Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,6,Mod(1,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("722.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(115.797117905\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2871 x^{13} - 4674 x^{12} + 3170019 x^{11} + 9081402 x^{10} - 1680307373 x^{9} - 6060225486 x^{8} + 437045334939 x^{7} + \cdots - 34\!\cdots\!72 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3\cdot 19^{6} \) |
Twist minimal: | no (minimal twist has level 38) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-12.5784\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −11.0464 | −0.708624 | −0.354312 | − | 0.935127i | \(-0.615285\pi\) | ||||
−0.354312 | + | 0.935127i | \(0.615285\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −52.2115 | −0.933988 | −0.466994 | − | 0.884261i | \(-0.654663\pi\) | ||||
−0.466994 | + | 0.884261i | \(0.654663\pi\) | |||||||
\(6\) | 44.1854 | 0.501073 | ||||||||
\(7\) | 215.645 | 1.66339 | 0.831697 | − | 0.555230i | \(-0.187370\pi\) | ||||
0.831697 | + | 0.555230i | \(0.187370\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | −120.978 | −0.497852 | ||||||||
\(10\) | 208.846 | 0.660429 | ||||||||
\(11\) | 546.889 | 1.36275 | 0.681377 | − | 0.731932i | \(-0.261381\pi\) | ||||
0.681377 | + | 0.731932i | \(0.261381\pi\) | |||||||
\(12\) | −176.742 | −0.354312 | ||||||||
\(13\) | −257.843 | −0.423152 | −0.211576 | − | 0.977362i | \(-0.567860\pi\) | ||||
−0.211576 | + | 0.977362i | \(0.567860\pi\) | |||||||
\(14\) | −862.581 | −1.17620 | ||||||||
\(15\) | 576.747 | 0.661846 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1895.04 | 1.59036 | 0.795181 | − | 0.606372i | \(-0.207376\pi\) | ||||
0.795181 | + | 0.606372i | \(0.207376\pi\) | |||||||
\(18\) | 483.912 | 0.352034 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −835.384 | −0.466994 | ||||||||
\(21\) | −2382.10 | −1.17872 | ||||||||
\(22\) | −2187.56 | −0.963613 | ||||||||
\(23\) | 2232.65 | 0.880038 | 0.440019 | − | 0.897989i | \(-0.354972\pi\) | ||||
0.440019 | + | 0.897989i | \(0.354972\pi\) | |||||||
\(24\) | 706.967 | 0.250536 | ||||||||
\(25\) | −398.958 | −0.127667 | ||||||||
\(26\) | 1031.37 | 0.299214 | ||||||||
\(27\) | 4020.63 | 1.06141 | ||||||||
\(28\) | 3450.32 | 0.831697 | ||||||||
\(29\) | 3582.58 | 0.791045 | 0.395522 | − | 0.918456i | \(-0.370564\pi\) | ||||
0.395522 | + | 0.918456i | \(0.370564\pi\) | |||||||
\(30\) | −2306.99 | −0.467996 | ||||||||
\(31\) | 8443.79 | 1.57809 | 0.789047 | − | 0.614332i | \(-0.210575\pi\) | ||||
0.789047 | + | 0.614332i | \(0.210575\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −6041.13 | −0.965681 | ||||||||
\(34\) | −7580.16 | −1.12456 | ||||||||
\(35\) | −11259.2 | −1.55359 | ||||||||
\(36\) | −1935.65 | −0.248926 | ||||||||
\(37\) | 3258.91 | 0.391353 | 0.195676 | − | 0.980669i | \(-0.437310\pi\) | ||||
0.195676 | + | 0.980669i | \(0.437310\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2848.22 | 0.299856 | ||||||||
\(40\) | 3341.54 | 0.330215 | ||||||||
\(41\) | −8960.15 | −0.832445 | −0.416222 | − | 0.909263i | \(-0.636646\pi\) | ||||
−0.416222 | + | 0.909263i | \(0.636646\pi\) | |||||||
\(42\) | 9528.38 | 0.833481 | ||||||||
\(43\) | 18035.6 | 1.48751 | 0.743753 | − | 0.668455i | \(-0.233044\pi\) | ||||
0.743753 | + | 0.668455i | \(0.233044\pi\) | |||||||
\(44\) | 8750.23 | 0.681377 | ||||||||
\(45\) | 6316.44 | 0.464988 | ||||||||
\(46\) | −8930.60 | −0.622281 | ||||||||
\(47\) | −20284.9 | −1.33945 | −0.669727 | − | 0.742607i | \(-0.733589\pi\) | ||||
−0.669727 | + | 0.742607i | \(0.733589\pi\) | |||||||
\(48\) | −2827.87 | −0.177156 | ||||||||
\(49\) | 29695.9 | 1.76688 | ||||||||
\(50\) | 1595.83 | 0.0902740 | ||||||||
\(51\) | −20933.3 | −1.12697 | ||||||||
\(52\) | −4125.48 | −0.211576 | ||||||||
\(53\) | −3592.76 | −0.175687 | −0.0878434 | − | 0.996134i | \(-0.527998\pi\) | ||||
−0.0878434 | + | 0.996134i | \(0.527998\pi\) | |||||||
\(54\) | −16082.5 | −0.750533 | ||||||||
\(55\) | −28553.9 | −1.27280 | ||||||||
\(56\) | −13801.3 | −0.588098 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −14330.3 | −0.559353 | ||||||||
\(59\) | 3069.98 | 0.114817 | 0.0574084 | − | 0.998351i | \(-0.481716\pi\) | ||||
0.0574084 | + | 0.998351i | \(0.481716\pi\) | |||||||
\(60\) | 9227.95 | 0.330923 | ||||||||
\(61\) | −5773.68 | −0.198668 | −0.0993340 | − | 0.995054i | \(-0.531671\pi\) | ||||
−0.0993340 | + | 0.995054i | \(0.531671\pi\) | |||||||
\(62\) | −33775.2 | −1.11588 | ||||||||
\(63\) | −26088.3 | −0.828123 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 13462.4 | 0.395219 | ||||||||
\(66\) | 24164.5 | 0.682839 | ||||||||
\(67\) | −38679.3 | −1.05267 | −0.526334 | − | 0.850278i | \(-0.676434\pi\) | ||||
−0.526334 | + | 0.850278i | \(0.676434\pi\) | |||||||
\(68\) | 30320.6 | 0.795181 | ||||||||
\(69\) | −24662.7 | −0.623616 | ||||||||
\(70\) | 45036.7 | 1.09855 | ||||||||
\(71\) | −42588.1 | −1.00263 | −0.501317 | − | 0.865264i | \(-0.667151\pi\) | ||||
−0.501317 | + | 0.865264i | \(0.667151\pi\) | |||||||
\(72\) | 7742.59 | 0.176017 | ||||||||
\(73\) | 44359.4 | 0.974269 | 0.487134 | − | 0.873327i | \(-0.338042\pi\) | ||||
0.487134 | + | 0.873327i | \(0.338042\pi\) | |||||||
\(74\) | −13035.6 | −0.276728 | ||||||||
\(75\) | 4407.04 | 0.0904677 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 117934. | 2.26680 | ||||||||
\(78\) | −11392.9 | −0.212030 | ||||||||
\(79\) | −11044.5 | −0.199104 | −0.0995520 | − | 0.995032i | \(-0.531741\pi\) | ||||
−0.0995520 | + | 0.995032i | \(0.531741\pi\) | |||||||
\(80\) | −13366.1 | −0.233497 | ||||||||
\(81\) | −15015.7 | −0.254292 | ||||||||
\(82\) | 35840.6 | 0.588627 | ||||||||
\(83\) | −21521.6 | −0.342910 | −0.171455 | − | 0.985192i | \(-0.554847\pi\) | ||||
−0.171455 | + | 0.985192i | \(0.554847\pi\) | |||||||
\(84\) | −38113.5 | −0.589360 | ||||||||
\(85\) | −98942.9 | −1.48538 | ||||||||
\(86\) | −72142.3 | −1.05183 | ||||||||
\(87\) | −39574.5 | −0.560554 | ||||||||
\(88\) | −35000.9 | −0.481807 | ||||||||
\(89\) | 61451.6 | 0.822353 | 0.411176 | − | 0.911556i | \(-0.365118\pi\) | ||||
0.411176 | + | 0.911556i | \(0.365118\pi\) | |||||||
\(90\) | −25265.8 | −0.328796 | ||||||||
\(91\) | −55602.6 | −0.703868 | ||||||||
\(92\) | 35722.4 | 0.440019 | ||||||||
\(93\) | −93273.1 | −1.11828 | ||||||||
\(94\) | 81139.5 | 0.947137 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 11311.5 | 0.125268 | ||||||||
\(97\) | −157318. | −1.69765 | −0.848827 | − | 0.528671i | \(-0.822691\pi\) | ||||
−0.848827 | + | 0.528671i | \(0.822691\pi\) | |||||||
\(98\) | −118784. | −1.24937 | ||||||||
\(99\) | −66161.6 | −0.678450 | ||||||||
\(100\) | −6383.33 | −0.0638333 | ||||||||
\(101\) | 77058.5 | 0.751652 | 0.375826 | − | 0.926690i | \(-0.377359\pi\) | ||||
0.375826 | + | 0.926690i | \(0.377359\pi\) | |||||||
\(102\) | 83733.1 | 0.796887 | ||||||||
\(103\) | −132907. | −1.23440 | −0.617200 | − | 0.786806i | \(-0.711733\pi\) | ||||
−0.617200 | + | 0.786806i | \(0.711733\pi\) | |||||||
\(104\) | 16501.9 | 0.149607 | ||||||||
\(105\) | 124373. | 1.10091 | ||||||||
\(106\) | 14371.1 | 0.124229 | ||||||||
\(107\) | −112225. | −0.947615 | −0.473808 | − | 0.880628i | \(-0.657121\pi\) | ||||
−0.473808 | + | 0.880628i | \(0.657121\pi\) | |||||||
\(108\) | 64330.1 | 0.530707 | ||||||||
\(109\) | 60711.5 | 0.489446 | 0.244723 | − | 0.969593i | \(-0.421303\pi\) | ||||
0.244723 | + | 0.969593i | \(0.421303\pi\) | |||||||
\(110\) | 114216. | 0.900003 | ||||||||
\(111\) | −35999.1 | −0.277322 | ||||||||
\(112\) | 55205.2 | 0.415848 | ||||||||
\(113\) | −44583.9 | −0.328459 | −0.164230 | − | 0.986422i | \(-0.552514\pi\) | ||||
−0.164230 | + | 0.986422i | \(0.552514\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −116570. | −0.821944 | ||||||||
\(116\) | 57321.3 | 0.395522 | ||||||||
\(117\) | 31193.3 | 0.210667 | ||||||||
\(118\) | −12279.9 | −0.0811877 | ||||||||
\(119\) | 408656. | 2.64540 | ||||||||
\(120\) | −36911.8 | −0.233998 | ||||||||
\(121\) | 138037. | 0.857100 | ||||||||
\(122\) | 23094.7 | 0.140479 | ||||||||
\(123\) | 98977.0 | 0.589891 | ||||||||
\(124\) | 135101. | 0.789047 | ||||||||
\(125\) | 183991. | 1.05323 | ||||||||
\(126\) | 104353. | 0.585572 | ||||||||
\(127\) | 306590. | 1.68674 | 0.843372 | − | 0.537331i | \(-0.180567\pi\) | ||||
0.843372 | + | 0.537331i | \(0.180567\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −199227. | −1.05408 | ||||||||
\(130\) | −53849.4 | −0.279462 | ||||||||
\(131\) | 19963.0 | 0.101636 | 0.0508181 | − | 0.998708i | \(-0.483817\pi\) | ||||
0.0508181 | + | 0.998708i | \(0.483817\pi\) | |||||||
\(132\) | −96658.1 | −0.482840 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 154717. | 0.744349 | ||||||||
\(135\) | −209923. | −0.991348 | ||||||||
\(136\) | −121283. | −0.562278 | ||||||||
\(137\) | 144949. | 0.659801 | 0.329900 | − | 0.944016i | \(-0.392985\pi\) | ||||
0.329900 | + | 0.944016i | \(0.392985\pi\) | |||||||
\(138\) | 98650.6 | 0.440963 | ||||||||
\(139\) | 91551.0 | 0.401907 | 0.200954 | − | 0.979601i | \(-0.435596\pi\) | ||||
0.200954 | + | 0.979601i | \(0.435596\pi\) | |||||||
\(140\) | −180147. | −0.776794 | ||||||||
\(141\) | 224074. | 0.949170 | ||||||||
\(142\) | 170352. | 0.708969 | ||||||||
\(143\) | −141011. | −0.576652 | ||||||||
\(144\) | −30970.4 | −0.124463 | ||||||||
\(145\) | −187052. | −0.738826 | ||||||||
\(146\) | −177438. | −0.688912 | ||||||||
\(147\) | −328031. | −1.25205 | ||||||||
\(148\) | 52142.6 | 0.195676 | ||||||||
\(149\) | −259829. | −0.958786 | −0.479393 | − | 0.877600i | \(-0.659143\pi\) | ||||
−0.479393 | + | 0.877600i | \(0.659143\pi\) | |||||||
\(150\) | −17628.1 | −0.0639703 | ||||||||
\(151\) | 172996. | 0.617438 | 0.308719 | − | 0.951153i | \(-0.400100\pi\) | ||||
0.308719 | + | 0.951153i | \(0.400100\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −229258. | −0.791764 | ||||||||
\(154\) | −471736. | −1.60287 | ||||||||
\(155\) | −440863. | −1.47392 | ||||||||
\(156\) | 45571.6 | 0.149928 | ||||||||
\(157\) | 32495.4 | 0.105214 | 0.0526070 | − | 0.998615i | \(-0.483247\pi\) | ||||
0.0526070 | + | 0.998615i | \(0.483247\pi\) | |||||||
\(158\) | 44178.2 | 0.140788 | ||||||||
\(159\) | 39687.0 | 0.124496 | ||||||||
\(160\) | 53464.6 | 0.165107 | ||||||||
\(161\) | 481461. | 1.46385 | ||||||||
\(162\) | 60062.7 | 0.179811 | ||||||||
\(163\) | 222554. | 0.656094 | 0.328047 | − | 0.944661i | \(-0.393610\pi\) | ||||
0.328047 | + | 0.944661i | \(0.393610\pi\) | |||||||
\(164\) | −143362. | −0.416222 | ||||||||
\(165\) | 315417. | 0.901934 | ||||||||
\(166\) | 86086.5 | 0.242474 | ||||||||
\(167\) | −401806. | −1.11487 | −0.557436 | − | 0.830220i | \(-0.688215\pi\) | ||||
−0.557436 | + | 0.830220i | \(0.688215\pi\) | |||||||
\(168\) | 152454. | 0.416741 | ||||||||
\(169\) | −304810. | −0.820942 | ||||||||
\(170\) | 395771. | 1.05032 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 288569. | 0.743753 | ||||||||
\(173\) | 289986. | 0.736652 | 0.368326 | − | 0.929697i | \(-0.379931\pi\) | ||||
0.368326 | + | 0.929697i | \(0.379931\pi\) | |||||||
\(174\) | 158298. | 0.396371 | ||||||||
\(175\) | −86033.5 | −0.212360 | ||||||||
\(176\) | 140004. | 0.340689 | ||||||||
\(177\) | −33912.1 | −0.0813619 | ||||||||
\(178\) | −245806. | −0.581491 | ||||||||
\(179\) | 308157. | 0.718852 | 0.359426 | − | 0.933174i | \(-0.382973\pi\) | ||||
0.359426 | + | 0.933174i | \(0.382973\pi\) | |||||||
\(180\) | 101063. | 0.232494 | ||||||||
\(181\) | 130725. | 0.296593 | 0.148296 | − | 0.988943i | \(-0.452621\pi\) | ||||
0.148296 | + | 0.988943i | \(0.452621\pi\) | |||||||
\(182\) | 222410. | 0.497710 | ||||||||
\(183\) | 63778.1 | 0.140781 | ||||||||
\(184\) | −142890. | −0.311140 | ||||||||
\(185\) | −170153. | −0.365519 | ||||||||
\(186\) | 373092. | 0.790741 | ||||||||
\(187\) | 1.03638e6 | 2.16727 | ||||||||
\(188\) | −324558. | −0.669727 | ||||||||
\(189\) | 867030. | 1.76555 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −828301. | −1.64288 | −0.821438 | − | 0.570297i | \(-0.806828\pi\) | ||||
−0.821438 | + | 0.570297i | \(0.806828\pi\) | |||||||
\(192\) | −45245.9 | −0.0885780 | ||||||||
\(193\) | 747808. | 1.44510 | 0.722548 | − | 0.691321i | \(-0.242971\pi\) | ||||
0.722548 | + | 0.691321i | \(0.242971\pi\) | |||||||
\(194\) | 629272. | 1.20042 | ||||||||
\(195\) | −148710. | −0.280062 | ||||||||
\(196\) | 475134. | 0.883438 | ||||||||
\(197\) | −716653. | −1.31566 | −0.657830 | − | 0.753167i | \(-0.728525\pi\) | ||||
−0.657830 | + | 0.753167i | \(0.728525\pi\) | |||||||
\(198\) | 264646. | 0.479736 | ||||||||
\(199\) | 256756. | 0.459608 | 0.229804 | − | 0.973237i | \(-0.426191\pi\) | ||||
0.229804 | + | 0.973237i | \(0.426191\pi\) | |||||||
\(200\) | 25533.3 | 0.0451370 | ||||||||
\(201\) | 427266. | 0.745947 | ||||||||
\(202\) | −308234. | −0.531498 | ||||||||
\(203\) | 772567. | 1.31582 | ||||||||
\(204\) | −334933. | −0.563484 | ||||||||
\(205\) | 467823. | 0.777493 | ||||||||
\(206\) | 531630. | 0.872853 | ||||||||
\(207\) | −270102. | −0.438128 | ||||||||
\(208\) | −66007.7 | −0.105788 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −497491. | −0.778461 | ||||||||
\(211\) | −300557. | −0.464751 | −0.232376 | − | 0.972626i | \(-0.574650\pi\) | ||||
−0.232376 | + | 0.972626i | \(0.574650\pi\) | |||||||
\(212\) | −57484.2 | −0.0878434 | ||||||||
\(213\) | 470443. | 0.710490 | ||||||||
\(214\) | 448902. | 0.670065 | ||||||||
\(215\) | −941664. | −1.38931 | ||||||||
\(216\) | −257320. | −0.375267 | ||||||||
\(217\) | 1.82086e6 | 2.62499 | ||||||||
\(218\) | −242846. | −0.346090 | ||||||||
\(219\) | −490010. | −0.690390 | ||||||||
\(220\) | −456863. | −0.636398 | ||||||||
\(221\) | −488622. | −0.672965 | ||||||||
\(222\) | 143996. | 0.196096 | ||||||||
\(223\) | 1.11984e6 | 1.50797 | 0.753984 | − | 0.656893i | \(-0.228130\pi\) | ||||
0.753984 | + | 0.656893i | \(0.228130\pi\) | |||||||
\(224\) | −220821. | −0.294049 | ||||||||
\(225\) | 48265.2 | 0.0635591 | ||||||||
\(226\) | 178335. | 0.232256 | ||||||||
\(227\) | −1.42711e6 | −1.83820 | −0.919099 | − | 0.394026i | \(-0.871082\pi\) | ||||
−0.919099 | + | 0.394026i | \(0.871082\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 843458. | 1.06286 | 0.531428 | − | 0.847103i | \(-0.321656\pi\) | ||||
0.531428 | + | 0.847103i | \(0.321656\pi\) | |||||||
\(230\) | 466280. | 0.581202 | ||||||||
\(231\) | −1.30274e6 | −1.60631 | ||||||||
\(232\) | −229285. | −0.279677 | ||||||||
\(233\) | 482086. | 0.581748 | 0.290874 | − | 0.956761i | \(-0.406054\pi\) | ||||
0.290874 | + | 0.956761i | \(0.406054\pi\) | |||||||
\(234\) | −124773. | −0.148964 | ||||||||
\(235\) | 1.05910e6 | 1.25103 | ||||||||
\(236\) | 49119.7 | 0.0574084 | ||||||||
\(237\) | 122002. | 0.141090 | ||||||||
\(238\) | −1.63463e6 | −1.87058 | ||||||||
\(239\) | 715888. | 0.810682 | 0.405341 | − | 0.914166i | \(-0.367153\pi\) | ||||
0.405341 | + | 0.914166i | \(0.367153\pi\) | |||||||
\(240\) | 147647. | 0.165462 | ||||||||
\(241\) | 1.58668e6 | 1.75973 | 0.879867 | − | 0.475220i | \(-0.157632\pi\) | ||||
0.879867 | + | 0.475220i | \(0.157632\pi\) | |||||||
\(242\) | −552147. | −0.606061 | ||||||||
\(243\) | −811145. | −0.881217 | ||||||||
\(244\) | −92378.8 | −0.0993340 | ||||||||
\(245\) | −1.55047e6 | −1.65024 | ||||||||
\(246\) | −395908. | −0.417116 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −540402. | −0.557941 | ||||||||
\(249\) | 237736. | 0.242994 | ||||||||
\(250\) | −735965. | −0.744744 | ||||||||
\(251\) | 280916. | 0.281444 | 0.140722 | − | 0.990049i | \(-0.455058\pi\) | ||||
0.140722 | + | 0.990049i | \(0.455058\pi\) | |||||||
\(252\) | −417413. | −0.414062 | ||||||||
\(253\) | 1.22101e6 | 1.19928 | ||||||||
\(254\) | −1.22636e6 | −1.19271 | ||||||||
\(255\) | 1.09296e6 | 1.05258 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.89954e6 | 1.79397 | 0.896985 | − | 0.442061i | \(-0.145752\pi\) | ||||
0.896985 | + | 0.442061i | \(0.145752\pi\) | |||||||
\(258\) | 796909. | 0.745349 | ||||||||
\(259\) | 702769. | 0.650973 | ||||||||
\(260\) | 215398. | 0.197609 | ||||||||
\(261\) | −433414. | −0.393823 | ||||||||
\(262\) | −79852.2 | −0.0718677 | ||||||||
\(263\) | 1.73196e6 | 1.54400 | 0.772000 | − | 0.635622i | \(-0.219256\pi\) | ||||
0.772000 | + | 0.635622i | \(0.219256\pi\) | |||||||
\(264\) | 386633. | 0.341420 | ||||||||
\(265\) | 187584. | 0.164089 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −678816. | −0.582739 | ||||||||
\(268\) | −618869. | −0.526334 | ||||||||
\(269\) | −575238. | −0.484693 | −0.242347 | − | 0.970190i | \(-0.577917\pi\) | ||||
−0.242347 | + | 0.970190i | \(0.577917\pi\) | |||||||
\(270\) | 839693. | 0.700989 | ||||||||
\(271\) | 1.71192e6 | 1.41599 | 0.707995 | − | 0.706218i | \(-0.249600\pi\) | ||||
0.707995 | + | 0.706218i | \(0.249600\pi\) | |||||||
\(272\) | 485130. | 0.397590 | ||||||||
\(273\) | 614206. | 0.498778 | ||||||||
\(274\) | −579795. | −0.466550 | ||||||||
\(275\) | −218186. | −0.173978 | ||||||||
\(276\) | −394603. | −0.311808 | ||||||||
\(277\) | −2.38150e6 | −1.86488 | −0.932442 | − | 0.361319i | \(-0.882326\pi\) | ||||
−0.932442 | + | 0.361319i | \(0.882326\pi\) | |||||||
\(278\) | −366204. | −0.284191 | ||||||||
\(279\) | −1.02151e6 | −0.785657 | ||||||||
\(280\) | 720587. | 0.549277 | ||||||||
\(281\) | 929370. | 0.702138 | 0.351069 | − | 0.936350i | \(-0.385818\pi\) | ||||
0.351069 | + | 0.936350i | \(0.385818\pi\) | |||||||
\(282\) | −896296. | −0.671164 | ||||||||
\(283\) | 321844. | 0.238880 | 0.119440 | − | 0.992841i | \(-0.461890\pi\) | ||||
0.119440 | + | 0.992841i | \(0.461890\pi\) | |||||||
\(284\) | −681409. | −0.501317 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 564046. | 0.407755 | ||||||||
\(287\) | −1.93221e6 | −1.38468 | ||||||||
\(288\) | 123881. | 0.0880086 | ||||||||
\(289\) | 2.17132e6 | 1.52925 | ||||||||
\(290\) | 748208. | 0.522429 | ||||||||
\(291\) | 1.73779e6 | 1.20300 | ||||||||
\(292\) | 709751. | 0.487134 | ||||||||
\(293\) | 287213. | 0.195450 | 0.0977250 | − | 0.995213i | \(-0.468843\pi\) | ||||
0.0977250 | + | 0.995213i | \(0.468843\pi\) | |||||||
\(294\) | 1.31213e6 | 0.885334 | ||||||||
\(295\) | −160288. | −0.107237 | ||||||||
\(296\) | −208570. | −0.138364 | ||||||||
\(297\) | 2.19884e6 | 1.44645 | ||||||||
\(298\) | 1.03932e6 | 0.677964 | ||||||||
\(299\) | −575673. | −0.372390 | ||||||||
\(300\) | 70512.6 | 0.0452338 | ||||||||
\(301\) | 3.88928e6 | 2.47431 | ||||||||
\(302\) | −691983. | −0.436595 | ||||||||
\(303\) | −851215. | −0.532639 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 301452. | 0.185554 | ||||||||
\(306\) | 917032. | 0.559862 | ||||||||
\(307\) | 71384.1 | 0.0432270 | 0.0216135 | − | 0.999766i | \(-0.493120\pi\) | ||||
0.0216135 | + | 0.999766i | \(0.493120\pi\) | |||||||
\(308\) | 1.88695e6 | 1.13340 | ||||||||
\(309\) | 1.46814e6 | 0.874726 | ||||||||
\(310\) | 1.76345e6 | 1.04222 | ||||||||
\(311\) | 1.91268e6 | 1.12135 | 0.560676 | − | 0.828035i | \(-0.310541\pi\) | ||||
0.560676 | + | 0.828035i | \(0.310541\pi\) | |||||||
\(312\) | −182286. | −0.106015 | ||||||||
\(313\) | 863929. | 0.498445 | 0.249222 | − | 0.968446i | \(-0.419825\pi\) | ||||
0.249222 | + | 0.968446i | \(0.419825\pi\) | |||||||
\(314\) | −129982. | −0.0743975 | ||||||||
\(315\) | 1.36211e6 | 0.773457 | ||||||||
\(316\) | −176713. | −0.0995520 | ||||||||
\(317\) | 2.49607e6 | 1.39511 | 0.697554 | − | 0.716532i | \(-0.254272\pi\) | ||||
0.697554 | + | 0.716532i | \(0.254272\pi\) | |||||||
\(318\) | −158748. | −0.0880319 | ||||||||
\(319\) | 1.95928e6 | 1.07800 | ||||||||
\(320\) | −213858. | −0.116748 | ||||||||
\(321\) | 1.23968e6 | 0.671503 | ||||||||
\(322\) | −1.92584e6 | −1.03510 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −240251. | −0.127146 | ||||||||
\(325\) | 102868. | 0.0540224 | ||||||||
\(326\) | −890215. | −0.463928 | ||||||||
\(327\) | −670641. | −0.346833 | ||||||||
\(328\) | 573449. | 0.294314 | ||||||||
\(329\) | −4.37434e6 | −2.22804 | ||||||||
\(330\) | −1.26167e6 | −0.637764 | ||||||||
\(331\) | −1.22909e6 | −0.616617 | −0.308308 | − | 0.951286i | \(-0.599763\pi\) | ||||
−0.308308 | + | 0.951286i | \(0.599763\pi\) | |||||||
\(332\) | −344346. | −0.171455 | ||||||||
\(333\) | −394257. | −0.194836 | ||||||||
\(334\) | 1.60722e6 | 0.788334 | ||||||||
\(335\) | 2.01951e6 | 0.983180 | ||||||||
\(336\) | −609816. | −0.294680 | ||||||||
\(337\) | −905116. | −0.434140 | −0.217070 | − | 0.976156i | \(-0.569650\pi\) | ||||
−0.217070 | + | 0.976156i | \(0.569650\pi\) | |||||||
\(338\) | 1.21924e6 | 0.580494 | ||||||||
\(339\) | 492489. | 0.232754 | ||||||||
\(340\) | −1.58309e6 | −0.742689 | ||||||||
\(341\) | 4.61782e6 | 2.15056 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.77943e6 | 1.27562 | ||||||||
\(344\) | −1.15428e6 | −0.525913 | ||||||||
\(345\) | 1.28767e6 | 0.582450 | ||||||||
\(346\) | −1.15995e6 | −0.520891 | ||||||||
\(347\) | −1.59170e6 | −0.709639 | −0.354819 | − | 0.934935i | \(-0.615458\pi\) | ||||
−0.354819 | + | 0.934935i | \(0.615458\pi\) | |||||||
\(348\) | −633192. | −0.280277 | ||||||||
\(349\) | −101389. | −0.0445582 | −0.0222791 | − | 0.999752i | \(-0.507092\pi\) | ||||
−0.0222791 | + | 0.999752i | \(0.507092\pi\) | |||||||
\(350\) | 344134. | 0.150161 | ||||||||
\(351\) | −1.03669e6 | −0.449140 | ||||||||
\(352\) | −560015. | −0.240903 | ||||||||
\(353\) | −1.12463e6 | −0.480365 | −0.240182 | − | 0.970728i | \(-0.577207\pi\) | ||||
−0.240182 | + | 0.970728i | \(0.577207\pi\) | |||||||
\(354\) | 135648. | 0.0575316 | ||||||||
\(355\) | 2.22359e6 | 0.936447 | ||||||||
\(356\) | 983225. | 0.411176 | ||||||||
\(357\) | −4.51416e6 | −1.87459 | ||||||||
\(358\) | −1.23263e6 | −0.508305 | ||||||||
\(359\) | −3.20159e6 | −1.31108 | −0.655540 | − | 0.755160i | \(-0.727559\pi\) | ||||
−0.655540 | + | 0.755160i | \(0.727559\pi\) | |||||||
\(360\) | −404252. | −0.164398 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −522898. | −0.209723 | ||||||||
\(363\) | −1.52480e6 | −0.607362 | ||||||||
\(364\) | −889641. | −0.351934 | ||||||||
\(365\) | −2.31607e6 | −0.909955 | ||||||||
\(366\) | −255112. | −0.0995472 | ||||||||
\(367\) | −1.66625e6 | −0.645764 | −0.322882 | − | 0.946439i | \(-0.604652\pi\) | ||||
−0.322882 | + | 0.946439i | \(0.604652\pi\) | |||||||
\(368\) | 571559. | 0.220009 | ||||||||
\(369\) | 1.08398e6 | 0.414434 | ||||||||
\(370\) | 680611. | 0.258461 | ||||||||
\(371\) | −774763. | −0.292236 | ||||||||
\(372\) | −1.49237e6 | −0.559138 | ||||||||
\(373\) | −4.06188e6 | −1.51166 | −0.755832 | − | 0.654765i | \(-0.772767\pi\) | ||||
−0.755832 | + | 0.654765i | \(0.772767\pi\) | |||||||
\(374\) | −4.14551e6 | −1.53249 | ||||||||
\(375\) | −2.03243e6 | −0.746342 | ||||||||
\(376\) | 1.29823e6 | 0.473569 | ||||||||
\(377\) | −923743. | −0.334732 | ||||||||
\(378\) | −3.46812e6 | −1.24843 | ||||||||
\(379\) | −122287. | −0.0437302 | −0.0218651 | − | 0.999761i | \(-0.506960\pi\) | ||||
−0.0218651 | + | 0.999761i | \(0.506960\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.38671e6 | −1.19527 | ||||||||
\(382\) | 3.31321e6 | 1.16169 | ||||||||
\(383\) | 1.42368e6 | 0.495925 | 0.247963 | − | 0.968770i | \(-0.420239\pi\) | ||||
0.247963 | + | 0.968770i | \(0.420239\pi\) | |||||||
\(384\) | 180984. | 0.0626341 | ||||||||
\(385\) | −6.15752e6 | −2.11716 | ||||||||
\(386\) | −2.99123e6 | −1.02184 | ||||||||
\(387\) | −2.18191e6 | −0.740557 | ||||||||
\(388\) | −2.51709e6 | −0.848827 | ||||||||
\(389\) | −2.08327e6 | −0.698026 | −0.349013 | − | 0.937118i | \(-0.613483\pi\) | ||||
−0.349013 | + | 0.937118i | \(0.613483\pi\) | |||||||
\(390\) | 594840. | 0.198034 | ||||||||
\(391\) | 4.23096e6 | 1.39958 | ||||||||
\(392\) | −1.90054e6 | −0.624685 | ||||||||
\(393\) | −220519. | −0.0720219 | ||||||||
\(394\) | 2.86661e6 | 0.930312 | ||||||||
\(395\) | 576652. | 0.185961 | ||||||||
\(396\) | −1.05858e6 | −0.339225 | ||||||||
\(397\) | 1.84336e6 | 0.586994 | 0.293497 | − | 0.955960i | \(-0.405181\pi\) | ||||
0.293497 | + | 0.955960i | \(0.405181\pi\) | |||||||
\(398\) | −1.02702e6 | −0.324992 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −102133. | −0.0319167 | ||||||||
\(401\) | 44488.5 | 0.0138161 | 0.00690807 | − | 0.999976i | \(-0.497801\pi\) | ||||
0.00690807 | + | 0.999976i | \(0.497801\pi\) | |||||||
\(402\) | −1.70906e6 | −0.527464 | ||||||||
\(403\) | −2.17717e6 | −0.667774 | ||||||||
\(404\) | 1.23294e6 | 0.375826 | ||||||||
\(405\) | 783991. | 0.237505 | ||||||||
\(406\) | −3.09027e6 | −0.930424 | ||||||||
\(407\) | 1.78226e6 | 0.533318 | ||||||||
\(408\) | 1.33973e6 | 0.398444 | ||||||||
\(409\) | 702028. | 0.207513 | 0.103757 | − | 0.994603i | \(-0.466914\pi\) | ||||
0.103757 | + | 0.994603i | \(0.466914\pi\) | |||||||
\(410\) | −1.87129e6 | −0.549771 | ||||||||
\(411\) | −1.60115e6 | −0.467551 | ||||||||
\(412\) | −2.12652e6 | −0.617200 | ||||||||
\(413\) | 662026. | 0.190985 | ||||||||
\(414\) | 1.08041e6 | 0.309803 | ||||||||
\(415\) | 1.12368e6 | 0.320274 | ||||||||
\(416\) | 264031. | 0.0748034 | ||||||||
\(417\) | −1.01131e6 | −0.284801 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.55566e6 | −1.54597 | −0.772984 | − | 0.634425i | \(-0.781237\pi\) | ||||
−0.772984 | + | 0.634425i | \(0.781237\pi\) | |||||||
\(420\) | 1.98996e6 | 0.550455 | ||||||||
\(421\) | 2.11205e6 | 0.580763 | 0.290382 | − | 0.956911i | \(-0.406218\pi\) | ||||
0.290382 | + | 0.956911i | \(0.406218\pi\) | |||||||
\(422\) | 1.20223e6 | 0.328629 | ||||||||
\(423\) | 2.45402e6 | 0.666850 | ||||||||
\(424\) | 229937. | 0.0621146 | ||||||||
\(425\) | −756042. | −0.203036 | ||||||||
\(426\) | −1.88177e6 | −0.502392 | ||||||||
\(427\) | −1.24507e6 | −0.330463 | ||||||||
\(428\) | −1.79561e6 | −0.473808 | ||||||||
\(429\) | 1.55766e6 | 0.408630 | ||||||||
\(430\) | 3.76666e6 | 0.982392 | ||||||||
\(431\) | −529667. | −0.137344 | −0.0686720 | − | 0.997639i | \(-0.521876\pi\) | ||||
−0.0686720 | + | 0.997639i | \(0.521876\pi\) | |||||||
\(432\) | 1.02928e6 | 0.265353 | ||||||||
\(433\) | −3.40387e6 | −0.872475 | −0.436238 | − | 0.899832i | \(-0.643689\pi\) | ||||
−0.436238 | + | 0.899832i | \(0.643689\pi\) | |||||||
\(434\) | −7.28345e6 | −1.85615 | ||||||||
\(435\) | 2.06624e6 | 0.523550 | ||||||||
\(436\) | 971384. | 0.244723 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 1.96004e6 | 0.488180 | ||||||||
\(439\) | −568141. | −0.140700 | −0.0703502 | − | 0.997522i | \(-0.522412\pi\) | ||||
−0.0703502 | + | 0.997522i | \(0.522412\pi\) | |||||||
\(440\) | 1.82745e6 | 0.450001 | ||||||||
\(441\) | −3.59255e6 | −0.879643 | ||||||||
\(442\) | 1.95449e6 | 0.475858 | ||||||||
\(443\) | 3.19364e6 | 0.773174 | 0.386587 | − | 0.922253i | \(-0.373654\pi\) | ||||
0.386587 | + | 0.922253i | \(0.373654\pi\) | |||||||
\(444\) | −575986. | −0.138661 | ||||||||
\(445\) | −3.20848e6 | −0.768067 | ||||||||
\(446\) | −4.47934e6 | −1.06629 | ||||||||
\(447\) | 2.87016e6 | 0.679419 | ||||||||
\(448\) | 883283. | 0.207924 | ||||||||
\(449\) | −1.27971e6 | −0.299567 | −0.149784 | − | 0.988719i | \(-0.547858\pi\) | ||||
−0.149784 | + | 0.988719i | \(0.547858\pi\) | |||||||
\(450\) | −193061. | −0.0449431 | ||||||||
\(451\) | −4.90021e6 | −1.13442 | ||||||||
\(452\) | −713342. | −0.164230 | ||||||||
\(453\) | −1.91097e6 | −0.437531 | ||||||||
\(454\) | 5.70843e6 | 1.29980 | ||||||||
\(455\) | 2.90309e6 | 0.657404 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.15509e6 | 1.15464 | 0.577319 | − | 0.816519i | \(-0.304099\pi\) | ||||
0.577319 | + | 0.816519i | \(0.304099\pi\) | |||||||
\(458\) | −3.37383e6 | −0.751553 | ||||||||
\(459\) | 7.61925e6 | 1.68803 | ||||||||
\(460\) | −1.86512e6 | −0.410972 | ||||||||
\(461\) | −3.73593e6 | −0.818742 | −0.409371 | − | 0.912368i | \(-0.634252\pi\) | ||||
−0.409371 | + | 0.912368i | \(0.634252\pi\) | |||||||
\(462\) | 5.21097e6 | 1.13583 | ||||||||
\(463\) | 7.57260e6 | 1.64170 | 0.820848 | − | 0.571147i | \(-0.193502\pi\) | ||||
0.820848 | + | 0.571147i | \(0.193502\pi\) | |||||||
\(464\) | 917141. | 0.197761 | ||||||||
\(465\) | 4.86993e6 | 1.04446 | ||||||||
\(466\) | −1.92834e6 | −0.411358 | ||||||||
\(467\) | −8.04618e6 | −1.70725 | −0.853626 | − | 0.520886i | \(-0.825602\pi\) | ||||
−0.853626 | + | 0.520886i | \(0.825602\pi\) | |||||||
\(468\) | 499093. | 0.105334 | ||||||||
\(469\) | −8.34101e6 | −1.75100 | ||||||||
\(470\) | −4.23642e6 | −0.884615 | ||||||||
\(471\) | −358956. | −0.0745571 | ||||||||
\(472\) | −196479. | −0.0405939 | ||||||||
\(473\) | 9.86346e6 | 2.02710 | ||||||||
\(474\) | −488008. | −0.0997656 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.53850e6 | 1.32270 | ||||||||
\(477\) | 434645. | 0.0874660 | ||||||||
\(478\) | −2.86355e6 | −0.573238 | ||||||||
\(479\) | −309721. | −0.0616782 | −0.0308391 | − | 0.999524i | \(-0.509818\pi\) | ||||
−0.0308391 | + | 0.999524i | \(0.509818\pi\) | |||||||
\(480\) | −590589. | −0.116999 | ||||||||
\(481\) | −840287. | −0.165602 | ||||||||
\(482\) | −6.34672e6 | −1.24432 | ||||||||
\(483\) | −5.31839e6 | −1.03732 | ||||||||
\(484\) | 2.20859e6 | 0.428550 | ||||||||
\(485\) | 8.21381e6 | 1.58559 | ||||||||
\(486\) | 3.24458e6 | 0.623114 | ||||||||
\(487\) | 3.23195e6 | 0.617508 | 0.308754 | − | 0.951142i | \(-0.400088\pi\) | ||||
0.308754 | + | 0.951142i | \(0.400088\pi\) | |||||||
\(488\) | 369515. | 0.0702397 | ||||||||
\(489\) | −2.45841e6 | −0.464924 | ||||||||
\(490\) | 6.20187e6 | 1.16690 | ||||||||
\(491\) | −7.32124e6 | −1.37051 | −0.685253 | − | 0.728305i | \(-0.740309\pi\) | ||||
−0.685253 | + | 0.728305i | \(0.740309\pi\) | |||||||
\(492\) | 1.58363e6 | 0.294945 | ||||||||
\(493\) | 6.78914e6 | 1.25805 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.45439e6 | 0.633664 | ||||||||
\(496\) | 2.16161e6 | 0.394524 | ||||||||
\(497\) | −9.18392e6 | −1.66777 | ||||||||
\(498\) | −950943. | −0.171823 | ||||||||
\(499\) | −4.31611e6 | −0.775963 | −0.387981 | − | 0.921667i | \(-0.626828\pi\) | ||||
−0.387981 | + | 0.921667i | \(0.626828\pi\) | |||||||
\(500\) | 2.94386e6 | 0.526613 | ||||||||
\(501\) | 4.43849e6 | 0.790026 | ||||||||
\(502\) | −1.12366e6 | −0.199011 | ||||||||
\(503\) | −4.64391e6 | −0.818396 | −0.409198 | − | 0.912446i | \(-0.634191\pi\) | ||||
−0.409198 | + | 0.912446i | \(0.634191\pi\) | |||||||
\(504\) | 1.66965e6 | 0.292786 | ||||||||
\(505\) | −4.02334e6 | −0.702034 | ||||||||
\(506\) | −4.88405e6 | −0.848016 | ||||||||
\(507\) | 3.36704e6 | 0.581740 | ||||||||
\(508\) | 4.90544e6 | 0.843372 | ||||||||
\(509\) | −7.29470e6 | −1.24800 | −0.623998 | − | 0.781426i | \(-0.714492\pi\) | ||||
−0.623998 | + | 0.781426i | \(0.714492\pi\) | |||||||
\(510\) | −4.37183e6 | −0.744283 | ||||||||
\(511\) | 9.56590e6 | 1.62059 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.59815e6 | −1.26853 | ||||||||
\(515\) | 6.93930e6 | 1.15292 | ||||||||
\(516\) | −3.18764e6 | −0.527041 | ||||||||
\(517\) | −1.10936e7 | −1.82535 | ||||||||
\(518\) | −2.81108e6 | −0.460308 | ||||||||
\(519\) | −3.20329e6 | −0.522009 | ||||||||
\(520\) | −861591. | −0.139731 | ||||||||
\(521\) | 7.11898e6 | 1.14901 | 0.574505 | − | 0.818501i | \(-0.305195\pi\) | ||||
0.574505 | + | 0.818501i | \(0.305195\pi\) | |||||||
\(522\) | 1.73365e6 | 0.278475 | ||||||||
\(523\) | 1.16755e7 | 1.86647 | 0.933237 | − | 0.359261i | \(-0.116971\pi\) | ||||
0.933237 | + | 0.359261i | \(0.116971\pi\) | |||||||
\(524\) | 319409. | 0.0508181 | ||||||||
\(525\) | 950357. | 0.150483 | ||||||||
\(526\) | −6.92782e6 | −1.09177 | ||||||||
\(527\) | 1.60013e7 | 2.50974 | ||||||||
\(528\) | −1.54653e6 | −0.241420 | ||||||||
\(529\) | −1.45161e6 | −0.225534 | ||||||||
\(530\) | −750335. | −0.116029 | ||||||||
\(531\) | −371400. | −0.0571617 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.31031e6 | 0.352251 | ||||||||
\(534\) | 2.71526e6 | 0.412059 | ||||||||
\(535\) | 5.85946e6 | 0.885061 | ||||||||
\(536\) | 2.47548e6 | 0.372175 | ||||||||
\(537\) | −3.40401e6 | −0.509396 | ||||||||
\(538\) | 2.30095e6 | 0.342730 | ||||||||
\(539\) | 1.62404e7 | 2.40782 | ||||||||
\(540\) | −3.35877e6 | −0.495674 | ||||||||
\(541\) | −5.42739e6 | −0.797256 | −0.398628 | − | 0.917113i | \(-0.630514\pi\) | ||||
−0.398628 | + | 0.917113i | \(0.630514\pi\) | |||||||
\(542\) | −6.84768e6 | −1.00126 | ||||||||
\(543\) | −1.44403e6 | −0.210173 | ||||||||
\(544\) | −1.94052e6 | −0.281139 | ||||||||
\(545\) | −3.16984e6 | −0.457136 | ||||||||
\(546\) | −2.45682e6 | −0.352689 | ||||||||
\(547\) | −1.85061e6 | −0.264452 | −0.132226 | − | 0.991220i | \(-0.542212\pi\) | ||||
−0.132226 | + | 0.991220i | \(0.542212\pi\) | |||||||
\(548\) | 2.31918e6 | 0.329900 | ||||||||
\(549\) | 698488. | 0.0989072 | ||||||||
\(550\) | 872744. | 0.123021 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1.57841e6 | 0.220482 | ||||||||
\(553\) | −2.38170e6 | −0.331188 | ||||||||
\(554\) | 9.52602e6 | 1.31867 | ||||||||
\(555\) | 1.87957e6 | 0.259015 | ||||||||
\(556\) | 1.46482e6 | 0.200954 | ||||||||
\(557\) | −3123.46 | −0.000426578 0 | −0.000213289 | − | 1.00000i | \(-0.500068\pi\) | ||||
−0.000213289 | 1.00000i | \(0.500068\pi\) | ||||||||
\(558\) | 4.08605e6 | 0.555544 | ||||||||
\(559\) | −4.65034e6 | −0.629441 | ||||||||
\(560\) | −2.88235e6 | −0.388397 | ||||||||
\(561\) | −1.14482e7 | −1.53578 | ||||||||
\(562\) | −3.71748e6 | −0.496487 | ||||||||
\(563\) | −3.45261e6 | −0.459068 | −0.229534 | − | 0.973301i | \(-0.573720\pi\) | ||||
−0.229534 | + | 0.973301i | \(0.573720\pi\) | |||||||
\(564\) | 3.58519e6 | 0.474585 | ||||||||
\(565\) | 2.32779e6 | 0.306777 | ||||||||
\(566\) | −1.28738e6 | −0.168914 | ||||||||
\(567\) | −3.23806e6 | −0.422987 | ||||||||
\(568\) | 2.72564e6 | 0.354484 | ||||||||
\(569\) | −9.38291e6 | −1.21495 | −0.607473 | − | 0.794341i | \(-0.707817\pi\) | ||||
−0.607473 | + | 0.794341i | \(0.707817\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.27080e6 | 1.06159 | 0.530796 | − | 0.847500i | \(-0.321893\pi\) | ||||
0.530796 | + | 0.847500i | \(0.321893\pi\) | |||||||
\(572\) | −2.25618e6 | −0.288326 | ||||||||
\(573\) | 9.14971e6 | 1.16418 | ||||||||
\(574\) | 7.72885e6 | 0.979119 | ||||||||
\(575\) | −890735. | −0.112351 | ||||||||
\(576\) | −495526. | −0.0622315 | ||||||||
\(577\) | −5.47580e6 | −0.684713 | −0.342356 | − | 0.939570i | \(-0.611225\pi\) | ||||
−0.342356 | + | 0.939570i | \(0.611225\pi\) | |||||||
\(578\) | −8.68527e6 | −1.08134 | ||||||||
\(579\) | −8.26055e6 | −1.02403 | ||||||||
\(580\) | −2.99283e6 | −0.369413 | ||||||||
\(581\) | −4.64104e6 | −0.570394 | ||||||||
\(582\) | −6.95116e6 | −0.850648 | ||||||||
\(583\) | −1.96484e6 | −0.239418 | ||||||||
\(584\) | −2.83900e6 | −0.344456 | ||||||||
\(585\) | −1.62865e6 | −0.196760 | ||||||||
\(586\) | −1.14885e6 | −0.138204 | ||||||||
\(587\) | −1.17010e7 | −1.40161 | −0.700806 | − | 0.713352i | \(-0.747176\pi\) | ||||
−0.700806 | + | 0.713352i | \(0.747176\pi\) | |||||||
\(588\) | −5.24850e6 | −0.626026 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 641153. | 0.0758283 | ||||||||
\(591\) | 7.91641e6 | 0.932308 | ||||||||
\(592\) | 834282. | 0.0978382 | ||||||||
\(593\) | −7.06987e6 | −0.825609 | −0.412805 | − | 0.910820i | \(-0.635451\pi\) | ||||
−0.412805 | + | 0.910820i | \(0.635451\pi\) | |||||||
\(594\) | −8.79536e6 | −1.02279 | ||||||||
\(595\) | −2.13366e7 | −2.47077 | ||||||||
\(596\) | −4.15726e6 | −0.479393 | ||||||||
\(597\) | −2.83622e6 | −0.325689 | ||||||||
\(598\) | 2.30269e6 | 0.263319 | ||||||||
\(599\) | 5.20555e6 | 0.592788 | 0.296394 | − | 0.955066i | \(-0.404216\pi\) | ||||
0.296394 | + | 0.955066i | \(0.404216\pi\) | |||||||
\(600\) | −282050. | −0.0319852 | ||||||||
\(601\) | 8.10399e6 | 0.915193 | 0.457597 | − | 0.889160i | \(-0.348710\pi\) | ||||
0.457597 | + | 0.889160i | \(0.348710\pi\) | |||||||
\(602\) | −1.55571e7 | −1.74960 | ||||||||
\(603\) | 4.67935e6 | 0.524073 | ||||||||
\(604\) | 2.76793e6 | 0.308719 | ||||||||
\(605\) | −7.20711e6 | −0.800521 | ||||||||
\(606\) | 3.40486e6 | 0.376633 | ||||||||
\(607\) | 5.55114e6 | 0.611520 | 0.305760 | − | 0.952109i | \(-0.401090\pi\) | ||||
0.305760 | + | 0.952109i | \(0.401090\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.53405e6 | −0.932421 | ||||||||
\(610\) | −1.20581e6 | −0.131206 | ||||||||
\(611\) | 5.23031e6 | 0.566793 | ||||||||
\(612\) | −3.66813e6 | −0.395882 | ||||||||
\(613\) | 1.00552e7 | 1.08079 | 0.540393 | − | 0.841413i | \(-0.318276\pi\) | ||||
0.540393 | + | 0.841413i | \(0.318276\pi\) | |||||||
\(614\) | −285536. | −0.0305661 | ||||||||
\(615\) | −5.16774e6 | −0.550951 | ||||||||
\(616\) | −7.54778e6 | −0.801434 | ||||||||
\(617\) | −1.57668e6 | −0.166736 | −0.0833681 | − | 0.996519i | \(-0.526568\pi\) | ||||
−0.0833681 | + | 0.996519i | \(0.526568\pi\) | |||||||
\(618\) | −5.87257e6 | −0.618525 | ||||||||
\(619\) | 1.15688e7 | 1.21356 | 0.606779 | − | 0.794871i | \(-0.292461\pi\) | ||||
0.606779 | + | 0.794871i | \(0.292461\pi\) | |||||||
\(620\) | −7.05381e6 | −0.736961 | ||||||||
\(621\) | 8.97666e6 | 0.934084 | ||||||||
\(622\) | −7.65073e6 | −0.792916 | ||||||||
\(623\) | 1.32517e7 | 1.36790 | ||||||||
\(624\) | 729145. | 0.0749639 | ||||||||
\(625\) | −8.35971e6 | −0.856035 | ||||||||
\(626\) | −3.45572e6 | −0.352454 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 519927. | 0.0526070 | ||||||||
\(629\) | 6.17577e6 | 0.622392 | ||||||||
\(630\) | −5.44844e6 | −0.546917 | ||||||||
\(631\) | −4.82735e6 | −0.482653 | −0.241327 | − | 0.970444i | \(-0.577583\pi\) | ||||
−0.241327 | + | 0.970444i | \(0.577583\pi\) | |||||||
\(632\) | 706851. | 0.0703939 | ||||||||
\(633\) | 3.32006e6 | 0.329334 | ||||||||
\(634\) | −9.98427e6 | −0.986491 | ||||||||
\(635\) | −1.60075e7 | −1.57540 | ||||||||
\(636\) | 634991. | 0.0622479 | ||||||||
\(637\) | −7.65687e6 | −0.747657 | ||||||||
\(638\) | −7.83710e6 | −0.762261 | ||||||||
\(639\) | 5.15222e6 | 0.499163 | ||||||||
\(640\) | 855433. | 0.0825536 | ||||||||
\(641\) | 2.00328e7 | 1.92573 | 0.962865 | − | 0.269982i | \(-0.0870177\pi\) | ||||
0.962865 | + | 0.269982i | \(0.0870177\pi\) | |||||||
\(642\) | −4.95873e6 | −0.474824 | ||||||||
\(643\) | 5.98749e6 | 0.571107 | 0.285553 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285553 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(644\) | 7.70337e6 | 0.731924 | ||||||||
\(645\) | 1.04020e7 | 0.984500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.64159e6 | 0.154172 | 0.0770859 | − | 0.997024i | \(-0.475438\pi\) | ||||
0.0770859 | + | 0.997024i | \(0.475438\pi\) | |||||||
\(648\) | 961003. | 0.0899057 | ||||||||
\(649\) | 1.67894e6 | 0.156467 | ||||||||
\(650\) | −411474. | −0.0381996 | ||||||||
\(651\) | −2.01139e7 | −1.86013 | ||||||||
\(652\) | 3.56086e6 | 0.328047 | ||||||||
\(653\) | −6.57658e6 | −0.603555 | −0.301778 | − | 0.953378i | \(-0.597580\pi\) | ||||
−0.301778 | + | 0.953378i | \(0.597580\pi\) | |||||||
\(654\) | 2.68256e6 | 0.245248 | ||||||||
\(655\) | −1.04230e6 | −0.0949270 | ||||||||
\(656\) | −2.29380e6 | −0.208111 | ||||||||
\(657\) | −5.36651e6 | −0.485041 | ||||||||
\(658\) | 1.74974e7 | 1.57546 | ||||||||
\(659\) | −1.35882e7 | −1.21884 | −0.609420 | − | 0.792847i | \(-0.708598\pi\) | ||||
−0.609420 | + | 0.792847i | \(0.708598\pi\) | |||||||
\(660\) | 5.04667e6 | 0.450967 | ||||||||
\(661\) | 9.37715e6 | 0.834771 | 0.417385 | − | 0.908730i | \(-0.362947\pi\) | ||||
0.417385 | + | 0.908730i | \(0.362947\pi\) | |||||||
\(662\) | 4.91638e6 | 0.436014 | ||||||||
\(663\) | 5.39749e6 | 0.476879 | ||||||||
\(664\) | 1.37738e6 | 0.121237 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.57703e6 | 0.137770 | ||||||||
\(667\) | 7.99866e6 | 0.696149 | ||||||||
\(668\) | −6.42890e6 | −0.557436 | ||||||||
\(669\) | −1.23701e7 | −1.06858 | ||||||||
\(670\) | −8.07802e6 | −0.695213 | ||||||||
\(671\) | −3.15756e6 | −0.270736 | ||||||||
\(672\) | 2.43927e6 | 0.208370 | ||||||||
\(673\) | 2.15238e7 | 1.83182 | 0.915908 | − | 0.401387i | \(-0.131472\pi\) | ||||
0.915908 | + | 0.401387i | \(0.131472\pi\) | |||||||
\(674\) | 3.62046e6 | 0.306983 | ||||||||
\(675\) | −1.60406e6 | −0.135507 | ||||||||
\(676\) | −4.87696e6 | −0.410471 | ||||||||
\(677\) | 1.44381e7 | 1.21071 | 0.605353 | − | 0.795957i | \(-0.293032\pi\) | ||||
0.605353 | + | 0.795957i | \(0.293032\pi\) | |||||||
\(678\) | −1.96996e6 | −0.164582 | ||||||||
\(679\) | −3.39249e7 | −2.82387 | ||||||||
\(680\) | 6.33234e6 | 0.525161 | ||||||||
\(681\) | 1.57644e7 | 1.30259 | ||||||||
\(682\) | −1.84713e7 | −1.52067 | ||||||||
\(683\) | −1.39407e7 | −1.14349 | −0.571747 | − | 0.820430i | \(-0.693734\pi\) | ||||
−0.571747 | + | 0.820430i | \(0.693734\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.56799e6 | −0.616246 | ||||||||
\(686\) | −1.11177e7 | −0.901997 | ||||||||
\(687\) | −9.31713e6 | −0.753166 | ||||||||
\(688\) | 4.61710e6 | 0.371876 | ||||||||
\(689\) | 926368. | 0.0743422 | ||||||||
\(690\) | −5.15070e6 | −0.411854 | ||||||||
\(691\) | 6.84023e6 | 0.544974 | 0.272487 | − | 0.962159i | \(-0.412154\pi\) | ||||
0.272487 | + | 0.962159i | \(0.412154\pi\) | |||||||
\(692\) | 4.63978e6 | 0.368326 | ||||||||
\(693\) | −1.42674e7 | −1.12853 | ||||||||
\(694\) | 6.36680e6 | 0.501790 | ||||||||
\(695\) | −4.78002e6 | −0.375377 | ||||||||
\(696\) | 2.53277e6 | 0.198186 | ||||||||
\(697\) | −1.69798e7 | −1.32389 | ||||||||
\(698\) | 405557. | 0.0315074 | ||||||||
\(699\) | −5.32529e6 | −0.412240 | ||||||||
\(700\) | −1.37654e6 | −0.106180 | ||||||||
\(701\) | −6.35337e6 | −0.488325 | −0.244162 | − | 0.969734i | \(-0.578513\pi\) | ||||
−0.244162 | + | 0.969734i | \(0.578513\pi\) | |||||||
\(702\) | 4.14676e6 | 0.317590 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.24006e6 | 0.170344 | ||||||||
\(705\) | −1.16992e7 | −0.886513 | ||||||||
\(706\) | 4.49850e6 | 0.339669 | ||||||||
\(707\) | 1.66173e7 | 1.25029 | ||||||||
\(708\) | −542593. | −0.0406810 | ||||||||
\(709\) | 1.29660e6 | 0.0968704 | 0.0484352 | − | 0.998826i | \(-0.484577\pi\) | ||||
0.0484352 | + | 0.998826i | \(0.484577\pi\) | |||||||
\(710\) | −8.89435e6 | −0.662168 | ||||||||
\(711\) | 1.33615e6 | 0.0991243 | ||||||||
\(712\) | −3.93290e6 | −0.290746 | ||||||||
\(713\) | 1.88520e7 | 1.38878 | ||||||||
\(714\) | 1.80567e7 | 1.32554 | ||||||||
\(715\) | 7.36242e6 | 0.538586 | ||||||||
\(716\) | 4.93051e6 | 0.359426 | ||||||||
\(717\) | −7.90795e6 | −0.574469 | ||||||||
\(718\) | 1.28064e7 | 0.927074 | ||||||||
\(719\) | 3.56565e6 | 0.257227 | 0.128614 | − | 0.991695i | \(-0.458947\pi\) | ||||
0.128614 | + | 0.991695i | \(0.458947\pi\) | |||||||
\(720\) | 1.61701e6 | 0.116247 | ||||||||
\(721\) | −2.86609e7 | −2.05329 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.75270e7 | −1.24699 | ||||||||
\(724\) | 2.09159e6 | 0.148296 | ||||||||
\(725\) | −1.42930e6 | −0.100990 | ||||||||
\(726\) | 6.09922e6 | 0.429470 | ||||||||
\(727\) | −4.17549e6 | −0.293003 | −0.146501 | − | 0.989210i | \(-0.546801\pi\) | ||||
−0.146501 | + | 0.989210i | \(0.546801\pi\) | |||||||
\(728\) | 3.55856e6 | 0.248855 | ||||||||
\(729\) | 1.26090e7 | 0.878743 | ||||||||
\(730\) | 9.26429e6 | 0.643435 | ||||||||
\(731\) | 3.41781e7 | 2.36567 | ||||||||
\(732\) | 1.02045e6 | 0.0703905 | ||||||||
\(733\) | 1.27641e7 | 0.877469 | 0.438734 | − | 0.898617i | \(-0.355427\pi\) | ||||
0.438734 | + | 0.898617i | \(0.355427\pi\) | |||||||
\(734\) | 6.66499e6 | 0.456624 | ||||||||
\(735\) | 1.71270e7 | 1.16940 | ||||||||
\(736\) | −2.28623e6 | −0.155570 | ||||||||
\(737\) | −2.11533e7 | −1.43453 | ||||||||
\(738\) | −4.33592e6 | −0.293049 | ||||||||
\(739\) | 1.59151e7 | 1.07201 | 0.536004 | − | 0.844215i | \(-0.319933\pi\) | ||||
0.536004 | + | 0.844215i | \(0.319933\pi\) | |||||||
\(740\) | −2.72244e6 | −0.182759 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.09905e6 | 0.206642 | ||||||||
\(743\) | 9.97067e6 | 0.662602 | 0.331301 | − | 0.943525i | \(-0.392513\pi\) | ||||
0.331301 | + | 0.943525i | \(0.392513\pi\) | |||||||
\(744\) | 5.96948e6 | 0.395370 | ||||||||
\(745\) | 1.35661e7 | 0.895495 | ||||||||
\(746\) | 1.62475e7 | 1.06891 | ||||||||
\(747\) | 2.60364e6 | 0.170718 | ||||||||
\(748\) | 1.65820e7 | 1.08364 | ||||||||
\(749\) | −2.42009e7 | −1.57626 | ||||||||
\(750\) | 8.12973e6 | 0.527744 | ||||||||
\(751\) | −550344. | −0.0356069 | −0.0178034 | − | 0.999842i | \(-0.505667\pi\) | ||||
−0.0178034 | + | 0.999842i | \(0.505667\pi\) | |||||||
\(752\) | −5.19293e6 | −0.334864 | ||||||||
\(753\) | −3.10309e6 | −0.199438 | ||||||||
\(754\) | 3.69497e6 | 0.236691 | ||||||||
\(755\) | −9.03237e6 | −0.576680 | ||||||||
\(756\) | 1.38725e7 | 0.882774 | ||||||||
\(757\) | −2.51587e7 | −1.59569 | −0.797843 | − | 0.602865i | \(-0.794026\pi\) | ||||
−0.797843 | + | 0.602865i | \(0.794026\pi\) | |||||||
\(758\) | 489147. | 0.0309219 | ||||||||
\(759\) | −1.34877e7 | −0.849835 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.64716e6 | 0.603862 | 0.301931 | − | 0.953330i | \(-0.402369\pi\) | ||||
0.301931 | + | 0.953330i | \(0.402369\pi\) | |||||||
\(762\) | 1.35468e7 | 0.845182 | ||||||||
\(763\) | 1.30921e7 | 0.814141 | ||||||||
\(764\) | −1.32528e7 | −0.821438 | ||||||||
\(765\) | 1.19699e7 | 0.739498 | ||||||||
\(766\) | −5.69473e6 | −0.350672 | ||||||||
\(767\) | −791572. | −0.0485849 | ||||||||
\(768\) | −723934. | −0.0442890 | ||||||||
\(769\) | −2.07985e7 | −1.26829 | −0.634143 | − | 0.773216i | \(-0.718647\pi\) | ||||
−0.634143 | + | 0.773216i | \(0.718647\pi\) | |||||||
\(770\) | 2.46301e7 | 1.49706 | ||||||||
\(771\) | −2.09830e7 | −1.27125 | ||||||||
\(772\) | 1.19649e7 | 0.722548 | ||||||||
\(773\) | 2.05987e7 | 1.23991 | 0.619955 | − | 0.784637i | \(-0.287151\pi\) | ||||
0.619955 | + | 0.784637i | \(0.287151\pi\) | |||||||
\(774\) | 8.72762e6 | 0.523653 | ||||||||
\(775\) | −3.36872e6 | −0.201470 | ||||||||
\(776\) | 1.00684e7 | 0.600211 | ||||||||
\(777\) | −7.76304e6 | −0.461296 | ||||||||
\(778\) | 8.33308e6 | 0.493579 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −2.37936e6 | −0.140031 | ||||||||
\(781\) | −2.32910e7 | −1.36634 | ||||||||
\(782\) | −1.69238e7 | −0.989651 | ||||||||
\(783\) | 1.44042e7 | 0.839626 | ||||||||
\(784\) | 7.60215e6 | 0.441719 | ||||||||
\(785\) | −1.69664e6 | −0.0982685 | ||||||||
\(786\) | 882076. | 0.0509272 | ||||||||
\(787\) | 3.14384e7 | 1.80935 | 0.904677 | − | 0.426098i | \(-0.140112\pi\) | ||||
0.904677 | + | 0.426098i | \(0.140112\pi\) | |||||||
\(788\) | −1.14665e7 | −0.657830 | ||||||||
\(789\) | −1.91318e7 | −1.09412 | ||||||||
\(790\) | −2.30661e6 | −0.131494 | ||||||||
\(791\) | −9.61430e6 | −0.546357 | ||||||||
\(792\) | 4.23434e6 | 0.239868 | ||||||||
\(793\) | 1.48870e6 | 0.0840668 | ||||||||
\(794\) | −7.37343e6 | −0.415067 | ||||||||
\(795\) | −2.07212e6 | −0.116278 | ||||||||
\(796\) | 4.10809e6 | 0.229804 | ||||||||
\(797\) | 1.25351e7 | 0.699006 | 0.349503 | − | 0.936935i | \(-0.386350\pi\) | ||||
0.349503 | + | 0.936935i | \(0.386350\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.84407e7 | −2.13022 | ||||||||
\(800\) | 408533. | 0.0225685 | ||||||||
\(801\) | −7.43429e6 | −0.409410 | ||||||||
\(802\) | −177954. | −0.00976949 | ||||||||
\(803\) | 2.42597e7 | 1.32769 | ||||||||
\(804\) | 6.83625e6 | 0.372973 | ||||||||
\(805\) | −2.51378e7 | −1.36722 | ||||||||
\(806\) | 8.70868e6 | 0.472188 | ||||||||
\(807\) | 6.35429e6 | 0.343465 | ||||||||
\(808\) | −4.93174e6 | −0.265749 | ||||||||
\(809\) | −1.51423e7 | −0.813432 | −0.406716 | − | 0.913555i | \(-0.633326\pi\) | ||||
−0.406716 | + | 0.913555i | \(0.633326\pi\) | |||||||
\(810\) | −3.13596e6 | −0.167942 | ||||||||
\(811\) | −3.18034e6 | −0.169793 | −0.0848967 | − | 0.996390i | \(-0.527056\pi\) | ||||
−0.0848967 | + | 0.996390i | \(0.527056\pi\) | |||||||
\(812\) | 1.23611e7 | 0.657909 | ||||||||
\(813\) | −1.89105e7 | −1.00340 | ||||||||
\(814\) | −7.12906e6 | −0.377113 | ||||||||
\(815\) | −1.16199e7 | −0.612784 | ||||||||
\(816\) | −5.35892e6 | −0.281742 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −2.80811e6 | −0.146734 | ||||||||
\(819\) | 6.72669e6 | 0.350422 | ||||||||
\(820\) | 7.48516e6 | 0.388747 | ||||||||
\(821\) | 1.60665e7 | 0.831885 | 0.415942 | − | 0.909391i | \(-0.363452\pi\) | ||||
0.415942 | + | 0.909391i | \(0.363452\pi\) | |||||||
\(822\) | 6.40462e6 | 0.330608 | ||||||||
\(823\) | 1.77578e7 | 0.913883 | 0.456941 | − | 0.889497i | \(-0.348945\pi\) | ||||
0.456941 | + | 0.889497i | \(0.348945\pi\) | |||||||
\(824\) | 8.50607e6 | 0.436426 | ||||||||
\(825\) | 2.41016e6 | 0.123285 | ||||||||
\(826\) | −2.64811e6 | −0.135047 | ||||||||
\(827\) | −1.79406e6 | −0.0912166 | −0.0456083 | − | 0.998959i | \(-0.514523\pi\) | ||||
−0.0456083 | + | 0.998959i | \(0.514523\pi\) | |||||||
\(828\) | −4.32163e6 | −0.219064 | ||||||||
\(829\) | −2.37927e7 | −1.20242 | −0.601212 | − | 0.799090i | \(-0.705315\pi\) | ||||
−0.601212 | + | 0.799090i | \(0.705315\pi\) | |||||||
\(830\) | −4.49471e6 | −0.226468 | ||||||||
\(831\) | 2.63069e7 | 1.32150 | ||||||||
\(832\) | −1.05612e6 | −0.0528940 | ||||||||
\(833\) | 5.62749e7 | 2.80997 | ||||||||
\(834\) | 4.04522e6 | 0.201385 | ||||||||
\(835\) | 2.09789e7 | 1.04128 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.39494e7 | 1.67501 | ||||||||
\(838\) | 2.22226e7 | 1.09316 | ||||||||
\(839\) | 4.82941e6 | 0.236859 | 0.118429 | − | 0.992962i | \(-0.462214\pi\) | ||||
0.118429 | + | 0.992962i | \(0.462214\pi\) | |||||||
\(840\) | −7.95986e6 | −0.389231 | ||||||||
\(841\) | −7.67625e6 | −0.374248 | ||||||||
\(842\) | −8.44820e6 | −0.410661 | ||||||||
\(843\) | −1.02661e7 | −0.497552 | ||||||||
\(844\) | −4.80891e6 | −0.232376 | ||||||||
\(845\) | 1.59146e7 | 0.766750 | ||||||||
\(846\) | −9.81610e6 | −0.471534 | ||||||||
\(847\) | 2.97670e7 | 1.42569 | ||||||||
\(848\) | −919748. | −0.0439217 | ||||||||
\(849\) | −3.55521e6 | −0.169276 | ||||||||
\(850\) | 3.02417e6 | 0.143568 | ||||||||
\(851\) | 7.27601e6 | 0.344405 | ||||||||
\(852\) | 7.52709e6 | 0.355245 | ||||||||
\(853\) | 2.91328e6 | 0.137091 | 0.0685456 | − | 0.997648i | \(-0.478164\pi\) | ||||
0.0685456 | + | 0.997648i | \(0.478164\pi\) | |||||||
\(854\) | 4.98027e6 | 0.233673 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.18243e6 | 0.335033 | ||||||||
\(857\) | −5.81789e6 | −0.270591 | −0.135295 | − | 0.990805i | \(-0.543198\pi\) | ||||
−0.135295 | + | 0.990805i | \(0.543198\pi\) | |||||||
\(858\) | −6.23065e6 | −0.288945 | ||||||||
\(859\) | 1.53027e7 | 0.707597 | 0.353799 | − | 0.935322i | \(-0.384890\pi\) | ||||
0.353799 | + | 0.935322i | \(0.384890\pi\) | |||||||
\(860\) | −1.50666e7 | −0.694656 | ||||||||
\(861\) | 2.13439e7 | 0.981220 | ||||||||
\(862\) | 2.11867e6 | 0.0971169 | ||||||||
\(863\) | 2.58064e7 | 1.17951 | 0.589754 | − | 0.807583i | \(-0.299225\pi\) | ||||
0.589754 | + | 0.807583i | \(0.299225\pi\) | |||||||
\(864\) | −4.11713e6 | −0.187633 | ||||||||
\(865\) | −1.51406e7 | −0.688024 | ||||||||
\(866\) | 1.36155e7 | 0.616933 | ||||||||
\(867\) | −2.39852e7 | −1.08366 | ||||||||
\(868\) | 2.91338e7 | 1.31250 | ||||||||
\(869\) | −6.04014e6 | −0.271330 | ||||||||
\(870\) | −8.26497e6 | −0.370206 | ||||||||
\(871\) | 9.97318e6 | 0.445439 | ||||||||
\(872\) | −3.88553e6 | −0.173045 | ||||||||
\(873\) | 1.90320e7 | 0.845180 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.96768e7 | 1.75193 | ||||||||
\(876\) | −7.84016e6 | −0.345195 | ||||||||
\(877\) | −4.01238e7 | −1.76158 | −0.880792 | − | 0.473503i | \(-0.842989\pi\) | ||||
−0.880792 | + | 0.473503i | \(0.842989\pi\) | |||||||
\(878\) | 2.27257e6 | 0.0994902 | ||||||||
\(879\) | −3.17266e6 | −0.138501 | ||||||||
\(880\) | −7.30980e6 | −0.318199 | ||||||||
\(881\) | −1.71504e7 | −0.744448 | −0.372224 | − | 0.928143i | \(-0.621405\pi\) | ||||
−0.372224 | + | 0.928143i | \(0.621405\pi\) | |||||||
\(882\) | 1.43702e7 | 0.622001 | ||||||||
\(883\) | 1.09709e7 | 0.473523 | 0.236762 | − | 0.971568i | \(-0.423914\pi\) | ||||
0.236762 | + | 0.971568i | \(0.423914\pi\) | |||||||
\(884\) | −7.81795e6 | −0.336482 | ||||||||
\(885\) | 1.77060e6 | 0.0759911 | ||||||||
\(886\) | −1.27746e7 | −0.546717 | ||||||||
\(887\) | 1.75319e7 | 0.748204 | 0.374102 | − | 0.927388i | \(-0.377951\pi\) | ||||
0.374102 | + | 0.927388i | \(0.377951\pi\) | |||||||
\(888\) | 2.30394e6 | 0.0980481 | ||||||||
\(889\) | 6.61147e7 | 2.80572 | ||||||||
\(890\) | 1.28339e7 | 0.543106 | ||||||||
\(891\) | −8.21191e6 | −0.346537 | ||||||||
\(892\) | 1.79174e7 | 0.753984 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −1.14807e7 | −0.480422 | ||||||||
\(895\) | −1.60893e7 | −0.671399 | ||||||||
\(896\) | −3.53313e6 | −0.147025 | ||||||||
\(897\) | 6.35909e6 | 0.263884 | ||||||||
\(898\) | 5.11882e6 | 0.211826 | ||||||||
\(899\) | 3.02506e7 | 1.24834 | ||||||||
\(900\) | 772243. | 0.0317795 | ||||||||
\(901\) | −6.80843e6 | −0.279406 | ||||||||
\(902\) | 1.96008e7 | 0.802155 | ||||||||
\(903\) | −4.29624e7 | −1.75335 | ||||||||
\(904\) | 2.85337e6 | 0.116128 | ||||||||
\(905\) | −6.82533e6 | −0.277014 | ||||||||
\(906\) | 7.64390e6 | 0.309381 | ||||||||
\(907\) | 4.35347e7 | 1.75718 | 0.878592 | − | 0.477573i | \(-0.158483\pi\) | ||||
0.878592 | + | 0.477573i | \(0.158483\pi\) | |||||||
\(908\) | −2.28337e7 | −0.919099 | ||||||||
\(909\) | −9.32238e6 | −0.374211 | ||||||||
\(910\) | −1.16124e7 | −0.464855 | ||||||||
\(911\) | 6.91498e6 | 0.276055 | 0.138027 | − | 0.990428i | \(-0.455924\pi\) | ||||
0.138027 | + | 0.990428i | \(0.455924\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.17699e7 | −0.467302 | ||||||||
\(914\) | −2.06204e7 | −0.816453 | ||||||||
\(915\) | −3.32995e6 | −0.131488 | ||||||||
\(916\) | 1.34953e7 | 0.531428 | ||||||||
\(917\) | 4.30494e6 | 0.169061 | ||||||||
\(918\) | −3.04770e7 | −1.19362 | ||||||||
\(919\) | 1.42108e7 | 0.555047 | 0.277523 | − | 0.960719i | \(-0.410486\pi\) | ||||
0.277523 | + | 0.960719i | \(0.410486\pi\) | |||||||
\(920\) | 7.46048e6 | 0.290601 | ||||||||
\(921\) | −788534. | −0.0306317 | ||||||||
\(922\) | 1.49437e7 | 0.578938 | ||||||||
\(923\) | 1.09810e7 | 0.424266 | ||||||||
\(924\) | −2.08439e7 | −0.803153 | ||||||||
\(925\) | −1.30017e6 | −0.0499627 | ||||||||
\(926\) | −3.02904e7 | −1.16085 | ||||||||
\(927\) | 1.60789e7 | 0.614549 | ||||||||
\(928\) | −3.66856e6 | −0.139838 | ||||||||
\(929\) | −4.49843e6 | −0.171010 | −0.0855051 | − | 0.996338i | \(-0.527250\pi\) | ||||
−0.0855051 | + | 0.996338i | \(0.527250\pi\) | |||||||
\(930\) | −1.94797e7 | −0.738542 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.71338e6 | 0.290874 | ||||||||
\(933\) | −2.11282e7 | −0.794618 | ||||||||
\(934\) | 3.21847e7 | 1.20721 | ||||||||
\(935\) | −5.41108e7 | −2.02421 | ||||||||
\(936\) | −1.99637e6 | −0.0744820 | ||||||||
\(937\) | −1.97821e7 | −0.736078 | −0.368039 | − | 0.929810i | \(-0.619971\pi\) | ||||
−0.368039 | + | 0.929810i | \(0.619971\pi\) | |||||||
\(938\) | 3.33640e7 | 1.23815 | ||||||||
\(939\) | −9.54327e6 | −0.353210 | ||||||||
\(940\) | 1.69457e7 | 0.625517 | ||||||||
\(941\) | 4.01748e6 | 0.147904 | 0.0739519 | − | 0.997262i | \(-0.476439\pi\) | ||||
0.0739519 | + | 0.997262i | \(0.476439\pi\) | |||||||
\(942\) | 1.43583e6 | 0.0527199 | ||||||||
\(943\) | −2.00049e7 | −0.732583 | ||||||||
\(944\) | 785914. | 0.0287042 | ||||||||
\(945\) | −4.52690e7 | −1.64900 | ||||||||
\(946\) | −3.94538e7 | −1.43338 | ||||||||
\(947\) | −1.27746e7 | −0.462884 | −0.231442 | − | 0.972849i | \(-0.574344\pi\) | ||||
−0.231442 | + | 0.972849i | \(0.574344\pi\) | |||||||
\(948\) | 1.95203e6 | 0.0705449 | ||||||||
\(949\) | −1.14378e7 | −0.412264 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.75725e7 | −0.988608 | ||||||||
\(952\) | −2.61540e7 | −0.935289 | ||||||||
\(953\) | 2.59500e7 | 0.925561 | 0.462781 | − | 0.886473i | \(-0.346852\pi\) | ||||
0.462781 | + | 0.886473i | \(0.346852\pi\) | |||||||
\(954\) | −1.73858e6 | −0.0618478 | ||||||||
\(955\) | 4.32469e7 | 1.53443 | ||||||||
\(956\) | 1.14542e7 | 0.405341 | ||||||||
\(957\) | −2.16429e7 | −0.763897 | ||||||||
\(958\) | 1.23888e6 | 0.0436131 | ||||||||
\(959\) | 3.12575e7 | 1.09751 | ||||||||
\(960\) | 2.36236e6 | 0.0827308 | ||||||||
\(961\) | 4.26684e7 | 1.49038 | ||||||||
\(962\) | 3.36115e6 | 0.117098 | ||||||||
\(963\) | 1.35768e7 | 0.471772 | ||||||||
\(964\) | 2.53869e7 | 0.879867 | ||||||||
\(965\) | −3.90442e7 | −1.34970 | ||||||||
\(966\) | 2.12735e7 | 0.733495 | ||||||||
\(967\) | 3.62654e7 | 1.24717 | 0.623586 | − | 0.781755i | \(-0.285675\pi\) | ||||
0.623586 | + | 0.781755i | \(0.285675\pi\) | |||||||
\(968\) | −8.83436e6 | −0.303031 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.28552e7 | −1.12118 | ||||||||
\(971\) | −7.02568e6 | −0.239133 | −0.119567 | − | 0.992826i | \(-0.538151\pi\) | ||||
−0.119567 | + | 0.992826i | \(0.538151\pi\) | |||||||
\(972\) | −1.29783e7 | −0.440608 | ||||||||
\(973\) | 1.97425e7 | 0.668530 | ||||||||
\(974\) | −1.29278e7 | −0.436644 | ||||||||
\(975\) | −1.13632e6 | −0.0382816 | ||||||||
\(976\) | −1.47806e6 | −0.0496670 | ||||||||
\(977\) | 3.44151e7 | 1.15349 | 0.576744 | − | 0.816925i | \(-0.304323\pi\) | ||||
0.576744 | + | 0.816925i | \(0.304323\pi\) | |||||||
\(978\) | 9.83363e6 | 0.328751 | ||||||||
\(979\) | 3.36072e7 | 1.12066 | ||||||||
\(980\) | −2.48075e7 | −0.825121 | ||||||||
\(981\) | −7.34475e6 | −0.243671 | ||||||||
\(982\) | 2.92850e7 | 0.969095 | ||||||||
\(983\) | −9.27370e6 | −0.306104 | −0.153052 | − | 0.988218i | \(-0.548910\pi\) | ||||
−0.153052 | + | 0.988218i | \(0.548910\pi\) | |||||||
\(984\) | −6.33453e6 | −0.208558 | ||||||||
\(985\) | 3.74176e7 | 1.22881 | ||||||||
\(986\) | −2.71565e7 | −0.889574 | ||||||||
\(987\) | 4.83205e7 | 1.57884 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.02671e7 | 1.30906 | ||||||||
\(990\) | −1.38176e7 | −0.448068 | ||||||||
\(991\) | −3.75908e7 | −1.21590 | −0.607950 | − | 0.793975i | \(-0.708008\pi\) | ||||
−0.607950 | + | 0.793975i | \(0.708008\pi\) | |||||||
\(992\) | −8.64644e6 | −0.278970 | ||||||||
\(993\) | 1.35770e7 | 0.436949 | ||||||||
\(994\) | 3.67357e7 | 1.17929 | ||||||||
\(995\) | −1.34056e7 | −0.429268 | ||||||||
\(996\) | 3.80377e6 | 0.121497 | ||||||||
\(997\) | −7.17501e6 | −0.228605 | −0.114302 | − | 0.993446i | \(-0.536463\pi\) | ||||
−0.114302 | + | 0.993446i | \(0.536463\pi\) | |||||||
\(998\) | 1.72644e7 | 0.548689 | ||||||||
\(999\) | 1.31029e7 | 0.415387 |
(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 | 722.6.a.q.1.5 | 15 | ||
19.14 | odd | 18 | 38.6.e.b.25.2 | ✓ | 30 | ||
19.15 | odd | 18 | 38.6.e.b.35.2 | yes | 30 | ||
19.18 | odd | 2 | 722.6.a.r.1.11 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.6.e.b.25.2 | ✓ | 30 | 19.14 | odd | 18 | ||
38.6.e.b.35.2 | yes | 30 | 19.15 | odd | 18 | ||
722.6.a.q.1.5 | 15 | 1.1 | even | 1 | trivial | ||
722.6.a.r.1.11 | 15 | 19.18 | odd | 2 |