Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,5,Mod(133,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.133");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.7773625799\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 133.13 | ||
Character | \(\chi\) | \(=\) | 201.133 |
Dual form | 201.5.b.a.133.34 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.05388i | − | 1.01347i | −0.862102 | − | 0.506736i | \(-0.830852\pi\) | ||
0.862102 | − | 0.506736i | \(-0.169148\pi\) | |||||||
\(3\) | − | 5.19615i | − | 0.577350i | ||||||
\(4\) | −0.433982 | −0.0271239 | ||||||||
\(5\) | 2.19375i | 0.0877500i | 0.999037 | + | 0.0438750i | \(0.0139703\pi\) | ||||
−0.999037 | + | 0.0438750i | \(0.986030\pi\) | |||||||
\(6\) | −21.0646 | −0.585128 | ||||||||
\(7\) | 19.8533i | 0.405170i | 0.979265 | + | 0.202585i | \(0.0649342\pi\) | ||||
−0.979265 | + | 0.202585i | \(0.935066\pi\) | |||||||
\(8\) | − | 63.1028i | − | 0.985982i | ||||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | 8.89321 | 0.0889321 | ||||||||
\(11\) | 61.3918i | 0.507371i | 0.967287 | + | 0.253685i | \(0.0816428\pi\) | ||||
−0.967287 | + | 0.253685i | \(0.918357\pi\) | |||||||
\(12\) | 2.25504i | 0.0156600i | ||||||||
\(13\) | − | 236.159i | − | 1.39739i | −0.715418 | − | 0.698696i | \(-0.753764\pi\) | ||
0.715418 | − | 0.698696i | \(-0.246236\pi\) | |||||||
\(14\) | 80.4831 | 0.410628 | ||||||||
\(15\) | 11.3991 | 0.0506625 | ||||||||
\(16\) | −262.755 | −1.02639 | ||||||||
\(17\) | −483.140 | −1.67176 | −0.835882 | − | 0.548909i | \(-0.815043\pi\) | ||||
−0.835882 | + | 0.548909i | \(0.815043\pi\) | |||||||
\(18\) | 109.455i | 0.337824i | ||||||||
\(19\) | −407.088 | −1.12767 | −0.563833 | − | 0.825889i | \(-0.690674\pi\) | ||||
−0.563833 | + | 0.825889i | \(0.690674\pi\) | |||||||
\(20\) | − | 0.952048i | − | 0.00238012i | ||||||
\(21\) | 103.161 | 0.233925 | ||||||||
\(22\) | 248.875 | 0.514206 | ||||||||
\(23\) | −331.409 | −0.626482 | −0.313241 | − | 0.949674i | \(-0.601415\pi\) | ||||
−0.313241 | + | 0.949674i | \(0.601415\pi\) | |||||||
\(24\) | −327.892 | −0.569257 | ||||||||
\(25\) | 620.187 | 0.992300 | ||||||||
\(26\) | −957.363 | −1.41622 | ||||||||
\(27\) | 140.296i | 0.192450i | ||||||||
\(28\) | − | 8.61599i | − | 0.0109898i | ||||||
\(29\) | −174.542 | −0.207541 | −0.103770 | − | 0.994601i | \(-0.533091\pi\) | ||||
−0.103770 | + | 0.994601i | \(0.533091\pi\) | |||||||
\(30\) | − | 46.2105i | − | 0.0513449i | ||||||
\(31\) | − | 1557.14i | − | 1.62033i | −0.586203 | − | 0.810164i | \(-0.699378\pi\) | ||
0.586203 | − | 0.810164i | \(-0.300622\pi\) | |||||||
\(32\) | 55.5345i | 0.0542329i | ||||||||
\(33\) | 319.001 | 0.292931 | ||||||||
\(34\) | 1958.59i | 1.69429i | ||||||||
\(35\) | −43.5532 | −0.0355536 | ||||||||
\(36\) | 11.7175 | 0.00904129 | ||||||||
\(37\) | −1375.04 | −1.00441 | −0.502207 | − | 0.864748i | \(-0.667478\pi\) | ||||
−0.502207 | + | 0.864748i | \(0.667478\pi\) | |||||||
\(38\) | 1650.29i | 1.14286i | ||||||||
\(39\) | −1227.12 | −0.806785 | ||||||||
\(40\) | 138.432 | 0.0865199 | ||||||||
\(41\) | 1731.82i | 1.03023i | 0.857120 | + | 0.515117i | \(0.172252\pi\) | ||||
−0.857120 | + | 0.515117i | \(0.827748\pi\) | |||||||
\(42\) | − | 418.202i | − | 0.237076i | ||||||
\(43\) | 806.745i | 0.436314i | 0.975914 | + | 0.218157i | \(0.0700045\pi\) | ||||
−0.975914 | + | 0.218157i | \(0.929995\pi\) | |||||||
\(44\) | − | 26.6430i | − | 0.0137619i | ||||||
\(45\) | − | 59.2312i | − | 0.0292500i | ||||||
\(46\) | 1343.49i | 0.634922i | ||||||||
\(47\) | 1725.60 | 0.781170 | 0.390585 | − | 0.920567i | \(-0.372273\pi\) | ||||
0.390585 | + | 0.920567i | \(0.372273\pi\) | |||||||
\(48\) | 1365.32i | 0.592585i | ||||||||
\(49\) | 2006.85 | 0.835837 | ||||||||
\(50\) | − | 2514.17i | − | 1.00567i | ||||||
\(51\) | 2510.47i | 0.965194i | ||||||||
\(52\) | 102.489i | 0.0379027i | ||||||||
\(53\) | 491.806i | 0.175082i | 0.996161 | + | 0.0875412i | \(0.0279009\pi\) | ||||
−0.996161 | + | 0.0875412i | \(0.972099\pi\) | |||||||
\(54\) | 568.744 | 0.195043 | ||||||||
\(55\) | −134.678 | −0.0445218 | ||||||||
\(56\) | 1252.80 | 0.399490 | ||||||||
\(57\) | 2115.29i | 0.651059i | ||||||||
\(58\) | 707.572i | 0.210336i | ||||||||
\(59\) | −5496.96 | −1.57913 | −0.789567 | − | 0.613665i | \(-0.789695\pi\) | ||||
−0.789567 | + | 0.613665i | \(0.789695\pi\) | |||||||
\(60\) | −4.94699 | −0.00137416 | ||||||||
\(61\) | 3388.09i | 0.910533i | 0.890355 | + | 0.455267i | \(0.150456\pi\) | ||||
−0.890355 | + | 0.455267i | \(0.849544\pi\) | |||||||
\(62\) | −6312.45 | −1.64216 | ||||||||
\(63\) | − | 536.040i | − | 0.135057i | ||||||
\(64\) | −3978.96 | −0.971425 | ||||||||
\(65\) | 518.074 | 0.122621 | ||||||||
\(66\) | − | 1293.19i | − | 0.296877i | ||||||
\(67\) | 3236.63 | − | 3110.52i | 0.721014 | − | 0.692920i | ||||
\(68\) | 209.674 | 0.0453447 | ||||||||
\(69\) | 1722.05i | 0.361700i | ||||||||
\(70\) | 176.560i | 0.0360326i | ||||||||
\(71\) | 465.285 | 0.0923001 | 0.0461500 | − | 0.998935i | \(-0.485305\pi\) | ||||
0.0461500 | + | 0.998935i | \(0.485305\pi\) | |||||||
\(72\) | 1703.78i | 0.328661i | ||||||||
\(73\) | 8586.98 | 1.61137 | 0.805684 | − | 0.592345i | \(-0.201798\pi\) | ||||
0.805684 | + | 0.592345i | \(0.201798\pi\) | |||||||
\(74\) | 5574.26i | 1.01794i | ||||||||
\(75\) | − | 3222.59i | − | 0.572905i | ||||||
\(76\) | 176.669 | 0.0305867 | ||||||||
\(77\) | −1218.83 | −0.205571 | ||||||||
\(78\) | 4974.60i | 0.817653i | ||||||||
\(79\) | − | 10742.8i | − | 1.72132i | −0.509176 | − | 0.860662i | \(-0.670050\pi\) | ||
0.509176 | − | 0.860662i | \(-0.329950\pi\) | |||||||
\(80\) | − | 576.419i | − | 0.0900655i | ||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 7020.61 | 1.04411 | ||||||||
\(83\) | −563.229 | −0.0817577 | −0.0408788 | − | 0.999164i | \(-0.513016\pi\) | ||||
−0.0408788 | + | 0.999164i | \(0.513016\pi\) | |||||||
\(84\) | −44.7700 | −0.00634495 | ||||||||
\(85\) | − | 1059.89i | − | 0.146697i | ||||||
\(86\) | 3270.45 | 0.442192 | ||||||||
\(87\) | 906.945i | 0.119824i | ||||||||
\(88\) | 3874.00 | 0.500258 | ||||||||
\(89\) | −12456.6 | −1.57261 | −0.786303 | − | 0.617841i | \(-0.788007\pi\) | ||||
−0.786303 | + | 0.617841i | \(0.788007\pi\) | |||||||
\(90\) | −240.117 | −0.0296440 | ||||||||
\(91\) | 4688.55 | 0.566181 | ||||||||
\(92\) | 143.826 | 0.0169926 | ||||||||
\(93\) | −8091.11 | −0.935497 | ||||||||
\(94\) | − | 6995.40i | − | 0.791693i | ||||||
\(95\) | − | 893.048i | − | 0.0989527i | ||||||
\(96\) | 288.566 | 0.0313114 | ||||||||
\(97\) | 10955.7i | 1.16438i | 0.813052 | + | 0.582191i | \(0.197804\pi\) | ||||
−0.813052 | + | 0.582191i | \(0.802196\pi\) | |||||||
\(98\) | − | 8135.52i | − | 0.847097i | ||||||
\(99\) | − | 1657.58i | − | 0.169124i | ||||||
\(100\) | −269.150 | −0.0269150 | ||||||||
\(101\) | − | 15359.3i | − | 1.50567i | −0.658209 | − | 0.752835i | \(-0.728686\pi\) | ||
0.658209 | − | 0.752835i | \(-0.271314\pi\) | |||||||
\(102\) | 10177.2 | 0.978196 | ||||||||
\(103\) | −4995.44 | −0.470868 | −0.235434 | − | 0.971890i | \(-0.575651\pi\) | ||||
−0.235434 | + | 0.971890i | \(0.575651\pi\) | |||||||
\(104\) | −14902.3 | −1.37780 | ||||||||
\(105\) | 226.309i | 0.0205269i | ||||||||
\(106\) | 1993.73 | 0.177441 | ||||||||
\(107\) | 2433.49 | 0.212550 | 0.106275 | − | 0.994337i | \(-0.466108\pi\) | ||||
0.106275 | + | 0.994337i | \(0.466108\pi\) | |||||||
\(108\) | − | 60.8860i | − | 0.00521999i | ||||||
\(109\) | − | 20839.0i | − | 1.75397i | −0.480514 | − | 0.876987i | \(-0.659550\pi\) | ||
0.480514 | − | 0.876987i | \(-0.340450\pi\) | |||||||
\(110\) | 545.970i | 0.0451215i | ||||||||
\(111\) | 7144.93i | 0.579898i | ||||||||
\(112\) | − | 5216.57i | − | 0.415862i | ||||||
\(113\) | − | 20065.6i | − | 1.57143i | −0.618589 | − | 0.785715i | \(-0.712295\pi\) | ||
0.618589 | − | 0.785715i | \(-0.287705\pi\) | |||||||
\(114\) | 8575.14 | 0.659829 | ||||||||
\(115\) | − | 727.029i | − | 0.0549738i | ||||||
\(116\) | 75.7479 | 0.00562931 | ||||||||
\(117\) | 6376.30i | 0.465798i | ||||||||
\(118\) | 22284.1i | 1.60041i | ||||||||
\(119\) | − | 9591.94i | − | 0.677349i | ||||||
\(120\) | − | 719.313i | − | 0.0499523i | ||||||
\(121\) | 10872.0 | 0.742575 | ||||||||
\(122\) | 13734.9 | 0.922799 | ||||||||
\(123\) | 8998.82 | 0.594806 | ||||||||
\(124\) | 675.769i | 0.0439496i | ||||||||
\(125\) | 2731.63i | 0.174824i | ||||||||
\(126\) | −2173.04 | −0.136876 | ||||||||
\(127\) | −9265.62 | −0.574470 | −0.287235 | − | 0.957860i | \(-0.592736\pi\) | ||||
−0.287235 | + | 0.957860i | \(0.592736\pi\) | |||||||
\(128\) | 17018.8i | 1.03874i | ||||||||
\(129\) | 4191.97 | 0.251906 | ||||||||
\(130\) | − | 2100.21i | − | 0.124273i | ||||||
\(131\) | 9285.00 | 0.541053 | 0.270526 | − | 0.962713i | \(-0.412802\pi\) | ||||
0.270526 | + | 0.962713i | \(0.412802\pi\) | |||||||
\(132\) | −138.441 | −0.00794541 | ||||||||
\(133\) | − | 8082.04i | − | 0.456897i | ||||||
\(134\) | −12609.7 | − | 13120.9i | −0.702255 | − | 0.730727i | ||||
\(135\) | −307.774 | −0.0168875 | ||||||||
\(136\) | 30487.5i | 1.64833i | ||||||||
\(137\) | − | 34125.1i | − | 1.81816i | −0.416620 | − | 0.909081i | \(-0.636785\pi\) | ||
0.416620 | − | 0.909081i | \(-0.363215\pi\) | |||||||
\(138\) | 6981.00 | 0.366572 | ||||||||
\(139\) | 6542.07i | 0.338599i | 0.985565 | + | 0.169300i | \(0.0541505\pi\) | ||||
−0.985565 | + | 0.169300i | \(0.945849\pi\) | |||||||
\(140\) | 18.9013 | 0.000964353 | ||||||||
\(141\) | − | 8966.50i | − | 0.451009i | ||||||
\(142\) | − | 1886.21i | − | 0.0935434i | ||||||
\(143\) | 14498.3 | 0.708996 | ||||||||
\(144\) | 7094.40 | 0.342129 | ||||||||
\(145\) | − | 382.900i | − | 0.0182117i | ||||||
\(146\) | − | 34810.6i | − | 1.63308i | ||||||
\(147\) | − | 10427.9i | − | 0.482571i | ||||||
\(148\) | 596.744 | 0.0272436 | ||||||||
\(149\) | 5798.85 | 0.261198 | 0.130599 | − | 0.991435i | \(-0.458310\pi\) | ||||
0.130599 | + | 0.991435i | \(0.458310\pi\) | |||||||
\(150\) | −13064.0 | −0.580622 | ||||||||
\(151\) | −11480.5 | −0.503507 | −0.251754 | − | 0.967791i | \(-0.581007\pi\) | ||||
−0.251754 | + | 0.967791i | \(0.581007\pi\) | |||||||
\(152\) | 25688.4i | 1.11186i | ||||||||
\(153\) | 13044.8 | 0.557255 | ||||||||
\(154\) | 4941.01i | 0.208341i | ||||||||
\(155\) | 3415.97 | 0.142184 | ||||||||
\(156\) | 532.548 | 0.0218831 | ||||||||
\(157\) | 32540.4 | 1.32015 | 0.660076 | − | 0.751199i | \(-0.270524\pi\) | ||||
0.660076 | + | 0.751199i | \(0.270524\pi\) | |||||||
\(158\) | −43550.0 | −1.74451 | ||||||||
\(159\) | 2555.50 | 0.101084 | ||||||||
\(160\) | −121.829 | −0.00475894 | ||||||||
\(161\) | − | 6579.57i | − | 0.253832i | ||||||
\(162\) | − | 2955.28i | − | 0.112608i | ||||||
\(163\) | 40283.9 | 1.51620 | 0.758099 | − | 0.652139i | \(-0.226128\pi\) | ||||
0.758099 | + | 0.652139i | \(0.226128\pi\) | |||||||
\(164\) | − | 751.580i | − | 0.0279439i | ||||||
\(165\) | 699.809i | 0.0257046i | ||||||||
\(166\) | 2283.26i | 0.0828591i | ||||||||
\(167\) | −30195.4 | −1.08270 | −0.541349 | − | 0.840798i | \(-0.682086\pi\) | ||||
−0.541349 | + | 0.840798i | \(0.682086\pi\) | |||||||
\(168\) | − | 6509.75i | − | 0.230646i | ||||||
\(169\) | −27210.2 | −0.952706 | ||||||||
\(170\) | −4296.66 | −0.148673 | ||||||||
\(171\) | 10991.4 | 0.375889 | ||||||||
\(172\) | − | 350.113i | − | 0.0118345i | ||||||
\(173\) | 11899.2 | 0.397580 | 0.198790 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198790 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(174\) | 3676.65 | 0.121438 | ||||||||
\(175\) | 12312.8i | 0.402050i | ||||||||
\(176\) | − | 16131.0i | − | 0.520759i | ||||||
\(177\) | 28563.1i | 0.911713i | ||||||||
\(178\) | 50497.7i | 1.59379i | ||||||||
\(179\) | 47223.6i | 1.47385i | 0.675975 | + | 0.736924i | \(0.263723\pi\) | ||||
−0.675975 | + | 0.736924i | \(0.736277\pi\) | |||||||
\(180\) | 25.7053i | 0.000793373i | ||||||||
\(181\) | −39859.4 | −1.21667 | −0.608336 | − | 0.793680i | \(-0.708163\pi\) | ||||
−0.608336 | + | 0.793680i | \(0.708163\pi\) | |||||||
\(182\) | − | 19006.8i | − | 0.573809i | ||||||
\(183\) | 17605.1 | 0.525697 | ||||||||
\(184\) | 20912.9i | 0.617700i | ||||||||
\(185\) | − | 3016.50i | − | 0.0881372i | ||||||
\(186\) | 32800.4i | 0.948099i | ||||||||
\(187\) | − | 29660.9i | − | 0.848204i | ||||||
\(188\) | −748.881 | −0.0211884 | ||||||||
\(189\) | −2785.34 | −0.0779750 | ||||||||
\(190\) | −3620.31 | −0.100286 | ||||||||
\(191\) | 52143.3i | 1.42933i | 0.699469 | + | 0.714663i | \(0.253420\pi\) | ||||
−0.699469 | + | 0.714663i | \(0.746580\pi\) | |||||||
\(192\) | 20675.3i | 0.560852i | ||||||||
\(193\) | 31454.2 | 0.844431 | 0.422216 | − | 0.906495i | \(-0.361252\pi\) | ||||
0.422216 | + | 0.906495i | \(0.361252\pi\) | |||||||
\(194\) | 44413.0 | 1.18007 | ||||||||
\(195\) | − | 2691.99i | − | 0.0707954i | ||||||
\(196\) | −870.935 | −0.0226712 | ||||||||
\(197\) | − | 27651.1i | − | 0.712492i | −0.934392 | − | 0.356246i | \(-0.884057\pi\) | ||
0.934392 | − | 0.356246i | \(-0.115943\pi\) | |||||||
\(198\) | −6719.64 | −0.171402 | ||||||||
\(199\) | −53743.2 | −1.35712 | −0.678558 | − | 0.734547i | \(-0.737395\pi\) | ||||
−0.678558 | + | 0.734547i | \(0.737395\pi\) | |||||||
\(200\) | − | 39135.6i | − | 0.978390i | ||||||
\(201\) | −16162.7 | − | 16818.0i | −0.400058 | − | 0.416278i | ||||
\(202\) | −62265.0 | −1.52595 | ||||||||
\(203\) | − | 3465.23i | − | 0.0840892i | ||||||
\(204\) | − | 1089.50i | − | 0.0261798i | ||||||
\(205\) | −3799.19 | −0.0904030 | ||||||||
\(206\) | 20250.9i | 0.477211i | ||||||||
\(207\) | 8948.05 | 0.208827 | ||||||||
\(208\) | 62052.1i | 1.43427i | ||||||||
\(209\) | − | 24991.9i | − | 0.572145i | ||||||
\(210\) | 917.431 | 0.0208034 | ||||||||
\(211\) | 50734.7 | 1.13957 | 0.569784 | − | 0.821795i | \(-0.307027\pi\) | ||||
0.569784 | + | 0.821795i | \(0.307027\pi\) | |||||||
\(212\) | − | 213.435i | − | 0.00474891i | ||||||
\(213\) | − | 2417.69i | − | 0.0532895i | ||||||
\(214\) | − | 9865.08i | − | 0.215413i | ||||||
\(215\) | −1769.80 | −0.0382866 | ||||||||
\(216\) | 8853.08 | 0.189752 | ||||||||
\(217\) | 30914.3 | 0.656508 | ||||||||
\(218\) | −84478.8 | −1.77760 | ||||||||
\(219\) | − | 44619.3i | − | 0.930324i | ||||||
\(220\) | 58.4480 | 0.00120760 | ||||||||
\(221\) | 114098.i | 2.33611i | ||||||||
\(222\) | 28964.7 | 0.587710 | ||||||||
\(223\) | 73794.1 | 1.48393 | 0.741963 | − | 0.670441i | \(-0.233895\pi\) | ||||
0.741963 | + | 0.670441i | \(0.233895\pi\) | |||||||
\(224\) | −1102.54 | −0.0219736 | ||||||||
\(225\) | −16745.1 | −0.330767 | ||||||||
\(226\) | −81343.6 | −1.59260 | ||||||||
\(227\) | −3603.56 | −0.0699326 | −0.0349663 | − | 0.999388i | \(-0.511132\pi\) | ||||
−0.0349663 | + | 0.999388i | \(0.511132\pi\) | |||||||
\(228\) | − | 917.998i | − | 0.0176592i | ||||||
\(229\) | 13896.7i | 0.264997i | 0.991183 | + | 0.132498i | \(0.0422999\pi\) | ||||
−0.991183 | + | 0.132498i | \(0.957700\pi\) | |||||||
\(230\) | −2947.29 | −0.0557144 | ||||||||
\(231\) | 6333.24i | 0.118687i | ||||||||
\(232\) | 11014.1i | 0.204631i | ||||||||
\(233\) | − | 68643.7i | − | 1.26441i | −0.774800 | − | 0.632206i | \(-0.782150\pi\) | ||
0.774800 | − | 0.632206i | \(-0.217850\pi\) | |||||||
\(234\) | 25848.8 | 0.472072 | ||||||||
\(235\) | 3785.54i | 0.0685476i | ||||||||
\(236\) | 2385.58 | 0.0428322 | ||||||||
\(237\) | −55821.2 | −0.993807 | ||||||||
\(238\) | −38884.6 | −0.686473 | ||||||||
\(239\) | 10929.4i | 0.191338i | 0.995413 | + | 0.0956692i | \(0.0304991\pi\) | ||||
−0.995413 | + | 0.0956692i | \(0.969501\pi\) | |||||||
\(240\) | −2995.16 | −0.0519994 | ||||||||
\(241\) | −86262.6 | −1.48521 | −0.742606 | − | 0.669728i | \(-0.766411\pi\) | ||||
−0.742606 | + | 0.669728i | \(0.766411\pi\) | |||||||
\(242\) | − | 44074.0i | − | 0.752578i | ||||||
\(243\) | − | 3788.00i | − | 0.0641500i | ||||||
\(244\) | − | 1470.37i | − | 0.0246972i | ||||||
\(245\) | 4402.52i | 0.0733447i | ||||||||
\(246\) | − | 36480.2i | − | 0.602819i | ||||||
\(247\) | 96137.5i | 1.57579i | ||||||||
\(248\) | −98259.7 | −1.59761 | ||||||||
\(249\) | 2926.62i | 0.0472028i | ||||||||
\(250\) | 11073.7 | 0.177179 | ||||||||
\(251\) | − | 29959.7i | − | 0.475544i | −0.971321 | − | 0.237772i | \(-0.923583\pi\) | ||
0.971321 | − | 0.237772i | \(-0.0764170\pi\) | |||||||
\(252\) | 232.632i | 0.00366326i | ||||||||
\(253\) | − | 20345.8i | − | 0.317859i | ||||||
\(254\) | 37561.8i | 0.582209i | ||||||||
\(255\) | −5507.34 | −0.0846957 | ||||||||
\(256\) | 5328.88 | 0.0813123 | ||||||||
\(257\) | 38523.2 | 0.583252 | 0.291626 | − | 0.956532i | \(-0.405804\pi\) | ||||
0.291626 | + | 0.956532i | \(0.405804\pi\) | |||||||
\(258\) | − | 16993.8i | − | 0.255300i | ||||||
\(259\) | − | 27299.2i | − | 0.406958i | ||||||
\(260\) | −224.835 | −0.00332596 | ||||||||
\(261\) | 4712.62 | 0.0691802 | ||||||||
\(262\) | − | 37640.3i | − | 0.548341i | ||||||
\(263\) | −53998.5 | −0.780675 | −0.390337 | − | 0.920672i | \(-0.627642\pi\) | ||||
−0.390337 | + | 0.920672i | \(0.627642\pi\) | |||||||
\(264\) | − | 20129.9i | − | 0.288824i | ||||||
\(265\) | −1078.90 | −0.0153635 | ||||||||
\(266\) | −32763.7 | −0.463051 | ||||||||
\(267\) | 64726.5i | 0.907944i | ||||||||
\(268\) | −1404.64 | + | 1349.91i | −0.0195567 | + | 0.0187947i | ||||
\(269\) | 51631.8 | 0.713531 | 0.356766 | − | 0.934194i | \(-0.383879\pi\) | ||||
0.356766 | + | 0.934194i | \(0.383879\pi\) | |||||||
\(270\) | 1247.68i | 0.0171150i | ||||||||
\(271\) | − | 121695.i | − | 1.65705i | −0.559954 | − | 0.828524i | \(-0.689181\pi\) | ||
0.559954 | − | 0.828524i | \(-0.310819\pi\) | |||||||
\(272\) | 126948. | 1.71588 | ||||||||
\(273\) | − | 24362.4i | − | 0.326885i | ||||||
\(274\) | −138339. | −1.84265 | ||||||||
\(275\) | 38074.5i | 0.503464i | ||||||||
\(276\) | − | 747.340i | − | 0.00981070i | ||||||
\(277\) | 30389.6 | 0.396065 | 0.198032 | − | 0.980196i | \(-0.436545\pi\) | ||||
0.198032 | + | 0.980196i | \(0.436545\pi\) | |||||||
\(278\) | 26520.8 | 0.343160 | ||||||||
\(279\) | 42042.7i | 0.540110i | ||||||||
\(280\) | 2748.33i | 0.0350553i | ||||||||
\(281\) | 64376.8i | 0.815298i | 0.913139 | + | 0.407649i | \(0.133651\pi\) | ||||
−0.913139 | + | 0.407649i | \(0.866349\pi\) | |||||||
\(282\) | −36349.2 | −0.457084 | ||||||||
\(283\) | −43342.2 | −0.541175 | −0.270588 | − | 0.962695i | \(-0.587218\pi\) | ||||
−0.270588 | + | 0.962695i | \(0.587218\pi\) | |||||||
\(284\) | −201.925 | −0.00250354 | ||||||||
\(285\) | −4640.41 | −0.0571304 | ||||||||
\(286\) | − | 58774.3i | − | 0.718547i | ||||||
\(287\) | −34382.5 | −0.417420 | ||||||||
\(288\) | − | 1499.43i | − | 0.0180776i | ||||||
\(289\) | 149903. | 1.79480 | ||||||||
\(290\) | −1552.23 | −0.0184570 | ||||||||
\(291\) | 56927.3 | 0.672256 | ||||||||
\(292\) | −3726.60 | −0.0437066 | ||||||||
\(293\) | 77718.3 | 0.905291 | 0.452646 | − | 0.891691i | \(-0.350480\pi\) | ||||
0.452646 | + | 0.891691i | \(0.350480\pi\) | |||||||
\(294\) | −42273.4 | −0.489072 | ||||||||
\(295\) | − | 12059.0i | − | 0.138569i | ||||||
\(296\) | 86769.1i | 0.990334i | ||||||||
\(297\) | −8613.04 | −0.0976435 | ||||||||
\(298\) | − | 23507.9i | − | 0.264716i | ||||||
\(299\) | 78265.4i | 0.875442i | ||||||||
\(300\) | 1398.55i | 0.0155394i | ||||||||
\(301\) | −16016.6 | −0.176781 | ||||||||
\(302\) | 46540.5i | 0.510290i | ||||||||
\(303\) | −79809.5 | −0.869299 | ||||||||
\(304\) | 106964. | 1.15742 | ||||||||
\(305\) | −7432.63 | −0.0798992 | ||||||||
\(306\) | − | 52882.0i | − | 0.564762i | ||||||
\(307\) | 98419.8 | 1.04425 | 0.522127 | − | 0.852868i | \(-0.325139\pi\) | ||||
0.522127 | + | 0.852868i | \(0.325139\pi\) | |||||||
\(308\) | 528.951 | 0.00557589 | ||||||||
\(309\) | 25957.1i | 0.271856i | ||||||||
\(310\) | − | 13847.9i | − | 0.144099i | ||||||
\(311\) | − | 118257.i | − | 1.22266i | −0.791376 | − | 0.611329i | \(-0.790635\pi\) | ||
0.791376 | − | 0.611329i | \(-0.209365\pi\) | |||||||
\(312\) | 77434.8i | 0.795475i | ||||||||
\(313\) | − | 94235.3i | − | 0.961889i | −0.876751 | − | 0.480945i | \(-0.840294\pi\) | ||
0.876751 | − | 0.480945i | \(-0.159706\pi\) | |||||||
\(314\) | − | 131915.i | − | 1.33794i | ||||||
\(315\) | 1175.94 | 0.0118512 | ||||||||
\(316\) | 4662.18i | 0.0466890i | ||||||||
\(317\) | 1669.41 | 0.0166128 | 0.00830642 | − | 0.999966i | \(-0.497356\pi\) | ||||
0.00830642 | + | 0.999966i | \(0.497356\pi\) | |||||||
\(318\) | − | 10359.7i | − | 0.102446i | ||||||
\(319\) | − | 10715.4i | − | 0.105300i | ||||||
\(320\) | − | 8728.83i | − | 0.0852425i | ||||||
\(321\) | − | 12644.8i | − | 0.122716i | ||||||
\(322\) | −26672.8 | −0.257251 | ||||||||
\(323\) | 196680. | 1.88519 | ||||||||
\(324\) | −316.373 | −0.00301376 | ||||||||
\(325\) | − | 146463.i | − | 1.38663i | ||||||
\(326\) | − | 163306.i | − | 1.53662i | ||||||
\(327\) | −108282. | −1.01266 | ||||||||
\(328\) | 109283. | 1.01579 | ||||||||
\(329\) | 34259.0i | 0.316507i | ||||||||
\(330\) | 2836.95 | 0.0260509 | ||||||||
\(331\) | − | 26818.3i | − | 0.244780i | −0.992482 | − | 0.122390i | \(-0.960944\pi\) | ||
0.992482 | − | 0.122390i | \(-0.0390559\pi\) | |||||||
\(332\) | 244.431 | 0.00221759 | ||||||||
\(333\) | 37126.1 | 0.334804 | ||||||||
\(334\) | 122408.i | 1.09728i | ||||||||
\(335\) | 6823.70 | + | 7100.36i | 0.0608037 | + | 0.0632690i | ||||
\(336\) | −27106.1 | −0.240098 | ||||||||
\(337\) | − | 126882.i | − | 1.11722i | −0.829430 | − | 0.558611i | \(-0.811335\pi\) | ||
0.829430 | − | 0.558611i | \(-0.188665\pi\) | |||||||
\(338\) | 110307.i | 0.965540i | ||||||||
\(339\) | −104264. | −0.907265 | ||||||||
\(340\) | 459.972i | 0.00397900i | ||||||||
\(341\) | 95595.4 | 0.822107 | ||||||||
\(342\) | − | 44557.7i | − | 0.380953i | ||||||
\(343\) | 87510.4i | 0.743826i | ||||||||
\(344\) | 50907.9 | 0.430198 | ||||||||
\(345\) | −3777.75 | −0.0317391 | ||||||||
\(346\) | − | 48237.9i | − | 0.402936i | ||||||
\(347\) | 215554.i | 1.79018i | 0.445886 | + | 0.895090i | \(0.352889\pi\) | ||||
−0.445886 | + | 0.895090i | \(0.647111\pi\) | |||||||
\(348\) | − | 393.598i | − | 0.00325008i | ||||||
\(349\) | 71512.4 | 0.587125 | 0.293562 | − | 0.955940i | \(-0.405159\pi\) | ||||
0.293562 | + | 0.955940i | \(0.405159\pi\) | |||||||
\(350\) | 49914.6 | 0.407466 | ||||||||
\(351\) | 33132.2 | 0.268928 | ||||||||
\(352\) | −3409.37 | −0.0275162 | ||||||||
\(353\) | 182287.i | 1.46287i | 0.681912 | + | 0.731434i | \(0.261149\pi\) | ||||
−0.681912 | + | 0.731434i | \(0.738851\pi\) | |||||||
\(354\) | 115791. | 0.923995 | ||||||||
\(355\) | 1020.72i | 0.00809933i | ||||||||
\(356\) | 5405.95 | 0.0426552 | ||||||||
\(357\) | −49841.2 | −0.391067 | ||||||||
\(358\) | 191439. | 1.49370 | ||||||||
\(359\) | −55541.3 | −0.430951 | −0.215475 | − | 0.976509i | \(-0.569130\pi\) | ||||
−0.215475 | + | 0.976509i | \(0.569130\pi\) | |||||||
\(360\) | −3737.66 | −0.0288400 | ||||||||
\(361\) | 35399.3 | 0.271632 | ||||||||
\(362\) | 161585.i | 1.23306i | ||||||||
\(363\) | − | 56492.8i | − | 0.428726i | ||||||
\(364\) | −2034.75 | −0.0153570 | ||||||||
\(365\) | 18837.7i | 0.141398i | ||||||||
\(366\) | − | 71368.9i | − | 0.532778i | ||||||
\(367\) | 99043.5i | 0.735350i | 0.929954 | + | 0.367675i | \(0.119846\pi\) | ||||
−0.929954 | + | 0.367675i | \(0.880154\pi\) | |||||||
\(368\) | 87079.5 | 0.643014 | ||||||||
\(369\) | − | 46759.2i | − | 0.343411i | ||||||
\(370\) | −12228.5 | −0.0893246 | ||||||||
\(371\) | −9763.99 | −0.0709381 | ||||||||
\(372\) | 3511.40 | 0.0253743 | ||||||||
\(373\) | − | 209435.i | − | 1.50533i | −0.658405 | − | 0.752664i | \(-0.728769\pi\) | ||
0.658405 | − | 0.752664i | \(-0.271231\pi\) | |||||||
\(374\) | −120242. | −0.859631 | ||||||||
\(375\) | 14194.0 | 0.100935 | ||||||||
\(376\) | − | 108891.i | − | 0.770219i | ||||||
\(377\) | 41219.6i | 0.290016i | ||||||||
\(378\) | 11291.5i | 0.0790254i | ||||||||
\(379\) | 33726.9i | 0.234800i | 0.993085 | + | 0.117400i | \(0.0374559\pi\) | ||||
−0.993085 | + | 0.117400i | \(0.962544\pi\) | |||||||
\(380\) | 387.567i | 0.00268398i | ||||||||
\(381\) | 48145.6i | 0.331670i | ||||||||
\(382\) | 211383. | 1.44858 | ||||||||
\(383\) | 29233.3i | 0.199288i | 0.995023 | + | 0.0996439i | \(0.0317704\pi\) | ||||
−0.995023 | + | 0.0996439i | \(0.968230\pi\) | |||||||
\(384\) | 88432.2 | 0.599719 | ||||||||
\(385\) | − | 2673.81i | − | 0.0180389i | ||||||
\(386\) | − | 127512.i | − | 0.855807i | ||||||
\(387\) | − | 21782.1i | − | 0.145438i | ||||||
\(388\) | − | 4754.57i | − | 0.0315826i | ||||||
\(389\) | 291228. | 1.92457 | 0.962286 | − | 0.272040i | \(-0.0876982\pi\) | ||||
0.962286 | + | 0.272040i | \(0.0876982\pi\) | |||||||
\(390\) | −10913.0 | −0.0717490 | ||||||||
\(391\) | 160117. | 1.04733 | ||||||||
\(392\) | − | 126638.i | − | 0.824121i | ||||||
\(393\) | − | 48246.3i | − | 0.312377i | ||||||
\(394\) | −112094. | −0.722090 | ||||||||
\(395\) | 23567.0 | 0.151046 | ||||||||
\(396\) | 719.360i | 0.00458729i | ||||||||
\(397\) | −266513. | −1.69098 | −0.845488 | − | 0.533995i | \(-0.820690\pi\) | ||||
−0.845488 | + | 0.533995i | \(0.820690\pi\) | |||||||
\(398\) | 217869.i | 1.37540i | ||||||||
\(399\) | −41995.5 | −0.263789 | ||||||||
\(400\) | −162958. | −1.01848 | ||||||||
\(401\) | 26541.3i | 0.165057i | 0.996589 | + | 0.0825283i | \(0.0262995\pi\) | ||||
−0.996589 | + | 0.0825283i | \(0.973701\pi\) | |||||||
\(402\) | −68178.4 | + | 65521.9i | −0.421885 | + | 0.405447i | ||||
\(403\) | −367732. | −2.26424 | ||||||||
\(404\) | 6665.68i | 0.0408396i | ||||||||
\(405\) | 1599.24i | 0.00975000i | ||||||||
\(406\) | −14047.6 | −0.0852220 | ||||||||
\(407\) | − | 84416.4i | − | 0.509610i | ||||||
\(408\) | 158418. | 0.951664 | ||||||||
\(409\) | − | 178774.i | − | 1.06871i | −0.845261 | − | 0.534354i | \(-0.820555\pi\) | ||
0.845261 | − | 0.534354i | \(-0.179445\pi\) | |||||||
\(410\) | 15401.5i | 0.0916208i | ||||||||
\(411\) | −177319. | −1.04972 | ||||||||
\(412\) | 2167.93 | 0.0127718 | ||||||||
\(413\) | − | 109133.i | − | 0.639817i | ||||||
\(414\) | − | 36274.4i | − | 0.211641i | ||||||
\(415\) | − | 1235.58i | − | 0.00717423i | ||||||
\(416\) | 13115.0 | 0.0757847 | ||||||||
\(417\) | 33993.6 | 0.195490 | ||||||||
\(418\) | −101314. | −0.579852 | ||||||||
\(419\) | −153113. | −0.872137 | −0.436069 | − | 0.899913i | \(-0.643630\pi\) | ||||
−0.436069 | + | 0.899913i | \(0.643630\pi\) | |||||||
\(420\) | − | 98.2141i | − | 0.000556769i | ||||||
\(421\) | −235921. | −1.33107 | −0.665536 | − | 0.746366i | \(-0.731797\pi\) | ||||
−0.665536 | + | 0.746366i | \(0.731797\pi\) | |||||||
\(422\) | − | 205673.i | − | 1.15492i | ||||||
\(423\) | −46591.3 | −0.260390 | ||||||||
\(424\) | 31034.4 | 0.172628 | ||||||||
\(425\) | −299637. | −1.65889 | ||||||||
\(426\) | −9801.03 | −0.0540073 | ||||||||
\(427\) | −67264.9 | −0.368921 | ||||||||
\(428\) | −1056.09 | −0.00576519 | ||||||||
\(429\) | − | 75335.2i | − | 0.409339i | ||||||
\(430\) | 7174.55i | 0.0388023i | ||||||||
\(431\) | 344575. | 1.85494 | 0.927468 | − | 0.373903i | \(-0.121981\pi\) | ||||
0.927468 | + | 0.373903i | \(0.121981\pi\) | |||||||
\(432\) | − | 36863.6i | − | 0.197528i | ||||||
\(433\) | 172115.i | 0.918002i | 0.888436 | + | 0.459001i | \(0.151793\pi\) | ||||
−0.888436 | + | 0.459001i | \(0.848207\pi\) | |||||||
\(434\) | − | 125323.i | − | 0.665352i | ||||||
\(435\) | −1989.61 | −0.0105145 | ||||||||
\(436\) | 9043.74i | 0.0475746i | ||||||||
\(437\) | 134913. | 0.706463 | ||||||||
\(438\) | −180881. | −0.942857 | ||||||||
\(439\) | −9717.32 | −0.0504217 | −0.0252108 | − | 0.999682i | \(-0.508026\pi\) | ||||
−0.0252108 | + | 0.999682i | \(0.508026\pi\) | |||||||
\(440\) | 8498.58i | 0.0438976i | ||||||||
\(441\) | −54184.8 | −0.278612 | ||||||||
\(442\) | 462540. | 2.36758 | ||||||||
\(443\) | 312138.i | 1.59052i | 0.606268 | + | 0.795261i | \(0.292666\pi\) | ||||
−0.606268 | + | 0.795261i | \(0.707334\pi\) | |||||||
\(444\) | − | 3100.77i | − | 0.0157291i | ||||||
\(445\) | − | 27326.7i | − | 0.137996i | ||||||
\(446\) | − | 299153.i | − | 1.50392i | ||||||
\(447\) | − | 30131.7i | − | 0.150803i | ||||||
\(448\) | − | 78995.5i | − | 0.393592i | ||||||
\(449\) | −299938. | −1.48778 | −0.743889 | − | 0.668303i | \(-0.767021\pi\) | ||||
−0.743889 | + | 0.668303i | \(0.767021\pi\) | |||||||
\(450\) | 67882.6i | 0.335222i | ||||||||
\(451\) | −106320. | −0.522710 | ||||||||
\(452\) | 8708.10i | 0.0426233i | ||||||||
\(453\) | 59654.3i | 0.290700i | ||||||||
\(454\) | 14608.4i | 0.0708747i | ||||||||
\(455\) | 10285.5i | 0.0496824i | ||||||||
\(456\) | 133481. | 0.641932 | ||||||||
\(457\) | −81434.1 | −0.389918 | −0.194959 | − | 0.980811i | \(-0.562457\pi\) | ||||
−0.194959 | + | 0.980811i | \(0.562457\pi\) | |||||||
\(458\) | 56335.6 | 0.268566 | ||||||||
\(459\) | − | 67782.7i | − | 0.321731i | ||||||
\(460\) | 315.517i | 0.00149110i | ||||||||
\(461\) | −350275. | −1.64819 | −0.824096 | − | 0.566450i | \(-0.808316\pi\) | ||||
−0.824096 | + | 0.566450i | \(0.808316\pi\) | |||||||
\(462\) | 25674.2 | 0.120286 | ||||||||
\(463\) | 9936.97i | 0.0463545i | 0.999731 | + | 0.0231772i | \(0.00737821\pi\) | ||||
−0.999731 | + | 0.0231772i | \(0.992622\pi\) | |||||||
\(464\) | 45861.7 | 0.213017 | ||||||||
\(465\) | − | 17749.9i | − | 0.0820898i | ||||||
\(466\) | −278274. | −1.28145 | ||||||||
\(467\) | 182819. | 0.838278 | 0.419139 | − | 0.907922i | \(-0.362332\pi\) | ||||
0.419139 | + | 0.907922i | \(0.362332\pi\) | |||||||
\(468\) | − | 2767.20i | − | 0.0126342i | ||||||
\(469\) | 61754.2 | + | 64257.9i | 0.280750 | + | 0.292133i | ||||
\(470\) | 15346.2 | 0.0694710 | ||||||||
\(471\) | − | 169085.i | − | 0.762190i | ||||||
\(472\) | 346874.i | 1.55700i | ||||||||
\(473\) | −49527.6 | −0.221373 | ||||||||
\(474\) | 226293.i | 1.00720i | ||||||||
\(475\) | −252471. | −1.11898 | ||||||||
\(476\) | 4162.73i | 0.0183723i | ||||||||
\(477\) | − | 13278.8i | − | 0.0583608i | ||||||
\(478\) | 44306.7 | 0.193916 | ||||||||
\(479\) | −199683. | −0.870300 | −0.435150 | − | 0.900358i | \(-0.643305\pi\) | ||||
−0.435150 | + | 0.900358i | \(0.643305\pi\) | |||||||
\(480\) | 633.041i | 0.00274757i | ||||||||
\(481\) | 324729.i | 1.40356i | ||||||||
\(482\) | 349699.i | 1.50522i | ||||||||
\(483\) | −34188.5 | −0.146550 | ||||||||
\(484\) | −4718.27 | −0.0201415 | ||||||||
\(485\) | −24034.0 | −0.102175 | ||||||||
\(486\) | −15356.1 | −0.0650142 | ||||||||
\(487\) | − | 120283.i | − | 0.507160i | −0.967314 | − | 0.253580i | \(-0.918392\pi\) | ||
0.967314 | − | 0.253580i | \(-0.0816080\pi\) | |||||||
\(488\) | 213798. | 0.897769 | ||||||||
\(489\) | − | 209321.i | − | 0.875378i | ||||||
\(490\) | 17847.3 | 0.0743327 | ||||||||
\(491\) | −292583. | −1.21363 | −0.606814 | − | 0.794844i | \(-0.707553\pi\) | ||||
−0.606814 | + | 0.794844i | \(0.707553\pi\) | |||||||
\(492\) | −3905.33 | −0.0161334 | ||||||||
\(493\) | 84328.0 | 0.346959 | ||||||||
\(494\) | 389731. | 1.59702 | ||||||||
\(495\) | 3636.31 | 0.0148406 | ||||||||
\(496\) | 409146.i | 1.66309i | ||||||||
\(497\) | 9237.45i | 0.0373972i | ||||||||
\(498\) | 11864.2 | 0.0478387 | ||||||||
\(499\) | − | 237737.i | − | 0.954762i | −0.878696 | − | 0.477381i | \(-0.841586\pi\) | ||
0.878696 | − | 0.477381i | \(-0.158414\pi\) | |||||||
\(500\) | − | 1185.48i | − | 0.00474191i | ||||||
\(501\) | 156900.i | 0.625096i | ||||||||
\(502\) | −121453. | −0.481950 | ||||||||
\(503\) | − | 101233.i | − | 0.400115i | −0.979784 | − | 0.200058i | \(-0.935887\pi\) | ||
0.979784 | − | 0.200058i | \(-0.0641129\pi\) | |||||||
\(504\) | −33825.6 | −0.133163 | ||||||||
\(505\) | 33694.6 | 0.132123 | ||||||||
\(506\) | −82479.6 | −0.322141 | ||||||||
\(507\) | 141389.i | 0.550045i | ||||||||
\(508\) | 4021.11 | 0.0155819 | ||||||||
\(509\) | 132814. | 0.512634 | 0.256317 | − | 0.966593i | \(-0.417491\pi\) | ||||
0.256317 | + | 0.966593i | \(0.417491\pi\) | |||||||
\(510\) | 22326.1i | 0.0858367i | ||||||||
\(511\) | 170480.i | 0.652878i | ||||||||
\(512\) | 250698.i | 0.956336i | ||||||||
\(513\) | − | 57112.8i | − | 0.217020i | ||||||
\(514\) | − | 156169.i | − | 0.591109i | ||||||
\(515\) | − | 10958.7i | − | 0.0413187i | ||||||
\(516\) | −1819.24 | −0.00683267 | ||||||||
\(517\) | 105938.i | 0.396343i | ||||||||
\(518\) | −110668. | −0.412440 | ||||||||
\(519\) | − | 61829.9i | − | 0.229543i | ||||||
\(520\) | − | 32692.0i | − | 0.120902i | ||||||
\(521\) | − | 347656.i | − | 1.28078i | −0.768051 | − | 0.640389i | \(-0.778773\pi\) | ||
0.768051 | − | 0.640389i | \(-0.221227\pi\) | |||||||
\(522\) | − | 19104.4i | − | 0.0701121i | ||||||
\(523\) | −286879. | −1.04881 | −0.524404 | − | 0.851470i | \(-0.675712\pi\) | ||||
−0.524404 | + | 0.851470i | \(0.675712\pi\) | |||||||
\(524\) | −4029.53 | −0.0146754 | ||||||||
\(525\) | 63979.1 | 0.232124 | ||||||||
\(526\) | 218904.i | 0.791192i | ||||||||
\(527\) | 752315.i | 2.70881i | ||||||||
\(528\) | −83819.3 | −0.300660 | ||||||||
\(529\) | −170009. | −0.607520 | ||||||||
\(530\) | 4373.74i | 0.0155704i | ||||||||
\(531\) | 148418. | 0.526378 | ||||||||
\(532\) | 3507.46i | 0.0123928i | ||||||||
\(533\) | 408986. | 1.43964 | ||||||||
\(534\) | 262394. | 0.920176 | ||||||||
\(535\) | 5338.46i | 0.0186513i | ||||||||
\(536\) | −196283. | − | 204241.i | −0.683207 | − | 0.710907i | ||||
\(537\) | 245381. | 0.850927 | ||||||||
\(538\) | − | 209310.i | − | 0.723144i | ||||||
\(539\) | 123204.i | 0.424079i | ||||||||
\(540\) | 133.569 | 0.000458054 | ||||||||
\(541\) | 17631.0i | 0.0602397i | 0.999546 | + | 0.0301198i | \(0.00958889\pi\) | ||||
−0.999546 | + | 0.0301198i | \(0.990411\pi\) | |||||||
\(542\) | −493338. | −1.67937 | ||||||||
\(543\) | 207115.i | 0.702446i | ||||||||
\(544\) | − | 26830.9i | − | 0.0906647i | ||||||
\(545\) | 45715.5 | 0.153911 | ||||||||
\(546\) | −98762.4 | −0.331289 | ||||||||
\(547\) | 333837.i | 1.11573i | 0.829931 | + | 0.557866i | \(0.188380\pi\) | ||||
−0.829931 | + | 0.557866i | \(0.811620\pi\) | |||||||
\(548\) | 14809.7i | 0.0493156i | ||||||||
\(549\) | − | 91478.5i | − | 0.303511i | ||||||
\(550\) | 154349. | 0.510246 | ||||||||
\(551\) | 71053.7 | 0.234037 | ||||||||
\(552\) | 108666. | 0.356629 | ||||||||
\(553\) | 213280. | 0.697429 | ||||||||
\(554\) | − | 123196.i | − | 0.401400i | ||||||
\(555\) | −15674.2 | −0.0508861 | ||||||||
\(556\) | − | 2839.14i | − | 0.00918412i | ||||||
\(557\) | −60637.0 | −0.195446 | −0.0977231 | − | 0.995214i | \(-0.531156\pi\) | ||||
−0.0977231 | + | 0.995214i | \(0.531156\pi\) | |||||||
\(558\) | 170436. | 0.547385 | ||||||||
\(559\) | 190520. | 0.609702 | ||||||||
\(560\) | 11443.8 | 0.0364918 | ||||||||
\(561\) | −154122. | −0.489711 | ||||||||
\(562\) | 260976. | 0.826281 | ||||||||
\(563\) | − | 57207.8i | − | 0.180484i | −0.995920 | − | 0.0902420i | \(-0.971236\pi\) | ||
0.995920 | − | 0.0902420i | \(-0.0287640\pi\) | |||||||
\(564\) | 3891.30i | 0.0122331i | ||||||||
\(565\) | 44018.9 | 0.137893 | ||||||||
\(566\) | 175704.i | 0.548465i | ||||||||
\(567\) | 14473.1i | 0.0450189i | ||||||||
\(568\) | − | 29360.8i | − | 0.0910062i | ||||||
\(569\) | 304897. | 0.941734 | 0.470867 | − | 0.882204i | \(-0.343941\pi\) | ||||
0.470867 | + | 0.882204i | \(0.343941\pi\) | |||||||
\(570\) | 18811.7i | 0.0579000i | ||||||||
\(571\) | −354457. | −1.08716 | −0.543578 | − | 0.839359i | \(-0.682931\pi\) | ||||
−0.543578 | + | 0.839359i | \(0.682931\pi\) | |||||||
\(572\) | −6291.99 | −0.0192307 | ||||||||
\(573\) | 270944. | 0.825222 | ||||||||
\(574\) | 139382.i | 0.423043i | ||||||||
\(575\) | −205536. | −0.621658 | ||||||||
\(576\) | 107432. | 0.323808 | ||||||||
\(577\) | 462510.i | 1.38922i | 0.719389 | + | 0.694608i | \(0.244422\pi\) | ||||
−0.719389 | + | 0.694608i | \(0.755578\pi\) | |||||||
\(578\) | − | 607690.i | − | 1.81897i | ||||||
\(579\) | − | 163441.i | − | 0.487533i | ||||||
\(580\) | 166.172i | 0.000493971i | ||||||||
\(581\) | − | 11182.0i | − | 0.0331258i | ||||||
\(582\) | − | 230777.i | − | 0.681313i | ||||||
\(583\) | −30192.9 | −0.0888317 | ||||||||
\(584\) | − | 541863.i | − | 1.58878i | ||||||
\(585\) | −13988.0 | −0.0408737 | ||||||||
\(586\) | − | 315061.i | − | 0.917486i | ||||||
\(587\) | 211848.i | 0.614820i | 0.951577 | + | 0.307410i | \(0.0994624\pi\) | ||||
−0.951577 | + | 0.307410i | \(0.900538\pi\) | |||||||
\(588\) | 4525.51i | 0.0130892i | ||||||||
\(589\) | 633891.i | 1.82719i | ||||||||
\(590\) | −48885.6 | −0.140436 | ||||||||
\(591\) | −143679. | −0.411357 | ||||||||
\(592\) | 361300. | 1.03092 | ||||||||
\(593\) | − | 182460.i | − | 0.518871i | −0.965760 | − | 0.259435i | \(-0.916464\pi\) | ||
0.965760 | − | 0.259435i | \(-0.0835365\pi\) | |||||||
\(594\) | 34916.3i | 0.0989589i | ||||||||
\(595\) | 21042.3 | 0.0594373 | ||||||||
\(596\) | −2516.60 | −0.00708470 | ||||||||
\(597\) | 279258.i | 0.783531i | ||||||||
\(598\) | 317279. | 0.887235 | ||||||||
\(599\) | − | 127925.i | − | 0.356534i | −0.983982 | − | 0.178267i | \(-0.942951\pi\) | ||
0.983982 | − | 0.178267i | \(-0.0570490\pi\) | |||||||
\(600\) | −203355. | −0.564874 | ||||||||
\(601\) | 376156. | 1.04140 | 0.520702 | − | 0.853738i | \(-0.325670\pi\) | ||||
0.520702 | + | 0.853738i | \(0.325670\pi\) | |||||||
\(602\) | 64929.3i | 0.179163i | ||||||||
\(603\) | −87389.1 | + | 83984.0i | −0.240338 | + | 0.230973i | ||||
\(604\) | 4982.32 | 0.0136571 | ||||||||
\(605\) | 23850.5i | 0.0651609i | ||||||||
\(606\) | 323539.i | 0.881010i | ||||||||
\(607\) | −552472. | −1.49945 | −0.749726 | − | 0.661748i | \(-0.769815\pi\) | ||||
−0.749726 | + | 0.661748i | \(0.769815\pi\) | |||||||
\(608\) | − | 22607.4i | − | 0.0611567i | ||||||
\(609\) | −18005.9 | −0.0485489 | ||||||||
\(610\) | 30131.0i | 0.0809756i | ||||||||
\(611\) | − | 407518.i | − | 1.09160i | ||||||
\(612\) | −5661.20 | −0.0151149 | ||||||||
\(613\) | 130656. | 0.347703 | 0.173851 | − | 0.984772i | \(-0.444379\pi\) | ||||
0.173851 | + | 0.984772i | \(0.444379\pi\) | |||||||
\(614\) | − | 398983.i | − | 1.05832i | ||||||
\(615\) | 19741.1i | 0.0521942i | ||||||||
\(616\) | 76911.8i | 0.202690i | ||||||||
\(617\) | 251274. | 0.660051 | 0.330026 | − | 0.943972i | \(-0.392943\pi\) | ||||
0.330026 | + | 0.943972i | \(0.392943\pi\) | |||||||
\(618\) | 105227. | 0.275518 | ||||||||
\(619\) | 101077. | 0.263797 | 0.131899 | − | 0.991263i | \(-0.457893\pi\) | ||||
0.131899 | + | 0.991263i | \(0.457893\pi\) | |||||||
\(620\) | −1482.47 | −0.00385658 | ||||||||
\(621\) | − | 46495.4i | − | 0.120567i | ||||||
\(622\) | −479399. | −1.23913 | ||||||||
\(623\) | − | 247305.i | − | 0.637173i | ||||||
\(624\) | 322432. | 0.828075 | ||||||||
\(625\) | 381625. | 0.976959 | ||||||||
\(626\) | −382019. | −0.974847 | ||||||||
\(627\) | −129862. | −0.330328 | ||||||||
\(628\) | −14122.0 | −0.0358076 | ||||||||
\(629\) | 664338. | 1.67914 | ||||||||
\(630\) | − | 4767.11i | − | 0.0120109i | ||||||
\(631\) | − | 89295.7i | − | 0.224270i | −0.993693 | − | 0.112135i | \(-0.964231\pi\) | ||
0.993693 | − | 0.112135i | \(-0.0357690\pi\) | |||||||
\(632\) | −677900. | −1.69720 | ||||||||
\(633\) | − | 263625.i | − | 0.657930i | ||||||
\(634\) | − | 6767.58i | − | 0.0168366i | ||||||
\(635\) | − | 20326.5i | − | 0.0504097i | ||||||
\(636\) | −1109.04 | −0.00274179 | ||||||||
\(637\) | − | 473935.i | − | 1.16799i | ||||||
\(638\) | −43439.1 | −0.106718 | ||||||||
\(639\) | −12562.7 | −0.0307667 | ||||||||
\(640\) | −37334.9 | −0.0911497 | ||||||||
\(641\) | − | 218971.i | − | 0.532932i | −0.963844 | − | 0.266466i | \(-0.914144\pi\) | ||
0.963844 | − | 0.266466i | \(-0.0858559\pi\) | |||||||
\(642\) | −51260.4 | −0.124369 | ||||||||
\(643\) | −286522. | −0.693004 | −0.346502 | − | 0.938049i | \(-0.612631\pi\) | ||||
−0.346502 | + | 0.938049i | \(0.612631\pi\) | |||||||
\(644\) | 2855.42i | 0.00688490i | ||||||||
\(645\) | 9196.13i | 0.0221048i | ||||||||
\(646\) | − | 797319.i | − | 1.91059i | ||||||
\(647\) | 474638.i | 1.13385i | 0.823771 | + | 0.566923i | \(0.191866\pi\) | ||||
−0.823771 | + | 0.566923i | \(0.808134\pi\) | |||||||
\(648\) | − | 46002.0i | − | 0.109554i | ||||||
\(649\) | − | 337469.i | − | 0.801206i | ||||||
\(650\) | −593744. | −1.40531 | ||||||||
\(651\) | − | 160636.i | − | 0.379035i | ||||||
\(652\) | −17482.5 | −0.0411252 | ||||||||
\(653\) | 392898.i | 0.921412i | 0.887553 | + | 0.460706i | \(0.152404\pi\) | ||||
−0.887553 | + | 0.460706i | \(0.847596\pi\) | |||||||
\(654\) | 438964.i | 1.02630i | ||||||||
\(655\) | 20369.0i | 0.0474774i | ||||||||
\(656\) | − | 455046.i | − | 1.05742i | ||||||
\(657\) | −231849. | −0.537123 | ||||||||
\(658\) | 138882. | 0.320770 | ||||||||
\(659\) | −96696.5 | −0.222659 | −0.111329 | − | 0.993784i | \(-0.535511\pi\) | ||||
−0.111329 | + | 0.993784i | \(0.535511\pi\) | |||||||
\(660\) | − | 303.705i | − | 0.000697210i | ||||||
\(661\) | 50931.1i | 0.116568i | 0.998300 | + | 0.0582841i | \(0.0185629\pi\) | ||||
−0.998300 | + | 0.0582841i | \(0.981437\pi\) | |||||||
\(662\) | −108718. | −0.248077 | ||||||||
\(663\) | 592871. | 1.34875 | ||||||||
\(664\) | 35541.3i | 0.0806116i | ||||||||
\(665\) | 17730.0 | 0.0400927 | ||||||||
\(666\) | − | 150505.i | − | 0.339315i | ||||||
\(667\) | 57844.7 | 0.130021 | ||||||||
\(668\) | 13104.2 | 0.0293670 | ||||||||
\(669\) | − | 383445.i | − | 0.856745i | ||||||
\(670\) | 28784.0 | − | 27662.5i | 0.0641213 | − | 0.0616228i | ||||
\(671\) | −208001. | −0.461978 | ||||||||
\(672\) | 5728.99i | 0.0126864i | ||||||||
\(673\) | − | 596582.i | − | 1.31716i | −0.752509 | − | 0.658582i | \(-0.771156\pi\) | ||
0.752509 | − | 0.658582i | \(-0.228844\pi\) | |||||||
\(674\) | −514364. | −1.13227 | ||||||||
\(675\) | 87009.9i | 0.190968i | ||||||||
\(676\) | 11808.8 | 0.0258411 | ||||||||
\(677\) | − | 674717.i | − | 1.47212i | −0.676915 | − | 0.736062i | \(-0.736683\pi\) | ||
0.676915 | − | 0.736062i | \(-0.263317\pi\) | |||||||
\(678\) | 422674.i | 0.919487i | ||||||||
\(679\) | −217507. | −0.471773 | ||||||||
\(680\) | −66881.9 | −0.144641 | ||||||||
\(681\) | 18724.6i | 0.0403756i | ||||||||
\(682\) | − | 387533.i | − | 0.833182i | ||||||
\(683\) | 86363.0i | 0.185134i | 0.995706 | + | 0.0925671i | \(0.0295073\pi\) | ||||
−0.995706 | + | 0.0925671i | \(0.970493\pi\) | |||||||
\(684\) | −4770.06 | −0.0101956 | ||||||||
\(685\) | 74861.8 | 0.159544 | ||||||||
\(686\) | 354757. | 0.753846 | ||||||||
\(687\) | 72209.3 | 0.152996 | ||||||||
\(688\) | − | 211977.i | − | 0.447828i | ||||||
\(689\) | 116145. | 0.244659 | ||||||||
\(690\) | 15314.6i | 0.0321667i | ||||||||
\(691\) | −295298. | −0.618450 | −0.309225 | − | 0.950989i | \(-0.600070\pi\) | ||||
−0.309225 | + | 0.950989i | \(0.600070\pi\) | |||||||
\(692\) | −5164.03 | −0.0107839 | ||||||||
\(693\) | 32908.5 | 0.0685238 | ||||||||
\(694\) | 873830. | 1.81430 | ||||||||
\(695\) | −14351.7 | −0.0297121 | ||||||||
\(696\) | 57230.8 | 0.118144 | ||||||||
\(697\) | − | 836713.i | − | 1.72231i | ||||||
\(698\) | − | 289903.i | − | 0.595034i | ||||||
\(699\) | −356683. | −0.730009 | ||||||||
\(700\) | − | 5343.53i | − | 0.0109052i | ||||||
\(701\) | − | 219670.i | − | 0.447028i | −0.974701 | − | 0.223514i | \(-0.928247\pi\) | ||
0.974701 | − | 0.223514i | \(-0.0717529\pi\) | |||||||
\(702\) | − | 134314.i | − | 0.272551i | ||||||
\(703\) | 559763. | 1.13264 | ||||||||
\(704\) | − | 244275.i | − | 0.492872i | ||||||
\(705\) | 19670.3 | 0.0395760 | ||||||||
\(706\) | 738969. | 1.48257 | ||||||||
\(707\) | 304934. | 0.610052 | ||||||||
\(708\) | − | 12395.9i | − | 0.0247292i | ||||||
\(709\) | 315595. | 0.627824 | 0.313912 | − | 0.949452i | \(-0.398360\pi\) | ||||
0.313912 | + | 0.949452i | \(0.398360\pi\) | |||||||
\(710\) | 4137.87 | 0.00820843 | ||||||||
\(711\) | 290055.i | 0.573775i | ||||||||
\(712\) | 786048.i | 1.55056i | ||||||||
\(713\) | 516049.i | 1.01511i | ||||||||
\(714\) | 202050.i | 0.396336i | ||||||||
\(715\) | 31805.5i | 0.0622144i | ||||||||
\(716\) | − | 20494.2i | − | 0.0399765i | ||||||
\(717\) | 56791.0 | 0.110469 | ||||||||
\(718\) | 225158.i | 0.436756i | ||||||||
\(719\) | 249888. | 0.483379 | 0.241689 | − | 0.970354i | \(-0.422299\pi\) | ||||
0.241689 | + | 0.970354i | \(0.422299\pi\) | |||||||
\(720\) | 15563.3i | 0.0300218i | ||||||||
\(721\) | − | 99176.1i | − | 0.190782i | ||||||
\(722\) | − | 143505.i | − | 0.275291i | ||||||
\(723\) | 448234.i | 0.857488i | ||||||||
\(724\) | 17298.3 | 0.0330009 | ||||||||
\(725\) | −108249. | −0.205942 | ||||||||
\(726\) | −229015. | −0.434501 | ||||||||
\(727\) | 377046.i | 0.713387i | 0.934221 | + | 0.356693i | \(0.116096\pi\) | ||||
−0.934221 | + | 0.356693i | \(0.883904\pi\) | |||||||
\(728\) | − | 295861.i | − | 0.558245i | ||||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 76365.8 | 0.143302 | ||||||||
\(731\) | − | 389771.i | − | 0.729415i | ||||||
\(732\) | −7640.28 | −0.0142589 | ||||||||
\(733\) | − | 64904.6i | − | 0.120800i | −0.998174 | − | 0.0604001i | \(-0.980762\pi\) | ||
0.998174 | − | 0.0604001i | \(-0.0192377\pi\) | |||||||
\(734\) | 401511. | 0.745256 | ||||||||
\(735\) | 22876.1 | 0.0423456 | ||||||||
\(736\) | − | 18404.7i | − | 0.0339760i | ||||||
\(737\) | 190961. | + | 198703.i | 0.351567 | + | 0.365821i | ||||
\(738\) | −189557. | −0.348037 | ||||||||
\(739\) | 309648.i | 0.566996i | 0.958973 | + | 0.283498i | \(0.0914949\pi\) | ||||
−0.958973 | + | 0.283498i | \(0.908505\pi\) | |||||||
\(740\) | 1309.11i | 0.00239062i | ||||||||
\(741\) | 499545. | 0.909784 | ||||||||
\(742\) | 39582.1i | 0.0718937i | ||||||||
\(743\) | −917129. | −1.66132 | −0.830659 | − | 0.556782i | \(-0.812036\pi\) | ||||
−0.830659 | + | 0.556782i | \(0.812036\pi\) | |||||||
\(744\) | 510572.i | 0.922383i | ||||||||
\(745\) | 12721.2i | 0.0229201i | ||||||||
\(746\) | −849024. | −1.52561 | ||||||||
\(747\) | 15207.2 | 0.0272526 | ||||||||
\(748\) | 12872.3i | 0.0230066i | ||||||||
\(749\) | 48312.8i | 0.0861189i | ||||||||
\(750\) | − | 57540.7i | − | 0.102295i | ||||||
\(751\) | 531941. | 0.943156 | 0.471578 | − | 0.881824i | \(-0.343685\pi\) | ||||
0.471578 | + | 0.881824i | \(0.343685\pi\) | |||||||
\(752\) | −453412. | −0.801784 | ||||||||
\(753\) | −155675. | −0.274555 | ||||||||
\(754\) | 167100. | 0.293922 | ||||||||
\(755\) | − | 25185.3i | − | 0.0441827i | ||||||
\(756\) | 1208.79 | 0.00211498 | ||||||||
\(757\) | 1.10930e6i | 1.93578i | 0.251380 | + | 0.967889i | \(0.419116\pi\) | ||||
−0.251380 | + | 0.967889i | \(0.580884\pi\) | |||||||
\(758\) | 136725. | 0.237963 | ||||||||
\(759\) | −105720. | −0.183516 | ||||||||
\(760\) | −56353.9 | −0.0975656 | ||||||||
\(761\) | −770312. | −1.33014 | −0.665070 | − | 0.746781i | \(-0.731598\pi\) | ||||
−0.665070 | + | 0.746781i | \(0.731598\pi\) | |||||||
\(762\) | 195177. | 0.336138 | ||||||||
\(763\) | 413723. | 0.710657 | ||||||||
\(764\) | − | 22629.2i | − | 0.0387689i | ||||||
\(765\) | 28617.0i | 0.0488991i | ||||||||
\(766\) | 118509. | 0.201972 | ||||||||
\(767\) | 1.29816e6i | 2.20667i | ||||||||
\(768\) | − | 27689.7i | − | 0.0469457i | ||||||
\(769\) | 336459.i | 0.568956i | 0.958683 | + | 0.284478i | \(0.0918203\pi\) | ||||
−0.958683 | + | 0.284478i | \(0.908180\pi\) | |||||||
\(770\) | −10839.3 | −0.0182819 | ||||||||
\(771\) | − | 200172.i | − | 0.336740i | ||||||
\(772\) | −13650.6 | −0.0229043 | ||||||||
\(773\) | 575355. | 0.962891 | 0.481445 | − | 0.876476i | \(-0.340112\pi\) | ||||
0.481445 | + | 0.876476i | \(0.340112\pi\) | |||||||
\(774\) | −88302.2 | −0.147397 | ||||||||
\(775\) | − | 965716.i | − | 1.60785i | ||||||
\(776\) | 691334. | 1.14806 | ||||||||
\(777\) | −141851. | −0.234957 | ||||||||
\(778\) | − | 1.18061e6i | − | 1.95050i | ||||||
\(779\) | − | 705004.i | − | 1.16176i | ||||||
\(780\) | 1168.28i | 0.00192024i | ||||||||
\(781\) | 28564.7i | 0.0468303i | ||||||||
\(782\) | − | 649096.i | − | 1.06144i | ||||||
\(783\) | − | 24487.5i | − | 0.0399412i | ||||||
\(784\) | −527309. | −0.857894 | ||||||||
\(785\) | 71385.5i | 0.115843i | ||||||||
\(786\) | −195585. | −0.316585 | ||||||||
\(787\) | 29692.7i | 0.0479402i | 0.999713 | + | 0.0239701i | \(0.00763065\pi\) | ||||
−0.999713 | + | 0.0239701i | \(0.992369\pi\) | |||||||
\(788\) | 12000.1i | 0.0193255i | ||||||||
\(789\) | 280584.i | 0.450723i | ||||||||
\(790\) | − | 95537.8i | − | 0.153081i | ||||||
\(791\) | 398369. | 0.636696 | ||||||||
\(792\) | −104598. | −0.166753 | ||||||||
\(793\) | 800130. | 1.27237 | ||||||||
\(794\) | 1.08041e6i | 1.71375i | ||||||||
\(795\) | 5606.13i | 0.00887010i | ||||||||
\(796\) | 23323.6 | 0.0368103 | ||||||||
\(797\) | 85596.4 | 0.134753 | 0.0673766 | − | 0.997728i | \(-0.478537\pi\) | ||||
0.0673766 | + | 0.997728i | \(0.478537\pi\) | |||||||
\(798\) | 170245.i | 0.267343i | ||||||||
\(799\) | −833708. | −1.30593 | ||||||||
\(800\) | 34441.8i | 0.0538153i | ||||||||
\(801\) | 336329. | 0.524202 | ||||||||
\(802\) | 107595. | 0.167280 | ||||||||
\(803\) | 527171.i | 0.817561i | ||||||||
\(804\) | 7014.34 | + | 7298.73i | 0.0108511 | + | 0.0112911i | ||||
\(805\) | 14433.9 | 0.0222737 | ||||||||
\(806\) | 1.49074e6i | 2.29474i | ||||||||
\(807\) | − | 268287.i | − | 0.411958i | ||||||
\(808\) | −969218. | −1.48456 | ||||||||
\(809\) | − | 762900.i | − | 1.16566i | −0.812595 | − | 0.582828i | \(-0.801946\pi\) | ||
0.812595 | − | 0.582828i | \(-0.198054\pi\) | |||||||
\(810\) | 6483.15 | 0.00988134 | ||||||||
\(811\) | 1.01687e6i | 1.54606i | 0.634371 | + | 0.773029i | \(0.281259\pi\) | ||||
−0.634371 | + | 0.773029i | \(0.718741\pi\) | |||||||
\(812\) | 1503.85i | 0.00228083i | ||||||||
\(813\) | −632347. | −0.956697 | ||||||||
\(814\) | −342214. | −0.516475 | ||||||||
\(815\) | 88372.7i | 0.133046i | ||||||||
\(816\) | − | 659639.i | − | 0.990663i | ||||||
\(817\) | − | 328416.i | − | 0.492017i | ||||||
\(818\) | −724731. | −1.08310 | ||||||||
\(819\) | −126591. | −0.188727 | ||||||||
\(820\) | 1648.78 | 0.00245208 | ||||||||
\(821\) | 278756. | 0.413559 | 0.206779 | − | 0.978388i | \(-0.433702\pi\) | ||||
0.206779 | + | 0.978388i | \(0.433702\pi\) | |||||||
\(822\) | 718831.i | 1.06386i | ||||||||
\(823\) | 126757. | 0.187142 | 0.0935711 | − | 0.995613i | \(-0.470172\pi\) | ||||
0.0935711 | + | 0.995613i | \(0.470172\pi\) | |||||||
\(824\) | 315227.i | 0.464268i | ||||||||
\(825\) | 197841. | 0.290675 | ||||||||
\(826\) | −442413. | −0.648436 | ||||||||
\(827\) | 717778. | 1.04949 | 0.524746 | − | 0.851259i | \(-0.324160\pi\) | ||||
0.524746 | + | 0.851259i | \(0.324160\pi\) | |||||||
\(828\) | −3883.29 | −0.00566421 | ||||||||
\(829\) | 564602. | 0.821548 | 0.410774 | − | 0.911737i | \(-0.365258\pi\) | ||||
0.410774 | + | 0.911737i | \(0.365258\pi\) | |||||||
\(830\) | −5008.91 | −0.00727088 | ||||||||
\(831\) | − | 157909.i | − | 0.228668i | ||||||
\(832\) | 939668.i | 1.35746i | ||||||||
\(833\) | −969587. | −1.39732 | ||||||||
\(834\) | − | 137806.i | − | 0.198124i | ||||||
\(835\) | − | 66241.0i | − | 0.0950067i | ||||||
\(836\) | 10846.0i | 0.0155188i | ||||||||
\(837\) | 218460. | 0.311832 | ||||||||
\(838\) | 620704.i | 0.883886i | ||||||||
\(839\) | 700709. | 0.995437 | 0.497719 | − | 0.867339i | \(-0.334171\pi\) | ||||
0.497719 | + | 0.867339i | \(0.334171\pi\) | |||||||
\(840\) | 14280.8 | 0.0202392 | ||||||||
\(841\) | −676816. | −0.956927 | ||||||||
\(842\) | 956395.i | 1.34900i | ||||||||
\(843\) | 334511. | 0.470713 | ||||||||
\(844\) | −22017.9 | −0.0309095 | ||||||||
\(845\) | − | 59692.4i | − | 0.0835999i | ||||||
\(846\) | 188876.i | 0.263898i | ||||||||
\(847\) | 215846.i | 0.300869i | ||||||||
\(848\) | − | 129225.i | − | 0.179702i | ||||||
\(849\) | 225213.i | 0.312448i | ||||||||
\(850\) | 1.21470e6i | 1.68124i | ||||||||
\(851\) | 455702. | 0.629247 | ||||||||
\(852\) | 1049.23i | 0.00144542i | ||||||||
\(853\) | 118032. | 0.162219 | 0.0811093 | − | 0.996705i | \(-0.474154\pi\) | ||||
0.0811093 | + | 0.996705i | \(0.474154\pi\) | |||||||
\(854\) | 272684.i | 0.373890i | ||||||||
\(855\) | 24112.3i | 0.0329842i | ||||||||
\(856\) | − | 153560.i | − | 0.209571i | ||||||
\(857\) | − | 1.06958e6i | − | 1.45630i | −0.685417 | − | 0.728151i | \(-0.740380\pi\) | ||
0.685417 | − | 0.728151i | \(-0.259620\pi\) | |||||||
\(858\) | −305400. | −0.414853 | ||||||||
\(859\) | −30306.7 | −0.0410726 | −0.0205363 | − | 0.999789i | \(-0.506537\pi\) | ||||
−0.0205363 | + | 0.999789i | \(0.506537\pi\) | |||||||
\(860\) | 768.060 | 0.00103848 | ||||||||
\(861\) | 178656.i | 0.240997i | ||||||||
\(862\) | − | 1.39687e6i | − | 1.87992i | ||||||
\(863\) | 218235. | 0.293024 | 0.146512 | − | 0.989209i | \(-0.453195\pi\) | ||||
0.146512 | + | 0.989209i | \(0.453195\pi\) | |||||||
\(864\) | −7791.28 | −0.0104371 | ||||||||
\(865\) | 26103.8i | 0.0348876i | ||||||||
\(866\) | 697735. | 0.930368 | ||||||||
\(867\) | − | 778920.i | − | 1.03623i | ||||||
\(868\) | −13416.3 | −0.0178071 | ||||||||
\(869\) | 659520. | 0.873350 | ||||||||
\(870\) | 8065.65i | 0.0106562i | ||||||||
\(871\) | −734578. | − | 764361.i | −0.968282 | − | 1.00754i | ||||
\(872\) | −1.31500e6 | −1.72939 | ||||||||
\(873\) | − | 295803.i | − | 0.388127i | ||||||
\(874\) | − | 546920.i | − | 0.715980i | ||||||
\(875\) | −54231.9 | −0.0708335 | ||||||||
\(876\) | 19364.0i | 0.0252340i | ||||||||
\(877\) | 40301.6 | 0.0523991 | 0.0261995 | − | 0.999657i | \(-0.491659\pi\) | ||||
0.0261995 | + | 0.999657i | \(0.491659\pi\) | |||||||
\(878\) | 39392.9i | 0.0511009i | ||||||||
\(879\) | − | 403836.i | − | 0.522670i | ||||||
\(880\) | 35387.4 | 0.0456966 | ||||||||
\(881\) | −623690. | −0.803557 | −0.401779 | − | 0.915737i | \(-0.631608\pi\) | ||||
−0.401779 | + | 0.915737i | \(0.631608\pi\) | |||||||
\(882\) | 219659.i | 0.282366i | ||||||||
\(883\) | 435337.i | 0.558346i | 0.960241 | + | 0.279173i | \(0.0900604\pi\) | ||||
−0.960241 | + | 0.279173i | \(0.909940\pi\) | |||||||
\(884\) | − | 49516.5i | − | 0.0633644i | ||||||
\(885\) | −62660.2 | −0.0800028 | ||||||||
\(886\) | 1.26537e6 | 1.61195 | ||||||||
\(887\) | −1.34469e6 | −1.70913 | −0.854563 | − | 0.519348i | \(-0.826175\pi\) | ||||
−0.854563 | + | 0.519348i | \(0.826175\pi\) | |||||||
\(888\) | 450865. | 0.571769 | ||||||||
\(889\) | − | 183953.i | − | 0.232758i | ||||||
\(890\) | −110779. | −0.139855 | ||||||||
\(891\) | 44754.7i | 0.0563745i | ||||||||
\(892\) | −32025.3 | −0.0402498 | ||||||||
\(893\) | −702472. | −0.880899 | ||||||||
\(894\) | −122151. | −0.152834 | ||||||||
\(895\) | −103597. | −0.129330 | ||||||||
\(896\) | −337879. | −0.420868 | ||||||||
\(897\) | 406679. | 0.505437 | ||||||||
\(898\) | 1.21591e6i | 1.50782i | ||||||||
\(899\) | 271785.i | 0.336284i | ||||||||
\(900\) | 7267.06 | 0.00897168 | ||||||||
\(901\) | − | 237611.i | − | 0.292697i | ||||||
\(902\) | 431008.i | 0.529752i | ||||||||
\(903\) | 83224.5i | 0.102065i | ||||||||
\(904\) | −1.26620e6 | −1.54940 | ||||||||
\(905\) | − | 87441.5i | − | 0.106763i | ||||||
\(906\) | 241832. | 0.294616 | ||||||||
\(907\) | −299833. | −0.364472 | −0.182236 | − | 0.983255i | \(-0.558334\pi\) | ||||
−0.182236 | + | 0.983255i | \(0.558334\pi\) | |||||||
\(908\) | 1563.88 | 0.00189684 | ||||||||
\(909\) | 414702.i | 0.501890i | ||||||||
\(910\) | 41696.2 | 0.0503517 | ||||||||
\(911\) | −406913. | −0.490304 | −0.245152 | − | 0.969485i | \(-0.578838\pi\) | ||||
−0.245152 | + | 0.969485i | \(0.578838\pi\) | |||||||
\(912\) | − | 555804.i | − | 0.668239i | ||||||
\(913\) | − | 34577.7i | − | 0.0414815i | ||||||
\(914\) | 330124.i | 0.395171i | ||||||||
\(915\) | 38621.1i | 0.0461299i | ||||||||
\(916\) | − | 6030.91i | − | 0.00718774i | ||||||
\(917\) | 184338.i | 0.219218i | ||||||||
\(918\) | −274783. | −0.326065 | ||||||||
\(919\) | 888551.i | 1.05209i | 0.850458 | + | 0.526043i | \(0.176325\pi\) | ||||
−0.850458 | + | 0.526043i | \(0.823675\pi\) | |||||||
\(920\) | −45877.6 | −0.0542032 | ||||||||
\(921\) | − | 511404.i | − | 0.602900i | ||||||
\(922\) | 1.41998e6i | 1.67039i | ||||||||
\(923\) | − | 109881.i | − | 0.128979i | ||||||
\(924\) | − | 2748.51i | − | 0.00321924i | ||||||
\(925\) | −852784. | −0.996679 | ||||||||
\(926\) | 40283.3 | 0.0469789 | ||||||||
\(927\) | 134877. | 0.156956 | ||||||||
\(928\) | − | 9693.08i | − | 0.0112555i | ||||||
\(929\) | − | 287037.i | − | 0.332588i | −0.986076 | − | 0.166294i | \(-0.946820\pi\) | ||
0.986076 | − | 0.166294i | \(-0.0531801\pi\) | |||||||
\(930\) | −71955.9 | −0.0831957 | ||||||||
\(931\) | −816962. | −0.942546 | ||||||||
\(932\) | 29790.1i | 0.0342958i | ||||||||
\(933\) | −614480. | −0.705902 | ||||||||
\(934\) | − | 741128.i | − | 0.849571i | ||||||
\(935\) | 65068.5 | 0.0744299 | ||||||||
\(936\) | 402363. | 0.459268 | ||||||||
\(937\) | 1213.00i | 0.00138160i | 1.00000 | 0.000690800i | \(0.000219888\pi\) | |||||
−1.00000 | 0.000690800i | \(0.999780\pi\) | ||||||||
\(938\) | 260494. | − | 250344.i | 0.296069 | − | 0.284533i | ||||
\(939\) | −489661. | −0.555347 | ||||||||
\(940\) | − | 1642.86i | − | 0.00185928i | ||||||
\(941\) | − | 650986.i | − | 0.735178i | −0.929988 | − | 0.367589i | \(-0.880183\pi\) | ||
0.929988 | − | 0.367589i | \(-0.119817\pi\) | |||||||
\(942\) | −685451. | −0.772458 | ||||||||
\(943\) | − | 573942.i | − | 0.645423i | ||||||
\(944\) | 1.44436e6 | 1.62080 | ||||||||
\(945\) | − | 6110.35i | − | 0.00684230i | ||||||
\(946\) | 200779.i | 0.224355i | ||||||||
\(947\) | 324996. | 0.362392 | 0.181196 | − | 0.983447i | \(-0.442003\pi\) | ||||
0.181196 | + | 0.983447i | \(0.442003\pi\) | |||||||
\(948\) | 24225.4 | 0.0269559 | ||||||||
\(949\) | − | 2.02790e6i | − | 2.25171i | ||||||
\(950\) | 1.02349e6i | 1.13406i | ||||||||
\(951\) | − | 8674.49i | − | 0.00959142i | ||||||
\(952\) | −605278. | −0.667854 | ||||||||
\(953\) | 1.41035e6 | 1.55290 | 0.776448 | − | 0.630181i | \(-0.217019\pi\) | ||||
0.776448 | + | 0.630181i | \(0.217019\pi\) | |||||||
\(954\) | −53830.6 | −0.0591470 | ||||||||
\(955\) | −114389. | −0.125423 | ||||||||
\(956\) | − | 4743.18i | − | 0.00518984i | ||||||
\(957\) | −55679.0 | −0.0607950 | ||||||||
\(958\) | 809490.i | 0.882024i | ||||||||
\(959\) | 677496. | 0.736664 | ||||||||
\(960\) | −45356.3 | −0.0492148 | ||||||||
\(961\) | −1.50115e6 | −1.62546 | ||||||||
\(962\) | 1.31641e6 | 1.42247 | ||||||||
\(963\) | −65704.1 | −0.0708501 | ||||||||
\(964\) | 37436.4 | 0.0402847 | ||||||||
\(965\) | 69002.7i | 0.0740988i | ||||||||
\(966\) | 138596.i | 0.148524i | ||||||||
\(967\) | −197552. | −0.211266 | −0.105633 | − | 0.994405i | \(-0.533687\pi\) | ||||
−0.105633 | + | 0.994405i | \(0.533687\pi\) | |||||||
\(968\) | − | 686057.i | − | 0.732166i | ||||||
\(969\) | − | 1.02198e6i | − | 1.08842i | ||||||
\(970\) | 97431.1i | 0.103551i | ||||||||
\(971\) | −480283. | −0.509400 | −0.254700 | − | 0.967020i | \(-0.581977\pi\) | ||||
−0.254700 | + | 0.967020i | \(0.581977\pi\) | |||||||
\(972\) | 1643.92i | 0.00174000i | ||||||||
\(973\) | −129882. | −0.137190 | ||||||||
\(974\) | −487611. | −0.513992 | ||||||||
\(975\) | −761044. | −0.800573 | ||||||||
\(976\) | − | 890240.i | − | 0.934560i | ||||||
\(977\) | 1.54035e6 | 1.61373 | 0.806866 | − | 0.590735i | \(-0.201162\pi\) | ||||
0.806866 | + | 0.590735i | \(0.201162\pi\) | |||||||
\(978\) | −848564. | −0.887170 | ||||||||
\(979\) | − | 764734.i | − | 0.797894i | ||||||
\(980\) | − | 1910.61i | − | 0.00198939i | ||||||
\(981\) | 562652.i | 0.584658i | ||||||||
\(982\) | 1.18610e6i | 1.22998i | ||||||||
\(983\) | 1.18578e6i | 1.22715i | 0.789636 | + | 0.613575i | \(0.210269\pi\) | ||||
−0.789636 | + | 0.613575i | \(0.789731\pi\) | |||||||
\(984\) | − | 567851.i | − | 0.586468i | ||||||
\(985\) | 60659.6 | 0.0625211 | ||||||||
\(986\) | − | 341856.i | − | 0.351633i | ||||||
\(987\) | 178015. | 0.182735 | ||||||||
\(988\) | − | 41722.0i | − | 0.0427416i | ||||||
\(989\) | − | 267363.i | − | 0.273343i | ||||||
\(990\) | − | 14741.2i | − | 0.0150405i | ||||||
\(991\) | 92429.5i | 0.0941160i | 0.998892 | + | 0.0470580i | \(0.0149846\pi\) | ||||
−0.998892 | + | 0.0470580i | \(0.985015\pi\) | |||||||
\(992\) | 86474.8 | 0.0878752 | ||||||||
\(993\) | −139352. | −0.141324 | ||||||||
\(994\) | 37447.5 | 0.0379010 | ||||||||
\(995\) | − | 117899.i | − | 0.119087i | ||||||
\(996\) | − | 1270.10i | − | 0.00128032i | ||||||
\(997\) | −668935. | −0.672967 | −0.336484 | − | 0.941689i | \(-0.609238\pi\) | ||||
−0.336484 | + | 0.941689i | \(0.609238\pi\) | |||||||
\(998\) | −963758. | −0.967624 | ||||||||
\(999\) | − | 192913.i | − | 0.193299i |
(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 | 201.5.b.a.133.13 | ✓ | 46 | |
67.66 | odd | 2 | inner | 201.5.b.a.133.34 | yes | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.5.b.a.133.13 | ✓ | 46 | 1.1 | even | 1 | trivial | |
201.5.b.a.133.34 | yes | 46 | 67.66 | odd | 2 | inner |