Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.11574317056.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 45x^{4} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.8 | ||
Root | \(0.386289 - 0.386289i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.e.369.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.25886i | 1.88150i | 0.339095 | + | 0.940752i | \(0.389879\pi\) | ||||
−0.339095 | + | 0.940752i | \(0.610121\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.386289 | − | 2.20245i | 0.172754 | − | 0.984965i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.44270i | − | 0.545290i | −0.962115 | − | 0.272645i | \(-0.912102\pi\) | ||
0.962115 | − | 0.272645i | \(-0.0878984\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.62018 | −2.54006 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.03144 | 0.612502 | 0.306251 | − | 0.951951i | \(-0.400925\pi\) | ||||
0.306251 | + | 0.951951i | \(0.400925\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.557299i | − | 0.154567i | −0.997009 | − | 0.0772835i | \(-0.975375\pi\) | ||
0.997009 | − | 0.0772835i | \(-0.0246246\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.17748 | + | 1.25886i | 1.85322 | + | 0.325037i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.91861i | − | 0.950403i | −0.879877 | − | 0.475202i | \(-0.842375\pi\) | ||
0.879877 | − | 0.475202i | \(-0.157625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.73300 | −1.54466 | −0.772328 | − | 0.635224i | \(-0.780908\pi\) | ||||
−0.772328 | + | 0.635224i | \(0.780908\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.70156 | 1.02596 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.70156 | − | 1.70156i | −0.940312 | − | 0.340312i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 15.0565i | − | 2.89763i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.69520 | 1.80035 | 0.900176 | − | 0.435525i | \(-0.143437\pi\) | ||||
0.900176 | + | 0.435525i | \(0.143437\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.07502 | 0.552290 | 0.276145 | − | 0.961116i | \(-0.410943\pi\) | ||||
0.276145 | + | 0.961116i | \(0.410943\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.62018i | 1.15242i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.17748 | − | 0.557299i | −0.537091 | − | 0.0942007i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.65798i | − | 0.601368i | −0.953724 | − | 0.300684i | \(-0.902785\pi\) | ||
0.953724 | − | 0.300684i | \(-0.0972150\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.81616 | 0.290818 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.03321 | 1.09840 | 0.549202 | − | 0.835690i | \(-0.314932\pi\) | ||||
0.549202 | + | 0.835690i | \(0.314932\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.06465i | − | 0.772352i | −0.922425 | − | 0.386176i | \(-0.873796\pi\) | ||
0.922425 | − | 0.386176i | \(-0.126204\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.94359 | + | 16.7830i | −0.438804 | + | 2.50187i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.659753i | − | 0.0962348i | −0.998842 | − | 0.0481174i | \(-0.984678\pi\) | ||
0.998842 | − | 0.0481174i | \(-0.0153222\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.91861 | 0.702659 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.7702 | 1.78819 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.1275i | − | 1.52848i | −0.644930 | − | 0.764242i | \(-0.723113\pi\) | ||
0.644930 | − | 0.764242i | \(-0.276887\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.784722 | − | 4.47414i | 0.105812 | − | 0.603293i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 21.9419i | − | 2.90628i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.7226 | 1.39597 | 0.697984 | − | 0.716114i | \(-0.254081\pi\) | ||||
0.697984 | + | 0.716114i | \(0.254081\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.73937 | 0.222703 | 0.111351 | − | 0.993781i | \(-0.464482\pi\) | ||||
0.111351 | + | 0.993781i | \(0.464482\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.9936i | 1.38507i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.22742 | − | 0.215278i | −0.152243 | − | 0.0267020i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.0129i | − | 1.46761i | −0.679359 | − | 0.733806i | \(-0.737742\pi\) | ||
0.679359 | − | 0.733806i | \(-0.262258\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.25886 | −0.392321 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4363 | −1.47592 | −0.737961 | − | 0.674844i | \(-0.764211\pi\) | ||||
−0.737961 | + | 0.674844i | \(0.764211\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.26464i | 1.08434i | 0.840267 | + | 0.542172i | \(0.182398\pi\) | ||||
−0.840267 | + | 0.542172i | \(0.817602\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.54515 | − | 15.3217i | 0.640299 | − | 1.76920i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.93076i | − | 0.333991i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.92439 | 0.666546 | 0.333273 | − | 0.942830i | \(-0.391847\pi\) | ||||
0.333273 | + | 0.942830i | \(0.391847\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 26.2066 | 2.91184 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 11.3775i | − | 1.24884i | −0.781089 | − | 0.624420i | \(-0.785336\pi\) | ||
0.781089 | − | 0.624420i | \(-0.214664\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.63055 | − | 1.51372i | −0.936114 | − | 0.164186i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 31.5953i | 3.38737i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.25308 | −0.556826 | −0.278413 | − | 0.960462i | \(-0.589808\pi\) | ||||
−0.278413 | + | 0.960462i | \(0.589808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.804016 | −0.0842838 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.0211i | 1.03914i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.60088 | + | 14.8291i | −0.266845 | + | 1.52143i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 0.0813861i | − | 0.00826350i | −0.999991 | − | 0.00413175i | \(-0.998685\pi\) | ||
0.999991 | − | 0.00413175i | \(-0.00131518\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15.4799 | −1.55579 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.31281 | 0.827156 | 0.413578 | − | 0.910469i | \(-0.364279\pi\) | ||||
0.413578 | + | 0.910469i | \(0.364279\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6.36991i | − | 0.627646i | −0.949481 | − | 0.313823i | \(-0.898390\pi\) | ||
0.949481 | − | 0.313823i | \(-0.101610\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.81616 | − | 10.3550i | 0.177239 | − | 1.01054i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.9226i | 1.63597i | 0.575239 | + | 0.817986i | \(0.304909\pi\) | ||||
−0.575239 | + | 0.817986i | \(0.695091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.218825 | 0.0209597 | 0.0104798 | − | 0.999945i | \(-0.496664\pi\) | ||||
0.0104798 | + | 0.999945i | \(0.496664\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.9208 | 1.13148 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 0.580599i | − | 0.0546182i | −0.999627 | − | 0.0273091i | \(-0.991306\pi\) | ||
0.999627 | − | 0.0273091i | \(-0.00869384\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.20245 | + | 0.386289i | 0.205379 | + | 0.0360216i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.24672i | 0.392609i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.65339 | −0.518245 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.87326 | −0.624842 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 22.9203i | 2.06665i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.56376 | + | 9.69766i | −0.497638 | + | 0.867385i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.56944i | − | 0.139266i | −0.997573 | − | 0.0696328i | \(-0.977817\pi\) | ||
0.997573 | − | 0.0696328i | \(-0.0221828\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.5050 | 1.45318 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.9208 | −1.39101 | −0.695505 | − | 0.718521i | \(-0.744819\pi\) | ||||
−0.695505 | + | 0.718521i | \(0.744819\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.71371i | 0.842285i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −33.1612 | − | 5.81616i | −2.85406 | − | 0.500575i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.47013i | − | 0.552781i | −0.961045 | − | 0.276390i | \(-0.910862\pi\) | ||
0.961045 | − | 0.276390i | \(-0.0891383\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.656206 | −0.0556586 | −0.0278293 | − | 0.999613i | \(-0.508859\pi\) | ||||
−0.0278293 | + | 0.999613i | \(0.508859\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.15004 | 0.181066 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.13212i | − | 0.0946725i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.74514 | − | 21.3532i | 0.311017 | − | 1.77328i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.0291i | 1.32206i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −23.8349 | −1.95263 | −0.976314 | − | 0.216357i | \(-0.930582\pi\) | ||||
−0.976314 | + | 0.216357i | \(0.930582\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.8669 | 1.20985 | 0.604925 | − | 0.796282i | \(-0.293203\pi\) | ||||
0.604925 | + | 0.796282i | \(0.293203\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.8605i | 2.41408i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.18785 | − | 6.77258i | 0.0954101 | − | 0.543987i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.24213i | 0.657793i | 0.944366 | + | 0.328897i | \(0.106677\pi\) | ||||
−0.944366 | + | 0.328897i | \(0.893323\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 36.2631 | 2.87585 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.44270 | 0.113701 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 10.3154i | − | 0.807962i | −0.914767 | − | 0.403981i | \(-0.867626\pi\) | ||
0.914767 | − | 0.403981i | \(-0.132374\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.5806 | + | 2.55730i | 1.13510 | + | 0.199085i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.65975i | 0.360582i | 0.983613 | + | 0.180291i | \(0.0577040\pi\) | ||||
−0.983613 | + | 0.180291i | \(0.942296\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6894 | 0.976109 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 51.3067 | 3.92352 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2.80402i | − | 0.213185i | −0.994303 | − | 0.106593i | \(-0.966006\pi\) | ||
0.994303 | − | 0.106593i | \(-0.0339941\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.45485 | + | 6.78295i | −0.185569 | + | 0.512743i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 34.9436i | 2.62652i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.44212 | −0.332019 | −0.166010 | − | 0.986124i | \(-0.553088\pi\) | ||||
−0.166010 | + | 0.986124i | \(0.553088\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.42019 | 0.179891 | 0.0899455 | − | 0.995947i | \(-0.471331\pi\) | ||||
0.0899455 | + | 0.995947i | \(0.471331\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.66835i | 0.419016i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.05651 | − | 1.41304i | −0.592327 | − | 0.103888i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7.96042i | − | 0.582124i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21.7220 | −1.58005 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.8934 | 1.51179 | 0.755897 | − | 0.654690i | \(-0.227201\pi\) | ||||
0.755897 | + | 0.654690i | \(0.227201\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.88540i | 0.207696i | 0.994593 | + | 0.103848i | \(0.0331155\pi\) | ||||
−0.994593 | + | 0.103848i | \(0.966884\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.701562 | − | 4.00000i | 0.0502399 | − | 0.286446i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.0925i | 1.36029i | 0.733079 | + | 0.680144i | \(0.238083\pi\) | ||||
−0.733079 | + | 0.680144i | \(0.761917\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.58060 | 0.466486 | 0.233243 | − | 0.972418i | \(-0.425066\pi\) | ||||
0.233243 | + | 0.972418i | \(0.425066\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 39.1485 | 2.76132 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 13.9873i | − | 0.981714i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.71685 | − | 15.4903i | 0.189753 | − | 1.08189i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 7.62018i | − | 0.529639i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.6777 | −0.946105 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.55986 | −0.451599 | −0.225800 | − | 0.974174i | \(-0.572499\pi\) | ||||
−0.225800 | + | 0.974174i | \(0.572499\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 40.5283i | − | 2.77695i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.1546 | − | 1.95642i | −0.760740 | − | 0.133427i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.43634i | − | 0.301158i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −30.1922 | −2.04020 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.18384 | −0.146901 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.2094i | 1.35332i | 0.736296 | + | 0.676660i | \(0.236573\pi\) | ||||
−0.736296 | + | 0.676660i | \(0.763427\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 35.8267 | + | 12.9662i | 2.38845 | + | 0.864414i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 15.0098i | − | 0.996234i | −0.867110 | − | 0.498117i | \(-0.834025\pi\) | ||
0.867110 | − | 0.498117i | \(-0.165975\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.7081 | −0.905859 | −0.452929 | − | 0.891546i | \(-0.649621\pi\) | ||||
−0.452929 | + | 0.891546i | \(0.649621\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.55093 | 0.628405 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.19822i | 0.602595i | 0.953530 | + | 0.301298i | \(0.0974198\pi\) | ||||
−0.953530 | + | 0.301298i | \(0.902580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.45307 | − | 0.254855i | −0.0947880 | − | 0.0166249i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.3068i | 1.25411i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.72618 | −0.176342 | −0.0881709 | − | 0.996105i | \(-0.528102\pi\) | ||||
−0.0881709 | + | 0.996105i | \(0.528102\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.26109 | 0.210066 | 0.105033 | − | 0.994469i | \(-0.466505\pi\) | ||||
0.105033 | + | 0.994469i | \(0.466505\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 40.2340i | 2.58101i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.90000 | − | 10.8330i | 0.121387 | − | 0.692095i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.75229i | 0.238753i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 37.0776 | 2.34970 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.9941 | −1.26202 | −0.631008 | − | 0.775776i | \(-0.717359\pi\) | ||||
−0.631008 | + | 0.775776i | \(0.717359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.03144i | 0.127715i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.93299 | − | 28.1258i | 0.308916 | − | 1.76130i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 26.7935i | − | 1.67133i | −0.549237 | − | 0.835667i | \(-0.685081\pi\) | ||
0.549237 | − | 0.835667i | \(-0.314919\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.27737 | −0.327920 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −73.8791 | −4.57300 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 15.8267i | − | 0.975918i | −0.872867 | − | 0.487959i | \(-0.837742\pi\) | ||
0.872867 | − | 0.487959i | \(-0.162258\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.5078 | − | 4.29844i | −1.50550 | − | 0.264051i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 17.1191i | − | 1.04767i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0872 | −0.736967 | −0.368484 | − | 0.929634i | \(-0.620123\pi\) | ||||
−0.368484 | + | 0.929634i | \(0.620123\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.40254 | −0.510418 | −0.255209 | − | 0.966886i | \(-0.582144\pi\) | ||||
−0.255209 | + | 0.966886i | \(0.582144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 2.62018i | − | 0.158580i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.55093 | − | 3.45662i | −0.575943 | − | 0.208442i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 13.8488i | − | 0.832093i | −0.909343 | − | 0.416046i | \(-0.863415\pi\) | ||
0.909343 | − | 0.416046i | \(-0.136585\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.4322 | −1.40285 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.15004 | −0.486191 | −0.243095 | − | 0.970002i | \(-0.578163\pi\) | ||||
−0.243095 | + | 0.970002i | \(0.578163\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 17.3532i | − | 1.03154i | −0.856727 | − | 0.515770i | \(-0.827506\pi\) | ||
0.856727 | − | 0.515770i | \(-0.172494\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −48.3259 | − | 8.47591i | −2.86258 | − | 0.502070i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 10.1468i | − | 0.598948i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.64446 | 0.0967332 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.265226 | 0.0155478 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.02252i | − | 0.410260i | −0.978735 | − | 0.205130i | \(-0.934238\pi\) | ||
0.978735 | − | 0.205130i | \(-0.0657617\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.14203 | − | 23.6160i | 0.241158 | − | 1.37498i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 30.5864i | − | 1.77480i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.557299 | 0.0322294 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.30678 | −0.421156 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.0903i | 1.55630i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.671897 | − | 3.83086i | 0.0384727 | − | 0.219355i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.4156i | − | 0.936887i | −0.883493 | − | 0.468444i | \(-0.844815\pi\) | ||
0.883493 | − | 0.468444i | \(-0.155185\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.7587 | 1.18092 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.35181 | −0.416883 | −0.208441 | − | 0.978035i | \(-0.566839\pi\) | ||||
−0.208441 | + | 0.978035i | \(0.566839\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.08972i | − | 0.231165i | −0.993298 | − | 0.115582i | \(-0.963127\pi\) | ||
0.993298 | − | 0.115582i | \(-0.0368734\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 24.2129 | + | 4.24672i | 1.36424 | + | 0.239275i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.91580i | 0.500761i | 0.968148 | + | 0.250381i | \(0.0805557\pi\) | ||||
−0.968148 | + | 0.250381i | \(0.919444\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.6952 | 1.10272 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −55.1485 | −3.07809 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.3840i | 1.46805i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.948279 | + | 2.62018i | −0.0526011 | + | 0.145341i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.713121i | 0.0394357i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.951826 | −0.0524759 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.3240 | −1.17207 | −0.586036 | − | 0.810285i | \(-0.699312\pi\) | ||||
−0.586036 | + | 0.810285i | \(0.699312\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 27.8744i | 1.52751i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.4579 | − | 4.64046i | −1.44555 | − | 0.253535i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.15417i | − | 0.171819i | −0.996303 | − | 0.0859094i | \(-0.972620\pi\) | ||
0.996303 | − | 0.0859094i | \(-0.0273796\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.89209 | 0.102764 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.24672 | 0.338279 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.1950i | − | 0.928443i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.25886 | + | 7.17748i | −0.0677748 | + | 0.386422i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.54739i | 0.190434i | 0.995457 | + | 0.0952169i | \(0.0303545\pi\) | ||||
−0.995457 | + | 0.0952169i | \(0.969646\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.9726 | 1.01558 | 0.507789 | − | 0.861481i | \(-0.330463\pi\) | ||||
0.507789 | + | 0.861481i | \(0.330463\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.39098 | −0.447877 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.5710i | 1.78680i | 0.449257 | + | 0.893402i | \(0.351689\pi\) | ||||
−0.449257 | + | 0.893402i | \(0.648311\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.80402 | + | 27.3904i | −0.254971 | + | 1.45373i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 18.4236i | − | 0.975081i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.53243 | −0.186434 | −0.0932171 | − | 0.995646i | \(-0.529715\pi\) | ||||
−0.0932171 | + | 0.995646i | \(0.529715\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.3333 | 1.38596 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 22.3990i | − | 1.17564i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.4049 | + | 3.57883i | 1.06804 | + | 0.187324i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.07444i | 0.421482i | 0.977542 | + | 0.210741i | \(0.0675877\pi\) | ||||
−0.977542 | + | 0.210741i | \(0.932412\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −53.5943 | −2.79001 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.0537 | −0.833466 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.31459i | − | 0.0680668i | −0.999421 | − | 0.0340334i | \(-0.989165\pi\) | ||
0.999421 | − | 0.0340334i | \(-0.0108353\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −31.6033 | − | 18.1315i | −1.63199 | − | 0.936308i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.40312i | − | 0.278275i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.311952 | 0.0160239 | 0.00801196 | − | 0.999968i | \(-0.497450\pi\) | ||||
0.00801196 | + | 0.999968i | \(0.497450\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.11460 | 0.262029 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 10.6805i | − | 0.545748i | −0.962050 | − | 0.272874i | \(-0.912026\pi\) | ||
0.962050 | − | 0.272874i | \(-0.0879742\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.45485 | − | 1.13212i | −0.328969 | − | 0.0576981i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 38.5935i | 1.96182i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.86867 | 0.398957 | 0.199479 | − | 0.979902i | \(-0.436075\pi\) | ||||
0.199479 | + | 0.979902i | \(0.436075\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.91861 | 0.198173 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 51.8838i | − | 2.61719i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.28853 | − | 13.0482i | 0.115148 | − | 0.656525i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 29.2334i | − | 1.46718i | −0.679591 | − | 0.733591i | \(-0.737843\pi\) | ||
0.679591 | − | 0.733591i | \(-0.262157\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −31.6556 | −1.58476 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.7130 | 1.18417 | 0.592086 | − | 0.805874i | \(-0.298304\pi\) | ||||
0.592086 | + | 0.805874i | \(0.298304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.71371i | − | 0.0853658i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.1233 | − | 57.7186i | 0.503031 | − | 2.86806i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7.43096i | − | 0.368339i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.2509 | 1.64415 | 0.822076 | − | 0.569378i | \(-0.192816\pi\) | ||||
0.822076 | + | 0.569378i | \(0.192816\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.0853 | 1.04006 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 15.4695i | − | 0.761207i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.0583 | − | 4.39499i | −1.23006 | − | 0.215741i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 2.13848i | − | 0.104722i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.28229 | 0.355763 | 0.177882 | − | 0.984052i | \(-0.443076\pi\) | ||||
0.177882 | + | 0.984052i | \(0.443076\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.71515 | −0.132329 | −0.0661643 | − | 0.997809i | \(-0.521076\pi\) | ||||
−0.0661643 | + | 0.997809i | \(0.521076\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.02743i | 0.244442i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.66777 | + | 18.4236i | −0.323434 | + | 0.893676i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2.50938i | − | 0.121438i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.68942 | 0.178127 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.3336 | −0.497750 | −0.248875 | − | 0.968536i | \(-0.580061\pi\) | ||||
−0.248875 | + | 0.968536i | \(0.580061\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.4153i | 1.36555i | 0.730628 | + | 0.682775i | \(0.239227\pi\) | ||||
−0.730628 | + | 0.682775i | \(0.760773\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 69.5870 | + | 12.2049i | 3.33644 | + | 0.585181i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.73300i | − | 0.322083i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.37313 | 0.304173 | 0.152087 | − | 0.988367i | \(-0.451401\pi\) | ||||
0.152087 | + | 0.988367i | \(0.451401\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −37.4807 | −1.78480 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.43114i | 0.448087i | 0.974579 | + | 0.224044i | \(0.0719258\pi\) | ||||
−0.974579 | + | 0.224044i | \(0.928074\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.02921 | + | 11.5696i | −0.0961936 | + | 0.548454i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 77.6745i | − | 3.67388i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.3185 | −0.534154 | −0.267077 | − | 0.963675i | \(-0.586058\pi\) | ||||
−0.267077 | + | 0.963675i | \(0.586058\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.2875 | 0.672774 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 48.4491i | 2.27634i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.310582 | + | 1.77080i | −0.0145603 | + | 0.0830166i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.96456i | − | 0.232232i | −0.993236 | − | 0.116116i | \(-0.962956\pi\) | ||
0.993236 | − | 0.116116i | \(-0.0370445\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −59.0007 | −2.75391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.9128 | 0.927433 | 0.463717 | − | 0.885984i | \(-0.346516\pi\) | ||||
0.463717 | + | 0.885984i | \(0.346516\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.9046i | 1.38978i | 0.719114 | + | 0.694892i | \(0.244548\pi\) | ||||
−0.719114 | + | 0.694892i | \(0.755452\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.0709 | + | 3.87102i | 1.02351 | + | 0.179514i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.1032i | 0.698895i | 0.936956 | + | 0.349447i | \(0.113631\pi\) | ||||
−0.936956 | + | 0.349447i | \(0.886369\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.3311 | −0.800274 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.8599 | −1.23764 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 10.2885i | − | 0.473067i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.6556 | + | 11.4566i | 1.45246 | + | 0.525666i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 84.7937i | 3.88244i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.6678 | 1.30986 | 0.654932 | − | 0.755688i | \(-0.272697\pi\) | ||||
0.654932 | + | 0.755688i | \(0.272697\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.03859 | −0.0929516 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.70156i | 0.213928i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.179249 | − | 0.0314385i | −0.00813926 | − | 0.00142755i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.15319i | 0.414770i | 0.978259 | + | 0.207385i | \(0.0664954\pi\) | ||||
−0.978259 | + | 0.207385i | \(0.933505\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 33.6164 | 1.52018 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.8098 | 0.939133 | 0.469566 | − | 0.882897i | \(-0.344410\pi\) | ||||
0.469566 | + | 0.882897i | \(0.344410\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 37.9917i | − | 1.71106i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.97972 | + | 34.0937i | −0.268768 | + | 1.53240i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.9419i | 0.804805i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.1293 | −0.811579 | −0.405789 | − | 0.913967i | \(-0.633003\pi\) | ||||
−0.405789 | + | 0.913967i | \(0.633003\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.1855 | −0.678438 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.4296i | 1.17844i | 0.807974 | + | 0.589218i | \(0.200564\pi\) | ||||
−0.807974 | + | 0.589218i | \(0.799436\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.21115 | − | 18.3085i | 0.142894 | − | 0.814720i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 41.3531i | 1.83655i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.0501 | 0.534113 | 0.267057 | − | 0.963681i | \(-0.413949\pi\) | ||||
0.267057 | + | 0.963681i | \(0.413949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.3661 | 0.591282 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 101.376i | 4.47584i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.0294 | − | 2.46062i | −0.618209 | − | 0.108428i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.34025i | − | 0.0589440i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.13790 | 0.401109 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.3697 | −1.11146 | −0.555732 | − | 0.831361i | \(-0.687562\pi\) | ||||
−0.555732 | + | 0.831361i | \(0.687562\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.0018i | 1.09325i | 0.837377 | + | 0.546626i | \(0.184088\pi\) | ||||
−0.837377 | + | 0.546626i | \(0.815912\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.1047 | − | 8.00000i | −0.964728 | − | 0.349149i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 12.0498i | − | 0.524898i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −81.7083 | −3.54584 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.91960i | − | 0.169777i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 37.2712 | + | 6.53702i | 1.61137 | + | 0.282620i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 14.4762i | − | 0.624696i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.99186 | 0.430380 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.7900 | 1.06580 | 0.532902 | − | 0.846177i | \(-0.321101\pi\) | ||||
0.532902 | + | 0.846177i | \(0.321101\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.88705i | 0.338466i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.0845298 | − | 0.481952i | 0.00362086 | − | 0.0206445i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 30.9508i | − | 1.32336i | −0.749785 | − | 0.661681i | \(-0.769843\pi\) | ||
0.749785 | − | 0.661681i | \(-0.230157\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.2543 | −0.565678 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −65.2778 | −2.78093 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 8.54713i | − | 0.363461i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.60489 | − | 26.2551i | 0.195467 | − | 1.11447i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.45307i | 0.315797i | 0.987455 | + | 0.157898i | \(0.0504718\pi\) | ||||
−0.987455 | + | 0.157898i | \(0.949528\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.82252 | −0.119380 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.9419 | 1.09527 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.96161i | 0.335542i | 0.985826 | + | 0.167771i | \(0.0536569\pi\) | ||||
−0.985826 | + | 0.167771i | \(0.946343\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.27874 | − | 0.224279i | −0.0537970 | − | 0.00943549i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 37.8082i | − | 1.58780i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.3873 | −1.35774 | −0.678872 | − | 0.734257i | \(-0.737531\pi\) | ||||
−0.678872 | + | 0.734257i | \(0.737531\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.38994 | 0.267410 | 0.133705 | − | 0.991021i | \(-0.457312\pi\) | ||||
0.133705 | + | 0.991021i | \(0.457312\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 68.0887i | 2.84445i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.70156 | − | 4.70156i | 0.0709600 | − | 0.196069i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.1728i | 1.63078i | 0.578910 | + | 0.815392i | \(0.303478\pi\) | ||||
−0.578910 | + | 0.815392i | \(0.696522\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.40312 | −0.390781 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.4143 | −0.680979 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 22.6049i | − | 0.936199i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.35318 | + | 1.64046i | 0.386706 | + | 0.0678246i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 21.3811i | − | 0.882491i | −0.897386 | − | 0.441246i | \(-0.854537\pi\) | ||
0.897386 | − | 0.441246i | \(-0.145463\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.7041 | −0.853098 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −62.2199 | −2.55939 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 2.45130i | − | 0.100663i | −0.998733 | − | 0.0503314i | \(-0.983972\pi\) | ||
0.998733 | − | 0.0503314i | \(-0.0160277\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.18384 | + | 12.4513i | −0.0895287 | + | 0.510453i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.4453i | 0.877696i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 38.5828 | 1.57645 | 0.788226 | − | 0.615386i | \(-0.211000\pi\) | ||||
0.788226 | + | 0.615386i | \(0.211000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.3416 | −1.44162 | −0.720808 | − | 0.693135i | \(-0.756229\pi\) | ||||
−0.720808 | + | 0.693135i | \(0.756229\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 91.5406i | 3.72782i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.65506 | + | 15.1380i | −0.107944 | + | 0.615447i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 17.8129i | − | 0.723005i | −0.932371 | − | 0.361502i | \(-0.882264\pi\) | ||
0.932371 | − | 0.361502i | \(-0.117736\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 45.5826 | 1.84710 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.367680 | −0.0148747 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 37.7547i | − | 1.52490i | −0.647048 | − | 0.762450i | \(-0.723997\pi\) | ||
0.647048 | − | 0.762450i | \(-0.276003\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 50.4807 | + | 8.85384i | 2.03558 | + | 0.357021i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 23.1248i | − | 0.930971i | −0.885055 | − | 0.465486i | \(-0.845880\pi\) | ||
0.885055 | − | 0.465486i | \(-0.154120\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.5428 | 0.785491 | 0.392746 | − | 0.919647i | \(-0.371525\pi\) | ||||
0.392746 | + | 0.919647i | \(0.371525\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.0565 | 0.604197 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.57863i | 0.303631i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.2094 | + | 16.0000i | 0.768375 | + | 0.640000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 44.5736i | − | 1.78010i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.3342 | −0.571542 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.4807 | 1.05418 | 0.527090 | − | 0.849809i | \(-0.323283\pi\) | ||||
0.527090 | + | 0.849809i | \(0.323283\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 21.3777i | − | 0.849686i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.45662 | − | 0.606258i | −0.137172 | − | 0.0240586i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.74114i | − | 0.108608i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 94.7671 | 3.74893 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.9594 | −1.42031 | −0.710156 | − | 0.704044i | \(-0.751376\pi\) | ||||
−0.710156 | + | 0.704044i | \(0.751376\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 14.6934i | − | 0.579452i | −0.957110 | − | 0.289726i | \(-0.906436\pi\) | ||
0.957110 | − | 0.289726i | \(-0.0935642\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.37569 | − | 36.3514i | 0.251043 | − | 1.43134i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.7763i | 1.05269i | 0.850272 | + | 0.526343i | \(0.176437\pi\) | ||||
−0.850272 | + | 0.526343i | \(0.823563\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.7824 | 0.855033 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.4574 | 0.566630 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.8331i | 0.736996i | 0.929629 | + | 0.368498i | \(0.120128\pi\) | ||||
−0.929629 | + | 0.368498i | \(0.879872\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.15004 | + | 35.0649i | −0.240302 | + | 1.37010i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 70.5982i | − | 2.75430i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0885 | −0.704629 | −0.352315 | − | 0.935882i | \(-0.614605\pi\) | ||||
−0.352315 | + | 0.935882i | \(0.614605\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.3235 | 1.17945 | 0.589724 | − | 0.807605i | \(-0.299237\pi\) | ||||
0.589724 | + | 0.807605i | \(0.299237\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 7.11683i | − | 0.276395i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.3939 | + | 3.75229i | 0.829621 | + | 0.145508i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.69520i | 0.375400i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −65.8595 | −2.54628 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.53341 | 0.136406 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.1496i | 0.429787i | 0.976637 | + | 0.214894i | \(0.0689404\pi\) | ||||
−0.976637 | + | 0.214894i | \(0.931060\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.6196 | + | 70.7891i | −0.986099 | + | 2.72467i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.5275i | 1.67290i | 0.548045 | + | 0.836449i | \(0.315372\pi\) | ||||
−0.548045 | + | 0.836449i | \(0.684628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.117416 | −0.00450600 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48.9148 | 1.87442 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 24.1375i | − | 0.923596i | −0.886985 | − | 0.461798i | \(-0.847205\pi\) | ||
0.886985 | − | 0.461798i | \(-0.152795\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.2501 | − | 2.49934i | −0.544470 | − | 0.0954948i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 44.6729i | − | 1.70438i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.20136 | −0.236253 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.8241 | 0.792186 | 0.396093 | − | 0.918210i | \(-0.370366\pi\) | ||||
0.396093 | + | 0.918210i | \(0.370366\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22.3329i | 0.848356i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.253485 | + | 1.44526i | −0.00961523 | + | 0.0548218i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 27.5604i | − | 1.04393i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.9757 | −1.13379 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.5301 | −1.19087 | −0.595437 | − | 0.803402i | \(-0.703021\pi\) | ||||
−0.595437 | + | 0.803402i | \(0.703021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.6292i | 0.928907i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.830537 | − | 4.73536i | 0.0312798 | − | 0.178344i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 11.9929i | − | 0.451040i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.12175 | −0.117240 | −0.0586199 | − | 0.998280i | \(-0.518670\pi\) | ||||
−0.0586199 | + | 0.998280i | \(0.518670\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −45.1449 | −1.69307 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.07502i | 0.115160i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.49343 | − | 0.437325i | −0.0932491 | − | 0.0163550i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 8.88423i | − | 0.331788i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.3945 | 0.760588 | 0.380294 | − | 0.924866i | \(-0.375823\pi\) | ||||
0.380294 | + | 0.924866i | \(0.375823\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.18988 | −0.342249 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.6275i | 0.395239i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −45.5826 | − | 16.4970i | −1.69289 | − | 0.612682i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.8896i | 1.47942i | 0.672924 | + | 0.739712i | \(0.265038\pi\) | ||||
−0.672924 | + | 0.739712i | \(0.734962\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −52.4973 | −1.94434 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.8464 | −0.734046 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.7761i | 0.841255i | 0.907233 | + | 0.420628i | \(0.138190\pi\) | ||||
−0.907233 | + | 0.420628i | \(0.861810\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 35.3032 | + | 6.19185i | 1.30218 | + | 0.228390i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 24.4035i | − | 0.898915i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.7661 | 1.24211 | 0.621053 | − | 0.783769i | \(-0.286705\pi\) | ||||
0.621053 | + | 0.783769i | \(0.286705\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.2282 | −0.449214 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.5880i | 1.74584i | 0.487868 | + | 0.872918i | \(0.337775\pi\) | ||||
−0.487868 | + | 0.872918i | \(0.662225\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.20714 | + | 52.4951i | −0.337324 | + | 1.92327i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 86.6983i | 3.17212i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.4143 | 0.892078 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.2698 | −1.87086 | −0.935430 | − | 0.353512i | \(-0.884987\pi\) | ||||
−0.935430 | + | 0.353512i | \(0.884987\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 65.1580i | − | 2.37449i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.74291 | − | 32.7436i | 0.209006 | − | 1.19166i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 26.2807i | − | 0.955189i | −0.878580 | − | 0.477594i | \(-0.841509\pi\) | ||
0.878580 | − | 0.477594i | \(-0.158491\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.62018 | −0.240297 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.18003 | −0.260276 | −0.130138 | − | 0.991496i | \(-0.541542\pi\) | ||||
−0.130138 | + | 0.991496i | \(0.541542\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 0.315700i | − | 0.0114291i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 65.7663 | + | 11.5348i | 2.37779 | + | 0.417041i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 5.97571i | − | 0.215770i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.2666 | 1.16356 | 0.581782 | − | 0.813345i | \(-0.302356\pi\) | ||||
0.581782 | + | 0.813345i | \(0.302356\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 87.3164 | 3.14462 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 3.75316i | − | 0.134992i | −0.997720 | − | 0.0674958i | \(-0.978499\pi\) | ||
0.997720 | − | 0.0674958i | \(-0.0215009\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.4574 | − | 5.23234i | −0.519325 | − | 0.187951i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 17.1982i | − | 0.616983i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −47.3546 | −1.69666 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.2637 | −0.904005 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 145.976i | − | 5.21675i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.1529 | + | 3.18384i | 0.647903 | + | 0.113636i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.9373i | 0.781981i | 0.920395 | + | 0.390991i | \(0.127867\pi\) | ||||
−0.920395 | + | 0.390991i | \(0.872133\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 51.5771 | 1.83619 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.837631 | −0.0297827 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.969347i | − | 0.0344225i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.0080 | − | 79.8676i | 0.496813 | − | 2.83261i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 7.57883i | − | 0.268456i | −0.990950 | − | 0.134228i | \(-0.957145\pi\) | ||
0.990950 | − | 0.134228i | \(-0.0428554\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.58532 | −0.0914619 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40.0294 | 1.41437 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.8205i | 0.664163i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.557299 | − | 3.17748i | 0.0196422 | − | 0.111991i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 39.3904i | − | 1.38661i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.9835 | −0.667423 | −0.333712 | − | 0.942675i | \(-0.608301\pi\) | ||||
−0.333712 | + | 0.942675i | \(0.608301\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.1851 | −0.498106 | −0.249053 | − | 0.968490i | \(-0.580119\pi\) | ||||
−0.249053 | + | 0.968490i | \(0.580119\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 27.3827i | − | 0.960354i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.7191 | − | 3.98471i | −0.795815 | − | 0.139578i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.1003i | 1.19302i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.12674 | 0.214086 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.8294 | −1.56456 | −0.782278 | − | 0.622930i | \(-0.785942\pi\) | ||||
−0.782278 | + | 0.622930i | \(0.785942\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.7652i | 0.549539i | 0.961510 | + | 0.274770i | \(0.0886016\pi\) | ||||
−0.961510 | + | 0.274770i | \(0.911398\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.2646 | − | 31.1252i | 0.392184 | − | 1.08364i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.4332i | 0.397573i | 0.980043 | + | 0.198786i | \(0.0637000\pi\) | ||||
−0.980043 | + | 0.198786i | \(0.936300\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.3924 | 0.986108 | 0.493054 | − | 0.869999i | \(-0.335881\pi\) | ||||
0.493054 | + | 0.869999i | \(0.335881\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 45.1313 | 1.56559 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 19.2741i | − | 0.667810i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.2629 | + | 1.80001i | 0.355161 | + | 0.0622919i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 46.2991i | − | 1.60033i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 54.3340 | 1.87582 | 0.937908 | − | 0.346883i | \(-0.112760\pi\) | ||||
0.937908 | + | 0.346883i | \(0.112760\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.9969 | 2.24127 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 26.5599i | − | 0.914770i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.90178 | − | 27.9478i | 0.168626 | − | 0.961433i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.91606i | 0.340720i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 56.5516 | 1.94085 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.65798 | 0.125394 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.8542i | 1.60426i | 0.597150 | + | 0.802129i | \(0.296300\pi\) | ||||
−0.597150 | + | 0.802129i | \(0.703700\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.8192 | − | 113.000i | 0.677802 | − | 3.86453i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.5356i | 0.974756i | 0.873191 | + | 0.487378i | \(0.162047\pi\) | ||||
−0.873191 | + | 0.487378i | \(0.837953\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.4417 | 0.663343 | 0.331671 | − | 0.943395i | \(-0.392387\pi\) | ||||
0.331671 | + | 0.943395i | \(0.392387\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 33.0671 | 1.12692 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.94514i | 0.0662132i | 0.999452 | + | 0.0331066i | \(0.0105401\pi\) | ||||
−0.999452 | + | 0.0331066i | \(0.989460\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.17570 | − | 1.08316i | −0.209980 | − | 0.0368285i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.35908i | 0.182004i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0350 | 0.408261 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.69479 | −0.226844 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.620176i | 0.0209898i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.9908 | + | 8.02685i | 0.472976 | + | 0.271357i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 38.6457i | − | 1.30497i | −0.757800 | − | 0.652486i | \(-0.773726\pi\) | ||
0.757800 | − | 0.652486i | \(-0.226274\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.8854 | 0.771905 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.6889 | −1.84252 | −0.921258 | − | 0.388952i | \(-0.872837\pi\) | ||||
−0.921258 | + | 0.388952i | \(0.872837\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 14.6273i | − | 0.492247i | −0.969238 | − | 0.246123i | \(-0.920843\pi\) | ||
0.969238 | − | 0.246123i | \(-0.0791569\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 76.9614 | + | 13.4983i | 2.58703 | + | 0.453740i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 40.2666i | − | 1.35202i | −0.736892 | − | 0.676010i | \(-0.763707\pi\) | ||
0.736892 | − | 0.676010i | \(-0.236293\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.26424 | −0.0759401 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 53.2370 | 1.78351 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.44212i | 0.148650i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.71594 | + | 9.78353i | −0.0573575 | + | 0.327027i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.81616i | 0.0606398i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29.8129 | 0.994317 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.6045 | −1.45268 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 23.8118i | − | 0.792406i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.934890 | − | 5.33034i | 0.0310768 | − | 0.177186i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 7.87090i | − | 0.261349i | −0.991425 | − | 0.130674i | \(-0.958286\pi\) | ||
0.991425 | − | 0.130674i | \(-0.0417143\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −63.3451 | −2.10102 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.586235 | −0.0194228 | −0.00971141 | − | 0.999953i | \(-0.503091\pi\) | ||||
−0.00971141 | + | 0.999953i | \(0.503091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 23.1126i | − | 0.764916i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.4843 | + | 2.18962i | 0.412717 | + | 0.0723866i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.9690i | 0.758504i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.9422 | −0.921729 | −0.460865 | − | 0.887470i | \(-0.652461\pi\) | ||||
−0.460865 | + | 0.887470i | \(0.652461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 53.4961 | 1.76276 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.93076i | 0.228129i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.22428 | + | 17.1982i | −0.204653 | + | 0.565474i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 48.5399i | 1.59426i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.79352 | 0.157270 | 0.0786351 | − | 0.996903i | \(-0.474944\pi\) | ||||
0.0786351 | + | 0.996903i | \(0.474944\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.1170 | −1.08537 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 23.9585i | − | 0.784367i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.5324 | − | 3.07502i | −0.573372 | − | 0.100564i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.110466i | 0.00360877i | 0.999998 | + | 0.00180438i | \(0.000574353\pi\) | ||||
−0.999998 | + | 0.00180438i | \(0.999426\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.3278 | 0.434938 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.2077 | 0.626155 | 0.313077 | − | 0.949728i | \(-0.398640\pi\) | ||||
0.313077 | + | 0.949728i | \(0.398640\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.03321i | 0.229033i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.39098 | + | 47.8417i | −0.272959 | + | 1.55629i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 20.0933i | − | 0.652944i | −0.945207 | − | 0.326472i | \(-0.894140\pi\) | ||
0.945207 | − | 0.326472i | \(-0.105860\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.16318 | 0.167604 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.0553 | −0.942184 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 55.4762i | − | 1.79705i | −0.438920 | − | 0.898526i | \(-0.644639\pi\) | ||
0.438920 | − | 0.898526i | \(-0.355361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.07089 | − | 46.0167i | 0.261168 | − | 1.48906i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 64.1839i | 2.07477i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.33447 | −0.301426 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.5442 | −0.694976 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 128.953i | − | 4.15546i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.35495 | + | 1.11460i | 0.204573 | + | 0.0358802i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.86228i | 0.0920448i | 0.998940 | + | 0.0460224i | \(0.0146546\pi\) | ||||
−0.998940 | + | 0.0460224i | \(0.985345\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −85.9819 | −2.76214 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.5901 | −1.36678 | −0.683391 | − | 0.730052i | \(-0.739496\pi\) | ||||
−0.683391 | + | 0.730052i | \(0.739496\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.946709i | 0.0303501i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.53879 | − | 3.09031i | −0.273460 | − | 0.0989691i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.5633i | 1.36172i | 0.732413 | + | 0.680861i | \(0.238394\pi\) | ||||
−0.732413 | + | 0.680861i | \(0.761606\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.6713 | −0.341057 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.66749 | −0.0532388 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.6691i | 1.04198i | 0.853562 | + | 0.520991i | \(0.174437\pi\) | ||||
−0.853562 | + | 0.520991i | \(0.825563\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42.0503 | + | 7.37523i | 1.33984 | + | 0.234994i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 3.10187i | − | 0.0987336i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.06465 | 0.161047 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.39775 | 0.139699 | 0.0698495 | − | 0.997558i | \(-0.477748\pi\) | ||||
0.0698495 | + | 0.997558i | \(0.477748\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 69.4919i | − | 2.20526i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.54201 | − | 14.4934i | 0.0805872 | − | 0.459473i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.4135i | 1.05822i | 0.848554 | + | 0.529108i | \(0.177473\pi\) | ||||
−0.848554 | + | 0.529108i | \(0.822527\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −55.0764 | −1.74254 |
(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 | 1840.2.e.e.369.8 | 8 | ||
4.3 | odd | 2 | 230.2.b.b.139.5 | yes | 8 | ||
5.2 | odd | 4 | 9200.2.a.cr.1.4 | 4 | |||
5.3 | odd | 4 | 9200.2.a.cj.1.1 | 4 | |||
5.4 | even | 2 | inner | 1840.2.e.e.369.1 | 8 | ||
12.11 | even | 2 | 2070.2.d.f.829.2 | 8 | |||
20.3 | even | 4 | 1150.2.a.s.1.4 | 4 | |||
20.7 | even | 4 | 1150.2.a.r.1.1 | 4 | |||
20.19 | odd | 2 | 230.2.b.b.139.4 | ✓ | 8 | ||
60.59 | even | 2 | 2070.2.d.f.829.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.b.b.139.4 | ✓ | 8 | 20.19 | odd | 2 | ||
230.2.b.b.139.5 | yes | 8 | 4.3 | odd | 2 | ||
1150.2.a.r.1.1 | 4 | 20.7 | even | 4 | |||
1150.2.a.s.1.4 | 4 | 20.3 | even | 4 | |||
1840.2.e.e.369.1 | 8 | 5.4 | even | 2 | inner | ||
1840.2.e.e.369.8 | 8 | 1.1 | even | 1 | trivial | ||
2070.2.d.f.829.2 | 8 | 12.11 | even | 2 | |||
2070.2.d.f.829.6 | 8 | 60.59 | even | 2 | |||
9200.2.a.cj.1.1 | 4 | 5.3 | odd | 4 | |||
9200.2.a.cr.1.4 | 4 | 5.2 | odd | 4 |