Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(191,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("960.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.h (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: | \(7.66563859404\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 480) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.3 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.191 |
Dual form | 960.2.h.a.191.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | + | 1.41421i | −0.577350 | + | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.82843i | 1.82497i | 0.409106 | + | 0.912487i | \(0.365841\pi\) | ||||
−0.409106 | + | 0.912487i | \(0.634159\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | − | 2.82843i | −0.333333 | − | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.82843 | −1.45583 | −0.727913 | − | 0.685670i | \(-0.759509\pi\) | ||||
−0.727913 | + | 0.685670i | \(0.759509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.17157 | −0.324936 | −0.162468 | − | 0.986714i | \(-0.551945\pi\) | ||||
−0.162468 | + | 0.986714i | \(0.551945\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.41421 | + | 1.00000i | 0.365148 | + | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.828427i | − | 0.200923i | −0.994941 | − | 0.100462i | \(-0.967968\pi\) | ||
0.994941 | − | 0.100462i | \(-0.0320319\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.00000i | − | 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.82843 | − | 4.82843i | −1.49008 | − | 1.05365i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.828427 | 0.172739 | 0.0863695 | − | 0.996263i | \(-0.472473\pi\) | ||||
0.0863695 | + | 0.996263i | \(0.472473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | + | 1.41421i | 0.962250 | + | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000i | 1.11417i | 0.830455 | + | 0.557086i | \(0.188081\pi\) | ||||
−0.830455 | + | 0.557086i | \(0.811919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.00000i | − | 0.359211i | −0.983739 | − | 0.179605i | \(-0.942518\pi\) | ||
0.983739 | − | 0.179605i | \(-0.0574821\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.82843 | − | 6.82843i | 0.840521 | − | 1.18868i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.82843 | 0.816153 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.82843 | −1.12259 | −0.561293 | − | 0.827617i | \(-0.689696\pi\) | ||||
−0.561293 | + | 0.827617i | \(0.689696\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.17157 | − | 1.65685i | 0.187602 | − | 0.265309i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.65685i | − | 1.50815i | −0.656790 | − | 0.754074i | \(-0.728086\pi\) | ||
0.656790 | − | 0.754074i | \(-0.271914\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.17157i | 0.178663i | 0.996002 | + | 0.0893316i | \(0.0284731\pi\) | ||||
−0.996002 | + | 0.0893316i | \(0.971527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.82843 | + | 1.00000i | −0.421637 | + | 0.149071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.17157 | −0.462621 | −0.231311 | − | 0.972880i | \(-0.574301\pi\) | ||||
−0.231311 | + | 0.972880i | \(0.574301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.3137 | −2.33053 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.17157 | + | 0.828427i | 0.164053 | + | 0.116003i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.65685i | − | 1.05175i | −0.850562 | − | 0.525875i | \(-0.823738\pi\) | ||
0.850562 | − | 0.525875i | \(-0.176262\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.82843i | 0.651065i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.48528 | + | 6.00000i | 1.12390 | + | 0.794719i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.8284 | −1.67012 | −0.835059 | − | 0.550160i | \(-0.814567\pi\) | ||||
−0.835059 | + | 0.550160i | \(0.814567\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.3137 | 1.70465 | 0.852323 | − | 0.523016i | \(-0.175193\pi\) | ||||
0.852323 | + | 0.523016i | \(0.175193\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.6569 | − | 4.82843i | 1.72060 | − | 0.608325i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.17157i | 0.145316i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.48528i | − | 0.547964i | −0.961735 | − | 0.273982i | \(-0.911659\pi\) | ||
0.961735 | − | 0.273982i | \(-0.0883409\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.828427 | + | 1.17157i | −0.0997309 | + | 0.141041i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3137 | −1.34269 | −0.671345 | − | 0.741145i | \(-0.734283\pi\) | ||||
−0.671345 | + | 0.741145i | \(0.734283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | − | 1.41421i | 0.115470 | − | 0.163299i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 23.3137i | − | 2.65684i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.00000i | − | 0.675053i | −0.941316 | − | 0.337526i | \(-0.890410\pi\) | ||
0.941316 | − | 0.337526i | \(-0.109590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.31371 | 0.583255 | 0.291628 | − | 0.956532i | \(-0.405803\pi\) | ||||
0.291628 | + | 0.956532i | \(0.405803\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.828427 | −0.0898555 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.48528 | − | 6.00000i | −0.909718 | − | 0.643268i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 5.65685i | − | 0.592999i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.82843 | + | 2.00000i | 0.293294 | + | 0.207390i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.00000 | −0.615587 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.82843 | + | 13.6569i | 0.485275 | + | 1.37257i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.65685i | 0.761885i | 0.924599 | + | 0.380943i | \(0.124401\pi\) | ||||
−0.924599 | + | 0.380943i | \(0.875599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.828427i | − | 0.0816274i | −0.999167 | − | 0.0408137i | \(-0.987005\pi\) | ||
0.999167 | − | 0.0408137i | \(-0.0129950\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.82843 | + | 6.82843i | −0.471206 | + | 0.666386i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.31371 | −0.513696 | −0.256848 | − | 0.966452i | \(-0.582684\pi\) | ||||
−0.256848 | + | 0.966452i | \(0.582684\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.65685 | −0.733394 | −0.366697 | − | 0.930341i | \(-0.619511\pi\) | ||||
−0.366697 | + | 0.930341i | \(0.619511\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.82843 | − | 9.65685i | 0.648126 | − | 0.916588i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 7.17157i | − | 0.674645i | −0.941389 | − | 0.337322i | \(-0.890479\pi\) | ||
0.941389 | − | 0.337322i | \(-0.109521\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 0.828427i | − | 0.0772512i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.17157 | + | 3.31371i | 0.108312 | + | 0.306352i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.6569 | + | 9.65685i | 1.23140 | + | 0.870729i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.48528i | 0.575476i | 0.957709 | + | 0.287738i | \(0.0929032\pi\) | ||||
−0.957709 | + | 0.287738i | \(0.907097\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.65685 | − | 1.17157i | −0.145878 | − | 0.103151i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.48528 | 0.217140 | 0.108570 | − | 0.994089i | \(-0.465373\pi\) | ||||
0.108570 | + | 0.994089i | \(0.465373\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 28.9706 | 2.51207 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.41421 | − | 5.00000i | 0.121716 | − | 0.430331i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.1421i | 1.37912i | 0.724231 | + | 0.689558i | \(0.242195\pi\) | ||||
−0.724231 | + | 0.689558i | \(0.757805\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.3137i | 1.80781i | 0.427738 | + | 0.903903i | \(0.359310\pi\) | ||||
−0.427738 | + | 0.903903i | \(0.640690\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.17157 | − | 4.48528i | 0.267095 | − | 0.377729i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.65685 | 0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.3137 | − | 23.0711i | 1.34553 | − | 1.90287i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.3431i | 1.01119i | 0.862771 | + | 0.505595i | \(0.168727\pi\) | ||||
−0.862771 | + | 0.505595i | \(0.831273\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.65685i | 0.623106i | 0.950229 | + | 0.311553i | \(0.100849\pi\) | ||||
−0.950229 | + | 0.311553i | \(0.899151\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.34315 | + | 0.828427i | −0.189432 | + | 0.0669744i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.485281 | −0.0387297 | −0.0193648 | − | 0.999812i | \(-0.506164\pi\) | ||||
−0.0193648 | + | 0.999812i | \(0.506164\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.8284 | + | 7.65685i | 0.858750 | + | 0.607228i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000i | 0.315244i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.485281i | 0.0380102i | 0.999819 | + | 0.0190051i | \(0.00604987\pi\) | ||||
−0.999819 | + | 0.0190051i | \(0.993950\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.82843 | − | 4.82843i | −0.531592 | − | 0.375893i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.8284 | −1.92128 | −0.960641 | − | 0.277794i | \(-0.910397\pi\) | ||||
−0.960641 | + | 0.277794i | \(0.910397\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6274 | −0.894417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.9706 | + | 6.00000i | −1.29777 | + | 0.458831i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9706i | 0.834076i | 0.908889 | + | 0.417038i | \(0.136932\pi\) | ||||
−0.908889 | + | 0.417038i | \(0.863068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.82843i | − | 0.364995i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.8284 | − | 18.1421i | 0.964244 | − | 1.36365i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.17157 | −0.237054 | −0.118527 | − | 0.992951i | \(-0.537817\pi\) | ||||
−0.118527 | + | 0.992951i | \(0.537817\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.3137 | + | 18.8284i | −0.984178 | + | 1.39184i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.82843i | 0.502036i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000i | 0.292509i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.82843 | + | 24.1421i | −0.496695 | + | 1.75608i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.9706 | 1.36553 | 0.682765 | − | 0.730638i | \(-0.260777\pi\) | ||||
0.682765 | + | 0.730638i | \(0.260777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.65685 | − | 1.17157i | −0.118650 | − | 0.0838981i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.3137i | 0.948562i | 0.880373 | + | 0.474281i | \(0.157292\pi\) | ||||
−0.880373 | + | 0.474281i | \(0.842708\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 7.65685i | − | 0.542780i | −0.962469 | − | 0.271390i | \(-0.912517\pi\) | ||
0.962469 | − | 0.271390i | \(-0.0874833\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.34315 | + | 4.48528i | 0.447411 | + | 0.316367i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −28.9706 | −2.03333 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.65685 | −0.674464 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.828427 | − | 2.34315i | −0.0575797 | − | 0.162860i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.9706i | 2.00394i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.97056i | 0.479873i | 0.970789 | + | 0.239937i | \(0.0771267\pi\) | ||||
−0.970789 | + | 0.239937i | \(0.922873\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.3137 | − | 16.0000i | 0.775203 | − | 1.09630i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.17157 | 0.0799006 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.65685 | 0.655550 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000 | − | 2.82843i | 0.135147 | − | 0.191127i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.970563i | 0.0652871i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.48528i | 0.434287i | 0.976140 | + | 0.217143i | \(0.0696739\pi\) | ||||
−0.976140 | + | 0.217143i | \(0.930326\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | + | 2.82843i | 0.0666667 | + | 0.188562i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.6569 | −0.773693 | −0.386846 | − | 0.922144i | \(-0.626436\pi\) | ||||
−0.386846 | + | 0.922144i | \(0.626436\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.9706 | −1.25361 | −0.626805 | − | 0.779176i | \(-0.715638\pi\) | ||||
−0.626805 | + | 0.779176i | \(0.715638\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 32.9706 | + | 23.3137i | 2.16930 | + | 1.53393i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 20.8284i | − | 1.36452i | −0.731112 | − | 0.682258i | \(-0.760998\pi\) | ||
0.731112 | − | 0.682258i | \(-0.239002\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.17157i | 0.206891i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.48528 | + | 6.00000i | 0.551178 | + | 0.389742i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9706 | 1.09773 | 0.548867 | − | 0.835910i | \(-0.315059\pi\) | ||||
0.548867 | + | 0.835910i | \(0.315059\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | − | 15.5563i | −0.0641500 | − | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.3137i | 1.04224i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.02944i | 0.447272i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.31371 | + | 7.51472i | −0.336743 | + | 0.476226i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.7990 | 1.12346 | 0.561731 | − | 0.827320i | \(-0.310136\pi\) | ||||
0.561731 | + | 0.827320i | \(0.310136\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.828427 | − | 1.17157i | 0.0518781 | − | 0.0733667i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.4853i | 1.65211i | 0.563592 | + | 0.826053i | \(0.309419\pi\) | ||||
−0.563592 | + | 0.826053i | \(0.690581\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 32.9706i | − | 2.04869i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.9706 | − | 6.00000i | 1.05045 | − | 0.371391i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.48528 | −0.153249 | −0.0766245 | − | 0.997060i | \(-0.524414\pi\) | ||||
−0.0766245 | + | 0.997060i | \(0.524414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.65685 | −0.470357 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.65685i | 0.222962i | 0.993767 | + | 0.111481i | \(0.0355595\pi\) | ||||
−0.993767 | + | 0.111481i | \(0.964441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 14.9706i | − | 0.909397i | −0.890645 | − | 0.454698i | \(-0.849747\pi\) | ||
0.890645 | − | 0.454698i | \(-0.150253\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.00000 | + | 5.65685i | 0.484182 | + | 0.342368i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.82843 | 0.291165 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.51472 | −0.211179 | −0.105589 | − | 0.994410i | \(-0.533673\pi\) | ||||
−0.105589 | + | 0.994410i | \(0.533673\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.65685 | + | 2.00000i | −0.338667 | + | 0.119737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 23.3137i | − | 1.39078i | −0.718633 | − | 0.695390i | \(-0.755232\pi\) | ||
0.718633 | − | 0.695390i | \(-0.244768\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 17.1716i | − | 1.02074i | −0.859954 | − | 0.510372i | \(-0.829508\pi\) | ||
0.859954 | − | 0.510372i | \(-0.170492\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.00000 | − | 8.48528i | 0.355409 | − | 0.502625i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 46.6274 | 2.75233 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3137 | 0.959630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | − | 8.48528i | 0.351726 | − | 0.497416i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.343146i | 0.0200468i | 0.999950 | + | 0.0100234i | \(0.00319060\pi\) | ||||
−0.999950 | + | 0.0100234i | \(0.996809\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.8284i | 0.746900i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.1421 | − | 6.82843i | −1.40087 | − | 0.396226i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.970563 | −0.0561291 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.65685 | −0.326056 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.8284 | − | 7.65685i | −0.622077 | − | 0.439875i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 13.3137i | − | 0.762341i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.4853i | 1.16916i | 0.811337 | + | 0.584578i | \(0.198740\pi\) | ||||
−0.811337 | + | 0.584578i | \(0.801260\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.17157 | + | 0.828427i | 0.0666485 | + | 0.0471276i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3137 | −0.641542 | −0.320771 | − | 0.947157i | \(-0.603942\pi\) | ||||
−0.320771 | + | 0.947157i | \(0.603942\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.3137 | 1.43082 | 0.715408 | − | 0.698707i | \(-0.246241\pi\) | ||||
0.715408 | + | 0.698707i | \(0.246241\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.82843 | − | 13.6569i | −0.272051 | − | 0.769477i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 5.31371i | − | 0.298448i | −0.988803 | − | 0.149224i | \(-0.952323\pi\) | ||
0.988803 | − | 0.149224i | \(-0.0476775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 28.9706i | − | 1.62204i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.31371 | − | 7.51472i | 0.296582 | − | 0.419431i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.97056 | −0.276570 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.17157 | 0.0649872 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.65685 | − | 10.8284i | 0.423425 | − | 0.598813i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 15.3137i | − | 0.844272i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 10.9706i | − | 0.602997i | −0.953467 | − | 0.301498i | \(-0.902513\pi\) | ||
0.953467 | − | 0.301498i | \(-0.0974868\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.82843 | + | 19.3137i | 0.374196 | + | 1.05838i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.48528 | −0.245057 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.9706 | 1.90497 | 0.952484 | − | 0.304589i | \(-0.0985190\pi\) | ||||
0.952484 | + | 0.304589i | \(0.0985190\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.1421 | + | 7.17157i | 0.550845 | + | 0.389506i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.65685i | 0.522948i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 44.9706i | − | 2.42818i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.17157 | + | 0.828427i | 0.0630754 | + | 0.0446010i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.3137 | 0.714717 | 0.357359 | − | 0.933967i | \(-0.383677\pi\) | ||||
0.357359 | + | 0.933967i | \(0.383677\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.9706 | −0.587241 | −0.293620 | − | 0.955922i | \(-0.594860\pi\) | ||||
−0.293620 | + | 0.955922i | \(0.594860\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.85786 | − | 1.65685i | −0.312670 | − | 0.0884363i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.8284i | 0.895687i | 0.894112 | + | 0.447843i | \(0.147808\pi\) | ||||
−0.894112 | + | 0.447843i | \(0.852192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.3137i | 0.600469i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.00000 | + | 5.65685i | −0.211702 | + | 0.299392i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.3137 | −1.65267 | −0.826337 | − | 0.563176i | \(-0.809579\pi\) | ||||
−0.826337 | + | 0.563176i | \(0.809579\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.3137 | + | 17.4142i | −0.646302 | + | 0.914009i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.00000i | 0.104685i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.1421i | 1.46901i | 0.678605 | + | 0.734504i | \(0.262585\pi\) | ||||
−0.678605 | + | 0.734504i | \(0.737415\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −27.3137 | + | 9.65685i | −1.42189 | + | 0.502716i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 36.9706 | 1.91942 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.4853 | −0.853576 | −0.426788 | − | 0.904352i | \(-0.640355\pi\) | ||||
−0.426788 | + | 0.904352i | \(0.640355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.41421 | − | 1.00000i | −0.0730297 | − | 0.0516398i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.02944i | − | 0.362034i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.6863i | − | 0.548918i | −0.961599 | − | 0.274459i | \(-0.911501\pi\) | ||
0.961599 | − | 0.274459i | \(-0.0884987\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.17157 | − | 6.48528i | −0.469874 | − | 0.332251i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.1421 | −1.23361 | −0.616803 | − | 0.787118i | \(-0.711572\pi\) | ||||
−0.616803 | + | 0.787118i | \(0.711572\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.3137 | −1.18818 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.31371 | − | 1.17157i | 0.168445 | − | 0.0595544i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 28.6274i | − | 1.45147i | −0.687976 | − | 0.725734i | \(-0.741500\pi\) | ||
0.687976 | − | 0.725734i | \(-0.258500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.686292i | − | 0.0347073i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.48528 | + | 3.51472i | −0.125366 | + | 0.177294i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.00000 | −0.301893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.4853 | 1.22888 | 0.614441 | − | 0.788963i | \(-0.289382\pi\) | ||||
0.614441 | + | 0.788963i | \(0.289382\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −28.9706 | + | 40.9706i | −1.45034 | + | 2.05109i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 16.9706i | − | 0.847469i | −0.905786 | − | 0.423735i | \(-0.860719\pi\) | ||
0.905786 | − | 0.423735i | \(-0.139281\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.34315i | 0.116720i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.65685 | + | 7.00000i | 0.281091 | + | 0.347833i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.9706 | 1.63429 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.6863 | −0.528403 | −0.264202 | − | 0.964467i | \(-0.585108\pi\) | ||||
−0.264202 | + | 0.964467i | \(0.585108\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.8284 | − | 16.1421i | −1.12604 | − | 0.796233i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 61.9411i | − | 3.04792i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 5.31371i | − | 0.260840i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.1421 | − | 21.3137i | −1.47607 | − | 1.04374i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.8284 | −0.822122 | −0.411061 | − | 0.911608i | \(-0.634842\pi\) | ||||
−0.411061 | + | 0.911608i | \(0.634842\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.17157 | + | 8.97056i | 0.154207 | + | 0.436164i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.828427i | 0.0401846i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 64.2843i | 3.11093i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.65685 | + | 8.00000i | −0.273115 | + | 0.386244i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.6569 | 0.850501 | 0.425250 | − | 0.905076i | \(-0.360186\pi\) | ||||
0.425250 | + | 0.905076i | \(0.360186\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.0000 | −1.44171 | −0.720854 | − | 0.693087i | \(-0.756250\pi\) | ||||
−0.720854 | + | 0.693087i | \(0.756250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.00000 | + | 8.48528i | −0.287678 | + | 0.406838i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 4.97056i | − | 0.237774i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.2843i | 1.25448i | 0.778826 | + | 0.627240i | \(0.215815\pi\) | ||||
−0.778826 | + | 0.627240i | \(0.784185\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.3137 | + | 46.1421i | 0.776843 | + | 2.19724i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.6569 | 0.933925 | 0.466963 | − | 0.884277i | \(-0.345348\pi\) | ||||
0.466963 | + | 0.884277i | \(0.345348\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.4558 | − | 12.3431i | −0.825633 | − | 0.583811i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.3431i | 1.05444i | 0.849729 | + | 0.527219i | \(0.176765\pi\) | ||||
−0.849729 | + | 0.527219i | \(0.823235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 46.6274i | 2.19560i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.8284 | − | 7.65685i | −0.508764 | − | 0.359750i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.65685 | −0.265197 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.9706 | −1.63585 | −0.817927 | − | 0.575322i | \(-0.804877\pi\) | ||||
−0.817927 | + | 0.575322i | \(0.804877\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.17157 | − | 4.14214i | 0.0546843 | − | 0.193338i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13.3137i | − | 0.620081i | −0.950723 | − | 0.310041i | \(-0.899657\pi\) | ||
0.950723 | − | 0.310041i | \(-0.100343\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.17157i | − | 0.333291i | −0.986017 | − | 0.166646i | \(-0.946706\pi\) | ||
0.986017 | − | 0.166646i | \(-0.0532936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.00000 | − | 2.82843i | 0.0927478 | − | 0.131165i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.6569 | −1.09471 | −0.547354 | − | 0.836901i | \(-0.684365\pi\) | ||||
−0.547354 | + | 0.836901i | \(0.684365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.6569 | 1.00002 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.485281 | − | 0.686292i | 0.0223606 | − | 0.0316226i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.65685i | − | 0.260102i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.00000i | 0.275299i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.6569 | + | 7.65685i | −0.991599 | + | 0.350583i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.34315 | 0.107061 | 0.0535305 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535305 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.65685 | − | 4.00000i | −0.257396 | − | 0.182006i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.00000i | 0.272446i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 23.4558i | − | 1.06289i | −0.847094 | − | 0.531443i | \(-0.821650\pi\) | ||
0.847094 | − | 0.531443i | \(-0.178350\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.686292 | − | 0.485281i | −0.0310352 | − | 0.0219452i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.1716 | −0.684683 | −0.342342 | − | 0.939576i | \(-0.611220\pi\) | ||||
−0.342342 | + | 0.939576i | \(0.611220\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.97056 | 0.223863 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.6569 | − | 4.82843i | 0.613830 | − | 0.217022i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 54.6274i | − | 2.45037i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 25.3137i | − | 1.13320i | −0.823994 | − | 0.566599i | \(-0.808259\pi\) | ||
0.823994 | − | 0.566599i | \(-0.191741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.8284 | − | 35.1127i | 1.10925 | − | 1.56872i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.828427 | 0.0369377 | 0.0184689 | − | 0.999829i | \(-0.494121\pi\) | ||||
0.0184689 | + | 0.999829i | \(0.494121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.65685 | 0.340726 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.6274 | − | 16.4437i | 0.516392 | − | 0.730288i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 12.3431i | − | 0.547100i | −0.961858 | − | 0.273550i | \(-0.911802\pi\) | ||
0.961858 | − | 0.273550i | \(-0.0881980\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 9.65685i | − | 0.427194i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.48528 | − | 30.0000i | 0.374634 | − | 1.32453i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.828427 | −0.0365049 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.3137 | 0.673496 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.5147 | − | 10.9706i | −0.681021 | − | 0.481554i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000i | 0.525730i | 0.964833 | + | 0.262865i | \(0.0846673\pi\) | ||||
−0.964833 | + | 0.262865i | \(0.915333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.48528i | − | 0.196128i | −0.995180 | − | 0.0980638i | \(-0.968735\pi\) | ||
0.995180 | − | 0.0980638i | \(-0.0312649\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.82843 | + | 4.82843i | 0.298017 | + | 0.210730i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.65685 | −0.0721737 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3137 | −0.970161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.8284 | + | 36.2843i | 0.556706 | + | 1.57460i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.3137i | 0.490051i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.31371i | 0.229732i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.17157 | − | 4.48528i | 0.136863 | − | 0.193554i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 78.7696 | 3.39284 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.6274 | −1.57474 | −0.787368 | − | 0.616483i | \(-0.788557\pi\) | ||||
−0.787368 | + | 0.616483i | \(0.788557\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.00000 | + | 2.82843i | −0.0858282 | + | 0.121379i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.65685i | 0.327984i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21.4558i | − | 0.917386i | −0.888595 | − | 0.458693i | \(-0.848318\pi\) | ||
0.888595 | − | 0.458693i | \(-0.151682\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.3137 | − | 37.6569i | −0.568215 | − | 1.60716i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.0000 | 1.53365 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.9706 | 1.23195 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.65685 | − | 6.82843i | −0.409911 | − | 0.289851i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.02944i | 0.0436187i | 0.999762 | + | 0.0218093i | \(0.00694268\pi\) | ||||
−0.999762 | + | 0.0218093i | \(0.993057\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.37258i | − | 0.0580541i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.65685 | − | 4.00000i | −0.238833 | − | 0.168880i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.3137 | 0.729686 | 0.364843 | − | 0.931069i | \(-0.381123\pi\) | ||||
0.364843 | + | 0.931069i | \(0.381123\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.17157 | −0.301710 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −27.3137 | − | 33.7990i | −1.14707 | − | 1.41942i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 34.9706i | − | 1.46347i | −0.681588 | − | 0.731736i | \(-0.738710\pi\) | ||
0.681588 | − | 0.731736i | \(-0.261290\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | − | 16.9706i | 0.501307 | − | 0.708955i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.828427 | −0.0345478 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.9706 | −0.623233 | −0.311616 | − | 0.950208i | \(-0.600870\pi\) | ||||
−0.311616 | + | 0.950208i | \(0.600870\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.9706 | + | 26.8284i | −0.788390 | + | 1.11495i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.6569i | 1.06443i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.9706i | 1.53116i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.31371 | − | 1.17157i | 0.137005 | − | 0.0484386i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.6274 | −0.686287 | −0.343143 | − | 0.939283i | \(-0.611492\pi\) | ||||
−0.343143 | + | 0.939283i | \(0.611492\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.8284 | − | 13.3137i | −0.774498 | − | 0.547653i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.1421i | 1.48418i | 0.670300 | + | 0.742090i | \(0.266165\pi\) | ||||
−0.670300 | + | 0.742090i | \(0.733835\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 4.00000i | − | 0.163984i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.8284 | + | 7.65685i | 0.443178 | + | 0.313374i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.6274 | 0.761096 | 0.380548 | − | 0.924761i | \(-0.375735\pi\) | ||||
0.380548 | + | 0.924761i | \(0.375735\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.6274 | −1.49406 | −0.747032 | − | 0.664788i | \(-0.768522\pi\) | ||||
−0.747032 | + | 0.664788i | \(0.768522\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.6863 | + | 4.48528i | −0.516626 | + | 0.182655i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 12.3137i | − | 0.500623i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5147i | 0.873255i | 0.899642 | + | 0.436628i | \(0.143827\pi\) | ||||
−0.899642 | + | 0.436628i | \(0.856173\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28.9706 | − | 40.9706i | 1.17395 | − | 1.66021i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.71573 | 0.150322 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.4558 | −1.02815 | −0.514076 | − | 0.857745i | \(-0.671865\pi\) | ||||
−0.514076 | + | 0.857745i | \(0.671865\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.65685 | − | 13.6569i | 0.389402 | − | 0.550698i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.17157i | − | 0.127683i | −0.997960 | − | 0.0638414i | \(-0.979665\pi\) | ||
0.997960 | − | 0.0638414i | \(-0.0203352\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.00000i | − | 0.241160i | −0.992704 | − | 0.120580i | \(-0.961525\pi\) | ||
0.992704 | − | 0.120580i | \(-0.0384755\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.14214 | + | 1.17157i | 0.166218 | + | 0.0470136i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −40.9706 | − | 28.9706i | −1.63621 | − | 1.15697i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.65685i | 0.225554i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.3137i | 1.32620i | 0.748532 | + | 0.663099i | \(0.230759\pi\) | ||||
−0.748532 | + | 0.663099i | \(0.769241\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.85786 | − | 6.97056i | −0.391815 | − | 0.277055i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.48528 | 0.257361 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.1127 | 0.757273 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.3137 | + | 32.0000i | 0.447563 | + | 1.26590i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 14.6274i | − | 0.577748i | −0.957367 | − | 0.288874i | \(-0.906719\pi\) | ||
0.957367 | − | 0.288874i | \(-0.0932809\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.17157i | 0.203947i | 0.994787 | + | 0.101973i | \(0.0325157\pi\) | ||||
−0.994787 | + | 0.101973i | \(0.967484\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.17157 | + | 1.65685i | −0.0461306 | + | 0.0652386i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.1716 | 0.596456 | 0.298228 | − | 0.954495i | \(-0.403604\pi\) | ||||
0.298228 | + | 0.954495i | \(0.403604\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 61.9411 | 2.43140 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.65685 | + | 13.6569i | −0.378482 | + | 0.535254i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.2843i | 1.18512i | 0.805528 | + | 0.592558i | \(0.201882\pi\) | ||||
−0.805528 | + | 0.592558i | \(0.798118\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.48528i | − | 0.0971080i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | + | 5.65685i | 0.0780274 | + | 0.220695i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.20101 | 0.241557 | 0.120779 | − | 0.992679i | \(-0.461461\pi\) | ||||
0.120779 | + | 0.992679i | \(0.461461\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.0000 | −0.544537 | −0.272268 | − | 0.962221i | \(-0.587774\pi\) | ||||
−0.272268 | + | 0.962221i | \(0.587774\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.37258 | − | 0.970563i | −0.0533067 | − | 0.0376935i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 28.9706i | − | 1.12343i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.97056i | 0.192461i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.17157 | − | 6.48528i | −0.354593 | − | 0.250735i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −64.2843 | −2.48167 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.9411 | −1.23124 | −0.615620 | − | 0.788043i | \(-0.711094\pi\) | ||||
−0.615620 | + | 0.788043i | \(0.711094\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.00000 | − | 1.41421i | −0.192450 | − | 0.0544331i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.6569i | 0.448009i | 0.974588 | + | 0.224005i | \(0.0719131\pi\) | ||||
−0.974588 | + | 0.224005i | \(0.928087\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 28.9706i | − | 1.11179i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.6569 | − | 16.4853i | 0.446692 | − | 0.631717i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.6569 | 1.21132 | 0.605658 | − | 0.795725i | \(-0.292910\pi\) | ||||
0.605658 | + | 0.795725i | \(0.292910\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.1421 | 0.616759 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.9706 | − | 26.8284i | 0.723772 | − | 1.02357i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.97056i | 0.341751i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 42.9706i | − | 1.63468i | −0.576158 | − | 0.817339i | \(-0.695449\pi\) | ||
0.576158 | − | 0.817339i | \(-0.304551\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −65.9411 | + | 23.3137i | −2.50490 | + | 0.885615i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.3137 | 0.808475 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.00000 | −0.303022 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.4558 | + | 20.8284i | 1.11412 | + | 0.787803i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.9411i | 1.50856i | 0.656555 | + | 0.754278i | \(0.272013\pi\) | ||||
−0.656555 | + | 0.754278i | \(0.727987\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.9706i | 1.54523i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.48528 | − | 3.17157i | −0.168925 | − | 0.119448i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −36.9706 | −1.39042 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.02944 | −0.339108 | −0.169554 | − | 0.985521i | \(-0.554233\pi\) | ||||
−0.169554 | + | 0.985521i | \(0.554233\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.9706 | + | 6.00000i | −0.636446 | + | 0.225018i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.65685i | − | 0.0620497i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.65685i | − | 0.211554i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.9706 | + | 24.0000i | −0.633777 | + | 0.896296i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.6863 | 0.771468 | 0.385734 | − | 0.922610i | \(-0.373948\pi\) | ||||
0.385734 | + | 0.922610i | \(0.373948\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | 0.148968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.00000 | + | 8.48528i | −0.223142 | + | 0.315571i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 6.00000i | − | 0.222834i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 24.8284i | − | 0.920835i | −0.887702 | − | 0.460418i | \(-0.847700\pi\) | ||
0.887702 | − | 0.460418i | \(-0.152300\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.970563 | 0.0358976 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.1716 | 0.929733 | 0.464867 | − | 0.885381i | \(-0.346102\pi\) | ||||
0.464867 | + | 0.885381i | \(0.346102\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −23.0711 | − | 16.3137i | −0.850989 | − | 0.601740i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.6569i | 0.797740i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.31371i | − | 0.0483255i | −0.999708 | − | 0.0241628i | \(-0.992308\pi\) | ||
0.999708 | − | 0.0241628i | \(-0.00769200\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.94113 | − | 7.02944i | −0.365196 | − | 0.258233i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.4558 | 1.15400 | 0.577001 | − | 0.816743i | \(-0.304223\pi\) | ||||
0.577001 | + | 0.816743i | \(0.304223\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.3431 | 0.452218 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.31371 | − | 15.0294i | −0.194418 | − | 0.549898i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 25.6569i | − | 0.937481i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.68629i | 0.0980242i | 0.998798 | + | 0.0490121i | \(0.0156073\pi\) | ||||
−0.998798 | + | 0.0490121i | \(0.984393\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.7990 | + | 25.1716i | −0.648631 | + | 0.917303i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.65685 | 0.278661 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.1421 | −0.659387 | −0.329694 | − | 0.944088i | \(-0.606945\pi\) | ||||
−0.329694 | + | 0.944088i | \(0.606945\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.00000 | − | 5.65685i | 0.145191 | − | 0.205331i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 8.68629i | − | 0.314878i | −0.987529 | − | 0.157439i | \(-0.949676\pi\) | ||
0.987529 | − | 0.157439i | \(-0.0503237\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 36.9706i | − | 1.33842i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.828427 | + | 2.34315i | 0.0299518 | + | 0.0847166i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.0294 | 0.542682 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.3137 | 1.20132 | 0.600662 | − | 0.799503i | \(-0.294904\pi\) | ||||
0.600662 | + | 0.799503i | \(0.294904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −37.4558 | − | 26.4853i | −1.34894 | − | 0.953844i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.68629i | 0.240489i | 0.992744 | + | 0.120245i | \(0.0383679\pi\) | ||||
−0.992744 | + | 0.120245i | \(0.961632\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.00000i | 0.0718421i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 46.6274 | + | 32.9706i | 1.67275 | + | 1.18281i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −57.9411 | −2.07596 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 54.6274 | 1.95472 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.48528 | + | 30.0000i | −0.303239 | + | 1.07211i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.485281i | 0.0173204i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.201010i | 0.00716524i | 0.999994 | + | 0.00358262i | \(0.00114039\pi\) | ||||
−0.999994 | + | 0.00358262i | \(0.998860\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.48528 | − | 3.51472i | 0.0884784 | − | 0.125127i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.6274 | 1.23121 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.5980 | −0.553901 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.65685 | − | 10.8284i | 0.271561 | − | 0.384045i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3.37258i | − | 0.119463i | −0.998214 | − | 0.0597315i | \(-0.980976\pi\) | ||
0.998214 | − | 0.0597315i | \(-0.0190245\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.62742i | 0.0929513i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.65685 | 0.340783 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | 0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.17157 | − | 3.65685i | −0.182048 | − | 0.128727i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.65685i | 0.198884i | 0.995043 | + | 0.0994422i | \(0.0317058\pi\) | ||||
−0.995043 | + | 0.0994422i | \(0.968294\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 38.2843i | − | 1.34434i | −0.740396 | − | 0.672171i | \(-0.765362\pi\) | ||
0.740396 | − | 0.672171i | \(-0.234638\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.1716 | + | 14.9706i | 0.742519 | + | 0.525041i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.485281 | 0.0169987 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.02944 | 0.245929 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.0000 | + | 5.65685i | −0.559085 | + | 0.197666i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 35.6569i | − | 1.24443i | −0.782845 | − | 0.622216i | \(-0.786232\pi\) | ||
0.782845 | − | 0.622216i | \(-0.213768\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 39.4558i | − | 1.37534i | −0.726021 | − | 0.687672i | \(-0.758633\pi\) | ||
0.726021 | − | 0.687672i | \(-0.241367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.82843 | + | 6.82843i | −0.168104 | + | 0.237735i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.3137 | 1.29752 | 0.648762 | − | 0.760991i | \(-0.275287\pi\) | ||||
0.648762 | + | 0.760991i | \(0.275287\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 56.9117 | 1.97662 | 0.988312 | − | 0.152443i | \(-0.0487139\pi\) | ||||
0.988312 | + | 0.152443i | \(0.0487139\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.51472 | − | 4.97056i | 0.121924 | − | 0.172427i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.5147i | 0.468257i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.8284i | 0.859223i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.82843 | − | 10.0000i | 0.0977647 | − | 0.345651i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.9411 | 0.757492 | 0.378746 | − | 0.925501i | \(-0.376355\pi\) | ||||
0.378746 | + | 0.925501i | \(0.376355\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.9706 | + | 23.3137i | 1.13557 | + | 0.802967i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.6274i | 0.399995i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 59.4558i | 2.04293i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.2843 | + | 17.1716i | 0.833434 | + | 0.589327i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.65685 | −0.193914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.4853 | 1.66010 | 0.830052 | − | 0.557686i | \(-0.188311\pi\) | ||||
0.830052 | + | 0.557686i | \(0.188311\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | + | 16.9706i | 0.205196 | + | 0.580381i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 9.79899i | − | 0.334727i | −0.985895 | − | 0.167364i | \(-0.946475\pi\) | ||
0.985895 | − | 0.167364i | \(-0.0535254\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 22.0000i | − | 0.750630i | −0.926897 | − | 0.375315i | \(-0.877534\pi\) | ||
0.926897 | − | 0.375315i | \(-0.122466\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −46.6274 | + | 65.9411i | −1.58906 | + | 2.24727i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 57.7990 | 1.96750 | 0.983750 | − | 0.179542i | \(-0.0574617\pi\) | ||||
0.983750 | + | 0.179542i | \(0.0574617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.9706 | 0.373010 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.3137 | + | 23.0711i | −0.554043 | + | 0.783535i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.9706i | 0.982759i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.25483i | 0.178053i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.00000 | + | 16.9706i | 0.203069 | + | 0.574367i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.82843 | −0.163231 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.7990 | −0.938705 | −0.469353 | − | 0.883011i | \(-0.655513\pi\) | ||||
−0.469353 | + | 0.883011i | \(0.655513\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.485281 | − | 0.343146i | −0.0163681 | − | 0.0115740i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.5980i | 1.33409i | 0.745018 | + | 0.667045i | \(0.232441\pi\) | ||||
−0.745018 | + | 0.667045i | \(0.767559\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 15.5147i | − | 0.522112i | −0.965324 | − | 0.261056i | \(-0.915929\pi\) | ||
0.965324 | − | 0.261056i | \(-0.0840707\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.1421 | − | 12.8284i | −0.609841 | − | 0.431223i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.8284 | −1.37088 | −0.685442 | − | 0.728127i | \(-0.740391\pi\) | ||||
−0.685442 | + | 0.728127i | \(0.740391\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.3137 | −1.05023 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.7990 | − | 27.3137i | 1.13231 | − | 0.915044i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.0294i | 0.636796i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.17157i | 0.106014i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.970563 | − | 1.37258i | 0.0324061 | − | 0.0458292i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.0000 | 0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.34315 | −0.211321 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.65685 | − | 8.00000i | 0.188248 | − | 0.266223i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.00000i | − | 0.0664822i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.8284i | 0.359552i | 0.983708 | + | 0.179776i | \(0.0575373\pi\) | ||||
−0.983708 | + | 0.179776i | \(0.942463\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.6569 | − | 7.65685i | 0.718313 | − | 0.253962i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.5980 | −1.70952 | −0.854759 | − | 0.519026i | \(-0.826295\pi\) | ||||
−0.854759 | + | 0.519026i | \(0.826295\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.6569 | −0.849118 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18.8284 | + | 13.3137i | 0.622449 | + | 0.440138i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.0000i | 0.396275i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 25.3137i | − | 0.835022i | −0.908672 | − | 0.417511i | \(-0.862902\pi\) | ||
0.908672 | − | 0.417511i | \(-0.137098\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.9706 | − | 20.4853i | −0.954612 | − | 0.675013i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.2548 | 0.436288 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.82843 | 0.224517 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.34315 | + | 0.828427i | −0.0769590 | + | 0.0272091i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 30.3431i | − | 0.995526i | −0.867313 | − | 0.497763i | \(-0.834155\pi\) | ||
0.867313 | − | 0.497763i | \(-0.165845\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 97.8823i | 3.20796i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.3137 | − | 16.0000i | 0.370394 | − | 0.523816i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.00000 | 0.130814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.97056 | 0.227718 | 0.113859 | − | 0.993497i | \(-0.463679\pi\) | ||||
0.113859 | + | 0.993497i | \(0.463679\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.3137 | + | 35.7990i | −0.826082 | + | 1.16826i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 41.5980i | − | 1.35606i | −0.735036 | − | 0.678028i | \(-0.762835\pi\) | ||
0.735036 | − | 0.678028i | \(-0.237165\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.00000i | − | 0.260516i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 24.1421 | + | 6.82843i | 0.785344 | + | 0.222129i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.2843 | 1.50404 | 0.752018 | − | 0.659142i | \(-0.229080\pi\) | ||||
0.752018 | + | 0.659142i | \(0.229080\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.34315 | 0.0760617 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.51472 | + | 5.31371i | 0.243681 | + | 0.172309i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.79899i | 0.0582750i | 0.999575 | + | 0.0291375i | \(0.00927607\pi\) | ||||
−0.999575 | + | 0.0291375i | \(0.990724\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.0000i | 0.388311i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 40.9706 | + | 28.9706i | 1.32439 | + | 0.936485i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −77.9411 | −2.51685 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000 | 0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.31371 | + | 15.0294i | 0.171232 | + | 0.484317i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 18.9706i | − | 0.610684i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.4853i | 0.594447i | 0.954808 | + | 0.297223i | \(0.0960606\pi\) | ||||
−0.954808 | + | 0.297223i | \(0.903939\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.97056 | − | 7.02944i | 0.159677 | − | 0.225818i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.7696 | −0.730710 | −0.365355 | − | 0.930868i | \(-0.619052\pi\) | ||||
−0.365355 | + | 0.930868i | \(0.619052\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −102.912 | −3.29920 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.17157 | + | 1.65685i | −0.0375204 | + | 0.0530618i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.7990i | 0.953354i | 0.879078 | + | 0.476677i | \(0.158159\pi\) | ||||
−0.879078 | + | 0.476677i | \(0.841841\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.65685 | + | 21.6569i | 0.244465 | + | 0.691450i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.1716 | −0.483898 | −0.241949 | − | 0.970289i | \(-0.577787\pi\) | ||||
−0.241949 | + | 0.970289i | \(0.577787\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.3137 | 0.424210 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.6569 | + | 15.3137i | 0.689345 | + | 0.487441i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.970563i | 0.0308621i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 42.2843i | − | 1.34320i | −0.740912 | − | 0.671602i | \(-0.765606\pi\) | ||
0.740912 | − | 0.671602i | \(-0.234394\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.5147 | + | 10.9706i | 0.492345 | + | 0.348140i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.65685 | −0.242739 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.5147 | 0.871400 | 0.435700 | − | 0.900092i | \(-0.356501\pi\) | ||||
0.435700 | + | 0.900092i | \(0.356501\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −34.1421 | − | 9.65685i | −1.08021 | − | 0.305529i |
(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 | 960.2.h.a.191.3 | 4 | ||
3.2 | odd | 2 | 960.2.h.e.191.4 | 4 | |||
4.3 | odd | 2 | 960.2.h.e.191.1 | 4 | |||
8.3 | odd | 2 | 480.2.h.a.191.4 | yes | 4 | ||
8.5 | even | 2 | 480.2.h.c.191.2 | yes | 4 | ||
12.11 | even | 2 | inner | 960.2.h.a.191.2 | 4 | ||
24.5 | odd | 2 | 480.2.h.a.191.1 | ✓ | 4 | ||
24.11 | even | 2 | 480.2.h.c.191.3 | yes | 4 | ||
40.3 | even | 4 | 2400.2.o.d.2399.1 | 4 | |||
40.13 | odd | 4 | 2400.2.o.g.2399.4 | 4 | |||
40.19 | odd | 2 | 2400.2.h.d.1151.2 | 4 | |||
40.27 | even | 4 | 2400.2.o.f.2399.4 | 4 | |||
40.29 | even | 2 | 2400.2.h.a.1151.3 | 4 | |||
40.37 | odd | 4 | 2400.2.o.e.2399.1 | 4 | |||
120.29 | odd | 2 | 2400.2.h.d.1151.3 | 4 | |||
120.53 | even | 4 | 2400.2.o.f.2399.3 | 4 | |||
120.59 | even | 2 | 2400.2.h.a.1151.2 | 4 | |||
120.77 | even | 4 | 2400.2.o.d.2399.2 | 4 | |||
120.83 | odd | 4 | 2400.2.o.e.2399.2 | 4 | |||
120.107 | odd | 4 | 2400.2.o.g.2399.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.2.h.a.191.1 | ✓ | 4 | 24.5 | odd | 2 | ||
480.2.h.a.191.4 | yes | 4 | 8.3 | odd | 2 | ||
480.2.h.c.191.2 | yes | 4 | 8.5 | even | 2 | ||
480.2.h.c.191.3 | yes | 4 | 24.11 | even | 2 | ||
960.2.h.a.191.2 | 4 | 12.11 | even | 2 | inner | ||
960.2.h.a.191.3 | 4 | 1.1 | even | 1 | trivial | ||
960.2.h.e.191.1 | 4 | 4.3 | odd | 2 | |||
960.2.h.e.191.4 | 4 | 3.2 | odd | 2 | |||
2400.2.h.a.1151.2 | 4 | 120.59 | even | 2 | |||
2400.2.h.a.1151.3 | 4 | 40.29 | even | 2 | |||
2400.2.h.d.1151.2 | 4 | 40.19 | odd | 2 | |||
2400.2.h.d.1151.3 | 4 | 120.29 | odd | 2 | |||
2400.2.o.d.2399.1 | 4 | 40.3 | even | 4 | |||
2400.2.o.d.2399.2 | 4 | 120.77 | even | 4 | |||
2400.2.o.e.2399.1 | 4 | 40.37 | odd | 4 | |||
2400.2.o.e.2399.2 | 4 | 120.83 | odd | 4 | |||
2400.2.o.f.2399.3 | 4 | 120.53 | even | 4 | |||
2400.2.o.f.2399.4 | 4 | 40.27 | even | 4 | |||
2400.2.o.g.2399.3 | 4 | 120.107 | odd | 4 | |||
2400.2.o.g.2399.4 | 4 | 40.13 | odd | 4 |