Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.8 | ||
Root | \(1.08982i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.h.1249.9 |
$q$-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 \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.0898194i | − 0.0635119i | −0.999496 | − | 0.0317560i | \(-0.989890\pi\) | ||||
0.999496 | − | 0.0317560i | \(-0.0101099\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.99193 | 0.995966 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0898194 | 0.0366686 | ||||||||
\(7\) | 4.36070i | 1.64819i | 0.566451 | + | 0.824095i | \(0.308316\pi\) | ||||
−0.566451 | + | 0.824095i | \(0.691684\pi\) | |||||||
\(8\) | − 0.358553i | − 0.126768i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.39094 | 1.32392 | 0.661959 | − | 0.749540i | \(-0.269725\pi\) | ||||
0.661959 | + | 0.749540i | \(0.269725\pi\) | |||||||
\(12\) | 1.99193i | 0.575021i | ||||||||
\(13\) | 1.98166i | 0.549612i | 0.961500 | + | 0.274806i | \(0.0886137\pi\) | ||||
−0.961500 | + | 0.274806i | \(0.911386\pi\) | |||||||
\(14\) | 0.391676 | 0.104680 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.95166 | 0.987915 | ||||||||
\(17\) | 0.997022i | 0.241813i | 0.992664 | + | 0.120907i | \(0.0385802\pi\) | ||||
−0.992664 | + | 0.120907i | \(0.961420\pi\) | |||||||
\(18\) | 0.0898194i | 0.0211706i | ||||||||
\(19\) | −1.35096 | −0.309931 | −0.154965 | − | 0.987920i | \(-0.549527\pi\) | ||||
−0.154965 | + | 0.987920i | \(0.549527\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.36070 | −0.951583 | ||||||||
\(22\) | − 0.394392i | − 0.0840846i | ||||||||
\(23\) | − 2.35651i | − 0.491366i | −0.969350 | − | 0.245683i | \(-0.920988\pi\) | ||||
0.969350 | − | 0.245683i | \(-0.0790122\pi\) | |||||||
\(24\) | 0.358553 | 0.0731893 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.177991 | 0.0349069 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 8.68622i | 1.64154i | ||||||||
\(29\) | 7.97856 | 1.48158 | 0.740790 | − | 0.671736i | \(-0.234451\pi\) | ||||
0.740790 | + | 0.671736i | \(0.234451\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.67761 | −0.660519 | −0.330259 | − | 0.943890i | \(-0.607136\pi\) | ||||
−0.330259 | + | 0.943890i | \(0.607136\pi\) | |||||||
\(32\) | − 1.07204i | − 0.189512i | ||||||||
\(33\) | 4.39094i | 0.764365i | ||||||||
\(34\) | 0.0895519 | 0.0153580 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.99193 | −0.331989 | ||||||||
\(37\) | − 1.43706i | − 0.236251i | −0.992999 | − | 0.118125i | \(-0.962312\pi\) | ||||
0.992999 | − | 0.118125i | \(-0.0376885\pi\) | |||||||
\(38\) | 0.121342i | 0.0196843i | ||||||||
\(39\) | −1.98166 | −0.317319 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.98248 | −0.934306 | −0.467153 | − | 0.884177i | \(-0.654720\pi\) | ||||
−0.467153 | + | 0.884177i | \(0.654720\pi\) | |||||||
\(42\) | 0.391676i | 0.0604369i | ||||||||
\(43\) | − 2.68554i | − 0.409541i | −0.978810 | − | 0.204770i | \(-0.934355\pi\) | ||||
0.978810 | − | 0.204770i | \(-0.0656447\pi\) | |||||||
\(44\) | 8.74646 | 1.31858 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.211660 | −0.0312076 | ||||||||
\(47\) | 10.9393i | 1.59566i | 0.602883 | + | 0.797829i | \(0.294018\pi\) | ||||
−0.602883 | + | 0.797829i | \(0.705982\pi\) | |||||||
\(48\) | 3.95166i | 0.570373i | ||||||||
\(49\) | −12.0157 | −1.71653 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.997022 | −0.139611 | ||||||||
\(52\) | 3.94732i | 0.547395i | ||||||||
\(53\) | − 11.0510i | − 1.51798i | −0.651104 | − | 0.758989i | \(-0.725694\pi\) | ||||
0.651104 | − | 0.758989i | \(-0.274306\pi\) | |||||||
\(54\) | −0.0898194 | −0.0122229 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.56354 | 0.208937 | ||||||||
\(57\) | − 1.35096i | − 0.178938i | ||||||||
\(58\) | − 0.716629i | − 0.0940980i | ||||||||
\(59\) | −6.68895 | −0.870827 | −0.435414 | − | 0.900231i | \(-0.643398\pi\) | ||||
−0.435414 | + | 0.900231i | \(0.643398\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.45570 | −1.21068 | −0.605339 | − | 0.795967i | \(-0.706963\pi\) | ||||
−0.605339 | + | 0.795967i | \(0.706963\pi\) | |||||||
\(62\) | 0.330321i | 0.0419508i | ||||||||
\(63\) | − 4.36070i | − 0.549397i | ||||||||
\(64\) | 7.80703 | 0.975879 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.394392 | 0.0485463 | ||||||||
\(67\) | 12.9219i | 1.57866i | 0.613972 | + | 0.789328i | \(0.289571\pi\) | ||||
−0.613972 | + | 0.789328i | \(0.710429\pi\) | |||||||
\(68\) | 1.98600i | 0.240838i | ||||||||
\(69\) | 2.35651 | 0.283690 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.32257 | 0.869029 | 0.434515 | − | 0.900665i | \(-0.356920\pi\) | ||||
0.434515 | + | 0.900665i | \(0.356920\pi\) | |||||||
\(72\) | 0.358553i | 0.0422559i | ||||||||
\(73\) | 0.424804i | 0.0497195i | 0.999691 | + | 0.0248598i | \(0.00791393\pi\) | ||||
−0.999691 | + | 0.0248598i | \(0.992086\pi\) | |||||||
\(74\) | −0.129076 | −0.0150047 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.69101 | −0.308680 | ||||||||
\(77\) | 19.1476i | 2.18207i | ||||||||
\(78\) | 0.177991i | 0.0201535i | ||||||||
\(79\) | 6.35531 | 0.715028 | 0.357514 | − | 0.933908i | \(-0.383624\pi\) | ||||
0.357514 | + | 0.933908i | \(0.383624\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.537343i | 0.0593396i | ||||||||
\(83\) | − 0.737011i | − 0.0808975i | −0.999182 | − | 0.0404487i | \(-0.987121\pi\) | ||||
0.999182 | − | 0.0404487i | \(-0.0128787\pi\) | |||||||
\(84\) | −8.68622 | −0.947745 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.241213 | −0.0260107 | ||||||||
\(87\) | 7.97856i | 0.855391i | ||||||||
\(88\) | − 1.57439i | − 0.167830i | ||||||||
\(89\) | 9.78736 | 1.03746 | 0.518729 | − | 0.854939i | \(-0.326405\pi\) | ||||
0.518729 | + | 0.854939i | \(0.326405\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.64141 | −0.905866 | ||||||||
\(92\) | − 4.69401i | − 0.489384i | ||||||||
\(93\) | − 3.67761i | − 0.381351i | ||||||||
\(94\) | 0.982560 | 0.101343 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.07204 | 0.109415 | ||||||||
\(97\) | 0.0337081i | 0.00342254i | 0.999999 | + | 0.00171127i | \(0.000544714\pi\) | ||||
−0.999999 | + | 0.00171127i | \(0.999455\pi\) | |||||||
\(98\) | 1.07925i | 0.109020i | ||||||||
\(99\) | −4.39094 | −0.441306 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.19390 | 0.317805 | 0.158902 | − | 0.987294i | \(-0.449204\pi\) | ||||
0.158902 | + | 0.987294i | \(0.449204\pi\) | |||||||
\(102\) | 0.0895519i | 0.00886696i | ||||||||
\(103\) | − 8.55342i | − 0.842794i | −0.906876 | − | 0.421397i | \(-0.861540\pi\) | ||||
0.906876 | − | 0.421397i | \(-0.138460\pi\) | |||||||
\(104\) | 0.710529 | 0.0696731 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.992598 | −0.0964097 | ||||||||
\(107\) | 2.22136i | 0.214747i | 0.994219 | + | 0.107373i | \(0.0342440\pi\) | ||||
−0.994219 | + | 0.107373i | \(0.965756\pi\) | |||||||
\(108\) | − 1.99193i | − 0.191674i | ||||||||
\(109\) | −11.0023 | −1.05383 | −0.526916 | − | 0.849917i | \(-0.676652\pi\) | ||||
−0.526916 | + | 0.849917i | \(0.676652\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.43706 | 0.136399 | ||||||||
\(112\) | 17.2320i | 1.62827i | ||||||||
\(113\) | − 1.71021i | − 0.160883i | −0.996759 | − | 0.0804415i | \(-0.974367\pi\) | ||||
0.996759 | − | 0.0804415i | \(-0.0256330\pi\) | |||||||
\(114\) | −0.121342 | −0.0113647 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 15.8927 | 1.47560 | ||||||||
\(117\) | − 1.98166i | − 0.183204i | ||||||||
\(118\) | 0.600798i | 0.0553079i | ||||||||
\(119\) | −4.34771 | −0.398554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.28037 | 0.752761 | ||||||||
\(122\) | 0.849306i | 0.0768925i | ||||||||
\(123\) | − 5.98248i | − 0.539422i | ||||||||
\(124\) | −7.32556 | −0.657855 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.391676 | −0.0348933 | ||||||||
\(127\) | − 12.5570i | − 1.11425i | −0.830429 | − | 0.557125i | \(-0.811905\pi\) | ||||
0.830429 | − | 0.557125i | \(-0.188095\pi\) | |||||||
\(128\) | − 2.84531i | − 0.251492i | ||||||||
\(129\) | 2.68554 | 0.236448 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.4718 | 1.43915 | 0.719574 | − | 0.694416i | \(-0.244337\pi\) | ||||
0.719574 | + | 0.694416i | \(0.244337\pi\) | |||||||
\(132\) | 8.74646i | 0.761282i | ||||||||
\(133\) | − 5.89112i | − 0.510825i | ||||||||
\(134\) | 1.16063 | 0.100263 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.357485 | 0.0306541 | ||||||||
\(137\) | − 9.66732i | − 0.825935i | −0.910746 | − | 0.412967i | \(-0.864492\pi\) | ||||
0.910746 | − | 0.412967i | \(-0.135508\pi\) | |||||||
\(138\) | − 0.211660i | − 0.0180177i | ||||||||
\(139\) | −13.5327 | −1.14783 | −0.573913 | − | 0.818916i | \(-0.694575\pi\) | ||||
−0.573913 | + | 0.818916i | \(0.694575\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.9393 | −0.921254 | ||||||||
\(142\) | − 0.657709i | − 0.0551937i | ||||||||
\(143\) | 8.70133i | 0.727642i | ||||||||
\(144\) | −3.95166 | −0.329305 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.0381557 | 0.00315778 | ||||||||
\(147\) | − 12.0157i | − 0.991040i | ||||||||
\(148\) | − 2.86252i | − 0.235298i | ||||||||
\(149\) | −13.6843 | −1.12106 | −0.560529 | − | 0.828134i | \(-0.689402\pi\) | ||||
−0.560529 | + | 0.828134i | \(0.689402\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.3204 | −0.921237 | −0.460619 | − | 0.887598i | \(-0.652372\pi\) | ||||
−0.460619 | + | 0.887598i | \(0.652372\pi\) | |||||||
\(152\) | 0.484389i | 0.0392892i | ||||||||
\(153\) | − 0.997022i | − 0.0806044i | ||||||||
\(154\) | 1.71983 | 0.138587 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.94732 | −0.316039 | ||||||||
\(157\) | 8.56070i | 0.683219i | 0.939842 | + | 0.341609i | \(0.110972\pi\) | ||||
−0.939842 | + | 0.341609i | \(0.889028\pi\) | |||||||
\(158\) | − 0.570830i | − 0.0454128i | ||||||||
\(159\) | 11.0510 | 0.876405 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.2760 | 0.809865 | ||||||||
\(162\) | − 0.0898194i | − 0.00705688i | ||||||||
\(163\) | − 4.58509i | − 0.359132i | −0.983746 | − | 0.179566i | \(-0.942531\pi\) | ||||
0.983746 | − | 0.179566i | \(-0.0574694\pi\) | |||||||
\(164\) | −11.9167 | −0.930537 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.0661979 | −0.00513795 | ||||||||
\(167\) | 7.21792i | 0.558540i | 0.960213 | + | 0.279270i | \(0.0900924\pi\) | ||||
−0.960213 | + | 0.279270i | \(0.909908\pi\) | |||||||
\(168\) | 1.56354i | 0.120630i | ||||||||
\(169\) | 9.07304 | 0.697926 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.35096 | 0.103310 | ||||||||
\(172\) | − 5.34941i | − 0.407889i | ||||||||
\(173\) | 4.65009i | 0.353540i | 0.984252 | + | 0.176770i | \(0.0565649\pi\) | ||||
−0.984252 | + | 0.176770i | \(0.943435\pi\) | |||||||
\(174\) | 0.716629 | 0.0543275 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 17.3515 | 1.30792 | ||||||||
\(177\) | − 6.68895i | − 0.502772i | ||||||||
\(178\) | − 0.879095i | − 0.0658909i | ||||||||
\(179\) | 7.20338 | 0.538406 | 0.269203 | − | 0.963083i | \(-0.413240\pi\) | ||||
0.269203 | + | 0.963083i | \(0.413240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.80424 | −0.282767 | −0.141383 | − | 0.989955i | \(-0.545155\pi\) | ||||
−0.141383 | + | 0.989955i | \(0.545155\pi\) | |||||||
\(182\) | 0.776167i | 0.0575333i | ||||||||
\(183\) | − 9.45570i | − 0.698986i | ||||||||
\(184\) | −0.844934 | −0.0622893 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.330321 | −0.0242203 | ||||||||
\(187\) | 4.37786i | 0.320141i | ||||||||
\(188\) | 21.7903i | 1.58922i | ||||||||
\(189\) | 4.36070 | 0.317194 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.5541 | 1.55960 | 0.779801 | − | 0.626027i | \(-0.215320\pi\) | ||||
0.779801 | + | 0.626027i | \(0.215320\pi\) | |||||||
\(192\) | 7.80703i | 0.563424i | ||||||||
\(193\) | − 3.15029i | − 0.226763i | −0.993552 | − | 0.113381i | \(-0.963832\pi\) | ||||
0.993552 | − | 0.113381i | \(-0.0361682\pi\) | |||||||
\(194\) | 0.00302764 | 0.000217372 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −23.9345 | −1.70961 | ||||||||
\(197\) | 26.0837i | 1.85839i | 0.369590 | + | 0.929195i | \(0.379498\pi\) | ||||
−0.369590 | + | 0.929195i | \(0.620502\pi\) | |||||||
\(198\) | 0.394392i | 0.0280282i | ||||||||
\(199\) | 24.2662 | 1.72018 | 0.860092 | − | 0.510139i | \(-0.170406\pi\) | ||||
0.860092 | + | 0.510139i | \(0.170406\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.9219 | −0.911437 | ||||||||
\(202\) | − 0.286874i | − 0.0201844i | ||||||||
\(203\) | 34.7921i | 2.44193i | ||||||||
\(204\) | −1.98600 | −0.139048 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.768264 | −0.0535275 | ||||||||
\(207\) | 2.35651i | 0.163789i | ||||||||
\(208\) | 7.83083i | 0.542970i | ||||||||
\(209\) | −5.93197 | −0.410323 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.3783 | 1.12753 | 0.563765 | − | 0.825935i | \(-0.309352\pi\) | ||||
0.563765 | + | 0.825935i | \(0.309352\pi\) | |||||||
\(212\) | − 22.0129i | − 1.51185i | ||||||||
\(213\) | 7.32257i | 0.501734i | ||||||||
\(214\) | 0.199521 | 0.0136390 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.358553 | −0.0243964 | ||||||||
\(217\) | − 16.0370i | − 1.08866i | ||||||||
\(218\) | 0.988224i | 0.0669310i | ||||||||
\(219\) | −0.424804 | −0.0287056 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.97575 | −0.132904 | ||||||||
\(222\) | − 0.129076i | − 0.00866299i | ||||||||
\(223\) | 5.68295i | 0.380558i | 0.981730 | + | 0.190279i | \(0.0609393\pi\) | ||||
−0.981730 | + | 0.190279i | \(0.939061\pi\) | |||||||
\(224\) | 4.67486 | 0.312352 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.153610 | −0.0102180 | ||||||||
\(227\) | 3.64374i | 0.241844i | 0.992662 | + | 0.120922i | \(0.0385850\pi\) | ||||
−0.992662 | + | 0.120922i | \(0.961415\pi\) | |||||||
\(228\) | − 2.69101i | − 0.178217i | ||||||||
\(229\) | −1.66125 | −0.109779 | −0.0548893 | − | 0.998492i | \(-0.517481\pi\) | ||||
−0.0548893 | + | 0.998492i | \(0.517481\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.1476 | −1.25982 | ||||||||
\(232\) | − 2.86074i | − 0.187817i | ||||||||
\(233\) | − 7.85899i | − 0.514860i | −0.966297 | − | 0.257430i | \(-0.917124\pi\) | ||||
0.966297 | − | 0.257430i | \(-0.0828756\pi\) | |||||||
\(234\) | −0.177991 | −0.0116356 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.3239 | −0.867314 | ||||||||
\(237\) | 6.35531i | 0.412821i | ||||||||
\(238\) | 0.390509i | 0.0253130i | ||||||||
\(239\) | 0.567301 | 0.0366956 | 0.0183478 | − | 0.999832i | \(-0.494159\pi\) | ||||
0.0183478 | + | 0.999832i | \(0.494159\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.0081 | −1.22442 | −0.612211 | − | 0.790695i | \(-0.709720\pi\) | ||||
−0.612211 | + | 0.790695i | \(0.709720\pi\) | |||||||
\(242\) | − 0.743738i | − 0.0478093i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −18.8351 | −1.20580 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.537343 | −0.0342597 | ||||||||
\(247\) | − 2.67713i | − 0.170342i | ||||||||
\(248\) | 1.31862i | 0.0837324i | ||||||||
\(249\) | 0.737011 | 0.0467062 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.02533 | 0.190957 | 0.0954787 | − | 0.995431i | \(-0.469562\pi\) | ||||
0.0954787 | + | 0.995431i | \(0.469562\pi\) | |||||||
\(252\) | − 8.68622i | − 0.547181i | ||||||||
\(253\) | − 10.3473i | − 0.650529i | ||||||||
\(254\) | −1.12786 | −0.0707681 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.3585 | 0.959906 | ||||||||
\(257\) | − 19.8613i | − 1.23891i | −0.785032 | − | 0.619456i | \(-0.787353\pi\) | ||||
0.785032 | − | 0.619456i | \(-0.212647\pi\) | |||||||
\(258\) | − 0.241213i | − 0.0150173i | ||||||||
\(259\) | 6.26658 | 0.389386 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.97856 | −0.493860 | ||||||||
\(262\) | − 1.47949i | − 0.0914030i | ||||||||
\(263\) | − 22.8299i | − 1.40775i | −0.710323 | − | 0.703876i | \(-0.751451\pi\) | ||||
0.710323 | − | 0.703876i | \(-0.248549\pi\) | |||||||
\(264\) | 1.57439 | 0.0968968 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.529137 | −0.0324435 | ||||||||
\(267\) | 9.78736i | 0.598977i | ||||||||
\(268\) | 25.7395i | 1.57229i | ||||||||
\(269\) | −14.8324 | −0.904347 | −0.452174 | − | 0.891930i | \(-0.649351\pi\) | ||||
−0.452174 | + | 0.891930i | \(0.649351\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.43720 | −0.391032 | −0.195516 | − | 0.980701i | \(-0.562638\pi\) | ||||
−0.195516 | + | 0.980701i | \(0.562638\pi\) | |||||||
\(272\) | 3.93989i | 0.238891i | ||||||||
\(273\) | − 8.64141i | − 0.523002i | ||||||||
\(274\) | −0.868313 | −0.0524567 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.69401 | 0.282546 | ||||||||
\(277\) | 6.70976i | 0.403150i | 0.979473 | + | 0.201575i | \(0.0646060\pi\) | ||||
−0.979473 | + | 0.201575i | \(0.935394\pi\) | |||||||
\(278\) | 1.21550i | 0.0729006i | ||||||||
\(279\) | 3.67761 | 0.220173 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.4867 | −1.22214 | −0.611068 | − | 0.791578i | \(-0.709260\pi\) | ||||
−0.611068 | + | 0.791578i | \(0.709260\pi\) | |||||||
\(282\) | 0.982560i | 0.0585106i | ||||||||
\(283\) | 11.4177i | 0.678715i | 0.940658 | + | 0.339357i | \(0.110210\pi\) | ||||
−0.940658 | + | 0.339357i | \(0.889790\pi\) | |||||||
\(284\) | 14.5861 | 0.865524 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.781549 | 0.0462140 | ||||||||
\(287\) | − 26.0878i | − 1.53991i | ||||||||
\(288\) | 1.07204i | 0.0631707i | ||||||||
\(289\) | 16.0059 | 0.941526 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0337081 | −0.00197600 | ||||||||
\(292\) | 0.846181i | 0.0495190i | ||||||||
\(293\) | − 28.5505i | − 1.66794i | −0.551812 | − | 0.833968i | \(-0.686063\pi\) | ||||
0.551812 | − | 0.833968i | \(-0.313937\pi\) | |||||||
\(294\) | −1.07925 | −0.0629429 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.515261 | −0.0299489 | ||||||||
\(297\) | − 4.39094i | − 0.254788i | ||||||||
\(298\) | 1.22911i | 0.0712006i | ||||||||
\(299\) | 4.66979 | 0.270061 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7108 | 0.675001 | ||||||||
\(302\) | 1.01679i | 0.0585095i | ||||||||
\(303\) | 3.19390i | 0.183485i | ||||||||
\(304\) | −5.33852 | −0.306185 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.0895519 | −0.00511934 | ||||||||
\(307\) | − 20.5417i | − 1.17238i | −0.810175 | − | 0.586188i | \(-0.800628\pi\) | ||||
0.810175 | − | 0.586188i | \(-0.199372\pi\) | |||||||
\(308\) | 38.1407i | 2.17327i | ||||||||
\(309\) | 8.55342 | 0.486587 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.5496 | 0.995146 | 0.497573 | − | 0.867422i | \(-0.334225\pi\) | ||||
0.497573 | + | 0.867422i | \(0.334225\pi\) | |||||||
\(312\) | 0.710529i | 0.0402258i | ||||||||
\(313\) | 2.98564i | 0.168758i | 0.996434 | + | 0.0843790i | \(0.0268907\pi\) | ||||
−0.996434 | + | 0.0843790i | \(0.973109\pi\) | |||||||
\(314\) | 0.768918 | 0.0433925 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.6593 | 0.712143 | ||||||||
\(317\) | − 16.1708i | − 0.908244i | −0.890940 | − | 0.454122i | \(-0.849953\pi\) | ||||
0.890940 | − | 0.454122i | \(-0.150047\pi\) | |||||||
\(318\) | − 0.992598i | − 0.0556621i | ||||||||
\(319\) | 35.0334 | 1.96149 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.22136 | −0.123984 | ||||||||
\(322\) | − 0.922988i | − 0.0514361i | ||||||||
\(323\) | − 1.34693i | − 0.0749453i | ||||||||
\(324\) | 1.99193 | 0.110663 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.411830 | −0.0228092 | ||||||||
\(327\) | − 11.0023i | − 0.608431i | ||||||||
\(328\) | 2.14504i | 0.118440i | ||||||||
\(329\) | −47.7030 | −2.62995 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0705 | −0.718418 | −0.359209 | − | 0.933257i | \(-0.616953\pi\) | ||||
−0.359209 | + | 0.933257i | \(0.616953\pi\) | |||||||
\(332\) | − 1.46808i | − 0.0805711i | ||||||||
\(333\) | 1.43706i | 0.0787502i | ||||||||
\(334\) | 0.648310 | 0.0354739 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −17.2320 | −0.940083 | ||||||||
\(337\) | 26.8049i | 1.46015i | 0.683365 | + | 0.730077i | \(0.260516\pi\) | ||||
−0.683365 | + | 0.730077i | \(0.739484\pi\) | |||||||
\(338\) | − 0.814935i | − 0.0443266i | ||||||||
\(339\) | 1.71021 | 0.0928858 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.1482 | −0.874473 | ||||||||
\(342\) | − 0.121342i | − 0.00656143i | ||||||||
\(343\) | − 21.8721i | − 1.18098i | ||||||||
\(344\) | −0.962908 | −0.0519165 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.417669 | 0.0224540 | ||||||||
\(347\) | − 25.4859i | − 1.36815i | −0.729410 | − | 0.684077i | \(-0.760205\pi\) | ||||
0.729410 | − | 0.684077i | \(-0.239795\pi\) | |||||||
\(348\) | 15.8927i | 0.851941i | ||||||||
\(349\) | 28.0435 | 1.50113 | 0.750566 | − | 0.660795i | \(-0.229781\pi\) | ||||
0.750566 | + | 0.660795i | \(0.229781\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.98166 | 0.105773 | ||||||||
\(352\) | − 4.70727i | − 0.250899i | ||||||||
\(353\) | − 14.6667i | − 0.780630i | −0.920681 | − | 0.390315i | \(-0.872366\pi\) | ||||
0.920681 | − | 0.390315i | \(-0.127634\pi\) | |||||||
\(354\) | −0.600798 | −0.0319320 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 19.4958 | 1.03327 | ||||||||
\(357\) | − 4.34771i | − 0.230105i | ||||||||
\(358\) | − 0.647004i | − 0.0341952i | ||||||||
\(359\) | 14.6205 | 0.771642 | 0.385821 | − | 0.922574i | \(-0.373918\pi\) | ||||
0.385821 | + | 0.922574i | \(0.373918\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1749 | −0.903943 | ||||||||
\(362\) | 0.341694i | 0.0179591i | ||||||||
\(363\) | 8.28037i | 0.434607i | ||||||||
\(364\) | −17.2131 | −0.902212 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.849306 | −0.0443939 | ||||||||
\(367\) | − 17.6940i | − 0.923617i | −0.886980 | − | 0.461808i | \(-0.847201\pi\) | ||||
0.886980 | − | 0.461808i | \(-0.152799\pi\) | |||||||
\(368\) | − 9.31212i | − 0.485428i | ||||||||
\(369\) | 5.98248 | 0.311435 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 48.1903 | 2.50192 | ||||||||
\(372\) | − 7.32556i | − 0.379813i | ||||||||
\(373\) | − 12.2293i | − 0.633210i | −0.948557 | − | 0.316605i | \(-0.897457\pi\) | ||||
0.948557 | − | 0.316605i | \(-0.102543\pi\) | |||||||
\(374\) | 0.393217 | 0.0203328 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.92231 | 0.202278 | ||||||||
\(377\) | 15.8107i | 0.814295i | ||||||||
\(378\) | − 0.391676i | − 0.0201456i | ||||||||
\(379\) | −28.0951 | −1.44315 | −0.721574 | − | 0.692338i | \(-0.756581\pi\) | ||||
−0.721574 | + | 0.692338i | \(0.756581\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.5570 | 0.643312 | ||||||||
\(382\) | − 1.93598i | − 0.0990533i | ||||||||
\(383\) | − 34.4334i | − 1.75947i | −0.475468 | − | 0.879733i | \(-0.657721\pi\) | ||||
0.475468 | − | 0.879733i | \(-0.342279\pi\) | |||||||
\(384\) | 2.84531 | 0.145199 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.282957 | −0.0144021 | ||||||||
\(387\) | 2.68554i | 0.136514i | ||||||||
\(388\) | 0.0671442i | 0.00340873i | ||||||||
\(389\) | −13.5225 | −0.685619 | −0.342809 | − | 0.939405i | \(-0.611378\pi\) | ||||
−0.342809 | + | 0.939405i | \(0.611378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.34949 | 0.118819 | ||||||||
\(392\) | 4.30827i | 0.217601i | ||||||||
\(393\) | 16.4718i | 0.830892i | ||||||||
\(394\) | 2.34283 | 0.118030 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.74646 | −0.439526 | ||||||||
\(397\) | − 35.9744i | − 1.80550i | −0.430164 | − | 0.902751i | \(-0.641544\pi\) | ||||
0.430164 | − | 0.902751i | \(-0.358456\pi\) | |||||||
\(398\) | − 2.17958i | − 0.109252i | ||||||||
\(399\) | 5.89112 | 0.294925 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.35977 | 0.217717 | 0.108858 | − | 0.994057i | \(-0.465281\pi\) | ||||
0.108858 | + | 0.994057i | \(0.465281\pi\) | |||||||
\(402\) | 1.16063i | 0.0578871i | ||||||||
\(403\) | − 7.28776i | − 0.363029i | ||||||||
\(404\) | 6.36203 | 0.316523 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.12501 | 0.155092 | ||||||||
\(407\) | − 6.31003i | − 0.312777i | ||||||||
\(408\) | 0.357485i | 0.0176982i | ||||||||
\(409\) | 18.1138 | 0.895668 | 0.447834 | − | 0.894117i | \(-0.352196\pi\) | ||||
0.447834 | + | 0.894117i | \(0.352196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.66732 | 0.476854 | ||||||||
\(412\) | − 17.0378i | − 0.839394i | ||||||||
\(413\) | − 29.1685i | − 1.43529i | ||||||||
\(414\) | 0.211660 | 0.0104025 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.12442 | 0.104158 | ||||||||
\(417\) | − 13.5327i | − 0.662698i | ||||||||
\(418\) | 0.532806i | 0.0260604i | ||||||||
\(419\) | −0.527867 | −0.0257880 | −0.0128940 | − | 0.999917i | \(-0.504104\pi\) | ||||
−0.0128940 | + | 0.999917i | \(0.504104\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.6586 | 0.909365 | 0.454682 | − | 0.890654i | \(-0.349753\pi\) | ||||
0.454682 | + | 0.890654i | \(0.349753\pi\) | |||||||
\(422\) | − 1.47109i | − 0.0716117i | ||||||||
\(423\) | − 10.9393i | − 0.531886i | ||||||||
\(424\) | −3.96239 | −0.192430 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.657709 | 0.0318661 | ||||||||
\(427\) | − 41.2335i | − 1.99543i | ||||||||
\(428\) | 4.42480i | 0.213881i | ||||||||
\(429\) | −8.70133 | −0.420104 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.9913 | 1.01112 | 0.505559 | − | 0.862792i | \(-0.331286\pi\) | ||||
0.505559 | + | 0.862792i | \(0.331286\pi\) | |||||||
\(432\) | − 3.95166i | − 0.190124i | ||||||||
\(433\) | 13.6639i | 0.656647i | 0.944565 | + | 0.328324i | \(0.106484\pi\) | ||||
−0.944565 | + | 0.328324i | \(0.893516\pi\) | |||||||
\(434\) | −1.44043 | −0.0691430 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.9159 | −1.04958 | ||||||||
\(437\) | 3.18354i | 0.152289i | ||||||||
\(438\) | 0.0381557i | 0.00182315i | ||||||||
\(439\) | 4.33339 | 0.206821 | 0.103411 | − | 0.994639i | \(-0.467024\pi\) | ||||
0.103411 | + | 0.994639i | \(0.467024\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.0157 | 0.572177 | ||||||||
\(442\) | 0.177461i | 0.00844096i | ||||||||
\(443\) | 1.60742i | 0.0763707i | 0.999271 | + | 0.0381854i | \(0.0121577\pi\) | ||||
−0.999271 | + | 0.0381854i | \(0.987842\pi\) | |||||||
\(444\) | 2.86252 | 0.135849 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.510439 | 0.0241700 | ||||||||
\(447\) | − 13.6843i | − 0.647244i | ||||||||
\(448\) | 34.0441i | 1.60843i | ||||||||
\(449\) | 13.8291 | 0.652634 | 0.326317 | − | 0.945260i | \(-0.394192\pi\) | ||||
0.326317 | + | 0.945260i | \(0.394192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.2687 | −1.23694 | ||||||||
\(452\) | − 3.40662i | − 0.160234i | ||||||||
\(453\) | − 11.3204i | − 0.531876i | ||||||||
\(454\) | 0.327279 | 0.0153600 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.484389 | −0.0226836 | ||||||||
\(457\) | 20.1345i | 0.941850i | 0.882173 | + | 0.470925i | \(0.156080\pi\) | ||||
−0.882173 | + | 0.470925i | \(0.843920\pi\) | |||||||
\(458\) | 0.149213i | 0.00697225i | ||||||||
\(459\) | 0.997022 | 0.0465370 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.5264 | 1.46833 | 0.734166 | − | 0.678970i | \(-0.237573\pi\) | ||||
0.734166 | + | 0.678970i | \(0.237573\pi\) | |||||||
\(462\) | 1.71983i | 0.0800135i | ||||||||
\(463\) | 0.0451697i | 0.00209921i | 0.999999 | + | 0.00104961i | \(0.000334100\pi\) | ||||
−0.999999 | + | 0.00104961i | \(0.999666\pi\) | |||||||
\(464\) | 31.5285 | 1.46368 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.705890 | −0.0326997 | ||||||||
\(467\) | − 32.8349i | − 1.51942i | −0.650265 | − | 0.759708i | \(-0.725342\pi\) | ||||
0.650265 | − | 0.759708i | \(-0.274658\pi\) | |||||||
\(468\) | − 3.94732i | − 0.182465i | ||||||||
\(469\) | −56.3484 | −2.60193 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.56070 | −0.394456 | ||||||||
\(472\) | 2.39834i | 0.110393i | ||||||||
\(473\) | − 11.7920i | − 0.542198i | ||||||||
\(474\) | 0.570830 | 0.0262191 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.66035 | −0.396947 | ||||||||
\(477\) | 11.0510i | 0.505992i | ||||||||
\(478\) | − 0.0509546i | − 0.00233061i | ||||||||
\(479\) | −7.48576 | −0.342033 | −0.171017 | − | 0.985268i | \(-0.554705\pi\) | ||||
−0.171017 | + | 0.985268i | \(0.554705\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.84775 | 0.129846 | ||||||||
\(482\) | 1.70730i | 0.0777654i | ||||||||
\(483\) | 10.2760i | 0.467576i | ||||||||
\(484\) | 16.4939 | 0.749724 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.0898194 | 0.00407429 | ||||||||
\(487\) | − 25.4295i | − 1.15232i | −0.817337 | − | 0.576160i | \(-0.804551\pi\) | ||||
0.817337 | − | 0.576160i | \(-0.195449\pi\) | |||||||
\(488\) | 3.39037i | 0.153475i | ||||||||
\(489\) | 4.58509 | 0.207345 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.0668 | −0.499438 | −0.249719 | − | 0.968318i | \(-0.580338\pi\) | ||||
−0.249719 | + | 0.968318i | \(0.580338\pi\) | |||||||
\(492\) | − 11.9167i | − 0.537246i | ||||||||
\(493\) | 7.95479i | 0.358266i | ||||||||
\(494\) | −0.240458 | −0.0108187 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.5327 | −0.652537 | ||||||||
\(497\) | 31.9315i | 1.43233i | ||||||||
\(498\) | − 0.0661979i | − 0.00296640i | ||||||||
\(499\) | −4.68157 | −0.209576 | −0.104788 | − | 0.994495i | \(-0.533416\pi\) | ||||
−0.104788 | + | 0.994495i | \(0.533416\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.21792 | −0.322473 | ||||||||
\(502\) | − 0.271734i | − 0.0121281i | ||||||||
\(503\) | − 10.8285i | − 0.482818i | −0.970423 | − | 0.241409i | \(-0.922391\pi\) | ||||
0.970423 | − | 0.241409i | \(-0.0776095\pi\) | |||||||
\(504\) | −1.56354 | −0.0696458 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.929388 | −0.0413163 | ||||||||
\(507\) | 9.07304i | 0.402948i | ||||||||
\(508\) | − 25.0126i | − 1.10975i | ||||||||
\(509\) | −11.5007 | −0.509757 | −0.254879 | − | 0.966973i | \(-0.582036\pi\) | ||||
−0.254879 | + | 0.966973i | \(0.582036\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.85244 | −0.0819473 | ||||||||
\(512\) | − 7.07011i | − 0.312457i | ||||||||
\(513\) | 1.35096i | 0.0596462i | ||||||||
\(514\) | −1.78393 | −0.0786856 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.34941 | 0.235495 | ||||||||
\(517\) | 48.0338i | 2.11252i | ||||||||
\(518\) | − 0.562860i | − 0.0247307i | ||||||||
\(519\) | −4.65009 | −0.204116 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.797807 | 0.0349525 | 0.0174763 | − | 0.999847i | \(-0.494437\pi\) | ||||
0.0174763 | + | 0.999847i | \(0.494437\pi\) | |||||||
\(522\) | 0.716629i | 0.0313660i | ||||||||
\(523\) | − 40.1429i | − 1.75533i | −0.479279 | − | 0.877663i | \(-0.659102\pi\) | ||||
0.479279 | − | 0.877663i | \(-0.340898\pi\) | |||||||
\(524\) | 32.8107 | 1.43334 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.05057 | −0.0894090 | ||||||||
\(527\) | − 3.66666i | − 0.159722i | ||||||||
\(528\) | 17.3515i | 0.755127i | ||||||||
\(529\) | 17.4469 | 0.758559 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.68895 | 0.290276 | ||||||||
\(532\) | − 11.7347i | − 0.508764i | ||||||||
\(533\) | − 11.8552i | − 0.513506i | ||||||||
\(534\) | 0.879095 | 0.0380422 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.63317 | 0.200123 | ||||||||
\(537\) | 7.20338i | 0.310849i | ||||||||
\(538\) | 1.33224i | 0.0574369i | ||||||||
\(539\) | −52.7603 | −2.27255 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.41016 | 0.0606277 | 0.0303138 | − | 0.999540i | \(-0.490349\pi\) | ||||
0.0303138 | + | 0.999540i | \(0.490349\pi\) | |||||||
\(542\) | 0.578185i | 0.0248352i | ||||||||
\(543\) | − 3.80424i | − 0.163255i | ||||||||
\(544\) | 1.06885 | 0.0458265 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.776167 | −0.0332169 | ||||||||
\(547\) | 15.4621i | 0.661110i | 0.943787 | + | 0.330555i | \(0.107236\pi\) | ||||
−0.943787 | + | 0.330555i | \(0.892764\pi\) | |||||||
\(548\) | − 19.2566i | − 0.822603i | ||||||||
\(549\) | 9.45570 | 0.403560 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.7787 | −0.459187 | ||||||||
\(552\) | − 0.844934i | − 0.0359628i | ||||||||
\(553\) | 27.7136i | 1.17850i | ||||||||
\(554\) | 0.602667 | 0.0256049 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26.9562 | −1.14320 | ||||||||
\(557\) | − 18.0445i | − 0.764568i | −0.924045 | − | 0.382284i | \(-0.875138\pi\) | ||||
0.924045 | − | 0.382284i | \(-0.124862\pi\) | |||||||
\(558\) | − 0.330321i | − 0.0139836i | ||||||||
\(559\) | 5.32181 | 0.225089 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.37786 | −0.184834 | ||||||||
\(562\) | 1.84011i | 0.0776202i | ||||||||
\(563\) | 28.5327i | 1.20251i | 0.799058 | + | 0.601254i | \(0.205332\pi\) | ||||
−0.799058 | + | 0.601254i | \(0.794668\pi\) | |||||||
\(564\) | −21.7903 | −0.917538 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.02554 | 0.0431065 | ||||||||
\(567\) | 4.36070i | 0.183132i | ||||||||
\(568\) | − 2.62553i | − 0.110165i | ||||||||
\(569\) | −16.4072 | −0.687826 | −0.343913 | − | 0.939001i | \(-0.611753\pi\) | ||||
−0.343913 | + | 0.939001i | \(0.611753\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.34705 | −0.349313 | −0.174657 | − | 0.984629i | \(-0.555882\pi\) | ||||
−0.174657 | + | 0.984629i | \(0.555882\pi\) | |||||||
\(572\) | 17.3325i | 0.724707i | ||||||||
\(573\) | 21.5541i | 0.900437i | ||||||||
\(574\) | −2.34319 | −0.0978029 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.80703 | −0.325293 | ||||||||
\(577\) | 8.43531i | 0.351167i | 0.984465 | + | 0.175583i | \(0.0561811\pi\) | ||||
−0.984465 | + | 0.175583i | \(0.943819\pi\) | |||||||
\(578\) | − 1.43765i | − 0.0597982i | ||||||||
\(579\) | 3.15029 | 0.130921 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.21389 | 0.133334 | ||||||||
\(582\) | 0.00302764i | 0 0.000125500i | ||||||||
\(583\) | − 48.5245i | − 2.00968i | ||||||||
\(584\) | 0.152315 | 0.00630283 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.56439 | −0.105934 | ||||||||
\(587\) | − 24.2852i | − 1.00236i | −0.865344 | − | 0.501179i | \(-0.832900\pi\) | ||||
0.865344 | − | 0.501179i | \(-0.167100\pi\) | |||||||
\(588\) | − 23.9345i | − 0.987042i | ||||||||
\(589\) | 4.96829 | 0.204715 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.0837 | −1.07294 | ||||||||
\(592\) | − 5.67876i | − 0.233396i | ||||||||
\(593\) | 28.4653i | 1.16893i | 0.811418 | + | 0.584466i | \(0.198696\pi\) | ||||
−0.811418 | + | 0.584466i | \(0.801304\pi\) | |||||||
\(594\) | −0.394392 | −0.0161821 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −27.2581 | −1.11654 | ||||||||
\(597\) | 24.2662i | 0.993149i | ||||||||
\(598\) | − 0.419438i | − 0.0171521i | ||||||||
\(599\) | −16.0387 | −0.655323 | −0.327662 | − | 0.944795i | \(-0.606261\pi\) | ||||
−0.327662 | + | 0.944795i | \(0.606261\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.09005 | −0.330000 | −0.165000 | − | 0.986294i | \(-0.552762\pi\) | ||||
−0.165000 | + | 0.986294i | \(0.552762\pi\) | |||||||
\(602\) | − 1.05186i | − 0.0428706i | ||||||||
\(603\) | − 12.9219i | − 0.526219i | ||||||||
\(604\) | −22.5494 | −0.917521 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.286874 | 0.0116535 | ||||||||
\(607\) | − 0.434608i | − 0.0176402i | −0.999961 | − | 0.00882010i | \(-0.997192\pi\) | ||||
0.999961 | − | 0.00882010i | \(-0.00280756\pi\) | |||||||
\(608\) | 1.44828i | 0.0587356i | ||||||||
\(609\) | −34.7921 | −1.40985 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.6779 | −0.876994 | ||||||||
\(612\) | − 1.98600i | − 0.0802793i | ||||||||
\(613\) | 39.3962i | 1.59120i | 0.605824 | + | 0.795599i | \(0.292844\pi\) | ||||
−0.605824 | + | 0.795599i | \(0.707156\pi\) | |||||||
\(614\) | −1.84504 | −0.0744599 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.86543 | 0.276616 | ||||||||
\(617\) | 15.4146i | 0.620568i | 0.950644 | + | 0.310284i | \(0.100424\pi\) | ||||
−0.950644 | + | 0.310284i | \(0.899576\pi\) | |||||||
\(618\) | − 0.768264i | − 0.0309041i | ||||||||
\(619\) | 10.6718 | 0.428935 | 0.214468 | − | 0.976731i | \(-0.431198\pi\) | ||||
0.214468 | + | 0.976731i | \(0.431198\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.35651 | −0.0945635 | ||||||||
\(622\) | − 1.57629i | − 0.0632036i | ||||||||
\(623\) | 42.6797i | 1.70993i | ||||||||
\(624\) | −7.83083 | −0.313484 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.268168 | 0.0107182 | ||||||||
\(627\) | − 5.93197i | − 0.236900i | ||||||||
\(628\) | 17.0523i | 0.680463i | ||||||||
\(629\) | 1.43278 | 0.0571285 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.4347 | −0.733874 | −0.366937 | − | 0.930246i | \(-0.619594\pi\) | ||||
−0.366937 | + | 0.930246i | \(0.619594\pi\) | |||||||
\(632\) | − 2.27871i | − 0.0906424i | ||||||||
\(633\) | 16.3783i | 0.650980i | ||||||||
\(634\) | −1.45245 | −0.0576843 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 22.0129 | 0.872869 | ||||||||
\(637\) | − 23.8110i | − 0.943427i | ||||||||
\(638\) | − 3.14668i | − 0.124578i | ||||||||
\(639\) | −7.32257 | −0.289676 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.4281 | 0.490882 | 0.245441 | − | 0.969412i | \(-0.421067\pi\) | ||||
0.245441 | + | 0.969412i | \(0.421067\pi\) | |||||||
\(642\) | 0.199521i | 0.00787447i | ||||||||
\(643\) | 1.84657i | 0.0728218i | 0.999337 | + | 0.0364109i | \(0.0115925\pi\) | ||||
−0.999337 | + | 0.0364109i | \(0.988407\pi\) | |||||||
\(644\) | 20.4692 | 0.806598 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.120981 | −0.00475992 | ||||||||
\(647\) | − 38.9760i | − 1.53230i | −0.642660 | − | 0.766152i | \(-0.722169\pi\) | ||||
0.642660 | − | 0.766152i | \(-0.277831\pi\) | |||||||
\(648\) | − 0.358553i | − 0.0140853i | ||||||||
\(649\) | −29.3708 | −1.15290 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.0370 | 0.628539 | ||||||||
\(652\) | − 9.13319i | − 0.357683i | ||||||||
\(653\) | − 28.3389i | − 1.10899i | −0.832189 | − | 0.554493i | \(-0.812912\pi\) | ||||
0.832189 | − | 0.554493i | \(-0.187088\pi\) | |||||||
\(654\) | −0.988224 | −0.0386426 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −23.6407 | −0.923015 | ||||||||
\(657\) | − 0.424804i | − 0.0165732i | ||||||||
\(658\) | 4.28465i | 0.167033i | ||||||||
\(659\) | 22.3561 | 0.870868 | 0.435434 | − | 0.900221i | \(-0.356595\pi\) | ||||
0.435434 | + | 0.900221i | \(0.356595\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.2143 | 1.13631 | 0.568153 | − | 0.822923i | \(-0.307658\pi\) | ||||
0.568153 | + | 0.822923i | \(0.307658\pi\) | |||||||
\(662\) | 1.17398i | 0.0456281i | ||||||||
\(663\) | − 1.97575i | − 0.0767319i | ||||||||
\(664\) | −0.264258 | −0.0102552 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.129076 | 0.00500158 | ||||||||
\(667\) | − 18.8015i | − 0.727998i | ||||||||
\(668\) | 14.3776i | 0.556287i | ||||||||
\(669\) | −5.68295 | −0.219715 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.5194 | −1.60284 | ||||||||
\(672\) | 4.67486i | 0.180336i | ||||||||
\(673\) | − 3.21546i | − 0.123947i | −0.998078 | − | 0.0619735i | \(-0.980261\pi\) | ||||
0.998078 | − | 0.0619735i | \(-0.0197394\pi\) | |||||||
\(674\) | 2.40760 | 0.0927372 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.0729 | 0.695111 | ||||||||
\(677\) | − 47.2470i | − 1.81585i | −0.419133 | − | 0.907925i | \(-0.637666\pi\) | ||||
0.419133 | − | 0.907925i | \(-0.362334\pi\) | |||||||
\(678\) | − 0.153610i | − 0.00589936i | ||||||||
\(679\) | −0.146991 | −0.00564099 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.64374 | −0.139629 | ||||||||
\(682\) | 1.45042i | 0.0555395i | ||||||||
\(683\) | 37.2527i | 1.42543i | 0.701452 | + | 0.712717i | \(0.252536\pi\) | ||||
−0.701452 | + | 0.712717i | \(0.747464\pi\) | |||||||
\(684\) | 2.69101 | 0.102893 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.96454 | −0.0750064 | ||||||||
\(687\) | − 1.66125i | − 0.0633807i | ||||||||
\(688\) | − 10.6123i | − 0.404591i | ||||||||
\(689\) | 21.8994 | 0.834299 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.9827 | −0.417803 | −0.208901 | − | 0.977937i | \(-0.566989\pi\) | ||||
−0.208901 | + | 0.977937i | \(0.566989\pi\) | |||||||
\(692\) | 9.26267i | 0.352114i | ||||||||
\(693\) | − 19.1476i | − 0.727357i | ||||||||
\(694\) | −2.28913 | −0.0868941 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.86074 | 0.108436 | ||||||||
\(697\) | − 5.96466i | − 0.225928i | ||||||||
\(698\) | − 2.51885i | − 0.0953399i | ||||||||
\(699\) | 7.85899 | 0.297254 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.4086 | 0.846361 | 0.423180 | − | 0.906046i | \(-0.360914\pi\) | ||||
0.423180 | + | 0.906046i | \(0.360914\pi\) | |||||||
\(702\) | − 0.177991i | − 0.00671784i | ||||||||
\(703\) | 1.94140i | 0.0732213i | ||||||||
\(704\) | 34.2802 | 1.29198 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.31736 | −0.0495793 | ||||||||
\(707\) | 13.9276i | 0.523803i | ||||||||
\(708\) | − 13.3239i | − 0.500744i | ||||||||
\(709\) | 14.6297 | 0.549431 | 0.274716 | − | 0.961526i | \(-0.411416\pi\) | ||||
0.274716 | + | 0.961526i | \(0.411416\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.35531 | −0.238343 | ||||||||
\(712\) | − 3.50929i | − 0.131516i | ||||||||
\(713\) | 8.66633i | 0.324557i | ||||||||
\(714\) | −0.390509 | −0.0146144 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.3486 | 0.536234 | ||||||||
\(717\) | 0.567301i | 0.0211862i | ||||||||
\(718\) | − 1.31321i | − 0.0490085i | ||||||||
\(719\) | 28.4977 | 1.06278 | 0.531392 | − | 0.847126i | \(-0.321669\pi\) | ||||
0.531392 | + | 0.847126i | \(0.321669\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.2989 | 1.38908 | ||||||||
\(722\) | 1.54264i | 0.0574112i | ||||||||
\(723\) | − 19.0081i | − 0.706920i | ||||||||
\(724\) | −7.57778 | −0.281626 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.743738 | 0.0276027 | ||||||||
\(727\) | 44.0064i | 1.63211i | 0.577976 | + | 0.816054i | \(0.303843\pi\) | ||||
−0.577976 | + | 0.816054i | \(0.696157\pi\) | |||||||
\(728\) | 3.09840i | 0.114835i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.67754 | 0.0990324 | ||||||||
\(732\) | − 18.8351i | − 0.696166i | ||||||||
\(733\) | 27.3227i | 1.00919i | 0.863357 | + | 0.504593i | \(0.168357\pi\) | ||||
−0.863357 | + | 0.504593i | \(0.831643\pi\) | |||||||
\(734\) | −1.58926 | −0.0586607 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.52628 | −0.0931198 | ||||||||
\(737\) | 56.7391i | 2.09001i | ||||||||
\(738\) | − 0.537343i | − 0.0197799i | ||||||||
\(739\) | −16.4678 | −0.605776 | −0.302888 | − | 0.953026i | \(-0.597951\pi\) | ||||
−0.302888 | + | 0.953026i | \(0.597951\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.67713 | 0.0983468 | ||||||||
\(742\) | − 4.32843i | − 0.158901i | ||||||||
\(743\) | 35.6012i | 1.30608i | 0.757322 | + | 0.653041i | \(0.226507\pi\) | ||||
−0.757322 | + | 0.653041i | \(0.773493\pi\) | |||||||
\(744\) | −1.31862 | −0.0483430 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.09843 | −0.0402164 | ||||||||
\(747\) | 0.737011i | 0.0269658i | ||||||||
\(748\) | 8.72041i | 0.318850i | ||||||||
\(749\) | −9.68668 | −0.353944 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.0748 | 1.68129 | 0.840647 | − | 0.541583i | \(-0.182175\pi\) | ||||
0.840647 | + | 0.541583i | \(0.182175\pi\) | |||||||
\(752\) | 43.2283i | 1.57638i | ||||||||
\(753\) | 3.02533i | 0.110249i | ||||||||
\(754\) | 1.42011 | 0.0517174 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.68622 | 0.315915 | ||||||||
\(757\) | 36.6482i | 1.33200i | 0.745951 | + | 0.666000i | \(0.231995\pi\) | ||||
−0.745951 | + | 0.666000i | \(0.768005\pi\) | |||||||
\(758\) | 2.52348i | 0.0916571i | ||||||||
\(759\) | 10.3473 | 0.375583 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.2078 | −0.986282 | −0.493141 | − | 0.869949i | \(-0.664151\pi\) | ||||
−0.493141 | + | 0.869949i | \(0.664151\pi\) | |||||||
\(762\) | − 1.12786i | − 0.0408580i | ||||||||
\(763\) | − 47.9779i | − 1.73692i | ||||||||
\(764\) | 42.9344 | 1.55331 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.09279 | −0.111747 | ||||||||
\(767\) | − 13.2552i | − 0.478617i | ||||||||
\(768\) | 15.3585i | 0.554202i | ||||||||
\(769\) | −26.5327 | −0.956794 | −0.478397 | − | 0.878144i | \(-0.658782\pi\) | ||||
−0.478397 | + | 0.878144i | \(0.658782\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.8613 | 0.715286 | ||||||||
\(772\) | − 6.27516i | − 0.225848i | ||||||||
\(773\) | 28.7677i | 1.03470i | 0.855773 | + | 0.517351i | \(0.173082\pi\) | ||||
−0.855773 | + | 0.517351i | \(0.826918\pi\) | |||||||
\(774\) | 0.241213 | 0.00867024 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.0120861 | 0.000433867 0 | ||||||||
\(777\) | 6.26658i | 0.224812i | ||||||||
\(778\) | 1.21458i | 0.0435450i | ||||||||
\(779\) | 8.08206 | 0.289570 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.1530 | 1.15052 | ||||||||
\(782\) | − 0.211030i | − 0.00754641i | ||||||||
\(783\) | − 7.97856i | − 0.285130i | ||||||||
\(784\) | −47.4820 | −1.69579 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.47949 | 0.0527716 | ||||||||
\(787\) | 24.8663i | 0.886387i | 0.896426 | + | 0.443193i | \(0.146155\pi\) | ||||
−0.896426 | + | 0.443193i | \(0.853845\pi\) | |||||||
\(788\) | 51.9571i | 1.85089i | ||||||||
\(789\) | 22.8299 | 0.812766 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.45771 | 0.265166 | ||||||||
\(792\) | 1.57439i | 0.0559434i | ||||||||
\(793\) | − 18.7379i | − 0.665404i | ||||||||
\(794\) | −3.23120 | −0.114671 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 48.3366 | 1.71325 | ||||||||
\(797\) | − 31.4206i | − 1.11298i | −0.830856 | − | 0.556488i | \(-0.812149\pi\) | ||||
0.830856 | − | 0.556488i | \(-0.187851\pi\) | |||||||
\(798\) | − 0.529137i | − 0.0187312i | ||||||||
\(799\) | −10.9067 | −0.385851 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.78736 | −0.345819 | ||||||||
\(802\) | − 0.391592i | − 0.0138276i | ||||||||
\(803\) | 1.86529i | 0.0658246i | ||||||||
\(804\) | −25.7395 | −0.907761 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.654583 | −0.0230567 | ||||||||
\(807\) | − 14.8324i | − 0.522125i | ||||||||
\(808\) | − 1.14518i | − 0.0402874i | ||||||||
\(809\) | −50.5027 | −1.77558 | −0.887790 | − | 0.460249i | \(-0.847760\pi\) | ||||
−0.887790 | + | 0.460249i | \(0.847760\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.1612 | 0.883528 | 0.441764 | − | 0.897131i | \(-0.354353\pi\) | ||||
0.441764 | + | 0.897131i | \(0.354353\pi\) | |||||||
\(812\) | 69.3035i | 2.43208i | ||||||||
\(813\) | − 6.43720i | − 0.225762i | ||||||||
\(814\) | −0.566763 | −0.0198650 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.93989 | −0.137924 | ||||||||
\(817\) | 3.62804i | 0.126929i | ||||||||
\(818\) | − 1.62697i | − 0.0568856i | ||||||||
\(819\) | 8.64141 | 0.301955 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.6307 | −0.720017 | −0.360009 | − | 0.932949i | \(-0.617226\pi\) | ||||
−0.360009 | + | 0.932949i | \(0.617226\pi\) | |||||||
\(822\) | − 0.868313i | − 0.0302859i | ||||||||
\(823\) | 35.8618i | 1.25006i | 0.780599 | + | 0.625032i | \(0.214914\pi\) | ||||
−0.780599 | + | 0.625032i | \(0.785086\pi\) | |||||||
\(824\) | −3.06686 | −0.106839 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.61990 | −0.0911580 | ||||||||
\(827\) | 4.73642i | 0.164701i | 0.996603 | + | 0.0823507i | \(0.0262428\pi\) | ||||
−0.996603 | + | 0.0823507i | \(0.973757\pi\) | |||||||
\(828\) | 4.69401i | 0.163128i | ||||||||
\(829\) | 28.4768 | 0.989039 | 0.494520 | − | 0.869166i | \(-0.335344\pi\) | ||||
0.494520 | + | 0.869166i | \(0.335344\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.70976 | −0.232759 | ||||||||
\(832\) | 15.4708i | 0.536355i | ||||||||
\(833\) | − 11.9799i | − 0.415080i | ||||||||
\(834\) | −1.21550 | −0.0420892 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −11.8161 | −0.408668 | ||||||||
\(837\) | 3.67761i | 0.127117i | ||||||||
\(838\) | 0.0474127i | 0.00163784i | ||||||||
\(839\) | 0.765715 | 0.0264354 | 0.0132177 | − | 0.999913i | \(-0.495793\pi\) | ||||
0.0132177 | + | 0.999913i | \(0.495793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.6574 | 1.19508 | ||||||||
\(842\) | − 1.67591i | − 0.0577555i | ||||||||
\(843\) | − 20.4867i | − 0.705600i | ||||||||
\(844\) | 32.6245 | 1.12298 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.982560 | −0.0337811 | ||||||||
\(847\) | 36.1082i | 1.24069i | ||||||||
\(848\) | − 43.6700i | − 1.49963i | ||||||||
\(849\) | −11.4177 | −0.391856 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.38644 | −0.116086 | ||||||||
\(852\) | 14.5861i | 0.499710i | ||||||||
\(853\) | − 34.7289i | − 1.18910i | −0.804060 | − | 0.594548i | \(-0.797331\pi\) | ||||
0.804060 | − | 0.594548i | \(-0.202669\pi\) | |||||||
\(854\) | −3.70357 | −0.126734 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.796475 | 0.0272230 | ||||||||
\(857\) | 54.2561i | 1.85335i | 0.375860 | + | 0.926676i | \(0.377347\pi\) | ||||
−0.375860 | + | 0.926676i | \(0.622653\pi\) | |||||||
\(858\) | 0.781549i | 0.0266816i | ||||||||
\(859\) | −15.9095 | −0.542824 | −0.271412 | − | 0.962463i | \(-0.587491\pi\) | ||||
−0.271412 | + | 0.962463i | \(0.587491\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.0878 | 0.889070 | ||||||||
\(862\) | − 1.88543i | − 0.0642180i | ||||||||
\(863\) | − 22.4714i | − 0.764935i | −0.923969 | − | 0.382467i | \(-0.875074\pi\) | ||||
0.923969 | − | 0.382467i | \(-0.124926\pi\) | |||||||
\(864\) | −1.07204 | −0.0364716 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.22729 | 0.0417049 | ||||||||
\(867\) | 16.0059i | 0.543590i | ||||||||
\(868\) | − 31.9446i | − 1.08427i | ||||||||
\(869\) | 27.9058 | 0.946639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.6067 | −0.867649 | ||||||||
\(872\) | 3.94492i | 0.133592i | ||||||||
\(873\) | − 0.0337081i | − 0.00114085i | ||||||||
\(874\) | 0.285944 | 0.00967219 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.846181 | −0.0285898 | ||||||||
\(877\) | 27.0756i | 0.914278i | 0.889395 | + | 0.457139i | \(0.151126\pi\) | ||||
−0.889395 | + | 0.457139i | \(0.848874\pi\) | |||||||
\(878\) | − 0.389222i | − 0.0131356i | ||||||||
\(879\) | 28.5505 | 0.962984 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.81317 | −0.263232 | −0.131616 | − | 0.991301i | \(-0.542017\pi\) | ||||
−0.131616 | + | 0.991301i | \(0.542017\pi\) | |||||||
\(882\) | − 1.07925i | − 0.0363401i | ||||||||
\(883\) | 58.3010i | 1.96199i | 0.194042 | + | 0.980993i | \(0.437840\pi\) | ||||
−0.194042 | + | 0.980993i | \(0.562160\pi\) | |||||||
\(884\) | −3.93557 | −0.132367 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.144377 | 0.00485045 | ||||||||
\(887\) | − 8.64610i | − 0.290307i | −0.989409 | − | 0.145154i | \(-0.953632\pi\) | ||||
0.989409 | − | 0.145154i | \(-0.0463677\pi\) | |||||||
\(888\) | − 0.515261i | − 0.0172910i | ||||||||
\(889\) | 54.7571 | 1.83650 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.39094 | 0.147102 | ||||||||
\(892\) | 11.3200i | 0.379023i | ||||||||
\(893\) | − 14.7785i | − 0.494543i | ||||||||
\(894\) | −1.22911 | −0.0411077 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 12.4075 | 0.414507 | ||||||||
\(897\) | 4.66979i | 0.155920i | ||||||||
\(898\) | − 1.24212i | − 0.0414500i | ||||||||
\(899\) | −29.3420 | −0.978612 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.0181 | 0.367067 | ||||||||
\(902\) | 2.35944i | 0.0785608i | ||||||||
\(903\) | 11.7108i | 0.389712i | ||||||||
\(904\) | −0.613201 | −0.0203948 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.01679 | −0.0337805 | ||||||||
\(907\) | − 40.4367i | − 1.34268i | −0.741151 | − | 0.671339i | \(-0.765720\pi\) | ||||
0.741151 | − | 0.671339i | \(-0.234280\pi\) | |||||||
\(908\) | 7.25809i | 0.240868i | ||||||||
\(909\) | −3.19390 | −0.105935 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.5643 | −1.67527 | −0.837635 | − | 0.546230i | \(-0.816063\pi\) | ||||
−0.837635 | + | 0.546230i | \(0.816063\pi\) | |||||||
\(912\) | − 5.33852i | − 0.176776i | ||||||||
\(913\) | − 3.23617i | − 0.107102i | ||||||||
\(914\) | 1.80847 | 0.0598187 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.30910 | −0.109336 | ||||||||
\(917\) | 71.8286i | 2.37199i | ||||||||
\(918\) | − 0.0895519i | − 0.00295565i | ||||||||
\(919\) | 43.3566 | 1.43020 | 0.715101 | − | 0.699021i | \(-0.246381\pi\) | ||||
0.715101 | + | 0.699021i | \(0.246381\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.5417 | 0.676871 | ||||||||
\(922\) | − 2.83169i | − 0.0932566i | ||||||||
\(923\) | 14.5108i | 0.477629i | ||||||||
\(924\) | −38.1407 | −1.25474 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.00405712 | 0.000133325 0 | ||||||||
\(927\) | 8.55342i | 0.280931i | ||||||||
\(928\) | − 8.55335i | − 0.280777i | ||||||||
\(929\) | 34.1746 | 1.12123 | 0.560617 | − | 0.828075i | \(-0.310564\pi\) | ||||
0.560617 | + | 0.828075i | \(0.310564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.2327 | 0.532006 | ||||||||
\(932\) | − 15.6546i | − 0.512783i | ||||||||
\(933\) | 17.5496i | 0.574548i | ||||||||
\(934\) | −2.94921 | −0.0965010 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.710529 | −0.0232244 | ||||||||
\(937\) | 27.8996i | 0.911441i | 0.890123 | + | 0.455720i | \(0.150618\pi\) | ||||
−0.890123 | + | 0.455720i | \(0.849382\pi\) | |||||||
\(938\) | 5.06118i | 0.165253i | ||||||||
\(939\) | −2.98564 | −0.0974325 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −54.3261 | −1.77098 | −0.885490 | − | 0.464659i | \(-0.846177\pi\) | ||||
−0.885490 | + | 0.464659i | \(0.846177\pi\) | |||||||
\(942\) | 0.768918i | 0.0250527i | ||||||||
\(943\) | 14.0978i | 0.459086i | ||||||||
\(944\) | −26.4325 | −0.860303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.05915 | −0.0344361 | ||||||||
\(947\) | 4.23171i | 0.137512i | 0.997633 | + | 0.0687561i | \(0.0219030\pi\) | ||||
−0.997633 | + | 0.0687561i | \(0.978097\pi\) | |||||||
\(948\) | 12.6593i | 0.411156i | ||||||||
\(949\) | −0.841815 | −0.0273265 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.1708 | 0.524375 | ||||||||
\(952\) | 1.55889i | 0.0505238i | ||||||||
\(953\) | 47.9307i | 1.55263i | 0.630346 | + | 0.776314i | \(0.282913\pi\) | ||||
−0.630346 | + | 0.776314i | \(0.717087\pi\) | |||||||
\(954\) | 0.992598 | 0.0321366 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.13002 | 0.0365476 | ||||||||
\(957\) | 35.0334i | 1.13247i | ||||||||
\(958\) | 0.672367i | 0.0217232i | ||||||||
\(959\) | 42.1563 | 1.36130 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.4752 | −0.563715 | ||||||||
\(962\) | − 0.255783i | − 0.00824679i | ||||||||
\(963\) | − 2.22136i | − 0.0715823i | ||||||||
\(964\) | −37.8629 | −1.21948 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.922988 | 0.0296966 | ||||||||
\(967\) | − 20.8827i | − 0.671544i | −0.941943 | − | 0.335772i | \(-0.891003\pi\) | ||||
0.941943 | − | 0.335772i | \(-0.108997\pi\) | |||||||
\(968\) | − 2.96895i | − 0.0954257i | ||||||||
\(969\) | 1.34693 | 0.0432697 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.0740 | 0.515838 | 0.257919 | − | 0.966167i | \(-0.416963\pi\) | ||||
0.257919 | + | 0.966167i | \(0.416963\pi\) | |||||||
\(972\) | 1.99193i | 0.0638913i | ||||||||
\(973\) | − 59.0119i | − 1.89184i | ||||||||
\(974\) | −2.28406 | −0.0731860 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37.3657 | −1.19605 | ||||||||
\(977\) | − 35.5665i | − 1.13787i | −0.822381 | − | 0.568937i | \(-0.807355\pi\) | ||||
0.822381 | − | 0.568937i | \(-0.192645\pi\) | |||||||
\(978\) | − 0.411830i | − 0.0131689i | ||||||||
\(979\) | 42.9757 | 1.37351 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.0023 | 0.351278 | ||||||||
\(982\) | 0.994014i | 0.0317202i | ||||||||
\(983\) | − 18.4711i | − 0.589138i | −0.955630 | − | 0.294569i | \(-0.904824\pi\) | ||||
0.955630 | − | 0.294569i | \(-0.0951761\pi\) | |||||||
\(984\) | −2.14504 | −0.0683812 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.714495 | 0.0227542 | ||||||||
\(987\) | − 47.7030i | − 1.51840i | ||||||||
\(988\) | − 5.33266i | − 0.169655i | ||||||||
\(989\) | −6.32849 | −0.201234 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.5907 | −1.32117 | −0.660586 | − | 0.750750i | \(-0.729692\pi\) | ||||
−0.660586 | + | 0.750750i | \(0.729692\pi\) | |||||||
\(992\) | 3.94256i | 0.125176i | ||||||||
\(993\) | − 13.0705i | − 0.414779i | ||||||||
\(994\) | 2.86807 | 0.0909698 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.46808 | 0.0465178 | ||||||||
\(997\) | 31.8374i | 1.00830i | 0.863616 | + | 0.504151i | \(0.168194\pi\) | ||||
−0.863616 | + | 0.504151i | \(0.831806\pi\) | |||||||
\(998\) | 0.420496i | 0.0133106i | ||||||||
\(999\) | −1.43706 | −0.0454665 |
(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 | 1875.2.b.h.1249.8 | 16 | ||
5.2 | odd | 4 | 1875.2.a.m.1.5 | 8 | |||
5.3 | odd | 4 | 1875.2.a.p.1.4 | 8 | |||
5.4 | even | 2 | inner | 1875.2.b.h.1249.9 | 16 | ||
15.2 | even | 4 | 5625.2.a.bd.1.4 | 8 | |||
15.8 | even | 4 | 5625.2.a.t.1.5 | 8 | |||
25.3 | odd | 20 | 375.2.g.d.76.3 | 16 | |||
25.4 | even | 10 | 75.2.i.a.34.3 | ✓ | 16 | ||
25.6 | even | 5 | 75.2.i.a.64.3 | yes | 16 | ||
25.8 | odd | 20 | 375.2.g.d.301.3 | 16 | |||
25.17 | odd | 20 | 375.2.g.e.301.2 | 16 | |||
25.19 | even | 10 | 375.2.i.c.199.2 | 16 | |||
25.21 | even | 5 | 375.2.i.c.49.2 | 16 | |||
25.22 | odd | 20 | 375.2.g.e.76.2 | 16 | |||
75.29 | odd | 10 | 225.2.m.b.109.2 | 16 | |||
75.56 | odd | 10 | 225.2.m.b.64.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.34.3 | ✓ | 16 | 25.4 | even | 10 | ||
75.2.i.a.64.3 | yes | 16 | 25.6 | even | 5 | ||
225.2.m.b.64.2 | 16 | 75.56 | odd | 10 | |||
225.2.m.b.109.2 | 16 | 75.29 | odd | 10 | |||
375.2.g.d.76.3 | 16 | 25.3 | odd | 20 | |||
375.2.g.d.301.3 | 16 | 25.8 | odd | 20 | |||
375.2.g.e.76.2 | 16 | 25.22 | odd | 20 | |||
375.2.g.e.301.2 | 16 | 25.17 | odd | 20 | |||
375.2.i.c.49.2 | 16 | 25.21 | even | 5 | |||
375.2.i.c.199.2 | 16 | 25.19 | even | 10 | |||
1875.2.a.m.1.5 | 8 | 5.2 | odd | 4 | |||
1875.2.a.p.1.4 | 8 | 5.3 | odd | 4 | |||
1875.2.b.h.1249.8 | 16 | 1.1 | even | 1 | trivial | ||
1875.2.b.h.1249.9 | 16 | 5.4 | even | 2 | inner | ||
5625.2.a.t.1.5 | 8 | 15.8 | even | 4 | |||
5625.2.a.bd.1.4 | 8 | 15.2 | even | 4 |