Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [725,2,Mod(157,725)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(725, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("725.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 725 = 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 725.e (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: | \(5.78915414654\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 3x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 157.1 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 725.157 |
Dual form | 725.2.e.a.568.2 |
$q$-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 \(\left(\mathbb{Z}/725\mathbb{Z}\right)^\times\).
\(n\) | \(176\) | \(552\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.23607i | − | 1.58114i | −0.612372 | − | 0.790569i | \(-0.709785\pi\) | ||
0.612372 | − | 0.790569i | \(-0.290215\pi\) | |||||||
\(3\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | −3.00000 | −1.50000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.23607 | + | 2.23607i | 0.845154 | + | 0.845154i | 0.989524 | − | 0.144370i | \(-0.0461154\pi\) |
−0.144370 | + | 0.989524i | \(0.546115\pi\) | |||||||
\(8\) | 2.23607i | 0.790569i | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | + | 4.00000i | 1.20605 | + | 1.20605i | 0.972297 | + | 0.233748i | \(0.0750991\pi\) |
0.233748 | + | 0.972297i | \(0.424901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214 | + | 4.47214i | 1.24035 | + | 1.24035i | 0.959857 | + | 0.280491i | \(0.0904971\pi\) |
0.280491 | + | 0.959857i | \(0.409503\pi\) | |||||||
\(14\) | 5.00000 | − | 5.00000i | 1.33631 | − | 1.33631i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.47214i | 1.08465i | 0.840168 | + | 0.542326i | \(0.182456\pi\) | ||||
−0.840168 | + | 0.542326i | \(0.817544\pi\) | |||||||
\(18\) | 6.70820i | 1.58114i | ||||||||
\(19\) | −2.00000 | + | 2.00000i | −0.458831 | + | 0.458831i | −0.898272 | − | 0.439440i | \(-0.855177\pi\) |
0.439440 | + | 0.898272i | \(0.355177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.94427 | − | 8.94427i | 1.90693 | − | 1.90693i | ||||
\(23\) | −2.23607 | + | 2.23607i | −0.466252 | + | 0.466252i | −0.900698 | − | 0.434446i | \(-0.856944\pi\) |
0.434446 | + | 0.900698i | \(0.356944\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 10.0000 | − | 10.0000i | 1.96116 | − | 1.96116i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.70820 | − | 6.70820i | −1.26773 | − | 1.26773i | ||||
\(29\) | 2.00000 | − | 5.00000i | 0.371391 | − | 0.928477i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | − | 4.00000i | −0.718421 | − | 0.718421i | 0.249861 | − | 0.968282i | \(-0.419615\pi\) |
−0.968282 | + | 0.249861i | \(0.919615\pi\) | |||||||
\(32\) | 6.70820i | 1.18585i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.0000 | 1.71499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.00000 | 1.50000 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | 4.47214 | + | 4.47214i | 0.725476 | + | 0.725476i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | − | 1.00000i | 0.156174 | − | 0.156174i | −0.624695 | − | 0.780869i | \(-0.714777\pi\) |
0.780869 | + | 0.624695i | \(0.214777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.47214 | 0.681994 | 0.340997 | − | 0.940064i | \(-0.389235\pi\) | ||||
0.340997 | + | 0.940064i | \(0.389235\pi\) | |||||||
\(44\) | −12.0000 | − | 12.0000i | −1.80907 | − | 1.80907i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.00000 | + | 5.00000i | 0.737210 | + | 0.737210i | ||||
\(47\) | 4.47214 | 0.652328 | 0.326164 | − | 0.945313i | \(-0.394244\pi\) | ||||
0.326164 | + | 0.945313i | \(0.394244\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000i | 0.428571i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.4164 | − | 13.4164i | −1.86052 | − | 1.86052i | ||||
\(53\) | 8.94427 | − | 8.94427i | 1.22859 | − | 1.22859i | 0.264093 | − | 0.964497i | \(-0.414927\pi\) |
0.964497 | − | 0.264093i | \(-0.0850726\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.00000 | + | 5.00000i | −0.668153 | + | 0.668153i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.1803 | − | 4.47214i | −1.46805 | − | 0.587220i | ||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.00000 | − | 9.00000i | −1.15233 | − | 1.15233i | −0.986084 | − | 0.166248i | \(-0.946835\pi\) |
−0.166248 | − | 0.986084i | \(-0.553165\pi\) | |||||||
\(62\) | −8.94427 | + | 8.94427i | −1.13592 | + | 1.13592i | ||||
\(63\) | −6.70820 | − | 6.70820i | −0.845154 | − | 0.845154i | ||||
\(64\) | 13.0000 | 1.62500 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.23607 | + | 2.23607i | −0.273179 | + | 0.273179i | −0.830379 | − | 0.557199i | \(-0.811876\pi\) |
0.557199 | + | 0.830379i | \(0.311876\pi\) | |||||||
\(68\) | − | 13.4164i | − | 1.62698i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000i | 1.42414i | 0.702109 | + | 0.712069i | \(0.252242\pi\) | ||||
−0.702109 | + | 0.712069i | \(0.747758\pi\) | |||||||
\(72\) | − | 6.70820i | − | 0.790569i | ||||||
\(73\) | − | 4.47214i | − | 0.523424i | −0.965146 | − | 0.261712i | \(-0.915713\pi\) | ||
0.965146 | − | 0.261712i | \(-0.0842870\pi\) | |||||||
\(74\) | 10.0000i | 1.16248i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000 | − | 6.00000i | 0.688247 | − | 0.688247i | ||||
\(77\) | 17.8885i | 2.03859i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.00000 | + | 2.00000i | −0.225018 | + | 0.225018i | −0.810607 | − | 0.585590i | \(-0.800863\pi\) |
0.585590 | + | 0.810607i | \(0.300863\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | −2.23607 | − | 2.23607i | −0.246932 | − | 0.246932i | ||||
\(83\) | 6.70820 | − | 6.70820i | 0.736321 | − | 0.736321i | −0.235543 | − | 0.971864i | \(-0.575687\pi\) |
0.971864 | + | 0.235543i | \(0.0756868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 10.0000i | − | 1.07833i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.94427 | + | 8.94427i | −0.953463 | + | 0.953463i | ||||
\(89\) | −7.00000 | + | 7.00000i | −0.741999 | + | 0.741999i | −0.972962 | − | 0.230964i | \(-0.925812\pi\) |
0.230964 | + | 0.972962i | \(0.425812\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.0000i | 2.09657i | ||||||||
\(92\) | 6.70820 | − | 6.70820i | 0.699379 | − | 0.699379i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 10.0000i | − | 1.03142i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.47214 | 0.454077 | 0.227038 | − | 0.973886i | \(-0.427096\pi\) | ||||
0.227038 | + | 0.973886i | \(0.427096\pi\) | |||||||
\(98\) | 6.70820 | 0.677631 | ||||||||
\(99\) | −12.0000 | − | 12.0000i | −1.20605 | − | 1.20605i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00000 | − | 1.00000i | −0.0995037 | − | 0.0995037i | 0.655602 | − | 0.755106i | \(-0.272415\pi\) |
−0.755106 | + | 0.655602i | \(0.772415\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.70820 | + | 6.70820i | −0.660979 | + | 0.660979i | −0.955611 | − | 0.294632i | \(-0.904803\pi\) |
0.294632 | + | 0.955611i | \(0.404803\pi\) | |||||||
\(104\) | −10.0000 | + | 10.0000i | −0.980581 | + | 0.980581i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.0000 | − | 20.0000i | −1.94257 | − | 1.94257i | ||||
\(107\) | 6.70820 | + | 6.70820i | 0.648507 | + | 0.648507i | 0.952632 | − | 0.304125i | \(-0.0983642\pi\) |
−0.304125 | + | 0.952632i | \(0.598364\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.23607 | − | 2.23607i | −0.211289 | − | 0.211289i | ||||
\(113\) | − | 4.47214i | − | 0.420703i | −0.977626 | − | 0.210352i | \(-0.932539\pi\) | ||
0.977626 | − | 0.210352i | \(-0.0674609\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.00000 | + | 15.0000i | −0.557086 | + | 1.39272i | ||||
\(117\) | −13.4164 | − | 13.4164i | −1.24035 | − | 1.24035i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.0000 | + | 10.0000i | −0.916698 | + | 0.916698i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.0000i | 1.90909i | ||||||||
\(122\) | −20.1246 | + | 20.1246i | −1.82200 | + | 1.82200i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.0000 | + | 12.0000i | 1.07763 | + | 1.07763i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −15.0000 | + | 15.0000i | −1.33631 | + | 1.33631i | ||||
\(127\) | 4.47214i | 0.396838i | 0.980117 | + | 0.198419i | \(0.0635807\pi\) | ||||
−0.980117 | + | 0.198419i | \(0.936419\pi\) | |||||||
\(128\) | − | 15.6525i | − | 1.38350i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.0000 | − | 14.0000i | 1.22319 | − | 1.22319i | 0.256693 | − | 0.966493i | \(-0.417367\pi\) |
0.966493 | − | 0.256693i | \(-0.0826328\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.94427 | −0.775567 | ||||||||
\(134\) | 5.00000 | + | 5.00000i | 0.431934 | + | 0.431934i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.0000 | −0.857493 | ||||||||
\(137\) | − | 13.4164i | − | 1.14624i | −0.819471 | − | 0.573121i | \(-0.805733\pi\) | ||
0.819471 | − | 0.573121i | \(-0.194267\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.00000i | − | 0.339276i | −0.985506 | − | 0.169638i | \(-0.945740\pi\) | ||
0.985506 | − | 0.169638i | \(-0.0542598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 26.8328 | 2.25176 | ||||||||
\(143\) | 35.7771i | 2.99183i | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.0000 | −0.827606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.4164 | 1.10282 | ||||||||
\(149\) | 20.0000 | 1.63846 | 0.819232 | − | 0.573462i | \(-0.194400\pi\) | ||||
0.819232 | + | 0.573462i | \(0.194400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.0000i | − | 0.976546i | −0.872691 | − | 0.488273i | \(-0.837627\pi\) | ||
0.872691 | − | 0.488273i | \(-0.162373\pi\) | |||||||
\(152\) | −4.47214 | − | 4.47214i | −0.362738 | − | 0.362738i | ||||
\(153\) | − | 13.4164i | − | 1.08465i | ||||||
\(154\) | 40.0000 | 3.22329 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4164 | 1.07075 | 0.535373 | − | 0.844616i | \(-0.320171\pi\) | ||||
0.535373 | + | 0.844616i | \(0.320171\pi\) | |||||||
\(158\) | 4.47214 | + | 4.47214i | 0.355784 | + | 0.355784i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.0000 | −0.788110 | ||||||||
\(162\) | − | 20.1246i | − | 1.58114i | ||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | −3.00000 | + | 3.00000i | −0.234261 | + | 0.234261i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.0000 | − | 15.0000i | −1.16423 | − | 1.16423i | ||||
\(167\) | 6.70820 | − | 6.70820i | 0.519096 | − | 0.519096i | −0.398202 | − | 0.917298i | \(-0.630366\pi\) |
0.917298 | + | 0.398202i | \(0.130366\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.0000i | 2.07692i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00000 | − | 6.00000i | 0.458831 | − | 0.458831i | ||||
\(172\) | −13.4164 | −1.02299 | ||||||||
\(173\) | 13.4164 | + | 13.4164i | 1.02003 | + | 1.02003i | 0.999795 | + | 0.0202354i | \(0.00644155\pi\) |
0.0202354 | + | 0.999795i | \(0.493558\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | − | 4.00000i | −0.301511 | − | 0.301511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.6525 | + | 15.6525i | 1.17320 | + | 1.17320i | ||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.0000 | −1.48659 | −0.743294 | − | 0.668965i | \(-0.766738\pi\) | ||||
−0.743294 | + | 0.668965i | \(0.766738\pi\) | |||||||
\(182\) | 44.7214 | 3.31497 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.00000 | − | 5.00000i | −0.368605 | − | 0.368605i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.8885 | + | 17.8885i | −1.30814 | + | 1.30814i | ||||
\(188\) | −13.4164 | −0.978492 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000 | + | 6.00000i | 0.434145 | + | 0.434145i | 0.890036 | − | 0.455891i | \(-0.150679\pi\) |
−0.455891 | + | 0.890036i | \(0.650679\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.47214 | −0.321911 | −0.160956 | − | 0.986962i | \(-0.551458\pi\) | ||||
−0.160956 | + | 0.986962i | \(0.551458\pi\) | |||||||
\(194\) | − | 10.0000i | − | 0.717958i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | − | 9.00000i | − | 0.642857i | ||||||
\(197\) | 13.4164 | + | 13.4164i | 0.955879 | + | 0.955879i | 0.999067 | − | 0.0431875i | \(-0.0137513\pi\) |
−0.0431875 | + | 0.999067i | \(0.513751\pi\) | |||||||
\(198\) | −26.8328 | + | 26.8328i | −1.90693 | + | 1.90693i | ||||
\(199\) | − | 20.0000i | − | 1.41776i | −0.705328 | − | 0.708881i | \(-0.749200\pi\) | ||
0.705328 | − | 0.708881i | \(-0.250800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.23607 | + | 2.23607i | −0.157329 | + | 0.157329i | ||||
\(203\) | 15.6525 | − | 6.70820i | 1.09859 | − | 0.470824i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.0000 | + | 15.0000i | 1.04510 | + | 1.04510i | ||||
\(207\) | 6.70820 | − | 6.70820i | 0.466252 | − | 0.466252i | ||||
\(208\) | −4.47214 | − | 4.47214i | −0.310087 | − | 0.310087i | ||||
\(209\) | −16.0000 | −1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | − | 16.0000i | 1.10149 | − | 1.10149i | 0.107254 | − | 0.994232i | \(-0.465794\pi\) |
0.994232 | − | 0.107254i | \(-0.0342057\pi\) | |||||||
\(212\) | −26.8328 | + | 26.8328i | −1.84289 | + | 1.84289i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.0000 | − | 15.0000i | 1.02538 | − | 1.02538i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 17.8885i | − | 1.21435i | ||||||
\(218\) | 22.3607i | 1.51446i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.0000 | + | 20.0000i | −1.34535 | + | 1.34535i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1803 | − | 11.1803i | 0.748691 | − | 0.748691i | −0.225542 | − | 0.974233i | \(-0.572415\pi\) |
0.974233 | + | 0.225542i | \(0.0724154\pi\) | |||||||
\(224\) | −15.0000 | + | 15.0000i | −1.00223 | + | 1.00223i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.0000 | −0.665190 | ||||||||
\(227\) | −6.70820 | − | 6.70820i | −0.445239 | − | 0.445239i | 0.448529 | − | 0.893768i | \(-0.351948\pi\) |
−0.893768 | + | 0.448529i | \(0.851948\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.00000 | − | 3.00000i | −0.198246 | − | 0.198246i | 0.601002 | − | 0.799248i | \(-0.294768\pi\) |
−0.799248 | + | 0.601002i | \(0.794768\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.1803 | + | 4.47214i | 0.734025 | + | 0.293610i | ||||
\(233\) | −8.94427 | + | 8.94427i | −0.585959 | + | 0.585959i | −0.936534 | − | 0.350576i | \(-0.885986\pi\) |
0.350576 | + | 0.936534i | \(0.385986\pi\) | |||||||
\(234\) | −30.0000 | + | 30.0000i | −1.96116 | + | 1.96116i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 22.3607 | + | 22.3607i | 1.44943 | + | 1.44943i | ||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00000i | 0.515325i | 0.966235 | + | 0.257663i | \(0.0829523\pi\) | ||||
−0.966235 | + | 0.257663i | \(0.917048\pi\) | |||||||
\(242\) | 46.9574 | 3.01854 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 27.0000 | + | 27.0000i | 1.72850 | + | 1.72850i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.8885 | −1.13822 | ||||||||
\(248\) | 8.94427 | − | 8.94427i | 0.567962 | − | 0.567962i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00000 | + | 4.00000i | 0.252478 | + | 0.252478i | 0.821986 | − | 0.569508i | \(-0.192866\pi\) |
−0.569508 | + | 0.821986i | \(0.692866\pi\) | |||||||
\(252\) | 20.1246 | + | 20.1246i | 1.26773 | + | 1.26773i | ||||
\(253\) | −17.8885 | −1.12464 | ||||||||
\(254\) | 10.0000 | 0.627456 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | −4.47214 | − | 4.47214i | −0.278964 | − | 0.278964i | 0.553731 | − | 0.832695i | \(-0.313203\pi\) |
−0.832695 | + | 0.553731i | \(0.813203\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.0000 | − | 10.0000i | −0.621370 | − | 0.621370i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | + | 15.0000i | −0.371391 | + | 0.928477i | ||||
\(262\) | −31.3050 | − | 31.3050i | −1.93403 | − | 1.93403i | ||||
\(263\) | −8.94427 | −0.551527 | −0.275764 | − | 0.961225i | \(-0.588931\pi\) | ||||
−0.275764 | + | 0.961225i | \(0.588931\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 20.0000i | 1.22628i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.70820 | − | 6.70820i | 0.409769 | − | 0.409769i | ||||
\(269\) | −7.00000 | − | 7.00000i | −0.426798 | − | 0.426798i | 0.460738 | − | 0.887536i | \(-0.347585\pi\) |
−0.887536 | + | 0.460738i | \(0.847585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0000 | − | 14.0000i | 0.850439 | − | 0.850439i | −0.139748 | − | 0.990187i | \(-0.544629\pi\) |
0.990187 | + | 0.139748i | \(0.0446292\pi\) | |||||||
\(272\) | − | 4.47214i | − | 0.271163i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −30.0000 | −1.81237 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.94427 | − | 8.94427i | −0.537409 | − | 0.537409i | 0.385358 | − | 0.922767i | \(-0.374078\pi\) |
−0.922767 | + | 0.385358i | \(0.874078\pi\) | |||||||
\(278\) | −8.94427 | −0.536442 | ||||||||
\(279\) | 12.0000 | + | 12.0000i | 0.718421 | + | 0.718421i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.1803 | − | 11.1803i | −0.664602 | − | 0.664602i | 0.291859 | − | 0.956461i | \(-0.405726\pi\) |
−0.956461 | + | 0.291859i | \(0.905726\pi\) | |||||||
\(284\) | − | 36.0000i | − | 2.13621i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 80.0000 | 4.73050 | ||||||||
\(287\) | 4.47214 | 0.263982 | ||||||||
\(288\) | − | 20.1246i | − | 1.18585i | ||||||
\(289\) | −3.00000 | −0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.4164i | 0.785136i | ||||||||
\(293\) | −4.47214 | −0.261265 | −0.130632 | − | 0.991431i | \(-0.541701\pi\) | ||||
−0.130632 | + | 0.991431i | \(0.541701\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 10.0000i | − | 0.581238i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 44.7214i | − | 2.59064i | ||||||
\(299\) | −20.0000 | −1.15663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0000 | + | 10.0000i | 0.576390 | + | 0.576390i | ||||
\(302\) | −26.8328 | −1.54406 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | − | 2.00000i | 0.114708 | − | 0.114708i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −30.0000 | −1.71499 | ||||||||
\(307\) | − | 31.3050i | − | 1.78667i | −0.449393 | − | 0.893334i | \(-0.648360\pi\) | ||
0.449393 | − | 0.893334i | \(-0.351640\pi\) | |||||||
\(308\) | − | 53.6656i | − | 3.05788i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.00000 | − | 4.00000i | −0.226819 | − | 0.226819i | 0.584543 | − | 0.811363i | \(-0.301274\pi\) |
−0.811363 | + | 0.584543i | \(0.801274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.3607 | + | 22.3607i | −1.26390 | + | 1.26390i | −0.314714 | + | 0.949187i | \(0.601909\pi\) |
−0.949187 | + | 0.314714i | \(0.898091\pi\) | |||||||
\(314\) | − | 30.0000i | − | 1.69300i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.00000 | − | 6.00000i | 0.337526 | − | 0.337526i | ||||
\(317\) | −31.3050 | −1.75826 | −0.879131 | − | 0.476581i | \(-0.841876\pi\) | ||||
−0.879131 | + | 0.476581i | \(0.841876\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.0000 | − | 12.0000i | 1.56770 | − | 0.671871i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 22.3607i | 1.24611i | ||||||||
\(323\) | −8.94427 | − | 8.94427i | −0.497673 | − | 0.497673i | ||||
\(324\) | −27.0000 | −1.50000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.23607 | + | 2.23607i | 0.123466 | + | 0.123466i | ||||
\(329\) | 10.0000 | + | 10.0000i | 0.551318 | + | 0.551318i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.00000 | + | 6.00000i | −0.329790 | + | 0.329790i | −0.852506 | − | 0.522717i | \(-0.824919\pi\) |
0.522717 | + | 0.852506i | \(0.324919\pi\) | |||||||
\(332\) | −20.1246 | + | 20.1246i | −1.10448 | + | 1.10448i | ||||
\(333\) | 13.4164 | 0.735215 | ||||||||
\(334\) | −15.0000 | − | 15.0000i | −0.820763 | − | 0.820763i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.4164 | 0.730838 | 0.365419 | − | 0.930843i | \(-0.380926\pi\) | ||||
0.365419 | + | 0.930843i | \(0.380926\pi\) | |||||||
\(338\) | 60.3738 | 3.28390 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 32.0000i | − | 1.73290i | ||||||
\(342\) | −13.4164 | − | 13.4164i | −0.725476 | − | 0.725476i | ||||
\(343\) | 8.94427 | − | 8.94427i | 0.482945 | − | 0.482945i | ||||
\(344\) | 10.0000i | 0.539164i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 30.0000 | − | 30.0000i | 1.61281 | − | 1.61281i | ||||
\(347\) | 15.6525 | − | 15.6525i | 0.840269 | − | 0.840269i | −0.148625 | − | 0.988894i | \(-0.547485\pi\) |
0.988894 | + | 0.148625i | \(0.0474846\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.0000i | 1.60586i | 0.596071 | + | 0.802932i | \(0.296728\pi\) | ||||
−0.596071 | + | 0.802932i | \(0.703272\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −26.8328 | + | 26.8328i | −1.43019 | + | 1.43019i | ||||
\(353\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 21.0000 | − | 21.0000i | 1.11300 | − | 1.11300i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.0000 | − | 12.0000i | 0.633336 | − | 0.633336i | −0.315567 | − | 0.948903i | \(-0.602195\pi\) |
0.948903 | + | 0.315567i | \(0.102195\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000i | 0.578947i | ||||||||
\(362\) | 44.7214i | 2.35050i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 60.0000i | − | 3.14485i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.8328i | 1.40066i | 0.713818 | + | 0.700331i | \(0.246964\pi\) | ||||
−0.713818 | + | 0.700331i | \(0.753036\pi\) | |||||||
\(368\) | 2.23607 | − | 2.23607i | 0.116563 | − | 0.116563i | ||||
\(369\) | −3.00000 | + | 3.00000i | −0.156174 | + | 0.156174i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.0000 | 2.07670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.4164 | + | 13.4164i | −0.694675 | + | 0.694675i | −0.963257 | − | 0.268582i | \(-0.913445\pi\) |
0.268582 | + | 0.963257i | \(0.413445\pi\) | |||||||
\(374\) | 40.0000 | + | 40.0000i | 2.06835 | + | 2.06835i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.0000i | 0.515711i | ||||||||
\(377\) | 31.3050 | − | 13.4164i | 1.61229 | − | 0.690980i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000 | − | 12.0000i | 0.616399 | − | 0.616399i | −0.328207 | − | 0.944606i | \(-0.606444\pi\) |
0.944606 | + | 0.328207i | \(0.106444\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.4164 | − | 13.4164i | 0.686443 | − | 0.686443i | ||||
\(383\) | −11.1803 | − | 11.1803i | −0.571289 | − | 0.571289i | 0.361200 | − | 0.932488i | \(-0.382367\pi\) |
−0.932488 | + | 0.361200i | \(0.882367\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.0000i | 0.508987i | ||||||||
\(387\) | −13.4164 | −0.681994 | ||||||||
\(388\) | −13.4164 | −0.681115 | ||||||||
\(389\) | 7.00000 | + | 7.00000i | 0.354914 | + | 0.354914i | 0.861934 | − | 0.507020i | \(-0.169253\pi\) |
−0.507020 | + | 0.861934i | \(0.669253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.0000 | − | 10.0000i | −0.505722 | − | 0.505722i | ||||
\(392\) | −6.70820 | −0.338815 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 30.0000 | − | 30.0000i | 1.51138 | − | 1.51138i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 36.0000 | + | 36.0000i | 1.80907 | + | 1.80907i | ||||
\(397\) | 13.4164 | + | 13.4164i | 0.673350 | + | 0.673350i | 0.958487 | − | 0.285137i | \(-0.0920390\pi\) |
−0.285137 | + | 0.958487i | \(0.592039\pi\) | |||||||
\(398\) | −44.7214 | −2.24168 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.0000 | −0.998752 | −0.499376 | − | 0.866385i | \(-0.666437\pi\) | ||||
−0.499376 | + | 0.866385i | \(0.666437\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 35.7771i | − | 1.78218i | ||||||
\(404\) | 3.00000 | + | 3.00000i | 0.149256 | + | 0.149256i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.0000 | − | 35.0000i | −0.744438 | − | 1.73702i | ||||
\(407\) | −17.8885 | − | 17.8885i | −0.886702 | − | 0.886702i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.00000 | − | 3.00000i | 0.148340 | − | 0.148340i | −0.629036 | − | 0.777376i | \(-0.716550\pi\) |
0.777376 | + | 0.629036i | \(0.216550\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 20.1246 | − | 20.1246i | 0.991468 | − | 0.991468i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −15.0000 | − | 15.0000i | −0.737210 | − | 0.737210i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −30.0000 | + | 30.0000i | −1.47087 | + | 1.47087i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 35.7771i | 1.74991i | ||||||||
\(419\) | −24.0000 | −1.17248 | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.00000 | − | 9.00000i | 0.438633 | − | 0.438633i | −0.452919 | − | 0.891552i | \(-0.649617\pi\) |
0.891552 | + | 0.452919i | \(0.149617\pi\) | |||||||
\(422\) | −35.7771 | − | 35.7771i | −1.74160 | − | 1.74160i | ||||
\(423\) | −13.4164 | −0.652328 | ||||||||
\(424\) | 20.0000 | + | 20.0000i | 0.971286 | + | 0.971286i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 40.2492i | − | 1.94780i | ||||||
\(428\) | −20.1246 | − | 20.1246i | −0.972760 | − | 0.972760i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 22.3607i | − | 1.07459i | −0.843396 | − | 0.537293i | \(-0.819447\pi\) | ||
0.843396 | − | 0.537293i | \(-0.180553\pi\) | |||||||
\(434\) | −40.0000 | −1.92006 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 30.0000 | 1.43674 | ||||||||
\(437\) | − | 8.94427i | − | 0.427863i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 9.00000i | − | 0.428571i | ||||||
\(442\) | 44.7214 | + | 44.7214i | 2.12718 | + | 2.12718i | ||||
\(443\) | 31.3050i | 1.48734i | 0.668545 | + | 0.743672i | \(0.266917\pi\) | ||||
−0.668545 | + | 0.743672i | \(0.733083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −25.0000 | − | 25.0000i | −1.18378 | − | 1.18378i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 29.0689 | + | 29.0689i | 1.37338 | + | 1.37338i | ||||
\(449\) | 13.0000 | − | 13.0000i | 0.613508 | − | 0.613508i | −0.330350 | − | 0.943858i | \(-0.607167\pi\) |
0.943858 | + | 0.330350i | \(0.107167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 13.4164i | 0.631055i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.0000 | + | 15.0000i | −0.703985 | + | 0.703985i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.8885 | − | 17.8885i | 0.836791 | − | 0.836791i | −0.151644 | − | 0.988435i | \(-0.548457\pi\) |
0.988435 | + | 0.151644i | \(0.0484568\pi\) | |||||||
\(458\) | −6.70820 | + | 6.70820i | −0.313454 | + | 0.313454i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.00000 | + | 9.00000i | −0.419172 | + | 0.419172i | −0.884918 | − | 0.465746i | \(-0.845786\pi\) |
0.465746 | + | 0.884918i | \(0.345786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.23607 | − | 2.23607i | −0.103919 | − | 0.103919i | 0.653236 | − | 0.757155i | \(-0.273411\pi\) |
−0.757155 | + | 0.653236i | \(0.773411\pi\) | |||||||
\(464\) | −2.00000 | + | 5.00000i | −0.0928477 | + | 0.232119i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.0000 | + | 20.0000i | 0.926482 | + | 0.926482i | ||||
\(467\) | 13.4164i | 0.620837i | 0.950600 | + | 0.310419i | \(0.100469\pi\) | ||||
−0.950600 | + | 0.310419i | \(0.899531\pi\) | |||||||
\(468\) | 40.2492 | + | 40.2492i | 1.86052 | + | 1.86052i | ||||
\(469\) | −10.0000 | −0.461757 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.8885 | + | 17.8885i | 0.822516 | + | 0.822516i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 30.0000 | − | 30.0000i | 1.37505 | − | 1.37505i | ||||
\(477\) | −26.8328 | + | 26.8328i | −1.22859 | + | 1.22859i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.0000 | − | 18.0000i | −0.822441 | − | 0.822441i | 0.164017 | − | 0.986458i | \(-0.447555\pi\) |
−0.986458 | + | 0.164017i | \(0.947555\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | − | 20.0000i | −0.911922 | − | 0.911922i | ||||
\(482\) | 17.8885 | 0.814801 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 63.0000i | − | 2.86364i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.1246 | − | 20.1246i | −0.911933 | − | 0.911933i | 0.0844910 | − | 0.996424i | \(-0.473074\pi\) |
−0.996424 | + | 0.0844910i | \(0.973074\pi\) | |||||||
\(488\) | 20.1246 | − | 20.1246i | 0.910998 | − | 0.910998i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.00000 | + | 6.00000i | −0.270776 | + | 0.270776i | −0.829413 | − | 0.558636i | \(-0.811325\pi\) |
0.558636 | + | 0.829413i | \(0.311325\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.3607 | + | 8.94427i | 1.00707 | + | 0.402830i | ||||
\(494\) | 40.0000i | 1.79969i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | + | 4.00000i | 0.179605 | + | 0.179605i | ||||
\(497\) | −26.8328 | + | 26.8328i | −1.20362 | + | 1.20362i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000 | 0.895323 | 0.447661 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447661 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.94427 | − | 8.94427i | 0.399202 | − | 0.399202i | ||||
\(503\) | − | 22.3607i | − | 0.997013i | −0.866886 | − | 0.498507i | \(-0.833882\pi\) | ||
0.866886 | − | 0.498507i | \(-0.166118\pi\) | |||||||
\(504\) | 15.0000 | − | 15.0000i | 0.668153 | − | 0.668153i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 40.0000i | 1.77822i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 13.4164i | − | 0.595257i | ||||||
\(509\) | − | 24.0000i | − | 1.06378i | −0.846813 | − | 0.531891i | \(-0.821482\pi\) | ||
0.846813 | − | 0.531891i | \(-0.178518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.0000 | − | 10.0000i | 0.442374 | − | 0.442374i | ||||
\(512\) | − | 11.1803i | − | 0.494106i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.0000 | + | 10.0000i | −0.441081 | + | 0.441081i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.8885 | + | 17.8885i | 0.786737 | + | 0.786737i | ||||
\(518\) | −22.3607 | + | 22.3607i | −0.982472 | + | 0.982472i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 10.0000i | − | 0.438108i | −0.975713 | − | 0.219054i | \(-0.929703\pi\) | ||
0.975713 | − | 0.219054i | \(-0.0702971\pi\) | |||||||
\(522\) | 33.5410 | + | 13.4164i | 1.46805 | + | 0.587220i | ||||
\(523\) | −15.6525 | + | 15.6525i | −0.684435 | + | 0.684435i | −0.960996 | − | 0.276561i | \(-0.910805\pi\) |
0.276561 | + | 0.960996i | \(0.410805\pi\) | |||||||
\(524\) | −42.0000 | + | 42.0000i | −1.83478 | + | 1.83478i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.0000i | 0.872041i | ||||||||
\(527\) | 17.8885 | − | 17.8885i | 0.779237 | − | 0.779237i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000i | 0.565217i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 26.8328 | 1.16335 | ||||||||
\(533\) | 8.94427 | 0.387419 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.00000 | − | 5.00000i | −0.215967 | − | 0.215967i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.6525 | + | 15.6525i | −0.674826 | + | 0.674826i | ||||
\(539\) | −12.0000 | + | 12.0000i | −0.516877 | + | 0.516877i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.00000 | − | 9.00000i | −0.386940 | − | 0.386940i | 0.486654 | − | 0.873595i | \(-0.338217\pi\) |
−0.873595 | + | 0.486654i | \(0.838217\pi\) | |||||||
\(542\) | −31.3050 | − | 31.3050i | −1.34466 | − | 1.34466i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −30.0000 | −1.28624 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.6525 | + | 15.6525i | 0.669252 | + | 0.669252i | 0.957543 | − | 0.288291i | \(-0.0930871\pi\) |
−0.288291 | + | 0.957543i | \(0.593087\pi\) | |||||||
\(548\) | 40.2492i | 1.71936i | ||||||||
\(549\) | 27.0000 | + | 27.0000i | 1.15233 | + | 1.15233i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | + | 14.0000i | 0.255609 | + | 0.596420i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.94427 | −0.380349 | ||||||||
\(554\) | −20.0000 | + | 20.0000i | −0.849719 | + | 0.849719i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.0000i | 0.508913i | ||||||||
\(557\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(558\) | 26.8328 | − | 26.8328i | 1.13592 | − | 1.13592i | ||||
\(559\) | 20.0000 | + | 20.0000i | 0.845910 | + | 0.845910i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.8328i | 1.13187i | ||||||||
\(563\) | 35.7771i | 1.50782i | 0.656975 | + | 0.753912i | \(0.271836\pi\) | ||||
−0.656975 | + | 0.753912i | \(0.728164\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −25.0000 | + | 25.0000i | −1.05083 | + | 1.05083i | ||||
\(567\) | 20.1246 | + | 20.1246i | 0.845154 | + | 0.845154i | ||||
\(568\) | −26.8328 | −1.12588 | ||||||||
\(569\) | −7.00000 | − | 7.00000i | −0.293455 | − | 0.293455i | 0.544988 | − | 0.838444i | \(-0.316534\pi\) |
−0.838444 | + | 0.544988i | \(0.816534\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.0000 | −0.502184 | −0.251092 | − | 0.967963i | \(-0.580790\pi\) | ||||
−0.251092 | + | 0.967963i | \(0.580790\pi\) | |||||||
\(572\) | − | 107.331i | − | 4.48775i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 10.0000i | − | 0.417392i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −39.0000 | −1.62500 | ||||||||
\(577\) | −40.2492 | −1.67560 | −0.837799 | − | 0.545979i | \(-0.816158\pi\) | ||||
−0.837799 | + | 0.545979i | \(0.816158\pi\) | |||||||
\(578\) | 6.70820i | 0.279024i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.0000 | 1.24461 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 71.5542 | 2.96347 | ||||||||
\(584\) | 10.0000 | 0.413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.0000i | 0.413096i | ||||||||
\(587\) | 20.1246 | + | 20.1246i | 0.830632 | + | 0.830632i | 0.987603 | − | 0.156972i | \(-0.0501731\pi\) |
−0.156972 | + | 0.987603i | \(0.550173\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.47214 | 0.183804 | ||||||||
\(593\) | 8.94427 | + | 8.94427i | 0.367297 | + | 0.367297i | 0.866491 | − | 0.499193i | \(-0.166370\pi\) |
−0.499193 | + | 0.866491i | \(0.666370\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −60.0000 | −2.45770 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 44.7214i | 1.82879i | ||||||||
\(599\) | 22.0000 | − | 22.0000i | 0.898896 | − | 0.898896i | −0.0964429 | − | 0.995339i | \(-0.530747\pi\) |
0.995339 | + | 0.0964429i | \(0.0307465\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.0000 | − | 21.0000i | −0.856608 | − | 0.856608i | 0.134329 | − | 0.990937i | \(-0.457112\pi\) |
−0.990937 | + | 0.134329i | \(0.957112\pi\) | |||||||
\(602\) | 22.3607 | − | 22.3607i | 0.911353 | − | 0.911353i | ||||
\(603\) | 6.70820 | − | 6.70820i | 0.273179 | − | 0.273179i | ||||
\(604\) | 36.0000i | 1.46482i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.4164 | 0.544555 | 0.272278 | − | 0.962219i | \(-0.412223\pi\) | ||||
0.272278 | + | 0.962219i | \(0.412223\pi\) | |||||||
\(608\) | −13.4164 | − | 13.4164i | −0.544107 | − | 0.544107i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.0000 | + | 20.0000i | 0.809113 | + | 0.809113i | ||||
\(612\) | 40.2492i | 1.62698i | ||||||||
\(613\) | −8.94427 | − | 8.94427i | −0.361256 | − | 0.361256i | 0.503019 | − | 0.864275i | \(-0.332222\pi\) |
−0.864275 | + | 0.503019i | \(0.832222\pi\) | |||||||
\(614\) | −70.0000 | −2.82497 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −40.0000 | −1.61165 | ||||||||
\(617\) | 40.2492 | 1.62037 | 0.810186 | − | 0.586172i | \(-0.199366\pi\) | ||||
0.810186 | + | 0.586172i | \(0.199366\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.0000 | − | 12.0000i | −0.482321 | − | 0.482321i | 0.423551 | − | 0.905872i | \(-0.360783\pi\) |
−0.905872 | + | 0.423551i | \(0.860783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.94427 | + | 8.94427i | −0.358633 | + | 0.358633i | ||||
\(623\) | −31.3050 | −1.25421 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 50.0000 | + | 50.0000i | 1.99840 | + | 1.99840i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −40.2492 | −1.60612 | ||||||||
\(629\) | − | 20.0000i | − | 0.797452i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000i | 1.59237i | 0.605050 | + | 0.796187i | \(0.293153\pi\) | ||||
−0.605050 | + | 0.796187i | \(0.706847\pi\) | |||||||
\(632\) | −4.47214 | − | 4.47214i | −0.177892 | − | 0.177892i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 70.0000i | 2.78006i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.4164 | + | 13.4164i | −0.531577 | + | 0.531577i | ||||
\(638\) | −26.8328 | − | 62.6099i | −1.06232 | − | 2.47875i | ||||
\(639\) | − | 36.0000i | − | 1.42414i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.00000 | + | 1.00000i | 0.0394976 | + | 0.0394976i | 0.726580 | − | 0.687082i | \(-0.241109\pi\) |
−0.687082 | + | 0.726580i | \(0.741109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.0689 | + | 29.0689i | 1.14636 | + | 1.14636i | 0.987262 | + | 0.159103i | \(0.0508601\pi\) |
0.159103 | + | 0.987262i | \(0.449140\pi\) | |||||||
\(644\) | 30.0000 | 1.18217 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.0000 | + | 20.0000i | −0.786889 | + | 0.786889i | ||||
\(647\) | −6.70820 | + | 6.70820i | −0.263727 | + | 0.263727i | −0.826566 | − | 0.562839i | \(-0.809709\pi\) |
0.562839 | + | 0.826566i | \(0.309709\pi\) | |||||||
\(648\) | 20.1246i | 0.790569i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.3050i | 1.22506i | 0.790448 | + | 0.612529i | \(0.209848\pi\) | ||||
−0.790448 | + | 0.612529i | \(0.790152\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.00000 | + | 1.00000i | −0.0390434 | + | 0.0390434i | ||||
\(657\) | 13.4164i | 0.523424i | ||||||||
\(658\) | 22.3607 | − | 22.3607i | 0.871710 | − | 0.871710i | ||||
\(659\) | 2.00000 | − | 2.00000i | 0.0779089 | − | 0.0779089i | −0.667078 | − | 0.744987i | \(-0.732455\pi\) |
0.744987 | + | 0.667078i | \(0.232455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.0000 | −1.55582 | −0.777910 | − | 0.628376i | \(-0.783720\pi\) | ||||
−0.777910 | + | 0.628376i | \(0.783720\pi\) | |||||||
\(662\) | 13.4164 | + | 13.4164i | 0.521443 | + | 0.521443i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.0000 | + | 15.0000i | 0.582113 | + | 0.582113i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 30.0000i | − | 1.16248i | ||||||
\(667\) | 6.70820 | + | 15.6525i | 0.259743 | + | 0.606066i | ||||
\(668\) | −20.1246 | + | 20.1246i | −0.778645 | + | 0.778645i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 72.0000i | − | 2.77953i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.47214 | − | 4.47214i | −0.172388 | − | 0.172388i | 0.615640 | − | 0.788028i | \(-0.288898\pi\) |
−0.788028 | + | 0.615640i | \(0.788898\pi\) | |||||||
\(674\) | − | 30.0000i | − | 1.15556i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | − | 81.0000i | − | 3.11538i | ||||||
\(677\) | 4.47214 | 0.171878 | 0.0859391 | − | 0.996300i | \(-0.472611\pi\) | ||||
0.0859391 | + | 0.996300i | \(0.472611\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0000 | + | 10.0000i | 0.383765 | + | 0.383765i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −71.5542 | −2.73995 | ||||||||
\(683\) | −33.5410 | + | 33.5410i | −1.28341 | + | 1.28341i | −0.344698 | + | 0.938714i | \(0.612019\pi\) |
−0.938714 | + | 0.344698i | \(0.887981\pi\) | |||||||
\(684\) | −18.0000 | + | 18.0000i | −0.688247 | + | 0.688247i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −20.0000 | − | 20.0000i | −0.763604 | − | 0.763604i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.47214 | −0.170499 | ||||||||
\(689\) | 80.0000 | 3.04776 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0000 | −0.760836 | −0.380418 | − | 0.924815i | \(-0.624220\pi\) | ||||
−0.380418 | + | 0.924815i | \(0.624220\pi\) | |||||||
\(692\) | −40.2492 | − | 40.2492i | −1.53005 | − | 1.53005i | ||||
\(693\) | − | 53.6656i | − | 2.03859i | ||||||
\(694\) | −35.0000 | − | 35.0000i | −1.32858 | − | 1.32858i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.47214 | + | 4.47214i | 0.169394 | + | 0.169394i | ||||
\(698\) | 67.0820 | 2.53909 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 18.0000i | − | 0.679851i | −0.940452 | − | 0.339925i | \(-0.889598\pi\) | ||
0.940452 | − | 0.339925i | \(-0.110402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.94427 | − | 8.94427i | 0.337340 | − | 0.337340i | ||||
\(704\) | 52.0000 | + | 52.0000i | 1.95982 | + | 1.95982i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.47214i | − | 0.168192i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0000 | 0.375558 | 0.187779 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187779 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.00000 | − | 6.00000i | 0.225018 | − | 0.225018i | ||||
\(712\) | −15.6525 | − | 15.6525i | −0.586601 | − | 0.586601i | ||||
\(713\) | 17.8885 | 0.669931 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −26.8328 | − | 26.8328i | −1.00139 | − | 1.00139i | ||||
\(719\) | 20.0000i | 0.745874i | 0.927857 | + | 0.372937i | \(0.121649\pi\) | ||||
−0.927857 | + | 0.372937i | \(0.878351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.0000 | −1.11726 | ||||||||
\(722\) | 24.5967 | 0.915396 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 60.0000 | 2.22988 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.7214i | 1.65862i | 0.558786 | + | 0.829312i | \(0.311267\pi\) | ||||
−0.558786 | + | 0.829312i | \(0.688733\pi\) | |||||||
\(728\) | −44.7214 | −1.65748 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.0000i | 0.739727i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.47214i | − | 0.165182i | −0.996584 | − | 0.0825911i | \(-0.973680\pi\) | ||
0.996584 | − | 0.0825911i | \(-0.0263195\pi\) | |||||||
\(734\) | 60.0000 | 2.21464 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.0000 | − | 15.0000i | −0.552907 | − | 0.552907i | ||||
\(737\) | −17.8885 | −0.658933 | ||||||||
\(738\) | 6.70820 | + | 6.70820i | 0.246932 | + | 0.246932i | ||||
\(739\) | −18.0000 | + | 18.0000i | −0.662141 | + | 0.662141i | −0.955884 | − | 0.293744i | \(-0.905099\pi\) |
0.293744 | + | 0.955884i | \(0.405099\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 89.4427i | − | 3.28355i | ||||||
\(743\) | − | 22.3607i | − | 0.820334i | −0.912010 | − | 0.410167i | \(-0.865470\pi\) | ||
0.912010 | − | 0.410167i | \(-0.134530\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 30.0000 | + | 30.0000i | 1.09838 | + | 1.09838i | ||||
\(747\) | −20.1246 | + | 20.1246i | −0.736321 | + | 0.736321i | ||||
\(748\) | 53.6656 | − | 53.6656i | 1.96221 | − | 1.96221i | ||||
\(749\) | 30.0000i | 1.09618i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0000 | − | 24.0000i | 0.875772 | − | 0.875772i | −0.117322 | − | 0.993094i | \(-0.537431\pi\) |
0.993094 | + | 0.117322i | \(0.0374308\pi\) | |||||||
\(752\) | −4.47214 | −0.163082 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −30.0000 | − | 70.0000i | −1.09254 | − | 2.54925i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 40.2492i | − | 1.46288i | −0.681904 | − | 0.731441i | \(-0.738848\pi\) | ||
0.681904 | − | 0.731441i | \(-0.261152\pi\) | |||||||
\(758\) | −26.8328 | − | 26.8328i | −0.974612 | − | 0.974612i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0000 | 0.362500 | 0.181250 | − | 0.983437i | \(-0.441986\pi\) | ||||
0.181250 | + | 0.983437i | \(0.441986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.3607 | − | 22.3607i | −0.809511 | − | 0.809511i | ||||
\(764\) | −18.0000 | − | 18.0000i | −0.651217 | − | 0.651217i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.0000 | + | 25.0000i | −0.903287 | + | 0.903287i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.0000 | + | 27.0000i | 0.973645 | + | 0.973645i | 0.999662 | − | 0.0260166i | \(-0.00828228\pi\) |
−0.0260166 | + | 0.999662i | \(0.508282\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.4164 | 0.482867 | ||||||||
\(773\) | 13.4164 | 0.482555 | 0.241277 | − | 0.970456i | \(-0.422434\pi\) | ||||
0.241277 | + | 0.970456i | \(0.422434\pi\) | |||||||
\(774\) | 30.0000i | 1.07833i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.0000i | 0.358979i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.6525 | − | 15.6525i | 0.561168 | − | 0.561168i | ||||
\(779\) | 4.00000i | 0.143315i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48.0000 | + | 48.0000i | −1.71758 | + | 1.71758i | ||||
\(782\) | −22.3607 | + | 22.3607i | −0.799616 | + | 0.799616i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 3.00000i | − | 0.107143i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.5410 | + | 33.5410i | −1.19561 | + | 1.19561i | −0.220140 | + | 0.975468i | \(0.570651\pi\) |
−0.975468 | + | 0.220140i | \(0.929349\pi\) | |||||||
\(788\) | −40.2492 | − | 40.2492i | −1.43382 | − | 1.43382i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.0000 | − | 10.0000i | 0.355559 | − | 0.355559i | ||||
\(792\) | 26.8328 | − | 26.8328i | 0.953463 | − | 0.953463i | ||||
\(793\) | − | 80.4984i | − | 2.85858i | ||||||
\(794\) | 30.0000 | − | 30.0000i | 1.06466 | − | 1.06466i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 60.0000i | 2.12664i | ||||||||
\(797\) | − | 4.47214i | − | 0.158411i | −0.996858 | − | 0.0792056i | \(-0.974762\pi\) | ||
0.996858 | − | 0.0792056i | \(-0.0252384\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.0000i | 0.707549i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.0000 | − | 21.0000i | 0.741999 | − | 0.741999i | ||||
\(802\) | 44.7214i | 1.57917i | ||||||||
\(803\) | 17.8885 | − | 17.8885i | 0.631273 | − | 0.631273i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −80.0000 | −2.81788 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.23607 | − | 2.23607i | 0.0786646 | − | 0.0786646i | ||||
\(809\) | −7.00000 | − | 7.00000i | −0.246107 | − | 0.246107i | 0.573264 | − | 0.819371i | \(-0.305677\pi\) |
−0.819371 | + | 0.573264i | \(0.805677\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000i | 0.702295i | 0.936320 | + | 0.351147i | \(0.114208\pi\) | ||||
−0.936320 | + | 0.351147i | \(0.885792\pi\) | |||||||
\(812\) | −46.9574 | + | 20.1246i | −1.64788 | + | 0.706235i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −40.0000 | + | 40.0000i | −1.40200 | + | 1.40200i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.94427 | + | 8.94427i | −0.312920 | + | 0.312920i | ||||
\(818\) | −6.70820 | − | 6.70820i | −0.234547 | − | 0.234547i | ||||
\(819\) | − | 60.0000i | − | 2.09657i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 20.0000i | − | 0.698005i | −0.937122 | − | 0.349002i | \(-0.886521\pi\) | ||
0.937122 | − | 0.349002i | \(-0.113479\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.7214 | 1.55889 | 0.779444 | − | 0.626472i | \(-0.215502\pi\) | ||||
0.779444 | + | 0.626472i | \(0.215502\pi\) | |||||||
\(824\) | −15.0000 | − | 15.0000i | −0.522550 | − | 0.522550i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.3607 | 0.777557 | 0.388779 | − | 0.921331i | \(-0.372897\pi\) | ||||
0.388779 | + | 0.921331i | \(0.372897\pi\) | |||||||
\(828\) | −20.1246 | + | 20.1246i | −0.699379 | + | 0.699379i | ||||
\(829\) | −27.0000 | + | 27.0000i | −0.937749 | + | 0.937749i | −0.998173 | − | 0.0604240i | \(-0.980755\pi\) |
0.0604240 | + | 0.998173i | \(0.480755\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 58.1378 | + | 58.1378i | 2.01556 | + | 2.01556i | ||||
\(833\) | −13.4164 | −0.464851 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 48.0000 | 1.66011 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 53.6656i | 1.85385i | ||||||||
\(839\) | 2.00000 | + | 2.00000i | 0.0690477 | + | 0.0690477i | 0.740787 | − | 0.671740i | \(-0.234453\pi\) |
−0.671740 | + | 0.740787i | \(0.734453\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | − | 20.0000i | −0.724138 | − | 0.689655i | ||||
\(842\) | −20.1246 | − | 20.1246i | −0.693540 | − | 0.693540i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −48.0000 | + | 48.0000i | −1.65223 | + | 1.65223i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 30.0000i | 1.03142i | ||||||||
\(847\) | −46.9574 | + | 46.9574i | −1.61348 | + | 1.61348i | ||||
\(848\) | −8.94427 | + | 8.94427i | −0.307148 | + | 0.307148i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.0000 | − | 10.0000i | 0.342796 | − | 0.342796i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 22.3607i | − | 0.765615i | −0.923828 | − | 0.382808i | \(-0.874957\pi\) | ||
0.923828 | − | 0.382808i | \(-0.125043\pi\) | |||||||
\(854\) | −90.0000 | −3.07974 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.0000 | + | 15.0000i | −0.512689 | + | 0.512689i | ||||
\(857\) | −13.4164 | − | 13.4164i | −0.458296 | − | 0.458296i | 0.439800 | − | 0.898096i | \(-0.355049\pi\) |
−0.898096 | + | 0.439800i | \(0.855049\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.0000 | + | 12.0000i | 0.409435 | + | 0.409435i | 0.881541 | − | 0.472107i | \(-0.156506\pi\) |
−0.472107 | + | 0.881541i | \(0.656506\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 26.8328i | − | 0.913929i | ||||||
\(863\) | 33.5410 | + | 33.5410i | 1.14175 | + | 1.14175i | 0.988130 | + | 0.153620i | \(0.0490930\pi\) |
0.153620 | + | 0.988130i | \(0.450907\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −50.0000 | −1.69907 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 53.6656i | 1.82153i | ||||||||
\(869\) | −16.0000 | −0.542763 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.0000 | −0.677674 | ||||||||
\(872\) | − | 22.3607i | − | 0.757228i | ||||||
\(873\) | −13.4164 | −0.454077 | ||||||||
\(874\) | −20.0000 | −0.676510 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.94427 | − | 8.94427i | −0.302027 | − | 0.302027i | 0.539780 | − | 0.841806i | \(-0.318508\pi\) |
−0.841806 | + | 0.539780i | \(0.818508\pi\) | |||||||
\(878\) | − | 35.7771i | − | 1.20742i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.0000 | + | 11.0000i | 0.370599 | + | 0.370599i | 0.867696 | − | 0.497096i | \(-0.165600\pi\) |
−0.497096 | + | 0.867696i | \(0.665600\pi\) | |||||||
\(882\) | −20.1246 | −0.677631 | ||||||||
\(883\) | −20.1246 | − | 20.1246i | −0.677247 | − | 0.677247i | 0.282129 | − | 0.959376i | \(-0.408959\pi\) |
−0.959376 | + | 0.282129i | \(0.908959\pi\) | |||||||
\(884\) | 60.0000 | − | 60.0000i | 2.01802 | − | 2.01802i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 70.0000 | 2.35170 | ||||||||
\(887\) | − | 31.3050i | − | 1.05112i | −0.850757 | − | 0.525559i | \(-0.823856\pi\) | ||
0.850757 | − | 0.525559i | \(-0.176144\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.0000 | + | 10.0000i | −0.335389 | + | 0.335389i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36.0000 | + | 36.0000i | 1.20605 | + | 1.20605i | ||||
\(892\) | −33.5410 | + | 33.5410i | −1.12304 | + | 1.12304i | ||||
\(893\) | −8.94427 | + | 8.94427i | −0.299309 | + | 0.299309i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 35.0000 | − | 35.0000i | 1.16927 | − | 1.16927i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −29.0689 | − | 29.0689i | −0.970041 | − | 0.970041i | ||||
\(899\) | −28.0000 | + | 12.0000i | −0.933852 | + | 0.400222i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.0000 | + | 40.0000i | 1.33259 | + | 1.33259i | ||||
\(902\) | − | 17.8885i | − | 0.595623i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.0000 | 0.332595 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.2492 | 1.33645 | 0.668227 | − | 0.743958i | \(-0.267054\pi\) | ||||
0.668227 | + | 0.743958i | \(0.267054\pi\) | |||||||
\(908\) | 20.1246 | + | 20.1246i | 0.667859 | + | 0.667859i | ||||
\(909\) | 3.00000 | + | 3.00000i | 0.0995037 | + | 0.0995037i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0000 | − | 16.0000i | 0.530104 | − | 0.530104i | −0.390499 | − | 0.920603i | \(-0.627698\pi\) |
0.920603 | + | 0.390499i | \(0.127698\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 53.6656 | 1.77607 | ||||||||
\(914\) | −40.0000 | − | 40.0000i | −1.32308 | − | 1.32308i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.00000 | + | 9.00000i | 0.297368 | + | 0.297368i | ||||
\(917\) | 62.6099 | 2.06756 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 20.0000i | − | 0.659739i | −0.944027 | − | 0.329870i | \(-0.892995\pi\) | ||
0.944027 | − | 0.329870i | \(-0.107005\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.1246 | + | 20.1246i | 0.662769 | + | 0.662769i | ||||
\(923\) | −53.6656 | + | 53.6656i | −1.76643 | + | 1.76643i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.00000 | + | 5.00000i | −0.164310 | + | 0.164310i | ||||
\(927\) | 20.1246 | − | 20.1246i | 0.660979 | − | 0.660979i | ||||
\(928\) | 33.5410 | + | 13.4164i | 1.10104 | + | 0.440415i | ||||
\(929\) | − | 14.0000i | − | 0.459325i | −0.973270 | − | 0.229663i | \(-0.926238\pi\) | ||
0.973270 | − | 0.229663i | \(-0.0737623\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.00000 | − | 6.00000i | −0.196642 | − | 0.196642i | ||||
\(932\) | 26.8328 | − | 26.8328i | 0.878938 | − | 0.878938i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.0000 | 0.981630 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 30.0000 | − | 30.0000i | 0.980581 | − | 0.980581i | ||||
\(937\) | −8.94427 | + | 8.94427i | −0.292197 | + | 0.292197i | −0.837947 | − | 0.545751i | \(-0.816245\pi\) |
0.545751 | + | 0.837947i | \(0.316245\pi\) | |||||||
\(938\) | 22.3607i | 0.730102i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 40.0000i | − | 1.30396i | −0.758235 | − | 0.651981i | \(-0.773938\pi\) | ||
0.758235 | − | 0.651981i | \(-0.226062\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.47214i | 0.145633i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.0000 | − | 40.0000i | 1.30051 | − | 1.30051i | ||||
\(947\) | − | 31.3050i | − | 1.01727i | −0.860981 | − | 0.508637i | \(-0.830149\pi\) | ||
0.860981 | − | 0.508637i | \(-0.169851\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.0000 | − | 20.0000i | 0.649227 | − | 0.649227i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −22.3607 | − | 22.3607i | −0.724714 | − | 0.724714i | ||||
\(953\) | −8.94427 | + | 8.94427i | −0.289733 | + | 0.289733i | −0.836975 | − | 0.547241i | \(-0.815678\pi\) |
0.547241 | + | 0.836975i | \(0.315678\pi\) | |||||||
\(954\) | 60.0000 | + | 60.0000i | 1.94257 | + | 1.94257i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −40.2492 | + | 40.2492i | −1.30039 | + | 1.30039i | ||||
\(959\) | 30.0000 | − | 30.0000i | 0.968751 | − | 0.968751i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000i | 0.0322581i | ||||||||
\(962\) | −44.7214 | + | 44.7214i | −1.44187 | + | 1.44187i | ||||
\(963\) | −20.1246 | − | 20.1246i | −0.648507 | − | 0.648507i | ||||
\(964\) | − | 24.0000i | − | 0.772988i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.94427 | 0.287628 | 0.143814 | − | 0.989605i | \(-0.454063\pi\) | ||||
0.143814 | + | 0.989605i | \(0.454063\pi\) | |||||||
\(968\) | −46.9574 | −1.50927 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.0000 | − | 14.0000i | −0.449281 | − | 0.449281i | 0.445834 | − | 0.895116i | \(-0.352907\pi\) |
−0.895116 | + | 0.445834i | \(0.852907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.94427 | − | 8.94427i | 0.286740 | − | 0.286740i | ||||
\(974\) | −45.0000 | + | 45.0000i | −1.44189 | + | 1.44189i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.00000 | + | 9.00000i | 0.288083 | + | 0.288083i | ||||
\(977\) | 4.47214 | + | 4.47214i | 0.143076 | + | 0.143076i | 0.775017 | − | 0.631941i | \(-0.217741\pi\) |
−0.631941 | + | 0.775017i | \(0.717741\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −56.0000 | −1.78977 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.0000 | 0.957826 | ||||||||
\(982\) | 13.4164 | + | 13.4164i | 0.428135 | + | 0.428135i | ||||
\(983\) | − | 13.4164i | − | 0.427917i | −0.976843 | − | 0.213958i | \(-0.931364\pi\) | ||
0.976843 | − | 0.213958i | \(-0.0686357\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 20.0000 | − | 50.0000i | 0.636930 | − | 1.59232i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 53.6656 | 1.70733 | ||||||||
\(989\) | −10.0000 | + | 10.0000i | −0.317982 | + | 0.317982i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 32.0000i | − | 1.01651i | −0.861206 | − | 0.508257i | \(-0.830290\pi\) | ||
0.861206 | − | 0.508257i | \(-0.169710\pi\) | |||||||
\(992\) | 26.8328 | − | 26.8328i | 0.851943 | − | 0.851943i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 60.0000 | + | 60.0000i | 1.90308 | + | 1.90308i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.4164i | 0.424902i | 0.977172 | + | 0.212451i | \(0.0681446\pi\) | ||||
−0.977172 | + | 0.212451i | \(0.931855\pi\) | |||||||
\(998\) | − | 44.7214i | − | 1.41563i | ||||||
\(999\) | 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 | 725.2.e.a.157.1 | ✓ | 4 | |
5.2 | odd | 4 | 725.2.j.a.418.2 | yes | 4 | ||
5.3 | odd | 4 | 725.2.j.a.418.1 | yes | 4 | ||
5.4 | even | 2 | inner | 725.2.e.a.157.2 | yes | 4 | |
29.17 | odd | 4 | 725.2.j.a.307.1 | yes | 4 | ||
145.17 | even | 4 | inner | 725.2.e.a.568.1 | yes | 4 | |
145.104 | odd | 4 | 725.2.j.a.307.2 | yes | 4 | ||
145.133 | even | 4 | inner | 725.2.e.a.568.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
725.2.e.a.157.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
725.2.e.a.157.2 | yes | 4 | 5.4 | even | 2 | inner | |
725.2.e.a.568.1 | yes | 4 | 145.17 | even | 4 | inner | |
725.2.e.a.568.2 | yes | 4 | 145.133 | even | 4 | inner | |
725.2.j.a.307.1 | yes | 4 | 29.17 | odd | 4 | ||
725.2.j.a.307.2 | yes | 4 | 145.104 | odd | 4 | ||
725.2.j.a.418.1 | yes | 4 | 5.3 | odd | 4 | ||
725.2.j.a.418.2 | yes | 4 | 5.2 | odd | 4 |