Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2850,2,Mod(799,2850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2850.799");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2850.d (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: | \(22.7573645761\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 799.3 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2850.799 |
Dual form | 2850.2.d.x.799.2 |
$q$-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 \(\left(\mathbb{Z}/2850\mathbb{Z}\right)^\times\).
\(n\) | \(1027\) | \(1351\) | \(1901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | − 0.732051i | − 0.276689i | −0.990384 | − | 0.138345i | \(-0.955822\pi\) | ||||
0.990384 | − | 0.138345i | \(-0.0441781\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.73205 | 1.12526 | 0.562628 | − | 0.826710i | \(-0.309790\pi\) | ||||
0.562628 | + | 0.826710i | \(0.309790\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | − 2.73205i | − 0.757735i | −0.925451 | − | 0.378867i | \(-0.876314\pi\) | ||||
0.925451 | − | 0.378867i | \(-0.123686\pi\) | |||||||
\(14\) | 0.732051 | 0.195649 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.19615i | 1.50279i | 0.659854 | + | 0.751394i | \(0.270618\pi\) | ||||
−0.659854 | + | 0.751394i | \(0.729382\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.732051 | −0.159747 | ||||||||
\(22\) | 3.73205i | 0.795676i | ||||||||
\(23\) | 5.92820i | 1.23612i | 0.786133 | + | 0.618058i | \(0.212080\pi\) | ||||
−0.786133 | + | 0.618058i | \(0.787920\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.73205 | 0.535799 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0.732051i | 0.138345i | ||||||||
\(29\) | 1.73205 | 0.321634 | 0.160817 | − | 0.986984i | \(-0.448587\pi\) | ||||
0.160817 | + | 0.986984i | \(0.448587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.46410 | −0.442566 | −0.221283 | − | 0.975210i | \(-0.571024\pi\) | ||||
−0.221283 | + | 0.975210i | \(0.571024\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 3.73205i | − 0.649667i | ||||||||
\(34\) | −6.19615 | −1.06263 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 1.00000i | 0.162221i | ||||||||
\(39\) | −2.73205 | −0.437478 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.92820 | −0.457309 | −0.228654 | − | 0.973508i | \(-0.573433\pi\) | ||||
−0.228654 | + | 0.973508i | \(0.573433\pi\) | |||||||
\(42\) | − 0.732051i | − 0.112958i | ||||||||
\(43\) | − 8.19615i | − 1.24990i | −0.780664 | − | 0.624951i | \(-0.785119\pi\) | ||||
0.780664 | − | 0.624951i | \(-0.214881\pi\) | |||||||
\(44\) | −3.73205 | −0.562628 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.92820 | −0.874066 | ||||||||
\(47\) | − 3.46410i | − 0.505291i | −0.967559 | − | 0.252646i | \(-0.918699\pi\) | ||||
0.967559 | − | 0.252646i | \(-0.0813007\pi\) | |||||||
\(48\) | − 1.00000i | − 0.144338i | ||||||||
\(49\) | 6.46410 | 0.923443 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.19615 | 0.867635 | ||||||||
\(52\) | 2.73205i | 0.378867i | ||||||||
\(53\) | − 1.73205i | − 0.237915i | −0.992899 | − | 0.118958i | \(-0.962045\pi\) | ||||
0.992899 | − | 0.118958i | \(-0.0379553\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.732051 | −0.0978244 | ||||||||
\(57\) | − 1.00000i | − 0.132453i | ||||||||
\(58\) | 1.73205i | 0.227429i | ||||||||
\(59\) | 8.19615 | 1.06705 | 0.533524 | − | 0.845785i | \(-0.320867\pi\) | ||||
0.533524 | + | 0.845785i | \(0.320867\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.6603 | 1.36491 | 0.682453 | − | 0.730930i | \(-0.260913\pi\) | ||||
0.682453 | + | 0.730930i | \(0.260913\pi\) | |||||||
\(62\) | − 2.46410i | − 0.312941i | ||||||||
\(63\) | 0.732051i | 0.0922297i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.73205 | 0.459384 | ||||||||
\(67\) | 0.267949i | 0.0327352i | 0.999866 | + | 0.0163676i | \(0.00521020\pi\) | ||||
−0.999866 | + | 0.0163676i | \(0.994790\pi\) | |||||||
\(68\) | − 6.19615i | − 0.751394i | ||||||||
\(69\) | 5.92820 | 0.713672 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1962 | 1.44742 | 0.723708 | − | 0.690106i | \(-0.242436\pi\) | ||||
0.723708 | + | 0.690106i | \(0.242436\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − 2.46410i | − 0.288401i | −0.989548 | − | 0.144201i | \(-0.953939\pi\) | ||||
0.989548 | − | 0.144201i | \(-0.0460611\pi\) | |||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | − 2.73205i | − 0.311346i | ||||||||
\(78\) | − 2.73205i | − 0.309344i | ||||||||
\(79\) | 5.53590 | 0.622837 | 0.311419 | − | 0.950273i | \(-0.399196\pi\) | ||||
0.311419 | + | 0.950273i | \(0.399196\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 2.92820i | − 0.323366i | ||||||||
\(83\) | 3.73205i | 0.409646i | 0.978799 | + | 0.204823i | \(0.0656618\pi\) | ||||
−0.978799 | + | 0.204823i | \(0.934338\pi\) | |||||||
\(84\) | 0.732051 | 0.0798733 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.19615 | 0.883814 | ||||||||
\(87\) | − 1.73205i | − 0.185695i | ||||||||
\(88\) | − 3.73205i | − 0.397838i | ||||||||
\(89\) | −10.8564 | −1.15078 | −0.575388 | − | 0.817880i | \(-0.695149\pi\) | ||||
−0.575388 | + | 0.817880i | \(0.695149\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | − 5.92820i | − 0.618058i | ||||||||
\(93\) | 2.46410i | 0.255515i | ||||||||
\(94\) | 3.46410 | 0.357295 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 15.1244i | 1.53565i | 0.640662 | + | 0.767823i | \(0.278660\pi\) | ||||
−0.640662 | + | 0.767823i | \(0.721340\pi\) | |||||||
\(98\) | 6.46410i | 0.652973i | ||||||||
\(99\) | −3.73205 | −0.375085 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.26795 | 0.922195 | 0.461098 | − | 0.887349i | \(-0.347456\pi\) | ||||
0.461098 | + | 0.887349i | \(0.347456\pi\) | |||||||
\(102\) | 6.19615i | 0.613511i | ||||||||
\(103\) | − 3.53590i | − 0.348402i | −0.984710 | − | 0.174201i | \(-0.944266\pi\) | ||||
0.984710 | − | 0.174201i | \(-0.0557343\pi\) | |||||||
\(104\) | −2.73205 | −0.267900 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.73205 | 0.168232 | ||||||||
\(107\) | − 2.19615i | − 0.212310i | −0.994350 | − | 0.106155i | \(-0.966146\pi\) | ||||
0.994350 | − | 0.106155i | \(-0.0338540\pi\) | |||||||
\(108\) | − 1.00000i | − 0.0962250i | ||||||||
\(109\) | −2.39230 | −0.229141 | −0.114571 | − | 0.993415i | \(-0.536549\pi\) | ||||
−0.114571 | + | 0.993415i | \(0.536549\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | − 0.732051i | − 0.0691723i | ||||||||
\(113\) | − 13.3923i | − 1.25984i | −0.776659 | − | 0.629921i | \(-0.783087\pi\) | ||||
0.776659 | − | 0.629921i | \(-0.216913\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.73205 | −0.160817 | ||||||||
\(117\) | 2.73205i | 0.252578i | ||||||||
\(118\) | 8.19615i | 0.754517i | ||||||||
\(119\) | 4.53590 | 0.415805 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.92820 | 0.266200 | ||||||||
\(122\) | 10.6603i | 0.965134i | ||||||||
\(123\) | 2.92820i | 0.264027i | ||||||||
\(124\) | 2.46410 | 0.221283 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.732051 | −0.0652163 | ||||||||
\(127\) | 5.00000i | 0.443678i | 0.975083 | + | 0.221839i | \(0.0712060\pi\) | ||||
−0.975083 | + | 0.221839i | \(0.928794\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −8.19615 | −0.721631 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2679 | 0.897115 | 0.448557 | − | 0.893754i | \(-0.351938\pi\) | ||||
0.448557 | + | 0.893754i | \(0.351938\pi\) | |||||||
\(132\) | 3.73205i | 0.324833i | ||||||||
\(133\) | − 0.732051i | − 0.0634769i | ||||||||
\(134\) | −0.267949 | −0.0231473 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.19615 | 0.531316 | ||||||||
\(137\) | 12.3923i | 1.05875i | 0.848389 | + | 0.529373i | \(0.177573\pi\) | ||||
−0.848389 | + | 0.529373i | \(0.822427\pi\) | |||||||
\(138\) | 5.92820i | 0.504642i | ||||||||
\(139\) | 21.1244 | 1.79174 | 0.895872 | − | 0.444312i | \(-0.146552\pi\) | ||||
0.895872 | + | 0.444312i | \(0.146552\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.46410 | −0.291730 | ||||||||
\(142\) | 12.1962i | 1.02348i | ||||||||
\(143\) | − 10.1962i | − 0.852645i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.46410 | 0.203931 | ||||||||
\(147\) | − 6.46410i | − 0.533150i | ||||||||
\(148\) | − 2.00000i | − 0.164399i | ||||||||
\(149\) | 21.8564 | 1.79055 | 0.895273 | − | 0.445517i | \(-0.146980\pi\) | ||||
0.895273 | + | 0.445517i | \(0.146980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4641 | −0.932935 | −0.466468 | − | 0.884538i | \(-0.654474\pi\) | ||||
−0.466468 | + | 0.884538i | \(0.654474\pi\) | |||||||
\(152\) | − 1.00000i | − 0.0811107i | ||||||||
\(153\) | − 6.19615i | − 0.500929i | ||||||||
\(154\) | 2.73205 | 0.220155 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.73205 | 0.218739 | ||||||||
\(157\) | − 13.8564i | − 1.10586i | −0.833227 | − | 0.552931i | \(-0.813509\pi\) | ||||
0.833227 | − | 0.552931i | \(-0.186491\pi\) | |||||||
\(158\) | 5.53590i | 0.440412i | ||||||||
\(159\) | −1.73205 | −0.137361 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.33975 | 0.342020 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − 2.00000i | − 0.156652i | −0.996928 | − | 0.0783260i | \(-0.975042\pi\) | ||||
0.996928 | − | 0.0783260i | \(-0.0249575\pi\) | |||||||
\(164\) | 2.92820 | 0.228654 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.73205 | −0.289663 | ||||||||
\(167\) | 8.92820i | 0.690885i | 0.938440 | + | 0.345443i | \(0.112271\pi\) | ||||
−0.938440 | + | 0.345443i | \(0.887729\pi\) | |||||||
\(168\) | 0.732051i | 0.0564789i | ||||||||
\(169\) | 5.53590 | 0.425838 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 8.19615i | 0.624951i | ||||||||
\(173\) | 13.5885i | 1.03311i | 0.856254 | + | 0.516556i | \(0.172786\pi\) | ||||
−0.856254 | + | 0.516556i | \(0.827214\pi\) | |||||||
\(174\) | 1.73205 | 0.131306 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.73205 | 0.281314 | ||||||||
\(177\) | − 8.19615i | − 0.616061i | ||||||||
\(178\) | − 10.8564i | − 0.813722i | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.5885 | −1.23301 | −0.616505 | − | 0.787351i | \(-0.711452\pi\) | ||||
−0.616505 | + | 0.787351i | \(0.711452\pi\) | |||||||
\(182\) | − 2.00000i | − 0.148250i | ||||||||
\(183\) | − 10.6603i | − 0.788029i | ||||||||
\(184\) | 5.92820 | 0.437033 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.46410 | −0.180677 | ||||||||
\(187\) | 23.1244i | 1.69102i | ||||||||
\(188\) | 3.46410i | 0.252646i | ||||||||
\(189\) | 0.732051 | 0.0532489 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | 0.217072 | 0.108536 | − | 0.994092i | \(-0.465384\pi\) | ||||
0.108536 | + | 0.994092i | \(0.465384\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 22.0526i | 1.58738i | 0.608324 | + | 0.793689i | \(0.291842\pi\) | ||||
−0.608324 | + | 0.793689i | \(0.708158\pi\) | |||||||
\(194\) | −15.1244 | −1.08587 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.46410 | −0.461722 | ||||||||
\(197\) | − 24.5885i | − 1.75186i | −0.482443 | − | 0.875928i | \(-0.660250\pi\) | ||||
0.482443 | − | 0.875928i | \(-0.339750\pi\) | |||||||
\(198\) | − 3.73205i | − 0.265225i | ||||||||
\(199\) | 14.0000 | 0.992434 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.267949 | 0.0188997 | ||||||||
\(202\) | 9.26795i | 0.652091i | ||||||||
\(203\) | − 1.26795i | − 0.0889926i | ||||||||
\(204\) | −6.19615 | −0.433817 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.53590 | 0.246358 | ||||||||
\(207\) | − 5.92820i | − 0.412039i | ||||||||
\(208\) | − 2.73205i | − 0.189434i | ||||||||
\(209\) | 3.73205 | 0.258151 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.2679 | −0.706875 | −0.353437 | − | 0.935458i | \(-0.614987\pi\) | ||||
−0.353437 | + | 0.935458i | \(0.614987\pi\) | |||||||
\(212\) | 1.73205i | 0.118958i | ||||||||
\(213\) | − 12.1962i | − 0.835667i | ||||||||
\(214\) | 2.19615 | 0.150126 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.80385i | 0.122453i | ||||||||
\(218\) | − 2.39230i | − 0.162027i | ||||||||
\(219\) | −2.46410 | −0.166509 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.9282 | 1.13871 | ||||||||
\(222\) | 2.00000i | 0.134231i | ||||||||
\(223\) | − 3.53590i | − 0.236781i | −0.992967 | − | 0.118391i | \(-0.962226\pi\) | ||||
0.992967 | − | 0.118391i | \(-0.0377735\pi\) | |||||||
\(224\) | 0.732051 | 0.0489122 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.3923 | 0.890843 | ||||||||
\(227\) | 6.00000i | 0.398234i | 0.979976 | + | 0.199117i | \(0.0638074\pi\) | ||||
−0.979976 | + | 0.199117i | \(0.936193\pi\) | |||||||
\(228\) | 1.00000i | 0.0662266i | ||||||||
\(229\) | 6.26795 | 0.414198 | 0.207099 | − | 0.978320i | \(-0.433598\pi\) | ||||
0.207099 | + | 0.978320i | \(0.433598\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.73205 | −0.179756 | ||||||||
\(232\) | − 1.73205i | − 0.113715i | ||||||||
\(233\) | − 21.1244i | − 1.38390i | −0.721944 | − | 0.691951i | \(-0.756751\pi\) | ||||
0.721944 | − | 0.691951i | \(-0.243249\pi\) | |||||||
\(234\) | −2.73205 | −0.178600 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.19615 | −0.533524 | ||||||||
\(237\) | − 5.53590i | − 0.359595i | ||||||||
\(238\) | 4.53590i | 0.294019i | ||||||||
\(239\) | 14.0000 | 0.905585 | 0.452792 | − | 0.891616i | \(-0.350428\pi\) | ||||
0.452792 | + | 0.891616i | \(0.350428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30.1962 | −1.94511 | −0.972553 | − | 0.232683i | \(-0.925249\pi\) | ||||
−0.972553 | + | 0.232683i | \(0.925249\pi\) | |||||||
\(242\) | 2.92820i | 0.188232i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −10.6603 | −0.682453 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.92820 | −0.186695 | ||||||||
\(247\) | − 2.73205i | − 0.173836i | ||||||||
\(248\) | 2.46410i | 0.156471i | ||||||||
\(249\) | 3.73205 | 0.236509 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.4641 | 0.723608 | 0.361804 | − | 0.932254i | \(-0.382161\pi\) | ||||
0.361804 | + | 0.932254i | \(0.382161\pi\) | |||||||
\(252\) | − 0.732051i | − 0.0461149i | ||||||||
\(253\) | 22.1244i | 1.39095i | ||||||||
\(254\) | −5.00000 | −0.313728 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 9.00000i | − 0.561405i | −0.959795 | − | 0.280702i | \(-0.909433\pi\) | ||||
0.959795 | − | 0.280702i | \(-0.0905674\pi\) | |||||||
\(258\) | − 8.19615i | − 0.510270i | ||||||||
\(259\) | 1.46410 | 0.0909748 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.73205 | −0.107211 | ||||||||
\(262\) | 10.2679i | 0.634356i | ||||||||
\(263\) | 15.0000i | 0.924940i | 0.886635 | + | 0.462470i | \(0.153037\pi\) | ||||
−0.886635 | + | 0.462470i | \(0.846963\pi\) | |||||||
\(264\) | −3.73205 | −0.229692 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.732051 | 0.0448849 | ||||||||
\(267\) | 10.8564i | 0.664401i | ||||||||
\(268\) | − 0.267949i | − 0.0163676i | ||||||||
\(269\) | 20.5359 | 1.25210 | 0.626048 | − | 0.779785i | \(-0.284671\pi\) | ||||
0.626048 | + | 0.779785i | \(0.284671\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.8038 | −0.960015 | −0.480008 | − | 0.877264i | \(-0.659366\pi\) | ||||
−0.480008 | + | 0.877264i | \(0.659366\pi\) | |||||||
\(272\) | 6.19615i | 0.375697i | ||||||||
\(273\) | 2.00000i | 0.121046i | ||||||||
\(274\) | −12.3923 | −0.748647 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.92820 | −0.356836 | ||||||||
\(277\) | − 11.1962i | − 0.672712i | −0.941735 | − | 0.336356i | \(-0.890806\pi\) | ||||
0.941735 | − | 0.336356i | \(-0.109194\pi\) | |||||||
\(278\) | 21.1244i | 1.26695i | ||||||||
\(279\) | 2.46410 | 0.147522 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.7846 | 1.06094 | 0.530470 | − | 0.847703i | \(-0.322015\pi\) | ||||
0.530470 | + | 0.847703i | \(0.322015\pi\) | |||||||
\(282\) | − 3.46410i | − 0.206284i | ||||||||
\(283\) | 4.00000i | 0.237775i | 0.992908 | + | 0.118888i | \(0.0379328\pi\) | ||||
−0.992908 | + | 0.118888i | \(0.962067\pi\) | |||||||
\(284\) | −12.1962 | −0.723708 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.1962 | 0.602911 | ||||||||
\(287\) | 2.14359i | 0.126532i | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −21.3923 | −1.25837 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.1244 | 0.886605 | ||||||||
\(292\) | 2.46410i | 0.144201i | ||||||||
\(293\) | − 27.7321i | − 1.62012i | −0.586344 | − | 0.810062i | \(-0.699433\pi\) | ||||
0.586344 | − | 0.810062i | \(-0.300567\pi\) | |||||||
\(294\) | 6.46410 | 0.376994 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.00000 | 0.116248 | ||||||||
\(297\) | 3.73205i | 0.216556i | ||||||||
\(298\) | 21.8564i | 1.26611i | ||||||||
\(299\) | 16.1962 | 0.936648 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | −0.345834 | ||||||||
\(302\) | − 11.4641i | − 0.659685i | ||||||||
\(303\) | − 9.26795i | − 0.532430i | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.19615 | 0.354210 | ||||||||
\(307\) | 20.2679i | 1.15675i | 0.815770 | + | 0.578376i | \(0.196314\pi\) | ||||
−0.815770 | + | 0.578376i | \(0.803686\pi\) | |||||||
\(308\) | 2.73205i | 0.155673i | ||||||||
\(309\) | −3.53590 | −0.201150 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.3205 | −1.66261 | −0.831307 | − | 0.555814i | \(-0.812407\pi\) | ||||
−0.831307 | + | 0.555814i | \(0.812407\pi\) | |||||||
\(312\) | 2.73205i | 0.154672i | ||||||||
\(313\) | − 3.92820i | − 0.222035i | −0.993818 | − | 0.111018i | \(-0.964589\pi\) | ||||
0.993818 | − | 0.111018i | \(-0.0354110\pi\) | |||||||
\(314\) | 13.8564 | 0.781962 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.53590 | −0.311419 | ||||||||
\(317\) | 1.73205i | 0.0972817i | 0.998816 | + | 0.0486408i | \(0.0154890\pi\) | ||||
−0.998816 | + | 0.0486408i | \(0.984511\pi\) | |||||||
\(318\) | − 1.73205i | − 0.0971286i | ||||||||
\(319\) | 6.46410 | 0.361920 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.19615 | −0.122577 | ||||||||
\(322\) | 4.33975i | 0.241845i | ||||||||
\(323\) | 6.19615i | 0.344763i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00000 | 0.110770 | ||||||||
\(327\) | 2.39230i | 0.132295i | ||||||||
\(328\) | 2.92820i | 0.161683i | ||||||||
\(329\) | −2.53590 | −0.139809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.2679 | −1.22396 | −0.611979 | − | 0.790874i | \(-0.709626\pi\) | ||||
−0.611979 | + | 0.790874i | \(0.709626\pi\) | |||||||
\(332\) | − 3.73205i | − 0.204823i | ||||||||
\(333\) | − 2.00000i | − 0.109599i | ||||||||
\(334\) | −8.92820 | −0.488530 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.732051 | −0.0399366 | ||||||||
\(337\) | − 10.5359i | − 0.573927i | −0.957942 | − | 0.286963i | \(-0.907354\pi\) | ||||
0.957942 | − | 0.286963i | \(-0.0926458\pi\) | |||||||
\(338\) | 5.53590i | 0.301113i | ||||||||
\(339\) | −13.3923 | −0.727370 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.19615 | −0.498000 | ||||||||
\(342\) | − 1.00000i | − 0.0540738i | ||||||||
\(343\) | − 9.85641i | − 0.532196i | ||||||||
\(344\) | −8.19615 | −0.441907 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.5885 | −0.730520 | ||||||||
\(347\) | 20.7846i | 1.11578i | 0.829916 | + | 0.557888i | \(0.188388\pi\) | ||||
−0.829916 | + | 0.557888i | \(0.811612\pi\) | |||||||
\(348\) | 1.73205i | 0.0928477i | ||||||||
\(349\) | 17.0526 | 0.912803 | 0.456401 | − | 0.889774i | \(-0.349138\pi\) | ||||
0.456401 | + | 0.889774i | \(0.349138\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.73205 | 0.145826 | ||||||||
\(352\) | 3.73205i | 0.198919i | ||||||||
\(353\) | 16.0526i | 0.854391i | 0.904159 | + | 0.427196i | \(0.140498\pi\) | ||||
−0.904159 | + | 0.427196i | \(0.859502\pi\) | |||||||
\(354\) | 8.19615 | 0.435621 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.8564 | 0.575388 | ||||||||
\(357\) | − 4.53590i | − 0.240065i | ||||||||
\(358\) | 12.0000i | 0.634220i | ||||||||
\(359\) | 16.9282 | 0.893436 | 0.446718 | − | 0.894675i | \(-0.352593\pi\) | ||||
0.446718 | + | 0.894675i | \(0.352593\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − 16.5885i | − 0.871870i | ||||||||
\(363\) | − 2.92820i | − 0.153691i | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.6603 | 0.557220 | ||||||||
\(367\) | 13.2679i | 0.692581i | 0.938127 | + | 0.346291i | \(0.112559\pi\) | ||||
−0.938127 | + | 0.346291i | \(0.887441\pi\) | |||||||
\(368\) | 5.92820i | 0.309029i | ||||||||
\(369\) | 2.92820 | 0.152436 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.26795 | −0.0658286 | ||||||||
\(372\) | − 2.46410i | − 0.127758i | ||||||||
\(373\) | − 31.5167i | − 1.63187i | −0.578143 | − | 0.815935i | \(-0.696222\pi\) | ||||
0.578143 | − | 0.815935i | \(-0.303778\pi\) | |||||||
\(374\) | −23.1244 | −1.19573 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.46410 | −0.178647 | ||||||||
\(377\) | − 4.73205i | − 0.243713i | ||||||||
\(378\) | 0.732051i | 0.0376526i | ||||||||
\(379\) | 0.392305 | 0.0201513 | 0.0100757 | − | 0.999949i | \(-0.496793\pi\) | ||||
0.0100757 | + | 0.999949i | \(0.496793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.00000 | 0.256158 | ||||||||
\(382\) | 3.00000i | 0.153493i | ||||||||
\(383\) | − 19.5167i | − 0.997255i | −0.866816 | − | 0.498627i | \(-0.833838\pi\) | ||||
0.866816 | − | 0.498627i | \(-0.166162\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.0526 | −1.12245 | ||||||||
\(387\) | 8.19615i | 0.416634i | ||||||||
\(388\) | − 15.1244i | − 0.767823i | ||||||||
\(389\) | −21.7128 | −1.10088 | −0.550442 | − | 0.834874i | \(-0.685541\pi\) | ||||
−0.550442 | + | 0.834874i | \(0.685541\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.7321 | −1.85762 | ||||||||
\(392\) | − 6.46410i | − 0.326486i | ||||||||
\(393\) | − 10.2679i | − 0.517950i | ||||||||
\(394\) | 24.5885 | 1.23875 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.73205 | 0.187543 | ||||||||
\(397\) | − 11.7321i | − 0.588815i | −0.955680 | − | 0.294407i | \(-0.904878\pi\) | ||||
0.955680 | − | 0.294407i | \(-0.0951222\pi\) | |||||||
\(398\) | 14.0000i | 0.701757i | ||||||||
\(399\) | −0.732051 | −0.0366484 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.8564 | 0.841769 | 0.420884 | − | 0.907114i | \(-0.361720\pi\) | ||||
0.420884 | + | 0.907114i | \(0.361720\pi\) | |||||||
\(402\) | 0.267949i | 0.0133641i | ||||||||
\(403\) | 6.73205i | 0.335347i | ||||||||
\(404\) | −9.26795 | −0.461098 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.26795 | 0.0629273 | ||||||||
\(407\) | 7.46410i | 0.369982i | ||||||||
\(408\) | − 6.19615i | − 0.306755i | ||||||||
\(409\) | −1.60770 | −0.0794954 | −0.0397477 | − | 0.999210i | \(-0.512655\pi\) | ||||
−0.0397477 | + | 0.999210i | \(0.512655\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.3923 | 0.611267 | ||||||||
\(412\) | 3.53590i | 0.174201i | ||||||||
\(413\) | − 6.00000i | − 0.295241i | ||||||||
\(414\) | 5.92820 | 0.291355 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.73205 | 0.133950 | ||||||||
\(417\) | − 21.1244i | − 1.03446i | ||||||||
\(418\) | 3.73205i | 0.182541i | ||||||||
\(419\) | −13.8564 | −0.676930 | −0.338465 | − | 0.940979i | \(-0.609908\pi\) | ||||
−0.338465 | + | 0.940979i | \(0.609908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.78461 | 0.330662 | 0.165331 | − | 0.986238i | \(-0.447131\pi\) | ||||
0.165331 | + | 0.986238i | \(0.447131\pi\) | |||||||
\(422\) | − 10.2679i | − 0.499836i | ||||||||
\(423\) | 3.46410i | 0.168430i | ||||||||
\(424\) | −1.73205 | −0.0841158 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.1962 | 0.590906 | ||||||||
\(427\) | − 7.80385i | − 0.377655i | ||||||||
\(428\) | 2.19615i | 0.106155i | ||||||||
\(429\) | −10.1962 | −0.492275 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.3205 | −1.41232 | −0.706160 | − | 0.708053i | \(-0.749574\pi\) | ||||
−0.706160 | + | 0.708053i | \(0.749574\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 24.1962i | 1.16279i | 0.813620 | + | 0.581396i | \(0.197493\pi\) | ||||
−0.813620 | + | 0.581396i | \(0.802507\pi\) | |||||||
\(434\) | −1.80385 | −0.0865875 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.39230 | 0.114571 | ||||||||
\(437\) | 5.92820i | 0.283584i | ||||||||
\(438\) | − 2.46410i | − 0.117739i | ||||||||
\(439\) | −25.7846 | −1.23063 | −0.615316 | − | 0.788280i | \(-0.710972\pi\) | ||||
−0.615316 | + | 0.788280i | \(0.710972\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.46410 | −0.307814 | ||||||||
\(442\) | 16.9282i | 0.805193i | ||||||||
\(443\) | 3.33975i | 0.158676i | 0.996848 | + | 0.0793381i | \(0.0252807\pi\) | ||||
−0.996848 | + | 0.0793381i | \(0.974719\pi\) | |||||||
\(444\) | −2.00000 | −0.0949158 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.53590 | 0.167430 | ||||||||
\(447\) | − 21.8564i | − 1.03377i | ||||||||
\(448\) | 0.732051i | 0.0345861i | ||||||||
\(449\) | −24.4641 | −1.15453 | −0.577266 | − | 0.816556i | \(-0.695880\pi\) | ||||
−0.577266 | + | 0.816556i | \(0.695880\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.9282 | −0.514589 | ||||||||
\(452\) | 13.3923i | 0.629921i | ||||||||
\(453\) | 11.4641i | 0.538630i | ||||||||
\(454\) | −6.00000 | −0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | − 5.07180i | − 0.237249i | −0.992939 | − | 0.118624i | \(-0.962152\pi\) | ||||
0.992939 | − | 0.118624i | \(-0.0378484\pi\) | |||||||
\(458\) | 6.26795i | 0.292882i | ||||||||
\(459\) | −6.19615 | −0.289212 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.8564 | −0.831656 | −0.415828 | − | 0.909443i | \(-0.636508\pi\) | ||||
−0.415828 | + | 0.909443i | \(0.636508\pi\) | |||||||
\(462\) | − 2.73205i | − 0.127107i | ||||||||
\(463\) | 35.3205i | 1.64148i | 0.571300 | + | 0.820742i | \(0.306439\pi\) | ||||
−0.571300 | + | 0.820742i | \(0.693561\pi\) | |||||||
\(464\) | 1.73205 | 0.0804084 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.1244 | 0.978567 | ||||||||
\(467\) | 7.19615i | 0.332998i | 0.986042 | + | 0.166499i | \(0.0532463\pi\) | ||||
−0.986042 | + | 0.166499i | \(0.946754\pi\) | |||||||
\(468\) | − 2.73205i | − 0.126289i | ||||||||
\(469\) | 0.196152 | 0.00905748 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.8564 | −0.638470 | ||||||||
\(472\) | − 8.19615i | − 0.377258i | ||||||||
\(473\) | − 30.5885i | − 1.40646i | ||||||||
\(474\) | 5.53590 | 0.254272 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.53590 | −0.207903 | ||||||||
\(477\) | 1.73205i | 0.0793052i | ||||||||
\(478\) | 14.0000i | 0.640345i | ||||||||
\(479\) | −3.14359 | −0.143634 | −0.0718172 | − | 0.997418i | \(-0.522880\pi\) | ||||
−0.0718172 | + | 0.997418i | \(0.522880\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.46410 | 0.249142 | ||||||||
\(482\) | − 30.1962i | − 1.37540i | ||||||||
\(483\) | − 4.33975i | − 0.197465i | ||||||||
\(484\) | −2.92820 | −0.133100 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 2.14359i | 0.0971355i | 0.998820 | + | 0.0485677i | \(0.0154657\pi\) | ||||
−0.998820 | + | 0.0485677i | \(0.984534\pi\) | |||||||
\(488\) | − 10.6603i | − 0.482567i | ||||||||
\(489\) | −2.00000 | −0.0904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.92820 | −0.132148 | −0.0660740 | − | 0.997815i | \(-0.521047\pi\) | ||||
−0.0660740 | + | 0.997815i | \(0.521047\pi\) | |||||||
\(492\) | − 2.92820i | − 0.132014i | ||||||||
\(493\) | 10.7321i | 0.483347i | ||||||||
\(494\) | 2.73205 | 0.122921 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.46410 | −0.110641 | ||||||||
\(497\) | − 8.92820i | − 0.400485i | ||||||||
\(498\) | 3.73205i | 0.167237i | ||||||||
\(499\) | −41.3731 | −1.85211 | −0.926056 | − | 0.377385i | \(-0.876823\pi\) | ||||
−0.926056 | + | 0.377385i | \(0.876823\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.92820 | 0.398883 | ||||||||
\(502\) | 11.4641i | 0.511668i | ||||||||
\(503\) | 17.8564i | 0.796178i | 0.917347 | + | 0.398089i | \(0.130326\pi\) | ||||
−0.917347 | + | 0.398089i | \(0.869674\pi\) | |||||||
\(504\) | 0.732051 | 0.0326081 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.1244 | −0.983548 | ||||||||
\(507\) | − 5.53590i | − 0.245858i | ||||||||
\(508\) | − 5.00000i | − 0.221839i | ||||||||
\(509\) | −13.8756 | −0.615027 | −0.307514 | − | 0.951544i | \(-0.599497\pi\) | ||||
−0.307514 | + | 0.951544i | \(0.599497\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.80385 | −0.0797975 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 1.00000i | 0.0441511i | ||||||||
\(514\) | 9.00000 | 0.396973 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.19615 | 0.360815 | ||||||||
\(517\) | − 12.9282i | − 0.568582i | ||||||||
\(518\) | 1.46410i | 0.0643289i | ||||||||
\(519\) | 13.5885 | 0.596467 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.1769 | 1.05921 | 0.529605 | − | 0.848244i | \(-0.322340\pi\) | ||||
0.529605 | + | 0.848244i | \(0.322340\pi\) | |||||||
\(522\) | − 1.73205i | − 0.0758098i | ||||||||
\(523\) | − 4.00000i | − 0.174908i | −0.996169 | − | 0.0874539i | \(-0.972127\pi\) | ||||
0.996169 | − | 0.0874539i | \(-0.0278730\pi\) | |||||||
\(524\) | −10.2679 | −0.448557 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.0000 | −0.654031 | ||||||||
\(527\) | − 15.2679i | − 0.665082i | ||||||||
\(528\) | − 3.73205i | − 0.162417i | ||||||||
\(529\) | −12.1436 | −0.527982 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.19615 | −0.355683 | ||||||||
\(532\) | 0.732051i | 0.0317384i | ||||||||
\(533\) | 8.00000i | 0.346518i | ||||||||
\(534\) | −10.8564 | −0.469803 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.267949 | 0.0115736 | ||||||||
\(537\) | − 12.0000i | − 0.517838i | ||||||||
\(538\) | 20.5359i | 0.885365i | ||||||||
\(539\) | 24.1244 | 1.03911 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.1962 | 0.739320 | 0.369660 | − | 0.929167i | \(-0.379474\pi\) | ||||
0.369660 | + | 0.929167i | \(0.379474\pi\) | |||||||
\(542\) | − 15.8038i | − 0.678833i | ||||||||
\(543\) | 16.5885i | 0.711879i | ||||||||
\(544\) | −6.19615 | −0.265658 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.00000 | −0.0855921 | ||||||||
\(547\) | − 43.4449i | − 1.85757i | −0.370621 | − | 0.928784i | \(-0.620855\pi\) | ||||
0.370621 | − | 0.928784i | \(-0.379145\pi\) | |||||||
\(548\) | − 12.3923i | − 0.529373i | ||||||||
\(549\) | −10.6603 | −0.454969 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.73205 | 0.0737878 | ||||||||
\(552\) | − 5.92820i | − 0.252321i | ||||||||
\(553\) | − 4.05256i | − 0.172332i | ||||||||
\(554\) | 11.1962 | 0.475679 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.1244 | −0.895872 | ||||||||
\(557\) | − 3.80385i | − 0.161174i | −0.996748 | − | 0.0805871i | \(-0.974320\pi\) | ||||
0.996748 | − | 0.0805871i | \(-0.0256795\pi\) | |||||||
\(558\) | 2.46410i | 0.104314i | ||||||||
\(559\) | −22.3923 | −0.947094 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.1244 | 0.976311 | ||||||||
\(562\) | 17.7846i | 0.750198i | ||||||||
\(563\) | 7.66025i | 0.322841i | 0.986886 | + | 0.161421i | \(0.0516076\pi\) | ||||
−0.986886 | + | 0.161421i | \(0.948392\pi\) | |||||||
\(564\) | 3.46410 | 0.145865 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | − 0.732051i | − 0.0307432i | ||||||||
\(568\) | − 12.1962i | − 0.511739i | ||||||||
\(569\) | −18.0000 | −0.754599 | −0.377300 | − | 0.926091i | \(-0.623147\pi\) | ||||
−0.377300 | + | 0.926091i | \(0.623147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.19615 | −0.259301 | −0.129650 | − | 0.991560i | \(-0.541386\pi\) | ||||
−0.129650 | + | 0.991560i | \(0.541386\pi\) | |||||||
\(572\) | 10.1962i | 0.426323i | ||||||||
\(573\) | − 3.00000i | − 0.125327i | ||||||||
\(574\) | −2.14359 | −0.0894719 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 17.2487i | 0.718073i | 0.933323 | + | 0.359037i | \(0.116895\pi\) | ||||
−0.933323 | + | 0.359037i | \(0.883105\pi\) | |||||||
\(578\) | − 21.3923i | − 0.889803i | ||||||||
\(579\) | 22.0526 | 0.916473 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.73205 | 0.113345 | ||||||||
\(582\) | 15.1244i | 0.626925i | ||||||||
\(583\) | − 6.46410i | − 0.267716i | ||||||||
\(584\) | −2.46410 | −0.101965 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.7321 | 1.14560 | ||||||||
\(587\) | 12.2679i | 0.506352i | 0.967420 | + | 0.253176i | \(0.0814752\pi\) | ||||
−0.967420 | + | 0.253176i | \(0.918525\pi\) | |||||||
\(588\) | 6.46410i | 0.266575i | ||||||||
\(589\) | −2.46410 | −0.101532 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.5885 | −1.01143 | ||||||||
\(592\) | 2.00000i | 0.0821995i | ||||||||
\(593\) | − 27.6077i | − 1.13371i | −0.823817 | − | 0.566856i | \(-0.808160\pi\) | ||||
0.823817 | − | 0.566856i | \(-0.191840\pi\) | |||||||
\(594\) | −3.73205 | −0.153128 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.8564 | −0.895273 | ||||||||
\(597\) | − 14.0000i | − 0.572982i | ||||||||
\(598\) | 16.1962i | 0.662310i | ||||||||
\(599\) | 3.66025 | 0.149554 | 0.0747770 | − | 0.997200i | \(-0.476176\pi\) | ||||
0.0747770 | + | 0.997200i | \(0.476176\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0526 | −0.410052 | −0.205026 | − | 0.978756i | \(-0.565728\pi\) | ||||
−0.205026 | + | 0.978756i | \(0.565728\pi\) | |||||||
\(602\) | − 6.00000i | − 0.244542i | ||||||||
\(603\) | − 0.267949i | − 0.0109117i | ||||||||
\(604\) | 11.4641 | 0.466468 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.26795 | 0.376485 | ||||||||
\(607\) | 11.7846i | 0.478323i | 0.970980 | + | 0.239161i | \(0.0768725\pi\) | ||||
−0.970980 | + | 0.239161i | \(0.923128\pi\) | |||||||
\(608\) | 1.00000i | 0.0405554i | ||||||||
\(609\) | −1.26795 | −0.0513799 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.46410 | −0.382877 | ||||||||
\(612\) | 6.19615i | 0.250465i | ||||||||
\(613\) | 38.7846i | 1.56650i | 0.621710 | + | 0.783248i | \(0.286438\pi\) | ||||
−0.621710 | + | 0.783248i | \(0.713562\pi\) | |||||||
\(614\) | −20.2679 | −0.817948 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.73205 | −0.110077 | ||||||||
\(617\) | − 46.3923i | − 1.86768i | −0.357686 | − | 0.933842i | \(-0.616434\pi\) | ||||
0.357686 | − | 0.933842i | \(-0.383566\pi\) | |||||||
\(618\) | − 3.53590i | − 0.142235i | ||||||||
\(619\) | 0.196152 | 0.00788403 | 0.00394202 | − | 0.999992i | \(-0.498745\pi\) | ||||
0.00394202 | + | 0.999992i | \(0.498745\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.92820 | −0.237891 | ||||||||
\(622\) | − 29.3205i | − 1.17565i | ||||||||
\(623\) | 7.94744i | 0.318408i | ||||||||
\(624\) | −2.73205 | −0.109370 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.92820 | 0.157003 | ||||||||
\(627\) | − 3.73205i | − 0.149044i | ||||||||
\(628\) | 13.8564i | 0.552931i | ||||||||
\(629\) | −12.3923 | −0.494114 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.92820 | 0.116570 | 0.0582850 | − | 0.998300i | \(-0.481437\pi\) | ||||
0.0582850 | + | 0.998300i | \(0.481437\pi\) | |||||||
\(632\) | − 5.53590i | − 0.220206i | ||||||||
\(633\) | 10.2679i | 0.408114i | ||||||||
\(634\) | −1.73205 | −0.0687885 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.73205 | 0.0686803 | ||||||||
\(637\) | − 17.6603i | − 0.699725i | ||||||||
\(638\) | 6.46410i | 0.255916i | ||||||||
\(639\) | −12.1962 | −0.482472 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.5359 | 0.416143 | 0.208071 | − | 0.978114i | \(-0.433281\pi\) | ||||
0.208071 | + | 0.978114i | \(0.433281\pi\) | |||||||
\(642\) | − 2.19615i | − 0.0866752i | ||||||||
\(643\) | 27.0718i | 1.06761i | 0.845608 | + | 0.533804i | \(0.179238\pi\) | ||||
−0.845608 | + | 0.533804i | \(0.820762\pi\) | |||||||
\(644\) | −4.33975 | −0.171010 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.19615 | −0.243784 | ||||||||
\(647\) | − 9.39230i | − 0.369250i | −0.982809 | − | 0.184625i | \(-0.940893\pi\) | ||||
0.982809 | − | 0.184625i | \(-0.0591070\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | 30.5885 | 1.20070 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.80385 | 0.0706984 | ||||||||
\(652\) | 2.00000i | 0.0783260i | ||||||||
\(653\) | − 17.4641i | − 0.683423i | −0.939805 | − | 0.341712i | \(-0.888993\pi\) | ||||
0.939805 | − | 0.341712i | \(-0.111007\pi\) | |||||||
\(654\) | −2.39230 | −0.0935465 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.92820 | −0.114327 | ||||||||
\(657\) | 2.46410i | 0.0961338i | ||||||||
\(658\) | − 2.53590i | − 0.0988596i | ||||||||
\(659\) | −7.41154 | −0.288713 | −0.144356 | − | 0.989526i | \(-0.546111\pi\) | ||||
−0.144356 | + | 0.989526i | \(0.546111\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.6410 | −0.880633 | −0.440317 | − | 0.897843i | \(-0.645134\pi\) | ||||
−0.440317 | + | 0.897843i | \(0.645134\pi\) | |||||||
\(662\) | − 22.2679i | − 0.865468i | ||||||||
\(663\) | − 16.9282i | − 0.657437i | ||||||||
\(664\) | 3.73205 | 0.144832 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.00000 | 0.0774984 | ||||||||
\(667\) | 10.2679i | 0.397577i | ||||||||
\(668\) | − 8.92820i | − 0.345443i | ||||||||
\(669\) | −3.53590 | −0.136706 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.7846 | 1.53587 | ||||||||
\(672\) | − 0.732051i | − 0.0282395i | ||||||||
\(673\) | 6.98076i | 0.269089i | 0.990908 | + | 0.134544i | \(0.0429571\pi\) | ||||
−0.990908 | + | 0.134544i | \(0.957043\pi\) | |||||||
\(674\) | 10.5359 | 0.405828 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.53590 | −0.212919 | ||||||||
\(677\) | 8.66025i | 0.332841i | 0.986055 | + | 0.166420i | \(0.0532208\pi\) | ||||
−0.986055 | + | 0.166420i | \(0.946779\pi\) | |||||||
\(678\) | − 13.3923i | − 0.514328i | ||||||||
\(679\) | 11.0718 | 0.424897 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | 0.229920 | ||||||||
\(682\) | − 9.19615i | − 0.352139i | ||||||||
\(683\) | 46.9808i | 1.79767i | 0.438288 | + | 0.898834i | \(0.355585\pi\) | ||||
−0.438288 | + | 0.898834i | \(0.644415\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.85641 | 0.376319 | ||||||||
\(687\) | − 6.26795i | − 0.239137i | ||||||||
\(688\) | − 8.19615i | − 0.312475i | ||||||||
\(689\) | −4.73205 | −0.180277 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.1962 | −0.844381 | −0.422191 | − | 0.906507i | \(-0.638739\pi\) | ||||
−0.422191 | + | 0.906507i | \(0.638739\pi\) | |||||||
\(692\) | − 13.5885i | − 0.516556i | ||||||||
\(693\) | 2.73205i | 0.103782i | ||||||||
\(694\) | −20.7846 | −0.788973 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.73205 | −0.0656532 | ||||||||
\(697\) | − 18.1436i | − 0.687238i | ||||||||
\(698\) | 17.0526i | 0.645449i | ||||||||
\(699\) | −21.1244 | −0.798997 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.60770 | 0.136261 | 0.0681304 | − | 0.997676i | \(-0.478297\pi\) | ||||
0.0681304 | + | 0.997676i | \(0.478297\pi\) | |||||||
\(702\) | 2.73205i | 0.103115i | ||||||||
\(703\) | 2.00000i | 0.0754314i | ||||||||
\(704\) | −3.73205 | −0.140657 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.0526 | −0.604146 | ||||||||
\(707\) | − 6.78461i | − 0.255162i | ||||||||
\(708\) | 8.19615i | 0.308030i | ||||||||
\(709\) | −47.3013 | −1.77644 | −0.888218 | − | 0.459422i | \(-0.848057\pi\) | ||||
−0.888218 | + | 0.459422i | \(0.848057\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.53590 | −0.207612 | ||||||||
\(712\) | 10.8564i | 0.406861i | ||||||||
\(713\) | − 14.6077i | − 0.547062i | ||||||||
\(714\) | 4.53590 | 0.169752 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | − 14.0000i | − 0.522840i | ||||||||
\(718\) | 16.9282i | 0.631755i | ||||||||
\(719\) | −12.1769 | −0.454122 | −0.227061 | − | 0.973881i | \(-0.572912\pi\) | ||||
−0.227061 | + | 0.973881i | \(0.572912\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.58846 | −0.0963992 | ||||||||
\(722\) | 1.00000i | 0.0372161i | ||||||||
\(723\) | 30.1962i | 1.12301i | ||||||||
\(724\) | 16.5885 | 0.616505 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.92820 | 0.108676 | ||||||||
\(727\) | 38.1051i | 1.41324i | 0.707593 | + | 0.706620i | \(0.249781\pi\) | ||||
−0.707593 | + | 0.706620i | \(0.750219\pi\) | |||||||
\(728\) | 2.00000i | 0.0741249i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.7846 | 1.87834 | ||||||||
\(732\) | 10.6603i | 0.394014i | ||||||||
\(733\) | − 20.5167i | − 0.757800i | −0.925438 | − | 0.378900i | \(-0.876302\pi\) | ||||
0.925438 | − | 0.378900i | \(-0.123698\pi\) | |||||||
\(734\) | −13.2679 | −0.489729 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.92820 | −0.218516 | ||||||||
\(737\) | 1.00000i | 0.0368355i | ||||||||
\(738\) | 2.92820i | 0.107789i | ||||||||
\(739\) | 53.1769 | 1.95614 | 0.978072 | − | 0.208266i | \(-0.0667820\pi\) | ||||
0.978072 | + | 0.208266i | \(0.0667820\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.73205 | −0.100364 | ||||||||
\(742\) | − 1.26795i | − 0.0465479i | ||||||||
\(743\) | − 5.07180i | − 0.186066i | −0.995663 | − | 0.0930331i | \(-0.970344\pi\) | ||||
0.995663 | − | 0.0930331i | \(-0.0296562\pi\) | |||||||
\(744\) | 2.46410 | 0.0903383 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 31.5167 | 1.15391 | ||||||||
\(747\) | − 3.73205i | − 0.136549i | ||||||||
\(748\) | − 23.1244i | − 0.845510i | ||||||||
\(749\) | −1.60770 | −0.0587439 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.46410 | 0.272369 | 0.136184 | − | 0.990683i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990683i | \(0.456516\pi\) | |||||||
\(752\) | − 3.46410i | − 0.126323i | ||||||||
\(753\) | − 11.4641i | − 0.417775i | ||||||||
\(754\) | 4.73205 | 0.172331 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.732051 | −0.0266244 | ||||||||
\(757\) | 13.5885i | 0.493881i | 0.969031 | + | 0.246940i | \(0.0794252\pi\) | ||||
−0.969031 | + | 0.246940i | \(0.920575\pi\) | |||||||
\(758\) | 0.392305i | 0.0142492i | ||||||||
\(759\) | 22.1244 | 0.803063 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.26795 | 0.0459631 | 0.0229816 | − | 0.999736i | \(-0.492684\pi\) | ||||
0.0229816 | + | 0.999736i | \(0.492684\pi\) | |||||||
\(762\) | 5.00000i | 0.181131i | ||||||||
\(763\) | 1.75129i | 0.0634009i | ||||||||
\(764\) | −3.00000 | −0.108536 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.5167 | 0.705166 | ||||||||
\(767\) | − 22.3923i | − 0.808539i | ||||||||
\(768\) | − 1.00000i | − 0.0360844i | ||||||||
\(769\) | 34.7128 | 1.25178 | 0.625888 | − | 0.779913i | \(-0.284737\pi\) | ||||
0.625888 | + | 0.779913i | \(0.284737\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.00000 | −0.324127 | ||||||||
\(772\) | − 22.0526i | − 0.793689i | ||||||||
\(773\) | − 45.3205i | − 1.63007i | −0.579415 | − | 0.815033i | \(-0.696719\pi\) | ||||
0.579415 | − | 0.815033i | \(-0.303281\pi\) | |||||||
\(774\) | −8.19615 | −0.294605 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15.1244 | 0.542933 | ||||||||
\(777\) | − 1.46410i | − 0.0525244i | ||||||||
\(778\) | − 21.7128i | − 0.778442i | ||||||||
\(779\) | −2.92820 | −0.104914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.5167 | 1.62871 | ||||||||
\(782\) | − 36.7321i | − 1.31354i | ||||||||
\(783\) | 1.73205i | 0.0618984i | ||||||||
\(784\) | 6.46410 | 0.230861 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10.2679 | 0.366246 | ||||||||
\(787\) | − 2.12436i | − 0.0757251i | −0.999283 | − | 0.0378626i | \(-0.987945\pi\) | ||||
0.999283 | − | 0.0378626i | \(-0.0120549\pi\) | |||||||
\(788\) | 24.5885i | 0.875928i | ||||||||
\(789\) | 15.0000 | 0.534014 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.80385 | −0.348585 | ||||||||
\(792\) | 3.73205i | 0.132613i | ||||||||
\(793\) | − 29.1244i | − 1.03424i | ||||||||
\(794\) | 11.7321 | 0.416355 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.0000 | −0.496217 | ||||||||
\(797\) | − 20.0000i | − 0.708436i | −0.935163 | − | 0.354218i | \(-0.884747\pi\) | ||||
0.935163 | − | 0.354218i | \(-0.115253\pi\) | |||||||
\(798\) | − 0.732051i | − 0.0259143i | ||||||||
\(799\) | 21.4641 | 0.759345 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.8564 | 0.383592 | ||||||||
\(802\) | 16.8564i | 0.595220i | ||||||||
\(803\) | − 9.19615i | − 0.324525i | ||||||||
\(804\) | −0.267949 | −0.00944984 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.73205 | −0.237126 | ||||||||
\(807\) | − 20.5359i | − 0.722898i | ||||||||
\(808\) | − 9.26795i | − 0.326045i | ||||||||
\(809\) | −37.5167 | −1.31902 | −0.659508 | − | 0.751698i | \(-0.729235\pi\) | ||||
−0.659508 | + | 0.751698i | \(0.729235\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.3731 | 0.645166 | 0.322583 | − | 0.946541i | \(-0.395449\pi\) | ||||
0.322583 | + | 0.946541i | \(0.395449\pi\) | |||||||
\(812\) | 1.26795i | 0.0444963i | ||||||||
\(813\) | 15.8038i | 0.554265i | ||||||||
\(814\) | −7.46410 | −0.261617 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.19615 | 0.216909 | ||||||||
\(817\) | − 8.19615i | − 0.286747i | ||||||||
\(818\) | − 1.60770i | − 0.0562117i | ||||||||
\(819\) | 2.00000 | 0.0698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.48334 | 0.0866691 | 0.0433346 | − | 0.999061i | \(-0.486202\pi\) | ||||
0.0433346 | + | 0.999061i | \(0.486202\pi\) | |||||||
\(822\) | 12.3923i | 0.432231i | ||||||||
\(823\) | − 6.78461i | − 0.236497i | −0.992984 | − | 0.118248i | \(-0.962272\pi\) | ||||
0.992984 | − | 0.118248i | \(-0.0377279\pi\) | |||||||
\(824\) | −3.53590 | −0.123179 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.00000 | 0.208767 | ||||||||
\(827\) | − 6.73205i | − 0.234096i | −0.993126 | − | 0.117048i | \(-0.962657\pi\) | ||||
0.993126 | − | 0.117048i | \(-0.0373432\pi\) | |||||||
\(828\) | 5.92820i | 0.206019i | ||||||||
\(829\) | −6.19615 | −0.215201 | −0.107601 | − | 0.994194i | \(-0.534317\pi\) | ||||
−0.107601 | + | 0.994194i | \(0.534317\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.1962 | −0.388390 | ||||||||
\(832\) | 2.73205i | 0.0947168i | ||||||||
\(833\) | 40.0526i | 1.38774i | ||||||||
\(834\) | 21.1244 | 0.731477 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.73205 | −0.129076 | ||||||||
\(837\) | − 2.46410i | − 0.0851718i | ||||||||
\(838\) | − 13.8564i | − 0.478662i | ||||||||
\(839\) | 46.5885 | 1.60841 | 0.804206 | − | 0.594351i | \(-0.202591\pi\) | ||||
0.804206 | + | 0.594351i | \(0.202591\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | −0.896552 | ||||||||
\(842\) | 6.78461i | 0.233813i | ||||||||
\(843\) | − 17.7846i | − 0.612534i | ||||||||
\(844\) | 10.2679 | 0.353437 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.46410 | −0.119098 | ||||||||
\(847\) | − 2.14359i | − 0.0736547i | ||||||||
\(848\) | − 1.73205i | − 0.0594789i | ||||||||
\(849\) | 4.00000 | 0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.8564 | −0.406432 | ||||||||
\(852\) | 12.1962i | 0.417833i | ||||||||
\(853\) | − 4.53590i | − 0.155306i | −0.996980 | − | 0.0776531i | \(-0.975257\pi\) | ||||
0.996980 | − | 0.0776531i | \(-0.0247427\pi\) | |||||||
\(854\) | 7.80385 | 0.267042 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.19615 | −0.0750629 | ||||||||
\(857\) | 42.9282i | 1.46640i | 0.680013 | + | 0.733200i | \(0.261974\pi\) | ||||
−0.680013 | + | 0.733200i | \(0.738026\pi\) | |||||||
\(858\) | − 10.1962i | − 0.348091i | ||||||||
\(859\) | −56.9282 | −1.94237 | −0.971183 | − | 0.238337i | \(-0.923398\pi\) | ||||
−0.971183 | + | 0.238337i | \(0.923398\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.14359 | 0.0730535 | ||||||||
\(862\) | − 29.3205i | − 0.998660i | ||||||||
\(863\) | − 55.3205i | − 1.88313i | −0.336829 | − | 0.941566i | \(-0.609354\pi\) | ||||
0.336829 | − | 0.941566i | \(-0.390646\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −24.1962 | −0.822219 | ||||||||
\(867\) | 21.3923i | 0.726521i | ||||||||
\(868\) | − 1.80385i | − 0.0612266i | ||||||||
\(869\) | 20.6603 | 0.700851 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.732051 | 0.0248046 | ||||||||
\(872\) | 2.39230i | 0.0810137i | ||||||||
\(873\) | − 15.1244i | − 0.511882i | ||||||||
\(874\) | −5.92820 | −0.200524 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.46410 | 0.0832543 | ||||||||
\(877\) | − 31.1769i | − 1.05277i | −0.850246 | − | 0.526385i | \(-0.823547\pi\) | ||||
0.850246 | − | 0.526385i | \(-0.176453\pi\) | |||||||
\(878\) | − 25.7846i | − 0.870188i | ||||||||
\(879\) | −27.7321 | −0.935379 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.5359 | −0.894017 | −0.447009 | − | 0.894530i | \(-0.647511\pi\) | ||||
−0.447009 | + | 0.894530i | \(0.647511\pi\) | |||||||
\(882\) | − 6.46410i | − 0.217658i | ||||||||
\(883\) | 27.2679i | 0.917640i | 0.888529 | + | 0.458820i | \(0.151728\pi\) | ||||
−0.888529 | + | 0.458820i | \(0.848272\pi\) | |||||||
\(884\) | −16.9282 | −0.569357 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.33975 | −0.112201 | ||||||||
\(887\) | 7.60770i | 0.255441i | 0.991810 | + | 0.127721i | \(0.0407661\pi\) | ||||
−0.991810 | + | 0.127721i | \(0.959234\pi\) | |||||||
\(888\) | − 2.00000i | − 0.0671156i | ||||||||
\(889\) | 3.66025 | 0.122761 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.73205 | 0.125028 | ||||||||
\(892\) | 3.53590i | 0.118391i | ||||||||
\(893\) | − 3.46410i | − 0.115922i | ||||||||
\(894\) | 21.8564 | 0.730988 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.732051 | −0.0244561 | ||||||||
\(897\) | − 16.1962i | − 0.540774i | ||||||||
\(898\) | − 24.4641i | − 0.816378i | ||||||||
\(899\) | −4.26795 | −0.142344 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.7321 | 0.357536 | ||||||||
\(902\) | − 10.9282i | − 0.363869i | ||||||||
\(903\) | 6.00000i | 0.199667i | ||||||||
\(904\) | −13.3923 | −0.445421 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11.4641 | −0.380869 | ||||||||
\(907\) | − 49.3205i | − 1.63766i | −0.574036 | − | 0.818830i | \(-0.694623\pi\) | ||||
0.574036 | − | 0.818830i | \(-0.305377\pi\) | |||||||
\(908\) | − 6.00000i | − 0.199117i | ||||||||
\(909\) | −9.26795 | −0.307398 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.1051 | 1.12995 | 0.564976 | − | 0.825107i | \(-0.308885\pi\) | ||||
0.564976 | + | 0.825107i | \(0.308885\pi\) | |||||||
\(912\) | − 1.00000i | − 0.0331133i | ||||||||
\(913\) | 13.9282i | 0.460956i | ||||||||
\(914\) | 5.07180 | 0.167760 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.26795 | −0.207099 | ||||||||
\(917\) | − 7.51666i | − 0.248222i | ||||||||
\(918\) | − 6.19615i | − 0.204504i | ||||||||
\(919\) | 4.48334 | 0.147892 | 0.0739459 | − | 0.997262i | \(-0.476441\pi\) | ||||
0.0739459 | + | 0.997262i | \(0.476441\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.2679 | 0.667852 | ||||||||
\(922\) | − 17.8564i | − 0.588069i | ||||||||
\(923\) | − 33.3205i | − 1.09676i | ||||||||
\(924\) | 2.73205 | 0.0898779 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −35.3205 | −1.16070 | ||||||||
\(927\) | 3.53590i | 0.116134i | ||||||||
\(928\) | 1.73205i | 0.0568574i | ||||||||
\(929\) | −42.9282 | −1.40843 | −0.704214 | − | 0.709987i | \(-0.748701\pi\) | ||||
−0.704214 | + | 0.709987i | \(0.748701\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.46410 | 0.211852 | ||||||||
\(932\) | 21.1244i | 0.691951i | ||||||||
\(933\) | 29.3205i | 0.959910i | ||||||||
\(934\) | −7.19615 | −0.235465 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.73205 | 0.0892999 | ||||||||
\(937\) | 13.2154i | 0.431728i | 0.976423 | + | 0.215864i | \(0.0692568\pi\) | ||||
−0.976423 | + | 0.215864i | \(0.930743\pi\) | |||||||
\(938\) | 0.196152i | 0.00640460i | ||||||||
\(939\) | −3.92820 | −0.128192 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.2679 | −0.399924 | −0.199962 | − | 0.979804i | \(-0.564082\pi\) | ||||
−0.199962 | + | 0.979804i | \(0.564082\pi\) | |||||||
\(942\) | − 13.8564i | − 0.451466i | ||||||||
\(943\) | − 17.3590i | − 0.565286i | ||||||||
\(944\) | 8.19615 | 0.266762 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.5885 | 0.994517 | ||||||||
\(947\) | − 5.85641i | − 0.190308i | −0.995463 | − | 0.0951538i | \(-0.969666\pi\) | ||||
0.995463 | − | 0.0951538i | \(-0.0303343\pi\) | |||||||
\(948\) | 5.53590i | 0.179798i | ||||||||
\(949\) | −6.73205 | −0.218532 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.73205 | 0.0561656 | ||||||||
\(952\) | − 4.53590i | − 0.147009i | ||||||||
\(953\) | 5.24871i | 0.170022i | 0.996380 | + | 0.0850112i | \(0.0270926\pi\) | ||||
−0.996380 | + | 0.0850112i | \(0.972907\pi\) | |||||||
\(954\) | −1.73205 | −0.0560772 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.0000 | −0.452792 | ||||||||
\(957\) | − 6.46410i | − 0.208955i | ||||||||
\(958\) | − 3.14359i | − 0.101565i | ||||||||
\(959\) | 9.07180 | 0.292944 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.9282 | −0.804136 | ||||||||
\(962\) | 5.46410i | 0.176170i | ||||||||
\(963\) | 2.19615i | 0.0707700i | ||||||||
\(964\) | 30.1962 | 0.972553 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.33975 | 0.139629 | ||||||||
\(967\) | 18.1051i | 0.582221i | 0.956689 | + | 0.291111i | \(0.0940248\pi\) | ||||
−0.956689 | + | 0.291111i | \(0.905975\pi\) | |||||||
\(968\) | − 2.92820i | − 0.0941160i | ||||||||
\(969\) | 6.19615 | 0.199049 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.7654 | −1.21195 | −0.605974 | − | 0.795484i | \(-0.707217\pi\) | ||||
−0.605974 | + | 0.795484i | \(0.707217\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − 15.4641i | − 0.495756i | ||||||||
\(974\) | −2.14359 | −0.0686852 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.6603 | 0.341226 | ||||||||
\(977\) | − 1.46410i | − 0.0468408i | −0.999726 | − | 0.0234204i | \(-0.992544\pi\) | ||||
0.999726 | − | 0.0234204i | \(-0.00745562\pi\) | |||||||
\(978\) | − 2.00000i | − 0.0639529i | ||||||||
\(979\) | −40.5167 | −1.29492 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.39230 | 0.0763804 | ||||||||
\(982\) | − 2.92820i | − 0.0934427i | ||||||||
\(983\) | 30.3397i | 0.967688i | 0.875154 | + | 0.483844i | \(0.160760\pi\) | ||||
−0.875154 | + | 0.483844i | \(0.839240\pi\) | |||||||
\(984\) | 2.92820 | 0.0933477 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.7321 | −0.341778 | ||||||||
\(987\) | 2.53590i | 0.0807185i | ||||||||
\(988\) | 2.73205i | 0.0869181i | ||||||||
\(989\) | 48.5885 | 1.54502 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.3205 | −1.28082 | −0.640412 | − | 0.768032i | \(-0.721236\pi\) | ||||
−0.640412 | + | 0.768032i | \(0.721236\pi\) | |||||||
\(992\) | − 2.46410i | − 0.0782353i | ||||||||
\(993\) | 22.2679i | 0.706652i | ||||||||
\(994\) | 8.92820 | 0.283185 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.73205 | −0.118255 | ||||||||
\(997\) | − 63.0526i | − 1.99689i | −0.0557047 | − | 0.998447i | \(-0.517741\pi\) | ||||
0.0557047 | − | 0.998447i | \(-0.482259\pi\) | |||||||
\(998\) | − 41.3731i | − 1.30964i | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 2850.2.d.x.799.3 | 4 | ||
5.2 | odd | 4 | 2850.2.a.bd.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 2850.2.a.bi.1.1 | yes | 2 | ||
5.4 | even | 2 | inner | 2850.2.d.x.799.2 | 4 | ||
15.2 | even | 4 | 8550.2.a.by.1.2 | 2 | |||
15.8 | even | 4 | 8550.2.a.bs.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2850.2.a.bd.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
2850.2.a.bi.1.1 | yes | 2 | 5.3 | odd | 4 | ||
2850.2.d.x.799.2 | 4 | 5.4 | even | 2 | inner | ||
2850.2.d.x.799.3 | 4 | 1.1 | even | 1 | trivial | ||
8550.2.a.bs.1.1 | 2 | 15.8 | even | 4 | |||
8550.2.a.by.1.2 | 2 | 15.2 | even | 4 |