Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7500,2,Mod(1249,7500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7500, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7500.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7500 = 2^{2} \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7500.d (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: | \(59.8878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.10 | ||
Character | \(\chi\) | \(=\) | 7500.1249 |
Dual form | 7500.2.d.g.1249.15 |
$q$-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 \(\left(\mathbb{Z}/7500\mathbb{Z}\right)^\times\).
\(n\) | \(2501\) | \(3751\) | \(6877\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.80992i | 1.44001i | 0.693968 | + | 0.720006i | \(0.255861\pi\) | ||||
−0.693968 | + | 0.720006i | \(0.744139\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.190733 | 0.0575081 | 0.0287541 | − | 0.999587i | \(-0.490846\pi\) | ||||
0.0287541 | + | 0.999587i | \(0.490846\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.67943i | − 0.465791i | −0.972502 | − | 0.232896i | \(-0.925180\pi\) | ||||
0.972502 | − | 0.232896i | \(-0.0748200\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 4.60324i | − 1.11645i | −0.829690 | − | 0.558225i | \(-0.811483\pi\) | ||||
0.829690 | − | 0.558225i | \(-0.188517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.64126 | 0.605946 | 0.302973 | − | 0.952999i | \(-0.402021\pi\) | ||||
0.302973 | + | 0.952999i | \(0.402021\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.80992 | 0.831392 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.35567i | 1.32525i | 0.748951 | + | 0.662625i | \(0.230558\pi\) | ||||
−0.748951 | + | 0.662625i | \(0.769442\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.52008 | −0.467966 | −0.233983 | − | 0.972241i | \(-0.575176\pi\) | ||||
−0.233983 | + | 0.972241i | \(0.575176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.74937 | 0.673407 | 0.336704 | − | 0.941611i | \(-0.390688\pi\) | ||||
0.336704 | + | 0.941611i | \(0.390688\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 0.190733i | − 0.0332023i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.8626i | 1.95019i | 0.221778 | + | 0.975097i | \(0.428814\pi\) | ||||
−0.221778 | + | 0.975097i | \(0.571186\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.67943 | −0.268925 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.18953 | −1.12282 | −0.561408 | − | 0.827539i | \(-0.689740\pi\) | ||||
−0.561408 | + | 0.827539i | \(0.689740\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 9.22619i | − 1.40698i | −0.710705 | − | 0.703491i | \(-0.751624\pi\) | ||||
0.710705 | − | 0.703491i | \(-0.248376\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.54848i | 0.663464i | 0.943374 | + | 0.331732i | \(0.107633\pi\) | ||||
−0.943374 | + | 0.331732i | \(0.892367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.51545 | −1.07364 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.60324 | −0.644583 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.43006i | 1.29532i | 0.761930 | + | 0.647659i | \(0.224252\pi\) | ||||
−0.761930 | + | 0.647659i | \(0.775748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 2.64126i | − 0.349843i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.14057 | −0.929623 | −0.464812 | − | 0.885410i | \(-0.653878\pi\) | ||||
−0.464812 | + | 0.885410i | \(0.653878\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.53012 | 1.22021 | 0.610103 | − | 0.792322i | \(-0.291128\pi\) | ||||
0.610103 | + | 0.792322i | \(0.291128\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 3.80992i | − 0.480004i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.05168i | − 0.739330i | −0.929165 | − | 0.369665i | \(-0.879472\pi\) | ||||
0.929165 | − | 0.369665i | \(-0.120528\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.35567 | 0.765133 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.2983 | 1.57822 | 0.789110 | − | 0.614252i | \(-0.210542\pi\) | ||||
0.789110 | + | 0.614252i | \(0.210542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 5.21152i | − 0.609963i | −0.952358 | − | 0.304981i | \(-0.901350\pi\) | ||||
0.952358 | − | 0.304981i | \(-0.0986502\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.726676i | 0.0828124i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.11168 | 0.350092 | 0.175046 | − | 0.984560i | \(-0.443993\pi\) | ||||
0.175046 | + | 0.984560i | \(0.443993\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.67837i | 0.513518i | 0.966475 | + | 0.256759i | \(0.0826546\pi\) | ||||
−0.966475 | + | 0.256759i | \(0.917345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.52008i | 0.270181i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.9423 | −1.47788 | −0.738939 | − | 0.673772i | \(-0.764673\pi\) | ||||
−0.738939 | + | 0.673772i | \(0.764673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.39850 | 0.670745 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 3.74937i | − 0.388792i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 6.69507i | − 0.679782i | −0.940465 | − | 0.339891i | \(-0.889610\pi\) | ||||
0.940465 | − | 0.339891i | \(-0.110390\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.190733 | −0.0191694 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.5147 | 1.04625 | 0.523127 | − | 0.852255i | \(-0.324765\pi\) | ||||
0.523127 | + | 0.852255i | \(0.324765\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 12.9648i | − 1.27746i | −0.769429 | − | 0.638732i | \(-0.779459\pi\) | ||||
0.769429 | − | 0.638732i | \(-0.220541\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.64606i | 0.932520i | 0.884648 | + | 0.466260i | \(0.154399\pi\) | ||||
−0.884648 | + | 0.466260i | \(0.845601\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.4454 | −1.95831 | −0.979157 | − | 0.203103i | \(-0.934898\pi\) | ||||
−0.979157 | + | 0.203103i | \(0.934898\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.8626 | 1.12595 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 4.04417i | − 0.380444i | −0.981741 | − | 0.190222i | \(-0.939079\pi\) | ||||
0.981741 | − | 0.190222i | \(-0.0609207\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.67943i | 0.155264i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.5380 | 1.60770 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9636 | −0.996693 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.18953i | 0.648258i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.7537i | 1.48665i | 0.668928 | + | 0.743327i | \(0.266753\pi\) | ||||
−0.668928 | + | 0.743327i | \(0.733247\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.22619 | −0.812321 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.30750 | −0.288978 | −0.144489 | − | 0.989506i | \(-0.546154\pi\) | ||||
−0.144489 | + | 0.989506i | \(0.546154\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.0630i | 0.872570i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.09916i | 0.179343i | 0.995971 | + | 0.0896717i | \(0.0285818\pi\) | ||||
−0.995971 | + | 0.0896717i | \(0.971418\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.2849 | 1.12681 | 0.563404 | − | 0.826181i | \(-0.309491\pi\) | ||||
0.563404 | + | 0.826181i | \(0.309491\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.54848 | 0.383051 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 0.320323i | − 0.0267868i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.51545i | 0.619864i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.79913 | 0.229313 | 0.114657 | − | 0.993405i | \(-0.463423\pi\) | ||||
0.114657 | + | 0.993405i | \(0.463423\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.71330 | −0.546320 | −0.273160 | − | 0.961969i | \(-0.588069\pi\) | ||||
−0.273160 | + | 0.961969i | \(0.588069\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.60324i | 0.372150i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.9495i | 1.11329i | 0.830750 | + | 0.556646i | \(0.187912\pi\) | ||||
−0.830750 | + | 0.556646i | \(0.812088\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.43006 | 0.747853 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.2146 | −1.90838 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.87503i | 0.695146i | 0.937653 | + | 0.347573i | \(0.112994\pi\) | ||||
−0.937653 | + | 0.347573i | \(0.887006\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.5944i | 1.90318i | 0.307378 | + | 0.951588i | \(0.400548\pi\) | ||||
−0.307378 | + | 0.951588i | \(0.599452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.1795 | 0.783039 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.64126 | −0.201982 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.9350i | 1.28755i | 0.765216 | + | 0.643774i | \(0.222632\pi\) | ||||
−0.765216 | + | 0.643774i | \(0.777368\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.14057i | 0.536718i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.7497 | −1.10244 | −0.551222 | − | 0.834358i | \(-0.685838\pi\) | ||||
−0.551222 | + | 0.834358i | \(0.685838\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9888 | −0.816791 | −0.408396 | − | 0.912805i | \(-0.633912\pi\) | ||||
−0.408396 | + | 0.912805i | \(0.633912\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 9.53012i | − 0.704486i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 0.877989i | − 0.0642049i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.80992 | −0.277131 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.0355 | −1.73915 | −0.869575 | − | 0.493801i | \(-0.835607\pi\) | ||||
−0.869575 | + | 0.493801i | \(0.835607\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50843i | 0.540469i | 0.962795 | + | 0.270234i | \(0.0871012\pi\) | ||||
−0.962795 | + | 0.270234i | \(0.912899\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.5522i | 0.894306i | 0.894457 | + | 0.447153i | \(0.147562\pi\) | ||||
−0.894457 | + | 0.447153i | \(0.852438\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.7618 | 1.40088 | 0.700440 | − | 0.713711i | \(-0.252987\pi\) | ||||
0.700440 | + | 0.713711i | \(0.252987\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.05168 | −0.426852 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 9.60128i | − 0.673877i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 6.35567i | − 0.441750i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.503774 | 0.0348468 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.2479 | −0.774336 | −0.387168 | − | 0.922009i | \(-0.626547\pi\) | ||||
−0.387168 | + | 0.922009i | \(0.626547\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 13.2983i | − 0.911186i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.2848i | 0.969715i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.21152 | −0.352162 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.73084 | −0.520033 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 7.27196i | − 0.486967i | −0.969905 | − | 0.243483i | \(-0.921710\pi\) | ||||
0.969905 | − | 0.243483i | \(-0.0782901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 9.46929i | − 0.628499i | −0.949340 | − | 0.314249i | \(-0.898247\pi\) | ||||
0.949340 | − | 0.314249i | \(-0.101753\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.2301 | −1.40292 | −0.701461 | − | 0.712708i | \(-0.747469\pi\) | ||||
−0.701461 | + | 0.712708i | \(0.747469\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.726676 | 0.0478118 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.08932i | 0.464437i | 0.972664 | + | 0.232218i | \(0.0745984\pi\) | ||||
−0.972664 | + | 0.232218i | \(0.925402\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 3.11168i | − 0.202126i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.0117 | 1.29445 | 0.647224 | − | 0.762300i | \(-0.275930\pi\) | ||||
0.647224 | + | 0.762300i | \(0.275930\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.8240 | 1.34139 | 0.670696 | − | 0.741732i | \(-0.265995\pi\) | ||||
0.670696 | + | 0.741732i | \(0.265995\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.43582i | − 0.282244i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.67837 | 0.296480 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.7741 | −1.87932 | −0.939662 | − | 0.342104i | \(-0.888861\pi\) | ||||
−0.939662 | + | 0.342104i | \(0.888861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.21224i | 0.0762126i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.2853i | 1.32774i | 0.747849 | + | 0.663869i | \(0.231087\pi\) | ||||
−0.747849 | + | 0.663869i | \(0.768913\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −45.1954 | −2.80830 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.52008 | 0.155989 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.8653i | 1.34827i | 0.738608 | + | 0.674135i | \(0.235483\pi\) | ||||
−0.738608 | + | 0.674135i | \(0.764517\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.9423i | 0.853253i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.56132 | 0.278109 | 0.139054 | − | 0.990285i | \(-0.455594\pi\) | ||||
0.139054 | + | 0.990285i | \(0.455594\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.9193 | −0.784791 | −0.392395 | − | 0.919797i | \(-0.628354\pi\) | ||||
−0.392395 | + | 0.919797i | \(0.628354\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 6.39850i | − 0.387255i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 8.83521i | − 0.530856i | −0.964131 | − | 0.265428i | \(-0.914487\pi\) | ||||
0.964131 | − | 0.265428i | \(-0.0855133\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.74937 | −0.224469 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.0305495 | 0.00182243 | 0.000911215 | − | 1.00000i | \(-0.499710\pi\) | ||||
0.000911215 | 1.00000i | \(0.499710\pi\) | ||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4.80719i | − 0.285758i | −0.989740 | − | 0.142879i | \(-0.954364\pi\) | ||||
0.989740 | − | 0.142879i | \(-0.0456359\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 27.3915i | − 1.61687i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.18984 | −0.246461 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.69507 | −0.392472 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.9705i | 0.874587i | 0.899319 | + | 0.437294i | \(0.144063\pi\) | ||||
−0.899319 | + | 0.437294i | \(0.855937\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.190733i | 0.0110674i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.6739 | 0.617290 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 35.1510 | 2.02607 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 10.5147i | − 0.604055i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.47622i | 0.255472i | 0.991808 | + | 0.127736i | \(0.0407710\pi\) | ||||
−0.991808 | + | 0.127736i | \(0.959229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.9648 | −0.737544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.296114 | 0.0167911 | 0.00839554 | − | 0.999965i | \(-0.497328\pi\) | ||||
0.00839554 | + | 0.999965i | \(0.497328\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.1569i | 1.19586i | 0.801548 | + | 0.597930i | \(0.204010\pi\) | ||||
−0.801548 | + | 0.597930i | \(0.795990\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.9166i | 1.45562i | 0.685777 | + | 0.727812i | \(0.259463\pi\) | ||||
−0.685777 | + | 0.727812i | \(0.740537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.480661 | −0.0269119 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.64606 | 0.538391 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 12.1583i | − 0.676509i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.4454i | 1.13063i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.3293 | −0.955397 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.07039 | −0.168764 | −0.0843819 | − | 0.996433i | \(-0.526892\pi\) | ||||
−0.0843819 | + | 0.996433i | \(0.526892\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 11.8626i | − 0.650065i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.2521i | 1.53899i | 0.638652 | + | 0.769495i | \(0.279492\pi\) | ||||
−0.638652 | + | 0.769495i | \(0.720508\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.04417 | −0.219649 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.715129 | 0.0387264 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.96383i | − 0.106037i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.6011i | 1.64275i | 0.570387 | + | 0.821376i | \(0.306793\pi\) | ||||
−0.570387 | + | 0.821376i | \(0.693207\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.1178 | 0.862764 | 0.431382 | − | 0.902169i | \(-0.358026\pi\) | ||||
0.431382 | + | 0.902169i | \(0.358026\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.67943 | 0.0896416 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.431010i | 0.0229404i | 0.999934 | + | 0.0114702i | \(0.00365115\pi\) | ||||
−0.999934 | + | 0.0114702i | \(0.996349\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 17.5380i | − 0.928207i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.4738 | −0.975008 | −0.487504 | − | 0.873121i | \(-0.662093\pi\) | ||||
−0.487504 | + | 0.873121i | \(0.662093\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.0238 | −0.632829 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.9636i | 0.575441i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2757i | 0.536386i | 0.963365 | + | 0.268193i | \(0.0864265\pi\) | ||||
−0.963365 | + | 0.268193i | \(0.913573\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.18953 | 0.374272 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.9277 | −1.86528 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 14.6433i | − 0.758201i | −0.925356 | − | 0.379100i | \(-0.876233\pi\) | ||||
0.925356 | − | 0.379100i | \(-0.123767\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.23230i | 0.217975i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.7051 | 0.549884 | 0.274942 | − | 0.961461i | \(-0.411341\pi\) | ||||
0.274942 | + | 0.961461i | \(0.411341\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.7537 | 0.858320 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 26.3174i | − 1.34476i | −0.740208 | − | 0.672378i | \(-0.765273\pi\) | ||||
0.740208 | − | 0.672378i | \(-0.234727\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.22619i | 0.468994i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.291780 | −0.0147938 | −0.00739692 | − | 0.999973i | \(-0.502355\pi\) | ||||
−0.00739692 | + | 0.999973i | \(0.502355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.2567 | 1.47958 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.30750i | 0.166841i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.01611i | 0.101185i | 0.998719 | + | 0.0505927i | \(0.0161110\pi\) | ||||
−0.998719 | + | 0.0505927i | \(0.983889\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.0630 | 0.503778 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.88760 | 0.493763 | 0.246882 | − | 0.969046i | \(-0.420594\pi\) | ||||
0.246882 | + | 0.969046i | \(0.420594\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 6.29683i | − 0.313667i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.26258i | 0.112152i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.6809 | 1.86320 | 0.931601 | − | 0.363483i | \(-0.118413\pi\) | ||||
0.931601 | + | 0.363483i | \(0.118413\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.09916 | 0.103544 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 27.2050i | − 1.33867i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 13.2849i | − 0.650563i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.6537 | 0.764734 | 0.382367 | − | 0.924011i | \(-0.375109\pi\) | ||||
0.382367 | + | 0.924011i | \(0.375109\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.5277 | 0.708036 | 0.354018 | − | 0.935239i | \(-0.384815\pi\) | ||||
0.354018 | + | 0.935239i | \(0.384815\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 4.54848i | − 0.221155i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.3089i | 1.75711i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.320323 | −0.0154653 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.6264 | −0.608192 | −0.304096 | − | 0.952641i | \(-0.598354\pi\) | ||||
−0.304096 | + | 0.952641i | \(0.598354\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.49014i | 0.167725i | 0.996477 | + | 0.0838626i | \(0.0267257\pi\) | ||||
−0.996477 | + | 0.0838626i | \(0.973274\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.7870i | 0.803030i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.5630 | 0.933689 | 0.466844 | − | 0.884340i | \(-0.345391\pi\) | ||||
0.466844 | + | 0.884340i | \(0.345391\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.51545 | 0.357879 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.77485i | 0.131837i | 0.997825 | + | 0.0659185i | \(0.0209977\pi\) | ||||
−0.997825 | + | 0.0659185i | \(0.979002\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 2.79913i | − 0.132394i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.4261 | 1.81344 | 0.906721 | − | 0.421732i | \(-0.138578\pi\) | ||||
0.906721 | + | 0.421732i | \(0.138578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.37128 | −0.0645710 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.71330i | 0.315418i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 36.0296i | − 1.68539i | −0.538389 | − | 0.842696i | \(-0.680967\pi\) | ||||
0.538389 | − | 0.842696i | \(-0.319033\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.60324 | 0.214861 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.857592 | 0.0399421 | 0.0199710 | − | 0.999801i | \(-0.493643\pi\) | ||||
0.0199710 | + | 0.999801i | \(0.493643\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 10.4068i | − 0.483643i | −0.970321 | − | 0.241822i | \(-0.922255\pi\) | ||||
0.970321 | − | 0.241822i | \(-0.0777449\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 20.5705i | − 0.951889i | −0.879475 | − | 0.475944i | \(-0.842106\pi\) | ||||
0.879475 | − | 0.475944i | \(-0.157894\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.0564 | 1.06464 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.9495 | 0.642759 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 1.75974i | − 0.0809128i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 9.43006i | − 0.431773i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.9380 | −1.45929 | −0.729643 | − | 0.683828i | \(-0.760314\pi\) | ||||
−0.729643 | + | 0.683828i | \(0.760314\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.9224 | 0.908383 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.2146i | 1.10180i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.6815i | 0.710599i | 0.934753 | + | 0.355299i | \(0.115621\pi\) | ||||
−0.934753 | + | 0.355299i | \(0.884379\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.87503 | 0.401343 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.4831 | 0.743870 | 0.371935 | − | 0.928259i | \(-0.378694\pi\) | ||||
0.371935 | + | 0.928259i | \(0.378694\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.6005i | 0.522461i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 50.6655i | 2.27266i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.4339 | −0.556618 | −0.278309 | − | 0.960492i | \(-0.589774\pi\) | ||||
−0.278309 | + | 0.960492i | \(0.589774\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.5944 | 1.09880 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 4.33327i | − 0.193211i | −0.995323 | − | 0.0966055i | \(-0.969201\pi\) | ||||
0.995323 | − | 0.0966055i | \(-0.0307985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 10.1795i | − 0.452088i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.0120 | −0.621072 | −0.310536 | − | 0.950562i | \(-0.600508\pi\) | ||||
−0.310536 | + | 0.950562i | \(0.600508\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.8555 | 0.878354 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.64126i | 0.116614i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.867545i | 0.0381546i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.9350 | 0.743366 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.92829 | 0.0844801 | 0.0422400 | − | 0.999107i | \(-0.486551\pi\) | ||||
0.0422400 | + | 0.999107i | \(0.486551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.95894i | 0.0856583i | 0.999082 | + | 0.0428291i | \(0.0136371\pi\) | ||||
−0.999082 | + | 0.0428291i | \(0.986363\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 17.2593i | − 0.751826i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.3946 | −0.756287 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.14057 | 0.309874 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0743i | 0.522998i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.7497i | 0.636497i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.43344 | −0.0617428 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.6132 | −1.48814 | −0.744069 | − | 0.668103i | \(-0.767107\pi\) | ||||
−0.744069 | + | 0.668103i | \(0.767107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.9888i | 0.471575i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.9494i | 0.681947i | 0.940073 | + | 0.340973i | \(0.110757\pi\) | ||||
−0.940073 | + | 0.340973i | \(0.889243\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.53012 | −0.406735 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.65617 | −0.283562 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.8552i | 0.504136i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.0343i | 1.82342i | 0.410831 | + | 0.911711i | \(0.365239\pi\) | ||||
−0.410831 | + | 0.911711i | \(0.634761\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.4948 | −0.655359 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.877989 | −0.0370687 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 18.8560i | − 0.794686i | −0.917670 | − | 0.397343i | \(-0.869932\pi\) | ||||
0.917670 | − | 0.397343i | \(-0.130068\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.80992i | 0.160001i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.3652 | 1.02144 | 0.510721 | − | 0.859747i | \(-0.329379\pi\) | ||||
0.510721 | + | 0.859747i | \(0.329379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.3391 | 0.641923 | 0.320962 | − | 0.947092i | \(-0.395994\pi\) | ||||
0.320962 | + | 0.947092i | \(0.395994\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.0355i | 1.00410i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.3401i | 0.596985i | 0.954412 | + | 0.298493i | \(0.0964838\pi\) | ||||
−0.954412 | + | 0.298493i | \(0.903516\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.50843 | 0.312040 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.8242 | −0.739472 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.79862i | 0.0744913i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 10.7026i | − 0.441744i | −0.975303 | − | 0.220872i | \(-0.929110\pi\) | ||||
0.975303 | − | 0.220872i | \(-0.0708903\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.90306 | 0.408048 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.5522 | 0.516328 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 23.5756i | − 0.968135i | −0.875031 | − | 0.484067i | \(-0.839159\pi\) | ||||
0.875031 | − | 0.484067i | \(-0.160841\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 19.7618i | − 0.808798i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.8055 | −0.564078 | −0.282039 | − | 0.959403i | \(-0.591011\pi\) | ||||
−0.282039 | + | 0.959403i | \(0.591011\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.61536 | 0.392219 | 0.196109 | − | 0.980582i | \(-0.437169\pi\) | ||||
0.196109 | + | 0.980582i | \(0.437169\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.05168i | 0.246443i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.7884i | 0.965539i | 0.875747 | + | 0.482770i | \(0.160369\pi\) | ||||
−0.875747 | + | 0.482770i | \(0.839631\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.60128 | −0.389063 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.63888 | 0.309036 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.0716i | 0.649127i | 0.945864 | + | 0.324563i | \(0.105217\pi\) | ||||
−0.945864 | + | 0.324563i | \(0.894783\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 9.34595i | − 0.376254i | −0.982145 | − | 0.188127i | \(-0.939758\pi\) | ||||
0.982145 | − | 0.188127i | \(-0.0602416\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.4768 | 0.742645 | 0.371323 | − | 0.928504i | \(-0.378904\pi\) | ||||
0.371323 | + | 0.928504i | \(0.378904\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.35567 | −0.255044 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 53.1189i | − 2.12816i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 0.503774i | − 0.0201188i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 54.6063 | 2.17729 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.5690 | 1.53541 | 0.767704 | − | 0.640804i | \(-0.221399\pi\) | ||||
0.767704 | + | 0.640804i | \(0.221399\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.2479i | 0.447063i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.6217i | 0.500090i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.2983 | −0.526073 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.8461 | −0.507389 | −0.253695 | − | 0.967284i | \(-0.581646\pi\) | ||||
−0.253695 | + | 0.967284i | \(0.581646\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.1030i | 0.792784i | 0.918081 | + | 0.396392i | \(0.129738\pi\) | ||||
−0.918081 | + | 0.396392i | \(0.870262\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 39.1895i | − 1.54070i | −0.637622 | − | 0.770350i | \(-0.720082\pi\) | ||||
0.637622 | − | 0.770350i | \(-0.279918\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.36194 | −0.0534609 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.2848 | 0.559865 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.9894i | 1.01704i | 0.861049 | + | 0.508522i | \(0.169808\pi\) | ||||
−0.861049 | + | 0.508522i | \(0.830192\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.21152i | 0.203321i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.42356 | 0.250226 | 0.125113 | − | 0.992142i | \(-0.460071\pi\) | ||||
0.125113 | + | 0.992142i | \(0.460071\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.5875 | 0.839657 | 0.419829 | − | 0.907603i | \(-0.362090\pi\) | ||||
0.419829 | + | 0.907603i | \(0.362090\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.73084i | 0.300241i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 16.0168i | − 0.620172i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.27196 | −0.281150 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.81771 | 0.0701718 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.94040i | 0.228986i | 0.993424 | + | 0.114493i | \(0.0365243\pi\) | ||||
−0.993424 | + | 0.114493i | \(0.963476\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 37.1784i | − 1.42888i | −0.699696 | − | 0.714441i | \(-0.746681\pi\) | ||||
0.699696 | − | 0.714441i | \(-0.253319\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.5077 | 0.978894 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.46929 | −0.362864 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 45.1024i | − 1.72580i | −0.505377 | − | 0.862899i | \(-0.668647\pi\) | ||||
0.505377 | − | 0.862899i | \(-0.331353\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.2301i | 0.809977i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.8372 | 0.603348 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5713 | −1.08691 | −0.543453 | − | 0.839440i | \(-0.682883\pi\) | ||||
−0.543453 | + | 0.839440i | \(0.682883\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 0.726676i | − 0.0276041i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.0952i | 1.25357i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.08932 | 0.268143 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.2636 | −1.67181 | −0.835907 | − | 0.548871i | \(-0.815058\pi\) | ||||
−0.835907 | + | 0.548871i | \(0.815058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.3321i | 1.18171i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 40.0602i | 1.50662i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0124 | −0.638913 | −0.319457 | − | 0.947601i | \(-0.603500\pi\) | ||||
−0.319457 | + | 0.947601i | \(0.603500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.11168 | −0.116697 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.8298i | 0.892433i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 20.0117i | − 0.747350i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.29496 | −0.309350 | −0.154675 | − | 0.987965i | \(-0.549433\pi\) | ||||
−0.154675 | + | 0.987965i | \(0.549433\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.3950 | 1.83956 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 20.8240i | − 0.774454i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.46319i | 0.276794i | 0.990377 | + | 0.138397i | \(0.0441950\pi\) | ||||
−0.990377 | + | 0.138397i | \(0.955805\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.4704 | −1.57082 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 12.0201i | − 0.443973i | −0.975050 | − | 0.221987i | \(-0.928746\pi\) | ||||
0.975050 | − | 0.221987i | \(-0.0712542\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.15425i | − 0.0425175i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.3335 | −0.931908 | −0.465954 | − | 0.884809i | \(-0.654289\pi\) | ||||
−0.465954 | + | 0.884809i | \(0.654289\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.43582 | −0.162954 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 21.0959i | − 0.773935i | −0.922093 | − | 0.386968i | \(-0.873523\pi\) | ||||
0.922093 | − | 0.386968i | \(-0.126477\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 4.67837i | − 0.171173i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36.7507 | −1.34284 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.3897 | −1.25490 | −0.627449 | − | 0.778658i | \(-0.715901\pi\) | ||||
−0.627449 | + | 0.778658i | \(0.715901\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.7741i | 1.08503i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 33.9762i | − 1.23488i | −0.786616 | − | 0.617442i | \(-0.788169\pi\) | ||||
0.786616 | − | 0.617442i | \(-0.211831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.21224 | 0.0440014 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.3872 | −0.485284 | −0.242642 | − | 0.970116i | \(-0.578014\pi\) | ||||
−0.242642 | + | 0.970116i | \(0.578014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 77.8953i | − 2.82000i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.9921i | 0.433010i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.94485 | 0.214377 | 0.107188 | − | 0.994239i | \(-0.465815\pi\) | ||||
0.107188 | + | 0.994239i | \(0.465815\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.2853 | 0.766570 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.0966i | 1.22637i | 0.789940 | + | 0.613184i | \(0.210112\pi\) | ||||
−0.789940 | + | 0.613184i | \(0.789888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 45.1954i | 1.62138i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.9894 | −0.680366 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.53643 | 0.0907604 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 2.52008i | − 0.0900602i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.97301i | 0.0703301i | 0.999382 | + | 0.0351651i | \(0.0111957\pi\) | ||||
−0.999382 | + | 0.0351651i | \(0.988804\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.8653 | 0.778424 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.4079 | 0.547843 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 16.0052i | − 0.568361i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 29.5512i | − 1.04676i | −0.852100 | − | 0.523379i | \(-0.824671\pi\) | ||||
0.852100 | − | 0.523379i | \(-0.175329\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.9378 | 0.740725 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.9423 | 0.492626 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 0.994009i | − 0.0350778i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 4.56132i | − 0.160566i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.94507 | −0.279334 | −0.139667 | − | 0.990199i | \(-0.544603\pi\) | ||||
−0.139667 | + | 0.990199i | \(0.544603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.5021 | 0.649698 | 0.324849 | − | 0.945766i | \(-0.394687\pi\) | ||||
0.324849 | + | 0.945766i | \(0.394687\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.9193i | 0.453099i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 24.3687i | − 0.852555i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.39850 | −0.223582 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.4242 | −0.538307 | −0.269154 | − | 0.963097i | \(-0.586744\pi\) | ||||
−0.269154 | + | 0.963097i | \(0.586744\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.5847i | 1.44955i | 0.688986 | + | 0.724775i | \(0.258056\pi\) | ||||
−0.688986 | + | 0.724775i | \(0.741944\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 34.8857i | − 1.21309i | −0.795048 | − | 0.606547i | \(-0.792554\pi\) | ||||
0.795048 | − | 0.606547i | \(-0.207446\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.6095 | −1.61882 | −0.809408 | − | 0.587247i | \(-0.800212\pi\) | ||||
−0.809408 | + | 0.587247i | \(0.800212\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.83521 | −0.306490 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.5955i | 1.19866i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.74937i | 0.129597i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.3953 | −1.46365 | −0.731825 | − | 0.681493i | \(-0.761331\pi\) | ||||
−0.731825 | + | 0.681493i | \(0.761331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.6492 | −0.781007 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 0.0305495i | − 0.00105218i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 41.7705i | − 1.43525i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.80719 | −0.164982 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −75.3946 | −2.58449 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.74484i | 0.128221i | 0.997943 | + | 0.0641104i | \(0.0204210\pi\) | ||||
−0.997943 | + | 0.0641104i | \(0.979579\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.9648i | 1.36517i | 0.730806 | + | 0.682586i | \(0.239145\pi\) | ||||
−0.730806 | + | 0.682586i | \(0.760855\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.1078 | 1.91437 | 0.957186 | − | 0.289472i | \(-0.0934798\pi\) | ||||
0.957186 | + | 0.289472i | \(0.0934798\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.3915 | −0.933500 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 18.5927i | − 0.632904i | −0.948609 | − | 0.316452i | \(-0.897508\pi\) | ||||
0.948609 | − | 0.316452i | \(-0.102492\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.18984i | 0.142294i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.593500 | 0.0201331 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.1634 | −0.344373 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.69507i | 0.226594i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.8792i | 0.367365i | 0.982986 | + | 0.183682i | \(0.0588018\pi\) | ||||
−0.982986 | + | 0.183682i | \(0.941198\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.9705 | 0.504943 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.9938 | 1.14528 | 0.572641 | − | 0.819806i | \(-0.305919\pi\) | ||||
0.572641 | + | 0.819806i | \(0.305919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 15.2549i | − 0.513367i | −0.966496 | − | 0.256683i | \(-0.917370\pi\) | ||||
0.966496 | − | 0.256683i | \(-0.0826298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 28.5046i | − 0.957090i | −0.878063 | − | 0.478545i | \(-0.841164\pi\) | ||||
0.878063 | − | 0.478545i | \(-0.158836\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −63.8303 | −2.14080 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.190733 | 0.00638979 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.0137i | 0.402024i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 10.6739i | − 0.356392i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.44871 | −0.315132 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.4089 | 1.44616 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 35.1510i | − 1.16975i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 22.1919i | − 0.736868i | −0.929654 | − | 0.368434i | \(-0.879894\pi\) | ||||
0.929654 | − | 0.368434i | \(-0.120106\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.5147 | −0.348751 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.6047 | 1.34529 | 0.672647 | − | 0.739963i | \(-0.265157\pi\) | ||||
0.672647 | + | 0.739963i | \(0.265157\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.892319i | 0.0295314i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 12.6013i | − 0.416132i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.5514 | −0.414031 | −0.207016 | − | 0.978338i | \(-0.566375\pi\) | ||||
−0.207016 | + | 0.978338i | \(0.566375\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.47622 | 0.147497 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 22.3336i | − 0.735121i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.9648i | 0.425821i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.4129 | 1.85085 | 0.925424 | − | 0.378932i | \(-0.123709\pi\) | ||||
0.925424 | + | 0.378932i | \(0.123709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.8502 | −0.650565 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 0.296114i | − 0.00969434i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 42.1247i | − 1.37616i | −0.725637 | − | 0.688078i | \(-0.758455\pi\) | ||||
0.725637 | − | 0.688078i | \(-0.241545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.1569 | 0.690430 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.7834 | −1.00351 | −0.501755 | − | 0.865010i | \(-0.667312\pi\) | ||||
−0.501755 | + | 0.865010i | \(0.667312\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 45.6943i | − 1.48801i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.741722i | 0.0241027i | 0.999927 | + | 0.0120514i | \(0.00383616\pi\) | ||||
−0.999927 | + | 0.0120514i | \(0.996164\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.75241 | −0.284115 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.9166 | 0.840405 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 39.3063i | − 1.27326i | −0.771171 | − | 0.636628i | \(-0.780329\pi\) | ||||
0.771171 | − | 0.636628i | \(-0.219671\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.480661i | 0.0155376i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.99763 | −0.258257 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.9422 | −0.546522 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 9.64606i | − 0.310840i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.7793i | 1.56864i | 0.620358 | + | 0.784319i | \(0.286987\pi\) | ||||
−0.620358 | + | 0.784319i | \(0.713013\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.1583 | −0.390582 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −61.2669 | −1.96615 | −0.983074 | − | 0.183210i | \(-0.941351\pi\) | ||||
−0.983074 | + | 0.183210i | \(0.941351\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 50.6143i | 1.62262i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.1646i | 0.357186i | 0.983923 | + | 0.178593i | \(0.0571545\pi\) | ||||
−0.983923 | + | 0.178593i | \(0.942845\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.65925 | −0.0849900 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.4454 | 0.652772 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.0074i | 0.988983i | 0.869182 | + | 0.494492i | \(0.164646\pi\) | ||||
−0.869182 | + | 0.494492i | \(0.835354\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.3293i | 0.551599i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 58.6387 | 1.86460 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.5575 | 0.938926 | 0.469463 | − | 0.882952i | \(-0.344447\pi\) | ||||
0.469463 | + | 0.882952i | \(0.344447\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.07039i | 0.0974358i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 54.0506i | − 1.71180i | −0.517142 | − | 0.855899i | \(-0.673004\pi\) | ||||
0.517142 | − | 0.855899i | \(-0.326996\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.8626 | −0.375315 |
(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 | 7500.2.d.g.1249.10 | 24 | ||
5.2 | odd | 4 | 7500.2.a.m.1.3 | 12 | |||
5.3 | odd | 4 | 7500.2.a.n.1.10 | 12 | |||
5.4 | even | 2 | inner | 7500.2.d.g.1249.15 | 24 | ||
25.2 | odd | 20 | 1500.2.m.d.601.2 | 24 | |||
25.9 | even | 10 | 300.2.o.a.169.3 | ✓ | 24 | ||
25.11 | even | 5 | 300.2.o.a.229.3 | yes | 24 | ||
25.12 | odd | 20 | 1500.2.m.d.901.2 | 24 | |||
25.13 | odd | 20 | 1500.2.m.c.901.5 | 24 | |||
25.14 | even | 10 | 1500.2.o.c.649.4 | 24 | |||
25.16 | even | 5 | 1500.2.o.c.349.4 | 24 | |||
25.23 | odd | 20 | 1500.2.m.c.601.5 | 24 | |||
75.11 | odd | 10 | 900.2.w.c.829.1 | 24 | |||
75.59 | odd | 10 | 900.2.w.c.469.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.169.3 | ✓ | 24 | 25.9 | even | 10 | ||
300.2.o.a.229.3 | yes | 24 | 25.11 | even | 5 | ||
900.2.w.c.469.1 | 24 | 75.59 | odd | 10 | |||
900.2.w.c.829.1 | 24 | 75.11 | odd | 10 | |||
1500.2.m.c.601.5 | 24 | 25.23 | odd | 20 | |||
1500.2.m.c.901.5 | 24 | 25.13 | odd | 20 | |||
1500.2.m.d.601.2 | 24 | 25.2 | odd | 20 | |||
1500.2.m.d.901.2 | 24 | 25.12 | odd | 20 | |||
1500.2.o.c.349.4 | 24 | 25.16 | even | 5 | |||
1500.2.o.c.649.4 | 24 | 25.14 | even | 10 | |||
7500.2.a.m.1.3 | 12 | 5.2 | odd | 4 | |||
7500.2.a.n.1.10 | 12 | 5.3 | odd | 4 | |||
7500.2.d.g.1249.10 | 24 | 1.1 | even | 1 | trivial | ||
7500.2.d.g.1249.15 | 24 | 5.4 | even | 2 | inner |