Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(7,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.7");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.d (of order \(6\), degree \(2\), 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: | \(9.89232559565\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 7.11 | ||
Character | \(\chi\) | \(=\) | 43.7 |
Dual form | 43.7.d.a.37.11 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.51738i | 0.189673i | 0.995493 | + | 0.0948365i | \(0.0302328\pi\) | ||||
−0.995493 | + | 0.0948365i | \(0.969767\pi\) | |||||||
\(3\) | 20.0424 | − | 11.5715i | 0.742310 | − | 0.428573i | −0.0805985 | − | 0.996747i | \(-0.525683\pi\) |
0.822909 | + | 0.568174i | \(0.192350\pi\) | |||||||
\(4\) | 61.6975 | 0.964024 | ||||||||
\(5\) | 211.318 | − | 122.005i | 1.69055 | − | 0.976037i | 0.736470 | − | 0.676470i | \(-0.236491\pi\) |
0.954075 | − | 0.299567i | \(-0.0968422\pi\) | |||||||
\(6\) | 17.5584 | + | 30.4120i | 0.0812887 | + | 0.140796i | ||||
\(7\) | −447.414 | − | 258.315i | −1.30442 | − | 0.753105i | −0.323257 | − | 0.946311i | \(-0.604778\pi\) |
−0.981158 | + | 0.193207i | \(0.938111\pi\) | |||||||
\(8\) | 190.731i | 0.372522i | ||||||||
\(9\) | −96.7022 | + | 167.493i | −0.132650 | + | 0.229757i | ||||
\(10\) | 185.128 | + | 320.651i | 0.185128 | + | 0.320651i | ||||
\(11\) | −593.709 | −0.446063 | −0.223031 | − | 0.974811i | \(-0.571595\pi\) | ||||
−0.223031 | + | 0.974811i | \(0.571595\pi\) | |||||||
\(12\) | 1236.57 | − | 713.931i | 0.715605 | − | 0.413155i | ||||
\(13\) | 651.631 | − | 1128.66i | 0.296600 | − | 0.513727i | −0.678755 | − | 0.734364i | \(-0.737480\pi\) |
0.975356 | + | 0.220637i | \(0.0708137\pi\) | |||||||
\(14\) | 391.963 | − | 678.899i | 0.142844 | − | 0.247412i | ||||
\(15\) | 2823.55 | − | 4890.52i | 0.836606 | − | 1.44904i | ||||
\(16\) | 3659.23 | 0.893367 | ||||||||
\(17\) | −1539.71 | + | 2666.85i | −0.313394 | + | 0.542815i | −0.979095 | − | 0.203404i | \(-0.934799\pi\) |
0.665701 | + | 0.746219i | \(0.268133\pi\) | |||||||
\(18\) | −254.151 | − | 146.734i | −0.0435788 | − | 0.0251602i | ||||
\(19\) | −3288.36 | + | 1898.54i | −0.479423 | + | 0.276795i | −0.720176 | − | 0.693791i | \(-0.755939\pi\) |
0.240753 | + | 0.970586i | \(0.422606\pi\) | |||||||
\(20\) | 13037.8 | − | 7527.39i | 1.62973 | − | 0.940923i | ||||
\(21\) | −11956.3 | −1.29104 | ||||||||
\(22\) | − | 900.885i | − | 0.0846060i | ||||||
\(23\) | 8014.01 | + | 13880.7i | 0.658668 | + | 1.14085i | 0.980961 | + | 0.194206i | \(0.0622132\pi\) |
−0.322293 | + | 0.946640i | \(0.604453\pi\) | |||||||
\(24\) | 2207.04 | + | 3822.71i | 0.159653 | + | 0.276527i | ||||
\(25\) | 21957.8 | − | 38031.9i | 1.40530 | − | 2.43404i | ||||
\(26\) | 1712.61 | + | 988.775i | 0.0974401 | + | 0.0562571i | ||||
\(27\) | 21347.1i | 1.08455i | ||||||||
\(28\) | −27604.4 | − | 15937.4i | −1.25749 | − | 0.726011i | ||||
\(29\) | 4728.25 | + | 2729.85i | 0.193868 | + | 0.111930i | 0.593792 | − | 0.804619i | \(-0.297630\pi\) |
−0.399924 | + | 0.916548i | \(0.630964\pi\) | |||||||
\(30\) | 7420.80 | + | 4284.40i | 0.274845 | + | 0.158682i | ||||
\(31\) | 7584.14 | + | 13136.1i | 0.254578 | + | 0.440942i | 0.964781 | − | 0.263055i | \(-0.0847301\pi\) |
−0.710203 | + | 0.703997i | \(0.751397\pi\) | |||||||
\(32\) | 17759.3i | 0.541970i | ||||||||
\(33\) | −11899.3 | + | 6870.09i | −0.331117 | + | 0.191170i | ||||
\(34\) | −4046.63 | − | 2336.33i | −0.102957 | − | 0.0594424i | ||||
\(35\) | −126062. | −2.94023 | ||||||||
\(36\) | −5966.29 | + | 10333.9i | −0.127878 | + | 0.221492i | ||||
\(37\) | 2862.28 | − | 1652.54i | 0.0565077 | − | 0.0326247i | −0.471480 | − | 0.881877i | \(-0.656280\pi\) |
0.527988 | + | 0.849252i | \(0.322947\pi\) | |||||||
\(38\) | −2880.81 | − | 4989.71i | −0.0525006 | − | 0.0909336i | ||||
\(39\) | − | 30161.3i | − | 0.508460i | ||||||
\(40\) | 23270.1 | + | 40305.0i | 0.363596 | + | 0.629766i | ||||
\(41\) | 85357.9 | 1.23849 | 0.619244 | − | 0.785198i | \(-0.287439\pi\) | ||||
0.619244 | + | 0.785198i | \(0.287439\pi\) | |||||||
\(42\) | − | 18142.3i | − | 0.244876i | ||||||
\(43\) | −57085.9 | + | 55340.4i | −0.717999 | + | 0.696044i | ||||
\(44\) | −36630.4 | −0.430015 | ||||||||
\(45\) | 47192.4i | 0.517887i | ||||||||
\(46\) | −21062.3 | + | 12160.3i | −0.216388 | + | 0.124932i | ||||
\(47\) | −22536.9 | −0.217070 | −0.108535 | − | 0.994093i | \(-0.534616\pi\) | ||||
−0.108535 | + | 0.994093i | \(0.534616\pi\) | |||||||
\(48\) | 73339.7 | − | 42342.7i | 0.663155 | − | 0.382873i | ||||
\(49\) | 74628.6 | + | 129261.i | 0.634333 | + | 1.09870i | ||||
\(50\) | 57709.1 | + | 33318.3i | 0.461672 | + | 0.266547i | ||||
\(51\) | 71266.6i | 0.537249i | ||||||||
\(52\) | 40204.0 | − | 69635.4i | 0.285930 | − | 0.495245i | ||||
\(53\) | −128928. | − | 223309.i | −0.866001 | − | 1.49996i | −0.866049 | − | 0.499959i | \(-0.833349\pi\) |
4.78358e−5 | − | 1.00000i | \(-0.499985\pi\) | |||||||
\(54\) | −32391.8 | −0.205709 | ||||||||
\(55\) | −125462. | + | 72435.3i | −0.754089 | + | 0.435374i | ||||
\(56\) | 49268.8 | − | 85336.0i | 0.280548 | − | 0.485924i | ||||
\(57\) | −43937.7 | + | 76102.4i | −0.237254 | + | 0.410936i | ||||
\(58\) | −4142.24 | + | 7174.57i | −0.0212300 | + | 0.0367715i | ||||
\(59\) | −107781. | −0.524793 | −0.262396 | − | 0.964960i | \(-0.584513\pi\) | ||||
−0.262396 | + | 0.964960i | \(0.584513\pi\) | |||||||
\(60\) | 174206. | − | 301733.i | 0.806508 | − | 1.39691i | ||||
\(61\) | −19167.1 | − | 11066.2i | −0.0844438 | − | 0.0487537i | 0.457184 | − | 0.889372i | \(-0.348858\pi\) |
−0.541627 | + | 0.840619i | \(0.682192\pi\) | |||||||
\(62\) | −19932.5 | + | 11508.0i | −0.0836348 | + | 0.0482866i | ||||
\(63\) | 86531.9 | − | 49959.2i | 0.346063 | − | 0.199799i | ||||
\(64\) | 207243. | 0.790570 | ||||||||
\(65\) | − | 318008.i | − | 1.15797i | ||||||
\(66\) | −10424.6 | − | 18055.9i | −0.0362599 | − | 0.0628039i | ||||
\(67\) | 230542. | + | 399311.i | 0.766525 | + | 1.32766i | 0.939436 | + | 0.342723i | \(0.111349\pi\) |
−0.172911 | + | 0.984937i | \(0.555317\pi\) | |||||||
\(68\) | −94996.1 | + | 164538.i | −0.302120 | + | 0.523287i | ||||
\(69\) | 321240. | + | 185468.i | 0.977872 | + | 0.564575i | ||||
\(70\) | − | 191285.i | − | 0.557682i | ||||||
\(71\) | 346473. | + | 200037.i | 0.968044 | + | 0.558900i | 0.898639 | − | 0.438688i | \(-0.144557\pi\) |
0.0694044 | + | 0.997589i | \(0.477890\pi\) | |||||||
\(72\) | −31946.2 | − | 18444.1i | −0.0855897 | − | 0.0494152i | ||||
\(73\) | −467725. | − | 270041.i | −1.20233 | − | 0.694163i | −0.241254 | − | 0.970462i | \(-0.577559\pi\) |
−0.961072 | + | 0.276299i | \(0.910892\pi\) | |||||||
\(74\) | 2507.54 | + | 4343.18i | 0.00618803 | + | 0.0107180i | ||||
\(75\) | − | 1.01633e6i | − | 2.40909i | ||||||
\(76\) | −202884. | + | 117135.i | −0.462176 | + | 0.266837i | ||||
\(77\) | 265634. | + | 153364.i | 0.581851 | + | 0.335932i | ||||
\(78\) | 45766.3 | 0.0964411 | ||||||||
\(79\) | −244212. | + | 422987.i | −0.495319 | + | 0.857918i | −0.999985 | − | 0.00539663i | \(-0.998282\pi\) |
0.504666 | + | 0.863314i | \(0.331616\pi\) | |||||||
\(80\) | 773262. | − | 446443.i | 1.51028 | − | 0.871959i | ||||
\(81\) | 176522. | + | 305745.i | 0.332157 | + | 0.575313i | ||||
\(82\) | 129521.i | 0.234908i | ||||||||
\(83\) | −360109. | − | 623728.i | −0.629796 | − | 1.09084i | −0.987592 | − | 0.157039i | \(-0.949805\pi\) |
0.357796 | − | 0.933800i | \(-0.383528\pi\) | |||||||
\(84\) | −737676. | −1.24459 | ||||||||
\(85\) | 751405.i | 1.22354i | ||||||||
\(86\) | −83972.6 | − | 86621.3i | −0.132021 | − | 0.136185i | ||||
\(87\) | 126354. | 0.191880 | ||||||||
\(88\) | − | 113239.i | − | 0.166168i | ||||||
\(89\) | −61258.8 | + | 35367.8i | −0.0868957 | + | 0.0501693i | −0.542818 | − | 0.839850i | \(-0.682643\pi\) |
0.455923 | + | 0.890019i | \(0.349309\pi\) | |||||||
\(90\) | −71609.1 | −0.0982292 | ||||||||
\(91\) | −583098. | + | 336652.i | −0.773780 | + | 0.446742i | ||||
\(92\) | 494445. | + | 856404.i | 0.634972 | + | 1.09980i | ||||
\(93\) | 304008. | + | 175519.i | 0.377952 | + | 0.218211i | ||||
\(94\) | − | 34197.1i | − | 0.0411724i | ||||||
\(95\) | −463261. | + | 802391.i | −0.540325 | + | 0.935870i | ||||
\(96\) | 205501. | + | 355938.i | 0.232274 | + | 0.402310i | ||||
\(97\) | −1.36624e6 | −1.49697 | −0.748483 | − | 0.663154i | \(-0.769217\pi\) | ||||
−0.748483 | + | 0.663154i | \(0.769217\pi\) | |||||||
\(98\) | −196138. | + | 113240.i | −0.208393 | + | 0.120316i | ||||
\(99\) | 57413.0 | − | 99442.2i | 0.0591704 | − | 0.102486i | ||||
\(100\) | 1.35474e6 | − | 2.34648e6i | 1.35474 | − | 2.34648i | ||||
\(101\) | −371051. | + | 642679.i | −0.360138 | + | 0.623778i | −0.987983 | − | 0.154560i | \(-0.950604\pi\) |
0.627845 | + | 0.778338i | \(0.283937\pi\) | |||||||
\(102\) | −108139. | −0.101902 | ||||||||
\(103\) | 434736. | − | 752985.i | 0.397845 | − | 0.689088i | −0.595615 | − | 0.803270i | \(-0.703091\pi\) |
0.993460 | + | 0.114182i | \(0.0364247\pi\) | |||||||
\(104\) | 215271. | + | 124287.i | 0.191375 | + | 0.110490i | ||||
\(105\) | −2.52659e6 | + | 1.45873e6i | −2.18256 | + | 1.26010i | ||||
\(106\) | 338846. | − | 195633.i | 0.284502 | − | 0.164257i | ||||
\(107\) | −1.59299e6 | −1.30035 | −0.650175 | − | 0.759784i | \(-0.725305\pi\) | ||||
−0.650175 | + | 0.759784i | \(0.725305\pi\) | |||||||
\(108\) | 1.31707e6i | 1.04553i | ||||||||
\(109\) | 615228. | + | 1.06561e6i | 0.475069 | + | 0.822843i | 0.999592 | − | 0.0285526i | \(-0.00908982\pi\) |
−0.524523 | + | 0.851396i | \(0.675756\pi\) | |||||||
\(110\) | −109912. | − | 190373.i | −0.0825786 | − | 0.143030i | ||||
\(111\) | 38244.6 | − | 66241.6i | 0.0279641 | − | 0.0484353i | ||||
\(112\) | −1.63719e6 | − | 945234.i | −1.16532 | − | 0.672799i | ||||
\(113\) | − | 1.79572e6i | − | 1.24453i | −0.782808 | − | 0.622263i | \(-0.786213\pi\) | ||
0.782808 | − | 0.622263i | \(-0.213787\pi\) | |||||||
\(114\) | −115477. | − | 66670.4i | −0.0779434 | − | 0.0450006i | ||||
\(115\) | 3.38701e6 | + | 1.95549e6i | 2.22702 | + | 1.28577i | ||||
\(116\) | 291721. | + | 168425.i | 0.186893 | + | 0.107903i | ||||
\(117\) | 126028. | + | 218287.i | 0.0786884 | + | 0.136292i | ||||
\(118\) | − | 163546.i | − | 0.0995390i | ||||||
\(119\) | 1.37777e6 | − | 795458.i | 0.817593 | − | 0.472037i | ||||
\(120\) | 932777. | + | 538539.i | 0.539801 | + | 0.311654i | ||||
\(121\) | −1.41907e6 | −0.801028 | ||||||||
\(122\) | 16791.6 | − | 29083.9i | 0.00924725 | − | 0.0160167i | ||||
\(123\) | 1.71077e6 | − | 987716.i | 0.919343 | − | 0.530783i | ||||
\(124\) | 467923. | + | 810466.i | 0.245419 | + | 0.425079i | ||||
\(125\) | − | 6.90314e6i | − | 3.53441i | ||||||
\(126\) | 75807.3 | + | 131302.i | 0.0378965 | + | 0.0656387i | ||||
\(127\) | 729609. | 0.356188 | 0.178094 | − | 0.984013i | \(-0.443007\pi\) | ||||
0.178094 | + | 0.984013i | \(0.443007\pi\) | |||||||
\(128\) | 1.45106e6i | 0.691920i | ||||||||
\(129\) | −503768. | + | 1.76972e6i | −0.234672 | + | 0.824396i | ||||
\(130\) | 482540. | 0.219636 | ||||||||
\(131\) | − | 3.33948e6i | − | 1.48547i | −0.669584 | − | 0.742737i | \(-0.733527\pi\) | ||
0.669584 | − | 0.742737i | \(-0.266473\pi\) | |||||||
\(132\) | −734160. | + | 423868.i | −0.319205 | + | 0.184293i | ||||
\(133\) | 1.96168e6 | 0.833823 | ||||||||
\(134\) | −605908. | + | 349821.i | −0.251821 | + | 0.145389i | ||||
\(135\) | 2.60445e6 | + | 4.51104e6i | 1.05856 | + | 1.83348i | ||||
\(136\) | −508652. | − | 293670.i | −0.202211 | − | 0.116746i | ||||
\(137\) | 612991.i | 0.238392i | 0.992871 | + | 0.119196i | \(0.0380317\pi\) | ||||
−0.992871 | + | 0.119196i | \(0.961968\pi\) | |||||||
\(138\) | −281426. | + | 487444.i | −0.107085 | + | 0.185476i | ||||
\(139\) | −1.82930e6 | − | 3.16845e6i | −0.681148 | − | 1.17978i | −0.974631 | − | 0.223818i | \(-0.928148\pi\) |
0.293483 | − | 0.955964i | \(-0.405186\pi\) | |||||||
\(140\) | −7.77774e6 | −2.83445 | ||||||||
\(141\) | −451693. | + | 260785.i | −0.161134 | + | 0.0930305i | ||||
\(142\) | −303532. | + | 525733.i | −0.106008 | + | 0.183612i | ||||
\(143\) | −386879. | + | 670095.i | −0.132302 | + | 0.229154i | ||||
\(144\) | −353856. | + | 612896.i | −0.118505 | + | 0.205258i | ||||
\(145\) | 1.33222e6 | 0.436990 | ||||||||
\(146\) | 409756. | − | 709719.i | 0.131664 | − | 0.228049i | ||||
\(147\) | 2.99147e6 | + | 1.72713e6i | 0.941744 | + | 0.543716i | ||||
\(148\) | 176596. | − | 101958.i | 0.0544748 | − | 0.0314510i | ||||
\(149\) | 5.56042e6 | − | 3.21031e6i | 1.68093 | − | 0.970483i | 0.719877 | − | 0.694101i | \(-0.244198\pi\) |
0.961048 | − | 0.276382i | \(-0.0891354\pi\) | |||||||
\(150\) | 1.54217e6 | 0.456939 | ||||||||
\(151\) | − | 1.00573e6i | − | 0.292113i | −0.989276 | − | 0.146056i | \(-0.953342\pi\) | ||
0.989276 | − | 0.146056i | \(-0.0466581\pi\) | |||||||
\(152\) | −362111. | − | 627194.i | −0.103112 | − | 0.178596i | ||||
\(153\) | −297786. | − | 515780.i | −0.0831438 | − | 0.144009i | ||||
\(154\) | −232712. | + | 403069.i | −0.0637172 | + | 0.110361i | ||||
\(155\) | 3.20533e6 | + | 1.85060e6i | 0.860752 | + | 0.496955i | ||||
\(156\) | − | 1.86088e6i | − | 0.490167i | ||||||
\(157\) | 1.25893e6 | + | 726845.i | 0.325315 | + | 0.187821i | 0.653759 | − | 0.756703i | \(-0.273191\pi\) |
−0.328444 | + | 0.944523i | \(0.606524\pi\) | |||||||
\(158\) | −641834. | − | 370563.i | −0.162724 | − | 0.0939487i | ||||
\(159\) | −5.16803e6 | − | 2.98377e6i | −1.28568 | − | 0.742290i | ||||
\(160\) | 2.16671e6 | + | 3.75286e6i | 0.528983 | + | 0.916225i | ||||
\(161\) | − | 8.28056e6i | − | 1.98418i | ||||||
\(162\) | −463933. | + | 267852.i | −0.109121 | + | 0.0630013i | ||||
\(163\) | 3.48059e6 | + | 2.00952e6i | 0.803692 | + | 0.464012i | 0.844761 | − | 0.535144i | \(-0.179743\pi\) |
−0.0410684 | + | 0.999156i | \(0.513076\pi\) | |||||||
\(164\) | 5.26637e6 | 1.19393 | ||||||||
\(165\) | −1.67637e6 | + | 2.90355e6i | −0.373179 | + | 0.646364i | ||||
\(166\) | 946434. | − | 546424.i | 0.206903 | − | 0.119455i | ||||
\(167\) | 385714. | + | 668076.i | 0.0828163 | + | 0.143442i | 0.904459 | − | 0.426561i | \(-0.140275\pi\) |
−0.821642 | + | 0.570003i | \(0.806942\pi\) | |||||||
\(168\) | − | 2.28045e6i | − | 0.480942i | ||||||
\(169\) | 1.56416e6 | + | 2.70920e6i | 0.324056 | + | 0.561282i | ||||
\(170\) | −1.14017e6 | −0.232072 | ||||||||
\(171\) | − | 734371.i | − | 0.146868i | ||||||
\(172\) | −3.52206e6 | + | 3.41437e6i | −0.692168 | + | 0.671004i | ||||
\(173\) | −2.99344e6 | −0.578140 | −0.289070 | − | 0.957308i | \(-0.593346\pi\) | ||||
−0.289070 | + | 0.957308i | \(0.593346\pi\) | |||||||
\(174\) | 191727.i | 0.0363945i | ||||||||
\(175\) | −1.96484e7 | + | 1.13440e7i | −3.66618 | + | 2.11667i | ||||
\(176\) | −2.17252e6 | −0.398497 | ||||||||
\(177\) | −2.16020e6 | + | 1.24719e6i | −0.389559 | + | 0.224912i | ||||
\(178\) | −53666.5 | − | 92953.1i | −0.00951575 | − | 0.0164818i | ||||
\(179\) | −2.93740e6 | − | 1.69591e6i | −0.512158 | − | 0.295695i | 0.221562 | − | 0.975146i | \(-0.428884\pi\) |
−0.733720 | + | 0.679452i | \(0.762218\pi\) | |||||||
\(180\) | 2.91166e6i | 0.499255i | ||||||||
\(181\) | −3.77377e6 | + | 6.53636e6i | −0.636414 | + | 1.10230i | 0.349800 | + | 0.936824i | \(0.386249\pi\) |
−0.986214 | + | 0.165476i | \(0.947084\pi\) | |||||||
\(182\) | −510830. | − | 884784.i | −0.0847349 | − | 0.146765i | ||||
\(183\) | −512207. | −0.0835780 | ||||||||
\(184\) | −2.64748e6 | + | 1.52852e6i | −0.424991 | + | 0.245369i | ||||
\(185\) | 403235. | − | 698424.i | 0.0636859 | − | 0.110307i | ||||
\(186\) | −266330. | + | 461297.i | −0.0413887 | + | 0.0716873i | ||||
\(187\) | 914138. | − | 1.58333e6i | 0.139793 | − | 0.242129i | ||||
\(188\) | −1.39047e6 | −0.209261 | ||||||||
\(189\) | 5.51429e6 | − | 9.55102e6i | 0.816778 | − | 1.41470i | ||||
\(190\) | −1.21754e6 | − | 702944.i | −0.177509 | − | 0.102485i | ||||
\(191\) | −6.30231e6 | + | 3.63864e6i | −0.904482 | + | 0.522203i | −0.878652 | − | 0.477463i | \(-0.841556\pi\) |
−0.0258303 | + | 0.999666i | \(0.508223\pi\) | |||||||
\(192\) | 4.15364e6 | − | 2.39811e6i | 0.586848 | − | 0.338817i | ||||
\(193\) | 8.26490e6 | 1.14965 | 0.574825 | − | 0.818277i | \(-0.305070\pi\) | ||||
0.574825 | + | 0.818277i | \(0.305070\pi\) | |||||||
\(194\) | − | 2.07311e6i | − | 0.283934i | ||||||
\(195\) | −3.67982e6 | − | 6.37364e6i | −0.496275 | − | 0.859574i | ||||
\(196\) | 4.60440e6 | + | 7.97506e6i | 0.611512 | + | 1.05917i | ||||
\(197\) | 1.37000e6 | − | 2.37291e6i | 0.179193 | − | 0.310372i | −0.762411 | − | 0.647093i | \(-0.775985\pi\) |
0.941604 | + | 0.336721i | \(0.109318\pi\) | |||||||
\(198\) | 150892. | + | 87117.5i | 0.0194389 | + | 0.0112230i | ||||
\(199\) | − | 2.84120e6i | − | 0.360531i | −0.983618 | − | 0.180266i | \(-0.942304\pi\) | ||
0.983618 | − | 0.180266i | \(-0.0576957\pi\) | |||||||
\(200\) | 7.25389e6 | + | 4.18803e6i | 0.906736 | + | 0.523504i | ||||
\(201\) | 9.24124e6 | + | 5.33543e6i | 1.13800 | + | 0.657024i | ||||
\(202\) | −975191. | − | 563027.i | −0.118314 | − | 0.0683085i | ||||
\(203\) | −1.41032e6 | − | 2.44275e6i | −0.168590 | − | 0.292006i | ||||
\(204\) | 4.39698e6i | 0.517921i | ||||||||
\(205\) | 1.80377e7 | − | 1.04141e7i | 2.09372 | − | 1.20881i | ||||
\(206\) | 1.14257e6 | + | 659662.i | 0.130701 | + | 0.0754605i | ||||
\(207\) | −3.09989e6 | −0.349490 | ||||||||
\(208\) | 2.38447e6 | − | 4.13002e6i | 0.264973 | − | 0.458947i | ||||
\(209\) | 1.95233e6 | − | 1.12718e6i | 0.213853 | − | 0.123468i | ||||
\(210\) | −2.21345e6 | − | 3.83381e6i | −0.239008 | − | 0.413973i | ||||
\(211\) | 1.50202e7i | 1.59893i | 0.600713 | + | 0.799464i | \(0.294883\pi\) | ||||
−0.600713 | + | 0.799464i | \(0.705117\pi\) | |||||||
\(212\) | −7.95452e6 | − | 1.37776e7i | −0.834846 | − | 1.44600i | ||||
\(213\) | 9.25887e6 | 0.958118 | ||||||||
\(214\) | − | 2.41717e6i | − | 0.246641i | ||||||
\(215\) | −5.31151e6 | + | 1.86592e7i | −0.534444 | + | 1.87749i | ||||
\(216\) | −4.07157e6 | −0.404018 | ||||||||
\(217\) | − | 7.83638e6i | − | 0.766896i | ||||||
\(218\) | −1.61693e6 | + | 933537.i | −0.156071 | + | 0.0901077i | ||||
\(219\) | −1.24991e7 | −1.19000 | ||||||||
\(220\) | −7.74067e6 | + | 4.46908e6i | −0.726960 | + | 0.419711i | ||||
\(221\) | 2.00664e6 | + | 3.47560e6i | 0.185906 | + | 0.321998i | ||||
\(222\) | 100514. | + | 58031.8i | 0.00918687 | + | 0.00530404i | ||||
\(223\) | − | 1.99339e7i | − | 1.79754i | −0.438423 | − | 0.898769i | \(-0.644463\pi\) | ||
0.438423 | − | 0.898769i | \(-0.355537\pi\) | |||||||
\(224\) | 4.58748e6 | − | 7.94575e6i | 0.408160 | − | 0.706954i | ||||
\(225\) | 4.24672e6 | + | 7.35554e6i | 0.372826 | + | 0.645754i | ||||
\(226\) | 2.72480e6 | 0.236053 | ||||||||
\(227\) | 1.06394e7 | − | 6.14269e6i | 0.909581 | − | 0.525147i | 0.0292848 | − | 0.999571i | \(-0.490677\pi\) |
0.880296 | + | 0.474424i | \(0.157344\pi\) | |||||||
\(228\) | −2.71085e6 | + | 4.69533e6i | −0.228718 | + | 0.396152i | ||||
\(229\) | 6.78715e6 | − | 1.17557e7i | 0.565173 | − | 0.978908i | −0.431861 | − | 0.901940i | \(-0.642143\pi\) |
0.997034 | − | 0.0769676i | \(-0.0245238\pi\) | |||||||
\(230\) | −2.96723e6 | + | 5.13940e6i | −0.243876 | + | 0.422405i | ||||
\(231\) | 7.09858e6 | 0.575885 | ||||||||
\(232\) | −520669. | + | 901825.i | −0.0416963 | + | 0.0722202i | ||||
\(233\) | −1.21498e7 | − | 7.01467e6i | −0.960506 | − | 0.554549i | −0.0641776 | − | 0.997938i | \(-0.520442\pi\) |
−0.896329 | + | 0.443390i | \(0.853776\pi\) | |||||||
\(234\) | −331226. | + | 191233.i | −0.0258510 | + | 0.0149251i | ||||
\(235\) | −4.76246e6 | + | 2.74960e6i | −0.366967 | + | 0.211869i | ||||
\(236\) | −6.64985e6 | −0.505913 | ||||||||
\(237\) | 1.13036e7i | 0.849121i | ||||||||
\(238\) | 1.20702e6 | + | 2.09061e6i | 0.0895327 | + | 0.155075i | ||||
\(239\) | −2.19866e6 | − | 3.80820e6i | −0.161052 | − | 0.278950i | 0.774194 | − | 0.632948i | \(-0.218155\pi\) |
−0.935246 | + | 0.353998i | \(0.884822\pi\) | |||||||
\(240\) | 1.03320e7 | − | 1.78956e7i | 0.747396 | − | 1.29453i | ||||
\(241\) | 238135. | + | 137488.i | 0.0170127 | + | 0.00982228i | 0.508482 | − | 0.861072i | \(-0.330207\pi\) |
−0.491470 | + | 0.870895i | \(0.663540\pi\) | |||||||
\(242\) | − | 2.15327e6i | − | 0.151933i | ||||||
\(243\) | −6.40131e6 | − | 3.69580e6i | −0.446118 | − | 0.257566i | ||||
\(244\) | −1.18257e6 | − | 682755.i | −0.0814059 | − | 0.0469997i | ||||
\(245\) | 3.15408e7 | + | 1.82101e7i | 2.14474 | + | 1.23826i | ||||
\(246\) | 1.49874e6 | + | 2.59590e6i | 0.100675 | + | 0.174374i | ||||
\(247\) | 4.94859e6i | 0.328390i | ||||||||
\(248\) | −2.50547e6 | + | 1.44653e6i | −0.164261 | + | 0.0948360i | ||||
\(249\) | −1.44349e7 | − | 8.33399e6i | −0.935008 | − | 0.539827i | ||||
\(250\) | 1.04747e7 | 0.670382 | ||||||||
\(251\) | 4.31496e6 | − | 7.47373e6i | 0.272870 | − | 0.472624i | −0.696726 | − | 0.717338i | \(-0.745361\pi\) |
0.969595 | + | 0.244713i | \(0.0786938\pi\) | |||||||
\(252\) | 5.33881e6 | − | 3.08236e6i | 0.333613 | − | 0.192611i | ||||
\(253\) | −4.75799e6 | − | 8.24109e6i | −0.293807 | − | 0.508889i | ||||
\(254\) | 1.10710e6i | 0.0675592i | ||||||||
\(255\) | 8.69486e6 | + | 1.50599e7i | 0.524375 | + | 0.908244i | ||||
\(256\) | 1.10617e7 | 0.659331 | ||||||||
\(257\) | 1.42453e7i | 0.839213i | 0.907706 | + | 0.419607i | \(0.137832\pi\) | ||||
−0.907706 | + | 0.419607i | \(0.862168\pi\) | |||||||
\(258\) | −2.68535e6 | − | 764409.i | −0.156366 | − | 0.0445109i | ||||
\(259\) | −1.70750e6 | −0.0982793 | ||||||||
\(260\) | − | 1.96203e7i | − | 1.11631i | ||||||
\(261\) | −914464. | + | 527966.i | −0.0514334 | + | 0.0296951i | ||||
\(262\) | 5.06727e6 | 0.281754 | ||||||||
\(263\) | −8.25963e6 | + | 4.76870e6i | −0.454039 | + | 0.262140i | −0.709534 | − | 0.704671i | \(-0.751095\pi\) |
0.255496 | + | 0.966810i | \(0.417761\pi\) | |||||||
\(264\) | −1.31034e6 | − | 2.26958e6i | −0.0712152 | − | 0.123348i | ||||
\(265\) | −5.44895e7 | − | 3.14595e7i | −2.92803 | − | 1.69050i | ||||
\(266\) | 2.97662e6i | 0.158154i | ||||||||
\(267\) | −818514. | + | 1.41771e6i | −0.0430024 | + | 0.0744823i | ||||
\(268\) | 1.42239e7 | + | 2.46365e7i | 0.738949 | + | 1.27990i | ||||
\(269\) | −1.66280e7 | −0.854249 | −0.427125 | − | 0.904193i | \(-0.640473\pi\) | ||||
−0.427125 | + | 0.904193i | \(0.640473\pi\) | |||||||
\(270\) | −6.84498e6 | + | 3.95195e6i | −0.347761 | + | 0.200780i | ||||
\(271\) | −1.07226e7 | + | 1.85721e7i | −0.538756 | + | 0.933152i | 0.460216 | + | 0.887807i | \(0.347772\pi\) |
−0.998971 | + | 0.0453452i | \(0.985561\pi\) | |||||||
\(272\) | −5.63414e6 | + | 9.75861e6i | −0.279976 | + | 0.484933i | ||||
\(273\) | −7.79112e6 | + | 1.34946e7i | −0.382923 | + | 0.663243i | ||||
\(274\) | −930142. | −0.0452166 | ||||||||
\(275\) | −1.30365e7 | + | 2.25799e7i | −0.626850 | + | 1.08574i | ||||
\(276\) | 1.98197e7 | + | 1.14429e7i | 0.942692 | + | 0.544264i | ||||
\(277\) | 3.54557e7 | − | 2.04703e7i | 1.66819 | − | 0.963132i | 0.699582 | − | 0.714552i | \(-0.253370\pi\) |
0.968611 | − | 0.248580i | \(-0.0799638\pi\) | |||||||
\(278\) | 4.80775e6 | − | 2.77576e6i | 0.223773 | − | 0.129195i | ||||
\(279\) | −2.93361e6 | −0.135080 | ||||||||
\(280\) | − | 2.40441e7i | − | 1.09530i | ||||||
\(281\) | 3.19875e6 | + | 5.54040e6i | 0.144166 | + | 0.249702i | 0.929061 | − | 0.369926i | \(-0.120617\pi\) |
−0.784896 | + | 0.619628i | \(0.787284\pi\) | |||||||
\(282\) | −395711. | − | 685391.i | −0.0176454 | − | 0.0305627i | ||||
\(283\) | −1.21713e7 | + | 2.10812e7i | −0.537002 | + | 0.930116i | 0.462061 | + | 0.886848i | \(0.347110\pi\) |
−0.999064 | + | 0.0432674i | \(0.986223\pi\) | |||||||
\(284\) | 2.13766e7 | + | 1.23418e7i | 0.933218 | + | 0.538793i | ||||
\(285\) | 2.14424e7i | 0.926274i | ||||||||
\(286\) | −1.01679e6 | − | 587045.i | −0.0434644 | − | 0.0250942i | ||||
\(287\) | −3.81904e7 | − | 2.20492e7i | −1.61550 | − | 0.932712i | ||||
\(288\) | −2.97455e6 | − | 1.71736e6i | −0.124522 | − | 0.0718925i | ||||
\(289\) | 7.32739e6 | + | 1.26914e7i | 0.303568 | + | 0.525795i | ||||
\(290\) | 2.02149e6i | 0.0828852i | ||||||||
\(291\) | −2.73827e7 | + | 1.58094e7i | −1.11121 | + | 0.641559i | ||||
\(292\) | −2.88575e7 | − | 1.66609e7i | −1.15907 | − | 0.669190i | ||||
\(293\) | 3.27806e7 | 1.30321 | 0.651605 | − | 0.758559i | \(-0.274096\pi\) | ||||
0.651605 | + | 0.758559i | \(0.274096\pi\) | |||||||
\(294\) | −2.62071e6 | + | 4.53921e6i | −0.103128 | + | 0.178623i | ||||
\(295\) | −2.27762e7 | + | 1.31498e7i | −0.887186 | + | 0.512217i | ||||
\(296\) | 315191. | + | 545927.i | 0.0121534 | + | 0.0210504i | ||||
\(297\) | − | 1.26740e7i | − | 0.483776i | ||||||
\(298\) | 4.87127e6 | + | 8.43728e6i | 0.184074 | + | 0.318826i | ||||
\(299\) | 2.08887e7 | 0.781445 | ||||||||
\(300\) | − | 6.27053e7i | − | 2.32242i | ||||||
\(301\) | 3.98363e7 | − | 1.00140e7i | 1.46076 | − | 0.367203i | ||||
\(302\) | 1.52608e6 | 0.0554059 | ||||||||
\(303\) | 1.71744e7i | 0.617382i | ||||||||
\(304\) | −1.20329e7 | + | 6.94719e6i | −0.428301 | + | 0.247280i | ||||
\(305\) | −5.40049e6 | −0.190342 | ||||||||
\(306\) | 782637. | − | 451855.i | 0.0273147 | − | 0.0157701i | ||||
\(307\) | −2.80741e6 | − | 4.86257e6i | −0.0970265 | − | 0.168055i | 0.813426 | − | 0.581668i | \(-0.197600\pi\) |
−0.910453 | + | 0.413613i | \(0.864266\pi\) | |||||||
\(308\) | 1.63890e7 | + | 9.46218e6i | 0.560918 | + | 0.323846i | ||||
\(309\) | − | 2.01222e7i | − | 0.682023i | ||||||
\(310\) | −2.80807e6 | + | 4.86372e6i | −0.0942590 | + | 0.163261i | ||||
\(311\) | −3.05334e6 | − | 5.28853e6i | −0.101506 | − | 0.175814i | 0.810799 | − | 0.585325i | \(-0.199033\pi\) |
−0.912305 | + | 0.409510i | \(0.865700\pi\) | |||||||
\(312\) | 5.75271e6 | 0.189413 | ||||||||
\(313\) | −6.58821e6 | + | 3.80370e6i | −0.214849 | + | 0.124043i | −0.603563 | − | 0.797315i | \(-0.706253\pi\) |
0.388714 | + | 0.921359i | \(0.372920\pi\) | |||||||
\(314\) | −1.10290e6 | + | 1.91028e6i | −0.0356245 | + | 0.0617034i | ||||
\(315\) | 1.21905e7 | − | 2.11146e7i | 0.390023 | − | 0.675540i | ||||
\(316\) | −1.50673e7 | + | 2.60973e7i | −0.477500 | + | 0.827054i | ||||
\(317\) | −5.38096e7 | −1.68920 | −0.844602 | − | 0.535394i | \(-0.820163\pi\) | ||||
−0.844602 | + | 0.535394i | \(0.820163\pi\) | |||||||
\(318\) | 4.52752e6 | − | 7.84189e6i | 0.140792 | − | 0.243859i | ||||
\(319\) | −2.80720e6 | − | 1.62074e6i | −0.0864773 | − | 0.0499277i | ||||
\(320\) | 4.37942e7 | − | 2.52846e7i | 1.33649 | − | 0.771625i | ||||
\(321\) | −3.19272e7 | + | 1.84332e7i | −0.965264 | + | 0.557295i | ||||
\(322\) | 1.25648e7 | 0.376346 | ||||||||
\(323\) | − | 1.16928e7i | − | 0.346984i | ||||||
\(324\) | 1.08910e7 | + | 1.88637e7i | 0.320208 | + | 0.554616i | ||||
\(325\) | −2.86167e7 | − | 4.95656e7i | −0.833623 | − | 1.44388i | ||||
\(326\) | −3.04921e6 | + | 5.28139e6i | −0.0880105 | + | 0.152439i | ||||
\(327\) | 2.46613e7 | + | 1.42382e7i | 0.705297 | + | 0.407203i | ||||
\(328\) | 1.62804e7i | 0.461365i | ||||||||
\(329\) | 1.00833e7 | + | 5.82161e6i | 0.283150 | + | 0.163477i | ||||
\(330\) | −4.40580e6 | − | 2.54369e6i | −0.122598 | − | 0.0707819i | ||||
\(331\) | 3.23977e7 | + | 1.87048e7i | 0.893367 | + | 0.515786i | 0.875042 | − | 0.484046i | \(-0.160833\pi\) |
0.0183247 | + | 0.999832i | \(0.494167\pi\) | |||||||
\(332\) | −2.22179e7 | − | 3.84825e7i | −0.607139 | − | 1.05160i | ||||
\(333\) | 639217.i | 0.0173107i | ||||||||
\(334\) | −1.01373e6 | + | 585276.i | −0.0272071 | + | 0.0157080i | ||||
\(335\) | 9.74356e7 | + | 5.62545e7i | 2.59169 | + | 1.49631i | ||||
\(336\) | −4.37510e7 | −1.15337 | ||||||||
\(337\) | 2.46048e7 | − | 4.26167e7i | 0.642880 | − | 1.11350i | −0.341907 | − | 0.939734i | \(-0.611073\pi\) |
0.984787 | − | 0.173766i | \(-0.0555938\pi\) | |||||||
\(338\) | −4.11090e6 | + | 2.37343e6i | −0.106460 | + | 0.0614647i | ||||
\(339\) | −2.07792e7 | − | 3.59906e7i | −0.533370 | − | 0.923824i | ||||
\(340\) | 4.63598e7i | 1.17952i | ||||||||
\(341\) | −4.50277e6 | − | 7.79903e6i | −0.113558 | − | 0.196688i | ||||
\(342\) | 1.11432e6 | 0.0278569 | ||||||||
\(343\) | − | 1.63298e7i | − | 0.404667i | ||||||
\(344\) | −1.05552e7 | − | 1.08881e7i | −0.259292 | − | 0.267471i | ||||
\(345\) | 9.05117e7 | 2.20418 | ||||||||
\(346\) | − | 4.54220e6i | − | 0.109657i | ||||||
\(347\) | 4.30351e7 | − | 2.48463e7i | 1.02999 | − | 0.594667i | 0.113011 | − | 0.993594i | \(-0.463951\pi\) |
0.916983 | + | 0.398927i | \(0.130617\pi\) | |||||||
\(348\) | 7.79571e6 | 0.184977 | ||||||||
\(349\) | −1.94695e7 | + | 1.12407e7i | −0.458013 | + | 0.264434i | −0.711209 | − | 0.702981i | \(-0.751852\pi\) |
0.253195 | + | 0.967415i | \(0.418518\pi\) | |||||||
\(350\) | −1.72132e7 | − | 2.98142e7i | −0.401475 | − | 0.695375i | ||||
\(351\) | 2.40936e7 | + | 1.39105e7i | 0.557161 | + | 0.321677i | ||||
\(352\) | − | 1.05438e7i | − | 0.241752i | ||||||
\(353\) | 1.73408e7 | − | 3.00352e7i | 0.394226 | − | 0.682820i | −0.598776 | − | 0.800917i | \(-0.704346\pi\) |
0.993002 | + | 0.118097i | \(0.0376792\pi\) | |||||||
\(354\) | −1.89247e6 | − | 3.27785e6i | −0.0426597 | − | 0.0738888i | ||||
\(355\) | 9.76215e7 | 2.18203 | ||||||||
\(356\) | −3.77952e6 | + | 2.18210e6i | −0.0837696 | + | 0.0483644i | ||||
\(357\) | 1.84092e7 | − | 3.18857e7i | 0.404605 | − | 0.700796i | ||||
\(358\) | 2.57335e6 | − | 4.45717e6i | 0.0560853 | − | 0.0971426i | ||||
\(359\) | 1.07648e6 | − | 1.86451e6i | 0.0232660 | − | 0.0402979i | −0.854158 | − | 0.520014i | \(-0.825927\pi\) |
0.877424 | + | 0.479716i | \(0.159260\pi\) | |||||||
\(360\) | −9.00108e6 | −0.192924 | ||||||||
\(361\) | −1.63140e7 | + | 2.82568e7i | −0.346769 | + | 0.600621i | ||||
\(362\) | −9.91816e6 | − | 5.72625e6i | −0.209077 | − | 0.120710i | ||||
\(363\) | −2.84415e7 | + | 1.64207e7i | −0.594611 | + | 0.343299i | ||||
\(364\) | −3.59757e7 | + | 2.07706e7i | −0.745943 | + | 0.430670i | ||||
\(365\) | −1.31785e8 | −2.71012 | ||||||||
\(366\) | − | 777214.i | − | 0.0158525i | ||||||
\(367\) | −3.80402e7 | − | 6.58876e7i | −0.769564 | − | 1.33292i | −0.937800 | − | 0.347177i | \(-0.887140\pi\) |
0.168236 | − | 0.985747i | \(-0.446193\pi\) | |||||||
\(368\) | 2.93251e7 | + | 5.07926e7i | 0.588432 | + | 1.01919i | ||||
\(369\) | −8.25429e6 | + | 1.42969e7i | −0.164286 | + | 0.284552i | ||||
\(370\) | 1.05978e6 | + | 611862.i | 0.0209223 | + | 0.0120795i | ||||
\(371\) | 1.33216e8i | 2.60876i | ||||||||
\(372\) | 1.87566e7 | + | 1.08291e7i | 0.364355 | + | 0.210360i | ||||
\(373\) | −4.95129e6 | − | 2.85863e6i | −0.0954095 | − | 0.0550847i | 0.451536 | − | 0.892253i | \(-0.350876\pi\) |
−0.546946 | + | 0.837168i | \(0.684210\pi\) | |||||||
\(374\) | 2.40252e6 | + | 1.38710e6i | 0.0459254 | + | 0.0265150i | ||||
\(375\) | −7.98795e7 | − | 1.38355e8i | −1.51475 | − | 2.62363i | ||||
\(376\) | − | 4.29849e6i | − | 0.0808635i | ||||||
\(377\) | 6.16215e6 | − | 3.55772e6i | 0.115003 | − | 0.0663968i | ||||
\(378\) | 1.44926e7 | + | 8.36729e6i | 0.268330 | + | 0.154921i | ||||
\(379\) | −3.82632e7 | −0.702851 | −0.351426 | − | 0.936216i | \(-0.614303\pi\) | ||||
−0.351426 | + | 0.936216i | \(0.614303\pi\) | |||||||
\(380\) | −2.85821e7 | + | 4.95056e7i | −0.520886 | + | 0.902201i | ||||
\(381\) | 1.46231e7 | − | 8.44265e6i | 0.264402 | − | 0.152652i | ||||
\(382\) | −5.52122e6 | − | 9.56303e6i | −0.0990478 | − | 0.171556i | ||||
\(383\) | 1.75291e7i | 0.312007i | 0.987756 | + | 0.156004i | \(0.0498611\pi\) | ||||
−0.987756 | + | 0.156004i | \(0.950139\pi\) | |||||||
\(384\) | 1.67909e7 | + | 2.90827e7i | 0.296538 | + | 0.513619i | ||||
\(385\) | 7.48444e7 | 1.31153 | ||||||||
\(386\) | 1.25410e7i | 0.218057i | ||||||||
\(387\) | −3.74880e6 | − | 1.49130e7i | −0.0646784 | − | 0.257296i | ||||
\(388\) | −8.42937e7 | −1.44311 | ||||||||
\(389\) | 7.18597e7i | 1.22078i | 0.792102 | + | 0.610389i | \(0.208987\pi\) | ||||
−0.792102 | + | 0.610389i | \(0.791013\pi\) | |||||||
\(390\) | 9.67125e6 | − | 5.58370e6i | 0.163038 | − | 0.0941300i | ||||
\(391\) | −4.93569e7 | −0.825691 | ||||||||
\(392\) | −2.46541e7 | + | 1.42340e7i | −0.409289 | + | 0.236303i | ||||
\(393\) | −3.86427e7 | − | 6.69311e7i | −0.636634 | − | 1.10268i | ||||
\(394\) | 3.60061e6 | + | 2.07881e6i | 0.0588692 | + | 0.0339881i | ||||
\(395\) | 1.19180e8i | 1.93380i | ||||||||
\(396\) | 3.54224e6 | − | 6.13534e6i | 0.0570417 | − | 0.0987991i | ||||
\(397\) | 2.45314e7 | + | 4.24897e7i | 0.392059 | + | 0.679066i | 0.992721 | − | 0.120437i | \(-0.0384296\pi\) |
−0.600662 | + | 0.799503i | \(0.705096\pi\) | |||||||
\(398\) | 4.31119e6 | 0.0683830 | ||||||||
\(399\) | 3.93168e7 | − | 2.26995e7i | 0.618955 | − | 0.357354i | ||||
\(400\) | 8.03485e7 | − | 1.39168e8i | 1.25544 | − | 2.17449i | ||||
\(401\) | 2.27838e7 | − | 3.94627e7i | 0.353340 | − | 0.612003i | −0.633492 | − | 0.773749i | \(-0.718379\pi\) |
0.986832 | + | 0.161746i | \(0.0517124\pi\) | |||||||
\(402\) | −8.09590e6 | + | 1.40225e7i | −0.124620 | + | 0.215848i | ||||
\(403\) | 1.97682e7 | 0.302032 | ||||||||
\(404\) | −2.28929e7 | + | 3.96517e7i | −0.347182 | + | 0.601337i | ||||
\(405\) | 7.46046e7 | + | 4.30730e7i | 1.12305 | + | 0.648396i | ||||
\(406\) | 3.70659e6 | − | 2.14000e6i | 0.0553856 | − | 0.0319769i | ||||
\(407\) | −1.69936e6 | + | 981128.i | −0.0252060 | + | 0.0145527i | ||||
\(408\) | −1.35928e7 | −0.200137 | ||||||||
\(409\) | 2.65415e7i | 0.387932i | 0.981008 | + | 0.193966i | \(0.0621352\pi\) | ||||
−0.981008 | + | 0.193966i | \(0.937865\pi\) | |||||||
\(410\) | 1.58021e7 | + | 2.73701e7i | 0.229279 | + | 0.397122i | ||||
\(411\) | 7.09320e6 | + | 1.22858e7i | 0.102169 | + | 0.176961i | ||||
\(412\) | 2.68222e7 | − | 4.64574e7i | 0.383533 | − | 0.664298i | ||||
\(413\) | 4.82230e7 | + | 2.78415e7i | 0.684548 | + | 0.395224i | ||||
\(414\) | − | 4.70372e6i | − | 0.0662889i | ||||||
\(415\) | −1.52195e8 | − | 8.78700e7i | −2.12940 | − | 1.22941i | ||||
\(416\) | 2.00441e7 | + | 1.15725e7i | 0.278425 | + | 0.160748i | ||||
\(417\) | −7.33272e7 | − | 4.23355e7i | −1.01125 | − | 0.583843i | ||||
\(418\) | 1.71036e6 | + | 2.96244e6i | 0.0234185 | + | 0.0405621i | ||||
\(419\) | − | 4.15078e7i | − | 0.564270i | −0.959375 | − | 0.282135i | \(-0.908957\pi\) | ||
0.959375 | − | 0.282135i | \(-0.0910427\pi\) | |||||||
\(420\) | −1.55884e8 | + | 8.99999e7i | −2.10404 | + | 1.21477i | ||||
\(421\) | −1.80073e6 | − | 1.03965e6i | −0.0241325 | − | 0.0139329i | 0.487885 | − | 0.872908i | \(-0.337768\pi\) |
−0.512018 | + | 0.858975i | \(0.671102\pi\) | |||||||
\(422\) | −2.27914e7 | −0.303274 | ||||||||
\(423\) | 2.17937e6 | − | 3.77477e6i | 0.0287945 | − | 0.0498735i | ||||
\(424\) | 4.25921e7 | − | 2.45906e7i | 0.558768 | − | 0.322605i | ||||
\(425\) | 6.76170e7 | + | 1.17116e8i | 0.880824 | + | 1.52563i | ||||
\(426\) | 1.40493e7i | 0.181729i | ||||||||
\(427\) | 5.71711e6 | + | 9.90232e6i | 0.0734332 | + | 0.127190i | ||||
\(428\) | −9.82833e7 | −1.25357 | ||||||||
\(429\) | 1.79071e7i | 0.226805i | ||||||||
\(430\) | −2.83131e7 | − | 8.05960e6i | −0.356109 | − | 0.101370i | ||||
\(431\) | 8.20353e6 | 0.102463 | 0.0512317 | − | 0.998687i | \(-0.483685\pi\) | ||||
0.0512317 | + | 0.998687i | \(0.483685\pi\) | |||||||
\(432\) | 7.81141e7i | 0.968899i | ||||||||
\(433\) | 8.98566e7 | − | 5.18787e7i | 1.10684 | − | 0.639037i | 0.168834 | − | 0.985645i | \(-0.446000\pi\) |
0.938010 | + | 0.346608i | \(0.112667\pi\) | |||||||
\(434\) | 1.18908e7 | 0.145459 | ||||||||
\(435\) | 2.67008e7 | − | 1.54157e7i | 0.324382 | − | 0.187282i | ||||
\(436\) | 3.79581e7 | + | 6.57453e7i | 0.457978 | + | 0.793241i | ||||
\(437\) | −5.27060e7 | − | 3.04298e7i | −0.631562 | − | 0.364632i | ||||
\(438\) | − | 1.89659e7i | − | 0.225711i | ||||||
\(439\) | −1.94516e7 | + | 3.36911e7i | −0.229912 | + | 0.398219i | −0.957782 | − | 0.287496i | \(-0.907177\pi\) |
0.727870 | + | 0.685715i | \(0.240510\pi\) | |||||||
\(440\) | −1.38157e7 | − | 2.39295e7i | −0.162186 | − | 0.280915i | ||||
\(441\) | −2.88670e7 | −0.336578 | ||||||||
\(442\) | −5.27383e6 | + | 3.04484e6i | −0.0610744 | + | 0.0352613i | ||||
\(443\) | 2.44303e7 | − | 4.23145e7i | 0.281007 | − | 0.486719i | −0.690626 | − | 0.723212i | \(-0.742665\pi\) |
0.971633 | + | 0.236493i | \(0.0759982\pi\) | |||||||
\(444\) | 2.35960e6 | − | 4.08695e6i | 0.0269581 | − | 0.0466928i | ||||
\(445\) | −8.63006e6 | + | 1.49477e7i | −0.0979341 | + | 0.169627i | ||||
\(446\) | 3.02474e7 | 0.340944 | ||||||||
\(447\) | 7.42960e7 | − | 1.28684e8i | 0.831845 | − | 1.44080i | ||||
\(448\) | −9.27236e7 | − | 5.35340e7i | −1.03123 | − | 0.595382i | ||||
\(449\) | 1.01162e8 | − | 5.84061e7i | 1.11758 | − | 0.645237i | 0.176800 | − | 0.984247i | \(-0.443425\pi\) |
0.940783 | + | 0.339010i | \(0.110092\pi\) | |||||||
\(450\) | −1.11612e7 | + | 6.44391e6i | −0.122482 | + | 0.0707151i | ||||
\(451\) | −5.06778e7 | −0.552443 | ||||||||
\(452\) | − | 1.10792e8i | − | 1.19975i | ||||||
\(453\) | −1.16378e7 | − | 2.01572e7i | −0.125192 | − | 0.216838i | ||||
\(454\) | 9.32081e6 | + | 1.61441e7i | 0.0996062 | + | 0.172523i | ||||
\(455\) | −8.21462e7 | + | 1.42281e8i | −0.872074 | + | 1.51048i | ||||
\(456\) | −1.45151e7 | − | 8.38031e6i | −0.153083 | − | 0.0883823i | ||||
\(457\) | − | 3.53543e7i | − | 0.370419i | −0.982699 | − | 0.185210i | \(-0.940704\pi\) | ||
0.982699 | − | 0.185210i | \(-0.0592964\pi\) | |||||||
\(458\) | 1.78379e7 | + | 1.02987e7i | 0.185672 | + | 0.107198i | ||||
\(459\) | −5.69296e7 | − | 3.28683e7i | −0.588708 | − | 0.339891i | ||||
\(460\) | 2.08970e8 | + | 1.20649e8i | 2.14690 | + | 1.23951i | ||||
\(461\) | 4.16039e7 | + | 7.20600e7i | 0.424650 | + | 0.735515i | 0.996388 | − | 0.0849213i | \(-0.0270639\pi\) |
−0.571738 | + | 0.820436i | \(0.693731\pi\) | |||||||
\(462\) | 1.07713e7i | 0.109230i | ||||||||
\(463\) | 2.26846e7 | − | 1.30969e7i | 0.228553 | − | 0.131955i | −0.381351 | − | 0.924430i | \(-0.624541\pi\) |
0.609905 | + | 0.792475i | \(0.291208\pi\) | |||||||
\(464\) | 1.73017e7 | + | 9.98917e6i | 0.173195 | + | 0.0999943i | ||||
\(465\) | 8.56566e7 | 0.851926 | ||||||||
\(466\) | 1.06440e7 | − | 1.84359e7i | 0.105183 | − | 0.182182i | ||||
\(467\) | 5.25464e7 | − | 3.03377e7i | 0.515932 | − | 0.297873i | −0.219337 | − | 0.975649i | \(-0.570389\pi\) |
0.735268 | + | 0.677776i | \(0.237056\pi\) | |||||||
\(468\) | 7.77564e6 | + | 1.34678e7i | 0.0758575 | + | 0.131389i | ||||
\(469\) | − | 2.38210e8i | − | 2.30909i | ||||||
\(470\) | −4.17221e6 | − | 7.22647e6i | −0.0401858 | − | 0.0696038i | ||||
\(471\) | 3.36427e7 | 0.321979 | ||||||||
\(472\) | − | 2.05573e7i | − | 0.195497i | ||||||
\(473\) | 3.38924e7 | − | 3.28561e7i | 0.320272 | − | 0.310479i | ||||
\(474\) | −1.71518e7 | −0.161055 | ||||||||
\(475\) | 1.66750e8i | 1.55592i | ||||||||
\(476\) | 8.50052e7 | − | 4.90778e7i | 0.788179 | − | 0.455055i | ||||
\(477\) | 4.98704e7 | 0.459502 | ||||||||
\(478\) | 5.77850e6 | − | 3.33622e6i | 0.0529092 | − | 0.0305472i | ||||
\(479\) | 8.69837e6 | + | 1.50660e7i | 0.0791464 | + | 0.137086i | 0.902882 | − | 0.429889i | \(-0.141447\pi\) |
−0.823735 | + | 0.566974i | \(0.808114\pi\) | |||||||
\(480\) | 8.68521e7 | + | 5.01441e7i | 0.785338 | + | 0.453415i | ||||
\(481\) | − | 4.30739e6i | − | 0.0387060i | ||||||
\(482\) | −208621. | + | 361343.i | −0.00186302 | + | 0.00322685i | ||||
\(483\) | −9.58182e7 | − | 1.65962e8i | −0.850367 | − | 1.47288i | ||||
\(484\) | −8.75532e7 | −0.772211 | ||||||||
\(485\) | −2.88711e8 | + | 1.66688e8i | −2.53069 | + | 1.46109i | ||||
\(486\) | 5.60794e6 | − | 9.71324e6i | 0.0488534 | − | 0.0846166i | ||||
\(487\) | −4.18992e7 | + | 7.25716e7i | −0.362760 | + | 0.628318i | −0.988414 | − | 0.151782i | \(-0.951499\pi\) |
0.625654 | + | 0.780100i | \(0.284832\pi\) | |||||||
\(488\) | 2.11066e6 | − | 3.65578e6i | 0.0181618 | − | 0.0314572i | ||||
\(489\) | 9.30123e7 | 0.795452 | ||||||||
\(490\) | −2.76317e7 | + | 4.78595e7i | −0.234865 | + | 0.406799i | ||||
\(491\) | 1.35911e8 | + | 7.84681e7i | 1.14818 | + | 0.662901i | 0.948443 | − | 0.316949i | \(-0.102658\pi\) |
0.199736 | + | 0.979850i | \(0.435992\pi\) | |||||||
\(492\) | 1.05551e8 | − | 6.09397e7i | 0.886269 | − | 0.511687i | ||||
\(493\) | −1.45602e7 | + | 8.40635e6i | −0.121514 | + | 0.0701563i | ||||
\(494\) | −7.50890e6 | −0.0622868 | ||||||||
\(495\) | − | 2.80186e7i | − | 0.231010i | ||||||
\(496\) | 2.77521e7 | + | 4.80680e7i | 0.227432 | + | 0.393923i | ||||
\(497\) | −1.03345e8 | − | 1.78999e8i | −0.841821 | − | 1.45808i | ||||
\(498\) | 1.26459e7 | − | 2.19033e7i | 0.102391 | − | 0.177346i | ||||
\(499\) | 1.19266e7 | + | 6.88584e6i | 0.0959878 | + | 0.0554186i | 0.547226 | − | 0.836985i | \(-0.315684\pi\) |
−0.451238 | + | 0.892404i | \(0.649017\pi\) | |||||||
\(500\) | − | 4.25907e8i | − | 3.40726i | ||||||
\(501\) | 1.54612e7 | + | 8.92655e6i | 0.122951 | + | 0.0709857i | ||||
\(502\) | 1.13405e7 | + | 6.54745e6i | 0.0896441 | + | 0.0517560i | ||||
\(503\) | −1.16420e8 | − | 6.72153e7i | −0.914797 | − | 0.528159i | −0.0328259 | − | 0.999461i | \(-0.510451\pi\) |
−0.881972 | + | 0.471303i | \(0.843784\pi\) | |||||||
\(504\) | 9.52879e6 | + | 1.65044e7i | 0.0744297 | + | 0.128916i | ||||
\(505\) | 1.81080e8i | 1.40603i | ||||||||
\(506\) | 1.25049e7 | − | 7.21970e6i | 0.0965225 | − | 0.0557273i | ||||
\(507\) | 6.26989e7 | + | 3.61992e7i | 0.481101 | + | 0.277764i | ||||
\(508\) | 4.50151e7 | 0.343374 | ||||||||
\(509\) | 9.38542e7 | − | 1.62560e8i | 0.711706 | − | 1.23271i | −0.252511 | − | 0.967594i | \(-0.581256\pi\) |
0.964216 | − | 0.265116i | \(-0.0854103\pi\) | |||||||
\(510\) | −2.28517e7 | + | 1.31934e7i | −0.172269 | + | 0.0994598i | ||||
\(511\) | 1.39511e8 | + | 2.41641e8i | 1.04556 | + | 1.81095i | ||||
\(512\) | 1.09653e8i | 0.816977i | ||||||||
\(513\) | −4.05284e7 | − | 7.01972e7i | −0.300197 | − | 0.519957i | ||||
\(514\) | −2.16156e7 | −0.159176 | ||||||||
\(515\) | − | 2.12159e8i | − | 1.55325i | ||||||
\(516\) | −3.10812e7 | + | 1.09187e8i | −0.226229 | + | 0.794737i | ||||
\(517\) | 1.33804e7 | 0.0968270 | ||||||||
\(518\) | − | 2.59094e6i | − | 0.0186409i | ||||||
\(519\) | −5.99957e7 | + | 3.46385e7i | −0.429159 | + | 0.247775i | ||||
\(520\) | 6.06541e7 | 0.431370 | ||||||||
\(521\) | −4.96331e6 | + | 2.86557e6i | −0.0350961 | + | 0.0202627i | −0.517445 | − | 0.855716i | \(-0.673117\pi\) |
0.482349 | + | 0.875979i | \(0.339784\pi\) | |||||||
\(522\) | −801127. | − | 1.38759e6i | −0.00563235 | − | 0.00975552i | ||||
\(523\) | −1.02249e8 | − | 5.90336e7i | −0.714751 | − | 0.412661i | 0.0980669 | − | 0.995180i | \(-0.468734\pi\) |
−0.812818 | + | 0.582518i | \(0.802067\pi\) | |||||||
\(524\) | − | 2.06038e8i | − | 1.43203i | ||||||
\(525\) | −2.62534e8 | + | 4.54722e8i | −1.81429 | + | 3.14245i | ||||
\(526\) | −7.23594e6 | − | 1.25330e7i | −0.0497208 | − | 0.0861189i | ||||
\(527\) | −4.67094e7 | −0.319133 | ||||||||
\(528\) | −4.35424e7 | + | 2.51392e7i | −0.295809 | + | 0.170785i | ||||
\(529\) | −5.44309e7 | + | 9.42771e7i | −0.367687 | + | 0.636853i | ||||
\(530\) | 4.77362e7 | − | 8.26815e7i | 0.320642 | − | 0.555368i | ||||
\(531\) | 1.04227e7 | − | 1.80526e7i | 0.0696140 | − | 0.120575i | ||||
\(532\) | 1.21031e8 | 0.803825 | ||||||||
\(533\) | 5.56219e7 | − | 9.63399e7i | 0.367336 | − | 0.636245i | ||||
\(534\) | −2.15121e6 | − | 1.24200e6i | −0.0141273 | − | 0.00815639i | ||||
\(535\) | −3.36627e8 | + | 1.94352e8i | −2.19830 | + | 1.26919i | ||||
\(536\) | −7.61612e7 | + | 4.39717e7i | −0.494583 | + | 0.285548i | ||||
\(537\) | −7.84967e7 | −0.506907 | ||||||||
\(538\) | − | 2.52311e7i | − | 0.162028i | ||||||
\(539\) | −4.43077e7 | − | 7.67432e7i | −0.282952 | − | 0.490088i | ||||
\(540\) | 1.60688e8 | + | 2.78320e8i | 1.02048 | + | 1.76752i | ||||
\(541\) | −1.06737e7 | + | 1.84874e7i | −0.0674098 | + | 0.116757i | −0.897760 | − | 0.440484i | \(-0.854807\pi\) |
0.830351 | + | 0.557241i | \(0.188140\pi\) | |||||||
\(542\) | −2.81810e7 | − | 1.62703e7i | −0.176994 | − | 0.102187i | ||||
\(543\) | 1.74672e8i | 1.09100i | ||||||||
\(544\) | −4.73613e7 | − | 2.73441e7i | −0.294189 | − | 0.169850i | ||||
\(545\) | 2.60018e8 | + | 1.50121e8i | 1.60625 | + | 0.927369i | ||||
\(546\) | −2.04765e7 | − | 1.18221e7i | −0.125799 | − | 0.0726302i | ||||
\(547\) | 8.26145e7 | + | 1.43093e8i | 0.504771 | + | 0.874289i | 0.999985 | + | 0.00551779i | \(0.00175638\pi\) |
−0.495214 | + | 0.868771i | \(0.664910\pi\) | |||||||
\(548\) | 3.78200e7i | 0.229816i | ||||||||
\(549\) | 3.70701e6 | − | 2.14024e6i | 0.0224030 | − | 0.0129344i | ||||
\(550\) | −3.42624e7 | − | 1.97814e7i | −0.205935 | − | 0.118897i | ||||
\(551\) | −2.07309e7 | −0.123926 | ||||||||
\(552\) | −3.53745e7 | + | 6.12705e7i | −0.210317 | + | 0.364279i | ||||
\(553\) | 2.18528e8 | − | 1.26167e8i | 1.29220 | − | 0.746054i | ||||
\(554\) | 3.10614e7 | + | 5.37999e7i | 0.182680 | + | 0.316411i | ||||
\(555\) | − | 1.86641e7i | − | 0.109176i | ||||||
\(556\) | −1.12864e8 | − | 1.95485e8i | −0.656643 | − | 1.13734i | ||||
\(557\) | −2.88414e8 | −1.66898 | −0.834490 | − | 0.551024i | \(-0.814237\pi\) | ||||
−0.834490 | + | 0.551024i | \(0.814237\pi\) | |||||||
\(558\) | − | 4.45141e6i | − | 0.0256209i | ||||||
\(559\) | 2.52614e7 | + | 1.00492e8i | 0.144618 | + | 0.575302i | ||||
\(560\) | −4.61291e8 | −2.62670 | ||||||||
\(561\) | − | 4.23117e7i | − | 0.239647i | ||||||
\(562\) | −8.40691e6 | + | 4.85373e6i | −0.0473617 | + | 0.0273443i | ||||
\(563\) | 4.68637e7 | 0.262610 | 0.131305 | − | 0.991342i | \(-0.458083\pi\) | ||||
0.131305 | + | 0.991342i | \(0.458083\pi\) | |||||||
\(564\) | −2.78683e7 | + | 1.60898e7i | −0.155337 | + | 0.0896836i | ||||
\(565\) | −2.19087e8 | − | 3.79469e8i | −1.21470 | − | 2.10393i | ||||
\(566\) | −3.19883e7 | − | 1.84685e7i | −0.176418 | − | 0.101855i | ||||
\(567\) | − | 1.82393e8i | − | 1.00060i | ||||||
\(568\) | −3.81533e7 | + | 6.60834e7i | −0.208203 | + | 0.360618i | ||||
\(569\) | −2.29989e7 | − | 3.98352e7i | −0.124845 | − | 0.216237i | 0.796828 | − | 0.604207i | \(-0.206510\pi\) |
−0.921672 | + | 0.387969i | \(0.873177\pi\) | |||||||
\(570\) | −3.25364e7 | −0.175689 | ||||||||
\(571\) | 8.22436e7 | − | 4.74834e7i | 0.441768 | − | 0.255055i | −0.262580 | − | 0.964910i | \(-0.584573\pi\) |
0.704347 | + | 0.709856i | \(0.251240\pi\) | |||||||
\(572\) | −2.38695e7 | + | 4.13432e7i | −0.127543 | + | 0.220910i | ||||
\(573\) | −8.42089e7 | + | 1.45854e8i | −0.447604 | + | 0.775273i | ||||
\(574\) | 3.34571e7 | − | 5.79494e7i | 0.176910 | − | 0.306417i | ||||
\(575\) | 7.03879e8 | 3.70249 | ||||||||
\(576\) | −2.00409e7 | + | 3.47118e7i | −0.104869 | + | 0.181639i | ||||
\(577\) | 1.02567e8 | + | 5.92171e7i | 0.533925 | + | 0.308262i | 0.742613 | − | 0.669721i | \(-0.233586\pi\) |
−0.208688 | + | 0.977982i | \(0.566919\pi\) | |||||||
\(578\) | −1.92578e7 | + | 1.11185e7i | −0.0997292 | + | 0.0575787i | ||||
\(579\) | 1.65648e8 | − | 9.56370e7i | 0.853396 | − | 0.492709i | ||||
\(580\) | 8.21947e7 | 0.421269 | ||||||||
\(581\) | 3.72086e8i | 1.89721i | ||||||||
\(582\) | −2.39889e7 | − | 4.15501e7i | −0.121686 | − | 0.210767i | ||||
\(583\) | 7.65456e7 | + | 1.32581e8i | 0.386291 | + | 0.669075i | ||||
\(584\) | 5.15054e7 | − | 8.92099e7i | 0.258591 | − | 0.447893i | ||||
\(585\) | 5.32641e7 | + | 3.07521e7i | 0.266052 | + | 0.153605i | ||||
\(586\) | 4.97408e7i | 0.247184i | ||||||||
\(587\) | −2.79439e8 | − | 1.61334e8i | −1.38157 | − | 0.797649i | −0.389224 | − | 0.921143i | \(-0.627257\pi\) |
−0.992345 | + | 0.123494i | \(0.960590\pi\) | |||||||
\(588\) | 1.84566e8 | + | 1.06559e8i | 0.907864 | + | 0.524155i | ||||
\(589\) | −4.98788e7 | − | 2.87975e7i | −0.244101 | − | 0.140932i | ||||
\(590\) | −1.99533e7 | − | 3.45602e7i | −0.0971538 | − | 0.168275i | ||||
\(591\) | − | 6.34116e7i | − | 0.307190i | ||||||
\(592\) | 1.04738e7 | − | 6.04702e6i | 0.0504821 | − | 0.0291458i | ||||
\(593\) | 2.26537e7 | + | 1.30791e7i | 0.108636 | + | 0.0627213i | 0.553334 | − | 0.832960i | \(-0.313355\pi\) |
−0.444697 | + | 0.895681i | \(0.646689\pi\) | |||||||
\(594\) | 1.92313e7 | 0.0917592 | ||||||||
\(595\) | 1.94099e8 | − | 3.36189e8i | 0.921452 | − | 1.59600i | ||||
\(596\) | 3.43064e8 | − | 1.98068e8i | 1.62045 | − | 0.935569i | ||||
\(597\) | −3.28769e7 | − | 5.69444e7i | −0.154514 | − | 0.267626i | ||||
\(598\) | 3.16962e7i | 0.148219i | ||||||||
\(599\) | −4.77747e7 | − | 8.27482e7i | −0.222289 | − | 0.385015i | 0.733214 | − | 0.679998i | \(-0.238019\pi\) |
−0.955503 | + | 0.294983i | \(0.904686\pi\) | |||||||
\(600\) | 1.93847e8 | 0.897439 | ||||||||
\(601\) | 3.95284e8i | 1.82090i | 0.413620 | + | 0.910450i | \(0.364264\pi\) | ||||
−0.413620 | + | 0.910450i | \(0.635736\pi\) | |||||||
\(602\) | 1.51950e7 | + | 6.04470e7i | 0.0696485 | + | 0.277067i | ||||
\(603\) | −8.91758e7 | −0.406720 | ||||||||
\(604\) | − | 6.20511e7i | − | 0.281604i | ||||||
\(605\) | −2.99875e8 | + | 1.73133e8i | −1.35417 | + | 0.781833i | ||||
\(606\) | −2.60602e7 | −0.117101 | ||||||||
\(607\) | −2.42388e7 | + | 1.39943e7i | −0.108379 | + | 0.0625727i | −0.553210 | − | 0.833042i | \(-0.686597\pi\) |
0.444831 | + | 0.895615i | \(0.353264\pi\) | |||||||
\(608\) | −3.37166e7 | − | 5.83989e7i | −0.150015 | − | 0.259833i | ||||
\(609\) | −5.65325e7 | − | 3.26390e7i | −0.250292 | − | 0.144506i | ||||
\(610\) | − | 8.19461e6i | − | 0.0361026i | ||||||
\(611\) | −1.46857e7 | + | 2.54365e7i | −0.0643832 | + | 0.111515i | ||||
\(612\) | −1.83727e7 | − | 3.18224e7i | −0.0801526 | − | 0.138828i | ||||
\(613\) | −1.02923e8 | −0.446819 | −0.223409 | − | 0.974725i | \(-0.571719\pi\) | ||||
−0.223409 | + | 0.974725i | \(0.571719\pi\) | |||||||
\(614\) | 7.37839e6 | − | 4.25991e6i | 0.0318755 | − | 0.0184033i | ||||
\(615\) | 2.41012e8 | − | 4.17445e8i | 1.03613 | − | 1.79462i | ||||
\(616\) | −2.92513e7 | + | 5.06648e7i | −0.125142 | + | 0.216752i | ||||
\(617\) | −1.38052e8 | + | 2.39114e8i | −0.587744 | + | 1.01800i | 0.406783 | + | 0.913525i | \(0.366651\pi\) |
−0.994527 | + | 0.104478i | \(0.966683\pi\) | |||||||
\(618\) | 3.05330e7 | 0.129361 | ||||||||
\(619\) | 5.78576e6 | − | 1.00212e7i | 0.0243943 | − | 0.0422522i | −0.853571 | − | 0.520977i | \(-0.825568\pi\) |
0.877965 | + | 0.478725i | \(0.158901\pi\) | |||||||
\(620\) | 1.97761e8 | + | 1.14177e8i | 0.829786 | + | 0.479077i | ||||
\(621\) | −2.96313e8 | + | 1.71076e8i | −1.23730 | + | 0.714357i | ||||
\(622\) | 8.02473e6 | − | 4.63308e6i | 0.0333472 | − | 0.0192530i | ||||
\(623\) | 3.65441e7 | 0.151131 | ||||||||
\(624\) | − | 1.10367e8i | − | 0.454241i | ||||||
\(625\) | −4.99126e8 | − | 8.64511e8i | −2.04442 | − | 3.54104i | ||||
\(626\) | −5.77168e6 | − | 9.99684e6i | −0.0235277 | − | 0.0407511i | ||||
\(627\) | 2.60862e7 | − | 4.51827e7i | 0.105830 | − | 0.183303i | ||||
\(628\) | 7.76731e7 | + | 4.48446e7i | 0.313611 | + | 0.181064i | ||||
\(629\) | 1.01777e7i | 0.0408976i | ||||||||
\(630\) | 3.20389e7 | + | 1.84977e7i | 0.128132 | + | 0.0739768i | ||||
\(631\) | 5.28793e7 | + | 3.05299e7i | 0.210474 | + | 0.121517i | 0.601531 | − | 0.798849i | \(-0.294557\pi\) |
−0.391058 | + | 0.920366i | \(0.627891\pi\) | |||||||
\(632\) | −8.06769e7 | − | 4.65788e7i | −0.319594 | − | 0.184517i | ||||
\(633\) | 1.73806e8 | + | 3.01041e8i | 0.685258 | + | 1.18690i | ||||
\(634\) | − | 8.16499e7i | − | 0.320397i | ||||||
\(635\) | 1.54180e8 | − | 8.90157e7i | 0.602152 | − | 0.347652i | ||||
\(636\) | −3.18855e8 | − | 1.84091e8i | −1.23943 | − | 0.715585i | ||||
\(637\) | 1.94521e8 | 0.752574 | ||||||||
\(638\) | 2.45928e6 | − | 4.25961e6i | 0.00946993 | − | 0.0164024i | ||||
\(639\) | −6.70095e7 | + | 3.86879e7i | −0.256823 | + | 0.148277i | ||||
\(640\) | 1.77036e8 | + | 3.06635e8i | 0.675339 | + | 1.16972i | ||||
\(641\) | 5.70618e7i | 0.216656i | 0.994115 | + | 0.108328i | \(0.0345497\pi\) | ||||
−0.994115 | + | 0.108328i | \(0.965450\pi\) | |||||||
\(642\) | −2.79702e7 | − | 4.84458e7i | −0.105704 | − | 0.183084i | ||||
\(643\) | 8.38216e7 | 0.315299 | 0.157650 | − | 0.987495i | \(-0.449608\pi\) | ||||
0.157650 | + | 0.987495i | \(0.449608\pi\) | |||||||
\(644\) | − | 5.10890e8i | − | 1.91280i | ||||||
\(645\) | 1.09459e8 | + | 4.35436e8i | 0.407917 | + | 1.62273i | ||||
\(646\) | 1.77424e7 | 0.0658135 | ||||||||
\(647\) | 3.93110e8i | 1.45145i | 0.687986 | + | 0.725724i | \(0.258495\pi\) | ||||
−0.687986 | + | 0.725724i | \(0.741505\pi\) | |||||||
\(648\) | −5.83152e7 | + | 3.36683e7i | −0.214317 | + | 0.123736i | ||||
\(649\) | 6.39908e7 | 0.234090 | ||||||||
\(650\) | 7.52100e7 | − | 4.34225e7i | 0.273864 | − | 0.158116i | ||||
\(651\) | −9.06784e7 | − | 1.57060e8i | −0.328671 | − | 0.569274i | ||||
\(652\) | 2.14744e8 | + | 1.23982e8i | 0.774779 | + | 0.447319i | ||||
\(653\) | 8.10400e7i | 0.291045i | 0.989355 | + | 0.145522i | \(0.0464863\pi\) | ||||
−0.989355 | + | 0.145522i | \(0.953514\pi\) | |||||||
\(654\) | −2.16048e7 | + | 3.74206e7i | −0.0772355 | + | 0.133776i | ||||
\(655\) | −4.07432e8 | − | 7.05693e8i | −1.44988 | − | 2.51126i | ||||
\(656\) | 3.12344e8 | 1.10642 | ||||||||
\(657\) | 9.04601e7 | − | 5.22272e7i | 0.318978 | − | 0.184162i | ||||
\(658\) | −8.83362e6 | + | 1.53003e7i | −0.0310071 | + | 0.0537059i | ||||
\(659\) | −1.23915e8 | + | 2.14628e8i | −0.432981 | + | 0.749946i | −0.997128 | − | 0.0757287i | \(-0.975872\pi\) |
0.564147 | + | 0.825674i | \(0.309205\pi\) | |||||||
\(660\) | −1.03428e8 | + | 1.79142e8i | −0.359753 | + | 0.623111i | ||||
\(661\) | −4.96868e7 | −0.172043 | −0.0860214 | − | 0.996293i | \(-0.527415\pi\) | ||||
−0.0860214 | + | 0.996293i | \(0.527415\pi\) | |||||||
\(662\) | −2.83824e7 | + | 4.91597e7i | −0.0978306 | + | 0.169448i | ||||
\(663\) | 8.04357e7 | + | 4.64396e7i | 0.275999 | + | 0.159348i | ||||
\(664\) | 1.18964e8 | − | 6.86842e7i | 0.406362 | − | 0.234613i | ||||
\(665\) | 4.14539e8 | − | 2.39334e8i | 1.40962 | − | 0.813842i | ||||
\(666\) | −969937. | −0.00328338 | ||||||||
\(667\) | 8.75084e7i | 0.294898i | ||||||||
\(668\) | 2.37976e7 | + | 4.12187e7i | 0.0798369 | + | 0.138282i | ||||
\(669\) | −2.30665e8 | − | 3.99523e8i | −0.770376 | − | 1.33433i | ||||
\(670\) | −8.53597e7 | + | 1.47847e8i | −0.283810 | + | 0.491574i | ||||
\(671\) | 1.13797e7 | + | 6.57008e6i | 0.0376672 | + | 0.0217472i | ||||
\(672\) | − | 2.12336e8i | − | 0.699705i | ||||||
\(673\) | 2.65859e8 | + | 1.53494e8i | 0.872181 | + | 0.503554i | 0.868072 | − | 0.496438i | \(-0.165359\pi\) |
0.00410868 | + | 0.999992i | \(0.498692\pi\) | |||||||
\(674\) | 6.46659e7 | + | 3.73349e7i | 0.211201 | + | 0.121937i | ||||
\(675\) | 8.11873e8 | + | 4.68735e8i | 2.63984 | + | 1.52411i | ||||
\(676\) | 9.65047e7 | + | 1.67151e8i | 0.312398 | + | 0.541090i | ||||
\(677\) | − | 2.43077e8i | − | 0.783388i | −0.920096 | − | 0.391694i | \(-0.871889\pi\) | ||
0.920096 | − | 0.391694i | \(-0.128111\pi\) | |||||||
\(678\) | 5.46115e7 | − | 3.15300e7i | 0.175225 | − | 0.101166i | ||||
\(679\) | 6.11276e8 | + | 3.52920e8i | 1.95267 | + | 1.12737i | ||||
\(680\) | −1.43317e8 | −0.455795 | ||||||||
\(681\) | 1.42160e8 | − | 2.46228e8i | 0.450128 | − | 0.779644i | ||||
\(682\) | 1.18341e7 | − | 6.83243e6i | 0.0373064 | − | 0.0215388i | ||||
\(683\) | −1.82732e8 | − | 3.16501e8i | −0.573524 | − | 0.993373i | −0.996200 | − | 0.0870924i | \(-0.972242\pi\) |
0.422676 | − | 0.906281i | \(-0.361091\pi\) | |||||||
\(684\) | − | 4.53089e7i | − | 0.141584i | ||||||
\(685\) | 7.47877e7 | + | 1.29536e8i | 0.232680 | + | 0.403013i | ||||
\(686\) | 2.47785e7 | 0.0767544 | ||||||||
\(687\) | − | 3.14149e8i | − | 0.968871i | ||||||
\(688\) | −2.08891e8 | + | 2.02503e8i | −0.641436 | + | 0.621823i | ||||
\(689\) | −3.36053e8 | −1.02743 | ||||||||
\(690\) | 1.37341e8i | 0.418074i | ||||||||
\(691\) | −1.14644e7 | + | 6.61898e6i | −0.0347470 | + | 0.0200612i | −0.517273 | − | 0.855821i | \(-0.673053\pi\) |
0.482526 | + | 0.875882i | \(0.339719\pi\) | |||||||
\(692\) | −1.84688e8 | −0.557341 | ||||||||
\(693\) | −5.13748e7 | + | 2.96613e7i | −0.154366 | + | 0.0891230i | ||||
\(694\) | 3.77014e7 | + | 6.53008e7i | 0.112792 | + | 0.195362i | ||||
\(695\) | −7.73130e8 | − | 4.46367e8i | −2.30302 | − | 1.32965i | ||||
\(696\) | 2.40996e7i | 0.0714797i | ||||||||
\(697\) | −1.31426e8 | + | 2.27637e8i | −0.388135 | + | 0.672270i | ||||
\(698\) | −1.70565e7 | − | 2.95427e7i | −0.0501560 | − | 0.0868727i | ||||
\(699\) | −3.24680e8 | −0.950658 | ||||||||
\(700\) | −1.21226e9 | + | 6.99899e8i | −3.53429 | + | 2.04052i | ||||
\(701\) | −4.75643e6 | + | 8.23837e6i | −0.0138079 | + | 0.0239159i | −0.872847 | − | 0.487994i | \(-0.837729\pi\) |
0.859039 | + | 0.511910i | \(0.171062\pi\) | |||||||
\(702\) | −2.11075e7 | + | 3.65593e7i | −0.0610135 | + | 0.105678i | ||||
\(703\) | −6.27482e6 | + | 1.08683e7i | −0.0180607 | + | 0.0312821i | ||||
\(704\) | −1.23042e8 | −0.352644 | ||||||||
\(705\) | −6.36339e7 | + | 1.10217e8i | −0.181602 | + | 0.314545i | ||||
\(706\) | 4.55749e7 | + | 2.63127e7i | 0.129513 | + | 0.0747741i | ||||
\(707\) | 3.32027e8 | − | 1.91696e8i | 0.939540 | − | 0.542444i | ||||
\(708\) | −1.33279e8 | + | 7.69485e7i | −0.375544 | + | 0.216821i | ||||
\(709\) | −1.07299e7 | −0.0301063 | −0.0150531 | − | 0.999887i | \(-0.504792\pi\) | ||||
−0.0150531 | + | 0.999887i | \(0.504792\pi\) | |||||||
\(710\) | 1.48129e8i | 0.413872i | ||||||||
\(711\) | −4.72316e7 | − | 8.18075e7i | −0.131409 | − | 0.227606i | ||||
\(712\) | −6.74575e6 | − | 1.16840e7i | −0.0186892 | − | 0.0323706i | ||||
\(713\) | −1.21559e8 | + | 2.10546e8i | −0.335365 | + | 0.580869i | ||||
\(714\) | 4.83829e7 | + | 2.79339e7i | 0.132922 | + | 0.0767426i | ||||
\(715\) | 1.88804e8i | 0.516528i | ||||||||
\(716\) | −1.81230e8 | − | 1.04633e8i | −0.493733 | − | 0.285057i | ||||
\(717\) | −8.81329e7 | − | 5.08836e7i | −0.239101 | − | 0.138045i | ||||
\(718\) | 2.82918e6 | + | 1.63343e6i | 0.00764342 | + | 0.00441293i | ||||
\(719\) | 1.71077e8 | + | 2.96313e8i | 0.460261 | + | 0.797195i | 0.998974 | − | 0.0452945i | \(-0.0144226\pi\) |
−0.538713 | + | 0.842489i | \(0.681089\pi\) | |||||||
\(720\) | 1.72688e8i | 0.462663i | ||||||||
\(721\) | −3.89015e8 | + | 2.24598e8i | −1.03791 | + | 0.599238i | ||||
\(722\) | −4.28764e7 | − | 2.47547e7i | −0.113922 | − | 0.0657727i | ||||
\(723\) | 6.36373e6 | 0.0168382 | ||||||||
\(724\) | −2.32832e8 | + | 4.03277e8i | −0.613518 | + | 1.06264i | ||||
\(725\) | 2.07643e8 | − | 1.19883e8i | 0.544884 | − | 0.314589i | ||||
\(726\) | −2.49165e7 | − | 4.31567e7i | −0.0651145 | − | 0.112782i | ||||
\(727\) | 8.56605e7i | 0.222935i | 0.993768 | + | 0.111467i | \(0.0355550\pi\) | ||||
−0.993768 | + | 0.111467i | \(0.964445\pi\) | |||||||
\(728\) | −6.42101e7 | − | 1.11215e8i | −0.166421 | − | 0.288250i | ||||
\(729\) | −4.28432e8 | −1.10586 | ||||||||
\(730\) | − | 1.99969e8i | − | 0.514036i | ||||||
\(731\) | −5.96890e7 | − | 2.37448e8i | −0.152807 | − | 0.607877i | ||||
\(732\) | −3.16019e7 | −0.0805712 | ||||||||
\(733\) | 6.61593e8i | 1.67988i | 0.542678 | + | 0.839941i | \(0.317410\pi\) | ||||
−0.542678 | + | 0.839941i | \(0.682590\pi\) | |||||||
\(734\) | 9.99768e7 | − | 5.77216e7i | 0.252820 | − | 0.145966i | ||||
\(735\) | 8.42869e8 | 2.12275 | ||||||||
\(736\) | −2.46511e8 | + | 1.42323e8i | −0.618304 | + | 0.356978i | ||||
\(737\) | −1.36875e8 | − | 2.37075e8i | −0.341918 | − | 0.592220i | ||||
\(738\) | −2.16938e7 | − | 1.25249e7i | −0.0539718 | − | 0.0311606i | ||||
\(739\) | − | 8.31473e7i | − | 0.206023i | −0.994680 | − | 0.103011i | \(-0.967152\pi\) | ||
0.994680 | − | 0.103011i | \(-0.0328478\pi\) | |||||||
\(740\) | 2.48786e7 | − | 4.30910e7i | 0.0613947 | − | 0.106339i | ||||
\(741\) | 5.72624e7 | + | 9.91814e7i | 0.140739 | + | 0.243767i | ||||
\(742\) | −2.02139e8 | −0.494811 | ||||||||
\(743\) | −5.72327e6 | + | 3.30433e6i | −0.0139533 | + | 0.00805596i | −0.506960 | − | 0.861969i | \(-0.669231\pi\) |
0.493007 | + | 0.870025i | \(0.335898\pi\) | |||||||
\(744\) | −3.34770e7 | + | 5.79839e7i | −0.0812883 | + | 0.140795i | ||||
\(745\) | 7.83345e8 | − | 1.35679e9i | 1.89445 | − | 3.28129i | ||||
\(746\) | 4.33764e6 | − | 7.51301e6i | 0.0104481 | − | 0.0180966i | ||||
\(747\) | 1.39293e8 | 0.334171 | ||||||||
\(748\) | 5.64001e7 | − | 9.76878e7i | 0.134764 | − | 0.233419i | ||||
\(749\) | 7.12725e8 | + | 4.11492e8i | 1.69620 | + | 0.979300i | ||||
\(750\) | 2.09938e8 | − | 1.21208e8i | 0.497631 | − | 0.287308i | ||||
\(751\) | −3.38651e8 | + | 1.95520e8i | −0.799526 | + | 0.461607i | −0.843305 | − | 0.537435i | \(-0.819393\pi\) |
0.0437794 | + | 0.999041i | \(0.486060\pi\) | |||||||
\(752\) | −8.24677e7 | −0.193923 | ||||||||
\(753\) | − | 1.99722e8i | − | 0.467778i | ||||||
\(754\) | 5.39842e6 | + | 9.35034e6i | 0.0125937 | + | 0.0218129i | ||||
\(755\) | −1.22704e8 | − | 2.12529e8i | −0.285113 | − | 0.493830i | ||||
\(756\) | 3.40218e8 | − | 5.89275e8i | 0.787393 | − | 1.36381i | ||||
\(757\) | 6.78883e8 | + | 3.91953e8i | 1.56498 | + | 0.903539i | 0.996741 | + | 0.0806723i | \(0.0257067\pi\) |
0.568235 | + | 0.822867i | \(0.307627\pi\) | |||||||
\(758\) | − | 5.80599e7i | − | 0.133312i | ||||||
\(759\) | −1.90723e8 | − | 1.10114e8i | −0.436192 | − | 0.251836i | ||||
\(760\) | −1.53041e8 | − | 8.83584e7i | −0.348632 | − | 0.201283i | ||||
\(761\) | 2.05333e8 | + | 1.18549e8i | 0.465913 | + | 0.268995i | 0.714527 | − | 0.699608i | \(-0.246642\pi\) |
−0.248614 | + | 0.968603i | \(0.579975\pi\) | |||||||
\(762\) | 1.28107e7 | + | 2.21889e7i | 0.0289541 | + | 0.0501499i | ||||
\(763\) | − | 6.35690e8i | − | 1.43111i | ||||||
\(764\) | −3.88837e8 | + | 2.24495e8i | −0.871942 | + | 0.503416i | ||||
\(765\) | −1.25855e8 | − | 7.26625e7i | −0.281117 | − | 0.162303i | ||||
\(766\) | −2.65984e7 | −0.0591793 | ||||||||
\(767\) | −7.02337e7 | + | 1.21648e8i | −0.155654 | + | 0.269600i | ||||
\(768\) | 2.21704e8 | − | 1.28001e8i | 0.489428 | − | 0.282572i | ||||
\(769\) | 1.05050e8 | + | 1.81952e8i | 0.231003 | + | 0.400110i | 0.958104 | − | 0.286422i | \(-0.0924658\pi\) |
−0.727100 | + | 0.686531i | \(0.759132\pi\) | |||||||
\(770\) | 1.13568e8i | 0.248761i | ||||||||
\(771\) | 1.64839e8 | + | 2.85510e8i | 0.359664 | + | 0.622957i | ||||
\(772\) | 5.09924e8 | 1.10829 | ||||||||
\(773\) | − | 1.66817e8i | − | 0.361161i | −0.983560 | − | 0.180580i | \(-0.942202\pi\) | ||
0.983560 | − | 0.180580i | \(-0.0577976\pi\) | |||||||
\(774\) | 2.26288e7 | − | 5.68837e6i | 0.0488021 | − | 0.0122678i | ||||
\(775\) | 6.66122e8 | 1.43103 | ||||||||
\(776\) | − | 2.60585e8i | − | 0.557653i | ||||||
\(777\) | −3.42224e7 | + | 1.97583e7i | −0.0729537 | + | 0.0421199i | ||||
\(778\) | −1.09039e8 | −0.231549 | ||||||||
\(779\) | −2.80688e8 | + | 1.62055e8i | −0.593760 | + | 0.342808i | ||||
\(780\) | −2.27036e8 | − | 3.93238e8i | −0.478421 | − | 0.828650i | ||||
\(781\) | −2.05705e8 | − | 1.18764e8i | −0.431808 | − | 0.249304i | ||||
\(782\) | − | 7.48934e7i | − | 0.156611i | ||||||
\(783\) | −5.82746e7 | + | 1.00935e8i | −0.121393 | + | 0.210259i | ||||
\(784\) | 2.73083e8 | + | 4.72994e8i | 0.566692 | + | 0.981539i | ||||
\(785\) | 3.54714e8 | 0.733279 | ||||||||
\(786\) | 1.01560e8 | − | 5.86358e7i | 0.209149 | − | 0.120752i | ||||
\(787\) | −2.16234e8 | + | 3.74529e8i | −0.443609 | + | 0.768353i | −0.997954 | − | 0.0639335i | \(-0.979635\pi\) |
0.554345 | + | 0.832287i | \(0.312969\pi\) | |||||||
\(788\) | 8.45256e7 | − | 1.46403e8i | 0.172747 | − | 0.299206i | ||||
\(789\) | −1.10362e8 | + | 1.91152e8i | −0.224692 | + | 0.389178i | ||||
\(790\) | −1.80841e8 | −0.366789 | ||||||||
\(791\) | −4.63862e8 | + | 8.03432e8i | −0.937258 | + | 1.62338i | ||||
\(792\) | 1.89668e7 | + | 1.09505e7i | 0.0381784 | + | 0.0220423i | ||||
\(793\) | −2.49798e7 | + | 1.44221e7i | −0.0500922 | + | 0.0289207i | ||||
\(794\) | −6.44732e7 | + | 3.72236e7i | −0.128800 | + | 0.0743630i | ||||
\(795\) | −1.45613e9 | −2.89801 | ||||||||
\(796\) | − | 1.75295e8i | − | 0.347561i | ||||||
\(797\) | −1.72478e7 | − | 2.98741e7i | −0.0340690 | − | 0.0590092i | 0.848488 | − | 0.529214i | \(-0.177513\pi\) |
−0.882557 | + | 0.470205i | \(0.844180\pi\) | |||||||
\(798\) | 3.44439e7 | + | 5.96586e7i | 0.0677804 | + | 0.117399i | ||||
\(799\) | 3.47002e7 | − | 6.01025e7i | 0.0680286 | − | 0.117829i | ||||
\(800\) | 6.75419e8 | + | 3.89954e8i | 1.31918 | + | 0.761628i | ||||
\(801\) | − | 1.36806e7i | − | 0.0266199i | ||||||
\(802\) | 5.98801e7 | + | 3.45718e7i | 0.116081 | + | 0.0670191i | ||||
\(803\) | 2.77693e8 | + | 1.60326e8i | 0.536313 | + | 0.309640i | ||||
\(804\) | 5.70162e8 | + | 3.29183e8i | 1.09706 | + | 0.633387i | ||||
\(805\) | −1.01027e9 | − | 1.74983e9i | −1.93664 | − | 3.35435i | ||||
\(806\) | 2.99960e7i | 0.0572873i | ||||||||
\(807\) | −3.33266e8 | + | 1.92411e8i | −0.634118 | + | 0.366108i | ||||
\(808\) | −1.22579e8 | − | 7.07711e7i | −0.232371 | − | 0.134160i | ||||
\(809\) | −2.86762e8 | −0.541597 | −0.270799 | − | 0.962636i | \(-0.587288\pi\) | ||||
−0.270799 | + | 0.962636i | \(0.587288\pi\) | |||||||
\(810\) | −6.53583e7 | + | 1.13204e8i | −0.122983 | + | 0.213013i | ||||
\(811\) | 7.23734e8 | − | 4.17848e8i | 1.35680 | − | 0.783350i | 0.367611 | − | 0.929980i | \(-0.380176\pi\) |
0.989191 | + | 0.146630i | \(0.0468425\pi\) | |||||||
\(812\) | −8.70135e7 | − | 1.50712e8i | −0.162524 | − | 0.281501i | ||||
\(813\) | 4.96305e8i | 0.923585i | ||||||||
\(814\) | −1.48875e6 | − | 2.57859e6i | −0.00276025 | − | 0.00478089i | ||||
\(815\) | 9.80682e8 | 1.81157 | ||||||||
\(816\) | 2.60781e8i | 0.479961i | ||||||||
\(817\) | 8.26535e7 | − | 2.90359e8i | 0.151564 | − | 0.532438i | ||||
\(818\) | −4.02737e7 | −0.0735802 | ||||||||
\(819\) | − | 1.30220e8i | − | 0.237042i | ||||||
\(820\) | 1.11288e9 | − | 6.42522e8i | 2.01840 | − | 1.16532i | ||||
\(821\) | 5.71064e8 | 1.03194 | 0.515971 | − | 0.856606i | \(-0.327431\pi\) | ||||
0.515971 | + | 0.856606i | \(0.327431\pi\) | |||||||
\(822\) | −1.86423e7 | + | 1.07631e7i | −0.0335647 | + | 0.0193786i | ||||
\(823\) | −5.09867e8 | − | 8.83116e8i | −0.914656 | − | 1.58423i | −0.807405 | − | 0.589998i | \(-0.799129\pi\) |
−0.107251 | − | 0.994232i | \(-0.534205\pi\) | |||||||
\(824\) | 1.43618e8 | + | 8.29179e7i | 0.256701 | + | 0.148206i | ||||
\(825\) | 6.03407e8i | 1.07460i | ||||||||
\(826\) | −4.22463e7 | + | 7.31728e7i | −0.0749633 | + | 0.129840i | ||||
\(827\) | 1.23406e8 | + | 2.13745e8i | 0.218182 | + | 0.377902i | 0.954252 | − | 0.299003i | \(-0.0966540\pi\) |
−0.736070 | + | 0.676905i | \(0.763321\pi\) | |||||||
\(828\) | −1.91256e8 | −0.336917 | ||||||||
\(829\) | −1.60390e8 | + | 9.26010e7i | −0.281522 | + | 0.162537i | −0.634112 | − | 0.773241i | \(-0.718634\pi\) |
0.352590 | + | 0.935778i | \(0.385301\pi\) | |||||||
\(830\) | 1.33333e8 | − | 2.30939e8i | 0.233186 | − | 0.403889i | ||||
\(831\) | 4.73744e8 | − | 8.20549e8i | 0.825545 | − | 1.42989i | ||||
\(832\) | 1.35046e8 | − | 2.33907e8i | 0.234483 | − | 0.406137i | ||||
\(833\) | −4.59625e8 | −0.795185 | ||||||||
\(834\) | 6.42392e7 | − | 1.11265e8i | 0.110739 | − | 0.191806i | ||||
\(835\) | 1.63017e8 | + | 9.41178e7i | 0.280010 | + | 0.161664i | ||||
\(836\) | 1.20454e8 | − | 6.95442e7i | 0.206159 | − | 0.119026i | ||||
\(837\) | −2.80418e8 | + | 1.61900e8i | −0.478223 | + | 0.276102i | ||||
\(838\) | 6.29832e7 | 0.107027 | ||||||||
\(839\) | − | 4.13910e8i | − | 0.700841i | −0.936592 | − | 0.350421i | \(-0.886039\pi\) | ||
0.936592 | − | 0.350421i | \(-0.113961\pi\) | |||||||
\(840\) | −2.78225e8 | − | 4.81900e8i | −0.469417 | − | 0.813054i | ||||
\(841\) | −2.82507e8 | − | 4.89317e8i | −0.474943 | − | 0.822626i | ||||
\(842\) | 1.57755e6 | − | 2.73240e6i | 0.00264270 | − | 0.00457729i | ||||
\(843\) | 1.28221e8 | + | 7.40285e7i | 0.214031 | + | 0.123571i | ||||
\(844\) | 9.26711e8i | 1.54141i | ||||||||
\(845\) | 6.61070e8 | + | 3.81669e8i | 1.09566 | + | 0.632582i | ||||
\(846\) | 5.72778e6 | + | 3.30694e6i | 0.00945965 | + | 0.00546153i | ||||
\(847\) | 6.34913e8 | + | 3.66567e8i | 1.04487 | + | 0.603258i | ||||
\(848\) | −4.71776e8 | − | 8.17140e8i | −0.773657 | − | 1.34001i | ||||
\(849\) | 5.63358e8i | 0.920579i | ||||||||
\(850\) | −1.77710e8 | + | 1.02601e8i | −0.289371 | + | 0.167068i | ||||
\(851\) | 4.58768e7 | + | 2.64870e7i | 0.0744396 | + | 0.0429777i | ||||
\(852\) | 5.71249e8 | 0.923649 | ||||||||
\(853\) | −1.66556e8 | + | 2.88483e8i | −0.268357 | + | 0.464808i | −0.968438 | − | 0.249256i | \(-0.919814\pi\) |
0.700081 | + | 0.714064i | \(0.253147\pi\) | |||||||
\(854\) | −1.50256e7 | + | 8.67504e6i | −0.0241245 | + | 0.0139283i | ||||
\(855\) | −8.95966e7 | − | 1.55186e8i | −0.143349 | − | 0.248287i | ||||
\(856\) | − | 3.03832e8i | − | 0.484410i | ||||||
\(857\) | −9.30821e7 | − | 1.61223e8i | −0.147885 | − | 0.256144i | 0.782561 | − | 0.622574i | \(-0.213913\pi\) |
−0.930446 | + | 0.366430i | \(0.880580\pi\) | |||||||
\(858\) | −2.71719e7 | −0.0430187 | ||||||||
\(859\) | 9.66258e7i | 0.152445i | 0.997091 | + | 0.0762225i | \(0.0242859\pi\) | ||||
−0.997091 | + | 0.0762225i | \(0.975714\pi\) | |||||||
\(860\) | −3.27707e8 | + | 1.15123e9i | −0.515217 | + | 1.80994i | ||||
\(861\) | −1.02057e9 | −1.59894 | ||||||||
\(862\) | 1.24479e7i | 0.0194345i | ||||||||
\(863\) | 4.14434e8 | − | 2.39274e8i | 0.644798 | − | 0.372274i | −0.141663 | − | 0.989915i | \(-0.545245\pi\) |
0.786460 | + | 0.617641i | \(0.211911\pi\) | |||||||
\(864\) | −3.79110e8 | −0.587792 | ||||||||
\(865\) | −6.32569e8 | + | 3.65214e8i | −0.977371 | + | 0.564286i | ||||
\(866\) | 7.87200e7 | + | 1.36347e8i | 0.121208 | + | 0.209938i | ||||
\(867\) | 2.93717e8 | + | 1.69577e8i | 0.450683 | + | 0.260202i | ||||
\(868\) | − | 4.83485e8i | − | 0.739306i | ||||||
\(869\) | 1.44991e8 | − | 2.51131e8i | 0.220943 | − | 0.382685i | ||||
\(870\) | 2.33916e7 | + | 4.05154e7i | 0.0355224 | + | 0.0615266i | ||||
\(871\) | 6.00915e8 | 0.909407 | ||||||||
\(872\) | −2.03245e8 | + | 1.17343e8i | −0.306528 | + | 0.176974i | ||||
\(873\) | 1.32118e8 | − | 2.28836e8i | 0.198573 | − | 0.343939i | ||||
\(874\) | 4.61737e7 | − | 7.99752e7i | 0.0691609 | − | 0.119790i | ||||
\(875\) | −1.78318e9 | + | 3.08857e9i | −2.66178 | + | 4.61034i | ||||
\(876\) | −7.71164e8 | −1.14719 | ||||||||
\(877\) | 3.69812e8 | − | 6.40534e8i | 0.548255 | − | 0.949605i | −0.450139 | − | 0.892958i | \(-0.648626\pi\) |
0.998394 | − | 0.0566471i | \(-0.0180410\pi\) | |||||||
\(878\) | −5.11224e7 | − | 2.95155e7i | −0.0755314 | − | 0.0436081i | ||||
\(879\) | 6.57001e8 | − | 3.79320e8i | 0.967385 | − | 0.558520i | ||||
\(880\) | −4.59093e8 | + | 2.65057e8i | −0.673678 | + | 0.388948i | ||||
\(881\) | −9.18084e8 | −1.34263 | −0.671313 | − | 0.741174i | \(-0.734269\pi\) | ||||
−0.671313 | + | 0.741174i | \(0.734269\pi\) | |||||||
\(882\) | − | 4.38023e7i | − | 0.0638398i | ||||||
\(883\) | −1.89295e8 | − | 3.27869e8i | −0.274953 | − | 0.476232i | 0.695171 | − | 0.718845i | \(-0.255329\pi\) |
−0.970123 | + | 0.242613i | \(0.921995\pi\) | |||||||
\(884\) | 1.23805e8 | + | 2.14436e8i | 0.179218 | + | 0.310414i | ||||
\(885\) | −3.04326e8 | + | 5.27108e8i | −0.439045 | + | 0.760448i | ||||
\(886\) | 6.42074e7 | + | 3.70701e7i | 0.0923174 | + | 0.0532995i | ||||
\(887\) | 1.71834e7i | 0.0246229i | 0.999924 | + | 0.0123114i | \(0.00391895\pi\) | ||||
−0.999924 | + | 0.0123114i | \(0.996081\pi\) | |||||||
\(888\) | 1.26344e7 | + | 7.29445e6i | 0.0180432 | + | 0.0104173i | ||||
\(889\) | −3.26438e8 | − | 1.88469e8i | −0.464617 | − | 0.268247i | ||||
\(890\) | −2.26814e7 | − | 1.30951e7i | −0.0321736 | − | 0.0185755i | ||||
\(891\) | −1.04803e8 | − | 1.81524e8i | −0.148163 | − | 0.256626i | ||||
\(892\) | − | 1.22987e9i | − | 1.73287i | ||||||
\(893\) | 7.41095e7 | − | 4.27871e7i | 0.104069 | − | 0.0600840i | ||||
\(894\) | 1.95264e8 | + | 1.12735e8i | 0.273281 | + | 0.157779i | ||||
\(895\) | −8.27635e8 | −1.15444 | ||||||||
\(896\) | 3.74830e8 | − | 6.49225e8i | 0.521088 | − | 0.902551i | ||||
\(897\) | 4.18660e8 | − | 2.41713e8i | 0.580074 | − | 0.334906i | ||||
\(898\) | 8.86244e7 | + | 1.53502e8i | 0.122384 | + | 0.211975i | ||||
\(899\) | 8.28144e7i | 0.113979i | ||||||||
\(900\) | 2.62012e8 | + | 4.53819e8i | 0.359414 | + | 0.622523i | ||||
\(901\) | 7.94043e8 | 1.08560 | ||||||||
\(902\) | − | 7.68976e7i | − | 0.104784i | ||||||
\(903\) | 6.82538e8 | − | 6.61668e8i | 0.926966 | − | 0.898622i | ||||
\(904\) | 3.42501e8 | 0.463614 | ||||||||
\(905\) | 1.84167e9i | 2.48465i | ||||||||
\(906\) | 3.05862e7 | − | 1.76590e7i | 0.0411284 | − | 0.0237455i | ||||
\(907\) | −1.05514e9 | −1.41413 | −0.707066 | − | 0.707147i | \(-0.749982\pi\) | ||||
−0.707066 | + | 0.707147i | \(0.749982\pi\) | |||||||
\(908\) | 6.56428e8 | − | 3.78989e8i | 0.876858 | − | 0.506254i | ||||
\(909\) | −7.17629e7 | − | 1.24297e8i | −0.0955450 | − | 0.165489i | ||||
\(910\) | −2.15895e8 | − | 1.24647e8i | −0.286497 | − | 0.165409i | ||||
\(911\) | − | 3.00713e8i | − | 0.397738i | −0.980026 | − | 0.198869i | \(-0.936273\pi\) | ||
0.980026 | − | 0.198869i | \(-0.0637268\pi\) | |||||||
\(912\) | −1.60778e8 | + | 2.78476e8i | −0.211955 | + | 0.367116i | ||||
\(913\) | 2.13800e8 | + | 3.70313e8i | 0.280929 | + | 0.486582i | ||||
\(914\) | 5.36460e7 | 0.0702585 | ||||||||
\(915\) | −1.08239e8 | + | 6.24916e7i | −0.141292 | + | 0.0815752i | ||||
\(916\) | 4.18751e8 | − | 7.25297e8i | 0.544840 | − | 0.943691i | ||||
\(917\) | −8.62637e8 | + | 1.49413e9i | −1.11872 | + | 1.93767i | ||||
\(918\) | 4.98739e7 | − | 8.63841e7i | 0.0644681 | − | 0.111662i | ||||
\(919\) | −3.52456e8 | −0.454108 | −0.227054 | − | 0.973882i | \(-0.572909\pi\) | ||||
−0.227054 | + | 0.973882i | \(0.572909\pi\) | |||||||
\(920\) | −3.72974e8 | + | 6.46010e8i | −0.478978 | + | 0.829613i | ||||
\(921\) | −1.12534e8 | − | 6.49717e7i | −0.144047 | − | 0.0831659i | ||||
\(922\) | −1.09343e8 | + | 6.31290e7i | −0.139507 | + | 0.0805446i | ||||
\(923\) | 4.51546e8 | − | 2.60700e8i | 0.574244 | − | 0.331540i | ||||
\(924\) | 4.37965e8 | 0.555167 | ||||||||
\(925\) | − | 1.45144e8i | − | 0.183390i | ||||||
\(926\) | 1.98731e7 | + | 3.44212e7i | 0.0250284 | + | 0.0433504i | ||||
\(927\) | 8.40799e7 | + | 1.45631e8i | 0.105549 | + | 0.182816i | ||||
\(928\) | −4.84802e7 | + | 8.39702e7i | −0.0606626 | + | 0.105071i | ||||
\(929\) | 1.05940e9 | + | 6.11645e8i | 1.32134 | + | 0.762873i | 0.983942 | − | 0.178490i | \(-0.0571213\pi\) |
0.337394 | + | 0.941364i | \(0.390455\pi\) | |||||||
\(930\) | 1.29974e8i | 0.161587i | ||||||||
\(931\) | −4.90812e8 | − | 2.83371e8i | −0.608228 | − | 0.351161i | ||||
\(932\) | −7.49611e8 | − | 4.32788e8i | −0.925951 | − | 0.534598i | ||||
\(933\) | −1.22392e8 | − | 7.06632e7i | −0.150698 | − | 0.0870058i | ||||
\(934\) | 4.60339e7 | + | 7.97330e7i | 0.0564985 | + | 0.0978583i | ||||
\(935\) | − | 4.46116e8i | − | 0.545774i | ||||||
\(936\) | −4.16343e7 | + | 2.40376e7i | −0.0507719 | + | 0.0293132i | ||||
\(937\) | 7.42998e8 | + | 4.28970e8i | 0.903168 | + | 0.521444i | 0.878227 | − | 0.478245i | \(-0.158727\pi\) |
0.0249415 | + | 0.999689i | \(0.492060\pi\) | |||||||
\(938\) | 3.61456e8 | 0.437973 | ||||||||
\(939\) | −8.80289e7 | + | 1.52470e8i | −0.106323 | + | 0.184157i | ||||
\(940\) | −2.93832e8 | + | 1.69644e8i | −0.353765 | + | 0.204247i | ||||
\(941\) | −3.83519e8 | − | 6.64274e8i | −0.460275 | − | 0.797220i | 0.538699 | − | 0.842498i | \(-0.318916\pi\) |
−0.998974 | + | 0.0452782i | \(0.985583\pi\) | |||||||
\(942\) | 5.10489e7i | 0.0610708i | ||||||||
\(943\) | 6.84059e8 | + | 1.18483e9i | 0.815753 | + | 1.41293i | ||||
\(944\) | −3.94397e8 | −0.468833 | ||||||||
\(945\) | − | 2.69107e9i | − | 3.18882i | ||||||
\(946\) | 4.98553e7 | + | 5.14278e7i | 0.0588895 | + | 0.0607470i | ||||
\(947\) | 3.69661e8 | 0.435265 | 0.217632 | − | 0.976031i | \(-0.430167\pi\) | ||||
0.217632 | + | 0.976031i | \(0.430167\pi\) | |||||||
\(948\) | 6.97401e8i | 0.818574i | ||||||||
\(949\) | −6.09569e8 | + | 3.51935e8i | −0.713221 | + | 0.411778i | ||||
\(950\) | −2.53025e8 | −0.295115 | ||||||||
\(951\) | −1.07847e9 | + | 6.22657e8i | −1.25391 | + | 0.723948i | ||||
\(952\) | 1.51719e8 | + | 2.62785e8i | 0.175844 | + | 0.304571i | ||||
\(953\) | −6.28941e8 | − | 3.63120e8i | −0.726660 | − | 0.419538i | 0.0905388 | − | 0.995893i | \(-0.471141\pi\) |
−0.817199 | + | 0.576355i | \(0.804474\pi\) | |||||||
\(954\) | 7.56725e7i | 0.0871551i | ||||||||
\(955\) | −8.87862e8 | + | 1.53782e9i | −1.01938 | + | 1.76562i | ||||
\(956\) | −1.35652e8 | − | 2.34957e8i | −0.155258 | − | 0.268914i | ||||
\(957\) | −7.50174e7 | −0.0855906 | ||||||||
\(958\) | −2.28609e7 | + | 1.31988e7i | −0.0260014 | + | 0.0150119i | ||||
\(959\) | 1.58345e8 | − | 2.74261e8i | 0.179534 | − | 0.310963i | ||||
\(960\) | 5.85160e8 | − | 1.01353e9i | 0.661395 | − | 1.14557i | ||||
\(961\) | 3.28714e8 | − | 5.69349e8i | 0.370380 | − | 0.641517i | ||||
\(962\) | 6.53596e6 | 0.00734149 | ||||||||
\(963\) | 1.54045e8 | − | 2.66814e8i | 0.172492 | − | 0.298765i | ||||
\(964\) | 1.46924e7 | + | 8.48264e6i | 0.0164006 | + | 0.00946891i | ||||
\(965\) | 1.74652e9 | − | 1.00836e9i | 1.94353 | − | 1.12210i | ||||
\(966\) | 2.51828e8 | − | 1.45393e8i | 0.279365 | − | 0.161292i | ||||
\(967\) | −3.71429e7 | −0.0410768 | −0.0205384 | − | 0.999789i | \(-0.506538\pi\) | ||||
−0.0205384 | + | 0.999789i | \(0.506538\pi\) | |||||||
\(968\) | − | 2.70661e8i | − | 0.298401i | ||||||
\(969\) | −1.35302e8 | − | 2.34351e8i | −0.148708 | − | 0.257570i | ||||
\(970\) | −2.52929e8 | − | 4.38086e8i | −0.277130 | − | 0.480003i | ||||
\(971\) | 5.24018e8 | − | 9.07626e8i | 0.572385 | − | 0.991400i | −0.423935 | − | 0.905693i | \(-0.639352\pi\) |
0.996320 | − | 0.0857077i | \(-0.0273151\pi\) | |||||||
\(972\) | −3.94945e8 | − | 2.28022e8i | −0.430069 | − | 0.248300i | ||||
\(973\) | 1.89015e9i | 2.05190i | ||||||||
\(974\) | −1.10119e8 | − | 6.35772e7i | −0.119175 | − | 0.0688057i | ||||
\(975\) | −1.14709e9 | − | 6.62275e8i | −1.23761 | − | 0.714536i | ||||
\(976\) | −7.01370e7 | − | 4.04936e7i | −0.0754393 | − | 0.0435549i | ||||
\(977\) | 2.43494e8 | + | 4.21744e8i | 0.261099 | + | 0.452237i | 0.966534 | − | 0.256538i | \(-0.0825818\pi\) |
−0.705435 | + | 0.708774i | \(0.749248\pi\) | |||||||
\(978\) | 1.41135e8i | 0.150876i | ||||||||
\(979\) | 3.63699e7 | − | 2.09982e7i | 0.0387609 | − | 0.0223786i | ||||
\(980\) | 1.94599e9 | + | 1.12352e9i | 2.06758 | + | 1.19372i | ||||
\(981\) | −2.37976e8 | −0.252072 | ||||||||
\(982\) | −1.19066e8 | + | 2.06229e8i | −0.125734 | + | 0.217778i | ||||
\(983\) | −7.87299e8 | + | 4.54547e8i | −0.828856 | + | 0.478540i | −0.853461 | − | 0.521157i | \(-0.825501\pi\) |
0.0246047 | + | 0.999697i | \(0.492167\pi\) | |||||||
\(984\) | 1.88389e8 | + | 3.26298e8i | 0.197728 | + | 0.342476i | ||||
\(985\) | − | 6.68585e8i | − | 0.699597i | ||||||
\(986\) | −1.27557e7 | − | 2.20934e7i | −0.0133068 | − | 0.0230480i | ||||
\(987\) | 2.69459e8 | 0.280247 | ||||||||
\(988\) | 3.05316e8i | 0.316576i | ||||||||
\(989\) | −1.22565e9 | − | 3.48893e8i | −1.26700 | − | 0.360664i | ||||
\(990\) | 4.25150e7 | 0.0438163 | ||||||||
\(991\) | − | 8.94447e8i | − | 0.919038i | −0.888168 | − | 0.459519i | \(-0.848022\pi\) | ||
0.888168 | − | 0.459519i | \(-0.151978\pi\) | |||||||
\(992\) | −2.33288e8 | + | 1.34689e8i | −0.238977 | + | 0.137974i | ||||
\(993\) | 8.65769e8 | 0.884207 | ||||||||
\(994\) | 2.71609e8 | − | 1.56814e8i | 0.276558 | − | 0.159671i | ||||
\(995\) | −3.46640e8 | − | 6.00398e8i | −0.351892 | − | 0.609495i | ||||
\(996\) | −8.90597e8 | − | 5.14187e8i | −0.901371 | − | 0.520407i | ||||
\(997\) | 1.42429e8i | 0.143718i | 0.997415 | + | 0.0718591i | \(0.0228932\pi\) | ||||
−0.997415 | + | 0.0718591i | \(0.977107\pi\) | |||||||
\(998\) | −1.04485e7 | + | 1.80973e7i | −0.0105114 | + | 0.0182063i | ||||
\(999\) | 3.52770e7 | + | 6.11016e7i | 0.0353831 | + | 0.0612853i |
(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 | 43.7.d.a.7.11 | ✓ | 42 | |
43.37 | odd | 6 | inner | 43.7.d.a.37.11 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.d.a.7.11 | ✓ | 42 | 1.1 | even | 1 | trivial | |
43.7.d.a.37.11 | yes | 42 | 43.37 | odd | 6 | inner |