Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,5,Mod(235,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, 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("354.235");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.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: | \(36.5929669317\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.18 | ||
Character | \(\chi\) | \(=\) | 354.235 |
Dual form | 354.5.d.a.235.17 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843i | 0.707107i | ||||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | −4.63644 | −0.185457 | −0.0927287 | − | 0.995691i | \(-0.529559\pi\) | ||||
−0.0927287 | + | 0.995691i | \(0.529559\pi\) | |||||||
\(6\) | 14.6969i | 0.408248i | ||||||||
\(7\) | −33.3282 | −0.680168 | −0.340084 | − | 0.940395i | \(-0.610456\pi\) | ||||
−0.340084 | + | 0.940395i | \(0.610456\pi\) | |||||||
\(8\) | − | 22.6274i | − | 0.353553i | ||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | − | 13.1138i | − | 0.131138i | ||||||
\(11\) | − | 4.16353i | − | 0.0344093i | −0.999852 | − | 0.0172047i | \(-0.994523\pi\) | ||
0.999852 | − | 0.0172047i | \(-0.00547669\pi\) | |||||||
\(12\) | −41.5692 | −0.288675 | ||||||||
\(13\) | 241.996i | 1.43193i | 0.698136 | + | 0.715965i | \(0.254013\pi\) | ||||
−0.698136 | + | 0.715965i | \(0.745987\pi\) | |||||||
\(14\) | − | 94.2665i | − | 0.480952i | ||||||
\(15\) | −24.0916 | −0.107074 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 291.659 | 1.00920 | 0.504600 | − | 0.863353i | \(-0.331640\pi\) | ||||
0.504600 | + | 0.863353i | \(0.331640\pi\) | |||||||
\(18\) | 76.3675i | 0.235702i | ||||||||
\(19\) | −369.712 | −1.02413 | −0.512067 | − | 0.858946i | \(-0.671120\pi\) | ||||
−0.512067 | + | 0.858946i | \(0.671120\pi\) | |||||||
\(20\) | 37.0915 | 0.0927287 | ||||||||
\(21\) | −173.179 | −0.392695 | ||||||||
\(22\) | 11.7762 | 0.0243311 | ||||||||
\(23\) | − | 496.520i | − | 0.938602i | −0.883038 | − | 0.469301i | \(-0.844506\pi\) | ||
0.883038 | − | 0.469301i | \(-0.155494\pi\) | |||||||
\(24\) | − | 117.576i | − | 0.204124i | ||||||
\(25\) | −603.503 | −0.965606 | ||||||||
\(26\) | −684.469 | −1.01253 | ||||||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | 266.626 | 0.340084 | ||||||||
\(29\) | −329.812 | −0.392166 | −0.196083 | − | 0.980587i | \(-0.562822\pi\) | ||||
−0.196083 | + | 0.980587i | \(0.562822\pi\) | |||||||
\(30\) | − | 68.1414i | − | 0.0757127i | ||||||
\(31\) | − | 1480.23i | − | 1.54030i | −0.637863 | − | 0.770150i | \(-0.720181\pi\) | ||
0.637863 | − | 0.770150i | \(-0.279819\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | − | 21.6343i | − | 0.0198662i | ||||||
\(34\) | 824.936i | 0.713612i | ||||||||
\(35\) | 154.524 | 0.126142 | ||||||||
\(36\) | −216.000 | −0.166667 | ||||||||
\(37\) | − | 727.964i | − | 0.531749i | −0.964008 | − | 0.265874i | \(-0.914339\pi\) | ||
0.964008 | − | 0.265874i | \(-0.0856606\pi\) | |||||||
\(38\) | − | 1045.70i | − | 0.724172i | ||||||
\(39\) | 1257.45i | 0.826726i | ||||||||
\(40\) | 104.911i | 0.0655691i | ||||||||
\(41\) | −1746.67 | −1.03907 | −0.519533 | − | 0.854451i | \(-0.673894\pi\) | ||||
−0.519533 | + | 0.854451i | \(0.673894\pi\) | |||||||
\(42\) | − | 489.823i | − | 0.277678i | ||||||
\(43\) | − | 1687.92i | − | 0.912883i | −0.889753 | − | 0.456442i | \(-0.849124\pi\) | ||
0.889753 | − | 0.456442i | \(-0.150876\pi\) | |||||||
\(44\) | 33.3082i | 0.0172047i | ||||||||
\(45\) | −125.184 | −0.0618192 | ||||||||
\(46\) | 1404.37 | 0.663692 | ||||||||
\(47\) | − | 2187.33i | − | 0.990190i | −0.868839 | − | 0.495095i | \(-0.835133\pi\) | ||
0.868839 | − | 0.495095i | \(-0.164867\pi\) | |||||||
\(48\) | 332.554 | 0.144338 | ||||||||
\(49\) | −1290.23 | −0.537371 | ||||||||
\(50\) | − | 1706.97i | − | 0.682786i | ||||||
\(51\) | 1515.50 | 0.582662 | ||||||||
\(52\) | − | 1935.97i | − | 0.715965i | ||||||
\(53\) | −2224.64 | −0.791968 | −0.395984 | − | 0.918258i | \(-0.629596\pi\) | ||||
−0.395984 | + | 0.918258i | \(0.629596\pi\) | |||||||
\(54\) | 396.817i | 0.136083i | ||||||||
\(55\) | 19.3039i | 0.00638147i | ||||||||
\(56\) | 754.132i | 0.240476i | ||||||||
\(57\) | −1921.08 | −0.591284 | ||||||||
\(58\) | − | 932.848i | − | 0.277303i | ||||||
\(59\) | −3416.38 | − | 667.631i | −0.981435 | − | 0.191793i | ||||
\(60\) | 192.733 | 0.0535370 | ||||||||
\(61\) | 4206.97i | 1.13060i | 0.824885 | + | 0.565301i | \(0.191240\pi\) | ||||
−0.824885 | + | 0.565301i | \(0.808760\pi\) | |||||||
\(62\) | 4186.72 | 1.08916 | ||||||||
\(63\) | −899.863 | −0.226723 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − | 1122.00i | − | 0.265562i | ||||||
\(66\) | 61.1911 | 0.0140476 | ||||||||
\(67\) | − | 279.854i | − | 0.0623422i | −0.999514 | − | 0.0311711i | \(-0.990076\pi\) | ||
0.999514 | − | 0.0311711i | \(-0.00992368\pi\) | |||||||
\(68\) | −2333.27 | −0.504600 | ||||||||
\(69\) | − | 2580.00i | − | 0.541902i | ||||||
\(70\) | 437.061i | 0.0891961i | ||||||||
\(71\) | −2456.24 | −0.487253 | −0.243627 | − | 0.969869i | \(-0.578337\pi\) | ||||
−0.243627 | + | 0.969869i | \(0.578337\pi\) | |||||||
\(72\) | − | 610.940i | − | 0.117851i | ||||||
\(73\) | − | 2001.19i | − | 0.375528i | −0.982214 | − | 0.187764i | \(-0.939876\pi\) | ||
0.982214 | − | 0.187764i | \(-0.0601241\pi\) | |||||||
\(74\) | 2058.99 | 0.376003 | ||||||||
\(75\) | −3135.90 | −0.557493 | ||||||||
\(76\) | 2957.70 | 0.512067 | ||||||||
\(77\) | 138.763i | 0.0234041i | ||||||||
\(78\) | −3556.61 | −0.584583 | ||||||||
\(79\) | 3622.55 | 0.580444 | 0.290222 | − | 0.956959i | \(-0.406271\pi\) | ||||
0.290222 | + | 0.956959i | \(0.406271\pi\) | |||||||
\(80\) | −296.732 | −0.0463644 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | − | 4940.33i | − | 0.734730i | ||||||
\(83\) | 2780.03i | 0.403546i | 0.979432 | + | 0.201773i | \(0.0646704\pi\) | ||||
−0.979432 | + | 0.201773i | \(0.935330\pi\) | |||||||
\(84\) | 1385.43 | 0.196348 | ||||||||
\(85\) | −1352.26 | −0.187164 | ||||||||
\(86\) | 4774.16 | 0.645506 | ||||||||
\(87\) | −1713.75 | −0.226417 | ||||||||
\(88\) | −94.2099 | −0.0121655 | ||||||||
\(89\) | − | 4088.90i | − | 0.516209i | −0.966117 | − | 0.258105i | \(-0.916902\pi\) | ||
0.966117 | − | 0.258105i | \(-0.0830980\pi\) | |||||||
\(90\) | − | 354.073i | − | 0.0437127i | ||||||
\(91\) | − | 8065.31i | − | 0.973954i | ||||||
\(92\) | 3972.16i | 0.469301i | ||||||||
\(93\) | − | 7691.49i | − | 0.889293i | ||||||
\(94\) | 6186.70 | 0.700170 | ||||||||
\(95\) | 1714.15 | 0.189933 | ||||||||
\(96\) | 940.604i | 0.102062i | ||||||||
\(97\) | − | 14089.3i | − | 1.49743i | −0.662892 | − | 0.748715i | \(-0.730671\pi\) | ||
0.662892 | − | 0.748715i | \(-0.269329\pi\) | |||||||
\(98\) | − | 3649.32i | − | 0.379979i | ||||||
\(99\) | − | 112.415i | − | 0.0114698i | ||||||
\(100\) | 4828.03 | 0.482803 | ||||||||
\(101\) | 4785.01i | 0.469073i | 0.972107 | + | 0.234536i | \(0.0753572\pi\) | ||||
−0.972107 | + | 0.234536i | \(0.924643\pi\) | |||||||
\(102\) | 4286.49i | 0.412004i | ||||||||
\(103\) | − | 5397.36i | − | 0.508753i | −0.967105 | − | 0.254376i | \(-0.918130\pi\) | ||
0.967105 | − | 0.254376i | \(-0.0818702\pi\) | |||||||
\(104\) | 5475.75 | 0.506264 | ||||||||
\(105\) | 802.932 | 0.0728283 | ||||||||
\(106\) | − | 6292.22i | − | 0.560006i | ||||||
\(107\) | 9551.89 | 0.834299 | 0.417150 | − | 0.908838i | \(-0.363029\pi\) | ||||
0.417150 | + | 0.908838i | \(0.363029\pi\) | |||||||
\(108\) | −1122.37 | −0.0962250 | ||||||||
\(109\) | 6217.45i | 0.523310i | 0.965161 | + | 0.261655i | \(0.0842683\pi\) | ||||
−0.965161 | + | 0.261655i | \(0.915732\pi\) | |||||||
\(110\) | −54.5998 | −0.00451238 | ||||||||
\(111\) | − | 3782.61i | − | 0.307005i | ||||||
\(112\) | −2133.01 | −0.170042 | ||||||||
\(113\) | 2816.11i | 0.220543i | 0.993902 | + | 0.110271i | \(0.0351720\pi\) | ||||
−0.993902 | + | 0.110271i | \(0.964828\pi\) | |||||||
\(114\) | − | 5433.64i | − | 0.418101i | ||||||
\(115\) | 2302.09i | 0.174071i | ||||||||
\(116\) | 2638.49 | 0.196083 | ||||||||
\(117\) | 6533.90i | 0.477310i | ||||||||
\(118\) | 1888.35 | − | 9662.97i | 0.135618 | − | 0.693980i | ||||
\(119\) | −9720.48 | −0.686426 | ||||||||
\(120\) | 545.131i | 0.0378564i | ||||||||
\(121\) | 14623.7 | 0.998816 | ||||||||
\(122\) | −11899.1 | −0.799456 | ||||||||
\(123\) | −9075.96 | −0.599905 | ||||||||
\(124\) | 11841.8i | 0.770150i | ||||||||
\(125\) | 5695.88 | 0.364536 | ||||||||
\(126\) | − | 2545.20i | − | 0.160317i | ||||||
\(127\) | −23586.6 | −1.46237 | −0.731185 | − | 0.682179i | \(-0.761033\pi\) | ||||
−0.731185 | + | 0.682179i | \(0.761033\pi\) | |||||||
\(128\) | − | 1448.15i | − | 0.0883883i | ||||||
\(129\) | − | 8770.70i | − | 0.527054i | ||||||
\(130\) | 3173.50 | 0.187781 | ||||||||
\(131\) | 14769.0i | 0.860612i | 0.902683 | + | 0.430306i | \(0.141594\pi\) | ||||
−0.902683 | + | 0.430306i | \(0.858406\pi\) | |||||||
\(132\) | 173.075i | 0.00993312i | ||||||||
\(133\) | 12321.9 | 0.696583 | ||||||||
\(134\) | 791.547 | 0.0440826 | ||||||||
\(135\) | −650.474 | −0.0356913 | ||||||||
\(136\) | − | 6599.49i | − | 0.356806i | ||||||
\(137\) | −30624.2 | −1.63164 | −0.815818 | − | 0.578308i | \(-0.803713\pi\) | ||||
−0.815818 | + | 0.578308i | \(0.803713\pi\) | |||||||
\(138\) | 7297.33 | 0.383183 | ||||||||
\(139\) | 25204.3 | 1.30450 | 0.652252 | − | 0.758002i | \(-0.273824\pi\) | ||||
0.652252 | + | 0.758002i | \(0.273824\pi\) | |||||||
\(140\) | −1236.19 | −0.0630711 | ||||||||
\(141\) | − | 11365.7i | − | 0.571687i | ||||||
\(142\) | − | 6947.31i | − | 0.344540i | ||||||
\(143\) | 1007.56 | 0.0492718 | ||||||||
\(144\) | 1728.00 | 0.0833333 | ||||||||
\(145\) | 1529.15 | 0.0727301 | ||||||||
\(146\) | 5660.22 | 0.265539 | ||||||||
\(147\) | −6704.22 | −0.310251 | ||||||||
\(148\) | 5823.71i | 0.265874i | ||||||||
\(149\) | − | 20530.3i | − | 0.924747i | −0.886685 | − | 0.462374i | \(-0.846998\pi\) | ||
0.886685 | − | 0.462374i | \(-0.153002\pi\) | |||||||
\(150\) | − | 8869.65i | − | 0.394207i | ||||||
\(151\) | − | 15895.5i | − | 0.697139i | −0.937283 | − | 0.348570i | \(-0.886668\pi\) | ||
0.937283 | − | 0.348570i | \(-0.113332\pi\) | |||||||
\(152\) | 8365.63i | 0.362086i | ||||||||
\(153\) | 7874.79 | 0.336400 | ||||||||
\(154\) | −392.481 | −0.0165492 | ||||||||
\(155\) | 6862.98i | 0.285660i | ||||||||
\(156\) | − | 10059.6i | − | 0.413363i | ||||||
\(157\) | − | 4402.72i | − | 0.178616i | −0.996004 | − | 0.0893082i | \(-0.971534\pi\) | ||
0.996004 | − | 0.0893082i | \(-0.0284656\pi\) | |||||||
\(158\) | 10246.1i | 0.410436i | ||||||||
\(159\) | −11559.6 | −0.457243 | ||||||||
\(160\) | − | 839.285i | − | 0.0327846i | ||||||
\(161\) | 16548.2i | 0.638407i | ||||||||
\(162\) | 2061.92i | 0.0785674i | ||||||||
\(163\) | 16309.9 | 0.613868 | 0.306934 | − | 0.951731i | \(-0.400697\pi\) | ||||
0.306934 | + | 0.951731i | \(0.400697\pi\) | |||||||
\(164\) | 13973.4 | 0.519533 | ||||||||
\(165\) | 100.306i | 0.00368434i | ||||||||
\(166\) | −7863.11 | −0.285350 | ||||||||
\(167\) | −29499.3 | −1.05774 | −0.528870 | − | 0.848703i | \(-0.677384\pi\) | ||||
−0.528870 | + | 0.848703i | \(0.677384\pi\) | |||||||
\(168\) | 3918.59i | 0.138839i | ||||||||
\(169\) | −30001.2 | −1.05043 | ||||||||
\(170\) | − | 3824.76i | − | 0.132345i | ||||||
\(171\) | −9982.23 | −0.341378 | ||||||||
\(172\) | 13503.4i | 0.456442i | ||||||||
\(173\) | 45951.4i | 1.53535i | 0.640841 | + | 0.767674i | \(0.278586\pi\) | ||||
−0.640841 | + | 0.767674i | \(0.721414\pi\) | |||||||
\(174\) | − | 4847.22i | − | 0.160101i | ||||||
\(175\) | 20113.7 | 0.656774 | ||||||||
\(176\) | − | 266.466i | − | 0.00860233i | ||||||
\(177\) | −17752.0 | − | 3469.11i | −0.566632 | − | 0.110732i | ||||
\(178\) | 11565.1 | 0.365015 | ||||||||
\(179\) | 50111.3i | 1.56397i | 0.623295 | + | 0.781987i | \(0.285793\pi\) | ||||
−0.623295 | + | 0.781987i | \(0.714207\pi\) | |||||||
\(180\) | 1001.47 | 0.0309096 | ||||||||
\(181\) | −55894.1 | −1.70612 | −0.853058 | − | 0.521816i | \(-0.825255\pi\) | ||||
−0.853058 | + | 0.521816i | \(0.825255\pi\) | |||||||
\(182\) | 22812.1 | 0.688689 | ||||||||
\(183\) | 21860.0i | 0.652753i | ||||||||
\(184\) | −11235.0 | −0.331846 | ||||||||
\(185\) | 3375.16i | 0.0986168i | ||||||||
\(186\) | 21754.8 | 0.628825 | ||||||||
\(187\) | − | 1214.33i | − | 0.0347259i | ||||||
\(188\) | 17498.6i | 0.495095i | ||||||||
\(189\) | −4675.82 | −0.130898 | ||||||||
\(190\) | 4848.34i | 0.134303i | ||||||||
\(191\) | 28684.0i | 0.786273i | 0.919480 | + | 0.393137i | \(0.128610\pi\) | ||||
−0.919480 | + | 0.393137i | \(0.871390\pi\) | |||||||
\(192\) | −2660.43 | −0.0721688 | ||||||||
\(193\) | 23152.2 | 0.621553 | 0.310777 | − | 0.950483i | \(-0.399411\pi\) | ||||
0.310777 | + | 0.950483i | \(0.399411\pi\) | |||||||
\(194\) | 39850.6 | 1.05884 | ||||||||
\(195\) | − | 5830.09i | − | 0.153322i | ||||||
\(196\) | 10321.8 | 0.268686 | ||||||||
\(197\) | 10420.0 | 0.268495 | 0.134248 | − | 0.990948i | \(-0.457138\pi\) | ||||
0.134248 | + | 0.990948i | \(0.457138\pi\) | |||||||
\(198\) | 317.958 | 0.00811036 | ||||||||
\(199\) | −46042.5 | −1.16266 | −0.581330 | − | 0.813668i | \(-0.697468\pi\) | ||||
−0.581330 | + | 0.813668i | \(0.697468\pi\) | |||||||
\(200\) | 13655.7i | 0.341393i | ||||||||
\(201\) | − | 1454.16i | − | 0.0359933i | ||||||
\(202\) | −13534.1 | −0.331685 | ||||||||
\(203\) | 10992.0 | 0.266739 | ||||||||
\(204\) | −12124.0 | −0.291331 | ||||||||
\(205\) | 8098.32 | 0.192702 | ||||||||
\(206\) | 15266.0 | 0.359743 | ||||||||
\(207\) | − | 13406.0i | − | 0.312867i | ||||||
\(208\) | 15487.8i | 0.357983i | ||||||||
\(209\) | 1539.31i | 0.0352397i | ||||||||
\(210\) | 2271.03i | 0.0514974i | ||||||||
\(211\) | 10156.2i | 0.228121i | 0.993474 | + | 0.114060i | \(0.0363857\pi\) | ||||
−0.993474 | + | 0.114060i | \(0.963614\pi\) | |||||||
\(212\) | 17797.1 | 0.395984 | ||||||||
\(213\) | −12763.0 | −0.281316 | ||||||||
\(214\) | 27016.8i | 0.589939i | ||||||||
\(215\) | 7825.94i | 0.169301i | ||||||||
\(216\) | − | 3174.54i | − | 0.0680414i | ||||||
\(217\) | 49333.4i | 1.04766i | ||||||||
\(218\) | −17585.6 | −0.370036 | ||||||||
\(219\) | − | 10398.5i | − | 0.216811i | ||||||
\(220\) | − | 154.432i | − | 0.00319073i | ||||||
\(221\) | 70580.4i | 1.44510i | ||||||||
\(222\) | 10698.8 | 0.217085 | ||||||||
\(223\) | 25793.8 | 0.518687 | 0.259343 | − | 0.965785i | \(-0.416494\pi\) | ||||
0.259343 | + | 0.965785i | \(0.416494\pi\) | |||||||
\(224\) | − | 6033.06i | − | 0.120238i | ||||||
\(225\) | −16294.6 | −0.321869 | ||||||||
\(226\) | −7965.17 | −0.155947 | ||||||||
\(227\) | 79731.8i | 1.54732i | 0.633601 | + | 0.773660i | \(0.281576\pi\) | ||||
−0.633601 | + | 0.773660i | \(0.718424\pi\) | |||||||
\(228\) | 15368.6 | 0.295642 | ||||||||
\(229\) | 4958.81i | 0.0945598i | 0.998882 | + | 0.0472799i | \(0.0150553\pi\) | ||||
−0.998882 | + | 0.0472799i | \(0.984945\pi\) | |||||||
\(230\) | −6511.28 | −0.123087 | ||||||||
\(231\) | 721.034i | 0.0135124i | ||||||||
\(232\) | 7462.78i | 0.138652i | ||||||||
\(233\) | 91557.2i | 1.68648i | 0.537539 | + | 0.843239i | \(0.319354\pi\) | ||||
−0.537539 | + | 0.843239i | \(0.680646\pi\) | |||||||
\(234\) | −18480.7 | −0.337509 | ||||||||
\(235\) | 10141.4i | 0.183638i | ||||||||
\(236\) | 27331.0 | + | 5341.05i | 0.490718 | + | 0.0958964i | ||||
\(237\) | 18823.3 | 0.335120 | ||||||||
\(238\) | − | 27493.7i | − | 0.485376i | ||||||
\(239\) | −44494.2 | −0.778946 | −0.389473 | − | 0.921038i | \(-0.627343\pi\) | ||||
−0.389473 | + | 0.921038i | \(0.627343\pi\) | |||||||
\(240\) | −1541.86 | −0.0267685 | ||||||||
\(241\) | 71057.7 | 1.22342 | 0.611712 | − | 0.791081i | \(-0.290481\pi\) | ||||
0.611712 | + | 0.791081i | \(0.290481\pi\) | |||||||
\(242\) | 41362.0i | 0.706270i | ||||||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | − | 33655.7i | − | 0.565301i | ||||||
\(245\) | 5982.06 | 0.0996595 | ||||||||
\(246\) | − | 25670.7i | − | 0.424197i | ||||||
\(247\) | − | 89469.0i | − | 1.46649i | ||||||
\(248\) | −33493.7 | −0.544578 | ||||||||
\(249\) | 14445.5i | 0.232988i | ||||||||
\(250\) | 16110.4i | 0.257766i | ||||||||
\(251\) | −60466.2 | −0.959765 | −0.479883 | − | 0.877333i | \(-0.659321\pi\) | ||||
−0.479883 | + | 0.877333i | \(0.659321\pi\) | |||||||
\(252\) | 7198.90 | 0.113361 | ||||||||
\(253\) | −2067.28 | −0.0322967 | ||||||||
\(254\) | − | 66712.9i | − | 1.03405i | ||||||
\(255\) | −7026.54 | −0.108059 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 94101.6 | 1.42472 | 0.712362 | − | 0.701812i | \(-0.247625\pi\) | ||||
0.712362 | + | 0.701812i | \(0.247625\pi\) | |||||||
\(258\) | 24807.3 | 0.372683 | ||||||||
\(259\) | 24261.8i | 0.361679i | ||||||||
\(260\) | 8976.01i | 0.132781i | ||||||||
\(261\) | −8904.91 | −0.130722 | ||||||||
\(262\) | −41772.9 | −0.608545 | ||||||||
\(263\) | −98841.3 | −1.42898 | −0.714491 | − | 0.699644i | \(-0.753342\pi\) | ||||
−0.714491 | + | 0.699644i | \(0.753342\pi\) | |||||||
\(264\) | −489.529 | −0.00702378 | ||||||||
\(265\) | 10314.4 | 0.146876 | ||||||||
\(266\) | 34851.5i | 0.492559i | ||||||||
\(267\) | − | 21246.5i | − | 0.298034i | ||||||
\(268\) | 2238.83i | 0.0311711i | ||||||||
\(269\) | − | 130957.i | − | 1.80977i | −0.425658 | − | 0.904884i | \(-0.639957\pi\) | ||
0.425658 | − | 0.904884i | \(-0.360043\pi\) | |||||||
\(270\) | − | 1839.82i | − | 0.0252376i | ||||||
\(271\) | −45179.0 | −0.615174 | −0.307587 | − | 0.951520i | \(-0.599521\pi\) | ||||
−0.307587 | + | 0.951520i | \(0.599521\pi\) | |||||||
\(272\) | 18666.2 | 0.252300 | ||||||||
\(273\) | − | 41908.6i | − | 0.562313i | ||||||
\(274\) | − | 86618.3i | − | 1.15374i | ||||||
\(275\) | 2512.70i | 0.0332258i | ||||||||
\(276\) | 20640.0i | 0.270951i | ||||||||
\(277\) | −102949. | −1.34173 | −0.670863 | − | 0.741582i | \(-0.734076\pi\) | ||||
−0.670863 | + | 0.741582i | \(0.734076\pi\) | |||||||
\(278\) | 71288.6i | 0.922424i | ||||||||
\(279\) | − | 39966.2i | − | 0.513433i | ||||||
\(280\) | − | 3496.49i | − | 0.0445980i | ||||||
\(281\) | 13476.5 | 0.170673 | 0.0853363 | − | 0.996352i | \(-0.472804\pi\) | ||||
0.0853363 | + | 0.996352i | \(0.472804\pi\) | |||||||
\(282\) | 32147.1 | 0.404243 | ||||||||
\(283\) | − | 36120.2i | − | 0.451000i | −0.974243 | − | 0.225500i | \(-0.927598\pi\) | ||
0.974243 | − | 0.225500i | \(-0.0724016\pi\) | |||||||
\(284\) | 19649.9 | 0.243627 | ||||||||
\(285\) | 8906.97 | 0.109658 | ||||||||
\(286\) | 2849.81i | 0.0348404i | ||||||||
\(287\) | 58213.4 | 0.706739 | ||||||||
\(288\) | 4887.52i | 0.0589256i | ||||||||
\(289\) | 1543.85 | 0.0184846 | ||||||||
\(290\) | 4325.09i | 0.0514280i | ||||||||
\(291\) | − | 73210.3i | − | 0.864542i | ||||||
\(292\) | 16009.5i | 0.187764i | ||||||||
\(293\) | 24607.5 | 0.286637 | 0.143318 | − | 0.989677i | \(-0.454223\pi\) | ||||
0.143318 | + | 0.989677i | \(0.454223\pi\) | |||||||
\(294\) | − | 18962.4i | − | 0.219381i | ||||||
\(295\) | 15839.8 | + | 3095.43i | 0.182015 | + | 0.0355694i | ||||
\(296\) | −16471.9 | −0.188002 | ||||||||
\(297\) | − | 584.127i | − | 0.00662208i | ||||||
\(298\) | 58068.5 | 0.653895 | ||||||||
\(299\) | 120156. | 1.34401 | ||||||||
\(300\) | 25087.2 | 0.278746 | ||||||||
\(301\) | 56255.5i | 0.620914i | ||||||||
\(302\) | 44959.2 | 0.492952 | ||||||||
\(303\) | 24863.7i | 0.270819i | ||||||||
\(304\) | −23661.6 | −0.256033 | ||||||||
\(305\) | − | 19505.3i | − | 0.209678i | ||||||
\(306\) | 22273.3i | 0.237871i | ||||||||
\(307\) | 120412. | 1.27760 | 0.638799 | − | 0.769374i | \(-0.279432\pi\) | ||||
0.638799 | + | 0.769374i | \(0.279432\pi\) | |||||||
\(308\) | − | 1110.11i | − | 0.0117021i | ||||||
\(309\) | − | 28045.5i | − | 0.293729i | ||||||
\(310\) | −19411.5 | −0.201992 | ||||||||
\(311\) | 122536. | 1.26690 | 0.633449 | − | 0.773784i | \(-0.281639\pi\) | ||||
0.633449 | + | 0.773784i | \(0.281639\pi\) | |||||||
\(312\) | 28452.8 | 0.292292 | ||||||||
\(313\) | − | 22938.9i | − | 0.234145i | −0.993123 | − | 0.117072i | \(-0.962649\pi\) | ||
0.993123 | − | 0.117072i | \(-0.0373510\pi\) | |||||||
\(314\) | 12452.8 | 0.126301 | ||||||||
\(315\) | 4172.16 | 0.0420474 | ||||||||
\(316\) | −28980.4 | −0.290222 | ||||||||
\(317\) | −21501.0 | −0.213964 | −0.106982 | − | 0.994261i | \(-0.534119\pi\) | ||||
−0.106982 | + | 0.994261i | \(0.534119\pi\) | |||||||
\(318\) | − | 32695.4i | − | 0.323319i | ||||||
\(319\) | 1373.18i | 0.0134942i | ||||||||
\(320\) | 2373.86 | 0.0231822 | ||||||||
\(321\) | 49633.1 | 0.481683 | ||||||||
\(322\) | −46805.2 | −0.451422 | ||||||||
\(323\) | −107830. | −1.03356 | ||||||||
\(324\) | −5832.00 | −0.0555556 | ||||||||
\(325\) | − | 146046.i | − | 1.38268i | ||||||
\(326\) | 46131.2i | 0.434070i | ||||||||
\(327\) | 32306.8i | 0.302133i | ||||||||
\(328\) | 39522.6i | 0.367365i | ||||||||
\(329\) | 72899.9i | 0.673496i | ||||||||
\(330\) | −283.709 | −0.00260522 | ||||||||
\(331\) | −141825. | −1.29449 | −0.647244 | − | 0.762283i | \(-0.724079\pi\) | ||||
−0.647244 | + | 0.762283i | \(0.724079\pi\) | |||||||
\(332\) | − | 22240.2i | − | 0.201773i | ||||||
\(333\) | − | 19655.0i | − | 0.177250i | ||||||
\(334\) | − | 83436.7i | − | 0.747935i | ||||||
\(335\) | 1297.53i | 0.0115618i | ||||||||
\(336\) | −11083.4 | −0.0981738 | ||||||||
\(337\) | − | 133252.i | − | 1.17331i | −0.809836 | − | 0.586657i | \(-0.800444\pi\) | ||
0.809836 | − | 0.586657i | \(-0.199556\pi\) | |||||||
\(338\) | − | 84856.3i | − | 0.742763i | ||||||
\(339\) | 14633.0i | 0.127331i | ||||||||
\(340\) | 10818.1 | 0.0935818 | ||||||||
\(341\) | −6162.97 | −0.0530007 | ||||||||
\(342\) | − | 28234.0i | − | 0.241391i | ||||||
\(343\) | 123022. | 1.04567 | ||||||||
\(344\) | −38193.3 | −0.322753 | ||||||||
\(345\) | 11962.0i | 0.100500i | ||||||||
\(346\) | −129970. | −1.08565 | ||||||||
\(347\) | − | 97310.6i | − | 0.808167i | −0.914722 | − | 0.404083i | \(-0.867591\pi\) | ||
0.914722 | − | 0.404083i | \(-0.132409\pi\) | |||||||
\(348\) | 13710.0 | 0.113209 | ||||||||
\(349\) | 102463.i | 0.841233i | 0.907239 | + | 0.420616i | \(0.138186\pi\) | ||||
−0.907239 | + | 0.420616i | \(0.861814\pi\) | |||||||
\(350\) | 56890.2i | 0.464410i | ||||||||
\(351\) | 33951.1i | 0.275575i | ||||||||
\(352\) | 753.679 | 0.00608277 | ||||||||
\(353\) | − | 16785.8i | − | 0.134708i | −0.997729 | − | 0.0673539i | \(-0.978544\pi\) | ||
0.997729 | − | 0.0673539i | \(-0.0214557\pi\) | |||||||
\(354\) | 9812.13 | − | 50210.3i | 0.0782991 | − | 0.400669i | ||||
\(355\) | 11388.2 | 0.0903648 | ||||||||
\(356\) | 32711.2i | 0.258105i | ||||||||
\(357\) | −50509.1 | −0.396308 | ||||||||
\(358\) | −141736. | −1.10590 | ||||||||
\(359\) | 204196. | 1.58438 | 0.792188 | − | 0.610277i | \(-0.208942\pi\) | ||||
0.792188 | + | 0.610277i | \(0.208942\pi\) | |||||||
\(360\) | 2832.59i | 0.0218564i | ||||||||
\(361\) | 6366.05 | 0.0488490 | ||||||||
\(362\) | − | 158092.i | − | 1.20641i | ||||||
\(363\) | 75986.8 | 0.576667 | ||||||||
\(364\) | 64522.5i | 0.486977i | ||||||||
\(365\) | 9278.40i | 0.0696446i | ||||||||
\(366\) | −61829.5 | −0.461566 | ||||||||
\(367\) | 107995.i | 0.801807i | 0.916120 | + | 0.400903i | \(0.131304\pi\) | ||||
−0.916120 | + | 0.400903i | \(0.868696\pi\) | |||||||
\(368\) | − | 31777.3i | − | 0.234650i | ||||||
\(369\) | −47160.1 | −0.346355 | ||||||||
\(370\) | −9546.39 | −0.0697326 | ||||||||
\(371\) | 74143.2 | 0.538671 | ||||||||
\(372\) | 61531.9i | 0.444646i | ||||||||
\(373\) | −259803. | −1.86735 | −0.933676 | − | 0.358120i | \(-0.883418\pi\) | ||||
−0.933676 | + | 0.358120i | \(0.883418\pi\) | |||||||
\(374\) | 3434.64 | 0.0245549 | ||||||||
\(375\) | 29596.7 | 0.210465 | ||||||||
\(376\) | −49493.6 | −0.350085 | ||||||||
\(377\) | − | 79813.2i | − | 0.561555i | ||||||
\(378\) | − | 13225.2i | − | 0.0925592i | ||||||
\(379\) | 180363. | 1.25565 | 0.627826 | − | 0.778354i | \(-0.283945\pi\) | ||||
0.627826 | + | 0.778354i | \(0.283945\pi\) | |||||||
\(380\) | −13713.2 | −0.0949666 | ||||||||
\(381\) | −122559. | −0.844300 | ||||||||
\(382\) | −81130.7 | −0.555979 | ||||||||
\(383\) | −53195.1 | −0.362639 | −0.181319 | − | 0.983424i | \(-0.558037\pi\) | ||||
−0.181319 | + | 0.983424i | \(0.558037\pi\) | |||||||
\(384\) | − | 7524.83i | − | 0.0510310i | ||||||
\(385\) | − | 643.367i | − | 0.00434047i | ||||||
\(386\) | 65484.4i | 0.439504i | ||||||||
\(387\) | − | 45573.9i | − | 0.304294i | ||||||
\(388\) | 112715.i | 0.748715i | ||||||||
\(389\) | −184071. | −1.21642 | −0.608212 | − | 0.793774i | \(-0.708113\pi\) | ||||
−0.608212 | + | 0.793774i | \(0.708113\pi\) | |||||||
\(390\) | 16490.0 | 0.108415 | ||||||||
\(391\) | − | 144815.i | − | 0.947237i | ||||||
\(392\) | 29194.5i | 0.189989i | ||||||||
\(393\) | 76741.8i | 0.496875i | ||||||||
\(394\) | 29472.3i | 0.189855i | ||||||||
\(395\) | −16795.7 | −0.107648 | ||||||||
\(396\) | 899.322i | 0.00573489i | ||||||||
\(397\) | − | 182691.i | − | 1.15914i | −0.814922 | − | 0.579570i | \(-0.803220\pi\) | ||
0.814922 | − | 0.579570i | \(-0.196780\pi\) | |||||||
\(398\) | − | 130228.i | − | 0.822125i | ||||||
\(399\) | 64026.2 | 0.402172 | ||||||||
\(400\) | −38624.2 | −0.241401 | ||||||||
\(401\) | 27488.4i | 0.170947i | 0.996340 | + | 0.0854733i | \(0.0272402\pi\) | ||||
−0.996340 | + | 0.0854733i | \(0.972760\pi\) | |||||||
\(402\) | 4113.00 | 0.0254511 | ||||||||
\(403\) | 358210. | 2.20560 | ||||||||
\(404\) | − | 38280.1i | − | 0.234536i | ||||||
\(405\) | −3379.96 | −0.0206064 | ||||||||
\(406\) | 31090.2i | 0.188613i | ||||||||
\(407\) | −3030.90 | −0.0182971 | ||||||||
\(408\) | − | 34291.9i | − | 0.206002i | ||||||
\(409\) | − | 185149.i | − | 1.10682i | −0.832910 | − | 0.553409i | \(-0.813327\pi\) | ||
0.832910 | − | 0.553409i | \(-0.186673\pi\) | |||||||
\(410\) | 22905.5i | 0.136261i | ||||||||
\(411\) | −159128. | −0.942026 | ||||||||
\(412\) | 43178.9i | 0.254376i | ||||||||
\(413\) | 113862. | + | 22251.0i | 0.667541 | + | 0.130451i | ||||
\(414\) | 37918.0 | 0.221231 | ||||||||
\(415\) | − | 12889.4i | − | 0.0748407i | ||||||
\(416\) | −43806.0 | −0.253132 | ||||||||
\(417\) | 130965. | 0.753156 | ||||||||
\(418\) | −4353.82 | −0.0249183 | ||||||||
\(419\) | − | 143622.i | − | 0.818077i | −0.912517 | − | 0.409038i | \(-0.865864\pi\) | ||
0.912517 | − | 0.409038i | \(-0.134136\pi\) | |||||||
\(420\) | −6423.46 | −0.0364141 | ||||||||
\(421\) | 240408.i | 1.35639i | 0.734883 | + | 0.678194i | \(0.237237\pi\) | ||||
−0.734883 | + | 0.678194i | \(0.762763\pi\) | |||||||
\(422\) | −28725.9 | −0.161306 | ||||||||
\(423\) | − | 59057.9i | − | 0.330063i | ||||||
\(424\) | 50337.8i | 0.280003i | ||||||||
\(425\) | −176017. | −0.974489 | ||||||||
\(426\) | − | 36099.3i | − | 0.198920i | ||||||
\(427\) | − | 140211.i | − | 0.768999i | ||||||
\(428\) | −76415.2 | −0.417150 | ||||||||
\(429\) | 5235.43 | 0.0284471 | ||||||||
\(430\) | −22135.1 | −0.119714 | ||||||||
\(431\) | − | 185431.i | − | 0.998223i | −0.866538 | − | 0.499112i | \(-0.833660\pi\) | ||
0.866538 | − | 0.499112i | \(-0.166340\pi\) | |||||||
\(432\) | 8978.95 | 0.0481125 | ||||||||
\(433\) | 5575.97 | 0.0297402 | 0.0148701 | − | 0.999889i | \(-0.495267\pi\) | ||||
0.0148701 | + | 0.999889i | \(0.495267\pi\) | |||||||
\(434\) | −139536. | −0.740810 | ||||||||
\(435\) | 7945.70 | 0.0419908 | ||||||||
\(436\) | − | 49739.6i | − | 0.261655i | ||||||
\(437\) | 183570.i | 0.961253i | ||||||||
\(438\) | 29411.4 | 0.153309 | ||||||||
\(439\) | 190431. | 0.988120 | 0.494060 | − | 0.869428i | \(-0.335512\pi\) | ||||
0.494060 | + | 0.869428i | \(0.335512\pi\) | |||||||
\(440\) | 436.798 | 0.00225619 | ||||||||
\(441\) | −34836.2 | −0.179124 | ||||||||
\(442\) | −199631. | −1.02184 | ||||||||
\(443\) | 190993.i | 0.973218i | 0.873620 | + | 0.486609i | \(0.161766\pi\) | ||||
−0.873620 | + | 0.486609i | \(0.838234\pi\) | |||||||
\(444\) | 30260.9i | 0.153503i | ||||||||
\(445\) | 18957.9i | 0.0957349i | ||||||||
\(446\) | 72955.8i | 0.366767i | ||||||||
\(447\) | − | 106679.i | − | 0.533903i | ||||||
\(448\) | 17064.1 | 0.0850210 | ||||||||
\(449\) | −166726. | −0.827010 | −0.413505 | − | 0.910502i | \(-0.635696\pi\) | ||||
−0.413505 | + | 0.910502i | \(0.635696\pi\) | |||||||
\(450\) | − | 46088.1i | − | 0.227595i | ||||||
\(451\) | 7272.31i | 0.0357535i | ||||||||
\(452\) | − | 22528.9i | − | 0.110271i | ||||||
\(453\) | − | 82595.3i | − | 0.402493i | ||||||
\(454\) | −225516. | −1.09412 | ||||||||
\(455\) | 37394.3i | 0.180627i | ||||||||
\(456\) | 43469.1i | 0.209050i | ||||||||
\(457\) | − | 383054.i | − | 1.83412i | −0.398748 | − | 0.917060i | \(-0.630555\pi\) | ||
0.398748 | − | 0.917060i | \(-0.369445\pi\) | |||||||
\(458\) | −14025.6 | −0.0668639 | ||||||||
\(459\) | 40918.6 | 0.194221 | ||||||||
\(460\) | − | 18416.7i | − | 0.0870354i | ||||||
\(461\) | −108184. | −0.509052 | −0.254526 | − | 0.967066i | \(-0.581919\pi\) | ||||
−0.254526 | + | 0.967066i | \(0.581919\pi\) | |||||||
\(462\) | −2039.39 | −0.00955470 | ||||||||
\(463\) | 199196.i | 0.929221i | 0.885515 | + | 0.464610i | \(0.153806\pi\) | ||||
−0.885515 | + | 0.464610i | \(0.846194\pi\) | |||||||
\(464\) | −21107.9 | −0.0980415 | ||||||||
\(465\) | 35661.1i | 0.164926i | ||||||||
\(466\) | −258963. | −1.19252 | ||||||||
\(467\) | − | 253351.i | − | 1.16169i | −0.814015 | − | 0.580844i | \(-0.802723\pi\) | ||
0.814015 | − | 0.580844i | \(-0.197277\pi\) | |||||||
\(468\) | − | 52271.2i | − | 0.238655i | ||||||
\(469\) | 9327.05i | 0.0424032i | ||||||||
\(470\) | −28684.3 | −0.129852 | ||||||||
\(471\) | − | 22877.2i | − | 0.103124i | ||||||
\(472\) | −15106.8 | + | 77303.8i | −0.0678090 | + | 0.346990i | ||||
\(473\) | −7027.71 | −0.0314117 | ||||||||
\(474\) | 53240.4i | 0.236965i | ||||||||
\(475\) | 223123. | 0.988909 | ||||||||
\(476\) | 77763.8 | 0.343213 | ||||||||
\(477\) | −60065.2 | −0.263989 | ||||||||
\(478\) | − | 125849.i | − | 0.550798i | ||||||
\(479\) | 7178.05 | 0.0312849 | 0.0156425 | − | 0.999878i | \(-0.495021\pi\) | ||||
0.0156425 | + | 0.999878i | \(0.495021\pi\) | |||||||
\(480\) | − | 4361.05i | − | 0.0189282i | ||||||
\(481\) | 176165. | 0.761427 | ||||||||
\(482\) | 200981.i | 0.865091i | ||||||||
\(483\) | 85986.7i | 0.368585i | ||||||||
\(484\) | −116989. | −0.499408 | ||||||||
\(485\) | 65324.3i | 0.277710i | ||||||||
\(486\) | 10714.1i | 0.0453609i | ||||||||
\(487\) | 183775. | 0.774869 | 0.387435 | − | 0.921897i | \(-0.373361\pi\) | ||||
0.387435 | + | 0.921897i | \(0.373361\pi\) | |||||||
\(488\) | 95192.8 | 0.399728 | ||||||||
\(489\) | 84748.5 | 0.354417 | ||||||||
\(490\) | 16919.8i | 0.0704699i | ||||||||
\(491\) | −693.629 | −0.00287716 | −0.00143858 | − | 0.999999i | \(-0.500458\pi\) | ||||
−0.00143858 | + | 0.999999i | \(0.500458\pi\) | |||||||
\(492\) | 72607.7 | 0.299952 | ||||||||
\(493\) | −96192.5 | −0.395774 | ||||||||
\(494\) | 253056. | 1.03696 | ||||||||
\(495\) | 521.206i | 0.00212716i | ||||||||
\(496\) | − | 94734.6i | − | 0.385075i | ||||||
\(497\) | 81862.3 | 0.331414 | ||||||||
\(498\) | −40857.9 | −0.164747 | ||||||||
\(499\) | 192263. | 0.772138 | 0.386069 | − | 0.922470i | \(-0.373833\pi\) | ||||
0.386069 | + | 0.922470i | \(0.373833\pi\) | |||||||
\(500\) | −45567.0 | −0.182268 | ||||||||
\(501\) | −153283. | −0.610687 | ||||||||
\(502\) | − | 171024.i | − | 0.678656i | ||||||
\(503\) | 240765.i | 0.951607i | 0.879552 | + | 0.475803i | \(0.157843\pi\) | ||||
−0.879552 | + | 0.475803i | \(0.842157\pi\) | |||||||
\(504\) | 20361.6i | 0.0801586i | ||||||||
\(505\) | − | 22185.4i | − | 0.0869931i | ||||||
\(506\) | − | 5847.14i | − | 0.0228372i | ||||||
\(507\) | −155891. | −0.606464 | ||||||||
\(508\) | 188693. | 0.731185 | ||||||||
\(509\) | 51894.8i | 0.200304i | 0.994972 | + | 0.100152i | \(0.0319328\pi\) | ||||
−0.994972 | + | 0.100152i | \(0.968067\pi\) | |||||||
\(510\) | − | 19874.0i | − | 0.0764093i | ||||||
\(511\) | 66696.2i | 0.255423i | ||||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | −51869.2 | −0.197095 | ||||||||
\(514\) | 266160.i | 1.00743i | ||||||||
\(515\) | 25024.5i | 0.0943520i | ||||||||
\(516\) | 70165.6i | 0.263527i | ||||||||
\(517\) | −9107.01 | −0.0340718 | ||||||||
\(518\) | −68622.6 | −0.255745 | ||||||||
\(519\) | 238771.i | 0.886433i | ||||||||
\(520\) | −25388.0 | −0.0938905 | ||||||||
\(521\) | −62938.8 | −0.231869 | −0.115935 | − | 0.993257i | \(-0.536986\pi\) | ||||
−0.115935 | + | 0.993257i | \(0.536986\pi\) | |||||||
\(522\) | − | 25186.9i | − | 0.0924344i | ||||||
\(523\) | −249247. | −0.911225 | −0.455613 | − | 0.890178i | \(-0.650580\pi\) | ||||
−0.455613 | + | 0.890178i | \(0.650580\pi\) | |||||||
\(524\) | − | 118152.i | − | 0.430306i | ||||||
\(525\) | 104514. | 0.379189 | ||||||||
\(526\) | − | 279565.i | − | 1.01044i | ||||||
\(527\) | − | 431722.i | − | 1.55447i | ||||||
\(528\) | − | 1384.60i | − | 0.00496656i | ||||||
\(529\) | 33308.6 | 0.119027 | ||||||||
\(530\) | 29173.5i | 0.103857i | ||||||||
\(531\) | −92242.2 | − | 18026.0i | −0.327145 | − | 0.0639310i | ||||
\(532\) | −98574.8 | −0.348291 | ||||||||
\(533\) | − | 422687.i | − | 1.48787i | ||||||
\(534\) | 60094.2 | 0.210742 | ||||||||
\(535\) | −44286.8 | −0.154727 | ||||||||
\(536\) | −6332.38 | −0.0220413 | ||||||||
\(537\) | 260386.i | 0.902960i | ||||||||
\(538\) | 370401. | 1.27970 | ||||||||
\(539\) | 5371.90i | 0.0184906i | ||||||||
\(540\) | 5203.79 | 0.0178457 | ||||||||
\(541\) | 488861.i | 1.67029i | 0.550032 | + | 0.835144i | \(0.314616\pi\) | ||||
−0.550032 | + | 0.835144i | \(0.685384\pi\) | |||||||
\(542\) | − | 127785.i | − | 0.434994i | ||||||
\(543\) | −290434. | −0.985026 | ||||||||
\(544\) | 52795.9i | 0.178403i | ||||||||
\(545\) | − | 28826.8i | − | 0.0970518i | ||||||
\(546\) | 118535. | 0.397615 | ||||||||
\(547\) | 253690. | 0.847869 | 0.423934 | − | 0.905693i | \(-0.360649\pi\) | ||||
0.423934 | + | 0.905693i | \(0.360649\pi\) | |||||||
\(548\) | 244994. | 0.815818 | ||||||||
\(549\) | 113588.i | 0.376867i | ||||||||
\(550\) | −7107.00 | −0.0234942 | ||||||||
\(551\) | 121935. | 0.401630 | ||||||||
\(552\) | −58378.6 | −0.191591 | ||||||||
\(553\) | −120733. | −0.394800 | ||||||||
\(554\) | − | 291184.i | − | 0.948743i | ||||||
\(555\) | 17537.8i | 0.0569364i | ||||||||
\(556\) | −201635. | −0.652252 | ||||||||
\(557\) | −56303.7 | −0.181479 | −0.0907396 | − | 0.995875i | \(-0.528923\pi\) | ||||
−0.0907396 | + | 0.995875i | \(0.528923\pi\) | |||||||
\(558\) | 113041. | 0.363052 | ||||||||
\(559\) | 408471. | 1.30719 | ||||||||
\(560\) | 9889.56 | 0.0315356 | ||||||||
\(561\) | − | 6309.84i | − | 0.0200490i | ||||||
\(562\) | 38117.2i | 0.120684i | ||||||||
\(563\) | − | 368407.i | − | 1.16228i | −0.813803 | − | 0.581141i | \(-0.802607\pi\) | ||
0.813803 | − | 0.581141i | \(-0.197393\pi\) | |||||||
\(564\) | 90925.6i | 0.285843i | ||||||||
\(565\) | − | 13056.7i | − | 0.0409013i | ||||||
\(566\) | 102163. | 0.318905 | ||||||||
\(567\) | −24296.3 | −0.0755743 | ||||||||
\(568\) | 55578.5i | 0.172270i | ||||||||
\(569\) | 373276.i | 1.15294i | 0.817119 | + | 0.576469i | \(0.195570\pi\) | ||||
−0.817119 | + | 0.576469i | \(0.804430\pi\) | |||||||
\(570\) | 25192.7i | 0.0775399i | ||||||||
\(571\) | − | 216523.i | − | 0.664097i | −0.943262 | − | 0.332049i | \(-0.892260\pi\) | ||
0.943262 | − | 0.332049i | \(-0.107740\pi\) | |||||||
\(572\) | −8060.47 | −0.0246359 | ||||||||
\(573\) | 149047.i | 0.453955i | ||||||||
\(574\) | 164652.i | 0.499740i | ||||||||
\(575\) | 299652.i | 0.906319i | ||||||||
\(576\) | −13824.0 | −0.0416667 | ||||||||
\(577\) | −30989.5 | −0.0930815 | −0.0465407 | − | 0.998916i | \(-0.514820\pi\) | ||||
−0.0465407 | + | 0.998916i | \(0.514820\pi\) | |||||||
\(578\) | 4366.66i | 0.0130706i | ||||||||
\(579\) | 120303. | 0.358854 | ||||||||
\(580\) | −12233.2 | −0.0363651 | ||||||||
\(581\) | − | 92653.6i | − | 0.274479i | ||||||
\(582\) | 207070. | 0.611324 | ||||||||
\(583\) | 9262.34i | 0.0272511i | ||||||||
\(584\) | −45281.8 | −0.132769 | ||||||||
\(585\) | − | 30294.0i | − | 0.0885208i | ||||||
\(586\) | 69600.5i | 0.202683i | ||||||||
\(587\) | 83561.5i | 0.242510i | 0.992621 | + | 0.121255i | \(0.0386919\pi\) | ||||
−0.992621 | + | 0.121255i | \(0.961308\pi\) | |||||||
\(588\) | 53633.8 | 0.155126 | ||||||||
\(589\) | 547258.i | 1.57747i | ||||||||
\(590\) | −8755.20 | + | 44801.8i | −0.0251514 | + | 0.128704i | ||||
\(591\) | 54144.1 | 0.155016 | ||||||||
\(592\) | − | 46589.7i | − | 0.132937i | ||||||
\(593\) | −351929. | −1.00080 | −0.500398 | − | 0.865795i | \(-0.666813\pi\) | ||||
−0.500398 | + | 0.865795i | \(0.666813\pi\) | |||||||
\(594\) | 1652.16 | 0.00468252 | ||||||||
\(595\) | 45068.4 | 0.127303 | ||||||||
\(596\) | 164243.i | 0.462374i | ||||||||
\(597\) | −239244. | −0.671262 | ||||||||
\(598\) | 339853.i | 0.950361i | ||||||||
\(599\) | −189155. | −0.527186 | −0.263593 | − | 0.964634i | \(-0.584908\pi\) | ||||
−0.263593 | + | 0.964634i | \(0.584908\pi\) | |||||||
\(600\) | 70957.2i | 0.197103i | ||||||||
\(601\) | 551712.i | 1.52744i | 0.645549 | + | 0.763719i | \(0.276629\pi\) | ||||
−0.645549 | + | 0.763719i | \(0.723371\pi\) | |||||||
\(602\) | −159114. | −0.439053 | ||||||||
\(603\) | − | 7556.06i | − | 0.0207807i | ||||||
\(604\) | 127164.i | 0.348570i | ||||||||
\(605\) | −67801.7 | −0.185238 | ||||||||
\(606\) | −70325.0 | −0.191498 | ||||||||
\(607\) | 237501. | 0.644598 | 0.322299 | − | 0.946638i | \(-0.395544\pi\) | ||||
0.322299 | + | 0.946638i | \(0.395544\pi\) | |||||||
\(608\) | − | 66925.0i | − | 0.181043i | ||||||
\(609\) | 57116.3 | 0.154002 | ||||||||
\(610\) | 55169.4 | 0.148265 | ||||||||
\(611\) | 529326. | 1.41788 | ||||||||
\(612\) | −62998.3 | −0.168200 | ||||||||
\(613\) | 496603.i | 1.32157i | 0.750577 | + | 0.660783i | \(0.229776\pi\) | ||||
−0.750577 | + | 0.660783i | \(0.770224\pi\) | |||||||
\(614\) | 340577.i | 0.903398i | ||||||||
\(615\) | 42080.1 | 0.111257 | ||||||||
\(616\) | 3139.85 | 0.00827461 | ||||||||
\(617\) | 125936. | 0.330811 | 0.165405 | − | 0.986226i | \(-0.447107\pi\) | ||||
0.165405 | + | 0.986226i | \(0.447107\pi\) | |||||||
\(618\) | 79324.7 | 0.207698 | ||||||||
\(619\) | 275923. | 0.720122 | 0.360061 | − | 0.932929i | \(-0.382756\pi\) | ||||
0.360061 | + | 0.932929i | \(0.382756\pi\) | |||||||
\(620\) | − | 54903.9i | − | 0.142830i | ||||||
\(621\) | − | 69659.9i | − | 0.180634i | ||||||
\(622\) | 346583.i | 0.895833i | ||||||||
\(623\) | 136276.i | 0.351109i | ||||||||
\(624\) | 80476.8i | 0.206681i | ||||||||
\(625\) | 350781. | 0.898000 | ||||||||
\(626\) | 64881.1 | 0.165565 | ||||||||
\(627\) | 7998.48i | 0.0203457i | ||||||||
\(628\) | 35221.7i | 0.0893082i | ||||||||
\(629\) | − | 212317.i | − | 0.536641i | ||||||
\(630\) | 11800.6i | 0.0297320i | ||||||||
\(631\) | 462752. | 1.16222 | 0.581112 | − | 0.813824i | \(-0.302618\pi\) | ||||
0.581112 | + | 0.813824i | \(0.302618\pi\) | |||||||
\(632\) | − | 81969.0i | − | 0.205218i | ||||||
\(633\) | 52772.9i | 0.131705i | ||||||||
\(634\) | − | 60814.1i | − | 0.151295i | ||||||
\(635\) | 109358. | 0.271208 | ||||||||
\(636\) | 92476.4 | 0.228621 | ||||||||
\(637\) | − | 312230.i | − | 0.769478i | ||||||
\(638\) | −3883.94 | −0.00954182 | ||||||||
\(639\) | −66318.6 | −0.162418 | ||||||||
\(640\) | 6714.28i | 0.0163923i | ||||||||
\(641\) | −351453. | −0.855364 | −0.427682 | − | 0.903929i | \(-0.640670\pi\) | ||||
−0.427682 | + | 0.903929i | \(0.640670\pi\) | |||||||
\(642\) | 140384.i | 0.340601i | ||||||||
\(643\) | −3965.89 | −0.00959220 | −0.00479610 | − | 0.999988i | \(-0.501527\pi\) | ||||
−0.00479610 | + | 0.999988i | \(0.501527\pi\) | |||||||
\(644\) | − | 132385.i | − | 0.319204i | ||||||
\(645\) | 40664.8i | 0.0977460i | ||||||||
\(646\) | − | 304989.i | − | 0.730834i | ||||||
\(647\) | −132862. | −0.317390 | −0.158695 | − | 0.987328i | \(-0.550729\pi\) | ||||
−0.158695 | + | 0.987328i | \(0.550729\pi\) | |||||||
\(648\) | − | 16495.4i | − | 0.0392837i | ||||||
\(649\) | −2779.70 | + | 14224.2i | −0.00659947 | + | 0.0337705i | ||||
\(650\) | 413079. | 0.977703 | ||||||||
\(651\) | 256344.i | 0.604869i | ||||||||
\(652\) | −130479. | −0.306934 | ||||||||
\(653\) | −363151. | −0.851650 | −0.425825 | − | 0.904805i | \(-0.640016\pi\) | ||||
−0.425825 | + | 0.904805i | \(0.640016\pi\) | |||||||
\(654\) | −91377.4 | −0.213640 | ||||||||
\(655\) | − | 68475.4i | − | 0.159607i | ||||||
\(656\) | −111787. | −0.259766 | ||||||||
\(657\) | − | 54032.2i | − | 0.125176i | ||||||
\(658\) | −206192. | −0.476234 | ||||||||
\(659\) | − | 281539.i | − | 0.648287i | −0.946008 | − | 0.324144i | \(-0.894924\pi\) | ||
0.946008 | − | 0.324144i | \(-0.105076\pi\) | |||||||
\(660\) | − | 802.450i | − | 0.00184217i | ||||||
\(661\) | 543997. | 1.24507 | 0.622534 | − | 0.782592i | \(-0.286103\pi\) | ||||
0.622534 | + | 0.782592i | \(0.286103\pi\) | |||||||
\(662\) | − | 401143.i | − | 0.915341i | ||||||
\(663\) | 366746.i | 0.834332i | ||||||||
\(664\) | 62904.9 | 0.142675 | ||||||||
\(665\) | −57129.5 | −0.129187 | ||||||||
\(666\) | 55592.8 | 0.125334 | ||||||||
\(667\) | 163758.i | 0.368088i | ||||||||
\(668\) | 235994. | 0.528870 | ||||||||
\(669\) | 134028. | 0.299464 | ||||||||
\(670\) | −3669.96 | −0.00817545 | ||||||||
\(671\) | 17515.8 | 0.0389032 | ||||||||
\(672\) | − | 31348.7i | − | 0.0694194i | ||||||
\(673\) | 19850.8i | 0.0438276i | 0.999760 | + | 0.0219138i | \(0.00697594\pi\) | ||||
−0.999760 | + | 0.0219138i | \(0.993024\pi\) | |||||||
\(674\) | 376894. | 0.829658 | ||||||||
\(675\) | −84669.2 | −0.185831 | ||||||||
\(676\) | 240010. | 0.525213 | ||||||||
\(677\) | −649848. | −1.41786 | −0.708932 | − | 0.705277i | \(-0.750822\pi\) | ||||
−0.708932 | + | 0.705277i | \(0.750822\pi\) | |||||||
\(678\) | −41388.2 | −0.0900363 | ||||||||
\(679\) | 469572.i | 1.01850i | ||||||||
\(680\) | 30598.1i | 0.0661724i | ||||||||
\(681\) | 414299.i | 0.893345i | ||||||||
\(682\) | − | 17431.5i | − | 0.0374771i | ||||||
\(683\) | 691295.i | 1.48191i | 0.671554 | + | 0.740955i | \(0.265627\pi\) | ||||
−0.671554 | + | 0.740955i | \(0.734373\pi\) | |||||||
\(684\) | 79857.8 | 0.170689 | ||||||||
\(685\) | 141987. | 0.302599 | ||||||||
\(686\) | 347959.i | 0.739401i | ||||||||
\(687\) | 25766.7i | 0.0545941i | ||||||||
\(688\) | − | 108027.i | − | 0.228221i | ||||||
\(689\) | − | 538354.i | − | 1.13404i | ||||||
\(690\) | −33833.6 | −0.0710641 | ||||||||
\(691\) | − | 115514.i | − | 0.241925i | −0.992657 | − | 0.120962i | \(-0.961402\pi\) | ||
0.992657 | − | 0.120962i | \(-0.0385980\pi\) | |||||||
\(692\) | − | 367611.i | − | 0.767674i | ||||||
\(693\) | 3746.60i | 0.00780138i | ||||||||
\(694\) | 275236. | 0.571460 | ||||||||
\(695\) | −116858. | −0.241930 | ||||||||
\(696\) | 38777.8i | 0.0800506i | ||||||||
\(697\) | −509431. | −1.04862 | ||||||||
\(698\) | −289809. | −0.594841 | ||||||||
\(699\) | 475745.i | 0.973688i | ||||||||
\(700\) | −160910. | −0.328387 | ||||||||
\(701\) | − | 824249.i | − | 1.67734i | −0.544636 | − | 0.838672i | \(-0.683332\pi\) | ||
0.544636 | − | 0.838672i | \(-0.316668\pi\) | |||||||
\(702\) | −96028.3 | −0.194861 | ||||||||
\(703\) | 269137.i | 0.544581i | ||||||||
\(704\) | 2131.73i | 0.00430117i | ||||||||
\(705\) | 52696.4i | 0.106024i | ||||||||
\(706\) | 47477.4 | 0.0952528 | ||||||||
\(707\) | − | 159476.i | − | 0.319048i | ||||||
\(708\) | 142016. | + | 27752.9i | 0.283316 | + | 0.0553658i | ||||
\(709\) | −902813. | −1.79599 | −0.897997 | − | 0.440001i | \(-0.854978\pi\) | ||||
−0.897997 | + | 0.440001i | \(0.854978\pi\) | |||||||
\(710\) | 32210.7i | 0.0638975i | ||||||||
\(711\) | 97808.9 | 0.193481 | ||||||||
\(712\) | −92521.1 | −0.182508 | ||||||||
\(713\) | −734963. | −1.44573 | ||||||||
\(714\) | − | 142861.i | − | 0.280232i | ||||||
\(715\) | −4671.48 | −0.00913782 | ||||||||
\(716\) | − | 400890.i | − | 0.781987i | ||||||
\(717\) | −231199. | −0.449725 | ||||||||
\(718\) | 577553.i | 1.12032i | ||||||||
\(719\) | 420448.i | 0.813307i | 0.913583 | + | 0.406653i | \(0.133304\pi\) | ||||
−0.913583 | + | 0.406653i | \(0.866696\pi\) | |||||||
\(720\) | −8011.76 | −0.0154548 | ||||||||
\(721\) | 179885.i | 0.346038i | ||||||||
\(722\) | 18005.9i | 0.0345414i | ||||||||
\(723\) | 369227. | 0.706344 | ||||||||
\(724\) | 447153. | 0.853058 | ||||||||
\(725\) | 199042. | 0.378678 | ||||||||
\(726\) | 214923.i | 0.407765i | ||||||||
\(727\) | −518451. | −0.980931 | −0.490466 | − | 0.871460i | \(-0.663173\pi\) | ||||
−0.490466 | + | 0.871460i | \(0.663173\pi\) | |||||||
\(728\) | −182497. | −0.344345 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | −26243.3 | −0.0492461 | ||||||||
\(731\) | − | 492297.i | − | 0.921282i | ||||||
\(732\) | − | 174880.i | − | 0.326376i | ||||||
\(733\) | −130264. | −0.242448 | −0.121224 | − | 0.992625i | \(-0.538682\pi\) | ||||
−0.121224 | + | 0.992625i | \(0.538682\pi\) | |||||||
\(734\) | −305455. | −0.566963 | ||||||||
\(735\) | 31083.7 | 0.0575384 | ||||||||
\(736\) | 89879.8 | 0.165923 | ||||||||
\(737\) | −1165.18 | −0.00214515 | ||||||||
\(738\) | − | 133389.i | − | 0.244910i | ||||||
\(739\) | − | 387178.i | − | 0.708960i | −0.935064 | − | 0.354480i | \(-0.884658\pi\) | ||
0.935064 | − | 0.354480i | \(-0.115342\pi\) | |||||||
\(740\) | − | 27001.3i | − | 0.0493084i | ||||||
\(741\) | − | 464894.i | − | 0.846677i | ||||||
\(742\) | 209709.i | 0.380898i | ||||||||
\(743\) | −430015. | −0.778943 | −0.389472 | − | 0.921038i | \(-0.627342\pi\) | ||||
−0.389472 | + | 0.921038i | \(0.627342\pi\) | |||||||
\(744\) | −174039. | −0.314412 | ||||||||
\(745\) | 95187.5i | 0.171501i | ||||||||
\(746\) | − | 734833.i | − | 1.32042i | ||||||
\(747\) | 75060.8i | 0.134515i | ||||||||
\(748\) | 9714.64i | 0.0173629i | ||||||||
\(749\) | −318348. | −0.567464 | ||||||||
\(750\) | 83712.0i | 0.148821i | ||||||||
\(751\) | − | 582052.i | − | 1.03200i | −0.856587 | − | 0.516002i | \(-0.827420\pi\) | ||
0.856587 | − | 0.516002i | \(-0.172580\pi\) | |||||||
\(752\) | − | 139989.i | − | 0.247548i | ||||||
\(753\) | −314191. | −0.554121 | ||||||||
\(754\) | 225746. | 0.397079 | ||||||||
\(755\) | 73698.3i | 0.129290i | ||||||||
\(756\) | 37406.6 | 0.0654492 | ||||||||
\(757\) | 254818. | 0.444671 | 0.222335 | − | 0.974970i | \(-0.428632\pi\) | ||||
0.222335 | + | 0.974970i | \(0.428632\pi\) | |||||||
\(758\) | 510144.i | 0.887880i | ||||||||
\(759\) | −10741.9 | −0.0186465 | ||||||||
\(760\) | − | 38786.7i | − | 0.0671515i | ||||||
\(761\) | 959024. | 1.65600 | 0.828000 | − | 0.560728i | \(-0.189479\pi\) | ||||
0.828000 | + | 0.560728i | \(0.189479\pi\) | |||||||
\(762\) | − | 346651.i | − | 0.597010i | ||||||
\(763\) | − | 207217.i | − | 0.355939i | ||||||
\(764\) | − | 229472.i | − | 0.393137i | ||||||
\(765\) | −36511.0 | −0.0623879 | ||||||||
\(766\) | − | 150459.i | − | 0.256424i | ||||||
\(767\) | 161564. | − | 826751.i | 0.274634 | − | 1.40535i | ||||
\(768\) | 21283.4 | 0.0360844 | ||||||||
\(769\) | − | 799674.i | − | 1.35226i | −0.736782 | − | 0.676130i | \(-0.763656\pi\) | ||
0.736782 | − | 0.676130i | \(-0.236344\pi\) | |||||||
\(770\) | 1819.72 | 0.00306918 | ||||||||
\(771\) | 488966. | 0.822565 | ||||||||
\(772\) | −185218. | −0.310777 | ||||||||
\(773\) | − | 906357.i | − | 1.51684i | −0.651765 | − | 0.758421i | \(-0.725971\pi\) | ||
0.651765 | − | 0.758421i | \(-0.274029\pi\) | |||||||
\(774\) | 128902. | 0.215169 | ||||||||
\(775\) | 893323.i | 1.48732i | ||||||||
\(776\) | −318805. | −0.529422 | ||||||||
\(777\) | 126068.i | 0.208815i | ||||||||
\(778\) | − | 520630.i | − | 0.860142i | ||||||
\(779\) | 645765. | 1.06414 | ||||||||
\(780\) | 46640.7i | 0.0766612i | ||||||||
\(781\) | 10226.6i | 0.0167661i | ||||||||
\(782\) | 409597. | 0.669798 | ||||||||
\(783\) | −46271.3 | −0.0754724 | ||||||||
\(784\) | −82574.6 | −0.134343 | ||||||||
\(785\) | 20412.9i | 0.0331258i | ||||||||
\(786\) | −217059. | −0.351343 | ||||||||
\(787\) | −1.16350e6 | −1.87852 | −0.939260 | − | 0.343206i | \(-0.888487\pi\) | ||||
−0.939260 | + | 0.343206i | \(0.888487\pi\) | |||||||
\(788\) | −83360.3 | −0.134248 | ||||||||
\(789\) | −513594. | −0.825023 | ||||||||
\(790\) | − | 47505.5i | − | 0.0761185i | ||||||
\(791\) | − | 93856.1i | − | 0.150006i | ||||||
\(792\) | −2543.67 | −0.00405518 | ||||||||
\(793\) | −1.01807e6 | −1.61894 | ||||||||
\(794\) | 516728. | 0.819636 | ||||||||
\(795\) | 53595.1 | 0.0847991 | ||||||||
\(796\) | 368340. | 0.581330 | ||||||||
\(797\) | 1.02880e6i | 1.61963i | 0.586685 | + | 0.809815i | \(0.300433\pi\) | ||||
−0.586685 | + | 0.809815i | \(0.699567\pi\) | |||||||
\(798\) | 181094.i | 0.284379i | ||||||||
\(799\) | − | 637954.i | − | 0.999300i | ||||||
\(800\) | − | 109246.i | − | 0.170697i | ||||||
\(801\) | − | 110400.i | − | 0.172070i | ||||||
\(802\) | −77748.9 | −0.120878 | ||||||||
\(803\) | −8332.02 | −0.0129217 | ||||||||
\(804\) | 11633.3i | 0.0179966i | ||||||||
\(805\) | − | 76724.5i | − | 0.118397i | ||||||
\(806\) | 1.01317e6i | 1.55960i | ||||||||
\(807\) | − | 680471.i | − | 1.04487i | ||||||
\(808\) | 108272. | 0.165842 | ||||||||
\(809\) | 218393.i | 0.333688i | 0.985983 | + | 0.166844i | \(0.0533577\pi\) | ||||
−0.985983 | + | 0.166844i | \(0.946642\pi\) | |||||||
\(810\) | − | 9559.98i | − | 0.0145709i | ||||||
\(811\) | 435909.i | 0.662757i | 0.943498 | + | 0.331378i | \(0.107514\pi\) | ||||
−0.943498 | + | 0.331378i | \(0.892486\pi\) | |||||||
\(812\) | −87936.3 | −0.133369 | ||||||||
\(813\) | −234757. | −0.355171 | ||||||||
\(814\) | − | 8572.68i | − | 0.0129380i | ||||||
\(815\) | −75619.6 | −0.113846 | ||||||||
\(816\) | 96992.2 | 0.145665 | ||||||||
\(817\) | 624045.i | 0.934914i | ||||||||
\(818\) | 523682. | 0.782638 | ||||||||
\(819\) | − | 217763.i | − | 0.324651i | ||||||
\(820\) | −64786.6 | −0.0963512 | ||||||||
\(821\) | 110620.i | 0.164115i | 0.996628 | + | 0.0820573i | \(0.0261490\pi\) | ||||
−0.996628 | + | 0.0820573i | \(0.973851\pi\) | |||||||
\(822\) | − | 450082.i | − | 0.666113i | ||||||
\(823\) | − | 722280.i | − | 1.06637i | −0.846000 | − | 0.533183i | \(-0.820996\pi\) | ||
0.846000 | − | 0.533183i | \(-0.179004\pi\) | |||||||
\(824\) | −122128. | −0.179871 | ||||||||
\(825\) | 13056.4i | 0.0191829i | ||||||||
\(826\) | −62935.3 | + | 322050.i | −0.0922431 | + | 0.472023i | ||||
\(827\) | 280361. | 0.409927 | 0.204964 | − | 0.978770i | \(-0.434292\pi\) | ||||
0.204964 | + | 0.978770i | \(0.434292\pi\) | |||||||
\(828\) | 107248.i | 0.156434i | ||||||||
\(829\) | −442043. | −0.643214 | −0.321607 | − | 0.946873i | \(-0.604223\pi\) | ||||
−0.321607 | + | 0.946873i | \(0.604223\pi\) | |||||||
\(830\) | 36456.8 | 0.0529204 | ||||||||
\(831\) | −534940. | −0.774645 | ||||||||
\(832\) | − | 123902.i | − | 0.178991i | ||||||
\(833\) | −376306. | −0.542315 | ||||||||
\(834\) | 370426.i | 0.532561i | ||||||||
\(835\) | 136772. | 0.196166 | ||||||||
\(836\) | − | 12314.5i | − | 0.0176199i | ||||||
\(837\) | − | 207670.i | − | 0.296431i | ||||||
\(838\) | 406225. | 0.578468 | ||||||||
\(839\) | − | 1.15312e6i | − | 1.63814i | −0.573696 | − | 0.819068i | \(-0.694491\pi\) | ||
0.573696 | − | 0.819068i | \(-0.305509\pi\) | |||||||
\(840\) | − | 18168.3i | − | 0.0257487i | ||||||
\(841\) | −598505. | −0.846206 | ||||||||
\(842\) | −679975. | −0.959111 | ||||||||
\(843\) | 70025.8 | 0.0985378 | ||||||||
\(844\) | − | 81249.2i | − | 0.114060i | ||||||
\(845\) | 139099. | 0.194809 | ||||||||
\(846\) | 167041. | 0.233390 | ||||||||
\(847\) | −487381. | −0.679363 | ||||||||
\(848\) | −142377. | −0.197992 | ||||||||
\(849\) | − | 187686.i | − | 0.260385i | ||||||
\(850\) | − | 497851.i | − | 0.689068i | ||||||
\(851\) | −361449. | −0.499100 | ||||||||
\(852\) | 102104. | 0.140658 | ||||||||
\(853\) | 46970.7 | 0.0645549 | 0.0322775 | − | 0.999479i | \(-0.489724\pi\) | ||||
0.0322775 | + | 0.999479i | \(0.489724\pi\) | |||||||
\(854\) | 396576. | 0.543765 | ||||||||
\(855\) | 46282.0 | 0.0633111 | ||||||||
\(856\) | − | 216135.i | − | 0.294969i | ||||||
\(857\) | 545280.i | 0.742435i | 0.928546 | + | 0.371217i | \(0.121059\pi\) | ||||
−0.928546 | + | 0.371217i | \(0.878941\pi\) | |||||||
\(858\) | 14808.0i | 0.0201151i | ||||||||
\(859\) | − | 303823.i | − | 0.411751i | −0.978578 | − | 0.205875i | \(-0.933996\pi\) | ||
0.978578 | − | 0.205875i | \(-0.0660042\pi\) | |||||||
\(860\) | − | 62607.5i | − | 0.0846505i | ||||||
\(861\) | 302486. | 0.408036 | ||||||||
\(862\) | 524478. | 0.705851 | ||||||||
\(863\) | − | 14279.4i | − | 0.0191730i | −0.999954 | − | 0.00958648i | \(-0.996948\pi\) | ||
0.999954 | − | 0.00958648i | \(-0.00305152\pi\) | |||||||
\(864\) | 25396.3i | 0.0340207i | ||||||||
\(865\) | − | 213051.i | − | 0.284742i | ||||||
\(866\) | 15771.2i | 0.0210295i | ||||||||
\(867\) | 8022.07 | 0.0106721 | ||||||||
\(868\) | − | 394667.i | − | 0.523832i | ||||||
\(869\) | − | 15082.6i | − | 0.0199727i | ||||||
\(870\) | 22473.8i | 0.0296919i | ||||||||
\(871\) | 67723.7 | 0.0892697 | ||||||||
\(872\) | 140685. | 0.185018 | ||||||||
\(873\) | − | 380412.i | − | 0.499144i | ||||||
\(874\) | −519213. | −0.679709 | ||||||||
\(875\) | −189834. | −0.247946 | ||||||||
\(876\) | 83187.9i | 0.108406i | ||||||||
\(877\) | 306520. | 0.398529 | 0.199264 | − | 0.979946i | \(-0.436145\pi\) | ||||
0.199264 | + | 0.979946i | \(0.436145\pi\) | |||||||
\(878\) | 538621.i | 0.698706i | ||||||||
\(879\) | 127864. | 0.165490 | ||||||||
\(880\) | 1235.45i | 0.00159537i | ||||||||
\(881\) | − | 100841.i | − | 0.129923i | −0.997888 | − | 0.0649613i | \(-0.979308\pi\) | ||
0.997888 | − | 0.0649613i | \(-0.0206924\pi\) | |||||||
\(882\) | − | 98531.5i | − | 0.126660i | ||||||
\(883\) | 295565. | 0.379080 | 0.189540 | − | 0.981873i | \(-0.439300\pi\) | ||||
0.189540 | + | 0.981873i | \(0.439300\pi\) | |||||||
\(884\) | − | 564643.i | − | 0.722552i | ||||||
\(885\) | 82306.1 | + | 16084.3i | 0.105086 | + | 0.0205360i | ||||
\(886\) | −540210. | −0.688169 | ||||||||
\(887\) | 910360.i | 1.15709i | 0.815652 | + | 0.578543i | \(0.196379\pi\) | ||||
−0.815652 | + | 0.578543i | \(0.803621\pi\) | |||||||
\(888\) | −85590.7 | −0.108543 | ||||||||
\(889\) | 786099. | 0.994658 | ||||||||
\(890\) | −53621.1 | −0.0676948 | ||||||||
\(891\) | − | 3035.21i | − | 0.00382326i | ||||||
\(892\) | −206350. | −0.259343 | ||||||||
\(893\) | 808682.i | 1.01409i | ||||||||
\(894\) | 301733. | 0.377527 | ||||||||
\(895\) | − | 232338.i | − | 0.290051i | ||||||
\(896\) | 48264.5i | 0.0601190i | ||||||||
\(897\) | 624349. | 0.775966 | ||||||||
\(898\) | − | 471572.i | − | 0.584784i | ||||||
\(899\) | 488196.i | 0.604053i | ||||||||
\(900\) | 130357. | 0.160934 | ||||||||
\(901\) | −648835. | −0.799254 | ||||||||
\(902\) | −20569.2 | −0.0252816 | ||||||||
\(903\) | 292312.i | 0.358485i | ||||||||
\(904\) | 63721.4 | 0.0779737 | ||||||||
\(905\) | 259149. | 0.316412 | ||||||||
\(906\) | 233615. | 0.284606 | ||||||||
\(907\) | 968919. | 1.17780 | 0.588902 | − | 0.808205i | \(-0.299560\pi\) | ||||
0.588902 | + | 0.808205i | \(0.299560\pi\) | |||||||
\(908\) | − | 637855.i | − | 0.773660i | ||||||
\(909\) | 129195.i | 0.156358i | ||||||||
\(910\) | −105767. | −0.127723 | ||||||||
\(911\) | −1.24637e6 | −1.50179 | −0.750897 | − | 0.660420i | \(-0.770378\pi\) | ||||
−0.750897 | + | 0.660420i | \(0.770378\pi\) | |||||||
\(912\) | −122949. | −0.147821 | ||||||||
\(913\) | 11574.7 | 0.0138858 | ||||||||
\(914\) | 1.08344e6 | 1.29692 | ||||||||
\(915\) | − | 101353.i | − | 0.121058i | ||||||
\(916\) | − | 39670.5i | − | 0.0472799i | ||||||
\(917\) | − | 492224.i | − | 0.585361i | ||||||
\(918\) | 115735.i | 0.137335i | ||||||||
\(919\) | 133235.i | 0.157757i | 0.996884 | + | 0.0788784i | \(0.0251339\pi\) | ||||
−0.996884 | + | 0.0788784i | \(0.974866\pi\) | |||||||
\(920\) | 52090.2 | 0.0615433 | ||||||||
\(921\) | 625680. | 0.737621 | ||||||||
\(922\) | − | 305991.i | − | 0.359954i | ||||||
\(923\) | − | 594402.i | − | 0.697713i | ||||||
\(924\) | − | 5768.28i | − | 0.00675619i | ||||||
\(925\) | 439329.i | 0.513459i | ||||||||
\(926\) | −563412. | −0.657058 | ||||||||
\(927\) | − | 145729.i | − | 0.169584i | ||||||
\(928\) | − | 59702.3i | − | 0.0693258i | ||||||
\(929\) | − | 989613.i | − | 1.14666i | −0.819325 | − | 0.573329i | \(-0.805652\pi\) | ||
0.819325 | − | 0.573329i | \(-0.194348\pi\) | |||||||
\(930\) | −100865. | −0.116620 | ||||||||
\(931\) | 477013. | 0.550340 | ||||||||
\(932\) | − | 732457.i | − | 0.843239i | ||||||
\(933\) | 636714. | 0.731444 | ||||||||
\(934\) | 716586. | 0.821438 | ||||||||
\(935\) | 5630.16i | 0.00644018i | ||||||||
\(936\) | 147845. | 0.168755 | ||||||||
\(937\) | − | 873861.i | − | 0.995321i | −0.867372 | − | 0.497661i | \(-0.834192\pi\) | ||
0.867372 | − | 0.497661i | \(-0.165808\pi\) | |||||||
\(938\) | −26380.9 | −0.0299836 | ||||||||
\(939\) | − | 119194.i | − | 0.135184i | ||||||
\(940\) | − | 81131.3i | − | 0.0918191i | ||||||
\(941\) | 506935.i | 0.572496i | 0.958156 | + | 0.286248i | \(0.0924082\pi\) | ||||
−0.958156 | + | 0.286248i | \(0.907592\pi\) | |||||||
\(942\) | 64706.5 | 0.0729199 | ||||||||
\(943\) | 867257.i | 0.975269i | ||||||||
\(944\) | −218648. | − | 42728.4i | −0.245359 | − | 0.0479482i | ||||
\(945\) | 21679.2 | 0.0242761 | ||||||||
\(946\) | − | 19877.4i | − | 0.0222114i | ||||||
\(947\) | 459717. | 0.512614 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(948\) | −150587. | −0.167560 | ||||||||
\(949\) | 484281. | 0.537731 | ||||||||
\(950\) | 631086.i | 0.699264i | ||||||||
\(951\) | −111723. | −0.123532 | ||||||||
\(952\) | 219949.i | 0.242688i | ||||||||
\(953\) | 1.27134e6 | 1.39984 | 0.699918 | − | 0.714223i | \(-0.253220\pi\) | ||||
0.699918 | + | 0.714223i | \(0.253220\pi\) | |||||||
\(954\) | − | 169890.i | − | 0.186669i | ||||||
\(955\) | − | 132992.i | − | 0.145820i | ||||||
\(956\) | 355953. | 0.389473 | ||||||||
\(957\) | 7135.25i | 0.00779086i | ||||||||
\(958\) | 20302.6i | 0.0221218i | ||||||||
\(959\) | 1.02065e6 | 1.10979 | ||||||||
\(960\) | 12334.9 | 0.0133842 | ||||||||
\(961\) | −1.26755e6 | −1.37252 | ||||||||
\(962\) | 498269.i | 0.538410i | ||||||||
\(963\) | 257901. | 0.278100 | ||||||||
\(964\) | −568461. | −0.611712 | ||||||||
\(965\) | −107344. | −0.115272 | ||||||||
\(966\) | −243207. | −0.260629 | ||||||||
\(967\) | − | 1.36038e6i | − | 1.45481i | −0.686208 | − | 0.727405i | \(-0.740726\pi\) | ||
0.686208 | − | 0.727405i | \(-0.259274\pi\) | |||||||
\(968\) | − | 330896.i | − | 0.353135i | ||||||
\(969\) | −560300. | −0.596723 | ||||||||
\(970\) | −184765. | −0.196370 | ||||||||
\(971\) | 669130. | 0.709695 | 0.354848 | − | 0.934924i | \(-0.384533\pi\) | ||||
0.354848 | + | 0.934924i | \(0.384533\pi\) | |||||||
\(972\) | −30304.0 | −0.0320750 | ||||||||
\(973\) | −840016. | −0.887282 | ||||||||
\(974\) | 519794.i | 0.547915i | ||||||||
\(975\) | − | 758875.i | − | 0.798291i | ||||||
\(976\) | 269246.i | 0.282650i | ||||||||
\(977\) | 33771.9i | 0.0353807i | 0.999844 | + | 0.0176904i | \(0.00563131\pi\) | ||||
−0.999844 | + | 0.0176904i | \(0.994369\pi\) | |||||||
\(978\) | 239705.i | 0.250611i | ||||||||
\(979\) | −17024.2 | −0.0177624 | ||||||||
\(980\) | −47856.5 | −0.0498297 | ||||||||
\(981\) | 167871.i | 0.174437i | ||||||||
\(982\) | − | 1961.88i | − | 0.00203446i | ||||||
\(983\) | − | 192587.i | − | 0.199306i | −0.995022 | − | 0.0996531i | \(-0.968227\pi\) | ||
0.995022 | − | 0.0996531i | \(-0.0317733\pi\) | |||||||
\(984\) | 205365.i | 0.212098i | ||||||||
\(985\) | −48311.8 | −0.0497945 | ||||||||
\(986\) | − | 272073.i | − | 0.279854i | ||||||
\(987\) | 378799.i | 0.388843i | ||||||||
\(988\) | 715752.i | 0.733244i | ||||||||
\(989\) | −838087. | −0.856834 | ||||||||
\(990\) | −1474.19 | −0.00150413 | ||||||||
\(991\) | 137261.i | 0.139766i | 0.997555 | + | 0.0698828i | \(0.0222625\pi\) | ||||
−0.997555 | + | 0.0698828i | \(0.977737\pi\) | |||||||
\(992\) | 267950. | 0.272289 | ||||||||
\(993\) | −736946. | −0.747373 | ||||||||
\(994\) | 231542.i | 0.234345i | ||||||||
\(995\) | 213473. | 0.215624 | ||||||||
\(996\) | − | 115564.i | − | 0.116494i | ||||||
\(997\) | −514755. | −0.517857 | −0.258929 | − | 0.965896i | \(-0.583369\pi\) | ||||
−0.258929 | + | 0.965896i | \(0.583369\pi\) | |||||||
\(998\) | 543802.i | 0.545984i | ||||||||
\(999\) | − | 102131.i | − | 0.102335i |
(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 | 354.5.d.a.235.18 | yes | 40 | |
3.2 | odd | 2 | 1062.5.d.b.235.11 | 40 | |||
59.58 | odd | 2 | inner | 354.5.d.a.235.17 | ✓ | 40 | |
177.176 | even | 2 | 1062.5.d.b.235.12 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.5.d.a.235.17 | ✓ | 40 | 59.58 | odd | 2 | inner | |
354.5.d.a.235.18 | yes | 40 | 1.1 | even | 1 | trivial | |
1062.5.d.b.235.11 | 40 | 3.2 | odd | 2 | |||
1062.5.d.b.235.12 | 40 | 177.176 | even | 2 |