Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(37,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.37");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.e (of order \(3\), degree \(2\), not 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: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 175x^{8} + 8800x^{6} + 124623x^{4} + 498609x^{2} + 442368 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{16} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 73.1 | ||
Root | \(-3.71922i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.73 |
Dual form | 108.6.e.a.37.1 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −40.7270 | − | 70.5412i | −0.728546 | − | 1.26188i | −0.957498 | − | 0.288441i | \(-0.906863\pi\) |
0.228951 | − | 0.973438i | \(-0.426470\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 89.6312 | − | 155.246i | 0.691376 | − | 1.19750i | −0.280012 | − | 0.959997i | \(-0.590338\pi\) |
0.971387 | − | 0.237501i | \(-0.0763283\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −250.250 | + | 433.446i | −0.623581 | + | 1.08007i | 0.365232 | + | 0.930916i | \(0.380990\pi\) |
−0.988813 | + | 0.149158i | \(0.952344\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 275.245 | + | 476.739i | 0.451712 | + | 0.782388i | 0.998493 | − | 0.0548877i | \(-0.0174801\pi\) |
−0.546780 | + | 0.837276i | \(0.684147\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −753.636 | −0.632469 | −0.316234 | − | 0.948681i | \(-0.602419\pi\) | ||||
−0.316234 | + | 0.948681i | \(0.602419\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2570.83 | −1.63376 | −0.816882 | − | 0.576805i | \(-0.804299\pi\) | ||||
−0.816882 | + | 0.576805i | \(0.804299\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1372.72 | − | 2377.63i | −0.541083 | − | 0.937183i | −0.998842 | − | 0.0481071i | \(-0.984681\pi\) |
0.457759 | − | 0.889076i | \(-0.348652\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1754.87 | + | 3039.53i | −0.561560 | + | 0.972650i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1954.86 | − | 3385.92i | 0.431639 | − | 0.747621i | −0.565376 | − | 0.824834i | \(-0.691269\pi\) |
0.997015 | + | 0.0772128i | \(0.0246021\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1552.42 | + | 2688.87i | 0.290138 | + | 0.502534i | 0.973842 | − | 0.227226i | \(-0.0729655\pi\) |
−0.683704 | + | 0.729759i | \(0.739632\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14601.6 | −2.01480 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9568.10 | −1.14900 | −0.574502 | − | 0.818503i | \(-0.694804\pi\) | ||||
−0.574502 | + | 0.818503i | \(0.694804\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1113.47 | + | 1928.59i | 0.103447 | + | 0.179176i | 0.913103 | − | 0.407730i | \(-0.133679\pi\) |
−0.809656 | + | 0.586905i | \(0.800346\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7143.42 | + | 12372.8i | −0.589162 | + | 1.02046i | 0.405180 | + | 0.914237i | \(0.367209\pi\) |
−0.994342 | + | 0.106222i | \(0.966125\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3236.07 | + | 5605.04i | −0.213685 | + | 0.370112i | −0.952865 | − | 0.303395i | \(-0.901880\pi\) |
0.739180 | + | 0.673508i | \(0.235213\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7664.00 | − | 13274.4i | −0.456000 | − | 0.789816i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13692.2 | −0.669553 | −0.334777 | − | 0.942298i | \(-0.608661\pi\) | ||||
−0.334777 | + | 0.942298i | \(0.608661\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 40767.8 | 1.81723 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2854.22 | + | 4943.65i | 0.106747 | + | 0.184892i | 0.914451 | − | 0.404697i | \(-0.132623\pi\) |
−0.807703 | + | 0.589589i | \(0.799290\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5899.59 | − | 10218.4i | 0.203000 | − | 0.351607i | −0.746493 | − | 0.665393i | \(-0.768264\pi\) |
0.949494 | + | 0.313786i | \(0.101597\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22419.8 | − | 38832.3i | 0.658186 | − | 1.14001i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1771.66 | + | 3068.60i | 0.0482162 | + | 0.0835129i | 0.889126 | − | 0.457662i | \(-0.151313\pi\) |
−0.840910 | + | 0.541175i | \(0.817980\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 58429.0 | 1.37557 | 0.687785 | − | 0.725914i | \(-0.258583\pi\) | ||||
0.687785 | + | 0.725914i | \(0.258583\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −60181.3 | −1.32176 | −0.660882 | − | 0.750490i | \(-0.729818\pi\) | ||||
−0.660882 | + | 0.750490i | \(0.729818\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 44860.5 | + | 77700.6i | 0.862258 | + | 1.49347i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 27811.7 | − | 48171.3i | 0.501372 | − | 0.868401i | −0.498627 | − | 0.866817i | \(-0.666162\pi\) |
0.999999 | − | 0.00158440i | \(-0.000504331\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 19990.3 | − | 34624.2i | 0.318511 | − | 0.551677i | −0.661667 | − | 0.749798i | \(-0.730151\pi\) |
0.980178 | + | 0.198121i | \(0.0634839\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 30693.3 | + | 53162.4i | 0.460783 | + | 0.798099i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −103171. | −1.38065 | −0.690327 | − | 0.723498i | \(-0.742533\pi\) | ||||
−0.690327 | + | 0.723498i | \(0.742533\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 98682.3 | 1.24921 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 104702. | + | 181349.i | 1.19027 | + | 2.06161i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 82996.9 | − | 143755.i | 0.895638 | − | 1.55129i | 0.0626259 | − | 0.998037i | \(-0.480053\pi\) |
0.833013 | − | 0.553254i | \(-0.186614\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 82524.4 | − | 142936.i | 0.804969 | − | 1.39425i | −0.111344 | − | 0.993782i | \(-0.535515\pi\) |
0.916312 | − | 0.400464i | \(-0.131151\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −36430.5 | − | 63099.4i | −0.338354 | − | 0.586047i | 0.645769 | − | 0.763533i | \(-0.276537\pi\) |
−0.984123 | + | 0.177486i | \(0.943204\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −123024. | −1.03880 | −0.519399 | − | 0.854532i | \(-0.673844\pi\) | ||||
−0.519399 | + | 0.854532i | \(0.673844\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 24274.5 | 0.195697 | 0.0978486 | − | 0.995201i | \(-0.468804\pi\) | ||||
0.0978486 | + | 0.995201i | \(0.468804\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −100686. | − | 174394.i | −0.741778 | − | 1.28480i | −0.951685 | − | 0.307075i | \(-0.900650\pi\) |
0.209908 | − | 0.977721i | \(-0.432684\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −111814. | + | 193667.i | −0.788408 | + | 1.36556i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −67549.3 | + | 116999.i | −0.437274 | + | 0.757380i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −44725.0 | − | 77465.9i | −0.277707 | − | 0.481002i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 31339.2 | 0.179396 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −104163. | −0.573067 | −0.286534 | − | 0.958070i | \(-0.592503\pi\) | ||||
−0.286534 | + | 0.958070i | \(0.592503\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 89424.9 | + | 154888.i | 0.455282 | + | 0.788571i | 0.998704 | − | 0.0508883i | \(-0.0162053\pi\) |
−0.543423 | + | 0.839459i | \(0.682872\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −230426. | + | 399110.i | −1.12954 | + | 1.95643i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 67651.3 | − | 117176.i | 0.307946 | − | 0.533378i | −0.669967 | − | 0.742391i | \(-0.733692\pi\) |
0.977913 | + | 0.209013i | \(0.0670250\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 113083. | + | 195866.i | 0.496434 | + | 0.859848i | 0.999992 | − | 0.00411320i | \(-0.00130927\pi\) |
−0.503558 | + | 0.863961i | \(0.667976\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −275521. | −1.12672 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −318462. | −1.25788 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −171449. | − | 296958.i | −0.632657 | − | 1.09579i | −0.987006 | − | 0.160680i | \(-0.948631\pi\) |
0.354350 | − | 0.935113i | \(-0.384702\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 121970. | − | 211258.i | 0.435322 | − | 0.754000i | −0.562000 | − | 0.827137i | \(-0.689968\pi\) |
0.997322 | + | 0.0731373i | \(0.0233011\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 126451. | − | 219019.i | 0.422758 | − | 0.732238i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −174438. | − | 302136.i | −0.564797 | − | 0.978257i | −0.997069 | − | 0.0765136i | \(-0.975621\pi\) |
0.432272 | − | 0.901743i | \(-0.357712\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −492156. | −1.49637 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 303629. | 0.895107 | 0.447553 | − | 0.894257i | \(-0.352295\pi\) | ||||
0.447553 | + | 0.894257i | \(0.352295\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16387.7 | − | 28384.4i | −0.0454703 | − | 0.0787568i | 0.842395 | − | 0.538861i | \(-0.181145\pi\) |
−0.887865 | + | 0.460104i | \(0.847812\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 34126.4 | − | 59108.7i | 0.0919123 | − | 0.159197i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −177651. | + | 307701.i | −0.451287 | + | 0.781652i | −0.998466 | − | 0.0553636i | \(-0.982368\pi\) |
0.547179 | + | 0.837015i | \(0.315702\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 314583. | + | 544873.i | 0.776497 | + | 1.34493i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 459272. | 1.07137 | 0.535683 | − | 0.844419i | \(-0.320054\pi\) | ||||
0.535683 | + | 0.844419i | \(0.320054\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −190088. | −0.431279 | −0.215640 | − | 0.976473i | \(-0.569184\pi\) | ||||
−0.215640 | + | 0.976473i | \(0.569184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 389680. | + | 674945.i | 0.837103 | + | 1.44990i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 188598. | − | 326661.i | 0.394396 | − | 0.683113i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −344280. | + | 596310.i | −0.682854 | + | 1.18274i | 0.291252 | + | 0.956646i | \(0.405928\pi\) |
−0.974106 | + | 0.226092i | \(0.927405\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −172138. | − | 298152.i | −0.332648 | − | 0.576163i | 0.650382 | − | 0.759607i | \(-0.274609\pi\) |
−0.983030 | + | 0.183444i | \(0.941275\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 596238. | 1.09460 | 0.547298 | − | 0.836938i | \(-0.315656\pi\) | ||||
0.547298 | + | 0.836938i | \(0.315656\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −49436.6 | −0.0884945 | −0.0442473 | − | 0.999021i | \(-0.514089\pi\) | ||||
−0.0442473 | + | 0.999021i | \(0.514089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −350433. | − | 606968.i | −0.596849 | − | 1.03377i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 90696.5 | − | 157091.i | 0.150732 | − | 0.261076i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 643351. | − | 1.11432e6i | 1.01878 | − | 1.76459i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 75999.1 | + | 131634.i | 0.117518 | + | 0.203546i | 0.918783 | − | 0.394762i | \(-0.129173\pi\) |
−0.801266 | + | 0.598309i | \(0.795840\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.16372e6 | 1.71693 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 556580. | 0.802377 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −207435. | − | 359288.i | −0.285694 | − | 0.494836i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 281057. | − | 486805.i | 0.378471 | − | 0.655531i | −0.612369 | − | 0.790572i | \(-0.709783\pi\) |
0.990840 | + | 0.135041i | \(0.0431167\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −630493. | + | 1.09205e6i | −0.812111 | + | 1.40662i | 0.0992724 | + | 0.995060i | \(0.468348\pi\) |
−0.911384 | + | 0.411558i | \(0.864985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −69803.7 | − | 120904.i | −0.0879609 | − | 0.152353i | 0.818688 | − | 0.574238i | \(-0.194702\pi\) |
−0.906649 | + | 0.421886i | \(0.861368\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.18799e6 | 1.43358 | 0.716790 | − | 0.697289i | \(-0.245610\pi\) | ||||
0.716790 | + | 0.697289i | \(0.245610\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 527181. | 0.622716 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −164952. | − | 285705.i | −0.186794 | − | 0.323536i | 0.757386 | − | 0.652968i | \(-0.226476\pi\) |
−0.944179 | + | 0.329432i | \(0.893143\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −84372.3 | + | 146137.i | −0.0935745 | + | 0.162076i | −0.909013 | − | 0.416768i | \(-0.863163\pi\) |
0.815438 | + | 0.578844i | \(0.196496\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −624263. | + | 1.08126e6i | −0.664435 | + | 1.15083i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −707609. | − | 1.22561e6i | −0.737991 | − | 1.27824i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 224796. | 0.225218 | 0.112609 | − | 0.993639i | \(-0.464079\pi\) | ||||
0.112609 | + | 0.993639i | \(0.464079\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.37410e6 | 1.34964 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 347968. | + | 602698.i | 0.328629 | + | 0.569203i | 0.982240 | − | 0.187628i | \(-0.0600799\pi\) |
−0.653611 | + | 0.756831i | \(0.726747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −857600. | + | 1.48541e6i | −0.794393 | + | 1.37593i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −241366. | + | 418057.i | −0.215172 | + | 0.372689i | −0.953326 | − | 0.301944i | \(-0.902365\pi\) |
0.738154 | + | 0.674633i | \(0.235698\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 557644. | + | 965867.i | 0.487800 | + | 0.844895i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.23733e6 | −1.88516 | −0.942581 | − | 0.333978i | \(-0.891609\pi\) | ||||
−0.942581 | + | 0.333978i | \(0.891609\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.74480e6 | −1.44318 | −0.721592 | − | 0.692318i | \(-0.756589\pi\) | ||||
−0.721592 | + | 0.692318i | \(0.756589\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −878315. | − | 1.52129e6i | −0.700356 | − | 1.21305i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 378971. | − | 656397.i | 0.296761 | − | 0.514005i | −0.678632 | − | 0.734478i | \(-0.737427\pi\) |
0.975393 | + | 0.220474i | \(0.0707603\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 215216. | − | 372764.i | 0.162595 | − | 0.281623i | −0.773203 | − | 0.634158i | \(-0.781347\pi\) |
0.935799 | + | 0.352535i | \(0.114680\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −478649. | − | 829044.i | −0.355264 | − | 0.615335i | 0.631899 | − | 0.775051i | \(-0.282276\pi\) |
−0.987163 | + | 0.159716i | \(0.948942\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 399206. | 0.286083 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −851890. | −0.599983 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −283147. | − | 490425.i | −0.192683 | − | 0.333737i | 0.753456 | − | 0.657499i | \(-0.228386\pi\) |
−0.946138 | + | 0.323762i | \(0.895052\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 232487. | − | 402680.i | 0.155541 | − | 0.269404i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 755673. | − | 1.30886e6i | 0.488828 | − | 0.846674i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.28055e6 | + | 2.21797e6i | 0.814665 | + | 1.41104i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −961090. | −0.591581 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.00565e6 | −1.21453 | −0.607265 | − | 0.794499i | \(-0.707733\pi\) | ||||
−0.607265 | + | 0.794499i | \(0.707733\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.05835e6 | − | 1.83312e6i | −0.620481 | − | 1.07471i | −0.989396 | − | 0.145242i | \(-0.953604\pi\) |
0.368915 | − | 0.929463i | \(-0.379729\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −606669. | + | 1.05078e6i | −0.350018 | + | 0.606249i | −0.986252 | − | 0.165247i | \(-0.947158\pi\) |
0.636234 | + | 0.771496i | \(0.280491\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.28378e6 | + | 2.22357e6i | −0.717533 | + | 1.24280i | 0.244441 | + | 0.969664i | \(0.421396\pi\) |
−0.961974 | + | 0.273140i | \(0.911938\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 978409. | + | 1.69465e6i | 0.538324 | + | 0.932404i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.93747e6 | 1.03330 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.93208e6 | −1.01465 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 580105. | + | 1.00477e6i | 0.295473 | + | 0.511773i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −721129. | + | 1.24903e6i | −0.361778 | + | 0.626619i | −0.988254 | − | 0.152823i | \(-0.951164\pi\) |
0.626475 | + | 0.779441i | \(0.284497\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 144309. | − | 249950.i | 0.0702555 | − | 0.121686i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −790934. | − | 1.36994e6i | −0.379372 | − | 0.657092i | 0.611599 | − | 0.791168i | \(-0.290527\pi\) |
−0.990971 | + | 0.134076i | \(0.957193\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.55397e6 | −0.723698 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 265129. | 0.121681 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −824985. | − | 1.42892e6i | −0.367809 | − | 0.637064i | 0.621414 | − | 0.783483i | \(-0.286559\pi\) |
−0.989223 | + | 0.146419i | \(0.953225\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −325183. | + | 563234.i | −0.142911 | + | 0.247528i | −0.928591 | − | 0.371104i | \(-0.878979\pi\) |
0.785681 | + | 0.618632i | \(0.212313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 590817. | − | 1.02333e6i | 0.252358 | − | 0.437096i | −0.711817 | − | 0.702365i | \(-0.752127\pi\) |
0.964174 | + | 0.265269i | \(0.0854607\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.37964e6 | − | 4.12165e6i | −1.00217 | − | 1.73580i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −985030. | −0.403379 | −0.201690 | − | 0.979449i | \(-0.564643\pi\) | ||||
−0.201690 | + | 0.979449i | \(0.564643\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.13306e6 | 1.66918 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.45100e6 | + | 4.24526e6i | 0.962967 | + | 1.66791i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 598436. | − | 1.03652e6i | 0.231928 | − | 0.401711i | −0.726448 | − | 0.687222i | \(-0.758830\pi\) |
0.958375 | + | 0.285511i | \(0.0921634\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.22725e6 | + | 2.12566e6i | −0.462913 | + | 0.801788i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.23230e6 | + | 2.13441e6i | 0.458611 | + | 0.794337i | 0.998888 | − | 0.0471500i | \(-0.0150139\pi\) |
−0.540277 | + | 0.841487i | \(0.681681\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.15227e6 | 0.779906 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.33540e6 | 1.90796 | 0.953979 | − | 0.299875i | \(-0.0969449\pi\) | ||||
0.953979 | + | 0.299875i | \(0.0969449\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 826117. | + | 1.43088e6i | 0.287770 | + | 0.498432i | 0.973277 | − | 0.229634i | \(-0.0737529\pi\) |
−0.685507 | + | 0.728066i | \(0.740420\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.65406e6 | − | 6.32902e6i | 1.25639 | − | 2.17613i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.83443e6 | − | 4.90938e6i | 0.949712 | − | 1.64495i | 0.203683 | − | 0.979037i | \(-0.434709\pi\) |
0.746029 | − | 0.665913i | \(-0.231958\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.03453e6 | + | 1.79187e6i | 0.342218 | + | 0.592739i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.53074e6 | −1.46109 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 418875. | 0.133385 | 0.0666927 | − | 0.997774i | \(-0.478755\pi\) | ||||
0.0666927 | + | 0.997774i | \(0.478755\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.43256e6 | + | 2.48126e6i | 0.444889 | + | 0.770570i | 0.998044 | − | 0.0625082i | \(-0.0199100\pi\) |
−0.553156 | + | 0.833078i | \(0.686577\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −854592. | + | 1.48020e6i | −0.262118 | + | 0.454001i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.39442e6 | − | 4.14726e6i | 0.716497 | − | 1.24101i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.65238e6 | − | 4.59406e6i | −0.784021 | − | 1.35796i | −0.929582 | − | 0.368615i | \(-0.879832\pi\) |
0.145561 | − | 0.989349i | \(-0.453501\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.02331e6 | 0.295210 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.25658e6 | −0.928200 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.42136e6 | + | 4.19393e6i | 0.673791 | + | 1.16704i | 0.976821 | + | 0.214059i | \(0.0686684\pi\) |
−0.303030 | + | 0.952981i | \(0.597998\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.28969e6 | + | 3.96586e6i | −0.629610 | + | 1.09052i | 0.358019 | + | 0.933714i | \(0.383452\pi\) |
−0.987630 | + | 0.156803i | \(0.949881\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.32254e6 | − | 2.29070e6i | 0.355169 | − | 0.615171i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.05757e6 | − | 1.83177e6i | −0.280699 | − | 0.486185i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.09717e6 | 0.803105 | 0.401552 | − | 0.915836i | \(-0.368471\pi\) | ||||
0.401552 | + | 0.915836i | \(0.368471\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −992453. | −0.254384 | −0.127192 | − | 0.991878i | \(-0.540596\pi\) | ||||
−0.127192 | + | 0.991878i | \(0.540596\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.52904e6 | + | 6.11248e6i | 0.884002 | + | 1.53114i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 442686. | − | 766755.i | 0.109631 | − | 0.189887i | −0.805990 | − | 0.591930i | \(-0.798366\pi\) |
0.915621 | + | 0.402043i | \(0.131700\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −270389. | + | 468327.i | −0.0654605 | + | 0.113381i | −0.896898 | − | 0.442237i | \(-0.854185\pi\) |
0.831438 | + | 0.555618i | \(0.187518\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.20186e6 | + | 7.27784e6i | 1.00587 | + | 1.74222i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.22193e6 | −0.520132 | −0.260066 | − | 0.965591i | \(-0.583744\pi\) | ||||
−0.260066 | + | 0.965591i | \(0.583744\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.11458e6 | −0.258031 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.01903e6 | − | 6.96117e6i | −0.910108 | − | 1.57635i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 288892. | − | 500376.i | 0.0647061 | − | 0.112074i | −0.831857 | − | 0.554989i | \(-0.812722\pi\) |
0.896564 | + | 0.442915i | \(0.146056\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.70719e6 | + | 2.95694e6i | −0.374137 | + | 0.648023i | −0.990197 | − | 0.139675i | \(-0.955394\pi\) |
0.616061 | + | 0.787699i | \(0.288728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 927775. | + | 1.60695e6i | 0.201136 | + | 0.348378i | 0.948895 | − | 0.315593i | \(-0.102203\pi\) |
−0.747759 | + | 0.663971i | \(0.768870\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.73338e6 | 0.792154 | 0.396077 | − | 0.918217i | \(-0.370371\pi\) | ||||
0.396077 | + | 0.918217i | \(0.370371\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 635184. | 0.133342 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.57528e6 | − | 6.19258e6i | −0.734781 | − | 1.27268i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.51148e6 | − | 7.81411e6i | 0.917455 | − | 1.58908i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.99246e6 | + | 3.45105e6i | −0.396782 | + | 0.687246i | −0.993327 | − | 0.115334i | \(-0.963206\pi\) |
0.596545 | + | 0.802579i | \(0.296540\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.63358e6 | − | 4.56149e6i | −0.519019 | − | 0.898967i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.35209e7 | −2.61006 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.19007e6 | 0.800570 | 0.400285 | − | 0.916391i | \(-0.368911\pi\) | ||||
0.400285 | + | 0.916391i | \(0.368911\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.09606e6 | + | 3.63049e6i | 0.392374 | + | 0.679612i | 0.992762 | − | 0.120097i | \(-0.0383204\pi\) |
−0.600388 | + | 0.799709i | \(0.704987\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.47325e6 | + | 2.55175e6i | −0.272998 | + | 0.472847i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.23706e6 | − | 9.07086e6i | 0.951036 | − | 1.64724i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.85169e6 | + | 3.20722e6i | 0.332903 | + | 0.576604i | 0.983080 | − | 0.183178i | \(-0.0586386\pi\) |
−0.650177 | + | 0.759783i | \(0.725305\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.03820e6 | −0.711653 | −0.355827 | − | 0.934552i | \(-0.615801\pi\) | ||||
−0.355827 | + | 0.934552i | \(0.615801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.34439e7 | −2.34583 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 83980.3 | + | 145458.i | 0.0143676 | + | 0.0248853i | 0.873120 | − | 0.487506i | \(-0.162093\pi\) |
−0.858752 | + | 0.512391i | \(0.828760\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.39412e6 | + | 9.34289e6i | −0.913836 | + | 1.58281i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.96741e6 | + | 5.13970e6i | −0.493014 | + | 0.853925i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.61965e6 | − | 2.80532e6i | −0.266499 | − | 0.461590i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.98731e6 | −0.643555 | −0.321777 | − | 0.946815i | \(-0.604280\pi\) | ||||
−0.321777 | + | 0.946815i | \(0.604280\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.41694e6 | −0.706102 | −0.353051 | − | 0.935604i | \(-0.614856\pi\) | ||||
−0.353051 | + | 0.935604i | \(0.614856\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.16996e6 | − | 2.02643e6i | −0.183503 | − | 0.317837i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −550576. | + | 953626.i | −0.0855418 | + | 0.148163i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −612955. | + | 1.06167e6i | −0.0934567 | + | 0.161872i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.01040e6 | + | 8.67827e6i | 0.756812 | + | 1.31084i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.67167e6 | 1.13741 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.24640e6 | 1.35825 | 0.679125 | − | 0.734023i | \(-0.262360\pi\) | ||||
0.679125 | + | 0.734023i | \(0.262360\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −988628. | − | 1.71235e6i | −0.142574 | − | 0.246946i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −762888. | + | 1.32136e6i | −0.109017 | + | 0.188822i | −0.915372 | − | 0.402609i | \(-0.868103\pi\) |
0.806356 | + | 0.591431i | \(0.201437\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.02561e6 | + | 8.70461e6i | −0.705196 | + | 1.22144i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.98559e6 | − | 8.63529e6i | −0.693272 | − | 1.20078i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.86988e6 | −0.801662 | −0.400831 | − | 0.916152i | \(-0.631279\pi\) | ||||
−0.400831 | + | 0.916152i | \(0.631279\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.86477e6 | −1.06453 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −106686. | − | 184785.i | −0.0141852 | − | 0.0245695i | 0.858846 | − | 0.512234i | \(-0.171182\pi\) |
−0.873031 | + | 0.487665i | \(0.837849\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.20129e6 | + | 1.42050e7i | −1.08084 | + | 1.87207i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.64514e6 | − | 9.77767e6i | 0.730961 | − | 1.26606i | −0.225512 | − | 0.974240i | \(-0.572405\pi\) |
0.956473 | − | 0.291821i | \(-0.0942612\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 232342. | + | 402427.i | 0.0298220 | + | 0.0516532i | 0.880551 | − | 0.473951i | \(-0.157173\pi\) |
−0.850729 | + | 0.525604i | \(0.823839\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.63583e6 | 1.21540 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.78227e6 | 1.09816 | 0.549082 | − | 0.835769i | \(-0.314978\pi\) | ||||
0.549082 | + | 0.835769i | \(0.314978\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.58351e6 | − | 6.20682e6i | −0.440421 | − | 0.762832i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.42649e6 | − | 5.93485e6i | 0.417521 | − | 0.723167i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.02083e6 | − | 8.69633e6i | 0.601423 | − | 1.04170i | −0.391183 | − | 0.920313i | \(-0.627934\pi\) |
0.992606 | − | 0.121382i | \(-0.0387327\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.99100e6 | − | 6.91262e6i | −0.474017 | − | 0.821021i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.15945e7 | 1.35399 | 0.676995 | − | 0.735988i | \(-0.263282\pi\) | ||||
0.676995 | + | 0.735988i | \(0.263282\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.10043e7 | 1.27430 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −744422. | − | 1.28938e6i | −0.0847720 | − | 0.146829i | 0.820522 | − | 0.571615i | \(-0.193683\pi\) |
−0.905294 | + | 0.424786i | \(0.860350\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.75503e6 | − | 8.23596e6i | 0.536992 | − | 0.930097i | −0.462073 | − | 0.886842i | \(-0.652894\pi\) |
0.999064 | − | 0.0432545i | \(-0.0137726\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.64303e6 | + | 6.30991e6i | −0.404645 | + | 0.700865i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.70203e6 | − | 6.41210e6i | −0.407819 | − | 0.706364i | 0.586826 | − | 0.809713i | \(-0.300377\pi\) |
−0.994645 | + | 0.103349i | \(0.967044\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.56285e6 | −0.386096 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.14368e6 | −0.767840 | −0.383920 | − | 0.923366i | \(-0.625426\pi\) | ||||
−0.383920 | + | 0.923366i | \(0.625426\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −502021. | − | 869525.i | −0.0530895 | − | 0.0919537i | 0.838259 | − | 0.545272i | \(-0.183574\pi\) |
−0.891349 | + | 0.453318i | \(0.850240\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.74328e6 | − | 6.48355e6i | 0.392668 | − | 0.680121i | −0.600132 | − | 0.799901i | \(-0.704885\pi\) |
0.992801 | + | 0.119779i | \(0.0382187\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.24738e6 | + | 1.60169e7i | −0.954550 | + | 1.65333i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.20763e6 | + | 7.28783e6i | 0.430861 | + | 0.746274i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.21086e6 | 0.726709 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.34648e7 | 1.34626 | 0.673128 | − | 0.739526i | \(-0.264950\pi\) | ||||
0.673128 | + | 0.739526i | \(0.264950\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.24226e6 | + | 7.34781e6i | 0.417506 | + | 0.723142i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.21896e6 | − | 7.30746e6i | 0.411962 | − | 0.713539i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.13083e6 | + | 1.40830e7i | −0.781610 | + | 1.35379i | 0.149394 | + | 0.988778i | \(0.452268\pi\) |
−0.931004 | + | 0.365010i | \(0.881065\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.68437e6 | + | 9.84561e6i | 0.542194 | + | 0.939108i | 0.998778 | + | 0.0494272i | \(0.0157396\pi\) |
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.18311e7 | 1.11113 | 0.555563 | − | 0.831474i | \(-0.312503\pi\) | ||||
0.555563 | + | 0.831474i | \(0.312503\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.85707e6 | −0.266262 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.67300e6 | − | 4.62977e6i | −0.245310 | − | 0.424890i | 0.716909 | − | 0.697167i | \(-0.245556\pi\) |
−0.962219 | + | 0.272278i | \(0.912223\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.28401e6 | − | 1.26163e7i | 0.663387 | − | 1.14902i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.18681e6 | + | 1.07159e7i | −0.554949 | + | 0.961200i | 0.442958 | + | 0.896542i | \(0.353929\pi\) |
−0.997907 | + | 0.0646581i | \(0.979404\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.04915e7 | + | 1.81718e7i | 0.933974 | + | 1.61769i | 0.776454 | + | 0.630174i | \(0.217016\pi\) |
0.157520 | + | 0.987516i | \(0.449650\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.75383e7 | 3.29170 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.07339e7 | −0.934210 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.95275e6 | + | 5.11431e6i | 0.253175 | + | 0.438511i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.30874e6 | − | 1.09271e7i | 0.536915 | − | 0.929963i | −0.462154 | − | 0.886800i | \(-0.652923\pi\) |
0.999068 | − | 0.0431633i | \(-0.0137436\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.99728e6 | − | 6.92349e6i | 0.335192 | − | 0.580569i | −0.648330 | − | 0.761359i | \(-0.724532\pi\) |
0.983522 | + | 0.180791i | \(0.0578656\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.48782e7 | − | 2.57698e7i | −1.23845 | − | 2.14505i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.23985e7 | −1.01699 | −0.508496 | − | 0.861064i | \(-0.669798\pi\) | ||||
−0.508496 | + | 0.861064i | \(0.669798\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.10209e7 | −0.897412 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.76873e6 | − | 6.52763e6i | −0.302445 | − | 0.523851i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.03172e7 | + | 1.78699e7i | −0.821990 | + | 1.42373i | 0.0822079 | + | 0.996615i | \(0.473803\pi\) |
−0.904198 | + | 0.427113i | \(0.859530\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.21108e6 | − | 1.59541e7i | 0.723350 | − | 1.25288i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −839150. | − | 1.45345e6i | −0.0654271 | − | 0.113323i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.28362e7 | −1.75521 | −0.877603 | − | 0.479388i | \(-0.840859\pi\) | ||||
−0.877603 | + | 0.479388i | \(0.840859\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.45980e7 | 1.87720 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.47935e7 | − | 2.56231e7i | −1.11307 | − | 1.92790i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.91237e6 | − | 1.54367e7i | 0.665852 | − | 1.15329i | −0.313202 | − | 0.949687i | \(-0.601402\pi\) |
0.979054 | − | 0.203603i | \(-0.0652651\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.26209e6 | − | 7.38215e6i | 0.313978 | − | 0.543825i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.12211e7 | + | 1.94356e7i | 0.820865 | + | 1.42178i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.10161e7 | 0.794702 | 0.397351 | − | 0.917667i | \(-0.369929\pi\) | ||||
0.397351 | + | 0.917667i | \(0.369929\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.30612e7 | −0.935720 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.86107e6 | + | 1.18837e7i | 0.484782 | + | 0.839667i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.30016e7 | + | 2.25195e7i | −0.912351 | + | 1.58024i | −0.101616 | + | 0.994824i | \(0.532401\pi\) |
−0.810734 | + | 0.585414i | \(0.800932\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.38353e6 | − | 9.32456e6i | 0.372627 | − | 0.645409i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.33355e7 | − | 2.30978e7i | −0.916750 | − | 1.58786i | −0.804319 | − | 0.594198i | \(-0.797470\pi\) |
−0.112431 | − | 0.993660i | \(-0.535864\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.77343e6 | −0.120267 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.31065e6 | 0.0882829 | 0.0441414 | − | 0.999025i | \(-0.485945\pi\) | ||||
0.0441414 | + | 0.999025i | \(0.485945\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.02502e7 | + | 1.77539e7i | 0.681178 | + | 1.17983i | 0.974622 | + | 0.223858i | \(0.0718653\pi\) |
−0.293444 | + | 0.955976i | \(0.594801\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.39652e7 | + | 2.41884e7i | −0.921839 | + | 1.59667i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.10268e7 | + | 1.90990e7i | −0.718199 | + | 1.24396i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.78701e6 | + | 1.17554e7i | 0.439115 | + | 0.760570i | 0.997621 | − | 0.0689306i | \(-0.0219587\pi\) |
−0.558506 | + | 0.829500i | \(0.688625\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.98699e7 | −1.26861 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −470115. | −0.0298171 | −0.0149085 | − | 0.999889i | \(-0.504746\pi\) | ||||
−0.0149085 | + | 0.999889i | \(0.504746\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.02690e6 | − | 1.77865e6i | −0.0642789 | − | 0.111334i | 0.832095 | − | 0.554633i | \(-0.187141\pi\) |
−0.896374 | + | 0.443299i | \(0.853808\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.17575e6 | − | 3.76852e6i | 0.135300 | − | 0.234347i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.57122e6 | + | 2.72143e6i | −0.0964381 | + | 0.167036i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.25600e6 | − | 2.17546e6i | −0.0765905 | − | 0.132659i | 0.825186 | − | 0.564861i | \(-0.191070\pi\) |
−0.901777 | + | 0.432202i | \(0.857737\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.03339e6 | 0.483560 | 0.241780 | − | 0.970331i | \(-0.422269\pi\) | ||||
0.241780 | + | 0.970331i | \(0.422269\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.08972e7 | −0.651719 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.86254e6 | − | 4.95806e6i | −0.169008 | − | 0.292731i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.46219e7 | + | 2.53258e7i | −0.857780 | + | 1.48572i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.42087e7 | + | 2.46102e7i | −0.822962 | + | 1.42541i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.57883e7 | − | 2.73461e7i | −0.908653 | − | 1.57383i | −0.815938 | − | 0.578140i | \(-0.803779\pi\) |
−0.0927148 | − | 0.995693i | \(-0.529554\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.60985e7 | −2.05139 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.49534e6 | 0.366791 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.33523e7 | − | 2.31268e7i | −0.744577 | − | 1.28965i | −0.950392 | − | 0.311055i | \(-0.899318\pi\) |
0.205815 | − | 0.978591i | \(-0.434016\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.43882e6 | − | 4.22416e6i | 0.135149 | − | 0.234085i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.50604e7 | − | 2.60853e7i | 0.824228 | − | 1.42760i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.00440e7 | + | 3.47173e7i | 1.09017 | + | 1.88823i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.27526e7 | −0.685057 | −0.342529 | − | 0.939507i | \(-0.611283\pi\) | ||||
−0.342529 | + | 0.939507i | \(0.611283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.34690e7 | −1.25297 | −0.626487 | − | 0.779432i | \(-0.715508\pi\) | ||||
−0.626487 | + | 0.779432i | \(0.715508\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.23659e7 | − | 2.14184e7i | −0.652127 | − | 1.12952i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.83645e7 | − | 3.18082e7i | 0.962552 | − | 1.66719i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.90381e6 | + | 1.36898e7i | −0.409240 | + | 0.708825i | −0.994805 | − | 0.101801i | \(-0.967540\pi\) |
0.585564 | + | 0.810626i | \(0.300873\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.12717e6 | − | 1.40767e7i | −0.418254 | − | 0.724437i | 0.577510 | − | 0.816383i | \(-0.304024\pi\) |
−0.995764 | + | 0.0919468i | \(0.970691\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.39257e7 | 0.708031 | 0.354016 | − | 0.935239i | \(-0.384816\pi\) | ||||
0.354016 | + | 0.935239i | \(0.384816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.52491e7 | 1.27603 | 0.638013 | − | 0.770026i | \(-0.279757\pi\) | ||||
0.638013 | + | 0.770026i | \(0.279757\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.77586e6 | + | 1.00041e7i | 0.288406 | + | 0.499534i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.33485e6 | + | 2.31202e6i | −0.0662544 | + | 0.114756i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.49554e6 | − | 4.32240e6i | 0.122394 | − | 0.211992i | −0.798317 | − | 0.602237i | \(-0.794276\pi\) |
0.920711 | + | 0.390245i | \(0.127610\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.61262e6 | + | 4.52518e6i | 0.127375 | + | 0.220621i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.55946e6 | −0.267850 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.60350e7 | −0.767999 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.31344e7 | + | 2.27494e7i | 0.621707 | + | 1.07683i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.76286e6 | + | 6.51746e6i | −0.177070 | + | 0.306694i | −0.940876 | − | 0.338752i | \(-0.889995\pi\) |
0.763806 | + | 0.645446i | \(0.223329\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.86940e7 | − | 3.23790e7i | 0.869461 | − | 1.50595i | 0.00691285 | − | 0.999976i | \(-0.497800\pi\) |
0.862548 | − | 0.505975i | \(-0.168867\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.21798e6 | + | 7.30575e6i | 0.195039 | + | 0.337817i | 0.946913 | − | 0.321489i | \(-0.104183\pi\) |
−0.751874 | + | 0.659306i | \(0.770850\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.10157e7 | 0.503482 | 0.251741 | − | 0.967795i | \(-0.418997\pi\) | ||||
0.251741 | + | 0.967795i | \(0.418997\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.89408e7 | 1.31513 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.39198e7 | + | 2.41097e7i | 0.625292 | + | 1.08304i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −975282. | + | 1.68924e6i | −0.0435597 | + | 0.0754476i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.80897e6 | − | 4.86527e6i | 0.124030 | − | 0.214826i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.42191e6 | + | 1.28551e7i | 0.325849 | + | 0.564387i | 0.981684 | − | 0.190517i | \(-0.0610166\pi\) |
−0.655835 | + | 0.754904i | \(0.727683\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.90839e7 | −1.26245 | −0.631224 | − | 0.775600i | \(-0.717447\pi\) | ||||
−0.631224 | + | 0.775600i | \(0.717447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.79255e7 | −1.63693 | −0.818464 | − | 0.574558i | \(-0.805174\pi\) | ||||
−0.818464 | + | 0.574558i | \(0.805174\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.65765e6 | + | 1.32634e7i | 0.326803 | + | 0.566040i | 0.981876 | − | 0.189526i | \(-0.0606952\pi\) |
−0.655072 | + | 0.755566i | \(0.727362\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.33629e6 | + | 1.61709e7i | −0.396205 | + | 0.686247i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.31938e6 | − | 1.44096e7i | 0.349110 | − | 0.604676i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.87048e7 | − | 3.23976e7i | −0.780540 | − | 1.35193i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.21390e7 | 0.500940 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.03190e7 | 0.423472 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.74171e6 | + | 1.34090e7i | 0.314207 | + | 0.544222i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.34234e7 | − | 2.32500e7i | 0.541806 | − | 0.938436i | −0.456994 | − | 0.889470i | \(-0.651074\pi\) |
0.998800 | − | 0.0489660i | \(-0.0155926\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.38433e6 | − | 4.12978e6i | 0.0951854 | − | 0.164866i | −0.814501 | − | 0.580163i | \(-0.802989\pi\) |
0.909686 | + | 0.415297i | \(0.136322\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.00052e7 | + | 1.73295e7i | 0.397235 | + | 0.688031i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.20610e7 | 1.25908 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.23134e7 | −0.871518 | −0.435759 | − | 0.900063i | \(-0.643520\pi\) | ||||
−0.435759 | + | 0.900063i | \(0.643520\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.60823e7 | + | 2.78554e7i | 0.621362 | + | 1.07623i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.67908e7 | − | 2.90825e7i | 0.645234 | − | 1.11758i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.15737e7 | − | 2.00463e7i | 0.439980 | − | 0.762068i | −0.557707 | − | 0.830038i | \(-0.688319\pi\) |
0.997687 | + | 0.0679696i | \(0.0216521\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.97028e7 | + | 3.41263e7i | 0.744997 | + | 1.29037i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.07240e7 | −1.14934 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.45453e6 | −0.128541 | −0.0642703 | − | 0.997933i | \(-0.520472\pi\) | ||||
−0.0642703 | + | 0.997933i | \(0.520472\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.77260e7 | + | 3.07024e7i | 0.652586 | + | 1.13031i | 0.982493 | + | 0.186298i | \(0.0596491\pi\) |
−0.329908 | + | 0.944013i | \(0.607018\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.05697e6 | − | 5.29483e6i | 0.111947 | − | 0.193898i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.95128e7 | − | 3.37971e7i | 0.707039 | − | 1.22463i | −0.258911 | − | 0.965901i | \(-0.583364\pi\) |
0.965950 | − | 0.258727i | \(-0.0833030\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.65646e7 | − | 2.86908e7i | −0.597057 | − | 1.03413i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.07434e6 | 0.0739858 | 0.0369929 | − | 0.999316i | \(-0.488222\pi\) | ||||
0.0369929 | + | 0.999316i | \(0.488222\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.60859e7 | 1.98996 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.21273e7 | − | 2.10052e7i | −0.425813 | − | 0.737530i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.49457e6 | − | 1.64451e7i | 0.331640 | − | 0.574417i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.40214e7 | + | 2.42857e7i | −0.484698 | + | 0.839522i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.74657e6 | + | 9.95336e6i | 0.197625 | + | 0.342297i | 0.947758 | − | 0.318990i | \(-0.103344\pi\) |
−0.750133 | + | 0.661287i | \(0.770010\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.36234e7 | −1.48481 | −0.742405 | − | 0.669951i | \(-0.766315\pi\) | ||||
−0.742405 | + | 0.669951i | \(0.766315\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.05431e7 | 1.37289 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.51800e7 | + | 2.62925e7i | 0.508785 | + | 0.881241i | 0.999948 | + | 0.0101736i | \(0.00323841\pi\) |
−0.491164 | + | 0.871067i | \(0.663428\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.58187e7 | − | 4.47193e7i | 0.860950 | − | 1.49121i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.14034e6 | + | 5.43924e6i | −0.103656 | + | 0.179537i | −0.913188 | − | 0.407538i | \(-0.866387\pi\) |
0.809532 | + | 0.587075i | \(0.199721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.42830e7 | − | 4.20593e7i | −0.797464 | − | 1.38125i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.92238e7 | 1.27514 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.30907e7 | 0.423428 | 0.211714 | − | 0.977332i | \(-0.432096\pi\) | ||||
0.211714 | + | 0.977332i | \(0.432096\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.01341e6 | + | 3.48732e6i | 0.0644723 | + | 0.111669i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.69254e6 | − | 2.93156e6i | 0.0539262 | − | 0.0934029i | −0.837802 | − | 0.545974i | \(-0.816160\pi\) |
0.891728 | + | 0.452571i | \(0.149493\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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.e.a.73.1 | 10 | ||
3.2 | odd | 2 | 36.6.e.a.25.3 | yes | 10 | ||
4.3 | odd | 2 | 432.6.i.d.289.1 | 10 | |||
9.2 | odd | 6 | 324.6.a.e.1.1 | 5 | |||
9.4 | even | 3 | inner | 108.6.e.a.37.1 | 10 | ||
9.5 | odd | 6 | 36.6.e.a.13.3 | ✓ | 10 | ||
9.7 | even | 3 | 324.6.a.d.1.5 | 5 | |||
12.11 | even | 2 | 144.6.i.d.97.3 | 10 | |||
36.23 | even | 6 | 144.6.i.d.49.3 | 10 | |||
36.31 | odd | 6 | 432.6.i.d.145.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.e.a.13.3 | ✓ | 10 | 9.5 | odd | 6 | ||
36.6.e.a.25.3 | yes | 10 | 3.2 | odd | 2 | ||
108.6.e.a.37.1 | 10 | 9.4 | even | 3 | inner | ||
108.6.e.a.73.1 | 10 | 1.1 | even | 1 | trivial | ||
144.6.i.d.49.3 | 10 | 36.23 | even | 6 | |||
144.6.i.d.97.3 | 10 | 12.11 | even | 2 | |||
324.6.a.d.1.5 | 5 | 9.7 | even | 3 | |||
324.6.a.e.1.1 | 5 | 9.2 | odd | 6 | |||
432.6.i.d.145.1 | 10 | 36.31 | odd | 6 | |||
432.6.i.d.289.1 | 10 | 4.3 | odd | 2 |