Newspace parameters
Level: | \( N \) | \(=\) | \( 650 = 2 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 650.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(5.19027613138\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
|
|
Defining polynomial: |
\( x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 650.307 |
Dual form | 650.2.j.d.343.1 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/650\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.00000 | − | 1.00000i | 0.577350 | − | 0.577350i | −0.356822 | − | 0.934172i | \(-0.616140\pi\) |
0.934172 | + | 0.356822i | \(0.116140\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | − | 1.00000i | −0.408248 | − | 0.408248i | ||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 1.00000i | 0.301511 | − | 0.301511i | −0.540094 | − | 0.841605i | \(-0.681611\pi\) |
0.841605 | + | 0.540094i | \(0.181611\pi\) | |||||||
\(12\) | −1.00000 | + | 1.00000i | −0.288675 | + | 0.288675i | ||||
\(13\) | −2.00000 | − | 3.00000i | −0.554700 | − | 0.832050i | ||||
\(14\) | − | 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 | \(-0.422021\pi\) |
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 3.00000 | − | 3.00000i | 0.688247 | − | 0.688247i | −0.273597 | − | 0.961844i | \(-0.588214\pi\) |
0.961844 | + | 0.273597i | \(0.0882135\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | − | 2.00000i | 0.436436 | − | 0.436436i | ||||
\(22\) | −1.00000 | − | 1.00000i | −0.213201 | − | 0.213201i | ||||
\(23\) | −5.00000 | − | 5.00000i | −1.04257 | − | 1.04257i | −0.999053 | − | 0.0435195i | \(-0.986143\pi\) |
−0.0435195 | − | 0.999053i | \(-0.513857\pi\) | |||||||
\(24\) | 1.00000 | + | 1.00000i | 0.204124 | + | 0.204124i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.00000 | + | 2.00000i | −0.588348 | + | 0.392232i | ||||
\(27\) | 4.00000 | + | 4.00000i | 0.769800 | + | 0.769800i | ||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | 4.00000i | 0.742781i | 0.928477 | + | 0.371391i | \(0.121119\pi\) | ||||
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | + | 1.00000i | 0.179605 | + | 0.179605i | 0.791184 | − | 0.611578i | \(-0.209465\pi\) |
−0.611578 | + | 0.791184i | \(0.709465\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | − | 2.00000i | − | 0.348155i | ||||||
\(34\) | −5.00000 | − | 5.00000i | −0.857493 | − | 0.857493i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −8.00000 | −1.31519 | −0.657596 | − | 0.753371i | \(-0.728427\pi\) | ||||
−0.657596 | + | 0.753371i | \(0.728427\pi\) | |||||||
\(38\) | −3.00000 | − | 3.00000i | −0.486664 | − | 0.486664i | ||||
\(39\) | −5.00000 | − | 1.00000i | −0.800641 | − | 0.160128i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | + | 1.00000i | 0.156174 | + | 0.156174i | 0.780869 | − | 0.624695i | \(-0.214777\pi\) |
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | −2.00000 | − | 2.00000i | −0.308607 | − | 0.308607i | ||||
\(43\) | 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 | ||||
\(47\) | 2.00000 | 0.291730 | 0.145865 | − | 0.989305i | \(-0.453403\pi\) | ||||
0.145865 | + | 0.989305i | \(0.453403\pi\) | |||||||
\(48\) | 1.00000 | − | 1.00000i | 0.144338 | − | 0.144338i | ||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 10.0000i | − | 1.40028i | ||||||
\(52\) | 2.00000 | + | 3.00000i | 0.277350 | + | 0.416025i | ||||
\(53\) | 1.00000 | − | 1.00000i | 0.137361 | − | 0.137361i | −0.635083 | − | 0.772444i | \(-0.719034\pi\) |
0.772444 | + | 0.635083i | \(0.219034\pi\) | |||||||
\(54\) | 4.00000 | − | 4.00000i | 0.544331 | − | 0.544331i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.00000i | 0.267261i | ||||||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | 4.00000 | 0.525226 | ||||||||
\(59\) | −3.00000 | − | 3.00000i | −0.390567 | − | 0.390567i | 0.484323 | − | 0.874889i | \(-0.339066\pi\) |
−0.874889 | + | 0.484323i | \(0.839066\pi\) | |||||||
\(60\) | 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 | ||||
\(63\) | 2.00000i | 0.251976i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.00000 | −0.246183 | ||||||||
\(67\) | 12.0000i | 1.46603i | 0.680211 | + | 0.733017i | \(0.261888\pi\) | ||||
−0.680211 | + | 0.733017i | \(0.738112\pi\) | |||||||
\(68\) | −5.00000 | + | 5.00000i | −0.606339 | + | 0.606339i | ||||
\(69\) | −10.0000 | −1.20386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.00000 | + | 1.00000i | 0.118678 | + | 0.118678i | 0.763952 | − | 0.645273i | \(-0.223257\pi\) |
−0.645273 | + | 0.763952i | \(0.723257\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | − | 6.00000i | − | 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | 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 | ||||
\(78\) | −1.00000 | + | 5.00000i | −0.113228 | + | 0.566139i | ||||
\(79\) | 14.0000i | 1.57512i | 0.616236 | + | 0.787562i | \(0.288657\pi\) | ||||
−0.616236 | + | 0.787562i | \(0.711343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 1.00000 | − | 1.00000i | 0.110432 | − | 0.110432i | ||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | −2.00000 | + | 2.00000i | −0.218218 | + | 0.218218i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.00000 | − | 5.00000i | 0.539164 | − | 0.539164i | ||||
\(87\) | 4.00000 | + | 4.00000i | 0.428845 | + | 0.428845i | ||||
\(88\) | 1.00000 | + | 1.00000i | 0.106600 | + | 0.106600i | ||||
\(89\) | 7.00000 | + | 7.00000i | 0.741999 | + | 0.741999i | 0.972962 | − | 0.230964i | \(-0.0741879\pi\) |
−0.230964 | + | 0.972962i | \(0.574188\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | − | 6.00000i | −0.419314 | − | 0.628971i | ||||
\(92\) | 5.00000 | + | 5.00000i | 0.521286 | + | 0.521286i | ||||
\(93\) | 2.00000 | 0.207390 | ||||||||
\(94\) | − | 2.00000i | − | 0.206284i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | − | 1.00000i | −0.102062 | − | 0.102062i | ||||
\(97\) | 2.00000i | 0.203069i | 0.994832 | + | 0.101535i | \(0.0323753\pi\) | ||||
−0.994832 | + | 0.101535i | \(0.967625\pi\) | |||||||
\(98\) | 3.00000i | 0.303046i | ||||||||
\(99\) | 1.00000 | + | 1.00000i | 0.100504 | + | 0.100504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | −10.0000 | −0.990148 | ||||||||
\(103\) | −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 | \(-0.598364\pi\) | |||||||
\(108\) | −4.00000 | − | 4.00000i | −0.384900 | − | 0.384900i | ||||
\(109\) | 13.0000 | − | 13.0000i | 1.24517 | − | 1.24517i | 0.287348 | − | 0.957826i | \(-0.407226\pi\) |
0.957826 | − | 0.287348i | \(-0.0927736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | + | 8.00000i | −0.759326 | + | 0.759326i | ||||
\(112\) | 2.00000 | 0.188982 | ||||||||
\(113\) | −9.00000 | + | 9.00000i | −0.846649 | + | 0.846649i | −0.989713 | − | 0.143065i | \(-0.954304\pi\) |
0.143065 | + | 0.989713i | \(0.454304\pi\) | |||||||
\(114\) | −6.00000 | −0.561951 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 4.00000i | − | 0.371391i | ||||||
\(117\) | 3.00000 | − | 2.00000i | 0.277350 | − | 0.184900i | ||||
\(118\) | −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 | ||||||||
\(122\) | − | 2.00000i | − | 0.181071i | ||||||
\(123\) | 2.00000 | 0.180334 | ||||||||
\(124\) | −1.00000 | − | 1.00000i | −0.0898027 | − | 0.0898027i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.00000 | 0.178174 | ||||||||
\(127\) | −15.0000 | + | 15.0000i | −1.33103 | + | 1.33103i | −0.426589 | + | 0.904445i | \(0.640285\pi\) |
−0.904445 | + | 0.426589i | \(0.859715\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 10.0000 | 0.880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 2.00000i | 0.174078i | ||||||||
\(133\) | 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 | ||||
\(137\) | 12.0000 | 1.02523 | 0.512615 | − | 0.858619i | \(-0.328677\pi\) | ||||
0.512615 | + | 0.858619i | \(0.328677\pi\) | |||||||
\(138\) | 10.0000i | 0.851257i | ||||||||
\(139\) | 14.0000i | 1.18746i | 0.804663 | + | 0.593732i | \(0.202346\pi\) | ||||
−0.804663 | + | 0.593732i | \(0.797654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00000 | − | 2.00000i | 0.168430 | − | 0.168430i | ||||
\(142\) | 1.00000 | − | 1.00000i | 0.0839181 | − | 0.0839181i | ||||
\(143\) | −5.00000 | − | 1.00000i | −0.418121 | − | 0.0836242i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.00000 | −0.496564 | ||||||||
\(147\) | −3.00000 | + | 3.00000i | −0.247436 | + | 0.247436i | ||||
\(148\) | 8.00000 | 0.657596 | ||||||||
\(149\) | 13.0000 | − | 13.0000i | 1.06500 | − | 1.06500i | 0.0672664 | − | 0.997735i | \(-0.478572\pi\) |
0.997735 | − | 0.0672664i | \(-0.0214278\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.00000 | + | 9.00000i | −0.732410 | + | 0.732410i | −0.971097 | − | 0.238687i | \(-0.923283\pi\) |
0.238687 | + | 0.971097i | \(0.423283\pi\) | |||||||
\(152\) | 3.00000 | + | 3.00000i | 0.243332 | + | 0.243332i | ||||
\(153\) | 5.00000 | + | 5.00000i | 0.404226 | + | 0.404226i | ||||
\(154\) | −2.00000 | − | 2.00000i | −0.161165 | − | 0.161165i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.00000 | + | 1.00000i | 0.400320 | + | 0.0800641i | ||||
\(157\) | −3.00000 | − | 3.00000i | −0.239426 | − | 0.239426i | 0.577186 | − | 0.816612i | \(-0.304151\pi\) |
−0.816612 | + | 0.577186i | \(0.804151\pi\) | |||||||
\(158\) | 14.0000 | 1.11378 | ||||||||
\(159\) | − | 2.00000i | − | 0.158610i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.0000 | − | 10.0000i | −0.788110 | − | 0.788110i | ||||
\(162\) | − | 5.00000i | − | 0.392837i | ||||||
\(163\) | 4.00000i | 0.313304i | 0.987654 | + | 0.156652i | \(0.0500701\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(164\) | −1.00000 | − | 1.00000i | −0.0780869 | − | 0.0780869i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 6.00000i | − | 0.465690i | ||||||
\(167\) | 2.00000 | 0.154765 | 0.0773823 | − | 0.997001i | \(-0.475344\pi\) | ||||
0.0773823 | + | 0.997001i | \(0.475344\pi\) | |||||||
\(168\) | 2.00000 | + | 2.00000i | 0.154303 | + | 0.154303i | ||||
\(169\) | −5.00000 | + | 12.0000i | −0.384615 | + | 0.923077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | + | 3.00000i | 0.229416 | + | 0.229416i | ||||
\(172\) | −5.00000 | − | 5.00000i | −0.381246 | − | 0.381246i | ||||
\(173\) | 15.0000 | + | 15.0000i | 1.14043 | + | 1.14043i | 0.988372 | + | 0.152057i | \(0.0485898\pi\) |
0.152057 | + | 0.988372i | \(0.451410\pi\) | |||||||
\(174\) | 4.00000 | − | 4.00000i | 0.303239 | − | 0.303239i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | − | 1.00000i | 0.0753778 | − | 0.0753778i | ||||
\(177\) | −6.00000 | −0.450988 | ||||||||
\(178\) | 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 | \(0.266738\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | −6.00000 | + | 4.00000i | −0.444750 | + | 0.296500i | ||||
\(183\) | 2.00000 | − | 2.00000i | 0.147844 | − | 0.147844i | ||||
\(184\) | 5.00000 | − | 5.00000i | 0.368605 | − | 0.368605i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 2.00000i | − | 0.146647i | ||||||
\(187\) | − | 10.0000i | − | 0.731272i | ||||||
\(188\) | −2.00000 | −0.145865 | ||||||||
\(189\) | 8.00000 | + | 8.00000i | 0.581914 | + | 0.581914i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | −1.00000 | + | 1.00000i | −0.0721688 | + | 0.0721688i | ||||
\(193\) | 14.0000i | 1.00774i | 0.863779 | + | 0.503871i | \(0.168091\pi\) | ||||
−0.863779 | + | 0.503871i | \(0.831909\pi\) | |||||||
\(194\) | 2.00000 | 0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 1.00000 | − | 1.00000i | 0.0710669 | − | 0.0710669i | ||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.0000 | + | 12.0000i | 0.846415 | + | 0.846415i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.00000i | 0.561490i | ||||||||
\(204\) | 10.0000i | 0.700140i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.00000 | + | 5.00000i | −0.348367 | + | 0.348367i | ||||
\(207\) | 5.00000 | − | 5.00000i | 0.347524 | − | 0.347524i | ||||
\(208\) | −2.00000 | − | 3.00000i | −0.138675 | − | 0.208013i | ||||
\(209\) | − | 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 | ||||
\(213\) | 2.00000 | 0.137038 | ||||||||
\(214\) | −13.0000 | + | 13.0000i | −0.888662 | + | 0.888662i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | + | 4.00000i | −0.272166 | + | 0.272166i | ||||
\(217\) | 2.00000 | + | 2.00000i | 0.135769 | + | 0.135769i | ||||
\(218\) | −13.0000 | − | 13.0000i | −0.880471 | − | 0.880471i | ||||
\(219\) | −6.00000 | − | 6.00000i | −0.405442 | − | 0.405442i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.0000 | − | 5.00000i | −1.68168 | − | 0.336336i | ||||
\(222\) | 8.00000 | + | 8.00000i | 0.536925 | + | 0.536925i | ||||
\(223\) | 6.00000 | 0.401790 | 0.200895 | − | 0.979613i | \(-0.435615\pi\) | ||||
0.200895 | + | 0.979613i | \(0.435615\pi\) | |||||||
\(224\) | − | 2.00000i | − | 0.133631i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.00000 | + | 9.00000i | 0.598671 | + | 0.598671i | ||||
\(227\) | 12.0000i | 0.796468i | 0.917284 | + | 0.398234i | \(0.130377\pi\) | ||||
−0.917284 | + | 0.398234i | \(0.869623\pi\) | |||||||
\(228\) | 6.00000i | 0.397360i | ||||||||
\(229\) | −3.00000 | − | 3.00000i | −0.198246 | − | 0.198246i | 0.601002 | − | 0.799248i | \(-0.294768\pi\) |
−0.799248 | + | 0.601002i | \(0.794768\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 4.00000i | − | 0.263181i | ||||||
\(232\) | −4.00000 | −0.262613 | ||||||||
\(233\) | 5.00000 | + | 5.00000i | 0.327561 | + | 0.327561i | 0.851658 | − | 0.524097i | \(-0.175597\pi\) |
−0.524097 | + | 0.851658i | \(0.675597\pi\) | |||||||
\(234\) | −2.00000 | − | 3.00000i | −0.130744 | − | 0.196116i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.00000 | + | 3.00000i | 0.195283 | + | 0.195283i | ||||
\(237\) | 14.0000 | + | 14.0000i | 0.909398 | + | 0.909398i | ||||
\(238\) | −10.0000 | − | 10.0000i | −0.648204 | − | 0.648204i | ||||
\(239\) | −7.00000 | + | 7.00000i | −0.452792 | + | 0.452792i | −0.896280 | − | 0.443488i | \(-0.853741\pi\) |
0.443488 | + | 0.896280i | \(0.353741\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | − | 1.00000i | 0.0644157 | − | 0.0644157i | −0.674165 | − | 0.738581i | \(-0.735496\pi\) |
0.738581 | + | 0.674165i | \(0.235496\pi\) | |||||||
\(242\) | 9.00000 | 0.578542 | ||||||||
\(243\) | −7.00000 | + | 7.00000i | −0.449050 | + | 0.449050i | ||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 2.00000i | − | 0.127515i | ||||||
\(247\) | −15.0000 | − | 3.00000i | −0.954427 | − | 0.190885i | ||||
\(248\) | −1.00000 | + | 1.00000i | −0.0635001 | + | 0.0635001i | ||||
\(249\) | 6.00000 | − | 6.00000i | 0.380235 | − | 0.380235i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 30.0000i | − | 1.89358i | −0.321847 | − | 0.946792i | \(-0.604304\pi\) | ||
0.321847 | − | 0.946792i | \(-0.395696\pi\) | |||||||
\(252\) | − | 2.00000i | − | 0.125988i | ||||||
\(253\) | −10.0000 | −0.628695 | ||||||||
\(254\) | 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 | −0.998053 | − | 0.0623783i | \(-0.980131\pi\) |
0.0623783 | + | 0.998053i | \(0.480131\pi\) | |||||||
\(258\) | − | 10.0000i | − | 0.622573i | ||||||
\(259\) | −16.0000 | −0.994192 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.00000 | −0.247594 | ||||||||
\(262\) | − | 12.0000i | − | 0.741362i | ||||||
\(263\) | −9.00000 | + | 9.00000i | −0.554964 | + | 0.554964i | −0.927869 | − | 0.372906i | \(-0.878362\pi\) |
0.372906 | + | 0.927869i | \(0.378362\pi\) | |||||||
\(264\) | 2.00000 | 0.123091 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.00000 | − | 6.00000i | −0.367884 | − | 0.367884i | ||||
\(267\) | 14.0000 | 0.856786 | ||||||||
\(268\) | − | 12.0000i | − | 0.733017i | ||||||
\(269\) | − | 16.0000i | − | 0.975537i | −0.872973 | − | 0.487769i | \(-0.837811\pi\) | ||
0.872973 | − | 0.487769i | \(-0.162189\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.00000 | + | 9.00000i | −0.546711 | + | 0.546711i | −0.925488 | − | 0.378777i | \(-0.876345\pi\) |
0.378777 | + | 0.925488i | \(0.376345\pi\) | |||||||
\(272\) | 5.00000 | − | 5.00000i | 0.303170 | − | 0.303170i | ||||
\(273\) | −10.0000 | − | 2.00000i | −0.605228 | − | 0.121046i | ||||
\(274\) | − | 12.0000i | − | 0.724947i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.0000 | 0.601929 | ||||||||
\(277\) | −5.00000 | + | 5.00000i | −0.300421 | + | 0.300421i | −0.841178 | − | 0.540758i | \(-0.818138\pi\) |
0.540758 | + | 0.841178i | \(0.318138\pi\) | |||||||
\(278\) | 14.0000 | 0.839664 | ||||||||
\(279\) | −1.00000 | + | 1.00000i | −0.0598684 | + | 0.0598684i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.0000 | − | 21.0000i | 1.25275 | − | 1.25275i | 0.298275 | − | 0.954480i | \(-0.403589\pi\) |
0.954480 | − | 0.298275i | \(-0.0964112\pi\) | |||||||
\(282\) | −2.00000 | − | 2.00000i | −0.119098 | − | 0.119098i | ||||
\(283\) | −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 | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | − | 33.0000i | − | 1.94118i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.00000 | + | 2.00000i | 0.117242 | + | 0.117242i | ||||
\(292\) | 6.00000i | 0.351123i | ||||||||
\(293\) | − | 26.0000i | − | 1.51894i | −0.650545 | − | 0.759468i | \(-0.725459\pi\) | ||
0.650545 | − | 0.759468i | \(-0.274541\pi\) | |||||||
\(294\) | 3.00000 | + | 3.00000i | 0.174964 | + | 0.174964i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 8.00000i | − | 0.464991i | ||||||
\(297\) | 8.00000 | 0.464207 | ||||||||
\(298\) | −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 | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.00000 | − | 5.00000i | 0.285831 | − | 0.285831i | ||||
\(307\) | 2.00000 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(308\) | −2.00000 | + | 2.00000i | −0.113961 | + | 0.113961i | ||||
\(309\) | −10.0000 | −0.568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0000i | 0.567048i | 0.958965 | + | 0.283524i | \(0.0915036\pi\) | ||||
−0.958965 | + | 0.283524i | \(0.908496\pi\) | |||||||
\(312\) | 1.00000 | − | 5.00000i | 0.0566139 | − | 0.283069i | ||||
\(313\) | −9.00000 | + | 9.00000i | −0.508710 | + | 0.508710i | −0.914130 | − | 0.405420i | \(-0.867125\pi\) |
0.405420 | + | 0.914130i | \(0.367125\pi\) | |||||||
\(314\) | −3.00000 | + | 3.00000i | −0.169300 | + | 0.169300i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 14.0000i | − | 0.787562i | ||||||
\(317\) | 2.00000i | 0.112331i | 0.998421 | + | 0.0561656i | \(0.0178875\pi\) | ||||
−0.998421 | + | 0.0561656i | \(0.982113\pi\) | |||||||
\(318\) | −2.00000 | −0.112154 | ||||||||
\(319\) | 4.00000 | + | 4.00000i | 0.223957 | + | 0.223957i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.0000 | −1.45118 | ||||||||
\(322\) | −10.0000 | + | 10.0000i | −0.557278 | + | 0.557278i | ||||
\(323\) | − | 30.0000i | − | 1.66924i | ||||||
\(324\) | −5.00000 | −0.277778 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.00000 | 0.221540 | ||||||||
\(327\) | − | 26.0000i | − | 1.43780i | ||||||
\(328\) | −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 | 0.415094 | − | 0.909779i | \(-0.363749\pi\) |
−0.909779 | + | 0.415094i | \(0.863749\pi\) | |||||||
\(332\) | −6.00000 | −0.329293 | ||||||||
\(333\) | − | 8.00000i | − | 0.438397i | ||||||
\(334\) | − | 2.00000i | − | 0.109435i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.00000 | − | 2.00000i | 0.109109 | − | 0.109109i | ||||
\(337\) | 5.00000 | − | 5.00000i | 0.272367 | − | 0.272367i | −0.557685 | − | 0.830053i | \(-0.688310\pi\) |
0.830053 | + | 0.557685i | \(0.188310\pi\) | |||||||
\(338\) | 12.0000 | + | 5.00000i | 0.652714 | + | 0.271964i | ||||
\(339\) | 18.0000i | 0.977626i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | 0.108306 | ||||||||
\(342\) | 3.00000 | − | 3.00000i | 0.162221 | − | 0.162221i | ||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | −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 | \(0.664392\pi\) | |||||||
\(348\) | −4.00000 | − | 4.00000i | −0.214423 | − | 0.214423i | ||||
\(349\) | −3.00000 | − | 3.00000i | −0.160586 | − | 0.160586i | 0.622240 | − | 0.782826i | \(-0.286223\pi\) |
−0.782826 | + | 0.622240i | \(0.786223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | − | 20.0000i | 0.213504 | − | 1.06752i | ||||
\(352\) | −1.00000 | − | 1.00000i | −0.0533002 | − | 0.0533002i | ||||
\(353\) | 16.0000 | 0.851594 | 0.425797 | − | 0.904819i | \(-0.359994\pi\) | ||||
0.425797 | + | 0.904819i | \(0.359994\pi\) | |||||||
\(354\) | 6.00000i | 0.318896i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.00000 | − | 7.00000i | −0.370999 | − | 0.370999i | ||||
\(357\) | − | 20.0000i | − | 1.05851i | ||||||
\(358\) | 20.0000i | 1.05703i | ||||||||
\(359\) | −13.0000 | − | 13.0000i | −0.686114 | − | 0.686114i | 0.275257 | − | 0.961371i | \(-0.411237\pi\) |
−0.961371 | + | 0.275257i | \(0.911237\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000i | 0.0526316i | ||||||||
\(362\) | 20.0000 | 1.05118 | ||||||||
\(363\) | 9.00000 | + | 9.00000i | 0.472377 | + | 0.472377i | ||||
\(364\) | 4.00000 | + | 6.00000i | 0.209657 | + | 0.314485i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.00000 | − | 2.00000i | −0.104542 | − | 0.104542i | ||||
\(367\) | −3.00000 | − | 3.00000i | −0.156599 | − | 0.156599i | 0.624459 | − | 0.781058i | \(-0.285320\pi\) |
−0.781058 | + | 0.624459i | \(0.785320\pi\) | |||||||
\(368\) | −5.00000 | − | 5.00000i | −0.260643 | − | 0.260643i | ||||
\(369\) | −1.00000 | + | 1.00000i | −0.0520579 | + | 0.0520579i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000 | − | 2.00000i | 0.103835 | − | 0.103835i | ||||
\(372\) | −2.00000 | −0.103695 | ||||||||
\(373\) | 1.00000 | − | 1.00000i | 0.0517780 | − | 0.0517780i | −0.680744 | − | 0.732522i | \(-0.738343\pi\) |
0.732522 | + | 0.680744i | \(0.238343\pi\) | |||||||
\(374\) | −10.0000 | −0.517088 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.00000i | 0.103142i | ||||||||
\(377\) | 12.0000 | − | 8.00000i | 0.618031 | − | 0.412021i | ||||
\(378\) | 8.00000 | − | 8.00000i | 0.411476 | − | 0.411476i | ||||
\(379\) | −17.0000 | + | 17.0000i | −0.873231 | + | 0.873231i | −0.992823 | − | 0.119592i | \(-0.961841\pi\) |
0.119592 | + | 0.992823i | \(0.461841\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.0000i | 1.53695i | ||||||||
\(382\) | 8.00000i | 0.409316i | ||||||||
\(383\) | 6.00000 | 0.306586 | 0.153293 | − | 0.988181i | \(-0.451012\pi\) | ||||
0.153293 | + | 0.988181i | \(0.451012\pi\) | |||||||
\(384\) | 1.00000 | + | 1.00000i | 0.0510310 | + | 0.0510310i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.0000 | 0.712581 | ||||||||
\(387\) | −5.00000 | + | 5.00000i | −0.254164 | + | 0.254164i | ||||
\(388\) | − | 2.00000i | − | 0.101535i | ||||||
\(389\) | 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 | ||||||||
\(392\) | − | 3.00000i | − | 0.151523i | ||||||
\(393\) | 12.0000 | − | 12.0000i | 0.605320 | − | 0.605320i | ||||
\(394\) | −18.0000 | −0.906827 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.00000 | − | 1.00000i | −0.0502519 | − | 0.0502519i | ||||
\(397\) | −8.00000 | −0.401508 | −0.200754 | − | 0.979642i | \(-0.564339\pi\) | ||||
−0.200754 | + | 0.979642i | \(0.564339\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 12.0000i | − | 0.600751i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | − | 1.00000i | 0.0499376 | − | 0.0499376i | −0.681697 | − | 0.731635i | \(-0.738758\pi\) |
0.731635 | + | 0.681697i | \(0.238758\pi\) | |||||||
\(402\) | 12.0000 | − | 12.0000i | 0.598506 | − | 0.598506i | ||||
\(403\) | 1.00000 | − | 5.00000i | 0.0498135 | − | 0.249068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.00000 | 0.397033 | ||||||||
\(407\) | −8.00000 | + | 8.00000i | −0.396545 | + | 0.396545i | ||||
\(408\) | 10.0000 | 0.495074 | ||||||||
\(409\) | 3.00000 | − | 3.00000i | 0.148340 | − | 0.148340i | −0.629036 | − | 0.777376i | \(-0.716550\pi\) |
0.777376 | + | 0.629036i | \(0.216550\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | − | 12.0000i | 0.591916 | − | 0.591916i | ||||
\(412\) | 5.00000 | + | 5.00000i | 0.246332 | + | 0.246332i | ||||
\(413\) | −6.00000 | − | 6.00000i | −0.295241 | − | 0.295241i | ||||
\(414\) | −5.00000 | − | 5.00000i | −0.245737 | − | 0.245737i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.00000 | + | 2.00000i | −0.147087 | + | 0.0980581i | ||||
\(417\) | 14.0000 | + | 14.0000i | 0.685583 | + | 0.685583i | ||||
\(418\) | −6.00000 | −0.293470 | ||||||||
\(419\) | − | 26.0000i | − | 1.27018i | −0.772437 | − | 0.635092i | \(-0.780962\pi\) | ||
0.772437 | − | 0.635092i | \(-0.219038\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.00000 | − | 9.00000i | −0.438633 | − | 0.438633i | 0.452919 | − | 0.891552i | \(-0.350383\pi\) |
−0.891552 | + | 0.452919i | \(0.850383\pi\) | |||||||
\(422\) | − | 12.0000i | − | 0.584151i | ||||||
\(423\) | 2.00000i | 0.0972433i | ||||||||
\(424\) | 1.00000 | + | 1.00000i | 0.0485643 | + | 0.0485643i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 2.00000i | − | 0.0969003i | ||||||
\(427\) | 4.00000 | 0.193574 | ||||||||
\(428\) | 13.0000 | + | 13.0000i | 0.628379 | + | 0.628379i | ||||
\(429\) | −6.00000 | + | 4.00000i | −0.289683 | + | 0.193122i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.0000 | + | 21.0000i | 1.01153 | + | 1.01153i | 0.999933 | + | 0.0116017i | \(0.00369302\pi\) |
0.0116017 | + | 0.999933i | \(0.496307\pi\) | |||||||
\(432\) | 4.00000 | + | 4.00000i | 0.192450 | + | 0.192450i | ||||
\(433\) | −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 | ||||
\(437\) | −30.0000 | −1.43509 | ||||||||
\(438\) | −6.00000 | + | 6.00000i | −0.286691 | + | 0.286691i | ||||
\(439\) | −40.0000 | −1.90910 | −0.954548 | − | 0.298057i | \(-0.903661\pi\) | ||||
−0.954548 | + | 0.298057i | \(0.903661\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 3.00000i | − | 0.142857i | ||||||
\(442\) | −5.00000 | + | 25.0000i | −0.237826 | + | 1.18913i | ||||
\(443\) | −19.0000 | + | 19.0000i | −0.902717 | + | 0.902717i | −0.995670 | − | 0.0929532i | \(-0.970369\pi\) |
0.0929532 | + | 0.995670i | \(0.470369\pi\) | |||||||
\(444\) | 8.00000 | − | 8.00000i | 0.379663 | − | 0.379663i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 6.00000i | − | 0.284108i | ||||||
\(447\) | − | 26.0000i | − | 1.22976i | ||||||
\(448\) | −2.00000 | −0.0944911 | ||||||||
\(449\) | 7.00000 | + | 7.00000i | 0.330350 | + | 0.330350i | 0.852720 | − | 0.522369i | \(-0.174952\pi\) |
−0.522369 | + | 0.852720i | \(0.674952\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.00000 | 0.0941763 | ||||||||
\(452\) | 9.00000 | − | 9.00000i | 0.423324 | − | 0.423324i | ||||
\(453\) | 18.0000i | 0.845714i | ||||||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | − | 38.0000i | − | 1.77757i | −0.458329 | − | 0.888783i | \(-0.651552\pi\) | ||
0.458329 | − | 0.888783i | \(-0.348448\pi\) | |||||||
\(458\) | −3.00000 | + | 3.00000i | −0.140181 | + | 0.140181i | ||||
\(459\) | 40.0000 | 1.86704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.0000 | + | 11.0000i | 0.512321 | + | 0.512321i | 0.915237 | − | 0.402916i | \(-0.132003\pi\) |
−0.402916 | + | 0.915237i | \(0.632003\pi\) | |||||||
\(462\) | −4.00000 | −0.186097 | ||||||||
\(463\) | − | 16.0000i | − | 0.743583i | −0.928316 | − | 0.371792i | \(-0.878744\pi\) | ||
0.928316 | − | 0.371792i | \(-0.121256\pi\) | |||||||
\(464\) | 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 | −0.813265 | − | 0.581893i | \(-0.802312\pi\) |
0.581893 | + | 0.813265i | \(0.302312\pi\) | |||||||
\(468\) | −3.00000 | + | 2.00000i | −0.138675 | + | 0.0924500i | ||||
\(469\) | 24.0000i | 1.10822i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.00000 | −0.276465 | ||||||||
\(472\) | 3.00000 | − | 3.00000i | 0.138086 | − | 0.138086i | ||||
\(473\) | 10.0000 | 0.459800 | ||||||||
\(474\) | 14.0000 | − | 14.0000i | 0.643041 | − | 0.643041i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10.0000 | + | 10.0000i | −0.458349 | + | 0.458349i | ||||
\(477\) | 1.00000 | + | 1.00000i | 0.0457869 | + | 0.0457869i | ||||
\(478\) | 7.00000 | + | 7.00000i | 0.320173 | + | 0.320173i | ||||
\(479\) | −13.0000 | − | 13.0000i | −0.593985 | − | 0.593985i | 0.344720 | − | 0.938705i | \(-0.387974\pi\) |
−0.938705 | + | 0.344720i | \(0.887974\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | + | 24.0000i | 0.729537 | + | 1.09431i | ||||
\(482\) | −1.00000 | − | 1.00000i | −0.0455488 | − | 0.0455488i | ||||
\(483\) | −20.0000 | −0.910032 | ||||||||
\(484\) | − | 9.00000i | − | 0.409091i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.00000 | + | 7.00000i | 0.317526 | + | 0.317526i | ||||
\(487\) | 32.0000i | 1.45006i | 0.688718 | + | 0.725029i | \(0.258174\pi\) | ||||
−0.688718 | + | 0.725029i | \(0.741826\pi\) | |||||||
\(488\) | 2.00000i | 0.0905357i | ||||||||
\(489\) | 4.00000 | + | 4.00000i | 0.180886 | + | 0.180886i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.0000i | 0.451294i | 0.974209 | + | 0.225647i | \(0.0724495\pi\) | ||||
−0.974209 | + | 0.225647i | \(0.927550\pi\) | |||||||
\(492\) | −2.00000 | −0.0901670 | ||||||||
\(493\) | 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 | ||||
\(498\) | −6.00000 | − | 6.00000i | −0.268866 | − | 0.268866i | ||||
\(499\) | 23.0000 | − | 23.0000i | 1.02962 | − | 1.02962i | 0.0300737 | − | 0.999548i | \(-0.490426\pi\) |
0.999548 | − | 0.0300737i | \(-0.00957421\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.00000 | − | 2.00000i | 0.0893534 | − | 0.0893534i | ||||
\(502\) | −30.0000 | −1.33897 | ||||||||
\(503\) | −9.00000 | + | 9.00000i | −0.401290 | + | 0.401290i | −0.878688 | − | 0.477397i | \(-0.841580\pi\) |
0.477397 | + | 0.878688i | \(0.341580\pi\) | |||||||
\(504\) | −2.00000 | −0.0890871 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.0000i | 0.444554i | ||||||||
\(507\) | 7.00000 | + | 17.0000i | 0.310881 | + | 0.754997i | ||||
\(508\) | 15.0000 | − | 15.0000i | 0.665517 | − | 0.665517i | ||||
\(509\) | 13.0000 | − | 13.0000i | 0.576215 | − | 0.576215i | −0.357643 | − | 0.933858i | \(-0.616420\pi\) |
0.933858 | + | 0.357643i | \(0.116420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 12.0000i | − | 0.530849i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 24.0000 | 1.05963 | ||||||||
\(514\) | 15.0000 | + | 15.0000i | 0.661622 | + | 0.661622i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −10.0000 | −0.440225 | ||||||||
\(517\) | 2.00000 | − | 2.00000i | 0.0879599 | − | 0.0879599i | ||||
\(518\) | 16.0000i | 0.703000i | ||||||||
\(519\) | 30.0000 | 1.31685 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.0000 | 0.963837 | 0.481919 | − | 0.876216i | \(-0.339940\pi\) | ||||
0.481919 | + | 0.876216i | \(0.339940\pi\) | |||||||
\(522\) | 4.00000i | 0.175075i | ||||||||
\(523\) | 21.0000 | − | 21.0000i | 0.918266 | − | 0.918266i | −0.0786374 | − | 0.996903i | \(-0.525057\pi\) |
0.996903 | + | 0.0786374i | \(0.0250569\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.00000 | + | 9.00000i | 0.392419 | + | 0.392419i | ||||
\(527\) | 10.0000 | 0.435607 | ||||||||
\(528\) | − | 2.00000i | − | 0.0870388i | ||||||
\(529\) | 27.0000i | 1.17391i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.00000 | − | 3.00000i | 0.130189 | − | 0.130189i | ||||
\(532\) | −6.00000 | + | 6.00000i | −0.260133 | + | 0.260133i | ||||
\(533\) | 1.00000 | − | 5.00000i | 0.0433148 | − | 0.216574i | ||||
\(534\) | − | 14.0000i | − | 0.605839i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.0000 | −0.518321 | ||||||||
\(537\) | −20.0000 | + | 20.0000i | −0.863064 | + | 0.863064i | ||||
\(538\) | −16.0000 | −0.689809 | ||||||||
\(539\) | −3.00000 | + | 3.00000i | −0.129219 | + | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.00000 | + | 9.00000i | −0.386940 | + | 0.386940i | −0.873595 | − | 0.486654i | \(-0.838217\pi\) |
0.486654 | + | 0.873595i | \(0.338217\pi\) | |||||||
\(542\) | 9.00000 | + | 9.00000i | 0.386583 | + | 0.386583i | ||||
\(543\) | 20.0000 | + | 20.0000i | 0.858282 | + | 0.858282i | ||||
\(544\) | −5.00000 | − | 5.00000i | −0.214373 | − | 0.214373i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.00000 | + | 10.0000i | −0.0855921 | + | 0.427960i | ||||
\(547\) | 7.00000 | + | 7.00000i | 0.299298 | + | 0.299298i | 0.840739 | − | 0.541441i | \(-0.182121\pi\) |
−0.541441 | + | 0.840739i | \(0.682121\pi\) | |||||||
\(548\) | −12.0000 | −0.512615 | ||||||||
\(549\) | 2.00000i | 0.0853579i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0000 | + | 12.0000i | 0.511217 | + | 0.511217i | ||||
\(552\) | − | 10.0000i | − | 0.425628i | ||||||
\(553\) | 28.0000i | 1.19068i | ||||||||
\(554\) | 5.00000 | + | 5.00000i | 0.212430 | + | 0.212430i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 14.0000i | − | 0.593732i | ||||||
\(557\) | −8.00000 | −0.338971 | −0.169485 | − | 0.985533i | \(-0.554211\pi\) | ||||
−0.169485 | + | 0.985533i | \(0.554211\pi\) | |||||||
\(558\) | 1.00000 | + | 1.00000i | 0.0423334 | + | 0.0423334i | ||||
\(559\) | 5.00000 | − | 25.0000i | 0.211477 | − | 1.05739i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.0000 | − | 10.0000i | −0.422200 | − | 0.422200i | ||||
\(562\) | −21.0000 | − | 21.0000i | −0.885832 | − | 0.885832i | ||||
\(563\) | 5.00000 | + | 5.00000i | 0.210725 | + | 0.210725i | 0.804575 | − | 0.593851i | \(-0.202393\pi\) |
−0.593851 | + | 0.804575i | \(0.702393\pi\) | |||||||
\(564\) | −2.00000 | + | 2.00000i | −0.0842152 | + | 0.0842152i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.0000 | + | 15.0000i | −0.630497 | + | 0.630497i | ||||
\(567\) | 10.0000 | 0.419961 | ||||||||
\(568\) | −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 | \(0.0671001\pi\) | ||||
−0.977864 | + | 0.209243i | \(0.932900\pi\) | |||||||
\(572\) | 5.00000 | + | 1.00000i | 0.209061 | + | 0.0418121i | ||||
\(573\) | −8.00000 | + | 8.00000i | −0.334205 | + | 0.334205i | ||||
\(574\) | 2.00000 | − | 2.00000i | 0.0834784 | − | 0.0834784i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 22.0000i | 0.915872i | 0.888985 | + | 0.457936i | \(0.151411\pi\) | ||||
−0.888985 | + | 0.457936i | \(0.848589\pi\) | |||||||
\(578\) | −33.0000 | −1.37262 | ||||||||
\(579\) | 14.0000 | + | 14.0000i | 0.581820 | + | 0.581820i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | 0.497844 | ||||||||
\(582\) | 2.00000 | − | 2.00000i | 0.0829027 | − | 0.0829027i | ||||
\(583\) | − | 2.00000i | − | 0.0828315i | ||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.0000 | −1.07405 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | 3.00000 | − | 3.00000i | 0.123718 | − | 0.123718i | ||||
\(589\) | 6.00000 | 0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.0000 | − | 18.0000i | −0.740421 | − | 0.740421i | ||||
\(592\) | −8.00000 | −0.328798 | ||||||||
\(593\) | 14.0000i | 0.574911i | 0.957794 | + | 0.287456i | \(0.0928094\pi\) | ||||
−0.957794 | + | 0.287456i | \(0.907191\pi\) | |||||||
\(594\) | − | 8.00000i | − | 0.328244i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.0000 | + | 13.0000i | −0.532501 | + | 0.532501i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 25.0000 | + | 5.00000i | 1.02233 | + | 0.204465i | ||||
\(599\) | 14.0000i | 0.572024i | 0.958226 | + | 0.286012i | \(0.0923298\pi\) | ||||
−0.958226 | + | 0.286012i | \(0.907670\pi\) | |||||||
\(600\) | 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 | ||||
\(603\) | −12.0000 | −0.488678 | ||||||||
\(604\) | 9.00000 | − | 9.00000i | 0.366205 | − | 0.366205i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.00000 | − | 3.00000i | −0.121766 | − | 0.121766i | 0.643598 | − | 0.765364i | \(-0.277441\pi\) |
−0.765364 | + | 0.643598i | \(0.777441\pi\) | |||||||
\(608\) | −3.00000 | − | 3.00000i | −0.121666 | − | 0.121666i | ||||
\(609\) | 8.00000 | + | 8.00000i | 0.324176 | + | 0.324176i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.00000 | − | 6.00000i | −0.161823 | − | 0.242734i | ||||
\(612\) | −5.00000 | − | 5.00000i | −0.202113 | − | 0.202113i | ||||
\(613\) | −4.00000 | −0.161558 | −0.0807792 | − | 0.996732i | \(-0.525741\pi\) | ||||
−0.0807792 | + | 0.996732i | \(0.525741\pi\) | |||||||
\(614\) | − | 2.00000i | − | 0.0807134i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | + | 2.00000i | 0.0805823 | + | 0.0805823i | ||||
\(617\) | − | 38.0000i | − | 1.52982i | −0.644136 | − | 0.764911i | \(-0.722783\pi\) | ||
0.644136 | − | 0.764911i | \(-0.277217\pi\) | |||||||
\(618\) | 10.0000i | 0.402259i | ||||||||
\(619\) | −3.00000 | − | 3.00000i | −0.120580 | − | 0.120580i | 0.644242 | − | 0.764822i | \(-0.277173\pi\) |
−0.764822 | + | 0.644242i | \(0.777173\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 40.0000i | − | 1.60514i | ||||||
\(622\) | 10.0000 | 0.400963 | ||||||||
\(623\) | 14.0000 | + | 14.0000i | 0.560898 | + | 0.560898i | ||||
\(624\) | −5.00000 | − | 1.00000i | −0.200160 | − | 0.0400320i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.00000 | + | 9.00000i | 0.359712 | + | 0.359712i | ||||
\(627\) | −6.00000 | − | 6.00000i | −0.239617 | − | 0.239617i | ||||
\(628\) | 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 | −0.453403 | − | 0.891306i | \(-0.649790\pi\) |
0.891306 | + | 0.453403i | \(0.149790\pi\) | |||||||
\(632\) | −14.0000 | −0.556890 | ||||||||
\(633\) | 12.0000 | − | 12.0000i | 0.476957 | − | 0.476957i | ||||
\(634\) | 2.00000 | 0.0794301 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.00000i | 0.0793052i | ||||||||
\(637\) | 6.00000 | + | 9.00000i | 0.237729 | + | 0.356593i | ||||
\(638\) | 4.00000 | − | 4.00000i | 0.158362 | − | 0.158362i | ||||
\(639\) | −1.00000 | + | 1.00000i | −0.0395594 | + | 0.0395594i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 26.0000i | 1.02614i | ||||||||
\(643\) | 46.0000 | 1.81406 | 0.907031 | − | 0.421063i | \(-0.138343\pi\) | ||||
0.907031 | + | 0.421063i | \(0.138343\pi\) | |||||||
\(644\) | 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 | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.798528 | + | 0.601958i | \(0.205612\pi\) | |||||||
\(648\) | 5.00000i | 0.196419i | ||||||||
\(649\) | −6.00000 | −0.235521 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | 0.156772 | ||||||||
\(652\) | − | 4.00000i | − | 0.156652i | ||||||
\(653\) | 21.0000 | − | 21.0000i | 0.821794 | − | 0.821794i | −0.164572 | − | 0.986365i | \(-0.552624\pi\) |
0.986365 | + | 0.164572i | \(0.0526242\pi\) | |||||||
\(654\) | −26.0000 | −1.01668 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.00000 | + | 1.00000i | 0.0390434 | + | 0.0390434i | ||||
\(657\) | 6.00000 | 0.234082 | ||||||||
\(658\) | − | 4.00000i | − | 0.155936i | ||||||
\(659\) | 14.0000i | 0.545363i | 0.962104 | + | 0.272681i | \(0.0879105\pi\) | ||||
−0.962104 | + | 0.272681i | \(0.912090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.0000 | − | 31.0000i | 1.20576 | − | 1.20576i | 0.233373 | − | 0.972387i | \(-0.425024\pi\) |
0.972387 | − | 0.233373i | \(-0.0749763\pi\) | |||||||
\(662\) | −9.00000 | + | 9.00000i | −0.349795 | + | 0.349795i | ||||
\(663\) | −30.0000 | + | 20.0000i | −1.16510 | + | 0.776736i | ||||
\(664\) | 6.00000i | 0.232845i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.00000 | −0.309994 | ||||||||
\(667\) | 20.0000 | − | 20.0000i | 0.774403 | − | 0.774403i | ||||
\(668\) | −2.00000 | −0.0773823 | ||||||||
\(669\) | 6.00000 | − | 6.00000i | 0.231973 | − | 0.231973i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.00000 | − | 2.00000i | 0.0772091 | − | 0.0772091i | ||||
\(672\) | −2.00000 | − | 2.00000i | −0.0771517 | − | 0.0771517i | ||||
\(673\) | 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 | \(0.964924\pi\) | |||||||
\(678\) | 18.0000 | 0.691286 | ||||||||
\(679\) | 4.00000i | 0.153506i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000 | + | 12.0000i | 0.459841 | + | 0.459841i | ||||
\(682\) | − | 2.00000i | − | 0.0765840i | ||||||
\(683\) | − | 36.0000i | − | 1.37750i | −0.724998 | − | 0.688751i | \(-0.758159\pi\) | ||
0.724998 | − | 0.688751i | \(-0.241841\pi\) | |||||||
\(684\) | −3.00000 | − | 3.00000i | −0.114708 | − | 0.114708i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.0000i | 0.763604i | ||||||||
\(687\) | −6.00000 | −0.228914 | ||||||||
\(688\) | 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 | 0.514884 | − | 0.857260i | \(-0.327835\pi\) |
−0.857260 | + | 0.514884i | \(0.827835\pi\) | |||||||
\(692\) | −15.0000 | − | 15.0000i | −0.570214 | − | 0.570214i | ||||
\(693\) | 2.00000 | + | 2.00000i | 0.0759737 | + | 0.0759737i | ||||
\(694\) | 7.00000 | − | 7.00000i | 0.265716 | − | 0.265716i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.00000 | + | 4.00000i | −0.151620 | + | 0.151620i | ||||
\(697\) | 10.0000 | 0.378777 | ||||||||
\(698\) | −3.00000 | + | 3.00000i | −0.113552 | + | 0.113552i | ||||
\(699\) | 10.0000 | 0.378235 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | −20.0000 | − | 4.00000i | −0.754851 | − | 0.150970i | ||||
\(703\) | −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 | ||||||||
\(708\) | 6.00000 | 0.225494 | ||||||||
\(709\) | −3.00000 | − | 3.00000i | −0.112667 | − | 0.112667i | 0.648526 | − | 0.761193i | \(-0.275386\pi\) |
−0.761193 | + | 0.648526i | \(0.775386\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.0000 | −0.525041 | ||||||||
\(712\) | −7.00000 | + | 7.00000i | −0.262336 | + | 0.262336i | ||||
\(713\) | − | 10.0000i | − | 0.374503i | ||||||
\(714\) | −20.0000 | −0.748481 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 20.0000 | 0.747435 | ||||||||
\(717\) | 14.0000i | 0.522840i | ||||||||
\(718\) | −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 | ||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | − | 2.00000i | − | 0.0743808i | ||||||
\(724\) | − | 20.0000i | − | 0.743294i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.00000 | − | 9.00000i | 0.334021 | − | 0.334021i | ||||
\(727\) | −35.0000 | + | 35.0000i | −1.29808 | + | 1.29808i | −0.368418 | + | 0.929660i | \(0.620100\pi\) |
−0.929660 | + | 0.368418i | \(0.879900\pi\) | |||||||
\(728\) | 6.00000 | − | 4.00000i | 0.222375 | − | 0.148250i | ||||
\(729\) | 29.0000i | 1.07407i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.0000 | 1.84932 | ||||||||
\(732\) | −2.00000 | + | 2.00000i | −0.0739221 | + | 0.0739221i | ||||
\(733\) | −44.0000 | −1.62518 | −0.812589 | − | 0.582838i | \(-0.801942\pi\) | ||||
−0.812589 | + | 0.582838i | \(0.801942\pi\) | |||||||
\(734\) | −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 | ||||
\(738\) | 1.00000 | + | 1.00000i | 0.0368105 | + | 0.0368105i | ||||
\(739\) | 37.0000 | + | 37.0000i | 1.36107 | + | 1.36107i | 0.872560 | + | 0.488507i | \(0.162458\pi\) |
0.488507 | + | 0.872560i | \(0.337542\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.0000 | + | 12.0000i | −0.661247 | + | 0.440831i | ||||
\(742\) | −2.00000 | − | 2.00000i | −0.0734223 | − | 0.0734223i | ||||
\(743\) | 6.00000 | 0.220119 | 0.110059 | − | 0.993925i | \(-0.464896\pi\) | ||||
0.110059 | + | 0.993925i | \(0.464896\pi\) | |||||||
\(744\) | 2.00000i | 0.0733236i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.00000 | − | 1.00000i | −0.0366126 | − | 0.0366126i | ||||
\(747\) | 6.00000i | 0.219529i | ||||||||
\(748\) | 10.0000i | 0.365636i | ||||||||
\(749\) | −26.0000 | − | 26.0000i | −0.950019 | − | 0.950019i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0000i | 0.364905i | 0.983215 | + | 0.182453i | \(0.0584036\pi\) | ||||
−0.983215 | + | 0.182453i | \(0.941596\pi\) | |||||||
\(752\) | 2.00000 | 0.0729325 | ||||||||
\(753\) | −30.0000 | − | 30.0000i | −1.09326 | − | 1.09326i | ||||
\(754\) | −8.00000 | − | 12.0000i | −0.291343 | − | 0.437014i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.00000 | − | 8.00000i | −0.290957 | − | 0.290957i | ||||
\(757\) | 17.0000 | + | 17.0000i | 0.617876 | + | 0.617876i | 0.944986 | − | 0.327111i | \(-0.106075\pi\) |
−0.327111 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(758\) | 17.0000 | + | 17.0000i | 0.617468 | + | 0.617468i | ||||
\(759\) | −10.0000 | + | 10.0000i | −0.362977 | + | 0.362977i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.0000 | + | 19.0000i | −0.688749 | + | 0.688749i | −0.961956 | − | 0.273206i | \(-0.911916\pi\) |
0.273206 | + | 0.961956i | \(0.411916\pi\) | |||||||
\(762\) | 30.0000 | 1.08679 | ||||||||
\(763\) | 26.0000 | − | 26.0000i | 0.941263 | − | 0.941263i | ||||
\(764\) | 8.00000 | 0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 6.00000i | − | 0.216789i | ||||||
\(767\) | −3.00000 | + | 15.0000i | −0.108324 | + | 0.541619i | ||||
\(768\) | 1.00000 | − | 1.00000i | 0.0360844 | − | 0.0360844i | ||||
\(769\) | 23.0000 | − | 23.0000i | 0.829401 | − | 0.829401i | −0.158033 | − | 0.987434i | \(-0.550515\pi\) |
0.987434 | + | 0.158033i | \(0.0505151\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.0000i | 1.08042i | ||||||||
\(772\) | − | 14.0000i | − | 0.503871i | ||||||
\(773\) | −24.0000 | −0.863220 | −0.431610 | − | 0.902060i | \(-0.642054\pi\) | ||||
−0.431610 | + | 0.902060i | \(0.642054\pi\) | |||||||
\(774\) | 5.00000 | + | 5.00000i | 0.179721 | + | 0.179721i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.00000 | −0.0717958 | ||||||||
\(777\) | −16.0000 | + | 16.0000i | −0.573997 | + | 0.573997i | ||||
\(778\) | − | 10.0000i | − | 0.358517i | ||||||
\(779\) | 6.00000 | 0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | 0.0715656 | ||||||||
\(782\) | 50.0000i | 1.78800i | ||||||||
\(783\) | −16.0000 | + | 16.0000i | −0.571793 | + | 0.571793i | ||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −12.0000 | − | 12.0000i | −0.428026 | − | 0.428026i | ||||
\(787\) | 42.0000 | 1.49714 | 0.748569 | − | 0.663057i | \(-0.230741\pi\) | ||||
0.748569 | + | 0.663057i | \(0.230741\pi\) | |||||||
\(788\) | 18.0000i | 0.641223i | ||||||||
\(789\) | 18.0000i | 0.640817i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.0000 | + | 18.0000i | −0.640006 | + | 0.640006i | ||||
\(792\) | −1.00000 | + | 1.00000i | −0.0355335 | + | 0.0355335i | ||||
\(793\) | −4.00000 | − | 6.00000i | −0.142044 | − | 0.213066i | ||||
\(794\) | 8.00000i | 0.283909i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.00000 | + | 5.00000i | −0.177109 | + | 0.177109i | −0.790094 | − | 0.612985i | \(-0.789968\pi\) |
0.612985 | + | 0.790094i | \(0.289968\pi\) | |||||||
\(798\) | −12.0000 | −0.424795 | ||||||||
\(799\) | 10.0000 | − | 10.0000i | 0.353775 | − | 0.353775i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.00000 | + | 7.00000i | −0.247333 | + | 0.247333i | ||||
\(802\) | −1.00000 | − | 1.00000i | −0.0353112 | − | 0.0353112i | ||||
\(803\) | −6.00000 | − | 6.00000i | −0.211735 | − | 0.211735i | ||||
\(804\) | −12.0000 | − | 12.0000i | −0.423207 | − | 0.423207i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.00000 | − | 1.00000i | −0.176117 | − | 0.0352235i | ||||
\(807\) | −16.0000 | − | 16.0000i | −0.563227 | − | 0.563227i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 36.0000i | − | 1.26569i | −0.774277 | − | 0.632846i | \(-0.781886\pi\) | ||
0.774277 | − | 0.632846i | \(-0.218114\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0000 | + | 11.0000i | 0.386262 | + | 0.386262i | 0.873352 | − | 0.487090i | \(-0.161942\pi\) |
−0.487090 | + | 0.873352i | \(0.661942\pi\) | |||||||
\(812\) | − | 8.00000i | − | 0.280745i | ||||||
\(813\) | 18.0000i | 0.631288i | ||||||||
\(814\) | 8.00000 | + | 8.00000i | 0.280400 | + | 0.280400i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 10.0000i | − | 0.350070i | ||||||
\(817\) | 30.0000 | 1.04957 | ||||||||
\(818\) | −3.00000 | − | 3.00000i | −0.104893 | − | 0.104893i | ||||
\(819\) | 6.00000 | − | 4.00000i | 0.209657 | − | 0.139771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.0000 | − | 29.0000i | −1.01211 | − | 1.01211i | −0.999926 | − | 0.0121812i | \(-0.996123\pi\) |
−0.0121812 | − | 0.999926i | \(-0.503877\pi\) | |||||||
\(822\) | −12.0000 | − | 12.0000i | −0.418548 | − | 0.418548i | ||||
\(823\) | 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 | ||||
\(827\) | 2.00000 | 0.0695468 | 0.0347734 | − | 0.999395i | \(-0.488929\pi\) | ||||
0.0347734 | + | 0.999395i | \(0.488929\pi\) | |||||||
\(828\) | −5.00000 | + | 5.00000i | −0.173762 | + | 0.173762i | ||||
\(829\) | 30.0000 | 1.04194 | 0.520972 | − | 0.853574i | \(-0.325570\pi\) | ||||
0.520972 | + | 0.853574i | \(0.325570\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.0000i | 0.346896i | ||||||||
\(832\) | 2.00000 | + | 3.00000i | 0.0693375 | + | 0.104006i | ||||
\(833\) | −15.0000 | + | 15.0000i | −0.519719 | + | 0.519719i | ||||
\(834\) | 14.0000 | − | 14.0000i | 0.484780 | − | 0.484780i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.00000i | 0.207514i | ||||||||
\(837\) | 8.00000i | 0.276520i | ||||||||
\(838\) | −26.0000 | −0.898155 | ||||||||
\(839\) | −13.0000 | − | 13.0000i | −0.448810 | − | 0.448810i | 0.446149 | − | 0.894959i | \(-0.352795\pi\) |
−0.894959 | + | 0.446149i | \(0.852795\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0000 | 0.448276 | ||||||||
\(842\) | −9.00000 | + | 9.00000i | −0.310160 | + | 0.310160i | ||||
\(843\) | − | 42.0000i | − | 1.44656i | ||||||
\(844\) | −12.0000 | −0.413057 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.00000 | 0.0687614 | ||||||||
\(847\) | 18.0000i | 0.618487i | ||||||||
\(848\) | 1.00000 | − | 1.00000i | 0.0343401 | − | 0.0343401i | ||||
\(849\) | −30.0000 | −1.02960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.0000 | + | 40.0000i | 1.37118 | + | 1.37118i | ||||
\(852\) | −2.00000 | −0.0685189 | ||||||||
\(853\) | − | 26.0000i | − | 0.890223i | −0.895475 | − | 0.445112i | \(-0.853164\pi\) | ||
0.895475 | − | 0.445112i | \(-0.146836\pi\) | |||||||
\(854\) | − | 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 | −0.616533 | − | 0.787329i | \(-0.711463\pi\) |
0.787329 | + | 0.616533i | \(0.211463\pi\) | |||||||
\(858\) | 4.00000 | + | 6.00000i | 0.136558 | + | 0.204837i | ||||
\(859\) | − | 26.0000i | − | 0.887109i | −0.896248 | − | 0.443554i | \(-0.853717\pi\) | ||
0.896248 | − | 0.443554i | \(-0.146283\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.00000 | 0.136320 | ||||||||
\(862\) | 21.0000 | − | 21.0000i | 0.715263 | − | 0.715263i | ||||
\(863\) | 46.0000 | 1.56586 | 0.782929 | − | 0.622111i | \(-0.213725\pi\) | ||||
0.782929 | + | 0.622111i | \(0.213725\pi\) | |||||||
\(864\) | 4.00000 | − | 4.00000i | 0.136083 | − | 0.136083i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −15.0000 | + | 15.0000i | −0.509721 | + | 0.509721i | ||||
\(867\) | −33.0000 | − | 33.0000i | −1.12074 | − | 1.12074i | ||||
\(868\) | −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 | ||||
\(873\) | −2.00000 | −0.0676897 | ||||||||
\(874\) | 30.0000i | 1.01477i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.00000 | + | 6.00000i | 0.202721 | + | 0.202721i | ||||
\(877\) | − | 18.0000i | − | 0.607817i | −0.952701 | − | 0.303908i | \(-0.901708\pi\) | ||
0.952701 | − | 0.303908i | \(-0.0982917\pi\) | |||||||
\(878\) | 40.0000i | 1.34993i | ||||||||
\(879\) | −26.0000 | − | 26.0000i | −0.876958 | − | 0.876958i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20.0000i | − | 0.673817i | −0.941537 | − | 0.336909i | \(-0.890619\pi\) | ||
0.941537 | − | 0.336909i | \(-0.109381\pi\) | |||||||
\(882\) | −3.00000 | −0.101015 | ||||||||
\(883\) | 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 | \(0.933878\pi\) | |||||||
\(888\) | −8.00000 | − | 8.00000i | −0.268462 | − | 0.268462i | ||||
\(889\) | −30.0000 | + | 30.0000i | −1.00617 | + | 1.00617i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.00000 | − | 5.00000i | 0.167506 | − | 0.167506i | ||||
\(892\) | −6.00000 | −0.200895 | ||||||||
\(893\) | 6.00000 | − | 6.00000i | 0.200782 | − | 0.200782i | ||||
\(894\) | −26.0000 | −0.869570 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000i | 0.0668153i | ||||||||
\(897\) | 20.0000 | + | 30.0000i | 0.667781 | + | 1.00167i | ||||
\(898\) | 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 | ||||||
\(902\) | − | 2.00000i | − | 0.0665927i | ||||||
\(903\) | 20.0000 | 0.665558 | ||||||||
\(904\) | −9.00000 | − | 9.00000i | −0.299336 | − | 0.299336i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 18.0000 | 0.598010 | ||||||||
\(907\) | 35.0000 | − | 35.0000i | 1.16216 | − | 1.16216i | 0.178153 | − | 0.984003i | \(-0.442988\pi\) |
0.984003 | − | 0.178153i | \(-0.0570122\pi\) | |||||||
\(908\) | − | 12.0000i | − | 0.398234i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | − | 6.00000i | − | 0.198680i | ||||||
\(913\) | 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 | ||||
\(917\) | 24.0000 | 0.792550 | ||||||||
\(918\) | − | 40.0000i | − | 1.32020i | ||||||
\(919\) | 14.0000i | 0.461817i | 0.972975 | + | 0.230909i | \(0.0741699\pi\) | ||||
−0.972975 | + | 0.230909i | \(0.925830\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.00000 | − | 2.00000i | 0.0659022 | − | 0.0659022i | ||||
\(922\) | 11.0000 | − | 11.0000i | 0.362266 | − | 0.362266i | ||||
\(923\) | 1.00000 | − | 5.00000i | 0.0329154 | − | 0.164577i | ||||
\(924\) | 4.00000i | 0.131590i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.0000 | −0.525793 | ||||||||
\(927\) | 5.00000 | − | 5.00000i | 0.164222 | − | 0.164222i | ||||
\(928\) | 4.00000 | 0.131306 | ||||||||
\(929\) | −17.0000 | + | 17.0000i | −0.557752 | + | 0.557752i | −0.928667 | − | 0.370915i | \(-0.879044\pi\) |
0.370915 | + | 0.928667i | \(0.379044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.00000 | + | 9.00000i | −0.294963 | + | 0.294963i | ||||
\(932\) | −5.00000 | − | 5.00000i | −0.163780 | − | 0.163780i | ||||
\(933\) | 10.0000 | + | 10.0000i | 0.327385 | + | 0.327385i | ||||
\(934\) | 5.00000 | + | 5.00000i | 0.163605 | + | 0.163605i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | + | 3.00000i | 0.0653720 | + | 0.0980581i | ||||
\(937\) | −33.0000 | − | 33.0000i | −1.07806 | − | 1.07806i | −0.996683 | − | 0.0813798i | \(-0.974067\pi\) |
−0.0813798 | − | 0.996683i | \(-0.525933\pi\) | |||||||
\(938\) | 24.0000 | 0.783628 | ||||||||
\(939\) | 18.0000i | 0.587408i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.0000 | − | 29.0000i | −0.945373 | − | 0.945373i | 0.0532103 | − | 0.998583i | \(-0.483055\pi\) |
−0.998583 | + | 0.0532103i | \(0.983055\pi\) | |||||||
\(942\) | 6.00000i | 0.195491i | ||||||||
\(943\) | − | 10.0000i | − | 0.325645i | ||||||
\(944\) | −3.00000 | − | 3.00000i | −0.0976417 | − | 0.0976417i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 10.0000i | − | 0.325128i | ||||||
\(947\) | −38.0000 | −1.23483 | −0.617417 | − | 0.786636i | \(-0.711821\pi\) | ||||
−0.617417 | + | 0.786636i | \(0.711821\pi\) | |||||||
\(948\) | −14.0000 | − | 14.0000i | −0.454699 | − | 0.454699i | ||||
\(949\) | −18.0000 | + | 12.0000i | −0.584305 | + | 0.389536i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.00000 | + | 2.00000i | 0.0648544 | + | 0.0648544i | ||||
\(952\) | 10.0000 | + | 10.0000i | 0.324102 | + | 0.324102i | ||||
\(953\) | −35.0000 | − | 35.0000i | −1.13376 | − | 1.13376i | −0.989546 | − | 0.144215i | \(-0.953934\pi\) |
−0.144215 | − | 0.989546i | \(-0.546066\pi\) | |||||||
\(954\) | 1.00000 | − | 1.00000i | 0.0323762 | − | 0.0323762i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.00000 | − | 7.00000i | 0.226396 | − | 0.226396i | ||||
\(957\) | 8.00000 | 0.258603 | ||||||||
\(958\) | −13.0000 | + | 13.0000i | −0.420011 | + | 0.420011i | ||||
\(959\) | 24.0000 | 0.775000 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 29.0000i | − | 0.935484i | ||||||
\(962\) | 24.0000 | − | 16.0000i | 0.773791 | − | 0.515861i | ||||
\(963\) | 13.0000 | − | 13.0000i | 0.418919 | − | 0.418919i | ||||
\(964\) | −1.00000 | + | 1.00000i | −0.0322078 | + | 0.0322078i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 20.0000i | 0.643489i | ||||||||
\(967\) | − | 48.0000i | − | 1.54358i | −0.635880 | − | 0.771788i | \(-0.719363\pi\) | ||
0.635880 | − | 0.771788i | \(-0.280637\pi\) | |||||||
\(968\) | −9.00000 | −0.289271 | ||||||||
\(969\) | −30.0000 | − | 30.0000i | −0.963739 | − | 0.963739i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | 0.385098 | 0.192549 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192549 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(972\) | 7.00000 | − | 7.00000i | 0.224525 | − | 0.224525i | ||||
\(973\) | 28.0000i | 0.897639i | ||||||||
\(974\) | 32.0000 | 1.02535 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 22.0000i | 0.703842i | 0.936030 | + | 0.351921i | \(0.114471\pi\) | ||||
−0.936030 | + | 0.351921i | \(0.885529\pi\) | |||||||
\(978\) | 4.00000 | − | 4.00000i | 0.127906 | − | 0.127906i | ||||
\(979\) | 14.0000 | 0.447442 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.0000 | + | 13.0000i | 0.415058 | + | 0.415058i | ||||
\(982\) | 10.0000 | 0.319113 | ||||||||
\(983\) | 24.0000i | 0.765481i | 0.923856 | + | 0.382741i | \(0.125020\pi\) | ||||
−0.923856 | + | 0.382741i | \(0.874980\pi\) | |||||||
\(984\) | 2.00000i | 0.0637577i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 20.0000 | − | 20.0000i | 0.636930 | − | 0.636930i | ||||
\(987\) | 4.00000 | − | 4.00000i | 0.127321 | − | 0.127321i | ||||
\(988\) | 15.0000 | + | 3.00000i | 0.477214 | + | 0.0954427i | ||||
\(989\) | − | 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 | ||||
\(993\) | −18.0000 | −0.571213 | ||||||||
\(994\) | 2.00000 | − | 2.00000i | 0.0634361 | − | 0.0634361i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.00000 | + | 6.00000i | −0.190117 | + | 0.190117i | ||||
\(997\) | 17.0000 | + | 17.0000i | 0.538395 | + | 0.538395i | 0.923057 | − | 0.384662i | \(-0.125682\pi\) |
−0.384662 | + | 0.923057i | \(0.625682\pi\) | |||||||
\(998\) | −23.0000 | − | 23.0000i | −0.728052 | − | 0.728052i | ||||
\(999\) | −32.0000 | − | 32.0000i | −1.01244 | − | 1.01244i |
(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 | 650.2.j.d.307.1 | 2 | ||
5.2 | odd | 4 | 130.2.g.c.73.1 | yes | 2 | ||
5.3 | odd | 4 | 650.2.g.b.593.1 | 2 | |||
5.4 | even | 2 | 130.2.j.b.47.1 | yes | 2 | ||
13.5 | odd | 4 | 650.2.g.b.57.1 | 2 | |||
15.2 | even | 4 | 1170.2.m.a.73.1 | 2 | |||
15.14 | odd | 2 | 1170.2.w.c.307.1 | 2 | |||
20.7 | even | 4 | 1040.2.bg.f.593.1 | 2 | |||
20.19 | odd | 2 | 1040.2.cd.e.177.1 | 2 | |||
65.18 | even | 4 | inner | 650.2.j.d.343.1 | 2 | ||
65.44 | odd | 4 | 130.2.g.c.57.1 | ✓ | 2 | ||
65.57 | even | 4 | 130.2.j.b.83.1 | yes | 2 | ||
195.44 | even | 4 | 1170.2.m.a.577.1 | 2 | |||
195.122 | odd | 4 | 1170.2.w.c.343.1 | 2 | |||
260.187 | odd | 4 | 1040.2.cd.e.993.1 | 2 | |||
260.239 | even | 4 | 1040.2.bg.f.577.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.g.c.57.1 | ✓ | 2 | 65.44 | odd | 4 | ||
130.2.g.c.73.1 | yes | 2 | 5.2 | odd | 4 | ||
130.2.j.b.47.1 | yes | 2 | 5.4 | even | 2 | ||
130.2.j.b.83.1 | yes | 2 | 65.57 | even | 4 | ||
650.2.g.b.57.1 | 2 | 13.5 | odd | 4 | |||
650.2.g.b.593.1 | 2 | 5.3 | odd | 4 | |||
650.2.j.d.307.1 | 2 | 1.1 | even | 1 | trivial | ||
650.2.j.d.343.1 | 2 | 65.18 | even | 4 | inner | ||
1040.2.bg.f.577.1 | 2 | 260.239 | even | 4 | |||
1040.2.bg.f.593.1 | 2 | 20.7 | even | 4 | |||
1040.2.cd.e.177.1 | 2 | 20.19 | odd | 2 | |||
1040.2.cd.e.993.1 | 2 | 260.187 | odd | 4 | |||
1170.2.m.a.73.1 | 2 | 15.2 | even | 4 | |||
1170.2.m.a.577.1 | 2 | 195.44 | even | 4 | |||
1170.2.w.c.307.1 | 2 | 15.14 | odd | 2 | |||
1170.2.w.c.343.1 | 2 | 195.122 | odd | 4 |