Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,5,Mod(10,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.10");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.41120878177\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 102x^{6} + 2913x^{4} + 23292x^{2} + 41364 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 10.1 | ||
Root | \(-7.70102i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.10 |
Dual form | 33.5.c.a.10.8 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 7.70102i | − | 1.92525i | −0.270830 | − | 0.962627i | \(-0.587298\pi\) | ||
0.270830 | − | 0.962627i | \(-0.412702\pi\) | |||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | −43.3057 | −2.70660 | ||||||||
\(5\) | −12.5296 | −0.501185 | −0.250593 | − | 0.968093i | \(-0.580625\pi\) | ||||
−0.250593 | + | 0.968093i | \(0.580625\pi\) | |||||||
\(6\) | − | 40.0157i | − | 1.11155i | ||||||
\(7\) | − | 63.6540i | − | 1.29906i | −0.760336 | − | 0.649530i | \(-0.774966\pi\) | ||
0.760336 | − | 0.649530i | \(-0.225034\pi\) | |||||||
\(8\) | 210.281i | 3.28565i | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 96.4909i | 0.964909i | ||||||||
\(11\) | 119.745 | + | 17.3819i | 0.989628 | + | 0.143652i | ||||
\(12\) | −225.023 | −1.56266 | ||||||||
\(13\) | − | 194.814i | − | 1.15274i | −0.817188 | − | 0.576371i | \(-0.804468\pi\) | ||
0.817188 | − | 0.576371i | \(-0.195532\pi\) | |||||||
\(14\) | −490.200 | −2.50102 | ||||||||
\(15\) | −65.1059 | −0.289359 | ||||||||
\(16\) | 926.491 | 3.61910 | ||||||||
\(17\) | − | 108.192i | − | 0.374366i | −0.982325 | − | 0.187183i | \(-0.940064\pi\) | ||
0.982325 | − | 0.187183i | \(-0.0599357\pi\) | |||||||
\(18\) | − | 207.927i | − | 0.641751i | ||||||
\(19\) | 69.0344i | 0.191231i | 0.995418 | + | 0.0956155i | \(0.0304819\pi\) | ||||
−0.995418 | + | 0.0956155i | \(0.969518\pi\) | |||||||
\(20\) | 542.604 | 1.35651 | ||||||||
\(21\) | − | 330.756i | − | 0.750013i | ||||||
\(22\) | 133.858 | − | 922.159i | 0.276567 | − | 1.90529i | ||||
\(23\) | 576.600 | 1.08998 | 0.544991 | − | 0.838442i | \(-0.316533\pi\) | ||||
0.544991 | + | 0.838442i | \(0.316533\pi\) | |||||||
\(24\) | 1092.65i | 1.89697i | ||||||||
\(25\) | −468.008 | −0.748813 | ||||||||
\(26\) | −1500.26 | −2.21932 | ||||||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | 2756.58i | 3.51604i | ||||||||
\(29\) | 382.039i | 0.454268i | 0.973864 | + | 0.227134i | \(0.0729356\pi\) | ||||
−0.973864 | + | 0.227134i | \(0.927064\pi\) | |||||||
\(30\) | 501.381i | 0.557090i | ||||||||
\(31\) | −36.6327 | −0.0381193 | −0.0190597 | − | 0.999818i | \(-0.506067\pi\) | ||||
−0.0190597 | + | 0.999818i | \(0.506067\pi\) | |||||||
\(32\) | − | 3770.42i | − | 3.68205i | ||||||
\(33\) | 622.213 | + | 90.3190i | 0.571362 | + | 0.0829376i | ||||
\(34\) | −833.186 | −0.720749 | ||||||||
\(35\) | 797.560i | 0.651070i | ||||||||
\(36\) | −1169.25 | −0.902202 | ||||||||
\(37\) | 1791.57 | 1.30867 | 0.654334 | − | 0.756205i | \(-0.272949\pi\) | ||||
0.654334 | + | 0.756205i | \(0.272949\pi\) | |||||||
\(38\) | 531.635 | 0.368168 | ||||||||
\(39\) | − | 1012.28i | − | 0.665536i | ||||||
\(40\) | − | 2634.75i | − | 1.64672i | ||||||
\(41\) | 2882.25i | 1.71460i | 0.514815 | + | 0.857301i | \(0.327861\pi\) | ||||
−0.514815 | + | 0.857301i | \(0.672139\pi\) | |||||||
\(42\) | −2547.16 | −1.44397 | ||||||||
\(43\) | 319.351i | 0.172716i | 0.996264 | + | 0.0863579i | \(0.0275228\pi\) | ||||
−0.996264 | + | 0.0863579i | \(0.972477\pi\) | |||||||
\(44\) | −5185.64 | − | 752.735i | −2.67853 | − | 0.388809i | ||||
\(45\) | −338.300 | −0.167062 | ||||||||
\(46\) | − | 4440.41i | − | 2.09849i | ||||||
\(47\) | 2299.80 | 1.04110 | 0.520552 | − | 0.853830i | \(-0.325726\pi\) | ||||
0.520552 | + | 0.853830i | \(0.325726\pi\) | |||||||
\(48\) | 4814.19 | 2.08949 | ||||||||
\(49\) | −1650.83 | −0.687558 | ||||||||
\(50\) | 3604.14i | 1.44166i | ||||||||
\(51\) | − | 562.181i | − | 0.216140i | ||||||
\(52\) | 8436.53i | 3.12002i | ||||||||
\(53\) | 857.015 | 0.305096 | 0.152548 | − | 0.988296i | \(-0.451252\pi\) | ||||
0.152548 | + | 0.988296i | \(0.451252\pi\) | |||||||
\(54\) | − | 1080.42i | − | 0.370515i | ||||||
\(55\) | −1500.36 | − | 217.789i | −0.495987 | − | 0.0719963i | ||||
\(56\) | 13385.2 | 4.26826 | ||||||||
\(57\) | 358.713i | 0.110407i | ||||||||
\(58\) | 2942.09 | 0.874582 | ||||||||
\(59\) | −2149.26 | −0.617427 | −0.308714 | − | 0.951155i | \(-0.599898\pi\) | ||||
−0.308714 | + | 0.951155i | \(0.599898\pi\) | |||||||
\(60\) | 2819.45 | 0.783182 | ||||||||
\(61\) | − | 4966.14i | − | 1.33462i | −0.744778 | − | 0.667312i | \(-0.767445\pi\) | ||
0.744778 | − | 0.667312i | \(-0.232555\pi\) | |||||||
\(62\) | 282.109i | 0.0733894i | ||||||||
\(63\) | − | 1718.66i | − | 0.433020i | ||||||
\(64\) | −14212.2 | −3.46978 | ||||||||
\(65\) | 2440.94i | 0.577738i | ||||||||
\(66\) | 695.548 | − | 4791.68i | 0.159676 | − | 1.10002i | ||||
\(67\) | −5369.49 | −1.19614 | −0.598072 | − | 0.801443i | \(-0.704066\pi\) | ||||
−0.598072 | + | 0.801443i | \(0.704066\pi\) | |||||||
\(68\) | 4685.32i | 1.01326i | ||||||||
\(69\) | 2996.10 | 0.629301 | ||||||||
\(70\) | 6142.03 | 1.25347 | ||||||||
\(71\) | −4954.38 | −0.982817 | −0.491408 | − | 0.870929i | \(-0.663518\pi\) | ||||
−0.491408 | + | 0.870929i | \(0.663518\pi\) | |||||||
\(72\) | 5677.60i | 1.09522i | ||||||||
\(73\) | − | 3583.14i | − | 0.672386i | −0.941793 | − | 0.336193i | \(-0.890861\pi\) | ||
0.941793 | − | 0.336193i | \(-0.109139\pi\) | |||||||
\(74\) | − | 13796.9i | − | 2.51952i | ||||||
\(75\) | −2431.84 | −0.432328 | ||||||||
\(76\) | − | 2989.58i | − | 0.517587i | ||||||
\(77\) | 1106.43 | − | 7622.24i | 0.186613 | − | 1.28559i | ||||
\(78\) | −7795.59 | −1.28133 | ||||||||
\(79\) | 7143.06i | 1.14454i | 0.820066 | + | 0.572269i | \(0.193937\pi\) | ||||
−0.820066 | + | 0.572269i | \(0.806063\pi\) | |||||||
\(80\) | −11608.6 | −1.81384 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 22196.2 | 3.30105 | ||||||||
\(83\) | − | 156.911i | − | 0.0227771i | −0.999935 | − | 0.0113885i | \(-0.996375\pi\) | ||
0.999935 | − | 0.0113885i | \(-0.00362516\pi\) | |||||||
\(84\) | 14323.6i | 2.02999i | ||||||||
\(85\) | 1355.60i | 0.187627i | ||||||||
\(86\) | 2459.33 | 0.332522 | ||||||||
\(87\) | 1985.14i | 0.262272i | ||||||||
\(88\) | −3655.09 | + | 25180.2i | −0.471990 | + | 3.25157i | ||||
\(89\) | 7181.21 | 0.906604 | 0.453302 | − | 0.891357i | \(-0.350246\pi\) | ||||
0.453302 | + | 0.891357i | \(0.350246\pi\) | |||||||
\(90\) | 2605.25i | 0.321636i | ||||||||
\(91\) | −12400.7 | −1.49748 | ||||||||
\(92\) | −24970.1 | −2.95015 | ||||||||
\(93\) | −190.349 | −0.0220082 | ||||||||
\(94\) | − | 17710.8i | − | 2.00439i | ||||||
\(95\) | − | 864.975i | − | 0.0958421i | ||||||
\(96\) | − | 19591.7i | − | 2.12583i | ||||||
\(97\) | 2419.65 | 0.257164 | 0.128582 | − | 0.991699i | \(-0.458958\pi\) | ||||
0.128582 | + | 0.991699i | \(0.458958\pi\) | |||||||
\(98\) | 12713.0i | 1.32372i | ||||||||
\(99\) | 3233.12 | + | 469.311i | 0.329876 | + | 0.0478840i | ||||
\(100\) | 20267.4 | 2.02674 | ||||||||
\(101\) | − | 3839.47i | − | 0.376381i | −0.982133 | − | 0.188191i | \(-0.939738\pi\) | ||
0.982133 | − | 0.188191i | \(-0.0602623\pi\) | |||||||
\(102\) | −4329.36 | −0.416125 | ||||||||
\(103\) | −6804.82 | −0.641420 | −0.320710 | − | 0.947177i | \(-0.603921\pi\) | ||||
−0.320710 | + | 0.947177i | \(0.603921\pi\) | |||||||
\(104\) | 40965.7 | 3.78751 | ||||||||
\(105\) | 4144.25i | 0.375895i | ||||||||
\(106\) | − | 6599.89i | − | 0.587388i | ||||||
\(107\) | − | 5960.40i | − | 0.520604i | −0.965527 | − | 0.260302i | \(-0.916178\pi\) | ||
0.965527 | − | 0.260302i | \(-0.0838222\pi\) | |||||||
\(108\) | −6075.62 | −0.520886 | ||||||||
\(109\) | 21808.4i | 1.83557i | 0.397080 | + | 0.917784i | \(0.370024\pi\) | ||||
−0.397080 | + | 0.917784i | \(0.629976\pi\) | |||||||
\(110\) | −1677.20 | + | 11554.3i | −0.138611 | + | 0.954901i | ||||
\(111\) | 9309.26 | 0.755560 | ||||||||
\(112\) | − | 58974.8i | − | 4.70144i | ||||||
\(113\) | 2293.56 | 0.179619 | 0.0898097 | − | 0.995959i | \(-0.471374\pi\) | ||||
0.0898097 | + | 0.995959i | \(0.471374\pi\) | |||||||
\(114\) | 2762.46 | 0.212562 | ||||||||
\(115\) | −7224.59 | −0.546283 | ||||||||
\(116\) | − | 16544.5i | − | 1.22952i | ||||||
\(117\) | − | 5259.96i | − | 0.384248i | ||||||
\(118\) | 16551.5i | 1.18870i | ||||||||
\(119\) | −6886.83 | −0.486324 | ||||||||
\(120\) | − | 13690.6i | − | 0.950733i | ||||||
\(121\) | 14036.7 | + | 4162.79i | 0.958728 | + | 0.284324i | ||||
\(122\) | −38244.3 | −2.56949 | ||||||||
\(123\) | 14976.6i | 0.989926i | ||||||||
\(124\) | 1586.40 | 0.103174 | ||||||||
\(125\) | 13695.0 | 0.876479 | ||||||||
\(126\) | −13235.4 | −0.833674 | ||||||||
\(127\) | 8755.61i | 0.542849i | 0.962460 | + | 0.271424i | \(0.0874947\pi\) | ||||
−0.962460 | + | 0.271424i | \(0.912505\pi\) | |||||||
\(128\) | 49121.7i | 2.99815i | ||||||||
\(129\) | 1659.40i | 0.0997175i | ||||||||
\(130\) | 18797.7 | 1.11229 | ||||||||
\(131\) | 13196.5i | 0.768981i | 0.923129 | + | 0.384490i | \(0.125623\pi\) | ||||
−0.923129 | + | 0.384490i | \(0.874377\pi\) | |||||||
\(132\) | −26945.4 | − | 3911.33i | −1.54645 | − | 0.224479i | ||||
\(133\) | 4394.31 | 0.248421 | ||||||||
\(134\) | 41350.5i | 2.30288i | ||||||||
\(135\) | −1757.86 | −0.0964531 | ||||||||
\(136\) | 22750.7 | 1.23003 | ||||||||
\(137\) | −2034.69 | −0.108407 | −0.0542034 | − | 0.998530i | \(-0.517262\pi\) | ||||
−0.0542034 | + | 0.998530i | \(0.517262\pi\) | |||||||
\(138\) | − | 23073.0i | − | 1.21157i | ||||||
\(139\) | − | 24766.1i | − | 1.28183i | −0.767614 | − | 0.640913i | \(-0.778556\pi\) | ||
0.767614 | − | 0.640913i | \(-0.221444\pi\) | |||||||
\(140\) | − | 34538.9i | − | 1.76219i | ||||||
\(141\) | 11950.1 | 0.601082 | ||||||||
\(142\) | 38153.8i | 1.89217i | ||||||||
\(143\) | 3386.23 | − | 23327.9i | 0.165594 | − | 1.14079i | ||||
\(144\) | 25015.3 | 1.20637 | ||||||||
\(145\) | − | 4786.81i | − | 0.227672i | ||||||
\(146\) | −27593.9 | −1.29451 | ||||||||
\(147\) | −8577.94 | −0.396962 | ||||||||
\(148\) | −77585.0 | −3.54205 | ||||||||
\(149\) | − | 20475.5i | − | 0.922277i | −0.887328 | − | 0.461138i | \(-0.847441\pi\) | ||
0.887328 | − | 0.461138i | \(-0.152559\pi\) | |||||||
\(150\) | 18727.7i | 0.832341i | ||||||||
\(151\) | − | 17123.5i | − | 0.750996i | −0.926823 | − | 0.375498i | \(-0.877472\pi\) | ||
0.926823 | − | 0.375498i | \(-0.122528\pi\) | |||||||
\(152\) | −14516.7 | −0.628318 | ||||||||
\(153\) | − | 2921.18i | − | 0.124789i | ||||||
\(154\) | −58699.0 | − | 8520.61i | −2.47508 | − | 0.359277i | ||||
\(155\) | 458.994 | 0.0191048 | ||||||||
\(156\) | 43837.5i | 1.80134i | ||||||||
\(157\) | 42755.1 | 1.73456 | 0.867279 | − | 0.497823i | \(-0.165867\pi\) | ||||
0.867279 | + | 0.497823i | \(0.165867\pi\) | |||||||
\(158\) | 55008.8 | 2.20353 | ||||||||
\(159\) | 4453.18 | 0.176147 | ||||||||
\(160\) | 47241.9i | 1.84539i | ||||||||
\(161\) | − | 36702.9i | − | 1.41595i | ||||||
\(162\) | − | 5614.04i | − | 0.213917i | ||||||
\(163\) | −32922.2 | −1.23912 | −0.619561 | − | 0.784949i | \(-0.712689\pi\) | ||||
−0.619561 | + | 0.784949i | \(0.712689\pi\) | |||||||
\(164\) | − | 124818.i | − | 4.64075i | ||||||
\(165\) | −7796.10 | − | 1131.66i | −0.286358 | − | 0.0415671i | ||||
\(166\) | −1208.38 | −0.0438516 | ||||||||
\(167\) | 22705.4i | 0.814136i | 0.913398 | + | 0.407068i | \(0.133449\pi\) | ||||
−0.913398 | + | 0.407068i | \(0.866551\pi\) | |||||||
\(168\) | 69551.8 | 2.46428 | ||||||||
\(169\) | −9391.31 | −0.328816 | ||||||||
\(170\) | 10439.5 | 0.361229 | ||||||||
\(171\) | 1863.93i | 0.0637437i | ||||||||
\(172\) | − | 13829.7i | − | 0.467473i | ||||||
\(173\) | 32607.5i | 1.08949i | 0.838600 | + | 0.544747i | \(0.183374\pi\) | ||||
−0.838600 | + | 0.544747i | \(0.816626\pi\) | |||||||
\(174\) | 15287.6 | 0.504940 | ||||||||
\(175\) | 29790.6i | 0.972754i | ||||||||
\(176\) | 110943. | + | 16104.2i | 3.58157 | + | 0.519892i | ||||
\(177\) | −11167.9 | −0.356472 | ||||||||
\(178\) | − | 55302.6i | − | 1.74544i | ||||||
\(179\) | 4293.51 | 0.134001 | 0.0670003 | − | 0.997753i | \(-0.478657\pi\) | ||||
0.0670003 | + | 0.997753i | \(0.478657\pi\) | |||||||
\(180\) | 14650.3 | 0.452170 | ||||||||
\(181\) | 24070.9 | 0.734743 | 0.367371 | − | 0.930074i | \(-0.380258\pi\) | ||||
0.367371 | + | 0.930074i | \(0.380258\pi\) | |||||||
\(182\) | 95497.6i | 2.88303i | ||||||||
\(183\) | − | 25804.8i | − | 0.770546i | ||||||
\(184\) | 121248.i | 3.58130i | ||||||||
\(185\) | −22447.7 | −0.655885 | ||||||||
\(186\) | 1465.88i | 0.0423714i | ||||||||
\(187\) | 1880.58 | − | 12955.4i | 0.0537784 | − | 0.370483i | ||||
\(188\) | −99594.4 | −2.81786 | ||||||||
\(189\) | − | 8930.40i | − | 0.250004i | ||||||
\(190\) | −6661.19 | −0.184520 | ||||||||
\(191\) | −15866.1 | −0.434913 | −0.217457 | − | 0.976070i | \(-0.569776\pi\) | ||||
−0.217457 | + | 0.976070i | \(0.569776\pi\) | |||||||
\(192\) | −73848.8 | −2.00328 | ||||||||
\(193\) | − | 29252.3i | − | 0.785319i | −0.919684 | − | 0.392659i | \(-0.871555\pi\) | ||
0.919684 | − | 0.392659i | \(-0.128445\pi\) | |||||||
\(194\) | − | 18633.8i | − | 0.495105i | ||||||
\(195\) | 12683.5i | 0.333557i | ||||||||
\(196\) | 71490.1 | 1.86095 | ||||||||
\(197\) | 54943.2i | 1.41573i | 0.706346 | + | 0.707867i | \(0.250342\pi\) | ||||
−0.706346 | + | 0.707867i | \(0.749658\pi\) | |||||||
\(198\) | 3614.17 | − | 24898.3i | 0.0921889 | − | 0.635095i | ||||
\(199\) | 31818.1 | 0.803468 | 0.401734 | − | 0.915756i | \(-0.368408\pi\) | ||||
0.401734 | + | 0.915756i | \(0.368408\pi\) | |||||||
\(200\) | − | 98413.5i | − | 2.46034i | ||||||
\(201\) | −27900.7 | −0.690594 | ||||||||
\(202\) | −29567.8 | −0.724630 | ||||||||
\(203\) | 24318.3 | 0.590122 | ||||||||
\(204\) | 24345.6i | 0.585006i | ||||||||
\(205\) | − | 36113.5i | − | 0.859333i | ||||||
\(206\) | 52404.1i | 1.23490i | ||||||||
\(207\) | 15568.2 | 0.363327 | ||||||||
\(208\) | − | 180493.i | − | 4.17190i | ||||||
\(209\) | −1199.95 | + | 8266.52i | −0.0274707 | + | 0.189248i | ||||
\(210\) | 31914.9 | 0.723694 | ||||||||
\(211\) | 59860.2i | 1.34454i | 0.740306 | + | 0.672270i | \(0.234680\pi\) | ||||
−0.740306 | + | 0.672270i | \(0.765320\pi\) | |||||||
\(212\) | −37113.6 | −0.825774 | ||||||||
\(213\) | −25743.7 | −0.567430 | ||||||||
\(214\) | −45901.1 | −1.00230 | ||||||||
\(215\) | − | 4001.35i | − | 0.0865626i | ||||||
\(216\) | 29501.7i | 0.632323i | ||||||||
\(217\) | 2331.81i | 0.0495193i | ||||||||
\(218\) | 167947. | 3.53394 | ||||||||
\(219\) | − | 18618.6i | − | 0.388202i | ||||||
\(220\) | 64974.1 | + | 9431.49i | 1.34244 | + | 0.194866i | ||||
\(221\) | −21077.2 | −0.431547 | ||||||||
\(222\) | − | 71690.8i | − | 1.45465i | ||||||
\(223\) | −8345.72 | −0.167824 | −0.0839120 | − | 0.996473i | \(-0.526741\pi\) | ||||
−0.0839120 | + | 0.996473i | \(0.526741\pi\) | |||||||
\(224\) | −240002. | −4.78320 | ||||||||
\(225\) | −12636.2 | −0.249604 | ||||||||
\(226\) | − | 17662.8i | − | 0.345813i | ||||||
\(227\) | 59279.0i | 1.15040i | 0.818013 | + | 0.575200i | \(0.195076\pi\) | ||||
−0.818013 | + | 0.575200i | \(0.804924\pi\) | |||||||
\(228\) | − | 15534.3i | − | 0.298829i | ||||||
\(229\) | −45919.1 | −0.875634 | −0.437817 | − | 0.899064i | \(-0.644248\pi\) | ||||
−0.437817 | + | 0.899064i | \(0.644248\pi\) | |||||||
\(230\) | 55636.7i | 1.05173i | ||||||||
\(231\) | 5749.16 | − | 39606.3i | 0.107741 | − | 0.742234i | ||||
\(232\) | −80335.8 | −1.49257 | ||||||||
\(233\) | 69926.9i | 1.28805i | 0.765005 | + | 0.644025i | \(0.222737\pi\) | ||||
−0.765005 | + | 0.644025i | \(0.777263\pi\) | |||||||
\(234\) | −40507.1 | −0.739774 | ||||||||
\(235\) | −28815.7 | −0.521786 | ||||||||
\(236\) | 93075.4 | 1.67113 | ||||||||
\(237\) | 37116.4i | 0.660799i | ||||||||
\(238\) | 53035.6i | 0.936297i | ||||||||
\(239\) | 16074.1i | 0.281404i | 0.990052 | + | 0.140702i | \(0.0449359\pi\) | ||||
−0.990052 | + | 0.140702i | \(0.955064\pi\) | |||||||
\(240\) | −60320.0 | −1.04722 | ||||||||
\(241\) | 6183.67i | 0.106466i | 0.998582 | + | 0.0532332i | \(0.0169527\pi\) | ||||
−0.998582 | + | 0.0532332i | \(0.983047\pi\) | |||||||
\(242\) | 32057.7 | − | 108097.i | 0.547397 | − | 1.84580i | ||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | 215062.i | 3.61230i | ||||||||
\(245\) | 20684.2 | 0.344594 | ||||||||
\(246\) | 115335. | 1.90586 | ||||||||
\(247\) | 13448.8 | 0.220440 | ||||||||
\(248\) | − | 7703.17i | − | 0.125247i | ||||||
\(249\) | − | 815.334i | − | 0.0131503i | ||||||
\(250\) | − | 105465.i | − | 1.68745i | ||||||
\(251\) | −50585.6 | −0.802933 | −0.401467 | − | 0.915874i | \(-0.631499\pi\) | ||||
−0.401467 | + | 0.915874i | \(0.631499\pi\) | |||||||
\(252\) | 74427.6i | 1.17201i | ||||||||
\(253\) | 69045.0 | + | 10022.4i | 1.07868 | + | 0.156578i | ||||
\(254\) | 67427.1 | 1.04512 | ||||||||
\(255\) | 7043.92i | 0.108326i | ||||||||
\(256\) | 150892. | 2.30243 | ||||||||
\(257\) | −26033.8 | −0.394159 | −0.197080 | − | 0.980387i | \(-0.563146\pi\) | ||||
−0.197080 | + | 0.980387i | \(0.563146\pi\) | |||||||
\(258\) | 12779.1 | 0.191982 | ||||||||
\(259\) | − | 114040.i | − | 1.70004i | ||||||
\(260\) | − | 105707.i | − | 1.56371i | ||||||
\(261\) | 10315.1i | 0.151423i | ||||||||
\(262\) | 101626. | 1.48048 | ||||||||
\(263\) | − | 79564.2i | − | 1.15029i | −0.818053 | − | 0.575143i | \(-0.804946\pi\) | ||
0.818053 | − | 0.575143i | \(-0.195054\pi\) | |||||||
\(264\) | −18992.4 | + | 130840.i | −0.272504 | + | 1.87730i | ||||
\(265\) | −10738.1 | −0.152910 | ||||||||
\(266\) | − | 33840.7i | − | 0.478273i | ||||||
\(267\) | 37314.6 | 0.523428 | ||||||||
\(268\) | 232529. | 3.23749 | ||||||||
\(269\) | −101837. | −1.40734 | −0.703671 | − | 0.710526i | \(-0.748457\pi\) | ||||
−0.703671 | + | 0.710526i | \(0.748457\pi\) | |||||||
\(270\) | 13537.3i | 0.185697i | ||||||||
\(271\) | 84386.2i | 1.14903i | 0.818493 | + | 0.574517i | \(0.194810\pi\) | ||||
−0.818493 | + | 0.574517i | \(0.805190\pi\) | |||||||
\(272\) | − | 100239.i | − | 1.35487i | ||||||
\(273\) | −64435.7 | −0.864572 | ||||||||
\(274\) | 15669.2i | 0.208711i | ||||||||
\(275\) | −56041.7 | − | 8134.88i | −0.741047 | − | 0.107569i | ||||
\(276\) | −129748. | −1.70327 | ||||||||
\(277\) | − | 77513.5i | − | 1.01022i | −0.863054 | − | 0.505112i | \(-0.831451\pi\) | ||
0.863054 | − | 0.505112i | \(-0.168549\pi\) | |||||||
\(278\) | −190725. | −2.46784 | ||||||||
\(279\) | −989.082 | −0.0127064 | ||||||||
\(280\) | −167712. | −2.13919 | ||||||||
\(281\) | − | 31892.6i | − | 0.403903i | −0.979395 | − | 0.201952i | \(-0.935272\pi\) | ||
0.979395 | − | 0.201952i | \(-0.0647284\pi\) | |||||||
\(282\) | − | 92028.0i | − | 1.15724i | ||||||
\(283\) | − | 91416.2i | − | 1.14143i | −0.821147 | − | 0.570716i | \(-0.806666\pi\) | ||
0.821147 | − | 0.570716i | \(-0.193334\pi\) | |||||||
\(284\) | 214553. | 2.66010 | ||||||||
\(285\) | − | 4494.54i | − | 0.0553345i | ||||||
\(286\) | −179649. | − | 26077.4i | −2.19630 | − | 0.318810i | ||||
\(287\) | 183466. | 2.22737 | ||||||||
\(288\) | − | 101801.i | − | 1.22735i | ||||||
\(289\) | 71815.6 | 0.859850 | ||||||||
\(290\) | −36863.3 | −0.438327 | ||||||||
\(291\) | 12572.9 | 0.148473 | ||||||||
\(292\) | 155170.i | 1.81988i | ||||||||
\(293\) | − | 98100.1i | − | 1.14271i | −0.820704 | − | 0.571353i | \(-0.806419\pi\) | ||
0.820704 | − | 0.571353i | \(-0.193581\pi\) | |||||||
\(294\) | 66058.9i | 0.764252i | ||||||||
\(295\) | 26929.5 | 0.309445 | ||||||||
\(296\) | 376733.i | 4.29982i | ||||||||
\(297\) | 16799.8 | + | 2438.61i | 0.190454 | + | 0.0276459i | ||||
\(298\) | −157682. | −1.77562 | ||||||||
\(299\) | − | 112330.i | − | 1.25647i | ||||||
\(300\) | 105313. | 1.17014 | ||||||||
\(301\) | 20328.0 | 0.224368 | ||||||||
\(302\) | −131868. | −1.44586 | ||||||||
\(303\) | − | 19950.4i | − | 0.217304i | ||||||
\(304\) | 63959.7i | 0.692085i | ||||||||
\(305\) | 62223.9i | 0.668894i | ||||||||
\(306\) | −22496.0 | −0.240250 | ||||||||
\(307\) | 142750.i | 1.51461i | 0.653063 | + | 0.757304i | \(0.273484\pi\) | ||||
−0.653063 | + | 0.757304i | \(0.726516\pi\) | |||||||
\(308\) | −47914.6 | + | 330086.i | −0.505087 | + | 3.47958i | ||||
\(309\) | −35358.9 | −0.370324 | ||||||||
\(310\) | − | 3534.72i | − | 0.0367817i | ||||||
\(311\) | 165392. | 1.70999 | 0.854996 | − | 0.518635i | \(-0.173560\pi\) | ||||
0.854996 | + | 0.518635i | \(0.173560\pi\) | |||||||
\(312\) | 212864. | 2.18672 | ||||||||
\(313\) | 73167.5 | 0.746843 | 0.373422 | − | 0.927662i | \(-0.378185\pi\) | ||||
0.373422 | + | 0.927662i | \(0.378185\pi\) | |||||||
\(314\) | − | 329258.i | − | 3.33946i | ||||||
\(315\) | 21534.1i | 0.217023i | ||||||||
\(316\) | − | 309335.i | − | 3.09781i | ||||||
\(317\) | −112606. | −1.12058 | −0.560292 | − | 0.828295i | \(-0.689311\pi\) | ||||
−0.560292 | + | 0.828295i | \(0.689311\pi\) | |||||||
\(318\) | − | 34294.0i | − | 0.339128i | ||||||
\(319\) | −6640.57 | + | 45747.3i | −0.0652566 | + | 0.449557i | ||||
\(320\) | 178074. | 1.73900 | ||||||||
\(321\) | − | 30971.1i | − | 0.300571i | ||||||
\(322\) | −282650. | −2.72607 | ||||||||
\(323\) | 7468.95 | 0.0715903 | ||||||||
\(324\) | −31569.8 | −0.300734 | ||||||||
\(325\) | 91174.4i | 0.863189i | ||||||||
\(326\) | 253535.i | 2.38562i | ||||||||
\(327\) | 113320.i | 1.05977i | ||||||||
\(328\) | −606083. | −5.63358 | ||||||||
\(329\) | − | 146391.i | − | 1.35246i | ||||||
\(330\) | −8714.96 | + | 60037.9i | −0.0800272 | + | 0.551312i | ||||
\(331\) | −72976.7 | −0.666083 | −0.333041 | − | 0.942912i | \(-0.608075\pi\) | ||||
−0.333041 | + | 0.942912i | \(0.608075\pi\) | |||||||
\(332\) | 6795.14i | 0.0616485i | ||||||||
\(333\) | 48372.3 | 0.436223 | ||||||||
\(334\) | 174855. | 1.56742 | ||||||||
\(335\) | 67277.7 | 0.599489 | ||||||||
\(336\) | − | 306442.i | − | 2.71437i | ||||||
\(337\) | 196562.i | 1.73077i | 0.501108 | + | 0.865384i | \(0.332926\pi\) | ||||
−0.501108 | + | 0.865384i | \(0.667074\pi\) | |||||||
\(338\) | 72322.6i | 0.633054i | ||||||||
\(339\) | 11917.7 | 0.103703 | ||||||||
\(340\) | − | 58705.3i | − | 0.507831i | ||||||
\(341\) | −4386.58 | − | 636.745i | −0.0377240 | − | 0.00547592i | ||||
\(342\) | 14354.1 | 0.122723 | ||||||||
\(343\) | − | 47751.5i | − | 0.405881i | ||||||
\(344\) | −67153.7 | −0.567483 | ||||||||
\(345\) | −37540.1 | −0.315397 | ||||||||
\(346\) | 251111. | 2.09755 | ||||||||
\(347\) | 206637.i | 1.71612i | 0.513546 | + | 0.858062i | \(0.328332\pi\) | ||||
−0.513546 | + | 0.858062i | \(0.671668\pi\) | |||||||
\(348\) | − | 85967.6i | − | 0.709866i | ||||||
\(349\) | − | 210273.i | − | 1.72636i | −0.504894 | − | 0.863181i | \(-0.668468\pi\) | ||
0.504894 | − | 0.863181i | \(-0.331532\pi\) | |||||||
\(350\) | 229418. | 1.87280 | ||||||||
\(351\) | − | 27331.6i | − | 0.221845i | ||||||
\(352\) | 65537.0 | − | 451489.i | 0.528934 | − | 3.64386i | ||||
\(353\) | −140022. | −1.12369 | −0.561847 | − | 0.827241i | \(-0.689909\pi\) | ||||
−0.561847 | + | 0.827241i | \(0.689909\pi\) | |||||||
\(354\) | 86004.2i | 0.686299i | ||||||||
\(355\) | 62076.5 | 0.492573 | ||||||||
\(356\) | −310987. | −2.45382 | ||||||||
\(357\) | −35785.0 | −0.280779 | ||||||||
\(358\) | − | 33064.4i | − | 0.257985i | ||||||
\(359\) | − | 90549.6i | − | 0.702583i | −0.936266 | − | 0.351292i | \(-0.885743\pi\) | ||
0.936266 | − | 0.351292i | \(-0.114257\pi\) | |||||||
\(360\) | − | 71138.2i | − | 0.548906i | ||||||
\(361\) | 125555. | 0.963431 | ||||||||
\(362\) | − | 185370.i | − | 1.41457i | ||||||
\(363\) | 72937.0 | + | 21630.5i | 0.553522 | + | 0.164155i | ||||
\(364\) | 537019. | 4.05309 | ||||||||
\(365\) | 44895.5i | 0.336990i | ||||||||
\(366\) | −198723. | −1.48350 | ||||||||
\(367\) | −60682.5 | −0.450538 | −0.225269 | − | 0.974297i | \(-0.572326\pi\) | ||||
−0.225269 | + | 0.974297i | \(0.572326\pi\) | |||||||
\(368\) | 534215. | 3.94476 | ||||||||
\(369\) | 77820.7i | 0.571534i | ||||||||
\(370\) | 172870.i | 1.26275i | ||||||||
\(371\) | − | 54552.4i | − | 0.396338i | ||||||
\(372\) | 8243.19 | 0.0595675 | ||||||||
\(373\) | 100208.i | 0.720252i | 0.932904 | + | 0.360126i | \(0.117266\pi\) | ||||
−0.932904 | + | 0.360126i | \(0.882734\pi\) | |||||||
\(374\) | −99769.9 | − | 14482.4i | −0.713274 | − | 0.103537i | ||||
\(375\) | 71161.3 | 0.506036 | ||||||||
\(376\) | 483606.i | 3.42070i | ||||||||
\(377\) | 74426.5 | 0.523654 | ||||||||
\(378\) | −68773.2 | −0.481322 | ||||||||
\(379\) | −228068. | −1.58777 | −0.793883 | − | 0.608070i | \(-0.791944\pi\) | ||||
−0.793883 | + | 0.608070i | \(0.791944\pi\) | |||||||
\(380\) | 37458.3i | 0.259407i | ||||||||
\(381\) | 45495.5i | 0.313414i | ||||||||
\(382\) | 122185.i | 0.837319i | ||||||||
\(383\) | −13819.4 | −0.0942091 | −0.0471045 | − | 0.998890i | \(-0.514999\pi\) | ||||
−0.0471045 | + | 0.998890i | \(0.514999\pi\) | |||||||
\(384\) | 255244.i | 1.73098i | ||||||||
\(385\) | −13863.1 | + | 95503.9i | −0.0935275 | + | 0.644317i | ||||
\(386\) | −225273. | −1.51194 | ||||||||
\(387\) | 8622.49i | 0.0575719i | ||||||||
\(388\) | −104785. | −0.696040 | ||||||||
\(389\) | −159107. | −1.05145 | −0.525726 | − | 0.850654i | \(-0.676206\pi\) | ||||
−0.525726 | + | 0.850654i | \(0.676206\pi\) | |||||||
\(390\) | 97675.9 | 0.642182 | ||||||||
\(391\) | − | 62383.4i | − | 0.408052i | ||||||
\(392\) | − | 347138.i | − | 2.25907i | ||||||
\(393\) | 68570.9i | 0.443971i | ||||||||
\(394\) | 423118. | 2.72565 | ||||||||
\(395\) | − | 89499.9i | − | 0.573625i | ||||||
\(396\) | −140012. | − | 20323.8i | −0.892844 | − | 0.129603i | ||||
\(397\) | −76802.1 | −0.487295 | −0.243648 | − | 0.969864i | \(-0.578344\pi\) | ||||
−0.243648 | + | 0.969864i | \(0.578344\pi\) | |||||||
\(398\) | − | 245032.i | − | 1.54688i | ||||||
\(399\) | 22833.5 | 0.143426 | ||||||||
\(400\) | −433605. | −2.71003 | ||||||||
\(401\) | 121201. | 0.753732 | 0.376866 | − | 0.926268i | \(-0.377002\pi\) | ||||
0.376866 | + | 0.926268i | \(0.377002\pi\) | |||||||
\(402\) | 214864.i | 1.32957i | ||||||||
\(403\) | 7136.54i | 0.0439418i | ||||||||
\(404\) | 166271.i | 1.01872i | ||||||||
\(405\) | −9134.10 | −0.0556872 | ||||||||
\(406\) | − | 187276.i | − | 1.13613i | ||||||
\(407\) | 214531. | + | 31140.8i | 1.29510 | + | 0.187993i | ||||
\(408\) | 118216. | 0.710161 | ||||||||
\(409\) | − | 81034.4i | − | 0.484421i | −0.970224 | − | 0.242210i | \(-0.922128\pi\) | ||
0.970224 | − | 0.242210i | \(-0.0778724\pi\) | |||||||
\(410\) | −278111. | −1.65444 | ||||||||
\(411\) | −10572.5 | −0.0625887 | ||||||||
\(412\) | 294687. | 1.73607 | ||||||||
\(413\) | 136809.i | 0.802075i | ||||||||
\(414\) | − | 119891.i | − | 0.699498i | ||||||
\(415\) | 1966.04i | 0.0114155i | ||||||||
\(416\) | −734528. | −4.24445 | ||||||||
\(417\) | − | 128689.i | − | 0.740062i | ||||||
\(418\) | 63660.6 | + | 9240.83i | 0.364350 | + | 0.0528881i | ||||
\(419\) | 160750. | 0.915635 | 0.457817 | − | 0.889046i | \(-0.348631\pi\) | ||||
0.457817 | + | 0.889046i | \(0.348631\pi\) | |||||||
\(420\) | − | 179469.i | − | 1.01740i | ||||||
\(421\) | −92831.1 | −0.523756 | −0.261878 | − | 0.965101i | \(-0.584342\pi\) | ||||
−0.261878 | + | 0.965101i | \(0.584342\pi\) | |||||||
\(422\) | 460985. | 2.58858 | ||||||||
\(423\) | 62094.6 | 0.347035 | ||||||||
\(424\) | 180214.i | 1.00244i | ||||||||
\(425\) | 50634.6i | 0.280330i | ||||||||
\(426\) | 198253.i | 1.09245i | ||||||||
\(427\) | −316114. | −1.73376 | ||||||||
\(428\) | 258119.i | 1.40907i | ||||||||
\(429\) | 17595.4 | − | 121216.i | 0.0956057 | − | 0.658634i | ||||
\(430\) | −30814.5 | −0.166655 | ||||||||
\(431\) | − | 213351.i | − | 1.14853i | −0.818671 | − | 0.574263i | \(-0.805289\pi\) | ||
0.818671 | − | 0.574263i | \(-0.194711\pi\) | |||||||
\(432\) | 129983. | 0.696497 | ||||||||
\(433\) | −33161.8 | −0.176873 | −0.0884366 | − | 0.996082i | \(-0.528187\pi\) | ||||
−0.0884366 | + | 0.996082i | \(0.528187\pi\) | |||||||
\(434\) | 17957.3 | 0.0953372 | ||||||||
\(435\) | − | 24873.0i | − | 0.131447i | ||||||
\(436\) | − | 944427.i | − | 4.96816i | ||||||
\(437\) | 39805.3i | 0.208438i | ||||||||
\(438\) | −143382. | −0.747388 | ||||||||
\(439\) | − | 293728.i | − | 1.52411i | −0.647513 | − | 0.762055i | \(-0.724191\pi\) | ||
0.647513 | − | 0.762055i | \(-0.275809\pi\) | |||||||
\(440\) | 45797.0 | − | 315498.i | 0.236555 | − | 1.62964i | ||||
\(441\) | −44572.3 | −0.229186 | ||||||||
\(442\) | 162316.i | 0.830839i | ||||||||
\(443\) | −274048. | −1.39643 | −0.698215 | − | 0.715888i | \(-0.746022\pi\) | ||||
−0.698215 | + | 0.715888i | \(0.746022\pi\) | |||||||
\(444\) | −403144. | −2.04500 | ||||||||
\(445\) | −89977.9 | −0.454376 | ||||||||
\(446\) | 64270.6i | 0.323104i | ||||||||
\(447\) | − | 106394.i | − | 0.532477i | ||||||
\(448\) | 904663.i | 4.50745i | ||||||||
\(449\) | −231379. | −1.14771 | −0.573854 | − | 0.818958i | \(-0.694552\pi\) | ||||
−0.573854 | + | 0.818958i | \(0.694552\pi\) | |||||||
\(450\) | 97311.8i | 0.480552i | ||||||||
\(451\) | −50098.9 | + | 345135.i | −0.246306 | + | 1.69682i | ||||
\(452\) | −99324.2 | −0.486159 | ||||||||
\(453\) | − | 88976.1i | − | 0.433588i | ||||||
\(454\) | 456509. | 2.21481 | ||||||||
\(455\) | 155376. | 0.750516 | ||||||||
\(456\) | −75430.7 | −0.362759 | ||||||||
\(457\) | − | 271864.i | − | 1.30172i | −0.759196 | − | 0.650862i | \(-0.774407\pi\) | ||
0.759196 | − | 0.650862i | \(-0.225593\pi\) | |||||||
\(458\) | 353624.i | 1.68582i | ||||||||
\(459\) | − | 15178.9i | − | 0.0720467i | ||||||
\(460\) | 312866. | 1.47857 | ||||||||
\(461\) | − | 264865.i | − | 1.24630i | −0.782102 | − | 0.623150i | \(-0.785852\pi\) | ||
0.782102 | − | 0.623150i | \(-0.214148\pi\) | |||||||
\(462\) | −305009. | − | 44274.4i | −1.42899 | − | 0.207429i | ||||
\(463\) | 255889. | 1.19369 | 0.596843 | − | 0.802358i | \(-0.296422\pi\) | ||||
0.596843 | + | 0.802358i | \(0.296422\pi\) | |||||||
\(464\) | 353956.i | 1.64404i | ||||||||
\(465\) | 2385.00 | 0.0110302 | ||||||||
\(466\) | 538508. | 2.47982 | ||||||||
\(467\) | −184125. | −0.844264 | −0.422132 | − | 0.906534i | \(-0.638718\pi\) | ||||
−0.422132 | + | 0.906534i | \(0.638718\pi\) | |||||||
\(468\) | 227786.i | 1.04001i | ||||||||
\(469\) | 341789.i | 1.55386i | ||||||||
\(470\) | 221910.i | 1.00457i | ||||||||
\(471\) | 222162. | 1.00145 | ||||||||
\(472\) | − | 451951.i | − | 2.02865i | ||||||
\(473\) | −5550.93 | + | 38240.7i | −0.0248110 | + | 0.170924i | ||||
\(474\) | 285834. | 1.27221 | ||||||||
\(475\) | − | 32308.7i | − | 0.143196i | ||||||
\(476\) | 298239. | 1.31629 | ||||||||
\(477\) | 23139.4 | 0.101699 | ||||||||
\(478\) | 123787. | 0.541774 | ||||||||
\(479\) | 452588.i | 1.97257i | 0.165062 | + | 0.986283i | \(0.447218\pi\) | ||||
−0.165062 | + | 0.986283i | \(0.552782\pi\) | |||||||
\(480\) | 245476.i | 1.06544i | ||||||||
\(481\) | − | 349022.i | − | 1.50856i | ||||||
\(482\) | 47620.6 | 0.204975 | ||||||||
\(483\) | − | 190714.i | − | 0.817500i | ||||||
\(484\) | −607870. | − | 180273.i | −2.59490 | − | 0.769554i | ||||
\(485\) | −30317.3 | −0.128887 | ||||||||
\(486\) | − | 29171.4i | − | 0.123505i | ||||||
\(487\) | 10896.3 | 0.0459432 | 0.0229716 | − | 0.999736i | \(-0.492687\pi\) | ||||
0.0229716 | + | 0.999736i | \(0.492687\pi\) | |||||||
\(488\) | 1.04429e6 | 4.38511 | ||||||||
\(489\) | −171069. | −0.715407 | ||||||||
\(490\) | − | 159290.i | − | 0.663431i | ||||||
\(491\) | 178944.i | 0.742256i | 0.928582 | + | 0.371128i | \(0.121029\pi\) | ||||
−0.928582 | + | 0.371128i | \(0.878971\pi\) | |||||||
\(492\) | − | 648572.i | − | 2.67934i | ||||||
\(493\) | 41333.5 | 0.170062 | ||||||||
\(494\) | − | 103570.i | − | 0.424403i | ||||||
\(495\) | −40509.7 | − | 5880.30i | −0.165329 | − | 0.0239988i | ||||
\(496\) | −33939.8 | −0.137958 | ||||||||
\(497\) | 315366.i | 1.27674i | ||||||||
\(498\) | −6278.90 | −0.0253177 | ||||||||
\(499\) | −402187. | −1.61520 | −0.807601 | − | 0.589729i | \(-0.799235\pi\) | ||||
−0.807601 | + | 0.589729i | \(0.799235\pi\) | |||||||
\(500\) | −593071. | −2.37228 | ||||||||
\(501\) | 117981.i | 0.470041i | ||||||||
\(502\) | 389561.i | 1.54585i | ||||||||
\(503\) | 211540.i | 0.836096i | 0.908425 | + | 0.418048i | \(0.137286\pi\) | ||||
−0.908425 | + | 0.418048i | \(0.862714\pi\) | |||||||
\(504\) | 361402. | 1.42275 | ||||||||
\(505\) | 48107.1i | 0.188637i | ||||||||
\(506\) | 77182.8 | − | 531717.i | 0.301453 | − | 2.07673i | ||||
\(507\) | −48798.7 | −0.189842 | ||||||||
\(508\) | − | 379167.i | − | 1.46928i | ||||||
\(509\) | 185877. | 0.717446 | 0.358723 | − | 0.933444i | \(-0.383212\pi\) | ||||
0.358723 | + | 0.933444i | \(0.383212\pi\) | |||||||
\(510\) | 54245.3 | 0.208556 | ||||||||
\(511\) | −228081. | −0.873470 | ||||||||
\(512\) | − | 376076.i | − | 1.43461i | ||||||
\(513\) | 9685.26i | 0.0368024i | ||||||||
\(514\) | 200487.i | 0.758857i | ||||||||
\(515\) | 85261.9 | 0.321470 | ||||||||
\(516\) | − | 71861.4i | − | 0.269896i | ||||||
\(517\) | 275390. | + | 39974.9i | 1.03031 | + | 0.149557i | ||||
\(518\) | −878227. | −3.27301 | ||||||||
\(519\) | 169433.i | 0.629020i | ||||||||
\(520\) | −513285. | −1.89824 | ||||||||
\(521\) | 324045. | 1.19380 | 0.596898 | − | 0.802317i | \(-0.296400\pi\) | ||||
0.596898 | + | 0.802317i | \(0.296400\pi\) | |||||||
\(522\) | 79436.5 | 0.291527 | ||||||||
\(523\) | − | 159328.i | − | 0.582492i | −0.956648 | − | 0.291246i | \(-0.905930\pi\) | ||
0.956648 | − | 0.291246i | \(-0.0940698\pi\) | |||||||
\(524\) | − | 571482.i | − | 2.08133i | ||||||
\(525\) | 154796.i | 0.561620i | ||||||||
\(526\) | −612725. | −2.21459 | ||||||||
\(527\) | 3963.35i | 0.0142706i | ||||||||
\(528\) | 576475. | + | 83679.7i | 2.06782 | + | 0.300160i | ||||
\(529\) | 52627.1 | 0.188061 | ||||||||
\(530\) | 82694.1i | 0.294390i | ||||||||
\(531\) | −58030.1 | −0.205809 | ||||||||
\(532\) | −190299. | −0.672376 | ||||||||
\(533\) | 561501. | 1.97650 | ||||||||
\(534\) | − | 287361.i | − | 1.00773i | ||||||
\(535\) | 74681.6i | 0.260919i | ||||||||
\(536\) | − | 1.12910e6i | − | 3.93011i | ||||||
\(537\) | 22309.7 | 0.0773653 | ||||||||
\(538\) | 784246.i | 2.70949i | ||||||||
\(539\) | −197678. | − | 28694.5i | −0.680426 | − | 0.0987691i | ||||
\(540\) | 76125.2 | 0.261061 | ||||||||
\(541\) | − | 94598.0i | − | 0.323212i | −0.986855 | − | 0.161606i | \(-0.948333\pi\) | ||
0.986855 | − | 0.161606i | \(-0.0516674\pi\) | |||||||
\(542\) | 649860. | 2.21218 | ||||||||
\(543\) | 125076. | 0.424204 | ||||||||
\(544\) | −407928. | −1.37843 | ||||||||
\(545\) | − | 273251.i | − | 0.919960i | ||||||
\(546\) | 496220.i | 1.66452i | ||||||||
\(547\) | − | 65315.6i | − | 0.218294i | −0.994026 | − | 0.109147i | \(-0.965188\pi\) | ||
0.994026 | − | 0.109147i | \(-0.0348119\pi\) | |||||||
\(548\) | 88113.5 | 0.293414 | ||||||||
\(549\) | − | 134086.i | − | 0.444875i | ||||||
\(550\) | −62646.8 | + | 431578.i | −0.207097 | + | 1.42670i | ||||
\(551\) | −26373.9 | −0.0868701 | ||||||||
\(552\) | 630025.i | 2.06766i | ||||||||
\(553\) | 454684. | 1.48682 | ||||||||
\(554\) | −596933. | −1.94494 | ||||||||
\(555\) | −116642. | −0.378676 | ||||||||
\(556\) | 1.07251e6i | 3.46939i | ||||||||
\(557\) | 334291.i | 1.07749i | 0.842468 | + | 0.538747i | \(0.181102\pi\) | ||||
−0.842468 | + | 0.538747i | \(0.818898\pi\) | |||||||
\(558\) | 7616.94i | 0.0244631i | ||||||||
\(559\) | 62214.0 | 0.199097 | ||||||||
\(560\) | 738932.i | 2.35629i | ||||||||
\(561\) | 9771.77 | − | 67318.3i | 0.0310490 | − | 0.213898i | ||||
\(562\) | −245606. | −0.777617 | ||||||||
\(563\) | − | 296644.i | − | 0.935876i | −0.883761 | − | 0.467938i | \(-0.844997\pi\) | ||
0.883761 | − | 0.467938i | \(-0.155003\pi\) | |||||||
\(564\) | −517508. | −1.62689 | ||||||||
\(565\) | −28737.5 | −0.0900226 | ||||||||
\(566\) | −703998. | −2.19755 | ||||||||
\(567\) | − | 46403.7i | − | 0.144340i | ||||||
\(568\) | − | 1.04181e6i | − | 3.22919i | ||||||
\(569\) | 87509.9i | 0.270292i | 0.990826 | + | 0.135146i | \(0.0431503\pi\) | ||||
−0.990826 | + | 0.135146i | \(0.956850\pi\) | |||||||
\(570\) | −34612.6 | −0.106533 | ||||||||
\(571\) | 615448.i | 1.88764i | 0.330462 | + | 0.943819i | \(0.392795\pi\) | ||||
−0.330462 | + | 0.943819i | \(0.607205\pi\) | |||||||
\(572\) | −146643. | + | 1.01023e6i | −0.448197 | + | 3.08766i | ||||
\(573\) | −82442.6 | −0.251097 | ||||||||
\(574\) | − | 1.41288e6i | − | 4.28826i | ||||||
\(575\) | −269854. | −0.816193 | ||||||||
\(576\) | −383729. | −1.15659 | ||||||||
\(577\) | 516552. | 1.55154 | 0.775770 | − | 0.631016i | \(-0.217362\pi\) | ||||
0.775770 | + | 0.631016i | \(0.217362\pi\) | |||||||
\(578\) | − | 553053.i | − | 1.65543i | ||||||
\(579\) | − | 152000.i | − | 0.453404i | ||||||
\(580\) | 207296.i | 0.616219i | ||||||||
\(581\) | −9988.01 | −0.0295888 | ||||||||
\(582\) | − | 96824.0i | − | 0.285849i | ||||||
\(583\) | 102623. | + | 14896.5i | 0.301932 | + | 0.0438277i | ||||
\(584\) | 753469. | 2.20922 | ||||||||
\(585\) | 65905.4i | 0.192579i | ||||||||
\(586\) | −755471. | −2.20000 | ||||||||
\(587\) | −523368. | −1.51891 | −0.759453 | − | 0.650562i | \(-0.774533\pi\) | ||||
−0.759453 | + | 0.650562i | \(0.774533\pi\) | |||||||
\(588\) | 371474. | 1.07442 | ||||||||
\(589\) | − | 2528.91i | − | 0.00728960i | ||||||
\(590\) | − | 207384.i | − | 0.595761i | ||||||
\(591\) | 285493.i | 0.817374i | ||||||||
\(592\) | 1.65987e6 | 4.73621 | ||||||||
\(593\) | − | 221167.i | − | 0.628942i | −0.949267 | − | 0.314471i | \(-0.898173\pi\) | ||
0.949267 | − | 0.314471i | \(-0.101827\pi\) | |||||||
\(594\) | 18779.8 | − | 129375.i | 0.0532253 | − | 0.366673i | ||||
\(595\) | 86289.4 | 0.243738 | ||||||||
\(596\) | 886704.i | 2.49624i | ||||||||
\(597\) | 165332. | 0.463882 | ||||||||
\(598\) | −865052. | −2.41902 | ||||||||
\(599\) | 293216. | 0.817210 | 0.408605 | − | 0.912711i | \(-0.366015\pi\) | ||||
0.408605 | + | 0.912711i | \(0.366015\pi\) | |||||||
\(600\) | − | 511372.i | − | 1.42048i | ||||||
\(601\) | − | 256959.i | − | 0.711401i | −0.934600 | − | 0.355701i | \(-0.884242\pi\) | ||
0.934600 | − | 0.355701i | \(-0.115758\pi\) | |||||||
\(602\) | − | 156546.i | − | 0.431966i | ||||||
\(603\) | −144976. | −0.398714 | ||||||||
\(604\) | 741543.i | 2.03265i | ||||||||
\(605\) | −175875. | − | 52158.2i | −0.480500 | − | 0.142499i | ||||
\(606\) | −153639. | −0.418365 | ||||||||
\(607\) | − | 182631.i | − | 0.495676i | −0.968802 | − | 0.247838i | \(-0.920280\pi\) | ||
0.968802 | − | 0.247838i | \(-0.0797200\pi\) | |||||||
\(608\) | 260288. | 0.704122 | ||||||||
\(609\) | 126362. | 0.340707 | ||||||||
\(610\) | 479187. | 1.28779 | ||||||||
\(611\) | − | 448032.i | − | 1.20013i | ||||||
\(612\) | 126504.i | 0.337753i | ||||||||
\(613\) | − | 199000.i | − | 0.529580i | −0.964306 | − | 0.264790i | \(-0.914697\pi\) | ||
0.964306 | − | 0.264790i | \(-0.0853026\pi\) | |||||||
\(614\) | 1.09932e6 | 2.91601 | ||||||||
\(615\) | − | 187651.i | − | 0.496136i | ||||||
\(616\) | 1.60282e6 | + | 232661.i | 4.22399 | + | 0.613144i | ||||
\(617\) | 385966. | 1.01386 | 0.506931 | − | 0.861987i | \(-0.330780\pi\) | ||||
0.506931 | + | 0.861987i | \(0.330780\pi\) | |||||||
\(618\) | 272300.i | 0.712968i | ||||||||
\(619\) | −287681. | −0.750809 | −0.375404 | − | 0.926861i | \(-0.622496\pi\) | ||||
−0.375404 | + | 0.926861i | \(0.622496\pi\) | |||||||
\(620\) | −19877.0 | −0.0517092 | ||||||||
\(621\) | 80894.8 | 0.209767 | ||||||||
\(622\) | − | 1.27369e6i | − | 3.29217i | ||||||
\(623\) | − | 457112.i | − | 1.17773i | ||||||
\(624\) | − | 937869.i | − | 2.40865i | ||||||
\(625\) | 120912. | 0.309535 | ||||||||
\(626\) | − | 563464.i | − | 1.43786i | ||||||
\(627\) | −6235.12 | + | 42954.1i | −0.0158602 | + | 0.109262i | ||||
\(628\) | −1.85154e6 | −4.69476 | ||||||||
\(629\) | − | 193833.i | − | 0.489921i | ||||||
\(630\) | 165835. | 0.417825 | ||||||||
\(631\) | 505556. | 1.26973 | 0.634863 | − | 0.772625i | \(-0.281056\pi\) | ||||
0.634863 | + | 0.772625i | \(0.281056\pi\) | |||||||
\(632\) | −1.50205e6 | −3.76055 | ||||||||
\(633\) | 311043.i | 0.776270i | ||||||||
\(634\) | 867184.i | 2.15741i | ||||||||
\(635\) | − | 109704.i | − | 0.272068i | ||||||
\(636\) | −192848. | −0.476761 | ||||||||
\(637\) | 321603.i | 0.792577i | ||||||||
\(638\) | 352301. | + | 51139.2i | 0.865511 | + | 0.125635i | ||||
\(639\) | −133768. | −0.327606 | ||||||||
\(640\) | − | 615477.i | − | 1.50263i | ||||||
\(641\) | −729128. | −1.77455 | −0.887274 | − | 0.461242i | \(-0.847404\pi\) | ||||
−0.887274 | + | 0.461242i | \(0.847404\pi\) | |||||||
\(642\) | −238509. | −0.578676 | ||||||||
\(643\) | −548088. | −1.32565 | −0.662824 | − | 0.748775i | \(-0.730642\pi\) | ||||
−0.662824 | + | 0.748775i | \(0.730642\pi\) | |||||||
\(644\) | 1.58944e6i | 3.83242i | ||||||||
\(645\) | − | 20791.6i | − | 0.0499769i | ||||||
\(646\) | − | 57518.5i | − | 0.137830i | ||||||
\(647\) | −301562. | −0.720390 | −0.360195 | − | 0.932877i | \(-0.617290\pi\) | ||||
−0.360195 | + | 0.932877i | \(0.617290\pi\) | |||||||
\(648\) | 153295.i | 0.365072i | ||||||||
\(649\) | −257364. | − | 37358.3i | −0.611024 | − | 0.0886947i | ||||
\(650\) | 702135. | 1.66186 | ||||||||
\(651\) | 12116.5i | 0.0285900i | ||||||||
\(652\) | 1.42572e6 | 3.35381 | ||||||||
\(653\) | 184146. | 0.431853 | 0.215926 | − | 0.976410i | \(-0.430723\pi\) | ||||
0.215926 | + | 0.976410i | \(0.430723\pi\) | |||||||
\(654\) | 872677. | 2.04032 | ||||||||
\(655\) | − | 165347.i | − | 0.385402i | ||||||
\(656\) | 2.67038e6i | 6.20533i | ||||||||
\(657\) | − | 96744.9i | − | 0.224129i | ||||||
\(658\) | −1.12736e6 | −2.60383 | ||||||||
\(659\) | 608904.i | 1.40210i | 0.713114 | + | 0.701048i | \(0.247284\pi\) | ||||
−0.713114 | + | 0.701048i | \(0.752716\pi\) | |||||||
\(660\) | 337616. | + | 49007.5i | 0.775059 | + | 0.112506i | ||||
\(661\) | −211140. | −0.483246 | −0.241623 | − | 0.970370i | \(-0.577680\pi\) | ||||
−0.241623 | + | 0.970370i | \(0.577680\pi\) | |||||||
\(662\) | 561995.i | 1.28238i | ||||||||
\(663\) | −109520. | −0.249154 | ||||||||
\(664\) | 32995.5 | 0.0748374 | ||||||||
\(665\) | −55059.1 | −0.124505 | ||||||||
\(666\) | − | 372516.i | − | 0.839840i | ||||||
\(667\) | 220284.i | 0.495144i | ||||||||
\(668\) | − | 983274.i | − | 2.20354i | ||||||
\(669\) | −43365.7 | −0.0968933 | ||||||||
\(670\) | − | 518107.i | − | 1.15417i | ||||||
\(671\) | 86320.9 | − | 594670.i | 0.191722 | − | 1.32078i | ||||
\(672\) | −1.24709e6 | −2.76158 | ||||||||
\(673\) | 207518.i | 0.458169i | 0.973406 | + | 0.229085i | \(0.0735733\pi\) | ||||
−0.973406 | + | 0.229085i | \(0.926427\pi\) | |||||||
\(674\) | 1.51373e6 | 3.33217 | ||||||||
\(675\) | −65659.8 | −0.144109 | ||||||||
\(676\) | 406697. | 0.889974 | ||||||||
\(677\) | − | 419679.i | − | 0.915673i | −0.889037 | − | 0.457836i | \(-0.848625\pi\) | ||
0.889037 | − | 0.457836i | \(-0.151375\pi\) | |||||||
\(678\) | − | 91778.4i | − | 0.199655i | ||||||
\(679\) | − | 154020.i | − | 0.334071i | ||||||
\(680\) | −285058. | −0.616475 | ||||||||
\(681\) | 308023.i | 0.664184i | ||||||||
\(682\) | −4903.59 | + | 33781.1i | −0.0105425 | + | 0.0726282i | ||||
\(683\) | 266045. | 0.570313 | 0.285156 | − | 0.958481i | \(-0.407954\pi\) | ||||
0.285156 | + | 0.958481i | \(0.407954\pi\) | |||||||
\(684\) | − | 80718.7i | − | 0.172529i | ||||||
\(685\) | 25493.9 | 0.0543319 | ||||||||
\(686\) | −367736. | −0.781425 | ||||||||
\(687\) | −238603. | −0.505547 | ||||||||
\(688\) | 295876.i | 0.625076i | ||||||||
\(689\) | − | 166958.i | − | 0.351697i | ||||||
\(690\) | 289097.i | 0.607219i | ||||||||
\(691\) | 594449. | 1.24497 | 0.622485 | − | 0.782632i | \(-0.286123\pi\) | ||||
0.622485 | + | 0.782632i | \(0.286123\pi\) | |||||||
\(692\) | − | 1.41209e6i | − | 2.94883i | ||||||
\(693\) | 29873.5 | − | 205801.i | 0.0622042 | − | 0.428529i | ||||
\(694\) | 1.59131e6 | 3.30398 | ||||||||
\(695\) | 310311.i | 0.642432i | ||||||||
\(696\) | −417437. | −0.861733 | ||||||||
\(697\) | 311835. | 0.641889 | ||||||||
\(698\) | −1.61931e6 | −3.32369 | ||||||||
\(699\) | 363351.i | 0.743656i | ||||||||
\(700\) | − | 1.29010e6i | − | 2.63286i | ||||||
\(701\) | 329130.i | 0.669779i | 0.942257 | + | 0.334890i | \(0.108699\pi\) | ||||
−0.942257 | + | 0.334890i | \(0.891301\pi\) | |||||||
\(702\) | −210481. | −0.427109 | ||||||||
\(703\) | 123680.i | 0.250258i | ||||||||
\(704\) | −1.70184e6 | − | 247035.i | −3.43379 | − | 0.498441i | ||||
\(705\) | −149731. | −0.301253 | ||||||||
\(706\) | 1.07832e6i | 2.16340i | ||||||||
\(707\) | −244397. | −0.488942 | ||||||||
\(708\) | 483634. | 0.964828 | ||||||||
\(709\) | −148161. | −0.294742 | −0.147371 | − | 0.989081i | \(-0.547081\pi\) | ||||
−0.147371 | + | 0.989081i | \(0.547081\pi\) | |||||||
\(710\) | − | 478053.i | − | 0.948329i | ||||||
\(711\) | 192863.i | 0.381513i | ||||||||
\(712\) | 1.51008e6i | 2.97878i | ||||||||
\(713\) | −21122.4 | −0.0415494 | ||||||||
\(714\) | 275581.i | 0.540571i | ||||||||
\(715\) | −42428.2 | + | 292291.i | −0.0829932 | + | 0.571745i | ||||
\(716\) | −185933. | −0.362687 | ||||||||
\(717\) | 83523.3i | 0.162469i | ||||||||
\(718\) | −697324. | −1.35265 | ||||||||
\(719\) | −140295. | −0.271384 | −0.135692 | − | 0.990751i | \(-0.543326\pi\) | ||||
−0.135692 | + | 0.990751i | \(0.543326\pi\) | |||||||
\(720\) | −313432. | −0.604614 | ||||||||
\(721\) | 433154.i | 0.833243i | ||||||||
\(722\) | − | 966903.i | − | 1.85485i | ||||||
\(723\) | 32131.3i | 0.0614684i | ||||||||
\(724\) | −1.04241e6 | −1.98866 | ||||||||
\(725\) | − | 178798.i | − | 0.340162i | ||||||
\(726\) | 166577. | − | 561689.i | 0.316040 | − | 1.06567i | ||||
\(727\) | −116812. | −0.221013 | −0.110507 | − | 0.993875i | \(-0.535247\pi\) | ||||
−0.110507 | + | 0.993875i | \(0.535247\pi\) | |||||||
\(728\) | − | 2.60763e6i | − | 4.92020i | ||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 345741. | 0.648791 | ||||||||
\(731\) | 34551.2 | 0.0646589 | ||||||||
\(732\) | 1.11749e6i | 2.08556i | ||||||||
\(733\) | − | 645954.i | − | 1.20225i | −0.799156 | − | 0.601123i | \(-0.794720\pi\) | ||
0.799156 | − | 0.601123i | \(-0.205280\pi\) | |||||||
\(734\) | 467317.i | 0.867400i | ||||||||
\(735\) | 107478. | 0.198951 | ||||||||
\(736\) | − | 2.17402e6i | − | 4.01337i | ||||||
\(737\) | −642969. | − | 93331.9i | −1.18374 | − | 0.171828i | ||||
\(738\) | 599298. | 1.10035 | ||||||||
\(739\) | 72867.2i | 0.133427i | 0.997772 | + | 0.0667134i | \(0.0212513\pi\) | ||||
−0.997772 | + | 0.0667134i | \(0.978749\pi\) | |||||||
\(740\) | 972112. | 1.77522 | ||||||||
\(741\) | 69882.2 | 0.127271 | ||||||||
\(742\) | −420109. | −0.763052 | ||||||||
\(743\) | 675603.i | 1.22381i | 0.790932 | + | 0.611905i | \(0.209596\pi\) | ||||
−0.790932 | + | 0.611905i | \(0.790404\pi\) | |||||||
\(744\) | − | 40026.9i | − | 0.0723112i | ||||||
\(745\) | 256550.i | 0.462231i | ||||||||
\(746\) | 771703. | 1.38667 | ||||||||
\(747\) | − | 4236.60i | − | 0.00759235i | ||||||
\(748\) | −81439.7 | + | 561043.i | −0.145557 | + | 1.00275i | ||||
\(749\) | −379403. | −0.676296 | ||||||||
\(750\) | − | 548014.i | − | 0.974247i | ||||||
\(751\) | −168392. | −0.298567 | −0.149283 | − | 0.988794i | \(-0.547697\pi\) | ||||
−0.149283 | + | 0.988794i | \(0.547697\pi\) | |||||||
\(752\) | 2.13074e6 | 3.76787 | ||||||||
\(753\) | −262850. | −0.463574 | ||||||||
\(754\) | − | 573159.i | − | 1.00817i | ||||||
\(755\) | 214551.i | 0.376388i | ||||||||
\(756\) | 386737.i | 0.676663i | ||||||||
\(757\) | −63422.1 | −0.110675 | −0.0553374 | − | 0.998468i | \(-0.517623\pi\) | ||||
−0.0553374 | + | 0.998468i | \(0.517623\pi\) | |||||||
\(758\) | 1.75636e6i | 3.05685i | ||||||||
\(759\) | 358769. | + | 52078.0i | 0.622774 | + | 0.0904004i | ||||
\(760\) | 181888. | 0.314904 | ||||||||
\(761\) | 377856.i | 0.652464i | 0.945290 | + | 0.326232i | \(0.105779\pi\) | ||||
−0.945290 | + | 0.326232i | \(0.894221\pi\) | |||||||
\(762\) | 350361. | 0.603401 | ||||||||
\(763\) | 1.38819e6 | 2.38451 | ||||||||
\(764\) | 687091. | 1.17714 | ||||||||
\(765\) | 36601.3i | 0.0625422i | ||||||||
\(766\) | 106424.i | 0.181376i | ||||||||
\(767\) | 418706.i | 0.711735i | ||||||||
\(768\) | 784059. | 1.32931 | ||||||||
\(769\) | 795673.i | 1.34549i | 0.739872 | + | 0.672747i | \(0.234886\pi\) | ||||
−0.739872 | + | 0.672747i | \(0.765114\pi\) | |||||||
\(770\) | 735477. | + | 106760.i | 1.24047 | + | 0.180064i | ||||
\(771\) | −135276. | −0.227568 | ||||||||
\(772\) | 1.26679e6i | 2.12555i | ||||||||
\(773\) | 929744. | 1.55598 | 0.777991 | − | 0.628276i | \(-0.216239\pi\) | ||||
0.777991 | + | 0.628276i | \(0.216239\pi\) | |||||||
\(774\) | 66401.9 | 0.110841 | ||||||||
\(775\) | 17144.4 | 0.0285443 | ||||||||
\(776\) | 508808.i | 0.844949i | ||||||||
\(777\) | − | 592571.i | − | 0.981518i | ||||||
\(778\) | 1.22528e6i | 2.02431i | ||||||||
\(779\) | −198974. | −0.327885 | ||||||||
\(780\) | − | 549268.i | − | 0.902807i | ||||||
\(781\) | −593262. | − | 86116.5i | −0.972623 | − | 0.141184i | ||||
\(782\) | −480416. | −0.785604 | ||||||||
\(783\) | 53598.7i | 0.0874239i | ||||||||
\(784\) | −1.52947e6 | −2.48834 | ||||||||
\(785\) | −535706. | −0.869334 | ||||||||
\(786\) | 528066. | 0.854757 | ||||||||
\(787\) | − | 852028.i | − | 1.37564i | −0.725882 | − | 0.687819i | \(-0.758568\pi\) | ||
0.725882 | − | 0.687819i | \(-0.241432\pi\) | |||||||
\(788\) | − | 2.37935e6i | − | 3.83183i | ||||||
\(789\) | − | 413428.i | − | 0.664118i | ||||||
\(790\) | −689240. | −1.10437 | ||||||||
\(791\) | − | 145994.i | − | 0.233337i | ||||||
\(792\) | −98687.5 | + | 679864.i | −0.157330 | + | 1.08386i | ||||
\(793\) | −967471. | −1.53848 | ||||||||
\(794\) | 591454.i | 0.938167i | ||||||||
\(795\) | −55796.7 | −0.0882824 | ||||||||
\(796\) | −1.37791e6 | −2.17467 | ||||||||
\(797\) | 691392. | 1.08845 | 0.544224 | − | 0.838940i | \(-0.316824\pi\) | ||||
0.544224 | + | 0.838940i | \(0.316824\pi\) | |||||||
\(798\) | − | 175841.i | − | 0.276131i | ||||||
\(799\) | − | 248819.i | − | 0.389754i | ||||||
\(800\) | 1.76459e6i | 2.75717i | ||||||||
\(801\) | 193893. | 0.302201 | ||||||||
\(802\) | − | 933370.i | − | 1.45113i | ||||||
\(803\) | 62281.9 | − | 429064.i | 0.0965896 | − | 0.665412i | ||||
\(804\) | 1.20826e6 | 1.86916 | ||||||||
\(805\) | 459874.i | 0.709654i | ||||||||
\(806\) | 54958.6 | 0.0845991 | ||||||||
\(807\) | −529159. | −0.812530 | ||||||||
\(808\) | 807369. | 1.23666 | ||||||||
\(809\) | 227949.i | 0.348289i | 0.984720 | + | 0.174145i | \(0.0557161\pi\) | ||||
−0.984720 | + | 0.174145i | \(0.944284\pi\) | |||||||
\(810\) | 70341.9i | 0.107212i | ||||||||
\(811\) | − | 1.02649e6i | − | 1.56068i | −0.625356 | − | 0.780340i | \(-0.715046\pi\) | ||
0.625356 | − | 0.780340i | \(-0.284954\pi\) | |||||||
\(812\) | −1.05312e6 | −1.59723 | ||||||||
\(813\) | 438484.i | 0.663395i | ||||||||
\(814\) | 239816. | − | 1.65211e6i | 0.361934 | − | 2.49339i | ||||
\(815\) | 412503. | 0.621029 | ||||||||
\(816\) | − | 520855.i | − | 0.782234i | ||||||
\(817\) | −22046.2 | −0.0330286 | ||||||||
\(818\) | −624047. | −0.932633 | ||||||||
\(819\) | −334818. | −0.499161 | ||||||||
\(820\) | 1.56392e6i | 2.32588i | ||||||||
\(821\) | − | 714226.i | − | 1.05962i | −0.848117 | − | 0.529809i | \(-0.822264\pi\) | ||
0.848117 | − | 0.529809i | \(-0.177736\pi\) | |||||||
\(822\) | 81419.4i | 0.120499i | ||||||||
\(823\) | 1.17206e6 | 1.73042 | 0.865210 | − | 0.501409i | \(-0.167185\pi\) | ||||
0.865210 | + | 0.501409i | \(0.167185\pi\) | |||||||
\(824\) | − | 1.43093e6i | − | 2.10748i | ||||||
\(825\) | −291201. | − | 42270.1i | −0.427844 | − | 0.0621048i | ||||
\(826\) | 1.05357e6 | 1.54420 | ||||||||
\(827\) | 788589.i | 1.15303i | 0.817087 | + | 0.576514i | \(0.195587\pi\) | ||||
−0.817087 | + | 0.576514i | \(0.804413\pi\) | |||||||
\(828\) | −674192. | −0.983383 | ||||||||
\(829\) | −1.30745e6 | −1.90246 | −0.951229 | − | 0.308484i | \(-0.900178\pi\) | ||||
−0.951229 | + | 0.308484i | \(0.900178\pi\) | |||||||
\(830\) | 15140.5 | 0.0219778 | ||||||||
\(831\) | − | 402772.i | − | 0.583253i | ||||||
\(832\) | 2.76873e6i | 3.99976i | ||||||||
\(833\) | 178606.i | 0.257398i | ||||||||
\(834\) | −991034. | −1.42481 | ||||||||
\(835\) | − | 284491.i | − | 0.408033i | ||||||
\(836\) | 51964.6 | − | 357987.i | 0.0743524 | − | 0.512218i | ||||
\(837\) | −5139.42 | −0.00733607 | ||||||||
\(838\) | − | 1.23794e6i | − | 1.76283i | ||||||
\(839\) | −872858. | −1.23999 | −0.619997 | − | 0.784604i | \(-0.712866\pi\) | ||||
−0.619997 | + | 0.784604i | \(0.712866\pi\) | |||||||
\(840\) | −871458. | −1.23506 | ||||||||
\(841\) | 561327. | 0.793640 | ||||||||
\(842\) | 714894.i | 1.00836i | ||||||||
\(843\) | − | 165719.i | − | 0.233194i | ||||||
\(844\) | − | 2.59229e6i | − | 3.63914i | ||||||
\(845\) | 117670. | 0.164798 | ||||||||
\(846\) | − | 478192.i | − | 0.668131i | ||||||
\(847\) | 264978. | − | 893494.i | 0.369354 | − | 1.24545i | ||||
\(848\) | 794016. | 1.10417 | ||||||||
\(849\) | − | 475013.i | − | 0.659007i | ||||||
\(850\) | 389938. | 0.539707 | ||||||||
\(851\) | 1.03302e6 | 1.42643 | ||||||||
\(852\) | 1.11485e6 | 1.53581 | ||||||||
\(853\) | − | 62382.2i | − | 0.0857359i | −0.999081 | − | 0.0428680i | \(-0.986351\pi\) | ||
0.999081 | − | 0.0428680i | \(-0.0136495\pi\) | |||||||
\(854\) | 2.43440e6i | 3.33793i | ||||||||
\(855\) | − | 23354.3i | − | 0.0319474i | ||||||
\(856\) | 1.25336e6 | 1.71052 | ||||||||
\(857\) | 378766.i | 0.515714i | 0.966183 | + | 0.257857i | \(0.0830163\pi\) | ||||
−0.966183 | + | 0.257857i | \(0.916984\pi\) | |||||||
\(858\) | −933483. | − | 135502.i | −1.26804 | − | 0.184065i | ||||
\(859\) | 128702. | 0.174421 | 0.0872106 | − | 0.996190i | \(-0.472205\pi\) | ||||
0.0872106 | + | 0.996190i | \(0.472205\pi\) | |||||||
\(860\) | 173281.i | 0.234291i | ||||||||
\(861\) | 953319. | 1.28597 | ||||||||
\(862\) | −1.64302e6 | −2.21120 | ||||||||
\(863\) | 692449. | 0.929750 | 0.464875 | − | 0.885376i | \(-0.346099\pi\) | ||||
0.464875 | + | 0.885376i | \(0.346099\pi\) | |||||||
\(864\) | − | 528975.i | − | 0.708611i | ||||||
\(865\) | − | 408560.i | − | 0.546038i | ||||||
\(866\) | 255379.i | 0.340526i | ||||||||
\(867\) | 373165. | 0.496435 | ||||||||
\(868\) | − | 100981.i | − | 0.134029i | ||||||
\(869\) | −124160. | + | 855346.i | −0.164415 | + | 1.13267i | ||||
\(870\) | −191548. | −0.253068 | ||||||||
\(871\) | 1.04605e6i | 1.37885i | ||||||||
\(872\) | −4.58590e6 | −6.03103 | ||||||||
\(873\) | 65330.6 | 0.0857212 | ||||||||
\(874\) | 306541. | 0.401297 | ||||||||
\(875\) | − | 871740.i | − | 1.13860i | ||||||
\(876\) | 806289.i | 1.05071i | ||||||||
\(877\) | − | 202045.i | − | 0.262694i | −0.991336 | − | 0.131347i | \(-0.958070\pi\) | ||
0.991336 | − | 0.131347i | \(-0.0419302\pi\) | |||||||
\(878\) | −2.26200e6 | −2.93430 | ||||||||
\(879\) | − | 509743.i | − | 0.659741i | ||||||
\(880\) | −1.39007e6 | − | 201779.i | −1.79503 | − | 0.260562i | ||||
\(881\) | −777238. | −1.00139 | −0.500694 | − | 0.865624i | \(-0.666922\pi\) | ||||
−0.500694 | + | 0.865624i | \(0.666922\pi\) | |||||||
\(882\) | 343252.i | 0.441241i | ||||||||
\(883\) | −138486. | −0.177617 | −0.0888083 | − | 0.996049i | \(-0.528306\pi\) | ||||
−0.0888083 | + | 0.996049i | \(0.528306\pi\) | |||||||
\(884\) | 912763. | 1.16803 | ||||||||
\(885\) | 139930. | 0.178658 | ||||||||
\(886\) | 2.11045e6i | 2.68848i | ||||||||
\(887\) | − | 637104.i | − | 0.809773i | −0.914367 | − | 0.404886i | \(-0.867311\pi\) | ||
0.914367 | − | 0.404886i | \(-0.132689\pi\) | |||||||
\(888\) | 1.95756e6i | 2.48251i | ||||||||
\(889\) | 557329. | 0.705193 | ||||||||
\(890\) | 692921.i | 0.874790i | ||||||||
\(891\) | 87294.1 | + | 12671.4i | 0.109959 | + | 0.0159613i | ||||
\(892\) | 361417. | 0.454233 | ||||||||
\(893\) | 158765.i | 0.199092i | ||||||||
\(894\) | −819339. | −1.02515 | ||||||||
\(895\) | −53796.1 | −0.0671591 | ||||||||
\(896\) | 3.12679e6 | 3.89478 | ||||||||
\(897\) | − | 583682.i | − | 0.725423i | ||||||
\(898\) | 1.78185e6i | 2.20963i | ||||||||
\(899\) | − | 13995.1i | − | 0.0173164i | ||||||
\(900\) | 547220. | 0.675581 | ||||||||
\(901\) | − | 92721.9i | − | 0.114218i | ||||||
\(902\) | 2.65789e6 | + | 385813.i | 3.26681 | + | 0.474202i | ||||
\(903\) | 105627. | 0.129539 | ||||||||
\(904\) | 482293.i | 0.590166i | ||||||||
\(905\) | −301600. | −0.368242 | ||||||||
\(906\) | −685206. | −0.834767 | ||||||||
\(907\) | −249854. | −0.303719 | −0.151859 | − | 0.988402i | \(-0.548526\pi\) | ||||
−0.151859 | + | 0.988402i | \(0.548526\pi\) | |||||||
\(908\) | − | 2.56712e6i | − | 3.11368i | ||||||
\(909\) | − | 103666.i | − | 0.125460i | ||||||
\(910\) | − | 1.19655e6i | − | 1.44493i | ||||||
\(911\) | 96364.5 | 0.116113 | 0.0580564 | − | 0.998313i | \(-0.481510\pi\) | ||||
0.0580564 | + | 0.998313i | \(0.481510\pi\) | |||||||
\(912\) | 332344.i | 0.399575i | ||||||||
\(913\) | 2727.41 | − | 18789.3i | 0.00327197 | − | 0.0225408i | ||||
\(914\) | −2.09363e6 | −2.50615 | ||||||||
\(915\) | 323325.i | 0.386186i | ||||||||
\(916\) | 1.98856e6 | 2.36999 | ||||||||
\(917\) | 840008. | 0.998952 | ||||||||
\(918\) | −116893. | −0.138708 | ||||||||
\(919\) | 586637.i | 0.694606i | 0.937753 | + | 0.347303i | \(0.112902\pi\) | ||||
−0.937753 | + | 0.347303i | \(0.887098\pi\) | |||||||
\(920\) | − | 1.51920e6i | − | 1.79489i | ||||||
\(921\) | 741752.i | 0.874459i | ||||||||
\(922\) | −2.03973e6 | −2.39945 | ||||||||
\(923\) | 965180.i | 1.13294i | ||||||||
\(924\) | −248971. | + | 1.71518e6i | −0.291612 | + | 2.00893i | ||||
\(925\) | −838469. | −0.979949 | ||||||||
\(926\) | − | 1.97061e6i | − | 2.29815i | ||||||
\(927\) | −183730. | −0.213807 | ||||||||
\(928\) | 1.44045e6 | 1.67264 | ||||||||
\(929\) | 702941. | 0.814494 | 0.407247 | − | 0.913318i | \(-0.366489\pi\) | ||||
0.407247 | + | 0.913318i | \(0.366489\pi\) | |||||||
\(930\) | − | 18366.9i | − | 0.0212359i | ||||||
\(931\) | − | 113964.i | − | 0.131482i | ||||||
\(932\) | − | 3.02823e6i | − | 3.48624i | ||||||
\(933\) | 859403. | 0.987264 | ||||||||
\(934\) | 1.41795e6i | 1.62542i | ||||||||
\(935\) | −23562.9 | + | 162327.i | −0.0269530 | + | 0.185681i | ||||
\(936\) | 1.10607e6 | 1.26250 | ||||||||
\(937\) | − | 1.34733e6i | − | 1.53459i | −0.641292 | − | 0.767297i | \(-0.721601\pi\) | ||
0.641292 | − | 0.767297i | \(-0.278399\pi\) | |||||||
\(938\) | 2.63212e6 | 2.99158 | ||||||||
\(939\) | 380189. | 0.431190 | ||||||||
\(940\) | 1.24788e6 | 1.41227 | ||||||||
\(941\) | − | 146016.i | − | 0.164900i | −0.996595 | − | 0.0824501i | \(-0.973725\pi\) | ||
0.996595 | − | 0.0824501i | \(-0.0262745\pi\) | |||||||
\(942\) | − | 1.71087e6i | − | 1.92804i | ||||||
\(943\) | 1.66190e6i | 1.86889i | ||||||||
\(944\) | −1.99127e6 | −2.23453 | ||||||||
\(945\) | 111895.i | 0.125298i | ||||||||
\(946\) | 294493. | + | 42747.8i | 0.329073 | + | 0.0477674i | ||||
\(947\) | 688104. | 0.767280 | 0.383640 | − | 0.923483i | \(-0.374670\pi\) | ||||
0.383640 | + | 0.923483i | \(0.374670\pi\) | |||||||
\(948\) | − | 1.60735e6i | − | 1.78852i | ||||||
\(949\) | −698045. | −0.775088 | ||||||||
\(950\) | −248810. | −0.275689 | ||||||||
\(951\) | −585120. | −0.646970 | ||||||||
\(952\) | − | 1.44817e6i | − | 1.59789i | ||||||
\(953\) | 93659.4i | 0.103125i | 0.998670 | + | 0.0515627i | \(0.0164202\pi\) | ||||
−0.998670 | + | 0.0515627i | \(0.983580\pi\) | |||||||
\(954\) | − | 178197.i | − | 0.195796i | ||||||
\(955\) | 198796. | 0.217972 | ||||||||
\(956\) | − | 696098.i | − | 0.761649i | ||||||
\(957\) | −34505.4 | + | 237710.i | −0.0376759 | + | 0.259552i | ||||
\(958\) | 3.48539e6 | 3.79769 | ||||||||
\(959\) | 129516.i | 0.140827i | ||||||||
\(960\) | 925298. | 1.00401 | ||||||||
\(961\) | −922179. | −0.998547 | ||||||||
\(962\) | −2.68782e6 | −2.90436 | ||||||||
\(963\) | − | 160931.i | − | 0.173535i | ||||||
\(964\) | − | 267788.i | − | 0.288162i | ||||||
\(965\) | 366521.i | 0.393590i | ||||||||
\(966\) | −1.46869e6 | −1.57390 | ||||||||
\(967\) | − | 4474.08i | − | 0.00478465i | −0.999997 | − | 0.00239233i | \(-0.999238\pi\) | ||
0.999997 | − | 0.00239233i | \(-0.000761502\pi\) | |||||||
\(968\) | −875358. | + | 2.95167e6i | −0.934190 | + | 3.15004i | ||||
\(969\) | 38809.8 | 0.0413327 | ||||||||
\(970\) | 233474.i | 0.248139i | ||||||||
\(971\) | −344326. | −0.365200 | −0.182600 | − | 0.983187i | \(-0.558451\pi\) | ||||
−0.182600 | + | 0.983187i | \(0.558451\pi\) | |||||||
\(972\) | −164042. | −0.173629 | ||||||||
\(973\) | −1.57646e6 | −1.66517 | ||||||||
\(974\) | − | 83912.7i | − | 0.0884524i | ||||||
\(975\) | 473756.i | 0.498363i | ||||||||
\(976\) | − | 4.60108e6i | − | 4.83015i | ||||||
\(977\) | 1.02530e6 | 1.07414 | 0.537069 | − | 0.843539i | \(-0.319532\pi\) | ||||
0.537069 | + | 0.843539i | \(0.319532\pi\) | |||||||
\(978\) | 1.31740e6i | 1.37734i | ||||||||
\(979\) | 859914. | + | 124823.i | 0.897201 | + | 0.130235i | ||||
\(980\) | −895745. | −0.932679 | ||||||||
\(981\) | 588826.i | 0.611856i | ||||||||
\(982\) | 1.37805e6 | 1.42903 | ||||||||
\(983\) | 230734. | 0.238784 | 0.119392 | − | 0.992847i | \(-0.461905\pi\) | ||||
0.119392 | + | 0.992847i | \(0.461905\pi\) | |||||||
\(984\) | −3.14930e6 | −3.25255 | ||||||||
\(985\) | − | 688418.i | − | 0.709544i | ||||||
\(986\) | − | 318310.i | − | 0.327414i | ||||||
\(987\) | − | 760672.i | − | 0.780842i | ||||||
\(988\) | −582411. | −0.596644 | ||||||||
\(989\) | 184138.i | 0.188257i | ||||||||
\(990\) | −45284.3 | + | 311966.i | −0.0462037 | + | 0.318300i | ||||
\(991\) | 378202. | 0.385103 | 0.192551 | − | 0.981287i | \(-0.438324\pi\) | ||||
0.192551 | + | 0.981287i | \(0.438324\pi\) | |||||||
\(992\) | 138120.i | 0.140357i | ||||||||
\(993\) | −379198. | −0.384563 | ||||||||
\(994\) | 2.42864e6 | 2.45805 | ||||||||
\(995\) | −398669. | −0.402686 | ||||||||
\(996\) | 35308.6i | 0.0355928i | ||||||||
\(997\) | 1.02115e6i | 1.02731i | 0.857997 | + | 0.513655i | \(0.171709\pi\) | ||||
−0.857997 | + | 0.513655i | \(0.828291\pi\) | |||||||
\(998\) | 3.09725e6i | 3.10968i | ||||||||
\(999\) | 251350. | 0.251853 |
(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 | 33.5.c.a.10.1 | ✓ | 8 | |
3.2 | odd | 2 | 99.5.c.c.10.8 | 8 | |||
4.3 | odd | 2 | 528.5.j.a.241.2 | 8 | |||
11.10 | odd | 2 | inner | 33.5.c.a.10.8 | yes | 8 | |
33.32 | even | 2 | 99.5.c.c.10.1 | 8 | |||
44.43 | even | 2 | 528.5.j.a.241.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.5.c.a.10.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
33.5.c.a.10.8 | yes | 8 | 11.10 | odd | 2 | inner | |
99.5.c.c.10.1 | 8 | 33.32 | even | 2 | |||
99.5.c.c.10.8 | 8 | 3.2 | odd | 2 | |||
528.5.j.a.241.1 | 8 | 44.43 | even | 2 | |||
528.5.j.a.241.2 | 8 | 4.3 | odd | 2 |