Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(176,177)]
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([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.176");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.3879361069\) |
Analytic rank: | \(0\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 176.3 | ||
Character | \(\chi\) | \(=\) | 177.176 |
Dual form | 177.6.d.b.176.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.7490 | −1.90017 | −0.950087 | − | 0.311984i | \(-0.899006\pi\) | ||||
−0.950087 | + | 0.311984i | \(0.899006\pi\) | |||||||
\(3\) | 9.69295 | + | 12.2085i | 0.621803 | + | 0.783174i | ||||
\(4\) | 83.5412 | 2.61066 | ||||||||
\(5\) | 33.1454i | 0.592924i | 0.955045 | + | 0.296462i | \(0.0958068\pi\) | ||||
−0.955045 | + | 0.296462i | \(0.904193\pi\) | |||||||
\(6\) | −104.190 | − | 131.229i | −1.18153 | − | 1.48817i | ||||
\(7\) | −174.539 | −1.34632 | −0.673160 | − | 0.739497i | \(-0.735063\pi\) | ||||
−0.673160 | + | 0.739497i | \(0.735063\pi\) | |||||||
\(8\) | −554.017 | −3.06054 | ||||||||
\(9\) | −55.0934 | + | 236.672i | −0.226722 | + | 0.973960i | ||||
\(10\) | − | 356.281i | − | 1.12666i | ||||||
\(11\) | −67.7482 | −0.168817 | −0.0844085 | − | 0.996431i | \(-0.526900\pi\) | ||||
−0.0844085 | + | 0.996431i | \(0.526900\pi\) | |||||||
\(12\) | 809.761 | + | 1019.91i | 1.62332 | + | 2.04460i | ||||
\(13\) | − | 762.395i | − | 1.25119i | −0.780150 | − | 0.625593i | \(-0.784857\pi\) | ||
0.780150 | − | 0.625593i | \(-0.215143\pi\) | |||||||
\(14\) | 1876.13 | 2.55824 | ||||||||
\(15\) | −404.655 | + | 321.277i | −0.464362 | + | 0.368682i | ||||
\(16\) | 3281.82 | 3.20490 | ||||||||
\(17\) | − | 1054.79i | − | 0.885203i | −0.896718 | − | 0.442602i | \(-0.854056\pi\) | ||
0.896718 | − | 0.442602i | \(-0.145944\pi\) | |||||||
\(18\) | 592.199 | − | 2543.99i | 0.430811 | − | 1.85069i | ||||
\(19\) | 1517.46 | 0.964344 | 0.482172 | − | 0.876077i | \(-0.339848\pi\) | ||||
0.482172 | + | 0.876077i | \(0.339848\pi\) | |||||||
\(20\) | 2769.01i | 1.54792i | ||||||||
\(21\) | −1691.80 | − | 2130.86i | −0.837146 | − | 1.05440i | ||||
\(22\) | 728.226 | 0.320782 | ||||||||
\(23\) | −1504.53 | −0.593036 | −0.296518 | − | 0.955027i | \(-0.595826\pi\) | ||||
−0.296518 | + | 0.955027i | \(0.595826\pi\) | |||||||
\(24\) | −5370.06 | − | 6763.70i | −1.90306 | − | 2.39694i | ||||
\(25\) | 2026.38 | 0.648442 | ||||||||
\(26\) | 8194.99i | 2.37747i | ||||||||
\(27\) | −3423.42 | + | 1621.45i | −0.903756 | + | 0.428049i | ||||
\(28\) | −14581.2 | −3.51479 | ||||||||
\(29\) | − | 4785.21i | − | 1.05659i | −0.849061 | − | 0.528294i | \(-0.822832\pi\) | ||
0.849061 | − | 0.528294i | \(-0.177168\pi\) | |||||||
\(30\) | 4349.64 | − | 3453.41i | 0.882369 | − | 0.700560i | ||||
\(31\) | 4004.32i | 0.748385i | 0.927351 | + | 0.374192i | \(0.122080\pi\) | ||||
−0.927351 | + | 0.374192i | \(0.877920\pi\) | |||||||
\(32\) | −17547.8 | −3.02933 | ||||||||
\(33\) | −656.680 | − | 827.102i | −0.104971 | − | 0.132213i | ||||
\(34\) | 11337.9i | 1.68204i | ||||||||
\(35\) | − | 5785.18i | − | 0.798265i | ||||||
\(36\) | −4602.57 | + | 19771.9i | −0.591894 | + | 2.54268i | ||||
\(37\) | − | 6219.64i | − | 0.746897i | −0.927651 | − | 0.373449i | \(-0.878175\pi\) | ||
0.927651 | − | 0.373449i | \(-0.121825\pi\) | |||||||
\(38\) | −16311.1 | −1.83242 | ||||||||
\(39\) | 9307.68 | − | 7389.86i | 0.979895 | − | 0.777991i | ||||
\(40\) | − | 18363.2i | − | 1.81467i | ||||||
\(41\) | − | 14687.7i | − | 1.36457i | −0.731088 | − | 0.682283i | \(-0.760987\pi\) | ||
0.731088 | − | 0.682283i | \(-0.239013\pi\) | |||||||
\(42\) | 18185.2 | + | 22904.6i | 1.59072 | + | 2.00355i | ||||
\(43\) | 19978.1i | 1.64772i | 0.566795 | + | 0.823859i | \(0.308183\pi\) | ||||
−0.566795 | + | 0.823859i | \(0.691817\pi\) | |||||||
\(44\) | −5659.77 | −0.440724 | ||||||||
\(45\) | −7844.60 | − | 1826.09i | −0.577484 | − | 0.134429i | ||||
\(46\) | 16172.2 | 1.12687 | ||||||||
\(47\) | 17461.3 | 1.15300 | 0.576502 | − | 0.817096i | \(-0.304417\pi\) | ||||
0.576502 | + | 0.817096i | \(0.304417\pi\) | |||||||
\(48\) | 31810.5 | + | 40066.0i | 1.99282 | + | 2.50999i | ||||
\(49\) | 13657.0 | 0.812578 | ||||||||
\(50\) | −21781.6 | −1.23215 | ||||||||
\(51\) | 12877.4 | − | 10224.0i | 0.693268 | − | 0.550422i | ||||
\(52\) | − | 63691.4i | − | 3.26642i | ||||||
\(53\) | 3262.05i | 0.159515i | 0.996814 | + | 0.0797574i | \(0.0254146\pi\) | ||||
−0.996814 | + | 0.0797574i | \(0.974585\pi\) | |||||||
\(54\) | 36798.4 | − | 17428.9i | 1.71729 | − | 0.813367i | ||||
\(55\) | − | 2245.54i | − | 0.100096i | ||||||
\(56\) | 96697.9 | 4.12047 | ||||||||
\(57\) | 14708.6 | + | 18525.8i | 0.599632 | + | 0.755248i | ||||
\(58\) | 51436.2i | 2.00770i | ||||||||
\(59\) | −16303.5 | + | 21192.4i | −0.609749 | + | 0.792594i | ||||
\(60\) | −33805.4 | + | 26839.9i | −1.21229 | + | 0.962504i | ||||
\(61\) | − | 21833.5i | − | 0.751276i | −0.926766 | − | 0.375638i | \(-0.877424\pi\) | ||
0.926766 | − | 0.375638i | \(-0.122576\pi\) | |||||||
\(62\) | − | 43042.5i | − | 1.42206i | ||||||
\(63\) | 9615.97 | − | 41308.6i | 0.305240 | − | 1.31126i | ||||
\(64\) | 83602.8 | 2.55136 | ||||||||
\(65\) | 25269.9 | 0.741857 | ||||||||
\(66\) | 7058.66 | + | 8890.53i | 0.199463 | + | 0.251228i | ||||
\(67\) | − | 20335.2i | − | 0.553427i | −0.960952 | − | 0.276714i | \(-0.910755\pi\) | ||
0.960952 | − | 0.276714i | \(-0.0892454\pi\) | |||||||
\(68\) | − | 88118.3i | − | 2.31097i | ||||||
\(69\) | −14583.3 | − | 18368.0i | −0.368752 | − | 0.464450i | ||||
\(70\) | 62185.0i | 1.51684i | ||||||||
\(71\) | 26490.5i | 0.623655i | 0.950139 | + | 0.311827i | \(0.100941\pi\) | ||||
−0.950139 | + | 0.311827i | \(0.899059\pi\) | |||||||
\(72\) | 30522.7 | − | 131121.i | 0.693892 | − | 2.98085i | ||||
\(73\) | 78490.3i | 1.72389i | 0.507003 | + | 0.861944i | \(0.330753\pi\) | ||||
−0.507003 | + | 0.861944i | \(0.669247\pi\) | |||||||
\(74\) | 66854.9i | 1.41923i | ||||||||
\(75\) | 19641.6 | + | 24739.0i | 0.403203 | + | 0.507842i | ||||
\(76\) | 126770. | 2.51758 | ||||||||
\(77\) | 11824.7 | 0.227282 | ||||||||
\(78\) | −100048. | + | 79433.7i | −1.86197 | + | 1.47832i | ||||
\(79\) | 78139.6 | 1.40865 | 0.704326 | − | 0.709877i | \(-0.251249\pi\) | ||||
0.704326 | + | 0.709877i | \(0.251249\pi\) | |||||||
\(80\) | 108777.i | 1.90026i | ||||||||
\(81\) | −52978.4 | − | 26078.1i | −0.897194 | − | 0.441636i | ||||
\(82\) | 157878.i | 2.59291i | ||||||||
\(83\) | −36801.4 | −0.586366 | −0.293183 | − | 0.956056i | \(-0.594715\pi\) | ||||
−0.293183 | + | 0.956056i | \(0.594715\pi\) | |||||||
\(84\) | −141335. | − | 178015.i | −2.18551 | − | 2.75269i | ||||
\(85\) | 34961.4 | 0.524858 | ||||||||
\(86\) | − | 214745.i | − | 3.13095i | ||||||
\(87\) | 58420.0 | − | 46382.8i | 0.827492 | − | 0.656990i | ||||
\(88\) | 37533.7 | 0.516671 | ||||||||
\(89\) | 93253.5 | 1.24793 | 0.623965 | − | 0.781453i | \(-0.285521\pi\) | ||||
0.623965 | + | 0.781453i | \(0.285521\pi\) | |||||||
\(90\) | 84321.7 | + | 19628.7i | 1.09732 | + | 0.255438i | ||||
\(91\) | 133068.i | 1.68450i | ||||||||
\(92\) | −125690. | −1.54822 | ||||||||
\(93\) | −48886.7 | + | 38813.7i | −0.586115 | + | 0.465348i | ||||
\(94\) | −187691. | −2.19091 | ||||||||
\(95\) | 50296.7i | 0.571782i | ||||||||
\(96\) | −170090. | − | 214231.i | −1.88365 | − | 2.37249i | ||||
\(97\) | − | 42572.4i | − | 0.459408i | −0.973261 | − | 0.229704i | \(-0.926224\pi\) | ||
0.973261 | − | 0.229704i | \(-0.0737759\pi\) | |||||||
\(98\) | −146799. | −1.54404 | ||||||||
\(99\) | 3732.48 | − | 16034.1i | 0.0382745 | − | 0.164421i | ||||
\(100\) | 169286. | 1.69286 | ||||||||
\(101\) | 130012. | 1.26817 | 0.634086 | − | 0.773262i | \(-0.281376\pi\) | ||||
0.634086 | + | 0.773262i | \(0.281376\pi\) | |||||||
\(102\) | −138419. | + | 109898.i | −1.31733 | + | 1.04590i | ||||
\(103\) | − | 183784.i | − | 1.70693i | −0.521150 | − | 0.853465i | \(-0.674497\pi\) | ||
0.521150 | − | 0.853465i | \(-0.325503\pi\) | |||||||
\(104\) | 422380.i | 3.82931i | ||||||||
\(105\) | 70628.2 | − | 56075.5i | 0.625180 | − | 0.496364i | ||||
\(106\) | − | 35063.8i | − | 0.303106i | ||||||
\(107\) | − | 142238.i | − | 1.20104i | −0.799610 | − | 0.600519i | \(-0.794961\pi\) | ||
0.799610 | − | 0.600519i | \(-0.205039\pi\) | |||||||
\(108\) | −285997. | + | 135458.i | −2.35940 | + | 1.11749i | ||||
\(109\) | 29378.8i | 0.236847i | 0.992963 | + | 0.118424i | \(0.0377841\pi\) | ||||
−0.992963 | + | 0.118424i | \(0.962216\pi\) | |||||||
\(110\) | 24137.4i | 0.190199i | ||||||||
\(111\) | 75932.2 | − | 60286.6i | 0.584950 | − | 0.464423i | ||||
\(112\) | −572807. | −4.31482 | ||||||||
\(113\) | −56037.4 | −0.412840 | −0.206420 | − | 0.978464i | \(-0.566181\pi\) | ||||
−0.206420 | + | 0.978464i | \(0.566181\pi\) | |||||||
\(114\) | −158103. | − | 199134.i | −1.13941 | − | 1.43510i | ||||
\(115\) | − | 49868.3i | − | 0.351625i | ||||||
\(116\) | − | 399762.i | − | 2.75840i | ||||||
\(117\) | 180438. | + | 42002.9i | 1.21860 | + | 0.283671i | ||||
\(118\) | 175247. | − | 227798.i | 1.15863 | − | 1.50607i | ||||
\(119\) | 184102.i | 1.19177i | ||||||||
\(120\) | 224186. | − | 177993.i | 1.42120 | − | 1.12837i | ||||
\(121\) | −156461. | −0.971501 | ||||||||
\(122\) | 234689.i | 1.42756i | ||||||||
\(123\) | 179314. | − | 142367.i | 1.06869 | − | 0.848491i | ||||
\(124\) | 334526.i | 1.95378i | ||||||||
\(125\) | 170745.i | 0.977400i | ||||||||
\(126\) | −103362. | + | 444027.i | −0.580009 | + | 2.49163i | ||||
\(127\) | 339103. | 1.86562 | 0.932808 | − | 0.360374i | \(-0.117351\pi\) | ||||
0.932808 | + | 0.360374i | \(0.117351\pi\) | |||||||
\(128\) | −337120. | −1.81869 | ||||||||
\(129\) | −243902. | + | 193647.i | −1.29045 | + | 1.02456i | ||||
\(130\) | −271627. | −1.40966 | ||||||||
\(131\) | 349637. | 1.78008 | 0.890039 | − | 0.455884i | \(-0.150677\pi\) | ||||
0.890039 | + | 0.455884i | \(0.150677\pi\) | |||||||
\(132\) | −54859.9 | − | 69097.1i | −0.274044 | − | 0.345164i | ||||
\(133\) | −264856. | −1.29832 | ||||||||
\(134\) | 218583.i | 1.05161i | ||||||||
\(135\) | −53743.5 | − | 113471.i | −0.253800 | − | 0.535858i | ||||
\(136\) | 584371.i | 2.70920i | ||||||||
\(137\) | − | 120090.i | − | 0.546643i | −0.961923 | − | 0.273322i | \(-0.911878\pi\) | ||
0.961923 | − | 0.273322i | \(-0.0881223\pi\) | |||||||
\(138\) | 156756. | + | 197438.i | 0.700693 | + | 0.882537i | ||||
\(139\) | 20574.2 | 0.0903204 | 0.0451602 | − | 0.998980i | \(-0.485620\pi\) | ||||
0.0451602 | + | 0.998980i | \(0.485620\pi\) | |||||||
\(140\) | − | 483301.i | − | 2.08400i | ||||||
\(141\) | 169251. | + | 213175.i | 0.716942 | + | 0.903003i | ||||
\(142\) | − | 284747.i | − | 1.18505i | ||||||
\(143\) | 51650.9i | 0.211221i | ||||||||
\(144\) | −180807. | + | 776715.i | −0.726621 | + | 3.12145i | ||||
\(145\) | 158608. | 0.626476 | ||||||||
\(146\) | − | 843694.i | − | 3.27569i | ||||||
\(147\) | 132377. | + | 166731.i | 0.505263 | + | 0.636389i | ||||
\(148\) | − | 519596.i | − | 1.94990i | ||||||
\(149\) | −172905. | −0.638031 | −0.319015 | − | 0.947750i | \(-0.603352\pi\) | ||||
−0.319015 | + | 0.947750i | \(0.603352\pi\) | |||||||
\(150\) | −211128. | − | 265920.i | −0.766156 | − | 0.964989i | ||||
\(151\) | 115365.i | 0.411747i | 0.978579 | + | 0.205873i | \(0.0660035\pi\) | ||||
−0.978579 | + | 0.205873i | \(0.933996\pi\) | |||||||
\(152\) | −840697. | −2.95142 | ||||||||
\(153\) | 249639. | + | 58111.9i | 0.862152 | + | 0.200695i | ||||
\(154\) | −127104. | −0.431875 | ||||||||
\(155\) | −132725. | −0.443735 | ||||||||
\(156\) | 777575. | − | 617358.i | 2.55818 | − | 2.03107i | ||||
\(157\) | − | 66650.4i | − | 0.215801i | −0.994162 | − | 0.107901i | \(-0.965587\pi\) | ||
0.994162 | − | 0.107901i | \(-0.0344128\pi\) | |||||||
\(158\) | −839924. | −2.67668 | ||||||||
\(159\) | −39824.7 | + | 31618.9i | −0.124928 | + | 0.0991868i | ||||
\(160\) | − | 581628.i | − | 1.79616i | ||||||
\(161\) | 262600. | 0.798417 | ||||||||
\(162\) | 569466. | + | 280314.i | 1.70483 | + | 0.839185i | ||||
\(163\) | −416761. | −1.22862 | −0.614311 | − | 0.789064i | \(-0.710566\pi\) | ||||
−0.614311 | + | 0.789064i | \(0.710566\pi\) | |||||||
\(164\) | − | 1.22703e6i | − | 3.56242i | ||||||
\(165\) | 27414.6 | − | 21765.9i | 0.0783922 | − | 0.0622397i | ||||
\(166\) | 395578. | 1.11420 | ||||||||
\(167\) | − | 650842.i | − | 1.80586i | −0.429785 | − | 0.902931i | \(-0.641411\pi\) | ||
0.429785 | − | 0.902931i | \(-0.358589\pi\) | |||||||
\(168\) | 937288. | + | 1.18053e6i | 2.56212 | + | 3.22704i | ||||
\(169\) | −209953. | −0.565465 | ||||||||
\(170\) | −375801. | −0.997322 | ||||||||
\(171\) | −83601.7 | + | 359139.i | −0.218638 | + | 0.939232i | ||||
\(172\) | 1.66899e6i | 4.30164i | ||||||||
\(173\) | 203386. | 0.516660 | 0.258330 | − | 0.966057i | \(-0.416828\pi\) | ||||
0.258330 | + | 0.966057i | \(0.416828\pi\) | |||||||
\(174\) | −627958. | + | 498569.i | −1.57238 | + | 1.24840i | ||||
\(175\) | −353683. | −0.873010 | ||||||||
\(176\) | −222337. | −0.541042 | ||||||||
\(177\) | −416756. | + | 6376.39i | −0.999883 | + | 0.0152983i | ||||
\(178\) | −1.00238e6 | −2.37128 | ||||||||
\(179\) | 465710. | 1.08638 | 0.543192 | − | 0.839609i | \(-0.317216\pi\) | ||||
0.543192 | + | 0.839609i | \(0.317216\pi\) | |||||||
\(180\) | −655348. | − | 152554.i | −1.50762 | − | 0.350948i | ||||
\(181\) | 863836. | 1.95990 | 0.979952 | − | 0.199234i | \(-0.0638455\pi\) | ||||
0.979952 | + | 0.199234i | \(0.0638455\pi\) | |||||||
\(182\) | − | 1.43035e6i | − | 3.20084i | ||||||
\(183\) | 266554. | − | 211631.i | 0.588380 | − | 0.467146i | ||||
\(184\) | 833536. | 1.81501 | ||||||||
\(185\) | 206153. | 0.442853 | ||||||||
\(186\) | 525483. | − | 417209.i | 1.11372 | − | 0.884243i | ||||
\(187\) | 71460.0i | 0.149437i | ||||||||
\(188\) | 1.45874e6 | 3.01011 | ||||||||
\(189\) | 597522. | − | 283006.i | 1.21674 | − | 0.576290i | ||||
\(190\) | − | 540640.i | − | 1.08649i | ||||||
\(191\) | 560153. | 1.11102 | 0.555512 | − | 0.831509i | \(-0.312522\pi\) | ||||
0.555512 | + | 0.831509i | \(0.312522\pi\) | |||||||
\(192\) | 810358. | + | 1.02066e6i | 1.58644 | + | 1.99816i | ||||
\(193\) | 27809.8 | 0.0537408 | 0.0268704 | − | 0.999639i | \(-0.491446\pi\) | ||||
0.0268704 | + | 0.999639i | \(0.491446\pi\) | |||||||
\(194\) | 457611.i | 0.872956i | ||||||||
\(195\) | 244940. | + | 308507.i | 0.461289 | + | 0.581003i | ||||
\(196\) | 1.14092e6 | 2.12137 | ||||||||
\(197\) | − | 151601.i | − | 0.278316i | −0.990270 | − | 0.139158i | \(-0.955560\pi\) | ||
0.990270 | − | 0.139158i | \(-0.0444395\pi\) | |||||||
\(198\) | −40120.4 | + | 172351.i | −0.0727282 | + | 0.312428i | ||||
\(199\) | 72452.3 | 0.129694 | 0.0648469 | − | 0.997895i | \(-0.479344\pi\) | ||||
0.0648469 | + | 0.997895i | \(0.479344\pi\) | |||||||
\(200\) | −1.12265e6 | −1.98458 | ||||||||
\(201\) | 248261. | − | 197108.i | 0.433430 | − | 0.344123i | ||||
\(202\) | −1.39750e6 | −2.40975 | ||||||||
\(203\) | 835207.i | 1.42251i | ||||||||
\(204\) | 1.07579e6 | − | 854127.i | 1.80989 | − | 1.43697i | ||||
\(205\) | 486831. | 0.809083 | ||||||||
\(206\) | 1.97550e6i | 3.24346i | ||||||||
\(207\) | 82889.7 | − | 356080.i | 0.134454 | − | 0.577594i | ||||
\(208\) | − | 2.50204e6i | − | 4.00993i | ||||||
\(209\) | −102805. | −0.162798 | ||||||||
\(210\) | −759184. | + | 602756.i | −1.18795 | + | 0.943178i | ||||
\(211\) | − | 923790.i | − | 1.42846i | −0.699913 | − | 0.714228i | \(-0.746778\pi\) | ||
0.699913 | − | 0.714228i | \(-0.253222\pi\) | |||||||
\(212\) | 272516.i | 0.416440i | ||||||||
\(213\) | −323408. | + | 256771.i | −0.488430 | + | 0.387790i | ||||
\(214\) | 1.52892e6i | 2.28218i | ||||||||
\(215\) | −662182. | −0.976971 | ||||||||
\(216\) | 1.89664e6 | − | 898309.i | 2.76598 | − | 1.31006i | ||||
\(217\) | − | 698912.i | − | 1.00757i | ||||||
\(218\) | − | 315793.i | − | 0.450051i | ||||||
\(219\) | −958247. | + | 760803.i | −1.35010 | + | 1.07192i | ||||
\(220\) | − | 187596.i | − | 0.261316i | ||||||
\(221\) | −804166. | −1.10755 | ||||||||
\(222\) | −816197. | + | 648022.i | −1.11151 | + | 0.882485i | ||||
\(223\) | −290482. | −0.391162 | −0.195581 | − | 0.980688i | \(-0.562659\pi\) | ||||
−0.195581 | + | 0.980688i | \(0.562659\pi\) | |||||||
\(224\) | 3.06278e6 | 4.07845 | ||||||||
\(225\) | −111640. | + | 479588.i | −0.147016 | + | 0.631556i | ||||
\(226\) | 602346. | 0.784468 | ||||||||
\(227\) | −1.29140e6 | −1.66340 | −0.831700 | − | 0.555225i | \(-0.812632\pi\) | ||||
−0.831700 | + | 0.555225i | \(0.812632\pi\) | |||||||
\(228\) | 1.22878e6 | + | 1.54767e6i | 1.56544 | + | 1.97170i | ||||
\(229\) | − | 1.12370e6i | − | 1.41600i | −0.706214 | − | 0.707998i | \(-0.749599\pi\) | ||
0.706214 | − | 0.707998i | \(-0.250401\pi\) | |||||||
\(230\) | 536035.i | 0.668150i | ||||||||
\(231\) | 114617. | + | 144362.i | 0.141324 | + | 0.178001i | ||||
\(232\) | 2.65109e6i | 3.23373i | ||||||||
\(233\) | −606409. | −0.731772 | −0.365886 | − | 0.930660i | \(-0.619234\pi\) | ||||
−0.365886 | + | 0.930660i | \(0.619234\pi\) | |||||||
\(234\) | −1.93953e6 | − | 451490.i | −2.31556 | − | 0.539024i | ||||
\(235\) | 578761.i | 0.683644i | ||||||||
\(236\) | −1.36202e6 | + | 1.77044e6i | −1.59185 | + | 2.06920i | ||||
\(237\) | 757404. | + | 953965.i | 0.875904 | + | 1.10322i | ||||
\(238\) | − | 1.97892e6i | − | 2.26457i | ||||||
\(239\) | 819859.i | 0.928420i | 0.885725 | + | 0.464210i | \(0.153662\pi\) | ||||
−0.885725 | + | 0.464210i | \(0.846338\pi\) | |||||||
\(240\) | −1.32800e6 | + | 1.05437e6i | −1.48824 | + | 1.18159i | ||||
\(241\) | −1.16362e6 | −1.29053 | −0.645266 | − | 0.763958i | \(-0.723253\pi\) | ||||
−0.645266 | + | 0.763958i | \(0.723253\pi\) | |||||||
\(242\) | 1.68180e6 | 1.84602 | ||||||||
\(243\) | −195143. | − | 899560.i | −0.212001 | − | 0.977269i | ||||
\(244\) | − | 1.82400e6i | − | 1.96133i | ||||||
\(245\) | 452667.i | 0.481797i | ||||||||
\(246\) | −1.92745e6 | + | 1.53031e6i | −2.03070 | + | 1.61228i | ||||
\(247\) | − | 1.15690e6i | − | 1.20657i | ||||||
\(248\) | − | 2.21847e6i | − | 2.29046i | ||||||
\(249\) | −356714. | − | 449288.i | −0.364604 | − | 0.459226i | ||||
\(250\) | − | 1.83534e6i | − | 1.85723i | ||||||
\(251\) | 1.79587e6i | 1.79925i | 0.436663 | + | 0.899625i | \(0.356160\pi\) | ||||
−0.436663 | + | 0.899625i | \(0.643840\pi\) | |||||||
\(252\) | 803330. | − | 3.45097e6i | 0.796879 | − | 3.42326i | ||||
\(253\) | 101929. | 0.100115 | ||||||||
\(254\) | −3.64502e6 | −3.54500 | ||||||||
\(255\) | 338879. | + | 426825.i | 0.326358 | + | 0.411055i | ||||
\(256\) | 948411. | 0.904476 | ||||||||
\(257\) | − | 1.48356e6i | − | 1.40111i | −0.713599 | − | 0.700554i | \(-0.752936\pi\) | ||
0.713599 | − | 0.700554i | \(-0.247064\pi\) | |||||||
\(258\) | 2.62170e6 | − | 2.08151e6i | 2.45208 | − | 1.94684i | ||||
\(259\) | 1.08557e6i | 1.00556i | ||||||||
\(260\) | 2.11108e6 | 1.93674 | ||||||||
\(261\) | 1.13253e6 | + | 263633.i | 1.02907 | + | 0.239552i | ||||
\(262\) | −3.75825e6 | −3.38246 | ||||||||
\(263\) | − | 485145.i | − | 0.432496i | −0.976338 | − | 0.216248i | \(-0.930618\pi\) | ||
0.976338 | − | 0.216248i | \(-0.0693820\pi\) | |||||||
\(264\) | 363812. | + | 458229.i | 0.321268 | + | 0.404643i | ||||
\(265\) | −108122. | −0.0945801 | ||||||||
\(266\) | 2.84694e6 | 2.46703 | ||||||||
\(267\) | 903901. | + | 1.13848e6i | 0.775966 | + | 0.977345i | ||||
\(268\) | − | 1.69882e6i | − | 1.44481i | ||||||
\(269\) | 324626. | 0.273528 | 0.136764 | − | 0.990604i | \(-0.456330\pi\) | ||||
0.136764 | + | 0.990604i | \(0.456330\pi\) | |||||||
\(270\) | 577690. | + | 1.21970e6i | 0.482265 | + | 1.01822i | ||||
\(271\) | −1.01698e6 | −0.841179 | −0.420589 | − | 0.907251i | \(-0.638177\pi\) | ||||
−0.420589 | + | 0.907251i | \(0.638177\pi\) | |||||||
\(272\) | − | 3.46163e6i | − | 2.83699i | ||||||
\(273\) | −1.62456e6 | + | 1.28982e6i | −1.31925 | + | 1.04742i | ||||
\(274\) | 1.29084e6i | 1.03872i | ||||||||
\(275\) | −137284. | −0.109468 | ||||||||
\(276\) | −1.21831e6 | − | 1.53449e6i | −0.962687 | − | 1.21252i | ||||
\(277\) | −49056.0 | −0.0384143 | −0.0192072 | − | 0.999816i | \(-0.506114\pi\) | ||||
−0.0192072 | + | 0.999816i | \(0.506114\pi\) | |||||||
\(278\) | −221152. | −0.171624 | ||||||||
\(279\) | −947712. | − | 220612.i | −0.728897 | − | 0.169675i | ||||
\(280\) | 3.20509e6i | 2.44312i | ||||||||
\(281\) | − | 720981.i | − | 0.544701i | −0.962198 | − | 0.272350i | \(-0.912199\pi\) | ||
0.962198 | − | 0.272350i | \(-0.0878010\pi\) | |||||||
\(282\) | −1.81928e6 | − | 2.29142e6i | −1.36231 | − | 1.71586i | ||||
\(283\) | − | 1.88644e6i | − | 1.40016i | −0.714066 | − | 0.700079i | \(-0.753148\pi\) | ||
0.714066 | − | 0.700079i | \(-0.246852\pi\) | |||||||
\(284\) | 2.21305e6i | 1.62815i | ||||||||
\(285\) | −614046. | + | 487524.i | −0.447805 | + | 0.355536i | ||||
\(286\) | − | 555196.i | − | 0.401357i | ||||||
\(287\) | 2.56358e6i | 1.83714i | ||||||||
\(288\) | 966766. | − | 4.15307e6i | 0.686815 | − | 2.95045i | ||||
\(289\) | 307278. | 0.216415 | ||||||||
\(290\) | −1.70488e6 | −1.19041 | ||||||||
\(291\) | 519744. | − | 412652.i | 0.359796 | − | 0.285661i | ||||
\(292\) | 6.55718e6i | 4.50049i | ||||||||
\(293\) | 645578.i | 0.439319i | 0.975577 | + | 0.219659i | \(0.0704946\pi\) | ||||
−0.975577 | + | 0.219659i | \(0.929505\pi\) | |||||||
\(294\) | −1.42292e6 | − | 1.79219e6i | −0.960089 | − | 1.20925i | ||||
\(295\) | −702433. | − | 540387.i | −0.469948 | − | 0.361535i | ||||
\(296\) | 3.44579e6i | 2.28591i | ||||||||
\(297\) | 231931. | − | 109850.i | 0.152569 | − | 0.0722619i | ||||
\(298\) | 1.85856e6 | 1.21237 | ||||||||
\(299\) | 1.14705e6i | 0.741999i | ||||||||
\(300\) | 1.64088e6 | + | 2.06673e6i | 1.05263 | + | 1.32581i | ||||
\(301\) | − | 3.48696e6i | − | 2.21836i | ||||||
\(302\) | − | 1.24006e6i | − | 0.782391i | ||||||
\(303\) | 1.26020e6 | + | 1.58724e6i | 0.788554 | + | 0.993199i | ||||
\(304\) | 4.98001e6 | 3.09063 | ||||||||
\(305\) | 723682. | 0.445449 | ||||||||
\(306\) | −2.68337e6 | − | 624645.i | −1.63824 | − | 0.381355i | ||||
\(307\) | −820548. | −0.496888 | −0.248444 | − | 0.968646i | \(-0.579919\pi\) | ||||
−0.248444 | + | 0.968646i | \(0.579919\pi\) | |||||||
\(308\) | 987852. | 0.593356 | ||||||||
\(309\) | 2.24373e6 | − | 1.78141e6i | 1.33682 | − | 1.06137i | ||||
\(310\) | 1.42666e6 | 0.843174 | ||||||||
\(311\) | − | 1.29992e6i | − | 0.762107i | −0.924553 | − | 0.381053i | \(-0.875561\pi\) | ||
0.924553 | − | 0.381053i | \(-0.124439\pi\) | |||||||
\(312\) | −5.15661e6 | + | 4.09411e6i | −2.99901 | + | 2.38107i | ||||
\(313\) | 769798.i | 0.444136i | 0.975031 | + | 0.222068i | \(0.0712807\pi\) | ||||
−0.975031 | + | 0.222068i | \(0.928719\pi\) | |||||||
\(314\) | 716426.i | 0.410060i | ||||||||
\(315\) | 1.36919e6 | + | 318725.i | 0.777478 | + | 0.180984i | ||||
\(316\) | 6.52788e6 | 3.67752 | ||||||||
\(317\) | − | 1.00921e6i | − | 0.564068i | −0.959404 | − | 0.282034i | \(-0.908991\pi\) | ||
0.959404 | − | 0.282034i | \(-0.0910092\pi\) | |||||||
\(318\) | 428076. | − | 339872.i | 0.237385 | − | 0.188472i | ||||
\(319\) | 324189.i | 0.178370i | ||||||||
\(320\) | 2.77105e6i | 1.51276i | ||||||||
\(321\) | 1.73651e6 | − | 1.37871e6i | 0.940622 | − | 0.746810i | ||||
\(322\) | −2.82269e6 | −1.51713 | ||||||||
\(323\) | − | 1.60059e6i | − | 0.853640i | ||||||
\(324\) | −4.42588e6 | − | 2.17860e6i | −2.34227 | − | 1.15296i | ||||
\(325\) | − | 1.54490e6i | − | 0.811321i | ||||||
\(326\) | 4.47977e6 | 2.33460 | ||||||||
\(327\) | −358670. | + | 284767.i | −0.185492 | + | 0.147272i | ||||
\(328\) | 8.13725e6i | 4.17631i | ||||||||
\(329\) | −3.04768e6 | −1.55231 | ||||||||
\(330\) | −294680. | + | 233962.i | −0.148959 | + | 0.118266i | ||||
\(331\) | 1.87477e6 | 0.940539 | 0.470270 | − | 0.882523i | \(-0.344157\pi\) | ||||
0.470270 | + | 0.882523i | \(0.344157\pi\) | |||||||
\(332\) | −3.07443e6 | −1.53080 | ||||||||
\(333\) | 1.47202e6 | + | 342661.i | 0.727447 | + | 0.169338i | ||||
\(334\) | 6.99591e6i | 3.43145i | ||||||||
\(335\) | 674018. | 0.328140 | ||||||||
\(336\) | −5.55219e6 | − | 6.99309e6i | −2.68297 | − | 3.37926i | ||||
\(337\) | 1.12324e6i | 0.538763i | 0.963034 | + | 0.269381i | \(0.0868192\pi\) | ||||
−0.963034 | + | 0.269381i | \(0.913181\pi\) | |||||||
\(338\) | 2.25679e6 | 1.07448 | ||||||||
\(339\) | −543167. | − | 684130.i | −0.256705 | − | 0.323325i | ||||
\(340\) | 2.92072e6 | 1.37023 | ||||||||
\(341\) | − | 271286.i | − | 0.126340i | ||||||
\(342\) | 898636. | − | 3.86039e6i | 0.415450 | − | 1.78470i | ||||
\(343\) | 549800. | 0.252330 | ||||||||
\(344\) | − | 1.10682e7i | − | 5.04291i | ||||||
\(345\) | 608816. | − | 483371.i | 0.275384 | − | 0.218642i | ||||
\(346\) | −2.18620e6 | −0.981745 | ||||||||
\(347\) | 827946. | 0.369129 | 0.184565 | − | 0.982820i | \(-0.440913\pi\) | ||||
0.184565 | + | 0.982820i | \(0.440913\pi\) | |||||||
\(348\) | 4.88048e6 | − | 3.87487e6i | 2.16030 | − | 1.71518i | ||||
\(349\) | − | 2.51515e6i | − | 1.10535i | −0.833396 | − | 0.552676i | \(-0.813607\pi\) | ||
0.833396 | − | 0.552676i | \(-0.186393\pi\) | |||||||
\(350\) | 3.80174e6 | 1.65887 | ||||||||
\(351\) | 1.23618e6 | + | 2.61000e6i | 0.535568 | + | 1.13077i | ||||
\(352\) | 1.18883e6 | 0.511402 | ||||||||
\(353\) | 3.47327e6 | 1.48355 | 0.741775 | − | 0.670649i | \(-0.233984\pi\) | ||||
0.741775 | + | 0.670649i | \(0.233984\pi\) | |||||||
\(354\) | 4.47972e6 | − | 68539.9i | 1.89995 | − | 0.0290694i | ||||
\(355\) | −878039. | −0.369780 | ||||||||
\(356\) | 7.79051e6 | 3.25792 | ||||||||
\(357\) | −2.24760e6 | + | 1.78449e6i | −0.933360 | + | 0.741044i | ||||
\(358\) | −5.00592e6 | −2.06432 | ||||||||
\(359\) | − | 1.49142e6i | − | 0.610751i | −0.952232 | − | 0.305376i | \(-0.901218\pi\) | ||
0.952232 | − | 0.305376i | \(-0.0987820\pi\) | |||||||
\(360\) | 4.34605e6 | + | 1.01169e6i | 1.76741 | + | 0.411425i | ||||
\(361\) | −173429. | −0.0700413 | ||||||||
\(362\) | −9.28538e6 | −3.72416 | ||||||||
\(363\) | −1.51657e6 | − | 1.91015e6i | −0.604082 | − | 0.760854i | ||||
\(364\) | 1.11167e7i | 4.39765i | ||||||||
\(365\) | −2.60160e6 | −1.02213 | ||||||||
\(366\) | −2.86519e6 | + | 2.27483e6i | −1.11802 | + | 0.887659i | ||||
\(367\) | − | 3.83867e6i | − | 1.48770i | −0.668346 | − | 0.743850i | \(-0.732997\pi\) | ||
0.668346 | − | 0.743850i | \(-0.267003\pi\) | |||||||
\(368\) | −4.93760e6 | −1.90062 | ||||||||
\(369\) | 3.47617e6 | + | 809196.i | 1.32903 | + | 0.309377i | ||||
\(370\) | −2.21594e6 | −0.841498 | ||||||||
\(371\) | − | 569356.i | − | 0.214758i | ||||||
\(372\) | −4.08405e6 | + | 3.24255e6i | −1.53015 | + | 1.21487i | ||||
\(373\) | 2.13313e6 | 0.793862 | 0.396931 | − | 0.917848i | \(-0.370075\pi\) | ||||
0.396931 | + | 0.917848i | \(0.370075\pi\) | |||||||
\(374\) | − | 768125.i | − | 0.283957i | ||||||
\(375\) | −2.08453e6 | + | 1.65502e6i | −0.765474 | + | 0.607750i | ||||
\(376\) | −9.67384e6 | −3.52882 | ||||||||
\(377\) | −3.64822e6 | −1.32199 | ||||||||
\(378\) | −6.42277e6 | + | 3.04204e6i | −2.31203 | + | 1.09505i | ||||
\(379\) | −341863. | −0.122252 | −0.0611258 | − | 0.998130i | \(-0.519469\pi\) | ||||
−0.0611258 | + | 0.998130i | \(0.519469\pi\) | |||||||
\(380\) | 4.20185e6i | 1.49273i | ||||||||
\(381\) | 3.28691e6 | + | 4.13993e6i | 1.16005 | + | 1.46110i | ||||
\(382\) | −6.02109e6 | −2.11114 | ||||||||
\(383\) | − | 2.17138e6i | − | 0.756378i | −0.925728 | − | 0.378189i | \(-0.876547\pi\) | ||
0.925728 | − | 0.378189i | \(-0.123453\pi\) | |||||||
\(384\) | −3.26768e6 | − | 4.11571e6i | −1.13087 | − | 1.42435i | ||||
\(385\) | 391936.i | 0.134761i | ||||||||
\(386\) | −298928. | −0.102117 | ||||||||
\(387\) | −4.72826e6 | − | 1.10066e6i | −1.60481 | − | 0.373573i | ||||
\(388\) | − | 3.55655e6i | − | 1.19936i | ||||||
\(389\) | 1.49102e6i | 0.499586i | 0.968299 | + | 0.249793i | \(0.0803625\pi\) | ||||
−0.968299 | + | 0.249793i | \(0.919638\pi\) | |||||||
\(390\) | −2.63286e6 | − | 3.31615e6i | −0.876530 | − | 1.10401i | ||||
\(391\) | 1.58696e6i | 0.524958i | ||||||||
\(392\) | −7.56621e6 | −2.48693 | ||||||||
\(393\) | 3.38902e6 | + | 4.26853e6i | 1.10686 | + | 1.39411i | ||||
\(394\) | 1.62957e6i | 0.528848i | ||||||||
\(395\) | 2.58997e6i | 0.835223i | ||||||||
\(396\) | 311816. | − | 1.33951e6i | 0.0999218 | − | 0.429248i | ||||
\(397\) | 89427.3i | 0.0284770i | 0.999899 | + | 0.0142385i | \(0.00453240\pi\) | ||||
−0.999899 | + | 0.0142385i | \(0.995468\pi\) | |||||||
\(398\) | −778790. | −0.246441 | ||||||||
\(399\) | −2.56723e6 | − | 3.23348e6i | −0.807296 | − | 1.01681i | ||||
\(400\) | 6.65021e6 | 2.07819 | ||||||||
\(401\) | −1.56878e6 | −0.487194 | −0.243597 | − | 0.969877i | \(-0.578327\pi\) | ||||
−0.243597 | + | 0.969877i | \(0.578327\pi\) | |||||||
\(402\) | −2.66856e6 | + | 2.11871e6i | −0.823592 | + | 0.653894i | ||||
\(403\) | 3.05288e6 | 0.936368 | ||||||||
\(404\) | 1.08613e7 | 3.31077 | ||||||||
\(405\) | 864372. | − | 1.75599e6i | 0.261856 | − | 0.531968i | ||||
\(406\) | − | 8.97765e6i | − | 2.70301i | ||||||
\(407\) | 421369.i | 0.126089i | ||||||||
\(408\) | −7.13428e6 | + | 5.66428e6i | −2.12178 | + | 1.68459i | ||||
\(409\) | − | 5.10075e6i | − | 1.50774i | −0.657025 | − | 0.753869i | \(-0.728185\pi\) | ||
0.657025 | − | 0.753869i | \(-0.271815\pi\) | |||||||
\(410\) | −5.23295e6 | −1.53740 | ||||||||
\(411\) | 1.46611e6 | − | 1.16402e6i | 0.428117 | − | 0.339904i | ||||
\(412\) | − | 1.53536e7i | − | 4.45622i | ||||||
\(413\) | 2.84561e6 | − | 3.69892e6i | 0.820918 | − | 1.06709i | ||||
\(414\) | −890982. | + | 3.82751e6i | −0.255487 | + | 1.09753i | ||||
\(415\) | − | 1.21980e6i | − | 0.347670i | ||||||
\(416\) | 1.33783e7i | 3.79026i | ||||||||
\(417\) | 199425. | + | 251179.i | 0.0561615 | + | 0.0707365i | ||||
\(418\) | 1.10505e6 | 0.309344 | ||||||||
\(419\) | 1.49547e6 | 0.416143 | 0.208071 | − | 0.978114i | \(-0.433281\pi\) | ||||
0.208071 | + | 0.978114i | \(0.433281\pi\) | |||||||
\(420\) | 5.90037e6 | − | 4.68462e6i | 1.63214 | − | 1.29584i | ||||
\(421\) | 4.23420e6i | 1.16430i | 0.813080 | + | 0.582151i | \(0.197789\pi\) | ||||
−0.813080 | + | 0.582151i | \(0.802211\pi\) | |||||||
\(422\) | 9.92983e6i | 2.71432i | ||||||||
\(423\) | −962000. | + | 4.13259e6i | −0.261411 | + | 1.12298i | ||||
\(424\) | − | 1.80723e6i | − | 0.488202i | ||||||
\(425\) | − | 2.13740e6i | − | 0.574003i | ||||||
\(426\) | 3.47632e6 | − | 2.76003e6i | 0.928102 | − | 0.736870i | ||||
\(427\) | 3.81081e6i | 1.01146i | ||||||||
\(428\) | − | 1.18828e7i | − | 3.13551i | ||||||
\(429\) | −630578. | + | 500650.i | −0.165423 | + | 0.131338i | ||||
\(430\) | 7.11781e6 | 1.85641 | ||||||||
\(431\) | 2.91462e6 | 0.755769 | 0.377885 | − | 0.925853i | \(-0.376652\pi\) | ||||
0.377885 | + | 0.925853i | \(0.376652\pi\) | |||||||
\(432\) | −1.12351e7 | + | 5.32129e6i | −2.89645 | + | 1.37185i | ||||
\(433\) | −2.84121e6 | −0.728256 | −0.364128 | − | 0.931349i | \(-0.618633\pi\) | ||||
−0.364128 | + | 0.931349i | \(0.618633\pi\) | |||||||
\(434\) | 7.51262e6i | 1.91455i | ||||||||
\(435\) | 1.53738e6 | + | 1.93636e6i | 0.389545 | + | 0.490640i | ||||
\(436\) | 2.45434e6i | 0.618328i | ||||||||
\(437\) | −2.28306e6 | −0.571891 | ||||||||
\(438\) | 1.03002e7 | − | 8.17788e6i | 2.56543 | − | 2.03683i | ||||
\(439\) | −6.42656e6 | −1.59154 | −0.795769 | − | 0.605600i | \(-0.792933\pi\) | ||||
−0.795769 | + | 0.605600i | \(0.792933\pi\) | |||||||
\(440\) | 1.24407e6i | 0.306347i | ||||||||
\(441\) | −752410. | + | 3.23223e6i | −0.184229 | + | 0.791418i | ||||
\(442\) | 8.64398e6 | 2.10455 | ||||||||
\(443\) | 5.11084e6 | 1.23732 | 0.618662 | − | 0.785657i | \(-0.287675\pi\) | ||||
0.618662 | + | 0.785657i | \(0.287675\pi\) | |||||||
\(444\) | 6.34347e6 | − | 5.03642e6i | 1.52711 | − | 1.21245i | ||||
\(445\) | 3.09093e6i | 0.739927i | ||||||||
\(446\) | 3.12239e6 | 0.743277 | ||||||||
\(447\) | −1.67596e6 | − | 2.11090e6i | −0.396729 | − | 0.499689i | ||||
\(448\) | −1.45920e7 | −3.43494 | ||||||||
\(449\) | − | 3.61586e6i | − | 0.846438i | −0.906027 | − | 0.423219i | \(-0.860900\pi\) | ||
0.906027 | − | 0.423219i | \(-0.139100\pi\) | |||||||
\(450\) | 1.20002e6 | − | 5.15509e6i | 0.279356 | − | 1.20007i | ||||
\(451\) | 995066.i | 0.230362i | ||||||||
\(452\) | −4.68143e6 | −1.07779 | ||||||||
\(453\) | −1.40843e6 | + | 1.11822e6i | −0.322469 | + | 0.256026i | ||||
\(454\) | 1.38813e7 | 3.16075 | ||||||||
\(455\) | −4.41060e6 | −0.998778 | ||||||||
\(456\) | −8.14883e6 | − | 1.02636e7i | −1.83520 | − | 2.31147i | ||||
\(457\) | 7.99940e6i | 1.79171i | 0.444350 | + | 0.895853i | \(0.353435\pi\) | ||||
−0.444350 | + | 0.895853i | \(0.646565\pi\) | |||||||
\(458\) | 1.20787e7i | 2.69064i | ||||||||
\(459\) | 1.71028e6 | + | 3.61099e6i | 0.378910 | + | 0.800008i | ||||
\(460\) | − | 4.16606e6i | − | 0.917976i | ||||||
\(461\) | − | 2.33966e6i | − | 0.512743i | −0.966578 | − | 0.256372i | \(-0.917473\pi\) | ||
0.966578 | − | 0.256372i | \(-0.0825271\pi\) | |||||||
\(462\) | −1.23201e6 | − | 1.55175e6i | −0.268541 | − | 0.338233i | ||||
\(463\) | 6.12417e6i | 1.32768i | 0.747873 | + | 0.663842i | \(0.231075\pi\) | ||||
−0.747873 | + | 0.663842i | \(0.768925\pi\) | |||||||
\(464\) | − | 1.57042e7i | − | 3.38626i | ||||||
\(465\) | −1.28650e6 | − | 1.62037e6i | −0.275916 | − | 0.347522i | ||||
\(466\) | 6.51829e6 | 1.39049 | ||||||||
\(467\) | 2.76756e6 | 0.587225 | 0.293612 | − | 0.955925i | \(-0.405142\pi\) | ||||
0.293612 | + | 0.955925i | \(0.405142\pi\) | |||||||
\(468\) | 1.50740e7 | + | 3.50898e6i | 3.18137 | + | 0.740570i | ||||
\(469\) | 3.54929e6i | 0.745090i | ||||||||
\(470\) | − | 6.22111e6i | − | 1.29904i | ||||||
\(471\) | 813700. | − | 646040.i | 0.169010 | − | 0.134186i | ||||
\(472\) | 9.03243e6 | − | 1.17410e7i | 1.86616 | − | 2.42577i | ||||
\(473\) | − | 1.35348e6i | − | 0.278163i | ||||||
\(474\) | −8.14134e6 | − | 1.02542e7i | −1.66437 | − | 2.09631i | ||||
\(475\) | 3.07494e6 | 0.625320 | ||||||||
\(476\) | 1.53801e7i | 3.11130i | ||||||||
\(477\) | −772037. | − | 179717.i | −0.155361 | − | 0.0361655i | ||||
\(478\) | − | 8.81268e6i | − | 1.76416i | ||||||
\(479\) | − | 3.22713e6i | − | 0.642656i | −0.946968 | − | 0.321328i | \(-0.895871\pi\) | ||
0.946968 | − | 0.321328i | \(-0.104129\pi\) | |||||||
\(480\) | 7.10079e6 | − | 5.63769e6i | 1.40671 | − | 1.11686i | ||||
\(481\) | −4.74182e6 | −0.934507 | ||||||||
\(482\) | 1.25078e7 | 2.45223 | ||||||||
\(483\) | 2.54537e6 | + | 3.20594e6i | 0.496458 | + | 0.625299i | ||||
\(484\) | −1.30710e7 | −2.53626 | ||||||||
\(485\) | 1.41108e6 | 0.272394 | ||||||||
\(486\) | 2.09760e6 | + | 9.66938e6i | 0.402839 | + | 1.85698i | ||||
\(487\) | 1.97410e6 | 0.377178 | 0.188589 | − | 0.982056i | \(-0.439609\pi\) | ||||
0.188589 | + | 0.982056i | \(0.439609\pi\) | |||||||
\(488\) | 1.20962e7i | 2.29931i | ||||||||
\(489\) | −4.03965e6 | − | 5.08802e6i | −0.763961 | − | 0.962225i | ||||
\(490\) | − | 4.86572e6i | − | 0.915498i | ||||||
\(491\) | 8.54422e6i | 1.59944i | 0.600371 | + | 0.799722i | \(0.295020\pi\) | ||||
−0.600371 | + | 0.799722i | \(0.704980\pi\) | |||||||
\(492\) | 1.49801e7 | − | 1.18935e7i | 2.78999 | − | 2.21513i | ||||
\(493\) | −5.04738e6 | −0.935295 | ||||||||
\(494\) | 1.24355e7i | 2.29270i | ||||||||
\(495\) | 531458. | + | 123715.i | 0.0974890 | + | 0.0226938i | ||||
\(496\) | 1.31415e7i | 2.39850i | ||||||||
\(497\) | − | 4.62363e6i | − | 0.839639i | ||||||
\(498\) | 3.83432e6 | + | 4.82941e6i | 0.692812 | + | 0.872610i | ||||
\(499\) | −5.53151e6 | −0.994472 | −0.497236 | − | 0.867615i | \(-0.665652\pi\) | ||||
−0.497236 | + | 0.867615i | \(0.665652\pi\) | |||||||
\(500\) | 1.42642e7i | 2.55166i | ||||||||
\(501\) | 7.94579e6 | − | 6.30858e6i | 1.41430 | − | 1.12289i | ||||
\(502\) | − | 1.93039e7i | − | 3.41889i | ||||||
\(503\) | 2.37831e6 | 0.419130 | 0.209565 | − | 0.977795i | \(-0.432795\pi\) | ||||
0.209565 | + | 0.977795i | \(0.432795\pi\) | |||||||
\(504\) | −5.32741e6 | + | 2.28857e7i | −0.934200 | + | 4.01317i | ||||
\(505\) | 4.30929e6i | 0.751930i | ||||||||
\(506\) | −1.09564e6 | −0.190235 | ||||||||
\(507\) | −2.03507e6 | − | 2.56321e6i | −0.351608 | − | 0.442857i | ||||
\(508\) | 2.83291e7 | 4.87050 | ||||||||
\(509\) | −9.30835e6 | −1.59250 | −0.796248 | − | 0.604971i | \(-0.793185\pi\) | ||||
−0.796248 | + | 0.604971i | \(0.793185\pi\) | |||||||
\(510\) | −3.64262e6 | − | 4.58795e6i | −0.620138 | − | 0.781076i | ||||
\(511\) | − | 1.36997e7i | − | 2.32090i | ||||||
\(512\) | 593343. | 0.100030 | ||||||||
\(513\) | −5.19489e6 | + | 2.46047e6i | −0.871531 | + | 0.412786i | ||||
\(514\) | 1.59468e7i | 2.66235i | ||||||||
\(515\) | 6.09162e6 | 1.01208 | ||||||||
\(516\) | −2.03759e7 | + | 1.61775e7i | −3.36893 | + | 2.67477i | ||||
\(517\) | −1.18297e6 | −0.194647 | ||||||||
\(518\) | − | 1.16688e7i | − | 1.91074i | ||||||
\(519\) | 1.97141e6 | + | 2.48303e6i | 0.321261 | + | 0.404635i | ||||
\(520\) | −1.40000e7 | −2.27049 | ||||||||
\(521\) | − | 7.87657e6i | − | 1.27129i | −0.771983 | − | 0.635643i | \(-0.780735\pi\) | ||
0.771983 | − | 0.635643i | \(-0.219265\pi\) | |||||||
\(522\) | −1.21735e7 | − | 2.83380e6i | −1.95542 | − | 0.455190i | ||||
\(523\) | −715534. | −0.114387 | −0.0571934 | − | 0.998363i | \(-0.518215\pi\) | ||||
−0.0571934 | + | 0.998363i | \(0.518215\pi\) | |||||||
\(524\) | 2.92091e7 | 4.64719 | ||||||||
\(525\) | −3.42823e6 | − | 4.31793e6i | −0.542840 | − | 0.683718i | ||||
\(526\) | 5.21483e6i | 0.821818i | ||||||||
\(527\) | 4.22372e6 | 0.662473 | ||||||||
\(528\) | −2.15511e6 | − | 2.71440e6i | −0.336421 | − | 0.423730i | ||||
\(529\) | −4.17273e6 | −0.648308 | ||||||||
\(530\) | 1.16221e6 | 0.179719 | ||||||||
\(531\) | −4.11745e6 | − | 5.02615e6i | −0.633712 | − | 0.773569i | ||||
\(532\) | −2.21264e7 | −3.38946 | ||||||||
\(533\) | −1.11978e7 | −1.70732 | ||||||||
\(534\) | −9.71605e6 | − | 1.22376e7i | −1.47447 | − | 1.85713i | ||||
\(535\) | 4.71455e6 | 0.712124 | ||||||||
\(536\) | 1.12660e7i | 1.69379i | ||||||||
\(537\) | 4.51411e6 | + | 5.68561e6i | 0.675517 | + | 0.850827i | ||||
\(538\) | −3.48941e6 | −0.519752 | ||||||||
\(539\) | −925237. | −0.137177 | ||||||||
\(540\) | −4.48980e6 | − | 9.47949e6i | −0.662587 | − | 1.39895i | ||||
\(541\) | 5.55517e6i | 0.816027i | 0.912976 | + | 0.408013i | \(0.133778\pi\) | ||||
−0.912976 | + | 0.408013i | \(0.866222\pi\) | |||||||
\(542\) | 1.09315e7 | 1.59839 | ||||||||
\(543\) | 8.37312e6 | + | 1.05461e7i | 1.21867 | + | 1.53494i | ||||
\(544\) | 1.85092e7i | 2.68157i | ||||||||
\(545\) | −973774. | −0.140432 | ||||||||
\(546\) | 1.74624e7 | − | 1.38643e7i | 2.50681 | − | 1.99029i | ||||
\(547\) | −2.56306e6 | −0.366261 | −0.183131 | − | 0.983089i | \(-0.558623\pi\) | ||||
−0.183131 | + | 0.983089i | \(0.558623\pi\) | |||||||
\(548\) | − | 1.00324e7i | − | 1.42710i | ||||||
\(549\) | 5.16739e6 | + | 1.20288e6i | 0.731712 | + | 0.170331i | ||||
\(550\) | 1.47566e6 | 0.208008 | ||||||||
\(551\) | − | 7.26134e6i | − | 1.01891i | ||||||
\(552\) | 8.07942e6 | + | 1.01762e7i | 1.12858 | + | 1.42147i | ||||
\(553\) | −1.36384e7 | −1.89650 | ||||||||
\(554\) | 527304. | 0.0729939 | ||||||||
\(555\) | 1.99823e6 | + | 2.51681e6i | 0.275367 | + | 0.346831i | ||||
\(556\) | 1.71879e6 | 0.235796 | ||||||||
\(557\) | − | 7.81111e6i | − | 1.06678i | −0.845870 | − | 0.533390i | \(-0.820918\pi\) | ||
0.845870 | − | 0.533390i | \(-0.179082\pi\) | |||||||
\(558\) | 1.01870e7 | + | 2.37136e6i | 1.38503 | + | 0.322412i | ||||
\(559\) | 1.52312e7 | 2.06160 | ||||||||
\(560\) | − | 1.89859e7i | − | 2.55836i | ||||||
\(561\) | −872417. | + | 692658.i | −0.117035 | + | 0.0929206i | ||||
\(562\) | 7.74984e6i | 1.03503i | ||||||||
\(563\) | 2.06962e6 | 0.275182 | 0.137591 | − | 0.990489i | \(-0.456064\pi\) | ||||
0.137591 | + | 0.990489i | \(0.456064\pi\) | |||||||
\(564\) | 1.41395e7 | + | 1.78089e7i | 1.87169 | + | 2.35744i | ||||
\(565\) | − | 1.85738e6i | − | 0.244782i | ||||||
\(566\) | 2.02774e7i | 2.66054i | ||||||||
\(567\) | 9.24682e6 | + | 4.55166e6i | 1.20791 | + | 0.594583i | ||||
\(568\) | − | 1.46762e7i | − | 1.90872i | ||||||
\(569\) | −4.95942e6 | −0.642170 | −0.321085 | − | 0.947050i | \(-0.604047\pi\) | ||||
−0.321085 | + | 0.947050i | \(0.604047\pi\) | |||||||
\(570\) | 6.60039e6 | − | 5.24040e6i | 0.850907 | − | 0.675580i | ||||
\(571\) | − | 1.32636e7i | − | 1.70244i | −0.524809 | − | 0.851220i | \(-0.675863\pi\) | ||
0.524809 | − | 0.851220i | \(-0.324137\pi\) | |||||||
\(572\) | 4.31498e6i | 0.551428i | ||||||||
\(573\) | 5.42954e6 | + | 6.83861e6i | 0.690838 | + | 0.870124i | ||||
\(574\) | − | 2.75560e7i | − | 3.49089i | ||||||
\(575\) | −3.04875e6 | −0.384549 | ||||||||
\(576\) | −4.60596e6 | + | 1.97865e7i | −0.578448 | + | 2.48492i | ||||
\(577\) | −5.63487e6 | −0.704603 | −0.352302 | − | 0.935887i | \(-0.614601\pi\) | ||||
−0.352302 | + | 0.935887i | \(0.614601\pi\) | |||||||
\(578\) | −3.30294e6 | −0.411226 | ||||||||
\(579\) | 269559. | + | 339515.i | 0.0334162 | + | 0.0420884i | ||||
\(580\) | 1.32503e7 | 1.63552 | ||||||||
\(581\) | 6.42329e6 | 0.789436 | ||||||||
\(582\) | −5.58673e6 | + | 4.43560e6i | −0.683676 | + | 0.542807i | ||||
\(583\) | − | 220998.i | − | 0.0269288i | ||||||
\(584\) | − | 4.34850e7i | − | 5.27603i | ||||||
\(585\) | −1.39221e6 | + | 5.98069e6i | −0.168195 | + | 0.722539i | ||||
\(586\) | − | 6.93933e6i | − | 0.834783i | ||||||
\(587\) | −2.95346e6 | −0.353782 | −0.176891 | − | 0.984230i | \(-0.556604\pi\) | ||||
−0.176891 | + | 0.984230i | \(0.556604\pi\) | |||||||
\(588\) | 1.10589e7 | + | 1.39289e7i | 1.31907 | + | 1.66140i | ||||
\(589\) | 6.07638e6i | 0.721700i | ||||||||
\(590\) | 7.55046e6 | + | 5.80863e6i | 0.892983 | + | 0.686979i | ||||
\(591\) | 1.85082e6 | − | 1.46947e6i | 0.217970 | − | 0.173058i | ||||
\(592\) | − | 2.04117e7i | − | 2.39373i | ||||||
\(593\) | 2.61462e6i | 0.305331i | 0.988278 | + | 0.152666i | \(0.0487858\pi\) | ||||
−0.988278 | + | 0.152666i | \(0.951214\pi\) | |||||||
\(594\) | −2.49303e6 | + | 1.18078e6i | −0.289908 | + | 0.137310i | ||||
\(595\) | −6.10215e6 | −0.706627 | ||||||||
\(596\) | −1.44447e7 | −1.66568 | ||||||||
\(597\) | 702276. | + | 884531.i | 0.0806440 | + | 0.101573i | ||||
\(598\) | − | 1.23296e7i | − | 1.40993i | ||||||
\(599\) | − | 5.62418e6i | − | 0.640460i | −0.947340 | − | 0.320230i | \(-0.896240\pi\) | ||
0.947340 | − | 0.320230i | \(-0.103760\pi\) | |||||||
\(600\) | −1.08818e7 | − | 1.37058e7i | −1.23402 | − | 1.55427i | ||||
\(601\) | 9.21924e6i | 1.04114i | 0.853819 | + | 0.520570i | \(0.174280\pi\) | ||||
−0.853819 | + | 0.520570i | \(0.825720\pi\) | |||||||
\(602\) | 3.74814e7i | 4.21526i | ||||||||
\(603\) | 4.81277e6 | + | 1.12033e6i | 0.539016 | + | 0.125474i | ||||
\(604\) | 9.63771e6i | 1.07493i | ||||||||
\(605\) | − | 5.18597e6i | − | 0.576026i | ||||||
\(606\) | −1.35459e7 | − | 1.70613e7i | −1.49839 | − | 1.88725i | ||||
\(607\) | 6.39908e6 | 0.704930 | 0.352465 | − | 0.935825i | \(-0.385344\pi\) | ||||
0.352465 | + | 0.935825i | \(0.385344\pi\) | |||||||
\(608\) | −2.66279e7 | −2.92132 | ||||||||
\(609\) | −1.01966e7 | + | 8.09562e6i | −1.11407 | + | 0.884518i | ||||
\(610\) | −7.77887e6 | −0.846432 | ||||||||
\(611\) | − | 1.33124e7i | − | 1.44262i | ||||||
\(612\) | 2.08552e7 | + | 4.85474e6i | 2.25079 | + | 0.523947i | ||||
\(613\) | − | 1.13754e7i | − | 1.22269i | −0.791366 | − | 0.611343i | \(-0.790630\pi\) | ||
0.791366 | − | 0.611343i | \(-0.209370\pi\) | |||||||
\(614\) | 8.82008e6 | 0.944173 | ||||||||
\(615\) | 4.71882e6 | + | 5.94346e6i | 0.503090 | + | 0.633653i | ||||
\(616\) | −6.55111e6 | −0.695605 | ||||||||
\(617\) | 4.96198e6i | 0.524737i | 0.964968 | + | 0.262369i | \(0.0845036\pi\) | ||||
−0.964968 | + | 0.262369i | \(0.915496\pi\) | |||||||
\(618\) | −2.41178e7 | + | 1.91484e7i | −2.54020 | + | 2.01680i | ||||
\(619\) | 7.34946e6 | 0.770955 | 0.385477 | − | 0.922717i | \(-0.374037\pi\) | ||||
0.385477 | + | 0.922717i | \(0.374037\pi\) | |||||||
\(620\) | −1.10880e7 | −1.15844 | ||||||||
\(621\) | 5.15064e6 | − | 2.43951e6i | 0.535960 | − | 0.253848i | ||||
\(622\) | 1.39729e7i | 1.44814i | ||||||||
\(623\) | −1.62764e7 | −1.68011 | ||||||||
\(624\) | 3.05461e7 | − | 2.42522e7i | 3.14047 | − | 2.49339i | ||||
\(625\) | 673027. | 0.0689180 | ||||||||
\(626\) | − | 8.27457e6i | − | 0.843936i | ||||||
\(627\) | −996482. | − | 1.25509e6i | −0.101228 | − | 0.127499i | ||||
\(628\) | − | 5.56806e6i | − | 0.563384i | ||||||
\(629\) | −6.56040e6 | −0.661156 | ||||||||
\(630\) | −1.47175e7 | − | 3.42598e6i | −1.47734 | − | 0.343901i | ||||
\(631\) | −5.08043e6 | −0.507957 | −0.253979 | − | 0.967210i | \(-0.581739\pi\) | ||||
−0.253979 | + | 0.967210i | \(0.581739\pi\) | |||||||
\(632\) | −4.32907e7 | −4.31124 | ||||||||
\(633\) | 1.12781e7 | − | 8.95425e6i | 1.11873 | − | 0.888219i | ||||
\(634\) | 1.08480e7i | 1.07183i | ||||||||
\(635\) | 1.12397e7i | 1.10617i | ||||||||
\(636\) | −3.32700e6 | + | 2.64148e6i | −0.326145 | + | 0.258944i | ||||
\(637\) | − | 1.04120e7i | − | 1.01669i | ||||||
\(638\) | − | 3.48471e6i | − | 0.338934i | ||||||
\(639\) | −6.26956e6 | − | 1.45945e6i | −0.607414 | − | 0.141396i | ||||
\(640\) | − | 1.11740e7i | − | 1.07835i | ||||||
\(641\) | − | 398727.i | − | 0.0383292i | −0.999816 | − | 0.0191646i | \(-0.993899\pi\) | ||
0.999816 | − | 0.0191646i | \(-0.00610066\pi\) | |||||||
\(642\) | −1.86658e7 | + | 1.48198e7i | −1.78735 | + | 1.41907i | ||||
\(643\) | 1.90598e7 | 1.81799 | 0.908994 | − | 0.416810i | \(-0.136852\pi\) | ||||
0.908994 | + | 0.416810i | \(0.136852\pi\) | |||||||
\(644\) | 2.19379e7 | 2.08440 | ||||||||
\(645\) | −6.41850e6 | − | 8.08423e6i | −0.607483 | − | 0.765138i | ||||
\(646\) | 1.72048e7i | 1.62207i | ||||||||
\(647\) | 1.69729e7i | 1.59403i | 0.603963 | + | 0.797013i | \(0.293588\pi\) | ||||
−0.603963 | + | 0.797013i | \(0.706412\pi\) | |||||||
\(648\) | 2.93510e7 | + | 1.44477e7i | 2.74590 | + | 1.35164i | ||||
\(649\) | 1.10453e6 | − | 1.43575e6i | 0.102936 | − | 0.133803i | ||||
\(650\) | 1.66062e7i | 1.54165i | ||||||||
\(651\) | 8.53265e6 | − | 6.77452e6i | 0.789099 | − | 0.626507i | ||||
\(652\) | −3.48168e7 | −3.20752 | ||||||||
\(653\) | 5.01672e6i | 0.460402i | 0.973143 | + | 0.230201i | \(0.0739384\pi\) | ||||
−0.973143 | + | 0.230201i | \(0.926062\pi\) | |||||||
\(654\) | 3.85535e6 | − | 3.06097e6i | 0.352468 | − | 0.279843i | ||||
\(655\) | 1.15889e7i | 1.05545i | ||||||||
\(656\) | − | 4.82024e7i | − | 4.37330i | ||||||
\(657\) | −1.85765e7 | − | 4.32430e6i | −1.67900 | − | 0.390843i | ||||
\(658\) | 3.27595e7 | 2.94967 | ||||||||
\(659\) | 1.03472e6 | 0.0928127 | 0.0464063 | − | 0.998923i | \(-0.485223\pi\) | ||||
0.0464063 | + | 0.998923i | \(0.485223\pi\) | |||||||
\(660\) | 2.29025e6 | − | 1.81835e6i | 0.204656 | − | 0.162487i | ||||
\(661\) | 2.39787e6 | 0.213463 | 0.106731 | − | 0.994288i | \(-0.465961\pi\) | ||||
0.106731 | + | 0.994288i | \(0.465961\pi\) | |||||||
\(662\) | −2.01519e7 | −1.78719 | ||||||||
\(663\) | −7.79474e6 | − | 9.81763e6i | −0.688680 | − | 0.867407i | ||||
\(664\) | 2.03886e7 | 1.79460 | ||||||||
\(665\) | − | 8.77876e6i | − | 0.769802i | ||||||
\(666\) | −1.58227e7 | − | 3.68327e6i | −1.38228 | − | 0.321771i | ||||
\(667\) | 7.19949e6i | 0.626595i | ||||||||
\(668\) | − | 5.43722e7i | − | 4.71450i | ||||||
\(669\) | −2.81563e6 | − | 3.54634e6i | −0.243226 | − | 0.306348i | ||||
\(670\) | −7.24503e6 | −0.623524 | ||||||||
\(671\) | 1.47918e6i | 0.126828i | ||||||||
\(672\) | 2.96873e7 | + | 3.73918e7i | 2.53599 | + | 3.19413i | ||||
\(673\) | 4.67594e6i | 0.397952i | 0.980004 | + | 0.198976i | \(0.0637617\pi\) | ||||
−0.980004 | + | 0.198976i | \(0.936238\pi\) | |||||||
\(674\) | − | 1.20737e7i | − | 1.02374i | ||||||
\(675\) | −6.93715e6 | + | 3.28567e6i | −0.586033 | + | 0.277564i | ||||
\(676\) | −1.75398e7 | −1.47624 | ||||||||
\(677\) | 5.07682e6i | 0.425716i | 0.977083 | + | 0.212858i | \(0.0682772\pi\) | ||||
−0.977083 | + | 0.212858i | \(0.931723\pi\) | |||||||
\(678\) | 5.83851e6 | + | 7.35372e6i | 0.487785 | + | 0.614374i | ||||
\(679\) | 7.43056e6i | 0.618511i | ||||||||
\(680\) | −1.93692e7 | −1.60635 | ||||||||
\(681\) | −1.25175e7 | − | 1.57660e7i | −1.03431 | − | 1.30273i | ||||
\(682\) | 2.91605e6i | 0.240068i | ||||||||
\(683\) | −2.30885e7 | −1.89384 | −0.946921 | − | 0.321467i | \(-0.895824\pi\) | ||||
−0.946921 | + | 0.321467i | \(0.895824\pi\) | |||||||
\(684\) | −6.98419e6 | + | 3.00030e7i | −0.570790 | + | 2.45202i | ||||
\(685\) | 3.98042e6 | 0.324118 | ||||||||
\(686\) | −5.90981e6 | −0.479472 | ||||||||
\(687\) | 1.37187e7 | − | 1.08920e7i | 1.10897 | − | 0.880471i | ||||
\(688\) | 6.55645e7i | 5.28077i | ||||||||
\(689\) | 2.48697e6 | 0.199583 | ||||||||
\(690\) | −6.54417e6 | + | 5.19576e6i | −0.523277 | + | 0.415457i | ||||
\(691\) | − | 1.33115e7i | − | 1.06055i | −0.847825 | − | 0.530277i | \(-0.822088\pi\) | ||
0.847825 | − | 0.530277i | \(-0.177912\pi\) | |||||||
\(692\) | 1.69911e7 | 1.34883 | ||||||||
\(693\) | −651464. | + | 2.79858e6i | −0.0515297 | + | 0.221363i | ||||
\(694\) | −8.89960e6 | −0.701410 | ||||||||
\(695\) | 681940.i | 0.0535531i | ||||||||
\(696\) | −3.23657e7 | + | 2.56969e7i | −2.53257 | + | 2.01075i | ||||
\(697\) | −1.54924e7 | −1.20792 | ||||||||
\(698\) | 2.70354e7i | 2.10036i | ||||||||
\(699\) | −5.87789e6 | − | 7.40332e6i | −0.455018 | − | 0.573104i | ||||
\(700\) | −2.95471e7 | −2.27914 | ||||||||
\(701\) | −9.60518e6 | −0.738262 | −0.369131 | − | 0.929377i | \(-0.620345\pi\) | ||||
−0.369131 | + | 0.929377i | \(0.620345\pi\) | |||||||
\(702\) | −1.32877e7 | − | 2.80549e7i | −1.01767 | − | 2.14865i | ||||
\(703\) | − | 9.43802e6i | − | 0.720265i | ||||||
\(704\) | −5.66394e6 | −0.430712 | ||||||||
\(705\) | −7.06579e6 | + | 5.60990e6i | −0.535412 | + | 0.425092i | ||||
\(706\) | −3.73342e7 | −2.81900 | ||||||||
\(707\) | −2.26921e7 | −1.70737 | ||||||||
\(708\) | −3.48164e7 | + | 532692.i | −2.61036 | + | 0.0399386i | ||||
\(709\) | 576086. | 0.0430400 | 0.0215200 | − | 0.999768i | \(-0.493149\pi\) | ||||
0.0215200 | + | 0.999768i | \(0.493149\pi\) | |||||||
\(710\) | 9.43805e6 | 0.702646 | ||||||||
\(711\) | −4.30498e6 | + | 1.84935e7i | −0.319372 | + | 1.37197i | ||||
\(712\) | −5.16640e7 | −3.81934 | ||||||||
\(713\) | − | 6.02463e6i | − | 0.443820i | ||||||
\(714\) | 2.41595e7 | − | 1.91815e7i | 1.77355 | − | 1.40811i | ||||
\(715\) | −1.71199e6 | −0.125238 | ||||||||
\(716\) | 3.89060e7 | 2.83618 | ||||||||
\(717\) | −1.00092e7 | + | 7.94686e6i | −0.727114 | + | 0.577295i | ||||
\(718\) | 1.60313e7i | 1.16053i | ||||||||
\(719\) | −4.40017e6 | −0.317430 | −0.158715 | − | 0.987324i | \(-0.550735\pi\) | ||||
−0.158715 | + | 0.987324i | \(0.550735\pi\) | |||||||
\(720\) | −2.57446e7 | − | 5.99291e6i | −1.85078 | − | 0.430831i | ||||
\(721\) | 3.20776e7i | 2.29807i | ||||||||
\(722\) | 1.86419e6 | 0.133091 | ||||||||
\(723\) | −1.12789e7 | − | 1.42060e7i | −0.802456 | − | 1.01071i | ||||
\(724\) | 7.21659e7 | 5.11665 | ||||||||
\(725\) | − | 9.69665e6i | − | 0.685136i | ||||||
\(726\) | 1.63016e7 | + | 2.05322e7i | 1.14786 | + | 1.44576i | ||||
\(727\) | 8.07553e6 | 0.566677 | 0.283338 | − | 0.959020i | \(-0.408558\pi\) | ||||
0.283338 | + | 0.959020i | \(0.408558\pi\) | |||||||
\(728\) | − | 7.37220e7i | − | 5.15547i | ||||||
\(729\) | 9.09073e6 | − | 1.11018e7i | 0.633549 | − | 0.773703i | ||||
\(730\) | 2.79646e7 | 1.94223 | ||||||||
\(731\) | 2.10727e7 | 1.45857 | ||||||||
\(732\) | 2.22683e7 | − | 1.76800e7i | 1.53606 | − | 1.21956i | ||||
\(733\) | −1.12591e7 | −0.774005 | −0.387002 | − | 0.922079i | \(-0.626489\pi\) | ||||
−0.387002 | + | 0.922079i | \(0.626489\pi\) | |||||||
\(734\) | 4.12619e7i | 2.82689i | ||||||||
\(735\) | −5.52637e6 | + | 4.38768e6i | −0.377330 | + | 0.299583i | ||||
\(736\) | 2.64011e7 | 1.79650 | ||||||||
\(737\) | 1.37767e6i | 0.0934279i | ||||||||
\(738\) | −3.73654e7 | − | 8.69805e6i | −2.52539 | − | 0.587870i | ||||
\(739\) | 5.14515e6i | 0.346567i | 0.984872 | + | 0.173283i | \(0.0554377\pi\) | ||||
−0.984872 | + | 0.173283i | \(0.944562\pi\) | |||||||
\(740\) | 1.72222e7 | 1.15614 | ||||||||
\(741\) | 1.41240e7 | − | 1.12138e7i | 0.944956 | − | 0.750251i | ||||
\(742\) | 6.12002e6i | 0.408078i | ||||||||
\(743\) | − | 4.93562e6i | − | 0.327997i | −0.986461 | − | 0.163998i | \(-0.947561\pi\) | ||
0.986461 | − | 0.163998i | \(-0.0524392\pi\) | |||||||
\(744\) | 2.70841e7 | − | 2.15035e7i | 1.79383 | − | 1.42422i | ||||
\(745\) | − | 5.73101e6i | − | 0.378303i | ||||||
\(746\) | −2.29290e7 | −1.50848 | ||||||||
\(747\) | 2.02751e6 | − | 8.70986e6i | 0.132942 | − | 0.571097i | ||||
\(748\) | 5.96986e6i | 0.390131i | ||||||||
\(749\) | 2.48262e7i | 1.61698i | ||||||||
\(750\) | 2.24067e7 | − | 1.77898e7i | 1.45453 | − | 1.15483i | ||||
\(751\) | − | 8.39631e6i | − | 0.543236i | −0.962405 | − | 0.271618i | \(-0.912441\pi\) | ||
0.962405 | − | 0.271618i | \(-0.0875588\pi\) | |||||||
\(752\) | 5.73047e7 | 3.69527 | ||||||||
\(753\) | −2.19249e7 | + | 1.74073e7i | −1.40913 | + | 1.11878i | ||||
\(754\) | 3.92147e7 | 2.51201 | ||||||||
\(755\) | −3.82381e6 | −0.244134 | ||||||||
\(756\) | 4.99177e7 | − | 2.36427e7i | 3.17651 | − | 1.50450i | ||||
\(757\) | 2.42372e7 | 1.53725 | 0.768623 | − | 0.639703i | \(-0.220942\pi\) | ||||
0.768623 | + | 0.639703i | \(0.220942\pi\) | |||||||
\(758\) | 3.67469e6 | 0.232299 | ||||||||
\(759\) | 987995. | + | 1.24440e6i | 0.0622516 | + | 0.0784071i | ||||
\(760\) | − | 2.78653e7i | − | 1.74996i | ||||||
\(761\) | 6.17608e6i | 0.386591i | 0.981141 | + | 0.193295i | \(0.0619175\pi\) | ||||
−0.981141 | + | 0.193295i | \(0.938082\pi\) | |||||||
\(762\) | −3.53310e7 | − | 4.45001e7i | −2.20429 | − | 2.77635i | ||||
\(763\) | − | 5.12776e6i | − | 0.318872i | ||||||
\(764\) | 4.67959e7 | 2.90051 | ||||||||
\(765\) | −1.92614e6 | + | 8.27440e6i | −0.118997 | + | 0.511190i | ||||
\(766\) | 2.33402e7i | 1.43725i | ||||||||
\(767\) | 1.61570e7 | + | 1.24297e7i | 0.991683 | + | 0.762909i | ||||
\(768\) | 9.19291e6 | + | 1.15787e7i | 0.562406 | + | 0.708361i | ||||
\(769\) | 1.75329e7i | 1.06915i | 0.845121 | + | 0.534575i | \(0.179528\pi\) | ||||
−0.845121 | + | 0.534575i | \(0.820472\pi\) | |||||||
\(770\) | − | 4.21292e6i | − | 0.256069i | ||||||
\(771\) | 1.81120e7 | − | 1.43801e7i | 1.09731 | − | 0.871213i | ||||
\(772\) | 2.32326e6 | 0.140299 | ||||||||
\(773\) | −1.85958e7 | −1.11935 | −0.559674 | − | 0.828713i | \(-0.689074\pi\) | ||||
−0.559674 | + | 0.828713i | \(0.689074\pi\) | |||||||
\(774\) | 5.08241e7 | + | 1.18310e7i | 3.04942 | + | 0.709855i | ||||
\(775\) | 8.11428e6i | 0.485284i | ||||||||
\(776\) | 2.35859e7i | 1.40604i | ||||||||
\(777\) | −1.32532e7 | + | 1.05224e7i | −0.787530 | + | 0.625262i | ||||
\(778\) | − | 1.60270e7i | − | 0.949300i | ||||||
\(779\) | − | 2.22879e7i | − | 1.31591i | ||||||
\(780\) | 2.04626e7 | + | 2.57731e7i | 1.20427 | + | 1.51680i | ||||
\(781\) | − | 1.79468e6i | − | 0.105283i | ||||||
\(782\) | − | 1.70583e7i | − | 0.997512i | ||||||
\(783\) | 7.75895e6 | + | 1.63818e7i | 0.452271 | + | 0.954898i | ||||
\(784\) | 4.48198e7 | 2.60423 | ||||||||
\(785\) | 2.20916e6 | 0.127954 | ||||||||
\(786\) | −3.64286e7 | − | 4.58825e7i | −2.10322 | − | 2.64905i | ||||
\(787\) | 2.03674e7 | 1.17219 | 0.586096 | − | 0.810242i | \(-0.300664\pi\) | ||||
0.586096 | + | 0.810242i | \(0.300664\pi\) | |||||||
\(788\) | − | 1.26650e7i | − | 0.726589i | ||||||
\(789\) | 5.92288e6 | − | 4.70249e6i | 0.338720 | − | 0.268928i | ||||
\(790\) | − | 2.78396e7i | − | 1.58707i | ||||||
\(791\) | 9.78073e6 | 0.555815 | ||||||||
\(792\) | −2.06786e6 | + | 8.88318e6i | −0.117141 | + | 0.503217i | ||||
\(793\) | −1.66458e7 | −0.939986 | ||||||||
\(794\) | − | 961255.i | − | 0.0541112i | ||||||
\(795\) | −1.04802e6 | − | 1.32001e6i | −0.0588102 | − | 0.0740727i | ||||
\(796\) | 6.05275e6 | 0.338587 | ||||||||
\(797\) | 1.94611e7 | 1.08523 | 0.542615 | − | 0.839982i | \(-0.317434\pi\) | ||||
0.542615 | + | 0.839982i | \(0.317434\pi\) | |||||||
\(798\) | 2.75952e7 | + | 3.47567e7i | 1.53400 | + | 1.93211i | ||||
\(799\) | − | 1.84179e7i | − | 1.02064i | ||||||
\(800\) | −3.55584e7 | −1.96434 | ||||||||
\(801\) | −5.13765e6 | + | 2.20705e7i | −0.282933 | + | 1.21543i | ||||
\(802\) | 1.68629e7 | 0.925753 | ||||||||
\(803\) | − | 5.31758e6i | − | 0.291022i | ||||||
\(804\) | 2.07400e7 | − | 1.64666e7i | 1.13154 | − | 0.898389i | ||||
\(805\) | 8.70399e6i | 0.473400i | ||||||||
\(806\) | −3.28154e7 | −1.77926 | ||||||||
\(807\) | 3.14658e6 | + | 3.96319e6i | 0.170081 | + | 0.214220i | ||||
\(808\) | −7.20287e7 | −3.88130 | ||||||||
\(809\) | 3.54946e6 | 0.190674 | 0.0953369 | − | 0.995445i | \(-0.469607\pi\) | ||||
0.0953369 | + | 0.995445i | \(0.469607\pi\) | |||||||
\(810\) | −9.29114e6 | + | 1.88752e7i | −0.497573 | + | 1.01083i | ||||
\(811\) | − | 1.40304e7i | − | 0.749064i | −0.927214 | − | 0.374532i | \(-0.877803\pi\) | ||
0.927214 | − | 0.374532i | \(-0.122197\pi\) | |||||||
\(812\) | 6.97742e7i | 3.71368i | ||||||||
\(813\) | −9.85752e6 | − | 1.24157e7i | −0.523047 | − | 0.658789i | ||||
\(814\) | − | 4.52930e6i | − | 0.239591i | ||||||
\(815\) | − | 1.38137e7i | − | 0.728479i | ||||||
\(816\) | 4.22611e7 | − | 3.35534e7i | 2.22186 | − | 1.76405i | ||||
\(817\) | 3.03158e7i | 1.58897i | ||||||||
\(818\) | 5.48280e7i | 2.86497i | ||||||||
\(819\) | −3.14935e7 | − | 7.33116e6i | −1.64063 | − | 0.381912i | ||||
\(820\) | 4.06704e7 | 2.11224 | ||||||||
\(821\) | 3.27873e7 | 1.69765 | 0.848825 | − | 0.528674i | \(-0.177311\pi\) | ||||
0.848825 | + | 0.528674i | \(0.177311\pi\) | |||||||
\(822\) | −1.57592e7 | + | 1.25121e7i | −0.813496 | + | 0.645878i | ||||
\(823\) | − | 2.33932e6i | − | 0.120390i | −0.998187 | − | 0.0601950i | \(-0.980828\pi\) | ||
0.998187 | − | 0.0601950i | \(-0.0191723\pi\) | |||||||
\(824\) | 1.01820e8i | 5.22413i | ||||||||
\(825\) | −1.33068e6 | − | 1.67602e6i | −0.0680675 | − | 0.0857324i | ||||
\(826\) | −3.05874e7 | + | 3.97597e7i | −1.55989 | + | 2.02765i | ||||
\(827\) | 1.57681e7i | 0.801709i | 0.916142 | + | 0.400855i | \(0.131287\pi\) | ||||
−0.916142 | + | 0.400855i | \(0.868713\pi\) | |||||||
\(828\) | 6.92471e6 | − | 2.97474e7i | 0.351015 | − | 1.50790i | ||||
\(829\) | −154501. | −0.00780811 | −0.00390405 | − | 0.999992i | \(-0.501243\pi\) | ||||
−0.00390405 | + | 0.999992i | \(0.501243\pi\) | |||||||
\(830\) | 1.31116e7i | 0.660634i | ||||||||
\(831\) | −475498. | − | 598899.i | −0.0238861 | − | 0.0300851i | ||||
\(832\) | − | 6.37384e7i | − | 3.19222i | ||||||
\(833\) | − | 1.44052e7i | − | 0.719296i | ||||||
\(834\) | −2.14362e6 | − | 2.69993e6i | −0.106717 | − | 0.134412i | ||||
\(835\) | 2.15725e7 | 1.07074 | ||||||||
\(836\) | −8.58844e6 | −0.425010 | ||||||||
\(837\) | −6.49280e6 | − | 1.37085e7i | −0.320345 | − | 0.676357i | ||||
\(838\) | −1.60748e7 | −0.790744 | ||||||||
\(839\) | 2.75824e7 | 1.35278 | 0.676390 | − | 0.736543i | \(-0.263543\pi\) | ||||
0.676390 | + | 0.736543i | \(0.263543\pi\) | |||||||
\(840\) | −3.91293e7 | + | 3.10668e7i | −1.91339 | + | 1.51914i | ||||
\(841\) | −2.38705e6 | −0.116378 | ||||||||
\(842\) | − | 4.55134e7i | − | 2.21238i | ||||||
\(843\) | 8.80208e6 | − | 6.98844e6i | 0.426595 | − | 0.338697i | ||||
\(844\) | − | 7.71745e7i | − | 3.72922i | ||||||
\(845\) | − | 6.95899e6i | − | 0.335278i | ||||||
\(846\) | 1.03405e7 | − | 4.44213e7i | 0.496727 | − | 2.13386i | ||||
\(847\) | 2.73086e7 | 1.30795 | ||||||||
\(848\) | 1.07055e7i | 0.511230i | ||||||||
\(849\) | 2.30305e7 | − | 1.82852e7i | 1.09657 | − | 0.870622i | ||||
\(850\) | 2.29750e7i | 1.09071i | ||||||||
\(851\) | 9.35763e6i | 0.442937i | ||||||||
\(852\) | −2.70179e7 | + | 2.14510e7i | −1.27513 | + | 1.01239i | ||||
\(853\) | 1.51712e7 | 0.713915 | 0.356958 | − | 0.934121i | \(-0.383814\pi\) | ||||
0.356958 | + | 0.934121i | \(0.383814\pi\) | |||||||
\(854\) | − | 4.09625e7i | − | 1.92195i | ||||||
\(855\) | −1.19038e7 | − | 2.77102e6i | −0.556893 | − | 0.129635i | ||||
\(856\) | 7.88025e7i | 3.67583i | ||||||||
\(857\) | −2.18772e7 | −1.01751 | −0.508757 | − | 0.860910i | \(-0.669895\pi\) | ||||
−0.508757 | + | 0.860910i | \(0.669895\pi\) | |||||||
\(858\) | 6.77809e6 | − | 5.38149e6i | 0.314333 | − | 0.249565i | ||||
\(859\) | − | 4.13582e7i | − | 1.91240i | −0.292711 | − | 0.956201i | \(-0.594557\pi\) | ||
0.292711 | − | 0.956201i | \(-0.405443\pi\) | |||||||
\(860\) | −5.53195e7 | −2.55054 | ||||||||
\(861\) | −3.12974e7 | + | 2.48487e7i | −1.43880 | + | 1.14234i | ||||
\(862\) | −3.13293e7 | −1.43609 | ||||||||
\(863\) | 7.13489e6 | 0.326107 | 0.163054 | − | 0.986617i | \(-0.447866\pi\) | ||||
0.163054 | + | 0.986617i | \(0.447866\pi\) | |||||||
\(864\) | 6.00734e7 | − | 2.84527e7i | 2.73778 | − | 1.29670i | ||||
\(865\) | 6.74131e6i | 0.306340i | ||||||||
\(866\) | 3.05402e7 | 1.38381 | ||||||||
\(867\) | 2.97843e6 | + | 3.75140e6i | 0.134568 | + | 0.169491i | ||||
\(868\) | − | 5.83880e7i | − | 2.63042i | ||||||
\(869\) | −5.29382e6 | −0.237804 | ||||||||
\(870\) | −1.65253e7 | − | 2.08139e7i | −0.740203 | − | 0.932301i | ||||
\(871\) | −1.55034e7 | −0.692440 | ||||||||
\(872\) | − | 1.62764e7i | − | 0.724881i | ||||||
\(873\) | 1.00757e7 | + | 2.34546e6i | 0.447445 | + | 0.104158i | ||||
\(874\) | 2.45406e7 | 1.08669 | ||||||||
\(875\) | − | 2.98017e7i | − | 1.31589i | ||||||
\(876\) | −8.00531e7 | + | 6.35584e7i | −3.52467 | + | 2.79842i | ||||
\(877\) | 1.06884e6 | 0.0469262 | 0.0234631 | − | 0.999725i | \(-0.492531\pi\) | ||||
0.0234631 | + | 0.999725i | \(0.492531\pi\) | |||||||
\(878\) | 6.90791e7 | 3.02420 | ||||||||
\(879\) | −7.88152e6 | + | 6.25756e6i | −0.344063 | + | 0.273170i | ||||
\(880\) | − | 7.36947e6i | − | 0.320796i | ||||||
\(881\) | −6.75682e6 | −0.293294 | −0.146647 | − | 0.989189i | \(-0.546848\pi\) | ||||
−0.146647 | + | 0.989189i | \(0.546848\pi\) | |||||||
\(882\) | 8.08766e6 | − | 3.47433e7i | 0.350067 | − | 1.50383i | ||||
\(883\) | −1.26215e7 | −0.544766 | −0.272383 | − | 0.962189i | \(-0.587812\pi\) | ||||
−0.272383 | + | 0.962189i | \(0.587812\pi\) | |||||||
\(884\) | −6.71810e7 | −2.89145 | ||||||||
\(885\) | −211348. | − | 1.38136e7i | −0.00907070 | − | 0.592854i | ||||
\(886\) | −5.49365e7 | −2.35113 | ||||||||
\(887\) | −4.16969e7 | −1.77949 | −0.889744 | − | 0.456459i | \(-0.849117\pi\) | ||||
−0.889744 | + | 0.456459i | \(0.849117\pi\) | |||||||
\(888\) | −4.20678e7 | + | 3.33998e7i | −1.79026 | + | 1.42139i | ||||
\(889\) | −5.91868e7 | −2.51172 | ||||||||
\(890\) | − | 3.32244e7i | − | 1.40599i | ||||||
\(891\) | 3.58919e6 | + | 1.76675e6i | 0.151462 | + | 0.0745556i | ||||
\(892\) | −2.42672e7 | −1.02119 | ||||||||
\(893\) | 2.64967e7 | 1.11189 | ||||||||
\(894\) | 1.80149e7 | + | 2.26901e7i | 0.753855 | + | 0.949496i | ||||
\(895\) | 1.54362e7i | 0.644143i | ||||||||
\(896\) | 5.88406e7 | 2.44854 | ||||||||
\(897\) | −1.40037e7 | + | 1.11183e7i | −0.581114 | + | 0.461377i | ||||
\(898\) | 3.88669e7i | 1.60838i | ||||||||
\(899\) | 1.91615e7 | 0.790735 | ||||||||
\(900\) | −9.32656e6 | + | 4.00654e7i | −0.383809 | + | 1.64878i | ||||
\(901\) | 3.44077e6 | 0.141203 | ||||||||
\(902\) | − | 1.06960e7i | − | 0.437728i | ||||||
\(903\) | 4.25705e7 | − | 3.37990e7i | 1.73736 | − | 1.37938i | ||||
\(904\) | 3.10457e7 | 1.26351 | ||||||||
\(905\) | 2.86322e7i | 1.16207i | ||||||||
\(906\) | 1.51392e7 | − | 1.20198e7i | 0.612748 | − | 0.486493i | ||||
\(907\) | 1.97646e7 | 0.797757 | 0.398879 | − | 0.917004i | \(-0.369399\pi\) | ||||
0.398879 | + | 0.917004i | \(0.369399\pi\) | |||||||
\(908\) | −1.07885e8 | −4.34258 | ||||||||
\(909\) | −7.16278e6 | + | 3.07701e7i | −0.287522 | + | 1.23515i | ||||
\(910\) | 4.74095e7 | 1.89785 | ||||||||
\(911\) | 2.84690e7i | 1.13652i | 0.822849 | + | 0.568259i | \(0.192383\pi\) | ||||
−0.822849 | + | 0.568259i | \(0.807617\pi\) | |||||||
\(912\) | 4.82710e7 | + | 6.07983e7i | 1.92176 | + | 2.42050i | ||||
\(913\) | 2.49323e6 | 0.0989885 | ||||||||
\(914\) | − | 8.59856e7i | − | 3.40456i | ||||||
\(915\) | 7.01462e6 | + | 8.83505e6i | 0.276982 | + | 0.348864i | ||||
\(916\) | − | 9.38754e7i | − | 3.69669i | ||||||
\(917\) | −6.10254e7 | −2.39656 | ||||||||
\(918\) | −1.83838e7 | − | 3.88145e7i | −0.719995 | − | 1.52015i | ||||
\(919\) | 3.60778e7i | 1.40913i | 0.709640 | + | 0.704564i | \(0.248858\pi\) | ||||
−0.709640 | + | 0.704564i | \(0.751142\pi\) | |||||||
\(920\) | 2.76279e7i | 1.07616i | ||||||||
\(921\) | −7.95353e6 | − | 1.00176e7i | −0.308966 | − | 0.389149i | ||||
\(922\) | 2.51490e7i | 0.974302i | ||||||||
\(923\) | 2.01962e7 | 0.780308 | ||||||||
\(924\) | 9.57521e6 | + | 1.20602e7i | 0.368951 | + | 0.464701i | ||||
\(925\) | − | 1.26033e7i | − | 0.484319i | ||||||
\(926\) | − | 6.58288e7i | − | 2.52283i | ||||||
\(927\) | 4.34967e7 | + | 1.01253e7i | 1.66248 | + | 0.386998i | ||||
\(928\) | 8.39697e7i | 3.20076i | ||||||||
\(929\) | 2.80879e7 | 1.06778 | 0.533889 | − | 0.845555i | \(-0.320730\pi\) | ||||
0.533889 | + | 0.845555i | \(0.320730\pi\) | |||||||
\(930\) | 1.38286e7 | + | 1.74174e7i | 0.524288 | + | 0.660352i | ||||
\(931\) | 2.07239e7 | 0.783604 | ||||||||
\(932\) | −5.06601e7 | −1.91041 | ||||||||
\(933\) | 1.58700e7 | − | 1.26001e7i | 0.596862 | − | 0.473880i | ||||
\(934\) | −2.97485e7 | −1.11583 | ||||||||
\(935\) | −2.36857e6 | −0.0886049 | ||||||||
\(936\) | −9.99656e7 | − | 2.32704e7i | −3.72959 | − | 0.868187i | ||||
\(937\) | − | 9.24927e6i | − | 0.344159i | −0.985083 | − | 0.172079i | \(-0.944951\pi\) | ||
0.985083 | − | 0.172079i | \(-0.0550485\pi\) | |||||||
\(938\) | − | 3.81513e7i | − | 1.41580i | ||||||
\(939\) | −9.39806e6 | + | 7.46162e6i | −0.347836 | + | 0.276165i | ||||
\(940\) | 4.83504e7i | 1.78476i | ||||||||
\(941\) | 3.26318e7 | 1.20134 | 0.600671 | − | 0.799496i | \(-0.294900\pi\) | ||||
0.600671 | + | 0.799496i | \(0.294900\pi\) | |||||||
\(942\) | −8.74647e6 | + | 6.94429e6i | −0.321148 | + | 0.254977i | ||||
\(943\) | 2.20981e7i | 0.809237i | ||||||||
\(944\) | −5.35052e7 | + | 6.95498e7i | −1.95419 | + | 2.54019i | ||||
\(945\) | 9.38036e6 | + | 1.98051e7i | 0.341696 | + | 0.721437i | ||||
\(946\) | 1.45486e7i | 0.528558i | ||||||||
\(947\) | 4.99180e7i | 1.80876i | 0.426723 | + | 0.904382i | \(0.359668\pi\) | ||||
−0.426723 | + | 0.904382i | \(0.640332\pi\) | |||||||
\(948\) | 6.32745e7 | + | 7.96955e7i | 2.28669 | + | 2.88013i | ||||
\(949\) | 5.98406e7 | 2.15690 | ||||||||
\(950\) | −3.30526e7 | −1.18822 | ||||||||
\(951\) | 1.23209e7 | − | 9.78219e6i | 0.441763 | − | 0.350739i | ||||
\(952\) | − | 1.01996e8i | − | 3.64745i | ||||||
\(953\) | − | 3.80787e7i | − | 1.35816i | −0.734066 | − | 0.679078i | \(-0.762380\pi\) | ||
0.734066 | − | 0.679078i | \(-0.237620\pi\) | |||||||
\(954\) | 8.29863e6 | + | 1.93179e6i | 0.295213 | + | 0.0687208i | ||||
\(955\) | 1.85665e7i | 0.658752i | ||||||||
\(956\) | 6.84921e7i | 2.42379i | ||||||||
\(957\) | −3.95785e6 | + | 3.14235e6i | −0.139695 | + | 0.110911i | ||||
\(958\) | 3.46885e7i | 1.22116i | ||||||||
\(959\) | 2.09604e7i | 0.735957i | ||||||||
\(960\) | −3.38303e7 | + | 2.68597e7i | −1.18475 | + | 0.940639i | ||||
\(961\) | 1.25945e7 | 0.439920 | ||||||||
\(962\) | 5.09699e7 | 1.77573 | ||||||||
\(963\) | 3.36638e7 | + | 7.83639e6i | 1.16976 | + | 0.272302i | ||||
\(964\) | −9.72102e7 | −3.36914 | ||||||||
\(965\) | 921767.i | 0.0318642i | ||||||||
\(966\) | −2.73602e7 | − | 3.44607e7i | −0.943357 | − | 1.18818i | ||||
\(967\) | − | 2.13883e7i | − | 0.735547i | −0.929915 | − | 0.367774i | \(-0.880120\pi\) | ||
0.929915 | − | 0.367774i | \(-0.119880\pi\) | |||||||
\(968\) | 8.66822e7 | 2.97332 | ||||||||
\(969\) | 1.95408e7 | − | 1.55145e7i | 0.668548 | − | 0.530796i | ||||
\(970\) | −1.51677e7 | −0.517596 | ||||||||
\(971\) | − | 2.63021e7i | − | 0.895245i | −0.894223 | − | 0.447623i | \(-0.852271\pi\) | ||
0.894223 | − | 0.447623i | \(-0.147729\pi\) | |||||||
\(972\) | −1.63025e7 | − | 7.51503e7i | −0.553463 | − | 2.55132i | ||||
\(973\) | −3.59101e6 | −0.121600 | ||||||||
\(974\) | −2.12196e7 | −0.716704 | ||||||||
\(975\) | 1.88609e7 | − | 1.49747e7i | 0.635405 | − | 0.504482i | ||||
\(976\) | − | 7.16537e7i | − | 2.40777i | ||||||
\(977\) | 4.11612e7 | 1.37960 | 0.689798 | − | 0.724002i | \(-0.257699\pi\) | ||||
0.689798 | + | 0.724002i | \(0.257699\pi\) | |||||||
\(978\) | 4.34222e7 | + | 5.46912e7i | 1.45166 | + | 1.82840i | ||||
\(979\) | −6.31775e6 | −0.210672 | ||||||||
\(980\) | 3.78164e7i | 1.25781i | ||||||||
\(981\) | −6.95315e6 | − | 1.61858e6i | −0.230679 | − | 0.0536984i | ||||
\(982\) | − | 9.18420e7i | − | 3.03922i | ||||||
\(983\) | −4.94781e7 | −1.63316 | −0.816581 | − | 0.577230i | \(-0.804133\pi\) | ||||
−0.816581 | + | 0.577230i | \(0.804133\pi\) | |||||||
\(984\) | −9.93433e7 | + | 7.88739e7i | −3.27078 | + | 2.59684i | ||||
\(985\) | 5.02490e6 | 0.165020 | ||||||||
\(986\) | 5.42544e7 | 1.77722 | ||||||||
\(987\) | −2.95410e7 | − | 3.72075e7i | −0.965233 | − | 1.21573i | ||||
\(988\) | − | 9.66489e7i | − | 3.14996i | ||||||
\(989\) | − | 3.00576e7i | − | 0.977157i | ||||||
\(990\) | −5.71265e6 | − | 1.32981e6i | −0.185246 | − | 0.0431223i | ||||
\(991\) | 1.23029e7i | 0.397944i | 0.980005 | + | 0.198972i | \(0.0637603\pi\) | ||||
−0.980005 | + | 0.198972i | \(0.936240\pi\) | |||||||
\(992\) | − | 7.02669e7i | − | 2.26711i | ||||||
\(993\) | 1.81720e7 | + | 2.28880e7i | 0.584830 | + | 0.736606i | ||||
\(994\) | 4.96995e7i | 1.59546i | ||||||||
\(995\) | 2.40146e6i | 0.0768985i | ||||||||
\(996\) | −2.98003e7 | − | 3.75341e7i | −0.951859 | − | 1.19889i | ||||
\(997\) | −9.61030e6 | −0.306196 | −0.153098 | − | 0.988211i | \(-0.548925\pi\) | ||||
−0.153098 | + | 0.988211i | \(0.548925\pi\) | |||||||
\(998\) | 5.94583e7 | 1.88967 | ||||||||
\(999\) | 1.00848e7 | + | 2.12924e7i | 0.319708 | + | 0.675012i |
(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 | 177.6.d.b.176.3 | ✓ | 92 | |
3.2 | odd | 2 | inner | 177.6.d.b.176.90 | yes | 92 | |
59.58 | odd | 2 | inner | 177.6.d.b.176.89 | yes | 92 | |
177.176 | even | 2 | inner | 177.6.d.b.176.4 | yes | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.d.b.176.3 | ✓ | 92 | 1.1 | even | 1 | trivial | |
177.6.d.b.176.4 | yes | 92 | 177.176 | even | 2 | inner | |
177.6.d.b.176.89 | yes | 92 | 59.58 | odd | 2 | inner | |
177.6.d.b.176.90 | yes | 92 | 3.2 | odd | 2 | inner |