Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,6,Mod(274,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.274");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.b (of order \(2\), degree \(1\), 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: | \(52.1247414392\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{12} + 326x^{10} + 38809x^{8} + 2034064x^{6} + 43897824x^{4} + 281822976x^{2} + 377913600 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.8 | ||
Root | \(2.75663i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.274 |
Dual form | 325.6.b.g.274.5 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.75663i | 0.487308i | 0.969862 | + | 0.243654i | \(0.0783462\pi\) | ||||
−0.969862 | + | 0.243654i | \(0.921654\pi\) | |||||||
\(3\) | 23.9621i | 1.53717i | 0.639748 | + | 0.768584i | \(0.279039\pi\) | ||||
−0.639748 | + | 0.768584i | \(0.720961\pi\) | |||||||
\(4\) | 24.4010 | 0.762531 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −66.0547 | −0.749075 | ||||||||
\(7\) | − 85.7300i | − 0.661284i | −0.943756 | − | 0.330642i | \(-0.892735\pi\) | ||||
0.943756 | − | 0.330642i | \(-0.107265\pi\) | |||||||
\(8\) | 155.477i | 0.858896i | ||||||||
\(9\) | −331.182 | −1.36289 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 431.046 | 1.07409 | 0.537046 | − | 0.843553i | \(-0.319540\pi\) | ||||
0.537046 | + | 0.843553i | \(0.319540\pi\) | |||||||
\(12\) | 584.699i | 1.17214i | ||||||||
\(13\) | 169.000i | 0.277350i | ||||||||
\(14\) | 236.326 | 0.322249 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 352.239 | 0.343984 | ||||||||
\(17\) | 438.894i | 0.368331i | 0.982895 | + | 0.184165i | \(0.0589582\pi\) | ||||
−0.982895 | + | 0.184165i | \(0.941042\pi\) | |||||||
\(18\) | − 912.946i | − 0.664147i | ||||||||
\(19\) | −1617.28 | −1.02778 | −0.513891 | − | 0.857856i | \(-0.671796\pi\) | ||||
−0.513891 | + | 0.857856i | \(0.671796\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2054.27 | 1.01650 | ||||||||
\(22\) | 1188.23i | 0.523414i | ||||||||
\(23\) | 2173.44i | 0.856700i | 0.903613 | + | 0.428350i | \(0.140905\pi\) | ||||
−0.903613 | + | 0.428350i | \(0.859095\pi\) | |||||||
\(24\) | −3725.55 | −1.32027 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −465.871 | −0.135155 | ||||||||
\(27\) | − 2113.02i | − 0.557821i | ||||||||
\(28\) | − 2091.90i | − 0.504249i | ||||||||
\(29\) | −8289.72 | −1.83040 | −0.915198 | − | 0.403005i | \(-0.867966\pi\) | ||||
−0.915198 | + | 0.403005i | \(0.867966\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2745.88 | −0.513190 | −0.256595 | − | 0.966519i | \(-0.582601\pi\) | ||||
−0.256595 | + | 0.966519i | \(0.582601\pi\) | |||||||
\(32\) | 5946.25i | 1.02652i | ||||||||
\(33\) | 10328.8i | 1.65106i | ||||||||
\(34\) | −1209.87 | −0.179491 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8081.16 | −1.03924 | ||||||||
\(37\) | 2137.03i | 0.256629i | 0.991734 | + | 0.128315i | \(0.0409567\pi\) | ||||
−0.991734 | + | 0.128315i | \(0.959043\pi\) | |||||||
\(38\) | − 4458.24i | − 0.500846i | ||||||||
\(39\) | −4049.59 | −0.426334 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −19520.9 | −1.81360 | −0.906799 | − | 0.421562i | \(-0.861482\pi\) | ||||
−0.906799 | + | 0.421562i | \(0.861482\pi\) | |||||||
\(42\) | 5662.87i | 0.495351i | ||||||||
\(43\) | 8153.29i | 0.672452i | 0.941781 | + | 0.336226i | \(0.109151\pi\) | ||||
−0.941781 | + | 0.336226i | \(0.890849\pi\) | |||||||
\(44\) | 10517.9 | 0.819029 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5991.39 | −0.417477 | ||||||||
\(47\) | 13235.5i | 0.873966i | 0.899470 | + | 0.436983i | \(0.143953\pi\) | ||||
−0.899470 | + | 0.436983i | \(0.856047\pi\) | |||||||
\(48\) | 8440.39i | 0.528761i | ||||||||
\(49\) | 9457.36 | 0.562704 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10516.8 | −0.566186 | ||||||||
\(52\) | 4123.77i | 0.211488i | ||||||||
\(53\) | 1753.17i | 0.0857303i | 0.999081 | + | 0.0428651i | \(0.0136486\pi\) | ||||
−0.999081 | + | 0.0428651i | \(0.986351\pi\) | |||||||
\(54\) | 5824.83 | 0.271831 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 13329.0 | 0.567974 | ||||||||
\(57\) | − 38753.4i | − 1.57987i | ||||||||
\(58\) | − 22851.7i | − 0.891967i | ||||||||
\(59\) | 1976.46 | 0.0739192 | 0.0369596 | − | 0.999317i | \(-0.488233\pi\) | ||||
0.0369596 | + | 0.999317i | \(0.488233\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 45578.3 | 1.56832 | 0.784158 | − | 0.620561i | \(-0.213095\pi\) | ||||
0.784158 | + | 0.620561i | \(0.213095\pi\) | |||||||
\(62\) | − 7569.39i | − 0.250082i | ||||||||
\(63\) | 28392.2i | 0.901256i | ||||||||
\(64\) | −5119.96 | −0.156249 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −28472.6 | −0.804576 | ||||||||
\(67\) | 19457.7i | 0.529546i | 0.964311 | + | 0.264773i | \(0.0852970\pi\) | ||||
−0.964311 | + | 0.264773i | \(0.914703\pi\) | |||||||
\(68\) | 10709.5i | 0.280863i | ||||||||
\(69\) | −52080.3 | −1.31689 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −64224.9 | −1.51202 | −0.756010 | − | 0.654561i | \(-0.772854\pi\) | ||||
−0.756010 | + | 0.654561i | \(0.772854\pi\) | |||||||
\(72\) | − 51491.1i | − 1.17058i | ||||||||
\(73\) | 1029.22i | 0.0226048i | 0.999936 | + | 0.0113024i | \(0.00359775\pi\) | ||||
−0.999936 | + | 0.0113024i | \(0.996402\pi\) | |||||||
\(74\) | −5891.00 | −0.125058 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −39463.2 | −0.783715 | ||||||||
\(77\) | − 36953.6i | − 0.710280i | ||||||||
\(78\) | − 11163.2i | − 0.207756i | ||||||||
\(79\) | 107661. | 1.94085 | 0.970424 | − | 0.241407i | \(-0.0776090\pi\) | ||||
0.970424 | + | 0.241407i | \(0.0776090\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −29844.7 | −0.505423 | ||||||||
\(82\) | − 53812.1i | − 0.883782i | ||||||||
\(83\) | − 46473.4i | − 0.740473i | −0.928938 | − | 0.370237i | \(-0.879277\pi\) | ||||
0.928938 | − | 0.370237i | \(-0.120723\pi\) | |||||||
\(84\) | 50126.2 | 0.775116 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −22475.6 | −0.327692 | ||||||||
\(87\) | − 198639.i | − 2.81363i | ||||||||
\(88\) | 67017.6i | 0.922534i | ||||||||
\(89\) | 3410.51 | 0.0456398 | 0.0228199 | − | 0.999740i | \(-0.492736\pi\) | ||||
0.0228199 | + | 0.999740i | \(0.492736\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14488.4 | 0.183407 | ||||||||
\(92\) | 53034.2i | 0.653260i | ||||||||
\(93\) | − 65797.1i | − 0.788859i | ||||||||
\(94\) | −36485.3 | −0.425891 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −142485. | −1.57794 | ||||||||
\(97\) | − 133264.i | − 1.43808i | −0.694967 | − | 0.719041i | \(-0.744581\pi\) | ||||
0.694967 | − | 0.719041i | \(-0.255419\pi\) | |||||||
\(98\) | 26070.5i | 0.274210i | ||||||||
\(99\) | −142755. | −1.46387 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 112628. | 1.09860 | 0.549302 | − | 0.835624i | \(-0.314894\pi\) | ||||
0.549302 | + | 0.835624i | \(0.314894\pi\) | |||||||
\(102\) | − 28991.0i | − 0.275907i | ||||||||
\(103\) | 102456.i | 0.951581i | 0.879559 | + | 0.475791i | \(0.157838\pi\) | ||||
−0.879559 | + | 0.475791i | \(0.842162\pi\) | |||||||
\(104\) | −26275.6 | −0.238215 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4832.84 | −0.0417771 | ||||||||
\(107\) | 90417.9i | 0.763475i | 0.924271 | + | 0.381738i | \(0.124674\pi\) | ||||
−0.924271 | + | 0.381738i | \(0.875326\pi\) | |||||||
\(108\) | − 51559.8i | − 0.425356i | ||||||||
\(109\) | −164916. | −1.32953 | −0.664764 | − | 0.747053i | \(-0.731468\pi\) | ||||
−0.664764 | + | 0.747053i | \(0.731468\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −51207.7 | −0.394483 | ||||||||
\(112\) | − 30197.5i | − 0.227471i | ||||||||
\(113\) | − 36453.6i | − 0.268562i | −0.990943 | − | 0.134281i | \(-0.957128\pi\) | ||||
0.990943 | − | 0.134281i | \(-0.0428724\pi\) | |||||||
\(114\) | 106829. | 0.769885 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −202277. | −1.39573 | ||||||||
\(117\) | − 55969.7i | − 0.377997i | ||||||||
\(118\) | 5448.36i | 0.0360214i | ||||||||
\(119\) | 37626.4 | 0.243571 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24749.6 | 0.153676 | ||||||||
\(122\) | 125643.i | 0.764253i | ||||||||
\(123\) | − 467763.i | − 2.78781i | ||||||||
\(124\) | −67002.3 | −0.391323 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −78266.9 | −0.439189 | ||||||||
\(127\) | − 178579.i | − 0.982476i | −0.871025 | − | 0.491238i | \(-0.836544\pi\) | ||||
0.871025 | − | 0.491238i | \(-0.163456\pi\) | |||||||
\(128\) | 176166.i | 0.950381i | ||||||||
\(129\) | −195370. | −1.03367 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 43555.7 | 0.221752 | 0.110876 | − | 0.993834i | \(-0.464634\pi\) | ||||
0.110876 | + | 0.993834i | \(0.464634\pi\) | |||||||
\(132\) | 252032.i | 1.25899i | ||||||||
\(133\) | 138649.i | 0.679655i | ||||||||
\(134\) | −53637.6 | −0.258052 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −68237.9 | −0.316358 | ||||||||
\(137\) | 347518.i | 1.58189i | 0.611888 | + | 0.790944i | \(0.290410\pi\) | ||||
−0.611888 | + | 0.790944i | \(0.709590\pi\) | |||||||
\(138\) | − 143566.i | − 0.641733i | ||||||||
\(139\) | −54594.1 | −0.239667 | −0.119834 | − | 0.992794i | \(-0.538236\pi\) | ||||
−0.119834 | + | 0.992794i | \(0.538236\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −317150. | −1.34343 | ||||||||
\(142\) | − 177044.i | − 0.736819i | ||||||||
\(143\) | 72846.8i | 0.297900i | ||||||||
\(144\) | −116655. | −0.468812 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2837.18 | −0.0110155 | ||||||||
\(147\) | 226618.i | 0.864971i | ||||||||
\(148\) | 52145.6i | 0.195688i | ||||||||
\(149\) | 249528. | 0.920777 | 0.460388 | − | 0.887718i | \(-0.347710\pi\) | ||||
0.460388 | + | 0.887718i | \(0.347710\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 398788. | 1.42331 | 0.711655 | − | 0.702529i | \(-0.247946\pi\) | ||||
0.711655 | + | 0.702529i | \(0.247946\pi\) | |||||||
\(152\) | − 251449.i | − 0.882757i | ||||||||
\(153\) | − 145354.i | − 0.501994i | ||||||||
\(154\) | 101867. | 0.346125 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −98814.1 | −0.325093 | ||||||||
\(157\) | − 432099.i | − 1.39905i | −0.714606 | − | 0.699527i | \(-0.753394\pi\) | ||||
0.714606 | − | 0.699527i | \(-0.246606\pi\) | |||||||
\(158\) | 296782.i | 0.945791i | ||||||||
\(159\) | −42009.6 | −0.131782 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 186329. | 0.566522 | ||||||||
\(162\) | − 82271.0i | − 0.246297i | ||||||||
\(163\) | 56309.9i | 0.166003i | 0.996549 | + | 0.0830014i | \(0.0264506\pi\) | ||||
−0.996549 | + | 0.0830014i | \(0.973549\pi\) | |||||||
\(164\) | −476330. | −1.38292 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 128110. | 0.360839 | ||||||||
\(167\) | 512611.i | 1.42232i | 0.703031 | + | 0.711160i | \(0.251830\pi\) | ||||
−0.703031 | + | 0.711160i | \(0.748170\pi\) | |||||||
\(168\) | 319391.i | 0.873072i | ||||||||
\(169\) | −28561.0 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 535613. | 1.40075 | ||||||||
\(172\) | 198948.i | 0.512766i | ||||||||
\(173\) | − 363030.i | − 0.922204i | −0.887347 | − | 0.461102i | \(-0.847454\pi\) | ||||
0.887347 | − | 0.461102i | \(-0.152546\pi\) | |||||||
\(174\) | 547575. | 1.37110 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 151831. | 0.369471 | ||||||||
\(177\) | 47360.0i | 0.113626i | ||||||||
\(178\) | 9401.51i | 0.0222406i | ||||||||
\(179\) | 812489. | 1.89533 | 0.947665 | − | 0.319265i | \(-0.103436\pi\) | ||||
0.947665 | + | 0.319265i | \(0.103436\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −464974. | −1.05495 | −0.527475 | − | 0.849570i | \(-0.676861\pi\) | ||||
−0.527475 | + | 0.849570i | \(0.676861\pi\) | |||||||
\(182\) | 39939.1i | 0.0893758i | ||||||||
\(183\) | 1.09215e6i | 2.41077i | ||||||||
\(184\) | −337920. | −0.735816 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 181378. | 0.384418 | ||||||||
\(187\) | 189184.i | 0.395621i | ||||||||
\(188\) | 322959.i | 0.666426i | ||||||||
\(189\) | −181150. | −0.368878 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15537.6 | −0.0308177 | −0.0154088 | − | 0.999881i | \(-0.504905\pi\) | ||||
−0.0154088 | + | 0.999881i | \(0.504905\pi\) | |||||||
\(192\) | − 122685.i | − 0.240181i | ||||||||
\(193\) | − 319408.i | − 0.617238i | −0.951186 | − | 0.308619i | \(-0.900133\pi\) | ||||
0.951186 | − | 0.308619i | \(-0.0998667\pi\) | |||||||
\(194\) | 367360. | 0.700789 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 230769. | 0.429079 | ||||||||
\(197\) | − 635878.i | − 1.16737i | −0.811980 | − | 0.583685i | \(-0.801610\pi\) | ||||
0.811980 | − | 0.583685i | \(-0.198390\pi\) | |||||||
\(198\) | − 393522.i | − 0.713355i | ||||||||
\(199\) | −57426.3 | −0.102797 | −0.0513983 | − | 0.998678i | \(-0.516368\pi\) | ||||
−0.0513983 | + | 0.998678i | \(0.516368\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −466246. | −0.814002 | ||||||||
\(202\) | 310473.i | 0.535359i | ||||||||
\(203\) | 710678.i | 1.21041i | ||||||||
\(204\) | −256621. | −0.431734 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −282434. | −0.463713 | ||||||||
\(207\) | − 719806.i | − 1.16759i | ||||||||
\(208\) | 59528.5i | 0.0954039i | ||||||||
\(209\) | −697121. | −1.10393 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −407094. | −0.629489 | −0.314745 | − | 0.949176i | \(-0.601919\pi\) | ||||
−0.314745 | + | 0.949176i | \(0.601919\pi\) | |||||||
\(212\) | 42779.1i | 0.0653720i | ||||||||
\(213\) | − 1.53896e6i | − 2.32423i | ||||||||
\(214\) | −249249. | −0.372048 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 328526. | 0.479110 | ||||||||
\(217\) | 235405.i | 0.339364i | ||||||||
\(218\) | − 454614.i | − 0.647890i | ||||||||
\(219\) | −24662.3 | −0.0347474 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −74173.2 | −0.102157 | ||||||||
\(222\) | − 141161.i | − 0.192235i | ||||||||
\(223\) | 94338.9i | 0.127037i | 0.997981 | + | 0.0635183i | \(0.0202321\pi\) | ||||
−0.997981 | + | 0.0635183i | \(0.979768\pi\) | |||||||
\(224\) | 509772. | 0.678822 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 100489. | 0.130872 | ||||||||
\(227\) | − 251896.i | − 0.324456i | −0.986753 | − | 0.162228i | \(-0.948132\pi\) | ||||
0.986753 | − | 0.162228i | \(-0.0518680\pi\) | |||||||
\(228\) | − 945620.i | − 1.20470i | ||||||||
\(229\) | 428033. | 0.539372 | 0.269686 | − | 0.962948i | \(-0.413080\pi\) | ||||
0.269686 | + | 0.962948i | \(0.413080\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 885485. | 1.09182 | ||||||||
\(232\) | − 1.28886e6i | − 1.57212i | ||||||||
\(233\) | 47973.8i | 0.0578914i | 0.999581 | + | 0.0289457i | \(0.00921499\pi\) | ||||
−0.999581 | + | 0.0289457i | \(0.990785\pi\) | |||||||
\(234\) | 154288. | 0.184201 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 48227.5 | 0.0563657 | ||||||||
\(237\) | 2.57979e6i | 2.98341i | ||||||||
\(238\) | 103722.i | 0.118694i | ||||||||
\(239\) | 1.39917e6 | 1.58444 | 0.792220 | − | 0.610236i | \(-0.208925\pi\) | ||||
0.792220 | + | 0.610236i | \(0.208925\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −576792. | −0.639700 | −0.319850 | − | 0.947468i | \(-0.603633\pi\) | ||||
−0.319850 | + | 0.947468i | \(0.603633\pi\) | |||||||
\(242\) | 68225.6i | 0.0748875i | ||||||||
\(243\) | − 1.22861e6i | − 1.33474i | ||||||||
\(244\) | 1.11216e6 | 1.19589 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.28945e6 | 1.35852 | ||||||||
\(247\) | − 273320.i | − 0.285055i | ||||||||
\(248\) | − 426921.i | − 0.440776i | ||||||||
\(249\) | 1.11360e6 | 1.13823 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 676974. | 0.678247 | 0.339124 | − | 0.940742i | \(-0.389870\pi\) | ||||
0.339124 | + | 0.940742i | \(0.389870\pi\) | |||||||
\(252\) | 692798.i | 0.687235i | ||||||||
\(253\) | 936855.i | 0.920176i | ||||||||
\(254\) | 492278. | 0.478769 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −649464. | −0.619377 | ||||||||
\(257\) | 2.05124e6i | 1.93724i | 0.248545 | + | 0.968620i | \(0.420047\pi\) | ||||
−0.248545 | + | 0.968620i | \(0.579953\pi\) | |||||||
\(258\) | − 538562.i | − 0.503717i | ||||||||
\(259\) | 183208. | 0.169705 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.74541e6 | 2.49462 | ||||||||
\(262\) | 120067.i | 0.108061i | ||||||||
\(263\) | 1.51723e6i | 1.35258i | 0.736636 | + | 0.676289i | \(0.236413\pi\) | ||||
−0.736636 | + | 0.676289i | \(0.763587\pi\) | |||||||
\(264\) | −1.60588e6 | −1.41809 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −382205. | −0.331201 | ||||||||
\(267\) | 81722.8i | 0.0701561i | ||||||||
\(268\) | 474786.i | 0.403795i | ||||||||
\(269\) | −180817. | −0.152355 | −0.0761777 | − | 0.997094i | \(-0.524272\pi\) | ||||
−0.0761777 | + | 0.997094i | \(0.524272\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.58203e6 | −1.30856 | −0.654278 | − | 0.756254i | \(-0.727028\pi\) | ||||
−0.654278 | + | 0.756254i | \(0.727028\pi\) | |||||||
\(272\) | 154596.i | 0.126700i | ||||||||
\(273\) | 347172.i | 0.281928i | ||||||||
\(274\) | −957979. | −0.770867 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.27081e6 | −1.00417 | ||||||||
\(277\) | 1.53514e6i | 1.20212i | 0.799202 | + | 0.601062i | \(0.205256\pi\) | ||||
−0.799202 | + | 0.601062i | \(0.794744\pi\) | |||||||
\(278\) | − 150496.i | − 0.116792i | ||||||||
\(279\) | 909387. | 0.699420 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 959201. | 0.724676 | 0.362338 | − | 0.932047i | \(-0.381979\pi\) | ||||
0.362338 | + | 0.932047i | \(0.381979\pi\) | |||||||
\(282\) | − 874265.i | − 0.654666i | ||||||||
\(283\) | 2.63997e6i | 1.95945i | 0.200353 | + | 0.979724i | \(0.435791\pi\) | ||||
−0.200353 | + | 0.979724i | \(0.564209\pi\) | |||||||
\(284\) | −1.56715e6 | −1.15296 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −200812. | −0.145169 | ||||||||
\(287\) | 1.67353e6i | 1.19930i | ||||||||
\(288\) | − 1.96929e6i | − 1.39903i | ||||||||
\(289\) | 1.22723e6 | 0.864333 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.19329e6 | 2.21058 | ||||||||
\(292\) | 25114.0i | 0.0172369i | ||||||||
\(293\) | 286709.i | 0.195106i | 0.995230 | + | 0.0975532i | \(0.0311016\pi\) | ||||
−0.995230 | + | 0.0975532i | \(0.968898\pi\) | |||||||
\(294\) | −624703. | −0.421507 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −332258. | −0.220418 | ||||||||
\(297\) | − 910810.i | − 0.599152i | ||||||||
\(298\) | 687858.i | 0.448702i | ||||||||
\(299\) | −367312. | −0.237606 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 698981. | 0.444682 | ||||||||
\(302\) | 1.09931e6i | 0.693591i | ||||||||
\(303\) | 2.69879e6i | 1.68874i | ||||||||
\(304\) | −569669. | −0.353540 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 400687. | 0.244626 | ||||||||
\(307\) | − 1.89896e6i | − 1.14993i | −0.818179 | − | 0.574963i | \(-0.805016\pi\) | ||||
0.818179 | − | 0.574963i | \(-0.194984\pi\) | |||||||
\(308\) | − 901704.i | − 0.541610i | ||||||||
\(309\) | −2.45507e6 | −1.46274 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.74416e6 | 1.02255 | 0.511277 | − | 0.859416i | \(-0.329173\pi\) | ||||
0.511277 | + | 0.859416i | \(0.329173\pi\) | |||||||
\(312\) | − 629618.i | − 0.366176i | ||||||||
\(313\) | 605507.i | 0.349348i | 0.984626 | + | 0.174674i | \(0.0558871\pi\) | ||||
−0.984626 | + | 0.174674i | \(0.944113\pi\) | |||||||
\(314\) | 1.19114e6 | 0.681770 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.62704e6 | 1.47996 | ||||||||
\(317\) | 2.19697e6i | 1.22793i | 0.789332 | + | 0.613967i | \(0.210427\pi\) | ||||
−0.789332 | + | 0.613967i | \(0.789573\pi\) | |||||||
\(318\) | − 115805.i | − 0.0642184i | ||||||||
\(319\) | −3.57325e6 | −1.96601 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.16660e6 | −1.17359 | ||||||||
\(322\) | 513642.i | 0.276071i | ||||||||
\(323\) | − 709814.i | − 0.378563i | ||||||||
\(324\) | −728241. | −0.385401 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −155226. | −0.0808945 | ||||||||
\(327\) | − 3.95174e6i | − 2.04371i | ||||||||
\(328\) | − 3.03505e6i | − 1.55769i | ||||||||
\(329\) | 1.13468e6 | 0.577940 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.68205e6 | −1.84722 | −0.923612 | − | 0.383329i | \(-0.874777\pi\) | ||||
−0.923612 | + | 0.383329i | \(0.874777\pi\) | |||||||
\(332\) | − 1.13400e6i | − 0.564633i | ||||||||
\(333\) | − 707745.i | − 0.349757i | ||||||||
\(334\) | −1.41308e6 | −0.693108 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 723595. | 0.349661 | ||||||||
\(337\) | 3.46729e6i | 1.66309i | 0.555460 | + | 0.831543i | \(0.312542\pi\) | ||||
−0.555460 | + | 0.831543i | \(0.687458\pi\) | |||||||
\(338\) | − 78732.2i | − 0.0374852i | ||||||||
\(339\) | 873504. | 0.412825 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.18360e6 | −0.551214 | ||||||||
\(342\) | 1.47649e6i | 0.682597i | ||||||||
\(343\) | − 2.25164e6i | − 1.03339i | ||||||||
\(344\) | −1.26765e6 | −0.577566 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.00074e6 | 0.449398 | ||||||||
\(347\) | − 3.91532e6i | − 1.74559i | −0.488083 | − | 0.872797i | \(-0.662304\pi\) | ||||
0.488083 | − | 0.872797i | \(-0.337696\pi\) | |||||||
\(348\) | − 4.84699e6i | − 2.14548i | ||||||||
\(349\) | 3.32051e6 | 1.45929 | 0.729644 | − | 0.683827i | \(-0.239686\pi\) | ||||
0.729644 | + | 0.683827i | \(0.239686\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 357101. | 0.154712 | ||||||||
\(352\) | 2.56311e6i | 1.10258i | ||||||||
\(353\) | 3.09575e6i | 1.32230i | 0.750255 | + | 0.661148i | \(0.229931\pi\) | ||||
−0.750255 | + | 0.661148i | \(0.770069\pi\) | |||||||
\(354\) | −130554. | −0.0553710 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 83219.7 | 0.0348017 | ||||||||
\(357\) | 901608.i | 0.374410i | ||||||||
\(358\) | 2.23973e6i | 0.923610i | ||||||||
\(359\) | 2.71429e6 | 1.11153 | 0.555764 | − | 0.831340i | \(-0.312426\pi\) | ||||
0.555764 | + | 0.831340i | \(0.312426\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 139488. | 0.0563340 | ||||||||
\(362\) | − 1.28176e6i | − 0.514086i | ||||||||
\(363\) | 593053.i | 0.236226i | ||||||||
\(364\) | 353531. | 0.139854 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.01066e6 | −1.17479 | ||||||||
\(367\) | − 2.54964e6i | − 0.988130i | −0.869425 | − | 0.494065i | \(-0.835511\pi\) | ||||
0.869425 | − | 0.494065i | \(-0.164489\pi\) | |||||||
\(368\) | 765573.i | 0.294691i | ||||||||
\(369\) | 6.46498e6 | 2.47173 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 150299. | 0.0566920 | ||||||||
\(372\) | − 1.60551e6i | − 0.601530i | ||||||||
\(373\) | 3.67946e6i | 1.36934i | 0.728852 | + | 0.684671i | \(0.240054\pi\) | ||||
−0.728852 | + | 0.684671i | \(0.759946\pi\) | |||||||
\(374\) | −521510. | −0.192790 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.05781e6 | −0.750646 | ||||||||
\(377\) | − 1.40096e6i | − 0.507660i | ||||||||
\(378\) | − 499362.i | − 0.179757i | ||||||||
\(379\) | 1.06822e6 | 0.382000 | 0.191000 | − | 0.981590i | \(-0.438827\pi\) | ||||
0.191000 | + | 0.981590i | \(0.438827\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.27914e6 | 1.51023 | ||||||||
\(382\) | − 42831.4i | − 0.0150177i | ||||||||
\(383\) | − 601784.i | − 0.209625i | −0.994492 | − | 0.104813i | \(-0.966576\pi\) | ||||
0.994492 | − | 0.104813i | \(-0.0334243\pi\) | |||||||
\(384\) | −4.22131e6 | −1.46090 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 880490. | 0.300785 | ||||||||
\(387\) | − 2.70022e6i | − 0.916478i | ||||||||
\(388\) | − 3.25178e6i | − 1.09658i | ||||||||
\(389\) | −5.00396e6 | −1.67664 | −0.838319 | − | 0.545180i | \(-0.816461\pi\) | ||||
−0.838319 | + | 0.545180i | \(0.816461\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −953913. | −0.315549 | ||||||||
\(392\) | 1.47040e6i | 0.483304i | ||||||||
\(393\) | 1.04369e6i | 0.340870i | ||||||||
\(394\) | 1.75288e6 | 0.568869 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.48335e6 | −1.11625 | ||||||||
\(397\) | − 3.47583e6i | − 1.10683i | −0.832904 | − | 0.553417i | \(-0.813323\pi\) | ||||
0.832904 | − | 0.553417i | \(-0.186677\pi\) | |||||||
\(398\) | − 158303.i | − 0.0500936i | ||||||||
\(399\) | −3.32233e6 | −1.04474 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.15091e6 | −1.59964 | −0.799822 | − | 0.600238i | \(-0.795073\pi\) | ||||
−0.799822 | + | 0.600238i | \(0.795073\pi\) | |||||||
\(402\) | − 1.28527e6i | − 0.396670i | ||||||||
\(403\) | − 464054.i | − 0.142333i | ||||||||
\(404\) | 2.74822e6 | 0.837719 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.95908e6 | −0.589843 | ||||||||
\(407\) | 921158.i | 0.275644i | ||||||||
\(408\) | − 1.63512e6i | − 0.486295i | ||||||||
\(409\) | 1.11646e6 | 0.330015 | 0.165008 | − | 0.986292i | \(-0.447235\pi\) | ||||
0.165008 | + | 0.986292i | \(0.447235\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.32726e6 | −2.43163 | ||||||||
\(412\) | 2.50004e6i | 0.725610i | ||||||||
\(413\) | − 169442.i | − 0.0488816i | ||||||||
\(414\) | 1.98424e6 | 0.568975 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00492e6 | −0.284706 | ||||||||
\(417\) | − 1.30819e6i | − 0.368409i | ||||||||
\(418\) | − 1.92171e6i | − 0.537955i | ||||||||
\(419\) | −1.79740e6 | −0.500160 | −0.250080 | − | 0.968225i | \(-0.580457\pi\) | ||||
−0.250080 | + | 0.968225i | \(0.580457\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.31302e6 | 1.46095 | 0.730477 | − | 0.682937i | \(-0.239298\pi\) | ||||
0.730477 | + | 0.682937i | \(0.239298\pi\) | |||||||
\(422\) | − 1.12221e6i | − 0.306755i | ||||||||
\(423\) | − 4.38335e6i | − 1.19112i | ||||||||
\(424\) | −272577. | −0.0736334 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.24235e6 | 1.13262 | ||||||||
\(427\) | − 3.90743e6i | − 1.03710i | ||||||||
\(428\) | 2.20629e6i | 0.582173i | ||||||||
\(429\) | −1.74556e6 | −0.457922 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.63630e6 | −1.20221 | −0.601103 | − | 0.799172i | \(-0.705272\pi\) | ||||
−0.601103 | + | 0.799172i | \(0.705272\pi\) | |||||||
\(432\) | − 744290.i | − 0.191881i | ||||||||
\(433\) | − 3.68664e6i | − 0.944955i | −0.881343 | − | 0.472478i | \(-0.843360\pi\) | ||||
0.881343 | − | 0.472478i | \(-0.156640\pi\) | |||||||
\(434\) | −648924. | −0.165375 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.02412e6 | −1.01381 | ||||||||
\(437\) | − 3.51506e6i | − 0.880501i | ||||||||
\(438\) | − 67984.8i | − 0.0169327i | ||||||||
\(439\) | 1.67032e6 | 0.413656 | 0.206828 | − | 0.978377i | \(-0.433686\pi\) | ||||
0.206828 | + | 0.978377i | \(0.433686\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.13211e6 | −0.766903 | ||||||||
\(442\) | − 204468.i | − 0.0497817i | ||||||||
\(443\) | 3.59209e6i | 0.869637i | 0.900518 | + | 0.434819i | \(0.143187\pi\) | ||||
−0.900518 | + | 0.434819i | \(0.856813\pi\) | |||||||
\(444\) | −1.24952e6 | −0.300805 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −260058. | −0.0619060 | ||||||||
\(447\) | 5.97922e6i | 1.41539i | ||||||||
\(448\) | 438934.i | 0.103325i | ||||||||
\(449\) | −80455.2 | −0.0188338 | −0.00941690 | − | 0.999956i | \(-0.502998\pi\) | ||||
−0.00941690 | + | 0.999956i | \(0.502998\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.41443e6 | −1.94797 | ||||||||
\(452\) | − 889503.i | − 0.204786i | ||||||||
\(453\) | 9.55579e6i | 2.18787i | ||||||||
\(454\) | 694384. | 0.158110 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.02525e6 | 1.35695 | ||||||||
\(457\) | − 2.87687e6i | − 0.644362i | −0.946678 | − | 0.322181i | \(-0.895584\pi\) | ||||
0.946678 | − | 0.322181i | \(-0.104416\pi\) | |||||||
\(458\) | 1.17993e6i | 0.262840i | ||||||||
\(459\) | 927394. | 0.205463 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 81644.7 | 0.0178927 | 0.00894635 | − | 0.999960i | \(-0.497152\pi\) | ||||
0.00894635 | + | 0.999960i | \(0.497152\pi\) | |||||||
\(462\) | 2.44096e6i | 0.532053i | ||||||||
\(463\) | − 2.50214e6i | − 0.542450i | −0.962516 | − | 0.271225i | \(-0.912571\pi\) | ||||
0.962516 | − | 0.271225i | \(-0.0874287\pi\) | |||||||
\(464\) | −2.91997e6 | −0.629626 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −132246. | −0.0282109 | ||||||||
\(467\) | − 1.38773e6i | − 0.294452i | −0.989103 | − | 0.147226i | \(-0.952966\pi\) | ||||
0.989103 | − | 0.147226i | \(-0.0470344\pi\) | |||||||
\(468\) | − 1.36572e6i | − 0.288235i | ||||||||
\(469\) | 1.66811e6 | 0.350180 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.03540e7 | 2.15058 | ||||||||
\(472\) | 307293.i | 0.0634889i | ||||||||
\(473\) | 3.51444e6i | 0.722276i | ||||||||
\(474\) | −7.11152e6 | −1.45384 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 918122. | 0.185730 | ||||||||
\(477\) | − 580618.i | − 0.116841i | ||||||||
\(478\) | 3.85700e6i | 0.772111i | ||||||||
\(479\) | 4.96374e6 | 0.988485 | 0.494243 | − | 0.869324i | \(-0.335445\pi\) | ||||
0.494243 | + | 0.869324i | \(0.335445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −361158. | −0.0711761 | ||||||||
\(482\) | − 1.59000e6i | − 0.311731i | ||||||||
\(483\) | 4.46484e6i | 0.870840i | ||||||||
\(484\) | 603915. | 0.117182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.38682e6 | 0.650431 | ||||||||
\(487\) | − 8.57371e6i | − 1.63812i | −0.573706 | − | 0.819061i | \(-0.694495\pi\) | ||||
0.573706 | − | 0.819061i | \(-0.305505\pi\) | |||||||
\(488\) | 7.08637e6i | 1.34702i | ||||||||
\(489\) | −1.34930e6 | −0.255174 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.55302e6 | 0.477915 | 0.238958 | − | 0.971030i | \(-0.423194\pi\) | ||||
0.238958 | + | 0.971030i | \(0.423194\pi\) | |||||||
\(492\) | − 1.14139e7i | − 2.12579i | ||||||||
\(493\) | − 3.63831e6i | − 0.674191i | ||||||||
\(494\) | 753442. | 0.138910 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −967209. | −0.176529 | ||||||||
\(497\) | 5.50600e6i | 0.999874i | ||||||||
\(498\) | 3.06979e6i | 0.554670i | ||||||||
\(499\) | −161861. | −0.0290999 | −0.0145500 | − | 0.999894i | \(-0.504632\pi\) | ||||
−0.0145500 | + | 0.999894i | \(0.504632\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.22832e7 | −2.18634 | ||||||||
\(502\) | 1.86617e6i | 0.330515i | ||||||||
\(503\) | 5.40474e6i | 0.952477i | 0.879316 | + | 0.476239i | \(0.158000\pi\) | ||||
−0.879316 | + | 0.476239i | \(0.842000\pi\) | |||||||
\(504\) | −4.41433e6 | −0.774085 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.58256e6 | −0.448409 | ||||||||
\(507\) | − 684381.i | − 0.118244i | ||||||||
\(508\) | − 4.35751e6i | − 0.749169i | ||||||||
\(509\) | −1.72999e6 | −0.295971 | −0.147985 | − | 0.988990i | \(-0.547279\pi\) | ||||
−0.147985 | + | 0.988990i | \(0.547279\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 88235.1 | 0.0149482 | ||||||||
\(512\) | 3.84698e6i | 0.648553i | ||||||||
\(513\) | 3.41735e6i | 0.573318i | ||||||||
\(514\) | −5.65451e6 | −0.944033 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.76721e6 | −0.788207 | ||||||||
\(517\) | 5.70510e6i | 0.938721i | ||||||||
\(518\) | 505036.i | 0.0826985i | ||||||||
\(519\) | 8.69896e6 | 1.41758 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.15642e6 | 1.31645 | 0.658226 | − | 0.752820i | \(-0.271307\pi\) | ||||
0.658226 | + | 0.752820i | \(0.271307\pi\) | |||||||
\(522\) | 7.56807e6i | 1.21565i | ||||||||
\(523\) | − 7.57602e6i | − 1.21112i | −0.795800 | − | 0.605559i | \(-0.792949\pi\) | ||||
0.795800 | − | 0.605559i | \(-0.207051\pi\) | |||||||
\(524\) | 1.06280e6 | 0.169093 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.18245e6 | −0.659123 | ||||||||
\(527\) | − 1.20515e6i | − 0.189023i | ||||||||
\(528\) | 3.63820e6i | 0.567939i | ||||||||
\(529\) | 1.71248e6 | 0.266064 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −654567. | −0.100744 | ||||||||
\(532\) | 3.38318e6i | 0.518258i | ||||||||
\(533\) | − 3.29904e6i | − 0.503002i | ||||||||
\(534\) | −225280. | −0.0341876 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.02521e6 | −0.454825 | ||||||||
\(537\) | 1.94689e7i | 2.91344i | ||||||||
\(538\) | − 498445.i | − 0.0742440i | ||||||||
\(539\) | 4.07656e6 | 0.604396 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.29055e7 | 1.89575 | 0.947876 | − | 0.318640i | \(-0.103226\pi\) | ||||
0.947876 | + | 0.318640i | \(0.103226\pi\) | |||||||
\(542\) | − 4.36108e6i | − 0.637670i | ||||||||
\(543\) | − 1.11417e7i | − 1.62164i | ||||||||
\(544\) | −2.60978e6 | −0.378099 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −957025. | −0.137386 | ||||||||
\(547\) | 7.61965e6i | 1.08885i | 0.838811 | + | 0.544423i | \(0.183252\pi\) | ||||
−0.838811 | + | 0.544423i | \(0.816748\pi\) | |||||||
\(548\) | 8.47978e6i | 1.20624i | ||||||||
\(549\) | −1.50947e7 | −2.13744 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.34068e7 | 1.88125 | ||||||||
\(552\) | − 8.09727e6i | − 1.13107i | ||||||||
\(553\) | − 9.22980e6i | − 1.28345i | ||||||||
\(554\) | −4.23182e6 | −0.585805 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.33215e6 | −0.182754 | ||||||||
\(557\) | 7.35984e6i | 1.00515i | 0.864534 | + | 0.502574i | \(0.167614\pi\) | ||||
−0.864534 | + | 0.502574i | \(0.832386\pi\) | |||||||
\(558\) | 2.50685e6i | 0.340833i | ||||||||
\(559\) | −1.37791e6 | −0.186505 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.53324e6 | −0.608137 | ||||||||
\(562\) | 2.64416e6i | 0.353140i | ||||||||
\(563\) | − 5.68526e6i | − 0.755927i | −0.925821 | − | 0.377963i | \(-0.876625\pi\) | ||||
0.925821 | − | 0.377963i | \(-0.123375\pi\) | |||||||
\(564\) | −7.73876e6 | −1.02441 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.27744e6 | −0.954855 | ||||||||
\(567\) | 2.55859e6i | 0.334228i | ||||||||
\(568\) | − 9.98547e6i | − 1.29867i | ||||||||
\(569\) | 1.43108e7 | 1.85304 | 0.926519 | − | 0.376249i | \(-0.122786\pi\) | ||||
0.926519 | + | 0.376249i | \(0.122786\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.95049e6 | −0.250354 | −0.125177 | − | 0.992134i | \(-0.539950\pi\) | ||||
−0.125177 | + | 0.992134i | \(0.539950\pi\) | |||||||
\(572\) | 1.77753e6i | 0.227158i | ||||||||
\(573\) | − 372313.i | − 0.0473720i | ||||||||
\(574\) | −4.61331e6 | −0.584430 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.69564e6 | 0.212950 | ||||||||
\(577\) | 987263.i | 0.123451i | 0.998093 | + | 0.0617253i | \(0.0196603\pi\) | ||||
−0.998093 | + | 0.0617253i | \(0.980340\pi\) | |||||||
\(578\) | 3.38302e6i | 0.421196i | ||||||||
\(579\) | 7.65368e6 | 0.948798 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.98417e6 | −0.489663 | ||||||||
\(582\) | 8.80272e6i | 1.07723i | ||||||||
\(583\) | 755697.i | 0.0920823i | ||||||||
\(584\) | −160020. | −0.0194152 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −790350. | −0.0950770 | ||||||||
\(587\) | − 1.11813e6i | − 0.133936i | −0.997755 | − | 0.0669679i | \(-0.978668\pi\) | ||||
0.997755 | − | 0.0669679i | \(-0.0213325\pi\) | |||||||
\(588\) | 5.52971e6i | 0.659567i | ||||||||
\(589\) | 4.44086e6 | 0.527447 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.52370e7 | 1.79445 | ||||||||
\(592\) | 752746.i | 0.0882763i | ||||||||
\(593\) | − 905001.i | − 0.105685i | −0.998603 | − | 0.0528424i | \(-0.983172\pi\) | ||||
0.998603 | − | 0.0528424i | \(-0.0168281\pi\) | |||||||
\(594\) | 2.51077e6 | 0.291971 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.08874e6 | 0.702121 | ||||||||
\(597\) | − 1.37606e6i | − 0.158016i | ||||||||
\(598\) | − 1.01254e6i | − 0.115787i | ||||||||
\(599\) | 5.11859e6 | 0.582885 | 0.291443 | − | 0.956588i | \(-0.405865\pi\) | ||||
0.291443 | + | 0.956588i | \(0.405865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.84991e6 | 0.999431 | 0.499716 | − | 0.866190i | \(-0.333438\pi\) | ||||
0.499716 | + | 0.866190i | \(0.333438\pi\) | |||||||
\(602\) | 1.92683e6i | 0.216697i | ||||||||
\(603\) | − 6.44403e6i | − 0.721712i | ||||||||
\(604\) | 9.73082e6 | 1.08532 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.43957e6 | −0.822937 | ||||||||
\(607\) | − 1.37995e7i | − 1.52017i | −0.649824 | − | 0.760085i | \(-0.725157\pi\) | ||||
0.649824 | − | 0.760085i | \(-0.274843\pi\) | |||||||
\(608\) | − 9.61674e6i | − 1.05504i | ||||||||
\(609\) | −1.70293e7 | −1.86061 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.23679e6 | −0.242395 | ||||||||
\(612\) | − 3.54678e6i | − 0.382785i | ||||||||
\(613\) | 1.55631e7i | 1.67280i | 0.548118 | + | 0.836401i | \(0.315345\pi\) | ||||
−0.548118 | + | 0.836401i | \(0.684655\pi\) | |||||||
\(614\) | 5.23473e6 | 0.560368 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.74542e6 | 0.610057 | ||||||||
\(617\) | − 1.57277e7i | − 1.66323i | −0.555353 | − | 0.831615i | \(-0.687417\pi\) | ||||
0.555353 | − | 0.831615i | \(-0.312583\pi\) | |||||||
\(618\) | − 6.76772e6i | − 0.712806i | ||||||||
\(619\) | 5.68261e6 | 0.596103 | 0.298051 | − | 0.954550i | \(-0.403663\pi\) | ||||
0.298051 | + | 0.954550i | \(0.403663\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.59254e6 | 0.477885 | ||||||||
\(622\) | 4.80802e6i | 0.498299i | ||||||||
\(623\) | − 292383.i | − 0.0301809i | ||||||||
\(624\) | −1.42643e6 | −0.146652 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.66916e6 | −0.170240 | ||||||||
\(627\) | − 1.67045e7i | − 1.69693i | ||||||||
\(628\) | − 1.05436e7i | − 1.06682i | ||||||||
\(629\) | −937930. | −0.0945244 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.92146e6 | 0.792012 | 0.396006 | − | 0.918248i | \(-0.370396\pi\) | ||||
0.396006 | + | 0.918248i | \(0.370396\pi\) | |||||||
\(632\) | 1.67388e7i | 1.66699i | ||||||||
\(633\) | − 9.75482e6i | − 0.967631i | ||||||||
\(634\) | −6.05622e6 | −0.598382 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.02508e6 | −0.100488 | ||||||||
\(637\) | 1.59829e6i | 0.156066i | ||||||||
\(638\) | − 9.85014e6i | − 0.958055i | ||||||||
\(639\) | 2.12701e7 | 2.06071 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.63330e6 | 0.829911 | 0.414956 | − | 0.909842i | \(-0.363797\pi\) | ||||
0.414956 | + | 0.909842i | \(0.363797\pi\) | |||||||
\(642\) | − 5.97252e6i | − 0.571900i | ||||||||
\(643\) | 5.41901e6i | 0.516884i | 0.966027 | + | 0.258442i | \(0.0832090\pi\) | ||||
−0.966027 | + | 0.258442i | \(0.916791\pi\) | |||||||
\(644\) | 4.54662e6 | 0.431990 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.95670e6 | 0.184477 | ||||||||
\(647\) | − 2.85189e6i | − 0.267838i | −0.990992 | − | 0.133919i | \(-0.957244\pi\) | ||||
0.990992 | − | 0.133919i | \(-0.0427562\pi\) | |||||||
\(648\) | − 4.64016e6i | − 0.434106i | ||||||||
\(649\) | 851944. | 0.0793961 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.64079e6 | −0.521660 | ||||||||
\(652\) | 1.37402e6i | 0.126582i | ||||||||
\(653\) | 1.31018e7i | 1.20239i | 0.799101 | + | 0.601197i | \(0.205309\pi\) | ||||
−0.799101 | + | 0.601197i | \(0.794691\pi\) | |||||||
\(654\) | 1.08935e7 | 0.995916 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.87605e6 | −0.623849 | ||||||||
\(657\) | − 340859.i | − 0.0308079i | ||||||||
\(658\) | 3.12789e6i | 0.281635i | ||||||||
\(659\) | 987681. | 0.0885937 | 0.0442969 | − | 0.999018i | \(-0.485895\pi\) | ||||
0.0442969 | + | 0.999018i | \(0.485895\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.30367e6 | 0.205077 | 0.102538 | − | 0.994729i | \(-0.467304\pi\) | ||||
0.102538 | + | 0.994729i | \(0.467304\pi\) | |||||||
\(662\) | − 1.01500e7i | − 0.900167i | ||||||||
\(663\) | − 1.77734e6i | − 0.157032i | ||||||||
\(664\) | 7.22553e6 | 0.635989 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.95099e6 | 0.170439 | ||||||||
\(667\) | − 1.80172e7i | − 1.56810i | ||||||||
\(668\) | 1.25082e7i | 1.08456i | ||||||||
\(669\) | −2.26056e6 | −0.195277 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.96464e7 | 1.68452 | ||||||||
\(672\) | 1.22152e7i | 1.04346i | ||||||||
\(673\) | − 3.89370e6i | − 0.331379i | −0.986178 | − | 0.165689i | \(-0.947015\pi\) | ||||
0.986178 | − | 0.165689i | \(-0.0529849\pi\) | |||||||
\(674\) | −9.55803e6 | −0.810436 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −696916. | −0.0586562 | ||||||||
\(677\) | − 2.83801e6i | − 0.237981i | −0.992895 | − | 0.118991i | \(-0.962034\pi\) | ||||
0.992895 | − | 0.118991i | \(-0.0379658\pi\) | |||||||
\(678\) | 2.40793e6i | 0.201173i | ||||||||
\(679\) | −1.14247e7 | −0.950981 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.03595e6 | 0.498744 | ||||||||
\(682\) | − 3.26276e6i | − 0.268611i | ||||||||
\(683\) | − 6.98711e6i | − 0.573121i | −0.958062 | − | 0.286560i | \(-0.907488\pi\) | ||||
0.958062 | − | 0.286560i | \(-0.0925119\pi\) | |||||||
\(684\) | 1.30695e7 | 1.06812 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.20695e6 | 0.503580 | ||||||||
\(687\) | 1.02566e7i | 0.829105i | ||||||||
\(688\) | 2.87191e6i | 0.231313i | ||||||||
\(689\) | −296286. | −0.0237773 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.58854e6 | 0.285905 | 0.142953 | − | 0.989730i | \(-0.454340\pi\) | ||||
0.142953 | + | 0.989730i | \(0.454340\pi\) | |||||||
\(692\) | − 8.85829e6i | − 0.703209i | ||||||||
\(693\) | 1.22384e7i | 0.968033i | ||||||||
\(694\) | 1.07931e7 | 0.850643 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.08838e7 | 2.41661 | ||||||||
\(697\) | − 8.56764e6i | − 0.668004i | ||||||||
\(698\) | 9.15342e6i | 0.711123i | ||||||||
\(699\) | −1.14955e6 | −0.0889888 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.07723e7 | −0.827971 | −0.413986 | − | 0.910283i | \(-0.635864\pi\) | ||||
−0.413986 | + | 0.910283i | \(0.635864\pi\) | |||||||
\(702\) | 984396.i | 0.0753923i | ||||||||
\(703\) | − 3.45617e6i | − 0.263759i | ||||||||
\(704\) | −2.20694e6 | −0.167826 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.53384e6 | −0.644366 | ||||||||
\(707\) | − 9.65556e6i | − 0.726489i | ||||||||
\(708\) | 1.15563e6i | 0.0866436i | ||||||||
\(709\) | −1.68465e7 | −1.25862 | −0.629309 | − | 0.777155i | \(-0.716662\pi\) | ||||
−0.629309 | + | 0.777155i | \(0.716662\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.56554e7 | −2.64516 | ||||||||
\(712\) | 530254.i | 0.0391998i | ||||||||
\(713\) | − 5.96803e6i | − 0.439650i | ||||||||
\(714\) | −2.48540e6 | −0.182453 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.98255e7 | 1.44525 | ||||||||
\(717\) | 3.35270e7i | 2.43555i | ||||||||
\(718\) | 7.48230e6i | 0.541656i | ||||||||
\(719\) | −7.10379e6 | −0.512470 | −0.256235 | − | 0.966615i | \(-0.582482\pi\) | ||||
−0.256235 | + | 0.966615i | \(0.582482\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.78359e6 | 0.629265 | ||||||||
\(722\) | 384518.i | 0.0274520i | ||||||||
\(723\) | − 1.38211e7i | − 0.983327i | ||||||||
\(724\) | −1.13458e7 | −0.804432 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.63483e6 | −0.115115 | ||||||||
\(727\) | 2.50048e7i | 1.75464i | 0.479908 | + | 0.877319i | \(0.340670\pi\) | ||||
−0.479908 | + | 0.877319i | \(0.659330\pi\) | |||||||
\(728\) | 2.25260e6i | 0.157528i | ||||||||
\(729\) | 2.21877e7 | 1.54630 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.57843e6 | −0.247685 | ||||||||
\(732\) | 2.66496e7i | 1.83828i | ||||||||
\(733\) | − 7.77802e6i | − 0.534699i | −0.963600 | − | 0.267349i | \(-0.913852\pi\) | ||||
0.963600 | − | 0.267349i | \(-0.0861477\pi\) | |||||||
\(734\) | 7.02842e6 | 0.481524 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.29238e7 | −0.879422 | ||||||||
\(737\) | 8.38715e6i | 0.568782i | ||||||||
\(738\) | 1.78216e7i | 1.20450i | ||||||||
\(739\) | −1.00573e7 | −0.677439 | −0.338720 | − | 0.940887i | \(-0.609994\pi\) | ||||
−0.338720 | + | 0.940887i | \(0.609994\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.54932e6 | 0.438178 | ||||||||
\(742\) | 414320.i | 0.0276265i | ||||||||
\(743\) | − 3.40838e6i | − 0.226504i | −0.993566 | − | 0.113252i | \(-0.963873\pi\) | ||||
0.993566 | − | 0.113252i | \(-0.0361268\pi\) | |||||||
\(744\) | 1.02299e7 | 0.677548 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.01429e7 | −0.667292 | ||||||||
\(747\) | 1.53912e7i | 1.00918i | ||||||||
\(748\) | 4.61627e6i | 0.301673i | ||||||||
\(749\) | 7.75153e6 | 0.504874 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.57084e7 | 1.01633 | 0.508163 | − | 0.861261i | \(-0.330325\pi\) | ||||
0.508163 | + | 0.861261i | \(0.330325\pi\) | |||||||
\(752\) | 4.66205e6i | 0.300630i | ||||||||
\(753\) | 1.62217e7i | 1.04258i | ||||||||
\(754\) | 3.86194e6 | 0.247387 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.42023e6 | −0.281281 | ||||||||
\(757\) | 2.52846e7i | 1.60367i | 0.597544 | + | 0.801836i | \(0.296143\pi\) | ||||
−0.597544 | + | 0.801836i | \(0.703857\pi\) | |||||||
\(758\) | 2.94469e6i | 0.186152i | ||||||||
\(759\) | −2.24490e7 | −1.41447 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.34808e7 | 0.843825 | 0.421913 | − | 0.906636i | \(-0.361359\pi\) | ||||
0.421913 | + | 0.906636i | \(0.361359\pi\) | |||||||
\(762\) | 1.17960e7i | 0.735949i | ||||||||
\(763\) | 1.41383e7i | 0.879195i | ||||||||
\(764\) | −379132. | −0.0234994 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.65890e6 | 0.102152 | ||||||||
\(767\) | 334021.i | 0.0205015i | ||||||||
\(768\) | − 1.55625e7i | − 0.952087i | ||||||||
\(769\) | −8.09020e6 | −0.493337 | −0.246668 | − | 0.969100i | \(-0.579336\pi\) | ||||
−0.246668 | + | 0.969100i | \(0.579336\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.91520e7 | −2.97787 | ||||||||
\(772\) | − 7.79387e6i | − 0.470663i | ||||||||
\(773\) | 2.75295e6i | 0.165710i | 0.996562 | + | 0.0828551i | \(0.0264039\pi\) | ||||
−0.996562 | + | 0.0828551i | \(0.973596\pi\) | |||||||
\(774\) | 7.44351e6 | 0.446607 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.07195e7 | 1.23516 | ||||||||
\(777\) | 4.39004e6i | 0.260865i | ||||||||
\(778\) | − 1.37941e7i | − 0.817040i | ||||||||
\(779\) | 3.15708e7 | 1.86398 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.76839e7 | −1.62405 | ||||||||
\(782\) | − 2.62959e6i | − 0.153770i | ||||||||
\(783\) | 1.75164e7i | 1.02103i | ||||||||
\(784\) | 3.33126e6 | 0.193561 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.87706e6 | −0.166109 | ||||||||
\(787\) | − 2.06536e7i | − 1.18867i | −0.804219 | − | 0.594333i | \(-0.797416\pi\) | ||||
0.804219 | − | 0.594333i | \(-0.202584\pi\) | |||||||
\(788\) | − 1.55161e7i | − 0.890156i | ||||||||
\(789\) | −3.63560e7 | −2.07914 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.12516e6 | −0.177595 | ||||||||
\(792\) | − 2.21950e7i | − 1.25731i | ||||||||
\(793\) | 7.70274e6i | 0.434973i | ||||||||
\(794\) | 9.58160e6 | 0.539370 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.40126e6 | −0.0783855 | ||||||||
\(797\) | − 5.27093e6i | − 0.293928i | −0.989142 | − | 0.146964i | \(-0.953050\pi\) | ||||
0.989142 | − | 0.146964i | \(-0.0469502\pi\) | |||||||
\(798\) | − 9.15843e6i | − 0.509113i | ||||||||
\(799\) | −5.80897e6 | −0.321909 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.12950e6 | −0.0622020 | ||||||||
\(802\) | − 1.41992e7i | − 0.779519i | ||||||||
\(803\) | 443641.i | 0.0242797i | ||||||||
\(804\) | −1.13769e7 | −0.620701 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.27923e6 | 0.0693602 | ||||||||
\(807\) | − 4.33275e6i | − 0.234196i | ||||||||
\(808\) | 1.75110e7i | 0.943586i | ||||||||
\(809\) | 2.62432e7 | 1.40976 | 0.704882 | − | 0.709325i | \(-0.251000\pi\) | ||||
0.704882 | + | 0.709325i | \(0.251000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.50454e7 | 0.803251 | 0.401626 | − | 0.915804i | \(-0.368445\pi\) | ||||
0.401626 | + | 0.915804i | \(0.368445\pi\) | |||||||
\(812\) | 1.73412e7i | 0.922975i | ||||||||
\(813\) | − 3.79088e7i | − 2.01147i | ||||||||
\(814\) | −2.53929e6 | −0.134323 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.70444e6 | −0.194759 | ||||||||
\(817\) | − 1.31861e7i | − 0.691134i | ||||||||
\(818\) | 3.07766e6i | 0.160819i | ||||||||
\(819\) | −4.79829e6 | −0.249963 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.82770e6 | 0.0946338 | 0.0473169 | − | 0.998880i | \(-0.484933\pi\) | ||||
0.0473169 | + | 0.998880i | \(0.484933\pi\) | |||||||
\(822\) | − 2.29552e7i | − 1.18495i | ||||||||
\(823\) | 2.45074e7i | 1.26124i | 0.776093 | + | 0.630619i | \(0.217199\pi\) | ||||
−0.776093 | + | 0.630619i | \(0.782801\pi\) | |||||||
\(824\) | −1.59296e7 | −0.817309 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 467088. | 0.0238204 | ||||||||
\(827\) | 7.03772e6i | 0.357823i | 0.983865 | + | 0.178911i | \(0.0572576\pi\) | ||||
−0.983865 | + | 0.178911i | \(0.942742\pi\) | |||||||
\(828\) | − 1.75640e7i | − 0.890321i | ||||||||
\(829\) | −3.44967e7 | −1.74338 | −0.871689 | − | 0.490059i | \(-0.836975\pi\) | ||||
−0.871689 | + | 0.490059i | \(0.836975\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.67852e7 | −1.84787 | ||||||||
\(832\) | − 865273.i | − 0.0433356i | ||||||||
\(833\) | 4.15078e6i | 0.207261i | ||||||||
\(834\) | 3.60619e6 | 0.179529 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.70104e7 | −0.841782 | ||||||||
\(837\) | 5.80212e6i | 0.286268i | ||||||||
\(838\) | − 4.95476e6i | − 0.243732i | ||||||||
\(839\) | −2.79128e6 | −0.136899 | −0.0684493 | − | 0.997655i | \(-0.521805\pi\) | ||||
−0.0684493 | + | 0.997655i | \(0.521805\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.82083e7 | 2.35035 | ||||||||
\(842\) | 1.46460e7i | 0.711935i | ||||||||
\(843\) | 2.29845e7i | 1.11395i | ||||||||
\(844\) | −9.93349e6 | −0.480005 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.20833e7 | 0.580442 | ||||||||
\(847\) | − 2.12179e6i | − 0.101623i | ||||||||
\(848\) | 617535.i | 0.0294898i | ||||||||
\(849\) | −6.32593e7 | −3.01200 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.64471e6 | −0.219854 | ||||||||
\(852\) | − 3.75522e7i | − 1.77230i | ||||||||
\(853\) | − 2.48047e7i | − 1.16724i | −0.812026 | − | 0.583621i | \(-0.801635\pi\) | ||||
0.812026 | − | 0.583621i | \(-0.198365\pi\) | |||||||
\(854\) | 1.07713e7 | 0.505388 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.40579e7 | −0.655746 | ||||||||
\(857\) | 1.83304e7i | 0.852550i | 0.904594 | + | 0.426275i | \(0.140174\pi\) | ||||
−0.904594 | + | 0.426275i | \(0.859826\pi\) | |||||||
\(858\) | − 4.81187e6i | − 0.223149i | ||||||||
\(859\) | −1.67092e7 | −0.772632 | −0.386316 | − | 0.922366i | \(-0.626253\pi\) | ||||
−0.386316 | + | 0.922366i | \(0.626253\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.01013e7 | −1.84353 | ||||||||
\(862\) | − 1.27806e7i | − 0.585844i | ||||||||
\(863\) | 8.29285e6i | 0.379033i | 0.981878 | + | 0.189516i | \(0.0606920\pi\) | ||||
−0.981878 | + | 0.189516i | \(0.939308\pi\) | |||||||
\(864\) | 1.25646e7 | 0.572615 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.01627e7 | 0.460484 | ||||||||
\(867\) | 2.94070e7i | 1.32863i | ||||||||
\(868\) | 5.74411e6i | 0.258775i | ||||||||
\(869\) | 4.64069e7 | 2.08465 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.28834e6 | −0.146870 | ||||||||
\(872\) | − 2.56407e7i | − 1.14193i | ||||||||
\(873\) | 4.41347e7i | 1.95995i | ||||||||
\(874\) | 9.68974e6 | 0.429075 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −601784. | −0.0264960 | ||||||||
\(877\) | 1.44569e7i | 0.634711i | 0.948307 | + | 0.317356i | \(0.102795\pi\) | ||||
−0.948307 | + | 0.317356i | \(0.897205\pi\) | |||||||
\(878\) | 4.60447e6i | 0.201578i | ||||||||
\(879\) | −6.87014e6 | −0.299912 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.42081e7 | −1.48487 | −0.742437 | − | 0.669916i | \(-0.766330\pi\) | ||||
−0.742437 | + | 0.669916i | \(0.766330\pi\) | |||||||
\(882\) | − 8.63407e6i | − 0.373718i | ||||||||
\(883\) | − 1.41341e7i | − 0.610051i | −0.952344 | − | 0.305026i | \(-0.901335\pi\) | ||||
0.952344 | − | 0.305026i | \(-0.0986650\pi\) | |||||||
\(884\) | −1.80990e6 | −0.0778975 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.90207e6 | −0.423781 | ||||||||
\(887\) | − 2.15650e7i | − 0.920325i | −0.887835 | − | 0.460163i | \(-0.847791\pi\) | ||||
0.887835 | − | 0.460163i | \(-0.152209\pi\) | |||||||
\(888\) | − 7.96160e6i | − 0.338819i | ||||||||
\(889\) | −1.53096e7 | −0.649696 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.28645e7 | −0.542872 | ||||||||
\(892\) | 2.30196e6i | 0.0968693i | ||||||||
\(893\) | − 2.14054e7i | − 0.898246i | ||||||||
\(894\) | −1.64825e7 | −0.689731 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.51027e7 | 0.628471 | ||||||||
\(897\) | − 8.80157e6i | − 0.365241i | ||||||||
\(898\) | − 221785.i | − 0.00917787i | ||||||||
\(899\) | 2.27626e7 | 0.939340 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −769456. | −0.0315771 | ||||||||
\(902\) | − 2.31955e7i | − 0.949264i | ||||||||
\(903\) | 1.67491e7i | 0.683551i | ||||||||
\(904\) | 5.66768e6 | 0.230666 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.63418e7 | −1.06617 | ||||||||
\(907\) | − 1.53494e7i | − 0.619547i | −0.950810 | − | 0.309773i | \(-0.899747\pi\) | ||||
0.950810 | − | 0.309773i | \(-0.100253\pi\) | |||||||
\(908\) | − 6.14650e6i | − 0.247408i | ||||||||
\(909\) | −3.73002e7 | −1.49727 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.00925e6 | −0.319739 | −0.159870 | − | 0.987138i | \(-0.551107\pi\) | ||||
−0.159870 | + | 0.987138i | \(0.551107\pi\) | |||||||
\(912\) | − 1.36505e7i | − 0.543451i | ||||||||
\(913\) | − 2.00322e7i | − 0.795337i | ||||||||
\(914\) | 7.93047e6 | 0.314003 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.04444e7 | 0.411287 | ||||||||
\(917\) | − 3.73403e6i | − 0.146641i | ||||||||
\(918\) | 2.55648e6i | 0.100124i | ||||||||
\(919\) | 1.00787e7 | 0.393655 | 0.196828 | − | 0.980438i | \(-0.436936\pi\) | ||||
0.196828 | + | 0.980438i | \(0.436936\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.55031e7 | 1.76763 | ||||||||
\(922\) | 225064.i | 0.00871926i | ||||||||
\(923\) | − 1.08540e7i | − 0.419359i | ||||||||
\(924\) | 2.16067e7 | 0.832547 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.89748e6 | 0.264340 | ||||||||
\(927\) | − 3.39317e7i | − 1.29690i | ||||||||
\(928\) | − 4.92927e7i | − 1.87894i | ||||||||
\(929\) | 1.20808e7 | 0.459257 | 0.229629 | − | 0.973278i | \(-0.426249\pi\) | ||||
0.229629 | + | 0.973278i | \(0.426249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.52952e7 | −0.578336 | ||||||||
\(932\) | 1.17061e6i | 0.0441440i | ||||||||
\(933\) | 4.17938e7i | 1.57184i | ||||||||
\(934\) | 3.82547e6 | 0.143489 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.70199e6 | 0.324660 | ||||||||
\(937\) | − 1.85069e7i | − 0.688628i | −0.938854 | − | 0.344314i | \(-0.888111\pi\) | ||||
0.938854 | − | 0.344314i | \(-0.111889\pi\) | |||||||
\(938\) | 4.59835e6i | 0.170646i | ||||||||
\(939\) | −1.45092e7 | −0.537007 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.31161e7 | −0.482871 | −0.241436 | − | 0.970417i | \(-0.577618\pi\) | ||||
−0.241436 | + | 0.970417i | \(0.577618\pi\) | |||||||
\(942\) | 2.85422e7i | 1.04800i | ||||||||
\(943\) | − 4.24277e7i | − 1.55371i | ||||||||
\(944\) | 696186. | 0.0254270 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.68802e6 | −0.351971 | ||||||||
\(947\) | 2.46835e7i | 0.894399i | 0.894434 | + | 0.447199i | \(0.147579\pi\) | ||||
−0.894434 | + | 0.447199i | \(0.852421\pi\) | |||||||
\(948\) | 6.29494e7i | 2.27494i | ||||||||
\(949\) | −173938. | −0.00626945 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.26439e7 | −1.88754 | ||||||||
\(952\) | 5.85003e6i | 0.209202i | ||||||||
\(953\) | 3.21978e7i | 1.14840i | 0.818715 | + | 0.574201i | \(0.194687\pi\) | ||||
−0.818715 | + | 0.574201i | \(0.805313\pi\) | |||||||
\(954\) | 1.60055e6 | 0.0569375 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.41411e7 | 1.20818 | ||||||||
\(957\) | − 8.56226e7i | − 3.02210i | ||||||||
\(958\) | 1.36832e7i | 0.481697i | ||||||||
\(959\) | 2.97927e7 | 1.04608 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.10893e7 | −0.736636 | ||||||||
\(962\) | − 995579.i | − 0.0346847i | ||||||||
\(963\) | − 2.99448e7i | − 1.04053i | ||||||||
\(964\) | −1.40743e7 | −0.487791 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.23079e7 | −0.424368 | ||||||||
\(967\) | − 2.28108e7i | − 0.784465i | −0.919866 | − | 0.392232i | \(-0.871703\pi\) | ||||
0.919866 | − | 0.392232i | \(-0.128297\pi\) | |||||||
\(968\) | 3.84799e6i | 0.131991i | ||||||||
\(969\) | 1.70086e7 | 0.581916 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.02182e7 | 1.36891 | 0.684455 | − | 0.729055i | \(-0.260040\pi\) | ||||
0.684455 | + | 0.729055i | \(0.260040\pi\) | |||||||
\(972\) | − 2.99792e7i | − 1.01778i | ||||||||
\(973\) | 4.68035e6i | 0.158488i | ||||||||
\(974\) | 2.36346e7 | 0.798271 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.60545e7 | 0.539475 | ||||||||
\(977\) | − 3.17409e7i | − 1.06386i | −0.846790 | − | 0.531928i | \(-0.821468\pi\) | ||||
0.846790 | − | 0.531928i | \(-0.178532\pi\) | |||||||
\(978\) | − 3.71953e6i | − 0.124349i | ||||||||
\(979\) | 1.47008e6 | 0.0490214 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.46173e7 | 1.81200 | ||||||||
\(982\) | 7.03774e6i | 0.232892i | ||||||||
\(983\) | 4.52276e6i | 0.149286i | 0.997210 | + | 0.0746431i | \(0.0237818\pi\) | ||||
−0.997210 | + | 0.0746431i | \(0.976218\pi\) | |||||||
\(984\) | 7.27262e7 | 2.39444 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.00295e7 | 0.328539 | ||||||||
\(987\) | 2.71892e7i | 0.888391i | ||||||||
\(988\) | − 6.66928e6i | − 0.217363i | ||||||||
\(989\) | −1.77207e7 | −0.576090 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.04730e7 | −0.662213 | −0.331107 | − | 0.943593i | \(-0.607422\pi\) | ||||
−0.331107 | + | 0.943593i | \(0.607422\pi\) | |||||||
\(992\) | − 1.63277e7i | − 0.526801i | ||||||||
\(993\) | − 8.82296e7i | − 2.83949i | ||||||||
\(994\) | −1.51780e7 | −0.487247 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.71729e7 | 0.867937 | ||||||||
\(997\) | 3.49736e7i | 1.11430i | 0.830412 | + | 0.557150i | \(0.188105\pi\) | ||||
−0.830412 | + | 0.557150i | \(0.811895\pi\) | |||||||
\(998\) | − 446192.i | − 0.0141806i | ||||||||
\(999\) | 4.51559e6 | 0.143153 |
(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 | 325.6.b.g.274.8 | 12 | ||
5.2 | odd | 4 | 65.6.a.d.1.3 | ✓ | 6 | ||
5.3 | odd | 4 | 325.6.a.g.1.4 | 6 | |||
5.4 | even | 2 | inner | 325.6.b.g.274.5 | 12 | ||
15.2 | even | 4 | 585.6.a.m.1.4 | 6 | |||
20.7 | even | 4 | 1040.6.a.q.1.2 | 6 | |||
65.12 | odd | 4 | 845.6.a.h.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.6.a.d.1.3 | ✓ | 6 | 5.2 | odd | 4 | ||
325.6.a.g.1.4 | 6 | 5.3 | odd | 4 | |||
325.6.b.g.274.5 | 12 | 5.4 | even | 2 | inner | ||
325.6.b.g.274.8 | 12 | 1.1 | even | 1 | trivial | ||
585.6.a.m.1.4 | 6 | 15.2 | even | 4 | |||
845.6.a.h.1.4 | 6 | 65.12 | odd | 4 | |||
1040.6.a.q.1.2 | 6 | 20.7 | even | 4 |