Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,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, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
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: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.13 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.28 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.44422i | − | 0.861054i | −0.902578 | − | 0.430527i | \(-0.858328\pi\) | ||
0.902578 | − | 0.430527i | \(-0.141672\pi\) | |||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | 4.13738 | 0.258586 | ||||||||
\(5\) | −16.2205 | −0.648821 | −0.324411 | − | 0.945916i | \(-0.605166\pi\) | ||||
−0.324411 | + | 0.945916i | \(0.605166\pi\) | |||||||
\(6\) | − | 17.8967i | − | 0.497130i | ||||||
\(7\) | 92.6602 | 1.89102 | 0.945512 | − | 0.325588i | \(-0.105562\pi\) | ||||
0.945512 | + | 0.325588i | \(0.105562\pi\) | |||||||
\(8\) | − | 69.3575i | − | 1.08371i | ||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 55.8670i | 0.558670i | ||||||||
\(11\) | 48.6771i | 0.402290i | 0.979561 | + | 0.201145i | \(0.0644663\pi\) | ||||
−0.979561 | + | 0.201145i | \(0.935534\pi\) | |||||||
\(12\) | 21.4985 | 0.149295 | ||||||||
\(13\) | 216.742i | 1.28250i | 0.767334 | + | 0.641248i | \(0.221583\pi\) | ||||
−0.767334 | + | 0.641248i | \(0.778417\pi\) | |||||||
\(14\) | − | 319.142i | − | 1.62827i | ||||||
\(15\) | −84.2844 | −0.374597 | ||||||||
\(16\) | −172.684 | −0.674547 | ||||||||
\(17\) | 171.979 | 0.595084 | 0.297542 | − | 0.954709i | \(-0.403833\pi\) | ||||
0.297542 | + | 0.954709i | \(0.403833\pi\) | |||||||
\(18\) | − | 92.9938i | − | 0.287018i | ||||||
\(19\) | 267.365 | 0.740624 | 0.370312 | − | 0.928907i | \(-0.379251\pi\) | ||||
0.370312 | + | 0.928907i | \(0.379251\pi\) | |||||||
\(20\) | −67.1105 | −0.167776 | ||||||||
\(21\) | 481.476 | 1.09178 | ||||||||
\(22\) | 167.654 | 0.346394 | ||||||||
\(23\) | − | 734.072i | − | 1.38766i | −0.720139 | − | 0.693830i | \(-0.755922\pi\) | ||
0.720139 | − | 0.693830i | \(-0.244078\pi\) | |||||||
\(24\) | − | 360.392i | − | 0.625681i | ||||||
\(25\) | −361.894 | −0.579031 | ||||||||
\(26\) | 746.506 | 1.10430 | ||||||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | 383.370 | 0.488993 | ||||||||
\(29\) | 999.352 | 1.18829 | 0.594145 | − | 0.804358i | \(-0.297490\pi\) | ||||
0.594145 | + | 0.804358i | \(0.297490\pi\) | |||||||
\(30\) | 290.294i | 0.322548i | ||||||||
\(31\) | 568.212i | 0.591272i | 0.955301 | + | 0.295636i | \(0.0955315\pi\) | ||||
−0.955301 | + | 0.295636i | \(0.904468\pi\) | |||||||
\(32\) | − | 514.959i | − | 0.502889i | ||||||
\(33\) | 252.934i | 0.232262i | ||||||||
\(34\) | − | 592.334i | − | 0.512400i | ||||||
\(35\) | −1503.00 | −1.22694 | ||||||||
\(36\) | 111.709 | 0.0861954 | ||||||||
\(37\) | − | 1003.07i | − | 0.732704i | −0.930476 | − | 0.366352i | \(-0.880607\pi\) | ||
0.930476 | − | 0.366352i | \(-0.119393\pi\) | |||||||
\(38\) | − | 920.864i | − | 0.637717i | ||||||
\(39\) | 1126.22i | 0.740449i | ||||||||
\(40\) | 1125.02i | 0.703135i | ||||||||
\(41\) | −2301.23 | −1.36897 | −0.684483 | − | 0.729029i | \(-0.739972\pi\) | ||||
−0.684483 | + | 0.729029i | \(0.739972\pi\) | |||||||
\(42\) | − | 1658.31i | − | 0.940084i | ||||||
\(43\) | − | 2157.18i | − | 1.16667i | −0.812231 | − | 0.583336i | \(-0.801747\pi\) | ||
0.812231 | − | 0.583336i | \(-0.198253\pi\) | |||||||
\(44\) | 201.396i | 0.104027i | ||||||||
\(45\) | −437.954 | −0.216274 | ||||||||
\(46\) | −2528.30 | −1.19485 | ||||||||
\(47\) | 1199.13i | 0.542840i | 0.962461 | + | 0.271420i | \(0.0874932\pi\) | ||||
−0.962461 | + | 0.271420i | \(0.912507\pi\) | |||||||
\(48\) | −897.293 | −0.389450 | ||||||||
\(49\) | 6184.90 | 2.57597 | ||||||||
\(50\) | 1246.44i | 0.498577i | ||||||||
\(51\) | 893.631 | 0.343572 | ||||||||
\(52\) | 896.743i | 0.331636i | ||||||||
\(53\) | −1101.00 | −0.391956 | −0.195978 | − | 0.980608i | \(-0.562788\pi\) | ||||
−0.195978 | + | 0.980608i | \(0.562788\pi\) | |||||||
\(54\) | − | 483.210i | − | 0.165710i | ||||||
\(55\) | − | 789.569i | − | 0.261015i | ||||||
\(56\) | − | 6426.67i | − | 2.04932i | ||||||
\(57\) | 1389.27 | 0.427599 | ||||||||
\(58\) | − | 3441.98i | − | 1.02318i | ||||||
\(59\) | −1324.95 | − | 3218.99i | −0.380623 | − | 0.924730i | ||||
\(60\) | −348.716 | −0.0968657 | ||||||||
\(61\) | − | 4030.40i | − | 1.08315i | −0.840653 | − | 0.541574i | \(-0.817828\pi\) | ||
0.840653 | − | 0.541574i | \(-0.182172\pi\) | |||||||
\(62\) | 1957.05 | 0.509117 | ||||||||
\(63\) | 2501.82 | 0.630341 | ||||||||
\(64\) | −4536.57 | −1.10756 | ||||||||
\(65\) | − | 3515.67i | − | 0.832111i | ||||||
\(66\) | 871.158 | 0.199990 | ||||||||
\(67\) | 8142.38i | 1.81385i | 0.421290 | + | 0.906926i | \(0.361577\pi\) | ||||
−0.421290 | + | 0.906926i | \(0.638423\pi\) | |||||||
\(68\) | 711.544 | 0.153881 | ||||||||
\(69\) | − | 3814.35i | − | 0.801165i | ||||||
\(70\) | 5176.65i | 1.05646i | ||||||||
\(71\) | −2537.07 | −0.503286 | −0.251643 | − | 0.967820i | \(-0.580971\pi\) | ||||
−0.251643 | + | 0.967820i | \(0.580971\pi\) | |||||||
\(72\) | − | 1872.65i | − | 0.361237i | ||||||
\(73\) | 792.331i | 0.148683i | 0.997233 | + | 0.0743414i | \(0.0236855\pi\) | ||||
−0.997233 | + | 0.0743414i | \(0.976315\pi\) | |||||||
\(74\) | −3454.80 | −0.630898 | ||||||||
\(75\) | −1880.46 | −0.334304 | ||||||||
\(76\) | 1106.19 | 0.191515 | ||||||||
\(77\) | 4510.43i | 0.760740i | ||||||||
\(78\) | 3878.96 | 0.637567 | ||||||||
\(79\) | −3214.46 | −0.515056 | −0.257528 | − | 0.966271i | \(-0.582908\pi\) | ||||
−0.257528 | + | 0.966271i | \(0.582908\pi\) | |||||||
\(80\) | 2801.03 | 0.437661 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 7925.93i | 1.17875i | ||||||||
\(83\) | 10537.1i | 1.52956i | 0.644292 | + | 0.764779i | \(0.277152\pi\) | ||||
−0.644292 | + | 0.764779i | \(0.722848\pi\) | |||||||
\(84\) | 1992.05 | 0.282320 | ||||||||
\(85\) | −2789.60 | −0.386103 | ||||||||
\(86\) | −7429.78 | −1.00457 | ||||||||
\(87\) | 5192.79 | 0.686060 | ||||||||
\(88\) | 3376.12 | 0.435966 | ||||||||
\(89\) | 226.497i | 0.0285945i | 0.999898 | + | 0.0142972i | \(0.00455111\pi\) | ||||
−0.999898 | + | 0.0142972i | \(0.995449\pi\) | |||||||
\(90\) | 1508.41i | 0.186223i | ||||||||
\(91\) | 20083.3i | 2.42523i | ||||||||
\(92\) | − | 3037.13i | − | 0.358829i | ||||||
\(93\) | 2952.52i | 0.341371i | ||||||||
\(94\) | 4130.07 | 0.467414 | ||||||||
\(95\) | −4336.81 | −0.480533 | ||||||||
\(96\) | − | 2675.80i | − | 0.290343i | ||||||
\(97\) | 7280.88i | 0.773821i | 0.922117 | + | 0.386911i | \(0.126458\pi\) | ||||
−0.922117 | + | 0.386911i | \(0.873542\pi\) | |||||||
\(98\) | − | 21302.1i | − | 2.21805i | ||||||
\(99\) | 1314.28i | 0.134097i | ||||||||
\(100\) | −1497.29 | −0.149729 | ||||||||
\(101\) | 11745.9i | 1.15145i | 0.817643 | + | 0.575725i | \(0.195280\pi\) | ||||
−0.817643 | + | 0.575725i | \(0.804720\pi\) | |||||||
\(102\) | − | 3077.86i | − | 0.295834i | ||||||
\(103\) | 19029.4i | 1.79370i | 0.442333 | + | 0.896851i | \(0.354151\pi\) | ||||
−0.442333 | + | 0.896851i | \(0.645849\pi\) | |||||||
\(104\) | 15032.7 | 1.38985 | ||||||||
\(105\) | −7809.80 | −0.708372 | ||||||||
\(106\) | 3792.10i | 0.337495i | ||||||||
\(107\) | 6751.89 | 0.589737 | 0.294868 | − | 0.955538i | \(-0.404724\pi\) | ||||
0.294868 | + | 0.955538i | \(0.404724\pi\) | |||||||
\(108\) | 580.458 | 0.0497649 | ||||||||
\(109\) | − | 22919.8i | − | 1.92911i | −0.263876 | − | 0.964556i | \(-0.585001\pi\) | ||
0.263876 | − | 0.964556i | \(-0.414999\pi\) | |||||||
\(110\) | −2719.45 | −0.224748 | ||||||||
\(111\) | − | 5212.12i | − | 0.423027i | ||||||
\(112\) | −16000.9 | −1.27558 | ||||||||
\(113\) | − | 1167.57i | − | 0.0914377i | −0.998954 | − | 0.0457188i | \(-0.985442\pi\) | ||
0.998954 | − | 0.0457188i | \(-0.0145578\pi\) | |||||||
\(114\) | − | 4784.95i | − | 0.368186i | ||||||
\(115\) | 11907.0i | 0.900343i | ||||||||
\(116\) | 4134.70 | 0.307276 | ||||||||
\(117\) | 5852.03i | 0.427499i | ||||||||
\(118\) | −11086.9 | + | 4563.41i | −0.796243 | + | 0.327737i | ||||
\(119\) | 15935.6 | 1.12532 | ||||||||
\(120\) | 5845.75i | 0.405955i | ||||||||
\(121\) | 12271.5 | 0.838163 | ||||||||
\(122\) | −13881.6 | −0.932649 | ||||||||
\(123\) | −11957.5 | −0.790372 | ||||||||
\(124\) | 2350.91i | 0.152895i | ||||||||
\(125\) | 16008.0 | 1.02451 | ||||||||
\(126\) | − | 8616.82i | − | 0.542758i | ||||||
\(127\) | −14064.3 | −0.871990 | −0.435995 | − | 0.899949i | \(-0.643603\pi\) | ||||
−0.435995 | + | 0.899949i | \(0.643603\pi\) | |||||||
\(128\) | 7385.60i | 0.450781i | ||||||||
\(129\) | − | 11209.0i | − | 0.673578i | ||||||
\(130\) | −12108.7 | −0.716492 | ||||||||
\(131\) | 15833.5i | 0.922644i | 0.887233 | + | 0.461322i | \(0.152625\pi\) | ||||
−0.887233 | + | 0.461322i | \(0.847375\pi\) | |||||||
\(132\) | 1046.48i | 0.0600598i | ||||||||
\(133\) | 24774.1 | 1.40054 | ||||||||
\(134\) | 28044.1 | 1.56182 | ||||||||
\(135\) | −2275.68 | −0.124866 | ||||||||
\(136\) | − | 11928.1i | − | 0.644899i | ||||||
\(137\) | −21940.7 | −1.16899 | −0.584493 | − | 0.811399i | \(-0.698707\pi\) | ||||
−0.584493 | + | 0.811399i | \(0.698707\pi\) | |||||||
\(138\) | −13137.4 | −0.689847 | ||||||||
\(139\) | −33025.6 | −1.70931 | −0.854655 | − | 0.519196i | \(-0.826231\pi\) | ||||
−0.854655 | + | 0.519196i | \(0.826231\pi\) | |||||||
\(140\) | −6218.47 | −0.317269 | ||||||||
\(141\) | 6230.88i | 0.313409i | ||||||||
\(142\) | 8738.20i | 0.433357i | ||||||||
\(143\) | −10550.4 | −0.515936 | ||||||||
\(144\) | −4662.47 | −0.224849 | ||||||||
\(145\) | −16210.0 | −0.770988 | ||||||||
\(146\) | 2728.96 | 0.128024 | ||||||||
\(147\) | 32137.7 | 1.48724 | ||||||||
\(148\) | − | 4150.09i | − | 0.189467i | ||||||
\(149\) | 20821.5i | 0.937863i | 0.883235 | + | 0.468932i | \(0.155361\pi\) | ||||
−0.883235 | + | 0.468932i | \(0.844639\pi\) | |||||||
\(150\) | 6476.70i | 0.287853i | ||||||||
\(151\) | − | 9654.62i | − | 0.423430i | −0.977331 | − | 0.211715i | \(-0.932095\pi\) | ||
0.977331 | − | 0.211715i | \(-0.0679048\pi\) | |||||||
\(152\) | − | 18543.8i | − | 0.802622i | ||||||
\(153\) | 4643.44 | 0.198361 | ||||||||
\(154\) | 15534.9 | 0.655038 | ||||||||
\(155\) | − | 9216.71i | − | 0.383630i | ||||||
\(156\) | 4659.61i | 0.191470i | ||||||||
\(157\) | 23483.9i | 0.952731i | 0.879247 | + | 0.476366i | \(0.158046\pi\) | ||||
−0.879247 | + | 0.476366i | \(0.841954\pi\) | |||||||
\(158\) | 11071.3i | 0.443491i | ||||||||
\(159\) | −5720.99 | −0.226296 | ||||||||
\(160\) | 8352.90i | 0.326285i | ||||||||
\(161\) | − | 68019.2i | − | 2.62410i | ||||||
\(162\) | − | 2510.83i | − | 0.0956727i | ||||||
\(163\) | 12805.6 | 0.481977 | 0.240988 | − | 0.970528i | \(-0.422528\pi\) | ||||
0.240988 | + | 0.970528i | \(0.422528\pi\) | |||||||
\(164\) | −9521.06 | −0.353995 | ||||||||
\(165\) | − | 4102.72i | − | 0.150697i | ||||||
\(166\) | 36292.2 | 1.31703 | ||||||||
\(167\) | −29956.3 | −1.07413 | −0.537063 | − | 0.843542i | \(-0.680466\pi\) | ||||
−0.537063 | + | 0.843542i | \(0.680466\pi\) | |||||||
\(168\) | − | 33394.0i | − | 1.18318i | ||||||
\(169\) | −18416.0 | −0.644796 | ||||||||
\(170\) | 9607.98i | 0.332456i | ||||||||
\(171\) | 7218.86 | 0.246875 | ||||||||
\(172\) | − | 8925.05i | − | 0.301685i | ||||||
\(173\) | − | 51496.1i | − | 1.72061i | −0.509781 | − | 0.860304i | \(-0.670274\pi\) | ||
0.509781 | − | 0.860304i | \(-0.329726\pi\) | |||||||
\(174\) | − | 17885.1i | − | 0.590735i | ||||||
\(175\) | −33533.2 | −1.09496 | ||||||||
\(176\) | − | 8405.76i | − | 0.271364i | ||||||
\(177\) | −6884.64 | − | 16726.3i | −0.219753 | − | 0.533893i | ||||
\(178\) | 780.104 | 0.0246214 | ||||||||
\(179\) | − | 17057.4i | − | 0.532363i | −0.963923 | − | 0.266181i | \(-0.914238\pi\) | ||
0.963923 | − | 0.266181i | \(-0.0857620\pi\) | |||||||
\(180\) | −1811.98 | −0.0559254 | ||||||||
\(181\) | 7526.56 | 0.229741 | 0.114871 | − | 0.993380i | \(-0.463355\pi\) | ||||
0.114871 | + | 0.993380i | \(0.463355\pi\) | |||||||
\(182\) | 69171.3 | 2.08825 | ||||||||
\(183\) | − | 20942.6i | − | 0.625356i | ||||||
\(184\) | −50913.4 | −1.50382 | ||||||||
\(185\) | 16270.4i | 0.475394i | ||||||||
\(186\) | 10169.1 | 0.293939 | ||||||||
\(187\) | 8371.46i | 0.239397i | ||||||||
\(188\) | 4961.27i | 0.140371i | ||||||||
\(189\) | 12999.9 | 0.363928 | ||||||||
\(190\) | 14936.9i | 0.413765i | ||||||||
\(191\) | 34367.0i | 0.942053i | 0.882119 | + | 0.471026i | \(0.156116\pi\) | ||||
−0.882119 | + | 0.471026i | \(0.843884\pi\) | |||||||
\(192\) | −23572.7 | −0.639451 | ||||||||
\(193\) | −35591.7 | −0.955507 | −0.477753 | − | 0.878494i | \(-0.658549\pi\) | ||||
−0.477753 | + | 0.878494i | \(0.658549\pi\) | |||||||
\(194\) | 25076.9 | 0.666302 | ||||||||
\(195\) | − | 18267.9i | − | 0.480419i | ||||||
\(196\) | 25589.3 | 0.666110 | ||||||||
\(197\) | −25127.2 | −0.647458 | −0.323729 | − | 0.946150i | \(-0.604937\pi\) | ||||
−0.323729 | + | 0.946150i | \(0.604937\pi\) | |||||||
\(198\) | 4526.67 | 0.115465 | ||||||||
\(199\) | 19989.2 | 0.504765 | 0.252382 | − | 0.967628i | \(-0.418786\pi\) | ||||
0.252382 | + | 0.967628i | \(0.418786\pi\) | |||||||
\(200\) | 25100.1i | 0.627502i | ||||||||
\(201\) | 42309.1i | 1.04723i | ||||||||
\(202\) | 40455.6 | 0.991460 | ||||||||
\(203\) | 92600.1 | 2.24709 | ||||||||
\(204\) | 3697.29 | 0.0888430 | ||||||||
\(205\) | 37327.2 | 0.888214 | ||||||||
\(206\) | 65541.3 | 1.54447 | ||||||||
\(207\) | − | 19819.9i | − | 0.462553i | ||||||
\(208\) | − | 37427.9i | − | 0.865104i | ||||||
\(209\) | 13014.6i | 0.297946i | ||||||||
\(210\) | 26898.6i | 0.609947i | ||||||||
\(211\) | − | 32244.7i | − | 0.724257i | −0.932128 | − | 0.362129i | \(-0.882050\pi\) | ||
0.932128 | − | 0.362129i | \(-0.117950\pi\) | |||||||
\(212\) | −4555.27 | −0.101354 | ||||||||
\(213\) | −13183.0 | −0.290573 | ||||||||
\(214\) | − | 23255.0i | − | 0.507795i | ||||||
\(215\) | 34990.5i | 0.756962i | ||||||||
\(216\) | − | 9730.58i | − | 0.208560i | ||||||
\(217\) | 52650.6i | 1.11811i | ||||||||
\(218\) | −78940.7 | −1.66107 | ||||||||
\(219\) | 4117.07i | 0.0858421i | ||||||||
\(220\) | − | 3266.75i | − | 0.0674948i | ||||||
\(221\) | 37275.1i | 0.763193i | ||||||||
\(222\) | −17951.7 | −0.364249 | ||||||||
\(223\) | −28806.5 | −0.579270 | −0.289635 | − | 0.957137i | \(-0.593534\pi\) | ||||
−0.289635 | + | 0.957137i | \(0.593534\pi\) | |||||||
\(224\) | − | 47716.1i | − | 0.950975i | ||||||
\(225\) | −9771.14 | −0.193010 | ||||||||
\(226\) | −4021.36 | −0.0787328 | ||||||||
\(227\) | − | 57367.6i | − | 1.11331i | −0.830745 | − | 0.556654i | \(-0.812085\pi\) | ||
0.830745 | − | 0.556654i | \(-0.187915\pi\) | |||||||
\(228\) | 5747.94 | 0.110571 | ||||||||
\(229\) | 8038.50i | 0.153287i | 0.997059 | + | 0.0766433i | \(0.0244203\pi\) | ||||
−0.997059 | + | 0.0766433i | \(0.975580\pi\) | |||||||
\(230\) | 41010.4 | 0.775244 | ||||||||
\(231\) | 23436.9i | 0.439214i | ||||||||
\(232\) | − | 69312.6i | − | 1.28776i | ||||||
\(233\) | 55821.9i | 1.02824i | 0.857719 | + | 0.514118i | \(0.171881\pi\) | ||||
−0.857719 | + | 0.514118i | \(0.828119\pi\) | |||||||
\(234\) | 20155.7 | 0.368099 | ||||||||
\(235\) | − | 19450.6i | − | 0.352206i | ||||||
\(236\) | −5481.82 | − | 13318.2i | −0.0984239 | − | 0.239122i | ||||
\(237\) | −16702.8 | −0.297368 | ||||||||
\(238\) | − | 54885.8i | − | 0.968960i | ||||||
\(239\) | −35079.1 | −0.614120 | −0.307060 | − | 0.951690i | \(-0.599345\pi\) | ||||
−0.307060 | + | 0.951690i | \(0.599345\pi\) | |||||||
\(240\) | 14554.6 | 0.252683 | ||||||||
\(241\) | 84946.1 | 1.46255 | 0.731273 | − | 0.682085i | \(-0.238927\pi\) | ||||
0.731273 | + | 0.682085i | \(0.238927\pi\) | |||||||
\(242\) | − | 42265.8i | − | 0.721703i | ||||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | − | 16675.3i | − | 0.280087i | ||||||
\(245\) | −100322. | −1.67134 | ||||||||
\(246\) | 41184.4i | 0.680553i | ||||||||
\(247\) | 57949.2i | 0.949847i | ||||||||
\(248\) | 39409.8 | 0.640768 | ||||||||
\(249\) | 54752.5i | 0.883091i | ||||||||
\(250\) | − | 55134.8i | − | 0.882157i | ||||||
\(251\) | −62187.4 | −0.987086 | −0.493543 | − | 0.869721i | \(-0.664298\pi\) | ||||
−0.493543 | + | 0.869721i | \(0.664298\pi\) | |||||||
\(252\) | 10351.0 | 0.162998 | ||||||||
\(253\) | 35732.5 | 0.558242 | ||||||||
\(254\) | 48440.5i | 0.750830i | ||||||||
\(255\) | −14495.2 | −0.222917 | ||||||||
\(256\) | −47147.6 | −0.719415 | ||||||||
\(257\) | −11454.6 | −0.173426 | −0.0867129 | − | 0.996233i | \(-0.527636\pi\) | ||||
−0.0867129 | + | 0.996233i | \(0.527636\pi\) | |||||||
\(258\) | −38606.3 | −0.579987 | ||||||||
\(259\) | − | 92944.8i | − | 1.38556i | ||||||
\(260\) | − | 14545.7i | − | 0.215172i | ||||||
\(261\) | 26982.5 | 0.396097 | ||||||||
\(262\) | 54533.9 | 0.794446 | ||||||||
\(263\) | 39389.7 | 0.569471 | 0.284735 | − | 0.958606i | \(-0.408094\pi\) | ||||
0.284735 | + | 0.958606i | \(0.408094\pi\) | |||||||
\(264\) | 17542.8 | 0.251705 | ||||||||
\(265\) | 17858.9 | 0.254310 | ||||||||
\(266\) | − | 85327.4i | − | 1.20594i | ||||||
\(267\) | 1176.91i | 0.0165090i | ||||||||
\(268\) | 33688.1i | 0.469037i | ||||||||
\(269\) | 13109.8i | 0.181172i | 0.995889 | + | 0.0905861i | \(0.0288740\pi\) | ||||
−0.995889 | + | 0.0905861i | \(0.971126\pi\) | |||||||
\(270\) | 7837.93i | 0.107516i | ||||||||
\(271\) | 63942.9 | 0.870670 | 0.435335 | − | 0.900268i | \(-0.356630\pi\) | ||||
0.435335 | + | 0.900268i | \(0.356630\pi\) | |||||||
\(272\) | −29698.1 | −0.401412 | ||||||||
\(273\) | 104356.i | 1.40021i | ||||||||
\(274\) | 75568.5i | 1.00656i | ||||||||
\(275\) | − | 17616.0i | − | 0.232938i | ||||||
\(276\) | − | 15781.4i | − | 0.207170i | ||||||
\(277\) | −26097.8 | −0.340130 | −0.170065 | − | 0.985433i | \(-0.554398\pi\) | ||||
−0.170065 | + | 0.985433i | \(0.554398\pi\) | |||||||
\(278\) | 113747.i | 1.47181i | ||||||||
\(279\) | 15341.7i | 0.197091i | ||||||||
\(280\) | 104244.i | 1.32964i | ||||||||
\(281\) | −33934.6 | −0.429765 | −0.214882 | − | 0.976640i | \(-0.568937\pi\) | ||||
−0.214882 | + | 0.976640i | \(0.568937\pi\) | |||||||
\(282\) | 21460.5 | 0.269862 | ||||||||
\(283\) | − | 50184.5i | − | 0.626609i | −0.949653 | − | 0.313305i | \(-0.898564\pi\) | ||
0.949653 | − | 0.313305i | \(-0.101436\pi\) | |||||||
\(284\) | −10496.8 | −0.130143 | ||||||||
\(285\) | −22534.7 | −0.277436 | ||||||||
\(286\) | 36337.7i | 0.444248i | ||||||||
\(287\) | −213232. | −2.58875 | ||||||||
\(288\) | − | 13903.9i | − | 0.167630i | ||||||
\(289\) | −53944.1 | −0.645875 | ||||||||
\(290\) | 55830.8i | 0.663863i | ||||||||
\(291\) | 37832.6i | 0.446766i | ||||||||
\(292\) | 3278.17i | 0.0384473i | ||||||||
\(293\) | −145740. | −1.69764 | −0.848819 | − | 0.528684i | \(-0.822686\pi\) | ||||
−0.848819 | + | 0.528684i | \(0.822686\pi\) | |||||||
\(294\) | − | 110689.i | − | 1.28059i | ||||||
\(295\) | 21491.4 | + | 52213.7i | 0.246957 | + | 0.599985i | ||||
\(296\) | −69570.6 | −0.794040 | ||||||||
\(297\) | 6829.21i | 0.0774208i | ||||||||
\(298\) | 71713.7 | 0.807551 | ||||||||
\(299\) | 159104. | 1.77967 | ||||||||
\(300\) | −7780.17 | −0.0864463 | ||||||||
\(301\) | − | 199884.i | − | 2.20620i | ||||||
\(302\) | −33252.6 | −0.364596 | ||||||||
\(303\) | 61033.7i | 0.664790i | ||||||||
\(304\) | −46169.7 | −0.499586 | ||||||||
\(305\) | 65375.2i | 0.702770i | ||||||||
\(306\) | − | 15993.0i | − | 0.170800i | ||||||
\(307\) | −37666.1 | −0.399645 | −0.199822 | − | 0.979832i | \(-0.564037\pi\) | ||||
−0.199822 | + | 0.979832i | \(0.564037\pi\) | |||||||
\(308\) | 18661.4i | 0.196717i | ||||||||
\(309\) | 98879.5i | 1.03559i | ||||||||
\(310\) | −31744.3 | −0.330326 | ||||||||
\(311\) | −145763. | −1.50704 | −0.753522 | − | 0.657423i | \(-0.771647\pi\) | ||||
−0.753522 | + | 0.657423i | \(0.771647\pi\) | |||||||
\(312\) | 78112.0 | 0.802433 | ||||||||
\(313\) | − | 28891.9i | − | 0.294908i | −0.989069 | − | 0.147454i | \(-0.952892\pi\) | ||
0.989069 | − | 0.147454i | \(-0.0471079\pi\) | |||||||
\(314\) | 80883.5 | 0.820353 | ||||||||
\(315\) | −40580.9 | −0.408979 | ||||||||
\(316\) | −13299.5 | −0.133186 | ||||||||
\(317\) | 149119. | 1.48393 | 0.741967 | − | 0.670437i | \(-0.233893\pi\) | ||||
0.741967 | + | 0.670437i | \(0.233893\pi\) | |||||||
\(318\) | 19704.3i | 0.194853i | ||||||||
\(319\) | 48645.6i | 0.478038i | ||||||||
\(320\) | 73585.6 | 0.718610 | ||||||||
\(321\) | 35083.9 | 0.340485 | ||||||||
\(322\) | −234273. | −2.25949 | ||||||||
\(323\) | 45981.3 | 0.440734 | ||||||||
\(324\) | 3016.15 | 0.0287318 | ||||||||
\(325\) | − | 78437.6i | − | 0.742605i | ||||||
\(326\) | − | 44105.4i | − | 0.415008i | ||||||
\(327\) | − | 119095.i | − | 1.11377i | ||||||
\(328\) | 159608.i | 1.48356i | ||||||||
\(329\) | 111112.i | 1.02652i | ||||||||
\(330\) | −14130.7 | −0.129758 | ||||||||
\(331\) | 20162.8 | 0.184033 | 0.0920164 | − | 0.995757i | \(-0.470669\pi\) | ||||
0.0920164 | + | 0.995757i | \(0.470669\pi\) | |||||||
\(332\) | 43596.1i | 0.395523i | ||||||||
\(333\) | − | 27083.0i | − | 0.244235i | ||||||
\(334\) | 103176.i | 0.924880i | ||||||||
\(335\) | − | 132074.i | − | 1.17687i | ||||||
\(336\) | −83143.3 | −0.736459 | ||||||||
\(337\) | − | 56644.5i | − | 0.498767i | −0.968405 | − | 0.249384i | \(-0.919772\pi\) | ||
0.968405 | − | 0.249384i | \(-0.0802280\pi\) | |||||||
\(338\) | 63428.7i | 0.555204i | ||||||||
\(339\) | − | 6066.86i | − | 0.0527916i | ||||||
\(340\) | −11541.6 | −0.0998410 | ||||||||
\(341\) | −27658.9 | −0.237863 | ||||||||
\(342\) | − | 24863.3i | − | 0.212572i | ||||||
\(343\) | 350617. | 2.98020 | ||||||||
\(344\) | −149616. | −1.26433 | ||||||||
\(345\) | 61870.8i | 0.519813i | ||||||||
\(346\) | −177364. | −1.48154 | ||||||||
\(347\) | − | 98468.3i | − | 0.817782i | −0.912583 | − | 0.408891i | \(-0.865916\pi\) | ||
0.912583 | − | 0.408891i | \(-0.134084\pi\) | |||||||
\(348\) | 21484.5 | 0.177406 | ||||||||
\(349\) | 11046.8i | 0.0906953i | 0.998971 | + | 0.0453476i | \(0.0144396\pi\) | ||||
−0.998971 | + | 0.0453476i | \(0.985560\pi\) | |||||||
\(350\) | 115495.i | 0.942820i | ||||||||
\(351\) | 30408.0i | 0.246816i | ||||||||
\(352\) | 25066.7 | 0.202307 | ||||||||
\(353\) | 82041.3i | 0.658390i | 0.944262 | + | 0.329195i | \(0.106777\pi\) | ||||
−0.944262 | + | 0.329195i | \(0.893223\pi\) | |||||||
\(354\) | −57609.1 | + | 23712.2i | −0.459711 | + | 0.189219i | ||||
\(355\) | 41152.6 | 0.326543 | ||||||||
\(356\) | 937.104i | 0.00739414i | ||||||||
\(357\) | 82804.0 | 0.649703 | ||||||||
\(358\) | −58749.5 | −0.458393 | ||||||||
\(359\) | −48438.3 | −0.375837 | −0.187919 | − | 0.982185i | \(-0.560174\pi\) | ||||
−0.187919 | + | 0.982185i | \(0.560174\pi\) | |||||||
\(360\) | 30375.4i | 0.234378i | ||||||||
\(361\) | −58836.8 | −0.451476 | ||||||||
\(362\) | − | 25923.1i | − | 0.197820i | ||||||
\(363\) | 63764.8 | 0.483913 | ||||||||
\(364\) | 83092.3i | 0.627131i | ||||||||
\(365\) | − | 12852.0i | − | 0.0964686i | ||||||
\(366\) | −72130.7 | −0.538465 | ||||||||
\(367\) | − | 206944.i | − | 1.53646i | −0.640175 | − | 0.768229i | \(-0.721138\pi\) | ||
0.640175 | − | 0.768229i | \(-0.278862\pi\) | |||||||
\(368\) | 126762.i | 0.936041i | ||||||||
\(369\) | −62133.2 | −0.456322 | ||||||||
\(370\) | 56038.7 | 0.409340 | ||||||||
\(371\) | −102019. | −0.741198 | ||||||||
\(372\) | 12215.7i | 0.0882738i | ||||||||
\(373\) | 96391.4 | 0.692821 | 0.346410 | − | 0.938083i | \(-0.387401\pi\) | ||||
0.346410 | + | 0.938083i | \(0.387401\pi\) | |||||||
\(374\) | 28833.1 | 0.206133 | ||||||||
\(375\) | 83179.8 | 0.591501 | ||||||||
\(376\) | 83168.8 | 0.588281 | ||||||||
\(377\) | 216601.i | 1.52398i | ||||||||
\(378\) | − | 44774.3i | − | 0.313361i | ||||||
\(379\) | 222227. | 1.54710 | 0.773549 | − | 0.633737i | \(-0.218480\pi\) | ||||
0.773549 | + | 0.633737i | \(0.218480\pi\) | |||||||
\(380\) | −17943.0 | −0.124259 | ||||||||
\(381\) | −73080.3 | −0.503443 | ||||||||
\(382\) | 118367. | 0.811158 | ||||||||
\(383\) | 251261. | 1.71288 | 0.856440 | − | 0.516246i | \(-0.172671\pi\) | ||||
0.856440 | + | 0.516246i | \(0.172671\pi\) | |||||||
\(384\) | 38376.7i | 0.260259i | ||||||||
\(385\) | − | 73161.6i | − | 0.493585i | ||||||
\(386\) | 122585.i | 0.822743i | ||||||||
\(387\) | − | 58243.7i | − | 0.388891i | ||||||
\(388\) | 30123.8i | 0.200100i | ||||||||
\(389\) | 247468. | 1.63538 | 0.817691 | − | 0.575657i | \(-0.195254\pi\) | ||||
0.817691 | + | 0.575657i | \(0.195254\pi\) | |||||||
\(390\) | −62918.8 | −0.413667 | ||||||||
\(391\) | − | 126245.i | − | 0.825774i | ||||||
\(392\) | − | 428969.i | − | 2.79161i | ||||||
\(393\) | 82273.2i | 0.532689i | ||||||||
\(394\) | 86543.4i | 0.557496i | ||||||||
\(395\) | 52140.3 | 0.334179 | ||||||||
\(396\) | 5437.68i | 0.0346756i | ||||||||
\(397\) | − | 15188.5i | − | 0.0963684i | −0.998838 | − | 0.0481842i | \(-0.984657\pi\) | ||
0.998838 | − | 0.0481842i | \(-0.0153435\pi\) | |||||||
\(398\) | − | 68847.1i | − | 0.434630i | ||||||
\(399\) | 128730. | 0.808601 | ||||||||
\(400\) | 62493.4 | 0.390583 | ||||||||
\(401\) | 41102.4i | 0.255611i | 0.991799 | + | 0.127805i | \(0.0407933\pi\) | ||||
−0.991799 | + | 0.127805i | \(0.959207\pi\) | |||||||
\(402\) | 145722. | 0.901720 | ||||||||
\(403\) | −123155. | −0.758304 | ||||||||
\(404\) | 48597.4i | 0.297749i | ||||||||
\(405\) | −11824.8 | −0.0720913 | ||||||||
\(406\) | − | 318935.i | − | 1.93486i | ||||||
\(407\) | 48826.7 | 0.294760 | ||||||||
\(408\) | − | 61980.0i | − | 0.372333i | ||||||
\(409\) | − | 119091.i | − | 0.711925i | −0.934500 | − | 0.355962i | \(-0.884153\pi\) | ||
0.934500 | − | 0.355962i | \(-0.115847\pi\) | |||||||
\(410\) | − | 128563.i | − | 0.764800i | ||||||
\(411\) | −114007. | −0.674915 | ||||||||
\(412\) | 78731.7i | 0.463826i | ||||||||
\(413\) | −122770. | − | 298272.i | −0.719768 | − | 1.74869i | ||||
\(414\) | −68264.1 | −0.398283 | ||||||||
\(415\) | − | 170918.i | − | 0.992411i | ||||||
\(416\) | 111613. | 0.644953 | ||||||||
\(417\) | −171606. | −0.986871 | ||||||||
\(418\) | 44825.0 | 0.256547 | ||||||||
\(419\) | 228690.i | 1.30263i | 0.758809 | + | 0.651313i | \(0.225782\pi\) | ||||
−0.758809 | + | 0.651313i | \(0.774218\pi\) | |||||||
\(420\) | −32312.1 | −0.183175 | ||||||||
\(421\) | − | 282680.i | − | 1.59489i | −0.603390 | − | 0.797447i | \(-0.706184\pi\) | ||
0.603390 | − | 0.797447i | \(-0.293816\pi\) | |||||||
\(422\) | −111058. | −0.623624 | ||||||||
\(423\) | 32376.6i | 0.180947i | ||||||||
\(424\) | 76362.9i | 0.424767i | ||||||||
\(425\) | −62238.3 | −0.344572 | ||||||||
\(426\) | 45405.0i | 0.250199i | ||||||||
\(427\) | − | 373457.i | − | 2.04826i | ||||||
\(428\) | 27935.1 | 0.152498 | ||||||||
\(429\) | −54821.3 | −0.297876 | ||||||||
\(430\) | 120515. | 0.651785 | ||||||||
\(431\) | 270326.i | 1.45524i | 0.685981 | + | 0.727619i | \(0.259373\pi\) | ||||
−0.685981 | + | 0.727619i | \(0.740627\pi\) | |||||||
\(432\) | −24226.9 | −0.129817 | ||||||||
\(433\) | −201414. | −1.07427 | −0.537136 | − | 0.843496i | \(-0.680494\pi\) | ||||
−0.537136 | + | 0.843496i | \(0.680494\pi\) | |||||||
\(434\) | 181340. | 0.962752 | ||||||||
\(435\) | −84229.8 | −0.445130 | ||||||||
\(436\) | − | 94827.9i | − | 0.498842i | ||||||
\(437\) | − | 196265.i | − | 1.02773i | ||||||
\(438\) | 14180.1 | 0.0739147 | ||||||||
\(439\) | −10876.9 | −0.0564388 | −0.0282194 | − | 0.999602i | \(-0.508984\pi\) | ||||
−0.0282194 | + | 0.999602i | \(0.508984\pi\) | |||||||
\(440\) | −54762.5 | −0.282864 | ||||||||
\(441\) | 166992. | 0.858657 | ||||||||
\(442\) | 128384. | 0.657151 | ||||||||
\(443\) | − | 28282.8i | − | 0.144117i | −0.997400 | − | 0.0720584i | \(-0.977043\pi\) | ||
0.997400 | − | 0.0720584i | \(-0.0229568\pi\) | |||||||
\(444\) | − | 21564.5i | − | 0.109389i | ||||||
\(445\) | − | 3673.90i | − | 0.0185527i | ||||||
\(446\) | 99215.8i | 0.498782i | ||||||||
\(447\) | 108192.i | 0.541475i | ||||||||
\(448\) | −420360. | −2.09443 | ||||||||
\(449\) | 158321. | 0.785320 | 0.392660 | − | 0.919684i | \(-0.371555\pi\) | ||||
0.392660 | + | 0.919684i | \(0.371555\pi\) | |||||||
\(450\) | 33653.9i | 0.166192i | ||||||||
\(451\) | − | 112017.i | − | 0.550721i | ||||||
\(452\) | − | 4830.67i | − | 0.0236445i | ||||||
\(453\) | − | 50166.9i | − | 0.244467i | ||||||
\(454\) | −197586. | −0.958618 | ||||||||
\(455\) | − | 325762.i | − | 1.57354i | ||||||
\(456\) | − | 96356.3i | − | 0.463394i | ||||||
\(457\) | 35833.3i | 0.171575i | 0.996313 | + | 0.0857876i | \(0.0273406\pi\) | ||||
−0.996313 | + | 0.0857876i | \(0.972659\pi\) | |||||||
\(458\) | 27686.3 | 0.131988 | ||||||||
\(459\) | 24128.0 | 0.114524 | ||||||||
\(460\) | 49263.9i | 0.232816i | ||||||||
\(461\) | 307571. | 1.44725 | 0.723625 | − | 0.690193i | \(-0.242474\pi\) | ||||
0.723625 | + | 0.690193i | \(0.242474\pi\) | |||||||
\(462\) | 80721.7 | 0.378187 | ||||||||
\(463\) | 272379.i | 1.27061i | 0.772262 | + | 0.635304i | \(0.219125\pi\) | ||||
−0.772262 | + | 0.635304i | \(0.780875\pi\) | |||||||
\(464\) | −172572. | −0.801558 | ||||||||
\(465\) | − | 47891.4i | − | 0.221489i | ||||||
\(466\) | 192263. | 0.885367 | ||||||||
\(467\) | 217459.i | 0.997111i | 0.866858 | + | 0.498556i | \(0.166136\pi\) | ||||
−0.866858 | + | 0.498556i | \(0.833864\pi\) | |||||||
\(468\) | 24212.1i | 0.110545i | ||||||||
\(469\) | 754474.i | 3.43004i | ||||||||
\(470\) | −66992.0 | −0.303268 | ||||||||
\(471\) | 122026.i | 0.550060i | ||||||||
\(472\) | −223261. | + | 91895.2i | −1.00214 | + | 0.412485i | ||||
\(473\) | 105005. | 0.469341 | ||||||||
\(474\) | 57528.2i | 0.256050i | ||||||||
\(475\) | −96757.9 | −0.428844 | ||||||||
\(476\) | 65931.8 | 0.290992 | ||||||||
\(477\) | −29727.1 | −0.130652 | ||||||||
\(478\) | 120820.i | 0.528790i | ||||||||
\(479\) | −56488.8 | −0.246202 | −0.123101 | − | 0.992394i | \(-0.539284\pi\) | ||||
−0.123101 | + | 0.992394i | \(0.539284\pi\) | |||||||
\(480\) | 43403.0i | 0.188381i | ||||||||
\(481\) | 217408. | 0.939691 | ||||||||
\(482\) | − | 292573.i | − | 1.25933i | ||||||
\(483\) | − | 353438.i | − | 1.51502i | ||||||
\(484\) | 50772.0 | 0.216737 | ||||||||
\(485\) | − | 118100.i | − | 0.502072i | ||||||
\(486\) | − | 13046.7i | − | 0.0552366i | ||||||
\(487\) | −374783. | −1.58024 | −0.790118 | − | 0.612954i | \(-0.789981\pi\) | ||||
−0.790118 | + | 0.612954i | \(0.789981\pi\) | |||||||
\(488\) | −279538. | −1.17382 | ||||||||
\(489\) | 66540.1 | 0.278270 | ||||||||
\(490\) | 345532.i | 1.43912i | ||||||||
\(491\) | −61744.1 | −0.256114 | −0.128057 | − | 0.991767i | \(-0.540874\pi\) | ||||
−0.128057 | + | 0.991767i | \(0.540874\pi\) | |||||||
\(492\) | −49472.9 | −0.204379 | ||||||||
\(493\) | 171868. | 0.707133 | ||||||||
\(494\) | 199590. | 0.817870 | ||||||||
\(495\) | − | 21318.4i | − | 0.0870048i | ||||||
\(496\) | − | 98121.2i | − | 0.398841i | ||||||
\(497\) | −235085. | −0.951726 | ||||||||
\(498\) | 188580. | 0.760389 | ||||||||
\(499\) | −212124. | −0.851901 | −0.425950 | − | 0.904747i | \(-0.640060\pi\) | ||||
−0.425950 | + | 0.904747i | \(0.640060\pi\) | |||||||
\(500\) | 66231.0 | 0.264924 | ||||||||
\(501\) | −155657. | −0.620147 | ||||||||
\(502\) | 214187.i | 0.849934i | ||||||||
\(503\) | − | 268106.i | − | 1.05967i | −0.848101 | − | 0.529834i | \(-0.822254\pi\) | ||
0.848101 | − | 0.529834i | \(-0.177746\pi\) | |||||||
\(504\) | − | 173520.i | − | 0.683107i | ||||||
\(505\) | − | 190525.i | − | 0.747085i | ||||||
\(506\) | − | 123070.i | − | 0.480676i | ||||||
\(507\) | −95692.4 | −0.372273 | ||||||||
\(508\) | −58189.4 | −0.225484 | ||||||||
\(509\) | 241532.i | 0.932265i | 0.884715 | + | 0.466133i | \(0.154353\pi\) | ||||
−0.884715 | + | 0.466133i | \(0.845647\pi\) | |||||||
\(510\) | 49924.5i | 0.191944i | ||||||||
\(511\) | 73417.5i | 0.281163i | ||||||||
\(512\) | 280556.i | 1.07024i | ||||||||
\(513\) | 37510.3 | 0.142533 | ||||||||
\(514\) | 39452.1i | 0.149329i | ||||||||
\(515\) | − | 308667.i | − | 1.16379i | ||||||
\(516\) | − | 46375.9i | − | 0.174178i | ||||||
\(517\) | −58370.3 | −0.218379 | ||||||||
\(518\) | −320122. | −1.19304 | ||||||||
\(519\) | − | 267581.i | − | 0.993394i | ||||||
\(520\) | −243838. | −0.901767 | ||||||||
\(521\) | 81137.0 | 0.298912 | 0.149456 | − | 0.988768i | \(-0.452248\pi\) | ||||
0.149456 | + | 0.988768i | \(0.452248\pi\) | |||||||
\(522\) | − | 92933.6i | − | 0.341061i | ||||||
\(523\) | 507362. | 1.85488 | 0.927438 | − | 0.373977i | \(-0.122006\pi\) | ||||
0.927438 | + | 0.373977i | \(0.122006\pi\) | |||||||
\(524\) | 65509.1i | 0.238583i | ||||||||
\(525\) | −174243. | −0.632176 | ||||||||
\(526\) | − | 135667.i | − | 0.490345i | ||||||
\(527\) | 97720.8i | 0.351857i | ||||||||
\(528\) | − | 43677.6i | − | 0.156672i | ||||||
\(529\) | −259020. | −0.925598 | ||||||||
\(530\) | − | 61509.9i | − | 0.218974i | ||||||
\(531\) | −35773.6 | − | 86912.6i | −0.126874 | − | 0.308243i | ||||
\(532\) | 102500. | 0.362160 | ||||||||
\(533\) | − | 498773.i | − | 1.75569i | ||||||
\(534\) | 4053.54 | 0.0142152 | ||||||||
\(535\) | −109519. | −0.382634 | ||||||||
\(536\) | 564735. | 1.96569 | ||||||||
\(537\) | − | 88633.0i | − | 0.307360i | ||||||
\(538\) | 45153.0 | 0.155999 | ||||||||
\(539\) | 301063.i | 1.03629i | ||||||||
\(540\) | −9415.34 | −0.0322886 | ||||||||
\(541\) | 303310.i | 1.03632i | 0.855285 | + | 0.518158i | \(0.173382\pi\) | ||||
−0.855285 | + | 0.518158i | \(0.826618\pi\) | |||||||
\(542\) | − | 220233.i | − | 0.749694i | ||||||
\(543\) | 39109.2 | 0.132641 | ||||||||
\(544\) | − | 88562.2i | − | 0.299261i | ||||||
\(545\) | 371771.i | 1.25165i | ||||||||
\(546\) | 359425. | 1.20565 | ||||||||
\(547\) | 185234. | 0.619077 | 0.309539 | − | 0.950887i | \(-0.399825\pi\) | ||||
0.309539 | + | 0.950887i | \(0.399825\pi\) | |||||||
\(548\) | −90777.0 | −0.302284 | ||||||||
\(549\) | − | 108821.i | − | 0.361050i | ||||||
\(550\) | −60673.2 | −0.200573 | ||||||||
\(551\) | 267192. | 0.880076 | ||||||||
\(552\) | −264554. | −0.868231 | ||||||||
\(553\) | −297853. | −0.973983 | ||||||||
\(554\) | 89886.5i | 0.292870i | ||||||||
\(555\) | 84543.3i | 0.274469i | ||||||||
\(556\) | −136639. | −0.442004 | ||||||||
\(557\) | 300545. | 0.968723 | 0.484361 | − | 0.874868i | \(-0.339052\pi\) | ||||
0.484361 | + | 0.874868i | \(0.339052\pi\) | |||||||
\(558\) | 52840.2 | 0.169706 | ||||||||
\(559\) | 467550. | 1.49625 | ||||||||
\(560\) | 259544. | 0.827626 | ||||||||
\(561\) | 43499.4i | 0.138216i | ||||||||
\(562\) | 116878.i | 0.370050i | ||||||||
\(563\) | − | 110761.i | − | 0.349437i | −0.984618 | − | 0.174719i | \(-0.944098\pi\) | ||
0.984618 | − | 0.174719i | \(-0.0559016\pi\) | |||||||
\(564\) | 25779.5i | 0.0810432i | ||||||||
\(565\) | 18938.6i | 0.0593267i | ||||||||
\(566\) | −172846. | −0.539544 | ||||||||
\(567\) | 67549.3 | 0.210114 | ||||||||
\(568\) | 175965.i | 0.545417i | ||||||||
\(569\) | 85112.7i | 0.262887i | 0.991324 | + | 0.131444i | \(0.0419612\pi\) | ||||
−0.991324 | + | 0.131444i | \(0.958039\pi\) | |||||||
\(570\) | 77614.4i | 0.238887i | ||||||||
\(571\) | − | 419082.i | − | 1.28537i | −0.766132 | − | 0.642683i | \(-0.777821\pi\) | ||
0.766132 | − | 0.642683i | \(-0.222179\pi\) | |||||||
\(572\) | −43650.9 | −0.133414 | ||||||||
\(573\) | 178576.i | 0.543894i | ||||||||
\(574\) | 734418.i | 2.22905i | ||||||||
\(575\) | 265656.i | 0.803497i | ||||||||
\(576\) | −122487. | −0.369187 | ||||||||
\(577\) | −210330. | −0.631757 | −0.315878 | − | 0.948800i | \(-0.602299\pi\) | ||||
−0.315878 | + | 0.948800i | \(0.602299\pi\) | |||||||
\(578\) | 185795.i | 0.556133i | ||||||||
\(579\) | −184940. | −0.551662 | ||||||||
\(580\) | −67067.0 | −0.199367 | ||||||||
\(581\) | 976372.i | 2.89243i | ||||||||
\(582\) | 130304. | 0.384690 | ||||||||
\(583\) | − | 53593.7i | − | 0.157680i | ||||||
\(584\) | 54954.1 | 0.161129 | ||||||||
\(585\) | − | 94923.1i | − | 0.277370i | ||||||
\(586\) | 501962.i | 1.46176i | ||||||||
\(587\) | − | 645237.i | − | 1.87259i | −0.351213 | − | 0.936296i | \(-0.614231\pi\) | ||
0.351213 | − | 0.936296i | \(-0.385769\pi\) | |||||||
\(588\) | 132966. | 0.384579 | ||||||||
\(589\) | 151920.i | 0.437910i | ||||||||
\(590\) | 179835. | − | 74021.0i | 0.516619 | − | 0.212643i | ||||
\(591\) | −130565. | −0.373810 | ||||||||
\(592\) | 173215.i | 0.494244i | ||||||||
\(593\) | −386221. | −1.09831 | −0.549157 | − | 0.835719i | \(-0.685051\pi\) | ||||
−0.549157 | + | 0.835719i | \(0.685051\pi\) | |||||||
\(594\) | 23521.3 | 0.0666635 | ||||||||
\(595\) | −258485. | −0.730131 | ||||||||
\(596\) | 86146.4i | 0.242518i | ||||||||
\(597\) | 103867. | 0.291426 | ||||||||
\(598\) | − | 547989.i | − | 1.53239i | ||||||
\(599\) | −388204. | −1.08195 | −0.540974 | − | 0.841039i | \(-0.681944\pi\) | ||||
−0.540974 | + | 0.841039i | \(0.681944\pi\) | |||||||
\(600\) | 130424.i | 0.362288i | ||||||||
\(601\) | 510006.i | 1.41197i | 0.708225 | + | 0.705987i | \(0.249496\pi\) | ||||
−0.708225 | + | 0.705987i | \(0.750504\pi\) | |||||||
\(602\) | −688444. | −1.89966 | ||||||||
\(603\) | 219844.i | 0.604617i | ||||||||
\(604\) | − | 39944.8i | − | 0.109493i | ||||||
\(605\) | −199051. | −0.543818 | ||||||||
\(606\) | 210213. | 0.572420 | ||||||||
\(607\) | −560179. | −1.52037 | −0.760185 | − | 0.649707i | \(-0.774892\pi\) | ||||
−0.760185 | + | 0.649707i | \(0.774892\pi\) | |||||||
\(608\) | − | 137682.i | − | 0.372452i | ||||||
\(609\) | 481164. | 1.29736 | ||||||||
\(610\) | 225166. | 0.605123 | ||||||||
\(611\) | −259902. | −0.696190 | ||||||||
\(612\) | 19211.7 | 0.0512935 | ||||||||
\(613\) | − | 306896.i | − | 0.816715i | −0.912822 | − | 0.408358i | \(-0.866102\pi\) | ||
0.912822 | − | 0.408358i | \(-0.133898\pi\) | |||||||
\(614\) | 129730.i | 0.344116i | ||||||||
\(615\) | 193958. | 0.512811 | ||||||||
\(616\) | 312832. | 0.824422 | ||||||||
\(617\) | 465889. | 1.22380 | 0.611902 | − | 0.790933i | \(-0.290405\pi\) | ||||
0.611902 | + | 0.790933i | \(0.290405\pi\) | |||||||
\(618\) | 340562. | 0.891702 | ||||||||
\(619\) | 608265. | 1.58749 | 0.793746 | − | 0.608250i | \(-0.208128\pi\) | ||||
0.793746 | + | 0.608250i | \(0.208128\pi\) | |||||||
\(620\) | − | 38133.0i | − | 0.0992014i | ||||||
\(621\) | − | 102987.i | − | 0.267055i | ||||||
\(622\) | 502039.i | 1.29765i | ||||||||
\(623\) | 20987.2i | 0.0540728i | ||||||||
\(624\) | − | 194481.i | − | 0.499468i | ||||||
\(625\) | −33473.7 | −0.0856927 | ||||||||
\(626\) | −99509.8 | −0.253932 | ||||||||
\(627\) | 67625.7i | 0.172019i | ||||||||
\(628\) | 97161.7i | 0.246363i | ||||||||
\(629\) | − | 172508.i | − | 0.436021i | ||||||
\(630\) | 139769.i | 0.352153i | ||||||||
\(631\) | −51223.1 | −0.128649 | −0.0643245 | − | 0.997929i | \(-0.520489\pi\) | ||||
−0.0643245 | + | 0.997929i | \(0.520489\pi\) | |||||||
\(632\) | 222947.i | 0.558171i | ||||||||
\(633\) | − | 167548.i | − | 0.418150i | ||||||
\(634\) | − | 513598.i | − | 1.27775i | ||||||
\(635\) | 228131. | 0.565766 | ||||||||
\(636\) | −23669.9 | −0.0585170 | ||||||||
\(637\) | 1.34053e6i | 3.30367i | ||||||||
\(638\) | 167546. | 0.411616 | ||||||||
\(639\) | −68500.8 | −0.167762 | ||||||||
\(640\) | − | 119798.i | − | 0.292476i | ||||||
\(641\) | −194528. | −0.473440 | −0.236720 | − | 0.971578i | \(-0.576072\pi\) | ||||
−0.236720 | + | 0.971578i | \(0.576072\pi\) | |||||||
\(642\) | − | 120836.i | − | 0.293176i | ||||||
\(643\) | −127058. | −0.307312 | −0.153656 | − | 0.988124i | \(-0.549105\pi\) | ||||
−0.153656 | + | 0.988124i | \(0.549105\pi\) | |||||||
\(644\) | − | 281421.i | − | 0.678555i | ||||||
\(645\) | 181816.i | 0.437032i | ||||||||
\(646\) | − | 158370.i | − | 0.379495i | ||||||
\(647\) | 298850. | 0.713912 | 0.356956 | − | 0.934121i | \(-0.383815\pi\) | ||||
0.356956 | + | 0.934121i | \(0.383815\pi\) | |||||||
\(648\) | − | 50561.6i | − | 0.120412i | ||||||
\(649\) | 156691. | − | 64494.7i | 0.372010 | − | 0.153121i | ||||
\(650\) | −270156. | −0.639423 | ||||||||
\(651\) | 273581.i | 0.645540i | ||||||||
\(652\) | 52981.8 | 0.124633 | ||||||||
\(653\) | −808235. | −1.89545 | −0.947723 | − | 0.319094i | \(-0.896621\pi\) | ||||
−0.947723 | + | 0.319094i | \(0.896621\pi\) | |||||||
\(654\) | −410188. | −0.959019 | ||||||||
\(655\) | − | 256828.i | − | 0.598631i | ||||||
\(656\) | 397386. | 0.923431 | ||||||||
\(657\) | 21392.9i | 0.0495609i | ||||||||
\(658\) | 382693. | 0.883891 | ||||||||
\(659\) | − | 205299.i | − | 0.472732i | −0.971664 | − | 0.236366i | \(-0.924044\pi\) | ||
0.971664 | − | 0.236366i | \(-0.0759565\pi\) | |||||||
\(660\) | − | 16974.5i | − | 0.0389681i | ||||||
\(661\) | −218321. | −0.499680 | −0.249840 | − | 0.968287i | \(-0.580378\pi\) | ||||
−0.249840 | + | 0.968287i | \(0.580378\pi\) | |||||||
\(662\) | − | 69445.1i | − | 0.158462i | ||||||
\(663\) | 193687.i | 0.440630i | ||||||||
\(664\) | 730829. | 1.65760 | ||||||||
\(665\) | −401849. | −0.908699 | ||||||||
\(666\) | −93279.5 | −0.210299 | ||||||||
\(667\) | − | 733596.i | − | 1.64894i | ||||||
\(668\) | −123940. | −0.277754 | ||||||||
\(669\) | −149683. | −0.334441 | ||||||||
\(670\) | −454891. | −1.01335 | ||||||||
\(671\) | 196188. | 0.435740 | ||||||||
\(672\) | − | 247940.i | − | 0.549046i | ||||||
\(673\) | − | 308870.i | − | 0.681939i | −0.940074 | − | 0.340970i | \(-0.889245\pi\) | ||
0.940074 | − | 0.340970i | \(-0.110755\pi\) | |||||||
\(674\) | −195096. | −0.429466 | ||||||||
\(675\) | −50772.4 | −0.111435 | ||||||||
\(676\) | −76194.0 | −0.166735 | ||||||||
\(677\) | −765077. | −1.66927 | −0.834637 | − | 0.550800i | \(-0.814323\pi\) | ||||
−0.834637 | + | 0.550800i | \(0.814323\pi\) | |||||||
\(678\) | −20895.6 | −0.0454564 | ||||||||
\(679\) | 674648.i | 1.46331i | ||||||||
\(680\) | 193479.i | 0.418424i | ||||||||
\(681\) | − | 298091.i | − | 0.642768i | ||||||
\(682\) | 95263.3i | 0.204813i | ||||||||
\(683\) | − | 32889.7i | − | 0.0705047i | −0.999378 | − | 0.0352523i | \(-0.988777\pi\) | ||
0.999378 | − | 0.0352523i | \(-0.0112235\pi\) | |||||||
\(684\) | 29867.2 | 0.0638384 | ||||||||
\(685\) | 355890. | 0.758463 | ||||||||
\(686\) | − | 1.20760e6i | − | 2.56611i | ||||||
\(687\) | 41769.3i | 0.0885000i | ||||||||
\(688\) | 372510.i | 0.786975i | ||||||||
\(689\) | − | 238634.i | − | 0.502682i | ||||||
\(690\) | 213096. | 0.447587 | ||||||||
\(691\) | − | 498934.i | − | 1.04493i | −0.852661 | − | 0.522465i | \(-0.825013\pi\) | ||
0.852661 | − | 0.522465i | \(-0.174987\pi\) | |||||||
\(692\) | − | 213059.i | − | 0.444925i | ||||||
\(693\) | 121782.i | 0.253580i | ||||||||
\(694\) | −339146. | −0.704154 | ||||||||
\(695\) | 535693. | 1.10904 | ||||||||
\(696\) | − | 360159.i | − | 0.743490i | ||||||
\(697\) | −395764. | −0.814650 | ||||||||
\(698\) | 38047.5 | 0.0780935 | ||||||||
\(699\) | 290059.i | 0.593653i | ||||||||
\(700\) | −138739. | −0.283142 | ||||||||
\(701\) | − | 70692.6i | − | 0.143859i | −0.997410 | − | 0.0719297i | \(-0.977084\pi\) | ||
0.997410 | − | 0.0719297i | \(-0.0229157\pi\) | |||||||
\(702\) | 104732. | 0.212522 | ||||||||
\(703\) | − | 268187.i | − | 0.542658i | ||||||
\(704\) | − | 220827.i | − | 0.445561i | ||||||
\(705\) | − | 101068.i | − | 0.203346i | ||||||
\(706\) | 282568. | 0.566909 | ||||||||
\(707\) | 1.08838e6i | 2.17742i | ||||||||
\(708\) | −28484.4 | − | 69203.2i | −0.0568251 | − | 0.138057i | ||||
\(709\) | −845715. | −1.68241 | −0.841204 | − | 0.540717i | \(-0.818153\pi\) | ||||
−0.841204 | + | 0.540717i | \(0.818153\pi\) | |||||||
\(710\) | − | 141738.i | − | 0.281171i | ||||||
\(711\) | −86790.5 | −0.171685 | ||||||||
\(712\) | 15709.3 | 0.0309881 | ||||||||
\(713\) | 417108. | 0.820484 | ||||||||
\(714\) | − | 285195.i | − | 0.559429i | ||||||
\(715\) | 171133. | 0.334750 | ||||||||
\(716\) | − | 70573.0i | − | 0.137662i | ||||||
\(717\) | −182277. | −0.354562 | ||||||||
\(718\) | 166832.i | 0.323616i | ||||||||
\(719\) | − | 541985.i | − | 1.04841i | −0.851593 | − | 0.524203i | \(-0.824363\pi\) | ||
0.851593 | − | 0.524203i | \(-0.175637\pi\) | |||||||
\(720\) | 75627.7 | 0.145887 | ||||||||
\(721\) | 1.76327e6i | 3.39193i | ||||||||
\(722\) | 202647.i | 0.388745i | ||||||||
\(723\) | 441393. | 0.844401 | ||||||||
\(724\) | 31140.2 | 0.0594080 | ||||||||
\(725\) | −361660. | −0.688057 | ||||||||
\(726\) | − | 219620.i | − | 0.416676i | ||||||
\(727\) | 324956. | 0.614832 | 0.307416 | − | 0.951575i | \(-0.400536\pi\) | ||||
0.307416 | + | 0.951575i | \(0.400536\pi\) | |||||||
\(728\) | 1.39293e6 | 2.62825 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | −44265.2 | −0.0830647 | ||||||||
\(731\) | − | 370990.i | − | 0.694268i | ||||||
\(732\) | − | 86647.3i | − | 0.161708i | ||||||
\(733\) | −228228. | −0.424777 | −0.212389 | − | 0.977185i | \(-0.568124\pi\) | ||||
−0.212389 | + | 0.977185i | \(0.568124\pi\) | |||||||
\(734\) | −712760. | −1.32297 | ||||||||
\(735\) | −521291. | −0.964951 | ||||||||
\(736\) | −378016. | −0.697839 | ||||||||
\(737\) | −396348. | −0.729695 | ||||||||
\(738\) | 214000.i | 0.392918i | ||||||||
\(739\) | 153824.i | 0.281667i | 0.990033 | + | 0.140834i | \(0.0449782\pi\) | ||||
−0.990033 | + | 0.140834i | \(0.955022\pi\) | |||||||
\(740\) | 67316.7i | 0.122930i | ||||||||
\(741\) | 301113.i | 0.548395i | ||||||||
\(742\) | 351376.i | 0.638212i | ||||||||
\(743\) | 40762.4 | 0.0738384 | 0.0369192 | − | 0.999318i | \(-0.488246\pi\) | ||||
0.0369192 | + | 0.999318i | \(0.488246\pi\) | |||||||
\(744\) | 204779. | 0.369947 | ||||||||
\(745\) | − | 337736.i | − | 0.608506i | ||||||
\(746\) | − | 331993.i | − | 0.596556i | ||||||
\(747\) | 284503.i | 0.509853i | ||||||||
\(748\) | 34635.9i | 0.0619047i | ||||||||
\(749\) | 625632. | 1.11521 | ||||||||
\(750\) | − | 286489.i | − | 0.509314i | ||||||
\(751\) | − | 947341.i | − | 1.67968i | −0.542834 | − | 0.839840i | \(-0.682649\pi\) | ||
0.542834 | − | 0.839840i | \(-0.317351\pi\) | |||||||
\(752\) | − | 207071.i | − | 0.366171i | ||||||
\(753\) | −323135. | −0.569894 | ||||||||
\(754\) | 746022. | 1.31223 | ||||||||
\(755\) | 156603.i | 0.274730i | ||||||||
\(756\) | 53785.3 | 0.0941067 | ||||||||
\(757\) | −384807. | −0.671508 | −0.335754 | − | 0.941950i | \(-0.608991\pi\) | ||||
−0.335754 | + | 0.941950i | \(0.608991\pi\) | |||||||
\(758\) | − | 765397.i | − | 1.33213i | ||||||
\(759\) | 185671. | 0.322301 | ||||||||
\(760\) | 300790.i | 0.520758i | ||||||||
\(761\) | 621369. | 1.07295 | 0.536476 | − | 0.843916i | \(-0.319755\pi\) | ||||
0.536476 | + | 0.843916i | \(0.319755\pi\) | |||||||
\(762\) | 251704.i | 0.433492i | ||||||||
\(763\) | − | 2.12375e6i | − | 3.64800i | ||||||
\(764\) | 142189.i | 0.243602i | ||||||||
\(765\) | −75319.1 | −0.128701 | ||||||||
\(766\) | − | 865396.i | − | 1.47488i | ||||||
\(767\) | 697689. | − | 287172.i | 1.18596 | − | 0.488148i | ||||
\(768\) | −244986. | −0.415354 | ||||||||
\(769\) | 140425.i | 0.237460i | 0.992927 | + | 0.118730i | \(0.0378823\pi\) | ||||
−0.992927 | + | 0.118730i | \(0.962118\pi\) | |||||||
\(770\) | −251984. | −0.425003 | ||||||||
\(771\) | −59519.9 | −0.100127 | ||||||||
\(772\) | −147256. | −0.247081 | ||||||||
\(773\) | 233110.i | 0.390124i | 0.980791 | + | 0.195062i | \(0.0624908\pi\) | ||||
−0.980791 | + | 0.195062i | \(0.937509\pi\) | |||||||
\(774\) | −200604. | −0.334856 | ||||||||
\(775\) | − | 205633.i | − | 0.342365i | ||||||
\(776\) | 504984. | 0.838598 | ||||||||
\(777\) | − | 482956.i | − | 0.799954i | ||||||
\(778\) | − | 852332.i | − | 1.40815i | ||||||
\(779\) | −615269. | −1.01389 | ||||||||
\(780\) | − | 75581.4i | − | 0.124230i | ||||||
\(781\) | − | 123497.i | − | 0.202467i | ||||||
\(782\) | −434816. | −0.711036 | ||||||||
\(783\) | 140205. | 0.228687 | ||||||||
\(784\) | −1.06803e6 | −1.73761 | ||||||||
\(785\) | − | 380921.i | − | 0.618153i | ||||||
\(786\) | 283367. | 0.458674 | ||||||||
\(787\) | 95032.6 | 0.153435 | 0.0767173 | − | 0.997053i | \(-0.475556\pi\) | ||||
0.0767173 | + | 0.997053i | \(0.475556\pi\) | |||||||
\(788\) | −103961. | −0.167424 | ||||||||
\(789\) | 204675. | 0.328784 | ||||||||
\(790\) | − | 179583.i | − | 0.287746i | ||||||
\(791\) | − | 108187.i | − | 0.172911i | ||||||
\(792\) | 91155.3 | 0.145322 | ||||||||
\(793\) | 873555. | 1.38913 | ||||||||
\(794\) | −52312.6 | −0.0829784 | ||||||||
\(795\) | 92797.5 | 0.146826 | ||||||||
\(796\) | 82702.9 | 0.130525 | ||||||||
\(797\) | 1.06273e6i | 1.67304i | 0.547936 | + | 0.836520i | \(0.315414\pi\) | ||||
−0.547936 | + | 0.836520i | \(0.684586\pi\) | |||||||
\(798\) | − | 443374.i | − | 0.696249i | ||||||
\(799\) | 206226.i | 0.323035i | ||||||||
\(800\) | 186361.i | 0.291188i | ||||||||
\(801\) | 6115.42i | 0.00953149i | ||||||||
\(802\) | 141566. | 0.220094 | ||||||||
\(803\) | −38568.4 | −0.0598137 | ||||||||
\(804\) | 175049.i | 0.270799i | ||||||||
\(805\) | 1.10331e6i | 1.70257i | ||||||||
\(806\) | 424174.i | 0.652940i | ||||||||
\(807\) | 68120.6i | 0.104600i | ||||||||
\(808\) | 814669. | 1.24784 | ||||||||
\(809\) | 961800.i | 1.46956i | 0.678305 | + | 0.734780i | \(0.262715\pi\) | ||||
−0.678305 | + | 0.734780i | \(0.737285\pi\) | |||||||
\(810\) | 40727.1i | 0.0620745i | ||||||||
\(811\) | − | 957274.i | − | 1.45544i | −0.685874 | − | 0.727721i | \(-0.740580\pi\) | ||
0.685874 | − | 0.727721i | \(-0.259420\pi\) | |||||||
\(812\) | 383122. | 0.581065 | ||||||||
\(813\) | 332257. | 0.502682 | ||||||||
\(814\) | − | 168170.i | − | 0.253804i | ||||||
\(815\) | −207714. | −0.312717 | ||||||||
\(816\) | −154316. | −0.231756 | ||||||||
\(817\) | − | 576754.i | − | 0.864065i | ||||||
\(818\) | −410177. | −0.613006 | ||||||||
\(819\) | 542250.i | 0.808410i | ||||||||
\(820\) | 154437. | 0.229680 | ||||||||
\(821\) | − | 698787.i | − | 1.03671i | −0.855165 | − | 0.518357i | \(-0.826544\pi\) | ||
0.855165 | − | 0.518357i | \(-0.173456\pi\) | |||||||
\(822\) | 392666.i | 0.581138i | ||||||||
\(823\) | − | 551034.i | − | 0.813540i | −0.913531 | − | 0.406770i | \(-0.866655\pi\) | ||
0.913531 | − | 0.406770i | \(-0.133345\pi\) | |||||||
\(824\) | 1.31983e6 | 1.94385 | ||||||||
\(825\) | − | 91535.3i | − | 0.134487i | ||||||
\(826\) | −1.02731e6 | + | 422846.i | −1.50571 | + | 0.619759i | ||||
\(827\) | 833437. | 1.21860 | 0.609301 | − | 0.792939i | \(-0.291450\pi\) | ||||
0.609301 | + | 0.792939i | \(0.291450\pi\) | |||||||
\(828\) | − | 82002.6i | − | 0.119610i | ||||||
\(829\) | 882949. | 1.28477 | 0.642387 | − | 0.766381i | \(-0.277944\pi\) | ||||
0.642387 | + | 0.766381i | \(0.277944\pi\) | |||||||
\(830\) | −588678. | −0.854519 | ||||||||
\(831\) | −135608. | −0.196374 | ||||||||
\(832\) | − | 983265.i | − | 1.42044i | ||||||
\(833\) | 1.06368e6 | 1.53292 | ||||||||
\(834\) | 591048.i | 0.849749i | ||||||||
\(835\) | 485907. | 0.696916 | ||||||||
\(836\) | 53846.2i | 0.0770447i | ||||||||
\(837\) | 79718.0i | 0.113790i | ||||||||
\(838\) | 787659. | 1.12163 | ||||||||
\(839\) | 959966.i | 1.36374i | 0.731473 | + | 0.681871i | \(0.238833\pi\) | ||||
−0.731473 | + | 0.681871i | \(0.761167\pi\) | |||||||
\(840\) | 541668.i | 0.767670i | ||||||||
\(841\) | 291424. | 0.412034 | ||||||||
\(842\) | −973612. | −1.37329 | ||||||||
\(843\) | −176330. | −0.248125 | ||||||||
\(844\) | − | 133408.i | − | 0.187283i | ||||||
\(845\) | 298718. | 0.418357 | ||||||||
\(846\) | 111512. | 0.155805 | ||||||||
\(847\) | 1.13708e6 | 1.58499 | ||||||||
\(848\) | 190126. | 0.264393 | ||||||||
\(849\) | − | 260766.i | − | 0.361773i | ||||||
\(850\) | 214362.i | 0.296695i | ||||||||
\(851\) | −736327. | −1.01674 | ||||||||
\(852\) | −54543.0 | −0.0751380 | ||||||||
\(853\) | 8821.74 | 0.0121243 | 0.00606214 | − | 0.999982i | \(-0.498070\pi\) | ||||
0.00606214 | + | 0.999982i | \(0.498070\pi\) | |||||||
\(854\) | −1.28627e6 | −1.76366 | ||||||||
\(855\) | −117094. | −0.160178 | ||||||||
\(856\) | − | 468294.i | − | 0.639104i | ||||||
\(857\) | 74384.0i | 0.101279i | 0.998717 | + | 0.0506394i | \(0.0161259\pi\) | ||||
−0.998717 | + | 0.0506394i | \(0.983874\pi\) | |||||||
\(858\) | 188816.i | 0.256487i | ||||||||
\(859\) | 106512.i | 0.144349i | 0.997392 | + | 0.0721746i | \(0.0229939\pi\) | ||||
−0.997392 | + | 0.0721746i | \(0.977006\pi\) | |||||||
\(860\) | 144769.i | 0.195740i | ||||||||
\(861\) | −1.10799e6 | −1.49461 | ||||||||
\(862\) | 931063. | 1.25304 | ||||||||
\(863\) | 662734.i | 0.889852i | 0.895567 | + | 0.444926i | \(0.146770\pi\) | ||||
−0.895567 | + | 0.444926i | \(0.853230\pi\) | |||||||
\(864\) | − | 72246.7i | − | 0.0967811i | ||||||
\(865\) | 835294.i | 1.11637i | ||||||||
\(866\) | 693714.i | 0.925006i | ||||||||
\(867\) | −280302. | −0.372896 | ||||||||
\(868\) | 217836.i | 0.289128i | ||||||||
\(869\) | − | 156471.i | − | 0.207202i | ||||||
\(870\) | 290106.i | 0.383281i | ||||||||
\(871\) | −1.76479e6 | −2.32626 | ||||||||
\(872\) | −1.58966e6 | −2.09060 | ||||||||
\(873\) | 196584.i | 0.257940i | ||||||||
\(874\) | −675980. | −0.884934 | ||||||||
\(875\) | 1.48330e6 | 1.93737 | ||||||||
\(876\) | 17033.9i | 0.0221976i | ||||||||
\(877\) | 1.48294e6 | 1.92808 | 0.964040 | − | 0.265757i | \(-0.0856217\pi\) | ||||
0.964040 | + | 0.265757i | \(0.0856217\pi\) | |||||||
\(878\) | 37462.5i | 0.0485968i | ||||||||
\(879\) | −757290. | −0.980132 | ||||||||
\(880\) | 136346.i | 0.176067i | ||||||||
\(881\) | − | 734191.i | − | 0.945926i | −0.881082 | − | 0.472963i | \(-0.843184\pi\) | ||
0.881082 | − | 0.472963i | \(-0.156816\pi\) | |||||||
\(882\) | − | 575158.i | − | 0.739350i | ||||||
\(883\) | 824634. | 1.05765 | 0.528823 | − | 0.848732i | \(-0.322634\pi\) | ||||
0.528823 | + | 0.848732i | \(0.322634\pi\) | |||||||
\(884\) | 154221.i | 0.197351i | ||||||||
\(885\) | 111673. | + | 271310.i | 0.142580 | + | 0.346401i | ||||
\(886\) | −97412.0 | −0.124092 | ||||||||
\(887\) | 786206.i | 0.999284i | 0.866232 | + | 0.499642i | \(0.166535\pi\) | ||||
−0.866232 | + | 0.499642i | \(0.833465\pi\) | |||||||
\(888\) | −361499. | −0.458439 | ||||||||
\(889\) | −1.30320e6 | −1.64895 | ||||||||
\(890\) | −12653.7 | −0.0159749 | ||||||||
\(891\) | 35485.6i | 0.0446989i | ||||||||
\(892\) | −119183. | −0.149791 | ||||||||
\(893\) | 320606.i | 0.402040i | ||||||||
\(894\) | 372635. | 0.466240 | ||||||||
\(895\) | 276681.i | 0.345408i | ||||||||
\(896\) | 684351.i | 0.852438i | ||||||||
\(897\) | 826729. | 1.02749 | ||||||||
\(898\) | − | 545293.i | − | 0.676203i | ||||||
\(899\) | 567844.i | 0.702603i | ||||||||
\(900\) | −40426.9 | −0.0499098 | ||||||||
\(901\) | −189350. | −0.233247 | ||||||||
\(902\) | −385812. | −0.474201 | ||||||||
\(903\) | − | 1.03863e6i | − | 1.27375i | ||||||
\(904\) | −80979.6 | −0.0990920 | ||||||||
\(905\) | −122085. | −0.149061 | ||||||||
\(906\) | −172786. | −0.210499 | ||||||||
\(907\) | −1.44869e6 | −1.76101 | −0.880504 | − | 0.474038i | \(-0.842796\pi\) | ||||
−0.880504 | + | 0.474038i | \(0.842796\pi\) | |||||||
\(908\) | − | 237352.i | − | 0.287886i | ||||||
\(909\) | 317140.i | 0.383817i | ||||||||
\(910\) | −1.12200e6 | −1.35490 | ||||||||
\(911\) | −812697. | −0.979246 | −0.489623 | − | 0.871934i | \(-0.662866\pi\) | ||||
−0.489623 | + | 0.871934i | \(0.662866\pi\) | |||||||
\(912\) | −239905. | −0.288436 | ||||||||
\(913\) | −512917. | −0.615327 | ||||||||
\(914\) | 123418. | 0.147735 | ||||||||
\(915\) | 339699.i | 0.405745i | ||||||||
\(916\) | 33258.3i | 0.0396378i | ||||||||
\(917\) | 1.46713e6i | 1.74474i | ||||||||
\(918\) | − | 83102.2i | − | 0.0986114i | ||||||
\(919\) | 851885.i | 1.00867i | 0.863507 | + | 0.504336i | \(0.168263\pi\) | ||||
−0.863507 | + | 0.504336i | \(0.831737\pi\) | |||||||
\(920\) | 825842. | 0.975711 | ||||||||
\(921\) | −195719. | −0.230735 | ||||||||
\(922\) | − | 1.05934e6i | − | 1.24616i | ||||||
\(923\) | − | 549888.i | − | 0.645463i | ||||||
\(924\) | 96967.2i | 0.113575i | ||||||||
\(925\) | 363006.i | 0.424258i | ||||||||
\(926\) | 938132. | 1.09406 | ||||||||
\(927\) | 513793.i | 0.597900i | ||||||||
\(928\) | − | 514625.i | − | 0.597578i | ||||||
\(929\) | − | 227195.i | − | 0.263250i | −0.991300 | − | 0.131625i | \(-0.957981\pi\) | ||
0.991300 | − | 0.131625i | \(-0.0420194\pi\) | |||||||
\(930\) | −164948. | −0.190714 | ||||||||
\(931\) | 1.65363e6 | 1.90782 | ||||||||
\(932\) | 230957.i | 0.265888i | ||||||||
\(933\) | −757406. | −0.870092 | ||||||||
\(934\) | 748976. | 0.858567 | ||||||||
\(935\) | − | 135790.i | − | 0.155326i | ||||||
\(936\) | 405882. | 0.463285 | ||||||||
\(937\) | − | 961855.i | − | 1.09554i | −0.836627 | − | 0.547772i | \(-0.815476\pi\) | ||
0.836627 | − | 0.547772i | \(-0.184524\pi\) | |||||||
\(938\) | 2.59857e6 | 2.95345 | ||||||||
\(939\) | − | 150127.i | − | 0.170265i | ||||||
\(940\) | − | 80474.4i | − | 0.0910756i | ||||||
\(941\) | 192956.i | 0.217911i | 0.994047 | + | 0.108955i | \(0.0347506\pi\) | ||||
−0.994047 | + | 0.108955i | \(0.965249\pi\) | |||||||
\(942\) | 420283. | 0.473631 | ||||||||
\(943\) | 1.68927e6i | 1.89966i | ||||||||
\(944\) | 228798. | + | 555867.i | 0.256748 | + | 0.623774i | ||||
\(945\) | −210865. | −0.236124 | ||||||||
\(946\) | − | 361660.i | − | 0.404128i | ||||||
\(947\) | −846036. | −0.943385 | −0.471693 | − | 0.881763i | \(-0.656357\pi\) | ||||
−0.471693 | + | 0.881763i | \(0.656357\pi\) | |||||||
\(948\) | −69106.0 | −0.0768952 | ||||||||
\(949\) | −171731. | −0.190685 | ||||||||
\(950\) | 333255.i | 0.369258i | ||||||||
\(951\) | 774845. | 0.856749 | ||||||||
\(952\) | − | 1.10526e6i | − | 1.21952i | ||||||
\(953\) | 596807. | 0.657125 | 0.328563 | − | 0.944482i | \(-0.393436\pi\) | ||||
0.328563 | + | 0.944482i | \(0.393436\pi\) | |||||||
\(954\) | 102387.i | 0.112498i | ||||||||
\(955\) | − | 557452.i | − | 0.611224i | ||||||
\(956\) | −145136. | −0.158803 | ||||||||
\(957\) | 252770.i | 0.275995i | ||||||||
\(958\) | 194560.i | 0.211993i | ||||||||
\(959\) | −2.03303e6 | −2.21058 | ||||||||
\(960\) | 382362. | 0.414890 | ||||||||
\(961\) | 600656. | 0.650398 | ||||||||
\(962\) | − | 748799.i | − | 0.809124i | ||||||
\(963\) | 182301. | 0.196579 | ||||||||
\(964\) | 351454. | 0.378194 | ||||||||
\(965\) | 577316. | 0.619953 | ||||||||
\(966\) | −1.21732e6 | −1.30452 | ||||||||
\(967\) | 380274.i | 0.406672i | 0.979109 | + | 0.203336i | \(0.0651784\pi\) | ||||
−0.979109 | + | 0.203336i | \(0.934822\pi\) | |||||||
\(968\) | − | 851123.i | − | 0.908326i | ||||||
\(969\) | 238926. | 0.254458 | ||||||||
\(970\) | −406761. | −0.432311 | ||||||||
\(971\) | 1.45439e6 | 1.54256 | 0.771281 | − | 0.636495i | \(-0.219616\pi\) | ||||
0.771281 | + | 0.636495i | \(0.219616\pi\) | |||||||
\(972\) | 15672.4 | 0.0165883 | ||||||||
\(973\) | −3.06016e6 | −3.23235 | ||||||||
\(974\) | 1.29083e6i | 1.36067i | ||||||||
\(975\) | − | 407574.i | − | 0.428743i | ||||||
\(976\) | 695985.i | 0.730635i | ||||||||
\(977\) | − | 1.71629e6i | − | 1.79805i | −0.437893 | − | 0.899027i | \(-0.644275\pi\) | ||
0.437893 | − | 0.899027i | \(-0.355725\pi\) | |||||||
\(978\) | − | 229178.i | − | 0.239605i | ||||||
\(979\) | −11025.2 | −0.0115033 | ||||||||
\(980\) | −415072. | −0.432187 | ||||||||
\(981\) | − | 618834.i | − | 0.643038i | ||||||
\(982\) | 212660.i | 0.220528i | ||||||||
\(983\) | − | 1.55447e6i | − | 1.60870i | −0.594155 | − | 0.804350i | \(-0.702513\pi\) | ||
0.594155 | − | 0.804350i | \(-0.297487\pi\) | |||||||
\(984\) | 829345.i | 0.856535i | ||||||||
\(985\) | 407576. | 0.420084 | ||||||||
\(986\) | − | 591950.i | − | 0.608880i | ||||||
\(987\) | 577354.i | 0.592663i | ||||||||
\(988\) | 239758.i | 0.245617i | ||||||||
\(989\) | −1.58352e6 | −1.61894 | ||||||||
\(990\) | −73425.0 | −0.0749159 | ||||||||
\(991\) | 1.55870e6i | 1.58714i | 0.608482 | + | 0.793568i | \(0.291779\pi\) | ||||
−0.608482 | + | 0.793568i | \(0.708221\pi\) | |||||||
\(992\) | 292606. | 0.297344 | ||||||||
\(993\) | 104769. | 0.106251 | ||||||||
\(994\) | 809683.i | 0.819488i | ||||||||
\(995\) | −324235. | −0.327502 | ||||||||
\(996\) | 226532.i | 0.228355i | ||||||||
\(997\) | −55668.1 | −0.0560037 | −0.0280018 | − | 0.999608i | \(-0.508914\pi\) | ||||
−0.0280018 | + | 0.999608i | \(0.508914\pi\) | |||||||
\(998\) | 730601.i | 0.733532i | ||||||||
\(999\) | − | 140727.i | − | 0.141009i |
(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 | 177.5.c.a.58.13 | ✓ | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.28 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.28 | yes | 40 | |
177.176 | even | 2 | 531.5.c.d.235.13 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.13 | ✓ | 40 | 1.1 | even | 1 | trivial | |
177.5.c.a.58.28 | yes | 40 | 59.58 | odd | 2 | inner | |
531.5.c.d.235.13 | 40 | 177.176 | even | 2 | |||
531.5.c.d.235.28 | 40 | 3.2 | odd | 2 |