Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(167.601091705\) |
Analytic rank: | \(1\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.8606 | −1.91989 | −0.959947 | − | 0.280182i | \(-0.909605\pi\) | ||||
−0.959947 | + | 0.280182i | \(0.909605\pi\) | |||||||
\(3\) | 27.1939 | 1.74449 | 0.872245 | − | 0.489069i | \(-0.162663\pi\) | ||||
0.872245 | + | 0.489069i | \(0.162663\pi\) | |||||||
\(4\) | 85.9518 | 2.68599 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −295.341 | −3.34924 | ||||||||
\(7\) | −206.298 | −1.59129 | −0.795647 | − | 0.605760i | \(-0.792869\pi\) | ||||
−0.795647 | + | 0.605760i | \(0.792869\pi\) | |||||||
\(8\) | −585.946 | −3.23693 | ||||||||
\(9\) | 496.509 | 2.04325 | ||||||||
\(10\) | −271.514 | −0.858603 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 2337.36 | 4.68569 | ||||||||
\(13\) | −408.237 | −0.669968 | −0.334984 | − | 0.942224i | \(-0.608731\pi\) | ||||
−0.334984 | + | 0.942224i | \(0.608731\pi\) | |||||||
\(14\) | 2240.51 | 3.05512 | ||||||||
\(15\) | 679.848 | 0.780160 | ||||||||
\(16\) | 3613.25 | 3.52856 | ||||||||
\(17\) | 1567.58 | 1.31555 | 0.657775 | − | 0.753214i | \(-0.271498\pi\) | ||||
0.657775 | + | 0.753214i | \(0.271498\pi\) | |||||||
\(18\) | −5392.36 | −3.92282 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | 2148.79 | 1.20121 | ||||||||
\(21\) | −5610.06 | −2.77600 | ||||||||
\(22\) | −1314.13 | −0.578870 | ||||||||
\(23\) | −2541.47 | −1.00176 | −0.500881 | − | 0.865516i | \(-0.666991\pi\) | ||||
−0.500881 | + | 0.865516i | \(0.666991\pi\) | |||||||
\(24\) | −15934.2 | −5.64679 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 4433.69 | 1.28627 | ||||||||
\(27\) | 6893.90 | 1.81993 | ||||||||
\(28\) | −17731.7 | −4.27420 | ||||||||
\(29\) | 4581.22 | 1.01155 | 0.505773 | − | 0.862666i | \(-0.331207\pi\) | ||||
0.505773 | + | 0.862666i | \(0.331207\pi\) | |||||||
\(30\) | −7383.53 | −1.49782 | ||||||||
\(31\) | −4714.60 | −0.881130 | −0.440565 | − | 0.897721i | \(-0.645222\pi\) | ||||
−0.440565 | + | 0.897721i | \(0.645222\pi\) | |||||||
\(32\) | −20491.6 | −3.53754 | ||||||||
\(33\) | 3290.46 | 0.525984 | ||||||||
\(34\) | −17024.8 | −2.52572 | ||||||||
\(35\) | −5157.46 | −0.711648 | ||||||||
\(36\) | 42675.8 | 5.48814 | ||||||||
\(37\) | 490.812 | 0.0589401 | 0.0294700 | − | 0.999566i | \(-0.490618\pi\) | ||||
0.0294700 | + | 0.999566i | \(0.490618\pi\) | |||||||
\(38\) | 3920.66 | 0.440454 | ||||||||
\(39\) | −11101.6 | −1.16875 | ||||||||
\(40\) | −14648.7 | −1.44760 | ||||||||
\(41\) | −11682.0 | −1.08532 | −0.542659 | − | 0.839953i | \(-0.682582\pi\) | ||||
−0.542659 | + | 0.839953i | \(0.682582\pi\) | |||||||
\(42\) | 60928.4 | 5.32962 | ||||||||
\(43\) | −21163.4 | −1.74547 | −0.872737 | − | 0.488191i | \(-0.837657\pi\) | ||||
−0.872737 | + | 0.488191i | \(0.837657\pi\) | |||||||
\(44\) | 10400.2 | 0.809857 | ||||||||
\(45\) | 12412.7 | 0.913767 | ||||||||
\(46\) | 27601.7 | 1.92328 | ||||||||
\(47\) | 27536.5 | 1.81829 | 0.909146 | − | 0.416478i | \(-0.136736\pi\) | ||||
0.909146 | + | 0.416478i | \(0.136736\pi\) | |||||||
\(48\) | 98258.4 | 6.15554 | ||||||||
\(49\) | 25752.0 | 1.53222 | ||||||||
\(50\) | −6787.85 | −0.383979 | ||||||||
\(51\) | 42628.6 | 2.29497 | ||||||||
\(52\) | −35088.7 | −1.79953 | ||||||||
\(53\) | 10377.5 | 0.507459 | 0.253730 | − | 0.967275i | \(-0.418343\pi\) | ||||
0.253730 | + | 0.967275i | \(0.418343\pi\) | |||||||
\(54\) | −74871.6 | −3.49408 | ||||||||
\(55\) | 3025.00 | 0.134840 | ||||||||
\(56\) | 120880. | 5.15090 | ||||||||
\(57\) | −9817.00 | −0.400213 | ||||||||
\(58\) | −49754.6 | −1.94206 | ||||||||
\(59\) | −74.2036 | −0.00277521 | −0.00138760 | − | 0.999999i | \(-0.500442\pi\) | ||||
−0.00138760 | + | 0.999999i | \(0.500442\pi\) | |||||||
\(60\) | 58434.1 | 2.09550 | ||||||||
\(61\) | 47574.4 | 1.63700 | 0.818500 | − | 0.574506i | \(-0.194806\pi\) | ||||
0.818500 | + | 0.574506i | \(0.194806\pi\) | |||||||
\(62\) | 51203.1 | 1.69168 | ||||||||
\(63\) | −102429. | −3.25141 | ||||||||
\(64\) | 106927. | 3.26314 | ||||||||
\(65\) | −10205.9 | −0.299619 | ||||||||
\(66\) | −35736.3 | −1.00983 | ||||||||
\(67\) | −50141.8 | −1.36462 | −0.682312 | − | 0.731061i | \(-0.739025\pi\) | ||||
−0.682312 | + | 0.731061i | \(0.739025\pi\) | |||||||
\(68\) | 134736. | 3.53356 | ||||||||
\(69\) | −69112.4 | −1.74756 | ||||||||
\(70\) | 56012.9 | 1.36629 | ||||||||
\(71\) | −20052.3 | −0.472084 | −0.236042 | − | 0.971743i | \(-0.575850\pi\) | ||||
−0.236042 | + | 0.971743i | \(0.575850\pi\) | |||||||
\(72\) | −290927. | −6.61384 | ||||||||
\(73\) | 30408.2 | 0.667858 | 0.333929 | − | 0.942598i | \(-0.391625\pi\) | ||||
0.333929 | + | 0.942598i | \(0.391625\pi\) | |||||||
\(74\) | −5330.49 | −0.113159 | ||||||||
\(75\) | 16996.2 | 0.348898 | ||||||||
\(76\) | −31028.6 | −0.616209 | ||||||||
\(77\) | −24962.1 | −0.479793 | ||||||||
\(78\) | 120569. | 2.24388 | ||||||||
\(79\) | −41210.0 | −0.742907 | −0.371454 | − | 0.928452i | \(-0.621141\pi\) | ||||
−0.371454 | + | 0.928452i | \(0.621141\pi\) | |||||||
\(80\) | 90331.2 | 1.57802 | ||||||||
\(81\) | 66820.3 | 1.13161 | ||||||||
\(82\) | 126873. | 2.08369 | ||||||||
\(83\) | −101109. | −1.61100 | −0.805500 | − | 0.592596i | \(-0.798103\pi\) | ||||
−0.805500 | + | 0.592596i | \(0.798103\pi\) | |||||||
\(84\) | −482194. | −7.45631 | ||||||||
\(85\) | 39189.5 | 0.588332 | ||||||||
\(86\) | 229846. | 3.35112 | ||||||||
\(87\) | 124581. | 1.76463 | ||||||||
\(88\) | −70899.5 | −0.975970 | ||||||||
\(89\) | 37971.6 | 0.508140 | 0.254070 | − | 0.967186i | \(-0.418231\pi\) | ||||
0.254070 | + | 0.967186i | \(0.418231\pi\) | |||||||
\(90\) | −134809. | −1.75434 | ||||||||
\(91\) | 84218.7 | 1.06612 | ||||||||
\(92\) | −218443. | −2.69073 | ||||||||
\(93\) | −128208. | −1.53712 | ||||||||
\(94\) | −299061. | −3.49093 | ||||||||
\(95\) | −9025.00 | −0.102598 | ||||||||
\(96\) | −557247. | −6.17120 | ||||||||
\(97\) | −149013. | −1.60803 | −0.804015 | − | 0.594610i | \(-0.797307\pi\) | ||||
−0.804015 | + | 0.594610i | \(0.797307\pi\) | |||||||
\(98\) | −279681. | −2.94169 | ||||||||
\(99\) | 60077.6 | 0.616062 | ||||||||
\(100\) | 53719.8 | 0.537198 | ||||||||
\(101\) | −24259.1 | −0.236631 | −0.118315 | − | 0.992976i | \(-0.537749\pi\) | ||||
−0.118315 | + | 0.992976i | \(0.537749\pi\) | |||||||
\(102\) | −462971. | −4.40609 | ||||||||
\(103\) | −114936. | −1.06749 | −0.533743 | − | 0.845647i | \(-0.679215\pi\) | ||||
−0.533743 | + | 0.845647i | \(0.679215\pi\) | |||||||
\(104\) | 239205. | 2.16864 | ||||||||
\(105\) | −140251. | −1.24146 | ||||||||
\(106\) | −112705. | −0.974268 | ||||||||
\(107\) | −118257. | −0.998548 | −0.499274 | − | 0.866444i | \(-0.666400\pi\) | ||||
−0.499274 | + | 0.866444i | \(0.666400\pi\) | |||||||
\(108\) | 592542. | 4.88832 | ||||||||
\(109\) | 166357. | 1.34114 | 0.670572 | − | 0.741845i | \(-0.266049\pi\) | ||||
0.670572 | + | 0.741845i | \(0.266049\pi\) | |||||||
\(110\) | −32853.2 | −0.258878 | ||||||||
\(111\) | 13347.1 | 0.102820 | ||||||||
\(112\) | −745407. | −5.61498 | ||||||||
\(113\) | 238291. | 1.75555 | 0.877773 | − | 0.479076i | \(-0.159028\pi\) | ||||
0.877773 | + | 0.479076i | \(0.159028\pi\) | |||||||
\(114\) | 106618. | 0.768367 | ||||||||
\(115\) | −63536.6 | −0.448002 | ||||||||
\(116\) | 393764. | 2.71701 | ||||||||
\(117\) | −202693. | −1.36891 | ||||||||
\(118\) | 805.893 | 0.00532810 | ||||||||
\(119\) | −323389. | −2.09343 | ||||||||
\(120\) | −398354. | −2.52532 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −516685. | −3.14287 | ||||||||
\(123\) | −317679. | −1.89333 | ||||||||
\(124\) | −405228. | −2.36671 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 1.11244e6 | 6.24235 | ||||||||
\(127\) | 140605. | 0.773556 | 0.386778 | − | 0.922173i | \(-0.373588\pi\) | ||||
0.386778 | + | 0.922173i | \(0.373588\pi\) | |||||||
\(128\) | −505550. | −2.72734 | ||||||||
\(129\) | −575514. | −3.04496 | ||||||||
\(130\) | 110842. | 0.575237 | ||||||||
\(131\) | 41443.2 | 0.210996 | 0.105498 | − | 0.994419i | \(-0.466356\pi\) | ||||
0.105498 | + | 0.994419i | \(0.466356\pi\) | |||||||
\(132\) | 282821. | 1.41279 | ||||||||
\(133\) | 74473.7 | 0.365068 | ||||||||
\(134\) | 544568. | 2.61993 | ||||||||
\(135\) | 172347. | 0.813899 | ||||||||
\(136\) | −918518. | −4.25834 | ||||||||
\(137\) | −382748. | −1.74225 | −0.871126 | − | 0.491059i | \(-0.836610\pi\) | ||||
−0.871126 | + | 0.491059i | \(0.836610\pi\) | |||||||
\(138\) | 750599. | 3.35514 | ||||||||
\(139\) | −55909.6 | −0.245442 | −0.122721 | − | 0.992441i | \(-0.539162\pi\) | ||||
−0.122721 | + | 0.992441i | \(0.539162\pi\) | |||||||
\(140\) | −443292. | −1.91148 | ||||||||
\(141\) | 748824. | 3.17199 | ||||||||
\(142\) | 217780. | 0.906351 | ||||||||
\(143\) | −49396.7 | −0.202003 | ||||||||
\(144\) | 1.79401e6 | 7.20972 | ||||||||
\(145\) | 114530. | 0.452377 | ||||||||
\(146\) | −330251. | −1.28222 | ||||||||
\(147\) | 700297. | 2.67294 | ||||||||
\(148\) | 42186.2 | 0.158313 | ||||||||
\(149\) | 218115. | 0.804860 | 0.402430 | − | 0.915451i | \(-0.368166\pi\) | ||||
0.402430 | + | 0.915451i | \(0.368166\pi\) | |||||||
\(150\) | −184588. | −0.669847 | ||||||||
\(151\) | −111973. | −0.399640 | −0.199820 | − | 0.979833i | \(-0.564036\pi\) | ||||
−0.199820 | + | 0.979833i | \(0.564036\pi\) | |||||||
\(152\) | 211527. | 0.742602 | ||||||||
\(153\) | 778318. | 2.68799 | ||||||||
\(154\) | 271102. | 0.921152 | ||||||||
\(155\) | −117865. | −0.394053 | ||||||||
\(156\) | −954199. | −3.13926 | ||||||||
\(157\) | 546460. | 1.76933 | 0.884666 | − | 0.466226i | \(-0.154387\pi\) | ||||
0.884666 | + | 0.466226i | \(0.154387\pi\) | |||||||
\(158\) | 447563. | 1.42630 | ||||||||
\(159\) | 282204. | 0.885258 | ||||||||
\(160\) | −512291. | −1.58204 | ||||||||
\(161\) | 524300. | 1.59410 | ||||||||
\(162\) | −725706. | −2.17257 | ||||||||
\(163\) | −224897. | −0.663002 | −0.331501 | − | 0.943455i | \(-0.607555\pi\) | ||||
−0.331501 | + | 0.943455i | \(0.607555\pi\) | |||||||
\(164\) | −1.00409e6 | −2.91515 | ||||||||
\(165\) | 82261.6 | 0.235227 | ||||||||
\(166\) | 1.09810e6 | 3.09295 | ||||||||
\(167\) | −504301. | −1.39926 | −0.699630 | − | 0.714505i | \(-0.746652\pi\) | ||||
−0.699630 | + | 0.714505i | \(0.746652\pi\) | |||||||
\(168\) | 3.28719e6 | 8.98570 | ||||||||
\(169\) | −204635. | −0.551142 | ||||||||
\(170\) | −425620. | −1.12954 | ||||||||
\(171\) | −179240. | −0.468753 | ||||||||
\(172\) | −1.81903e6 | −4.68833 | ||||||||
\(173\) | −564549. | −1.43412 | −0.717061 | − | 0.697010i | \(-0.754513\pi\) | ||||
−0.717061 | + | 0.697010i | \(0.754513\pi\) | |||||||
\(174\) | −1.35302e6 | −3.38791 | ||||||||
\(175\) | −128936. | −0.318259 | ||||||||
\(176\) | 437203. | 1.06390 | ||||||||
\(177\) | −2017.89 | −0.00484132 | ||||||||
\(178\) | −412393. | −0.975575 | ||||||||
\(179\) | −64849.4 | −0.151277 | −0.0756386 | − | 0.997135i | \(-0.524100\pi\) | ||||
−0.0756386 | + | 0.997135i | \(0.524100\pi\) | |||||||
\(180\) | 1.06690e6 | 2.45437 | ||||||||
\(181\) | 37008.4 | 0.0839662 | 0.0419831 | − | 0.999118i | \(-0.486632\pi\) | ||||
0.0419831 | + | 0.999118i | \(0.486632\pi\) | |||||||
\(182\) | −914662. | −2.04683 | ||||||||
\(183\) | 1.29373e6 | 2.85573 | ||||||||
\(184\) | 1.48916e6 | 3.24263 | ||||||||
\(185\) | 12270.3 | 0.0263588 | ||||||||
\(186\) | 1.39241e6 | 2.95111 | ||||||||
\(187\) | 189677. | 0.396653 | ||||||||
\(188\) | 2.36681e6 | 4.88392 | ||||||||
\(189\) | −1.42220e6 | −2.89605 | ||||||||
\(190\) | 98016.6 | 0.196977 | ||||||||
\(191\) | −660056. | −1.30917 | −0.654587 | − | 0.755987i | \(-0.727157\pi\) | ||||
−0.654587 | + | 0.755987i | \(0.727157\pi\) | |||||||
\(192\) | 2.90775e6 | 5.69251 | ||||||||
\(193\) | −832746. | −1.60923 | −0.804617 | − | 0.593794i | \(-0.797630\pi\) | ||||
−0.804617 | + | 0.593794i | \(0.797630\pi\) | |||||||
\(194\) | 1.61836e6 | 3.08725 | ||||||||
\(195\) | −277539. | −0.522682 | ||||||||
\(196\) | 2.21343e6 | 4.11552 | ||||||||
\(197\) | −419852. | −0.770780 | −0.385390 | − | 0.922754i | \(-0.625933\pi\) | ||||
−0.385390 | + | 0.922754i | \(0.625933\pi\) | |||||||
\(198\) | −652476. | −1.18277 | ||||||||
\(199\) | −397097. | −0.710828 | −0.355414 | − | 0.934709i | \(-0.615660\pi\) | ||||
−0.355414 | + | 0.934709i | \(0.615660\pi\) | |||||||
\(200\) | −366216. | −0.647385 | ||||||||
\(201\) | −1.36355e6 | −2.38057 | ||||||||
\(202\) | 263468. | 0.454306 | ||||||||
\(203\) | −945097. | −1.60967 | ||||||||
\(204\) | 3.66401e6 | 6.16426 | ||||||||
\(205\) | −292049. | −0.485369 | ||||||||
\(206\) | 1.24827e6 | 2.04946 | ||||||||
\(207\) | −1.26186e6 | −2.04685 | ||||||||
\(208\) | −1.47506e6 | −2.36403 | ||||||||
\(209\) | −43681.0 | −0.0691714 | ||||||||
\(210\) | 1.52321e6 | 2.38348 | ||||||||
\(211\) | 139757. | 0.216106 | 0.108053 | − | 0.994145i | \(-0.465538\pi\) | ||||
0.108053 | + | 0.994145i | \(0.465538\pi\) | |||||||
\(212\) | 891961. | 1.36303 | ||||||||
\(213\) | −545302. | −0.823546 | ||||||||
\(214\) | 1.28434e6 | 1.91711 | ||||||||
\(215\) | −529084. | −0.780600 | ||||||||
\(216\) | −4.03945e6 | −5.89099 | ||||||||
\(217\) | 972613. | 1.40214 | ||||||||
\(218\) | −1.80673e6 | −2.57485 | ||||||||
\(219\) | 826919. | 1.16507 | ||||||||
\(220\) | 260004. | 0.362179 | ||||||||
\(221\) | −639945. | −0.881377 | ||||||||
\(222\) | −144957. | −0.197404 | ||||||||
\(223\) | 501213. | 0.674932 | 0.337466 | − | 0.941338i | \(-0.390430\pi\) | ||||
0.337466 | + | 0.941338i | \(0.390430\pi\) | |||||||
\(224\) | 4.22739e6 | 5.62927 | ||||||||
\(225\) | 310318. | 0.408649 | ||||||||
\(226\) | −2.58798e6 | −3.37046 | ||||||||
\(227\) | 435429. | 0.560858 | 0.280429 | − | 0.959875i | \(-0.409523\pi\) | ||||
0.280429 | + | 0.959875i | \(0.409523\pi\) | |||||||
\(228\) | −843789. | −1.07497 | ||||||||
\(229\) | −864868. | −1.08984 | −0.544918 | − | 0.838489i | \(-0.683439\pi\) | ||||
−0.544918 | + | 0.838489i | \(0.683439\pi\) | |||||||
\(230\) | 690044. | 0.860116 | ||||||||
\(231\) | −678817. | −0.836995 | ||||||||
\(232\) | −2.68435e6 | −3.27430 | ||||||||
\(233\) | 332203. | 0.400880 | 0.200440 | − | 0.979706i | \(-0.435763\pi\) | ||||
0.200440 | + | 0.979706i | \(0.435763\pi\) | |||||||
\(234\) | 2.20136e6 | 2.62816 | ||||||||
\(235\) | 688412. | 0.813165 | ||||||||
\(236\) | −6377.93 | −0.00745418 | ||||||||
\(237\) | −1.12066e6 | −1.29599 | ||||||||
\(238\) | 3.51219e6 | 4.01916 | ||||||||
\(239\) | 367382. | 0.416029 | 0.208014 | − | 0.978126i | \(-0.433300\pi\) | ||||
0.208014 | + | 0.978126i | \(0.433300\pi\) | |||||||
\(240\) | 2.45646e6 | 2.75284 | ||||||||
\(241\) | −583630. | −0.647284 | −0.323642 | − | 0.946180i | \(-0.604907\pi\) | ||||
−0.323642 | + | 0.946180i | \(0.604907\pi\) | |||||||
\(242\) | −159009. | −0.174536 | ||||||||
\(243\) | 141890. | 0.154147 | ||||||||
\(244\) | 4.08910e6 | 4.39697 | ||||||||
\(245\) | 643799. | 0.685228 | ||||||||
\(246\) | 3.45017e6 | 3.63498 | ||||||||
\(247\) | 147374. | 0.153701 | ||||||||
\(248\) | 2.76250e6 | 2.85215 | ||||||||
\(249\) | −2.74956e6 | −2.81037 | ||||||||
\(250\) | −169696. | −0.171721 | ||||||||
\(251\) | −281672. | −0.282201 | −0.141101 | − | 0.989995i | \(-0.545064\pi\) | ||||
−0.141101 | + | 0.989995i | \(0.545064\pi\) | |||||||
\(252\) | −8.80394e6 | −8.73325 | ||||||||
\(253\) | −307517. | −0.302043 | ||||||||
\(254\) | −1.52705e6 | −1.48514 | ||||||||
\(255\) | 1.06572e6 | 1.02634 | ||||||||
\(256\) | 2.06891e6 | 1.97306 | ||||||||
\(257\) | −1.19452e6 | −1.12813 | −0.564067 | − | 0.825729i | \(-0.690764\pi\) | ||||
−0.564067 | + | 0.825729i | \(0.690764\pi\) | |||||||
\(258\) | 6.25041e6 | 5.84600 | ||||||||
\(259\) | −101254. | −0.0937910 | ||||||||
\(260\) | −877218. | −0.804774 | ||||||||
\(261\) | 2.27461e6 | 2.06684 | ||||||||
\(262\) | −450096. | −0.405091 | ||||||||
\(263\) | 465453. | 0.414941 | 0.207471 | − | 0.978241i | \(-0.433477\pi\) | ||||
0.207471 | + | 0.978241i | \(0.433477\pi\) | |||||||
\(264\) | −1.92803e6 | −1.70257 | ||||||||
\(265\) | 259436. | 0.226943 | ||||||||
\(266\) | −808826. | −0.700892 | ||||||||
\(267\) | 1.03260e6 | 0.886446 | ||||||||
\(268\) | −4.30977e6 | −3.66537 | ||||||||
\(269\) | −1.45085e6 | −1.22248 | −0.611241 | − | 0.791444i | \(-0.709330\pi\) | ||||
−0.611241 | + | 0.791444i | \(0.709330\pi\) | |||||||
\(270\) | −1.87179e6 | −1.56260 | ||||||||
\(271\) | −572165. | −0.473258 | −0.236629 | − | 0.971600i | \(-0.576043\pi\) | ||||
−0.236629 | + | 0.971600i | \(0.576043\pi\) | |||||||
\(272\) | 5.66406e6 | 4.64200 | ||||||||
\(273\) | 2.29023e6 | 1.85983 | ||||||||
\(274\) | 4.15685e6 | 3.34494 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | −5.94033e6 | −4.69395 | ||||||||
\(277\) | 2.36440e6 | 1.85149 | 0.925747 | − | 0.378144i | \(-0.123438\pi\) | ||||
0.925747 | + | 0.378144i | \(0.123438\pi\) | |||||||
\(278\) | 607209. | 0.471223 | ||||||||
\(279\) | −2.34084e6 | −1.80037 | ||||||||
\(280\) | 3.02199e6 | 2.30355 | ||||||||
\(281\) | 246360. | 0.186125 | 0.0930623 | − | 0.995660i | \(-0.470334\pi\) | ||||
0.0930623 | + | 0.995660i | \(0.470334\pi\) | |||||||
\(282\) | −8.13265e6 | −6.08989 | ||||||||
\(283\) | −1.24324e6 | −0.922760 | −0.461380 | − | 0.887203i | \(-0.652646\pi\) | ||||
−0.461380 | + | 0.887203i | \(0.652646\pi\) | |||||||
\(284\) | −1.72353e6 | −1.26801 | ||||||||
\(285\) | −245425. | −0.178981 | ||||||||
\(286\) | 536476. | 0.387824 | ||||||||
\(287\) | 2.40997e6 | 1.72706 | ||||||||
\(288\) | −1.01743e7 | −7.22806 | ||||||||
\(289\) | 1.03745e6 | 0.730674 | ||||||||
\(290\) | −1.24386e6 | −0.868516 | ||||||||
\(291\) | −4.05224e6 | −2.80519 | ||||||||
\(292\) | 2.61364e6 | 1.79386 | ||||||||
\(293\) | −32060.4 | −0.0218172 | −0.0109086 | − | 0.999940i | \(-0.503472\pi\) | ||||
−0.0109086 | + | 0.999940i | \(0.503472\pi\) | |||||||
\(294\) | −7.60562e6 | −5.13176 | ||||||||
\(295\) | −1855.09 | −0.00124111 | ||||||||
\(296\) | −287589. | −0.190785 | ||||||||
\(297\) | 834161. | 0.548730 | ||||||||
\(298\) | −2.36885e6 | −1.54525 | ||||||||
\(299\) | 1.03752e6 | 0.671149 | ||||||||
\(300\) | 1.46085e6 | 0.937138 | ||||||||
\(301\) | 4.36596e6 | 2.77756 | ||||||||
\(302\) | 1.21608e6 | 0.767267 | ||||||||
\(303\) | −659700. | −0.412800 | ||||||||
\(304\) | −1.30438e6 | −0.809508 | ||||||||
\(305\) | 1.18936e6 | 0.732089 | ||||||||
\(306\) | −8.45296e6 | −5.16066 | ||||||||
\(307\) | −1.00441e6 | −0.608228 | −0.304114 | − | 0.952636i | \(-0.598360\pi\) | ||||
−0.304114 | + | 0.952636i | \(0.598360\pi\) | |||||||
\(308\) | −2.14554e6 | −1.28872 | ||||||||
\(309\) | −3.12555e6 | −1.86222 | ||||||||
\(310\) | 1.28008e6 | 0.756541 | ||||||||
\(311\) | −2.72507e6 | −1.59763 | −0.798816 | − | 0.601575i | \(-0.794540\pi\) | ||||
−0.798816 | + | 0.601575i | \(0.794540\pi\) | |||||||
\(312\) | 6.50492e6 | 3.78317 | ||||||||
\(313\) | 1.11018e6 | 0.640518 | 0.320259 | − | 0.947330i | \(-0.396230\pi\) | ||||
0.320259 | + | 0.947330i | \(0.396230\pi\) | |||||||
\(314\) | −5.93486e6 | −3.39693 | ||||||||
\(315\) | −2.56072e6 | −1.45407 | ||||||||
\(316\) | −3.54207e6 | −1.99544 | ||||||||
\(317\) | 2.00207e6 | 1.11900 | 0.559500 | − | 0.828830i | \(-0.310993\pi\) | ||||
0.559500 | + | 0.828830i | \(0.310993\pi\) | |||||||
\(318\) | −3.06489e6 | −1.69960 | ||||||||
\(319\) | 554327. | 0.304993 | ||||||||
\(320\) | 2.67316e6 | 1.45932 | ||||||||
\(321\) | −3.21588e6 | −1.74196 | ||||||||
\(322\) | −5.69419e6 | −3.06050 | ||||||||
\(323\) | −565897. | −0.301808 | ||||||||
\(324\) | 5.74333e6 | 3.03949 | ||||||||
\(325\) | −255148. | −0.133994 | ||||||||
\(326\) | 2.44251e6 | 1.27289 | ||||||||
\(327\) | 4.52390e6 | 2.33961 | ||||||||
\(328\) | 6.84501e6 | 3.51309 | ||||||||
\(329\) | −5.68073e6 | −2.89344 | ||||||||
\(330\) | −893407. | −0.451611 | ||||||||
\(331\) | 103312. | 0.0518300 | 0.0259150 | − | 0.999664i | \(-0.491750\pi\) | ||||
0.0259150 | + | 0.999664i | \(0.491750\pi\) | |||||||
\(332\) | −8.69052e6 | −4.32713 | ||||||||
\(333\) | 243692. | 0.120429 | ||||||||
\(334\) | 5.47699e6 | 2.68643 | ||||||||
\(335\) | −1.25354e6 | −0.610278 | ||||||||
\(336\) | −2.02705e7 | −9.79528 | ||||||||
\(337\) | −2.05576e6 | −0.986046 | −0.493023 | − | 0.870016i | \(-0.664108\pi\) | ||||
−0.493023 | + | 0.870016i | \(0.664108\pi\) | |||||||
\(338\) | 2.22245e6 | 1.05813 | ||||||||
\(339\) | 6.48008e6 | 3.06253 | ||||||||
\(340\) | 3.36841e6 | 1.58026 | ||||||||
\(341\) | −570466. | −0.265671 | ||||||||
\(342\) | 1.94664e6 | 0.899956 | ||||||||
\(343\) | −1.84533e6 | −0.846915 | ||||||||
\(344\) | 1.24006e7 | 5.64997 | ||||||||
\(345\) | −1.72781e6 | −0.781535 | ||||||||
\(346\) | 6.13132e6 | 2.75336 | ||||||||
\(347\) | −1.17926e6 | −0.525757 | −0.262879 | − | 0.964829i | \(-0.584672\pi\) | ||||
−0.262879 | + | 0.964829i | \(0.584672\pi\) | |||||||
\(348\) | 1.07080e7 | 4.73979 | ||||||||
\(349\) | 4.04136e6 | 1.77609 | 0.888043 | − | 0.459761i | \(-0.152065\pi\) | ||||
0.888043 | + | 0.459761i | \(0.152065\pi\) | |||||||
\(350\) | 1.40032e6 | 0.611023 | ||||||||
\(351\) | −2.81435e6 | −1.21930 | ||||||||
\(352\) | −2.47949e6 | −1.06661 | ||||||||
\(353\) | 2.72359e6 | 1.16334 | 0.581668 | − | 0.813426i | \(-0.302400\pi\) | ||||
0.581668 | + | 0.813426i | \(0.302400\pi\) | |||||||
\(354\) | 21915.4 | 0.00929482 | ||||||||
\(355\) | −501309. | −0.211122 | ||||||||
\(356\) | 3.26372e6 | 1.36486 | ||||||||
\(357\) | −8.79422e6 | −3.65197 | ||||||||
\(358\) | 704300. | 0.290436 | ||||||||
\(359\) | −1.77817e6 | −0.728178 | −0.364089 | − | 0.931364i | \(-0.618620\pi\) | ||||
−0.364089 | + | 0.931364i | \(0.618620\pi\) | |||||||
\(360\) | −7.27319e6 | −2.95780 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | −401932. | −0.161206 | ||||||||
\(363\) | 398146. | 0.158590 | ||||||||
\(364\) | 7.23874e6 | 2.86358 | ||||||||
\(365\) | 760206. | 0.298675 | ||||||||
\(366\) | −1.40507e7 | −5.48270 | ||||||||
\(367\) | 1.61301e6 | 0.625131 | 0.312565 | − | 0.949896i | \(-0.398812\pi\) | ||||
0.312565 | + | 0.949896i | \(0.398812\pi\) | |||||||
\(368\) | −9.18295e6 | −3.53478 | ||||||||
\(369\) | −5.80020e6 | −2.21757 | ||||||||
\(370\) | −133262. | −0.0506061 | ||||||||
\(371\) | −2.14085e6 | −0.807517 | ||||||||
\(372\) | −1.10197e7 | −4.12870 | ||||||||
\(373\) | −3.82168e6 | −1.42227 | −0.711135 | − | 0.703056i | \(-0.751818\pi\) | ||||
−0.711135 | + | 0.703056i | \(0.751818\pi\) | |||||||
\(374\) | −2.06000e6 | −0.761533 | ||||||||
\(375\) | 424905. | 0.156032 | ||||||||
\(376\) | −1.61349e7 | −5.88568 | ||||||||
\(377\) | −1.87022e6 | −0.677704 | ||||||||
\(378\) | 1.54459e7 | 5.56011 | ||||||||
\(379\) | 2.49903e6 | 0.893662 | 0.446831 | − | 0.894618i | \(-0.352552\pi\) | ||||
0.446831 | + | 0.894618i | \(0.352552\pi\) | |||||||
\(380\) | −775715. | −0.275577 | ||||||||
\(381\) | 3.82360e6 | 1.34946 | ||||||||
\(382\) | 7.16857e6 | 2.51347 | ||||||||
\(383\) | −4.32573e6 | −1.50682 | −0.753411 | − | 0.657550i | \(-0.771593\pi\) | ||||
−0.753411 | + | 0.657550i | \(0.771593\pi\) | |||||||
\(384\) | −1.37479e7 | −4.75782 | ||||||||
\(385\) | −624052. | −0.214570 | ||||||||
\(386\) | 9.04409e6 | 3.08956 | ||||||||
\(387\) | −1.05078e7 | −3.56643 | ||||||||
\(388\) | −1.28079e7 | −4.31915 | ||||||||
\(389\) | 3.80671e6 | 1.27549 | 0.637743 | − | 0.770249i | \(-0.279868\pi\) | ||||
0.637743 | + | 0.770249i | \(0.279868\pi\) | |||||||
\(390\) | 3.01423e6 | 1.00349 | ||||||||
\(391\) | −3.98395e6 | −1.31787 | ||||||||
\(392\) | −1.50893e7 | −4.95968 | ||||||||
\(393\) | 1.12700e6 | 0.368081 | ||||||||
\(394\) | 4.55983e6 | 1.47982 | ||||||||
\(395\) | −1.03025e6 | −0.332238 | ||||||||
\(396\) | 5.16377e6 | 1.65474 | ||||||||
\(397\) | −3.67790e6 | −1.17118 | −0.585590 | − | 0.810608i | \(-0.699137\pi\) | ||||
−0.585590 | + | 0.810608i | \(0.699137\pi\) | |||||||
\(398\) | 4.31270e6 | 1.36471 | ||||||||
\(399\) | 2.02523e6 | 0.636857 | ||||||||
\(400\) | 2.25828e6 | 0.705713 | ||||||||
\(401\) | −2.67650e6 | −0.831201 | −0.415600 | − | 0.909547i | \(-0.636429\pi\) | ||||
−0.415600 | + | 0.909547i | \(0.636429\pi\) | |||||||
\(402\) | 1.48089e7 | 4.57045 | ||||||||
\(403\) | 1.92467e6 | 0.590330 | ||||||||
\(404\) | −2.08511e6 | −0.635589 | ||||||||
\(405\) | 1.67051e6 | 0.506071 | ||||||||
\(406\) | 1.02643e7 | 3.09039 | ||||||||
\(407\) | 59388.3 | 0.0177711 | ||||||||
\(408\) | −2.49781e7 | −7.42863 | ||||||||
\(409\) | 234395. | 0.0692851 | 0.0346426 | − | 0.999400i | \(-0.488971\pi\) | ||||
0.0346426 | + | 0.999400i | \(0.488971\pi\) | |||||||
\(410\) | 3.17182e6 | 0.931856 | ||||||||
\(411\) | −1.04084e7 | −3.03934 | ||||||||
\(412\) | −9.87893e6 | −2.86726 | ||||||||
\(413\) | 15308.1 | 0.00441617 | ||||||||
\(414\) | 1.37045e7 | 3.92973 | ||||||||
\(415\) | −2.52773e6 | −0.720461 | ||||||||
\(416\) | 8.36544e6 | 2.37004 | ||||||||
\(417\) | −1.52040e6 | −0.428172 | ||||||||
\(418\) | 474400. | 0.132802 | ||||||||
\(419\) | −472881. | −0.131588 | −0.0657941 | − | 0.997833i | \(-0.520958\pi\) | ||||
−0.0657941 | + | 0.997833i | \(0.520958\pi\) | |||||||
\(420\) | −1.20549e7 | −3.33456 | ||||||||
\(421\) | 907027. | 0.249411 | 0.124705 | − | 0.992194i | \(-0.460201\pi\) | ||||
0.124705 | + | 0.992194i | \(0.460201\pi\) | |||||||
\(422\) | −1.51784e6 | −0.414900 | ||||||||
\(423\) | 1.36721e7 | 3.71522 | ||||||||
\(424\) | −6.08063e6 | −1.64261 | ||||||||
\(425\) | 979738. | 0.263110 | ||||||||
\(426\) | 5.92228e6 | 1.58112 | ||||||||
\(427\) | −9.81452e6 | −2.60495 | ||||||||
\(428\) | −1.01644e7 | −2.68209 | ||||||||
\(429\) | −1.34329e6 | −0.352392 | ||||||||
\(430\) | 5.74615e6 | 1.49867 | ||||||||
\(431\) | 2.24031e6 | 0.580917 | 0.290459 | − | 0.956888i | \(-0.406192\pi\) | ||||
0.290459 | + | 0.956888i | \(0.406192\pi\) | |||||||
\(432\) | 2.49094e7 | 6.42175 | ||||||||
\(433\) | −395485. | −0.101370 | −0.0506852 | − | 0.998715i | \(-0.516141\pi\) | ||||
−0.0506852 | + | 0.998715i | \(0.516141\pi\) | |||||||
\(434\) | −1.05631e7 | −2.69196 | ||||||||
\(435\) | 3.11453e6 | 0.789168 | ||||||||
\(436\) | 1.42987e7 | 3.60230 | ||||||||
\(437\) | 917469. | 0.229820 | ||||||||
\(438\) | −8.98081e6 | −2.23681 | ||||||||
\(439\) | −1.73873e6 | −0.430596 | −0.215298 | − | 0.976548i | \(-0.569072\pi\) | ||||
−0.215298 | + | 0.976548i | \(0.569072\pi\) | |||||||
\(440\) | −1.77249e6 | −0.436467 | ||||||||
\(441\) | 1.27861e7 | 3.13070 | ||||||||
\(442\) | 6.95016e6 | 1.69215 | ||||||||
\(443\) | −5.52681e6 | −1.33803 | −0.669015 | − | 0.743249i | \(-0.733284\pi\) | ||||
−0.669015 | + | 0.743249i | \(0.733284\pi\) | |||||||
\(444\) | 1.14721e6 | 0.276175 | ||||||||
\(445\) | 949289. | 0.227247 | ||||||||
\(446\) | −5.44345e6 | −1.29580 | ||||||||
\(447\) | 5.93140e6 | 1.40407 | ||||||||
\(448\) | −2.20588e7 | −5.19261 | ||||||||
\(449\) | 6.53068e6 | 1.52877 | 0.764385 | − | 0.644760i | \(-0.223043\pi\) | ||||
0.764385 | + | 0.644760i | \(0.223043\pi\) | |||||||
\(450\) | −3.37023e6 | −0.784563 | ||||||||
\(451\) | −1.41352e6 | −0.327235 | ||||||||
\(452\) | 2.04816e7 | 4.71538 | ||||||||
\(453\) | −3.04497e6 | −0.697169 | ||||||||
\(454\) | −4.72900e6 | −1.07679 | ||||||||
\(455\) | 2.10547e6 | 0.476782 | ||||||||
\(456\) | 5.75224e6 | 1.29546 | ||||||||
\(457\) | 326134. | 0.0730475 | 0.0365237 | − | 0.999333i | \(-0.488372\pi\) | ||||
0.0365237 | + | 0.999333i | \(0.488372\pi\) | |||||||
\(458\) | 9.39295e6 | 2.09237 | ||||||||
\(459\) | 1.08067e7 | 2.39421 | ||||||||
\(460\) | −5.46109e6 | −1.20333 | ||||||||
\(461\) | 2.89122e6 | 0.633621 | 0.316810 | − | 0.948489i | \(-0.397388\pi\) | ||||
0.316810 | + | 0.948489i | \(0.397388\pi\) | |||||||
\(462\) | 7.37233e6 | 1.60694 | ||||||||
\(463\) | 7.86562e6 | 1.70522 | 0.852610 | − | 0.522548i | \(-0.175019\pi\) | ||||
0.852610 | + | 0.522548i | \(0.175019\pi\) | |||||||
\(464\) | 1.65531e7 | 3.56931 | ||||||||
\(465\) | −3.20521e6 | −0.687422 | ||||||||
\(466\) | −3.60791e6 | −0.769647 | ||||||||
\(467\) | −4.15802e6 | −0.882255 | −0.441127 | − | 0.897444i | \(-0.645421\pi\) | ||||
−0.441127 | + | 0.897444i | \(0.645421\pi\) | |||||||
\(468\) | −1.74219e7 | −3.67688 | ||||||||
\(469\) | 1.03442e7 | 2.17152 | ||||||||
\(470\) | −7.47654e6 | −1.56119 | ||||||||
\(471\) | 1.48604e7 | 3.08658 | ||||||||
\(472\) | 43479.4 | 0.00898314 | ||||||||
\(473\) | −2.56077e6 | −0.526280 | ||||||||
\(474\) | 1.21710e7 | 2.48817 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | −2.77959e7 | −5.62293 | ||||||||
\(477\) | 5.15250e6 | 1.03686 | ||||||||
\(478\) | −3.98998e6 | −0.798731 | ||||||||
\(479\) | −7.81837e6 | −1.55696 | −0.778480 | − | 0.627669i | \(-0.784009\pi\) | ||||
−0.778480 | + | 0.627669i | \(0.784009\pi\) | |||||||
\(480\) | −1.39312e7 | −2.75985 | ||||||||
\(481\) | −200368. | −0.0394880 | ||||||||
\(482\) | 6.33854e6 | 1.24272 | ||||||||
\(483\) | 1.42578e7 | 2.78089 | ||||||||
\(484\) | 1.25842e6 | 0.244181 | ||||||||
\(485\) | −3.72532e6 | −0.719132 | ||||||||
\(486\) | −1.54100e6 | −0.295946 | ||||||||
\(487\) | −3.61636e6 | −0.690955 | −0.345477 | − | 0.938427i | \(-0.612283\pi\) | ||||
−0.345477 | + | 0.938427i | \(0.612283\pi\) | |||||||
\(488\) | −2.78760e7 | −5.29885 | ||||||||
\(489\) | −6.11583e6 | −1.15660 | ||||||||
\(490\) | −6.99202e6 | −1.31557 | ||||||||
\(491\) | 221811. | 0.0415221 | 0.0207610 | − | 0.999784i | \(-0.493391\pi\) | ||||
0.0207610 | + | 0.999784i | \(0.493391\pi\) | |||||||
\(492\) | −2.73050e7 | −5.08546 | ||||||||
\(493\) | 7.18143e6 | 1.33074 | ||||||||
\(494\) | −1.60056e6 | −0.295090 | ||||||||
\(495\) | 1.50194e6 | 0.275511 | ||||||||
\(496\) | −1.70350e7 | −3.10912 | ||||||||
\(497\) | 4.13676e6 | 0.751224 | ||||||||
\(498\) | 2.98617e7 | 5.39562 | ||||||||
\(499\) | 5.72243e6 | 1.02880 | 0.514398 | − | 0.857552i | \(-0.328015\pi\) | ||||
0.514398 | + | 0.857552i | \(0.328015\pi\) | |||||||
\(500\) | 1.34300e6 | 0.240242 | ||||||||
\(501\) | −1.37139e7 | −2.44100 | ||||||||
\(502\) | 3.05911e6 | 0.541797 | ||||||||
\(503\) | 610801. | 0.107641 | 0.0538207 | − | 0.998551i | \(-0.482860\pi\) | ||||
0.0538207 | + | 0.998551i | \(0.482860\pi\) | |||||||
\(504\) | 6.00178e7 | 10.5246 | ||||||||
\(505\) | −606478. | −0.105825 | ||||||||
\(506\) | 3.33981e6 | 0.579890 | ||||||||
\(507\) | −5.56483e6 | −0.961462 | ||||||||
\(508\) | 1.20852e7 | 2.07776 | ||||||||
\(509\) | −6.82079e6 | −1.16692 | −0.583459 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583459 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(510\) | −1.15743e7 | −1.97046 | ||||||||
\(511\) | −6.27317e6 | −1.06276 | ||||||||
\(512\) | −6.29189e6 | −1.06073 | ||||||||
\(513\) | −2.48870e6 | −0.417521 | ||||||||
\(514\) | 1.29732e7 | 2.16590 | ||||||||
\(515\) | −2.87339e6 | −0.477394 | ||||||||
\(516\) | −4.94665e7 | −8.17875 | ||||||||
\(517\) | 3.33191e6 | 0.548236 | ||||||||
\(518\) | 1.09967e6 | 0.180069 | ||||||||
\(519\) | −1.53523e7 | −2.50181 | ||||||||
\(520\) | 5.98013e6 | 0.969845 | ||||||||
\(521\) | −2.41165e6 | −0.389242 | −0.194621 | − | 0.980878i | \(-0.562348\pi\) | ||||
−0.194621 | + | 0.980878i | \(0.562348\pi\) | |||||||
\(522\) | −2.47036e7 | −3.96811 | ||||||||
\(523\) | −520796. | −0.0832556 | −0.0416278 | − | 0.999133i | \(-0.513254\pi\) | ||||
−0.0416278 | + | 0.999133i | \(0.513254\pi\) | |||||||
\(524\) | 3.56212e6 | 0.566735 | ||||||||
\(525\) | −3.50629e6 | −0.555199 | ||||||||
\(526\) | −5.05508e6 | −0.796643 | ||||||||
\(527\) | −7.39051e6 | −1.15917 | ||||||||
\(528\) | 1.18893e7 | 1.85597 | ||||||||
\(529\) | 22705.8 | 0.00352775 | ||||||||
\(530\) | −2.81762e6 | −0.435706 | ||||||||
\(531\) | −36842.8 | −0.00567043 | ||||||||
\(532\) | 6.40114e6 | 0.980570 | ||||||||
\(533\) | 4.76902e6 | 0.727128 | ||||||||
\(534\) | −1.12146e7 | −1.70188 | ||||||||
\(535\) | −2.95644e6 | −0.446564 | ||||||||
\(536\) | 2.93804e7 | 4.41719 | ||||||||
\(537\) | −1.76351e6 | −0.263901 | ||||||||
\(538\) | 1.57571e7 | 2.34704 | ||||||||
\(539\) | 3.11599e6 | 0.461981 | ||||||||
\(540\) | 1.48136e7 | 2.18613 | ||||||||
\(541\) | 241426. | 0.0354643 | 0.0177322 | − | 0.999843i | \(-0.494355\pi\) | ||||
0.0177322 | + | 0.999843i | \(0.494355\pi\) | |||||||
\(542\) | 6.21403e6 | 0.908605 | ||||||||
\(543\) | 1.00640e6 | 0.146478 | ||||||||
\(544\) | −3.21223e7 | −4.65381 | ||||||||
\(545\) | 4.15893e6 | 0.599778 | ||||||||
\(546\) | −2.48732e7 | −3.57068 | ||||||||
\(547\) | 9.15785e6 | 1.30865 | 0.654327 | − | 0.756211i | \(-0.272952\pi\) | ||||
0.654327 | + | 0.756211i | \(0.272952\pi\) | |||||||
\(548\) | −3.28978e7 | −4.67968 | ||||||||
\(549\) | 2.36211e7 | 3.34479 | ||||||||
\(550\) | −821330. | −0.115774 | ||||||||
\(551\) | −1.65382e6 | −0.232065 | ||||||||
\(552\) | 4.04962e7 | 5.65674 | ||||||||
\(553\) | 8.50155e6 | 1.18218 | ||||||||
\(554\) | −2.56787e7 | −3.55467 | ||||||||
\(555\) | 333677. | 0.0459827 | ||||||||
\(556\) | −4.80553e6 | −0.659256 | ||||||||
\(557\) | 9.92387e6 | 1.35532 | 0.677662 | − | 0.735374i | \(-0.262993\pi\) | ||||
0.677662 | + | 0.735374i | \(0.262993\pi\) | |||||||
\(558\) | 2.54228e7 | 3.45651 | ||||||||
\(559\) | 8.63967e6 | 1.16941 | ||||||||
\(560\) | −1.86352e7 | −2.51110 | ||||||||
\(561\) | 5.15807e6 | 0.691958 | ||||||||
\(562\) | −2.67560e6 | −0.357339 | ||||||||
\(563\) | 8.17891e6 | 1.08749 | 0.543744 | − | 0.839251i | \(-0.317006\pi\) | ||||
0.543744 | + | 0.839251i | \(0.317006\pi\) | |||||||
\(564\) | 6.43628e7 | 8.51995 | ||||||||
\(565\) | 5.95729e6 | 0.785104 | ||||||||
\(566\) | 1.35023e7 | 1.77160 | ||||||||
\(567\) | −1.37849e7 | −1.80072 | ||||||||
\(568\) | 1.17496e7 | 1.52810 | ||||||||
\(569\) | −2.14200e6 | −0.277357 | −0.138678 | − | 0.990337i | \(-0.544285\pi\) | ||||
−0.138678 | + | 0.990337i | \(0.544285\pi\) | |||||||
\(570\) | 2.66545e6 | 0.343624 | ||||||||
\(571\) | −5.17031e6 | −0.663631 | −0.331815 | − | 0.943344i | \(-0.607661\pi\) | ||||
−0.331815 | + | 0.943344i | \(0.607661\pi\) | |||||||
\(572\) | −4.24573e6 | −0.542579 | ||||||||
\(573\) | −1.79495e7 | −2.28384 | ||||||||
\(574\) | −2.61736e7 | −3.31577 | ||||||||
\(575\) | −1.58842e6 | −0.200352 | ||||||||
\(576\) | 5.30900e7 | 6.66739 | ||||||||
\(577\) | −9.16003e6 | −1.14540 | −0.572700 | − | 0.819765i | \(-0.694104\pi\) | ||||
−0.572700 | + | 0.819765i | \(0.694104\pi\) | |||||||
\(578\) | −1.12673e7 | −1.40282 | ||||||||
\(579\) | −2.26456e7 | −2.80729 | ||||||||
\(580\) | 9.84409e6 | 1.21508 | ||||||||
\(581\) | 2.08587e7 | 2.56358 | ||||||||
\(582\) | 4.40096e7 | 5.38567 | ||||||||
\(583\) | 1.25567e6 | 0.153005 | ||||||||
\(584\) | −1.78176e7 | −2.16181 | ||||||||
\(585\) | −5.06734e6 | −0.612195 | ||||||||
\(586\) | 348194. | 0.0418868 | ||||||||
\(587\) | −5.13979e6 | −0.615673 | −0.307836 | − | 0.951439i | \(-0.599605\pi\) | ||||
−0.307836 | + | 0.951439i | \(0.599605\pi\) | |||||||
\(588\) | 6.01918e7 | 7.17949 | ||||||||
\(589\) | 1.70197e6 | 0.202145 | ||||||||
\(590\) | 20147.3 | 0.00238280 | ||||||||
\(591\) | −1.14174e7 | −1.34462 | ||||||||
\(592\) | 1.77343e6 | 0.207974 | ||||||||
\(593\) | −1.43471e7 | −1.67543 | −0.837716 | − | 0.546106i | \(-0.816110\pi\) | ||||
−0.837716 | + | 0.546106i | \(0.816110\pi\) | |||||||
\(594\) | −9.05946e6 | −1.05350 | ||||||||
\(595\) | −8.08473e6 | −0.936210 | ||||||||
\(596\) | 1.87474e7 | 2.16185 | ||||||||
\(597\) | −1.07986e7 | −1.24003 | ||||||||
\(598\) | −1.12681e7 | −1.28854 | ||||||||
\(599\) | −8.13507e6 | −0.926391 | −0.463195 | − | 0.886256i | \(-0.653297\pi\) | ||||
−0.463195 | + | 0.886256i | \(0.653297\pi\) | |||||||
\(600\) | −9.95886e6 | −1.12936 | ||||||||
\(601\) | 1.16339e7 | 1.31383 | 0.656917 | − | 0.753963i | \(-0.271860\pi\) | ||||
0.656917 | + | 0.753963i | \(0.271860\pi\) | |||||||
\(602\) | −4.74168e7 | −5.33263 | ||||||||
\(603\) | −2.48958e7 | −2.78826 | ||||||||
\(604\) | −9.62424e6 | −1.07343 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | 7.16471e6 | 0.792533 | ||||||||
\(607\) | −9.14190e6 | −1.00708 | −0.503541 | − | 0.863972i | \(-0.667970\pi\) | ||||
−0.503541 | + | 0.863972i | \(0.667970\pi\) | |||||||
\(608\) | 7.39748e6 | 0.811567 | ||||||||
\(609\) | −2.57009e7 | −2.80805 | ||||||||
\(610\) | −1.29171e7 | −1.40553 | ||||||||
\(611\) | −1.12414e7 | −1.21820 | ||||||||
\(612\) | 6.68978e7 | 7.21993 | ||||||||
\(613\) | 1.03428e7 | 1.11170 | 0.555852 | − | 0.831282i | \(-0.312392\pi\) | ||||
0.555852 | + | 0.831282i | \(0.312392\pi\) | |||||||
\(614\) | 1.09085e7 | 1.16773 | ||||||||
\(615\) | −7.94197e6 | −0.846721 | ||||||||
\(616\) | 1.46264e7 | 1.55306 | ||||||||
\(617\) | −1.16522e7 | −1.23224 | −0.616119 | − | 0.787653i | \(-0.711296\pi\) | ||||
−0.616119 | + | 0.787653i | \(0.711296\pi\) | |||||||
\(618\) | 3.39452e7 | 3.57526 | ||||||||
\(619\) | 1.18202e7 | 1.23993 | 0.619965 | − | 0.784629i | \(-0.287147\pi\) | ||||
0.619965 | + | 0.784629i | \(0.287147\pi\) | |||||||
\(620\) | −1.01307e7 | −1.05842 | ||||||||
\(621\) | −1.75206e7 | −1.82314 | ||||||||
\(622\) | 2.95958e7 | 3.06729 | ||||||||
\(623\) | −7.83347e6 | −0.808601 | ||||||||
\(624\) | −4.01127e7 | −4.12402 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −1.20571e7 | −1.22973 | ||||||||
\(627\) | −1.18786e6 | −0.120669 | ||||||||
\(628\) | 4.69692e7 | 4.75241 | ||||||||
\(629\) | 769387. | 0.0775387 | ||||||||
\(630\) | 2.78109e7 | 2.79167 | ||||||||
\(631\) | −4.00568e6 | −0.400500 | −0.200250 | − | 0.979745i | \(-0.564175\pi\) | ||||
−0.200250 | + | 0.979745i | \(0.564175\pi\) | |||||||
\(632\) | 2.41468e7 | 2.40474 | ||||||||
\(633\) | 3.80053e6 | 0.376995 | ||||||||
\(634\) | −2.17436e7 | −2.14836 | ||||||||
\(635\) | 3.51513e6 | 0.345945 | ||||||||
\(636\) | 2.42559e7 | 2.37780 | ||||||||
\(637\) | −1.05129e7 | −1.02654 | ||||||||
\(638\) | −6.02030e6 | −0.585554 | ||||||||
\(639\) | −9.95616e6 | −0.964584 | ||||||||
\(640\) | −1.26388e7 | −1.21970 | ||||||||
\(641\) | 1.12013e7 | 1.07677 | 0.538385 | − | 0.842699i | \(-0.319035\pi\) | ||||
0.538385 | + | 0.842699i | \(0.319035\pi\) | |||||||
\(642\) | 3.49263e7 | 3.34437 | ||||||||
\(643\) | −1.24947e7 | −1.19178 | −0.595892 | − | 0.803064i | \(-0.703201\pi\) | ||||
−0.595892 | + | 0.803064i | \(0.703201\pi\) | |||||||
\(644\) | 4.50645e7 | 4.28174 | ||||||||
\(645\) | −1.43879e7 | −1.36175 | ||||||||
\(646\) | 6.14595e6 | 0.579439 | ||||||||
\(647\) | −1.73939e7 | −1.63356 | −0.816781 | − | 0.576948i | \(-0.804243\pi\) | ||||
−0.816781 | + | 0.576948i | \(0.804243\pi\) | |||||||
\(648\) | −3.91531e7 | −3.66293 | ||||||||
\(649\) | −8978.64 | −0.000836756 0 | ||||||||
\(650\) | 2.77105e6 | 0.257254 | ||||||||
\(651\) | 2.64491e7 | 2.44602 | ||||||||
\(652\) | −1.93303e7 | −1.78082 | ||||||||
\(653\) | −7.05606e6 | −0.647559 | −0.323779 | − | 0.946133i | \(-0.604954\pi\) | ||||
−0.323779 | + | 0.946133i | \(0.604954\pi\) | |||||||
\(654\) | −4.91321e7 | −4.49181 | ||||||||
\(655\) | 1.03608e6 | 0.0943604 | ||||||||
\(656\) | −4.22099e7 | −3.82961 | ||||||||
\(657\) | 1.50980e7 | 1.36460 | ||||||||
\(658\) | 6.16959e7 | 5.55509 | ||||||||
\(659\) | −2.04727e7 | −1.83637 | −0.918186 | − | 0.396149i | \(-0.870346\pi\) | ||||
−0.918186 | + | 0.396149i | \(0.870346\pi\) | |||||||
\(660\) | 7.07053e6 | 0.631818 | ||||||||
\(661\) | −4.05521e6 | −0.361002 | −0.180501 | − | 0.983575i | \(-0.557772\pi\) | ||||
−0.180501 | + | 0.983575i | \(0.557772\pi\) | |||||||
\(662\) | −1.12203e6 | −0.0995080 | ||||||||
\(663\) | −1.74026e7 | −1.53755 | ||||||||
\(664\) | 5.92446e7 | 5.21469 | ||||||||
\(665\) | 1.86184e6 | 0.163263 | ||||||||
\(666\) | −2.64664e6 | −0.231211 | ||||||||
\(667\) | −1.16430e7 | −1.01333 | ||||||||
\(668\) | −4.33455e7 | −3.75840 | ||||||||
\(669\) | 1.36299e7 | 1.17741 | ||||||||
\(670\) | 1.36142e7 | 1.17167 | ||||||||
\(671\) | 5.75650e6 | 0.493574 | ||||||||
\(672\) | 1.14959e8 | 9.82020 | ||||||||
\(673\) | −9.18537e6 | −0.781734 | −0.390867 | − | 0.920447i | \(-0.627825\pi\) | ||||
−0.390867 | + | 0.920447i | \(0.627825\pi\) | |||||||
\(674\) | 2.23267e7 | 1.89310 | ||||||||
\(675\) | 4.30868e6 | 0.363986 | ||||||||
\(676\) | −1.75888e7 | −1.48036 | ||||||||
\(677\) | 5.98964e6 | 0.502261 | 0.251130 | − | 0.967953i | \(-0.419198\pi\) | ||||
0.251130 | + | 0.967953i | \(0.419198\pi\) | |||||||
\(678\) | −7.03773e7 | −5.87974 | ||||||||
\(679\) | 3.07411e7 | 2.55885 | ||||||||
\(680\) | −2.29630e7 | −1.90439 | ||||||||
\(681\) | 1.18410e7 | 0.978410 | ||||||||
\(682\) | 6.19558e6 | 0.510060 | ||||||||
\(683\) | 1.28056e7 | 1.05038 | 0.525190 | − | 0.850985i | \(-0.323994\pi\) | ||||
0.525190 | + | 0.850985i | \(0.323994\pi\) | |||||||
\(684\) | −1.54060e7 | −1.25907 | ||||||||
\(685\) | −9.56869e6 | −0.779159 | ||||||||
\(686\) | 2.00414e7 | 1.62599 | ||||||||
\(687\) | −2.35191e7 | −1.90121 | ||||||||
\(688\) | −7.64685e7 | −6.15901 | ||||||||
\(689\) | −4.23646e6 | −0.339982 | ||||||||
\(690\) | 1.87650e7 | 1.50046 | ||||||||
\(691\) | −6.05307e6 | −0.482260 | −0.241130 | − | 0.970493i | \(-0.577518\pi\) | ||||
−0.241130 | + | 0.970493i | \(0.577518\pi\) | |||||||
\(692\) | −4.85240e7 | −3.85204 | ||||||||
\(693\) | −1.23939e7 | −0.980336 | ||||||||
\(694\) | 1.28074e7 | 1.00940 | ||||||||
\(695\) | −1.39774e6 | −0.109765 | ||||||||
\(696\) | −7.29979e7 | −5.71199 | ||||||||
\(697\) | −1.83124e7 | −1.42779 | ||||||||
\(698\) | −4.38914e7 | −3.40990 | ||||||||
\(699\) | 9.03391e6 | 0.699331 | ||||||||
\(700\) | −1.10823e7 | −0.854841 | ||||||||
\(701\) | 1.27500e7 | 0.979973 | 0.489986 | − | 0.871730i | \(-0.337002\pi\) | ||||
0.489986 | + | 0.871730i | \(0.337002\pi\) | |||||||
\(702\) | 3.05654e7 | 2.34092 | ||||||||
\(703\) | −177183. | −0.0135218 | ||||||||
\(704\) | 1.29381e7 | 0.983873 | ||||||||
\(705\) | 1.87206e7 | 1.41856 | ||||||||
\(706\) | −2.95797e7 | −2.23348 | ||||||||
\(707\) | 5.00461e6 | 0.376550 | ||||||||
\(708\) | −173441. | −0.0130037 | ||||||||
\(709\) | −1.87488e7 | −1.40074 | −0.700372 | − | 0.713778i | \(-0.746982\pi\) | ||||
−0.700372 | + | 0.713778i | \(0.746982\pi\) | |||||||
\(710\) | 5.44449e6 | 0.405333 | ||||||||
\(711\) | −2.04611e7 | −1.51794 | ||||||||
\(712\) | −2.22493e7 | −1.64481 | ||||||||
\(713\) | 1.19820e7 | 0.882683 | ||||||||
\(714\) | 9.55101e7 | 7.01139 | ||||||||
\(715\) | −1.23492e6 | −0.0903385 | ||||||||
\(716\) | −5.57392e6 | −0.406329 | ||||||||
\(717\) | 9.99056e6 | 0.725758 | ||||||||
\(718\) | 1.93119e7 | 1.39803 | ||||||||
\(719\) | −2.60285e7 | −1.87771 | −0.938853 | − | 0.344318i | \(-0.888110\pi\) | ||||
−0.938853 | + | 0.344318i | \(0.888110\pi\) | |||||||
\(720\) | 4.48502e7 | 3.22429 | ||||||||
\(721\) | 2.37110e7 | 1.69868 | ||||||||
\(722\) | −1.41536e6 | −0.101047 | ||||||||
\(723\) | −1.58712e7 | −1.12918 | ||||||||
\(724\) | 3.18094e6 | 0.225533 | ||||||||
\(725\) | 2.86326e6 | 0.202309 | ||||||||
\(726\) | −4.32409e6 | −0.304476 | ||||||||
\(727\) | 1.34044e7 | 0.940611 | 0.470306 | − | 0.882504i | \(-0.344144\pi\) | ||||
0.470306 | + | 0.882504i | \(0.344144\pi\) | |||||||
\(728\) | −4.93476e7 | −3.45094 | ||||||||
\(729\) | −1.23788e7 | −0.862700 | ||||||||
\(730\) | −8.25626e6 | −0.573425 | ||||||||
\(731\) | −3.31753e7 | −2.29626 | ||||||||
\(732\) | 1.11199e8 | 7.67047 | ||||||||
\(733\) | 1.46451e7 | 1.00677 | 0.503386 | − | 0.864062i | \(-0.332087\pi\) | ||||
0.503386 | + | 0.864062i | \(0.332087\pi\) | |||||||
\(734\) | −1.75181e7 | −1.20018 | ||||||||
\(735\) | 1.75074e7 | 1.19537 | ||||||||
\(736\) | 5.20788e7 | 3.54377 | ||||||||
\(737\) | −6.06716e6 | −0.411449 | ||||||||
\(738\) | 6.29935e7 | 4.25750 | ||||||||
\(739\) | 1.76852e7 | 1.19124 | 0.595619 | − | 0.803267i | \(-0.296907\pi\) | ||||
0.595619 | + | 0.803267i | \(0.296907\pi\) | |||||||
\(740\) | 1.05465e6 | 0.0707996 | ||||||||
\(741\) | 4.00767e6 | 0.268130 | ||||||||
\(742\) | 2.32508e7 | 1.55035 | ||||||||
\(743\) | −1.58234e7 | −1.05154 | −0.525772 | − | 0.850625i | \(-0.676224\pi\) | ||||
−0.525772 | + | 0.850625i | \(0.676224\pi\) | |||||||
\(744\) | 7.51232e7 | 4.97556 | ||||||||
\(745\) | 5.45288e6 | 0.359944 | ||||||||
\(746\) | 4.15056e7 | 2.73061 | ||||||||
\(747\) | −5.02016e7 | −3.29167 | ||||||||
\(748\) | 1.63031e7 | 1.06541 | ||||||||
\(749\) | 2.43963e7 | 1.58898 | ||||||||
\(750\) | −4.61470e6 | −0.299565 | ||||||||
\(751\) | 2.49465e7 | 1.61402 | 0.807012 | − | 0.590535i | \(-0.201083\pi\) | ||||
0.807012 | + | 0.590535i | \(0.201083\pi\) | |||||||
\(752\) | 9.94961e7 | 6.41596 | ||||||||
\(753\) | −7.65976e6 | −0.492298 | ||||||||
\(754\) | 2.03117e7 | 1.30112 | ||||||||
\(755\) | −2.79931e6 | −0.178725 | ||||||||
\(756\) | −1.22240e8 | −7.77876 | ||||||||
\(757\) | −2.58220e7 | −1.63776 | −0.818880 | − | 0.573964i | \(-0.805405\pi\) | ||||
−0.818880 | + | 0.573964i | \(0.805405\pi\) | |||||||
\(758\) | −2.71409e7 | −1.71574 | ||||||||
\(759\) | −8.36260e6 | −0.526911 | ||||||||
\(760\) | 5.28817e6 | 0.332102 | ||||||||
\(761\) | 3.62267e6 | 0.226760 | 0.113380 | − | 0.993552i | \(-0.463832\pi\) | ||||
0.113380 | + | 0.993552i | \(0.463832\pi\) | |||||||
\(762\) | −4.15264e7 | −2.59082 | ||||||||
\(763\) | −3.43192e7 | −2.13415 | ||||||||
\(764\) | −5.67329e7 | −3.51643 | ||||||||
\(765\) | 1.94579e7 | 1.20211 | ||||||||
\(766\) | 4.69798e7 | 2.89294 | ||||||||
\(767\) | 30292.7 | 0.00185930 | ||||||||
\(768\) | 5.62617e7 | 3.44199 | ||||||||
\(769\) | 2.15093e7 | 1.31163 | 0.655813 | − | 0.754923i | \(-0.272326\pi\) | ||||
0.655813 | + | 0.754923i | \(0.272326\pi\) | |||||||
\(770\) | 6.77756e6 | 0.411952 | ||||||||
\(771\) | −3.24837e7 | −1.96802 | ||||||||
\(772\) | −7.15760e7 | −4.32239 | ||||||||
\(773\) | 1.80078e7 | 1.08396 | 0.541979 | − | 0.840392i | \(-0.317675\pi\) | ||||
0.541979 | + | 0.840392i | \(0.317675\pi\) | |||||||
\(774\) | 1.14120e8 | 6.84717 | ||||||||
\(775\) | −2.94662e6 | −0.176226 | ||||||||
\(776\) | 8.73134e7 | 5.20507 | ||||||||
\(777\) | −2.75348e6 | −0.163618 | ||||||||
\(778\) | −4.13430e7 | −2.44880 | ||||||||
\(779\) | 4.21719e6 | 0.248989 | ||||||||
\(780\) | −2.38550e7 | −1.40392 | ||||||||
\(781\) | −2.42633e6 | −0.142339 | ||||||||
\(782\) | 4.32680e7 | 2.53017 | ||||||||
\(783\) | 3.15824e7 | 1.84095 | ||||||||
\(784\) | 9.30483e7 | 5.40653 | ||||||||
\(785\) | 1.36615e7 | 0.791269 | ||||||||
\(786\) | −1.22399e7 | −0.706677 | ||||||||
\(787\) | −1.27927e6 | −0.0736250 | −0.0368125 | − | 0.999322i | \(-0.511720\pi\) | ||||
−0.0368125 | + | 0.999322i | \(0.511720\pi\) | |||||||
\(788\) | −3.60870e7 | −2.07031 | ||||||||
\(789\) | 1.26575e7 | 0.723861 | ||||||||
\(790\) | 1.11891e7 | 0.637862 | ||||||||
\(791\) | −4.91591e7 | −2.79359 | ||||||||
\(792\) | −3.52022e7 | −1.99415 | ||||||||
\(793\) | −1.94216e7 | −1.09674 | ||||||||
\(794\) | 3.99440e7 | 2.24854 | ||||||||
\(795\) | 7.05509e6 | 0.395899 | ||||||||
\(796\) | −3.41312e7 | −1.90928 | ||||||||
\(797\) | 837805. | 0.0467194 | 0.0233597 | − | 0.999727i | \(-0.492564\pi\) | ||||
0.0233597 | + | 0.999727i | \(0.492564\pi\) | |||||||
\(798\) | −2.19951e7 | −1.22270 | ||||||||
\(799\) | 4.31656e7 | 2.39206 | ||||||||
\(800\) | −1.28073e7 | −0.707508 | ||||||||
\(801\) | 1.88532e7 | 1.03826 | ||||||||
\(802\) | 2.90683e7 | 1.59582 | ||||||||
\(803\) | 3.67940e6 | 0.201367 | ||||||||
\(804\) | −1.17200e8 | −6.39420 | ||||||||
\(805\) | 1.31075e7 | 0.712903 | ||||||||
\(806\) | −2.09030e7 | −1.13337 | ||||||||
\(807\) | −3.94544e7 | −2.13261 | ||||||||
\(808\) | 1.42145e7 | 0.765957 | ||||||||
\(809\) | −2.07886e7 | −1.11674 | −0.558372 | − | 0.829590i | \(-0.688574\pi\) | ||||
−0.558372 | + | 0.829590i | \(0.688574\pi\) | |||||||
\(810\) | −1.81427e7 | −0.971602 | ||||||||
\(811\) | −5.89050e6 | −0.314485 | −0.157243 | − | 0.987560i | \(-0.550260\pi\) | ||||
−0.157243 | + | 0.987560i | \(0.550260\pi\) | |||||||
\(812\) | −8.12328e7 | −4.32356 | ||||||||
\(813\) | −1.55594e7 | −0.825594 | ||||||||
\(814\) | −644990. | −0.0341186 | ||||||||
\(815\) | −5.62243e6 | −0.296504 | ||||||||
\(816\) | 1.54028e8 | 8.09793 | ||||||||
\(817\) | 7.63997e6 | 0.400439 | ||||||||
\(818\) | −2.54566e6 | −0.133020 | ||||||||
\(819\) | 4.18153e7 | 2.17834 | ||||||||
\(820\) | −2.51022e7 | −1.30370 | ||||||||
\(821\) | −2.56535e7 | −1.32828 | −0.664138 | − | 0.747610i | \(-0.731201\pi\) | ||||
−0.664138 | + | 0.747610i | \(0.731201\pi\) | |||||||
\(822\) | 1.13041e8 | 5.83521 | ||||||||
\(823\) | −2.65216e7 | −1.36490 | −0.682449 | − | 0.730933i | \(-0.739085\pi\) | ||||
−0.682449 | + | 0.730933i | \(0.739085\pi\) | |||||||
\(824\) | 6.73462e7 | 3.45537 | ||||||||
\(825\) | 2.05654e6 | 0.105197 | ||||||||
\(826\) | −166254. | −0.00847858 | ||||||||
\(827\) | −1.15781e7 | −0.588673 | −0.294336 | − | 0.955702i | \(-0.595099\pi\) | ||||
−0.294336 | + | 0.955702i | \(0.595099\pi\) | |||||||
\(828\) | −1.08459e8 | −5.49782 | ||||||||
\(829\) | 1.23572e6 | 0.0624502 | 0.0312251 | − | 0.999512i | \(-0.490059\pi\) | ||||
0.0312251 | + | 0.999512i | \(0.490059\pi\) | |||||||
\(830\) | 2.74526e7 | 1.38321 | ||||||||
\(831\) | 6.42974e7 | 3.22991 | ||||||||
\(832\) | −4.36514e7 | −2.18620 | ||||||||
\(833\) | 4.03683e7 | 2.01571 | ||||||||
\(834\) | 1.65124e7 | 0.822044 | ||||||||
\(835\) | −1.26075e7 | −0.625768 | ||||||||
\(836\) | −3.75446e6 | −0.185794 | ||||||||
\(837\) | −3.25019e7 | −1.60360 | ||||||||
\(838\) | 5.13576e6 | 0.252635 | ||||||||
\(839\) | 7.88637e6 | 0.386787 | 0.193394 | − | 0.981121i | \(-0.438051\pi\) | ||||
0.193394 | + | 0.981121i | \(0.438051\pi\) | |||||||
\(840\) | 8.21798e7 | 4.01853 | ||||||||
\(841\) | 476397. | 0.0232263 | ||||||||
\(842\) | −9.85082e6 | −0.478842 | ||||||||
\(843\) | 6.69948e6 | 0.324693 | ||||||||
\(844\) | 1.20123e7 | 0.580459 | ||||||||
\(845\) | −5.11588e6 | −0.246478 | ||||||||
\(846\) | −1.48487e8 | −7.13282 | ||||||||
\(847\) | −3.02041e6 | −0.144663 | ||||||||
\(848\) | 3.74963e7 | 1.79060 | ||||||||
\(849\) | −3.38086e7 | −1.60975 | ||||||||
\(850\) | −1.06405e7 | −0.505144 | ||||||||
\(851\) | −1.24738e6 | −0.0590440 | ||||||||
\(852\) | −4.68696e7 | −2.21204 | ||||||||
\(853\) | 4.18337e6 | 0.196858 | 0.0984292 | − | 0.995144i | \(-0.468618\pi\) | ||||
0.0984292 | + | 0.995144i | \(0.468618\pi\) | |||||||
\(854\) | 1.06591e8 | 5.00123 | ||||||||
\(855\) | −4.48099e6 | −0.209633 | ||||||||
\(856\) | 6.92925e7 | 3.23223 | ||||||||
\(857\) | −1.99149e6 | −0.0926243 | −0.0463122 | − | 0.998927i | \(-0.514747\pi\) | ||||
−0.0463122 | + | 0.998927i | \(0.514747\pi\) | |||||||
\(858\) | 1.45889e7 | 0.676556 | ||||||||
\(859\) | 6.09514e6 | 0.281839 | 0.140919 | − | 0.990021i | \(-0.454994\pi\) | ||||
0.140919 | + | 0.990021i | \(0.454994\pi\) | |||||||
\(860\) | −4.54757e7 | −2.09668 | ||||||||
\(861\) | 6.55366e7 | 3.01284 | ||||||||
\(862\) | −2.43310e7 | −1.11530 | ||||||||
\(863\) | 8.49981e6 | 0.388492 | 0.194246 | − | 0.980953i | \(-0.437774\pi\) | ||||
0.194246 | + | 0.980953i | \(0.437774\pi\) | |||||||
\(864\) | −1.41267e8 | −6.43808 | ||||||||
\(865\) | −1.41137e7 | −0.641359 | ||||||||
\(866\) | 4.29519e6 | 0.194620 | ||||||||
\(867\) | 2.82124e7 | 1.27465 | ||||||||
\(868\) | 8.35978e7 | 3.76613 | ||||||||
\(869\) | −4.98641e6 | −0.223995 | ||||||||
\(870\) | −3.38255e7 | −1.51512 | ||||||||
\(871\) | 2.04697e7 | 0.914255 | ||||||||
\(872\) | −9.74764e7 | −4.34118 | ||||||||
\(873\) | −7.39861e7 | −3.28560 | ||||||||
\(874\) | −9.96423e6 | −0.441230 | ||||||||
\(875\) | −3.22341e6 | −0.142330 | ||||||||
\(876\) | 7.10752e7 | 3.12937 | ||||||||
\(877\) | 1.76101e7 | 0.773150 | 0.386575 | − | 0.922258i | \(-0.373658\pi\) | ||||
0.386575 | + | 0.922258i | \(0.373658\pi\) | |||||||
\(878\) | 1.88836e7 | 0.826699 | ||||||||
\(879\) | −871847. | −0.0380599 | ||||||||
\(880\) | 1.09301e7 | 0.475791 | ||||||||
\(881\) | −1.17321e7 | −0.509254 | −0.254627 | − | 0.967039i | \(-0.581953\pi\) | ||||
−0.254627 | + | 0.967039i | \(0.581953\pi\) | |||||||
\(882\) | −1.38864e8 | −6.01061 | ||||||||
\(883\) | −1.78593e7 | −0.770839 | −0.385419 | − | 0.922742i | \(-0.625943\pi\) | ||||
−0.385419 | + | 0.922742i | \(0.625943\pi\) | |||||||
\(884\) | −5.50044e7 | −2.36737 | ||||||||
\(885\) | −50447.2 | −0.00216510 | ||||||||
\(886\) | 6.00243e7 | 2.56887 | ||||||||
\(887\) | 2.45054e7 | 1.04581 | 0.522904 | − | 0.852392i | \(-0.324849\pi\) | ||||
0.522904 | + | 0.852392i | \(0.324849\pi\) | |||||||
\(888\) | −7.82068e6 | −0.332822 | ||||||||
\(889\) | −2.90066e7 | −1.23095 | ||||||||
\(890\) | −1.03098e7 | −0.436291 | ||||||||
\(891\) | 8.08526e6 | 0.341193 | ||||||||
\(892\) | 4.30801e7 | 1.81286 | ||||||||
\(893\) | −9.94067e6 | −0.417145 | ||||||||
\(894\) | −6.44184e7 | −2.69566 | ||||||||
\(895\) | −1.62123e6 | −0.0676532 | ||||||||
\(896\) | 1.04294e8 | 4.34000 | ||||||||
\(897\) | 2.82143e7 | 1.17081 | ||||||||
\(898\) | −7.09268e7 | −2.93508 | ||||||||
\(899\) | −2.15986e7 | −0.891304 | ||||||||
\(900\) | 2.66724e7 | 1.09763 | ||||||||
\(901\) | 1.62675e7 | 0.667588 | ||||||||
\(902\) | 1.53516e7 | 0.628257 | ||||||||
\(903\) | 1.18728e8 | 4.84543 | ||||||||
\(904\) | −1.39626e8 | −5.68257 | ||||||||
\(905\) | 925211. | 0.0375508 | ||||||||
\(906\) | 3.30701e7 | 1.33849 | ||||||||
\(907\) | 2.03431e7 | 0.821105 | 0.410552 | − | 0.911837i | \(-0.365336\pi\) | ||||
0.410552 | + | 0.911837i | \(0.365336\pi\) | |||||||
\(908\) | 3.74259e7 | 1.50646 | ||||||||
\(909\) | −1.20449e7 | −0.483495 | ||||||||
\(910\) | −2.28665e7 | −0.915371 | ||||||||
\(911\) | 2.86098e7 | 1.14214 | 0.571070 | − | 0.820901i | \(-0.306528\pi\) | ||||
0.571070 | + | 0.820901i | \(0.306528\pi\) | |||||||
\(912\) | −3.54713e7 | −1.41218 | ||||||||
\(913\) | −1.22342e7 | −0.485735 | ||||||||
\(914\) | −3.54199e6 | −0.140243 | ||||||||
\(915\) | 3.23434e7 | 1.27712 | ||||||||
\(916\) | −7.43369e7 | −2.92729 | ||||||||
\(917\) | −8.54966e6 | −0.335757 | ||||||||
\(918\) | −1.17367e8 | −4.59664 | ||||||||
\(919\) | 2.76381e7 | 1.07949 | 0.539746 | − | 0.841828i | \(-0.318520\pi\) | ||||
0.539746 | + | 0.841828i | \(0.318520\pi\) | |||||||
\(920\) | 3.72291e7 | 1.45015 | ||||||||
\(921\) | −2.73139e7 | −1.06105 | ||||||||
\(922\) | −3.14003e7 | −1.21648 | ||||||||
\(923\) | 8.18611e6 | 0.316281 | ||||||||
\(924\) | −5.83455e7 | −2.24816 | ||||||||
\(925\) | 306757. | 0.0117880 | ||||||||
\(926\) | −8.54250e7 | −3.27384 | ||||||||
\(927\) | −5.70666e7 | −2.18114 | ||||||||
\(928\) | −9.38766e7 | −3.57839 | ||||||||
\(929\) | 2.10798e7 | 0.801361 | 0.400680 | − | 0.916218i | \(-0.368774\pi\) | ||||
0.400680 | + | 0.916218i | \(0.368774\pi\) | |||||||
\(930\) | 3.48103e7 | 1.31978 | ||||||||
\(931\) | −9.29646e6 | −0.351515 | ||||||||
\(932\) | 2.85535e7 | 1.07676 | ||||||||
\(933\) | −7.41054e7 | −2.78705 | ||||||||
\(934\) | 4.51584e7 | 1.69384 | ||||||||
\(935\) | 4.74193e6 | 0.177389 | ||||||||
\(936\) | 1.18767e8 | 4.43106 | ||||||||
\(937\) | −4.78560e7 | −1.78068 | −0.890342 | − | 0.455292i | \(-0.849535\pi\) | ||||
−0.890342 | + | 0.455292i | \(0.849535\pi\) | |||||||
\(938\) | −1.12343e8 | −4.16908 | ||||||||
\(939\) | 3.01901e7 | 1.11738 | ||||||||
\(940\) | 5.91702e7 | 2.18415 | ||||||||
\(941\) | 2.32341e7 | 0.855366 | 0.427683 | − | 0.903929i | \(-0.359330\pi\) | ||||
0.427683 | + | 0.903929i | \(0.359330\pi\) | |||||||
\(942\) | −1.61392e8 | −5.92591 | ||||||||
\(943\) | 2.96893e7 | 1.08723 | ||||||||
\(944\) | −268116. | −0.00979249 | ||||||||
\(945\) | −3.55550e7 | −1.29515 | ||||||||
\(946\) | 2.78114e7 | 1.01040 | ||||||||
\(947\) | 1.29421e7 | 0.468954 | 0.234477 | − | 0.972122i | \(-0.424662\pi\) | ||||
0.234477 | + | 0.972122i | \(0.424662\pi\) | |||||||
\(948\) | −9.63227e7 | −3.48103 | ||||||||
\(949\) | −1.24138e7 | −0.447444 | ||||||||
\(950\) | 2.45041e6 | 0.0880908 | ||||||||
\(951\) | 5.44440e7 | 1.95209 | ||||||||
\(952\) | 1.89489e8 | 6.77627 | ||||||||
\(953\) | 1.17497e7 | 0.419079 | 0.209540 | − | 0.977800i | \(-0.432804\pi\) | ||||
0.209540 | + | 0.977800i | \(0.432804\pi\) | |||||||
\(954\) | −5.59590e7 | −1.99067 | ||||||||
\(955\) | −1.65014e7 | −0.585480 | ||||||||
\(956\) | 3.15772e7 | 1.11745 | ||||||||
\(957\) | 1.50743e7 | 0.532057 | ||||||||
\(958\) | 8.49119e7 | 2.98920 | ||||||||
\(959\) | 7.89602e7 | 2.77244 | ||||||||
\(960\) | 7.26938e7 | 2.54577 | ||||||||
\(961\) | −6.40174e6 | −0.223609 | ||||||||
\(962\) | 2.17611e6 | 0.0758128 | ||||||||
\(963\) | −5.87159e7 | −2.04028 | ||||||||
\(964\) | −5.01640e7 | −1.73860 | ||||||||
\(965\) | −2.08187e7 | −0.719672 | ||||||||
\(966\) | −1.54847e8 | −5.33901 | ||||||||
\(967\) | 1.70389e7 | 0.585971 | 0.292985 | − | 0.956117i | \(-0.405351\pi\) | ||||
0.292985 | + | 0.956117i | \(0.405351\pi\) | |||||||
\(968\) | −8.57884e6 | −0.294266 | ||||||||
\(969\) | −1.53889e7 | −0.526501 | ||||||||
\(970\) | 4.04590e7 | 1.38066 | ||||||||
\(971\) | 4.13436e7 | 1.40721 | 0.703607 | − | 0.710589i | \(-0.251572\pi\) | ||||
0.703607 | + | 0.710589i | \(0.251572\pi\) | |||||||
\(972\) | 1.21957e7 | 0.414038 | ||||||||
\(973\) | 1.15341e7 | 0.390571 | ||||||||
\(974\) | 3.92757e7 | 1.32656 | ||||||||
\(975\) | −6.93848e6 | −0.233751 | ||||||||
\(976\) | 1.71898e8 | 5.77626 | ||||||||
\(977\) | −2.59627e7 | −0.870187 | −0.435094 | − | 0.900385i | \(-0.643285\pi\) | ||||
−0.435094 | + | 0.900385i | \(0.643285\pi\) | |||||||
\(978\) | 6.64214e7 | 2.22055 | ||||||||
\(979\) | 4.59456e6 | 0.153210 | ||||||||
\(980\) | 5.53357e7 | 1.84052 | ||||||||
\(981\) | 8.25978e7 | 2.74029 | ||||||||
\(982\) | −2.40899e6 | −0.0797180 | ||||||||
\(983\) | −2.51752e7 | −0.830978 | −0.415489 | − | 0.909598i | \(-0.636390\pi\) | ||||
−0.415489 | + | 0.909598i | \(0.636390\pi\) | |||||||
\(984\) | 1.86143e8 | 6.12856 | ||||||||
\(985\) | −1.04963e7 | −0.344704 | ||||||||
\(986\) | −7.79943e7 | −2.55488 | ||||||||
\(987\) | −1.54481e8 | −5.04757 | ||||||||
\(988\) | 1.26670e7 | 0.412841 | ||||||||
\(989\) | 5.37859e7 | 1.74855 | ||||||||
\(990\) | −1.63119e7 | −0.528952 | ||||||||
\(991\) | 4.63976e7 | 1.50076 | 0.750381 | − | 0.661006i | \(-0.229870\pi\) | ||||
0.750381 | + | 0.661006i | \(0.229870\pi\) | |||||||
\(992\) | 9.66097e7 | 3.11703 | ||||||||
\(993\) | 2.80946e6 | 0.0904169 | ||||||||
\(994\) | −4.49276e7 | −1.44227 | ||||||||
\(995\) | −9.92744e6 | −0.317892 | ||||||||
\(996\) | −2.36329e8 | −7.54864 | ||||||||
\(997\) | −1.29196e7 | −0.411633 | −0.205816 | − | 0.978591i | \(-0.565985\pi\) | ||||
−0.205816 | + | 0.978591i | \(0.565985\pi\) | |||||||
\(998\) | −6.21488e7 | −1.97518 | ||||||||
\(999\) | 3.38361e6 | 0.107267 |
(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 | 1045.6.a.e.1.2 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.e.1.2 | ✓ | 38 | 1.1 | even | 1 | trivial |