Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(83,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.83");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.w (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: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 167.1 | ||
Root | \(-0.323042 + 0.323042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 420.167 |
Dual form | 420.2.w.a.83.2 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.707107 | − | 0.707107i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.707107 | + | 0.707107i | ||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | 1.22474 | − | 1.87083i | 0.547723 | − | 0.836660i | ||||
\(6\) | 2.44949 | 1.00000 | ||||||||
\(7\) | 1.87083 | + | 1.87083i | 0.707107 | + | 0.707107i | ||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | − | 3.00000i | − | 1.00000i | ||||||
\(10\) | −3.09557 | + | 0.646084i | −0.978906 | + | 0.204310i | ||||
\(11\) | −3.58258 | −1.08019 | −0.540094 | − | 0.841605i | \(-0.681611\pi\) | ||||
−0.540094 | + | 0.841605i | \(0.681611\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.707107 | − | 0.707107i | ||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | − | 3.74166i | − | 1.00000i | ||||||
\(15\) | 0.791288 | + | 3.79129i | 0.204310 | + | 0.978906i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 5.54506 | + | 5.54506i | 1.34488 | + | 1.34488i | 0.891133 | + | 0.453743i | \(0.149911\pi\) |
0.453743 | + | 0.891133i | \(0.350089\pi\) | |||||||
\(18\) | −3.00000 | + | 3.00000i | −0.707107 | + | 0.707107i | ||||
\(19\) | 1.15732i | 0.265508i | 0.991149 | + | 0.132754i | \(0.0423820\pi\) | ||||
−0.991149 | + | 0.132754i | \(0.957618\pi\) | |||||||
\(20\) | 3.74166 | + | 2.44949i | 0.836660 | + | 0.547723i | ||||
\(21\) | −4.58258 | −1.00000 | ||||||||
\(22\) | 3.58258 | + | 3.58258i | 0.763808 | + | 0.763808i | ||||
\(23\) | 4.58258 | − | 4.58258i | 0.955533 | − | 0.955533i | −0.0435195 | − | 0.999053i | \(-0.513857\pi\) |
0.999053 | + | 0.0435195i | \(0.0138571\pi\) | |||||||
\(24\) | 4.89898i | 1.00000i | ||||||||
\(25\) | −2.00000 | − | 4.58258i | −0.400000 | − | 0.916515i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.707107 | + | 0.707107i | ||||
\(28\) | −3.74166 | + | 3.74166i | −0.707107 | + | 0.707107i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 3.00000 | − | 4.58258i | 0.547723 | − | 0.836660i | ||||
\(31\) | 9.93280 | 1.78398 | 0.891992 | − | 0.452051i | \(-0.149307\pi\) | ||||
0.891992 | + | 0.452051i | \(0.149307\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.707107 | + | 0.707107i | ||||
\(33\) | 4.38774 | − | 4.38774i | 0.763808 | − | 0.763808i | ||||
\(34\) | − | 11.0901i | − | 1.90194i | ||||||
\(35\) | 5.79129 | − | 1.20871i | 0.978906 | − | 0.204310i | ||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 8.58258 | + | 8.58258i | 1.41097 | + | 1.41097i | 0.753371 | + | 0.657596i | \(0.228427\pi\) |
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | 1.15732 | − | 1.15732i | 0.187742 | − | 0.187742i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.29217 | − | 6.19115i | −0.204310 | − | 0.978906i | ||||
\(41\) | −3.74166 | −0.584349 | −0.292174 | − | 0.956365i | \(-0.594379\pi\) | ||||
−0.292174 | + | 0.956365i | \(0.594379\pi\) | |||||||
\(42\) | 4.58258 | + | 4.58258i | 0.707107 | + | 0.707107i | ||||
\(43\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(44\) | − | 7.16515i | − | 1.08019i | ||||||
\(45\) | −5.61249 | − | 3.67423i | −0.836660 | − | 0.547723i | ||||
\(46\) | −9.16515 | −1.35133 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.707107 | − | 0.707107i | ||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | −2.58258 | + | 6.58258i | −0.365231 | + | 0.930917i | ||||
\(51\) | −13.5826 | −1.90194 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(54\) | − | 7.34847i | − | 1.00000i | ||||||
\(55\) | −4.38774 | + | 6.70239i | −0.591643 | + | 0.903749i | ||||
\(56\) | 7.48331 | 1.00000 | ||||||||
\(57\) | −1.41742 | − | 1.41742i | −0.187742 | − | 0.187742i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | −7.58258 | + | 1.58258i | −0.978906 | + | 0.204310i | ||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | −9.93280 | − | 9.93280i | −1.26147 | − | 1.26147i | ||||
\(63\) | 5.61249 | − | 5.61249i | 0.707107 | − | 0.707107i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.77548 | −1.08019 | ||||||||
\(67\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(68\) | −11.0901 | + | 11.0901i | −1.34488 | + | 1.34488i | ||||
\(69\) | 11.2250i | 1.35133i | ||||||||
\(70\) | −7.00000 | − | 4.58258i | −0.836660 | − | 0.547723i | ||||
\(71\) | 6.41742 | 0.761608 | 0.380804 | − | 0.924656i | \(-0.375647\pi\) | ||||
0.380804 | + | 0.924656i | \(0.375647\pi\) | |||||||
\(72\) | −6.00000 | − | 6.00000i | −0.707107 | − | 0.707107i | ||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | − | 17.1652i | − | 1.99541i | ||||||
\(75\) | 8.06198 | + | 3.16300i | 0.930917 | + | 0.365231i | ||||
\(76\) | −2.31464 | −0.265508 | ||||||||
\(77\) | −6.70239 | − | 6.70239i | −0.763808 | − | 0.763808i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −4.89898 | + | 7.48331i | −0.547723 | + | 0.836660i | ||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 3.74166 | + | 3.74166i | 0.413197 | + | 0.413197i | ||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | − | 9.16515i | − | 1.00000i | ||||||
\(85\) | 17.1652 | − | 3.58258i | 1.86182 | − | 0.388585i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.16515 | + | 7.16515i | −0.763808 | + | 0.763808i | ||||
\(89\) | − | 2.44949i | − | 0.259645i | −0.991537 | − | 0.129823i | \(-0.958559\pi\) | ||
0.991537 | − | 0.129823i | \(-0.0414408\pi\) | |||||||
\(90\) | 1.93825 | + | 9.28672i | 0.204310 | + | 0.978906i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.16515 | + | 9.16515i | 0.955533 | + | 0.955533i | ||||
\(93\) | −12.1652 | + | 12.1652i | −1.26147 | + | 1.26147i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.16515 | + | 1.41742i | 0.222140 | + | 0.145425i | ||||
\(96\) | −9.79796 | −1.00000 | ||||||||
\(97\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(98\) | 7.00000 | − | 7.00000i | 0.707107 | − | 0.707107i | ||||
\(99\) | 10.7477i | 1.08019i | ||||||||
\(100\) | 9.16515 | − | 4.00000i | 0.916515 | − | 0.400000i | ||||
\(101\) | −7.34847 | −0.731200 | −0.365600 | − | 0.930772i | \(-0.619136\pi\) | ||||
−0.365600 | + | 0.930772i | \(0.619136\pi\) | |||||||
\(102\) | 13.5826 | + | 13.5826i | 1.34488 | + | 1.34488i | ||||
\(103\) | −7.48331 | + | 7.48331i | −0.737353 | + | 0.737353i | −0.972065 | − | 0.234712i | \(-0.924585\pi\) |
0.234712 | + | 0.972065i | \(0.424585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.61249 | + | 8.57321i | −0.547723 | + | 0.836660i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.7477 | − | 13.7477i | −1.32904 | − | 1.32904i | −0.906206 | − | 0.422837i | \(-0.861034\pi\) |
−0.422837 | − | 0.906206i | \(-0.638966\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.707107 | + | 0.707107i | ||||
\(109\) | − | 18.3303i | − | 1.75572i | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||
0.478913 | − | 0.877862i | \(-0.341031\pi\) | |||||||
\(110\) | 11.0901 | − | 2.31464i | 1.05740 | − | 0.220693i | ||||
\(111\) | −21.0229 | −1.99541 | ||||||||
\(112\) | −7.48331 | − | 7.48331i | −0.707107 | − | 0.707107i | ||||
\(113\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(114\) | 2.83485i | 0.265508i | ||||||||
\(115\) | −2.96073 | − | 14.1857i | −0.276089 | − | 1.32282i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.7477i | 1.90194i | ||||||||
\(120\) | 9.16515 | + | 6.00000i | 0.836660 | + | 0.547723i | ||||
\(121\) | 1.83485 | 0.166804 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.58258 | − | 4.58258i | 0.413197 | − | 0.413197i | ||||
\(124\) | 19.8656i | 1.78398i | ||||||||
\(125\) | −11.0227 | − | 1.87083i | −0.985901 | − | 0.167332i | ||||
\(126\) | −11.2250 | −1.00000 | ||||||||
\(127\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.707107 | + | 0.707107i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 8.77548 | + | 8.77548i | 0.763808 | + | 0.763808i | ||||
\(133\) | −2.16515 | + | 2.16515i | −0.187742 | + | 0.187742i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.3739 | − | 2.37386i | 0.978906 | − | 0.204310i | ||||
\(136\) | 22.1803 | 1.90194 | ||||||||
\(137\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(138\) | 11.2250 | − | 11.2250i | 0.955533 | − | 0.955533i | ||||
\(139\) | 7.61816i | 0.646164i | 0.946371 | + | 0.323082i | \(0.104719\pi\) | ||||
−0.946371 | + | 0.323082i | \(0.895281\pi\) | |||||||
\(140\) | 2.41742 | + | 11.5826i | 0.204310 | + | 0.978906i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.41742 | − | 6.41742i | −0.538538 | − | 0.538538i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.0000i | 1.00000i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.57321 | − | 8.57321i | −0.707107 | − | 0.707107i | ||||
\(148\) | −17.1652 | + | 17.1652i | −1.41097 | + | 1.41097i | ||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | −4.89898 | − | 11.2250i | −0.400000 | − | 0.916515i | ||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 2.31464 | + | 2.31464i | 0.187742 | + | 0.187742i | ||||
\(153\) | 16.6352 | − | 16.6352i | 1.34488 | − | 1.34488i | ||||
\(154\) | 13.4048i | 1.08019i | ||||||||
\(155\) | 12.1652 | − | 18.5826i | 0.977128 | − | 1.49259i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.3823 | − | 2.58434i | 0.978906 | − | 0.204310i | ||||
\(161\) | 17.1464 | 1.35133 | ||||||||
\(162\) | 9.00000 | + | 9.00000i | 0.707107 | + | 0.707107i | ||||
\(163\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(164\) | − | 7.48331i | − | 0.584349i | ||||||
\(165\) | −2.83485 | − | 13.5826i | −0.220693 | − | 1.05740i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | −9.16515 | + | 9.16515i | −0.707107 | + | 0.707107i | ||||
\(169\) | − | 13.0000i | − | 1.00000i | ||||||
\(170\) | −20.7477 | − | 13.5826i | −1.59128 | − | 1.04174i | ||||
\(171\) | 3.47197 | 0.265508 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.3205 | + | 14.3205i | −1.08877 | + | 1.08877i | −0.0931156 | + | 0.995655i | \(0.529683\pi\) |
−0.995655 | + | 0.0931156i | \(0.970317\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.83156 | − | 12.3149i | 0.365231 | − | 0.930917i | ||||
\(176\) | 14.3303 | 1.08019 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.44949 | + | 2.44949i | −0.183597 | + | 0.183597i | ||||
\(179\) | 0.747727i | 0.0558877i | 0.999609 | + | 0.0279439i | \(0.00889597\pi\) | ||||
−0.999609 | + | 0.0279439i | \(0.991104\pi\) | |||||||
\(180\) | 7.34847 | − | 11.2250i | 0.547723 | − | 0.836660i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 18.3303i | − | 1.35133i | ||||||
\(185\) | 26.5680 | − | 5.54506i | 1.95332 | − | 0.407681i | ||||
\(186\) | 24.3303 | 1.78398 | ||||||||
\(187\) | −19.8656 | − | 19.8656i | −1.45272 | − | 1.45272i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.7477i | 1.00000i | ||||||||
\(190\) | −0.747727 | − | 3.58258i | −0.0542458 | − | 0.259907i | ||||
\(191\) | −23.5826 | −1.70638 | −0.853188 | − | 0.521604i | \(-0.825334\pi\) | ||||
−0.853188 | + | 0.521604i | \(0.825334\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.707107 | + | 0.707107i | ||||
\(193\) | 15.7477 | − | 15.7477i | 1.13355 | − | 1.13355i | 0.143963 | − | 0.989583i | \(-0.454015\pi\) |
0.989583 | − | 0.143963i | \(-0.0459847\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −1.00000 | ||||||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 10.7477 | − | 10.7477i | 0.763808 | − | 0.763808i | ||||
\(199\) | − | 23.3376i | − | 1.65436i | −0.561939 | − | 0.827178i | \(-0.689945\pi\) | ||
0.561939 | − | 0.827178i | \(-0.310055\pi\) | |||||||
\(200\) | −13.1652 | − | 5.16515i | −0.930917 | − | 0.365231i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.34847 | + | 7.34847i | 0.517036 | + | 0.517036i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 27.1652i | − | 1.90194i | ||||||
\(205\) | −4.58258 | + | 7.00000i | −0.320061 | + | 0.488901i | ||||
\(206\) | 14.9666 | 1.04277 | ||||||||
\(207\) | −13.7477 | − | 13.7477i | −0.955533 | − | 0.955533i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.14619i | − | 0.286798i | ||||||
\(210\) | 14.1857 | − | 2.96073i | 0.978906 | − | 0.204310i | ||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.85971 | + | 7.85971i | −0.538538 | + | 0.538538i | ||||
\(214\) | 27.4955i | 1.87955i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969 | 1.00000 | ||||||||
\(217\) | 18.5826 | + | 18.5826i | 1.26147 | + | 1.26147i | ||||
\(218\) | −18.3303 | + | 18.3303i | −1.24148 | + | 1.24148i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13.4048 | − | 8.77548i | −0.903749 | − | 0.591643i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 21.0229 | + | 21.0229i | 1.41097 | + | 1.41097i | ||||
\(223\) | 9.79796 | − | 9.79796i | 0.656120 | − | 0.656120i | −0.298340 | − | 0.954460i | \(-0.596433\pi\) |
0.954460 | + | 0.298340i | \(0.0964329\pi\) | |||||||
\(224\) | 14.9666i | 1.00000i | ||||||||
\(225\) | −13.7477 | + | 6.00000i | −0.916515 | + | 0.400000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | 2.83485 | − | 2.83485i | 0.187742 | − | 0.187742i | ||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | −11.2250 | + | 17.1464i | −0.740153 | + | 1.13060i | ||||
\(231\) | 16.4174 | 1.08019 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 20.7477 | − | 20.7477i | 1.34488 | − | 1.34488i | ||||
\(239\) | 30.7477i | 1.98891i | 0.105186 | + | 0.994453i | \(0.466456\pi\) | ||||
−0.105186 | + | 0.994453i | \(0.533544\pi\) | |||||||
\(240\) | −3.16515 | − | 15.1652i | −0.204310 | − | 0.978906i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −1.83485 | − | 1.83485i | −0.117949 | − | 0.117949i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.707107 | − | 0.707107i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.0958 | + | 8.57321i | 0.836660 | + | 0.547723i | ||||
\(246\) | −9.16515 | −0.584349 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 19.8656 | − | 19.8656i | 1.26147 | − | 1.26147i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.15188 | + | 12.8935i | 0.578815 | + | 0.815459i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 11.2250 | + | 11.2250i | 0.707107 | + | 0.707107i | ||||
\(253\) | −16.4174 | + | 16.4174i | −1.03215 | + | 1.03215i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.6352 | + | 25.4107i | −1.04174 | + | 1.59128i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 17.7925 | + | 17.7925i | 1.10987 | + | 1.10987i | 0.993167 | + | 0.116699i | \(0.0372313\pi\) |
0.116699 | + | 0.993167i | \(0.462769\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 32.1131i | 1.99541i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.00000 | + | 1.00000i | −0.0616626 | + | 0.0616626i | −0.737266 | − | 0.675603i | \(-0.763883\pi\) |
0.675603 | + | 0.737266i | \(0.263883\pi\) | |||||||
\(264\) | − | 17.5510i | − | 1.08019i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.33030 | 0.265508 | ||||||||
\(267\) | 3.00000 | + | 3.00000i | 0.183597 | + | 0.183597i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 26.9444i | − | 1.64283i | −0.570332 | − | 0.821414i | \(-0.693186\pi\) | ||
0.570332 | − | 0.821414i | \(-0.306814\pi\) | |||||||
\(270\) | −13.7477 | − | 9.00000i | −0.836660 | − | 0.547723i | ||||
\(271\) | −14.5621 | −0.884584 | −0.442292 | − | 0.896871i | \(-0.645835\pi\) | ||||
−0.442292 | + | 0.896871i | \(0.645835\pi\) | |||||||
\(272\) | −22.1803 | − | 22.1803i | −1.34488 | − | 1.34488i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.16515 | + | 16.4174i | 0.432075 | + | 0.990008i | ||||
\(276\) | −22.4499 | −1.35133 | ||||||||
\(277\) | −11.4174 | − | 11.4174i | −0.686007 | − | 0.686007i | 0.275340 | − | 0.961347i | \(-0.411209\pi\) |
−0.961347 | + | 0.275340i | \(0.911209\pi\) | |||||||
\(278\) | 7.61816 | − | 7.61816i | 0.456907 | − | 0.456907i | ||||
\(279\) | − | 29.7984i | − | 1.78398i | ||||||
\(280\) | 9.16515 | − | 14.0000i | 0.547723 | − | 0.836660i | ||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.6969 | + | 14.6969i | −0.873642 | + | 0.873642i | −0.992867 | − | 0.119225i | \(-0.961959\pi\) |
0.119225 | + | 0.992867i | \(0.461959\pi\) | |||||||
\(284\) | 12.8348i | 0.761608i | ||||||||
\(285\) | −4.38774 | + | 0.915775i | −0.259907 | + | 0.0542458i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.00000 | − | 7.00000i | −0.413197 | − | 0.413197i | ||||
\(288\) | 12.0000 | − | 12.0000i | 0.707107 | − | 0.707107i | ||||
\(289\) | 44.4955i | 2.61738i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.07310 | + | 2.07310i | −0.121112 | + | 0.121112i | −0.765065 | − | 0.643953i | \(-0.777293\pi\) |
0.643953 | + | 0.765065i | \(0.277293\pi\) | |||||||
\(294\) | 17.1464i | 1.00000i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 34.3303 | 1.99541 | ||||||||
\(297\) | −13.1632 | − | 13.1632i | −0.763808 | − | 0.763808i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −6.32599 | + | 16.1240i | −0.365231 | + | 0.930917i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.00000 | − | 9.00000i | 0.517036 | − | 0.517036i | ||||
\(304\) | − | 4.62929i | − | 0.265508i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −33.2704 | −1.90194 | ||||||||
\(307\) | 3.74166 | + | 3.74166i | 0.213548 | + | 0.213548i | 0.805773 | − | 0.592225i | \(-0.201750\pi\) |
−0.592225 | + | 0.805773i | \(0.701750\pi\) | |||||||
\(308\) | 13.4048 | − | 13.4048i | 0.763808 | − | 0.763808i | ||||
\(309\) | − | 18.3303i | − | 1.04277i | ||||||
\(310\) | −30.7477 | + | 6.41742i | −1.74635 | + | 0.364485i | ||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.62614 | − | 17.3739i | −0.204310 | − | 0.978906i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −14.9666 | − | 9.79796i | −0.836660 | − | 0.547723i | ||||
\(321\) | 33.6749 | 1.87955 | ||||||||
\(322\) | −17.1464 | − | 17.1464i | −0.955533 | − | 0.955533i | ||||
\(323\) | −6.41742 | + | 6.41742i | −0.357075 | + | 0.357075i | ||||
\(324\) | − | 18.0000i | − | 1.00000i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.4499 | + | 22.4499i | 1.24148 | + | 1.24148i | ||||
\(328\) | −7.48331 | + | 7.48331i | −0.413197 | + | 0.413197i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10.7477 | + | 16.4174i | −0.591643 | + | 0.903749i | ||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.7477 | − | 25.7477i | 1.41097 | − | 1.41097i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 18.3303 | 1.00000 | ||||||||
\(337\) | −19.3303 | − | 19.3303i | −1.05299 | − | 1.05299i | −0.998515 | − | 0.0544735i | \(-0.982652\pi\) |
−0.0544735 | − | 0.998515i | \(-0.517348\pi\) | |||||||
\(338\) | −13.0000 | + | 13.0000i | −0.707107 | + | 0.707107i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.16515 | + | 34.3303i | 0.388585 | + | 1.86182i | ||||
\(341\) | −35.5850 | −1.92704 | ||||||||
\(342\) | −3.47197 | − | 3.47197i | −0.187742 | − | 0.187742i | ||||
\(343\) | −13.0958 | + | 13.0958i | −0.707107 | + | 0.707107i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.0000 | + | 13.7477i | 1.13060 | + | 0.740153i | ||||
\(346\) | 28.6411 | 1.53975 | ||||||||
\(347\) | 13.0000 | + | 13.0000i | 0.697877 | + | 0.697877i | 0.963952 | − | 0.266076i | \(-0.0857271\pi\) |
−0.266076 | + | 0.963952i | \(0.585727\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | −17.1464 | + | 7.48331i | −0.916515 | + | 0.400000i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −14.3303 | − | 14.3303i | −0.763808 | − | 0.763808i | ||||
\(353\) | −26.5680 | + | 26.5680i | −1.41407 | + | 1.41407i | −0.697019 | + | 0.717053i | \(0.745491\pi\) |
−0.717053 | + | 0.697019i | \(0.754509\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.85971 | − | 12.0059i | 0.417150 | − | 0.637207i | ||||
\(356\) | 4.89898 | 0.259645 | ||||||||
\(357\) | −25.4107 | − | 25.4107i | −1.34488 | − | 1.34488i | ||||
\(358\) | 0.747727 | − | 0.747727i | 0.0395186 | − | 0.0395186i | ||||
\(359\) | − | 9.25227i | − | 0.488316i | −0.969735 | − | 0.244158i | \(-0.921488\pi\) | ||
0.969735 | − | 0.244158i | \(-0.0785116\pi\) | |||||||
\(360\) | −18.5734 | + | 3.87650i | −0.978906 | + | 0.204310i | ||||
\(361\) | 17.6606 | 0.929506 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.24722 | + | 2.24722i | −0.117949 | + | 0.117949i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.5959 | + | 19.5959i | 1.02290 | + | 1.02290i | 0.999732 | + | 0.0231670i | \(0.00737494\pi\) |
0.0231670 | + | 0.999732i | \(0.492625\pi\) | |||||||
\(368\) | −18.3303 | + | 18.3303i | −0.955533 | + | 0.955533i | ||||
\(369\) | 11.2250i | 0.584349i | ||||||||
\(370\) | −32.1131 | − | 21.0229i | −1.66948 | − | 1.09293i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −24.3303 | − | 24.3303i | −1.26147 | − | 1.26147i | ||||
\(373\) | 7.83485 | − | 7.83485i | 0.405673 | − | 0.405673i | −0.474554 | − | 0.880227i | \(-0.657390\pi\) |
0.880227 | + | 0.474554i | \(0.157390\pi\) | |||||||
\(374\) | 39.7312i | 2.05445i | ||||||||
\(375\) | 15.7913 | − | 11.2087i | 0.815459 | − | 0.578815i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 13.7477 | − | 13.7477i | 0.707107 | − | 0.707107i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | −2.83485 | + | 4.33030i | −0.145425 | + | 0.222140i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 23.5826 | + | 23.5826i | 1.20659 | + | 1.20659i | ||||
\(383\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(384\) | − | 19.5959i | − | 1.00000i | ||||||
\(385\) | −20.7477 | + | 4.33030i | −1.05740 | + | 0.220693i | ||||
\(386\) | −31.4955 | −1.60308 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 50.8213 | 2.57015 | ||||||||
\(392\) | 14.0000 | + | 14.0000i | 0.707107 | + | 0.707107i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −21.4955 | −1.08019 | ||||||||
\(397\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(398\) | −23.3376 | + | 23.3376i | −1.16981 | + | 1.16981i | ||||
\(399\) | − | 5.30352i | − | 0.265508i | ||||||
\(400\) | 8.00000 | + | 18.3303i | 0.400000 | + | 0.916515i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 14.6969i | − | 0.731200i | ||||||
\(405\) | −11.0227 | + | 16.8375i | −0.547723 | + | 0.836660i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −30.7477 | − | 30.7477i | −1.52411 | − | 1.52411i | ||||
\(408\) | −27.1652 | + | 27.1652i | −1.34488 | + | 1.34488i | ||||
\(409\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 11.5826 | − | 2.41742i | 0.572023 | − | 0.119388i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.9666 | − | 14.9666i | −0.737353 | − | 0.737353i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 27.4955i | 1.35133i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.33030 | − | 9.33030i | −0.456907 | − | 0.456907i | ||||
\(418\) | −4.14619 | + | 4.14619i | −0.202797 | + | 0.202797i | ||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | −17.1464 | − | 11.2250i | −0.836660 | − | 0.547723i | ||||
\(421\) | −9.16515 | −0.446682 | −0.223341 | − | 0.974740i | \(-0.571696\pi\) | ||||
−0.223341 | + | 0.974740i | \(0.571696\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.3205 | − | 36.5008i | 0.694649 | − | 1.77055i | ||||
\(426\) | 15.7194 | 0.761608 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 27.4955 | − | 27.4955i | 1.32904 | − | 1.32904i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.5826 | −1.61762 | −0.808808 | − | 0.588073i | \(-0.799887\pi\) | ||||
−0.808808 | + | 0.588073i | \(0.799887\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.707107 | − | 0.707107i | ||||
\(433\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(434\) | − | 37.1652i | − | 1.78398i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 36.6606 | 1.75572 | ||||||||
\(437\) | 5.30352 | + | 5.30352i | 0.253702 | + | 0.253702i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.6522i | 1.22431i | 0.790736 | + | 0.612157i | \(0.209698\pi\) | ||||
−0.790736 | + | 0.612157i | \(0.790302\pi\) | |||||||
\(440\) | 4.62929 | + | 22.1803i | 0.220693 | + | 1.05740i | ||||
\(441\) | 21.0000 | 1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.0000 | − | 19.0000i | 0.902717 | − | 0.902717i | −0.0929532 | − | 0.995670i | \(-0.529631\pi\) |
0.995670 | + | 0.0929532i | \(0.0296307\pi\) | |||||||
\(444\) | − | 42.0459i | − | 1.99541i | ||||||
\(445\) | −4.58258 | − | 3.00000i | −0.217235 | − | 0.142214i | ||||
\(446\) | −19.5959 | −0.927894 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14.9666 | − | 14.9666i | 0.707107 | − | 0.707107i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 19.7477 | + | 7.74773i | 0.930917 | + | 0.365231i | ||||
\(451\) | 13.4048 | 0.631206 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.66970 | −0.265508 | ||||||||
\(457\) | −29.3303 | − | 29.3303i | −1.37201 | − | 1.37201i | −0.857455 | − | 0.514558i | \(-0.827956\pi\) |
−0.514558 | − | 0.857455i | \(-0.672044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 40.7477i | 1.90194i | ||||||||
\(460\) | 28.3714 | − | 5.92146i | 1.32282 | − | 0.276089i | ||||
\(461\) | −41.1582 | −1.91693 | −0.958465 | − | 0.285210i | \(-0.907937\pi\) | ||||
−0.958465 | + | 0.285210i | \(0.907937\pi\) | |||||||
\(462\) | −16.4174 | − | 16.4174i | −0.763808 | − | 0.763808i | ||||
\(463\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.85971 | + | 37.6581i | 0.364485 | + | 1.74635i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.30352 | − | 2.31464i | 0.243342 | − | 0.106203i | ||||
\(476\) | −41.4955 | −1.90194 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 30.7477 | − | 30.7477i | 1.40637 | − | 1.40637i | ||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | −12.0000 | + | 18.3303i | −0.547723 | + | 0.836660i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −21.0000 | + | 21.0000i | −0.955533 | + | 0.955533i | ||||
\(484\) | 3.66970i | 0.166804i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −22.0454 | −1.00000 | ||||||||
\(487\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.52259 | − | 21.6690i | −0.204310 | − | 0.978906i | ||||
\(491\) | 26.4174 | 1.19220 | 0.596101 | − | 0.802910i | \(-0.296716\pi\) | ||||
0.596101 | + | 0.802910i | \(0.296716\pi\) | |||||||
\(492\) | 9.16515 | + | 9.16515i | 0.413197 | + | 0.413197i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 20.1072 | + | 13.1632i | 0.903749 | + | 0.591643i | ||||
\(496\) | −39.7312 | −1.78398 | ||||||||
\(497\) | 12.0059 | + | 12.0059i | 0.538538 | + | 0.538538i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 3.74166 | − | 22.0454i | 0.167332 | − | 0.985901i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(504\) | − | 22.4499i | − | 1.00000i | ||||||
\(505\) | −9.00000 | + | 13.7477i | −0.400495 | + | 0.611766i | ||||
\(506\) | 32.8348 | 1.45969 | ||||||||
\(507\) | 15.9217 | + | 15.9217i | 0.707107 | + | 0.707107i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 26.1916i | − | 1.16092i | −0.814288 | − | 0.580461i | \(-0.802872\pi\) | ||
0.814288 | − | 0.580461i | \(-0.197128\pi\) | |||||||
\(510\) | 42.0459 | − | 8.77548i | 1.86182 | − | 0.388585i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | −4.25227 | + | 4.25227i | −0.187742 | + | 0.187742i | ||||
\(514\) | − | 35.5850i | − | 1.56959i | ||||||
\(515\) | 4.83485 | + | 23.1652i | 0.213049 | + | 1.02078i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 32.1131 | − | 32.1131i | 1.41097 | − | 1.41097i | ||||
\(519\) | − | 35.0780i | − | 1.53975i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.6413 | 1.82434 | 0.912170 | − | 0.409812i | \(-0.134406\pi\) | ||||
0.912170 | + | 0.409812i | \(0.134406\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.9333 | − | 29.9333i | 1.30889 | − | 1.30889i | 0.386673 | − | 0.922217i | \(-0.373624\pi\) |
0.922217 | − | 0.386673i | \(-0.126376\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.16515 | + | 21.0000i | 0.400000 | + | 0.916515i | ||||
\(526\) | 2.00000 | 0.0872041 | ||||||||
\(527\) | 55.0780 | + | 55.0780i | 2.39924 | + | 2.39924i | ||||
\(528\) | −17.5510 | + | 17.5510i | −0.763808 | + | 0.763808i | ||||
\(529\) | − | 19.0000i | − | 0.826087i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.33030 | − | 4.33030i | −0.187742 | − | 0.187742i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | − | 6.00000i | − | 0.259645i | ||||||
\(535\) | −42.5571 | + | 8.88218i | −1.83990 | + | 0.384010i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.915775 | − | 0.915775i | −0.0395186 | − | 0.0395186i | ||||
\(538\) | −26.9444 | + | 26.9444i | −1.16166 | + | 1.16166i | ||||
\(539\) | − | 25.0780i | − | 1.08019i | ||||||
\(540\) | 4.74773 | + | 22.7477i | 0.204310 | + | 0.978906i | ||||
\(541\) | −8.00000 | −0.343947 | −0.171973 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171973 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(542\) | 14.5621 | + | 14.5621i | 0.625495 | + | 0.625495i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 44.3605i | 1.90194i | ||||||||
\(545\) | −34.2929 | − | 22.4499i | −1.46894 | − | 0.961650i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.25227 | − | 23.5826i | 0.394518 | − | 1.00556i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 22.4499 | + | 22.4499i | 0.955533 | + | 0.955533i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22.8348i | 0.970160i | ||||||||
\(555\) | −25.7477 | + | 39.3303i | −1.09293 | + | 1.66948i | ||||
\(556\) | −15.2363 | −0.646164 | ||||||||
\(557\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(558\) | −29.7984 | + | 29.7984i | −1.26147 | + | 1.26147i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −23.1652 | + | 4.83485i | −0.978906 | + | 0.204310i | ||||
\(561\) | 48.6606 | 2.05445 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 29.3939 | 1.23552 | ||||||||
\(567\) | −16.8375 | − | 16.8375i | −0.707107 | − | 0.707107i | ||||
\(568\) | 12.8348 | − | 12.8348i | 0.538538 | − | 0.538538i | ||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 5.30352 | + | 3.47197i | 0.222140 | + | 0.145425i | ||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 28.8826 | − | 28.8826i | 1.20659 | − | 1.20659i | ||||
\(574\) | 14.0000i | 0.584349i | ||||||||
\(575\) | −30.1652 | − | 11.8348i | −1.25797 | − | 0.493547i | ||||
\(576\) | −24.0000 | −1.00000 | ||||||||
\(577\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(578\) | 44.4955 | − | 44.4955i | 1.85077 | − | 1.85077i | ||||
\(579\) | 38.5739i | 1.60308i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.14619 | 0.171278 | ||||||||
\(587\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(588\) | 17.1464 | − | 17.1464i | 0.707107 | − | 0.707107i | ||||
\(589\) | 11.4955i | 0.473662i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −34.3303 | − | 34.3303i | −1.41097 | − | 1.41097i | ||||
\(593\) | 23.0960 | − | 23.0960i | 0.948440 | − | 0.948440i | −0.0502942 | − | 0.998734i | \(-0.516016\pi\) |
0.998734 | + | 0.0502942i | \(0.0160159\pi\) | |||||||
\(594\) | 26.3264i | 1.08019i | ||||||||
\(595\) | 38.8154 | + | 25.4107i | 1.59128 | + | 1.04174i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 28.5826 | + | 28.5826i | 1.16981 | + | 1.16981i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 45.0780i | − | 1.84184i | −0.389754 | − | 0.920919i | \(-0.627440\pi\) | ||
0.389754 | − | 0.920919i | \(-0.372560\pi\) | |||||||
\(600\) | 22.4499 | − | 9.79796i | 0.916515 | − | 0.400000i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.24722 | − | 3.43269i | 0.0913625 | − | 0.139559i | ||||
\(606\) | −18.0000 | −0.731200 | ||||||||
\(607\) | −29.3939 | − | 29.3939i | −1.19306 | − | 1.19306i | −0.976203 | − | 0.216857i | \(-0.930419\pi\) |
−0.216857 | − | 0.976203i | \(-0.569581\pi\) | |||||||
\(608\) | −4.62929 | + | 4.62929i | −0.187742 | + | 0.187742i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 33.2704 | + | 33.2704i | 1.34488 | + | 1.34488i | ||||
\(613\) | −32.1652 | + | 32.1652i | −1.29914 | + | 1.29914i | −0.370177 | + | 0.928961i | \(0.620703\pi\) |
−0.928961 | + | 0.370177i | \(0.879297\pi\) | |||||||
\(614\) | − | 7.48331i | − | 0.302002i | ||||||
\(615\) | −2.96073 | − | 14.1857i | −0.119388 | − | 0.572023i | ||||
\(616\) | −26.8095 | −1.08019 | ||||||||
\(617\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(618\) | −18.3303 | + | 18.3303i | −0.737353 | + | 0.737353i | ||||
\(619\) | − | 16.8767i | − | 0.678333i | −0.940726 | − | 0.339167i | \(-0.889855\pi\) | ||
0.940726 | − | 0.339167i | \(-0.110145\pi\) | |||||||
\(620\) | 37.1652 | + | 24.3303i | 1.49259 | + | 0.977128i | ||||
\(621\) | 33.6749 | 1.35133 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.58258 | − | 4.58258i | 0.183597 | − | 0.183597i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.0000 | + | 18.3303i | −0.680000 | + | 0.733212i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.07803 | + | 5.07803i | 0.202797 | + | 0.202797i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 95.1819i | 3.79515i | ||||||||
\(630\) | −13.7477 | + | 21.0000i | −0.547723 | + | 0.836660i | ||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 19.2523i | − | 0.761608i | ||||||
\(640\) | 5.16867 | + | 24.7646i | 0.204310 | + | 0.978906i | ||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | −33.6749 | − | 33.6749i | −1.32904 | − | 1.32904i | ||||
\(643\) | −26.1916 | + | 26.1916i | −1.03290 | + | 1.03290i | −0.0334557 | + | 0.999440i | \(0.510651\pi\) |
−0.999440 | + | 0.0334557i | \(0.989349\pi\) | |||||||
\(644\) | 34.2929i | 1.35133i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.8348 | 0.504980 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | −18.0000 | + | 18.0000i | −0.707107 | + | 0.707107i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −45.5178 | −1.78398 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(654\) | − | 44.8999i | − | 1.75572i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.9666 | 0.584349 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 15.0780i | − | 0.587357i | −0.955904 | − | 0.293678i | \(-0.905121\pi\) | ||
0.955904 | − | 0.293678i | \(-0.0948794\pi\) | |||||||
\(660\) | 27.1652 | − | 5.66970i | 1.05740 | − | 0.220693i | ||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.39887 | + | 6.70239i | 0.0542458 | + | 0.259907i | ||||
\(666\) | −51.4955 | −1.99541 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0000i | 0.927894i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −18.3303 | − | 18.3303i | −0.707107 | − | 0.707107i | ||||
\(673\) | 35.7477 | − | 35.7477i | 1.37797 | − | 1.37797i | 0.529936 | − | 0.848038i | \(-0.322216\pi\) |
0.848038 | − | 0.529936i | \(-0.177784\pi\) | |||||||
\(674\) | 38.6606i | 1.48915i | ||||||||
\(675\) | 9.48899 | − | 24.1859i | 0.365231 | − | 0.930917i | ||||
\(676\) | 26.0000 | 1.00000 | ||||||||
\(677\) | 36.5008 | + | 36.5008i | 1.40284 | + | 1.40284i | 0.790920 | + | 0.611920i | \(0.209603\pi\) |
0.611920 | + | 0.790920i | \(0.290397\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 27.1652 | − | 41.4955i | 1.04174 | − | 1.59128i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 35.5850 | + | 35.5850i | 1.36262 | + | 1.36262i | ||||
\(683\) | 29.0000 | − | 29.0000i | 1.10965 | − | 1.10965i | 0.116459 | − | 0.993196i | \(-0.462846\pi\) |
0.993196 | − | 0.116459i | \(-0.0371542\pi\) | |||||||
\(684\) | 6.94393i | 0.265508i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916 | 1.00000 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −7.25227 | − | 34.7477i | −0.276089 | − | 1.32282i | ||||
\(691\) | −51.9787 | −1.97736 | −0.988681 | − | 0.150034i | \(-0.952062\pi\) | ||||
−0.988681 | + | 0.150034i | \(0.952062\pi\) | |||||||
\(692\) | −28.6411 | − | 28.6411i | −1.08877 | − | 1.08877i | ||||
\(693\) | −20.1072 | + | 20.1072i | −0.763808 | + | 0.763808i | ||||
\(694\) | − | 26.0000i | − | 0.986947i | ||||||
\(695\) | 14.2523 | + | 9.33030i | 0.540620 | + | 0.353919i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.7477 | − | 20.7477i | −0.785876 | − | 0.785876i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 24.6297 | + | 9.66311i | 0.930917 | + | 0.365231i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.93280 | + | 9.93280i | −0.374623 | + | 0.374623i | ||||
\(704\) | 28.6606i | 1.08019i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 53.1360 | 1.99980 | ||||||||
\(707\) | −13.7477 | − | 13.7477i | −0.517036 | − | 0.517036i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 18.3303i | − | 0.688409i | −0.938895 | − | 0.344204i | \(-0.888149\pi\) | ||
0.938895 | − | 0.344204i | \(-0.111851\pi\) | |||||||
\(710\) | −19.8656 | + | 4.14619i | −0.745543 | + | 0.155604i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.89898 | − | 4.89898i | −0.183597 | − | 0.183597i | ||||
\(713\) | 45.5178 | − | 45.5178i | 1.70466 | − | 1.70466i | ||||
\(714\) | 50.8213i | 1.90194i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.49545 | −0.0558877 | ||||||||
\(717\) | −37.6581 | − | 37.6581i | −1.40637 | − | 1.40637i | ||||
\(718\) | −9.25227 | + | 9.25227i | −0.345292 | + | 0.345292i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 22.4499 | + | 14.6969i | 0.836660 | + | 0.547723i | ||||
\(721\) | −28.0000 | −1.04277 | ||||||||
\(722\) | −17.6606 | − | 17.6606i | −0.657260 | − | 0.657260i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.49444 | 0.166804 | ||||||||
\(727\) | 7.34847 | + | 7.34847i | 0.272540 | + | 0.272540i | 0.830122 | − | 0.557582i | \(-0.188271\pi\) |
−0.557582 | + | 0.830122i | \(0.688271\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(734\) | − | 39.1918i | − | 1.44660i | ||||||
\(735\) | −26.5390 | + | 5.53901i | −0.978906 | + | 0.204310i | ||||
\(736\) | 36.6606 | 1.35133 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 11.2250 | − | 11.2250i | 0.413197 | − | 0.413197i | ||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 11.0901 | + | 53.1360i | 0.407681 | + | 1.95332i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.0000 | + | 31.0000i | −1.13728 | + | 1.13728i | −0.148344 | + | 0.988936i | \(0.547394\pi\) |
−0.988936 | + | 0.148344i | \(0.952606\pi\) | |||||||
\(744\) | 48.6606i | 1.78398i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.6697 | −0.573708 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 39.7312 | − | 39.7312i | 1.45272 | − | 1.45272i | ||||
\(749\) | − | 51.4393i | − | 1.87955i | ||||||
\(750\) | −27.0000 | − | 4.58258i | −0.985901 | − | 0.167332i | ||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −27.4955 | −1.00000 | ||||||||
\(757\) | 26.4955 | + | 26.4955i | 0.962994 | + | 0.962994i | 0.999339 | − | 0.0363456i | \(-0.0115717\pi\) |
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 40.2143i | − | 1.45969i | ||||||
\(760\) | 7.16515 | − | 1.49545i | 0.259907 | − | 0.0542458i | ||||
\(761\) | −41.1582 | −1.49198 | −0.745992 | − | 0.665955i | \(-0.768024\pi\) | ||||
−0.745992 | + | 0.665955i | \(0.768024\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.2929 | − | 34.2929i | 1.24148 | − | 1.24148i | ||||
\(764\) | − | 47.1652i | − | 1.70638i | ||||||
\(765\) | −10.7477 | − | 51.4955i | −0.388585 | − | 1.86182i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −19.5959 | + | 19.5959i | −0.707107 | + | 0.707107i | ||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 25.0780 | + | 16.4174i | 0.903749 | + | 0.591643i | ||||
\(771\) | −43.5826 | −1.56959 | ||||||||
\(772\) | 31.4955 | + | 31.4955i | 1.13355 | + | 1.13355i | ||||
\(773\) | 10.8486 | − | 10.8486i | 0.390196 | − | 0.390196i | −0.484561 | − | 0.874757i | \(-0.661021\pi\) |
0.874757 | + | 0.484561i | \(0.161021\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.8656 | − | 45.5178i | −0.713594 | − | 1.63505i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −39.3303 | − | 39.3303i | −1.41097 | − | 1.41097i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 4.33030i | − | 0.155149i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.9909 | −0.822679 | ||||||||
\(782\) | −50.8213 | − | 50.8213i | −1.81737 | − | 1.81737i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 28.0000i | − | 1.00000i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.9666 | − | 14.9666i | −0.533503 | − | 0.533503i | 0.388110 | − | 0.921613i | \(-0.373128\pi\) |
−0.921613 | + | 0.388110i | \(0.873128\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 2.44949i | − | 0.0872041i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 21.4955 | + | 21.4955i | 0.763808 | + | 0.763808i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 46.6752 | 1.65436 | ||||||||
\(797\) | 30.0400 | + | 30.0400i | 1.06407 | + | 1.06407i | 0.997802 | + | 0.0662682i | \(0.0211093\pi\) |
0.0662682 | + | 0.997802i | \(0.478891\pi\) | |||||||
\(798\) | −5.30352 | + | 5.30352i | −0.187742 | + | 0.187742i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 10.3303 | − | 26.3303i | 0.365231 | − | 0.930917i | ||||
\(801\) | −7.34847 | −0.259645 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.0000 | − | 32.0780i | 0.740153 | − | 1.13060i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.0000 | + | 33.0000i | 1.16166 | + | 1.16166i | ||||
\(808\) | −14.6969 | + | 14.6969i | −0.517036 | + | 0.517036i | ||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 27.8602 | − | 5.81475i | 0.978906 | − | 0.204310i | ||||
\(811\) | −2.98887 | −0.104953 | −0.0524767 | − | 0.998622i | \(-0.516712\pi\) | ||||
−0.0524767 | + | 0.998622i | \(0.516712\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.8348 | − | 17.8348i | 0.625495 | − | 0.625495i | ||||
\(814\) | 61.4955i | 2.15541i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 54.3303 | 1.90194 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.0000 | − | 9.16515i | −0.488901 | − | 0.320061i | ||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(824\) | 29.9333i | 1.04277i | ||||||||
\(825\) | −28.8826 | − | 11.3317i | −1.00556 | − | 0.394518i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.0780 | + | 32.0780i | 1.11546 | + | 1.11546i | 0.992399 | + | 0.123064i | \(0.0392719\pi\) |
0.123064 | + | 0.992399i | \(0.460728\pi\) | |||||||
\(828\) | 27.4955 | − | 27.4955i | 0.955533 | − | 0.955533i | ||||
\(829\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.9669 | 0.970160 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.8154 | + | 38.8154i | −1.34488 | + | 1.34488i | ||||
\(834\) | 18.6606i | 0.646164i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.29239 | 0.286798 | ||||||||
\(837\) | 36.4955 | + | 36.4955i | 1.26147 | + | 1.26147i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 5.92146 | + | 28.3714i | 0.204310 | + | 0.978906i | ||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 9.16515 | + | 9.16515i | 0.315852 | + | 0.315852i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.3208 | − | 15.9217i | −0.836660 | − | 0.547723i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.43269 | + | 3.43269i | 0.117949 | + | 0.117949i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 36.0000i | − | 1.23552i | ||||||
\(850\) | −50.8213 | + | 22.1803i | −1.74316 | + | 0.760776i | ||||
\(851\) | 78.6606 | 2.69645 | ||||||||
\(852\) | −15.7194 | − | 15.7194i | −0.538538 | − | 0.538538i | ||||
\(853\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.25227 | − | 6.49545i | 0.145425 | − | 0.222140i | ||||
\(856\) | −54.9909 | −1.87955 | ||||||||
\(857\) | −0.241547 | − | 0.241547i | −0.00825109 | − | 0.00825109i | 0.702969 | − | 0.711220i | \(-0.251857\pi\) |
−0.711220 | + | 0.702969i | \(0.751857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 36.2593i | − | 1.23715i | −0.785726 | − | 0.618575i | \(-0.787710\pi\) | ||
0.785726 | − | 0.618575i | \(-0.212290\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.1464 | 0.584349 | ||||||||
\(862\) | 33.5826 | + | 33.5826i | 1.14383 | + | 1.14383i | ||||
\(863\) | −41.2432 | + | 41.2432i | −1.40393 | + | 1.40393i | −0.616866 | + | 0.787068i | \(0.711598\pi\) |
−0.787068 | + | 0.616866i | \(0.788402\pi\) | |||||||
\(864\) | 29.3939i | 1.00000i | ||||||||
\(865\) | 9.25227 | + | 44.3303i | 0.314587 | + | 1.50728i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −54.4956 | − | 54.4956i | −1.85077 | − | 1.85077i | ||||
\(868\) | −37.1652 | + | 37.1652i | −1.26147 | + | 1.26147i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −36.6606 | − | 36.6606i | −1.24148 | − | 1.24148i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 10.6070i | − | 0.358788i | ||||||
\(875\) | −17.1216 | − | 24.1216i | −0.578815 | − | 0.815459i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.4955 | + | 16.4955i | 0.557012 | + | 0.557012i | 0.928456 | − | 0.371444i | \(-0.121137\pi\) |
−0.371444 | + | 0.928456i | \(0.621137\pi\) | |||||||
\(878\) | 25.6522 | − | 25.6522i | 0.865720 | − | 0.865720i | ||||
\(879\) | − | 5.07803i | − | 0.171278i | ||||||
\(880\) | 17.5510 | − | 26.8095i | 0.591643 | − | 0.903749i | ||||
\(881\) | −56.3383 | −1.89808 | −0.949042 | − | 0.315149i | \(-0.897945\pi\) | ||||
−0.949042 | + | 0.315149i | \(0.897945\pi\) | |||||||
\(882\) | −21.0000 | − | 21.0000i | −0.707107 | − | 0.707107i | ||||
\(883\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38.0000 | −1.27663 | ||||||||
\(887\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(888\) | −42.0459 | + | 42.0459i | −1.41097 | + | 1.41097i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.58258 | + | 7.58258i | 0.0530481 | + | 0.254169i | ||||
\(891\) | 32.2432 | 1.08019 | ||||||||
\(892\) | 19.5959 | + | 19.5959i | 0.656120 | + | 0.656120i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.39887 | + | 0.915775i | 0.0467590 | + | 0.0306110i | ||||
\(896\) | −29.9333 | −1.00000 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −12.0000 | − | 27.4955i | −0.400000 | − | 0.916515i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −13.4048 | − | 13.4048i | −0.446330 | − | 0.446330i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.0454i | 0.731200i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.2432 | 1.73089 | 0.865447 | − | 0.501001i | \(-0.167035\pi\) | ||||
0.865447 | + | 0.501001i | \(0.167035\pi\) | |||||||
\(912\) | 5.66970 | + | 5.66970i | 0.187742 | + | 0.187742i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 58.6606i | 1.94032i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 40.7477 | − | 40.7477i | 1.34488 | − | 1.34488i | ||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | −34.2929 | − | 22.4499i | −1.13060 | − | 0.740153i | ||||
\(921\) | −9.16515 | −0.302002 | ||||||||
\(922\) | 41.1582 | + | 41.1582i | 1.35547 | + | 1.35547i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 32.8348i | 1.08019i | ||||||||
\(925\) | 22.1652 | − | 56.4955i | 0.728786 | − | 1.85756i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.4499 | + | 22.4499i | 0.737353 | + | 0.737353i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48.6415i | 1.59588i | 0.602739 | + | 0.797939i | \(0.294076\pi\) | ||||
−0.602739 | + | 0.797939i | \(0.705924\pi\) | |||||||
\(930\) | 29.7984 | − | 45.5178i | 0.977128 | − | 1.49259i | ||||
\(931\) | −8.10125 | −0.265508 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −61.4955 | + | 12.8348i | −2.01112 | + | 0.419744i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.74166 | −0.121975 | −0.0609873 | − | 0.998139i | \(-0.519425\pi\) | ||||
−0.0609873 | + | 0.998139i | \(0.519425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.1464 | + | 17.1464i | −0.558365 | + | 0.558365i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 25.7196 | + | 16.8375i | 0.836660 | + | 0.547723i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.0000 | − | 37.0000i | −1.20234 | − | 1.20234i | −0.973453 | − | 0.228885i | \(-0.926492\pi\) |
−0.228885 | − | 0.973453i | \(-0.573508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −7.61816 | − | 2.98887i | −0.247166 | − | 0.0969718i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 41.4955 | + | 41.4955i | 1.34488 | + | 1.34488i | ||||
\(953\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.8826 | + | 44.1190i | −0.934620 | + | 1.42766i | ||||
\(956\) | −61.4955 | −1.98891 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 30.3303 | − | 6.33030i | 0.978906 | − | 0.204310i | ||||
\(961\) | 67.6606 | 2.18260 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −41.2432 | + | 41.2432i | −1.32904 | + | 1.32904i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.1744 | − | 48.7482i | −0.327524 | − | 1.56926i | ||||
\(966\) | 42.0000 | 1.35133 | ||||||||
\(967\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(968\) | 3.66970 | − | 3.66970i | 0.117949 | − | 0.117949i | ||||
\(969\) | − | 15.7194i | − | 0.504980i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | 22.0454 | + | 22.0454i | 0.707107 | + | 0.707107i | ||||
\(973\) | −14.2523 | + | 14.2523i | −0.456907 | + | 0.456907i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.77548i | 0.280466i | ||||||||
\(980\) | −17.1464 | + | 26.1916i | −0.547723 | + | 0.836660i | ||||
\(981\) | −54.9909 | −1.75572 | ||||||||
\(982\) | −26.4174 | − | 26.4174i | −0.843014 | − | 0.843014i | ||||
\(983\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(984\) | − | 18.3303i | − | 0.584349i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −6.94393 | − | 33.2704i | −0.220693 | − | 1.05740i | ||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 39.7312 | + | 39.7312i | 1.26147 | + | 1.26147i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 24.0118i | − | 0.761608i | ||||||
\(995\) | −43.6606 | − | 28.5826i | −1.38413 | − | 0.906129i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 63.0688i | 1.99541i |
(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 | 420.2.w.a.167.1 | yes | 8 | |
3.2 | odd | 2 | 420.2.w.b.167.2 | yes | 8 | ||
4.3 | odd | 2 | 420.2.w.b.167.3 | yes | 8 | ||
5.3 | odd | 4 | inner | 420.2.w.a.83.2 | ✓ | 8 | |
7.6 | odd | 2 | inner | 420.2.w.a.167.4 | yes | 8 | |
12.11 | even | 2 | inner | 420.2.w.a.167.4 | yes | 8 | |
15.8 | even | 4 | 420.2.w.b.83.1 | yes | 8 | ||
20.3 | even | 4 | 420.2.w.b.83.4 | yes | 8 | ||
21.20 | even | 2 | 420.2.w.b.167.3 | yes | 8 | ||
28.27 | even | 2 | 420.2.w.b.167.2 | yes | 8 | ||
35.13 | even | 4 | inner | 420.2.w.a.83.3 | yes | 8 | |
60.23 | odd | 4 | inner | 420.2.w.a.83.3 | yes | 8 | |
84.83 | odd | 2 | CM | 420.2.w.a.167.1 | yes | 8 | |
105.83 | odd | 4 | 420.2.w.b.83.4 | yes | 8 | ||
140.83 | odd | 4 | 420.2.w.b.83.1 | yes | 8 | ||
420.83 | even | 4 | inner | 420.2.w.a.83.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.w.a.83.2 | ✓ | 8 | 5.3 | odd | 4 | inner | |
420.2.w.a.83.2 | ✓ | 8 | 420.83 | even | 4 | inner | |
420.2.w.a.83.3 | yes | 8 | 35.13 | even | 4 | inner | |
420.2.w.a.83.3 | yes | 8 | 60.23 | odd | 4 | inner | |
420.2.w.a.167.1 | yes | 8 | 1.1 | even | 1 | trivial | |
420.2.w.a.167.1 | yes | 8 | 84.83 | odd | 2 | CM | |
420.2.w.a.167.4 | yes | 8 | 7.6 | odd | 2 | inner | |
420.2.w.a.167.4 | yes | 8 | 12.11 | even | 2 | inner | |
420.2.w.b.83.1 | yes | 8 | 15.8 | even | 4 | ||
420.2.w.b.83.1 | yes | 8 | 140.83 | odd | 4 | ||
420.2.w.b.83.4 | yes | 8 | 20.3 | even | 4 | ||
420.2.w.b.83.4 | yes | 8 | 105.83 | odd | 4 | ||
420.2.w.b.167.2 | yes | 8 | 3.2 | odd | 2 | ||
420.2.w.b.167.2 | yes | 8 | 28.27 | even | 2 | ||
420.2.w.b.167.3 | yes | 8 | 4.3 | odd | 2 | ||
420.2.w.b.167.3 | yes | 8 | 21.20 | even | 2 |