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: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 799.1 | ||
Root | \(1.58114 - 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2850.799 |
Dual form | 2850.2.d.v.799.4 |
$q$-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 | ||||||||
\(7\) | − 3.16228i | − 1.19523i | −0.801784 | − | 0.597614i | \(-0.796115\pi\) | ||||
0.801784 | − | 0.597614i | \(-0.203885\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.16228 | 1.25497 | 0.627487 | − | 0.778627i | \(-0.284084\pi\) | ||||
0.627487 | + | 0.778627i | \(0.284084\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 5.16228i | 1.43176i | 0.698224 | + | 0.715879i | \(0.253974\pi\) | ||||
−0.698224 | + | 0.715879i | \(0.746026\pi\) | |||||||
\(14\) | −3.16228 | −0.845154 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 0.837722i | − 0.203178i | −0.994826 | − | 0.101589i | \(-0.967607\pi\) | ||||
0.994826 | − | 0.101589i | \(-0.0323926\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.16228 | −0.690066 | ||||||||
\(22\) | − 4.16228i | − 0.887401i | ||||||||
\(23\) | − 5.32456i | − 1.11025i | −0.831768 | − | 0.555123i | \(-0.812671\pi\) | ||||
0.831768 | − | 0.555123i | \(-0.187329\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.16228 | 1.01241 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 3.16228i | 0.597614i | ||||||||
\(29\) | 3.83772 | 0.712647 | 0.356324 | − | 0.934363i | \(-0.384030\pi\) | ||||
0.356324 | + | 0.934363i | \(0.384030\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.32456 | 0.956318 | 0.478159 | − | 0.878273i | \(-0.341304\pi\) | ||||
0.478159 | + | 0.878273i | \(0.341304\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 4.16228i | − 0.724560i | ||||||||
\(34\) | −0.837722 | −0.143668 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − 10.0000i | − 1.64399i | −0.569495 | − | 0.821995i | \(-0.692861\pi\) | ||||
0.569495 | − | 0.821995i | \(-0.307139\pi\) | |||||||
\(38\) | − 1.00000i | − 0.162221i | ||||||||
\(39\) | 5.16228 | 0.826626 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.32456 | −0.987730 | −0.493865 | − | 0.869539i | \(-0.664416\pi\) | ||||
−0.493865 | + | 0.869539i | \(0.664416\pi\) | |||||||
\(42\) | 3.16228i | 0.487950i | ||||||||
\(43\) | − 9.16228i | − 1.39723i | −0.715496 | − | 0.698617i | \(-0.753799\pi\) | ||||
0.715496 | − | 0.698617i | \(-0.246201\pi\) | |||||||
\(44\) | −4.16228 | −0.627487 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.32456 | −0.785063 | ||||||||
\(47\) | − 6.00000i | − 0.875190i | −0.899172 | − | 0.437595i | \(-0.855830\pi\) | ||||
0.899172 | − | 0.437595i | \(-0.144170\pi\) | |||||||
\(48\) | − 1.00000i | − 0.144338i | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.837722 | −0.117305 | ||||||||
\(52\) | − 5.16228i | − 0.715879i | ||||||||
\(53\) | 1.83772i | 0.252431i | 0.992003 | + | 0.126215i | \(0.0402830\pi\) | ||||
−0.992003 | + | 0.126215i | \(0.959717\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.16228 | 0.422577 | ||||||||
\(57\) | − 1.00000i | − 0.132453i | ||||||||
\(58\) | − 3.83772i | − 0.503918i | ||||||||
\(59\) | 7.48683 | 0.974703 | 0.487351 | − | 0.873206i | \(-0.337963\pi\) | ||||
0.487351 | + | 0.873206i | \(0.337963\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.16228 | −0.532925 | −0.266463 | − | 0.963845i | \(-0.585855\pi\) | ||||
−0.266463 | + | 0.963845i | \(0.585855\pi\) | |||||||
\(62\) | − 5.32456i | − 0.676219i | ||||||||
\(63\) | 3.16228i | 0.398410i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.16228 | −0.512341 | ||||||||
\(67\) | 6.48683i | 0.792493i | 0.918144 | + | 0.396246i | \(0.129687\pi\) | ||||
−0.918144 | + | 0.396246i | \(0.870313\pi\) | |||||||
\(68\) | 0.837722i | 0.101589i | ||||||||
\(69\) | −5.32456 | −0.641001 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.16228 | 0.137937 | 0.0689685 | − | 0.997619i | \(-0.478029\pi\) | ||||
0.0689685 | + | 0.997619i | \(0.478029\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | − 1.00000i | − 0.117041i | −0.998286 | − | 0.0585206i | \(-0.981362\pi\) | ||||
0.998286 | − | 0.0585206i | \(-0.0186383\pi\) | |||||||
\(74\) | −10.0000 | −1.16248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | − 13.1623i | − 1.49998i | ||||||||
\(78\) | − 5.16228i | − 0.584513i | ||||||||
\(79\) | 5.32456 | 0.599059 | 0.299530 | − | 0.954087i | \(-0.403170\pi\) | ||||
0.299530 | + | 0.954087i | \(0.403170\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.32456i | 0.698430i | ||||||||
\(83\) | 6.48683i | 0.712022i | 0.934482 | + | 0.356011i | \(0.115864\pi\) | ||||
−0.934482 | + | 0.356011i | \(0.884136\pi\) | |||||||
\(84\) | 3.16228 | 0.345033 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.16228 | −0.987994 | ||||||||
\(87\) | − 3.83772i | − 0.411447i | ||||||||
\(88\) | 4.16228i | 0.443700i | ||||||||
\(89\) | 7.32456 | 0.776401 | 0.388201 | − | 0.921575i | \(-0.373097\pi\) | ||||
0.388201 | + | 0.921575i | \(0.373097\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.3246 | 1.71128 | ||||||||
\(92\) | 5.32456i | 0.555123i | ||||||||
\(93\) | − 5.32456i | − 0.552131i | ||||||||
\(94\) | −6.00000 | −0.618853 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | − 0.513167i | − 0.0521042i | −0.999661 | − | 0.0260521i | \(-0.991706\pi\) | ||||
0.999661 | − | 0.0260521i | \(-0.00829358\pi\) | |||||||
\(98\) | 3.00000i | 0.303046i | ||||||||
\(99\) | −4.16228 | −0.418325 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.8114 | −1.37428 | −0.687142 | − | 0.726523i | \(-0.741135\pi\) | ||||
−0.687142 | + | 0.726523i | \(0.741135\pi\) | |||||||
\(102\) | 0.837722i | 0.0829469i | ||||||||
\(103\) | 15.6491i | 1.54195i | 0.636864 | + | 0.770976i | \(0.280231\pi\) | ||||
−0.636864 | + | 0.770976i | \(0.719769\pi\) | |||||||
\(104\) | −5.16228 | −0.506203 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.83772 | 0.178495 | ||||||||
\(107\) | − 12.8377i | − 1.24107i | −0.784179 | − | 0.620535i | \(-0.786916\pi\) | ||||
0.784179 | − | 0.620535i | \(-0.213084\pi\) | |||||||
\(108\) | − 1.00000i | − 0.0962250i | ||||||||
\(109\) | −7.67544 | −0.735174 | −0.367587 | − | 0.929989i | \(-0.619816\pi\) | ||||
−0.367587 | + | 0.929989i | \(0.619816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0000 | −0.949158 | ||||||||
\(112\) | − 3.16228i | − 0.298807i | ||||||||
\(113\) | 9.64911i | 0.907712i | 0.891075 | + | 0.453856i | \(0.149952\pi\) | ||||
−0.891075 | + | 0.453856i | \(0.850048\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.83772 | −0.356324 | ||||||||
\(117\) | − 5.16228i | − 0.477253i | ||||||||
\(118\) | − 7.48683i | − 0.689219i | ||||||||
\(119\) | −2.64911 | −0.242844 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.32456 | 0.574960 | ||||||||
\(122\) | 4.16228i | 0.376835i | ||||||||
\(123\) | 6.32456i | 0.570266i | ||||||||
\(124\) | −5.32456 | −0.478159 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.16228 | 0.281718 | ||||||||
\(127\) | − 15.6491i | − 1.38863i | −0.719669 | − | 0.694317i | \(-0.755707\pi\) | ||||
0.719669 | − | 0.694317i | \(-0.244293\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −9.16228 | −0.806694 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.4868 | −1.09098 | −0.545490 | − | 0.838117i | \(-0.683656\pi\) | ||||
−0.545490 | + | 0.838117i | \(0.683656\pi\) | |||||||
\(132\) | 4.16228i | 0.362280i | ||||||||
\(133\) | − 3.16228i | − 0.274204i | ||||||||
\(134\) | 6.48683 | 0.560377 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.837722 | 0.0718341 | ||||||||
\(137\) | − 2.32456i | − 0.198600i | −0.995058 | − | 0.0993001i | \(-0.968340\pi\) | ||||
0.995058 | − | 0.0993001i | \(-0.0316604\pi\) | |||||||
\(138\) | 5.32456i | 0.453256i | ||||||||
\(139\) | −21.4868 | −1.82249 | −0.911245 | − | 0.411865i | \(-0.864877\pi\) | ||||
−0.911245 | + | 0.411865i | \(0.864877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | − 1.16228i | − 0.0975362i | ||||||||
\(143\) | 21.4868i | 1.79682i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.00000 | −0.0827606 | ||||||||
\(147\) | 3.00000i | 0.247436i | ||||||||
\(148\) | 10.0000i | 0.821995i | ||||||||
\(149\) | −16.6491 | −1.36395 | −0.681974 | − | 0.731376i | \(-0.738878\pi\) | ||||
−0.681974 | + | 0.731376i | \(0.738878\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | −0.813788 | −0.406894 | − | 0.913475i | \(-0.633388\pi\) | ||||
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(152\) | 1.00000i | 0.0811107i | ||||||||
\(153\) | 0.837722i | 0.0677258i | ||||||||
\(154\) | −13.1623 | −1.06065 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.16228 | −0.413313 | ||||||||
\(157\) | − 18.3246i | − 1.46246i | −0.682132 | − | 0.731229i | \(-0.738947\pi\) | ||||
0.682132 | − | 0.731229i | \(-0.261053\pi\) | |||||||
\(158\) | − 5.32456i | − 0.423599i | ||||||||
\(159\) | 1.83772 | 0.145741 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.8377 | −1.32700 | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | − 22.6491i | − 1.77402i | −0.461755 | − | 0.887008i | \(-0.652780\pi\) | ||||
0.461755 | − | 0.887008i | \(-0.347220\pi\) | |||||||
\(164\) | 6.32456 | 0.493865 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.48683 | 0.503476 | ||||||||
\(167\) | − 2.64911i | − 0.204994i | −0.994733 | − | 0.102497i | \(-0.967317\pi\) | ||||
0.994733 | − | 0.102497i | \(-0.0326833\pi\) | |||||||
\(168\) | − 3.16228i | − 0.243975i | ||||||||
\(169\) | −13.6491 | −1.04993 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 9.16228i | 0.698617i | ||||||||
\(173\) | − 2.16228i | − 0.164395i | −0.996616 | − | 0.0821975i | \(-0.973806\pi\) | ||||
0.996616 | − | 0.0821975i | \(-0.0261938\pi\) | |||||||
\(174\) | −3.83772 | −0.290937 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.16228 | 0.313743 | ||||||||
\(177\) | − 7.48683i | − 0.562745i | ||||||||
\(178\) | − 7.32456i | − 0.548999i | ||||||||
\(179\) | 20.6491 | 1.54339 | 0.771693 | − | 0.635995i | \(-0.219410\pi\) | ||||
0.771693 | + | 0.635995i | \(0.219410\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.16228 | 0.681027 | 0.340513 | − | 0.940240i | \(-0.389399\pi\) | ||||
0.340513 | + | 0.940240i | \(0.389399\pi\) | |||||||
\(182\) | − 16.3246i | − 1.21006i | ||||||||
\(183\) | 4.16228i | 0.307684i | ||||||||
\(184\) | 5.32456 | 0.392531 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.32456 | −0.390415 | ||||||||
\(187\) | − 3.48683i | − 0.254982i | ||||||||
\(188\) | 6.00000i | 0.437595i | ||||||||
\(189\) | 3.16228 | 0.230022 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.6491 | 1.56647 | 0.783237 | − | 0.621723i | \(-0.213567\pi\) | ||||
0.783237 | + | 0.621723i | \(0.213567\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − 9.16228i | − 0.659515i | −0.944066 | − | 0.329758i | \(-0.893033\pi\) | ||||
0.944066 | − | 0.329758i | \(-0.106967\pi\) | |||||||
\(194\) | −0.513167 | −0.0368432 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | 24.1359i | 1.71961i | 0.510618 | + | 0.859807i | \(0.329416\pi\) | ||||
−0.510618 | + | 0.859807i | \(0.670584\pi\) | |||||||
\(198\) | 4.16228i | 0.295800i | ||||||||
\(199\) | 18.6491 | 1.32200 | 0.661000 | − | 0.750386i | \(-0.270132\pi\) | ||||
0.661000 | + | 0.750386i | \(0.270132\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.48683 | 0.457546 | ||||||||
\(202\) | 13.8114i | 0.971766i | ||||||||
\(203\) | − 12.1359i | − 0.851776i | ||||||||
\(204\) | 0.837722 | 0.0586523 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.6491 | 1.09033 | ||||||||
\(207\) | 5.32456i | 0.370082i | ||||||||
\(208\) | 5.16228i | 0.357940i | ||||||||
\(209\) | 4.16228 | 0.287911 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.8114 | −1.29503 | −0.647515 | − | 0.762053i | \(-0.724192\pi\) | ||||
−0.647515 | + | 0.762053i | \(0.724192\pi\) | |||||||
\(212\) | − 1.83772i | − 0.126215i | ||||||||
\(213\) | − 1.16228i | − 0.0796380i | ||||||||
\(214\) | −12.8377 | −0.877569 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | − 16.8377i | − 1.14302i | ||||||||
\(218\) | 7.67544i | 0.519847i | ||||||||
\(219\) | −1.00000 | −0.0675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.32456 | 0.290901 | ||||||||
\(222\) | 10.0000i | 0.671156i | ||||||||
\(223\) | − 25.6491i | − 1.71759i | −0.512318 | − | 0.858796i | \(-0.671213\pi\) | ||||
0.512318 | − | 0.858796i | \(-0.328787\pi\) | |||||||
\(224\) | −3.16228 | −0.211289 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.64911 | 0.641849 | ||||||||
\(227\) | 2.00000i | 0.132745i | 0.997795 | + | 0.0663723i | \(0.0211425\pi\) | ||||
−0.997795 | + | 0.0663723i | \(0.978857\pi\) | |||||||
\(228\) | 1.00000i | 0.0662266i | ||||||||
\(229\) | −8.16228 | −0.539378 | −0.269689 | − | 0.962947i | \(-0.586921\pi\) | ||||
−0.269689 | + | 0.962947i | \(0.586921\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.1623 | −0.866014 | ||||||||
\(232\) | 3.83772i | 0.251959i | ||||||||
\(233\) | − 11.8114i | − 0.773790i | −0.922124 | − | 0.386895i | \(-0.873548\pi\) | ||||
0.922124 | − | 0.386895i | \(-0.126452\pi\) | |||||||
\(234\) | −5.16228 | −0.337469 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.48683 | −0.487351 | ||||||||
\(237\) | − 5.32456i | − 0.345867i | ||||||||
\(238\) | 2.64911i | 0.171716i | ||||||||
\(239\) | 24.3246 | 1.57342 | 0.786712 | − | 0.617320i | \(-0.211782\pi\) | ||||
0.786712 | + | 0.617320i | \(0.211782\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.5132 | 0.677213 | 0.338606 | − | 0.940928i | \(-0.390045\pi\) | ||||
0.338606 | + | 0.940928i | \(0.390045\pi\) | |||||||
\(242\) | − 6.32456i | − 0.406558i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 4.16228 | 0.266463 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.32456 | 0.403239 | ||||||||
\(247\) | 5.16228i | 0.328468i | ||||||||
\(248\) | 5.32456i | 0.338110i | ||||||||
\(249\) | 6.48683 | 0.411086 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.6491 | −0.672166 | −0.336083 | − | 0.941832i | \(-0.609102\pi\) | ||||
−0.336083 | + | 0.941832i | \(0.609102\pi\) | |||||||
\(252\) | − 3.16228i | − 0.199205i | ||||||||
\(253\) | − 22.1623i | − 1.39333i | ||||||||
\(254\) | −15.6491 | −0.981913 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.3246i | 1.20543i | 0.797956 | + | 0.602716i | \(0.205915\pi\) | ||||
−0.797956 | + | 0.602716i | \(0.794085\pi\) | |||||||
\(258\) | 9.16228i | 0.570418i | ||||||||
\(259\) | −31.6228 | −1.96494 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.83772 | −0.237549 | ||||||||
\(262\) | 12.4868i | 0.771439i | ||||||||
\(263\) | 31.9737i | 1.97158i | 0.167980 | + | 0.985790i | \(0.446275\pi\) | ||||
−0.167980 | + | 0.985790i | \(0.553725\pi\) | |||||||
\(264\) | 4.16228 | 0.256170 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.16228 | −0.193892 | ||||||||
\(267\) | − 7.32456i | − 0.448256i | ||||||||
\(268\) | − 6.48683i | − 0.396246i | ||||||||
\(269\) | −12.3246 | −0.751441 | −0.375721 | − | 0.926733i | \(-0.622605\pi\) | ||||
−0.375721 | + | 0.926733i | \(0.622605\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.16228 | −0.0706033 | −0.0353017 | − | 0.999377i | \(-0.511239\pi\) | ||||
−0.0353017 | + | 0.999377i | \(0.511239\pi\) | |||||||
\(272\) | − 0.837722i | − 0.0507944i | ||||||||
\(273\) | − 16.3246i | − 0.988007i | ||||||||
\(274\) | −2.32456 | −0.140432 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.32456 | 0.320501 | ||||||||
\(277\) | − 24.8114i | − 1.49077i | −0.666633 | − | 0.745386i | \(-0.732265\pi\) | ||||
0.666633 | − | 0.745386i | \(-0.267735\pi\) | |||||||
\(278\) | 21.4868i | 1.28869i | ||||||||
\(279\) | −5.32456 | −0.318773 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.64911 | 0.456308 | 0.228154 | − | 0.973625i | \(-0.426731\pi\) | ||||
0.228154 | + | 0.973625i | \(0.426731\pi\) | |||||||
\(282\) | 6.00000i | 0.357295i | ||||||||
\(283\) | 24.6491i | 1.46524i | 0.680639 | + | 0.732619i | \(0.261702\pi\) | ||||
−0.680639 | + | 0.732619i | \(0.738298\pi\) | |||||||
\(284\) | −1.16228 | −0.0689685 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.4868 | 1.27054 | ||||||||
\(287\) | 20.0000i | 1.18056i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 16.2982 | 0.958719 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.513167 | −0.0300824 | ||||||||
\(292\) | 1.00000i | 0.0585206i | ||||||||
\(293\) | 16.4868i | 0.963171i | 0.876399 | + | 0.481586i | \(0.159939\pi\) | ||||
−0.876399 | + | 0.481586i | \(0.840061\pi\) | |||||||
\(294\) | 3.00000 | 0.174964 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.0000 | 0.581238 | ||||||||
\(297\) | 4.16228i | 0.241520i | ||||||||
\(298\) | 16.6491i | 0.964457i | ||||||||
\(299\) | 27.4868 | 1.58960 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.9737 | −1.67001 | ||||||||
\(302\) | 10.0000i | 0.575435i | ||||||||
\(303\) | 13.8114i | 0.793444i | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.837722 | 0.0478894 | ||||||||
\(307\) | − 13.5132i | − 0.771237i | −0.922658 | − | 0.385619i | \(-0.873988\pi\) | ||||
0.922658 | − | 0.385619i | \(-0.126012\pi\) | |||||||
\(308\) | 13.1623i | 0.749990i | ||||||||
\(309\) | 15.6491 | 0.890247 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.0000 | −1.47432 | −0.737162 | − | 0.675716i | \(-0.763835\pi\) | ||||
−0.737162 | + | 0.675716i | \(0.763835\pi\) | |||||||
\(312\) | 5.16228i | 0.292256i | ||||||||
\(313\) | − 10.6754i | − 0.603412i | −0.953401 | − | 0.301706i | \(-0.902444\pi\) | ||||
0.953401 | − | 0.301706i | \(-0.0975561\pi\) | |||||||
\(314\) | −18.3246 | −1.03411 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.32456 | −0.299530 | ||||||||
\(317\) | − 4.16228i | − 0.233777i | −0.993145 | − | 0.116888i | \(-0.962708\pi\) | ||||
0.993145 | − | 0.116888i | \(-0.0372920\pi\) | |||||||
\(318\) | − 1.83772i | − 0.103054i | ||||||||
\(319\) | 15.9737 | 0.894354 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.8377 | −0.716532 | ||||||||
\(322\) | 16.8377i | 0.938330i | ||||||||
\(323\) | − 0.837722i | − 0.0466121i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −22.6491 | −1.25442 | ||||||||
\(327\) | 7.67544i | 0.424453i | ||||||||
\(328\) | − 6.32456i | − 0.349215i | ||||||||
\(329\) | −18.9737 | −1.04605 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.18861 | −0.175262 | −0.0876310 | − | 0.996153i | \(-0.527930\pi\) | ||||
−0.0876310 | + | 0.996153i | \(0.527930\pi\) | |||||||
\(332\) | − 6.48683i | − 0.356011i | ||||||||
\(333\) | 10.0000i | 0.547997i | ||||||||
\(334\) | −2.64911 | −0.144953 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.16228 | −0.172516 | ||||||||
\(337\) | 2.97367i | 0.161986i | 0.996715 | + | 0.0809930i | \(0.0258091\pi\) | ||||
−0.996715 | + | 0.0809930i | \(0.974191\pi\) | |||||||
\(338\) | 13.6491i | 0.742414i | ||||||||
\(339\) | 9.64911 | 0.524068 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.1623 | 1.20015 | ||||||||
\(342\) | 1.00000i | 0.0540738i | ||||||||
\(343\) | − 12.6491i | − 0.682988i | ||||||||
\(344\) | 9.16228 | 0.493997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.16228 | −0.116245 | ||||||||
\(347\) | 20.0000i | 1.07366i | 0.843692 | + | 0.536828i | \(0.180378\pi\) | ||||
−0.843692 | + | 0.536828i | \(0.819622\pi\) | |||||||
\(348\) | 3.83772i | 0.205724i | ||||||||
\(349\) | 17.8377 | 0.954831 | 0.477416 | − | 0.878678i | \(-0.341574\pi\) | ||||
0.477416 | + | 0.878678i | \(0.341574\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.16228 | −0.275542 | ||||||||
\(352\) | − 4.16228i | − 0.221850i | ||||||||
\(353\) | 23.8114i | 1.26735i | 0.773598 | + | 0.633676i | \(0.218455\pi\) | ||||
−0.773598 | + | 0.633676i | \(0.781545\pi\) | |||||||
\(354\) | −7.48683 | −0.397921 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.32456 | −0.388201 | ||||||||
\(357\) | 2.64911i | 0.140206i | ||||||||
\(358\) | − 20.6491i | − 1.09134i | ||||||||
\(359\) | 11.6754 | 0.616206 | 0.308103 | − | 0.951353i | \(-0.400306\pi\) | ||||
0.308103 | + | 0.951353i | \(0.400306\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − 9.16228i | − 0.481559i | ||||||||
\(363\) | − 6.32456i | − 0.331953i | ||||||||
\(364\) | −16.3246 | −0.855639 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.16228 | 0.217566 | ||||||||
\(367\) | 7.48683i | 0.390810i | 0.980723 | + | 0.195405i | \(0.0626020\pi\) | ||||
−0.980723 | + | 0.195405i | \(0.937398\pi\) | |||||||
\(368\) | − 5.32456i | − 0.277562i | ||||||||
\(369\) | 6.32456 | 0.329243 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.81139 | 0.301712 | ||||||||
\(372\) | 5.32456i | 0.276065i | ||||||||
\(373\) | − 16.1359i | − 0.835487i | −0.908565 | − | 0.417744i | \(-0.862821\pi\) | ||||
0.908565 | − | 0.417744i | \(-0.137179\pi\) | |||||||
\(374\) | −3.48683 | −0.180300 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | 19.8114i | 1.02034i | ||||||||
\(378\) | − 3.16228i | − 0.162650i | ||||||||
\(379\) | −22.9737 | −1.18008 | −0.590039 | − | 0.807375i | \(-0.700888\pi\) | ||||
−0.590039 | + | 0.807375i | \(0.700888\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.6491 | −0.801728 | ||||||||
\(382\) | − 21.6491i | − 1.10766i | ||||||||
\(383\) | − 3.48683i | − 0.178169i | −0.996024 | − | 0.0890844i | \(-0.971606\pi\) | ||||
0.996024 | − | 0.0890844i | \(-0.0283941\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.16228 | −0.466348 | ||||||||
\(387\) | 9.16228i | 0.465745i | ||||||||
\(388\) | 0.513167i | 0.0260521i | ||||||||
\(389\) | 34.6491 | 1.75678 | 0.878390 | − | 0.477945i | \(-0.158618\pi\) | ||||
0.878390 | + | 0.477945i | \(0.158618\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.46050 | −0.225577 | ||||||||
\(392\) | − 3.00000i | − 0.151523i | ||||||||
\(393\) | 12.4868i | 0.629877i | ||||||||
\(394\) | 24.1359 | 1.21595 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.16228 | 0.209162 | ||||||||
\(397\) | − 17.1359i | − 0.860028i | −0.902822 | − | 0.430014i | \(-0.858509\pi\) | ||||
0.902822 | − | 0.430014i | \(-0.141491\pi\) | |||||||
\(398\) | − 18.6491i | − 0.934795i | ||||||||
\(399\) | −3.16228 | −0.158312 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.6491 | 0.681604 | 0.340802 | − | 0.940135i | \(-0.389301\pi\) | ||||
0.340802 | + | 0.940135i | \(0.389301\pi\) | |||||||
\(402\) | − 6.48683i | − 0.323534i | ||||||||
\(403\) | 27.4868i | 1.36922i | ||||||||
\(404\) | 13.8114 | 0.687142 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.1359 | −0.602297 | ||||||||
\(407\) | − 41.6228i | − 2.06316i | ||||||||
\(408\) | − 0.837722i | − 0.0414734i | ||||||||
\(409\) | 7.67544 | 0.379526 | 0.189763 | − | 0.981830i | \(-0.439228\pi\) | ||||
0.189763 | + | 0.981830i | \(0.439228\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.32456 | −0.114662 | ||||||||
\(412\) | − 15.6491i | − 0.770976i | ||||||||
\(413\) | − 23.6754i | − 1.16499i | ||||||||
\(414\) | 5.32456 | 0.261688 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.16228 | 0.253101 | ||||||||
\(417\) | 21.4868i | 1.05221i | ||||||||
\(418\) | − 4.16228i | − 0.203584i | ||||||||
\(419\) | −8.00000 | −0.390826 | −0.195413 | − | 0.980721i | \(-0.562605\pi\) | ||||
−0.195413 | + | 0.980721i | \(0.562605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.6491 | 0.908902 | 0.454451 | − | 0.890772i | \(-0.349835\pi\) | ||||
0.454451 | + | 0.890772i | \(0.349835\pi\) | |||||||
\(422\) | 18.8114i | 0.915724i | ||||||||
\(423\) | 6.00000i | 0.291730i | ||||||||
\(424\) | −1.83772 | −0.0892477 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.16228 | −0.0563125 | ||||||||
\(427\) | 13.1623i | 0.636967i | ||||||||
\(428\) | 12.8377i | 0.620535i | ||||||||
\(429\) | 21.4868 | 1.03739 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.324555 | −0.0156333 | −0.00781664 | − | 0.999969i | \(-0.502488\pi\) | ||||
−0.00781664 | + | 0.999969i | \(0.502488\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 28.1359i | 1.35213i | 0.736843 | + | 0.676064i | \(0.236316\pi\) | ||||
−0.736843 | + | 0.676064i | \(0.763684\pi\) | |||||||
\(434\) | −16.8377 | −0.808237 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.67544 | 0.367587 | ||||||||
\(437\) | − 5.32456i | − 0.254708i | ||||||||
\(438\) | 1.00000i | 0.0477818i | ||||||||
\(439\) | −13.6491 | −0.651437 | −0.325718 | − | 0.945467i | \(-0.605606\pi\) | ||||
−0.325718 | + | 0.945467i | \(0.605606\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | − 4.32456i | − 0.205698i | ||||||||
\(443\) | − 11.8377i | − 0.562427i | −0.959645 | − | 0.281214i | \(-0.909263\pi\) | ||||
0.959645 | − | 0.281214i | \(-0.0907369\pi\) | |||||||
\(444\) | 10.0000 | 0.474579 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −25.6491 | −1.21452 | ||||||||
\(447\) | 16.6491i | 0.787476i | ||||||||
\(448\) | 3.16228i | 0.149404i | ||||||||
\(449\) | 11.0000 | 0.519122 | 0.259561 | − | 0.965727i | \(-0.416422\pi\) | ||||
0.259561 | + | 0.965727i | \(0.416422\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.3246 | −1.23957 | ||||||||
\(452\) | − 9.64911i | − 0.453856i | ||||||||
\(453\) | 10.0000i | 0.469841i | ||||||||
\(454\) | 2.00000 | 0.0938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | − 9.67544i | − 0.452598i | −0.974058 | − | 0.226299i | \(-0.927337\pi\) | ||||
0.974058 | − | 0.226299i | \(-0.0726627\pi\) | |||||||
\(458\) | 8.16228i | 0.381398i | ||||||||
\(459\) | 0.837722 | 0.0391015 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 13.1623i | 0.612365i | ||||||||
\(463\) | − 21.6754i | − 1.00734i | −0.863895 | − | 0.503672i | \(-0.831982\pi\) | ||||
0.863895 | − | 0.503672i | \(-0.168018\pi\) | |||||||
\(464\) | 3.83772 | 0.178162 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.8114 | −0.547152 | ||||||||
\(467\) | 37.1359i | 1.71845i | 0.511601 | + | 0.859223i | \(0.329053\pi\) | ||||
−0.511601 | + | 0.859223i | \(0.670947\pi\) | |||||||
\(468\) | 5.16228i | 0.238626i | ||||||||
\(469\) | 20.5132 | 0.947210 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.3246 | −0.844351 | ||||||||
\(472\) | 7.48683i | 0.344609i | ||||||||
\(473\) | − 38.1359i | − 1.75349i | ||||||||
\(474\) | −5.32456 | −0.244565 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.64911 | 0.121422 | ||||||||
\(477\) | − 1.83772i | − 0.0841435i | ||||||||
\(478\) | − 24.3246i | − 1.11258i | ||||||||
\(479\) | 39.9737 | 1.82644 | 0.913222 | − | 0.407463i | \(-0.133586\pi\) | ||||
0.913222 | + | 0.407463i | \(0.133586\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 51.6228 | 2.35380 | ||||||||
\(482\) | − 10.5132i | − 0.478862i | ||||||||
\(483\) | 16.8377i | 0.766143i | ||||||||
\(484\) | −6.32456 | −0.287480 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 28.6491i | 1.29822i | 0.760697 | + | 0.649108i | \(0.224857\pi\) | ||||
−0.760697 | + | 0.649108i | \(0.775143\pi\) | |||||||
\(488\) | − 4.16228i | − 0.188417i | ||||||||
\(489\) | −22.6491 | −1.02423 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | − 6.32456i | − 0.285133i | ||||||||
\(493\) | − 3.21495i | − 0.144794i | ||||||||
\(494\) | 5.16228 | 0.232262 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.32456 | 0.239080 | ||||||||
\(497\) | − 3.67544i | − 0.164866i | ||||||||
\(498\) | − 6.48683i | − 0.290682i | ||||||||
\(499\) | 5.81139 | 0.260153 | 0.130077 | − | 0.991504i | \(-0.458478\pi\) | ||||
0.130077 | + | 0.991504i | \(0.458478\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.64911 | −0.118354 | ||||||||
\(502\) | 10.6491i | 0.475293i | ||||||||
\(503\) | − 29.2982i | − 1.30634i | −0.757210 | − | 0.653172i | \(-0.773438\pi\) | ||||
0.757210 | − | 0.653172i | \(-0.226562\pi\) | |||||||
\(504\) | −3.16228 | −0.140859 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.1623 | −0.985233 | ||||||||
\(507\) | 13.6491i | 0.606178i | ||||||||
\(508\) | 15.6491i | 0.694317i | ||||||||
\(509\) | −16.8114 | −0.745152 | −0.372576 | − | 0.928002i | \(-0.621525\pi\) | ||||
−0.372576 | + | 0.928002i | \(0.621525\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.16228 | −0.139891 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 1.00000i | 0.0441511i | ||||||||
\(514\) | 19.3246 | 0.852370 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.16228 | 0.403347 | ||||||||
\(517\) | − 24.9737i | − 1.09834i | ||||||||
\(518\) | 31.6228i | 1.38943i | ||||||||
\(519\) | −2.16228 | −0.0949135 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.9737 | 0.875062 | 0.437531 | − | 0.899203i | \(-0.355853\pi\) | ||||
0.437531 | + | 0.899203i | \(0.355853\pi\) | |||||||
\(522\) | 3.83772i | 0.167973i | ||||||||
\(523\) | − 16.6491i | − 0.728015i | −0.931396 | − | 0.364007i | \(-0.881408\pi\) | ||||
0.931396 | − | 0.364007i | \(-0.118592\pi\) | |||||||
\(524\) | 12.4868 | 0.545490 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.9737 | 1.39412 | ||||||||
\(527\) | − 4.46050i | − 0.194302i | ||||||||
\(528\) | − 4.16228i | − 0.181140i | ||||||||
\(529\) | −5.35089 | −0.232647 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.48683 | −0.324901 | ||||||||
\(532\) | 3.16228i | 0.137102i | ||||||||
\(533\) | − 32.6491i | − 1.41419i | ||||||||
\(534\) | −7.32456 | −0.316965 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.48683 | −0.280189 | ||||||||
\(537\) | − 20.6491i | − 0.891075i | ||||||||
\(538\) | 12.3246i | 0.531349i | ||||||||
\(539\) | −12.4868 | −0.537846 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.162278 | −0.00697686 | −0.00348843 | − | 0.999994i | \(-0.501110\pi\) | ||||
−0.00348843 | + | 0.999994i | \(0.501110\pi\) | |||||||
\(542\) | 1.16228i | 0.0499241i | ||||||||
\(543\) | − 9.16228i | − 0.393191i | ||||||||
\(544\) | −0.837722 | −0.0359170 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −16.3246 | −0.698626 | ||||||||
\(547\) | 16.8114i | 0.718803i | 0.933183 | + | 0.359402i | \(0.117019\pi\) | ||||
−0.933183 | + | 0.359402i | \(0.882981\pi\) | |||||||
\(548\) | 2.32456i | 0.0993001i | ||||||||
\(549\) | 4.16228 | 0.177642 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.83772 | 0.163492 | ||||||||
\(552\) | − 5.32456i | − 0.226628i | ||||||||
\(553\) | − 16.8377i | − 0.716013i | ||||||||
\(554\) | −24.8114 | −1.05413 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.4868 | 0.911245 | ||||||||
\(557\) | 22.8377i | 0.967665i | 0.875161 | + | 0.483833i | \(0.160756\pi\) | ||||
−0.875161 | + | 0.483833i | \(0.839244\pi\) | |||||||
\(558\) | 5.32456i | 0.225406i | ||||||||
\(559\) | 47.2982 | 2.00050 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.48683 | −0.147214 | ||||||||
\(562\) | − 7.64911i | − 0.322658i | ||||||||
\(563\) | 31.1623i | 1.31333i | 0.754181 | + | 0.656667i | \(0.228034\pi\) | ||||
−0.754181 | + | 0.656667i | \(0.771966\pi\) | |||||||
\(564\) | 6.00000 | 0.252646 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.6491 | 1.03608 | ||||||||
\(567\) | − 3.16228i | − 0.132803i | ||||||||
\(568\) | 1.16228i | 0.0487681i | ||||||||
\(569\) | −22.0000 | −0.922288 | −0.461144 | − | 0.887325i | \(-0.652561\pi\) | ||||
−0.461144 | + | 0.887325i | \(0.652561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.8114 | −0.661686 | −0.330843 | − | 0.943686i | \(-0.607333\pi\) | ||||
−0.330843 | + | 0.943686i | \(0.607333\pi\) | |||||||
\(572\) | − 21.4868i | − 0.898410i | ||||||||
\(573\) | − 21.6491i | − 0.904405i | ||||||||
\(574\) | 20.0000 | 0.834784 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 16.6754i | 0.694208i | 0.937827 | + | 0.347104i | \(0.112835\pi\) | ||||
−0.937827 | + | 0.347104i | \(0.887165\pi\) | |||||||
\(578\) | − 16.2982i | − 0.677917i | ||||||||
\(579\) | −9.16228 | −0.380771 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.5132 | 0.851030 | ||||||||
\(582\) | 0.513167i | 0.0212715i | ||||||||
\(583\) | 7.64911i | 0.316794i | ||||||||
\(584\) | 1.00000 | 0.0413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.4868 | 0.681065 | ||||||||
\(587\) | 18.8114i | 0.776429i | 0.921569 | + | 0.388215i | \(0.126908\pi\) | ||||
−0.921569 | + | 0.388215i | \(0.873092\pi\) | |||||||
\(588\) | − 3.00000i | − 0.123718i | ||||||||
\(589\) | 5.32456 | 0.219394 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.1359 | 0.992820 | ||||||||
\(592\) | − 10.0000i | − 0.410997i | ||||||||
\(593\) | − 2.32456i | − 0.0954580i | −0.998860 | − | 0.0477290i | \(-0.984802\pi\) | ||||
0.998860 | − | 0.0477290i | \(-0.0151984\pi\) | |||||||
\(594\) | 4.16228 | 0.170780 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.6491 | 0.681974 | ||||||||
\(597\) | − 18.6491i | − 0.763257i | ||||||||
\(598\) | − 27.4868i | − 1.12402i | ||||||||
\(599\) | 4.18861 | 0.171142 | 0.0855710 | − | 0.996332i | \(-0.472729\pi\) | ||||
0.0855710 | + | 0.996332i | \(0.472729\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.8114 | 1.86869 | 0.934343 | − | 0.356376i | \(-0.115988\pi\) | ||||
0.934343 | + | 0.356376i | \(0.115988\pi\) | |||||||
\(602\) | 28.9737i | 1.18088i | ||||||||
\(603\) | − 6.48683i | − 0.264164i | ||||||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.8114 | 0.561049 | ||||||||
\(607\) | − 2.02633i | − 0.0822464i | −0.999154 | − | 0.0411232i | \(-0.986906\pi\) | ||||
0.999154 | − | 0.0411232i | \(-0.0130936\pi\) | |||||||
\(608\) | − 1.00000i | − 0.0405554i | ||||||||
\(609\) | −12.1359 | −0.491773 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.9737 | 1.25306 | ||||||||
\(612\) | − 0.837722i | − 0.0338629i | ||||||||
\(613\) | − 27.2982i | − 1.10256i | −0.834319 | − | 0.551282i | \(-0.814139\pi\) | ||||
0.834319 | − | 0.551282i | \(-0.185861\pi\) | |||||||
\(614\) | −13.5132 | −0.545347 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.1623 | 0.530323 | ||||||||
\(617\) | 11.6754i | 0.470036i | 0.971991 | + | 0.235018i | \(0.0755149\pi\) | ||||
−0.971991 | + | 0.235018i | \(0.924485\pi\) | |||||||
\(618\) | − 15.6491i | − 0.629500i | ||||||||
\(619\) | −10.8377 | −0.435605 | −0.217802 | − | 0.975993i | \(-0.569889\pi\) | ||||
−0.217802 | + | 0.975993i | \(0.569889\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.32456 | 0.213667 | ||||||||
\(622\) | 26.0000i | 1.04251i | ||||||||
\(623\) | − 23.1623i | − 0.927977i | ||||||||
\(624\) | 5.16228 | 0.206656 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.6754 | −0.426677 | ||||||||
\(627\) | − 4.16228i | − 0.166225i | ||||||||
\(628\) | 18.3246i | 0.731229i | ||||||||
\(629\) | −8.37722 | −0.334022 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.2982 | 1.80329 | 0.901647 | − | 0.432473i | \(-0.142359\pi\) | ||||
0.901647 | + | 0.432473i | \(0.142359\pi\) | |||||||
\(632\) | 5.32456i | 0.211799i | ||||||||
\(633\) | 18.8114i | 0.747686i | ||||||||
\(634\) | −4.16228 | −0.165305 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.83772 | −0.0728704 | ||||||||
\(637\) | − 15.4868i | − 0.613611i | ||||||||
\(638\) | − 15.9737i | − 0.632403i | ||||||||
\(639\) | −1.16228 | −0.0459790 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.2982 | −1.47319 | −0.736596 | − | 0.676333i | \(-0.763568\pi\) | ||||
−0.736596 | + | 0.676333i | \(0.763568\pi\) | |||||||
\(642\) | 12.8377i | 0.506664i | ||||||||
\(643\) | 6.64911i | 0.262215i | 0.991368 | + | 0.131108i | \(0.0418534\pi\) | ||||
−0.991368 | + | 0.131108i | \(0.958147\pi\) | |||||||
\(644\) | 16.8377 | 0.663499 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.837722 | −0.0329597 | ||||||||
\(647\) | 9.00000i | 0.353827i | 0.984226 | + | 0.176913i | \(0.0566112\pi\) | ||||
−0.984226 | + | 0.176913i | \(0.943389\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 31.1623 | 1.22323 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.8377 | −0.659922 | ||||||||
\(652\) | 22.6491i | 0.887008i | ||||||||
\(653\) | 6.97367i | 0.272901i | 0.990647 | + | 0.136450i | \(0.0435694\pi\) | ||||
−0.990647 | + | 0.136450i | \(0.956431\pi\) | |||||||
\(654\) | 7.67544 | 0.300134 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.32456 | −0.246932 | ||||||||
\(657\) | 1.00000i | 0.0390137i | ||||||||
\(658\) | 18.9737i | 0.739671i | ||||||||
\(659\) | 49.8114 | 1.94038 | 0.970188 | − | 0.242353i | \(-0.0779193\pi\) | ||||
0.970188 | + | 0.242353i | \(0.0779193\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.2982 | 1.45073 | 0.725366 | − | 0.688363i | \(-0.241670\pi\) | ||||
0.725366 | + | 0.688363i | \(0.241670\pi\) | |||||||
\(662\) | 3.18861i | 0.123929i | ||||||||
\(663\) | − 4.32456i | − 0.167952i | ||||||||
\(664\) | −6.48683 | −0.251738 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.0000 | 0.387492 | ||||||||
\(667\) | − 20.4342i | − 0.791214i | ||||||||
\(668\) | 2.64911i | 0.102497i | ||||||||
\(669\) | −25.6491 | −0.991652 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.3246 | −0.668807 | ||||||||
\(672\) | 3.16228i | 0.121988i | ||||||||
\(673\) | − 32.4605i | − 1.25126i | −0.780120 | − | 0.625630i | \(-0.784842\pi\) | ||||
0.780120 | − | 0.625630i | \(-0.215158\pi\) | |||||||
\(674\) | 2.97367 | 0.114541 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.6491 | 0.524966 | ||||||||
\(677\) | − 18.4868i | − 0.710507i | −0.934770 | − | 0.355253i | \(-0.884395\pi\) | ||||
0.934770 | − | 0.355253i | \(-0.115605\pi\) | |||||||
\(678\) | − 9.64911i | − 0.370572i | ||||||||
\(679\) | −1.62278 | −0.0622765 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.00000 | 0.0766402 | ||||||||
\(682\) | − 22.1623i | − 0.848637i | ||||||||
\(683\) | − 37.1096i | − 1.41996i | −0.704222 | − | 0.709980i | \(-0.748704\pi\) | ||||
0.704222 | − | 0.709980i | \(-0.251296\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.6491 | −0.482945 | ||||||||
\(687\) | 8.16228i | 0.311410i | ||||||||
\(688\) | − 9.16228i | − 0.349309i | ||||||||
\(689\) | −9.48683 | −0.361420 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4868 | 0.513063 | 0.256532 | − | 0.966536i | \(-0.417420\pi\) | ||||
0.256532 | + | 0.966536i | \(0.417420\pi\) | |||||||
\(692\) | 2.16228i | 0.0821975i | ||||||||
\(693\) | 13.1623i | 0.499994i | ||||||||
\(694\) | 20.0000 | 0.759190 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.83772 | 0.145468 | ||||||||
\(697\) | 5.29822i | 0.200684i | ||||||||
\(698\) | − 17.8377i | − 0.675168i | ||||||||
\(699\) | −11.8114 | −0.446748 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.9737 | −1.16986 | −0.584930 | − | 0.811084i | \(-0.698878\pi\) | ||||
−0.584930 | + | 0.811084i | \(0.698878\pi\) | |||||||
\(702\) | 5.16228i | 0.194838i | ||||||||
\(703\) | − 10.0000i | − 0.377157i | ||||||||
\(704\) | −4.16228 | −0.156872 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.8114 | 0.896153 | ||||||||
\(707\) | 43.6754i | 1.64258i | ||||||||
\(708\) | 7.48683i | 0.281372i | ||||||||
\(709\) | −23.5132 | −0.883056 | −0.441528 | − | 0.897248i | \(-0.645563\pi\) | ||||
−0.441528 | + | 0.897248i | \(0.645563\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.32456 | −0.199686 | ||||||||
\(712\) | 7.32456i | 0.274499i | ||||||||
\(713\) | − 28.3509i | − 1.06175i | ||||||||
\(714\) | 2.64911 | 0.0991405 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −20.6491 | −0.771693 | ||||||||
\(717\) | − 24.3246i | − 0.908417i | ||||||||
\(718\) | − 11.6754i | − 0.435724i | ||||||||
\(719\) | −19.3246 | −0.720684 | −0.360342 | − | 0.932820i | \(-0.617340\pi\) | ||||
−0.360342 | + | 0.932820i | \(0.617340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.4868 | 1.84299 | ||||||||
\(722\) | − 1.00000i | − 0.0372161i | ||||||||
\(723\) | − 10.5132i | − 0.390989i | ||||||||
\(724\) | −9.16228 | −0.340513 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.32456 | −0.234726 | ||||||||
\(727\) | 49.6228i | 1.84041i | 0.391440 | + | 0.920203i | \(0.371977\pi\) | ||||
−0.391440 | + | 0.920203i | \(0.628023\pi\) | |||||||
\(728\) | 16.3246i | 0.605028i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.67544 | −0.283887 | ||||||||
\(732\) | − 4.16228i | − 0.153842i | ||||||||
\(733\) | 50.4868i | 1.86477i | 0.361462 | + | 0.932387i | \(0.382278\pi\) | ||||
−0.361462 | + | 0.932387i | \(0.617722\pi\) | |||||||
\(734\) | 7.48683 | 0.276344 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.32456 | −0.196266 | ||||||||
\(737\) | 27.0000i | 0.994558i | ||||||||
\(738\) | − 6.32456i | − 0.232810i | ||||||||
\(739\) | −6.32456 | −0.232653 | −0.116326 | − | 0.993211i | \(-0.537112\pi\) | ||||
−0.116326 | + | 0.993211i | \(0.537112\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.16228 | 0.189641 | ||||||||
\(742\) | − 5.81139i | − 0.213343i | ||||||||
\(743\) | 4.64911i | 0.170559i | 0.996357 | + | 0.0852797i | \(0.0271784\pi\) | ||||
−0.996357 | + | 0.0852797i | \(0.972822\pi\) | |||||||
\(744\) | 5.32456 | 0.195208 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −16.1359 | −0.590779 | ||||||||
\(747\) | − 6.48683i | − 0.237341i | ||||||||
\(748\) | 3.48683i | 0.127491i | ||||||||
\(749\) | −40.5964 | −1.48336 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.0000 | −0.948753 | −0.474377 | − | 0.880322i | \(-0.657327\pi\) | ||||
−0.474377 | + | 0.880322i | \(0.657327\pi\) | |||||||
\(752\) | − 6.00000i | − 0.218797i | ||||||||
\(753\) | 10.6491i | 0.388075i | ||||||||
\(754\) | 19.8114 | 0.721488 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.16228 | −0.115011 | ||||||||
\(757\) | 4.86406i | 0.176787i | 0.996086 | + | 0.0883936i | \(0.0281733\pi\) | ||||
−0.996086 | + | 0.0883936i | \(0.971827\pi\) | |||||||
\(758\) | 22.9737i | 0.834441i | ||||||||
\(759\) | −22.1623 | −0.804440 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.4868 | −1.43140 | −0.715698 | − | 0.698410i | \(-0.753891\pi\) | ||||
−0.715698 | + | 0.698410i | \(0.753891\pi\) | |||||||
\(762\) | 15.6491i | 0.566907i | ||||||||
\(763\) | 24.2719i | 0.878701i | ||||||||
\(764\) | −21.6491 | −0.783237 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.48683 | −0.125984 | ||||||||
\(767\) | 38.6491i | 1.39554i | ||||||||
\(768\) | − 1.00000i | − 0.0360844i | ||||||||
\(769\) | −34.6754 | −1.25043 | −0.625214 | − | 0.780453i | \(-0.714988\pi\) | ||||
−0.625214 | + | 0.780453i | \(0.714988\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.3246 | 0.695957 | ||||||||
\(772\) | 9.16228i | 0.329758i | ||||||||
\(773\) | 8.97367i | 0.322760i | 0.986892 | + | 0.161380i | \(0.0515945\pi\) | ||||
−0.986892 | + | 0.161380i | \(0.948405\pi\) | |||||||
\(774\) | 9.16228 | 0.329331 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.513167 | 0.0184216 | ||||||||
\(777\) | 31.6228i | 1.13446i | ||||||||
\(778\) | − 34.6491i | − 1.24223i | ||||||||
\(779\) | −6.32456 | −0.226601 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.83772 | 0.173107 | ||||||||
\(782\) | 4.46050i | 0.159507i | ||||||||
\(783\) | 3.83772i | 0.137149i | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.4868 | 0.445391 | ||||||||
\(787\) | − 34.4868i | − 1.22932i | −0.788791 | − | 0.614661i | \(-0.789293\pi\) | ||||
0.788791 | − | 0.614661i | \(-0.210707\pi\) | |||||||
\(788\) | − 24.1359i | − 0.859807i | ||||||||
\(789\) | 31.9737 | 1.13829 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.5132 | 1.08492 | ||||||||
\(792\) | − 4.16228i | − 0.147900i | ||||||||
\(793\) | − 21.4868i | − 0.763020i | ||||||||
\(794\) | −17.1359 | −0.608132 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.6491 | −0.661000 | ||||||||
\(797\) | − 47.6228i | − 1.68689i | −0.537219 | − | 0.843443i | \(-0.680525\pi\) | ||||
0.537219 | − | 0.843443i | \(-0.319475\pi\) | |||||||
\(798\) | 3.16228i | 0.111943i | ||||||||
\(799\) | −5.02633 | −0.177819 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.32456 | −0.258800 | ||||||||
\(802\) | − 13.6491i | − 0.481967i | ||||||||
\(803\) | − 4.16228i | − 0.146884i | ||||||||
\(804\) | −6.48683 | −0.228773 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 27.4868 | 0.968182 | ||||||||
\(807\) | 12.3246i | 0.433845i | ||||||||
\(808\) | − 13.8114i | − 0.485883i | ||||||||
\(809\) | 23.1623 | 0.814342 | 0.407171 | − | 0.913352i | \(-0.366515\pi\) | ||||
0.407171 | + | 0.913352i | \(0.366515\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.1886 | 0.392885 | 0.196443 | − | 0.980515i | \(-0.437061\pi\) | ||||
0.196443 | + | 0.980515i | \(0.437061\pi\) | |||||||
\(812\) | 12.1359i | 0.425888i | ||||||||
\(813\) | 1.16228i | 0.0407629i | ||||||||
\(814\) | −41.6228 | −1.45888 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.837722 | −0.0293261 | ||||||||
\(817\) | − 9.16228i | − 0.320548i | ||||||||
\(818\) | − 7.67544i | − 0.268366i | ||||||||
\(819\) | −16.3246 | −0.570426 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.8377 | 1.28565 | 0.642823 | − | 0.766015i | \(-0.277763\pi\) | ||||
0.642823 | + | 0.766015i | \(0.277763\pi\) | |||||||
\(822\) | 2.32456i | 0.0810782i | ||||||||
\(823\) | − 27.2982i | − 0.951556i | −0.879565 | − | 0.475778i | \(-0.842167\pi\) | ||||
0.879565 | − | 0.475778i | \(-0.157833\pi\) | |||||||
\(824\) | −15.6491 | −0.545163 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23.6754 | −0.823774 | ||||||||
\(827\) | − 5.16228i | − 0.179510i | −0.995964 | − | 0.0897550i | \(-0.971392\pi\) | ||||
0.995964 | − | 0.0897550i | \(-0.0286084\pi\) | |||||||
\(828\) | − 5.32456i | − 0.185041i | ||||||||
\(829\) | 22.7851 | 0.791358 | 0.395679 | − | 0.918389i | \(-0.370509\pi\) | ||||
0.395679 | + | 0.918389i | \(0.370509\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.8114 | −0.860698 | ||||||||
\(832\) | − 5.16228i | − 0.178970i | ||||||||
\(833\) | 2.51317i | 0.0870761i | ||||||||
\(834\) | 21.4868 | 0.744028 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.16228 | −0.143955 | ||||||||
\(837\) | 5.32456i | 0.184044i | ||||||||
\(838\) | 8.00000i | 0.276355i | ||||||||
\(839\) | 12.8377 | 0.443207 | 0.221604 | − | 0.975137i | \(-0.428871\pi\) | ||||
0.221604 | + | 0.975137i | \(0.428871\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.2719 | −0.492134 | ||||||||
\(842\) | − 18.6491i | − 0.642691i | ||||||||
\(843\) | − 7.64911i | − 0.263449i | ||||||||
\(844\) | 18.8114 | 0.647515 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | − 20.0000i | − 0.687208i | ||||||||
\(848\) | 1.83772i | 0.0631076i | ||||||||
\(849\) | 24.6491 | 0.845955 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −53.2456 | −1.82523 | ||||||||
\(852\) | 1.16228i | 0.0398190i | ||||||||
\(853\) | 32.3246i | 1.10677i | 0.832925 | + | 0.553386i | \(0.186664\pi\) | ||||
−0.832925 | + | 0.553386i | \(0.813336\pi\) | |||||||
\(854\) | 13.1623 | 0.450404 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.8377 | 0.438784 | ||||||||
\(857\) | − 25.6754i | − 0.877056i | −0.898717 | − | 0.438528i | \(-0.855500\pi\) | ||||
0.898717 | − | 0.438528i | \(-0.144500\pi\) | |||||||
\(858\) | − 21.4868i | − 0.733548i | ||||||||
\(859\) | 5.35089 | 0.182570 | 0.0912850 | − | 0.995825i | \(-0.470903\pi\) | ||||
0.0912850 | + | 0.995825i | \(0.470903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.0000 | 0.681598 | ||||||||
\(862\) | 0.324555i | 0.0110544i | ||||||||
\(863\) | 54.9737i | 1.87133i | 0.352896 | + | 0.935663i | \(0.385197\pi\) | ||||
−0.352896 | + | 0.935663i | \(0.614803\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 28.1359 | 0.956098 | ||||||||
\(867\) | − 16.2982i | − 0.553517i | ||||||||
\(868\) | 16.8377i | 0.571510i | ||||||||
\(869\) | 22.1623 | 0.751804 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.4868 | −1.13466 | ||||||||
\(872\) | − 7.67544i | − 0.259923i | ||||||||
\(873\) | 0.513167i | 0.0173681i | ||||||||
\(874\) | −5.32456 | −0.180106 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.00000 | 0.0337869 | ||||||||
\(877\) | − 45.6228i | − 1.54057i | −0.637699 | − | 0.770286i | \(-0.720114\pi\) | ||||
0.637699 | − | 0.770286i | \(-0.279886\pi\) | |||||||
\(878\) | 13.6491i | 0.460635i | ||||||||
\(879\) | 16.4868 | 0.556087 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.3246 | 0.482607 | 0.241303 | − | 0.970450i | \(-0.422425\pi\) | ||||
0.241303 | + | 0.970450i | \(0.422425\pi\) | |||||||
\(882\) | − 3.00000i | − 0.101015i | ||||||||
\(883\) | − 29.4868i | − 0.992311i | −0.868234 | − | 0.496155i | \(-0.834745\pi\) | ||||
0.868234 | − | 0.496155i | \(-0.165255\pi\) | |||||||
\(884\) | −4.32456 | −0.145451 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.8377 | −0.397696 | ||||||||
\(887\) | − 21.6754i | − 0.727790i | −0.931440 | − | 0.363895i | \(-0.881447\pi\) | ||||
0.931440 | − | 0.363895i | \(-0.118553\pi\) | |||||||
\(888\) | − 10.0000i | − 0.335578i | ||||||||
\(889\) | −49.4868 | −1.65974 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.16228 | 0.139442 | ||||||||
\(892\) | 25.6491i | 0.858796i | ||||||||
\(893\) | − 6.00000i | − 0.200782i | ||||||||
\(894\) | 16.6491 | 0.556830 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.16228 | 0.105644 | ||||||||
\(897\) | − 27.4868i | − 0.917759i | ||||||||
\(898\) | − 11.0000i | − 0.367075i | ||||||||
\(899\) | 20.4342 | 0.681518 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.53950 | 0.0512882 | ||||||||
\(902\) | 26.3246i | 0.876512i | ||||||||
\(903\) | 28.9737i | 0.964183i | ||||||||
\(904\) | −9.64911 | −0.320925 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.0000 | 0.332228 | ||||||||
\(907\) | 38.6491i | 1.28332i | 0.766988 | + | 0.641661i | \(0.221755\pi\) | ||||
−0.766988 | + | 0.641661i | \(0.778245\pi\) | |||||||
\(908\) | − 2.00000i | − 0.0663723i | ||||||||
\(909\) | 13.8114 | 0.458095 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.02633 | −0.232793 | −0.116396 | − | 0.993203i | \(-0.537134\pi\) | ||||
−0.116396 | + | 0.993203i | \(0.537134\pi\) | |||||||
\(912\) | − 1.00000i | − 0.0331133i | ||||||||
\(913\) | 27.0000i | 0.893570i | ||||||||
\(914\) | −9.67544 | −0.320035 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.16228 | 0.269689 | ||||||||
\(917\) | 39.4868i | 1.30397i | ||||||||
\(918\) | − 0.837722i | − 0.0276490i | ||||||||
\(919\) | 18.8377 | 0.621399 | 0.310700 | − | 0.950508i | \(-0.399437\pi\) | ||||
0.310700 | + | 0.950508i | \(0.399437\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.5132 | −0.445274 | ||||||||
\(922\) | − 12.0000i | − 0.395199i | ||||||||
\(923\) | 6.00000i | 0.197492i | ||||||||
\(924\) | 13.1623 | 0.433007 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21.6754 | −0.712299 | ||||||||
\(927\) | − 15.6491i | − 0.513984i | ||||||||
\(928\) | − 3.83772i | − 0.125979i | ||||||||
\(929\) | 37.2982 | 1.22371 | 0.611857 | − | 0.790968i | \(-0.290423\pi\) | ||||
0.611857 | + | 0.790968i | \(0.290423\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.00000 | −0.0983210 | ||||||||
\(932\) | 11.8114i | 0.386895i | ||||||||
\(933\) | 26.0000i | 0.851202i | ||||||||
\(934\) | 37.1359 | 1.21513 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.16228 | 0.168734 | ||||||||
\(937\) | 26.6491i | 0.870588i | 0.900288 | + | 0.435294i | \(0.143356\pi\) | ||||
−0.900288 | + | 0.435294i | \(0.856644\pi\) | |||||||
\(938\) | − 20.5132i | − 0.669779i | ||||||||
\(939\) | −10.6754 | −0.348380 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.8114 | 1.06962 | 0.534810 | − | 0.844972i | \(-0.320383\pi\) | ||||
0.534810 | + | 0.844972i | \(0.320383\pi\) | |||||||
\(942\) | 18.3246i | 0.597046i | ||||||||
\(943\) | 33.6754i | 1.09662i | ||||||||
\(944\) | 7.48683 | 0.243676 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.1359 | −1.23991 | ||||||||
\(947\) | 48.0000i | 1.55979i | 0.625910 | + | 0.779895i | \(0.284728\pi\) | ||||
−0.625910 | + | 0.779895i | \(0.715272\pi\) | |||||||
\(948\) | 5.32456i | 0.172934i | ||||||||
\(949\) | 5.16228 | 0.167575 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.16228 | −0.134971 | ||||||||
\(952\) | − 2.64911i | − 0.0858582i | ||||||||
\(953\) | − 40.6754i | − 1.31761i | −0.752315 | − | 0.658803i | \(-0.771063\pi\) | ||||
0.752315 | − | 0.658803i | \(-0.228937\pi\) | |||||||
\(954\) | −1.83772 | −0.0594985 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −24.3246 | −0.786712 | ||||||||
\(957\) | − 15.9737i | − 0.516355i | ||||||||
\(958\) | − 39.9737i | − 1.29149i | ||||||||
\(959\) | −7.35089 | −0.237373 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.64911 | −0.0854552 | ||||||||
\(962\) | − 51.6228i | − 1.66439i | ||||||||
\(963\) | 12.8377i | 0.413690i | ||||||||
\(964\) | −10.5132 | −0.338606 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.8377 | 0.541745 | ||||||||
\(967\) | − 24.3246i | − 0.782225i | −0.920343 | − | 0.391112i | \(-0.872090\pi\) | ||||
0.920343 | − | 0.391112i | \(-0.127910\pi\) | |||||||
\(968\) | 6.32456i | 0.203279i | ||||||||
\(969\) | −0.837722 | −0.0269115 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.5132 | 0.401567 | 0.200783 | − | 0.979636i | \(-0.435651\pi\) | ||||
0.200783 | + | 0.979636i | \(0.435651\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 67.9473i | 2.17829i | ||||||||
\(974\) | 28.6491 | 0.917977 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.16228 | −0.133231 | ||||||||
\(977\) | 53.9473i | 1.72593i | 0.505265 | + | 0.862964i | \(0.331395\pi\) | ||||
−0.505265 | + | 0.862964i | \(0.668605\pi\) | |||||||
\(978\) | 22.6491i | 0.724239i | ||||||||
\(979\) | 30.4868 | 0.974363 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.67544 | 0.245058 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 36.1359i | − 1.15256i | −0.817253 | − | 0.576279i | \(-0.804504\pi\) | ||||
0.817253 | − | 0.576279i | \(-0.195496\pi\) | |||||||
\(984\) | −6.32456 | −0.201619 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.21495 | −0.102385 | ||||||||
\(987\) | 18.9737i | 0.603938i | ||||||||
\(988\) | − 5.16228i | − 0.164234i | ||||||||
\(989\) | −48.7851 | −1.55127 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.2982 | 0.771858 | 0.385929 | − | 0.922528i | \(-0.373881\pi\) | ||||
0.385929 | + | 0.922528i | \(0.373881\pi\) | |||||||
\(992\) | − 5.32456i | − 0.169055i | ||||||||
\(993\) | 3.18861i | 0.101188i | ||||||||
\(994\) | −3.67544 | −0.116578 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.48683 | −0.205543 | ||||||||
\(997\) | − 13.5132i | − 0.427966i | −0.976837 | − | 0.213983i | \(-0.931356\pi\) | ||||
0.976837 | − | 0.213983i | \(-0.0686438\pi\) | |||||||
\(998\) | − 5.81139i | − 0.183956i | ||||||||
\(999\) | 10.0000 | 0.316386 |
(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.v.799.1 | 4 | ||
5.2 | odd | 4 | 2850.2.a.bg.1.2 | yes | 2 | ||
5.3 | odd | 4 | 2850.2.a.bf.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 2850.2.d.v.799.4 | 4 | ||
15.2 | even | 4 | 8550.2.a.bq.1.2 | 2 | |||
15.8 | even | 4 | 8550.2.a.ca.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2850.2.a.bf.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
2850.2.a.bg.1.2 | yes | 2 | 5.2 | odd | 4 | ||
2850.2.d.v.799.1 | 4 | 1.1 | even | 1 | trivial | ||
2850.2.d.v.799.4 | 4 | 5.4 | even | 2 | inner | ||
8550.2.a.bq.1.2 | 2 | 15.2 | even | 4 | |||
8550.2.a.ca.1.1 | 2 | 15.8 | even | 4 |