Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(197,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.m (of order \(4\), degree \(2\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 197.2 | ||
Root | \(-2.16053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.197 |
Dual form | 630.2.m.d.323.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 2.23483 | − | 0.0743018i | 0.999448 | − | 0.0332288i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.52773 | + | 1.63280i | −0.483109 | + | 0.516338i | ||||
\(11\) | 5.26561i | 1.58764i | 0.608152 | + | 0.793821i | \(0.291911\pi\) | ||||
−0.608152 | + | 0.793821i | \(0.708089\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.16053 | + | 3.16053i | −0.876574 | + | 0.876574i | −0.993178 | − | 0.116605i | \(-0.962799\pi\) |
0.116605 | + | 0.993178i | \(0.462799\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.05545 | − | 3.05545i | 0.741056 | − | 0.741056i | −0.231725 | − | 0.972781i | \(-0.574437\pi\) |
0.972781 | + | 0.231725i | \(0.0744370\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | −0.0743018 | − | 2.23483i | −0.0166144 | − | 0.499724i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.72335 | − | 3.72335i | −0.793821 | − | 0.793821i | ||||
\(23\) | 4.32106 | + | 4.32106i | 0.901004 | + | 0.901004i | 0.995523 | − | 0.0945192i | \(-0.0301314\pi\) |
−0.0945192 | + | 0.995523i | \(0.530131\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.98896 | − | 0.332104i | 0.997792 | − | 0.0664208i | ||||
\(26\) | − | 4.46967i | − | 0.876574i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.707107 | + | 0.707107i | −0.133631 | + | 0.133631i | ||||
\(29\) | 9.96230 | 1.84995 | 0.924977 | − | 0.380024i | \(-0.124084\pi\) | ||||
0.924977 | + | 0.380024i | \(0.124084\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.26561 | 0.227310 | 0.113655 | − | 0.993520i | \(-0.463744\pi\) | ||||
0.113655 | + | 0.993520i | \(0.463744\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.32106i | 0.741056i | ||||||||
\(35\) | −1.63280 | − | 1.52773i | −0.275994 | − | 0.258233i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.93351 | − | 2.93351i | −0.482265 | − | 0.482265i | 0.423589 | − | 0.905854i | \(-0.360770\pi\) |
−0.905854 | + | 0.423589i | \(0.860770\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.63280 | + | 1.52773i | 0.258169 | + | 0.241555i | ||||
\(41\) | 10.6798i | 1.66791i | 0.551834 | + | 0.833954i | \(0.313928\pi\) | ||||
−0.551834 | + | 0.833954i | \(0.686072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.597714 | − | 0.597714i | 0.0911506 | − | 0.0911506i | −0.660061 | − | 0.751212i | \(-0.729470\pi\) |
0.751212 | + | 0.660061i | \(0.229470\pi\) | |||||||
\(44\) | 5.26561 | 0.793821 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.11091 | −0.901004 | ||||||||
\(47\) | −3.42614 | + | 3.42614i | −0.499754 | + | 0.499754i | −0.911361 | − | 0.411607i | \(-0.864968\pi\) |
0.411607 | + | 0.911361i | \(0.364968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | −3.29289 | + | 3.76256i | −0.465685 | + | 0.532106i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.16053 | + | 3.16053i | 0.438287 | + | 0.438287i | ||||
\(53\) | −9.88388 | − | 9.88388i | −1.35766 | − | 1.35766i | −0.876800 | − | 0.480855i | \(-0.840326\pi\) |
−0.480855 | − | 0.876800i | \(-0.659674\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.391244 | + | 11.7678i | 0.0527554 | + | 1.58676i | ||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.04441 | + | 7.04441i | −0.924977 | + | 0.924977i | ||||
\(59\) | 3.12563 | 0.406923 | 0.203461 | − | 0.979083i | \(-0.434781\pi\) | ||||
0.203461 | + | 0.979083i | \(0.434781\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.05545 | 0.391211 | 0.195605 | − | 0.980683i | \(-0.437333\pi\) | ||||
0.195605 | + | 0.980683i | \(0.437333\pi\) | |||||||
\(62\) | −0.894921 | + | 0.894921i | −0.113655 | + | 0.113655i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −6.82843 | + | 7.29809i | −0.846962 | + | 0.905217i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.59771 | + | 4.59771i | 0.561700 | + | 0.561700i | 0.929790 | − | 0.368090i | \(-0.119988\pi\) |
−0.368090 | + | 0.929790i | \(0.619988\pi\) | |||||||
\(68\) | −3.05545 | − | 3.05545i | −0.370528 | − | 0.370528i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.23483 | − | 0.0743018i | 0.267114 | − | 0.00888076i | ||||
\(71\) | 9.23654i | 1.09618i | 0.836421 | + | 0.548088i | \(0.184644\pi\) | ||||
−0.836421 | + | 0.548088i | \(0.815356\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2160 | − | 10.2160i | 1.19569 | − | 1.19569i | 0.220246 | − | 0.975444i | \(-0.429314\pi\) |
0.975444 | − | 0.220246i | \(-0.0706861\pi\) | |||||||
\(74\) | 4.14860 | 0.482265 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.72335 | − | 3.72335i | 0.424315 | − | 0.424315i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.57969i | 0.402746i | 0.979515 | + | 0.201373i | \(0.0645403\pi\) | ||||
−0.979515 | + | 0.201373i | \(0.935460\pi\) | |||||||
\(80\) | −2.23483 | + | 0.0743018i | −0.249862 | + | 0.00830719i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.55178 | − | 7.55178i | −0.833954 | − | 0.833954i | ||||
\(83\) | −6.21016 | − | 6.21016i | −0.681653 | − | 0.681653i | 0.278719 | − | 0.960373i | \(-0.410090\pi\) |
−0.960373 | + | 0.278719i | \(0.910090\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.60140 | − | 7.05545i | 0.716023 | − | 0.765271i | ||||
\(86\) | 0.845296i | 0.0911506i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.72335 | + | 3.72335i | −0.396910 | + | 0.396910i | ||||
\(89\) | −3.61916 | −0.383630 | −0.191815 | − | 0.981431i | \(-0.561437\pi\) | ||||
−0.191815 | + | 0.981431i | \(0.561437\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.46967 | 0.468548 | ||||||||
\(92\) | 4.32106 | − | 4.32106i | 0.450502 | − | 0.450502i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 4.84530i | − | 0.499754i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.63630 | − | 4.63630i | −0.470745 | − | 0.470745i | 0.431411 | − | 0.902156i | \(-0.358016\pi\) |
−0.902156 | + | 0.431411i | \(0.858016\pi\) | |||||||
\(98\) | −0.707107 | − | 0.707107i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.332104 | − | 4.98896i | −0.0332104 | − | 0.498896i | ||||
\(101\) | − | 2.12652i | − | 0.211597i | −0.994388 | − | 0.105798i | \(-0.966260\pi\) | ||
0.994388 | − | 0.105798i | \(-0.0337398\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.9225 | + | 10.9225i | −1.07622 | + | 1.07622i | −0.0793778 | + | 0.996845i | \(0.525293\pi\) |
−0.996845 | + | 0.0793778i | \(0.974707\pi\) | |||||||
\(104\) | −4.46967 | −0.438287 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.9779 | 1.35766 | ||||||||
\(107\) | −6.40811 | + | 6.40811i | −0.619496 | + | 0.619496i | −0.945402 | − | 0.325906i | \(-0.894331\pi\) |
0.325906 | + | 0.945402i | \(0.394331\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.55760i | − | 0.915452i | −0.889093 | − | 0.457726i | \(-0.848664\pi\) | ||
0.889093 | − | 0.457726i | \(-0.151336\pi\) | |||||||
\(110\) | −8.59771 | − | 8.04441i | −0.819760 | − | 0.767005i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.707107 | + | 0.707107i | 0.0668153 | + | 0.0668153i | ||||
\(113\) | 3.29809 | + | 3.29809i | 0.310259 | + | 0.310259i | 0.845010 | − | 0.534751i | \(-0.179595\pi\) |
−0.534751 | + | 0.845010i | \(0.679595\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.97792 | + | 9.33579i | 0.930446 | + | 0.870567i | ||||
\(116\) | − | 9.96230i | − | 0.924977i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.21016 | + | 2.21016i | −0.203461 | + | 0.203461i | ||||
\(119\) | −4.32106 | −0.396111 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.7266 | −1.52060 | ||||||||
\(122\) | −2.16053 | + | 2.16053i | −0.195605 | + | 0.195605i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 1.26561i | − | 0.113655i | ||||||
\(125\) | 11.1248 | − | 1.11289i | 0.995034 | − | 0.0995396i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.32106 | − | 8.32106i | −0.738375 | − | 0.738375i | 0.233889 | − | 0.972263i | \(-0.424855\pi\) |
−0.972263 | + | 0.233889i | \(0.924855\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.332104 | − | 9.98896i | −0.0291275 | − | 0.876090i | ||||
\(131\) | − | 17.4246i | − | 1.52240i | −0.648520 | − | 0.761198i | \(-0.724612\pi\) | ||
0.648520 | − | 0.761198i | \(-0.275388\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.50215 | −0.561700 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.32106 | 0.370528 | ||||||||
\(137\) | 2.35876 | − | 2.35876i | 0.201523 | − | 0.201523i | −0.599130 | − | 0.800652i | \(-0.704487\pi\) |
0.800652 | + | 0.599130i | \(0.204487\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 21.8449i | − | 1.85286i | −0.376464 | − | 0.926431i | \(-0.622860\pi\) | ||
0.376464 | − | 0.926431i | \(-0.377140\pi\) | |||||||
\(140\) | −1.52773 | + | 1.63280i | −0.129116 | + | 0.137997i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.53122 | − | 6.53122i | −0.548088 | − | 0.548088i | ||||
\(143\) | −16.6421 | − | 16.6421i | −1.39168 | − | 1.39168i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.2641 | − | 0.740217i | 1.84893 | − | 0.0614717i | ||||
\(146\) | 14.4476i | 1.19569i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.93351 | + | 2.93351i | −0.241133 | + | 0.241133i | ||||
\(149\) | 6.08541 | 0.498536 | 0.249268 | − | 0.968435i | \(-0.419810\pi\) | ||||
0.249268 | + | 0.968435i | \(0.419810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.7530 | 1.85162 | 0.925808 | − | 0.377995i | \(-0.123386\pi\) | ||||
0.925808 | + | 0.377995i | \(0.123386\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.26561i | 0.424315i | ||||||||
\(155\) | 2.82843 | − | 0.0940371i | 0.227185 | − | 0.00755324i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.7181 | − | 10.7181i | −0.855400 | − | 0.855400i | 0.135392 | − | 0.990792i | \(-0.456771\pi\) |
−0.990792 | + | 0.135392i | \(0.956771\pi\) | |||||||
\(158\) | −2.53122 | − | 2.53122i | −0.201373 | − | 0.201373i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.52773 | − | 1.63280i | 0.120777 | − | 0.129085i | ||||
\(161\) | − | 6.11091i | − | 0.481607i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.04441 | + | 4.04441i | −0.316783 | + | 0.316783i | −0.847530 | − | 0.530747i | \(-0.821911\pi\) |
0.530747 | + | 0.847530i | \(0.321911\pi\) | |||||||
\(164\) | 10.6798 | 0.833954 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.78249 | 0.681653 | ||||||||
\(167\) | 5.76929 | − | 5.76929i | 0.446441 | − | 0.446441i | −0.447729 | − | 0.894169i | \(-0.647767\pi\) |
0.894169 | + | 0.447729i | \(0.147767\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 6.97792i | − | 0.536763i | ||||||
\(170\) | 0.321063 | + | 9.65685i | 0.0246244 | + | 0.740647i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.597714 | − | 0.597714i | −0.0455753 | − | 0.0455753i | ||||
\(173\) | −6.14492 | − | 6.14492i | −0.467189 | − | 0.467189i | 0.433813 | − | 0.901003i | \(-0.357168\pi\) |
−0.901003 | + | 0.433813i | \(0.857168\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.76256 | − | 3.29289i | −0.284423 | − | 0.248919i | ||||
\(176\) | − | 5.26561i | − | 0.396910i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.55913 | − | 2.55913i | 0.191815 | − | 0.191815i | ||||
\(179\) | 0.391244 | 0.0292430 | 0.0146215 | − | 0.999893i | \(-0.495346\pi\) | ||||
0.0146215 | + | 0.999893i | \(0.495346\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0113 | −1.11578 | −0.557890 | − | 0.829915i | \(-0.688389\pi\) | ||||
−0.557890 | + | 0.829915i | \(0.688389\pi\) | |||||||
\(182\) | −3.16053 | + | 3.16053i | −0.234274 | + | 0.234274i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.11091i | 0.450502i | ||||||||
\(185\) | −6.77386 | − | 6.33793i | −0.498024 | − | 0.465974i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.0888 | + | 16.0888i | 1.17653 | + | 1.17653i | ||||
\(188\) | 3.42614 | + | 3.42614i | 0.249877 | + | 0.249877i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.3474i | 1.68936i | 0.535270 | + | 0.844681i | \(0.320210\pi\) | ||||
−0.535270 | + | 0.844681i | \(0.679790\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.69059 | − | 6.69059i | 0.481599 | − | 0.481599i | −0.424043 | − | 0.905642i | \(-0.639389\pi\) |
0.905642 | + | 0.424043i | \(0.139389\pi\) | |||||||
\(194\) | 6.55672 | 0.470745 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −0.375629 | + | 0.375629i | −0.0267625 | + | 0.0267625i | −0.720361 | − | 0.693599i | \(-0.756024\pi\) |
0.693599 | + | 0.720361i | \(0.256024\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 18.0481i | − | 1.27940i | −0.768626 | − | 0.639698i | \(-0.779059\pi\) | ||
0.768626 | − | 0.639698i | \(-0.220941\pi\) | |||||||
\(200\) | 3.76256 | + | 3.29289i | 0.266053 | + | 0.232843i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.50368 | + | 1.50368i | 0.105798 | + | 0.105798i | ||||
\(203\) | −7.04441 | − | 7.04441i | −0.494421 | − | 0.494421i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.793530 | + | 23.8676i | 0.0554225 | + | 1.66699i | ||||
\(206\) | − | 15.4467i | − | 1.07622i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.16053 | − | 3.16053i | 0.219143 | − | 0.219143i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.22181 | −0.566013 | −0.283006 | − | 0.959118i | \(-0.591332\pi\) | ||||
−0.283006 | + | 0.959118i | \(0.591332\pi\) | |||||||
\(212\) | −9.88388 | + | 9.88388i | −0.678828 | + | 0.678828i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 9.06244i | − | 0.619496i | ||||||
\(215\) | 1.29138 | − | 1.38020i | 0.0880714 | − | 0.0941290i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.894921 | − | 0.894921i | −0.0607512 | − | 0.0607512i | ||||
\(218\) | 6.75825 | + | 6.75825i | 0.457726 | + | 0.457726i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.7678 | − | 0.391244i | 0.793382 | − | 0.0263777i | ||||
\(221\) | 19.3137i | 1.29918i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.2365 | + | 13.2365i | −0.886384 | + | 0.886384i | −0.994174 | − | 0.107789i | \(-0.965623\pi\) |
0.107789 | + | 0.994174i | \(0.465623\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.66421 | −0.310259 | ||||||||
\(227\) | 5.46878 | − | 5.46878i | 0.362976 | − | 0.362976i | −0.501932 | − | 0.864907i | \(-0.667377\pi\) |
0.864907 | + | 0.501932i | \(0.167377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.0966i | − | 0.865445i | −0.901527 | − | 0.432723i | \(-0.857553\pi\) | ||
0.901527 | − | 0.432723i | \(-0.142447\pi\) | |||||||
\(230\) | −13.6569 | + | 0.454051i | −0.900506 | + | 0.0299393i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.04441 | + | 7.04441i | 0.462488 | + | 0.462488i | ||||
\(233\) | 0.642125 | + | 0.642125i | 0.0420670 | + | 0.0420670i | 0.727827 | − | 0.685760i | \(-0.240530\pi\) |
−0.685760 | + | 0.727827i | \(0.740530\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.40229 | + | 7.91142i | −0.482872 | + | 0.516084i | ||||
\(236\) | − | 3.12563i | − | 0.203461i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.05545 | − | 3.05545i | 0.198056 | − | 0.198056i | ||||
\(239\) | −25.4246 | −1.64458 | −0.822291 | − | 0.569068i | \(-0.807304\pi\) | ||||
−0.822291 | + | 0.569068i | \(0.807304\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.46878 | −0.481106 | −0.240553 | − | 0.970636i | \(-0.577329\pi\) | ||||
−0.240553 | + | 0.970636i | \(0.577329\pi\) | |||||||
\(242\) | 11.8275 | − | 11.8275i | 0.760302 | − | 0.760302i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 3.05545i | − | 0.195605i | ||||||
\(245\) | 0.0743018 | + | 2.23483i | 0.00474697 | + | 0.142778i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.894921 | + | 0.894921i | 0.0568276 | + | 0.0568276i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.07950 | + | 8.65336i | −0.447747 | + | 0.547287i | ||||
\(251\) | 1.23654i | 0.0780497i | 0.999238 | + | 0.0390249i | \(0.0124252\pi\) | ||||
−0.999238 | + | 0.0390249i | \(0.987575\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.7530 | + | 22.7530i | −1.43047 | + | 1.43047i | ||||
\(254\) | 11.7678 | 0.738375 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.8076 | − | 10.8076i | 0.674159 | − | 0.674159i | −0.284513 | − | 0.958672i | \(-0.591832\pi\) |
0.958672 | + | 0.284513i | \(0.0918318\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.14860i | 0.257782i | ||||||||
\(260\) | 7.29809 | + | 6.82843i | 0.452609 | + | 0.423481i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.3211 | + | 12.3211i | 0.761198 | + | 0.761198i | ||||
\(263\) | −6.99265 | − | 6.99265i | −0.431185 | − | 0.431185i | 0.457846 | − | 0.889031i | \(-0.348621\pi\) |
−0.889031 | + | 0.457846i | \(0.848621\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.8232 | − | 21.3544i | −1.40202 | − | 1.31179i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.59771 | − | 4.59771i | 0.280850 | − | 0.280850i | ||||
\(269\) | 21.7374 | 1.32535 | 0.662677 | − | 0.748905i | \(-0.269420\pi\) | ||||
0.662677 | + | 0.748905i | \(0.269420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.98566 | −0.302857 | −0.151429 | − | 0.988468i | \(-0.548387\pi\) | ||||
−0.151429 | + | 0.988468i | \(0.548387\pi\) | |||||||
\(272\) | −3.05545 | + | 3.05545i | −0.185264 | + | 0.185264i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.33579i | 0.201523i | ||||||||
\(275\) | 1.74873 | + | 26.2699i | 0.105452 | + | 1.58414i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.80787 | + | 1.80787i | 0.108624 | + | 0.108624i | 0.759330 | − | 0.650706i | \(-0.225527\pi\) |
−0.650706 | + | 0.759330i | \(0.725527\pi\) | |||||||
\(278\) | 15.4467 | + | 15.4467i | 0.926431 | + | 0.926431i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.0743018 | − | 2.23483i | −0.00444038 | − | 0.133557i | ||||
\(281\) | 8.66296i | 0.516789i | 0.966040 | + | 0.258394i | \(0.0831934\pi\) | ||||
−0.966040 | + | 0.258394i | \(0.916807\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.55760 | + | 1.55760i | −0.0925899 | + | 0.0925899i | −0.751885 | − | 0.659295i | \(-0.770855\pi\) |
0.659295 | + | 0.751885i | \(0.270855\pi\) | |||||||
\(284\) | 9.23654 | 0.548088 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 23.5355 | 1.39168 | ||||||||
\(287\) | 7.55178 | − | 7.55178i | 0.445767 | − | 0.445767i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.67158i | − | 0.0983284i | ||||||
\(290\) | −15.2197 | + | 16.2665i | −0.893730 | + | 0.955202i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.2160 | − | 10.2160i | −0.597845 | − | 0.597845i | ||||
\(293\) | 5.39366 | + | 5.39366i | 0.315101 | + | 0.315101i | 0.846882 | − | 0.531781i | \(-0.178477\pi\) |
−0.531781 | + | 0.846882i | \(0.678477\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.98527 | − | 0.232240i | 0.406698 | − | 0.0135215i | ||||
\(296\) | − | 4.14860i | − | 0.241133i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.30303 | + | 4.30303i | −0.249268 | + | 0.249268i | ||||
\(299\) | −27.3137 | −1.57959 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.845296 | −0.0487220 | ||||||||
\(302\) | −16.0888 | + | 16.0888i | −0.925808 | + | 0.925808i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.82843 | − | 0.227026i | 0.390995 | − | 0.0129994i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.46878 | − | 1.46878i | −0.0838277 | − | 0.0838277i | 0.663950 | − | 0.747777i | \(-0.268879\pi\) |
−0.747777 | + | 0.663950i | \(0.768879\pi\) | |||||||
\(308\) | −3.72335 | − | 3.72335i | −0.212157 | − | 0.212157i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.93351 | + | 2.06649i | −0.109816 | + | 0.117369i | ||||
\(311\) | − | 30.9822i | − | 1.75684i | −0.477889 | − | 0.878420i | \(-0.658598\pi\) | ||
0.477889 | − | 0.878420i | \(-0.341402\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.74720 | − | 6.74720i | 0.381375 | − | 0.381375i | −0.490223 | − | 0.871597i | \(-0.663085\pi\) |
0.871597 | + | 0.490223i | \(0.163085\pi\) | |||||||
\(314\) | 15.1577 | 0.855400 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.57969 | 0.201373 | ||||||||
\(317\) | 20.4151 | − | 20.4151i | 1.14663 | − | 1.14663i | 0.159415 | − | 0.987212i | \(-0.449039\pi\) |
0.987212 | − | 0.159415i | \(-0.0509606\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 52.4576i | 2.93706i | ||||||||
\(320\) | 0.0743018 | + | 2.23483i | 0.00415360 | + | 0.124931i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.32106 | + | 4.32106i | 0.240803 | + | 0.240803i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.7181 | + | 16.8174i | −0.816415 | + | 0.932861i | ||||
\(326\) | − | 5.71966i | − | 0.316783i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.55178 | + | 7.55178i | −0.416977 | + | 0.416977i | ||||
\(329\) | 4.84530 | 0.267130 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.2513 | −1.00318 | −0.501590 | − | 0.865105i | \(-0.667251\pi\) | ||||
−0.501590 | + | 0.865105i | \(0.667251\pi\) | |||||||
\(332\) | −6.21016 | + | 6.21016i | −0.340827 | + | 0.340827i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.15900i | 0.446441i | ||||||||
\(335\) | 10.6167 | + | 9.93351i | 0.580055 | + | 0.542725i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.21016 | − | 7.21016i | −0.392762 | − | 0.392762i | 0.482909 | − | 0.875671i | \(-0.339580\pi\) |
−0.875671 | + | 0.482909i | \(0.839580\pi\) | |||||||
\(338\) | 4.93413 | + | 4.93413i | 0.268381 | + | 0.268381i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.05545 | − | 6.60140i | −0.382636 | − | 0.358011i | ||||
\(341\) | 6.66421i | 0.360887i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | 0.845296 | 0.0455753 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.69022 | 0.467189 | ||||||||
\(347\) | 10.8284 | − | 10.8284i | 0.581300 | − | 0.581300i | −0.353960 | − | 0.935261i | \(-0.615165\pi\) |
0.935261 | + | 0.353960i | \(0.115165\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0598i | 0.859659i | 0.902910 | + | 0.429829i | \(0.141426\pi\) | ||||
−0.902910 | + | 0.429829i | \(0.858574\pi\) | |||||||
\(350\) | 4.98896 | − | 0.332104i | 0.266671 | − | 0.0177517i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.72335 | + | 3.72335i | 0.198455 | + | 0.198455i | ||||
\(353\) | 9.26561 | + | 9.26561i | 0.493159 | + | 0.493159i | 0.909300 | − | 0.416141i | \(-0.136618\pi\) |
−0.416141 | + | 0.909300i | \(0.636618\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.686292 | + | 20.6421i | 0.0364246 | + | 1.09557i | ||||
\(356\) | 3.61916i | 0.191815i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.276651 | + | 0.276651i | −0.0146215 | + | 0.0146215i | ||||
\(359\) | −7.35787 | −0.388334 | −0.194167 | − | 0.980969i | \(-0.562200\pi\) | ||||
−0.194167 | + | 0.980969i | \(0.562200\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 10.6146 | − | 10.6146i | 0.557890 | − | 0.557890i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 4.46967i | − | 0.234274i | ||||||
\(365\) | 22.0720 | − | 23.5901i | 1.15530 | − | 1.23476i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.1443 | + | 23.1443i | 1.20812 | + | 1.20812i | 0.971635 | + | 0.236487i | \(0.0759959\pi\) |
0.236487 | + | 0.971635i | \(0.424004\pi\) | |||||||
\(368\) | −4.32106 | − | 4.32106i | −0.225251 | − | 0.225251i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.27144 | − | 0.308249i | 0.481999 | − | 0.0160251i | ||||
\(371\) | 13.9779i | 0.725697i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.0812231 | − | 0.0812231i | 0.00420557 | − | 0.00420557i | −0.705001 | − | 0.709206i | \(-0.749053\pi\) |
0.709206 | + | 0.705001i | \(0.249053\pi\) | |||||||
\(374\) | −22.7530 | −1.17653 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.84530 | −0.249877 | ||||||||
\(377\) | −31.4862 | + | 31.4862i | −1.62162 | + | 1.62162i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.3548i | 0.634623i | 0.948321 | + | 0.317312i | \(0.102780\pi\) | ||||
−0.948321 | + | 0.317312i | \(0.897220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.5091 | − | 16.5091i | −0.844681 | − | 0.844681i | ||||
\(383\) | 11.7546 | + | 11.7546i | 0.600631 | + | 0.600631i | 0.940480 | − | 0.339849i | \(-0.110376\pi\) |
−0.339849 | + | 0.940480i | \(0.610376\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.04441 | − | 8.59771i | 0.409981 | − | 0.438180i | ||||
\(386\) | 9.46192i | 0.481599i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.63630 | + | 4.63630i | −0.235372 | + | 0.235372i | ||||
\(389\) | −11.4960 | −0.582873 | −0.291436 | − | 0.956590i | \(-0.594133\pi\) | ||||
−0.291436 | + | 0.956590i | \(0.594133\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.4056 | 1.33539 | ||||||||
\(392\) | −0.707107 | + | 0.707107i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 0.531220i | − | 0.0267625i | ||||||
\(395\) | 0.265977 | + | 8.00000i | 0.0133828 | + | 0.402524i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.2424 | − | 11.2424i | −0.564238 | − | 0.564238i | 0.366270 | − | 0.930509i | \(-0.380635\pi\) |
−0.930509 | + | 0.366270i | \(0.880635\pi\) | |||||||
\(398\) | 12.7619 | + | 12.7619i | 0.639698 | + | 0.639698i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.98896 | + | 0.332104i | −0.249448 | + | 0.0166052i | ||||
\(401\) | 29.5269i | 1.47450i | 0.675619 | + | 0.737251i | \(0.263877\pi\) | ||||
−0.675619 | + | 0.737251i | \(0.736123\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | + | 4.00000i | −0.199254 | + | 0.199254i | ||||
\(404\) | −2.12652 | −0.105798 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.96230 | 0.494421 | ||||||||
\(407\) | 15.4467 | − | 15.4467i | 0.765664 | − | 0.765664i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 26.2916i | − | 1.30004i | −0.759919 | − | 0.650018i | \(-0.774761\pi\) | ||
0.759919 | − | 0.650018i | \(-0.225239\pi\) | |||||||
\(410\) | −17.4381 | − | 16.3158i | −0.861205 | − | 0.805782i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.9225 | + | 10.9225i | 0.538111 | + | 0.538111i | ||||
\(413\) | −2.21016 | − | 2.21016i | −0.108755 | − | 0.108755i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.3401 | − | 13.4172i | −0.703927 | − | 0.658626i | ||||
\(416\) | 4.46967i | 0.219143i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.5980 | 1.00628 | 0.503138 | − | 0.864206i | \(-0.332179\pi\) | ||||
0.503138 | + | 0.864206i | \(0.332179\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.73402 | −0.0845111 | −0.0422556 | − | 0.999107i | \(-0.513454\pi\) | ||||
−0.0422556 | + | 0.999107i | \(0.513454\pi\) | |||||||
\(422\) | 5.81370 | − | 5.81370i | 0.283006 | − | 0.283006i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 13.9779i | − | 0.678828i | ||||||
\(425\) | 14.2288 | − | 16.2583i | 0.690198 | − | 0.788641i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.16053 | − | 2.16053i | −0.104555 | − | 0.104555i | ||||
\(428\) | 6.40811 | + | 6.40811i | 0.309748 | + | 0.309748i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.0628070 | + | 1.88909i | 0.00302882 | + | 0.0911002i | ||||
\(431\) | − | 1.70102i | − | 0.0819353i | −0.999160 | − | 0.0409676i | \(-0.986956\pi\) | ||
0.999160 | − | 0.0409676i | \(-0.0130441\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.88757 | − | 2.88757i | 0.138768 | − | 0.138768i | −0.634311 | − | 0.773078i | \(-0.718716\pi\) |
0.773078 | + | 0.634311i | \(0.218716\pi\) | |||||||
\(434\) | 1.26561 | 0.0607512 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.55760 | −0.457726 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 32.8011i | − | 1.56551i | −0.622328 | − | 0.782756i | \(-0.713813\pi\) | ||
0.622328 | − | 0.782756i | \(-0.286187\pi\) | |||||||
\(440\) | −8.04441 | + | 8.59771i | −0.383502 | + | 0.409880i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.6569 | − | 13.6569i | −0.649590 | − | 0.649590i | ||||
\(443\) | 20.0650 | + | 20.0650i | 0.953315 | + | 0.953315i | 0.998958 | − | 0.0456425i | \(-0.0145335\pi\) |
−0.0456425 | + | 0.998958i | \(0.514534\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.08821 | + | 0.268910i | −0.383418 | + | 0.0127475i | ||||
\(446\) | − | 18.7193i | − | 0.886384i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.707107 | − | 0.707107i | 0.0334077 | − | 0.0334077i | ||||
\(449\) | −11.9767 | −0.565214 | −0.282607 | − | 0.959236i | \(-0.591199\pi\) | ||||
−0.282607 | + | 0.959236i | \(0.591199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −56.2358 | −2.64804 | ||||||||
\(452\) | 3.29809 | − | 3.29809i | 0.155129 | − | 0.155129i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.73402i | 0.362976i | ||||||||
\(455\) | 9.98896 | − | 0.332104i | 0.468290 | − | 0.0155693i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.46878 | + | 6.46878i | 0.302597 | + | 0.302597i | 0.842029 | − | 0.539432i | \(-0.181361\pi\) |
−0.539432 | + | 0.842029i | \(0.681361\pi\) | |||||||
\(458\) | 9.26067 | + | 9.26067i | 0.432723 | + | 0.432723i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.33579 | − | 9.97792i | 0.435284 | − | 0.465223i | ||||
\(461\) | − | 37.0915i | − | 1.72752i | −0.503901 | − | 0.863761i | \(-0.668102\pi\) | ||
0.503901 | − | 0.863761i | \(-0.331898\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.232240 | + | 0.232240i | −0.0107931 | + | 0.0107931i | −0.712483 | − | 0.701690i | \(-0.752429\pi\) |
0.701690 | + | 0.712483i | \(0.252429\pi\) | |||||||
\(464\) | −9.96230 | −0.462488 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.908103 | −0.0420670 | ||||||||
\(467\) | −22.1997 | + | 22.1997i | −1.02728 | + | 1.02728i | −0.0276636 | + | 0.999617i | \(0.508807\pi\) |
−0.999617 | + | 0.0276636i | \(0.991193\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.50215i | − | 0.300241i | ||||||
\(470\) | −0.360014 | − | 10.8284i | −0.0166062 | − | 0.499478i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.21016 | + | 2.21016i | 0.101731 | + | 0.101731i | ||||
\(473\) | 3.14733 | + | 3.14733i | 0.144714 | + | 0.144714i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.32106i | 0.198056i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.9779 | − | 17.9779i | 0.822291 | − | 0.822291i | ||||
\(479\) | −20.7751 | −0.949239 | −0.474620 | − | 0.880191i | \(-0.657414\pi\) | ||||
−0.474620 | + | 0.880191i | \(0.657414\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.5429 | 0.845482 | ||||||||
\(482\) | 5.28123 | − | 5.28123i | 0.240553 | − | 0.240553i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.7266i | 0.760302i | ||||||||
\(485\) | −10.7058 | − | 10.0169i | −0.486127 | − | 0.454843i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.00735 | − | 1.00735i | −0.0456476 | − | 0.0456476i | 0.683915 | − | 0.729562i | \(-0.260276\pi\) |
−0.729562 | + | 0.683915i | \(0.760276\pi\) | |||||||
\(488\) | 2.16053 | + | 2.16053i | 0.0978027 | + | 0.0978027i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.63280 | − | 1.52773i | −0.0737626 | − | 0.0690156i | ||||
\(491\) | − | 6.95620i | − | 0.313929i | −0.987604 | − | 0.156964i | \(-0.949829\pi\) | ||
0.987604 | − | 0.156964i | \(-0.0501708\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.4393 | − | 30.4393i | 1.37092 | − | 1.37092i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.26561 | −0.0568276 | ||||||||
\(497\) | 6.53122 | − | 6.53122i | 0.292965 | − | 0.292965i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 20.9969i | − | 0.939951i | −0.882679 | − | 0.469976i | \(-0.844263\pi\) | ||
0.882679 | − | 0.469976i | \(-0.155737\pi\) | |||||||
\(500\) | −1.11289 | − | 11.1248i | −0.0497698 | − | 0.497517i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.874366 | − | 0.874366i | −0.0390249 | − | 0.0390249i | ||||
\(503\) | −7.29315 | − | 7.29315i | −0.325186 | − | 0.325186i | 0.525567 | − | 0.850752i | \(-0.323853\pi\) |
−0.850752 | + | 0.525567i | \(0.823853\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.158004 | − | 4.75242i | −0.00703110 | − | 0.211480i | ||||
\(506\) | − | 32.1776i | − | 1.43047i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.32106 | + | 8.32106i | −0.369187 | + | 0.369187i | ||||
\(509\) | −0.545062 | −0.0241595 | −0.0120797 | − | 0.999927i | \(-0.503845\pi\) | ||||
−0.0120797 | + | 0.999927i | \(0.503845\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.4476 | −0.639123 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.2843i | 0.674159i | ||||||||
\(515\) | −23.5983 | + | 25.2214i | −1.03987 | + | 1.11139i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.0407 | − | 18.0407i | −0.793430 | − | 0.793430i | ||||
\(518\) | −2.93351 | − | 2.93351i | −0.128891 | − | 0.128891i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.98896 | + | 0.332104i | −0.438045 | + | 0.0145637i | ||||
\(521\) | − | 21.6963i | − | 0.950533i | −0.879842 | − | 0.475267i | \(-0.842352\pi\) | ||
0.879842 | − | 0.475267i | \(-0.157648\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.9822 | − | 26.9822i | 1.17985 | − | 1.17985i | 0.200068 | − | 0.979782i | \(-0.435884\pi\) |
0.979782 | − | 0.200068i | \(-0.0641163\pi\) | |||||||
\(524\) | −17.4246 | −0.761198 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.88909 | 0.431185 | ||||||||
\(527\) | 3.86701 | − | 3.86701i | 0.168450 | − | 0.168450i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.3432i | 0.623616i | ||||||||
\(530\) | 31.2383 | − | 1.03858i | 1.35691 | − | 0.0451132i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.7539 | − | 33.7539i | −1.46204 | − | 1.46204i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.8449 | + | 14.7972i | −0.598568 | + | 0.639739i | ||||
\(536\) | 6.50215i | 0.280850i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.3707 | + | 15.3707i | −0.662677 | + | 0.662677i | ||||
\(539\) | −5.26561 | −0.226806 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.2249 | −0.654569 | −0.327284 | − | 0.944926i | \(-0.606134\pi\) | ||||
−0.327284 | + | 0.944926i | \(0.606134\pi\) | |||||||
\(542\) | 3.52539 | − | 3.52539i | 0.151429 | − | 0.151429i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 4.32106i | − | 0.185264i | ||||||
\(545\) | −0.710147 | − | 21.3596i | −0.0304194 | − | 0.914947i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.84898 | + | 6.84898i | 0.292841 | + | 0.292841i | 0.838202 | − | 0.545360i | \(-0.183607\pi\) |
−0.545360 | + | 0.838202i | \(0.683607\pi\) | |||||||
\(548\) | −2.35876 | − | 2.35876i | −0.100761 | − | 0.100761i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −19.8122 | − | 17.3391i | −0.844794 | − | 0.739341i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.53122 | − | 2.53122i | 0.107638 | − | 0.107638i | ||||
\(554\) | −2.55672 | −0.108624 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.8449 | −0.926431 | ||||||||
\(557\) | −25.8839 | + | 25.8839i | −1.09674 | + | 1.09674i | −0.101945 | + | 0.994790i | \(0.532507\pi\) |
−0.994790 | + | 0.101945i | \(0.967493\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.77819i | 0.159800i | ||||||||
\(560\) | 1.63280 | + | 1.52773i | 0.0689986 | + | 0.0645582i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.12563 | − | 6.12563i | −0.258394 | − | 0.258394i | ||||
\(563\) | 14.9926 | + | 14.9926i | 0.631865 | + | 0.631865i | 0.948535 | − | 0.316671i | \(-0.102565\pi\) |
−0.316671 | + | 0.948535i | \(0.602565\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.61574 | + | 7.12563i | 0.320397 | + | 0.299778i | ||||
\(566\) | − | 2.20278i | − | 0.0925899i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.53122 | + | 6.53122i | −0.274044 | + | 0.274044i | ||||
\(569\) | 4.97742 | 0.208664 | 0.104332 | − | 0.994543i | \(-0.466730\pi\) | ||||
0.104332 | + | 0.994543i | \(0.466730\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.6949 | 1.45194 | 0.725968 | − | 0.687728i | \(-0.241392\pi\) | ||||
0.725968 | + | 0.687728i | \(0.241392\pi\) | |||||||
\(572\) | −16.6421 | + | 16.6421i | −0.695842 | + | 0.695842i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.6798i | 0.445767i | ||||||||
\(575\) | 22.9926 | + | 20.1226i | 0.958860 | + | 0.839169i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.5782 | + | 32.5782i | 1.35625 | + | 1.35625i | 0.878495 | + | 0.477751i | \(0.158548\pi\) |
0.477751 | + | 0.878495i | \(0.341452\pi\) | |||||||
\(578\) | 1.18199 | + | 1.18199i | 0.0491642 | + | 0.0491642i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.740217 | − | 22.2641i | −0.0307358 | − | 0.924466i | ||||
\(581\) | 8.78249i | 0.364359i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 52.0447 | − | 52.0447i | 2.15547 | − | 2.15547i | ||||
\(584\) | 14.4476 | 0.597845 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.62778 | −0.315101 | ||||||||
\(587\) | 18.4320 | − | 18.4320i | 0.760769 | − | 0.760769i | −0.215693 | − | 0.976461i | \(-0.569201\pi\) |
0.976461 | + | 0.215693i | \(0.0692009\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −4.77511 | + | 5.10355i | −0.196588 | + | 0.210110i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.93351 | + | 2.93351i | 0.120566 | + | 0.120566i | ||||
\(593\) | 22.1213 | + | 22.1213i | 0.908413 | + | 0.908413i | 0.996144 | − | 0.0877310i | \(-0.0279616\pi\) |
−0.0877310 | + | 0.996144i | \(0.527962\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.65685 | + | 0.321063i | −0.395892 | + | 0.0131623i | ||||
\(596\) | − | 6.08541i | − | 0.249268i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 19.3137 | − | 19.3137i | 0.789796 | − | 0.789796i | ||||
\(599\) | −17.6906 | −0.722818 | −0.361409 | − | 0.932407i | \(-0.617704\pi\) | ||||
−0.361409 | + | 0.932407i | \(0.617704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.6979 | 0.762705 | 0.381353 | − | 0.924430i | \(-0.375458\pi\) | ||||
0.381353 | + | 0.924430i | \(0.375458\pi\) | |||||||
\(602\) | 0.597714 | − | 0.597714i | 0.0243610 | − | 0.0243610i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 22.7530i | − | 0.925808i | ||||||
\(605\) | −37.3813 | + | 1.24282i | −1.51976 | + | 0.0505278i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.23654 | + | 5.23654i | 0.212545 | + | 0.212545i | 0.805348 | − | 0.592803i | \(-0.201979\pi\) |
−0.592803 | + | 0.805348i | \(0.701979\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.66790 | + | 4.98896i | −0.188998 | + | 0.201997i | ||||
\(611\) | − | 21.6569i | − | 0.876143i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.4426 | − | 21.4426i | 0.866060 | − | 0.866060i | −0.125973 | − | 0.992034i | \(-0.540205\pi\) |
0.992034 | + | 0.125973i | \(0.0402054\pi\) | |||||||
\(614\) | 2.07717 | 0.0838277 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.26561 | 0.212157 | ||||||||
\(617\) | 2.18109 | − | 2.18109i | 0.0878073 | − | 0.0878073i | −0.661839 | − | 0.749646i | \(-0.730224\pi\) |
0.749646 | + | 0.661839i | \(0.230224\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.7573i | 0.794114i | 0.917794 | + | 0.397057i | \(0.129969\pi\) | ||||
−0.917794 | + | 0.397057i | \(0.870031\pi\) | |||||||
\(620\) | −0.0940371 | − | 2.82843i | −0.00377662 | − | 0.113592i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.9077 | + | 21.9077i | 0.878420 | + | 0.878420i | ||||
\(623\) | 2.55913 | + | 2.55913i | 0.102529 | + | 0.102529i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7794 | − | 3.31371i | 0.991177 | − | 0.132548i | ||||
\(626\) | 9.54199i | 0.381375i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.7181 | + | 10.7181i | −0.427700 | + | 0.427700i | ||||
\(629\) | −17.9264 | −0.714771 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.15507 | 0.0857920 | 0.0428960 | − | 0.999080i | \(-0.486342\pi\) | ||||
0.0428960 | + | 0.999080i | \(0.486342\pi\) | |||||||
\(632\) | −2.53122 | + | 2.53122i | −0.100687 | + | 0.100687i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28.8713i | 1.14663i | ||||||||
\(635\) | −19.2145 | − | 17.9779i | −0.762502 | − | 0.713432i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.16053 | − | 3.16053i | −0.125225 | − | 0.125225i | ||||
\(638\) | −37.0931 | − | 37.0931i | −1.46853 | − | 1.46853i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.63280 | − | 1.52773i | −0.0645423 | − | 0.0603887i | ||||
\(641\) | 39.5147i | 1.56074i | 0.625320 | + | 0.780368i | \(0.284968\pi\) | ||||
−0.625320 | + | 0.780368i | \(0.715032\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.61574 | − | 9.61574i | 0.379208 | − | 0.379208i | −0.491608 | − | 0.870816i | \(-0.663591\pi\) |
0.870816 | + | 0.491608i | \(0.163591\pi\) | |||||||
\(644\) | −6.11091 | −0.240803 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.6510 | + | 14.6510i | −0.575991 | + | 0.575991i | −0.933796 | − | 0.357805i | \(-0.883525\pi\) |
0.357805 | + | 0.933796i | \(0.383525\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.4584i | 0.646048i | ||||||||
\(650\) | −1.48440 | − | 22.2990i | −0.0582228 | − | 0.874638i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.04441 | + | 4.04441i | 0.158391 | + | 0.158391i | ||||
\(653\) | −32.0836 | − | 32.0836i | −1.25553 | − | 1.25553i | −0.953206 | − | 0.302323i | \(-0.902238\pi\) |
−0.302323 | − | 0.953206i | \(-0.597762\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.29468 | − | 38.9411i | −0.0505873 | − | 1.52155i | ||||
\(656\) | − | 10.6798i | − | 0.416977i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.42614 | + | 3.42614i | −0.133565 | + | 0.133565i | ||||
\(659\) | −38.5499 | −1.50169 | −0.750845 | − | 0.660479i | \(-0.770353\pi\) | ||||
−0.750845 | + | 0.660479i | \(0.770353\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.4176 | −1.53317 | −0.766584 | − | 0.642144i | \(-0.778045\pi\) | ||||
−0.766584 | + | 0.642144i | \(0.778045\pi\) | |||||||
\(662\) | 12.9056 | − | 12.9056i | 0.501590 | − | 0.501590i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 8.78249i | − | 0.340827i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 43.0477 | + | 43.0477i | 1.66681 | + | 1.66681i | ||||
\(668\) | −5.76929 | − | 5.76929i | −0.223220 | − | 0.223220i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.5312 | + | 0.483121i | −0.561390 | + | 0.0186646i | ||||
\(671\) | 16.0888i | 0.621102i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.3431 | + | 13.3431i | −0.514340 | + | 0.514340i | −0.915853 | − | 0.401513i | \(-0.868484\pi\) |
0.401513 | + | 0.915853i | \(0.368484\pi\) | |||||||
\(674\) | 10.1967 | 0.392762 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.97792 | −0.268381 | ||||||||
\(677\) | −18.1024 | + | 18.1024i | −0.695731 | + | 0.695731i | −0.963487 | − | 0.267755i | \(-0.913718\pi\) |
0.267755 | + | 0.963487i | \(0.413718\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.55672i | 0.251624i | ||||||||
\(680\) | 9.65685 | − | 0.321063i | 0.370323 | − | 0.0123122i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.71231 | − | 4.71231i | −0.180444 | − | 0.180444i | ||||
\(683\) | −27.4077 | − | 27.4077i | −1.04873 | − | 1.04873i | −0.998750 | − | 0.0499779i | \(-0.984085\pi\) |
−0.0499779 | − | 0.998750i | \(-0.515915\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.09618 | − | 5.44670i | 0.194715 | − | 0.208108i | ||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.597714 | + | 0.597714i | −0.0227876 | + | 0.0227876i | ||||
\(689\) | 62.4766 | 2.38017 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.9221 | −0.491579 | −0.245789 | − | 0.969323i | \(-0.579047\pi\) | ||||
−0.245789 | + | 0.969323i | \(0.579047\pi\) | |||||||
\(692\) | −6.14492 | + | 6.14492i | −0.233595 | + | 0.233595i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.3137i | 0.581300i | ||||||||
\(695\) | −1.62312 | − | 48.8198i | −0.0615684 | − | 1.85184i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.6317 | + | 32.6317i | 1.23601 | + | 1.23601i | ||||
\(698\) | −11.3560 | − | 11.3560i | −0.429829 | − | 0.429829i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.29289 | + | 3.76256i | −0.124460 | + | 0.142211i | ||||
\(701\) | 13.5732i | 0.512653i | 0.966590 | + | 0.256327i | \(0.0825123\pi\) | ||||
−0.966590 | + | 0.256327i | \(0.917488\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −5.26561 | −0.198455 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.1036 | −0.493159 | ||||||||
\(707\) | −1.50368 | + | 1.50368i | −0.0565516 | + | 0.0565516i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.4429i | 1.51886i | 0.650586 | + | 0.759432i | \(0.274523\pi\) | ||||
−0.650586 | + | 0.759432i | \(0.725477\pi\) | |||||||
\(710\) | −15.0815 | − | 14.1109i | −0.565997 | − | 0.529573i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.55913 | − | 2.55913i | −0.0959074 | − | 0.0959074i | ||||
\(713\) | 5.46878 | + | 5.46878i | 0.204807 | + | 0.204807i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −38.4289 | − | 35.9558i | −1.43716 | − | 1.34467i | ||||
\(716\) | − | 0.391244i | − | 0.0146215i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.20280 | − | 5.20280i | 0.194167 | − | 0.194167i | ||||
\(719\) | −16.9706 | −0.632895 | −0.316448 | − | 0.948610i | \(-0.602490\pi\) | ||||
−0.316448 | + | 0.948610i | \(0.602490\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.4467 | 0.575265 | ||||||||
\(722\) | −13.4350 | + | 13.4350i | −0.500000 | + | 0.500000i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.0113i | 0.557890i | ||||||||
\(725\) | 49.7015 | − | 3.30852i | 1.84587 | − | 0.122875i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.8787 | − | 29.8787i | −1.10814 | − | 1.10814i | −0.993395 | − | 0.114743i | \(-0.963395\pi\) |
−0.114743 | − | 0.993395i | \(-0.536605\pi\) | |||||||
\(728\) | 3.16053 | + | 3.16053i | 0.117137 | + | 0.117137i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.07348 | + | 32.2879i | 0.0397313 | + | 1.19503i | ||||
\(731\) | − | 3.65258i | − | 0.135095i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.55913 | + | 8.55913i | −0.316139 | + | 0.316139i | −0.847282 | − | 0.531143i | \(-0.821763\pi\) |
0.531143 | + | 0.847282i | \(0.321763\pi\) | |||||||
\(734\) | −32.7309 | −1.20812 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.11091 | 0.225251 | ||||||||
\(737\) | −24.2098 | + | 24.2098i | −0.891778 | + | 0.891778i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 35.3584i | − | 1.30068i | −0.759644 | − | 0.650339i | \(-0.774627\pi\) | ||
0.759644 | − | 0.650339i | \(-0.225373\pi\) | |||||||
\(740\) | −6.33793 | + | 6.77386i | −0.232987 | + | 0.249012i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.88388 | − | 9.88388i | −0.362849 | − | 0.362849i | ||||
\(743\) | 35.1733 | + | 35.1733i | 1.29038 | + | 1.29038i | 0.934548 | + | 0.355837i | \(0.115804\pi\) |
0.355837 | + | 0.934548i | \(0.384196\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5999 | − | 0.452157i | 0.498261 | − | 0.0165657i | ||||
\(746\) | 0.114867i | 0.00420557i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.0888 | − | 16.0888i | 0.588266 | − | 0.588266i | ||||
\(749\) | 9.06244 | 0.331134 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.2358 | 0.592452 | 0.296226 | − | 0.955118i | \(-0.404272\pi\) | ||||
0.296226 | + | 0.955118i | \(0.404272\pi\) | |||||||
\(752\) | 3.42614 | − | 3.42614i | 0.124939 | − | 0.124939i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 44.5282i | − | 1.62162i | ||||||
\(755\) | 50.8492 | − | 1.69059i | 1.85059 | − | 0.0615269i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.76016 | − | 1.76016i | −0.0639741 | − | 0.0639741i | 0.674396 | − | 0.738370i | \(-0.264404\pi\) |
−0.738370 | + | 0.674396i | \(0.764404\pi\) | |||||||
\(758\) | −8.73616 | − | 8.73616i | −0.317312 | − | 0.317312i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.0125i | 1.05170i | 0.850576 | + | 0.525852i | \(0.176253\pi\) | ||||
−0.850576 | + | 0.525852i | \(0.823747\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.75825 | + | 6.75825i | −0.244665 | + | 0.244665i | ||||
\(764\) | 23.3474 | 0.844681 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.6235 | −0.600631 | ||||||||
\(767\) | −9.87867 | + | 9.87867i | −0.356698 | + | 0.356698i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.2439i | 1.05456i | 0.849691 | + | 0.527281i | \(0.176789\pi\) | ||||
−0.849691 | + | 0.527281i | \(0.823211\pi\) | |||||||
\(770\) | 0.391244 | + | 11.7678i | 0.0140995 | + | 0.424081i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.69059 | − | 6.69059i | −0.240800 | − | 0.240800i | ||||
\(773\) | 8.95467 | + | 8.95467i | 0.322077 | + | 0.322077i | 0.849564 | − | 0.527486i | \(-0.176865\pi\) |
−0.527486 | + | 0.849564i | \(0.676865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.31408 | − | 0.420314i | 0.226808 | − | 0.0150981i | ||||
\(776\) | − | 6.55672i | − | 0.235372i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.12893 | − | 8.12893i | 0.291436 | − | 0.291436i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48.6360 | −1.74033 | ||||||||
\(782\) | −18.6716 | + | 18.6716i | −0.667694 | + | 0.667694i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | −24.7496 | − | 23.1569i | −0.883352 | − | 0.826504i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.9264 | − | 29.9264i | −1.06676 | − | 1.06676i | −0.997606 | − | 0.0691541i | \(-0.977970\pi\) |
−0.0691541 | − | 0.997606i | \(-0.522030\pi\) | |||||||
\(788\) | 0.375629 | + | 0.375629i | 0.0133812 | + | 0.0133812i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.84493 | − | 5.46878i | −0.207953 | − | 0.194570i | ||||
\(791\) | − | 4.66421i | − | 0.165840i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.65685 | + | 9.65685i | −0.342925 | + | 0.342925i | ||||
\(794\) | 15.8991 | 0.564238 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.0481 | −0.639698 | ||||||||
\(797\) | −7.21473 | + | 7.21473i | −0.255559 | + | 0.255559i | −0.823245 | − | 0.567686i | \(-0.807839\pi\) |
0.567686 | + | 0.823245i | \(0.307839\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.9368i | 0.740692i | ||||||||
\(800\) | 3.29289 | − | 3.76256i | 0.116421 | − | 0.133027i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.8787 | − | 20.8787i | −0.737251 | − | 0.737251i | ||||
\(803\) | 53.7934 | + | 53.7934i | 1.89833 | + | 1.89833i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.454051 | − | 13.6569i | −0.0160032 | − | 0.481341i | ||||
\(806\) | − | 5.65685i | − | 0.199254i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.50368 | − | 1.50368i | 0.0528992 | − | 0.0528992i | ||||
\(809\) | 33.5606 | 1.17993 | 0.589964 | − | 0.807429i | \(-0.299142\pi\) | ||||
0.589964 | + | 0.807429i | \(0.299142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.7236 | 1.57046 | 0.785229 | − | 0.619206i | \(-0.212545\pi\) | ||||
0.785229 | + | 0.619206i | \(0.212545\pi\) | |||||||
\(812\) | −7.04441 | + | 7.04441i | −0.247210 | + | 0.247210i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21.8449i | 0.765664i | ||||||||
\(815\) | −8.73808 | + | 9.33909i | −0.306081 | + | 0.327134i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 18.5910 | + | 18.5910i | 0.650018 | + | 0.650018i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.8676 | − | 0.793530i | 0.833494 | − | 0.0277113i | ||||
\(821\) | − | 47.8955i | − | 1.67156i | −0.549061 | − | 0.835782i | \(-0.685015\pi\) | ||
0.549061 | − | 0.835782i | \(-0.314985\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.8926 | + | 37.8926i | −1.32085 | + | 1.32085i | −0.407769 | + | 0.913085i | \(0.633693\pi\) |
−0.913085 | + | 0.407769i | \(0.866307\pi\) | |||||||
\(824\) | −15.4467 | −0.538111 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.12563 | 0.108755 | ||||||||
\(827\) | 13.7405 | − | 13.7405i | 0.477803 | − | 0.477803i | −0.426626 | − | 0.904428i | \(-0.640298\pi\) |
0.904428 | + | 0.426626i | \(0.140298\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 12.9445i | − | 0.449583i | −0.974407 | − | 0.224791i | \(-0.927830\pi\) | ||
0.974407 | − | 0.224791i | \(-0.0721701\pi\) | |||||||
\(830\) | 19.6274 | − | 0.652555i | 0.681277 | − | 0.0226505i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.16053 | − | 3.16053i | −0.109572 | − | 0.109572i | ||||
\(833\) | 3.05545 | + | 3.05545i | 0.105865 | + | 0.105865i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.4647 | − | 13.3221i | 0.431360 | − | 0.461029i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.5650 | + | 14.5650i | −0.503138 | + | 0.503138i | ||||
\(839\) | 6.27763 | 0.216728 | 0.108364 | − | 0.994111i | \(-0.465439\pi\) | ||||
0.108364 | + | 0.994111i | \(0.465439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 70.2475 | 2.42233 | ||||||||
\(842\) | 1.22614 | − | 1.22614i | 0.0422556 | − | 0.0422556i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.22181i | 0.283006i | ||||||||
\(845\) | −0.518472 | − | 15.5945i | −0.0178360 | − | 0.536466i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.8275 | + | 11.8275i | 0.406399 | + | 0.406399i | ||||
\(848\) | 9.88388 | + | 9.88388i | 0.339414 | + | 0.339414i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.43504 | + | 21.5576i | 0.0492216 | + | 0.739420i | ||||
\(851\) | − | 25.3517i | − | 0.869046i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.2350 | − | 16.2350i | 0.555876 | − | 0.555876i | −0.372254 | − | 0.928131i | \(-0.621415\pi\) |
0.928131 | + | 0.372254i | \(0.121415\pi\) | |||||||
\(854\) | 3.05545 | 0.104555 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.06244 | −0.309748 | ||||||||
\(857\) | −33.9488 | + | 33.9488i | −1.15967 | + | 1.15967i | −0.175124 | + | 0.984546i | \(0.556033\pi\) |
−0.984546 | + | 0.175124i | \(0.943967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.2444i | 1.71432i | 0.515053 | + | 0.857158i | \(0.327772\pi\) | ||||
−0.515053 | + | 0.857158i | \(0.672228\pi\) | |||||||
\(860\) | −1.38020 | − | 1.29138i | −0.0470645 | − | 0.0440357i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.20280 | + | 1.20280i | 0.0409676 | + | 0.0409676i | ||||
\(863\) | 7.09190 | + | 7.09190i | 0.241411 | + | 0.241411i | 0.817434 | − | 0.576023i | \(-0.195396\pi\) |
−0.576023 | + | 0.817434i | \(0.695396\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.1894 | − | 13.2763i | −0.482455 | − | 0.451407i | ||||
\(866\) | 4.08364i | 0.138768i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.894921 | + | 0.894921i | −0.0303756 | + | 0.0303756i | ||||
\(869\) | −18.8492 | −0.639416 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.0624 | −0.984743 | ||||||||
\(872\) | 6.75825 | − | 6.75825i | 0.228863 | − | 0.228863i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.65336 | − | 7.07950i | −0.292537 | − | 0.239331i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.0150 | + | 29.0150i | 0.979765 | + | 0.979765i | 0.999799 | − | 0.0200339i | \(-0.00637743\pi\) |
−0.0200339 | + | 0.999799i | \(0.506377\pi\) | |||||||
\(878\) | 23.1939 | + | 23.1939i | 0.782756 | + | 0.782756i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.391244 | − | 11.7678i | −0.0131888 | − | 0.396691i | ||||
\(881\) | − | 15.5887i | − | 0.525197i | −0.964905 | − | 0.262598i | \(-0.915421\pi\) | ||
0.964905 | − | 0.262598i | \(-0.0845794\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.8048 | − | 22.8048i | 0.767443 | − | 0.767443i | −0.210213 | − | 0.977656i | \(-0.567416\pi\) |
0.977656 | + | 0.210213i | \(0.0674156\pi\) | |||||||
\(884\) | 19.3137 | 0.649590 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.3761 | −0.953315 | ||||||||
\(887\) | 16.2013 | − | 16.2013i | 0.543985 | − | 0.543985i | −0.380710 | − | 0.924695i | \(-0.624320\pi\) |
0.924695 | + | 0.380710i | \(0.124320\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.7678i | 0.394678i | ||||||||
\(890\) | 5.52908 | − | 5.90938i | 0.185335 | − | 0.198083i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.2365 | + | 13.2365i | 0.443192 | + | 0.443192i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.874366 | − | 0.0290702i | 0.0292268 | − | 0.000971708i | ||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.46878 | − | 8.46878i | 0.282607 | − | 0.282607i | ||||
\(899\) | 12.6084 | 0.420513 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −60.3995 | −2.01220 | ||||||||
\(902\) | 39.7647 | − | 39.7647i | 1.32402 | − | 1.32402i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.66421i | 0.155129i | ||||||||
\(905\) | −33.5477 | + | 1.11537i | −1.11516 | + | 0.0370760i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.9114 | − | 19.9114i | −0.661148 | − | 0.661148i | 0.294503 | − | 0.955651i | \(-0.404846\pi\) |
−0.955651 | + | 0.294503i | \(0.904846\pi\) | |||||||
\(908\) | −5.46878 | − | 5.46878i | −0.181488 | − | 0.181488i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.82843 | + | 7.29809i | −0.226360 | + | 0.241929i | ||||
\(911\) | 28.4723i | 0.943331i | 0.881778 | + | 0.471665i | \(0.156347\pi\) | ||||
−0.881778 | + | 0.471665i | \(0.843653\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.7003 | − | 32.7003i | 1.08222 | − | 1.08222i | ||||
\(914\) | −9.14824 | −0.302597 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.0966 | −0.432723 | ||||||||
\(917\) | −12.3211 | + | 12.3211i | −0.406877 | + | 0.406877i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 57.2261i | − | 1.88772i | −0.330353 | − | 0.943858i | \(-0.607168\pi\) | ||
0.330353 | − | 0.943858i | \(-0.392832\pi\) | |||||||
\(920\) | 0.454051 | + | 13.6569i | 0.0149696 | + | 0.450253i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 26.2276 | + | 26.2276i | 0.863761 | + | 0.863761i | ||||
\(923\) | −29.1924 | − | 29.1924i | −0.960879 | − | 0.960879i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.6094 | − | 13.6609i | −0.513233 | − | 0.449168i | ||||
\(926\) | − | 0.328437i | − | 0.0107931i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.04441 | − | 7.04441i | 0.231244 | − | 0.231244i | ||||
\(929\) | 28.6166 | 0.938881 | 0.469441 | − | 0.882964i | \(-0.344456\pi\) | ||||
0.469441 | + | 0.882964i | \(0.344456\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.642125 | − | 0.642125i | 0.0210335 | − | 0.0210335i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 31.3952i | − | 1.02728i | ||||||
\(935\) | 37.1513 | + | 34.7604i | 1.21498 | + | 1.13679i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.09342 | − | 4.09342i | −0.133726 | − | 0.133726i | 0.637075 | − | 0.770802i | \(-0.280144\pi\) |
−0.770802 | + | 0.637075i | \(0.780144\pi\) | |||||||
\(938\) | 4.59771 | + | 4.59771i | 0.150121 | + | 0.150121i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.91142 | + | 7.40229i | 0.258042 | + | 0.241436i | ||||
\(941\) | 18.7890i | 0.612502i | 0.951951 | + | 0.306251i | \(0.0990748\pi\) | ||||
−0.951951 | + | 0.306251i | \(0.900925\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −46.1482 | + | 46.1482i | −1.50279 | + | 1.50279i | ||||
\(944\) | −3.12563 | −0.101731 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.45100 | −0.144714 | ||||||||
\(947\) | 22.6009 | − | 22.6009i | 0.734429 | − | 0.734429i | −0.237065 | − | 0.971494i | \(-0.576185\pi\) |
0.971494 | + | 0.237065i | \(0.0761854\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 64.5759i | 2.09622i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.05545 | − | 3.05545i | −0.0990278 | − | 0.0990278i | ||||
\(953\) | 29.8241 | + | 29.8241i | 0.966097 | + | 0.966097i | 0.999444 | − | 0.0333465i | \(-0.0106165\pi\) |
−0.0333465 | + | 0.999444i | \(0.510616\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.73476 | + | 52.1776i | 0.0561354 | + | 1.68843i | ||||
\(956\) | 25.4246i | 0.822291i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.6902 | − | 14.6902i | 0.474620 | − | 0.474620i | ||||
\(959\) | −3.33579 | −0.107718 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3982 | −0.948330 | ||||||||
\(962\) | −13.1118 | + | 13.1118i | −0.422741 | + | 0.422741i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.46878i | 0.240553i | ||||||||
\(965\) | 14.4552 | − | 15.4495i | 0.465330 | − | 0.497336i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.4975 | + | 10.4975i | 0.337576 | + | 0.337576i | 0.855454 | − | 0.517878i | \(-0.173278\pi\) |
−0.517878 | + | 0.855454i | \(0.673278\pi\) | |||||||
\(968\) | −11.8275 | − | 11.8275i | −0.380151 | − | 0.380151i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.6532 | − | 0.487176i | 0.470485 | − | 0.0156423i | ||||
\(971\) | − | 15.3579i | − | 0.492858i | −0.969161 | − | 0.246429i | \(-0.920743\pi\) | ||
0.969161 | − | 0.246429i | \(-0.0792572\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.4467 | + | 15.4467i | −0.495198 | + | 0.495198i | ||||
\(974\) | 1.42461 | 0.0456476 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.05545 | −0.0978027 | ||||||||
\(977\) | −15.5459 | + | 15.5459i | −0.497359 | + | 0.497359i | −0.910615 | − | 0.413256i | \(-0.864391\pi\) |
0.413256 | + | 0.910615i | \(0.364391\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 19.0571i | − | 0.609066i | ||||||
\(980\) | 2.23483 | − | 0.0743018i | 0.0713891 | − | 0.00237348i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.91878 | + | 4.91878i | 0.156964 | + | 0.156964i | ||||
\(983\) | 42.6546 | + | 42.6546i | 1.36047 | + | 1.36047i | 0.873317 | + | 0.487153i | \(0.161965\pi\) |
0.487153 | + | 0.873317i | \(0.338035\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.811559 | + | 0.867379i | −0.0258584 | + | 0.0276370i | ||||
\(986\) | 43.0477i | 1.37092i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.16552 | 0.164254 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.98099 | 0.285291 | 0.142645 | − | 0.989774i | \(-0.454439\pi\) | ||||
0.142645 | + | 0.989774i | \(0.454439\pi\) | |||||||
\(992\) | 0.894921 | − | 0.894921i | 0.0284138 | − | 0.0284138i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.23654i | 0.292965i | ||||||||
\(995\) | −1.34101 | − | 40.3345i | −0.0425128 | − | 1.27869i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.7038 | − | 25.7038i | −0.814047 | − | 0.814047i | 0.171191 | − | 0.985238i | \(-0.445239\pi\) |
−0.985238 | + | 0.171191i | \(0.945239\pi\) | |||||||
\(998\) | 14.8471 | + | 14.8471i | 0.469976 | + | 0.469976i | ||||
\(999\) | 0 | 0 |
(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 | 630.2.m.d.197.2 | yes | 8 | |
3.2 | odd | 2 | 630.2.m.c.197.3 | ✓ | 8 | ||
5.2 | odd | 4 | 3150.2.m.i.2843.2 | 8 | |||
5.3 | odd | 4 | 630.2.m.c.323.3 | yes | 8 | ||
5.4 | even | 2 | 3150.2.m.j.1457.4 | 8 | |||
15.2 | even | 4 | 3150.2.m.j.2843.3 | 8 | |||
15.8 | even | 4 | inner | 630.2.m.d.323.2 | yes | 8 | |
15.14 | odd | 2 | 3150.2.m.i.1457.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.m.c.197.3 | ✓ | 8 | 3.2 | odd | 2 | ||
630.2.m.c.323.3 | yes | 8 | 5.3 | odd | 4 | ||
630.2.m.d.197.2 | yes | 8 | 1.1 | even | 1 | trivial | |
630.2.m.d.323.2 | yes | 8 | 15.8 | even | 4 | inner | |
3150.2.m.i.1457.1 | 8 | 15.14 | odd | 2 | |||
3150.2.m.i.2843.2 | 8 | 5.2 | odd | 4 | |||
3150.2.m.j.1457.4 | 8 | 5.4 | even | 2 | |||
3150.2.m.j.2843.3 | 8 | 15.2 | even | 4 |