Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1121,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.b (of order \(2\), degree \(1\), 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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 35 x^{10} - 120 x^{9} + 362 x^{8} - 794 x^{7} + 1463 x^{6} - 2048 x^{5} + 2258 x^{4} + \cdots + 61 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1121.7 | ||
Root | \(0.500000 - 2.51441i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1121 |
Dual form | 2240.2.b.g.1121.6 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.191804i | 0.110738i | 0.998466 | + | 0.0553690i | \(0.0176335\pi\) | ||||
−0.998466 | + | 0.0553690i | \(0.982366\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.96321 | 0.987737 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.28284i | 0.688303i | 0.938914 | + | 0.344152i | \(0.111833\pi\) | ||||
−0.938914 | + | 0.344152i | \(0.888167\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 7.09308i | − 1.96727i | −0.180185 | − | 0.983633i | \(-0.557670\pi\) | ||||
0.180185 | − | 0.983633i | \(-0.442330\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.191804 | −0.0495236 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.56906 | −1.10816 | −0.554080 | − | 0.832464i | \(-0.686930\pi\) | ||||
−0.554080 | + | 0.832464i | \(0.686930\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.962523i | 0.220818i | 0.993886 | + | 0.110409i | \(0.0352161\pi\) | ||||
−0.993886 | + | 0.110409i | \(0.964784\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 0.191804i | − 0.0418551i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.09510 | 1.47943 | 0.739715 | − | 0.672920i | \(-0.234960\pi\) | ||||
0.739715 | + | 0.672920i | \(0.234960\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.14377i | 0.220118i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8.27096i | − 1.53588i | −0.640522 | − | 0.767940i | \(-0.721282\pi\) | ||||
0.640522 | − | 0.767940i | \(-0.278718\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.79834 | 1.04141 | 0.520706 | − | 0.853736i | \(-0.325669\pi\) | ||||
0.520706 | + | 0.853736i | \(0.325669\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.437858 | −0.0762214 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.00000i | − 0.169031i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.01460i | 0.659997i | 0.943981 | + | 0.329998i | \(0.107048\pi\) | ||||
−0.943981 | + | 0.329998i | \(0.892952\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.36048 | 0.217851 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.14580 | 0.647466 | 0.323733 | − | 0.946149i | \(-0.395062\pi\) | ||||
0.323733 | + | 0.946149i | \(0.395062\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.77547i | − 1.33825i | −0.743152 | − | 0.669123i | \(-0.766670\pi\) | ||||
0.743152 | − | 0.669123i | \(-0.233330\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.96321i | 0.441729i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.18259 | 0.318364 | 0.159182 | − | 0.987249i | \(-0.449114\pi\) | ||||
0.159182 | + | 0.987249i | \(0.449114\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 0.876363i | − 0.122715i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4.79700i | − 0.658919i | −0.944170 | − | 0.329460i | \(-0.893133\pi\) | ||||
0.944170 | − | 0.329460i | \(-0.106867\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.28284 | −0.307819 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.184616 | −0.0244530 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.2877i | 1.72992i | 0.501844 | + | 0.864958i | \(0.332655\pi\) | ||||
−0.501844 | + | 0.864958i | \(0.667345\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.486527i | 0.0622934i | 0.999515 | + | 0.0311467i | \(0.00991591\pi\) | ||||
−0.999515 | + | 0.0311467i | \(0.990084\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.96321 | −0.373330 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.09308 | 0.879788 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 7.20902i | − 0.880722i | −0.897821 | − | 0.440361i | \(-0.854850\pi\) | ||||
0.897821 | − | 0.440361i | \(-0.145150\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.36087i | 0.163829i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.30311 | −0.154651 | −0.0773256 | − | 0.997006i | \(-0.524638\pi\) | ||||
−0.0773256 | + | 0.997006i | \(0.524638\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.33844 | −0.975941 | −0.487970 | − | 0.872860i | \(-0.662263\pi\) | ||||
−0.487970 | + | 0.872860i | \(0.662263\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 0.191804i | − 0.0221476i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.28284i | − 0.260154i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.6482 | 1.42304 | 0.711518 | − | 0.702668i | \(-0.248008\pi\) | ||||
0.711518 | + | 0.702668i | \(0.248008\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.67025 | 0.963362 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.6474i | 1.38823i | 0.719864 | + | 0.694115i | \(0.244204\pi\) | ||||
−0.719864 | + | 0.694115i | \(0.755796\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 4.56906i | − 0.495584i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.58640 | 0.170080 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.09510 | 0.964079 | 0.482039 | − | 0.876150i | \(-0.339896\pi\) | ||||
0.482039 | + | 0.876150i | \(0.339896\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.09308i | 0.743556i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.11214i | 0.115324i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.962523 | −0.0987528 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.64085 | 0.166604 | 0.0833018 | − | 0.996524i | \(-0.473453\pi\) | ||||
0.0833018 | + | 0.996524i | \(0.473453\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.76455i | 0.679863i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 2.67268i | − 0.265942i | −0.991120 | − | 0.132971i | \(-0.957548\pi\) | ||||
0.991120 | − | 0.132971i | \(-0.0424516\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.18259 | −0.215057 | −0.107529 | − | 0.994202i | \(-0.534294\pi\) | ||||
−0.107529 | + | 0.994202i | \(0.534294\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.191804 | 0.0187182 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.66710i | 0.257838i | 0.991655 | + | 0.128919i | \(0.0411507\pi\) | ||||
−0.991655 | + | 0.128919i | \(0.958849\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 5.63437i | − 0.539675i | −0.962906 | − | 0.269837i | \(-0.913030\pi\) | ||||
0.962906 | − | 0.269837i | \(-0.0869699\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.770017 | −0.0730868 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.3892 | 1.91805 | 0.959027 | − | 0.283315i | \(-0.0914343\pi\) | ||||
0.959027 | + | 0.283315i | \(0.0914343\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.09510i | 0.661621i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 21.0183i | − 1.94314i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.56906 | 0.418845 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.78863 | 0.526239 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.795182i | 0.0716991i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.31003 | 0.737396 | 0.368698 | − | 0.929549i | \(-0.379804\pi\) | ||||
0.368698 | + | 0.929549i | \(0.379804\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.68317 | 0.148195 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.60724i | 0.839388i | 0.907666 | + | 0.419694i | \(0.137863\pi\) | ||||
−0.907666 | + | 0.419694i | \(0.862137\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 0.962523i | − 0.0834613i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.14377 | −0.0984398 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.486527 | −0.0415668 | −0.0207834 | − | 0.999784i | \(-0.506616\pi\) | ||||
−0.0207834 | + | 0.999784i | \(0.506616\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 17.6713i | − 1.49886i | −0.662081 | − | 0.749432i | \(-0.730327\pi\) | ||||
0.662081 | − | 0.749432i | \(-0.269673\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.418630i | 0.0352550i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.1924 | 1.35407 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.27096 | 0.686866 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.191804i | 0.0158197i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.66847i | 0.382456i | 0.981546 | + | 0.191228i | \(0.0612470\pi\) | ||||
−0.981546 | + | 0.191228i | \(0.938753\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5733 | 1.18596 | 0.592978 | − | 0.805219i | \(-0.297952\pi\) | ||||
0.592978 | + | 0.805219i | \(0.297952\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.5391 | −1.09457 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.79834i | 0.465734i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 15.2593i | − 1.21783i | −0.793237 | − | 0.608913i | \(-0.791606\pi\) | ||||
0.793237 | − | 0.608913i | \(-0.208394\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.920084 | 0.0729674 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.09510 | −0.559172 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 5.31448i | − 0.416262i | −0.978101 | − | 0.208131i | \(-0.933262\pi\) | ||||
0.978101 | − | 0.208131i | \(-0.0667381\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 0.437858i | − 0.0340872i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.3701 | 1.42152 | 0.710761 | − | 0.703433i | \(-0.248351\pi\) | ||||
0.710761 | + | 0.703433i | \(0.248351\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −37.3117 | −2.87013 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.85216i | 0.218110i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.83246i | − 0.139319i | −0.997571 | − | 0.0696596i | \(-0.977809\pi\) | ||||
0.997571 | − | 0.0696596i | \(-0.0221913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.54864 | −0.191568 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 12.4499i | − 0.930551i | −0.885166 | − | 0.465276i | \(-0.845955\pi\) | ||||
0.885166 | − | 0.465276i | \(-0.154045\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3.81930i | − 0.283886i | −0.989875 | − | 0.141943i | \(-0.954665\pi\) | ||||
0.989875 | − | 0.141943i | \(-0.0453350\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.0933179 | −0.00689826 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.01460 | −0.295160 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 10.4304i | − 0.762749i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.14377i | − 0.0831969i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.5957 | −1.63497 | −0.817485 | − | 0.575950i | \(-0.804632\pi\) | ||||
−0.817485 | + | 0.575950i | \(0.804632\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.5300 | 1.69372 | 0.846862 | − | 0.531812i | \(-0.178489\pi\) | ||||
0.846862 | + | 0.531812i | \(0.178489\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.36048i | 0.0974260i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 6.06709i | − 0.432262i | −0.976364 | − | 0.216131i | \(-0.930656\pi\) | ||||
0.976364 | − | 0.216131i | \(-0.0693439\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.4683 | −1.73452 | −0.867258 | − | 0.497860i | \(-0.834119\pi\) | ||||
−0.867258 | + | 0.497860i | \(0.834119\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.38272 | 0.0975295 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.27096i | 0.580508i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.14580i | 0.289556i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.0243 | 1.46129 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.19729 | −0.151990 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.0643i | 1.24360i | 0.783177 | + | 0.621799i | \(0.213598\pi\) | ||||
−0.783177 | + | 0.621799i | \(0.786402\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 0.249942i | − 0.0171258i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.77547 | 0.598482 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.79834 | −0.393617 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 1.59935i | − 0.108074i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.4087i | 2.18004i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.8582 | −1.79856 | −0.899279 | − | 0.437376i | \(-0.855908\pi\) | ||||
−0.899279 | + | 0.437376i | \(0.855908\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.96321 | −0.197547 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 14.9436i | − 0.991844i | −0.868367 | − | 0.495922i | \(-0.834830\pi\) | ||||
0.868367 | − | 0.495922i | \(-0.165170\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.0859i | 1.06299i | 0.847063 | + | 0.531493i | \(0.178369\pi\) | ||||
−0.847063 | + | 0.531493i | \(0.821631\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.437858 | 0.0288090 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.5949 | −0.956143 | −0.478072 | − | 0.878321i | \(-0.658664\pi\) | ||||
−0.478072 | + | 0.878321i | \(0.658664\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.18259i | 0.142377i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.42598i | 0.157584i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.1332 | −0.720149 | −0.360075 | − | 0.932924i | \(-0.617249\pi\) | ||||
−0.360075 | + | 0.932924i | \(0.617249\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.7887 | 1.14587 | 0.572937 | − | 0.819600i | \(-0.305804\pi\) | ||||
0.572937 | + | 0.819600i | \(0.305804\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.09429i | 0.326799i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000i | 0.0638877i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.82725 | 0.434408 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.42582 | −0.153730 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.1989i | 1.14870i | 0.818608 | + | 0.574352i | \(0.194746\pi\) | ||||
−0.818608 | + | 0.574352i | \(0.805254\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.1970i | 1.01830i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.876363 | 0.0548800 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.71531 | 0.543646 | 0.271823 | − | 0.962347i | \(-0.412373\pi\) | ||||
0.271823 | + | 0.962347i | \(0.412373\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 4.01460i | − 0.249455i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 24.5086i | − 1.51704i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.22578 | 0.445561 | 0.222780 | − | 0.974869i | \(-0.428487\pi\) | ||||
0.222780 | + | 0.974869i | \(0.428487\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.79700 | 0.294678 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.74448i | 0.106760i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 24.0081i | − 1.46380i | −0.681412 | − | 0.731900i | \(-0.738634\pi\) | ||||
0.681412 | − | 0.731900i | \(-0.261366\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.6009 | −0.704703 | −0.352352 | − | 0.935868i | \(-0.614618\pi\) | ||||
−0.352352 | + | 0.935868i | \(0.614618\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.36048 | −0.0823400 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 2.28284i | − 0.137661i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.2267i | 1.33547i | 0.744397 | + | 0.667737i | \(0.232737\pi\) | ||||
−0.744397 | + | 0.667737i | \(0.767263\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.1817 | 1.02864 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.0524 | 1.13657 | 0.568286 | − | 0.822831i | \(-0.307607\pi\) | ||||
0.568286 | + | 0.822831i | \(0.307607\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 6.75611i | − 0.401609i | −0.979631 | − | 0.200805i | \(-0.935644\pi\) | ||||
0.979631 | − | 0.200805i | \(-0.0643556\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 0.184616i | − 0.0109357i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.14580 | −0.244719 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.87629 | 0.228017 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.314722i | 0.0184494i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 10.5274i | − 0.615017i | −0.951545 | − | 0.307508i | \(-0.900505\pi\) | ||||
0.951545 | − | 0.307508i | \(-0.0994952\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.2877 | −0.773642 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.61104 | −0.151508 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 50.3261i | − 2.91043i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.77547i | 0.505809i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.512630 | 0.0294499 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.486527 | −0.0278585 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.6866i | 0.609915i | 0.952366 | + | 0.304958i | \(0.0986423\pi\) | ||||
−0.952366 | + | 0.304958i | \(0.901358\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 0.418630i | − 0.0238150i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.2196 | −1.94041 | −0.970207 | − | 0.242278i | \(-0.922105\pi\) | ||||
−0.970207 | + | 0.242278i | \(0.922105\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.3322 | −0.866627 | −0.433314 | − | 0.901243i | \(-0.642656\pi\) | ||||
−0.433314 | + | 0.901243i | \(0.642656\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 2.96321i | − 0.166958i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 8.05495i | − 0.452411i | −0.974080 | − | 0.226206i | \(-0.927368\pi\) | ||||
0.974080 | − | 0.226206i | \(-0.0726321\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.8813 | 1.05715 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.511560 | −0.0285525 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 4.39782i | − 0.244701i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.09308i | 0.393453i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.08069 | 0.0597625 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.18259 | −0.120330 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.7492i | 0.700758i | 0.936608 | + | 0.350379i | \(0.113947\pi\) | ||||
−0.936608 | + | 0.350379i | \(0.886053\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.8961i | 0.651903i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.20902 | 0.393871 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.80570 | −0.479677 | −0.239839 | − | 0.970813i | \(-0.577095\pi\) | ||||
−0.239839 | + | 0.970813i | \(0.577095\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.91073i | 0.212402i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.2367i | 0.716807i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.36087 | −0.0732667 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 29.8409i | − 1.60194i | −0.598702 | − | 0.800972i | \(-0.704317\pi\) | ||||
0.598702 | − | 0.800972i | \(-0.295683\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 18.9719i | − 1.01554i | −0.861492 | − | 0.507772i | \(-0.830469\pi\) | ||||
0.861492 | − | 0.507772i | \(-0.169531\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.11283 | 0.433031 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.853924 | −0.0454498 | −0.0227249 | − | 0.999742i | \(-0.507234\pi\) | ||||
−0.0227249 | + | 0.999742i | \(0.507234\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.30311i | − 0.0691621i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.876363i | 0.0463821i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.1272 | 0.534491 | 0.267245 | − | 0.963629i | \(-0.413887\pi\) | ||||
0.267245 | + | 0.963629i | \(0.413887\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0735 | 0.951239 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.11028i | 0.0582747i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 8.33844i | − 0.436454i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.0927 | −1.51863 | −0.759315 | − | 0.650724i | \(-0.774466\pi\) | ||||
−0.759315 | + | 0.650724i | \(0.774466\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.2849 | 0.639526 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.79700i | 0.249048i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.6342i | 0.550617i | 0.961356 | + | 0.275309i | \(0.0887800\pi\) | ||||
−0.961356 | + | 0.275309i | \(0.911220\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.191804 | 0.00990471 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −58.6666 | −3.02148 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.7389i | 1.78442i | 0.451625 | + | 0.892208i | \(0.350844\pi\) | ||||
−0.451625 | + | 0.892208i | \(0.649156\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.59390i | 0.0816578i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.23011 | 0.471637 | 0.235818 | − | 0.971797i | \(-0.424223\pi\) | ||||
0.235818 | + | 0.971797i | \(0.424223\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.28284 | 0.116344 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 26.0036i | − 1.32184i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 2.25392i | − 0.114278i | −0.998366 | − | 0.0571391i | \(-0.981802\pi\) | ||||
0.998366 | − | 0.0571391i | \(-0.0181978\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.4179 | −1.63944 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.84271 | −0.0929522 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.6482i | 0.636401i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.14020i | 0.358356i | 0.983817 | + | 0.179178i | \(0.0573438\pi\) | ||||
−0.983817 | + | 0.179178i | \(0.942656\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.184616 | 0.00924235 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.5177 | 1.27429 | 0.637147 | − | 0.770743i | \(-0.280115\pi\) | ||||
0.637147 | + | 0.770743i | \(0.280115\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 41.1281i | − 2.04873i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.67025i | 0.430828i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.16471 | −0.454278 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.9071 | −1.33047 | −0.665236 | − | 0.746634i | \(-0.731669\pi\) | ||||
−0.665236 | + | 0.746634i | \(0.731669\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 0.0933179i | − 0.00460303i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 13.2877i | − 0.653847i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.6474 | −0.620836 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.38943 | 0.165981 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.57935i | 0.467982i | 0.972239 | + | 0.233991i | \(0.0751786\pi\) | ||||
−0.972239 | + | 0.233991i | \(0.924821\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.7603i | 1.84032i | 0.391539 | + | 0.920161i | \(0.371943\pi\) | ||||
−0.391539 | + | 0.920161i | \(0.628057\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.46748 | 0.314460 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.56906 | 0.221632 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 0.486527i | − 0.0235447i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.10576i | 0.149948i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.5243 | −0.699613 | −0.349806 | − | 0.936822i | \(-0.613753\pi\) | ||||
−0.349806 | + | 0.936822i | \(0.613753\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.0665 | −1.01239 | −0.506196 | − | 0.862419i | \(-0.668949\pi\) | ||||
−0.506196 | + | 0.862419i | \(0.668949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.58640i | 0.0760622i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.82920i | 0.326685i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.15309 | 0.102761 | 0.0513807 | − | 0.998679i | \(-0.483638\pi\) | ||||
0.0513807 | + | 0.998679i | \(0.483638\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.96321 | 0.141105 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.3536i | 1.58468i | 0.610081 | + | 0.792339i | \(0.291137\pi\) | ||||
−0.610081 | + | 0.792339i | \(0.708863\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.09510i | 0.431149i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.895432 | −0.0423525 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.9197 | −1.03446 | −0.517228 | − | 0.855848i | \(-0.673036\pi\) | ||||
−0.517228 | + | 0.855848i | \(0.673036\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.46422i | 0.445653i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.79521i | 0.131330i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.09308 | −0.332529 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.2437 | −0.993740 | −0.496870 | − | 0.867825i | \(-0.665517\pi\) | ||||
−0.496870 | + | 0.867825i | \(0.665517\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 5.22594i | − 0.243926i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.02516i | 0.280620i | 0.990108 | + | 0.140310i | \(0.0448099\pi\) | ||||
−0.990108 | + | 0.140310i | \(0.955190\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.26475 | −0.244674 | −0.122337 | − | 0.992489i | \(-0.539039\pi\) | ||||
−0.122337 | + | 0.992489i | \(0.539039\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.11214 | −0.0515745 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 25.5467i | − 1.18216i | −0.806614 | − | 0.591079i | \(-0.798702\pi\) | ||||
0.806614 | − | 0.591079i | \(-0.201298\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.20902i | 0.332882i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.92680 | 0.134860 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.0330 | 0.921119 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 0.962523i | − 0.0441636i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 14.2145i | − 0.650839i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.4709 | 1.02672 | 0.513360 | − | 0.858173i | \(-0.328401\pi\) | ||||
0.513360 | + | 0.858173i | \(0.328401\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.4759 | 1.29839 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.36087i | − 0.0619216i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.64085i | 0.0745074i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.4033 | −1.42302 | −0.711510 | − | 0.702676i | \(-0.751988\pi\) | ||||
−0.711510 | + | 0.702676i | \(0.751988\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.01934 | 0.0460961 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 4.61526i | − 0.208284i | −0.994562 | − | 0.104142i | \(-0.966790\pi\) | ||||
0.994562 | − | 0.104142i | \(-0.0332096\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.7905i | 1.70200i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.76455 | −0.304044 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.30311 | 0.0584527 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 13.2110i | − 0.591408i | −0.955280 | − | 0.295704i | \(-0.904446\pi\) | ||||
0.955280 | − | 0.295704i | \(-0.0955541\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.52346i | 0.157417i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0644 | −0.537926 | −0.268963 | − | 0.963150i | \(-0.586681\pi\) | ||||
−0.268963 | + | 0.963150i | \(0.586681\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.67268 | 0.118933 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 7.15654i | − 0.317833i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.8433i | 1.10116i | 0.834782 | + | 0.550580i | \(0.185594\pi\) | ||||
−0.834782 | + | 0.550580i | \(0.814406\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.33844 | 0.368871 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.10090 | −0.0486060 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2.18259i | − 0.0961765i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.98252i | 0.219131i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.351473 | 0.0154279 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.8102 | −0.736470 | −0.368235 | − | 0.929733i | \(-0.620038\pi\) | ||||
−0.368235 | + | 0.929733i | \(0.620038\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 0.150199i | − 0.00656775i | −0.999995 | − | 0.00328388i | \(-0.998955\pi\) | ||||
0.999995 | − | 0.00328388i | \(-0.00104529\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.191804i | 0.00837101i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.4929 | −1.15405 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.3404 | 1.18871 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 39.3744i | 1.70870i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 29.4065i | − 1.27374i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.66710 | −0.115309 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.38795 | 0.103047 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.28284i | 0.0983290i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.0978i | 1.59496i | 0.603347 | + | 0.797479i | \(0.293833\pi\) | ||||
−0.603347 | + | 0.797479i | \(0.706167\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.732556 | 0.0314370 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.63437 | 0.241350 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 24.2098i | − 1.03514i | −0.855642 | − | 0.517568i | \(-0.826838\pi\) | ||||
0.855642 | − | 0.517568i | \(-0.173162\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.44168i | 0.0615295i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.96099 | 0.339150 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.6482 | −0.537857 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 0.770017i | − 0.0326854i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.17924i | 0.304194i | 0.988366 | + | 0.152097i | \(0.0486026\pi\) | ||||
−0.988366 | + | 0.152097i | \(0.951397\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −62.2451 | −2.63269 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.00060 | 0.0844654 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.9927i | 1.43262i | 0.697781 | + | 0.716312i | \(0.254171\pi\) | ||||
−0.697781 | + | 0.716312i | \(0.745829\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.3892i | 0.857780i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.67025 | −0.364116 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.38269 | −0.0579654 | −0.0289827 | − | 0.999580i | \(-0.509227\pi\) | ||||
−0.0289827 | + | 0.999580i | \(0.509227\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 27.5840i | − 1.15435i | −0.816619 | − | 0.577177i | \(-0.804154\pi\) | ||||
0.816619 | − | 0.577177i | \(-0.195846\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 4.33395i | − 0.181053i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.09510 | −0.295886 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.1968 | −1.04895 | −0.524477 | − | 0.851424i | \(-0.675739\pi\) | ||||
−0.524477 | + | 0.851424i | \(0.675739\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.51314i | 0.187560i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 12.6474i | − 0.524702i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.9508 | 0.453536 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 21.0183 | 0.868999 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.3370i | 0.715574i | 0.933803 | + | 0.357787i | \(0.116469\pi\) | ||||
−0.933803 | + | 0.357787i | \(0.883531\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.58104i | 0.229963i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.16369 | 0.0478679 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.02762 | 0.124329 | 0.0621647 | − | 0.998066i | \(-0.480200\pi\) | ||||
0.0621647 | + | 0.998066i | \(0.480200\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.56906i | 0.187313i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 4.69313i | − 0.192077i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.0391 | −0.818774 | −0.409387 | − | 0.912361i | \(-0.634257\pi\) | ||||
−0.409387 | + | 0.912361i | \(0.634257\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.5248 | −1.69383 | −0.846915 | − | 0.531728i | \(-0.821543\pi\) | ||||
−0.846915 | + | 0.531728i | \(0.821543\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 21.3619i | − 0.869922i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.78863i | 0.235341i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.6125 | 1.16134 | 0.580672 | − | 0.814138i | \(-0.302790\pi\) | ||||
0.580672 | + | 0.814138i | \(0.302790\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.58640 | −0.0642843 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 15.4813i | − 0.626306i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 14.5762i | − 0.588727i | −0.955694 | − | 0.294363i | \(-0.904892\pi\) | ||||
0.955694 | − | 0.294363i | \(-0.0951076\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.795182 | −0.0320648 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.9847 | −0.724035 | −0.362017 | − | 0.932171i | \(-0.617912\pi\) | ||||
−0.362017 | + | 0.932171i | \(0.617912\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 11.7216i | − 0.471132i | −0.971858 | − | 0.235566i | \(-0.924306\pi\) | ||||
0.971858 | − | 0.235566i | \(-0.0756943\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.11514i | 0.325650i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.09510 | −0.364387 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 0.421449i | − 0.0168310i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 18.3430i | − 0.731382i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.9398 | −0.992839 | −0.496419 | − | 0.868083i | \(-0.665352\pi\) | ||||
−0.496419 | + | 0.868083i | \(0.665352\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.46480 | −0.137714 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.31003i | 0.329773i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 7.09308i | − 0.281038i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.86140 | −0.152755 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.5072 | 1.32346 | 0.661728 | − | 0.749744i | \(-0.269823\pi\) | ||||
0.661728 | + | 0.749744i | \(0.269823\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 30.4807i | − 1.20204i | −0.799233 | − | 0.601022i | \(-0.794761\pi\) | ||||
0.799233 | − | 0.601022i | \(-0.205239\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.68317i | 0.0662747i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.4027 | 1.43114 | 0.715568 | − | 0.698543i | \(-0.246168\pi\) | ||||
0.715568 | + | 0.698543i | \(0.246168\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.3338 | −1.19071 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 1.11214i | − 0.0435884i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.4937i | 0.449782i | 0.974384 | + | 0.224891i | \(0.0722026\pi\) | ||||
−0.974384 | + | 0.224891i | \(0.927797\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.60724 | −0.375386 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.7086 | −0.963973 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 5.83329i | − 0.227233i | −0.993525 | − | 0.113616i | \(-0.963757\pi\) | ||||
0.993525 | − | 0.113616i | \(-0.0362435\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 20.9106i | − 0.813326i | −0.913578 | − | 0.406663i | \(-0.866692\pi\) | ||||
0.913578 | − | 0.406663i | \(-0.133308\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.21611 | −0.241414 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.962523 | 0.0373250 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 58.6833i | − 2.27223i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 5.15151i | − 0.199169i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.11067 | −0.0428768 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.0222 | −1.42710 | −0.713551 | − | 0.700603i | \(-0.752914\pi\) | ||||
−0.713551 | + | 0.700603i | \(0.752914\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1.14377i | − 0.0440236i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 9.39877i | − 0.361224i | −0.983554 | − | 0.180612i | \(-0.942192\pi\) | ||||
0.983554 | − | 0.180612i | \(-0.0578078\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.64085 | −0.0629702 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.86625 | 0.109835 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 46.4388i | − 1.77693i | −0.458945 | − | 0.888465i | \(-0.651772\pi\) | ||||
0.458945 | − | 0.888465i | \(-0.348228\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 0.486527i | − 0.0185893i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.08534 | −0.117713 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −34.0255 | −1.29627 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 12.7719i | − 0.485865i | −0.970043 | − | 0.242932i | \(-0.921891\pi\) | ||||
0.970043 | − | 0.242932i | \(-0.0781093\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 6.76455i | − 0.256964i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.6713 | 0.670312 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.9424 | −0.717495 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 2.79936i | − 0.105881i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 3.07006i | − 0.115954i | −0.998318 | − | 0.0579772i | \(-0.981535\pi\) | ||||
0.998318 | − | 0.0579772i | \(-0.0184651\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.86415 | −0.145739 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.418630 | −0.0157665 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.67268i | 0.100516i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.3877i | 1.25390i | 0.779059 | + | 0.626951i | \(0.215697\pi\) | ||||
−0.779059 | + | 0.626951i | \(0.784303\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.4793 | 1.40558 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 41.1398 | 1.54070 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.1924i | 0.605561i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.13540i | − 0.0797479i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.8589 | 1.26273 | 0.631363 | − | 0.775488i | \(-0.282496\pi\) | ||||
0.631363 | + | 0.775488i | \(0.282496\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.18259 | 0.0812840 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.41195i | 0.126892i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.27096i | 0.307176i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.0976 | 1.07917 | 0.539585 | − | 0.841931i | \(-0.318581\pi\) | ||||
0.539585 | + | 0.841931i | \(0.318581\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.0337 | 0.927173 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.0956i | 1.48299i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.5192i | 1.38580i | 0.721032 | + | 0.692902i | \(0.243668\pi\) | ||||
−0.721032 | + | 0.692902i | \(0.756332\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.191804 | −0.00707480 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.4571 | 0.606204 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 34.3673i | − 1.26422i | −0.774878 | − | 0.632111i | \(-0.782189\pi\) | ||||
0.774878 | − | 0.632111i | \(-0.217811\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.30949i | 0.0481055i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.67144 | −0.171378 | −0.0856892 | − | 0.996322i | \(-0.527309\pi\) | ||||
−0.0856892 | + | 0.996322i | \(0.527309\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.66847 | −0.171040 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 37.4769i | 1.37121i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 2.66710i | − 0.0974536i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.1081 | −0.478321 | −0.239161 | − | 0.970980i | \(-0.576872\pi\) | ||||
−0.239161 | + | 0.970980i | \(0.576872\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.49062 | −0.127205 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.5733i | 0.530375i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 34.7064i | − 1.26142i | −0.776017 | − | 0.630712i | \(-0.782763\pi\) | ||||
0.776017 | − | 0.630712i | \(-0.217237\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.10665 | −0.112764 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.0543 | 0.690718 | 0.345359 | − | 0.938471i | \(-0.387757\pi\) | ||||
0.345359 | + | 0.938471i | \(0.387757\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.63437i | 0.203978i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 13.5391i | − 0.489507i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 94.2509 | 3.40320 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.3346 | 0.841466 | 0.420733 | − | 0.907184i | \(-0.361773\pi\) | ||||
0.420733 | + | 0.907184i | \(0.361773\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.67163i | 0.0602023i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 11.9937i | − 0.431384i | −0.976461 | − | 0.215692i | \(-0.930799\pi\) | ||||
0.976461 | − | 0.215692i | \(-0.0692007\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.79834 | −0.208282 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.770017 | 0.0276242 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.99043i | 0.142972i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 2.97481i | − 0.106447i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.46006 | 0.338075 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.2593 | 0.544629 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 52.5461i | 1.87306i | 0.350581 | + | 0.936532i | \(0.385984\pi\) | ||||
−0.350581 | + | 0.936532i | \(0.614016\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.38593i | 0.0493405i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.3892 | −0.724956 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.45098 | 0.122548 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.920084i | 0.0326320i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.5448i | 0.373515i | 0.982406 | + | 0.186758i | \(0.0597979\pi\) | ||||
−0.982406 | + | 0.186758i | \(0.940202\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.97239 | −0.352798 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26.9507 | 0.952256 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 19.0354i | − 0.671743i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 7.09510i | − 0.250069i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.60485 | 0.162098 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.7886 | 1.01215 | 0.506077 | − | 0.862488i | \(-0.331095\pi\) | ||||
0.506077 | + | 0.862488i | \(0.331095\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.60362i | − 0.0563108i | −0.999604 | − | 0.0281554i | \(-0.991037\pi\) | ||||
0.999604 | − | 0.0281554i | \(-0.00896332\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.22510i | − 0.0780375i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.31448 | 0.186158 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.44659 | 0.295509 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.0183i | 0.734438i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.8725i | 1.46136i | 0.682720 | + | 0.730680i | \(0.260797\pi\) | ||||
−0.682720 | + | 0.730680i | \(0.739203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.8752 | −0.588234 | −0.294117 | − | 0.955769i | \(-0.595025\pi\) | ||||
−0.294117 | + | 0.955769i | \(0.595025\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.437858 | 0.0152443 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.789683i | 0.0274600i | 0.999906 | + | 0.0137300i | \(0.00437053\pi\) | ||||
−0.999906 | + | 0.0137300i | \(0.995629\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 25.8343i | − 0.897261i | −0.893717 | − | 0.448631i | \(-0.851912\pi\) | ||||
0.893717 | − | 0.448631i | \(-0.148088\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.26317 | −0.147888 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.56906 | −0.158308 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.3701i | 0.635724i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.63195i | 0.229234i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.8432 | −0.650538 | −0.325269 | − | 0.945621i | \(-0.605455\pi\) | ||||
−0.325269 | + | 0.945621i | \(0.605455\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −39.4088 | −1.35893 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.65433i | 0.125862i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 37.3117i | − 1.28356i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.78863 | −0.198900 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.29585 | 0.0444734 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.4840i | 0.976420i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 24.8587i | − 0.851145i | −0.904924 | − | 0.425572i | \(-0.860073\pi\) | ||||
0.904924 | − | 0.425572i | \(-0.139927\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.85216 | −0.0975418 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.8448 | −0.677885 | −0.338943 | − | 0.940807i | \(-0.610069\pi\) | ||||
−0.338943 | + | 0.940807i | \(0.610069\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.1860i | 0.791094i | 0.918446 | + | 0.395547i | \(0.129445\pi\) | ||||
−0.918446 | + | 0.395547i | \(0.870555\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 0.795182i | − 0.0270997i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.5878 | −0.462532 | −0.231266 | − | 0.972891i | \(-0.574287\pi\) | ||||
−0.231266 | + | 0.972891i | \(0.574287\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.83246 | 0.0623054 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.743488i | 0.0252502i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.8739i | 0.979480i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −51.1342 | −1.73261 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.86220 | 0.164560 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000i | 0.0338062i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 36.5476i | − 1.23412i | −0.786914 | − | 0.617062i | \(-0.788323\pi\) | ||||
0.786914 | − | 0.617062i | \(-0.211677\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.01920 | 0.0681058 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.7800 | 1.23915 | 0.619575 | − | 0.784937i | \(-0.287305\pi\) | ||||
0.619575 | + | 0.784937i | \(0.287305\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.3640i | 1.45931i | 0.683813 | + | 0.729657i | \(0.260320\pi\) | ||||
−0.683813 | + | 0.729657i | \(0.739680\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 2.54864i | − 0.0856716i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.6046 | −0.826142 | −0.413071 | − | 0.910699i | \(-0.635544\pi\) | ||||
−0.413071 | + | 0.910699i | \(0.635544\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.31003 | −0.278709 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.7928i | 0.663085i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.10080i | 0.0703005i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.4499 | 0.416155 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.65274 | 0.322296 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 47.9578i | − 1.59948i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.9178i | 0.730187i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.68317 | −0.0560124 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.81930 | 0.126958 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 19.2254i | − 0.638368i | −0.947693 | − | 0.319184i | \(-0.896591\pi\) | ||||
0.947693 | − | 0.319184i | \(-0.103409\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 7.91971i | − 0.262680i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.7858 | 0.920585 | 0.460293 | − | 0.887767i | \(-0.347745\pi\) | ||||
0.460293 | + | 0.887767i | \(0.347745\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.8720 | −0.955523 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 0.0933179i | − 0.00308499i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 9.60724i | − 0.317259i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.0084 | 1.61664 | 0.808320 | − | 0.588744i | \(-0.200377\pi\) | ||||
0.808320 | + | 0.588744i | \(0.200377\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.04973 | −0.0675409 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.24309i | 0.304240i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 4.01460i | − 0.131999i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.46748 | −0.212420 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.9803 | −0.589914 | −0.294957 | − | 0.955511i | \(-0.595305\pi\) | ||||
−0.294957 | + | 0.955511i | \(0.595305\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.962523i | 0.0315454i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 6.56345i | − 0.214878i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.4304 | 0.341112 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.8426 | 0.550224 | 0.275112 | − | 0.961412i | \(-0.411285\pi\) | ||||
0.275112 | + | 0.961412i | \(0.411285\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 2.94078i | − 0.0959686i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 9.51080i | − 0.310043i | −0.987911 | − | 0.155022i | \(-0.950455\pi\) | ||||
0.987911 | − | 0.155022i | \(-0.0495447\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.4149 | 0.957881 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.14377 | 0.0372068 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.3596i | 0.694093i | 0.937848 | + | 0.347046i | \(0.112815\pi\) | ||||
−0.937848 | + | 0.347046i | \(0.887185\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 59.1452i | 1.91993i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.54497 | 0.0500991 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.7813 | −0.932317 | −0.466158 | − | 0.884701i | \(-0.654362\pi\) | ||||
−0.466158 | + | 0.884701i | \(0.654362\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 22.5957i | − 0.731181i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.62151i | 0.117067i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.486527 | 0.0157108 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.62073 | 0.0845397 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.90317i | 0.254676i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.5300i | 0.757457i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.14801 | 0.197707 | 0.0988534 | − | 0.995102i | \(-0.468483\pi\) | ||||
0.0988534 | + | 0.995102i | \(0.468483\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.843520 | 0.0270978 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.7772i | 1.18024i | 0.807316 | + | 0.590119i | \(0.200919\pi\) | ||||
−0.807316 | + | 0.590119i | \(0.799081\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.6713i | 0.566517i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.36048 | −0.0435702 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.4277 | 1.10144 | 0.550719 | − | 0.834690i | \(-0.314353\pi\) | ||||
0.550719 | + | 0.834690i | \(0.314353\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.7627i | 0.663578i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 16.6958i | − 0.533057i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.4682 | −0.971786 | −0.485893 | − | 0.874018i | \(-0.661505\pi\) | ||||
−0.485893 | + | 0.874018i | \(0.661505\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.06709 | 0.193314 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 0.418630i | − 0.0133251i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 62.2628i | − 1.97984i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.7242 | −1.42071 | −0.710356 | − | 0.703843i | \(-0.751466\pi\) | ||||
−0.710356 | + | 0.703843i | \(0.751466\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.44534 | −0.0776006 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 24.4683i | − 0.775699i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 10.5274i | − 0.333406i | −0.986007 | − | 0.166703i | \(-0.946688\pi\) | ||||
0.986007 | − | 0.166703i | \(-0.0533121\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.59178 | −0.145277 |
(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 | 2240.2.b.g.1121.7 | yes | 12 | |
4.3 | odd | 2 | 2240.2.b.h.1121.6 | yes | 12 | ||
8.3 | odd | 2 | 2240.2.b.h.1121.7 | yes | 12 | ||
8.5 | even | 2 | inner | 2240.2.b.g.1121.6 | ✓ | 12 | |
16.3 | odd | 4 | 8960.2.a.ce.1.3 | 6 | |||
16.5 | even | 4 | 8960.2.a.cc.1.3 | 6 | |||
16.11 | odd | 4 | 8960.2.a.cb.1.4 | 6 | |||
16.13 | even | 4 | 8960.2.a.ch.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.b.g.1121.6 | ✓ | 12 | 8.5 | even | 2 | inner | |
2240.2.b.g.1121.7 | yes | 12 | 1.1 | even | 1 | trivial | |
2240.2.b.h.1121.6 | yes | 12 | 4.3 | odd | 2 | ||
2240.2.b.h.1121.7 | yes | 12 | 8.3 | odd | 2 | ||
8960.2.a.cb.1.4 | 6 | 16.11 | odd | 4 | |||
8960.2.a.cc.1.3 | 6 | 16.5 | even | 4 | |||
8960.2.a.ce.1.3 | 6 | 16.3 | odd | 4 | |||
8960.2.a.ch.1.4 | 6 | 16.13 | even | 4 |