Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(1,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.a (trivial) |
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: | yes |
Analytic conductor: | \(30.9760027530\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 525.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.00000 | 1.06066 | 0.530330 | − | 0.847791i | \(-0.322068\pi\) | ||||
0.530330 | + | 0.847791i | \(0.322068\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.125000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 9.00000 | 0.612372 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −21.0000 | −0.928078 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.00000 | −0.164461 | −0.0822304 | − | 0.996613i | \(-0.526204\pi\) | ||||
−0.0822304 | + | 0.996613i | \(0.526204\pi\) | |||||||
\(12\) | 3.00000 | 0.0721688 | ||||||||
\(13\) | −41.0000 | −0.874720 | −0.437360 | − | 0.899287i | \(-0.644086\pi\) | ||||
−0.437360 | + | 0.899287i | \(0.644086\pi\) | |||||||
\(14\) | −21.0000 | −0.400892 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | −27.0000 | −0.385204 | −0.192602 | − | 0.981277i | \(-0.561693\pi\) | ||||
−0.192602 | + | 0.981277i | \(0.561693\pi\) | |||||||
\(18\) | 27.0000 | 0.353553 | ||||||||
\(19\) | −4.00000 | −0.0482980 | −0.0241490 | − | 0.999708i | \(-0.507688\pi\) | ||||
−0.0241490 | + | 0.999708i | \(0.507688\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | −18.0000 | −0.174437 | ||||||||
\(23\) | −75.0000 | −0.679938 | −0.339969 | − | 0.940437i | \(-0.610417\pi\) | ||||
−0.339969 | + | 0.940437i | \(0.610417\pi\) | |||||||
\(24\) | −63.0000 | −0.535826 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −123.000 | −0.927780 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −7.00000 | −0.0472456 | ||||||||
\(29\) | −123.000 | −0.787604 | −0.393802 | − | 0.919195i | \(-0.628841\pi\) | ||||
−0.393802 | + | 0.919195i | \(0.628841\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −205.000 | −1.18771 | −0.593856 | − | 0.804571i | \(-0.702395\pi\) | ||||
−0.593856 | + | 0.804571i | \(0.702395\pi\) | |||||||
\(32\) | −45.0000 | −0.248592 | ||||||||
\(33\) | −18.0000 | −0.0949514 | ||||||||
\(34\) | −81.0000 | −0.408570 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.00000 | 0.0416667 | ||||||||
\(37\) | 262.000 | 1.16412 | 0.582061 | − | 0.813145i | \(-0.302246\pi\) | ||||
0.582061 | + | 0.813145i | \(0.302246\pi\) | |||||||
\(38\) | −12.0000 | −0.0512278 | ||||||||
\(39\) | −123.000 | −0.505020 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 57.0000 | 0.217120 | 0.108560 | − | 0.994090i | \(-0.465376\pi\) | ||||
0.108560 | + | 0.994090i | \(0.465376\pi\) | |||||||
\(42\) | −63.0000 | −0.231455 | ||||||||
\(43\) | −407.000 | −1.44342 | −0.721708 | − | 0.692197i | \(-0.756643\pi\) | ||||
−0.721708 | + | 0.692197i | \(0.756643\pi\) | |||||||
\(44\) | −6.00000 | −0.0205576 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −225.000 | −0.721183 | ||||||||
\(47\) | 60.0000 | 0.186211 | 0.0931053 | − | 0.995656i | \(-0.470321\pi\) | ||||
0.0931053 | + | 0.995656i | \(0.470321\pi\) | |||||||
\(48\) | −213.000 | −0.640498 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −81.0000 | −0.222397 | ||||||||
\(52\) | −41.0000 | −0.109340 | ||||||||
\(53\) | −327.000 | −0.847489 | −0.423744 | − | 0.905782i | \(-0.639285\pi\) | ||||
−0.423744 | + | 0.905782i | \(0.639285\pi\) | |||||||
\(54\) | 81.0000 | 0.204124 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 147.000 | 0.350780 | ||||||||
\(57\) | −12.0000 | −0.0278849 | ||||||||
\(58\) | −369.000 | −0.835381 | ||||||||
\(59\) | 33.0000 | 0.0728175 | 0.0364088 | − | 0.999337i | \(-0.488408\pi\) | ||||
0.0364088 | + | 0.999337i | \(0.488408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −427.000 | −0.896258 | −0.448129 | − | 0.893969i | \(-0.647910\pi\) | ||||
−0.448129 | + | 0.893969i | \(0.647910\pi\) | |||||||
\(62\) | −615.000 | −1.25976 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −54.0000 | −0.100711 | ||||||||
\(67\) | 628.000 | 1.14511 | 0.572555 | − | 0.819866i | \(-0.305952\pi\) | ||||
0.572555 | + | 0.819866i | \(0.305952\pi\) | |||||||
\(68\) | −27.0000 | −0.0481505 | ||||||||
\(69\) | −225.000 | −0.392563 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 300.000 | 0.501457 | 0.250729 | − | 0.968057i | \(-0.419330\pi\) | ||||
0.250729 | + | 0.968057i | \(0.419330\pi\) | |||||||
\(72\) | −189.000 | −0.309359 | ||||||||
\(73\) | −98.0000 | −0.157124 | −0.0785619 | − | 0.996909i | \(-0.525033\pi\) | ||||
−0.0785619 | + | 0.996909i | \(0.525033\pi\) | |||||||
\(74\) | 786.000 | 1.23474 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | −0.00603726 | ||||||||
\(77\) | 42.0000 | 0.0621603 | ||||||||
\(78\) | −369.000 | −0.535654 | ||||||||
\(79\) | 686.000 | 0.976975 | 0.488488 | − | 0.872571i | \(-0.337549\pi\) | ||||
0.488488 | + | 0.872571i | \(0.337549\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 171.000 | 0.230290 | ||||||||
\(83\) | −1401.00 | −1.85277 | −0.926384 | − | 0.376580i | \(-0.877100\pi\) | ||||
−0.926384 | + | 0.376580i | \(0.877100\pi\) | |||||||
\(84\) | −21.0000 | −0.0272772 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1221.00 | −1.53097 | ||||||||
\(87\) | −369.000 | −0.454724 | ||||||||
\(88\) | 126.000 | 0.152632 | ||||||||
\(89\) | 714.000 | 0.850380 | 0.425190 | − | 0.905104i | \(-0.360207\pi\) | ||||
0.425190 | + | 0.905104i | \(0.360207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 287.000 | 0.330613 | ||||||||
\(92\) | −75.0000 | −0.0849923 | ||||||||
\(93\) | −615.000 | −0.685726 | ||||||||
\(94\) | 180.000 | 0.197506 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −135.000 | −0.143525 | ||||||||
\(97\) | −494.000 | −0.517094 | −0.258547 | − | 0.965999i | \(-0.583244\pi\) | ||||
−0.258547 | + | 0.965999i | \(0.583244\pi\) | |||||||
\(98\) | 147.000 | 0.151523 | ||||||||
\(99\) | −54.0000 | −0.0548202 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 624.000 | 0.614756 | 0.307378 | − | 0.951588i | \(-0.400548\pi\) | ||||
0.307378 | + | 0.951588i | \(0.400548\pi\) | |||||||
\(102\) | −243.000 | −0.235888 | ||||||||
\(103\) | 769.000 | 0.735649 | 0.367824 | − | 0.929895i | \(-0.380103\pi\) | ||||
0.367824 | + | 0.929895i | \(0.380103\pi\) | |||||||
\(104\) | 861.000 | 0.811808 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −981.000 | −0.898898 | ||||||||
\(107\) | −1662.00 | −1.50160 | −0.750802 | − | 0.660527i | \(-0.770333\pi\) | ||||
−0.750802 | + | 0.660527i | \(0.770333\pi\) | |||||||
\(108\) | 27.0000 | 0.0240563 | ||||||||
\(109\) | 188.000 | 0.165203 | 0.0826015 | − | 0.996583i | \(-0.473677\pi\) | ||||
0.0826015 | + | 0.996583i | \(0.473677\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 786.000 | 0.672106 | ||||||||
\(112\) | 497.000 | 0.419304 | ||||||||
\(113\) | 18.0000 | 0.0149849 | 0.00749247 | − | 0.999972i | \(-0.497615\pi\) | ||||
0.00749247 | + | 0.999972i | \(0.497615\pi\) | |||||||
\(114\) | −36.0000 | −0.0295764 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −123.000 | −0.0984505 | ||||||||
\(117\) | −369.000 | −0.291573 | ||||||||
\(118\) | 99.0000 | 0.0772347 | ||||||||
\(119\) | 189.000 | 0.145593 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1295.00 | −0.972953 | ||||||||
\(122\) | −1281.00 | −0.950625 | ||||||||
\(123\) | 171.000 | 0.125354 | ||||||||
\(124\) | −205.000 | −0.148464 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −189.000 | −0.133631 | ||||||||
\(127\) | 1450.00 | 1.01312 | 0.506562 | − | 0.862204i | \(-0.330916\pi\) | ||||
0.506562 | + | 0.862204i | \(0.330916\pi\) | |||||||
\(128\) | 1659.00 | 1.14560 | ||||||||
\(129\) | −1221.00 | −0.833357 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2664.00 | 1.77675 | 0.888377 | − | 0.459115i | \(-0.151833\pi\) | ||||
0.888377 | + | 0.459115i | \(0.151833\pi\) | |||||||
\(132\) | −18.0000 | −0.0118689 | ||||||||
\(133\) | 28.0000 | 0.0182549 | ||||||||
\(134\) | 1884.00 | 1.21457 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 567.000 | 0.357499 | ||||||||
\(137\) | −1692.00 | −1.05516 | −0.527581 | − | 0.849504i | \(-0.676901\pi\) | ||||
−0.527581 | + | 0.849504i | \(0.676901\pi\) | |||||||
\(138\) | −675.000 | −0.416375 | ||||||||
\(139\) | 1268.00 | 0.773744 | 0.386872 | − | 0.922134i | \(-0.373556\pi\) | ||||
0.386872 | + | 0.922134i | \(0.373556\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 180.000 | 0.107509 | ||||||||
\(142\) | 900.000 | 0.531876 | ||||||||
\(143\) | 246.000 | 0.143857 | ||||||||
\(144\) | −639.000 | −0.369792 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −294.000 | −0.166655 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 262.000 | 0.145515 | ||||||||
\(149\) | 2169.00 | 1.19256 | 0.596280 | − | 0.802777i | \(-0.296645\pi\) | ||||
0.596280 | + | 0.802777i | \(0.296645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 518.000 | 0.279167 | 0.139584 | − | 0.990210i | \(-0.455424\pi\) | ||||
0.139584 | + | 0.990210i | \(0.455424\pi\) | |||||||
\(152\) | 84.0000 | 0.0448243 | ||||||||
\(153\) | −243.000 | −0.128401 | ||||||||
\(154\) | 126.000 | 0.0659310 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −123.000 | −0.0631274 | ||||||||
\(157\) | 886.000 | 0.450385 | 0.225193 | − | 0.974314i | \(-0.427699\pi\) | ||||
0.225193 | + | 0.974314i | \(0.427699\pi\) | |||||||
\(158\) | 2058.00 | 1.03624 | ||||||||
\(159\) | −981.000 | −0.489298 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 525.000 | 0.256993 | ||||||||
\(162\) | 243.000 | 0.117851 | ||||||||
\(163\) | −3893.00 | −1.87070 | −0.935348 | − | 0.353730i | \(-0.884913\pi\) | ||||
−0.935348 | + | 0.353730i | \(0.884913\pi\) | |||||||
\(164\) | 57.0000 | 0.0271400 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4203.00 | −1.96516 | ||||||||
\(167\) | −2046.00 | −0.948049 | −0.474025 | − | 0.880512i | \(-0.657199\pi\) | ||||
−0.474025 | + | 0.880512i | \(0.657199\pi\) | |||||||
\(168\) | 441.000 | 0.202523 | ||||||||
\(169\) | −516.000 | −0.234866 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −36.0000 | −0.0160993 | ||||||||
\(172\) | −407.000 | −0.180427 | ||||||||
\(173\) | 3540.00 | 1.55573 | 0.777865 | − | 0.628432i | \(-0.216303\pi\) | ||||
0.777865 | + | 0.628432i | \(0.216303\pi\) | |||||||
\(174\) | −1107.00 | −0.482307 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 426.000 | 0.182449 | ||||||||
\(177\) | 99.0000 | 0.0420412 | ||||||||
\(178\) | 2142.00 | 0.901965 | ||||||||
\(179\) | −3246.00 | −1.35540 | −0.677702 | − | 0.735336i | \(-0.737024\pi\) | ||||
−0.677702 | + | 0.735336i | \(0.737024\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1334.00 | 0.547820 | 0.273910 | − | 0.961755i | \(-0.411683\pi\) | ||||
0.273910 | + | 0.961755i | \(0.411683\pi\) | |||||||
\(182\) | 861.000 | 0.350668 | ||||||||
\(183\) | −1281.00 | −0.517455 | ||||||||
\(184\) | 1575.00 | 0.631036 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1845.00 | −0.727322 | ||||||||
\(187\) | 162.000 | 0.0633509 | ||||||||
\(188\) | 60.0000 | 0.0232763 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −873.000 | −0.330723 | −0.165361 | − | 0.986233i | \(-0.552879\pi\) | ||||
−0.165361 | + | 0.986233i | \(0.552879\pi\) | |||||||
\(192\) | 1299.00 | 0.488267 | ||||||||
\(193\) | 1006.00 | 0.375199 | 0.187600 | − | 0.982246i | \(-0.439929\pi\) | ||||
0.187600 | + | 0.982246i | \(0.439929\pi\) | |||||||
\(194\) | −1482.00 | −0.548461 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 49.0000 | 0.0178571 | ||||||||
\(197\) | −591.000 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | −162.000 | −0.0581456 | ||||||||
\(199\) | −2584.00 | −0.920477 | −0.460238 | − | 0.887795i | \(-0.652236\pi\) | ||||
−0.460238 | + | 0.887795i | \(0.652236\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1884.00 | 0.661130 | ||||||||
\(202\) | 1872.00 | 0.652047 | ||||||||
\(203\) | 861.000 | 0.297686 | ||||||||
\(204\) | −81.0000 | −0.0277997 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2307.00 | 0.780273 | ||||||||
\(207\) | −675.000 | −0.226646 | ||||||||
\(208\) | 2911.00 | 0.970392 | ||||||||
\(209\) | 24.0000 | 0.00794313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1441.00 | −0.470154 | −0.235077 | − | 0.971977i | \(-0.575534\pi\) | ||||
−0.235077 | + | 0.971977i | \(0.575534\pi\) | |||||||
\(212\) | −327.000 | −0.105936 | ||||||||
\(213\) | 900.000 | 0.289516 | ||||||||
\(214\) | −4986.00 | −1.59269 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −567.000 | −0.178609 | ||||||||
\(217\) | 1435.00 | 0.448913 | ||||||||
\(218\) | 564.000 | 0.175224 | ||||||||
\(219\) | −294.000 | −0.0907154 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1107.00 | 0.336945 | ||||||||
\(222\) | 2358.00 | 0.712877 | ||||||||
\(223\) | −3827.00 | −1.14921 | −0.574607 | − | 0.818429i | \(-0.694845\pi\) | ||||
−0.574607 | + | 0.818429i | \(0.694845\pi\) | |||||||
\(224\) | 315.000 | 0.0939590 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 54.0000 | 0.0158939 | ||||||||
\(227\) | 5421.00 | 1.58504 | 0.792521 | − | 0.609845i | \(-0.208768\pi\) | ||||
0.792521 | + | 0.609845i | \(0.208768\pi\) | |||||||
\(228\) | −12.0000 | −0.00348561 | ||||||||
\(229\) | −5290.00 | −1.52652 | −0.763260 | − | 0.646092i | \(-0.776402\pi\) | ||||
−0.763260 | + | 0.646092i | \(0.776402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 126.000 | 0.0358883 | ||||||||
\(232\) | 2583.00 | 0.730958 | ||||||||
\(233\) | −4908.00 | −1.37997 | −0.689987 | − | 0.723822i | \(-0.742384\pi\) | ||||
−0.689987 | + | 0.723822i | \(0.742384\pi\) | |||||||
\(234\) | −1107.00 | −0.309260 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 33.0000 | 0.00910219 | ||||||||
\(237\) | 2058.00 | 0.564057 | ||||||||
\(238\) | 567.000 | 0.154425 | ||||||||
\(239\) | 1056.00 | 0.285803 | 0.142902 | − | 0.989737i | \(-0.454357\pi\) | ||||
0.142902 | + | 0.989737i | \(0.454357\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5342.00 | 1.42784 | 0.713918 | − | 0.700229i | \(-0.246919\pi\) | ||||
0.713918 | + | 0.700229i | \(0.246919\pi\) | |||||||
\(242\) | −3885.00 | −1.03197 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −427.000 | −0.112032 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 513.000 | 0.132958 | ||||||||
\(247\) | 164.000 | 0.0422472 | ||||||||
\(248\) | 4305.00 | 1.10229 | ||||||||
\(249\) | −4203.00 | −1.06970 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5805.00 | 1.45979 | 0.729897 | − | 0.683557i | \(-0.239568\pi\) | ||||
0.729897 | + | 0.683557i | \(0.239568\pi\) | |||||||
\(252\) | −63.0000 | −0.0157485 | ||||||||
\(253\) | 450.000 | 0.111823 | ||||||||
\(254\) | 4350.00 | 1.07458 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | −543.000 | −0.131795 | −0.0658977 | − | 0.997826i | \(-0.520991\pi\) | ||||
−0.0658977 | + | 0.997826i | \(0.520991\pi\) | |||||||
\(258\) | −3663.00 | −0.883909 | ||||||||
\(259\) | −1834.00 | −0.439997 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1107.00 | −0.262535 | ||||||||
\(262\) | 7992.00 | 1.88453 | ||||||||
\(263\) | 5193.00 | 1.21754 | 0.608772 | − | 0.793345i | \(-0.291662\pi\) | ||||
0.608772 | + | 0.793345i | \(0.291662\pi\) | |||||||
\(264\) | 378.000 | 0.0881223 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 84.0000 | 0.0193623 | ||||||||
\(267\) | 2142.00 | 0.490967 | ||||||||
\(268\) | 628.000 | 0.143139 | ||||||||
\(269\) | 2154.00 | 0.488222 | 0.244111 | − | 0.969747i | \(-0.421504\pi\) | ||||
0.244111 | + | 0.969747i | \(0.421504\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2396.00 | 0.537072 | 0.268536 | − | 0.963270i | \(-0.413460\pi\) | ||||
0.268536 | + | 0.963270i | \(0.413460\pi\) | |||||||
\(272\) | 1917.00 | 0.427335 | ||||||||
\(273\) | 861.000 | 0.190879 | ||||||||
\(274\) | −5076.00 | −1.11917 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −225.000 | −0.0490703 | ||||||||
\(277\) | −4286.00 | −0.929678 | −0.464839 | − | 0.885395i | \(-0.653888\pi\) | ||||
−0.464839 | + | 0.885395i | \(0.653888\pi\) | |||||||
\(278\) | 3804.00 | 0.820679 | ||||||||
\(279\) | −1845.00 | −0.395904 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2208.00 | 0.468748 | 0.234374 | − | 0.972146i | \(-0.424696\pi\) | ||||
0.234374 | + | 0.972146i | \(0.424696\pi\) | |||||||
\(282\) | 540.000 | 0.114030 | ||||||||
\(283\) | −3620.00 | −0.760377 | −0.380188 | − | 0.924909i | \(-0.624141\pi\) | ||||
−0.380188 | + | 0.924909i | \(0.624141\pi\) | |||||||
\(284\) | 300.000 | 0.0626821 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 738.000 | 0.152583 | ||||||||
\(287\) | −399.000 | −0.0820635 | ||||||||
\(288\) | −405.000 | −0.0828641 | ||||||||
\(289\) | −4184.00 | −0.851618 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1482.00 | −0.298544 | ||||||||
\(292\) | −98.0000 | −0.0196405 | ||||||||
\(293\) | 1392.00 | 0.277548 | 0.138774 | − | 0.990324i | \(-0.455684\pi\) | ||||
0.138774 | + | 0.990324i | \(0.455684\pi\) | |||||||
\(294\) | 441.000 | 0.0874818 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5502.00 | −1.08040 | ||||||||
\(297\) | −162.000 | −0.0316505 | ||||||||
\(298\) | 6507.00 | 1.26490 | ||||||||
\(299\) | 3075.00 | 0.594755 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2849.00 | 0.545560 | ||||||||
\(302\) | 1554.00 | 0.296101 | ||||||||
\(303\) | 1872.00 | 0.354929 | ||||||||
\(304\) | 284.000 | 0.0535806 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −729.000 | −0.136190 | ||||||||
\(307\) | −9002.00 | −1.67352 | −0.836761 | − | 0.547568i | \(-0.815554\pi\) | ||||
−0.836761 | + | 0.547568i | \(0.815554\pi\) | |||||||
\(308\) | 42.0000 | 0.00777004 | ||||||||
\(309\) | 2307.00 | 0.424727 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6666.00 | 1.21542 | 0.607708 | − | 0.794161i | \(-0.292089\pi\) | ||||
0.607708 | + | 0.794161i | \(0.292089\pi\) | |||||||
\(312\) | 2583.00 | 0.468697 | ||||||||
\(313\) | 2878.00 | 0.519726 | 0.259863 | − | 0.965646i | \(-0.416323\pi\) | ||||
0.259863 | + | 0.965646i | \(0.416323\pi\) | |||||||
\(314\) | 2658.00 | 0.477706 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 686.000 | 0.122122 | ||||||||
\(317\) | −4611.00 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(318\) | −2943.00 | −0.518979 | ||||||||
\(319\) | 738.000 | 0.129530 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4986.00 | −0.866951 | ||||||||
\(322\) | 1575.00 | 0.272582 | ||||||||
\(323\) | 108.000 | 0.0186046 | ||||||||
\(324\) | 81.0000 | 0.0138889 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11679.0 | −1.98417 | ||||||||
\(327\) | 564.000 | 0.0953800 | ||||||||
\(328\) | −1197.00 | −0.201504 | ||||||||
\(329\) | −420.000 | −0.0703810 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7459.00 | −1.23862 | −0.619311 | − | 0.785146i | \(-0.712588\pi\) | ||||
−0.619311 | + | 0.785146i | \(0.712588\pi\) | |||||||
\(332\) | −1401.00 | −0.231596 | ||||||||
\(333\) | 2358.00 | 0.388041 | ||||||||
\(334\) | −6138.00 | −1.00556 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1491.00 | 0.242085 | ||||||||
\(337\) | −5843.00 | −0.944476 | −0.472238 | − | 0.881471i | \(-0.656554\pi\) | ||||
−0.472238 | + | 0.881471i | \(0.656554\pi\) | |||||||
\(338\) | −1548.00 | −0.249113 | ||||||||
\(339\) | 54.0000 | 0.00865156 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1230.00 | 0.195332 | ||||||||
\(342\) | −108.000 | −0.0170759 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 8547.00 | 1.33960 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10620.0 | 1.65010 | ||||||||
\(347\) | −2346.00 | −0.362939 | −0.181470 | − | 0.983397i | \(-0.558085\pi\) | ||||
−0.181470 | + | 0.983397i | \(0.558085\pi\) | |||||||
\(348\) | −369.000 | −0.0568404 | ||||||||
\(349\) | 5807.00 | 0.890664 | 0.445332 | − | 0.895366i | \(-0.353086\pi\) | ||||
0.445332 | + | 0.895366i | \(0.353086\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1107.00 | −0.168340 | ||||||||
\(352\) | 270.000 | 0.0408837 | ||||||||
\(353\) | 5190.00 | 0.782538 | 0.391269 | − | 0.920276i | \(-0.372036\pi\) | ||||
0.391269 | + | 0.920276i | \(0.372036\pi\) | |||||||
\(354\) | 297.000 | 0.0445914 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 714.000 | 0.106298 | ||||||||
\(357\) | 567.000 | 0.0840583 | ||||||||
\(358\) | −9738.00 | −1.43762 | ||||||||
\(359\) | 8883.00 | 1.30592 | 0.652962 | − | 0.757391i | \(-0.273526\pi\) | ||||
0.652962 | + | 0.757391i | \(0.273526\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6843.00 | −0.997667 | ||||||||
\(362\) | 4002.00 | 0.581051 | ||||||||
\(363\) | −3885.00 | −0.561734 | ||||||||
\(364\) | 287.000 | 0.0413266 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3843.00 | −0.548844 | ||||||||
\(367\) | −9965.00 | −1.41735 | −0.708677 | − | 0.705533i | \(-0.750708\pi\) | ||||
−0.708677 | + | 0.705533i | \(0.750708\pi\) | |||||||
\(368\) | 5325.00 | 0.754307 | ||||||||
\(369\) | 513.000 | 0.0723732 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2289.00 | 0.320321 | ||||||||
\(372\) | −615.000 | −0.0857158 | ||||||||
\(373\) | −11660.0 | −1.61858 | −0.809292 | − | 0.587406i | \(-0.800149\pi\) | ||||
−0.809292 | + | 0.587406i | \(0.800149\pi\) | |||||||
\(374\) | 486.000 | 0.0671937 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1260.00 | −0.172818 | ||||||||
\(377\) | 5043.00 | 0.688933 | ||||||||
\(378\) | −567.000 | −0.0771517 | ||||||||
\(379\) | 3203.00 | 0.434108 | 0.217054 | − | 0.976160i | \(-0.430355\pi\) | ||||
0.217054 | + | 0.976160i | \(0.430355\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4350.00 | 0.584927 | ||||||||
\(382\) | −2619.00 | −0.350785 | ||||||||
\(383\) | 8220.00 | 1.09666 | 0.548332 | − | 0.836261i | \(-0.315263\pi\) | ||||
0.548332 | + | 0.836261i | \(0.315263\pi\) | |||||||
\(384\) | 4977.00 | 0.661410 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3018.00 | 0.397959 | ||||||||
\(387\) | −3663.00 | −0.481139 | ||||||||
\(388\) | −494.000 | −0.0646367 | ||||||||
\(389\) | −2226.00 | −0.290135 | −0.145068 | − | 0.989422i | \(-0.546340\pi\) | ||||
−0.145068 | + | 0.989422i | \(0.546340\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2025.00 | 0.261915 | ||||||||
\(392\) | −1029.00 | −0.132583 | ||||||||
\(393\) | 7992.00 | 1.02581 | ||||||||
\(394\) | −1773.00 | −0.226707 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −54.0000 | −0.00685253 | ||||||||
\(397\) | −10451.0 | −1.32121 | −0.660605 | − | 0.750733i | \(-0.729700\pi\) | ||||
−0.660605 | + | 0.750733i | \(0.729700\pi\) | |||||||
\(398\) | −7752.00 | −0.976313 | ||||||||
\(399\) | 84.0000 | 0.0105395 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1320.00 | −0.164383 | −0.0821916 | − | 0.996617i | \(-0.526192\pi\) | ||||
−0.0821916 | + | 0.996617i | \(0.526192\pi\) | |||||||
\(402\) | 5652.00 | 0.701234 | ||||||||
\(403\) | 8405.00 | 1.03892 | ||||||||
\(404\) | 624.000 | 0.0768445 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2583.00 | 0.315744 | ||||||||
\(407\) | −1572.00 | −0.191452 | ||||||||
\(408\) | 1701.00 | 0.206402 | ||||||||
\(409\) | 2402.00 | 0.290394 | 0.145197 | − | 0.989403i | \(-0.453618\pi\) | ||||
0.145197 | + | 0.989403i | \(0.453618\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5076.00 | −0.609199 | ||||||||
\(412\) | 769.000 | 0.0919561 | ||||||||
\(413\) | −231.000 | −0.0275224 | ||||||||
\(414\) | −2025.00 | −0.240394 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1845.00 | 0.217448 | ||||||||
\(417\) | 3804.00 | 0.446721 | ||||||||
\(418\) | 72.0000 | 0.00842496 | ||||||||
\(419\) | −3333.00 | −0.388610 | −0.194305 | − | 0.980941i | \(-0.562245\pi\) | ||||
−0.194305 | + | 0.980941i | \(0.562245\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1462.00 | −0.169248 | −0.0846241 | − | 0.996413i | \(-0.526969\pi\) | ||||
−0.0846241 | + | 0.996413i | \(0.526969\pi\) | |||||||
\(422\) | −4323.00 | −0.498674 | ||||||||
\(423\) | 540.000 | 0.0620702 | ||||||||
\(424\) | 6867.00 | 0.786535 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2700.00 | 0.307078 | ||||||||
\(427\) | 2989.00 | 0.338754 | ||||||||
\(428\) | −1662.00 | −0.187700 | ||||||||
\(429\) | 738.000 | 0.0830559 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10089.0 | −1.12754 | −0.563770 | − | 0.825932i | \(-0.690650\pi\) | ||||
−0.563770 | + | 0.825932i | \(0.690650\pi\) | |||||||
\(432\) | −1917.00 | −0.213499 | ||||||||
\(433\) | −3242.00 | −0.359817 | −0.179908 | − | 0.983683i | \(-0.557580\pi\) | ||||
−0.179908 | + | 0.983683i | \(0.557580\pi\) | |||||||
\(434\) | 4305.00 | 0.476144 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 188.000 | 0.0206504 | ||||||||
\(437\) | 300.000 | 0.0328397 | ||||||||
\(438\) | −882.000 | −0.0962182 | ||||||||
\(439\) | 1799.00 | 0.195584 | 0.0977922 | − | 0.995207i | \(-0.468822\pi\) | ||||
0.0977922 | + | 0.995207i | \(0.468822\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 3321.00 | 0.357384 | ||||||||
\(443\) | −8772.00 | −0.940791 | −0.470395 | − | 0.882456i | \(-0.655889\pi\) | ||||
−0.470395 | + | 0.882456i | \(0.655889\pi\) | |||||||
\(444\) | 786.000 | 0.0840133 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11481.0 | −1.21893 | ||||||||
\(447\) | 6507.00 | 0.688525 | ||||||||
\(448\) | −3031.00 | −0.319646 | ||||||||
\(449\) | 1560.00 | 0.163966 | 0.0819832 | − | 0.996634i | \(-0.473875\pi\) | ||||
0.0819832 | + | 0.996634i | \(0.473875\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −342.000 | −0.0357077 | ||||||||
\(452\) | 18.0000 | 0.00187312 | ||||||||
\(453\) | 1554.00 | 0.161177 | ||||||||
\(454\) | 16263.0 | 1.68119 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 252.000 | 0.0258793 | ||||||||
\(457\) | −11615.0 | −1.18890 | −0.594449 | − | 0.804133i | \(-0.702630\pi\) | ||||
−0.594449 | + | 0.804133i | \(0.702630\pi\) | |||||||
\(458\) | −15870.0 | −1.61912 | ||||||||
\(459\) | −729.000 | −0.0741325 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6960.00 | 0.703166 | 0.351583 | − | 0.936157i | \(-0.385644\pi\) | ||||
0.351583 | + | 0.936157i | \(0.385644\pi\) | |||||||
\(462\) | 378.000 | 0.0380653 | ||||||||
\(463\) | −13052.0 | −1.31010 | −0.655052 | − | 0.755584i | \(-0.727353\pi\) | ||||
−0.655052 | + | 0.755584i | \(0.727353\pi\) | |||||||
\(464\) | 8733.00 | 0.873749 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14724.0 | −1.46368 | ||||||||
\(467\) | −14013.0 | −1.38853 | −0.694266 | − | 0.719719i | \(-0.744271\pi\) | ||||
−0.694266 | + | 0.719719i | \(0.744271\pi\) | |||||||
\(468\) | −369.000 | −0.0364466 | ||||||||
\(469\) | −4396.00 | −0.432811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2658.00 | 0.260030 | ||||||||
\(472\) | −693.000 | −0.0675803 | ||||||||
\(473\) | 2442.00 | 0.237385 | ||||||||
\(474\) | 6174.00 | 0.598273 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 189.000 | 0.0181992 | ||||||||
\(477\) | −2943.00 | −0.282496 | ||||||||
\(478\) | 3168.00 | 0.303140 | ||||||||
\(479\) | 1056.00 | 0.100730 | 0.0503652 | − | 0.998731i | \(-0.483961\pi\) | ||||
0.0503652 | + | 0.998731i | \(0.483961\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10742.0 | −1.01828 | ||||||||
\(482\) | 16026.0 | 1.51445 | ||||||||
\(483\) | 1575.00 | 0.148375 | ||||||||
\(484\) | −1295.00 | −0.121619 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 729.000 | 0.0680414 | ||||||||
\(487\) | −7886.00 | −0.733776 | −0.366888 | − | 0.930265i | \(-0.619577\pi\) | ||||
−0.366888 | + | 0.930265i | \(0.619577\pi\) | |||||||
\(488\) | 8967.00 | 0.831797 | ||||||||
\(489\) | −11679.0 | −1.08005 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10590.0 | 0.973361 | 0.486680 | − | 0.873580i | \(-0.338208\pi\) | ||||
0.486680 | + | 0.873580i | \(0.338208\pi\) | |||||||
\(492\) | 171.000 | 0.0156693 | ||||||||
\(493\) | 3321.00 | 0.303388 | ||||||||
\(494\) | 492.000 | 0.0448100 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14555.0 | 1.31762 | ||||||||
\(497\) | −2100.00 | −0.189533 | ||||||||
\(498\) | −12609.0 | −1.13458 | ||||||||
\(499\) | −14899.0 | −1.33661 | −0.668307 | − | 0.743885i | \(-0.732981\pi\) | ||||
−0.668307 | + | 0.743885i | \(0.732981\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6138.00 | −0.547357 | ||||||||
\(502\) | 17415.0 | 1.54835 | ||||||||
\(503\) | −21558.0 | −1.91098 | −0.955491 | − | 0.295021i | \(-0.904673\pi\) | ||||
−0.955491 | + | 0.295021i | \(0.904673\pi\) | |||||||
\(504\) | 1323.00 | 0.116927 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1350.00 | 0.118606 | ||||||||
\(507\) | −1548.00 | −0.135600 | ||||||||
\(508\) | 1450.00 | 0.126640 | ||||||||
\(509\) | −15240.0 | −1.32711 | −0.663557 | − | 0.748126i | \(-0.730954\pi\) | ||||
−0.663557 | + | 0.748126i | \(0.730954\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 686.000 | 0.0593872 | ||||||||
\(512\) | −8733.00 | −0.753804 | ||||||||
\(513\) | −108.000 | −0.00929496 | ||||||||
\(514\) | −1629.00 | −0.139790 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1221.00 | −0.104170 | ||||||||
\(517\) | −360.000 | −0.0306243 | ||||||||
\(518\) | −5502.00 | −0.466687 | ||||||||
\(519\) | 10620.0 | 0.898201 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16797.0 | −1.41246 | −0.706228 | − | 0.707984i | \(-0.749605\pi\) | ||||
−0.706228 | + | 0.707984i | \(0.749605\pi\) | |||||||
\(522\) | −3321.00 | −0.278460 | ||||||||
\(523\) | −22520.0 | −1.88285 | −0.941425 | − | 0.337222i | \(-0.890513\pi\) | ||||
−0.941425 | + | 0.337222i | \(0.890513\pi\) | |||||||
\(524\) | 2664.00 | 0.222094 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15579.0 | 1.29140 | ||||||||
\(527\) | 5535.00 | 0.457511 | ||||||||
\(528\) | 1278.00 | 0.105337 | ||||||||
\(529\) | −6542.00 | −0.537684 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 297.000 | 0.0242725 | ||||||||
\(532\) | 28.0000 | 0.00228187 | ||||||||
\(533\) | −2337.00 | −0.189919 | ||||||||
\(534\) | 6426.00 | 0.520749 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13188.0 | −1.06275 | ||||||||
\(537\) | −9738.00 | −0.782543 | ||||||||
\(538\) | 6462.00 | 0.517838 | ||||||||
\(539\) | −294.000 | −0.0234944 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12004.0 | −0.953960 | −0.476980 | − | 0.878914i | \(-0.658269\pi\) | ||||
−0.476980 | + | 0.878914i | \(0.658269\pi\) | |||||||
\(542\) | 7188.00 | 0.569651 | ||||||||
\(543\) | 4002.00 | 0.316284 | ||||||||
\(544\) | 1215.00 | 0.0957586 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2583.00 | 0.202458 | ||||||||
\(547\) | 16423.0 | 1.28372 | 0.641862 | − | 0.766820i | \(-0.278162\pi\) | ||||
0.641862 | + | 0.766820i | \(0.278162\pi\) | |||||||
\(548\) | −1692.00 | −0.131895 | ||||||||
\(549\) | −3843.00 | −0.298753 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 492.000 | 0.0380398 | ||||||||
\(552\) | 4725.00 | 0.364329 | ||||||||
\(553\) | −4802.00 | −0.369262 | ||||||||
\(554\) | −12858.0 | −0.986072 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1268.00 | 0.0967179 | ||||||||
\(557\) | −714.000 | −0.0543145 | −0.0271572 | − | 0.999631i | \(-0.508645\pi\) | ||||
−0.0271572 | + | 0.999631i | \(0.508645\pi\) | |||||||
\(558\) | −5535.00 | −0.419920 | ||||||||
\(559\) | 16687.0 | 1.26258 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 486.000 | 0.0365756 | ||||||||
\(562\) | 6624.00 | 0.497183 | ||||||||
\(563\) | −16293.0 | −1.21966 | −0.609830 | − | 0.792533i | \(-0.708762\pi\) | ||||
−0.609830 | + | 0.792533i | \(0.708762\pi\) | |||||||
\(564\) | 180.000 | 0.0134386 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10860.0 | −0.806501 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | −6300.00 | −0.465391 | ||||||||
\(569\) | −17370.0 | −1.27977 | −0.639884 | − | 0.768471i | \(-0.721018\pi\) | ||||
−0.639884 | + | 0.768471i | \(0.721018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12589.0 | −0.922650 | −0.461325 | − | 0.887231i | \(-0.652626\pi\) | ||||
−0.461325 | + | 0.887231i | \(0.652626\pi\) | |||||||
\(572\) | 246.000 | 0.0179821 | ||||||||
\(573\) | −2619.00 | −0.190943 | ||||||||
\(574\) | −1197.00 | −0.0870415 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3897.00 | 0.281901 | ||||||||
\(577\) | 13318.0 | 0.960894 | 0.480447 | − | 0.877024i | \(-0.340475\pi\) | ||||
0.480447 | + | 0.877024i | \(0.340475\pi\) | |||||||
\(578\) | −12552.0 | −0.903277 | ||||||||
\(579\) | 3018.00 | 0.216621 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9807.00 | 0.700280 | ||||||||
\(582\) | −4446.00 | −0.316654 | ||||||||
\(583\) | 1962.00 | 0.139379 | ||||||||
\(584\) | 2058.00 | 0.145823 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4176.00 | 0.294384 | ||||||||
\(587\) | 7551.00 | 0.530942 | 0.265471 | − | 0.964119i | \(-0.414472\pi\) | ||||
0.265471 | + | 0.964119i | \(0.414472\pi\) | |||||||
\(588\) | 147.000 | 0.0103098 | ||||||||
\(589\) | 820.000 | 0.0573642 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1773.00 | −0.123404 | ||||||||
\(592\) | −18602.0 | −1.29145 | ||||||||
\(593\) | 6402.00 | 0.443337 | 0.221668 | − | 0.975122i | \(-0.428850\pi\) | ||||
0.221668 | + | 0.975122i | \(0.428850\pi\) | |||||||
\(594\) | −486.000 | −0.0335704 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2169.00 | 0.149070 | ||||||||
\(597\) | −7752.00 | −0.531438 | ||||||||
\(598\) | 9225.00 | 0.630833 | ||||||||
\(599\) | −15753.0 | −1.07454 | −0.537271 | − | 0.843410i | \(-0.680545\pi\) | ||||
−0.537271 | + | 0.843410i | \(0.680545\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9764.00 | 0.662699 | 0.331349 | − | 0.943508i | \(-0.392496\pi\) | ||||
0.331349 | + | 0.943508i | \(0.392496\pi\) | |||||||
\(602\) | 8547.00 | 0.578654 | ||||||||
\(603\) | 5652.00 | 0.381704 | ||||||||
\(604\) | 518.000 | 0.0348959 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5616.00 | 0.376459 | ||||||||
\(607\) | −7772.00 | −0.519696 | −0.259848 | − | 0.965649i | \(-0.583673\pi\) | ||||
−0.259848 | + | 0.965649i | \(0.583673\pi\) | |||||||
\(608\) | 180.000 | 0.0120065 | ||||||||
\(609\) | 2583.00 | 0.171869 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2460.00 | −0.162882 | ||||||||
\(612\) | −243.000 | −0.0160502 | ||||||||
\(613\) | 24262.0 | 1.59859 | 0.799293 | − | 0.600942i | \(-0.205208\pi\) | ||||
0.799293 | + | 0.600942i | \(0.205208\pi\) | |||||||
\(614\) | −27006.0 | −1.77504 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −882.000 | −0.0576896 | ||||||||
\(617\) | 25818.0 | 1.68459 | 0.842296 | − | 0.539015i | \(-0.181203\pi\) | ||||
0.842296 | + | 0.539015i | \(0.181203\pi\) | |||||||
\(618\) | 6921.00 | 0.450491 | ||||||||
\(619\) | 22430.0 | 1.45644 | 0.728221 | − | 0.685342i | \(-0.240347\pi\) | ||||
0.728221 | + | 0.685342i | \(0.240347\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2025.00 | −0.130854 | ||||||||
\(622\) | 19998.0 | 1.28914 | ||||||||
\(623\) | −4998.00 | −0.321414 | ||||||||
\(624\) | 8733.00 | 0.560256 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8634.00 | 0.551252 | ||||||||
\(627\) | 72.0000 | 0.00458597 | ||||||||
\(628\) | 886.000 | 0.0562982 | ||||||||
\(629\) | −7074.00 | −0.448424 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2830.00 | −0.178543 | −0.0892714 | − | 0.996007i | \(-0.528454\pi\) | ||||
−0.0892714 | + | 0.996007i | \(0.528454\pi\) | |||||||
\(632\) | −14406.0 | −0.906709 | ||||||||
\(633\) | −4323.00 | −0.271444 | ||||||||
\(634\) | −13833.0 | −0.866528 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −981.000 | −0.0611622 | ||||||||
\(637\) | −2009.00 | −0.124960 | ||||||||
\(638\) | 2214.00 | 0.137387 | ||||||||
\(639\) | 2700.00 | 0.167152 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5202.00 | −0.320541 | −0.160270 | − | 0.987073i | \(-0.551237\pi\) | ||||
−0.160270 | + | 0.987073i | \(0.551237\pi\) | |||||||
\(642\) | −14958.0 | −0.919541 | ||||||||
\(643\) | 22030.0 | 1.35113 | 0.675566 | − | 0.737299i | \(-0.263899\pi\) | ||||
0.675566 | + | 0.737299i | \(0.263899\pi\) | |||||||
\(644\) | 525.000 | 0.0321241 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 324.000 | 0.0197331 | ||||||||
\(647\) | 20370.0 | 1.23775 | 0.618877 | − | 0.785488i | \(-0.287588\pi\) | ||||
0.618877 | + | 0.785488i | \(0.287588\pi\) | |||||||
\(648\) | −1701.00 | −0.103120 | ||||||||
\(649\) | −198.000 | −0.0119756 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4305.00 | 0.259180 | ||||||||
\(652\) | −3893.00 | −0.233837 | ||||||||
\(653\) | 31626.0 | 1.89528 | 0.947642 | − | 0.319333i | \(-0.103459\pi\) | ||||
0.947642 | + | 0.319333i | \(0.103459\pi\) | |||||||
\(654\) | 1692.00 | 0.101166 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4047.00 | −0.240867 | ||||||||
\(657\) | −882.000 | −0.0523746 | ||||||||
\(658\) | −1260.00 | −0.0746503 | ||||||||
\(659\) | −11142.0 | −0.658620 | −0.329310 | − | 0.944222i | \(-0.606816\pi\) | ||||
−0.329310 | + | 0.944222i | \(0.606816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5518.00 | −0.324698 | −0.162349 | − | 0.986733i | \(-0.551907\pi\) | ||||
−0.162349 | + | 0.986733i | \(0.551907\pi\) | |||||||
\(662\) | −22377.0 | −1.31376 | ||||||||
\(663\) | 3321.00 | 0.194535 | ||||||||
\(664\) | 29421.0 | 1.71951 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7074.00 | 0.411579 | ||||||||
\(667\) | 9225.00 | 0.535522 | ||||||||
\(668\) | −2046.00 | −0.118506 | ||||||||
\(669\) | −11481.0 | −0.663499 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2562.00 | 0.147399 | ||||||||
\(672\) | 945.000 | 0.0542473 | ||||||||
\(673\) | 12517.0 | 0.716931 | 0.358466 | − | 0.933543i | \(-0.383300\pi\) | ||||
0.358466 | + | 0.933543i | \(0.383300\pi\) | |||||||
\(674\) | −17529.0 | −1.00177 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −516.000 | −0.0293582 | ||||||||
\(677\) | 2604.00 | 0.147828 | 0.0739142 | − | 0.997265i | \(-0.476451\pi\) | ||||
0.0739142 | + | 0.997265i | \(0.476451\pi\) | |||||||
\(678\) | 162.000 | 0.00917636 | ||||||||
\(679\) | 3458.00 | 0.195443 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16263.0 | 0.915124 | ||||||||
\(682\) | 3690.00 | 0.207181 | ||||||||
\(683\) | −25986.0 | −1.45582 | −0.727911 | − | 0.685671i | \(-0.759509\pi\) | ||||
−0.727911 | + | 0.685671i | \(0.759509\pi\) | |||||||
\(684\) | −36.0000 | −0.00201242 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1029.00 | −0.0572703 | ||||||||
\(687\) | −15870.0 | −0.881337 | ||||||||
\(688\) | 28897.0 | 1.60129 | ||||||||
\(689\) | 13407.0 | 0.741315 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24610.0 | −1.35486 | −0.677430 | − | 0.735587i | \(-0.736906\pi\) | ||||
−0.677430 | + | 0.735587i | \(0.736906\pi\) | |||||||
\(692\) | 3540.00 | 0.194466 | ||||||||
\(693\) | 378.000 | 0.0207201 | ||||||||
\(694\) | −7038.00 | −0.384955 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7749.00 | 0.422019 | ||||||||
\(697\) | −1539.00 | −0.0836353 | ||||||||
\(698\) | 17421.0 | 0.944691 | ||||||||
\(699\) | −14724.0 | −0.796728 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10725.0 | 0.577857 | 0.288928 | − | 0.957351i | \(-0.406701\pi\) | ||||
0.288928 | + | 0.957351i | \(0.406701\pi\) | |||||||
\(702\) | −3321.00 | −0.178551 | ||||||||
\(703\) | −1048.00 | −0.0562248 | ||||||||
\(704\) | −2598.00 | −0.139085 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15570.0 | 0.830007 | ||||||||
\(707\) | −4368.00 | −0.232356 | ||||||||
\(708\) | 99.0000 | 0.00525515 | ||||||||
\(709\) | −34516.0 | −1.82832 | −0.914158 | − | 0.405359i | \(-0.867147\pi\) | ||||
−0.914158 | + | 0.405359i | \(0.867147\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6174.00 | 0.325658 | ||||||||
\(712\) | −14994.0 | −0.789219 | ||||||||
\(713\) | 15375.0 | 0.807571 | ||||||||
\(714\) | 1701.00 | 0.0891573 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3246.00 | −0.169426 | ||||||||
\(717\) | 3168.00 | 0.165009 | ||||||||
\(718\) | 26649.0 | 1.38514 | ||||||||
\(719\) | 17958.0 | 0.931461 | 0.465730 | − | 0.884927i | \(-0.345792\pi\) | ||||
0.465730 | + | 0.884927i | \(0.345792\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5383.00 | −0.278049 | ||||||||
\(722\) | −20529.0 | −1.05819 | ||||||||
\(723\) | 16026.0 | 0.824361 | ||||||||
\(724\) | 1334.00 | 0.0684775 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −11655.0 | −0.595809 | ||||||||
\(727\) | −2255.00 | −0.115039 | −0.0575195 | − | 0.998344i | \(-0.518319\pi\) | ||||
−0.0575195 | + | 0.998344i | \(0.518319\pi\) | |||||||
\(728\) | −6027.00 | −0.306834 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10989.0 | 0.556009 | ||||||||
\(732\) | −1281.00 | −0.0646819 | ||||||||
\(733\) | −9539.00 | −0.480670 | −0.240335 | − | 0.970690i | \(-0.577257\pi\) | ||||
−0.240335 | + | 0.970690i | \(0.577257\pi\) | |||||||
\(734\) | −29895.0 | −1.50333 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3375.00 | 0.169027 | ||||||||
\(737\) | −3768.00 | −0.188326 | ||||||||
\(738\) | 1539.00 | 0.0767634 | ||||||||
\(739\) | 37979.0 | 1.89050 | 0.945250 | − | 0.326346i | \(-0.105817\pi\) | ||||
0.945250 | + | 0.326346i | \(0.105817\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 492.000 | 0.0243915 | ||||||||
\(742\) | 6867.00 | 0.339751 | ||||||||
\(743\) | 20535.0 | 1.01394 | 0.506969 | − | 0.861964i | \(-0.330766\pi\) | ||||
0.506969 | + | 0.861964i | \(0.330766\pi\) | |||||||
\(744\) | 12915.0 | 0.636407 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −34980.0 | −1.71677 | ||||||||
\(747\) | −12609.0 | −0.617589 | ||||||||
\(748\) | 162.000 | 0.00791886 | ||||||||
\(749\) | 11634.0 | 0.567553 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2452.00 | −0.119141 | −0.0595704 | − | 0.998224i | \(-0.518973\pi\) | ||||
−0.0595704 | + | 0.998224i | \(0.518973\pi\) | |||||||
\(752\) | −4260.00 | −0.206577 | ||||||||
\(753\) | 17415.0 | 0.842813 | ||||||||
\(754\) | 15129.0 | 0.730724 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −189.000 | −0.00909241 | ||||||||
\(757\) | 36850.0 | 1.76927 | 0.884634 | − | 0.466286i | \(-0.154408\pi\) | ||||
0.884634 | + | 0.466286i | \(0.154408\pi\) | |||||||
\(758\) | 9609.00 | 0.460441 | ||||||||
\(759\) | 1350.00 | 0.0645611 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30258.0 | 1.44133 | 0.720665 | − | 0.693284i | \(-0.243837\pi\) | ||||
0.720665 | + | 0.693284i | \(0.243837\pi\) | |||||||
\(762\) | 13050.0 | 0.620409 | ||||||||
\(763\) | −1316.00 | −0.0624409 | ||||||||
\(764\) | −873.000 | −0.0413404 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24660.0 | 1.16319 | ||||||||
\(767\) | −1353.00 | −0.0636949 | ||||||||
\(768\) | 4539.00 | 0.213264 | ||||||||
\(769\) | 29288.0 | 1.37341 | 0.686705 | − | 0.726936i | \(-0.259056\pi\) | ||||
0.686705 | + | 0.726936i | \(0.259056\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1629.00 | −0.0760921 | ||||||||
\(772\) | 1006.00 | 0.0468999 | ||||||||
\(773\) | −40668.0 | −1.89227 | −0.946136 | − | 0.323769i | \(-0.895050\pi\) | ||||
−0.946136 | + | 0.323769i | \(0.895050\pi\) | |||||||
\(774\) | −10989.0 | −0.510325 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10374.0 | 0.479903 | ||||||||
\(777\) | −5502.00 | −0.254032 | ||||||||
\(778\) | −6678.00 | −0.307735 | ||||||||
\(779\) | −228.000 | −0.0104865 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1800.00 | −0.0824700 | ||||||||
\(782\) | 6075.00 | 0.277803 | ||||||||
\(783\) | −3321.00 | −0.151575 | ||||||||
\(784\) | −3479.00 | −0.158482 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 23976.0 | 1.08804 | ||||||||
\(787\) | −13118.0 | −0.594163 | −0.297081 | − | 0.954852i | \(-0.596013\pi\) | ||||
−0.297081 | + | 0.954852i | \(0.596013\pi\) | |||||||
\(788\) | −591.000 | −0.0267176 | ||||||||
\(789\) | 15579.0 | 0.702949 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −126.000 | −0.00566377 | ||||||||
\(792\) | 1134.00 | 0.0508774 | ||||||||
\(793\) | 17507.0 | 0.783975 | ||||||||
\(794\) | −31353.0 | −1.40136 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2584.00 | −0.115060 | ||||||||
\(797\) | 37278.0 | 1.65678 | 0.828391 | − | 0.560151i | \(-0.189257\pi\) | ||||
0.828391 | + | 0.560151i | \(0.189257\pi\) | |||||||
\(798\) | 252.000 | 0.0111788 | ||||||||
\(799\) | −1620.00 | −0.0717290 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6426.00 | 0.283460 | ||||||||
\(802\) | −3960.00 | −0.174355 | ||||||||
\(803\) | 588.000 | 0.0258407 | ||||||||
\(804\) | 1884.00 | 0.0826412 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25215.0 | 1.10194 | ||||||||
\(807\) | 6462.00 | 0.281875 | ||||||||
\(808\) | −13104.0 | −0.570541 | ||||||||
\(809\) | 5268.00 | 0.228941 | 0.114470 | − | 0.993427i | \(-0.463483\pi\) | ||||
0.114470 | + | 0.993427i | \(0.463483\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34994.0 | 1.51517 | 0.757587 | − | 0.652735i | \(-0.226378\pi\) | ||||
0.757587 | + | 0.652735i | \(0.226378\pi\) | |||||||
\(812\) | 861.000 | 0.0372108 | ||||||||
\(813\) | 7188.00 | 0.310079 | ||||||||
\(814\) | −4716.00 | −0.203066 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5751.00 | 0.246722 | ||||||||
\(817\) | 1628.00 | 0.0697142 | ||||||||
\(818\) | 7206.00 | 0.308010 | ||||||||
\(819\) | 2583.00 | 0.110204 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28818.0 | 1.22504 | 0.612518 | − | 0.790456i | \(-0.290157\pi\) | ||||
0.612518 | + | 0.790456i | \(0.290157\pi\) | |||||||
\(822\) | −15228.0 | −0.646153 | ||||||||
\(823\) | 20962.0 | 0.887836 | 0.443918 | − | 0.896067i | \(-0.353588\pi\) | ||||
0.443918 | + | 0.896067i | \(0.353588\pi\) | |||||||
\(824\) | −16149.0 | −0.682739 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −693.000 | −0.0291920 | ||||||||
\(827\) | 28266.0 | 1.18852 | 0.594259 | − | 0.804273i | \(-0.297445\pi\) | ||||
0.594259 | + | 0.804273i | \(0.297445\pi\) | |||||||
\(828\) | −675.000 | −0.0283308 | ||||||||
\(829\) | 42491.0 | 1.78019 | 0.890093 | − | 0.455780i | \(-0.150640\pi\) | ||||
0.890093 | + | 0.455780i | \(0.150640\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12858.0 | −0.536750 | ||||||||
\(832\) | −17753.0 | −0.739753 | ||||||||
\(833\) | −1323.00 | −0.0550291 | ||||||||
\(834\) | 11412.0 | 0.473819 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 24.0000 | 0.000992892 0 | ||||||||
\(837\) | −5535.00 | −0.228575 | ||||||||
\(838\) | −9999.00 | −0.412183 | ||||||||
\(839\) | −40512.0 | −1.66702 | −0.833510 | − | 0.552505i | \(-0.813672\pi\) | ||||
−0.833510 | + | 0.552505i | \(0.813672\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9260.00 | −0.379679 | ||||||||
\(842\) | −4386.00 | −0.179515 | ||||||||
\(843\) | 6624.00 | 0.270632 | ||||||||
\(844\) | −1441.00 | −0.0587693 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1620.00 | 0.0658354 | ||||||||
\(847\) | 9065.00 | 0.367742 | ||||||||
\(848\) | 23217.0 | 0.940183 | ||||||||
\(849\) | −10860.0 | −0.439004 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19650.0 | −0.791532 | ||||||||
\(852\) | 900.000 | 0.0361895 | ||||||||
\(853\) | 40525.0 | 1.62667 | 0.813335 | − | 0.581796i | \(-0.197650\pi\) | ||||
0.813335 | + | 0.581796i | \(0.197650\pi\) | |||||||
\(854\) | 8967.00 | 0.359303 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 34902.0 | 1.39360 | ||||||||
\(857\) | 7182.00 | 0.286269 | 0.143134 | − | 0.989703i | \(-0.454282\pi\) | ||||
0.143134 | + | 0.989703i | \(0.454282\pi\) | |||||||
\(858\) | 2214.00 | 0.0880941 | ||||||||
\(859\) | −7864.00 | −0.312359 | −0.156179 | − | 0.987729i | \(-0.549918\pi\) | ||||
−0.156179 | + | 0.987729i | \(0.549918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1197.00 | −0.0473794 | ||||||||
\(862\) | −30267.0 | −1.19594 | ||||||||
\(863\) | −28872.0 | −1.13883 | −0.569417 | − | 0.822049i | \(-0.692831\pi\) | ||||
−0.569417 | + | 0.822049i | \(0.692831\pi\) | |||||||
\(864\) | −1215.00 | −0.0478416 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9726.00 | −0.381643 | ||||||||
\(867\) | −12552.0 | −0.491682 | ||||||||
\(868\) | 1435.00 | 0.0561141 | ||||||||
\(869\) | −4116.00 | −0.160674 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25748.0 | −1.00165 | ||||||||
\(872\) | −3948.00 | −0.153321 | ||||||||
\(873\) | −4446.00 | −0.172365 | ||||||||
\(874\) | 900.000 | 0.0348318 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −294.000 | −0.0113394 | ||||||||
\(877\) | 47392.0 | 1.82476 | 0.912380 | − | 0.409345i | \(-0.134243\pi\) | ||||
0.912380 | + | 0.409345i | \(0.134243\pi\) | |||||||
\(878\) | 5397.00 | 0.207449 | ||||||||
\(879\) | 4176.00 | 0.160242 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17769.0 | 0.679515 | 0.339758 | − | 0.940513i | \(-0.389655\pi\) | ||||
0.339758 | + | 0.940513i | \(0.389655\pi\) | |||||||
\(882\) | 1323.00 | 0.0505076 | ||||||||
\(883\) | −32549.0 | −1.24050 | −0.620250 | − | 0.784404i | \(-0.712969\pi\) | ||||
−0.620250 | + | 0.784404i | \(0.712969\pi\) | |||||||
\(884\) | 1107.00 | 0.0421181 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26316.0 | −0.997859 | ||||||||
\(887\) | −6714.00 | −0.254153 | −0.127077 | − | 0.991893i | \(-0.540559\pi\) | ||||
−0.127077 | + | 0.991893i | \(0.540559\pi\) | |||||||
\(888\) | −16506.0 | −0.623767 | ||||||||
\(889\) | −10150.0 | −0.382925 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −486.000 | −0.0182734 | ||||||||
\(892\) | −3827.00 | −0.143652 | ||||||||
\(893\) | −240.000 | −0.00899361 | ||||||||
\(894\) | 19521.0 | 0.730291 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −11613.0 | −0.432995 | ||||||||
\(897\) | 9225.00 | 0.343382 | ||||||||
\(898\) | 4680.00 | 0.173913 | ||||||||
\(899\) | 25215.0 | 0.935448 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8829.00 | 0.326456 | ||||||||
\(902\) | −1026.00 | −0.0378737 | ||||||||
\(903\) | 8547.00 | 0.314979 | ||||||||
\(904\) | −378.000 | −0.0139072 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4662.00 | 0.170954 | ||||||||
\(907\) | −29693.0 | −1.08703 | −0.543517 | − | 0.839398i | \(-0.682908\pi\) | ||||
−0.543517 | + | 0.839398i | \(0.682908\pi\) | |||||||
\(908\) | 5421.00 | 0.198130 | ||||||||
\(909\) | 5616.00 | 0.204919 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8199.00 | −0.298183 | −0.149092 | − | 0.988823i | \(-0.547635\pi\) | ||||
−0.149092 | + | 0.988823i | \(0.547635\pi\) | |||||||
\(912\) | 852.000 | 0.0309348 | ||||||||
\(913\) | 8406.00 | 0.304708 | ||||||||
\(914\) | −34845.0 | −1.26102 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5290.00 | −0.190815 | ||||||||
\(917\) | −18648.0 | −0.671550 | ||||||||
\(918\) | −2187.00 | −0.0786294 | ||||||||
\(919\) | −15388.0 | −0.552343 | −0.276172 | − | 0.961108i | \(-0.589066\pi\) | ||||
−0.276172 | + | 0.961108i | \(0.589066\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27006.0 | −0.966208 | ||||||||
\(922\) | 20880.0 | 0.745820 | ||||||||
\(923\) | −12300.0 | −0.438634 | ||||||||
\(924\) | 126.000 | 0.00448603 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −39156.0 | −1.38957 | ||||||||
\(927\) | 6921.00 | 0.245216 | ||||||||
\(928\) | 5535.00 | 0.195792 | ||||||||
\(929\) | −411.000 | −0.0145150 | −0.00725752 | − | 0.999974i | \(-0.502310\pi\) | ||||
−0.00725752 | + | 0.999974i | \(0.502310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −196.000 | −0.00689972 | ||||||||
\(932\) | −4908.00 | −0.172497 | ||||||||
\(933\) | 19998.0 | 0.701720 | ||||||||
\(934\) | −42039.0 | −1.47276 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7749.00 | 0.270603 | ||||||||
\(937\) | −26066.0 | −0.908793 | −0.454397 | − | 0.890800i | \(-0.650145\pi\) | ||||
−0.454397 | + | 0.890800i | \(0.650145\pi\) | |||||||
\(938\) | −13188.0 | −0.459066 | ||||||||
\(939\) | 8634.00 | 0.300064 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24048.0 | 0.833095 | 0.416548 | − | 0.909114i | \(-0.363240\pi\) | ||||
0.416548 | + | 0.909114i | \(0.363240\pi\) | |||||||
\(942\) | 7974.00 | 0.275804 | ||||||||
\(943\) | −4275.00 | −0.147628 | ||||||||
\(944\) | −2343.00 | −0.0807819 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7326.00 | 0.251785 | ||||||||
\(947\) | 22968.0 | 0.788131 | 0.394065 | − | 0.919082i | \(-0.371068\pi\) | ||||
0.394065 | + | 0.919082i | \(0.371068\pi\) | |||||||
\(948\) | 2058.00 | 0.0705071 | ||||||||
\(949\) | 4018.00 | 0.137439 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13833.0 | −0.471678 | ||||||||
\(952\) | −3969.00 | −0.135122 | ||||||||
\(953\) | 10248.0 | 0.348337 | 0.174169 | − | 0.984716i | \(-0.444276\pi\) | ||||
0.174169 | + | 0.984716i | \(0.444276\pi\) | |||||||
\(954\) | −8829.00 | −0.299633 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1056.00 | 0.0357254 | ||||||||
\(957\) | 2214.00 | 0.0747842 | ||||||||
\(958\) | 3168.00 | 0.106841 | ||||||||
\(959\) | 11844.0 | 0.398814 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12234.0 | 0.410661 | ||||||||
\(962\) | −32226.0 | −1.08005 | ||||||||
\(963\) | −14958.0 | −0.500535 | ||||||||
\(964\) | 5342.00 | 0.178479 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4725.00 | 0.157375 | ||||||||
\(967\) | 43060.0 | 1.43197 | 0.715986 | − | 0.698115i | \(-0.245978\pi\) | ||||
0.715986 | + | 0.698115i | \(0.245978\pi\) | |||||||
\(968\) | 27195.0 | 0.902976 | ||||||||
\(969\) | 324.000 | 0.0107414 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12348.0 | −0.408101 | −0.204051 | − | 0.978960i | \(-0.565411\pi\) | ||||
−0.204051 | + | 0.978960i | \(0.565411\pi\) | |||||||
\(972\) | 243.000 | 0.00801875 | ||||||||
\(973\) | −8876.00 | −0.292448 | ||||||||
\(974\) | −23658.0 | −0.778287 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30317.0 | 0.994286 | ||||||||
\(977\) | 44190.0 | 1.44705 | 0.723523 | − | 0.690301i | \(-0.242522\pi\) | ||||
0.723523 | + | 0.690301i | \(0.242522\pi\) | |||||||
\(978\) | −35037.0 | −1.14556 | ||||||||
\(979\) | −4284.00 | −0.139854 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1692.00 | 0.0550677 | ||||||||
\(982\) | 31770.0 | 1.03240 | ||||||||
\(983\) | −60168.0 | −1.95225 | −0.976125 | − | 0.217211i | \(-0.930304\pi\) | ||||
−0.976125 | + | 0.217211i | \(0.930304\pi\) | |||||||
\(984\) | −3591.00 | −0.116338 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9963.00 | 0.321792 | ||||||||
\(987\) | −1260.00 | −0.0406345 | ||||||||
\(988\) | 164.000 | 0.00528091 | ||||||||
\(989\) | 30525.0 | 0.981434 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8804.00 | 0.282208 | 0.141104 | − | 0.989995i | \(-0.454935\pi\) | ||||
0.141104 | + | 0.989995i | \(0.454935\pi\) | |||||||
\(992\) | 9225.00 | 0.295256 | ||||||||
\(993\) | −22377.0 | −0.715118 | ||||||||
\(994\) | −6300.00 | −0.201030 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4203.00 | −0.133712 | ||||||||
\(997\) | −15302.0 | −0.486077 | −0.243039 | − | 0.970017i | \(-0.578144\pi\) | ||||
−0.243039 | + | 0.970017i | \(0.578144\pi\) | |||||||
\(998\) | −44697.0 | −1.41769 | ||||||||
\(999\) | 7074.00 | 0.224035 |
(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 | 525.4.a.h.1.1 | yes | 1 | |
3.2 | odd | 2 | 1575.4.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 525.4.d.d.274.2 | 2 | |||
5.3 | odd | 4 | 525.4.d.d.274.1 | 2 | |||
5.4 | even | 2 | 525.4.a.c.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 1575.4.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.4.a.c.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
525.4.a.h.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
525.4.d.d.274.1 | 2 | 5.3 | odd | 4 | |||
525.4.d.d.274.2 | 2 | 5.2 | odd | 4 | |||
1575.4.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
1575.4.a.j.1.1 | 1 | 15.14 | odd | 2 |