Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(107,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, 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("108.107");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.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: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 94 x^{18} + 5872 x^{16} - 207192 x^{14} + 5271952 x^{12} - 76648960 x^{10} + 792478720 x^{8} + \cdots + 41943040000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{50}\cdot 3^{40} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.14 | ||
Root | \(1.93085 + 1.11477i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.107 |
Dual form | 108.6.b.c.107.13 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.63934 | + | 4.33073i | 0.643351 | + | 0.765571i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.51036 | + | 31.5220i | −0.172199 | + | 0.985062i | ||||
\(5\) | − | 80.5384i | − | 1.44071i | −0.693603 | − | 0.720357i | \(-0.743978\pi\) | ||
0.693603 | − | 0.720357i | \(-0.256022\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 216.819i | 1.67245i | 0.548388 | + | 0.836224i | \(0.315242\pi\) | ||||
−0.548388 | + | 0.836224i | \(0.684758\pi\) | |||||||
\(8\) | −156.567 | + | 90.8555i | −0.864920 | + | 0.501910i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 348.790 | − | 293.107i | 1.10297 | − | 0.926885i | ||||
\(11\) | 153.345 | 0.382110 | 0.191055 | − | 0.981579i | \(-0.438809\pi\) | ||||
0.191055 | + | 0.981579i | \(0.438809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −945.747 | −1.55209 | −0.776044 | − | 0.630679i | \(-0.782777\pi\) | ||||
−0.776044 | + | 0.630679i | \(0.782777\pi\) | |||||||
\(14\) | −938.984 | + | 789.079i | −1.28038 | + | 1.07597i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −963.272 | − | 347.395i | −0.940695 | − | 0.339253i | ||||
\(17\) | 2184.11i | 1.83296i | 0.400084 | + | 0.916478i | \(0.368981\pi\) | ||||
−0.400084 | + | 0.916478i | \(0.631019\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 719.706i | 0.457373i | 0.973500 | + | 0.228687i | \(0.0734431\pi\) | ||||
−0.973500 | + | 0.228687i | \(0.926557\pi\) | |||||||
\(20\) | 2538.73 | + | 443.796i | 1.41919 | + | 0.248089i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 558.076 | + | 664.096i | 0.245831 | + | 0.292532i | ||||
\(23\) | −2622.17 | −1.03357 | −0.516786 | − | 0.856115i | \(-0.672872\pi\) | ||||
−0.516786 | + | 0.856115i | \(0.672872\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3361.43 | −1.07566 | ||||||||
\(26\) | −3441.90 | − | 4095.77i | −0.998538 | − | 1.18823i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6834.57 | − | 1194.75i | −1.64747 | − | 0.287994i | ||||
\(29\) | 155.049i | 0.0342353i | 0.999853 | + | 0.0171177i | \(0.00544899\pi\) | ||||
−0.999853 | + | 0.0171177i | \(0.994551\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4909.55i | − | 0.917567i | −0.888548 | − | 0.458783i | \(-0.848285\pi\) | ||
0.888548 | − | 0.458783i | \(-0.151715\pi\) | |||||||
\(32\) | −2001.20 | − | 5435.96i | −0.345475 | − | 0.938428i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9458.78 | + | 7948.73i | −1.40326 | + | 1.17923i | ||||
\(35\) | 17462.3 | 2.40952 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 114.620 | 0.0137644 | 0.00688218 | − | 0.999976i | \(-0.497809\pi\) | ||||
0.00688218 | + | 0.999976i | \(0.497809\pi\) | |||||||
\(38\) | −3116.85 | + | 2619.26i | −0.350152 | + | 0.294252i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7317.35 | + | 12609.7i | 0.723109 | + | 1.24610i | ||||
\(41\) | − | 3356.63i | − | 0.311849i | −0.987769 | − | 0.155924i | \(-0.950164\pi\) | ||
0.987769 | − | 0.155924i | \(-0.0498356\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13109.4i | 1.08121i | 0.841276 | + | 0.540606i | \(0.181805\pi\) | ||||
−0.841276 | + | 0.540606i | \(0.818195\pi\) | |||||||
\(44\) | −844.988 | + | 4833.74i | −0.0657989 | + | 0.376402i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9542.96 | − | 11355.9i | −0.664949 | − | 0.791273i | ||||
\(47\) | 9409.97 | 0.621360 | 0.310680 | − | 0.950515i | \(-0.399443\pi\) | ||||
0.310680 | + | 0.950515i | \(0.399443\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −30203.6 | −1.79708 | ||||||||
\(50\) | −12233.4 | − | 14557.4i | −0.692026 | − | 0.823493i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5211.41 | − | 29811.8i | 0.267268 | − | 1.52890i | ||||
\(53\) | 19619.3i | 0.959388i | 0.877436 | + | 0.479694i | \(0.159252\pi\) | ||||
−0.877436 | + | 0.479694i | \(0.840748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 12350.2i | − | 0.550511i | ||||||
\(56\) | −19699.2 | − | 33946.8i | −0.839419 | − | 1.44653i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −671.476 | + | 564.277i | −0.0262096 | + | 0.0220253i | ||||
\(59\) | 21595.2 | 0.807658 | 0.403829 | − | 0.914835i | \(-0.367679\pi\) | ||||
0.403829 | + | 0.914835i | \(0.367679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 33298.2 | 1.14577 | 0.572884 | − | 0.819637i | \(-0.305825\pi\) | ||||
0.572884 | + | 0.819637i | \(0.305825\pi\) | |||||||
\(62\) | 21261.9 | − | 17867.5i | 0.702463 | − | 0.590317i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 16258.6 | − | 28450.0i | 0.496172 | − | 0.868224i | ||||
\(65\) | 76168.9i | 2.23612i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 23493.1i | 0.639371i | 0.947524 | + | 0.319685i | \(0.103577\pi\) | ||||
−0.947524 | + | 0.319685i | \(0.896423\pi\) | |||||||
\(68\) | −68847.5 | − | 12035.2i | −1.80558 | − | 0.315633i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 63551.2 | + | 75624.3i | 1.55017 | + | 1.84466i | ||||
\(71\) | 2402.72 | 0.0565662 | 0.0282831 | − | 0.999600i | \(-0.490996\pi\) | ||||
0.0282831 | + | 0.999600i | \(0.490996\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4867.76 | 0.106911 | 0.0534555 | − | 0.998570i | \(-0.482976\pi\) | ||||
0.0534555 | + | 0.998570i | \(0.482976\pi\) | |||||||
\(74\) | 417.141 | + | 496.388i | 0.00885531 | + | 0.0105376i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −22686.6 | − | 3965.84i | −0.450541 | − | 0.0787592i | ||||
\(77\) | 33248.2i | 0.639059i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11925.5i | 0.214985i | 0.994206 | + | 0.107492i | \(0.0342821\pi\) | ||||
−0.994206 | + | 0.107492i | \(0.965718\pi\) | |||||||
\(80\) | −27978.7 | + | 77580.4i | −0.488767 | + | 1.35527i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14536.6 | − | 12215.9i | 0.238742 | − | 0.200628i | ||||
\(83\) | 83940.6 | 1.33745 | 0.668724 | − | 0.743511i | \(-0.266841\pi\) | ||||
0.668724 | + | 0.743511i | \(0.266841\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 175905. | 2.64077 | ||||||||
\(86\) | −56773.1 | + | 47709.5i | −0.827745 | + | 0.695599i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −24008.8 | + | 13932.2i | −0.330494 | + | 0.191785i | ||||
\(89\) | − | 36800.9i | − | 0.492474i | −0.969210 | − | 0.246237i | \(-0.920806\pi\) | ||
0.969210 | − | 0.246237i | \(-0.0791941\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 205056.i | − | 2.59579i | ||||||
\(92\) | 14449.1 | − | 82655.9i | 0.177980 | − | 1.01813i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 34246.1 | + | 40752.0i | 0.399753 | + | 0.475696i | ||||
\(95\) | 57963.9 | 0.658945 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −28249.7 | −0.304849 | −0.152424 | − | 0.988315i | \(-0.548708\pi\) | ||||
−0.152424 | + | 0.988315i | \(0.548708\pi\) | |||||||
\(98\) | −109921. | − | 130803.i | −1.15616 | − | 1.37579i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 18522.7 | − | 105959.i | 0.185227 | − | 1.05959i | ||||
\(101\) | − | 4051.50i | − | 0.0395196i | −0.999805 | − | 0.0197598i | \(-0.993710\pi\) | ||
0.999805 | − | 0.0197598i | \(-0.00629015\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 108384.i | 1.00663i | 0.864103 | + | 0.503316i | \(0.167887\pi\) | ||||
−0.864103 | + | 0.503316i | \(0.832113\pi\) | |||||||
\(104\) | 148073. | − | 85926.3i | 1.34243 | − | 0.779009i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −84965.9 | + | 71401.4i | −0.734480 | + | 0.617223i | ||||
\(107\) | 94762.1 | 0.800157 | 0.400079 | − | 0.916481i | \(-0.368983\pi\) | ||||
0.400079 | + | 0.916481i | \(0.368983\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −105703. | −0.852160 | −0.426080 | − | 0.904685i | \(-0.640106\pi\) | ||||
−0.426080 | + | 0.904685i | \(0.640106\pi\) | |||||||
\(110\) | 53485.2 | − | 44946.5i | 0.421456 | − | 0.354172i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 75322.0 | − | 208856.i | 0.567383 | − | 1.57326i | ||||
\(113\) | − | 80853.1i | − | 0.595663i | −0.954618 | − | 0.297832i | \(-0.903737\pi\) | ||
0.954618 | − | 0.297832i | \(-0.0962634\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 211185.i | 1.48908i | ||||||||
\(116\) | −4887.46 | − | 854.378i | −0.0337239 | − | 0.00589529i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 78592.4 | + | 93522.9i | 0.519607 | + | 0.618319i | ||||
\(119\) | −473557. | −3.06552 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −137536. | −0.853992 | ||||||||
\(122\) | 121184. | + | 144205.i | 0.737131 | + | 0.877166i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 154759. | + | 27053.4i | 0.903860 | + | 0.158004i | ||||
\(125\) | 19041.9i | 0.109002i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 47941.0i | − | 0.263753i | −0.991266 | − | 0.131877i | \(-0.957900\pi\) | ||
0.991266 | − | 0.131877i | \(-0.0421003\pi\) | |||||||
\(128\) | 182380. | − | 33127.8i | 0.983900 | − | 0.178718i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −329867. | + | 277205.i | −1.71191 | + | 1.43861i | ||||
\(131\) | 301162. | 1.53328 | 0.766640 | − | 0.642077i | \(-0.221927\pi\) | ||||
0.766640 | + | 0.642077i | \(0.221927\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −156046. | −0.764933 | ||||||||
\(134\) | −101742. | + | 85499.4i | −0.489484 | + | 0.411340i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −198438. | − | 341960.i | −0.919980 | − | 1.58536i | ||||
\(137\) | 134846.i | 0.613814i | 0.951739 | + | 0.306907i | \(0.0992941\pi\) | ||||
−0.951739 | + | 0.306907i | \(0.900706\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 88215.4i | 0.387264i | 0.981074 | + | 0.193632i | \(0.0620268\pi\) | ||||
−0.981074 | + | 0.193632i | \(0.937973\pi\) | |||||||
\(140\) | −96223.5 | + | 550446.i | −0.414917 | + | 2.37353i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8744.31 | + | 10405.5i | 0.0363919 | + | 0.0433054i | ||||
\(143\) | −145026. | −0.593068 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12487.4 | 0.0493233 | ||||||||
\(146\) | 17715.5 | + | 21080.9i | 0.0687813 | + | 0.0818480i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −631.598 | + | 3613.05i | −0.00237021 | + | 0.0135587i | ||||
\(149\) | − | 424905.i | − | 1.56793i | −0.620806 | − | 0.783965i | \(-0.713194\pi\) | ||
0.620806 | − | 0.783965i | \(-0.286806\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 188045.i | − | 0.671150i | −0.942014 | − | 0.335575i | \(-0.891069\pi\) | ||
0.942014 | − | 0.335575i | \(-0.108931\pi\) | |||||||
\(152\) | −65389.2 | − | 112682.i | −0.229560 | − | 0.395591i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −143989. | + | 121002.i | −0.489245 | + | 0.411139i | ||||
\(155\) | −395407. | −1.32195 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −348168. | −1.12730 | −0.563650 | − | 0.826014i | \(-0.690603\pi\) | ||||
−0.563650 | + | 0.826014i | \(0.690603\pi\) | |||||||
\(158\) | −51645.9 | + | 43400.9i | −0.164586 | + | 0.138311i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −437803. | + | 161174.i | −1.35201 | + | 0.497730i | ||||
\(161\) | − | 568536.i | − | 1.72859i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 25262.9i | 0.0744756i | 0.999306 | + | 0.0372378i | \(0.0118559\pi\) | ||||
−0.999306 | + | 0.0372378i | \(0.988144\pi\) | |||||||
\(164\) | 105808. | + | 18496.2i | 0.307190 | + | 0.0537000i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 305489. | + | 363524.i | 0.860448 | + | 1.02391i | ||||
\(167\) | −385026. | −1.06831 | −0.534157 | − | 0.845386i | \(-0.679371\pi\) | ||||
−0.534157 | + | 0.845386i | \(0.679371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 523144. | 1.40898 | ||||||||
\(170\) | 640178. | + | 761795.i | 1.69894 | + | 2.02170i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −413233. | − | 72237.4i | −1.06506 | − | 0.186183i | ||||
\(173\) | 547742.i | 1.39143i | 0.718318 | + | 0.695715i | \(0.244912\pi\) | ||||
−0.718318 | + | 0.695715i | \(0.755088\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 728823.i | − | 1.79898i | ||||||
\(176\) | −147713. | − | 53271.4i | −0.359449 | − | 0.129632i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 159374. | − | 133931.i | 0.377024 | − | 0.316834i | ||||
\(179\) | −450824. | −1.05166 | −0.525829 | − | 0.850590i | \(-0.676245\pi\) | ||||
−0.525829 | + | 0.850590i | \(0.676245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1585.85 | 0.00359805 | 0.00179902 | − | 0.999998i | \(-0.499427\pi\) | ||||
0.00179902 | + | 0.999998i | \(0.499427\pi\) | |||||||
\(182\) | 888041. | − | 746269.i | 1.98726 | − | 1.67000i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 410545. | − | 238238.i | 0.893956 | − | 0.518760i | ||||
\(185\) | − | 9231.31i | − | 0.0198305i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 334923.i | 0.700391i | ||||||||
\(188\) | −51852.3 | + | 296621.i | −0.106998 | + | 0.612078i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 210951. | + | 251026.i | 0.423933 | + | 0.504469i | ||||
\(191\) | 310556. | 0.615966 | 0.307983 | − | 0.951392i | \(-0.400346\pi\) | ||||
0.307983 | + | 0.951392i | \(0.400346\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 86770.6 | 0.167679 | 0.0838397 | − | 0.996479i | \(-0.473282\pi\) | ||||
0.0838397 | + | 0.996479i | \(0.473282\pi\) | |||||||
\(194\) | −102810. | − | 122342.i | −0.196125 | − | 0.233383i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 166433. | − | 952077.i | 0.309456 | − | 1.77024i | ||||
\(197\) | − | 406767.i | − | 0.746758i | −0.927679 | − | 0.373379i | \(-0.878199\pi\) | ||
0.927679 | − | 0.373379i | \(-0.121801\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.07477e6i | 1.92389i | 0.273235 | + | 0.961947i | \(0.411906\pi\) | ||||
−0.273235 | + | 0.961947i | \(0.588094\pi\) | |||||||
\(200\) | 526290. | − | 305404.i | 0.930358 | − | 0.539884i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17546.0 | − | 14744.8i | 0.0302551 | − | 0.0254250i | ||||
\(203\) | −33617.6 | −0.0572568 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −270338. | −0.449285 | ||||||||
\(206\) | −469380. | + | 394445.i | −0.770648 | + | 0.647618i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 911011. | + | 328548.i | 1.46004 | + | 0.526551i | ||||
\(209\) | 110363.i | 0.174767i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 629852.i | 0.973941i | 0.873419 | + | 0.486970i | \(0.161898\pi\) | ||||
−0.873419 | + | 0.486970i | \(0.838102\pi\) | |||||||
\(212\) | −618440. | − | 108110.i | −0.945057 | − | 0.165206i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 344872. | + | 410389.i | 0.514782 | + | 0.612577i | ||||
\(215\) | 1.05581e6 | 1.55772 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.06449e6 | 1.53458 | ||||||||
\(218\) | −384690. | − | 457771.i | −0.548238 | − | 0.652389i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 389302. | + | 68053.9i | 0.542288 | + | 0.0947974i | ||||
\(221\) | − | 2.06561e6i | − | 2.84491i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.27771e6i | − | 1.72056i | −0.509825 | − | 0.860278i | \(-0.670290\pi\) | ||
0.509825 | − | 0.860278i | \(-0.329710\pi\) | |||||||
\(224\) | 1.17862e6 | − | 433899.i | 1.56947 | − | 0.577788i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 350153. | − | 294252.i | 0.456023 | − | 0.383221i | ||||
\(227\) | −1.43061e6 | −1.84271 | −0.921354 | − | 0.388724i | \(-0.872916\pi\) | ||||
−0.921354 | + | 0.388724i | \(0.872916\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 618971. | 0.779977 | 0.389988 | − | 0.920820i | \(-0.372479\pi\) | ||||
0.389988 | + | 0.920820i | \(0.372479\pi\) | |||||||
\(230\) | −914584. | + | 768575.i | −1.14000 | + | 0.958002i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14087.1 | − | 24275.6i | −0.0171831 | − | 0.0296108i | ||||
\(233\) | 391086.i | 0.471936i | 0.971761 | + | 0.235968i | \(0.0758260\pi\) | ||||
−0.971761 | + | 0.235968i | \(0.924174\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 757864.i | − | 0.895203i | ||||||
\(236\) | −118997. | + | 680724.i | −0.139078 | + | 0.795593i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.72344e6 | − | 2.05085e6i | −1.97221 | − | 2.34688i | ||||
\(239\) | 1.39491e6 | 1.57961 | 0.789806 | − | 0.613356i | \(-0.210181\pi\) | ||||
0.789806 | + | 0.613356i | \(0.210181\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −745913. | −0.827266 | −0.413633 | − | 0.910444i | \(-0.635740\pi\) | ||||
−0.413633 | + | 0.910444i | \(0.635740\pi\) | |||||||
\(242\) | −500542. | − | 595632.i | −0.549417 | − | 0.653792i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −183485. | + | 1.04963e6i | −0.197300 | + | 1.12865i | ||||
\(245\) | 2.43255e6i | 2.58908i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 680659.i | − | 0.709884i | ||||||
\(248\) | 446060. | + | 768675.i | 0.460536 | + | 0.793621i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −82465.1 | + | 69299.9i | −0.0834488 | + | 0.0701266i | ||||
\(251\) | 1.22222e6 | 1.22452 | 0.612260 | − | 0.790657i | \(-0.290261\pi\) | ||||
0.612260 | + | 0.790657i | \(0.290261\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −402096. | −0.394938 | ||||||||
\(254\) | 207619. | − | 174474.i | 0.201922 | − | 0.169686i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 807209. | + | 669272.i | 0.769815 | + | 0.638268i | ||||
\(257\) | 1.79287e6i | 1.69323i | 0.532207 | + | 0.846614i | \(0.321363\pi\) | ||||
−0.532207 | + | 0.846614i | \(0.678637\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24851.8i | 0.0230202i | ||||||||
\(260\) | −2.40100e6 | − | 419718.i | −2.20271 | − | 0.385057i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.09603e6 | + | 1.30425e6i | 0.986438 | + | 1.17384i | ||||
\(263\) | −996371. | −0.888243 | −0.444122 | − | 0.895967i | \(-0.646484\pi\) | ||||
−0.444122 | + | 0.895967i | \(0.646484\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.58011e6 | 1.38220 | ||||||||
\(266\) | −567905. | − | 675793.i | −0.492121 | − | 0.585611i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −740549. | − | 129455.i | −0.629820 | − | 0.110099i | ||||
\(269\) | 2.16053e6i | 1.82045i | 0.414109 | + | 0.910227i | \(0.364093\pi\) | ||||
−0.414109 | + | 0.910227i | \(0.635907\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.68130e6i | 1.39066i | 0.718688 | + | 0.695332i | \(0.244743\pi\) | ||||
−0.718688 | + | 0.695332i | \(0.755257\pi\) | |||||||
\(272\) | 758749. | − | 2.10389e6i | 0.621836 | − | 1.72425i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −583982. | + | 490751.i | −0.469919 | + | 0.394898i | ||||
\(275\) | −515459. | −0.411020 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.08867e6 | 0.852507 | 0.426254 | − | 0.904604i | \(-0.359833\pi\) | ||||
0.426254 | + | 0.904604i | \(0.359833\pi\) | |||||||
\(278\) | −382036. | + | 321046.i | −0.296478 | + | 0.249147i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.73402e6 | + | 1.58654e6i | −2.08404 | + | 1.20936i | ||||
\(281\) | − | 728495.i | − | 0.550377i | −0.961390 | − | 0.275189i | \(-0.911260\pi\) | ||
0.961390 | − | 0.275189i | \(-0.0887403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 733677.i | 0.544551i | 0.962219 | + | 0.272276i | \(0.0877762\pi\) | ||||
−0.962219 | + | 0.272276i | \(0.912224\pi\) | |||||||
\(284\) | −13239.8 | + | 75738.4i | −0.00974063 | + | 0.0557212i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −527798. | − | 628066.i | −0.381551 | − | 0.454036i | ||||
\(287\) | 727782. | 0.521551 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.35048e6 | −2.35973 | ||||||||
\(290\) | 45446.0 | + | 54079.6i | 0.0317322 | + | 0.0377605i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −26823.1 | + | 153442.i | −0.0184099 | + | 0.105314i | ||||
\(293\) | − | 400766.i | − | 0.272723i | −0.990659 | − | 0.136361i | \(-0.956459\pi\) | ||
0.990659 | − | 0.136361i | \(-0.0435409\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.73924e6i | − | 1.16360i | ||||||
\(296\) | −17945.7 | + | 10413.9i | −0.0119051 | + | 0.00690847i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.84015e6 | − | 1.54638e6i | 1.20036 | − | 1.00873i | ||||
\(299\) | 2.47990e6 | 1.60419 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.84236e6 | −1.80827 | ||||||||
\(302\) | 814371. | − | 684360.i | 0.513813 | − | 0.431785i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 250022. | − | 693272.i | 0.155165 | − | 0.430249i | ||||
\(305\) | − | 2.68178e6i | − | 1.65072i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.18446e6i | 0.717258i | 0.933480 | + | 0.358629i | \(0.116756\pi\) | ||||
−0.933480 | + | 0.358629i | \(0.883244\pi\) | |||||||
\(308\) | −1.04805e6 | − | 183210.i | −0.629513 | − | 0.110045i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.43902e6 | − | 1.71240e6i | −0.850479 | − | 1.01205i | ||||
\(311\) | 2.98276e6 | 1.74871 | 0.874354 | − | 0.485289i | \(-0.161286\pi\) | ||||
0.874354 | + | 0.485289i | \(0.161286\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.44466e6 | −1.41045 | −0.705224 | − | 0.708984i | \(-0.749154\pi\) | ||||
−0.705224 | + | 0.708984i | \(0.749154\pi\) | |||||||
\(314\) | −1.26710e6 | − | 1.50782e6i | −0.725249 | − | 0.863028i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −375914. | − | 65713.6i | −0.211773 | − | 0.0370201i | ||||
\(317\) | − | 164872.i | − | 0.0921508i | −0.998938 | − | 0.0460754i | \(-0.985329\pi\) | ||
0.998938 | − | 0.0460754i | \(-0.0146715\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23776.0i | 0.0130817i | ||||||||
\(320\) | −2.29131e6 | − | 1.30944e6i | −1.25086 | − | 0.714842i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.46217e6 | − | 2.06910e6i | 1.32336 | − | 1.11209i | ||||
\(323\) | −1.57192e6 | −0.838346 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.17906e6 | 1.66952 | ||||||||
\(326\) | −109407. | + | 91940.4i | −0.0570164 | + | 0.0479140i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 304968. | + | 525538.i | 0.156520 | + | 0.269724i | ||||
\(329\) | 2.04026e6i | 1.03919i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.03272e6i | 1.52147i | 0.649065 | + | 0.760733i | \(0.275160\pi\) | ||||
−0.649065 | + | 0.760733i | \(0.724840\pi\) | |||||||
\(332\) | −462543. | + | 2.64597e6i | −0.230307 | + | 1.31747i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.40124e6 | − | 1.66744e6i | −0.687300 | − | 0.817870i | ||||
\(335\) | 1.89209e6 | 0.921151 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.77189e6 | −1.32954 | −0.664769 | − | 0.747049i | \(-0.731470\pi\) | ||||
−0.664769 | + | 0.747049i | \(0.731470\pi\) | |||||||
\(338\) | 1.90390e6 | + | 2.26559e6i | 0.906468 | + | 1.07867i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −969299. | + | 5.54487e6i | −0.454737 | + | 2.60132i | ||||
\(341\) | − | 752856.i | − | 0.350611i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.90463e6i | − | 1.33308i | ||||||
\(344\) | −1.19106e6 | − | 2.05250e6i | −0.542671 | − | 0.935161i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.37212e6 | + | 1.99342e6i | −1.06524 | + | 0.895177i | ||||
\(347\) | 1.11916e6 | 0.498961 | 0.249481 | − | 0.968380i | \(-0.419740\pi\) | ||||
0.249481 | + | 0.968380i | \(0.419740\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.08395e6 | 0.915849 | 0.457925 | − | 0.888991i | \(-0.348593\pi\) | ||||
0.457925 | + | 0.888991i | \(0.348593\pi\) | |||||||
\(350\) | 3.15633e6 | − | 2.65244e6i | 1.37725 | − | 1.15738i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −306875. | − | 833578.i | −0.132009 | − | 0.358583i | ||||
\(353\) | 2.22872e6i | 0.951961i | 0.879456 | + | 0.475980i | \(0.157907\pi\) | ||||
−0.879456 | + | 0.475980i | \(0.842093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 193511.i | − | 0.0814957i | ||||||
\(356\) | 1.16004e6 | + | 202786.i | 0.485117 | + | 0.0848034i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.64070e6 | − | 1.95239e6i | −0.676585 | − | 0.805119i | ||||
\(359\) | −3.79795e6 | −1.55530 | −0.777649 | − | 0.628699i | \(-0.783588\pi\) | ||||
−0.777649 | + | 0.628699i | \(0.783588\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.95812e6 | 0.790810 | ||||||||
\(362\) | 5771.47 | + | 6867.90i | 0.00231481 | + | 0.00275456i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.46377e6 | + | 1.12993e6i | 2.55701 | + | 0.446992i | ||||
\(365\) | − | 392042.i | − | 0.154028i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.00563e6i | − | 0.389737i | −0.980829 | − | 0.194868i | \(-0.937572\pi\) | ||
0.980829 | − | 0.194868i | \(-0.0624280\pi\) | |||||||
\(368\) | 2.52586e6 | + | 910928.i | 0.972276 | + | 0.350642i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 39978.3 | − | 33595.9i | 0.0151817 | − | 0.0127580i | ||||
\(371\) | −4.25385e6 | −1.60453 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.13554e6 | 1.16692 | 0.583458 | − | 0.812143i | \(-0.301699\pi\) | ||||
0.583458 | + | 0.812143i | \(0.301699\pi\) | |||||||
\(374\) | −1.45046e6 | + | 1.21890e6i | −0.536199 | + | 0.450597i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.47329e6 | + | 854947.i | −0.537427 | + | 0.311867i | ||||
\(377\) | − | 146637.i | − | 0.0531363i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.35382e6i | 0.484133i | 0.970260 | + | 0.242066i | \(0.0778251\pi\) | ||||
−0.970260 | + | 0.242066i | \(0.922175\pi\) | |||||||
\(380\) | −319402. | + | 1.82714e6i | −0.113470 | + | 0.649101i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.13022e6 | + | 1.34493e6i | 0.396283 | + | 0.471566i | ||||
\(383\) | −3.31845e6 | −1.15595 | −0.577974 | − | 0.816055i | \(-0.696157\pi\) | ||||
−0.577974 | + | 0.816055i | \(0.696157\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.67775e6 | 0.920702 | ||||||||
\(386\) | 315788. | + | 375780.i | 0.107877 | + | 0.128370i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 155666. | − | 890486.i | 0.0524946 | − | 0.300295i | ||||
\(389\) | − | 3.73290e6i | − | 1.25076i | −0.780322 | − | 0.625378i | \(-0.784945\pi\) | ||
0.780322 | − | 0.625378i | \(-0.215055\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.72710e6i | − | 1.89449i | ||||||
\(392\) | 4.72889e6 | − | 2.74416e6i | 1.55433 | − | 0.901974i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.76160e6 | − | 1.48036e6i | 0.571697 | − | 0.480428i | ||||
\(395\) | 960458. | 0.309732 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −908240. | −0.289217 | −0.144609 | − | 0.989489i | \(-0.546192\pi\) | ||||
−0.144609 | + | 0.989489i | \(0.546192\pi\) | |||||||
\(398\) | −4.65452e6 | + | 3.91144e6i | −1.47288 | + | 1.23774i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.23797e6 | + | 1.16775e6i | 1.01187 | + | 0.364921i | ||||
\(401\) | − | 128575.i | − | 0.0399297i | −0.999801 | − | 0.0199649i | \(-0.993645\pi\) | ||
0.999801 | − | 0.0199649i | \(-0.00635544\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.64319e6i | 1.42414i | ||||||||
\(404\) | 127711. | + | 22325.3i | 0.0389293 | + | 0.00680524i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −122346. | − | 145589.i | −0.0368362 | − | 0.0438342i | ||||
\(407\) | 17576.4 | 0.00525950 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.22625e6 | 1.24924 | 0.624622 | − | 0.780927i | \(-0.285253\pi\) | ||||
0.624622 | + | 0.780927i | \(0.285253\pi\) | |||||||
\(410\) | −983851. | − | 1.17076e6i | −0.289048 | − | 0.343960i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.41647e6 | − | 597233.i | −0.991595 | − | 0.173341i | ||||
\(413\) | 4.68225e6i | 1.35077i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 6.76044e6i | − | 1.92688i | ||||||
\(416\) | 1.89263e6 | + | 5.14104e6i | 0.536207 | + | 1.45652i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −477954. | + | 401650.i | −0.133797 | + | 0.112437i | ||||
\(419\) | −2.78414e6 | −0.774739 | −0.387370 | − | 0.921924i | \(-0.626616\pi\) | ||||
−0.387370 | + | 0.921924i | \(0.626616\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.45303e6 | −0.674525 | −0.337262 | − | 0.941411i | \(-0.609501\pi\) | ||||
−0.337262 | + | 0.941411i | \(0.609501\pi\) | |||||||
\(422\) | −2.72772e6 | + | 2.29225e6i | −0.745621 | + | 0.626586i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.78252e6 | − | 3.07174e6i | −0.481527 | − | 0.829794i | ||||
\(425\) | − | 7.34174e6i | − | 1.97164i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.21969e6i | 1.91624i | ||||||||
\(428\) | −522174. | + | 2.98709e6i | −0.137786 | + | 0.788204i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.84245e6 | + | 4.57241e6i | 1.00216 | + | 1.19254i | ||||
\(431\) | 1.70611e6 | 0.442397 | 0.221199 | − | 0.975229i | \(-0.429003\pi\) | ||||
0.221199 | + | 0.975229i | \(0.429003\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 194630. | 0.0498872 | 0.0249436 | − | 0.999689i | \(-0.492059\pi\) | ||||
0.0249436 | + | 0.999689i | \(0.492059\pi\) | |||||||
\(434\) | 3.87403e6 | + | 4.60999e6i | 0.987275 | + | 1.17483i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 582462. | − | 3.33197e6i | 0.146741 | − | 0.839431i | ||||
\(437\) | − | 1.88719e6i | − | 0.472728i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 550852.i | 0.136419i | 0.997671 | + | 0.0682093i | \(0.0217286\pi\) | ||||
−0.997671 | + | 0.0682093i | \(0.978271\pi\) | |||||||
\(440\) | 1.12208e6 | + | 1.93363e6i | 0.276307 | + | 0.476148i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.94561e6 | − | 7.51748e6i | 2.17798 | − | 1.83028i | ||||
\(443\) | 5.84486e6 | 1.41503 | 0.707514 | − | 0.706700i | \(-0.249817\pi\) | ||||
0.707514 | + | 0.706700i | \(0.249817\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.96388e6 | −0.709514 | ||||||||
\(446\) | 5.53339e6 | − | 4.65001e6i | 1.31721 | − | 1.10692i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.16850e6 | + | 3.52517e6i | 1.45206 | + | 0.829822i | ||||
\(449\) | − | 3.10126e6i | − | 0.725977i | −0.931794 | − | 0.362989i | \(-0.881756\pi\) | ||
0.931794 | − | 0.362989i | \(-0.118244\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 514723.i | − | 0.119160i | ||||||
\(452\) | 2.54865e6 | + | 445530.i | 0.586765 | + | 0.102573i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.20648e6 | − | 6.19558e6i | −1.18551 | − | 1.41072i | ||||
\(455\) | −1.65149e7 | −3.73979 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 917472. | 0.205496 | 0.102748 | − | 0.994707i | \(-0.467237\pi\) | ||||
0.102748 | + | 0.994707i | \(0.467237\pi\) | |||||||
\(458\) | 2.25265e6 | + | 2.68059e6i | 0.501799 | + | 0.597128i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.65697e6 | − | 1.16371e6i | −1.46684 | − | 0.256418i | ||||
\(461\) | − | 7.26023e6i | − | 1.59110i | −0.605886 | − | 0.795552i | \(-0.707181\pi\) | ||
0.605886 | − | 0.795552i | \(-0.292819\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.02175e6i | 1.52227i | 0.648591 | + | 0.761137i | \(0.275359\pi\) | ||||
−0.648591 | + | 0.761137i | \(0.724641\pi\) | |||||||
\(464\) | 53863.4 | − | 149355.i | 0.0116144 | − | 0.0322050i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.69369e6 | + | 1.42330e6i | −0.361300 | + | 0.303620i | ||||
\(467\) | 2.85330e6 | 0.605417 | 0.302709 | − | 0.953083i | \(-0.402109\pi\) | ||||
0.302709 | + | 0.953083i | \(0.402109\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.09375e6 | −1.06931 | ||||||||
\(470\) | 3.28210e6 | − | 2.75813e6i | 0.685342 | − | 0.575930i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.38110e6 | + | 1.96204e6i | −0.698559 | + | 0.405372i | ||||
\(473\) | 2.01026e6i | 0.413142i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.41924e6i | − | 0.491978i | ||||||
\(476\) | 2.60947e6 | − | 1.49275e7i | 0.527880 | − | 3.01973i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.07655e6 | + | 6.04096e6i | 1.01625 | + | 1.20931i | ||||
\(479\) | 919797. | 0.183169 | 0.0915847 | − | 0.995797i | \(-0.470807\pi\) | ||||
0.0915847 | + | 0.995797i | \(0.470807\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −108401. | −0.0213635 | ||||||||
\(482\) | −2.71463e6 | − | 3.23034e6i | −0.532223 | − | 0.633331i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 757875. | − | 4.33542e6i | 0.147056 | − | 0.841235i | ||||
\(485\) | 2.27518e6i | 0.439200i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.70621e6i | − | 1.09025i | −0.838355 | − | 0.545124i | \(-0.816483\pi\) | ||
0.838355 | − | 0.545124i | \(-0.183517\pi\) | |||||||
\(488\) | −5.21341e6 | + | 3.02533e6i | −0.990997 | + | 0.575072i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.05347e7 | + | 8.85287e6i | −1.98213 | + | 1.66569i | ||||
\(491\) | 2.01852e6 | 0.377859 | 0.188930 | − | 0.981991i | \(-0.439498\pi\) | ||||
0.188930 | + | 0.981991i | \(0.439498\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −338645. | −0.0627519 | ||||||||
\(494\) | 2.94775e6 | − | 2.47715e6i | 0.543467 | − | 0.456705i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.70556e6 | + | 4.72923e6i | −0.311287 | + | 0.863150i | ||||
\(497\) | 520955.i | 0.0946040i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1.19282e6i | − | 0.214448i | −0.994235 | − | 0.107224i | \(-0.965804\pi\) | ||
0.994235 | − | 0.107224i | \(-0.0341962\pi\) | |||||||
\(500\) | −600238. | − | 104928.i | −0.107374 | − | 0.0187700i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.44808e6 | + | 5.29310e6i | 0.787796 | + | 0.937457i | ||||
\(503\) | −9.18424e6 | −1.61854 | −0.809270 | − | 0.587437i | \(-0.800137\pi\) | ||||
−0.809270 | + | 0.587437i | \(0.800137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −326302. | −0.0569365 | ||||||||
\(506\) | −1.46337e6 | − | 1.74137e6i | −0.254084 | − | 0.302353i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.51120e6 | + | 264172.i | 0.259813 | + | 0.0454180i | ||||
\(509\) | − | 1.17272e6i | − | 0.200632i | −0.994956 | − | 0.100316i | \(-0.968015\pi\) | ||
0.994956 | − | 0.100316i | \(-0.0319853\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.05542e6i | 0.178803i | ||||||||
\(512\) | 39277.0 | + | 5.93151e6i | 0.00662161 | + | 0.999978i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.76442e6 | + | 6.52486e6i | −1.29629 | + | 1.08934i | ||||
\(515\) | 8.72904e6 | 1.45027 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.44297e6 | 0.237428 | ||||||||
\(518\) | −107626. | + | 90444.3i | −0.0176236 | + | 0.0148101i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.92036e6 | − | 1.19256e7i | −1.12233 | − | 1.93406i | ||||
\(521\) | 6.12848e6i | 0.989141i | 0.869137 | + | 0.494571i | \(0.164675\pi\) | ||||
−0.869137 | + | 0.494571i | \(0.835325\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.43682e6i | 1.02900i | 0.857489 | + | 0.514502i | \(0.172023\pi\) | ||||
−0.857489 | + | 0.514502i | \(0.827977\pi\) | |||||||
\(524\) | −1.65951e6 | + | 9.49322e6i | −0.264029 | + | 1.51038i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.62614e6 | − | 4.31501e6i | −0.571452 | − | 0.680013i | ||||
\(527\) | 1.07230e7 | 1.68186 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 439409. | 0.0682700 | ||||||||
\(530\) | 5.75056e6 | + | 6.84302e6i | 0.889242 | + | 1.05818i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 859870. | − | 4.91888e6i | 0.131721 | − | 0.753507i | ||||
\(533\) | 3.17452e6i | 0.484016i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 7.63199e6i | − | 1.15280i | ||||||
\(536\) | −2.13447e6 | − | 3.67825e6i | −0.320907 | − | 0.553005i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.35667e6 | + | 7.86291e6i | −1.39369 | + | 1.17119i | ||||
\(539\) | −4.63157e6 | −0.686683 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.06503e7 | −1.56448 | −0.782238 | − | 0.622980i | \(-0.785922\pi\) | ||||
−0.782238 | + | 0.622980i | \(0.785922\pi\) | |||||||
\(542\) | −7.28126e6 | + | 6.11883e6i | −1.06465 | + | 0.894686i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.18727e7 | − | 4.37085e6i | 1.72010 | − | 0.633240i | ||||
\(545\) | 8.51315e6i | 1.22772i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.81400e6i | − | 0.259220i | −0.991565 | − | 0.129610i | \(-0.958628\pi\) | ||
0.991565 | − | 0.129610i | \(-0.0413725\pi\) | |||||||
\(548\) | −4.25062e6 | − | 743051.i | −0.604645 | − | 0.105698i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.87593e6 | − | 2.23231e6i | −0.264430 | − | 0.314665i | ||||
\(551\) | −111590. | −0.0156583 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.58567e6 | −0.359551 | ||||||||
\(554\) | 3.96206e6 | + | 4.71475e6i | 0.548462 | + | 0.652655i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.78072e6 | − | 486099.i | −0.381479 | − | 0.0666864i | ||||
\(557\) | − | 6.09580e6i | − | 0.832517i | −0.909246 | − | 0.416258i | \(-0.863341\pi\) | ||
0.909246 | − | 0.416258i | \(-0.136659\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.23981e7i | − | 1.67814i | ||||||
\(560\) | −1.68209e7 | − | 6.06631e6i | −2.26662 | − | 0.817437i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.15491e6 | − | 2.65124e6i | 0.421353 | − | 0.354086i | ||||
\(563\) | −2.10559e6 | −0.279964 | −0.139982 | − | 0.990154i | \(-0.544704\pi\) | ||||
−0.139982 | + | 0.990154i | \(0.544704\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.51178e6 | −0.858181 | ||||||||
\(566\) | −3.17735e6 | + | 2.67010e6i | −0.416893 | + | 0.350338i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −376187. | + | 218300.i | −0.0489252 | + | 0.0283911i | ||||
\(569\) | − | 8.26598e6i | − | 1.07032i | −0.844751 | − | 0.535160i | \(-0.820251\pi\) | ||
0.844751 | − | 0.535160i | \(-0.179749\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.32978e6i | 0.812453i | 0.913772 | + | 0.406227i | \(0.133156\pi\) | ||||
−0.913772 | + | 0.406227i | \(0.866844\pi\) | |||||||
\(572\) | 799144. | − | 4.57150e6i | 0.102126 | − | 0.584209i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.64865e6 | + | 3.15182e6i | 0.335540 | + | 0.399284i | ||||
\(575\) | 8.81423e6 | 1.11177 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.46843e7 | 1.83617 | 0.918087 | − | 0.396380i | \(-0.129734\pi\) | ||||
0.918087 | + | 0.396380i | \(0.129734\pi\) | |||||||
\(578\) | −1.21935e7 | − | 1.45100e7i | −1.51813 | − | 1.80654i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −68810.2 | + | 393628.i | −0.00849342 | + | 0.0485866i | ||||
\(581\) | 1.81999e7i | 2.23681i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.00853e6i | 0.366592i | ||||||||
\(584\) | −762132. | + | 442263.i | −0.0924694 | + | 0.0536597i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.73561e6 | − | 1.45852e6i | 0.208789 | − | 0.175457i | ||||
\(587\) | 3.94562e6 | 0.472628 | 0.236314 | − | 0.971677i | \(-0.424061\pi\) | ||||
0.236314 | + | 0.971677i | \(0.424061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.53343e6 | 0.419671 | ||||||||
\(590\) | 7.53218e6 | − | 6.32970e6i | 0.890822 | − | 0.748606i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −110410. | − | 39818.4i | −0.0129481 | − | 0.00466960i | ||||
\(593\) | 2.10090e6i | 0.245341i | 0.992447 | + | 0.122670i | \(0.0391458\pi\) | ||||
−0.992447 | + | 0.122670i | \(0.960854\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.81395e7i | 4.41655i | ||||||||
\(596\) | 1.33939e7 | + | 2.34138e6i | 1.54451 | + | 0.269996i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.02522e6 | + | 1.07398e7i | 1.03206 | + | 1.22813i | ||||
\(599\) | 1.27405e7 | 1.45084 | 0.725420 | − | 0.688307i | \(-0.241646\pi\) | ||||
0.725420 | + | 0.688307i | \(0.241646\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.23040e7 | −1.38951 | −0.694755 | − | 0.719246i | \(-0.744487\pi\) | ||||
−0.694755 | + | 0.719246i | \(0.744487\pi\) | |||||||
\(602\) | −1.03443e7 | − | 1.23095e7i | −1.16335 | − | 1.38436i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.92755e6 | + | 1.03620e6i | 0.661124 | + | 0.115571i | ||||
\(605\) | 1.10769e7i | 1.23036i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.64207e6i | − | 1.06218i | −0.847315 | − | 0.531091i | \(-0.821782\pi\) | ||
0.847315 | − | 0.531091i | \(-0.178218\pi\) | |||||||
\(608\) | 3.91229e6 | − | 1.44028e6i | 0.429212 | − | 0.158011i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.16141e7 | − | 9.75993e6i | 1.26375 | − | 1.06199i | ||||
\(611\) | −8.89944e6 | −0.964406 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.91038e6 | 1.06522 | 0.532610 | − | 0.846361i | \(-0.321211\pi\) | ||||
0.532610 | + | 0.846361i | \(0.321211\pi\) | |||||||
\(614\) | −5.12958e6 | + | 4.31067e6i | −0.549112 | + | 0.461449i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.02078e6 | − | 5.20557e6i | −0.320750 | − | 0.552735i | ||||
\(617\) | 1.03111e6i | 0.109041i | 0.998513 | + | 0.0545207i | \(0.0173631\pi\) | ||||
−0.998513 | + | 0.0545207i | \(0.982637\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3.43026e6i | − | 0.359833i | −0.983682 | − | 0.179917i | \(-0.942417\pi\) | ||
0.983682 | − | 0.179917i | \(-0.0575828\pi\) | |||||||
\(620\) | 2.17884e6 | − | 1.24640e7i | 0.227639 | − | 1.30220i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.08553e7 | + | 1.29175e7i | 1.12503 | + | 1.33876i | ||||
\(623\) | 7.97914e6 | 0.823637 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.97087e6 | −0.918618 | ||||||||
\(626\) | −8.89695e6 | − | 1.05871e7i | −0.907413 | − | 1.07980i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.91853e6 | − | 1.09749e7i | 0.194120 | − | 1.11046i | ||||
\(629\) | 250343.i | 0.0252295i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 3.03674e6i | − | 0.303623i | −0.988409 | − | 0.151811i | \(-0.951489\pi\) | ||
0.988409 | − | 0.151811i | \(-0.0485106\pi\) | |||||||
\(632\) | −1.08349e6 | − | 1.86714e6i | −0.107903 | − | 0.185944i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 714016. | − | 600026.i | 0.0705480 | − | 0.0592853i | ||||
\(635\) | −3.86109e6 | −0.379993 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.85649e7 | 2.78923 | ||||||||
\(638\) | −102968. | + | 86529.2i | −0.0100149 | + | 0.00841610i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.66806e6 | − | 1.46886e7i | −0.257481 | − | 1.41752i | ||||
\(641\) | − | 2.28706e6i | − | 0.219853i | −0.993940 | − | 0.109927i | \(-0.964938\pi\) | ||
0.993940 | − | 0.109927i | \(-0.0350616\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.33547e7i | − | 1.27382i | −0.770940 | − | 0.636908i | \(-0.780213\pi\) | ||
0.770940 | − | 0.636908i | \(-0.219787\pi\) | |||||||
\(644\) | 1.79214e7 | + | 3.13284e6i | 1.70277 | + | 0.297662i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.72074e6 | − | 6.80754e6i | −0.539351 | − | 0.641813i | ||||
\(647\) | 1.21139e7 | 1.13769 | 0.568843 | − | 0.822446i | \(-0.307391\pi\) | ||||
0.568843 | + | 0.822446i | \(0.307391\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.31152e6 | 0.308614 | ||||||||
\(650\) | 1.15697e7 | + | 1.37676e7i | 1.07409 | + | 1.27813i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −796337. | − | 139208.i | −0.0733631 | − | 0.0128246i | ||||
\(653\) | − | 5.51376e6i | − | 0.506017i | −0.967464 | − | 0.253008i | \(-0.918580\pi\) | ||
0.967464 | − | 0.253008i | \(-0.0814200\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.42551e7i | − | 2.20902i | ||||||
\(656\) | −1.16608e6 | + | 3.23335e6i | −0.105796 | + | 0.293354i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.83581e6 | + | 7.42521e6i | −0.795576 | + | 0.668566i | ||||
\(659\) | −7.16100e6 | −0.642333 | −0.321166 | − | 0.947023i | \(-0.604075\pi\) | ||||
−0.321166 | + | 0.947023i | \(0.604075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.29525e6 | −0.382371 | −0.191186 | − | 0.981554i | \(-0.561233\pi\) | ||||
−0.191186 | + | 0.981554i | \(0.561233\pi\) | |||||||
\(662\) | −1.31339e7 | + | 1.10371e7i | −1.16479 | + | 0.978836i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.31423e7 | + | 7.62646e6i | −1.15678 | + | 0.671279i | ||||
\(665\) | 1.25677e7i | 1.10205i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 406565.i | − | 0.0353847i | ||||||
\(668\) | 2.12163e6 | − | 1.21368e7i | 0.183962 | − | 1.05235i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.88598e6 | + | 8.19414e6i | 0.592623 | + | 0.705207i | ||||
\(671\) | 5.10612e6 | 0.437809 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.72112e6 | 0.742224 | 0.371112 | − | 0.928588i | \(-0.378977\pi\) | ||||
0.371112 | + | 0.928588i | \(0.378977\pi\) | |||||||
\(674\) | −1.00878e7 | − | 1.20043e7i | −0.855359 | − | 1.01786i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.88271e6 | + | 1.64905e7i | −0.242624 | + | 1.38793i | ||||
\(677\) | − | 1.55598e7i | − | 1.30476i | −0.757890 | − | 0.652382i | \(-0.773770\pi\) | ||
0.757890 | − | 0.652382i | \(-0.226230\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6.12507e6i | − | 0.509843i | ||||||
\(680\) | −2.75409e7 | + | 1.59819e7i | −2.28405 | + | 1.32543i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.26041e6 | − | 2.73990e6i | 0.268418 | − | 0.225566i | ||||
\(683\) | 1.62106e7 | 1.32968 | 0.664840 | − | 0.746986i | \(-0.268500\pi\) | ||||
0.664840 | + | 0.746986i | \(0.268500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.08603e7 | 0.884331 | ||||||||
\(686\) | 1.25792e7 | − | 1.05710e7i | 1.02057 | − | 0.857638i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.55413e6 | − | 1.26279e7i | 0.366804 | − | 1.01709i | ||||
\(689\) | − | 1.85549e7i | − | 1.48905i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.77172e7i | 1.41156i | 0.708429 | + | 0.705782i | \(0.249404\pi\) | ||||
−0.708429 | + | 0.705782i | \(0.750596\pi\) | |||||||
\(692\) | −1.72659e7 | − | 3.01826e6i | −1.37064 | − | 0.239603i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.07299e6 | + | 4.84676e6i | 0.321007 | + | 0.381990i | ||||
\(695\) | 7.10472e6 | 0.557937 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.33125e6 | 0.571605 | ||||||||
\(698\) | 7.58422e6 | + | 9.02502e6i | 0.589213 | + | 0.701148i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.29740e7 | + | 4.01608e6i | 1.77211 | + | 0.309783i | ||||
\(701\) | − | 1.38386e6i | − | 0.106364i | −0.998585 | − | 0.0531821i | \(-0.983064\pi\) | ||
0.998585 | − | 0.0531821i | \(-0.0169364\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 82492.7i | 0.00629545i | ||||||||
\(704\) | 2.49317e6 | − | 4.36267e6i | 0.189592 | − | 0.331757i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.65198e6 | + | 8.11108e6i | −0.728794 | + | 0.612445i | ||||
\(707\) | 878444. | 0.0660945 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.82723e6 | −0.285936 | −0.142968 | − | 0.989727i | \(-0.545665\pi\) | ||||
−0.142968 | + | 0.989727i | \(0.545665\pi\) | |||||||
\(710\) | 838043. | − | 704253.i | 0.0623908 | − | 0.0524304i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.34356e6 | + | 5.76181e6i | 0.247178 | + | 0.425950i | ||||
\(713\) | 1.28737e7i | 0.948371i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.16801e7i | 0.854442i | ||||||||
\(716\) | 2.48420e6 | − | 1.42109e7i | 0.181094 | − | 1.03595i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.38221e7 | − | 1.64479e7i | −1.00060 | − | 1.19069i | ||||
\(719\) | −1.09144e7 | −0.787365 | −0.393682 | − | 0.919247i | \(-0.628799\pi\) | ||||
−0.393682 | + | 0.919247i | \(0.628799\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.34997e7 | −1.68354 | ||||||||
\(722\) | 7.12628e6 | + | 8.48009e6i | 0.508768 | + | 0.605421i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8738.63 | + | 49989.3i | −0.000619580 | + | 0.00354430i | ||||
\(725\) | − | 521187.i | − | 0.0368255i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.42329e6i | − | 0.240219i | −0.992761 | − | 0.120110i | \(-0.961675\pi\) | ||
0.992761 | − | 0.120110i | \(-0.0383246\pi\) | |||||||
\(728\) | 1.86305e7 | + | 3.21050e7i | 1.30285 | + | 2.24515i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.69783e6 | − | 1.42677e6i | 0.117920 | − | 0.0990942i | ||||
\(731\) | −2.86323e7 | −1.98181 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.27970e6 | 0.0879724 | 0.0439862 | − | 0.999032i | \(-0.485994\pi\) | ||||
0.0439862 | + | 0.999032i | \(0.485994\pi\) | |||||||
\(734\) | 4.35509e6 | − | 3.65982e6i | 0.298371 | − | 0.250737i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.24749e6 | + | 1.42540e7i | 0.357073 | + | 0.969932i | ||||
\(737\) | 3.60255e6i | 0.244310i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 73084.4i | − | 0.00492281i | −0.999997 | − | 0.00246141i | \(-0.999217\pi\) | ||
0.999997 | − | 0.00246141i | \(-0.000783491\pi\) | |||||||
\(740\) | 290989. | + | 50867.9i | 0.0195343 | + | 0.00341479i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.54812e7 | − | 1.84222e7i | −1.03227 | − | 1.22838i | ||||
\(743\) | −2.23684e7 | −1.48649 | −0.743247 | − | 0.669017i | \(-0.766715\pi\) | ||||
−0.743247 | + | 0.669017i | \(0.766715\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.42212e7 | −2.25894 | ||||||||
\(746\) | 1.14113e7 | + | 1.35792e7i | 0.750737 | + | 0.893358i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.05574e7 | − | 1.84555e6i | −0.689929 | − | 0.120607i | ||||
\(749\) | 2.05462e7i | 1.33822i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.91551e7i | 1.23932i | 0.784869 | + | 0.619662i | \(0.212730\pi\) | ||||
−0.784869 | + | 0.619662i | \(0.787270\pi\) | |||||||
\(752\) | −9.06436e6 | − | 3.26898e6i | −0.584511 | − | 0.210798i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 635046. | − | 533663.i | 0.0406796 | − | 0.0341853i | ||||
\(755\) | −1.51448e7 | −0.966935 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.56784e6 | −0.416565 | −0.208283 | − | 0.978069i | \(-0.566787\pi\) | ||||
−0.208283 | + | 0.978069i | \(0.566787\pi\) | |||||||
\(758\) | −5.86304e6 | + | 4.92703e6i | −0.370638 | + | 0.311467i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.07525e6 | + | 5.26634e6i | −0.569934 | + | 0.330731i | ||||
\(761\) | − | 1.18923e7i | − | 0.744397i | −0.928153 | − | 0.372199i | \(-0.878604\pi\) | ||
0.928153 | − | 0.372199i | \(-0.121396\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 2.29185e7i | − | 1.42519i | ||||||
\(764\) | −1.71128e6 | + | 9.78935e6i | −0.106069 | + | 0.606765i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.20770e7 | − | 1.43713e7i | −0.743681 | − | 0.884961i | ||||
\(767\) | −2.04236e7 | −1.25356 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.93438e7 | 1.78937 | 0.894686 | − | 0.446695i | \(-0.147399\pi\) | ||||
0.894686 | + | 0.446695i | \(0.147399\pi\) | |||||||
\(770\) | 9.74527e6 | + | 1.15966e7i | 0.592334 | + | 0.704863i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −478138. | + | 2.73518e6i | −0.0288742 | + | 0.165175i | ||||
\(773\) | − | 2.17877e7i | − | 1.31148i | −0.754986 | − | 0.655741i | \(-0.772356\pi\) | ||
0.754986 | − | 0.655741i | \(-0.227644\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.65031e7i | 0.986988i | ||||||||
\(776\) | 4.42297e6 | − | 2.56664e6i | 0.263670 | − | 0.153007i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.61662e7 | − | 1.35853e7i | 0.957542 | − | 0.804675i | ||||
\(779\) | 2.41579e6 | 0.142631 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 368445. | 0.0216145 | ||||||||
\(782\) | 2.48025e7 | − | 2.08429e7i | 1.45037 | − | 1.21882i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.90942e7 | + | 1.04926e7i | 1.69051 | + | 0.609666i | ||||
\(785\) | 2.80409e7i | 1.62412i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.15045e7i | 1.23763i | 0.785536 | + | 0.618816i | \(0.212387\pi\) | ||||
−0.785536 | + | 0.618816i | \(0.787613\pi\) | |||||||
\(788\) | 1.28221e7 | + | 2.24143e6i | 0.735603 | + | 0.128591i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.49543e6 | + | 4.15948e6i | 0.199266 | + | 0.237122i | ||||
\(791\) | 1.75305e7 | 0.996216 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.14917e7 | −1.77833 | ||||||||
\(794\) | −3.30540e6 | − | 3.93334e6i | −0.186068 | − | 0.221417i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.38788e7 | − | 5.92235e6i | −1.89516 | − | 0.331292i | ||||
\(797\) | 1.17517e7i | 0.655322i | 0.944795 | + | 0.327661i | \(0.106260\pi\) | ||||
−0.944795 | + | 0.327661i | \(0.893740\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.05524e7i | 1.13893i | ||||||||
\(800\) | 6.72691e6 | + | 1.82726e7i | 0.371613 | + | 1.00943i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 556824. | − | 467930.i | 0.0305691 | − | 0.0256888i | ||||
\(803\) | 746448. | 0.0408517 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.57890e7 | −2.49041 | ||||||||
\(806\) | −2.01084e7 | + | 1.68982e7i | −1.09028 | + | 0.916225i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 368101. | + | 634333.i | 0.0198353 | + | 0.0341813i | ||||
\(809\) | − | 2.46613e7i | − | 1.32479i | −0.749157 | − | 0.662393i | \(-0.769541\pi\) | ||
0.749157 | − | 0.662393i | \(-0.230459\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.20425e7i | − | 1.71070i | −0.518047 | − | 0.855352i | \(-0.673341\pi\) | ||
0.518047 | − | 0.855352i | \(-0.326659\pi\) | |||||||
\(812\) | 185245. | − | 1.05970e6i | 0.00985956 | − | 0.0564015i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 63966.6 | + | 76118.6i | 0.00338370 | + | 0.00402652i | ||||
\(815\) | 2.03463e6 | 0.107298 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.43489e6 | −0.494517 | ||||||||
\(818\) | 1.53808e7 | + | 1.83027e7i | 0.803702 | + | 0.956385i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.48966e6 | − | 8.52158e6i | 0.0773663 | − | 0.442573i | ||||
\(821\) | − | 2.68961e7i | − | 1.39262i | −0.717743 | − | 0.696308i | \(-0.754825\pi\) | ||
0.717743 | − | 0.696308i | \(-0.245175\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 3.24237e7i | − | 1.66864i | −0.551278 | − | 0.834321i | \(-0.685860\pi\) | ||
0.551278 | − | 0.834321i | \(-0.314140\pi\) | |||||||
\(824\) | −9.84724e6 | − | 1.69693e7i | −0.505239 | − | 0.870656i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.02776e7 | + | 1.70403e7i | −1.03411 | + | 0.869016i | ||||
\(827\) | −1.20579e6 | −0.0613065 | −0.0306533 | − | 0.999530i | \(-0.509759\pi\) | ||||
−0.0306533 | + | 0.999530i | \(0.509759\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.69091e7 | 0.854545 | 0.427273 | − | 0.904123i | \(-0.359474\pi\) | ||||
0.427273 | + | 0.904123i | \(0.359474\pi\) | |||||||
\(830\) | 2.92776e7 | − | 2.46036e7i | 1.47516 | − | 1.23966i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.53765e7 | + | 2.69065e7i | −0.770103 | + | 1.34756i | ||||
\(833\) | − | 6.59679e7i | − | 3.29397i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.10094e7i | 1.53913i | ||||||||
\(836\) | −3.47887e6 | − | 608142.i | −0.172156 | − | 0.0300947i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.01324e7 | − | 1.20573e7i | −0.498429 | − | 0.593118i | ||||
\(839\) | −3.21837e6 | −0.157845 | −0.0789226 | − | 0.996881i | \(-0.525148\pi\) | ||||
−0.0789226 | + | 0.996881i | \(0.525148\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.04871e7 | 0.998828 | ||||||||
\(842\) | −8.92742e6 | − | 1.06234e7i | −0.433956 | − | 0.516397i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.98542e7 | − | 3.47071e6i | −0.959392 | − | 0.167711i | ||||
\(845\) | − | 4.21332e7i | − | 2.02994i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.98205e7i | − | 1.42826i | ||||||
\(848\) | 6.81566e6 | − | 1.88987e7i | 0.325475 | − | 0.902492i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.17950e7 | − | 2.67191e7i | 1.50943 | − | 1.26845i | ||||
\(851\) | −300553. | −0.0142264 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.33124e7 | 1.09702 | 0.548510 | − | 0.836144i | \(-0.315195\pi\) | ||||
0.548510 | + | 0.836144i | \(0.315195\pi\) | |||||||
\(854\) | −3.12665e7 | + | 2.62749e7i | −1.46702 | + | 1.23281i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.48366e7 | + | 8.60965e6i | −0.692072 | + | 0.401607i | ||||
\(857\) | 1.65961e7i | 0.771885i | 0.922523 | + | 0.385943i | \(0.126124\pi\) | ||||
−0.922523 | + | 0.385943i | \(0.873876\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 3.87503e6i | − | 0.179181i | −0.995979 | − | 0.0895906i | \(-0.971444\pi\) | ||
0.995979 | − | 0.0895906i | \(-0.0285559\pi\) | |||||||
\(860\) | −5.81788e6 | + | 3.32812e7i | −0.268237 | + | 1.53445i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.20910e6 | + | 7.38867e6i | 0.284617 | + | 0.338687i | ||||
\(863\) | −2.73653e7 | −1.25076 | −0.625380 | − | 0.780321i | \(-0.715056\pi\) | ||||
−0.625380 | + | 0.780321i | \(0.715056\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.41143e7 | 2.00465 | ||||||||
\(866\) | 708324. | + | 842888.i | 0.0320950 | + | 0.0381922i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.86570e6 | + | 3.35547e7i | −0.264253 | + | 1.51166i | ||||
\(869\) | 1.82871e6i | 0.0821478i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.22185e7i | − | 0.992360i | ||||||
\(872\) | 1.65496e7 | − | 9.60370e6i | 0.737050 | − | 0.427708i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.17289e6 | − | 6.86812e6i | 0.361907 | − | 0.304130i | ||||
\(875\) | −4.12864e6 | −0.182300 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.11018e6 | 0.180452 | 0.0902260 | − | 0.995921i | \(-0.471241\pi\) | ||||
0.0902260 | + | 0.995921i | \(0.471241\pi\) | |||||||
\(878\) | −2.38559e6 | + | 2.00474e6i | −0.104438 | + | 0.0877650i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.29039e6 | + | 1.18966e7i | −0.186763 | + | 0.517863i | ||||
\(881\) | 2.51778e7i | 1.09289i | 0.837494 | + | 0.546446i | \(0.184020\pi\) | ||||
−0.837494 | + | 0.546446i | \(0.815980\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.79618e7i | − | 0.775261i | −0.921815 | − | 0.387631i | \(-0.873294\pi\) | ||
0.921815 | − | 0.387631i | \(-0.126706\pi\) | |||||||
\(884\) | 6.51123e7 | + | 1.13823e7i | 2.80241 | + | 0.489890i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.12714e7 | + | 2.53125e7i | 0.910359 | + | 1.08330i | ||||
\(887\) | 3.60977e7 | 1.54053 | 0.770266 | − | 0.637723i | \(-0.220124\pi\) | ||||
0.770266 | + | 0.637723i | \(0.220124\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.03945e7 | 0.441114 | ||||||||
\(890\) | −1.07866e7 | − | 1.28358e7i | −0.456467 | − | 0.543184i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.02758e7 | + | 7.04062e6i | 1.69485 | + | 0.296278i | ||||
\(893\) | 6.77241e6i | 0.284194i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.63086e7i | 1.51514i | ||||||||
\(896\) | 7.18274e6 | + | 3.95434e7i | 0.298896 | + | 1.64552i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.34307e7 | − | 1.12866e7i | 0.555787 | − | 0.467058i | ||||
\(899\) | 761222. | 0.0314132 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.28508e7 | −1.75852 | ||||||||
\(902\) | 2.22912e6 | − | 1.87325e6i | 0.0912258 | − | 0.0766620i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.34595e6 | + | 1.26589e7i | 0.298969 | + | 0.515201i | ||||
\(905\) | − | 127722.i | − | 0.00518376i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.22058e7i | 1.29992i | 0.759970 | + | 0.649958i | \(0.225214\pi\) | ||||
−0.759970 | + | 0.649958i | \(0.774786\pi\) | |||||||
\(908\) | 7.88318e6 | − | 4.50957e7i | 0.317312 | − | 1.81518i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.01033e7 | − | 7.15214e7i | −2.40600 | − | 2.86307i | ||||
\(911\) | −3.74348e7 | −1.49444 | −0.747222 | − | 0.664574i | \(-0.768613\pi\) | ||||
−0.747222 | + | 0.664574i | \(0.768613\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.28719e7 | 0.511052 | ||||||||
\(914\) | 3.33900e6 | + | 3.97332e6i | 0.132206 | + | 0.157322i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.41075e6 | + | 1.95112e7i | −0.134311 | + | 0.768325i | ||||
\(917\) | 6.52977e7i | 2.56433i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.15460e7i | 1.23213i | 0.787696 | + | 0.616064i | \(0.211274\pi\) | ||||
−0.787696 | + | 0.616064i | \(0.788726\pi\) | |||||||
\(920\) | −1.91873e7 | − | 3.30646e7i | −0.747385 | − | 1.28794i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.14421e7 | − | 2.64225e7i | 1.21810 | − | 1.02364i | ||||
\(923\) | −2.27236e6 | −0.0877957 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −385287. | −0.0148057 | ||||||||
\(926\) | −3.04093e7 | + | 2.55546e7i | −1.16541 | + | 0.979357i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 842841. | − | 310285.i | 0.0321274 | − | 0.0118274i | ||||
\(929\) | 3.56283e7i | 1.35443i | 0.735786 | + | 0.677214i | \(0.236813\pi\) | ||||
−0.735786 | + | 0.677214i | \(0.763187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.17377e7i | − | 0.821938i | ||||||
\(932\) | −1.23278e7 | − | 2.15503e6i | −0.464886 | − | 0.0812668i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.03841e7 | + | 1.23568e7i | 0.389496 | + | 0.463490i | ||||
\(935\) | 2.69741e7 | 1.00906 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.27092e7 | 1.58918 | 0.794588 | − | 0.607149i | \(-0.207687\pi\) | ||||
0.794588 | + | 0.607149i | \(0.207687\pi\) | |||||||
\(938\) | −1.85379e7 | − | 2.20596e7i | −0.687945 | − | 0.818637i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.38894e7 | + | 4.17610e6i | 0.881830 | + | 0.154153i | ||||
\(941\) | 2.64684e7i | 0.974435i | 0.873281 | + | 0.487218i | \(0.161988\pi\) | ||||
−0.873281 | + | 0.487218i | \(0.838012\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.80164e6i | 0.322318i | ||||||||
\(944\) | −2.08020e7 | − | 7.50207e6i | −0.759759 | − | 0.274000i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.70588e6 | + | 7.31602e6i | −0.316289 | + | 0.265795i | ||||
\(947\) | 8.86252e6 | 0.321131 | 0.160566 | − | 0.987025i | \(-0.448668\pi\) | ||||
0.160566 | + | 0.987025i | \(0.448668\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.60367e6 | −0.165935 | ||||||||
\(950\) | 1.04771e7 | − | 8.80445e6i | 0.376644 | − | 0.316514i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.41435e7 | − | 4.30252e7i | 2.65143 | − | 1.53862i | ||||
\(953\) | − | 2.07166e7i | − | 0.738901i | −0.929250 | − | 0.369450i | \(-0.879546\pi\) | ||
0.929250 | − | 0.369450i | \(-0.120454\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2.50117e7i | − | 0.887432i | ||||||
\(956\) | −7.68645e6 | + | 4.39703e7i | −0.272007 | + | 1.55602i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.34746e6 | + | 3.98339e6i | 0.117842 | + | 0.140229i | ||||
\(959\) | −2.92372e7 | −1.02657 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.52545e6 | 0.158072 | ||||||||
\(962\) | −394510. | − | 469457.i | −0.0137442 | − | 0.0163553i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.11025e6 | − | 2.35127e7i | 0.142454 | − | 0.814909i | ||||
\(965\) | − | 6.98837e6i | − | 0.241578i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.43752e7i | − | 1.52607i | −0.646358 | − | 0.763035i | \(-0.723709\pi\) | ||
0.646358 | − | 0.763035i | \(-0.276291\pi\) | |||||||
\(968\) | 2.15337e7 | − | 1.24959e7i | 0.738634 | − | 0.428627i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.85320e6 | + | 8.28017e6i | −0.336239 | + | 0.282560i | ||||
\(971\) | 2.88625e7 | 0.982396 | 0.491198 | − | 0.871048i | \(-0.336559\pi\) | ||||
0.491198 | + | 0.871048i | \(0.336559\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.91268e7 | −0.647679 | ||||||||
\(974\) | 2.47120e7 | − | 2.07669e7i | 0.834663 | − | 0.701412i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.20752e7 | − | 1.15676e7i | −1.07782 | − | 0.388705i | ||||
\(977\) | 4.81221e6i | 0.161290i | 0.996743 | + | 0.0806451i | \(0.0256980\pi\) | ||||
−0.996743 | + | 0.0806451i | \(0.974302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5.64324e6i | − | 0.188179i | ||||||
\(980\) | −7.66787e7 | − | 1.34042e7i | −2.55041 | − | 0.445837i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.34610e6 | + | 8.74168e6i | 0.243096 | + | 0.289278i | ||||
\(983\) | −2.99778e7 | −0.989502 | −0.494751 | − | 0.869035i | \(-0.664741\pi\) | ||||
−0.494751 | + | 0.869035i | \(0.664741\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.27603e7 | −1.07587 | ||||||||
\(986\) | −1.23244e6 | − | 1.46658e6i | −0.0403715 | − | 0.0480410i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.14557e7 | + | 3.75068e6i | 0.699280 | + | 0.122241i | ||||
\(989\) | − | 3.43749e7i | − | 1.11751i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.75969e6i | 0.315683i | 0.987464 | + | 0.157842i | \(0.0504536\pi\) | ||||
−0.987464 | + | 0.157842i | \(0.949546\pi\) | |||||||
\(992\) | −2.66881e7 | + | 9.82501e6i | −0.861070 | + | 0.316996i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.25611e6 | + | 1.89593e6i | −0.0724261 | + | 0.0608636i | ||||
\(995\) | 8.65599e7 | 2.77178 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.77818e7 | 1.52238 | 0.761192 | − | 0.648527i | \(-0.224614\pi\) | ||||
0.761192 | + | 0.648527i | \(0.224614\pi\) | |||||||
\(998\) | 5.16576e6 | − | 4.34107e6i | 0.164175 | − | 0.137965i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.6.b.c.107.14 | yes | 20 | |
3.2 | odd | 2 | inner | 108.6.b.c.107.7 | ✓ | 20 | |
4.3 | odd | 2 | inner | 108.6.b.c.107.8 | yes | 20 | |
12.11 | even | 2 | inner | 108.6.b.c.107.13 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.b.c.107.7 | ✓ | 20 | 3.2 | odd | 2 | inner | |
108.6.b.c.107.8 | yes | 20 | 4.3 | odd | 2 | inner | |
108.6.b.c.107.13 | yes | 20 | 12.11 | even | 2 | inner | |
108.6.b.c.107.14 | yes | 20 | 1.1 | even | 1 | trivial |