Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(361,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.bs (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.361 |
Dual form | 1170.2.bs.b.901.2 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | 2.59808 | − | 1.50000i | 0.783349 | − | 0.452267i | −0.0542666 | − | 0.998526i | \(-0.517282\pi\) |
0.837616 | + | 0.546259i | \(0.183949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | − | 3.46410i | −0.277350 | − | 0.960769i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | − | 1.73205i | −0.688247 | − | 0.397360i | 0.114708 | − | 0.993399i | \(-0.463407\pi\) |
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | −0.866025 | − | 0.500000i | −0.193649 | − | 0.111803i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.50000 | − | 2.59808i | 0.319801 | − | 0.553912i | ||||
\(23\) | 0.866025 | + | 1.50000i | 0.180579 | + | 0.312772i | 0.942078 | − | 0.335394i | \(-0.108870\pi\) |
−0.761499 | + | 0.648166i | \(0.775536\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −2.59808 | − | 2.50000i | −0.509525 | − | 0.490290i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.866025 | + | 1.50000i | 0.160817 | + | 0.278543i | 0.935162 | − | 0.354221i | \(-0.115254\pi\) |
−0.774345 | + | 0.632764i | \(0.781920\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.19615i | − | 0.933257i | −0.884454 | − | 0.466628i | \(-0.845469\pi\) | ||
0.884454 | − | 0.466628i | \(-0.154531\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.50000 | − | 0.866025i | 0.246598 | − | 0.142374i | −0.371607 | − | 0.928390i | \(-0.621193\pi\) |
0.618206 | + | 0.786016i | \(0.287860\pi\) | |||||||
\(38\) | −3.46410 | −0.561951 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 5.19615 | − | 3.00000i | 0.811503 | − | 0.468521i | −0.0359748 | − | 0.999353i | \(-0.511454\pi\) |
0.847477 | + | 0.530831i | \(0.178120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.500000 | − | 0.866025i | 0.0762493 | − | 0.132068i | −0.825380 | − | 0.564578i | \(-0.809039\pi\) |
0.901629 | + | 0.432511i | \(0.142372\pi\) | |||||||
\(44\) | − | 3.00000i | − | 0.452267i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.50000 | + | 0.866025i | 0.221163 | + | 0.127688i | ||||
\(47\) | − | 3.00000i | − | 0.437595i | −0.975770 | − | 0.218797i | \(-0.929787\pi\) | ||
0.975770 | − | 0.218797i | \(-0.0702134\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.50000 | − | 6.06218i | −0.500000 | − | 0.866025i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.50000 | − | 0.866025i | −0.485363 | − | 0.120096i | ||||
\(53\) | −6.92820 | −0.951662 | −0.475831 | − | 0.879537i | \(-0.657853\pi\) | ||||
−0.475831 | + | 0.879537i | \(0.657853\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50000 | − | 2.59808i | −0.202260 | − | 0.350325i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.50000 | + | 0.866025i | 0.196960 | + | 0.113715i | ||||
\(59\) | 7.79423 | + | 4.50000i | 1.01472 | + | 0.585850i | 0.912571 | − | 0.408919i | \(-0.134094\pi\) |
0.102151 | + | 0.994769i | \(0.467427\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | − | 6.92820i | 0.512148 | − | 0.887066i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.999901 | − | 0.0140840i | \(-0.00448323\pi\) | |||||||
\(62\) | −2.59808 | − | 4.50000i | −0.329956 | − | 0.571501i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.46410 | + | 1.00000i | −0.429669 | + | 0.124035i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00000 | + | 1.73205i | −0.366508 | + | 0.211604i | −0.671932 | − | 0.740613i | \(-0.734535\pi\) |
0.305424 | + | 0.952217i | \(0.401202\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.19615 | + | 3.00000i | 0.616670 | + | 0.356034i | 0.775571 | − | 0.631260i | \(-0.217462\pi\) |
−0.158901 | + | 0.987294i | \(0.550795\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0.866025 | − | 1.50000i | 0.100673 | − | 0.174371i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.00000 | + | 1.73205i | −0.344124 | + | 0.198680i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.0000 | −1.23760 | −0.618798 | − | 0.785550i | \(-0.712380\pi\) | ||||
−0.618798 | + | 0.785550i | \(0.712380\pi\) | |||||||
\(80\) | −0.866025 | + | 0.500000i | −0.0968246 | + | 0.0559017i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 1.00000i | − | 0.107833i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.50000 | − | 2.59808i | −0.159901 | − | 0.276956i | ||||
\(89\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.73205 | 0.180579 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.50000 | − | 2.59808i | −0.154713 | − | 0.267971i | ||||
\(95\) | −1.73205 | + | 3.00000i | −0.177705 | + | 0.307794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.00000 | − | 1.73205i | −0.304604 | − | 0.175863i | 0.339905 | − | 0.940460i | \(-0.389605\pi\) |
−0.644509 | + | 0.764597i | \(0.722938\pi\) | |||||||
\(98\) | −6.06218 | − | 3.50000i | −0.612372 | − | 0.353553i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 6.92820 | + | 12.0000i | 0.689382 | + | 1.19404i | 0.972038 | + | 0.234823i | \(0.0754512\pi\) |
−0.282656 | + | 0.959221i | \(0.591216\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | −3.46410 | + | 1.00000i | −0.339683 | + | 0.0980581i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | + | 3.46410i | −0.582772 | + | 0.336463i | ||||
\(107\) | 3.46410 | + | 6.00000i | 0.334887 | + | 0.580042i | 0.983463 | − | 0.181108i | \(-0.0579684\pi\) |
−0.648576 | + | 0.761150i | \(0.724635\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | −2.59808 | − | 1.50000i | −0.247717 | − | 0.143019i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.06218 | + | 10.5000i | −0.570282 | + | 0.987757i | 0.426255 | + | 0.904603i | \(0.359833\pi\) |
−0.996537 | + | 0.0831539i | \(0.973501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50000 | − | 0.866025i | 0.139876 | − | 0.0807573i | ||||
\(116\) | 1.73205 | 0.160817 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.00000 | 0.828517 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | + | 1.73205i | −0.0909091 | + | 0.157459i | ||||
\(122\) | − | 8.00000i | − | 0.724286i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.50000 | − | 2.59808i | −0.404112 | − | 0.233314i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | + | 1.73205i | 0.0887357 | + | 0.153695i | 0.906977 | − | 0.421180i | \(-0.138384\pi\) |
−0.818241 | + | 0.574875i | \(0.805051\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.50000 | + | 2.59808i | −0.219265 | + | 0.227866i | ||||
\(131\) | 12.1244 | 1.05931 | 0.529655 | − | 0.848213i | \(-0.322321\pi\) | ||||
0.529655 | + | 0.848213i | \(0.322321\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.73205 | + | 3.00000i | −0.149626 | + | 0.259161i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.59808 | + | 1.50000i | 0.221969 | + | 0.128154i | 0.606861 | − | 0.794808i | \(-0.292428\pi\) |
−0.384893 | + | 0.922961i | \(0.625762\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.00000 | − | 8.66025i | 0.424094 | − | 0.734553i | −0.572241 | − | 0.820086i | \(-0.693926\pi\) |
0.996335 | + | 0.0855324i | \(0.0272591\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | −7.79423 | − | 7.50000i | −0.651786 | − | 0.627182i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.50000 | − | 0.866025i | 0.124568 | − | 0.0719195i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.73205i | − | 0.142374i | ||||||
\(149\) | 2.59808 | + | 1.50000i | 0.212843 | + | 0.122885i | 0.602632 | − | 0.798019i | \(-0.294119\pi\) |
−0.389789 | + | 0.920904i | \(0.627452\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.46410i | 0.281905i | 0.990016 | + | 0.140952i | \(0.0450164\pi\) | ||||
−0.990016 | + | 0.140952i | \(0.954984\pi\) | |||||||
\(152\) | −1.73205 | + | 3.00000i | −0.140488 | + | 0.243332i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.19615 | −0.417365 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | −0.558661 | −0.279330 | − | 0.960195i | \(-0.590112\pi\) | ||||
−0.279330 | + | 0.960195i | \(0.590112\pi\) | |||||||
\(158\) | −9.52628 | + | 5.50000i | −0.757870 | + | 0.437557i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.5000 | + | 11.2583i | 1.52736 | + | 0.881820i | 0.999472 | + | 0.0325054i | \(0.0103486\pi\) |
0.527886 | + | 0.849315i | \(0.322985\pi\) | |||||||
\(164\) | − | 6.00000i | − | 0.468521i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | + | 5.19615i | 0.232845 | + | 0.403300i | ||||
\(167\) | 18.1865 | − | 10.5000i | 1.40732 | − | 0.812514i | 0.412188 | − | 0.911099i | \(-0.364765\pi\) |
0.995129 | + | 0.0985846i | \(0.0314315\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.500000 | − | 0.866025i | −0.0381246 | − | 0.0660338i | ||||
\(173\) | −10.3923 | + | 18.0000i | −0.790112 | + | 1.36851i | 0.135785 | + | 0.990738i | \(0.456644\pi\) |
−0.925897 | + | 0.377776i | \(0.876689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.59808 | − | 1.50000i | −0.195837 | − | 0.113067i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.33013 | + | 7.50000i | 0.323649 | + | 0.560576i | 0.981238 | − | 0.192800i | \(-0.0617570\pi\) |
−0.657589 | + | 0.753377i | \(0.728424\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.50000 | − | 0.866025i | 0.110581 | − | 0.0638442i | ||||
\(185\) | −0.866025 | − | 1.50000i | −0.0636715 | − | 0.110282i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.59808 | − | 1.50000i | −0.189484 | − | 0.109399i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.46410i | 0.251312i | ||||||||
\(191\) | 8.66025 | − | 15.0000i | 0.626634 | − | 1.08536i | −0.361588 | − | 0.932338i | \(-0.617765\pi\) |
0.988222 | − | 0.153024i | \(-0.0489012\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.00000 | + | 5.19615i | −0.647834 | + | 0.374027i | −0.787626 | − | 0.616154i | \(-0.788690\pi\) |
0.139792 | + | 0.990181i | \(0.455357\pi\) | |||||||
\(194\) | −3.46410 | −0.248708 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | −5.19615 | + | 3.00000i | −0.370211 | + | 0.213741i | −0.673550 | − | 0.739141i | \(-0.735232\pi\) |
0.303340 | + | 0.952882i | \(0.401898\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | + | 13.8564i | −0.567105 | + | 0.982255i | 0.429745 | + | 0.902950i | \(0.358603\pi\) |
−0.996850 | + | 0.0793045i | \(0.974730\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.0000 | + | 6.92820i | 0.844317 | + | 0.487467i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | − | 5.19615i | −0.209529 | − | 0.362915i | ||||
\(206\) | 12.1244 | − | 7.00000i | 0.844744 | − | 0.487713i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.50000 | + | 2.59808i | −0.173344 | + | 0.180144i | ||||
\(209\) | −10.3923 | −0.718851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.00000 | + | 1.73205i | 0.0688428 | + | 0.119239i | 0.898392 | − | 0.439194i | \(-0.144736\pi\) |
−0.829549 | + | 0.558433i | \(0.811403\pi\) | |||||||
\(212\) | −3.46410 | + | 6.00000i | −0.237915 | + | 0.412082i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | + | 3.46410i | 0.410152 | + | 0.236801i | ||||
\(215\) | −0.866025 | − | 0.500000i | −0.0590624 | − | 0.0340997i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.00000 | −0.202260 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.0000 | + | 8.66025i | −1.00447 | + | 0.579934i | −0.909569 | − | 0.415553i | \(-0.863588\pi\) |
−0.0949052 | + | 0.995486i | \(0.530255\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.1244i | 0.806500i | ||||||||
\(227\) | 15.5885 | + | 9.00000i | 1.03464 | + | 0.597351i | 0.918311 | − | 0.395860i | \(-0.129553\pi\) |
0.116331 | + | 0.993210i | \(0.462887\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.92820i | 0.457829i | 0.973447 | + | 0.228914i | \(0.0735176\pi\) | ||||
−0.973447 | + | 0.228914i | \(0.926482\pi\) | |||||||
\(230\) | 0.866025 | − | 1.50000i | 0.0571040 | − | 0.0989071i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.50000 | − | 0.866025i | 0.0984798 | − | 0.0568574i | ||||
\(233\) | −19.0526 | −1.24817 | −0.624087 | − | 0.781355i | \(-0.714529\pi\) | ||||
−0.624087 | + | 0.781355i | \(0.714529\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00000 | −0.195698 | ||||||||
\(236\) | 7.79423 | − | 4.50000i | 0.507361 | − | 0.292925i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000i | 0.388108i | 0.980991 | + | 0.194054i | \(0.0621637\pi\) | ||||
−0.980991 | + | 0.194054i | \(0.937836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.5000 | + | 7.79423i | 0.869611 | + | 0.502070i | 0.867219 | − | 0.497927i | \(-0.165905\pi\) |
0.00239235 | + | 0.999997i | \(0.499238\pi\) | |||||||
\(242\) | 2.00000i | 0.128565i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.00000 | − | 6.92820i | −0.256074 | − | 0.443533i | ||||
\(245\) | −6.06218 | + | 3.50000i | −0.387298 | + | 0.223607i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.00000 | + | 12.1244i | −0.190885 | + | 0.771454i | ||||
\(248\) | −5.19615 | −0.329956 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | 2.59808 | − | 4.50000i | 0.163989 | − | 0.284037i | −0.772307 | − | 0.635250i | \(-0.780897\pi\) |
0.936296 | + | 0.351212i | \(0.114230\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.50000 | + | 2.59808i | 0.282913 | + | 0.163340i | ||||
\(254\) | 1.73205 | + | 1.00000i | 0.108679 | + | 0.0627456i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 4.33013 | + | 7.50000i | 0.270106 | + | 0.467837i | 0.968889 | − | 0.247497i | \(-0.0796080\pi\) |
−0.698783 | + | 0.715334i | \(0.746275\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.866025 | + | 3.50000i | −0.0537086 | + | 0.217061i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.5000 | − | 6.06218i | 0.648692 | − | 0.374523i | ||||
\(263\) | −7.79423 | − | 13.5000i | −0.480613 | − | 0.832446i | 0.519140 | − | 0.854689i | \(-0.326252\pi\) |
−0.999753 | + | 0.0222436i | \(0.992919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.92820i | 0.425596i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.46410i | 0.211604i | ||||||||
\(269\) | 13.8564 | − | 24.0000i | 0.844840 | − | 1.46331i | −0.0409201 | − | 0.999162i | \(-0.513029\pi\) |
0.885760 | − | 0.464143i | \(-0.153638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.5000 | − | 6.06218i | 0.637830 | − | 0.368251i | −0.145948 | − | 0.989292i | \(-0.546623\pi\) |
0.783778 | + | 0.621041i | \(0.213290\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.00000 | 0.181237 | ||||||||
\(275\) | −2.59808 | + | 1.50000i | −0.156670 | + | 0.0904534i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.50000 | + | 14.7224i | −0.510716 | + | 0.884585i | 0.489207 | + | 0.872167i | \(0.337286\pi\) |
−0.999923 | + | 0.0124177i | \(0.996047\pi\) | |||||||
\(278\) | − | 10.0000i | − | 0.599760i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.00000i | − | 0.357930i | −0.983855 | − | 0.178965i | \(-0.942725\pi\) | ||
0.983855 | − | 0.178965i | \(-0.0572749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.50000 | + | 4.33013i | 0.148610 | + | 0.257399i | 0.930714 | − | 0.365748i | \(-0.119187\pi\) |
−0.782104 | + | 0.623148i | \(0.785854\pi\) | |||||||
\(284\) | 5.19615 | − | 3.00000i | 0.308335 | − | 0.178017i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.5000 | − | 2.59808i | −0.620878 | − | 0.153627i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0.866025 | − | 1.50000i | 0.0508548 | − | 0.0880830i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.5885 | − | 9.00000i | −0.910687 | − | 0.525786i | −0.0300351 | − | 0.999549i | \(-0.509562\pi\) |
−0.880652 | + | 0.473763i | \(0.842895\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.50000 | − | 7.79423i | 0.262000 | − | 0.453798i | ||||
\(296\) | −0.866025 | − | 1.50000i | −0.0503367 | − | 0.0871857i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | 0.173785 | ||||||||
\(299\) | 4.33013 | − | 4.50000i | 0.250418 | − | 0.260242i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.73205 | + | 3.00000i | 0.0996683 | + | 0.172631i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.46410i | 0.198680i | ||||||||
\(305\) | −6.92820 | − | 4.00000i | −0.396708 | − | 0.229039i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.1769i | 1.77936i | 0.456584 | + | 0.889680i | \(0.349073\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.50000 | + | 2.59808i | −0.255583 | + | 0.147561i | ||||
\(311\) | 24.2487 | 1.37502 | 0.687509 | − | 0.726176i | \(-0.258704\pi\) | ||||
0.687509 | + | 0.726176i | \(0.258704\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.00000 | −0.452187 | −0.226093 | − | 0.974106i | \(-0.572595\pi\) | ||||
−0.226093 | + | 0.974106i | \(0.572595\pi\) | |||||||
\(314\) | −6.06218 | + | 3.50000i | −0.342108 | + | 0.197516i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.50000 | + | 9.52628i | −0.309399 | + | 0.535895i | ||||
\(317\) | − | 6.00000i | − | 0.336994i | −0.985702 | − | 0.168497i | \(-0.946109\pi\) | ||
0.985702 | − | 0.168497i | \(-0.0538913\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.50000 | + | 2.59808i | 0.251952 | + | 0.145464i | ||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | + | 3.46410i | 0.0554700 | + | 0.192154i | ||||
\(326\) | 22.5167 | 1.24708 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.00000 | − | 5.19615i | −0.165647 | − | 0.286910i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | 5.19615 | + | 3.00000i | 0.285176 | + | 0.164646i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.5000 | − | 18.1865i | 0.574534 | − | 0.995123i | ||||
\(335\) | 1.73205 | + | 3.00000i | 0.0946320 | + | 0.163908i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.00000 | 0.217894 | 0.108947 | − | 0.994048i | \(-0.465252\pi\) | ||||
0.108947 | + | 0.994048i | \(0.465252\pi\) | |||||||
\(338\) | −6.06218 | + | 11.5000i | −0.329739 | + | 0.625518i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.79423 | − | 13.5000i | −0.422081 | − | 0.731066i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.866025 | − | 0.500000i | −0.0466930 | − | 0.0269582i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.7846i | 1.11739i | ||||||||
\(347\) | 8.66025 | − | 15.0000i | 0.464907 | − | 0.805242i | −0.534291 | − | 0.845301i | \(-0.679421\pi\) |
0.999197 | + | 0.0400587i | \(0.0127545\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.0000 | + | 15.5885i | −1.44528 | + | 0.834431i | −0.998195 | − | 0.0600619i | \(-0.980870\pi\) |
−0.447082 | + | 0.894493i | \(0.647537\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | −15.5885 | + | 9.00000i | −0.829690 | + | 0.479022i | −0.853746 | − | 0.520689i | \(-0.825675\pi\) |
0.0240566 | + | 0.999711i | \(0.492342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.00000 | − | 5.19615i | 0.159223 | − | 0.275783i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.50000 | + | 4.33013i | 0.396387 | + | 0.228854i | ||||
\(359\) | − | 24.0000i | − | 1.26667i | −0.773877 | − | 0.633336i | \(-0.781685\pi\) | ||
0.773877 | − | 0.633336i | \(-0.218315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.50000 | − | 6.06218i | −0.184211 | − | 0.319062i | ||||
\(362\) | 17.3205 | − | 10.0000i | 0.910346 | − | 0.525588i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.0000 | − | 22.5167i | −0.678594 | − | 1.17536i | −0.975404 | − | 0.220423i | \(-0.929256\pi\) |
0.296810 | − | 0.954937i | \(-0.404077\pi\) | |||||||
\(368\) | 0.866025 | − | 1.50000i | 0.0451447 | − | 0.0781929i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.50000 | − | 0.866025i | −0.0779813 | − | 0.0450225i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.50000 | − | 14.7224i | 0.440113 | − | 0.762299i | −0.557584 | − | 0.830120i | \(-0.688272\pi\) |
0.997697 | + | 0.0678218i | \(0.0216049\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | −0.154713 | ||||||||
\(377\) | 4.33013 | − | 4.50000i | 0.223013 | − | 0.231762i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000 | − | 6.92820i | 0.616399 | − | 0.355878i | −0.159067 | − | 0.987268i | \(-0.550849\pi\) |
0.775466 | + | 0.631390i | \(0.217515\pi\) | |||||||
\(380\) | 1.73205 | + | 3.00000i | 0.0888523 | + | 0.153897i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 17.3205i | − | 0.886194i | ||||||
\(383\) | 7.79423 | + | 4.50000i | 0.398266 | + | 0.229939i | 0.685736 | − | 0.727851i | \(-0.259481\pi\) |
−0.287469 | + | 0.957790i | \(0.592814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.19615 | + | 9.00000i | −0.264477 | + | 0.458088i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.00000 | + | 1.73205i | −0.152302 | + | 0.0879316i | ||||
\(389\) | −29.4449 | −1.49291 | −0.746457 | − | 0.665434i | \(-0.768247\pi\) | ||||
−0.746457 | + | 0.665434i | \(0.768247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −6.06218 | + | 3.50000i | −0.306186 | + | 0.176777i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.00000 | + | 5.19615i | −0.151138 | + | 0.261778i | ||||
\(395\) | 11.0000i | 0.553470i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.5000 | + | 14.7224i | 1.27981 | + | 0.738898i | 0.976813 | − | 0.214094i | \(-0.0686800\pi\) |
0.302995 | + | 0.952992i | \(0.402013\pi\) | |||||||
\(398\) | 16.0000i | 0.802008i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.0000 | + | 5.19615i | −0.896644 | + | 0.258839i | ||||
\(404\) | 13.8564 | 0.689382 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.59808 | − | 4.50000i | 0.128782 | − | 0.223057i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.0000 | + | 17.3205i | 1.48340 | + | 0.856444i | 0.999822 | − | 0.0188549i | \(-0.00600205\pi\) |
0.483582 | + | 0.875299i | \(0.339335\pi\) | |||||||
\(410\) | −5.19615 | − | 3.00000i | −0.256620 | − | 0.148159i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.00000 | − | 12.1244i | 0.344865 | − | 0.597324i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | −0.866025 | + | 3.50000i | −0.0424604 | + | 0.171602i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.00000 | + | 5.19615i | −0.440204 | + | 0.254152i | ||||
\(419\) | 8.66025 | + | 15.0000i | 0.423081 | + | 0.732798i | 0.996239 | − | 0.0866469i | \(-0.0276152\pi\) |
−0.573158 | + | 0.819445i | \(0.694282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 38.1051i | − | 1.85713i | −0.371170 | − | 0.928565i | \(-0.621043\pi\) | ||
0.371170 | − | 0.928565i | \(-0.378957\pi\) | |||||||
\(422\) | 1.73205 | + | 1.00000i | 0.0843149 | + | 0.0486792i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.92820i | 0.336463i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.92820 | 0.334887 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.00000 | −0.0482243 | ||||||||
\(431\) | 15.5885 | − | 9.00000i | 0.750870 | − | 0.433515i | −0.0751385 | − | 0.997173i | \(-0.523940\pi\) |
0.826008 | + | 0.563658i | \(0.190607\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.00000 | − | 12.1244i | 0.336399 | − | 0.582659i | −0.647354 | − | 0.762190i | \(-0.724124\pi\) |
0.983752 | + | 0.179530i | \(0.0574578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.00000i | − | 0.287019i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0000 | − | 27.7128i | −0.763638 | − | 1.32266i | −0.940963 | − | 0.338508i | \(-0.890078\pi\) |
0.177325 | − | 0.984152i | \(-0.443256\pi\) | |||||||
\(440\) | −2.59808 | + | 1.50000i | −0.123858 | + | 0.0715097i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.1769 | −1.48126 | −0.740630 | − | 0.671913i | \(-0.765473\pi\) | ||||
−0.740630 | + | 0.671913i | \(0.765473\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.66025 | + | 15.0000i | −0.410075 | + | 0.710271i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.3923 | − | 6.00000i | −0.490443 | − | 0.283158i | 0.234315 | − | 0.972161i | \(-0.424715\pi\) |
−0.724758 | + | 0.689003i | \(0.758049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | − | 15.5885i | 0.423793 | − | 0.734032i | ||||
\(452\) | 6.06218 | + | 10.5000i | 0.285141 | + | 0.493878i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.0000 | 0.844782 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.0000 | + | 12.1244i | −0.982339 | + | 0.567153i | −0.902975 | − | 0.429692i | \(-0.858622\pi\) |
−0.0793632 | + | 0.996846i | \(0.525289\pi\) | |||||||
\(458\) | 3.46410 | + | 6.00000i | 0.161867 | + | 0.280362i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 1.73205i | − | 0.0807573i | ||||||
\(461\) | 18.1865 | + | 10.5000i | 0.847031 | + | 0.489034i | 0.859648 | − | 0.510887i | \(-0.170683\pi\) |
−0.0126168 | + | 0.999920i | \(0.504016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0.866025 | − | 1.50000i | 0.0402042 | − | 0.0696358i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.5000 | + | 9.52628i | −0.764348 | + | 0.441296i | ||||
\(467\) | −13.8564 | −0.641198 | −0.320599 | − | 0.947215i | \(-0.603884\pi\) | ||||
−0.320599 | + | 0.947215i | \(0.603884\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.59808 | + | 1.50000i | −0.119840 | + | 0.0691898i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.50000 | − | 7.79423i | 0.207129 | − | 0.358758i | ||||
\(473\) | − | 3.00000i | − | 0.137940i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.00000 | + | 1.73205i | 0.137649 | + | 0.0794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.00000 | + | 5.19615i | 0.137217 | + | 0.237666i | ||||
\(479\) | 5.19615 | − | 3.00000i | 0.237418 | − | 0.137073i | −0.376571 | − | 0.926388i | \(-0.622897\pi\) |
0.613990 | + | 0.789314i | \(0.289564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.50000 | − | 4.33013i | −0.205182 | − | 0.197437i | ||||
\(482\) | 15.5885 | 0.710035 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | −1.73205 | + | 3.00000i | −0.0786484 | + | 0.136223i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.00000 | − | 5.19615i | −0.407829 | − | 0.235460i | 0.282028 | − | 0.959406i | \(-0.408993\pi\) |
−0.689856 | + | 0.723946i | \(0.742326\pi\) | |||||||
\(488\) | −6.92820 | − | 4.00000i | −0.313625 | − | 0.181071i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.50000 | + | 6.06218i | −0.158114 | + | 0.273861i | ||||
\(491\) | 8.66025 | + | 15.0000i | 0.390832 | + | 0.676941i | 0.992559 | − | 0.121761i | \(-0.0388541\pi\) |
−0.601728 | + | 0.798701i | \(0.705521\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 3.46410 | + | 12.0000i | 0.155857 | + | 0.539906i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.50000 | + | 2.59808i | −0.202056 | + | 0.116657i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.3205i | − | 0.775372i | −0.921791 | − | 0.387686i | \(-0.873274\pi\) | ||
0.921791 | − | 0.387686i | \(-0.126726\pi\) | |||||||
\(500\) | 0.866025 | + | 0.500000i | 0.0387298 | + | 0.0223607i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 5.19615i | − | 0.231916i | ||||||
\(503\) | 1.73205 | − | 3.00000i | 0.0772283 | − | 0.133763i | −0.824825 | − | 0.565388i | \(-0.808726\pi\) |
0.902053 | + | 0.431625i | \(0.142060\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | − | 6.92820i | 0.533993 | − | 0.308301i | ||||
\(506\) | 5.19615 | 0.230997 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.00000 | 0.0887357 | ||||||||
\(509\) | −18.1865 | + | 10.5000i | −0.806104 | + | 0.465404i | −0.845601 | − | 0.533815i | \(-0.820758\pi\) |
0.0394971 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.50000 | + | 4.33013i | 0.330811 | + | 0.190994i | ||||
\(515\) | − | 14.0000i | − | 0.616914i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.50000 | − | 7.79423i | −0.197910 | − | 0.342790i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.00000 | + | 3.46410i | 0.0438529 | + | 0.151911i | ||||
\(521\) | −38.1051 | −1.66942 | −0.834708 | − | 0.550693i | \(-0.814363\pi\) | ||||
−0.834708 | + | 0.550693i | \(0.814363\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.50000 | − | 14.7224i | −0.371679 | − | 0.643767i | 0.618145 | − | 0.786064i | \(-0.287884\pi\) |
−0.989824 | + | 0.142297i | \(0.954551\pi\) | |||||||
\(524\) | 6.06218 | − | 10.5000i | 0.264827 | − | 0.458695i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.5000 | − | 7.79423i | −0.588628 | − | 0.339845i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.0000 | − | 17.3205i | 0.434783 | − | 0.753066i | ||||
\(530\) | 3.46410 | + | 6.00000i | 0.150471 | + | 0.260623i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.5885 | − | 15.0000i | −0.675211 | − | 0.649722i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | − | 3.46410i | 0.259403 | − | 0.149766i | ||||
\(536\) | 1.73205 | + | 3.00000i | 0.0748132 | + | 0.129580i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 27.7128i | − | 1.19478i | ||||||
\(539\) | −18.1865 | − | 10.5000i | −0.783349 | − | 0.452267i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 13.8564i | − | 0.595733i | −0.954607 | − | 0.297867i | \(-0.903725\pi\) | ||
0.954607 | − | 0.297867i | \(-0.0962751\pi\) | |||||||
\(542\) | 6.06218 | − | 10.5000i | 0.260393 | − | 0.451014i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 2.59808 | − | 1.50000i | 0.110984 | − | 0.0640768i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.50000 | + | 2.59808i | −0.0639602 | + | 0.110782i | ||||
\(551\) | − | 6.00000i | − | 0.255609i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 17.0000i | 0.722261i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.00000 | − | 8.66025i | −0.212047 | − | 0.367277i | ||||
\(557\) | −25.9808 | + | 15.0000i | −1.10084 | + | 0.635570i | −0.936442 | − | 0.350824i | \(-0.885902\pi\) |
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.50000 | − | 0.866025i | −0.148034 | − | 0.0366290i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.00000 | − | 5.19615i | −0.126547 | − | 0.219186i | ||||
\(563\) | −8.66025 | + | 15.0000i | −0.364986 | + | 0.632175i | −0.988774 | − | 0.149419i | \(-0.952260\pi\) |
0.623788 | + | 0.781594i | \(0.285593\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.5000 | + | 6.06218i | 0.441738 | + | 0.255038i | ||||
\(566\) | 4.33013 | + | 2.50000i | 0.182009 | + | 0.105083i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.00000 | − | 5.19615i | 0.125877 | − | 0.218026i | ||||
\(569\) | 12.1244 | + | 21.0000i | 0.508279 | + | 0.880366i | 0.999954 | + | 0.00958679i | \(0.00305162\pi\) |
−0.491675 | + | 0.870779i | \(0.663615\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.00000 | −0.0836974 | −0.0418487 | − | 0.999124i | \(-0.513325\pi\) | ||||
−0.0418487 | + | 0.999124i | \(0.513325\pi\) | |||||||
\(572\) | −10.3923 | + | 3.00000i | −0.434524 | + | 0.125436i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.866025 | − | 1.50000i | −0.0361158 | − | 0.0625543i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 6.92820i | − | 0.288425i | −0.989547 | − | 0.144212i | \(-0.953935\pi\) | ||
0.989547 | − | 0.144212i | \(-0.0460649\pi\) | |||||||
\(578\) | 14.7224 | + | 8.50000i | 0.612372 | + | 0.353553i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 1.73205i | − | 0.0719195i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0000 | + | 10.3923i | −0.745484 | + | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.00000 | + | 15.5885i | −0.370839 | + | 0.642311i | ||||
\(590\) | − | 9.00000i | − | 0.370524i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.50000 | − | 0.866025i | −0.0616496 | − | 0.0355934i | ||||
\(593\) | 3.00000i | 0.123195i | 0.998101 | + | 0.0615976i | \(0.0196196\pi\) | ||||
−0.998101 | + | 0.0615976i | \(0.980380\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.59808 | − | 1.50000i | 0.106421 | − | 0.0614424i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.50000 | − | 6.06218i | 0.0613396 | − | 0.247901i | ||||
\(599\) | 17.3205 | 0.707697 | 0.353848 | − | 0.935303i | \(-0.384873\pi\) | ||||
0.353848 | + | 0.935303i | \(0.384873\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.5000 | − | 32.0429i | −0.754631 | − | 1.30706i | −0.945558 | − | 0.325455i | \(-0.894483\pi\) |
0.190927 | − | 0.981604i | \(-0.438851\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.00000 | + | 1.73205i | 0.122068 | + | 0.0704761i | ||||
\(605\) | 1.73205 | + | 1.00000i | 0.0704179 | + | 0.0406558i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000 | − | 13.8564i | 0.324710 | − | 0.562414i | −0.656744 | − | 0.754114i | \(-0.728067\pi\) |
0.981454 | + | 0.191700i | \(0.0614000\pi\) | |||||||
\(608\) | 1.73205 | + | 3.00000i | 0.0702439 | + | 0.121666i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.00000 | −0.323911 | ||||||||
\(611\) | −10.3923 | + | 3.00000i | −0.420428 | + | 0.121367i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.5000 | + | 7.79423i | −0.545260 | + | 0.314806i | −0.747208 | − | 0.664590i | \(-0.768606\pi\) |
0.201948 | + | 0.979396i | \(0.435273\pi\) | |||||||
\(614\) | 15.5885 | + | 27.0000i | 0.629099 | + | 1.08963i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.59808 | + | 1.50000i | 0.104595 | + | 0.0603877i | 0.551385 | − | 0.834251i | \(-0.314100\pi\) |
−0.446790 | + | 0.894639i | \(0.647433\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.3923i | − | 0.417702i | −0.977947 | − | 0.208851i | \(-0.933028\pi\) | ||
0.977947 | − | 0.208851i | \(-0.0669724\pi\) | |||||||
\(620\) | −2.59808 | + | 4.50000i | −0.104341 | + | 0.180724i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.0000 | − | 12.1244i | 0.842023 | − | 0.486142i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −6.92820 | + | 4.00000i | −0.276907 | + | 0.159872i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.50000 | + | 6.06218i | −0.139665 | + | 0.241907i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.0000 | + | 19.0526i | 1.31371 | + | 0.758470i | 0.982708 | − | 0.185160i | \(-0.0592804\pi\) |
0.331001 | + | 0.943630i | \(0.392614\pi\) | |||||||
\(632\) | 11.0000i | 0.437557i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.00000 | − | 5.19615i | −0.119145 | − | 0.206366i | ||||
\(635\) | 1.73205 | − | 1.00000i | 0.0687343 | − | 0.0396838i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.5000 | + | 18.1865i | −0.693375 | + | 0.720577i | ||||
\(638\) | 5.19615 | 0.205718 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 3.46410 | − | 6.00000i | 0.136824 | − | 0.236986i | −0.789469 | − | 0.613791i | \(-0.789644\pi\) |
0.926293 | + | 0.376805i | \(0.122977\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.00000 | + | 1.73205i | 0.118308 | + | 0.0683054i | 0.557986 | − | 0.829850i | \(-0.311574\pi\) |
−0.439678 | + | 0.898155i | \(0.644907\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.19615 | + | 9.00000i | 0.204282 | + | 0.353827i | 0.949904 | − | 0.312543i | \(-0.101181\pi\) |
−0.745622 | + | 0.666369i | \(0.767847\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.0000 | 1.05984 | ||||||||
\(650\) | 2.59808 | + | 2.50000i | 0.101905 | + | 0.0980581i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.5000 | − | 11.2583i | 0.763679 | − | 0.440910i | ||||
\(653\) | −5.19615 | − | 9.00000i | −0.203341 | − | 0.352197i | 0.746262 | − | 0.665653i | \(-0.231847\pi\) |
−0.949603 | + | 0.313455i | \(0.898513\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 12.1244i | − | 0.473738i | ||||||
\(656\) | −5.19615 | − | 3.00000i | −0.202876 | − | 0.117130i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.06218 | − | 10.5000i | 0.236149 | − | 0.409022i | −0.723457 | − | 0.690369i | \(-0.757448\pi\) |
0.959606 | + | 0.281347i | \(0.0907813\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.0000 | + | 19.0526i | −1.28355 | + | 0.741059i | −0.977496 | − | 0.210955i | \(-0.932343\pi\) |
−0.306055 | + | 0.952014i | \(0.599009\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.50000 | + | 2.59808i | −0.0580802 | + | 0.100598i | ||||
\(668\) | − | 21.0000i | − | 0.812514i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.00000 | + | 1.73205i | 0.115900 | + | 0.0669150i | ||||
\(671\) | − | 24.0000i | − | 0.926510i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.0000 | − | 38.1051i | −0.848038 | − | 1.46884i | −0.882957 | − | 0.469454i | \(-0.844451\pi\) |
0.0349191 | − | 0.999390i | \(-0.488883\pi\) | |||||||
\(674\) | 3.46410 | − | 2.00000i | 0.133432 | − | 0.0770371i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.500000 | + | 12.9904i | 0.0192308 | + | 0.499630i | ||||
\(677\) | −45.0333 | −1.73077 | −0.865386 | − | 0.501107i | \(-0.832926\pi\) | ||||
−0.865386 | + | 0.501107i | \(0.832926\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13.5000 | − | 7.79423i | −0.516942 | − | 0.298456i | ||||
\(683\) | 31.1769 | + | 18.0000i | 1.19295 | + | 0.688751i | 0.958975 | − | 0.283491i | \(-0.0914927\pi\) |
0.233977 | + | 0.972242i | \(0.424826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.50000 | − | 2.59808i | 0.0573121 | − | 0.0992674i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00000 | −0.0381246 | ||||||||
\(689\) | 6.92820 | + | 24.0000i | 0.263944 | + | 0.914327i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.0000 | − | 12.1244i | 0.798878 | − | 0.461232i | −0.0442009 | − | 0.999023i | \(-0.514074\pi\) |
0.843079 | + | 0.537790i | \(0.180741\pi\) | |||||||
\(692\) | 10.3923 | + | 18.0000i | 0.395056 | + | 0.684257i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 17.3205i | − | 0.657477i | ||||||
\(695\) | −8.66025 | − | 5.00000i | −0.328502 | − | 0.189661i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −15.5885 | + | 27.0000i | −0.590032 | + | 1.02197i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.5167 | 0.850443 | 0.425221 | − | 0.905089i | \(-0.360196\pi\) | ||||
0.425221 | + | 0.905089i | \(0.360196\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | −0.226294 | ||||||||
\(704\) | −2.59808 | + | 1.50000i | −0.0979187 | + | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.00000 | + | 15.5885i | −0.338719 | + | 0.586679i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.0000 | + | 10.3923i | 0.676004 | + | 0.390291i | 0.798348 | − | 0.602197i | \(-0.205708\pi\) |
−0.122344 | + | 0.992488i | \(0.539041\pi\) | |||||||
\(710\) | − | 6.00000i | − | 0.225176i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.79423 | − | 4.50000i | 0.291896 | − | 0.168526i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.50000 | + | 7.79423i | −0.280484 | + | 0.291488i | ||||
\(716\) | 8.66025 | 0.323649 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.0000 | − | 20.7846i | −0.447836 | − | 0.775675i | ||||
\(719\) | 13.8564 | − | 24.0000i | 0.516757 | − | 0.895049i | −0.483054 | − | 0.875591i | \(-0.660472\pi\) |
0.999811 | − | 0.0194584i | \(-0.00619418\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.06218 | − | 3.50000i | −0.225611 | − | 0.130257i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.0000 | − | 17.3205i | 0.371647 | − | 0.643712i | ||||
\(725\) | −0.866025 | − | 1.50000i | −0.0321634 | − | 0.0557086i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 27.7128i | − | 1.02360i | −0.859106 | − | 0.511798i | \(-0.828980\pi\) | ||
0.859106 | − | 0.511798i | \(-0.171020\pi\) | |||||||
\(734\) | −22.5167 | − | 13.0000i | −0.831105 | − | 0.479839i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 1.73205i | − | 0.0638442i | ||||||
\(737\) | −5.19615 | + | 9.00000i | −0.191403 | + | 0.331519i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.00000 | + | 5.19615i | −0.331070 | + | 0.191144i | −0.656316 | − | 0.754486i | \(-0.727886\pi\) |
0.325246 | + | 0.945629i | \(0.394553\pi\) | |||||||
\(740\) | −1.73205 | −0.0636715 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.9711 | − | 22.5000i | 1.42971 | − | 0.825445i | 0.432615 | − | 0.901579i | \(-0.357591\pi\) |
0.997098 | + | 0.0761338i | \(0.0242576\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.50000 | − | 2.59808i | 0.0549557 | − | 0.0951861i | ||||
\(746\) | − | 17.0000i | − | 0.622414i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.50000 | − | 4.33013i | −0.0912263 | − | 0.158009i | 0.816801 | − | 0.576919i | \(-0.195745\pi\) |
−0.908027 | + | 0.418911i | \(0.862412\pi\) | |||||||
\(752\) | −2.59808 | + | 1.50000i | −0.0947421 | + | 0.0546994i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.50000 | − | 6.06218i | 0.0546268 | − | 0.220771i | ||||
\(755\) | 3.46410 | 0.126072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.0000 | − | 39.8372i | −0.835949 | − | 1.44791i | −0.893255 | − | 0.449550i | \(-0.851584\pi\) |
0.0573060 | − | 0.998357i | \(-0.481749\pi\) | |||||||
\(758\) | 6.92820 | − | 12.0000i | 0.251644 | − | 0.435860i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.00000 | + | 1.73205i | 0.108821 | + | 0.0628281i | ||||
\(761\) | −31.1769 | − | 18.0000i | −1.13016 | − | 0.652499i | −0.186187 | − | 0.982514i | \(-0.559613\pi\) |
−0.943976 | + | 0.330015i | \(0.892946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.66025 | − | 15.0000i | −0.313317 | − | 0.542681i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.00000 | 0.325183 | ||||||||
\(767\) | 7.79423 | − | 31.5000i | 0.281433 | − | 1.13740i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.5000 | + | 7.79423i | −0.486822 | + | 0.281067i | −0.723255 | − | 0.690581i | \(-0.757355\pi\) |
0.236433 | + | 0.971648i | \(0.424022\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.3923i | 0.374027i | ||||||||
\(773\) | 20.7846 | + | 12.0000i | 0.747570 | + | 0.431610i | 0.824815 | − | 0.565402i | \(-0.191279\pi\) |
−0.0772449 | + | 0.997012i | \(0.524612\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.19615i | 0.186651i | ||||||||
\(776\) | −1.73205 | + | 3.00000i | −0.0621770 | + | 0.107694i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.5000 | + | 14.7224i | −0.914219 | + | 0.527825i | ||||
\(779\) | −20.7846 | −0.744686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | 0.644091 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.50000 | + | 6.06218i | −0.125000 | + | 0.216506i | ||||
\(785\) | 7.00000i | 0.249841i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.5000 | + | 16.4545i | 1.01592 | + | 0.586539i | 0.912918 | − | 0.408143i | \(-0.133823\pi\) |
0.102997 | + | 0.994682i | \(0.467157\pi\) | |||||||
\(788\) | 6.00000i | 0.213741i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.50000 | + | 9.52628i | 0.195681 | + | 0.338930i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.0000 | − | 6.92820i | −0.994309 | − | 0.246028i | ||||
\(794\) | 29.4449 | 1.04496 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00000 | + | 13.8564i | 0.283552 | + | 0.491127i | ||||
\(797\) | 24.2487 | − | 42.0000i | 0.858933 | − | 1.48772i | −0.0140139 | − | 0.999902i | \(-0.504461\pi\) |
0.872947 | − | 0.487815i | \(-0.162206\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.9904 | + | 13.5000i | −0.457567 | + | 0.475517i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.0000 | − | 6.92820i | 0.422159 | − | 0.243733i | ||||
\(809\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.7128i | − | 0.973128i | −0.873645 | − | 0.486564i | \(-0.838250\pi\) | ||
0.873645 | − | 0.486564i | \(-0.161750\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 5.19615i | − | 0.182125i | ||||||
\(815\) | 11.2583 | − | 19.5000i | 0.394362 | − | 0.683055i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.00000 | + | 1.73205i | −0.104957 | + | 0.0605968i | ||||
\(818\) | 34.6410 | 1.21119 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.00000 | −0.209529 | ||||||||
\(821\) | −12.9904 | + | 7.50000i | −0.453367 | + | 0.261752i | −0.709251 | − | 0.704956i | \(-0.750967\pi\) |
0.255884 | + | 0.966708i | \(0.417634\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.0000 | + | 38.1051i | −0.766872 | + | 1.32826i | 0.172379 | + | 0.985031i | \(0.444854\pi\) |
−0.939251 | + | 0.343230i | \(0.888479\pi\) | |||||||
\(824\) | − | 14.0000i | − | 0.487713i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000i | 1.25184i | 0.779886 | + | 0.625921i | \(0.215277\pi\) | ||||
−0.779886 | + | 0.625921i | \(0.784723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.0000 | + | 27.7128i | 0.555703 | + | 0.962506i | 0.997848 | + | 0.0655624i | \(0.0208842\pi\) |
−0.442145 | + | 0.896943i | \(0.645783\pi\) | |||||||
\(830\) | 5.19615 | − | 3.00000i | 0.180361 | − | 0.104132i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000 | + | 3.46410i | 0.0346688 | + | 0.120096i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.5000 | − | 18.1865i | −0.363367 | − | 0.629371i | ||||
\(836\) | −5.19615 | + | 9.00000i | −0.179713 | + | 0.311272i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.0000 | + | 8.66025i | 0.518166 | + | 0.299164i | ||||
\(839\) | 15.5885 | + | 9.00000i | 0.538173 | + | 0.310715i | 0.744338 | − | 0.667803i | \(-0.232765\pi\) |
−0.206165 | + | 0.978517i | \(0.566098\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0000 | − | 22.5167i | 0.448276 | − | 0.776437i | ||||
\(842\) | −19.0526 | − | 33.0000i | −0.656595 | − | 1.13726i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.00000 | 0.0688428 | ||||||||
\(845\) | 6.92820 | + | 11.0000i | 0.238337 | + | 0.378412i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.46410 | + | 6.00000i | 0.118958 | + | 0.206041i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.59808 | + | 1.50000i | 0.0890609 | + | 0.0514193i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.73205i | − | 0.0593043i | −0.999560 | − | 0.0296521i | \(-0.990560\pi\) | ||
0.999560 | − | 0.0296521i | \(-0.00943995\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.00000 | − | 3.46410i | 0.205076 | − | 0.118401i | ||||
\(857\) | −22.5167 | −0.769154 | −0.384577 | − | 0.923093i | \(-0.625653\pi\) | ||||
−0.384577 | + | 0.923093i | \(0.625653\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.0000 | 0.545913 | 0.272956 | − | 0.962026i | \(-0.411998\pi\) | ||||
0.272956 | + | 0.962026i | \(0.411998\pi\) | |||||||
\(860\) | −0.866025 | + | 0.500000i | −0.0295312 | + | 0.0170499i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.00000 | − | 15.5885i | 0.306541 | − | 0.530945i | ||||
\(863\) | 3.00000i | 0.102121i | 0.998696 | + | 0.0510606i | \(0.0162602\pi\) | ||||
−0.998696 | + | 0.0510606i | \(0.983740\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.0000 | + | 10.3923i | 0.612018 | + | 0.353349i | ||||
\(866\) | − | 14.0000i | − | 0.475739i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.5788 | + | 16.5000i | −0.969471 | + | 0.559724i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.00000 | + | 8.66025i | 0.304953 | + | 0.293442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.00000 | − | 5.19615i | −0.101477 | − | 0.175762i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.50000 | + | 0.866025i | 0.0506514 | + | 0.0292436i | 0.525112 | − | 0.851033i | \(-0.324023\pi\) |
−0.474460 | + | 0.880277i | \(0.657357\pi\) | |||||||
\(878\) | −27.7128 | − | 16.0000i | −0.935262 | − | 0.539974i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.50000 | + | 2.59808i | −0.0505650 | + | 0.0875811i | ||||
\(881\) | 6.92820 | + | 12.0000i | 0.233417 | + | 0.404290i | 0.958811 | − | 0.284043i | \(-0.0916759\pi\) |
−0.725394 | + | 0.688333i | \(0.758343\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.0000 | 0.841317 | 0.420658 | − | 0.907219i | \(-0.361799\pi\) | ||||
0.420658 | + | 0.907219i | \(0.361799\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.0000 | + | 15.5885i | −0.907083 | + | 0.523704i | ||||
\(887\) | −18.1865 | − | 31.5000i | −0.610644 | − | 1.05767i | −0.991132 | − | 0.132881i | \(-0.957577\pi\) |
0.380488 | − | 0.924786i | \(-0.375756\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.3205i | 0.579934i | ||||||||
\(893\) | −5.19615 | + | 9.00000i | −0.173883 | + | 0.301174i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.50000 | − | 4.33013i | 0.250697 | − | 0.144740i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.0000 | −0.400445 | ||||||||
\(899\) | 7.79423 | − | 4.50000i | 0.259952 | − | 0.150083i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | − | 18.0000i | − | 0.599334i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.5000 | + | 6.06218i | 0.349225 | + | 0.201625i | ||||
\(905\) | − | 20.0000i | − | 0.664822i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.50000 | + | 14.7224i | 0.282238 | + | 0.488850i | 0.971936 | − | 0.235247i | \(-0.0755899\pi\) |
−0.689698 | + | 0.724097i | \(0.742257\pi\) | |||||||
\(908\) | 15.5885 | − | 9.00000i | 0.517321 | − | 0.298675i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.0333 | −1.49202 | −0.746010 | − | 0.665934i | \(-0.768033\pi\) | ||||
−0.746010 | + | 0.665934i | \(0.768033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.00000 | + | 15.5885i | 0.297857 | + | 0.515903i | ||||
\(914\) | −12.1244 | + | 21.0000i | −0.401038 | + | 0.694618i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.00000 | + | 3.46410i | 0.198246 | + | 0.114457i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000 | − | 6.92820i | 0.131948 | − | 0.228540i | −0.792480 | − | 0.609898i | \(-0.791210\pi\) |
0.924427 | + | 0.381358i | \(0.124544\pi\) | |||||||
\(920\) | −0.866025 | − | 1.50000i | −0.0285520 | − | 0.0494535i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 21.0000 | 0.691598 | ||||||||
\(923\) | 5.19615 | − | 21.0000i | 0.171033 | − | 0.691223i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.50000 | + | 0.866025i | −0.0493197 | + | 0.0284747i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 1.73205i | − | 0.0568574i | ||||||
\(929\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.2487i | 0.794719i | ||||||||
\(932\) | −9.52628 | + | 16.5000i | −0.312044 | + | 0.540475i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.0000 | + | 6.92820i | −0.392652 | + | 0.226698i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.50000 | + | 2.59808i | −0.0489246 | + | 0.0847399i | ||||
\(941\) | 18.0000i | 0.586783i | 0.955992 | + | 0.293392i | \(0.0947840\pi\) | ||||
−0.955992 | + | 0.293392i | \(0.905216\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.00000 | + | 5.19615i | 0.293080 | + | 0.169210i | ||||
\(944\) | − | 9.00000i | − | 0.292925i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.50000 | − | 2.59808i | −0.0487692 | − | 0.0844707i | ||||
\(947\) | −5.19615 | + | 3.00000i | −0.168852 | + | 0.0974869i | −0.582045 | − | 0.813157i | \(-0.697747\pi\) |
0.413192 | + | 0.910644i | \(0.364414\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.46410 | 0.112390 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.1865 | − | 31.5000i | 0.589120 | − | 1.02039i | −0.405228 | − | 0.914215i | \(-0.632808\pi\) |
0.994348 | − | 0.106170i | \(-0.0338587\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.0000 | − | 8.66025i | −0.485389 | − | 0.280239i | ||||
\(956\) | 5.19615 | + | 3.00000i | 0.168056 | + | 0.0970269i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.00000 | − | 5.19615i | 0.0969256 | − | 0.167880i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.00000 | 0.129032 | ||||||||
\(962\) | −6.06218 | − | 1.50000i | −0.195452 | − | 0.0483619i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.5000 | − | 7.79423i | 0.434806 | − | 0.251035i | ||||
\(965\) | 5.19615 | + | 9.00000i | 0.167270 | + | 0.289720i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.2487i | − | 0.779786i | −0.920860 | − | 0.389893i | \(-0.872512\pi\) | ||
0.920860 | − | 0.389893i | \(-0.127488\pi\) | |||||||
\(968\) | 1.73205 | + | 1.00000i | 0.0556702 | + | 0.0321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.46410i | 0.111226i | ||||||||
\(971\) | −25.9808 | + | 45.0000i | −0.833762 | + | 1.44412i | 0.0612718 | + | 0.998121i | \(0.480484\pi\) |
−0.895034 | + | 0.445998i | \(0.852849\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.3923 | −0.332991 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | 28.5788 | − | 16.5000i | 0.914318 | − | 0.527882i | 0.0325001 | − | 0.999472i | \(-0.489653\pi\) |
0.881818 | + | 0.471590i | \(0.156320\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 7.00000i | 0.223607i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.0000 | + | 8.66025i | 0.478669 | + | 0.276360i | ||||
\(983\) | 9.00000i | 0.287055i | 0.989646 | + | 0.143528i | \(0.0458446\pi\) | ||||
−0.989646 | + | 0.143528i | \(0.954155\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.00000 | + | 5.19615i | 0.0955879 | + | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.00000 | + | 8.66025i | 0.286328 | + | 0.275519i | ||||
\(989\) | 1.73205 | 0.0550760 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.50000 | + | 6.06218i | 0.111181 | + | 0.192571i | 0.916247 | − | 0.400614i | \(-0.131203\pi\) |
−0.805066 | + | 0.593186i | \(0.797870\pi\) | |||||||
\(992\) | −2.59808 | + | 4.50000i | −0.0824890 | + | 0.142875i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.8564 | + | 8.00000i | 0.439278 | + | 0.253617i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.0000 | + | 22.5167i | −0.411714 | + | 0.713110i | −0.995077 | − | 0.0991016i | \(-0.968403\pi\) |
0.583363 | + | 0.812211i | \(0.301736\pi\) | |||||||
\(998\) | −8.66025 | − | 15.0000i | −0.274136 | − | 0.474817i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1170.2.bs.b.361.2 | yes | 4 | |
3.2 | odd | 2 | inner | 1170.2.bs.b.361.1 | ✓ | 4 | |
13.4 | even | 6 | inner | 1170.2.bs.b.901.2 | yes | 4 | |
39.17 | odd | 6 | inner | 1170.2.bs.b.901.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1170.2.bs.b.361.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
1170.2.bs.b.361.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1170.2.bs.b.901.1 | yes | 4 | 39.17 | odd | 6 | inner | |
1170.2.bs.b.901.2 | yes | 4 | 13.4 | even | 6 | inner |