Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,7,Mod(19,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.f (of order \(6\), degree \(2\), not 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: | \(33.8179502921\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.4 | ||
Root | \(-6.30797 - 10.9257i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.31 |
Dual form | 147.7.f.d.19.4 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.80797 | + | 10.0597i | 0.725996 | + | 1.25746i | 0.958563 | + | 0.284881i | \(0.0919542\pi\) |
−0.232567 | + | 0.972580i | \(0.574712\pi\) | |||||||
\(3\) | 13.5000 | + | 7.79423i | 0.500000 | + | 0.288675i | ||||
\(4\) | −35.4650 | + | 61.4271i | −0.554140 | + | 0.959799i | ||||
\(5\) | 165.302 | − | 95.4373i | 1.32242 | − | 0.763498i | 0.338304 | − | 0.941037i | \(-0.390147\pi\) |
0.984114 | + | 0.177539i | \(0.0568136\pi\) | |||||||
\(6\) | 181.074i | 0.838308i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −80.4975 | −0.157222 | ||||||||
\(9\) | 121.500 | + | 210.444i | 0.166667 | + | 0.288675i | ||||
\(10\) | 1920.14 | + | 1108.59i | 1.92014 | + | 1.10859i | ||||
\(11\) | 1027.55 | − | 1779.77i | 0.772015 | − | 1.33717i | −0.164442 | − | 0.986387i | \(-0.552582\pi\) |
0.936457 | − | 0.350783i | \(-0.114084\pi\) | |||||||
\(12\) | −957.554 | + | 552.844i | −0.554140 | + | 0.319933i | ||||
\(13\) | − | 3059.97i | − | 1.39279i | −0.717657 | − | 0.696396i | \(-0.754786\pi\) | ||
0.717657 | − | 0.696396i | \(-0.245214\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2975.44 | 0.881612 | ||||||||
\(16\) | 1802.23 | + | 3121.55i | 0.439998 | + | 0.762098i | ||||
\(17\) | −2468.38 | − | 1425.12i | −0.502419 | − | 0.290072i | 0.227293 | − | 0.973826i | \(-0.427012\pi\) |
−0.729712 | + | 0.683755i | \(0.760346\pi\) | |||||||
\(18\) | −1411.34 | + | 2444.51i | −0.241999 | + | 0.419154i | ||||
\(19\) | 3420.04 | − | 1974.56i | 0.498622 | − | 0.287879i | −0.229523 | − | 0.973303i | \(-0.573716\pi\) |
0.728144 | + | 0.685424i | \(0.240383\pi\) | |||||||
\(20\) | 13538.7i | 1.69234i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 23872.0 | 2.24192 | ||||||||
\(23\) | −330.272 | − | 572.047i | −0.0271449 | − | 0.0470163i | 0.852134 | − | 0.523324i | \(-0.175308\pi\) |
−0.879279 | + | 0.476308i | \(0.841975\pi\) | |||||||
\(24\) | −1086.72 | − | 627.416i | −0.0786109 | − | 0.0453860i | ||||
\(25\) | 10404.0 | − | 18020.3i | 0.665859 | − | 1.15330i | ||||
\(26\) | 30782.3 | − | 17772.2i | 1.75138 | − | 1.01116i | ||||
\(27\) | 3788.00i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9282.66 | −0.380609 | −0.190304 | − | 0.981725i | \(-0.560947\pi\) | ||||
−0.190304 | + | 0.981725i | \(0.560947\pi\) | |||||||
\(30\) | 17281.3 | + | 29932.0i | 0.640046 | + | 1.10859i | ||||
\(31\) | −2426.36 | − | 1400.86i | −0.0814460 | − | 0.0470229i | 0.458724 | − | 0.888579i | \(-0.348307\pi\) |
−0.540170 | + | 0.841556i | \(0.681640\pi\) | |||||||
\(32\) | −23510.5 | + | 40721.4i | −0.717484 | + | 1.24272i | ||||
\(33\) | 27743.9 | − | 16018.0i | 0.772015 | − | 0.445723i | ||||
\(34\) | − | 33108.2i | − | 0.842363i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −17236.0 | −0.369427 | ||||||||
\(37\) | 18466.2 | + | 31984.5i | 0.364563 | + | 0.631442i | 0.988706 | − | 0.149868i | \(-0.0478849\pi\) |
−0.624143 | + | 0.781310i | \(0.714552\pi\) | |||||||
\(38\) | 39727.0 | + | 22936.4i | 0.723994 | + | 0.417998i | ||||
\(39\) | 23850.1 | − | 41309.5i | 0.402065 | − | 0.696396i | ||||
\(40\) | −13306.4 | + | 7682.46i | −0.207913 | + | 0.120039i | ||||
\(41\) | 67941.3i | 0.985785i | 0.870090 | + | 0.492892i | \(0.164060\pi\) | ||||
−0.870090 | + | 0.492892i | \(0.835940\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12336.3 | 0.155160 | 0.0775799 | − | 0.996986i | \(-0.475281\pi\) | ||||
0.0775799 | + | 0.996986i | \(0.475281\pi\) | |||||||
\(44\) | 72884.2 | + | 126239.i | 0.855609 | + | 1.48196i | ||||
\(45\) | 40168.4 | + | 23191.3i | 0.440806 | + | 0.254499i | ||||
\(46\) | 3836.41 | − | 6644.86i | 0.0394141 | − | 0.0682673i | ||||
\(47\) | −127836. | + | 73806.3i | −1.23129 | + | 0.710886i | −0.967299 | − | 0.253639i | \(-0.918372\pi\) |
−0.263991 | + | 0.964525i | \(0.585039\pi\) | |||||||
\(48\) | 56188.0i | 0.508066i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 241705. | 1.93364 | ||||||||
\(51\) | −22215.4 | − | 38478.3i | −0.167473 | − | 0.290072i | ||||
\(52\) | 187965. | + | 108522.i | 1.33680 | + | 0.771802i | ||||
\(53\) | −109818. | + | 190210.i | −0.737641 | + | 1.27763i | 0.215914 | + | 0.976412i | \(0.430727\pi\) |
−0.953555 | + | 0.301219i | \(0.902607\pi\) | |||||||
\(54\) | −38106.1 | + | 22000.6i | −0.241999 | + | 0.139718i | ||||
\(55\) | − | 392267.i | − | 2.35773i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 61560.8 | 0.332414 | ||||||||
\(58\) | −53913.4 | − | 93380.8i | −0.276320 | − | 0.478601i | ||||
\(59\) | −166725. | − | 96258.8i | −0.811792 | − | 0.468689i | 0.0357855 | − | 0.999359i | \(-0.488607\pi\) |
−0.847578 | + | 0.530671i | \(0.821940\pi\) | |||||||
\(60\) | −105524. | + | 182773.i | −0.488536 | + | 0.846170i | ||||
\(61\) | −288244. | + | 166418.i | −1.26990 | + | 0.733180i | −0.974970 | − | 0.222338i | \(-0.928631\pi\) |
−0.294935 | + | 0.955517i | \(0.595298\pi\) | |||||||
\(62\) | − | 32544.5i | − | 0.136554i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −315508. | −1.20357 | ||||||||
\(65\) | −292035. | − | 505819.i | −1.06339 | − | 1.84185i | ||||
\(66\) | 322271. | + | 186063.i | 1.12096 | + | 0.647186i | ||||
\(67\) | −174592. | + | 302402.i | −0.580496 | + | 1.00545i | 0.414924 | + | 0.909856i | \(0.363808\pi\) |
−0.995420 | + | 0.0955931i | \(0.969525\pi\) | |||||||
\(68\) | 175082. | − | 101084.i | 0.556821 | − | 0.321481i | ||||
\(69\) | − | 10296.9i | − | 0.0313442i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 305650. | 0.853984 | 0.426992 | − | 0.904255i | \(-0.359573\pi\) | ||||
0.426992 | + | 0.904255i | \(0.359573\pi\) | |||||||
\(72\) | −9780.45 | − | 16940.2i | −0.0262036 | − | 0.0453860i | ||||
\(73\) | 204814. | + | 118249.i | 0.526490 | + | 0.303969i | 0.739586 | − | 0.673062i | \(-0.235021\pi\) |
−0.213096 | + | 0.977031i | \(0.568355\pi\) | |||||||
\(74\) | −214503. | + | 371529.i | −0.529343 | + | 0.916849i | ||||
\(75\) | 280909. | − | 162183.i | 0.665859 | − | 0.384434i | ||||
\(76\) | 280111.i | 0.638102i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 554082. | 1.16759 | ||||||||
\(79\) | 293218. | + | 507869.i | 0.594716 | + | 1.03008i | 0.993587 | + | 0.113072i | \(0.0360690\pi\) |
−0.398871 | + | 0.917007i | \(0.630598\pi\) | |||||||
\(80\) | 595825. | + | 344000.i | 1.16372 | + | 0.671875i | ||||
\(81\) | −29524.5 | + | 51137.9i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −683468. | + | 394601.i | −1.23959 | + | 0.715675i | ||||
\(83\) | − | 106377.i | − | 0.186044i | −0.995664 | − | 0.0930218i | \(-0.970347\pi\) | ||
0.995664 | − | 0.0930218i | \(-0.0296526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −544039. | −0.885876 | ||||||||
\(86\) | 71648.8 | + | 124099.i | 0.112645 | + | 0.195108i | ||||
\(87\) | −125316. | − | 72351.2i | −0.190304 | − | 0.109872i | ||||
\(88\) | −82715.4 | + | 143267.i | −0.121378 | + | 0.210232i | ||||
\(89\) | −11308.5 | + | 6528.95i | −0.0160411 | + | 0.00926134i | −0.507999 | − | 0.861358i | \(-0.669615\pi\) |
0.491958 | + | 0.870619i | \(0.336281\pi\) | |||||||
\(90\) | 538776.i | 0.739062i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 46852.3 | 0.0601682 | ||||||||
\(93\) | −21837.2 | − | 37823.2i | −0.0271487 | − | 0.0470229i | ||||
\(94\) | −1.48494e6 | − | 857329.i | −1.78782 | − | 1.03220i | ||||
\(95\) | 376894. | − | 652799.i | 0.439591 | − | 0.761393i | ||||
\(96\) | −634784. | + | 366493.i | −0.717484 | + | 0.414240i | ||||
\(97\) | − | 205209.i | − | 0.224844i | −0.993661 | − | 0.112422i | \(-0.964139\pi\) | ||
0.993661 | − | 0.112422i | \(-0.0358609\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 499390. | 0.514677 | ||||||||
\(100\) | 737958. | + | 1.27818e6i | 0.737958 | + | 1.27818i | ||||
\(101\) | 1.21339e6 | + | 700549.i | 1.17770 | + | 0.679946i | 0.955482 | − | 0.295050i | \(-0.0953364\pi\) |
0.222220 | + | 0.974997i | \(0.428670\pi\) | |||||||
\(102\) | 258053. | − | 446961.i | 0.243169 | − | 0.421182i | ||||
\(103\) | −448291. | + | 258821.i | −0.410250 | + | 0.236858i | −0.690897 | − | 0.722953i | \(-0.742784\pi\) |
0.280647 | + | 0.959811i | \(0.409451\pi\) | |||||||
\(104\) | 246320.i | 0.218977i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.55127e6 | −2.14210 | ||||||||
\(107\) | −323372. | − | 560097.i | −0.263968 | − | 0.457206i | 0.703325 | − | 0.710869i | \(-0.251698\pi\) |
−0.967293 | + | 0.253663i | \(0.918365\pi\) | |||||||
\(108\) | −232686. | − | 134341.i | −0.184713 | − | 0.106644i | ||||
\(109\) | 343631. | − | 595186.i | 0.265346 | − | 0.459593i | −0.702308 | − | 0.711873i | \(-0.747847\pi\) |
0.967654 | + | 0.252280i | \(0.0811805\pi\) | |||||||
\(110\) | 3.94609e6 | − | 2.27827e6i | 2.96475 | − | 1.71170i | ||||
\(111\) | 575720.i | 0.420962i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.11668e6 | 1.46697 | 0.733483 | − | 0.679708i | \(-0.237893\pi\) | ||||
0.733483 | + | 0.679708i | \(0.237893\pi\) | |||||||
\(114\) | 357543. | + | 619283.i | 0.241331 | + | 0.417998i | ||||
\(115\) | −109189. | − | 63040.4i | −0.0717937 | − | 0.0414501i | ||||
\(116\) | 329209. | − | 570207.i | 0.210910 | − | 0.365308i | ||||
\(117\) | 643952. | − | 371786.i | 0.402065 | − | 0.232132i | ||||
\(118\) | − | 2.23627e6i | − | 1.36106i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −239516. | −0.138609 | ||||||||
\(121\) | −1.22595e6 | − | 2.12340e6i | −0.692015 | − | 1.19860i | ||||
\(122\) | −3.34823e6 | − | 1.93310e6i | −1.84389 | − | 1.06457i | ||||
\(123\) | −529550. | + | 917207.i | −0.284571 | + | 0.492892i | ||||
\(124\) | 172101. | − | 99362.7i | 0.0902649 | − | 0.0521145i | ||||
\(125\) | − | 989318.i | − | 0.506531i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.29012e6 | 1.60620 | 0.803102 | − | 0.595841i | \(-0.203181\pi\) | ||||
0.803102 | + | 0.595841i | \(0.203181\pi\) | |||||||
\(128\) | −327785. | − | 567740.i | −0.156300 | − | 0.270720i | ||||
\(129\) | 166540. | + | 96151.9i | 0.0775799 | + | 0.0447908i | ||||
\(130\) | 3.39226e6 | − | 5.87556e6i | 1.54404 | − | 2.67436i | ||||
\(131\) | −193424. | + | 111674.i | −0.0860394 | + | 0.0496748i | −0.542402 | − | 0.840119i | \(-0.682485\pi\) |
0.456363 | + | 0.889794i | \(0.349152\pi\) | |||||||
\(132\) | 2.27230e6i | 0.987972i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.05609e6 | −1.68575 | ||||||||
\(135\) | 361516. | + | 626164.i | 0.146935 | + | 0.254499i | ||||
\(136\) | 198699. | + | 114719.i | 0.0789912 | + | 0.0456056i | ||||
\(137\) | 1.58525e6 | − | 2.74573e6i | 0.616504 | − | 1.06782i | −0.373615 | − | 0.927584i | \(-0.621882\pi\) |
0.990119 | − | 0.140232i | \(-0.0447849\pi\) | |||||||
\(138\) | 103583. | − | 59803.8i | 0.0394141 | − | 0.0227558i | ||||
\(139\) | − | 774740.i | − | 0.288477i | −0.989543 | − | 0.144239i | \(-0.953927\pi\) | ||
0.989543 | − | 0.144239i | \(-0.0460733\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.30105e6 | −0.820860 | ||||||||
\(142\) | 1.77521e6 | + | 3.07475e6i | 0.619989 | + | 1.07385i | ||||
\(143\) | −5.44604e6 | − | 3.14427e6i | −1.86240 | − | 1.07526i | ||||
\(144\) | −437942. | + | 758538.i | −0.146666 | + | 0.254033i | ||||
\(145\) | −1.53444e6 | + | 885912.i | −0.503323 | + | 0.290594i | ||||
\(146\) | 2.74715e6i | 0.882722i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.61962e6 | −0.808077 | ||||||||
\(149\) | −1.75461e6 | − | 3.03907e6i | −0.530421 | − | 0.918716i | −0.999370 | − | 0.0354908i | \(-0.988701\pi\) |
0.468949 | − | 0.883225i | \(-0.344633\pi\) | |||||||
\(150\) | 3.26302e6 | + | 1.88391e6i | 0.966821 | + | 0.558194i | ||||
\(151\) | −3.22601e6 | + | 5.58761e6i | −0.936989 | + | 1.62291i | −0.165940 | + | 0.986136i | \(0.553066\pi\) |
−0.771049 | + | 0.636776i | \(0.780268\pi\) | |||||||
\(152\) | −275305. | + | 158948.i | −0.0783942 | + | 0.0452609i | ||||
\(153\) | − | 692609.i | − | 0.193381i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −534776. | −0.143607 | ||||||||
\(156\) | 1.69168e6 | + | 2.93008e6i | 0.445600 | + | 0.771802i | ||||
\(157\) | 4.05557e6 | + | 2.34148e6i | 1.04798 | + | 0.605051i | 0.922083 | − | 0.386992i | \(-0.126486\pi\) |
0.125896 | + | 0.992043i | \(0.459819\pi\) | |||||||
\(158\) | −3.40600e6 | + | 5.89937e6i | −0.863523 | + | 1.49567i | ||||
\(159\) | −2.96508e6 | + | 1.71189e6i | −0.737641 | + | 0.425877i | ||||
\(160\) | 8.97512e6i | 2.19119i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −685909. | −0.161332 | ||||||||
\(163\) | −2.59116e6 | − | 4.48803e6i | −0.598318 | − | 1.03632i | −0.993069 | − | 0.117529i | \(-0.962503\pi\) |
0.394752 | − | 0.918788i | \(-0.370831\pi\) | |||||||
\(164\) | −4.17344e6 | − | 2.40953e6i | −0.946155 | − | 0.546263i | ||||
\(165\) | 3.05742e6 | − | 5.29560e6i | 0.680617 | − | 1.17886i | ||||
\(166\) | 1.07012e6 | − | 617836.i | 0.233943 | − | 0.135067i | ||||
\(167\) | − | 1.56630e6i | − | 0.336298i | −0.985762 | − | 0.168149i | \(-0.946221\pi\) | ||
0.985762 | − | 0.168149i | \(-0.0537790\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.53658e6 | −0.939871 | ||||||||
\(170\) | −3.15976e6 | − | 5.47286e6i | −0.643143 | − | 1.11396i | ||||
\(171\) | 831071. | + | 479819.i | 0.166207 | + | 0.0959598i | ||||
\(172\) | −437506. | + | 757783.i | −0.0859803 | + | 0.148922i | ||||
\(173\) | 1.07788e6 | − | 622312.i | 0.208176 | − | 0.120190i | −0.392287 | − | 0.919843i | \(-0.628316\pi\) |
0.600463 | + | 0.799652i | \(0.294983\pi\) | |||||||
\(174\) | − | 1.68085e6i | − | 0.319067i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.40754e6 | 1.35874 | ||||||||
\(177\) | −1.50053e6 | − | 2.59899e6i | −0.270597 | − | 0.468689i | ||||
\(178\) | −131359. | − | 75839.9i | −0.0232916 | − | 0.0134474i | ||||
\(179\) | −1.12800e6 | + | 1.95375e6i | −0.196675 | + | 0.340651i | −0.947448 | − | 0.319909i | \(-0.896348\pi\) |
0.750773 | + | 0.660560i | \(0.229681\pi\) | |||||||
\(180\) | −2.84914e6 | + | 1.64495e6i | −0.488536 | + | 0.282057i | ||||
\(181\) | − | 7.97198e6i | − | 1.34441i | −0.740367 | − | 0.672203i | \(-0.765348\pi\) | ||
0.740367 | − | 0.672203i | \(-0.234652\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.18839e6 | −0.846603 | ||||||||
\(184\) | 26586.1 | + | 46048.4i | 0.00426776 | + | 0.00739199i | ||||
\(185\) | 6.10502e6 | + | 3.52473e6i | 0.964210 | + | 0.556687i | ||||
\(186\) | 253660. | − | 439351.i | 0.0394196 | − | 0.0682768i | ||||
\(187\) | −5.07278e6 | + | 2.92877e6i | −0.775750 | + | 0.447879i | ||||
\(188\) | − | 1.04701e7i | − | 1.57572i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.75595e6 | 1.27656 | ||||||||
\(191\) | −2.13087e6 | − | 3.69078e6i | −0.305814 | − | 0.529685i | 0.671628 | − | 0.740888i | \(-0.265595\pi\) |
−0.977442 | + | 0.211203i | \(0.932262\pi\) | |||||||
\(192\) | −4.25935e6 | − | 2.45914e6i | −0.601783 | − | 0.347440i | ||||
\(193\) | 72886.7 | − | 126243.i | 0.0101386 | − | 0.0175605i | −0.860912 | − | 0.508755i | \(-0.830106\pi\) |
0.871050 | + | 0.491194i | \(0.163439\pi\) | |||||||
\(194\) | 2.06434e6 | − | 1.19185e6i | 0.282733 | − | 0.163236i | ||||
\(195\) | − | 9.10474e6i | − | 1.22790i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.21313e6 | −0.943463 | −0.471732 | − | 0.881742i | \(-0.656371\pi\) | ||||
−0.471732 | + | 0.881742i | \(0.656371\pi\) | |||||||
\(198\) | 2.90044e6 | + | 5.02371e6i | 0.373653 | + | 0.647186i | ||||
\(199\) | −1.52836e6 | − | 882399.i | −0.193940 | − | 0.111971i | 0.399886 | − | 0.916565i | \(-0.369050\pi\) |
−0.593826 | + | 0.804594i | \(0.702383\pi\) | |||||||
\(200\) | −837500. | + | 1.45059e6i | −0.104687 | + | 0.181324i | ||||
\(201\) | −4.71398e6 | + | 2.72162e6i | −0.580496 | + | 0.335150i | ||||
\(202\) | 1.62751e7i | 1.97455i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.15148e6 | 0.371214 | ||||||||
\(205\) | 6.48413e6 | + | 1.12308e7i | 0.752645 | + | 1.30362i | ||||
\(206\) | −5.20732e6 | − | 3.00645e6i | −0.595680 | − | 0.343916i | ||||
\(207\) | 80256.0 | − | 139007.i | 0.00904829 | − | 0.0156721i | ||||
\(208\) | 9.55185e6 | − | 5.51476e6i | 1.06144 | − | 0.612825i | ||||
\(209\) | − | 8.11587e6i | − | 0.888989i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.37033e7 | 1.45874 | 0.729369 | − | 0.684121i | \(-0.239814\pi\) | ||||
0.729369 | + | 0.684121i | \(0.239814\pi\) | |||||||
\(212\) | −7.78936e6 | − | 1.34916e7i | −0.817512 | − | 1.41597i | ||||
\(213\) | 4.12628e6 | + | 2.38231e6i | 0.426992 | + | 0.246524i | ||||
\(214\) | 3.75627e6 | − | 6.50605e6i | 0.383279 | − | 0.663859i | ||||
\(215\) | 2.03922e6 | − | 1.17734e6i | 0.205186 | − | 0.118464i | ||||
\(216\) | − | 304924.i | − | 0.0302573i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.98318e6 | 0.770560 | ||||||||
\(219\) | 1.84332e6 | + | 3.19273e6i | 0.175497 | + | 0.303969i | ||||
\(220\) | 2.40958e7 | + | 1.39117e7i | 2.26294 | + | 1.30651i | ||||
\(221\) | −4.36082e6 | + | 7.55317e6i | −0.404010 | + | 0.699765i | ||||
\(222\) | −5.79157e6 | + | 3.34376e6i | −0.529343 | + | 0.305616i | ||||
\(223\) | 2.15029e7i | 1.93902i | 0.245055 | + | 0.969509i | \(0.421194\pi\) | ||||
−0.245055 | + | 0.969509i | \(0.578806\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.05636e6 | 0.443906 | ||||||||
\(226\) | 1.22936e7 | + | 2.12932e7i | 1.06501 | + | 1.84465i | ||||
\(227\) | −3.40461e6 | − | 1.96565e6i | −0.291065 | − | 0.168046i | 0.347357 | − | 0.937733i | \(-0.387079\pi\) |
−0.638422 | + | 0.769687i | \(0.720412\pi\) | |||||||
\(228\) | −2.18325e6 | + | 3.78150e6i | −0.184204 | + | 0.319051i | ||||
\(229\) | −486988. | + | 281163.i | −0.0405520 | + | 0.0234127i | −0.520139 | − | 0.854082i | \(-0.674120\pi\) |
0.479587 | + | 0.877494i | \(0.340787\pi\) | |||||||
\(230\) | − | 1.46455e6i | − | 0.120370i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 747232. | 0.0598400 | ||||||||
\(233\) | 8.16657e6 | + | 1.41449e7i | 0.645612 | + | 1.11823i | 0.984160 | + | 0.177284i | \(0.0567310\pi\) |
−0.338548 | + | 0.940949i | \(0.609936\pi\) | |||||||
\(234\) | 7.48010e6 | + | 4.31864e6i | 0.583794 | + | 0.337054i | ||||
\(235\) | −1.40877e7 | + | 2.44007e7i | −1.08552 | + | 1.88018i | ||||
\(236\) | 1.18258e7 | − | 6.82763e6i | 0.899693 | − | 0.519438i | ||||
\(237\) | 9.14164e6i | 0.686719i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.96132e7 | −1.43666 | −0.718331 | − | 0.695702i | \(-0.755094\pi\) | ||||
−0.718331 | + | 0.695702i | \(0.755094\pi\) | |||||||
\(240\) | 5.36243e6 | + | 9.28800e6i | 0.387907 | + | 0.671875i | ||||
\(241\) | −3.11683e6 | − | 1.79950e6i | −0.222670 | − | 0.128559i | 0.384516 | − | 0.923118i | \(-0.374368\pi\) |
−0.607186 | + | 0.794560i | \(0.707702\pi\) | |||||||
\(242\) | 1.42405e7 | − | 2.46653e7i | 1.00480 | − | 1.74036i | ||||
\(243\) | −797162. | + | 460241.i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | − | 2.36080e7i | − | 1.62514i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.23024e7 | −0.826391 | ||||||||
\(247\) | −6.04210e6 | − | 1.04652e7i | −0.400956 | − | 0.694476i | ||||
\(248\) | 195316. | + | 112766.i | 0.0128051 | + | 0.00739302i | ||||
\(249\) | 829129. | − | 1.43609e6i | 0.0537061 | − | 0.0930218i | ||||
\(250\) | 9.95223e6 | − | 5.74592e6i | 0.636943 | − | 0.367739i | ||||
\(251\) | 6.49855e6i | 0.410956i | 0.978662 | + | 0.205478i | \(0.0658749\pi\) | ||||
−0.978662 | + | 0.205478i | \(0.934125\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.35749e6 | −0.0838250 | ||||||||
\(254\) | 1.91089e7 | + | 3.30976e7i | 1.16610 | + | 2.01974i | ||||
\(255\) | −7.34452e6 | − | 4.24036e6i | −0.442938 | − | 0.255730i | ||||
\(256\) | −6.28871e6 | + | 1.08924e7i | −0.374837 | + | 0.649236i | ||||
\(257\) | −2.47506e6 | + | 1.42897e6i | −0.145810 | + | 0.0841832i | −0.571130 | − | 0.820860i | \(-0.693495\pi\) |
0.425320 | + | 0.905043i | \(0.360161\pi\) | |||||||
\(258\) | 2.23379e6i | 0.130072i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.14280e7 | 2.35708 | ||||||||
\(261\) | −1.12784e6 | − | 1.95348e6i | −0.0634348 | − | 0.109872i | ||||
\(262\) | −2.24680e6 | − | 1.29719e6i | −0.124928 | − | 0.0721275i | ||||
\(263\) | 2.49913e6 | − | 4.32862e6i | 0.137380 | − | 0.237948i | −0.789124 | − | 0.614233i | \(-0.789465\pi\) |
0.926504 | + | 0.376285i | \(0.122799\pi\) | |||||||
\(264\) | −2.23332e6 | + | 1.28941e6i | −0.121378 | + | 0.0700774i | ||||
\(265\) | 4.19228e7i | 2.25275i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −203553. | −0.0106941 | ||||||||
\(268\) | −1.23838e7 | − | 2.14493e7i | −0.643352 | − | 1.11432i | ||||
\(269\) | 1.76842e7 | + | 1.02100e7i | 0.908507 | + | 0.524527i | 0.879951 | − | 0.475065i | \(-0.157576\pi\) |
0.0285567 | + | 0.999592i | \(0.490909\pi\) | |||||||
\(270\) | −4.19934e6 | + | 7.27348e6i | −0.213349 | + | 0.369531i | ||||
\(271\) | −1.06885e7 | + | 6.17102e6i | −0.537044 | + | 0.310062i | −0.743880 | − | 0.668313i | \(-0.767017\pi\) |
0.206836 | + | 0.978376i | \(0.433683\pi\) | |||||||
\(272\) | − | 1.02736e7i | − | 0.510523i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.68283e7 | 1.79032 | ||||||||
\(275\) | −2.13814e7 | − | 3.70336e7i | −1.02811 | − | 1.78073i | ||||
\(276\) | 632506. | + | 365177.i | 0.0300841 | + | 0.0173691i | ||||
\(277\) | 1.04151e7 | − | 1.80395e7i | 0.490031 | − | 0.848758i | −0.509903 | − | 0.860232i | \(-0.670319\pi\) |
0.999934 | + | 0.0114733i | \(0.00365216\pi\) | |||||||
\(278\) | 7.79365e6 | − | 4.49966e6i | 0.362749 | − | 0.209433i | ||||
\(279\) | − | 680817.i | − | 0.0313486i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.10143e7 | 0.947100 | 0.473550 | − | 0.880767i | \(-0.342972\pi\) | ||||
0.473550 | + | 0.880767i | \(0.342972\pi\) | |||||||
\(282\) | −1.33644e7 | − | 2.31479e7i | −0.595941 | − | 1.03220i | ||||
\(283\) | −9.02737e6 | − | 5.21195e6i | −0.398292 | − | 0.229954i | 0.287455 | − | 0.957794i | \(-0.407191\pi\) |
−0.685747 | + | 0.727840i | \(0.740524\pi\) | |||||||
\(284\) | −1.08399e7 | + | 1.87752e7i | −0.473227 | + | 0.819653i | ||||
\(285\) | 1.01761e7 | − | 5.87519e6i | 0.439591 | − | 0.253798i | ||||
\(286\) | − | 7.30474e7i | − | 3.12253i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.14261e7 | −0.478323 | ||||||||
\(289\) | −8.00684e6 | − | 1.38683e7i | −0.331717 | − | 0.574551i | ||||
\(290\) | −1.78240e7 | − | 1.02907e7i | −0.730821 | − | 0.421940i | ||||
\(291\) | 1.59945e6 | − | 2.77033e6i | 0.0649070 | − | 0.112422i | ||||
\(292\) | −1.45274e7 | + | 8.38741e6i | −0.583499 | + | 0.336883i | ||||
\(293\) | − | 2.85328e7i | − | 1.13433i | −0.823603 | − | 0.567167i | \(-0.808039\pi\) | ||
0.823603 | − | 0.567167i | \(-0.191961\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.67467e7 | −1.43137 | ||||||||
\(296\) | −1.48649e6 | − | 2.57467e6i | −0.0573173 | − | 0.0992765i | ||||
\(297\) | 6.74177e6 | + | 3.89236e6i | 0.257338 | + | 0.148574i | ||||
\(298\) | 2.03814e7 | − | 3.53016e7i | 0.770167 | − | 1.33397i | ||||
\(299\) | −1.75044e6 | + | 1.01062e6i | −0.0654839 | + | 0.0378072i | ||||
\(300\) | 2.30072e7i | 0.852120i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.49461e7 | −2.72100 | ||||||||
\(303\) | 1.09205e7 | + | 1.89148e7i | 0.392567 | + | 0.679946i | ||||
\(304\) | 1.23274e7 | + | 7.11724e6i | 0.438785 | + | 0.253332i | ||||
\(305\) | −3.17649e7 | + | 5.50185e7i | −1.11956 | + | 1.93914i | ||||
\(306\) | 6.96744e6 | − | 4.02265e6i | 0.243169 | − | 0.140394i | ||||
\(307\) | − | 1.02269e7i | − | 0.353450i | −0.984260 | − | 0.176725i | \(-0.943450\pi\) | ||
0.984260 | − | 0.176725i | \(-0.0565503\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.06925e6 | −0.273500 | ||||||||
\(310\) | −3.10596e6 | − | 5.37968e6i | −0.104258 | − | 0.180581i | ||||
\(311\) | 1.36331e7 | + | 7.87108e6i | 0.453225 | + | 0.261669i | 0.709191 | − | 0.705016i | \(-0.249060\pi\) |
−0.255966 | + | 0.966686i | \(0.582394\pi\) | |||||||
\(312\) | −1.91987e6 | + | 3.32532e6i | −0.0632133 | + | 0.109489i | ||||
\(313\) | −4.80881e7 | + | 2.77637e7i | −1.56821 | + | 0.905408i | −0.571834 | + | 0.820369i | \(0.693768\pi\) |
−0.996378 | + | 0.0850387i | \(0.972899\pi\) | |||||||
\(314\) | 5.43970e7i | 1.75706i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.15959e7 | −1.31822 | ||||||||
\(317\) | 3.01539e6 | + | 5.22282e6i | 0.0946600 | + | 0.163956i | 0.909467 | − | 0.415777i | \(-0.136490\pi\) |
−0.814807 | + | 0.579733i | \(0.803157\pi\) | |||||||
\(318\) | −3.44422e7 | − | 1.98852e7i | −1.07105 | − | 0.618370i | ||||
\(319\) | −9.53842e6 | + | 1.65210e7i | −0.293836 | + | 0.508938i | ||||
\(320\) | −5.21541e7 | + | 3.01112e7i | −1.59162 | + | 0.918920i | ||||
\(321\) | − | 1.00817e7i | − | 0.304804i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.12560e7 | −0.334022 | ||||||||
\(324\) | −2.09417e6 | − | 3.62721e6i | −0.0615711 | − | 0.106644i | ||||
\(325\) | −5.51416e7 | − | 3.18360e7i | −1.60631 | − | 0.927403i | ||||
\(326\) | 3.00988e7 | − | 5.21326e7i | 0.868752 | − | 1.50472i | ||||
\(327\) | 9.27803e6 | − | 5.35667e6i | 0.265346 | − | 0.153198i | ||||
\(328\) | − | 5.46910e6i | − | 0.154987i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.10295e7 | 1.97650 | ||||||||
\(331\) | −4.88277e6 | − | 8.45720e6i | −0.134643 | − | 0.233208i | 0.790818 | − | 0.612051i | \(-0.209655\pi\) |
−0.925461 | + | 0.378843i | \(0.876322\pi\) | |||||||
\(332\) | 6.53445e6 | + | 3.77267e6i | 0.178564 | + | 0.103094i | ||||
\(333\) | −4.48729e6 | + | 7.77222e6i | −0.121521 | + | 0.210481i | ||||
\(334\) | 1.57564e7 | − | 9.09699e6i | 0.422882 | − | 0.244151i | ||||
\(335\) | 6.66502e7i | 1.77283i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.70025e7 | −1.48938 | −0.744688 | − | 0.667412i | \(-0.767402\pi\) | ||||
−0.744688 | + | 0.667412i | \(0.767402\pi\) | |||||||
\(338\) | −2.63483e7 | − | 4.56366e7i | −0.682343 | − | 1.18185i | ||||
\(339\) | 2.85752e7 | + | 1.64979e7i | 0.733483 | + | 0.423477i | ||||
\(340\) | 1.92943e7 | − | 3.34187e7i | 0.490900 | − | 0.850263i | ||||
\(341\) | −4.98642e6 | + | 2.87891e6i | −0.125755 | + | 0.0726047i | ||||
\(342\) | 1.11471e7i | 0.278666i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −993041. | −0.0243945 | ||||||||
\(345\) | −982703. | − | 1.70209e6i | −0.0239312 | − | 0.0414501i | ||||
\(346\) | 1.25205e7 | + | 7.22874e6i | 0.302270 | + | 0.174516i | ||||
\(347\) | 1.83677e7 | − | 3.18139e7i | 0.439610 | − | 0.761426i | −0.558050 | − | 0.829808i | \(-0.688450\pi\) |
0.997659 | + | 0.0683813i | \(0.0217834\pi\) | |||||||
\(348\) | 8.88865e6 | − | 5.13187e6i | 0.210910 | − | 0.121769i | ||||
\(349\) | − | 6.58421e7i | − | 1.54891i | −0.632626 | − | 0.774457i | \(-0.718023\pi\) | ||
0.632626 | − | 0.774457i | \(-0.281977\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.15911e7 | 0.268043 | ||||||||
\(352\) | 4.83166e7 | + | 8.36867e7i | 1.10782 | + | 1.91879i | ||||
\(353\) | −2.76008e7 | − | 1.59353e7i | −0.627476 | − | 0.362273i | 0.152298 | − | 0.988335i | \(-0.451333\pi\) |
−0.779774 | + | 0.626061i | \(0.784666\pi\) | |||||||
\(354\) | 1.74300e7 | − | 3.01897e7i | 0.392905 | − | 0.680532i | ||||
\(355\) | 5.05247e7 | − | 2.91704e7i | 1.12932 | − | 0.652015i | ||||
\(356\) | − | 926197.i | − | 0.0205283i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.62055e7 | −0.571141 | ||||||||
\(359\) | 1.91128e7 | + | 3.31044e7i | 0.413087 | + | 0.715488i | 0.995226 | − | 0.0976018i | \(-0.0311171\pi\) |
−0.582138 | + | 0.813090i | \(0.697784\pi\) | |||||||
\(360\) | −3.23346e6 | − | 1.86684e6i | −0.0693043 | − | 0.0400128i | ||||
\(361\) | −1.57251e7 | + | 2.72367e7i | −0.334251 | + | 0.578940i | ||||
\(362\) | 8.01957e7 | − | 4.63010e7i | 1.69054 | − | 0.976033i | ||||
\(363\) | − | 3.82212e7i | − | 0.799070i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.51415e7 | 0.928320 | ||||||||
\(366\) | −3.01340e7 | − | 5.21937e7i | −0.614630 | − | 1.06457i | ||||
\(367\) | −8.43371e7 | − | 4.86920e7i | −1.70616 | − | 0.985053i | −0.939206 | − | 0.343354i | \(-0.888437\pi\) |
−0.766956 | − | 0.641699i | \(-0.778230\pi\) | |||||||
\(368\) | 1.19045e6 | − | 2.06192e6i | 0.0238874 | − | 0.0413741i | ||||
\(369\) | −1.42978e7 | + | 8.25486e6i | −0.284571 | + | 0.164297i | ||||
\(370\) | 8.18861e7i | 1.61661i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.09782e6 | 0.0601766 | ||||||||
\(373\) | −1.05213e7 | − | 1.82235e7i | −0.202742 | − | 0.351160i | 0.746669 | − | 0.665196i | \(-0.231652\pi\) |
−0.949411 | + | 0.314036i | \(0.898319\pi\) | |||||||
\(374\) | −5.89251e7 | − | 3.40204e7i | −1.12638 | − | 0.650317i | ||||
\(375\) | 7.71097e6 | − | 1.33558e7i | 0.146223 | − | 0.253265i | ||||
\(376\) | 1.02905e7 | − | 5.94122e6i | 0.193586 | − | 0.111767i | ||||
\(377\) | 2.84046e7i | 0.530109i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.11794e7 | −0.756418 | −0.378209 | − | 0.925720i | \(-0.623460\pi\) | ||||
−0.378209 | + | 0.925720i | \(0.623460\pi\) | |||||||
\(380\) | 2.67331e7 | + | 4.63030e7i | 0.487189 | + | 0.843837i | ||||
\(381\) | 4.44166e7 | + | 2.56440e7i | 0.803102 | + | 0.463671i | ||||
\(382\) | 2.47521e7 | − | 4.28718e7i | 0.444039 | − | 0.769098i | ||||
\(383\) | 1.31798e7 | − | 7.60939e6i | 0.234592 | − | 0.135442i | −0.378096 | − | 0.925766i | \(-0.623421\pi\) |
0.612689 | + | 0.790324i | \(0.290088\pi\) | |||||||
\(384\) | − | 1.02193e7i | − | 0.180480i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.69329e6 | 0.0294422 | ||||||||
\(387\) | 1.49886e6 | + | 2.59610e6i | 0.0258600 | + | 0.0447908i | ||||
\(388\) | 1.26054e7 | + | 7.27774e6i | 0.215805 | + | 0.124595i | ||||
\(389\) | 3.37497e7 | − | 5.84563e7i | 0.573353 | − | 0.993076i | −0.422866 | − | 0.906192i | \(-0.638976\pi\) |
0.996218 | − | 0.0868835i | \(-0.0276908\pi\) | |||||||
\(390\) | 9.15909e7 | − | 5.28800e7i | 1.54404 | − | 0.891452i | ||||
\(391\) | 1.88271e6i | 0.0314958i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.48164e6 | −0.0573596 | ||||||||
\(394\) | −4.18936e7 | − | 7.25619e7i | −0.684951 | − | 1.18637i | ||||
\(395\) | 9.69393e7 | + | 5.59679e7i | 1.57293 | + | 0.908130i | ||||
\(396\) | −1.77109e7 | + | 3.06761e7i | −0.285203 | + | 0.493986i | ||||
\(397\) | −8.14198e6 | + | 4.70078e6i | −0.130124 | + | 0.0751273i | −0.563649 | − | 0.826014i | \(-0.690603\pi\) |
0.433525 | + | 0.901142i | \(0.357270\pi\) | |||||||
\(398\) | − | 2.04998e7i | − | 0.325162i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.50019e7 | 1.17190 | ||||||||
\(401\) | 2.77486e7 | + | 4.80620e7i | 0.430336 | + | 0.745364i | 0.996902 | − | 0.0786521i | \(-0.0250616\pi\) |
−0.566566 | + | 0.824016i | \(0.691728\pi\) | |||||||
\(402\) | −5.47573e7 | − | 3.16141e7i | −0.842876 | − | 0.486635i | ||||
\(403\) | −4.28658e6 | + | 7.42457e6i | −0.0654931 | + | 0.113437i | ||||
\(404\) | −8.60654e7 | + | 4.96899e7i | −1.30522 | + | 0.753571i | ||||
\(405\) | 1.12709e7i | 0.169666i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.59001e7 | 1.12579 | ||||||||
\(408\) | 1.78829e6 | + | 3.09741e6i | 0.0263304 | + | 0.0456056i | ||||
\(409\) | −1.41570e7 | − | 8.17357e6i | −0.206920 | − | 0.119465i | 0.392959 | − | 0.919556i | \(-0.371451\pi\) |
−0.599879 | + | 0.800091i | \(0.704785\pi\) | |||||||
\(410\) | −7.53192e7 | + | 1.30457e8i | −1.09283 | + | 1.89284i | ||||
\(411\) | 4.28017e7 | − | 2.47116e7i | 0.616504 | − | 0.355939i | ||||
\(412\) | − | 3.67163e7i | − | 0.525010i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.86450e6 | 0.0262761 | ||||||||
\(415\) | −1.01524e7 | − | 1.75844e7i | −0.142044 | − | 0.246027i | ||||
\(416\) | 1.24606e8 | + | 7.19413e7i | 1.73085 | + | 0.999306i | ||||
\(417\) | 6.03850e6 | − | 1.04590e7i | 0.0832762 | − | 0.144239i | ||||
\(418\) | 8.16432e7 | − | 4.71367e7i | 1.11787 | − | 0.645402i | ||||
\(419\) | − | 3.75022e7i | − | 0.509818i | −0.966965 | − | 0.254909i | \(-0.917955\pi\) | ||
0.966965 | − | 0.254909i | \(-0.0820455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.17501e7 | 1.22959 | 0.614795 | − | 0.788687i | \(-0.289239\pi\) | ||||
0.614795 | + | 0.788687i | \(0.289239\pi\) | |||||||
\(422\) | 7.95882e7 | + | 1.37851e8i | 1.05904 | + | 1.83431i | ||||
\(423\) | −3.10642e7 | − | 1.79349e7i | −0.410430 | − | 0.236962i | ||||
\(424\) | 8.84006e6 | − | 1.53114e7i | 0.115973 | − | 0.200871i | ||||
\(425\) | −5.13623e7 | + | 2.96540e7i | −0.669080 | + | 0.386293i | ||||
\(426\) | 5.53455e7i | 0.715902i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.58735e7 | 0.585101 | ||||||||
\(429\) | −4.90144e7 | − | 8.48954e7i | −0.620800 | − | 1.07526i | ||||
\(430\) | 2.36874e7 | + | 1.36759e7i | 0.297928 | + | 0.172009i | ||||
\(431\) | 6.89035e7 | − | 1.19344e8i | 0.860616 | − | 1.49063i | −0.0107202 | − | 0.999943i | \(-0.503412\pi\) |
0.871336 | − | 0.490687i | \(-0.163254\pi\) | |||||||
\(432\) | −1.18244e7 | + | 6.82684e6i | −0.146666 | + | 0.0846776i | ||||
\(433\) | 2.00324e7i | 0.246757i | 0.992360 | + | 0.123378i | \(0.0393729\pi\) | ||||
−0.992360 | + | 0.123378i | \(0.960627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.76200e7 | −0.335549 | ||||||||
\(436\) | 2.43737e7 | + | 4.22165e7i | 0.294078 | + | 0.509357i | ||||
\(437\) | −2.25909e6 | − | 1.30428e6i | −0.0270700 | − | 0.0156289i | ||||
\(438\) | −2.14119e7 | + | 3.70865e7i | −0.254820 | + | 0.441361i | ||||
\(439\) | −7.45669e7 | + | 4.30512e7i | −0.881359 | + | 0.508853i | −0.871106 | − | 0.491095i | \(-0.836597\pi\) |
−0.0102525 | + | 0.999947i | \(0.503264\pi\) | |||||||
\(440\) | 3.15765e7i | 0.370686i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.01310e8 | −1.17324 | ||||||||
\(443\) | 4.03937e6 | + | 6.99640e6i | 0.0464625 | + | 0.0804754i | 0.888321 | − | 0.459222i | \(-0.151872\pi\) |
−0.841859 | + | 0.539698i | \(0.818539\pi\) | |||||||
\(444\) | −3.53648e7 | − | 2.04179e7i | −0.404038 | − | 0.233272i | ||||
\(445\) | −1.24621e6 | + | 2.15850e6i | −0.0141420 | + | 0.0244947i | ||||
\(446\) | −2.16312e8 | + | 1.24888e8i | −2.43824 | + | 1.40772i | ||||
\(447\) | − | 5.47032e7i | − | 0.612477i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.16486e7 | −0.570584 | −0.285292 | − | 0.958441i | \(-0.592091\pi\) | ||||
−0.285292 | + | 0.958441i | \(0.592091\pi\) | |||||||
\(450\) | 2.93672e7 | + | 5.08655e7i | 0.322274 | + | 0.558194i | ||||
\(451\) | 1.20920e8 | + | 6.98132e7i | 1.31816 | + | 0.761041i | ||||
\(452\) | −7.50680e7 | + | 1.30022e8i | −0.812904 | + | 1.40799i | ||||
\(453\) | −8.71022e7 | + | 5.02885e7i | −0.936989 | + | 0.540971i | ||||
\(454\) | − | 4.56657e7i | − | 0.488004i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.95549e6 | −0.0522628 | ||||||||
\(457\) | 1.99697e7 | + | 3.45885e7i | 0.209229 | + | 0.362396i | 0.951472 | − | 0.307735i | \(-0.0995711\pi\) |
−0.742243 | + | 0.670131i | \(0.766238\pi\) | |||||||
\(458\) | −5.65682e6 | − | 3.26597e6i | −0.0588811 | − | 0.0339950i | ||||
\(459\) | 5.39835e6 | − | 9.35022e6i | 0.0558243 | − | 0.0966905i | ||||
\(460\) | 7.74478e6 | − | 4.47145e6i | 0.0795675 | − | 0.0459383i | ||||
\(461\) | − | 1.40914e7i | − | 0.143831i | −0.997411 | − | 0.0719153i | \(-0.977089\pi\) | ||
0.997411 | − | 0.0719153i | \(-0.0229111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.25200e8 | 1.26142 | 0.630712 | − | 0.776017i | \(-0.282763\pi\) | ||||
0.630712 | + | 0.776017i | \(0.282763\pi\) | |||||||
\(464\) | −1.67295e7 | − | 2.89763e7i | −0.167467 | − | 0.290061i | ||||
\(465\) | −7.21948e6 | − | 4.16817e6i | −0.0718037 | − | 0.0414559i | ||||
\(466\) | −9.48623e7 | + | 1.64306e8i | −0.937423 | + | 1.62367i | ||||
\(467\) | 8.96567e7 | − | 5.17633e7i | 0.880303 | − | 0.508243i | 0.00954455 | − | 0.999954i | \(-0.496962\pi\) |
0.870758 | + | 0.491711i | \(0.163628\pi\) | |||||||
\(468\) | 5.27415e7i | 0.514535i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.27284e8 | −3.15233 | ||||||||
\(471\) | 3.65001e7 | + | 6.32200e7i | 0.349326 | + | 0.605051i | ||||
\(472\) | 1.34210e7 | + | 7.74860e6i | 0.127631 | + | 0.0736880i | ||||
\(473\) | 1.26762e7 | − | 2.19558e7i | 0.119786 | − | 0.207475i | ||||
\(474\) | −9.19621e7 | + | 5.30944e7i | −0.863523 | + | 0.498555i | ||||
\(475\) | − | 8.21738e7i | − | 0.766747i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.33714e7 | −0.491760 | ||||||||
\(478\) | −1.13913e8 | − | 1.97303e8i | −1.04301 | − | 1.80655i | ||||
\(479\) | 6.75301e7 | + | 3.89885e7i | 0.614456 | + | 0.354757i | 0.774708 | − | 0.632320i | \(-0.217897\pi\) |
−0.160251 | + | 0.987076i | \(0.551230\pi\) | |||||||
\(480\) | −6.99541e7 | + | 1.21164e8i | −0.632542 | + | 1.09560i | ||||
\(481\) | 9.78713e7 | − | 5.65060e7i | 0.879468 | − | 0.507761i | ||||
\(482\) | − | 4.18058e7i | − | 0.373333i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.73913e8 | 1.53389 | ||||||||
\(485\) | −1.95846e7 | − | 3.39216e7i | −0.171668 | − | 0.297338i | ||||
\(486\) | −9.25978e6 | − | 5.34613e6i | −0.0806662 | − | 0.0465727i | ||||
\(487\) | −7.13992e7 | + | 1.23667e8i | −0.618168 | + | 1.07070i | 0.371651 | + | 0.928372i | \(0.378792\pi\) |
−0.989820 | + | 0.142327i | \(0.954542\pi\) | |||||||
\(488\) | 2.32029e7 | − | 1.33962e7i | 0.199657 | − | 0.115272i | ||||
\(489\) | − | 8.07845e7i | − | 0.690878i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.07818e7 | 0.429006 | 0.214503 | − | 0.976723i | \(-0.431187\pi\) | ||||
0.214503 | + | 0.976723i | \(0.431187\pi\) | |||||||
\(492\) | −3.75609e7 | − | 6.50574e7i | −0.315385 | − | 0.546263i | ||||
\(493\) | 2.29132e7 | + | 1.32289e7i | 0.191225 | + | 0.110404i | ||||
\(494\) | 7.01846e7 | − | 1.21563e8i | 0.582185 | − | 1.00837i | ||||
\(495\) | 8.25503e7 | − | 4.76604e7i | 0.680617 | − | 0.392955i | ||||
\(496\) | − | 1.00987e7i | − | 0.0827598i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.92622e7 | 0.155962 | ||||||||
\(499\) | −6.32522e7 | − | 1.09556e8i | −0.509065 | − | 0.881727i | −0.999945 | − | 0.0104998i | \(-0.996658\pi\) |
0.490879 | − | 0.871228i | \(-0.336676\pi\) | |||||||
\(500\) | 6.07709e7 | + | 3.50861e7i | 0.486167 | + | 0.280689i | ||||
\(501\) | 1.22081e7 | − | 2.11450e7i | 0.0970808 | − | 0.168149i | ||||
\(502\) | −6.53735e7 | + | 3.77434e7i | −0.516762 | + | 0.298353i | ||||
\(503\) | − | 7.36652e6i | − | 0.0578840i | −0.999581 | − | 0.0289420i | \(-0.990786\pi\) | ||
0.999581 | − | 0.0289420i | \(-0.00921381\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.67434e8 | 2.07655 | ||||||||
\(506\) | −7.88423e6 | − | 1.36559e7i | −0.0608566 | − | 0.105407i | ||||
\(507\) | −6.12438e7 | − | 3.53591e7i | −0.469936 | − | 0.271317i | ||||
\(508\) | −1.16684e8 | + | 2.02103e8i | −0.890062 | + | 1.54163i | ||||
\(509\) | 1.98695e8 | − | 1.14716e8i | 1.50672 | − | 0.869906i | 0.506753 | − | 0.862092i | \(-0.330846\pi\) |
0.999969 | − | 0.00781491i | \(-0.00248759\pi\) | |||||||
\(510\) | − | 9.85116e7i | − | 0.742637i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.88055e8 | −1.40112 | ||||||||
\(513\) | 7.47964e6 | + | 1.29551e7i | 0.0554024 | + | 0.0959598i | ||||
\(514\) | −2.87501e7 | − | 1.65989e7i | −0.211714 | − | 0.122233i | ||||
\(515\) | −4.94024e7 | + | 8.55674e7i | −0.361681 | + | 0.626450i | ||||
\(516\) | −1.18127e7 | + | 6.82004e6i | −0.0859803 | + | 0.0496407i | ||||
\(517\) | 3.03359e8i | 2.19526i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.94018e7 | 0.138784 | ||||||||
\(520\) | 2.35081e7 | + | 4.07172e7i | 0.167189 | + | 0.289579i | ||||
\(521\) | 9.29834e7 | + | 5.36840e7i | 0.657495 | + | 0.379605i | 0.791322 | − | 0.611400i | \(-0.209393\pi\) |
−0.133827 | + | 0.991005i | \(0.542727\pi\) | |||||||
\(522\) | 1.31010e7 | − | 2.26915e7i | 0.0921068 | − | 0.159534i | ||||
\(523\) | −1.30357e8 | + | 7.52614e7i | −0.911230 | + | 0.526099i | −0.880827 | − | 0.473439i | \(-0.843013\pi\) |
−0.0304034 | + | 0.999538i | \(0.509679\pi\) | |||||||
\(524\) | − | 1.58420e7i | − | 0.110107i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.80595e7 | 0.398948 | ||||||||
\(527\) | 3.99279e6 | + | 6.91571e6i | 0.0272800 | + | 0.0472503i | ||||
\(528\) | 1.00002e8 | + | 5.77361e7i | 0.679370 | + | 0.392234i | ||||
\(529\) | 7.37998e7 | − | 1.27825e8i | 0.498526 | − | 0.863473i | ||||
\(530\) | −4.21731e8 | + | 2.43486e8i | −2.83275 | + | 1.63549i | ||||
\(531\) | − | 4.67818e7i | − | 0.312459i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.07898e8 | 1.37299 | ||||||||
\(534\) | −1.18223e6 | − | 2.04768e6i | −0.00776385 | − | 0.0134474i | ||||
\(535\) | −1.06908e8 | − | 6.17235e7i | −0.698151 | − | 0.403078i | ||||
\(536\) | 1.40542e7 | − | 2.43426e7i | 0.0912666 | − | 0.158078i | ||||
\(537\) | −3.04560e7 | + | 1.75838e7i | −0.196675 | + | 0.113550i | ||||
\(538\) | 2.37197e8i | 1.52322i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.12846e7 | −0.325691 | ||||||||
\(541\) | 3.02874e7 | + | 5.24593e7i | 0.191280 | + | 0.331307i | 0.945675 | − | 0.325114i | \(-0.105403\pi\) |
−0.754395 | + | 0.656421i | \(0.772069\pi\) | |||||||
\(542\) | −1.24157e8 | − | 7.16821e7i | −0.779783 | − | 0.450208i | ||||
\(543\) | 6.21354e7 | − | 1.07622e8i | 0.388097 | − | 0.672203i | ||||
\(544\) | 1.16066e8 | − | 6.70107e7i | 0.720955 | − | 0.416243i | ||||
\(545\) | − | 1.31181e8i | − | 0.810365i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.68955e8 | −1.64330 | −0.821651 | − | 0.569992i | \(-0.806946\pi\) | ||||
−0.821651 | + | 0.569992i | \(0.806946\pi\) | |||||||
\(548\) | 1.12442e8 | + | 1.94755e8i | 0.683259 | + | 1.18344i | ||||
\(549\) | −7.00433e7 | − | 4.04395e7i | −0.423301 | − | 0.244393i | ||||
\(550\) | 2.48365e8 | − | 4.30180e8i | 1.49280 | − | 2.58561i | ||||
\(551\) | −3.17471e7 | + | 1.83292e7i | −0.189780 | + | 0.109569i | ||||
\(552\) | 828871.i | 0.00492799i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.41962e8 | 1.42304 | ||||||||
\(555\) | 5.49451e7 | + | 9.51678e7i | 0.321403 | + | 0.556687i | ||||
\(556\) | 4.75900e7 | + | 2.74761e7i | 0.276880 | + | 0.159857i | ||||
\(557\) | −1.00886e8 | + | 1.74739e8i | −0.583800 | + | 1.01117i | 0.411223 | + | 0.911535i | \(0.365102\pi\) |
−0.995024 | + | 0.0996375i | \(0.968232\pi\) | |||||||
\(558\) | 6.84881e6 | − | 3.95416e6i | 0.0394196 | − | 0.0227589i | ||||
\(559\) | − | 3.77486e7i | − | 0.216105i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.13101e7 | −0.517166 | ||||||||
\(562\) | 1.22050e8 | + | 2.11397e8i | 0.687591 | + | 1.19094i | ||||
\(563\) | −1.52694e8 | − | 8.81577e7i | −0.855650 | − | 0.494010i | 0.00690346 | − | 0.999976i | \(-0.497803\pi\) |
−0.862553 | + | 0.505967i | \(0.831136\pi\) | |||||||
\(564\) | 8.16067e7 | − | 1.41347e8i | 0.454871 | − | 0.787860i | ||||
\(565\) | 3.49892e8 | − | 2.02010e8i | 1.93994 | − | 1.12003i | ||||
\(566\) | − | 1.21083e8i | − | 0.667783i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.46041e7 | −0.134265 | ||||||||
\(569\) | −1.00368e8 | − | 1.73843e8i | −0.544828 | − | 0.943669i | −0.998618 | − | 0.0525605i | \(-0.983262\pi\) |
0.453790 | − | 0.891109i | \(-0.350072\pi\) | |||||||
\(570\) | 1.18205e8 | + | 6.82459e7i | 0.638282 | + | 0.368512i | ||||
\(571\) | 2.23204e7 | − | 3.86600e7i | 0.119893 | − | 0.207660i | −0.799832 | − | 0.600224i | \(-0.795078\pi\) |
0.919725 | + | 0.392563i | \(0.128412\pi\) | |||||||
\(572\) | 3.86287e8 | − | 2.23023e8i | 2.06406 | − | 1.19169i | ||||
\(573\) | − | 6.64340e7i | − | 0.353123i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.37446e7 | −0.0722986 | ||||||||
\(576\) | −3.83342e7 | − | 6.63967e7i | −0.200594 | − | 0.347440i | ||||
\(577\) | 2.24118e8 | + | 1.29395e8i | 1.16668 | + | 0.673581i | 0.952895 | − | 0.303301i | \(-0.0980887\pi\) |
0.213781 | + | 0.976882i | \(0.431422\pi\) | |||||||
\(578\) | 9.30069e7 | − | 1.61093e8i | 0.481650 | − | 0.834243i | ||||
\(579\) | 1.96794e6 | − | 1.13619e6i | 0.0101386 | − | 0.00585350i | ||||
\(580\) | − | 1.25675e8i | − | 0.644119i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.71582e7 | 0.188489 | ||||||||
\(583\) | 2.25687e8 | + | 3.90901e8i | 1.13894 | + | 1.97270i | ||||
\(584\) | −1.64870e7 | − | 9.51877e6i | −0.0827757 | − | 0.0477906i | ||||
\(585\) | 7.09644e7 | − | 1.22914e8i | 0.354465 | − | 0.613951i | ||||
\(586\) | 2.87031e8 | − | 1.65717e8i | 1.42638 | − | 0.823522i | ||||
\(587\) | 3.41902e8i | 1.69039i | 0.534457 | + | 0.845196i | \(0.320516\pi\) | ||||
−0.534457 | + | 0.845196i | \(0.679484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.10643e7 | −0.0541476 | ||||||||
\(590\) | −2.13424e8 | − | 3.69661e8i | −1.03917 | − | 1.79989i | ||||
\(591\) | −9.73773e7 | − | 5.62208e7i | −0.471732 | − | 0.272354i | ||||
\(592\) | −6.65608e7 | + | 1.15287e8i | −0.320814 | + | 0.555666i | ||||
\(593\) | −1.27791e8 | + | 7.37803e7i | −0.612826 | + | 0.353815i | −0.774071 | − | 0.633099i | \(-0.781782\pi\) |
0.161245 | + | 0.986914i | \(0.448449\pi\) | |||||||
\(594\) | 9.04268e7i | 0.431458i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.48908e8 | 1.17571 | ||||||||
\(597\) | −1.37552e7 | − | 2.38248e7i | −0.0646465 | − | 0.111971i | ||||
\(598\) | −2.03331e7 | − | 1.17393e7i | −0.0950822 | − | 0.0548957i | ||||
\(599\) | 3.32461e7 | − | 5.75840e7i | 0.154690 | − | 0.267930i | −0.778256 | − | 0.627947i | \(-0.783896\pi\) |
0.932946 | + | 0.360017i | \(0.117229\pi\) | |||||||
\(600\) | −2.26125e7 | + | 1.30553e7i | −0.104687 | + | 0.0604413i | ||||
\(601\) | 3.71302e7i | 0.171042i | 0.996336 | + | 0.0855212i | \(0.0272555\pi\) | ||||
−0.996336 | + | 0.0855212i | \(0.972744\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.48516e7 | −0.386998 | ||||||||
\(604\) | −2.28820e8 | − | 3.96328e8i | −1.03845 | − | 1.79864i | ||||
\(605\) | −4.05303e8 | − | 2.34002e8i | −1.83026 | − | 1.05670i | ||||
\(606\) | −1.26852e8 | + | 2.19713e8i | −0.570004 | + | 0.987276i | ||||
\(607\) | −1.10132e8 | + | 6.35850e7i | −0.492436 | + | 0.284308i | −0.725584 | − | 0.688133i | \(-0.758430\pi\) |
0.233149 | + | 0.972441i | \(0.425097\pi\) | |||||||
\(608\) | 1.85692e8i | 0.826195i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.37959e8 | −3.25119 | ||||||||
\(611\) | 2.25845e8 | + | 3.91174e8i | 0.990116 | + | 1.71493i | ||||
\(612\) | 4.25450e7 | + | 2.45634e7i | 0.185607 | + | 0.107160i | ||||
\(613\) | 7.14975e7 | − | 1.23837e8i | 0.310391 | − | 0.537614i | −0.668056 | − | 0.744111i | \(-0.732873\pi\) |
0.978447 | + | 0.206498i | \(0.0662066\pi\) | |||||||
\(614\) | 1.02879e8 | − | 5.93974e7i | 0.444450 | − | 0.256603i | ||||
\(615\) | 2.02155e8i | 0.869079i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.96115e8 | −1.26068 | −0.630339 | − | 0.776320i | \(-0.717084\pi\) | ||||
−0.630339 | + | 0.776320i | \(0.717084\pi\) | |||||||
\(618\) | −4.68659e7 | − | 8.11742e7i | −0.198560 | − | 0.343916i | ||||
\(619\) | −2.81343e8 | − | 1.62433e8i | −1.18622 | − | 0.684862i | −0.228771 | − | 0.973480i | \(-0.573471\pi\) |
−0.957444 | + | 0.288619i | \(0.906804\pi\) | |||||||
\(620\) | 1.89658e7 | − | 3.28498e7i | 0.0795786 | − | 0.137834i | ||||
\(621\) | 2.16691e6 | − | 1.25107e6i | 0.00904829 | − | 0.00522403i | ||||
\(622\) | 1.82860e8i | 0.759884i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.71933e8 | 0.707630 | ||||||||
\(625\) | 6.81453e7 | + | 1.18031e8i | 0.279123 | + | 0.483456i | ||||
\(626\) | −5.58588e8 | − | 3.22501e8i | −2.27703 | − | 1.31464i | ||||
\(627\) | 6.32569e7 | − | 1.09564e8i | 0.256629 | − | 0.444494i | ||||
\(628\) | −2.87661e8 | + | 1.66081e8i | −1.16145 | + | 0.670566i | ||||
\(629\) | − | 1.05267e8i | − | 0.422998i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.40735e8 | −0.560163 | −0.280082 | − | 0.959976i | \(-0.590362\pi\) | ||||
−0.280082 | + | 0.959976i | \(0.590362\pi\) | |||||||
\(632\) | −2.36034e7 | − | 4.08822e7i | −0.0935023 | − | 0.161951i | ||||
\(633\) | 1.84994e8 | + | 1.06806e8i | 0.729369 | + | 0.421101i | ||||
\(634\) | −3.50266e7 | + | 6.06679e7i | −0.137446 | + | 0.238063i | ||||
\(635\) | 5.43864e8 | − | 3.14000e8i | 2.12407 | − | 1.22633i | ||||
\(636\) | − | 2.42848e8i | − | 0.943982i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.21595e8 | −0.853294 | ||||||||
\(639\) | 3.71365e7 | + | 6.43224e7i | 0.142331 | + | 0.246524i | ||||
\(640\) | −1.08367e8 | − | 6.25658e7i | −0.413388 | − | 0.238670i | ||||
\(641\) | 1.08339e8 | − | 1.87648e8i | 0.411348 | − | 0.712476i | −0.583689 | − | 0.811977i | \(-0.698391\pi\) |
0.995037 | + | 0.0995014i | \(0.0317248\pi\) | |||||||
\(642\) | 1.01419e8 | − | 5.85544e7i | 0.383279 | − | 0.221286i | ||||
\(643\) | − | 2.61645e8i | − | 0.984192i | −0.870541 | − | 0.492096i | \(-0.836231\pi\) | ||
0.870541 | − | 0.492096i | \(-0.163769\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.67059e7 | 0.136791 | ||||||||
\(646\) | −6.53743e7 | − | 1.13232e8i | −0.242499 | − | 0.420020i | ||||
\(647\) | 9.29409e7 | + | 5.36595e7i | 0.343158 | + | 0.198122i | 0.661668 | − | 0.749797i | \(-0.269849\pi\) |
−0.318510 | + | 0.947920i | \(0.603182\pi\) | |||||||
\(648\) | 2.37665e6 | − | 4.11648e6i | 0.00873454 | − | 0.0151287i | ||||
\(649\) | −3.42637e8 | + | 1.97822e8i | −1.25343 | + | 0.723669i | ||||
\(650\) | − | 7.39610e8i | − | 2.69316i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.67582e8 | 1.32621 | ||||||||
\(653\) | −2.21977e8 | − | 3.84475e8i | −0.797200 | − | 1.38079i | −0.921432 | − | 0.388539i | \(-0.872980\pi\) |
0.124232 | − | 0.992253i | \(-0.460353\pi\) | |||||||
\(654\) | 1.07773e8 | + | 6.22228e7i | 0.385280 | + | 0.222442i | ||||
\(655\) | −2.13156e7 | + | 3.69198e7i | −0.0758533 | + | 0.131382i | ||||
\(656\) | −2.12082e8 | + | 1.22446e8i | −0.751265 | + | 0.433743i | ||||
\(657\) | 5.74691e7i | 0.202646i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.87037e7 | −0.0653538 | −0.0326769 | − | 0.999466i | \(-0.510403\pi\) | ||||
−0.0326769 | + | 0.999466i | \(0.510403\pi\) | |||||||
\(660\) | 2.16862e8 | + | 3.75617e8i | 0.754315 | + | 1.30651i | ||||
\(661\) | 1.85577e7 | + | 1.07143e7i | 0.0642570 | + | 0.0370988i | 0.531784 | − | 0.846880i | \(-0.321522\pi\) |
−0.467527 | + | 0.883979i | \(0.654855\pi\) | |||||||
\(662\) | 5.67179e7 | − | 9.82383e7i | 0.195500 | − | 0.338616i | ||||
\(663\) | −1.17742e8 | + | 6.79785e7i | −0.404010 | + | 0.233255i | ||||
\(664\) | 8.56311e6i | 0.0292501i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.04248e8 | −0.352895 | ||||||||
\(667\) | 3.06580e6 | + | 5.31012e6i | 0.0103316 | + | 0.0178948i | ||||
\(668\) | 9.62130e7 | + | 5.55486e7i | 0.322778 | + | 0.186356i | ||||
\(669\) | −1.67598e8 | + | 2.90289e8i | −0.559746 | + | 0.969509i | ||||
\(670\) | −6.70481e8 | + | 3.87102e8i | −2.22927 | + | 1.28707i | ||||
\(671\) | 6.84012e8i | 2.26410i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.29593e8 | 0.753205 | 0.376603 | − | 0.926375i | \(-0.377092\pi\) | ||||
0.376603 | + | 0.926375i | \(0.377092\pi\) | |||||||
\(674\) | −3.31069e8 | − | 5.73428e8i | −1.08128 | − | 1.87283i | ||||
\(675\) | 6.82609e7 | + | 3.94105e7i | 0.221953 | + | 0.128145i | ||||
\(676\) | 1.60890e8 | − | 2.78669e8i | 0.520820 | − | 0.902087i | ||||
\(677\) | −1.96110e7 | + | 1.13224e7i | −0.0632024 | + | 0.0364899i | −0.531268 | − | 0.847204i | \(-0.678284\pi\) |
0.468066 | + | 0.883694i | \(0.344951\pi\) | |||||||
\(678\) | 3.83277e8i | 1.22977i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.37938e7 | 0.139279 | ||||||||
\(681\) | −3.06415e7 | − | 5.30726e7i | −0.0970216 | − | 0.168046i | ||||
\(682\) | −5.79219e7 | − | 3.34412e7i | −0.182595 | − | 0.105421i | ||||
\(683\) | −1.12310e8 | + | 1.94527e8i | −0.352499 | + | 0.610546i | −0.986687 | − | 0.162633i | \(-0.948001\pi\) |
0.634188 | + | 0.773179i | \(0.281335\pi\) | |||||||
\(684\) | −5.89478e7 | + | 3.40335e7i | −0.184204 | + | 0.106350i | ||||
\(685\) | − | 6.05167e8i | − | 1.88280i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.76579e6 | −0.0270346 | ||||||||
\(688\) | 2.22328e7 | + | 3.85084e7i | 0.0682700 | + | 0.118247i | ||||
\(689\) | 5.82036e8 | + | 3.36038e8i | 1.77947 | + | 1.02738i | ||||
\(690\) | 1.14150e7 | − | 1.97714e7i | 0.0347480 | − | 0.0601852i | ||||
\(691\) | −2.19279e8 | + | 1.26601e8i | −0.664603 | + | 0.383709i | −0.794029 | − | 0.607880i | \(-0.792020\pi\) |
0.129426 | + | 0.991589i | \(0.458687\pi\) | |||||||
\(692\) | 8.82811e7i | 0.266409i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.26717e8 | 1.27662 | ||||||||
\(695\) | −7.39390e7 | − | 1.28066e8i | −0.220252 | − | 0.381487i | ||||
\(696\) | 1.00876e7 | + | 5.82409e6i | 0.0299200 | + | 0.0172743i | ||||
\(697\) | 9.68246e7 | − | 1.67705e8i | 0.285948 | − | 0.495277i | ||||
\(698\) | 6.62351e8 | − | 3.82409e8i | 1.94770 | − | 1.12451i | ||||
\(699\) | 2.54608e8i | 0.745489i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.18180e8 | 0.923674 | 0.461837 | − | 0.886965i | \(-0.347191\pi\) | ||||
0.461837 | + | 0.886965i | \(0.347191\pi\) | |||||||
\(702\) | 6.73209e7 | + | 1.16603e8i | 0.194598 | + | 0.337054i | ||||
\(703\) | 1.26311e8 | + | 7.29255e7i | 0.363558 | + | 0.209900i | ||||
\(704\) | −3.24201e8 | + | 5.61532e8i | −0.929171 | + | 1.60937i | ||||
\(705\) | −3.80369e8 | + | 2.19606e8i | −1.08552 | + | 0.626725i | ||||
\(706\) | − | 3.70207e8i | − | 1.05204i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.12864e8 | 0.599796 | ||||||||
\(709\) | −1.35142e8 | − | 2.34072e8i | −0.379185 | − | 0.656767i | 0.611759 | − | 0.791044i | \(-0.290462\pi\) |
−0.990944 | + | 0.134277i | \(0.957129\pi\) | |||||||
\(710\) | 5.86891e8 | + | 3.38842e8i | 1.63977 | + | 0.946721i | ||||
\(711\) | −7.12521e7 | + | 1.23412e8i | −0.198239 | + | 0.343360i | ||||
\(712\) | 910305. | − | 525565.i | 0.00252201 | − | 0.00145608i | ||||
\(713\) | 1.85065e6i | 0.00510572i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.20032e9 | −3.28383 | ||||||||
\(716\) | −8.00089e7 | − | 1.38579e8i | −0.217971 | − | 0.377537i | ||||
\(717\) | −2.64778e8 | − | 1.52870e8i | −0.718331 | − | 0.414728i | ||||
\(718\) | −2.22013e8 | + | 3.84538e8i | −0.599799 | + | 1.03888i | ||||
\(719\) | −9.13702e7 | + | 5.27526e7i | −0.245820 | + | 0.141924i | −0.617849 | − | 0.786297i | \(-0.711996\pi\) |
0.372029 | + | 0.928221i | \(0.378662\pi\) | |||||||
\(720\) | 1.67184e8i | 0.447916i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.65324e8 | −0.970660 | ||||||||
\(723\) | −2.80515e7 | − | 4.85866e7i | −0.0742234 | − | 0.128559i | ||||
\(724\) | 4.89696e8 | + | 2.82726e8i | 1.29036 | + | 0.744989i | ||||
\(725\) | −9.65772e7 | + | 1.67277e8i | −0.253431 | + | 0.438956i | ||||
\(726\) | 3.84494e8 | − | 2.21988e8i | 1.00480 | − | 0.580121i | ||||
\(727\) | 3.47133e8i | 0.903425i | 0.892164 | + | 0.451713i | \(0.149187\pi\) | ||||
−0.892164 | + | 0.451713i | \(0.850813\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | 2.62180e8 | + | 4.54110e8i | 0.673956 | + | 1.16733i | ||||
\(731\) | −3.04507e7 | − | 1.75807e7i | −0.0779552 | − | 0.0450074i | ||||
\(732\) | 1.84006e8 | − | 3.18708e8i | 0.469137 | − | 0.812568i | ||||
\(733\) | 4.04599e8 | − | 2.33596e8i | 1.02734 | − | 0.593134i | 0.111117 | − | 0.993807i | \(-0.464557\pi\) |
0.916221 | + | 0.400673i | \(0.131224\pi\) | |||||||
\(734\) | − | 1.13121e9i | − | 2.86058i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.10594e7 | 0.0779040 | ||||||||
\(737\) | 3.58804e8 | + | 6.21467e8i | 0.896304 | + | 1.55244i | ||||
\(738\) | −1.66083e8 | − | 9.58879e7i | −0.413195 | − | 0.238558i | ||||
\(739\) | −1.98814e8 | + | 3.44356e8i | −0.492623 | + | 0.853247i | −0.999964 | − | 0.00849788i | \(-0.997295\pi\) |
0.507341 | + | 0.861745i | \(0.330628\pi\) | |||||||
\(740\) | −4.33028e8 | + | 2.50009e8i | −1.06861 | + | 0.616965i | ||||
\(741\) | − | 1.88374e8i | − | 0.462984i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.88913e8 | 1.67957 | 0.839784 | − | 0.542920i | \(-0.182681\pi\) | ||||
0.839784 | + | 0.542920i | \(0.182681\pi\) | |||||||
\(744\) | 1.75784e6 | + | 3.04467e6i | 0.00426836 | + | 0.00739302i | ||||
\(745\) | −5.80080e8 | − | 3.34909e8i | −1.40288 | − | 0.809951i | ||||
\(746\) | 1.22215e8 | − | 2.11683e8i | 0.294380 | − | 0.509881i | ||||
\(747\) | 2.23865e7 | − | 1.29248e7i | 0.0537061 | − | 0.0310073i | ||||
\(748\) | − | 4.15475e8i | − | 0.992751i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.79140e8 | 0.424629 | ||||||||
\(751\) | −1.83282e8 | − | 3.17453e8i | −0.432712 | − | 0.749480i | 0.564393 | − | 0.825506i | \(-0.309110\pi\) |
−0.997106 | + | 0.0760260i | \(0.975777\pi\) | |||||||
\(752\) | −4.60781e8 | − | 2.66032e8i | −1.08353 | − | 0.625576i | ||||
\(753\) | −5.06512e7 | + | 8.77305e7i | −0.118633 | + | 0.205478i | ||||
\(754\) | −2.85742e8 | + | 1.64973e8i | −0.666592 | + | 0.384857i | ||||
\(755\) | 1.23152e9i | 2.86156i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.07241e8 | −0.477735 | −0.238868 | − | 0.971052i | \(-0.576776\pi\) | ||||
−0.238868 | + | 0.971052i | \(0.576776\pi\) | |||||||
\(758\) | −2.39168e8 | − | 4.14252e8i | −0.549157 | − | 0.951167i | ||||
\(759\) | −1.83261e7 | − | 1.05806e7i | −0.0419125 | − | 0.0241982i | ||||
\(760\) | −3.03390e7 | + | 5.25487e7i | −0.0691132 | + | 0.119708i | ||||
\(761\) | 5.86021e8 | − | 3.38339e8i | 1.32972 | − | 0.767712i | 0.344461 | − | 0.938801i | \(-0.388062\pi\) |
0.985256 | + | 0.171088i | \(0.0547283\pi\) | |||||||
\(762\) | 5.95757e8i | 1.34649i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.02285e8 | 0.677854 | ||||||||
\(765\) | −6.61007e7 | − | 1.14490e8i | −0.147646 | − | 0.255730i | ||||
\(766\) | 1.53096e8 | + | 8.83901e7i | 0.340626 | + | 0.196661i | ||||
\(767\) | −2.94549e8 | + | 5.10173e8i | −0.652786 | + | 1.13066i | ||||
\(768\) | −1.69795e8 | + | 9.80314e7i | −0.374837 | + | 0.216412i | ||||
\(769\) | − | 5.58023e8i | − | 1.22708i | −0.789663 | − | 0.613540i | \(-0.789745\pi\) | ||
0.789663 | − | 0.613540i | \(-0.210255\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.45510e7 | −0.0972063 | ||||||||
\(772\) | 5.16985e6 | + | 8.95443e6i | 0.0112364 | + | 0.0194619i | ||||
\(773\) | −7.17689e7 | − | 4.14358e7i | −0.155381 | − | 0.0897093i | 0.420293 | − | 0.907388i | \(-0.361927\pi\) |
−0.575675 | + | 0.817679i | \(0.695260\pi\) | |||||||
\(774\) | −1.74107e7 | + | 3.01561e7i | −0.0375485 | + | 0.0650358i | ||||
\(775\) | −5.04878e7 | + | 2.91492e7i | −0.108463 | + | 0.0626211i | ||||
\(776\) | 1.65188e7i | 0.0353504i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.84070e8 | 1.66501 | ||||||||
\(779\) | 1.34154e8 | + | 2.32362e8i | 0.283787 | + | 0.491533i | ||||
\(780\) | 5.59278e8 | + | 3.22899e8i | 1.17854 | + | 0.680430i | ||||
\(781\) | 3.14072e8 | − | 5.43988e8i | 0.659289 | − | 1.14192i | ||||
\(782\) | −1.89395e7 | + | 1.09347e7i | −0.0396048 | + | 0.0228658i | ||||
\(783\) | − | 3.51627e7i | − | 0.0732482i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.93859e8 | 1.84782 | ||||||||
\(786\) | −2.02212e7 | − | 3.50242e7i | −0.0416428 | − | 0.0721275i | ||||
\(787\) | 4.59435e8 | + | 2.65255e8i | 0.942541 | + | 0.544176i | 0.890756 | − | 0.454482i | \(-0.150176\pi\) |
0.0517851 | + | 0.998658i | \(0.483509\pi\) | |||||||
\(788\) | 2.55813e8 | − | 4.43082e8i | 0.522811 | − | 0.905535i | ||||
\(789\) | 6.74766e7 | − | 3.89576e7i | 0.137380 | − | 0.0793161i | ||||
\(790\) | 1.30024e9i | 2.63719i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.01997e7 | −0.0809184 | ||||||||
\(793\) | 5.09233e8 | + | 8.82017e8i | 1.02117 | + | 1.76871i | ||||
\(794\) | −9.45767e7 | − | 5.46039e7i | −0.188939 | − | 0.109084i | ||||
\(795\) | −3.26756e8 | + | 5.65958e8i | −0.650313 | + | 1.12637i | ||||
\(796\) | 1.08406e8 | − | 6.25885e7i | 0.214939 | − | 0.124095i | ||||
\(797\) | − | 4.96880e8i | − | 0.981469i | −0.871309 | − | 0.490735i | \(-0.836728\pi\) | ||
0.871309 | − | 0.490735i | \(-0.163272\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.20732e8 | 0.824831 | ||||||||
\(800\) | 4.89209e8 | + | 8.47334e8i | 0.955486 | + | 1.65495i | ||||
\(801\) | −2.74796e6 | − | 1.58654e6i | −0.00534703 | − | 0.00308711i | ||||
\(802\) | −3.22326e8 | + | 5.58285e8i | −0.624845 | + | 1.08226i | ||||
\(803\) | 4.20913e8 | − | 2.43014e8i | 0.812917 | − | 0.469338i | ||||
\(804\) | − | 3.86088e8i | − | 0.742879i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.95852e7 | −0.190191 | ||||||||
\(807\) | 1.59158e8 | + | 2.75669e8i | 0.302836 | + | 0.524527i | ||||
\(808\) | −9.76747e7 | − | 5.63925e7i | −0.185160 | − | 0.106902i | ||||
\(809\) | 2.10152e8 | − | 3.63994e8i | 0.396906 | − | 0.687461i | −0.596437 | − | 0.802660i | \(-0.703417\pi\) |
0.993342 | + | 0.115199i | \(0.0367506\pi\) | |||||||
\(810\) | −1.13382e8 | + | 6.54613e7i | −0.213349 | + | 0.123177i | ||||
\(811\) | 4.27809e8i | 0.802025i | 0.916073 | + | 0.401012i | \(0.131342\pi\) | ||||
−0.916073 | + | 0.401012i | \(0.868658\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.92393e8 | −0.358029 | ||||||||
\(814\) | 4.40825e8 | + | 7.63531e8i | 0.817322 | + | 1.41564i | ||||
\(815\) | −8.56650e8 | − | 4.94587e8i | −1.58245 | − | 0.913629i | ||||
\(816\) | 8.00747e7 | − | 1.38693e8i | 0.147375 | − | 0.255262i | ||||
\(817\) | 4.21907e7 | − | 2.43588e7i | 0.0773660 | − | 0.0446673i | ||||
\(818\) | − | 1.89887e8i | − | 0.346925i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.19837e8 | −1.66828 | ||||||||
\(821\) | −4.76401e8 | − | 8.25152e8i | −0.860882 | − | 1.49109i | −0.871079 | − | 0.491143i | \(-0.836579\pi\) |
0.0101968 | − | 0.999948i | \(-0.496754\pi\) | |||||||
\(822\) | 4.97182e8 | + | 2.87048e8i | 0.895159 | + | 0.516820i | ||||
\(823\) | 3.70614e8 | − | 6.41923e8i | 0.664848 | − | 1.15155i | −0.314478 | − | 0.949265i | \(-0.601829\pi\) |
0.979326 | − | 0.202287i | \(-0.0648372\pi\) | |||||||
\(824\) | 3.60864e7 | − | 2.08345e7i | 0.0645003 | − | 0.0372392i | ||||
\(825\) | − | 6.66606e8i | − | 1.18715i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.61072e8 | −1.34558 | −0.672790 | − | 0.739834i | \(-0.734904\pi\) | ||||
−0.672790 | + | 0.739834i | \(0.734904\pi\) | |||||||
\(828\) | 5.69255e6 | + | 9.85979e6i | 0.0100280 | + | 0.0173691i | ||||
\(829\) | 7.06469e8 | + | 4.07880e8i | 1.24002 | + | 0.715928i | 0.969099 | − | 0.246673i | \(-0.0793373\pi\) |
0.270924 | + | 0.962601i | \(0.412671\pi\) | |||||||
\(830\) | 1.17929e8 | − | 2.04259e8i | 0.206247 | − | 0.357230i | ||||
\(831\) | 2.81207e8 | − | 1.62355e8i | 0.490031 | − | 0.282919i | ||||
\(832\) | 9.65442e8i | 1.67632i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.40286e8 | 0.241833 | ||||||||
\(835\) | −1.49483e8 | − | 2.58912e8i | −0.256763 | − | 0.444726i | ||||
\(836\) | 4.98534e8 | + | 2.87829e8i | 0.853250 | + | 0.492624i | ||||
\(837\) | 5.30644e6 | − | 9.19103e6i | 0.00904955 | − | 0.0156743i | ||||
\(838\) | 3.77261e8 | − | 2.17812e8i | 0.641076 | − | 0.370126i | ||||
\(839\) | − | 1.07654e9i | − | 1.82283i | −0.411491 | − | 0.911414i | \(-0.634992\pi\) | ||
0.411491 | − | 0.911414i | \(-0.365008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.08655e8 | −0.855137 | ||||||||
\(842\) | 5.32881e8 | + | 9.22978e8i | 0.892677 | + | 1.54616i | ||||
\(843\) | 2.83693e8 | + | 1.63790e8i | 0.473550 | + | 0.273404i | ||||
\(844\) | −4.85986e8 | + | 8.41753e8i | −0.808345 | + | 1.40009i | ||||
\(845\) | −7.49906e8 | + | 4.32959e8i | −1.24290 | + | 0.717590i | ||||
\(846\) | − | 4.16662e8i | − | 0.688133i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.91667e8 | −1.29824 | ||||||||
\(849\) | −8.12463e7 | − | 1.40723e8i | −0.132764 | − | 0.229954i | ||||
\(850\) | −5.96621e8 | − | 3.44459e8i | −0.971498 | − | 0.560895i | ||||
\(851\) | 1.21977e7 | − | 2.11271e7i | 0.0197921 | − | 0.0342808i | ||||
\(852\) | −2.92677e8 | + | 1.68977e8i | −0.473227 | + | 0.273218i | ||||
\(853\) | − | 9.74565e8i | − | 1.57023i | −0.619349 | − | 0.785116i | \(-0.712603\pi\) | ||
0.619349 | − | 0.785116i | \(-0.287397\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.83170e8 | 0.293060 | ||||||||
\(856\) | 2.60307e7 | + | 4.50864e7i | 0.0415015 | + | 0.0718827i | ||||
\(857\) | 8.31953e8 | + | 4.80328e8i | 1.32177 | + | 0.763125i | 0.984011 | − | 0.178107i | \(-0.0569974\pi\) |
0.337760 | + | 0.941232i | \(0.390331\pi\) | |||||||
\(858\) | 5.69348e8 | − | 9.86139e8i | 0.901396 | − | 1.56126i | ||||
\(859\) | −4.22688e8 | + | 2.44039e8i | −0.666869 | + | 0.385017i | −0.794889 | − | 0.606755i | \(-0.792471\pi\) |
0.128020 | + | 0.991772i | \(0.459138\pi\) | |||||||
\(860\) | 1.67018e8i | 0.262583i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.60076e9 | 2.49921 | ||||||||
\(863\) | −1.61373e8 | − | 2.79507e8i | −0.251073 | − | 0.434871i | 0.712749 | − | 0.701420i | \(-0.247450\pi\) |
−0.963821 | + | 0.266549i | \(0.914117\pi\) | |||||||
\(864\) | −1.54252e8 | − | 8.90577e7i | −0.239161 | − | 0.138080i | ||||
\(865\) | 1.18784e8 | − | 2.05739e8i | 0.183530 | − | 0.317884i | ||||
\(866\) | −2.01520e8 | + | 1.16348e8i | −0.310287 | + | 0.179144i | ||||
\(867\) | − | 2.49629e8i | − | 0.383034i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.20519e9 | 1.83652 | ||||||||
\(870\) | −1.60416e8 | − | 2.77849e8i | −0.243607 | − | 0.421940i | ||||
\(871\) | 9.25339e8 | + | 5.34245e8i | 1.40038 | + | 0.808511i | ||||
\(872\) | −2.76614e7 | + | 4.79110e7i | −0.0417182 | + | 0.0722580i | ||||
\(873\) | 4.31851e7 | − | 2.49329e7i | 0.0649070 | − | 0.0374741i | ||||
\(874\) | − | 3.03010e7i | − | 0.0453860i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.61494e8 | −0.388999 | ||||||||
\(877\) | −4.68948e8 | − | 8.12242e8i | −0.695226 | − | 1.20417i | −0.970104 | − | 0.242688i | \(-0.921971\pi\) |
0.274878 | − | 0.961479i | \(-0.411362\pi\) | |||||||
\(878\) | −8.66164e8 | − | 5.00080e8i | −1.27973 | − | 0.738850i | ||||
\(879\) | 2.22391e8 | − | 3.85192e8i | 0.327454 | − | 0.567167i | ||||
\(880\) | 1.22448e9 | − | 7.06956e8i | 1.79682 | − | 1.03739i | ||||
\(881\) | 9.47337e8i | 1.38540i | 0.721224 | + | 0.692702i | \(0.243580\pi\) | ||||
−0.721224 | + | 0.692702i | \(0.756420\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.52054e8 | 0.220860 | 0.110430 | − | 0.993884i | \(-0.464777\pi\) | ||||
0.110430 | + | 0.993884i | \(0.464777\pi\) | |||||||
\(884\) | −3.09313e8 | − | 5.35746e8i | −0.447756 | − | 0.775536i | ||||
\(885\) | −4.96080e8 | − | 2.86412e8i | −0.715686 | − | 0.413201i | ||||
\(886\) | −4.69211e7 | + | 8.12697e7i | −0.0674632 | + | 0.116850i | ||||
\(887\) | −1.02528e9 | + | 5.91948e8i | −1.46917 | + | 0.848228i | −0.999403 | − | 0.0345605i | \(-0.988997\pi\) |
−0.469771 | + | 0.882788i | \(0.655664\pi\) | |||||||
\(888\) | − | 4.63441e7i | − | 0.0661843i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.89518e7 | −0.0410682 | ||||||||
\(891\) | 6.06759e7 | + | 1.05094e8i | 0.0857795 | + | 0.148574i | ||||
\(892\) | −1.32086e9 | − | 7.62599e8i | −1.86107 | − | 1.07449i | ||||
\(893\) | −2.91470e8 | + | 5.04842e8i | −0.409298 | + | 0.708926i | ||||
\(894\) | 5.50297e8 | − | 3.17714e8i | 0.770167 | − | 0.444656i | ||||
\(895\) | 4.30612e8i | 0.600644i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.15080e7 | −0.0436560 | ||||||||
\(898\) | −2.99974e8 | − | 5.19569e8i | −0.414242 | − | 0.717488i | ||||
\(899\) | 2.25231e7 | + | 1.30037e7i | 0.0309990 | + | 0.0178973i | ||||
\(900\) | −1.79324e8 | + | 3.10598e8i | −0.245986 | + | 0.426060i | ||||
\(901\) | 5.42144e8 | − | 3.13007e8i | 0.741209 | − | 0.427937i | ||||
\(902\) | 1.62189e9i | 2.21005i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.70388e8 | −0.230639 | ||||||||
\(905\) | −7.60824e8 | − | 1.31779e9i | −1.02645 | − | 1.77787i | ||||
\(906\) | −1.01177e9 | − | 5.84147e8i | −1.36050 | − | 0.785485i | ||||
\(907\) | −1.69886e8 | + | 2.94252e8i | −0.227686 | + | 0.394364i | −0.957122 | − | 0.289685i | \(-0.906449\pi\) |
0.729436 | + | 0.684049i | \(0.239783\pi\) | |||||||
\(908\) | 2.41489e8 | − | 1.39423e8i | 0.322581 | − | 0.186242i | ||||
\(909\) | 3.40467e8i | 0.453297i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.44286e8 | −1.24896 | −0.624480 | − | 0.781041i | \(-0.714689\pi\) | ||||
−0.624480 | + | 0.781041i | \(0.714689\pi\) | |||||||
\(912\) | 1.10947e8 | + | 1.92165e8i | 0.146262 | + | 0.253332i | ||||
\(913\) | −1.89327e8 | − | 1.09308e8i | −0.248772 | − | 0.143628i | ||||
\(914\) | −2.31967e8 | + | 4.01778e8i | −0.303799 | + | 0.526196i | ||||
\(915\) | −8.57653e8 | + | 4.95166e8i | −1.11956 | + | 0.646380i | ||||
\(916\) | − | 3.98857e7i | − | 0.0518956i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.25414e8 | 0.162113 | ||||||||
\(919\) | 1.87277e8 | + | 3.24374e8i | 0.241290 | + | 0.417926i | 0.961082 | − | 0.276264i | \(-0.0890963\pi\) |
−0.719792 | + | 0.694189i | \(0.755763\pi\) | |||||||
\(920\) | 8.78947e6 | + | 5.07460e6i | 0.0112875 | + | 0.00651686i | ||||
\(921\) | 7.97106e7 | − | 1.38063e8i | 0.102032 | − | 0.176725i | ||||
\(922\) | 1.41755e8 | − | 8.18424e7i | 0.180862 | − | 0.104420i | ||||
\(923\) | − | 9.35280e8i | − | 1.18942i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.68494e8 | 0.970991 | ||||||||
\(926\) | 7.27157e8 | + | 1.25947e9i | 0.915788 | + | 1.58619i | ||||
\(927\) | −1.08935e8 | − | 6.28936e7i | −0.136750 | − | 0.0789527i | ||||
\(928\) | 2.18240e8 | − | 3.78003e8i | 0.273081 | − | 0.472989i | ||||
\(929\) | −7.89503e8 | + | 4.55820e8i | −0.984707 | + | 0.568521i | −0.903688 | − | 0.428192i | \(-0.859151\pi\) |
−0.0810189 | + | 0.996713i | \(0.525817\pi\) | |||||||
\(930\) | − | 9.68343e7i | − | 0.120387i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.15851e9 | −1.43104 | ||||||||
\(933\) | 1.22698e8 | + | 2.12519e8i | 0.151075 | + | 0.261669i | ||||
\(934\) | 1.04145e9 | + | 6.01279e8i | 1.27819 | + | 0.737965i | ||||
\(935\) | −5.59028e8 | + | 9.68265e8i | −0.683910 | + | 1.18457i | ||||
\(936\) | −5.18365e7 | + | 2.99278e7i | −0.0632133 | + | 0.0364962i | ||||
\(937\) | − | 3.76597e8i | − | 0.457781i | −0.973452 | − | 0.228890i | \(-0.926490\pi\) | ||
0.973452 | − | 0.228890i | \(-0.0735097\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.65586e8 | −1.04547 | ||||||||
\(940\) | −9.99242e8 | − | 1.73074e9i | −1.20306 | − | 2.08376i | ||||
\(941\) | −2.17999e8 | − | 1.25862e8i | −0.261629 | − | 0.151051i | 0.363449 | − | 0.931614i | \(-0.381599\pi\) |
−0.625077 | + | 0.780563i | \(0.714933\pi\) | |||||||
\(942\) | −4.23983e8 | + | 7.34360e8i | −0.507219 | + | 0.878529i | ||||
\(943\) | 3.88656e7 | − | 2.24391e7i | 0.0463479 | − | 0.0267590i | ||||
\(944\) | − | 6.93922e8i | − | 0.824888i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.94491e8 | 0.347856 | ||||||||
\(947\) | 1.32933e8 | + | 2.30247e8i | 0.156525 | + | 0.271109i | 0.933613 | − | 0.358282i | \(-0.116637\pi\) |
−0.777088 | + | 0.629392i | \(0.783304\pi\) | |||||||
\(948\) | −5.61545e8 | − | 3.24208e8i | −0.659112 | − | 0.380539i | ||||
\(949\) | 3.61838e8 | − | 6.26723e8i | 0.423366 | − | 0.733292i | ||||
\(950\) | 8.26643e8 | − | 4.77262e8i | 0.964156 | − | 0.556655i | ||||
\(951\) | 9.40107e7i | 0.109304i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.38039e8 | −0.621635 | −0.310817 | − | 0.950470i | \(-0.600603\pi\) | ||||
−0.310817 | + | 0.950470i | \(0.600603\pi\) | |||||||
\(954\) | −3.09979e8 | − | 5.36900e8i | −0.357016 | − | 0.618370i | ||||
\(955\) | −7.04475e8 | − | 4.06729e8i | −0.808827 | − | 0.466976i | ||||
\(956\) | 6.95581e8 | − | 1.20478e9i | 0.796112 | − | 1.37891i | ||||
\(957\) | −2.57537e8 | + | 1.48689e8i | −0.293836 | + | 0.169646i | ||||
\(958\) | 9.05777e8i | 1.03021i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −9.38774e8 | −1.06108 | ||||||||
\(961\) | −4.39827e8 | − | 7.61803e8i | −0.495578 | − | 0.858366i | ||||
\(962\) | 1.13687e9 | + | 6.56370e8i | 1.27698 | + | 0.737265i | ||||
\(963\) | 7.85794e7 | − | 1.36104e8i | 0.0879893 | − | 0.152402i | ||||
\(964\) | 2.21077e8 | − | 1.27639e8i | 0.246781 | − | 0.142479i | ||||
\(965\) | − | 2.78244e7i | − | 0.0309631i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.16138e9 | −1.28439 | −0.642194 | − | 0.766542i | \(-0.721976\pi\) | ||||
−0.642194 | + | 0.766542i | \(0.721976\pi\) | |||||||
\(968\) | 9.86856e7 | + | 1.70929e8i | 0.108800 | + | 0.188447i | ||||
\(969\) | −1.51956e8 | − | 8.77316e7i | −0.167011 | − | 0.0964240i | ||||
\(970\) | 2.27494e8 | − | 3.94031e8i | 0.249261 | − | 0.431732i | ||||
\(971\) | −1.30640e9 | + | 7.54248e8i | −1.42698 | + | 0.823866i | −0.996881 | − | 0.0789166i | \(-0.974854\pi\) |
−0.430097 | + | 0.902783i | \(0.641521\pi\) | |||||||
\(972\) | − | 6.52898e7i | − | 0.0710962i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.65874e9 | −1.79515 | ||||||||
\(975\) | −4.96274e8 | − | 8.59572e8i | −0.535436 | − | 0.927403i | ||||
\(976\) | −1.03896e9 | − | 5.99847e8i | −1.11751 | − | 0.645195i | ||||
\(977\) | 6.03772e7 | − | 1.04576e8i | 0.0647425 | − | 0.112137i | −0.831837 | − | 0.555020i | \(-0.812711\pi\) |
0.896580 | + | 0.442882i | \(0.146044\pi\) | |||||||
\(978\) | 8.12667e8 | − | 4.69194e8i | 0.868752 | − | 0.501574i | ||||
\(979\) | 2.68354e7i | 0.0285996i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.67005e8 | 0.176897 | ||||||||
\(982\) | 2.94939e8 | + | 5.10849e8i | 0.311457 | + | 0.539459i | ||||
\(983\) | 1.86333e7 | + | 1.07580e7i | 0.0196169 | + | 0.0113258i | 0.509776 | − | 0.860307i | \(-0.329728\pi\) |
−0.490159 | + | 0.871633i | \(0.663061\pi\) | |||||||
\(984\) | 4.26274e7 | − | 7.38329e7i | 0.0447408 | − | 0.0774934i | ||||
\(985\) | −1.19235e9 | + | 6.88401e8i | −1.24765 | + | 0.720333i | ||||
\(986\) | 3.07333e8i | 0.320611i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.57131e8 | 0.888743 | ||||||||
\(989\) | −4.07433e6 | − | 7.05694e6i | −0.00421179 | − | 0.00729504i | ||||
\(990\) | 9.58899e8 | + | 5.53621e8i | 0.988251 | + | 0.570567i | ||||
\(991\) | 3.07940e7 | − | 5.33368e7i | 0.0316407 | − | 0.0548033i | −0.849771 | − | 0.527151i | \(-0.823260\pi\) |
0.881412 | + | 0.472348i | \(0.156593\pi\) | |||||||
\(992\) | 1.14090e8 | − | 6.58698e7i | 0.116872 | − | 0.0674763i | ||||
\(993\) | − | 1.52230e8i | − | 0.155472i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.36855e8 | −0.341959 | ||||||||
\(996\) | 5.88100e7 | + | 1.01862e8i | 0.0595215 | + | 0.103094i | ||||
\(997\) | −6.72319e8 | − | 3.88164e8i | −0.678406 | − | 0.391678i | 0.120848 | − | 0.992671i | \(-0.461439\pi\) |
−0.799254 | + | 0.600993i | \(0.794772\pi\) | |||||||
\(998\) | 7.34733e8 | − | 1.27259e9i | 0.739159 | − | 1.28026i | ||||
\(999\) | −1.21157e8 | + | 6.99500e7i | −0.121521 | + | 0.0701603i |
(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 | 147.7.f.d.31.4 | 8 | ||
7.2 | even | 3 | 21.7.f.a.19.4 | yes | 8 | ||
7.3 | odd | 6 | 147.7.d.b.97.2 | 8 | |||
7.4 | even | 3 | 147.7.d.b.97.1 | 8 | |||
7.5 | odd | 6 | inner | 147.7.f.d.19.4 | 8 | ||
7.6 | odd | 2 | 21.7.f.a.10.4 | ✓ | 8 | ||
21.2 | odd | 6 | 63.7.m.d.19.1 | 8 | |||
21.11 | odd | 6 | 441.7.d.c.244.7 | 8 | |||
21.17 | even | 6 | 441.7.d.c.244.8 | 8 | |||
21.20 | even | 2 | 63.7.m.d.10.1 | 8 | |||
28.23 | odd | 6 | 336.7.bh.d.145.1 | 8 | |||
28.27 | even | 2 | 336.7.bh.d.241.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.7.f.a.10.4 | ✓ | 8 | 7.6 | odd | 2 | ||
21.7.f.a.19.4 | yes | 8 | 7.2 | even | 3 | ||
63.7.m.d.10.1 | 8 | 21.20 | even | 2 | |||
63.7.m.d.19.1 | 8 | 21.2 | odd | 6 | |||
147.7.d.b.97.1 | 8 | 7.4 | even | 3 | |||
147.7.d.b.97.2 | 8 | 7.3 | odd | 6 | |||
147.7.f.d.19.4 | 8 | 7.5 | odd | 6 | inner | ||
147.7.f.d.31.4 | 8 | 1.1 | even | 1 | trivial | ||
336.7.bh.d.145.1 | 8 | 28.23 | odd | 6 | |||
336.7.bh.d.241.1 | 8 | 28.27 | even | 2 | |||
441.7.d.c.244.7 | 8 | 21.11 | odd | 6 | |||
441.7.d.c.244.8 | 8 | 21.17 | even | 6 |