Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,6,Mod(75,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.75");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.1891703058\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 75.9 | ||
Character | \(\chi\) | \(=\) | 76.75 |
Dual form | 76.6.d.a.75.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.77452 | − | 3.03380i | −0.844024 | − | 0.536306i | ||||
\(3\) | 25.5646 | 1.63997 | 0.819986 | − | 0.572384i | \(-0.193981\pi\) | ||||
0.819986 | + | 0.572384i | \(0.193981\pi\) | |||||||
\(4\) | 13.5921 | + | 28.9699i | 0.424752 | + | 0.905310i | ||||
\(5\) | 94.0869 | 1.68308 | 0.841539 | − | 0.540196i | \(-0.181650\pi\) | ||||
0.841539 | + | 0.540196i | \(0.181650\pi\) | |||||||
\(6\) | −122.059 | − | 77.5580i | −1.38417 | − | 0.879526i | ||||
\(7\) | − | 166.433i | − | 1.28379i | −0.766793 | − | 0.641894i | \(-0.778149\pi\) | ||
0.766793 | − | 0.641894i | \(-0.221851\pi\) | |||||||
\(8\) | 22.9933 | − | 179.553i | 0.127022 | − | 0.991900i | ||||
\(9\) | 410.550 | 1.68951 | ||||||||
\(10\) | −449.220 | − | 285.441i | −1.42056 | − | 0.902645i | ||||
\(11\) | 721.639i | 1.79820i | 0.437743 | + | 0.899100i | \(0.355778\pi\) | ||||
−0.437743 | + | 0.899100i | \(0.644222\pi\) | |||||||
\(12\) | 347.476 | + | 740.605i | 0.696582 | + | 1.48468i | ||||
\(13\) | − | 430.611i | − | 0.706686i | −0.935494 | − | 0.353343i | \(-0.885045\pi\) | ||
0.935494 | − | 0.353343i | \(-0.114955\pi\) | |||||||
\(14\) | −504.924 | + | 794.636i | −0.688503 | + | 1.08355i | ||||
\(15\) | 2405.30 | 2.76020 | ||||||||
\(16\) | −654.511 | + | 787.522i | −0.639171 | + | 0.769065i | ||||
\(17\) | −541.677 | −0.454588 | −0.227294 | − | 0.973826i | \(-0.572988\pi\) | ||||
−0.227294 | + | 0.973826i | \(0.572988\pi\) | |||||||
\(18\) | −1960.18 | − | 1245.53i | −1.42598 | − | 0.906092i | ||||
\(19\) | −1417.04 | + | 684.177i | −0.900529 | + | 0.434795i | ||||
\(20\) | 1278.84 | + | 2725.69i | 0.714892 | + | 1.52371i | ||||
\(21\) | − | 4254.79i | − | 2.10538i | ||||||
\(22\) | 2189.31 | − | 3445.48i | 0.964385 | − | 1.51772i | ||||
\(23\) | − | 9.20716i | − | 0.00362916i | −0.999998 | − | 0.00181458i | \(-0.999422\pi\) | ||
0.999998 | − | 0.00181458i | \(-0.000577599\pi\) | |||||||
\(24\) | 587.816 | − | 4590.21i | 0.208312 | − | 1.62669i | ||||
\(25\) | 5727.35 | 1.83275 | ||||||||
\(26\) | −1306.39 | + | 2055.96i | −0.379000 | + | 0.596460i | ||||
\(27\) | 4283.35 | 1.13077 | ||||||||
\(28\) | 4821.54 | − | 2262.17i | 1.16223 | − | 0.545292i | ||||
\(29\) | − | 3732.49i | − | 0.824145i | −0.911151 | − | 0.412073i | \(-0.864805\pi\) | ||
0.911151 | − | 0.412073i | \(-0.135195\pi\) | |||||||
\(30\) | −11484.1 | − | 7297.20i | −2.32967 | − | 1.48031i | ||||
\(31\) | −3182.34 | −0.594761 | −0.297380 | − | 0.954759i | \(-0.596113\pi\) | ||||
−0.297380 | + | 0.954759i | \(0.596113\pi\) | |||||||
\(32\) | 5514.16 | − | 1774.38i | 0.951929 | − | 0.306318i | ||||
\(33\) | 18448.4i | 2.94900i | ||||||||
\(34\) | 2586.25 | + | 1643.34i | 0.383684 | + | 0.243798i | ||||
\(35\) | − | 15659.1i | − | 2.16072i | ||||||
\(36\) | 5580.23 | + | 11893.6i | 0.717622 | + | 1.52953i | ||||
\(37\) | 49.0739i | 0.00589313i | 0.999996 | + | 0.00294656i | \(0.000937922\pi\) | ||||
−0.999996 | + | 0.00294656i | \(0.999062\pi\) | |||||||
\(38\) | 8841.34 | + | 1032.40i | 0.993251 | + | 0.115982i | ||||
\(39\) | − | 11008.4i | − | 1.15894i | ||||||
\(40\) | 2163.37 | − | 16893.6i | 0.213787 | − | 1.66945i | ||||
\(41\) | − | 798.065i | − | 0.0741444i | −0.999313 | − | 0.0370722i | \(-0.988197\pi\) | ||
0.999313 | − | 0.0370722i | \(-0.0118032\pi\) | |||||||
\(42\) | −12908.2 | + | 20314.6i | −1.12913 | + | 1.77699i | ||||
\(43\) | 8741.19i | 0.720941i | 0.932771 | + | 0.360470i | \(0.117384\pi\) | ||||
−0.932771 | + | 0.360470i | \(0.882616\pi\) | |||||||
\(44\) | −20905.8 | + | 9808.57i | −1.62793 | + | 0.763790i | ||||
\(45\) | 38627.4 | 2.84357 | ||||||||
\(46\) | −27.9327 | + | 43.9598i | −0.00194634 | + | 0.00306310i | ||||
\(47\) | − | 15993.5i | − | 1.05609i | −0.849218 | − | 0.528043i | \(-0.822926\pi\) | ||
0.849218 | − | 0.528043i | \(-0.177074\pi\) | |||||||
\(48\) | −16732.3 | + | 20132.7i | −1.04822 | + | 1.26124i | ||||
\(49\) | −10892.8 | −0.648112 | ||||||||
\(50\) | −27345.4 | − | 17375.7i | −1.54689 | − | 0.982916i | ||||
\(51\) | −13847.8 | −0.745512 | ||||||||
\(52\) | 12474.8 | − | 5852.89i | 0.639770 | − | 0.300167i | ||||
\(53\) | 28325.1i | 1.38510i | 0.721370 | + | 0.692550i | \(0.243513\pi\) | ||||
−0.721370 | + | 0.692550i | \(0.756487\pi\) | |||||||
\(54\) | −20451.0 | − | 12994.8i | −0.954397 | − | 0.606439i | ||||
\(55\) | 67896.8i | 3.02651i | ||||||||
\(56\) | −29883.5 | − | 3826.84i | −1.27339 | − | 0.163069i | ||||
\(57\) | −36226.1 | + | 17490.7i | −1.47684 | + | 0.713052i | ||||
\(58\) | −11323.6 | + | 17820.9i | −0.441994 | + | 0.695598i | ||||
\(59\) | −11895.3 | −0.444884 | −0.222442 | − | 0.974946i | \(-0.571403\pi\) | ||||
−0.222442 | + | 0.974946i | \(0.571403\pi\) | |||||||
\(60\) | 32693.0 | + | 69681.2i | 1.17240 | + | 2.49884i | ||||
\(61\) | 19568.1 | 0.673324 | 0.336662 | − | 0.941625i | \(-0.390702\pi\) | ||||
0.336662 | + | 0.941625i | \(0.390702\pi\) | |||||||
\(62\) | 15194.1 | + | 9654.59i | 0.501992 | + | 0.318973i | ||||
\(63\) | − | 68328.9i | − | 2.16897i | ||||||
\(64\) | −31710.6 | − | 8257.05i | −0.967731 | − | 0.251985i | ||||
\(65\) | − | 40514.9i | − | 1.18941i | ||||||
\(66\) | 55968.9 | − | 88082.3i | 1.58156 | − | 2.48902i | ||||
\(67\) | 25458.9 | 0.692872 | 0.346436 | − | 0.938074i | \(-0.387392\pi\) | ||||
0.346436 | + | 0.938074i | \(0.387392\pi\) | |||||||
\(68\) | −7362.52 | − | 15692.3i | −0.193088 | − | 0.411543i | ||||
\(69\) | − | 235.378i | − | 0.00595172i | ||||||
\(70\) | −47506.7 | + | 74764.9i | −1.15880 | + | 1.82370i | ||||
\(71\) | 35628.2 | 0.838780 | 0.419390 | − | 0.907806i | \(-0.362244\pi\) | ||||
0.419390 | + | 0.907806i | \(0.362244\pi\) | |||||||
\(72\) | 9439.92 | − | 73715.5i | 0.214604 | − | 1.67582i | ||||
\(73\) | −18156.0 | −0.398761 | −0.199381 | − | 0.979922i | \(-0.563893\pi\) | ||||
−0.199381 | + | 0.979922i | \(0.563893\pi\) | |||||||
\(74\) | 148.880 | − | 234.304i | 0.00316052 | − | 0.00497394i | ||||
\(75\) | 146418. | 3.00566 | ||||||||
\(76\) | −39081.1 | − | 31752.1i | −0.776126 | − | 0.630578i | ||||
\(77\) | 120104. | 2.30851 | ||||||||
\(78\) | −33397.3 | + | 52559.8i | −0.621549 | + | 0.978177i | ||||
\(79\) | −96443.4 | −1.73862 | −0.869310 | − | 0.494267i | \(-0.835436\pi\) | ||||
−0.869310 | + | 0.494267i | \(0.835436\pi\) | |||||||
\(80\) | −61580.9 | + | 74095.6i | −1.07577 | + | 1.29440i | ||||
\(81\) | 9738.65 | 0.164925 | ||||||||
\(82\) | −2421.17 | + | 3810.38i | −0.0397641 | + | 0.0625796i | ||||
\(83\) | − | 34700.1i | − | 0.552887i | −0.961030 | − | 0.276443i | \(-0.910844\pi\) | ||
0.961030 | − | 0.276443i | \(-0.0891558\pi\) | |||||||
\(84\) | 123261. | − | 57831.4i | 1.90602 | − | 0.894264i | ||||
\(85\) | −50964.8 | −0.765108 | ||||||||
\(86\) | 26519.1 | − | 41735.0i | 0.386645 | − | 0.608491i | ||||
\(87\) | − | 95419.7i | − | 1.35157i | ||||||
\(88\) | 129572. | + | 16592.9i | 1.78363 | + | 0.228410i | ||||
\(89\) | 32267.6i | 0.431808i | 0.976415 | + | 0.215904i | \(0.0692699\pi\) | ||||
−0.976415 | + | 0.215904i | \(0.930730\pi\) | |||||||
\(90\) | −184427. | − | 117188.i | −2.40004 | − | 1.52502i | ||||
\(91\) | −71667.7 | −0.907235 | ||||||||
\(92\) | 266.731 | − | 125.144i | 0.00328551 | − | 0.00154149i | ||||
\(93\) | −81355.3 | −0.975390 | ||||||||
\(94\) | −48521.1 | + | 76361.3i | −0.566385 | + | 0.891361i | ||||
\(95\) | −133325. | + | 64372.2i | −1.51566 | + | 0.731794i | ||||
\(96\) | 140968. | − | 45361.5i | 1.56114 | − | 0.502353i | ||||
\(97\) | − | 6031.95i | − | 0.0650922i | −0.999470 | − | 0.0325461i | \(-0.989638\pi\) | ||
0.999470 | − | 0.0325461i | \(-0.0103616\pi\) | |||||||
\(98\) | 52008.0 | + | 33046.7i | 0.547022 | + | 0.347586i | ||||
\(99\) | 296269.i | 3.03807i | ||||||||
\(100\) | 77846.6 | + | 165921.i | 0.778466 | + | 1.65921i | ||||
\(101\) | −108403. | −1.05739 | −0.528697 | − | 0.848811i | \(-0.677319\pi\) | ||||
−0.528697 | + | 0.848811i | \(0.677319\pi\) | |||||||
\(102\) | 66116.5 | + | 42011.4i | 0.629230 | + | 0.399822i | ||||
\(103\) | −77927.4 | −0.723765 | −0.361882 | − | 0.932224i | \(-0.617866\pi\) | ||||
−0.361882 | + | 0.932224i | \(0.617866\pi\) | |||||||
\(104\) | −77317.5 | − | 9901.18i | −0.700962 | − | 0.0897643i | ||||
\(105\) | − | 400320.i | − | 3.54351i | ||||||
\(106\) | 85932.7 | − | 135239.i | 0.742837 | − | 1.16906i | ||||
\(107\) | 94800.4 | 0.800481 | 0.400240 | − | 0.916410i | \(-0.368927\pi\) | ||||
0.400240 | + | 0.916410i | \(0.368927\pi\) | |||||||
\(108\) | 58219.7 | + | 124088.i | 0.480297 | + | 1.02370i | ||||
\(109\) | 226846.i | 1.82880i | 0.404816 | + | 0.914398i | \(0.367336\pi\) | ||||
−0.404816 | + | 0.914398i | \(0.632664\pi\) | |||||||
\(110\) | 205985. | − | 324174.i | 1.62314 | − | 2.55445i | ||||
\(111\) | 1254.55i | 0.00966456i | ||||||||
\(112\) | 131069. | + | 108932.i | 0.987316 | + | 0.820560i | ||||
\(113\) | 39331.1i | 0.289761i | 0.989449 | + | 0.144880i | \(0.0462797\pi\) | ||||
−0.989449 | + | 0.144880i | \(0.953720\pi\) | |||||||
\(114\) | 226026. | + | 26392.9i | 1.62890 | + | 0.190207i | ||||
\(115\) | − | 866.274i | − | 0.00610816i | ||||||
\(116\) | 108130. | − | 50732.3i | 0.746107 | − | 0.350058i | ||||
\(117\) | − | 176787.i | − | 1.19395i | ||||||
\(118\) | 56794.6 | + | 36088.1i | 0.375493 | + | 0.238594i | ||||
\(119\) | 90152.8i | 0.583595i | ||||||||
\(120\) | 55305.8 | − | 431879.i | 0.350605 | − | 2.73784i | ||||
\(121\) | −359711. | −2.23352 | ||||||||
\(122\) | −93428.3 | − | 59365.8i | −0.568302 | − | 0.361108i | ||||
\(123\) | − | 20402.2i | − | 0.121595i | ||||||
\(124\) | −43254.6 | − | 92192.0i | −0.252626 | − | 0.538442i | ||||
\(125\) | 244848. | 1.40159 | ||||||||
\(126\) | −207296. | + | 326238.i | −1.16323 | + | 1.83066i | ||||
\(127\) | −164306. | −0.903950 | −0.451975 | − | 0.892031i | \(-0.649280\pi\) | ||||
−0.451975 | + | 0.892031i | \(0.649280\pi\) | |||||||
\(128\) | 126353. | + | 135627.i | 0.681647 | + | 0.731681i | ||||
\(129\) | 223465.i | 1.18232i | ||||||||
\(130\) | −122914. | + | 193439.i | −0.637886 | + | 1.00389i | ||||
\(131\) | − | 345339.i | − | 1.75819i | −0.476642 | − | 0.879097i | \(-0.658146\pi\) | ||
0.476642 | − | 0.879097i | \(-0.341854\pi\) | |||||||
\(132\) | −534449. | + | 250752.i | −2.66975 | + | 1.25259i | ||||
\(133\) | 113869. | + | 235842.i | 0.558185 | + | 1.15609i | ||||
\(134\) | −121554. | − | 77237.3i | −0.584800 | − | 0.371591i | ||||
\(135\) | 403008. | 1.90318 | ||||||||
\(136\) | −12455.0 | + | 97259.8i | −0.0577425 | + | 0.450906i | ||||
\(137\) | −269095. | −1.22491 | −0.612455 | − | 0.790506i | \(-0.709818\pi\) | ||||
−0.612455 | + | 0.790506i | \(0.709818\pi\) | |||||||
\(138\) | −714.089 | + | 1123.81i | −0.00319194 | + | 0.00502339i | ||||
\(139\) | 105247.i | 0.462033i | 0.972950 | + | 0.231016i | \(0.0742051\pi\) | ||||
−0.972950 | + | 0.231016i | \(0.925795\pi\) | |||||||
\(140\) | 453644. | − | 212840.i | 1.95612 | − | 0.917770i | ||||
\(141\) | − | 408868.i | − | 1.73195i | ||||||
\(142\) | −170108. | − | 108089.i | −0.707950 | − | 0.449842i | ||||
\(143\) | 310745. | 1.27076 | ||||||||
\(144\) | −268709. | + | 323317.i | −1.07988 | + | 1.29934i | ||||
\(145\) | − | 351179.i | − | 1.38710i | ||||||
\(146\) | 86686.2 | + | 55081.7i | 0.336564 | + | 0.213858i | ||||
\(147\) | −278471. | −1.06289 | ||||||||
\(148\) | −1421.66 | + | 667.016i | −0.00533510 | + | 0.00250312i | ||||
\(149\) | 9590.81 | 0.0353908 | 0.0176954 | − | 0.999843i | \(-0.494367\pi\) | ||||
0.0176954 | + | 0.999843i | \(0.494367\pi\) | |||||||
\(150\) | −699074. | − | 444202.i | −2.53685 | − | 1.61195i | ||||
\(151\) | 93897.3 | 0.335128 | 0.167564 | − | 0.985861i | \(-0.446410\pi\) | ||||
0.167564 | + | 0.985861i | \(0.446410\pi\) | |||||||
\(152\) | 90263.7 | + | 270165.i | 0.316887 | + | 0.948463i | ||||
\(153\) | −222386. | −0.768030 | ||||||||
\(154\) | −573440. | − | 364373.i | −1.94844 | − | 1.23807i | ||||
\(155\) | −299417. | −1.00103 | ||||||||
\(156\) | 318912. | − | 149627.i | 1.04920 | − | 0.492265i | ||||
\(157\) | 499368. | 1.61686 | 0.808428 | − | 0.588595i | \(-0.200319\pi\) | ||||
0.808428 | + | 0.588595i | \(0.200319\pi\) | |||||||
\(158\) | 460471. | + | 292590.i | 1.46744 | + | 0.932432i | ||||
\(159\) | 724120.i | 2.27153i | ||||||||
\(160\) | 518811. | − | 166946.i | 1.60217 | − | 0.515557i | ||||
\(161\) | −1532.37 | −0.00465907 | ||||||||
\(162\) | −46497.4 | − | 29545.1i | −0.139201 | − | 0.0884501i | ||||
\(163\) | − | 225573.i | − | 0.664993i | −0.943104 | − | 0.332497i | \(-0.892109\pi\) | ||
0.943104 | − | 0.332497i | \(-0.107891\pi\) | |||||||
\(164\) | 23119.9 | − | 10847.4i | 0.0671236 | − | 0.0314930i | ||||
\(165\) | 1.73576e6i | 4.96339i | ||||||||
\(166\) | −105273. | + | 165677.i | −0.296516 | + | 0.466649i | ||||
\(167\) | 352587. | 0.978306 | 0.489153 | − | 0.872198i | \(-0.337306\pi\) | ||||
0.489153 | + | 0.872198i | \(0.337306\pi\) | |||||||
\(168\) | −763960. | − | 97831.8i | −2.08832 | − | 0.267428i | ||||
\(169\) | 185867. | 0.500595 | ||||||||
\(170\) | 243332. | + | 154617.i | 0.645769 | + | 0.410332i | ||||
\(171\) | −581765. | + | 280889.i | −1.52145 | + | 0.734589i | ||||
\(172\) | −253231. | + | 118811.i | −0.652674 | + | 0.306221i | ||||
\(173\) | − | 542727.i | − | 1.37869i | −0.724434 | − | 0.689344i | \(-0.757899\pi\) | ||
0.724434 | − | 0.689344i | \(-0.242101\pi\) | |||||||
\(174\) | −289485. | + | 455583.i | −0.724857 | + | 1.14076i | ||||
\(175\) | − | 953219.i | − | 2.35287i | ||||||
\(176\) | −568307. | − | 472320.i | −1.38293 | − | 1.14936i | ||||
\(177\) | −304100. | −0.729597 | ||||||||
\(178\) | 97893.4 | − | 154062.i | 0.231581 | − | 0.364457i | ||||
\(179\) | −429784. | −1.00258 | −0.501288 | − | 0.865280i | \(-0.667140\pi\) | ||||
−0.501288 | + | 0.865280i | \(0.667140\pi\) | |||||||
\(180\) | 525027. | + | 1.11903e6i | 1.20781 | + | 2.57431i | ||||
\(181\) | − | 175918.i | − | 0.399131i | −0.979885 | − | 0.199565i | \(-0.936047\pi\) | ||
0.979885 | − | 0.199565i | \(-0.0639530\pi\) | |||||||
\(182\) | 342179. | + | 217426.i | 0.765728 | + | 0.486555i | ||||
\(183\) | 500251. | 1.10423 | ||||||||
\(184\) | −1653.17 | − | 211.703i | −0.00359976 | − | 0.000460981i | ||||
\(185\) | 4617.21i | 0.00991860i | ||||||||
\(186\) | 388432. | + | 246816.i | 0.823253 | + | 0.523107i | ||||
\(187\) | − | 390895.i | − | 0.817441i | ||||||
\(188\) | 463330. | − | 217385.i | 0.956084 | − | 0.448575i | ||||
\(189\) | − | 712890.i | − | 1.45167i | ||||||
\(190\) | 831855. | + | 97135.4i | 1.67172 | + | 0.195206i | ||||
\(191\) | 95349.0i | 0.189118i | 0.995519 | + | 0.0945590i | \(0.0301441\pi\) | ||||
−0.995519 | + | 0.0945590i | \(0.969856\pi\) | |||||||
\(192\) | −810670. | − | 211088.i | −1.58705 | − | 0.413249i | ||||
\(193\) | 912221.i | 1.76281i | 0.472357 | + | 0.881407i | \(0.343403\pi\) | ||||
−0.472357 | + | 0.881407i | \(0.656597\pi\) | |||||||
\(194\) | −18299.8 | + | 28799.7i | −0.0349093 | + | 0.0549393i | ||||
\(195\) | − | 1.03575e6i | − | 1.95060i | ||||||
\(196\) | −148056. | − | 315564.i | −0.275287 | − | 0.586742i | ||||
\(197\) | 144265. | 0.264847 | 0.132424 | − | 0.991193i | \(-0.457724\pi\) | ||||
0.132424 | + | 0.991193i | \(0.457724\pi\) | |||||||
\(198\) | 898821. | − | 1.41454e6i | 1.62933 | − | 2.56420i | ||||
\(199\) | 607857.i | 1.08810i | 0.839053 | + | 0.544050i | \(0.183110\pi\) | ||||
−0.839053 | + | 0.544050i | \(0.816890\pi\) | |||||||
\(200\) | 131691. | − | 1.02836e6i | 0.232799 | − | 1.81791i | ||||
\(201\) | 650847. | 1.13629 | ||||||||
\(202\) | 517571. | + | 328873.i | 0.892466 | + | 0.567086i | ||||
\(203\) | −621208. | −1.05803 | ||||||||
\(204\) | −188220. | − | 401169.i | −0.316658 | − | 0.674919i | ||||
\(205\) | − | 75087.5i | − | 0.124791i | ||||||
\(206\) | 372066. | + | 236417.i | 0.610875 | + | 0.388159i | ||||
\(207\) | − | 3780.00i | − | 0.00613149i | ||||||
\(208\) | 339116. | + | 281839.i | 0.543487 | + | 0.451693i | ||||
\(209\) | −493729. | − | 1.02259e6i | −0.781849 | − | 1.61933i | ||||
\(210\) | −1.21449e6 | + | 1.91134e6i | −1.90041 | + | 2.99081i | ||||
\(211\) | 778502. | 1.20380 | 0.601899 | − | 0.798572i | \(-0.294411\pi\) | ||||
0.601899 | + | 0.798572i | \(0.294411\pi\) | |||||||
\(212\) | −820575. | + | 384997.i | −1.25394 | + | 0.588325i | ||||
\(213\) | 910822. | 1.37558 | ||||||||
\(214\) | −452627. | − | 287606.i | −0.675625 | − | 0.429302i | ||||
\(215\) | 822432.i | 1.21340i | ||||||||
\(216\) | 98488.6 | − | 769089.i | 0.143632 | − | 1.12161i | ||||
\(217\) | 529645.i | 0.763547i | ||||||||
\(218\) | 688207. | − | 1.08308e6i | 0.980794 | − | 1.54355i | ||||
\(219\) | −464151. | −0.653957 | ||||||||
\(220\) | −1.96696e6 | + | 922858.i | −2.73993 | + | 1.28552i | ||||
\(221\) | 233252.i | 0.321251i | ||||||||
\(222\) | 3806.07 | − | 5989.90i | 0.00518316 | − | 0.00815712i | ||||
\(223\) | −281144. | −0.378588 | −0.189294 | − | 0.981920i | \(-0.560620\pi\) | ||||
−0.189294 | + | 0.981920i | \(0.560620\pi\) | |||||||
\(224\) | −295315. | − | 917737.i | −0.393248 | − | 1.22208i | ||||
\(225\) | 2.35136e6 | 3.09645 | ||||||||
\(226\) | 119323. | − | 187787.i | 0.155400 | − | 0.244565i | ||||
\(227\) | 541554. | 0.697553 | 0.348777 | − | 0.937206i | \(-0.386597\pi\) | ||||
0.348777 | + | 0.937206i | \(0.386597\pi\) | |||||||
\(228\) | −999093. | − | 811731.i | −1.27282 | − | 1.03413i | ||||
\(229\) | 786356. | 0.990901 | 0.495451 | − | 0.868636i | \(-0.335003\pi\) | ||||
0.495451 | + | 0.868636i | \(0.335003\pi\) | |||||||
\(230\) | −2628.10 | + | 4136.04i | −0.00327584 | + | 0.00515543i | ||||
\(231\) | 3.07042e6 | 3.78589 | ||||||||
\(232\) | −670180. | − | 85822.5i | −0.817470 | − | 0.104684i | ||||
\(233\) | 355481. | 0.428969 | 0.214485 | − | 0.976727i | \(-0.431193\pi\) | ||||
0.214485 | + | 0.976727i | \(0.431193\pi\) | |||||||
\(234\) | −536338. | + | 844074.i | −0.640322 | + | 1.00772i | ||||
\(235\) | − | 1.50478e6i | − | 1.77747i | ||||||
\(236\) | −161682. | − | 344607.i | −0.188966 | − | 0.402758i | ||||
\(237\) | −2.46554e6 | −2.85129 | ||||||||
\(238\) | 273506. | − | 430436.i | 0.312986 | − | 0.492568i | ||||
\(239\) | 104233.i | 0.118034i | 0.998257 | + | 0.0590172i | \(0.0187967\pi\) | ||||
−0.998257 | + | 0.0590172i | \(0.981203\pi\) | |||||||
\(240\) | −1.57429e6 | + | 1.89423e6i | −1.76424 | + | 2.12277i | ||||
\(241\) | 306180.i | 0.339574i | 0.985481 | + | 0.169787i | \(0.0543080\pi\) | ||||
−0.985481 | + | 0.169787i | \(0.945692\pi\) | |||||||
\(242\) | 1.71745e6 | + | 1.09129e6i | 1.88515 | + | 1.19785i | ||||
\(243\) | −791890. | −0.860298 | ||||||||
\(244\) | 265971. | + | 566886.i | 0.285996 | + | 0.609567i | ||||
\(245\) | −1.02487e6 | −1.09082 | ||||||||
\(246\) | −61896.3 | + | 97410.8i | −0.0652119 | + | 0.102629i | ||||
\(247\) | 294614. | + | 610192.i | 0.307264 | + | 0.636392i | ||||
\(248\) | −73172.6 | + | 571399.i | −0.0755474 | + | 0.589943i | ||||
\(249\) | − | 887096.i | − | 0.906718i | ||||||
\(250\) | −1.16903e6 | − | 742819.i | −1.18297 | − | 0.751680i | ||||
\(251\) | 248473.i | 0.248940i | 0.992223 | + | 0.124470i | \(0.0397231\pi\) | ||||
−0.992223 | + | 0.124470i | \(0.960277\pi\) | |||||||
\(252\) | 1.97948e6 | − | 928732.i | 1.96359 | − | 0.921274i | ||||
\(253\) | 6644.24 | 0.00652596 | ||||||||
\(254\) | 784483. | + | 498472.i | 0.762955 | + | 0.484793i | ||||
\(255\) | −1.30290e6 | −1.25476 | ||||||||
\(256\) | −191807. | − | 1.03088e6i | −0.182921 | − | 0.983128i | ||||
\(257\) | − | 878165.i | − | 0.829361i | −0.909967 | − | 0.414680i | \(-0.863893\pi\) | ||
0.909967 | − | 0.414680i | \(-0.136107\pi\) | |||||||
\(258\) | 677950. | − | 1.06694e6i | 0.634086 | − | 0.997908i | ||||
\(259\) | 8167.49 | 0.00756553 | ||||||||
\(260\) | 1.17371e6 | − | 550681.i | 1.07678 | − | 0.505204i | ||||
\(261\) | − | 1.53237e6i | − | 1.39240i | ||||||
\(262\) | −1.04769e6 | + | 1.64883e6i | −0.942930 | + | 1.48396i | ||||
\(263\) | − | 1.28149e6i | − | 1.14242i | −0.820804 | − | 0.571211i | \(-0.806474\pi\) | ||
0.820804 | − | 0.571211i | \(-0.193526\pi\) | |||||||
\(264\) | 3.31247e6 | + | 424191.i | 2.92511 | + | 0.374586i | ||||
\(265\) | 2.66502e6i | 2.33123i | ||||||||
\(266\) | 171825. | − | 1.47149e6i | 0.148896 | − | 1.27512i | ||||
\(267\) | 824908.i | 0.708153i | ||||||||
\(268\) | 346039. | + | 737542.i | 0.294299 | + | 0.627263i | ||||
\(269\) | − | 1.88601e6i | − | 1.58914i | −0.607171 | − | 0.794571i | \(-0.707696\pi\) | ||
0.607171 | − | 0.794571i | \(-0.292304\pi\) | |||||||
\(270\) | −1.92417e6 | − | 1.22265e6i | −1.60633 | − | 1.02068i | ||||
\(271\) | − | 1.37764e6i | − | 1.13949i | −0.821820 | − | 0.569747i | \(-0.807041\pi\) | ||
0.821820 | − | 0.569747i | \(-0.192959\pi\) | |||||||
\(272\) | 354534. | − | 426583.i | 0.290560 | − | 0.349608i | ||||
\(273\) | −1.83216e6 | −1.48784 | ||||||||
\(274\) | 1.28480e6 | + | 816381.i | 1.03385 | + | 0.656926i | ||||
\(275\) | 4.13308e6i | 3.29566i | ||||||||
\(276\) | 6818.87 | − | 3199.27i | 0.00538815 | − | 0.00252801i | ||||
\(277\) | 1.34891e6 | 1.05629 | 0.528147 | − | 0.849153i | \(-0.322887\pi\) | ||||
0.528147 | + | 0.849153i | \(0.322887\pi\) | |||||||
\(278\) | 319299. | − | 502504.i | 0.247791 | − | 0.389967i | ||||
\(279\) | −1.30651e6 | −1.00485 | ||||||||
\(280\) | −2.81165e6 | − | 360056.i | −2.14321 | − | 0.274457i | ||||
\(281\) | − | 454809.i | − | 0.343608i | −0.985131 | − | 0.171804i | \(-0.945040\pi\) | ||
0.985131 | − | 0.171804i | \(-0.0549596\pi\) | |||||||
\(282\) | −1.24042e6 | + | 1.95215e6i | −0.928854 | + | 1.46181i | ||||
\(283\) | 1.15530e6i | 0.857487i | 0.903426 | + | 0.428744i | \(0.141044\pi\) | ||||
−0.903426 | + | 0.428744i | \(0.858956\pi\) | |||||||
\(284\) | 484261. | + | 1.03215e6i | 0.356274 | + | 0.759355i | ||||
\(285\) | −3.40840e6 | + | 1.64565e6i | −2.48564 | + | 1.20012i | ||||
\(286\) | −1.48366e6 | − | 942740.i | −1.07255 | − | 0.681517i | ||||
\(287\) | −132824. | −0.0951857 | ||||||||
\(288\) | 2.26384e6 | − | 728473.i | 1.60829 | − | 0.517526i | ||||
\(289\) | −1.12644e6 | −0.793349 | ||||||||
\(290\) | −1.06541e6 | + | 1.67671e6i | −0.743910 | + | 1.17075i | ||||
\(291\) | − | 154205.i | − | 0.106749i | ||||||
\(292\) | −246778. | − | 525978.i | −0.169375 | − | 0.361002i | ||||
\(293\) | 2.20787e6i | 1.50247i | 0.660036 | + | 0.751234i | \(0.270541\pi\) | ||||
−0.660036 | + | 0.751234i | \(0.729459\pi\) | |||||||
\(294\) | 1.32957e6 | + | 844826.i | 0.897101 | + | 0.570032i | ||||
\(295\) | −1.11920e6 | −0.748775 | ||||||||
\(296\) | 8811.36 | + | 1128.37i | 0.00584539 | + | 0.000748554i | ||||
\(297\) | 3.09103e6i | 2.03335i | ||||||||
\(298\) | −45791.5 | − | 29096.6i | −0.0298706 | − | 0.0189803i | ||||
\(299\) | −3964.70 | −0.00256468 | ||||||||
\(300\) | 1.99012e6 | + | 4.24171e6i | 1.27666 | + | 2.72106i | ||||
\(301\) | 1.45482e6 | 0.925535 | ||||||||
\(302\) | −448314. | − | 284866.i | −0.282856 | − | 0.179731i | ||||
\(303\) | −2.77128e6 | −1.73410 | ||||||||
\(304\) | 388663. | − | 1.56375e6i | 0.241206 | − | 0.970474i | ||||
\(305\) | 1.84110e6 | 1.13326 | ||||||||
\(306\) | 1.06178e6 | + | 674674.i | 0.648236 | + | 0.411899i | ||||
\(307\) | −2.72997e6 | −1.65315 | −0.826575 | − | 0.562826i | \(-0.809714\pi\) | ||||
−0.826575 | + | 0.562826i | \(0.809714\pi\) | |||||||
\(308\) | 1.63247e6 | + | 3.47941e6i | 0.980544 | + | 2.08991i | ||||
\(309\) | −1.99219e6 | −1.18695 | ||||||||
\(310\) | 1.42957e6 | + | 908371.i | 0.844892 | + | 0.536857i | ||||
\(311\) | − | 102980.i | − | 0.0603741i | −0.999544 | − | 0.0301870i | \(-0.990390\pi\) | ||
0.999544 | − | 0.0301870i | \(-0.00961030\pi\) | |||||||
\(312\) | −1.97659e6 | − | 253120.i | −1.14956 | − | 0.147211i | ||||
\(313\) | −1.53929e6 | −0.888094 | −0.444047 | − | 0.896003i | \(-0.646458\pi\) | ||||
−0.444047 | + | 0.896003i | \(0.646458\pi\) | |||||||
\(314\) | −2.38424e6 | − | 1.51498e6i | −1.36467 | − | 0.867129i | ||||
\(315\) | − | 6.42886e6i | − | 3.65054i | ||||||
\(316\) | −1.31087e6 | − | 2.79396e6i | −0.738483 | − | 1.57399i | ||||
\(317\) | − | 1.52122e6i | − | 0.850244i | −0.905136 | − | 0.425122i | \(-0.860231\pi\) | ||
0.905136 | − | 0.425122i | \(-0.139769\pi\) | |||||||
\(318\) | 2.19684e6 | − | 3.45732e6i | 1.21823 | − | 1.91722i | ||||
\(319\) | 2.69351e6 | 1.48198 | ||||||||
\(320\) | −2.98355e6 | − | 776881.i | −1.62877 | − | 0.424111i | ||||
\(321\) | 2.42354e6 | 1.31277 | ||||||||
\(322\) | 7316.34 | + | 4648.91i | 0.00393237 | + | 0.00249869i | ||||
\(323\) | 767578. | − | 370603.i | 0.409370 | − | 0.197653i | ||||
\(324\) | 132368. | + | 282128.i | 0.0700522 | + | 0.149308i | ||||
\(325\) | − | 2.46626e6i | − | 1.29518i | ||||||
\(326\) | −684343. | + | 1.07700e6i | −0.356640 | + | 0.561270i | ||||
\(327\) | 5.79924e6i | 2.99917i | ||||||||
\(328\) | −143295. | − | 18350.2i | −0.0735438 | − | 0.00941793i | ||||
\(329\) | −2.66184e6 | −1.35579 | ||||||||
\(330\) | 5.26594e6 | − | 8.28740e6i | 2.66190 | − | 4.18922i | ||||
\(331\) | 1.34814e6 | 0.676338 | 0.338169 | − | 0.941085i | \(-0.390192\pi\) | ||||
0.338169 | + | 0.941085i | \(0.390192\pi\) | |||||||
\(332\) | 1.00526e6 | − | 471647.i | 0.500533 | − | 0.234840i | ||||
\(333\) | 20147.3i | 0.00995648i | ||||||||
\(334\) | −1.68343e6 | − | 1.06968e6i | −0.825714 | − | 0.524671i | ||||
\(335\) | 2.39535e6 | 1.16616 | ||||||||
\(336\) | 3.35074e6 | + | 2.78480e6i | 1.61917 | + | 1.34569i | ||||
\(337\) | − | 3.02702e6i | − | 1.45191i | −0.687741 | − | 0.725956i | \(-0.741397\pi\) | ||
0.687741 | − | 0.725956i | \(-0.258603\pi\) | |||||||
\(338\) | −887427. | − | 563885.i | −0.422514 | − | 0.268472i | ||||
\(339\) | 1.00548e6i | 0.475199i | ||||||||
\(340\) | −692717. | − | 1.47644e6i | −0.324982 | − | 0.692660i | ||||
\(341\) | − | 2.29650e6i | − | 1.06950i | ||||||
\(342\) | 3.62981e6 | + | 423852.i | 1.67810 | + | 0.195952i | ||||
\(343\) | − | 984312.i | − | 0.451749i | ||||||
\(344\) | 1.56951e6 | + | 200989.i | 0.715101 | + | 0.0915750i | ||||
\(345\) | − | 22146.0i | − | 0.0100172i | ||||||
\(346\) | −1.64653e6 | + | 2.59126e6i | −0.739399 | + | 1.16365i | ||||
\(347\) | − | 1.14412e6i | − | 0.510092i | −0.966929 | − | 0.255046i | \(-0.917909\pi\) | ||
0.966929 | − | 0.255046i | \(-0.0820906\pi\) | |||||||
\(348\) | 2.76430e6 | − | 1.29695e6i | 1.22359 | − | 0.574085i | ||||
\(349\) | −1.73948e6 | −0.764463 | −0.382232 | − | 0.924067i | \(-0.624844\pi\) | ||||
−0.382232 | + | 0.924067i | \(0.624844\pi\) | |||||||
\(350\) | −2.89188e6 | + | 4.55116e6i | −1.26186 | + | 1.98588i | ||||
\(351\) | − | 1.84446e6i | − | 0.799100i | ||||||
\(352\) | 1.28046e6 | + | 3.97923e6i | 0.550821 | + | 1.71176i | ||||
\(353\) | 3.46233e6 | 1.47888 | 0.739438 | − | 0.673225i | \(-0.235091\pi\) | ||||
0.739438 | + | 0.673225i | \(0.235091\pi\) | |||||||
\(354\) | 1.45193e6 | + | 922580.i | 0.615798 | + | 0.391287i | ||||
\(355\) | 3.35215e6 | 1.41173 | ||||||||
\(356\) | −934788. | + | 438583.i | −0.390920 | + | 0.183412i | ||||
\(357\) | 2.30472e6i | 0.957080i | ||||||||
\(358\) | 2.05201e6 | + | 1.30388e6i | 0.846199 | + | 0.537688i | ||||
\(359\) | 1.15342e6i | 0.472336i | 0.971712 | + | 0.236168i | \(0.0758916\pi\) | ||||
−0.971712 | + | 0.236168i | \(0.924108\pi\) | |||||||
\(360\) | 888173. | − | 6.93567e6i | 0.361195 | − | 2.82054i | ||||
\(361\) | 1.53990e6 | − | 1.93901e6i | 0.621906 | − | 0.783092i | ||||
\(362\) | −533702. | + | 839926.i | −0.214056 | + | 0.336876i | ||||
\(363\) | −9.19588e6 | −3.66291 | ||||||||
\(364\) | −974113. | − | 2.07621e6i | −0.385350 | − | 0.821329i | ||||
\(365\) | −1.70824e6 | −0.671147 | ||||||||
\(366\) | −2.38846e6 | − | 1.51766e6i | −0.931999 | − | 0.592206i | ||||
\(367\) | 2.03678e6i | 0.789368i | 0.918817 | + | 0.394684i | \(0.129146\pi\) | ||||
−0.918817 | + | 0.394684i | \(0.870854\pi\) | |||||||
\(368\) | 7250.84 | + | 6026.19i | 0.00279106 | + | 0.00231965i | ||||
\(369\) | − | 327645.i | − | 0.125267i | ||||||
\(370\) | 14007.7 | − | 22045.0i | 0.00531940 | − | 0.00837153i | ||||
\(371\) | 4.71422e6 | 1.77818 | ||||||||
\(372\) | −1.10579e6 | − | 2.35685e6i | −0.414299 | − | 0.883030i | ||||
\(373\) | 878299.i | 0.326867i | 0.986554 | + | 0.163433i | \(0.0522568\pi\) | ||||
−0.986554 | + | 0.163433i | \(0.947743\pi\) | |||||||
\(374\) | −1.18590e6 | + | 1.86634e6i | −0.438398 | + | 0.689940i | ||||
\(375\) | 6.25943e6 | 2.29857 | ||||||||
\(376\) | −2.87168e6 | − | 367744.i | −1.04753 | − | 0.134146i | ||||
\(377\) | −1.60725e6 | −0.582412 | ||||||||
\(378\) | −2.16277e6 | + | 3.40371e6i | −0.778539 | + | 1.22524i | ||||
\(379\) | 3.41881e6 | 1.22258 | 0.611289 | − | 0.791407i | \(-0.290651\pi\) | ||||
0.611289 | + | 0.791407i | \(0.290651\pi\) | |||||||
\(380\) | −3.67702e6 | − | 2.98746e6i | −1.30628 | − | 1.06131i | ||||
\(381\) | −4.20042e6 | −1.48245 | ||||||||
\(382\) | 289270. | − | 455246.i | 0.101425 | − | 0.159620i | ||||
\(383\) | 1.14090e6 | 0.397420 | 0.198710 | − | 0.980058i | \(-0.436325\pi\) | ||||
0.198710 | + | 0.980058i | \(0.436325\pi\) | |||||||
\(384\) | 3.23016e6 | + | 3.46726e6i | 1.11788 | + | 1.19994i | ||||
\(385\) | 1.13002e7 | 3.88540 | ||||||||
\(386\) | 2.76750e6 | − | 4.35542e6i | 0.945407 | − | 1.48786i | ||||
\(387\) | 3.58870e6i | 1.21803i | ||||||||
\(388\) | 174745. | − | 81986.8i | 0.0589286 | − | 0.0276481i | ||||
\(389\) | 2.91802e6 | 0.977719 | 0.488860 | − | 0.872362i | \(-0.337413\pi\) | ||||
0.488860 | + | 0.872362i | \(0.337413\pi\) | |||||||
\(390\) | −3.14225e6 | + | 4.94519e6i | −1.04612 | + | 1.64635i | ||||
\(391\) | 4987.31i | 0.00164977i | ||||||||
\(392\) | −250463. | + | 1.95584e6i | −0.0823242 | + | 0.642863i | ||||
\(393\) | − | 8.82845e6i | − | 2.88339i | ||||||
\(394\) | −688796. | − | 437671.i | −0.223537 | − | 0.142039i | ||||
\(395\) | −9.07406e6 | −2.92623 | ||||||||
\(396\) | −8.58288e6 | + | 4.02691e6i | −2.75039 | + | 1.29043i | ||||
\(397\) | −1.50445e6 | −0.479072 | −0.239536 | − | 0.970887i | \(-0.576995\pi\) | ||||
−0.239536 | + | 0.970887i | \(0.576995\pi\) | |||||||
\(398\) | 1.84412e6 | − | 2.90223e6i | 0.583554 | − | 0.918382i | ||||
\(399\) | 2.91103e6 | + | 6.02920e6i | 0.915407 | + | 1.89595i | ||||
\(400\) | −3.74862e6 | + | 4.51042e6i | −1.17144 | + | 1.40951i | ||||
\(401\) | 6.12590e6i | 1.90243i | 0.308525 | + | 0.951216i | \(0.400165\pi\) | ||||
−0.308525 | + | 0.951216i | \(0.599835\pi\) | |||||||
\(402\) | −3.10748e6 | − | 1.97454e6i | −0.959055 | − | 0.609399i | ||||
\(403\) | 1.37035e6i | 0.420309i | ||||||||
\(404\) | −1.47342e6 | − | 3.14042e6i | −0.449131 | − | 0.957269i | ||||
\(405\) | 916280. | 0.277581 | ||||||||
\(406\) | 2.96597e6 | + | 1.88462e6i | 0.893001 | + | 0.567426i | ||||
\(407\) | −35413.6 | −0.0105970 | ||||||||
\(408\) | −318407. | + | 2.48641e6i | −0.0946961 | + | 0.739473i | ||||
\(409\) | 2.85001e6i | 0.842439i | 0.906959 | + | 0.421220i | \(0.138398\pi\) | ||||
−0.906959 | + | 0.421220i | \(0.861602\pi\) | |||||||
\(410\) | −227801. | + | 358507.i | −0.0669260 | + | 0.105326i | ||||
\(411\) | −6.87931e6 | −2.00882 | ||||||||
\(412\) | −1.05920e6 | − | 2.25755e6i | −0.307421 | − | 0.655231i | ||||
\(413\) | 1.97977e6i | 0.571137i | ||||||||
\(414\) | −11467.8 | + | 18047.7i | −0.00328835 | + | 0.00517512i | ||||
\(415\) | − | 3.26483e6i | − | 0.930551i | ||||||
\(416\) | −764069. | − | 2.37446e6i | −0.216471 | − | 0.672715i | ||||
\(417\) | 2.69060e6i | 0.757721i | ||||||||
\(418\) | −745020. | + | 6.38025e6i | −0.208558 | + | 1.78606i | ||||
\(419\) | − | 5.03769e6i | − | 1.40183i | −0.713244 | − | 0.700916i | \(-0.752775\pi\) | ||
0.713244 | − | 0.700916i | \(-0.247225\pi\) | |||||||
\(420\) | 1.15972e7 | − | 5.44118e6i | 3.20798 | − | 1.50512i | ||||
\(421\) | 2.24346e6i | 0.616898i | 0.951241 | + | 0.308449i | \(0.0998100\pi\) | ||||
−0.951241 | + | 0.308449i | \(0.900190\pi\) | |||||||
\(422\) | −3.71697e6 | − | 2.36182e6i | −1.01603 | − | 0.645603i | ||||
\(423\) | − | 6.56613e6i | − | 1.78426i | ||||||
\(424\) | 5.08585e6 | + | 651288.i | 1.37388 | + | 0.175938i | ||||
\(425\) | −3.10238e6 | −0.833148 | ||||||||
\(426\) | −4.34874e6 | − | 2.76325e6i | −1.16102 | − | 0.737729i | ||||
\(427\) | − | 3.25677e6i | − | 0.864406i | ||||||
\(428\) | 1.28853e6 | + | 2.74636e6i | 0.340006 | + | 0.724683i | ||||
\(429\) | 7.94409e6 | 2.08401 | ||||||||
\(430\) | 2.49510e6 | − | 3.92672e6i | 0.650753 | − | 1.02414i | ||||
\(431\) | 5.37467e6 | 1.39366 | 0.696832 | − | 0.717234i | \(-0.254592\pi\) | ||||
0.696832 | + | 0.717234i | \(0.254592\pi\) | |||||||
\(432\) | −2.80350e6 | + | 3.37324e6i | −0.722755 | + | 0.869636i | ||||
\(433\) | 1.19123e6i | 0.305334i | 0.988278 | + | 0.152667i | \(0.0487862\pi\) | ||||
−0.988278 | + | 0.152667i | \(0.951214\pi\) | |||||||
\(434\) | 1.60684e6 | − | 2.52880e6i | 0.409494 | − | 0.644452i | ||||
\(435\) | − | 8.97775e6i | − | 2.27481i | ||||||
\(436\) | −6.57171e6 | + | 3.08331e6i | −1.65563 | + | 0.776786i | ||||
\(437\) | 6299.33 | + | 13046.9i | 0.00157794 | + | 0.00326817i | ||||
\(438\) | 2.21610e6 | + | 1.40814e6i | 0.551955 | + | 0.350721i | ||||
\(439\) | 200583. | 0.0496743 | 0.0248372 | − | 0.999692i | \(-0.492093\pi\) | ||||
0.0248372 | + | 0.999692i | \(0.492093\pi\) | |||||||
\(440\) | 1.21911e7 | + | 1.56117e6i | 3.00200 | + | 0.384432i | ||||
\(441\) | −4.47205e6 | −1.09499 | ||||||||
\(442\) | 707641. | − | 1.11367e6i | 0.172289 | − | 0.271144i | ||||
\(443\) | − | 86536.0i | − | 0.0209502i | −0.999945 | − | 0.0104751i | \(-0.996666\pi\) | ||
0.999945 | − | 0.0104751i | \(-0.00333438\pi\) | |||||||
\(444\) | −36344.3 | + | 17052.0i | −0.00874942 | + | 0.00410505i | ||||
\(445\) | 3.03596e6i | 0.726767i | ||||||||
\(446\) | 1.34233e6 | + | 852936.i | 0.319537 | + | 0.203039i | ||||
\(447\) | 245186. | 0.0580398 | ||||||||
\(448\) | −1.37424e6 | + | 5.27768e6i | −0.323496 | + | 1.24236i | ||||
\(449\) | 5.85475e6i | 1.37054i | 0.728288 | + | 0.685271i | \(0.240316\pi\) | ||||
−0.728288 | + | 0.685271i | \(0.759684\pi\) | |||||||
\(450\) | −1.12266e7 | − | 7.13358e6i | −2.61348 | − | 1.66064i | ||||
\(451\) | 575914. | 0.133326 | ||||||||
\(452\) | −1.13942e6 | + | 534591.i | −0.262323 | + | 0.123077i | ||||
\(453\) | 2.40045e6 | 0.549600 | ||||||||
\(454\) | −2.58566e6 | − | 1.64297e6i | −0.588752 | − | 0.374102i | ||||
\(455\) | −6.74299e6 | −1.52695 | ||||||||
\(456\) | 2.30756e6 | + | 6.90667e6i | 0.519685 | + | 1.55545i | ||||
\(457\) | 5.23690e6 | 1.17296 | 0.586481 | − | 0.809963i | \(-0.300513\pi\) | ||||
0.586481 | + | 0.809963i | \(0.300513\pi\) | |||||||
\(458\) | −3.75447e6 | − | 2.38565e6i | −0.836344 | − | 0.531426i | ||||
\(459\) | −2.32020e6 | −0.514035 | ||||||||
\(460\) | 25095.9 | − | 11774.5i | 0.00552978 | − | 0.00259446i | ||||
\(461\) | 778640. | 0.170641 | 0.0853207 | − | 0.996354i | \(-0.472809\pi\) | ||||
0.0853207 | + | 0.996354i | \(0.472809\pi\) | |||||||
\(462\) | −1.46598e7 | − | 9.31505e6i | −3.19538 | − | 2.03039i | ||||
\(463\) | − | 6.79131e6i | − | 1.47232i | −0.676809 | − | 0.736158i | \(-0.736638\pi\) | ||
0.676809 | − | 0.736158i | \(-0.263362\pi\) | |||||||
\(464\) | 2.93942e6 | + | 2.44296e6i | 0.633821 | + | 0.526770i | ||||
\(465\) | −7.65447e6 | −1.64166 | ||||||||
\(466\) | −1.69725e6 | − | 1.07846e6i | −0.362060 | − | 0.230059i | ||||
\(467\) | − | 1.18854e6i | − | 0.252187i | −0.992018 | − | 0.126094i | \(-0.959756\pi\) | ||
0.992018 | − | 0.126094i | \(-0.0402440\pi\) | |||||||
\(468\) | 5.12151e6 | − | 2.40291e6i | 1.08089 | − | 0.507133i | ||||
\(469\) | − | 4.23719e6i | − | 0.889500i | ||||||
\(470\) | −4.56521e6 | + | 7.18460e6i | −0.953270 | + | 1.50023i | ||||
\(471\) | 1.27661e7 | 2.65160 | ||||||||
\(472\) | −273514. | + | 2.13585e6i | −0.0565099 | + | 0.441281i | ||||
\(473\) | −6.30798e6 | −1.29640 | ||||||||
\(474\) | 1.17718e7 | + | 7.47996e6i | 2.40655 | + | 1.52916i | ||||
\(475\) | −8.11589e6 | + | 3.91853e6i | −1.65045 | + | 0.796872i | ||||
\(476\) | −2.61172e6 | + | 1.22536e6i | −0.528334 | + | 0.247884i | ||||
\(477\) | 1.16289e7i | 2.34014i | ||||||||
\(478\) | 316221. | − | 497660.i | 0.0633025 | − | 0.0996238i | ||||
\(479\) | − | 3.09162e6i | − | 0.615669i | −0.951440 | − | 0.307834i | \(-0.900396\pi\) | ||
0.951440 | − | 0.307834i | \(-0.0996042\pi\) | |||||||
\(480\) | 1.32632e7 | − | 4.26792e6i | 2.62752 | − | 0.845499i | ||||
\(481\) | 21131.7 | 0.00416459 | ||||||||
\(482\) | 928891. | − | 1.46186e6i | 0.182116 | − | 0.286609i | ||||
\(483\) | −39174.5 | −0.00764075 | ||||||||
\(484\) | −4.88922e6 | − | 1.04208e7i | −0.948695 | − | 2.02203i | ||||
\(485\) | − | 567528.i | − | 0.109555i | ||||||
\(486\) | 3.78089e6 | + | 2.40244e6i | 0.726112 | + | 0.461383i | ||||
\(487\) | −3.59773e6 | −0.687394 | −0.343697 | − | 0.939081i | \(-0.611679\pi\) | ||||
−0.343697 | + | 0.939081i | \(0.611679\pi\) | |||||||
\(488\) | 449936. | − | 3.51351e6i | 0.0855267 | − | 0.667870i | ||||
\(489\) | − | 5.76668e6i | − | 1.09057i | ||||||
\(490\) | 4.89327e6 | + | 3.10926e6i | 0.920681 | + | 0.585015i | ||||
\(491\) | 6.96091e6i | 1.30305i | 0.758626 | + | 0.651527i | \(0.225871\pi\) | ||||
−0.758626 | + | 0.651527i | \(0.774129\pi\) | |||||||
\(492\) | 591050. | − | 277309.i | 0.110081 | − | 0.0516476i | ||||
\(493\) | 2.02181e6i | 0.374647i | ||||||||
\(494\) | 444563. | − | 3.80718e6i | 0.0819626 | − | 0.701917i | ||||
\(495\) | 2.78750e7i | 5.11331i | ||||||||
\(496\) | 2.08288e6 | − | 2.50616e6i | 0.380154 | − | 0.457409i | ||||
\(497\) | − | 5.92970e6i | − | 1.07682i | ||||||
\(498\) | −2.69127e6 | + | 4.23546e6i | −0.486278 | + | 0.765292i | ||||
\(499\) | − | 3.09077e6i | − | 0.555668i | −0.960629 | − | 0.277834i | \(-0.910384\pi\) | ||
0.960629 | − | 0.277834i | \(-0.0896165\pi\) | |||||||
\(500\) | 3.32799e6 | + | 7.09321e6i | 0.595328 | + | 1.26887i | ||||
\(501\) | 9.01375e6 | 1.60439 | ||||||||
\(502\) | 753819. | − | 1.18634e6i | 0.133508 | − | 0.210112i | ||||
\(503\) | 8.48635e6i | 1.49555i | 0.663952 | + | 0.747775i | \(0.268878\pi\) | ||||
−0.663952 | + | 0.747775i | \(0.731122\pi\) | |||||||
\(504\) | −1.22687e7 | − | 1.57111e6i | −2.15140 | − | 0.275506i | ||||
\(505\) | −1.01993e7 | −1.77968 | ||||||||
\(506\) | −31723.1 | − | 20157.3i | −0.00550806 | − | 0.00349991i | ||||
\(507\) | 4.75163e6 | 0.820961 | ||||||||
\(508\) | −2.23326e6 | − | 4.75993e6i | −0.383955 | − | 0.818354i | ||||
\(509\) | − | 5.87480e6i | − | 1.00507i | −0.864555 | − | 0.502537i | \(-0.832400\pi\) | ||
0.864555 | − | 0.502537i | \(-0.167600\pi\) | |||||||
\(510\) | 6.22070e6 | + | 3.95273e6i | 1.05904 | + | 0.672932i | ||||
\(511\) | 3.02175e6i | 0.511925i | ||||||||
\(512\) | −2.21171e6 | + | 5.50388e6i | −0.372867 | + | 0.927885i | ||||
\(513\) | −6.06968e6 | + | 2.93057e6i | −1.01829 | + | 0.491653i | ||||
\(514\) | −2.66418e6 | + | 4.19282e6i | −0.444791 | + | 0.700000i | ||||
\(515\) | −7.33196e6 | −1.21815 | ||||||||
\(516\) | −6.47377e6 | + | 3.03736e6i | −1.07037 | + | 0.502194i | ||||
\(517\) | 1.15415e7 | 1.89905 | ||||||||
\(518\) | −38995.8 | − | 24778.6i | −0.00638549 | − | 0.00405744i | ||||
\(519\) | − | 1.38746e7i | − | 2.26101i | ||||||
\(520\) | −7.27457e6 | − | 931572.i | −1.17977 | − | 0.151080i | ||||
\(521\) | − | 1.13055e7i | − | 1.82471i | −0.409397 | − | 0.912357i | \(-0.634261\pi\) | ||
0.409397 | − | 0.912357i | \(-0.365739\pi\) | |||||||
\(522\) | −4.64892e6 | + | 7.31635e6i | −0.746751 | + | 1.17522i | ||||
\(523\) | 9.51562e6 | 1.52119 | 0.760594 | − | 0.649228i | \(-0.224908\pi\) | ||||
0.760594 | + | 0.649228i | \(0.224908\pi\) | |||||||
\(524\) | 1.00044e7 | − | 4.69387e6i | 1.59171 | − | 0.746797i | ||||
\(525\) | − | 2.43687e7i | − | 3.85863i | ||||||
\(526\) | −3.88779e6 | + | 6.11851e6i | −0.612687 | + | 0.964231i | ||||
\(527\) | 1.72380e6 | 0.270371 | ||||||||
\(528\) | −1.45285e7 | − | 1.20747e7i | −2.26797 | − | 1.88491i | ||||
\(529\) | 6.43626e6 | 0.999987 | ||||||||
\(530\) | 8.08514e6 | − | 1.27242e7i | 1.25025 | − | 1.96762i | ||||
\(531\) | −4.88363e6 | −0.751635 | ||||||||
\(532\) | −5.28459e6 | + | 6.50436e6i | −0.809528 | + | 0.996382i | ||||
\(533\) | −343655. | −0.0523968 | ||||||||
\(534\) | 2.50261e6 | − | 3.93854e6i | 0.379787 | − | 0.597698i | ||||
\(535\) | 8.91948e6 | 1.34727 | ||||||||
\(536\) | 585386. | − | 4.57122e6i | 0.0880096 | − | 0.687259i | ||||
\(537\) | −1.09873e7 | −1.64420 | ||||||||
\(538\) | −5.72178e6 | + | 9.00478e6i | −0.852266 | + | 1.34127i | ||||
\(539\) | − | 7.86068e6i | − | 1.16544i | ||||||
\(540\) | 5.47771e6 | + | 1.16751e7i | 0.808378 | + | 1.72296i | ||||
\(541\) | −1.63250e6 | −0.239806 | −0.119903 | − | 0.992786i | \(-0.538258\pi\) | ||||
−0.119903 | + | 0.992786i | \(0.538258\pi\) | |||||||
\(542\) | −4.17949e6 | + | 6.57757e6i | −0.611118 | + | 0.961761i | ||||
\(543\) | − | 4.49729e6i | − | 0.654563i | ||||||
\(544\) | −2.98690e6 | + | 961144.i | −0.432736 | + | 0.139249i | ||||
\(545\) | 2.13433e7i | 3.07801i | ||||||||
\(546\) | 8.74767e6 | + | 5.55841e6i | 1.25577 | + | 0.797937i | ||||
\(547\) | 6.46710e6 | 0.924148 | 0.462074 | − | 0.886841i | \(-0.347106\pi\) | ||||
0.462074 | + | 0.886841i | \(0.347106\pi\) | |||||||
\(548\) | −3.65756e6 | − | 7.79565e6i | −0.520283 | − | 1.10892i | ||||
\(549\) | 8.03369e6 | 1.13759 | ||||||||
\(550\) | 1.25389e7 | − | 1.97335e7i | 1.76748 | − | 2.78161i | ||||
\(551\) | 2.55369e6 | + | 5.28909e6i | 0.358334 | + | 0.742167i | ||||
\(552\) | −42262.8 | − | 5412.12i | −0.00590351 | − | 0.000755996i | ||||
\(553\) | 1.60513e7i | 2.23202i | ||||||||
\(554\) | −6.44042e6 | − | 4.09234e6i | −0.891537 | − | 0.566496i | ||||
\(555\) | 118037.i | 0.0162662i | ||||||||
\(556\) | −3.04900e6 | + | 1.43053e6i | −0.418283 | + | 0.196250i | ||||
\(557\) | −5.16001e6 | −0.704714 | −0.352357 | − | 0.935866i | \(-0.614620\pi\) | ||||
−0.352357 | + | 0.935866i | \(0.614620\pi\) | |||||||
\(558\) | 6.23795e6 | + | 3.96369e6i | 0.848119 | + | 0.538908i | ||||
\(559\) | 3.76405e6 | 0.509479 | ||||||||
\(560\) | 1.23319e7 | + | 1.02491e7i | 1.66173 | + | 1.38107i | ||||
\(561\) | − | 9.99309e6i | − | 1.34058i | ||||||
\(562\) | −1.37980e6 | + | 2.17149e6i | −0.184279 | + | 0.290013i | ||||
\(563\) | −5.95975e6 | −0.792423 | −0.396211 | − | 0.918159i | \(-0.629675\pi\) | ||||
−0.396211 | + | 0.918159i | \(0.629675\pi\) | |||||||
\(564\) | 1.18449e7 | − | 5.55736e6i | 1.56795 | − | 0.735650i | ||||
\(565\) | 3.70054e6i | 0.487690i | ||||||||
\(566\) | 3.50494e6 | − | 5.51599e6i | 0.459875 | − | 0.723740i | ||||
\(567\) | − | 1.62083e6i | − | 0.211729i | ||||||
\(568\) | 819212. | − | 6.39715e6i | 0.106543 | − | 0.831986i | ||||
\(569\) | − | 1.04555e7i | − | 1.35383i | −0.736063 | − | 0.676914i | \(-0.763317\pi\) | ||
0.736063 | − | 0.676914i | \(-0.236683\pi\) | |||||||
\(570\) | 2.12661e7 | + | 2.48323e6i | 2.74157 | + | 0.320133i | ||||
\(571\) | − | 4.60322e6i | − | 0.590842i | −0.955367 | − | 0.295421i | \(-0.904540\pi\) | ||
0.955367 | − | 0.295421i | \(-0.0954599\pi\) | |||||||
\(572\) | 4.22367e6 | + | 9.00226e6i | 0.539760 | + | 1.15043i | ||||
\(573\) | 2.43756e6i | 0.310148i | ||||||||
\(574\) | 634171. | + | 402962.i | 0.0803390 | + | 0.0510486i | ||||
\(575\) | − | 52732.7i | − | 0.00665135i | ||||||
\(576\) | −1.30188e7 | − | 3.38993e6i | −1.63499 | − | 0.425731i | ||||
\(577\) | 1.29728e7 | 1.62216 | 0.811080 | − | 0.584936i | \(-0.198880\pi\) | ||||
0.811080 | + | 0.584936i | \(0.198880\pi\) | |||||||
\(578\) | 5.37822e6 | + | 3.41741e6i | 0.669606 | + | 0.425478i | ||||
\(579\) | 2.33206e7i | 2.89097i | ||||||||
\(580\) | 1.01736e7 | − | 4.77325e6i | 1.25576 | − | 0.589175i | ||||
\(581\) | −5.77524e6 | −0.709789 | ||||||||
\(582\) | −467827. | + | 736253.i | −0.0572503 | + | 0.0900989i | ||||
\(583\) | −2.04405e7 | −2.49069 | ||||||||
\(584\) | −417467. | + | 3.25997e6i | −0.0506513 | + | 0.395531i | ||||
\(585\) | − | 1.66334e7i | − | 2.00951i | ||||||
\(586\) | 6.69825e6 | − | 1.05415e7i | 0.805782 | − | 1.26812i | ||||
\(587\) | − | 9.89340e6i | − | 1.18509i | −0.805538 | − | 0.592544i | \(-0.798124\pi\) | ||
0.805538 | − | 0.592544i | \(-0.201876\pi\) | |||||||
\(588\) | −3.78500e6 | − | 8.06728e6i | −0.451463 | − | 0.962241i | ||||
\(589\) | 4.50950e6 | − | 2.17728e6i | 0.535599 | − | 0.258599i | ||||
\(590\) | 5.34363e6 | + | 3.39542e6i | 0.631984 | + | 0.401572i | ||||
\(591\) | 3.68808e6 | 0.434342 | ||||||||
\(592\) | −38646.8 | − | 32119.4i | −0.00453220 | − | 0.00376671i | ||||
\(593\) | −9.91998e6 | −1.15844 | −0.579220 | − | 0.815171i | \(-0.696643\pi\) | ||||
−0.579220 | + | 0.815171i | \(0.696643\pi\) | |||||||
\(594\) | 9.37758e6 | − | 1.47582e7i | 1.09050 | − | 1.71620i | ||||
\(595\) | 8.48220e6i | 0.982237i | ||||||||
\(596\) | 130359. | + | 277845.i | 0.0150323 | + | 0.0320396i | ||||
\(597\) | 1.55396e7i | 1.78445i | ||||||||
\(598\) | 18929.5 | + | 12028.1i | 0.00216465 | + | 0.00137545i | ||||
\(599\) | −3.56054e6 | −0.405460 | −0.202730 | − | 0.979235i | \(-0.564981\pi\) | ||||
−0.202730 | + | 0.979235i | \(0.564981\pi\) | |||||||
\(600\) | 3.36663e6 | − | 2.62897e7i | 0.381784 | − | 2.98132i | ||||
\(601\) | − | 1.35986e7i | − | 1.53571i | −0.640624 | − | 0.767855i | \(-0.721324\pi\) | ||
0.640624 | − | 0.767855i | \(-0.278676\pi\) | |||||||
\(602\) | −6.94607e6 | − | 4.41364e6i | −0.781174 | − | 0.496370i | ||||
\(603\) | 1.04522e7 | 1.17061 | ||||||||
\(604\) | 1.27626e6 | + | 2.72020e6i | 0.142346 | + | 0.303395i | ||||
\(605\) | −3.38441e7 | −3.75920 | ||||||||
\(606\) | 1.32315e7 | + | 8.40750e6i | 1.46362 | + | 0.930006i | ||||
\(607\) | −1.54890e7 | −1.70629 | −0.853145 | − | 0.521675i | \(-0.825308\pi\) | ||||
−0.853145 | + | 0.521675i | \(0.825308\pi\) | |||||||
\(608\) | −6.59979e6 | + | 6.28704e6i | −0.724055 | + | 0.689743i | ||||
\(609\) | −1.58810e7 | −1.73514 | ||||||||
\(610\) | −8.79039e6 | − | 5.58555e6i | −0.956497 | − | 0.607773i | ||||
\(611\) | −6.88698e6 | −0.746321 | ||||||||
\(612\) | −3.02268e6 | − | 6.44249e6i | −0.326223 | − | 0.695305i | ||||
\(613\) | −521655. | −0.0560703 | −0.0280351 | − | 0.999607i | \(-0.508925\pi\) | ||||
−0.0280351 | + | 0.999607i | \(0.508925\pi\) | |||||||
\(614\) | 1.30343e7 | + | 8.28220e6i | 1.39530 | + | 0.886594i | ||||
\(615\) | − | 1.91958e6i | − | 0.204653i | ||||||
\(616\) | 2.76160e6 | − | 2.15651e7i | 0.293230 | − | 2.28981i | ||||
\(617\) | −6.54779e6 | −0.692440 | −0.346220 | − | 0.938153i | \(-0.612535\pi\) | ||||
−0.346220 | + | 0.938153i | \(0.612535\pi\) | |||||||
\(618\) | 9.51173e6 | + | 6.04390e6i | 1.00182 | + | 0.636570i | ||||
\(619\) | 8.13536e6i | 0.853395i | 0.904394 | + | 0.426697i | \(0.140323\pi\) | ||||
−0.904394 | + | 0.426697i | \(0.859677\pi\) | |||||||
\(620\) | −4.06969e6 | − | 8.67407e6i | −0.425189 | − | 0.906241i | ||||
\(621\) | − | 39437.5i | − | 0.00410375i | ||||||
\(622\) | −312420. | + | 491679.i | −0.0323790 | + | 0.0509572i | ||||
\(623\) | 5.37038e6 | 0.554351 | ||||||||
\(624\) | 8.66936e6 | + | 7.20512e6i | 0.891304 | + | 0.740764i | ||||
\(625\) | 5.13897e6 | 0.526231 | ||||||||
\(626\) | 7.34936e6 | + | 4.66990e6i | 0.749573 | + | 0.476290i | ||||
\(627\) | −1.26220e7 | − | 2.61421e7i | −1.28221 | − | 2.65566i | ||||
\(628\) | 6.78745e6 | + | 1.44666e7i | 0.686764 | + | 1.46376i | ||||
\(629\) | − | 26582.2i | − | 0.00267895i | ||||||
\(630\) | −1.95039e7 | + | 3.06947e7i | −1.95781 | + | 3.08115i | ||||
\(631\) | 7.55707e6i | 0.755580i | 0.925891 | + | 0.377790i | \(0.123316\pi\) | ||||
−0.925891 | + | 0.377790i | \(0.876684\pi\) | |||||||
\(632\) | −2.21756e6 | + | 1.73167e7i | −0.220842 | + | 1.72454i | ||||
\(633\) | 1.99021e7 | 1.97419 | ||||||||
\(634\) | −4.61508e6 | + | 7.26309e6i | −0.455991 | + | 0.717626i | ||||
\(635\) | −1.54591e7 | −1.52142 | ||||||||
\(636\) | −2.09777e7 | + | 9.84229e6i | −2.05643 | + | 0.964836i | ||||
\(637\) | 4.69057e6i | 0.458012i | ||||||||
\(638\) | −1.28602e7 | − | 8.17158e6i | −1.25082 | − | 0.794793i | ||||
\(639\) | 1.46272e7 | 1.41712 | ||||||||
\(640\) | 1.18881e7 | + | 1.27608e7i | 1.14727 | + | 1.23148i | ||||
\(641\) | 1.35581e7i | 1.30333i | 0.758507 | + | 0.651665i | \(0.225929\pi\) | ||||
−0.758507 | + | 0.651665i | \(0.774071\pi\) | |||||||
\(642\) | −1.15712e7 | − | 7.35254e6i | −1.10801 | − | 0.704044i | ||||
\(643\) | 3.16596e6i | 0.301979i | 0.988535 | + | 0.150990i | \(0.0482460\pi\) | ||||
−0.988535 | + | 0.150990i | \(0.951754\pi\) | |||||||
\(644\) | −20828.1 | − | 44392.7i | −0.00197895 | − | 0.00421790i | ||||
\(645\) | 2.10252e7i | 1.98994i | ||||||||
\(646\) | −4.78915e6 | − | 559228.i | −0.451521 | − | 0.0527239i | ||||
\(647\) | − | 2.06733e6i | − | 0.194156i | −0.995277 | − | 0.0970778i | \(-0.969050\pi\) | ||
0.995277 | − | 0.0970778i | \(-0.0309496\pi\) | |||||||
\(648\) | 223924. | − | 1.74860e6i | 0.0209490 | − | 0.163589i | ||||
\(649\) | − | 8.58414e6i | − | 0.799991i | ||||||
\(650\) | −7.48215e6 | + | 1.17752e7i | −0.694613 | + | 1.09316i | ||||
\(651\) | 1.35402e7i | 1.25219i | ||||||||
\(652\) | 6.53481e6 | − | 3.06600e6i | 0.602025 | − | 0.282457i | ||||
\(653\) | 1.70976e7 | 1.56911 | 0.784555 | − | 0.620059i | \(-0.212891\pi\) | ||||
0.784555 | + | 0.620059i | \(0.212891\pi\) | |||||||
\(654\) | 1.75937e7 | − | 2.76886e7i | 1.60847 | − | 2.53137i | ||||
\(655\) | − | 3.24919e7i | − | 2.95918i | ||||||
\(656\) | 628494. | + | 522342.i | 0.0570219 | + | 0.0473909i | ||||
\(657\) | −7.45395e6 | −0.673710 | ||||||||
\(658\) | 1.27090e7 | + | 8.07550e6i | 1.14432 | + | 0.727118i | ||||
\(659\) | −948534. | −0.0850823 | −0.0425412 | − | 0.999095i | \(-0.513545\pi\) | ||||
−0.0425412 | + | 0.999095i | \(0.513545\pi\) | |||||||
\(660\) | −5.02847e7 | + | 2.35925e7i | −4.49341 | + | 2.10821i | ||||
\(661\) | − | 6.92093e6i | − | 0.616113i | −0.951368 | − | 0.308057i | \(-0.900321\pi\) | ||
0.951368 | − | 0.308057i | \(-0.0996787\pi\) | |||||||
\(662\) | −6.43670e6 | − | 4.08998e6i | −0.570845 | − | 0.362724i | ||||
\(663\) | 5.96300e6i | 0.526843i | ||||||||
\(664\) | −6.23052e6 | − | 797873.i | −0.548408 | − | 0.0702285i | ||||
\(665\) | 1.07136e7 | + | 2.21896e7i | 0.939469 | + | 1.94579i | ||||
\(666\) | 61122.9 | − | 96193.5i | 0.00533971 | − | 0.00840350i | ||||
\(667\) | −34365.6 | −0.00299096 | ||||||||
\(668\) | 4.79239e6 | + | 1.02144e7i | 0.415538 | + | 0.885670i | ||||
\(669\) | −7.18735e6 | −0.620874 | ||||||||
\(670\) | −1.14366e7 | − | 7.26702e6i | −0.984264 | − | 0.625417i | ||||
\(671\) | 1.41211e7i | 1.21077i | ||||||||
\(672\) | −7.54963e6 | − | 2.34616e7i | −0.644915 | − | 2.00417i | ||||
\(673\) | − | 7.01210e6i | − | 0.596775i | −0.954445 | − | 0.298388i | \(-0.903551\pi\) | ||
0.954445 | − | 0.298388i | \(-0.0964488\pi\) | |||||||
\(674\) | −9.18338e6 | + | 1.44526e7i | −0.778669 | + | 1.22545i | ||||
\(675\) | 2.45323e7 | 2.07242 | ||||||||
\(676\) | 2.52632e6 | + | 5.38456e6i | 0.212629 | + | 0.453193i | ||||
\(677\) | 1.41401e7i | 1.18572i | 0.805307 | + | 0.592858i | \(0.202001\pi\) | ||||
−0.805307 | + | 0.592858i | \(0.797999\pi\) | |||||||
\(678\) | 3.05044e6 | − | 4.80070e6i | 0.254852 | − | 0.401080i | ||||
\(679\) | −1.00391e6 | −0.0835646 | ||||||||
\(680\) | −1.17185e6 | + | 9.15088e6i | −0.0971852 | + | 0.758911i | ||||
\(681\) | 1.38446e7 | 1.14397 | ||||||||
\(682\) | −6.96712e6 | + | 1.09647e7i | −0.573578 | + | 0.902682i | ||||
\(683\) | 7.13798e6 | 0.585495 | 0.292748 | − | 0.956190i | \(-0.405430\pi\) | ||||
0.292748 | + | 0.956190i | \(0.405430\pi\) | |||||||
\(684\) | −1.60447e7 | − | 1.30358e7i | −1.31127 | − | 1.06536i | ||||
\(685\) | −2.53183e7 | −2.06162 | ||||||||
\(686\) | −2.98621e6 | + | 4.69962e6i | −0.242276 | + | 0.381287i | ||||
\(687\) | 2.01029e7 | 1.62505 | ||||||||
\(688\) | −6.88388e6 | − | 5.72121e6i | −0.554450 | − | 0.460804i | ||||
\(689\) | 1.21971e7 | 0.978831 | ||||||||
\(690\) | −67186.5 | + | 105736.i | −0.00537229 | + | 0.00845476i | ||||
\(691\) | − | 2.28937e7i | − | 1.82399i | −0.410206 | − | 0.911993i | \(-0.634543\pi\) | ||
0.410206 | − | 0.911993i | \(-0.365457\pi\) | |||||||
\(692\) | 1.57228e7 | − | 7.37679e6i | 1.24814 | − | 0.585601i | ||||
\(693\) | 4.93088e7 | 3.90024 | ||||||||
\(694\) | −3.47104e6 | + | 5.46263e6i | −0.273565 | + | 0.430530i | ||||
\(695\) | 9.90237e6i | 0.777638i | ||||||||
\(696\) | −1.71329e7 | − | 2.19402e6i | −1.34063 | − | 0.171679i | ||||
\(697\) | 432294.i | 0.0337052i | ||||||||
\(698\) | 8.30520e6 | + | 5.27725e6i | 0.645225 | + | 0.409986i | ||||
\(699\) | 9.08773e6 | 0.703497 | ||||||||
\(700\) | 2.76147e7 | − | 1.29562e7i | 2.13007 | − | 0.999386i | ||||
\(701\) | 1.65026e7 | 1.26841 | 0.634203 | − | 0.773167i | \(-0.281329\pi\) | ||||
0.634203 | + | 0.773167i | \(0.281329\pi\) | |||||||
\(702\) | −5.59572e6 | + | 8.80640e6i | −0.428562 | + | 0.674459i | ||||
\(703\) | −33575.2 | − | 69539.6i | −0.00256230 | − | 0.00530693i | ||||
\(704\) | 5.95861e6 | − | 2.28836e7i | 0.453120 | − | 1.74017i | ||||
\(705\) | − | 3.84691e7i | − | 2.91501i | ||||||
\(706\) | −1.65310e7 | − | 1.05040e7i | −1.24821 | − | 0.793129i | ||||
\(707\) | 1.80418e7i | 1.35747i | ||||||||
\(708\) | −4.13335e6 | − | 8.80975e6i | −0.309898 | − | 0.660512i | ||||
\(709\) | −1.71958e7 | −1.28472 | −0.642359 | − | 0.766404i | \(-0.722044\pi\) | ||||
−0.642359 | + | 0.766404i | \(0.722044\pi\) | |||||||
\(710\) | −1.60049e7 | − | 1.01698e7i | −1.19154 | − | 0.757120i | ||||
\(711\) | −3.95948e7 | −2.93741 | ||||||||
\(712\) | 5.79374e6 | + | 741939.i | 0.428311 | + | 0.0548490i | ||||
\(713\) | 29300.3i | 0.00215848i | ||||||||
\(714\) | 6.99207e6 | − | 1.10039e7i | 0.513287 | − | 0.807798i | ||||
\(715\) | 2.92371e7 | 2.13879 | ||||||||
\(716\) | −5.84166e6 | − | 1.24508e7i | −0.425847 | − | 0.907642i | ||||
\(717\) | 2.66467e6i | 0.193573i | ||||||||
\(718\) | 3.49925e6 | − | 5.50703e6i | 0.253317 | − | 0.398663i | ||||
\(719\) | − | 1.09124e7i | − | 0.787227i | −0.919276 | − | 0.393613i | \(-0.871225\pi\) | ||
0.919276 | − | 0.393613i | \(-0.128775\pi\) | |||||||
\(720\) | −2.52821e7 | + | 3.04199e7i | −1.81753 | + | 2.18689i | ||||
\(721\) | 1.29697e7i | 0.929161i | ||||||||
\(722\) | −1.32349e7 | + | 4.58609e6i | −0.944880 | + | 0.327416i | ||||
\(723\) | 7.82738e6i | 0.556892i | ||||||||
\(724\) | 5.09634e6 | − | 2.39110e6i | 0.361337 | − | 0.169532i | ||||
\(725\) | − | 2.13773e7i | − | 1.51045i | ||||||
\(726\) | 4.39059e7 | + | 2.78985e7i | 3.09159 | + | 1.96444i | ||||
\(727\) | − | 2.03681e7i | − | 1.42927i | −0.699497 | − | 0.714636i | \(-0.746593\pi\) | ||
0.699497 | − | 0.714636i | \(-0.253407\pi\) | |||||||
\(728\) | −1.64788e6 | + | 1.28682e7i | −0.115238 | + | 0.899887i | ||||
\(729\) | −2.26109e7 | −1.57579 | ||||||||
\(730\) | 8.15604e6 | + | 5.18247e6i | 0.566464 | + | 0.359940i | ||||
\(731\) | − | 4.73491e6i | − | 0.327731i | ||||||
\(732\) | 6.79946e6 | + | 1.44922e7i | 0.469025 | + | 0.999672i | ||||
\(733\) | 5.38904e6 | 0.370468 | 0.185234 | − | 0.982694i | \(-0.440696\pi\) | ||||
0.185234 | + | 0.982694i | \(0.440696\pi\) | |||||||
\(734\) | 6.17920e6 | − | 9.72466e6i | 0.423343 | − | 0.666246i | ||||
\(735\) | −2.62005e7 | −1.78892 | ||||||||
\(736\) | −16337.0 | − | 50769.8i | −0.00111168 | − | 0.00345470i | ||||
\(737\) | 1.83721e7i | 1.24592i | ||||||||
\(738\) | −994012. | + | 1.56435e6i | −0.0671816 | + | 0.105729i | ||||
\(739\) | 1.79505e7i | 1.20911i | 0.796563 | + | 0.604555i | \(0.206649\pi\) | ||||
−0.796563 | + | 0.604555i | \(0.793351\pi\) | |||||||
\(740\) | −133760. | + | 62757.5i | −0.00897940 | + | 0.00421295i | ||||
\(741\) | 7.53170e6 | + | 1.55993e7i | 0.503904 | + | 1.04366i | ||||
\(742\) | −2.25081e7 | − | 1.43020e7i | −1.50082 | − | 0.953646i | ||||
\(743\) | −235415. | −0.0156445 | −0.00782225 | − | 0.999969i | \(-0.502490\pi\) | ||||
−0.00782225 | + | 0.999969i | \(0.502490\pi\) | |||||||
\(744\) | −1.87063e6 | + | 1.46076e7i | −0.123896 | + | 0.967490i | ||||
\(745\) | 902370. | 0.0595654 | ||||||||
\(746\) | 2.66459e6 | − | 4.19346e6i | 0.175300 | − | 0.275883i | ||||
\(747\) | − | 1.42461e7i | − | 0.934105i | ||||||
\(748\) | 1.13242e7 | − | 5.31308e6i | 0.740037 | − | 0.347210i | ||||
\(749\) | − | 1.57779e7i | − | 1.02765i | ||||||
\(750\) | −2.98858e7 | − | 1.89899e7i | −1.94004 | − | 1.23273i | ||||
\(751\) | −4.45310e6 | −0.288113 | −0.144056 | − | 0.989569i | \(-0.546015\pi\) | ||||
−0.144056 | + | 0.989569i | \(0.546015\pi\) | |||||||
\(752\) | 1.25952e7 | + | 1.04679e7i | 0.812198 | + | 0.675019i | ||||
\(753\) | 6.35212e6i | 0.408255i | ||||||||
\(754\) | 7.67385e6 | + | 4.87608e6i | 0.491570 | + | 0.312351i | ||||
\(755\) | 8.83451e6 | 0.564047 | ||||||||
\(756\) | 2.06523e7 | − | 9.68965e6i | 1.31421 | − | 0.616600i | ||||
\(757\) | −2.02606e7 | −1.28503 | −0.642516 | − | 0.766273i | \(-0.722109\pi\) | ||||
−0.642516 | + | 0.766273i | \(0.722109\pi\) | |||||||
\(758\) | −1.63232e7 | − | 1.03720e7i | −1.03189 | − | 0.655676i | ||||
\(759\) | 169858. | 0.0107024 | ||||||||
\(760\) | 8.49263e6 | + | 2.54190e7i | 0.533345 | + | 1.59634i | ||||
\(761\) | 1.48612e7 | 0.930236 | 0.465118 | − | 0.885249i | \(-0.346012\pi\) | ||||
0.465118 | + | 0.885249i | \(0.346012\pi\) | |||||||
\(762\) | 2.00550e7 | + | 1.27433e7i | 1.25122 | + | 0.795047i | ||||
\(763\) | 3.77546e7 | 2.34779 | ||||||||
\(764\) | −2.76225e6 | + | 1.29599e6i | −0.171210 | + | 0.0803283i | ||||
\(765\) | −2.09236e7 | −1.29265 | ||||||||
\(766\) | −5.44723e6 | − | 3.46126e6i | −0.335432 | − | 0.213138i | ||||
\(767\) | 5.12226e6i | 0.314393i | ||||||||
\(768\) | −4.90347e6 | − | 2.63542e7i | −0.299986 | − | 1.61230i | ||||
\(769\) | 6.53060e6 | 0.398233 | 0.199117 | − | 0.979976i | \(-0.436193\pi\) | ||||
0.199117 | + | 0.979976i | \(0.436193\pi\) | |||||||
\(770\) | −5.39532e7 | − | 3.42827e7i | −3.27937 | − | 2.08376i | ||||
\(771\) | − | 2.24500e7i | − | 1.36013i | ||||||
\(772\) | −2.64269e7 | + | 1.23990e7i | −1.59589 | + | 0.748760i | ||||
\(773\) | − | 6.08632e6i | − | 0.366358i | −0.983080 | − | 0.183179i | \(-0.941361\pi\) | ||
0.983080 | − | 0.183179i | \(-0.0586389\pi\) | |||||||
\(774\) | 1.08874e7 | − | 1.71343e7i | 0.653238 | − | 1.02805i | ||||
\(775\) | −1.82264e7 | −1.09005 | ||||||||
\(776\) | −1.08306e6 | − | 138695.i | −0.0645649 | − | 0.00826811i | ||||
\(777\) | 208799. | 0.0124072 | ||||||||
\(778\) | −1.39321e7 | − | 8.85270e6i | −0.825218 | − | 0.524356i | ||||
\(779\) | 546018. | + | 1.13089e6i | 0.0322376 | + | 0.0667692i | ||||
\(780\) | 3.00055e7 | − | 1.40780e7i | 1.76589 | − | 0.828520i | ||||
\(781\) | 2.57107e7i | 1.50829i | ||||||||
\(782\) | 15130.5 | − | 23812.0i | 0.000884783 | − | 0.00139245i | ||||
\(783\) | − | 1.59876e7i | − | 0.931919i | ||||||
\(784\) | 7.12947e6 | − | 8.57834e6i | 0.414255 | − | 0.498440i | ||||
\(785\) | 4.69840e7 | 2.72130 | ||||||||
\(786\) | −2.67838e7 | + | 4.21516e7i | −1.54638 | + | 2.43365i | ||||
\(787\) | −9.74658e6 | −0.560939 | −0.280469 | − | 0.959863i | \(-0.590490\pi\) | ||||
−0.280469 | + | 0.959863i | \(0.590490\pi\) | |||||||
\(788\) | 1.96086e6 | + | 4.17934e6i | 0.112494 | + | 0.239769i | ||||
\(789\) | − | 3.27608e7i | − | 1.87354i | ||||||
\(790\) | 4.33243e7 | + | 2.75289e7i | 2.46981 | + | 1.56936i | ||||
\(791\) | 6.54597e6 | 0.371992 | ||||||||
\(792\) | 5.31960e7 | + | 6.81221e6i | 3.01346 | + | 0.385900i | ||||
\(793\) | − | 8.42624e6i | − | 0.475829i | ||||||
\(794\) | 7.18302e6 | + | 4.56420e6i | 0.404348 | + | 0.256929i | ||||
\(795\) | 6.81302e7i | 3.82316i | ||||||||
\(796\) | −1.76096e7 | + | 8.26204e6i | −0.985067 | + | 0.462173i | ||||
\(797\) | − | 2.43081e7i | − | 1.35552i | −0.735284 | − | 0.677759i | \(-0.762951\pi\) | ||
0.735284 | − | 0.677759i | \(-0.237049\pi\) | |||||||
\(798\) | 4.39264e6 | − | 3.76180e7i | 0.244185 | − | 2.09117i | ||||
\(799\) | 8.66332e6i | 0.480084i | ||||||||
\(800\) | 3.15816e7 | − | 1.01625e7i | 1.74465 | − | 0.561405i | ||||
\(801\) | 1.32474e7i | 0.729543i | ||||||||
\(802\) | 1.85848e7 | − | 2.92483e7i | 1.02029 | − | 1.60570i | ||||
\(803\) | − | 1.31021e7i | − | 0.717053i | ||||||
\(804\) | 8.84637e6 | + | 1.88550e7i | 0.482642 | + | 1.02869i | ||||
\(805\) | −144176. | −0.00784159 | ||||||||
\(806\) | 4.15737e6 | − | 6.54276e6i | 0.225414 | − | 0.354751i | ||||
\(807\) | − | 4.82151e7i | − | 2.60615i | ||||||
\(808\) | −2.49254e6 | + | 1.94640e7i | −0.134312 | + | 1.04883i | ||||
\(809\) | −1.34685e7 | −0.723513 | −0.361757 | − | 0.932273i | \(-0.617823\pi\) | ||||
−0.361757 | + | 0.932273i | \(0.617823\pi\) | |||||||
\(810\) | −4.37480e6 | − | 2.77981e6i | −0.234285 | − | 0.148869i | ||||
\(811\) | −3.56801e7 | −1.90491 | −0.952454 | − | 0.304681i | \(-0.901450\pi\) | ||||
−0.952454 | + | 0.304681i | \(0.901450\pi\) | |||||||
\(812\) | −8.44351e6 | − | 1.79963e7i | −0.449400 | − | 0.957843i | ||||
\(813\) | − | 3.52188e7i | − | 1.86874i | ||||||
\(814\) | 169083. | + | 107438.i | 0.00894414 | + | 0.00568324i | ||||
\(815\) | − | 2.12234e7i | − | 1.11924i | ||||||
\(816\) | 9.06352e6 | − | 1.09054e7i | 0.476510 | − | 0.573347i | ||||
\(817\) | −5.98052e6 | − | 1.23866e7i | −0.313461 | − | 0.649228i | ||||
\(818\) | 8.64638e6 | − | 1.36074e7i | 0.451805 | − | 0.711039i | ||||
\(819\) | −2.94232e7 | −1.53278 | ||||||||
\(820\) | 2.17528e6 | − | 1.02059e6i | 0.112974 | − | 0.0530052i | ||||
\(821\) | 4.06465e6 | 0.210458 | 0.105229 | − | 0.994448i | \(-0.466442\pi\) | ||||
0.105229 | + | 0.994448i | \(0.466442\pi\) | |||||||
\(822\) | 3.28454e7 | + | 2.08705e7i | 1.69549 | + | 1.07734i | ||||
\(823\) | − | 1.59194e7i | − | 0.819272i | −0.912249 | − | 0.409636i | \(-0.865656\pi\) | ||
0.912249 | − | 0.409636i | \(-0.134344\pi\) | |||||||
\(824\) | −1.79181e6 | + | 1.39921e7i | −0.0919337 | + | 0.717902i | ||||
\(825\) | 1.05661e8i | 5.40478i | ||||||||
\(826\) | 6.00624e6 | − | 9.45247e6i | 0.306304 | − | 0.482053i | ||||
\(827\) | 3.72616e7 | 1.89452 | 0.947258 | − | 0.320472i | \(-0.103842\pi\) | ||||
0.947258 | + | 0.320472i | \(0.103842\pi\) | |||||||
\(828\) | 109506. | − | 51378.0i | 0.00555089 | − | 0.00260436i | ||||
\(829\) | 1.08401e7i | 0.547829i | 0.961754 | + | 0.273915i | \(0.0883186\pi\) | ||||
−0.961754 | + | 0.273915i | \(0.911681\pi\) | |||||||
\(830\) | −9.90485e6 | + | 1.55880e7i | −0.499060 | + | 0.785408i | ||||
\(831\) | 3.44845e7 | 1.73229 | ||||||||
\(832\) | −3.55558e6 | + | 1.36549e7i | −0.178074 | + | 0.683882i | ||||
\(833\) | 5.90040e6 | 0.294624 | ||||||||
\(834\) | 8.16275e6 | − | 1.28463e7i | 0.406370 | − | 0.639534i | ||||
\(835\) | 3.31738e7 | 1.64657 | ||||||||
\(836\) | 2.29135e7 | − | 2.82024e7i | 1.13390 | − | 1.39563i | ||||
\(837\) | −1.36311e7 | −0.672538 | ||||||||
\(838\) | −1.52833e7 | + | 2.40525e7i | −0.751811 | + | 1.18318i | ||||
\(839\) | −3.51785e7 | −1.72533 | −0.862666 | − | 0.505774i | \(-0.831207\pi\) | ||||
−0.862666 | + | 0.505774i | \(0.831207\pi\) | |||||||
\(840\) | −7.18787e7 | − | 9.20470e6i | −3.51481 | − | 0.450102i | ||||
\(841\) | 6.57966e6 | 0.320785 | ||||||||
\(842\) | 6.80622e6 | − | 1.07115e7i | 0.330846 | − | 0.520677i | ||||
\(843\) | − | 1.16270e7i | − | 0.563507i | ||||||
\(844\) | 1.05815e7 | + | 2.25531e7i | 0.511316 | + | 1.08981i | ||||
\(845\) | 1.74877e7 | 0.842540 | ||||||||
\(846\) | −1.99204e7 | + | 3.13501e7i | −0.956910 | + | 1.50596i | ||||
\(847\) | 5.98677e7i | 2.86737i | ||||||||
\(848\) | −2.23066e7 | − | 1.85391e7i | −1.06523 | − | 0.885316i | ||||
\(849\) | 2.95347e7i | 1.40625i | ||||||||
\(850\) | 1.48124e7 | + | 9.41200e6i | 0.703197 | + | 0.446822i | ||||
\(851\) | 451.831 | 2.13871e−5 | ||||||||
\(852\) | 1.23800e7 | + | 2.63864e7i | 0.584279 | + | 1.24532i | ||||
\(853\) | −3.24795e7 | −1.52840 | −0.764199 | − | 0.644980i | \(-0.776866\pi\) | ||||
−0.764199 | + | 0.644980i | \(0.776866\pi\) | |||||||
\(854\) | −9.88041e6 | + | 1.55495e7i | −0.463586 | + | 0.729579i | ||||
\(855\) | −5.47365e7 | + | 2.64280e7i | −2.56072 | + | 1.23637i | ||||
\(856\) | 2.17978e6 | − | 1.70217e7i | 0.101678 | − | 0.793997i | ||||
\(857\) | − | 9.87730e6i | − | 0.459395i | −0.973262 | − | 0.229697i | \(-0.926226\pi\) | ||
0.973262 | − | 0.229697i | \(-0.0737737\pi\) | |||||||
\(858\) | −3.79292e7 | − | 2.41008e7i | −1.75896 | − | 1.11767i | ||||
\(859\) | 1.03156e7i | 0.476994i | 0.971143 | + | 0.238497i | \(0.0766547\pi\) | ||||
−0.971143 | + | 0.238497i | \(0.923345\pi\) | |||||||
\(860\) | −2.38258e7 | + | 1.11786e7i | −1.09850 | + | 0.515394i | ||||
\(861\) | −3.39560e6 | −0.156102 | ||||||||
\(862\) | −2.56614e7 | − | 1.63057e7i | −1.17629 | − | 0.747430i | ||||
\(863\) | 2.29287e7 | 1.04798 | 0.523988 | − | 0.851725i | \(-0.324444\pi\) | ||||
0.523988 | + | 0.851725i | \(0.324444\pi\) | |||||||
\(864\) | 2.36191e7 | − | 7.60031e6i | 1.07641 | − | 0.346375i | ||||
\(865\) | − | 5.10635e7i | − | 2.32044i | ||||||
\(866\) | 3.61395e6 | − | 5.68755e6i | 0.163752 | − | 0.257709i | ||||
\(867\) | −2.87971e7 | −1.30107 | ||||||||
\(868\) | −1.53438e7 | + | 7.19898e6i | −0.691246 | + | 0.324318i | ||||
\(869\) | − | 6.95973e7i | − | 3.12639i | ||||||
\(870\) | −2.72367e7 | + | 4.28645e7i | −1.21999 | + | 1.91999i | ||||
\(871\) | − | 1.09629e7i | − | 0.489643i | ||||||
\(872\) | 4.07309e7 | + | 5.21596e6i | 1.81398 | + | 0.232296i | ||||
\(873\) | − | 2.47642e6i | − | 0.109974i | ||||||
\(874\) | 9505.48 | − | 81403.6i | 0.000420916 | − | 0.00360467i | ||||
\(875\) | − | 4.07506e7i | − | 1.79934i | ||||||
\(876\) | −6.30878e6 | − | 1.34464e7i | −0.277770 | − | 0.592034i | ||||
\(877\) | 1.21889e7i | 0.535138i | 0.963539 | + | 0.267569i | \(0.0862204\pi\) | ||||
−0.963539 | + | 0.267569i | \(0.913780\pi\) | |||||||
\(878\) | −957685. | − | 608528.i | −0.0419263 | − | 0.0266406i | ||||
\(879\) | 5.64435e7i | 2.46400i | ||||||||
\(880\) | −5.34702e7 | − | 4.44392e7i | −2.32758 | − | 1.93446i | ||||
\(881\) | 2.02657e7 | 0.879675 | 0.439837 | − | 0.898077i | \(-0.355036\pi\) | ||||
0.439837 | + | 0.898077i | \(0.355036\pi\) | |||||||
\(882\) | 2.13519e7 | + | 1.35673e7i | 0.924198 | + | 0.587249i | ||||
\(883\) | 2.17676e7i | 0.939525i | 0.882793 | + | 0.469762i | \(0.155660\pi\) | ||||
−0.882793 | + | 0.469762i | \(0.844340\pi\) | |||||||
\(884\) | −6.75729e6 | + | 3.17038e6i | −0.290832 | + | 0.136452i | ||||
\(885\) | −2.86118e7 | −1.22797 | ||||||||
\(886\) | −262533. | + | 413168.i | −0.0112357 | + | 0.0176824i | ||||
\(887\) | 4.67578e7 | 1.99547 | 0.997734 | − | 0.0672753i | \(-0.0214306\pi\) | ||||
0.997734 | + | 0.0672753i | \(0.0214306\pi\) | |||||||
\(888\) | 225259. | + | 28846.4i | 0.00958628 | + | 0.00122761i | ||||
\(889\) | 2.73459e7i | 1.16048i | ||||||||
\(890\) | 9.21049e6 | − | 1.44952e7i | 0.389770 | − | 0.613409i | ||||
\(891\) | 7.02778e6i | 0.296568i | ||||||||
\(892\) | −3.82133e6 | − | 8.14472e6i | −0.160806 | − | 0.342739i | ||||
\(893\) | 1.09424e7 | + | 2.26634e7i | 0.459181 | + | 0.951036i | ||||
\(894\) | −1.17064e6 | − | 743845.i | −0.0489870 | − | 0.0311271i | ||||
\(895\) | −4.04371e7 | −1.68742 | ||||||||
\(896\) | 2.25728e7 | − | 2.10292e7i | 0.939324 | − | 0.875090i | ||||
\(897\) | −101356. | −0.00420600 | ||||||||
\(898\) | 1.77622e7 | − | 2.79536e7i | 0.735029 | − | 1.15677i | ||||
\(899\) | 1.18781e7i | 0.490169i | ||||||||
\(900\) | 3.19599e7 | + | 6.81188e7i | 1.31522 | + | 2.80324i | ||||
\(901\) | − | 1.53431e7i | − | 0.629651i | ||||||
\(902\) | −2.74971e6 | − | 1.74721e6i | −0.112531 | − | 0.0715038i | ||||
\(903\) | 3.71919e7 | 1.51785 | ||||||||
\(904\) | 7.06201e6 | + | 904353.i | 0.287414 | + | 0.0368059i | ||||
\(905\) | − | 1.65516e7i | − | 0.671768i | ||||||
\(906\) | −1.14610e7 | − | 7.28249e6i | −0.463876 | − | 0.294754i | ||||
\(907\) | −1.19607e7 | −0.482768 | −0.241384 | − | 0.970430i | \(-0.577601\pi\) | ||||
−0.241384 | + | 0.970430i | \(0.577601\pi\) | |||||||
\(908\) | 7.36085e6 | + | 1.56888e7i | 0.296287 | + | 0.631502i | ||||
\(909\) | −4.45047e7 | −1.78647 | ||||||||
\(910\) | 3.21946e7 | + | 2.04569e7i | 1.28878 | + | 0.818911i | ||||
\(911\) | 3.75316e6 | 0.149831 | 0.0749154 | − | 0.997190i | \(-0.476131\pi\) | ||||
0.0749154 | + | 0.997190i | \(0.476131\pi\) | |||||||
\(912\) | 9.93602e6 | − | 3.99767e7i | 0.395572 | − | 1.59155i | ||||
\(913\) | 2.50410e7 | 0.994201 | ||||||||
\(914\) | −2.50037e7 | − | 1.58877e7i | −0.990008 | − | 0.629066i | ||||
\(915\) | 4.70671e7 | 1.85851 | ||||||||
\(916\) | 1.06882e7 | + | 2.27807e7i | 0.420888 | + | 0.897073i | ||||
\(917\) | −5.74756e7 | −2.25715 | ||||||||
\(918\) | 1.10778e7 | + | 7.03902e6i | 0.433858 | + | 0.275680i | ||||
\(919\) | 2.96847e7i | 1.15943i | 0.814820 | + | 0.579713i | \(0.196835\pi\) | ||||
−0.814820 | + | 0.579713i | \(0.803165\pi\) | |||||||
\(920\) | −155542. | − | 19918.5i | −0.00605868 | − | 0.000775868i | ||||
\(921\) | −6.97907e7 | −2.71112 | ||||||||
\(922\) | −3.71763e6 | − | 2.36224e6i | −0.144025 | − | 0.0915159i | ||||
\(923\) | − | 1.53419e7i | − | 0.592754i | ||||||
\(924\) | 4.17334e7 | + | 8.89497e7i | 1.60806 | + | 3.42740i | ||||
\(925\) | 281063.i | 0.0108006i | ||||||||
\(926\) | −2.06035e7 | + | 3.24253e7i | −0.789612 | + | 1.24267i | ||||
\(927\) | −3.19931e7 | −1.22280 | ||||||||
\(928\) | −6.62287e6 | − | 2.05816e7i | −0.252451 | − | 0.784528i | ||||
\(929\) | −3.17744e7 | −1.20792 | −0.603960 | − | 0.797015i | \(-0.706411\pi\) | ||||
−0.603960 | + | 0.797015i | \(0.706411\pi\) | |||||||
\(930\) | 3.65464e7 | + | 2.32222e7i | 1.38560 | + | 0.880431i | ||||
\(931\) | 1.54356e7 | − | 7.45262e6i | 0.583644 | − | 0.281796i | ||||
\(932\) | 4.83172e6 | + | 1.02982e7i | 0.182206 | + | 0.388350i | ||||
\(933\) | − | 2.63264e6i | − | 0.0990118i | ||||||
\(934\) | −3.60581e6 | + | 5.67473e6i | −0.135250 | + | 0.212852i | ||||
\(935\) | − | 3.67781e7i | − | 1.37582i | ||||||
\(936\) | −3.17427e7 | − | 4.06493e6i | −1.18428 | − | 0.151657i | ||||
\(937\) | −1.15538e7 | −0.429909 | −0.214954 | − | 0.976624i | \(-0.568960\pi\) | ||||
−0.214954 | + | 0.976624i | \(0.568960\pi\) | |||||||
\(938\) | −1.28548e7 | + | 2.02306e7i | −0.477044 | + | 0.750760i | ||||
\(939\) | −3.93513e7 | −1.45645 | ||||||||
\(940\) | 4.35933e7 | − | 2.04531e7i | 1.60916 | − | 0.754987i | ||||
\(941\) | 1.49823e7i | 0.551574i | 0.961219 | + | 0.275787i | \(0.0889384\pi\) | ||||
−0.961219 | + | 0.275787i | \(0.911062\pi\) | |||||||
\(942\) | −6.09522e7 | − | 3.87300e7i | −2.23801 | − | 1.42207i | ||||
\(943\) | −7347.91 | −0.000269082 | ||||||||
\(944\) | 7.78563e6 | − | 9.36785e6i | 0.284357 | − | 0.342145i | ||||
\(945\) | − | 6.70736e7i | − | 2.44327i | ||||||
\(946\) | 3.01176e7 | + | 1.91372e7i | 1.09419 | + | 0.695264i | ||||
\(947\) | 6.25833e6i | 0.226769i | 0.993551 | + | 0.113384i | \(0.0361692\pi\) | ||||
−0.993551 | + | 0.113384i | \(0.963831\pi\) | |||||||
\(948\) | −3.35118e7 | − | 7.14264e7i | −1.21109 | − | 2.58130i | ||||
\(949\) | 7.81817e6i | 0.281799i | ||||||||
\(950\) | 5.06375e7 | + | 5.91292e6i | 1.82038 | + | 0.212566i | ||||
\(951\) | − | 3.88894e7i | − | 1.39438i | ||||||
\(952\) | 1.61872e7 | + | 2.07291e6i | 0.578868 | + | 0.0741292i | ||||
\(953\) | − | 2.60023e7i | − | 0.927426i | −0.885985 | − | 0.463713i | \(-0.846517\pi\) | ||
0.885985 | − | 0.463713i | \(-0.153483\pi\) | |||||||
\(954\) | 3.52797e7 | − | 5.55222e7i | 1.25503 | − | 1.97513i | ||||
\(955\) | 8.97110e6i | 0.318300i | ||||||||
\(956\) | −3.01961e6 | + | 1.41674e6i | −0.106858 | + | 0.0501354i | ||||
\(957\) | 6.88586e7 | 2.43040 | ||||||||
\(958\) | −9.37936e6 | + | 1.47610e7i | −0.330187 | + | 0.519639i | ||||
\(959\) | 4.47862e7i | 1.57252i | ||||||||
\(960\) | −7.62735e7 | − | 1.98607e7i | −2.67113 | − | 0.695530i | ||||
\(961\) | −1.85019e7 | −0.646260 | ||||||||
\(962\) | −100894. | − | 64109.5i | −0.00351501 | − | 0.00223349i | ||||
\(963\) | 3.89203e7 | 1.35242 | ||||||||
\(964\) | −8.87001e6 | + | 4.16163e6i | −0.307420 | + | 0.144235i | ||||
\(965\) | 8.58280e7i | 2.96695i | ||||||||
\(966\) | 187039. | + | 118848.i | 0.00644897 | + | 0.00409778i | ||||
\(967\) | 1.89582e6i | 0.0651973i | 0.999469 | + | 0.0325987i | \(0.0103783\pi\) | ||||
−0.999469 | + | 0.0325987i | \(0.989622\pi\) | |||||||
\(968\) | −8.27097e6 | + | 6.45873e7i | −0.283706 | + | 2.21543i | ||||
\(969\) | 1.96228e7 | − | 9.47434e6i | 0.671356 | − | 0.324145i | ||||
\(970\) | −1.72177e6 | + | 2.70967e6i | −0.0587551 | + | 0.0924672i | ||||
\(971\) | −1.71402e7 | −0.583401 | −0.291700 | − | 0.956510i | \(-0.594221\pi\) | ||||
−0.291700 | + | 0.956510i | \(0.594221\pi\) | |||||||
\(972\) | −1.07634e7 | − | 2.29410e7i | −0.365414 | − | 0.778836i | ||||
\(973\) | 1.75165e7 | 0.593152 | ||||||||
\(974\) | 1.71774e7 | + | 1.09148e7i | 0.580177 | + | 0.368654i | ||||
\(975\) | − | 6.30490e7i | − | 2.12406i | ||||||
\(976\) | −1.28075e7 | + | 1.54103e7i | −0.430369 | + | 0.517830i | ||||
\(977\) | − | 1.93553e6i | − | 0.0648729i | −0.999474 | − | 0.0324365i | \(-0.989673\pi\) | ||
0.999474 | − | 0.0324365i | \(-0.0103267\pi\) | |||||||
\(978\) | −1.74950e7 | + | 2.75331e7i | −0.584879 | + | 0.920467i | ||||
\(979\) | −2.32855e7 | −0.776478 | ||||||||
\(980\) | −1.39301e7 | − | 2.96905e7i | −0.463330 | − | 0.987533i | ||||
\(981\) | 9.31317e7i | 3.08976i | ||||||||
\(982\) | 2.11180e7 | − | 3.32350e7i | 0.698835 | − | 1.09981i | ||||
\(983\) | 9.93053e6 | 0.327785 | 0.163892 | − | 0.986478i | \(-0.447595\pi\) | ||||
0.163892 | + | 0.986478i | \(0.447595\pi\) | |||||||
\(984\) | −3.66328e6 | − | 469115.i | −0.120610 | − | 0.0154451i | ||||
\(985\) | 1.35734e7 | 0.445758 | ||||||||
\(986\) | 6.13376e6 | − | 9.65315e6i | 0.200925 | − | 0.316211i | ||||
\(987\) | −6.80490e7 | −2.22346 | ||||||||
\(988\) | −1.36728e7 | + | 1.68287e7i | −0.445620 | + | 0.548478i | ||||
\(989\) | 80481.5 | 0.00261641 | ||||||||
\(990\) | 8.45673e7 | − | 1.33090e8i | 2.74230 | − | 4.31576i | ||||
\(991\) | 4.04697e7 | 1.30902 | 0.654510 | − | 0.756054i | \(-0.272875\pi\) | ||||
0.654510 | + | 0.756054i | \(0.272875\pi\) | |||||||
\(992\) | −1.75479e7 | + | 5.64669e6i | −0.566170 | + | 0.182186i | ||||
\(993\) | 3.44646e7 | 1.10917 | ||||||||
\(994\) | −1.79895e7 | + | 2.83114e7i | −0.577502 | + | 0.908858i | ||||
\(995\) | 5.71914e7i | 1.83136i | ||||||||
\(996\) | 2.56991e7 | − | 1.20575e7i | 0.820861 | − | 0.385131i | ||||
\(997\) | 2.76211e7 | 0.880041 | 0.440020 | − | 0.897988i | \(-0.354971\pi\) | ||||
0.440020 | + | 0.897988i | \(0.354971\pi\) | |||||||
\(998\) | −9.37679e6 | + | 1.47569e7i | −0.298008 | + | 0.468997i | ||||
\(999\) | 210201.i | 0.00666377i |
(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 | 76.6.d.a.75.9 | ✓ | 48 | |
4.3 | odd | 2 | inner | 76.6.d.a.75.39 | yes | 48 | |
19.18 | odd | 2 | inner | 76.6.d.a.75.40 | yes | 48 | |
76.75 | even | 2 | inner | 76.6.d.a.75.10 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.d.a.75.9 | ✓ | 48 | 1.1 | even | 1 | trivial | |
76.6.d.a.75.10 | yes | 48 | 76.75 | even | 2 | inner | |
76.6.d.a.75.39 | yes | 48 | 4.3 | odd | 2 | inner | |
76.6.d.a.75.40 | yes | 48 | 19.18 | odd | 2 | inner |