Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(3005,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6012.3005");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.h (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: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3005.18 | ||
Character | \(\chi\) | \(=\) | 6012.3005 |
Dual form | 6012.2.h.a.3005.17 |
$q$-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 \(\left(\mathbb{Z}/6012\mathbb{Z}\right)^\times\).
\(n\) | \(3007\) | \(3341\) | \(4681\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.39469 | −0.623726 | −0.311863 | − | 0.950127i | \(-0.600953\pi\) | ||||
−0.311863 | + | 0.950127i | \(0.600953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.57475 | −1.72909 | −0.864547 | − | 0.502552i | \(-0.832394\pi\) | ||||
−0.864547 | + | 0.502552i | \(0.832394\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.16668i | 0.954791i | 0.878689 | + | 0.477395i | \(0.158419\pi\) | ||||
−0.878689 | + | 0.477395i | \(0.841581\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.678448i | − | 0.188168i | −0.995564 | − | 0.0940839i | \(-0.970008\pi\) | ||
0.995564 | − | 0.0940839i | \(-0.0299922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.04770 | 0.496641 | 0.248320 | − | 0.968678i | \(-0.420121\pi\) | ||||
0.248320 | + | 0.968678i | \(0.420121\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.83917 | −0.880765 | −0.440383 | − | 0.897810i | \(-0.645157\pi\) | ||||
−0.440383 | + | 0.897810i | \(0.645157\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.63709 | 0.341356 | 0.170678 | − | 0.985327i | \(-0.445404\pi\) | ||||
0.170678 | + | 0.985327i | \(0.445404\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.05483 | −0.610966 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.49162i | − | 0.462681i | −0.972873 | − | 0.231341i | \(-0.925689\pi\) | ||
0.972873 | − | 0.231341i | \(-0.0743112\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.99578 | −0.897269 | −0.448635 | − | 0.893715i | \(-0.648090\pi\) | ||||
−0.448635 | + | 0.893715i | \(0.648090\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.38038 | 1.07848 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.1215i | 1.66396i | 0.554802 | + | 0.831982i | \(0.312794\pi\) | ||||
−0.554802 | + | 0.831982i | \(0.687206\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.1835 | −1.90275 | −0.951374 | − | 0.308037i | \(-0.900328\pi\) | ||||
−0.951374 | + | 0.308037i | \(0.900328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.71460i | 0.718970i | 0.933151 | + | 0.359485i | \(0.117048\pi\) | ||||
−0.933151 | + | 0.359485i | \(0.882952\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.25120i | − | 0.474237i | −0.971481 | − | 0.237118i | \(-0.923797\pi\) | ||
0.971481 | − | 0.237118i | \(-0.0762029\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.9284 | 1.98977 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.08207 | −0.972797 | −0.486398 | − | 0.873737i | \(-0.661690\pi\) | ||||
−0.486398 | + | 0.873737i | \(0.661690\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.41655i | − | 0.595528i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.99637 | 0.780661 | 0.390330 | − | 0.920675i | \(-0.372361\pi\) | ||||
0.390330 | + | 0.920675i | \(0.372361\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.50097 | 1.21647 | 0.608237 | − | 0.793755i | \(-0.291877\pi\) | ||||
0.608237 | + | 0.793755i | \(0.291877\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.946227i | 0.117365i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.54542i | 1.16616i | 0.812415 | + | 0.583079i | \(0.198152\pi\) | ||||
−0.812415 | + | 0.583079i | \(0.801848\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.35726 | −1.11050 | −0.555251 | − | 0.831683i | \(-0.687378\pi\) | ||||
−0.555251 | + | 0.831683i | \(0.687378\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.4904i | − | 1.22781i | −0.789381 | − | 0.613903i | \(-0.789598\pi\) | ||
0.789381 | − | 0.613903i | \(-0.210402\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 14.4868i | − | 1.65092i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 17.2275i | − | 1.93824i | −0.246590 | − | 0.969120i | \(-0.579310\pi\) | ||
0.246590 | − | 0.969120i | \(-0.420690\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.9720 | −1.75316 | −0.876580 | − | 0.481257i | \(-0.840180\pi\) | ||||
−0.876580 | + | 0.481257i | \(0.840180\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.85592 | −0.309768 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.3957i | 1.63194i | 0.578094 | + | 0.815970i | \(0.303797\pi\) | ||||
−0.578094 | + | 0.815970i | \(0.696203\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.10373i | 0.325360i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.35446 | 0.549356 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.44085 | 0.755503 | 0.377752 | − | 0.925907i | \(-0.376697\pi\) | ||||
0.377752 | + | 0.925907i | \(0.376697\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.07700 | 0.604684 | 0.302342 | − | 0.953200i | \(-0.402232\pi\) | ||||
0.302342 | + | 0.953200i | \(0.402232\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.5730i | 1.43592i | 0.696083 | + | 0.717961i | \(0.254924\pi\) | ||||
−0.696083 | + | 0.717961i | \(0.745076\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.24282i | 0.410169i | 0.978744 | + | 0.205084i | \(0.0657469\pi\) | ||||
−0.978744 | + | 0.205084i | \(0.934253\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.51313i | − | 0.528062i | −0.964514 | − | 0.264031i | \(-0.914948\pi\) | ||
0.964514 | − | 0.264031i | \(-0.0850521\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.6859 | 1.00524 | 0.502620 | − | 0.864507i | \(-0.332369\pi\) | ||||
0.502620 | + | 0.864507i | \(0.332369\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.28323 | −0.212913 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.36773 | −0.858738 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.972122 | 0.0883747 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.2340 | 1.00480 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.3908 | 1.27698 | 0.638490 | − | 0.769630i | \(-0.279559\pi\) | ||||
0.638490 | + | 0.769630i | \(0.279559\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.21806 | −0.368534 | −0.184267 | − | 0.982876i | \(-0.558991\pi\) | ||||
−0.184267 | + | 0.982876i | \(0.558991\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.5632 | 1.52293 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15.7664i | − | 1.34701i | −0.739182 | − | 0.673505i | \(-0.764788\pi\) | ||
0.739182 | − | 0.673505i | \(-0.235212\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.32836i | 0.112670i | 0.998412 | + | 0.0563350i | \(0.0179415\pi\) | ||||
−0.998412 | + | 0.0563350i | \(0.982059\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.14843 | 0.179661 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.47504i | 0.288586i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.7715 | 0.964362 | 0.482181 | − | 0.876072i | \(-0.339845\pi\) | ||||
0.482181 | + | 0.876072i | \(0.339845\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.5889i | − | 0.861709i | −0.902421 | − | 0.430854i | \(-0.858212\pi\) | ||
0.902421 | − | 0.430854i | \(-0.141788\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.96759 | 0.559650 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.4110 | 1.22993 | 0.614965 | − | 0.788555i | \(-0.289170\pi\) | ||||
0.614965 | + | 0.788555i | \(0.289170\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.48927 | −0.590237 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 12.6578i | − | 0.991436i | −0.868484 | − | 0.495718i | \(-0.834905\pi\) | ||
0.868484 | − | 0.495718i | \(-0.165095\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.96454 | − | 12.7726i | 0.152021 | − | 0.988377i | ||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5397 | 0.964593 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 20.4501i | − | 1.55479i | −0.629013 | − | 0.777395i | \(-0.716541\pi\) | ||
0.629013 | − | 0.777395i | \(-0.283459\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.9751 | 1.05642 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 0.305626i | − | 0.0228436i | −0.999935 | − | 0.0114218i | \(-0.996364\pi\) | ||
0.999935 | − | 0.0114218i | \(-0.00363574\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.4692 | 0.778168 | 0.389084 | − | 0.921202i | \(-0.372792\pi\) | ||||
0.389084 | + | 0.921202i | \(0.372792\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 14.1164i | − | 1.03786i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.48442i | 0.474188i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 14.0013i | − | 1.01310i | −0.862212 | − | 0.506548i | \(-0.830921\pi\) | ||
0.862212 | − | 0.506548i | \(-0.169079\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 11.7565i | − | 0.846255i | −0.906070 | − | 0.423127i | \(-0.860932\pi\) | ||
0.906070 | − | 0.423127i | \(-0.139068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.3280 | −1.51956 | −0.759780 | − | 0.650181i | \(-0.774693\pi\) | ||||
−0.759780 | + | 0.650181i | \(0.774693\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0439 | −0.711992 | −0.355996 | − | 0.934488i | \(-0.615858\pi\) | ||||
−0.355996 | + | 0.934488i | \(0.615858\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.3985i | 0.800020i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.9923 | 1.18679 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 12.1574i | − | 0.840947i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.36608 | −0.162888 | −0.0814438 | − | 0.996678i | \(-0.525953\pi\) | ||||
−0.0814438 | + | 0.996678i | \(0.525953\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 6.57542i | − | 0.448440i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.8545 | 1.55146 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.38926i | − | 0.0934517i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.63935 | 0.377639 | 0.188819 | − | 0.982012i | \(-0.439534\pi\) | ||||
0.188819 | + | 0.982012i | \(0.439534\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.2355 | 0.944844 | 0.472422 | − | 0.881372i | \(-0.343380\pi\) | ||||
0.472422 | + | 0.881372i | \(0.343380\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.42754 | 0.358662 | 0.179331 | − | 0.983789i | \(-0.442607\pi\) | ||||
0.179331 | + | 0.983789i | \(0.442607\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 7.63054i | − | 0.499894i | −0.968260 | − | 0.249947i | \(-0.919587\pi\) | ||
0.968260 | − | 0.249947i | \(-0.0804131\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.53443i | 0.295794i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.38304i | − | 0.412884i | −0.978459 | − | 0.206442i | \(-0.933811\pi\) | ||
0.978459 | − | 0.206442i | \(-0.0661885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.0010i | 1.09513i | 0.836764 | + | 0.547564i | \(0.184445\pi\) | ||||
−0.836764 | + | 0.547564i | \(0.815555\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −19.4258 | −1.24107 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.60468i | 0.165732i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.5787i | 0.983316i | 0.870788 | + | 0.491658i | \(0.163609\pi\) | ||||
−0.870788 | + | 0.491658i | \(0.836391\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.18413i | 0.325924i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.5886 | −1.40904 | −0.704520 | − | 0.709684i | \(-0.748838\pi\) | ||||
−0.704520 | + | 0.709684i | \(0.748838\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 46.3034i | − | 2.87715i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.71783i | − | 0.290914i | −0.989365 | − | 0.145457i | \(-0.953535\pi\) | ||
0.989365 | − | 0.145457i | \(-0.0464652\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.87731 | 0.606758 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.3567 | 1.36311 | 0.681556 | − | 0.731766i | \(-0.261303\pi\) | ||||
0.681556 | + | 0.731766i | \(0.261303\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.60680i | 0.401335i | 0.979659 | + | 0.200667i | \(0.0643110\pi\) | ||||
−0.979659 | + | 0.200667i | \(0.935689\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 9.67368i | − | 0.583345i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 26.6210i | − | 1.59950i | −0.600334 | − | 0.799749i | \(-0.704966\pi\) | ||
0.600334 | − | 0.799749i | \(-0.295034\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 32.8224i | − | 1.95802i | −0.203805 | − | 0.979011i | \(-0.565331\pi\) | ||
0.203805 | − | 0.979011i | \(-0.434669\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.71459 | 0.101922 | 0.0509609 | − | 0.998701i | \(-0.483772\pi\) | ||||
0.0509609 | + | 0.998701i | \(0.483772\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 55.7367 | 3.29003 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.8069 | −0.753348 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.20416i | − | 0.479292i | −0.970860 | − | 0.239646i | \(-0.922969\pi\) | ||
0.970860 | − | 0.239646i | \(-0.0770314\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.36310 | −0.486918 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.11068i | − | 0.0642322i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 21.5681i | − | 1.24317i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.2509 | −0.758747 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.84943i | 0.276772i | 0.990378 | + | 0.138386i | \(0.0441914\pi\) | ||||
−0.990378 | + | 0.138386i | \(0.955809\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7.14797i | − | 0.405324i | −0.979249 | − | 0.202662i | \(-0.935041\pi\) | ||
0.979249 | − | 0.202662i | \(-0.0649593\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0218i | 0.622988i | 0.950248 | + | 0.311494i | \(0.100829\pi\) | ||||
−0.950248 | + | 0.311494i | \(0.899171\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.26539i | 0.295734i | 0.989007 | + | 0.147867i | \(0.0472408\pi\) | ||||
−0.989007 | + | 0.147867i | \(0.952759\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.89016 | 0.441764 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.86147 | −0.437424 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.07254i | 0.114964i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.8734i | 0.820000i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.27343i | 0.454749i | 0.973807 | + | 0.227374i | \(0.0730141\pi\) | ||||
−0.973807 | + | 0.227374i | \(0.926986\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 13.3129i | − | 0.727363i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.1026 | 1.85769 | 0.928844 | − | 0.370471i | \(-0.120804\pi\) | ||||
0.928844 | + | 0.370471i | \(0.120804\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 15.8201i | − | 0.856704i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −31.6955 | −1.71140 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.7405 | −0.952359 | −0.476179 | − | 0.879348i | \(-0.657979\pi\) | ||||
−0.476179 | + | 0.879348i | \(0.657979\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.9216i | 1.76226i | 0.472879 | + | 0.881128i | \(0.343215\pi\) | ||||
−0.472879 | + | 0.881128i | \(0.656785\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 23.4839i | − | 1.24992i | −0.780656 | − | 0.624961i | \(-0.785115\pi\) | ||
0.780656 | − | 0.624961i | \(-0.214885\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.0505 | 0.692649 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.7233i | 1.04096i | 0.853875 | + | 0.520479i | \(0.174246\pi\) | ||||
−0.853875 | + | 0.520479i | \(0.825754\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.26079 | −0.224252 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.6309i | 0.765815i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.6349 | 1.28593 | 0.642967 | − | 0.765894i | \(-0.277703\pi\) | ||||
0.642967 | + | 0.765894i | \(0.277703\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32.3987 | 1.68206 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.09861i | 0.263996i | 0.991250 | + | 0.131998i | \(0.0421393\pi\) | ||||
−0.991250 | + | 0.131998i | \(0.957861\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.69043 | −0.0870617 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.07234i | 0.106449i | 0.998583 | + | 0.0532244i | \(0.0169498\pi\) | ||||
−0.998583 | + | 0.0532244i | \(0.983050\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.5206i | 1.09965i | 0.835280 | + | 0.549825i | \(0.185305\pi\) | ||||
−0.835280 | + | 0.549825i | \(0.814695\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.2046i | 1.02972i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.7818 | 0.597359 | 0.298679 | − | 0.954354i | \(-0.403454\pi\) | ||||
0.298679 | + | 0.954354i | \(0.403454\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.35227 | 0.169531 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.0270i | 1.20893i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.66291 | −0.0834590 | −0.0417295 | − | 0.999129i | \(-0.513287\pi\) | ||||
−0.0417295 | + | 0.999129i | \(0.513287\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.873382 | 0.0436146 | 0.0218073 | − | 0.999762i | \(-0.493058\pi\) | ||||
0.0218073 | + | 0.999762i | \(0.493058\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.38938i | 0.168837i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −32.0516 | −1.58874 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.8880 | −1.13174 | −0.565869 | − | 0.824495i | \(-0.691459\pi\) | ||||
−0.565869 | + | 0.824495i | \(0.691459\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.4319 | −1.34984 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.2761 | 1.09349 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 0.989747i | − | 0.0483523i | −0.999708 | − | 0.0241762i | \(-0.992304\pi\) | ||
0.999708 | − | 0.0241762i | \(-0.00769626\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0798 | −0.637468 | −0.318734 | − | 0.947844i | \(-0.603258\pi\) | ||||
−0.318734 | + | 0.947844i | \(0.603258\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.25538 | −0.303431 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −43.4646 | −2.10340 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 25.2048i | − | 1.21407i | −0.794674 | − | 0.607037i | \(-0.792358\pi\) | ||
0.794674 | − | 0.607037i | \(-0.207642\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.31288 | −0.351435 | −0.175717 | − | 0.984441i | \(-0.556224\pi\) | ||||
−0.175717 | + | 0.984441i | \(0.556224\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.28505 | −0.300655 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.2996i | 1.54158i | 0.637090 | + | 0.770789i | \(0.280138\pi\) | ||||
−0.637090 | + | 0.770789i | \(0.719862\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.0186 | 0.856092 | 0.428046 | − | 0.903757i | \(-0.359202\pi\) | ||||
0.428046 | + | 0.903757i | \(0.359202\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 21.4723i | − | 1.01788i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.4917i | 1.91092i | 0.295119 | + | 0.955460i | \(0.404641\pi\) | ||||
−0.295119 | + | 0.955460i | \(0.595359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 38.5814i | − | 1.81673i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 4.32876i | − | 0.202935i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 29.5031i | − | 1.38010i | −0.723763 | − | 0.690049i | \(-0.757589\pi\) | ||
0.723763 | − | 0.690049i | \(-0.242411\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.5480i | 0.863865i | 0.901906 | + | 0.431932i | \(0.142168\pi\) | ||||
−0.901906 | + | 0.431932i | \(0.857832\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 34.3790i | − | 1.59773i | −0.601513 | − | 0.798863i | \(-0.705435\pi\) | ||
0.601513 | − | 0.798863i | \(-0.294565\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.5733i | 0.859470i | 0.902955 | + | 0.429735i | \(0.141393\pi\) | ||||
−0.902955 | + | 0.429735i | \(0.858607\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 43.6679i | − | 2.01640i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.9296 | −0.686466 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.7280 | 0.538118 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.6138 | −0.941868 | −0.470934 | − | 0.882169i | \(-0.656083\pi\) | ||||
−0.470934 | + | 0.882169i | \(0.656083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.86691 | 0.313104 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.3777 | −0.471227 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.2837i | 1.32697i | 0.748190 | + | 0.663485i | \(0.230923\pi\) | ||||
−0.748190 | + | 0.663485i | \(0.769077\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.2853i | − | 1.45701i | −0.685038 | − | 0.728507i | \(-0.740214\pi\) | ||
0.685038 | − | 0.728507i | \(-0.259786\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.10209i | − | 0.229786i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 42.8071 | 1.92016 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7516i | 0.660373i | 0.943916 | + | 0.330187i | \(0.107112\pi\) | ||||
−0.943916 | + | 0.330187i | \(0.892888\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.1022i | 0.807137i | 0.914949 | + | 0.403569i | \(0.132230\pi\) | ||||
−0.914949 | + | 0.403569i | \(0.867770\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.47555 | −0.377157 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 38.7177i | − | 1.71613i | −0.513541 | − | 0.858065i | \(-0.671666\pi\) | ||
0.513541 | − | 0.858065i | \(-0.328334\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 47.9909i | 2.12299i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 20.3249i | − | 0.895621i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.2955 | 0.452797 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.1043 | 1.09984 | 0.549919 | − | 0.835218i | \(-0.314659\pi\) | ||||
0.549919 | + | 0.835218i | \(0.314659\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.4808 | −1.33283 | −0.666416 | − | 0.745580i | \(-0.732173\pi\) | ||||
−0.666416 | + | 0.745580i | \(0.732173\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.2299 | −0.445620 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.3199 | −0.883476 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.26590i | 0.358036i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 5.91743i | − | 0.255833i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 44.1067i | 1.89981i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 9.04366i | − | 0.388817i | −0.980921 | − | 0.194409i | \(-0.937721\pi\) | ||
0.980921 | − | 0.194409i | \(-0.0622788\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.68912i | 0.329366i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 39.1689i | − | 1.67474i | −0.546635 | − | 0.837371i | \(-0.684092\pi\) | ||
0.546635 | − | 0.837371i | \(-0.315908\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.56573i | 0.407514i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 78.8113i | 3.35140i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 7.61535i | − | 0.322673i | −0.986899 | − | 0.161336i | \(-0.948420\pi\) | ||
0.986899 | − | 0.161336i | \(-0.0515804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.19861 | 0.135287 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.6553i | 1.75556i | 0.479062 | + | 0.877781i | \(0.340977\pi\) | ||||
−0.479062 | + | 0.877781i | \(0.659023\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.9035 | −0.626995 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.2979 | −1.01862 | −0.509311 | − | 0.860582i | \(-0.670100\pi\) | ||||
−0.509311 | + | 0.860582i | \(0.670100\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.5904i | 1.65681i | 0.560133 | + | 0.828403i | \(0.310750\pi\) | ||||
−0.560133 | + | 0.828403i | \(0.689250\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.00102 | −0.208557 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.4711 | 0.560807 | 0.280404 | − | 0.959882i | \(-0.409532\pi\) | ||||
0.280404 | + | 0.959882i | \(0.409532\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 73.0681 | 3.03138 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 22.4267i | − | 0.928817i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.30680 | −0.0539376 | −0.0269688 | − | 0.999636i | \(-0.508585\pi\) | ||||
−0.0269688 | + | 0.999636i | \(0.508585\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.1797 | 0.790284 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.0491 | 0.535862 | 0.267931 | − | 0.963438i | \(-0.413660\pi\) | ||||
0.267931 | + | 0.963438i | \(0.413660\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.0651 | 0.535617 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.3900i | 0.628820i | 0.949287 | + | 0.314410i | \(0.101807\pi\) | ||||
−0.949287 | + | 0.314410i | \(0.898193\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.7420 | 1.82506 | 0.912532 | − | 0.409006i | \(-0.134124\pi\) | ||||
0.912532 | + | 0.409006i | \(0.134124\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.35581 | −0.0551216 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.47030i | − | 0.303210i | −0.988441 | − | 0.151605i | \(-0.951556\pi\) | ||
0.988441 | − | 0.151605i | \(-0.0484442\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.20577 | −0.0892360 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.4294 | 0.421238 | 0.210619 | − | 0.977568i | \(-0.432452\pi\) | ||||
0.210619 | + | 0.977568i | \(0.432452\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.7728i | 0.796021i | 0.917381 | + | 0.398011i | \(0.130299\pi\) | ||||
−0.917381 | + | 0.398011i | \(0.869701\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13.2880i | − | 0.534090i | −0.963684 | − | 0.267045i | \(-0.913953\pi\) | ||
0.963684 | − | 0.267045i | \(-0.0860473\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 70.4315i | − | 2.82178i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.393856 | −0.0157543 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.7258i | 0.826392i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.7439 | 1.46275 | 0.731375 | − | 0.681975i | \(-0.238879\pi\) | ||||
0.731375 | + | 0.681975i | \(0.238879\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.0708 | −0.796486 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 9.44967i | − | 0.374410i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.1486 | −1.23029 | −0.615147 | − | 0.788412i | \(-0.710904\pi\) | ||||
−0.615147 | + | 0.788412i | \(0.710904\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.0760i | 1.06777i | 0.845556 | + | 0.533887i | \(0.179269\pi\) | ||||
−0.845556 | + | 0.533887i | \(0.820731\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.5380 | −1.00400 | −0.502000 | − | 0.864867i | \(-0.667402\pi\) | ||||
−0.502000 | + | 0.864867i | \(0.667402\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.9886i | 0.745368i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 26.2589i | − | 1.02759i | −0.857913 | − | 0.513794i | \(-0.828239\pi\) | ||
0.857913 | − | 0.513794i | \(-0.171761\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.88291 | 0.229864 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.7145 | −1.15751 | −0.578756 | − | 0.815501i | \(-0.696462\pi\) | ||||
−0.578756 | + | 0.815501i | \(0.696462\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 2.40757i | − | 0.0936436i | −0.998903 | − | 0.0468218i | \(-0.985091\pi\) | ||
0.998903 | − | 0.0468218i | \(-0.0149093\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −24.4953 | −0.949888 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 4.07899i | − | 0.157939i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.0866i | 1.16148i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.5706i | 0.484561i | 0.970206 | + | 0.242280i | \(0.0778954\pi\) | ||||
−0.970206 | + | 0.242280i | \(0.922105\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 51.1838i | − | 1.96715i | −0.180495 | − | 0.983576i | \(-0.557770\pi\) | ||
0.180495 | − | 0.983576i | \(-0.442230\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.0400 | −1.30634 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.4862 | 1.24305 | 0.621524 | − | 0.783395i | \(-0.286514\pi\) | ||||
0.621524 | + | 0.783395i | \(0.286514\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.9892i | 0.840165i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.80482i | 0.183049i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 14.5875i | − | 0.554936i | −0.960735 | − | 0.277468i | \(-0.910505\pi\) | ||
0.960735 | − | 0.277468i | \(-0.0894953\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 1.85265i | − | 0.0702752i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.9482 | −0.944982 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 34.6612i | − | 1.30913i | −0.756004 | − | 0.654567i | \(-0.772851\pi\) | ||
0.756004 | − | 0.654567i | \(-0.227149\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 38.8581i | − | 1.46556i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.8008 | −1.04555 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.6451i | 0.587563i | 0.955873 | + | 0.293781i | \(0.0949138\pi\) | ||||
−0.955873 | + | 0.293781i | \(0.905086\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.17853 | −0.306288 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.99640 | −0.112059 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.1948 | 0.678550 | 0.339275 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339275 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 66.6679i | − | 2.48284i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.61146i | 0.282683i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.38903i | 0.0886041i | 0.999018 | + | 0.0443021i | \(0.0141064\pi\) | ||||
−0.999018 | + | 0.0443021i | \(0.985894\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.65410i | 0.357070i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.8454 | 0.400585 | 0.200292 | − | 0.979736i | \(-0.435811\pi\) | ||||
0.200292 | + | 0.979736i | \(0.435811\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30.2273 | −1.11344 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.9673i | 1.80129i | 0.434555 | + | 0.900645i | \(0.356906\pi\) | ||||
−0.434555 | + | 0.900645i | \(0.643094\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.09351i | − | 0.113490i | −0.998389 | − | 0.0567448i | \(-0.981928\pi\) | ||
0.998389 | − | 0.0567448i | \(-0.0180722\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.4177 | −0.601497 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 19.4098i | − | 0.709220i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.99295i | − | 0.0727238i | −0.999339 | − | 0.0363619i | \(-0.988423\pi\) | ||
0.999339 | − | 0.0363619i | \(-0.0115769\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.7682i | 0.537470i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.4304 | 0.524483 | 0.262241 | − | 0.965002i | \(-0.415538\pi\) | ||||
0.262241 | + | 0.965002i | \(0.415538\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 31.3336i | − | 1.13584i | −0.823083 | − | 0.567921i | \(-0.807748\pi\) | ||
0.823083 | − | 0.567921i | \(-0.192252\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.2212i | 0.913068i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 4.06823i | − | 0.146895i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.6037i | 1.50027i | 0.661287 | + | 0.750133i | \(0.270011\pi\) | ||||
−0.661287 | + | 0.750133i | \(0.729989\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.95828 | −0.286240 | −0.143120 | − | 0.989705i | \(-0.545713\pi\) | ||||
−0.143120 | + | 0.989705i | \(0.545713\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.2613 | 0.548201 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 46.7746 | 1.67588 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 29.6315i | − | 1.06030i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.4936 | −0.767139 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.0474i | 1.89093i | 0.325718 | + | 0.945467i | \(0.394394\pi\) | ||||
−0.325718 | + | 0.945467i | \(0.605606\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −48.8851 | −1.73816 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.44592i | − | 0.228901i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.5774 | −0.374671 | −0.187336 | − | 0.982296i | \(-0.559985\pi\) | ||||
−0.187336 | + | 0.982296i | \(0.559985\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.65749i | − | 0.235525i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.2197 | 1.17230 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.4452 | 0.368146 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.2800i | 0.748166i | 0.927395 | + | 0.374083i | \(0.122043\pi\) | ||||
−0.927395 | + | 0.374083i | \(0.877957\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 41.6959i | − | 1.46414i | −0.681229 | − | 0.732070i | \(-0.738554\pi\) | ||
0.681229 | − | 0.732070i | \(-0.261446\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.6538i | 0.618384i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 18.1001i | − | 0.633244i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.0559 | 0.455653 | 0.227826 | − | 0.973702i | \(-0.426838\pi\) | ||||
0.227826 | + | 0.973702i | \(0.426838\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 39.1714i | − | 1.36543i | −0.730686 | − | 0.682714i | \(-0.760800\pi\) | ||
0.730686 | − | 0.682714i | \(-0.239200\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.7523 | 0.443441 | 0.221720 | − | 0.975110i | \(-0.428833\pi\) | ||||
0.221720 | + | 0.975110i | \(0.428833\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.5270i | 0.400350i | 0.979760 | + | 0.200175i | \(0.0641511\pi\) | ||||
−0.979760 | + | 0.200175i | \(0.935849\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.5211 | 0.988198 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.73993 | + | 17.8139i | −0.0948192 | + | 0.616476i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 33.9357i | − | 1.17159i | −0.810459 | − | 0.585795i | \(-0.800782\pi\) | ||
0.810459 | − | 0.585795i | \(-0.199218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.7918 | 0.785926 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.4890 | −0.601641 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.44722 | −0.152808 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.5698i | 0.568005i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.1652 | −0.416527 | −0.208264 | − | 0.978073i | \(-0.566781\pi\) | ||||
−0.208264 | + | 0.978073i | \(0.566781\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 20.1719i | − | 0.689061i | −0.938775 | − | 0.344530i | \(-0.888038\pi\) | ||
0.938775 | − | 0.344530i | \(-0.111962\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.7396 | −0.605268 | −0.302634 | − | 0.953107i | \(-0.597866\pi\) | ||||
−0.302634 | + | 0.953107i | \(0.597866\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 45.6561i | − | 1.55415i | −0.629407 | − | 0.777076i | \(-0.716702\pi\) | ||
0.629407 | − | 0.777076i | \(-0.283298\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.5216i | 0.969762i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 54.5539 | 1.85061 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.47607 | 0.219433 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −51.3928 | −1.73740 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.2228 | 1.39200 | 0.695998 | − | 0.718044i | \(-0.254962\pi\) | ||||
0.695998 | + | 0.718044i | \(0.254962\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.4484 | 0.958451 | 0.479226 | − | 0.877692i | \(-0.340918\pi\) | ||||
0.479226 | + | 0.877692i | \(0.340918\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.99349 | 0.134392 | 0.0671958 | − | 0.997740i | \(-0.478595\pi\) | ||||
0.0671958 | + | 0.997740i | \(0.478595\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.8899 | 0.802145 | 0.401073 | − | 0.916046i | \(-0.368637\pi\) | ||||
0.401073 | + | 0.916046i | \(0.368637\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −65.8345 | −2.20802 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.4819i | 0.417691i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.426255i | 0.0142481i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.4476i | 0.415150i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.5020 | −0.483130 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.6013 | −0.485363 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.31375 | −0.143236 | −0.0716178 | − | 0.997432i | \(-0.522816\pi\) | ||||
−0.0716178 | + | 0.997432i | \(0.522816\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 31.8083i | − | 1.05386i | −0.849910 | − | 0.526928i | \(-0.823344\pi\) | ||
0.849910 | − | 0.526928i | \(-0.176656\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 50.5784i | − | 1.67390i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.2966 | 0.637230 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.2542 | 0.602152 | 0.301076 | − | 0.953600i | \(-0.402654\pi\) | ||||
0.301076 | + | 0.953600i | \(0.402654\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.34842i | 0.208961i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 30.9195i | − | 1.01663i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.2625i | 1.12412i | 0.827098 | + | 0.562058i | \(0.189990\pi\) | ||||
−0.827098 | + | 0.562058i | \(0.810010\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −53.4733 | −1.75252 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 9.04378i | − | 0.295763i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 20.0049i | − | 0.653531i | −0.945105 | − | 0.326766i | \(-0.894041\pi\) | ||
0.945105 | − | 0.326766i | \(-0.105959\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −58.9337 | −1.92118 | −0.960592 | − | 0.277961i | \(-0.910341\pi\) | ||||
−0.960592 | + | 0.277961i | \(0.910341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.9455 | −0.649515 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 55.1149i | − | 1.79099i | −0.445069 | − | 0.895496i | \(-0.646821\pi\) | ||
0.445069 | − | 0.895496i | \(-0.353179\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.11718 | −0.231034 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.8692 | 1.97175 | 0.985873 | − | 0.167494i | \(-0.0535674\pi\) | ||||
0.985873 | + | 0.167494i | \(0.0535674\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.5275i | 0.631894i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 72.1272i | 2.32911i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.04215 | −0.194908 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.3968i | 0.527831i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.91549 | 0.254545 | 0.127273 | − | 0.991868i | \(-0.459378\pi\) | ||||
0.127273 | + | 0.991868i | \(0.459378\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.8769 | 0.509515 | 0.254757 | − | 0.967005i | \(-0.418004\pi\) | ||||
0.254757 | + | 0.967005i | \(0.418004\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 6.07692i | − | 0.194817i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.3902 | −1.03625 | −0.518127 | − | 0.855304i | \(-0.673370\pi\) | ||||
−0.518127 | + | 0.855304i | \(0.673370\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.7533 | −1.55816 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.0878 | −1.02344 | −0.511720 | − | 0.859152i | \(-0.670992\pi\) | ||||
−0.511720 | + | 0.859152i | \(0.670992\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.7461 | 0.947788 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.71821i | 0.245425i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.6089i | 1.41705i | 0.705687 | + | 0.708524i | \(0.250639\pi\) | ||||
−0.705687 | + | 0.708524i | \(0.749361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.0081 | 0.444087 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.1850 | 0.955969 | 0.477985 | − | 0.878368i | \(-0.341367\pi\) | ||||
0.477985 | + | 0.878368i | \(0.341367\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6012.2.h.a.3005.18 | yes | 56 | |
3.2 | odd | 2 | inner | 6012.2.h.a.3005.40 | yes | 56 | |
167.166 | odd | 2 | inner | 6012.2.h.a.3005.39 | yes | 56 | |
501.500 | even | 2 | inner | 6012.2.h.a.3005.17 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6012.2.h.a.3005.17 | ✓ | 56 | 501.500 | even | 2 | inner | |
6012.2.h.a.3005.18 | yes | 56 | 1.1 | even | 1 | trivial | |
6012.2.h.a.3005.39 | yes | 56 | 167.166 | odd | 2 | inner | |
6012.2.h.a.3005.40 | yes | 56 | 3.2 | odd | 2 | inner |