Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(2157,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.2157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.m (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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2157.16 | ||
Character | \(\chi\) | \(=\) | 4004.2157 |
Dual form | 4004.2.m.c.2157.15 |
$q$-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 \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.819032 | −0.472869 | −0.236434 | − | 0.971647i | \(-0.575979\pi\) | ||||
−0.236434 | + | 0.971647i | \(0.575979\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.69723i | − | 0.759023i | −0.925187 | − | 0.379511i | \(-0.876092\pi\) | ||
0.925187 | − | 0.379511i | \(-0.123908\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.32919 | −0.776395 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.93282 | + | 3.04372i | −0.536067 | + | 0.844175i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.39008i | 0.358918i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.32085 | −0.562890 | −0.281445 | − | 0.959577i | \(-0.590814\pi\) | ||||
−0.281445 | + | 0.959577i | \(0.590814\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.77344i | − | 0.636271i | −0.948045 | − | 0.318136i | \(-0.896943\pi\) | ||
0.948045 | − | 0.318136i | \(-0.103057\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.819032i | 0.178728i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.366187 | −0.0763553 | −0.0381776 | − | 0.999271i | \(-0.512155\pi\) | ||||
−0.0381776 | + | 0.999271i | \(0.512155\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.11942 | 0.423884 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.36478 | 0.840002 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.95197 | 0.548168 | 0.274084 | − | 0.961706i | \(-0.411625\pi\) | ||||
0.274084 | + | 0.961706i | \(0.411625\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.83529i | − | 1.76647i | −0.468931 | − | 0.883235i | \(-0.655361\pi\) | ||
0.468931 | − | 0.883235i | \(-0.344639\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.819032i | − | 0.142575i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.69723 | −0.286884 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.39804i | 1.21623i | 0.793849 | + | 0.608115i | \(0.208074\pi\) | ||||
−0.793849 | + | 0.608115i | \(0.791926\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.58304 | − | 2.49290i | 0.253489 | − | 0.399184i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.67457i | − | 1.51091i | −0.655199 | − | 0.755457i | \(-0.727415\pi\) | ||
0.655199 | − | 0.755457i | \(-0.272585\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.1237 | −1.54385 | −0.771924 | − | 0.635715i | \(-0.780705\pi\) | ||||
−0.771924 | + | 0.635715i | \(0.780705\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.95316i | 0.589302i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4378i | 1.52250i | 0.648457 | + | 0.761251i | \(0.275415\pi\) | ||||
−0.648457 | + | 0.761251i | \(0.724585\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.90085 | 0.266173 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.02888 | −0.965490 | −0.482745 | − | 0.875761i | \(-0.660360\pi\) | ||||
−0.482745 | + | 0.875761i | \(0.660360\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.69723 | 0.228854 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.27154i | 0.300873i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.9025i | 1.54958i | 0.632219 | + | 0.774790i | \(0.282144\pi\) | ||||
−0.632219 | + | 0.774790i | \(0.717856\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.21477 | −1.05179 | −0.525897 | − | 0.850548i | \(-0.676270\pi\) | ||||
−0.525897 | + | 0.850548i | \(0.676270\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.32919i | 0.293450i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.16588 | + | 3.28043i | 0.640748 | + | 0.406887i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3012i | 1.25849i | 0.777208 | + | 0.629244i | \(0.216635\pi\) | ||||
−0.777208 | + | 0.629244i | \(0.783365\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.299919 | 0.0361060 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.127032i | − | 0.0150759i | −0.999972 | − | 0.00753794i | \(-0.997601\pi\) | ||
0.999972 | − | 0.00753794i | \(-0.00239942\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.1281i | 1.30244i | 0.758888 | + | 0.651221i | \(0.225743\pi\) | ||||
−0.758888 | + | 0.651221i | \(0.774257\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.73587 | −0.200441 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.2135 | 1.59915 | 0.799574 | − | 0.600567i | \(-0.205058\pi\) | ||||
0.799574 | + | 0.600567i | \(0.205058\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.41266 | 0.379185 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.44302i | − | 0.487684i | −0.969815 | − | 0.243842i | \(-0.921592\pi\) | ||
0.969815 | − | 0.243842i | \(-0.0784079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.93902i | 0.427246i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.41776 | −0.259211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.15887i | 0.546839i | 0.961895 | + | 0.273419i | \(0.0881547\pi\) | ||||
−0.961895 | + | 0.273419i | \(0.911845\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.04372 | + | 1.93282i | 0.319068 | + | 0.202614i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.05542i | 0.835308i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.70716 | −0.482945 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.55893i | − | 0.462890i | −0.972848 | − | 0.231445i | \(-0.925655\pi\) | ||
0.972848 | − | 0.231445i | \(-0.0743453\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.32919i | − | 0.234092i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.4229 | 1.63414 | 0.817068 | − | 0.576541i | \(-0.195598\pi\) | ||||
0.817068 | + | 0.576541i | \(0.195598\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.61320 | −0.553085 | −0.276543 | − | 0.961002i | \(-0.589189\pi\) | ||||
−0.276543 | + | 0.961002i | \(0.589189\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.39008 | 0.135658 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.32562 | 0.611520 | 0.305760 | − | 0.952109i | \(-0.401089\pi\) | ||||
0.305760 | + | 0.952109i | \(0.401089\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 0.445333i | − | 0.0426552i | −0.999773 | − | 0.0213276i | \(-0.993211\pi\) | ||
0.999773 | − | 0.0213276i | \(-0.00678930\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 6.05924i | − | 0.575117i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.69007 | 0.158988 | 0.0794940 | − | 0.996835i | \(-0.474670\pi\) | ||||
0.0794940 | + | 0.996835i | \(0.474670\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.621502i | 0.0579554i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.50189 | − | 7.08938i | 0.416200 | − | 0.655414i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.32085i | 0.212752i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.92378i | 0.714463i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.0833i | − | 1.08076i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.3288 | 1.18274 | 0.591369 | − | 0.806401i | \(-0.298588\pi\) | ||||
0.591369 | + | 0.806401i | \(0.298588\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.29163 | 0.730037 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.1942 | −1.32752 | −0.663761 | − | 0.747944i | \(-0.731041\pi\) | ||||
−0.663761 | + | 0.747944i | \(0.731041\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.77344 | −0.240488 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 7.40802i | − | 0.637581i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.05099i | − | 0.260663i | −0.991470 | − | 0.130332i | \(-0.958396\pi\) | ||
0.991470 | − | 0.130332i | \(-0.0416042\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.1151 | 1.28205 | 0.641023 | − | 0.767522i | \(-0.278510\pi\) | ||||
0.641023 | + | 0.767522i | \(0.278510\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 8.54886i | − | 0.719944i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.04372 | − | 1.93282i | −0.254528 | − | 0.161630i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 5.01017i | − | 0.416072i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.819032 | 0.0675527 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.07402i | 0.333757i | 0.985977 | + | 0.166878i | \(0.0533688\pi\) | ||||
−0.985977 | + | 0.166878i | \(0.946631\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.4602i | 1.42089i | 0.703750 | + | 0.710447i | \(0.251507\pi\) | ||||
−0.703750 | + | 0.710447i | \(0.748493\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.40570 | 0.437025 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.6927 | −1.34079 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0108 | 1.11818 | 0.559091 | − | 0.829106i | \(-0.311150\pi\) | ||||
0.559091 | + | 0.829106i | \(0.311150\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.75688 | 0.456550 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.366187i | 0.0288596i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.1130i | 0.948766i | 0.880319 | + | 0.474383i | \(0.157329\pi\) | ||||
−0.880319 | + | 0.474383i | \(0.842671\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.39008 | −0.108218 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.6051i | 0.898033i | 0.893523 | + | 0.449016i | \(0.148226\pi\) | ||||
−0.893523 | + | 0.449016i | \(0.851774\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.52843 | − | 11.7659i | −0.425264 | − | 0.905069i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.45986i | 0.493998i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.4572 | 1.09916 | 0.549582 | − | 0.835440i | \(-0.314787\pi\) | ||||
0.549582 | + | 0.835440i | \(0.314787\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.11942i | − | 0.160213i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 9.74857i | − | 0.732747i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.06658 | −0.154464 | −0.0772318 | − | 0.997013i | \(-0.524608\pi\) | ||||
−0.0772318 | + | 0.997013i | \(0.524608\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.45225 | 0.702580 | 0.351290 | − | 0.936267i | \(-0.385743\pi\) | ||||
0.351290 | + | 0.936267i | \(0.385743\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.72817 | 0.497360 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.5562 | 0.923147 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.32085i | − | 0.169718i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 4.36478i | − | 0.317491i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.193160 | −0.0139765 | −0.00698827 | − | 0.999976i | \(-0.502224\pi\) | ||||
−0.00698827 | + | 0.999976i | \(0.502224\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.0349i | 1.51413i | 0.653340 | + | 0.757064i | \(0.273367\pi\) | ||||
−0.653340 | + | 0.757064i | \(0.726633\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.23102 | − | 2.68678i | −0.302990 | − | 0.192404i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.65046i | 0.473826i | 0.971531 | + | 0.236913i | \(0.0761356\pi\) | ||||
−0.971531 | + | 0.236913i | \(0.923864\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.4598 | 1.37947 | 0.689735 | − | 0.724062i | \(-0.257727\pi\) | ||||
0.689735 | + | 0.724062i | \(0.257727\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 8.43699i | − | 0.595099i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2.95197i | − | 0.207188i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.4199 | −1.14682 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.852917 | 0.0592819 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.77344 | 0.191843 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1153 | 0.696367 | 0.348183 | − | 0.937426i | \(-0.386799\pi\) | ||||
0.348183 | + | 0.937426i | \(0.386799\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.104043i | 0.00712891i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.1822i | 1.17182i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.83529 | −0.667663 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 9.11425i | − | 0.615884i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.48579 | − | 7.06402i | 0.301747 | − | 0.475178i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.6441i | 1.38243i | 0.722647 | + | 0.691217i | \(0.242925\pi\) | ||||
−0.722647 | + | 0.691217i | \(0.757075\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.93652 | −0.329102 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 29.0731i | 1.92965i | 0.262896 | + | 0.964824i | \(0.415322\pi\) | ||||
−0.262896 | + | 0.964824i | \(0.584678\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.72489i | 0.113984i | 0.998375 | + | 0.0569921i | \(0.0181510\pi\) | ||||
−0.998375 | + | 0.0569921i | \(0.981849\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.819032 | −0.0538884 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.70662 | 0.635902 | 0.317951 | − | 0.948107i | \(-0.397005\pi\) | ||||
0.317951 | + | 0.948107i | \(0.397005\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.7152 | 1.15561 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.6414 | −0.756187 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.18724i | 0.594273i | 0.954835 | + | 0.297137i | \(0.0960317\pi\) | ||||
−0.954835 | + | 0.297137i | \(0.903968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 14.7453i | − | 0.949826i | −0.880033 | − | 0.474913i | \(-0.842480\pi\) | ||
0.880033 | − | 0.474913i | \(-0.157520\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.8894 | −1.01931 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.69723i | 0.108432i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.44158 | + | 5.36056i | 0.537125 | + | 0.341084i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.63897i | 0.230611i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.9720 | 1.89182 | 0.945909 | − | 0.324432i | \(-0.105173\pi\) | ||||
0.945909 | + | 0.324432i | \(0.105173\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.366187i | − | 0.0230220i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 3.22618i | − | 0.202031i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.6901 | −0.916345 | −0.458173 | − | 0.888863i | \(-0.651496\pi\) | ||||
−0.458173 | + | 0.888863i | \(0.651496\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.39804 | 0.459692 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.87570 | −0.425595 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.47278 | 0.522454 | 0.261227 | − | 0.965277i | \(-0.415873\pi\) | ||||
0.261227 | + | 0.965277i | \(0.415873\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.9296i | 0.732829i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 4.22528i | − | 0.258583i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.9317 | −1.03234 | −0.516171 | − | 0.856486i | \(-0.672643\pi\) | ||||
−0.516171 | + | 0.856486i | \(0.672643\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.06282i | − | 0.0645616i | −0.999479 | − | 0.0322808i | \(-0.989723\pi\) | ||
0.999479 | − | 0.0322808i | \(-0.0102771\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.49290 | − | 1.58304i | −0.150877 | − | 0.0958100i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.11942i | 0.127806i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.9601 | −1.01904 | −0.509518 | − | 0.860460i | \(-0.670176\pi\) | ||||
−0.509518 | + | 0.860460i | \(0.670176\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.9082i | 1.37148i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.53421i | − | 0.0915236i | −0.998952 | − | 0.0457618i | \(-0.985428\pi\) | ||
0.998952 | − | 0.0457618i | \(-0.0145715\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.4847 | 1.45546 | 0.727732 | − | 0.685861i | \(-0.240574\pi\) | ||||
0.727732 | + | 0.685861i | \(0.240574\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.85532 | 0.228369 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.67457 | −0.571072 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.6136 | −0.683155 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.73392i | 0.218886i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 11.4585i | − | 0.669414i | −0.942322 | − | 0.334707i | \(-0.891363\pi\) | ||
0.942322 | − | 0.334707i | \(-0.108637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.2013 | 1.17617 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.36478i | 0.253270i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.707773 | − | 1.11457i | 0.0409315 | − | 0.0644572i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.1237i | 0.583519i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.4509 | −0.772732 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.9423i | 0.798336i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.2231i | − | 0.925902i | −0.886384 | − | 0.462951i | \(-0.846791\pi\) | ||
0.886384 | − | 0.462951i | \(-0.153209\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.59740 | 0.261537 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.9393 | −1.86782 | −0.933908 | − | 0.357514i | \(-0.883625\pi\) | ||||
−0.933908 | + | 0.357514i | \(0.883625\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.11898 | −0.345865 | −0.172933 | − | 0.984934i | \(-0.555324\pi\) | ||||
−0.172933 | + | 0.984934i | \(0.555324\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.95316 | 0.222735 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 5.56290i | − | 0.312444i | −0.987722 | − | 0.156222i | \(-0.950069\pi\) | ||
0.987722 | − | 0.156222i | \(-0.0499315\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.95197i | 0.165279i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.18089 | −0.289169 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.43675i | 0.358151i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.09645 | + | 6.45092i | −0.227230 | + | 0.357832i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.364743i | 0.0201703i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.4378 | 0.575452 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.30178i | 0.346377i | 0.984889 | + | 0.173188i | \(0.0554070\pi\) | ||||
−0.984889 | + | 0.173188i | \(0.944593\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 17.2314i | − | 0.944276i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.4834 | 0.955221 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.2305 | −0.720709 | −0.360355 | − | 0.932815i | \(-0.617344\pi\) | ||||
−0.360355 | + | 0.932815i | \(0.617344\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.38422 | −0.0751805 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.83529 | 0.532611 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 0.509031i | − | 0.0274053i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33.1097 | −1.77742 | −0.888710 | − | 0.458470i | \(-0.848398\pi\) | ||||
−0.888710 | + | 0.458470i | \(0.848398\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.39507i | 0.181734i | 0.995863 | + | 0.0908670i | \(0.0289638\pi\) | ||||
−0.995863 | + | 0.0908670i | \(0.971036\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.43632 | + | 13.2851i | −0.450297 | + | 0.709109i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 26.9734i | − | 1.43565i | −0.696224 | − | 0.717824i | \(-0.745138\pi\) | ||
0.696224 | − | 0.717824i | \(-0.254862\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.215601 | −0.0114429 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1.90085i | − | 0.100604i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.2390i | 1.17373i | 0.809684 | + | 0.586866i | \(0.199638\pi\) | ||||
−0.809684 | + | 0.586866i | \(0.800362\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.3080 | 0.595159 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.819032 | 0.0429881 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.8869 | 0.988584 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.31898 | −0.486447 | −0.243223 | − | 0.969970i | \(-0.578205\pi\) | ||||
−0.243223 | + | 0.969970i | \(0.578205\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 22.5339i | 1.17307i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.02888i | 0.364921i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.75842 | −0.298160 | −0.149080 | − | 0.988825i | \(-0.547631\pi\) | ||||
−0.149080 | + | 0.988825i | \(0.547631\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.89659i | 0.511058i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.70563 | + | 8.98498i | −0.293855 | + | 0.462750i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.5494i | 0.593251i | 0.954994 | + | 0.296625i | \(0.0958613\pi\) | ||||
−0.954994 | + | 0.296625i | \(0.904139\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.9167 | −0.559280 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 1.63226i | − | 0.0834043i | −0.999130 | − | 0.0417022i | \(-0.986722\pi\) | ||
0.999130 | − | 0.0417022i | \(-0.0132781\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 1.69723i | − | 0.0864987i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 23.5799 | 1.19864 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −34.1493 | −1.73144 | −0.865720 | − | 0.500528i | \(-0.833139\pi\) | ||||
−0.865720 | + | 0.500528i | \(0.833139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.849866 | 0.0429796 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.4445 | 0.627744 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 24.1236i | − | 1.21379i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.1368i | 1.11102i | 0.831511 | + | 0.555508i | \(0.187476\pi\) | ||||
−0.831511 | + | 0.555508i | \(0.812524\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.27154 | 0.113719 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.3380i | 0.865819i | 0.901437 | + | 0.432910i | \(0.142513\pi\) | ||||
−0.901437 | + | 0.432910i | \(0.857487\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.9358 | + | 19.0098i | 1.49121 | + | 0.946946i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 5.79206i | − | 0.287810i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.39804 | −0.366707 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.96973i | − | 0.295184i | −0.989048 | − | 0.147592i | \(-0.952848\pi\) | ||
0.989048 | − | 0.147592i | \(-0.0471523\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.49886i | 0.123260i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.9025 | 0.585686 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.54081 | −0.370164 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.3798 | −0.606239 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.1740 | −0.839006 | −0.419503 | − | 0.907754i | \(-0.637796\pi\) | ||||
−0.419503 | + | 0.907754i | \(0.637796\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 14.8026i | − | 0.721436i | −0.932675 | − | 0.360718i | \(-0.882532\pi\) | ||
0.932675 | − | 0.360718i | \(-0.117468\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 24.3115i | − | 1.18206i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.91887 | −0.238600 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.21477i | 0.397541i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.49290 | + | 1.58304i | 0.120359 | + | 0.0764299i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.17641i | 0.0566655i | 0.999599 | + | 0.0283327i | \(0.00901980\pi\) | ||||
−0.999599 | + | 0.0283327i | \(0.990980\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.7302 | 1.62097 | 0.810485 | − | 0.585760i | \(-0.199204\pi\) | ||||
0.810485 | + | 0.585760i | \(0.199204\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.10349i | 0.196747i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.01560i | 0.0485827i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.0484 | −1.57731 | −0.788656 | − | 0.614835i | \(-0.789223\pi\) | ||||
−0.788656 | + | 0.614835i | \(0.789223\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.32919 | 0.110914 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.5853 | 1.35813 | 0.679064 | − | 0.734079i | \(-0.262386\pi\) | ||||
0.679064 | + | 0.734079i | \(0.262386\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.75577 | 0.415063 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 3.33676i | − | 0.157823i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.750950i | 0.0354395i | 0.999843 | + | 0.0177198i | \(0.00564067\pi\) | ||||
−0.999843 | + | 0.0177198i | \(0.994359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.67457 | 0.455557 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 14.3005i | − | 0.671897i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.28043 | − | 5.16588i | 0.153789 | − | 0.242180i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 22.9719i | − | 1.07458i | −0.843398 | − | 0.537290i | \(-0.819448\pi\) | ||
0.843398 | − | 0.537290i | \(-0.180552\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.1300 | −0.472828 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13.4739i | − | 0.627541i | −0.949499 | − | 0.313770i | \(-0.898408\pi\) | ||
0.949499 | − | 0.313770i | \(-0.101592\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.5879i | 1.09622i | 0.836405 | + | 0.548112i | \(0.184653\pi\) | ||||
−0.836405 | + | 0.548112i | \(0.815347\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.6719 | 0.634018 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.0362 | 1.25109 | 0.625544 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625544 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.3012 | 0.475664 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.4753 | −0.528753 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 10.1237i | − | 0.465487i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.87809i | − | 0.269705i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.3716 | 0.749602 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.28707i | 0.332955i | 0.986045 | + | 0.166477i | \(0.0532393\pi\) | ||||
−0.986045 | + | 0.166477i | \(0.946761\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.5175 | − | 14.2991i | −1.02671 | − | 0.651981i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 0.299919i | − | 0.0136468i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.73755 | −0.351344 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 19.3351i | − | 0.876155i | −0.898937 | − | 0.438077i | \(-0.855660\pi\) | ||
0.898937 | − | 0.438077i | \(-0.144340\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 9.92096i | − | 0.448642i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.36812 | 0.106872 | 0.0534358 | − | 0.998571i | \(-0.482983\pi\) | ||||
0.0534358 | + | 0.998571i | \(0.482983\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.85110 | −0.308558 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.95316 | −0.177681 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.127032 | −0.00569814 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.6681i | 1.77579i | 0.460048 | + | 0.887894i | \(0.347832\pi\) | ||||
−0.460048 | + | 0.887894i | \(0.652168\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 9.50499i | − | 0.424652i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.75868 | 0.212179 | 0.106089 | − | 0.994357i | \(-0.466167\pi\) | ||||
0.106089 | + | 0.994357i | \(0.466167\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 27.8733i | − | 1.24035i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.52797 | + | 9.63666i | 0.201094 | + | 0.427979i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.79819i | 0.212676i | 0.994330 | + | 0.106338i | \(0.0339126\pi\) | ||||
−0.994330 | + | 0.106338i | \(0.966087\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.1281 | 0.492277 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 12.1055i | − | 0.534469i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.52688i | 0.419804i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.4378 | −0.459052 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.8410 | −0.519760 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.9554 | −1.44380 | −0.721902 | − | 0.691996i | \(-0.756732\pi\) | ||||
−0.721902 | + | 0.691996i | \(0.756732\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.616555 | −0.0269601 | −0.0134800 | − | 0.999909i | \(-0.504291\pi\) | ||||
−0.0134800 | + | 0.999909i | \(0.504291\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.73587i | 0.0757598i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.8263i | 0.994328i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8659 | −0.994170 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 27.7232i | − | 1.20309i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.4466 | + | 18.6992i | 1.27548 | + | 0.809951i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 10.7360i | − | 0.464158i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.69260 | 0.0730410 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.00000i | − | 0.0430730i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.2915i | 1.51730i | 0.651499 | + | 0.758650i | \(0.274141\pi\) | ||||
−0.651499 | + | 0.758650i | \(0.725859\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.74170 | −0.332228 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.755832 | −0.0323763 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.8694 | −1.19161 | −0.595804 | − | 0.803130i | \(-0.703166\pi\) | ||||
−0.595804 | + | 0.803130i | \(0.703166\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19.1337 | 0.816608 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.18713i | − | 0.348784i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 14.2135i | − | 0.604421i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.2839 | −0.436527 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 20.7880i | − | 0.880815i | −0.897798 | − | 0.440408i | \(-0.854834\pi\) | ||
0.897798 | − | 0.440408i | \(-0.145166\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.5672 | − | 30.8136i | 0.827606 | − | 1.30328i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.90085i | 0.0802542i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.3083 | 1.53021 | 0.765106 | − | 0.643905i | \(-0.222687\pi\) | ||||
0.765106 | + | 0.643905i | \(0.222687\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.86843i | − | 0.120676i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 3.41266i | − | 0.143318i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.4117 | −1.27493 | −0.637463 | − | 0.770481i | \(-0.720016\pi\) | ||||
−0.637463 | + | 0.770481i | \(0.720016\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.8569 | 1.16578 | 0.582888 | − | 0.812553i | \(-0.301923\pi\) | ||||
0.582888 | + | 0.812553i | \(0.301923\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.158204 | 0.00660906 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.776104 | −0.0323658 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 21.5422i | − | 0.896812i | −0.893830 | − | 0.448406i | \(-0.851992\pi\) | ||
0.893830 | − | 0.448406i | \(-0.148008\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 17.2283i | − | 0.715984i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.44302 | −0.184327 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7.02888i | − | 0.291106i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.0323 | − | 7.64073i | −0.497474 | − | 0.315905i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.25568i | − | 0.340748i | −0.985379 | − | 0.170374i | \(-0.945502\pi\) | ||
0.985379 | − | 0.170374i | \(-0.0544977\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.2776 | −1.12395 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 5.44694i | − | 0.224057i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 0.692417i | − | 0.0284342i | −0.999899 | − | 0.0142171i | \(-0.995474\pi\) | ||
0.999899 | − | 0.0142171i | \(-0.00452559\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.93902 | 0.161484 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.9382 | −0.652308 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.4964 | −0.551450 | −0.275725 | − | 0.961237i | \(-0.588918\pi\) | ||||
−0.275725 | + | 0.961237i | \(0.588918\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.9950 | 1.67222 | 0.836111 | − | 0.548560i | \(-0.184824\pi\) | ||||
0.836111 | + | 0.548560i | \(0.184824\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 23.9933i | − | 0.977084i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.69723i | 0.0690021i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.68506 | −0.393105 | −0.196552 | − | 0.980493i | \(-0.562975\pi\) | ||||
−0.196552 | + | 0.980493i | \(0.562975\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.41776i | 0.0979727i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.7696 | − | 20.1743i | −1.28526 | − | 0.816164i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.2799i | 1.90962i | 0.297223 | + | 0.954808i | \(0.403940\pi\) | ||||
−0.297223 | + | 0.954808i | \(0.596060\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.4485 | 0.542294 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.4585i | − | 0.501562i | −0.968044 | − | 0.250781i | \(-0.919313\pi\) | ||
0.968044 | − | 0.250781i | \(-0.0806873\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.8410i | 1.40038i | 0.713958 | + | 0.700188i | \(0.246901\pi\) | ||||
−0.713958 | + | 0.700188i | \(0.753099\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.59832 | −0.0641385 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.15887 | 0.206686 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.91095 | −0.396438 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.27154 | −0.0907165 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 17.1698i | − | 0.684604i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.9578i | − | 1.23241i | −0.787586 | − | 0.616205i | \(-0.788669\pi\) | ||
0.787586 | − | 0.616205i | \(-0.211331\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.28477 | −0.329290 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 22.6220i | − | 0.897726i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.93282 | − | 3.04372i | 0.0765810 | − | 0.120596i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.295880i | 0.0117048i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.1952 | −1.46912 | −0.734560 | − | 0.678543i | \(-0.762612\pi\) | ||||
−0.734560 | + | 0.678543i | \(0.762612\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.449713i | 0.0177349i | 0.999961 | + | 0.00886747i | \(0.00282264\pi\) | ||||
−0.999961 | + | 0.00886747i | \(0.997177\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 14.0728i | − | 0.554115i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.79899 | −0.345924 | −0.172962 | − | 0.984928i | \(-0.555334\pi\) | ||||
−0.172962 | + | 0.984928i | \(0.555334\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.9025 | −0.467216 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.05542 | 0.315717 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −36.0064 | −1.40904 | −0.704519 | − | 0.709685i | \(-0.748837\pi\) | ||||
−0.704519 | + | 0.709685i | \(0.748837\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.7880i | 1.00762i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 25.9194i | − | 1.01121i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.969131 | 0.0377520 | 0.0188760 | − | 0.999822i | \(-0.493991\pi\) | ||||
0.0188760 | + | 0.999822i | \(0.493991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.92011i | 0.113579i | 0.998386 | + | 0.0567896i | \(0.0180864\pi\) | ||||
−0.998386 | + | 0.0567896i | \(0.981914\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.67401 | + | 5.78567i | −0.142687 | + | 0.224697i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.70716i | 0.182536i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.08097 | −0.0418555 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 16.9082i | − | 0.653710i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 8.21477i | − | 0.317128i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.8429 | 0.726342 | 0.363171 | − | 0.931723i | \(-0.381694\pi\) | ||||
0.363171 | + | 0.931723i | \(0.381694\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.25080 | 0.356063 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.6292 | −0.754410 | −0.377205 | − | 0.926130i | \(-0.623115\pi\) | ||||
−0.377205 | + | 0.926130i | \(0.623115\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.55893 | −0.174956 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 23.8118i | − | 0.912470i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.0865i | 1.61040i | 0.593006 | + | 0.805198i | \(0.297941\pi\) | ||||
−0.593006 | + | 0.805198i | \(0.702059\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.17822 | −0.197849 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1.41274i | − | 0.0538995i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.5855 | − | 21.3939i | 0.517568 | − | 0.815043i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.595349i | 0.0226481i | 0.999936 | + | 0.0113241i | \(0.00360464\pi\) | ||||
−0.999936 | + | 0.0113241i | \(0.996395\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.32919 | −0.0884785 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 25.6537i | − | 0.973102i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.4533i | 0.850478i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.95004 | −0.300698 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.54504 | −0.322742 | −0.161371 | − | 0.986894i | \(-0.551592\pi\) | ||||
−0.161371 | + | 0.986894i | \(0.551592\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.5180 | 0.773853 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.5094 | −0.546454 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 16.4229i | − | 0.617646i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 2.69377i | − | 0.101167i | −0.998720 | − | 0.0505833i | \(-0.983892\pi\) | ||
0.998720 | − | 0.0505833i | \(-0.0161080\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −33.1060 | −1.24157 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.60155i | 0.134879i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.28043 | + | 5.16588i | −0.122681 | + | 0.193193i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 7.52465i | − | 0.281013i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.17053 | −0.267416 | −0.133708 | − | 0.991021i | \(-0.542688\pi\) | ||||
−0.133708 | + | 0.991021i | \(0.542688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.61320i | 0.209047i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.0769i | 0.449143i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.25648 | 0.232360 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.7863 | −0.437128 | −0.218564 | − | 0.975823i | \(-0.570137\pi\) | ||||
−0.218564 | + | 0.975823i | \(0.570137\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.77595 | 0.102813 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.4956 | 0.869016 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.2355i | 0.599673i | 0.953991 | + | 0.299837i | \(0.0969321\pi\) | ||||
−0.953991 | + | 0.299837i | \(0.903068\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 1.39008i | − | 0.0512740i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.3012 | −0.379448 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4.53787i | − | 0.166928i | −0.996511 | − | 0.0834642i | \(-0.973402\pi\) | ||
0.996511 | − | 0.0834642i | \(-0.0265984\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.91392 | − | 4.39047i | −0.253989 | − | 0.161288i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7.32658i | − | 0.268786i | −0.990928 | − | 0.134393i | \(-0.957092\pi\) | ||
0.990928 | − | 0.134393i | \(-0.0429085\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.91454 | 0.253329 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.3486i | 0.378636i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 6.32562i | − | 0.231133i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.03656 | −0.256768 | −0.128384 | − | 0.991725i | \(-0.540979\pi\) | ||||
−0.128384 | + | 0.991725i | \(0.540979\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.5481 | −0.894582 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.6340 | 1.07849 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.4980 | 0.490594 | 0.245297 | − | 0.969448i | \(-0.421114\pi\) | ||||
0.245297 | + | 0.969448i | \(0.421114\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.299919i | 0.0108864i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 13.4622i | − | 0.488005i | −0.969775 | − | 0.244002i | \(-0.921540\pi\) | ||
0.969775 | − | 0.244002i | \(-0.0784605\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.445333 | −0.0161222 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 9.17470i | − | 0.331712i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −36.2280 | − | 23.0054i | −1.30812 | − | 0.830678i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.3243i | 0.408366i | 0.978933 | + | 0.204183i | \(0.0654538\pi\) | ||||
−0.978933 | + | 0.204183i | \(0.934546\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.0317 | 0.433311 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 39.8536i | − | 1.43343i | −0.697364 | − | 0.716717i | \(-0.745644\pi\) | ||
0.697364 | − | 0.716717i | \(-0.254356\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 20.8451i | − | 0.748778i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.05924 | −0.217374 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.8318 | −0.961351 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.127032 | 0.00454555 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.8847 | 0.460462 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 23.7795i | − | 0.848726i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.8270i | 0.671109i | 0.942021 | + | 0.335555i | \(0.108924\pi\) | ||||
−0.942021 | + | 0.335555i | \(0.891076\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.93948 | −0.247052 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.69007i | − | 0.0600918i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.8777 | − | 25.0035i | 0.563832 | − | 0.887899i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 9.77073i | − | 0.346532i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.21225 | −0.326315 | −0.163157 | − | 0.986600i | \(-0.552168\pi\) | ||||
−0.163157 | + | 0.986600i | \(0.552168\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 24.2245i | − | 0.857001i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 12.0160i | − | 0.424563i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.1281 | −0.392701 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.621502 | 0.0219051 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.8676 | 0.488162 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.3347 | 1.55873 | 0.779363 | − | 0.626573i | \(-0.215543\pi\) | ||||
0.779363 | + | 0.626573i | \(0.215543\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.16307i | 0.0759558i | 0.999279 | + | 0.0379779i | \(0.0120916\pi\) | ||||
−0.999279 | + | 0.0379779i | \(0.987908\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.870483i | 0.0305292i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.5586 | 0.720135 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.0775i | 0.982306i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.08938 | − | 4.50189i | −0.247723 | − | 0.157309i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.7421i | 1.24741i | 0.781661 | + | 0.623704i | \(0.214373\pi\) | ||||
−0.781661 | + | 0.623704i | \(0.785627\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.2244 | 0.948982 | 0.474491 | − | 0.880260i | \(-0.342632\pi\) | ||||
0.474491 | + | 0.880260i | \(0.342632\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.73587i | − | 0.0604354i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 39.2293i | − | 1.36414i | −0.731289 | − | 0.682068i | \(-0.761081\pi\) | ||
0.731289 | − | 0.682068i | \(-0.238919\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.0601 | 0.766179 | 0.383090 | − | 0.923711i | \(-0.374860\pi\) | ||||
0.383090 | + | 0.923711i | \(0.374860\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.8909 | 0.481870 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.32085 | 0.0804128 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.6966 | 0.681628 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 42.9288i | − | 1.48384i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 7.55390i | − | 0.260790i | −0.991462 | − | 0.130395i | \(-0.958375\pi\) | ||
0.991462 | − | 0.130395i | \(-0.0416245\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.2858 | −0.699512 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.25657i | 0.0432786i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.9694 | + | 9.38300i | −0.686968 | + | 0.322785i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.0538 | −0.688244 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.70907i | − | 0.0928656i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.6952i | 1.01674i | 0.861138 | + | 0.508371i | \(0.169752\pi\) | ||||
−0.861138 | + | 0.508371i | \(0.830248\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.9639 | 0.374956 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.967791 | −0.0330591 | −0.0165296 | − | 0.999863i | \(-0.505262\pi\) | ||||
−0.0165296 | + | 0.999863i | \(0.505262\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.2839 | 1.34035 | 0.670175 | − | 0.742204i | \(-0.266219\pi\) | ||||
0.670175 | + | 0.742204i | \(0.266219\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.92378 | 0.270042 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 42.0058i | − | 1.42989i | −0.699179 | − | 0.714947i | \(-0.746451\pi\) | ||
0.699179 | − | 0.714947i | \(-0.253549\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 24.5372i | − | 0.834291i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.51195 | 0.323043 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.2135i | 0.482161i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.3538 | − | 19.9103i | −1.06238 | − | 0.674634i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.6186i | 0.359385i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.0833 | −0.408489 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.72454i | 0.260839i | 0.991459 | + | 0.130420i | \(0.0416325\pi\) | ||||
−0.991459 | + | 0.130420i | \(0.958368\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.38490i | 0.316545i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.91245 | −0.333959 | −0.166979 | − | 0.985960i | \(-0.553401\pi\) | ||||
−0.166979 | + | 0.985960i | \(0.553401\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.8090 | −1.37333 | −0.686667 | − | 0.726972i | \(-0.740927\pi\) | ||||
−0.686667 | + | 0.726972i | \(0.740927\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.5455 | −0.556172 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.0574 | 1.27784 | 0.638922 | − | 0.769272i | \(-0.279381\pi\) | ||||
0.638922 | + | 0.769272i | \(0.279381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 13.3288i | − | 0.447033i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.41266i | 0.114329i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.9485 | 0.968725 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.50746i | 0.117241i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.579689 | + | 0.912869i | −0.0193552 | + | 0.0304798i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 29.0335i | − | 0.968322i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.3130 | 0.543465 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 8.29163i | − | 0.275928i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 16.0426i | − | 0.533274i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.2584 | −0.573057 | −0.286529 | − | 0.958072i | \(-0.592501\pi\) | ||||
−0.286529 | + | 0.958072i | \(0.592501\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −38.2519 | −1.26874 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.99574 | −0.264911 | −0.132455 | − | 0.991189i | \(-0.542286\pi\) | ||||
−0.132455 | + | 0.991189i | \(0.542286\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.44302 | 0.147042 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 11.4192i | − | 0.377508i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.1942i | 0.501756i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.5336 | −0.380458 | −0.190229 | − | 0.981740i | \(-0.560923\pi\) | ||||
−0.190229 | + | 0.981740i | \(0.560923\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.2873i | 0.437830i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.386648 | + | 0.245529i | 0.0127267 | + | 0.00808168i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.6796i | 0.515541i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.0742 | 0.429413 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.35914i | 0.274255i | 0.990553 | + | 0.137127i | \(0.0437869\pi\) | ||||
−0.990553 | + | 0.137127i | \(0.956213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.77344i | 0.0908959i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.9784 | 0.883232 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.93902 | −0.128820 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.2457 | 1.54345 | 0.771726 | − | 0.635956i | \(-0.219394\pi\) | ||||
0.771726 | + | 0.635956i | \(0.219394\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.01164 | 0.163549 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 43.7421i | − | 1.42595i | −0.701189 | − | 0.712975i | \(-0.747347\pi\) | ||
0.701189 | − | 0.712975i | \(-0.252653\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.54270i | 0.115366i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.40802 | −0.240983 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.25908i | 0.0409145i | 0.999791 | + | 0.0204572i | \(0.00651220\pi\) | ||||
−0.999791 | + | 0.0204572i | \(0.993488\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.8707 | − | 21.5085i | −1.09949 | − | 0.698197i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.55620i | 0.147745i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.1190 | −0.424965 | −0.212483 | − | 0.977165i | \(-0.568155\pi\) | ||||
−0.212483 | + | 0.977165i | \(0.568155\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.327836i | 0.0106085i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 2.41776i | − | 0.0781552i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.05099 | −0.0985215 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −65.7329 | −2.12041 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.7335 | −0.474782 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.7011 | 1.14926 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.7342i | 1.18129i | 0.806931 | + | 0.590646i | \(0.201127\pi\) | ||||
−0.806931 | + | 0.590646i | \(0.798873\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 5.27191i | − | 0.169358i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.5486 | −1.71846 | −0.859228 | − | 0.511593i | \(-0.829056\pi\) | ||||
−0.859228 | + | 0.511593i | \(0.829056\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 15.1151i | − | 0.484568i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.35513 | − | 5.28351i | 0.107450 | − | 0.169208i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 23.1365i | − | 0.740203i | −0.928991 | − | 0.370102i | \(-0.879323\pi\) | ||
0.928991 | − | 0.370102i | \(-0.120677\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.15887 | −0.164878 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.03726i | 0.0331173i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.48080i | 0.0472303i | 0.999721 | + | 0.0236151i | \(0.00751763\pi\) | ||||
−0.999721 | + | 0.0236151i | \(0.992482\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.2873 | 0.359644 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.54886 | −0.272113 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.70716 | 0.117881 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.6329 | −1.35428 | −0.677139 | − | 0.735855i | \(-0.736780\pi\) | ||||
−0.677139 | + | 0.735855i | \(0.736780\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 5.16136i | − | 0.163791i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 33.0277i | − | 1.04705i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.29043 | −0.104209 | −0.0521045 | − | 0.998642i | \(-0.516593\pi\) | ||||
−0.0521045 | + | 0.998642i | \(0.516593\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32.2908i | 1.02164i |
(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 | 4004.2.m.c.2157.16 | yes | 36 | |
13.12 | even | 2 | inner | 4004.2.m.c.2157.15 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.m.c.2157.15 | ✓ | 36 | 13.12 | even | 2 | inner | |
4004.2.m.c.2157.16 | yes | 36 | 1.1 | even | 1 | trivial |