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 | 19.2 | ||
Root | \(2.26350 - 3.92050i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.19 |
Dual form | 147.7.f.d.31.2 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.76350 | + | 4.78652i | −0.345438 | + | 0.598316i | −0.985433 | − | 0.170063i | \(-0.945603\pi\) |
0.639996 | + | 0.768379i | \(0.278936\pi\) | |||||||
\(3\) | 13.5000 | − | 7.79423i | 0.500000 | − | 0.288675i | ||||
\(4\) | 16.7261 | + | 28.9705i | 0.261346 | + | 0.452664i | ||||
\(5\) | 57.9943 | + | 33.4830i | 0.463955 | + | 0.267864i | 0.713706 | − | 0.700446i | \(-0.247015\pi\) |
−0.249751 | + | 0.968310i | \(0.580349\pi\) | |||||||
\(6\) | 86.1574i | 0.398877i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −538.619 | −1.05199 | ||||||||
\(9\) | 121.500 | − | 210.444i | 0.166667 | − | 0.288675i | ||||
\(10\) | −320.535 | + | 185.061i | −0.320535 | + | 0.185061i | ||||
\(11\) | −862.868 | − | 1494.53i | −0.648285 | − | 1.12286i | −0.983532 | − | 0.180733i | \(-0.942153\pi\) |
0.335247 | − | 0.942130i | \(-0.391180\pi\) | |||||||
\(12\) | 451.605 | + | 260.734i | 0.261346 | + | 0.150888i | ||||
\(13\) | − | 2807.43i | − | 1.27785i | −0.769271 | − | 0.638923i | \(-0.779380\pi\) | ||
0.769271 | − | 0.638923i | \(-0.220620\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1043.90 | 0.309303 | ||||||||
\(16\) | 418.002 | − | 724.000i | 0.102051 | − | 0.176758i | ||||
\(17\) | 5323.58 | − | 3073.57i | 1.08357 | − | 0.625599i | 0.151712 | − | 0.988425i | \(-0.451521\pi\) |
0.931857 | + | 0.362826i | \(0.118188\pi\) | |||||||
\(18\) | 671.531 | + | 1163.13i | 0.115146 | + | 0.199439i | ||||
\(19\) | −7737.30 | − | 4467.13i | −1.12805 | − | 0.651281i | −0.184607 | − | 0.982812i | \(-0.559101\pi\) |
−0.943444 | + | 0.331532i | \(0.892435\pi\) | |||||||
\(20\) | 2240.17i | 0.280021i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9538.15 | 0.895769 | ||||||||
\(23\) | −4950.64 | + | 8574.76i | −0.406891 | + | 0.704755i | −0.994540 | − | 0.104361i | \(-0.966720\pi\) |
0.587649 | + | 0.809116i | \(0.300054\pi\) | |||||||
\(24\) | −7271.35 | + | 4198.12i | −0.525995 | + | 0.303683i | ||||
\(25\) | −5570.27 | − | 9648.00i | −0.356497 | − | 0.617472i | ||||
\(26\) | 13437.8 | + | 7758.32i | 0.764555 | + | 0.441416i | ||||
\(27\) | − | 3788.00i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −13610.4 | −0.558054 | −0.279027 | − | 0.960283i | \(-0.590012\pi\) | ||||
−0.279027 | + | 0.960283i | \(0.590012\pi\) | |||||||
\(30\) | −2884.81 | + | 4996.64i | −0.106845 | + | 0.185061i | ||||
\(31\) | 21833.0 | − | 12605.3i | 0.732871 | − | 0.423123i | −0.0866007 | − | 0.996243i | \(-0.527600\pi\) |
0.819472 | + | 0.573120i | \(0.194267\pi\) | |||||||
\(32\) | −14925.5 | − | 25851.7i | −0.455490 | − | 0.788932i | ||||
\(33\) | −23297.4 | − | 13450.8i | −0.648285 | − | 0.374288i | ||||
\(34\) | 33975.2i | 0.864422i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8128.90 | 0.174230 | ||||||||
\(37\) | −11366.4 | + | 19687.1i | −0.224397 | + | 0.388666i | −0.956138 | − | 0.292916i | \(-0.905374\pi\) |
0.731742 | + | 0.681582i | \(0.238708\pi\) | |||||||
\(38\) | 42764.1 | − | 24689.9i | 0.779343 | − | 0.449954i | ||||
\(39\) | −21881.7 | − | 37900.2i | −0.368882 | − | 0.638923i | ||||
\(40\) | −31236.8 | − | 18034.6i | −0.488075 | − | 0.281790i | ||||
\(41\) | 37897.2i | 0.549865i | 0.961464 | + | 0.274932i | \(0.0886554\pi\) | ||||
−0.961464 | + | 0.274932i | \(0.911345\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 73646.2 | 0.926286 | 0.463143 | − | 0.886284i | \(-0.346722\pi\) | ||||
0.463143 | + | 0.886284i | \(0.346722\pi\) | |||||||
\(44\) | 28864.9 | − | 49995.4i | 0.338853 | − | 0.586911i | ||||
\(45\) | 14092.6 | − | 8136.38i | 0.154652 | − | 0.0892881i | ||||
\(46\) | −27362.2 | − | 47392.7i | −0.281111 | − | 0.486898i | ||||
\(47\) | −120523. | − | 69583.9i | −1.16085 | − | 0.670216i | −0.209342 | − | 0.977843i | \(-0.567132\pi\) |
−0.951507 | + | 0.307626i | \(0.900465\pi\) | |||||||
\(48\) | − | 13032.0i | − | 0.117839i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 61573.8 | 0.492591 | ||||||||
\(51\) | 47912.2 | − | 82986.3i | 0.361190 | − | 0.625599i | ||||
\(52\) | 81332.5 | − | 46957.3i | 0.578434 | − | 0.333959i | ||||
\(53\) | 8258.79 | + | 14304.7i | 0.0554739 | + | 0.0960837i | 0.892429 | − | 0.451188i | \(-0.149000\pi\) |
−0.836955 | + | 0.547272i | \(0.815666\pi\) | |||||||
\(54\) | 18131.3 | + | 10468.1i | 0.115146 | + | 0.0664795i | ||||
\(55\) | − | 115566.i | − | 0.694610i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −139271. | −0.752034 | ||||||||
\(58\) | 37612.3 | − | 65146.4i | 0.192773 | − | 0.333892i | ||||
\(59\) | 61989.7 | − | 35789.8i | 0.301831 | − | 0.174262i | −0.341434 | − | 0.939906i | \(-0.610913\pi\) |
0.643265 | + | 0.765644i | \(0.277579\pi\) | |||||||
\(60\) | 17460.4 | + | 30242.2i | 0.0808350 | + | 0.140010i | ||||
\(61\) | 228557. | + | 131958.i | 1.00695 | + | 0.581360i | 0.910296 | − | 0.413958i | \(-0.135854\pi\) |
0.0966496 | + | 0.995318i | \(0.469187\pi\) | |||||||
\(62\) | 139339.i | 0.584651i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 218491. | 0.833476 | ||||||||
\(65\) | 94001.1 | − | 162815.i | 0.342289 | − | 0.592862i | ||||
\(66\) | 128765. | − | 74342.5i | 0.447884 | − | 0.258586i | ||||
\(67\) | −274333. | − | 475159.i | −0.912125 | − | 1.57985i | −0.811057 | − | 0.584967i | \(-0.801107\pi\) |
−0.101068 | − | 0.994880i | \(-0.532226\pi\) | |||||||
\(68\) | 178086. | + | 102818.i | 0.566372 | + | 0.326995i | ||||
\(69\) | 154346.i | 0.469837i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 465655. | 1.30103 | 0.650517 | − | 0.759491i | \(-0.274552\pi\) | ||||
0.650517 | + | 0.759491i | \(0.274552\pi\) | |||||||
\(72\) | −65442.2 | + | 113349.i | −0.175332 | + | 0.303683i | ||||
\(73\) | 289020. | − | 166866.i | 0.742950 | − | 0.428942i | −0.0801910 | − | 0.996780i | \(-0.525553\pi\) |
0.823141 | + | 0.567837i | \(0.192220\pi\) | |||||||
\(74\) | −62821.9 | − | 108811.i | −0.155030 | − | 0.268520i | ||||
\(75\) | −150397. | − | 86832.0i | −0.356497 | − | 0.205824i | ||||
\(76\) | − | 298871.i | − | 0.680837i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 241881. | 0.509703 | ||||||||
\(79\) | 205012. | − | 355091.i | 0.415813 | − | 0.720209i | −0.579700 | − | 0.814830i | \(-0.696830\pi\) |
0.995513 | + | 0.0946203i | \(0.0301637\pi\) | |||||||
\(80\) | 48483.5 | − | 27991.9i | 0.0946942 | − | 0.0546717i | ||||
\(81\) | −29524.5 | − | 51137.9i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −181396. | − | 104729.i | −0.328993 | − | 0.189944i | ||||
\(83\) | − | 71948.9i | − | 0.125832i | −0.998019 | − | 0.0629158i | \(-0.979960\pi\) | ||
0.998019 | − | 0.0629158i | \(-0.0200400\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 411649. | 0.670302 | ||||||||
\(86\) | −203521. | + | 352509.i | −0.319974 | + | 0.554211i | ||||
\(87\) | −183740. | + | 106082.i | −0.279027 | + | 0.161096i | ||||
\(88\) | 464757. | + | 804983.i | 0.681990 | + | 1.18124i | ||||
\(89\) | 141505. | + | 81698.0i | 0.200725 | + | 0.115889i | 0.596994 | − | 0.802246i | \(-0.296362\pi\) |
−0.396269 | + | 0.918135i | \(0.629695\pi\) | |||||||
\(90\) | 89939.6i | 0.123374i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −331220. | −0.425357 | ||||||||
\(93\) | 196497. | − | 340342.i | 0.244290 | − | 0.423123i | ||||
\(94\) | 666130. | − | 384590.i | 0.802002 | − | 0.463036i | ||||
\(95\) | −299146. | − | 518137.i | −0.348910 | − | 0.604329i | ||||
\(96\) | −402989. | − | 232666.i | −0.455490 | − | 0.262977i | ||||
\(97\) | − | 651914.i | − | 0.714291i | −0.934049 | − | 0.357146i | \(-0.883750\pi\) | ||
0.934049 | − | 0.357146i | \(-0.116250\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −419354. | −0.432190 | ||||||||
\(100\) | 186338. | − | 322747.i | 0.186338 | − | 0.322747i | ||||
\(101\) | −883850. | + | 510291.i | −0.857856 | + | 0.495283i | −0.863294 | − | 0.504702i | \(-0.831602\pi\) |
0.00543765 | + | 0.999985i | \(0.498269\pi\) | |||||||
\(102\) | 264811. | + | 458666.i | 0.249537 | + | 0.432211i | ||||
\(103\) | −363147. | − | 209663.i | −0.332331 | − | 0.191871i | 0.324545 | − | 0.945870i | \(-0.394789\pi\) |
−0.656875 | + | 0.753999i | \(0.728122\pi\) | |||||||
\(104\) | 1.51213e6i | 1.34428i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −91292.8 | −0.0766512 | ||||||||
\(107\) | −1.10621e6 | + | 1.91600e6i | −0.902993 | + | 1.56403i | −0.0794039 | + | 0.996843i | \(0.525302\pi\) |
−0.823589 | + | 0.567187i | \(0.808032\pi\) | |||||||
\(108\) | 109740. | − | 63358.5i | 0.0871152 | − | 0.0502960i | ||||
\(109\) | −382955. | − | 663297.i | −0.295711 | − | 0.512187i | 0.679439 | − | 0.733732i | \(-0.262223\pi\) |
−0.975150 | + | 0.221545i | \(0.928890\pi\) | |||||||
\(110\) | 553158. | + | 319366.i | 0.415596 | + | 0.239944i | ||||
\(111\) | 354368.i | 0.259111i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.66096e6 | −1.84418 | −0.922090 | − | 0.386976i | \(-0.873520\pi\) | ||||
−0.922090 | + | 0.386976i | \(0.873520\pi\) | |||||||
\(114\) | 384877. | − | 666626.i | 0.259781 | − | 0.449954i | ||||
\(115\) | −574218. | + | 331525.i | −0.377558 | + | 0.217983i | ||||
\(116\) | −227649. | − | 394299.i | −0.145845 | − | 0.252611i | ||||
\(117\) | −590806. | − | 341102.i | −0.368882 | − | 0.212974i | ||||
\(118\) | 395620.i | 0.240787i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −562263. | −0.325384 | ||||||||
\(121\) | −603302. | + | 1.04495e6i | −0.340548 | + | 0.589847i | ||||
\(122\) | −1.26324e6 | + | 729331.i | −0.695674 | + | 0.401647i | ||||
\(123\) | 295380. | + | 511612.i | 0.158732 | + | 0.274932i | ||||
\(124\) | 730361. | + | 421674.i | 0.383065 | + | 0.221163i | ||||
\(125\) | − | 1.79238e6i | − | 0.917700i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.11648e6 | −0.545055 | −0.272527 | − | 0.962148i | \(-0.587859\pi\) | ||||
−0.272527 | + | 0.962148i | \(0.587859\pi\) | |||||||
\(128\) | 351433. | − | 608699.i | 0.167576 | − | 0.290250i | ||||
\(129\) | 994224. | − | 574015.i | 0.463143 | − | 0.267396i | ||||
\(130\) | 519544. | + | 899877.i | 0.236479 | + | 0.409594i | ||||
\(131\) | −247826. | − | 143083.i | −0.110239 | − | 0.0636463i | 0.443867 | − | 0.896093i | \(-0.353606\pi\) |
−0.554106 | + | 0.832446i | \(0.686940\pi\) | |||||||
\(132\) | − | 899918.i | − | 0.391274i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.03248e6 | 1.26033 | ||||||||
\(135\) | 126834. | − | 219682.i | 0.0515505 | − | 0.0892881i | ||||
\(136\) | −2.86738e6 | + | 1.65548e6i | −1.13990 | + | 0.658124i | ||||
\(137\) | 1.86697e6 | + | 3.23368e6i | 0.726063 | + | 1.25758i | 0.958535 | + | 0.284975i | \(0.0919854\pi\) |
−0.232472 | + | 0.972603i | \(0.574681\pi\) | |||||||
\(138\) | −738779. | − | 426534.i | −0.281111 | − | 0.162299i | ||||
\(139\) | − | 618216.i | − | 0.230195i | −0.993354 | − | 0.115097i | \(-0.963282\pi\) | ||
0.993354 | − | 0.115097i | \(-0.0367180\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.16941e6 | −0.773899 | ||||||||
\(142\) | −1.28684e6 | + | 2.22887e6i | −0.449426 | + | 0.778429i | ||||
\(143\) | −4.19579e6 | + | 2.42244e6i | −1.43485 | + | 0.828408i | ||||
\(144\) | −101574. | − | 175932.i | −0.0340171 | − | 0.0589193i | ||||
\(145\) | −789324. | − | 455716.i | −0.258911 | − | 0.149483i | ||||
\(146\) | 1.84454e6i | 0.592691i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −760461. | −0.234580 | ||||||||
\(149\) | −1.86160e6 | + | 3.22438e6i | −0.562765 | + | 0.974737i | 0.434489 | + | 0.900677i | \(0.356929\pi\) |
−0.997254 | + | 0.0740601i | \(0.976404\pi\) | |||||||
\(150\) | 831247. | − | 479920.i | 0.246295 | − | 0.142199i | ||||
\(151\) | 1.27599e6 | + | 2.21009e6i | 0.370611 | + | 0.641917i | 0.989660 | − | 0.143436i | \(-0.0458151\pi\) |
−0.619049 | + | 0.785352i | \(0.712482\pi\) | |||||||
\(152\) | 4.16746e6 | + | 2.40608e6i | 1.18670 | + | 0.685140i | ||||
\(153\) | − | 1.49375e6i | − | 0.417066i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.68825e6 | 0.453358 | ||||||||
\(156\) | 731993. | − | 1.26785e6i | 0.192811 | − | 0.333959i | ||||
\(157\) | 5.87057e6 | − | 3.38938e6i | 1.51699 | − | 0.875832i | 0.517186 | − | 0.855873i | \(-0.326980\pi\) |
0.999801 | − | 0.0199592i | \(-0.00635363\pi\) | |||||||
\(158\) | 1.13310e6 | + | 1.96259e6i | 0.287275 | + | 0.497575i | ||||
\(159\) | 222987. | + | 128742.i | 0.0554739 | + | 0.0320279i | ||||
\(160\) | − | 1.99900e6i | − | 0.488038i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 326364. | 0.0767639 | ||||||||
\(163\) | 4.13571e6 | − | 7.16325e6i | 0.954964 | − | 1.65405i | 0.220513 | − | 0.975384i | \(-0.429227\pi\) |
0.734451 | − | 0.678662i | \(-0.237440\pi\) | |||||||
\(164\) | −1.09790e6 | + | 633874.i | −0.248904 | + | 0.143705i | ||||
\(165\) | −900746. | − | 1.56014e6i | −0.200517 | − | 0.347305i | ||||
\(166\) | 344385. | + | 198831.i | 0.0752871 | + | 0.0434670i | ||||
\(167\) | 2.59960e6i | 0.558158i | 0.960268 | + | 0.279079i | \(0.0900291\pi\) | ||||
−0.960268 | + | 0.279079i | \(0.909971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.05483e6 | −0.632888 | ||||||||
\(170\) | −1.13759e6 | + | 1.97037e6i | −0.231548 | + | 0.401052i | ||||
\(171\) | −1.88016e6 | + | 1.08551e6i | −0.376017 | + | 0.217094i | ||||
\(172\) | 1.23182e6 | + | 2.13357e6i | 0.242081 | + | 0.419296i | ||||
\(173\) | 7.10612e6 | + | 4.10272e6i | 1.37244 | + | 0.792380i | 0.991235 | − | 0.132109i | \(-0.0421749\pi\) |
0.381208 | + | 0.924489i | \(0.375508\pi\) | |||||||
\(174\) | − | 1.17263e6i | − | 0.222595i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.44272e6 | −0.264633 | ||||||||
\(177\) | 557907. | − | 966324.i | 0.100610 | − | 0.174262i | ||||
\(178\) | −782099. | + | 451545.i | −0.138676 | + | 0.0800647i | ||||
\(179\) | −4.09401e6 | − | 7.09104e6i | −0.713822 | − | 1.23638i | −0.963412 | − | 0.268025i | \(-0.913629\pi\) |
0.249590 | − | 0.968352i | \(-0.419704\pi\) | |||||||
\(180\) | 471430. | + | 272180.i | 0.0808350 | + | 0.0466701i | ||||
\(181\) | 3.25606e6i | 0.549106i | 0.961572 | + | 0.274553i | \(0.0885298\pi\) | ||||
−0.961572 | + | 0.274553i | \(0.911470\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.11403e6 | 0.671297 | ||||||||
\(184\) | 2.66651e6 | − | 4.61853e6i | 0.428045 | − | 0.741395i | ||||
\(185\) | −1.31837e6 | + | 761161.i | −0.208220 | + | 0.120216i | ||||
\(186\) | 1.08604e6 | + | 1.88107e6i | 0.168774 | + | 0.292325i | ||||
\(187\) | −9.18709e6 | − | 5.30417e6i | −1.40492 | − | 0.811133i | ||||
\(188\) | − | 4.65547e6i | − | 0.700633i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.30677e6 | 0.482106 | ||||||||
\(191\) | −4.30425e6 | + | 7.45518e6i | −0.617728 | + | 1.06994i | 0.372171 | + | 0.928164i | \(0.378614\pi\) |
−0.989899 | + | 0.141773i | \(0.954720\pi\) | |||||||
\(192\) | 2.94963e6 | − | 1.70297e6i | 0.416738 | − | 0.240604i | ||||
\(193\) | 89943.0 | + | 155786.i | 0.0125111 | + | 0.0216699i | 0.872213 | − | 0.489126i | \(-0.162684\pi\) |
−0.859702 | + | 0.510796i | \(0.829351\pi\) | |||||||
\(194\) | 3.12040e6 | + | 1.80157e6i | 0.427372 | + | 0.246743i | ||||
\(195\) | − | 2.93067e6i | − | 0.395241i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.69333e6 | 0.352283 | 0.176141 | − | 0.984365i | \(-0.443638\pi\) | ||||
0.176141 | + | 0.984365i | \(0.443638\pi\) | |||||||
\(198\) | 1.15888e6 | − | 2.00725e6i | 0.149295 | − | 0.258586i | ||||
\(199\) | −5.23271e6 | + | 3.02111e6i | −0.663999 | + | 0.383360i | −0.793799 | − | 0.608180i | \(-0.791900\pi\) |
0.129800 | + | 0.991540i | \(0.458566\pi\) | |||||||
\(200\) | 3.00025e6 | + | 5.19659e6i | 0.375032 | + | 0.649574i | ||||
\(201\) | −7.40700e6 | − | 4.27643e6i | −0.912125 | − | 0.526616i | ||||
\(202\) | − | 5.64076e6i | − | 0.684358i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.20554e6 | 0.377581 | ||||||||
\(205\) | −1.26891e6 | + | 2.19782e6i | −0.147289 | + | 0.255112i | ||||
\(206\) | 2.00711e6 | − | 1.15881e6i | 0.229599 | − | 0.132559i | ||||
\(207\) | 1.20301e6 | + | 2.08367e6i | 0.135630 | + | 0.234918i | ||||
\(208\) | −2.03258e6 | − | 1.17351e6i | −0.225869 | − | 0.130406i | ||||
\(209\) | 1.54182e7i | 1.68886i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.38113e7 | −1.47024 | −0.735118 | − | 0.677939i | \(-0.762873\pi\) | ||||
−0.735118 | + | 0.677939i | \(0.762873\pi\) | |||||||
\(212\) | −276275. | + | 478523.i | −0.0289958 | + | 0.0502221i | ||||
\(213\) | 6.28634e6 | − | 3.62942e6i | 0.650517 | − | 0.375576i | ||||
\(214\) | −6.11400e6 | − | 1.05898e7i | −0.623855 | − | 1.08055i | ||||
\(215\) | 4.27106e6 | + | 2.46590e6i | 0.429755 | + | 0.248119i | ||||
\(216\) | 2.04029e6i | 0.202456i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.23318e6 | 0.408599 | ||||||||
\(219\) | 2.60118e6 | − | 4.50538e6i | 0.247650 | − | 0.428942i | ||||
\(220\) | 3.34800e6 | − | 1.93297e6i | 0.314425 | − | 0.181533i | ||||
\(221\) | −8.62881e6 | − | 1.49455e7i | −0.799419 | − | 1.38463i | ||||
\(222\) | −1.69619e6 | − | 979297.i | −0.155030 | − | 0.0895067i | ||||
\(223\) | 9.81400e6i | 0.884976i | 0.896774 | + | 0.442488i | \(0.145904\pi\) | ||||
−0.896774 | + | 0.442488i | \(0.854096\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.70715e6 | −0.237665 | ||||||||
\(226\) | 7.35357e6 | − | 1.27368e7i | 0.637049 | − | 1.10340i | ||||
\(227\) | 1.26217e7 | − | 7.28715e6i | 1.07905 | − | 0.622989i | 0.148408 | − | 0.988926i | \(-0.452585\pi\) |
0.930639 | + | 0.365938i | \(0.119252\pi\) | |||||||
\(228\) | −2.32947e6 | − | 4.03476e6i | −0.196541 | − | 0.340419i | ||||
\(229\) | −1.27292e7 | − | 7.34923e6i | −1.05998 | − | 0.611978i | −0.134551 | − | 0.990907i | \(-0.542959\pi\) |
−0.925426 | + | 0.378929i | \(0.876292\pi\) | |||||||
\(230\) | − | 3.66468e6i | − | 0.301198i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.33080e6 | 0.587067 | ||||||||
\(233\) | −2.87597e6 | + | 4.98133e6i | −0.227362 | + | 0.393802i | −0.957025 | − | 0.290004i | \(-0.906343\pi\) |
0.729664 | + | 0.683806i | \(0.239677\pi\) | |||||||
\(234\) | 3.26539e6 | − | 1.88527e6i | 0.254852 | − | 0.147139i | ||||
\(235\) | −4.65976e6 | − | 8.07094e6i | −0.359054 | − | 0.621900i | ||||
\(236\) | 2.07369e6 | + | 1.19725e6i | 0.157764 | + | 0.0910853i | ||||
\(237\) | − | 6.39164e6i | − | 0.480140i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.60167e7 | 1.17322 | 0.586610 | − | 0.809869i | \(-0.300462\pi\) | ||||
0.586610 | + | 0.809869i | \(0.300462\pi\) | |||||||
\(240\) | 436351. | − | 755782.i | 0.0315647 | − | 0.0546717i | ||||
\(241\) | 2.23613e7 | − | 1.29103e7i | 1.59752 | − | 0.922327i | 0.605553 | − | 0.795805i | \(-0.292952\pi\) |
0.991964 | − | 0.126522i | \(-0.0403816\pi\) | |||||||
\(242\) | −3.33445e6 | − | 5.77544e6i | −0.235276 | − | 0.407510i | ||||
\(243\) | −797162. | − | 460241.i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 8.82856e6i | 0.607744i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.26513e6 | −0.219328 | ||||||||
\(247\) | −1.25411e7 | + | 2.17219e7i | −0.832236 | + | 1.44147i | ||||
\(248\) | −1.17596e7 | + | 6.78943e6i | −0.770973 | + | 0.445121i | ||||
\(249\) | −560786. | − | 971311.i | −0.0363245 | − | 0.0629158i | ||||
\(250\) | 8.57929e6 | + | 4.95325e6i | 0.549074 | + | 0.317008i | ||||
\(251\) | − | 9.51912e6i | − | 0.601971i | −0.953629 | − | 0.300985i | \(-0.902684\pi\) | ||
0.953629 | − | 0.300985i | \(-0.0973156\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.70870e7 | 1.05513 | ||||||||
\(254\) | 3.08539e6 | − | 5.34406e6i | 0.188282 | − | 0.326115i | ||||
\(255\) | 5.55727e6 | − | 3.20849e6i | 0.335151 | − | 0.193500i | ||||
\(256\) | 8.93408e6 | + | 1.54743e7i | 0.532512 | + | 0.922339i | ||||
\(257\) | −1.93872e7 | − | 1.11932e7i | −1.14213 | − | 0.659408i | −0.195171 | − | 0.980769i | \(-0.562526\pi\) |
−0.946957 | + | 0.321361i | \(0.895860\pi\) | |||||||
\(258\) | 6.34517e6i | 0.369474i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.28910e6 | 0.357823 | ||||||||
\(261\) | −1.65366e6 | + | 2.86422e6i | −0.0930089 | + | 0.161096i | ||||
\(262\) | 1.36974e6 | − | 790818.i | 0.0761612 | − | 0.0439717i | ||||
\(263\) | −5.24659e6 | − | 9.08736e6i | −0.288410 | − | 0.499540i | 0.685021 | − | 0.728524i | \(-0.259793\pi\) |
−0.973430 | + | 0.228983i | \(0.926460\pi\) | |||||||
\(264\) | 1.25484e7 | + | 7.24484e6i | 0.681990 | + | 0.393747i | ||||
\(265\) | 1.10612e6i | 0.0594380i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.54709e6 | 0.133817 | ||||||||
\(268\) | 9.17707e6 | − | 1.58951e7i | 0.476760 | − | 0.825772i | ||||
\(269\) | −2.33663e7 | + | 1.34905e7i | −1.20042 | + | 0.693063i | −0.960649 | − | 0.277766i | \(-0.910406\pi\) |
−0.239772 | + | 0.970829i | \(0.577073\pi\) | |||||||
\(270\) | 701009. | + | 1.21418e6i | 0.0356150 | + | 0.0616869i | ||||
\(271\) | 1.09955e6 | + | 634826.i | 0.0552468 | + | 0.0318968i | 0.527369 | − | 0.849636i | \(-0.323179\pi\) |
−0.472122 | + | 0.881533i | \(0.656512\pi\) | |||||||
\(272\) | − | 5.13903e6i | − | 0.255373i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.06374e7 | −1.00324 | ||||||||
\(275\) | −9.61282e6 | + | 1.66499e7i | −0.462224 | + | 0.800596i | ||||
\(276\) | −4.47147e6 | + | 2.58160e6i | −0.212678 | + | 0.122790i | ||||
\(277\) | 3.35016e6 | + | 5.80265e6i | 0.157626 | + | 0.273016i | 0.934012 | − | 0.357242i | \(-0.116283\pi\) |
−0.776386 | + | 0.630257i | \(0.782949\pi\) | |||||||
\(278\) | 2.95911e6 | + | 1.70844e6i | 0.137729 | + | 0.0795180i | ||||
\(279\) | − | 6.12616e6i | − | 0.282082i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −321000. | −0.0144673 | −0.00723363 | − | 0.999974i | \(-0.502303\pi\) | ||||
−0.00723363 | + | 0.999974i | \(0.502303\pi\) | |||||||
\(282\) | 5.99517e6 | − | 1.03839e7i | 0.267334 | − | 0.463036i | ||||
\(283\) | −2.77311e6 | + | 1.60105e6i | −0.122351 | + | 0.0706394i | −0.559926 | − | 0.828542i | \(-0.689171\pi\) |
0.437575 | + | 0.899182i | \(0.355837\pi\) | |||||||
\(284\) | 7.78860e6 | + | 1.34902e7i | 0.340020 | + | 0.588931i | ||||
\(285\) | −8.07695e6 | − | 4.66323e6i | −0.348910 | − | 0.201443i | ||||
\(286\) | − | 2.67776e7i | − | 1.14465i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.25380e6 | −0.303660 | ||||||||
\(289\) | 6.82485e6 | − | 1.18210e7i | 0.282748 | − | 0.489734i | ||||
\(290\) | 4.36260e6 | − | 2.51875e6i | 0.178876 | − | 0.103274i | ||||
\(291\) | −5.08117e6 | − | 8.80084e6i | −0.206198 | − | 0.357146i | ||||
\(292\) | 9.66837e6 | + | 5.58204e6i | 0.388333 | + | 0.224204i | ||||
\(293\) | − | 2.67440e6i | − | 0.106322i | −0.998586 | − | 0.0531610i | \(-0.983070\pi\) | ||
0.998586 | − | 0.0531610i | \(-0.0169297\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.79340e6 | 0.186714 | ||||||||
\(296\) | 6.12214e6 | − | 1.06039e7i | 0.236063 | − | 0.408873i | ||||
\(297\) | −5.66128e6 | + | 3.26854e6i | −0.216095 | + | 0.124763i | ||||
\(298\) | −1.02891e7 | − | 1.78212e7i | −0.388800 | − | 0.673422i | ||||
\(299\) | 2.40730e7 | + | 1.38986e7i | 0.900568 | + | 0.519943i | ||||
\(300\) | − | 5.80945e6i | − | 0.215165i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.41048e7 | −0.512092 | ||||||||
\(303\) | −7.95465e6 | + | 1.37779e7i | −0.285952 | + | 0.495283i | ||||
\(304\) | −6.46841e6 | + | 3.73454e6i | −0.230238 | + | 0.132928i | ||||
\(305\) | 8.83669e6 | + | 1.53056e7i | 0.311451 | + | 0.539449i | ||||
\(306\) | 7.14989e6 | + | 4.12799e6i | 0.249537 | + | 0.144070i | ||||
\(307\) | 1.98765e7i | 0.686950i | 0.939162 | + | 0.343475i | \(0.111604\pi\) | ||||
−0.939162 | + | 0.343475i | \(0.888396\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.53664e6 | −0.221554 | ||||||||
\(310\) | −4.66548e6 | + | 8.08085e6i | −0.156607 | + | 0.271251i | ||||
\(311\) | 1.36580e7 | − | 7.88548e6i | 0.454054 | − | 0.262148i | −0.255487 | − | 0.966813i | \(-0.582236\pi\) |
0.709541 | + | 0.704664i | \(0.248902\pi\) | |||||||
\(312\) | 1.17859e7 | + | 2.04138e7i | 0.388060 | + | 0.672140i | ||||
\(313\) | 9.13939e6 | + | 5.27663e6i | 0.298047 | + | 0.172077i | 0.641565 | − | 0.767069i | \(-0.278285\pi\) |
−0.343518 | + | 0.939146i | \(0.611619\pi\) | |||||||
\(314\) | 3.74662e7i | 1.21018i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.37162e7 | 0.434684 | ||||||||
\(317\) | 1.61613e7 | − | 2.79923e7i | 0.507341 | − | 0.878740i | −0.492623 | − | 0.870243i | \(-0.663962\pi\) |
0.999964 | − | 0.00849733i | \(-0.00270482\pi\) | |||||||
\(318\) | −1.23245e6 | + | 711557.i | −0.0383256 | + | 0.0221273i | ||||
\(319\) | 1.17440e7 | + | 2.03411e7i | 0.361778 | + | 0.626618i | ||||
\(320\) | 1.26712e7 | + | 7.31574e6i | 0.386695 | + | 0.223259i | ||||
\(321\) | 3.44881e7i | 1.04269i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.49201e7 | −1.62976 | ||||||||
\(324\) | 987661. | − | 1.71068e6i | 0.0290384 | − | 0.0502960i | ||||
\(325\) | −2.70860e7 | + | 1.56381e7i | −0.789033 | + | 0.455549i | ||||
\(326\) | 2.28581e7 | + | 3.95913e7i | 0.659761 | + | 1.14274i | ||||
\(327\) | −1.03398e7 | − | 5.96968e6i | −0.295711 | − | 0.170729i | ||||
\(328\) | − | 2.04122e7i | − | 0.578452i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 9.95685e6 | 0.277064 | ||||||||
\(331\) | −1.00165e7 | + | 1.73490e7i | −0.276205 | + | 0.478400i | −0.970438 | − | 0.241349i | \(-0.922410\pi\) |
0.694234 | + | 0.719750i | \(0.255743\pi\) | |||||||
\(332\) | 2.08440e6 | − | 1.20343e6i | 0.0569595 | − | 0.0328856i | ||||
\(333\) | 2.76203e6 | + | 4.78397e6i | 0.0747989 | + | 0.129555i | ||||
\(334\) | −1.24430e7 | − | 7.18400e6i | −0.333955 | − | 0.192809i | ||||
\(335\) | − | 3.67421e7i | − | 0.977303i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.66702e6 | −0.0958128 | −0.0479064 | − | 0.998852i | \(-0.515255\pi\) | ||||
−0.0479064 | + | 0.998852i | \(0.515255\pi\) | |||||||
\(338\) | 8.44203e6 | − | 1.46220e7i | 0.218623 | − | 0.378667i | ||||
\(339\) | −3.59230e7 | + | 2.07401e7i | −0.922090 | + | 0.532369i | ||||
\(340\) | 6.88530e6 | + | 1.19257e7i | 0.175181 | + | 0.303422i | ||||
\(341\) | −3.76779e7 | − | 2.17534e7i | −0.950219 | − | 0.548609i | ||||
\(342\) | − | 1.19993e7i | − | 0.299969i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.96672e7 | −0.974443 | ||||||||
\(345\) | −5.16796e6 | + | 8.95117e6i | −0.125853 | + | 0.217983i | ||||
\(346\) | −3.92756e7 | + | 2.26758e7i | −0.948187 | + | 0.547436i | ||||
\(347\) | −3.22802e6 | − | 5.59109e6i | −0.0772587 | − | 0.133816i | 0.824808 | − | 0.565414i | \(-0.191283\pi\) |
−0.902066 | + | 0.431598i | \(0.857950\pi\) | |||||||
\(348\) | −6.14652e6 | − | 3.54869e6i | −0.145845 | − | 0.0842036i | ||||
\(349\) | − | 4.01536e7i | − | 0.944600i | −0.881438 | − | 0.472300i | \(-0.843424\pi\) | ||
0.881438 | − | 0.472300i | \(-0.156576\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.06345e7 | −0.245921 | ||||||||
\(352\) | −2.57575e7 | + | 4.46133e7i | −0.590575 | + | 1.02291i | ||||
\(353\) | −7.02915e6 | + | 4.05828e6i | −0.159801 | + | 0.0922610i | −0.577768 | − | 0.816201i | \(-0.696076\pi\) |
0.417967 | + | 0.908462i | \(0.362743\pi\) | |||||||
\(354\) | 3.08356e6 | + | 5.34087e6i | 0.0695091 | + | 0.120393i | ||||
\(355\) | 2.70053e7 | + | 1.55915e7i | 0.603621 | + | 0.348501i | ||||
\(356\) | 5.46596e6i | 0.121148i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.52552e7 | 0.986324 | ||||||||
\(359\) | −1.84586e7 | + | 3.19712e7i | −0.398946 | + | 0.690996i | −0.993596 | − | 0.112989i | \(-0.963957\pi\) |
0.594650 | + | 0.803985i | \(0.297291\pi\) | |||||||
\(360\) | −7.59055e6 | + | 4.38241e6i | −0.162692 | + | 0.0939302i | ||||
\(361\) | 1.63876e7 | + | 2.83842e7i | 0.348333 | + | 0.603330i | ||||
\(362\) | −1.55852e7 | − | 8.99811e6i | −0.328539 | − | 0.189682i | ||||
\(363\) | 1.88091e7i | 0.393231i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.23487e7 | 0.459593 | ||||||||
\(366\) | −1.13691e7 | + | 1.96919e7i | −0.231891 | + | 0.401647i | ||||
\(367\) | −1.70742e7 | + | 9.85777e6i | −0.345415 | + | 0.199425i | −0.662664 | − | 0.748917i | \(-0.730574\pi\) |
0.317249 | + | 0.948342i | \(0.397241\pi\) | |||||||
\(368\) | 4.13875e6 | + | 7.16853e6i | 0.0830474 | + | 0.143842i | ||||
\(369\) | 7.97525e6 | + | 4.60451e6i | 0.158732 | + | 0.0916441i | ||||
\(370\) | − | 8.41387e6i | − | 0.166108i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.31465e7 | 0.255377 | ||||||||
\(373\) | −5.21653e6 | + | 9.03530e6i | −0.100521 | + | 0.174107i | −0.911899 | − | 0.410414i | \(-0.865384\pi\) |
0.811379 | + | 0.584521i | \(0.198718\pi\) | |||||||
\(374\) | 5.07770e7 | − | 2.93161e7i | 0.970627 | − | 0.560392i | ||||
\(375\) | −1.39702e7 | − | 2.41972e7i | −0.264917 | − | 0.458850i | ||||
\(376\) | 6.49158e7 | + | 3.74792e7i | 1.22120 | + | 0.705061i | ||||
\(377\) | 3.82101e7i | 0.713106i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.26018e7 | −0.966235 | −0.483118 | − | 0.875556i | \(-0.660496\pi\) | ||||
−0.483118 | + | 0.875556i | \(0.660496\pi\) | |||||||
\(380\) | 1.00071e7 | − | 1.73328e7i | 0.182372 | − | 0.315878i | ||||
\(381\) | −1.50725e7 | + | 8.70210e6i | −0.272527 | + | 0.157344i | ||||
\(382\) | −2.37896e7 | − | 4.12048e7i | −0.426773 | − | 0.739193i | ||||
\(383\) | −6.36846e7 | − | 3.67683e7i | −1.13354 | − | 0.654451i | −0.188719 | − | 0.982031i | \(-0.560434\pi\) |
−0.944823 | + | 0.327580i | \(0.893767\pi\) | |||||||
\(384\) | − | 1.09566e7i | − | 0.193500i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −994230. | −0.0172872 | ||||||||
\(387\) | 8.94802e6 | − | 1.54984e7i | 0.154381 | − | 0.267396i | ||||
\(388\) | 1.88863e7 | − | 1.09040e7i | 0.323334 | − | 0.186677i | ||||
\(389\) | −8.60695e6 | − | 1.49077e7i | −0.146218 | − | 0.253257i | 0.783609 | − | 0.621255i | \(-0.213377\pi\) |
−0.929827 | + | 0.367998i | \(0.880043\pi\) | |||||||
\(390\) | 1.40277e7 | + | 8.09890e6i | 0.236479 | + | 0.136531i | ||||
\(391\) | 6.08645e7i | 1.01820i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.46088e6 | −0.0734924 | ||||||||
\(394\) | −7.44303e6 | + | 1.28917e7i | −0.121692 | + | 0.210776i | ||||
\(395\) | 2.37791e7 | − | 1.37289e7i | 0.385837 | − | 0.222763i | ||||
\(396\) | −7.01416e6 | − | 1.21489e7i | −0.112951 | − | 0.195637i | ||||
\(397\) | 5.31024e7 | + | 3.06587e7i | 0.848678 | + | 0.489984i | 0.860205 | − | 0.509949i | \(-0.170336\pi\) |
−0.0115267 | + | 0.999934i | \(0.503669\pi\) | |||||||
\(398\) | − | 3.33953e7i | − | 0.529708i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.31354e6 | −0.145524 | ||||||||
\(401\) | 2.30735e7 | − | 3.99645e7i | 0.357833 | − | 0.619785i | −0.629765 | − | 0.776785i | \(-0.716849\pi\) |
0.987599 | + | 0.157000i | \(0.0501823\pi\) | |||||||
\(402\) | 4.09385e7 | − | 2.36359e7i | 0.630165 | − | 0.363826i | ||||
\(403\) | −3.53883e7 | − | 6.12944e7i | −0.540686 | − | 0.936495i | ||||
\(404\) | −2.95668e7 | − | 1.70704e7i | −0.448394 | − | 0.258880i | ||||
\(405\) | − | 3.95428e6i | − | 0.0595254i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.92307e7 | 0.581892 | ||||||||
\(408\) | −2.58064e7 | + | 4.46980e7i | −0.379968 | + | 0.658124i | ||||
\(409\) | 5.25613e7 | − | 3.03463e7i | 0.768239 | − | 0.443543i | −0.0640071 | − | 0.997949i | \(-0.520388\pi\) |
0.832246 | + | 0.554406i | \(0.187055\pi\) | |||||||
\(410\) | −7.01329e6 | − | 1.21474e7i | −0.101758 | − | 0.176251i | ||||
\(411\) | 5.04081e7 | + | 2.91031e7i | 0.726063 | + | 0.419193i | ||||
\(412\) | − | 1.40274e7i | − | 0.200579i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.32980e7 | −0.187407 | ||||||||
\(415\) | 2.40907e6 | − | 4.17263e6i | 0.0337058 | − | 0.0583802i | ||||
\(416\) | −7.25768e7 | + | 4.19022e7i | −1.00813 | + | 0.582046i | ||||
\(417\) | −4.81852e6 | − | 8.34592e6i | −0.0664516 | − | 0.115097i | ||||
\(418\) | −7.37995e7 | − | 4.26082e7i | −1.01047 | − | 0.583397i | ||||
\(419\) | − | 1.17371e8i | − | 1.59558i | −0.602939 | − | 0.797788i | \(-0.706004\pi\) | ||
0.602939 | − | 0.797788i | \(-0.293996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.28510e7 | −0.172222 | −0.0861111 | − | 0.996286i | \(-0.527444\pi\) | ||||
−0.0861111 | + | 0.996286i | \(0.527444\pi\) | |||||||
\(422\) | 3.81676e7 | − | 6.61081e7i | 0.507875 | − | 0.879666i | ||||
\(423\) | −2.92870e7 | + | 1.69089e7i | −0.386950 | + | 0.223405i | ||||
\(424\) | −4.44834e6 | − | 7.70475e6i | −0.0583580 | − | 0.101079i | ||||
\(425\) | −5.93075e7 | − | 3.42412e7i | −0.772579 | − | 0.446049i | ||||
\(426\) | 4.01196e7i | 0.518953i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.40101e7 | −0.943973 | ||||||||
\(429\) | −3.77621e7 | + | 6.54058e7i | −0.478282 | + | 0.828408i | ||||
\(430\) | −2.36062e7 | + | 1.36290e7i | −0.296907 | + | 0.171419i | ||||
\(431\) | 5.69282e7 | + | 9.86026e7i | 0.711043 | + | 1.23156i | 0.964466 | + | 0.264207i | \(0.0851102\pi\) |
−0.253423 | + | 0.967356i | \(0.581556\pi\) | |||||||
\(432\) | −2.74251e6 | − | 1.58339e6i | −0.0340171 | − | 0.0196398i | ||||
\(433\) | − | 2.76112e7i | − | 0.340111i | −0.985434 | − | 0.170056i | \(-0.945605\pi\) | ||
0.985434 | − | 0.170056i | \(-0.0543947\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.42078e7 | −0.172608 | ||||||||
\(436\) | 1.28107e7 | − | 2.21888e7i | 0.154566 | − | 0.267716i | ||||
\(437\) | 7.66092e7 | − | 4.42303e7i | 0.917987 | − | 0.530000i | ||||
\(438\) | 1.43767e7 | + | 2.49012e7i | 0.171095 | + | 0.296346i | ||||
\(439\) | −6.22452e7 | − | 3.59373e7i | −0.735720 | − | 0.424768i | 0.0847914 | − | 0.996399i | \(-0.472978\pi\) |
−0.820511 | + | 0.571631i | \(0.806311\pi\) | |||||||
\(440\) | 6.22459e7i | 0.730723i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.53829e7 | 1.10460 | ||||||||
\(443\) | 4.75145e7 | − | 8.22975e7i | 0.546531 | − | 0.946620i | −0.451978 | − | 0.892029i | \(-0.649281\pi\) |
0.998509 | − | 0.0545904i | \(-0.0173853\pi\) | |||||||
\(444\) | −1.02662e7 | + | 5.92721e6i | −0.117290 | + | 0.0677175i | ||||
\(445\) | 5.47099e6 | + | 9.47603e6i | 0.0620849 | + | 0.107534i | ||||
\(446\) | −4.69750e7 | − | 2.71210e7i | −0.529495 | − | 0.305704i | ||||
\(447\) | 5.80389e7i | 0.649825i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.15401e8 | 1.27488 | 0.637440 | − | 0.770500i | \(-0.279993\pi\) | ||||
0.637440 | + | 0.770500i | \(0.279993\pi\) | |||||||
\(450\) | 7.48122e6 | − | 1.29579e7i | 0.0820984 | − | 0.142199i | ||||
\(451\) | 5.66386e7 | − | 3.27003e7i | 0.617423 | − | 0.356469i | ||||
\(452\) | −4.45076e7 | − | 7.70894e7i | −0.481968 | − | 0.834794i | ||||
\(453\) | 3.44518e7 | + | 1.98908e7i | 0.370611 | + | 0.213972i | ||||
\(454\) | 8.05522e7i | 0.860815i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.50142e7 | 0.791132 | ||||||||
\(457\) | −4.58763e6 | + | 7.94601e6i | −0.0480662 | + | 0.0832531i | −0.889058 | − | 0.457796i | \(-0.848639\pi\) |
0.840991 | + | 0.541049i | \(0.181973\pi\) | |||||||
\(458\) | 7.03546e7 | − | 4.06192e7i | 0.732311 | − | 0.422800i | ||||
\(459\) | −1.16427e7 | − | 2.01657e7i | −0.120397 | − | 0.208533i | ||||
\(460\) | −1.92089e7 | − | 1.10903e7i | −0.197346 | − | 0.113938i | ||||
\(461\) | − | 5.79354e7i | − | 0.591346i | −0.955289 | − | 0.295673i | \(-0.904456\pi\) | ||
0.955289 | − | 0.295673i | \(-0.0955438\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.51781e7 | 0.656687 | 0.328344 | − | 0.944558i | \(-0.393510\pi\) | ||||
0.328344 | + | 0.944558i | \(0.393510\pi\) | |||||||
\(464\) | −5.68916e6 | + | 9.85391e6i | −0.0569500 | + | 0.0986404i | ||||
\(465\) | 2.27914e7 | − | 1.31586e7i | 0.226679 | − | 0.130873i | ||||
\(466\) | −1.58955e7 | − | 2.75318e7i | −0.157079 | − | 0.272068i | ||||
\(467\) | 1.46749e8 | + | 8.47258e7i | 1.44087 | + | 0.831888i | 0.997908 | − | 0.0646508i | \(-0.0205933\pi\) |
0.442965 | + | 0.896539i | \(0.353927\pi\) | |||||||
\(468\) | − | 2.28213e7i | − | 0.222640i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.15090e7 | 0.496123 | ||||||||
\(471\) | 5.28352e7 | − | 9.15132e7i | 0.505662 | − | 0.875832i | ||||
\(472\) | −3.33888e7 | + | 1.92770e7i | −0.317523 | + | 0.183322i | ||||
\(473\) | −6.35470e7 | − | 1.10067e8i | −0.600498 | − | 1.04009i | ||||
\(474\) | 3.05938e7 | + | 1.76633e7i | 0.287275 | + | 0.165858i | ||||
\(475\) | 9.95326e7i | 0.928719i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.01377e6 | 0.0369826 | ||||||||
\(478\) | −4.42622e7 | + | 7.66644e7i | −0.405275 | + | 0.701956i | ||||
\(479\) | 7.92689e7 | − | 4.57659e7i | 0.721268 | − | 0.416424i | −0.0939514 | − | 0.995577i | \(-0.529950\pi\) |
0.815219 | + | 0.579153i | \(0.196617\pi\) | |||||||
\(480\) | −1.55807e7 | − | 2.69866e7i | −0.140885 | − | 0.244019i | ||||
\(481\) | 5.52701e7 | + | 3.19102e7i | 0.496656 | + | 0.286744i | ||||
\(482\) | 1.42710e8i | 1.27443i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.03636e7 | −0.356003 | ||||||||
\(485\) | 2.18281e7 | − | 3.78073e7i | 0.191333 | − | 0.331399i | ||||
\(486\) | 4.40591e6 | − | 2.54376e6i | 0.0383820 | − | 0.0221598i | ||||
\(487\) | 6.56199e7 | + | 1.13657e8i | 0.568131 | + | 0.984032i | 0.996751 | + | 0.0805467i | \(0.0256666\pi\) |
−0.428620 | + | 0.903485i | \(0.641000\pi\) | |||||||
\(488\) | −1.23105e8 | − | 7.10749e7i | −1.05930 | − | 0.611585i | ||||
\(489\) | − | 1.28939e8i | − | 1.10270i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.81776e7 | −0.744927 | −0.372463 | − | 0.928047i | \(-0.621487\pi\) | ||||
−0.372463 | + | 0.928047i | \(0.621487\pi\) | |||||||
\(492\) | −9.88111e6 | + | 1.71146e7i | −0.0829680 | + | 0.143705i | ||||
\(493\) | −7.24558e7 | + | 4.18324e7i | −0.604690 | + | 0.349118i | ||||
\(494\) | −6.93149e7 | − | 1.20057e8i | −0.574971 | − | 0.995879i | ||||
\(495\) | −2.43201e7 | − | 1.40412e7i | −0.200517 | − | 0.115768i | ||||
\(496\) | − | 2.10761e7i | − | 0.172721i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.19894e6 | 0.0501914 | ||||||||
\(499\) | 1.14235e8 | − | 1.97862e8i | 0.919389 | − | 1.59243i | 0.119043 | − | 0.992889i | \(-0.462017\pi\) |
0.800346 | − | 0.599539i | \(-0.204649\pi\) | |||||||
\(500\) | 5.19262e7 | − | 2.99796e7i | 0.415410 | − | 0.239837i | ||||
\(501\) | 2.02619e7 | + | 3.50946e7i | 0.161126 | + | 0.279079i | ||||
\(502\) | 4.55635e7 | + | 2.63061e7i | 0.360169 | + | 0.207943i | ||||
\(503\) | − | 2.07735e8i | − | 1.63232i | −0.577824 | − | 0.816161i | \(-0.696098\pi\) | ||
0.577824 | − | 0.816161i | \(-0.303902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.83444e7 | −0.530675 | ||||||||
\(506\) | −4.72199e7 | + | 8.17873e7i | −0.364480 | + | 0.631298i | ||||
\(507\) | −4.12402e7 | + | 2.38100e7i | −0.316444 | + | 0.182699i | ||||
\(508\) | −1.86744e7 | − | 3.23450e7i | −0.142448 | − | 0.246727i | ||||
\(509\) | 4.74960e7 | + | 2.74218e7i | 0.360167 | + | 0.207942i | 0.669154 | − | 0.743124i | \(-0.266657\pi\) |
−0.308987 | + | 0.951066i | \(0.599990\pi\) | |||||||
\(510\) | 3.54667e7i | 0.267368i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −5.37739e7 | −0.400647 | ||||||||
\(513\) | −1.69215e7 | + | 2.93089e7i | −0.125339 | + | 0.217094i | ||||
\(514\) | 1.07153e8 | − | 6.18647e7i | 0.789068 | − | 0.455569i | ||||
\(515\) | −1.40403e7 | − | 2.43185e7i | −0.102791 | − | 0.178039i | ||||
\(516\) | 3.32590e7 | + | 1.92021e7i | 0.242081 | + | 0.139765i | ||||
\(517\) | 2.40167e8i | 1.73797i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.27910e8 | 0.914962 | ||||||||
\(520\) | −5.06308e7 | + | 8.76951e7i | −0.360085 | + | 0.623685i | ||||
\(521\) | 2.47035e7 | − | 1.42626e7i | 0.174681 | − | 0.100852i | −0.410110 | − | 0.912036i | \(-0.634510\pi\) |
0.584791 | + | 0.811184i | \(0.301176\pi\) | |||||||
\(522\) | −9.13978e6 | − | 1.58306e7i | −0.0642576 | − | 0.111297i | ||||
\(523\) | 9.32394e7 | + | 5.38318e7i | 0.651770 | + | 0.376300i | 0.789134 | − | 0.614221i | \(-0.210530\pi\) |
−0.137364 | + | 0.990521i | \(0.543863\pi\) | |||||||
\(524\) | − | 9.57287e6i | − | 0.0665347i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.79958e7 | 0.398510 | ||||||||
\(527\) | 7.74863e7 | − | 1.34210e8i | 0.529411 | − | 0.916966i | ||||
\(528\) | −1.94767e7 | + | 1.12449e7i | −0.132317 | + | 0.0763930i | ||||
\(529\) | 2.50003e7 | + | 4.33018e7i | 0.168880 | + | 0.292509i | ||||
\(530\) | −5.29446e6 | − | 3.05676e6i | −0.0355627 | − | 0.0205321i | ||||
\(531\) | − | 1.73938e7i | − | 0.116175i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.06394e8 | 0.702642 | ||||||||
\(534\) | −7.03889e6 | + | 1.21917e7i | −0.0462253 | + | 0.0800647i | ||||
\(535\) | −1.28307e8 | + | 7.40782e7i | −0.837895 | + | 0.483759i | ||||
\(536\) | 1.47761e8 | + | 2.55930e8i | 0.959546 | + | 1.66198i | ||||
\(537\) | −1.10538e8 | − | 6.38193e7i | −0.713822 | − | 0.412125i | ||||
\(538\) | − | 1.49125e8i | − | 0.957640i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.48574e6 | 0.0538900 | ||||||||
\(541\) | −2.77877e7 | + | 4.81297e7i | −0.175493 | + | 0.303963i | −0.940332 | − | 0.340259i | \(-0.889485\pi\) |
0.764839 | + | 0.644222i | \(0.222819\pi\) | |||||||
\(542\) | −6.07722e6 | + | 3.50868e6i | −0.0381686 | + | 0.0220367i | ||||
\(543\) | 2.53784e7 | + | 4.39567e7i | 0.158513 | + | 0.274553i | ||||
\(544\) | −1.58914e8 | − | 9.17491e7i | −0.987110 | − | 0.569908i | ||||
\(545\) | − | 5.12900e7i | − | 0.316842i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.44170e7 | 0.332485 | 0.166243 | − | 0.986085i | \(-0.446837\pi\) | ||||
0.166243 | + | 0.986085i | \(0.446837\pi\) | |||||||
\(548\) | −6.24542e7 | + | 1.08174e8i | −0.379507 | + | 0.657325i | ||||
\(549\) | 5.55395e7 | − | 3.20657e7i | 0.335648 | − | 0.193787i | ||||
\(550\) | −5.31301e7 | − | 9.20240e7i | −0.319339 | − | 0.553112i | ||||
\(551\) | 1.05308e8 | + | 6.07993e7i | 0.629513 | + | 0.363449i | ||||
\(552\) | − | 8.31335e7i | − | 0.494264i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.70327e7 | −0.217799 | ||||||||
\(555\) | −1.18653e7 | + | 2.05513e7i | −0.0694066 | + | 0.120216i | ||||
\(556\) | 1.79100e7 | − | 1.03404e7i | 0.104201 | − | 0.0601605i | ||||
\(557\) | −6.26135e6 | − | 1.08450e7i | −0.0362329 | − | 0.0627571i | 0.847340 | − | 0.531050i | \(-0.178202\pi\) |
−0.883573 | + | 0.468293i | \(0.844869\pi\) | |||||||
\(558\) | 2.93230e7 | + | 1.69296e7i | 0.168774 | + | 0.0974418i | ||||
\(559\) | − | 2.06756e8i | − | 1.18365i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.65368e8 | −0.936616 | ||||||||
\(562\) | 887085. | − | 1.53648e6i | 0.00499754 | − | 0.00865599i | ||||
\(563\) | −1.50742e8 | + | 8.70310e7i | −0.844713 | + | 0.487695i | −0.858864 | − | 0.512204i | \(-0.828829\pi\) |
0.0141502 | + | 0.999900i | \(0.495496\pi\) | |||||||
\(564\) | −3.62858e7 | − | 6.28489e7i | −0.202255 | − | 0.350316i | ||||
\(565\) | −1.54321e8 | − | 8.90971e7i | −0.855616 | − | 0.493990i | ||||
\(566\) | − | 1.76981e7i | − | 0.0976060i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.50810e8 | −1.36868 | ||||||||
\(569\) | −2.37803e7 | + | 4.11886e7i | −0.129086 | + | 0.223584i | −0.923323 | − | 0.384025i | \(-0.874538\pi\) |
0.794237 | + | 0.607609i | \(0.207871\pi\) | |||||||
\(570\) | 4.46413e7 | − | 2.57737e7i | 0.241053 | − | 0.139172i | ||||
\(571\) | −8.27707e7 | − | 1.43363e8i | −0.444599 | − | 0.770068i | 0.553425 | − | 0.832899i | \(-0.313320\pi\) |
−0.998024 | + | 0.0628311i | \(0.979987\pi\) | |||||||
\(572\) | −1.40358e8 | − | 8.10360e7i | −0.749981 | − | 0.433002i | ||||
\(573\) | 1.34193e8i | 0.713291i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.10306e8 | 0.580222 | ||||||||
\(576\) | 2.65466e7 | − | 4.59801e7i | 0.138913 | − | 0.240604i | ||||
\(577\) | 4.44692e7 | − | 2.56743e7i | 0.231490 | − | 0.133651i | −0.379769 | − | 0.925081i | \(-0.623997\pi\) |
0.611259 | + | 0.791431i | \(0.290663\pi\) | |||||||
\(578\) | 3.77210e7 | + | 6.53346e7i | 0.195344 | + | 0.338345i | ||||
\(579\) | 2.42846e6 | + | 1.40207e6i | 0.0125111 | + | 0.00722328i | ||||
\(580\) | − | 3.04895e7i | − | 0.156267i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.61673e7 | 0.284914 | ||||||||
\(583\) | 1.42525e7 | − | 2.46861e7i | 0.0719259 | − | 0.124579i | ||||
\(584\) | −1.55672e8 | + | 8.98771e7i | −0.781576 | + | 0.451243i | ||||
\(585\) | −2.28423e7 | − | 3.95640e7i | −0.114096 | − | 0.197621i | ||||
\(586\) | 1.28011e7 | + | 7.39070e6i | 0.0636141 | + | 0.0367276i | ||||
\(587\) | 2.37624e8i | 1.17483i | 0.809285 | + | 0.587416i | \(0.199855\pi\) | ||||
−0.809285 | + | 0.587416i | \(0.800145\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.25238e8 | −1.10229 | ||||||||
\(590\) | −1.32466e7 | + | 2.29437e7i | −0.0644982 | + | 0.111714i | ||||
\(591\) | 3.63600e7 | − | 2.09925e7i | 0.176141 | − | 0.101695i | ||||
\(592\) | 9.50232e6 | + | 1.64585e7i | 0.0457999 | + | 0.0793278i | ||||
\(593\) | 3.20624e8 | + | 1.85112e8i | 1.53756 | + | 0.887711i | 0.998981 | + | 0.0451361i | \(0.0143722\pi\) |
0.538579 | + | 0.842575i | \(0.318961\pi\) | |||||||
\(594\) | − | 3.61305e7i | − | 0.172391i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.24549e8 | −0.588305 | ||||||||
\(597\) | −4.70944e7 | + | 8.15699e7i | −0.221333 | + | 0.383360i | ||||
\(598\) | −1.33052e8 | + | 7.68173e7i | −0.622180 | + | 0.359216i | ||||
\(599\) | 1.87938e7 | + | 3.25519e7i | 0.0874451 | + | 0.151459i | 0.906430 | − | 0.422355i | \(-0.138796\pi\) |
−0.818985 | + | 0.573814i | \(0.805463\pi\) | |||||||
\(600\) | 8.10068e7 | + | 4.67693e7i | 0.375032 | + | 0.216525i | ||||
\(601\) | 2.67605e7i | 0.123274i | 0.998099 | + | 0.0616369i | \(0.0196321\pi\) | ||||
−0.998099 | + | 0.0616369i | \(0.980368\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.33326e8 | −0.608083 | ||||||||
\(604\) | −4.26849e7 | + | 7.39324e7i | −0.193715 | + | 0.335524i | ||||
\(605\) | −6.99761e7 | + | 4.04007e7i | −0.315998 | + | 0.182441i | ||||
\(606\) | −4.39654e7 | − | 7.61503e7i | −0.197557 | − | 0.342179i | ||||
\(607\) | −6.69071e7 | − | 3.86288e7i | −0.299162 | − | 0.172721i | 0.342905 | − | 0.939370i | \(-0.388589\pi\) |
−0.642066 | + | 0.766649i | \(0.721923\pi\) | |||||||
\(608\) | 2.66697e8i | 1.18661i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.76808e7 | −0.430348 | ||||||||
\(611\) | −1.95352e8 | + | 3.38359e8i | −0.856433 | + | 1.48338i | ||||
\(612\) | 4.32748e7 | − | 2.49847e7i | 0.188791 | − | 0.108998i | ||||
\(613\) | 1.76486e8 | + | 3.05682e8i | 0.766174 | + | 1.32705i | 0.939623 | + | 0.342210i | \(0.111175\pi\) |
−0.173449 | + | 0.984843i | \(0.555491\pi\) | |||||||
\(614\) | −9.51394e7 | − | 5.49288e7i | −0.411013 | − | 0.237298i | ||||
\(615\) | 3.95608e7i | 0.170075i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.82109e8 | 0.775310 | 0.387655 | − | 0.921805i | \(-0.373285\pi\) | ||||
0.387655 | + | 0.921805i | \(0.373285\pi\) | |||||||
\(618\) | 1.80640e7 | − | 3.12878e7i | 0.0765330 | − | 0.132559i | ||||
\(619\) | −8.43335e7 | + | 4.86900e7i | −0.355573 | + | 0.205290i | −0.667137 | − | 0.744935i | \(-0.732480\pi\) |
0.311564 | + | 0.950225i | \(0.399147\pi\) | |||||||
\(620\) | 2.82379e7 | + | 4.89094e7i | 0.118483 | + | 0.205219i | ||||
\(621\) | 3.24811e7 | + | 1.87530e7i | 0.135630 | + | 0.0783062i | ||||
\(622\) | 8.71661e7i | 0.362223i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.65864e7 | −0.150579 | ||||||||
\(625\) | −2.70211e7 | + | 4.68019e7i | −0.110678 | + | 0.191701i | ||||
\(626\) | −5.05134e7 | + | 2.91639e7i | −0.205913 | + | 0.118884i | ||||
\(627\) | 1.20173e8 | + | 2.08145e8i | 0.487533 | + | 0.844431i | ||||
\(628\) | 1.96384e8 | + | 1.13382e8i | 0.792916 | + | 0.457790i | ||||
\(629\) | 1.39741e8i | 0.561529i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.37285e8 | −0.546430 | −0.273215 | − | 0.961953i | \(-0.588087\pi\) | ||||
−0.273215 | + | 0.961953i | \(0.588087\pi\) | |||||||
\(632\) | −1.10423e8 | + | 1.91259e8i | −0.437431 | + | 0.757653i | ||||
\(633\) | −1.86453e8 | + | 1.07648e8i | −0.735118 | + | 0.424421i | ||||
\(634\) | 8.93238e7 | + | 1.54713e8i | 0.350509 | + | 0.607100i | ||||
\(635\) | −6.47495e7 | − | 3.73832e7i | −0.252881 | − | 0.146001i | ||||
\(636\) | 8.61341e6i | 0.0334814i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.29818e8 | −0.499887 | ||||||||
\(639\) | 5.65770e7 | − | 9.79943e7i | 0.216839 | − | 0.375576i | ||||
\(640\) | 4.07622e7 | − | 2.35341e7i | 0.155495 | − | 0.0897753i | ||||
\(641\) | 1.04673e8 | + | 1.81298e8i | 0.397428 | + | 0.688366i | 0.993408 | − | 0.114633i | \(-0.0365693\pi\) |
−0.595979 | + | 0.803000i | \(0.703236\pi\) | |||||||
\(642\) | −1.65078e8 | − | 9.53078e7i | −0.623855 | − | 0.360183i | ||||
\(643\) | − | 3.49818e8i | − | 1.31586i | −0.753079 | − | 0.657930i | \(-0.771432\pi\) | ||
0.753079 | − | 0.657930i | \(-0.228568\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.68791e7 | 0.286503 | ||||||||
\(646\) | 1.51772e8 | − | 2.62877e8i | 0.562981 | − | 0.975112i | ||||
\(647\) | −3.20197e8 | + | 1.84866e8i | −1.18224 | + | 0.682566i | −0.956531 | − | 0.291630i | \(-0.905803\pi\) |
−0.225707 | + | 0.974195i | \(0.572469\pi\) | |||||||
\(648\) | 1.59025e7 | + | 2.75439e7i | 0.0584439 | + | 0.101228i | ||||
\(649\) | −1.06978e8 | − | 6.17637e7i | −0.391345 | − | 0.225943i | ||||
\(650\) | − | 1.72864e8i | − | 0.629454i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.76697e8 | 0.998303 | ||||||||
\(653\) | 1.97623e7 | − | 3.42293e7i | 0.0709737 | − | 0.122930i | −0.828355 | − | 0.560204i | \(-0.810723\pi\) |
0.899328 | + | 0.437274i | \(0.144056\pi\) | |||||||
\(654\) | 5.71480e7 | − | 3.29944e7i | 0.204300 | − | 0.117952i | ||||
\(655\) | −9.58169e6 | − | 1.65960e7i | −0.0340971 | − | 0.0590580i | ||||
\(656\) | 2.74376e7 | + | 1.58411e7i | 0.0971929 | + | 0.0561144i | ||||
\(657\) | − | 8.10968e7i | − | 0.285962i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.29124e8 | −1.15002 | −0.575008 | − | 0.818148i | \(-0.695001\pi\) | ||||
−0.575008 | + | 0.818148i | \(0.695001\pi\) | |||||||
\(660\) | 3.01320e7 | − | 5.21901e7i | 0.104808 | − | 0.181533i | ||||
\(661\) | 1.39292e8 | − | 8.04205e7i | 0.482306 | − | 0.278460i | −0.239071 | − | 0.971002i | \(-0.576843\pi\) |
0.721377 | + | 0.692543i | \(0.243509\pi\) | |||||||
\(662\) | −5.53611e7 | − | 9.58882e7i | −0.190823 | − | 0.330515i | ||||
\(663\) | −2.32978e8 | − | 1.34510e8i | −0.799419 | − | 0.461545i | ||||
\(664\) | 3.87530e7i | 0.132374i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.05315e7 | −0.103353 | ||||||||
\(667\) | 6.73800e7 | − | 1.16706e8i | 0.227067 | − | 0.393291i | ||||
\(668\) | −7.53117e7 | + | 4.34812e7i | −0.252658 | + | 0.145872i | ||||
\(669\) | 7.64926e7 | + | 1.32489e8i | 0.255471 | + | 0.442488i | ||||
\(670\) | 1.75867e8 | + | 1.01537e8i | 0.584735 | + | 0.337597i | ||||
\(671\) | − | 4.55448e8i | − | 1.50755i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.32162e8 | 1.74582 | 0.872908 | − | 0.487886i | \(-0.162232\pi\) | ||||
0.872908 | + | 0.487886i | \(0.162232\pi\) | |||||||
\(674\) | 1.01338e7 | − | 1.75523e7i | 0.0330974 | − | 0.0573263i | ||||
\(675\) | −3.65466e7 | + | 2.11002e7i | −0.118832 | + | 0.0686080i | ||||
\(676\) | −5.10955e7 | − | 8.84999e7i | −0.165403 | − | 0.286486i | ||||
\(677\) | 4.68878e8 | + | 2.70707e8i | 1.51110 | + | 0.872435i | 0.999916 | + | 0.0129645i | \(0.00412684\pi\) |
0.511186 | + | 0.859470i | \(0.329206\pi\) | |||||||
\(678\) | − | 2.29262e8i | − | 0.735601i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.21722e8 | −0.705151 | ||||||||
\(681\) | 1.13595e8 | − | 1.96753e8i | 0.359683 | − | 0.622989i | ||||
\(682\) | 2.08246e8 | − | 1.20231e8i | 0.656483 | − | 0.379021i | ||||
\(683\) | −1.24469e8 | − | 2.15587e8i | −0.390662 | − | 0.676646i | 0.601875 | − | 0.798590i | \(-0.294420\pi\) |
−0.992537 | + | 0.121944i | \(0.961087\pi\) | |||||||
\(684\) | −6.28957e7 | − | 3.63129e7i | −0.196541 | − | 0.113473i | ||||
\(685\) | 2.50047e8i | 0.777946i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.29126e8 | −0.706651 | ||||||||
\(688\) | 3.07843e7 | − | 5.33199e7i | 0.0945286 | − | 0.163728i | ||||
\(689\) | 4.01592e7 | − | 2.31860e7i | 0.122780 | − | 0.0708871i | ||||
\(690\) | −2.85633e7 | − | 4.94731e7i | −0.0869484 | − | 0.150599i | ||||
\(691\) | −8.00565e7 | − | 4.62206e7i | −0.242640 | − | 0.140088i | 0.373749 | − | 0.927530i | \(-0.378072\pi\) |
−0.616390 | + | 0.787441i | \(0.711405\pi\) | |||||||
\(692\) | 2.74491e8i | 0.828341i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.56825e7 | 0.106752 | ||||||||
\(695\) | 2.06997e7 | − | 3.58530e7i | 0.0616610 | − | 0.106800i | ||||
\(696\) | 9.89658e7 | − | 5.71379e7i | 0.293533 | − | 0.169472i | ||||
\(697\) | 1.16480e8 | + | 2.01749e8i | 0.343995 | + | 0.595816i | ||||
\(698\) | 1.92196e8 | + | 1.10964e8i | 0.565169 | + | 0.326300i | ||||
\(699\) | 8.96640e7i | 0.262535i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.38435e8 | 1.56307 | 0.781537 | − | 0.623859i | \(-0.214436\pi\) | ||||
0.781537 | + | 0.623859i | \(0.214436\pi\) | |||||||
\(702\) | 2.93885e7 | − | 5.09024e7i | 0.0849505 | − | 0.147139i | ||||
\(703\) | 1.75890e8 | − | 1.01550e8i | 0.506262 | − | 0.292290i | ||||
\(704\) | −1.88529e8 | − | 3.26541e8i | −0.540331 | − | 0.935880i | ||||
\(705\) | −1.25813e8 | − | 7.26384e7i | −0.359054 | − | 0.207300i | ||||
\(706\) | − | 4.48603e7i | − | 0.127482i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.73265e7 | 0.105176 | ||||||||
\(709\) | −3.53455e7 | + | 6.12202e7i | −0.0991735 | + | 0.171773i | −0.911343 | − | 0.411648i | \(-0.864953\pi\) |
0.812169 | + | 0.583422i | \(0.198287\pi\) | |||||||
\(710\) | −1.49258e8 | + | 8.61744e7i | −0.417027 | + | 0.240771i | ||||
\(711\) | −4.98179e7 | − | 8.62872e7i | −0.138604 | − | 0.240070i | ||||
\(712\) | −7.62173e7 | − | 4.40041e7i | −0.211161 | − | 0.121914i | ||||
\(713\) | 2.49616e8i | 0.688660i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.24442e8 | −0.887604 | ||||||||
\(716\) | 1.36954e8 | − | 2.37211e8i | 0.373109 | − | 0.646243i | ||||
\(717\) | 2.16226e8 | − | 1.24838e8i | 0.586610 | − | 0.338680i | ||||
\(718\) | −1.02021e8 | − | 1.76705e8i | −0.275622 | − | 0.477392i | ||||
\(719\) | 3.38940e8 | + | 1.95687e8i | 0.911876 | + | 0.526472i | 0.881034 | − | 0.473053i | \(-0.156848\pi\) |
0.0308415 | + | 0.999524i | \(0.490181\pi\) | |||||||
\(720\) | − | 1.36041e7i | − | 0.0364478i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.81149e8 | −0.481309 | ||||||||
\(723\) | 2.01252e8 | − | 3.48578e8i | 0.532506 | − | 0.922327i | ||||
\(724\) | −9.43295e7 | + | 5.44612e7i | −0.248560 | + | 0.143506i | ||||
\(725\) | 7.58135e7 | + | 1.31313e8i | 0.198945 | + | 0.344582i | ||||
\(726\) | −9.00302e7 | − | 5.19789e7i | −0.235276 | − | 0.135837i | ||||
\(727\) | − | 4.83550e8i | − | 1.25846i | −0.777221 | − | 0.629228i | \(-0.783371\pi\) | ||
0.777221 | − | 0.629228i | \(-0.216629\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | −6.17607e7 | + | 1.06973e8i | −0.158761 | + | 0.274982i | ||||
\(731\) | 3.92061e8 | − | 2.26357e8i | 1.00369 | − | 0.579484i | ||||
\(732\) | 6.88118e7 | + | 1.19186e8i | 0.175441 | + | 0.303872i | ||||
\(733\) | 2.76711e8 | + | 1.59759e8i | 0.702611 | + | 0.405653i | 0.808319 | − | 0.588745i | \(-0.200378\pi\) |
−0.105708 | + | 0.994397i | \(0.533711\pi\) | |||||||
\(734\) | − | 1.08968e8i | − | 0.275556i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.95563e8 | 0.741339 | ||||||||
\(737\) | −4.73427e8 | + | 8.20000e8i | −1.18263 | + | 2.04838i | ||||
\(738\) | −4.40792e7 | + | 2.54491e7i | −0.109664 | + | 0.0633146i | ||||
\(739\) | −1.76757e8 | − | 3.06151e8i | −0.437968 | − | 0.758582i | 0.559565 | − | 0.828787i | \(-0.310968\pi\) |
−0.997533 | + | 0.0702042i | \(0.977635\pi\) | |||||||
\(740\) | −4.41024e7 | − | 2.54625e7i | −0.108835 | − | 0.0628357i | ||||
\(741\) | 3.90994e8i | 0.960983i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.63396e8 | 1.12976 | 0.564880 | − | 0.825173i | \(-0.308923\pi\) | ||||
0.564880 | + | 0.825173i | \(0.308923\pi\) | |||||||
\(744\) | −1.05837e8 | + | 1.83315e8i | −0.256991 | + | 0.445121i | ||||
\(745\) | −2.15924e8 | + | 1.24664e8i | −0.522195 | + | 0.301489i | ||||
\(746\) | −2.88318e7 | − | 4.99381e7i | −0.0694472 | − | 0.120286i | ||||
\(747\) | −1.51412e7 | − | 8.74179e6i | −0.0363245 | − | 0.0209719i | ||||
\(748\) | − | 3.54873e8i | − | 0.847945i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.54427e8 | 0.366050 | ||||||||
\(751\) | 1.48510e7 | − | 2.57226e7i | 0.0350618 | − | 0.0607289i | −0.847962 | − | 0.530057i | \(-0.822171\pi\) |
0.883024 | + | 0.469328i | \(0.155504\pi\) | |||||||
\(752\) | −1.00757e8 | + | 5.81724e7i | −0.236932 | + | 0.136793i | ||||
\(753\) | −7.41942e7 | − | 1.28508e8i | −0.173774 | − | 0.300985i | ||||
\(754\) | −1.82894e8 | − | 1.05594e8i | −0.426662 | − | 0.246334i | ||||
\(755\) | 1.70897e8i | 0.397093i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.11235e8 | 1.63955 | 0.819776 | − | 0.572684i | \(-0.194098\pi\) | ||||
0.819776 | + | 0.572684i | \(0.194098\pi\) | |||||||
\(758\) | 1.45365e8 | − | 2.51780e8i | 0.333774 | − | 0.578113i | ||||
\(759\) | 2.30674e8 | − | 1.33180e8i | 0.527563 | − | 0.304588i | ||||
\(760\) | 1.61126e8 | + | 2.79078e8i | 0.367049 | + | 0.635748i | ||||
\(761\) | −3.18255e8 | − | 1.83745e8i | −0.722140 | − | 0.416928i | 0.0933998 | − | 0.995629i | \(-0.470227\pi\) |
−0.815540 | + | 0.578701i | \(0.803560\pi\) | |||||||
\(762\) | − | 9.61931e7i | − | 0.217410i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.87974e8 | −0.645763 | ||||||||
\(765\) | 5.00154e7 | − | 8.66292e7i | 0.111717 | − | 0.193500i | ||||
\(766\) | 3.51985e8 | − | 2.03218e8i | 0.783137 | − | 0.452144i | ||||
\(767\) | −1.00477e8 | − | 1.74031e8i | −0.222680 | − | 0.385693i | ||||
\(768\) | 2.41220e8 | + | 1.39268e8i | 0.532512 | + | 0.307446i | ||||
\(769\) | 3.18891e8i | 0.701235i | 0.936519 | + | 0.350617i | \(0.114028\pi\) | ||||
−0.936519 | + | 0.350617i | \(0.885972\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.48969e8 | −0.761419 | ||||||||
\(772\) | −3.00879e6 | + | 5.21138e6i | −0.00653944 | + | 0.0113266i | ||||
\(773\) | −1.35153e8 | + | 7.80307e7i | −0.292609 | + | 0.168938i | −0.639118 | − | 0.769109i | \(-0.720700\pi\) |
0.346509 | + | 0.938047i | \(0.387367\pi\) | |||||||
\(774\) | 4.94557e7 | + | 8.56598e7i | 0.106658 | + | 0.184737i | ||||
\(775\) | −2.43231e8 | − | 1.40430e8i | −0.522533 | − | 0.301685i | ||||
\(776\) | 3.51133e8i | 0.751427i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.51413e7 | 0.202037 | ||||||||
\(779\) | 1.69292e8 | − | 2.93222e8i | 0.358116 | − | 0.620275i | ||||
\(780\) | 8.49028e7 | − | 4.90187e7i | 0.178912 | − | 0.103295i | ||||
\(781\) | −4.01798e8 | − | 6.95935e8i | −0.843442 | − | 1.46088i | ||||
\(782\) | −2.91329e8 | − | 1.68199e8i | −0.609206 | − | 0.351725i | ||||
\(783\) | 5.15560e7i | 0.107397i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.53947e8 | 0.938417 | ||||||||
\(786\) | 1.23276e7 | − | 2.13521e7i | 0.0253871 | − | 0.0439717i | ||||
\(787\) | 6.50044e8 | − | 3.75303e8i | 1.33358 | − | 0.769942i | 0.347733 | − | 0.937594i | \(-0.386952\pi\) |
0.985846 | + | 0.167651i | \(0.0536183\pi\) | |||||||
\(788\) | 4.50490e7 | + | 7.80272e7i | 0.0920676 | + | 0.159466i | ||||
\(789\) | −1.41658e8 | − | 8.17862e7i | −0.288410 | − | 0.166513i | ||||
\(790\) | 1.51759e8i | 0.307803i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.25872e8 | 0.454660 | ||||||||
\(793\) | 3.70462e8 | − | 6.41658e8i | 0.742888 | − | 1.28672i | ||||
\(794\) | −2.93497e8 | + | 1.69451e8i | −0.586331 | + | 0.338518i | ||||
\(795\) | 8.62134e6 | + | 1.49326e7i | 0.0171583 | + | 0.0297190i | ||||
\(796\) | −1.75046e8 | − | 1.01063e8i | −0.347067 | − | 0.200379i | ||||
\(797\) | − | 1.08408e6i | − | 0.00214134i | −0.999999 | − | 0.00107067i | \(-0.999659\pi\) | ||
0.999999 | − | 0.00107067i | \(-0.000340806\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.55483e8 | −1.67715 | ||||||||
\(800\) | −1.66278e8 | + | 2.88002e8i | −0.324762 | + | 0.562505i | ||||
\(801\) | 3.43857e7 | − | 1.98526e7i | 0.0669084 | − | 0.0386296i | ||||
\(802\) | 1.27527e8 | + | 2.20884e8i | 0.247218 | + | 0.428194i | ||||
\(803\) | −4.98772e8 | − | 2.87966e8i | −0.963287 | − | 0.556154i | ||||
\(804\) | − | 2.86113e8i | − | 0.550515i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.91183e8 | 0.747093 | ||||||||
\(807\) | −2.10297e8 | + | 3.64245e8i | −0.400140 | + | 0.693063i | ||||
\(808\) | 4.76058e8 | − | 2.74852e8i | 0.902456 | − | 0.521033i | ||||
\(809\) | −2.23887e8 | − | 3.87784e8i | −0.422847 | − | 0.732392i | 0.573370 | − | 0.819297i | \(-0.305636\pi\) |
−0.996217 | + | 0.0869044i | \(0.972303\pi\) | |||||||
\(810\) | 1.89273e7 | + | 1.09277e7i | 0.0356150 | + | 0.0205623i | ||||
\(811\) | 7.02416e8i | 1.31684i | 0.752652 | + | 0.658418i | \(0.228774\pi\) | ||||
−0.752652 | + | 0.658418i | \(0.771226\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.97919e7 | 0.0368312 | ||||||||
\(814\) | −1.08414e8 | + | 1.87779e8i | −0.201008 | + | 0.348155i | ||||
\(815\) | 4.79695e8 | − | 2.76952e8i | 0.886120 | − | 0.511601i | ||||
\(816\) | −4.00548e7 | − | 6.93769e7i | −0.0737197 | − | 0.127686i | ||||
\(817\) | −5.69823e8 | − | 3.28987e8i | −1.04490 | − | 0.603272i | ||||
\(818\) | 3.35448e8i | 0.612866i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.48960e7 | −0.153973 | ||||||||
\(821\) | −3.31937e8 | + | 5.74932e8i | −0.599828 | + | 1.03893i | 0.393018 | + | 0.919531i | \(0.371431\pi\) |
−0.992846 | + | 0.119402i | \(0.961902\pi\) | |||||||
\(822\) | −2.78605e8 | + | 1.60853e8i | −0.501619 | + | 0.289610i | ||||
\(823\) | −2.08427e8 | − | 3.61007e8i | −0.373900 | − | 0.647614i | 0.616262 | − | 0.787541i | \(-0.288646\pi\) |
−0.990162 | + | 0.139928i | \(0.955313\pi\) | |||||||
\(824\) | 1.95598e8 | + | 1.12928e8i | 0.349609 | + | 0.201847i | ||||
\(825\) | 2.99698e8i | 0.533731i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.14598e8 | 0.202609 | 0.101305 | − | 0.994855i | \(-0.467698\pi\) | ||||
0.101305 | + | 0.994855i | \(0.467698\pi\) | |||||||
\(828\) | −4.02432e7 | + | 6.97033e7i | −0.0708928 | + | 0.122790i | ||||
\(829\) | −4.05381e8 | + | 2.34047e8i | −0.711541 | + | 0.410808i | −0.811631 | − | 0.584170i | \(-0.801420\pi\) |
0.100090 | + | 0.994978i | \(0.468087\pi\) | |||||||
\(830\) | 1.33149e7 | + | 2.30621e7i | 0.0232865 | + | 0.0403334i | ||||
\(831\) | 9.04544e7 | + | 5.22239e7i | 0.157626 | + | 0.0910052i | ||||
\(832\) | − | 6.13397e8i | − | 1.06505i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5.32639e7 | 0.0918195 | ||||||||
\(835\) | −8.70425e7 | + | 1.50762e8i | −0.149511 | + | 0.258960i | ||||
\(836\) | −4.46672e8 | + | 2.57886e8i | −0.764487 | + | 0.441377i | ||||
\(837\) | −4.77487e7 | − | 8.27031e7i | −0.0814301 | − | 0.141041i | ||||
\(838\) | 5.61797e8 | + | 3.24354e8i | 0.954657 | + | 0.551172i | ||||
\(839\) | − | 6.49855e8i | − | 1.10035i | −0.835050 | − | 0.550174i | \(-0.814561\pi\) | ||
0.835050 | − | 0.550174i | \(-0.185439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.09581e8 | −0.688576 | ||||||||
\(842\) | 3.55136e7 | − | 6.15114e7i | 0.0594920 | − | 0.103043i | ||||
\(843\) | −4.33350e6 | + | 2.50195e6i | −0.00723363 | + | 0.00417634i | ||||
\(844\) | −2.31010e8 | − | 4.00120e8i | −0.384240 | − | 0.665523i | ||||
\(845\) | −1.77163e8 | − | 1.02285e8i | −0.293631 | − | 0.169528i | ||||
\(846\) | − | 1.86911e8i | − | 0.308691i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.38088e7 | 0.0226447 | ||||||||
\(849\) | −2.49580e7 | + | 4.32285e7i | −0.0407837 | + | 0.0706394i | ||||
\(850\) | 3.27793e8 | − | 1.89251e8i | 0.533756 | − | 0.308164i | ||||
\(851\) | −1.12542e8 | − | 1.94928e8i | −0.182610 | − | 0.316290i | ||||
\(852\) | 2.10292e8 | + | 1.21412e8i | 0.340020 | + | 0.196310i | ||||
\(853\) | 7.47082e7i | 0.120371i | 0.998187 | + | 0.0601854i | \(0.0191692\pi\) | ||||
−0.998187 | + | 0.0601854i | \(0.980831\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.45385e8 | −0.232606 | ||||||||
\(856\) | 5.95823e8 | − | 1.03200e9i | 0.949939 | − | 1.64534i | ||||
\(857\) | 7.50588e8 | − | 4.33352e8i | 1.19250 | − | 0.688491i | 0.233629 | − | 0.972326i | \(-0.424940\pi\) |
0.958873 | + | 0.283835i | \(0.0916066\pi\) | |||||||
\(858\) | −2.08711e8 | − | 3.61498e8i | −0.330433 | − | 0.572327i | ||||
\(859\) | 1.51273e7 | + | 8.73376e6i | 0.0238662 | + | 0.0137791i | 0.511886 | − | 0.859054i | \(-0.328947\pi\) |
−0.488019 | + | 0.872833i | \(0.662280\pi\) | |||||||
\(860\) | 1.64980e8i | 0.259379i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.29285e8 | −0.982484 | ||||||||
\(863\) | 5.59542e8 | − | 9.69155e8i | 0.870563 | − | 1.50786i | 0.00914866 | − | 0.999958i | \(-0.497088\pi\) |
0.861415 | − | 0.507902i | \(-0.169579\pi\) | |||||||
\(864\) | −9.79262e7 | + | 5.65377e7i | −0.151830 | + | 0.0876591i | ||||
\(865\) | 2.74743e8 | + | 4.75869e8i | 0.424501 | + | 0.735257i | ||||
\(866\) | 1.32161e8 | + | 7.63035e7i | 0.203494 | + | 0.117487i | ||||
\(867\) | − | 2.12778e8i | − | 0.326489i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.07593e8 | −1.07826 | ||||||||
\(870\) | 3.92634e7 | − | 6.80061e7i | 0.0596252 | − | 0.103274i | ||||
\(871\) | −1.33397e9 | + | 7.70171e8i | −2.01880 | + | 1.16555i | ||||
\(872\) | 2.06267e8 | + | 3.57264e8i | 0.311085 | + | 0.538816i | ||||
\(873\) | −1.37192e8 | − | 7.92076e7i | −0.206198 | − | 0.119049i | ||||
\(874\) | 4.88922e8i | 0.732328i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.74031e8 | 0.258889 | ||||||||
\(877\) | −5.82730e8 | + | 1.00932e9i | −0.863910 | + | 1.49634i | 0.00421521 | + | 0.999991i | \(0.498658\pi\) |
−0.868125 | + | 0.496345i | \(0.834675\pi\) | |||||||
\(878\) | 3.44029e8 | − | 1.98625e8i | 0.508290 | − | 0.293462i | ||||
\(879\) | −2.08449e7 | − | 3.61044e7i | −0.0306925 | − | 0.0531610i | ||||
\(880\) | −8.36696e7 | − | 4.83067e7i | −0.122778 | − | 0.0708858i | ||||
\(881\) | − | 2.07806e8i | − | 0.303900i | −0.988388 | − | 0.151950i | \(-0.951445\pi\) | ||
0.988388 | − | 0.151950i | \(-0.0485553\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.48816e8 | −0.506657 | −0.253329 | − | 0.967380i | \(-0.581525\pi\) | ||||
−0.253329 | + | 0.967380i | \(0.581525\pi\) | |||||||
\(884\) | 2.88653e8 | − | 4.99962e8i | 0.417849 | − | 0.723736i | ||||
\(885\) | 6.47109e7 | − | 3.73609e7i | 0.0933572 | − | 0.0538998i | ||||
\(886\) | 2.62613e8 | + | 4.54859e8i | 0.377585 | + | 0.653996i | ||||
\(887\) | 7.31382e8 | + | 4.22263e8i | 1.04803 | + | 0.605080i | 0.922097 | − | 0.386959i | \(-0.126475\pi\) |
0.125932 | + | 0.992039i | \(0.459808\pi\) | |||||||
\(888\) | − | 1.90869e8i | − | 0.272582i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.04764e7 | −0.0857858 | ||||||||
\(891\) | −5.09515e7 | + | 8.82506e7i | −0.0720317 | + | 0.124763i | ||||
\(892\) | −2.84317e8 | + | 1.64150e8i | −0.400597 | + | 0.231285i | ||||
\(893\) | 6.21681e8 | + | 1.07678e9i | 0.872998 | + | 1.51208i | ||||
\(894\) | −2.77804e8 | − | 1.60390e8i | −0.388800 | − | 0.224474i | ||||
\(895\) | − | 5.48320e8i | − | 0.764830i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.33314e8 | 0.600379 | ||||||||
\(898\) | −3.18910e8 | + | 5.52368e8i | −0.440391 | + | 0.762780i | ||||
\(899\) | −2.97155e8 | + | 1.71562e8i | −0.408981 | + | 0.236125i | ||||
\(900\) | −4.52802e7 | − | 7.84276e7i | −0.0621127 | − | 0.107582i | ||||
\(901\) | 8.79326e7 | + | 5.07679e7i | 0.120220 | + | 0.0694089i | ||||
\(902\) | 3.61469e8i | 0.492552i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.43324e9 | 1.94006 | ||||||||
\(905\) | −1.09023e8 | + | 1.88833e8i | −0.147086 | + | 0.254760i | ||||
\(906\) | −1.90415e8 | + | 1.09936e8i | −0.256046 | + | 0.147828i | ||||
\(907\) | 3.99924e8 | + | 6.92689e8i | 0.535989 | + | 0.928360i | 0.999115 | + | 0.0420677i | \(0.0133945\pi\) |
−0.463126 | + | 0.886293i | \(0.653272\pi\) | |||||||
\(908\) | 4.22225e8 | + | 2.43771e8i | 0.564009 | + | 0.325631i | ||||
\(909\) | 2.48001e8i | 0.330189i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.54047e8 | 0.203750 | 0.101875 | − | 0.994797i | \(-0.467516\pi\) | ||||
0.101875 | + | 0.994797i | \(0.467516\pi\) | |||||||
\(912\) | −5.82157e7 | + | 1.00833e8i | −0.0767460 | + | 0.132928i | ||||
\(913\) | −1.07530e8 | + | 6.20824e7i | −0.141292 | + | 0.0815749i | ||||
\(914\) | −2.53559e7 | − | 4.39176e7i | −0.0332078 | − | 0.0575175i | ||||
\(915\) | 2.38591e8 | + | 1.37750e8i | 0.311451 | + | 0.179816i | ||||
\(916\) | − | 4.91697e8i | − | 0.639751i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.28698e8 | 0.166358 | ||||||||
\(919\) | −3.43544e8 | + | 5.95036e8i | −0.442625 | + | 0.766649i | −0.997883 | − | 0.0650288i | \(-0.979286\pi\) |
0.555258 | + | 0.831678i | \(0.312619\pi\) | |||||||
\(920\) | 3.09285e8 | − | 1.78566e8i | 0.397187 | − | 0.229316i | ||||
\(921\) | 1.54922e8 | + | 2.68333e8i | 0.198305 | + | 0.343475i | ||||
\(922\) | 2.77309e8 | + | 1.60105e8i | 0.353811 | + | 0.204273i | ||||
\(923\) | − | 1.30729e9i | − | 1.66252i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.53255e8 | 0.319987 | ||||||||
\(926\) | −1.80120e8 | + | 3.11977e8i | −0.226845 | + | 0.392906i | ||||
\(927\) | −8.82447e7 | + | 5.09481e7i | −0.110777 | + | 0.0639571i | ||||
\(928\) | 2.03142e8 | + | 3.51852e8i | 0.254188 | + | 0.440266i | ||||
\(929\) | −3.27395e8 | − | 1.89021e8i | −0.408342 | − | 0.235757i | 0.281735 | − | 0.959492i | \(-0.409090\pi\) |
−0.690077 | + | 0.723736i | \(0.742423\pi\) | |||||||
\(930\) | 1.45455e8i | 0.180834i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.92416e8 | −0.237680 | ||||||||
\(933\) | 1.22922e8 | − | 2.12908e8i | 0.151351 | − | 0.262148i | ||||
\(934\) | −8.11084e8 | + | 4.68280e8i | −0.995463 | + | 0.574731i | ||||
\(935\) | −3.55199e8 | − | 6.15223e8i | −0.434547 | − | 0.752658i | ||||
\(936\) | 3.18219e8 | + | 1.83724e8i | 0.388060 | + | 0.224047i | ||||
\(937\) | 1.27190e9i | 1.54609i | 0.634351 | + | 0.773045i | \(0.281268\pi\) | ||||
−0.634351 | + | 0.773045i | \(0.718732\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.64509e8 | 0.198698 | ||||||||
\(940\) | 1.55879e8 | − | 2.69991e8i | 0.187674 | − | 0.325062i | ||||
\(941\) | 6.05181e8 | − | 3.49402e8i | 0.726301 | − | 0.419330i | −0.0907665 | − | 0.995872i | \(-0.528932\pi\) |
0.817067 | + | 0.576542i | \(0.195598\pi\) | |||||||
\(942\) | 2.92020e8 | + | 5.05794e8i | 0.349349 | + | 0.605091i | ||||
\(943\) | −3.24960e8 | − | 1.87615e8i | −0.387520 | − | 0.223735i | ||||
\(944\) | − | 5.98408e7i | − | 0.0711346i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.02448e8 | 0.829738 | ||||||||
\(947\) | 1.95719e8 | − | 3.38995e8i | 0.230453 | − | 0.399157i | −0.727488 | − | 0.686120i | \(-0.759312\pi\) |
0.957942 | + | 0.286963i | \(0.0926458\pi\) | |||||||
\(948\) | 1.85169e8 | − | 1.06907e8i | 0.217342 | − | 0.125482i | ||||
\(949\) | −4.68464e8 | − | 8.11403e8i | −0.548122 | − | 0.949375i | ||||
\(950\) | −4.76415e8 | − | 2.75058e8i | −0.555667 | − | 0.320815i | ||||
\(951\) | − | 5.03861e8i | − | 0.585827i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.05418e8 | −1.04609 | −0.523047 | − | 0.852304i | \(-0.675205\pi\) | ||||
−0.523047 | + | 0.852304i | \(0.675205\pi\) | |||||||
\(954\) | −1.10921e7 | + | 1.92120e7i | −0.0127752 | + | 0.0221273i | ||||
\(955\) | −4.99244e8 | + | 2.88239e8i | −0.573196 | + | 0.330935i | ||||
\(956\) | 2.67897e8 | + | 4.64012e8i | 0.306616 | + | 0.531075i | ||||
\(957\) | 3.17087e8 | + | 1.83070e8i | 0.361778 | + | 0.208873i | ||||
\(958\) | 5.05897e8i | 0.575394i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.28082e8 | 0.257797 | ||||||||
\(961\) | −1.25967e8 | + | 2.18180e8i | −0.141934 | + | 0.245836i | ||||
\(962\) | −3.05478e8 | + | 1.76368e8i | −0.343127 | + | 0.198104i | ||||
\(963\) | 2.68808e8 | + | 4.65589e8i | 0.300998 | + | 0.521343i | ||||
\(964\) | 7.48035e8 | + | 4.31878e8i | 0.835008 | + | 0.482092i | ||||
\(965\) | 1.20463e7i | 0.0134051i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.33523e9 | −1.47665 | −0.738323 | − | 0.674448i | \(-0.764382\pi\) | ||||
−0.738323 | + | 0.674448i | \(0.764382\pi\) | |||||||
\(968\) | 3.24950e8 | − | 5.62829e8i | 0.358253 | − | 0.620513i | ||||
\(969\) | −7.41422e8 | + | 4.28060e8i | −0.814881 | + | 0.470472i | ||||
\(970\) | 1.20644e8 | + | 2.08961e8i | 0.132187 | + | 0.228955i | ||||
\(971\) | 5.45806e8 | + | 3.15121e8i | 0.596184 | + | 0.344207i | 0.767539 | − | 0.641002i | \(-0.221481\pi\) |
−0.171355 | + | 0.985209i | \(0.554814\pi\) | |||||||
\(972\) | − | 3.07922e7i | − | 0.0335307i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7.25362e8 | −0.785015 | ||||||||
\(975\) | −2.43774e8 | + | 4.22229e8i | −0.263011 | + | 0.455549i | ||||
\(976\) | 1.91075e8 | − | 1.10317e8i | 0.205520 | − | 0.118657i | ||||
\(977\) | 2.04552e8 | + | 3.54294e8i | 0.219341 | + | 0.379910i | 0.954607 | − | 0.297869i | \(-0.0962760\pi\) |
−0.735266 | + | 0.677779i | \(0.762943\pi\) | |||||||
\(978\) | 6.17168e8 | + | 3.56322e8i | 0.659761 | + | 0.380913i | ||||
\(979\) | − | 2.81978e8i | − | 0.300516i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.86116e8 | −0.197141 | ||||||||
\(982\) | 2.43679e8 | − | 4.22064e8i | 0.257326 | − | 0.445701i | ||||
\(983\) | −7.95291e8 | + | 4.59161e8i | −0.837270 | + | 0.483398i | −0.856335 | − | 0.516420i | \(-0.827264\pi\) |
0.0190654 | + | 0.999818i | \(0.493931\pi\) | |||||||
\(984\) | −1.59097e8 | − | 2.75564e8i | −0.166985 | − | 0.289226i | ||||
\(985\) | 1.56198e8 | + | 9.01810e7i | 0.163443 | + | 0.0943640i | ||||
\(986\) | − | 4.62415e8i | − | 0.482394i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.39059e8 | −0.870005 | ||||||||
\(989\) | −3.64596e8 | + | 6.31499e8i | −0.376897 | + | 0.652805i | ||||
\(990\) | 1.34417e8 | − | 7.76060e7i | 0.138532 | − | 0.0799815i | ||||
\(991\) | 2.59369e8 | + | 4.49241e8i | 0.266500 | + | 0.461592i | 0.967956 | − | 0.251122i | \(-0.0807994\pi\) |
−0.701455 | + | 0.712713i | \(0.747466\pi\) | |||||||
\(992\) | −6.51736e8 | − | 3.76280e8i | −0.667631 | − | 0.385457i | ||||
\(993\) | 3.12283e8i | 0.318934i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.04623e8 | −0.410754 | ||||||||
\(996\) | 1.87596e7 | − | 3.24925e7i | 0.0189865 | − | 0.0328856i | ||||
\(997\) | −3.12596e8 | + | 1.80477e8i | −0.315426 | + | 0.182111i | −0.649352 | − | 0.760488i | \(-0.724960\pi\) |
0.333926 | + | 0.942599i | \(0.391626\pi\) | |||||||
\(998\) | 6.31379e8 | + | 1.09358e9i | 0.635183 | + | 1.10017i | ||||
\(999\) | 7.45747e7 | + | 4.30557e7i | 0.0747989 | + | 0.0431852i |
(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.19.2 | 8 | ||
7.2 | even | 3 | 147.7.d.b.97.6 | 8 | |||
7.3 | odd | 6 | inner | 147.7.f.d.31.2 | 8 | ||
7.4 | even | 3 | 21.7.f.a.10.2 | ✓ | 8 | ||
7.5 | odd | 6 | 147.7.d.b.97.5 | 8 | |||
7.6 | odd | 2 | 21.7.f.a.19.2 | yes | 8 | ||
21.2 | odd | 6 | 441.7.d.c.244.4 | 8 | |||
21.5 | even | 6 | 441.7.d.c.244.3 | 8 | |||
21.11 | odd | 6 | 63.7.m.d.10.3 | 8 | |||
21.20 | even | 2 | 63.7.m.d.19.3 | 8 | |||
28.11 | odd | 6 | 336.7.bh.d.241.2 | 8 | |||
28.27 | even | 2 | 336.7.bh.d.145.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.7.f.a.10.2 | ✓ | 8 | 7.4 | even | 3 | ||
21.7.f.a.19.2 | yes | 8 | 7.6 | odd | 2 | ||
63.7.m.d.10.3 | 8 | 21.11 | odd | 6 | |||
63.7.m.d.19.3 | 8 | 21.20 | even | 2 | |||
147.7.d.b.97.5 | 8 | 7.5 | odd | 6 | |||
147.7.d.b.97.6 | 8 | 7.2 | even | 3 | |||
147.7.f.d.19.2 | 8 | 1.1 | even | 1 | trivial | ||
147.7.f.d.31.2 | 8 | 7.3 | odd | 6 | inner | ||
336.7.bh.d.145.2 | 8 | 28.27 | even | 2 | |||
336.7.bh.d.241.2 | 8 | 28.11 | odd | 6 | |||
441.7.d.c.244.3 | 8 | 21.5 | even | 6 | |||
441.7.d.c.244.4 | 8 | 21.2 | odd | 6 |