Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,8,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.a (trivial) |
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: | yes |
Analytic conductor: | \(170.562223914\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 367021x^{4} - 17702143x^{3} + 34815194576x^{2} + 1422988371620x - 933871993059968 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-264.243\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −262.243 | −0.938227 | −0.469114 | − | 0.883138i | \(-0.655427\pi\) | ||||
−0.469114 | + | 0.883138i | \(0.655427\pi\) | |||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −2097.94 | −0.663427 | ||||||||
\(11\) | 8089.34 | 1.83248 | 0.916239 | − | 0.400632i | \(-0.131209\pi\) | ||||
0.916239 | + | 0.400632i | \(0.131209\pi\) | |||||||
\(12\) | −1728.00 | −0.288675 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | 2744.00 | 0.267261 | ||||||||
\(15\) | 7080.55 | 0.541686 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 36358.9 | 1.79490 | 0.897448 | − | 0.441120i | \(-0.145419\pi\) | ||||
0.897448 | + | 0.441120i | \(0.145419\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | 7942.87 | 0.265668 | 0.132834 | − | 0.991138i | \(-0.457592\pi\) | ||||
0.132834 | + | 0.991138i | \(0.457592\pi\) | |||||||
\(20\) | −16783.5 | −0.469114 | ||||||||
\(21\) | −9261.00 | −0.218218 | ||||||||
\(22\) | 64714.7 | 1.29576 | ||||||||
\(23\) | 80499.5 | 1.37958 | 0.689788 | − | 0.724012i | \(-0.257704\pi\) | ||||
0.689788 | + | 0.724012i | \(0.257704\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | −9353.86 | −0.119729 | ||||||||
\(26\) | −17576.0 | −0.196116 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 21952.0 | 0.188982 | ||||||||
\(29\) | −98927.0 | −0.753220 | −0.376610 | − | 0.926372i | \(-0.622910\pi\) | ||||
−0.376610 | + | 0.926372i | \(0.622910\pi\) | |||||||
\(30\) | 56644.4 | 0.383030 | ||||||||
\(31\) | −315959. | −1.90487 | −0.952434 | − | 0.304745i | \(-0.901429\pi\) | ||||
−0.952434 | + | 0.304745i | \(0.901429\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | −218412. | −1.05798 | ||||||||
\(34\) | 290871. | 1.26918 | ||||||||
\(35\) | −89949.2 | −0.354617 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | −533705. | −1.73219 | −0.866094 | − | 0.499881i | \(-0.833377\pi\) | ||||
−0.866094 | + | 0.499881i | \(0.833377\pi\) | |||||||
\(38\) | 63543.0 | 0.187856 | ||||||||
\(39\) | 59319.0 | 0.160128 | ||||||||
\(40\) | −134268. | −0.331713 | ||||||||
\(41\) | 293184. | 0.664350 | 0.332175 | − | 0.943218i | \(-0.392217\pi\) | ||||
0.332175 | + | 0.943218i | \(0.392217\pi\) | |||||||
\(42\) | −74088.0 | −0.154303 | ||||||||
\(43\) | 438998. | 0.842021 | 0.421010 | − | 0.907056i | \(-0.361676\pi\) | ||||
0.421010 | + | 0.907056i | \(0.361676\pi\) | |||||||
\(44\) | 517718. | 0.916239 | ||||||||
\(45\) | −191175. | −0.312742 | ||||||||
\(46\) | 643996. | 0.975507 | ||||||||
\(47\) | −410797. | −0.577145 | −0.288572 | − | 0.957458i | \(-0.593181\pi\) | ||||
−0.288572 | + | 0.957458i | \(0.593181\pi\) | |||||||
\(48\) | −110592. | −0.144338 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | −74830.9 | −0.0846615 | ||||||||
\(51\) | −981690. | −1.03628 | ||||||||
\(52\) | −140608. | −0.138675 | ||||||||
\(53\) | 1.31693e6 | 1.21506 | 0.607529 | − | 0.794298i | \(-0.292161\pi\) | ||||
0.607529 | + | 0.794298i | \(0.292161\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | −2.12137e6 | −1.71928 | ||||||||
\(56\) | 175616. | 0.133631 | ||||||||
\(57\) | −214457. | −0.153384 | ||||||||
\(58\) | −791416. | −0.532607 | ||||||||
\(59\) | 1.45055e6 | 0.919497 | 0.459748 | − | 0.888049i | \(-0.347940\pi\) | ||||
0.459748 | + | 0.888049i | \(0.347940\pi\) | |||||||
\(60\) | 453155. | 0.270843 | ||||||||
\(61\) | −1.08338e6 | −0.611119 | −0.305559 | − | 0.952173i | \(-0.598843\pi\) | ||||
−0.305559 | + | 0.952173i | \(0.598843\pi\) | |||||||
\(62\) | −2.52767e6 | −1.34694 | ||||||||
\(63\) | 250047. | 0.125988 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 576147. | 0.260217 | ||||||||
\(66\) | −1.74730e6 | −0.748106 | ||||||||
\(67\) | 258422. | 0.104970 | 0.0524852 | − | 0.998622i | \(-0.483286\pi\) | ||||
0.0524852 | + | 0.998622i | \(0.483286\pi\) | |||||||
\(68\) | 2.32697e6 | 0.897448 | ||||||||
\(69\) | −2.17349e6 | −0.796498 | ||||||||
\(70\) | −719593. | −0.250752 | ||||||||
\(71\) | 2.75251e6 | 0.912694 | 0.456347 | − | 0.889802i | \(-0.349158\pi\) | ||||
0.456347 | + | 0.889802i | \(0.349158\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | 574512. | 0.172850 | 0.0864250 | − | 0.996258i | \(-0.472456\pi\) | ||||
0.0864250 | + | 0.996258i | \(0.472456\pi\) | |||||||
\(74\) | −4.26964e6 | −1.22484 | ||||||||
\(75\) | 252554. | 0.0691258 | ||||||||
\(76\) | 508344. | 0.132834 | ||||||||
\(77\) | 2.77464e6 | 0.692612 | ||||||||
\(78\) | 474552. | 0.113228 | ||||||||
\(79\) | −2.14531e6 | −0.489547 | −0.244774 | − | 0.969580i | \(-0.578714\pi\) | ||||
−0.244774 | + | 0.969580i | \(0.578714\pi\) | |||||||
\(80\) | −1.07415e6 | −0.234557 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 2.34547e6 | 0.469767 | ||||||||
\(83\) | 5.48945e6 | 1.05379 | 0.526897 | − | 0.849929i | \(-0.323355\pi\) | ||||
0.526897 | + | 0.849929i | \(0.323355\pi\) | |||||||
\(84\) | −592704. | −0.109109 | ||||||||
\(85\) | −9.53485e6 | −1.68402 | ||||||||
\(86\) | 3.51198e6 | 0.595398 | ||||||||
\(87\) | 2.67103e6 | 0.434872 | ||||||||
\(88\) | 4.14174e6 | 0.647879 | ||||||||
\(89\) | −8.91294e6 | −1.34016 | −0.670079 | − | 0.742290i | \(-0.733740\pi\) | ||||
−0.670079 | + | 0.742290i | \(0.733740\pi\) | |||||||
\(90\) | −1.52940e6 | −0.221142 | ||||||||
\(91\) | −753571. | −0.104828 | ||||||||
\(92\) | 5.15196e6 | 0.689788 | ||||||||
\(93\) | 8.53089e6 | 1.09978 | ||||||||
\(94\) | −3.28637e6 | −0.408103 | ||||||||
\(95\) | −2.08296e6 | −0.249257 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | −1.12731e7 | −1.25413 | −0.627064 | − | 0.778967i | \(-0.715744\pi\) | ||||
−0.627064 | + | 0.778967i | \(0.715744\pi\) | |||||||
\(98\) | 941192. | 0.101015 | ||||||||
\(99\) | 5.89713e6 | 0.610826 | ||||||||
\(100\) | −598647. | −0.0598647 | ||||||||
\(101\) | 9.54170e6 | 0.921512 | 0.460756 | − | 0.887527i | \(-0.347578\pi\) | ||||
0.460756 | + | 0.887527i | \(0.347578\pi\) | |||||||
\(102\) | −7.85352e6 | −0.732763 | ||||||||
\(103\) | 1.57024e7 | 1.41591 | 0.707955 | − | 0.706257i | \(-0.249618\pi\) | ||||
0.707955 | + | 0.706257i | \(0.249618\pi\) | |||||||
\(104\) | −1.12486e6 | −0.0980581 | ||||||||
\(105\) | 2.42863e6 | 0.204738 | ||||||||
\(106\) | 1.05354e7 | 0.859175 | ||||||||
\(107\) | 1.39745e7 | 1.10279 | 0.551395 | − | 0.834244i | \(-0.314096\pi\) | ||||
0.551395 | + | 0.834244i | \(0.314096\pi\) | |||||||
\(108\) | −1.25971e6 | −0.0962250 | ||||||||
\(109\) | 2.91571e6 | 0.215651 | 0.107825 | − | 0.994170i | \(-0.465611\pi\) | ||||
0.107825 | + | 0.994170i | \(0.465611\pi\) | |||||||
\(110\) | −1.69710e7 | −1.21572 | ||||||||
\(111\) | 1.44100e7 | 1.00008 | ||||||||
\(112\) | 1.40493e6 | 0.0944911 | ||||||||
\(113\) | −462016. | −0.0301219 | −0.0150610 | − | 0.999887i | \(-0.504794\pi\) | ||||
−0.0150610 | + | 0.999887i | \(0.504794\pi\) | |||||||
\(114\) | −1.71566e6 | −0.108459 | ||||||||
\(115\) | −2.11104e7 | −1.29436 | ||||||||
\(116\) | −6.33133e6 | −0.376610 | ||||||||
\(117\) | −1.60161e6 | −0.0924500 | ||||||||
\(118\) | 1.16044e7 | 0.650182 | ||||||||
\(119\) | 1.24711e7 | 0.678407 | ||||||||
\(120\) | 3.62524e6 | 0.191515 | ||||||||
\(121\) | 4.59503e7 | 2.35798 | ||||||||
\(122\) | −8.66702e6 | −0.432126 | ||||||||
\(123\) | −7.91598e6 | −0.383563 | ||||||||
\(124\) | −2.02214e7 | −0.952434 | ||||||||
\(125\) | 2.29407e7 | 1.05056 | ||||||||
\(126\) | 2.00038e6 | 0.0890871 | ||||||||
\(127\) | 4.31989e7 | 1.87137 | 0.935685 | − | 0.352836i | \(-0.114783\pi\) | ||||
0.935685 | + | 0.352836i | \(0.114783\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −1.18529e7 | −0.486141 | ||||||||
\(130\) | 4.60917e6 | 0.184002 | ||||||||
\(131\) | −3.79145e7 | −1.47352 | −0.736760 | − | 0.676154i | \(-0.763645\pi\) | ||||
−0.736760 | + | 0.676154i | \(0.763645\pi\) | |||||||
\(132\) | −1.39784e7 | −0.528991 | ||||||||
\(133\) | 2.72440e6 | 0.100413 | ||||||||
\(134\) | 2.06737e6 | 0.0742253 | ||||||||
\(135\) | 5.16172e6 | 0.180562 | ||||||||
\(136\) | 1.86157e7 | 0.634592 | ||||||||
\(137\) | 1.99944e7 | 0.664333 | 0.332166 | − | 0.943221i | \(-0.392220\pi\) | ||||
0.332166 | + | 0.943221i | \(0.392220\pi\) | |||||||
\(138\) | −1.73879e7 | −0.563209 | ||||||||
\(139\) | 5.72515e7 | 1.80815 | 0.904076 | − | 0.427371i | \(-0.140560\pi\) | ||||
0.904076 | + | 0.427371i | \(0.140560\pi\) | |||||||
\(140\) | −5.75675e6 | −0.177308 | ||||||||
\(141\) | 1.10915e7 | 0.333215 | ||||||||
\(142\) | 2.20201e7 | 0.645372 | ||||||||
\(143\) | −1.77723e7 | −0.508238 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | 2.59429e7 | 0.706692 | ||||||||
\(146\) | 4.59610e6 | 0.122223 | ||||||||
\(147\) | −3.17652e6 | −0.0824786 | ||||||||
\(148\) | −3.41571e7 | −0.866094 | ||||||||
\(149\) | −7.54723e7 | −1.86911 | −0.934557 | − | 0.355813i | \(-0.884204\pi\) | ||||
−0.934557 | + | 0.355813i | \(0.884204\pi\) | |||||||
\(150\) | 2.02043e6 | 0.0488793 | ||||||||
\(151\) | −1.79894e7 | −0.425203 | −0.212602 | − | 0.977139i | \(-0.568194\pi\) | ||||
−0.212602 | + | 0.977139i | \(0.568194\pi\) | |||||||
\(152\) | 4.06675e6 | 0.0939279 | ||||||||
\(153\) | 2.65056e7 | 0.598299 | ||||||||
\(154\) | 2.21972e7 | 0.489750 | ||||||||
\(155\) | 8.28579e7 | 1.78720 | ||||||||
\(156\) | 3.79642e6 | 0.0800641 | ||||||||
\(157\) | −2.15622e7 | −0.444677 | −0.222338 | − | 0.974970i | \(-0.571369\pi\) | ||||
−0.222338 | + | 0.974970i | \(0.571369\pi\) | |||||||
\(158\) | −1.71625e7 | −0.346162 | ||||||||
\(159\) | −3.55571e7 | −0.701514 | ||||||||
\(160\) | −8.59316e6 | −0.165857 | ||||||||
\(161\) | 2.76113e7 | 0.521431 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | −3.58850e7 | −0.649017 | −0.324509 | − | 0.945883i | \(-0.605199\pi\) | ||||
−0.324509 | + | 0.945883i | \(0.605199\pi\) | |||||||
\(164\) | 1.87638e7 | 0.332175 | ||||||||
\(165\) | 5.72770e7 | 0.992627 | ||||||||
\(166\) | 4.39156e7 | 0.745145 | ||||||||
\(167\) | −6.65864e7 | −1.10631 | −0.553156 | − | 0.833077i | \(-0.686577\pi\) | ||||
−0.553156 | + | 0.833077i | \(0.686577\pi\) | |||||||
\(168\) | −4.74163e6 | −0.0771517 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | −7.62788e7 | −1.19078 | ||||||||
\(171\) | 5.79035e6 | 0.0885561 | ||||||||
\(172\) | 2.80959e7 | 0.421010 | ||||||||
\(173\) | −1.04765e8 | −1.53835 | −0.769173 | − | 0.639040i | \(-0.779332\pi\) | ||||
−0.769173 | + | 0.639040i | \(0.779332\pi\) | |||||||
\(174\) | 2.13682e7 | 0.307501 | ||||||||
\(175\) | −3.20837e6 | −0.0452535 | ||||||||
\(176\) | 3.31339e7 | 0.458120 | ||||||||
\(177\) | −3.91648e7 | −0.530872 | ||||||||
\(178\) | −7.13035e7 | −0.947635 | ||||||||
\(179\) | 9.04976e7 | 1.17937 | 0.589687 | − | 0.807632i | \(-0.299251\pi\) | ||||
0.589687 | + | 0.807632i | \(0.299251\pi\) | |||||||
\(180\) | −1.22352e7 | −0.156371 | ||||||||
\(181\) | −365955. | −0.00458726 | −0.00229363 | − | 0.999997i | \(-0.500730\pi\) | ||||
−0.00229363 | + | 0.999997i | \(0.500730\pi\) | |||||||
\(182\) | −6.02857e6 | −0.0741249 | ||||||||
\(183\) | 2.92512e7 | 0.352830 | ||||||||
\(184\) | 4.12157e7 | 0.487754 | ||||||||
\(185\) | 1.39960e8 | 1.62519 | ||||||||
\(186\) | 6.82471e7 | 0.777659 | ||||||||
\(187\) | 2.94119e8 | 3.28911 | ||||||||
\(188\) | −2.62910e7 | −0.288572 | ||||||||
\(189\) | −6.75127e6 | −0.0727393 | ||||||||
\(190\) | −1.66637e7 | −0.176252 | ||||||||
\(191\) | 4.38236e7 | 0.455084 | 0.227542 | − | 0.973768i | \(-0.426931\pi\) | ||||
0.227542 | + | 0.973768i | \(0.426931\pi\) | |||||||
\(192\) | −7.07789e6 | −0.0721688 | ||||||||
\(193\) | 1.53764e8 | 1.53958 | 0.769791 | − | 0.638295i | \(-0.220360\pi\) | ||||
0.769791 | + | 0.638295i | \(0.220360\pi\) | |||||||
\(194\) | −9.01848e7 | −0.886803 | ||||||||
\(195\) | −1.55560e7 | −0.150237 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | −9.46327e7 | −0.881880 | −0.440940 | − | 0.897537i | \(-0.645355\pi\) | ||||
−0.440940 | + | 0.897537i | \(0.645355\pi\) | |||||||
\(198\) | 4.71770e7 | 0.431919 | ||||||||
\(199\) | −9.12893e7 | −0.821172 | −0.410586 | − | 0.911822i | \(-0.634676\pi\) | ||||
−0.410586 | + | 0.911822i | \(0.634676\pi\) | |||||||
\(200\) | −4.78918e6 | −0.0423307 | ||||||||
\(201\) | −6.97738e6 | −0.0606047 | ||||||||
\(202\) | 7.63336e7 | 0.651608 | ||||||||
\(203\) | −3.39320e7 | −0.284690 | ||||||||
\(204\) | −6.28282e7 | −0.518142 | ||||||||
\(205\) | −7.68854e7 | −0.623312 | ||||||||
\(206\) | 1.25619e8 | 1.00120 | ||||||||
\(207\) | 5.86841e7 | 0.459859 | ||||||||
\(208\) | −8.99891e6 | −0.0693375 | ||||||||
\(209\) | 6.42526e7 | 0.486831 | ||||||||
\(210\) | 1.94290e7 | 0.144772 | ||||||||
\(211\) | 2.32329e8 | 1.70261 | 0.851306 | − | 0.524670i | \(-0.175811\pi\) | ||||
0.851306 | + | 0.524670i | \(0.175811\pi\) | |||||||
\(212\) | 8.42834e7 | 0.607529 | ||||||||
\(213\) | −7.43179e7 | −0.526944 | ||||||||
\(214\) | 1.11796e8 | 0.779790 | ||||||||
\(215\) | −1.15124e8 | −0.790007 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | −1.08374e8 | −0.719972 | ||||||||
\(218\) | 2.33256e7 | 0.152488 | ||||||||
\(219\) | −1.55118e7 | −0.0997950 | ||||||||
\(220\) | −1.35768e8 | −0.859641 | ||||||||
\(221\) | −7.98805e7 | −0.497815 | ||||||||
\(222\) | 1.15280e8 | 0.707163 | ||||||||
\(223\) | 3.59293e7 | 0.216961 | 0.108480 | − | 0.994099i | \(-0.465401\pi\) | ||||
0.108480 | + | 0.994099i | \(0.465401\pi\) | |||||||
\(224\) | 1.12394e7 | 0.0668153 | ||||||||
\(225\) | −6.81897e6 | −0.0399098 | ||||||||
\(226\) | −3.69613e6 | −0.0212994 | ||||||||
\(227\) | −1.12121e8 | −0.636202 | −0.318101 | − | 0.948057i | \(-0.603045\pi\) | ||||
−0.318101 | + | 0.948057i | \(0.603045\pi\) | |||||||
\(228\) | −1.37253e7 | −0.0766918 | ||||||||
\(229\) | 1.33685e7 | 0.0735628 | 0.0367814 | − | 0.999323i | \(-0.488289\pi\) | ||||
0.0367814 | + | 0.999323i | \(0.488289\pi\) | |||||||
\(230\) | −1.68883e8 | −0.915248 | ||||||||
\(231\) | −7.49154e7 | −0.399879 | ||||||||
\(232\) | −5.06506e7 | −0.266304 | ||||||||
\(233\) | −2.46179e7 | −0.127499 | −0.0637493 | − | 0.997966i | \(-0.520306\pi\) | ||||
−0.0637493 | + | 0.997966i | \(0.520306\pi\) | |||||||
\(234\) | −1.28129e7 | −0.0653720 | ||||||||
\(235\) | 1.07728e8 | 0.541493 | ||||||||
\(236\) | 9.28351e7 | 0.459748 | ||||||||
\(237\) | 5.79233e7 | 0.282640 | ||||||||
\(238\) | 9.97688e7 | 0.479706 | ||||||||
\(239\) | 3.25624e8 | 1.54285 | 0.771425 | − | 0.636320i | \(-0.219544\pi\) | ||||
0.771425 | + | 0.636320i | \(0.219544\pi\) | |||||||
\(240\) | 2.90019e7 | 0.135421 | ||||||||
\(241\) | −3.13928e8 | −1.44467 | −0.722337 | − | 0.691541i | \(-0.756932\pi\) | ||||
−0.722337 | + | 0.691541i | \(0.756932\pi\) | |||||||
\(242\) | 3.67602e8 | 1.66734 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −6.93362e7 | −0.305559 | ||||||||
\(245\) | −3.08526e7 | −0.134032 | ||||||||
\(246\) | −6.33278e7 | −0.271220 | ||||||||
\(247\) | −1.74505e7 | −0.0736831 | ||||||||
\(248\) | −1.61771e8 | −0.673472 | ||||||||
\(249\) | −1.48215e8 | −0.608408 | ||||||||
\(250\) | 1.83525e8 | 0.742859 | ||||||||
\(251\) | 1.69788e8 | 0.677717 | 0.338858 | − | 0.940837i | \(-0.389959\pi\) | ||||
0.338858 | + | 0.940837i | \(0.389959\pi\) | |||||||
\(252\) | 1.60030e7 | 0.0629941 | ||||||||
\(253\) | 6.51188e8 | 2.52804 | ||||||||
\(254\) | 3.45591e8 | 1.32326 | ||||||||
\(255\) | 2.57441e8 | 0.972270 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −2.46021e7 | −0.0904080 | −0.0452040 | − | 0.998978i | \(-0.514394\pi\) | ||||
−0.0452040 | + | 0.998978i | \(0.514394\pi\) | |||||||
\(258\) | −9.48235e7 | −0.343753 | ||||||||
\(259\) | −1.83061e8 | −0.654706 | ||||||||
\(260\) | 3.68734e7 | 0.130109 | ||||||||
\(261\) | −7.21178e7 | −0.251073 | ||||||||
\(262\) | −3.03316e8 | −1.04194 | ||||||||
\(263\) | 3.74298e8 | 1.26874 | 0.634369 | − | 0.773030i | \(-0.281260\pi\) | ||||
0.634369 | + | 0.773030i | \(0.281260\pi\) | |||||||
\(264\) | −1.11827e8 | −0.374053 | ||||||||
\(265\) | −3.45355e8 | −1.14000 | ||||||||
\(266\) | 2.17952e7 | 0.0710028 | ||||||||
\(267\) | 2.40649e8 | 0.773741 | ||||||||
\(268\) | 1.65390e7 | 0.0524852 | ||||||||
\(269\) | 5.22987e7 | 0.163817 | 0.0819083 | − | 0.996640i | \(-0.473899\pi\) | ||||
0.0819083 | + | 0.996640i | \(0.473899\pi\) | |||||||
\(270\) | 4.12938e7 | 0.127677 | ||||||||
\(271\) | 1.27694e8 | 0.389743 | 0.194871 | − | 0.980829i | \(-0.437571\pi\) | ||||
0.194871 | + | 0.980829i | \(0.437571\pi\) | |||||||
\(272\) | 1.48926e8 | 0.448724 | ||||||||
\(273\) | 2.03464e7 | 0.0605228 | ||||||||
\(274\) | 1.59955e8 | 0.469754 | ||||||||
\(275\) | −7.56666e7 | −0.219402 | ||||||||
\(276\) | −1.39103e8 | −0.398249 | ||||||||
\(277\) | 3.96501e8 | 1.12089 | 0.560447 | − | 0.828190i | \(-0.310629\pi\) | ||||
0.560447 | + | 0.828190i | \(0.310629\pi\) | |||||||
\(278\) | 4.58012e8 | 1.27856 | ||||||||
\(279\) | −2.30334e8 | −0.634956 | ||||||||
\(280\) | −4.60540e7 | −0.125376 | ||||||||
\(281\) | −9.05068e7 | −0.243337 | −0.121669 | − | 0.992571i | \(-0.538825\pi\) | ||||
−0.121669 | + | 0.992571i | \(0.538825\pi\) | |||||||
\(282\) | 8.87321e7 | 0.235618 | ||||||||
\(283\) | 6.65988e8 | 1.74668 | 0.873341 | − | 0.487109i | \(-0.161949\pi\) | ||||
0.873341 | + | 0.487109i | \(0.161949\pi\) | |||||||
\(284\) | 1.76161e8 | 0.456347 | ||||||||
\(285\) | 5.62399e7 | 0.143909 | ||||||||
\(286\) | −1.42178e8 | −0.359379 | ||||||||
\(287\) | 1.00562e8 | 0.251101 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | 9.11630e8 | 2.22165 | ||||||||
\(290\) | 2.07543e8 | 0.499707 | ||||||||
\(291\) | 3.04374e8 | 0.724072 | ||||||||
\(292\) | 3.67688e7 | 0.0864250 | ||||||||
\(293\) | −8.54906e7 | −0.198555 | −0.0992776 | − | 0.995060i | \(-0.531653\pi\) | ||||
−0.0992776 | + | 0.995060i | \(0.531653\pi\) | |||||||
\(294\) | −2.54122e7 | −0.0583212 | ||||||||
\(295\) | −3.80396e8 | −0.862697 | ||||||||
\(296\) | −2.73257e8 | −0.612421 | ||||||||
\(297\) | −1.59223e8 | −0.352661 | ||||||||
\(298\) | −6.03779e8 | −1.32166 | ||||||||
\(299\) | −1.76857e8 | −0.382625 | ||||||||
\(300\) | 1.61635e7 | 0.0345629 | ||||||||
\(301\) | 1.50576e8 | 0.318254 | ||||||||
\(302\) | −1.43915e8 | −0.300664 | ||||||||
\(303\) | −2.57626e8 | −0.532035 | ||||||||
\(304\) | 3.25340e7 | 0.0664171 | ||||||||
\(305\) | 2.84108e8 | 0.573368 | ||||||||
\(306\) | 2.12045e8 | 0.423061 | ||||||||
\(307\) | 6.78551e7 | 0.133844 | 0.0669219 | − | 0.997758i | \(-0.478682\pi\) | ||||
0.0669219 | + | 0.997758i | \(0.478682\pi\) | |||||||
\(308\) | 1.77577e8 | 0.346306 | ||||||||
\(309\) | −4.23965e8 | −0.817476 | ||||||||
\(310\) | 6.62863e8 | 1.26374 | ||||||||
\(311\) | −1.14569e7 | −0.0215976 | −0.0107988 | − | 0.999942i | \(-0.503437\pi\) | ||||
−0.0107988 | + | 0.999942i | \(0.503437\pi\) | |||||||
\(312\) | 3.03713e7 | 0.0566139 | ||||||||
\(313\) | −2.31158e8 | −0.426092 | −0.213046 | − | 0.977042i | \(-0.568338\pi\) | ||||
−0.213046 | + | 0.977042i | \(0.568338\pi\) | |||||||
\(314\) | −1.72498e8 | −0.314434 | ||||||||
\(315\) | −6.55730e7 | −0.118206 | ||||||||
\(316\) | −1.37300e8 | −0.244774 | ||||||||
\(317\) | 8.98774e8 | 1.58468 | 0.792342 | − | 0.610077i | \(-0.208861\pi\) | ||||
0.792342 | + | 0.610077i | \(0.208861\pi\) | |||||||
\(318\) | −2.84457e8 | −0.496045 | ||||||||
\(319\) | −8.00254e8 | −1.38026 | ||||||||
\(320\) | −6.87453e7 | −0.117278 | ||||||||
\(321\) | −3.77311e8 | −0.636696 | ||||||||
\(322\) | 2.20890e8 | 0.368707 | ||||||||
\(323\) | 2.88794e8 | 0.476847 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | 2.05504e7 | 0.0332070 | ||||||||
\(326\) | −2.87080e8 | −0.458924 | ||||||||
\(327\) | −7.87241e7 | −0.124506 | ||||||||
\(328\) | 1.50110e8 | 0.234883 | ||||||||
\(329\) | −1.40903e8 | −0.218140 | ||||||||
\(330\) | 4.58216e8 | 0.701894 | ||||||||
\(331\) | −9.20059e8 | −1.39450 | −0.697249 | − | 0.716829i | \(-0.745593\pi\) | ||||
−0.697249 | + | 0.716829i | \(0.745593\pi\) | |||||||
\(332\) | 3.51325e8 | 0.526897 | ||||||||
\(333\) | −3.89071e8 | −0.577396 | ||||||||
\(334\) | −5.32691e8 | −0.782281 | ||||||||
\(335\) | −6.77691e7 | −0.0984861 | ||||||||
\(336\) | −3.79331e7 | −0.0545545 | ||||||||
\(337\) | −1.14771e9 | −1.63353 | −0.816765 | − | 0.576970i | \(-0.804235\pi\) | ||||
−0.816765 | + | 0.576970i | \(0.804235\pi\) | |||||||
\(338\) | 3.86145e7 | 0.0543928 | ||||||||
\(339\) | 1.24744e7 | 0.0173909 | ||||||||
\(340\) | −6.10230e8 | −0.842010 | ||||||||
\(341\) | −2.55590e9 | −3.49063 | ||||||||
\(342\) | 4.63228e7 | 0.0626186 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | 2.24767e8 | 0.297699 | ||||||||
\(345\) | 5.69980e8 | 0.747297 | ||||||||
\(346\) | −8.38119e8 | −1.08778 | ||||||||
\(347\) | 1.20200e9 | 1.54437 | 0.772187 | − | 0.635396i | \(-0.219163\pi\) | ||||
0.772187 | + | 0.635396i | \(0.219163\pi\) | |||||||
\(348\) | 1.70946e8 | 0.217436 | ||||||||
\(349\) | −7.46699e7 | −0.0940279 | −0.0470140 | − | 0.998894i | \(-0.514971\pi\) | ||||
−0.0470140 | + | 0.998894i | \(0.514971\pi\) | |||||||
\(350\) | −2.56670e7 | −0.0319990 | ||||||||
\(351\) | 4.32436e7 | 0.0533761 | ||||||||
\(352\) | 2.65072e8 | 0.323939 | ||||||||
\(353\) | 1.09945e9 | 1.33035 | 0.665173 | − | 0.746689i | \(-0.268358\pi\) | ||||
0.665173 | + | 0.746689i | \(0.268358\pi\) | |||||||
\(354\) | −3.13319e8 | −0.375383 | ||||||||
\(355\) | −7.21826e8 | −0.856315 | ||||||||
\(356\) | −5.70428e8 | −0.670079 | ||||||||
\(357\) | −3.36720e8 | −0.391678 | ||||||||
\(358\) | 7.23981e8 | 0.833943 | ||||||||
\(359\) | −5.37432e8 | −0.613046 | −0.306523 | − | 0.951863i | \(-0.599166\pi\) | ||||
−0.306523 | + | 0.951863i | \(0.599166\pi\) | |||||||
\(360\) | −9.78815e7 | −0.110571 | ||||||||
\(361\) | −8.30783e8 | −0.929420 | ||||||||
\(362\) | −2.92764e6 | −0.00324368 | ||||||||
\(363\) | −1.24066e9 | −1.36138 | ||||||||
\(364\) | −4.82285e7 | −0.0524142 | ||||||||
\(365\) | −1.50662e8 | −0.162173 | ||||||||
\(366\) | 2.34010e8 | 0.249488 | ||||||||
\(367\) | 8.15959e8 | 0.861662 | 0.430831 | − | 0.902433i | \(-0.358220\pi\) | ||||
0.430831 | + | 0.902433i | \(0.358220\pi\) | |||||||
\(368\) | 3.29726e8 | 0.344894 | ||||||||
\(369\) | 2.13731e8 | 0.221450 | ||||||||
\(370\) | 1.11968e9 | 1.14918 | ||||||||
\(371\) | 4.51707e8 | 0.459248 | ||||||||
\(372\) | 5.45977e8 | 0.549888 | ||||||||
\(373\) | −6.16286e8 | −0.614896 | −0.307448 | − | 0.951565i | \(-0.599475\pi\) | ||||
−0.307448 | + | 0.951565i | \(0.599475\pi\) | |||||||
\(374\) | 2.35296e9 | 2.32575 | ||||||||
\(375\) | −6.19398e8 | −0.606542 | ||||||||
\(376\) | −2.10328e8 | −0.204051 | ||||||||
\(377\) | 2.17343e8 | 0.208906 | ||||||||
\(378\) | −5.40102e7 | −0.0514344 | ||||||||
\(379\) | 4.67684e8 | 0.441281 | 0.220641 | − | 0.975355i | \(-0.429185\pi\) | ||||
0.220641 | + | 0.975355i | \(0.429185\pi\) | |||||||
\(380\) | −1.33309e8 | −0.124629 | ||||||||
\(381\) | −1.16637e9 | −1.08044 | ||||||||
\(382\) | 3.50589e8 | 0.321793 | ||||||||
\(383\) | 1.42413e9 | 1.29525 | 0.647626 | − | 0.761958i | \(-0.275762\pi\) | ||||
0.647626 | + | 0.761958i | \(0.275762\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | −7.27630e8 | −0.649827 | ||||||||
\(386\) | 1.23011e9 | 1.08865 | ||||||||
\(387\) | 3.20029e8 | 0.280674 | ||||||||
\(388\) | −7.21478e8 | −0.627064 | ||||||||
\(389\) | −1.84423e8 | −0.158852 | −0.0794260 | − | 0.996841i | \(-0.525309\pi\) | ||||
−0.0794260 | + | 0.996841i | \(0.525309\pi\) | |||||||
\(390\) | −1.24448e8 | −0.106233 | ||||||||
\(391\) | 2.92687e9 | 2.47619 | ||||||||
\(392\) | 6.02363e7 | 0.0505076 | ||||||||
\(393\) | 1.02369e9 | 0.850738 | ||||||||
\(394\) | −7.57062e8 | −0.623583 | ||||||||
\(395\) | 5.62591e8 | 0.459307 | ||||||||
\(396\) | 3.77416e8 | 0.305413 | ||||||||
\(397\) | 1.13782e9 | 0.912653 | 0.456327 | − | 0.889812i | \(-0.349165\pi\) | ||||
0.456327 | + | 0.889812i | \(0.349165\pi\) | |||||||
\(398\) | −7.30315e8 | −0.580656 | ||||||||
\(399\) | −7.35589e7 | −0.0579736 | ||||||||
\(400\) | −3.83134e7 | −0.0299324 | ||||||||
\(401\) | −2.16316e9 | −1.67526 | −0.837631 | − | 0.546237i | \(-0.816060\pi\) | ||||
−0.837631 | + | 0.546237i | \(0.816060\pi\) | |||||||
\(402\) | −5.58191e7 | −0.0428540 | ||||||||
\(403\) | 6.94162e8 | 0.528315 | ||||||||
\(404\) | 6.10669e8 | 0.460756 | ||||||||
\(405\) | −1.39366e8 | −0.104247 | ||||||||
\(406\) | −2.71456e8 | −0.201307 | ||||||||
\(407\) | −4.31732e9 | −3.17420 | ||||||||
\(408\) | −5.02625e8 | −0.366382 | ||||||||
\(409\) | 1.67587e9 | 1.21118 | 0.605590 | − | 0.795777i | \(-0.292937\pi\) | ||||
0.605590 | + | 0.795777i | \(0.292937\pi\) | |||||||
\(410\) | −6.15083e8 | −0.440748 | ||||||||
\(411\) | −5.39848e8 | −0.383553 | ||||||||
\(412\) | 1.00495e9 | 0.707955 | ||||||||
\(413\) | 4.97538e8 | 0.347537 | ||||||||
\(414\) | 4.69473e8 | 0.325169 | ||||||||
\(415\) | −1.43957e9 | −0.988698 | ||||||||
\(416\) | −7.19913e7 | −0.0490290 | ||||||||
\(417\) | −1.54579e9 | −1.04394 | ||||||||
\(418\) | 5.14021e8 | 0.344242 | ||||||||
\(419\) | 1.95050e9 | 1.29538 | 0.647689 | − | 0.761905i | \(-0.275736\pi\) | ||||
0.647689 | + | 0.761905i | \(0.275736\pi\) | |||||||
\(420\) | 1.55432e8 | 0.102369 | ||||||||
\(421\) | 2.04077e9 | 1.33293 | 0.666464 | − | 0.745537i | \(-0.267807\pi\) | ||||
0.666464 | + | 0.745537i | \(0.267807\pi\) | |||||||
\(422\) | 1.85864e9 | 1.20393 | ||||||||
\(423\) | −2.99471e8 | −0.192382 | ||||||||
\(424\) | 6.74267e8 | 0.429588 | ||||||||
\(425\) | −3.40096e8 | −0.214902 | ||||||||
\(426\) | −5.94543e8 | −0.372606 | ||||||||
\(427\) | −3.71599e8 | −0.230981 | ||||||||
\(428\) | 8.94367e8 | 0.551395 | ||||||||
\(429\) | 4.79852e8 | 0.293431 | ||||||||
\(430\) | −9.20991e8 | −0.558619 | ||||||||
\(431\) | −1.76452e8 | −0.106159 | −0.0530795 | − | 0.998590i | \(-0.516904\pi\) | ||||
−0.0530795 | + | 0.998590i | \(0.516904\pi\) | |||||||
\(432\) | −8.06216e7 | −0.0481125 | ||||||||
\(433\) | −9.70906e8 | −0.574737 | −0.287369 | − | 0.957820i | \(-0.592780\pi\) | ||||
−0.287369 | + | 0.957820i | \(0.592780\pi\) | |||||||
\(434\) | −8.66992e8 | −0.509097 | ||||||||
\(435\) | −7.00457e8 | −0.408009 | ||||||||
\(436\) | 1.86605e8 | 0.107825 | ||||||||
\(437\) | 6.39397e8 | 0.366510 | ||||||||
\(438\) | −1.24095e8 | −0.0705657 | ||||||||
\(439\) | −2.81547e9 | −1.58827 | −0.794137 | − | 0.607738i | \(-0.792077\pi\) | ||||
−0.794137 | + | 0.607738i | \(0.792077\pi\) | |||||||
\(440\) | −1.08614e9 | −0.607858 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | −6.39044e8 | −0.352008 | ||||||||
\(443\) | 3.55508e7 | 0.0194283 | 0.00971417 | − | 0.999953i | \(-0.496908\pi\) | ||||
0.00971417 | + | 0.999953i | \(0.496908\pi\) | |||||||
\(444\) | 9.22242e8 | 0.500040 | ||||||||
\(445\) | 2.33735e9 | 1.25737 | ||||||||
\(446\) | 2.87434e8 | 0.153415 | ||||||||
\(447\) | 2.03775e9 | 1.07913 | ||||||||
\(448\) | 8.99154e7 | 0.0472456 | ||||||||
\(449\) | 1.95787e9 | 1.02075 | 0.510377 | − | 0.859951i | \(-0.329506\pi\) | ||||
0.510377 | + | 0.859951i | \(0.329506\pi\) | |||||||
\(450\) | −5.45517e7 | −0.0282205 | ||||||||
\(451\) | 2.37167e9 | 1.21741 | ||||||||
\(452\) | −2.95690e7 | −0.0150610 | ||||||||
\(453\) | 4.85713e8 | 0.245491 | ||||||||
\(454\) | −8.96965e8 | −0.449863 | ||||||||
\(455\) | 1.97618e8 | 0.0983530 | ||||||||
\(456\) | −1.09802e8 | −0.0542293 | ||||||||
\(457\) | 2.17951e9 | 1.06820 | 0.534100 | − | 0.845422i | \(-0.320651\pi\) | ||||
0.534100 | + | 0.845422i | \(0.320651\pi\) | |||||||
\(458\) | 1.06948e8 | 0.0520168 | ||||||||
\(459\) | −7.15652e8 | −0.345428 | ||||||||
\(460\) | −1.35106e9 | −0.647178 | ||||||||
\(461\) | −8.06597e8 | −0.383445 | −0.191723 | − | 0.981449i | \(-0.561407\pi\) | ||||
−0.191723 | + | 0.981449i | \(0.561407\pi\) | |||||||
\(462\) | −5.99323e8 | −0.282758 | ||||||||
\(463\) | 1.67835e9 | 0.785866 | 0.392933 | − | 0.919567i | \(-0.371460\pi\) | ||||
0.392933 | + | 0.919567i | \(0.371460\pi\) | |||||||
\(464\) | −4.05205e8 | −0.188305 | ||||||||
\(465\) | −2.23716e9 | −1.03184 | ||||||||
\(466\) | −1.96943e8 | −0.0901552 | ||||||||
\(467\) | 2.87764e9 | 1.30746 | 0.653728 | − | 0.756729i | \(-0.273204\pi\) | ||||
0.653728 | + | 0.756729i | \(0.273204\pi\) | |||||||
\(468\) | −1.02503e8 | −0.0462250 | ||||||||
\(469\) | 8.86386e7 | 0.0396751 | ||||||||
\(470\) | 8.61827e8 | 0.382893 | ||||||||
\(471\) | 5.82180e8 | 0.256734 | ||||||||
\(472\) | 7.42681e8 | 0.325091 | ||||||||
\(473\) | 3.55120e9 | 1.54298 | ||||||||
\(474\) | 4.63386e8 | 0.199857 | ||||||||
\(475\) | −7.42965e7 | −0.0318083 | ||||||||
\(476\) | 7.98150e8 | 0.339203 | ||||||||
\(477\) | 9.60041e8 | 0.405019 | ||||||||
\(478\) | 2.60499e9 | 1.09096 | ||||||||
\(479\) | −9.17628e8 | −0.381498 | −0.190749 | − | 0.981639i | \(-0.561092\pi\) | ||||
−0.190749 | + | 0.981639i | \(0.561092\pi\) | |||||||
\(480\) | 2.32015e8 | 0.0957574 | ||||||||
\(481\) | 1.17255e9 | 0.480423 | ||||||||
\(482\) | −2.51142e9 | −1.02154 | ||||||||
\(483\) | −7.45505e8 | −0.301048 | ||||||||
\(484\) | 2.94082e9 | 1.17899 | ||||||||
\(485\) | 2.95628e9 | 1.17666 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | −3.05087e9 | −1.19694 | −0.598469 | − | 0.801146i | \(-0.704224\pi\) | ||||
−0.598469 | + | 0.801146i | \(0.704224\pi\) | |||||||
\(488\) | −5.54690e8 | −0.216063 | ||||||||
\(489\) | 9.68895e8 | 0.374710 | ||||||||
\(490\) | −2.46821e8 | −0.0947753 | ||||||||
\(491\) | 8.68118e8 | 0.330974 | 0.165487 | − | 0.986212i | \(-0.447080\pi\) | ||||
0.165487 | + | 0.986212i | \(0.447080\pi\) | |||||||
\(492\) | −5.06622e8 | −0.191781 | ||||||||
\(493\) | −3.59688e9 | −1.35195 | ||||||||
\(494\) | −1.39604e8 | −0.0521018 | ||||||||
\(495\) | −1.54648e9 | −0.573094 | ||||||||
\(496\) | −1.29417e9 | −0.476217 | ||||||||
\(497\) | 9.44112e8 | 0.344966 | ||||||||
\(498\) | −1.18572e9 | −0.430209 | ||||||||
\(499\) | −3.54412e9 | −1.27690 | −0.638450 | − | 0.769664i | \(-0.720424\pi\) | ||||
−0.638450 | + | 0.769664i | \(0.720424\pi\) | |||||||
\(500\) | 1.46820e9 | 0.525280 | ||||||||
\(501\) | 1.79783e9 | 0.638730 | ||||||||
\(502\) | 1.35830e9 | 0.479218 | ||||||||
\(503\) | −3.81317e9 | −1.33597 | −0.667987 | − | 0.744173i | \(-0.732844\pi\) | ||||
−0.667987 | + | 0.744173i | \(0.732844\pi\) | |||||||
\(504\) | 1.28024e8 | 0.0445435 | ||||||||
\(505\) | −2.50224e9 | −0.864588 | ||||||||
\(506\) | 5.20950e9 | 1.78760 | ||||||||
\(507\) | −1.30324e8 | −0.0444116 | ||||||||
\(508\) | 2.76473e9 | 0.935685 | ||||||||
\(509\) | 5.60514e9 | 1.88397 | 0.941985 | − | 0.335654i | \(-0.108957\pi\) | ||||
0.941985 | + | 0.335654i | \(0.108957\pi\) | |||||||
\(510\) | 2.05953e9 | 0.687499 | ||||||||
\(511\) | 1.97058e8 | 0.0653311 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | −1.56339e8 | −0.0511279 | ||||||||
\(514\) | −1.96817e8 | −0.0639281 | ||||||||
\(515\) | −4.11784e9 | −1.32845 | ||||||||
\(516\) | −7.58588e8 | −0.243070 | ||||||||
\(517\) | −3.32308e9 | −1.05760 | ||||||||
\(518\) | −1.46449e9 | −0.462947 | ||||||||
\(519\) | 2.82865e9 | 0.888165 | ||||||||
\(520\) | 2.94987e8 | 0.0920008 | ||||||||
\(521\) | −2.78007e9 | −0.861240 | −0.430620 | − | 0.902533i | \(-0.641705\pi\) | ||||
−0.430620 | + | 0.902533i | \(0.641705\pi\) | |||||||
\(522\) | −5.76942e8 | −0.177536 | ||||||||
\(523\) | 4.86040e8 | 0.148565 | 0.0742824 | − | 0.997237i | \(-0.476333\pi\) | ||||
0.0742824 | + | 0.997237i | \(0.476333\pi\) | |||||||
\(524\) | −2.42653e9 | −0.736760 | ||||||||
\(525\) | 8.66261e7 | 0.0261271 | ||||||||
\(526\) | 2.99438e9 | 0.897133 | ||||||||
\(527\) | −1.14879e10 | −3.41904 | ||||||||
\(528\) | −8.94616e8 | −0.264495 | ||||||||
\(529\) | 3.07534e9 | 0.903229 | ||||||||
\(530\) | −2.76284e9 | −0.806102 | ||||||||
\(531\) | 1.05745e9 | 0.306499 | ||||||||
\(532\) | 1.74362e8 | 0.0502066 | ||||||||
\(533\) | −6.44126e8 | −0.184258 | ||||||||
\(534\) | 1.92520e9 | 0.547117 | ||||||||
\(535\) | −3.66470e9 | −1.03467 | ||||||||
\(536\) | 1.32312e8 | 0.0371127 | ||||||||
\(537\) | −2.44343e9 | −0.680912 | ||||||||
\(538\) | 4.18390e8 | 0.115836 | ||||||||
\(539\) | 9.51703e8 | 0.261783 | ||||||||
\(540\) | 3.30350e8 | 0.0902810 | ||||||||
\(541\) | −2.92864e9 | −0.795197 | −0.397599 | − | 0.917559i | \(-0.630156\pi\) | ||||
−0.397599 | + | 0.917559i | \(0.630156\pi\) | |||||||
\(542\) | 1.02155e9 | 0.275590 | ||||||||
\(543\) | 9.88079e6 | 0.00264845 | ||||||||
\(544\) | 1.19141e9 | 0.317296 | ||||||||
\(545\) | −7.64622e8 | −0.202329 | ||||||||
\(546\) | 1.62771e8 | 0.0427960 | ||||||||
\(547\) | 4.76852e9 | 1.24574 | 0.622871 | − | 0.782325i | \(-0.285966\pi\) | ||||
0.622871 | + | 0.782325i | \(0.285966\pi\) | |||||||
\(548\) | 1.27964e9 | 0.332166 | ||||||||
\(549\) | −7.89783e8 | −0.203706 | ||||||||
\(550\) | −6.05333e8 | −0.155140 | ||||||||
\(551\) | −7.85764e8 | −0.200107 | ||||||||
\(552\) | −1.11282e9 | −0.281605 | ||||||||
\(553\) | −7.35840e8 | −0.185031 | ||||||||
\(554\) | 3.17200e9 | 0.792592 | ||||||||
\(555\) | −3.77892e9 | −0.938302 | ||||||||
\(556\) | 3.66410e9 | 0.904076 | ||||||||
\(557\) | 2.40126e9 | 0.588769 | 0.294385 | − | 0.955687i | \(-0.404885\pi\) | ||||
0.294385 | + | 0.955687i | \(0.404885\pi\) | |||||||
\(558\) | −1.84267e9 | −0.448982 | ||||||||
\(559\) | −9.64478e8 | −0.233535 | ||||||||
\(560\) | −3.68432e8 | −0.0886542 | ||||||||
\(561\) | −7.94122e9 | −1.89897 | ||||||||
\(562\) | −7.24054e8 | −0.172066 | ||||||||
\(563\) | 5.35882e8 | 0.126558 | 0.0632790 | − | 0.997996i | \(-0.479844\pi\) | ||||
0.0632790 | + | 0.997996i | \(0.479844\pi\) | |||||||
\(564\) | 7.09857e8 | 0.166607 | ||||||||
\(565\) | 1.21160e8 | 0.0282612 | ||||||||
\(566\) | 5.32791e9 | 1.23509 | ||||||||
\(567\) | 1.82284e8 | 0.0419961 | ||||||||
\(568\) | 1.40929e9 | 0.322686 | ||||||||
\(569\) | 2.50427e9 | 0.569887 | 0.284943 | − | 0.958544i | \(-0.408025\pi\) | ||||
0.284943 | + | 0.958544i | \(0.408025\pi\) | |||||||
\(570\) | 4.49919e8 | 0.101759 | ||||||||
\(571\) | −3.94023e9 | −0.885717 | −0.442859 | − | 0.896591i | \(-0.646036\pi\) | ||||
−0.442859 | + | 0.896591i | \(0.646036\pi\) | |||||||
\(572\) | −1.13743e9 | −0.254119 | ||||||||
\(573\) | −1.18324e9 | −0.262743 | ||||||||
\(574\) | 8.04498e8 | 0.177555 | ||||||||
\(575\) | −7.52981e8 | −0.165176 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | −5.67394e9 | −1.22962 | −0.614808 | − | 0.788677i | \(-0.710766\pi\) | ||||
−0.614808 | + | 0.788677i | \(0.710766\pi\) | |||||||
\(578\) | 7.29304e9 | 1.57095 | ||||||||
\(579\) | −4.15162e9 | −0.888879 | ||||||||
\(580\) | 1.66034e9 | 0.353346 | ||||||||
\(581\) | 1.88288e9 | 0.398297 | ||||||||
\(582\) | 2.43499e9 | 0.511996 | ||||||||
\(583\) | 1.06531e10 | 2.22657 | ||||||||
\(584\) | 2.94150e8 | 0.0611117 | ||||||||
\(585\) | 4.20011e8 | 0.0867391 | ||||||||
\(586\) | −6.83924e8 | −0.140400 | ||||||||
\(587\) | 7.19268e9 | 1.46777 | 0.733884 | − | 0.679275i | \(-0.237706\pi\) | ||||
0.733884 | + | 0.679275i | \(0.237706\pi\) | |||||||
\(588\) | −2.03297e8 | −0.0412393 | ||||||||
\(589\) | −2.50962e9 | −0.506063 | ||||||||
\(590\) | −3.04316e9 | −0.610019 | ||||||||
\(591\) | 2.55508e9 | 0.509154 | ||||||||
\(592\) | −2.18605e9 | −0.433047 | ||||||||
\(593\) | 2.65660e9 | 0.523161 | 0.261581 | − | 0.965182i | \(-0.415756\pi\) | ||||
0.261581 | + | 0.965182i | \(0.415756\pi\) | |||||||
\(594\) | −1.27378e9 | −0.249369 | ||||||||
\(595\) | −3.27045e9 | −0.636500 | ||||||||
\(596\) | −4.83023e9 | −0.934557 | ||||||||
\(597\) | 2.46481e9 | 0.474104 | ||||||||
\(598\) | −1.41486e9 | −0.270557 | ||||||||
\(599\) | 4.83838e9 | 0.919826 | 0.459913 | − | 0.887964i | \(-0.347881\pi\) | ||||
0.459913 | + | 0.887964i | \(0.347881\pi\) | |||||||
\(600\) | 1.29308e8 | 0.0244397 | ||||||||
\(601\) | −6.40961e9 | −1.20440 | −0.602201 | − | 0.798345i | \(-0.705709\pi\) | ||||
−0.602201 | + | 0.798345i | \(0.705709\pi\) | |||||||
\(602\) | 1.20461e9 | 0.225039 | ||||||||
\(603\) | 1.88389e8 | 0.0349901 | ||||||||
\(604\) | −1.15132e9 | −0.212602 | ||||||||
\(605\) | −1.20501e10 | −2.21232 | ||||||||
\(606\) | −2.06101e9 | −0.376206 | ||||||||
\(607\) | −4.61181e9 | −0.836973 | −0.418486 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418486 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(608\) | 2.60272e8 | 0.0469640 | ||||||||
\(609\) | 9.16163e8 | 0.164366 | ||||||||
\(610\) | 2.27286e9 | 0.405433 | ||||||||
\(611\) | 9.02521e8 | 0.160071 | ||||||||
\(612\) | 1.69636e9 | 0.299149 | ||||||||
\(613\) | −1.68984e9 | −0.296301 | −0.148151 | − | 0.988965i | \(-0.547332\pi\) | ||||
−0.148151 | + | 0.988965i | \(0.547332\pi\) | |||||||
\(614\) | 5.42841e8 | 0.0946418 | ||||||||
\(615\) | 2.07591e9 | 0.359869 | ||||||||
\(616\) | 1.42062e9 | 0.244875 | ||||||||
\(617\) | −1.03250e10 | −1.76966 | −0.884831 | − | 0.465912i | \(-0.845726\pi\) | ||||
−0.884831 | + | 0.465912i | \(0.845726\pi\) | |||||||
\(618\) | −3.39172e9 | −0.578043 | ||||||||
\(619\) | 2.48042e9 | 0.420347 | 0.210174 | − | 0.977664i | \(-0.432597\pi\) | ||||
0.210174 | + | 0.977664i | \(0.432597\pi\) | |||||||
\(620\) | 5.30290e9 | 0.893600 | ||||||||
\(621\) | −1.58447e9 | −0.265499 | ||||||||
\(622\) | −9.16551e7 | −0.0152718 | ||||||||
\(623\) | −3.05714e9 | −0.506532 | ||||||||
\(624\) | 2.42971e8 | 0.0400320 | ||||||||
\(625\) | −5.28525e9 | −0.865935 | ||||||||
\(626\) | −1.84926e9 | −0.301292 | ||||||||
\(627\) | −1.73482e9 | −0.281072 | ||||||||
\(628\) | −1.37998e9 | −0.222338 | ||||||||
\(629\) | −1.94049e10 | −3.10910 | ||||||||
\(630\) | −5.24584e8 | −0.0835839 | ||||||||
\(631\) | −1.66794e9 | −0.264288 | −0.132144 | − | 0.991231i | \(-0.542186\pi\) | ||||
−0.132144 | + | 0.991231i | \(0.542186\pi\) | |||||||
\(632\) | −1.09840e9 | −0.173081 | ||||||||
\(633\) | −6.27290e9 | −0.983003 | ||||||||
\(634\) | 7.19019e9 | 1.12054 | ||||||||
\(635\) | −1.13286e10 | −1.75577 | ||||||||
\(636\) | −2.27565e9 | −0.350757 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | −6.40204e9 | −0.975991 | ||||||||
\(639\) | 2.00658e9 | 0.304231 | ||||||||
\(640\) | −5.49962e8 | −0.0829284 | ||||||||
\(641\) | 5.95360e9 | 0.892846 | 0.446423 | − | 0.894822i | \(-0.352698\pi\) | ||||
0.446423 | + | 0.894822i | \(0.352698\pi\) | |||||||
\(642\) | −3.01849e9 | −0.450212 | ||||||||
\(643\) | −8.74492e9 | −1.29723 | −0.648616 | − | 0.761116i | \(-0.724652\pi\) | ||||
−0.648616 | + | 0.761116i | \(0.724652\pi\) | |||||||
\(644\) | 1.76712e9 | 0.260715 | ||||||||
\(645\) | 3.10834e9 | 0.456111 | ||||||||
\(646\) | 2.31035e9 | 0.337182 | ||||||||
\(647\) | −7.84651e9 | −1.13897 | −0.569484 | − | 0.822002i | \(-0.692857\pi\) | ||||
−0.569484 | + | 0.822002i | \(0.692857\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | 1.17340e10 | 1.68496 | ||||||||
\(650\) | 1.64403e8 | 0.0234809 | ||||||||
\(651\) | 2.92610e9 | 0.415676 | ||||||||
\(652\) | −2.29664e9 | −0.324509 | ||||||||
\(653\) | −1.36993e10 | −1.92532 | −0.962662 | − | 0.270708i | \(-0.912742\pi\) | ||||
−0.962662 | + | 0.270708i | \(0.912742\pi\) | |||||||
\(654\) | −6.29792e8 | −0.0880390 | ||||||||
\(655\) | 9.94280e9 | 1.38250 | ||||||||
\(656\) | 1.20088e9 | 0.166088 | ||||||||
\(657\) | 4.18819e8 | 0.0576167 | ||||||||
\(658\) | −1.12723e9 | −0.154248 | ||||||||
\(659\) | 5.88214e9 | 0.800638 | 0.400319 | − | 0.916376i | \(-0.368899\pi\) | ||||
0.400319 | + | 0.916376i | \(0.368899\pi\) | |||||||
\(660\) | 3.66573e9 | 0.496314 | ||||||||
\(661\) | −1.06870e10 | −1.43929 | −0.719646 | − | 0.694341i | \(-0.755696\pi\) | ||||
−0.719646 | + | 0.694341i | \(0.755696\pi\) | |||||||
\(662\) | −7.36047e9 | −0.986059 | ||||||||
\(663\) | 2.15677e9 | 0.287413 | ||||||||
\(664\) | 2.81060e9 | 0.372572 | ||||||||
\(665\) | −7.14455e8 | −0.0942104 | ||||||||
\(666\) | −3.11257e9 | −0.408281 | ||||||||
\(667\) | −7.96357e9 | −1.03912 | ||||||||
\(668\) | −4.26153e9 | −0.553156 | ||||||||
\(669\) | −9.70091e8 | −0.125262 | ||||||||
\(670\) | −5.42153e8 | −0.0696402 | ||||||||
\(671\) | −8.76381e9 | −1.11986 | ||||||||
\(672\) | −3.03464e8 | −0.0385758 | ||||||||
\(673\) | 9.41563e9 | 1.19068 | 0.595342 | − | 0.803472i | \(-0.297016\pi\) | ||||
0.595342 | + | 0.803472i | \(0.297016\pi\) | |||||||
\(674\) | −9.18168e9 | −1.15508 | ||||||||
\(675\) | 1.84112e8 | 0.0230419 | ||||||||
\(676\) | 3.08916e8 | 0.0384615 | ||||||||
\(677\) | 1.00850e8 | 0.0124916 | 0.00624579 | − | 0.999980i | \(-0.498012\pi\) | ||||
0.00624579 | + | 0.999980i | \(0.498012\pi\) | |||||||
\(678\) | 9.97955e7 | 0.0122972 | ||||||||
\(679\) | −3.86667e9 | −0.474016 | ||||||||
\(680\) | −4.88184e9 | −0.595391 | ||||||||
\(681\) | 3.02726e9 | 0.367311 | ||||||||
\(682\) | −2.04472e10 | −2.46825 | ||||||||
\(683\) | −5.72351e9 | −0.687369 | −0.343685 | − | 0.939085i | \(-0.611675\pi\) | ||||
−0.343685 | + | 0.939085i | \(0.611675\pi\) | |||||||
\(684\) | 3.70582e8 | 0.0442781 | ||||||||
\(685\) | −5.24337e9 | −0.623295 | ||||||||
\(686\) | 3.22829e8 | 0.0381802 | ||||||||
\(687\) | −3.60950e8 | −0.0424715 | ||||||||
\(688\) | 1.79813e9 | 0.210505 | ||||||||
\(689\) | −2.89329e9 | −0.336996 | ||||||||
\(690\) | 4.55984e9 | 0.528418 | ||||||||
\(691\) | 1.06363e10 | 1.22636 | 0.613180 | − | 0.789943i | \(-0.289890\pi\) | ||||
0.613180 | + | 0.789943i | \(0.289890\pi\) | |||||||
\(692\) | −6.70495e9 | −0.769173 | ||||||||
\(693\) | 2.02272e9 | 0.230871 | ||||||||
\(694\) | 9.61602e9 | 1.09204 | ||||||||
\(695\) | −1.50138e10 | −1.69646 | ||||||||
\(696\) | 1.36757e9 | 0.153750 | ||||||||
\(697\) | 1.06599e10 | 1.19244 | ||||||||
\(698\) | −5.97360e8 | −0.0664878 | ||||||||
\(699\) | 6.64684e8 | 0.0736114 | ||||||||
\(700\) | −2.05336e8 | −0.0226267 | ||||||||
\(701\) | −1.82601e9 | −0.200212 | −0.100106 | − | 0.994977i | \(-0.531918\pi\) | ||||
−0.100106 | + | 0.994977i | \(0.531918\pi\) | |||||||
\(702\) | 3.45948e8 | 0.0377426 | ||||||||
\(703\) | −4.23915e9 | −0.460188 | ||||||||
\(704\) | 2.12057e9 | 0.229060 | ||||||||
\(705\) | −2.90867e9 | −0.312631 | ||||||||
\(706\) | 8.79562e9 | 0.940697 | ||||||||
\(707\) | 3.27280e9 | 0.348299 | ||||||||
\(708\) | −2.50655e9 | −0.265436 | ||||||||
\(709\) | 6.35699e9 | 0.669869 | 0.334935 | − | 0.942241i | \(-0.391286\pi\) | ||||
0.334935 | + | 0.942241i | \(0.391286\pi\) | |||||||
\(710\) | −5.77461e9 | −0.605506 | ||||||||
\(711\) | −1.56393e9 | −0.163182 | ||||||||
\(712\) | −4.56343e9 | −0.473818 | ||||||||
\(713\) | −2.54345e10 | −2.62791 | ||||||||
\(714\) | −2.69376e9 | −0.276958 | ||||||||
\(715\) | 4.66065e9 | 0.476843 | ||||||||
\(716\) | 5.79185e9 | 0.589687 | ||||||||
\(717\) | −8.79185e9 | −0.890765 | ||||||||
\(718\) | −4.29946e9 | −0.433489 | ||||||||
\(719\) | 1.31687e10 | 1.32127 | 0.660633 | − | 0.750709i | \(-0.270288\pi\) | ||||
0.660633 | + | 0.750709i | \(0.270288\pi\) | |||||||
\(720\) | −7.83052e8 | −0.0781856 | ||||||||
\(721\) | 5.38592e9 | 0.535164 | ||||||||
\(722\) | −6.64626e9 | −0.657199 | ||||||||
\(723\) | 8.47604e9 | 0.834083 | ||||||||
\(724\) | −2.34211e7 | −0.00229363 | ||||||||
\(725\) | 9.25350e8 | 0.0901826 | ||||||||
\(726\) | −9.92526e9 | −0.962640 | ||||||||
\(727\) | −7.56453e9 | −0.730149 | −0.365074 | − | 0.930978i | \(-0.618956\pi\) | ||||
−0.365074 | + | 0.930978i | \(0.618956\pi\) | |||||||
\(728\) | −3.85828e8 | −0.0370625 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −1.20529e9 | −0.114673 | ||||||||
\(731\) | 1.59615e10 | 1.51134 | ||||||||
\(732\) | 1.87208e9 | 0.176415 | ||||||||
\(733\) | 5.51700e9 | 0.517415 | 0.258707 | − | 0.965956i | \(-0.416703\pi\) | ||||
0.258707 | + | 0.965956i | \(0.416703\pi\) | |||||||
\(734\) | 6.52767e9 | 0.609287 | ||||||||
\(735\) | 8.33019e8 | 0.0773837 | ||||||||
\(736\) | 2.63781e9 | 0.243877 | ||||||||
\(737\) | 2.09046e9 | 0.192356 | ||||||||
\(738\) | 1.70985e9 | 0.156589 | ||||||||
\(739\) | −9.43656e9 | −0.860118 | −0.430059 | − | 0.902801i | \(-0.641507\pi\) | ||||
−0.430059 | + | 0.902801i | \(0.641507\pi\) | |||||||
\(740\) | 8.95745e9 | 0.812593 | ||||||||
\(741\) | 4.71163e8 | 0.0425410 | ||||||||
\(742\) | 3.61365e9 | 0.324738 | ||||||||
\(743\) | −1.76347e10 | −1.57727 | −0.788637 | − | 0.614859i | \(-0.789213\pi\) | ||||
−0.788637 | + | 0.614859i | \(0.789213\pi\) | |||||||
\(744\) | 4.36782e9 | 0.388830 | ||||||||
\(745\) | 1.97921e10 | 1.75365 | ||||||||
\(746\) | −4.93029e9 | −0.434797 | ||||||||
\(747\) | 4.00181e9 | 0.351265 | ||||||||
\(748\) | 1.88236e10 | 1.64455 | ||||||||
\(749\) | 4.79325e9 | 0.416815 | ||||||||
\(750\) | −4.95519e9 | −0.428890 | ||||||||
\(751\) | 1.51261e10 | 1.30313 | 0.651564 | − | 0.758593i | \(-0.274113\pi\) | ||||
0.651564 | + | 0.758593i | \(0.274113\pi\) | |||||||
\(752\) | −1.68262e9 | −0.144286 | ||||||||
\(753\) | −4.58427e9 | −0.391280 | ||||||||
\(754\) | 1.73874e9 | 0.147719 | ||||||||
\(755\) | 4.71758e9 | 0.398937 | ||||||||
\(756\) | −4.32081e8 | −0.0363696 | ||||||||
\(757\) | 8.50906e9 | 0.712929 | 0.356464 | − | 0.934309i | \(-0.383982\pi\) | ||||
0.356464 | + | 0.934309i | \(0.383982\pi\) | |||||||
\(758\) | 3.74147e9 | 0.312033 | ||||||||
\(759\) | −1.75821e10 | −1.45957 | ||||||||
\(760\) | −1.06647e9 | −0.0881258 | ||||||||
\(761\) | 1.27843e9 | 0.105155 | 0.0525777 | − | 0.998617i | \(-0.483256\pi\) | ||||
0.0525777 | + | 0.998617i | \(0.483256\pi\) | |||||||
\(762\) | −9.33097e9 | −0.763984 | ||||||||
\(763\) | 1.00009e9 | 0.0815083 | ||||||||
\(764\) | 2.80471e9 | 0.227542 | ||||||||
\(765\) | −6.95090e9 | −0.561340 | ||||||||
\(766\) | 1.13931e10 | 0.915882 | ||||||||
\(767\) | −3.18686e9 | −0.255023 | ||||||||
\(768\) | −4.52985e8 | −0.0360844 | ||||||||
\(769\) | 6.26123e9 | 0.496498 | 0.248249 | − | 0.968696i | \(-0.420145\pi\) | ||||
0.248249 | + | 0.968696i | \(0.420145\pi\) | |||||||
\(770\) | −5.82104e9 | −0.459497 | ||||||||
\(771\) | 6.64258e8 | 0.0521971 | ||||||||
\(772\) | 9.84087e9 | 0.769791 | ||||||||
\(773\) | −3.35252e9 | −0.261062 | −0.130531 | − | 0.991444i | \(-0.541668\pi\) | ||||
−0.130531 | + | 0.991444i | \(0.541668\pi\) | |||||||
\(774\) | 2.56024e9 | 0.198466 | ||||||||
\(775\) | 2.95544e9 | 0.228069 | ||||||||
\(776\) | −5.77182e9 | −0.443401 | ||||||||
\(777\) | 4.94264e9 | 0.377994 | ||||||||
\(778\) | −1.47539e9 | −0.112325 | ||||||||
\(779\) | 2.32872e9 | 0.176497 | ||||||||
\(780\) | −9.95582e8 | −0.0751183 | ||||||||
\(781\) | 2.22660e10 | 1.67249 | ||||||||
\(782\) | 2.34150e10 | 1.75093 | ||||||||
\(783\) | 1.94718e9 | 0.144957 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | 5.65453e9 | 0.417208 | ||||||||
\(786\) | 8.18954e9 | 0.601562 | ||||||||
\(787\) | −2.38346e9 | −0.174300 | −0.0871499 | − | 0.996195i | \(-0.527776\pi\) | ||||
−0.0871499 | + | 0.996195i | \(0.527776\pi\) | |||||||
\(788\) | −6.05649e9 | −0.440940 | ||||||||
\(789\) | −1.01060e10 | −0.732506 | ||||||||
\(790\) | 4.50073e9 | 0.324779 | ||||||||
\(791\) | −1.58471e8 | −0.0113850 | ||||||||
\(792\) | 3.01933e9 | 0.215960 | ||||||||
\(793\) | 2.38018e9 | 0.169494 | ||||||||
\(794\) | 9.10254e9 | 0.645343 | ||||||||
\(795\) | 9.32458e9 | 0.658179 | ||||||||
\(796\) | −5.84252e9 | −0.410586 | ||||||||
\(797\) | −1.33613e10 | −0.934855 | −0.467427 | − | 0.884031i | \(-0.654819\pi\) | ||||
−0.467427 | + | 0.884031i | \(0.654819\pi\) | |||||||
\(798\) | −5.88471e8 | −0.0409935 | ||||||||
\(799\) | −1.49361e10 | −1.03591 | ||||||||
\(800\) | −3.06507e8 | −0.0211654 | ||||||||
\(801\) | −6.49754e9 | −0.446719 | ||||||||
\(802\) | −1.73053e10 | −1.18459 | ||||||||
\(803\) | 4.64743e9 | 0.316744 | ||||||||
\(804\) | −4.46552e8 | −0.0303024 | ||||||||
\(805\) | −7.24086e9 | −0.489220 | ||||||||
\(806\) | 5.55330e9 | 0.373575 | ||||||||
\(807\) | −1.41207e9 | −0.0945796 | ||||||||
\(808\) | 4.88535e9 | 0.325804 | ||||||||
\(809\) | −7.57292e9 | −0.502856 | −0.251428 | − | 0.967876i | \(-0.580900\pi\) | ||||
−0.251428 | + | 0.967876i | \(0.580900\pi\) | |||||||
\(810\) | −1.11493e9 | −0.0737141 | ||||||||
\(811\) | −9.58451e7 | −0.00630953 | −0.00315476 | − | 0.999995i | \(-0.501004\pi\) | ||||
−0.00315476 | + | 0.999995i | \(0.501004\pi\) | |||||||
\(812\) | −2.17165e9 | −0.142345 | ||||||||
\(813\) | −3.44774e9 | −0.225018 | ||||||||
\(814\) | −3.45386e10 | −2.24450 | ||||||||
\(815\) | 9.41057e9 | 0.608926 | ||||||||
\(816\) | −4.02100e9 | −0.259071 | ||||||||
\(817\) | 3.48690e9 | 0.223698 | ||||||||
\(818\) | 1.34069e10 | 0.856433 | ||||||||
\(819\) | −5.49353e8 | −0.0349428 | ||||||||
\(820\) | −4.92066e9 | −0.311656 | ||||||||
\(821\) | 3.05920e10 | 1.92933 | 0.964667 | − | 0.263472i | \(-0.0848677\pi\) | ||||
0.964667 | + | 0.263472i | \(0.0848677\pi\) | |||||||
\(822\) | −4.31878e9 | −0.271213 | ||||||||
\(823\) | −2.67508e10 | −1.67278 | −0.836388 | − | 0.548137i | \(-0.815337\pi\) | ||||
−0.836388 | + | 0.548137i | \(0.815337\pi\) | |||||||
\(824\) | 8.03963e9 | 0.500600 | ||||||||
\(825\) | 2.04300e9 | 0.126672 | ||||||||
\(826\) | 3.98031e9 | 0.245746 | ||||||||
\(827\) | 1.13389e10 | 0.697112 | 0.348556 | − | 0.937288i | \(-0.386672\pi\) | ||||
0.348556 | + | 0.937288i | \(0.386672\pi\) | |||||||
\(828\) | 3.75578e9 | 0.229929 | ||||||||
\(829\) | 7.95356e9 | 0.484865 | 0.242432 | − | 0.970168i | \(-0.422055\pi\) | ||||
0.242432 | + | 0.970168i | \(0.422055\pi\) | |||||||
\(830\) | −1.15165e10 | −0.699115 | ||||||||
\(831\) | −1.07055e10 | −0.647149 | ||||||||
\(832\) | −5.75930e8 | −0.0346688 | ||||||||
\(833\) | 4.27759e9 | 0.256414 | ||||||||
\(834\) | −1.23663e10 | −0.738175 | ||||||||
\(835\) | 1.74618e10 | 1.03797 | ||||||||
\(836\) | 4.11217e9 | 0.243416 | ||||||||
\(837\) | 6.21902e9 | 0.366592 | ||||||||
\(838\) | 1.56040e10 | 0.915970 | ||||||||
\(839\) | 1.58689e10 | 0.927640 | 0.463820 | − | 0.885929i | \(-0.346478\pi\) | ||||
0.463820 | + | 0.885929i | \(0.346478\pi\) | |||||||
\(840\) | 1.24346e9 | 0.0723858 | ||||||||
\(841\) | −7.46332e9 | −0.432659 | ||||||||
\(842\) | 1.63262e10 | 0.942522 | ||||||||
\(843\) | 2.44368e9 | 0.140491 | ||||||||
\(844\) | 1.48691e10 | 0.851306 | ||||||||
\(845\) | −1.26579e9 | −0.0721713 | ||||||||
\(846\) | −2.39577e9 | −0.136034 | ||||||||
\(847\) | 1.57609e10 | 0.891231 | ||||||||
\(848\) | 5.39414e9 | 0.303764 | ||||||||
\(849\) | −1.79817e10 | −1.00845 | ||||||||
\(850\) | −2.72077e9 | −0.151959 | ||||||||
\(851\) | −4.29629e10 | −2.38968 | ||||||||
\(852\) | −4.75634e9 | −0.263472 | ||||||||
\(853\) | 1.04522e10 | 0.576615 | 0.288308 | − | 0.957538i | \(-0.406907\pi\) | ||||
0.288308 | + | 0.957538i | \(0.406907\pi\) | |||||||
\(854\) | −2.97279e9 | −0.163328 | ||||||||
\(855\) | −1.51848e9 | −0.0830858 | ||||||||
\(856\) | 7.15494e9 | 0.389895 | ||||||||
\(857\) | 2.43883e10 | 1.32358 | 0.661789 | − | 0.749690i | \(-0.269798\pi\) | ||||
0.661789 | + | 0.749690i | \(0.269798\pi\) | |||||||
\(858\) | 3.83881e9 | 0.207487 | ||||||||
\(859\) | −1.53166e10 | −0.824493 | −0.412246 | − | 0.911072i | \(-0.635256\pi\) | ||||
−0.412246 | + | 0.911072i | \(0.635256\pi\) | |||||||
\(860\) | −7.36793e9 | −0.395003 | ||||||||
\(861\) | −2.71518e9 | −0.144973 | ||||||||
\(862\) | −1.41162e9 | −0.0750657 | ||||||||
\(863\) | −6.85504e9 | −0.363055 | −0.181528 | − | 0.983386i | \(-0.558104\pi\) | ||||
−0.181528 | + | 0.983386i | \(0.558104\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | 2.74738e10 | 1.44332 | ||||||||
\(866\) | −7.76725e9 | −0.406401 | ||||||||
\(867\) | −2.46140e10 | −1.28267 | ||||||||
\(868\) | −6.93593e9 | −0.359986 | ||||||||
\(869\) | −1.73541e10 | −0.897085 | ||||||||
\(870\) | −5.60366e9 | −0.288506 | ||||||||
\(871\) | −5.67752e8 | −0.0291136 | ||||||||
\(872\) | 1.49284e9 | 0.0762441 | ||||||||
\(873\) | −8.21809e9 | −0.418043 | ||||||||
\(874\) | 5.11517e9 | 0.259161 | ||||||||
\(875\) | 7.86865e9 | 0.397075 | ||||||||
\(876\) | −9.92757e8 | −0.0498975 | ||||||||
\(877\) | 1.83666e10 | 0.919453 | 0.459726 | − | 0.888061i | \(-0.347947\pi\) | ||||
0.459726 | + | 0.888061i | \(0.347947\pi\) | |||||||
\(878\) | −2.25238e10 | −1.12308 | ||||||||
\(879\) | 2.30825e9 | 0.114636 | ||||||||
\(880\) | −8.68913e9 | −0.429820 | ||||||||
\(881\) | 3.29732e9 | 0.162460 | 0.0812299 | − | 0.996695i | \(-0.474115\pi\) | ||||
0.0812299 | + | 0.996695i | \(0.474115\pi\) | |||||||
\(882\) | 6.86129e8 | 0.0336718 | ||||||||
\(883\) | −2.94976e10 | −1.44186 | −0.720932 | − | 0.693005i | \(-0.756286\pi\) | ||||
−0.720932 | + | 0.693005i | \(0.756286\pi\) | |||||||
\(884\) | −5.11235e9 | −0.248907 | ||||||||
\(885\) | 1.02707e10 | 0.498078 | ||||||||
\(886\) | 2.84406e8 | 0.0137379 | ||||||||
\(887\) | −2.61083e9 | −0.125616 | −0.0628081 | − | 0.998026i | \(-0.520006\pi\) | ||||
−0.0628081 | + | 0.998026i | \(0.520006\pi\) | |||||||
\(888\) | 7.37794e9 | 0.353581 | ||||||||
\(889\) | 1.48172e10 | 0.707312 | ||||||||
\(890\) | 1.86988e10 | 0.889097 | ||||||||
\(891\) | 4.29901e9 | 0.203609 | ||||||||
\(892\) | 2.29947e9 | 0.108480 | ||||||||
\(893\) | −3.26291e9 | −0.153329 | ||||||||
\(894\) | 1.63020e10 | 0.763063 | ||||||||
\(895\) | −2.37323e10 | −1.10652 | ||||||||
\(896\) | 7.19323e8 | 0.0334077 | ||||||||
\(897\) | 4.77515e9 | 0.220909 | ||||||||
\(898\) | 1.56629e10 | 0.721782 | ||||||||
\(899\) | 3.12569e10 | 1.43478 | ||||||||
\(900\) | −4.36414e8 | −0.0199549 | ||||||||
\(901\) | 4.78821e10 | 2.18090 | ||||||||
\(902\) | 1.89733e10 | 0.860837 | ||||||||
\(903\) | −4.06556e9 | −0.183744 | ||||||||
\(904\) | −2.36552e8 | −0.0106497 | ||||||||
\(905\) | 9.59690e7 | 0.00430389 | ||||||||
\(906\) | 3.88570e9 | 0.173588 | ||||||||
\(907\) | 2.81292e10 | 1.25179 | 0.625896 | − | 0.779907i | \(-0.284733\pi\) | ||||
0.625896 | + | 0.779907i | \(0.284733\pi\) | |||||||
\(908\) | −7.17572e9 | −0.318101 | ||||||||
\(909\) | 6.95590e9 | 0.307171 | ||||||||
\(910\) | 1.58095e9 | 0.0695460 | ||||||||
\(911\) | −3.77491e10 | −1.65422 | −0.827108 | − | 0.562043i | \(-0.810016\pi\) | ||||
−0.827108 | + | 0.562043i | \(0.810016\pi\) | |||||||
\(912\) | −8.78418e8 | −0.0383459 | ||||||||
\(913\) | 4.44060e10 | 1.93105 | ||||||||
\(914\) | 1.74361e10 | 0.755331 | ||||||||
\(915\) | −7.67091e9 | −0.331034 | ||||||||
\(916\) | 8.55584e8 | 0.0367814 | ||||||||
\(917\) | −1.30047e10 | −0.556938 | ||||||||
\(918\) | −5.72522e9 | −0.244254 | ||||||||
\(919\) | −2.24933e10 | −0.955981 | −0.477990 | − | 0.878365i | \(-0.658635\pi\) | ||||
−0.477990 | + | 0.878365i | \(0.658635\pi\) | |||||||
\(920\) | −1.08085e10 | −0.457624 | ||||||||
\(921\) | −1.83209e9 | −0.0772747 | ||||||||
\(922\) | −6.45278e9 | −0.271137 | ||||||||
\(923\) | −6.04727e9 | −0.253136 | ||||||||
\(924\) | −4.79459e9 | −0.199940 | ||||||||
\(925\) | 4.99220e9 | 0.207394 | ||||||||
\(926\) | 1.34268e10 | 0.555691 | ||||||||
\(927\) | 1.14470e10 | 0.471970 | ||||||||
\(928\) | −3.24164e9 | −0.133152 | ||||||||
\(929\) | 1.01665e10 | 0.416020 | 0.208010 | − | 0.978127i | \(-0.433301\pi\) | ||||
0.208010 | + | 0.978127i | \(0.433301\pi\) | |||||||
\(930\) | −1.78973e10 | −0.729621 | ||||||||
\(931\) | 9.34471e8 | 0.0379526 | ||||||||
\(932\) | −1.57555e9 | −0.0637493 | ||||||||
\(933\) | 3.09336e8 | 0.0124694 | ||||||||
\(934\) | 2.30211e10 | 0.924512 | ||||||||
\(935\) | −7.71306e10 | −3.08593 | ||||||||
\(936\) | −8.20026e8 | −0.0326860 | ||||||||
\(937\) | 2.91223e10 | 1.15648 | 0.578240 | − | 0.815867i | \(-0.303740\pi\) | ||||
0.578240 | + | 0.815867i | \(0.303740\pi\) | |||||||
\(938\) | 7.09109e8 | 0.0280545 | ||||||||
\(939\) | 6.24125e9 | 0.246004 | ||||||||
\(940\) | 6.89462e9 | 0.270746 | ||||||||
\(941\) | −6.31351e9 | −0.247006 | −0.123503 | − | 0.992344i | \(-0.539413\pi\) | ||||
−0.123503 | + | 0.992344i | \(0.539413\pi\) | |||||||
\(942\) | 4.65744e9 | 0.181539 | ||||||||
\(943\) | 2.36012e10 | 0.916521 | ||||||||
\(944\) | 5.94145e9 | 0.229874 | ||||||||
\(945\) | 1.77047e9 | 0.0682460 | ||||||||
\(946\) | 2.84096e10 | 1.09105 | ||||||||
\(947\) | 1.94677e10 | 0.744885 | 0.372443 | − | 0.928055i | \(-0.378520\pi\) | ||||
0.372443 | + | 0.928055i | \(0.378520\pi\) | |||||||
\(948\) | 3.70709e9 | 0.141320 | ||||||||
\(949\) | −1.26220e9 | −0.0479400 | ||||||||
\(950\) | −5.94372e8 | −0.0224919 | ||||||||
\(951\) | −2.42669e10 | −0.914918 | ||||||||
\(952\) | 6.38520e9 | 0.239853 | ||||||||
\(953\) | −1.40644e10 | −0.526376 | −0.263188 | − | 0.964745i | \(-0.584774\pi\) | ||||
−0.263188 | + | 0.964745i | \(0.584774\pi\) | |||||||
\(954\) | 7.68033e9 | 0.286392 | ||||||||
\(955\) | −1.14924e10 | −0.426972 | ||||||||
\(956\) | 2.08399e10 | 0.771425 | ||||||||
\(957\) | 2.16069e10 | 0.796893 | ||||||||
\(958\) | −7.34102e9 | −0.269760 | ||||||||
\(959\) | 6.85807e9 | 0.251094 | ||||||||
\(960\) | 1.85612e9 | 0.0677107 | ||||||||
\(961\) | 7.23175e10 | 2.62852 | ||||||||
\(962\) | 9.38040e9 | 0.339710 | ||||||||
\(963\) | 1.01874e10 | 0.367597 | ||||||||
\(964\) | −2.00914e10 | −0.722337 | ||||||||
\(965\) | −4.03234e10 | −1.44448 | ||||||||
\(966\) | −5.96404e9 | −0.212873 | ||||||||
\(967\) | −2.63668e10 | −0.937703 | −0.468852 | − | 0.883277i | \(-0.655332\pi\) | ||||
−0.468852 | + | 0.883277i | \(0.655332\pi\) | |||||||
\(968\) | 2.35265e10 | 0.833670 | ||||||||
\(969\) | −7.79743e9 | −0.275308 | ||||||||
\(970\) | 2.36503e10 | 0.832023 | ||||||||
\(971\) | −1.38855e10 | −0.486735 | −0.243368 | − | 0.969934i | \(-0.578252\pi\) | ||||
−0.243368 | + | 0.969934i | \(0.578252\pi\) | |||||||
\(972\) | −9.18330e8 | −0.0320750 | ||||||||
\(973\) | 1.96373e10 | 0.683417 | ||||||||
\(974\) | −2.44069e10 | −0.846364 | ||||||||
\(975\) | −5.54862e8 | −0.0191721 | ||||||||
\(976\) | −4.43752e9 | −0.152780 | ||||||||
\(977\) | 2.36190e9 | 0.0810270 | 0.0405135 | − | 0.999179i | \(-0.487101\pi\) | ||||
0.0405135 | + | 0.999179i | \(0.487101\pi\) | |||||||
\(978\) | 7.75116e9 | 0.264960 | ||||||||
\(979\) | −7.20998e10 | −2.45581 | ||||||||
\(980\) | −1.97456e9 | −0.0670162 | ||||||||
\(981\) | 2.12555e9 | 0.0718836 | ||||||||
\(982\) | 6.94494e9 | 0.234034 | ||||||||
\(983\) | 4.42618e10 | 1.48625 | 0.743125 | − | 0.669153i | \(-0.233343\pi\) | ||||
0.743125 | + | 0.669153i | \(0.233343\pi\) | |||||||
\(984\) | −4.05298e9 | −0.135610 | ||||||||
\(985\) | 2.48167e10 | 0.827404 | ||||||||
\(986\) | −2.87750e10 | −0.955974 | ||||||||
\(987\) | 3.80439e9 | 0.125943 | ||||||||
\(988\) | −1.11683e9 | −0.0368416 | ||||||||
\(989\) | 3.53391e10 | 1.16163 | ||||||||
\(990\) | −1.23718e10 | −0.405238 | ||||||||
\(991\) | 4.03463e10 | 1.31688 | 0.658440 | − | 0.752634i | \(-0.271217\pi\) | ||||
0.658440 | + | 0.752634i | \(0.271217\pi\) | |||||||
\(992\) | −1.03533e10 | −0.336736 | ||||||||
\(993\) | 2.48416e10 | 0.805114 | ||||||||
\(994\) | 7.55290e9 | 0.243928 | ||||||||
\(995\) | 2.39399e10 | 0.770446 | ||||||||
\(996\) | −9.48577e9 | −0.304204 | ||||||||
\(997\) | −2.59706e10 | −0.829944 | −0.414972 | − | 0.909834i | \(-0.636209\pi\) | ||||
−0.414972 | + | 0.909834i | \(0.636209\pi\) | |||||||
\(998\) | −2.83530e10 | −0.902904 | ||||||||
\(999\) | 1.05049e10 | 0.333360 |
(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 | 546.8.a.q.1.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.8.a.q.1.3 | ✓ | 6 | 1.1 | even | 1 | trivial |