Newspace parameters
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(9.34249703649\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
|
|
Defining polynomial: |
\( x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 577.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.577 |
Dual form | 1170.2.m.a.73.1 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | − | 2.00000i | −0.447214 | − | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.00000i | − | 0.755929i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) | ||
0.925820 | − | 0.377964i | \(-0.123376\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | + | 2.00000i | 0.316228 | + | 0.632456i | ||||
\(11\) | −1.00000 | − | 1.00000i | −0.301511 | − | 0.301511i | 0.540094 | − | 0.841605i | \(-0.318389\pi\) |
−0.841605 | + | 0.540094i | \(0.818389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | − | 2.00000i | −0.832050 | − | 0.554700i | ||||
\(14\) | 2.00000i | 0.534522i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.00000 | + | 5.00000i | −1.21268 | + | 1.21268i | −0.242536 | + | 0.970143i | \(0.577979\pi\) |
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | − | 3.00000i | −0.688247 | − | 0.688247i | 0.273597 | − | 0.961844i | \(-0.411786\pi\) |
−0.961844 | + | 0.273597i | \(0.911786\pi\) | |||||||
\(20\) | −1.00000 | − | 2.00000i | −0.223607 | − | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | + | 1.00000i | 0.213201 | + | 0.213201i | ||||
\(23\) | 5.00000 | + | 5.00000i | 1.04257 | + | 1.04257i | 0.999053 | + | 0.0435195i | \(0.0138571\pi\) |
0.0435195 | + | 0.999053i | \(0.486143\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | 3.00000 | + | 2.00000i | 0.588348 | + | 0.392232i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 2.00000i | − | 0.377964i | ||||||
\(29\) | − | 4.00000i | − | 0.742781i | −0.928477 | − | 0.371391i | \(-0.878881\pi\) | ||
0.928477 | − | 0.371391i | \(-0.121119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | − | 1.00000i | 0.179605 | − | 0.179605i | −0.611578 | − | 0.791184i | \(-0.709465\pi\) |
0.791184 | + | 0.611578i | \(0.209465\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.00000 | − | 5.00000i | 0.857493 | − | 0.857493i | ||||
\(35\) | −4.00000 | + | 2.00000i | −0.676123 | + | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.00000i | 1.31519i | 0.753371 | + | 0.657596i | \(0.228427\pi\) | ||||
−0.753371 | + | 0.657596i | \(0.771573\pi\) | |||||||
\(38\) | 3.00000 | + | 3.00000i | 0.486664 | + | 0.486664i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | + | 2.00000i | 0.158114 | + | 0.316228i | ||||
\(41\) | −1.00000 | + | 1.00000i | −0.156174 | + | 0.156174i | −0.780869 | − | 0.624695i | \(-0.785223\pi\) |
0.624695 | + | 0.780869i | \(0.285223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | + | 5.00000i | 0.762493 | + | 0.762493i | 0.976772 | − | 0.214280i | \(-0.0687403\pi\) |
−0.214280 | + | 0.976772i | \(0.568740\pi\) | |||||||
\(44\) | −1.00000 | − | 1.00000i | −0.150756 | − | 0.150756i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.00000 | − | 5.00000i | −0.737210 | − | 0.737210i | ||||
\(47\) | 2.00000i | 0.291730i | 0.989305 | + | 0.145865i | \(0.0465965\pi\) | ||||
−0.989305 | + | 0.145865i | \(0.953403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 3.00000 | − | 4.00000i | 0.424264 | − | 0.565685i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.00000 | − | 2.00000i | −0.416025 | − | 0.277350i | ||||
\(53\) | 1.00000 | − | 1.00000i | 0.137361 | − | 0.137361i | −0.635083 | − | 0.772444i | \(-0.719034\pi\) |
0.772444 | + | 0.635083i | \(0.219034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | + | 3.00000i | −0.134840 | + | 0.404520i | ||||
\(56\) | 2.00000i | 0.267261i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000i | 0.525226i | ||||||||
\(59\) | −3.00000 | + | 3.00000i | −0.390567 | + | 0.390567i | −0.874889 | − | 0.484323i | \(-0.839066\pi\) |
0.484323 | + | 0.874889i | \(0.339066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | −1.00000 | + | 1.00000i | −0.127000 | + | 0.127000i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00000 | + | 8.00000i | −0.124035 | + | 0.992278i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0000 | −1.46603 | −0.733017 | − | 0.680211i | \(-0.761888\pi\) | ||||
−0.733017 | + | 0.680211i | \(0.761888\pi\) | |||||||
\(68\) | −5.00000 | + | 5.00000i | −0.606339 | + | 0.606339i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.00000 | − | 2.00000i | 0.478091 | − | 0.239046i | ||||
\(71\) | −1.00000 | + | 1.00000i | −0.118678 | + | 0.118678i | −0.763952 | − | 0.645273i | \(-0.776743\pi\) |
0.645273 | + | 0.763952i | \(0.276743\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | − | 8.00000i | − | 0.929981i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.00000 | − | 3.00000i | −0.344124 | − | 0.344124i | ||||
\(77\) | −2.00000 | + | 2.00000i | −0.227921 | + | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0000i | 1.57512i | 0.616236 | + | 0.787562i | \(0.288657\pi\) | ||||
−0.616236 | + | 0.787562i | \(0.711343\pi\) | |||||||
\(80\) | −1.00000 | − | 2.00000i | −0.111803 | − | 0.223607i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.00000 | − | 1.00000i | 0.110432 | − | 0.110432i | ||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.0000 | + | 5.00000i | 1.62698 | + | 0.542326i | ||||
\(86\) | −5.00000 | − | 5.00000i | −0.539164 | − | 0.539164i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | + | 1.00000i | 0.106600 | + | 0.106600i | ||||
\(89\) | 7.00000 | − | 7.00000i | 0.741999 | − | 0.741999i | −0.230964 | − | 0.972962i | \(-0.574188\pi\) |
0.972962 | + | 0.230964i | \(0.0741879\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | + | 6.00000i | −0.419314 | + | 0.628971i | ||||
\(92\) | 5.00000 | + | 5.00000i | 0.521286 | + | 0.521286i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 2.00000i | − | 0.206284i | ||||||
\(95\) | −3.00000 | + | 9.00000i | −0.307794 | + | 0.923381i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | −3.00000 | −0.303046 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | + | 4.00000i | −0.300000 | + | 0.400000i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.00000 | − | 5.00000i | −0.492665 | − | 0.492665i | 0.416480 | − | 0.909145i | \(-0.363264\pi\) |
−0.909145 | + | 0.416480i | \(0.863264\pi\) | |||||||
\(104\) | 3.00000 | + | 2.00000i | 0.294174 | + | 0.196116i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.00000 | + | 1.00000i | −0.0971286 | + | 0.0971286i | ||||
\(107\) | −13.0000 | − | 13.0000i | −1.25676 | − | 1.25676i | −0.952632 | − | 0.304125i | \(-0.901636\pi\) |
−0.304125 | − | 0.952632i | \(-0.598364\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.0000 | − | 13.0000i | −1.24517 | − | 1.24517i | −0.957826 | − | 0.287348i | \(-0.907226\pi\) |
−0.287348 | − | 0.957826i | \(-0.592774\pi\) | |||||||
\(110\) | 1.00000 | − | 3.00000i | 0.0953463 | − | 0.286039i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 2.00000i | − | 0.188982i | ||||||
\(113\) | −9.00000 | + | 9.00000i | −0.846649 | + | 0.846649i | −0.989713 | − | 0.143065i | \(-0.954304\pi\) |
0.143065 | + | 0.989713i | \(0.454304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.00000 | − | 15.0000i | 0.466252 | − | 1.39876i | ||||
\(116\) | − | 4.00000i | − | 0.371391i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.00000 | − | 3.00000i | 0.276172 | − | 0.276172i | ||||
\(119\) | 10.0000 | + | 10.0000i | 0.916698 | + | 0.916698i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 9.00000i | − | 0.818182i | ||||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.00000 | − | 1.00000i | 0.0898027 | − | 0.0898027i | ||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.0000 | + | 15.0000i | −1.33103 | + | 1.33103i | −0.426589 | + | 0.904445i | \(0.640285\pi\) |
−0.904445 | + | 0.426589i | \(0.859715\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.00000 | − | 8.00000i | 0.0877058 | − | 0.701646i | ||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 6.00000i | −0.520266 | + | 0.520266i | ||||
\(134\) | 12.0000 | 1.03664 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.00000 | − | 5.00000i | 0.428746 | − | 0.428746i | ||||
\(137\) | 12.0000i | 1.02523i | 0.858619 | + | 0.512615i | \(0.171323\pi\) | ||||
−0.858619 | + | 0.512615i | \(0.828677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0000i | 1.18746i | 0.804663 | + | 0.593732i | \(0.202346\pi\) | ||||
−0.804663 | + | 0.593732i | \(0.797654\pi\) | |||||||
\(140\) | −4.00000 | + | 2.00000i | −0.338062 | + | 0.169031i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.00000 | − | 1.00000i | 0.0839181 | − | 0.0839181i | ||||
\(143\) | 1.00000 | + | 5.00000i | 0.0836242 | + | 0.418121i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.00000 | + | 4.00000i | −0.664364 | + | 0.332182i | ||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.00000i | 0.657596i | ||||||||
\(149\) | 13.0000 | + | 13.0000i | 1.06500 | + | 1.06500i | 0.997735 | + | 0.0672664i | \(0.0214278\pi\) |
0.0672664 | + | 0.997735i | \(0.478572\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.00000 | − | 9.00000i | −0.732410 | − | 0.732410i | 0.238687 | − | 0.971097i | \(-0.423283\pi\) |
−0.971097 | + | 0.238687i | \(0.923283\pi\) | |||||||
\(152\) | 3.00000 | + | 3.00000i | 0.243332 | + | 0.243332i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | − | 2.00000i | 0.161165 | − | 0.161165i | ||||
\(155\) | −3.00000 | − | 1.00000i | −0.240966 | − | 0.0803219i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.00000 | + | 3.00000i | 0.239426 | + | 0.239426i | 0.816612 | − | 0.577186i | \(-0.195849\pi\) |
−0.577186 | + | 0.816612i | \(0.695849\pi\) | |||||||
\(158\) | − | 14.0000i | − | 1.11378i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | + | 2.00000i | 0.0790569 | + | 0.158114i | ||||
\(161\) | 10.0000 | − | 10.0000i | 0.788110 | − | 0.788110i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | −1.00000 | + | 1.00000i | −0.0780869 | + | 0.0780869i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000i | 0.465690i | ||||||||
\(167\) | 2.00000i | 0.154765i | 0.997001 | + | 0.0773823i | \(0.0246562\pi\) | ||||
−0.997001 | + | 0.0773823i | \(0.975344\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | + | 12.0000i | 0.384615 | + | 0.923077i | ||||
\(170\) | −15.0000 | − | 5.00000i | −1.15045 | − | 0.383482i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.00000 | + | 5.00000i | 0.381246 | + | 0.381246i | ||||
\(173\) | −15.0000 | − | 15.0000i | −1.14043 | − | 1.14043i | −0.988372 | − | 0.152057i | \(-0.951410\pi\) |
−0.152057 | − | 0.988372i | \(-0.548590\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.00000 | + | 6.00000i | 0.604743 | + | 0.453557i | ||||
\(176\) | −1.00000 | − | 1.00000i | −0.0753778 | − | 0.0753778i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.00000 | + | 7.00000i | −0.524672 | + | 0.524672i | ||||
\(179\) | −20.0000 | −1.49487 | −0.747435 | − | 0.664335i | \(-0.768715\pi\) | ||||
−0.747435 | + | 0.664335i | \(0.768715\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.0000i | − | 1.48659i | −0.668965 | − | 0.743294i | \(-0.733262\pi\) | ||
0.668965 | − | 0.743294i | \(-0.266738\pi\) | |||||||
\(182\) | 4.00000 | − | 6.00000i | 0.296500 | − | 0.444750i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.00000 | − | 5.00000i | −0.368605 | − | 0.368605i | ||||
\(185\) | 16.0000 | − | 8.00000i | 1.17634 | − | 0.588172i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0000 | 0.731272 | ||||||||
\(188\) | 2.00000i | 0.145865i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.00000 | − | 9.00000i | 0.217643 | − | 0.652929i | ||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | 2.00000 | 0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 3.00000 | − | 4.00000i | 0.212132 | − | 0.282843i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.00000 | −0.561490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | + | 1.00000i | 0.209529 | + | 0.0698430i | ||||
\(206\) | 5.00000 | + | 5.00000i | 0.348367 | + | 0.348367i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.00000 | − | 2.00000i | −0.208013 | − | 0.138675i | ||||
\(209\) | 6.00000i | 0.415029i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 1.00000 | − | 1.00000i | 0.0686803 | − | 0.0686803i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.0000 | + | 13.0000i | 0.888662 | + | 0.888662i | ||||
\(215\) | 5.00000 | − | 15.0000i | 0.340997 | − | 1.02299i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | − | 2.00000i | −0.135769 | − | 0.135769i | ||||
\(218\) | 13.0000 | + | 13.0000i | 0.880471 | + | 0.880471i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.00000 | + | 3.00000i | −0.0674200 | + | 0.202260i | ||||
\(221\) | 25.0000 | − | 5.00000i | 1.68168 | − | 0.336336i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.00000i | 0.401790i | 0.979613 | + | 0.200895i | \(0.0643850\pi\) | ||||
−0.979613 | + | 0.200895i | \(0.935615\pi\) | |||||||
\(224\) | 2.00000i | 0.133631i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.00000 | − | 9.00000i | 0.598671 | − | 0.598671i | ||||
\(227\) | 12.0000 | 0.796468 | 0.398234 | − | 0.917284i | \(-0.369623\pi\) | ||||
0.398234 | + | 0.917284i | \(0.369623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.00000 | − | 3.00000i | 0.198246 | − | 0.198246i | −0.601002 | − | 0.799248i | \(-0.705232\pi\) |
0.799248 | + | 0.601002i | \(0.205232\pi\) | |||||||
\(230\) | −5.00000 | + | 15.0000i | −0.329690 | + | 0.989071i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.00000i | 0.262613i | ||||||||
\(233\) | −5.00000 | − | 5.00000i | −0.327561 | − | 0.327561i | 0.524097 | − | 0.851658i | \(-0.324403\pi\) |
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | − | 2.00000i | 0.260931 | − | 0.130466i | ||||
\(236\) | −3.00000 | + | 3.00000i | −0.195283 | + | 0.195283i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.0000 | − | 10.0000i | −0.648204 | − | 0.648204i | ||||
\(239\) | −7.00000 | − | 7.00000i | −0.452792 | − | 0.452792i | 0.443488 | − | 0.896280i | \(-0.353741\pi\) |
−0.896280 | + | 0.443488i | \(0.853741\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | + | 1.00000i | 0.0644157 | + | 0.0644157i | 0.738581 | − | 0.674165i | \(-0.235496\pi\) |
−0.674165 | + | 0.738581i | \(0.735496\pi\) | |||||||
\(242\) | 9.00000i | 0.578542i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | −3.00000 | − | 6.00000i | −0.191663 | − | 0.383326i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.00000 | + | 15.0000i | 0.190885 | + | 0.954427i | ||||
\(248\) | −1.00000 | + | 1.00000i | −0.0635001 | + | 0.0635001i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.0000 | − | 2.00000i | −0.695701 | − | 0.126491i | ||||
\(251\) | − | 30.0000i | − | 1.89358i | −0.321847 | − | 0.946792i | \(-0.604304\pi\) | ||
0.321847 | − | 0.946792i | \(-0.395696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 10.0000i | − | 0.628695i | ||||||
\(254\) | 15.0000 | − | 15.0000i | 0.941184 | − | 0.941184i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.0000 | − | 15.0000i | 0.935674 | − | 0.935674i | −0.0623783 | − | 0.998053i | \(-0.519869\pi\) |
0.998053 | + | 0.0623783i | \(0.0198685\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.0000 | 0.994192 | ||||||||
\(260\) | −1.00000 | + | 8.00000i | −0.0620174 | + | 0.496139i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.0000 | 0.741362 | ||||||||
\(263\) | −9.00000 | + | 9.00000i | −0.554964 | + | 0.554964i | −0.927869 | − | 0.372906i | \(-0.878362\pi\) |
0.372906 | + | 0.927869i | \(0.378362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00000 | − | 1.00000i | −0.184289 | − | 0.0614295i | ||||
\(266\) | 6.00000 | − | 6.00000i | 0.367884 | − | 0.367884i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.0000 | −0.733017 | ||||||||
\(269\) | 16.0000i | 0.975537i | 0.872973 | + | 0.487769i | \(0.162189\pi\) | ||||
−0.872973 | + | 0.487769i | \(0.837811\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.00000 | − | 9.00000i | −0.546711 | − | 0.546711i | 0.378777 | − | 0.925488i | \(-0.376345\pi\) |
−0.925488 | + | 0.378777i | \(0.876345\pi\) | |||||||
\(272\) | −5.00000 | + | 5.00000i | −0.303170 | + | 0.303170i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 12.0000i | − | 0.724947i | ||||||
\(275\) | 7.00000 | − | 1.00000i | 0.422116 | − | 0.0603023i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.00000 | + | 5.00000i | −0.300421 | + | 0.300421i | −0.841178 | − | 0.540758i | \(-0.818138\pi\) |
0.540758 | + | 0.841178i | \(0.318138\pi\) | |||||||
\(278\) | − | 14.0000i | − | 0.839664i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.00000 | − | 2.00000i | 0.239046 | − | 0.119523i | ||||
\(281\) | −21.0000 | − | 21.0000i | −1.25275 | − | 1.25275i | −0.954480 | − | 0.298275i | \(-0.903589\pi\) |
−0.298275 | − | 0.954480i | \(-0.596411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.0000 | − | 15.0000i | −0.891657 | − | 0.891657i | 0.103022 | − | 0.994679i | \(-0.467149\pi\) |
−0.994679 | + | 0.103022i | \(0.967149\pi\) | |||||||
\(284\) | −1.00000 | + | 1.00000i | −0.0593391 | + | 0.0593391i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.00000 | − | 5.00000i | −0.0591312 | − | 0.295656i | ||||
\(287\) | 2.00000 | + | 2.00000i | 0.118056 | + | 0.118056i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 33.0000i | − | 1.94118i | ||||||
\(290\) | 8.00000 | − | 4.00000i | 0.469776 | − | 0.234888i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.00000 | −0.351123 | ||||||||
\(293\) | 26.0000 | 1.51894 | 0.759468 | − | 0.650545i | \(-0.225459\pi\) | ||||
0.759468 | + | 0.650545i | \(0.225459\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.00000 | + | 3.00000i | 0.524000 | + | 0.174667i | ||||
\(296\) | − | 8.00000i | − | 0.464991i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.0000 | − | 13.0000i | −0.753070 | − | 0.753070i | ||||
\(299\) | −5.00000 | − | 25.0000i | −0.289157 | − | 1.44579i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0000 | − | 10.0000i | 0.576390 | − | 0.576390i | ||||
\(302\) | 9.00000 | + | 9.00000i | 0.517892 | + | 0.517892i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.00000 | − | 3.00000i | −0.172062 | − | 0.172062i | ||||
\(305\) | −2.00000 | − | 4.00000i | −0.114520 | − | 0.229039i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.00000i | − | 0.114146i | −0.998370 | − | 0.0570730i | \(-0.981823\pi\) | ||
0.998370 | − | 0.0570730i | \(-0.0181768\pi\) | |||||||
\(308\) | −2.00000 | + | 2.00000i | −0.113961 | + | 0.113961i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.00000 | + | 1.00000i | 0.170389 | + | 0.0567962i | ||||
\(311\) | 10.0000i | 0.567048i | 0.958965 | + | 0.283524i | \(0.0915036\pi\) | ||||
−0.958965 | + | 0.283524i | \(0.908496\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.00000 | − | 9.00000i | 0.508710 | − | 0.508710i | −0.405420 | − | 0.914130i | \(-0.632875\pi\) |
0.914130 | + | 0.405420i | \(0.132875\pi\) | |||||||
\(314\) | −3.00000 | − | 3.00000i | −0.169300 | − | 0.169300i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.0000i | 0.787562i | ||||||||
\(317\) | 2.00000 | 0.112331 | 0.0561656 | − | 0.998421i | \(-0.482113\pi\) | ||||
0.0561656 | + | 0.998421i | \(0.482113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | + | 4.00000i | −0.223957 | + | 0.223957i | ||||
\(320\) | −1.00000 | − | 2.00000i | −0.0559017 | − | 0.111803i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.0000 | + | 10.0000i | −0.557278 | + | 0.557278i | ||||
\(323\) | 30.0000 | 1.66924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.0000 | − | 6.00000i | 0.942990 | − | 0.332820i | ||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.00000 | − | 1.00000i | 0.0552158 | − | 0.0552158i | ||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.00000 | + | 9.00000i | −0.494685 | + | 0.494685i | −0.909779 | − | 0.415094i | \(-0.863749\pi\) |
0.415094 | + | 0.909779i | \(0.363749\pi\) | |||||||
\(332\) | − | 6.00000i | − | 0.329293i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 2.00000i | − | 0.109435i | ||||||
\(335\) | 12.0000 | + | 24.0000i | 0.655630 | + | 1.31126i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00000 | − | 5.00000i | 0.272367 | − | 0.272367i | −0.557685 | − | 0.830053i | \(-0.688310\pi\) |
0.830053 | + | 0.557685i | \(0.188310\pi\) | |||||||
\(338\) | −5.00000 | − | 12.0000i | −0.271964 | − | 0.652714i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 15.0000 | + | 5.00000i | 0.813489 | + | 0.271163i | ||||
\(341\) | −2.00000 | −0.108306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.0000i | − | 1.07990i | ||||||
\(344\) | −5.00000 | − | 5.00000i | −0.269582 | − | 0.269582i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.0000 | + | 15.0000i | 0.806405 | + | 0.806405i | ||||
\(347\) | 7.00000 | + | 7.00000i | 0.375780 | + | 0.375780i | 0.869577 | − | 0.493797i | \(-0.164392\pi\) |
−0.493797 | + | 0.869577i | \(0.664392\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.00000 | − | 3.00000i | 0.160586 | − | 0.160586i | −0.622240 | − | 0.782826i | \(-0.713777\pi\) |
0.782826 | + | 0.622240i | \(0.213777\pi\) | |||||||
\(350\) | −8.00000 | − | 6.00000i | −0.427618 | − | 0.320713i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | + | 1.00000i | 0.0533002 | + | 0.0533002i | ||||
\(353\) | − | 16.0000i | − | 0.851594i | −0.904819 | − | 0.425797i | \(-0.859994\pi\) | ||
0.904819 | − | 0.425797i | \(-0.140006\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.00000 | + | 1.00000i | 0.159223 | + | 0.0530745i | ||||
\(356\) | 7.00000 | − | 7.00000i | 0.370999 | − | 0.370999i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.0000 | 1.05703 | ||||||||
\(359\) | −13.0000 | + | 13.0000i | −0.686114 | + | 0.686114i | −0.961371 | − | 0.275257i | \(-0.911237\pi\) |
0.275257 | + | 0.961371i | \(0.411237\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.00000i | − | 0.0526316i | ||||||
\(362\) | 20.0000i | 1.05118i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.00000 | + | 6.00000i | −0.209657 | + | 0.314485i | ||||
\(365\) | 6.00000 | + | 12.0000i | 0.314054 | + | 0.628109i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.00000 | + | 3.00000i | 0.156599 | + | 0.156599i | 0.781058 | − | 0.624459i | \(-0.214680\pi\) |
−0.624459 | + | 0.781058i | \(0.714680\pi\) | |||||||
\(368\) | 5.00000 | + | 5.00000i | 0.260643 | + | 0.260643i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −16.0000 | + | 8.00000i | −0.831800 | + | 0.415900i | ||||
\(371\) | −2.00000 | − | 2.00000i | −0.103835 | − | 0.103835i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.00000 | + | 1.00000i | −0.0517780 | + | 0.0517780i | −0.732522 | − | 0.680744i | \(-0.761657\pi\) |
0.680744 | + | 0.732522i | \(0.261657\pi\) | |||||||
\(374\) | −10.0000 | −0.517088 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 2.00000i | − | 0.103142i | ||||||
\(377\) | −8.00000 | + | 12.0000i | −0.412021 | + | 0.618031i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.0000 | + | 17.0000i | 0.873231 | + | 0.873231i | 0.992823 | − | 0.119592i | \(-0.0381586\pi\) |
−0.119592 | + | 0.992823i | \(0.538159\pi\) | |||||||
\(380\) | −3.00000 | + | 9.00000i | −0.153897 | + | 0.461690i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.00000 | −0.409316 | ||||||||
\(383\) | − | 6.00000i | − | 0.306586i | −0.988181 | − | 0.153293i | \(-0.951012\pi\) | ||
0.988181 | − | 0.153293i | \(-0.0489878\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | + | 2.00000i | 0.305788 | + | 0.101929i | ||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.00000 | −0.101535 | ||||||||
\(389\) | 10.0000 | 0.507020 | 0.253510 | − | 0.967333i | \(-0.418415\pi\) | ||||
0.253510 | + | 0.967333i | \(0.418415\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −50.0000 | −2.52861 | ||||||||
\(392\) | −3.00000 | −0.151523 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.0000 | 0.906827 | ||||||||
\(395\) | 28.0000 | − | 14.0000i | 1.40883 | − | 0.704416i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.00000i | 0.401508i | 0.979642 | + | 0.200754i | \(0.0643393\pi\) | ||||
−0.979642 | + | 0.200754i | \(0.935661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | −1.00000 | − | 1.00000i | −0.0499376 | − | 0.0499376i | 0.681697 | − | 0.731635i | \(-0.261242\pi\) |
−0.731635 | + | 0.681697i | \(0.761242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.00000 | + | 1.00000i | −0.249068 | + | 0.0498135i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.00000 | 0.397033 | ||||||||
\(407\) | 8.00000 | − | 8.00000i | 0.396545 | − | 0.396545i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.00000 | − | 3.00000i | −0.148340 | − | 0.148340i | 0.629036 | − | 0.777376i | \(-0.283450\pi\) |
−0.777376 | + | 0.629036i | \(0.783450\pi\) | |||||||
\(410\) | −3.00000 | − | 1.00000i | −0.148159 | − | 0.0493865i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.00000 | − | 5.00000i | −0.246332 | − | 0.246332i | ||||
\(413\) | 6.00000 | + | 6.00000i | 0.295241 | + | 0.295241i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | + | 6.00000i | −0.589057 | + | 0.294528i | ||||
\(416\) | 3.00000 | + | 2.00000i | 0.147087 | + | 0.0980581i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 6.00000i | − | 0.293470i | ||||||
\(419\) | 26.0000i | 1.27018i | 0.772437 | + | 0.635092i | \(0.219038\pi\) | ||||
−0.772437 | + | 0.635092i | \(0.780962\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.00000 | + | 9.00000i | −0.438633 | + | 0.438633i | −0.891552 | − | 0.452919i | \(-0.850383\pi\) |
0.452919 | + | 0.891552i | \(0.350383\pi\) | |||||||
\(422\) | −12.0000 | −0.584151 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.00000 | + | 1.00000i | −0.0485643 | + | 0.0485643i | ||||
\(425\) | −5.00000 | − | 35.0000i | −0.242536 | − | 1.69775i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 4.00000i | − | 0.193574i | ||||||
\(428\) | −13.0000 | − | 13.0000i | −0.628379 | − | 0.628379i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.00000 | + | 15.0000i | −0.241121 | + | 0.723364i | ||||
\(431\) | −21.0000 | + | 21.0000i | −1.01153 | + | 1.01153i | −0.0116017 | + | 0.999933i | \(0.503693\pi\) |
−0.999933 | + | 0.0116017i | \(0.996307\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.0000 | − | 15.0000i | −0.720854 | − | 0.720854i | 0.247925 | − | 0.968779i | \(-0.420251\pi\) |
−0.968779 | + | 0.247925i | \(0.920251\pi\) | |||||||
\(434\) | 2.00000 | + | 2.00000i | 0.0960031 | + | 0.0960031i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.0000 | − | 13.0000i | −0.622587 | − | 0.622587i | ||||
\(437\) | − | 30.0000i | − | 1.43509i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.0000 | 1.90910 | 0.954548 | − | 0.298057i | \(-0.0963387\pi\) | ||||
0.954548 | + | 0.298057i | \(0.0963387\pi\) | |||||||
\(440\) | 1.00000 | − | 3.00000i | 0.0476731 | − | 0.143019i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −25.0000 | + | 5.00000i | −1.18913 | + | 0.237826i | ||||
\(443\) | −19.0000 | + | 19.0000i | −0.902717 | + | 0.902717i | −0.995670 | − | 0.0929532i | \(-0.970369\pi\) |
0.0929532 | + | 0.995670i | \(0.470369\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.0000 | − | 7.00000i | −0.995495 | − | 0.331832i | ||||
\(446\) | − | 6.00000i | − | 0.284108i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 2.00000i | − | 0.0944911i | ||||||
\(449\) | 7.00000 | − | 7.00000i | 0.330350 | − | 0.330350i | −0.522369 | − | 0.852720i | \(-0.674952\pi\) |
0.852720 | + | 0.522369i | \(0.174952\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.00000 | 0.0941763 | ||||||||
\(452\) | −9.00000 | + | 9.00000i | −0.423324 | + | 0.423324i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.0000 | −0.563188 | ||||||||
\(455\) | 16.0000 | + | 2.00000i | 0.750092 | + | 0.0937614i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.0000 | 1.77757 | 0.888783 | − | 0.458329i | \(-0.151552\pi\) | ||||
0.888783 | + | 0.458329i | \(0.151552\pi\) | |||||||
\(458\) | −3.00000 | + | 3.00000i | −0.140181 | + | 0.140181i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.00000 | − | 15.0000i | 0.233126 | − | 0.699379i | ||||
\(461\) | −11.0000 | + | 11.0000i | −0.512321 | + | 0.512321i | −0.915237 | − | 0.402916i | \(-0.867997\pi\) |
0.402916 | + | 0.915237i | \(0.367997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | − | 4.00000i | − | 0.185695i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.00000 | + | 5.00000i | 0.231621 | + | 0.231621i | ||||
\(467\) | 5.00000 | − | 5.00000i | 0.231372 | − | 0.231372i | −0.581893 | − | 0.813265i | \(-0.697688\pi\) |
0.813265 | + | 0.581893i | \(0.197688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0000i | 1.10822i | ||||||||
\(470\) | −4.00000 | + | 2.00000i | −0.184506 | + | 0.0922531i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.00000 | − | 3.00000i | 0.138086 | − | 0.138086i | ||||
\(473\) | − | 10.0000i | − | 0.459800i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.0000 | − | 3.00000i | 0.963546 | − | 0.137649i | ||||
\(476\) | 10.0000 | + | 10.0000i | 0.458349 | + | 0.458349i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.00000 | + | 7.00000i | 0.320173 | + | 0.320173i | ||||
\(479\) | −13.0000 | + | 13.0000i | −0.593985 | + | 0.593985i | −0.938705 | − | 0.344720i | \(-0.887974\pi\) |
0.344720 | + | 0.938705i | \(0.387974\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | − | 24.0000i | 0.729537 | − | 1.09431i | ||||
\(482\) | −1.00000 | − | 1.00000i | −0.0455488 | − | 0.0455488i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 9.00000i | − | 0.409091i | ||||||
\(485\) | 2.00000 | + | 4.00000i | 0.0908153 | + | 0.181631i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.0000 | −1.45006 | −0.725029 | − | 0.688718i | \(-0.758174\pi\) | ||||
−0.725029 | + | 0.688718i | \(0.758174\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.00000 | + | 6.00000i | 0.135526 | + | 0.271052i | ||||
\(491\) | 10.0000i | 0.451294i | 0.974209 | + | 0.225647i | \(0.0724495\pi\) | ||||
−0.974209 | + | 0.225647i | \(0.927550\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | + | 20.0000i | 0.900755 | + | 0.900755i | ||||
\(494\) | −3.00000 | − | 15.0000i | −0.134976 | − | 0.674882i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | − | 1.00000i | 0.0449013 | − | 0.0449013i | ||||
\(497\) | 2.00000 | + | 2.00000i | 0.0897123 | + | 0.0897123i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.0000 | − | 23.0000i | −1.02962 | − | 1.02962i | −0.999548 | − | 0.0300737i | \(-0.990426\pi\) |
−0.0300737 | − | 0.999548i | \(-0.509574\pi\) | |||||||
\(500\) | 11.0000 | + | 2.00000i | 0.491935 | + | 0.0894427i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 30.0000i | 1.33897i | ||||||||
\(503\) | −9.00000 | + | 9.00000i | −0.401290 | + | 0.401290i | −0.878688 | − | 0.477397i | \(-0.841580\pi\) |
0.477397 | + | 0.878688i | \(0.341580\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.0000i | 0.444554i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.0000 | + | 15.0000i | −0.665517 | + | 0.665517i | ||||
\(509\) | 13.0000 | + | 13.0000i | 0.576215 | + | 0.576215i | 0.933858 | − | 0.357643i | \(-0.116420\pi\) |
−0.357643 | + | 0.933858i | \(0.616420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000i | 0.530849i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.0000 | + | 15.0000i | −0.661622 | + | 0.661622i | ||||
\(515\) | −5.00000 | + | 15.0000i | −0.220326 | + | 0.660979i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.00000 | − | 2.00000i | 0.0879599 | − | 0.0879599i | ||||
\(518\) | −16.0000 | −0.703000 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.00000 | − | 8.00000i | 0.0438529 | − | 0.350823i | ||||
\(521\) | −22.0000 | −0.963837 | −0.481919 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481919 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.0000 | + | 21.0000i | −0.918266 | + | 0.918266i | −0.996903 | − | 0.0786374i | \(-0.974943\pi\) |
0.0786374 | + | 0.996903i | \(0.474943\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.00000 | − | 9.00000i | 0.392419 | − | 0.392419i | ||||
\(527\) | 10.0000i | 0.435607i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.0000i | 1.17391i | ||||||||
\(530\) | 3.00000 | + | 1.00000i | 0.130312 | + | 0.0434372i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.00000 | + | 6.00000i | −0.260133 | + | 0.260133i | ||||
\(533\) | 5.00000 | − | 1.00000i | 0.216574 | − | 0.0433148i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.0000 | + | 39.0000i | −0.562039 | + | 1.68612i | ||||
\(536\) | 12.0000 | 0.518321 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 16.0000i | − | 0.689809i | ||||||
\(539\) | −3.00000 | − | 3.00000i | −0.129219 | − | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.00000 | − | 9.00000i | −0.386940 | − | 0.386940i | 0.486654 | − | 0.873595i | \(-0.338217\pi\) |
−0.873595 | + | 0.486654i | \(0.838217\pi\) | |||||||
\(542\) | 9.00000 | + | 9.00000i | 0.386583 | + | 0.386583i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.00000 | − | 5.00000i | 0.214373 | − | 0.214373i | ||||
\(545\) | −13.0000 | + | 39.0000i | −0.556859 | + | 1.67058i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.00000 | − | 7.00000i | −0.299298 | − | 0.299298i | 0.541441 | − | 0.840739i | \(-0.317879\pi\) |
−0.840739 | + | 0.541441i | \(0.817879\pi\) | |||||||
\(548\) | 12.0000i | 0.512615i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.00000 | + | 1.00000i | −0.298481 | + | 0.0426401i | ||||
\(551\) | −12.0000 | + | 12.0000i | −0.511217 | + | 0.511217i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.0000 | 1.19068 | ||||||||
\(554\) | 5.00000 | − | 5.00000i | 0.212430 | − | 0.212430i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.0000i | 0.593732i | ||||||||
\(557\) | − | 8.00000i | − | 0.338971i | −0.985533 | − | 0.169485i | \(-0.945789\pi\) | ||
0.985533 | − | 0.169485i | \(-0.0542106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.00000 | − | 25.0000i | −0.211477 | − | 1.05739i | ||||
\(560\) | −4.00000 | + | 2.00000i | −0.169031 | + | 0.0845154i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21.0000 | + | 21.0000i | 0.885832 | + | 0.885832i | ||||
\(563\) | −5.00000 | − | 5.00000i | −0.210725 | − | 0.210725i | 0.593851 | − | 0.804575i | \(-0.297607\pi\) |
−0.804575 | + | 0.593851i | \(0.797607\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.0000 | + | 9.00000i | 1.13590 | + | 0.378633i | ||||
\(566\) | 15.0000 | + | 15.0000i | 0.630497 | + | 0.630497i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.00000 | − | 1.00000i | 0.0419591 | − | 0.0419591i | ||||
\(569\) | 10.0000 | 0.419222 | 0.209611 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209611 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 10.0000i | − | 0.418487i | −0.977864 | − | 0.209243i | \(-0.932900\pi\) | ||
0.977864 | − | 0.209243i | \(-0.0671001\pi\) | |||||||
\(572\) | 1.00000 | + | 5.00000i | 0.0418121 | + | 0.209061i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.00000 | − | 2.00000i | −0.0834784 | − | 0.0834784i | ||||
\(575\) | −35.0000 | + | 5.00000i | −1.45960 | + | 0.208514i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.0000 | −0.915872 | −0.457936 | − | 0.888985i | \(-0.651411\pi\) | ||||
−0.457936 | + | 0.888985i | \(0.651411\pi\) | |||||||
\(578\) | 33.0000i | 1.37262i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.00000 | + | 4.00000i | −0.332182 | + | 0.166091i | ||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.00000 | −0.0828315 | ||||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.0000 | −1.07405 | ||||||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.00000 | −0.247226 | ||||||||
\(590\) | −9.00000 | − | 3.00000i | −0.370524 | − | 0.123508i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.00000i | 0.328798i | ||||||||
\(593\) | −14.0000 | −0.574911 | −0.287456 | − | 0.957794i | \(-0.592809\pi\) | ||||
−0.287456 | + | 0.957794i | \(0.592809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0000 | − | 30.0000i | 0.409960 | − | 1.22988i | ||||
\(596\) | 13.0000 | + | 13.0000i | 0.532501 | + | 0.532501i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.00000 | + | 25.0000i | 0.204465 | + | 1.02233i | ||||
\(599\) | − | 14.0000i | − | 0.572024i | −0.958226 | − | 0.286012i | \(-0.907670\pi\) | ||
0.958226 | − | 0.286012i | \(-0.0923298\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | −10.0000 | + | 10.0000i | −0.407570 | + | 0.407570i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.00000 | − | 9.00000i | −0.366205 | − | 0.366205i | ||||
\(605\) | −18.0000 | + | 9.00000i | −0.731804 | + | 0.365902i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.00000 | + | 3.00000i | 0.121766 | + | 0.121766i | 0.765364 | − | 0.643598i | \(-0.222559\pi\) |
−0.643598 | + | 0.765364i | \(0.722559\pi\) | |||||||
\(608\) | 3.00000 | + | 3.00000i | 0.121666 | + | 0.121666i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.00000 | + | 4.00000i | 0.0809776 | + | 0.161955i | ||||
\(611\) | 4.00000 | − | 6.00000i | 0.161823 | − | 0.242734i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 4.00000i | − | 0.161558i | −0.996732 | − | 0.0807792i | \(-0.974259\pi\) | ||
0.996732 | − | 0.0807792i | \(-0.0257409\pi\) | |||||||
\(614\) | 2.00000i | 0.0807134i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | − | 2.00000i | 0.0805823 | − | 0.0805823i | ||||
\(617\) | −38.0000 | −1.52982 | −0.764911 | − | 0.644136i | \(-0.777217\pi\) | ||||
−0.764911 | + | 0.644136i | \(0.777217\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.00000 | − | 3.00000i | 0.120580 | − | 0.120580i | −0.644242 | − | 0.764822i | \(-0.722827\pi\) |
0.764822 | + | 0.644242i | \(0.222827\pi\) | |||||||
\(620\) | −3.00000 | − | 1.00000i | −0.120483 | − | 0.0401610i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 10.0000i | − | 0.400963i | ||||||
\(623\) | −14.0000 | − | 14.0000i | −0.560898 | − | 0.560898i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | −9.00000 | + | 9.00000i | −0.359712 | + | 0.359712i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.00000 | + | 3.00000i | 0.119713 | + | 0.119713i | ||||
\(629\) | −40.0000 | − | 40.0000i | −1.59490 | − | 1.59490i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.0000 | + | 11.0000i | 0.437903 | + | 0.437903i | 0.891306 | − | 0.453403i | \(-0.149790\pi\) |
−0.453403 | + | 0.891306i | \(0.649790\pi\) | |||||||
\(632\) | − | 14.0000i | − | 0.556890i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.00000 | −0.0794301 | ||||||||
\(635\) | 45.0000 | + | 15.0000i | 1.78577 | + | 0.595257i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.00000 | − | 6.00000i | −0.356593 | − | 0.237729i | ||||
\(638\) | 4.00000 | − | 4.00000i | 0.158362 | − | 0.158362i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | + | 2.00000i | 0.0395285 | + | 0.0790569i | ||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.0000i | 1.81406i | 0.421063 | + | 0.907031i | \(0.361657\pi\) | ||||
−0.421063 | + | 0.907031i | \(0.638343\pi\) | |||||||
\(644\) | 10.0000 | − | 10.0000i | 0.394055 | − | 0.394055i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30.0000 | −1.18033 | ||||||||
\(647\) | −5.00000 | + | 5.00000i | −0.196570 | + | 0.196570i | −0.798528 | − | 0.601958i | \(-0.794388\pi\) |
0.601958 | + | 0.798528i | \(0.294388\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.00000 | 0.235521 | ||||||||
\(650\) | −17.0000 | + | 6.00000i | −0.666795 | + | 0.235339i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.00000 | 0.156652 | ||||||||
\(653\) | 21.0000 | − | 21.0000i | 0.821794 | − | 0.821794i | −0.164572 | − | 0.986365i | \(-0.552624\pi\) |
0.986365 | + | 0.164572i | \(0.0526242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0000 | + | 24.0000i | 0.468879 | + | 0.937758i | ||||
\(656\) | −1.00000 | + | 1.00000i | −0.0390434 | + | 0.0390434i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.00000 | −0.155936 | ||||||||
\(659\) | − | 14.0000i | − | 0.545363i | −0.962104 | − | 0.272681i | \(-0.912090\pi\) | ||
0.962104 | − | 0.272681i | \(-0.0879105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.0000 | + | 31.0000i | 1.20576 | + | 1.20576i | 0.972387 | + | 0.233373i | \(0.0749763\pi\) |
0.233373 | + | 0.972387i | \(0.425024\pi\) | |||||||
\(662\) | 9.00000 | − | 9.00000i | 0.349795 | − | 0.349795i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000i | 0.232845i | ||||||||
\(665\) | 18.0000 | + | 6.00000i | 0.698010 | + | 0.232670i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.0000 | − | 20.0000i | 0.774403 | − | 0.774403i | ||||
\(668\) | 2.00000i | 0.0773823i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.0000 | − | 24.0000i | −0.463600 | − | 0.927201i | ||||
\(671\) | −2.00000 | − | 2.00000i | −0.0772091 | − | 0.0772091i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.00000 | + | 5.00000i | 0.192736 | + | 0.192736i | 0.796877 | − | 0.604141i | \(-0.206484\pi\) |
−0.604141 | + | 0.796877i | \(0.706484\pi\) | |||||||
\(674\) | −5.00000 | + | 5.00000i | −0.192593 | + | 0.192593i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.00000 | + | 12.0000i | 0.192308 | + | 0.461538i | ||||
\(677\) | −23.0000 | − | 23.0000i | −0.883962 | − | 0.883962i | 0.109973 | − | 0.993935i | \(-0.464924\pi\) |
−0.993935 | + | 0.109973i | \(0.964924\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.00000i | 0.153506i | ||||||||
\(680\) | −15.0000 | − | 5.00000i | −0.575224 | − | 0.191741i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.00000 | 0.0765840 | ||||||||
\(683\) | 36.0000 | 1.37750 | 0.688751 | − | 0.724998i | \(-0.258159\pi\) | ||||
0.688751 | + | 0.724998i | \(0.258159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0000 | − | 12.0000i | 0.916993 | − | 0.458496i | ||||
\(686\) | 20.0000i | 0.763604i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.00000 | + | 5.00000i | 0.190623 | + | 0.190623i | ||||
\(689\) | −5.00000 | + | 1.00000i | −0.190485 | + | 0.0380970i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.00000 | + | 9.00000i | −0.342376 | + | 0.342376i | −0.857260 | − | 0.514884i | \(-0.827835\pi\) |
0.514884 | + | 0.857260i | \(0.327835\pi\) | |||||||
\(692\) | −15.0000 | − | 15.0000i | −0.570214 | − | 0.570214i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.00000 | − | 7.00000i | −0.265716 | − | 0.265716i | ||||
\(695\) | 28.0000 | − | 14.0000i | 1.06210 | − | 0.531050i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10.0000i | − | 0.378777i | ||||||
\(698\) | −3.00000 | + | 3.00000i | −0.113552 | + | 0.113552i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.00000 | + | 6.00000i | 0.302372 | + | 0.226779i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000 | − | 24.0000i | 0.905177 | − | 0.905177i | ||||
\(704\) | −1.00000 | − | 1.00000i | −0.0376889 | − | 0.0376889i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.0000i | 0.602168i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.00000 | − | 3.00000i | 0.112667 | − | 0.112667i | −0.648526 | − | 0.761193i | \(-0.724614\pi\) |
0.761193 | + | 0.648526i | \(0.224614\pi\) | |||||||
\(710\) | −3.00000 | − | 1.00000i | −0.112588 | − | 0.0375293i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.00000 | + | 7.00000i | −0.262336 | + | 0.262336i | ||||
\(713\) | 10.0000 | 0.374503 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.00000 | − | 7.00000i | 0.336581 | − | 0.261785i | ||||
\(716\) | −20.0000 | −0.747435 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.0000 | − | 13.0000i | 0.485156 | − | 0.485156i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | + | 10.0000i | −0.372419 | + | 0.372419i | ||||
\(722\) | 1.00000i | 0.0372161i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 20.0000i | − | 0.743294i | ||||||
\(725\) | 16.0000 | + | 12.0000i | 0.594225 | + | 0.445669i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.0000 | + | 35.0000i | −1.29808 | + | 1.29808i | −0.368418 | + | 0.929660i | \(0.620100\pi\) |
−0.929660 | + | 0.368418i | \(0.879900\pi\) | |||||||
\(728\) | 4.00000 | − | 6.00000i | 0.148250 | − | 0.222375i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.00000 | − | 12.0000i | −0.222070 | − | 0.444140i | ||||
\(731\) | −50.0000 | −1.84932 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 44.0000i | − | 1.62518i | −0.582838 | − | 0.812589i | \(-0.698058\pi\) | ||
0.582838 | − | 0.812589i | \(-0.301942\pi\) | |||||||
\(734\) | −3.00000 | − | 3.00000i | −0.110732 | − | 0.110732i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.00000 | − | 5.00000i | −0.184302 | − | 0.184302i | ||||
\(737\) | 12.0000 | + | 12.0000i | 0.442026 | + | 0.442026i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.0000 | + | 37.0000i | −1.36107 | + | 1.36107i | −0.488507 | + | 0.872560i | \(0.662458\pi\) |
−0.872560 | + | 0.488507i | \(0.837542\pi\) | |||||||
\(740\) | 16.0000 | − | 8.00000i | 0.588172 | − | 0.294086i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.00000 | + | 2.00000i | 0.0734223 | + | 0.0734223i | ||||
\(743\) | − | 6.00000i | − | 0.220119i | −0.993925 | − | 0.110059i | \(-0.964896\pi\) | ||
0.993925 | − | 0.110059i | \(-0.0351041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.0000 | − | 39.0000i | 0.476283 | − | 1.42885i | ||||
\(746\) | 1.00000 | − | 1.00000i | 0.0366126 | − | 0.0366126i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.0000 | 0.365636 | ||||||||
\(749\) | −26.0000 | + | 26.0000i | −0.950019 | + | 0.950019i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 10.0000i | − | 0.364905i | −0.983215 | − | 0.182453i | \(-0.941596\pi\) | ||
0.983215 | − | 0.182453i | \(-0.0584036\pi\) | |||||||
\(752\) | 2.00000i | 0.0729325i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.00000 | − | 12.0000i | 0.291343 | − | 0.437014i | ||||
\(755\) | −9.00000 | + | 27.0000i | −0.327544 | + | 0.982631i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.0000 | − | 17.0000i | −0.617876 | − | 0.617876i | 0.327111 | − | 0.944986i | \(-0.393925\pi\) |
−0.944986 | + | 0.327111i | \(0.893925\pi\) | |||||||
\(758\) | −17.0000 | − | 17.0000i | −0.617468 | − | 0.617468i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.00000 | − | 9.00000i | 0.108821 | − | 0.326464i | ||||
\(761\) | 19.0000 | + | 19.0000i | 0.688749 | + | 0.688749i | 0.961956 | − | 0.273206i | \(-0.0880841\pi\) |
−0.273206 | + | 0.961956i | \(0.588084\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.0000 | + | 26.0000i | −0.941263 | + | 0.941263i | ||||
\(764\) | 8.00000 | 0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.00000i | 0.216789i | ||||||||
\(767\) | 15.0000 | − | 3.00000i | 0.541619 | − | 0.108324i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.0000 | − | 23.0000i | −0.829401 | − | 0.829401i | 0.158033 | − | 0.987434i | \(-0.449485\pi\) |
−0.987434 | + | 0.158033i | \(0.949485\pi\) | |||||||
\(770\) | −6.00000 | − | 2.00000i | −0.216225 | − | 0.0720750i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.0000 | 0.503871 | ||||||||
\(773\) | 24.0000i | 0.863220i | 0.902060 | + | 0.431610i | \(0.142054\pi\) | ||||
−0.902060 | + | 0.431610i | \(0.857946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.00000 | + | 7.00000i | 0.0359211 | + | 0.251447i | ||||
\(776\) | 2.00000 | 0.0717958 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.0000 | −0.358517 | ||||||||
\(779\) | 6.00000 | 0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | 0.0715656 | ||||||||
\(782\) | 50.0000 | 1.78800 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 3.00000 | − | 9.00000i | 0.107075 | − | 0.321224i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 42.0000i | − | 1.49714i | −0.663057 | − | 0.748569i | \(-0.730741\pi\) | ||
0.663057 | − | 0.748569i | \(-0.269259\pi\) | |||||||
\(788\) | −18.0000 | −0.641223 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −28.0000 | + | 14.0000i | −0.996195 | + | 0.498098i | ||||
\(791\) | 18.0000 | + | 18.0000i | 0.640006 | + | 0.640006i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.00000 | − | 4.00000i | −0.213066 | − | 0.142044i | ||||
\(794\) | − | 8.00000i | − | 0.283909i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.00000 | − | 5.00000i | 0.177109 | − | 0.177109i | −0.612985 | − | 0.790094i | \(-0.710032\pi\) |
0.790094 | + | 0.612985i | \(0.210032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.0000 | − | 10.0000i | −0.353775 | − | 0.353775i | ||||
\(800\) | 3.00000 | − | 4.00000i | 0.106066 | − | 0.141421i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.00000 | + | 1.00000i | 0.0353112 | + | 0.0353112i | ||||
\(803\) | 6.00000 | + | 6.00000i | 0.211735 | + | 0.211735i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30.0000 | − | 10.0000i | −1.05736 | − | 0.352454i | ||||
\(806\) | 5.00000 | − | 1.00000i | 0.176117 | − | 0.0352235i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.0000i | 1.26569i | 0.774277 | + | 0.632846i | \(0.218114\pi\) | ||||
−0.774277 | + | 0.632846i | \(0.781886\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0000 | − | 11.0000i | 0.386262 | − | 0.386262i | −0.487090 | − | 0.873352i | \(-0.661942\pi\) |
0.873352 | + | 0.487090i | \(0.161942\pi\) | |||||||
\(812\) | −8.00000 | −0.280745 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.00000 | + | 8.00000i | −0.280400 | + | 0.280400i | ||||
\(815\) | −4.00000 | − | 8.00000i | −0.140114 | − | 0.280228i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 30.0000i | − | 1.04957i | ||||||
\(818\) | 3.00000 | + | 3.00000i | 0.104893 | + | 0.104893i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.00000 | + | 1.00000i | 0.104765 | + | 0.0349215i | ||||
\(821\) | 29.0000 | − | 29.0000i | 1.01211 | − | 1.01211i | 0.0121812 | − | 0.999926i | \(-0.496123\pi\) |
0.999926 | − | 0.0121812i | \(-0.00387748\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.0000 | + | 15.0000i | 0.522867 | + | 0.522867i | 0.918436 | − | 0.395569i | \(-0.129453\pi\) |
−0.395569 | + | 0.918436i | \(0.629453\pi\) | |||||||
\(824\) | 5.00000 | + | 5.00000i | 0.174183 | + | 0.174183i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | − | 6.00000i | −0.208767 | − | 0.208767i | ||||
\(827\) | 2.00000i | 0.0695468i | 0.999395 | + | 0.0347734i | \(0.0110710\pi\) | ||||
−0.999395 | + | 0.0347734i | \(0.988929\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.0000 | −1.04194 | −0.520972 | − | 0.853574i | \(-0.674430\pi\) | ||||
−0.520972 | + | 0.853574i | \(0.674430\pi\) | |||||||
\(830\) | 12.0000 | − | 6.00000i | 0.416526 | − | 0.208263i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.00000 | − | 2.00000i | −0.104006 | − | 0.0693375i | ||||
\(833\) | −15.0000 | + | 15.0000i | −0.519719 | + | 0.519719i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.00000 | − | 2.00000i | 0.138426 | − | 0.0692129i | ||||
\(836\) | 6.00000i | 0.207514i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 26.0000i | − | 0.898155i | ||||||
\(839\) | −13.0000 | + | 13.0000i | −0.448810 | + | 0.448810i | −0.894959 | − | 0.446149i | \(-0.852795\pi\) |
0.446149 | + | 0.894959i | \(0.352795\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0000 | 0.448276 | ||||||||
\(842\) | 9.00000 | − | 9.00000i | 0.310160 | − | 0.310160i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.0000 | 0.413057 | ||||||||
\(845\) | 19.0000 | − | 22.0000i | 0.653620 | − | 0.756823i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.0000 | −0.618487 | ||||||||
\(848\) | 1.00000 | − | 1.00000i | 0.0343401 | − | 0.0343401i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.00000 | + | 35.0000i | 0.171499 | + | 1.20049i | ||||
\(851\) | −40.0000 | + | 40.0000i | −1.37118 | + | 1.37118i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.0000 | −0.890223 | −0.445112 | − | 0.895475i | \(-0.646836\pi\) | ||||
−0.445112 | + | 0.895475i | \(0.646836\pi\) | |||||||
\(854\) | 4.00000i | 0.136877i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.0000 | + | 13.0000i | 0.444331 | + | 0.444331i | ||||
\(857\) | −5.00000 | + | 5.00000i | −0.170797 | + | 0.170797i | −0.787329 | − | 0.616533i | \(-0.788537\pi\) |
0.616533 | + | 0.787329i | \(0.288537\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 26.0000i | − | 0.887109i | −0.896248 | − | 0.443554i | \(-0.853717\pi\) | ||
0.896248 | − | 0.443554i | \(-0.146283\pi\) | |||||||
\(860\) | 5.00000 | − | 15.0000i | 0.170499 | − | 0.511496i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.0000 | − | 21.0000i | 0.715263 | − | 0.715263i | ||||
\(863\) | − | 46.0000i | − | 1.56586i | −0.622111 | − | 0.782929i | \(-0.713725\pi\) | ||
0.622111 | − | 0.782929i | \(-0.286275\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.0000 | + | 45.0000i | −0.510015 | + | 1.53005i | ||||
\(866\) | 15.0000 | + | 15.0000i | 0.509721 | + | 0.509721i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.00000 | − | 2.00000i | −0.0678844 | − | 0.0678844i | ||||
\(869\) | 14.0000 | − | 14.0000i | 0.474917 | − | 0.474917i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.0000 | + | 24.0000i | 1.21981 | + | 0.813209i | ||||
\(872\) | 13.0000 | + | 13.0000i | 0.440236 | + | 0.440236i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 30.0000i | 1.01477i | ||||||||
\(875\) | 4.00000 | − | 22.0000i | 0.135225 | − | 0.743736i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.0000 | 0.607817 | 0.303908 | − | 0.952701i | \(-0.401708\pi\) | ||||
0.303908 | + | 0.952701i | \(0.401708\pi\) | |||||||
\(878\) | −40.0000 | −1.34993 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | + | 3.00000i | −0.0337100 | + | 0.101130i | ||||
\(881\) | − | 20.0000i | − | 0.673817i | −0.941537 | − | 0.336909i | \(-0.890619\pi\) | ||
0.941537 | − | 0.336909i | \(-0.109381\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.00000 | + | 5.00000i | 0.168263 | + | 0.168263i | 0.786216 | − | 0.617952i | \(-0.212037\pi\) |
−0.617952 | + | 0.786216i | \(0.712037\pi\) | |||||||
\(884\) | 25.0000 | − | 5.00000i | 0.840841 | − | 0.168168i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.0000 | − | 19.0000i | 0.638317 | − | 0.638317i | ||||
\(887\) | −23.0000 | − | 23.0000i | −0.772264 | − | 0.772264i | 0.206238 | − | 0.978502i | \(-0.433878\pi\) |
−0.978502 | + | 0.206238i | \(0.933878\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.0000 | + | 30.0000i | 1.00617 | + | 1.00617i | ||||
\(890\) | 21.0000 | + | 7.00000i | 0.703922 | + | 0.234641i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.00000i | 0.200895i | ||||||||
\(893\) | 6.00000 | − | 6.00000i | 0.200782 | − | 0.200782i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.0000 | + | 40.0000i | 0.668526 | + | 1.33705i | ||||
\(896\) | 2.00000i | 0.0668153i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.00000 | + | 7.00000i | −0.233593 | + | 0.233593i | ||||
\(899\) | −4.00000 | − | 4.00000i | −0.133407 | − | 0.133407i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0000i | 0.333148i | ||||||||
\(902\) | −2.00000 | −0.0665927 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.00000 | − | 9.00000i | 0.299336 | − | 0.299336i | ||||
\(905\) | −40.0000 | + | 20.0000i | −1.32964 | + | 0.664822i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.0000 | − | 35.0000i | 1.16216 | − | 1.16216i | 0.178153 | − | 0.984003i | \(-0.442988\pi\) |
0.984003 | − | 0.178153i | \(-0.0570122\pi\) | |||||||
\(908\) | 12.0000 | 0.398234 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −16.0000 | − | 2.00000i | −0.530395 | − | 0.0662994i | ||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.00000 | + | 6.00000i | −0.198571 | + | 0.198571i | ||||
\(914\) | −38.0000 | −1.25693 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.00000 | − | 3.00000i | 0.0991228 | − | 0.0991228i | ||||
\(917\) | 24.0000i | 0.792550i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.0000i | 0.461817i | 0.972975 | + | 0.230909i | \(0.0741699\pi\) | ||||
−0.972975 | + | 0.230909i | \(0.925830\pi\) | |||||||
\(920\) | −5.00000 | + | 15.0000i | −0.164845 | + | 0.494535i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.0000 | − | 11.0000i | 0.362266 | − | 0.362266i | ||||
\(923\) | 5.00000 | − | 1.00000i | 0.164577 | − | 0.0329154i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.0000 | − | 24.0000i | −1.05215 | − | 0.789115i | ||||
\(926\) | 16.0000 | 0.525793 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.00000i | 0.131306i | ||||||||
\(929\) | −17.0000 | − | 17.0000i | −0.557752 | − | 0.557752i | 0.370915 | − | 0.928667i | \(-0.379044\pi\) |
−0.928667 | + | 0.370915i | \(0.879044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.00000 | − | 9.00000i | −0.294963 | − | 0.294963i | ||||
\(932\) | −5.00000 | − | 5.00000i | −0.163780 | − | 0.163780i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.00000 | + | 5.00000i | −0.163605 | + | 0.163605i | ||||
\(935\) | −10.0000 | − | 20.0000i | −0.327035 | − | 0.654070i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.0000 | + | 33.0000i | 1.07806 | + | 1.07806i | 0.996683 | + | 0.0813798i | \(0.0259327\pi\) |
0.0813798 | + | 0.996683i | \(0.474067\pi\) | |||||||
\(938\) | − | 24.0000i | − | 0.783628i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.00000 | − | 2.00000i | 0.130466 | − | 0.0652328i | ||||
\(941\) | 29.0000 | − | 29.0000i | 0.945373 | − | 0.945373i | −0.0532103 | − | 0.998583i | \(-0.516945\pi\) |
0.998583 | + | 0.0532103i | \(0.0169454\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.0000 | −0.325645 | ||||||||
\(944\) | −3.00000 | + | 3.00000i | −0.0976417 | + | 0.0976417i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.0000i | 0.325128i | ||||||||
\(947\) | − | 38.0000i | − | 1.23483i | −0.786636 | − | 0.617417i | \(-0.788179\pi\) | ||
0.786636 | − | 0.617417i | \(-0.211821\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.0000 | + | 12.0000i | 0.584305 | + | 0.389536i | ||||
\(950\) | −21.0000 | + | 3.00000i | −0.681330 | + | 0.0973329i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.0000 | − | 10.0000i | −0.324102 | − | 0.324102i | ||||
\(953\) | 35.0000 | + | 35.0000i | 1.13376 | + | 1.13376i | 0.989546 | + | 0.144215i | \(0.0460656\pi\) |
0.144215 | + | 0.989546i | \(0.453934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00000 | − | 16.0000i | −0.258874 | − | 0.517748i | ||||
\(956\) | −7.00000 | − | 7.00000i | −0.226396 | − | 0.226396i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.0000 | − | 13.0000i | 0.420011 | − | 0.420011i | ||||
\(959\) | 24.0000 | 0.775000 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.0000i | 0.935484i | ||||||||
\(962\) | −16.0000 | + | 24.0000i | −0.515861 | + | 0.773791i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.00000 | + | 1.00000i | 0.0322078 | + | 0.0322078i | ||||
\(965\) | −14.0000 | − | 28.0000i | −0.450676 | − | 0.901352i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.0000 | 1.54358 | 0.771788 | − | 0.635880i | \(-0.219363\pi\) | ||||
0.771788 | + | 0.635880i | \(0.219363\pi\) | |||||||
\(968\) | 9.00000i | 0.289271i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.00000 | − | 4.00000i | −0.0642161 | − | 0.128432i | ||||
\(971\) | −12.0000 | −0.385098 | −0.192549 | − | 0.981287i | \(-0.561675\pi\) | ||||
−0.192549 | + | 0.981287i | \(0.561675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.0000 | 0.897639 | ||||||||
\(974\) | 32.0000 | 1.02535 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 22.0000 | 0.703842 | 0.351921 | − | 0.936030i | \(-0.385529\pi\) | ||||
0.351921 | + | 0.936030i | \(0.385529\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.0000 | −0.447442 | ||||||||
\(980\) | −3.00000 | − | 6.00000i | −0.0958315 | − | 0.191663i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 10.0000i | − | 0.319113i | ||||||
\(983\) | −24.0000 | −0.765481 | −0.382741 | − | 0.923856i | \(-0.625020\pi\) | ||||
−0.382741 | + | 0.923856i | \(0.625020\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.0000 | + | 36.0000i | 0.573528 | + | 1.14706i | ||||
\(986\) | −20.0000 | − | 20.0000i | −0.636930 | − | 0.636930i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.00000 | + | 15.0000i | 0.0954427 | + | 0.477214i | ||||
\(989\) | 50.0000i | 1.58991i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | −1.00000 | + | 1.00000i | −0.0317500 | + | 0.0317500i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.00000 | − | 2.00000i | −0.0634361 | − | 0.0634361i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.0000 | − | 17.0000i | −0.538395 | − | 0.538395i | 0.384662 | − | 0.923057i | \(-0.374318\pi\) |
−0.923057 | + | 0.384662i | \(0.874318\pi\) | |||||||
\(998\) | 23.0000 | + | 23.0000i | 0.728052 | + | 0.728052i | ||||
\(999\) | 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 | 1170.2.m.a.577.1 | 2 | ||
3.2 | odd | 2 | 130.2.g.c.57.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1170.2.w.c.343.1 | 2 | |||
12.11 | even | 2 | 1040.2.bg.f.577.1 | 2 | |||
13.8 | odd | 4 | 1170.2.w.c.307.1 | 2 | |||
15.2 | even | 4 | 650.2.j.d.343.1 | 2 | |||
15.8 | even | 4 | 130.2.j.b.83.1 | yes | 2 | ||
15.14 | odd | 2 | 650.2.g.b.57.1 | 2 | |||
39.8 | even | 4 | 130.2.j.b.47.1 | yes | 2 | ||
60.23 | odd | 4 | 1040.2.cd.e.993.1 | 2 | |||
65.8 | even | 4 | inner | 1170.2.m.a.73.1 | 2 | ||
156.47 | odd | 4 | 1040.2.cd.e.177.1 | 2 | |||
195.8 | odd | 4 | 130.2.g.c.73.1 | yes | 2 | ||
195.47 | odd | 4 | 650.2.g.b.593.1 | 2 | |||
195.164 | even | 4 | 650.2.j.d.307.1 | 2 | |||
780.203 | even | 4 | 1040.2.bg.f.593.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.g.c.57.1 | ✓ | 2 | 3.2 | odd | 2 | ||
130.2.g.c.73.1 | yes | 2 | 195.8 | odd | 4 | ||
130.2.j.b.47.1 | yes | 2 | 39.8 | even | 4 | ||
130.2.j.b.83.1 | yes | 2 | 15.8 | even | 4 | ||
650.2.g.b.57.1 | 2 | 15.14 | odd | 2 | |||
650.2.g.b.593.1 | 2 | 195.47 | odd | 4 | |||
650.2.j.d.307.1 | 2 | 195.164 | even | 4 | |||
650.2.j.d.343.1 | 2 | 15.2 | even | 4 | |||
1040.2.bg.f.577.1 | 2 | 12.11 | even | 2 | |||
1040.2.bg.f.593.1 | 2 | 780.203 | even | 4 | |||
1040.2.cd.e.177.1 | 2 | 156.47 | odd | 4 | |||
1040.2.cd.e.993.1 | 2 | 60.23 | odd | 4 | |||
1170.2.m.a.73.1 | 2 | 65.8 | even | 4 | inner | ||
1170.2.m.a.577.1 | 2 | 1.1 | even | 1 | trivial | ||
1170.2.w.c.307.1 | 2 | 13.8 | odd | 4 | |||
1170.2.w.c.343.1 | 2 | 5.3 | odd | 4 |