Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(146,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.146");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.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: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.37 | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.6.c.d.146.38 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 9.64154i | − | 1.70440i | −0.523216 | − | 0.852200i | \(-0.675268\pi\) | ||
0.523216 | − | 0.852200i | \(-0.324732\pi\) | |||||||
\(3\) | −2.14483 | + | 15.4402i | −0.137591 | + | 0.990489i | ||||
\(4\) | −60.9593 | −1.90498 | ||||||||
\(5\) | 95.0200 | 1.69977 | 0.849885 | − | 0.526968i | \(-0.176671\pi\) | ||||
0.849885 | + | 0.526968i | \(0.176671\pi\) | |||||||
\(6\) | 148.867 | + | 20.6794i | 1.68819 | + | 0.234510i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 279.213i | 1.54245i | ||||||||
\(9\) | −233.799 | − | 66.2331i | −0.962138 | − | 0.272564i | ||||
\(10\) | − | 916.140i | − | 2.89709i | ||||||
\(11\) | 151.751i | 0.378137i | 0.981964 | + | 0.189068i | \(0.0605468\pi\) | ||||
−0.981964 | + | 0.189068i | \(0.939453\pi\) | |||||||
\(12\) | 130.747 | − | 941.224i | 0.262107 | − | 1.88686i | ||||
\(13\) | 901.601i | 1.47964i | 0.672805 | + | 0.739820i | \(0.265089\pi\) | ||||
−0.672805 | + | 0.739820i | \(0.734911\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −203.801 | + | 1467.13i | −0.233872 | + | 1.68360i | ||||
\(16\) | 741.343 | 0.723968 | ||||||||
\(17\) | −488.591 | −0.410037 | −0.205019 | − | 0.978758i | \(-0.565726\pi\) | ||||
−0.205019 | + | 0.978758i | \(0.565726\pi\) | |||||||
\(18\) | −638.589 | + | 2254.19i | −0.464558 | + | 1.63987i | ||||
\(19\) | 2181.83i | 1.38656i | 0.720670 | + | 0.693278i | \(0.243834\pi\) | ||||
−0.720670 | + | 0.693278i | \(0.756166\pi\) | |||||||
\(20\) | −5792.36 | −3.23803 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1463.11 | 0.644497 | ||||||||
\(23\) | − | 1380.63i | − | 0.544201i | −0.962269 | − | 0.272100i | \(-0.912282\pi\) | ||
0.962269 | − | 0.272100i | \(-0.0877182\pi\) | |||||||
\(24\) | −4311.10 | − | 598.863i | −1.52778 | − | 0.212226i | ||||
\(25\) | 5903.81 | 1.88922 | ||||||||
\(26\) | 8692.82 | 2.52190 | ||||||||
\(27\) | 1524.11 | − | 3467.85i | 0.402353 | − | 0.915485i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5152.42i | 1.13767i | 0.822452 | + | 0.568835i | \(0.192606\pi\) | ||||
−0.822452 | + | 0.568835i | \(0.807394\pi\) | |||||||
\(30\) | 14145.4 | + | 1964.96i | 2.86953 | + | 0.398612i | ||||
\(31\) | 1259.55i | 0.235403i | 0.993049 | + | 0.117701i | \(0.0375526\pi\) | ||||
−0.993049 | + | 0.117701i | \(0.962447\pi\) | |||||||
\(32\) | 1787.12i | 0.308517i | ||||||||
\(33\) | −2343.06 | − | 325.479i | −0.374541 | − | 0.0520281i | ||||
\(34\) | 4710.77i | 0.698868i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 14252.3 | + | 4037.52i | 1.83285 | + | 0.519229i | ||||
\(37\) | −3684.15 | −0.442418 | −0.221209 | − | 0.975226i | \(-0.571000\pi\) | ||||
−0.221209 | + | 0.975226i | \(0.571000\pi\) | |||||||
\(38\) | 21036.2 | 2.36325 | ||||||||
\(39\) | −13920.9 | − | 1933.78i | −1.46557 | − | 0.203585i | ||||
\(40\) | 26530.8i | 2.62181i | ||||||||
\(41\) | 14410.3 | 1.33879 | 0.669397 | − | 0.742905i | \(-0.266553\pi\) | ||||
0.669397 | + | 0.742905i | \(0.266553\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10096.1 | 0.832689 | 0.416345 | − | 0.909207i | \(-0.363311\pi\) | ||||
0.416345 | + | 0.909207i | \(0.363311\pi\) | |||||||
\(44\) | − | 9250.63i | − | 0.720343i | ||||||
\(45\) | −22215.6 | − | 6293.47i | −1.63541 | − | 0.463296i | ||||
\(46\) | −13311.4 | −0.927535 | ||||||||
\(47\) | −9270.49 | −0.612150 | −0.306075 | − | 0.952007i | \(-0.599016\pi\) | ||||
−0.306075 | + | 0.952007i | \(0.599016\pi\) | |||||||
\(48\) | −1590.05 | + | 11446.5i | −0.0996112 | + | 0.717082i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 56921.8i | − | 3.21998i | ||||||
\(51\) | 1047.94 | − | 7543.95i | 0.0564173 | − | 0.406138i | ||||
\(52\) | − | 54961.0i | − | 2.81868i | ||||||
\(53\) | 16719.0i | 0.817562i | 0.912633 | + | 0.408781i | \(0.134046\pi\) | ||||
−0.912633 | + | 0.408781i | \(0.865954\pi\) | |||||||
\(54\) | −33435.4 | − | 14694.8i | −1.56035 | − | 0.685770i | ||||
\(55\) | 14419.4i | 0.642746i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −33687.9 | − | 4679.65i | −1.37337 | − | 0.190777i | ||||
\(58\) | 49677.3 | 1.93904 | ||||||||
\(59\) | 2365.92 | 0.0884850 | 0.0442425 | − | 0.999021i | \(-0.485913\pi\) | ||||
0.0442425 | + | 0.999021i | \(0.485913\pi\) | |||||||
\(60\) | 12423.6 | − | 89435.2i | 0.445522 | − | 3.20723i | ||||
\(61\) | 7948.63i | 0.273506i | 0.990605 | + | 0.136753i | \(0.0436667\pi\) | ||||
−0.990605 | + | 0.136753i | \(0.956333\pi\) | |||||||
\(62\) | 12144.0 | 0.401221 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 40953.6 | 1.24980 | ||||||||
\(65\) | 85670.1i | 2.51505i | ||||||||
\(66\) | −3138.12 | + | 22590.7i | −0.0886767 | + | 0.638367i | ||||
\(67\) | 33927.2 | 0.923337 | 0.461669 | − | 0.887052i | \(-0.347251\pi\) | ||||
0.461669 | + | 0.887052i | \(0.347251\pi\) | |||||||
\(68\) | 29784.2 | 0.781113 | ||||||||
\(69\) | 21317.3 | + | 2961.22i | 0.539025 | + | 0.0748769i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 43126.9i | − | 1.01532i | −0.861558 | − | 0.507659i | \(-0.830511\pi\) | ||
0.861558 | − | 0.507659i | \(-0.169489\pi\) | |||||||
\(72\) | 18493.1 | − | 65279.8i | 0.420416 | − | 1.48405i | ||||
\(73\) | 21559.1i | 0.473504i | 0.971570 | + | 0.236752i | \(0.0760829\pi\) | ||||
−0.971570 | + | 0.236752i | \(0.923917\pi\) | |||||||
\(74\) | 35520.8i | 0.754057i | ||||||||
\(75\) | −12662.6 | + | 91156.0i | −0.259939 | + | 1.87125i | ||||
\(76\) | − | 133003.i | − | 2.64136i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −18644.6 | + | 134219.i | −0.346989 | + | 2.49791i | ||||
\(79\) | −10123.5 | −0.182501 | −0.0912503 | − | 0.995828i | \(-0.529086\pi\) | ||||
−0.0912503 | + | 0.995828i | \(0.529086\pi\) | |||||||
\(80\) | 70442.4 | 1.23058 | ||||||||
\(81\) | 50275.4 | + | 30970.5i | 0.851418 | + | 0.524488i | ||||
\(82\) | − | 138938.i | − | 2.28184i | ||||||
\(83\) | −2968.57 | −0.0472990 | −0.0236495 | − | 0.999720i | \(-0.507529\pi\) | ||||
−0.0236495 | + | 0.999720i | \(0.507529\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −46426.0 | −0.696969 | ||||||||
\(86\) | − | 97342.1i | − | 1.41924i | ||||||
\(87\) | −79554.4 | − | 11051.0i | −1.12685 | − | 0.156533i | ||||
\(88\) | −42370.7 | −0.583256 | ||||||||
\(89\) | 84489.6 | 1.13065 | 0.565325 | − | 0.824868i | \(-0.308751\pi\) | ||||
0.565325 | + | 0.824868i | \(0.308751\pi\) | |||||||
\(90\) | −60678.8 | + | 214193.i | −0.789642 | + | 2.78740i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 84162.5i | 1.03669i | ||||||||
\(93\) | −19447.7 | − | 2701.52i | −0.233164 | − | 0.0323892i | ||||
\(94\) | 89381.8i | 1.04335i | ||||||||
\(95\) | 207318.i | 2.35683i | ||||||||
\(96\) | −27593.5 | − | 3833.06i | −0.305583 | − | 0.0424490i | ||||
\(97\) | − | 60769.2i | − | 0.655774i | −0.944717 | − | 0.327887i | \(-0.893664\pi\) | ||
0.944717 | − | 0.327887i | \(-0.106336\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10050.9 | − | 35479.2i | 0.103067 | − | 0.363820i | ||||
\(100\) | −359892. | −3.59892 | ||||||||
\(101\) | 26945.9 | 0.262838 | 0.131419 | − | 0.991327i | \(-0.458047\pi\) | ||||
0.131419 | + | 0.991327i | \(0.458047\pi\) | |||||||
\(102\) | −72735.3 | − | 10103.8i | −0.692221 | − | 0.0961577i | ||||
\(103\) | − | 461.131i | − | 0.00428284i | −0.999998 | − | 0.00214142i | \(-0.999318\pi\) | ||
0.999998 | − | 0.00214142i | \(-0.000681635\pi\) | |||||||
\(104\) | −251738. | −2.28227 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 161197. | 1.39345 | ||||||||
\(107\) | 131955.i | 1.11421i | 0.830442 | + | 0.557106i | \(0.188088\pi\) | ||||
−0.830442 | + | 0.557106i | \(0.811912\pi\) | |||||||
\(108\) | −92908.8 | + | 211398.i | −0.766474 | + | 1.74398i | ||||
\(109\) | −218127. | −1.75850 | −0.879252 | − | 0.476357i | \(-0.841957\pi\) | ||||
−0.879252 | + | 0.476357i | \(0.841957\pi\) | |||||||
\(110\) | 139025. | 1.09550 | ||||||||
\(111\) | 7901.85 | − | 56883.9i | 0.0608725 | − | 0.438210i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 178165.i | 1.31258i | 0.754509 | + | 0.656290i | \(0.227875\pi\) | ||||
−0.754509 | + | 0.656290i | \(0.772125\pi\) | |||||||
\(114\) | −45119.1 | + | 324804.i | −0.325161 | + | 2.34077i | ||||
\(115\) | − | 131188.i | − | 0.925016i | ||||||
\(116\) | − | 314088.i | − | 2.16724i | ||||||
\(117\) | 59715.8 | − | 210794.i | 0.403297 | − | 1.42362i | ||||
\(118\) | − | 22811.1i | − | 0.150814i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −409641. | − | 56904.0i | −2.59687 | − | 0.360736i | ||||
\(121\) | 138023. | 0.857012 | ||||||||
\(122\) | 76637.0 | 0.466164 | ||||||||
\(123\) | −30907.6 | + | 222498.i | −0.184206 | + | 1.32606i | ||||
\(124\) | − | 76781.4i | − | 0.448438i | ||||||
\(125\) | 264042. | 1.51147 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −180683. | −0.994050 | −0.497025 | − | 0.867736i | \(-0.665574\pi\) | ||||
−0.497025 | + | 0.867736i | \(0.665574\pi\) | |||||||
\(128\) | − | 337668.i | − | 1.82165i | ||||||
\(129\) | −21654.4 | + | 155886.i | −0.114570 | + | 0.824770i | ||||
\(130\) | 825992. | 4.28665 | ||||||||
\(131\) | −372251. | −1.89521 | −0.947605 | − | 0.319444i | \(-0.896504\pi\) | ||||
−0.947605 | + | 0.319444i | \(0.896504\pi\) | |||||||
\(132\) | 142831. | + | 19841.0i | 0.713492 | + | 0.0991125i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 327110.i | − | 1.57374i | ||||||
\(135\) | 144821. | − | 329515.i | 0.683907 | − | 1.55611i | ||||
\(136\) | − | 136421.i | − | 0.632461i | ||||||
\(137\) | − | 329194.i | − | 1.49848i | −0.662301 | − | 0.749238i | \(-0.730420\pi\) | ||
0.662301 | − | 0.749238i | \(-0.269580\pi\) | |||||||
\(138\) | 28550.7 | − | 205531.i | 0.127620 | − | 0.918714i | ||||
\(139\) | − | 379210.i | − | 1.66473i | −0.554230 | − | 0.832363i | \(-0.686987\pi\) | ||
0.554230 | − | 0.832363i | \(-0.313013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19883.6 | − | 143138.i | 0.0842262 | − | 0.606328i | ||||
\(142\) | −415810. | −1.73051 | ||||||||
\(143\) | −136819. | −0.559506 | ||||||||
\(144\) | −173326. | − | 49101.4i | −0.696556 | − | 0.197328i | ||||
\(145\) | 489583.i | 1.93378i | ||||||||
\(146\) | 207863. | 0.807041 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 224583. | 0.842797 | ||||||||
\(149\) | 173846.i | 0.641502i | 0.947164 | + | 0.320751i | \(0.103935\pi\) | ||||
−0.947164 | + | 0.320751i | \(0.896065\pi\) | |||||||
\(150\) | 878884. | + | 122087.i | 3.18936 | + | 0.443040i | ||||
\(151\) | −117976. | −0.421066 | −0.210533 | − | 0.977587i | \(-0.567520\pi\) | ||||
−0.210533 | + | 0.977587i | \(0.567520\pi\) | |||||||
\(152\) | −609195. | −2.13869 | ||||||||
\(153\) | 114232. | + | 32360.9i | 0.394512 | + | 0.111761i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 119683.i | 0.400131i | ||||||||
\(156\) | 848609. | + | 117882.i | 2.79187 | + | 0.387824i | ||||
\(157\) | 39454.9i | 0.127747i | 0.997958 | + | 0.0638736i | \(0.0203454\pi\) | ||||
−0.997958 | + | 0.0638736i | \(0.979655\pi\) | |||||||
\(158\) | 97606.5i | 0.311054i | ||||||||
\(159\) | −258145. | − | 35859.3i | −0.809786 | − | 0.112489i | ||||
\(160\) | 169812.i | 0.524408i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 298604. | − | 484732.i | 0.893938 | − | 1.45116i | ||||
\(163\) | −432587. | −1.27528 | −0.637639 | − | 0.770335i | \(-0.720089\pi\) | ||||
−0.637639 | + | 0.770335i | \(0.720089\pi\) | |||||||
\(164\) | −878443. | −2.55038 | ||||||||
\(165\) | −222638. | − | 30927.0i | −0.636633 | − | 0.0884358i | ||||
\(166\) | 28621.6i | 0.0806165i | ||||||||
\(167\) | −264429. | −0.733698 | −0.366849 | − | 0.930280i | \(-0.619563\pi\) | ||||
−0.366849 | + | 0.930280i | \(0.619563\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −441591. | −1.18933 | ||||||||
\(170\) | 447618.i | 1.18791i | ||||||||
\(171\) | 144509. | − | 510111.i | 0.377925 | − | 1.33406i | ||||
\(172\) | −615452. | −1.58626 | ||||||||
\(173\) | 559625. | 1.42161 | 0.710807 | − | 0.703387i | \(-0.248330\pi\) | ||||
0.710807 | + | 0.703387i | \(0.248330\pi\) | |||||||
\(174\) | −106549. | + | 767027.i | −0.266794 | + | 1.92060i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 112499.i | 0.273759i | ||||||||
\(177\) | −5074.48 | + | 36530.2i | −0.0121747 | + | 0.0876434i | ||||
\(178\) | − | 814610.i | − | 1.92708i | ||||||
\(179\) | − | 535665.i | − | 1.24957i | −0.780796 | − | 0.624786i | \(-0.785186\pi\) | ||
0.780796 | − | 0.624786i | \(-0.214814\pi\) | |||||||
\(180\) | 1.35425e6 | + | 383646.i | 3.11543 | + | 0.882570i | ||||
\(181\) | − | 4383.91i | − | 0.00994639i | −0.999988 | − | 0.00497319i | \(-0.998417\pi\) | ||
0.999988 | − | 0.00497319i | \(-0.00158302\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −122728. | − | 17048.4i | −0.270905 | − | 0.0376319i | ||||
\(184\) | 385491. | 0.839401 | ||||||||
\(185\) | −350068. | −0.752008 | ||||||||
\(186\) | −26046.8 | + | 187506.i | −0.0552042 | + | 0.397405i | ||||
\(187\) | − | 74144.1i | − | 0.155050i | ||||||
\(188\) | 565123. | 1.16613 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.99886e6 | 4.01698 | ||||||||
\(191\) | − | 401981.i | − | 0.797301i | −0.917103 | − | 0.398650i | \(-0.869479\pi\) | ||
0.917103 | − | 0.398650i | \(-0.130521\pi\) | |||||||
\(192\) | −87838.3 | + | 632331.i | −0.171961 | + | 1.23792i | ||||
\(193\) | −179908. | −0.347662 | −0.173831 | − | 0.984776i | \(-0.555615\pi\) | ||||
−0.173831 | + | 0.984776i | \(0.555615\pi\) | |||||||
\(194\) | −585909. | −1.11770 | ||||||||
\(195\) | −1.32276e6 | − | 183748.i | −2.49113 | − | 0.346047i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 516773.i | 0.948711i | 0.880333 | + | 0.474355i | \(0.157319\pi\) | ||||
−0.880333 | + | 0.474355i | \(0.842681\pi\) | |||||||
\(198\) | −342075. | − | 96906.3i | −0.620094 | − | 0.175667i | ||||
\(199\) | 393200.i | 0.703851i | 0.936028 | + | 0.351925i | \(0.114473\pi\) | ||||
−0.936028 | + | 0.351925i | \(0.885527\pi\) | |||||||
\(200\) | 1.64842e6i | 2.91402i | ||||||||
\(201\) | −72767.8 | + | 523842.i | −0.127043 | + | 0.914556i | ||||
\(202\) | − | 259800.i | − | 0.447982i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −63881.9 | + | 459874.i | −0.107474 | + | 0.773684i | ||||
\(205\) | 1.36927e6 | 2.27564 | ||||||||
\(206\) | −4446.02 | −0.00729967 | ||||||||
\(207\) | −91443.6 | + | 322791.i | −0.148330 | + | 0.523596i | ||||
\(208\) | 668395.i | 1.07121i | ||||||||
\(209\) | −331095. | −0.524308 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 288681. | 0.446387 | 0.223194 | − | 0.974774i | \(-0.428352\pi\) | ||||
0.223194 | + | 0.974774i | \(0.428352\pi\) | |||||||
\(212\) | − | 1.01918e6i | − | 1.55744i | ||||||
\(213\) | 665888. | + | 92499.7i | 1.00566 | + | 0.139698i | ||||
\(214\) | 1.27225e6 | 1.89906 | ||||||||
\(215\) | 959333. | 1.41538 | ||||||||
\(216\) | 968268. | + | 425551.i | 1.41209 | + | 0.620608i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.10308e6i | 2.99719i | ||||||||
\(219\) | −332877. | − | 46240.6i | −0.469001 | − | 0.0651498i | ||||
\(220\) | − | 878995.i | − | 1.22442i | ||||||
\(221\) | − | 440514.i | − | 0.606708i | ||||||
\(222\) | −548449. | − | 76186.0i | −0.746885 | − | 0.103751i | ||||
\(223\) | − | 445560.i | − | 0.599991i | −0.953941 | − | 0.299995i | \(-0.903015\pi\) | ||
0.953941 | − | 0.299995i | \(-0.0969851\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.38031e6 | − | 391027.i | −1.81769 | − | 0.514933i | ||||
\(226\) | 1.71778e6 | 2.23716 | ||||||||
\(227\) | 1.08495e6 | 1.39748 | 0.698742 | − | 0.715374i | \(-0.253744\pi\) | ||||
0.698742 | + | 0.715374i | \(0.253744\pi\) | |||||||
\(228\) | 2.05359e6 | + | 285268.i | 2.61624 | + | 0.363427i | ||||
\(229\) | − | 677435.i | − | 0.853648i | −0.904335 | − | 0.426824i | \(-0.859632\pi\) | ||
0.904335 | − | 0.426824i | \(-0.140368\pi\) | |||||||
\(230\) | −1.26485e6 | −1.57660 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.43862e6 | −1.75480 | ||||||||
\(233\) | − | 142166.i | − | 0.171556i | −0.996314 | − | 0.0857779i | \(-0.972662\pi\) | ||
0.996314 | − | 0.0857779i | \(-0.0273376\pi\) | |||||||
\(234\) | −2.03238e6 | − | 575752.i | −2.42641 | − | 0.687379i | ||||
\(235\) | −880882. | −1.04051 | ||||||||
\(236\) | −144225. | −0.168562 | ||||||||
\(237\) | 21713.2 | − | 156309.i | 0.0251104 | − | 0.180765i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.10854e6i | − | 1.25532i | −0.778486 | − | 0.627662i | \(-0.784012\pi\) | ||
0.778486 | − | 0.627662i | \(-0.215988\pi\) | |||||||
\(240\) | −151087. | + | 1.08764e6i | −0.169316 | + | 1.21887i | ||||
\(241\) | − | 528785.i | − | 0.586458i | −0.956042 | − | 0.293229i | \(-0.905270\pi\) | ||
0.956042 | − | 0.293229i | \(-0.0947298\pi\) | |||||||
\(242\) | − | 1.33075e6i | − | 1.46069i | ||||||
\(243\) | −586023. | + | 709835.i | −0.636647 | + | 0.771155i | ||||
\(244\) | − | 484543.i | − | 0.521024i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.14522e6 | + | 297997.i | 2.26014 | + | 0.313960i | ||||
\(247\) | −1.96714e6 | −2.05160 | ||||||||
\(248\) | −351683. | −0.363096 | ||||||||
\(249\) | 6367.07 | − | 45835.3i | 0.00650791 | − | 0.0468492i | ||||
\(250\) | − | 2.54578e6i | − | 2.57615i | ||||||
\(251\) | 852997. | 0.854600 | 0.427300 | − | 0.904110i | \(-0.359465\pi\) | ||||
0.427300 | + | 0.904110i | \(0.359465\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 209512. | 0.205782 | ||||||||
\(254\) | 1.74206e6i | 1.69426i | ||||||||
\(255\) | 99575.6 | − | 716826.i | 0.0958965 | − | 0.690341i | ||||
\(256\) | −1.94512e6 | −1.85501 | ||||||||
\(257\) | 1.73250e6 | 1.63621 | 0.818107 | − | 0.575066i | \(-0.195024\pi\) | ||||
0.818107 | + | 0.575066i | \(0.195024\pi\) | |||||||
\(258\) | 1.50298e6 | + | 208782.i | 1.40574 | + | 0.195274i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 5.22240e6i | − | 4.79111i | ||||||
\(261\) | 341261. | − | 1.20463e6i | 0.310088 | − | 1.09460i | ||||
\(262\) | 3.58907e6i | 3.23020i | ||||||||
\(263\) | − | 1.30449e6i | − | 1.16292i | −0.813573 | − | 0.581462i | \(-0.802481\pi\) | ||
0.813573 | − | 0.581462i | \(-0.197519\pi\) | |||||||
\(264\) | 90877.9 | − | 654213.i | 0.0802506 | − | 0.577709i | ||||
\(265\) | 1.58864e6i | 1.38967i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −181215. | + | 1.30454e6i | −0.155567 | + | 1.11990i | ||||
\(268\) | −2.06818e6 | −1.75894 | ||||||||
\(269\) | 935876. | 0.788565 | 0.394283 | − | 0.918989i | \(-0.370993\pi\) | ||||
0.394283 | + | 0.918989i | \(0.370993\pi\) | |||||||
\(270\) | −3.17704e6 | − | 1.39630e6i | −2.65224 | − | 1.16565i | ||||
\(271\) | 2.23522e6i | 1.84883i | 0.381386 | + | 0.924416i | \(0.375447\pi\) | ||||
−0.381386 | + | 0.924416i | \(0.624553\pi\) | |||||||
\(272\) | −362214. | −0.296854 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.17393e6 | −2.55400 | ||||||||
\(275\) | 895907.i | 0.714383i | ||||||||
\(276\) | −1.29949e6 | − | 180514.i | −1.02683 | − | 0.142639i | ||||
\(277\) | 1.24448e6 | 0.974512 | 0.487256 | − | 0.873259i | \(-0.337998\pi\) | ||||
0.487256 | + | 0.873259i | \(0.337998\pi\) | |||||||
\(278\) | −3.65617e6 | −2.83736 | ||||||||
\(279\) | 83424.0 | − | 294482.i | 0.0641624 | − | 0.226490i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 622353.i | 0.470187i | 0.971973 | + | 0.235094i | \(0.0755397\pi\) | ||||
−0.971973 | + | 0.235094i | \(0.924460\pi\) | |||||||
\(282\) | −1.38007e6 | − | 191708.i | −1.03343 | − | 0.143555i | ||||
\(283\) | − | 1.01477e6i | − | 0.753182i | −0.926380 | − | 0.376591i | \(-0.877096\pi\) | ||
0.926380 | − | 0.376591i | \(-0.122904\pi\) | |||||||
\(284\) | 2.62899e6i | 1.93416i | ||||||||
\(285\) | −3.20103e6 | − | 444661.i | −2.33441 | − | 0.324277i | ||||
\(286\) | 1.31914e6i | 0.953623i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 118366. | − | 417828.i | 0.0840906 | − | 0.296836i | ||||
\(289\) | −1.18114e6 | −0.831869 | ||||||||
\(290\) | 4.72034e6 | 3.29593 | ||||||||
\(291\) | 938288. | + | 130339.i | 0.649537 | + | 0.0902283i | ||||
\(292\) | − | 1.31423e6i | − | 0.902016i | ||||||
\(293\) | 816319. | 0.555509 | 0.277754 | − | 0.960652i | \(-0.410410\pi\) | ||||
0.277754 | + | 0.960652i | \(0.410410\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 224810. | 0.150404 | ||||||||
\(296\) | − | 1.02866e6i | − | 0.682406i | ||||||
\(297\) | 526249. | + | 231285.i | 0.346179 | + | 0.152144i | ||||
\(298\) | 1.67614e6 | 1.09338 | ||||||||
\(299\) | 1.24478e6 | 0.805221 | ||||||||
\(300\) | 771906. | − | 5.55681e6i | 0.495178 | − | 3.56469i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.13747e6i | 0.717665i | ||||||||
\(303\) | −57794.2 | + | 416049.i | −0.0361641 | + | 0.260338i | ||||
\(304\) | 1.61749e6i | 1.00382i | ||||||||
\(305\) | 755279.i | 0.464898i | ||||||||
\(306\) | 312009. | − | 1.10138e6i | 0.190486 | − | 0.672407i | ||||
\(307\) | − | 711458.i | − | 0.430827i | −0.976523 | − | 0.215414i | \(-0.930890\pi\) | ||
0.976523 | − | 0.215414i | \(-0.0691100\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7119.96 | + | 989.047i | 0.00424211 | + | 0.000589279i | ||||
\(310\) | 1.15393e6 | 0.681983 | ||||||||
\(311\) | −2.05317e6 | −1.20372 | −0.601859 | − | 0.798602i | \(-0.705573\pi\) | ||||
−0.601859 | + | 0.798602i | \(0.705573\pi\) | |||||||
\(312\) | 539935. | − | 3.88689e6i | 0.314018 | − | 2.26056i | ||||
\(313\) | 2.12331e6i | 1.22505i | 0.790452 | + | 0.612524i | \(0.209846\pi\) | ||||
−0.790452 | + | 0.612524i | \(0.790154\pi\) | |||||||
\(314\) | 380406. | 0.217732 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 617124. | 0.347660 | ||||||||
\(317\) | − | 1.73845e6i | − | 0.971660i | −0.874053 | − | 0.485830i | \(-0.838517\pi\) | ||
0.874053 | − | 0.485830i | \(-0.161483\pi\) | |||||||
\(318\) | −345739. | + | 2.48891e6i | −0.191726 | + | 1.38020i | ||||
\(319\) | −781884. | −0.430195 | ||||||||
\(320\) | 3.89141e6 | 2.12438 | ||||||||
\(321\) | −2.03742e6 | − | 283021.i | −1.10361 | − | 0.153305i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.06602e6i | − | 0.568540i | ||||||
\(324\) | −3.06475e6 | − | 1.88794e6i | −1.62193 | − | 0.999140i | ||||
\(325\) | 5.32288e6i | 2.79536i | ||||||||
\(326\) | 4.17081e6i | 2.17358i | ||||||||
\(327\) | 467845. | − | 3.36793e6i | 0.241954 | − | 1.74178i | ||||
\(328\) | 4.02354e6i | 2.06502i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −298184. | + | 2.14657e6i | −0.150730 | + | 1.08508i | ||||
\(331\) | 2.88004e6 | 1.44487 | 0.722434 | − | 0.691440i | \(-0.243023\pi\) | ||||
0.722434 | + | 0.691440i | \(0.243023\pi\) | |||||||
\(332\) | 180962. | 0.0901037 | ||||||||
\(333\) | 861351. | + | 244012.i | 0.425667 | + | 0.120587i | ||||
\(334\) | 2.54950e6i | 1.25052i | ||||||||
\(335\) | 3.22376e6 | 1.56946 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.45918e6 | −0.699898 | −0.349949 | − | 0.936769i | \(-0.613801\pi\) | ||||
−0.349949 | + | 0.936769i | \(0.613801\pi\) | |||||||
\(338\) | 4.25762e6i | 2.02710i | ||||||||
\(339\) | −2.75090e6 | − | 382132.i | −1.30010 | − | 0.180599i | ||||
\(340\) | 2.83010e6 | 1.32771 | ||||||||
\(341\) | −191138. | −0.0890145 | ||||||||
\(342\) | −4.91826e6 | − | 1.39329e6i | −2.27377 | − | 0.644136i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.81896e6i | 1.28438i | ||||||||
\(345\) | 2.02557e6 | + | 281375.i | 0.916218 | + | 0.127274i | ||||
\(346\) | − | 5.39565e6i | − | 2.42300i | ||||||
\(347\) | − | 1.25367e6i | − | 0.558932i | −0.960156 | − | 0.279466i | \(-0.909843\pi\) | ||
0.960156 | − | 0.279466i | \(-0.0901574\pi\) | |||||||
\(348\) | 4.84958e6 | + | 673665.i | 2.14663 | + | 0.298192i | ||||
\(349\) | − | 1.47601e6i | − | 0.648673i | −0.945942 | − | 0.324337i | \(-0.894859\pi\) | ||
0.945942 | − | 0.324337i | \(-0.105141\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.12662e6 | + | 1.37414e6i | 1.35459 | + | 0.595337i | ||||
\(352\) | −271197. | −0.116662 | ||||||||
\(353\) | −3.04428e6 | −1.30031 | −0.650157 | − | 0.759800i | \(-0.725297\pi\) | ||||
−0.650157 | + | 0.759800i | \(0.725297\pi\) | |||||||
\(354\) | 352208. | + | 48925.8i | 0.149379 | + | 0.0207506i | ||||
\(355\) | − | 4.09792e6i | − | 1.72581i | ||||||
\(356\) | −5.15043e6 | −2.15387 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.16464e6 | −2.12977 | ||||||||
\(359\) | 4.49259e6i | 1.83976i | 0.392201 | + | 0.919879i | \(0.371714\pi\) | ||||
−0.392201 | + | 0.919879i | \(0.628286\pi\) | |||||||
\(360\) | 1.75722e6 | − | 6.20289e6i | 0.714610 | − | 2.52254i | ||||
\(361\) | −2.28429e6 | −0.922537 | ||||||||
\(362\) | −42267.7 | −0.0169526 | ||||||||
\(363\) | −296035. | + | 2.13110e6i | −0.117917 | + | 0.848862i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.04855e6i | 0.804849i | ||||||||
\(366\) | −164373. | + | 1.18329e6i | −0.0641399 | + | 0.461731i | ||||
\(367\) | − | 3.34198e6i | − | 1.29521i | −0.761977 | − | 0.647604i | \(-0.775771\pi\) | ||
0.761977 | − | 0.647604i | \(-0.224229\pi\) | |||||||
\(368\) | − | 1.02352e6i | − | 0.393984i | ||||||
\(369\) | −3.36912e6 | − | 954439.i | −1.28810 | − | 0.364907i | ||||
\(370\) | 3.37519e6i | 1.28172i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.18552e6 | + | 164683.i | 0.444173 | + | 0.0617008i | ||||
\(373\) | −578295. | −0.215218 | −0.107609 | − | 0.994193i | \(-0.534319\pi\) | ||||
−0.107609 | + | 0.994193i | \(0.534319\pi\) | |||||||
\(374\) | −714863. | −0.264268 | ||||||||
\(375\) | −566325. | + | 4.07687e6i | −0.207964 | + | 1.49709i | ||||
\(376\) | − | 2.58844e6i | − | 0.944210i | ||||||
\(377\) | −4.64543e6 | −1.68334 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.69943e6 | 0.965327 | 0.482663 | − | 0.875806i | \(-0.339669\pi\) | ||||
0.482663 | + | 0.875806i | \(0.339669\pi\) | |||||||
\(380\) | − | 1.26380e7i | − | 4.48971i | ||||||
\(381\) | 387534. | − | 2.78978e6i | 0.136772 | − | 0.984595i | ||||
\(382\) | −3.87572e6 | −1.35892 | ||||||||
\(383\) | −708579. | −0.246826 | −0.123413 | − | 0.992355i | \(-0.539384\pi\) | ||||
−0.123413 | + | 0.992355i | \(0.539384\pi\) | |||||||
\(384\) | 5.21366e6 | + | 724238.i | 1.80432 | + | 0.250642i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.73459e6i | 0.592554i | ||||||||
\(387\) | −2.36047e6 | − | 668696.i | −0.801162 | − | 0.226961i | ||||
\(388\) | 3.70445e6i | 1.24924i | ||||||||
\(389\) | 5.64956e6i | 1.89296i | 0.322766 | + | 0.946479i | \(0.395387\pi\) | ||||
−0.322766 | + | 0.946479i | \(0.604613\pi\) | |||||||
\(390\) | −1.77161e6 | + | 1.27535e7i | −0.589802 | + | 4.24588i | ||||
\(391\) | 674566.i | 0.223143i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 798413. | − | 5.74763e6i | 0.260763 | − | 1.87719i | ||||
\(394\) | 4.98249e6 | 1.61698 | ||||||||
\(395\) | −961939. | −0.310209 | ||||||||
\(396\) | −612697. | + | 2.16279e6i | −0.196340 | + | 0.693069i | ||||
\(397\) | − | 957286.i | − | 0.304835i | −0.988316 | − | 0.152418i | \(-0.951294\pi\) | ||
0.988316 | − | 0.152418i | \(-0.0487059\pi\) | |||||||
\(398\) | 3.79105e6 | 1.19964 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.37675e6 | 1.36773 | ||||||||
\(401\) | 4.82361e6i | 1.49800i | 0.662572 | + | 0.748998i | \(0.269465\pi\) | ||||
−0.662572 | + | 0.748998i | \(0.730535\pi\) | |||||||
\(402\) | 5.05065e6 | + | 701594.i | 1.55877 | + | 0.216531i | ||||
\(403\) | −1.13561e6 | −0.348311 | ||||||||
\(404\) | −1.64260e6 | −0.500702 | ||||||||
\(405\) | 4.77717e6 | + | 2.94282e6i | 1.44721 | + | 0.891510i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 559072.i | − | 0.167294i | ||||||
\(408\) | 2.10637e6 | + | 292599.i | 0.626446 | + | 0.0870207i | ||||
\(409\) | 5.31324e6i | 1.57055i | 0.619148 | + | 0.785274i | \(0.287478\pi\) | ||||
−0.619148 | + | 0.785274i | \(0.712522\pi\) | |||||||
\(410\) | − | 1.32019e7i | − | 3.87860i | ||||||
\(411\) | 5.08281e6 | + | 706063.i | 1.48422 | + | 0.206176i | ||||
\(412\) | 28110.3i | 0.00815872i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.11221e6 | + | 881658.i | 0.892417 | + | 0.252813i | ||||
\(415\) | −282074. | −0.0803975 | ||||||||
\(416\) | −1.61127e6 | −0.456494 | ||||||||
\(417\) | 5.85508e6 | + | 813340.i | 1.64889 | + | 0.229051i | ||||
\(418\) | 3.19226e6i | 0.893631i | ||||||||
\(419\) | 5.20890e6 | 1.44948 | 0.724738 | − | 0.689025i | \(-0.241961\pi\) | ||||
0.724738 | + | 0.689025i | \(0.241961\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.34116e6 | 1.46869 | 0.734345 | − | 0.678776i | \(-0.237489\pi\) | ||||
0.734345 | + | 0.678776i | \(0.237489\pi\) | |||||||
\(422\) | − | 2.78333e6i | − | 0.760822i | ||||||
\(423\) | 2.16744e6 | + | 614013.i | 0.588973 | + | 0.166850i | ||||
\(424\) | −4.66816e6 | −1.26105 | ||||||||
\(425\) | −2.88455e6 | −0.774650 | ||||||||
\(426\) | 891840. | − | 6.42019e6i | 0.238102 | − | 1.71405i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 8.04391e6i | − | 2.12255i | ||||||
\(429\) | 293452. | − | 2.11251e6i | 0.0769828 | − | 0.554185i | ||||
\(430\) | − | 9.24945e6i | − | 2.41237i | ||||||
\(431\) | − | 3.83470e6i | − | 0.994349i | −0.867651 | − | 0.497174i | \(-0.834371\pi\) | ||
0.867651 | − | 0.497174i | \(-0.165629\pi\) | |||||||
\(432\) | 1.12989e6 | − | 2.57087e6i | 0.291290 | − | 0.662781i | ||||
\(433\) | − | 3.78196e6i | − | 0.969388i | −0.874684 | − | 0.484694i | \(-0.838931\pi\) | ||
0.874684 | − | 0.484694i | \(-0.161069\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.55926e6 | − | 1.05007e6i | −1.91539 | − | 0.266070i | ||||
\(436\) | 1.32969e7 | 3.34991 | ||||||||
\(437\) | 3.01231e6 | 0.754564 | ||||||||
\(438\) | −445830. | + | 3.20945e6i | −0.111041 | + | 0.799365i | ||||
\(439\) | 2.56622e6i | 0.635524i | 0.948170 | + | 0.317762i | \(0.102931\pi\) | ||||
−0.948170 | + | 0.317762i | \(0.897069\pi\) | |||||||
\(440\) | −4.02607e6 | −0.991402 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.24724e6 | −1.03407 | ||||||||
\(443\) | − | 526826.i | − | 0.127543i | −0.997965 | − | 0.0637717i | \(-0.979687\pi\) | ||
0.997965 | − | 0.0637717i | \(-0.0203130\pi\) | |||||||
\(444\) | −481692. | + | 3.46761e6i | −0.115961 | + | 0.834781i | ||||
\(445\) | 8.02821e6 | 1.92185 | ||||||||
\(446\) | −4.29589e6 | −1.02262 | ||||||||
\(447\) | −2.68421e6 | − | 372869.i | −0.635401 | − | 0.0882647i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 44350.8i | 0.0103821i | 0.999987 | + | 0.00519106i | \(0.00165237\pi\) | ||||
−0.999987 | + | 0.00519106i | \(0.998348\pi\) | |||||||
\(450\) | −3.77011e6 | + | 1.33083e7i | −0.877652 | + | 3.09807i | ||||
\(451\) | 2.18678e6i | 0.506247i | ||||||||
\(452\) | − | 1.08608e7i | − | 2.50044i | ||||||
\(453\) | 253037. | − | 1.82157e6i | 0.0579348 | − | 0.417061i | ||||
\(454\) | − | 1.04606e7i | − | 2.38187i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.30662e6 | − | 9.40610e6i | 0.294264 | − | 2.11835i | ||||
\(457\) | 4.26707e6 | 0.955739 | 0.477870 | − | 0.878431i | \(-0.341409\pi\) | ||||
0.477870 | + | 0.878431i | \(0.341409\pi\) | |||||||
\(458\) | −6.53152e6 | −1.45496 | ||||||||
\(459\) | −744667. | + | 1.69436e6i | −0.164980 | + | 0.375383i | ||||
\(460\) | 7.99713e6i | 1.76214i | ||||||||
\(461\) | 6.35979e6 | 1.39377 | 0.696884 | − | 0.717183i | \(-0.254569\pi\) | ||||
0.696884 | + | 0.717183i | \(0.254569\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.65409e6 | 1.44257 | 0.721284 | − | 0.692640i | \(-0.243552\pi\) | ||||
0.721284 | + | 0.692640i | \(0.243552\pi\) | |||||||
\(464\) | 3.81971e6i | 0.823636i | ||||||||
\(465\) | −1.84792e6 | − | 256698.i | −0.396325 | − | 0.0550542i | ||||
\(466\) | −1.37070e6 | −0.292400 | ||||||||
\(467\) | −3.02259e6 | −0.641338 | −0.320669 | − | 0.947191i | \(-0.603908\pi\) | ||||
−0.320669 | + | 0.947191i | \(0.603908\pi\) | |||||||
\(468\) | −3.64024e6 | + | 1.28498e7i | −0.768272 | + | 2.71196i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.49307e6i | 1.77345i | ||||||||
\(471\) | −609191. | − | 84623.8i | −0.126532 | − | 0.0175768i | ||||
\(472\) | 660594.i | 0.136483i | ||||||||
\(473\) | 1.53209e6i | 0.314871i | ||||||||
\(474\) | −1.50706e6 | − | 209349.i | −0.308096 | − | 0.0427981i | ||||
\(475\) | 1.28811e7i | 2.61951i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.10735e6 | − | 3.90889e6i | 0.222838 | − | 0.786607i | ||||
\(478\) | −1.06880e7 | −2.13958 | ||||||||
\(479\) | 6.51777e6 | 1.29796 | 0.648978 | − | 0.760807i | \(-0.275197\pi\) | ||||
0.648978 | + | 0.760807i | \(0.275197\pi\) | |||||||
\(480\) | −2.62194e6 | − | 364218.i | −0.519420 | − | 0.0721536i | ||||
\(481\) | − | 3.32163e6i | − | 0.654619i | ||||||
\(482\) | −5.09830e6 | −0.999558 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.41377e6 | −1.63259 | ||||||||
\(485\) | − | 5.77429e6i | − | 1.11466i | ||||||
\(486\) | 6.84391e6 | + | 5.65016e6i | 1.31436 | + | 1.08510i | ||||
\(487\) | −6.70316e6 | −1.28073 | −0.640364 | − | 0.768072i | \(-0.721216\pi\) | ||||
−0.640364 | + | 0.768072i | \(0.721216\pi\) | |||||||
\(488\) | −2.21936e6 | −0.421869 | ||||||||
\(489\) | 927825. | − | 6.67924e6i | 0.175466 | − | 1.26315i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 915570.i | − | 0.171391i | −0.996321 | − | 0.0856954i | \(-0.972689\pi\) | ||
0.996321 | − | 0.0856954i | \(-0.0273112\pi\) | |||||||
\(492\) | 1.88411e6 | − | 1.35633e7i | 0.350908 | − | 2.52612i | ||||
\(493\) | − | 2.51743e6i | − | 0.466487i | ||||||
\(494\) | 1.89663e7i | 3.49675i | ||||||||
\(495\) | 955039. | − | 3.37124e6i | 0.175189 | − | 0.618410i | ||||
\(496\) | 933759.i | 0.170424i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −441923. | − | 61388.4i | −0.0798498 | − | 0.0110921i | ||||
\(499\) | −9.00297e6 | −1.61858 | −0.809291 | − | 0.587408i | \(-0.800148\pi\) | ||||
−0.809291 | + | 0.587408i | \(0.800148\pi\) | |||||||
\(500\) | −1.60959e7 | −2.87931 | ||||||||
\(501\) | 567154. | − | 4.08283e6i | 0.100950 | − | 0.726720i | ||||
\(502\) | − | 8.22420e6i | − | 1.45658i | ||||||
\(503\) | −3.22643e6 | −0.568595 | −0.284297 | − | 0.958736i | \(-0.591760\pi\) | ||||
−0.284297 | + | 0.958736i | \(0.591760\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.56040e6 | 0.446765 | ||||||||
\(506\) | − | 2.02002e6i | − | 0.350735i | ||||||
\(507\) | 947136. | − | 6.81825e6i | 0.163641 | − | 1.17802i | ||||
\(508\) | 1.10143e7 | 1.89364 | ||||||||
\(509\) | 3.20046e6 | 0.547542 | 0.273771 | − | 0.961795i | \(-0.411729\pi\) | ||||
0.273771 | + | 0.961795i | \(0.411729\pi\) | |||||||
\(510\) | −6.91131e6 | − | 960063.i | −1.17662 | − | 0.163446i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7.94862e6i | 1.34004i | ||||||||
\(513\) | 7.56627e6 | + | 3.32535e6i | 1.26937 | + | 0.557885i | ||||
\(514\) | − | 1.67040e7i | − | 2.78876i | ||||||
\(515\) | − | 43816.7i | − | 0.00727984i | ||||||
\(516\) | 1.32004e6 | − | 9.50271e6i | 0.218254 | − | 1.57117i | ||||
\(517\) | − | 1.40680e6i | − | 0.231477i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.20030e6 | + | 8.64072e6i | −0.195601 | + | 1.40809i | ||||
\(520\) | −2.39202e7 | −3.87933 | ||||||||
\(521\) | −3.36968e6 | −0.543869 | −0.271935 | − | 0.962316i | \(-0.587663\pi\) | ||||
−0.271935 | + | 0.962316i | \(0.587663\pi\) | |||||||
\(522\) | −1.16145e7 | − | 3.29028e6i | −1.86563 | − | 0.528514i | ||||
\(523\) | − | 5.59447e6i | − | 0.894344i | −0.894448 | − | 0.447172i | \(-0.852431\pi\) | ||
0.894448 | − | 0.447172i | \(-0.147569\pi\) | |||||||
\(524\) | 2.26922e7 | 3.61034 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.25773e7 | −1.98209 | ||||||||
\(527\) | − | 615406.i | − | 0.0965240i | ||||||
\(528\) | −1.73701e6 | − | 241291.i | −0.271155 | − | 0.0376667i | ||||
\(529\) | 4.53019e6 | 0.703846 | ||||||||
\(530\) | 1.53169e7 | 2.36855 | ||||||||
\(531\) | −553150. | − | 156702.i | −0.0851347 | − | 0.0241178i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.29923e7i | 1.98093i | ||||||||
\(534\) | 1.25777e7 | + | 1.74720e6i | 1.90875 | + | 0.265148i | ||||
\(535\) | 1.25384e7i | 1.89390i | ||||||||
\(536\) | 9.47290e6i | 1.42420i | ||||||||
\(537\) | 8.27078e6 | + | 1.14891e6i | 1.23769 | + | 0.171929i | ||||
\(538\) | − | 9.02329e6i | − | 1.34403i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8.82820e6 | + | 2.00870e7i | −1.30283 | + | 2.96436i | ||||
\(541\) | −7.06104e6 | −1.03723 | −0.518616 | − | 0.855007i | \(-0.673553\pi\) | ||||
−0.518616 | + | 0.855007i | \(0.673553\pi\) | |||||||
\(542\) | 2.15510e7 | 3.15115 | ||||||||
\(543\) | 67688.5 | + | 9402.73i | 0.00985179 | + | 0.00136853i | ||||
\(544\) | − | 873172.i | − | 0.126503i | ||||||
\(545\) | −2.07264e7 | −2.98905 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.45678e6 | 0.779773 | 0.389887 | − | 0.920863i | \(-0.372514\pi\) | ||||
0.389887 | + | 0.920863i | \(0.372514\pi\) | |||||||
\(548\) | 2.00674e7i | 2.85457i | ||||||||
\(549\) | 526462. | − | 1.85838e6i | 0.0745480 | − | 0.263151i | ||||
\(550\) | 8.63793e6 | 1.21759 | ||||||||
\(551\) | −1.12417e7 | −1.57744 | ||||||||
\(552\) | −826810. | + | 5.95205e6i | −0.115494 | + | 0.831417i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 1.19987e7i | − | 1.66096i | ||||||
\(555\) | 750834. | − | 5.40511e6i | 0.103469 | − | 0.744856i | ||||
\(556\) | 2.31164e7i | 3.17127i | ||||||||
\(557\) | − | 1.11070e7i | − | 1.51691i | −0.651725 | − | 0.758456i | \(-0.725954\pi\) | ||
0.651725 | − | 0.758456i | \(-0.274046\pi\) | |||||||
\(558\) | −2.83926e6 | − | 804336.i | −0.386029 | − | 0.109358i | ||||
\(559\) | 9.10266e6i | 1.23208i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.14480e6 | + | 159026.i | 0.153576 | + | 0.0213335i | ||||
\(562\) | 6.00044e6 | 0.801387 | ||||||||
\(563\) | −7.35807e6 | −0.978347 | −0.489174 | − | 0.872186i | \(-0.662702\pi\) | ||||
−0.489174 | + | 0.872186i | \(0.662702\pi\) | |||||||
\(564\) | −1.21209e6 | + | 8.72561e6i | −0.160449 | + | 1.15504i | ||||
\(565\) | 1.69292e7i | 2.23108i | ||||||||
\(566\) | −9.78391e6 | −1.28372 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.20416e7 | 1.56608 | ||||||||
\(569\) | 1.05911e6i | 0.137139i | 0.997646 | + | 0.0685697i | \(0.0218435\pi\) | ||||
−0.997646 | + | 0.0685697i | \(0.978156\pi\) | |||||||
\(570\) | −4.28721e6 | + | 3.08628e7i | −0.552698 | + | 3.97877i | ||||
\(571\) | −3.23975e6 | −0.415836 | −0.207918 | − | 0.978146i | \(-0.566669\pi\) | ||||
−0.207918 | + | 0.978146i | \(0.566669\pi\) | |||||||
\(572\) | 8.34037e6 | 1.06585 | ||||||||
\(573\) | 6.20667e6 | + | 862179.i | 0.789718 | + | 0.109701i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8.15100e6i | − | 1.02811i | ||||||
\(576\) | −9.57492e6 | − | 2.71248e6i | −1.20248 | − | 0.340652i | ||||
\(577\) | − | 1.84253e6i | − | 0.230396i | −0.993343 | − | 0.115198i | \(-0.963250\pi\) | ||
0.993343 | − | 0.115198i | \(-0.0367502\pi\) | |||||||
\(578\) | 1.13880e7i | 1.41784i | ||||||||
\(579\) | 385871. | − | 2.77781e6i | 0.0478350 | − | 0.344355i | ||||
\(580\) | − | 2.98447e7i | − | 3.68381i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.25667e6 | − | 9.04655e6i | 0.153785 | − | 1.10707i | ||||
\(583\) | −2.53712e6 | −0.309150 | ||||||||
\(584\) | −6.01958e6 | −0.730355 | ||||||||
\(585\) | 5.67420e6 | − | 2.00296e7i | 0.685511 | − | 2.41982i | ||||
\(586\) | − | 7.87058e6i | − | 0.946809i | ||||||
\(587\) | −2.89532e6 | −0.346818 | −0.173409 | − | 0.984850i | \(-0.555478\pi\) | ||||
−0.173409 | + | 0.984850i | \(0.555478\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.74813e6 | −0.326399 | ||||||||
\(590\) | − | 2.16751e6i | − | 0.256349i | ||||||
\(591\) | −7.97907e6 | − | 1.10839e6i | −0.939688 | − | 0.130534i | ||||
\(592\) | −2.73121e6 | −0.320296 | ||||||||
\(593\) | 1.31439e7 | 1.53493 | 0.767465 | − | 0.641090i | \(-0.221518\pi\) | ||||
0.767465 | + | 0.641090i | \(0.221518\pi\) | |||||||
\(594\) | 2.22994e6 | − | 5.07385e6i | 0.259315 | − | 0.590027i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 1.05975e7i | − | 1.22205i | ||||||
\(597\) | −6.07108e6 | − | 843345.i | −0.697156 | − | 0.0968433i | ||||
\(598\) | − | 1.20016e7i | − | 1.37242i | ||||||
\(599\) | 6.86660e6i | 0.781942i | 0.920403 | + | 0.390971i | \(0.127861\pi\) | ||||
−0.920403 | + | 0.390971i | \(0.872139\pi\) | |||||||
\(600\) | −2.54519e7 | − | 3.53557e6i | −2.88631 | − | 0.400942i | ||||
\(601\) | − | 7.09487e6i | − | 0.801232i | −0.916246 | − | 0.400616i | \(-0.868796\pi\) | ||
0.916246 | − | 0.400616i | \(-0.131204\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.93215e6 | − | 2.24710e6i | −0.888378 | − | 0.251669i | ||||
\(604\) | 7.19172e6 | 0.802122 | ||||||||
\(605\) | 1.31149e7 | 1.45672 | ||||||||
\(606\) | 4.01136e6 | + | 557225.i | 0.443721 | + | 0.0616381i | ||||
\(607\) | 6.58484e6i | 0.725393i | 0.931907 | + | 0.362696i | \(0.118144\pi\) | ||||
−0.931907 | + | 0.362696i | \(0.881856\pi\) | |||||||
\(608\) | −3.89920e6 | −0.427776 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.28205e6 | 0.792372 | ||||||||
\(611\) | − | 8.35828e6i | − | 0.905762i | ||||||
\(612\) | −6.96353e6 | − | 1.97270e6i | −0.751538 | − | 0.212903i | ||||
\(613\) | 8.95805e6 | 0.962859 | 0.481429 | − | 0.876485i | \(-0.340118\pi\) | ||||
0.481429 | + | 0.876485i | \(0.340118\pi\) | |||||||
\(614\) | −6.85955e6 | −0.734302 | ||||||||
\(615\) | −2.93684e6 | + | 2.11418e7i | −0.313107 | + | 2.25400i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.76138e7i | − | 1.86269i | −0.364140 | − | 0.931344i | \(-0.618637\pi\) | ||
0.364140 | − | 0.931344i | \(-0.381363\pi\) | |||||||
\(618\) | 9535.94 | − | 68647.4i | 0.00100437 | − | 0.00723024i | ||||
\(619\) | − | 7.47775e6i | − | 0.784412i | −0.919877 | − | 0.392206i | \(-0.871712\pi\) | ||
0.919877 | − | 0.392206i | \(-0.128288\pi\) | |||||||
\(620\) | − | 7.29577e6i | − | 0.762241i | ||||||
\(621\) | −4.78783e6 | − | 2.10424e6i | −0.498207 | − | 0.218961i | ||||
\(622\) | 1.97958e7i | 2.05162i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.03202e7 | − | 1.43359e6i | −1.06102 | − | 0.147389i | ||||
\(625\) | 6.63993e6 | 0.679929 | ||||||||
\(626\) | 2.04720e7 | 2.08797 | ||||||||
\(627\) | 710140. | − | 5.11217e6i | 0.0721399 | − | 0.519321i | ||||
\(628\) | − | 2.40514e6i | − | 0.243356i | ||||||
\(629\) | 1.80004e6 | 0.181408 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.60645e7 | −1.60618 | −0.803090 | − | 0.595857i | \(-0.796812\pi\) | ||||
−0.803090 | + | 0.595857i | \(0.796812\pi\) | |||||||
\(632\) | − | 2.82662e6i | − | 0.281498i | ||||||
\(633\) | −619170. | + | 4.45729e6i | −0.0614187 | + | 0.442142i | ||||
\(634\) | −1.67613e7 | −1.65610 | ||||||||
\(635\) | −1.71685e7 | −1.68966 | ||||||||
\(636\) | 1.57363e7 | + | 2.18596e6i | 1.54263 | + | 0.214289i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.53856e6i | 0.733224i | ||||||||
\(639\) | −2.85643e6 | + | 1.00830e7i | −0.276739 | + | 0.976876i | ||||
\(640\) | − | 3.20852e7i | − | 3.09638i | ||||||
\(641\) | − | 7.99813e6i | − | 0.768853i | −0.923156 | − | 0.384426i | \(-0.874399\pi\) | ||
0.923156 | − | 0.384426i | \(-0.125601\pi\) | |||||||
\(642\) | −2.72876e6 | + | 1.96438e7i | −0.261293 | + | 1.88100i | ||||
\(643\) | − | 6.81245e6i | − | 0.649794i | −0.945749 | − | 0.324897i | \(-0.894670\pi\) | ||
0.945749 | − | 0.324897i | \(-0.105330\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.05760e6 | + | 1.48123e7i | −0.194743 | + | 1.40192i | ||||
\(646\) | −1.02781e7 | −0.969019 | ||||||||
\(647\) | 1.89337e7 | 1.77817 | 0.889087 | − | 0.457739i | \(-0.151340\pi\) | ||||
0.889087 | + | 0.457739i | \(0.151340\pi\) | |||||||
\(648\) | −8.64736e6 | + | 1.40375e7i | −0.808996 | + | 1.31327i | ||||
\(649\) | 359030.i | 0.0334594i | ||||||||
\(650\) | 5.13208e7 | 4.76442 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.63703e7 | 2.42938 | ||||||||
\(653\) | − | 3.73214e6i | − | 0.342511i | −0.985227 | − | 0.171256i | \(-0.945218\pi\) | ||
0.985227 | − | 0.171256i | \(-0.0547824\pi\) | |||||||
\(654\) | −3.24720e7 | − | 4.51074e6i | −2.96869 | − | 0.412386i | ||||
\(655\) | −3.53713e7 | −3.22142 | ||||||||
\(656\) | 1.06830e7 | 0.969243 | ||||||||
\(657\) | 1.42793e6 | − | 5.04051e6i | 0.129060 | − | 0.455576i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 3.02429e6i | − | 0.271276i | −0.990758 | − | 0.135638i | \(-0.956692\pi\) | ||
0.990758 | − | 0.135638i | \(-0.0433083\pi\) | |||||||
\(660\) | 1.35719e7 | + | 1.88529e6i | 1.21277 | + | 0.168468i | ||||
\(661\) | 1.49262e7i | 1.32876i | 0.747396 | + | 0.664378i | \(0.231304\pi\) | ||||
−0.747396 | + | 0.664378i | \(0.768696\pi\) | |||||||
\(662\) | − | 2.77680e7i | − | 2.46263i | ||||||
\(663\) | 6.80163e6 | + | 944827.i | 0.600937 | + | 0.0834773i | ||||
\(664\) | − | 828863.i | − | 0.0729563i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.35265e6 | − | 8.30475e6i | 0.205529 | − | 0.725506i | ||||
\(667\) | 7.11361e6 | 0.619121 | ||||||||
\(668\) | 1.61194e7 | 1.39768 | ||||||||
\(669\) | 6.87954e6 | + | 955650.i | 0.594284 | + | 0.0825531i | ||||
\(670\) | − | 3.10820e7i | − | 2.67499i | ||||||
\(671\) | −1.20621e6 | −0.103423 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.60991e7 | 1.37014 | 0.685069 | − | 0.728478i | \(-0.259772\pi\) | ||||
0.685069 | + | 0.728478i | \(0.259772\pi\) | |||||||
\(674\) | 1.40688e7i | 1.19291i | ||||||||
\(675\) | 8.99806e6 | − | 2.04735e7i | 0.760133 | − | 1.72955i | ||||
\(676\) | 2.69191e7 | 2.26565 | ||||||||
\(677\) | 1.22188e7 | 1.02460 | 0.512302 | − | 0.858805i | \(-0.328793\pi\) | ||||
0.512302 | + | 0.858805i | \(0.328793\pi\) | |||||||
\(678\) | −3.68434e6 | + | 2.65229e7i | −0.307812 | + | 2.21588i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 1.29627e7i | − | 1.07504i | ||||||
\(681\) | −2.32704e6 | + | 1.67519e7i | −0.192281 | + | 1.38419i | ||||
\(682\) | 1.84286e6i | 0.151716i | ||||||||
\(683\) | 1.63451e7i | 1.34071i | 0.742040 | + | 0.670356i | \(0.233858\pi\) | ||||
−0.742040 | + | 0.670356i | \(0.766142\pi\) | |||||||
\(684\) | −8.80920e6 | + | 3.10960e7i | −0.719940 | + | 2.54135i | ||||
\(685\) | − | 3.12800e7i | − | 2.54707i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.04597e7 | + | 1.45298e6i | 0.845529 | + | 0.117454i | ||||
\(688\) | 7.48468e6 | 0.602840 | ||||||||
\(689\) | −1.50739e7 | −1.20970 | ||||||||
\(690\) | 2.71289e6 | − | 1.95296e7i | 0.216925 | − | 1.56160i | ||||
\(691\) | − | 7.73168e6i | − | 0.615997i | −0.951387 | − | 0.307999i | \(-0.900341\pi\) | ||
0.951387 | − | 0.307999i | \(-0.0996592\pi\) | |||||||
\(692\) | −3.41144e7 | −2.70815 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.20873e7 | −0.952643 | ||||||||
\(695\) | − | 3.60326e7i | − | 2.82965i | ||||||
\(696\) | 3.08559e6 | − | 2.22126e7i | 0.241444 | − | 1.73811i | ||||
\(697\) | −7.04075e6 | −0.548956 | ||||||||
\(698\) | −1.42310e7 | −1.10560 | ||||||||
\(699\) | 2.19507e6 | + | 304921.i | 0.169924 | + | 0.0236045i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.04372e6i | 0.464525i | 0.972653 | + | 0.232263i | \(0.0746129\pi\) | ||||
−0.972653 | + | 0.232263i | \(0.925387\pi\) | |||||||
\(702\) | 1.32488e7 | − | 3.01454e7i | 1.01469 | − | 2.30876i | ||||
\(703\) | − | 8.03819e6i | − | 0.613437i | ||||||
\(704\) | 6.21473e6i | 0.472597i | ||||||||
\(705\) | 1.88934e6 | − | 1.36010e7i | 0.143165 | − | 1.03062i | ||||
\(706\) | 2.93516e7i | 2.21625i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 309337. | − | 2.22686e6i | 0.0231926 | − | 0.166959i | ||||
\(709\) | 1.65966e7 | 1.23995 | 0.619976 | − | 0.784621i | \(-0.287142\pi\) | ||||
0.619976 | + | 0.784621i | \(0.287142\pi\) | |||||||
\(710\) | −3.95103e7 | −2.94147 | ||||||||
\(711\) | 2.36688e6 | + | 670513.i | 0.175591 | + | 0.0497431i | ||||
\(712\) | 2.35906e7i | 1.74397i | ||||||||
\(713\) | 1.73898e6 | 0.128106 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.30005e7 | −0.951032 | ||||||||
\(716\) | 3.26538e7i | 2.38041i | ||||||||
\(717\) | 1.71161e7 | + | 2.37762e6i | 1.24339 | + | 0.172721i | ||||
\(718\) | 4.33155e7 | 3.13568 | ||||||||
\(719\) | 9.21557e6 | 0.664814 | 0.332407 | − | 0.943136i | \(-0.392139\pi\) | ||||
0.332407 | + | 0.943136i | \(0.392139\pi\) | |||||||
\(720\) | −1.64694e7 | − | 4.66562e6i | −1.18399 | − | 0.335411i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.20241e7i | 1.57237i | ||||||||
\(723\) | 8.16455e6 | + | 1.13415e6i | 0.580880 | + | 0.0806911i | ||||
\(724\) | 267240.i | 0.0189477i | ||||||||
\(725\) | 3.04189e7i | 2.14931i | ||||||||
\(726\) | 2.05471e7 | + | 2.85423e6i | 1.44680 | + | 0.200978i | ||||
\(727\) | − | 1.28807e6i | − | 0.0903867i | −0.998978 | − | 0.0451934i | \(-0.985610\pi\) | ||
0.998978 | − | 0.0451934i | \(-0.0143904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.70308e6 | − | 1.05708e7i | −0.676224 | − | 0.736696i | ||||
\(730\) | 1.97512e7 | 1.37178 | ||||||||
\(731\) | −4.93287e6 | −0.341434 | ||||||||
\(732\) | 7.48144e6 | + | 1.03926e6i | 0.516069 | + | 0.0716880i | ||||
\(733\) | 9.37579e6i | 0.644537i | 0.946648 | + | 0.322269i | \(0.104445\pi\) | ||||
−0.946648 | + | 0.322269i | \(0.895555\pi\) | |||||||
\(734\) | −3.22219e7 | −2.20755 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.46736e6 | 0.167895 | ||||||||
\(737\) | 5.14847e6i | 0.349148i | ||||||||
\(738\) | −9.20227e6 | + | 3.24835e7i | −0.621948 | + | 2.19544i | ||||
\(739\) | 3.50492e6 | 0.236084 | 0.118042 | − | 0.993009i | \(-0.462338\pi\) | ||||
0.118042 | + | 0.993009i | \(0.462338\pi\) | |||||||
\(740\) | 2.13399e7 | 1.43256 | ||||||||
\(741\) | 4.21918e6 | − | 3.03731e7i | 0.282281 | − | 2.03209i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.35976e6i | − | 0.223273i | −0.993749 | − | 0.111636i | \(-0.964391\pi\) | ||
0.993749 | − | 0.111636i | \(-0.0356092\pi\) | |||||||
\(744\) | 754298. | − | 5.43005e6i | 0.0499587 | − | 0.359643i | ||||
\(745\) | 1.65188e7i | 1.09041i | ||||||||
\(746\) | 5.57566e6i | 0.366817i | ||||||||
\(747\) | 694051. | + | 196618.i | 0.0455082 | + | 0.0128920i | ||||
\(748\) | 4.51978e6i | 0.295368i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.93073e7 | + | 5.46025e6i | 2.55164 | + | 0.354453i | ||||
\(751\) | −1.52035e7 | −0.983658 | −0.491829 | − | 0.870692i | \(-0.663671\pi\) | ||||
−0.491829 | + | 0.870692i | \(0.663671\pi\) | |||||||
\(752\) | −6.87261e6 | −0.443177 | ||||||||
\(753\) | −1.82953e6 | + | 1.31704e7i | −0.117585 | + | 0.846472i | ||||
\(754\) | 4.47891e7i | 2.86909i | ||||||||
\(755\) | −1.12101e7 | −0.715716 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.72166e6 | −0.489746 | −0.244873 | − | 0.969555i | \(-0.578746\pi\) | ||||
−0.244873 | + | 0.969555i | \(0.578746\pi\) | |||||||
\(758\) | − | 2.60267e7i | − | 1.64530i | ||||||
\(759\) | −449367. | + | 3.23491e6i | −0.0283137 | + | 0.203825i | ||||
\(760\) | −5.78858e7 | −3.63528 | ||||||||
\(761\) | −2.63085e7 | −1.64678 | −0.823388 | − | 0.567479i | \(-0.807919\pi\) | ||||
−0.823388 | + | 0.567479i | \(0.807919\pi\) | |||||||
\(762\) | −2.68978e7 | − | 3.73642e6i | −1.67814 | − | 0.233114i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.45045e7i | 1.51884i | ||||||||
\(765\) | 1.08544e7 | + | 3.07493e6i | 0.670580 | + | 0.189969i | ||||
\(766\) | 6.83180e6i | 0.420691i | ||||||||
\(767\) | 2.13311e6i | 0.130926i | ||||||||
\(768\) | 4.17195e6 | − | 3.00331e7i | 0.255233 | − | 1.83737i | ||||
\(769\) | 8.35031e6i | 0.509198i | 0.967047 | + | 0.254599i | \(0.0819435\pi\) | ||||
−0.967047 | + | 0.254599i | \(0.918056\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.71591e6 | + | 2.67501e7i | −0.225128 | + | 1.62065i | ||||
\(772\) | 1.09671e7 | 0.662288 | ||||||||
\(773\) | −4.65556e6 | −0.280236 | −0.140118 | − | 0.990135i | \(-0.544748\pi\) | ||||
−0.140118 | + | 0.990135i | \(0.544748\pi\) | |||||||
\(774\) | −6.44727e6 | + | 2.27585e7i | −0.386833 | + | 1.36550i | ||||
\(775\) | 7.43615e6i | 0.444727i | ||||||||
\(776\) | 1.69675e7 | 1.01150 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.44705e7 | 3.22636 | ||||||||
\(779\) | 3.14409e7i | 1.85631i | ||||||||
\(780\) | 8.06348e7 | + | 1.12011e7i | 4.74555 | + | 0.659212i | ||||
\(781\) | 6.54454e6 | 0.383929 | ||||||||
\(782\) | 6.50386e6 | 0.380324 | ||||||||
\(783\) | 1.78678e7 | + | 7.85286e6i | 1.04152 | + | 0.457745i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.74900e6i | 0.217141i | ||||||||
\(786\) | −5.54160e7 | − | 7.69793e6i | −3.19947 | − | 0.444445i | ||||
\(787\) | − | 2.50495e7i | − | 1.44166i | −0.693114 | − | 0.720828i | \(-0.743762\pi\) | ||
0.693114 | − | 0.720828i | \(-0.256238\pi\) | |||||||
\(788\) | − | 3.15021e7i | − | 1.80727i | ||||||
\(789\) | 2.01416e7 | + | 2.79791e6i | 1.15186 | + | 0.160008i | ||||
\(790\) | 9.27457e6i | 0.528721i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.90626e6 | + | 2.80634e6i | 0.561173 | + | 0.158975i | ||||
\(793\) | −7.16649e6 | −0.404691 | ||||||||
\(794\) | −9.22971e6 | −0.519561 | ||||||||
\(795\) | −2.45289e7 | − | 3.40736e6i | −1.37645 | − | 0.191205i | ||||
\(796\) | − | 2.39692e7i | − | 1.34082i | ||||||
\(797\) | 2.26401e7 | 1.26250 | 0.631252 | − | 0.775578i | \(-0.282541\pi\) | ||||
0.631252 | + | 0.775578i | \(0.282541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.52948e6 | 0.251005 | ||||||||
\(800\) | 1.05508e7i | 0.582856i | ||||||||
\(801\) | −1.97536e7 | − | 5.59601e6i | −1.08784 | − | 0.308175i | ||||
\(802\) | 4.65070e7 | 2.55319 | ||||||||
\(803\) | −3.27161e6 | −0.179049 | ||||||||
\(804\) | 4.43588e6 | − | 3.19331e7i | 0.242014 | − | 1.74221i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.09491e7i | 0.593662i | ||||||||
\(807\) | −2.00729e6 | + | 1.44501e7i | −0.108499 | + | 0.781066i | ||||
\(808\) | 7.52363e6i | 0.405414i | ||||||||
\(809\) | − | 2.46698e6i | − | 0.132524i | −0.997802 | − | 0.0662619i | \(-0.978893\pi\) | ||
0.997802 | − | 0.0662619i | \(-0.0211073\pi\) | |||||||
\(810\) | 2.83733e7 | − | 4.60593e7i | 1.51949 | − | 2.46663i | ||||
\(811\) | 3.47087e7i | 1.85304i | 0.376241 | + | 0.926522i | \(0.377216\pi\) | ||||
−0.376241 | + | 0.926522i | \(0.622784\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.45123e7 | − | 4.79416e6i | −1.83125 | − | 0.254382i | ||||
\(814\) | −5.39031e6 | −0.285137 | ||||||||
\(815\) | −4.11045e7 | −2.16768 | ||||||||
\(816\) | 776885. | − | 5.59265e6i | 0.0408443 | − | 0.294030i | ||||
\(817\) | 2.20280e7i | 1.15457i | ||||||||
\(818\) | 5.12279e7 | 2.67684 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.34697e7 | −4.33505 | ||||||||
\(821\) | − | 1.35642e7i | − | 0.702321i | −0.936315 | − | 0.351160i | \(-0.885787\pi\) | ||
0.936315 | − | 0.351160i | \(-0.114213\pi\) | |||||||
\(822\) | 6.80754e6 | − | 4.90062e7i | 0.351407 | − | 2.52971i | ||||
\(823\) | −3.25080e7 | −1.67298 | −0.836490 | − | 0.547983i | \(-0.815396\pi\) | ||||
−0.836490 | + | 0.547983i | \(0.815396\pi\) | |||||||
\(824\) | 128754. | 0.00660605 | ||||||||
\(825\) | −1.38330e7 | − | 1.92157e6i | −0.707589 | − | 0.0982925i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.01138e6i | 0.254797i | 0.991852 | + | 0.127398i | \(0.0406627\pi\) | ||||
−0.991852 | + | 0.127398i | \(0.959337\pi\) | |||||||
\(828\) | 5.57434e6 | − | 1.96772e7i | 0.282565 | − | 0.997439i | ||||
\(829\) | 4.44010e6i | 0.224392i | 0.993686 | + | 0.112196i | \(0.0357884\pi\) | ||||
−0.993686 | + | 0.112196i | \(0.964212\pi\) | |||||||
\(830\) | 2.71963e6i | 0.137030i | ||||||||
\(831\) | −2.66918e6 | + | 1.92150e7i | −0.134084 | + | 0.965244i | ||||
\(832\) | 3.69238e7i | 1.84926i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.84185e6 | − | 5.64520e7i | 0.390394 | − | 2.81037i | ||||
\(835\) | −2.51260e7 | −1.24712 | ||||||||
\(836\) | 2.01833e7 | 0.998796 | ||||||||
\(837\) | 4.36794e6 | + | 1.91970e6i | 0.215508 | + | 0.0947150i | ||||
\(838\) | − | 5.02218e7i | − | 2.47049i | ||||||
\(839\) | 4.45699e6 | 0.218593 | 0.109297 | − | 0.994009i | \(-0.465140\pi\) | ||||
0.109297 | + | 0.994009i | \(0.465140\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.03629e6 | −0.294293 | ||||||||
\(842\) | − | 5.14970e7i | − | 2.50324i | ||||||
\(843\) | −9.60925e6 | − | 1.33484e6i | −0.465715 | − | 0.0646934i | ||||
\(844\) | −1.75978e7 | −0.850359 | ||||||||
\(845\) | −4.19600e7 | −2.02159 | ||||||||
\(846\) | 5.92003e6 | − | 2.08974e7i | 0.284379 | − | 1.00385i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.23945e7i | 0.591888i | ||||||||
\(849\) | 1.56682e7 | + | 2.17650e6i | 0.746018 | + | 0.103631i | ||||
\(850\) | 2.78115e7i | 1.32031i | ||||||||
\(851\) | 5.08646e6i | 0.240764i | ||||||||
\(852\) | −4.05921e7 | − | 5.63872e6i | −1.91577 | − | 0.266123i | ||||
\(853\) | − | 4.50408e6i | − | 0.211950i | −0.994369 | − | 0.105975i | \(-0.966204\pi\) | ||
0.994369 | − | 0.105975i | \(-0.0337964\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.37313e7 | − | 4.84708e7i | 0.642386 | − | 2.26759i | ||||
\(856\) | −3.68436e7 | −1.71861 | ||||||||
\(857\) | −3.62211e6 | −0.168465 | −0.0842326 | − | 0.996446i | \(-0.526844\pi\) | ||||
−0.0842326 | + | 0.996446i | \(0.526844\pi\) | |||||||
\(858\) | −2.03678e7 | − | 2.82933e6i | −0.944553 | − | 0.131210i | ||||
\(859\) | − | 1.27436e7i | − | 0.589263i | −0.955611 | − | 0.294632i | \(-0.904803\pi\) | ||
0.955611 | − | 0.294632i | \(-0.0951969\pi\) | |||||||
\(860\) | −5.84803e7 | −2.69627 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.69725e7 | −1.69477 | ||||||||
\(863\) | 1.22085e7i | 0.558000i | 0.960291 | + | 0.279000i | \(0.0900029\pi\) | ||||
−0.960291 | + | 0.279000i | \(0.909997\pi\) | |||||||
\(864\) | 6.19747e6 | + | 2.72377e6i | 0.282442 | + | 0.124133i | ||||
\(865\) | 5.31756e7 | 2.41642 | ||||||||
\(866\) | −3.64640e7 | −1.65223 | ||||||||
\(867\) | 2.53333e6 | − | 1.82370e7i | 0.114457 | − | 0.823958i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.53625e6i | − | 0.0690103i | ||||||
\(870\) | −1.01243e7 | + | 7.28830e7i | −0.453489 | + | 3.26458i | ||||
\(871\) | 3.05887e7i | 1.36621i | ||||||||
\(872\) | − | 6.09039e7i | − | 2.71240i | ||||||
\(873\) | −4.02493e6 | + | 1.42078e7i | −0.178740 | + | 0.630945i | ||||
\(874\) | − | 2.90433e7i | − | 1.28608i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.02920e7 | + | 2.81879e6i | 0.893437 | + | 0.124109i | ||||
\(877\) | 1.36721e7 | 0.600255 | 0.300127 | − | 0.953899i | \(-0.402971\pi\) | ||||
0.300127 | + | 0.953899i | \(0.402971\pi\) | |||||||
\(878\) | 2.47423e7 | 1.08319 | ||||||||
\(879\) | −1.75086e6 | + | 1.26041e7i | −0.0764328 | + | 0.550226i | ||||
\(880\) | 1.06897e7i | 0.465327i | ||||||||
\(881\) | −1.97267e7 | −0.856279 | −0.428140 | − | 0.903713i | \(-0.640831\pi\) | ||||
−0.428140 | + | 0.903713i | \(0.640831\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.09920e7 | 0.474434 | 0.237217 | − | 0.971457i | \(-0.423765\pi\) | ||||
0.237217 | + | 0.971457i | \(0.423765\pi\) | |||||||
\(884\) | 2.68535e7i | 1.15577i | ||||||||
\(885\) | −482177. | + | 3.47110e6i | −0.0206942 | + | 0.148974i | ||||
\(886\) | −5.07942e6 | −0.217385 | ||||||||
\(887\) | 3.17812e7 | 1.35632 | 0.678158 | − | 0.734916i | \(-0.262778\pi\) | ||||
0.678158 | + | 0.734916i | \(0.262778\pi\) | |||||||
\(888\) | 1.58827e7 | + | 2.20630e6i | 0.675916 | + | 0.0938927i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 7.74043e7i | − | 3.27559i | ||||||
\(891\) | −4.69980e6 | + | 7.62932e6i | −0.198328 | + | 0.321952i | ||||
\(892\) | 2.71611e7i | 1.14297i | ||||||||
\(893\) | − | 2.02267e7i | − | 0.848781i | ||||||
\(894\) | −3.59503e6 | + | 2.58799e7i | −0.150438 | + | 1.08298i | ||||
\(895\) | − | 5.08989e7i | − | 2.12398i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.66984e6 | + | 1.92197e7i | −0.110791 | + | 0.797562i | ||||
\(898\) | 427610. | 0.0176953 | ||||||||
\(899\) | −6.48974e6 | −0.267811 | ||||||||
\(900\) | 8.41426e7 | + | 2.38368e7i | 3.46266 | + | 0.980937i | ||||
\(901\) | − | 8.16876e6i | − | 0.335231i | ||||||
\(902\) | 2.10839e7 | 0.862848 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.97459e7 | −2.02458 | ||||||||
\(905\) | − | 416560.i | − | 0.0169066i | ||||||
\(906\) | −1.75627e7 | − | 2.43967e6i | −0.710840 | − | 0.0987440i | ||||
\(907\) | −4.25373e6 | −0.171693 | −0.0858463 | − | 0.996308i | \(-0.527359\pi\) | ||||
−0.0858463 | + | 0.996308i | \(0.527359\pi\) | |||||||
\(908\) | −6.61381e7 | −2.66218 | ||||||||
\(909\) | −6.29993e6 | − | 1.78471e6i | −0.252887 | − | 0.0716403i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.87743e7i | 1.14870i | 0.818608 | + | 0.574352i | \(0.194746\pi\) | ||||
−0.818608 | + | 0.574352i | \(0.805254\pi\) | |||||||
\(912\) | −2.49743e7 | − | 3.46923e6i | −0.994274 | − | 0.138116i | ||||
\(913\) | − | 450483.i | − | 0.0178855i | ||||||
\(914\) | − | 4.11412e7i | − | 1.62896i | ||||||
\(915\) | −1.16617e7 | − | 1.61994e6i | −0.460476 | − | 0.0639656i | ||||
\(916\) | 4.12960e7i | 1.62618i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.63363e7 | + | 7.17974e6i | 0.639803 | + | 0.281192i | ||||
\(919\) | 1.79842e7 | 0.702429 | 0.351215 | − | 0.936295i | \(-0.385769\pi\) | ||||
0.351215 | + | 0.936295i | \(0.385769\pi\) | |||||||
\(920\) | 3.66293e7 | 1.42679 | ||||||||
\(921\) | 1.09851e7 | + | 1.52595e6i | 0.426730 | + | 0.0592778i | ||||
\(922\) | − | 6.13182e7i | − | 2.37554i | ||||||
\(923\) | 3.88832e7 | 1.50231 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.17505e7 | −0.835824 | ||||||||
\(926\) | − | 6.41557e7i | − | 2.45871i | ||||||
\(927\) | −30542.2 | + | 107812.i | −0.00116735 | + | 0.00412068i | ||||
\(928\) | −9.20800e6 | −0.350990 | ||||||||
\(929\) | −1.63681e7 | −0.622240 | −0.311120 | − | 0.950371i | \(-0.600704\pi\) | ||||
−0.311120 | + | 0.950371i | \(0.600704\pi\) | |||||||
\(930\) | −2.47497e6 | + | 1.78168e7i | −0.0938345 | + | 0.675497i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.66634e6i | 0.326810i | ||||||||
\(933\) | 4.40370e6 | − | 3.17014e7i | 0.165620 | − | 1.19227i | ||||
\(934\) | 2.91424e7i | 1.09310i | ||||||||
\(935\) | − | 7.04518e6i | − | 0.263550i | ||||||
\(936\) | 5.88563e7 | + | 1.66734e7i | 2.19585 | + | 0.622064i | ||||
\(937\) | 1.56678e7i | 0.582986i | 0.956573 | + | 0.291493i | \(0.0941520\pi\) | ||||
−0.956573 | + | 0.291493i | \(0.905848\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.27844e7 | − | 4.55413e6i | −1.21340 | − | 0.168555i | ||||
\(940\) | 5.36980e7 | 1.98216 | ||||||||
\(941\) | −464968. | −0.0171179 | −0.00855893 | − | 0.999963i | \(-0.502724\pi\) | ||||
−0.00855893 | + | 0.999963i | \(0.502724\pi\) | |||||||
\(942\) | −815904. | + | 5.87354e6i | −0.0299579 | + | 0.215662i | ||||
\(943\) | − | 1.98954e7i | − | 0.728572i | ||||||
\(944\) | 1.75396e6 | 0.0640603 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.47717e7 | 0.536665 | ||||||||
\(947\) | 3.83949e7i | 1.39123i | 0.718415 | + | 0.695615i | \(0.244868\pi\) | ||||
−0.718415 | + | 0.695615i | \(0.755132\pi\) | |||||||
\(948\) | −1.32362e6 | + | 9.52852e6i | −0.0478348 | + | 0.344354i | ||||
\(949\) | −1.94377e7 | −0.700616 | ||||||||
\(950\) | 1.24194e8 | 4.46469 | ||||||||
\(951\) | 2.68420e7 | + | 3.72867e6i | 0.962419 | + | 0.133691i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.66890e7i | − | 1.30859i | −0.756240 | − | 0.654294i | \(-0.772966\pi\) | ||
0.756240 | − | 0.654294i | \(-0.227034\pi\) | |||||||
\(954\) | −3.76878e7 | − | 1.06766e7i | −1.34069 | − | 0.379805i | ||||
\(955\) | − | 3.81962e7i | − | 1.35523i | ||||||
\(956\) | 6.75758e7i | 2.39137i | ||||||||
\(957\) | 1.67700e6 | − | 1.20724e7i | 0.0591908 | − | 0.426104i | ||||
\(958\) | − | 6.28414e7i | − | 2.21224i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −8.34640e6 | + | 6.00841e7i | −0.292295 | + | 2.10417i | ||||
\(961\) | 2.70427e7 | 0.944586 | ||||||||
\(962\) | −3.20256e7 | −1.11573 | ||||||||
\(963\) | 8.73981e6 | − | 3.08511e7i | 0.303694 | − | 1.07202i | ||||
\(964\) | 3.22344e7i | 1.11719i | ||||||||
\(965\) | −1.70948e7 | −0.590945 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.57252e7 | 1.22860 | 0.614298 | − | 0.789074i | \(-0.289439\pi\) | ||||
0.614298 | + | 0.789074i | \(0.289439\pi\) | |||||||
\(968\) | 3.85377e7i | 1.32190i | ||||||||
\(969\) | 1.64596e7 | + | 2.28644e6i | 0.563133 | + | 0.0782258i | ||||
\(970\) | −5.56731e7 | −1.89983 | ||||||||
\(971\) | 3.60215e7 | 1.22606 | 0.613032 | − | 0.790058i | \(-0.289949\pi\) | ||||
0.613032 | + | 0.790058i | \(0.289949\pi\) | |||||||
\(972\) | 3.57236e7 | − | 4.32711e7i | 1.21280 | − | 1.46904i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 6.46288e7i | 2.18287i | ||||||||
\(975\) | −8.21863e7 | − | 1.14166e7i | −2.76878 | − | 0.384616i | ||||
\(976\) | 5.89266e6i | 0.198010i | ||||||||
\(977\) | 2.10574e7i | 0.705779i | 0.935665 | + | 0.352889i | \(0.114801\pi\) | ||||
−0.935665 | + | 0.352889i | \(0.885199\pi\) | |||||||
\(978\) | −6.43981e7 | − | 8.94566e6i | −2.15291 | − | 0.299065i | ||||
\(979\) | 1.28214e7i | 0.427541i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.09980e7 | + | 1.44472e7i | 1.69192 | + | 0.479305i | ||||
\(982\) | −8.82750e6 | −0.292119 | ||||||||
\(983\) | 4.42821e7 | 1.46165 | 0.730827 | − | 0.682563i | \(-0.239135\pi\) | ||||
0.730827 | + | 0.682563i | \(0.239135\pi\) | |||||||
\(984\) | −6.21243e7 | − | 8.62980e6i | −2.04538 | − | 0.284127i | ||||
\(985\) | 4.91038e7i | 1.61259i | ||||||||
\(986\) | −2.42719e7 | −0.795081 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.19916e8 | 3.90826 | ||||||||
\(989\) | − | 1.39390e7i | − | 0.453150i | ||||||
\(990\) | −3.25039e7 | − | 9.20805e6i | −1.05402 | − | 0.298593i | ||||
\(991\) | −3.34563e7 | −1.08216 | −0.541082 | − | 0.840970i | \(-0.681985\pi\) | ||||
−0.541082 | + | 0.840970i | \(0.681985\pi\) | |||||||
\(992\) | −2.25097e6 | −0.0726257 | ||||||||
\(993\) | −6.17718e6 | + | 4.44684e7i | −0.198800 | + | 1.43113i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.73619e7i | 1.19638i | ||||||||
\(996\) | −388132. | + | 2.79409e6i | −0.0123974 | + | 0.0892468i | ||||
\(997\) | 1.90479e7i | 0.606890i | 0.952849 | + | 0.303445i | \(0.0981369\pi\) | ||||
−0.952849 | + | 0.303445i | \(0.901863\pi\) | |||||||
\(998\) | 8.68025e7i | 2.75871i | ||||||||
\(999\) | −5.61505e6 | + | 1.27761e7i | −0.178008 | + | 0.405027i |
(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 | 147.6.c.d.146.37 | yes | 40 | |
3.2 | odd | 2 | inner | 147.6.c.d.146.4 | yes | 40 | |
7.6 | odd | 2 | inner | 147.6.c.d.146.3 | ✓ | 40 | |
21.20 | even | 2 | inner | 147.6.c.d.146.38 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.6.c.d.146.3 | ✓ | 40 | 7.6 | odd | 2 | inner | |
147.6.c.d.146.4 | yes | 40 | 3.2 | odd | 2 | inner | |
147.6.c.d.146.37 | yes | 40 | 1.1 | even | 1 | trivial | |
147.6.c.d.146.38 | yes | 40 | 21.20 | even | 2 | inner |