348.840i | 0.828599i | 0.910141 | + | 0.414299i | \(0.135973\pi\) | ||||
−0.910141 | + | 0.414299i | \(0.864027\pi\) | |||||||
\(422\) | 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 | \(-0.889552\pi\) | ||
0.940403 | − | 0.340061i | \(-0.110448\pi\) | |||||||
\(432\) | −35.3478 | −0.0818236 | ||||||||
\(433\) | − | 345.030i | − | 0.796835i | −0.917204 | − | 0.398418i | \(-0.869560\pi\) | ||
0.917204 | − | 0.398418i | \(-0.130440\pi\) | |||||||
\(434\) | − | 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 | \(-0.715257\pi\) | ||
0.625872 | − | 0.779926i | \(-0.284743\pi\) | |||||||
\(458\) | − | 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 | \(0.299094\pi\) | ||||
−0.590085 | + | 0.807341i | \(0.700906\pi\) | |||||||
\(468\) | −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 | \(-0.956903\pi\) | ||
0.990848 | − | 0.134979i | \(-0.0430967\pi\) | |||||||
\(480\) | 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 | \(-0.935621\pi\) | ||
0.979617 | − | 0.200877i | \(-0.0643790\pi\) | |||||||
\(504\) | − | 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 | \(-0.850567\pi\) | ||
0.891814 | − | 0.452403i | \(-0.149433\pi\) | |||||||
\(522\) | 102.780 | 0.196897 | ||||||||
\(523\) | − | 141.188i | − | 0.269958i | −0.990848 | − | 0.134979i | \(-0.956903\pi\) | ||
0.990848 | − | 0.134979i | \(-0.0430967\pi\) | |||||||
\(524\) | −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 | \(0.110066\pi\) | ||||
−0.940811 | + | 0.338933i | \(0.889934\pi\) | |||||||
\(558\) | 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 | \(0.0803362\pi\) | ||||
−0.968320 | + | 0.249713i | \(0.919664\pi\) | |||||||
\(564\) | 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 | \(0.217313\pi\) | ||||
−0.775867 | + | 0.630897i | \(0.782687\pi\) | |||||||
\(570\) | −4.65221 | −0.00816177 | ||||||||
\(571\) | − | 828.411i | − | 1.45081i | −0.688324 | − | 0.725404i | \(-0.741653\pi\) | ||
0.688324 | − | 0.725404i | \(-0.258347\pi\) | |||||||
\(572\) | 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 | \(-0.778061\pi\) | ||
0.766615 | − | 0.642106i | \(-0.221939\pi\) | |||||||
\(614\) | −137.421 | −0.223813 | ||||||||
\(615\) | 9.26659i | 0.0150676i | ||||||||
\(616\) | −1085.33 | −1.76189 | ||||||||
\(617\) | 47.1461i | 0.0764119i | 0.999270 | + | 0.0382059i | \(0.0121643\pi\) | ||||
−0.999270 | + | 0.0382059i | \(0.987836\pi\) | |||||||
\(618\) | 47.5512i | 0.0769437i | ||||||||
\(619\) | 738.262i | 1.19267i | 0.802736 | + | 0.596335i | \(0.203377\pi\) | ||||
−0.802736 | + | 0.596335i | \(0.796623\pi\) | |||||||
\(620\) | 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 | \(-0.815206\pi\) | ||
0.836163 | − | 0.548482i | \(-0.184794\pi\) | |||||||
\(632\) | 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 | \(0.150210\pi\) | ||||
−0.890706 | + | 0.454580i | \(0.849790\pi\) | |||||||
\(642\) | − | 75.8287i | − | 0.118113i | ||||||
\(643\) | 600.348i | 0.933668i | 0.884345 | + | 0.466834i | \(0.154605\pi\) | ||||
−0.884345 | + | 0.466834i | \(0.845395\pi\) | |||||||
\(644\) | 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 | \(-0.977237\pi\) | ||
0.997444 | − | 0.0714516i | \(-0.0227632\pi\) | |||||||
\(660\) | −50.4685 | −0.0764674 | ||||||||
\(661\) | 705.908i | 1.06794i | 0.845504 | + | 0.533970i | \(0.179300\pi\) | ||||
−0.845504 | + | 0.533970i | \(0.820700\pi\) | |||||||
\(662\) | 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 | \(-0.761210\pi\) | ||
0.731566 | − | 0.681771i | \(-0.238790\pi\) | |||||||
\(678\) | − | 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 | \(0.106965\pi\) | ||||
−0.944067 | + | 0.329753i | \(0.893035\pi\) | |||||||
\(702\) | −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 | \(-0.763452\pi\) | ||
0.736349 | − | 0.676601i | \(-0.236548\pi\) | |||||||
\(710\) | − | 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 | \(0.229392\pi\) | ||||
−0.751373 | + | 0.659877i | \(0.770608\pi\) | |||||||
\(728\) | − | 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 | \(0.459975\pi\) | ||||
−0.125412 | + | 0.992105i | \(0.540025\pi\) | |||||||
\(734\) | 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 | \(0.0716439\pi\) | ||||
−0.974777 | + | 0.223180i | \(0.928356\pi\) | |||||||
\(744\) | 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 | \(0.0117564\pi\) | ||||
−0.999318 | + | 0.0369256i | \(0.988244\pi\) | |||||||
\(752\) | −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 | \(0.0535874\pi\) | ||||
−0.985863 | + | 0.167556i | \(0.946413\pi\) | |||||||
\(758\) | 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 | \(-0.811341\pi\) | ||
0.829442 | − | 0.558593i | \(-0.188659\pi\) | |||||||
\(770\) | − | 346.695i | − | 0.450253i | ||||||
\(771\) | −34.8722 | −0.0452298 | ||||||||
\(772\) | 342.766 | 0.443997 | ||||||||
\(773\) | 1350.61i | 1.74724i | 0.486612 | + | 0.873618i | \(0.338232\pi\) | ||||
−0.486612 | + | 0.873618i | \(0.661768\pi\) | |||||||
\(774\) | − | 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 | \(0.221925\pi\) | ||||
−0.766644 | + | 0.642072i | \(0.778075\pi\) | |||||||
\(788\) | −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 | \(0.236704\pi\) | ||||
−0.736017 | + | 0.676963i | \(0.763296\pi\) | |||||||
\(798\) | 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 | \(-0.969393\pi\) | ||
0.995381 | − | 0.0960063i | \(-0.0306069\pi\) | |||||||
\(828\) | −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 | \(-0.838047\pi\) | ||
0.873335 | − | 0.487120i | \(-0.161953\pi\) | |||||||
\(840\) | 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 | \(0.0468040\pi\) | ||||
−0.989209 | + | 0.146510i | \(0.953196\pi\) | |||||||
\(882\) | −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 | \(0.180371\pi\) | ||||
−0.843702 | + | 0.536812i | \(0.819629\pi\) | |||||||
\(908\) | 577.234i | 0.635720i | ||||||||
\(909\) | −1299.21 | −1.42927 | ||||||||
\(910\) | 340.249 | 0.373900 | ||||||||
\(911\) | 564.279i | 0.619406i | 0.950833 | + | 0.309703i | \(0.100230\pi\) | ||||
−0.950833 | + | 0.309703i | \(0.899770\pi\) | |||||||
\(912\) | 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 | \(-0.979339\pi\) | ||
0.997894 | − | 0.0648638i | \(-0.0206613\pi\) | |||||||
\(920\) | 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 | \(0.0385545\pi\) | ||||
−0.992674 | + | 0.120827i | \(0.961445\pi\) | |||||||
\(938\) | −286.298 | −0.305222 | ||||||||
\(939\) | − | 149.085i | − | 0.158769i | ||||||
\(940\) | − | 102.440i | − | 0.108979i | ||||||
\(941\) | 523.829i | 0.556672i | 0.960484 | + | 0.278336i | \(0.0897829\pi\) | ||||
−0.960484 | + | 0.278336i | \(0.910217\pi\) | |||||||
\(942\) | − | 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 | \(-0.570342\pi\) | ||
0.219192 | − | 0.975682i | \(-0.429658\pi\) | |||||||
\(954\) | 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 | \(-0.886471\pi\) | ||
0.937068 | − | 0.349148i | \(-0.113529\pi\) | |||||||
\(972\) | −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 | \(-0.950597\pi\) | ||
0.987980 | − | 0.154581i | \(-0.0494026\pi\) | |||||||
\(978\) | −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 | \(0.00311027\pi\) | ||||
−0.999952 | + | 0.00977105i | \(0.996890\pi\) | |||||||
\(984\) | −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.91.3 | ✓ | 6 | |
3.2 | odd | 2 | 1035.3.g.a.91.6 | 6 | |||
4.3 | odd | 2 | 1840.3.k.a.321.3 | 6 | |||
5.2 | odd | 4 | 575.3.c.c.574.3 | 12 | |||
5.3 | odd | 4 | 575.3.c.c.574.10 | 12 | |||
5.4 | even | 2 | 575.3.d.e.551.3 | 6 | |||
23.22 | odd | 2 | inner | 115.3.d.a.91.4 | yes | 6 | |
69.68 | even | 2 | 1035.3.g.a.91.1 | 6 | |||
92.91 | even | 2 | 1840.3.k.a.321.4 | 6 | |||
115.22 | even | 4 | 575.3.c.c.574.4 | 12 | |||
115.68 | even | 4 | 575.3.c.c.574.9 | 12 | |||
115.114 | odd | 2 | 575.3.d.e.551.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.3.d.a.91.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
115.3.d.a.91.4 | yes | 6 | 23.22 | odd | 2 | inner | |
575.3.c.c.574.3 | 12 | 5.2 | odd | 4 | |||
575.3.c.c.574.4 | 12 | 115.22 | even | 4 | |||
575.3.c.c.574.9 | 12 | 115.68 | even | 4 | |||
575.3.c.c.574.10 | 12 | 5.3 | odd | 4 | |||
575.3.d.e.551.3 | 6 | 5.4 | even | 2 | |||
575.3.d.e.551.4 | 6 | 115.114 | odd | 2 | |||
1035.3.g.a.91.1 | 6 | 69.68 | even | 2 | |||
1035.3.g.a.91.6 | 6 | 3.2 | odd | 2 | |||
1840.3.k.a.321.3 | 6 | 4.3 | odd | 2 | |||
1840.3.k.a.321.4 | 6 | 92.91 | even | 2 |