Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,7,Mod(114,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("115.114");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.c (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: | \(26.4562196163\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 114.10 | ||
Character | \(\chi\) | \(=\) | 115.114 |
Dual form | 115.7.c.c.114.9 |
$q$-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 \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 14.4471i | 1.80589i | 0.429754 | + | 0.902946i | \(0.358600\pi\) | ||||
−0.429754 | + | 0.902946i | \(0.641400\pi\) | |||||||
\(3\) | 3.70784i | 0.137327i | 0.997640 | + | 0.0686637i | \(0.0218735\pi\) | ||||
−0.997640 | + | 0.0686637i | \(0.978126\pi\) | |||||||
\(4\) | −144.720 | −2.26125 | ||||||||
\(5\) | 95.5216 | + | 80.6265i | 0.764173 | + | 0.645012i | ||||
\(6\) | −53.5677 | −0.247998 | ||||||||
\(7\) | 454.114 | 1.32395 | 0.661974 | − | 0.749527i | \(-0.269719\pi\) | ||||
0.661974 | + | 0.749527i | \(0.269719\pi\) | |||||||
\(8\) | − | 1166.17i | − | 2.27768i | ||||||
\(9\) | 715.252 | 0.981141 | ||||||||
\(10\) | −1164.82 | + | 1380.01i | −1.16482 | + | 1.38001i | ||||
\(11\) | 1344.78i | 1.01036i | 0.863015 | + | 0.505178i | \(0.168573\pi\) | ||||
−0.863015 | + | 0.505178i | \(0.831427\pi\) | |||||||
\(12\) | − | 536.598i | − | 0.310531i | ||||||
\(13\) | 3188.96i | 1.45151i | 0.687954 | + | 0.725754i | \(0.258509\pi\) | ||||
−0.687954 | + | 0.725754i | \(0.741491\pi\) | |||||||
\(14\) | 6560.65i | 2.39091i | ||||||||
\(15\) | −298.950 | + | 354.179i | −0.0885778 | + | 0.104942i | ||||
\(16\) | 7585.76 | 1.85199 | ||||||||
\(17\) | 2309.58 | 0.470096 | 0.235048 | − | 0.971984i | \(-0.424475\pi\) | ||||
0.235048 | + | 0.971984i | \(0.424475\pi\) | |||||||
\(18\) | 10333.3i | 1.77184i | ||||||||
\(19\) | − | 2898.81i | − | 0.422629i | −0.977418 | − | 0.211314i | \(-0.932226\pi\) | ||
0.977418 | − | 0.211314i | \(-0.0677743\pi\) | |||||||
\(20\) | −13823.9 | − | 11668.3i | −1.72798 | − | 1.45853i | ||||
\(21\) | 1683.78i | 0.181814i | ||||||||
\(22\) | −19428.3 | −1.82459 | ||||||||
\(23\) | 5950.46 | − | 10612.6i | 0.489066 | − | 0.872247i | ||||
\(24\) | 4323.97 | 0.312787 | ||||||||
\(25\) | 2623.74 | + | 15403.1i | 0.167919 | + | 0.985801i | ||||
\(26\) | −46071.4 | −2.62127 | ||||||||
\(27\) | 5355.05i | 0.272065i | ||||||||
\(28\) | −65719.3 | −2.99377 | ||||||||
\(29\) | 40194.1 | 1.64804 | 0.824020 | − | 0.566561i | \(-0.191726\pi\) | ||||
0.824020 | + | 0.566561i | \(0.191726\pi\) | |||||||
\(30\) | −5116.87 | − | 4318.97i | −0.189514 | − | 0.159962i | ||||
\(31\) | 5774.59 | 0.193837 | 0.0969184 | − | 0.995292i | \(-0.469101\pi\) | ||||
0.0969184 | + | 0.995292i | \(0.469101\pi\) | |||||||
\(32\) | 34957.6i | 1.06682i | ||||||||
\(33\) | −4986.24 | −0.138749 | ||||||||
\(34\) | 33366.9i | 0.848943i | ||||||||
\(35\) | 43377.7 | + | 36613.6i | 1.01172 | + | 0.853962i | ||||
\(36\) | −103511. | −2.21860 | ||||||||
\(37\) | −100068. | −1.97556 | −0.987781 | − | 0.155849i | \(-0.950189\pi\) | ||||
−0.987781 | + | 0.155849i | \(0.950189\pi\) | |||||||
\(38\) | 41879.5 | 0.763222 | ||||||||
\(39\) | −11824.2 | −0.199332 | ||||||||
\(40\) | 94024.2 | − | 111394.i | 1.46913 | − | 1.74054i | ||||
\(41\) | −65360.8 | −0.948344 | −0.474172 | − | 0.880432i | \(-0.657253\pi\) | ||||
−0.474172 | + | 0.880432i | \(0.657253\pi\) | |||||||
\(42\) | −24325.8 | −0.328337 | ||||||||
\(43\) | 87522.8 | 1.10082 | 0.550409 | − | 0.834895i | \(-0.314472\pi\) | ||||
0.550409 | + | 0.834895i | \(0.314472\pi\) | |||||||
\(44\) | − | 194617.i | − | 2.28466i | ||||||
\(45\) | 68322.0 | + | 57668.2i | 0.749761 | + | 0.632848i | ||||
\(46\) | 153322. | + | 85967.1i | 1.57518 | + | 0.883200i | ||||
\(47\) | − | 167340.i | − | 1.61178i | −0.592064 | − | 0.805891i | \(-0.701687\pi\) | ||
0.592064 | − | 0.805891i | \(-0.298313\pi\) | |||||||
\(48\) | 28126.8i | 0.254329i | ||||||||
\(49\) | 88570.6 | 0.752838 | ||||||||
\(50\) | −222531. | + | 37905.5i | −1.78025 | + | 0.303244i | ||||
\(51\) | 8563.56i | 0.0645571i | ||||||||
\(52\) | − | 461506.i | − | 3.28222i | ||||||
\(53\) | −83815.9 | −0.562988 | −0.281494 | − | 0.959563i | \(-0.590830\pi\) | ||||
−0.281494 | + | 0.959563i | \(0.590830\pi\) | |||||||
\(54\) | −77365.2 | −0.491320 | ||||||||
\(55\) | −108425. | + | 128456.i | −0.651691 | + | 0.772086i | ||||
\(56\) | − | 529575.i | − | 3.01553i | ||||||
\(57\) | 10748.3 | 0.0580385 | ||||||||
\(58\) | 580689.i | 2.97618i | ||||||||
\(59\) | −33392.8 | −0.162591 | −0.0812956 | − | 0.996690i | \(-0.525906\pi\) | ||||
−0.0812956 | + | 0.996690i | \(0.525906\pi\) | |||||||
\(60\) | 43264.0 | − | 51256.7i | 0.200296 | − | 0.237299i | ||||
\(61\) | − | 229407.i | − | 1.01069i | −0.862918 | − | 0.505345i | \(-0.831365\pi\) | ||
0.862918 | − | 0.505345i | \(-0.168635\pi\) | |||||||
\(62\) | 83426.3i | 0.350048i | ||||||||
\(63\) | 324806. | 1.29898 | ||||||||
\(64\) | −19548.9 | −0.0745730 | ||||||||
\(65\) | −257115. | + | 304615.i | −0.936240 | + | 1.10920i | ||||
\(66\) | − | 72036.9i | − | 0.250567i | ||||||
\(67\) | −441802. | −1.46894 | −0.734469 | − | 0.678642i | \(-0.762569\pi\) | ||||
−0.734469 | + | 0.678642i | \(0.762569\pi\) | |||||||
\(68\) | −334242. | −1.06300 | ||||||||
\(69\) | 39349.9 | + | 22063.4i | 0.119783 | + | 0.0671621i | ||||
\(70\) | −528962. | + | 626684.i | −1.54216 | + | 1.82707i | ||||
\(71\) | 73472.2 | 0.205281 | 0.102640 | − | 0.994719i | \(-0.467271\pi\) | ||||
0.102640 | + | 0.994719i | \(0.467271\pi\) | |||||||
\(72\) | − | 834106.i | − | 2.23472i | ||||||
\(73\) | − | 242444.i | − | 0.623223i | −0.950210 | − | 0.311612i | \(-0.899131\pi\) | ||
0.950210 | − | 0.311612i | \(-0.100869\pi\) | |||||||
\(74\) | − | 1.44570e6i | − | 3.56765i | ||||||
\(75\) | −57112.4 | + | 9728.41i | −0.135377 | + | 0.0230599i | ||||
\(76\) | 419515.i | 0.955668i | ||||||||
\(77\) | 610685.i | 1.33766i | ||||||||
\(78\) | − | 170825.i | − | 0.359972i | ||||||
\(79\) | 547549.i | 1.11056i | 0.831663 | + | 0.555280i | \(0.187389\pi\) | ||||
−0.831663 | + | 0.555280i | \(0.812611\pi\) | |||||||
\(80\) | 724604. | + | 611613.i | 1.41524 | + | 1.19456i | ||||
\(81\) | 501563. | 0.943779 | ||||||||
\(82\) | − | 944277.i | − | 1.71261i | ||||||
\(83\) | −640953. | −1.12096 | −0.560482 | − | 0.828167i | \(-0.689384\pi\) | ||||
−0.560482 | + | 0.828167i | \(0.689384\pi\) | |||||||
\(84\) | − | 243677.i | − | 0.411127i | ||||||
\(85\) | 220615. | + | 186213.i | 0.359235 | + | 0.303218i | ||||
\(86\) | 1.26445e6i | 1.98796i | ||||||||
\(87\) | 149033.i | 0.226321i | ||||||||
\(88\) | 1.56825e6 | 2.30126 | ||||||||
\(89\) | 504452.i | 0.715566i | 0.933805 | + | 0.357783i | \(0.116467\pi\) | ||||
−0.933805 | + | 0.357783i | \(0.883533\pi\) | |||||||
\(90\) | −833141. | + | 987057.i | −1.14285 | + | 1.35399i | ||||
\(91\) | 1.44815e6i | 1.92172i | ||||||||
\(92\) | −861150. | + | 1.53586e6i | −1.10590 | + | 1.97237i | ||||
\(93\) | 21411.3i | 0.0266191i | ||||||||
\(94\) | 2.41758e6 | 2.91070 | ||||||||
\(95\) | 233721. | − | 276899.i | 0.272600 | − | 0.322961i | ||||
\(96\) | −129617. | −0.146504 | ||||||||
\(97\) | −100060. | −0.109634 | −0.0548168 | − | 0.998496i | \(-0.517457\pi\) | ||||
−0.0548168 | + | 0.998496i | \(0.517457\pi\) | |||||||
\(98\) | 1.27959e6i | 1.35954i | ||||||||
\(99\) | 961859.i | 0.991301i | ||||||||
\(100\) | −379707. | − | 2.22914e6i | −0.379707 | − | 2.22914i | ||||
\(101\) | −511425. | −0.496384 | −0.248192 | − | 0.968711i | \(-0.579836\pi\) | ||||
−0.248192 | + | 0.968711i | \(0.579836\pi\) | |||||||
\(102\) | −123719. | −0.116583 | ||||||||
\(103\) | 866738. | 0.793188 | 0.396594 | − | 0.917994i | \(-0.370192\pi\) | ||||
0.396594 | + | 0.917994i | \(0.370192\pi\) | |||||||
\(104\) | 3.71887e6 | 3.30607 | ||||||||
\(105\) | −135757. | + | 160838.i | −0.117272 | + | 0.138937i | ||||
\(106\) | − | 1.21090e6i | − | 1.01670i | ||||||
\(107\) | −809076. | −0.660447 | −0.330223 | − | 0.943903i | \(-0.607124\pi\) | ||||
−0.330223 | + | 0.943903i | \(0.607124\pi\) | |||||||
\(108\) | − | 774983.i | − | 0.615206i | ||||||
\(109\) | − | 1.57882e6i | − | 1.21914i | −0.792733 | − | 0.609569i | \(-0.791342\pi\) | ||
0.792733 | − | 0.609569i | \(-0.208658\pi\) | |||||||
\(110\) | −1.85582e6 | − | 1.56643e6i | −1.39430 | − | 1.17688i | ||||
\(111\) | − | 371037.i | − | 0.271299i | ||||||
\(112\) | 3.44480e6 | 2.45194 | ||||||||
\(113\) | −1.32022e6 | −0.914982 | −0.457491 | − | 0.889214i | \(-0.651252\pi\) | ||||
−0.457491 | + | 0.889214i | \(0.651252\pi\) | |||||||
\(114\) | 155282.i | 0.104811i | ||||||||
\(115\) | 1.42406e6 | − | 533970.i | 0.936340 | − | 0.351094i | ||||
\(116\) | −5.81688e6 | −3.72663 | ||||||||
\(117\) | 2.28091e6i | 1.42413i | ||||||||
\(118\) | − | 482431.i | − | 0.293622i | ||||||
\(119\) | 1.04881e6 | 0.622383 | ||||||||
\(120\) | 413033. | + | 348627.i | 0.239024 | + | 0.201752i | ||||
\(121\) | −36880.9 | −0.0208183 | ||||||||
\(122\) | 3.31428e6 | 1.82520 | ||||||||
\(123\) | − | 242347.i | − | 0.130234i | ||||||
\(124\) | −835698. | −0.438313 | ||||||||
\(125\) | −991277. | + | 1.68287e6i | −0.507534 | + | 0.861632i | ||||
\(126\) | 4.69252e6i | 2.34582i | ||||||||
\(127\) | − | 2.80478e6i | − | 1.36926i | −0.728889 | − | 0.684632i | \(-0.759963\pi\) | ||
0.728889 | − | 0.684632i | \(-0.240037\pi\) | |||||||
\(128\) | 1.95486e6i | 0.932151i | ||||||||
\(129\) | 324521.i | 0.151173i | ||||||||
\(130\) | −4.40081e6 | − | 3.71457e6i | −2.00310 | − | 1.69075i | ||||
\(131\) | −490972. | −0.218395 | −0.109198 | − | 0.994020i | \(-0.534828\pi\) | ||||
−0.109198 | + | 0.994020i | \(0.534828\pi\) | |||||||
\(132\) | 721608. | 0.313747 | ||||||||
\(133\) | − | 1.31639e6i | − | 0.559538i | ||||||
\(134\) | − | 6.38278e6i | − | 2.65274i | ||||||
\(135\) | −431759. | + | 511523.i | −0.175485 | + | 0.207905i | ||||
\(136\) | − | 2.69337e6i | − | 1.07073i | ||||||
\(137\) | 1.65858e6 | 0.645022 | 0.322511 | − | 0.946566i | \(-0.395473\pi\) | ||||
0.322511 | + | 0.946566i | \(0.395473\pi\) | |||||||
\(138\) | −318752. | + | 568494.i | −0.121288 | + | 0.216316i | ||||
\(139\) | 4.55698e6 | 1.69681 | 0.848405 | − | 0.529348i | \(-0.177563\pi\) | ||||
0.848405 | + | 0.529348i | \(0.177563\pi\) | |||||||
\(140\) | −6.27761e6 | − | 5.29872e6i | −2.28776 | − | 1.93102i | ||||
\(141\) | 620470. | 0.221342 | ||||||||
\(142\) | 1.06146e6i | 0.370715i | ||||||||
\(143\) | −4.28846e6 | −1.46654 | ||||||||
\(144\) | 5.42573e6 | 1.81707 | ||||||||
\(145\) | 3.83940e6 | + | 3.24071e6i | 1.25939 | + | 1.06301i | ||||
\(146\) | 3.50263e6 | 1.12547 | ||||||||
\(147\) | 328406.i | 0.103385i | ||||||||
\(148\) | 1.44818e7 | 4.46723 | ||||||||
\(149\) | 3.48875e6i | 1.05466i | 0.849662 | + | 0.527328i | \(0.176806\pi\) | ||||
−0.849662 | + | 0.527328i | \(0.823194\pi\) | |||||||
\(150\) | −140548. | − | 825110.i | −0.0416437 | − | 0.244477i | ||||
\(151\) | −914162. | −0.265517 | −0.132759 | − | 0.991148i | \(-0.542383\pi\) | ||||
−0.132759 | + | 0.991148i | \(0.542383\pi\) | |||||||
\(152\) | −3.38051e6 | −0.962611 | ||||||||
\(153\) | 1.65193e6 | 0.461231 | ||||||||
\(154\) | −8.82265e6 | −2.41567 | ||||||||
\(155\) | 551598. | + | 465585.i | 0.148125 | + | 0.125027i | ||||
\(156\) | 1.71119e6 | 0.450738 | ||||||||
\(157\) | 5.72267e6 | 1.47877 | 0.739383 | − | 0.673285i | \(-0.235117\pi\) | ||||
0.739383 | + | 0.673285i | \(0.235117\pi\) | |||||||
\(158\) | −7.91052e6 | −2.00555 | ||||||||
\(159\) | − | 310776.i | − | 0.0773136i | ||||||
\(160\) | −2.81851e6 | + | 3.33921e6i | −0.688113 | + | 0.815236i | ||||
\(161\) | 2.70219e6 | − | 4.81934e6i | 0.647497 | − | 1.15481i | ||||
\(162\) | 7.24615e6i | 1.70436i | ||||||||
\(163\) | 27407.0i | 0.00632847i | 0.999995 | + | 0.00316423i | \(0.00100721\pi\) | ||||
−0.999995 | + | 0.00316423i | \(0.998993\pi\) | |||||||
\(164\) | 9.45901e6 | 2.14444 | ||||||||
\(165\) | −476294. | − | 402023.i | −0.106029 | − | 0.0894951i | ||||
\(166\) | − | 9.25993e6i | − | 2.02434i | ||||||
\(167\) | 243555.i | 0.0522936i | 0.999658 | + | 0.0261468i | \(0.00832373\pi\) | ||||
−0.999658 | + | 0.0261468i | \(0.991676\pi\) | |||||||
\(168\) | 1.96358e6 | 0.414114 | ||||||||
\(169\) | −5.34267e6 | −1.10688 | ||||||||
\(170\) | −2.69025e6 | + | 3.18725e6i | −0.547578 | + | 0.648739i | ||||
\(171\) | − | 2.07338e6i | − | 0.414658i | ||||||
\(172\) | −1.26663e7 | −2.48922 | ||||||||
\(173\) | − | 496614.i | − | 0.0959137i | −0.998849 | − | 0.0479569i | \(-0.984729\pi\) | ||
0.998849 | − | 0.0479569i | \(-0.0152710\pi\) | |||||||
\(174\) | −2.15310e6 | −0.408712 | ||||||||
\(175\) | 1.19148e6 | + | 6.99478e6i | 0.222316 | + | 1.30515i | ||||
\(176\) | 1.02012e7i | 1.87117i | ||||||||
\(177\) | − | 123815.i | − | 0.0223282i | ||||||
\(178\) | −7.28789e6 | −1.29224 | ||||||||
\(179\) | 6.20825e6 | 1.08246 | 0.541228 | − | 0.840876i | \(-0.317960\pi\) | ||||
0.541228 | + | 0.840876i | \(0.317960\pi\) | |||||||
\(180\) | −9.88755e6 | − | 8.34574e6i | −1.69540 | − | 1.43103i | ||||
\(181\) | 5.95741e6i | 1.00467i | 0.864674 | + | 0.502333i | \(0.167525\pi\) | ||||
−0.864674 | + | 0.502333i | \(0.832475\pi\) | |||||||
\(182\) | −2.09217e7 | −3.47042 | ||||||||
\(183\) | 850605. | 0.138795 | ||||||||
\(184\) | −1.23761e7 | − | 6.93925e6i | −1.98670 | − | 1.11393i | ||||
\(185\) | −9.55867e6 | − | 8.06814e6i | −1.50967 | − | 1.27426i | ||||
\(186\) | −309331. | −0.0480712 | ||||||||
\(187\) | 3.10589e6i | 0.474964i | ||||||||
\(188\) | 2.42174e7i | 3.64464i | ||||||||
\(189\) | 2.43181e6i | 0.360200i | ||||||||
\(190\) | 4.00040e6 | + | 3.37660e6i | 0.583233 | + | 0.492287i | ||||
\(191\) | − | 1.83210e6i | − | 0.262936i | −0.991320 | − | 0.131468i | \(-0.958031\pi\) | ||
0.991320 | − | 0.131468i | \(-0.0419690\pi\) | |||||||
\(192\) | − | 72484.1i | − | 0.0102409i | ||||||
\(193\) | 5.97069e6i | 0.830524i | 0.909702 | + | 0.415262i | \(0.136310\pi\) | ||||
−0.909702 | + | 0.415262i | \(0.863690\pi\) | |||||||
\(194\) | − | 1.44558e6i | − | 0.197987i | ||||||
\(195\) | −1.12946e6 | − | 953341.i | −0.152324 | − | 0.128571i | ||||
\(196\) | −1.28179e7 | −1.70235 | ||||||||
\(197\) | − | 1.28195e7i | − | 1.67677i | −0.545077 | − | 0.838386i | \(-0.683500\pi\) | ||
0.545077 | − | 0.838386i | \(-0.316500\pi\) | |||||||
\(198\) | −1.38961e7 | −1.79018 | ||||||||
\(199\) | − | 1.04999e7i | − | 1.33237i | −0.745787 | − | 0.666184i | \(-0.767926\pi\) | ||
0.745787 | − | 0.666184i | \(-0.232074\pi\) | |||||||
\(200\) | 1.79627e7 | − | 3.05973e6i | 2.24534 | − | 0.382466i | ||||
\(201\) | − | 1.63813e6i | − | 0.201725i | ||||||
\(202\) | − | 7.38863e6i | − | 0.896417i | ||||||
\(203\) | 1.82527e7 | 2.18192 | ||||||||
\(204\) | − | 1.23932e6i | − | 0.145980i | ||||||
\(205\) | −6.24337e6 | − | 5.26981e6i | −0.724698 | − | 0.611693i | ||||
\(206\) | 1.25219e7i | 1.43241i | ||||||||
\(207\) | 4.25608e6 | − | 7.59070e6i | 0.479842 | − | 0.855797i | ||||
\(208\) | 2.41907e7i | 2.68818i | ||||||||
\(209\) | 3.89827e6 | 0.427005 | ||||||||
\(210\) | −2.32364e6 | − | 1.96131e6i | −0.250906 | − | 0.211781i | ||||
\(211\) | −1.45098e6 | −0.154459 | −0.0772295 | − | 0.997013i | \(-0.524607\pi\) | ||||
−0.0772295 | + | 0.997013i | \(0.524607\pi\) | |||||||
\(212\) | 1.21298e7 | 1.27305 | ||||||||
\(213\) | 272423.i | 0.0281907i | ||||||||
\(214\) | − | 1.16888e7i | − | 1.19270i | ||||||
\(215\) | 8.36032e6 | + | 7.05666e6i | 0.841216 | + | 0.710041i | ||||
\(216\) | 6.24491e6 | 0.619676 | ||||||||
\(217\) | 2.62232e6 | 0.256630 | ||||||||
\(218\) | 2.28094e7 | 2.20163 | ||||||||
\(219\) | 898945. | 0.0855856 | ||||||||
\(220\) | 1.56913e7 | − | 1.85901e7i | 1.47364 | − | 1.74588i | ||||
\(221\) | 7.36517e6i | 0.682348i | ||||||||
\(222\) | 5.36042e6 | 0.489936 | ||||||||
\(223\) | − | 9.39033e6i | − | 0.846771i | −0.905950 | − | 0.423386i | \(-0.860842\pi\) | ||
0.905950 | − | 0.423386i | \(-0.139158\pi\) | |||||||
\(224\) | 1.58747e7i | 1.41242i | ||||||||
\(225\) | 1.87664e6 | + | 1.10171e7i | 0.164753 | + | 0.967210i | ||||
\(226\) | − | 1.90735e7i | − | 1.65236i | ||||||
\(227\) | 2.01506e6 | 0.172270 | 0.0861350 | − | 0.996283i | \(-0.472548\pi\) | ||||
0.0861350 | + | 0.996283i | \(0.472548\pi\) | |||||||
\(228\) | −1.55549e6 | −0.131239 | ||||||||
\(229\) | 1.84118e7i | 1.53317i | 0.642142 | + | 0.766586i | \(0.278046\pi\) | ||||
−0.642142 | + | 0.766586i | \(0.721954\pi\) | |||||||
\(230\) | 7.71434e6 | + | 2.05735e7i | 0.634038 | + | 1.69093i | ||||
\(231\) | −2.26432e6 | −0.183697 | ||||||||
\(232\) | − | 4.68731e7i | − | 3.75370i | ||||||
\(233\) | − | 1.63387e7i | − | 1.29167i | −0.763478 | − | 0.645833i | \(-0.776510\pi\) | ||
0.763478 | − | 0.645833i | \(-0.223490\pi\) | |||||||
\(234\) | −3.29526e7 | −2.57183 | ||||||||
\(235\) | 1.34920e7 | − | 1.59846e7i | 1.03962 | − | 1.23168i | ||||
\(236\) | 4.83260e6 | 0.367659 | ||||||||
\(237\) | −2.03023e6 | −0.152510 | ||||||||
\(238\) | 1.51524e7i | 1.12396i | ||||||||
\(239\) | −4.95176e6 | −0.362715 | −0.181358 | − | 0.983417i | \(-0.558049\pi\) | ||||
−0.181358 | + | 0.983417i | \(0.558049\pi\) | |||||||
\(240\) | −2.26776e6 | + | 2.68671e6i | −0.164045 | + | 0.194351i | ||||
\(241\) | − | 2.54349e7i | − | 1.81710i | −0.417777 | − | 0.908550i | \(-0.637191\pi\) | ||
0.417777 | − | 0.908550i | \(-0.362809\pi\) | |||||||
\(242\) | − | 532823.i | − | 0.0375956i | ||||||
\(243\) | 5.76355e6i | 0.401672i | ||||||||
\(244\) | 3.31998e7i | 2.28542i | ||||||||
\(245\) | 8.46040e6 | + | 7.14114e6i | 0.575298 | + | 0.485589i | ||||
\(246\) | 3.50123e6 | 0.235188 | ||||||||
\(247\) | 9.24419e6 | 0.613449 | ||||||||
\(248\) | − | 6.73416e6i | − | 0.441498i | ||||||
\(249\) | − | 2.37655e6i | − | 0.153939i | ||||||
\(250\) | −2.43127e7 | − | 1.43211e7i | −1.55601 | − | 0.916551i | ||||
\(251\) | 2.34408e7i | 1.48235i | 0.671309 | + | 0.741177i | \(0.265732\pi\) | ||||
−0.671309 | + | 0.741177i | \(0.734268\pi\) | |||||||
\(252\) | −4.70059e7 | −2.93731 | ||||||||
\(253\) | 1.42717e7 | + | 8.00208e6i | 0.881280 | + | 0.494130i | ||||
\(254\) | 4.05210e7 | 2.47274 | ||||||||
\(255\) | −690450. | + | 818005.i | −0.0416401 | + | 0.0493327i | ||||
\(256\) | −2.94933e7 | −1.75794 | ||||||||
\(257\) | − | 9.81416e6i | − | 0.578168i | −0.957304 | − | 0.289084i | \(-0.906649\pi\) | ||
0.957304 | − | 0.289084i | \(-0.0933506\pi\) | |||||||
\(258\) | −4.68839e6 | −0.273001 | ||||||||
\(259\) | −4.54424e7 | −2.61554 | ||||||||
\(260\) | 3.72096e7 | − | 4.40838e7i | 2.11707 | − | 2.50818i | ||||
\(261\) | 2.87489e7 | 1.61696 | ||||||||
\(262\) | − | 7.09314e6i | − | 0.394398i | ||||||
\(263\) | 1.56511e7 | 0.860357 | 0.430178 | − | 0.902744i | \(-0.358451\pi\) | ||||
0.430178 | + | 0.902744i | \(0.358451\pi\) | |||||||
\(264\) | 5.81481e6i | 0.316027i | ||||||||
\(265\) | −8.00623e6 | − | 6.75778e6i | −0.430220 | − | 0.363134i | ||||
\(266\) | 1.90181e7 | 1.01047 | ||||||||
\(267\) | −1.87043e6 | −0.0982668 | ||||||||
\(268\) | 6.39375e7 | 3.32163 | ||||||||
\(269\) | −2.42990e7 | −1.24834 | −0.624169 | − | 0.781289i | \(-0.714562\pi\) | ||||
−0.624169 | + | 0.781289i | \(0.714562\pi\) | |||||||
\(270\) | −7.39005e6 | − | 6.23769e6i | −0.375453 | − | 0.316907i | ||||
\(271\) | 1.90357e7 | 0.956449 | 0.478224 | − | 0.878238i | \(-0.341281\pi\) | ||||
0.478224 | + | 0.878238i | \(0.341281\pi\) | |||||||
\(272\) | 1.75199e7 | 0.870614 | ||||||||
\(273\) | −5.36952e6 | −0.263905 | ||||||||
\(274\) | 2.39617e7i | 1.16484i | ||||||||
\(275\) | −2.07139e7 | + | 3.52836e6i | −0.996009 | + | 0.169658i | ||||
\(276\) | −5.69471e6 | − | 3.19301e6i | −0.270860 | − | 0.151870i | ||||
\(277\) | 1.57122e6i | 0.0739263i | 0.999317 | + | 0.0369632i | \(0.0117684\pi\) | ||||
−0.999317 | + | 0.0369632i | \(0.988232\pi\) | |||||||
\(278\) | 6.58354e7i | 3.06426i | ||||||||
\(279\) | 4.13029e6 | 0.190181 | ||||||||
\(280\) | 4.26977e7 | − | 5.05858e7i | 1.94505 | − | 2.30438i | ||||
\(281\) | − | 1.42810e7i | − | 0.643637i | −0.946801 | − | 0.321819i | \(-0.895706\pi\) | ||
0.946801 | − | 0.321819i | \(-0.104294\pi\) | |||||||
\(282\) | 8.96402e6i | 0.399719i | ||||||||
\(283\) | 8.38454e6 | 0.369930 | 0.184965 | − | 0.982745i | \(-0.440783\pi\) | ||||
0.184965 | + | 0.982745i | \(0.440783\pi\) | |||||||
\(284\) | −1.06329e7 | −0.464190 | ||||||||
\(285\) | 1.02670e6 | + | 866599.i | 0.0443514 | + | 0.0374355i | ||||
\(286\) | − | 6.19560e7i | − | 2.64841i | ||||||
\(287\) | −2.96813e7 | −1.25556 | ||||||||
\(288\) | 2.50035e7i | 1.04670i | ||||||||
\(289\) | −1.88034e7 | −0.779010 | ||||||||
\(290\) | −4.68189e7 | + | 5.54683e7i | −1.91967 | + | 2.27432i | ||||
\(291\) | − | 371005.i | − | 0.0150557i | ||||||
\(292\) | 3.50865e7i | 1.40926i | ||||||||
\(293\) | −2.43170e7 | −0.966733 | −0.483367 | − | 0.875418i | \(-0.660586\pi\) | ||||
−0.483367 | + | 0.875418i | \(0.660586\pi\) | |||||||
\(294\) | −4.74452e6 | −0.186703 | ||||||||
\(295\) | −3.18973e6 | − | 2.69234e6i | −0.124248 | − | 0.104873i | ||||
\(296\) | 1.16697e8i | 4.49969i | ||||||||
\(297\) | −7.20139e6 | −0.274882 | ||||||||
\(298\) | −5.04024e7 | −1.90460 | ||||||||
\(299\) | 3.38433e7 | + | 1.89758e7i | 1.26607 | + | 0.709883i | ||||
\(300\) | 8.26529e6 | − | 1.40789e6i | 0.306122 | − | 0.0521442i | ||||
\(301\) | 3.97453e7 | 1.45743 | ||||||||
\(302\) | − | 1.32070e7i | − | 0.479495i | ||||||
\(303\) | − | 1.89628e6i | − | 0.0681672i | ||||||
\(304\) | − | 2.19897e7i | − | 0.782705i | ||||||
\(305\) | 1.84963e7 | − | 2.19133e7i | 0.651907 | − | 0.772341i | ||||
\(306\) | 2.38657e7i | 0.832933i | ||||||||
\(307\) | − | 1.78458e6i | − | 0.0616765i | −0.999524 | − | 0.0308383i | \(-0.990182\pi\) | ||
0.999524 | − | 0.0308383i | \(-0.00981768\pi\) | |||||||
\(308\) | − | 8.83782e7i | − | 3.02478i | ||||||
\(309\) | 3.21373e6i | 0.108926i | ||||||||
\(310\) | −6.72637e6 | + | 7.96901e6i | −0.225785 | + | 0.267497i | ||||
\(311\) | 2.38789e7 | 0.793839 | 0.396920 | − | 0.917853i | \(-0.370079\pi\) | ||||
0.396920 | + | 0.917853i | \(0.370079\pi\) | |||||||
\(312\) | 1.37890e7i | 0.454013i | ||||||||
\(313\) | 1.08463e7 | 0.353711 | 0.176856 | − | 0.984237i | \(-0.443407\pi\) | ||||
0.176856 | + | 0.984237i | \(0.443407\pi\) | |||||||
\(314\) | 8.26762e7i | 2.67049i | ||||||||
\(315\) | 3.10260e7 | + | 2.61880e7i | 0.992645 | + | 0.837857i | ||||
\(316\) | − | 7.92413e7i | − | 2.51125i | ||||||
\(317\) | 2.02018e7i | 0.634178i | 0.948396 | + | 0.317089i | \(0.102705\pi\) | ||||
−0.948396 | + | 0.317089i | \(0.897295\pi\) | |||||||
\(318\) | 4.48982e6 | 0.139620 | ||||||||
\(319\) | 5.40523e7i | 1.66511i | ||||||||
\(320\) | −1.86734e6 | − | 1.57616e6i | −0.0569867 | − | 0.0481005i | ||||
\(321\) | − | 2.99992e6i | − | 0.0906974i | ||||||
\(322\) | 6.96257e7 | + | 3.90389e7i | 2.08546 | + | 1.16931i | ||||
\(323\) | − | 6.69504e6i | − | 0.198676i | ||||||
\(324\) | −7.25861e7 | −2.13412 | ||||||||
\(325\) | −4.91200e7 | + | 8.36701e6i | −1.43090 | + | 0.243736i | ||||
\(326\) | −395953. | −0.0114285 | ||||||||
\(327\) | 5.85401e6 | 0.167421 | ||||||||
\(328\) | 7.62219e7i | 2.16002i | ||||||||
\(329\) | − | 7.59915e7i | − | 2.13391i | ||||||
\(330\) | 5.80808e6 | − | 6.88108e6i | 0.161618 | − | 0.191476i | ||||
\(331\) | 1.56904e7 | 0.432664 | 0.216332 | − | 0.976320i | \(-0.430591\pi\) | ||||
0.216332 | + | 0.976320i | \(0.430591\pi\) | |||||||
\(332\) | 9.27585e7 | 2.53478 | ||||||||
\(333\) | −7.15739e7 | −1.93831 | ||||||||
\(334\) | −3.51868e6 | −0.0944365 | ||||||||
\(335\) | −4.22016e7 | − | 3.56210e7i | −1.12252 | − | 0.947483i | ||||
\(336\) | 1.27728e7i | 0.336719i | ||||||||
\(337\) | 6.50165e6 | 0.169877 | 0.0849384 | − | 0.996386i | \(-0.472931\pi\) | ||||
0.0849384 | + | 0.996386i | \(0.472931\pi\) | |||||||
\(338\) | − | 7.71864e7i | − | 1.99890i | ||||||
\(339\) | − | 4.89518e6i | − | 0.125652i | ||||||
\(340\) | −3.19274e7 | − | 2.69488e7i | −0.812318 | − | 0.685650i | ||||
\(341\) | 7.76557e6i | 0.195844i | ||||||||
\(342\) | 2.99544e7 | 0.748828 | ||||||||
\(343\) | −1.32049e7 | −0.327230 | ||||||||
\(344\) | − | 1.02067e8i | − | 2.50731i | ||||||
\(345\) | 1.97988e6 | + | 5.28017e6i | 0.0482148 | + | 0.128585i | ||||
\(346\) | 7.17465e6 | 0.173210 | ||||||||
\(347\) | 5.93954e7i | 1.42156i | 0.703416 | + | 0.710779i | \(0.251657\pi\) | ||||
−0.703416 | + | 0.710779i | \(0.748343\pi\) | |||||||
\(348\) | − | 2.15680e7i | − | 0.511768i | ||||||
\(349\) | 6.08567e6 | 0.143163 | 0.0715817 | − | 0.997435i | \(-0.477195\pi\) | ||||
0.0715817 | + | 0.997435i | \(0.477195\pi\) | |||||||
\(350\) | −1.01055e8 | + | 1.72134e7i | −2.35696 | + | 0.401480i | ||||
\(351\) | −1.70771e7 | −0.394904 | ||||||||
\(352\) | −4.70104e7 | −1.07787 | ||||||||
\(353\) | 4.52737e7i | 1.02925i | 0.857415 | + | 0.514626i | \(0.172069\pi\) | ||||
−0.857415 | + | 0.514626i | \(0.827931\pi\) | |||||||
\(354\) | 1.78878e6 | 0.0403224 | ||||||||
\(355\) | 7.01818e6 | + | 5.92381e6i | 0.156870 | + | 0.132408i | ||||
\(356\) | − | 7.30042e7i | − | 1.61807i | ||||||
\(357\) | 3.88883e6i | 0.0854702i | ||||||||
\(358\) | 8.96915e7i | 1.95480i | ||||||||
\(359\) | 7.47898e7i | 1.61644i | 0.588881 | + | 0.808219i | \(0.299568\pi\) | ||||
−0.588881 | + | 0.808219i | \(0.700432\pi\) | |||||||
\(360\) | 6.72510e7 | − | 7.96751e7i | 1.44142 | − | 1.70771i | ||||
\(361\) | 3.86428e7 | 0.821385 | ||||||||
\(362\) | −8.60676e7 | −1.81432 | ||||||||
\(363\) | − | 136748.i | − | 0.00285892i | ||||||
\(364\) | − | 2.09576e8i | − | 4.34549i | ||||||
\(365\) | 1.95474e7 | − | 2.31587e7i | 0.401986 | − | 0.476250i | ||||
\(366\) | 1.22888e7i | 0.250649i | ||||||||
\(367\) | −7.56972e7 | −1.53137 | −0.765687 | − | 0.643213i | \(-0.777601\pi\) | ||||
−0.765687 | + | 0.643213i | \(0.777601\pi\) | |||||||
\(368\) | 4.51388e7 | − | 8.05049e7i | 0.905746 | − | 1.61539i | ||||
\(369\) | −4.67494e7 | −0.930459 | ||||||||
\(370\) | 1.16562e8 | − | 1.38095e8i | 2.30118 | − | 2.72630i | ||||
\(371\) | −3.80620e7 | −0.745366 | ||||||||
\(372\) | − | 3.09863e6i | − | 0.0601924i | ||||||
\(373\) | 1.58831e7 | 0.306062 | 0.153031 | − | 0.988221i | \(-0.451097\pi\) | ||||
0.153031 | + | 0.988221i | \(0.451097\pi\) | |||||||
\(374\) | −4.48712e7 | −0.857734 | ||||||||
\(375\) | −6.23983e6 | − | 3.67550e6i | −0.118326 | − | 0.0696983i | ||||
\(376\) | −1.95147e8 | −3.67112 | ||||||||
\(377\) | 1.28177e8i | 2.39214i | ||||||||
\(378\) | −3.51326e7 | −0.650482 | ||||||||
\(379\) | 2.29476e7i | 0.421521i | 0.977538 | + | 0.210760i | \(0.0675940\pi\) | ||||
−0.977538 | + | 0.210760i | \(0.932406\pi\) | |||||||
\(380\) | −3.38240e7 | + | 4.00727e7i | −0.616417 | + | 0.730295i | ||||
\(381\) | 1.03997e7 | 0.188037 | ||||||||
\(382\) | 2.64686e7 | 0.474834 | ||||||||
\(383\) | −3.12689e7 | −0.556565 | −0.278282 | − | 0.960499i | \(-0.589765\pi\) | ||||
−0.278282 | + | 0.960499i | \(0.589765\pi\) | |||||||
\(384\) | −7.24832e6 | −0.128010 | ||||||||
\(385\) | −4.92374e7 | + | 5.83336e7i | −0.862805 | + | 1.02220i | ||||
\(386\) | −8.62593e7 | −1.49984 | ||||||||
\(387\) | 6.26009e7 | 1.08006 | ||||||||
\(388\) | 1.44806e7 | 0.247909 | ||||||||
\(389\) | − | 9.23294e7i | − | 1.56852i | −0.620430 | − | 0.784262i | \(-0.713042\pi\) | ||
0.620430 | − | 0.784262i | \(-0.286958\pi\) | |||||||
\(390\) | 1.37730e7 | − | 1.63175e7i | 0.232186 | − | 0.275081i | ||||
\(391\) | 1.37431e7 | − | 2.45107e7i | 0.229908 | − | 0.410040i | ||||
\(392\) | − | 1.03288e8i | − | 1.71472i | ||||||
\(393\) | − | 1.82045e6i | − | 0.0299916i | ||||||
\(394\) | 1.85206e8 | 3.02807 | ||||||||
\(395\) | −4.41470e7 | + | 5.23028e7i | −0.716324 | + | 0.848660i | ||||
\(396\) | − | 1.39200e8i | − | 2.24158i | ||||||
\(397\) | − | 3.93714e7i | − | 0.629230i | −0.949219 | − | 0.314615i | \(-0.898125\pi\) | ||
0.949219 | − | 0.314615i | \(-0.101875\pi\) | |||||||
\(398\) | 1.51693e8 | 2.40611 | ||||||||
\(399\) | 4.88096e6 | 0.0768399 | ||||||||
\(400\) | 1.99031e7 | + | 1.16845e8i | 0.310985 | + | 1.82570i | ||||
\(401\) | − | 3.14689e7i | − | 0.488032i | −0.969771 | − | 0.244016i | \(-0.921535\pi\) | ||
0.969771 | − | 0.244016i | \(-0.0784650\pi\) | |||||||
\(402\) | 2.36663e7 | 0.364294 | ||||||||
\(403\) | 1.84150e7i | 0.281356i | ||||||||
\(404\) | 7.40134e7 | 1.12245 | ||||||||
\(405\) | 4.79101e7 | + | 4.04393e7i | 0.721210 | + | 0.608749i | ||||
\(406\) | 2.63699e8i | 3.94031i | ||||||||
\(407\) | − | 1.34570e8i | − | 1.99602i | ||||||
\(408\) | 9.98657e6 | 0.147040 | ||||||||
\(409\) | 6.18938e7 | 0.904643 | 0.452321 | − | 0.891855i | \(-0.350596\pi\) | ||||
0.452321 | + | 0.891855i | \(0.350596\pi\) | |||||||
\(410\) | 7.61337e7 | − | 9.01988e7i | 1.10465 | − | 1.30873i | ||||
\(411\) | 6.14975e6i | 0.0885792i | ||||||||
\(412\) | −1.25434e8 | −1.79359 | ||||||||
\(413\) | −1.51641e7 | −0.215262 | ||||||||
\(414\) | 1.09664e8 | + | 6.14882e7i | 1.54548 | + | 0.866544i | ||||
\(415\) | −6.12248e7 | − | 5.16778e7i | −0.856610 | − | 0.723035i | ||||
\(416\) | −1.11479e8 | −1.54850 | ||||||||
\(417\) | 1.68966e7i | 0.233018i | ||||||||
\(418\) | 5.63188e7i | 0.771125i | ||||||||
\(419\) | − | 2.52204e7i | − | 0.342854i | −0.985197 | − | 0.171427i | \(-0.945162\pi\) | ||
0.985197 | − | 0.171427i | \(-0.0548378\pi\) | |||||||
\(420\) | 1.96468e7 | − | 2.32764e7i | 0.265182 | − | 0.314172i | ||||
\(421\) | 5.51391e7i | 0.738948i | 0.929241 | + | 0.369474i | \(0.120462\pi\) | ||||
−0.929241 | + | 0.369474i | \(0.879538\pi\) | |||||||
\(422\) | − | 2.09625e7i | − | 0.278936i | ||||||
\(423\) | − | 1.19690e8i | − | 1.58139i | ||||||
\(424\) | 9.77437e7i | 1.28230i | ||||||||
\(425\) | 6.05974e6 | + | 3.55748e7i | 0.0789382 | + | 0.463421i | ||||
\(426\) | −3.93574e6 | −0.0509093 | ||||||||
\(427\) | − | 1.04177e8i | − | 1.33810i | ||||||
\(428\) | 1.17089e8 | 1.49343 | ||||||||
\(429\) | − | 1.59009e7i | − | 0.201396i | ||||||
\(430\) | −1.01948e8 | + | 1.20783e8i | −1.28226 | + | 1.51914i | ||||
\(431\) | − | 3.63184e7i | − | 0.453623i | −0.973939 | − | 0.226812i | \(-0.927170\pi\) | ||
0.973939 | − | 0.226812i | \(-0.0728302\pi\) | |||||||
\(432\) | 4.06222e7i | 0.503862i | ||||||||
\(433\) | −1.41519e8 | −1.74322 | −0.871609 | − | 0.490203i | \(-0.836923\pi\) | ||||
−0.871609 | + | 0.490203i | \(0.836923\pi\) | |||||||
\(434\) | 3.78851e7i | 0.463446i | ||||||||
\(435\) | −1.20160e7 | + | 1.42359e7i | −0.145980 | + | 0.172948i | ||||
\(436\) | 2.28486e8i | 2.75677i | ||||||||
\(437\) | −3.07640e7 | − | 1.72493e7i | −0.368636 | − | 0.206693i | ||||
\(438\) | 1.29872e7i | 0.154558i | ||||||||
\(439\) | 2.37952e7 | 0.281252 | 0.140626 | − | 0.990063i | \(-0.455089\pi\) | ||||
0.140626 | + | 0.990063i | \(0.455089\pi\) | |||||||
\(440\) | 1.49801e8 | + | 1.26442e8i | 1.75856 | + | 1.48434i | ||||
\(441\) | 6.33503e7 | 0.738640 | ||||||||
\(442\) | −1.06406e8 | −1.23225 | ||||||||
\(443\) | 5.76395e7i | 0.662993i | 0.943456 | + | 0.331497i | \(0.107554\pi\) | ||||
−0.943456 | + | 0.331497i | \(0.892446\pi\) | |||||||
\(444\) | 5.36964e7i | 0.613474i | ||||||||
\(445\) | −4.06722e7 | + | 4.81860e7i | −0.461549 | + | 0.546816i | ||||
\(446\) | 1.35663e8 | 1.52918 | ||||||||
\(447\) | −1.29357e7 | −0.144833 | ||||||||
\(448\) | −8.87742e6 | −0.0987308 | ||||||||
\(449\) | 8.94417e7 | 0.988101 | 0.494050 | − | 0.869433i | \(-0.335516\pi\) | ||||
0.494050 | + | 0.869433i | \(0.335516\pi\) | |||||||
\(450\) | −1.59166e8 | + | 2.71120e7i | −1.74668 | + | 0.297525i | ||||
\(451\) | − | 8.78961e7i | − | 0.958165i | ||||||
\(452\) | 1.91063e8 | 2.06900 | ||||||||
\(453\) | − | 3.38957e6i | − | 0.0364628i | ||||||
\(454\) | 2.91118e7i | 0.311101i | ||||||||
\(455\) | −1.16759e8 | + | 1.38330e8i | −1.23953 | + | 1.46853i | ||||
\(456\) | − | 1.25344e7i | − | 0.132193i | ||||||
\(457\) | −4.30619e7 | −0.451175 | −0.225587 | − | 0.974223i | \(-0.572430\pi\) | ||||
−0.225587 | + | 0.974223i | \(0.572430\pi\) | |||||||
\(458\) | −2.65998e8 | −2.76874 | ||||||||
\(459\) | 1.23679e7i | 0.127897i | ||||||||
\(460\) | −2.06089e8 | + | 7.72761e7i | −2.11730 | + | 0.793911i | ||||
\(461\) | 3.20062e7 | 0.326686 | 0.163343 | − | 0.986569i | \(-0.447772\pi\) | ||||
0.163343 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(462\) | − | 3.27130e7i | − | 0.331737i | ||||||
\(463\) | 7.62354e7i | 0.768092i | 0.923314 | + | 0.384046i | \(0.125470\pi\) | ||||
−0.923314 | + | 0.384046i | \(0.874530\pi\) | |||||||
\(464\) | 3.04902e8 | 3.05216 | ||||||||
\(465\) | −1.72631e6 | + | 2.04524e6i | −0.0171696 | + | 0.0203416i | ||||
\(466\) | 2.36048e8 | 2.33261 | ||||||||
\(467\) | −1.14370e8 | −1.12296 | −0.561479 | − | 0.827491i | \(-0.689767\pi\) | ||||
−0.561479 | + | 0.827491i | \(0.689767\pi\) | |||||||
\(468\) | − | 3.30093e8i | − | 3.22032i | ||||||
\(469\) | −2.00629e8 | −1.94480 | ||||||||
\(470\) | 2.30931e8 | + | 1.94921e8i | 2.22428 | + | 1.87744i | ||||
\(471\) | 2.12187e7i | 0.203075i | ||||||||
\(472\) | 3.89417e7i | 0.370330i | ||||||||
\(473\) | 1.17699e8i | 1.11222i | ||||||||
\(474\) | − | 2.93310e7i | − | 0.275417i | ||||||
\(475\) | 4.46508e7 | − | 7.60572e6i | 0.416628 | − | 0.0709675i | ||||
\(476\) | −1.51784e8 | −1.40736 | ||||||||
\(477\) | −5.99495e7 | −0.552371 | ||||||||
\(478\) | − | 7.15388e7i | − | 0.655025i | ||||||
\(479\) | − | 4.61367e7i | − | 0.419798i | −0.977723 | − | 0.209899i | \(-0.932687\pi\) | ||
0.977723 | − | 0.209899i | \(-0.0673135\pi\) | |||||||
\(480\) | −1.23812e7 | − | 1.04506e7i | −0.111954 | − | 0.0944967i | ||||
\(481\) | − | 3.19114e8i | − | 2.86754i | ||||||
\(482\) | 3.67461e8 | 3.28149 | ||||||||
\(483\) | 1.78694e7 | + | 1.00193e7i | 0.158587 | + | 0.0889191i | ||||
\(484\) | 5.33740e6 | 0.0470753 | ||||||||
\(485\) | −9.55786e6 | − | 8.06746e6i | −0.0837790 | − | 0.0707150i | ||||
\(486\) | −8.32668e7 | −0.725376 | ||||||||
\(487\) | − | 1.13979e8i | − | 0.986824i | −0.869796 | − | 0.493412i | \(-0.835750\pi\) | ||
0.869796 | − | 0.493412i | \(-0.164250\pi\) | |||||||
\(488\) | −2.67528e8 | −2.30202 | ||||||||
\(489\) | −101621. | −0.000869072 | ||||||||
\(490\) | −1.03169e8 | + | 1.22229e8i | −0.876922 | + | 1.03893i | ||||
\(491\) | 1.62610e8 | 1.37373 | 0.686866 | − | 0.726784i | \(-0.258986\pi\) | ||||
0.686866 | + | 0.726784i | \(0.258986\pi\) | |||||||
\(492\) | 3.50725e7i | 0.294490i | ||||||||
\(493\) | 9.28315e7 | 0.774737 | ||||||||
\(494\) | 1.33552e8i | 1.10782i | ||||||||
\(495\) | −7.75513e7 | + | 9.18783e7i | −0.639401 | + | 0.757525i | ||||
\(496\) | 4.38047e7 | 0.358984 | ||||||||
\(497\) | 3.33648e7 | 0.271781 | ||||||||
\(498\) | 3.43343e7 | 0.277997 | ||||||||
\(499\) | 1.23715e8 | 0.995679 | 0.497839 | − | 0.867269i | \(-0.334127\pi\) | ||||
0.497839 | + | 0.867269i | \(0.334127\pi\) | |||||||
\(500\) | 1.43457e8 | − | 2.43545e8i | 1.14766 | − | 1.94836i | ||||
\(501\) | −903064. | −0.00718134 | ||||||||
\(502\) | −3.38653e8 | −2.67697 | ||||||||
\(503\) | 2.02011e8 | 1.58735 | 0.793673 | − | 0.608344i | \(-0.208166\pi\) | ||||
0.793673 | + | 0.608344i | \(0.208166\pi\) | |||||||
\(504\) | − | 3.78779e8i | − | 2.95866i | ||||||
\(505\) | −4.88521e7 | − | 4.12344e7i | −0.379323 | − | 0.320174i | ||||
\(506\) | −1.15607e8 | + | 2.06185e8i | −0.892346 | + | 1.59150i | ||||
\(507\) | − | 1.98098e7i | − | 0.152004i | ||||||
\(508\) | 4.05907e8i | 3.09624i | ||||||||
\(509\) | −2.49247e8 | −1.89007 | −0.945033 | − | 0.326976i | \(-0.893970\pi\) | ||||
−0.945033 | + | 0.326976i | \(0.893970\pi\) | |||||||
\(510\) | −1.18178e7 | − | 9.97502e6i | −0.0890896 | − | 0.0751975i | ||||
\(511\) | − | 1.10097e8i | − | 0.825115i | ||||||
\(512\) | − | 3.00983e8i | − | 2.24249i | ||||||
\(513\) | 1.55233e7 | 0.114982 | ||||||||
\(514\) | 1.41787e8 | 1.04411 | ||||||||
\(515\) | 8.27922e7 | + | 6.98821e7i | 0.606133 | + | 0.511616i | ||||
\(516\) | − | 4.69646e7i | − | 0.341839i | ||||||
\(517\) | 2.25036e8 | 1.62847 | ||||||||
\(518\) | − | 6.56512e8i | − | 4.72339i | ||||||
\(519\) | 1.84137e6 | 0.0131716 | ||||||||
\(520\) | 3.55233e8 | + | 2.99840e8i | 2.52640 | + | 2.13245i | ||||
\(521\) | 4.86877e6i | 0.0344276i | 0.999852 | + | 0.0172138i | \(0.00547959\pi\) | ||||
−0.999852 | + | 0.0172138i | \(0.994520\pi\) | |||||||
\(522\) | 4.15339e8i | 2.92006i | ||||||||
\(523\) | 2.56582e8 | 1.79358 | 0.896790 | − | 0.442457i | \(-0.145893\pi\) | ||||
0.896790 | + | 0.442457i | \(0.145893\pi\) | |||||||
\(524\) | 7.10534e7 | 0.493845 | ||||||||
\(525\) | −2.59355e7 | + | 4.41781e6i | −0.179233 | + | 0.0305301i | ||||
\(526\) | 2.26114e8i | 1.55371i | ||||||||
\(527\) | 1.33369e7 | 0.0911219 | ||||||||
\(528\) | −3.78244e7 | −0.256963 | ||||||||
\(529\) | −7.72199e7 | − | 1.26300e8i | −0.521630 | − | 0.853172i | ||||
\(530\) | 9.76306e7 | − | 1.15667e8i | 0.655781 | − | 0.776931i | ||||
\(531\) | −2.38843e7 | −0.159525 | ||||||||
\(532\) | 1.90508e8i | 1.26525i | ||||||||
\(533\) | − | 2.08433e8i | − | 1.37653i | ||||||
\(534\) | − | 2.70223e7i | − | 0.177459i | ||||||
\(535\) | −7.72842e7 | − | 6.52329e7i | −0.504695 | − | 0.425996i | ||||
\(536\) | 5.15217e8i | 3.34577i | ||||||||
\(537\) | 2.30192e7i | 0.148651i | ||||||||
\(538\) | − | 3.51052e8i | − | 2.25437i | ||||||
\(539\) | 1.19108e8i | 0.760634i | ||||||||
\(540\) | 6.24841e7 | − | 7.40276e7i | 0.396815 | − | 0.470124i | ||||
\(541\) | 9.49861e7 | 0.599886 | 0.299943 | − | 0.953957i | \(-0.403032\pi\) | ||||
0.299943 | + | 0.953957i | \(0.403032\pi\) | |||||||
\(542\) | 2.75012e8i | 1.72724i | ||||||||
\(543\) | −2.20891e7 | −0.137968 | ||||||||
\(544\) | 8.07375e7i | 0.501509i | ||||||||
\(545\) | 1.27295e8 | − | 1.50811e8i | 0.786359 | − | 0.931632i | ||||
\(546\) | − | 7.75742e7i | − | 0.476584i | ||||||
\(547\) | − | 9.47033e7i | − | 0.578633i | −0.957234 | − | 0.289316i | \(-0.906572\pi\) | ||
0.957234 | − | 0.289316i | \(-0.0934279\pi\) | |||||||
\(548\) | −2.40029e8 | −1.45855 | ||||||||
\(549\) | − | 1.64084e8i | − | 0.991629i | ||||||
\(550\) | −5.09747e7 | − | 2.99256e8i | −0.306385 | − | 1.79869i | ||||
\(551\) | − | 1.16515e8i | − | 0.696509i | ||||||
\(552\) | 2.57296e7 | − | 4.58887e7i | 0.152974 | − | 0.272828i | ||||
\(553\) | 2.48650e8i | 1.47032i | ||||||||
\(554\) | −2.26997e7 | −0.133503 | ||||||||
\(555\) | 2.99154e7 | − | 3.54420e7i | 0.174991 | − | 0.207319i | ||||
\(556\) | −6.59486e8 | −3.83691 | ||||||||
\(557\) | −1.75817e8 | −1.01741 | −0.508703 | − | 0.860942i | \(-0.669875\pi\) | ||||
−0.508703 | + | 0.860942i | \(0.669875\pi\) | |||||||
\(558\) | 5.96708e7i | 0.343447i | ||||||||
\(559\) | 2.79107e8i | 1.59785i | ||||||||
\(560\) | 3.29053e8 | + | 2.77742e8i | 1.87371 | + | 1.58153i | ||||
\(561\) | −1.15161e7 | −0.0652256 | ||||||||
\(562\) | 2.06320e8 | 1.16234 | ||||||||
\(563\) | 1.56046e7 | 0.0874433 | 0.0437217 | − | 0.999044i | \(-0.486079\pi\) | ||||
0.0437217 | + | 0.999044i | \(0.486079\pi\) | |||||||
\(564\) | −8.97943e7 | −0.500509 | ||||||||
\(565\) | −1.26110e8 | − | 1.06445e8i | −0.699204 | − | 0.590174i | ||||
\(566\) | 1.21133e8i | 0.668055i | ||||||||
\(567\) | 2.27767e8 | 1.24951 | ||||||||
\(568\) | − | 8.56811e7i | − | 0.467563i | ||||||
\(569\) | 3.44560e7i | 0.187037i | 0.995618 | + | 0.0935186i | \(0.0298115\pi\) | ||||
−0.995618 | + | 0.0935186i | \(0.970189\pi\) | |||||||
\(570\) | −1.25199e7 | + | 1.48328e7i | −0.0676045 | + | 0.0800939i | ||||
\(571\) | − | 2.36637e8i | − | 1.27108i | −0.772066 | − | 0.635542i | \(-0.780777\pi\) | ||
0.772066 | − | 0.635542i | \(-0.219223\pi\) | |||||||
\(572\) | 6.20626e8 | 3.31621 | ||||||||
\(573\) | 6.79314e6 | 0.0361083 | ||||||||
\(574\) | − | 4.28809e8i | − | 2.26740i | ||||||
\(575\) | 1.79080e8 | + | 6.38110e7i | 0.941985 | + | 0.335654i | ||||
\(576\) | −1.39824e7 | −0.0731667 | ||||||||
\(577\) | − | 1.63773e8i | − | 0.852542i | −0.904596 | − | 0.426271i | \(-0.859827\pi\) | ||
0.904596 | − | 0.426271i | \(-0.140173\pi\) | |||||||
\(578\) | − | 2.71655e8i | − | 1.40681i | ||||||
\(579\) | −2.21383e7 | −0.114054 | ||||||||
\(580\) | −5.55637e8 | − | 4.68994e8i | −2.84779 | − | 2.40372i | ||||
\(581\) | −2.91066e8 | −1.48410 | ||||||||
\(582\) | 5.35996e6 | 0.0271890 | ||||||||
\(583\) | − | 1.12714e8i | − | 0.568818i | ||||||
\(584\) | −2.82732e8 | −1.41950 | ||||||||
\(585\) | −1.83902e8 | + | 2.17876e8i | −0.918583 | + | 1.08828i | ||||
\(586\) | − | 3.51311e8i | − | 1.74582i | ||||||
\(587\) | 2.66853e8i | 1.31935i | 0.751553 | + | 0.659673i | \(0.229305\pi\) | ||||
−0.751553 | + | 0.659673i | \(0.770695\pi\) | |||||||
\(588\) | − | 4.75268e7i | − | 0.233780i | ||||||
\(589\) | − | 1.67394e7i | − | 0.0819209i | ||||||
\(590\) | 3.88967e7 | − | 4.60825e7i | 0.189390 | − | 0.224378i | ||||
\(591\) | 4.75328e7 | 0.230267 | ||||||||
\(592\) | −7.59093e8 | −3.65873 | ||||||||
\(593\) | − | 2.52270e8i | − | 1.20976i | −0.796315 | − | 0.604882i | \(-0.793220\pi\) | ||
0.796315 | − | 0.604882i | \(-0.206780\pi\) | |||||||
\(594\) | − | 1.04039e8i | − | 0.496408i | ||||||
\(595\) | 1.00184e8 | + | 8.45622e7i | 0.475608 | + | 0.401444i | ||||
\(596\) | − | 5.04891e8i | − | 2.38484i | ||||||
\(597\) | 3.89318e7 | 0.182971 | ||||||||
\(598\) | −2.74146e8 | + | 4.88939e8i | −1.28197 | + | 2.28639i | ||||
\(599\) | −1.04813e8 | −0.487680 | −0.243840 | − | 0.969815i | \(-0.578407\pi\) | ||||
−0.243840 | + | 0.969815i | \(0.578407\pi\) | |||||||
\(600\) | 1.13450e7 | + | 6.66028e7i | 0.0525231 | + | 0.308346i | ||||
\(601\) | −1.37629e8 | −0.633998 | −0.316999 | − | 0.948426i | \(-0.602675\pi\) | ||||
−0.316999 | + | 0.948426i | \(0.602675\pi\) | |||||||
\(602\) | 5.74206e8i | 2.63196i | ||||||||
\(603\) | −3.16000e8 | −1.44124 | ||||||||
\(604\) | 1.32297e8 | 0.600400 | ||||||||
\(605\) | −3.52292e6 | − | 2.97358e6i | −0.0159088 | − | 0.0134281i | ||||
\(606\) | 2.73959e7 | 0.123103 | ||||||||
\(607\) | − | 2.47318e7i | − | 0.110583i | −0.998470 | − | 0.0552917i | \(-0.982391\pi\) | ||
0.998470 | − | 0.0552917i | \(-0.0176089\pi\) | |||||||
\(608\) | 1.01335e8 | 0.450869 | ||||||||
\(609\) | 6.76780e7i | 0.299637i | ||||||||
\(610\) | 3.16585e8 | + | 2.67219e8i | 1.39476 | + | 1.17727i | ||||
\(611\) | 5.33641e8 | 2.33951 | ||||||||
\(612\) | −2.39067e8 | −1.04296 | ||||||||
\(613\) | −3.84237e7 | −0.166808 | −0.0834042 | − | 0.996516i | \(-0.526579\pi\) | ||||
−0.0834042 | + | 0.996516i | \(0.526579\pi\) | |||||||
\(614\) | 2.57820e7 | 0.111381 | ||||||||
\(615\) | 1.95396e7 | − | 2.31494e7i | 0.0840022 | − | 0.0995209i | ||||
\(616\) | 7.12163e8 | 3.04675 | ||||||||
\(617\) | −2.42571e8 | −1.03272 | −0.516360 | − | 0.856372i | \(-0.672713\pi\) | ||||
−0.516360 | + | 0.856372i | \(0.672713\pi\) | |||||||
\(618\) | −4.64292e7 | −0.196709 | ||||||||
\(619\) | 1.37558e8i | 0.579980i | 0.957030 | + | 0.289990i | \(0.0936519\pi\) | ||||
−0.957030 | + | 0.289990i | \(0.906348\pi\) | |||||||
\(620\) | −7.98272e7 | − | 6.73794e7i | −0.334947 | − | 0.282717i | ||||
\(621\) | 5.68312e7 | + | 3.18650e7i | 0.237308 | + | 0.133058i | ||||
\(622\) | 3.44981e8i | 1.43359i | ||||||||
\(623\) | 2.29079e8i | 0.947372i | ||||||||
\(624\) | −8.96953e7 | −0.369161 | ||||||||
\(625\) | −2.30373e8 | + | 8.08277e7i | −0.943606 | + | 0.331070i | ||||
\(626\) | 1.56698e8i | 0.638764i | ||||||||
\(627\) | 1.44542e7i | 0.0586395i | ||||||||
\(628\) | −8.28184e8 | −3.34386 | ||||||||
\(629\) | −2.31116e8 | −0.928704 | ||||||||
\(630\) | −3.78341e8 | + | 4.48237e8i | −1.51308 | + | 1.79261i | ||||
\(631\) | 4.40692e8i | 1.75407i | 0.480427 | + | 0.877035i | \(0.340482\pi\) | ||||
−0.480427 | + | 0.877035i | \(0.659518\pi\) | |||||||
\(632\) | 6.38536e8 | 2.52950 | ||||||||
\(633\) | − | 5.37999e6i | − | 0.0212115i | ||||||
\(634\) | −2.91858e8 | −1.14526 | ||||||||
\(635\) | 2.26139e8 | − | 2.67917e8i | 0.883191 | − | 1.04635i | ||||
\(636\) | 4.49755e7i | 0.174825i | ||||||||
\(637\) | 2.82448e8i | 1.09275i | ||||||||
\(638\) | −7.80901e8 | −3.00700 | ||||||||
\(639\) | 5.25511e7 | 0.201409 | ||||||||
\(640\) | −1.57614e8 | + | 1.86731e8i | −0.601248 | + | 0.712324i | ||||
\(641\) | 1.28432e8i | 0.487639i | 0.969821 | + | 0.243820i | \(0.0784005\pi\) | ||||
−0.969821 | + | 0.243820i | \(0.921600\pi\) | |||||||
\(642\) | 4.33403e7 | 0.163790 | ||||||||
\(643\) | 2.80441e8 | 1.05489 | 0.527447 | − | 0.849588i | \(-0.323149\pi\) | ||||
0.527447 | + | 0.849588i | \(0.323149\pi\) | |||||||
\(644\) | −3.91060e8 | + | 6.97455e8i | −1.46415 | + | 2.61131i | ||||
\(645\) | −2.61649e7 | + | 3.09987e7i | −0.0975081 | + | 0.115522i | ||||
\(646\) | 9.67241e7 | 0.358788 | ||||||||
\(647\) | − | 2.37356e8i | − | 0.876369i | −0.898885 | − | 0.438184i | \(-0.855622\pi\) | ||
0.898885 | − | 0.438184i | \(-0.144378\pi\) | |||||||
\(648\) | − | 5.84908e8i | − | 2.14962i | ||||||
\(649\) | − | 4.49061e7i | − | 0.164275i | ||||||
\(650\) | −1.20879e8 | − | 7.09644e8i | −0.440161 | − | 2.58405i | ||||
\(651\) | 9.72315e6i | 0.0352423i | ||||||||
\(652\) | − | 3.96633e6i | − | 0.0143102i | ||||||
\(653\) | − | 3.05149e8i | − | 1.09590i | −0.836510 | − | 0.547951i | \(-0.815408\pi\) | ||
0.836510 | − | 0.547951i | \(-0.184592\pi\) | |||||||
\(654\) | 8.45737e7i | 0.302344i | ||||||||
\(655\) | −4.68984e7 | − | 3.95854e7i | −0.166892 | − | 0.140867i | ||||
\(656\) | −4.95811e8 | −1.75633 | ||||||||
\(657\) | − | 1.73409e8i | − | 0.611470i | ||||||
\(658\) | 1.09786e9 | 3.85362 | ||||||||
\(659\) | 4.53455e8i | 1.58445i | 0.610232 | + | 0.792223i | \(0.291076\pi\) | ||||
−0.610232 | + | 0.792223i | \(0.708924\pi\) | |||||||
\(660\) | 6.89291e7 | + | 5.81807e7i | 0.239757 | + | 0.202370i | ||||
\(661\) | − | 1.68737e8i | − | 0.584258i | −0.956379 | − | 0.292129i | \(-0.905636\pi\) | ||
0.956379 | − | 0.292129i | \(-0.0943637\pi\) | |||||||
\(662\) | 2.26682e8i | 0.781345i | ||||||||
\(663\) | −2.73089e7 | −0.0937051 | ||||||||
\(664\) | 7.47460e8i | 2.55319i | ||||||||
\(665\) | 1.06136e8 | − | 1.25744e8i | 0.360909 | − | 0.427584i | ||||
\(666\) | − | 1.03404e9i | − | 3.50037i | ||||||
\(667\) | 2.39173e8 | − | 4.26565e8i | 0.806000 | − | 1.43750i | ||||
\(668\) | − | 3.52473e7i | − | 0.118249i | ||||||
\(669\) | 3.48178e7 | 0.116285 | ||||||||
\(670\) | 5.14621e8 | − | 6.09693e8i | 1.71105 | − | 2.02715i | ||||
\(671\) | 3.08503e8 | 1.02116 | ||||||||
\(672\) | −5.88610e7 | −0.193963 | ||||||||
\(673\) | 5.50540e8i | 1.80611i | 0.429525 | + | 0.903055i | \(0.358681\pi\) | ||||
−0.429525 | + | 0.903055i | \(0.641319\pi\) | |||||||
\(674\) | 9.39302e7i | 0.306779i | ||||||||
\(675\) | −8.24846e7 | + | 1.40503e7i | −0.268202 | + | 0.0456850i | ||||
\(676\) | 7.73191e8 | 2.50292 | ||||||||
\(677\) | −5.21033e8 | −1.67919 | −0.839593 | − | 0.543215i | \(-0.817207\pi\) | ||||
−0.839593 | + | 0.543215i | \(0.817207\pi\) | |||||||
\(678\) | 7.07214e7 | 0.226914 | ||||||||
\(679\) | −4.54385e7 | −0.145149 | ||||||||
\(680\) | 2.17157e8 | − | 2.57275e8i | 0.690632 | − | 0.818220i | ||||
\(681\) | 7.47150e6i | 0.0236574i | ||||||||
\(682\) | −1.12190e8 | −0.353673 | ||||||||
\(683\) | 4.43281e7i | 0.139129i | 0.997577 | + | 0.0695644i | \(0.0221609\pi\) | ||||
−0.997577 | + | 0.0695644i | \(0.977839\pi\) | |||||||
\(684\) | 3.00059e8i | 0.937645i | ||||||||
\(685\) | 1.58430e8 | + | 1.33725e8i | 0.492908 | + | 0.416047i | ||||
\(686\) | − | 1.90773e8i | − | 0.590942i | ||||||
\(687\) | −6.82682e7 | −0.210546 | ||||||||
\(688\) | 6.63927e8 | 2.03871 | ||||||||
\(689\) | − | 2.67286e8i | − | 0.817181i | ||||||
\(690\) | −7.62834e7 | + | 2.86035e7i | −0.232211 | + | 0.0870708i | ||||
\(691\) | 4.02116e8 | 1.21876 | 0.609378 | − | 0.792880i | \(-0.291419\pi\) | ||||
0.609378 | + | 0.792880i | \(0.291419\pi\) | |||||||
\(692\) | 7.18699e7i | 0.216885i | ||||||||
\(693\) | 4.36794e8i | 1.31243i | ||||||||
\(694\) | −8.58093e8 | −2.56718 | ||||||||
\(695\) | 4.35290e8 | + | 3.67414e8i | 1.29666 | + | 1.09446i | ||||
\(696\) | 1.73798e8 | 0.515486 | ||||||||
\(697\) | −1.50956e8 | −0.445813 | ||||||||
\(698\) | 8.79205e7i | 0.258538i | ||||||||
\(699\) | 6.05814e7 | 0.177381 | ||||||||
\(700\) | −1.72430e8 | − | 1.01228e9i | −0.502713 | − | 2.95126i | ||||
\(701\) | 8.41138e7i | 0.244182i | 0.992519 | + | 0.122091i | \(0.0389599\pi\) | ||||
−0.992519 | + | 0.122091i | \(0.961040\pi\) | |||||||
\(702\) | − | 2.46715e8i | − | 0.713155i | ||||||
\(703\) | 2.90078e8i | 0.834929i | ||||||||
\(704\) | − | 2.62890e7i | − | 0.0753453i | ||||||
\(705\) | 5.92683e7 | + | 5.00263e7i | 0.169143 | + | 0.142768i | ||||
\(706\) | −6.54075e8 | −1.85872 | ||||||||
\(707\) | −2.32245e8 | −0.657187 | ||||||||
\(708\) | 1.79185e7i | 0.0504896i | ||||||||
\(709\) | 7.87448e7i | 0.220945i | 0.993879 | + | 0.110472i | \(0.0352363\pi\) | ||||
−0.993879 | + | 0.110472i | \(0.964764\pi\) | |||||||
\(710\) | −8.55821e7 | + | 1.01393e8i | −0.239115 | + | 0.283290i | ||||
\(711\) | 3.91636e8i | 1.08962i | ||||||||
\(712\) | 5.88277e8 | 1.62983 | ||||||||
\(713\) | 3.43615e7 | − | 6.12836e7i | 0.0947989 | − | 0.169074i | ||||
\(714\) | −5.61825e7 | −0.154350 | ||||||||
\(715\) | −4.09641e8 | − | 3.45764e8i | −1.12069 | − | 0.945935i | ||||
\(716\) | −8.98457e8 | −2.44770 | ||||||||
\(717\) | − | 1.83603e7i | − | 0.0498108i | ||||||
\(718\) | −1.08050e9 | −2.91911 | ||||||||
\(719\) | 5.20406e8 | 1.40009 | 0.700045 | − | 0.714099i | \(-0.253163\pi\) | ||||
0.700045 | + | 0.714099i | \(0.253163\pi\) | |||||||
\(720\) | 5.18274e8 | + | 4.37458e8i | 1.38855 | + | 1.17203i | ||||
\(721\) | 3.93598e8 | 1.05014 | ||||||||
\(722\) | 5.58278e8i | 1.48333i | ||||||||
\(723\) | 9.43085e7 | 0.249538 | ||||||||
\(724\) | − | 8.62156e8i | − | 2.27180i | ||||||
\(725\) | 1.05459e8 | + | 6.19115e8i | 0.276738 | + | 1.62464i | ||||
\(726\) | 1.97562e6 | 0.00516291 | ||||||||
\(727\) | 5.88183e8 | 1.53077 | 0.765383 | − | 0.643575i | \(-0.222549\pi\) | ||||
0.765383 | + | 0.643575i | \(0.222549\pi\) | |||||||
\(728\) | 1.68879e9 | 4.37706 | ||||||||
\(729\) | 3.44269e8 | 0.888619 | ||||||||
\(730\) | 3.34577e8 | + | 2.82405e8i | 0.860056 | + | 0.725944i | ||||
\(731\) | 2.02141e8 | 0.517491 | ||||||||
\(732\) | −1.23099e8 | −0.313851 | ||||||||
\(733\) | −1.34273e8 | −0.340939 | −0.170469 | − | 0.985363i | \(-0.554528\pi\) | ||||
−0.170469 | + | 0.985363i | \(0.554528\pi\) | |||||||
\(734\) | − | 1.09361e9i | − | 2.76550i | ||||||
\(735\) | −2.64782e7 | + | 3.13698e7i | −0.0666847 | + | 0.0790042i | ||||
\(736\) | 3.70992e8 | + | 2.08014e8i | 0.930532 | + | 0.521746i | ||||
\(737\) | − | 5.94128e8i | − | 1.48415i | ||||||
\(738\) | − | 6.75396e8i | − | 1.68031i | ||||||
\(739\) | 2.24429e8 | 0.556090 | 0.278045 | − | 0.960568i | \(-0.410314\pi\) | ||||
0.278045 | + | 0.960568i | \(0.410314\pi\) | |||||||
\(740\) | 1.38333e9 | + | 1.16762e9i | 3.41374 | + | 2.88142i | ||||
\(741\) | 3.42760e7i | 0.0842433i | ||||||||
\(742\) | − | 5.49887e8i | − | 1.34605i | ||||||
\(743\) | −2.96463e8 | −0.722776 | −0.361388 | − | 0.932416i | \(-0.617697\pi\) | ||||
−0.361388 | + | 0.932416i | \(0.617697\pi\) | |||||||
\(744\) | 2.49692e7 | 0.0606297 | ||||||||
\(745\) | −2.81286e8 | + | 3.33251e8i | −0.680266 | + | 0.805939i | ||||
\(746\) | 2.29466e8i | 0.552715i | ||||||||
\(747\) | −4.58443e8 | −1.09982 | ||||||||
\(748\) | − | 4.49483e8i | − | 1.07401i | ||||||
\(749\) | −3.67413e8 | −0.874397 | ||||||||
\(750\) | 5.31004e7 | − | 9.01477e7i | 0.125868 | − | 0.213683i | ||||
\(751\) | 2.54254e8i | 0.600272i | 0.953896 | + | 0.300136i | \(0.0970321\pi\) | ||||
−0.953896 | + | 0.300136i | \(0.902968\pi\) | |||||||
\(752\) | − | 1.26940e9i | − | 2.98501i | ||||||
\(753\) | −8.69149e7 | −0.203568 | ||||||||
\(754\) | −1.85180e9 | −4.31995 | ||||||||
\(755\) | −8.73222e7 | − | 7.37057e7i | −0.202901 | − | 0.171262i | ||||
\(756\) | − | 3.51931e8i | − | 0.814501i | ||||||
\(757\) | −1.64432e8 | −0.379052 | −0.189526 | − | 0.981876i | \(-0.560695\pi\) | ||||
−0.189526 | + | 0.981876i | \(0.560695\pi\) | |||||||
\(758\) | −3.31527e8 | −0.761221 | ||||||||
\(759\) | −2.96704e7 | + | 5.29171e7i | −0.0678576 | + | 0.121024i | ||||
\(760\) | −3.22911e8 | − | 2.72558e8i | −0.735601 | − | 0.620896i | ||||
\(761\) | −5.23690e8 | −1.18828 | −0.594142 | − | 0.804360i | \(-0.702508\pi\) | ||||
−0.594142 | + | 0.804360i | \(0.702508\pi\) | |||||||
\(762\) | 1.50245e8i | 0.339575i | ||||||||
\(763\) | − | 7.16964e8i | − | 1.61408i | ||||||
\(764\) | 2.65141e8i | 0.594563i | ||||||||
\(765\) | 1.57795e8 | + | 1.33190e8i | 0.352460 | + | 0.297499i | ||||
\(766\) | − | 4.51746e8i | − | 1.00510i | ||||||
\(767\) | − | 1.06488e8i | − | 0.236002i | ||||||
\(768\) | − | 1.09356e8i | − | 0.241413i | ||||||
\(769\) | − | 5.01267e8i | − | 1.10228i | −0.834414 | − | 0.551138i | \(-0.814194\pi\) | ||
0.834414 | − | 0.551138i | \(-0.185806\pi\) | |||||||
\(770\) | −8.42754e8 | − | 7.11339e8i | −1.84599 | − | 1.55813i | ||||
\(771\) | 3.63893e7 | 0.0793983 | ||||||||
\(772\) | − | 8.64077e8i | − | 1.87802i | ||||||
\(773\) | −5.04958e8 | −1.09324 | −0.546622 | − | 0.837380i | \(-0.684086\pi\) | ||||
−0.546622 | + | 0.837380i | \(0.684086\pi\) | |||||||
\(774\) | 9.04403e8i | 1.95047i | ||||||||
\(775\) | 1.51510e7 | + | 8.89468e7i | 0.0325489 | + | 0.191084i | ||||
\(776\) | 1.16687e8i | 0.249710i | ||||||||
\(777\) | − | 1.68493e8i | − | 0.359185i | ||||||
\(778\) | 1.33390e9 | 2.83259 | ||||||||
\(779\) | 1.89469e8i | 0.400797i | ||||||||
\(780\) | 1.63456e8 | + | 1.37967e8i | 0.344442 | + | 0.290732i | ||||
\(781\) | 9.88042e7i | 0.207406i | ||||||||
\(782\) | 3.54110e8 | + | 1.98548e8i | 0.740488 | + | 0.415189i | ||||
\(783\) | 2.15241e8i | 0.448374i | ||||||||
\(784\) | 6.71875e8 | 1.39425 | ||||||||
\(785\) | 5.46638e8 | + | 4.61399e8i | 1.13003 | + | 0.953822i | ||||
\(786\) | 2.63002e7 | 0.0541617 | ||||||||
\(787\) | 2.32789e8 | 0.477572 | 0.238786 | − | 0.971072i | \(-0.423251\pi\) | ||||
0.238786 | + | 0.971072i | \(0.423251\pi\) | |||||||
\(788\) | 1.85524e9i | 3.79159i | ||||||||
\(789\) | 5.80319e7i | 0.118151i | ||||||||
\(790\) | −7.55626e8 | − | 6.37798e8i | −1.53259 | − | 1.29360i | ||||
\(791\) | −5.99533e8 | −1.21139 | ||||||||
\(792\) | 1.12169e9 | 2.25786 | ||||||||
\(793\) | 7.31571e8 | 1.46702 | ||||||||
\(794\) | 5.68804e8 | 1.13632 | ||||||||
\(795\) | 2.50568e7 | − | 2.96858e7i | 0.0498682 | − | 0.0590810i | ||||
\(796\) | 1.51954e9i | 3.01282i | ||||||||
\(797\) | −3.58693e7 | −0.0708513 | −0.0354257 | − | 0.999372i | \(-0.511279\pi\) | ||||
−0.0354257 | + | 0.999372i | \(0.511279\pi\) | |||||||
\(798\) | 7.05160e7i | 0.138765i | ||||||||
\(799\) | − | 3.86486e8i | − | 0.757692i | ||||||
\(800\) | −5.38457e8 | + | 9.17197e7i | −1.05167 | + | 0.179140i | ||||
\(801\) | 3.60810e8i | 0.702071i | ||||||||
\(802\) | 4.54636e8 | 0.881334 | ||||||||
\(803\) | 3.26035e8 | 0.629677 | ||||||||
\(804\) | 2.37070e8i | 0.456151i | ||||||||
\(805\) | 6.46684e8 | − | 2.42483e8i | 1.23967 | − | 0.464830i | ||||
\(806\) | −2.66043e8 | −0.508098 | ||||||||
\(807\) | − | 9.00970e7i | − | 0.171431i | ||||||
\(808\) | 5.96409e8i | 1.13060i | ||||||||
\(809\) | 7.27782e8 | 1.37453 | 0.687267 | − | 0.726405i | \(-0.258810\pi\) | ||||
0.687267 | + | 0.726405i | \(0.258810\pi\) | |||||||
\(810\) | −5.84232e8 | + | 6.92164e8i | −1.09933 | + | 1.30243i | ||||
\(811\) | −3.64238e8 | −0.682845 | −0.341423 | − | 0.939910i | \(-0.610909\pi\) | ||||
−0.341423 | + | 0.939910i | \(0.610909\pi\) | |||||||
\(812\) | −2.64153e9 | −4.93386 | ||||||||
\(813\) | 7.05814e7i | 0.131347i | ||||||||
\(814\) | 1.94415e9 | 3.60460 | ||||||||
\(815\) | −2.20973e6 | + | 2.61796e6i | −0.00408194 | + | 0.00483604i | ||||
\(816\) | 6.49611e7i | 0.119559i | ||||||||
\(817\) | − | 2.53712e8i | − | 0.465237i | ||||||
\(818\) | 8.94188e8i | 1.63369i | ||||||||
\(819\) | 1.03579e9i | 1.88548i | ||||||||
\(820\) | 9.03539e8 | + | 7.62646e8i | 1.63872 | + | 1.38319i | ||||
\(821\) | −5.66091e8 | −1.02296 | −0.511478 | − | 0.859296i | \(-0.670902\pi\) | ||||
−0.511478 | + | 0.859296i | \(0.670902\pi\) | |||||||
\(822\) | −8.88462e7 | −0.159964 | ||||||||
\(823\) | − | 2.92339e8i | − | 0.524430i | −0.965009 | − | 0.262215i | \(-0.915547\pi\) | ||
0.965009 | − | 0.262215i | \(-0.0844530\pi\) | |||||||
\(824\) | − | 1.01076e9i | − | 1.80663i | ||||||
\(825\) | −1.30826e7 | − | 7.68037e7i | −0.0232987 | − | 0.136779i | ||||
\(826\) | − | 2.19079e8i | − | 0.388740i | ||||||
\(827\) | −4.03764e8 | −0.713856 | −0.356928 | − | 0.934132i | \(-0.616176\pi\) | ||||
−0.356928 | + | 0.934132i | \(0.616176\pi\) | |||||||
\(828\) | −6.15939e8 | + | 1.09853e9i | −1.08504 | + | 1.93517i | ||||
\(829\) | 8.52671e7 | 0.149664 | 0.0748321 | − | 0.997196i | \(-0.476158\pi\) | ||||
0.0748321 | + | 0.997196i | \(0.476158\pi\) | |||||||
\(830\) | 7.46596e8 | − | 8.84523e8i | 1.30572 | − | 1.54695i | ||||
\(831\) | −5.82585e6 | −0.0101521 | ||||||||
\(832\) | − | 6.23406e7i | − | 0.108243i | ||||||
\(833\) | 2.04561e8 | 0.353906 | ||||||||
\(834\) | −2.44107e8 | −0.420806 | ||||||||
\(835\) | −1.96370e7 | + | 2.32648e7i | −0.0337300 | + | 0.0399613i | ||||
\(836\) | −5.64157e8 | −0.965564 | ||||||||
\(837\) | 3.09233e7i | 0.0527362i | ||||||||
\(838\) | 3.64362e8 | 0.619158 | ||||||||
\(839\) | 1.26265e8i | 0.213795i | 0.994270 | + | 0.106897i | \(0.0340916\pi\) | ||||
−0.994270 | + | 0.106897i | \(0.965908\pi\) | |||||||
\(840\) | 1.87564e8 | + | 1.58316e8i | 0.316455 | + | 0.267109i | ||||
\(841\) | 1.02074e9 | 1.71604 | ||||||||
\(842\) | −7.96603e8 | −1.33446 | ||||||||
\(843\) | 5.29518e7 | 0.0883890 | ||||||||
\(844\) | 2.09985e8 | 0.349270 | ||||||||
\(845\) | −5.10341e8 | − | 4.30761e8i | −0.845844 | − | 0.713948i | ||||
\(846\) | 1.72918e9 | 2.85581 | ||||||||
\(847\) | −1.67481e7 | −0.0275623 | ||||||||
\(848\) | −6.35808e8 | −1.04265 | ||||||||
\(849\) | 3.10885e7i | 0.0508016i | ||||||||
\(850\) | −5.13954e8 | + | 8.75460e7i | −0.836889 | + | 0.142554i | ||||
\(851\) | −5.95452e8 | + | 1.06199e9i | −0.966179 | + | 1.72318i | ||||
\(852\) | − | 3.94250e7i | − | 0.0637461i | ||||||
\(853\) | 4.78036e8i | 0.770218i | 0.922871 | + | 0.385109i | \(0.125836\pi\) | ||||
−0.922871 | + | 0.385109i | \(0.874164\pi\) | |||||||
\(854\) | 1.50506e9 | 2.41646 | ||||||||
\(855\) | 1.67169e8 | − | 1.98052e8i | 0.267459 | − | 0.316870i | ||||
\(856\) | 9.43520e8i | 1.50428i | ||||||||
\(857\) | 7.02998e8i | 1.11689i | 0.829540 | + | 0.558447i | \(0.188603\pi\) | ||||
−0.829540 | + | 0.558447i | \(0.811397\pi\) | |||||||
\(858\) | 2.29723e8 | 0.363699 | ||||||||
\(859\) | −8.88962e8 | −1.40250 | −0.701251 | − | 0.712914i | \(-0.747375\pi\) | ||||
−0.701251 | + | 0.712914i | \(0.747375\pi\) | |||||||
\(860\) | −1.20990e9 | − | 1.02124e9i | −1.90220 | − | 1.60558i | ||||
\(861\) | − | 1.10053e8i | − | 0.172423i | ||||||
\(862\) | 5.24697e8 | 0.819195 | ||||||||
\(863\) | − | 5.56119e8i | − | 0.865237i | −0.901577 | − | 0.432619i | \(-0.857590\pi\) | ||
0.901577 | − | 0.432619i | \(-0.142410\pi\) | |||||||
\(864\) | −1.87200e8 | −0.290245 | ||||||||
\(865\) | 4.00402e7 | − | 4.74374e7i | 0.0618655 | − | 0.0732946i | ||||
\(866\) | − | 2.04455e9i | − | 3.14806i | ||||||
\(867\) | − | 6.97200e7i | − | 0.106979i | ||||||
\(868\) | −3.79502e8 | −0.580303 | ||||||||
\(869\) | −7.36335e8 | −1.12206 | ||||||||
\(870\) | −2.05668e8 | − | 1.73597e8i | −0.312326 | − | 0.263624i | ||||
\(871\) | − | 1.40889e9i | − | 2.13218i | ||||||
\(872\) | −1.84117e9 | −2.77680 | ||||||||
\(873\) | −7.15679e7 | −0.107566 | ||||||||
\(874\) | 2.49202e8 | − | 4.44452e8i | 0.373265 | − | 0.665718i | ||||
\(875\) | −4.50153e8 | + | 7.64217e8i | −0.671948 | + | 1.14076i | ||||
\(876\) | −1.30095e8 | −0.193530 | ||||||||
\(877\) | − | 8.31734e8i | − | 1.23306i | −0.787330 | − | 0.616532i | \(-0.788537\pi\) | ||
0.787330 | − | 0.616532i | \(-0.211463\pi\) | |||||||
\(878\) | 3.43772e8i | 0.507910i | ||||||||
\(879\) | − | 9.01634e7i | − | 0.132759i | ||||||
\(880\) | −8.22487e8 | + | 9.74435e8i | −1.20693 | + | 1.42990i | ||||
\(881\) | − | 3.75024e8i | − | 0.548443i | −0.961667 | − | 0.274221i | \(-0.911580\pi\) | ||
0.961667 | − | 0.274221i | \(-0.0884201\pi\) | |||||||
\(882\) | 9.15231e8i | 1.33390i | ||||||||
\(883\) | − | 6.76061e8i | − | 0.981982i | −0.871165 | − | 0.490991i | \(-0.836635\pi\) | ||
0.871165 | − | 0.490991i | \(-0.163365\pi\) | |||||||
\(884\) | − | 1.06589e9i | − | 1.54296i | ||||||
\(885\) | 9.98278e6 | − | 1.18270e7i | 0.0144020 | − | 0.0170626i | ||||
\(886\) | −8.32726e8 | −1.19729 | ||||||||
\(887\) | 6.52558e8i | 0.935079i | 0.883972 | + | 0.467539i | \(0.154859\pi\) | ||||
−0.883972 | + | 0.467539i | \(0.845141\pi\) | |||||||
\(888\) | −4.32692e8 | −0.617931 | ||||||||
\(889\) | − | 1.27369e9i | − | 1.81283i | ||||||
\(890\) | −6.96150e8 | − | 5.87597e8i | −0.987491 | − | 0.833507i | ||||
\(891\) | 6.74493e8i | 0.953553i | ||||||||
\(892\) | 1.35897e9i | 1.91476i | ||||||||
\(893\) | −4.85087e8 | −0.681185 | ||||||||
\(894\) | − | 1.86884e8i | − | 0.261553i | ||||||
\(895\) | 5.93022e8 | + | 5.00550e8i | 0.827183 | + | 0.698197i | ||||
\(896\) | 8.87730e8i | 1.23412i | ||||||||
\(897\) | −7.03592e7 | + | 1.25485e8i | −0.0974863 | + | 0.173867i | ||||
\(898\) | 1.29218e9i | 1.78440i | ||||||||
\(899\) | 2.32104e8 | 0.319451 | ||||||||
\(900\) | −2.71586e8 | − | 1.59440e9i | −0.372546 | − | 2.18710i | ||||
\(901\) | −1.93580e8 | −0.264658 | ||||||||
\(902\) | 1.26985e9 | 1.73034 | ||||||||
\(903\) | 1.47369e8i | 0.200145i | ||||||||
\(904\) | 1.53961e9i | 2.08403i | ||||||||
\(905\) | −4.80325e8 | + | 5.69061e8i | −0.648022 | + | 0.767739i | ||||
\(906\) | 4.89696e7 | 0.0658478 | ||||||||
\(907\) | 9.61845e8 | 1.28909 | 0.644545 | − | 0.764566i | \(-0.277047\pi\) | ||||
0.644545 | + | 0.764566i | \(0.277047\pi\) | |||||||
\(908\) | −2.91619e8 | −0.389545 | ||||||||
\(909\) | −3.65798e8 | −0.487023 | ||||||||
\(910\) | −1.99847e9 | − | 1.68684e9i | −2.65200 | − | 2.23846i | ||||
\(911\) | 3.13110e8i | 0.414134i | 0.978327 | + | 0.207067i | \(0.0663919\pi\) | ||||
−0.978327 | + | 0.207067i | \(0.933608\pi\) | |||||||
\(912\) | 8.15342e7 | 0.107487 | ||||||||
\(913\) | − | 8.61942e8i | − | 1.13257i | ||||||
\(914\) | − | 6.22122e8i | − | 0.814773i | ||||||
\(915\) | 8.12512e7 | + | 6.85813e7i | 0.106064 | + | 0.0895246i | ||||
\(916\) | − | 2.66456e9i | − | 3.46688i | ||||||
\(917\) | −2.22957e8 | −0.289144 | ||||||||
\(918\) | −1.78681e8 | −0.230968 | ||||||||
\(919\) | 2.11882e8i | 0.272990i | 0.990641 | + | 0.136495i | \(0.0435838\pi\) | ||||
−0.990641 | + | 0.136495i | \(0.956416\pi\) | |||||||
\(920\) | −6.22700e8 | − | 1.66069e9i | −0.799679 | − | 2.13268i | ||||
\(921\) | 6.61692e6 | 0.00846988 | ||||||||
\(922\) | 4.62398e8i | 0.589960i | ||||||||
\(923\) | 2.34300e8i | 0.297967i | ||||||||
\(924\) | 3.27692e8 | 0.415385 | ||||||||
\(925\) | −2.62553e8 | − | 1.54136e9i | −0.331735 | − | 1.94751i | ||||
\(926\) | −1.10138e9 | −1.38709 | ||||||||
\(927\) | 6.19936e8 | 0.778230 | ||||||||
\(928\) | 1.40509e9i | 1.75817i | ||||||||
\(929\) | 4.27927e8 | 0.533732 | 0.266866 | − | 0.963734i | \(-0.414012\pi\) | ||||
0.266866 | + | 0.963734i | \(0.414012\pi\) | |||||||
\(930\) | −2.95478e7 | − | 2.49403e7i | −0.0367347 | − | 0.0310065i | ||||
\(931\) | − | 2.56749e8i | − | 0.318171i | ||||||
\(932\) | 2.36454e9i | 2.92078i | ||||||||
\(933\) | 8.85390e7i | 0.109016i | ||||||||
\(934\) | − | 1.65233e9i | − | 2.02794i | ||||||
\(935\) | −2.50417e8 | + | 2.96679e8i | −0.306358 | + | 0.362955i | ||||
\(936\) | 2.65993e9 | 3.24372 | ||||||||
\(937\) | 1.94631e8 | 0.236588 | 0.118294 | − | 0.992979i | \(-0.462257\pi\) | ||||
0.118294 | + | 0.992979i | \(0.462257\pi\) | |||||||
\(938\) | − | 2.89851e9i | − | 3.51209i | ||||||
\(939\) | 4.02163e7i | 0.0485742i | ||||||||
\(940\) | −1.95257e9 | + | 2.31329e9i | −2.35083 | + | 2.78513i | ||||
\(941\) | − | 6.86546e7i | − | 0.0823949i | −0.999151 | − | 0.0411975i | \(-0.986883\pi\) | ||
0.999151 | − | 0.0411975i | \(-0.0131173\pi\) | |||||||
\(942\) | −3.06550e8 | −0.366732 | ||||||||
\(943\) | −3.88927e8 | + | 6.93650e8i | −0.463802 | + | 0.827190i | ||||
\(944\) | −2.53310e8 | −0.301118 | ||||||||
\(945\) | −1.96068e8 | + | 2.32290e8i | −0.232333 | + | 0.275255i | ||||
\(946\) | −1.70042e9 | −2.00855 | ||||||||
\(947\) | − | 4.61667e8i | − | 0.543600i | −0.962354 | − | 0.271800i | \(-0.912381\pi\) | ||
0.962354 | − | 0.271800i | \(-0.0876189\pi\) | |||||||
\(948\) | 2.93814e8 | 0.344864 | ||||||||
\(949\) | 7.73146e8 | 0.904613 | ||||||||
\(950\) | 1.09881e8 | + | 6.45076e8i | 0.128160 | + | 0.752384i | ||||
\(951\) | −7.49049e7 | −0.0870901 | ||||||||
\(952\) | − | 1.22310e9i | − | 1.41759i | ||||||
\(953\) | 1.53760e9 | 1.77650 | 0.888248 | − | 0.459365i | \(-0.151923\pi\) | ||||
0.888248 | + | 0.459365i | \(0.151923\pi\) | |||||||
\(954\) | − | 8.66099e8i | − | 0.997522i | ||||||
\(955\) | 1.47716e8 | − | 1.75005e8i | 0.169597 | − | 0.200928i | ||||
\(956\) | 7.16618e8 | 0.820189 | ||||||||
\(957\) | −2.00417e8 | −0.228665 | ||||||||
\(958\) | 6.66544e8 | 0.758110 | ||||||||
\(959\) | 7.53184e8 | 0.853975 | ||||||||
\(960\) | 5.84414e6 | − | 6.92379e6i | 0.00660551 | − | 0.00782583i | ||||
\(961\) | −8.54158e8 | −0.962427 | ||||||||
\(962\) | 4.61028e9 | 5.17848 | ||||||||
\(963\) | −5.78693e8 | −0.647991 | ||||||||
\(964\) | 3.68093e9i | 4.10891i | ||||||||
\(965\) | −4.81395e8 | + | 5.70329e8i | −0.535698 | + | 0.634664i | ||||
\(966\) | −1.44750e8 | + | 2.58161e8i | −0.160578 | + | 0.286391i | ||||
\(967\) | − | 1.67835e9i | − | 1.85610i | −0.372452 | − | 0.928051i | \(-0.621483\pi\) | ||
0.372452 | − | 0.928051i | \(-0.378517\pi\) | |||||||
\(968\) | 4.30094e7i | 0.0474174i | ||||||||
\(969\) | 2.48241e7 | 0.0272837 | ||||||||
\(970\) | 1.16552e8 | − | 1.38084e8i | 0.127704 | − | 0.151296i | ||||
\(971\) | 2.64977e8i | 0.289435i | 0.989473 | + | 0.144717i | \(0.0462273\pi\) | ||||
−0.989473 | + | 0.144717i | \(0.953773\pi\) | |||||||
\(972\) | − | 8.34100e8i | − | 0.908279i | ||||||
\(973\) | 2.06939e9 | 2.24649 | ||||||||
\(974\) | 1.64668e9 | 1.78210 | ||||||||
\(975\) | −3.10235e7 | − | 1.82129e8i | −0.0334717 | − | 0.196501i | ||||
\(976\) | − | 1.74023e9i | − | 1.87179i | ||||||
\(977\) | −2.69731e8 | −0.289233 | −0.144616 | − | 0.989488i | \(-0.546195\pi\) | ||||
−0.144616 | + | 0.989488i | \(0.546195\pi\) | |||||||
\(978\) | − | 1.46813e6i | − | 0.00156945i | ||||||
\(979\) | −6.78379e8 | −0.722976 | ||||||||
\(980\) | −1.22439e9 | − | 1.03346e9i | −1.30089 | − | 1.09804i | ||||
\(981\) | − | 1.12925e9i | − | 1.19615i | ||||||
\(982\) | 2.34924e9i | 2.48081i | ||||||||
\(983\) | 5.21470e8 | 0.548995 | 0.274498 | − | 0.961588i | \(-0.411488\pi\) | ||||
0.274498 | + | 0.961588i | \(0.411488\pi\) | |||||||
\(984\) | −2.82618e8 | −0.296630 | ||||||||
\(985\) | 1.03359e9 | − | 1.22454e9i | 1.08154 | − | 1.28134i | ||||
\(986\) | 1.34115e9i | 1.39909i | ||||||||
\(987\) | 2.81764e8 | 0.293045 | ||||||||
\(988\) | −1.33782e9 | −1.38716 | ||||||||
\(989\) | 5.20801e8 | − | 9.28847e8i | 0.538373 | − | 0.960186i | ||||
\(990\) | −1.32738e9 | − | 1.12039e9i | −1.36801 | − | 1.15469i | ||||
\(991\) | −7.80432e7 | −0.0801889 | −0.0400944 | − | 0.999196i | \(-0.512766\pi\) | ||||
−0.0400944 | + | 0.999196i | \(0.512766\pi\) | |||||||
\(992\) | 2.01866e8i | 0.206789i | ||||||||
\(993\) | 5.81776e7i | 0.0594166i | ||||||||
\(994\) | 4.82025e8i | 0.490807i | ||||||||
\(995\) | 8.46567e8 | − | 1.00296e9i | 0.859394 | − | 1.01816i | ||||
\(996\) | 3.43934e8i | 0.348094i | ||||||||
\(997\) | − | 5.05761e8i | − | 0.510340i | −0.966896 | − | 0.255170i | \(-0.917869\pi\) | ||
0.966896 | − | 0.255170i | \(-0.0821315\pi\) | |||||||
\(998\) | 1.78732e9i | 1.79809i | ||||||||
\(999\) | − | 5.35870e8i | − | 0.537481i |
(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 | 115.7.c.c.114.10 | yes | 68 | |
5.4 | even | 2 | inner | 115.7.c.c.114.59 | yes | 68 | |
23.22 | odd | 2 | inner | 115.7.c.c.114.60 | yes | 68 | |
115.114 | odd | 2 | inner | 115.7.c.c.114.9 | ✓ | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.7.c.c.114.9 | ✓ | 68 | 115.114 | odd | 2 | inner | |
115.7.c.c.114.10 | yes | 68 | 1.1 | even | 1 | trivial | |
115.7.c.c.114.59 | yes | 68 | 5.4 | even | 2 | inner | |
115.7.c.c.114.60 | yes | 68 | 23.22 | odd | 2 | inner |