Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,6,Mod(36,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.36");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.b (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: | \(5.93420133308\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 390 x^{14} + 60701 x^{12} + 4799932 x^{10} + 203487156 x^{8} + 4519465040 x^{6} + \cdots + 178006118400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 36.10 | ||
Root | \(2.85171i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.36 |
Dual form | 37.6.b.a.36.7 |
$q$-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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.85171i | 0.504117i | 0.967712 | + | 0.252058i | \(0.0811075\pi\) | ||||
−0.967712 | + | 0.252058i | \(0.918893\pi\) | |||||||
\(3\) | −12.3080 | −0.789560 | −0.394780 | − | 0.918776i | \(-0.629179\pi\) | ||||
−0.394780 | + | 0.918776i | \(0.629179\pi\) | |||||||
\(4\) | 23.8677 | 0.745866 | ||||||||
\(5\) | 38.2713i | 0.684618i | 0.939587 | + | 0.342309i | \(0.111209\pi\) | ||||
−0.939587 | + | 0.342309i | \(0.888791\pi\) | |||||||
\(6\) | − | 35.0990i | − | 0.398030i | ||||||
\(7\) | −96.3094 | −0.742888 | −0.371444 | − | 0.928455i | \(-0.621137\pi\) | ||||
−0.371444 | + | 0.928455i | \(0.621137\pi\) | |||||||
\(8\) | 159.319i | 0.880120i | ||||||||
\(9\) | −91.5127 | −0.376595 | ||||||||
\(10\) | −109.139 | −0.345127 | ||||||||
\(11\) | −564.497 | −1.40663 | −0.703315 | − | 0.710878i | \(-0.748298\pi\) | ||||
−0.703315 | + | 0.710878i | \(0.748298\pi\) | |||||||
\(12\) | −293.764 | −0.588906 | ||||||||
\(13\) | 678.423i | 1.11338i | 0.830721 | + | 0.556688i | \(0.187928\pi\) | ||||
−0.830721 | + | 0.556688i | \(0.812072\pi\) | |||||||
\(14\) | − | 274.647i | − | 0.374502i | ||||||
\(15\) | − | 471.044i | − | 0.540547i | ||||||
\(16\) | 309.435 | 0.302183 | ||||||||
\(17\) | − | 2074.76i | − | 1.74119i | −0.492002 | − | 0.870594i | \(-0.663735\pi\) | ||
0.492002 | − | 0.870594i | \(-0.336265\pi\) | |||||||
\(18\) | − | 260.968i | − | 0.189848i | ||||||
\(19\) | 2693.06i | 1.71144i | 0.517440 | + | 0.855719i | \(0.326885\pi\) | ||||
−0.517440 | + | 0.855719i | \(0.673115\pi\) | |||||||
\(20\) | 913.449i | 0.510634i | ||||||||
\(21\) | 1185.38 | 0.586555 | ||||||||
\(22\) | − | 1609.78i | − | 0.709106i | ||||||
\(23\) | 3071.93i | 1.21085i | 0.795901 | + | 0.605427i | \(0.206998\pi\) | ||||
−0.795901 | + | 0.605427i | \(0.793002\pi\) | |||||||
\(24\) | − | 1960.90i | − | 0.694908i | ||||||
\(25\) | 1660.31 | 0.531298 | ||||||||
\(26\) | −1934.67 | −0.561272 | ||||||||
\(27\) | 4117.19 | 1.08690 | ||||||||
\(28\) | −2298.69 | −0.554095 | ||||||||
\(29\) | − | 2966.43i | − | 0.654996i | −0.944852 | − | 0.327498i | \(-0.893794\pi\) | ||
0.944852 | − | 0.327498i | \(-0.106206\pi\) | |||||||
\(30\) | 1343.28 | 0.272499 | ||||||||
\(31\) | − | 5199.33i | − | 0.971725i | −0.874035 | − | 0.485863i | \(-0.838506\pi\) | ||
0.874035 | − | 0.485863i | \(-0.161494\pi\) | |||||||
\(32\) | 5980.62i | 1.03246i | ||||||||
\(33\) | 6947.84 | 1.11062 | ||||||||
\(34\) | 5916.63 | 0.877762 | ||||||||
\(35\) | − | 3685.89i | − | 0.508595i | ||||||
\(36\) | −2184.20 | −0.280890 | ||||||||
\(37\) | 7849.71 | + | 2779.56i | 0.942648 | + | 0.333789i | ||||
\(38\) | −7679.83 | −0.862765 | ||||||||
\(39\) | − | 8350.04i | − | 0.879078i | ||||||
\(40\) | −6097.34 | −0.602546 | ||||||||
\(41\) | −6499.88 | −0.603873 | −0.301937 | − | 0.953328i | \(-0.597633\pi\) | ||||
−0.301937 | + | 0.953328i | \(0.597633\pi\) | |||||||
\(42\) | 3380.36i | 0.295692i | ||||||||
\(43\) | 8586.79i | 0.708206i | 0.935206 | + | 0.354103i | \(0.115214\pi\) | ||||
−0.935206 | + | 0.354103i | \(0.884786\pi\) | |||||||
\(44\) | −13473.3 | −1.04916 | ||||||||
\(45\) | − | 3502.31i | − | 0.257824i | ||||||
\(46\) | −8760.27 | −0.610412 | ||||||||
\(47\) | −8498.42 | −0.561169 | −0.280584 | − | 0.959829i | \(-0.590528\pi\) | ||||
−0.280584 | + | 0.959829i | \(0.590528\pi\) | |||||||
\(48\) | −3808.54 | −0.238591 | ||||||||
\(49\) | −7531.50 | −0.448117 | ||||||||
\(50\) | 4734.72i | 0.267836i | ||||||||
\(51\) | 25536.2i | 1.37477i | ||||||||
\(52\) | 16192.4i | 0.830430i | ||||||||
\(53\) | 22725.8 | 1.11130 | 0.555648 | − | 0.831418i | \(-0.312470\pi\) | ||||
0.555648 | + | 0.831418i | \(0.312470\pi\) | |||||||
\(54\) | 11741.0i | 0.547927i | ||||||||
\(55\) | − | 21604.0i | − | 0.963004i | ||||||
\(56\) | − | 15343.9i | − | 0.653831i | ||||||
\(57\) | − | 33146.2i | − | 1.35128i | ||||||
\(58\) | 8459.41 | 0.330195 | ||||||||
\(59\) | 23622.9i | 0.883492i | 0.897140 | + | 0.441746i | \(0.145641\pi\) | ||||
−0.897140 | + | 0.441746i | \(0.854359\pi\) | |||||||
\(60\) | − | 11242.7i | − | 0.403176i | ||||||
\(61\) | 14456.4i | 0.497435i | 0.968576 | + | 0.248718i | \(0.0800091\pi\) | ||||
−0.968576 | + | 0.248718i | \(0.919991\pi\) | |||||||
\(62\) | 14827.0 | 0.489863 | ||||||||
\(63\) | 8813.53 | 0.279768 | ||||||||
\(64\) | −7153.11 | −0.218295 | ||||||||
\(65\) | −25964.1 | −0.762238 | ||||||||
\(66\) | 19813.3i | 0.559881i | ||||||||
\(67\) | −4980.51 | −0.135546 | −0.0677730 | − | 0.997701i | \(-0.521589\pi\) | ||||
−0.0677730 | + | 0.997701i | \(0.521589\pi\) | |||||||
\(68\) | − | 49519.8i | − | 1.29869i | ||||||
\(69\) | − | 37809.4i | − | 0.956042i | ||||||
\(70\) | 10511.1 | 0.256391 | ||||||||
\(71\) | −7644.87 | −0.179980 | −0.0899900 | − | 0.995943i | \(-0.528684\pi\) | ||||
−0.0899900 | + | 0.995943i | \(0.528684\pi\) | |||||||
\(72\) | − | 14579.7i | − | 0.331449i | ||||||
\(73\) | 76611.5 | 1.68262 | 0.841312 | − | 0.540550i | \(-0.181784\pi\) | ||||
0.841312 | + | 0.540550i | \(0.181784\pi\) | |||||||
\(74\) | −7926.51 | + | 22385.1i | −0.168268 | + | 0.475205i | ||||
\(75\) | −20435.1 | −0.419492 | ||||||||
\(76\) | 64277.1i | 1.27650i | ||||||||
\(77\) | 54366.4 | 1.04497 | ||||||||
\(78\) | 23811.9 | 0.443158 | ||||||||
\(79\) | − | 43134.5i | − | 0.777601i | −0.921322 | − | 0.388800i | \(-0.872890\pi\) | ||
0.921322 | − | 0.388800i | \(-0.127110\pi\) | |||||||
\(80\) | 11842.5i | 0.206880i | ||||||||
\(81\) | −28436.9 | −0.481581 | ||||||||
\(82\) | − | 18535.8i | − | 0.304423i | ||||||
\(83\) | −48677.9 | −0.775599 | −0.387799 | − | 0.921744i | \(-0.626765\pi\) | ||||
−0.387799 | + | 0.921744i | \(0.626765\pi\) | |||||||
\(84\) | 28292.3 | 0.437491 | ||||||||
\(85\) | 79403.8 | 1.19205 | ||||||||
\(86\) | −24487.1 | −0.357019 | ||||||||
\(87\) | 36510.9i | 0.517159i | ||||||||
\(88\) | − | 89935.0i | − | 1.23800i | ||||||
\(89\) | 46571.1i | 0.623220i | 0.950210 | + | 0.311610i | \(0.100868\pi\) | ||||
−0.950210 | + | 0.311610i | \(0.899132\pi\) | |||||||
\(90\) | 9987.59 | 0.129973 | ||||||||
\(91\) | − | 65338.5i | − | 0.827114i | ||||||
\(92\) | 73320.0i | 0.903135i | ||||||||
\(93\) | 63993.5i | 0.767235i | ||||||||
\(94\) | − | 24235.1i | − | 0.282894i | ||||||
\(95\) | −103067. | −1.17168 | ||||||||
\(96\) | − | 73609.6i | − | 0.815186i | ||||||
\(97\) | 135193.i | 1.45889i | 0.684038 | + | 0.729446i | \(0.260222\pi\) | ||||
−0.684038 | + | 0.729446i | \(0.739778\pi\) | |||||||
\(98\) | − | 21477.7i | − | 0.225903i | ||||||
\(99\) | 51658.6 | 0.529730 | ||||||||
\(100\) | 39627.7 | 0.396277 | ||||||||
\(101\) | −200856. | −1.95921 | −0.979605 | − | 0.200933i | \(-0.935603\pi\) | ||||
−0.979605 | + | 0.200933i | \(0.935603\pi\) | |||||||
\(102\) | −72821.9 | −0.693046 | ||||||||
\(103\) | 62474.9i | 0.580247i | 0.956989 | + | 0.290123i | \(0.0936963\pi\) | ||||
−0.956989 | + | 0.290123i | \(0.906304\pi\) | |||||||
\(104\) | −108086. | −0.979906 | ||||||||
\(105\) | 45366.0i | 0.401566i | ||||||||
\(106\) | 64807.6i | 0.560223i | ||||||||
\(107\) | −39477.9 | −0.333345 | −0.166673 | − | 0.986012i | \(-0.553302\pi\) | ||||
−0.166673 | + | 0.986012i | \(0.553302\pi\) | |||||||
\(108\) | 98267.9 | 0.810685 | ||||||||
\(109\) | − | 117545.i | − | 0.947628i | −0.880625 | − | 0.473814i | \(-0.842877\pi\) | ||
0.880625 | − | 0.473814i | \(-0.157123\pi\) | |||||||
\(110\) | 61608.6 | 0.485467 | ||||||||
\(111\) | −96614.4 | − | 34210.9i | −0.744277 | − | 0.263546i | ||||
\(112\) | −29801.5 | −0.224488 | ||||||||
\(113\) | − | 158580.i | − | 1.16830i | −0.811647 | − | 0.584148i | \(-0.801429\pi\) | ||
0.811647 | − | 0.584148i | \(-0.198571\pi\) | |||||||
\(114\) | 94523.5 | 0.681205 | ||||||||
\(115\) | −117567. | −0.828972 | ||||||||
\(116\) | − | 70801.9i | − | 0.488540i | ||||||
\(117\) | − | 62084.3i | − | 0.419292i | ||||||
\(118\) | −67365.7 | −0.445383 | ||||||||
\(119\) | 199819.i | 1.29351i | ||||||||
\(120\) | 75046.2 | 0.475746 | ||||||||
\(121\) | 157606. | 0.978608 | ||||||||
\(122\) | −41225.6 | −0.250765 | ||||||||
\(123\) | 80000.7 | 0.476794 | ||||||||
\(124\) | − | 124096.i | − | 0.724777i | ||||||
\(125\) | 183140.i | 1.04835i | ||||||||
\(126\) | 25133.7i | 0.141036i | ||||||||
\(127\) | 77966.9 | 0.428944 | 0.214472 | − | 0.976730i | \(-0.431197\pi\) | ||||
0.214472 | + | 0.976730i | \(0.431197\pi\) | |||||||
\(128\) | 170981.i | 0.922409i | ||||||||
\(129\) | − | 105686.i | − | 0.559171i | ||||||
\(130\) | − | 74042.3i | − | 0.384257i | ||||||
\(131\) | 160530.i | 0.817294i | 0.912693 | + | 0.408647i | \(0.133999\pi\) | ||||
−0.912693 | + | 0.408647i | \(0.866001\pi\) | |||||||
\(132\) | 165829. | 0.828373 | ||||||||
\(133\) | − | 259367.i | − | 1.27141i | ||||||
\(134\) | − | 14203.0i | − | 0.0683310i | ||||||
\(135\) | 157570.i | 0.744114i | ||||||||
\(136\) | 330548. | 1.53246 | ||||||||
\(137\) | 51981.2 | 0.236616 | 0.118308 | − | 0.992977i | \(-0.462253\pi\) | ||||
0.118308 | + | 0.992977i | \(0.462253\pi\) | |||||||
\(138\) | 107822. | 0.481957 | ||||||||
\(139\) | −402175. | −1.76554 | −0.882771 | − | 0.469803i | \(-0.844325\pi\) | ||||
−0.882771 | + | 0.469803i | \(0.844325\pi\) | |||||||
\(140\) | − | 87973.7i | − | 0.379344i | ||||||
\(141\) | 104599. | 0.443076 | ||||||||
\(142\) | − | 21801.0i | − | 0.0907309i | ||||||
\(143\) | − | 382968.i | − | 1.56611i | ||||||
\(144\) | −28317.2 | −0.113801 | ||||||||
\(145\) | 113529. | 0.448422 | ||||||||
\(146\) | 218474.i | 0.848239i | ||||||||
\(147\) | 92697.9 | 0.353815 | ||||||||
\(148\) | 187355. | + | 66341.8i | 0.703089 | + | 0.248962i | ||||
\(149\) | 33622.9 | 0.124071 | 0.0620353 | − | 0.998074i | \(-0.480241\pi\) | ||||
0.0620353 | + | 0.998074i | \(0.480241\pi\) | |||||||
\(150\) | − | 58275.0i | − | 0.211473i | ||||||
\(151\) | 46126.5 | 0.164630 | 0.0823148 | − | 0.996606i | \(-0.473769\pi\) | ||||
0.0823148 | + | 0.996606i | \(0.473769\pi\) | |||||||
\(152\) | −429055. | −1.50627 | ||||||||
\(153\) | 189867.i | 0.655723i | ||||||||
\(154\) | 155037.i | 0.526786i | ||||||||
\(155\) | 198985. | 0.665261 | ||||||||
\(156\) | − | 199296.i | − | 0.655674i | ||||||
\(157\) | −189721. | −0.614281 | −0.307140 | − | 0.951664i | \(-0.599372\pi\) | ||||
−0.307140 | + | 0.951664i | \(0.599372\pi\) | |||||||
\(158\) | 123007. | 0.392002 | ||||||||
\(159\) | −279710. | −0.877435 | ||||||||
\(160\) | −228886. | −0.706838 | ||||||||
\(161\) | − | 295856.i | − | 0.899529i | ||||||
\(162\) | − | 81093.8i | − | 0.242773i | ||||||
\(163\) | − | 89298.7i | − | 0.263255i | −0.991299 | − | 0.131627i | \(-0.957980\pi\) | ||
0.991299 | − | 0.131627i | \(-0.0420202\pi\) | |||||||
\(164\) | −155137. | −0.450409 | ||||||||
\(165\) | 265903.i | 0.760350i | ||||||||
\(166\) | − | 138816.i | − | 0.390992i | ||||||
\(167\) | 84828.3i | 0.235369i | 0.993051 | + | 0.117685i | \(0.0375472\pi\) | ||||
−0.993051 | + | 0.117685i | \(0.962453\pi\) | |||||||
\(168\) | 188853.i | 0.516239i | ||||||||
\(169\) | −88964.7 | −0.239608 | ||||||||
\(170\) | 226437.i | 0.600932i | ||||||||
\(171\) | − | 246449.i | − | 0.644520i | ||||||
\(172\) | 204947.i | 0.528227i | ||||||||
\(173\) | 352138. | 0.894536 | 0.447268 | − | 0.894400i | \(-0.352397\pi\) | ||||
0.447268 | + | 0.894400i | \(0.352397\pi\) | |||||||
\(174\) | −104119. | −0.260708 | ||||||||
\(175\) | −159903. | −0.394695 | ||||||||
\(176\) | −174675. | −0.425059 | ||||||||
\(177\) | − | 290751.i | − | 0.697570i | ||||||
\(178\) | −132808. | −0.314176 | ||||||||
\(179\) | 167857.i | 0.391568i | 0.980647 | + | 0.195784i | \(0.0627252\pi\) | ||||
−0.980647 | + | 0.195784i | \(0.937275\pi\) | |||||||
\(180\) | − | 83592.1i | − | 0.192302i | ||||||
\(181\) | 416443. | 0.944842 | 0.472421 | − | 0.881373i | \(-0.343380\pi\) | ||||
0.472421 | + | 0.881373i | \(0.343380\pi\) | |||||||
\(182\) | 186327. | 0.416962 | ||||||||
\(183\) | − | 177930.i | − | 0.392755i | ||||||
\(184\) | −489416. | −1.06570 | ||||||||
\(185\) | −106377. | + | 300419.i | −0.228518 | + | 0.645354i | ||||
\(186\) | −182491. | −0.386776 | ||||||||
\(187\) | 1.17120e6i | 2.44921i | ||||||||
\(188\) | −202838. | −0.418557 | ||||||||
\(189\) | −396524. | −0.807448 | ||||||||
\(190\) | − | 293917.i | − | 0.590664i | ||||||
\(191\) | − | 713843.i | − | 1.41586i | −0.706284 | − | 0.707929i | \(-0.749630\pi\) | ||
0.706284 | − | 0.707929i | \(-0.250370\pi\) | |||||||
\(192\) | 88040.6 | 0.172357 | ||||||||
\(193\) | 133580.i | 0.258136i | 0.991636 | + | 0.129068i | \(0.0411986\pi\) | ||||
−0.991636 | + | 0.129068i | \(0.958801\pi\) | |||||||
\(194\) | −385531. | −0.735452 | ||||||||
\(195\) | 319567. | 0.601832 | ||||||||
\(196\) | −179760. | −0.334235 | ||||||||
\(197\) | 637649. | 1.17062 | 0.585310 | − | 0.810809i | \(-0.300973\pi\) | ||||
0.585310 | + | 0.810809i | \(0.300973\pi\) | |||||||
\(198\) | 147316.i | 0.267046i | ||||||||
\(199\) | 363643.i | 0.650942i | 0.945552 | + | 0.325471i | \(0.105523\pi\) | ||||
−0.945552 | + | 0.325471i | \(0.894477\pi\) | |||||||
\(200\) | 264518.i | 0.467606i | ||||||||
\(201\) | 61300.2 | 0.107022 | ||||||||
\(202\) | − | 572784.i | − | 0.987671i | ||||||
\(203\) | 285695.i | 0.486589i | ||||||||
\(204\) | 609491.i | 1.02540i | ||||||||
\(205\) | − | 248759.i | − | 0.413423i | ||||||
\(206\) | −178161. | −0.292512 | ||||||||
\(207\) | − | 281120.i | − | 0.456002i | ||||||
\(208\) | 209928.i | 0.336443i | ||||||||
\(209\) | − | 1.52022e6i | − | 2.40736i | ||||||
\(210\) | −129371. | −0.202436 | ||||||||
\(211\) | 1.19996e6 | 1.85550 | 0.927752 | − | 0.373197i | \(-0.121738\pi\) | ||||
0.927752 | + | 0.373197i | \(0.121738\pi\) | |||||||
\(212\) | 542413. | 0.828878 | ||||||||
\(213\) | 94093.2 | 0.142105 | ||||||||
\(214\) | − | 112580.i | − | 0.168045i | ||||||
\(215\) | −328628. | −0.484851 | ||||||||
\(216\) | 655946.i | 0.956607i | ||||||||
\(217\) | 500745.i | 0.721883i | ||||||||
\(218\) | 335205. | 0.477715 | ||||||||
\(219\) | −942936. | −1.32853 | ||||||||
\(220\) | − | 515639.i | − | 0.718272i | ||||||
\(221\) | 1.40757e6 | 1.93860 | ||||||||
\(222\) | 97559.7 | − | 275517.i | 0.132858 | − | 0.375202i | ||||
\(223\) | −54778.0 | −0.0737640 | −0.0368820 | − | 0.999320i | \(-0.511743\pi\) | ||||
−0.0368820 | + | 0.999320i | \(0.511743\pi\) | |||||||
\(224\) | − | 575990.i | − | 0.766999i | ||||||
\(225\) | −151939. | −0.200084 | ||||||||
\(226\) | 452225. | 0.588957 | ||||||||
\(227\) | − | 802415.i | − | 1.03356i | −0.856119 | − | 0.516778i | \(-0.827131\pi\) | ||
0.856119 | − | 0.516778i | \(-0.172869\pi\) | |||||||
\(228\) | − | 791124.i | − | 1.00788i | ||||||
\(229\) | 710586. | 0.895423 | 0.447711 | − | 0.894178i | \(-0.352239\pi\) | ||||
0.447711 | + | 0.894178i | \(0.352239\pi\) | |||||||
\(230\) | − | 335267.i | − | 0.417899i | ||||||
\(231\) | −669142. | −0.825065 | ||||||||
\(232\) | 472608. | 0.576476 | ||||||||
\(233\) | 307185. | 0.370689 | 0.185345 | − | 0.982674i | \(-0.440660\pi\) | ||||
0.185345 | + | 0.982674i | \(0.440660\pi\) | |||||||
\(234\) | 177047. | 0.211372 | ||||||||
\(235\) | − | 325246.i | − | 0.384186i | ||||||
\(236\) | 563824.i | 0.658967i | ||||||||
\(237\) | 530900.i | 0.613962i | ||||||||
\(238\) | −569827. | −0.652079 | ||||||||
\(239\) | 1.34121e6i | 1.51881i | 0.650621 | + | 0.759403i | \(0.274509\pi\) | ||||
−0.650621 | + | 0.759403i | \(0.725491\pi\) | |||||||
\(240\) | − | 145758.i | − | 0.163344i | ||||||
\(241\) | 1.02266e6i | 1.13420i | 0.823650 | + | 0.567099i | \(0.191934\pi\) | ||||
−0.823650 | + | 0.567099i | \(0.808066\pi\) | |||||||
\(242\) | 449447.i | 0.493333i | ||||||||
\(243\) | −650475. | −0.706668 | ||||||||
\(244\) | 345042.i | 0.371020i | ||||||||
\(245\) | − | 288241.i | − | 0.306789i | ||||||
\(246\) | 228139.i | 0.240360i | ||||||||
\(247\) | −1.82703e6 | −1.90548 | ||||||||
\(248\) | 828352. | 0.855235 | ||||||||
\(249\) | 599129. | 0.612381 | ||||||||
\(250\) | −522263. | −0.528493 | ||||||||
\(251\) | − | 25154.5i | − | 0.0252018i | −0.999921 | − | 0.0126009i | \(-0.995989\pi\) | ||
0.999921 | − | 0.0126009i | \(-0.00401110\pi\) | |||||||
\(252\) | 210359. | 0.208670 | ||||||||
\(253\) | − | 1.73410e6i | − | 1.70322i | ||||||
\(254\) | 222339.i | 0.216238i | ||||||||
\(255\) | −977304. | −0.941194 | ||||||||
\(256\) | −716489. | −0.683298 | ||||||||
\(257\) | 815697.i | 0.770364i | 0.922841 | + | 0.385182i | \(0.125861\pi\) | ||||
−0.922841 | + | 0.385182i | \(0.874139\pi\) | |||||||
\(258\) | 301387. | 0.281888 | ||||||||
\(259\) | −756001. | − | 267698.i | −0.700282 | − | 0.247968i | ||||
\(260\) | −619705. | −0.568527 | ||||||||
\(261\) | 271466.i | 0.246669i | ||||||||
\(262\) | −457786. | −0.412011 | ||||||||
\(263\) | 323462. | 0.288359 | 0.144180 | − | 0.989552i | \(-0.453946\pi\) | ||||
0.144180 | + | 0.989552i | \(0.453946\pi\) | |||||||
\(264\) | 1.10692e6i | 0.977478i | ||||||||
\(265\) | 869747.i | 0.760813i | ||||||||
\(266\) | 739640. | 0.640938 | ||||||||
\(267\) | − | 573198.i | − | 0.492070i | ||||||
\(268\) | −118873. | −0.101099 | ||||||||
\(269\) | 866044. | 0.729725 | 0.364863 | − | 0.931061i | \(-0.381116\pi\) | ||||
0.364863 | + | 0.931061i | \(0.381116\pi\) | |||||||
\(270\) | −449345. | −0.375120 | ||||||||
\(271\) | 120109. | 0.0993463 | 0.0496732 | − | 0.998766i | \(-0.484182\pi\) | ||||
0.0496732 | + | 0.998766i | \(0.484182\pi\) | |||||||
\(272\) | − | 642004.i | − | 0.526157i | ||||||
\(273\) | 804187.i | 0.653056i | ||||||||
\(274\) | 148236.i | 0.119282i | ||||||||
\(275\) | −937238. | −0.747340 | ||||||||
\(276\) | − | 902424.i | − | 0.713079i | ||||||
\(277\) | − | 1.46087e6i | − | 1.14397i | −0.820265 | − | 0.571983i | \(-0.806174\pi\) | ||
0.820265 | − | 0.571983i | \(-0.193826\pi\) | |||||||
\(278\) | − | 1.14689e6i | − | 0.890039i | ||||||
\(279\) | 475805.i | 0.365947i | ||||||||
\(280\) | 587231. | 0.447625 | ||||||||
\(281\) | − | 755744.i | − | 0.570964i | −0.958384 | − | 0.285482i | \(-0.907846\pi\) | ||
0.958384 | − | 0.285482i | \(-0.0921537\pi\) | |||||||
\(282\) | 298286.i | 0.223362i | ||||||||
\(283\) | 2.59322e6i | 1.92474i | 0.271735 | + | 0.962372i | \(0.412402\pi\) | ||||
−0.271735 | + | 0.962372i | \(0.587598\pi\) | |||||||
\(284\) | −182466. | −0.134241 | ||||||||
\(285\) | 1.26855e6 | 0.925113 | ||||||||
\(286\) | 1.09211e6 | 0.789502 | ||||||||
\(287\) | 626000. | 0.448610 | ||||||||
\(288\) | − | 547303.i | − | 0.388818i | ||||||
\(289\) | −2.88477e6 | −2.03174 | ||||||||
\(290\) | 323753.i | 0.226057i | ||||||||
\(291\) | − | 1.66395e6i | − | 1.15188i | ||||||
\(292\) | 1.82854e6 | 1.25501 | ||||||||
\(293\) | −433664. | −0.295111 | −0.147555 | − | 0.989054i | \(-0.547140\pi\) | ||||
−0.147555 | + | 0.989054i | \(0.547140\pi\) | |||||||
\(294\) | 264348.i | 0.178364i | ||||||||
\(295\) | −904078. | −0.604854 | ||||||||
\(296\) | −442836. | + | 1.25061e6i | −0.293774 | + | 0.829644i | ||||
\(297\) | −2.32414e6 | −1.52887 | ||||||||
\(298\) | 95882.8i | 0.0625461i | ||||||||
\(299\) | −2.08407e6 | −1.34814 | ||||||||
\(300\) | −487739. | −0.312885 | ||||||||
\(301\) | − | 826988.i | − | 0.526118i | ||||||
\(302\) | 131540.i | 0.0829925i | ||||||||
\(303\) | 2.47214e6 | 1.54691 | ||||||||
\(304\) | 833326.i | 0.517167i | ||||||||
\(305\) | −553267. | −0.340553 | ||||||||
\(306\) | −541446. | −0.330561 | ||||||||
\(307\) | 1.00344e6 | 0.607641 | 0.303820 | − | 0.952729i | \(-0.401738\pi\) | ||||
0.303820 | + | 0.952729i | \(0.401738\pi\) | |||||||
\(308\) | 1.29760e6 | 0.779407 | ||||||||
\(309\) | − | 768943.i | − | 0.458139i | ||||||
\(310\) | 567449.i | 0.335369i | ||||||||
\(311\) | − | 1.51587e6i | − | 0.888714i | −0.895850 | − | 0.444357i | \(-0.853432\pi\) | ||
0.895850 | − | 0.444357i | \(-0.146568\pi\) | |||||||
\(312\) | 1.33032e6 | 0.773694 | ||||||||
\(313\) | 141947.i | 0.0818963i | 0.999161 | + | 0.0409482i | \(0.0130378\pi\) | ||||
−0.999161 | + | 0.0409482i | \(0.986962\pi\) | |||||||
\(314\) | − | 541031.i | − | 0.309669i | ||||||
\(315\) | 337305.i | 0.191534i | ||||||||
\(316\) | − | 1.02952e6i | − | 0.579986i | ||||||
\(317\) | 1.48491e6 | 0.829948 | 0.414974 | − | 0.909833i | \(-0.363791\pi\) | ||||
0.414974 | + | 0.909833i | \(0.363791\pi\) | |||||||
\(318\) | − | 797653.i | − | 0.442330i | ||||||
\(319\) | 1.67454e6i | 0.921338i | ||||||||
\(320\) | − | 273759.i | − | 0.149449i | ||||||
\(321\) | 485895. | 0.263196 | ||||||||
\(322\) | 843696. | 0.453468 | ||||||||
\(323\) | 5.58745e6 | 2.97994 | ||||||||
\(324\) | −678723. | −0.359195 | ||||||||
\(325\) | 1.12639e6i | 0.591535i | ||||||||
\(326\) | 254655. | 0.132711 | ||||||||
\(327\) | 1.44675e6i | 0.748209i | ||||||||
\(328\) | − | 1.03555e6i | − | 0.531481i | ||||||
\(329\) | 818477. | 0.416886 | ||||||||
\(330\) | −758279. | −0.383305 | ||||||||
\(331\) | − | 2.66337e6i | − | 1.33617i | −0.744085 | − | 0.668085i | \(-0.767114\pi\) | ||
0.744085 | − | 0.668085i | \(-0.232886\pi\) | |||||||
\(332\) | −1.16183e6 | −0.578493 | ||||||||
\(333\) | −718348. | − | 254365.i | −0.354997 | − | 0.125703i | ||||
\(334\) | −241906. | −0.118654 | ||||||||
\(335\) | − | 190611.i | − | 0.0927973i | ||||||
\(336\) | 366798. | 0.177247 | ||||||||
\(337\) | −2.02951e6 | −0.973458 | −0.486729 | − | 0.873553i | \(-0.661810\pi\) | ||||
−0.486729 | + | 0.873553i | \(0.661810\pi\) | |||||||
\(338\) | − | 253702.i | − | 0.120790i | ||||||
\(339\) | 1.95181e6i | 0.922439i | ||||||||
\(340\) | 1.89519e6 | 0.889109 | ||||||||
\(341\) | 2.93501e6i | 1.36686i | ||||||||
\(342\) | 702801. | 0.324913 | ||||||||
\(343\) | 2.34403e6 | 1.07579 | ||||||||
\(344\) | −1.36804e6 | −0.623307 | ||||||||
\(345\) | 1.44701e6 | 0.654523 | ||||||||
\(346\) | 1.00420e6i | 0.450951i | ||||||||
\(347\) | − | 3.16483e6i | − | 1.41100i | −0.708710 | − | 0.705500i | \(-0.750723\pi\) | ||
0.708710 | − | 0.705500i | \(-0.249277\pi\) | |||||||
\(348\) | 871431.i | 0.385731i | ||||||||
\(349\) | −1.43841e6 | −0.632147 | −0.316073 | − | 0.948735i | \(-0.602365\pi\) | ||||
−0.316073 | + | 0.948735i | \(0.602365\pi\) | |||||||
\(350\) | − | 455998.i | − | 0.198972i | ||||||
\(351\) | 2.79319e6i | 1.21013i | ||||||||
\(352\) | − | 3.37604e6i | − | 1.45228i | ||||||
\(353\) | − | 677495.i | − | 0.289381i | −0.989477 | − | 0.144690i | \(-0.953781\pi\) | ||
0.989477 | − | 0.144690i | \(-0.0462186\pi\) | |||||||
\(354\) | 829138. | 0.351657 | ||||||||
\(355\) | − | 292579.i | − | 0.123218i | ||||||
\(356\) | 1.11155e6i | 0.464839i | ||||||||
\(357\) | − | 2.45938e6i | − | 1.02130i | ||||||
\(358\) | −478681. | −0.197396 | ||||||||
\(359\) | −1.97222e6 | −0.807642 | −0.403821 | − | 0.914838i | \(-0.632318\pi\) | ||||
−0.403821 | + | 0.914838i | \(0.632318\pi\) | |||||||
\(360\) | 557984. | 0.226916 | ||||||||
\(361\) | −4.77645e6 | −1.92902 | ||||||||
\(362\) | 1.18758e6i | 0.476311i | ||||||||
\(363\) | −1.93982e6 | −0.772670 | ||||||||
\(364\) | − | 1.55948e6i | − | 0.616917i | ||||||
\(365\) | 2.93202e6i | 1.15195i | ||||||||
\(366\) | 507406. | 0.197994 | ||||||||
\(367\) | −2.97537e6 | −1.15312 | −0.576562 | − | 0.817053i | \(-0.695606\pi\) | ||||
−0.576562 | + | 0.817053i | \(0.695606\pi\) | |||||||
\(368\) | 950563.i | 0.365899i | ||||||||
\(369\) | 594821. | 0.227416 | ||||||||
\(370\) | −856709. | − | 303358.i | −0.325334 | − | 0.115200i | ||||
\(371\) | −2.18871e6 | −0.825569 | ||||||||
\(372\) | 1.52738e6i | 0.572255i | ||||||||
\(373\) | −2.19422e6 | −0.816597 | −0.408299 | − | 0.912848i | \(-0.633878\pi\) | ||||
−0.408299 | + | 0.912848i | \(0.633878\pi\) | |||||||
\(374\) | −3.33992e6 | −1.23469 | ||||||||
\(375\) | − | 2.25409e6i | − | 0.827738i | ||||||
\(376\) | − | 1.35396e6i | − | 0.493896i | ||||||
\(377\) | 2.01249e6 | 0.729258 | ||||||||
\(378\) | − | 1.13077e6i | − | 0.407048i | ||||||
\(379\) | 2.44142e6 | 0.873061 | 0.436530 | − | 0.899689i | \(-0.356207\pi\) | ||||
0.436530 | + | 0.899689i | \(0.356207\pi\) | |||||||
\(380\) | −2.45997e6 | −0.873918 | ||||||||
\(381\) | −959618. | −0.338677 | ||||||||
\(382\) | 2.03568e6 | 0.713757 | ||||||||
\(383\) | 685919.i | 0.238933i | 0.992838 | + | 0.119466i | \(0.0381184\pi\) | ||||
−0.992838 | + | 0.119466i | \(0.961882\pi\) | |||||||
\(384\) | − | 2.10444e6i | − | 0.728297i | ||||||
\(385\) | 2.08067e6i | 0.715405i | ||||||||
\(386\) | −380933. | −0.130131 | ||||||||
\(387\) | − | 785800.i | − | 0.266707i | ||||||
\(388\) | 3.22674e6i | 1.08814i | ||||||||
\(389\) | 4.07598e6i | 1.36571i | 0.730554 | + | 0.682855i | \(0.239262\pi\) | ||||
−0.730554 | + | 0.682855i | \(0.760738\pi\) | |||||||
\(390\) | 911314.i | 0.303394i | ||||||||
\(391\) | 6.37352e6 | 2.10832 | ||||||||
\(392\) | − | 1.19991e6i | − | 0.394397i | ||||||
\(393\) | − | 1.97581e6i | − | 0.645302i | ||||||
\(394\) | 1.81839e6i | 0.590129i | ||||||||
\(395\) | 1.65081e6 | 0.532360 | ||||||||
\(396\) | 1.23297e6 | 0.395108 | ||||||||
\(397\) | 862797. | 0.274746 | 0.137373 | − | 0.990519i | \(-0.456134\pi\) | ||||
0.137373 | + | 0.990519i | \(0.456134\pi\) | |||||||
\(398\) | −1.03701e6 | −0.328151 | ||||||||
\(399\) | 3.19229e6i | 1.00385i | ||||||||
\(400\) | 513757. | 0.160549 | ||||||||
\(401\) | − | 121613.i | − | 0.0377676i | −0.999822 | − | 0.0188838i | \(-0.993989\pi\) | ||
0.999822 | − | 0.0188838i | \(-0.00601125\pi\) | |||||||
\(402\) | 174811.i | 0.0539514i | ||||||||
\(403\) | 3.52735e6 | 1.08190 | ||||||||
\(404\) | −4.79397e6 | −1.46131 | ||||||||
\(405\) | − | 1.08832e6i | − | 0.329699i | ||||||
\(406\) | −814720. | −0.245298 | ||||||||
\(407\) | −4.43114e6 | − | 1.56905e6i | −1.32596 | − | 0.469517i | ||||
\(408\) | −4.06840e6 | −1.20997 | ||||||||
\(409\) | − | 5.72992e6i | − | 1.69372i | −0.531819 | − | 0.846858i | \(-0.678491\pi\) | ||
0.531819 | − | 0.846858i | \(-0.321509\pi\) | |||||||
\(410\) | 709390. | 0.208413 | ||||||||
\(411\) | −639785. | −0.186823 | ||||||||
\(412\) | 1.49113e6i | 0.432786i | ||||||||
\(413\) | − | 2.27510e6i | − | 0.656336i | ||||||
\(414\) | 801675. | 0.229878 | ||||||||
\(415\) | − | 1.86297e6i | − | 0.530989i | ||||||
\(416\) | −4.05739e6 | −1.14951 | ||||||||
\(417\) | 4.94998e6 | 1.39400 | ||||||||
\(418\) | 4.33524e6 | 1.21359 | ||||||||
\(419\) | 5.11602e6 | 1.42363 | 0.711816 | − | 0.702366i | \(-0.247873\pi\) | ||||
0.711816 | + | 0.702366i | \(0.247873\pi\) | |||||||
\(420\) | 1.08278e6i | 0.299515i | ||||||||
\(421\) | 972912.i | 0.267527i | 0.991013 | + | 0.133764i | \(0.0427063\pi\) | ||||
−0.991013 | + | 0.133764i | \(0.957294\pi\) | |||||||
\(422\) | 3.42195e6i | 0.935391i | ||||||||
\(423\) | 777713. | 0.211333 | ||||||||
\(424\) | 3.62065e6i | 0.978075i | ||||||||
\(425\) | − | 3.44474e6i | − | 0.925090i | ||||||
\(426\) | 268327.i | 0.0716375i | ||||||||
\(427\) | − | 1.39229e6i | − | 0.369539i | ||||||
\(428\) | −942247. | −0.248631 | ||||||||
\(429\) | 4.71357e6i | 1.23654i | ||||||||
\(430\) | − | 937152.i | − | 0.244421i | ||||||
\(431\) | 2.25886e6i | 0.585728i | 0.956154 | + | 0.292864i | \(0.0946084\pi\) | ||||
−0.956154 | + | 0.292864i | \(0.905392\pi\) | |||||||
\(432\) | 1.27400e6 | 0.328444 | ||||||||
\(433\) | 4.76746e6 | 1.22199 | 0.610994 | − | 0.791635i | \(-0.290770\pi\) | ||||
0.610994 | + | 0.791635i | \(0.290770\pi\) | |||||||
\(434\) | −1.42798e6 | −0.363913 | ||||||||
\(435\) | −1.39732e6 | −0.354056 | ||||||||
\(436\) | − | 2.80553e6i | − | 0.706804i | ||||||
\(437\) | −8.27288e6 | −2.07230 | ||||||||
\(438\) | − | 2.68898e6i | − | 0.669735i | ||||||
\(439\) | − | 6.47953e6i | − | 1.60466i | −0.596882 | − | 0.802329i | \(-0.703594\pi\) | ||
0.596882 | − | 0.802329i | \(-0.296406\pi\) | |||||||
\(440\) | 3.44193e6 | 0.847560 | ||||||||
\(441\) | 689228. | 0.168759 | ||||||||
\(442\) | 4.01397e6i | 0.977280i | ||||||||
\(443\) | 7.13256e6 | 1.72678 | 0.863389 | − | 0.504540i | \(-0.168338\pi\) | ||||
0.863389 | + | 0.504540i | \(0.168338\pi\) | |||||||
\(444\) | −2.30597e6 | − | 816536.i | −0.555131 | − | 0.196570i | ||||
\(445\) | −1.78234e6 | −0.426668 | ||||||||
\(446\) | − | 156211.i | − | 0.0371856i | ||||||
\(447\) | −413831. | −0.0979612 | ||||||||
\(448\) | 688911. | 0.162169 | ||||||||
\(449\) | 6.31912e6i | 1.47925i | 0.673021 | + | 0.739624i | \(0.264997\pi\) | ||||
−0.673021 | + | 0.739624i | \(0.735003\pi\) | |||||||
\(450\) | − | 433287.i | − | 0.100866i | ||||||
\(451\) | 3.66916e6 | 0.849426 | ||||||||
\(452\) | − | 3.78495e6i | − | 0.871392i | ||||||
\(453\) | −567725. | −0.129985 | ||||||||
\(454\) | 2.28826e6 | 0.521033 | ||||||||
\(455\) | 2.50059e6 | 0.566257 | ||||||||
\(456\) | 5.28081e6 | 1.18929 | ||||||||
\(457\) | 7.64055e6i | 1.71133i | 0.517529 | + | 0.855666i | \(0.326852\pi\) | ||||
−0.517529 | + | 0.855666i | \(0.673148\pi\) | |||||||
\(458\) | 2.02639e6i | 0.451398i | ||||||||
\(459\) | − | 8.54218e6i | − | 1.89250i | ||||||
\(460\) | −2.80605e6 | −0.618303 | ||||||||
\(461\) | − | 3.92010e6i | − | 0.859102i | −0.903043 | − | 0.429551i | \(-0.858672\pi\) | ||
0.903043 | − | 0.429551i | \(-0.141328\pi\) | |||||||
\(462\) | − | 1.90820e6i | − | 0.415929i | ||||||
\(463\) | − | 6.57986e6i | − | 1.42647i | −0.700923 | − | 0.713237i | \(-0.747228\pi\) | ||
0.700923 | − | 0.713237i | \(-0.252772\pi\) | |||||||
\(464\) | − | 917917.i | − | 0.197929i | ||||||
\(465\) | −2.44912e6 | −0.525263 | ||||||||
\(466\) | 876004.i | 0.186871i | ||||||||
\(467\) | − | 3.88545e6i | − | 0.824421i | −0.911089 | − | 0.412211i | \(-0.864757\pi\) | ||
0.911089 | − | 0.412211i | \(-0.135243\pi\) | |||||||
\(468\) | − | 1.48181e6i | − | 0.312736i | ||||||
\(469\) | 479670. | 0.100696 | ||||||||
\(470\) | 927508. | 0.193675 | ||||||||
\(471\) | 2.33509e6 | 0.485012 | ||||||||
\(472\) | −3.76357e6 | −0.777579 | ||||||||
\(473\) | − | 4.84722e6i | − | 0.996184i | ||||||
\(474\) | −1.51398e6 | −0.309509 | ||||||||
\(475\) | 4.47130e6i | 0.909284i | ||||||||
\(476\) | 4.76922e6i | 0.964784i | ||||||||
\(477\) | −2.07970e6 | −0.418509 | ||||||||
\(478\) | −3.82475e6 | −0.765656 | ||||||||
\(479\) | 752587.i | 0.149871i | 0.997188 | + | 0.0749355i | \(0.0238751\pi\) | ||||
−0.997188 | + | 0.0749355i | \(0.976125\pi\) | |||||||
\(480\) | 2.81714e6 | 0.558091 | ||||||||
\(481\) | −1.88572e6 | + | 5.32543e6i | −0.371633 | + | 1.04952i | ||||
\(482\) | −2.91634e6 | −0.571768 | ||||||||
\(483\) | 3.64140e6i | 0.710232i | ||||||||
\(484\) | 3.76169e6 | 0.729911 | ||||||||
\(485\) | −5.17400e6 | −0.998784 | ||||||||
\(486\) | − | 1.85497e6i | − | 0.356243i | ||||||
\(487\) | 1.01221e7i | 1.93396i | 0.254846 | + | 0.966982i | \(0.417975\pi\) | ||||
−0.254846 | + | 0.966982i | \(0.582025\pi\) | |||||||
\(488\) | −2.30318e6 | −0.437803 | ||||||||
\(489\) | 1.09909e6i | 0.207855i | ||||||||
\(490\) | 821980. | 0.154657 | ||||||||
\(491\) | 3.12950e6 | 0.585829 | 0.292915 | − | 0.956139i | \(-0.405375\pi\) | ||||
0.292915 | + | 0.956139i | \(0.405375\pi\) | |||||||
\(492\) | 1.90943e6 | 0.355625 | ||||||||
\(493\) | −6.15463e6 | −1.14047 | ||||||||
\(494\) | − | 5.21017e6i | − | 0.960582i | ||||||
\(495\) | 1.97704e6i | 0.362663i | ||||||||
\(496\) | − | 1.60886e6i | − | 0.293639i | ||||||
\(497\) | 736273. | 0.133705 | ||||||||
\(498\) | 1.70855e6i | 0.308712i | ||||||||
\(499\) | 5032.18i | 0.000904700i | 1.00000 | 0.000452350i | \(0.000143987\pi\) | |||||
−1.00000 | 0.000452350i | \(0.999856\pi\) | ||||||||
\(500\) | 4.37113e6i | 0.781932i | ||||||||
\(501\) | − | 1.04407e6i | − | 0.185838i | ||||||
\(502\) | 71733.5 | 0.0127046 | ||||||||
\(503\) | 1.88460e6i | 0.332123i | 0.986115 | + | 0.166062i | \(0.0531050\pi\) | ||||
−0.986115 | + | 0.166062i | \(0.946895\pi\) | |||||||
\(504\) | 1.40416e6i | 0.246230i | ||||||||
\(505\) | − | 7.68702e6i | − | 1.34131i | ||||||
\(506\) | 4.94515e6 | 0.858624 | ||||||||
\(507\) | 1.09498e6 | 0.189185 | ||||||||
\(508\) | 1.86089e6 | 0.319935 | ||||||||
\(509\) | −6.71398e6 | −1.14864 | −0.574322 | − | 0.818629i | \(-0.694734\pi\) | ||||
−0.574322 | + | 0.818629i | \(0.694734\pi\) | |||||||
\(510\) | − | 2.78699e6i | − | 0.474472i | ||||||
\(511\) | −7.37841e6 | −1.25000 | ||||||||
\(512\) | 3.42818e6i | 0.577948i | ||||||||
\(513\) | 1.10878e7i | 1.86017i | ||||||||
\(514\) | −2.32613e6 | −0.388353 | ||||||||
\(515\) | −2.39100e6 | −0.397247 | ||||||||
\(516\) | − | 2.52249e6i | − | 0.417067i | ||||||
\(517\) | 4.79733e6 | 0.789357 | ||||||||
\(518\) | 763397. | − | 2.15590e6i | 0.125005 | − | 0.353024i | ||||
\(519\) | −4.33412e6 | −0.706290 | ||||||||
\(520\) | − | 4.13658e6i | − | 0.670861i | ||||||
\(521\) | −3.33825e6 | −0.538796 | −0.269398 | − | 0.963029i | \(-0.586825\pi\) | ||||
−0.269398 | + | 0.963029i | \(0.586825\pi\) | |||||||
\(522\) | −774143. | −0.124350 | ||||||||
\(523\) | 5.47242e6i | 0.874832i | 0.899259 | + | 0.437416i | \(0.144106\pi\) | ||||
−0.899259 | + | 0.437416i | \(0.855894\pi\) | |||||||
\(524\) | 3.83149e6i | 0.609592i | ||||||||
\(525\) | 1.96809e6 | 0.311635 | ||||||||
\(526\) | 922421.i | 0.145367i | ||||||||
\(527\) | −1.07874e7 | −1.69196 | ||||||||
\(528\) | 2.14991e6 | 0.335610 | ||||||||
\(529\) | −3.00041e6 | −0.466167 | ||||||||
\(530\) | −2.48027e6 | −0.383539 | ||||||||
\(531\) | − | 2.16179e6i | − | 0.332719i | ||||||
\(532\) | − | 6.19049e6i | − | 0.948300i | ||||||
\(533\) | − | 4.40967e6i | − | 0.672338i | ||||||
\(534\) | 1.63460e6 | 0.248061 | ||||||||
\(535\) | − | 1.51087e6i | − | 0.228214i | ||||||
\(536\) | − | 793489.i | − | 0.119297i | ||||||
\(537\) | − | 2.06599e6i | − | 0.309166i | ||||||
\(538\) | 2.46971e6i | 0.367867i | ||||||||
\(539\) | 4.25151e6 | 0.630335 | ||||||||
\(540\) | 3.76084e6i | 0.555010i | ||||||||
\(541\) | 850109.i | 0.124877i | 0.998049 | + | 0.0624383i | \(0.0198877\pi\) | ||||
−0.998049 | + | 0.0624383i | \(0.980112\pi\) | |||||||
\(542\) | 342516.i | 0.0500821i | ||||||||
\(543\) | −5.12559e6 | −0.746010 | ||||||||
\(544\) | 1.24084e7 | 1.79770 | ||||||||
\(545\) | 4.49860e6 | 0.648763 | ||||||||
\(546\) | −2.29331e6 | −0.329217 | ||||||||
\(547\) | − | 4.42050e6i | − | 0.631688i | −0.948811 | − | 0.315844i | \(-0.897712\pi\) | ||
0.948811 | − | 0.315844i | \(-0.102288\pi\) | |||||||
\(548\) | 1.24067e6 | 0.176484 | ||||||||
\(549\) | − | 1.32295e6i | − | 0.187332i | ||||||
\(550\) | − | 2.67274e6i | − | 0.376747i | ||||||
\(551\) | 7.98876e6 | 1.12099 | ||||||||
\(552\) | 6.02375e6 | 0.841432 | ||||||||
\(553\) | 4.15425e6i | 0.577670i | ||||||||
\(554\) | 4.16599e6 | 0.576692 | ||||||||
\(555\) | 1.30930e6 | − | 3.69756e6i | 0.180428 | − | 0.509545i | ||||
\(556\) | −9.59900e6 | −1.31686 | ||||||||
\(557\) | 5.79127e6i | 0.790926i | 0.918482 | + | 0.395463i | \(0.129416\pi\) | ||||
−0.918482 | + | 0.395463i | \(0.870584\pi\) | |||||||
\(558\) | −1.35686e6 | −0.184480 | ||||||||
\(559\) | −5.82547e6 | −0.788500 | ||||||||
\(560\) | − | 1.14054e6i | − | 0.153689i | ||||||
\(561\) | − | 1.44151e7i | − | 1.93380i | ||||||
\(562\) | 2.15517e6 | 0.287833 | ||||||||
\(563\) | 5.05335e6i | 0.671906i | 0.941879 | + | 0.335953i | \(0.109058\pi\) | ||||
−0.941879 | + | 0.335953i | \(0.890942\pi\) | |||||||
\(564\) | 2.49653e6 | 0.330476 | ||||||||
\(565\) | 6.06907e6 | 0.799836 | ||||||||
\(566\) | −7.39512e6 | −0.970296 | ||||||||
\(567\) | 2.73874e6 | 0.357761 | ||||||||
\(568\) | − | 1.21797e6i | − | 0.158404i | ||||||
\(569\) | − | 3.57229e6i | − | 0.462558i | −0.972888 | − | 0.231279i | \(-0.925709\pi\) | ||
0.972888 | − | 0.231279i | \(-0.0742910\pi\) | |||||||
\(570\) | 3.61754e6i | 0.466365i | ||||||||
\(571\) | 1.29233e7 | 1.65876 | 0.829380 | − | 0.558684i | \(-0.188694\pi\) | ||||
0.829380 | + | 0.558684i | \(0.188694\pi\) | |||||||
\(572\) | − | 9.14057e6i | − | 1.16811i | ||||||
\(573\) | 8.78600e6i | 1.11790i | ||||||||
\(574\) | 1.78517e6i | 0.226152i | ||||||||
\(575\) | 5.10035e6i | 0.643324i | ||||||||
\(576\) | 654600. | 0.0822090 | ||||||||
\(577\) | − | 1.61007e6i | − | 0.201329i | −0.994920 | − | 0.100664i | \(-0.967903\pi\) | ||
0.994920 | − | 0.100664i | \(-0.0320968\pi\) | |||||||
\(578\) | − | 8.22656e6i | − | 1.02423i | ||||||
\(579\) | − | 1.64411e6i | − | 0.203814i | ||||||
\(580\) | 2.70968e6 | 0.334463 | ||||||||
\(581\) | 4.68814e6 | 0.576183 | ||||||||
\(582\) | 4.74512e6 | 0.580684 | ||||||||
\(583\) | −1.28287e7 | −1.56318 | ||||||||
\(584\) | 1.22057e7i | 1.48091i | ||||||||
\(585\) | 2.37605e6 | 0.287055 | ||||||||
\(586\) | − | 1.23669e6i | − | 0.148770i | ||||||
\(587\) | 4.70903e6i | 0.564075i | 0.959403 | + | 0.282037i | \(0.0910102\pi\) | ||||
−0.959403 | + | 0.282037i | \(0.908990\pi\) | |||||||
\(588\) | 2.21249e6 | 0.263899 | ||||||||
\(589\) | 1.40021e7 | 1.66305 | ||||||||
\(590\) | − | 2.57817e6i | − | 0.304917i | ||||||
\(591\) | −7.84820e6 | −0.924275 | ||||||||
\(592\) | 2.42898e6 | + | 860094.i | 0.284852 | + | 0.100865i | ||||
\(593\) | 6.00154e6 | 0.700851 | 0.350426 | − | 0.936591i | \(-0.386037\pi\) | ||||
0.350426 | + | 0.936591i | \(0.386037\pi\) | |||||||
\(594\) | − | 6.62779e6i | − | 0.770730i | ||||||
\(595\) | −7.64733e6 | −0.885559 | ||||||||
\(596\) | 802501. | 0.0925401 | ||||||||
\(597\) | − | 4.47572e6i | − | 0.513958i | ||||||
\(598\) | − | 5.94317e6i | − | 0.679618i | ||||||
\(599\) | 1.17352e7 | 1.33636 | 0.668179 | − | 0.744000i | \(-0.267074\pi\) | ||||
0.668179 | + | 0.744000i | \(0.267074\pi\) | |||||||
\(600\) | − | 3.25569e6i | − | 0.369203i | ||||||
\(601\) | −9.96280e6 | −1.12511 | −0.562555 | − | 0.826760i | \(-0.690182\pi\) | ||||
−0.562555 | + | 0.826760i | \(0.690182\pi\) | |||||||
\(602\) | 2.35833e6 | 0.265225 | ||||||||
\(603\) | 455780. | 0.0510460 | ||||||||
\(604\) | 1.10093e6 | 0.122792 | ||||||||
\(605\) | 6.03178e6i | 0.669973i | ||||||||
\(606\) | 7.04983e6i | 0.779825i | ||||||||
\(607\) | − | 1.17448e6i | − | 0.129382i | −0.997905 | − | 0.0646908i | \(-0.979394\pi\) | ||
0.997905 | − | 0.0646908i | \(-0.0206061\pi\) | |||||||
\(608\) | −1.61062e7 | −1.76699 | ||||||||
\(609\) | − | 3.51634e6i | − | 0.384191i | ||||||
\(610\) | − | 1.57776e6i | − | 0.171679i | ||||||
\(611\) | − | 5.76552e6i | − | 0.624792i | ||||||
\(612\) | 4.53169e6i | 0.489082i | ||||||||
\(613\) | −1.45455e7 | −1.56343 | −0.781715 | − | 0.623636i | \(-0.785655\pi\) | ||||
−0.781715 | + | 0.623636i | \(0.785655\pi\) | |||||||
\(614\) | 2.86153e6i | 0.306322i | ||||||||
\(615\) | 3.06173e6i | 0.326422i | ||||||||
\(616\) | 8.66158e6i | 0.919699i | ||||||||
\(617\) | 8.19052e6 | 0.866161 | 0.433081 | − | 0.901355i | \(-0.357427\pi\) | ||||
0.433081 | + | 0.901355i | \(0.357427\pi\) | |||||||
\(618\) | 2.19281e6 | 0.230956 | ||||||||
\(619\) | 595920. | 0.0625117 | 0.0312558 | − | 0.999511i | \(-0.490049\pi\) | ||||
0.0312558 | + | 0.999511i | \(0.490049\pi\) | |||||||
\(620\) | 4.74933e6 | 0.496195 | ||||||||
\(621\) | 1.26477e7i | 1.31608i | ||||||||
\(622\) | 4.32284e6 | 0.448016 | ||||||||
\(623\) | − | 4.48524e6i | − | 0.462983i | ||||||
\(624\) | − | 2.58380e6i | − | 0.265642i | ||||||
\(625\) | −1.82055e6 | −0.186424 | ||||||||
\(626\) | −404791. | −0.0412853 | ||||||||
\(627\) | 1.87109e7i | 1.90076i | ||||||||
\(628\) | −4.52822e6 | −0.458171 | ||||||||
\(629\) | 5.76692e6 | − | 1.62863e7i | 0.581189 | − | 1.64133i | ||||
\(630\) | −961898. | −0.0965557 | ||||||||
\(631\) | 2.68979e6i | 0.268934i | 0.990918 | + | 0.134467i | \(0.0429322\pi\) | ||||
−0.990918 | + | 0.134467i | \(0.957068\pi\) | |||||||
\(632\) | 6.87213e6 | 0.684382 | ||||||||
\(633\) | −1.47692e7 | −1.46503 | ||||||||
\(634\) | 4.23453e6i | 0.418390i | ||||||||
\(635\) | 2.98390e6i | 0.293663i | ||||||||
\(636\) | −6.67604e6 | −0.654449 | ||||||||
\(637\) | − | 5.10954e6i | − | 0.498923i | ||||||
\(638\) | −4.77531e6 | −0.464462 | ||||||||
\(639\) | 699602. | 0.0677796 | ||||||||
\(640\) | −6.54368e6 | −0.631498 | ||||||||
\(641\) | 1.40540e6 | 0.135100 | 0.0675498 | − | 0.997716i | \(-0.478482\pi\) | ||||
0.0675498 | + | 0.997716i | \(0.478482\pi\) | |||||||
\(642\) | 1.38563e6i | 0.132682i | ||||||||
\(643\) | − | 1.06168e7i | − | 1.01267i | −0.862337 | − | 0.506335i | \(-0.831000\pi\) | ||
0.862337 | − | 0.506335i | \(-0.169000\pi\) | |||||||
\(644\) | − | 7.06140e6i | − | 0.670928i | ||||||
\(645\) | 4.04476e6 | 0.382819 | ||||||||
\(646\) | 1.59338e7i | 1.50224i | ||||||||
\(647\) | 2.90444e6i | 0.272773i | 0.990656 | + | 0.136387i | \(0.0435489\pi\) | ||||
−0.990656 | + | 0.136387i | \(0.956451\pi\) | |||||||
\(648\) | − | 4.53053e6i | − | 0.423849i | ||||||
\(649\) | − | 1.33350e7i | − | 1.24275i | ||||||
\(650\) | −3.21214e6 | −0.298203 | ||||||||
\(651\) | − | 6.16317e6i | − | 0.569970i | ||||||
\(652\) | − | 2.13136e6i | − | 0.196353i | ||||||
\(653\) | 6.64094e6i | 0.609462i | 0.952438 | + | 0.304731i | \(0.0985666\pi\) | ||||
−0.952438 | + | 0.304731i | \(0.901433\pi\) | |||||||
\(654\) | −4.12571e6 | −0.377185 | ||||||||
\(655\) | −6.14370e6 | −0.559534 | ||||||||
\(656\) | −2.01129e6 | −0.182480 | ||||||||
\(657\) | −7.01092e6 | −0.633668 | ||||||||
\(658\) | 2.33406e6i | 0.210159i | ||||||||
\(659\) | 1.05401e6 | 0.0945431 | 0.0472716 | − | 0.998882i | \(-0.484947\pi\) | ||||
0.0472716 | + | 0.998882i | \(0.484947\pi\) | |||||||
\(660\) | 6.34650e6i | 0.567119i | ||||||||
\(661\) | − | 6.02242e6i | − | 0.536126i | −0.963401 | − | 0.268063i | \(-0.913616\pi\) | ||
0.963401 | − | 0.268063i | \(-0.0863836\pi\) | |||||||
\(662\) | 7.59518e6 | 0.673586 | ||||||||
\(663\) | −1.73243e7 | −1.53064 | ||||||||
\(664\) | − | 7.75531e6i | − | 0.682620i | ||||||
\(665\) | 9.92630e6 | 0.870429 | ||||||||
\(666\) | 725376. | − | 2.04852e6i | 0.0633691 | − | 0.178960i | ||||
\(667\) | 9.11266e6 | 0.793105 | ||||||||
\(668\) | 2.02466e6i | 0.175554i | ||||||||
\(669\) | 674209. | 0.0582411 | ||||||||
\(670\) | 543567. | 0.0467807 | ||||||||
\(671\) | − | 8.16061e6i | − | 0.699707i | ||||||
\(672\) | 7.08930e6i | 0.605592i | ||||||||
\(673\) | 6.71709e6 | 0.571667 | 0.285834 | − | 0.958279i | \(-0.407730\pi\) | ||||
0.285834 | + | 0.958279i | \(0.407730\pi\) | |||||||
\(674\) | − | 5.78759e6i | − | 0.490736i | ||||||
\(675\) | 6.83580e6 | 0.577470 | ||||||||
\(676\) | −2.12338e6 | −0.178715 | ||||||||
\(677\) | −1.24184e7 | −1.04134 | −0.520670 | − | 0.853758i | \(-0.674318\pi\) | ||||
−0.520670 | + | 0.853758i | \(0.674318\pi\) | |||||||
\(678\) | −5.56600e6 | −0.465017 | ||||||||
\(679\) | − | 1.30203e7i | − | 1.08379i | ||||||
\(680\) | 1.26505e7i | 1.04915i | ||||||||
\(681\) | 9.87613e6i | 0.816055i | ||||||||
\(682\) | −8.36981e6 | −0.689056 | ||||||||
\(683\) | 1.47559e6i | 0.121036i | 0.998167 | + | 0.0605180i | \(0.0192753\pi\) | ||||
−0.998167 | + | 0.0605180i | \(0.980725\pi\) | |||||||
\(684\) | − | 5.88217e6i | − | 0.480726i | ||||||
\(685\) | 1.98939e6i | 0.161992i | ||||||||
\(686\) | 6.68449e6i | 0.542323i | ||||||||
\(687\) | −8.74591e6 | −0.706990 | ||||||||
\(688\) | 2.65706e6i | 0.214008i | ||||||||
\(689\) | 1.54177e7i | 1.23729i | ||||||||
\(690\) | 4.12647e6i | 0.329956i | ||||||||
\(691\) | −7.94552e6 | −0.633034 | −0.316517 | − | 0.948587i | \(-0.602513\pi\) | ||||
−0.316517 | + | 0.948587i | \(0.602513\pi\) | |||||||
\(692\) | 8.40473e6 | 0.667204 | ||||||||
\(693\) | −4.97521e6 | −0.393530 | ||||||||
\(694\) | 9.02520e6 | 0.711308 | ||||||||
\(695\) | − | 1.53918e7i | − | 1.20872i | ||||||
\(696\) | −5.81687e6 | −0.455162 | ||||||||
\(697\) | 1.34857e7i | 1.05146i | ||||||||
\(698\) | − | 4.10192e6i | − | 0.318676i | ||||||
\(699\) | −3.78084e6 | −0.292681 | ||||||||
\(700\) | −3.81652e6 | −0.294390 | ||||||||
\(701\) | − | 1.46257e7i | − | 1.12414i | −0.827088 | − | 0.562072i | \(-0.810004\pi\) | ||
0.827088 | − | 0.562072i | \(-0.189996\pi\) | |||||||
\(702\) | −7.96540e6 | −0.610049 | ||||||||
\(703\) | −7.48551e6 | + | 2.11397e7i | −0.571259 | + | 1.61328i | ||||
\(704\) | 4.03791e6 | 0.307061 | ||||||||
\(705\) | 4.00313e6i | 0.303338i | ||||||||
\(706\) | 1.93202e6 | 0.145882 | ||||||||
\(707\) | 1.93443e7 | 1.45547 | ||||||||
\(708\) | − | 6.93956e6i | − | 0.520294i | ||||||
\(709\) | 2.36304e7i | 1.76545i | 0.469892 | + | 0.882724i | \(0.344293\pi\) | ||||
−0.469892 | + | 0.882724i | \(0.655707\pi\) | |||||||
\(710\) | 834352. | 0.0621160 | ||||||||
\(711\) | 3.94735e6i | 0.292841i | ||||||||
\(712\) | −7.41966e6 | −0.548509 | ||||||||
\(713\) | 1.59720e7 | 1.17662 | ||||||||
\(714\) | 7.01344e6 | 0.514855 | ||||||||
\(715\) | 1.46567e7 | 1.07219 | ||||||||
\(716\) | 4.00637e6i | 0.292057i | ||||||||
\(717\) | − | 1.65076e7i | − | 1.19919i | ||||||
\(718\) | − | 5.62421e6i | − | 0.407146i | ||||||
\(719\) | −5.85300e6 | −0.422237 | −0.211118 | − | 0.977460i | \(-0.567711\pi\) | ||||
−0.211118 | + | 0.977460i | \(0.567711\pi\) | |||||||
\(720\) | − | 1.08374e6i | − | 0.0779100i | ||||||
\(721\) | − | 6.01692e6i | − | 0.431058i | ||||||
\(722\) | − | 1.36211e7i | − | 0.972453i | ||||||
\(723\) | − | 1.25869e7i | − | 0.895517i | ||||||
\(724\) | 9.93955e6 | 0.704726 | ||||||||
\(725\) | − | 4.92518e6i | − | 0.347998i | ||||||
\(726\) | − | 5.53180e6i | − | 0.389516i | ||||||
\(727\) | − | 636687.i | − | 0.0446776i | −0.999750 | − | 0.0223388i | \(-0.992889\pi\) | ||
0.999750 | − | 0.0223388i | \(-0.00711126\pi\) | |||||||
\(728\) | 1.04097e7 | 0.727960 | ||||||||
\(729\) | 1.49162e7 | 1.03954 | ||||||||
\(730\) | −8.36129e6 | −0.580719 | ||||||||
\(731\) | 1.78155e7 | 1.23312 | ||||||||
\(732\) | − | 4.24678e6i | − | 0.292943i | ||||||
\(733\) | 1.67411e7 | 1.15087 | 0.575433 | − | 0.817849i | \(-0.304833\pi\) | ||||
0.575433 | + | 0.817849i | \(0.304833\pi\) | |||||||
\(734\) | − | 8.48491e6i | − | 0.581309i | ||||||
\(735\) | 3.54767e6i | 0.242228i | ||||||||
\(736\) | −1.83721e7 | −1.25015 | ||||||||
\(737\) | 2.81148e6 | 0.190663 | ||||||||
\(738\) | 1.69626e6i | 0.114644i | ||||||||
\(739\) | 1.36468e7 | 0.919217 | 0.459609 | − | 0.888122i | \(-0.347990\pi\) | ||||
0.459609 | + | 0.888122i | \(0.347990\pi\) | |||||||
\(740\) | −2.53899e6 | + | 7.17031e6i | −0.170444 | + | 0.481348i | ||||
\(741\) | 2.24871e7 | 1.50449 | ||||||||
\(742\) | − | 6.24158e6i | − | 0.416183i | ||||||
\(743\) | −1.59940e6 | −0.106288 | −0.0531440 | − | 0.998587i | \(-0.516924\pi\) | ||||
−0.0531440 | + | 0.998587i | \(0.516924\pi\) | |||||||
\(744\) | −1.01954e7 | −0.675259 | ||||||||
\(745\) | 1.28679e6i | 0.0849410i | ||||||||
\(746\) | − | 6.25729e6i | − | 0.411660i | ||||||
\(747\) | 4.45465e6 | 0.292087 | ||||||||
\(748\) | 2.79538e7i | 1.82678i | ||||||||
\(749\) | 3.80209e6 | 0.247638 | ||||||||
\(750\) | 6.42802e6 | 0.417277 | ||||||||
\(751\) | −1.94616e6 | −0.125915 | −0.0629575 | − | 0.998016i | \(-0.520053\pi\) | ||||
−0.0629575 | + | 0.998016i | \(0.520053\pi\) | |||||||
\(752\) | −2.62971e6 | −0.169576 | ||||||||
\(753\) | 309602.i | 0.0198983i | ||||||||
\(754\) | 5.73906e6i | 0.367631i | ||||||||
\(755\) | 1.76532e6i | 0.112708i | ||||||||
\(756\) | −9.46412e6 | −0.602249 | ||||||||
\(757\) | − | 2.01297e7i | − | 1.27673i | −0.769735 | − | 0.638364i | \(-0.779611\pi\) | ||
0.769735 | − | 0.638364i | \(-0.220389\pi\) | |||||||
\(758\) | 6.96223e6i | 0.440125i | ||||||||
\(759\) | 2.13433e7i | 1.34480i | ||||||||
\(760\) | − | 1.64205e7i | − | 1.03122i | ||||||
\(761\) | 7.09820e6 | 0.444310 | 0.222155 | − | 0.975011i | \(-0.428691\pi\) | ||||
0.222155 | + | 0.975011i | \(0.428691\pi\) | |||||||
\(762\) | − | 2.73656e6i | − | 0.170733i | ||||||
\(763\) | 1.13207e7i | 0.703982i | ||||||||
\(764\) | − | 1.70378e7i | − | 1.05604i | ||||||
\(765\) | −7.26645e6 | −0.448920 | ||||||||
\(766\) | −1.95604e6 | −0.120450 | ||||||||
\(767\) | −1.60263e7 | −0.983659 | ||||||||
\(768\) | 8.81857e6 | 0.539504 | ||||||||
\(769\) | − | 6.44116e6i | − | 0.392779i | −0.980526 | − | 0.196389i | \(-0.937078\pi\) | ||
0.980526 | − | 0.196389i | \(-0.0629217\pi\) | |||||||
\(770\) | −5.93348e6 | −0.360647 | ||||||||
\(771\) | − | 1.00396e7i | − | 0.608248i | ||||||
\(772\) | 3.18826e6i | 0.192535i | ||||||||
\(773\) | −9.51628e6 | −0.572820 | −0.286410 | − | 0.958107i | \(-0.592462\pi\) | ||||
−0.286410 | + | 0.958107i | \(0.592462\pi\) | |||||||
\(774\) | 2.24088e6 | 0.134451 | ||||||||
\(775\) | − | 8.63249e6i | − | 0.516276i | ||||||
\(776\) | −2.15387e7 | −1.28400 | ||||||||
\(777\) | 9.30488e6 | + | 3.29483e6i | 0.552915 | + | 0.195785i | ||||
\(778\) | −1.16235e7 | −0.688477 | ||||||||
\(779\) | − | 1.75045e7i | − | 1.03349i | ||||||
\(780\) | 7.62734e6 | 0.448886 | ||||||||
\(781\) | 4.31550e6 | 0.253165 | ||||||||
\(782\) | 1.81755e7i | 1.06284i | ||||||||
\(783\) | − | 1.22133e7i | − | 0.711918i | ||||||
\(784\) | −2.33051e6 | −0.135413 | ||||||||
\(785\) | − | 7.26088e6i | − | 0.420548i | ||||||
\(786\) | 5.63444e6 | 0.325308 | ||||||||
\(787\) | −2.72531e7 | −1.56848 | −0.784241 | − | 0.620457i | \(-0.786947\pi\) | ||||
−0.784241 | + | 0.620457i | \(0.786947\pi\) | |||||||
\(788\) | 1.52192e7 | 0.873126 | ||||||||
\(789\) | −3.98118e6 | −0.227677 | ||||||||
\(790\) | 4.70765e6i | 0.268371i | ||||||||
\(791\) | 1.52728e7i | 0.867913i | ||||||||
\(792\) | 8.23019e6i | 0.466226i | ||||||||
\(793\) | −9.80757e6 | −0.553833 | ||||||||
\(794\) | 2.46045e6i | 0.138504i | ||||||||
\(795\) | − | 1.07049e7i | − | 0.600708i | ||||||
\(796\) | 8.67932e6i | 0.485516i | ||||||||
\(797\) | 2.81998e7i | 1.57253i | 0.617888 | + | 0.786266i | \(0.287988\pi\) | ||||
−0.617888 | + | 0.786266i | \(0.712012\pi\) | |||||||
\(798\) | −9.10350e6 | −0.506059 | ||||||||
\(799\) | 1.76322e7i | 0.977100i | ||||||||
\(800\) | 9.92967e6i | 0.548542i | ||||||||
\(801\) | − | 4.26185e6i | − | 0.234702i | ||||||
\(802\) | 346806. | 0.0190393 | ||||||||
\(803\) | −4.32470e7 | −2.36683 | ||||||||
\(804\) | 1.46310e6 | 0.0798239 | ||||||||
\(805\) | 1.13228e7 | 0.615834 | ||||||||
\(806\) | 1.00590e7i | 0.545402i | ||||||||
\(807\) | −1.06593e7 | −0.576162 | ||||||||
\(808\) | − | 3.20001e7i | − | 1.72434i | ||||||
\(809\) | − | 1.93886e7i | − | 1.04154i | −0.853698 | − | 0.520768i | \(-0.825646\pi\) | ||
0.853698 | − | 0.520768i | \(-0.174354\pi\) | |||||||
\(810\) | 3.10357e6 | 0.166207 | ||||||||
\(811\) | 4.62132e6 | 0.246725 | 0.123363 | − | 0.992362i | \(-0.460632\pi\) | ||||
0.123363 | + | 0.992362i | \(0.460632\pi\) | |||||||
\(812\) | 6.81889e6i | 0.362930i | ||||||||
\(813\) | −1.47830e6 | −0.0784399 | ||||||||
\(814\) | 4.47449e6 | − | 1.26363e7i | 0.236692 | − | 0.668437i | ||||
\(815\) | 3.41758e6 | 0.180229 | ||||||||
\(816\) | 7.90180e6i | 0.415433i | ||||||||
\(817\) | −2.31247e7 | −1.21205 | ||||||||
\(818\) | 1.63401e7 | 0.853831 | ||||||||
\(819\) | 5.97930e6i | 0.311487i | ||||||||
\(820\) | − | 5.93731e6i | − | 0.308358i | ||||||
\(821\) | −2.53220e7 | −1.31111 | −0.655557 | − | 0.755145i | \(-0.727566\pi\) | ||||
−0.655557 | + | 0.755145i | \(0.727566\pi\) | |||||||
\(822\) | − | 1.82449e6i | − | 0.0941805i | ||||||
\(823\) | 3.21181e7 | 1.65291 | 0.826457 | − | 0.563001i | \(-0.190353\pi\) | ||||
0.826457 | + | 0.563001i | \(0.190353\pi\) | |||||||
\(824\) | −9.95343e6 | −0.510687 | ||||||||
\(825\) | 1.15355e7 | 0.590070 | ||||||||
\(826\) | 6.48795e6 | 0.330870 | ||||||||
\(827\) | 1.20543e7i | 0.612883i | 0.951889 | + | 0.306442i | \(0.0991384\pi\) | ||||
−0.951889 | + | 0.306442i | \(0.900862\pi\) | |||||||
\(828\) | − | 6.70971e6i | − | 0.340116i | ||||||
\(829\) | 1.95634e7i | 0.988684i | 0.869267 | + | 0.494342i | \(0.164591\pi\) | ||||
−0.869267 | + | 0.494342i | \(0.835409\pi\) | |||||||
\(830\) | 5.31266e6 | 0.267680 | ||||||||
\(831\) | 1.79805e7i | 0.903230i | ||||||||
\(832\) | − | 4.85283e6i | − | 0.243045i | ||||||
\(833\) | 1.56261e7i | 0.780256i | ||||||||
\(834\) | 1.41159e7i | 0.702739i | ||||||||
\(835\) | −3.24649e6 | −0.161138 | ||||||||
\(836\) | − | 3.62842e7i | − | 1.79557i | ||||||
\(837\) | − | 2.14066e7i | − | 1.05617i | ||||||
\(838\) | 1.45894e7i | 0.717676i | ||||||||
\(839\) | −1.14371e7 | −0.560931 | −0.280466 | − | 0.959864i | \(-0.590489\pi\) | ||||
−0.280466 | + | 0.959864i | \(0.590489\pi\) | |||||||
\(840\) | −7.22765e6 | −0.353426 | ||||||||
\(841\) | 1.17115e7 | 0.570980 | ||||||||
\(842\) | −2.77447e6 | −0.134865 | ||||||||
\(843\) | 9.30171e6i | 0.450810i | ||||||||
\(844\) | 2.86404e7 | 1.38396 | ||||||||
\(845\) | − | 3.40479e6i | − | 0.164040i | ||||||
\(846\) | 2.21781e6i | 0.106537i | ||||||||
\(847\) | −1.51789e7 | −0.726996 | ||||||||
\(848\) | 7.03217e6 | 0.335815 | ||||||||
\(849\) | − | 3.19174e7i | − | 1.51970i | ||||||
\(850\) | 9.82341e6 | 0.466353 | ||||||||
\(851\) | −8.53861e6 | + | 2.41138e7i | −0.404169 | + | 1.14141i | ||||
\(852\) | 2.24579e6 | 0.105991 | ||||||||
\(853\) | 1.88357e7i | 0.886359i | 0.896433 | + | 0.443180i | \(0.146150\pi\) | ||||
−0.896433 | + | 0.443180i | \(0.853850\pi\) | |||||||
\(854\) | 3.97041e6 | 0.186291 | ||||||||
\(855\) | 9.43192e6 | 0.441250 | ||||||||
\(856\) | − | 6.28957e6i | − | 0.293384i | ||||||
\(857\) | − | 1.22399e7i | − | 0.569280i | −0.958635 | − | 0.284640i | \(-0.908126\pi\) | ||
0.958635 | − | 0.284640i | \(-0.0918740\pi\) | |||||||
\(858\) | −1.34418e7 | −0.623359 | ||||||||
\(859\) | − | 2.16729e7i | − | 1.00216i | −0.865402 | − | 0.501078i | \(-0.832937\pi\) | ||
0.865402 | − | 0.501078i | \(-0.167063\pi\) | |||||||
\(860\) | −7.84359e6 | −0.361634 | ||||||||
\(861\) | −7.70482e6 | −0.354205 | ||||||||
\(862\) | −6.44162e6 | −0.295275 | ||||||||
\(863\) | −4.04170e7 | −1.84730 | −0.923649 | − | 0.383240i | \(-0.874808\pi\) | ||||
−0.923649 | + | 0.383240i | \(0.874808\pi\) | |||||||
\(864\) | 2.46234e7i | 1.12218i | ||||||||
\(865\) | 1.34768e7i | 0.612415i | ||||||||
\(866\) | 1.35954e7i | 0.616025i | ||||||||
\(867\) | 3.55059e7 | 1.60418 | ||||||||
\(868\) | 1.19516e7i | 0.538428i | ||||||||
\(869\) | 2.43493e7i | 1.09380i | ||||||||
\(870\) | − | 3.98475e6i | − | 0.178486i | ||||||
\(871\) | − | 3.37889e6i | − | 0.150914i | ||||||
\(872\) | 1.87271e7 | 0.834027 | ||||||||
\(873\) | − | 1.23718e7i | − | 0.549412i | ||||||
\(874\) | − | 2.35919e7i | − | 1.04468i | ||||||
\(875\) | − | 1.76381e7i | − | 0.778810i | ||||||
\(876\) | −2.25057e7 | −0.990907 | ||||||||
\(877\) | −1.77282e7 | −0.778333 | −0.389166 | − | 0.921167i | \(-0.627237\pi\) | ||||
−0.389166 | + | 0.921167i | \(0.627237\pi\) | |||||||
\(878\) | 1.84778e7 | 0.808935 | ||||||||
\(879\) | 5.33755e6 | 0.233007 | ||||||||
\(880\) | − | 6.68505e6i | − | 0.291003i | ||||||
\(881\) | −2.08301e7 | −0.904172 | −0.452086 | − | 0.891974i | \(-0.649320\pi\) | ||||
−0.452086 | + | 0.891974i | \(0.649320\pi\) | |||||||
\(882\) | 1.96548e6i | 0.0850741i | ||||||||
\(883\) | 1.01542e7i | 0.438270i | 0.975695 | + | 0.219135i | \(0.0703236\pi\) | ||||
−0.975695 | + | 0.219135i | \(0.929676\pi\) | |||||||
\(884\) | 3.35954e7 | 1.44594 | ||||||||
\(885\) | 1.11274e7 | 0.477569 | ||||||||
\(886\) | 2.03400e7i | 0.870497i | ||||||||
\(887\) | −3.19961e7 | −1.36549 | −0.682744 | − | 0.730657i | \(-0.739214\pi\) | ||||
−0.682744 | + | 0.730657i | \(0.739214\pi\) | |||||||
\(888\) | 5.45044e6 | − | 1.53925e7i | 0.231952 | − | 0.655053i | ||||
\(889\) | −7.50894e6 | −0.318658 | ||||||||
\(890\) | − | 5.08272e6i | − | 0.215090i | ||||||
\(891\) | 1.60525e7 | 0.677406 | ||||||||
\(892\) | −1.30743e6 | −0.0550181 | ||||||||
\(893\) | − | 2.28867e7i | − | 0.960406i | ||||||
\(894\) | − | 1.18013e6i | − | 0.0493839i | ||||||
\(895\) | −6.42411e6 | −0.268075 | ||||||||
\(896\) | − | 1.64671e7i | − | 0.685247i | ||||||
\(897\) | 2.56507e7 | 1.06443 | ||||||||
\(898\) | −1.80203e7 | −0.745713 | ||||||||
\(899\) | −1.54235e7 | −0.636476 | ||||||||
\(900\) | −3.62644e6 | −0.149236 | ||||||||
\(901\) | − | 4.71506e7i | − | 1.93498i | ||||||
\(902\) | 1.04634e7i | 0.428210i | ||||||||
\(903\) | 1.01786e7i | 0.415402i | ||||||||
\(904\) | 2.52648e7 | 1.02824 | ||||||||
\(905\) | 1.59378e7i | 0.646856i | ||||||||
\(906\) | − | 1.61899e6i | − | 0.0655275i | ||||||
\(907\) | − | 1.27218e7i | − | 0.513486i | −0.966480 | − | 0.256743i | \(-0.917351\pi\) | ||
0.966480 | − | 0.256743i | \(-0.0826494\pi\) | |||||||
\(908\) | − | 1.91518e7i | − | 0.770895i | ||||||
\(909\) | 1.83808e7 | 0.737829 | ||||||||
\(910\) | 7.13097e6i | 0.285460i | ||||||||
\(911\) | 1.63465e7i | 0.652571i | 0.945271 | + | 0.326285i | \(0.105797\pi\) | ||||
−0.945271 | + | 0.326285i | \(0.894203\pi\) | |||||||
\(912\) | − | 1.02566e7i | − | 0.408335i | ||||||
\(913\) | 2.74786e7 | 1.09098 | ||||||||
\(914\) | −2.17887e7 | −0.862711 | ||||||||
\(915\) | 6.80962e6 | 0.268887 | ||||||||
\(916\) | 1.69601e7 | 0.667866 | ||||||||
\(917\) | − | 1.54606e7i | − | 0.607158i | ||||||
\(918\) | 2.43599e7 | 0.954043 | ||||||||
\(919\) | 3.39032e7i | 1.32419i | 0.749418 | + | 0.662097i | \(0.230333\pi\) | ||||
−0.749418 | + | 0.662097i | \(0.769667\pi\) | |||||||
\(920\) | − | 1.87306e7i | − | 0.729596i | ||||||
\(921\) | −1.23504e7 | −0.479769 | ||||||||
\(922\) | 1.11790e7 | 0.433088 | ||||||||
\(923\) | − | 5.18645e6i | − | 0.200385i | ||||||
\(924\) | −1.59709e7 | −0.615389 | ||||||||
\(925\) | 1.30329e7 | + | 4.61492e6i | 0.500827 | + | 0.177341i | ||||
\(926\) | 1.87639e7 | 0.719110 | ||||||||
\(927\) | − | 5.71725e6i | − | 0.218518i | ||||||
\(928\) | 1.77411e7 | 0.676255 | ||||||||
\(929\) | 4.54616e7 | 1.72824 | 0.864122 | − | 0.503282i | \(-0.167874\pi\) | ||||
0.864122 | + | 0.503282i | \(0.167874\pi\) | |||||||
\(930\) | − | 6.98418e6i | − | 0.264794i | ||||||
\(931\) | − | 2.02828e7i | − | 0.766925i | ||||||
\(932\) | 7.33180e6 | 0.276485 | ||||||||
\(933\) | 1.86574e7i | 0.701693i | ||||||||
\(934\) | 1.10802e7 | 0.415605 | ||||||||
\(935\) | −4.48232e7 | −1.67677 | ||||||||
\(936\) | 9.89119e6 | 0.369028 | ||||||||
\(937\) | −1.11969e6 | −0.0416629 | −0.0208314 | − | 0.999783i | \(-0.506631\pi\) | ||||
−0.0208314 | + | 0.999783i | \(0.506631\pi\) | |||||||
\(938\) | 1.36788e6i | 0.0507623i | ||||||||
\(939\) | − | 1.74708e6i | − | 0.0646620i | ||||||
\(940\) | − | 7.76287e6i | − | 0.286551i | ||||||
\(941\) | 2.25114e7 | 0.828760 | 0.414380 | − | 0.910104i | \(-0.363999\pi\) | ||||
0.414380 | + | 0.910104i | \(0.363999\pi\) | |||||||
\(942\) | 6.65902e6i | 0.244502i | ||||||||
\(943\) | − | 1.99672e7i | − | 0.731202i | ||||||
\(944\) | 7.30975e6i | 0.266976i | ||||||||
\(945\) | − | 1.51755e7i | − | 0.552794i | ||||||
\(946\) | 1.38229e7 | 0.502193 | ||||||||
\(947\) | 3.50838e7i | 1.27125i | 0.771997 | + | 0.635626i | \(0.219258\pi\) | ||||
−0.771997 | + | 0.635626i | \(0.780742\pi\) | |||||||
\(948\) | 1.26714e7i | 0.457934i | ||||||||
\(949\) | 5.19750e7i | 1.87339i | ||||||||
\(950\) | −1.27509e7 | −0.458385 | ||||||||
\(951\) | −1.82762e7 | −0.655293 | ||||||||
\(952\) | −3.18349e7 | −1.13844 | ||||||||
\(953\) | 8.82460e6 | 0.314748 | 0.157374 | − | 0.987539i | \(-0.449697\pi\) | ||||
0.157374 | + | 0.987539i | \(0.449697\pi\) | |||||||
\(954\) | − | 5.93071e6i | − | 0.210977i | ||||||
\(955\) | 2.73197e7 | 0.969322 | ||||||||
\(956\) | 3.20116e7i | 1.13283i | ||||||||
\(957\) | − | 2.06103e7i | − | 0.727451i | ||||||
\(958\) | −2.14616e6 | −0.0755525 | ||||||||
\(959\) | −5.00628e6 | −0.175779 | ||||||||
\(960\) | 3.36943e6i | 0.117999i | ||||||||
\(961\) | 1.59608e6 | 0.0557501 | ||||||||
\(962\) | −1.51866e7 | − | 5.37753e6i | −0.529082 | − | 0.187346i | ||||
\(963\) | 3.61273e6 | 0.125536 | ||||||||
\(964\) | 2.44086e7i | 0.845960i | ||||||||
\(965\) | −5.11229e6 | −0.176725 | ||||||||
\(966\) | −1.03842e7 | −0.358040 | ||||||||
\(967\) | − | 2.91030e7i | − | 1.00086i | −0.865778 | − | 0.500428i | \(-0.833176\pi\) | ||
0.865778 | − | 0.500428i | \(-0.166824\pi\) | |||||||
\(968\) | 2.51096e7i | 0.861293i | ||||||||
\(969\) | −6.87704e7 | −2.35284 | ||||||||
\(970\) | − | 1.47548e7i | − | 0.503504i | ||||||
\(971\) | −1.31598e7 | −0.447921 | −0.223961 | − | 0.974598i | \(-0.571899\pi\) | ||||
−0.223961 | + | 0.974598i | \(0.571899\pi\) | |||||||
\(972\) | −1.55254e7 | −0.527080 | ||||||||
\(973\) | 3.87332e7 | 1.31160 | ||||||||
\(974\) | −2.88653e7 | −0.974943 | ||||||||
\(975\) | − | 1.38636e7i | − | 0.467052i | ||||||
\(976\) | 4.47333e6i | 0.150316i | ||||||||
\(977\) | − | 3.87316e7i | − | 1.29816i | −0.760720 | − | 0.649080i | \(-0.775154\pi\) | ||
0.760720 | − | 0.649080i | \(-0.224846\pi\) | |||||||
\(978\) | −3.13429e6 | −0.104783 | ||||||||
\(979\) | − | 2.62893e7i | − | 0.876641i | ||||||
\(980\) | − | 6.87964e6i | − | 0.228824i | ||||||
\(981\) | 1.07569e7i | 0.356872i | ||||||||
\(982\) | 8.92444e6i | 0.295326i | ||||||||
\(983\) | −1.63230e7 | −0.538788 | −0.269394 | − | 0.963030i | \(-0.586823\pi\) | ||||
−0.269394 | + | 0.963030i | \(0.586823\pi\) | |||||||
\(984\) | 1.27456e7i | 0.419636i | ||||||||
\(985\) | 2.44037e7i | 0.801428i | ||||||||
\(986\) | − | 1.75512e7i | − | 0.574931i | ||||||
\(987\) | −1.00738e7 | −0.329156 | ||||||||
\(988\) | −4.36071e7 | −1.42123 | ||||||||
\(989\) | −2.63780e7 | −0.857534 | ||||||||
\(990\) | −5.63796e6 | −0.182824 | ||||||||
\(991\) | − | 1.49634e7i | − | 0.484001i | −0.970276 | − | 0.242000i | \(-0.922196\pi\) | ||
0.970276 | − | 0.242000i | \(-0.0778035\pi\) | |||||||
\(992\) | 3.10953e7 | 1.00326 | ||||||||
\(993\) | 3.27808e7i | 1.05499i | ||||||||
\(994\) | 2.09964e6i | 0.0674029i | ||||||||
\(995\) | −1.39171e7 | −0.445647 | ||||||||
\(996\) | 1.42998e7 | 0.456755 | ||||||||
\(997\) | 2.63578e7i | 0.839791i | 0.907572 | + | 0.419896i | \(0.137933\pi\) | ||||
−0.907572 | + | 0.419896i | \(0.862067\pi\) | |||||||
\(998\) | −14350.3 | −0.000456074 | ||||||||
\(999\) | 3.23187e7 | + | 1.14440e7i | 1.02457 | + | 0.362796i |
(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 | 37.6.b.a.36.10 | yes | 16 | |
3.2 | odd | 2 | 333.6.c.d.73.7 | 16 | |||
4.3 | odd | 2 | 592.6.g.c.369.12 | 16 | |||
37.36 | even | 2 | inner | 37.6.b.a.36.7 | ✓ | 16 | |
111.110 | odd | 2 | 333.6.c.d.73.10 | 16 | |||
148.147 | odd | 2 | 592.6.g.c.369.11 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.6.b.a.36.7 | ✓ | 16 | 37.36 | even | 2 | inner | |
37.6.b.a.36.10 | yes | 16 | 1.1 | even | 1 | trivial | |
333.6.c.d.73.7 | 16 | 3.2 | odd | 2 | |||
333.6.c.d.73.10 | 16 | 111.110 | odd | 2 | |||
592.6.g.c.369.11 | 16 | 148.147 | odd | 2 | |||
592.6.g.c.369.12 | 16 | 4.3 | odd | 2 |