Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(235,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, 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("531.235");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | no (minimal twist has level 177) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.13 | ||
Character | \(\chi\) | \(=\) | 531.235 |
Dual form | 531.5.c.d.235.28 |
$q$-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 \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | \(-0.141672\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.13738 | 0.258586 | ||||||||
\(5\) | 16.2205 | 0.648821 | 0.324411 | − | 0.945916i | \(-0.394834\pi\) | ||||
0.324411 | + | 0.945916i | \(0.394834\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 92.6602 | 1.89102 | 0.945512 | − | 0.325588i | \(-0.105562\pi\) | ||||
0.945512 | + | 0.325588i | \(0.105562\pi\) | |||||||
\(8\) | − | 69.3575i | − | 1.08371i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 55.8670i | − | 0.558670i | ||||||
\(11\) | 48.6771i | 0.402290i | 0.979561 | + | 0.201145i | \(0.0644663\pi\) | ||||
−0.979561 | + | 0.201145i | \(0.935534\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 216.742i | − | 1.28250i | −0.767334 | − | 0.641248i | \(-0.778417\pi\) | ||
0.767334 | − | 0.641248i | \(-0.221583\pi\) | |||||||
\(14\) | − | 319.142i | − | 1.62827i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −172.684 | −0.674547 | ||||||||
\(17\) | −171.979 | −0.595084 | −0.297542 | − | 0.954709i | \(-0.596167\pi\) | ||||
−0.297542 | + | 0.954709i | \(0.596167\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 267.365 | 0.740624 | 0.370312 | − | 0.928907i | \(-0.379251\pi\) | ||||
0.370312 | + | 0.928907i | \(0.379251\pi\) | |||||||
\(20\) | 67.1105 | 0.167776 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 167.654 | 0.346394 | ||||||||
\(23\) | − | 734.072i | − | 1.38766i | −0.720139 | − | 0.693830i | \(-0.755922\pi\) | ||
0.720139 | − | 0.693830i | \(-0.244078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −361.894 | −0.579031 | ||||||||
\(26\) | −746.506 | −1.10430 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 383.370 | 0.488993 | ||||||||
\(29\) | −999.352 | −1.18829 | −0.594145 | − | 0.804358i | \(-0.702510\pi\) | ||||
−0.594145 | + | 0.804358i | \(0.702510\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 568.212i | − | 0.591272i | −0.955301 | − | 0.295636i | \(-0.904468\pi\) | ||
0.955301 | − | 0.295636i | \(-0.0955315\pi\) | |||||||
\(32\) | − | 514.959i | − | 0.502889i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 592.334i | 0.512400i | ||||||||
\(35\) | 1503.00 | 1.22694 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1003.07i | 0.732704i | 0.930476 | + | 0.366352i | \(0.119393\pi\) | ||||
−0.930476 | + | 0.366352i | \(0.880607\pi\) | |||||||
\(38\) | − | 920.864i | − | 0.637717i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 1125.02i | − | 0.703135i | ||||||
\(41\) | 2301.23 | 1.36897 | 0.684483 | − | 0.729029i | \(-0.260028\pi\) | ||||
0.684483 | + | 0.729029i | \(0.260028\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2157.18i | 1.16667i | 0.812231 | + | 0.583336i | \(0.198253\pi\) | ||||
−0.812231 | + | 0.583336i | \(0.801747\pi\) | |||||||
\(44\) | 201.396i | 0.104027i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2528.30 | −1.19485 | ||||||||
\(47\) | 1199.13i | 0.542840i | 0.962461 | + | 0.271420i | \(0.0874932\pi\) | ||||
−0.962461 | + | 0.271420i | \(0.912507\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6184.90 | 2.57597 | ||||||||
\(50\) | 1246.44i | 0.498577i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 896.743i | − | 0.331636i | ||||||
\(53\) | 1101.00 | 0.391956 | 0.195978 | − | 0.980608i | \(-0.437212\pi\) | ||||
0.195978 | + | 0.980608i | \(0.437212\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 789.569i | 0.261015i | ||||||||
\(56\) | − | 6426.67i | − | 2.04932i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3441.98i | 1.02318i | ||||||||
\(59\) | 1324.95 | − | 3218.99i | 0.380623 | − | 0.924730i | ||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4030.40i | 1.08315i | 0.840653 | + | 0.541574i | \(0.182172\pi\) | ||||
−0.840653 | + | 0.541574i | \(0.817828\pi\) | |||||||
\(62\) | −1957.05 | −0.509117 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4536.57 | −1.10756 | ||||||||
\(65\) | − | 3515.67i | − | 0.832111i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8142.38i | − | 1.81385i | −0.421290 | − | 0.906926i | \(-0.638423\pi\) | ||
0.421290 | − | 0.906926i | \(-0.361577\pi\) | |||||||
\(68\) | −711.544 | −0.153881 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 5176.65i | − | 1.05646i | ||||||
\(71\) | 2537.07 | 0.503286 | 0.251643 | − | 0.967820i | \(-0.419029\pi\) | ||||
0.251643 | + | 0.967820i | \(0.419029\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 792.331i | − | 0.148683i | −0.997233 | − | 0.0743414i | \(-0.976315\pi\) | ||
0.997233 | − | 0.0743414i | \(-0.0236855\pi\) | |||||||
\(74\) | 3454.80 | 0.630898 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1106.19 | 0.191515 | ||||||||
\(77\) | 4510.43i | 0.760740i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3214.46 | −0.515056 | −0.257528 | − | 0.966271i | \(-0.582908\pi\) | ||||
−0.257528 | + | 0.966271i | \(0.582908\pi\) | |||||||
\(80\) | −2801.03 | −0.437661 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 7925.93i | − | 1.17875i | ||||||
\(83\) | 10537.1i | 1.52956i | 0.644292 | + | 0.764779i | \(0.277152\pi\) | ||||
−0.644292 | + | 0.764779i | \(0.722848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2789.60 | −0.386103 | ||||||||
\(86\) | 7429.78 | 1.00457 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3376.12 | 0.435966 | ||||||||
\(89\) | 226.497i | 0.0285945i | 0.999898 | + | 0.0142972i | \(0.00455111\pi\) | ||||
−0.999898 | + | 0.0142972i | \(0.995449\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 20083.3i | − | 2.42523i | ||||||
\(92\) | − | 3037.13i | − | 0.358829i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4130.07 | 0.467414 | ||||||||
\(95\) | 4336.81 | 0.480533 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7280.88i | − | 0.773821i | −0.922117 | − | 0.386911i | \(-0.873542\pi\) | ||
0.922117 | − | 0.386911i | \(-0.126458\pi\) | |||||||
\(98\) | − | 21302.1i | − | 2.21805i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1497.29 | −0.149729 | ||||||||
\(101\) | 11745.9i | 1.15145i | 0.817643 | + | 0.575725i | \(0.195280\pi\) | ||||
−0.817643 | + | 0.575725i | \(0.804720\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 19029.4i | − | 1.79370i | −0.442333 | − | 0.896851i | \(-0.645849\pi\) | ||
0.442333 | − | 0.896851i | \(-0.354151\pi\) | |||||||
\(104\) | −15032.7 | −1.38985 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 3792.10i | − | 0.337495i | ||||||
\(107\) | −6751.89 | −0.589737 | −0.294868 | − | 0.955538i | \(-0.595276\pi\) | ||||
−0.294868 | + | 0.955538i | \(0.595276\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 22919.8i | 1.92911i | 0.263876 | + | 0.964556i | \(0.414999\pi\) | ||||
−0.263876 | + | 0.964556i | \(0.585001\pi\) | |||||||
\(110\) | 2719.45 | 0.224748 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −16000.9 | −1.27558 | ||||||||
\(113\) | − | 1167.57i | − | 0.0914377i | −0.998954 | − | 0.0457188i | \(-0.985442\pi\) | ||
0.998954 | − | 0.0457188i | \(-0.0145578\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 11907.0i | − | 0.900343i | ||||||
\(116\) | −4134.70 | −0.307276 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11086.9 | − | 4563.41i | −0.796243 | − | 0.327737i | ||||
\(119\) | −15935.6 | −1.12532 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12271.5 | 0.838163 | ||||||||
\(122\) | 13881.6 | 0.932649 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 2350.91i | − | 0.152895i | ||||||
\(125\) | −16008.0 | −1.02451 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14064.3 | −0.871990 | −0.435995 | − | 0.899949i | \(-0.643603\pi\) | ||||
−0.435995 | + | 0.899949i | \(0.643603\pi\) | |||||||
\(128\) | 7385.60i | 0.450781i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12108.7 | −0.716492 | ||||||||
\(131\) | 15833.5i | 0.922644i | 0.887233 | + | 0.461322i | \(0.152625\pi\) | ||||
−0.887233 | + | 0.461322i | \(0.847375\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24774.1 | 1.40054 | ||||||||
\(134\) | −28044.1 | −1.56182 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11928.1i | 0.644899i | ||||||||
\(137\) | 21940.7 | 1.16899 | 0.584493 | − | 0.811399i | \(-0.301293\pi\) | ||||
0.584493 | + | 0.811399i | \(0.301293\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −33025.6 | −1.70931 | −0.854655 | − | 0.519196i | \(-0.826231\pi\) | ||||
−0.854655 | + | 0.519196i | \(0.826231\pi\) | |||||||
\(140\) | 6218.47 | 0.317269 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 8738.20i | − | 0.433357i | ||||||
\(143\) | 10550.4 | 0.515936 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16210.0 | −0.770988 | ||||||||
\(146\) | −2728.96 | −0.128024 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4150.09i | 0.189467i | ||||||||
\(149\) | 20821.5i | 0.937863i | 0.883235 | + | 0.468932i | \(0.155361\pi\) | ||||
−0.883235 | + | 0.468932i | \(0.844639\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9654.62i | 0.423430i | 0.977331 | + | 0.211715i | \(0.0679048\pi\) | ||||
−0.977331 | + | 0.211715i | \(0.932095\pi\) | |||||||
\(152\) | − | 18543.8i | − | 0.802622i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 15534.9 | 0.655038 | ||||||||
\(155\) | − | 9216.71i | − | 0.383630i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 23483.9i | − | 0.952731i | −0.879247 | − | 0.476366i | \(-0.841954\pi\) | ||
0.879247 | − | 0.476366i | \(-0.158046\pi\) | |||||||
\(158\) | 11071.3i | 0.443491i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 8352.90i | − | 0.326285i | ||||||
\(161\) | − | 68019.2i | − | 2.62410i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12805.6 | 0.481977 | 0.240988 | − | 0.970528i | \(-0.422528\pi\) | ||||
0.240988 | + | 0.970528i | \(0.422528\pi\) | |||||||
\(164\) | 9521.06 | 0.353995 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 36292.2 | 1.31703 | ||||||||
\(167\) | 29956.3 | 1.07413 | 0.537063 | − | 0.843542i | \(-0.319534\pi\) | ||||
0.537063 | + | 0.843542i | \(0.319534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18416.0 | −0.644796 | ||||||||
\(170\) | 9607.98i | 0.332456i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8925.05i | 0.301685i | ||||||||
\(173\) | − | 51496.1i | − | 1.72061i | −0.509781 | − | 0.860304i | \(-0.670274\pi\) | ||
0.509781 | − | 0.860304i | \(-0.329726\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −33533.2 | −1.09496 | ||||||||
\(176\) | − | 8405.76i | − | 0.271364i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 780.104 | 0.0246214 | ||||||||
\(179\) | − | 17057.4i | − | 0.532363i | −0.963923 | − | 0.266181i | \(-0.914238\pi\) | ||
0.963923 | − | 0.266181i | \(-0.0857620\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7526.56 | 0.229741 | 0.114871 | − | 0.993380i | \(-0.463355\pi\) | ||||
0.114871 | + | 0.993380i | \(0.463355\pi\) | |||||||
\(182\) | −69171.3 | −2.08825 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −50913.4 | −1.50382 | ||||||||
\(185\) | 16270.4i | 0.475394i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 8371.46i | − | 0.239397i | ||||||
\(188\) | 4961.27i | 0.140371i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 14936.9i | − | 0.413765i | ||||||
\(191\) | 34367.0i | 0.942053i | 0.882119 | + | 0.471026i | \(0.156116\pi\) | ||||
−0.882119 | + | 0.471026i | \(0.843884\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −35591.7 | −0.955507 | −0.477753 | − | 0.878494i | \(-0.658549\pi\) | ||||
−0.477753 | + | 0.878494i | \(0.658549\pi\) | |||||||
\(194\) | −25076.9 | −0.666302 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 25589.3 | 0.666110 | ||||||||
\(197\) | 25127.2 | 0.647458 | 0.323729 | − | 0.946150i | \(-0.395063\pi\) | ||||
0.323729 | + | 0.946150i | \(0.395063\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19989.2 | 0.504765 | 0.252382 | − | 0.967628i | \(-0.418786\pi\) | ||||
0.252382 | + | 0.967628i | \(0.418786\pi\) | |||||||
\(200\) | 25100.1i | 0.627502i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 40455.6 | 0.991460 | ||||||||
\(203\) | −92600.1 | −2.24709 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 37327.2 | 0.888214 | ||||||||
\(206\) | −65541.3 | −1.54447 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 37427.9i | 0.865104i | ||||||||
\(209\) | 13014.6i | 0.297946i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 32244.7i | 0.724257i | 0.932128 | + | 0.362129i | \(0.117950\pi\) | ||||
−0.932128 | + | 0.362129i | \(0.882050\pi\) | |||||||
\(212\) | 4555.27 | 0.101354 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 23255.0i | 0.507795i | ||||||||
\(215\) | 34990.5i | 0.756962i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 52650.6i | − | 1.11811i | ||||||
\(218\) | 78940.7 | 1.66107 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3266.75i | 0.0674948i | ||||||||
\(221\) | 37275.1i | 0.763193i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28806.5 | −0.579270 | −0.289635 | − | 0.957137i | \(-0.593534\pi\) | ||||
−0.289635 | + | 0.957137i | \(0.593534\pi\) | |||||||
\(224\) | − | 47716.1i | − | 0.950975i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4021.36 | −0.0787328 | ||||||||
\(227\) | − | 57367.6i | − | 1.11331i | −0.830745 | − | 0.556654i | \(-0.812085\pi\) | ||
0.830745 | − | 0.556654i | \(-0.187915\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 8038.50i | − | 0.153287i | −0.997059 | − | 0.0766433i | \(-0.975580\pi\) | ||
0.997059 | − | 0.0766433i | \(-0.0244203\pi\) | |||||||
\(230\) | −41010.4 | −0.775244 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 69312.6i | 1.28776i | ||||||||
\(233\) | 55821.9i | 1.02824i | 0.857719 | + | 0.514118i | \(0.171881\pi\) | ||||
−0.857719 | + | 0.514118i | \(0.828119\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19450.6i | 0.352206i | ||||||||
\(236\) | 5481.82 | − | 13318.2i | 0.0984239 | − | 0.239122i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 54885.8i | 0.968960i | ||||||||
\(239\) | 35079.1 | 0.614120 | 0.307060 | − | 0.951690i | \(-0.400655\pi\) | ||||
0.307060 | + | 0.951690i | \(0.400655\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 84946.1 | 1.46255 | 0.731273 | − | 0.682085i | \(-0.238927\pi\) | ||||
0.731273 | + | 0.682085i | \(0.238927\pi\) | |||||||
\(242\) | − | 42265.8i | − | 0.721703i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 16675.3i | 0.280087i | ||||||||
\(245\) | 100322. | 1.67134 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 57949.2i | − | 0.949847i | ||||||
\(248\) | −39409.8 | −0.640768 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 55134.8i | 0.882157i | ||||||||
\(251\) | 62187.4 | 0.987086 | 0.493543 | − | 0.869721i | \(-0.335702\pi\) | ||||
0.493543 | + | 0.869721i | \(0.335702\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 35732.5 | 0.558242 | ||||||||
\(254\) | 48440.5i | 0.750830i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −47147.6 | −0.719415 | ||||||||
\(257\) | 11454.6 | 0.173426 | 0.0867129 | − | 0.996233i | \(-0.472364\pi\) | ||||
0.0867129 | + | 0.996233i | \(0.472364\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 92944.8i | 1.38556i | ||||||||
\(260\) | − | 14545.7i | − | 0.215172i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 54533.9 | 0.794446 | ||||||||
\(263\) | −39389.7 | −0.569471 | −0.284735 | − | 0.958606i | \(-0.591906\pi\) | ||||
−0.284735 | + | 0.958606i | \(0.591906\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17858.9 | 0.254310 | ||||||||
\(266\) | − | 85327.4i | − | 1.20594i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 33688.1i | − | 0.469037i | ||||||
\(269\) | 13109.8i | 0.181172i | 0.995889 | + | 0.0905861i | \(0.0288740\pi\) | ||||
−0.995889 | + | 0.0905861i | \(0.971126\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 63942.9 | 0.870670 | 0.435335 | − | 0.900268i | \(-0.356630\pi\) | ||||
0.435335 | + | 0.900268i | \(0.356630\pi\) | |||||||
\(272\) | 29698.1 | 0.401412 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 75568.5i | − | 1.00656i | ||||||
\(275\) | − | 17616.0i | − | 0.232938i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26097.8 | −0.340130 | −0.170065 | − | 0.985433i | \(-0.554398\pi\) | ||||
−0.170065 | + | 0.985433i | \(0.554398\pi\) | |||||||
\(278\) | 113747.i | 1.47181i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 104244.i | − | 1.32964i | ||||||
\(281\) | 33934.6 | 0.429765 | 0.214882 | − | 0.976640i | \(-0.431063\pi\) | ||||
0.214882 | + | 0.976640i | \(0.431063\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 50184.5i | 0.626609i | 0.949653 | + | 0.313305i | \(0.101436\pi\) | ||||
−0.949653 | + | 0.313305i | \(0.898564\pi\) | |||||||
\(284\) | 10496.8 | 0.130143 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 36337.7i | − | 0.444248i | ||||||
\(287\) | 213232. | 2.58875 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −53944.1 | −0.645875 | ||||||||
\(290\) | 55830.8i | 0.663863i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 3278.17i | − | 0.0384473i | ||||||
\(293\) | 145740. | 1.69764 | 0.848819 | − | 0.528684i | \(-0.177314\pi\) | ||||
0.848819 | + | 0.528684i | \(0.177314\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21491.4 | − | 52213.7i | 0.246957 | − | 0.599985i | ||||
\(296\) | 69570.6 | 0.794040 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 71713.7 | 0.807551 | ||||||||
\(299\) | −159104. | −1.77967 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 199884.i | 2.20620i | ||||||||
\(302\) | 33252.6 | 0.364596 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −46169.7 | −0.499586 | ||||||||
\(305\) | 65375.2i | 0.702770i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −37666.1 | −0.399645 | −0.199822 | − | 0.979832i | \(-0.564037\pi\) | ||||
−0.199822 | + | 0.979832i | \(0.564037\pi\) | |||||||
\(308\) | 18661.4i | 0.196717i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −31744.3 | −0.330326 | ||||||||
\(311\) | 145763. | 1.50704 | 0.753522 | − | 0.657423i | \(-0.228353\pi\) | ||||
0.753522 | + | 0.657423i | \(0.228353\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28891.9i | 0.294908i | 0.989069 | + | 0.147454i | \(0.0471079\pi\) | ||||
−0.989069 | + | 0.147454i | \(0.952892\pi\) | |||||||
\(314\) | −80883.5 | −0.820353 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13299.5 | −0.133186 | ||||||||
\(317\) | −149119. | −1.48393 | −0.741967 | − | 0.670437i | \(-0.766107\pi\) | ||||
−0.741967 | + | 0.670437i | \(0.766107\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 48645.6i | − | 0.478038i | ||||||
\(320\) | −73585.6 | −0.718610 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −234273. | −2.25949 | ||||||||
\(323\) | −45981.3 | −0.440734 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 78437.6i | 0.742605i | ||||||||
\(326\) | − | 44105.4i | − | 0.415008i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 159608.i | − | 1.48356i | ||||||
\(329\) | 111112.i | 1.02652i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20162.8 | 0.184033 | 0.0920164 | − | 0.995757i | \(-0.470669\pi\) | ||||
0.0920164 | + | 0.995757i | \(0.470669\pi\) | |||||||
\(332\) | 43596.1i | 0.395523i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 103176.i | − | 0.924880i | ||||||
\(335\) | − | 132074.i | − | 1.17687i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 56644.5i | 0.498767i | 0.968405 | + | 0.249384i | \(0.0802280\pi\) | ||||
−0.968405 | + | 0.249384i | \(0.919772\pi\) | |||||||
\(338\) | 63428.7i | 0.555204i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11541.6 | −0.0998410 | ||||||||
\(341\) | 27658.9 | 0.237863 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 350617. | 2.98020 | ||||||||
\(344\) | 149616. | 1.26433 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −177364. | −1.48154 | ||||||||
\(347\) | − | 98468.3i | − | 0.817782i | −0.912583 | − | 0.408891i | \(-0.865916\pi\) | ||
0.912583 | − | 0.408891i | \(-0.134084\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 11046.8i | − | 0.0906953i | −0.998971 | − | 0.0453476i | \(-0.985560\pi\) | ||
0.998971 | − | 0.0453476i | \(-0.0144396\pi\) | |||||||
\(350\) | 115495.i | 0.942820i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 25066.7 | 0.202307 | ||||||||
\(353\) | 82041.3i | 0.658390i | 0.944262 | + | 0.329195i | \(0.106777\pi\) | ||||
−0.944262 | + | 0.329195i | \(0.893223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 41152.6 | 0.326543 | ||||||||
\(356\) | 937.104i | 0.00739414i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −58749.5 | −0.458393 | ||||||||
\(359\) | 48438.3 | 0.375837 | 0.187919 | − | 0.982185i | \(-0.439826\pi\) | ||||
0.187919 | + | 0.982185i | \(0.439826\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −58836.8 | −0.451476 | ||||||||
\(362\) | − | 25923.1i | − | 0.197820i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 83092.3i | − | 0.627131i | ||||||
\(365\) | − | 12852.0i | − | 0.0964686i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 206944.i | 1.53646i | 0.640175 | + | 0.768229i | \(0.278862\pi\) | ||||
−0.640175 | + | 0.768229i | \(0.721138\pi\) | |||||||
\(368\) | 126762.i | 0.936041i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 56038.7 | 0.409340 | ||||||||
\(371\) | 102019. | 0.741198 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 96391.4 | 0.692821 | 0.346410 | − | 0.938083i | \(-0.387401\pi\) | ||||
0.346410 | + | 0.938083i | \(0.387401\pi\) | |||||||
\(374\) | −28833.1 | −0.206133 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 83168.8 | 0.588281 | ||||||||
\(377\) | 216601.i | 1.52398i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 222227. | 1.54710 | 0.773549 | − | 0.633737i | \(-0.218480\pi\) | ||||
0.773549 | + | 0.633737i | \(0.218480\pi\) | |||||||
\(380\) | 17943.0 | 0.124259 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 118367. | 0.811158 | ||||||||
\(383\) | −251261. | −1.71288 | −0.856440 | − | 0.516246i | \(-0.827329\pi\) | ||||
−0.856440 | + | 0.516246i | \(0.827329\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 73161.6i | 0.493585i | ||||||||
\(386\) | 122585.i | 0.822743i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 30123.8i | − | 0.200100i | ||||||
\(389\) | −247468. | −1.63538 | −0.817691 | − | 0.575657i | \(-0.804746\pi\) | ||||
−0.817691 | + | 0.575657i | \(0.804746\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 126245.i | 0.825774i | ||||||||
\(392\) | − | 428969.i | − | 2.79161i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 86543.4i | − | 0.557496i | ||||||
\(395\) | −52140.3 | −0.334179 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15188.5i | 0.0963684i | 0.998838 | + | 0.0481842i | \(0.0153435\pi\) | ||||
−0.998838 | + | 0.0481842i | \(0.984657\pi\) | |||||||
\(398\) | − | 68847.1i | − | 0.434630i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 62493.4 | 0.390583 | ||||||||
\(401\) | 41102.4i | 0.255611i | 0.991799 | + | 0.127805i | \(0.0407933\pi\) | ||||
−0.991799 | + | 0.127805i | \(0.959207\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −123155. | −0.758304 | ||||||||
\(404\) | 48597.4i | 0.297749i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 318935.i | 1.93486i | ||||||||
\(407\) | −48826.7 | −0.294760 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 119091.i | 0.711925i | 0.934500 | + | 0.355962i | \(0.115847\pi\) | ||||
−0.934500 | + | 0.355962i | \(0.884153\pi\) | |||||||
\(410\) | − | 128563.i | − | 0.764800i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 78731.7i | − | 0.463826i | ||||||
\(413\) | 122770. | − | 298272.i | 0.719768 | − | 1.74869i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 170918.i | 0.992411i | ||||||||
\(416\) | −111613. | −0.644953 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 44825.0 | 0.256547 | ||||||||
\(419\) | 228690.i | 1.30263i | 0.758809 | + | 0.651313i | \(0.225782\pi\) | ||||
−0.758809 | + | 0.651313i | \(0.774218\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 282680.i | 1.59489i | 0.603390 | + | 0.797447i | \(0.293816\pi\) | ||||
−0.603390 | + | 0.797447i | \(0.706184\pi\) | |||||||
\(422\) | 111058. | 0.623624 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 76362.9i | − | 0.424767i | ||||||
\(425\) | 62238.3 | 0.344572 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 373457.i | 2.04826i | ||||||||
\(428\) | −27935.1 | −0.152498 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 120515. | 0.651785 | ||||||||
\(431\) | 270326.i | 1.45524i | 0.685981 | + | 0.727619i | \(0.259373\pi\) | ||||
−0.685981 | + | 0.727619i | \(0.740627\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −201414. | −1.07427 | −0.537136 | − | 0.843496i | \(-0.680494\pi\) | ||||
−0.537136 | + | 0.843496i | \(0.680494\pi\) | |||||||
\(434\) | −181340. | −0.962752 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 94827.9i | 0.498842i | ||||||||
\(437\) | − | 196265.i | − | 1.02773i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10876.9 | −0.0564388 | −0.0282194 | − | 0.999602i | \(-0.508984\pi\) | ||||
−0.0282194 | + | 0.999602i | \(0.508984\pi\) | |||||||
\(440\) | 54762.5 | 0.282864 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 128384. | 0.657151 | ||||||||
\(443\) | − | 28282.8i | − | 0.144117i | −0.997400 | − | 0.0720584i | \(-0.977043\pi\) | ||
0.997400 | − | 0.0720584i | \(-0.0229568\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3673.90i | 0.0185527i | ||||||||
\(446\) | 99215.8i | 0.498782i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −420360. | −2.09443 | ||||||||
\(449\) | −158321. | −0.785320 | −0.392660 | − | 0.919684i | \(-0.628445\pi\) | ||||
−0.392660 | + | 0.919684i | \(0.628445\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 112017.i | 0.550721i | ||||||||
\(452\) | − | 4830.67i | − | 0.0236445i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −197586. | −0.958618 | ||||||||
\(455\) | − | 325762.i | − | 1.57354i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 35833.3i | − | 0.171575i | −0.996313 | − | 0.0857876i | \(-0.972659\pi\) | ||
0.996313 | − | 0.0857876i | \(-0.0273406\pi\) | |||||||
\(458\) | −27686.3 | −0.131988 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 49263.9i | − | 0.232816i | ||||||
\(461\) | −307571. | −1.44725 | −0.723625 | − | 0.690193i | \(-0.757526\pi\) | ||||
−0.723625 | + | 0.690193i | \(0.757526\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 272379.i | − | 1.27061i | −0.772262 | − | 0.635304i | \(-0.780875\pi\) | ||
0.772262 | − | 0.635304i | \(-0.219125\pi\) | |||||||
\(464\) | 172572. | 0.801558 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 192263. | 0.885367 | ||||||||
\(467\) | 217459.i | 0.997111i | 0.866858 | + | 0.498556i | \(0.166136\pi\) | ||||
−0.866858 | + | 0.498556i | \(0.833864\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 754474.i | − | 3.43004i | ||||||
\(470\) | 66992.0 | 0.303268 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −223261. | − | 91895.2i | −1.00214 | − | 0.412485i | ||||
\(473\) | −105005. | −0.469341 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −96757.9 | −0.428844 | ||||||||
\(476\) | −65931.8 | −0.290992 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 120820.i | − | 0.528790i | ||||||
\(479\) | 56488.8 | 0.246202 | 0.123101 | − | 0.992394i | \(-0.460716\pi\) | ||||
0.123101 | + | 0.992394i | \(0.460716\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 217408. | 0.939691 | ||||||||
\(482\) | − | 292573.i | − | 1.25933i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 50772.0 | 0.216737 | ||||||||
\(485\) | − | 118100.i | − | 0.502072i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −374783. | −1.58024 | −0.790118 | − | 0.612954i | \(-0.789981\pi\) | ||||
−0.790118 | + | 0.612954i | \(0.789981\pi\) | |||||||
\(488\) | 279538. | 1.17382 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 345532.i | − | 1.43912i | ||||||
\(491\) | 61744.1 | 0.256114 | 0.128057 | − | 0.991767i | \(-0.459126\pi\) | ||||
0.128057 | + | 0.991767i | \(0.459126\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 171868. | 0.707133 | ||||||||
\(494\) | −199590. | −0.817870 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 98121.2i | 0.398841i | ||||||||
\(497\) | 235085. | 0.951726 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −212124. | −0.851901 | −0.425950 | − | 0.904747i | \(-0.640060\pi\) | ||||
−0.425950 | + | 0.904747i | \(0.640060\pi\) | |||||||
\(500\) | −66231.0 | −0.264924 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 214187.i | − | 0.849934i | ||||||
\(503\) | − | 268106.i | − | 1.05967i | −0.848101 | − | 0.529834i | \(-0.822254\pi\) | ||
0.848101 | − | 0.529834i | \(-0.177746\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 190525.i | 0.747085i | ||||||||
\(506\) | − | 123070.i | − | 0.480676i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −58189.4 | −0.225484 | ||||||||
\(509\) | 241532.i | 0.932265i | 0.884715 | + | 0.466133i | \(0.154353\pi\) | ||||
−0.884715 | + | 0.466133i | \(0.845647\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 73417.5i | − | 0.281163i | ||||||
\(512\) | 280556.i | 1.07024i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 39452.1i | − | 0.149329i | ||||||
\(515\) | − | 308667.i | − | 1.16379i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −58370.3 | −0.218379 | ||||||||
\(518\) | 320122. | 1.19304 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −243838. | −0.901767 | ||||||||
\(521\) | −81137.0 | −0.298912 | −0.149456 | − | 0.988768i | \(-0.547752\pi\) | ||||
−0.149456 | + | 0.988768i | \(0.547752\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 507362. | 1.85488 | 0.927438 | − | 0.373977i | \(-0.122006\pi\) | ||||
0.927438 | + | 0.373977i | \(0.122006\pi\) | |||||||
\(524\) | 65509.1i | 0.238583i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 135667.i | 0.490345i | ||||||||
\(527\) | 97720.8i | 0.351857i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −259020. | −0.925598 | ||||||||
\(530\) | − | 61509.9i | − | 0.218974i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 102500. | 0.362160 | ||||||||
\(533\) | − | 498773.i | − | 1.75569i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −109519. | −0.382634 | ||||||||
\(536\) | −564735. | −1.96569 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 45153.0 | 0.155999 | ||||||||
\(539\) | 301063.i | 1.03629i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 303310.i | − | 1.03632i | −0.855285 | − | 0.518158i | \(-0.826618\pi\) | ||
0.855285 | − | 0.518158i | \(-0.173382\pi\) | |||||||
\(542\) | − | 220233.i | − | 0.749694i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 88562.2i | 0.299261i | ||||||||
\(545\) | 371771.i | 1.25165i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 185234. | 0.619077 | 0.309539 | − | 0.950887i | \(-0.399825\pi\) | ||||
0.309539 | + | 0.950887i | \(0.399825\pi\) | |||||||
\(548\) | 90777.0 | 0.302284 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −60673.2 | −0.200573 | ||||||||
\(551\) | −267192. | −0.880076 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −297853. | −0.973983 | ||||||||
\(554\) | 89886.5i | 0.292870i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −136639. | −0.442004 | ||||||||
\(557\) | −300545. | −0.968723 | −0.484361 | − | 0.874868i | \(-0.660948\pi\) | ||||
−0.484361 | + | 0.874868i | \(0.660948\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 467550. | 1.49625 | ||||||||
\(560\) | −259544. | −0.827626 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 116878.i | − | 0.370050i | ||||||
\(563\) | − | 110761.i | − | 0.349437i | −0.984618 | − | 0.174719i | \(-0.944098\pi\) | ||
0.984618 | − | 0.174719i | \(-0.0559016\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 18938.6i | − | 0.0593267i | ||||||
\(566\) | 172846. | 0.539544 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 175965.i | − | 0.545417i | ||||||
\(569\) | 85112.7i | 0.262887i | 0.991324 | + | 0.131444i | \(0.0419612\pi\) | ||||
−0.991324 | + | 0.131444i | \(0.958039\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 419082.i | 1.28537i | 0.766132 | + | 0.642683i | \(0.222179\pi\) | ||||
−0.766132 | + | 0.642683i | \(0.777821\pi\) | |||||||
\(572\) | 43650.9 | 0.133414 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 734418.i | − | 2.22905i | ||||||
\(575\) | 265656.i | 0.803497i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −210330. | −0.631757 | −0.315878 | − | 0.948800i | \(-0.602299\pi\) | ||||
−0.315878 | + | 0.948800i | \(0.602299\pi\) | |||||||
\(578\) | 185795.i | 0.556133i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −67067.0 | −0.199367 | ||||||||
\(581\) | 976372.i | 2.89243i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 53593.7i | 0.157680i | ||||||||
\(584\) | −54954.1 | −0.161129 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 501962.i | − | 1.46176i | ||||||
\(587\) | − | 645237.i | − | 1.87259i | −0.351213 | − | 0.936296i | \(-0.614231\pi\) | ||
0.351213 | − | 0.936296i | \(-0.385769\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 151920.i | − | 0.437910i | ||||||
\(590\) | −179835. | − | 74021.0i | −0.516619 | − | 0.212643i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 173215.i | − | 0.494244i | ||||||
\(593\) | 386221. | 1.09831 | 0.549157 | − | 0.835719i | \(-0.314949\pi\) | ||||
0.549157 | + | 0.835719i | \(0.314949\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −258485. | −0.730131 | ||||||||
\(596\) | 86146.4i | 0.242518i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 547989.i | 1.53239i | ||||||||
\(599\) | 388204. | 1.08195 | 0.540974 | − | 0.841039i | \(-0.318056\pi\) | ||||
0.540974 | + | 0.841039i | \(0.318056\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 510006.i | − | 1.41197i | −0.708225 | − | 0.705987i | \(-0.750504\pi\) | ||
0.708225 | − | 0.705987i | \(-0.249496\pi\) | |||||||
\(602\) | 688444. | 1.89966 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 39944.8i | 0.109493i | ||||||||
\(605\) | 199051. | 0.543818 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −560179. | −1.52037 | −0.760185 | − | 0.649707i | \(-0.774892\pi\) | ||||
−0.760185 | + | 0.649707i | \(0.774892\pi\) | |||||||
\(608\) | − | 137682.i | − | 0.372452i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 225166. | 0.605123 | ||||||||
\(611\) | 259902. | 0.696190 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 306896.i | 0.816715i | 0.912822 | + | 0.408358i | \(0.133898\pi\) | ||||
−0.912822 | + | 0.408358i | \(0.866102\pi\) | |||||||
\(614\) | 129730.i | 0.344116i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 312832. | 0.824422 | ||||||||
\(617\) | −465889. | −1.22380 | −0.611902 | − | 0.790933i | \(-0.709595\pi\) | ||||
−0.611902 | + | 0.790933i | \(0.709595\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 608265. | 1.58749 | 0.793746 | − | 0.608250i | \(-0.208128\pi\) | ||||
0.793746 | + | 0.608250i | \(0.208128\pi\) | |||||||
\(620\) | − | 38133.0i | − | 0.0992014i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 502039.i | − | 1.29765i | ||||||
\(623\) | 20987.2i | 0.0540728i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −33473.7 | −0.0856927 | ||||||||
\(626\) | 99509.8 | 0.253932 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 97161.7i | − | 0.246363i | ||||||
\(629\) | − | 172508.i | − | 0.436021i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −51223.1 | −0.128649 | −0.0643245 | − | 0.997929i | \(-0.520489\pi\) | ||||
−0.0643245 | + | 0.997929i | \(0.520489\pi\) | |||||||
\(632\) | 222947.i | 0.558171i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 513598.i | 1.27775i | ||||||||
\(635\) | −228131. | −0.565766 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.34053e6i | − | 3.30367i | ||||||
\(638\) | −167546. | −0.411616 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 119798.i | 0.292476i | ||||||||
\(641\) | 194528. | 0.473440 | 0.236720 | − | 0.971578i | \(-0.423928\pi\) | ||||
0.236720 | + | 0.971578i | \(0.423928\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −127058. | −0.307312 | −0.153656 | − | 0.988124i | \(-0.549105\pi\) | ||||
−0.153656 | + | 0.988124i | \(0.549105\pi\) | |||||||
\(644\) | − | 281421.i | − | 0.678555i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 158370.i | 0.379495i | ||||||||
\(647\) | −298850. | −0.713912 | −0.356956 | − | 0.934121i | \(-0.616185\pi\) | ||||
−0.356956 | + | 0.934121i | \(0.616185\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 156691. | + | 64494.7i | 0.372010 | + | 0.153121i | ||||
\(650\) | 270156. | 0.639423 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 52981.8 | 0.124633 | ||||||||
\(653\) | 808235. | 1.89545 | 0.947723 | − | 0.319094i | \(-0.103379\pi\) | ||||
0.947723 | + | 0.319094i | \(0.103379\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 256828.i | 0.598631i | ||||||||
\(656\) | −397386. | −0.923431 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 382693. | 0.883891 | ||||||||
\(659\) | − | 205299.i | − | 0.472732i | −0.971664 | − | 0.236366i | \(-0.924044\pi\) | ||
0.971664 | − | 0.236366i | \(-0.0759565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −218321. | −0.499680 | −0.249840 | − | 0.968287i | \(-0.580378\pi\) | ||||
−0.249840 | + | 0.968287i | \(0.580378\pi\) | |||||||
\(662\) | − | 69445.1i | − | 0.158462i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 730829. | 1.65760 | ||||||||
\(665\) | 401849. | 0.908699 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 733596.i | 1.64894i | ||||||||
\(668\) | 123940. | 0.277754 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −454891. | −1.01335 | ||||||||
\(671\) | −196188. | −0.435740 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 308870.i | 0.681939i | 0.940074 | + | 0.340970i | \(0.110755\pi\) | ||||
−0.940074 | + | 0.340970i | \(0.889245\pi\) | |||||||
\(674\) | 195096. | 0.429466 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −76194.0 | −0.166735 | ||||||||
\(677\) | 765077. | 1.66927 | 0.834637 | − | 0.550800i | \(-0.185677\pi\) | ||||
0.834637 | + | 0.550800i | \(0.185677\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 674648.i | − | 1.46331i | ||||||
\(680\) | 193479.i | 0.418424i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 95263.3i | − | 0.204813i | ||||||
\(683\) | − | 32889.7i | − | 0.0705047i | −0.999378 | − | 0.0352523i | \(-0.988777\pi\) | ||
0.999378 | − | 0.0352523i | \(-0.0112235\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 355890. | 0.758463 | ||||||||
\(686\) | − | 1.20760e6i | − | 2.56611i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 372510.i | − | 0.786975i | ||||||
\(689\) | − | 238634.i | − | 0.502682i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 498934.i | 1.04493i | 0.852661 | + | 0.522465i | \(0.174987\pi\) | ||||
−0.852661 | + | 0.522465i | \(0.825013\pi\) | |||||||
\(692\) | − | 213059.i | − | 0.444925i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −339146. | −0.704154 | ||||||||
\(695\) | −535693. | −1.10904 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −395764. | −0.814650 | ||||||||
\(698\) | −38047.5 | −0.0780935 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −138739. | −0.283142 | ||||||||
\(701\) | − | 70692.6i | − | 0.143859i | −0.997410 | − | 0.0719297i | \(-0.977084\pi\) | ||
0.997410 | − | 0.0719297i | \(-0.0229157\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 268187.i | 0.542658i | ||||||||
\(704\) | − | 220827.i | − | 0.445561i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 282568. | 0.566909 | ||||||||
\(707\) | 1.08838e6i | 2.17742i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −845715. | −1.68241 | −0.841204 | − | 0.540717i | \(-0.818153\pi\) | ||||
−0.841204 | + | 0.540717i | \(0.818153\pi\) | |||||||
\(710\) | − | 141738.i | − | 0.281171i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15709.3 | 0.0309881 | ||||||||
\(713\) | −417108. | −0.820484 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 171133. | 0.334750 | ||||||||
\(716\) | − | 70573.0i | − | 0.137662i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 166832.i | − | 0.323616i | ||||||
\(719\) | − | 541985.i | − | 1.04841i | −0.851593 | − | 0.524203i | \(-0.824363\pi\) | ||
0.851593 | − | 0.524203i | \(-0.175637\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1.76327e6i | − | 3.39193i | ||||||
\(722\) | 202647.i | 0.388745i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 31140.2 | 0.0594080 | ||||||||
\(725\) | 361660. | 0.688057 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 324956. | 0.614832 | 0.307416 | − | 0.951575i | \(-0.400536\pi\) | ||||
0.307416 | + | 0.951575i | \(0.400536\pi\) | |||||||
\(728\) | −1.39293e6 | −2.62825 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −44265.2 | −0.0830647 | ||||||||
\(731\) | − | 370990.i | − | 0.694268i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −228228. | −0.424777 | −0.212389 | − | 0.977185i | \(-0.568124\pi\) | ||||
−0.212389 | + | 0.977185i | \(0.568124\pi\) | |||||||
\(734\) | 712760. | 1.32297 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −378016. | −0.697839 | ||||||||
\(737\) | 396348. | 0.729695 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 153824.i | − | 0.281667i | −0.990033 | − | 0.140834i | \(-0.955022\pi\) | ||
0.990033 | − | 0.140834i | \(-0.0449782\pi\) | |||||||
\(740\) | 67316.7i | 0.122930i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 351376.i | − | 0.638212i | ||||||
\(743\) | −40762.4 | −0.0738384 | −0.0369192 | − | 0.999318i | \(-0.511754\pi\) | ||||
−0.0369192 | + | 0.999318i | \(0.511754\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 337736.i | 0.608506i | ||||||||
\(746\) | − | 331993.i | − | 0.596556i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 34635.9i | − | 0.0619047i | ||||||
\(749\) | −625632. | −1.11521 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 947341.i | 1.67968i | 0.542834 | + | 0.839840i | \(0.317351\pi\) | ||||
−0.542834 | + | 0.839840i | \(0.682649\pi\) | |||||||
\(752\) | − | 207071.i | − | 0.366171i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 746022. | 1.31223 | ||||||||
\(755\) | 156603.i | 0.274730i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −384807. | −0.671508 | −0.335754 | − | 0.941950i | \(-0.608991\pi\) | ||||
−0.335754 | + | 0.941950i | \(0.608991\pi\) | |||||||
\(758\) | − | 765397.i | − | 1.33213i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 300790.i | − | 0.520758i | ||||||
\(761\) | −621369. | −1.07295 | −0.536476 | − | 0.843916i | \(-0.680245\pi\) | ||||
−0.536476 | + | 0.843916i | \(0.680245\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.12375e6i | 3.64800i | ||||||||
\(764\) | 142189.i | 0.243602i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 865396.i | 1.47488i | ||||||||
\(767\) | −697689. | − | 287172.i | −1.18596 | − | 0.488148i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 140425.i | − | 0.237460i | −0.992927 | − | 0.118730i | \(-0.962118\pi\) | ||
0.992927 | − | 0.118730i | \(-0.0378823\pi\) | |||||||
\(770\) | 251984. | 0.425003 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −147256. | −0.247081 | ||||||||
\(773\) | 233110.i | 0.390124i | 0.980791 | + | 0.195062i | \(0.0624908\pi\) | ||||
−0.980791 | + | 0.195062i | \(0.937509\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 205633.i | 0.342365i | ||||||||
\(776\) | −504984. | −0.838598 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 852332.i | 1.40815i | ||||||||
\(779\) | 615269. | 1.01389 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 123497.i | 0.202467i | ||||||||
\(782\) | 434816. | 0.711036 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.06803e6 | −1.73761 | ||||||||
\(785\) | − | 380921.i | − | 0.618153i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 95032.6 | 0.153435 | 0.0767173 | − | 0.997053i | \(-0.475556\pi\) | ||||
0.0767173 | + | 0.997053i | \(0.475556\pi\) | |||||||
\(788\) | 103961. | 0.167424 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 179583.i | 0.287746i | ||||||||
\(791\) | − | 108187.i | − | 0.172911i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 873555. | 1.38913 | ||||||||
\(794\) | 52312.6 | 0.0829784 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 82702.9 | 0.130525 | ||||||||
\(797\) | 1.06273e6i | 1.67304i | 0.547936 | + | 0.836520i | \(0.315414\pi\) | ||||
−0.547936 | + | 0.836520i | \(0.684586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 206226.i | − | 0.323035i | ||||||
\(800\) | 186361.i | 0.291188i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 141566. | 0.220094 | ||||||||
\(803\) | 38568.4 | 0.0598137 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.10331e6i | − | 1.70257i | ||||||
\(806\) | 424174.i | 0.652940i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 814669. | 1.24784 | ||||||||
\(809\) | 961800.i | 1.46956i | 0.678305 | + | 0.734780i | \(0.262715\pi\) | ||||
−0.678305 | + | 0.734780i | \(0.737285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 957274.i | 1.45544i | 0.685874 | + | 0.727721i | \(0.259420\pi\) | ||||
−0.685874 | + | 0.727721i | \(0.740580\pi\) | |||||||
\(812\) | −383122. | −0.581065 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 168170.i | 0.253804i | ||||||||
\(815\) | 207714. | 0.312717 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 576754.i | 0.864065i | ||||||||
\(818\) | 410177. | 0.613006 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 154437. | 0.229680 | ||||||||
\(821\) | − | 698787.i | − | 1.03671i | −0.855165 | − | 0.518357i | \(-0.826544\pi\) | ||
0.855165 | − | 0.518357i | \(-0.173456\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 551034.i | 0.813540i | 0.913531 | + | 0.406770i | \(0.133345\pi\) | ||||
−0.913531 | + | 0.406770i | \(0.866655\pi\) | |||||||
\(824\) | −1.31983e6 | −1.94385 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.02731e6 | − | 422846.i | −1.50571 | − | 0.619759i | ||||
\(827\) | −833437. | −1.21860 | −0.609301 | − | 0.792939i | \(-0.708550\pi\) | ||||
−0.609301 | + | 0.792939i | \(0.708550\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 882949. | 1.28477 | 0.642387 | − | 0.766381i | \(-0.277944\pi\) | ||||
0.642387 | + | 0.766381i | \(0.277944\pi\) | |||||||
\(830\) | 588678. | 0.854519 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 983265.i | 1.42044i | ||||||||
\(833\) | −1.06368e6 | −1.53292 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 485907. | 0.696916 | ||||||||
\(836\) | 53846.2i | 0.0770447i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 787659. | 1.12163 | ||||||||
\(839\) | 959966.i | 1.36374i | 0.731473 | + | 0.681871i | \(0.238833\pi\) | ||||
−0.731473 | + | 0.681871i | \(0.761167\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 291424. | 0.412034 | ||||||||
\(842\) | 973612. | 1.37329 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 133408.i | 0.187283i | ||||||||
\(845\) | −298718. | −0.418357 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.13708e6 | 1.58499 | ||||||||
\(848\) | −190126. | −0.264393 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 214362.i | − | 0.296695i | ||||||
\(851\) | 736327. | 1.01674 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8821.74 | 0.0121243 | 0.00606214 | − | 0.999982i | \(-0.498070\pi\) | ||||
0.00606214 | + | 0.999982i | \(0.498070\pi\) | |||||||
\(854\) | 1.28627e6 | 1.76366 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 468294.i | 0.639104i | ||||||||
\(857\) | 74384.0i | 0.101279i | 0.998717 | + | 0.0506394i | \(0.0161259\pi\) | ||||
−0.998717 | + | 0.0506394i | \(0.983874\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 106512.i | − | 0.144349i | −0.997392 | − | 0.0721746i | \(-0.977006\pi\) | ||
0.997392 | − | 0.0721746i | \(-0.0229939\pi\) | |||||||
\(860\) | 144769.i | 0.195740i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 931063. | 1.25304 | ||||||||
\(863\) | 662734.i | 0.889852i | 0.895567 | + | 0.444926i | \(0.146770\pi\) | ||||
−0.895567 | + | 0.444926i | \(0.853230\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 835294.i | − | 1.11637i | ||||||
\(866\) | 693714.i | 0.925006i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 217836.i | − | 0.289128i | ||||||
\(869\) | − | 156471.i | − | 0.207202i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.76479e6 | −2.32626 | ||||||||
\(872\) | 1.58966e6 | 2.09060 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −675980. | −0.884934 | ||||||||
\(875\) | −1.48330e6 | −1.93737 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.48294e6 | 1.92808 | 0.964040 | − | 0.265757i | \(-0.0856217\pi\) | ||||
0.964040 | + | 0.265757i | \(0.0856217\pi\) | |||||||
\(878\) | 37462.5i | 0.0485968i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 136346.i | − | 0.176067i | ||||||
\(881\) | − | 734191.i | − | 0.945926i | −0.881082 | − | 0.472963i | \(-0.843184\pi\) | ||
0.881082 | − | 0.472963i | \(-0.156816\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 824634. | 1.05765 | 0.528823 | − | 0.848732i | \(-0.322634\pi\) | ||||
0.528823 | + | 0.848732i | \(0.322634\pi\) | |||||||
\(884\) | 154221.i | 0.197351i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −97412.0 | −0.124092 | ||||||||
\(887\) | 786206.i | 0.999284i | 0.866232 | + | 0.499642i | \(0.166535\pi\) | ||||
−0.866232 | + | 0.499642i | \(0.833465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.30320e6 | −1.64895 | ||||||||
\(890\) | 12653.7 | 0.0159749 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −119183. | −0.149791 | ||||||||
\(893\) | 320606.i | 0.402040i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 276681.i | − | 0.345408i | ||||||
\(896\) | 684351.i | 0.852438i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 545293.i | 0.676203i | ||||||||
\(899\) | 567844.i | 0.702603i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −189350. | −0.233247 | ||||||||
\(902\) | 385812. | 0.474201 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −80979.6 | −0.0990920 | ||||||||
\(905\) | 122085. | 0.149061 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.44869e6 | −1.76101 | −0.880504 | − | 0.474038i | \(-0.842796\pi\) | ||||
−0.880504 | + | 0.474038i | \(0.842796\pi\) | |||||||
\(908\) | − | 237352.i | − | 0.287886i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.12200e6 | −1.35490 | ||||||||
\(911\) | 812697. | 0.979246 | 0.489623 | − | 0.871934i | \(-0.337134\pi\) | ||||
0.489623 | + | 0.871934i | \(0.337134\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −512917. | −0.615327 | ||||||||
\(914\) | −123418. | −0.147735 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 33258.3i | − | 0.0396378i | ||||||
\(917\) | 1.46713e6i | 1.74474i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 851885.i | − | 1.00867i | −0.863507 | − | 0.504336i | \(-0.831737\pi\) | ||
0.863507 | − | 0.504336i | \(-0.168263\pi\) | |||||||
\(920\) | −825842. | −0.975711 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.05934e6i | 1.24616i | ||||||||
\(923\) | − | 549888.i | − | 0.645463i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 363006.i | − | 0.424258i | ||||||
\(926\) | −938132. | −1.09406 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 514625.i | 0.597578i | ||||||||
\(929\) | − | 227195.i | − | 0.263250i | −0.991300 | − | 0.131625i | \(-0.957981\pi\) | ||
0.991300 | − | 0.131625i | \(-0.0420194\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.65363e6 | 1.90782 | ||||||||
\(932\) | 230957.i | 0.265888i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 748976. | 0.858567 | ||||||||
\(935\) | − | 135790.i | − | 0.155326i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 961855.i | 1.09554i | 0.836627 | + | 0.547772i | \(0.184524\pi\) | ||||
−0.836627 | + | 0.547772i | \(0.815476\pi\) | |||||||
\(938\) | −2.59857e6 | −2.95345 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 80474.4i | 0.0910756i | ||||||||
\(941\) | 192956.i | 0.217911i | 0.994047 | + | 0.108955i | \(0.0347506\pi\) | ||||
−0.994047 | + | 0.108955i | \(0.965249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.68927e6i | − | 1.89966i | ||||||
\(944\) | −228798. | + | 555867.i | −0.256748 | + | 0.623774i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 361660.i | 0.404128i | ||||||||
\(947\) | 846036. | 0.943385 | 0.471693 | − | 0.881763i | \(-0.343643\pi\) | ||||
0.471693 | + | 0.881763i | \(0.343643\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −171731. | −0.190685 | ||||||||
\(950\) | 333255.i | 0.369258i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.10526e6i | 1.21952i | ||||||||
\(953\) | −596807. | −0.657125 | −0.328563 | − | 0.944482i | \(-0.606564\pi\) | ||||
−0.328563 | + | 0.944482i | \(0.606564\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 557452.i | 0.611224i | ||||||||
\(956\) | 145136. | 0.158803 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 194560.i | − | 0.211993i | ||||||
\(959\) | 2.03303e6 | 2.21058 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 600656. | 0.650398 | ||||||||
\(962\) | − | 748799.i | − | 0.809124i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 351454. | 0.378194 | ||||||||
\(965\) | −577316. | −0.619953 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 380274.i | − | 0.406672i | −0.979109 | − | 0.203336i | \(-0.934822\pi\) | ||
0.979109 | − | 0.203336i | \(-0.0651784\pi\) | |||||||
\(968\) | − | 851123.i | − | 0.908326i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −406761. | −0.432311 | ||||||||
\(971\) | −1.45439e6 | −1.54256 | −0.771281 | − | 0.636495i | \(-0.780384\pi\) | ||||
−0.771281 | + | 0.636495i | \(0.780384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.06016e6 | −3.23235 | ||||||||
\(974\) | 1.29083e6i | 1.36067i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 695985.i | − | 0.730635i | ||||||
\(977\) | − | 1.71629e6i | − | 1.79805i | −0.437893 | − | 0.899027i | \(-0.644275\pi\) | ||
0.437893 | − | 0.899027i | \(-0.355725\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11025.2 | −0.0115033 | ||||||||
\(980\) | 415072. | 0.432187 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 212660.i | − | 0.220528i | ||||||
\(983\) | − | 1.55447e6i | − | 1.60870i | −0.594155 | − | 0.804350i | \(-0.702513\pi\) | ||
0.594155 | − | 0.804350i | \(-0.297487\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 407576. | 0.420084 | ||||||||
\(986\) | − | 591950.i | − | 0.608880i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 239758.i | − | 0.245617i | ||||||
\(989\) | 1.58352e6 | 1.61894 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.55870e6i | − | 1.58714i | −0.608482 | − | 0.793568i | \(-0.708221\pi\) | ||
0.608482 | − | 0.793568i | \(-0.291779\pi\) | |||||||
\(992\) | −292606. | −0.297344 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 809683.i | − | 0.819488i | ||||||
\(995\) | 324235. | 0.327502 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55668.1 | −0.0560037 | −0.0280018 | − | 0.999608i | \(-0.508914\pi\) | ||||
−0.0280018 | + | 0.999608i | \(0.508914\pi\) | |||||||
\(998\) | 730601.i | 0.733532i | ||||||||
\(999\) | 0 | 0 |
(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 | 531.5.c.d.235.13 | 40 | ||
3.2 | odd | 2 | 177.5.c.a.58.28 | yes | 40 | ||
59.58 | odd | 2 | inner | 531.5.c.d.235.28 | 40 | ||
177.176 | even | 2 | 177.5.c.a.58.13 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.13 | ✓ | 40 | 177.176 | even | 2 | ||
177.5.c.a.58.28 | yes | 40 | 3.2 | odd | 2 | ||
531.5.c.d.235.13 | 40 | 1.1 | even | 1 | trivial | ||
531.5.c.d.235.28 | 40 | 59.58 | odd | 2 | inner |