Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(55.2921495107\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + \cdots + 24\!\cdots\!16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(21.8139\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 21.8139 | 1.92809 | 0.964045 | − | 0.265738i | \(-0.0856157\pi\) | ||||
0.964045 | + | 0.265738i | \(0.0856157\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 347.844 | 2.71753 | ||||||||
\(5\) | 424.937 | 1.52030 | 0.760151 | − | 0.649747i | \(-0.225125\pi\) | ||||
0.760151 | + | 0.649747i | \(0.225125\pi\) | |||||||
\(6\) | −588.974 | −1.11318 | ||||||||
\(7\) | 1192.89 | 1.31449 | 0.657243 | − | 0.753679i | \(-0.271723\pi\) | ||||
0.657243 | + | 0.753679i | \(0.271723\pi\) | |||||||
\(8\) | 4795.65 | 3.31156 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 9269.52 | 2.93128 | ||||||||
\(11\) | −3093.76 | −0.700829 | −0.350415 | − | 0.936595i | \(-0.613959\pi\) | ||||
−0.350415 | + | 0.936595i | \(0.613959\pi\) | |||||||
\(12\) | −9391.79 | −1.56897 | ||||||||
\(13\) | 1043.61 | 0.131746 | 0.0658729 | − | 0.997828i | \(-0.479017\pi\) | ||||
0.0658729 | + | 0.997828i | \(0.479017\pi\) | |||||||
\(14\) | 26021.4 | 2.53445 | ||||||||
\(15\) | −11473.3 | −0.877746 | ||||||||
\(16\) | 60087.5 | 3.66745 | ||||||||
\(17\) | −16626.4 | −0.820780 | −0.410390 | − | 0.911910i | \(-0.634607\pi\) | ||||
−0.410390 | + | 0.911910i | \(0.634607\pi\) | |||||||
\(18\) | 15902.3 | 0.642697 | ||||||||
\(19\) | 25587.3 | 0.855829 | 0.427915 | − | 0.903819i | \(-0.359248\pi\) | ||||
0.427915 | + | 0.903819i | \(0.359248\pi\) | |||||||
\(20\) | 147812. | 4.13147 | ||||||||
\(21\) | −32207.9 | −0.758919 | ||||||||
\(22\) | −67486.8 | −1.35126 | ||||||||
\(23\) | −98700.2 | −1.69149 | −0.845747 | − | 0.533584i | \(-0.820845\pi\) | ||||
−0.845747 | + | 0.533584i | \(0.820845\pi\) | |||||||
\(24\) | −129482. | −1.91193 | ||||||||
\(25\) | 102447. | 1.31132 | ||||||||
\(26\) | 22765.2 | 0.254018 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 414938. | 3.57216 | ||||||||
\(29\) | −241457. | −1.83842 | −0.919212 | − | 0.393762i | \(-0.871173\pi\) | ||||
−0.919212 | + | 0.393762i | \(0.871173\pi\) | |||||||
\(30\) | −250277. | −1.69237 | ||||||||
\(31\) | −117145. | −0.706248 | −0.353124 | − | 0.935576i | \(-0.614881\pi\) | ||||
−0.353124 | + | 0.935576i | \(0.614881\pi\) | |||||||
\(32\) | 696897. | 3.75962 | ||||||||
\(33\) | 83531.5 | 0.404624 | ||||||||
\(34\) | −362686. | −1.58254 | ||||||||
\(35\) | 506902. | 1.99841 | ||||||||
\(36\) | 253578. | 0.905844 | ||||||||
\(37\) | 73455.9 | 0.238408 | 0.119204 | − | 0.992870i | \(-0.461966\pi\) | ||||
0.119204 | + | 0.992870i | \(0.461966\pi\) | |||||||
\(38\) | 558158. | 1.65012 | ||||||||
\(39\) | −28177.5 | −0.0760635 | ||||||||
\(40\) | 2.03785e6 | 5.03457 | ||||||||
\(41\) | −333204. | −0.755035 | −0.377517 | − | 0.926003i | \(-0.623222\pi\) | ||||
−0.377517 | + | 0.926003i | \(0.623222\pi\) | |||||||
\(42\) | −702579. | −1.46326 | ||||||||
\(43\) | 608971. | 1.16804 | 0.584019 | − | 0.811740i | \(-0.301479\pi\) | ||||
0.584019 | + | 0.811740i | \(0.301479\pi\) | |||||||
\(44\) | −1.07615e6 | −1.90453 | ||||||||
\(45\) | 309779. | 0.506767 | ||||||||
\(46\) | −2.15303e6 | −3.26135 | ||||||||
\(47\) | −923874. | −1.29799 | −0.648993 | − | 0.760794i | \(-0.724810\pi\) | ||||
−0.648993 | + | 0.760794i | \(0.724810\pi\) | |||||||
\(48\) | −1.62236e6 | −2.11740 | ||||||||
\(49\) | 599434. | 0.727872 | ||||||||
\(50\) | 2.23475e6 | 2.52834 | ||||||||
\(51\) | 448913. | 0.473878 | ||||||||
\(52\) | 363014. | 0.358024 | ||||||||
\(53\) | 617858. | 0.570064 | 0.285032 | − | 0.958518i | \(-0.407996\pi\) | ||||
0.285032 | + | 0.958518i | \(0.407996\pi\) | |||||||
\(54\) | −429362. | −0.371061 | ||||||||
\(55\) | −1.31465e6 | −1.06547 | ||||||||
\(56\) | 5.72066e6 | 4.35299 | ||||||||
\(57\) | −690858. | −0.494113 | ||||||||
\(58\) | −5.26710e6 | −3.54465 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | −3.99092e6 | −2.38530 | ||||||||
\(61\) | 3.02318e6 | 1.70533 | 0.852667 | − | 0.522455i | \(-0.174984\pi\) | ||||
0.852667 | + | 0.522455i | \(0.174984\pi\) | |||||||
\(62\) | −2.55538e6 | −1.36171 | ||||||||
\(63\) | 869614. | 0.438162 | ||||||||
\(64\) | 7.51081e6 | 3.58143 | ||||||||
\(65\) | 443469. | 0.200293 | ||||||||
\(66\) | 1.82214e6 | 0.780152 | ||||||||
\(67\) | 4.24635e6 | 1.72486 | 0.862429 | − | 0.506177i | \(-0.168942\pi\) | ||||
0.862429 | + | 0.506177i | \(0.168942\pi\) | |||||||
\(68\) | −5.78339e6 | −2.23050 | ||||||||
\(69\) | 2.66490e6 | 0.976584 | ||||||||
\(70\) | 1.10575e7 | 3.85312 | ||||||||
\(71\) | 809917. | 0.268557 | 0.134278 | − | 0.990944i | \(-0.457128\pi\) | ||||
0.134278 | + | 0.990944i | \(0.457128\pi\) | |||||||
\(72\) | 3.49603e6 | 1.10385 | ||||||||
\(73\) | 1.31862e6 | 0.396726 | 0.198363 | − | 0.980129i | \(-0.436437\pi\) | ||||
0.198363 | + | 0.980129i | \(0.436437\pi\) | |||||||
\(74\) | 1.60236e6 | 0.459672 | ||||||||
\(75\) | −2.76606e6 | −0.757089 | ||||||||
\(76\) | 8.90040e6 | 2.32574 | ||||||||
\(77\) | −3.69050e6 | −0.921230 | ||||||||
\(78\) | −614660. | −0.146657 | ||||||||
\(79\) | 5.69982e6 | 1.30067 | 0.650334 | − | 0.759649i | \(-0.274629\pi\) | ||||
0.650334 | + | 0.759649i | \(0.274629\pi\) | |||||||
\(80\) | 2.55334e7 | 5.57563 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −7.26847e6 | −1.45577 | ||||||||
\(83\) | −3.55052e6 | −0.681583 | −0.340791 | − | 0.940139i | \(-0.610695\pi\) | ||||
−0.340791 | + | 0.940139i | \(0.610695\pi\) | |||||||
\(84\) | −1.12033e7 | −2.06239 | ||||||||
\(85\) | −7.06517e6 | −1.24783 | ||||||||
\(86\) | 1.32840e7 | 2.25208 | ||||||||
\(87\) | 6.51933e6 | 1.06142 | ||||||||
\(88\) | −1.48366e7 | −2.32084 | ||||||||
\(89\) | −1.13503e7 | −1.70664 | −0.853318 | − | 0.521390i | \(-0.825414\pi\) | ||||
−0.853318 | + | 0.521390i | \(0.825414\pi\) | |||||||
\(90\) | 6.75748e6 | 0.977093 | ||||||||
\(91\) | 1.24491e6 | 0.173178 | ||||||||
\(92\) | −3.43323e7 | −4.59669 | ||||||||
\(93\) | 3.16291e6 | 0.407753 | ||||||||
\(94\) | −2.01532e7 | −2.50264 | ||||||||
\(95\) | 1.08730e7 | 1.30112 | ||||||||
\(96\) | −1.88162e7 | −2.17062 | ||||||||
\(97\) | −3.73640e6 | −0.415673 | −0.207837 | − | 0.978164i | \(-0.566642\pi\) | ||||
−0.207837 | + | 0.978164i | \(0.566642\pi\) | |||||||
\(98\) | 1.30760e7 | 1.40340 | ||||||||
\(99\) | −2.25535e6 | −0.233610 | ||||||||
\(100\) | 3.56354e7 | 3.56354 | ||||||||
\(101\) | 1.81426e6 | 0.175216 | 0.0876080 | − | 0.996155i | \(-0.472078\pi\) | ||||
0.0876080 | + | 0.996155i | \(0.472078\pi\) | |||||||
\(102\) | 9.79251e6 | 0.913679 | ||||||||
\(103\) | −2.08845e7 | −1.88318 | −0.941592 | − | 0.336755i | \(-0.890671\pi\) | ||||
−0.941592 | + | 0.336755i | \(0.890671\pi\) | |||||||
\(104\) | 5.00479e6 | 0.436284 | ||||||||
\(105\) | −1.36863e7 | −1.15378 | ||||||||
\(106\) | 1.34779e7 | 1.09913 | ||||||||
\(107\) | 3.03824e6 | 0.239761 | 0.119881 | − | 0.992788i | \(-0.461749\pi\) | ||||
0.119881 | + | 0.992788i | \(0.461749\pi\) | |||||||
\(108\) | −6.84662e6 | −0.522989 | ||||||||
\(109\) | −7.65394e6 | −0.566099 | −0.283049 | − | 0.959105i | \(-0.591346\pi\) | ||||
−0.283049 | + | 0.959105i | \(0.591346\pi\) | |||||||
\(110\) | −2.86777e7 | −2.05433 | ||||||||
\(111\) | −1.98331e6 | −0.137645 | ||||||||
\(112\) | 7.16775e7 | 4.82081 | ||||||||
\(113\) | 1.47494e6 | 0.0961611 | 0.0480805 | − | 0.998843i | \(-0.484690\pi\) | ||||
0.0480805 | + | 0.998843i | \(0.484690\pi\) | |||||||
\(114\) | −1.50703e7 | −0.952695 | ||||||||
\(115\) | −4.19414e7 | −2.57158 | ||||||||
\(116\) | −8.39892e7 | −4.99598 | ||||||||
\(117\) | 760793. | 0.0439153 | ||||||||
\(118\) | −4.48011e6 | −0.251016 | ||||||||
\(119\) | −1.98334e7 | −1.07890 | ||||||||
\(120\) | −5.50219e7 | −2.90671 | ||||||||
\(121\) | −9.91582e6 | −0.508838 | ||||||||
\(122\) | 6.59472e7 | 3.28804 | ||||||||
\(123\) | 8.99651e6 | 0.435919 | ||||||||
\(124\) | −4.07482e7 | −1.91925 | ||||||||
\(125\) | 1.03351e7 | 0.473294 | ||||||||
\(126\) | 1.89696e7 | 0.844816 | ||||||||
\(127\) | −3.33858e7 | −1.44627 | −0.723134 | − | 0.690708i | \(-0.757299\pi\) | ||||
−0.723134 | + | 0.690708i | \(0.757299\pi\) | |||||||
\(128\) | 7.46368e7 | 3.14571 | ||||||||
\(129\) | −1.64422e7 | −0.674367 | ||||||||
\(130\) | 9.67377e6 | 0.386184 | ||||||||
\(131\) | 4.37782e7 | 1.70141 | 0.850704 | − | 0.525645i | \(-0.176176\pi\) | ||||
0.850704 | + | 0.525645i | \(0.176176\pi\) | |||||||
\(132\) | 2.90560e7 | 1.09958 | ||||||||
\(133\) | 3.05228e7 | 1.12498 | ||||||||
\(134\) | 9.26292e7 | 3.32568 | ||||||||
\(135\) | −8.36404e6 | −0.292582 | ||||||||
\(136\) | −7.97343e7 | −2.71806 | ||||||||
\(137\) | −2.96908e7 | −0.986507 | −0.493254 | − | 0.869886i | \(-0.664193\pi\) | ||||
−0.493254 | + | 0.869886i | \(0.664193\pi\) | |||||||
\(138\) | 5.81318e7 | 1.88294 | ||||||||
\(139\) | −6.45869e6 | −0.203983 | −0.101991 | − | 0.994785i | \(-0.532521\pi\) | ||||
−0.101991 | + | 0.994785i | \(0.532521\pi\) | |||||||
\(140\) | 1.76323e8 | 5.43076 | ||||||||
\(141\) | 2.49446e7 | 0.749393 | ||||||||
\(142\) | 1.76674e7 | 0.517802 | ||||||||
\(143\) | −3.22868e6 | −0.0923314 | ||||||||
\(144\) | 4.38038e7 | 1.22248 | ||||||||
\(145\) | −1.02604e8 | −2.79496 | ||||||||
\(146\) | 2.87643e7 | 0.764924 | ||||||||
\(147\) | −1.61847e7 | −0.420237 | ||||||||
\(148\) | 2.55512e7 | 0.647881 | ||||||||
\(149\) | 3.19641e6 | 0.0791608 | 0.0395804 | − | 0.999216i | \(-0.487398\pi\) | ||||
0.0395804 | + | 0.999216i | \(0.487398\pi\) | |||||||
\(150\) | −6.03384e7 | −1.45974 | ||||||||
\(151\) | −1.51144e7 | −0.357250 | −0.178625 | − | 0.983917i | \(-0.557165\pi\) | ||||
−0.178625 | + | 0.983917i | \(0.557165\pi\) | |||||||
\(152\) | 1.22708e8 | 2.83413 | ||||||||
\(153\) | −1.21206e7 | −0.273593 | ||||||||
\(154\) | −8.05041e7 | −1.77621 | ||||||||
\(155\) | −4.97792e7 | −1.07371 | ||||||||
\(156\) | −9.80138e6 | −0.206705 | ||||||||
\(157\) | 6.70787e7 | 1.38336 | 0.691681 | − | 0.722203i | \(-0.256870\pi\) | ||||
0.691681 | + | 0.722203i | \(0.256870\pi\) | |||||||
\(158\) | 1.24335e8 | 2.50780 | ||||||||
\(159\) | −1.66822e7 | −0.329126 | ||||||||
\(160\) | 2.96137e8 | 5.71575 | ||||||||
\(161\) | −1.17738e8 | −2.22344 | ||||||||
\(162\) | 1.15928e7 | 0.214232 | ||||||||
\(163\) | −7.17787e7 | −1.29819 | −0.649096 | − | 0.760707i | \(-0.724853\pi\) | ||||
−0.649096 | + | 0.760707i | \(0.724853\pi\) | |||||||
\(164\) | −1.15903e8 | −2.05183 | ||||||||
\(165\) | 3.54956e7 | 0.615150 | ||||||||
\(166\) | −7.74505e7 | −1.31415 | ||||||||
\(167\) | 6.81851e7 | 1.13287 | 0.566437 | − | 0.824105i | \(-0.308321\pi\) | ||||
0.566437 | + | 0.824105i | \(0.308321\pi\) | |||||||
\(168\) | −1.54458e8 | −2.51320 | ||||||||
\(169\) | −6.16594e7 | −0.982643 | ||||||||
\(170\) | −1.54119e8 | −2.40593 | ||||||||
\(171\) | 1.86532e7 | 0.285276 | ||||||||
\(172\) | 2.11827e8 | 3.17418 | ||||||||
\(173\) | 5.64546e7 | 0.828968 | 0.414484 | − | 0.910057i | \(-0.363962\pi\) | ||||
0.414484 | + | 0.910057i | \(0.363962\pi\) | |||||||
\(174\) | 1.42212e8 | 2.04650 | ||||||||
\(175\) | 1.22207e8 | 1.72371 | ||||||||
\(176\) | −1.85896e8 | −2.57026 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | −2.47593e8 | −3.29055 | ||||||||
\(179\) | 6.74593e7 | 0.879136 | 0.439568 | − | 0.898209i | \(-0.355132\pi\) | ||||
0.439568 | + | 0.898209i | \(0.355132\pi\) | |||||||
\(180\) | 1.07755e8 | 1.37716 | ||||||||
\(181\) | 2.62245e7 | 0.328724 | 0.164362 | − | 0.986400i | \(-0.447443\pi\) | ||||
0.164362 | + | 0.986400i | \(0.447443\pi\) | |||||||
\(182\) | 2.71563e7 | 0.333903 | ||||||||
\(183\) | −8.16258e7 | −0.984575 | ||||||||
\(184\) | −4.73331e8 | −5.60148 | ||||||||
\(185\) | 3.12141e7 | 0.362452 | ||||||||
\(186\) | 6.89953e7 | 0.786184 | ||||||||
\(187\) | 5.14381e7 | 0.575227 | ||||||||
\(188\) | −3.21364e8 | −3.52732 | ||||||||
\(189\) | −2.34796e7 | −0.252973 | ||||||||
\(190\) | 2.37182e8 | 2.50867 | ||||||||
\(191\) | 1.01202e8 | 1.05092 | 0.525461 | − | 0.850818i | \(-0.323893\pi\) | ||||
0.525461 | + | 0.850818i | \(0.323893\pi\) | |||||||
\(192\) | −2.02792e8 | −2.06774 | ||||||||
\(193\) | 9.77806e7 | 0.979044 | 0.489522 | − | 0.871991i | \(-0.337171\pi\) | ||||
0.489522 | + | 0.871991i | \(0.337171\pi\) | |||||||
\(194\) | −8.15052e7 | −0.801455 | ||||||||
\(195\) | −1.19737e7 | −0.115639 | ||||||||
\(196\) | 2.08510e8 | 1.97802 | ||||||||
\(197\) | −2.53181e7 | −0.235939 | −0.117969 | − | 0.993017i | \(-0.537638\pi\) | ||||
−0.117969 | + | 0.993017i | \(0.537638\pi\) | |||||||
\(198\) | −4.91979e7 | −0.450421 | ||||||||
\(199\) | 1.47608e8 | 1.32778 | 0.663888 | − | 0.747832i | \(-0.268905\pi\) | ||||
0.663888 | + | 0.747832i | \(0.268905\pi\) | |||||||
\(200\) | 4.91298e8 | 4.34250 | ||||||||
\(201\) | −1.14651e8 | −0.995848 | ||||||||
\(202\) | 3.95759e7 | 0.337832 | ||||||||
\(203\) | −2.88030e8 | −2.41658 | ||||||||
\(204\) | 1.56152e8 | 1.28778 | ||||||||
\(205\) | −1.41591e8 | −1.14788 | ||||||||
\(206\) | −4.55571e8 | −3.63095 | ||||||||
\(207\) | −7.19524e7 | −0.563831 | ||||||||
\(208\) | 6.27080e7 | 0.483171 | ||||||||
\(209\) | −7.91610e7 | −0.599790 | ||||||||
\(210\) | −2.98552e8 | −2.22460 | ||||||||
\(211\) | −1.08855e7 | −0.0797736 | −0.0398868 | − | 0.999204i | \(-0.512700\pi\) | ||||
−0.0398868 | + | 0.999204i | \(0.512700\pi\) | |||||||
\(212\) | 2.14918e8 | 1.54917 | ||||||||
\(213\) | −2.18677e7 | −0.155051 | ||||||||
\(214\) | 6.62757e7 | 0.462281 | ||||||||
\(215\) | 2.58774e8 | 1.77577 | ||||||||
\(216\) | −9.43927e7 | −0.637310 | ||||||||
\(217\) | −1.39740e8 | −0.928353 | ||||||||
\(218\) | −1.66962e8 | −1.09149 | ||||||||
\(219\) | −3.56028e7 | −0.229050 | ||||||||
\(220\) | −4.57295e8 | −2.89545 | ||||||||
\(221\) | −1.73515e7 | −0.108134 | ||||||||
\(222\) | −4.32636e7 | −0.265392 | ||||||||
\(223\) | 2.34198e8 | 1.41421 | 0.707107 | − | 0.707106i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707106i | \(0.250000\pi\) | |||||||
\(224\) | 8.31319e8 | 4.94196 | ||||||||
\(225\) | 7.46836e7 | 0.437105 | ||||||||
\(226\) | 3.21741e7 | 0.185407 | ||||||||
\(227\) | 2.70843e8 | 1.53683 | 0.768417 | − | 0.639949i | \(-0.221045\pi\) | ||||
0.768417 | + | 0.639949i | \(0.221045\pi\) | |||||||
\(228\) | −2.40311e8 | −1.34277 | ||||||||
\(229\) | 7.25435e7 | 0.399185 | 0.199592 | − | 0.979879i | \(-0.436038\pi\) | ||||
0.199592 | + | 0.979879i | \(0.436038\pi\) | |||||||
\(230\) | −9.14903e8 | −4.95824 | ||||||||
\(231\) | 9.96436e7 | 0.531872 | ||||||||
\(232\) | −1.15794e9 | −6.08805 | ||||||||
\(233\) | 6.86130e7 | 0.355354 | 0.177677 | − | 0.984089i | \(-0.443142\pi\) | ||||
0.177677 | + | 0.984089i | \(0.443142\pi\) | |||||||
\(234\) | 1.65958e7 | 0.0846727 | ||||||||
\(235\) | −3.92588e8 | −1.97333 | ||||||||
\(236\) | −7.14399e7 | −0.353793 | ||||||||
\(237\) | −1.53895e8 | −0.750941 | ||||||||
\(238\) | −4.32643e8 | −2.08022 | ||||||||
\(239\) | −1.66795e8 | −0.790298 | −0.395149 | − | 0.918617i | \(-0.629307\pi\) | ||||
−0.395149 | + | 0.918617i | \(0.629307\pi\) | |||||||
\(240\) | −6.89402e8 | −3.21909 | ||||||||
\(241\) | −1.09566e8 | −0.504213 | −0.252107 | − | 0.967699i | \(-0.581123\pi\) | ||||
−0.252107 | + | 0.967699i | \(0.581123\pi\) | |||||||
\(242\) | −2.16302e8 | −0.981086 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 1.05160e9 | 4.63430 | ||||||||
\(245\) | 2.54722e8 | 1.10659 | ||||||||
\(246\) | 1.96249e8 | 0.840492 | ||||||||
\(247\) | 2.67032e7 | 0.112752 | ||||||||
\(248\) | −5.61786e8 | −2.33878 | ||||||||
\(249\) | 9.58640e7 | 0.393512 | ||||||||
\(250\) | 2.25449e8 | 0.912554 | ||||||||
\(251\) | −2.24011e8 | −0.894154 | −0.447077 | − | 0.894496i | \(-0.647535\pi\) | ||||
−0.447077 | + | 0.894496i | \(0.647535\pi\) | |||||||
\(252\) | 3.02490e8 | 1.19072 | ||||||||
\(253\) | 3.05355e8 | 1.18545 | ||||||||
\(254\) | −7.28273e8 | −2.78853 | ||||||||
\(255\) | 1.90760e8 | 0.720437 | ||||||||
\(256\) | 6.66733e8 | 2.48378 | ||||||||
\(257\) | 4.92524e8 | 1.80993 | 0.904964 | − | 0.425489i | \(-0.139898\pi\) | ||||
0.904964 | + | 0.425489i | \(0.139898\pi\) | |||||||
\(258\) | −3.58668e8 | −1.30024 | ||||||||
\(259\) | 8.76245e7 | 0.313384 | ||||||||
\(260\) | 1.54258e8 | 0.544304 | ||||||||
\(261\) | −1.76022e8 | −0.612808 | ||||||||
\(262\) | 9.54971e8 | 3.28047 | ||||||||
\(263\) | −4.27801e8 | −1.45010 | −0.725049 | − | 0.688698i | \(-0.758183\pi\) | ||||
−0.725049 | + | 0.688698i | \(0.758183\pi\) | |||||||
\(264\) | 4.00588e8 | 1.33994 | ||||||||
\(265\) | 2.62551e8 | 0.866669 | ||||||||
\(266\) | 6.65819e8 | 2.16905 | ||||||||
\(267\) | 3.06457e8 | 0.985327 | ||||||||
\(268\) | 1.47707e9 | 4.68736 | ||||||||
\(269\) | 1.72598e8 | 0.540633 | 0.270316 | − | 0.962772i | \(-0.412872\pi\) | ||||
0.270316 | + | 0.962772i | \(0.412872\pi\) | |||||||
\(270\) | −1.82452e8 | −0.564125 | ||||||||
\(271\) | 2.54060e8 | 0.775431 | 0.387716 | − | 0.921779i | \(-0.373264\pi\) | ||||
0.387716 | + | 0.921779i | \(0.373264\pi\) | |||||||
\(272\) | −9.99038e8 | −3.01017 | ||||||||
\(273\) | −3.36126e7 | −0.0999844 | ||||||||
\(274\) | −6.47671e8 | −1.90208 | ||||||||
\(275\) | −3.16945e8 | −0.919009 | ||||||||
\(276\) | 9.26971e8 | 2.65390 | ||||||||
\(277\) | −3.42400e8 | −0.967954 | −0.483977 | − | 0.875081i | \(-0.660808\pi\) | ||||
−0.483977 | + | 0.875081i | \(0.660808\pi\) | |||||||
\(278\) | −1.40889e8 | −0.393297 | ||||||||
\(279\) | −8.53986e7 | −0.235416 | ||||||||
\(280\) | 2.43092e9 | 6.61786 | ||||||||
\(281\) | −6.48885e8 | −1.74460 | −0.872300 | − | 0.488971i | \(-0.837372\pi\) | ||||
−0.872300 | + | 0.488971i | \(0.837372\pi\) | |||||||
\(282\) | 5.44138e8 | 1.44490 | ||||||||
\(283\) | −1.70974e8 | −0.448413 | −0.224206 | − | 0.974542i | \(-0.571979\pi\) | ||||
−0.224206 | + | 0.974542i | \(0.571979\pi\) | |||||||
\(284\) | 2.81725e8 | 0.729812 | ||||||||
\(285\) | −2.93571e8 | −0.751201 | ||||||||
\(286\) | −7.04300e7 | −0.178023 | ||||||||
\(287\) | −3.97475e8 | −0.992482 | ||||||||
\(288\) | 5.08038e8 | 1.25321 | ||||||||
\(289\) | −1.33902e8 | −0.326320 | ||||||||
\(290\) | −2.23818e9 | −5.38894 | ||||||||
\(291\) | 1.00883e8 | 0.239989 | ||||||||
\(292\) | 4.58676e8 | 1.07812 | ||||||||
\(293\) | −7.65359e8 | −1.77758 | −0.888789 | − | 0.458316i | \(-0.848453\pi\) | ||||
−0.888789 | + | 0.458316i | \(0.848453\pi\) | |||||||
\(294\) | −3.53051e8 | −0.810255 | ||||||||
\(295\) | −8.72732e7 | −0.197926 | ||||||||
\(296\) | 3.52268e8 | 0.789501 | ||||||||
\(297\) | 6.08945e7 | 0.134875 | ||||||||
\(298\) | 6.97260e7 | 0.152629 | ||||||||
\(299\) | −1.03005e8 | −0.222847 | ||||||||
\(300\) | −9.62157e8 | −2.05741 | ||||||||
\(301\) | 7.26433e8 | 1.53537 | ||||||||
\(302\) | −3.29704e8 | −0.688811 | ||||||||
\(303\) | −4.89849e7 | −0.101161 | ||||||||
\(304\) | 1.53748e9 | 3.13871 | ||||||||
\(305\) | 1.28466e9 | 2.59262 | ||||||||
\(306\) | −2.64398e8 | −0.527513 | ||||||||
\(307\) | 1.89113e8 | 0.373024 | 0.186512 | − | 0.982453i | \(-0.440282\pi\) | ||||
0.186512 | + | 0.982453i | \(0.440282\pi\) | |||||||
\(308\) | −1.28372e9 | −2.50347 | ||||||||
\(309\) | 5.63880e8 | 1.08726 | ||||||||
\(310\) | −1.08588e9 | −2.07021 | ||||||||
\(311\) | 2.41634e8 | 0.455508 | 0.227754 | − | 0.973719i | \(-0.426862\pi\) | ||||
0.227754 | + | 0.973719i | \(0.426862\pi\) | |||||||
\(312\) | −1.35129e8 | −0.251889 | ||||||||
\(313\) | −4.22149e8 | −0.778145 | −0.389073 | − | 0.921207i | \(-0.627204\pi\) | ||||
−0.389073 | + | 0.921207i | \(0.627204\pi\) | |||||||
\(314\) | 1.46325e9 | 2.66725 | ||||||||
\(315\) | 3.69531e8 | 0.666138 | ||||||||
\(316\) | 1.98265e9 | 3.53461 | ||||||||
\(317\) | 1.02142e9 | 1.80093 | 0.900467 | − | 0.434925i | \(-0.143225\pi\) | ||||
0.900467 | + | 0.434925i | \(0.143225\pi\) | |||||||
\(318\) | −3.63903e8 | −0.634586 | ||||||||
\(319\) | 7.47008e8 | 1.28842 | ||||||||
\(320\) | 3.19162e9 | 5.44486 | ||||||||
\(321\) | −8.20324e7 | −0.138426 | ||||||||
\(322\) | −2.56832e9 | −4.28700 | ||||||||
\(323\) | −4.25425e8 | −0.702448 | ||||||||
\(324\) | 1.84859e8 | 0.301948 | ||||||||
\(325\) | 1.06914e8 | 0.172760 | ||||||||
\(326\) | −1.56577e9 | −2.50303 | ||||||||
\(327\) | 2.06656e8 | 0.326837 | ||||||||
\(328\) | −1.59793e9 | −2.50034 | ||||||||
\(329\) | −1.10208e9 | −1.70618 | ||||||||
\(330\) | 7.74297e8 | 1.18607 | ||||||||
\(331\) | 8.62048e8 | 1.30657 | 0.653286 | − | 0.757111i | \(-0.273390\pi\) | ||||
0.653286 | + | 0.757111i | \(0.273390\pi\) | |||||||
\(332\) | −1.23503e9 | −1.85222 | ||||||||
\(333\) | 5.35493e7 | 0.0794693 | ||||||||
\(334\) | 1.48738e9 | 2.18428 | ||||||||
\(335\) | 1.80443e9 | 2.62231 | ||||||||
\(336\) | −1.93529e9 | −2.78330 | ||||||||
\(337\) | −9.09270e8 | −1.29416 | −0.647080 | − | 0.762422i | \(-0.724010\pi\) | ||||
−0.647080 | + | 0.762422i | \(0.724010\pi\) | |||||||
\(338\) | −1.34503e9 | −1.89462 | ||||||||
\(339\) | −3.98233e7 | −0.0555186 | ||||||||
\(340\) | −2.45758e9 | −3.39103 | ||||||||
\(341\) | 3.62418e8 | 0.494959 | ||||||||
\(342\) | 4.06897e8 | 0.550039 | ||||||||
\(343\) | −2.67336e8 | −0.357708 | ||||||||
\(344\) | 2.92041e9 | 3.86803 | ||||||||
\(345\) | 1.13242e9 | 1.48470 | ||||||||
\(346\) | 1.23149e9 | 1.59833 | ||||||||
\(347\) | 4.58759e8 | 0.589428 | 0.294714 | − | 0.955585i | \(-0.404776\pi\) | ||||
0.294714 | + | 0.955585i | \(0.404776\pi\) | |||||||
\(348\) | 2.26771e9 | 2.88443 | ||||||||
\(349\) | −9.57438e8 | −1.20565 | −0.602826 | − | 0.797873i | \(-0.705959\pi\) | ||||
−0.602826 | + | 0.797873i | \(0.705959\pi\) | |||||||
\(350\) | 2.66581e9 | 3.32346 | ||||||||
\(351\) | −2.05414e7 | −0.0253545 | ||||||||
\(352\) | −2.15603e9 | −2.63485 | ||||||||
\(353\) | 3.43926e8 | 0.416154 | 0.208077 | − | 0.978112i | \(-0.433280\pi\) | ||||
0.208077 | + | 0.978112i | \(0.433280\pi\) | |||||||
\(354\) | 1.20963e8 | 0.144924 | ||||||||
\(355\) | 3.44164e8 | 0.408287 | ||||||||
\(356\) | −3.94812e9 | −4.63784 | ||||||||
\(357\) | 5.35501e8 | 0.622905 | ||||||||
\(358\) | 1.47155e9 | 1.69505 | ||||||||
\(359\) | −9.03951e8 | −1.03113 | −0.515566 | − | 0.856850i | \(-0.672418\pi\) | ||||
−0.515566 | + | 0.856850i | \(0.672418\pi\) | |||||||
\(360\) | 1.48559e9 | 1.67819 | ||||||||
\(361\) | −2.39161e8 | −0.267556 | ||||||||
\(362\) | 5.72057e8 | 0.633810 | ||||||||
\(363\) | 2.67727e8 | 0.293778 | ||||||||
\(364\) | 4.33034e8 | 0.470617 | ||||||||
\(365\) | 5.60332e8 | 0.603144 | ||||||||
\(366\) | −1.78057e9 | −1.89835 | ||||||||
\(367\) | 1.55115e9 | 1.63804 | 0.819019 | − | 0.573767i | \(-0.194518\pi\) | ||||
0.819019 | + | 0.573767i | \(0.194518\pi\) | |||||||
\(368\) | −5.93065e9 | −6.20347 | ||||||||
\(369\) | −2.42906e8 | −0.251678 | ||||||||
\(370\) | 6.80900e8 | 0.698840 | ||||||||
\(371\) | 7.37035e8 | 0.749341 | ||||||||
\(372\) | 1.10020e9 | 1.10808 | ||||||||
\(373\) | −1.60756e9 | −1.60393 | −0.801967 | − | 0.597368i | \(-0.796213\pi\) | ||||
−0.801967 | + | 0.597368i | \(0.796213\pi\) | |||||||
\(374\) | 1.12206e9 | 1.10909 | ||||||||
\(375\) | −2.79049e8 | −0.273257 | ||||||||
\(376\) | −4.43057e9 | −4.29836 | ||||||||
\(377\) | −2.51987e8 | −0.242205 | ||||||||
\(378\) | −5.12180e8 | −0.487755 | ||||||||
\(379\) | 5.29474e8 | 0.499583 | 0.249791 | − | 0.968300i | \(-0.419638\pi\) | ||||
0.249791 | + | 0.968300i | \(0.419638\pi\) | |||||||
\(380\) | 3.78211e9 | 3.53583 | ||||||||
\(381\) | 9.01416e8 | 0.835003 | ||||||||
\(382\) | 2.20760e9 | 2.02627 | ||||||||
\(383\) | −1.13814e9 | −1.03515 | −0.517573 | − | 0.855639i | \(-0.673164\pi\) | ||||
−0.517573 | + | 0.855639i | \(0.673164\pi\) | |||||||
\(384\) | −2.01519e9 | −1.81617 | ||||||||
\(385\) | −1.56823e9 | −1.40055 | ||||||||
\(386\) | 2.13297e9 | 1.88769 | ||||||||
\(387\) | 4.43940e8 | 0.389346 | ||||||||
\(388\) | −1.29968e9 | −1.12961 | ||||||||
\(389\) | −8.63651e8 | −0.743900 | −0.371950 | − | 0.928253i | \(-0.621311\pi\) | ||||
−0.371950 | + | 0.928253i | \(0.621311\pi\) | |||||||
\(390\) | −2.61192e8 | −0.222963 | ||||||||
\(391\) | 1.64103e9 | 1.38834 | ||||||||
\(392\) | 2.87467e9 | 2.41039 | ||||||||
\(393\) | −1.18201e9 | −0.982308 | ||||||||
\(394\) | −5.52285e8 | −0.454911 | ||||||||
\(395\) | 2.42206e9 | 1.97741 | ||||||||
\(396\) | −7.84511e8 | −0.634842 | ||||||||
\(397\) | 3.54481e7 | 0.0284332 | 0.0142166 | − | 0.999899i | \(-0.495475\pi\) | ||||
0.0142166 | + | 0.999899i | \(0.495475\pi\) | |||||||
\(398\) | 3.21991e9 | 2.56007 | ||||||||
\(399\) | −8.24114e8 | −0.649505 | ||||||||
\(400\) | 6.15576e9 | 4.80919 | ||||||||
\(401\) | 2.17381e8 | 0.168351 | 0.0841756 | − | 0.996451i | \(-0.473174\pi\) | ||||
0.0841756 | + | 0.996451i | \(0.473174\pi\) | |||||||
\(402\) | −2.50099e9 | −1.92008 | ||||||||
\(403\) | −1.22254e8 | −0.0930453 | ||||||||
\(404\) | 6.31078e8 | 0.476155 | ||||||||
\(405\) | 2.25829e8 | 0.168922 | ||||||||
\(406\) | −6.28305e9 | −4.65939 | ||||||||
\(407\) | −2.27255e8 | −0.167083 | ||||||||
\(408\) | 2.15283e9 | 1.56927 | ||||||||
\(409\) | 2.43499e9 | 1.75981 | 0.879904 | − | 0.475151i | \(-0.157607\pi\) | ||||
0.879904 | + | 0.475151i | \(0.157607\pi\) | |||||||
\(410\) | −3.08864e9 | −2.21322 | ||||||||
\(411\) | 8.01652e8 | 0.569560 | ||||||||
\(412\) | −7.26454e9 | −5.11762 | ||||||||
\(413\) | −2.44994e8 | −0.171131 | ||||||||
\(414\) | −1.56956e9 | −1.08712 | ||||||||
\(415\) | −1.50875e9 | −1.03621 | ||||||||
\(416\) | 7.27290e8 | 0.495314 | ||||||||
\(417\) | 1.74385e8 | 0.117769 | ||||||||
\(418\) | −1.72681e9 | −1.15645 | ||||||||
\(419\) | −4.11950e8 | −0.273587 | −0.136794 | − | 0.990600i | \(-0.543680\pi\) | ||||
−0.136794 | + | 0.990600i | \(0.543680\pi\) | |||||||
\(420\) | −4.76071e9 | −3.13545 | ||||||||
\(421\) | −1.54001e9 | −1.00585 | −0.502927 | − | 0.864329i | \(-0.667744\pi\) | ||||
−0.502927 | + | 0.864329i | \(0.667744\pi\) | |||||||
\(422\) | −2.37454e8 | −0.153811 | ||||||||
\(423\) | −6.73504e8 | −0.432662 | ||||||||
\(424\) | 2.96303e9 | 1.88780 | ||||||||
\(425\) | −1.70332e9 | −1.07630 | ||||||||
\(426\) | −4.77020e8 | −0.298953 | ||||||||
\(427\) | 3.60631e9 | 2.24164 | ||||||||
\(428\) | 1.05683e9 | 0.651559 | ||||||||
\(429\) | 8.71744e7 | 0.0533075 | ||||||||
\(430\) | 5.64487e9 | 3.42385 | ||||||||
\(431\) | 2.03052e9 | 1.22162 | 0.610811 | − | 0.791776i | \(-0.290843\pi\) | ||||
0.610811 | + | 0.791776i | \(0.290843\pi\) | |||||||
\(432\) | −1.18270e9 | −0.705801 | ||||||||
\(433\) | 6.40897e8 | 0.379385 | 0.189693 | − | 0.981844i | \(-0.439251\pi\) | ||||
0.189693 | + | 0.981844i | \(0.439251\pi\) | |||||||
\(434\) | −3.04828e9 | −1.78995 | ||||||||
\(435\) | 2.77030e9 | 1.61367 | ||||||||
\(436\) | −2.66238e9 | −1.53839 | ||||||||
\(437\) | −2.52547e9 | −1.44763 | ||||||||
\(438\) | −7.76635e8 | −0.441629 | ||||||||
\(439\) | −4.52255e8 | −0.255128 | −0.127564 | − | 0.991830i | \(-0.540716\pi\) | ||||
−0.127564 | + | 0.991830i | \(0.540716\pi\) | |||||||
\(440\) | −6.30462e9 | −3.52837 | ||||||||
\(441\) | 4.36987e8 | 0.242624 | ||||||||
\(442\) | −3.78503e8 | −0.208493 | ||||||||
\(443\) | 1.95166e9 | 1.06657 | 0.533287 | − | 0.845935i | \(-0.320957\pi\) | ||||
0.533287 | + | 0.845935i | \(0.320957\pi\) | |||||||
\(444\) | −6.89882e8 | −0.374054 | ||||||||
\(445\) | −4.82315e9 | −2.59460 | ||||||||
\(446\) | 5.10875e9 | 2.72673 | ||||||||
\(447\) | −8.63030e7 | −0.0457035 | ||||||||
\(448\) | 8.95954e9 | 4.70774 | ||||||||
\(449\) | −7.36502e8 | −0.383983 | −0.191991 | − | 0.981397i | \(-0.561495\pi\) | ||||
−0.191991 | + | 0.981397i | \(0.561495\pi\) | |||||||
\(450\) | 1.62914e9 | 0.842779 | ||||||||
\(451\) | 1.03085e9 | 0.529150 | ||||||||
\(452\) | 5.13049e8 | 0.261321 | ||||||||
\(453\) | 4.08090e8 | 0.206259 | ||||||||
\(454\) | 5.90813e9 | 2.96316 | ||||||||
\(455\) | 5.29008e8 | 0.263283 | ||||||||
\(456\) | −3.31311e9 | −1.63628 | ||||||||
\(457\) | 8.44943e8 | 0.414115 | 0.207057 | − | 0.978329i | \(-0.433611\pi\) | ||||
0.207057 | + | 0.978329i | \(0.433611\pi\) | |||||||
\(458\) | 1.58245e9 | 0.769664 | ||||||||
\(459\) | 3.27257e8 | 0.157959 | ||||||||
\(460\) | −1.45891e10 | −6.98835 | ||||||||
\(461\) | 2.59377e8 | 0.123305 | 0.0616523 | − | 0.998098i | \(-0.480363\pi\) | ||||
0.0616523 | + | 0.998098i | \(0.480363\pi\) | |||||||
\(462\) | 2.17361e9 | 1.02550 | ||||||||
\(463\) | 4.01914e8 | 0.188191 | 0.0940957 | − | 0.995563i | \(-0.470004\pi\) | ||||
0.0940957 | + | 0.995563i | \(0.470004\pi\) | |||||||
\(464\) | −1.45085e10 | −6.74233 | ||||||||
\(465\) | 1.34404e9 | 0.619907 | ||||||||
\(466\) | 1.49671e9 | 0.685154 | ||||||||
\(467\) | −3.10097e9 | −1.40893 | −0.704463 | − | 0.709740i | \(-0.748812\pi\) | ||||
−0.704463 | + | 0.709740i | \(0.748812\pi\) | |||||||
\(468\) | 2.64637e8 | 0.119341 | ||||||||
\(469\) | 5.06541e9 | 2.26730 | ||||||||
\(470\) | −8.56386e9 | −3.80476 | ||||||||
\(471\) | −1.81113e9 | −0.798685 | ||||||||
\(472\) | −9.84925e8 | −0.431128 | ||||||||
\(473\) | −1.88401e9 | −0.818596 | ||||||||
\(474\) | −3.35705e9 | −1.44788 | ||||||||
\(475\) | 2.62133e9 | 1.12226 | ||||||||
\(476\) | −6.89893e9 | −2.93195 | ||||||||
\(477\) | 4.50419e8 | 0.190021 | ||||||||
\(478\) | −3.63844e9 | −1.52377 | ||||||||
\(479\) | 3.79632e9 | 1.57829 | 0.789147 | − | 0.614204i | \(-0.210523\pi\) | ||||
0.789147 | + | 0.614204i | \(0.210523\pi\) | |||||||
\(480\) | −7.99571e9 | −3.29999 | ||||||||
\(481\) | 7.66594e7 | 0.0314092 | ||||||||
\(482\) | −2.39005e9 | −0.972169 | ||||||||
\(483\) | 3.17893e9 | 1.28371 | ||||||||
\(484\) | −3.44916e9 | −1.38278 | ||||||||
\(485\) | −1.58773e9 | −0.631948 | ||||||||
\(486\) | −3.13005e8 | −0.123687 | ||||||||
\(487\) | 7.82358e6 | 0.00306940 | 0.00153470 | − | 0.999999i | \(-0.499511\pi\) | ||||
0.00153470 | + | 0.999999i | \(0.499511\pi\) | |||||||
\(488\) | 1.44981e10 | 5.64731 | ||||||||
\(489\) | 1.93802e9 | 0.749511 | ||||||||
\(490\) | 5.55646e9 | 2.13360 | ||||||||
\(491\) | −2.48479e9 | −0.947336 | −0.473668 | − | 0.880704i | \(-0.657070\pi\) | ||||
−0.473668 | + | 0.880704i | \(0.657070\pi\) | |||||||
\(492\) | 3.12938e9 | 1.18463 | ||||||||
\(493\) | 4.01455e9 | 1.50894 | ||||||||
\(494\) | 5.82500e8 | 0.217396 | ||||||||
\(495\) | −9.58382e8 | −0.355157 | ||||||||
\(496\) | −7.03894e9 | −2.59013 | ||||||||
\(497\) | 9.66138e8 | 0.353014 | ||||||||
\(498\) | 2.09116e9 | 0.758727 | ||||||||
\(499\) | 3.32153e9 | 1.19670 | 0.598352 | − | 0.801234i | \(-0.295823\pi\) | ||||
0.598352 | + | 0.801234i | \(0.295823\pi\) | |||||||
\(500\) | 3.59502e9 | 1.28619 | ||||||||
\(501\) | −1.84100e9 | −0.654065 | ||||||||
\(502\) | −4.88655e9 | −1.72401 | ||||||||
\(503\) | 2.45772e9 | 0.861082 | 0.430541 | − | 0.902571i | \(-0.358323\pi\) | ||||
0.430541 | + | 0.902571i | \(0.358323\pi\) | |||||||
\(504\) | 4.17036e9 | 1.45100 | ||||||||
\(505\) | 7.70945e8 | 0.266381 | ||||||||
\(506\) | 6.66096e9 | 2.28565 | ||||||||
\(507\) | 1.66480e9 | 0.567329 | ||||||||
\(508\) | −1.16131e10 | −3.93028 | ||||||||
\(509\) | −4.91205e8 | −0.165101 | −0.0825507 | − | 0.996587i | \(-0.526307\pi\) | ||||
−0.0825507 | + | 0.996587i | \(0.526307\pi\) | |||||||
\(510\) | 4.16120e9 | 1.38907 | ||||||||
\(511\) | 1.57297e9 | 0.521491 | ||||||||
\(512\) | 4.99051e9 | 1.64324 | ||||||||
\(513\) | −5.03635e8 | −0.164704 | ||||||||
\(514\) | 1.07438e10 | 3.48970 | ||||||||
\(515\) | −8.87458e9 | −2.86301 | ||||||||
\(516\) | −5.71933e9 | −1.83262 | ||||||||
\(517\) | 2.85824e9 | 0.909667 | ||||||||
\(518\) | 1.91143e9 | 0.604232 | ||||||||
\(519\) | −1.52427e9 | −0.478605 | ||||||||
\(520\) | 2.12672e9 | 0.663283 | ||||||||
\(521\) | 3.12235e9 | 0.967275 | 0.483638 | − | 0.875268i | \(-0.339315\pi\) | ||||
0.483638 | + | 0.875268i | \(0.339315\pi\) | |||||||
\(522\) | −3.83971e9 | −1.18155 | ||||||||
\(523\) | 1.24953e9 | 0.381938 | 0.190969 | − | 0.981596i | \(-0.438837\pi\) | ||||
0.190969 | + | 0.981596i | \(0.438837\pi\) | |||||||
\(524\) | 1.52280e10 | 4.62363 | ||||||||
\(525\) | −3.29959e9 | −0.995182 | ||||||||
\(526\) | −9.33200e9 | −2.79592 | ||||||||
\(527\) | 1.94770e9 | 0.579674 | ||||||||
\(528\) | 5.01920e9 | 1.48394 | ||||||||
\(529\) | 6.33690e9 | 1.86115 | ||||||||
\(530\) | 5.72725e9 | 1.67102 | ||||||||
\(531\) | −1.49721e8 | −0.0433963 | ||||||||
\(532\) | 1.06172e10 | 3.05716 | ||||||||
\(533\) | −3.47736e8 | −0.0994727 | ||||||||
\(534\) | 6.68501e9 | 1.89980 | ||||||||
\(535\) | 1.29106e9 | 0.364509 | ||||||||
\(536\) | 2.03640e10 | 5.71197 | ||||||||
\(537\) | −1.82140e9 | −0.507569 | ||||||||
\(538\) | 3.76502e9 | 1.04239 | ||||||||
\(539\) | −1.85451e9 | −0.510114 | ||||||||
\(540\) | −2.90938e9 | −0.795101 | ||||||||
\(541\) | 8.58513e8 | 0.233108 | 0.116554 | − | 0.993184i | \(-0.462815\pi\) | ||||
0.116554 | + | 0.993184i | \(0.462815\pi\) | |||||||
\(542\) | 5.54202e9 | 1.49510 | ||||||||
\(543\) | −7.08061e8 | −0.189789 | ||||||||
\(544\) | −1.15869e10 | −3.08582 | ||||||||
\(545\) | −3.25244e9 | −0.860641 | ||||||||
\(546\) | −7.33219e8 | −0.192779 | ||||||||
\(547\) | 6.72132e9 | 1.75590 | 0.877948 | − | 0.478755i | \(-0.158912\pi\) | ||||
0.877948 | + | 0.478755i | \(0.158912\pi\) | |||||||
\(548\) | −1.03278e10 | −2.68087 | ||||||||
\(549\) | 2.20390e9 | 0.568445 | ||||||||
\(550\) | −6.91379e9 | −1.77193 | ||||||||
\(551\) | −6.17823e9 | −1.57338 | ||||||||
\(552\) | 1.27799e10 | 3.23402 | ||||||||
\(553\) | 6.79923e9 | 1.70971 | ||||||||
\(554\) | −7.46907e9 | −1.86630 | ||||||||
\(555\) | −8.42781e8 | −0.209262 | ||||||||
\(556\) | −2.24662e9 | −0.554329 | ||||||||
\(557\) | −2.12425e9 | −0.520850 | −0.260425 | − | 0.965494i | \(-0.583863\pi\) | ||||
−0.260425 | + | 0.965494i | \(0.583863\pi\) | |||||||
\(558\) | −1.86287e9 | −0.453903 | ||||||||
\(559\) | 6.35529e8 | 0.153884 | ||||||||
\(560\) | 3.04584e10 | 7.32908 | ||||||||
\(561\) | −1.38883e9 | −0.332107 | ||||||||
\(562\) | −1.41547e10 | −3.36375 | ||||||||
\(563\) | 1.69196e9 | 0.399587 | 0.199793 | − | 0.979838i | \(-0.435973\pi\) | ||||
0.199793 | + | 0.979838i | \(0.435973\pi\) | |||||||
\(564\) | 8.67683e9 | 2.03650 | ||||||||
\(565\) | 6.26756e8 | 0.146194 | ||||||||
\(566\) | −3.72961e9 | −0.864580 | ||||||||
\(567\) | 6.33949e8 | 0.146054 | ||||||||
\(568\) | 3.88407e9 | 0.889341 | ||||||||
\(569\) | −7.54396e8 | −0.171675 | −0.0858374 | − | 0.996309i | \(-0.527357\pi\) | ||||
−0.0858374 | + | 0.996309i | \(0.527357\pi\) | |||||||
\(570\) | −6.40392e9 | −1.44838 | ||||||||
\(571\) | −3.56448e9 | −0.801254 | −0.400627 | − | 0.916241i | \(-0.631208\pi\) | ||||
−0.400627 | + | 0.916241i | \(0.631208\pi\) | |||||||
\(572\) | −1.12308e9 | −0.250913 | ||||||||
\(573\) | −2.73244e9 | −0.606750 | ||||||||
\(574\) | −8.67045e9 | −1.91360 | ||||||||
\(575\) | −1.01115e10 | −2.21808 | ||||||||
\(576\) | 5.47538e9 | 1.19381 | ||||||||
\(577\) | −6.20845e9 | −1.34545 | −0.672725 | − | 0.739892i | \(-0.734876\pi\) | ||||
−0.672725 | + | 0.739892i | \(0.734876\pi\) | |||||||
\(578\) | −2.92091e9 | −0.629175 | ||||||||
\(579\) | −2.64008e9 | −0.565251 | ||||||||
\(580\) | −3.56901e10 | −7.59539 | ||||||||
\(581\) | −4.23537e9 | −0.895931 | ||||||||
\(582\) | 2.20064e9 | 0.462720 | ||||||||
\(583\) | −1.91151e9 | −0.399517 | ||||||||
\(584\) | 6.32366e9 | 1.31378 | ||||||||
\(585\) | 3.23289e8 | 0.0667645 | ||||||||
\(586\) | −1.66954e10 | −3.42733 | ||||||||
\(587\) | −1.55164e9 | −0.316635 | −0.158317 | − | 0.987388i | \(-0.550607\pi\) | ||||
−0.158317 | + | 0.987388i | \(0.550607\pi\) | |||||||
\(588\) | −5.62976e9 | −1.14201 | ||||||||
\(589\) | −2.99742e9 | −0.604428 | ||||||||
\(590\) | −1.90376e9 | −0.381620 | ||||||||
\(591\) | 6.83589e8 | 0.136219 | ||||||||
\(592\) | 4.41378e9 | 0.874349 | ||||||||
\(593\) | 6.42351e9 | 1.26497 | 0.632486 | − | 0.774572i | \(-0.282035\pi\) | ||||
0.632486 | + | 0.774572i | \(0.282035\pi\) | |||||||
\(594\) | 1.32834e9 | 0.260051 | ||||||||
\(595\) | −8.42794e9 | −1.64026 | ||||||||
\(596\) | 1.11185e9 | 0.215122 | ||||||||
\(597\) | −3.98543e9 | −0.766592 | ||||||||
\(598\) | −2.24693e9 | −0.429670 | ||||||||
\(599\) | −3.92988e9 | −0.747111 | −0.373556 | − | 0.927608i | \(-0.621861\pi\) | ||||
−0.373556 | + | 0.927608i | \(0.621861\pi\) | |||||||
\(600\) | −1.32650e10 | −2.50714 | ||||||||
\(601\) | −5.05280e9 | −0.949448 | −0.474724 | − | 0.880135i | \(-0.657452\pi\) | ||||
−0.474724 | + | 0.880135i | \(0.657452\pi\) | |||||||
\(602\) | 1.58463e10 | 2.96033 | ||||||||
\(603\) | 3.09559e9 | 0.574953 | ||||||||
\(604\) | −5.25747e9 | −0.970839 | ||||||||
\(605\) | −4.21360e9 | −0.773588 | ||||||||
\(606\) | −1.06855e9 | −0.195048 | ||||||||
\(607\) | −7.19598e9 | −1.30596 | −0.652979 | − | 0.757376i | \(-0.726481\pi\) | ||||
−0.652979 | + | 0.757376i | \(0.726481\pi\) | |||||||
\(608\) | 1.78317e10 | 3.21759 | ||||||||
\(609\) | 7.77681e9 | 1.39521 | ||||||||
\(610\) | 2.80234e10 | 4.99881 | ||||||||
\(611\) | −9.64165e8 | −0.171004 | ||||||||
\(612\) | −4.21609e9 | −0.743499 | ||||||||
\(613\) | −4.01935e9 | −0.704765 | −0.352383 | − | 0.935856i | \(-0.614628\pi\) | ||||
−0.352383 | + | 0.935856i | \(0.614628\pi\) | |||||||
\(614\) | 4.12528e9 | 0.719223 | ||||||||
\(615\) | 3.82295e9 | 0.662729 | ||||||||
\(616\) | −1.76984e10 | −3.05071 | ||||||||
\(617\) | 2.76235e9 | 0.473458 | 0.236729 | − | 0.971576i | \(-0.423925\pi\) | ||||
0.236729 | + | 0.971576i | \(0.423925\pi\) | |||||||
\(618\) | 1.23004e10 | 2.09633 | ||||||||
\(619\) | 6.94825e9 | 1.17749 | 0.588746 | − | 0.808318i | \(-0.299622\pi\) | ||||
0.588746 | + | 0.808318i | \(0.299622\pi\) | |||||||
\(620\) | −1.73154e10 | −2.91784 | ||||||||
\(621\) | 1.94272e9 | 0.325528 | ||||||||
\(622\) | 5.27096e9 | 0.878261 | ||||||||
\(623\) | −1.35396e10 | −2.24335 | ||||||||
\(624\) | −1.69312e9 | −0.278959 | ||||||||
\(625\) | −3.61185e9 | −0.591766 | ||||||||
\(626\) | −9.20870e9 | −1.50033 | ||||||||
\(627\) | 2.13735e9 | 0.346289 | ||||||||
\(628\) | 2.33329e10 | 3.75933 | ||||||||
\(629\) | −1.22131e9 | −0.195680 | ||||||||
\(630\) | 8.06090e9 | 1.28437 | ||||||||
\(631\) | 4.84723e9 | 0.768052 | 0.384026 | − | 0.923322i | \(-0.374537\pi\) | ||||
0.384026 | + | 0.923322i | \(0.374537\pi\) | |||||||
\(632\) | 2.73343e10 | 4.30723 | ||||||||
\(633\) | 2.93908e8 | 0.0460573 | ||||||||
\(634\) | 2.22811e10 | 3.47236 | ||||||||
\(635\) | −1.41869e10 | −2.19876 | ||||||||
\(636\) | −5.80280e9 | −0.894412 | ||||||||
\(637\) | 6.25576e8 | 0.0958942 | ||||||||
\(638\) | 1.62951e10 | 2.48419 | ||||||||
\(639\) | 5.90429e8 | 0.0895189 | ||||||||
\(640\) | 3.17160e10 | 4.78242 | ||||||||
\(641\) | −1.40292e9 | −0.210393 | −0.105196 | − | 0.994451i | \(-0.533547\pi\) | ||||
−0.105196 | + | 0.994451i | \(0.533547\pi\) | |||||||
\(642\) | −1.78944e9 | −0.266898 | ||||||||
\(643\) | −8.62484e9 | −1.27942 | −0.639709 | − | 0.768617i | \(-0.720945\pi\) | ||||
−0.639709 | + | 0.768617i | \(0.720945\pi\) | |||||||
\(644\) | −4.09545e10 | −6.04228 | ||||||||
\(645\) | −6.98691e9 | −1.02524 | ||||||||
\(646\) | −9.28015e9 | −1.35438 | ||||||||
\(647\) | −2.56483e9 | −0.372300 | −0.186150 | − | 0.982521i | \(-0.559601\pi\) | ||||
−0.186150 | + | 0.982521i | \(0.559601\pi\) | |||||||
\(648\) | 2.54860e9 | 0.367951 | ||||||||
\(649\) | 6.35393e8 | 0.0912402 | ||||||||
\(650\) | 2.33221e9 | 0.333098 | ||||||||
\(651\) | 3.77299e9 | 0.535985 | ||||||||
\(652\) | −2.49678e10 | −3.52788 | ||||||||
\(653\) | −2.05512e9 | −0.288829 | −0.144414 | − | 0.989517i | \(-0.546130\pi\) | ||||
−0.144414 | + | 0.989517i | \(0.546130\pi\) | |||||||
\(654\) | 4.50797e9 | 0.630172 | ||||||||
\(655\) | 1.86030e10 | 2.58665 | ||||||||
\(656\) | −2.00214e10 | −2.76905 | ||||||||
\(657\) | 9.61277e8 | 0.132242 | ||||||||
\(658\) | −2.40405e10 | −3.28968 | ||||||||
\(659\) | −7.82229e9 | −1.06472 | −0.532360 | − | 0.846518i | \(-0.678695\pi\) | ||||
−0.532360 | + | 0.846518i | \(0.678695\pi\) | |||||||
\(660\) | 1.23470e10 | 1.67169 | ||||||||
\(661\) | −4.59162e8 | −0.0618388 | −0.0309194 | − | 0.999522i | \(-0.509844\pi\) | ||||
−0.0309194 | + | 0.999522i | \(0.509844\pi\) | |||||||
\(662\) | 1.88046e10 | 2.51919 | ||||||||
\(663\) | 4.68490e8 | 0.0624314 | ||||||||
\(664\) | −1.70270e10 | −2.25710 | ||||||||
\(665\) | 1.29703e10 | 1.71030 | ||||||||
\(666\) | 1.16812e9 | 0.153224 | ||||||||
\(667\) | 2.38318e10 | 3.10968 | ||||||||
\(668\) | 2.37178e10 | 3.07862 | ||||||||
\(669\) | −6.32333e9 | −0.816497 | ||||||||
\(670\) | 3.93616e10 | 5.05604 | ||||||||
\(671\) | −9.35299e9 | −1.19515 | ||||||||
\(672\) | −2.24456e10 | −2.85324 | ||||||||
\(673\) | −6.96032e9 | −0.880190 | −0.440095 | − | 0.897951i | \(-0.645055\pi\) | ||||
−0.440095 | + | 0.897951i | \(0.645055\pi\) | |||||||
\(674\) | −1.98347e10 | −2.49526 | ||||||||
\(675\) | −2.01646e9 | −0.252363 | ||||||||
\(676\) | −2.14479e10 | −2.67036 | ||||||||
\(677\) | 1.09451e10 | 1.35568 | 0.677842 | − | 0.735208i | \(-0.262915\pi\) | ||||
0.677842 | + | 0.735208i | \(0.262915\pi\) | |||||||
\(678\) | −8.68700e8 | −0.107045 | ||||||||
\(679\) | −4.45710e9 | −0.546396 | ||||||||
\(680\) | −3.38821e10 | −4.13227 | ||||||||
\(681\) | −7.31276e9 | −0.887292 | ||||||||
\(682\) | 7.90574e9 | 0.954326 | ||||||||
\(683\) | 2.98731e9 | 0.358763 | 0.179382 | − | 0.983780i | \(-0.442590\pi\) | ||||
0.179382 | + | 0.983780i | \(0.442590\pi\) | |||||||
\(684\) | 6.48839e9 | 0.775248 | ||||||||
\(685\) | −1.26167e10 | −1.49979 | ||||||||
\(686\) | −5.83164e9 | −0.689693 | ||||||||
\(687\) | −1.95867e9 | −0.230469 | ||||||||
\(688\) | 3.65916e10 | 4.28372 | ||||||||
\(689\) | 6.44804e8 | 0.0751036 | ||||||||
\(690\) | 2.47024e10 | 2.86264 | ||||||||
\(691\) | 5.37053e9 | 0.619219 | 0.309609 | − | 0.950864i | \(-0.399802\pi\) | ||||
0.309609 | + | 0.950864i | \(0.399802\pi\) | |||||||
\(692\) | 1.96374e10 | 2.25275 | ||||||||
\(693\) | −2.69038e9 | −0.307077 | ||||||||
\(694\) | 1.00073e10 | 1.13647 | ||||||||
\(695\) | −2.74454e9 | −0.310115 | ||||||||
\(696\) | 3.12644e10 | 3.51494 | ||||||||
\(697\) | 5.53998e9 | 0.619717 | ||||||||
\(698\) | −2.08854e10 | −2.32461 | ||||||||
\(699\) | −1.85255e9 | −0.205163 | ||||||||
\(700\) | 4.25090e10 | 4.68423 | ||||||||
\(701\) | 6.64856e9 | 0.728979 | 0.364489 | − | 0.931208i | \(-0.381244\pi\) | ||||
0.364489 | + | 0.931208i | \(0.381244\pi\) | |||||||
\(702\) | −4.48087e8 | −0.0488858 | ||||||||
\(703\) | 1.87954e9 | 0.204036 | ||||||||
\(704\) | −2.32366e10 | −2.50997 | ||||||||
\(705\) | 1.05999e10 | 1.13930 | ||||||||
\(706\) | 7.50236e9 | 0.802382 | ||||||||
\(707\) | 2.16420e9 | 0.230319 | ||||||||
\(708\) | 1.92888e9 | 0.204262 | ||||||||
\(709\) | 5.41047e8 | 0.0570129 | 0.0285064 | − | 0.999594i | \(-0.490925\pi\) | ||||
0.0285064 | + | 0.999594i | \(0.490925\pi\) | |||||||
\(710\) | 7.50753e9 | 0.787215 | ||||||||
\(711\) | 4.15517e9 | 0.433556 | ||||||||
\(712\) | −5.44319e10 | −5.65163 | ||||||||
\(713\) | 1.15622e10 | 1.19461 | ||||||||
\(714\) | 1.16814e10 | 1.20102 | ||||||||
\(715\) | −1.37199e9 | −0.140372 | ||||||||
\(716\) | 2.34653e10 | 2.38908 | ||||||||
\(717\) | 4.50347e9 | 0.456278 | ||||||||
\(718\) | −1.97186e10 | −1.98812 | ||||||||
\(719\) | 9.95307e9 | 0.998633 | 0.499316 | − | 0.866420i | \(-0.333585\pi\) | ||||
0.499316 | + | 0.866420i | \(0.333585\pi\) | |||||||
\(720\) | 1.86139e10 | 1.85854 | ||||||||
\(721\) | −2.49128e10 | −2.47542 | ||||||||
\(722\) | −5.21702e9 | −0.515872 | ||||||||
\(723\) | 2.95827e9 | 0.291108 | ||||||||
\(724\) | 9.12203e9 | 0.893319 | ||||||||
\(725\) | −2.47364e10 | −2.41076 | ||||||||
\(726\) | 5.84016e9 | 0.566430 | ||||||||
\(727\) | −1.32542e10 | −1.27933 | −0.639665 | − | 0.768654i | \(-0.720927\pi\) | ||||
−0.639665 | + | 0.768654i | \(0.720927\pi\) | |||||||
\(728\) | 5.97015e9 | 0.573489 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 1.22230e10 | 1.16292 | ||||||||
\(731\) | −1.01250e10 | −0.958703 | ||||||||
\(732\) | −2.83931e10 | −2.67561 | ||||||||
\(733\) | 6.98110e8 | 0.0654727 | 0.0327363 | − | 0.999464i | \(-0.489578\pi\) | ||||
0.0327363 | + | 0.999464i | \(0.489578\pi\) | |||||||
\(734\) | 3.38367e10 | 3.15828 | ||||||||
\(735\) | −6.87749e9 | −0.638887 | ||||||||
\(736\) | −6.87838e10 | −6.35937 | ||||||||
\(737\) | −1.31372e10 | −1.20883 | ||||||||
\(738\) | −5.29871e9 | −0.485258 | ||||||||
\(739\) | 5.01583e9 | 0.457180 | 0.228590 | − | 0.973523i | \(-0.426588\pi\) | ||||
0.228590 | + | 0.973523i | \(0.426588\pi\) | |||||||
\(740\) | 1.08576e10 | 0.984974 | ||||||||
\(741\) | −7.20987e8 | −0.0650974 | ||||||||
\(742\) | 1.60776e10 | 1.44480 | ||||||||
\(743\) | 1.65206e10 | 1.47763 | 0.738814 | − | 0.673910i | \(-0.235386\pi\) | ||||
0.738814 | + | 0.673910i | \(0.235386\pi\) | |||||||
\(744\) | 1.51682e10 | 1.35030 | ||||||||
\(745\) | 1.35827e9 | 0.120348 | ||||||||
\(746\) | −3.50671e10 | −3.09253 | ||||||||
\(747\) | −2.58833e9 | −0.227194 | ||||||||
\(748\) | 1.78924e10 | 1.56320 | ||||||||
\(749\) | 3.62427e9 | 0.315162 | ||||||||
\(750\) | −6.08713e9 | −0.526863 | ||||||||
\(751\) | 1.65574e10 | 1.42643 | 0.713216 | − | 0.700944i | \(-0.247238\pi\) | ||||
0.713216 | + | 0.700944i | \(0.247238\pi\) | |||||||
\(752\) | −5.55133e10 | −4.76030 | ||||||||
\(753\) | 6.04831e9 | 0.516240 | ||||||||
\(754\) | −5.49680e9 | −0.466993 | ||||||||
\(755\) | −6.42269e9 | −0.543128 | ||||||||
\(756\) | −8.16723e9 | −0.687462 | ||||||||
\(757\) | −8.37645e9 | −0.701818 | −0.350909 | − | 0.936410i | \(-0.614127\pi\) | ||||
−0.350909 | + | 0.936410i | \(0.614127\pi\) | |||||||
\(758\) | 1.15499e10 | 0.963240 | ||||||||
\(759\) | −8.24458e9 | −0.684419 | ||||||||
\(760\) | 5.21431e10 | 4.30873 | ||||||||
\(761\) | 2.25820e9 | 0.185745 | 0.0928725 | − | 0.995678i | \(-0.470395\pi\) | ||||
0.0928725 | + | 0.995678i | \(0.470395\pi\) | |||||||
\(762\) | 1.96634e10 | 1.60996 | ||||||||
\(763\) | −9.13028e9 | −0.744129 | ||||||||
\(764\) | 3.52024e10 | 2.85592 | ||||||||
\(765\) | −5.15051e9 | −0.415944 | ||||||||
\(766\) | −2.48273e10 | −1.99585 | ||||||||
\(767\) | −2.14336e8 | −0.0171519 | ||||||||
\(768\) | −1.80018e10 | −1.43401 | ||||||||
\(769\) | 5.84510e9 | 0.463500 | 0.231750 | − | 0.972775i | \(-0.425555\pi\) | ||||
0.231750 | + | 0.972775i | \(0.425555\pi\) | |||||||
\(770\) | −3.42092e10 | −2.70038 | ||||||||
\(771\) | −1.32981e10 | −1.04496 | ||||||||
\(772\) | 3.40124e10 | 2.66058 | ||||||||
\(773\) | −4.05810e9 | −0.316005 | −0.158003 | − | 0.987439i | \(-0.550505\pi\) | ||||
−0.158003 | + | 0.987439i | \(0.550505\pi\) | |||||||
\(774\) | 9.68404e9 | 0.750695 | ||||||||
\(775\) | −1.20011e10 | −0.926115 | ||||||||
\(776\) | −1.79184e10 | −1.37653 | ||||||||
\(777\) | −2.36586e9 | −0.180932 | ||||||||
\(778\) | −1.88396e10 | −1.43431 | ||||||||
\(779\) | −8.52580e9 | −0.646181 | ||||||||
\(780\) | −4.16497e9 | −0.314254 | ||||||||
\(781\) | −2.50569e9 | −0.188212 | ||||||||
\(782\) | 3.57971e10 | 2.67685 | ||||||||
\(783\) | 4.75259e9 | 0.353805 | ||||||||
\(784\) | 3.60185e10 | 2.66943 | ||||||||
\(785\) | 2.85042e10 | 2.10313 | ||||||||
\(786\) | −2.57842e10 | −1.89398 | ||||||||
\(787\) | −1.54824e10 | −1.13221 | −0.566106 | − | 0.824333i | \(-0.691551\pi\) | ||||
−0.566106 | + | 0.824333i | \(0.691551\pi\) | |||||||
\(788\) | −8.80675e9 | −0.641171 | ||||||||
\(789\) | 1.15506e10 | 0.837214 | ||||||||
\(790\) | 5.28346e10 | 3.81262 | ||||||||
\(791\) | 1.75943e9 | 0.126402 | ||||||||
\(792\) | −1.08159e10 | −0.773612 | ||||||||
\(793\) | 3.15502e9 | 0.224671 | ||||||||
\(794\) | 7.73260e8 | 0.0548218 | ||||||||
\(795\) | −7.08888e9 | −0.500371 | ||||||||
\(796\) | 5.13447e10 | 3.60828 | ||||||||
\(797\) | 2.07763e10 | 1.45366 | 0.726831 | − | 0.686816i | \(-0.240992\pi\) | ||||
0.726831 | + | 0.686816i | \(0.240992\pi\) | |||||||
\(798\) | −1.79771e10 | −1.25230 | ||||||||
\(799\) | 1.53607e10 | 1.06536 | ||||||||
\(800\) | 7.13947e10 | 4.93005 | ||||||||
\(801\) | −8.27434e9 | −0.568879 | ||||||||
\(802\) | 4.74192e9 | 0.324596 | ||||||||
\(803\) | −4.07951e9 | −0.278037 | ||||||||
\(804\) | −3.98808e10 | −2.70625 | ||||||||
\(805\) | −5.00313e10 | −3.38031 | ||||||||
\(806\) | −2.66682e9 | −0.179400 | ||||||||
\(807\) | −4.66014e9 | −0.312134 | ||||||||
\(808\) | 8.70053e9 | 0.580238 | ||||||||
\(809\) | 1.24188e10 | 0.824628 | 0.412314 | − | 0.911042i | \(-0.364721\pi\) | ||||
0.412314 | + | 0.911042i | \(0.364721\pi\) | |||||||
\(810\) | 4.92620e9 | 0.325698 | ||||||||
\(811\) | −2.86382e10 | −1.88526 | −0.942632 | − | 0.333835i | \(-0.891657\pi\) | ||||
−0.942632 | + | 0.333835i | \(0.891657\pi\) | |||||||
\(812\) | −1.00190e11 | −6.56714 | ||||||||
\(813\) | −6.85961e9 | −0.447695 | ||||||||
\(814\) | −4.95730e9 | −0.322151 | ||||||||
\(815\) | −3.05014e10 | −1.97364 | ||||||||
\(816\) | 2.69740e10 | 1.73792 | ||||||||
\(817\) | 1.55819e10 | 0.999642 | ||||||||
\(818\) | 5.31165e10 | 3.39307 | ||||||||
\(819\) | 9.07539e8 | 0.0577260 | ||||||||
\(820\) | −4.92515e10 | −3.11940 | ||||||||
\(821\) | 6.53708e9 | 0.412271 | 0.206135 | − | 0.978523i | \(-0.433911\pi\) | ||||
0.206135 | + | 0.978523i | \(0.433911\pi\) | |||||||
\(822\) | 1.74871e10 | 1.09816 | ||||||||
\(823\) | −6.03479e8 | −0.0377366 | −0.0188683 | − | 0.999822i | \(-0.506006\pi\) | ||||
−0.0188683 | + | 0.999822i | \(0.506006\pi\) | |||||||
\(824\) | −1.00155e11 | −6.23628 | ||||||||
\(825\) | 8.55752e9 | 0.530590 | ||||||||
\(826\) | −5.34426e9 | −0.329957 | ||||||||
\(827\) | −1.88036e10 | −1.15604 | −0.578020 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578020 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(828\) | −2.50282e10 | −1.53223 | ||||||||
\(829\) | 1.67240e10 | 1.01953 | 0.509763 | − | 0.860315i | \(-0.329733\pi\) | ||||
0.509763 | + | 0.860315i | \(0.329733\pi\) | |||||||
\(830\) | −3.29116e10 | −1.99791 | ||||||||
\(831\) | 9.24480e9 | 0.558849 | ||||||||
\(832\) | 7.83836e9 | 0.471839 | ||||||||
\(833\) | −9.96642e9 | −0.597423 | ||||||||
\(834\) | 3.80400e9 | 0.227070 | ||||||||
\(835\) | 2.89744e10 | 1.72231 | ||||||||
\(836\) | −2.75357e10 | −1.62995 | ||||||||
\(837\) | 2.30576e9 | 0.135918 | ||||||||
\(838\) | −8.98622e9 | −0.527501 | ||||||||
\(839\) | 2.23616e10 | 1.30718 | 0.653592 | − | 0.756847i | \(-0.273261\pi\) | ||||
0.653592 | + | 0.756847i | \(0.273261\pi\) | |||||||
\(840\) | −6.56349e10 | −3.82083 | ||||||||
\(841\) | 4.10514e10 | 2.37981 | ||||||||
\(842\) | −3.35935e10 | −1.93938 | ||||||||
\(843\) | 1.75199e10 | 1.00725 | ||||||||
\(844\) | −3.78645e9 | −0.216787 | ||||||||
\(845\) | −2.62014e10 | −1.49391 | ||||||||
\(846\) | −1.46917e10 | −0.834212 | ||||||||
\(847\) | −1.18284e10 | −0.668861 | ||||||||
\(848\) | 3.71256e10 | 2.09068 | ||||||||
\(849\) | 4.61630e9 | 0.258891 | ||||||||
\(850\) | −3.71559e10 | −2.07521 | ||||||||
\(851\) | −7.25011e9 | −0.403265 | ||||||||
\(852\) | −7.60657e9 | −0.421357 | ||||||||
\(853\) | −1.44921e9 | −0.0799483 | −0.0399742 | − | 0.999201i | \(-0.512728\pi\) | ||||
−0.0399742 | + | 0.999201i | \(0.512728\pi\) | |||||||
\(854\) | 7.86675e10 | 4.32208 | ||||||||
\(855\) | 7.92642e9 | 0.433706 | ||||||||
\(856\) | 1.45703e10 | 0.793983 | ||||||||
\(857\) | −8.02175e9 | −0.435347 | −0.217674 | − | 0.976022i | \(-0.569847\pi\) | ||||
−0.217674 | + | 0.976022i | \(0.569847\pi\) | |||||||
\(858\) | 1.90161e9 | 0.102782 | ||||||||
\(859\) | 1.19930e10 | 0.645584 | 0.322792 | − | 0.946470i | \(-0.395379\pi\) | ||||
0.322792 | + | 0.946470i | \(0.395379\pi\) | |||||||
\(860\) | 9.00132e10 | 4.82571 | ||||||||
\(861\) | 1.07318e10 | 0.573010 | ||||||||
\(862\) | 4.42935e10 | 2.35540 | ||||||||
\(863\) | −2.67440e10 | −1.41641 | −0.708205 | − | 0.706007i | \(-0.750495\pi\) | ||||
−0.708205 | + | 0.706007i | \(0.750495\pi\) | |||||||
\(864\) | −1.37170e10 | −0.723539 | ||||||||
\(865\) | 2.39896e10 | 1.26028 | ||||||||
\(866\) | 1.39804e10 | 0.731489 | ||||||||
\(867\) | 3.61535e9 | 0.188401 | ||||||||
\(868\) | −4.86079e10 | −2.52283 | ||||||||
\(869\) | −1.76339e10 | −0.911546 | ||||||||
\(870\) | 6.04310e10 | 3.11130 | ||||||||
\(871\) | 4.43153e9 | 0.227243 | ||||||||
\(872\) | −3.67056e10 | −1.87467 | ||||||||
\(873\) | −2.72383e9 | −0.138558 | ||||||||
\(874\) | −5.50903e10 | −2.79116 | ||||||||
\(875\) | 1.23286e10 | 0.622139 | ||||||||
\(876\) | −1.23842e10 | −0.622451 | ||||||||
\(877\) | −6.68932e8 | −0.0334875 | −0.0167438 | − | 0.999860i | \(-0.505330\pi\) | ||||
−0.0167438 | + | 0.999860i | \(0.505330\pi\) | |||||||
\(878\) | −9.86542e9 | −0.491909 | ||||||||
\(879\) | 2.06647e10 | 1.02629 | ||||||||
\(880\) | −7.89942e10 | −3.90756 | ||||||||
\(881\) | 2.73982e10 | 1.34992 | 0.674958 | − | 0.737856i | \(-0.264162\pi\) | ||||
0.674958 | + | 0.737856i | \(0.264162\pi\) | |||||||
\(882\) | 9.53238e9 | 0.467801 | ||||||||
\(883\) | 1.56749e9 | 0.0766198 | 0.0383099 | − | 0.999266i | \(-0.487803\pi\) | ||||
0.0383099 | + | 0.999266i | \(0.487803\pi\) | |||||||
\(884\) | −6.03561e9 | −0.293859 | ||||||||
\(885\) | 2.35638e9 | 0.114273 | ||||||||
\(886\) | 4.25732e10 | 2.05645 | ||||||||
\(887\) | 6.07648e9 | 0.292361 | 0.146181 | − | 0.989258i | \(-0.453302\pi\) | ||||
0.146181 | + | 0.989258i | \(0.453302\pi\) | |||||||
\(888\) | −9.51125e9 | −0.455819 | ||||||||
\(889\) | −3.98254e10 | −1.90110 | ||||||||
\(890\) | −1.05211e11 | −5.00263 | ||||||||
\(891\) | −1.64415e9 | −0.0778699 | ||||||||
\(892\) | 8.14643e10 | 3.84317 | ||||||||
\(893\) | −2.36395e10 | −1.11086 | ||||||||
\(894\) | −1.88260e9 | −0.0881205 | ||||||||
\(895\) | 2.86659e10 | 1.33655 | ||||||||
\(896\) | 8.90332e10 | 4.13499 | ||||||||
\(897\) | 2.78112e9 | 0.128661 | ||||||||
\(898\) | −1.60659e10 | −0.740354 | ||||||||
\(899\) | 2.82854e10 | 1.29838 | ||||||||
\(900\) | 2.59782e10 | 1.18785 | ||||||||
\(901\) | −1.02728e10 | −0.467897 | ||||||||
\(902\) | 2.24869e10 | 1.02025 | ||||||||
\(903\) | −1.96137e10 | −0.886446 | ||||||||
\(904\) | 7.07329e9 | 0.318443 | ||||||||
\(905\) | 1.11438e10 | 0.499760 | ||||||||
\(906\) | 8.90201e9 | 0.397685 | ||||||||
\(907\) | −3.19626e10 | −1.42238 | −0.711191 | − | 0.702999i | \(-0.751844\pi\) | ||||
−0.711191 | + | 0.702999i | \(0.751844\pi\) | |||||||
\(908\) | 9.42112e10 | 4.17640 | ||||||||
\(909\) | 1.32259e9 | 0.0584053 | ||||||||
\(910\) | 1.15397e10 | 0.507633 | ||||||||
\(911\) | 3.33824e10 | 1.46286 | 0.731430 | − | 0.681916i | \(-0.238853\pi\) | ||||
0.731430 | + | 0.681916i | \(0.238853\pi\) | |||||||
\(912\) | −4.15119e10 | −1.81214 | ||||||||
\(913\) | 1.09845e10 | 0.477673 | ||||||||
\(914\) | 1.84315e10 | 0.798451 | ||||||||
\(915\) | −3.46859e10 | −1.49685 | ||||||||
\(916\) | 2.52338e10 | 1.08480 | ||||||||
\(917\) | 5.22224e10 | 2.23648 | ||||||||
\(918\) | 7.13874e9 | 0.304560 | ||||||||
\(919\) | −8.98427e9 | −0.381837 | −0.190919 | − | 0.981606i | \(-0.561147\pi\) | ||||
−0.190919 | + | 0.981606i | \(0.561147\pi\) | |||||||
\(920\) | −2.01136e11 | −8.51594 | ||||||||
\(921\) | −5.10604e9 | −0.215365 | ||||||||
\(922\) | 5.65802e9 | 0.237742 | ||||||||
\(923\) | 8.45238e8 | 0.0353812 | ||||||||
\(924\) | 3.46604e10 | 1.44538 | ||||||||
\(925\) | 7.52530e9 | 0.312628 | ||||||||
\(926\) | 8.76730e9 | 0.362850 | ||||||||
\(927\) | −1.52248e10 | −0.627728 | ||||||||
\(928\) | −1.68270e11 | −6.91177 | ||||||||
\(929\) | −4.29286e10 | −1.75668 | −0.878339 | − | 0.478039i | \(-0.841348\pi\) | ||||
−0.878339 | + | 0.478039i | \(0.841348\pi\) | |||||||
\(930\) | 2.93187e10 | 1.19524 | ||||||||
\(931\) | 1.53379e10 | 0.622934 | ||||||||
\(932\) | 2.38666e10 | 0.965685 | ||||||||
\(933\) | −6.52411e9 | −0.262988 | ||||||||
\(934\) | −6.76441e10 | −2.71654 | ||||||||
\(935\) | 2.18579e10 | 0.874518 | ||||||||
\(936\) | 3.64849e9 | 0.145428 | ||||||||
\(937\) | −2.92971e9 | −0.116342 | −0.0581710 | − | 0.998307i | \(-0.518527\pi\) | ||||
−0.0581710 | + | 0.998307i | \(0.518527\pi\) | |||||||
\(938\) | 1.10496e11 | 4.37156 | ||||||||
\(939\) | 1.13980e10 | 0.449262 | ||||||||
\(940\) | −1.36560e11 | −5.36259 | ||||||||
\(941\) | 1.23877e10 | 0.484650 | 0.242325 | − | 0.970195i | \(-0.422090\pi\) | ||||
0.242325 | + | 0.970195i | \(0.422090\pi\) | |||||||
\(942\) | −3.95076e10 | −1.53994 | ||||||||
\(943\) | 3.28873e10 | 1.27714 | ||||||||
\(944\) | −1.23407e10 | −0.477461 | ||||||||
\(945\) | −9.97734e9 | −0.384595 | ||||||||
\(946\) | −4.10975e10 | −1.57833 | ||||||||
\(947\) | 5.27697e9 | 0.201911 | 0.100955 | − | 0.994891i | \(-0.467810\pi\) | ||||
0.100955 | + | 0.994891i | \(0.467810\pi\) | |||||||
\(948\) | −5.35315e10 | −2.04071 | ||||||||
\(949\) | 1.37613e9 | 0.0522671 | ||||||||
\(950\) | 5.71814e10 | 2.16382 | ||||||||
\(951\) | −2.75784e10 | −1.03977 | ||||||||
\(952\) | −9.51139e10 | −3.57285 | ||||||||
\(953\) | −1.49617e10 | −0.559959 | −0.279980 | − | 0.960006i | \(-0.590328\pi\) | ||||
−0.279980 | + | 0.960006i | \(0.590328\pi\) | |||||||
\(954\) | 9.82537e9 | 0.366378 | ||||||||
\(955\) | 4.30043e10 | 1.59772 | ||||||||
\(956\) | −5.80187e10 | −2.14766 | ||||||||
\(957\) | −2.01692e10 | −0.743871 | ||||||||
\(958\) | 8.28123e10 | 3.04309 | ||||||||
\(959\) | −3.54178e10 | −1.29675 | ||||||||
\(960\) | −8.61738e10 | −3.14359 | ||||||||
\(961\) | −1.37897e10 | −0.501213 | ||||||||
\(962\) | 1.67224e9 | 0.0605599 | ||||||||
\(963\) | 2.21488e9 | 0.0799204 | ||||||||
\(964\) | −3.81117e10 | −1.37022 | ||||||||
\(965\) | 4.15506e10 | 1.48844 | ||||||||
\(966\) | 6.93446e10 | 2.47510 | ||||||||
\(967\) | 3.49771e10 | 1.24392 | 0.621958 | − | 0.783051i | \(-0.286337\pi\) | ||||
0.621958 | + | 0.783051i | \(0.286337\pi\) | |||||||
\(968\) | −4.75528e10 | −1.68505 | ||||||||
\(969\) | 1.14865e10 | 0.405558 | ||||||||
\(970\) | −3.46346e10 | −1.21845 | ||||||||
\(971\) | 4.12202e10 | 1.44492 | 0.722459 | − | 0.691414i | \(-0.243012\pi\) | ||||
0.722459 | + | 0.691414i | \(0.243012\pi\) | |||||||
\(972\) | −4.99118e9 | −0.174330 | ||||||||
\(973\) | −7.70449e9 | −0.268132 | ||||||||
\(974\) | 1.70662e8 | 0.00591809 | ||||||||
\(975\) | −2.88669e9 | −0.0997433 | ||||||||
\(976\) | 1.81655e11 | 6.25423 | ||||||||
\(977\) | −3.74910e10 | −1.28616 | −0.643081 | − | 0.765798i | \(-0.722344\pi\) | ||||
−0.643081 | + | 0.765798i | \(0.722344\pi\) | |||||||
\(978\) | 4.22758e10 | 1.44513 | ||||||||
\(979\) | 3.51150e10 | 1.19606 | ||||||||
\(980\) | 8.86035e10 | 3.00718 | ||||||||
\(981\) | −5.57972e9 | −0.188700 | ||||||||
\(982\) | −5.42028e10 | −1.82655 | ||||||||
\(983\) | 5.07263e9 | 0.170332 | 0.0851660 | − | 0.996367i | \(-0.472858\pi\) | ||||
0.0851660 | + | 0.996367i | \(0.472858\pi\) | |||||||
\(984\) | 4.31441e10 | 1.44357 | ||||||||
\(985\) | −1.07586e10 | −0.358698 | ||||||||
\(986\) | 8.75728e10 | 2.90938 | ||||||||
\(987\) | 2.97561e10 | 0.985066 | ||||||||
\(988\) | 9.28856e9 | 0.306407 | ||||||||
\(989\) | −6.01056e10 | −1.97573 | ||||||||
\(990\) | −2.09060e10 | −0.684775 | ||||||||
\(991\) | 1.45130e10 | 0.473694 | 0.236847 | − | 0.971547i | \(-0.423886\pi\) | ||||
0.236847 | + | 0.971547i | \(0.423886\pi\) | |||||||
\(992\) | −8.16379e10 | −2.65522 | ||||||||
\(993\) | −2.32753e10 | −0.754350 | ||||||||
\(994\) | 2.10752e10 | 0.680643 | ||||||||
\(995\) | 6.27243e10 | 2.01862 | ||||||||
\(996\) | 3.33457e10 | 1.06938 | ||||||||
\(997\) | 1.97848e10 | 0.632265 | 0.316132 | − | 0.948715i | \(-0.397616\pi\) | ||||
0.316132 | + | 0.948715i | \(0.397616\pi\) | |||||||
\(998\) | 7.24554e10 | 2.30735 | ||||||||
\(999\) | −1.44583e9 | −0.0458816 |
(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 | 177.8.a.c.1.17 | ✓ | 17 | |
3.2 | odd | 2 | 531.8.a.c.1.1 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.c.1.17 | ✓ | 17 | 1.1 | even | 1 | trivial | |
531.8.a.c.1.1 | 17 | 3.2 | odd | 2 |