Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(39,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.39");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 39.8 | ||
Character | \(\chi\) | \(=\) | 76.39 |
Dual form | 76.7.b.a.39.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.53857 | + | 2.67768i | −0.942321 | + | 0.334710i | ||||
\(3\) | − | 14.2612i | − | 0.528191i | −0.964497 | − | 0.264096i | \(-0.914927\pi\) | ||
0.964497 | − | 0.264096i | \(-0.0850734\pi\) | |||||||
\(4\) | 49.6600 | − | 40.3718i | 0.775938 | − | 0.630809i | ||||
\(5\) | −201.264 | −1.61011 | −0.805057 | − | 0.593197i | \(-0.797866\pi\) | ||||
−0.805057 | + | 0.593197i | \(0.797866\pi\) | |||||||
\(6\) | 38.1869 | + | 107.509i | 0.176791 | + | 0.497726i | ||||
\(7\) | 304.241i | 0.886999i | 0.896275 | + | 0.443499i | \(0.146263\pi\) | ||||
−0.896275 | + | 0.443499i | \(0.853737\pi\) | |||||||
\(8\) | −266.263 | + | 437.319i | −0.520044 | + | 0.854139i | ||||
\(9\) | 525.619 | 0.721014 | ||||||||
\(10\) | 1517.25 | − | 538.922i | 1.51725 | − | 0.538922i | ||||
\(11\) | 933.491i | 0.701346i | 0.936498 | + | 0.350673i | \(0.114047\pi\) | ||||
−0.936498 | + | 0.350673i | \(0.885953\pi\) | |||||||
\(12\) | −575.749 | − | 708.210i | −0.333188 | − | 0.409843i | ||||
\(13\) | −219.305 | −0.0998201 | −0.0499100 | − | 0.998754i | \(-0.515893\pi\) | ||||
−0.0499100 | + | 0.998754i | \(0.515893\pi\) | |||||||
\(14\) | −814.660 | − | 2293.54i | −0.296888 | − | 0.835837i | ||||
\(15\) | 2870.26i | 0.850448i | ||||||||
\(16\) | 836.237 | − | 4009.73i | 0.204159 | − | 0.978938i | ||||
\(17\) | −4130.81 | −0.840791 | −0.420396 | − | 0.907341i | \(-0.638109\pi\) | ||||
−0.420396 | + | 0.907341i | \(0.638109\pi\) | |||||||
\(18\) | −3962.42 | + | 1407.44i | −0.679427 | + | 0.241331i | ||||
\(19\) | − | 1573.56i | − | 0.229416i | ||||||
\(20\) | −9994.79 | + | 8125.40i | −1.24935 | + | 1.01568i | ||||
\(21\) | 4338.82 | 0.468505 | ||||||||
\(22\) | −2499.59 | − | 7037.19i | −0.234748 | − | 0.660893i | ||||
\(23\) | − | 11056.4i | − | 0.908719i | −0.890818 | − | 0.454359i | \(-0.849868\pi\) | ||
0.890818 | − | 0.454359i | \(-0.150132\pi\) | |||||||
\(24\) | 6236.68 | + | 3797.21i | 0.451149 | + | 0.274683i | ||||
\(25\) | 24882.3 | 1.59247 | ||||||||
\(26\) | 1653.24 | − | 587.229i | 0.0940626 | − | 0.0334108i | ||||
\(27\) | − | 17892.3i | − | 0.909024i | ||||||
\(28\) | 12282.7 | + | 15108.6i | 0.559527 | + | 0.688256i | ||||
\(29\) | 13109.4 | 0.537512 | 0.268756 | − | 0.963208i | \(-0.413387\pi\) | ||||
0.268756 | + | 0.963208i | \(0.413387\pi\) | |||||||
\(30\) | −7685.66 | − | 21637.7i | −0.284654 | − | 0.801395i | ||||
\(31\) | − | 47617.4i | − | 1.59838i | −0.601078 | − | 0.799191i | \(-0.705262\pi\) | ||
0.601078 | − | 0.799191i | \(-0.294738\pi\) | |||||||
\(32\) | 4432.76 | + | 32466.8i | 0.135277 | + | 0.990808i | ||||
\(33\) | 13312.7 | 0.370445 | ||||||||
\(34\) | 31140.4 | − | 11061.0i | 0.792295 | − | 0.281422i | ||||
\(35\) | − | 61232.8i | − | 1.42817i | ||||||
\(36\) | 26102.3 | − | 21220.2i | 0.559462 | − | 0.454822i | ||||
\(37\) | 48926.0 | 0.965906 | 0.482953 | − | 0.875646i | \(-0.339564\pi\) | ||||
0.482953 | + | 0.875646i | \(0.339564\pi\) | |||||||
\(38\) | 4213.50 | + | 11862.4i | 0.0767878 | + | 0.216183i | ||||
\(39\) | 3127.54i | 0.0527241i | ||||||||
\(40\) | 53589.2 | − | 88016.8i | 0.837331 | − | 1.37526i | ||||
\(41\) | 30436.0 | 0.441607 | 0.220803 | − | 0.975318i | \(-0.429132\pi\) | ||||
0.220803 | + | 0.975318i | \(0.429132\pi\) | |||||||
\(42\) | −32708.5 | + | 11618.0i | −0.441482 | + | 0.156813i | ||||
\(43\) | − | 50390.6i | − | 0.633789i | −0.948461 | − | 0.316894i | \(-0.897360\pi\) | ||
0.948461 | − | 0.316894i | \(-0.102640\pi\) | |||||||
\(44\) | 37686.7 | + | 46357.2i | 0.442416 | + | 0.544201i | ||||
\(45\) | −105788. | −1.16092 | ||||||||
\(46\) | 29605.5 | + | 83349.3i | 0.304158 | + | 0.856305i | ||||
\(47\) | 117012.i | 1.12703i | 0.826105 | + | 0.563517i | \(0.190552\pi\) | ||||
−0.826105 | + | 0.563517i | \(0.809448\pi\) | |||||||
\(48\) | −57183.4 | − | 11925.7i | −0.517066 | − | 0.107835i | ||||
\(49\) | 25086.7 | 0.213234 | ||||||||
\(50\) | −187577. | + | 66627.0i | −1.50062 | + | 0.533016i | ||||
\(51\) | 58910.1i | 0.444098i | ||||||||
\(52\) | −10890.7 | + | 8853.73i | −0.0774542 | + | 0.0629674i | ||||
\(53\) | −135594. | −0.910778 | −0.455389 | − | 0.890293i | \(-0.650500\pi\) | ||||
−0.455389 | + | 0.890293i | \(0.650500\pi\) | |||||||
\(54\) | 47910.0 | + | 134883.i | 0.304260 | + | 0.856593i | ||||
\(55\) | − | 187879.i | − | 1.12925i | ||||||
\(56\) | −133050. | − | 81007.9i | −0.757620 | − | 0.461278i | ||||
\(57\) | −22440.8 | −0.121175 | ||||||||
\(58\) | −98826.0 | + | 35102.8i | −0.506509 | + | 0.179911i | ||||
\(59\) | − | 326096.i | − | 1.58778i | −0.608065 | − | 0.793888i | \(-0.708054\pi\) | ||
0.608065 | − | 0.793888i | \(-0.291946\pi\) | |||||||
\(60\) | 115878. | + | 142537.i | 0.536471 | + | 0.659895i | ||||
\(61\) | 282709. | 1.24552 | 0.622758 | − | 0.782414i | \(-0.286012\pi\) | ||||
0.622758 | + | 0.782414i | \(0.286012\pi\) | |||||||
\(62\) | 127504. | + | 358967.i | 0.534995 | + | 1.50619i | ||||
\(63\) | 159915.i | 0.639539i | ||||||||
\(64\) | −120352. | − | 232884.i | −0.459108 | − | 0.888380i | ||||
\(65\) | 44138.2 | 0.160722 | ||||||||
\(66\) | −100358. | + | 35647.1i | −0.349078 | + | 0.123992i | ||||
\(67\) | − | 359557.i | − | 1.19548i | −0.801689 | − | 0.597742i | \(-0.796065\pi\) | ||
0.801689 | − | 0.597742i | \(-0.203935\pi\) | |||||||
\(68\) | −205136. | + | 166768.i | −0.652402 | + | 0.530379i | ||||
\(69\) | −157677. | −0.479977 | ||||||||
\(70\) | 163962. | + | 461607.i | 0.478023 | + | 1.34579i | ||||
\(71\) | 133998.i | 0.374390i | 0.982323 | + | 0.187195i | \(0.0599396\pi\) | ||||
−0.982323 | + | 0.187195i | \(0.940060\pi\) | |||||||
\(72\) | −139953. | + | 229863.i | −0.374959 | + | 0.615847i | ||||
\(73\) | −227670. | −0.585244 | −0.292622 | − | 0.956228i | \(-0.594528\pi\) | ||||
−0.292622 | + | 0.956228i | \(0.594528\pi\) | |||||||
\(74\) | −368832. | + | 131008.i | −0.910194 | + | 0.323299i | ||||
\(75\) | − | 354851.i | − | 0.841129i | ||||||
\(76\) | −63527.5 | − | 78143.2i | −0.144718 | − | 0.178012i | ||||
\(77\) | −284006. | −0.622093 | ||||||||
\(78\) | −8374.56 | − | 23577.2i | −0.0176473 | − | 0.0496830i | ||||
\(79\) | 746350.i | 1.51377i | 0.653545 | + | 0.756887i | \(0.273281\pi\) | ||||
−0.653545 | + | 0.756887i | \(0.726719\pi\) | |||||||
\(80\) | −168305. | + | 807016.i | −0.328720 | + | 1.57620i | ||||
\(81\) | 128011. | 0.240876 | ||||||||
\(82\) | −229444. | + | 81497.9i | −0.416135 | + | 0.147810i | ||||
\(83\) | − | 459386.i | − | 0.803421i | −0.915767 | − | 0.401710i | \(-0.868416\pi\) | ||
0.915767 | − | 0.401710i | \(-0.131584\pi\) | |||||||
\(84\) | 215466. | − | 175166.i | 0.363531 | − | 0.295537i | ||||
\(85\) | 831384. | 1.35377 | ||||||||
\(86\) | 134930. | + | 379873.i | 0.212136 | + | 0.597232i | ||||
\(87\) | − | 186955.i | − | 0.283909i | ||||||
\(88\) | −408234. | − | 248554.i | −0.599047 | − | 0.364731i | ||||
\(89\) | 905466. | 1.28440 | 0.642202 | − | 0.766535i | \(-0.278021\pi\) | ||||
0.642202 | + | 0.766535i | \(0.278021\pi\) | |||||||
\(90\) | 797493. | − | 283268.i | 1.09396 | − | 0.388571i | ||||
\(91\) | − | 66721.4i | − | 0.0885403i | ||||||
\(92\) | −446366. | − | 549060.i | −0.573228 | − | 0.705109i | ||||
\(93\) | −679079. | −0.844251 | ||||||||
\(94\) | −313321. | − | 882103.i | −0.377230 | − | 1.06203i | ||||
\(95\) | 316702.i | 0.369386i | ||||||||
\(96\) | 463014. | − | 63216.2i | 0.523336 | − | 0.0714521i | ||||
\(97\) | 1.58577e6 | 1.73750 | 0.868752 | − | 0.495247i | \(-0.164922\pi\) | ||||
0.868752 | + | 0.495247i | \(0.164922\pi\) | |||||||
\(98\) | −189118. | + | 67174.3i | −0.200934 | + | 0.0713715i | ||||
\(99\) | 490661.i | 0.505680i | ||||||||
\(100\) | 1.23566e6 | − | 1.00454e6i | 1.23566 | − | 1.00454i | ||||
\(101\) | −924935. | −0.897732 | −0.448866 | − | 0.893599i | \(-0.648172\pi\) | ||||
−0.448866 | + | 0.893599i | \(0.648172\pi\) | |||||||
\(102\) | −157743. | − | 444098.i | −0.148644 | − | 0.418483i | ||||
\(103\) | 72807.1i | 0.0666288i | 0.999445 | + | 0.0333144i | \(0.0106063\pi\) | ||||
−0.999445 | + | 0.0333144i | \(0.989394\pi\) | |||||||
\(104\) | 58392.7 | − | 95906.2i | 0.0519109 | − | 0.0852603i | ||||
\(105\) | −873250. | −0.754346 | ||||||||
\(106\) | 1.02218e6 | − | 363077.i | 0.858245 | − | 0.304847i | ||||
\(107\) | − | 1.36704e6i | − | 1.11591i | −0.829871 | − | 0.557955i | \(-0.811586\pi\) | ||
0.829871 | − | 0.557955i | \(-0.188414\pi\) | |||||||
\(108\) | −722345. | − | 888533.i | −0.573421 | − | 0.705346i | ||||
\(109\) | −382830. | −0.295615 | −0.147808 | − | 0.989016i | \(-0.547222\pi\) | ||||
−0.147808 | + | 0.989016i | \(0.547222\pi\) | |||||||
\(110\) | 503079. | + | 1.41634e6i | 0.377971 | + | 1.06411i | ||||
\(111\) | − | 697742.i | − | 0.510183i | ||||||
\(112\) | 1.21992e6 | + | 254417.i | 0.868316 | + | 0.181089i | ||||
\(113\) | −1.55925e6 | −1.08064 | −0.540318 | − | 0.841461i | \(-0.681696\pi\) | ||||
−0.540318 | + | 0.841461i | \(0.681696\pi\) | |||||||
\(114\) | 169172. | − | 60089.4i | 0.114186 | − | 0.0405586i | ||||
\(115\) | 2.22526e6i | 1.46314i | ||||||||
\(116\) | 651012. | − | 529249.i | 0.417076 | − | 0.339068i | ||||
\(117\) | −115271. | −0.0719717 | ||||||||
\(118\) | 873181. | + | 2.45829e6i | 0.531445 | + | 1.49619i | ||||
\(119\) | − | 1.25676e6i | − | 0.745780i | ||||||
\(120\) | −1.25522e6 | − | 764244.i | −0.726401 | − | 0.442271i | ||||
\(121\) | 900155. | 0.508114 | ||||||||
\(122\) | −2.13122e6 | + | 757004.i | −1.17368 | + | 0.416887i | ||||
\(123\) | − | 434052.i | − | 0.233253i | ||||||
\(124\) | −1.92240e6 | − | 2.36468e6i | −1.00827 | − | 1.24024i | ||||
\(125\) | −1.86317e6 | −0.953945 | ||||||||
\(126\) | −428201. | − | 1.20553e6i | −0.214060 | − | 0.602651i | ||||
\(127\) | 1.85216e6i | 0.904208i | 0.891965 | + | 0.452104i | \(0.149326\pi\) | ||||
−0.891965 | + | 0.452104i | \(0.850674\pi\) | |||||||
\(128\) | 1.53087e6 | + | 1.43334e6i | 0.729977 | + | 0.683471i | ||||
\(129\) | −718629. | −0.334762 | ||||||||
\(130\) | −332739. | + | 118188.i | −0.151452 | + | 0.0537953i | ||||
\(131\) | − | 226361.i | − | 0.100690i | −0.998732 | − | 0.0503451i | \(-0.983968\pi\) | ||
0.998732 | − | 0.0503451i | \(-0.0160321\pi\) | |||||||
\(132\) | 661108. | − | 537456.i | 0.287442 | − | 0.233680i | ||||
\(133\) | 478741. | 0.203491 | ||||||||
\(134\) | 962781. | + | 2.71055e6i | 0.400141 | + | 1.12653i | ||||
\(135\) | 3.60109e6i | 1.46363i | ||||||||
\(136\) | 1.09988e6 | − | 1.80648e6i | 0.437249 | − | 0.718153i | ||||
\(137\) | 4.89900e6 | 1.90522 | 0.952611 | − | 0.304192i | \(-0.0983863\pi\) | ||||
0.952611 | + | 0.304192i | \(0.0983863\pi\) | |||||||
\(138\) | 1.18866e6 | − | 422209.i | 0.452293 | − | 0.160653i | ||||
\(139\) | − | 5.05499e6i | − | 1.88224i | −0.338066 | − | 0.941122i | \(-0.609773\pi\) | ||
0.338066 | − | 0.941122i | \(-0.390227\pi\) | |||||||
\(140\) | −2.47208e6 | − | 3.04082e6i | −0.900903 | − | 1.10817i | ||||
\(141\) | 1.66873e6 | 0.595289 | ||||||||
\(142\) | −358805. | − | 1.01016e6i | −0.125312 | − | 0.352796i | ||||
\(143\) | − | 204719.i | − | 0.0700084i | ||||||
\(144\) | 439542. | − | 2.10759e6i | 0.147202 | − | 0.705828i | ||||
\(145\) | −2.63845e6 | −0.865456 | ||||||||
\(146\) | 1.71630e6 | − | 609627.i | 0.551487 | − | 0.195887i | ||||
\(147\) | − | 357766.i | − | 0.112628i | ||||||
\(148\) | 2.42967e6 | − | 1.97523e6i | 0.749483 | − | 0.609302i | ||||
\(149\) | 2.74913e6 | 0.831066 | 0.415533 | − | 0.909578i | \(-0.363595\pi\) | ||||
0.415533 | + | 0.909578i | \(0.363595\pi\) | |||||||
\(150\) | 950179. | + | 2.67507e6i | 0.281534 | + | 0.792613i | ||||
\(151\) | 3.60493e6i | 1.04705i | 0.852011 | + | 0.523523i | \(0.175383\pi\) | ||||
−0.852011 | + | 0.523523i | \(0.824617\pi\) | |||||||
\(152\) | 688149. | + | 418981.i | 0.195953 | + | 0.119306i | ||||
\(153\) | −2.17123e6 | −0.606222 | ||||||||
\(154\) | 2.14100e6 | − | 760478.i | 0.586211 | − | 0.208221i | ||||
\(155\) | 9.58368e6i | 2.57358i | ||||||||
\(156\) | 126264. | + | 155314.i | 0.0332588 | + | 0.0409106i | ||||
\(157\) | −3.36977e6 | −0.870766 | −0.435383 | − | 0.900245i | \(-0.643387\pi\) | ||||
−0.435383 | + | 0.900245i | \(0.643387\pi\) | |||||||
\(158\) | −1.99849e6 | − | 5.62641e6i | −0.506676 | − | 1.42646i | ||||
\(159\) | 1.93373e6i | 0.481065i | ||||||||
\(160\) | −892156. | − | 6.53441e6i | −0.217811 | − | 1.59531i | ||||
\(161\) | 3.36380e6 | 0.806032 | ||||||||
\(162\) | −965021. | + | 342773.i | −0.226982 | + | 0.0806236i | ||||
\(163\) | 1.68728e6i | 0.389606i | 0.980842 | + | 0.194803i | \(0.0624067\pi\) | ||||
−0.980842 | + | 0.194803i | \(0.937593\pi\) | |||||||
\(164\) | 1.51145e6 | − | 1.22876e6i | 0.342659 | − | 0.278570i | ||||
\(165\) | −2.67937e6 | −0.596458 | ||||||||
\(166\) | 1.23009e6 | + | 3.46311e6i | 0.268913 | + | 0.757080i | ||||
\(167\) | 12054.9i | 0.00258830i | 0.999999 | + | 0.00129415i | \(0.000411941\pi\) | ||||
−0.999999 | + | 0.00129415i | \(0.999588\pi\) | |||||||
\(168\) | −1.15527e6 | + | 1.89745e6i | −0.243643 | + | 0.400168i | ||||
\(169\) | −4.77871e6 | −0.990036 | ||||||||
\(170\) | −6.26745e6 | + | 2.22618e6i | −1.27569 | + | 0.453121i | ||||
\(171\) | − | 827095.i | − | 0.165412i | ||||||
\(172\) | −2.03436e6 | − | 2.50240e6i | −0.399800 | − | 0.491781i | ||||
\(173\) | −2.14415e6 | −0.414110 | −0.207055 | − | 0.978329i | \(-0.566388\pi\) | ||||
−0.207055 | + | 0.978329i | \(0.566388\pi\) | |||||||
\(174\) | 500606. | + | 1.40937e6i | 0.0950273 | + | 0.267533i | ||||
\(175\) | 7.57022e6i | 1.41252i | ||||||||
\(176\) | 3.74305e6 | + | 780620.i | 0.686574 | + | 0.143186i | ||||
\(177\) | −4.65050e6 | −0.838649 | ||||||||
\(178\) | −6.82592e6 | + | 2.42455e6i | −1.21032 | + | 0.429904i | ||||
\(179\) | 351257.i | 0.0612443i | 0.999531 | + | 0.0306221i | \(0.00974885\pi\) | ||||
−0.999531 | + | 0.0306221i | \(0.990251\pi\) | |||||||
\(180\) | −5.25346e6 | + | 4.27087e6i | −0.900799 | + | 0.732316i | ||||
\(181\) | 6.47595e6 | 1.09211 | 0.546057 | − | 0.837748i | \(-0.316128\pi\) | ||||
0.546057 | + | 0.837748i | \(0.316128\pi\) | |||||||
\(182\) | 178659. | + | 502984.i | 0.0296353 | + | 0.0834334i | ||||
\(183\) | − | 4.03175e6i | − | 0.657871i | ||||||
\(184\) | 4.83517e6 | + | 2.94390e6i | 0.776173 | + | 0.472574i | ||||
\(185\) | −9.84707e6 | −1.55522 | ||||||||
\(186\) | 5.11928e6 | − | 1.81836e6i | 0.795555 | − | 0.282579i | ||||
\(187\) | − | 3.85607e6i | − | 0.589685i | ||||||
\(188\) | 4.72399e6 | + | 5.81082e6i | 0.710943 | + | 0.874508i | ||||
\(189\) | 5.44357e6 | 0.806303 | ||||||||
\(190\) | −848028. | − | 2.38748e6i | −0.123637 | − | 0.348080i | ||||
\(191\) | − | 2.10096e6i | − | 0.301521i | −0.988570 | − | 0.150761i | \(-0.951828\pi\) | ||
0.988570 | − | 0.150761i | \(-0.0481722\pi\) | |||||||
\(192\) | −3.32119e6 | + | 1.71636e6i | −0.469235 | + | 0.242497i | ||||
\(193\) | 1.09660e7 | 1.52538 | 0.762689 | − | 0.646765i | \(-0.223879\pi\) | ||||
0.762689 | + | 0.646765i | \(0.223879\pi\) | |||||||
\(194\) | −1.19545e7 | + | 4.24620e6i | −1.63729 | + | 0.581561i | ||||
\(195\) | − | 629462.i | − | 0.0848918i | ||||||
\(196\) | 1.24581e6 | − | 1.01280e6i | 0.165456 | − | 0.134510i | ||||
\(197\) | −963490. | −0.126023 | −0.0630113 | − | 0.998013i | \(-0.520070\pi\) | ||||
−0.0630113 | + | 0.998013i | \(0.520070\pi\) | |||||||
\(198\) | −1.31383e6 | − | 3.69888e6i | −0.169256 | − | 0.476513i | ||||
\(199\) | − | 1.30813e7i | − | 1.65994i | −0.557807 | − | 0.829971i | \(-0.688357\pi\) | ||
0.557807 | − | 0.829971i | \(-0.311643\pi\) | |||||||
\(200\) | −6.62524e6 | + | 1.08815e7i | −0.828155 | + | 1.36019i | ||||
\(201\) | −5.12770e6 | −0.631444 | ||||||||
\(202\) | 6.97268e6 | − | 2.47668e6i | 0.845952 | − | 0.300480i | ||||
\(203\) | 3.98840e6i | 0.476772i | ||||||||
\(204\) | 2.37831e6 | + | 2.92548e6i | 0.280141 | + | 0.344593i | ||||
\(205\) | −6.12568e6 | −0.711038 | ||||||||
\(206\) | −194954. | − | 548861.i | −0.0223013 | − | 0.0627857i | ||||
\(207\) | − | 5.81145e6i | − | 0.655199i | ||||||
\(208\) | −183391. | + | 879352.i | −0.0203792 | + | 0.0977176i | ||||
\(209\) | 1.46891e6 | 0.160900 | ||||||||
\(210\) | 6.58306e6 | − | 2.33829e6i | 0.710837 | − | 0.252488i | ||||
\(211\) | − | 4.72673e6i | − | 0.503168i | −0.967835 | − | 0.251584i | \(-0.919049\pi\) | ||
0.967835 | − | 0.251584i | \(-0.0809515\pi\) | |||||||
\(212\) | −6.73359e6 | + | 5.47417e6i | −0.706707 | + | 0.574527i | ||||
\(213\) | 1.91097e6 | 0.197749 | ||||||||
\(214\) | 3.66049e6 | + | 1.03055e7i | 0.373507 | + | 1.05155i | ||||
\(215\) | 1.01418e7i | 1.02047i | ||||||||
\(216\) | 7.82466e6 | + | 4.76406e6i | 0.776433 | + | 0.472733i | ||||
\(217\) | 1.44871e7 | 1.41776 | ||||||||
\(218\) | 2.88599e6 | − | 1.02510e6i | 0.278565 | − | 0.0989455i | ||||
\(219\) | 3.24683e6i | 0.309121i | ||||||||
\(220\) | −7.58499e6 | − | 9.33005e6i | −0.712340 | − | 0.876226i | ||||
\(221\) | 905905. | 0.0839278 | ||||||||
\(222\) | 1.86833e6 | + | 5.25998e6i | 0.170764 | + | 0.480756i | ||||
\(223\) | − | 1.60135e7i | − | 1.44401i | −0.691886 | − | 0.722007i | \(-0.743220\pi\) | ||
0.691886 | − | 0.722007i | \(-0.256780\pi\) | |||||||
\(224\) | −9.87771e6 | + | 1.34862e6i | −0.878845 | + | 0.119990i | ||||
\(225\) | 1.30786e7 | 1.14819 | ||||||||
\(226\) | 1.17545e7 | − | 4.17517e6i | 1.01831 | − | 0.361700i | ||||
\(227\) | 1.44440e7i | 1.23484i | 0.786635 | + | 0.617419i | \(0.211822\pi\) | ||||
−0.786635 | + | 0.617419i | \(0.788178\pi\) | |||||||
\(228\) | −1.11441e6 | + | 905976.i | −0.0940245 | + | 0.0764385i | ||||
\(229\) | −2.13524e7 | −1.77804 | −0.889018 | − | 0.457873i | \(-0.848611\pi\) | ||||
−0.889018 | + | 0.457873i | \(0.848611\pi\) | |||||||
\(230\) | −5.95853e6 | − | 1.67752e7i | −0.489729 | − | 1.37875i | ||||
\(231\) | 4.05025e6i | 0.328584i | ||||||||
\(232\) | −3.49054e6 | + | 5.73299e6i | −0.279530 | + | 0.459110i | ||||
\(233\) | −2.21591e7 | −1.75180 | −0.875901 | − | 0.482491i | \(-0.839732\pi\) | ||||
−0.875901 | + | 0.482491i | \(0.839732\pi\) | |||||||
\(234\) | 868977. | − | 308659.i | 0.0678204 | − | 0.0240897i | ||||
\(235\) | − | 2.35504e7i | − | 1.81465i | ||||||
\(236\) | −1.31651e7 | − | 1.61939e7i | −1.00158 | − | 1.23201i | ||||
\(237\) | 1.06438e7 | 0.799562 | ||||||||
\(238\) | 3.36520e6 | + | 9.47416e6i | 0.249620 | + | 0.702765i | ||||
\(239\) | − | 1.95371e7i | − | 1.43109i | −0.698567 | − | 0.715544i | \(-0.746179\pi\) | ||
0.698567 | − | 0.715544i | \(-0.253821\pi\) | |||||||
\(240\) | 1.15090e7 | + | 2.40022e6i | 0.832536 | + | 0.173627i | ||||
\(241\) | 2.28838e7 | 1.63485 | 0.817424 | − | 0.576036i | \(-0.195401\pi\) | ||||
0.817424 | + | 0.576036i | \(0.195401\pi\) | |||||||
\(242\) | −6.78588e6 | + | 2.41033e6i | −0.478806 | + | 0.170071i | ||||
\(243\) | − | 1.48691e7i | − | 1.03625i | ||||||
\(244\) | 1.40393e7 | − | 1.14135e7i | 0.966444 | − | 0.785683i | ||||
\(245\) | −5.04906e6 | −0.343331 | ||||||||
\(246\) | 1.16225e6 | + | 3.27213e6i | 0.0780721 | + | 0.219799i | ||||
\(247\) | 345090.i | 0.0229003i | ||||||||
\(248\) | 2.08240e7 | + | 1.26787e7i | 1.36524 | + | 0.831229i | ||||
\(249\) | −6.55137e6 | −0.424360 | ||||||||
\(250\) | 1.40457e7 | − | 4.98899e6i | 0.898923 | − | 0.319295i | ||||
\(251\) | − | 1.64716e7i | − | 1.04163i | −0.853670 | − | 0.520815i | \(-0.825628\pi\) | ||
0.853670 | − | 0.520815i | \(-0.174372\pi\) | |||||||
\(252\) | 6.45604e6 | + | 7.94137e6i | 0.403427 | + | 0.496242i | ||||
\(253\) | 1.03210e7 | 0.637326 | ||||||||
\(254\) | −4.95951e6 | − | 1.39627e7i | −0.302648 | − | 0.852054i | ||||
\(255\) | − | 1.18565e7i | − | 0.715049i | ||||||
\(256\) | −1.53786e7 | − | 6.70616e6i | −0.916638 | − | 0.399719i | ||||
\(257\) | 2.44386e7 | 1.43972 | 0.719859 | − | 0.694120i | \(-0.244206\pi\) | ||||
0.719859 | + | 0.694120i | \(0.244206\pi\) | |||||||
\(258\) | 5.41743e6 | − | 1.92426e6i | 0.315453 | − | 0.112048i | ||||
\(259\) | 1.48853e7i | 0.856757i | ||||||||
\(260\) | 2.19191e6 | − | 1.78194e6i | 0.124710 | − | 0.101385i | ||||
\(261\) | 6.89054e6 | 0.387554 | ||||||||
\(262\) | 606123. | + | 1.70644e6i | 0.0337021 | + | 0.0948825i | ||||
\(263\) | 2.00725e7i | 1.10340i | 0.834041 | + | 0.551702i | \(0.186021\pi\) | ||||
−0.834041 | + | 0.551702i | \(0.813979\pi\) | |||||||
\(264\) | −3.54467e6 | + | 5.82189e6i | −0.192648 | + | 0.316411i | ||||
\(265\) | 2.72902e7 | 1.46646 | ||||||||
\(266\) | −3.60903e6 | + | 1.28192e6i | −0.191754 | + | 0.0681107i | ||||
\(267\) | − | 1.29130e7i | − | 0.678411i | ||||||
\(268\) | −1.45160e7 | − | 1.78556e7i | −0.754122 | − | 0.927621i | ||||
\(269\) | 796563. | 0.0409226 | 0.0204613 | − | 0.999791i | \(-0.493487\pi\) | ||||
0.0204613 | + | 0.999791i | \(0.493487\pi\) | |||||||
\(270\) | −9.64257e6 | − | 2.71470e7i | −0.489893 | − | 1.37921i | ||||
\(271\) | − | 1.04185e6i | − | 0.0523474i | −0.999657 | − | 0.0261737i | \(-0.991668\pi\) | ||
0.999657 | − | 0.0261737i | \(-0.00833230\pi\) | |||||||
\(272\) | −3.45433e6 | + | 1.65634e7i | −0.171655 | + | 0.823082i | ||||
\(273\) | −951524. | −0.0467662 | ||||||||
\(274\) | −3.69314e7 | + | 1.31180e7i | −1.79533 | + | 0.637698i | ||||
\(275\) | 2.32275e7i | 1.11687i | ||||||||
\(276\) | −7.83024e6 | + | 6.36570e6i | −0.372433 | + | 0.302774i | ||||
\(277\) | −2.26267e7 | −1.06459 | −0.532293 | − | 0.846560i | \(-0.678670\pi\) | ||||
−0.532293 | + | 0.846560i | \(0.678670\pi\) | |||||||
\(278\) | 1.35357e7 | + | 3.81074e7i | 0.630007 | + | 1.77368i | ||||
\(279\) | − | 2.50286e7i | − | 1.15246i | ||||||
\(280\) | 2.67783e7 | + | 1.63040e7i | 1.21986 | + | 0.742711i | ||||
\(281\) | 2.62054e6 | 0.118106 | 0.0590531 | − | 0.998255i | \(-0.481192\pi\) | ||||
0.0590531 | + | 0.998255i | \(0.481192\pi\) | |||||||
\(282\) | −1.25798e7 | + | 4.46832e6i | −0.560954 | + | 0.199249i | ||||
\(283\) | − | 1.42323e7i | − | 0.627935i | −0.949434 | − | 0.313967i | \(-0.898342\pi\) | ||
0.949434 | − | 0.313967i | \(-0.101658\pi\) | |||||||
\(284\) | 5.40975e6 | + | 6.65436e6i | 0.236169 | + | 0.290503i | ||||
\(285\) | 4.51654e6 | 0.195106 | ||||||||
\(286\) | 548173. | + | 1.54329e6i | 0.0234325 | + | 0.0659704i | ||||
\(287\) | 9.25986e6i | 0.391705i | ||||||||
\(288\) | 2.32994e6 | + | 1.70652e7i | 0.0975366 | + | 0.714386i | ||||
\(289\) | −7.07401e6 | −0.293070 | ||||||||
\(290\) | 1.98901e7 | − | 7.06494e6i | 0.815538 | − | 0.289677i | ||||
\(291\) | − | 2.26150e7i | − | 0.917734i | ||||||
\(292\) | −1.13061e7 | + | 9.19144e6i | −0.454113 | + | 0.369177i | ||||
\(293\) | −9.23155e6 | −0.367005 | −0.183502 | − | 0.983019i | \(-0.558743\pi\) | ||||
−0.183502 | + | 0.983019i | \(0.558743\pi\) | |||||||
\(294\) | 957983. | + | 2.69704e6i | 0.0376978 | + | 0.106132i | ||||
\(295\) | 6.56314e7i | 2.55650i | ||||||||
\(296\) | −1.30272e7 | + | 2.13963e7i | −0.502314 | + | 0.825018i | ||||
\(297\) | 1.67023e7 | 0.637541 | ||||||||
\(298\) | −2.07245e7 | + | 7.36129e6i | −0.783131 | + | 0.278167i | ||||
\(299\) | 2.42472e6i | 0.0907084i | ||||||||
\(300\) | −1.43260e7 | − | 1.76219e7i | −0.530592 | − | 0.652664i | ||||
\(301\) | 1.53309e7 | 0.562170 | ||||||||
\(302\) | −9.65286e6 | − | 2.71760e7i | −0.350457 | − | 0.986654i | ||||
\(303\) | 1.31906e7i | 0.474174i | ||||||||
\(304\) | −6.30956e6 | − | 1.31587e6i | −0.224584 | − | 0.0468374i | ||||
\(305\) | −5.68992e7 | −2.00543 | ||||||||
\(306\) | 1.63680e7 | − | 5.81387e6i | 0.571256 | − | 0.202909i | ||||
\(307\) | 4.33908e7i | 1.49962i | 0.661651 | + | 0.749812i | \(0.269856\pi\) | ||||
−0.661651 | + | 0.749812i | \(0.730144\pi\) | |||||||
\(308\) | −1.41037e7 | + | 1.14658e7i | −0.482705 | + | 0.392422i | ||||
\(309\) | 1.03831e6 | 0.0351927 | ||||||||
\(310\) | −2.56621e7 | − | 7.22472e7i | −0.861403 | − | 2.42514i | ||||
\(311\) | − | 3.03615e7i | − | 1.00935i | −0.863309 | − | 0.504676i | \(-0.831612\pi\) | ||
0.863309 | − | 0.504676i | \(-0.168388\pi\) | |||||||
\(312\) | −1.36773e6 | − | 832747.i | −0.0450337 | − | 0.0274189i | ||||
\(313\) | −4.96666e7 | −1.61969 | −0.809844 | − | 0.586645i | \(-0.800448\pi\) | ||||
−0.809844 | + | 0.586645i | \(0.800448\pi\) | |||||||
\(314\) | 2.54032e7 | − | 9.02318e6i | 0.820541 | − | 0.291454i | ||||
\(315\) | − | 3.21851e7i | − | 1.02973i | ||||||
\(316\) | 3.01315e7 | + | 3.70638e7i | 0.954903 | + | 1.17460i | ||||
\(317\) | −3.88885e7 | −1.22080 | −0.610398 | − | 0.792095i | \(-0.708991\pi\) | ||||
−0.610398 | + | 0.792095i | \(0.708991\pi\) | |||||||
\(318\) | −5.17790e6 | − | 1.45775e7i | −0.161017 | − | 0.453317i | ||||
\(319\) | 1.22375e7i | 0.376982i | ||||||||
\(320\) | 2.42227e7 | + | 4.68712e7i | 0.739217 | + | 1.43039i | ||||
\(321\) | −1.94955e7 | −0.589414 | ||||||||
\(322\) | −2.53582e7 | + | 9.00719e6i | −0.759541 | + | 0.269787i | ||||
\(323\) | 6.50008e6i | 0.192891i | ||||||||
\(324\) | 6.35704e6 | − | 5.16804e6i | 0.186905 | − | 0.151947i | ||||
\(325\) | −5.45682e6 | −0.158961 | ||||||||
\(326\) | −4.51801e6 | − | 1.27197e7i | −0.130405 | − | 0.367134i | ||||
\(327\) | 5.45961e6i | 0.156141i | ||||||||
\(328\) | −8.10397e6 | + | 1.33102e7i | −0.229655 | + | 0.377194i | ||||
\(329\) | −3.55998e7 | −0.999677 | ||||||||
\(330\) | 2.01986e7 | − | 7.17449e6i | 0.562055 | − | 0.199641i | ||||
\(331\) | 2.42937e7i | 0.669900i | 0.942236 | + | 0.334950i | \(0.108719\pi\) | ||||
−0.942236 | + | 0.334950i | \(0.891281\pi\) | |||||||
\(332\) | −1.85462e7 | − | 2.28131e7i | −0.506805 | − | 0.623405i | ||||
\(333\) | 2.57165e7 | 0.696432 | ||||||||
\(334\) | −32279.2 | − | 90876.7i | −0.000866330 | − | 0.00243901i | ||||
\(335\) | 7.23661e7i | 1.92487i | ||||||||
\(336\) | 3.62828e6 | − | 1.73975e7i | 0.0956496 | − | 0.458637i | ||||
\(337\) | −3.56079e7 | −0.930373 | −0.465186 | − | 0.885213i | \(-0.654013\pi\) | ||||
−0.465186 | + | 0.885213i | \(0.654013\pi\) | |||||||
\(338\) | 3.60247e7 | − | 1.27959e7i | 0.932932 | − | 0.331375i | ||||
\(339\) | 2.22367e7i | 0.570783i | ||||||||
\(340\) | 4.12866e7 | − | 3.35645e7i | 1.05044 | − | 0.853971i | ||||
\(341\) | 4.44504e7 | 1.12102 | ||||||||
\(342\) | 2.21470e6 | + | 6.23511e6i | 0.0553651 | + | 0.155871i | ||||
\(343\) | 4.34260e7i | 1.07614i | ||||||||
\(344\) | 2.20368e7 | + | 1.34171e7i | 0.541344 | + | 0.329598i | ||||
\(345\) | 3.17347e7 | 0.772818 | ||||||||
\(346\) | 1.61638e7 | − | 5.74134e6i | 0.390225 | − | 0.138607i | ||||
\(347\) | − | 1.40341e6i | − | 0.0335890i | −0.999859 | − | 0.0167945i | \(-0.994654\pi\) | ||
0.999859 | − | 0.0167945i | \(-0.00534610\pi\) | |||||||
\(348\) | −7.54771e6 | − | 9.28419e6i | −0.179092 | − | 0.220296i | ||||
\(349\) | −1.27027e7 | −0.298827 | −0.149413 | − | 0.988775i | \(-0.547739\pi\) | ||||
−0.149413 | + | 0.988775i | \(0.547739\pi\) | |||||||
\(350\) | −2.02706e7 | − | 5.70686e7i | −0.472785 | − | 1.33105i | ||||
\(351\) | 3.92387e6i | 0.0907389i | ||||||||
\(352\) | −3.03075e7 | + | 4.13794e6i | −0.694899 | + | 0.0948760i | ||||
\(353\) | 4.78227e7 | 1.08720 | 0.543601 | − | 0.839344i | \(-0.317061\pi\) | ||||
0.543601 | + | 0.839344i | \(0.317061\pi\) | |||||||
\(354\) | 3.50581e7 | − | 1.24526e7i | 0.790276 | − | 0.280704i | ||||
\(355\) | − | 2.69691e7i | − | 0.602811i | ||||||
\(356\) | 4.49655e7 | − | 3.65553e7i | 0.996619 | − | 0.810215i | ||||
\(357\) | −1.79228e7 | −0.393915 | ||||||||
\(358\) | −940554. | − | 2.64797e6i | −0.0204991 | − | 0.0577118i | ||||
\(359\) | 7.00860e7i | 1.51477i | 0.652966 | + | 0.757387i | \(0.273525\pi\) | ||||
−0.652966 | + | 0.757387i | \(0.726475\pi\) | |||||||
\(360\) | 2.81675e7 | − | 4.62633e7i | 0.603728 | − | 0.991584i | ||||
\(361\) | −2.47610e6 | −0.0526316 | ||||||||
\(362\) | −4.88194e7 | + | 1.73406e7i | −1.02912 | + | 0.365542i | ||||
\(363\) | − | 1.28373e7i | − | 0.268381i | ||||||
\(364\) | −2.69366e6 | − | 3.31339e6i | −0.0558520 | − | 0.0687018i | ||||
\(365\) | 4.58218e7 | 0.942310 | ||||||||
\(366\) | 1.07958e7 | + | 3.03936e7i | 0.220196 | + | 0.619926i | ||||
\(367\) | − | 1.78296e7i | − | 0.360699i | −0.983603 | − | 0.180349i | \(-0.942277\pi\) | ||
0.983603 | − | 0.180349i | \(-0.0577228\pi\) | |||||||
\(368\) | −4.43331e7 | − | 9.24575e6i | −0.889579 | − | 0.185523i | ||||
\(369\) | 1.59977e7 | 0.318405 | ||||||||
\(370\) | 7.42328e7 | − | 2.63673e7i | 1.46552 | − | 0.520548i | ||||
\(371\) | − | 4.12531e7i | − | 0.807858i | ||||||
\(372\) | −3.37231e7 | + | 2.74156e7i | −0.655086 | + | 0.532561i | ||||
\(373\) | −3.47591e7 | −0.669795 | −0.334898 | − | 0.942254i | \(-0.608702\pi\) | ||||
−0.334898 | + | 0.942254i | \(0.608702\pi\) | |||||||
\(374\) | 1.03253e7 | + | 2.90693e7i | 0.197374 | + | 0.555673i | ||||
\(375\) | 2.65710e7i | 0.503865i | ||||||||
\(376\) | −5.11716e7 | − | 3.11559e7i | −0.962644 | − | 0.586107i | ||||
\(377\) | −2.87495e6 | −0.0536545 | ||||||||
\(378\) | −4.10367e7 | + | 1.45762e7i | −0.759797 | + | 0.269878i | ||||
\(379\) | − | 4.69020e7i | − | 0.861536i | −0.902463 | − | 0.430768i | \(-0.858243\pi\) | ||
0.902463 | − | 0.430768i | \(-0.141757\pi\) | |||||||
\(380\) | 1.27858e7 | + | 1.57274e7i | 0.233012 | + | 0.286620i | ||||
\(381\) | 2.64140e7 | 0.477595 | ||||||||
\(382\) | 5.62570e6 | + | 1.58382e7i | 0.100922 | + | 0.284130i | ||||
\(383\) | − | 2.59506e7i | − | 0.461903i | −0.972965 | − | 0.230952i | \(-0.925816\pi\) | ||
0.972965 | − | 0.230952i | \(-0.0741839\pi\) | |||||||
\(384\) | 2.04411e7 | − | 2.18320e7i | 0.361003 | − | 0.385568i | ||||
\(385\) | 5.71603e7 | 1.00164 | ||||||||
\(386\) | −8.26682e7 | + | 2.93636e7i | −1.43740 | + | 0.510560i | ||||
\(387\) | − | 2.64863e7i | − | 0.456971i | ||||||
\(388\) | 7.87496e7 | − | 6.40205e7i | 1.34820 | − | 1.09603i | ||||
\(389\) | 5.98509e7 | 1.01677 | 0.508384 | − | 0.861130i | \(-0.330243\pi\) | ||||
0.508384 | + | 0.861130i | \(0.330243\pi\) | |||||||
\(390\) | 1.68550e6 | + | 4.74524e6i | 0.0284142 | + | 0.0799954i | ||||
\(391\) | 4.56718e7i | 0.764043i | ||||||||
\(392\) | −6.67966e6 | + | 1.09709e7i | −0.110891 | + | 0.182131i | ||||
\(393\) | −3.22817e6 | −0.0531837 | ||||||||
\(394\) | 7.26333e6 | − | 2.57992e6i | 0.118754 | − | 0.0421811i | ||||
\(395\) | − | 1.50214e8i | − | 2.43735i | ||||||
\(396\) | 1.98089e7 | + | 2.43662e7i | 0.318988 | + | 0.392377i | ||||
\(397\) | −5.66329e7 | −0.905101 | −0.452551 | − | 0.891739i | \(-0.649486\pi\) | ||||
−0.452551 | + | 0.891739i | \(0.649486\pi\) | |||||||
\(398\) | 3.50277e7 | + | 9.86145e7i | 0.555600 | + | 1.56420i | ||||
\(399\) | − | 6.82741e6i | − | 0.107482i | ||||||
\(400\) | 2.08075e7 | − | 9.97715e7i | 0.325118 | − | 1.55893i | ||||
\(401\) | −2.81556e7 | −0.436649 | −0.218324 | − | 0.975876i | \(-0.570059\pi\) | ||||
−0.218324 | + | 0.975876i | \(0.570059\pi\) | |||||||
\(402\) | 3.86556e7 | − | 1.37304e7i | 0.595023 | − | 0.211351i | ||||
\(403\) | 1.04427e7i | 0.159551i | ||||||||
\(404\) | −4.59323e7 | + | 3.73413e7i | −0.696585 | + | 0.566298i | ||||
\(405\) | −2.57641e7 | −0.387837 | ||||||||
\(406\) | −1.06797e7 | − | 3.00669e7i | −0.159581 | − | 0.449273i | ||||
\(407\) | 4.56720e7i | 0.677434i | ||||||||
\(408\) | −2.57625e7 | − | 1.56856e7i | −0.379322 | − | 0.230951i | ||||
\(409\) | −5.69492e7 | −0.832373 | −0.416187 | − | 0.909279i | \(-0.636634\pi\) | ||||
−0.416187 | + | 0.909279i | \(0.636634\pi\) | |||||||
\(410\) | 4.61788e7 | − | 1.64026e7i | 0.670026 | − | 0.237992i | ||||
\(411\) | − | 6.98654e7i | − | 1.00632i | ||||||
\(412\) | 2.93935e6 | + | 3.61560e6i | 0.0420301 | + | 0.0516998i | ||||
\(413\) | 9.92115e7 | 1.40835 | ||||||||
\(414\) | 1.55612e7 | + | 4.38100e7i | 0.219302 | + | 0.617408i | ||||
\(415\) | 9.24580e7i | 1.29360i | ||||||||
\(416\) | −972124. | − | 7.12012e6i | −0.0135034 | − | 0.0989025i | ||||
\(417\) | −7.20901e7 | −0.994185 | ||||||||
\(418\) | −1.10735e7 | + | 3.93327e6i | −0.151619 | + | 0.0538548i | ||||
\(419\) | − | 1.28188e8i | − | 1.74263i | −0.490724 | − | 0.871315i | \(-0.663268\pi\) | ||
0.490724 | − | 0.871315i | \(-0.336732\pi\) | |||||||
\(420\) | −4.33656e7 | + | 3.52547e7i | −0.585326 | + | 0.475849i | ||||
\(421\) | 1.38826e8 | 1.86048 | 0.930238 | − | 0.366957i | \(-0.119600\pi\) | ||||
0.930238 | + | 0.366957i | \(0.119600\pi\) | |||||||
\(422\) | 1.26567e7 | + | 3.56327e7i | 0.168416 | + | 0.474146i | ||||
\(423\) | 6.15038e7i | 0.812607i | ||||||||
\(424\) | 3.61036e7 | − | 5.92978e7i | 0.473645 | − | 0.777931i | ||||
\(425\) | −1.02784e8 | −1.33893 | ||||||||
\(426\) | −1.44060e7 | + | 5.11698e6i | −0.186344 | + | 0.0661888i | ||||
\(427\) | 8.60114e7i | 1.10477i | ||||||||
\(428\) | −5.51897e7 | − | 6.78871e7i | −0.703926 | − | 0.865877i | ||||
\(429\) | −2.91953e6 | −0.0369778 | ||||||||
\(430\) | −2.71566e7 | − | 7.64550e7i | −0.341563 | − | 0.961613i | ||||
\(431\) | 5.38586e7i | 0.672703i | 0.941737 | + | 0.336351i | \(0.109193\pi\) | ||||
−0.941737 | + | 0.336351i | \(0.890807\pi\) | |||||||
\(432\) | −7.17434e7 | − | 1.49622e7i | −0.889878 | − | 0.185586i | ||||
\(433\) | −2.00516e7 | −0.246994 | −0.123497 | − | 0.992345i | \(-0.539411\pi\) | ||||
−0.123497 | + | 0.992345i | \(0.539411\pi\) | |||||||
\(434\) | −1.09212e8 | + | 3.87920e7i | −1.33599 | + | 0.474540i | ||||
\(435\) | 3.76274e7i | 0.457126i | ||||||||
\(436\) | −1.90114e7 | + | 1.54556e7i | −0.229379 | + | 0.186477i | ||||
\(437\) | −1.73979e7 | −0.208474 | ||||||||
\(438\) | −8.69399e6 | − | 2.44765e7i | −0.103466 | − | 0.291291i | ||||
\(439\) | 4.22684e7i | 0.499600i | 0.968297 | + | 0.249800i | \(0.0803649\pi\) | ||||
−0.968297 | + | 0.249800i | \(0.919635\pi\) | |||||||
\(440\) | 8.21629e7 | + | 5.00250e7i | 0.964535 | + | 0.587259i | ||||
\(441\) | 1.31861e7 | 0.153744 | ||||||||
\(442\) | −6.82923e6 | + | 2.42573e6i | −0.0790870 | + | 0.0280915i | ||||
\(443\) | − | 1.28540e8i | − | 1.47852i | −0.673418 | − | 0.739262i | \(-0.735174\pi\) | ||
0.673418 | − | 0.739262i | \(-0.264826\pi\) | |||||||
\(444\) | −2.81691e7 | − | 3.46499e7i | −0.321828 | − | 0.395870i | ||||
\(445\) | −1.82238e8 | −2.06804 | ||||||||
\(446\) | 4.28790e7 | + | 1.20719e8i | 0.483326 | + | 1.36072i | ||||
\(447\) | − | 3.92057e7i | − | 0.438962i | ||||||
\(448\) | 7.08526e7 | − | 3.66161e7i | 0.787992 | − | 0.407228i | ||||
\(449\) | 7.85801e7 | 0.868108 | 0.434054 | − | 0.900887i | \(-0.357083\pi\) | ||||
0.434054 | + | 0.900887i | \(0.357083\pi\) | |||||||
\(450\) | −9.85942e7 | + | 3.50205e7i | −1.08197 | + | 0.384312i | ||||
\(451\) | 2.84117e7i | 0.309719i | ||||||||
\(452\) | −7.74323e7 | + | 6.29496e7i | −0.838507 | + | 0.681675i | ||||
\(453\) | 5.14105e7 | 0.553041 | ||||||||
\(454\) | −3.86764e7 | − | 1.08887e8i | −0.413313 | − | 1.16361i | ||||
\(455\) | 1.34286e7i | 0.142560i | ||||||||
\(456\) | 5.97515e6 | − | 9.81381e6i | 0.0630165 | − | 0.103501i | ||||
\(457\) | −3.52825e6 | −0.0369667 | −0.0184833 | − | 0.999829i | \(-0.505884\pi\) | ||||
−0.0184833 | + | 0.999829i | \(0.505884\pi\) | |||||||
\(458\) | 1.60967e8 | − | 5.71750e7i | 1.67548 | − | 0.595127i | ||||
\(459\) | 7.39097e7i | 0.764300i | ||||||||
\(460\) | 8.98376e7 | + | 1.10506e8i | 0.922963 | + | 1.13531i | ||||
\(461\) | 1.35044e8 | 1.37839 | 0.689194 | − | 0.724577i | \(-0.257965\pi\) | ||||
0.689194 | + | 0.724577i | \(0.257965\pi\) | |||||||
\(462\) | −1.08453e7 | − | 3.05331e7i | −0.109980 | − | 0.309632i | ||||
\(463\) | − | 1.53732e8i | − | 1.54890i | −0.632637 | − | 0.774448i | \(-0.718027\pi\) | ||
0.632637 | − | 0.774448i | \(-0.281973\pi\) | |||||||
\(464\) | 1.09625e7 | − | 5.25651e7i | 0.109738 | − | 0.526191i | ||||
\(465\) | 1.36674e8 | 1.35934 | ||||||||
\(466\) | 1.67048e8 | − | 5.93351e7i | 1.65076 | − | 0.586346i | ||||
\(467\) | − | 4.70204e7i | − | 0.461675i | −0.972992 | − | 0.230837i | \(-0.925854\pi\) | ||
0.972992 | − | 0.230837i | \(-0.0741465\pi\) | |||||||
\(468\) | −5.72435e6 | + | 4.65369e6i | −0.0558456 | + | 0.0454004i | ||||
\(469\) | 1.09392e8 | 1.06039 | ||||||||
\(470\) | 6.30604e7 | + | 1.77536e8i | 0.607383 | + | 1.70999i | ||||
\(471\) | 4.80568e7i | 0.459931i | ||||||||
\(472\) | 1.42608e8 | + | 8.68271e7i | 1.35618 | + | 0.825713i | ||||
\(473\) | 4.70392e7 | 0.444505 | ||||||||
\(474\) | −8.02391e7 | + | 2.85008e7i | −0.753444 | + | 0.267622i | ||||
\(475\) | − | 3.91539e7i | − | 0.365338i | ||||||
\(476\) | −5.07376e7 | − | 6.24107e7i | −0.470445 | − | 0.578679i | ||||
\(477\) | −7.12707e7 | −0.656683 | ||||||||
\(478\) | 5.23142e7 | + | 1.47282e8i | 0.479000 | + | 1.34854i | ||||
\(479\) | − | 1.05499e8i | − | 0.959938i | −0.877285 | − | 0.479969i | \(-0.840648\pi\) | ||
0.877285 | − | 0.479969i | \(-0.159352\pi\) | |||||||
\(480\) | −9.31882e7 | + | 1.27232e7i | −0.842631 | + | 0.115046i | ||||
\(481\) | −1.07297e7 | −0.0964168 | ||||||||
\(482\) | −1.72511e8 | + | 6.12756e7i | −1.54055 | + | 0.547201i | ||||
\(483\) | − | 4.79717e7i | − | 0.425739i | ||||||
\(484\) | 4.47017e7 | − | 3.63409e7i | 0.394265 | − | 0.320523i | ||||
\(485\) | −3.19160e8 | −2.79758 | ||||||||
\(486\) | 3.98147e7 | + | 1.12092e8i | 0.346845 | + | 0.976483i | ||||
\(487\) | 7.29337e7i | 0.631454i | 0.948850 | + | 0.315727i | \(0.102248\pi\) | ||||
−0.948850 | + | 0.315727i | \(0.897752\pi\) | |||||||
\(488\) | −7.52747e7 | + | 1.23634e8i | −0.647724 | + | 1.06384i | ||||
\(489\) | 2.40626e7 | 0.205786 | ||||||||
\(490\) | 3.80627e7 | − | 1.35198e7i | 0.323528 | − | 0.114916i | ||||
\(491\) | − | 1.76733e8i | − | 1.49305i | −0.665359 | − | 0.746524i | \(-0.731722\pi\) | ||
0.665359 | − | 0.746524i | \(-0.268278\pi\) | |||||||
\(492\) | −1.75235e7 | − | 2.15551e7i | −0.147138 | − | 0.180990i | ||||
\(493\) | −5.41523e7 | −0.451935 | ||||||||
\(494\) | −924041. | − | 2.60148e6i | −0.00766497 | − | 0.0215794i | ||||
\(495\) | − | 9.87526e7i | − | 0.814203i | ||||||
\(496\) | −1.90933e8 | − | 3.98194e7i | −1.56472 | − | 0.326324i | ||||
\(497\) | −4.07677e7 | −0.332083 | ||||||||
\(498\) | 4.93880e7 | − | 1.75425e7i | 0.399883 | − | 0.142038i | ||||
\(499\) | 4.09661e7i | 0.329703i | 0.986318 | + | 0.164852i | \(0.0527145\pi\) | ||||
−0.986318 | + | 0.164852i | \(0.947285\pi\) | |||||||
\(500\) | −9.25253e7 | + | 7.52197e7i | −0.740202 | + | 0.601757i | ||||
\(501\) | 171917. | 0.00136712 | ||||||||
\(502\) | 4.41056e7 | + | 1.24172e8i | 0.348644 | + | 0.981550i | ||||
\(503\) | 2.79451e7i | 0.219584i | 0.993955 | + | 0.109792i | \(0.0350185\pi\) | ||||
−0.993955 | + | 0.109792i | \(0.964981\pi\) | |||||||
\(504\) | −6.99338e7 | − | 4.25793e7i | −0.546255 | − | 0.332588i | ||||
\(505\) | 1.86156e8 | 1.44545 | ||||||||
\(506\) | −7.78058e7 | + | 2.76365e7i | −0.600566 | + | 0.213320i | ||||
\(507\) | 6.81500e7i | 0.522928i | ||||||||
\(508\) | 7.47752e7 | + | 9.19785e7i | 0.570383 | + | 0.701609i | ||||
\(509\) | −1.06277e7 | −0.0805911 | −0.0402956 | − | 0.999188i | \(-0.512830\pi\) | ||||
−0.0402956 | + | 0.999188i | \(0.512830\pi\) | |||||||
\(510\) | 3.17480e7 | + | 8.93811e7i | 0.239334 | + | 0.673806i | ||||
\(511\) | − | 6.92664e7i | − | 0.519110i | ||||||
\(512\) | 1.33890e8 | + | 9.37577e6i | 0.997557 | + | 0.0698549i | ||||
\(513\) | −2.81547e7 | −0.208544 | ||||||||
\(514\) | −1.84232e8 | + | 6.54389e7i | −1.35668 | + | 0.481889i | ||||
\(515\) | − | 1.46535e7i | − | 0.107280i | ||||||
\(516\) | −3.56871e7 | + | 2.90123e7i | −0.259754 | + | 0.211171i | ||||
\(517\) | −1.09230e8 | −0.790441 | ||||||||
\(518\) | −3.98581e7 | − | 1.12214e8i | −0.286766 | − | 0.807340i | ||||
\(519\) | 3.05780e7i | 0.218729i | ||||||||
\(520\) | −1.17524e7 | + | 1.93025e7i | −0.0835825 | + | 0.137279i | ||||
\(521\) | −3.34642e7 | −0.236629 | −0.118314 | − | 0.992976i | \(-0.537749\pi\) | ||||
−0.118314 | + | 0.992976i | \(0.537749\pi\) | |||||||
\(522\) | −5.19448e7 | + | 1.84507e7i | −0.365200 | + | 0.129718i | ||||
\(523\) | − | 2.51990e8i | − | 1.76148i | −0.473601 | − | 0.880740i | \(-0.657046\pi\) | ||
0.473601 | − | 0.880740i | \(-0.342954\pi\) | |||||||
\(524\) | −9.13859e6 | − | 1.12411e7i | −0.0635163 | − | 0.0781294i | ||||
\(525\) | 1.07960e8 | 0.746080 | ||||||||
\(526\) | −5.37478e7 | − | 1.51318e8i | −0.369321 | − | 1.03976i | ||||
\(527\) | 1.96698e8i | 1.34390i | ||||||||
\(528\) | 1.11325e7 | − | 5.33802e7i | 0.0756297 | − | 0.362642i | ||||
\(529\) | 2.57923e7 | 0.174230 | ||||||||
\(530\) | −2.05729e8 | + | 7.30745e7i | −1.38187 | + | 0.490838i | ||||
\(531\) | − | 1.71402e8i | − | 1.14481i | ||||||
\(532\) | 2.37743e7 | − | 1.93277e7i | 0.157897 | − | 0.128364i | ||||
\(533\) | −6.67476e6 | −0.0440812 | ||||||||
\(534\) | 3.45769e7 | + | 9.73455e7i | 0.227071 | + | 0.639281i | ||||
\(535\) | 2.75136e8i | 1.79674i | ||||||||
\(536\) | 1.57241e8 | + | 9.57367e7i | 1.02111 | + | 0.621705i | ||||
\(537\) | 5.00933e6 | 0.0323487 | ||||||||
\(538\) | −6.00494e6 | + | 2.13294e6i | −0.0385622 | + | 0.0136972i | ||||
\(539\) | 2.34182e7i | 0.149550i | ||||||||
\(540\) | 1.45382e8 | + | 1.78830e8i | 0.923274 | + | 1.13569i | ||||
\(541\) | −1.23124e8 | −0.777593 | −0.388796 | − | 0.921324i | \(-0.627109\pi\) | ||||
−0.388796 | + | 0.921324i | \(0.627109\pi\) | |||||||
\(542\) | 2.78973e6 | + | 7.85402e6i | 0.0175212 | + | 0.0493281i | ||||
\(543\) | − | 9.23546e7i | − | 0.576845i | ||||||
\(544\) | −1.83109e7 | − | 1.34114e8i | −0.113740 | − | 0.833062i | ||||
\(545\) | 7.70501e7 | 0.475975 | ||||||||
\(546\) | 7.17313e6 | − | 2.54788e6i | 0.0440688 | − | 0.0156531i | ||||
\(547\) | 1.61396e8i | 0.986120i | 0.869995 | + | 0.493060i | \(0.164122\pi\) | ||||
−0.869995 | + | 0.493060i | \(0.835878\pi\) | |||||||
\(548\) | 2.43284e8 | − | 1.97781e8i | 1.47833 | − | 1.20183i | ||||
\(549\) | 1.48597e8 | 0.898035 | ||||||||
\(550\) | −6.21958e7 | − | 1.75102e8i | −0.373829 | − | 1.05245i | ||||
\(551\) | − | 2.06284e7i | − | 0.123314i | ||||||
\(552\) | 4.19834e7 | − | 6.89551e7i | 0.249609 | − | 0.409967i | ||||
\(553\) | −2.27070e8 | −1.34272 | ||||||||
\(554\) | 1.70573e8 | − | 6.05870e7i | 1.00318 | − | 0.356328i | ||||
\(555\) | 1.40431e8i | 0.821453i | ||||||||
\(556\) | −2.04079e8 | − | 2.51031e8i | −1.18734 | − | 1.46051i | ||||
\(557\) | 6.79124e7 | 0.392992 | 0.196496 | − | 0.980505i | \(-0.437044\pi\) | ||||
0.196496 | + | 0.980505i | \(0.437044\pi\) | |||||||
\(558\) | 6.70187e7 | + | 1.88680e8i | 0.385739 | + | 1.08598i | ||||
\(559\) | 1.10509e7i | 0.0632648i | ||||||||
\(560\) | −2.45527e8 | − | 5.12051e7i | −1.39809 | − | 0.291574i | ||||
\(561\) | −5.49921e7 | −0.311467 | ||||||||
\(562\) | −1.97552e7 | + | 7.01699e6i | −0.111294 | + | 0.0395314i | ||||
\(563\) | 1.63874e8i | 0.918300i | 0.888359 | + | 0.459150i | \(0.151846\pi\) | ||||
−0.888359 | + | 0.459150i | \(0.848154\pi\) | |||||||
\(564\) | 8.28690e7 | − | 6.73695e7i | 0.461907 | − | 0.375514i | ||||
\(565\) | 3.13821e8 | 1.73995 | ||||||||
\(566\) | 3.81095e7 | + | 1.07291e8i | 0.210176 | + | 0.591716i | ||||
\(567\) | 3.89462e7i | 0.213656i | ||||||||
\(568\) | −5.86001e7 | − | 3.56787e7i | −0.319781 | − | 0.194699i | ||||
\(569\) | 4.76512e7 | 0.258664 | 0.129332 | − | 0.991601i | \(-0.458717\pi\) | ||||
0.129332 | + | 0.991601i | \(0.458717\pi\) | |||||||
\(570\) | −3.40482e7 | + | 1.20939e7i | −0.183853 | + | 0.0653041i | ||||
\(571\) | 2.89473e8i | 1.55489i | 0.628950 | + | 0.777446i | \(0.283485\pi\) | ||||
−0.628950 | + | 0.777446i | \(0.716515\pi\) | |||||||
\(572\) | −8.26488e6 | − | 1.01664e7i | −0.0441620 | − | 0.0543222i | ||||
\(573\) | −2.99621e7 | −0.159261 | ||||||||
\(574\) | −2.47950e7 | − | 6.98061e7i | −0.131108 | − | 0.369111i | ||||
\(575\) | − | 2.75109e8i | − | 1.44711i | ||||||
\(576\) | −6.32596e7 | − | 1.22408e8i | −0.331023 | − | 0.640535i | ||||
\(577\) | −1.68949e8 | −0.879487 | −0.439744 | − | 0.898123i | \(-0.644931\pi\) | ||||
−0.439744 | + | 0.898123i | \(0.644931\pi\) | |||||||
\(578\) | 5.33279e7 | − | 1.89419e7i | 0.276166 | − | 0.0980937i | ||||
\(579\) | − | 1.56388e8i | − | 0.805691i | ||||||
\(580\) | −1.31026e8 | + | 1.06519e8i | −0.671540 | + | 0.545938i | ||||
\(581\) | 1.39764e8 | 0.712633 | ||||||||
\(582\) | 6.05557e7 | + | 1.70484e8i | 0.307175 | + | 0.864801i | ||||
\(583\) | − | 1.26576e8i | − | 0.638770i | ||||||
\(584\) | 6.06199e7 | − | 9.95644e7i | 0.304353 | − | 0.499880i | ||||
\(585\) | 2.31999e7 | 0.115883 | ||||||||
\(586\) | 6.95926e7 | − | 2.47192e7i | 0.345836 | − | 0.122840i | ||||
\(587\) | − | 887448.i | − | 0.00438762i | −0.999998 | − | 0.00219381i | \(-0.999302\pi\) | ||
0.999998 | − | 0.00219381i | \(-0.000698311\pi\) | |||||||
\(588\) | −1.44436e7 | − | 1.77667e7i | −0.0710468 | − | 0.0873924i | ||||
\(589\) | −7.49289e7 | −0.366694 | ||||||||
\(590\) | −1.75740e8 | − | 4.94767e8i | −0.855687 | − | 2.40904i | ||||
\(591\) | 1.37405e7i | 0.0665640i | ||||||||
\(592\) | 4.09137e7 | − | 1.96180e8i | 0.197199 | − | 0.945562i | ||||
\(593\) | −2.75935e7 | −0.132325 | −0.0661627 | − | 0.997809i | \(-0.521076\pi\) | ||||
−0.0661627 | + | 0.997809i | \(0.521076\pi\) | |||||||
\(594\) | −1.25912e8 | + | 4.47236e7i | −0.600768 | + | 0.213391i | ||||
\(595\) | 2.52941e8i | 1.20079i | ||||||||
\(596\) | 1.36522e8 | − | 1.10987e8i | 0.644856 | − | 0.524244i | ||||
\(597\) | −1.86555e8 | −0.876766 | ||||||||
\(598\) | −6.49262e6 | − | 1.82789e7i | −0.0303610 | − | 0.0854764i | ||||
\(599\) | − | 1.16393e8i | − | 0.541562i | −0.962641 | − | 0.270781i | \(-0.912718\pi\) | ||
0.962641 | − | 0.270781i | \(-0.0872819\pi\) | |||||||
\(600\) | 1.55183e8 | + | 9.44836e7i | 0.718441 | + | 0.437424i | ||||
\(601\) | 1.62465e8 | 0.748402 | 0.374201 | − | 0.927348i | \(-0.377917\pi\) | ||||
0.374201 | + | 0.927348i | \(0.377917\pi\) | |||||||
\(602\) | −1.15573e8 | + | 4.10512e7i | −0.529744 | + | 0.188164i | ||||
\(603\) | − | 1.88990e8i | − | 0.861961i | ||||||
\(604\) | 1.45538e8 | + | 1.79021e8i | 0.660487 | + | 0.812443i | ||||
\(605\) | −1.81169e8 | −0.818122 | ||||||||
\(606\) | −3.53204e7 | − | 9.94385e7i | −0.158711 | − | 0.446824i | ||||
\(607\) | 1.74742e8i | 0.781324i | 0.920534 | + | 0.390662i | \(0.127754\pi\) | ||||
−0.920534 | + | 0.390662i | \(0.872246\pi\) | |||||||
\(608\) | 5.10885e7 | − | 6.97522e6i | 0.227307 | − | 0.0310347i | ||||
\(609\) | 5.68793e7 | 0.251827 | ||||||||
\(610\) | 4.28938e8 | − | 1.52358e8i | 1.88975 | − | 0.671237i | ||||
\(611\) | − | 2.56613e7i | − | 0.112501i | ||||||
\(612\) | −1.07823e8 | + | 8.76565e7i | −0.470391 | + | 0.382411i | ||||
\(613\) | 7.67842e7 | 0.333342 | 0.166671 | − | 0.986013i | \(-0.446698\pi\) | ||||
0.166671 | + | 0.986013i | \(0.446698\pi\) | |||||||
\(614\) | −1.16187e8 | − | 3.27105e8i | −0.501940 | − | 1.41313i | ||||
\(615\) | 8.73593e7i | 0.375564i | ||||||||
\(616\) | 7.56202e7 | − | 1.24201e8i | 0.323516 | − | 0.531354i | ||||
\(617\) | 2.39522e8 | 1.01974 | 0.509872 | − | 0.860251i | \(-0.329693\pi\) | ||||
0.509872 | + | 0.860251i | \(0.329693\pi\) | |||||||
\(618\) | −7.82740e6 | + | 2.78027e6i | −0.0331629 | + | 0.0117794i | ||||
\(619\) | 2.49504e8i | 1.05198i | 0.850492 | + | 0.525988i | \(0.176304\pi\) | ||||
−0.850492 | + | 0.525988i | \(0.823696\pi\) | |||||||
\(620\) | 3.86910e8 | + | 4.75926e8i | 1.62344 | + | 1.99694i | ||||
\(621\) | −1.97824e8 | −0.826048 | ||||||||
\(622\) | 8.12985e7 | + | 2.28882e8i | 0.337840 | + | 0.951133i | ||||
\(623\) | 2.75479e8i | 1.13927i | ||||||||
\(624\) | 1.25406e7 | + | 2.61536e6i | 0.0516136 | + | 0.0107641i | ||||
\(625\) | −1.37961e7 | −0.0565089 | ||||||||
\(626\) | 3.74415e8 | − | 1.32991e8i | 1.52627 | − | 0.542126i | ||||
\(627\) | − | 2.09483e7i | − | 0.0849858i | ||||||
\(628\) | −1.67343e8 | + | 1.36044e8i | −0.675660 | + | 0.549287i | ||||
\(629\) | −2.02104e8 | −0.812125 | ||||||||
\(630\) | 8.61816e7 | + | 2.42630e8i | 0.344662 | + | 0.970337i | ||||
\(631\) | − | 1.47158e8i | − | 0.585727i | −0.956154 | − | 0.292863i | \(-0.905392\pi\) | ||
0.956154 | − | 0.292863i | \(-0.0946081\pi\) | |||||||
\(632\) | −3.26393e8 | − | 1.98725e8i | −1.29297 | − | 0.787230i | ||||
\(633\) | −6.74086e7 | −0.265769 | ||||||||
\(634\) | 2.93163e8 | − | 1.04131e8i | 1.15038 | − | 0.408613i | ||||
\(635\) | − | 3.72775e8i | − | 1.45588i | ||||||
\(636\) | 7.80680e7 | + | 9.60288e7i | 0.303460 | + | 0.373276i | ||||
\(637\) | −5.50164e6 | −0.0212850 | ||||||||
\(638\) | −3.27681e7 | − | 9.22532e7i | −0.126180 | − | 0.355238i | ||||
\(639\) | 7.04321e7i | 0.269941i | ||||||||
\(640\) | −3.08110e8 | − | 2.88481e8i | −1.17535 | − | 1.10047i | ||||
\(641\) | 1.03678e8 | 0.393653 | 0.196826 | − | 0.980438i | \(-0.436936\pi\) | ||||
0.196826 | + | 0.980438i | \(0.436936\pi\) | |||||||
\(642\) | 1.46968e8 | − | 5.22029e7i | 0.555417 | − | 0.197283i | ||||
\(643\) | 2.23604e8i | 0.841098i | 0.907270 | + | 0.420549i | \(0.138163\pi\) | ||||
−0.907270 | + | 0.420549i | \(0.861837\pi\) | |||||||
\(644\) | 1.67046e8 | − | 1.35803e8i | 0.625431 | − | 0.508453i | ||||
\(645\) | 1.44634e8 | 0.539005 | ||||||||
\(646\) | −1.74052e7 | − | 4.90013e7i | −0.0645625 | − | 0.181765i | ||||
\(647\) | − | 4.10400e8i | − | 1.51529i | −0.652670 | − | 0.757643i | \(-0.726351\pi\) | ||
0.652670 | − | 0.757643i | \(-0.273649\pi\) | |||||||
\(648\) | −3.40846e7 | + | 5.59818e7i | −0.125266 | + | 0.205741i | ||||
\(649\) | 3.04407e8 | 1.11358 | ||||||||
\(650\) | 4.11366e7 | − | 1.46116e7i | 0.149792 | − | 0.0532057i | ||||
\(651\) | − | 2.06603e8i | − | 0.748849i | ||||||
\(652\) | 6.81187e7 | + | 8.37905e7i | 0.245767 | + | 0.302310i | ||||
\(653\) | 2.37002e8 | 0.851164 | 0.425582 | − | 0.904920i | \(-0.360069\pi\) | ||||
0.425582 | + | 0.904920i | \(0.360069\pi\) | |||||||
\(654\) | −1.46191e7 | − | 4.11576e7i | −0.0522621 | − | 0.147135i | ||||
\(655\) | 4.55584e7i | 0.162123i | ||||||||
\(656\) | 2.54517e7 | − | 1.22040e8i | 0.0901581 | − | 0.432306i | ||||
\(657\) | −1.19668e8 | −0.421969 | ||||||||
\(658\) | 2.68372e8 | − | 9.53250e7i | 0.942017 | − | 0.334602i | ||||
\(659\) | − | 2.57956e8i | − | 0.901342i | −0.892690 | − | 0.450671i | \(-0.851185\pi\) | ||
0.892690 | − | 0.450671i | \(-0.148815\pi\) | |||||||
\(660\) | −1.33057e8 | + | 1.08171e8i | −0.462815 | + | 0.376252i | ||||
\(661\) | −1.44446e8 | −0.500152 | −0.250076 | − | 0.968226i | \(-0.580456\pi\) | ||||
−0.250076 | + | 0.968226i | \(0.580456\pi\) | |||||||
\(662\) | −6.50509e7 | − | 1.83140e8i | −0.224222 | − | 0.631261i | ||||
\(663\) | − | 1.29193e7i | − | 0.0443299i | ||||||
\(664\) | 2.00898e8 | + | 1.22317e8i | 0.686233 | + | 0.417814i | ||||
\(665\) | −9.63536e7 | −0.327645 | ||||||||
\(666\) | −1.93865e8 | + | 6.88606e7i | −0.656262 | + | 0.233103i | ||||
\(667\) | − | 1.44942e8i | − | 0.488447i | ||||||
\(668\) | 486678. | + | 598647.i | 0.00163272 | + | 0.00200836i | ||||
\(669\) | −2.28371e8 | −0.762715 | ||||||||
\(670\) | −1.93773e8 | − | 5.45537e8i | −0.644273 | − | 1.81384i | ||||
\(671\) | 2.63906e8i | 0.873538i | ||||||||
\(672\) | 1.92329e7 | + | 1.40868e8i | 0.0633779 | + | 0.464198i | ||||
\(673\) | 1.41439e8 | 0.464006 | 0.232003 | − | 0.972715i | \(-0.425472\pi\) | ||||
0.232003 | + | 0.972715i | \(0.425472\pi\) | |||||||
\(674\) | 2.68433e8 | − | 9.53467e7i | 0.876710 | − | 0.311405i | ||||
\(675\) | − | 4.45203e8i | − | 1.44759i | ||||||
\(676\) | −2.37311e8 | + | 1.92925e8i | −0.768206 | + | 0.624524i | ||||
\(677\) | 1.65808e8 | 0.534368 | 0.267184 | − | 0.963645i | \(-0.413907\pi\) | ||||
0.267184 | + | 0.963645i | \(0.413907\pi\) | |||||||
\(678\) | −5.95428e7 | − | 1.67633e8i | −0.191047 | − | 0.537860i | ||||
\(679\) | 4.82457e8i | 1.54116i | ||||||||
\(680\) | −2.21367e8 | + | 3.63580e8i | −0.704020 | + | 1.15631i | ||||
\(681\) | 2.05988e8 | 0.652230 | ||||||||
\(682\) | −3.35092e8 | + | 1.19024e8i | −1.05636 | + | 0.375216i | ||||
\(683\) | 4.13870e8i | 1.29898i | 0.760371 | + | 0.649490i | \(0.225017\pi\) | ||||
−0.760371 | + | 0.649490i | \(0.774983\pi\) | |||||||
\(684\) | −3.33913e7 | − | 4.10736e7i | −0.104343 | − | 0.128349i | ||||
\(685\) | −9.85994e8 | −3.06763 | ||||||||
\(686\) | −1.16281e8 | − | 3.27370e8i | −0.360194 | − | 1.01407i | ||||
\(687\) | 3.04510e8i | 0.939142i | ||||||||
\(688\) | −2.02053e8 | − | 4.21385e7i | −0.620440 | − | 0.129394i | ||||
\(689\) | 2.97364e7 | 0.0909139 | ||||||||
\(690\) | −2.39234e8 | + | 8.49755e7i | −0.728243 | + | 0.258670i | ||||
\(691\) | 1.36723e8i | 0.414388i | 0.978300 | + | 0.207194i | \(0.0664331\pi\) | ||||
−0.978300 | + | 0.207194i | \(0.933567\pi\) | |||||||
\(692\) | −1.06478e8 | + | 8.65630e7i | −0.321324 | + | 0.261225i | ||||
\(693\) | −1.49279e8 | −0.448538 | ||||||||
\(694\) | 3.75789e6 | + | 1.05797e7i | 0.0112426 | + | 0.0316516i | ||||
\(695\) | 1.01739e9i | 3.03063i | ||||||||
\(696\) | 8.17590e7 | + | 4.97791e7i | 0.242498 | + | 0.147645i | ||||
\(697\) | −1.25725e8 | −0.371299 | ||||||||
\(698\) | 9.57602e7 | − | 3.40138e7i | 0.281591 | − | 0.100020i | ||||
\(699\) | 3.16015e8i | 0.925286i | ||||||||
\(700\) | 3.05623e8 | + | 3.75937e8i | 0.891030 | + | 1.09603i | ||||
\(701\) | 1.37569e8 | 0.399361 | 0.199680 | − | 0.979861i | \(-0.436010\pi\) | ||||
0.199680 | + | 0.979861i | \(0.436010\pi\) | |||||||
\(702\) | −1.05069e7 | − | 2.95804e7i | −0.0303712 | − | 0.0855052i | ||||
\(703\) | − | 7.69882e7i | − | 0.221594i | ||||||
\(704\) | 2.17395e8 | − | 1.12348e8i | 0.623062 | − | 0.321994i | ||||
\(705\) | −3.35855e8 | −0.958484 | ||||||||
\(706\) | −3.60515e8 | + | 1.28054e8i | −1.02449 | + | 0.363898i | ||||
\(707\) | − | 2.81403e8i | − | 0.796287i | ||||||
\(708\) | −2.30944e8 | + | 1.87749e8i | −0.650739 | + | 0.529027i | ||||
\(709\) | 3.87826e8 | 1.08817 | 0.544087 | − | 0.839029i | \(-0.316876\pi\) | ||||
0.544087 | + | 0.839029i | \(0.316876\pi\) | |||||||
\(710\) | 7.22147e7 | + | 2.03308e8i | 0.201767 | + | 0.568042i | ||||
\(711\) | 3.92296e8i | 1.09145i | ||||||||
\(712\) | −2.41092e8 | + | 3.95978e8i | −0.667947 | + | 1.09706i | ||||
\(713\) | −5.26476e8 | −1.45248 | ||||||||
\(714\) | 1.35113e8 | − | 4.79917e7i | 0.371194 | − | 0.131847i | ||||
\(715\) | 4.12027e7i | 0.112722i | ||||||||
\(716\) | 1.41809e7 | + | 1.74434e7i | 0.0386334 | + | 0.0475217i | ||||
\(717\) | −2.78622e8 | −0.755888 | ||||||||
\(718\) | −1.87668e8 | − | 5.28348e8i | −0.507011 | − | 1.42740i | ||||
\(719\) | 1.23338e8i | 0.331826i | 0.986140 | + | 0.165913i | \(0.0530571\pi\) | ||||
−0.986140 | + | 0.165913i | \(0.946943\pi\) | |||||||
\(720\) | −8.84642e7 | + | 4.24183e8i | −0.237012 | + | 1.13646i | ||||
\(721\) | −2.21509e7 | −0.0590996 | ||||||||
\(722\) | 1.86662e7 | − | 6.63021e6i | 0.0495958 | − | 0.0176163i | ||||
\(723\) | − | 3.26350e8i | − | 0.863512i | ||||||
\(724\) | 3.21596e8 | − | 2.61446e8i | 0.847413 | − | 0.688916i | ||||
\(725\) | 3.26192e8 | 0.855972 | ||||||||
\(726\) | 3.43741e7 | + | 9.67745e7i | 0.0898300 | + | 0.252901i | ||||
\(727\) | 6.02562e8i | 1.56819i | 0.620641 | + | 0.784095i | \(0.286873\pi\) | ||||
−0.620641 | + | 0.784095i | \(0.713127\pi\) | |||||||
\(728\) | 2.91786e7 | + | 1.77654e7i | 0.0756257 | + | 0.0460449i | ||||
\(729\) | −1.18730e8 | −0.306464 | ||||||||
\(730\) | −3.45431e8 | + | 1.22696e8i | −0.887958 | + | 0.315401i | ||||
\(731\) | 2.08154e8i | 0.532884i | ||||||||
\(732\) | −1.62769e8 | − | 2.00217e8i | −0.414991 | − | 0.510467i | ||||
\(733\) | −3.48940e7 | −0.0886010 | −0.0443005 | − | 0.999018i | \(-0.514106\pi\) | ||||
−0.0443005 | + | 0.999018i | \(0.514106\pi\) | |||||||
\(734\) | 4.77421e7 | + | 1.34410e8i | 0.120730 | + | 0.339894i | ||||
\(735\) | 7.20055e7i | 0.181344i | ||||||||
\(736\) | 3.58965e8 | − | 4.90102e7i | 0.900366 | − | 0.122929i | ||||
\(737\) | 3.35644e8 | 0.838448 | ||||||||
\(738\) | −1.20600e8 | + | 4.28369e7i | −0.300040 | + | 0.106573i | ||||
\(739\) | − | 2.60560e8i | − | 0.645616i | −0.946464 | − | 0.322808i | \(-0.895373\pi\) | ||
0.946464 | − | 0.322808i | \(-0.104627\pi\) | |||||||
\(740\) | −4.89006e8 | + | 3.97544e8i | −1.20675 | + | 0.981047i | ||||
\(741\) | 4.92138e6 | 0.0120957 | ||||||||
\(742\) | 1.10463e8 | + | 3.10990e8i | 0.270399 | + | 0.761262i | ||||
\(743\) | − | 6.93870e8i | − | 1.69166i | −0.533456 | − | 0.845828i | \(-0.679107\pi\) | ||
0.533456 | − | 0.845828i | \(-0.320893\pi\) | |||||||
\(744\) | 1.80813e8 | − | 2.96974e8i | 0.439048 | − | 0.721108i | ||||
\(745\) | −5.53301e8 | −1.33811 | ||||||||
\(746\) | 2.62034e8 | − | 9.30739e7i | 0.631162 | − | 0.224187i | ||||
\(747\) | − | 2.41462e8i | − | 0.579278i | ||||||
\(748\) | −1.55677e8 | − | 1.91493e8i | −0.371979 | − | 0.457559i | ||||
\(749\) | 4.15908e8 | 0.989810 | ||||||||
\(750\) | −7.11488e7 | − | 2.00307e8i | −0.168649 | − | 0.474803i | ||||
\(751\) | 3.01857e8i | 0.712658i | 0.934361 | + | 0.356329i | \(0.115972\pi\) | ||||
−0.934361 | + | 0.356329i | \(0.884028\pi\) | |||||||
\(752\) | 4.69186e8 | + | 9.78497e7i | 1.10330 | + | 0.230094i | ||||
\(753\) | −2.34903e8 | −0.550180 | ||||||||
\(754\) | 2.16730e7 | − | 7.69820e6i | 0.0505598 | − | 0.0179587i | ||||
\(755\) | − | 7.25544e8i | − | 1.68587i | ||||||
\(756\) | 2.70328e8 | − | 2.19767e8i | 0.625641 | − | 0.508624i | ||||
\(757\) | 4.78490e8 | 1.10302 | 0.551512 | − | 0.834167i | \(-0.314051\pi\) | ||||
0.551512 | + | 0.834167i | \(0.314051\pi\) | |||||||
\(758\) | 1.25589e8 | + | 3.53574e8i | 0.288365 | + | 0.811844i | ||||
\(759\) | − | 1.47190e8i | − | 0.336630i | ||||||
\(760\) | −1.38500e8 | − | 8.43259e7i | −0.315507 | − | 0.192097i | ||||
\(761\) | −5.95860e8 | −1.35204 | −0.676021 | − | 0.736882i | \(-0.736297\pi\) | ||||
−0.676021 | + | 0.736882i | \(0.736297\pi\) | |||||||
\(762\) | −1.99124e8 | + | 7.07283e7i | −0.450047 | + | 0.159856i | ||||
\(763\) | − | 1.16473e8i | − | 0.262210i | ||||||
\(764\) | −8.48195e7 | − | 1.04334e8i | −0.190202 | − | 0.233962i | ||||
\(765\) | 4.36992e8 | 0.976088 | ||||||||
\(766\) | 6.94875e7 | + | 1.95630e8i | 0.154604 | + | 0.435261i | ||||
\(767\) | 7.15143e7i | 0.158492i | ||||||||
\(768\) | −9.56377e7 | + | 2.19317e8i | −0.211128 | + | 0.484160i | ||||
\(769\) | 6.50131e8 | 1.42962 | 0.714812 | − | 0.699317i | \(-0.246512\pi\) | ||||
0.714812 | + | 0.699317i | \(0.246512\pi\) | |||||||
\(770\) | −4.30907e8 | + | 1.53057e8i | −0.943867 | + | 0.335260i | ||||
\(771\) | − | 3.48523e8i | − | 0.760446i | ||||||
\(772\) | 5.44574e8 | − | 4.42718e8i | 1.18360 | − | 0.962223i | ||||
\(773\) | 5.61377e8 | 1.21539 | 0.607696 | − | 0.794170i | \(-0.292094\pi\) | ||||
0.607696 | + | 0.794170i | \(0.292094\pi\) | |||||||
\(774\) | 7.09219e7 | + | 1.99669e8i | 0.152953 | + | 0.430613i | ||||
\(775\) | − | 1.18483e9i | − | 2.54537i | ||||||
\(776\) | −4.22232e8 | + | 6.93489e8i | −0.903579 | + | 1.48407i | ||||
\(777\) | 2.12281e8 | 0.452532 | ||||||||
\(778\) | −4.51190e8 | + | 1.60262e8i | −0.958122 | + | 0.340323i | ||||
\(779\) | − | 4.78929e7i | − | 0.101312i | ||||||
\(780\) | −2.54125e7 | − | 3.12591e7i | −0.0535506 | − | 0.0658708i | ||||
\(781\) | −1.25086e8 | −0.262577 | ||||||||
\(782\) | −1.22295e8 | − | 3.44300e8i | −0.255733 | − | 0.719974i | ||||
\(783\) | − | 2.34557e8i | − | 0.488612i | ||||||
\(784\) | 2.09784e7 | − | 1.00591e8i | 0.0435336 | − | 0.208742i | ||||
\(785\) | 6.78215e8 | 1.40203 | ||||||||
\(786\) | 2.43358e7 | − | 8.64401e6i | 0.0501161 | − | 0.0178011i | ||||
\(787\) | 2.56259e8i | 0.525721i | 0.964834 | + | 0.262860i | \(0.0846658\pi\) | ||||
−0.964834 | + | 0.262860i | \(0.915334\pi\) | |||||||
\(788\) | −4.78469e7 | + | 3.88978e7i | −0.0977857 | + | 0.0794962i | ||||
\(789\) | 2.86257e8 | 0.582808 | ||||||||
\(790\) | 4.02225e8 | + | 1.13240e9i | 0.815807 | + | 2.29677i | ||||
\(791\) | − | 4.74386e8i | − | 0.958523i | ||||||
\(792\) | −2.14576e8 | − | 1.30645e8i | −0.431921 | − | 0.262976i | ||||
\(793\) | −6.19993e7 | −0.124328 | ||||||||
\(794\) | 4.26931e8 | − | 1.51645e8i | 0.852896 | − | 0.302947i | ||||
\(795\) | − | 3.89190e8i | − | 0.774569i | ||||||
\(796\) | −5.28117e8 | − | 6.49619e8i | −1.04711 | − | 1.28801i | ||||
\(797\) | −3.41309e7 | −0.0674176 | −0.0337088 | − | 0.999432i | \(-0.510732\pi\) | ||||
−0.0337088 | + | 0.999432i | \(0.510732\pi\) | |||||||
\(798\) | 1.82816e7 | + | 5.14689e7i | 0.0359755 | + | 0.101283i | ||||
\(799\) | − | 4.83354e8i | − | 0.947600i | ||||||
\(800\) | 1.10297e8 | + | 8.07850e8i | 0.215425 | + | 1.57783i | ||||
\(801\) | 4.75930e8 | 0.926074 | ||||||||
\(802\) | 2.12253e8 | − | 7.53918e7i | 0.411463 | − | 0.146151i | ||||
\(803\) | − | 2.12528e8i | − | 0.410458i | ||||||
\(804\) | −2.54642e8 | + | 2.07015e8i | −0.489961 | + | 0.398321i | ||||
\(805\) | −6.77013e8 | −1.29780 | ||||||||
\(806\) | −2.79623e7 | − | 7.87231e7i | −0.0534032 | − | 0.150348i | ||||
\(807\) | − | 1.13599e7i | − | 0.0216149i | ||||||
\(808\) | 2.46276e8 | − | 4.04492e8i | 0.466861 | − | 0.766789i | ||||
\(809\) | 1.12820e8 | 0.213078 | 0.106539 | − | 0.994308i | \(-0.466023\pi\) | ||||
0.106539 | + | 0.994308i | \(0.466023\pi\) | |||||||
\(810\) | 1.94224e8 | − | 6.89881e7i | 0.365467 | − | 0.129813i | ||||
\(811\) | 1.85497e8i | 0.347756i | 0.984767 | + | 0.173878i | \(0.0556299\pi\) | ||||
−0.984767 | + | 0.173878i | \(0.944370\pi\) | |||||||
\(812\) | 1.61019e8 | + | 1.98064e8i | 0.300752 | + | 0.369946i | ||||
\(813\) | −1.48579e7 | −0.0276494 | ||||||||
\(814\) | −1.22295e8 | − | 3.44302e8i | −0.226744 | − | 0.638361i | ||||
\(815\) | − | 3.39590e8i | − | 0.627310i | ||||||
\(816\) | 2.36213e8 | + | 4.92628e7i | 0.434745 | + | 0.0906668i | ||||
\(817\) | −7.92928e7 | −0.145401 | ||||||||
\(818\) | 4.29316e8 | − | 1.52492e8i | 0.784363 | − | 0.278604i | ||||
\(819\) | − | 3.50700e7i | − | 0.0638388i | ||||||
\(820\) | −3.04201e8 | + | 2.47305e8i | −0.551721 | + | 0.448529i | ||||
\(821\) | 6.47897e8 | 1.17078 | 0.585391 | − | 0.810751i | \(-0.300941\pi\) | ||||
0.585391 | + | 0.810751i | \(0.300941\pi\) | |||||||
\(822\) | 1.87077e8 | + | 5.26685e8i | 0.336826 | + | 0.948278i | ||||
\(823\) | 4.02842e8i | 0.722661i | 0.932438 | + | 0.361331i | \(0.117677\pi\) | ||||
−0.932438 | + | 0.361331i | \(0.882323\pi\) | |||||||
\(824\) | −3.18399e7 | − | 1.93858e7i | −0.0569103 | − | 0.0346499i | ||||
\(825\) | 3.31250e8 | 0.589922 | ||||||||
\(826\) | −7.47913e8 | + | 2.65657e8i | −1.32712 | + | 0.471391i | ||||
\(827\) | − | 2.64980e7i | − | 0.0468486i | −0.999726 | − | 0.0234243i | \(-0.992543\pi\) | ||
0.999726 | − | 0.0234243i | \(-0.00745687\pi\) | |||||||
\(828\) | −2.34619e8 | − | 2.88597e8i | −0.413306 | − | 0.508394i | ||||
\(829\) | −5.15025e8 | −0.903992 | −0.451996 | − | 0.892020i | \(-0.649288\pi\) | ||||
−0.451996 | + | 0.892020i | \(0.649288\pi\) | |||||||
\(830\) | −2.47573e8 | − | 6.97001e8i | −0.432981 | − | 1.21899i | ||||
\(831\) | 3.22682e8i | 0.562305i | ||||||||
\(832\) | 2.63939e7 | + | 5.10725e7i | 0.0458282 | + | 0.0886782i | ||||
\(833\) | −1.03628e8 | −0.179285 | ||||||||
\(834\) | 5.43456e8 | − | 1.93034e8i | 0.936841 | − | 0.332764i | ||||
\(835\) | − | 2.42622e6i | − | 0.00416746i | ||||||
\(836\) | 7.29460e7 | − | 5.93024e7i | 0.124848 | − | 0.101497i | ||||
\(837\) | −8.51986e8 | −1.45297 | ||||||||
\(838\) | 3.43247e8 | + | 9.66354e8i | 0.583277 | + | 1.64212i | ||||
\(839\) | − | 6.99663e8i | − | 1.18468i | −0.805686 | − | 0.592342i | \(-0.798203\pi\) | ||
0.805686 | − | 0.592342i | \(-0.201797\pi\) | |||||||
\(840\) | 2.32514e8 | − | 3.81889e8i | 0.392294 | − | 0.644317i | ||||
\(841\) | −4.22967e8 | −0.711081 | ||||||||
\(842\) | −1.04655e9 | + | 3.71732e8i | −1.75317 | + | 0.622721i | ||||
\(843\) | − | 3.73720e7i | − | 0.0623826i | ||||||
\(844\) | −1.90826e8 | − | 2.34729e8i | −0.317403 | − | 0.390427i | ||||
\(845\) | 9.61785e8 | 1.59407 | ||||||||
\(846\) | −1.64688e8 | − | 4.63650e8i | −0.271988 | − | 0.765737i | ||||
\(847\) | 2.73864e8i | 0.450696i | ||||||||
\(848\) | −1.13389e8 | + | 5.43694e8i | −0.185944 | + | 0.891594i | ||||
\(849\) | −2.02969e8 | −0.331670 | ||||||||
\(850\) | 7.74845e8 | − | 2.75223e8i | 1.26171 | − | 0.448155i | ||||
\(851\) | − | 5.40945e8i | − | 0.877737i | ||||||
\(852\) | 9.48989e7 | − | 7.71493e7i | 0.153441 | − | 0.124742i | ||||
\(853\) | −9.64213e8 | −1.55355 | −0.776776 | − | 0.629777i | \(-0.783146\pi\) | ||||
−0.776776 | + | 0.629777i | \(0.783146\pi\) | |||||||
\(854\) | −2.30311e8 | − | 6.48403e8i | −0.369778 | − | 1.04105i | ||||
\(855\) | 1.66465e8i | 0.266332i | ||||||||
\(856\) | 5.97832e8 | + | 3.63991e8i | 0.953142 | + | 0.580322i | ||||
\(857\) | −2.61569e7 | −0.0415570 | −0.0207785 | − | 0.999784i | \(-0.506614\pi\) | ||||
−0.0207785 | + | 0.999784i | \(0.506614\pi\) | |||||||
\(858\) | 2.20091e7 | − | 7.81758e6i | 0.0348450 | − | 0.0123769i | ||||
\(859\) | 9.37229e8i | 1.47865i | 0.673347 | + | 0.739326i | \(0.264856\pi\) | ||||
−0.673347 | + | 0.739326i | \(0.735144\pi\) | |||||||
\(860\) | 4.09444e8 | + | 5.03644e8i | 0.643724 | + | 0.791823i | ||||
\(861\) | 1.32056e8 | 0.206895 | ||||||||
\(862\) | −1.44216e8 | − | 4.06017e8i | −0.225161 | − | 0.633902i | ||||
\(863\) | − | 1.49852e8i | − | 0.233147i | −0.993182 | − | 0.116574i | \(-0.962809\pi\) | ||
0.993182 | − | 0.116574i | \(-0.0371911\pi\) | |||||||
\(864\) | 5.80906e8 | − | 7.93123e7i | 0.900668 | − | 0.122970i | ||||
\(865\) | 4.31540e8 | 0.666765 | ||||||||
\(866\) | 1.51161e8 | − | 5.36920e7i | 0.232748 | − | 0.0826714i | ||||
\(867\) | 1.00884e8i | 0.154797i | ||||||||
\(868\) | 7.19431e8 | − | 5.84872e8i | 1.10010 | − | 0.894337i | ||||
\(869\) | −6.96711e8 | −1.06168 | ||||||||
\(870\) | −1.00754e8 | − | 2.83657e8i | −0.153005 | − | 0.430760i | ||||
\(871\) | 7.88526e7i | 0.119333i | ||||||||
\(872\) | 1.01933e8 | − | 1.67419e8i | 0.153733 | − | 0.252497i | ||||
\(873\) | 8.33513e8 | 1.25277 | ||||||||
\(874\) | 1.31155e8 | − | 4.65861e7i | 0.196450 | − | 0.0697785i | ||||
\(875\) | − | 5.66853e8i | − | 0.846148i | ||||||
\(876\) | 1.31081e8 | + | 1.61238e8i | 0.194996 | + | 0.239858i | ||||
\(877\) | −3.76755e7 | −0.0558547 | −0.0279274 | − | 0.999610i | \(-0.508891\pi\) | ||||
−0.0279274 | + | 0.999610i | \(0.508891\pi\) | |||||||
\(878\) | −1.13182e8 | − | 3.18644e8i | −0.167221 | − | 0.470784i | ||||
\(879\) | 1.31653e8i | 0.193849i | ||||||||
\(880\) | −7.53342e8 | − | 1.57111e8i | −1.10546 | − | 0.230546i | ||||
\(881\) | −4.58408e8 | −0.670386 | −0.335193 | − | 0.942150i | \(-0.608801\pi\) | ||||
−0.335193 | + | 0.942150i | \(0.608801\pi\) | |||||||
\(882\) | −9.94040e7 | + | 3.53081e7i | −0.144877 | + | 0.0514599i | ||||
\(883\) | 2.11933e8i | 0.307834i | 0.988084 | + | 0.153917i | \(0.0491889\pi\) | ||||
−0.988084 | + | 0.153917i | \(0.950811\pi\) | |||||||
\(884\) | 4.49873e7 | − | 3.65730e7i | 0.0651228 | − | 0.0529425i | ||||
\(885\) | 9.35980e8 | 1.35032 | ||||||||
\(886\) | 3.44190e8 | + | 9.69011e8i | 0.494877 | + | 1.39324i | ||||
\(887\) | 2.52427e8i | 0.361713i | 0.983509 | + | 0.180857i | \(0.0578870\pi\) | ||||
−0.983509 | + | 0.180857i | \(0.942113\pi\) | |||||||
\(888\) | 3.05136e8 | + | 1.85783e8i | 0.435767 | + | 0.265318i | ||||
\(889\) | −5.63503e8 | −0.802031 | ||||||||
\(890\) | 1.37381e9 | − | 4.87976e8i | 1.94876 | − | 0.692194i | ||||
\(891\) | 1.19497e8i | 0.168937i | ||||||||
\(892\) | −6.46493e8 | − | 7.95230e8i | −0.910897 | − | 1.12046i | ||||
\(893\) | 1.84126e8 | 0.258559 | ||||||||
\(894\) | 1.04980e8 | + | 2.95555e8i | 0.146925 | + | 0.413643i | ||||
\(895\) | − | 7.06954e7i | − | 0.0986103i | ||||||
\(896\) | −4.36081e8 | + | 4.65754e8i | −0.606238 | + | 0.647489i | ||||
\(897\) | 3.45793e7 | 0.0479114 | ||||||||
\(898\) | −5.92382e8 | + | 2.10413e8i | −0.818036 | + | 0.290565i | ||||
\(899\) | − | 6.24234e8i | − | 0.859149i | ||||||
\(900\) | 6.49486e8 | − | 5.28008e8i | 0.890927 | − | 0.724291i | ||||
\(901\) | 5.60112e8 | 0.765774 | ||||||||
\(902\) | −7.60776e7 | − | 2.14184e8i | −0.103666 | − | 0.291855i | ||||
\(903\) | − | 2.18636e8i | − | 0.296933i | ||||||
\(904\) | 4.15169e8 | − | 6.81889e8i | 0.561979 | − | 0.923014i | ||||
\(905\) | −1.30338e9 | −1.75843 | ||||||||
\(906\) | −3.87561e8 | + | 1.37661e8i | −0.521142 | + | 0.185108i | ||||
\(907\) | 1.27485e9i | 1.70859i | 0.519789 | + | 0.854294i | \(0.326010\pi\) | ||||
−0.519789 | + | 0.854294i | \(0.673990\pi\) | |||||||
\(908\) | 5.83130e8 | + | 7.17289e8i | 0.778947 | + | 0.958157i | ||||
\(909\) | −4.86164e8 | −0.647278 | ||||||||
\(910\) | −3.59576e7 | − | 1.01233e8i | −0.0477163 | − | 0.134337i | ||||
\(911\) | 9.61222e7i | 0.127136i | 0.997978 | + | 0.0635680i | \(0.0202480\pi\) | ||||
−0.997978 | + | 0.0635680i | \(0.979752\pi\) | |||||||
\(912\) | −1.87658e7 | + | 8.99816e7i | −0.0247391 | + | 0.118623i | ||||
\(913\) | 4.28833e8 | 0.563476 | ||||||||
\(914\) | 2.65979e7 | − | 9.44753e6i | 0.0348345 | − | 0.0123731i | ||||
\(915\) | 8.11448e8i | 1.05925i | ||||||||
\(916\) | −1.06036e9 | + | 8.62035e8i | −1.37964 | + | 1.12160i | ||||
\(917\) | 6.88681e7 | 0.0893121 | ||||||||
\(918\) | −1.97907e8 | − | 5.57174e8i | −0.255819 | − | 0.720216i | ||||
\(919\) | − | 1.40009e9i | − | 1.80389i | −0.431849 | − | 0.901946i | \(-0.642139\pi\) | ||
0.431849 | − | 0.901946i | \(-0.357861\pi\) | |||||||
\(920\) | −9.73147e8 | − | 5.92502e8i | −1.24973 | − | 0.760898i | ||||
\(921\) | 6.18803e8 | 0.792088 | ||||||||
\(922\) | −1.01804e9 | + | 3.61604e8i | −1.29888 | + | 0.461361i | ||||
\(923\) | − | 2.93865e7i | − | 0.0373716i | ||||||
\(924\) | 1.63516e8 | + | 2.01136e8i | 0.207274 | + | 0.254961i | ||||
\(925\) | 1.21739e9 | 1.53818 | ||||||||
\(926\) | 4.11647e8 | + | 1.15892e9i | 0.518432 | + | 1.45956i | ||||
\(927\) | 3.82688e7i | 0.0480403i | ||||||||
\(928\) | 5.81107e7 | + | 4.25620e8i | 0.0727130 | + | 0.532571i | ||||
\(929\) | −9.90092e8 | −1.23489 | −0.617445 | − | 0.786614i | \(-0.711832\pi\) | ||||
−0.617445 | + | 0.786614i | \(0.711832\pi\) | |||||||
\(930\) | −1.03033e9 | + | 3.65971e8i | −1.28094 | + | 0.454985i | ||||
\(931\) | − | 3.94755e7i | − | 0.0489191i | ||||||
\(932\) | −1.10042e9 | + | 8.94604e8i | −1.35929 | + | 1.10505i | ||||
\(933\) | −4.32990e8 | −0.533130 | ||||||||
\(934\) | 1.25906e8 | + | 3.54467e8i | 0.154527 | + | 0.435046i | ||||
\(935\) | 7.76090e8i | 0.949461i | ||||||||
\(936\) | 3.06923e7 | − | 5.04102e7i | 0.0374285 | − | 0.0614739i | ||||
\(937\) | 6.25355e8 | 0.760165 | 0.380082 | − | 0.924953i | \(-0.375896\pi\) | ||||
0.380082 | + | 0.924953i | \(0.375896\pi\) | |||||||
\(938\) | −8.24658e8 | + | 2.92917e8i | −0.999230 | + | 0.354924i | ||||
\(939\) | 7.08303e8i | 0.855505i | ||||||||
\(940\) | −9.50770e8 | − | 1.16951e9i | −1.14470 | − | 1.40806i | ||||
\(941\) | −8.66106e8 | −1.03945 | −0.519724 | − | 0.854335i | \(-0.673965\pi\) | ||||
−0.519724 | + | 0.854335i | \(0.673965\pi\) | |||||||
\(942\) | −1.28681e8 | − | 3.62280e8i | −0.153944 | − | 0.433402i | ||||
\(943\) | − | 3.36512e8i | − | 0.401296i | ||||||
\(944\) | −1.30756e9 | − | 2.72693e8i | −1.55433 | − | 0.324159i | ||||
\(945\) | −1.09560e9 | −1.29824 | ||||||||
\(946\) | −3.54608e8 | + | 1.25956e8i | −0.418867 | + | 0.148780i | ||||
\(947\) | 1.05653e9i | 1.24403i | 0.783006 | + | 0.622014i | \(0.213685\pi\) | ||||
−0.783006 | + | 0.622014i | \(0.786315\pi\) | |||||||
\(948\) | 5.28572e8 | − | 4.29710e8i | 0.620411 | − | 0.504371i | ||||
\(949\) | 4.99291e7 | 0.0584191 | ||||||||
\(950\) | 1.04842e8 | + | 2.95165e8i | 0.122282 | + | 0.344265i | ||||
\(951\) | 5.54595e8i | 0.644814i | ||||||||
\(952\) | 5.49605e8 | + | 3.34628e8i | 0.637000 | + | 0.387839i | ||||
\(953\) | 1.53579e9 | 1.77441 | 0.887205 | − | 0.461376i | \(-0.152644\pi\) | ||||
0.887205 | + | 0.461376i | \(0.152644\pi\) | |||||||
\(954\) | 5.37279e8 | − | 1.90840e8i | 0.618807 | − | 0.219799i | ||||
\(955\) | 4.22848e8i | 0.485483i | ||||||||
\(956\) | −7.88748e8 | − | 9.70213e8i | −0.902744 | − | 1.11044i | ||||
\(957\) | 1.74521e8 | 0.199118 | ||||||||
\(958\) | 2.82494e8 | + | 7.95314e8i | 0.321301 | + | 0.904570i | ||||
\(959\) | 1.49047e9i | 1.68993i | ||||||||
\(960\) | 6.68437e8 | − | 3.45443e8i | 0.755522 | − | 0.390448i | ||||
\(961\) | −1.37991e9 | −1.55482 | ||||||||
\(962\) | 8.08867e7 | − | 2.87308e7i | 0.0908556 | − | 0.0322717i | ||||
\(963\) | − | 7.18541e8i | − | 0.804587i | ||||||
\(964\) | 1.13641e9 | − | 9.23861e8i | 1.26854 | − | 1.03128i | ||||
\(965\) | −2.20707e9 | −2.45604 | ||||||||
\(966\) | 1.28453e8 | + | 3.61638e8i | 0.142499 | + | 0.401183i | ||||
\(967\) | − | 9.05532e8i | − | 1.00144i | −0.865610 | − | 0.500719i | \(-0.833069\pi\) | ||
0.865610 | − | 0.500719i | \(-0.166931\pi\) | |||||||
\(968\) | −2.39678e8 | + | 3.93655e8i | −0.264242 | + | 0.434000i | ||||
\(969\) | 9.26987e7 | 0.101883 | ||||||||
\(970\) | 2.40601e9 | − | 8.54609e8i | 2.63622 | − | 0.936380i | ||||
\(971\) | − | 4.03780e8i | − | 0.441049i | −0.975381 | − | 0.220524i | \(-0.929223\pi\) | ||
0.975381 | − | 0.220524i | \(-0.0707769\pi\) | |||||||
\(972\) | −6.00292e8 | − | 7.38400e8i | −0.653678 | − | 0.804068i | ||||
\(973\) | 1.53793e9 | 1.66955 | ||||||||
\(974\) | −1.95293e8 | − | 5.49816e8i | −0.211354 | − | 0.595032i | ||||
\(975\) | 7.78205e7i | 0.0839615i | ||||||||
\(976\) | 2.36411e8 | − | 1.13358e9i | 0.254284 | − | 1.21928i | ||||
\(977\) | 6.46229e8 | 0.692951 | 0.346475 | − | 0.938059i | \(-0.387378\pi\) | ||||
0.346475 | + | 0.938059i | \(0.387378\pi\) | |||||||
\(978\) | −1.81398e8 | + | 6.44321e7i | −0.193917 | + | 0.0688788i | ||||
\(979\) | 8.45244e8i | 0.900812i | ||||||||
\(980\) | −2.50737e8 | + | 2.03840e8i | −0.266403 | + | 0.216576i | ||||
\(981\) | −2.01223e8 | −0.213143 | ||||||||
\(982\) | 4.73235e8 | + | 1.33231e9i | 0.499738 | + | 1.40693i | ||||
\(983\) | − | 1.04005e9i | − | 1.09495i | −0.836822 | − | 0.547475i | \(-0.815589\pi\) | ||
0.836822 | − | 0.547475i | \(-0.184411\pi\) | |||||||
\(984\) | 1.89820e8 | + | 1.15572e8i | 0.199230 | + | 0.121302i | ||||
\(985\) | 1.93916e8 | 0.202911 | ||||||||
\(986\) | 4.08231e8 | − | 1.45003e8i | 0.425868 | − | 0.151267i | ||||
\(987\) | 5.07694e8i | 0.528021i | ||||||||
\(988\) | 1.39319e7 | + | 1.71372e7i | 0.0144457 | + | 0.0177692i | ||||
\(989\) | −5.57138e8 | −0.575936 | ||||||||
\(990\) | 2.64428e8 | + | 7.44453e8i | 0.272522 | + | 0.767241i | ||||
\(991\) | − | 1.59559e9i | − | 1.63946i | −0.572750 | − | 0.819730i | \(-0.694123\pi\) | ||
0.572750 | − | 0.819730i | \(-0.305877\pi\) | |||||||
\(992\) | 1.54598e9 | − | 2.11076e8i | 1.58369 | − | 0.216224i | ||||
\(993\) | 3.46456e8 | 0.353835 | ||||||||
\(994\) | 3.07330e8 | − | 1.09163e8i | 0.312929 | − | 0.111152i | ||||
\(995\) | 2.63281e9i | 2.67270i | ||||||||
\(996\) | −3.25341e8 | + | 2.64491e8i | −0.329277 | + | 0.267690i | ||||
\(997\) | 3.15622e8 | 0.318480 | 0.159240 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159240 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(998\) | −1.09694e8 | − | 3.08826e8i | −0.110355 | − | 0.310686i | ||||
\(999\) | − | 8.75401e8i | − | 0.878032i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 76.7.b.a.39.8 | yes | 54 | |
4.3 | odd | 2 | inner | 76.7.b.a.39.7 | ✓ | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.b.a.39.7 | ✓ | 54 | 4.3 | odd | 2 | inner | |
76.7.b.a.39.8 | yes | 54 | 1.1 | even | 1 | trivial |