Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(287,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.287");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.d (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: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 287.11 | ||
Character | \(\chi\) | \(=\) | 624.287 |
Dual form | 624.4.d.c.287.12 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.486351 | − | 5.17334i | −0.0935984 | − | 0.995610i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.15078i | 0.371257i | 0.982620 | + | 0.185628i | \(0.0594320\pi\) | ||||
−0.982620 | + | 0.185628i | \(0.940568\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.70503i | 0.362038i | 0.983480 | + | 0.181019i | \(0.0579395\pi\) | ||||
−0.983480 | + | 0.181019i | \(0.942061\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.5269 | + | 5.03212i | −0.982479 | + | 0.186375i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 32.5924 | 0.893361 | 0.446680 | − | 0.894694i | \(-0.352606\pi\) | ||||
0.446680 | + | 0.894694i | \(0.352606\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 21.4734 | − | 2.01874i | 0.369627 | − | 0.0347490i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 99.7981i | − | 1.42380i | −0.702281 | − | 0.711900i | \(-0.747835\pi\) | ||
0.702281 | − | 0.711900i | \(-0.252165\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 73.6834i | 0.889691i | 0.895607 | + | 0.444846i | \(0.146741\pi\) | ||||
−0.895607 | + | 0.444846i | \(0.853259\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 34.6874 | − | 3.26100i | 0.360448 | − | 0.0338861i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −193.704 | −1.75609 | −0.878044 | − | 0.478580i | \(-0.841152\pi\) | ||||
−0.878044 | + | 0.478580i | \(0.841152\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 107.771 | 0.862168 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 38.9343 | + | 134.785i | 0.277515 | + | 0.960721i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 138.975i | 0.889895i | 0.895557 | + | 0.444948i | \(0.146778\pi\) | ||||
−0.895557 | + | 0.444948i | \(0.853222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 165.252i | 0.957426i | 0.877971 | + | 0.478713i | \(0.158897\pi\) | ||||
−0.877971 | + | 0.478713i | \(0.841103\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15.8513 | − | 168.611i | −0.0836171 | − | 0.889439i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −27.8311 | −0.134409 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −54.1147 | −0.240443 | −0.120222 | − | 0.992747i | \(-0.538361\pi\) | ||||
−0.120222 | + | 0.992747i | \(0.538361\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.32257 | + | 67.2534i | 0.0259595 | + | 0.276133i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 512.529i | 1.95228i | 0.217133 | + | 0.976142i | \(0.430329\pi\) | ||||
−0.217133 | + | 0.976142i | \(0.569671\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 336.614i | 1.19379i | 0.802318 | + | 0.596897i | \(0.203600\pi\) | ||||
−0.802318 | + | 0.596897i | \(0.796400\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −20.8872 | − | 110.107i | −0.0691929 | − | 0.364752i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 495.587 | 1.53806 | 0.769029 | − | 0.639214i | \(-0.220740\pi\) | ||||
0.769029 | + | 0.639214i | \(0.220740\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 298.043 | 0.868929 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −516.289 | + | 48.5369i | −1.41755 | + | 0.133265i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 537.479i | − | 1.39299i | −0.717562 | − | 0.696495i | \(-0.754742\pi\) | ||
0.717562 | − | 0.696495i | \(-0.245258\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 135.284i | 0.331666i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 381.189 | − | 35.8360i | 0.885786 | − | 0.0832737i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 315.255 | 0.695640 | 0.347820 | − | 0.937561i | \(-0.386922\pi\) | ||||
0.347820 | + | 0.937561i | \(0.386922\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −133.740 | −0.280715 | −0.140358 | − | 0.990101i | \(-0.544825\pi\) | ||||
−0.140358 | + | 0.990101i | \(0.544825\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −33.7405 | − | 177.864i | −0.0674747 | − | 0.355694i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 53.9601i | − | 0.102968i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 131.721i | 0.240182i | 0.992763 | + | 0.120091i | \(0.0383187\pi\) | ||||
−0.992763 | + | 0.120091i | \(0.961681\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 94.2081 | + | 1002.10i | 0.164367 | + | 1.74838i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1073.24 | −1.79394 | −0.896970 | − | 0.442091i | \(-0.854237\pi\) | ||||
−0.896970 | + | 0.442091i | \(0.854237\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1023.67 | 1.64125 | 0.820626 | − | 0.571465i | \(-0.193625\pi\) | ||||
0.820626 | + | 0.571465i | \(0.193625\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −52.4146 | − | 557.537i | −0.0806976 | − | 0.858384i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 218.533i | 0.323430i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 108.143i | 0.154013i | 0.997031 | + | 0.0770067i | \(0.0245363\pi\) | ||||
−0.997031 | + | 0.0770067i | \(0.975464\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 678.355 | − | 266.974i | 0.930529 | − | 0.366219i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1032.79 | 1.36582 | 0.682910 | − | 0.730503i | \(-0.260714\pi\) | ||||
0.682910 | + | 0.730503i | \(0.260714\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 414.239 | 0.528595 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 718.964 | − | 67.5906i | 0.885989 | − | 0.0832927i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 139.135i | 0.165711i | 0.996562 | + | 0.0828554i | \(0.0264040\pi\) | ||||
−0.996562 | + | 0.0828554i | \(0.973596\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 87.1654i | − | 0.100411i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 854.907 | − | 80.3707i | 0.953223 | − | 0.0896135i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −305.843 | −0.330304 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1458.52 | 1.52670 | 0.763352 | − | 0.645983i | \(-0.223552\pi\) | ||||
0.763352 | + | 0.645983i | \(0.223552\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −864.575 | + | 164.009i | −0.877708 | + | 0.166500i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1373.84i | − | 1.35349i | −0.736220 | − | 0.676743i | \(-0.763391\pi\) | ||
0.736220 | − | 0.676743i | \(-0.236609\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1505.44i | 1.44015i | 0.693898 | + | 0.720073i | \(0.255892\pi\) | ||||
−0.693898 | + | 0.720073i | \(0.744108\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.5357 | + | 143.980i | 0.0125804 | + | 0.133819i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −632.092 | −0.571090 | −0.285545 | − | 0.958365i | \(-0.592175\pi\) | ||||
−0.285545 | + | 0.958365i | \(0.592175\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 922.022 | 0.810218 | 0.405109 | − | 0.914268i | \(-0.367234\pi\) | ||||
0.405109 | + | 0.914268i | \(0.367234\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.3187 | + | 279.954i | 0.0225051 | + | 0.239388i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 903.296i | 0.751990i | 0.926622 | + | 0.375995i | \(0.122699\pi\) | ||||
−0.926622 | + | 0.375995i | \(0.877301\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 804.021i | − | 0.651959i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 344.850 | − | 65.4176i | 0.272491 | − | 0.0516911i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 669.149 | 0.515469 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −268.737 | −0.201906 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2651.49 | − | 249.269i | 1.94371 | − | 0.182731i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 966.180i | 0.691342i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 31.2951i | − | 0.0218660i | −0.999940 | − | 0.0109330i | \(-0.996520\pi\) | ||
0.999940 | − | 0.0109330i | \(-0.00348016\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1741.42 | − | 163.713i | 1.18855 | − | 0.111737i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −306.642 | −0.204515 | −0.102257 | − | 0.994758i | \(-0.532607\pi\) | ||||
−0.102257 | + | 0.994758i | \(0.532607\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −494.049 | −0.322102 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −559.464 | + | 161.608i | −0.356674 | + | 0.103029i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 70.7897i | − | 0.0441458i | −0.999756 | − | 0.0220729i | \(-0.992973\pi\) | ||
0.999756 | − | 0.0220729i | \(-0.00702659\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 725.665i | 0.442807i | 0.975182 | + | 0.221403i | \(0.0710637\pi\) | ||||
−0.975182 | + | 0.221403i | \(0.928936\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −241.029 | − | 2563.84i | −0.143960 | − | 1.53131i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −423.701 | −0.247774 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −576.853 | −0.330380 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −144.953 | − | 1541.88i | −0.0813303 | − | 0.865114i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2069.01i | 1.13759i | 0.822481 | + | 0.568793i | \(0.192589\pi\) | ||||
−0.822481 | + | 0.568793i | \(0.807411\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3034.60i | 1.63545i | 0.575612 | + | 0.817723i | \(0.304764\pi\) | ||||
−0.575612 | + | 0.817723i | \(0.695236\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 502.196 | + | 2647.34i | 0.265360 | + | 1.39885i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −685.926 | −0.355451 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3473.41 | −1.76566 | −0.882829 | − | 0.469694i | \(-0.844364\pi\) | ||||
−0.882829 | + | 0.469694i | \(0.844364\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2780.56 | + | 261.404i | −1.38688 | + | 0.130382i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1298.79i | − | 0.635770i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2996.56i | 1.43993i | 0.694010 | + | 0.719965i | \(0.255842\pi\) | ||||
−0.694010 | + | 0.719965i | \(0.744158\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 699.868 | − | 65.7954i | 0.330210 | − | 0.0310434i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 46.8590 | 0.0217129 | 0.0108565 | − | 0.999941i | \(-0.496544\pi\) | ||||
0.0108565 | + | 0.999941i | \(0.496544\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −370.784 | − | 1954.59i | −0.165816 | − | 0.874103i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2189.42i | − | 0.962189i | −0.876669 | − | 0.481095i | \(-0.840239\pi\) | ||
0.876669 | − | 0.481095i | \(-0.159761\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 722.608i | 0.312137i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −153.325 | − | 1630.92i | −0.0651108 | − | 0.692586i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 675.873 | 0.282218 | 0.141109 | − | 0.989994i | \(-0.454933\pi\) | ||||
0.141109 | + | 0.989994i | \(0.454933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −157.711 | −0.0647656 | −0.0323828 | − | 0.999476i | \(-0.510310\pi\) | ||||
−0.0323828 | + | 0.999476i | \(0.510310\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 65.0445 | + | 691.882i | 0.0262745 | + | 0.279483i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 224.618i | − | 0.0892661i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3252.66i | − | 1.27197i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −903.740 | + | 261.056i | −0.347817 | + | 0.100471i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1013.12 | 0.383806 | 0.191903 | − | 0.981414i | \(-0.438534\pi\) | ||||
0.191903 | + | 0.981414i | \(0.438534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 38.4793 | 0.0143513 | 0.00717566 | − | 0.999974i | \(-0.497716\pi\) | ||||
0.00717566 | + | 0.999974i | \(0.497716\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −279.154 | + | 26.2436i | −0.102516 | + | 0.00963764i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 46.5566i | − | 0.0168377i | −0.999965 | − | 0.00841883i | \(-0.997320\pi\) | ||
0.999965 | − | 0.00841883i | \(-0.00267983\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3751.71i | 1.33644i | 0.743964 | + | 0.668220i | \(0.232944\pi\) | ||||
−0.743964 | + | 0.668220i | \(0.767056\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 681.435 | − | 64.0625i | 0.239128 | − | 0.0224807i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −931.830 | −0.322175 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2127.39 | −0.724798 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5138.36 | − | 974.741i | 1.72532 | − | 0.327291i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2401.52i | 0.794815i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3034.14i | 0.989948i | 0.868908 | + | 0.494974i | \(0.164823\pi\) | ||||
−0.868908 | + | 0.494974i | \(0.835177\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 521.970 | + | 5552.22i | 0.167910 | + | 1.78606i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1397.21 | −0.443204 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1108.02 | −0.346624 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −497.863 | − | 5295.79i | −0.153619 | − | 1.63405i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1297.37i | 0.394891i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 502.348i | 0.150851i | 0.997151 | + | 0.0754253i | \(0.0240314\pi\) | ||||
−0.997151 | + | 0.0754253i | \(0.975969\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2858.83 | + | 542.317i | −0.847062 | + | 0.160687i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4630.13 | −1.35380 | −0.676899 | − | 0.736076i | \(-0.736677\pi\) | ||||
−0.676899 | + | 0.736076i | \(0.736677\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1411.21 | 0.407228 | 0.203614 | − | 0.979051i | \(-0.434731\pi\) | ||||
0.203614 | + | 0.979051i | \(0.434731\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1130.54 | − | 106.284i | 0.322010 | − | 0.0302725i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6006.04i | − | 1.68871i | −0.535786 | − | 0.844354i | \(-0.679985\pi\) | ||
0.535786 | − | 0.844354i | \(-0.320015\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2057.07i | 0.571014i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 559.462 | − | 52.5956i | 0.153337 | − | 0.0144154i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −588.425 | −0.159255 | −0.0796277 | − | 0.996825i | \(-0.525373\pi\) | ||||
−0.0796277 | + | 0.996825i | \(0.525373\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6547.37 | −1.75001 | −0.875006 | − | 0.484112i | \(-0.839143\pi\) | ||||
−0.875006 | + | 0.484112i | \(0.839143\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1711.06 | − | 3379.52i | −0.451707 | − | 0.892166i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1237.11i | 0.322596i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 957.884i | − | 0.246756i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −502.297 | − | 5342.96i | −0.127838 | − | 1.35982i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2477.90 | 0.623122 | 0.311561 | − | 0.950226i | \(-0.399148\pi\) | ||||
0.311561 | + | 0.950226i | \(0.399148\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6313.26 | −1.56882 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −201.466 | − | 2143.00i | −0.0494756 | − | 0.526274i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 375.601i | − | 0.0911648i | −0.998961 | − | 0.0455824i | \(-0.985486\pi\) | ||
0.998961 | − | 0.0455824i | \(-0.0145144\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 362.840i | − | 0.0870494i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −699.338 | − | 3686.57i | −0.165854 | − | 0.874303i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7331.67 | 1.71897 | 0.859487 | − | 0.511158i | \(-0.170783\pi\) | ||||
0.859487 | + | 0.511158i | \(0.170783\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2230.96 | 0.517157 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 719.792 | − | 67.6684i | 0.164983 | − | 0.0155103i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1947.22i | − | 0.441352i | −0.975347 | − | 0.220676i | \(-0.929174\pi\) | ||
0.975347 | − | 0.220676i | \(-0.0708264\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2443.85i | − | 0.547798i | −0.961758 | − | 0.273899i | \(-0.911687\pi\) | ||
0.961758 | − | 0.273899i | \(-0.0883135\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −450.936 | + | 42.3930i | −0.0999704 | + | 0.00939832i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3512.51 | 0.770228 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3761.28 | −0.815861 | −0.407930 | − | 0.913013i | \(-0.633749\pi\) | ||||
−0.407930 | + | 0.913013i | \(0.633749\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −831.571 | − | 4383.64i | −0.178440 | − | 0.940651i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5014.21i | 1.06449i | 0.846590 | + | 0.532246i | \(0.178652\pi\) | ||||
−0.846590 | + | 0.532246i | \(0.821348\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7204.17i | − | 1.51323i | −0.653862 | − | 0.756614i | \(-0.726852\pi\) | ||
0.653862 | − | 0.756614i | \(-0.273148\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 148.747 | + | 1582.23i | 0.0309159 | + | 0.328854i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3436.52 | −0.706800 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5046.65 | −1.02720 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −709.353 | − | 7545.42i | −0.142897 | − | 1.52000i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6452.30i | − | 1.28651i | −0.765652 | − | 0.643254i | \(-0.777584\pi\) | ||
0.765652 | − | 0.643254i | \(-0.222416\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1308.55i | 0.258261i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1268.96 | + | 4392.98i | 0.247921 | + | 0.858271i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2518.15 | 0.487051 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2257.01 | −0.432199 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7107.34 | + | 668.168i | −1.34754 | + | 0.126684i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 555.124i | − | 0.104217i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3644.73i | − | 0.677576i | −0.940863 | − | 0.338788i | \(-0.889983\pi\) | ||
0.940863 | − | 0.338788i | \(-0.110017\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7788.14 | − | 732.171i | 1.43382 | − | 0.134795i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4488.18 | −0.818332 | −0.409166 | − | 0.912460i | \(-0.634180\pi\) | ||||
−0.409166 | + | 0.912460i | \(0.634180\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1619.80 | −0.292514 | −0.146257 | − | 0.989247i | \(-0.546723\pi\) | ||||
−0.146257 | + | 0.989247i | \(0.546723\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 738.273 | − | 140.049i | 0.132054 | − | 0.0250504i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3052.76i | − | 0.540884i | −0.962736 | − | 0.270442i | \(-0.912830\pi\) | ||
0.962736 | − | 0.270442i | \(-0.0871698\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4529.52i | 0.794998i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 307.419 | + | 3270.03i | 0.0534531 | + | 0.568583i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7353.46 | 1.26674 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1401.02 | −0.239123 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −448.427 | − | 4769.94i | −0.0758351 | − | 0.806661i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3322.92i | 0.556835i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2819.23i | − | 0.468154i | −0.972218 | − | 0.234077i | \(-0.924793\pi\) | ||
0.972218 | − | 0.234077i | \(-0.0752067\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1435.50 | − | 272.312i | 0.236230 | − | 0.0448126i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −546.742 | −0.0891693 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6094.96 | −0.985203 | −0.492601 | − | 0.870255i | \(-0.663954\pi\) | ||||
−0.492601 | + | 0.870255i | \(0.663954\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4673.06 | − | 439.319i | 0.748689 | − | 0.0703851i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5385.97i | 0.855327i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4298.21i | 0.676622i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4159.47 | + | 391.037i | −0.649097 | + | 0.0610223i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9811.05 | −1.51782 | −0.758912 | − | 0.651193i | \(-0.774269\pi\) | ||||
−0.758912 | + | 0.651193i | \(0.774269\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3209.72 | 0.492299 | 0.246149 | − | 0.969232i | \(-0.420835\pi\) | ||||
0.246149 | + | 0.969232i | \(0.420835\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −506.146 | − | 1752.21i | −0.0769689 | − | 0.266456i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8538.15i | 1.28736i | 0.765293 | + | 0.643682i | \(0.222594\pi\) | ||||
−0.765293 | + | 0.643682i | \(0.777406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 4454.76i | − | 0.666012i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −325.442 | − | 3461.74i | −0.0482470 | − | 0.513206i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5268.60 | 0.774557 | 0.387278 | − | 0.921963i | \(-0.373415\pi\) | ||||
0.387278 | + | 0.921963i | \(0.373415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1429.76 | 0.208450 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 130.701 | + | 1390.27i | 0.0188981 | + | 0.201020i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4249.02i | 0.609326i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11294.8i | 1.60649i | 0.595647 | + | 0.803246i | \(0.296896\pi\) | ||||
−0.595647 | + | 0.803246i | \(0.703104\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2579.11 | − | 13595.8i | −0.363857 | − | 1.91808i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3603.82 | 0.504315 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10199.9 | 1.41590 | 0.707948 | − | 0.706265i | \(-0.249621\pi\) | ||||
0.707948 | + | 0.706265i | \(0.249621\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4998.38 | − | 469.903i | 0.688307 | − | 0.0647085i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1806.67i | − | 0.246813i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 11233.0i | − | 1.52243i | −0.648500 | − | 0.761215i | \(-0.724603\pi\) | ||
0.648500 | − | 0.761215i | \(-0.275397\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −161.900 | + | 15.2204i | −0.0217701 | + | 0.00204663i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4415.99 | 0.589155 | 0.294577 | − | 0.955628i | \(-0.404821\pi\) | ||||
0.294577 | + | 0.955628i | \(0.404821\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −907.081 | −0.120076 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1693.88 | − | 8929.34i | −0.222493 | − | 1.17288i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4900.14i | 0.638681i | 0.947640 | + | 0.319340i | \(0.103461\pi\) | ||||
−0.947640 | + | 0.319340i | \(0.896539\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19331.3i | 2.50032i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 149.136 | + | 1586.36i | 0.0191422 | + | 0.203617i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −448.878 | −0.0571785 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13149.3 | −1.66233 | −0.831165 | − | 0.556025i | \(-0.812326\pi\) | ||||
−0.831165 | + | 0.556025i | \(0.812326\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 240.282 | + | 2555.89i | 0.0301482 | + | 0.320688i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4490.95i | − | 0.559270i | −0.960106 | − | 0.279635i | \(-0.909787\pi\) | ||
0.960106 | − | 0.279635i | \(-0.0902135\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 2148.28i | − | 0.265542i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1108.15 | + | 2815.70i | 0.135961 | + | 0.345465i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1763.73 | −0.214803 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1405.54 | −0.169925 | −0.0849627 | − | 0.996384i | \(-0.527077\pi\) | ||||
−0.0849627 | + | 0.996384i | \(0.527077\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −366.220 | + | 34.4287i | −0.0439520 | + | 0.00413198i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2113.80i | 0.251848i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4286.86i | 0.507070i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3754.11 | − | 352.928i | 0.440863 | − | 0.0414460i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12751.3 | −1.48674 | −0.743370 | − | 0.668880i | \(-0.766774\pi\) | ||||
−0.743370 | + | 0.668880i | \(0.766774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6483.29 | −0.750537 | −0.375269 | − | 0.926916i | \(-0.622450\pi\) | ||||
−0.375269 | + | 0.926916i | \(0.622450\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13146.4 | + | 2493.85i | −1.51111 | + | 0.286656i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 10755.3i | − | 1.22755i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 896.729i | − | 0.101629i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 206.067 | + | 2191.95i | 0.0231912 | + | 0.246686i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10523.9 | −1.17615 | −0.588074 | − | 0.808807i | \(-0.700114\pi\) | ||||
−0.588074 | + | 0.808807i | \(0.700114\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9569.70 | −1.06210 | −0.531051 | − | 0.847340i | \(-0.678203\pi\) | ||||
−0.531051 | + | 0.847340i | \(0.678203\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 280.553 | + | 2984.26i | 0.0309230 | + | 0.328929i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 14272.8i | − | 1.56238i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 226.844i | 0.0246621i | 0.999924 | + | 0.0123310i | \(0.00392519\pi\) | ||||
−0.999924 | + | 0.0123310i | \(0.996075\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7906.15 | + | 1499.79i | −0.853704 | + | 0.161947i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5366.00 | −0.575499 | −0.287750 | − | 0.957706i | \(-0.592907\pi\) | ||||
−0.287750 | + | 0.957706i | \(0.592907\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −577.518 | −0.0615213 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10703.7 | − | 1006.27i | 1.13259 | − | 0.106476i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1825.33i | − | 0.191854i | −0.995388 | − | 0.0959272i | \(-0.969418\pi\) | ||
0.995388 | − | 0.0959272i | \(-0.0305816\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16704.5i | 1.74409i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15699.0 | − | 1475.88i | 1.62827 | − | 0.153075i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 361.804 | 0.0372783 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5835.87 | 0.597353 | 0.298677 | − | 0.954354i | \(-0.403455\pi\) | ||||
0.298677 | + | 0.954354i | \(0.403455\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13451.3 | − | 3885.57i | 1.36787 | − | 0.395126i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3767.02i | 0.380581i | 0.981728 | + | 0.190290i | \(0.0609429\pi\) | ||||
−0.981728 | + | 0.190290i | \(0.939057\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8214.87i | 0.824573i | 0.911054 | + | 0.412286i | \(0.135270\pi\) | ||||
−0.911054 | + | 0.412286i | \(0.864730\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 333.601 | + | 3548.53i | 0.0332696 | + | 0.353890i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11066.2 | 1.09653 | 0.548267 | − | 0.836303i | \(-0.315288\pi\) | ||||
0.548267 | + | 0.836303i | \(0.315288\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −883.190 | −0.0869551 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1689.30 | + | 17969.1i | 0.165263 | + | 1.75791i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10971.1i | 1.06649i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7940.94i | 0.767064i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2704.66 | + | 14257.7i | 0.259618 | + | 1.36858i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7515.92 | −0.716933 | −0.358467 | − | 0.933542i | \(-0.616700\pi\) | ||||
−0.358467 | + | 0.933542i | \(0.616700\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 703.491 | 0.0666869 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6719.08 | + | 631.668i | −0.632979 | + | 0.0595070i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6053.99i | 0.566799i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2472.60i | − | 0.230071i | −0.993361 | − | 0.115035i | \(-0.963302\pi\) | ||
0.993361 | − | 0.115035i | \(-0.0366981\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15502.2 | − | 1457.38i | 1.43361 | − | 0.134775i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14395.4 | 1.32312 | 0.661562 | − | 0.749891i | \(-0.269894\pi\) | ||||
0.661562 | + | 0.749891i | \(0.269894\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13869.4 | 1.26703 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −680.764 | − | 3588.66i | −0.0618143 | − | 0.325855i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 7196.08i | − | 0.649474i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8887.34i | − | 0.797299i | −0.917103 | − | 0.398649i | \(-0.869479\pi\) | ||
0.917103 | − | 0.398649i | \(-0.130521\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.7900 | − | 242.418i | −0.00203230 | − | 0.0216176i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11212.4 | 0.993911 | 0.496956 | − | 0.867776i | \(-0.334451\pi\) | ||||
0.496956 | + | 0.867776i | \(0.334451\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5702.50 | 0.502491 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −82.1934 | − | 874.295i | −0.00719987 | − | 0.0765854i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 10375.7i | − | 0.903530i | −0.892137 | − | 0.451765i | \(-0.850795\pi\) | ||
0.892137 | − | 0.451765i | \(-0.149205\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6863.73i | 0.594195i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9931.45 | + | 2868.81i | −0.854745 | + | 0.246903i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6248.73 | −0.534664 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16152.3 | 1.37404 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11326.6 | + | 1064.83i | −0.957965 | + | 0.0900593i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13512.4i | − | 1.13625i | −0.822941 | − | 0.568127i | \(-0.807668\pi\) | ||
0.822941 | − | 0.568127i | \(-0.192332\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11963.6i | 1.00025i | 0.865952 | + | 0.500126i | \(0.166713\pi\) | ||||
−0.865952 | + | 0.500126i | \(0.833287\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3738.30 | − | 351.441i | 0.310767 | − | 0.0292156i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16491.9 | 1.36318 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25354.1 | 2.08385 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8362.76 | + | 1586.40i | −0.683451 | + | 0.129650i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6662.88i | − | 0.541466i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2623.67i | − | 0.212021i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −328.712 | − | 3496.52i | −0.0264152 | − | 0.280980i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9713.91 | 0.776267 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13732.3 | 1.09131 | 0.545654 | − | 0.838011i | \(-0.316281\pi\) | ||||
0.545654 | + | 0.838011i | \(0.316281\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 76.7030 | + | 815.893i | 0.00606195 | + | 0.0644813i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3827.11i | 0.300799i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5437.61i | − | 0.425037i | −0.977157 | − | 0.212519i | \(-0.931833\pi\) | ||
0.977157 | − | 0.212519i | \(-0.0681666\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3547.71 | − | 672.995i | 0.275797 | − | 0.0523183i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10240.1 | −0.791732 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −725.104 | −0.0557587 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1162.02 | + | 109.243i | −0.0888742 | + | 0.00835516i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15910.5i | 1.21032i | 0.796104 | + | 0.605159i | \(0.206891\pi\) | ||||
−0.796104 | + | 0.605159i | \(0.793109\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4375.98i | − | 0.331099i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16827.1 | + | 1581.93i | −1.26638 | + | 0.119054i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14833.6 | −1.11041 | −0.555207 | − | 0.831712i | \(-0.687361\pi\) | ||||
−0.555207 | + | 0.831712i | \(0.687361\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3749.38 | −0.279181 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1790.07 | + | 4548.39i | 0.132585 | + | 0.336886i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11064.8i | 0.815224i | 0.913155 | + | 0.407612i | \(0.133638\pi\) | ||||
−0.913155 | + | 0.407612i | \(0.866362\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 10460.9i | − | 0.766684i | −0.923606 | − | 0.383342i | \(-0.874773\pi\) | ||
0.923606 | − | 0.383342i | \(-0.125227\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −492.734 | − | 5241.23i | −0.0359237 | − | 0.382121i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20875.7 | −1.51404 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17525.4 | 1.26446 | 0.632228 | − | 0.774782i | \(-0.282141\pi\) | ||||
0.632228 | + | 0.774782i | \(0.282141\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.7145 | − | 199.067i | −0.00134326 | − | 0.0142883i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6924.86i | 0.494478i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 17517.7i | − | 1.24444i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 271.534 | + | 1431.40i | 0.0191907 | + | 0.101164i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8469.95 | 0.595558 | 0.297779 | − | 0.954635i | \(-0.403754\pi\) | ||||
0.297779 | + | 0.954635i | \(0.403754\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12176.4 | −0.851814 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −240.853 | + | 22.6429i | −0.0167638 | + | 0.00157598i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24461.7i | 1.69397i | 0.531619 | + | 0.846984i | \(0.321584\pi\) | ||||
−0.531619 | + | 0.846984i | \(0.678416\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2777.49i | 0.191371i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19408.9 | − | 1824.65i | 1.33057 | − | 0.125089i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4337.40 | 0.295862 | 0.147931 | − | 0.988998i | \(-0.452739\pi\) | ||||
0.147931 | + | 0.988998i | \(0.452739\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15309.5 | 1.03908 | 0.519541 | − | 0.854445i | \(-0.326103\pi\) | ||||
0.519541 | + | 0.854445i | \(0.326103\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −662.834 | − | 3494.14i | −0.0447640 | − | 0.235974i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 1115.47i | − | 0.0749591i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2011.88i | − | 0.134530i | −0.997735 | − | 0.0672651i | \(-0.978573\pi\) | ||
0.997735 | − | 0.0672651i | \(-0.0214273\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 453.197 | + | 4820.67i | 0.0301551 | + | 0.320761i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6442.63 | −0.426581 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3790.69 | 0.249763 | 0.124881 | − | 0.992172i | \(-0.460145\pi\) | ||||
0.124881 | + | 0.992172i | \(0.460145\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1034.66 | + | 11005.7i | 0.0678400 | + | 0.721617i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 4591.08i | − | 0.299562i | −0.988719 | − | 0.149781i | \(-0.952143\pi\) | ||
0.988719 | − | 0.149781i | \(-0.0478569\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 4037.57i | − | 0.262171i | −0.991371 | − | 0.131085i | \(-0.958154\pi\) | ||
0.991371 | − | 0.131085i | \(-0.0418462\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7541.72 | − | 26108.4i | −0.487341 | − | 1.68711i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −932.903 | −0.0599935 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9460.98 | 0.605503 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12423.9 | − | 1167.98i | 0.791326 | − | 0.0743934i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5400.54i | 0.342343i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6235.96i | 0.393423i | 0.980461 | + | 0.196711i | \(0.0630262\pi\) | ||||
−0.980461 | + | 0.196711i | \(0.936974\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15696.7 | − | 1475.66i | 0.985603 | − | 0.0926576i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 129.899 | 0.00811791 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3874.55 | −0.240997 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28469.7 | − | 5400.66i | 1.76251 | − | 0.334345i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 21379.2i | − | 1.31736i | −0.752423 | − | 0.658681i | \(-0.771115\pi\) | ||
0.752423 | − | 0.658681i | \(-0.228885\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5718.32i | 0.350713i | 0.984505 | + | 0.175356i | \(0.0561078\pi\) | ||||
−0.984505 | + | 0.175356i | \(0.943892\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 679.535 | + | 7228.24i | 0.0414832 | + | 0.441259i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12501.6 | −0.759643 | −0.379822 | − | 0.925060i | \(-0.624015\pi\) | ||||
−0.379822 | + | 0.925060i | \(0.624015\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10274.9 | 0.621458 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 538.888 | + | 5732.18i | 0.0324435 | + | 0.345103i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 19195.3i | − | 1.15034i | −0.818035 | − | 0.575169i | \(-0.804936\pi\) | ||
0.818035 | − | 0.575169i | \(-0.195064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1272.80i | − | 0.0759274i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27154.8 | + | 5151.23i | −1.61250 | + | 0.305888i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16527.6 | 0.976972 | 0.488486 | − | 0.872572i | \(-0.337549\pi\) | ||||
0.488486 | + | 0.872572i | \(0.337549\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22315.8 | −1.31314 | −0.656569 | − | 0.754266i | \(-0.727993\pi\) | ||||
−0.656569 | + | 0.754266i | \(0.727993\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6711.76 | − | 630.980i | 0.393157 | − | 0.0369611i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2050.69i | − | 0.119582i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 26919.9i | − | 1.56273i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2598.82 | − | 244.317i | 0.150188 | − | 0.0141194i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4358.90 | −0.250780 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12686.7 | 0.726653 | 0.363326 | − | 0.931662i | \(-0.381641\pi\) | ||||
0.363326 | + | 0.931662i | \(0.381641\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4195.99 | + | 14526.0i | 0.239265 | + | 0.828304i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31590.2i | 1.79337i | 0.442673 | + | 0.896683i | \(0.354030\pi\) | ||||
−0.442673 | + | 0.896683i | \(0.645970\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9779.42i | 0.552724i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2251.87 | + | 23953.2i | 0.126713 | + | 1.34786i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32381.3 | −1.81411 | −0.907055 | − | 0.421013i | \(-0.861675\pi\) | ||||
−0.907055 | + | 0.421013i | \(0.861675\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 293.832 | 0.0163894 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −686.343 | − | 7300.66i | −0.0381159 | − | 0.405441i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6987.23i | 0.386346i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1530.62i | − | 0.0842658i | −0.999112 | − | 0.0421329i | \(-0.986585\pi\) | ||
0.999112 | − | 0.0421329i | \(-0.0134153\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1099.68 | − | 5797.00i | −0.0602793 | − | 0.317763i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3012.07 | −0.164395 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 51149.4 | 2.77966 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −31071.3 | + | 2921.05i | −1.68129 | + | 0.158060i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8696.96i | − | 0.468587i | −0.972166 | − | 0.234294i | \(-0.924722\pi\) | ||
0.972166 | − | 0.234294i | \(-0.0752777\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3987.35i | − | 0.213920i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10641.9 | − | 1000.46i | 0.568508 | − | 0.0534460i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9211.63 | 0.490013 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31191.9 | −1.65224 | −0.826120 | − | 0.563494i | \(-0.809457\pi\) | ||||
−0.826120 | + | 0.563494i | \(0.809457\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −544.190 | − | 2868.71i | −0.0287043 | − | 0.151315i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 32010.0i | − | 1.68132i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1758.69i | − | 0.0919876i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 286.181 | + | 3044.12i | 0.0149061 | + | 0.158556i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25726.2 | 1.33439 | 0.667194 | − | 0.744884i | \(-0.267495\pi\) | ||||
0.667194 | + | 0.744884i | \(0.267495\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10094.0 | −0.521387 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3184.32 | + | 33871.8i | 0.163798 | + | 1.74233i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14977.5i | 0.767240i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4644.52i | − | 0.236940i | −0.992958 | − | 0.118470i | \(-0.962201\pi\) | ||
0.992958 | − | 0.118470i | \(-0.0377990\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16651.2 | + | 10495.6i | −0.845971 | + | 0.533229i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33593.4 | 1.69972 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −463.154 | −0.0233383 | −0.0116692 | − | 0.999932i | \(-0.503714\pi\) | ||||
−0.0116692 | + | 0.999932i | \(0.503714\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6399.98 | − | 601.669i | 0.321179 | − | 0.0301944i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4293.08i | 0.214570i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2346.21i | 0.116789i | 0.998294 | + | 0.0583943i | \(0.0185981\pi\) | ||||
−0.998294 | + | 0.0583943i | \(0.981402\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4955.46 | + | 465.868i | −0.245673 | + | 0.0230960i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14287.4 | 0.705454 | 0.352727 | − | 0.935726i | \(-0.385254\pi\) | ||||
0.352727 | + | 0.935726i | \(0.385254\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8588.01 | −0.422336 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −27396.6 | + | 5197.11i | −1.34189 | + | 0.254555i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 4238.20i | − | 0.206756i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 5991.43i | − | 0.291119i | −0.989350 | − | 0.145559i | \(-0.953502\pi\) | ||
0.989350 | − | 0.145559i | \(-0.0464982\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1205.13 | − | 12819.0i | −0.0583232 | − | 0.620387i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12595.9 | −0.607170 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15089.4 | 0.724481 | 0.362240 | − | 0.932085i | \(-0.382012\pi\) | ||||
0.362240 | + | 0.932085i | \(0.382012\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3070.47 | + | 32660.7i | 0.146839 | + | 1.56193i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26872.4i | 1.28006i | 0.768352 | + | 0.640028i | \(0.221077\pi\) | ||||
−0.768352 | + | 0.640028i | \(0.778923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6182.19i | 0.293329i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10988.5 | + | 2084.50i | −0.519333 | + | 0.0985168i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4098.32 | −0.192936 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23951.3 | −1.12316 | −0.561578 | − | 0.827424i | \(-0.689806\pi\) | ||||
−0.561578 | + | 0.827424i | \(0.689806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1943.11 | + | 182.674i | −0.0907646 | + | 0.00853287i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 26706.8i | − | 1.24266i | −0.783548 | − | 0.621331i | \(-0.786592\pi\) | ||
0.783548 | − | 0.621331i | \(-0.213408\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17809.4i | 0.825463i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1877.10 | + | 176.468i | −0.0866673 | + | 0.00814769i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −37764.9 | −1.73693 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34979.3 | −1.60264 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18731.8 | + | 5410.88i | −0.854941 | + | 0.246959i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 14417.3i | − | 0.655512i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 29838.7i | − | 1.35151i | −0.737128 | − | 0.675753i | \(-0.763819\pi\) | ||
0.737128 | − | 0.675753i | \(-0.236181\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3565.77 | − | 37929.2i | −0.160893 | − | 1.71143i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6056.62 | −0.272249 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1738.62 | 0.0778564 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1085.03 | − | 11541.5i | −0.0484050 | − | 0.514887i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 9775.89i | − | 0.434479i | −0.976118 | − | 0.217240i | \(-0.930295\pi\) | ||
0.976118 | − | 0.217240i | \(-0.0697053\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 49458.6i | − | 2.18989i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −700.144 | − | 3690.82i | −0.0308844 | − | 0.162807i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33363.8 | 1.46623 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5390.98 | 0.236034 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10073.6 | + | 947.031i | −0.439415 | + | 0.0413099i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20854.3i | 0.906303i | 0.891433 | + | 0.453152i | \(0.149700\pi\) | ||||
−0.891433 | + | 0.453152i | \(0.850300\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5752.41i | − | 0.249068i | −0.992215 | − | 0.124534i | \(-0.960256\pi\) | ||
0.992215 | − | 0.124534i | \(-0.0397436\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12642.9 | + | 1188.57i | −0.545393 | + | 0.0512730i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12438.0 | −0.534584 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24802.9 | −1.06211 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 438.627 | + | 2312.23i | 0.0187141 | + | 0.0986518i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6934.64i | 0.294788i | 0.989078 | + | 0.147394i | \(0.0470885\pi\) | ||||
−0.989078 | + | 0.147394i | \(0.952912\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26056.7i | − | 1.10362i | −0.833970 | − | 0.551810i | \(-0.813937\pi\) | ||
0.833970 | − | 0.551810i | \(-0.186063\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1708.32 | − | 18171.4i | −0.0720921 | − | 0.766846i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19162.5 | 0.805740 | 0.402870 | − | 0.915257i | \(-0.368013\pi\) | ||||
0.402870 | + | 0.915257i | \(0.368013\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36255.5 | −1.51895 | −0.759473 | − | 0.650539i | \(-0.774543\pi\) | ||||
−0.759473 | + | 0.650539i | \(0.774543\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1829.30 | + | 19458.4i | 0.0763632 | + | 0.812279i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 29744.1i | − | 1.23718i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 194.501i | 0.00806107i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22273.6 | + | 6433.99i | −0.919820 | + | 0.265700i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14044.0 | 0.577894 | 0.288947 | − | 0.957345i | \(-0.406695\pi\) | ||||
0.288947 | + | 0.957345i | \(0.406695\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5075.02 | 0.208087 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25940.2 | − | 2438.67i | 1.05982 | − | 0.0996348i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 701.481i | 0.0285582i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1801.89i | − | 0.0730977i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −37269.6 | + | 3503.76i | −1.50658 | + | 0.141636i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10482.2 | 0.422239 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33205.3 | 1.33286 | 0.666428 | − | 0.745569i | \(-0.267822\pi\) | ||||
0.666428 | + | 0.745569i | \(0.267822\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8113.08 | − | 1539.04i | 0.324516 | − | 0.0615604i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24286.2i | 0.968028i | 0.875060 | + | 0.484014i | \(0.160822\pi\) | ||||
−0.875060 | + | 0.484014i | \(0.839178\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 28543.6i | − | 1.13375i | −0.823803 | − | 0.566876i | \(-0.808152\pi\) | ||
0.823803 | − | 0.566876i | \(-0.191848\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1671.36 | + | 17778.3i | 0.0661553 | + | 0.703697i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5973.84 | −0.235634 | −0.117817 | − | 0.993035i | \(-0.537590\pi\) | ||||
−0.117817 | + | 0.993035i | \(0.537590\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9087.80 | 0.357219 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2454.45 | + | 26108.1i | 0.0961446 | + | 1.02269i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3524.64i | 0.137590i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1712.37i | − | 0.0666146i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −38690.0 | + | 7339.45i | −1.49995 | + | 0.284539i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6478.27 | −0.250292 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18301.3 | −0.704665 | −0.352332 | − | 0.935875i | \(-0.614611\pi\) | ||||
−0.352332 | + | 0.935875i | \(0.614611\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −33379.9 | + | 3138.08i | −1.28086 | + | 0.120415i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 40284.2i | − | 1.54053i | −0.637722 | − | 0.770266i | \(-0.720123\pi\) | ||
0.637722 | − | 0.770266i | \(-0.279877\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37019.3i | 1.41087i | 0.708774 | + | 0.705435i | \(0.249248\pi\) | ||||
−0.708774 | + | 0.705435i | \(0.750752\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6769.60 | − | 636.417i | 0.257127 | − | 0.0241728i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5439.74 | −0.205917 | −0.102959 | − | 0.994686i | \(-0.532831\pi\) | ||||
−0.102959 | + | 0.994686i | \(0.532831\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 209.834 | 0.00791633 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22109.2 | − | 8701.30i | 0.831298 | − | 0.327166i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36516.5i | 1.36840i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2805.40i | 0.104775i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1224.71 | − | 13027.2i | −0.0455872 | − | 0.484913i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22965.9 | −0.852009 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53639.4 | −1.98334 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1097.70 | + | 11676.3i | 0.0404531 | + | 0.430301i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 654.623i | − | 0.0240447i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 14617.8i | − | 0.535144i | −0.963538 | − | 0.267572i | \(-0.913779\pi\) | ||
0.963538 | − | 0.267572i | \(-0.0862213\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6913.33 | + | 36443.7i | 0.252256 | + | 1.32977i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21082.5 | 0.766735 | 0.383368 | − | 0.923596i | \(-0.374764\pi\) | ||||
0.383368 | + | 0.923596i | \(0.374764\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33661.0 | 1.22017 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2871.85 | + | 269.985i | −0.103760 | + | 0.00975458i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2056.04i | − | 0.0740420i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23894.1i | 0.857666i | 0.903384 | + | 0.428833i | \(0.141075\pi\) | ||||
−0.903384 | + | 0.428833i | \(0.858925\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18855.4 | + | 1772.62i | −0.674602 | + | 0.0634200i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13952.1 | 0.497549 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5832.00 | −0.207303 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7575.54 | − | 39934.6i | −0.268407 | − | 1.41491i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51500.7i | 1.81882i | 0.415903 | + | 0.909409i | \(0.363466\pi\) | ||||
−0.415903 | + | 0.909409i | \(0.636534\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21960.8i | 0.773078i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2182.83 | + | 23218.9i | 0.0765946 | + | 0.814740i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13501.0 | 0.472226 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2862.58 | 0.0998041 | 0.0499021 | − | 0.998754i | \(-0.484109\pi\) | ||||
0.0499021 | + | 0.998754i | \(0.484109\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 787.794 | + | 8379.80i | 0.0273788 | + | 0.291230i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 27932.6i | − | 0.967671i | −0.875159 | − | 0.483835i | \(-0.839243\pi\) | ||
0.875159 | − | 0.483835i | \(-0.160757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 99278.9i | − | 3.42838i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1083.58 | − | 3751.22i | −0.0373005 | − | 0.129129i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32402.3 | −1.11186 | −0.555930 | − | 0.831229i | \(-0.687638\pi\) | ||||
−0.555930 | + | 0.831229i | \(0.687638\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13307.7 | −0.455202 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15793.0 | + | 1484.72i | −0.538509 | + | 0.0506258i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15804.2i | 0.537197i | 0.963252 | + | 0.268598i | \(0.0865605\pi\) | ||||
−0.963252 | + | 0.268598i | \(0.913440\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4205.25i | 0.142491i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23432.7 | − | 2202.94i | 0.791508 | − | 0.0744105i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 474.647 | 0.0159824 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2482.64 | 0.0833353 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16767.5 | − | 3180.77i | 0.561084 | − | 0.106437i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 159.719i | 0.00532802i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 39370.7i | − | 1.30928i | −0.755939 | − | 0.654642i | \(-0.772820\pi\) | ||
0.755939 | − | 0.654642i | \(-0.227180\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3576.37 | − | 38042.0i | −0.118565 | − | 1.26118i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28551.2 | −0.943616 | −0.471808 | − | 0.881701i | \(-0.656398\pi\) | ||||
−0.471808 | + | 0.881701i | \(0.656398\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4865.61 | −0.160313 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 681.390 | + | 7247.97i | 0.0223815 | + | 0.238073i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 39675.1i | − | 1.29920i | −0.760275 | − | 0.649601i | \(-0.774936\pi\) | ||
0.760275 | − | 0.649601i | \(-0.225064\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4534.73i | 0.148040i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24458.4 | + | 4639.73i | −0.796022 | + | 0.151004i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7940.67 | −0.257648 | −0.128824 | − | 0.991667i | \(-0.541120\pi\) | ||||
−0.128824 | + | 0.991667i | \(0.541120\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 193.246 | 0.00625110 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17190.6 | − | 1616.11i | 0.554390 | − | 0.0521188i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 65203.4i | − | 2.09641i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 46308.7i | − | 1.48440i | −0.670177 | − | 0.742201i | \(-0.733782\pi\) | ||
0.670177 | − | 0.742201i | \(-0.266218\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14584.8 | + | 1371.14i | −0.466099 | + | 0.0438184i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15572.5 | −0.496162 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46001.3 | 1.46126 | 0.730630 | − | 0.682774i | \(-0.239226\pi\) | ||||
0.730630 | + | 0.682774i | \(0.239226\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2106.92 | − | 7293.87i | −0.0667266 | − | 0.230999i |
(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 | 624.4.d.c.287.11 | ✓ | 24 | |
3.2 | odd | 2 | inner | 624.4.d.c.287.13 | yes | 24 | |
4.3 | odd | 2 | inner | 624.4.d.c.287.14 | yes | 24 | |
12.11 | even | 2 | inner | 624.4.d.c.287.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
624.4.d.c.287.11 | ✓ | 24 | 1.1 | even | 1 | trivial | |
624.4.d.c.287.12 | yes | 24 | 12.11 | even | 2 | inner | |
624.4.d.c.287.13 | yes | 24 | 3.2 | odd | 2 | inner | |
624.4.d.c.287.14 | yes | 24 | 4.3 | odd | 2 | inner |