Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,3,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(4.82290067918\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.16 | ||
Root | \(2.72775i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.3.c.a.58.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.72775i | 1.36387i | 0.731411 | + | 0.681937i | \(0.238862\pi\) | ||||
−0.731411 | + | 0.681937i | \(0.761138\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −3.44061 | −0.860153 | ||||||||
\(5\) | 5.71516 | 1.14303 | 0.571516 | − | 0.820591i | \(-0.306356\pi\) | ||||
0.571516 | + | 0.820591i | \(0.306356\pi\) | |||||||
\(6\) | − | 4.72460i | − | 0.787433i | ||||||
\(7\) | 8.69147 | 1.24164 | 0.620819 | − | 0.783954i | \(-0.286800\pi\) | ||||
0.620819 | + | 0.783954i | \(0.286800\pi\) | |||||||
\(8\) | 1.52587i | 0.190733i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 15.5895i | 1.55895i | ||||||||
\(11\) | 6.01328i | 0.546662i | 0.961920 | + | 0.273331i | \(0.0881254\pi\) | ||||
−0.961920 | + | 0.273331i | \(0.911875\pi\) | |||||||
\(12\) | 5.95932 | 0.496610 | ||||||||
\(13\) | − | 4.81519i | − | 0.370399i | −0.982701 | − | 0.185200i | \(-0.940707\pi\) | ||
0.982701 | − | 0.185200i | \(-0.0592932\pi\) | |||||||
\(14\) | 23.7081i | 1.69344i | ||||||||
\(15\) | −9.89894 | −0.659930 | ||||||||
\(16\) | −17.9246 | −1.12029 | ||||||||
\(17\) | 10.8327 | 0.637220 | 0.318610 | − | 0.947886i | \(-0.396784\pi\) | ||||
0.318610 | + | 0.947886i | \(0.396784\pi\) | |||||||
\(18\) | 8.18325i | 0.454625i | ||||||||
\(19\) | −18.4655 | −0.971869 | −0.485935 | − | 0.873995i | \(-0.661521\pi\) | ||||
−0.485935 | + | 0.873995i | \(0.661521\pi\) | |||||||
\(20\) | −19.6636 | −0.983182 | ||||||||
\(21\) | −15.0541 | −0.716860 | ||||||||
\(22\) | −16.4027 | −0.745578 | ||||||||
\(23\) | 15.4084i | 0.669930i | 0.942231 | + | 0.334965i | \(0.108724\pi\) | ||||
−0.942231 | + | 0.334965i | \(0.891276\pi\) | |||||||
\(24\) | − | 2.64288i | − | 0.110120i | ||||||
\(25\) | 7.66303 | 0.306521 | ||||||||
\(26\) | 13.1346 | 0.505178 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −29.9040 | −1.06800 | ||||||||
\(29\) | 15.5293 | 0.535492 | 0.267746 | − | 0.963489i | \(-0.413721\pi\) | ||||
0.267746 | + | 0.963489i | \(0.413721\pi\) | |||||||
\(30\) | − | 27.0018i | − | 0.900061i | ||||||
\(31\) | − | 6.38687i | − | 0.206028i | −0.994680 | − | 0.103014i | \(-0.967151\pi\) | ||
0.994680 | − | 0.103014i | \(-0.0328487\pi\) | |||||||
\(32\) | − | 42.7904i | − | 1.33720i | ||||||
\(33\) | − | 10.4153i | − | 0.315615i | ||||||
\(34\) | 29.5490i | 0.869087i | ||||||||
\(35\) | 49.6731 | 1.41923 | ||||||||
\(36\) | −10.3218 | −0.286718 | ||||||||
\(37\) | − | 0.527041i | − | 0.0142444i | −0.999975 | − | 0.00712218i | \(-0.997733\pi\) | ||
0.999975 | − | 0.00712218i | \(-0.00226708\pi\) | |||||||
\(38\) | − | 50.3693i | − | 1.32551i | ||||||
\(39\) | 8.34016i | 0.213850i | ||||||||
\(40\) | 8.72058i | 0.218014i | ||||||||
\(41\) | 9.31080 | 0.227093 | 0.113546 | − | 0.993533i | \(-0.463779\pi\) | ||||
0.113546 | + | 0.993533i | \(0.463779\pi\) | |||||||
\(42\) | − | 41.0637i | − | 0.977707i | ||||||
\(43\) | 52.9611i | 1.23165i | 0.787882 | + | 0.615827i | \(0.211178\pi\) | ||||
−0.787882 | + | 0.615827i | \(0.788822\pi\) | |||||||
\(44\) | − | 20.6894i | − | 0.470213i | ||||||
\(45\) | 17.1455 | 0.381011 | ||||||||
\(46\) | −42.0302 | −0.913700 | ||||||||
\(47\) | − | 78.0549i | − | 1.66074i | −0.557211 | − | 0.830371i | \(-0.688128\pi\) | ||
0.557211 | − | 0.830371i | \(-0.311872\pi\) | |||||||
\(48\) | 31.0464 | 0.646800 | ||||||||
\(49\) | 26.5417 | 0.541666 | ||||||||
\(50\) | 20.9028i | 0.418056i | ||||||||
\(51\) | −18.7628 | −0.367899 | ||||||||
\(52\) | 16.5672i | 0.318600i | ||||||||
\(53\) | −10.2232 | −0.192891 | −0.0964457 | − | 0.995338i | \(-0.530747\pi\) | ||||
−0.0964457 | + | 0.995338i | \(0.530747\pi\) | |||||||
\(54\) | − | 14.1738i | − | 0.262478i | ||||||
\(55\) | 34.3668i | 0.624851i | ||||||||
\(56\) | 13.2620i | 0.236822i | ||||||||
\(57\) | 31.9832 | 0.561109 | ||||||||
\(58\) | 42.3600i | 0.730344i | ||||||||
\(59\) | 29.4888 | + | 51.1020i | 0.499810 | + | 0.866135i | ||||
\(60\) | 34.0584 | 0.567641 | ||||||||
\(61\) | − | 41.5604i | − | 0.681318i | −0.940187 | − | 0.340659i | \(-0.889350\pi\) | ||
0.940187 | − | 0.340659i | \(-0.110650\pi\) | |||||||
\(62\) | 17.4218 | 0.280997 | ||||||||
\(63\) | 26.0744 | 0.413880 | ||||||||
\(64\) | 45.0230 | 0.703484 | ||||||||
\(65\) | − | 27.5196i | − | 0.423378i | ||||||
\(66\) | 28.4103 | 0.430460 | ||||||||
\(67\) | − | 92.4125i | − | 1.37929i | −0.724147 | − | 0.689646i | \(-0.757766\pi\) | ||
0.724147 | − | 0.689646i | \(-0.242234\pi\) | |||||||
\(68\) | −37.2712 | −0.548106 | ||||||||
\(69\) | − | 26.6881i | − | 0.386784i | ||||||
\(70\) | 135.496i | 1.93565i | ||||||||
\(71\) | 93.8038 | 1.32118 | 0.660590 | − | 0.750747i | \(-0.270306\pi\) | ||||
0.660590 | + | 0.750747i | \(0.270306\pi\) | |||||||
\(72\) | 4.57760i | 0.0635778i | ||||||||
\(73\) | − | 88.0161i | − | 1.20570i | −0.797854 | − | 0.602850i | \(-0.794032\pi\) | ||
0.797854 | − | 0.602850i | \(-0.205968\pi\) | |||||||
\(74\) | 1.43764 | 0.0194275 | ||||||||
\(75\) | −13.2728 | −0.176970 | ||||||||
\(76\) | 63.5327 | 0.835957 | ||||||||
\(77\) | 52.2642i | 0.678756i | ||||||||
\(78\) | −22.7499 | −0.291665 | ||||||||
\(79\) | −81.2111 | −1.02799 | −0.513994 | − | 0.857794i | \(-0.671835\pi\) | ||||
−0.513994 | + | 0.857794i | \(0.671835\pi\) | |||||||
\(80\) | −102.442 | −1.28053 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 25.3975i | 0.309726i | ||||||||
\(83\) | − | 2.92193i | − | 0.0352040i | −0.999845 | − | 0.0176020i | \(-0.994397\pi\) | ||
0.999845 | − | 0.0176020i | \(-0.00560318\pi\) | |||||||
\(84\) | 51.7952 | 0.616610 | ||||||||
\(85\) | 61.9108 | 0.728362 | ||||||||
\(86\) | −144.465 | −1.67982 | ||||||||
\(87\) | −26.8975 | −0.309167 | ||||||||
\(88\) | −9.17547 | −0.104267 | ||||||||
\(89\) | − | 168.718i | − | 1.89571i | −0.318699 | − | 0.947856i | \(-0.603246\pi\) | ||
0.318699 | − | 0.947856i | \(-0.396754\pi\) | |||||||
\(90\) | 46.7685i | 0.519650i | ||||||||
\(91\) | − | 41.8511i | − | 0.459902i | ||||||
\(92\) | − | 53.0143i | − | 0.576242i | ||||||
\(93\) | 11.0624i | 0.118950i | ||||||||
\(94\) | 212.914 | 2.26504 | ||||||||
\(95\) | −105.533 | −1.11088 | ||||||||
\(96\) | 74.1152i | 0.772033i | ||||||||
\(97\) | − | 169.166i | − | 1.74397i | −0.489528 | − | 0.871987i | \(-0.662831\pi\) | ||
0.489528 | − | 0.871987i | \(-0.337169\pi\) | |||||||
\(98\) | 72.3990i | 0.738765i | ||||||||
\(99\) | 18.0398i | 0.182221i | ||||||||
\(100\) | −26.3655 | −0.263655 | ||||||||
\(101\) | − | 6.43636i | − | 0.0637263i | −0.999492 | − | 0.0318631i | \(-0.989856\pi\) | ||
0.999492 | − | 0.0318631i | \(-0.0101441\pi\) | |||||||
\(102\) | − | 51.1803i | − | 0.501768i | ||||||
\(103\) | 176.969i | 1.71814i | 0.511854 | + | 0.859072i | \(0.328959\pi\) | ||||
−0.511854 | + | 0.859072i | \(0.671041\pi\) | |||||||
\(104\) | 7.34735 | 0.0706476 | ||||||||
\(105\) | −86.0364 | −0.819394 | ||||||||
\(106\) | − | 27.8864i | − | 0.263080i | ||||||
\(107\) | −183.573 | −1.71564 | −0.857818 | − | 0.513953i | \(-0.828181\pi\) | ||||
−0.857818 | + | 0.513953i | \(0.828181\pi\) | |||||||
\(108\) | 17.8779 | 0.165537 | ||||||||
\(109\) | − | 105.308i | − | 0.966132i | −0.875584 | − | 0.483066i | \(-0.839523\pi\) | ||
0.875584 | − | 0.483066i | \(-0.160477\pi\) | |||||||
\(110\) | −93.7441 | −0.852219 | ||||||||
\(111\) | 0.912863i | 0.00822399i | ||||||||
\(112\) | −155.791 | −1.39099 | ||||||||
\(113\) | 100.717i | 0.891297i | 0.895208 | + | 0.445648i | \(0.147027\pi\) | ||||
−0.895208 | + | 0.445648i | \(0.852973\pi\) | |||||||
\(114\) | 87.2422i | 0.765282i | ||||||||
\(115\) | 88.0614i | 0.765751i | ||||||||
\(116\) | −53.4302 | −0.460606 | ||||||||
\(117\) | − | 14.4456i | − | 0.123466i | ||||||
\(118\) | −139.393 | + | 80.4379i | −1.18130 | + | 0.681677i | ||||
\(119\) | 94.1524 | 0.791196 | ||||||||
\(120\) | − | 15.1045i | − | 0.125871i | ||||||
\(121\) | 84.8405 | 0.701161 | ||||||||
\(122\) | 113.366 | 0.929233 | ||||||||
\(123\) | −16.1268 | −0.131112 | ||||||||
\(124\) | 21.9748i | 0.177216i | ||||||||
\(125\) | −99.0835 | −0.792668 | ||||||||
\(126\) | 71.1244i | 0.564480i | ||||||||
\(127\) | −206.165 | −1.62335 | −0.811675 | − | 0.584110i | \(-0.801444\pi\) | ||||
−0.811675 | + | 0.584110i | \(0.801444\pi\) | |||||||
\(128\) | − | 48.3503i | − | 0.377737i | ||||||
\(129\) | − | 91.7313i | − | 0.711095i | ||||||
\(130\) | 75.0665 | 0.577435 | ||||||||
\(131\) | 152.579i | 1.16473i | 0.812929 | + | 0.582363i | \(0.197872\pi\) | ||||
−0.812929 | + | 0.582363i | \(0.802128\pi\) | |||||||
\(132\) | 35.8350i | 0.271477i | ||||||||
\(133\) | −160.493 | −1.20671 | ||||||||
\(134\) | 252.078 | 1.88118 | ||||||||
\(135\) | −29.6968 | −0.219977 | ||||||||
\(136\) | 16.5293i | 0.121539i | ||||||||
\(137\) | 193.341 | 1.41125 | 0.705624 | − | 0.708586i | \(-0.250667\pi\) | ||||
0.705624 | + | 0.708586i | \(0.250667\pi\) | |||||||
\(138\) | 72.7985 | 0.527525 | ||||||||
\(139\) | 172.850 | 1.24353 | 0.621763 | − | 0.783206i | \(-0.286417\pi\) | ||||
0.621763 | + | 0.783206i | \(0.286417\pi\) | |||||||
\(140\) | −170.906 | −1.22076 | ||||||||
\(141\) | 135.195i | 0.958830i | ||||||||
\(142\) | 255.873i | 1.80192i | ||||||||
\(143\) | 28.9551 | 0.202483 | ||||||||
\(144\) | −53.7739 | −0.373430 | ||||||||
\(145\) | 88.7523 | 0.612085 | ||||||||
\(146\) | 240.086 | 1.64442 | ||||||||
\(147\) | −45.9715 | −0.312731 | ||||||||
\(148\) | 1.81335i | 0.0122523i | ||||||||
\(149\) | 181.616i | 1.21890i | 0.792826 | + | 0.609448i | \(0.208609\pi\) | ||||
−0.792826 | + | 0.609448i | \(0.791391\pi\) | |||||||
\(150\) | − | 36.2047i | − | 0.241365i | ||||||
\(151\) | − | 1.21185i | − | 0.00802549i | −0.999992 | − | 0.00401275i | \(-0.998723\pi\) | ||
0.999992 | − | 0.00401275i | \(-0.00127730\pi\) | |||||||
\(152\) | − | 28.1759i | − | 0.185368i | ||||||
\(153\) | 32.4982 | 0.212407 | ||||||||
\(154\) | −142.564 | −0.925738 | ||||||||
\(155\) | − | 36.5020i | − | 0.235497i | ||||||
\(156\) | − | 28.6953i | − | 0.183944i | ||||||
\(157\) | − | 184.394i | − | 1.17449i | −0.809410 | − | 0.587244i | \(-0.800213\pi\) | ||
0.809410 | − | 0.587244i | \(-0.199787\pi\) | |||||||
\(158\) | − | 221.523i | − | 1.40205i | ||||||
\(159\) | 17.7072 | 0.111366 | ||||||||
\(160\) | − | 244.554i | − | 1.52846i | ||||||
\(161\) | 133.922i | 0.831811i | ||||||||
\(162\) | 24.5497i | 0.151542i | ||||||||
\(163\) | 8.96097 | 0.0549752 | 0.0274876 | − | 0.999622i | \(-0.491249\pi\) | ||||
0.0274876 | + | 0.999622i | \(0.491249\pi\) | |||||||
\(164\) | −32.0348 | −0.195334 | ||||||||
\(165\) | − | 59.5251i | − | 0.360758i | ||||||
\(166\) | 7.97030 | 0.0480139 | ||||||||
\(167\) | −143.336 | −0.858298 | −0.429149 | − | 0.903234i | \(-0.641187\pi\) | ||||
−0.429149 | + | 0.903234i | \(0.641187\pi\) | |||||||
\(168\) | − | 22.9705i | − | 0.136729i | ||||||
\(169\) | 145.814 | 0.862804 | ||||||||
\(170\) | 168.877i | 0.993394i | ||||||||
\(171\) | −55.3966 | −0.323956 | ||||||||
\(172\) | − | 182.219i | − | 1.05941i | ||||||
\(173\) | 57.4482i | 0.332070i | 0.986120 | + | 0.166035i | \(0.0530965\pi\) | ||||
−0.986120 | + | 0.166035i | \(0.946903\pi\) | |||||||
\(174\) | − | 73.3696i | − | 0.421665i | ||||||
\(175\) | 66.6030 | 0.380588 | ||||||||
\(176\) | − | 107.786i | − | 0.612419i | ||||||
\(177\) | −51.0760 | − | 88.5112i | −0.288565 | − | 0.500063i | ||||
\(178\) | 460.221 | 2.58551 | ||||||||
\(179\) | 90.1857i | 0.503831i | 0.967749 | + | 0.251915i | \(0.0810604\pi\) | ||||
−0.967749 | + | 0.251915i | \(0.918940\pi\) | |||||||
\(180\) | −58.9909 | −0.327727 | ||||||||
\(181\) | 123.939 | 0.684745 | 0.342373 | − | 0.939564i | \(-0.388769\pi\) | ||||
0.342373 | + | 0.939564i | \(0.388769\pi\) | |||||||
\(182\) | 114.159 | 0.627249 | ||||||||
\(183\) | 71.9848i | 0.393359i | ||||||||
\(184\) | −23.5112 | −0.127778 | ||||||||
\(185\) | − | 3.01213i | − | 0.0162818i | ||||||
\(186\) | −30.1754 | −0.162233 | ||||||||
\(187\) | 65.1402i | 0.348343i | ||||||||
\(188\) | 268.557i | 1.42849i | ||||||||
\(189\) | −45.1622 | −0.238953 | ||||||||
\(190\) | − | 287.868i | − | 1.51510i | ||||||
\(191\) | 150.842i | 0.789751i | 0.918735 | + | 0.394876i | \(0.129212\pi\) | ||||
−0.918735 | + | 0.394876i | \(0.870788\pi\) | |||||||
\(192\) | −77.9821 | −0.406157 | ||||||||
\(193\) | −84.8208 | −0.439486 | −0.219743 | − | 0.975558i | \(-0.570522\pi\) | ||||
−0.219743 | + | 0.975558i | \(0.570522\pi\) | |||||||
\(194\) | 461.441 | 2.37856 | ||||||||
\(195\) | 47.6653i | 0.244438i | ||||||||
\(196\) | −91.3195 | −0.465916 | ||||||||
\(197\) | −190.721 | −0.968127 | −0.484063 | − | 0.875033i | \(-0.660840\pi\) | ||||
−0.484063 | + | 0.875033i | \(0.660840\pi\) | |||||||
\(198\) | −49.2081 | −0.248526 | ||||||||
\(199\) | −200.054 | −1.00529 | −0.502647 | − | 0.864492i | \(-0.667641\pi\) | ||||
−0.502647 | + | 0.864492i | \(0.667641\pi\) | |||||||
\(200\) | 11.6928i | 0.0584638i | ||||||||
\(201\) | 160.063i | 0.796334i | ||||||||
\(202\) | 17.5568 | 0.0869147 | ||||||||
\(203\) | 134.972 | 0.664888 | ||||||||
\(204\) | 64.5557 | 0.316449 | ||||||||
\(205\) | 53.2127 | 0.259574 | ||||||||
\(206\) | −482.727 | −2.34333 | ||||||||
\(207\) | 46.2252i | 0.223310i | ||||||||
\(208\) | 86.3106i | 0.414955i | ||||||||
\(209\) | − | 111.038i | − | 0.531284i | ||||||
\(210\) | − | 234.686i | − | 1.11755i | ||||||
\(211\) | − | 412.135i | − | 1.95325i | −0.214955 | − | 0.976624i | \(-0.568961\pi\) | ||
0.214955 | − | 0.976624i | \(-0.431039\pi\) | |||||||
\(212\) | 35.1742 | 0.165916 | ||||||||
\(213\) | −162.473 | −0.762784 | ||||||||
\(214\) | − | 500.741i | − | 2.33991i | ||||||
\(215\) | 302.681i | 1.40782i | ||||||||
\(216\) | − | 7.92864i | − | 0.0367067i | ||||||
\(217\) | − | 55.5113i | − | 0.255813i | ||||||
\(218\) | 287.255 | 1.31768 | ||||||||
\(219\) | 152.448i | 0.696111i | ||||||||
\(220\) | − | 118.243i | − | 0.537468i | ||||||
\(221\) | − | 52.1617i | − | 0.236026i | ||||||
\(222\) | −2.49006 | −0.0112165 | ||||||||
\(223\) | −22.4832 | −0.100821 | −0.0504107 | − | 0.998729i | \(-0.516053\pi\) | ||||
−0.0504107 | + | 0.998729i | \(0.516053\pi\) | |||||||
\(224\) | − | 371.912i | − | 1.66032i | ||||||
\(225\) | 22.9891 | 0.102174 | ||||||||
\(226\) | −274.729 | −1.21562 | ||||||||
\(227\) | − | 276.847i | − | 1.21959i | −0.792559 | − | 0.609795i | \(-0.791252\pi\) | ||
0.792559 | − | 0.609795i | \(-0.208748\pi\) | |||||||
\(228\) | −110.042 | −0.482640 | ||||||||
\(229\) | 160.926i | 0.702732i | 0.936238 | + | 0.351366i | \(0.114283\pi\) | ||||
−0.936238 | + | 0.351366i | \(0.885717\pi\) | |||||||
\(230\) | −240.209 | −1.04439 | ||||||||
\(231\) | − | 90.5243i | − | 0.391880i | ||||||
\(232\) | 23.6956i | 0.102136i | ||||||||
\(233\) | − | 10.6284i | − | 0.0456153i | −0.999740 | − | 0.0228076i | \(-0.992739\pi\) | ||
0.999740 | − | 0.0228076i | \(-0.00726052\pi\) | |||||||
\(234\) | 39.4039 | 0.168393 | ||||||||
\(235\) | − | 446.096i | − | 1.89828i | ||||||
\(236\) | −101.459 | − | 175.822i | −0.429913 | − | 0.745009i | ||||
\(237\) | 140.662 | 0.593510 | ||||||||
\(238\) | 256.824i | 1.07909i | ||||||||
\(239\) | 223.594 | 0.935540 | 0.467770 | − | 0.883850i | \(-0.345058\pi\) | ||||
0.467770 | + | 0.883850i | \(0.345058\pi\) | |||||||
\(240\) | 177.435 | 0.739312 | ||||||||
\(241\) | 64.6207 | 0.268136 | 0.134068 | − | 0.990972i | \(-0.457196\pi\) | ||||
0.134068 | + | 0.990972i | \(0.457196\pi\) | |||||||
\(242\) | 231.424i | 0.956296i | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 142.993i | 0.586038i | ||||||||
\(245\) | 151.690 | 0.619142 | ||||||||
\(246\) | − | 43.9898i | − | 0.178820i | ||||||
\(247\) | 88.9150i | 0.359980i | ||||||||
\(248\) | 9.74553 | 0.0392965 | ||||||||
\(249\) | 5.06094i | 0.0203251i | ||||||||
\(250\) | − | 270.275i | − | 1.08110i | ||||||
\(251\) | −142.392 | −0.567299 | −0.283650 | − | 0.958928i | \(-0.591545\pi\) | ||||
−0.283650 | + | 0.958928i | \(0.591545\pi\) | |||||||
\(252\) | −89.7119 | −0.356000 | ||||||||
\(253\) | −92.6549 | −0.366225 | ||||||||
\(254\) | − | 562.367i | − | 2.21405i | ||||||
\(255\) | −107.233 | −0.420520 | ||||||||
\(256\) | 311.979 | 1.21867 | ||||||||
\(257\) | 13.2725 | 0.0516440 | 0.0258220 | − | 0.999667i | \(-0.491780\pi\) | ||||
0.0258220 | + | 0.999667i | \(0.491780\pi\) | |||||||
\(258\) | 250.220 | 0.969844 | ||||||||
\(259\) | − | 4.58077i | − | 0.0176864i | ||||||
\(260\) | 94.6843i | 0.364170i | ||||||||
\(261\) | 46.5878 | 0.178497 | ||||||||
\(262\) | −416.198 | −1.58854 | ||||||||
\(263\) | −54.0179 | −0.205391 | −0.102696 | − | 0.994713i | \(-0.532747\pi\) | ||||
−0.102696 | + | 0.994713i | \(0.532747\pi\) | |||||||
\(264\) | 15.8924 | 0.0601984 | ||||||||
\(265\) | −58.4274 | −0.220481 | ||||||||
\(266\) | − | 437.783i | − | 1.64580i | ||||||
\(267\) | 292.229i | 1.09449i | ||||||||
\(268\) | 317.956i | 1.18640i | ||||||||
\(269\) | 372.720i | 1.38558i | 0.721140 | + | 0.692789i | \(0.243618\pi\) | ||||
−0.721140 | + | 0.692789i | \(0.756382\pi\) | |||||||
\(270\) | − | 81.0055i | − | 0.300020i | ||||||
\(271\) | 531.359 | 1.96074 | 0.980368 | − | 0.197177i | \(-0.0631773\pi\) | ||||
0.980368 | + | 0.197177i | \(0.0631773\pi\) | |||||||
\(272\) | −194.173 | −0.713871 | ||||||||
\(273\) | 72.4882i | 0.265525i | ||||||||
\(274\) | 527.386i | 1.92477i | ||||||||
\(275\) | 46.0799i | 0.167563i | ||||||||
\(276\) | 91.8235i | 0.332694i | ||||||||
\(277\) | 136.910 | 0.494260 | 0.247130 | − | 0.968982i | \(-0.420512\pi\) | ||||
0.247130 | + | 0.968982i | \(0.420512\pi\) | |||||||
\(278\) | 471.492i | 1.69601i | ||||||||
\(279\) | − | 19.1606i | − | 0.0686761i | ||||||
\(280\) | 75.7946i | 0.270695i | ||||||||
\(281\) | −186.333 | −0.663108 | −0.331554 | − | 0.943436i | \(-0.607573\pi\) | ||||
−0.331554 | + | 0.943436i | \(0.607573\pi\) | |||||||
\(282\) | −368.778 | −1.30772 | ||||||||
\(283\) | 370.038i | 1.30755i | 0.756687 | + | 0.653777i | \(0.226817\pi\) | ||||
−0.756687 | + | 0.653777i | \(0.773183\pi\) | |||||||
\(284\) | −322.743 | −1.13642 | ||||||||
\(285\) | 182.789 | 0.641365 | ||||||||
\(286\) | 78.9822i | 0.276162i | ||||||||
\(287\) | 80.9245 | 0.281967 | ||||||||
\(288\) | − | 128.371i | − | 0.445734i | ||||||
\(289\) | −171.652 | −0.593951 | ||||||||
\(290\) | 242.094i | 0.834807i | ||||||||
\(291\) | 293.003i | 1.00688i | ||||||||
\(292\) | 302.829i | 1.03709i | ||||||||
\(293\) | 299.019 | 1.02054 | 0.510271 | − | 0.860013i | \(-0.329545\pi\) | ||||
0.510271 | + | 0.860013i | \(0.329545\pi\) | |||||||
\(294\) | − | 125.399i | − | 0.426526i | ||||||
\(295\) | 168.533 | + | 292.056i | 0.571298 | + | 0.990020i | ||||
\(296\) | 0.804196 | 0.00271688 | ||||||||
\(297\) | − | 31.2459i | − | 0.105205i | ||||||
\(298\) | −495.402 | −1.66242 | ||||||||
\(299\) | 74.1944 | 0.248142 | ||||||||
\(300\) | 45.6664 | 0.152221 | ||||||||
\(301\) | 460.310i | 1.52927i | ||||||||
\(302\) | 3.30562 | 0.0109458 | ||||||||
\(303\) | 11.1481i | 0.0367924i | ||||||||
\(304\) | 330.988 | 1.08878 | ||||||||
\(305\) | − | 237.524i | − | 0.778768i | ||||||
\(306\) | 88.6469i | 0.289696i | ||||||||
\(307\) | 27.6515 | 0.0900700 | 0.0450350 | − | 0.998985i | \(-0.485660\pi\) | ||||
0.0450350 | + | 0.998985i | \(0.485660\pi\) | |||||||
\(308\) | − | 179.821i | − | 0.583834i | ||||||
\(309\) | − | 306.519i | − | 0.991971i | ||||||
\(310\) | 99.5682 | 0.321188 | ||||||||
\(311\) | −364.708 | −1.17269 | −0.586347 | − | 0.810060i | \(-0.699434\pi\) | ||||
−0.586347 | + | 0.810060i | \(0.699434\pi\) | |||||||
\(312\) | −12.7260 | −0.0407884 | ||||||||
\(313\) | 174.644i | 0.557969i | 0.960296 | + | 0.278984i | \(0.0899978\pi\) | ||||
−0.960296 | + | 0.278984i | \(0.910002\pi\) | |||||||
\(314\) | 502.982 | 1.60185 | ||||||||
\(315\) | 149.019 | 0.473077 | ||||||||
\(316\) | 279.416 | 0.884228 | ||||||||
\(317\) | −505.102 | −1.59338 | −0.796691 | − | 0.604387i | \(-0.793418\pi\) | ||||
−0.796691 | + | 0.604387i | \(0.793418\pi\) | |||||||
\(318\) | 48.3007i | 0.151889i | ||||||||
\(319\) | 93.3819i | 0.292733i | ||||||||
\(320\) | 257.313 | 0.804105 | ||||||||
\(321\) | 317.958 | 0.990523 | ||||||||
\(322\) | −365.304 | −1.13449 | ||||||||
\(323\) | −200.032 | −0.619294 | ||||||||
\(324\) | −30.9655 | −0.0955726 | ||||||||
\(325\) | − | 36.8990i | − | 0.113535i | ||||||
\(326\) | 24.4433i | 0.0749793i | ||||||||
\(327\) | 182.400i | 0.557797i | ||||||||
\(328\) | 14.2070i | 0.0433142i | ||||||||
\(329\) | − | 678.412i | − | 2.06204i | ||||||
\(330\) | 162.370 | 0.492029 | ||||||||
\(331\) | 3.99311 | 0.0120638 | 0.00603188 | − | 0.999982i | \(-0.498080\pi\) | ||||
0.00603188 | + | 0.999982i | \(0.498080\pi\) | |||||||
\(332\) | 10.0532i | 0.0302809i | ||||||||
\(333\) | − | 1.58112i | − | 0.00474812i | ||||||
\(334\) | − | 390.984i | − | 1.17061i | ||||||
\(335\) | − | 528.152i | − | 1.57657i | ||||||
\(336\) | 269.839 | 0.803091 | ||||||||
\(337\) | − | 347.538i | − | 1.03127i | −0.856808 | − | 0.515636i | \(-0.827556\pi\) | ||
0.856808 | − | 0.515636i | \(-0.172444\pi\) | |||||||
\(338\) | 397.744i | 1.17676i | ||||||||
\(339\) | − | 174.446i | − | 0.514591i | ||||||
\(340\) | −213.011 | −0.626503 | ||||||||
\(341\) | 38.4060 | 0.112628 | ||||||||
\(342\) | − | 151.108i | − | 0.441836i | ||||||
\(343\) | −195.196 | −0.569085 | ||||||||
\(344\) | −80.8116 | −0.234917 | ||||||||
\(345\) | − | 152.527i | − | 0.442107i | ||||||
\(346\) | −156.704 | −0.452902 | ||||||||
\(347\) | 587.431i | 1.69289i | 0.532480 | + | 0.846443i | \(0.321260\pi\) | ||||
−0.532480 | + | 0.846443i | \(0.678740\pi\) | |||||||
\(348\) | 92.5439 | 0.265931 | ||||||||
\(349\) | 395.445i | 1.13308i | 0.824034 | + | 0.566540i | \(0.191718\pi\) | ||||
−0.824034 | + | 0.566540i | \(0.808282\pi\) | |||||||
\(350\) | 181.676i | 0.519075i | ||||||||
\(351\) | 25.0205i | 0.0712834i | ||||||||
\(352\) | 257.311 | 0.730996 | ||||||||
\(353\) | − | 201.884i | − | 0.571909i | −0.958243 | − | 0.285955i | \(-0.907689\pi\) | ||
0.958243 | − | 0.285955i | \(-0.0923106\pi\) | |||||||
\(354\) | 241.436 | − | 139.323i | 0.682024 | − | 0.393567i | ||||
\(355\) | 536.104 | 1.51015 | ||||||||
\(356\) | 580.494i | 1.63060i | ||||||||
\(357\) | −163.077 | −0.456797 | ||||||||
\(358\) | −246.004 | −0.687162 | ||||||||
\(359\) | −529.552 | −1.47507 | −0.737537 | − | 0.675307i | \(-0.764011\pi\) | ||||
−0.737537 | + | 0.675307i | \(0.764011\pi\) | |||||||
\(360\) | 26.1617i | 0.0726715i | ||||||||
\(361\) | −20.0246 | −0.0554698 | ||||||||
\(362\) | 338.074i | 0.933906i | ||||||||
\(363\) | −146.948 | −0.404816 | ||||||||
\(364\) | 143.993i | 0.395586i | ||||||||
\(365\) | − | 503.026i | − | 1.37815i | ||||||
\(366\) | −196.356 | −0.536493 | ||||||||
\(367\) | − | 359.579i | − | 0.979779i | −0.871785 | − | 0.489889i | \(-0.837037\pi\) | ||
0.871785 | − | 0.489889i | \(-0.162963\pi\) | |||||||
\(368\) | − | 276.190i | − | 0.750516i | ||||||
\(369\) | 27.9324 | 0.0756975 | ||||||||
\(370\) | 8.21632 | 0.0222063 | ||||||||
\(371\) | −88.8550 | −0.239501 | ||||||||
\(372\) | − | 38.0614i | − | 0.102316i | ||||||
\(373\) | −439.679 | −1.17876 | −0.589382 | − | 0.807854i | \(-0.700629\pi\) | ||||
−0.589382 | + | 0.807854i | \(0.700629\pi\) | |||||||
\(374\) | −177.686 | −0.475097 | ||||||||
\(375\) | 171.618 | 0.457647 | ||||||||
\(376\) | 119.101 | 0.316759 | ||||||||
\(377\) | − | 74.7765i | − | 0.198346i | ||||||
\(378\) | − | 123.191i | − | 0.325902i | ||||||
\(379\) | −580.426 | −1.53147 | −0.765734 | − | 0.643158i | \(-0.777624\pi\) | ||||
−0.765734 | + | 0.643158i | \(0.777624\pi\) | |||||||
\(380\) | 363.099 | 0.955525 | ||||||||
\(381\) | 357.089 | 0.937241 | ||||||||
\(382\) | −411.460 | −1.07712 | ||||||||
\(383\) | −343.315 | −0.896384 | −0.448192 | − | 0.893937i | \(-0.647932\pi\) | ||||
−0.448192 | + | 0.893937i | \(0.647932\pi\) | |||||||
\(384\) | 83.7452i | 0.218086i | ||||||||
\(385\) | 298.698i | 0.775840i | ||||||||
\(386\) | − | 231.370i | − | 0.599404i | ||||||
\(387\) | 158.883i | 0.410551i | ||||||||
\(388\) | 582.033i | 1.50009i | ||||||||
\(389\) | 303.425 | 0.780013 | 0.390007 | − | 0.920812i | \(-0.372473\pi\) | ||||
0.390007 | + | 0.920812i | \(0.372473\pi\) | |||||||
\(390\) | −130.019 | −0.333382 | ||||||||
\(391\) | 166.915i | 0.426893i | ||||||||
\(392\) | 40.4991i | 0.103314i | ||||||||
\(393\) | − | 264.275i | − | 0.672455i | ||||||
\(394\) | − | 520.239i | − | 1.32040i | ||||||
\(395\) | −464.134 | −1.17502 | ||||||||
\(396\) | − | 62.0681i | − | 0.156738i | ||||||
\(397\) | 159.184i | 0.400967i | 0.979697 | + | 0.200484i | \(0.0642513\pi\) | ||||
−0.979697 | + | 0.200484i | \(0.935749\pi\) | |||||||
\(398\) | − | 545.696i | − | 1.37110i | ||||||
\(399\) | 277.981 | 0.696695 | ||||||||
\(400\) | −137.357 | −0.343392 | ||||||||
\(401\) | − | 421.293i | − | 1.05061i | −0.850915 | − | 0.525303i | \(-0.823952\pi\) | ||
0.850915 | − | 0.525303i | \(-0.176048\pi\) | |||||||
\(402\) | −436.612 | −1.08610 | ||||||||
\(403\) | −30.7540 | −0.0763127 | ||||||||
\(404\) | 22.1450i | 0.0548144i | ||||||||
\(405\) | 51.4364 | 0.127004 | ||||||||
\(406\) | 368.170i | 0.906824i | ||||||||
\(407\) | 3.16925 | 0.00778685 | ||||||||
\(408\) | − | 28.6296i | − | 0.0701706i | ||||||
\(409\) | 662.202i | 1.61908i | 0.587068 | + | 0.809538i | \(0.300282\pi\) | ||||
−0.587068 | + | 0.809538i | \(0.699718\pi\) | |||||||
\(410\) | 145.151i | 0.354026i | ||||||||
\(411\) | −334.877 | −0.814785 | ||||||||
\(412\) | − | 608.881i | − | 1.47787i | ||||||
\(413\) | 256.301 | + | 444.151i | 0.620583 | + | 1.07543i | ||||
\(414\) | −126.091 | −0.304567 | ||||||||
\(415\) | − | 16.6993i | − | 0.0402393i | ||||||
\(416\) | −206.044 | −0.495299 | ||||||||
\(417\) | −299.385 | −0.717950 | ||||||||
\(418\) | 302.885 | 0.724604 | ||||||||
\(419\) | 338.057i | 0.806818i | 0.915020 | + | 0.403409i | \(0.132175\pi\) | ||||
−0.915020 | + | 0.403409i | \(0.867825\pi\) | |||||||
\(420\) | 296.018 | 0.704804 | ||||||||
\(421\) | 101.363i | 0.240766i | 0.992727 | + | 0.120383i | \(0.0384123\pi\) | ||||
−0.992727 | + | 0.120383i | \(0.961588\pi\) | |||||||
\(422\) | 1124.20 | 2.66398 | ||||||||
\(423\) | − | 234.165i | − | 0.553581i | ||||||
\(424\) | − | 15.5993i | − | 0.0367908i | ||||||
\(425\) | 83.0115 | 0.195321 | ||||||||
\(426\) | − | 443.185i | − | 1.04034i | ||||||
\(427\) | − | 361.221i | − | 0.845951i | ||||||
\(428\) | 631.604 | 1.47571 | ||||||||
\(429\) | −50.1517 | −0.116904 | ||||||||
\(430\) | −825.637 | −1.92009 | ||||||||
\(431\) | − | 47.6635i | − | 0.110588i | −0.998470 | − | 0.0552941i | \(-0.982390\pi\) | ||
0.998470 | − | 0.0552941i | \(-0.0176096\pi\) | |||||||
\(432\) | 93.1391 | 0.215600 | ||||||||
\(433\) | −172.895 | −0.399294 | −0.199647 | − | 0.979868i | \(-0.563980\pi\) | ||||
−0.199647 | + | 0.979868i | \(0.563980\pi\) | |||||||
\(434\) | 151.421 | 0.348896 | ||||||||
\(435\) | −153.723 | −0.353387 | ||||||||
\(436\) | 362.325i | 0.831022i | ||||||||
\(437\) | − | 284.524i | − | 0.651084i | ||||||
\(438\) | −415.841 | −0.949409 | ||||||||
\(439\) | 384.161 | 0.875081 | 0.437540 | − | 0.899199i | \(-0.355850\pi\) | ||||
0.437540 | + | 0.899199i | \(0.355850\pi\) | |||||||
\(440\) | −52.4392 | −0.119180 | ||||||||
\(441\) | 79.6250 | 0.180555 | ||||||||
\(442\) | 142.284 | 0.321910 | ||||||||
\(443\) | − | 172.202i | − | 0.388717i | −0.980931 | − | 0.194359i | \(-0.937737\pi\) | ||
0.980931 | − | 0.194359i | \(-0.0622625\pi\) | |||||||
\(444\) | − | 3.14081i | − | 0.00707389i | ||||||
\(445\) | − | 964.252i | − | 2.16686i | ||||||
\(446\) | − | 61.3285i | − | 0.137508i | ||||||
\(447\) | − | 314.567i | − | 0.703730i | ||||||
\(448\) | 391.316 | 0.873473 | ||||||||
\(449\) | 613.309 | 1.36595 | 0.682973 | − | 0.730444i | \(-0.260687\pi\) | ||||
0.682973 | + | 0.730444i | \(0.260687\pi\) | |||||||
\(450\) | 62.7084i | 0.139352i | ||||||||
\(451\) | 55.9884i | 0.124143i | ||||||||
\(452\) | − | 346.527i | − | 0.766652i | ||||||
\(453\) | 2.09898i | 0.00463352i | ||||||||
\(454\) | 755.168 | 1.66337 | ||||||||
\(455\) | − | 239.186i | − | 0.525683i | ||||||
\(456\) | 48.8022i | 0.107022i | ||||||||
\(457\) | 279.448i | 0.611484i | 0.952114 | + | 0.305742i | \(0.0989046\pi\) | ||||
−0.952114 | + | 0.305742i | \(0.901095\pi\) | |||||||
\(458\) | −438.965 | −0.958438 | ||||||||
\(459\) | −56.2885 | −0.122633 | ||||||||
\(460\) | − | 302.985i | − | 0.658663i | ||||||
\(461\) | −555.187 | −1.20431 | −0.602155 | − | 0.798379i | \(-0.705691\pi\) | ||||
−0.602155 | + | 0.798379i | \(0.705691\pi\) | |||||||
\(462\) | 246.928 | 0.534475 | ||||||||
\(463\) | − | 672.785i | − | 1.45310i | −0.687114 | − | 0.726550i | \(-0.741123\pi\) | ||
0.687114 | − | 0.726550i | \(-0.258877\pi\) | |||||||
\(464\) | −278.357 | −0.599907 | ||||||||
\(465\) | 63.2233i | 0.135964i | ||||||||
\(466\) | 28.9915 | 0.0622135 | ||||||||
\(467\) | 436.023i | 0.933669i | 0.884345 | + | 0.466834i | \(0.154606\pi\) | ||||
−0.884345 | + | 0.466834i | \(0.845394\pi\) | |||||||
\(468\) | 49.7016i | 0.106200i | ||||||||
\(469\) | − | 803.201i | − | 1.71258i | ||||||
\(470\) | 1216.84 | 2.58902 | ||||||||
\(471\) | 319.381i | 0.678090i | ||||||||
\(472\) | −77.9749 | + | 44.9960i | −0.165201 | + | 0.0953304i | ||||
\(473\) | −318.470 | −0.673297 | ||||||||
\(474\) | 383.690i | 0.809472i | ||||||||
\(475\) | −141.502 | −0.297899 | ||||||||
\(476\) | −323.942 | −0.680550 | ||||||||
\(477\) | −30.6697 | −0.0642971 | ||||||||
\(478\) | 609.908i | 1.27596i | ||||||||
\(479\) | 620.966 | 1.29638 | 0.648190 | − | 0.761479i | \(-0.275526\pi\) | ||||
0.648190 | + | 0.761479i | \(0.275526\pi\) | |||||||
\(480\) | 423.580i | 0.882458i | ||||||||
\(481\) | −2.53781 | −0.00527611 | ||||||||
\(482\) | 176.269i | 0.365704i | ||||||||
\(483\) | − | 231.959i | − | 0.480246i | ||||||
\(484\) | −291.903 | −0.603106 | ||||||||
\(485\) | − | 966.808i | − | 1.99342i | ||||||
\(486\) | − | 42.5214i | − | 0.0874926i | ||||||
\(487\) | 683.788 | 1.40408 | 0.702041 | − | 0.712136i | \(-0.252272\pi\) | ||||
0.702041 | + | 0.712136i | \(0.252272\pi\) | |||||||
\(488\) | 63.4157 | 0.129950 | ||||||||
\(489\) | −15.5208 | −0.0317400 | ||||||||
\(490\) | 413.771i | 0.844432i | ||||||||
\(491\) | 650.610 | 1.32507 | 0.662536 | − | 0.749030i | \(-0.269480\pi\) | ||||
0.662536 | + | 0.749030i | \(0.269480\pi\) | |||||||
\(492\) | 55.4860 | 0.112776 | ||||||||
\(493\) | 168.225 | 0.341226 | ||||||||
\(494\) | −242.538 | −0.490967 | ||||||||
\(495\) | 103.100i | 0.208284i | ||||||||
\(496\) | 114.482i | 0.230811i | ||||||||
\(497\) | 815.293 | 1.64043 | ||||||||
\(498\) | −13.8050 | −0.0277208 | ||||||||
\(499\) | −503.786 | −1.00959 | −0.504796 | − | 0.863239i | \(-0.668432\pi\) | ||||
−0.504796 | + | 0.863239i | \(0.668432\pi\) | |||||||
\(500\) | 340.908 | 0.681816 | ||||||||
\(501\) | 248.265 | 0.495539 | ||||||||
\(502\) | − | 388.410i | − | 0.773725i | ||||||
\(503\) | 622.714i | 1.23800i | 0.785391 | + | 0.619000i | \(0.212462\pi\) | ||||
−0.785391 | + | 0.619000i | \(0.787538\pi\) | |||||||
\(504\) | 39.7861i | 0.0789407i | ||||||||
\(505\) | − | 36.7848i | − | 0.0728412i | ||||||
\(506\) | − | 252.739i | − | 0.499485i | ||||||
\(507\) | −252.557 | −0.498140 | ||||||||
\(508\) | 709.335 | 1.39633 | ||||||||
\(509\) | 338.691i | 0.665405i | 0.943032 | + | 0.332702i | \(0.107960\pi\) | ||||
−0.943032 | + | 0.332702i | \(0.892040\pi\) | |||||||
\(510\) | − | 292.504i | − | 0.573536i | ||||||
\(511\) | − | 764.990i | − | 1.49704i | ||||||
\(512\) | 657.600i | 1.28438i | ||||||||
\(513\) | 95.9497 | 0.187036 | ||||||||
\(514\) | 36.2041i | 0.0704360i | ||||||||
\(515\) | 1011.41i | 1.96389i | ||||||||
\(516\) | 315.612i | 0.611651i | ||||||||
\(517\) | 469.366 | 0.907864 | ||||||||
\(518\) | 12.4952 | 0.0241220 | ||||||||
\(519\) | − | 99.5032i | − | 0.191721i | ||||||
\(520\) | 41.9913 | 0.0807524 | ||||||||
\(521\) | 144.363 | 0.277088 | 0.138544 | − | 0.990356i | \(-0.455758\pi\) | ||||
0.138544 | + | 0.990356i | \(0.455758\pi\) | |||||||
\(522\) | 127.080i | 0.243448i | ||||||||
\(523\) | −81.3990 | −0.155639 | −0.0778193 | − | 0.996967i | \(-0.524796\pi\) | ||||
−0.0778193 | + | 0.996967i | \(0.524796\pi\) | |||||||
\(524\) | − | 524.966i | − | 1.00184i | ||||||
\(525\) | −115.360 | −0.219733 | ||||||||
\(526\) | − | 147.347i | − | 0.280128i | ||||||
\(527\) | − | 69.1873i | − | 0.131285i | ||||||
\(528\) | 186.690i | 0.353580i | ||||||||
\(529\) | 291.582 | 0.551194 | ||||||||
\(530\) | − | 159.375i | − | 0.300708i | ||||||
\(531\) | 88.4663 | + | 153.306i | 0.166603 | + | 0.288712i | ||||
\(532\) | 552.193 | 1.03796 | ||||||||
\(533\) | − | 44.8333i | − | 0.0841150i | ||||||
\(534\) | −797.127 | −1.49275 | ||||||||
\(535\) | −1049.15 | −1.96103 | ||||||||
\(536\) | 141.009 | 0.263077 | ||||||||
\(537\) | − | 156.206i | − | 0.290887i | ||||||
\(538\) | −1016.69 | −1.88975 | ||||||||
\(539\) | 159.602i | 0.296108i | ||||||||
\(540\) | 102.175 | 0.189214 | ||||||||
\(541\) | 52.0841i | 0.0962738i | 0.998841 | + | 0.0481369i | \(0.0153284\pi\) | ||||
−0.998841 | + | 0.0481369i | \(0.984672\pi\) | |||||||
\(542\) | 1449.41i | 2.67420i | ||||||||
\(543\) | −214.668 | −0.395338 | ||||||||
\(544\) | − | 463.537i | − | 0.852091i | ||||||
\(545\) | − | 601.854i | − | 1.10432i | ||||||
\(546\) | −197.730 | −0.362142 | ||||||||
\(547\) | 477.454 | 0.872859 | 0.436429 | − | 0.899738i | \(-0.356243\pi\) | ||||
0.436429 | + | 0.899738i | \(0.356243\pi\) | |||||||
\(548\) | −665.212 | −1.21389 | ||||||||
\(549\) | − | 124.681i | − | 0.227106i | ||||||
\(550\) | −125.694 | −0.228535 | ||||||||
\(551\) | −286.756 | −0.520429 | ||||||||
\(552\) | 40.7225 | 0.0737727 | ||||||||
\(553\) | −705.844 | −1.27639 | ||||||||
\(554\) | 373.456i | 0.674109i | ||||||||
\(555\) | 5.21715i | 0.00940028i | ||||||||
\(556\) | −594.710 | −1.06962 | ||||||||
\(557\) | 313.535 | 0.562899 | 0.281449 | − | 0.959576i | \(-0.409185\pi\) | ||||
0.281449 | + | 0.959576i | \(0.409185\pi\) | |||||||
\(558\) | 52.2654 | 0.0936655 | ||||||||
\(559\) | 255.018 | 0.456204 | ||||||||
\(560\) | −890.373 | −1.58995 | ||||||||
\(561\) | − | 112.826i | − | 0.201116i | ||||||
\(562\) | − | 508.270i | − | 0.904395i | ||||||
\(563\) | 49.8387i | 0.0885234i | 0.999020 | + | 0.0442617i | \(0.0140935\pi\) | ||||
−0.999020 | + | 0.0442617i | \(0.985906\pi\) | |||||||
\(564\) | − | 465.154i | − | 0.824741i | ||||||
\(565\) | 575.611i | 1.01878i | ||||||||
\(566\) | −1009.37 | −1.78334 | ||||||||
\(567\) | 78.2232 | 0.137960 | ||||||||
\(568\) | 143.132i | 0.251993i | ||||||||
\(569\) | 197.517i | 0.347131i | 0.984822 | + | 0.173565i | \(0.0555288\pi\) | ||||
−0.984822 | + | 0.173565i | \(0.944471\pi\) | |||||||
\(570\) | 498.603i | 0.874742i | ||||||||
\(571\) | − | 18.9985i | − | 0.0332723i | −0.999862 | − | 0.0166362i | \(-0.994704\pi\) | ||
0.999862 | − | 0.0166362i | \(-0.00529570\pi\) | |||||||
\(572\) | −99.6233 | −0.174167 | ||||||||
\(573\) | − | 261.267i | − | 0.455963i | ||||||
\(574\) | 220.742i | 0.384567i | ||||||||
\(575\) | 118.075i | 0.205348i | ||||||||
\(576\) | 135.069 | 0.234495 | ||||||||
\(577\) | −248.509 | −0.430691 | −0.215346 | − | 0.976538i | \(-0.569088\pi\) | ||||
−0.215346 | + | 0.976538i | \(0.569088\pi\) | |||||||
\(578\) | − | 468.223i | − | 0.810075i | ||||||
\(579\) | 146.914 | 0.253737 | ||||||||
\(580\) | −305.362 | −0.526487 | ||||||||
\(581\) | − | 25.3959i | − | 0.0437107i | ||||||
\(582\) | −799.239 | −1.37326 | ||||||||
\(583\) | − | 61.4752i | − | 0.105446i | ||||||
\(584\) | 134.301 | 0.229967 | ||||||||
\(585\) | − | 82.5588i | − | 0.141126i | ||||||
\(586\) | 815.649i | 1.39189i | ||||||||
\(587\) | 736.598i | 1.25485i | 0.778676 | + | 0.627426i | \(0.215892\pi\) | ||||
−0.778676 | + | 0.627426i | \(0.784108\pi\) | |||||||
\(588\) | 158.170 | 0.268997 | ||||||||
\(589\) | 117.937i | 0.200232i | ||||||||
\(590\) | −796.655 | + | 459.716i | −1.35026 | + | 0.779179i | ||||
\(591\) | 330.338 | 0.558948 | ||||||||
\(592\) | 9.44703i | 0.0159578i | ||||||||
\(593\) | −83.9607 | −0.141586 | −0.0707932 | − | 0.997491i | \(-0.522553\pi\) | ||||
−0.0707932 | + | 0.997491i | \(0.522553\pi\) | |||||||
\(594\) | 85.2310 | 0.143487 | ||||||||
\(595\) | 538.096 | 0.904362 | ||||||||
\(596\) | − | 624.869i | − | 1.04844i | ||||||
\(597\) | 346.503 | 0.580407 | ||||||||
\(598\) | 202.384i | 0.338434i | ||||||||
\(599\) | −93.6816 | −0.156397 | −0.0781983 | − | 0.996938i | \(-0.524917\pi\) | ||||
−0.0781983 | + | 0.996938i | \(0.524917\pi\) | |||||||
\(600\) | − | 20.2525i | − | 0.0337541i | ||||||
\(601\) | 931.300i | 1.54958i | 0.632216 | + | 0.774792i | \(0.282146\pi\) | ||||
−0.632216 | + | 0.774792i | \(0.717854\pi\) | |||||||
\(602\) | −1255.61 | −2.08573 | ||||||||
\(603\) | − | 277.238i | − | 0.459764i | ||||||
\(604\) | 4.16950i | 0.00690315i | ||||||||
\(605\) | 484.877 | 0.801449 | ||||||||
\(606\) | −30.4092 | −0.0501802 | ||||||||
\(607\) | −217.894 | −0.358969 | −0.179484 | − | 0.983761i | \(-0.557443\pi\) | ||||
−0.179484 | + | 0.983761i | \(0.557443\pi\) | |||||||
\(608\) | 790.147i | 1.29958i | ||||||||
\(609\) | −233.779 | −0.383873 | ||||||||
\(610\) | 647.907 | 1.06214 | ||||||||
\(611\) | −375.849 | −0.615138 | ||||||||
\(612\) | −111.814 | −0.182702 | ||||||||
\(613\) | 46.8619i | 0.0764468i | 0.999269 | + | 0.0382234i | \(0.0121698\pi\) | ||||
−0.999269 | + | 0.0382234i | \(0.987830\pi\) | |||||||
\(614\) | 75.4263i | 0.122844i | ||||||||
\(615\) | −92.1670 | −0.149865 | ||||||||
\(616\) | −79.7483 | −0.129462 | ||||||||
\(617\) | 994.661 | 1.61209 | 0.806046 | − | 0.591853i | \(-0.201603\pi\) | ||||
0.806046 | + | 0.591853i | \(0.201603\pi\) | |||||||
\(618\) | 836.107 | 1.35292 | ||||||||
\(619\) | 801.130 | 1.29423 | 0.647116 | − | 0.762391i | \(-0.275975\pi\) | ||||
0.647116 | + | 0.762391i | \(0.275975\pi\) | |||||||
\(620\) | 125.589i | 0.202563i | ||||||||
\(621\) | − | 80.0643i | − | 0.128928i | ||||||
\(622\) | − | 994.831i | − | 1.59941i | ||||||
\(623\) | − | 1466.41i | − | 2.35379i | ||||||
\(624\) | − | 149.494i | − | 0.239574i | ||||||
\(625\) | −757.854 | −1.21257 | ||||||||
\(626\) | −476.385 | −0.760999 | ||||||||
\(627\) | 192.324i | 0.306737i | ||||||||
\(628\) | 634.430i | 1.01024i | ||||||||
\(629\) | − | 5.70930i | − | 0.00907679i | ||||||
\(630\) | 406.487i | 0.645218i | ||||||||
\(631\) | 891.594 | 1.41299 | 0.706493 | − | 0.707720i | \(-0.250276\pi\) | ||||
0.706493 | + | 0.707720i | \(0.250276\pi\) | |||||||
\(632\) | − | 123.917i | − | 0.196072i | ||||||
\(633\) | 713.839i | 1.12771i | ||||||||
\(634\) | − | 1377.79i | − | 2.17317i | ||||||
\(635\) | −1178.27 | −1.85554 | ||||||||
\(636\) | −60.9235 | −0.0957917 | ||||||||
\(637\) | − | 127.803i | − | 0.200633i | ||||||
\(638\) | −254.722 | −0.399251 | ||||||||
\(639\) | 281.411 | 0.440394 | ||||||||
\(640\) | − | 276.330i | − | 0.431765i | ||||||
\(641\) | −790.983 | −1.23398 | −0.616991 | − | 0.786970i | \(-0.711649\pi\) | ||||
−0.616991 | + | 0.786970i | \(0.711649\pi\) | |||||||
\(642\) | 867.309i | 1.35095i | ||||||||
\(643\) | −348.723 | −0.542337 | −0.271169 | − | 0.962532i | \(-0.587410\pi\) | ||||
−0.271169 | + | 0.962532i | \(0.587410\pi\) | |||||||
\(644\) | − | 460.772i | − | 0.715485i | ||||||
\(645\) | − | 524.259i | − | 0.812804i | ||||||
\(646\) | − | 545.637i | − | 0.844639i | ||||||
\(647\) | 746.195 | 1.15332 | 0.576658 | − | 0.816986i | \(-0.304357\pi\) | ||||
0.576658 | + | 0.816986i | \(0.304357\pi\) | |||||||
\(648\) | 13.7328i | 0.0211926i | ||||||||
\(649\) | −307.290 | + | 177.324i | −0.473483 | + | 0.273227i | ||||
\(650\) | 100.651 | 0.154848 | ||||||||
\(651\) | 96.1484i | 0.147693i | ||||||||
\(652\) | −30.8312 | −0.0472871 | ||||||||
\(653\) | −945.003 | −1.44717 | −0.723586 | − | 0.690234i | \(-0.757507\pi\) | ||||
−0.723586 | + | 0.690234i | \(0.757507\pi\) | |||||||
\(654\) | −497.540 | −0.760765 | ||||||||
\(655\) | 872.014i | 1.33132i | ||||||||
\(656\) | −166.893 | −0.254409 | ||||||||
\(657\) | − | 264.048i | − | 0.401900i | ||||||
\(658\) | 1850.54 | 2.81237 | ||||||||
\(659\) | − | 907.745i | − | 1.37746i | −0.725018 | − | 0.688729i | \(-0.758169\pi\) | ||
0.725018 | − | 0.688729i | \(-0.241831\pi\) | |||||||
\(660\) | 204.803i | 0.310307i | ||||||||
\(661\) | −1024.26 | −1.54957 | −0.774783 | − | 0.632227i | \(-0.782141\pi\) | ||||
−0.774783 | + | 0.632227i | \(0.782141\pi\) | |||||||
\(662\) | 10.8922i | 0.0164535i | ||||||||
\(663\) | 90.3467i | 0.136270i | ||||||||
\(664\) | 4.45849 | 0.00671459 | ||||||||
\(665\) | −917.240 | −1.37931 | ||||||||
\(666\) | 4.31291 | 0.00647584 | ||||||||
\(667\) | 239.281i | 0.358742i | ||||||||
\(668\) | 493.163 | 0.738268 | ||||||||
\(669\) | 38.9420 | 0.0582093 | ||||||||
\(670\) | 1440.67 | 2.15025 | ||||||||
\(671\) | 249.914 | 0.372451 | ||||||||
\(672\) | 644.170i | 0.958586i | ||||||||
\(673\) | 629.364i | 0.935163i | 0.883950 | + | 0.467581i | \(0.154874\pi\) | ||||
−0.883950 | + | 0.467581i | \(0.845126\pi\) | |||||||
\(674\) | 947.997 | 1.40652 | ||||||||
\(675\) | −39.8183 | −0.0589900 | ||||||||
\(676\) | −501.689 | −0.742144 | ||||||||
\(677\) | 671.976 | 0.992579 | 0.496289 | − | 0.868157i | \(-0.334695\pi\) | ||||
0.496289 | + | 0.868157i | \(0.334695\pi\) | |||||||
\(678\) | 475.845 | 0.701837 | ||||||||
\(679\) | − | 1470.30i | − | 2.16539i | ||||||
\(680\) | 94.4677i | 0.138923i | ||||||||
\(681\) | 479.513i | 0.704130i | ||||||||
\(682\) | 104.762i | 0.153610i | ||||||||
\(683\) | 683.994i | 1.00145i | 0.865605 | + | 0.500727i | \(0.166934\pi\) | ||||
−0.865605 | + | 0.500727i | \(0.833066\pi\) | |||||||
\(684\) | 190.598 | 0.278652 | ||||||||
\(685\) | 1104.97 | 1.61310 | ||||||||
\(686\) | − | 532.446i | − | 0.776160i | ||||||
\(687\) | − | 278.731i | − | 0.405722i | ||||||
\(688\) | − | 949.308i | − | 1.37981i | ||||||
\(689\) | 49.2269i | 0.0714468i | ||||||||
\(690\) | 416.055 | 0.602978 | ||||||||
\(691\) | − | 69.2046i | − | 0.100151i | −0.998745 | − | 0.0500757i | \(-0.984054\pi\) | ||
0.998745 | − | 0.0500757i | \(-0.0159463\pi\) | |||||||
\(692\) | − | 197.657i | − | 0.285631i | ||||||
\(693\) | 156.793i | 0.226252i | ||||||||
\(694\) | −1602.36 | −2.30888 | ||||||||
\(695\) | 987.865 | 1.42139 | ||||||||
\(696\) | − | 41.0420i | − | 0.0589685i | ||||||
\(697\) | 100.861 | 0.144708 | ||||||||
\(698\) | −1078.67 | −1.54538 | ||||||||
\(699\) | 18.4088i | 0.0263360i | ||||||||
\(700\) | −229.155 | −0.327364 | ||||||||
\(701\) | 1173.53i | 1.67408i | 0.547143 | + | 0.837039i | \(0.315715\pi\) | ||||
−0.547143 | + | 0.837039i | \(0.684285\pi\) | |||||||
\(702\) | −68.2496 | −0.0972216 | ||||||||
\(703\) | 9.73209i | 0.0138437i | ||||||||
\(704\) | 270.736i | 0.384568i | ||||||||
\(705\) | 772.661i | 1.09597i | ||||||||
\(706\) | 550.689 | 0.780012 | ||||||||
\(707\) | − | 55.9414i | − | 0.0791250i | ||||||
\(708\) | 175.733 | + | 304.533i | 0.248210 | + | 0.430131i | ||||
\(709\) | −291.385 | −0.410980 | −0.205490 | − | 0.978659i | \(-0.565879\pi\) | ||||
−0.205490 | + | 0.978659i | \(0.565879\pi\) | |||||||
\(710\) | 1462.36i | 2.05966i | ||||||||
\(711\) | −243.633 | −0.342663 | ||||||||
\(712\) | 257.442 | 0.361576 | ||||||||
\(713\) | 98.4114 | 0.138024 | ||||||||
\(714\) | − | 444.832i | − | 0.623014i | ||||||
\(715\) | 165.483 | 0.231445 | ||||||||
\(716\) | − | 310.294i | − | 0.433371i | ||||||
\(717\) | −387.276 | −0.540134 | ||||||||
\(718\) | − | 1444.48i | − | 2.01182i | ||||||
\(719\) | − | 1045.70i | − | 1.45438i | −0.686434 | − | 0.727192i | \(-0.740825\pi\) | ||
0.686434 | − | 0.727192i | \(-0.259175\pi\) | |||||||
\(720\) | −307.326 | −0.426842 | ||||||||
\(721\) | 1538.12i | 2.13331i | ||||||||
\(722\) | − | 54.6221i | − | 0.0756538i | ||||||
\(723\) | −111.926 | −0.154808 | ||||||||
\(724\) | −426.426 | −0.588986 | ||||||||
\(725\) | 119.001 | 0.164140 | ||||||||
\(726\) | − | 400.837i | − | 0.552118i | ||||||
\(727\) | −96.8300 | −0.133191 | −0.0665956 | − | 0.997780i | \(-0.521214\pi\) | ||||
−0.0665956 | + | 0.997780i | \(0.521214\pi\) | |||||||
\(728\) | 63.8593 | 0.0877188 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 1372.13 | 1.87963 | ||||||||
\(731\) | 573.713i | 0.784833i | ||||||||
\(732\) | − | 247.672i | − | 0.338349i | ||||||
\(733\) | 63.9954 | 0.0873061 | 0.0436531 | − | 0.999047i | \(-0.486100\pi\) | ||||
0.0436531 | + | 0.999047i | \(0.486100\pi\) | |||||||
\(734\) | 980.840 | 1.33629 | ||||||||
\(735\) | −262.734 | −0.357462 | ||||||||
\(736\) | 659.332 | 0.895831 | ||||||||
\(737\) | 555.702 | 0.754006 | ||||||||
\(738\) | 76.1925i | 0.103242i | ||||||||
\(739\) | 234.644i | 0.317515i | 0.987318 | + | 0.158758i | \(0.0507489\pi\) | ||||
−0.987318 | + | 0.158758i | \(0.949251\pi\) | |||||||
\(740\) | 10.3636i | 0.0140048i | ||||||||
\(741\) | − | 154.005i | − | 0.207835i | ||||||
\(742\) | − | 242.374i | − | 0.326650i | ||||||
\(743\) | 724.236 | 0.974746 | 0.487373 | − | 0.873194i | \(-0.337955\pi\) | ||||
0.487373 | + | 0.873194i | \(0.337955\pi\) | |||||||
\(744\) | −16.8797 | −0.0226878 | ||||||||
\(745\) | 1037.96i | 1.39324i | ||||||||
\(746\) | − | 1199.33i | − | 1.60769i | ||||||
\(747\) | − | 8.76580i | − | 0.0117347i | ||||||
\(748\) | − | 224.122i | − | 0.299629i | ||||||
\(749\) | −1595.52 | −2.13020 | ||||||||
\(750\) | 468.130i | 0.624173i | ||||||||
\(751\) | − | 539.064i | − | 0.717795i | −0.933377 | − | 0.358897i | \(-0.883153\pi\) | ||
0.933377 | − | 0.358897i | \(-0.116847\pi\) | |||||||
\(752\) | 1399.11i | 1.86051i | ||||||||
\(753\) | 246.630 | 0.327531 | ||||||||
\(754\) | 203.971 | 0.270519 | ||||||||
\(755\) | − | 6.92591i | − | 0.00917339i | ||||||
\(756\) | 155.386 | 0.205537 | ||||||||
\(757\) | 669.143 | 0.883941 | 0.441970 | − | 0.897030i | \(-0.354280\pi\) | ||||
0.441970 | + | 0.897030i | \(0.354280\pi\) | |||||||
\(758\) | − | 1583.26i | − | 2.08873i | ||||||
\(759\) | 160.483 | 0.211440 | ||||||||
\(760\) | − | 161.030i | − | 0.211882i | ||||||
\(761\) | 896.609 | 1.17820 | 0.589099 | − | 0.808061i | \(-0.299483\pi\) | ||||
0.589099 | + | 0.808061i | \(0.299483\pi\) | |||||||
\(762\) | 974.049i | 1.27828i | ||||||||
\(763\) | − | 915.285i | − | 1.19959i | ||||||
\(764\) | − | 518.990i | − | 0.679307i | ||||||
\(765\) | 185.732 | 0.242787 | ||||||||
\(766\) | − | 936.477i | − | 1.22255i | ||||||
\(767\) | 246.066 | − | 141.994i | 0.320816 | − | 0.185129i | ||||
\(768\) | −540.364 | −0.703599 | ||||||||
\(769\) | 294.155i | 0.382516i | 0.981540 | + | 0.191258i | \(0.0612567\pi\) | ||||
−0.981540 | + | 0.191258i | \(0.938743\pi\) | |||||||
\(770\) | −814.774 | −1.05815 | ||||||||
\(771\) | −22.9887 | −0.0298167 | ||||||||
\(772\) | 291.836 | 0.378025 | ||||||||
\(773\) | − | 118.806i | − | 0.153694i | −0.997043 | − | 0.0768471i | \(-0.975515\pi\) | ||
0.997043 | − | 0.0768471i | \(-0.0244853\pi\) | |||||||
\(774\) | −433.394 | −0.559940 | ||||||||
\(775\) | − | 48.9428i | − | 0.0631520i | ||||||
\(776\) | 258.124 | 0.332634 | ||||||||
\(777\) | 7.93412i | 0.0102112i | ||||||||
\(778\) | 827.668i | 1.06384i | ||||||||
\(779\) | −171.929 | −0.220704 | ||||||||
\(780\) | − | 163.998i | − | 0.210254i | ||||||
\(781\) | 564.068i | 0.722239i | ||||||||
\(782\) | −455.302 | −0.582228 | ||||||||
\(783\) | −80.6925 | −0.103056 | ||||||||
\(784\) | −475.749 | −0.606823 | ||||||||
\(785\) | − | 1053.84i | − | 1.34248i | ||||||
\(786\) | 720.876 | 0.917144 | ||||||||
\(787\) | 67.0954 | 0.0852546 | 0.0426273 | − | 0.999091i | \(-0.486427\pi\) | ||||
0.0426273 | + | 0.999091i | \(0.486427\pi\) | |||||||
\(788\) | 656.197 | 0.832737 | ||||||||
\(789\) | 93.5618 | 0.118583 | ||||||||
\(790\) | − | 1266.04i | − | 1.60258i | ||||||
\(791\) | 875.375i | 1.10667i | ||||||||
\(792\) | −27.5264 | −0.0347556 | ||||||||
\(793\) | −200.121 | −0.252360 | ||||||||
\(794\) | −434.214 | −0.546869 | ||||||||
\(795\) | 101.199 | 0.127295 | ||||||||
\(796\) | 688.307 | 0.864707 | ||||||||
\(797\) | 390.810i | 0.490352i | 0.969479 | + | 0.245176i | \(0.0788457\pi\) | ||||
−0.969479 | + | 0.245176i | \(0.921154\pi\) | |||||||
\(798\) | 758.263i | 0.950204i | ||||||||
\(799\) | − | 845.548i | − | 1.05826i | ||||||
\(800\) | − | 327.904i | − | 0.409880i | ||||||
\(801\) | − | 506.155i | − | 0.631904i | ||||||
\(802\) | 1149.18 | 1.43290 | ||||||||
\(803\) | 529.265 | 0.659110 | ||||||||
\(804\) | − | 550.716i | − | 0.684970i | ||||||
\(805\) | 765.383i | 0.950786i | ||||||||
\(806\) | − | 83.8893i | − | 0.104081i | ||||||
\(807\) | − | 645.571i | − | 0.799964i | ||||||
\(808\) | 9.82103 | 0.0121547 | ||||||||
\(809\) | − | 296.341i | − | 0.366305i | −0.983084 | − | 0.183153i | \(-0.941370\pi\) | ||
0.983084 | − | 0.183153i | \(-0.0586302\pi\) | |||||||
\(810\) | 140.306i | 0.173217i | ||||||||
\(811\) | 1396.97i | 1.72253i | 0.508158 | + | 0.861264i | \(0.330327\pi\) | ||||
−0.508158 | + | 0.861264i | \(0.669673\pi\) | |||||||
\(812\) | −464.387 | −0.571906 | ||||||||
\(813\) | −920.342 | −1.13203 | ||||||||
\(814\) | 8.64491i | 0.0106203i | ||||||||
\(815\) | 51.2133 | 0.0628384 | ||||||||
\(816\) | 336.317 | 0.412153 | ||||||||
\(817\) | − | 977.954i | − | 1.19701i | ||||||
\(818\) | −1806.32 | −2.20821 | ||||||||
\(819\) | − | 125.553i | − | 0.153301i | ||||||
\(820\) | −183.084 | −0.223273 | ||||||||
\(821\) | 62.3621i | 0.0759587i | 0.999279 | + | 0.0379793i | \(0.0120921\pi\) | ||||
−0.999279 | + | 0.0379793i | \(0.987908\pi\) | |||||||
\(822\) | − | 913.459i | − | 1.11126i | ||||||
\(823\) | − | 1509.54i | − | 1.83419i | −0.398667 | − | 0.917096i | \(-0.630527\pi\) | ||
0.398667 | − | 0.917096i | \(-0.369473\pi\) | |||||||
\(824\) | −270.031 | −0.327708 | ||||||||
\(825\) | − | 79.8128i | − | 0.0967427i | ||||||
\(826\) | −1211.53 | + | 699.124i | −1.46675 | + | 0.846397i | ||||
\(827\) | 427.575 | 0.517019 | 0.258509 | − | 0.966009i | \(-0.416769\pi\) | ||||
0.258509 | + | 0.966009i | \(0.416769\pi\) | |||||||
\(828\) | − | 159.043i | − | 0.192081i | ||||||
\(829\) | −1352.03 | −1.63092 | −0.815459 | − | 0.578814i | \(-0.803516\pi\) | ||||
−0.815459 | + | 0.578814i | \(0.803516\pi\) | |||||||
\(830\) | 45.5515 | 0.0548814 | ||||||||
\(831\) | −237.135 | −0.285361 | ||||||||
\(832\) | − | 216.794i | − | 0.260570i | ||||||
\(833\) | 287.519 | 0.345160 | ||||||||
\(834\) | − | 816.647i | − | 0.979193i | ||||||
\(835\) | −819.187 | −0.981062 | ||||||||
\(836\) | 382.040i | 0.456985i | ||||||||
\(837\) | 33.1872i | 0.0396501i | ||||||||
\(838\) | −922.134 | −1.10040 | ||||||||
\(839\) | − | 849.147i | − | 1.01209i | −0.862506 | − | 0.506047i | \(-0.831106\pi\) | ||
0.862506 | − | 0.506047i | \(-0.168894\pi\) | |||||||
\(840\) | − | 131.280i | − | 0.156286i | ||||||
\(841\) | −599.841 | −0.713248 | ||||||||
\(842\) | −276.492 | −0.328375 | ||||||||
\(843\) | 322.739 | 0.382845 | ||||||||
\(844\) | 1418.00i | 1.68009i | ||||||||
\(845\) | 833.350 | 0.986212 | ||||||||
\(846\) | 638.742 | 0.755015 | ||||||||
\(847\) | 737.389 | 0.870589 | ||||||||
\(848\) | 183.248 | 0.216094 | ||||||||
\(849\) | − | 640.925i | − | 0.754917i | ||||||
\(850\) | 226.435i | 0.266394i | ||||||||
\(851\) | 8.12086 | 0.00954273 | ||||||||
\(852\) | 559.007 | 0.656111 | ||||||||
\(853\) | −529.505 | −0.620757 | −0.310378 | − | 0.950613i | \(-0.600456\pi\) | ||||
−0.310378 | + | 0.950613i | \(0.600456\pi\) | |||||||
\(854\) | 985.321 | 1.15377 | ||||||||
\(855\) | −316.600 | −0.370292 | ||||||||
\(856\) | − | 280.108i | − | 0.327229i | ||||||
\(857\) | 437.967i | 0.511047i | 0.966803 | + | 0.255523i | \(0.0822478\pi\) | ||||
−0.966803 | + | 0.255523i | \(0.917752\pi\) | |||||||
\(858\) | − | 136.801i | − | 0.159442i | ||||||
\(859\) | 1046.52i | 1.21831i | 0.793053 | + | 0.609153i | \(0.208490\pi\) | ||||
−0.793053 | + | 0.609153i | \(0.791510\pi\) | |||||||
\(860\) | − | 1041.41i | − | 1.21094i | ||||||
\(861\) | −140.165 | −0.162794 | ||||||||
\(862\) | 130.014 | 0.150828 | ||||||||
\(863\) | 560.329i | 0.649281i | 0.945838 | + | 0.324640i | \(0.105243\pi\) | ||||
−0.945838 | + | 0.324640i | \(0.894757\pi\) | |||||||
\(864\) | 222.346i | 0.257344i | ||||||||
\(865\) | 328.325i | 0.379567i | ||||||||
\(866\) | − | 471.613i | − | 0.544587i | ||||||
\(867\) | 297.310 | 0.342918 | ||||||||
\(868\) | 190.993i | 0.220038i | ||||||||
\(869\) | − | 488.345i | − | 0.561962i | ||||||
\(870\) | − | 419.319i | − | 0.481976i | ||||||
\(871\) | −444.984 | −0.510889 | ||||||||
\(872\) | 160.687 | 0.184274 | ||||||||
\(873\) | − | 507.497i | − | 0.581325i | ||||||
\(874\) | 776.110 | 0.887997 | ||||||||
\(875\) | −861.182 | −0.984207 | ||||||||
\(876\) | − | 524.516i | − | 0.598762i | ||||||
\(877\) | −1008.15 | −1.14954 | −0.574771 | − | 0.818314i | \(-0.694909\pi\) | ||||
−0.574771 | + | 0.818314i | \(0.694909\pi\) | |||||||
\(878\) | 1047.89i | 1.19350i | ||||||||
\(879\) | −517.916 | −0.589211 | ||||||||
\(880\) | − | 616.013i | − | 0.700015i | ||||||
\(881\) | − | 498.377i | − | 0.565695i | −0.959165 | − | 0.282847i | \(-0.908721\pi\) | ||
0.959165 | − | 0.282847i | \(-0.0912790\pi\) | |||||||
\(882\) | 217.197i | 0.246255i | ||||||||
\(883\) | −1428.37 | −1.61763 | −0.808817 | − | 0.588061i | \(-0.799891\pi\) | ||||
−0.808817 | + | 0.588061i | \(0.799891\pi\) | |||||||
\(884\) | 179.468i | 0.203018i | ||||||||
\(885\) | −291.908 | − | 505.856i | −0.329839 | − | 0.571588i | ||||
\(886\) | 469.723 | 0.530161 | ||||||||
\(887\) | − | 886.165i | − | 0.999058i | −0.866297 | − | 0.499529i | \(-0.833506\pi\) | ||
0.866297 | − | 0.499529i | \(-0.166494\pi\) | |||||||
\(888\) | −1.39291 | −0.00156859 | ||||||||
\(889\) | −1791.88 | −2.01561 | ||||||||
\(890\) | 2630.24 | 2.95532 | ||||||||
\(891\) | 54.1195i | 0.0607402i | ||||||||
\(892\) | 77.3559 | 0.0867219 | ||||||||
\(893\) | 1441.32i | 1.61402i | ||||||||
\(894\) | 858.061 | 0.959799 | ||||||||
\(895\) | 515.425i | 0.575894i | ||||||||
\(896\) | − | 420.235i | − | 0.469013i | ||||||
\(897\) | −128.508 | −0.143265 | ||||||||
\(898\) | 1672.95i | 1.86298i | ||||||||
\(899\) | − | 99.1836i | − | 0.110327i | ||||||
\(900\) | −79.0965 | −0.0878850 | ||||||||
\(901\) | −110.746 | −0.122914 | ||||||||
\(902\) | −152.722 | −0.169315 | ||||||||
\(903\) | − | 797.280i | − | 0.882923i | ||||||
\(904\) | −153.680 | −0.170000 | ||||||||
\(905\) | 708.330 | 0.782685 | ||||||||
\(906\) | −5.72550 | −0.00631954 | ||||||||
\(907\) | −1277.00 | −1.40794 | −0.703971 | − | 0.710229i | \(-0.748591\pi\) | ||||
−0.703971 | + | 0.710229i | \(0.748591\pi\) | |||||||
\(908\) | 952.522i | 1.04903i | ||||||||
\(909\) | − | 19.3091i | − | 0.0212421i | ||||||
\(910\) | 652.438 | 0.716965 | ||||||||
\(911\) | 12.8533 | 0.0141090 | 0.00705452 | − | 0.999975i | \(-0.497754\pi\) | ||||
0.00705452 | + | 0.999975i | \(0.497754\pi\) | |||||||
\(912\) | −573.288 | −0.628605 | ||||||||
\(913\) | 17.5704 | 0.0192447 | ||||||||
\(914\) | −762.265 | −0.833988 | ||||||||
\(915\) | 411.404i | 0.449622i | ||||||||
\(916\) | − | 553.683i | − | 0.604457i | ||||||
\(917\) | 1326.14i | 1.44617i | ||||||||
\(918\) | − | 153.541i | − | 0.167256i | ||||||
\(919\) | 728.935i | 0.793182i | 0.917995 | + | 0.396591i | \(0.129807\pi\) | ||||
−0.917995 | + | 0.396591i | \(0.870193\pi\) | |||||||
\(920\) | −134.370 | −0.146054 | ||||||||
\(921\) | −47.8938 | −0.0520019 | ||||||||
\(922\) | − | 1514.41i | − | 1.64253i | ||||||
\(923\) | − | 451.684i | − | 0.489365i | ||||||
\(924\) | 311.459i | 0.337077i | ||||||||
\(925\) | − | 4.03873i | − | 0.00436620i | ||||||
\(926\) | 1835.19 | 1.98184 | ||||||||
\(927\) | 530.907i | 0.572715i | ||||||||
\(928\) | − | 664.505i | − | 0.716061i | ||||||
\(929\) | 498.588i | 0.536694i | 0.963322 | + | 0.268347i | \(0.0864773\pi\) | ||||
−0.963322 | + | 0.268347i | \(0.913523\pi\) | |||||||
\(930\) | −172.457 | −0.185438 | ||||||||
\(931\) | −490.105 | −0.526429 | ||||||||
\(932\) | 36.5680i | 0.0392361i | ||||||||
\(933\) | 631.692 | 0.677055 | ||||||||
\(934\) | −1189.36 | −1.27341 | ||||||||
\(935\) | 372.287i | 0.398168i | ||||||||
\(936\) | 22.0420 | 0.0235492 | ||||||||
\(937\) | 12.3168i | 0.0131449i | 0.999978 | + | 0.00657247i | \(0.00209210\pi\) | ||||
−0.999978 | + | 0.00657247i | \(0.997908\pi\) | |||||||
\(938\) | 2190.93 | 2.33575 | ||||||||
\(939\) | − | 302.493i | − | 0.322143i | ||||||
\(940\) | 1534.84i | 1.63281i | ||||||||
\(941\) | 974.832i | 1.03595i | 0.855395 | + | 0.517976i | \(0.173314\pi\) | ||||
−0.855395 | + | 0.517976i | \(0.826686\pi\) | |||||||
\(942\) | −871.190 | −0.924830 | ||||||||
\(943\) | 143.464i | 0.152136i | ||||||||
\(944\) | −528.575 | − | 915.984i | −0.559932 | − | 0.970322i | ||||
\(945\) | −258.109 | −0.273131 | ||||||||
\(946\) | − | 868.705i | − | 0.918293i | ||||||
\(947\) | 247.178 | 0.261012 | 0.130506 | − | 0.991448i | \(-0.458340\pi\) | ||||
0.130506 | + | 0.991448i | \(0.458340\pi\) | |||||||
\(948\) | −483.963 | −0.510509 | ||||||||
\(949\) | −423.815 | −0.446591 | ||||||||
\(950\) | − | 385.981i | − | 0.406296i | ||||||
\(951\) | 874.863 | 0.919940 | ||||||||
\(952\) | 143.664i | 0.150908i | ||||||||
\(953\) | 19.6401 | 0.0206087 | 0.0103043 | − | 0.999947i | \(-0.496720\pi\) | ||||
0.0103043 | + | 0.999947i | \(0.496720\pi\) | |||||||
\(954\) | − | 83.6593i | − | 0.0876932i | ||||||
\(955\) | 862.088i | 0.902710i | ||||||||
\(956\) | −769.300 | −0.804707 | ||||||||
\(957\) | − | 161.742i | − | 0.169010i | ||||||
\(958\) | 1693.84i | 1.76810i | ||||||||
\(959\) | 1680.42 | 1.75226 | ||||||||
\(960\) | −445.680 | −0.464250 | ||||||||
\(961\) | 920.208 | 0.957552 | ||||||||
\(962\) | − | 6.92250i | − | 0.00719594i | ||||||
\(963\) | −550.719 | −0.571879 | ||||||||
\(964\) | −222.335 | −0.230638 | ||||||||
\(965\) | −484.764 | −0.502347 | ||||||||
\(966\) | 632.726 | 0.654996 | ||||||||
\(967\) | − | 1501.84i | − | 1.55309i | −0.630062 | − | 0.776545i | \(-0.716970\pi\) | ||
0.630062 | − | 0.776545i | \(-0.283030\pi\) | |||||||
\(968\) | 129.455i | 0.133735i | ||||||||
\(969\) | 346.466 | 0.357550 | ||||||||
\(970\) | 2637.21 | 2.71877 | ||||||||
\(971\) | −1557.05 | −1.60355 | −0.801776 | − | 0.597624i | \(-0.796111\pi\) | ||||
−0.801776 | + | 0.597624i | \(0.796111\pi\) | |||||||
\(972\) | 53.6338 | 0.0551789 | ||||||||
\(973\) | 1502.32 | 1.54401 | ||||||||
\(974\) | 1865.20i | 1.91499i | ||||||||
\(975\) | 63.9109i | 0.0655496i | ||||||||
\(976\) | 744.955i | 0.763274i | ||||||||
\(977\) | 220.988i | 0.226191i | 0.993584 | + | 0.113095i | \(0.0360766\pi\) | ||||
−0.993584 | + | 0.113095i | \(0.963923\pi\) | |||||||
\(978\) | − | 42.3370i | − | 0.0432893i | ||||||
\(979\) | 1014.55 | 1.03631 | ||||||||
\(980\) | −521.906 | −0.532557 | ||||||||
\(981\) | − | 315.925i | − | 0.322044i | ||||||
\(982\) | 1774.70i | 1.80723i | ||||||||
\(983\) | 9.44684i | 0.00961021i | 0.999988 | + | 0.00480510i | \(0.00152952\pi\) | ||||
−0.999988 | + | 0.00480510i | \(0.998470\pi\) | |||||||
\(984\) | − | 24.6073i | − | 0.0250074i | ||||||
\(985\) | −1090.00 | −1.10660 | ||||||||
\(986\) | 458.874i | 0.465390i | ||||||||
\(987\) | 1175.04i | 1.19052i | ||||||||
\(988\) | − | 305.922i | − | 0.309638i | ||||||
\(989\) | −816.045 | −0.825121 | ||||||||
\(990\) | −281.232 | −0.284073 | ||||||||
\(991\) | − | 86.9654i | − | 0.0877552i | −0.999037 | − | 0.0438776i | \(-0.986029\pi\) | ||
0.999037 | − | 0.0438776i | \(-0.0139712\pi\) | |||||||
\(992\) | −273.297 | −0.275501 | ||||||||
\(993\) | −6.91626 | −0.00696502 | ||||||||
\(994\) | 2223.91i | 2.23734i | ||||||||
\(995\) | −1143.34 | −1.14908 | ||||||||
\(996\) | − | 17.4127i | − | 0.0174827i | ||||||
\(997\) | 728.589 | 0.730781 | 0.365390 | − | 0.930854i | \(-0.380935\pi\) | ||||
0.365390 | + | 0.930854i | \(0.380935\pi\) | |||||||
\(998\) | − | 1374.20i | − | 1.37696i | ||||||
\(999\) | 2.73859i | 0.00274133i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.3.c.a.58.16 | yes | 20 | |
3.2 | odd | 2 | 531.3.c.c.235.5 | 20 | |||
59.58 | odd | 2 | inner | 177.3.c.a.58.5 | ✓ | 20 | |
177.176 | even | 2 | 531.3.c.c.235.16 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.3.c.a.58.5 | ✓ | 20 | 59.58 | odd | 2 | inner | |
177.3.c.a.58.16 | yes | 20 | 1.1 | even | 1 | trivial | |
531.3.c.c.235.5 | 20 | 3.2 | odd | 2 | |||
531.3.c.c.235.16 | 20 | 177.176 | even | 2 |