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 | 91.1 | ||
Root | \(-4.73103 + 2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 115.91 |
Dual form | 115.3.d.a.91.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | \(0.580431\pi\) | |||||||
\(3\) | −4.73103 | −1.57701 | −0.788505 | − | 0.615028i | \(-0.789145\pi\) | ||||
−0.788505 | + | 0.615028i | \(0.789145\pi\) | |||||||
\(4\) | −3.00000 | −0.750000 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 4.73103 | 0.788505 | ||||||||
\(7\) | 7.39757i | 1.05680i | 0.848997 | + | 0.528398i | \(0.177207\pi\) | ||||
−0.848997 | + | 0.528398i | \(0.822793\pi\) | |||||||
\(8\) | 7.00000 | 0.875000 | ||||||||
\(9\) | 13.3827 | 1.48696 | ||||||||
\(10\) | 2.23607i | 0.223607i | ||||||||
\(11\) | − | 16.9416i | − | 1.54015i | −0.637956 | − | 0.770073i | \(-0.720220\pi\) | ||
0.637956 | − | 0.770073i | \(-0.279780\pi\) | |||||||
\(12\) | 14.1931 | 1.18276 | ||||||||
\(13\) | 13.8447 | 1.06498 | 0.532490 | − | 0.846436i | \(-0.321256\pi\) | ||||
0.532490 | + | 0.846436i | \(0.321256\pi\) | |||||||
\(14\) | − | 7.39757i | − | 0.528398i | ||||||
\(15\) | 10.5789i | 0.705261i | ||||||||
\(16\) | 5.00000 | 0.312500 | ||||||||
\(17\) | 30.3580i | 1.78577i | 0.450290 | + | 0.892883i | \(0.351321\pi\) | ||||
−0.450290 | + | 0.892883i | \(0.648679\pi\) | |||||||
\(18\) | −13.3827 | −0.743482 | ||||||||
\(19\) | 6.01884i | 0.316781i | 0.987377 | + | 0.158391i | \(0.0506305\pi\) | ||||
−0.987377 | + | 0.158391i | \(0.949369\pi\) | |||||||
\(20\) | 6.70820i | 0.335410i | ||||||||
\(21\) | − | 34.9981i | − | 1.66658i | ||||||
\(22\) | 16.9416i | 0.770073i | ||||||||
\(23\) | −1.34836 | − | 22.9604i | −0.0586244 | − | 0.998280i | ||||
\(24\) | −33.1172 | −1.37988 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | −13.8447 | −0.532490 | ||||||||
\(27\) | −20.7346 | −0.767947 | ||||||||
\(28\) | − | 22.1927i | − | 0.792596i | ||||||
\(29\) | 42.3862 | 1.46159 | 0.730796 | − | 0.682595i | \(-0.239149\pi\) | ||||
0.730796 | + | 0.682595i | \(0.239149\pi\) | |||||||
\(30\) | − | 10.5789i | − | 0.352630i | ||||||
\(31\) | −17.1480 | −0.553162 | −0.276581 | − | 0.960991i | \(-0.589201\pi\) | ||||
−0.276581 | + | 0.960991i | \(0.589201\pi\) | |||||||
\(32\) | −33.0000 | −1.03125 | ||||||||
\(33\) | 80.1513i | 2.42883i | ||||||||
\(34\) | − | 30.3580i | − | 0.892883i | ||||||
\(35\) | 16.5415 | 0.472613 | ||||||||
\(36\) | −40.1480 | −1.11522 | ||||||||
\(37\) | − | 28.2115i | − | 0.762474i | −0.924477 | − | 0.381237i | \(-0.875498\pi\) | ||
0.924477 | − | 0.381237i | \(-0.124502\pi\) | |||||||
\(38\) | − | 6.01884i | − | 0.158391i | ||||||
\(39\) | −65.4999 | −1.67948 | ||||||||
\(40\) | − | 15.6525i | − | 0.391312i | ||||||
\(41\) | 69.8826 | 1.70445 | 0.852226 | − | 0.523173i | \(-0.175252\pi\) | ||||
0.852226 | + | 0.523173i | \(0.175252\pi\) | |||||||
\(42\) | 34.9981i | 0.833289i | ||||||||
\(43\) | 17.7093i | 0.411845i | 0.978568 | + | 0.205923i | \(0.0660195\pi\) | ||||
−0.978568 | + | 0.205923i | \(0.933980\pi\) | |||||||
\(44\) | 50.8248i | 1.15511i | ||||||||
\(45\) | − | 29.9246i | − | 0.664990i | ||||||
\(46\) | 1.34836 | + | 22.9604i | 0.0293122 | + | 0.499140i | ||||
\(47\) | 49.6895 | 1.05722 | 0.528611 | − | 0.848864i | \(-0.322713\pi\) | ||||
0.528611 | + | 0.848864i | \(0.322713\pi\) | |||||||
\(48\) | −23.6552 | −0.492816 | ||||||||
\(49\) | −5.72398 | −0.116816 | ||||||||
\(50\) | 5.00000 | 0.100000 | ||||||||
\(51\) | − | 143.625i | − | 2.81617i | ||||||
\(52\) | −41.5342 | −0.798735 | ||||||||
\(53\) | 40.2492i | 0.759419i | 0.925106 | + | 0.379710i | \(0.123976\pi\) | ||||
−0.925106 | + | 0.379710i | \(0.876024\pi\) | |||||||
\(54\) | 20.7346 | 0.383973 | ||||||||
\(55\) | −37.8826 | −0.688774 | ||||||||
\(56\) | 51.7830i | 0.924696i | ||||||||
\(57\) | − | 28.4753i | − | 0.499567i | ||||||
\(58\) | −42.3862 | −0.730796 | ||||||||
\(59\) | 40.6066 | 0.688247 | 0.344123 | − | 0.938924i | \(-0.388176\pi\) | ||||
0.344123 | + | 0.938924i | \(0.388176\pi\) | |||||||
\(60\) | − | 31.7367i | − | 0.528946i | ||||||
\(61\) | 2.84083i | 0.0465710i | 0.999729 | + | 0.0232855i | \(0.00741267\pi\) | ||||
−0.999729 | + | 0.0232855i | \(0.992587\pi\) | |||||||
\(62\) | 17.1480 | 0.276581 | ||||||||
\(63\) | 98.9992i | 1.57142i | ||||||||
\(64\) | 13.0000 | 0.203125 | ||||||||
\(65\) | − | 30.9578i | − | 0.476273i | ||||||
\(66\) | − | 80.1513i | − | 1.21441i | ||||||
\(67\) | 35.2619i | 0.526297i | 0.964755 | + | 0.263149i | \(0.0847610\pi\) | ||||
−0.964755 | + | 0.263149i | \(0.915239\pi\) | |||||||
\(68\) | − | 91.0740i | − | 1.33932i | ||||||
\(69\) | 6.37914 | + | 108.627i | 0.0924514 | + | 1.57430i | ||||
\(70\) | −16.5415 | −0.236307 | ||||||||
\(71\) | 9.88257 | 0.139191 | 0.0695956 | − | 0.997575i | \(-0.477829\pi\) | ||||
0.0695956 | + | 0.997575i | \(0.477829\pi\) | |||||||
\(72\) | 93.6787 | 1.30109 | ||||||||
\(73\) | 30.3862 | 0.416249 | 0.208125 | − | 0.978102i | \(-0.433264\pi\) | ||||
0.208125 | + | 0.978102i | \(0.433264\pi\) | |||||||
\(74\) | 28.2115i | 0.381237i | ||||||||
\(75\) | 23.6552 | 0.315402 | ||||||||
\(76\) | − | 18.0565i | − | 0.237586i | ||||||
\(77\) | 125.327 | 1.62762 | ||||||||
\(78\) | 65.4999 | 0.839742 | ||||||||
\(79\) | 98.0510i | 1.24115i | 0.784146 | + | 0.620576i | \(0.213101\pi\) | ||||
−0.784146 | + | 0.620576i | \(0.786899\pi\) | |||||||
\(80\) | − | 11.1803i | − | 0.139754i | ||||||
\(81\) | −22.3482 | −0.275903 | ||||||||
\(82\) | −69.8826 | −0.852226 | ||||||||
\(83\) | − | 100.271i | − | 1.20808i | −0.796953 | − | 0.604041i | \(-0.793556\pi\) | ||
0.796953 | − | 0.604041i | \(-0.206444\pi\) | |||||||
\(84\) | 104.994i | 1.24993i | ||||||||
\(85\) | 67.8826 | 0.798618 | ||||||||
\(86\) | − | 17.7093i | − | 0.205923i | ||||||
\(87\) | −200.530 | −2.30495 | ||||||||
\(88\) | − | 118.591i | − | 1.34763i | ||||||
\(89\) | − | 28.3683i | − | 0.318745i | −0.987219 | − | 0.159373i | \(-0.949053\pi\) | ||
0.987219 | − | 0.159373i | \(-0.0509471\pi\) | |||||||
\(90\) | 29.9246i | 0.332495i | ||||||||
\(91\) | 102.417i | 1.12547i | ||||||||
\(92\) | 4.04509 | + | 68.8813i | 0.0439683 | + | 0.748710i | ||||
\(93\) | 81.1278 | 0.872342 | ||||||||
\(94\) | −49.6895 | −0.528611 | ||||||||
\(95\) | 13.4585 | 0.141669 | ||||||||
\(96\) | 156.124 | 1.62629 | ||||||||
\(97\) | − | 174.330i | − | 1.79722i | −0.438753 | − | 0.898608i | \(-0.644580\pi\) | ||
0.438753 | − | 0.898608i | \(-0.355420\pi\) | |||||||
\(98\) | 5.72398 | 0.0584080 | ||||||||
\(99\) | − | 226.724i | − | 2.29014i | ||||||
\(100\) | 15.0000 | 0.150000 | ||||||||
\(101\) | −13.7651 | −0.136289 | −0.0681443 | − | 0.997675i | \(-0.521708\pi\) | ||||
−0.0681443 | + | 0.997675i | \(0.521708\pi\) | |||||||
\(102\) | 143.625i | 1.40809i | ||||||||
\(103\) | 65.7767i | 0.638609i | 0.947652 | + | 0.319304i | \(0.103449\pi\) | ||||
−0.947652 | + | 0.319304i | \(0.896551\pi\) | |||||||
\(104\) | 96.9132 | 0.931857 | ||||||||
\(105\) | −78.2582 | −0.745316 | ||||||||
\(106\) | − | 40.2492i | − | 0.379710i | ||||||
\(107\) | 116.455i | 1.08836i | 0.838968 | + | 0.544181i | \(0.183160\pi\) | ||||
−0.838968 | + | 0.544181i | \(0.816840\pi\) | |||||||
\(108\) | 62.2037 | 0.575960 | ||||||||
\(109\) | − | 130.903i | − | 1.20094i | −0.799647 | − | 0.600471i | \(-0.794980\pi\) | ||
0.799647 | − | 0.600471i | \(-0.205020\pi\) | |||||||
\(110\) | 37.8826 | 0.344387 | ||||||||
\(111\) | 133.470i | 1.20243i | ||||||||
\(112\) | 36.9878i | 0.330248i | ||||||||
\(113\) | 10.5022i | 0.0929398i | 0.998920 | + | 0.0464699i | \(0.0147972\pi\) | ||||
−0.998920 | + | 0.0464699i | \(0.985203\pi\) | |||||||
\(114\) | 28.4753i | 0.249784i | ||||||||
\(115\) | −51.3411 | + | 3.01503i | −0.446444 | + | 0.0262176i | ||||
\(116\) | −127.159 | −1.09619 | ||||||||
\(117\) | 185.280 | 1.58359 | ||||||||
\(118\) | −40.6066 | −0.344123 | ||||||||
\(119\) | −224.575 | −1.88719 | ||||||||
\(120\) | 74.0524i | 0.617103i | ||||||||
\(121\) | −166.018 | −1.37205 | ||||||||
\(122\) | − | 2.84083i | − | 0.0232855i | ||||||
\(123\) | −330.617 | −2.68794 | ||||||||
\(124\) | 51.4440 | 0.414871 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | − | 98.9992i | − | 0.785708i | ||||||
\(127\) | −188.758 | −1.48628 | −0.743141 | − | 0.669135i | \(-0.766665\pi\) | ||||
−0.743141 | + | 0.669135i | \(0.766665\pi\) | |||||||
\(128\) | 119.000 | 0.929688 | ||||||||
\(129\) | − | 83.7835i | − | 0.649484i | ||||||
\(130\) | 30.9578i | 0.238137i | ||||||||
\(131\) | 99.4691 | 0.759306 | 0.379653 | − | 0.925129i | \(-0.376043\pi\) | ||||
0.379653 | + | 0.925129i | \(0.376043\pi\) | |||||||
\(132\) | − | 240.454i | − | 1.82162i | ||||||
\(133\) | −44.5248 | −0.334773 | ||||||||
\(134\) | − | 35.2619i | − | 0.263149i | ||||||
\(135\) | 46.3639i | 0.343436i | ||||||||
\(136\) | 212.506i | 1.56254i | ||||||||
\(137\) | 80.6789i | 0.588897i | 0.955667 | + | 0.294448i | \(0.0951359\pi\) | ||||
−0.955667 | + | 0.294448i | \(0.904864\pi\) | |||||||
\(138\) | −6.37914 | − | 108.627i | −0.0462257 | − | 0.787149i | ||||
\(139\) | 125.870 | 0.905538 | 0.452769 | − | 0.891628i | \(-0.350436\pi\) | ||||
0.452769 | + | 0.891628i | \(0.350436\pi\) | |||||||
\(140\) | −49.6244 | −0.354460 | ||||||||
\(141\) | −235.083 | −1.66725 | ||||||||
\(142\) | −9.88257 | −0.0695956 | ||||||||
\(143\) | − | 234.552i | − | 1.64022i | ||||||
\(144\) | 66.9134 | 0.464676 | ||||||||
\(145\) | − | 94.7784i | − | 0.653644i | ||||||
\(146\) | −30.3862 | −0.208125 | ||||||||
\(147\) | 27.0803 | 0.184220 | ||||||||
\(148\) | 84.6346i | 0.571856i | ||||||||
\(149\) | 68.6512i | 0.460746i | 0.973102 | + | 0.230373i | \(0.0739947\pi\) | ||||
−0.973102 | + | 0.230373i | \(0.926005\pi\) | |||||||
\(150\) | −23.6552 | −0.157701 | ||||||||
\(151\) | 83.8681 | 0.555418 | 0.277709 | − | 0.960665i | \(-0.410425\pi\) | ||||
0.277709 | + | 0.960665i | \(0.410425\pi\) | |||||||
\(152\) | 42.1319i | 0.277184i | ||||||||
\(153\) | 406.271i | 2.65537i | ||||||||
\(154\) | −125.327 | −0.813809 | ||||||||
\(155\) | 38.3441i | 0.247381i | ||||||||
\(156\) | 196.500 | 1.25961 | ||||||||
\(157\) | 26.6761i | 0.169911i | 0.996385 | + | 0.0849556i | \(0.0270748\pi\) | ||||
−0.996385 | + | 0.0849556i | \(0.972925\pi\) | |||||||
\(158\) | − | 98.0510i | − | 0.620576i | ||||||
\(159\) | − | 190.420i | − | 1.19761i | ||||||
\(160\) | 73.7902i | 0.461189i | ||||||||
\(161\) | 169.851 | − | 9.97460i | 1.05498 | − | 0.0619540i | ||||
\(162\) | 22.3482 | 0.137952 | ||||||||
\(163\) | −57.5342 | −0.352971 | −0.176485 | − | 0.984303i | \(-0.556473\pi\) | ||||
−0.176485 | + | 0.984303i | \(0.556473\pi\) | |||||||
\(164\) | −209.648 | −1.27834 | ||||||||
\(165\) | 179.224 | 1.08620 | ||||||||
\(166\) | 100.271i | 0.604041i | ||||||||
\(167\) | 11.3934 | 0.0682242 | 0.0341121 | − | 0.999418i | \(-0.489140\pi\) | ||||
0.0341121 | + | 0.999418i | \(0.489140\pi\) | |||||||
\(168\) | − | 244.987i | − | 1.45826i | ||||||
\(169\) | 22.6767 | 0.134182 | ||||||||
\(170\) | −67.8826 | −0.399309 | ||||||||
\(171\) | 80.5482i | 0.471042i | ||||||||
\(172\) | − | 53.1280i | − | 0.308884i | ||||||
\(173\) | 229.875 | 1.32876 | 0.664378 | − | 0.747397i | \(-0.268697\pi\) | ||||
0.664378 | + | 0.747397i | \(0.268697\pi\) | |||||||
\(174\) | 200.530 | 1.15247 | ||||||||
\(175\) | − | 36.9878i | − | 0.211359i | ||||||
\(176\) | − | 84.7080i | − | 0.481295i | ||||||
\(177\) | −192.111 | −1.08537 | ||||||||
\(178\) | 28.3683i | 0.159373i | ||||||||
\(179\) | 75.4691 | 0.421615 | 0.210808 | − | 0.977528i | \(-0.432391\pi\) | ||||
0.210808 | + | 0.977528i | \(0.432391\pi\) | |||||||
\(180\) | 89.7737i | 0.498743i | ||||||||
\(181\) | 119.179i | 0.658445i | 0.944252 | + | 0.329222i | \(0.106787\pi\) | ||||
−0.944252 | + | 0.329222i | \(0.893213\pi\) | |||||||
\(182\) | − | 102.417i | − | 0.562733i | ||||||
\(183\) | − | 13.4401i | − | 0.0734429i | ||||||
\(184\) | −9.43853 | − | 160.723i | −0.0512964 | − | 0.873495i | ||||
\(185\) | −63.0829 | −0.340989 | ||||||||
\(186\) | −81.1278 | −0.436171 | ||||||||
\(187\) | 514.313 | 2.75034 | ||||||||
\(188\) | −149.068 | −0.792917 | ||||||||
\(189\) | − | 153.385i | − | 0.811562i | ||||||
\(190\) | −13.4585 | −0.0708344 | ||||||||
\(191\) | 111.457i | 0.583547i | 0.956487 | + | 0.291773i | \(0.0942453\pi\) | ||||
−0.956487 | + | 0.291773i | \(0.905755\pi\) | |||||||
\(192\) | −61.5034 | −0.320330 | ||||||||
\(193\) | 125.123 | 0.648305 | 0.324153 | − | 0.946005i | \(-0.394921\pi\) | ||||
0.324153 | + | 0.946005i | \(0.394921\pi\) | |||||||
\(194\) | 174.330i | 0.898608i | ||||||||
\(195\) | 146.462i | 0.751088i | ||||||||
\(196\) | 17.1719 | 0.0876120 | ||||||||
\(197\) | −296.716 | −1.50617 | −0.753087 | − | 0.657921i | \(-0.771436\pi\) | ||||
−0.753087 | + | 0.657921i | \(0.771436\pi\) | |||||||
\(198\) | 226.724i | 1.14507i | ||||||||
\(199\) | − | 195.027i | − | 0.980034i | −0.871713 | − | 0.490017i | \(-0.836990\pi\) | ||
0.871713 | − | 0.490017i | \(-0.163010\pi\) | |||||||
\(200\) | −35.0000 | −0.175000 | ||||||||
\(201\) | − | 166.825i | − | 0.829977i | ||||||
\(202\) | 13.7651 | 0.0681443 | ||||||||
\(203\) | 313.555i | 1.54460i | ||||||||
\(204\) | 430.874i | 2.11213i | ||||||||
\(205\) | − | 156.262i | − | 0.762255i | ||||||
\(206\) | − | 65.7767i | − | 0.319304i | ||||||
\(207\) | −18.0447 | − | 307.272i | −0.0871724 | − | 1.48441i | ||||
\(208\) | 69.2237 | 0.332806 | ||||||||
\(209\) | 101.969 | 0.487889 | ||||||||
\(210\) | 78.2582 | 0.372658 | ||||||||
\(211\) | 195.386 | 0.925998 | 0.462999 | − | 0.886359i | \(-0.346773\pi\) | ||||
0.462999 | + | 0.886359i | \(0.346773\pi\) | |||||||
\(212\) | − | 120.748i | − | 0.569564i | ||||||
\(213\) | −46.7548 | −0.219506 | ||||||||
\(214\) | − | 116.455i | − | 0.544181i | ||||||
\(215\) | 39.5993 | 0.184183 | ||||||||
\(216\) | −145.142 | −0.671953 | ||||||||
\(217\) | − | 126.854i | − | 0.584579i | ||||||
\(218\) | 130.903i | 0.600471i | ||||||||
\(219\) | −143.758 | −0.656430 | ||||||||
\(220\) | 113.648 | 0.516581 | ||||||||
\(221\) | 420.299i | 1.90180i | ||||||||
\(222\) | − | 133.470i | − | 0.601215i | ||||||
\(223\) | −65.3033 | −0.292840 | −0.146420 | − | 0.989223i | \(-0.546775\pi\) | ||||
−0.146420 | + | 0.989223i | \(0.546775\pi\) | |||||||
\(224\) | − | 244.120i | − | 1.08982i | ||||||
\(225\) | −66.9134 | −0.297393 | ||||||||
\(226\) | − | 10.5022i | − | 0.0464699i | ||||||
\(227\) | − | 248.917i | − | 1.09655i | −0.836299 | − | 0.548274i | \(-0.815285\pi\) | ||
0.836299 | − | 0.548274i | \(-0.184715\pi\) | |||||||
\(228\) | 85.4260i | 0.374676i | ||||||||
\(229\) | 203.690i | 0.889476i | 0.895661 | + | 0.444738i | \(0.146703\pi\) | ||||
−0.895661 | + | 0.444738i | \(0.853297\pi\) | |||||||
\(230\) | 51.3411 | − | 3.01503i | 0.223222 | − | 0.0131088i | ||||
\(231\) | −592.924 | −2.56677 | ||||||||
\(232\) | 296.703 | 1.27889 | ||||||||
\(233\) | 170.311 | 0.730946 | 0.365473 | − | 0.930822i | \(-0.380907\pi\) | ||||
0.365473 | + | 0.930822i | \(0.380907\pi\) | |||||||
\(234\) | −185.280 | −0.791793 | ||||||||
\(235\) | − | 111.109i | − | 0.472804i | ||||||
\(236\) | −121.820 | −0.516185 | ||||||||
\(237\) | − | 463.883i | − | 1.95731i | ||||||
\(238\) | 224.575 | 0.943594 | ||||||||
\(239\) | 232.938 | 0.974637 | 0.487318 | − | 0.873224i | \(-0.337975\pi\) | ||||
0.487318 | + | 0.873224i | \(0.337975\pi\) | |||||||
\(240\) | 52.8946i | 0.220394i | ||||||||
\(241\) | 373.790i | 1.55100i | 0.631349 | + | 0.775499i | \(0.282502\pi\) | ||||
−0.631349 | + | 0.775499i | \(0.717498\pi\) | |||||||
\(242\) | 166.018 | 0.686024 | ||||||||
\(243\) | 292.341 | 1.20305 | ||||||||
\(244\) | − | 8.52249i | − | 0.0349282i | ||||||
\(245\) | 12.7992i | 0.0522417i | ||||||||
\(246\) | 330.617 | 1.34397 | ||||||||
\(247\) | 83.3293i | 0.337366i | ||||||||
\(248\) | −120.036 | −0.484016 | ||||||||
\(249\) | 474.385i | 1.90516i | ||||||||
\(250\) | − | 11.1803i | − | 0.0447214i | ||||||
\(251\) | − | 84.1207i | − | 0.335142i | −0.985860 | − | 0.167571i | \(-0.946408\pi\) | ||
0.985860 | − | 0.167571i | \(-0.0535924\pi\) | |||||||
\(252\) | − | 296.998i | − | 1.17856i | ||||||
\(253\) | −388.987 | + | 22.8434i | −1.53750 | + | 0.0902902i | ||||
\(254\) | 188.758 | 0.743141 | ||||||||
\(255\) | −321.155 | −1.25943 | ||||||||
\(256\) | −171.000 | −0.667969 | ||||||||
\(257\) | −327.255 | −1.27337 | −0.636684 | − | 0.771125i | \(-0.719694\pi\) | ||||
−0.636684 | + | 0.771125i | \(0.719694\pi\) | |||||||
\(258\) | 83.7835i | 0.324742i | ||||||||
\(259\) | 208.697 | 0.805779 | ||||||||
\(260\) | 92.8733i | 0.357205i | ||||||||
\(261\) | 567.241 | 2.17334 | ||||||||
\(262\) | −99.4691 | −0.379653 | ||||||||
\(263\) | − | 434.052i | − | 1.65039i | −0.564849 | − | 0.825194i | \(-0.691066\pi\) | ||
0.564849 | − | 0.825194i | \(-0.308934\pi\) | |||||||
\(264\) | 561.059i | 2.12522i | ||||||||
\(265\) | 90.0000 | 0.339623 | ||||||||
\(266\) | 44.5248 | 0.167386 | ||||||||
\(267\) | 134.211i | 0.502664i | ||||||||
\(268\) | − | 105.786i | − | 0.394723i | ||||||
\(269\) | −2.80140 | −0.0104141 | −0.00520706 | − | 0.999986i | \(-0.501657\pi\) | ||||
−0.00520706 | + | 0.999986i | \(0.501657\pi\) | |||||||
\(270\) | − | 46.3639i | − | 0.171718i | ||||||
\(271\) | 192.728 | 0.711175 | 0.355588 | − | 0.934643i | \(-0.384281\pi\) | ||||
0.355588 | + | 0.934643i | \(0.384281\pi\) | |||||||
\(272\) | 151.790i | 0.558052i | ||||||||
\(273\) | − | 484.540i | − | 1.77487i | ||||||
\(274\) | − | 80.6789i | − | 0.294448i | ||||||
\(275\) | 84.7080i | 0.308029i | ||||||||
\(276\) | −19.1374 | − | 325.880i | −0.0693385 | − | 1.18072i | ||||
\(277\) | 320.620 | 1.15747 | 0.578736 | − | 0.815515i | \(-0.303546\pi\) | ||||
0.578736 | + | 0.815515i | \(0.303546\pi\) | |||||||
\(278\) | −125.870 | −0.452769 | ||||||||
\(279\) | −229.486 | −0.822531 | ||||||||
\(280\) | 115.790 | 0.413537 | ||||||||
\(281\) | − | 481.983i | − | 1.71524i | −0.514283 | − | 0.857621i | \(-0.671942\pi\) | ||
0.514283 | − | 0.857621i | \(-0.328058\pi\) | |||||||
\(282\) | 235.083 | 0.833626 | ||||||||
\(283\) | 88.7608i | 0.313642i | 0.987627 | + | 0.156821i | \(0.0501246\pi\) | ||||
−0.987627 | + | 0.156821i | \(0.949875\pi\) | |||||||
\(284\) | −29.6477 | −0.104393 | ||||||||
\(285\) | −63.6728 | −0.223413 | ||||||||
\(286\) | 234.552i | 0.820112i | ||||||||
\(287\) | 516.961i | 1.80126i | ||||||||
\(288\) | −441.628 | −1.53343 | ||||||||
\(289\) | −632.609 | −2.18896 | ||||||||
\(290\) | 94.7784i | 0.326822i | ||||||||
\(291\) | 824.761i | 2.83423i | ||||||||
\(292\) | −91.1586 | −0.312187 | ||||||||
\(293\) | − | 212.736i | − | 0.726062i | −0.931777 | − | 0.363031i | \(-0.881742\pi\) | ||
0.931777 | − | 0.363031i | \(-0.118258\pi\) | |||||||
\(294\) | −27.0803 | −0.0921100 | ||||||||
\(295\) | − | 90.7990i | − | 0.307793i | ||||||
\(296\) | − | 197.481i | − | 0.667165i | ||||||
\(297\) | 351.277i | 1.18275i | ||||||||
\(298\) | − | 68.6512i | − | 0.230373i | ||||||
\(299\) | −18.6677 | − | 317.881i | −0.0624338 | − | 1.06315i | ||||
\(300\) | −70.9655 | −0.236552 | ||||||||
\(301\) | −131.006 | −0.435236 | ||||||||
\(302\) | −83.8681 | −0.277709 | ||||||||
\(303\) | 65.1233 | 0.214928 | ||||||||
\(304\) | 30.0942i | 0.0989941i | ||||||||
\(305\) | 6.35229 | 0.0208272 | ||||||||
\(306\) | − | 406.271i | − | 1.32768i | ||||||
\(307\) | −411.377 | −1.33999 | −0.669995 | − | 0.742365i | \(-0.733704\pi\) | ||||
−0.669995 | + | 0.742365i | \(0.733704\pi\) | |||||||
\(308\) | −375.980 | −1.22071 | ||||||||
\(309\) | − | 311.192i | − | 1.00709i | ||||||
\(310\) | − | 38.3441i | − | 0.123691i | ||||||
\(311\) | −146.924 | −0.472424 | −0.236212 | − | 0.971702i | \(-0.575906\pi\) | ||||
−0.236212 | + | 0.971702i | \(0.575906\pi\) | |||||||
\(312\) | −458.499 | −1.46955 | ||||||||
\(313\) | 336.949i | 1.07652i | 0.842780 | + | 0.538258i | \(0.180917\pi\) | ||||
−0.842780 | + | 0.538258i | \(0.819083\pi\) | |||||||
\(314\) | − | 26.6761i | − | 0.0849556i | ||||||
\(315\) | 221.369 | 0.702758 | ||||||||
\(316\) | − | 294.153i | − | 0.930864i | ||||||
\(317\) | −400.963 | −1.26487 | −0.632434 | − | 0.774614i | \(-0.717944\pi\) | ||||
−0.632434 | + | 0.774614i | \(0.717944\pi\) | |||||||
\(318\) | 190.420i | 0.598806i | ||||||||
\(319\) | − | 718.090i | − | 2.25107i | ||||||
\(320\) | − | 29.0689i | − | 0.0908403i | ||||||
\(321\) | − | 550.951i | − | 1.71636i | ||||||
\(322\) | −169.851 | + | 9.97460i | −0.527489 | + | 0.0309770i | ||||
\(323\) | −182.720 | −0.565697 | ||||||||
\(324\) | 67.0445 | 0.206927 | ||||||||
\(325\) | −69.2237 | −0.212996 | ||||||||
\(326\) | 57.5342 | 0.176485 | ||||||||
\(327\) | 619.305i | 1.89390i | ||||||||
\(328\) | 489.178 | 1.49140 | ||||||||
\(329\) | 367.581i | 1.11727i | ||||||||
\(330\) | −179.224 | −0.543102 | ||||||||
\(331\) | −605.346 | −1.82884 | −0.914419 | − | 0.404768i | \(-0.867352\pi\) | ||||
−0.914419 | + | 0.404768i | \(0.867352\pi\) | |||||||
\(332\) | 300.813i | 0.906062i | ||||||||
\(333\) | − | 377.546i | − | 1.13377i | ||||||
\(334\) | −11.3934 | −0.0341121 | ||||||||
\(335\) | 78.8481 | 0.235367 | ||||||||
\(336\) | − | 174.991i | − | 0.520805i | ||||||
\(337\) | 381.287i | 1.13142i | 0.824605 | + | 0.565708i | \(0.191397\pi\) | ||||
−0.824605 | + | 0.565708i | \(0.808603\pi\) | |||||||
\(338\) | −22.6767 | −0.0670909 | ||||||||
\(339\) | − | 49.6862i | − | 0.146567i | ||||||
\(340\) | −203.648 | −0.598964 | ||||||||
\(341\) | 290.515i | 0.851949i | ||||||||
\(342\) | − | 80.5482i | − | 0.235521i | ||||||
\(343\) | 320.137i | 0.933345i | ||||||||
\(344\) | 123.965i | 0.360365i | ||||||||
\(345\) | 242.896 | − | 14.2642i | 0.704048 | − | 0.0413455i | ||||
\(346\) | −229.875 | −0.664378 | ||||||||
\(347\) | 549.405 | 1.58330 | 0.791650 | − | 0.610975i | \(-0.209222\pi\) | ||||
0.791650 | + | 0.610975i | \(0.209222\pi\) | |||||||
\(348\) | 601.591 | 1.72871 | ||||||||
\(349\) | 355.772 | 1.01940 | 0.509702 | − | 0.860351i | \(-0.329756\pi\) | ||||
0.509702 | + | 0.860351i | \(0.329756\pi\) | |||||||
\(350\) | 36.9878i | 0.105680i | ||||||||
\(351\) | −287.064 | −0.817848 | ||||||||
\(352\) | 559.073i | 1.58828i | ||||||||
\(353\) | −123.524 | −0.349925 | −0.174963 | − | 0.984575i | \(-0.555980\pi\) | ||||
−0.174963 | + | 0.984575i | \(0.555980\pi\) | |||||||
\(354\) | 192.111 | 0.542686 | ||||||||
\(355\) | − | 22.0981i | − | 0.0622482i | ||||||
\(356\) | 85.1049i | 0.239059i | ||||||||
\(357\) | 1062.47 | 2.97612 | ||||||||
\(358\) | −75.4691 | −0.210808 | ||||||||
\(359\) | − | 231.668i | − | 0.645313i | −0.946516 | − | 0.322657i | \(-0.895424\pi\) | ||
0.946516 | − | 0.322657i | \(-0.104576\pi\) | |||||||
\(360\) | − | 209.472i | − | 0.581866i | ||||||
\(361\) | 324.774 | 0.899650 | ||||||||
\(362\) | − | 119.179i | − | 0.329222i | ||||||
\(363\) | 785.436 | 2.16373 | ||||||||
\(364\) | − | 307.252i | − | 0.844099i | ||||||
\(365\) | − | 67.9456i | − | 0.186152i | ||||||
\(366\) | 13.4401i | 0.0367215i | ||||||||
\(367\) | 200.756i | 0.547019i | 0.961869 | + | 0.273509i | \(0.0881844\pi\) | ||||
−0.961869 | + | 0.273509i | \(0.911816\pi\) | |||||||
\(368\) | −6.74181 | − | 114.802i | −0.0183201 | − | 0.311963i | ||||
\(369\) | 935.215 | 2.53446 | ||||||||
\(370\) | 63.0829 | 0.170494 | ||||||||
\(371\) | −297.746 | −0.802551 | ||||||||
\(372\) | −243.383 | −0.654257 | ||||||||
\(373\) | − | 147.414i | − | 0.395211i | −0.980282 | − | 0.197606i | \(-0.936683\pi\) | ||
0.980282 | − | 0.197606i | \(-0.0633165\pi\) | |||||||
\(374\) | −514.313 | −1.37517 | ||||||||
\(375\) | − | 52.8946i | − | 0.141052i | ||||||
\(376\) | 347.826 | 0.925070 | ||||||||
\(377\) | 586.826 | 1.55657 | ||||||||
\(378\) | 153.385i | 0.405781i | ||||||||
\(379\) | − | 234.528i | − | 0.618808i | −0.950931 | − | 0.309404i | \(-0.899870\pi\) | ||
0.950931 | − | 0.309404i | \(-0.100130\pi\) | |||||||
\(380\) | −40.3756 | −0.106252 | ||||||||
\(381\) | 893.020 | 2.34388 | ||||||||
\(382\) | − | 111.457i | − | 0.291773i | ||||||
\(383\) | − | 234.044i | − | 0.611081i | −0.952179 | − | 0.305541i | \(-0.901163\pi\) | ||
0.952179 | − | 0.305541i | \(-0.0988372\pi\) | |||||||
\(384\) | −562.993 | −1.46613 | ||||||||
\(385\) | − | 280.239i | − | 0.727893i | ||||||
\(386\) | −125.123 | −0.324153 | ||||||||
\(387\) | 236.998i | 0.612399i | ||||||||
\(388\) | 522.990i | 1.34791i | ||||||||
\(389\) | 131.490i | 0.338021i | 0.985614 | + | 0.169010i | \(0.0540571\pi\) | ||||
−0.985614 | + | 0.169010i | \(0.945943\pi\) | |||||||
\(390\) | − | 146.462i | − | 0.375544i | ||||||
\(391\) | 697.033 | − | 40.9336i | 1.78269 | − | 0.104689i | ||||
\(392\) | −40.0679 | −0.102214 | ||||||||
\(393\) | −470.592 | −1.19743 | ||||||||
\(394\) | 296.716 | 0.753087 | ||||||||
\(395\) | 219.249 | 0.555060 | ||||||||
\(396\) | 680.172i | 1.71761i | ||||||||
\(397\) | −126.113 | −0.317665 | −0.158833 | − | 0.987306i | \(-0.550773\pi\) | ||||
−0.158833 | + | 0.987306i | \(0.550773\pi\) | |||||||
\(398\) | 195.027i | 0.490017i | ||||||||
\(399\) | 210.648 | 0.527940 | ||||||||
\(400\) | −25.0000 | −0.0625000 | ||||||||
\(401\) | − | 761.107i | − | 1.89802i | −0.315244 | − | 0.949011i | \(-0.602086\pi\) | ||
0.315244 | − | 0.949011i | \(-0.397914\pi\) | |||||||
\(402\) | 166.825i | 0.414988i | ||||||||
\(403\) | −237.410 | −0.589106 | ||||||||
\(404\) | 41.2954 | 0.102216 | ||||||||
\(405\) | 49.9720i | 0.123388i | ||||||||
\(406\) | − | 313.555i | − | 0.772302i | ||||||
\(407\) | −477.949 | −1.17432 | ||||||||
\(408\) | − | 1005.37i | − | 2.46415i | ||||||
\(409\) | −115.134 | −0.281500 | −0.140750 | − | 0.990045i | \(-0.544951\pi\) | ||||
−0.140750 | + | 0.990045i | \(0.544951\pi\) | |||||||
\(410\) | 156.262i | 0.381127i | ||||||||
\(411\) | − | 381.694i | − | 0.928697i | ||||||
\(412\) | − | 197.330i | − | 0.478957i | ||||||
\(413\) | 300.390i | 0.727336i | ||||||||
\(414\) | 18.0447 | + | 307.272i | 0.0435862 | + | 0.742203i | ||||
\(415\) | −224.213 | −0.540271 | ||||||||
\(416\) | −456.876 | −1.09826 | ||||||||
\(417\) | −595.494 | −1.42804 | ||||||||
\(418\) | −101.969 | −0.243945 | ||||||||
\(419\) | 253.837i | 0.605815i | 0.953020 | + | 0.302908i | \(0.0979574\pi\) | ||||
−0.953020 | + | 0.302908i | \(0.902043\pi\) | |||||||
\(420\) | 234.775 | 0.558987 | ||||||||
\(421\) | − | 378.206i | − | 0.898353i | −0.893443 | − | 0.449176i | \(-0.851718\pi\) | ||
0.893443 | − | 0.449176i | \(-0.148282\pi\) | |||||||
\(422\) | −195.386 | −0.462999 | ||||||||
\(423\) | 664.978 | 1.57205 | ||||||||
\(424\) | 281.745i | 0.664492i | ||||||||
\(425\) | − | 151.790i | − | 0.357153i | ||||||
\(426\) | 46.7548 | 0.109753 | ||||||||
\(427\) | −21.0152 | −0.0492160 | ||||||||
\(428\) | − | 349.364i | − | 0.816271i | ||||||
\(429\) | 1109.67i | 2.58665i | ||||||||
\(430\) | −39.5993 | −0.0920914 | ||||||||
\(431\) | 801.659i | 1.86000i | 0.367561 | + | 0.929999i | \(0.380193\pi\) | ||||
−0.367561 | + | 0.929999i | \(0.619807\pi\) | |||||||
\(432\) | −103.673 | −0.239983 | ||||||||
\(433\) | 651.032i | 1.50354i | 0.659427 | + | 0.751769i | \(0.270799\pi\) | ||||
−0.659427 | + | 0.751769i | \(0.729201\pi\) | |||||||
\(434\) | 126.854i | 0.292289i | ||||||||
\(435\) | 448.400i | 1.03080i | ||||||||
\(436\) | 392.708i | 0.900707i | ||||||||
\(437\) | 138.195 | − | 8.11558i | 0.316236 | − | 0.0185711i | ||||
\(438\) | 143.758 | 0.328215 | ||||||||
\(439\) | −247.011 | −0.562668 | −0.281334 | − | 0.959610i | \(-0.590777\pi\) | ||||
−0.281334 | + | 0.959610i | \(0.590777\pi\) | |||||||
\(440\) | −265.178 | −0.602677 | ||||||||
\(441\) | −76.6022 | −0.173701 | ||||||||
\(442\) | − | 420.299i | − | 0.950902i | ||||||
\(443\) | −221.043 | −0.498969 | −0.249485 | − | 0.968379i | \(-0.580261\pi\) | ||||
−0.249485 | + | 0.968379i | \(0.580261\pi\) | |||||||
\(444\) | − | 400.409i | − | 0.901822i | ||||||
\(445\) | −63.4335 | −0.142547 | ||||||||
\(446\) | 65.3033 | 0.146420 | ||||||||
\(447\) | − | 324.791i | − | 0.726602i | ||||||
\(448\) | 96.1684i | 0.214662i | ||||||||
\(449\) | −768.822 | −1.71230 | −0.856149 | − | 0.516729i | \(-0.827149\pi\) | ||||
−0.856149 | + | 0.516729i | \(0.827149\pi\) | |||||||
\(450\) | 66.9134 | 0.148696 | ||||||||
\(451\) | − | 1183.92i | − | 2.62511i | ||||||
\(452\) | − | 31.5066i | − | 0.0697048i | ||||||
\(453\) | −396.783 | −0.875900 | ||||||||
\(454\) | 248.917i | 0.548274i | ||||||||
\(455\) | 229.012 | 0.503323 | ||||||||
\(456\) | − | 199.327i | − | 0.437121i | ||||||
\(457\) | 112.926i | 0.247102i | 0.992338 | + | 0.123551i | \(0.0394283\pi\) | ||||
−0.992338 | + | 0.123551i | \(0.960572\pi\) | |||||||
\(458\) | − | 203.690i | − | 0.444738i | ||||||
\(459\) | − | 629.460i | − | 1.37137i | ||||||
\(460\) | 154.023 | − | 9.04509i | 0.334833 | − | 0.0196632i | ||||
\(461\) | −388.330 | −0.842365 | −0.421183 | − | 0.906976i | \(-0.638385\pi\) | ||||
−0.421183 | + | 0.906976i | \(0.638385\pi\) | |||||||
\(462\) | 592.924 | 1.28339 | ||||||||
\(463\) | 51.6362 | 0.111525 | 0.0557626 | − | 0.998444i | \(-0.482241\pi\) | ||||
0.0557626 | + | 0.998444i | \(0.482241\pi\) | |||||||
\(464\) | 211.931 | 0.456748 | ||||||||
\(465\) | − | 181.407i | − | 0.390123i | ||||||
\(466\) | −170.311 | −0.365473 | ||||||||
\(467\) | − | 388.028i | − | 0.830895i | −0.909617 | − | 0.415447i | \(-0.863625\pi\) | ||
0.909617 | − | 0.415447i | \(-0.136375\pi\) | |||||||
\(468\) | −555.839 | −1.18769 | ||||||||
\(469\) | −260.852 | −0.556189 | ||||||||
\(470\) | 111.109i | 0.236402i | ||||||||
\(471\) | − | 126.205i | − | 0.267952i | ||||||
\(472\) | 284.246 | 0.602216 | ||||||||
\(473\) | 300.025 | 0.634302 | ||||||||
\(474\) | 463.883i | 0.978655i | ||||||||
\(475\) | − | 30.0942i | − | 0.0633562i | ||||||
\(476\) | 673.726 | 1.41539 | ||||||||
\(477\) | 538.642i | 1.12923i | ||||||||
\(478\) | −232.938 | −0.487318 | ||||||||
\(479\) | 393.672i | 0.821863i | 0.911666 | + | 0.410931i | \(0.134796\pi\) | ||||
−0.911666 | + | 0.410931i | \(0.865204\pi\) | |||||||
\(480\) | − | 349.104i | − | 0.727300i | ||||||
\(481\) | − | 390.581i | − | 0.812019i | ||||||
\(482\) | − | 373.790i | − | 0.775499i | ||||||
\(483\) | −803.572 | + | 47.1901i | −1.66371 | + | 0.0977022i | ||||
\(484\) | 498.053 | 1.02904 | ||||||||
\(485\) | −389.814 | −0.803739 | ||||||||
\(486\) | −292.341 | −0.601525 | ||||||||
\(487\) | −551.219 | −1.13187 | −0.565933 | − | 0.824451i | \(-0.691484\pi\) | ||||
−0.565933 | + | 0.824451i | \(0.691484\pi\) | |||||||
\(488\) | 19.8858i | 0.0407496i | ||||||||
\(489\) | 272.196 | 0.556638 | ||||||||
\(490\) | − | 12.7992i | − | 0.0261208i | ||||||
\(491\) | −429.833 | −0.875424 | −0.437712 | − | 0.899115i | \(-0.644211\pi\) | ||||
−0.437712 | + | 0.899115i | \(0.644211\pi\) | |||||||
\(492\) | 991.850 | 2.01596 | ||||||||
\(493\) | 1286.76i | 2.61006i | ||||||||
\(494\) | − | 83.3293i | − | 0.168683i | ||||||
\(495\) | −506.970 | −1.02418 | ||||||||
\(496\) | −85.7401 | −0.172863 | ||||||||
\(497\) | 73.1070i | 0.147097i | ||||||||
\(498\) | − | 474.385i | − | 0.952580i | ||||||
\(499\) | 695.248 | 1.39328 | 0.696641 | − | 0.717420i | \(-0.254677\pi\) | ||||
0.696641 | + | 0.717420i | \(0.254677\pi\) | |||||||
\(500\) | − | 33.5410i | − | 0.0670820i | ||||||
\(501\) | −53.9028 | −0.107590 | ||||||||
\(502\) | 84.1207i | 0.167571i | ||||||||
\(503\) | 79.9845i | 0.159015i | 0.996834 | + | 0.0795075i | \(0.0253347\pi\) | ||||
−0.996834 | + | 0.0795075i | \(0.974665\pi\) | |||||||
\(504\) | 692.994i | 1.37499i | ||||||||
\(505\) | 30.7798i | 0.0609501i | ||||||||
\(506\) | 388.987 | − | 22.8434i | 0.768748 | − | 0.0451451i | ||||
\(507\) | −107.284 | −0.211606 | ||||||||
\(508\) | 566.274 | 1.11471 | ||||||||
\(509\) | 5.84516 | 0.0114836 | 0.00574181 | − | 0.999984i | \(-0.498172\pi\) | ||||
0.00574181 | + | 0.999984i | \(0.498172\pi\) | |||||||
\(510\) | 321.155 | 0.629715 | ||||||||
\(511\) | 224.784i | 0.439890i | ||||||||
\(512\) | −305.000 | −0.595703 | ||||||||
\(513\) | − | 124.798i | − | 0.243271i | ||||||
\(514\) | 327.255 | 0.636684 | ||||||||
\(515\) | 147.081 | 0.285595 | ||||||||
\(516\) | 251.350i | 0.487113i | ||||||||
\(517\) | − | 841.819i | − | 1.62828i | ||||||
\(518\) | −208.697 | −0.402889 | ||||||||
\(519\) | −1087.54 | −2.09546 | ||||||||
\(520\) | − | 216.704i | − | 0.416739i | ||||||
\(521\) | − | 925.289i | − | 1.77599i | −0.459856 | − | 0.887993i | \(-0.652099\pi\) | ||
0.459856 | − | 0.887993i | \(-0.347901\pi\) | |||||||
\(522\) | −567.241 | −1.08667 | ||||||||
\(523\) | 578.949i | 1.10698i | 0.832857 | + | 0.553488i | \(0.186704\pi\) | ||||
−0.832857 | + | 0.553488i | \(0.813296\pi\) | |||||||
\(524\) | −298.407 | −0.569480 | ||||||||
\(525\) | 174.991i | 0.333315i | ||||||||
\(526\) | 434.052i | 0.825194i | ||||||||
\(527\) | − | 520.579i | − | 0.987817i | ||||||
\(528\) | 400.756i | 0.759008i | ||||||||
\(529\) | −525.364 | + | 61.9180i | −0.993126 | + | 0.117047i | ||||
\(530\) | −90.0000 | −0.169811 | ||||||||
\(531\) | 543.424 | 1.02340 | ||||||||
\(532\) | 133.574 | 0.251080 | ||||||||
\(533\) | 967.506 | 1.81521 | ||||||||
\(534\) | − | 134.211i | − | 0.251332i | ||||||
\(535\) | 260.401 | 0.486730 | ||||||||
\(536\) | 246.833i | 0.460510i | ||||||||
\(537\) | −357.047 | −0.664892 | ||||||||
\(538\) | 2.80140 | 0.00520706 | ||||||||
\(539\) | 96.9734i | 0.179914i | ||||||||
\(540\) | − | 139.092i | − | 0.257577i | ||||||
\(541\) | −161.610 | −0.298725 | −0.149363 | − | 0.988782i | \(-0.547722\pi\) | ||||
−0.149363 | + | 0.988782i | \(0.547722\pi\) | |||||||
\(542\) | −192.728 | −0.355588 | ||||||||
\(543\) | − | 563.838i | − | 1.03837i | ||||||
\(544\) | − | 1001.81i | − | 1.84157i | ||||||
\(545\) | −292.707 | −0.537078 | ||||||||
\(546\) | 484.540i | 0.887436i | ||||||||
\(547\) | −39.5119 | −0.0722337 | −0.0361169 | − | 0.999348i | \(-0.511499\pi\) | ||||
−0.0361169 | + | 0.999348i | \(0.511499\pi\) | |||||||
\(548\) | − | 242.037i | − | 0.441673i | ||||||
\(549\) | 38.0179i | 0.0692493i | ||||||||
\(550\) | − | 84.7080i | − | 0.154015i | ||||||
\(551\) | 255.116i | 0.463005i | ||||||||
\(552\) | 44.6540 | + | 760.386i | 0.0808950 | + | 1.37751i | ||||
\(553\) | −725.339 | −1.31164 | ||||||||
\(554\) | −320.620 | −0.578736 | ||||||||
\(555\) | 298.447 | 0.537743 | ||||||||
\(556\) | −377.609 | −0.679154 | ||||||||
\(557\) | − | 587.320i | − | 1.05444i | −0.849730 | − | 0.527218i | \(-0.823235\pi\) | ||
0.849730 | − | 0.527218i | \(-0.176765\pi\) | |||||||
\(558\) | 229.486 | 0.411266 | ||||||||
\(559\) | 245.181i | 0.438607i | ||||||||
\(560\) | 82.7073 | 0.147692 | ||||||||
\(561\) | −2433.23 | −4.33731 | ||||||||
\(562\) | 481.983i | 0.857621i | ||||||||
\(563\) | 180.142i | 0.319968i | 0.987120 | + | 0.159984i | \(0.0511443\pi\) | ||||
−0.987120 | + | 0.159984i | \(0.948856\pi\) | |||||||
\(564\) | 705.248 | 1.25044 | ||||||||
\(565\) | 23.4836 | 0.0415639 | ||||||||
\(566\) | − | 88.7608i | − | 0.156821i | ||||||
\(567\) | − | 165.322i | − | 0.291573i | ||||||
\(568\) | 69.1780 | 0.121792 | ||||||||
\(569\) | 759.111i | 1.33411i | 0.745007 | + | 0.667057i | \(0.232446\pi\) | ||||
−0.745007 | + | 0.667057i | \(0.767554\pi\) | |||||||
\(570\) | 63.6728 | 0.111707 | ||||||||
\(571\) | − | 243.396i | − | 0.426262i | −0.977024 | − | 0.213131i | \(-0.931634\pi\) | ||
0.977024 | − | 0.213131i | \(-0.0683661\pi\) | |||||||
\(572\) | 703.656i | 1.23017i | ||||||||
\(573\) | − | 527.309i | − | 0.920260i | ||||||
\(574\) | − | 516.961i | − | 0.900629i | ||||||
\(575\) | 6.74181 | + | 114.802i | 0.0117249 | + | 0.199656i | ||||
\(576\) | 173.975 | 0.302039 | ||||||||
\(577\) | −224.674 | −0.389384 | −0.194692 | − | 0.980864i | \(-0.562371\pi\) | ||||
−0.194692 | + | 0.980864i | \(0.562371\pi\) | |||||||
\(578\) | 632.609 | 1.09448 | ||||||||
\(579\) | −591.961 | −1.02238 | ||||||||
\(580\) | 284.335i | 0.490233i | ||||||||
\(581\) | 741.760 | 1.27670 | ||||||||
\(582\) | − | 824.761i | − | 1.41711i | ||||||
\(583\) | 681.886 | 1.16962 | ||||||||
\(584\) | 212.703 | 0.364218 | ||||||||
\(585\) | − | 414.298i | − | 0.708201i | ||||||
\(586\) | 212.736i | 0.363031i | ||||||||
\(587\) | 355.464 | 0.605561 | 0.302780 | − | 0.953060i | \(-0.402085\pi\) | ||||
0.302780 | + | 0.953060i | \(0.402085\pi\) | |||||||
\(588\) | −81.2410 | −0.138165 | ||||||||
\(589\) | − | 103.211i | − | 0.175231i | ||||||
\(590\) | 90.7990i | 0.153897i | ||||||||
\(591\) | 1403.77 | 2.37525 | ||||||||
\(592\) | − | 141.058i | − | 0.238273i | ||||||
\(593\) | −614.157 | −1.03568 | −0.517839 | − | 0.855478i | \(-0.673263\pi\) | ||||
−0.517839 | + | 0.855478i | \(0.673263\pi\) | |||||||
\(594\) | − | 351.277i | − | 0.591375i | ||||||
\(595\) | 502.166i | 0.843976i | ||||||||
\(596\) | − | 205.954i | − | 0.345560i | ||||||
\(597\) | 922.678i | 1.54553i | ||||||||
\(598\) | 18.6677 | + | 317.881i | 0.0312169 | + | 0.531574i | ||||
\(599\) | 557.741 | 0.931120 | 0.465560 | − | 0.885016i | \(-0.345853\pi\) | ||||
0.465560 | + | 0.885016i | \(0.345853\pi\) | |||||||
\(600\) | 165.586 | 0.275977 | ||||||||
\(601\) | −588.078 | −0.978500 | −0.489250 | − | 0.872144i | \(-0.662729\pi\) | ||||
−0.489250 | + | 0.872144i | \(0.662729\pi\) | |||||||
\(602\) | 131.006 | 0.217618 | ||||||||
\(603\) | 471.899i | 0.782585i | ||||||||
\(604\) | −251.604 | −0.416563 | ||||||||
\(605\) | 371.227i | 0.613599i | ||||||||
\(606\) | −65.1233 | −0.107464 | ||||||||
\(607\) | 154.978 | 0.255318 | 0.127659 | − | 0.991818i | \(-0.459254\pi\) | ||||
0.127659 | + | 0.991818i | \(0.459254\pi\) | |||||||
\(608\) | − | 198.622i | − | 0.326681i | ||||||
\(609\) | − | 1483.44i | − | 2.43586i | ||||||
\(610\) | −6.35229 | −0.0104136 | ||||||||
\(611\) | 687.938 | 1.12592 | ||||||||
\(612\) | − | 1218.81i | − | 1.99153i | ||||||
\(613\) | − | 952.132i | − | 1.55323i | −0.629974 | − | 0.776617i | \(-0.716934\pi\) | ||
0.629974 | − | 0.776617i | \(-0.283066\pi\) | |||||||
\(614\) | 411.377 | 0.669995 | ||||||||
\(615\) | 739.281i | 1.20208i | ||||||||
\(616\) | 877.286 | 1.42417 | ||||||||
\(617\) | − | 844.964i | − | 1.36947i | −0.728792 | − | 0.684735i | \(-0.759918\pi\) | ||
0.728792 | − | 0.684735i | \(-0.240082\pi\) | |||||||
\(618\) | 311.192i | 0.503546i | ||||||||
\(619\) | 303.263i | 0.489924i | 0.969533 | + | 0.244962i | \(0.0787755\pi\) | ||||
−0.969533 | + | 0.244962i | \(0.921225\pi\) | |||||||
\(620\) | − | 115.032i | − | 0.185536i | ||||||
\(621\) | 27.9577 | + | 476.075i | 0.0450204 | + | 0.766626i | ||||
\(622\) | 146.924 | 0.236212 | ||||||||
\(623\) | 209.856 | 0.336848 | ||||||||
\(624\) | −327.499 | −0.524839 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 336.949i | − | 0.538258i | ||||||
\(627\) | −482.418 | −0.769406 | ||||||||
\(628\) | − | 80.0282i | − | 0.127433i | ||||||
\(629\) | 856.446 | 1.36160 | ||||||||
\(630\) | −221.369 | −0.351379 | ||||||||
\(631\) | 1211.50i | 1.91996i | 0.280066 | + | 0.959981i | \(0.409644\pi\) | ||||
−0.280066 | + | 0.959981i | \(0.590356\pi\) | |||||||
\(632\) | 686.357i | 1.08601i | ||||||||
\(633\) | −924.376 | −1.46031 | ||||||||
\(634\) | 400.963 | 0.632434 | ||||||||
\(635\) | 422.075i | 0.664686i | ||||||||
\(636\) | 571.261i | 0.898209i | ||||||||
\(637\) | −79.2470 | −0.124407 | ||||||||
\(638\) | 718.090i | 1.12553i | ||||||||
\(639\) | 132.255 | 0.206972 | ||||||||
\(640\) | − | 266.092i | − | 0.415769i | ||||||
\(641\) | 492.485i | 0.768307i | 0.923269 | + | 0.384154i | \(0.125507\pi\) | ||||
−0.923269 | + | 0.384154i | \(0.874493\pi\) | |||||||
\(642\) | 550.951i | 0.858179i | ||||||||
\(643\) | 448.951i | 0.698213i | 0.937083 | + | 0.349106i | \(0.113515\pi\) | ||||
−0.937083 | + | 0.349106i | \(0.886485\pi\) | |||||||
\(644\) | −509.554 | + | 29.9238i | −0.791233 | + | 0.0464655i | ||||
\(645\) | −187.346 | −0.290458 | ||||||||
\(646\) | 182.720 | 0.282848 | ||||||||
\(647\) | 1045.09 | 1.61528 | 0.807641 | − | 0.589675i | \(-0.200744\pi\) | ||||
0.807641 | + | 0.589675i | \(0.200744\pi\) | |||||||
\(648\) | −156.437 | −0.241415 | ||||||||
\(649\) | − | 687.940i | − | 1.06000i | ||||||
\(650\) | 69.2237 | 0.106498 | ||||||||
\(651\) | 600.148i | 0.921887i | ||||||||
\(652\) | 172.603 | 0.264728 | ||||||||
\(653\) | 775.801 | 1.18806 | 0.594029 | − | 0.804444i | \(-0.297537\pi\) | ||||
0.594029 | + | 0.804444i | \(0.297537\pi\) | |||||||
\(654\) | − | 619.305i | − | 0.946949i | ||||||
\(655\) | − | 222.420i | − | 0.339572i | ||||||
\(656\) | 349.413 | 0.532642 | ||||||||
\(657\) | 406.648 | 0.618947 | ||||||||
\(658\) | − | 367.581i | − | 0.558634i | ||||||
\(659\) | 184.054i | 0.279293i | 0.990201 | + | 0.139647i | \(0.0445967\pi\) | ||||
−0.990201 | + | 0.139647i | \(0.955403\pi\) | |||||||
\(660\) | −537.671 | −0.814653 | ||||||||
\(661\) | − | 507.423i | − | 0.767660i | −0.923404 | − | 0.383830i | \(-0.874605\pi\) | ||
0.923404 | − | 0.383830i | \(-0.125395\pi\) | |||||||
\(662\) | 605.346 | 0.914419 | ||||||||
\(663\) | − | 1988.45i | − | 2.99917i | ||||||
\(664\) | − | 701.896i | − | 1.05707i | ||||||
\(665\) | 99.5604i | 0.149715i | ||||||||
\(666\) | 377.546i | 0.566886i | ||||||||
\(667\) | −57.1519 | − | 973.206i | −0.0856851 | − | 1.45908i | ||||
\(668\) | −34.1803 | −0.0511682 | ||||||||
\(669\) | 308.952 | 0.461812 | ||||||||
\(670\) | −78.8481 | −0.117684 | ||||||||
\(671\) | 48.1282 | 0.0717261 | ||||||||
\(672\) | 1154.94i | 1.71866i | ||||||||
\(673\) | −767.114 | −1.13984 | −0.569921 | − | 0.821699i | \(-0.693026\pi\) | ||||
−0.569921 | + | 0.821699i | \(0.693026\pi\) | |||||||
\(674\) | − | 381.287i | − | 0.565708i | ||||||
\(675\) | 103.673 | 0.153589 | ||||||||
\(676\) | −68.0302 | −0.100636 | ||||||||
\(677\) | 62.9632i | 0.0930032i | 0.998918 | + | 0.0465016i | \(0.0148073\pi\) | ||||
−0.998918 | + | 0.0465016i | \(0.985193\pi\) | |||||||
\(678\) | 49.6862i | 0.0732835i | ||||||||
\(679\) | 1289.62 | 1.89929 | ||||||||
\(680\) | 475.178 | 0.698791 | ||||||||
\(681\) | 1177.63i | 1.72927i | ||||||||
\(682\) | − | 290.515i | − | 0.425975i | ||||||
\(683\) | −644.810 | −0.944084 | −0.472042 | − | 0.881576i | \(-0.656483\pi\) | ||||
−0.472042 | + | 0.881576i | \(0.656483\pi\) | |||||||
\(684\) | − | 241.645i | − | 0.353281i | ||||||
\(685\) | 180.403 | 0.263363 | ||||||||
\(686\) | − | 320.137i | − | 0.466672i | ||||||
\(687\) | − | 963.664i | − | 1.40271i | ||||||
\(688\) | 88.5467i | 0.128702i | ||||||||
\(689\) | 557.240i | 0.808766i | ||||||||
\(690\) | −242.896 | + | 14.2642i | −0.352024 | + | 0.0206728i | ||||
\(691\) | −65.6173 | −0.0949599 | −0.0474800 | − | 0.998872i | \(-0.515119\pi\) | ||||
−0.0474800 | + | 0.998872i | \(0.515119\pi\) | |||||||
\(692\) | −689.624 | −0.996567 | ||||||||
\(693\) | 1677.20 | 2.42021 | ||||||||
\(694\) | −549.405 | −0.791650 | ||||||||
\(695\) | − | 281.453i | − | 0.404969i | ||||||
\(696\) | −1403.71 | −2.01683 | ||||||||
\(697\) | 2121.50i | 3.04375i | ||||||||
\(698\) | −355.772 | −0.509702 | ||||||||
\(699\) | −805.745 | −1.15271 | ||||||||
\(700\) | 110.963i | 0.158519i | ||||||||
\(701\) | − | 510.716i | − | 0.728553i | −0.931291 | − | 0.364276i | \(-0.881316\pi\) | ||
0.931291 | − | 0.364276i | \(-0.118684\pi\) | |||||||
\(702\) | 287.064 | 0.408924 | ||||||||
\(703\) | 169.801 | 0.241537 | ||||||||
\(704\) | − | 220.241i | − | 0.312842i | ||||||
\(705\) | 525.660i | 0.745618i | ||||||||
\(706\) | 123.524 | 0.174963 | ||||||||
\(707\) | − | 101.829i | − | 0.144029i | ||||||
\(708\) | 576.333 | 0.814029 | ||||||||
\(709\) | − | 776.700i | − | 1.09549i | −0.836647 | − | 0.547743i | \(-0.815487\pi\) | ||
0.836647 | − | 0.547743i | \(-0.184513\pi\) | |||||||
\(710\) | 22.0981i | 0.0311241i | ||||||||
\(711\) | 1312.18i | 1.84555i | ||||||||
\(712\) | − | 198.578i | − | 0.278902i | ||||||
\(713\) | 23.1217 | + | 393.726i | 0.0324288 | + | 0.552210i | ||||
\(714\) | −1062.47 | −1.48806 | ||||||||
\(715\) | −524.474 | −0.733530 | ||||||||
\(716\) | −226.407 | −0.316211 | ||||||||
\(717\) | −1102.04 | −1.53701 | ||||||||
\(718\) | 231.668i | 0.322657i | ||||||||
\(719\) | 871.038 | 1.21146 | 0.605729 | − | 0.795671i | \(-0.292882\pi\) | ||||
0.605729 | + | 0.795671i | \(0.292882\pi\) | |||||||
\(720\) | − | 149.623i | − | 0.207809i | ||||||
\(721\) | −486.587 | −0.674879 | ||||||||
\(722\) | −324.774 | −0.449825 | ||||||||
\(723\) | − | 1768.41i | − | 2.44594i | ||||||
\(724\) | − | 357.536i | − | 0.493834i | ||||||
\(725\) | −211.931 | −0.292319 | ||||||||
\(726\) | −785.436 | −1.08187 | ||||||||
\(727\) | 67.3522i | 0.0926440i | 0.998927 | + | 0.0463220i | \(0.0147500\pi\) | ||||
−0.998927 | + | 0.0463220i | \(0.985250\pi\) | |||||||
\(728\) | 716.921i | 0.984782i | ||||||||
\(729\) | −1181.94 | −1.62132 | ||||||||
\(730\) | 67.9456i | 0.0930762i | ||||||||
\(731\) | −537.620 | −0.735459 | ||||||||
\(732\) | 40.3202i | 0.0550822i | ||||||||
\(733\) | − | 330.102i | − | 0.450343i | −0.974319 | − | 0.225172i | \(-0.927706\pi\) | ||
0.974319 | − | 0.225172i | \(-0.0722943\pi\) | |||||||
\(734\) | − | 200.756i | − | 0.273509i | ||||||
\(735\) | − | 60.5535i | − | 0.0823857i | ||||||
\(736\) | 44.4959 | + | 757.695i | 0.0604565 | + | 1.02948i | ||||
\(737\) | 597.393 | 0.810575 | ||||||||
\(738\) | −935.215 | −1.26723 | ||||||||
\(739\) | −256.434 | −0.347001 | −0.173501 | − | 0.984834i | \(-0.555508\pi\) | ||||
−0.173501 | + | 0.984834i | \(0.555508\pi\) | |||||||
\(740\) | 189.249 | 0.255742 | ||||||||
\(741\) | − | 394.234i | − | 0.532029i | ||||||
\(742\) | 297.746 | 0.401275 | ||||||||
\(743\) | − | 129.457i | − | 0.174235i | −0.996198 | − | 0.0871175i | \(-0.972234\pi\) | ||
0.996198 | − | 0.0871175i | \(-0.0277656\pi\) | |||||||
\(744\) | 567.895 | 0.763299 | ||||||||
\(745\) | 153.509 | 0.206052 | ||||||||
\(746\) | 147.414i | 0.197606i | ||||||||
\(747\) | − | 1341.89i | − | 1.79638i | ||||||
\(748\) | −1542.94 | −2.06275 | ||||||||
\(749\) | −861.482 | −1.15018 | ||||||||
\(750\) | 52.8946i | 0.0705261i | ||||||||
\(751\) | − | 25.6109i | − | 0.0341023i | −0.999855 | − | 0.0170512i | \(-0.994572\pi\) | ||
0.999855 | − | 0.0170512i | \(-0.00542782\pi\) | |||||||
\(752\) | 248.447 | 0.330382 | ||||||||
\(753\) | 397.978i | 0.528523i | ||||||||
\(754\) | −586.826 | −0.778283 | ||||||||
\(755\) | − | 187.535i | − | 0.248390i | ||||||
\(756\) | 460.156i | 0.608672i | ||||||||
\(757\) | 1057.96i | 1.39757i | 0.715332 | + | 0.698785i | \(0.246275\pi\) | ||||
−0.715332 | + | 0.698785i | \(0.753725\pi\) | |||||||
\(758\) | 234.528i | 0.309404i | ||||||||
\(759\) | 1840.31 | − | 108.073i | 2.42465 | − | 0.142389i | ||||
\(760\) | 94.2098 | 0.123960 | ||||||||
\(761\) | 1074.33 | 1.41174 | 0.705869 | − | 0.708343i | \(-0.250557\pi\) | ||||
0.705869 | + | 0.708343i | \(0.250557\pi\) | |||||||
\(762\) | −893.020 | −1.17194 | ||||||||
\(763\) | 968.361 | 1.26915 | ||||||||
\(764\) | − | 334.372i | − | 0.437660i | ||||||
\(765\) | 908.450 | 1.18752 | ||||||||
\(766\) | 234.044i | 0.305541i | ||||||||
\(767\) | 562.187 | 0.732969 | ||||||||
\(768\) | 809.007 | 1.05339 | ||||||||
\(769\) | 354.829i | 0.461416i | 0.973023 | + | 0.230708i | \(0.0741043\pi\) | ||||
−0.973023 | + | 0.230708i | \(0.925896\pi\) | |||||||
\(770\) | 280.239i | 0.363947i | ||||||||
\(771\) | 1548.26 | 2.00811 | ||||||||
\(772\) | −375.369 | −0.486229 | ||||||||
\(773\) | − | 421.630i | − | 0.545446i | −0.962093 | − | 0.272723i | \(-0.912076\pi\) | ||
0.962093 | − | 0.272723i | \(-0.0879243\pi\) | |||||||
\(774\) | − | 236.998i | − | 0.306199i | ||||||
\(775\) | 85.7401 | 0.110632 | ||||||||
\(776\) | − | 1220.31i | − | 1.57256i | ||||||
\(777\) | −987.351 | −1.27072 | ||||||||
\(778\) | − | 131.490i | − | 0.169010i | ||||||
\(779\) | 420.612i | 0.539939i | ||||||||
\(780\) | − | 439.387i | − | 0.563316i | ||||||
\(781\) | − | 167.427i | − | 0.214375i | ||||||
\(782\) | −697.033 | + | 40.9336i | −0.891347 | + | 0.0523447i | ||||
\(783\) | −878.859 | −1.12243 | ||||||||
\(784\) | −28.6199 | −0.0365050 | ||||||||
\(785\) | 59.6495 | 0.0759866 | ||||||||
\(786\) | 470.592 | 0.598717 | ||||||||
\(787\) | − | 818.127i | − | 1.03955i | −0.854303 | − | 0.519776i | \(-0.826016\pi\) | ||
0.854303 | − | 0.519776i | \(-0.173984\pi\) | |||||||
\(788\) | 890.148 | 1.12963 | ||||||||
\(789\) | 2053.52i | 2.60268i | ||||||||
\(790\) | −219.249 | −0.277530 | ||||||||
\(791\) | −77.6907 | −0.0982183 | ||||||||
\(792\) | − | 1587.07i | − | 2.00387i | ||||||
\(793\) | 39.3305i | 0.0495971i | ||||||||
\(794\) | 126.113 | 0.158833 | ||||||||
\(795\) | −425.793 | −0.535589 | ||||||||
\(796\) | 585.081i | 0.735026i | ||||||||
\(797\) | − | 948.359i | − | 1.18991i | −0.803759 | − | 0.594955i | \(-0.797170\pi\) | ||
0.803759 | − | 0.594955i | \(-0.202830\pi\) | |||||||
\(798\) | −210.648 | −0.263970 | ||||||||
\(799\) | 1508.47i | 1.88795i | ||||||||
\(800\) | 165.000 | 0.206250 | ||||||||
\(801\) | − | 379.644i | − | 0.473962i | ||||||
\(802\) | 761.107i | 0.949011i | ||||||||
\(803\) | − | 514.791i | − | 0.641084i | ||||||
\(804\) | 500.476i | 0.622483i | ||||||||
\(805\) | −22.3039 | − | 379.799i | −0.0277067 | − | 0.471800i | ||||
\(806\) | 237.410 | 0.294553 | ||||||||
\(807\) | 13.2535 | 0.0164232 | ||||||||
\(808\) | −96.3560 | −0.119252 | ||||||||
\(809\) | −672.293 | −0.831017 | −0.415509 | − | 0.909589i | \(-0.636396\pi\) | ||||
−0.415509 | + | 0.909589i | \(0.636396\pi\) | |||||||
\(810\) | − | 49.9720i | − | 0.0616938i | ||||||
\(811\) | −378.524 | −0.466738 | −0.233369 | − | 0.972388i | \(-0.574975\pi\) | ||||
−0.233369 | + | 0.972388i | \(0.574975\pi\) | |||||||
\(812\) | − | 940.664i | − | 1.15845i | ||||||
\(813\) | −911.805 | −1.12153 | ||||||||
\(814\) | 477.949 | 0.587160 | ||||||||
\(815\) | 128.650i | 0.157853i | ||||||||
\(816\) | − | 718.124i | − | 0.880054i | ||||||
\(817\) | −106.590 | −0.130465 | ||||||||
\(818\) | 115.134 | 0.140750 | ||||||||
\(819\) | 1370.62i | 1.67353i | ||||||||
\(820\) | 468.787i | 0.571691i | ||||||||
\(821\) | −797.381 | −0.971231 | −0.485616 | − | 0.874172i | \(-0.661405\pi\) | ||||
−0.485616 | + | 0.874172i | \(0.661405\pi\) | |||||||
\(822\) | 381.694i | 0.464348i | ||||||||
\(823\) | 557.455 | 0.677345 | 0.338672 | − | 0.940904i | \(-0.390022\pi\) | ||||
0.338672 | + | 0.940904i | \(0.390022\pi\) | |||||||
\(824\) | 460.437i | 0.558783i | ||||||||
\(825\) | − | 400.756i | − | 0.485765i | ||||||
\(826\) | − | 300.390i | − | 0.363668i | ||||||
\(827\) | − | 534.678i | − | 0.646527i | −0.946309 | − | 0.323264i | \(-0.895220\pi\) | ||
0.946309 | − | 0.323264i | \(-0.104780\pi\) | |||||||
\(828\) | 54.1341 | + | 921.816i | 0.0653793 | + | 1.11330i | ||||
\(829\) | −1218.60 | −1.46997 | −0.734984 | − | 0.678085i | \(-0.762810\pi\) | ||||
−0.734984 | + | 0.678085i | \(0.762810\pi\) | |||||||
\(830\) | 224.213 | 0.270136 | ||||||||
\(831\) | −1516.86 | −1.82535 | ||||||||
\(832\) | 179.982 | 0.216324 | ||||||||
\(833\) | − | 173.769i | − | 0.208606i | ||||||
\(834\) | 595.494 | 0.714022 | ||||||||
\(835\) | − | 25.4765i | − | 0.0305108i | ||||||
\(836\) | −305.906 | −0.365917 | ||||||||
\(837\) | 355.556 | 0.424799 | ||||||||
\(838\) | − | 253.837i | − | 0.302908i | ||||||
\(839\) | 1512.85i | 1.80315i | 0.432619 | + | 0.901577i | \(0.357589\pi\) | ||||
−0.432619 | + | 0.901577i | \(0.642411\pi\) | |||||||
\(840\) | −547.807 | −0.652152 | ||||||||
\(841\) | 955.590 | 1.13625 | ||||||||
\(842\) | 378.206i | 0.449176i | ||||||||
\(843\) | 2280.28i | 2.70495i | ||||||||
\(844\) | −586.157 | −0.694499 | ||||||||
\(845\) | − | 50.7067i | − | 0.0600079i | ||||||
\(846\) | −664.978 | −0.786026 | ||||||||
\(847\) | − | 1228.13i | − | 1.44997i | ||||||
\(848\) | 201.246i | 0.237319i | ||||||||
\(849\) | − | 419.930i | − | 0.494617i | ||||||
\(850\) | 151.790i | 0.178577i | ||||||||
\(851\) | −647.749 | + | 38.0394i | −0.761163 | + | 0.0446996i | ||||
\(852\) | 140.264 | 0.164629 | ||||||||
\(853\) | 741.519 | 0.869307 | 0.434653 | − | 0.900598i | \(-0.356871\pi\) | ||||
0.434653 | + | 0.900598i | \(0.356871\pi\) | |||||||
\(854\) | 21.0152 | 0.0246080 | ||||||||
\(855\) | 180.111 | 0.210656 | ||||||||
\(856\) | 815.183i | 0.952317i | ||||||||
\(857\) | −277.933 | −0.324310 | −0.162155 | − | 0.986765i | \(-0.551844\pi\) | ||||
−0.162155 | + | 0.986765i | \(0.551844\pi\) | |||||||
\(858\) | − | 1109.67i | − | 1.29333i | ||||||
\(859\) | −1512.21 | −1.76043 | −0.880215 | − | 0.474574i | \(-0.842602\pi\) | ||||
−0.880215 | + | 0.474574i | \(0.842602\pi\) | |||||||
\(860\) | −118.798 | −0.138137 | ||||||||
\(861\) | − | 2445.76i | − | 2.84060i | ||||||
\(862\) | − | 801.659i | − | 0.929999i | ||||||
\(863\) | −1008.72 | −1.16885 | −0.584424 | − | 0.811448i | \(-0.698679\pi\) | ||||
−0.584424 | + | 0.811448i | \(0.698679\pi\) | |||||||
\(864\) | 684.240 | 0.791945 | ||||||||
\(865\) | − | 514.015i | − | 0.594238i | ||||||
\(866\) | − | 651.032i | − | 0.751769i | ||||||
\(867\) | 2992.89 | 3.45201 | ||||||||
\(868\) | 380.561i | 0.438434i | ||||||||
\(869\) | 1661.14 | 1.91156 | ||||||||
\(870\) | − | 448.400i | − | 0.515402i | ||||||
\(871\) | 488.192i | 0.560496i | ||||||||
\(872\) | − | 916.319i | − | 1.05082i | ||||||
\(873\) | − | 2333.00i | − | 2.67239i | ||||||
\(874\) | −138.195 | + | 8.11558i | −0.158118 | + | 0.00928556i | ||||
\(875\) | −82.7073 | −0.0945226 | ||||||||
\(876\) | 431.274 | 0.492322 | ||||||||
\(877\) | −1314.49 | −1.49885 | −0.749423 | − | 0.662092i | \(-0.769669\pi\) | ||||
−0.749423 | + | 0.662092i | \(0.769669\pi\) | |||||||
\(878\) | 247.011 | 0.281334 | ||||||||
\(879\) | 1006.46i | 1.14501i | ||||||||
\(880\) | −189.413 | −0.215242 | ||||||||
\(881\) | 1048.30i | 1.18990i | 0.803762 | + | 0.594951i | \(0.202829\pi\) | ||||
−0.803762 | + | 0.594951i | \(0.797171\pi\) | |||||||
\(882\) | 76.6022 | 0.0868505 | ||||||||
\(883\) | 641.613 | 0.726629 | 0.363314 | − | 0.931667i | \(-0.381645\pi\) | ||||
0.363314 | + | 0.931667i | \(0.381645\pi\) | |||||||
\(884\) | − | 1260.90i | − | 1.42635i | ||||||
\(885\) | 429.573i | 0.485393i | ||||||||
\(886\) | 221.043 | 0.249485 | ||||||||
\(887\) | 418.361 | 0.471658 | 0.235829 | − | 0.971795i | \(-0.424219\pi\) | ||||
0.235829 | + | 0.971795i | \(0.424219\pi\) | |||||||
\(888\) | 934.288i | 1.05213i | ||||||||
\(889\) | − | 1396.35i | − | 1.57070i | ||||||
\(890\) | 63.4335 | 0.0712735 | ||||||||
\(891\) | 378.614i | 0.424931i | ||||||||
\(892\) | 195.910 | 0.219630 | ||||||||
\(893\) | 299.073i | 0.334908i | ||||||||
\(894\) | 324.791i | 0.363301i | ||||||||
\(895\) | − | 168.754i | − | 0.188552i | ||||||
\(896\) | 880.310i | 0.982489i | ||||||||
\(897\) | 88.3176 | + | 1503.91i | 0.0984588 | + | 1.67660i | ||||
\(898\) | 768.822 | 0.856149 | ||||||||
\(899\) | −726.839 | −0.808497 | ||||||||
\(900\) | 200.740 | 0.223045 | ||||||||
\(901\) | −1221.89 | −1.35614 | ||||||||
\(902\) | 1183.92i | 1.31255i | ||||||||
\(903\) | 619.794 | 0.686372 | ||||||||
\(904\) | 73.5154i | 0.0813223i | ||||||||
\(905\) | 266.491 | 0.294466 | ||||||||
\(906\) | 396.783 | 0.437950 | ||||||||
\(907\) | 41.1303i | 0.0453477i | 0.999743 | + | 0.0226738i | \(0.00721793\pi\) | ||||
−0.999743 | + | 0.0226738i | \(0.992782\pi\) | |||||||
\(908\) | 746.750i | 0.822412i | ||||||||
\(909\) | −184.214 | −0.202656 | ||||||||
\(910\) | −229.012 | −0.251662 | ||||||||
\(911\) | 142.023i | 0.155898i | 0.996957 | + | 0.0779492i | \(0.0248372\pi\) | ||||
−0.996957 | + | 0.0779492i | \(0.975163\pi\) | |||||||
\(912\) | − | 142.377i | − | 0.156115i | ||||||
\(913\) | −1698.75 | −1.86062 | ||||||||
\(914\) | − | 112.926i | − | 0.123551i | ||||||
\(915\) | −30.0529 | −0.0328447 | ||||||||
\(916\) | − | 611.070i | − | 0.667107i | ||||||
\(917\) | 735.829i | 0.802431i | ||||||||
\(918\) | 629.460i | 0.685686i | ||||||||
\(919\) | − | 1288.94i | − | 1.40255i | −0.712891 | − | 0.701275i | \(-0.752615\pi\) | ||
0.712891 | − | 0.701275i | \(-0.247385\pi\) | |||||||
\(920\) | −359.388 | + | 21.1052i | −0.390639 | + | 0.0229404i | ||||
\(921\) | 1946.24 | 2.11318 | ||||||||
\(922\) | 388.330 | 0.421183 | ||||||||
\(923\) | 136.822 | 0.148236 | ||||||||
\(924\) | 1778.77 | 1.92508 | ||||||||
\(925\) | 141.058i | 0.152495i | ||||||||
\(926\) | −51.6362 | −0.0557626 | ||||||||
\(927\) | 880.268i | 0.949588i | ||||||||
\(928\) | −1398.74 | −1.50727 | ||||||||
\(929\) | 981.566 | 1.05658 | 0.528291 | − | 0.849063i | \(-0.322833\pi\) | ||||
0.528291 | + | 0.849063i | \(0.322833\pi\) | |||||||
\(930\) | 181.407i | 0.195062i | ||||||||
\(931\) | − | 34.4517i | − | 0.0370051i | ||||||
\(932\) | −510.932 | −0.548210 | ||||||||
\(933\) | 695.101 | 0.745017 | ||||||||
\(934\) | 388.028i | 0.415447i | ||||||||
\(935\) | − | 1150.04i | − | 1.22999i | ||||||
\(936\) | 1296.96 | 1.38564 | ||||||||
\(937\) | − | 1180.83i | − | 1.26023i | −0.776504 | − | 0.630113i | \(-0.783009\pi\) | ||
0.776504 | − | 0.630113i | \(-0.216991\pi\) | |||||||
\(938\) | 260.852 | 0.278094 | ||||||||
\(939\) | − | 1594.12i | − | 1.69768i | ||||||
\(940\) | 333.327i | 0.354603i | ||||||||
\(941\) | 104.030i | 0.110553i | 0.998471 | + | 0.0552764i | \(0.0176040\pi\) | ||||
−0.998471 | + | 0.0552764i | \(0.982396\pi\) | |||||||
\(942\) | 126.205i | 0.133976i | ||||||||
\(943\) | −94.2270 | − | 1604.53i | −0.0999226 | − | 1.70152i | ||||
\(944\) | 203.033 | 0.215077 | ||||||||
\(945\) | −342.980 | −0.362942 | ||||||||
\(946\) | −300.025 | −0.317151 | ||||||||
\(947\) | −806.025 | −0.851135 | −0.425568 | − | 0.904927i | \(-0.639926\pi\) | ||||
−0.425568 | + | 0.904927i | \(0.639926\pi\) | |||||||
\(948\) | 1391.65i | 1.46798i | ||||||||
\(949\) | 420.689 | 0.443297 | ||||||||
\(950\) | 30.0942i | 0.0316781i | ||||||||
\(951\) | 1896.97 | 1.99471 | ||||||||
\(952\) | −1572.03 | −1.65129 | ||||||||
\(953\) | 133.702i | 0.140296i | 0.997537 | + | 0.0701480i | \(0.0223471\pi\) | ||||
−0.997537 | + | 0.0701480i | \(0.977653\pi\) | |||||||
\(954\) | − | 538.642i | − | 0.564614i | ||||||
\(955\) | 249.226 | 0.260970 | ||||||||
\(956\) | −698.815 | −0.730978 | ||||||||
\(957\) | 3397.31i | 3.54996i | ||||||||
\(958\) | − | 393.672i | − | 0.410931i | ||||||
\(959\) | −596.827 | −0.622343 | ||||||||
\(960\) | 137.526i | 0.143256i | ||||||||
\(961\) | −666.946 | −0.694012 | ||||||||
\(962\) | 390.581i | 0.406010i | ||||||||
\(963\) | 1558.48i | 1.61835i | ||||||||
\(964\) | − | 1121.37i | − | 1.16325i | ||||||
\(965\) | − | 279.783i | − | 0.289931i | ||||||
\(966\) | 803.572 | − | 47.1901i | 0.831856 | − | 0.0488511i | ||||
\(967\) | 1392.07 | 1.43958 | 0.719790 | − | 0.694192i | \(-0.244238\pi\) | ||||
0.719790 | + | 0.694192i | \(0.244238\pi\) | |||||||
\(968\) | −1162.12 | −1.20054 | ||||||||
\(969\) | 864.455 | 0.892110 | ||||||||
\(970\) | 389.814 | 0.401870 | ||||||||
\(971\) | 44.5482i | 0.0458787i | 0.999737 | + | 0.0229394i | \(0.00730247\pi\) | ||||
−0.999737 | + | 0.0229394i | \(0.992698\pi\) | |||||||
\(972\) | −877.023 | −0.902287 | ||||||||
\(973\) | 931.130i | 0.956968i | ||||||||
\(974\) | 551.219 | 0.565933 | ||||||||
\(975\) | 327.499 | 0.335897 | ||||||||
\(976\) | 14.2041i | 0.0145534i | ||||||||
\(977\) | 796.273i | 0.815018i | 0.913201 | + | 0.407509i | \(0.133603\pi\) | ||||
−0.913201 | + | 0.407509i | \(0.866397\pi\) | |||||||
\(978\) | −272.196 | −0.278319 | ||||||||
\(979\) | −480.604 | −0.490914 | ||||||||
\(980\) | − | 38.3976i | − | 0.0391813i | ||||||
\(981\) | − | 1751.83i | − | 1.78576i | ||||||
\(982\) | 429.833 | 0.437712 | ||||||||
\(983\) | − | 207.733i | − | 0.211325i | −0.994402 | − | 0.105663i | \(-0.966304\pi\) | ||
0.994402 | − | 0.105663i | \(-0.0336964\pi\) | |||||||
\(984\) | −2314.32 | −2.35195 | ||||||||
\(985\) | 663.477i | 0.673581i | ||||||||
\(986\) | − | 1286.76i | − | 1.30503i | ||||||
\(987\) | − | 1739.04i | − | 1.76194i | ||||||
\(988\) | − | 249.988i | − | 0.253024i | ||||||
\(989\) | 406.614 | − | 23.8786i | 0.411137 | − | 0.0241442i | ||||
\(990\) | 506.970 | 0.512091 | ||||||||
\(991\) | 28.3036 | 0.0285606 | 0.0142803 | − | 0.999898i | \(-0.495454\pi\) | ||||
0.0142803 | + | 0.999898i | \(0.495454\pi\) | |||||||
\(992\) | 565.884 | 0.570448 | ||||||||
\(993\) | 2863.91 | 2.88410 | ||||||||
\(994\) | − | 73.1070i | − | 0.0735483i | ||||||
\(995\) | −436.093 | −0.438285 | ||||||||
\(996\) | − | 1423.15i | − | 1.42887i | ||||||
\(997\) | 1747.49 | 1.75275 | 0.876376 | − | 0.481628i | \(-0.159954\pi\) | ||||
0.876376 | + | 0.481628i | \(0.159954\pi\) | |||||||
\(998\) | −695.248 | −0.696641 | ||||||||
\(999\) | 584.954i | 0.585539i |
(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.91.1 | ✓ | 6 | |
3.2 | odd | 2 | 1035.3.g.a.91.5 | 6 | |||
4.3 | odd | 2 | 1840.3.k.a.321.5 | 6 | |||
5.2 | odd | 4 | 575.3.c.c.574.5 | 12 | |||
5.3 | odd | 4 | 575.3.c.c.574.8 | 12 | |||
5.4 | even | 2 | 575.3.d.e.551.5 | 6 | |||
23.22 | odd | 2 | inner | 115.3.d.a.91.2 | yes | 6 | |
69.68 | even | 2 | 1035.3.g.a.91.2 | 6 | |||
92.91 | even | 2 | 1840.3.k.a.321.6 | 6 | |||
115.22 | even | 4 | 575.3.c.c.574.6 | 12 | |||
115.68 | even | 4 | 575.3.c.c.574.7 | 12 | |||
115.114 | odd | 2 | 575.3.d.e.551.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.3.d.a.91.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
115.3.d.a.91.2 | yes | 6 | 23.22 | odd | 2 | inner | |
575.3.c.c.574.5 | 12 | 5.2 | odd | 4 | |||
575.3.c.c.574.6 | 12 | 115.22 | even | 4 | |||
575.3.c.c.574.7 | 12 | 115.68 | even | 4 | |||
575.3.c.c.574.8 | 12 | 5.3 | odd | 4 | |||
575.3.d.e.551.5 | 6 | 5.4 | even | 2 | |||
575.3.d.e.551.6 | 6 | 115.114 | odd | 2 | |||
1035.3.g.a.91.2 | 6 | 69.68 | even | 2 | |||
1035.3.g.a.91.5 | 6 | 3.2 | odd | 2 | |||
1840.3.k.a.321.5 | 6 | 4.3 | odd | 2 | |||
1840.3.k.a.321.6 | 6 | 92.91 | even | 2 |