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 | 1.7 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.88488 | −1.57064 | −0.785320 | − | 0.619091i | \(-0.787501\pi\) | ||||
−0.785320 | + | 0.619091i | \(0.787501\pi\) | |||||||
\(3\) | −24.9356 | −1.59962 | −0.799810 | − | 0.600253i | \(-0.795066\pi\) | ||||
−0.799810 | + | 0.600253i | \(0.795066\pi\) | |||||||
\(4\) | 46.9410 | 1.46691 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 221.550 | 2.51243 | ||||||||
\(7\) | −188.162 | −1.45140 | −0.725700 | − | 0.688011i | \(-0.758484\pi\) | ||||
−0.725700 | + | 0.688011i | \(0.758484\pi\) | |||||||
\(8\) | −132.749 | −0.733343 | ||||||||
\(9\) | 378.784 | 1.55878 | ||||||||
\(10\) | −222.122 | −0.702411 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −1170.50 | −2.34649 | ||||||||
\(13\) | 1013.16 | 1.66272 | 0.831361 | − | 0.555732i | \(-0.187562\pi\) | ||||
0.831361 | + | 0.555732i | \(0.187562\pi\) | |||||||
\(14\) | 1671.80 | 2.27963 | ||||||||
\(15\) | −623.390 | −0.715372 | ||||||||
\(16\) | −322.653 | −0.315090 | ||||||||
\(17\) | 136.931 | 0.114915 | 0.0574577 | − | 0.998348i | \(-0.481701\pi\) | ||||
0.0574577 | + | 0.998348i | \(0.481701\pi\) | |||||||
\(18\) | −3365.45 | −2.44829 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | 1173.53 | 0.656021 | ||||||||
\(21\) | 4691.94 | 2.32169 | ||||||||
\(22\) | −1075.07 | −0.473566 | ||||||||
\(23\) | −2499.86 | −0.985364 | −0.492682 | − | 0.870209i | \(-0.663983\pi\) | ||||
−0.492682 | + | 0.870209i | \(0.663983\pi\) | |||||||
\(24\) | 3310.18 | 1.17307 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −9001.81 | −2.61154 | ||||||||
\(27\) | −3385.87 | −0.893842 | ||||||||
\(28\) | −8832.53 | −2.12907 | ||||||||
\(29\) | 6928.91 | 1.52992 | 0.764962 | − | 0.644075i | \(-0.222758\pi\) | ||||
0.764962 | + | 0.644075i | \(0.222758\pi\) | |||||||
\(30\) | 5538.74 | 1.12359 | ||||||||
\(31\) | 1840.68 | 0.344013 | 0.172006 | − | 0.985096i | \(-0.444975\pi\) | ||||
0.172006 | + | 0.985096i | \(0.444975\pi\) | |||||||
\(32\) | 7114.70 | 1.22824 | ||||||||
\(33\) | −3017.21 | −0.482304 | ||||||||
\(34\) | −1216.61 | −0.180490 | ||||||||
\(35\) | −4704.05 | −0.649086 | ||||||||
\(36\) | 17780.5 | 2.28659 | ||||||||
\(37\) | −10033.0 | −1.20484 | −0.602418 | − | 0.798181i | \(-0.705796\pi\) | ||||
−0.602418 | + | 0.798181i | \(0.705796\pi\) | |||||||
\(38\) | 3207.44 | 0.360329 | ||||||||
\(39\) | −25263.8 | −2.65972 | ||||||||
\(40\) | −3318.73 | −0.327961 | ||||||||
\(41\) | 11841.6 | 1.10015 | 0.550073 | − | 0.835117i | \(-0.314600\pi\) | ||||
0.550073 | + | 0.835117i | \(0.314600\pi\) | |||||||
\(42\) | −41687.3 | −3.64653 | ||||||||
\(43\) | −3911.61 | −0.322615 | −0.161308 | − | 0.986904i | \(-0.551571\pi\) | ||||
−0.161308 | + | 0.986904i | \(0.551571\pi\) | |||||||
\(44\) | 5679.86 | 0.442289 | ||||||||
\(45\) | 9469.61 | 0.697109 | ||||||||
\(46\) | 22211.0 | 1.54765 | ||||||||
\(47\) | −16417.7 | −1.08409 | −0.542047 | − | 0.840348i | \(-0.682351\pi\) | ||||
−0.542047 | + | 0.840348i | \(0.682351\pi\) | |||||||
\(48\) | 8045.54 | 0.504025 | ||||||||
\(49\) | 18598.0 | 1.10656 | ||||||||
\(50\) | −5553.05 | −0.314128 | ||||||||
\(51\) | −3414.45 | −0.183821 | ||||||||
\(52\) | 47558.8 | 2.43906 | ||||||||
\(53\) | −35920.1 | −1.75650 | −0.878250 | − | 0.478202i | \(-0.841289\pi\) | ||||
−0.878250 | + | 0.478202i | \(0.841289\pi\) | |||||||
\(54\) | 30083.0 | 1.40390 | ||||||||
\(55\) | 3025.00 | 0.134840 | ||||||||
\(56\) | 24978.4 | 1.06437 | ||||||||
\(57\) | 9001.75 | 0.366978 | ||||||||
\(58\) | −61562.5 | −2.40296 | ||||||||
\(59\) | −20681.9 | −0.773502 | −0.386751 | − | 0.922184i | \(-0.626403\pi\) | ||||
−0.386751 | + | 0.922184i | \(0.626403\pi\) | |||||||
\(60\) | −29262.6 | −1.04938 | ||||||||
\(61\) | −2228.28 | −0.0766734 | −0.0383367 | − | 0.999265i | \(-0.512206\pi\) | ||||
−0.0383367 | + | 0.999265i | \(0.512206\pi\) | |||||||
\(62\) | −16354.2 | −0.540320 | ||||||||
\(63\) | −71272.9 | −2.26242 | ||||||||
\(64\) | −52888.4 | −1.61403 | ||||||||
\(65\) | 25329.0 | 0.743592 | ||||||||
\(66\) | 26807.5 | 0.757525 | ||||||||
\(67\) | −29275.7 | −0.796748 | −0.398374 | − | 0.917223i | \(-0.630425\pi\) | ||||
−0.398374 | + | 0.917223i | \(0.630425\pi\) | |||||||
\(68\) | 6427.66 | 0.168570 | ||||||||
\(69\) | 62335.6 | 1.57621 | ||||||||
\(70\) | 41794.9 | 1.01948 | ||||||||
\(71\) | −25545.3 | −0.601403 | −0.300702 | − | 0.953718i | \(-0.597221\pi\) | ||||
−0.300702 | + | 0.953718i | \(0.597221\pi\) | |||||||
\(72\) | −50283.3 | −1.14312 | ||||||||
\(73\) | 31498.9 | 0.691812 | 0.345906 | − | 0.938269i | \(-0.387572\pi\) | ||||
0.345906 | + | 0.938269i | \(0.387572\pi\) | |||||||
\(74\) | 89142.3 | 1.89236 | ||||||||
\(75\) | −15584.8 | −0.319924 | ||||||||
\(76\) | −16945.7 | −0.336532 | ||||||||
\(77\) | −22767.6 | −0.437614 | ||||||||
\(78\) | 224465. | 4.17747 | ||||||||
\(79\) | −92865.9 | −1.67413 | −0.837063 | − | 0.547106i | \(-0.815729\pi\) | ||||
−0.837063 | + | 0.547106i | \(0.815729\pi\) | |||||||
\(80\) | −8066.31 | −0.140913 | ||||||||
\(81\) | −7615.96 | −0.128977 | ||||||||
\(82\) | −105211. | −1.72793 | ||||||||
\(83\) | 88852.5 | 1.41571 | 0.707855 | − | 0.706358i | \(-0.249663\pi\) | ||||
0.707855 | + | 0.706358i | \(0.249663\pi\) | |||||||
\(84\) | 220244. | 3.40570 | ||||||||
\(85\) | 3423.26 | 0.0513917 | ||||||||
\(86\) | 34754.2 | 0.506712 | ||||||||
\(87\) | −172777. | −2.44730 | ||||||||
\(88\) | −16062.7 | −0.221111 | ||||||||
\(89\) | 127748. | 1.70954 | 0.854770 | − | 0.519007i | \(-0.173698\pi\) | ||||
0.854770 | + | 0.519007i | \(0.173698\pi\) | |||||||
\(90\) | −84136.3 | −1.09491 | ||||||||
\(91\) | −190638. | −2.41328 | ||||||||
\(92\) | −117346. | −1.44544 | ||||||||
\(93\) | −45898.5 | −0.550290 | ||||||||
\(94\) | 145869. | 1.70272 | ||||||||
\(95\) | −9025.00 | −0.102598 | ||||||||
\(96\) | −177409. | −1.96471 | ||||||||
\(97\) | −35272.3 | −0.380631 | −0.190316 | − | 0.981723i | \(-0.560951\pi\) | ||||
−0.190316 | + | 0.981723i | \(0.560951\pi\) | |||||||
\(98\) | −165241. | −1.73801 | ||||||||
\(99\) | 45832.9 | 0.469991 | ||||||||
\(100\) | 29338.1 | 0.293381 | ||||||||
\(101\) | −110956. | −1.08230 | −0.541149 | − | 0.840926i | \(-0.682011\pi\) | ||||
−0.541149 | + | 0.840926i | \(0.682011\pi\) | |||||||
\(102\) | 30336.9 | 0.288716 | ||||||||
\(103\) | 56546.7 | 0.525187 | 0.262594 | − | 0.964906i | \(-0.415422\pi\) | ||||
0.262594 | + | 0.964906i | \(0.415422\pi\) | |||||||
\(104\) | −134496. | −1.21935 | ||||||||
\(105\) | 117298. | 1.03829 | ||||||||
\(106\) | 319146. | 2.75883 | ||||||||
\(107\) | 29592.8 | 0.249877 | 0.124939 | − | 0.992164i | \(-0.460127\pi\) | ||||
0.124939 | + | 0.992164i | \(0.460127\pi\) | |||||||
\(108\) | −158936. | −1.31118 | ||||||||
\(109\) | 131250. | 1.05812 | 0.529059 | − | 0.848585i | \(-0.322545\pi\) | ||||
0.529059 | + | 0.848585i | \(0.322545\pi\) | |||||||
\(110\) | −26876.8 | −0.211785 | ||||||||
\(111\) | 250180. | 1.92728 | ||||||||
\(112\) | 60711.0 | 0.457322 | ||||||||
\(113\) | 33785.7 | 0.248907 | 0.124453 | − | 0.992225i | \(-0.460282\pi\) | ||||
0.124453 | + | 0.992225i | \(0.460282\pi\) | |||||||
\(114\) | −79979.5 | −0.576390 | ||||||||
\(115\) | −62496.6 | −0.440668 | ||||||||
\(116\) | 325250. | 2.24426 | ||||||||
\(117\) | 383769. | 2.59183 | ||||||||
\(118\) | 183756. | 1.21489 | ||||||||
\(119\) | −25765.1 | −0.166788 | ||||||||
\(120\) | 82754.6 | 0.524613 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 19798.0 | 0.120426 | ||||||||
\(123\) | −295277. | −1.75981 | ||||||||
\(124\) | 86403.6 | 0.504635 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 633251. | 3.55344 | ||||||||
\(127\) | −154895. | −0.852171 | −0.426085 | − | 0.904683i | \(-0.640108\pi\) | ||||
−0.426085 | + | 0.904683i | \(0.640108\pi\) | |||||||
\(128\) | 242236. | 1.30682 | ||||||||
\(129\) | 97538.5 | 0.516062 | ||||||||
\(130\) | −225045. | −1.16792 | ||||||||
\(131\) | 290721. | 1.48013 | 0.740063 | − | 0.672537i | \(-0.234795\pi\) | ||||
0.740063 | + | 0.672537i | \(0.234795\pi\) | |||||||
\(132\) | −141631. | −0.707495 | ||||||||
\(133\) | 67926.5 | 0.332974 | ||||||||
\(134\) | 260111. | 1.25140 | ||||||||
\(135\) | −84646.7 | −0.399738 | ||||||||
\(136\) | −18177.4 | −0.0842723 | ||||||||
\(137\) | 32993.2 | 0.150184 | 0.0750919 | − | 0.997177i | \(-0.476075\pi\) | ||||
0.0750919 | + | 0.997177i | \(0.476075\pi\) | |||||||
\(138\) | −553844. | −2.47565 | ||||||||
\(139\) | 174089. | 0.764247 | 0.382123 | − | 0.924111i | \(-0.375193\pi\) | ||||
0.382123 | + | 0.924111i | \(0.375193\pi\) | |||||||
\(140\) | −220813. | −0.952149 | ||||||||
\(141\) | 409385. | 1.73414 | ||||||||
\(142\) | 226967. | 0.944588 | ||||||||
\(143\) | 122592. | 0.501330 | ||||||||
\(144\) | −122216. | −0.491158 | ||||||||
\(145\) | 173223. | 0.684203 | ||||||||
\(146\) | −279864. | −1.08659 | ||||||||
\(147\) | −463752. | −1.77008 | ||||||||
\(148\) | −470961. | −1.76738 | ||||||||
\(149\) | 435723. | 1.60785 | 0.803924 | − | 0.594732i | \(-0.202742\pi\) | ||||
0.803924 | + | 0.594732i | \(0.202742\pi\) | |||||||
\(150\) | 138469. | 0.502485 | ||||||||
\(151\) | −155989. | −0.556738 | −0.278369 | − | 0.960474i | \(-0.589794\pi\) | ||||
−0.278369 | + | 0.960474i | \(0.589794\pi\) | |||||||
\(152\) | 47922.5 | 0.168240 | ||||||||
\(153\) | 51867.1 | 0.179128 | ||||||||
\(154\) | 202287. | 0.687333 | ||||||||
\(155\) | 46017.1 | 0.153847 | ||||||||
\(156\) | −1.18591e6 | −3.90157 | ||||||||
\(157\) | −125610. | −0.406702 | −0.203351 | − | 0.979106i | \(-0.565183\pi\) | ||||
−0.203351 | + | 0.979106i | \(0.565183\pi\) | |||||||
\(158\) | 825102. | 2.62945 | ||||||||
\(159\) | 895690. | 2.80973 | ||||||||
\(160\) | 177868. | 0.549284 | ||||||||
\(161\) | 470380. | 1.43016 | ||||||||
\(162\) | 67666.9 | 0.202576 | ||||||||
\(163\) | 488373. | 1.43974 | 0.719868 | − | 0.694111i | \(-0.244202\pi\) | ||||
0.719868 | + | 0.694111i | \(0.244202\pi\) | |||||||
\(164\) | 555856. | 1.61381 | ||||||||
\(165\) | −75430.2 | −0.215693 | ||||||||
\(166\) | −789443. | −2.22357 | ||||||||
\(167\) | 261701. | 0.726130 | 0.363065 | − | 0.931764i | \(-0.381730\pi\) | ||||
0.363065 | + | 0.931764i | \(0.381730\pi\) | |||||||
\(168\) | −622851. | −1.70259 | ||||||||
\(169\) | 655201. | 1.76465 | ||||||||
\(170\) | −30415.3 | −0.0807178 | ||||||||
\(171\) | −136741. | −0.357610 | ||||||||
\(172\) | −183615. | −0.473247 | ||||||||
\(173\) | −14891.8 | −0.0378297 | −0.0189149 | − | 0.999821i | \(-0.506021\pi\) | ||||
−0.0189149 | + | 0.999821i | \(0.506021\pi\) | |||||||
\(174\) | 1.53510e6 | 3.84382 | ||||||||
\(175\) | −117601. | −0.290280 | ||||||||
\(176\) | −39041.0 | −0.0950033 | ||||||||
\(177\) | 515717. | 1.23731 | ||||||||
\(178\) | −1.13503e6 | −2.68507 | ||||||||
\(179\) | 456700. | 1.06537 | 0.532683 | − | 0.846315i | \(-0.321184\pi\) | ||||
0.532683 | + | 0.846315i | \(0.321184\pi\) | |||||||
\(180\) | 444513. | 1.02259 | ||||||||
\(181\) | −349168. | −0.792206 | −0.396103 | − | 0.918206i | \(-0.629638\pi\) | ||||
−0.396103 | + | 0.918206i | \(0.629638\pi\) | |||||||
\(182\) | 1.69380e6 | 3.79039 | ||||||||
\(183\) | 55563.5 | 0.122648 | ||||||||
\(184\) | 331855. | 0.722610 | ||||||||
\(185\) | −250826. | −0.538819 | ||||||||
\(186\) | 407803. | 0.864307 | ||||||||
\(187\) | 16568.6 | 0.0346483 | ||||||||
\(188\) | −770663. | −1.59027 | ||||||||
\(189\) | 637092. | 1.29732 | ||||||||
\(190\) | 80186.0 | 0.161144 | ||||||||
\(191\) | 442443. | 0.877555 | 0.438777 | − | 0.898596i | \(-0.355412\pi\) | ||||
0.438777 | + | 0.898596i | \(0.355412\pi\) | |||||||
\(192\) | 1.31880e6 | 2.58183 | ||||||||
\(193\) | −135166. | −0.261201 | −0.130601 | − | 0.991435i | \(-0.541691\pi\) | ||||
−0.130601 | + | 0.991435i | \(0.541691\pi\) | |||||||
\(194\) | 313390. | 0.597834 | ||||||||
\(195\) | −631594. | −1.18947 | ||||||||
\(196\) | 873009. | 1.62322 | ||||||||
\(197\) | −476036. | −0.873924 | −0.436962 | − | 0.899480i | \(-0.643946\pi\) | ||||
−0.436962 | + | 0.899480i | \(0.643946\pi\) | |||||||
\(198\) | −407220. | −0.738186 | ||||||||
\(199\) | −698847. | −1.25098 | −0.625489 | − | 0.780233i | \(-0.715100\pi\) | ||||
−0.625489 | + | 0.780233i | \(0.715100\pi\) | |||||||
\(200\) | −82968.3 | −0.146669 | ||||||||
\(201\) | 730008. | 1.27449 | ||||||||
\(202\) | 985830. | 1.69990 | ||||||||
\(203\) | −1.30376e6 | −2.22053 | ||||||||
\(204\) | −160278. | −0.269648 | ||||||||
\(205\) | 296039. | 0.492000 | ||||||||
\(206\) | −502411. | −0.824880 | ||||||||
\(207\) | −946910. | −1.53597 | ||||||||
\(208\) | −326899. | −0.523908 | ||||||||
\(209\) | −43681.0 | −0.0691714 | ||||||||
\(210\) | −1.04218e6 | −1.63078 | ||||||||
\(211\) | −332407. | −0.514001 | −0.257001 | − | 0.966411i | \(-0.582734\pi\) | ||||
−0.257001 | + | 0.966411i | \(0.582734\pi\) | |||||||
\(212\) | −1.68613e6 | −2.57662 | ||||||||
\(213\) | 636989. | 0.962017 | ||||||||
\(214\) | −262928. | −0.392467 | ||||||||
\(215\) | −97790.3 | −0.144278 | ||||||||
\(216\) | 449471. | 0.655492 | ||||||||
\(217\) | −346347. | −0.499300 | ||||||||
\(218\) | −1.16614e6 | −1.66192 | ||||||||
\(219\) | −785443. | −1.10664 | ||||||||
\(220\) | 141997. | 0.197798 | ||||||||
\(221\) | 138733. | 0.191072 | ||||||||
\(222\) | −2.22282e6 | −3.02706 | ||||||||
\(223\) | 1.38186e6 | 1.86082 | 0.930408 | − | 0.366527i | \(-0.119453\pi\) | ||||
0.930408 | + | 0.366527i | \(0.119453\pi\) | |||||||
\(224\) | −1.33872e6 | −1.78266 | ||||||||
\(225\) | 236740. | 0.311757 | ||||||||
\(226\) | −300182. | −0.390943 | ||||||||
\(227\) | −404074. | −0.520471 | −0.260235 | − | 0.965545i | \(-0.583800\pi\) | ||||
−0.260235 | + | 0.965545i | \(0.583800\pi\) | |||||||
\(228\) | 422552. | 0.538323 | ||||||||
\(229\) | 1.34341e6 | 1.69286 | 0.846430 | − | 0.532499i | \(-0.178747\pi\) | ||||
0.846430 | + | 0.532499i | \(0.178747\pi\) | |||||||
\(230\) | 555275. | 0.692131 | ||||||||
\(231\) | 567724. | 0.700015 | ||||||||
\(232\) | −919808. | −1.12196 | ||||||||
\(233\) | −1.42763e6 | −1.72276 | −0.861381 | − | 0.507960i | \(-0.830400\pi\) | ||||
−0.861381 | + | 0.507960i | \(0.830400\pi\) | |||||||
\(234\) | −3.40974e6 | −4.07082 | ||||||||
\(235\) | −410442. | −0.484822 | ||||||||
\(236\) | −970832. | −1.13466 | ||||||||
\(237\) | 2.31567e6 | 2.67797 | ||||||||
\(238\) | 228920. | 0.261964 | ||||||||
\(239\) | −403793. | −0.457261 | −0.228630 | − | 0.973513i | \(-0.573425\pi\) | ||||
−0.228630 | + | 0.973513i | \(0.573425\pi\) | |||||||
\(240\) | 201138. | 0.225407 | ||||||||
\(241\) | −1.07591e6 | −1.19325 | −0.596627 | − | 0.802519i | \(-0.703493\pi\) | ||||
−0.596627 | + | 0.802519i | \(0.703493\pi\) | |||||||
\(242\) | −130083. | −0.142785 | ||||||||
\(243\) | 1.01267e6 | 1.10016 | ||||||||
\(244\) | −104598. | −0.112473 | ||||||||
\(245\) | 464950. | 0.494870 | ||||||||
\(246\) | 2.62350e6 | 2.76403 | ||||||||
\(247\) | −365751. | −0.381455 | ||||||||
\(248\) | −244349. | −0.252279 | ||||||||
\(249\) | −2.21559e6 | −2.26460 | ||||||||
\(250\) | −138826. | −0.140482 | ||||||||
\(251\) | −356261. | −0.356931 | −0.178465 | − | 0.983946i | \(-0.557113\pi\) | ||||
−0.178465 | + | 0.983946i | \(0.557113\pi\) | |||||||
\(252\) | −3.34562e6 | −3.31876 | ||||||||
\(253\) | −302484. | −0.297099 | ||||||||
\(254\) | 1.37622e6 | 1.33845 | ||||||||
\(255\) | −85361.1 | −0.0822072 | ||||||||
\(256\) | −459811. | −0.438510 | ||||||||
\(257\) | −757207. | −0.715125 | −0.357562 | − | 0.933889i | \(-0.616392\pi\) | ||||
−0.357562 | + | 0.933889i | \(0.616392\pi\) | |||||||
\(258\) | −866617. | −0.810547 | ||||||||
\(259\) | 1.88784e6 | 1.74870 | ||||||||
\(260\) | 1.18897e6 | 1.09078 | ||||||||
\(261\) | 2.62456e6 | 2.38482 | ||||||||
\(262\) | −2.58302e6 | −2.32474 | ||||||||
\(263\) | −1.51030e6 | −1.34640 | −0.673199 | − | 0.739461i | \(-0.735080\pi\) | ||||
−0.673199 | + | 0.739461i | \(0.735080\pi\) | |||||||
\(264\) | 400532. | 0.353694 | ||||||||
\(265\) | −898003. | −0.785530 | ||||||||
\(266\) | −603519. | −0.522982 | ||||||||
\(267\) | −3.18547e6 | −2.73461 | ||||||||
\(268\) | −1.37423e6 | −1.16876 | ||||||||
\(269\) | 292026. | 0.246060 | 0.123030 | − | 0.992403i | \(-0.460739\pi\) | ||||
0.123030 | + | 0.992403i | \(0.460739\pi\) | |||||||
\(270\) | 752075. | 0.627844 | ||||||||
\(271\) | 1.45925e6 | 1.20700 | 0.603500 | − | 0.797363i | \(-0.293772\pi\) | ||||
0.603500 | + | 0.797363i | \(0.293772\pi\) | |||||||
\(272\) | −44181.0 | −0.0362087 | ||||||||
\(273\) | 4.75369e6 | 3.86032 | ||||||||
\(274\) | −293140. | −0.235885 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | 2.92610e6 | 2.31215 | ||||||||
\(277\) | 553858. | 0.433709 | 0.216855 | − | 0.976204i | \(-0.430420\pi\) | ||||
0.216855 | + | 0.976204i | \(0.430420\pi\) | |||||||
\(278\) | −1.54676e6 | −1.20036 | ||||||||
\(279\) | 697222. | 0.536242 | ||||||||
\(280\) | 624459. | 0.476002 | ||||||||
\(281\) | 869175. | 0.656662 | 0.328331 | − | 0.944563i | \(-0.393514\pi\) | ||||
0.328331 | + | 0.944563i | \(0.393514\pi\) | |||||||
\(282\) | −3.63733e6 | −2.72371 | ||||||||
\(283\) | −1.26603e6 | −0.939675 | −0.469837 | − | 0.882753i | \(-0.655687\pi\) | ||||
−0.469837 | + | 0.882753i | \(0.655687\pi\) | |||||||
\(284\) | −1.19912e6 | −0.882203 | ||||||||
\(285\) | 225044. | 0.164118 | ||||||||
\(286\) | −1.08922e6 | −0.787408 | ||||||||
\(287\) | −2.22814e6 | −1.59675 | ||||||||
\(288\) | 2.69494e6 | 1.91455 | ||||||||
\(289\) | −1.40111e6 | −0.986794 | ||||||||
\(290\) | −1.53906e6 | −1.07464 | ||||||||
\(291\) | 879536. | 0.608865 | ||||||||
\(292\) | 1.47859e6 | 1.01482 | ||||||||
\(293\) | −690423. | −0.469836 | −0.234918 | − | 0.972015i | \(-0.575482\pi\) | ||||
−0.234918 | + | 0.972015i | \(0.575482\pi\) | |||||||
\(294\) | 4.12038e6 | 2.78016 | ||||||||
\(295\) | −517048. | −0.345920 | ||||||||
\(296\) | 1.33188e6 | 0.883558 | ||||||||
\(297\) | −409690. | −0.269503 | ||||||||
\(298\) | −3.87135e6 | −2.52535 | ||||||||
\(299\) | −2.53276e6 | −1.63839 | ||||||||
\(300\) | −731564. | −0.469299 | ||||||||
\(301\) | 736018. | 0.468244 | ||||||||
\(302\) | 1.38594e6 | 0.874434 | ||||||||
\(303\) | 2.76675e6 | 1.73127 | ||||||||
\(304\) | 116478. | 0.0722867 | ||||||||
\(305\) | −55707.0 | −0.0342894 | ||||||||
\(306\) | −460833. | −0.281346 | ||||||||
\(307\) | 616049. | 0.373052 | 0.186526 | − | 0.982450i | \(-0.440277\pi\) | ||||
0.186526 | + | 0.982450i | \(0.440277\pi\) | |||||||
\(308\) | −1.06874e6 | −0.641939 | ||||||||
\(309\) | −1.41003e6 | −0.840100 | ||||||||
\(310\) | −408856. | −0.241639 | ||||||||
\(311\) | 1.66166e6 | 0.974182 | 0.487091 | − | 0.873351i | \(-0.338058\pi\) | ||||
0.487091 | + | 0.873351i | \(0.338058\pi\) | |||||||
\(312\) | 3.35375e6 | 1.95049 | ||||||||
\(313\) | 1.35601e6 | 0.782354 | 0.391177 | − | 0.920315i | \(-0.372068\pi\) | ||||
0.391177 | + | 0.920315i | \(0.372068\pi\) | |||||||
\(314\) | 1.11603e6 | 0.638781 | ||||||||
\(315\) | −1.78182e6 | −1.01178 | ||||||||
\(316\) | −4.35922e6 | −2.45579 | ||||||||
\(317\) | 1.23272e6 | 0.688998 | 0.344499 | − | 0.938787i | \(-0.388049\pi\) | ||||
0.344499 | + | 0.938787i | \(0.388049\pi\) | |||||||
\(318\) | −7.95809e6 | −4.41307 | ||||||||
\(319\) | 838398. | 0.461290 | ||||||||
\(320\) | −1.32221e6 | −0.721814 | ||||||||
\(321\) | −737914. | −0.399708 | ||||||||
\(322\) | −4.17927e6 | −2.24626 | ||||||||
\(323\) | −49431.9 | −0.0263634 | ||||||||
\(324\) | −357501. | −0.189197 | ||||||||
\(325\) | 633225. | 0.332545 | ||||||||
\(326\) | −4.33914e6 | −2.26131 | ||||||||
\(327\) | −3.27280e6 | −1.69259 | ||||||||
\(328\) | −1.57196e6 | −0.806784 | ||||||||
\(329\) | 3.08919e6 | 1.57346 | ||||||||
\(330\) | 670188. | 0.338775 | ||||||||
\(331\) | −899915. | −0.451473 | −0.225736 | − | 0.974188i | \(-0.572479\pi\) | ||||
−0.225736 | + | 0.974188i | \(0.572479\pi\) | |||||||
\(332\) | 4.17083e6 | 2.07672 | ||||||||
\(333\) | −3.80036e6 | −1.87808 | ||||||||
\(334\) | −2.32518e6 | −1.14049 | ||||||||
\(335\) | −731893. | −0.356316 | ||||||||
\(336\) | −1.51387e6 | −0.731542 | ||||||||
\(337\) | −3.37808e6 | −1.62030 | −0.810150 | − | 0.586223i | \(-0.800614\pi\) | ||||
−0.810150 | + | 0.586223i | \(0.800614\pi\) | |||||||
\(338\) | −5.82138e6 | −2.77162 | ||||||||
\(339\) | −842467. | −0.398156 | ||||||||
\(340\) | 160691. | 0.0753868 | ||||||||
\(341\) | 222723. | 0.103724 | ||||||||
\(342\) | 1.21493e6 | 0.561675 | ||||||||
\(343\) | −336997. | −0.154665 | ||||||||
\(344\) | 519264. | 0.236588 | ||||||||
\(345\) | 1.55839e6 | 0.704902 | ||||||||
\(346\) | 132312. | 0.0594169 | ||||||||
\(347\) | −3.33946e6 | −1.48886 | −0.744428 | − | 0.667703i | \(-0.767278\pi\) | ||||
−0.744428 | + | 0.667703i | \(0.767278\pi\) | |||||||
\(348\) | −8.11031e6 | −3.58996 | ||||||||
\(349\) | 3.42925e6 | 1.50708 | 0.753538 | − | 0.657404i | \(-0.228345\pi\) | ||||
0.753538 | + | 0.657404i | \(0.228345\pi\) | |||||||
\(350\) | 1.04487e6 | 0.455925 | ||||||||
\(351\) | −3.43043e6 | −1.48621 | ||||||||
\(352\) | 860879. | 0.370327 | ||||||||
\(353\) | 790575. | 0.337681 | 0.168840 | − | 0.985643i | \(-0.445998\pi\) | ||||
0.168840 | + | 0.985643i | \(0.445998\pi\) | |||||||
\(354\) | −4.58208e6 | −1.94337 | ||||||||
\(355\) | −638634. | −0.268956 | ||||||||
\(356\) | 5.99662e6 | 2.50774 | ||||||||
\(357\) | 642469. | 0.266798 | ||||||||
\(358\) | −4.05773e6 | −1.67330 | ||||||||
\(359\) | −3.75551e6 | −1.53792 | −0.768959 | − | 0.639299i | \(-0.779225\pi\) | ||||
−0.768959 | + | 0.639299i | \(0.779225\pi\) | |||||||
\(360\) | −1.25708e6 | −0.511220 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 3.10232e6 | 1.24427 | ||||||||
\(363\) | −365082. | −0.145420 | ||||||||
\(364\) | −8.94877e6 | −3.54005 | ||||||||
\(365\) | 787472. | 0.309388 | ||||||||
\(366\) | −493675. | −0.192636 | ||||||||
\(367\) | −96283.1 | −0.0373151 | −0.0186576 | − | 0.999826i | \(-0.505939\pi\) | ||||
−0.0186576 | + | 0.999826i | \(0.505939\pi\) | |||||||
\(368\) | 806588. | 0.310479 | ||||||||
\(369\) | 4.48541e6 | 1.71489 | ||||||||
\(370\) | 2.22856e6 | 0.846290 | ||||||||
\(371\) | 6.75881e6 | 2.54938 | ||||||||
\(372\) | −2.15453e6 | −0.807224 | ||||||||
\(373\) | 1.32162e6 | 0.491852 | 0.245926 | − | 0.969289i | \(-0.420908\pi\) | ||||
0.245926 | + | 0.969289i | \(0.420908\pi\) | |||||||
\(374\) | −147210. | −0.0544199 | ||||||||
\(375\) | −389619. | −0.143074 | ||||||||
\(376\) | 2.17943e6 | 0.795013 | ||||||||
\(377\) | 7.02010e6 | 2.54384 | ||||||||
\(378\) | −5.66048e6 | −2.03762 | ||||||||
\(379\) | 784562. | 0.280562 | 0.140281 | − | 0.990112i | \(-0.455199\pi\) | ||||
0.140281 | + | 0.990112i | \(0.455199\pi\) | |||||||
\(380\) | −423643. | −0.150502 | ||||||||
\(381\) | 3.86239e6 | 1.36315 | ||||||||
\(382\) | −3.93105e6 | −1.37832 | ||||||||
\(383\) | 3.13193e6 | 1.09098 | 0.545489 | − | 0.838118i | \(-0.316344\pi\) | ||||
0.545489 | + | 0.838118i | \(0.316344\pi\) | |||||||
\(384\) | −6.04031e6 | −2.09041 | ||||||||
\(385\) | −569190. | −0.195707 | ||||||||
\(386\) | 1.20094e6 | 0.410253 | ||||||||
\(387\) | −1.48166e6 | −0.502887 | ||||||||
\(388\) | −1.65572e6 | −0.558351 | ||||||||
\(389\) | −2.33290e6 | −0.781669 | −0.390834 | − | 0.920461i | \(-0.627813\pi\) | ||||
−0.390834 | + | 0.920461i | \(0.627813\pi\) | |||||||
\(390\) | 5.61164e6 | 1.86822 | ||||||||
\(391\) | −342308. | −0.113233 | ||||||||
\(392\) | −2.46887e6 | −0.811490 | ||||||||
\(393\) | −7.24932e6 | −2.36764 | ||||||||
\(394\) | 4.22952e6 | 1.37262 | ||||||||
\(395\) | −2.32165e6 | −0.748692 | ||||||||
\(396\) | 2.15144e6 | 0.689433 | ||||||||
\(397\) | 4.61021e6 | 1.46806 | 0.734031 | − | 0.679116i | \(-0.237637\pi\) | ||||
0.734031 | + | 0.679116i | \(0.237637\pi\) | |||||||
\(398\) | 6.20917e6 | 1.96483 | ||||||||
\(399\) | −1.69379e6 | −0.532632 | ||||||||
\(400\) | −201658. | −0.0630181 | ||||||||
\(401\) | 2.26692e6 | 0.704005 | 0.352002 | − | 0.935999i | \(-0.385501\pi\) | ||||
0.352002 | + | 0.935999i | \(0.385501\pi\) | |||||||
\(402\) | −6.48603e6 | −2.00177 | ||||||||
\(403\) | 1.86491e6 | 0.571998 | ||||||||
\(404\) | −5.20839e6 | −1.58763 | ||||||||
\(405\) | −190399. | −0.0576803 | ||||||||
\(406\) | 1.15837e7 | 3.48766 | ||||||||
\(407\) | −1.21400e6 | −0.363272 | ||||||||
\(408\) | 453265. | 0.134804 | ||||||||
\(409\) | −5.53987e6 | −1.63754 | −0.818769 | − | 0.574124i | \(-0.805343\pi\) | ||||
−0.818769 | + | 0.574124i | \(0.805343\pi\) | |||||||
\(410\) | −2.63027e6 | −0.772754 | ||||||||
\(411\) | −822705. | −0.240237 | ||||||||
\(412\) | 2.65436e6 | 0.770401 | ||||||||
\(413\) | 3.89156e6 | 1.12266 | ||||||||
\(414\) | 8.41318e6 | 2.41245 | ||||||||
\(415\) | 2.22131e6 | 0.633125 | ||||||||
\(416\) | 7.20834e6 | 2.04222 | ||||||||
\(417\) | −4.34101e6 | −1.22250 | ||||||||
\(418\) | 388100. | 0.108643 | ||||||||
\(419\) | 5.61196e6 | 1.56164 | 0.780818 | − | 0.624759i | \(-0.214803\pi\) | ||||
0.780818 | + | 0.624759i | \(0.214803\pi\) | |||||||
\(420\) | 5.50611e6 | 1.52308 | ||||||||
\(421\) | −4.63665e6 | −1.27497 | −0.637483 | − | 0.770464i | \(-0.720024\pi\) | ||||
−0.637483 | + | 0.770464i | \(0.720024\pi\) | |||||||
\(422\) | 2.95340e6 | 0.807311 | ||||||||
\(423\) | −6.21876e6 | −1.68987 | ||||||||
\(424\) | 4.76837e6 | 1.28812 | ||||||||
\(425\) | 85581.6 | 0.0229831 | ||||||||
\(426\) | −5.65956e6 | −1.51098 | ||||||||
\(427\) | 419278. | 0.111284 | ||||||||
\(428\) | 1.38912e6 | 0.366547 | ||||||||
\(429\) | −3.05692e6 | −0.801937 | ||||||||
\(430\) | 868855. | 0.226608 | ||||||||
\(431\) | −2.50316e6 | −0.649076 | −0.324538 | − | 0.945873i | \(-0.605209\pi\) | ||||
−0.324538 | + | 0.945873i | \(0.605209\pi\) | |||||||
\(432\) | 1.09246e6 | 0.281641 | ||||||||
\(433\) | −2.77523e6 | −0.711344 | −0.355672 | − | 0.934611i | \(-0.615748\pi\) | ||||
−0.355672 | + | 0.934611i | \(0.615748\pi\) | |||||||
\(434\) | 3.07725e6 | 0.784221 | ||||||||
\(435\) | −4.31942e6 | −1.09446 | ||||||||
\(436\) | 6.16102e6 | 1.55216 | ||||||||
\(437\) | 902451. | 0.226058 | ||||||||
\(438\) | 6.97857e6 | 1.73812 | ||||||||
\(439\) | 6.81783e6 | 1.68844 | 0.844219 | − | 0.535999i | \(-0.180065\pi\) | ||||
0.844219 | + | 0.535999i | \(0.180065\pi\) | |||||||
\(440\) | −401566. | −0.0988839 | ||||||||
\(441\) | 7.04463e6 | 1.72489 | ||||||||
\(442\) | −1.23262e6 | −0.300106 | ||||||||
\(443\) | 427517. | 0.103501 | 0.0517505 | − | 0.998660i | \(-0.483520\pi\) | ||||
0.0517505 | + | 0.998660i | \(0.483520\pi\) | |||||||
\(444\) | 1.17437e7 | 2.82714 | ||||||||
\(445\) | 3.19370e6 | 0.764529 | ||||||||
\(446\) | −1.22777e7 | −2.92267 | ||||||||
\(447\) | −1.08650e7 | −2.57195 | ||||||||
\(448\) | 9.95159e6 | 2.34260 | ||||||||
\(449\) | −8.49047e6 | −1.98754 | −0.993770 | − | 0.111448i | \(-0.964451\pi\) | ||||
−0.993770 | + | 0.111448i | \(0.964451\pi\) | |||||||
\(450\) | −2.10341e6 | −0.489657 | ||||||||
\(451\) | 1.43283e6 | 0.331706 | ||||||||
\(452\) | 1.58594e6 | 0.365123 | ||||||||
\(453\) | 3.88967e6 | 0.890569 | ||||||||
\(454\) | 3.59015e6 | 0.817472 | ||||||||
\(455\) | −4.76596e6 | −1.07925 | ||||||||
\(456\) | −1.19498e6 | −0.269121 | ||||||||
\(457\) | 6.49877e6 | 1.45560 | 0.727798 | − | 0.685792i | \(-0.240544\pi\) | ||||
0.727798 | + | 0.685792i | \(0.240544\pi\) | |||||||
\(458\) | −1.19361e7 | −2.65887 | ||||||||
\(459\) | −463629. | −0.102716 | ||||||||
\(460\) | −2.93366e6 | −0.646420 | ||||||||
\(461\) | 4.71758e6 | 1.03387 | 0.516937 | − | 0.856024i | \(-0.327072\pi\) | ||||
0.516937 | + | 0.856024i | \(0.327072\pi\) | |||||||
\(462\) | −5.04416e6 | −1.09947 | ||||||||
\(463\) | 5.90781e6 | 1.28078 | 0.640389 | − | 0.768051i | \(-0.278773\pi\) | ||||
0.640389 | + | 0.768051i | \(0.278773\pi\) | |||||||
\(464\) | −2.23563e6 | −0.482065 | ||||||||
\(465\) | −1.14746e6 | −0.246097 | ||||||||
\(466\) | 1.26843e7 | 2.70584 | ||||||||
\(467\) | 5.03866e6 | 1.06911 | 0.534556 | − | 0.845133i | \(-0.320479\pi\) | ||||
0.534556 | + | 0.845133i | \(0.320479\pi\) | |||||||
\(468\) | 1.80145e7 | 3.80197 | ||||||||
\(469\) | 5.50859e6 | 1.15640 | ||||||||
\(470\) | 3.64673e6 | 0.761480 | ||||||||
\(471\) | 3.13217e6 | 0.650568 | ||||||||
\(472\) | 2.74551e6 | 0.567242 | ||||||||
\(473\) | −473305. | −0.0972721 | ||||||||
\(474\) | −2.05744e7 | −4.20612 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | −1.20944e6 | −0.244663 | ||||||||
\(477\) | −1.36060e7 | −2.73800 | ||||||||
\(478\) | 3.58765e6 | 0.718191 | ||||||||
\(479\) | −1.78762e6 | −0.355989 | −0.177995 | − | 0.984031i | \(-0.556961\pi\) | ||||
−0.177995 | + | 0.984031i | \(0.556961\pi\) | |||||||
\(480\) | −4.43524e6 | −0.878645 | ||||||||
\(481\) | −1.01651e7 | −2.00331 | ||||||||
\(482\) | 9.55932e6 | 1.87417 | ||||||||
\(483\) | −1.17292e7 | −2.28771 | ||||||||
\(484\) | 687264. | 0.133355 | ||||||||
\(485\) | −881808. | −0.170224 | ||||||||
\(486\) | −8.99749e6 | −1.72795 | ||||||||
\(487\) | 3.29188e6 | 0.628958 | 0.314479 | − | 0.949264i | \(-0.398170\pi\) | ||||
0.314479 | + | 0.949264i | \(0.398170\pi\) | |||||||
\(488\) | 295802. | 0.0562279 | ||||||||
\(489\) | −1.21779e7 | −2.30303 | ||||||||
\(490\) | −4.13102e6 | −0.777262 | ||||||||
\(491\) | −1.03906e7 | −1.94508 | −0.972541 | − | 0.232733i | \(-0.925233\pi\) | ||||
−0.972541 | + | 0.232733i | \(0.925233\pi\) | |||||||
\(492\) | −1.38606e7 | −2.58148 | ||||||||
\(493\) | 948779. | 0.175812 | ||||||||
\(494\) | 3.24965e6 | 0.599128 | ||||||||
\(495\) | 1.14582e6 | 0.210186 | ||||||||
\(496\) | −593901. | −0.108395 | ||||||||
\(497\) | 4.80667e6 | 0.872877 | ||||||||
\(498\) | 1.96852e7 | 3.55687 | ||||||||
\(499\) | −3.54549e6 | −0.637419 | −0.318710 | − | 0.947852i | \(-0.603250\pi\) | ||||
−0.318710 | + | 0.947852i | \(0.603250\pi\) | |||||||
\(500\) | 733454. | 0.131204 | ||||||||
\(501\) | −6.52567e6 | −1.16153 | ||||||||
\(502\) | 3.16533e6 | 0.560609 | ||||||||
\(503\) | 3.87983e6 | 0.683743 | 0.341872 | − | 0.939747i | \(-0.388939\pi\) | ||||
0.341872 | + | 0.939747i | \(0.388939\pi\) | |||||||
\(504\) | 9.46142e6 | 1.65913 | ||||||||
\(505\) | −2.77390e6 | −0.484019 | ||||||||
\(506\) | 2.68753e6 | 0.466635 | ||||||||
\(507\) | −1.63378e7 | −2.82277 | ||||||||
\(508\) | −7.27091e6 | −1.25006 | ||||||||
\(509\) | −6.20042e6 | −1.06078 | −0.530392 | − | 0.847753i | \(-0.677955\pi\) | ||||
−0.530392 | + | 0.847753i | \(0.677955\pi\) | |||||||
\(510\) | 758423. | 0.129118 | ||||||||
\(511\) | −5.92689e6 | −1.00410 | ||||||||
\(512\) | −3.66620e6 | −0.618075 | ||||||||
\(513\) | 1.22230e6 | 0.205061 | ||||||||
\(514\) | 6.72769e6 | 1.12320 | ||||||||
\(515\) | 1.41367e6 | 0.234871 | ||||||||
\(516\) | 4.57856e6 | 0.757015 | ||||||||
\(517\) | −1.98654e6 | −0.326867 | ||||||||
\(518\) | −1.67732e7 | −2.74658 | ||||||||
\(519\) | 371337. | 0.0605132 | ||||||||
\(520\) | −3.36241e6 | −0.545308 | ||||||||
\(521\) | −1.15408e7 | −1.86269 | −0.931347 | − | 0.364132i | \(-0.881366\pi\) | ||||
−0.931347 | + | 0.364132i | \(0.881366\pi\) | |||||||
\(522\) | −2.33189e7 | −3.74569 | ||||||||
\(523\) | −4.76148e6 | −0.761181 | −0.380591 | − | 0.924744i | \(-0.624279\pi\) | ||||
−0.380591 | + | 0.924744i | \(0.624279\pi\) | |||||||
\(524\) | 1.36468e7 | 2.17121 | ||||||||
\(525\) | 2.93246e6 | 0.464338 | ||||||||
\(526\) | 1.34188e7 | 2.11471 | ||||||||
\(527\) | 252046. | 0.0395324 | ||||||||
\(528\) | 973510. | 0.151969 | ||||||||
\(529\) | −187022. | −0.0290572 | ||||||||
\(530\) | 7.97864e6 | 1.23378 | ||||||||
\(531\) | −7.83400e6 | −1.20572 | ||||||||
\(532\) | 3.18854e6 | 0.488442 | ||||||||
\(533\) | 1.19974e7 | 1.82924 | ||||||||
\(534\) | 2.83025e7 | 4.29509 | ||||||||
\(535\) | 739820. | 0.111748 | ||||||||
\(536\) | 3.88633e6 | 0.584289 | ||||||||
\(537\) | −1.13881e7 | −1.70418 | ||||||||
\(538\) | −2.59462e6 | −0.386472 | ||||||||
\(539\) | 2.25036e6 | 0.333641 | ||||||||
\(540\) | −3.97340e6 | −0.586379 | ||||||||
\(541\) | −2.61622e6 | −0.384309 | −0.192154 | − | 0.981365i | \(-0.561547\pi\) | ||||
−0.192154 | + | 0.981365i | \(0.561547\pi\) | |||||||
\(542\) | −1.29653e7 | −1.89576 | ||||||||
\(543\) | 8.70672e6 | 1.26723 | ||||||||
\(544\) | 974220. | 0.141143 | ||||||||
\(545\) | 3.28126e6 | 0.473205 | ||||||||
\(546\) | −4.22359e7 | −6.06318 | ||||||||
\(547\) | −3.57422e6 | −0.510756 | −0.255378 | − | 0.966841i | \(-0.582200\pi\) | ||||
−0.255378 | + | 0.966841i | \(0.582200\pi\) | |||||||
\(548\) | 1.54873e6 | 0.220306 | ||||||||
\(549\) | −844037. | −0.119517 | ||||||||
\(550\) | −671919. | −0.0947131 | ||||||||
\(551\) | −2.50134e6 | −0.350989 | ||||||||
\(552\) | −8.27501e6 | −1.15590 | ||||||||
\(553\) | 1.74738e7 | 2.42983 | ||||||||
\(554\) | −4.92096e6 | −0.681201 | ||||||||
\(555\) | 6.25449e6 | 0.861906 | ||||||||
\(556\) | 8.17190e6 | 1.12108 | ||||||||
\(557\) | 1.23683e7 | 1.68917 | 0.844585 | − | 0.535422i | \(-0.179847\pi\) | ||||
0.844585 | + | 0.535422i | \(0.179847\pi\) | |||||||
\(558\) | −6.19473e6 | −0.842242 | ||||||||
\(559\) | −3.96309e6 | −0.536420 | ||||||||
\(560\) | 1.51777e6 | 0.204521 | ||||||||
\(561\) | −413148. | −0.0554241 | ||||||||
\(562\) | −7.72252e6 | −1.03138 | ||||||||
\(563\) | −6.02685e6 | −0.801345 | −0.400672 | − | 0.916221i | \(-0.631223\pi\) | ||||
−0.400672 | + | 0.916221i | \(0.631223\pi\) | |||||||
\(564\) | 1.92169e7 | 2.54382 | ||||||||
\(565\) | 844643. | 0.111315 | ||||||||
\(566\) | 1.12485e7 | 1.47589 | ||||||||
\(567\) | 1.43304e6 | 0.187197 | ||||||||
\(568\) | 3.39112e6 | 0.441035 | ||||||||
\(569\) | 1.27503e7 | 1.65097 | 0.825487 | − | 0.564421i | \(-0.190901\pi\) | ||||
0.825487 | + | 0.564421i | \(0.190901\pi\) | |||||||
\(570\) | −1.99949e6 | −0.257769 | ||||||||
\(571\) | 2.46819e6 | 0.316802 | 0.158401 | − | 0.987375i | \(-0.449366\pi\) | ||||
0.158401 | + | 0.987375i | \(0.449366\pi\) | |||||||
\(572\) | 5.75461e6 | 0.735404 | ||||||||
\(573\) | −1.10326e7 | −1.40375 | ||||||||
\(574\) | 1.97967e7 | 2.50792 | ||||||||
\(575\) | −1.56242e6 | −0.197073 | ||||||||
\(576\) | −2.00333e7 | −2.51592 | ||||||||
\(577\) | 139823. | 0.0174839 | 0.00874197 | − | 0.999962i | \(-0.497217\pi\) | ||||
0.00874197 | + | 0.999962i | \(0.497217\pi\) | |||||||
\(578\) | 1.24487e7 | 1.54990 | ||||||||
\(579\) | 3.37045e6 | 0.417823 | ||||||||
\(580\) | 8.13126e6 | 1.00366 | ||||||||
\(581\) | −1.67187e7 | −2.05476 | ||||||||
\(582\) | −7.81457e6 | −0.956308 | ||||||||
\(583\) | −4.34633e6 | −0.529604 | ||||||||
\(584\) | −4.18145e6 | −0.507335 | ||||||||
\(585\) | 9.59424e6 | 1.15910 | ||||||||
\(586\) | 6.13432e6 | 0.737943 | ||||||||
\(587\) | 5.33599e6 | 0.639175 | 0.319588 | − | 0.947557i | \(-0.396456\pi\) | ||||
0.319588 | + | 0.947557i | \(0.396456\pi\) | |||||||
\(588\) | −2.17690e7 | −2.59654 | ||||||||
\(589\) | −664487. | −0.0789220 | ||||||||
\(590\) | 4.59391e6 | 0.543316 | ||||||||
\(591\) | 1.18702e7 | 1.39795 | ||||||||
\(592\) | 3.23718e6 | 0.379632 | ||||||||
\(593\) | −1.22305e7 | −1.42826 | −0.714130 | − | 0.700013i | \(-0.753177\pi\) | ||||
−0.714130 | + | 0.700013i | \(0.753177\pi\) | |||||||
\(594\) | 3.64004e6 | 0.423293 | ||||||||
\(595\) | −644128. | −0.0745899 | ||||||||
\(596\) | 2.04533e7 | 2.35856 | ||||||||
\(597\) | 1.74262e7 | 2.00109 | ||||||||
\(598\) | 2.25033e7 | 2.57332 | ||||||||
\(599\) | −1.15256e7 | −1.31249 | −0.656247 | − | 0.754546i | \(-0.727857\pi\) | ||||
−0.656247 | + | 0.754546i | \(0.727857\pi\) | |||||||
\(600\) | 2.06886e6 | 0.234614 | ||||||||
\(601\) | 3.52237e6 | 0.397786 | 0.198893 | − | 0.980021i | \(-0.436265\pi\) | ||||
0.198893 | + | 0.980021i | \(0.436265\pi\) | |||||||
\(602\) | −6.53943e6 | −0.735442 | ||||||||
\(603\) | −1.10892e7 | −1.24196 | ||||||||
\(604\) | −7.32227e6 | −0.816682 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | −2.45823e7 | −2.71919 | ||||||||
\(607\) | −3.87019e6 | −0.426344 | −0.213172 | − | 0.977015i | \(-0.568380\pi\) | ||||
−0.213172 | + | 0.977015i | \(0.568380\pi\) | |||||||
\(608\) | −2.56841e6 | −0.281777 | ||||||||
\(609\) | 3.25100e7 | 3.55201 | ||||||||
\(610\) | 494950. | 0.0538563 | ||||||||
\(611\) | −1.66337e7 | −1.80255 | ||||||||
\(612\) | 2.43470e6 | 0.262764 | ||||||||
\(613\) | 5.31523e6 | 0.571309 | 0.285655 | − | 0.958333i | \(-0.407789\pi\) | ||||
0.285655 | + | 0.958333i | \(0.407789\pi\) | |||||||
\(614\) | −5.47352e6 | −0.585930 | ||||||||
\(615\) | −7.38192e6 | −0.787013 | ||||||||
\(616\) | 3.02238e6 | 0.320921 | ||||||||
\(617\) | −5.68939e6 | −0.601663 | −0.300831 | − | 0.953677i | \(-0.597264\pi\) | ||||
−0.300831 | + | 0.953677i | \(0.597264\pi\) | |||||||
\(618\) | 1.25279e7 | 1.31949 | ||||||||
\(619\) | −1.27931e6 | −0.134199 | −0.0670997 | − | 0.997746i | \(-0.521375\pi\) | ||||
−0.0670997 | + | 0.997746i | \(0.521375\pi\) | |||||||
\(620\) | 2.16009e6 | 0.225680 | ||||||||
\(621\) | 8.46421e6 | 0.880760 | ||||||||
\(622\) | −1.47636e7 | −1.53009 | ||||||||
\(623\) | −2.40373e7 | −2.48123 | ||||||||
\(624\) | 8.15142e6 | 0.838054 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −1.20480e7 | −1.22880 | ||||||||
\(627\) | 1.08921e6 | 0.110648 | ||||||||
\(628\) | −5.89627e6 | −0.596593 | ||||||||
\(629\) | −1.37383e6 | −0.138454 | ||||||||
\(630\) | 1.58313e7 | 1.58915 | ||||||||
\(631\) | 3.51100e6 | 0.351041 | 0.175521 | − | 0.984476i | \(-0.443839\pi\) | ||||
0.175521 | + | 0.984476i | \(0.443839\pi\) | |||||||
\(632\) | 1.23279e7 | 1.22771 | ||||||||
\(633\) | 8.28878e6 | 0.822207 | ||||||||
\(634\) | −1.09526e7 | −1.08217 | ||||||||
\(635\) | −3.87236e6 | −0.381102 | ||||||||
\(636\) | 4.20446e7 | 4.12162 | ||||||||
\(637\) | 1.88428e7 | 1.83991 | ||||||||
\(638\) | −7.44907e6 | −0.724520 | ||||||||
\(639\) | −9.67618e6 | −0.937458 | ||||||||
\(640\) | 6.05591e6 | 0.584425 | ||||||||
\(641\) | −1.25302e6 | −0.120452 | −0.0602258 | − | 0.998185i | \(-0.519182\pi\) | ||||
−0.0602258 | + | 0.998185i | \(0.519182\pi\) | |||||||
\(642\) | 6.55628e6 | 0.627798 | ||||||||
\(643\) | 1.36373e7 | 1.30077 | 0.650386 | − | 0.759604i | \(-0.274607\pi\) | ||||
0.650386 | + | 0.759604i | \(0.274607\pi\) | |||||||
\(644\) | 2.20801e7 | 2.09791 | ||||||||
\(645\) | 2.43846e6 | 0.230790 | ||||||||
\(646\) | 439196. | 0.0414074 | ||||||||
\(647\) | −4.55963e6 | −0.428222 | −0.214111 | − | 0.976809i | \(-0.568685\pi\) | ||||
−0.214111 | + | 0.976809i | \(0.568685\pi\) | |||||||
\(648\) | 1.01101e6 | 0.0945843 | ||||||||
\(649\) | −2.50251e6 | −0.233220 | ||||||||
\(650\) | −5.62613e6 | −0.522308 | ||||||||
\(651\) | 8.63637e6 | 0.798691 | ||||||||
\(652\) | 2.29248e7 | 2.11196 | ||||||||
\(653\) | −1.74990e7 | −1.60594 | −0.802971 | − | 0.596019i | \(-0.796748\pi\) | ||||
−0.802971 | + | 0.596019i | \(0.796748\pi\) | |||||||
\(654\) | 2.90785e7 | 2.65844 | ||||||||
\(655\) | 7.26804e6 | 0.661933 | ||||||||
\(656\) | −3.82072e6 | −0.346645 | ||||||||
\(657\) | 1.19313e7 | 1.07838 | ||||||||
\(658\) | −2.74470e7 | −2.47133 | ||||||||
\(659\) | 1.41476e7 | 1.26902 | 0.634512 | − | 0.772913i | \(-0.281201\pi\) | ||||
0.634512 | + | 0.772913i | \(0.281201\pi\) | |||||||
\(660\) | −3.54077e6 | −0.316401 | ||||||||
\(661\) | −9.25386e6 | −0.823795 | −0.411897 | − | 0.911230i | \(-0.635134\pi\) | ||||
−0.411897 | + | 0.911230i | \(0.635134\pi\) | |||||||
\(662\) | 7.99563e6 | 0.709101 | ||||||||
\(663\) | −3.45938e6 | −0.305643 | ||||||||
\(664\) | −1.17951e7 | −1.03820 | ||||||||
\(665\) | 1.69816e6 | 0.148911 | ||||||||
\(666\) | 3.37657e7 | 2.94978 | ||||||||
\(667\) | −1.73213e7 | −1.50753 | ||||||||
\(668\) | 1.22845e7 | 1.06517 | ||||||||
\(669\) | −3.44576e7 | −2.97660 | ||||||||
\(670\) | 6.50278e6 | 0.559644 | ||||||||
\(671\) | −269622. | −0.0231179 | ||||||||
\(672\) | 3.33817e7 | 2.85158 | ||||||||
\(673\) | 1.31201e7 | 1.11660 | 0.558301 | − | 0.829638i | \(-0.311453\pi\) | ||||
0.558301 | + | 0.829638i | \(0.311453\pi\) | |||||||
\(674\) | 3.00138e7 | 2.54491 | ||||||||
\(675\) | −2.11617e6 | −0.178768 | ||||||||
\(676\) | 3.07558e7 | 2.58857 | ||||||||
\(677\) | 1.75189e7 | 1.46904 | 0.734521 | − | 0.678586i | \(-0.237407\pi\) | ||||
0.734521 | + | 0.678586i | \(0.237407\pi\) | |||||||
\(678\) | 7.48522e6 | 0.625360 | ||||||||
\(679\) | 6.63691e6 | 0.552448 | ||||||||
\(680\) | −454435. | −0.0376877 | ||||||||
\(681\) | 1.00758e7 | 0.832555 | ||||||||
\(682\) | −1.97886e6 | −0.162913 | ||||||||
\(683\) | −6.94169e6 | −0.569395 | −0.284698 | − | 0.958617i | \(-0.591893\pi\) | ||||
−0.284698 | + | 0.958617i | \(0.591893\pi\) | |||||||
\(684\) | −6.41877e6 | −0.524580 | ||||||||
\(685\) | 824830. | 0.0671642 | ||||||||
\(686\) | 2.99418e6 | 0.242922 | ||||||||
\(687\) | −3.34989e7 | −2.70793 | ||||||||
\(688\) | 1.26209e6 | 0.101653 | ||||||||
\(689\) | −3.63928e7 | −2.92057 | ||||||||
\(690\) | −1.38461e7 | −1.10715 | ||||||||
\(691\) | −743833. | −0.0592625 | −0.0296313 | − | 0.999561i | \(-0.509433\pi\) | ||||
−0.0296313 | + | 0.999561i | \(0.509433\pi\) | |||||||
\(692\) | −699039. | −0.0554927 | ||||||||
\(693\) | −8.62402e6 | −0.682145 | ||||||||
\(694\) | 2.96707e7 | 2.33846 | ||||||||
\(695\) | 4.35222e6 | 0.341782 | ||||||||
\(696\) | 2.29360e7 | 1.79471 | ||||||||
\(697\) | 1.62147e6 | 0.126424 | ||||||||
\(698\) | −3.04684e7 | −2.36707 | ||||||||
\(699\) | 3.55988e7 | 2.75576 | ||||||||
\(700\) | −5.52033e6 | −0.425814 | ||||||||
\(701\) | 2.12345e6 | 0.163210 | 0.0816049 | − | 0.996665i | \(-0.473995\pi\) | ||||
0.0816049 | + | 0.996665i | \(0.473995\pi\) | |||||||
\(702\) | 3.04789e7 | 2.33430 | ||||||||
\(703\) | 3.62193e6 | 0.276408 | ||||||||
\(704\) | −6.39949e6 | −0.486647 | ||||||||
\(705\) | 1.02346e7 | 0.775531 | ||||||||
\(706\) | −7.02416e6 | −0.530375 | ||||||||
\(707\) | 2.08777e7 | 1.57085 | ||||||||
\(708\) | 2.42083e7 | 1.81502 | ||||||||
\(709\) | −1.34560e7 | −1.00531 | −0.502654 | − | 0.864488i | \(-0.667643\pi\) | ||||
−0.502654 | + | 0.864488i | \(0.667643\pi\) | |||||||
\(710\) | 5.67418e6 | 0.422432 | ||||||||
\(711\) | −3.51761e7 | −2.60960 | ||||||||
\(712\) | −1.69585e7 | −1.25368 | ||||||||
\(713\) | −4.60146e6 | −0.338978 | ||||||||
\(714\) | −5.70826e6 | −0.419043 | ||||||||
\(715\) | 3.06481e6 | 0.224202 | ||||||||
\(716\) | 2.14380e7 | 1.56279 | ||||||||
\(717\) | 1.00688e7 | 0.731443 | ||||||||
\(718\) | 3.33673e7 | 2.41551 | ||||||||
\(719\) | 791399. | 0.0570917 | 0.0285459 | − | 0.999592i | \(-0.490912\pi\) | ||||
0.0285459 | + | 0.999592i | \(0.490912\pi\) | |||||||
\(720\) | −3.05539e6 | −0.219652 | ||||||||
\(721\) | −1.06400e7 | −0.762257 | ||||||||
\(722\) | −1.15789e6 | −0.0826652 | ||||||||
\(723\) | 2.68284e7 | 1.90875 | ||||||||
\(724\) | −1.63903e7 | −1.16209 | ||||||||
\(725\) | 4.33057e6 | 0.305985 | ||||||||
\(726\) | 3.24371e6 | 0.228402 | ||||||||
\(727\) | −532721. | −0.0373821 | −0.0186911 | − | 0.999825i | \(-0.505950\pi\) | ||||
−0.0186911 | + | 0.999825i | \(0.505950\pi\) | |||||||
\(728\) | 2.53071e7 | 1.76976 | ||||||||
\(729\) | −2.34010e7 | −1.63085 | ||||||||
\(730\) | −6.99659e6 | −0.485936 | ||||||||
\(731\) | −535619. | −0.0370734 | ||||||||
\(732\) | 2.60821e6 | 0.179914 | ||||||||
\(733\) | −5.86911e6 | −0.403471 | −0.201735 | − | 0.979440i | \(-0.564658\pi\) | ||||
−0.201735 | + | 0.979440i | \(0.564658\pi\) | |||||||
\(734\) | 855464. | 0.0586086 | ||||||||
\(735\) | −1.15938e7 | −0.791603 | ||||||||
\(736\) | −1.77858e7 | −1.21026 | ||||||||
\(737\) | −3.54236e6 | −0.240228 | ||||||||
\(738\) | −3.98523e7 | −2.69347 | ||||||||
\(739\) | −1.14369e7 | −0.770368 | −0.385184 | − | 0.922840i | \(-0.625862\pi\) | ||||
−0.385184 | + | 0.922840i | \(0.625862\pi\) | |||||||
\(740\) | −1.17740e7 | −0.790398 | ||||||||
\(741\) | 9.12022e6 | 0.610183 | ||||||||
\(742\) | −6.00511e7 | −4.00416 | ||||||||
\(743\) | −1.57238e7 | −1.04492 | −0.522462 | − | 0.852662i | \(-0.674986\pi\) | ||||
−0.522462 | + | 0.852662i | \(0.674986\pi\) | |||||||
\(744\) | 6.09300e6 | 0.403551 | ||||||||
\(745\) | 1.08931e7 | 0.719052 | ||||||||
\(746\) | −1.17424e7 | −0.772522 | ||||||||
\(747\) | 3.36559e7 | 2.20679 | ||||||||
\(748\) | 777747. | 0.0508258 | ||||||||
\(749\) | −5.56824e6 | −0.362672 | ||||||||
\(750\) | 3.46172e6 | 0.224718 | ||||||||
\(751\) | 1.38162e7 | 0.893902 | 0.446951 | − | 0.894558i | \(-0.352510\pi\) | ||||
0.446951 | + | 0.894558i | \(0.352510\pi\) | |||||||
\(752\) | 5.29721e6 | 0.341588 | ||||||||
\(753\) | 8.88358e6 | 0.570953 | ||||||||
\(754\) | −6.23727e7 | −3.99546 | ||||||||
\(755\) | −3.89972e6 | −0.248981 | ||||||||
\(756\) | 2.99058e7 | 1.90305 | ||||||||
\(757\) | −1.29929e6 | −0.0824073 | −0.0412037 | − | 0.999151i | \(-0.513119\pi\) | ||||
−0.0412037 | + | 0.999151i | \(0.513119\pi\) | |||||||
\(758\) | −6.97074e6 | −0.440662 | ||||||||
\(759\) | 7.54261e6 | 0.475245 | ||||||||
\(760\) | 1.19806e6 | 0.0752394 | ||||||||
\(761\) | −1.25864e7 | −0.787843 | −0.393922 | − | 0.919144i | \(-0.628882\pi\) | ||||
−0.393922 | + | 0.919144i | \(0.628882\pi\) | |||||||
\(762\) | −3.43168e7 | −2.14102 | ||||||||
\(763\) | −2.46963e7 | −1.53575 | ||||||||
\(764\) | 2.07687e7 | 1.28729 | ||||||||
\(765\) | 1.29668e6 | 0.0801085 | ||||||||
\(766\) | −2.78268e7 | −1.71353 | ||||||||
\(767\) | −2.09541e7 | −1.28612 | ||||||||
\(768\) | 1.14657e7 | 0.701449 | ||||||||
\(769\) | −5.78962e6 | −0.353048 | −0.176524 | − | 0.984296i | \(-0.556485\pi\) | ||||
−0.176524 | + | 0.984296i | \(0.556485\pi\) | |||||||
\(770\) | 5.05719e6 | 0.307385 | ||||||||
\(771\) | 1.88814e7 | 1.14393 | ||||||||
\(772\) | −6.34485e6 | −0.383158 | ||||||||
\(773\) | 2.03165e6 | 0.122293 | 0.0611464 | − | 0.998129i | \(-0.480524\pi\) | ||||
0.0611464 | + | 0.998129i | \(0.480524\pi\) | |||||||
\(774\) | 1.31644e7 | 0.789854 | ||||||||
\(775\) | 1.15043e6 | 0.0688026 | ||||||||
\(776\) | 4.68237e6 | 0.279133 | ||||||||
\(777\) | −4.70744e7 | −2.79725 | ||||||||
\(778\) | 2.07276e7 | 1.22772 | ||||||||
\(779\) | −4.27481e6 | −0.252391 | ||||||||
\(780\) | −2.96477e7 | −1.74483 | ||||||||
\(781\) | −3.09099e6 | −0.181330 | ||||||||
\(782\) | 3.04136e6 | 0.177849 | ||||||||
\(783\) | −2.34604e7 | −1.36751 | ||||||||
\(784\) | −6.00069e6 | −0.348667 | ||||||||
\(785\) | −3.14026e6 | −0.181882 | ||||||||
\(786\) | 6.44093e7 | 3.71871 | ||||||||
\(787\) | 1.29592e7 | 0.745833 | 0.372917 | − | 0.927865i | \(-0.378358\pi\) | ||||
0.372917 | + | 0.927865i | \(0.378358\pi\) | |||||||
\(788\) | −2.23456e7 | −1.28197 | ||||||||
\(789\) | 3.76602e7 | 2.15372 | ||||||||
\(790\) | 2.06275e7 | 1.17593 | ||||||||
\(791\) | −6.35719e6 | −0.361263 | ||||||||
\(792\) | −6.08428e6 | −0.344664 | ||||||||
\(793\) | −2.25760e6 | −0.127487 | ||||||||
\(794\) | −4.09611e7 | −2.30579 | ||||||||
\(795\) | 2.23922e7 | 1.25655 | ||||||||
\(796\) | −3.28046e7 | −1.83507 | ||||||||
\(797\) | −2.70442e6 | −0.150810 | −0.0754048 | − | 0.997153i | \(-0.524025\pi\) | ||||
−0.0754048 | + | 0.997153i | \(0.524025\pi\) | |||||||
\(798\) | 1.50491e7 | 0.836572 | ||||||||
\(799\) | −2.24808e6 | −0.124579 | ||||||||
\(800\) | 4.44669e6 | 0.245647 | ||||||||
\(801\) | 4.83890e7 | 2.66480 | ||||||||
\(802\) | −2.01413e7 | −1.10574 | ||||||||
\(803\) | 3.81136e6 | 0.208589 | ||||||||
\(804\) | 3.42673e7 | 1.86956 | ||||||||
\(805\) | 1.17595e7 | 0.639586 | ||||||||
\(806\) | −1.65695e7 | −0.898403 | ||||||||
\(807\) | −7.28186e6 | −0.393603 | ||||||||
\(808\) | 1.47293e7 | 0.793696 | ||||||||
\(809\) | 1.45890e7 | 0.783708 | 0.391854 | − | 0.920027i | \(-0.371834\pi\) | ||||
0.391854 | + | 0.920027i | \(0.371834\pi\) | |||||||
\(810\) | 1.69167e6 | 0.0905949 | ||||||||
\(811\) | 1.41263e7 | 0.754181 | 0.377090 | − | 0.926177i | \(-0.376925\pi\) | ||||
0.377090 | + | 0.926177i | \(0.376925\pi\) | |||||||
\(812\) | −6.11998e7 | −3.25732 | ||||||||
\(813\) | −3.63874e7 | −1.93074 | ||||||||
\(814\) | 1.07862e7 | 0.570569 | ||||||||
\(815\) | 1.22093e7 | 0.643870 | ||||||||
\(816\) | 1.10168e6 | 0.0579202 | ||||||||
\(817\) | 1.41209e6 | 0.0740130 | ||||||||
\(818\) | 4.92211e7 | 2.57198 | ||||||||
\(819\) | −7.22109e7 | −3.76178 | ||||||||
\(820\) | 1.38964e7 | 0.721718 | ||||||||
\(821\) | 6.20587e6 | 0.321325 | 0.160663 | − | 0.987009i | \(-0.448637\pi\) | ||||
0.160663 | + | 0.987009i | \(0.448637\pi\) | |||||||
\(822\) | 7.30964e6 | 0.377326 | ||||||||
\(823\) | 1.55160e6 | 0.0798512 | 0.0399256 | − | 0.999203i | \(-0.487288\pi\) | ||||
0.0399256 | + | 0.999203i | \(0.487288\pi\) | |||||||
\(824\) | −7.50653e6 | −0.385142 | ||||||||
\(825\) | −1.88576e6 | −0.0964607 | ||||||||
\(826\) | −3.45760e7 | −1.76329 | ||||||||
\(827\) | 2.67852e7 | 1.36186 | 0.680928 | − | 0.732350i | \(-0.261577\pi\) | ||||
0.680928 | + | 0.732350i | \(0.261577\pi\) | |||||||
\(828\) | −4.44489e7 | −2.25313 | ||||||||
\(829\) | 2.26034e7 | 1.14232 | 0.571160 | − | 0.820839i | \(-0.306493\pi\) | ||||
0.571160 | + | 0.820839i | \(0.306493\pi\) | |||||||
\(830\) | −1.97361e7 | −0.994411 | ||||||||
\(831\) | −1.38108e7 | −0.693770 | ||||||||
\(832\) | −5.35844e7 | −2.68368 | ||||||||
\(833\) | 2.54663e6 | 0.127161 | ||||||||
\(834\) | 3.85693e7 | 1.92011 | ||||||||
\(835\) | 6.54253e6 | 0.324735 | ||||||||
\(836\) | −2.05043e6 | −0.101468 | ||||||||
\(837\) | −6.23231e6 | −0.307493 | ||||||||
\(838\) | −4.98616e7 | −2.45277 | ||||||||
\(839\) | −3.86543e7 | −1.89580 | −0.947901 | − | 0.318565i | \(-0.896799\pi\) | ||||
−0.947901 | + | 0.318565i | \(0.896799\pi\) | |||||||
\(840\) | −1.55713e7 | −0.761423 | ||||||||
\(841\) | 2.74987e7 | 1.34067 | ||||||||
\(842\) | 4.11960e7 | 2.00251 | ||||||||
\(843\) | −2.16734e7 | −1.05041 | ||||||||
\(844\) | −1.56035e7 | −0.753992 | ||||||||
\(845\) | 1.63800e7 | 0.789174 | ||||||||
\(846\) | 5.52529e7 | 2.65417 | ||||||||
\(847\) | −2.75488e6 | −0.131945 | ||||||||
\(848\) | 1.15897e7 | 0.553456 | ||||||||
\(849\) | 3.15692e7 | 1.50312 | ||||||||
\(850\) | −760382. | −0.0360981 | ||||||||
\(851\) | 2.50812e7 | 1.18720 | ||||||||
\(852\) | 2.99009e7 | 1.41119 | ||||||||
\(853\) | 2.27225e7 | 1.06926 | 0.534631 | − | 0.845086i | \(-0.320451\pi\) | ||||
0.534631 | + | 0.845086i | \(0.320451\pi\) | |||||||
\(854\) | −3.72523e6 | −0.174787 | ||||||||
\(855\) | −3.41853e6 | −0.159928 | ||||||||
\(856\) | −3.92842e6 | −0.183246 | ||||||||
\(857\) | −2.68485e6 | −0.124873 | −0.0624365 | − | 0.998049i | \(-0.519887\pi\) | ||||
−0.0624365 | + | 0.998049i | \(0.519887\pi\) | |||||||
\(858\) | 2.71603e7 | 1.25955 | ||||||||
\(859\) | 2.12982e7 | 0.984827 | 0.492413 | − | 0.870361i | \(-0.336115\pi\) | ||||
0.492413 | + | 0.870361i | \(0.336115\pi\) | |||||||
\(860\) | −4.59038e6 | −0.211642 | ||||||||
\(861\) | 5.55599e7 | 2.55419 | ||||||||
\(862\) | 2.22403e7 | 1.01946 | ||||||||
\(863\) | −4.00704e7 | −1.83146 | −0.915729 | − | 0.401796i | \(-0.868386\pi\) | ||||
−0.915729 | + | 0.401796i | \(0.868386\pi\) | |||||||
\(864\) | −2.40894e7 | −1.09785 | ||||||||
\(865\) | −372296. | −0.0169180 | ||||||||
\(866\) | 2.46576e7 | 1.11726 | ||||||||
\(867\) | 3.49375e7 | 1.57850 | ||||||||
\(868\) | −1.62579e7 | −0.732427 | ||||||||
\(869\) | −1.12368e7 | −0.504768 | ||||||||
\(870\) | 3.83775e7 | 1.71901 | ||||||||
\(871\) | −2.96610e7 | −1.32477 | ||||||||
\(872\) | −1.74234e7 | −0.775963 | ||||||||
\(873\) | −1.33606e7 | −0.593322 | ||||||||
\(874\) | −8.01817e6 | −0.355056 | ||||||||
\(875\) | −2.94003e6 | −0.129817 | ||||||||
\(876\) | −3.68695e7 | −1.62333 | ||||||||
\(877\) | 1.13767e7 | 0.499479 | 0.249739 | − | 0.968313i | \(-0.419655\pi\) | ||||
0.249739 | + | 0.968313i | \(0.419655\pi\) | |||||||
\(878\) | −6.05756e7 | −2.65193 | ||||||||
\(879\) | 1.72161e7 | 0.751559 | ||||||||
\(880\) | −976024. | −0.0424868 | ||||||||
\(881\) | −3.26303e7 | −1.41639 | −0.708193 | − | 0.706019i | \(-0.750489\pi\) | ||||
−0.708193 | + | 0.706019i | \(0.750489\pi\) | |||||||
\(882\) | −6.25907e7 | −2.70918 | ||||||||
\(883\) | 1.50901e7 | 0.651315 | 0.325657 | − | 0.945488i | \(-0.394414\pi\) | ||||
0.325657 | + | 0.945488i | \(0.394414\pi\) | |||||||
\(884\) | 6.51225e6 | 0.280285 | ||||||||
\(885\) | 1.28929e7 | 0.553341 | ||||||||
\(886\) | −3.79844e6 | −0.162563 | ||||||||
\(887\) | 1.37870e7 | 0.588384 | 0.294192 | − | 0.955746i | \(-0.404950\pi\) | ||||
0.294192 | + | 0.955746i | \(0.404950\pi\) | |||||||
\(888\) | −3.32112e7 | −1.41336 | ||||||||
\(889\) | 2.91453e7 | 1.23684 | ||||||||
\(890\) | −2.83756e7 | −1.20080 | ||||||||
\(891\) | −921531. | −0.0388880 | ||||||||
\(892\) | 6.48661e7 | 2.72964 | ||||||||
\(893\) | 5.92678e6 | 0.248708 | ||||||||
\(894\) | 9.65344e7 | 4.03960 | ||||||||
\(895\) | 1.14175e7 | 0.476446 | ||||||||
\(896\) | −4.55797e7 | −1.89671 | ||||||||
\(897\) | 6.31560e7 | 2.62080 | ||||||||
\(898\) | 7.54368e7 | 3.12171 | ||||||||
\(899\) | 1.27539e7 | 0.526314 | ||||||||
\(900\) | 1.11128e7 | 0.457318 | ||||||||
\(901\) | −4.91856e6 | −0.201849 | ||||||||
\(902\) | −1.27305e7 | −0.520991 | ||||||||
\(903\) | −1.83530e7 | −0.749012 | ||||||||
\(904\) | −4.48503e6 | −0.182534 | ||||||||
\(905\) | −8.72921e6 | −0.354285 | ||||||||
\(906\) | −3.45592e7 | −1.39876 | ||||||||
\(907\) | 2.49739e7 | 1.00802 | 0.504009 | − | 0.863698i | \(-0.331858\pi\) | ||||
0.504009 | + | 0.863698i | \(0.331858\pi\) | |||||||
\(908\) | −1.89676e7 | −0.763482 | ||||||||
\(909\) | −4.20284e7 | −1.68707 | ||||||||
\(910\) | 4.23450e7 | 1.69511 | ||||||||
\(911\) | 2.39786e7 | 0.957256 | 0.478628 | − | 0.878018i | \(-0.341134\pi\) | ||||
0.478628 | + | 0.878018i | \(0.341134\pi\) | |||||||
\(912\) | −2.90444e6 | −0.115631 | ||||||||
\(913\) | 1.07512e7 | 0.426853 | ||||||||
\(914\) | −5.77408e7 | −2.28622 | ||||||||
\(915\) | 1.38909e6 | 0.0548500 | ||||||||
\(916\) | 6.30613e7 | 2.48327 | ||||||||
\(917\) | −5.47028e7 | −2.14826 | ||||||||
\(918\) | 4.11928e6 | 0.161330 | ||||||||
\(919\) | 6.14797e6 | 0.240128 | 0.120064 | − | 0.992766i | \(-0.461690\pi\) | ||||
0.120064 | + | 0.992766i | \(0.461690\pi\) | |||||||
\(920\) | 8.29638e6 | 0.323161 | ||||||||
\(921\) | −1.53616e7 | −0.596741 | ||||||||
\(922\) | −4.19151e7 | −1.62384 | ||||||||
\(923\) | −2.58815e7 | −0.999967 | ||||||||
\(924\) | 2.66496e7 | 1.02686 | ||||||||
\(925\) | −6.27065e6 | −0.240967 | ||||||||
\(926\) | −5.24902e7 | −2.01164 | ||||||||
\(927\) | 2.14190e7 | 0.818654 | ||||||||
\(928\) | 4.92972e7 | 1.87911 | ||||||||
\(929\) | 3.50835e7 | 1.33372 | 0.666858 | − | 0.745185i | \(-0.267639\pi\) | ||||
0.666858 | + | 0.745185i | \(0.267639\pi\) | |||||||
\(930\) | 1.01951e7 | 0.386530 | ||||||||
\(931\) | −6.71388e6 | −0.253863 | ||||||||
\(932\) | −6.70143e7 | −2.52713 | ||||||||
\(933\) | −4.14344e7 | −1.55832 | ||||||||
\(934\) | −4.47679e7 | −1.67919 | ||||||||
\(935\) | 414215. | 0.0154952 | ||||||||
\(936\) | −5.09451e7 | −1.90070 | ||||||||
\(937\) | 2.05030e7 | 0.762902 | 0.381451 | − | 0.924389i | \(-0.375424\pi\) | ||||
0.381451 | + | 0.924389i | \(0.375424\pi\) | |||||||
\(938\) | −4.89431e7 | −1.81629 | ||||||||
\(939\) | −3.38130e7 | −1.25147 | ||||||||
\(940\) | −1.92666e7 | −0.711189 | ||||||||
\(941\) | 2.06647e7 | 0.760774 | 0.380387 | − | 0.924827i | \(-0.375791\pi\) | ||||
0.380387 | + | 0.924827i | \(0.375791\pi\) | |||||||
\(942\) | −2.78289e7 | −1.02181 | ||||||||
\(943\) | −2.96023e7 | −1.08404 | ||||||||
\(944\) | 6.67308e6 | 0.243723 | ||||||||
\(945\) | 1.59273e7 | 0.580180 | ||||||||
\(946\) | 4.20526e6 | 0.152779 | ||||||||
\(947\) | −1.98587e6 | −0.0719573 | −0.0359786 | − | 0.999353i | \(-0.511455\pi\) | ||||
−0.0359786 | + | 0.999353i | \(0.511455\pi\) | |||||||
\(948\) | 1.08700e8 | 3.92833 | ||||||||
\(949\) | 3.19134e7 | 1.15029 | ||||||||
\(950\) | 2.00465e6 | 0.0720659 | ||||||||
\(951\) | −3.07387e7 | −1.10213 | ||||||||
\(952\) | 3.42030e6 | 0.122313 | ||||||||
\(953\) | −5.07140e7 | −1.80882 | −0.904410 | − | 0.426664i | \(-0.859689\pi\) | ||||
−0.904410 | + | 0.426664i | \(0.859689\pi\) | |||||||
\(954\) | 1.20887e8 | 4.30041 | ||||||||
\(955\) | 1.10611e7 | 0.392454 | ||||||||
\(956\) | −1.89544e7 | −0.670759 | ||||||||
\(957\) | −2.09060e7 | −0.737888 | ||||||||
\(958\) | 1.58828e7 | 0.559131 | ||||||||
\(959\) | −6.20807e6 | −0.217977 | ||||||||
\(960\) | 3.29701e7 | 1.15463 | ||||||||
\(961\) | −2.52410e7 | −0.881655 | ||||||||
\(962\) | 9.03154e7 | 3.14647 | ||||||||
\(963\) | 1.12093e7 | 0.389504 | ||||||||
\(964\) | −5.05043e7 | −1.75039 | ||||||||
\(965\) | −3.37916e6 | −0.116813 | ||||||||
\(966\) | 1.04213e8 | 3.59317 | ||||||||
\(967\) | 2.75220e7 | 0.946486 | 0.473243 | − | 0.880932i | \(-0.343083\pi\) | ||||
0.473243 | + | 0.880932i | \(0.343083\pi\) | |||||||
\(968\) | −1.94358e6 | −0.0666675 | ||||||||
\(969\) | 1.23261e6 | 0.0421714 | ||||||||
\(970\) | 7.83475e6 | 0.267360 | ||||||||
\(971\) | −3.59377e6 | −0.122321 | −0.0611607 | − | 0.998128i | \(-0.519480\pi\) | ||||
−0.0611607 | + | 0.998128i | \(0.519480\pi\) | |||||||
\(972\) | 4.75360e7 | 1.61383 | ||||||||
\(973\) | −3.27569e7 | −1.10923 | ||||||||
\(974\) | −2.92480e7 | −0.987867 | ||||||||
\(975\) | −1.57899e7 | −0.531945 | ||||||||
\(976\) | 718960. | 0.0241591 | ||||||||
\(977\) | −4.51616e7 | −1.51368 | −0.756838 | − | 0.653603i | \(-0.773257\pi\) | ||||
−0.756838 | + | 0.653603i | \(0.773257\pi\) | |||||||
\(978\) | 1.08199e8 | 3.61723 | ||||||||
\(979\) | 1.54575e7 | 0.515446 | ||||||||
\(980\) | 2.18252e7 | 0.725928 | ||||||||
\(981\) | 4.97156e7 | 1.64938 | ||||||||
\(982\) | 9.23194e7 | 3.05502 | ||||||||
\(983\) | 1.42881e7 | 0.471619 | 0.235810 | − | 0.971799i | \(-0.424226\pi\) | ||||
0.235810 | + | 0.971799i | \(0.424226\pi\) | |||||||
\(984\) | 3.91978e7 | 1.29055 | ||||||||
\(985\) | −1.19009e7 | −0.390831 | ||||||||
\(986\) | −8.42979e6 | −0.276137 | ||||||||
\(987\) | −7.70307e7 | −2.51693 | ||||||||
\(988\) | −1.71687e7 | −0.559559 | ||||||||
\(989\) | 9.77850e6 | 0.317893 | ||||||||
\(990\) | −1.01805e7 | −0.330127 | ||||||||
\(991\) | 3.52970e7 | 1.14171 | 0.570853 | − | 0.821053i | \(-0.306613\pi\) | ||||
0.570853 | + | 0.821053i | \(0.306613\pi\) | |||||||
\(992\) | 1.30959e7 | 0.422529 | ||||||||
\(993\) | 2.24399e7 | 0.722185 | ||||||||
\(994\) | −4.27066e7 | −1.37097 | ||||||||
\(995\) | −1.74712e7 | −0.559454 | ||||||||
\(996\) | −1.04002e8 | −3.32196 | ||||||||
\(997\) | 3.52946e7 | 1.12453 | 0.562264 | − | 0.826958i | \(-0.309931\pi\) | ||||
0.562264 | + | 0.826958i | \(0.309931\pi\) | |||||||
\(998\) | 3.15013e7 | 1.00116 | ||||||||
\(999\) | 3.39705e7 | 1.07693 |
(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.1.7 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.e.1.7 | ✓ | 38 | 1.1 | even | 1 | trivial |