Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,6,Mod(385,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("768.385");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.d (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: | \(123.174773616\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 6) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 385.2 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.385 |
Dual form | 768.6.d.c.385.1 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 66.0000i | − 1.18064i | −0.807168 | − | 0.590322i | \(-0.799001\pi\) | ||||
0.807168 | − | 0.590322i | \(-0.200999\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −176.000 | −1.35759 | −0.678793 | − | 0.734329i | \(-0.737497\pi\) | ||||
−0.678793 | + | 0.734329i | \(0.737497\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 60.0000i | − 0.149510i | −0.997202 | − | 0.0747549i | \(-0.976183\pi\) | ||||
0.997202 | − | 0.0747549i | \(-0.0238174\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 658.000i | 1.07986i | 0.841710 | + | 0.539930i | \(0.181549\pi\) | ||||
−0.841710 | + | 0.539930i | \(0.818451\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 594.000 | 0.681645 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −414.000 | −0.347439 | −0.173719 | − | 0.984795i | \(-0.555579\pi\) | ||||
−0.173719 | + | 0.984795i | \(0.555579\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 956.000i | − 0.607539i | −0.952746 | − | 0.303769i | \(-0.901755\pi\) | ||||
0.952746 | − | 0.303769i | \(-0.0982452\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 1584.00i | − 0.783803i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −600.000 | −0.236500 | −0.118250 | − | 0.992984i | \(-0.537728\pi\) | ||||
−0.118250 | + | 0.992984i | \(0.537728\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1231.00 | −0.393920 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 729.000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 5574.00i | − 1.23076i | −0.788232 | − | 0.615378i | \(-0.789003\pi\) | ||||
0.788232 | − | 0.615378i | \(-0.210997\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3592.00 | −0.671324 | −0.335662 | − | 0.941983i | \(-0.608960\pi\) | ||||
−0.335662 | + | 0.941983i | \(0.608960\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 540.000 | 0.0863195 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11616.0i | 1.60283i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 8458.00i | − 1.01570i | −0.861447 | − | 0.507848i | \(-0.830441\pi\) | ||||
0.861447 | − | 0.507848i | \(-0.169559\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5922.00 | −0.623458 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −19194.0 | −1.78322 | −0.891612 | − | 0.452800i | \(-0.850425\pi\) | ||||
−0.891612 | + | 0.452800i | \(0.850425\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13316.0i | 1.09825i | 0.835739 | + | 0.549127i | \(0.185040\pi\) | ||||
−0.835739 | + | 0.549127i | \(0.814960\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5346.00i | 0.393548i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −19680.0 | −1.29951 | −0.649756 | − | 0.760143i | \(-0.725129\pi\) | ||||
−0.649756 | + | 0.760143i | \(0.725129\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14169.0 | 0.843042 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 3726.00i | − 0.200594i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 31266.0i | − 1.52891i | −0.644676 | − | 0.764456i | \(-0.723008\pi\) | ||||
0.644676 | − | 0.764456i | \(-0.276992\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3960.00 | −0.176518 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8604.00 | 0.350763 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 26340.0i | 0.985112i | 0.870281 | + | 0.492556i | \(0.163937\pi\) | ||||
−0.870281 | + | 0.492556i | \(0.836063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 31090.0i | 1.06978i | 0.844920 | + | 0.534892i | \(0.179648\pi\) | ||||
−0.844920 | + | 0.534892i | \(0.820352\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14256.0 | 0.452529 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 43428.0 | 1.27493 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16804.0i | 0.457326i | 0.973506 | + | 0.228663i | \(0.0734353\pi\) | ||||
−0.973506 | + | 0.228663i | \(0.926565\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 5400.00i | − 0.136544i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6120.00 | −0.144081 | −0.0720403 | − | 0.997402i | \(-0.522951\pi\) | ||||
−0.0720403 | + | 0.997402i | \(0.522951\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 25558.0 | 0.561332 | 0.280666 | − | 0.959806i | \(-0.409445\pi\) | ||||
0.280666 | + | 0.959806i | \(0.409445\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 11079.0i | − 0.227430i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10560.0i | 0.202972i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74408.0 | 1.34138 | 0.670690 | − | 0.741738i | \(-0.265998\pi\) | ||||
0.670690 | + | 0.741738i | \(0.265998\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6468.00i | 0.103056i | 0.998672 | + | 0.0515282i | \(0.0164092\pi\) | ||||
−0.998672 | + | 0.0515282i | \(0.983591\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 27324.0i | 0.410201i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 50166.0 | 0.710577 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 32742.0 | 0.438157 | 0.219079 | − | 0.975707i | \(-0.429695\pi\) | ||||
0.219079 | + | 0.975707i | \(0.429695\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 115808.i | − 1.46600i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 32328.0i | − 0.387589i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −63096.0 | −0.717287 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 166082. | 1.79223 | 0.896114 | − | 0.443824i | \(-0.146378\pi\) | ||||
0.896114 | + | 0.443824i | \(0.146378\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4860.00i | 0.0498366i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 22002.0i | − 0.214614i | −0.994226 | − | 0.107307i | \(-0.965777\pi\) | ||||
0.994226 | − | 0.107307i | \(-0.0342228\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 79264.0 | 0.736178 | 0.368089 | − | 0.929791i | \(-0.380012\pi\) | ||||
0.368089 | + | 0.929791i | \(0.380012\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −104544. | −0.925392 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 227988.i | 1.92510i | 0.271110 | + | 0.962548i | \(0.412609\pi\) | ||||
−0.271110 | + | 0.962548i | \(0.587391\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8530.00i | 0.0687674i | 0.999409 | + | 0.0343837i | \(0.0109468\pi\) | ||||
−0.999409 | + | 0.0343837i | \(0.989053\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 76122.0 | 0.586412 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −195438. | −1.43984 | −0.719918 | − | 0.694059i | \(-0.755821\pi\) | ||||
−0.719918 | + | 0.694059i | \(0.755821\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 39600.0i | 0.279223i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 53298.0i | − 0.359953i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 72864.0 | 0.471678 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 157451. | 0.977647 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 172746.i | − 1.02954i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 125004.i | − 0.715565i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 173000. | 0.951780 | 0.475890 | − | 0.879505i | \(-0.342126\pi\) | ||||
0.475890 | + | 0.879505i | \(0.342126\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −119844. | −0.634077 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 151260.i | − 0.770098i | −0.922896 | − | 0.385049i | \(-0.874185\pi\) | ||||
0.922896 | − | 0.385049i | \(-0.125815\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 168256.i | 0.824786i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −48114.0 | −0.227215 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 128454. | 0.584718 | 0.292359 | − | 0.956309i | \(-0.405560\pi\) | ||||
0.292359 | + | 0.956309i | \(0.405560\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 154196.i | 0.676918i | 0.940981 | + | 0.338459i | \(0.109906\pi\) | ||||
−0.940981 | + | 0.338459i | \(0.890094\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 177120.i | − 0.750274i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 39480.0 | 0.161450 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −367884. | −1.45308 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 127521.i | 0.486730i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 29454.0i | 0.108687i | 0.998522 | + | 0.0543436i | \(0.0173066\pi\) | ||||
−0.998522 | + | 0.0543436i | \(0.982693\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 203872. | 0.727638 | 0.363819 | − | 0.931470i | \(-0.381473\pi\) | ||||
0.363819 | + | 0.931470i | \(0.381473\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 33534.0 | 0.115813 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 237072.i | 0.792594i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 136142.i | − 0.440801i | −0.975409 | − | 0.220401i | \(-0.929263\pi\) | ||||
0.975409 | − | 0.220401i | \(-0.0707365\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 281394. | 0.882718 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 105600. | 0.321070 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 171124.i | 0.504478i | 0.967665 | + | 0.252239i | \(0.0811669\pi\) | ||||
−0.967665 | + | 0.252239i | \(0.918833\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 35640.0i | − 0.101913i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 676200. | 1.87622 | 0.938110 | − | 0.346336i | \(-0.112574\pi\) | ||||
0.938110 | + | 0.346336i | \(0.112574\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −61671.0 | −0.166098 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 77436.0i | 0.202513i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 133158.i | − 0.338261i | −0.985594 | − | 0.169131i | \(-0.945904\pi\) | ||||
0.985594 | − | 0.169131i | \(-0.0540959\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 216656. | 0.534781 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −237060. | −0.568755 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 693396.i | 1.61752i | 0.588141 | + | 0.808758i | \(0.299860\pi\) | ||||
−0.588141 | + | 0.808758i | \(0.700140\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 377174.i | 0.855747i | 0.903839 | + | 0.427873i | \(0.140737\pi\) | ||||
−0.903839 | + | 0.427873i | \(0.859263\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −279810. | −0.617640 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −558228. | −1.19917 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24840.0i | 0.0519455i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 128304.i | 0.261268i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −265344. | −0.526291 | −0.263145 | − | 0.964756i | \(-0.584760\pi\) | ||||
−0.263145 | + | 0.964756i | \(0.584760\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 295298. | 0.570647 | 0.285323 | − | 0.958431i | \(-0.407899\pi\) | ||||
0.285323 | + | 0.958431i | \(0.407899\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 390852.i | 0.736081i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 201294.i | 0.369543i | 0.982781 | + | 0.184772i | \(0.0591545\pi\) | ||||
−0.982781 | + | 0.184772i | \(0.940845\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −652448. | −1.16792 | −0.583960 | − | 0.811782i | \(-0.698498\pi\) | ||||
−0.583960 | + | 0.811782i | \(0.698498\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −151236. | −0.264037 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 981024.i | 1.67086i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.26680e6i | 2.10535i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 48600.0 | 0.0788334 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −57360.0 | −0.0908330 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.14706e6i | 1.77370i | 0.462058 | + | 0.886850i | \(0.347111\pi\) | ||||
−0.462058 | + | 0.886850i | \(0.652889\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 55080.0i | − 0.0831850i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 878856. | 1.29665 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 632192. | 0.911380 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 230022.i | 0.324085i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 272412.i | − 0.375185i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 701960. | 0.945258 | 0.472629 | − | 0.881262i | \(-0.343305\pi\) | ||||
0.472629 | + | 0.881262i | \(0.343305\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 99711.0 | 0.131307 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1.23611e6i | − 1.59218i | −0.605179 | − | 0.796089i | \(-0.706899\pi\) | ||||
0.605179 | − | 0.796089i | \(-0.293101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 105830.i | 0.133358i | 0.997774 | + | 0.0666792i | \(0.0212404\pi\) | ||||
−0.997774 | + | 0.0666792i | \(0.978760\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −95040.0 | −0.117186 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 438678. | 0.529366 | 0.264683 | − | 0.964335i | \(-0.414733\pi\) | ||||
0.264683 | + | 0.964335i | \(0.414733\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.29888e6i | 1.53426i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 669672.i | 0.774446i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28464.0 | 0.0322330 | 0.0161165 | − | 0.999870i | \(-0.494870\pi\) | ||||
0.0161165 | + | 0.999870i | \(0.494870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 892562. | 0.989910 | 0.494955 | − | 0.868919i | \(-0.335185\pi\) | ||||
0.494955 | + | 0.868919i | \(0.335185\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 935154.i | − 0.995332i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 629048. | 0.656057 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −58212.0 | −0.0594996 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 110124.i | − 0.110331i | −0.998477 | − | 0.0551655i | \(-0.982431\pi\) | ||||
0.998477 | − | 0.0551655i | \(-0.0175686\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36000.0i | 0.0353591i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −245916. | −0.236830 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 140802. | 0.132977 | 0.0664884 | − | 0.997787i | \(-0.478820\pi\) | ||||
0.0664884 | + | 0.997787i | \(0.478820\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.48861e6i | 1.37889i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 451494.i | 0.410252i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 938760. | 0.836884 | 0.418442 | − | 0.908244i | \(-0.362576\pi\) | ||||
0.418442 | + | 0.908244i | \(0.362576\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.06356e6 | −1.80510 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 294678.i | 0.252970i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.11451e6i | 0.939078i | 0.882912 | + | 0.469539i | \(0.155580\pi\) | ||||
−0.882912 | + | 0.469539i | \(0.844420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 567704. | 0.469568 | 0.234784 | − | 0.972048i | \(-0.424562\pi\) | ||||
0.234784 | + | 0.972048i | \(0.424562\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.04227e6 | 0.846398 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 73860.0i | 0.0588949i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.21326e6i | − 0.950066i | −0.879968 | − | 0.475033i | \(-0.842436\pi\) | ||||
0.879968 | − | 0.475033i | \(-0.157564\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 290952. | 0.223775 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −687738. | −0.519586 | −0.259793 | − | 0.965664i | \(-0.583654\pi\) | ||||
−0.259793 | + | 0.965664i | \(0.583654\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 830908.i | − 0.616718i | −0.951270 | − | 0.308359i | \(-0.900220\pi\) | ||||
0.951270 | − | 0.308359i | \(-0.0997799\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 567864.i | − 0.414126i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.37814e6 | 2.42088 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.24846e6 | −0.879286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.49474e6i | 1.03474i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.31263e6i | − 0.893248i | −0.894722 | − | 0.446624i | \(-0.852626\pi\) | ||||
0.894722 | − | 0.446624i | \(-0.147374\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.73844e6 | 1.16307 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −43740.0 | −0.0287732 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 394800.i | − 0.255387i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2.34362e6i | − 1.49097i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 198018. | 0.123908 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.05194e6 | 1.26303 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.69022e6i | − 1.02352i | −0.859128 | − | 0.511761i | \(-0.828993\pi\) | ||||
0.859128 | − | 0.511761i | \(-0.171007\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 713376.i | 0.425033i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.50204e6 | 0.880604 | 0.440302 | − | 0.897850i | \(-0.354871\pi\) | ||||
0.440302 | + | 0.897850i | \(0.354871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −810842. | −0.467816 | −0.233908 | − | 0.972259i | \(-0.575152\pi\) | ||||
−0.233908 | + | 0.972259i | \(0.575152\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 940896.i | − 0.534275i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 903558.i | − 0.505019i | −0.967594 | − | 0.252510i | \(-0.918744\pi\) | ||||
0.967594 | − | 0.252510i | \(-0.0812559\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −334440. | −0.184010 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.05189e6 | −1.11146 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 395784.i | 0.211082i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 809998.i | − 0.425379i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −76770.0 | −0.0397029 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.46368e6 | 1.76420 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.12197e6i | 0.562875i | 0.959580 | + | 0.281438i | \(0.0908112\pi\) | ||||
−0.959580 | + | 0.281438i | \(0.909189\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 685098.i | 0.338565i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.10906e6 | 0.539939 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.75217e6 | −1.32008 | −0.660041 | − | 0.751229i | \(-0.729461\pi\) | ||||
−0.660041 | + | 0.751229i | \(0.729461\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1.75894e6i | − 0.831289i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 215520.i | 0.100369i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 464288. | 0.213085 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −356400. | −0.161209 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.91749e6i | 0.854889i | 0.904042 | + | 0.427445i | \(0.140586\pi\) | ||||
−0.904042 | + | 0.427445i | \(0.859414\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1.83659e6i | − 0.807140i | −0.914949 | − | 0.403570i | \(-0.867769\pi\) | ||||
0.914949 | − | 0.403570i | \(-0.132231\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 479682. | 0.207819 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −622014. | −0.265683 | −0.132841 | − | 0.991137i | \(-0.542410\pi\) | ||||
−0.132841 | + | 0.991137i | \(0.542410\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 403920.i | 0.170108i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 655776.i | 0.272323i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.74062e6 | −1.53182 | −0.765909 | − | 0.642949i | \(-0.777711\pi\) | ||||
−0.765909 | + | 0.642949i | \(0.777711\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.56216e6 | 0.630897 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.41706e6i | 0.564445i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.68683e6i | − 0.662733i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16232.0 | 0.00629081 | 0.00314541 | − | 0.999995i | \(-0.498999\pi\) | ||||
0.00314541 | + | 0.999995i | \(0.498999\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.55471e6 | 0.594408 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.50282e6i | 2.07563i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 293606.i | 0.109268i | 0.998506 | + | 0.0546340i | \(0.0173992\pi\) | ||||
−0.998506 | + | 0.0546340i | \(0.982601\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.12504e6 | 0.413131 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.66769e6 | 1.32904 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.18012e6i | 1.13722i | 0.822607 | + | 0.568611i | \(0.192519\pi\) | ||||
−0.822607 | + | 0.568611i | \(0.807481\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.55700e6i | 0.549511i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.97984e6 | −1.03800 | −0.518998 | − | 0.854775i | \(-0.673695\pi\) | ||||
−0.518998 | + | 0.854775i | \(0.673695\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 696960. | 0.239638 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.07860e6i | − 0.366085i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.45977e6i | 1.15924i | 0.814887 | + | 0.579620i | \(0.196799\pi\) | ||||
−0.814887 | + | 0.579620i | \(0.803201\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 248400. | 0.0821693 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.36134e6 | 0.444616 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 4.91093e6i | − 1.58369i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.90416e6i | 1.24323i | 0.783323 | + | 0.621615i | \(0.213523\pi\) | ||||
−0.783323 | + | 0.621615i | \(0.786477\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.51430e6 | −0.476191 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.44115e6 | 1.68978 | 0.844890 | − | 0.534940i | \(-0.179666\pi\) | ||||
0.844890 | + | 0.534940i | \(0.179666\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2.36354e6i | − 0.724936i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 433026.i | − 0.131183i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −507480. | −0.151856 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.96995e6 | −0.582299 | −0.291150 | − | 0.956678i | \(-0.594038\pi\) | ||||
−0.291150 | + | 0.956678i | \(0.594038\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.15609e6i | 0.337587i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.63584e6i | − 1.33738i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 426888. | 0.121673 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.38776e6 | −0.390819 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 139020.i | − 0.0386850i | −0.999813 | − | 0.0193425i | \(-0.993843\pi\) | ||||
0.999813 | − | 0.0193425i | \(-0.00615729\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.32743e6i | 1.18994i | 0.803748 | + | 0.594970i | \(0.202836\pi\) | ||||
−0.803748 | + | 0.594970i | \(0.797164\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.59408e6 | 0.433171 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 509634. | 0.136863 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5.47184e6i | − 1.45232i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 355320.i | 0.0932130i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.79936e6 | −0.725881 | −0.362941 | − | 0.931812i | \(-0.618227\pi\) | ||||
−0.362941 | + | 0.931812i | \(0.618227\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.90241e6 | −1.51290 | −0.756449 | − | 0.654052i | \(-0.773068\pi\) | ||||
−0.756449 | + | 0.654052i | \(0.773068\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 3.31096e6i | − 0.838939i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 573600.i | 0.143683i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 446512. | 0.110579 | 0.0552894 | − | 0.998470i | \(-0.482392\pi\) | ||||
0.0552894 | + | 0.998470i | \(0.482392\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.14769e6 | −0.281014 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.49525e6i | 0.846193i | 0.906085 | + | 0.423096i | \(0.139057\pi\) | ||||
−0.906085 | + | 0.423096i | \(0.860943\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.16097e6i | − 0.517308i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −265086. | −0.0627506 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.20613e6 | −0.282343 | −0.141171 | − | 0.989985i | \(-0.545087\pi\) | ||||
−0.141171 | + | 0.989985i | \(0.545087\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.15164e6i | 0.266609i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.83485e6i | 0.420102i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.64333e6 | −1.73083 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −233546. | −0.0523097 | −0.0261548 | − | 0.999658i | \(-0.508326\pi\) | ||||
−0.0261548 | + | 0.999658i | \(0.508326\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 301806.i | 0.0668646i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.74489e6i | 0.382398i | 0.981551 | + | 0.191199i | \(0.0612376\pi\) | ||||
−0.981551 | + | 0.191199i | \(0.938762\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.91786e6 | −0.632576 | −0.316288 | − | 0.948663i | \(-0.602437\pi\) | ||||
−0.316288 | + | 0.948663i | \(0.602437\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.13365e6 | −0.457605 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.31076e6i | 1.12684i | 0.826169 | + | 0.563422i | \(0.190516\pi\) | ||||
−0.826169 | + | 0.563422i | \(0.809484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 2.95750e6i | − 0.620859i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.22528e6 | 0.254497 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 798960. | 0.164200 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.17684e6i | 0.239322i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.53255e6i | 0.509638i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.34466e6 | 0.466918 | 0.233459 | − | 0.972367i | \(-0.424996\pi\) | ||||
0.233459 | + | 0.972367i | \(0.424996\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.56536e6 | 1.09681 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 950400.i | 0.185370i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1.09614e7i | − 2.11598i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.81531e6 | −1.87535 | −0.937674 | − | 0.347517i | \(-0.887025\pi\) | ||||
−0.937674 | + | 0.347517i | \(0.887025\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.54012e6 | −0.291260 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 5.94520e6i | − 1.11292i | −0.830876 | − | 0.556458i | \(-0.812160\pi\) | ||||
0.830876 | − | 0.556458i | \(-0.187840\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.30764e6i | 0.427612i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 320760. | 0.0588393 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.07712e6 | 0.195602 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 6.47832e6i | − 1.16469i | −0.812941 | − | 0.582346i | \(-0.802135\pi\) | ||||
0.812941 | − | 0.582346i | \(-0.197865\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.08580e6i | 1.08324i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.71794e6 | −0.831444 | −0.415722 | − | 0.909492i | \(-0.636471\pi\) | ||||
−0.415722 | + | 0.909492i | \(0.636471\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.45213e6 | −0.253383 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 555039.i | − 0.0958967i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.90771e6i | 0.326375i | 0.986595 | + | 0.163188i | \(0.0521776\pi\) | ||||
−0.986595 | + | 0.163188i | \(0.947822\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.49821e6 | −0.762057 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −696924. | −0.116921 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 5.23142e6i | − 0.869164i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.18080e6i | 0.194290i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.19842e6 | 0.195295 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.01974e6 | −1.29439 | −0.647196 | − | 0.762324i | \(-0.724059\pi\) | ||||
−0.647196 | + | 0.762324i | \(0.724059\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.91162e6i | 0.305596i | 0.988257 | + | 0.152798i | \(0.0488284\pi\) | ||||
−0.988257 | + | 0.152798i | \(0.951172\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.94990e6i | 0.308756i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.48709e6 | 0.233244 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.07634e6 | −0.944068 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 2.13354e6i | − 0.328371i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.26297e7i | − 1.92563i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.50472e7 | 2.27285 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.24056e6 | −0.933874 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 850140.i | − 0.126043i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.19900e7i | 1.76128i | 0.473788 | + | 0.880639i | \(0.342886\pi\) | ||||
−0.473788 | + | 0.880639i | \(0.657114\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.39457e6 | −0.494066 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 562980. | 0.0811898 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 4.45809e6i | − 0.637061i | −0.947913 | − | 0.318530i | \(-0.896811\pi\) | ||||
0.947913 | − | 0.318530i | \(-0.103189\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 2.51829e6i | − 0.356595i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.32874e6 | −0.747732 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.30958e7 | −1.82104 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 5.02405e6i | − 0.692344i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 9.02612e6i | − 1.23272i | −0.787466 | − | 0.616358i | \(-0.788607\pi\) | ||||
0.787466 | − | 0.616358i | \(-0.211393\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.76193e6 | −1.18596 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −223560. | −0.0299907 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 6.84899e6i | − 0.910658i | −0.890323 | − | 0.455329i | \(-0.849522\pi\) | ||||
0.890323 | − | 0.455329i | \(-0.150478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.28989e7i | 1.69993i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.15474e6 | −0.150843 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.46322e6 | 0.707405 | 0.353703 | − | 0.935358i | \(-0.384923\pi\) | ||||
0.353703 | + | 0.935358i | \(0.384923\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 1.02324e7i | − 1.31337i | −0.754166 | − | 0.656684i | \(-0.771959\pi\) | ||||
0.754166 | − | 0.656684i | \(-0.228041\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 2.38810e6i | − 0.303854i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 738600. | 0.0931622 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.59437e7 | 1.99365 | 0.996825 | − | 0.0796186i | \(-0.0253702\pi\) | ||||
0.996825 | + | 0.0796186i | \(0.0253702\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.65768e6i | 0.329463i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1.13837e6i | − 0.139908i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.87596e6 | −0.228587 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.51767e6 | −0.424977 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 9.47713e6i | − 1.13522i | −0.823296 | − | 0.567612i | \(-0.807867\pi\) | ||||
0.823296 | − | 0.567612i | \(-0.192133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.43395e6i | 0.407855i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.81165e6 | −0.213356 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.45349e6 | 0.286515 | 0.143258 | − | 0.989685i | \(-0.454242\pi\) | ||||
0.143258 | + | 0.989685i | \(0.454242\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4.80902e6i | − 0.556884i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 5.87203e6i | − 0.674299i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.29978e6 | 1.05902 | 0.529512 | − | 0.848302i | \(-0.322375\pi\) | ||||
0.529512 | + | 0.848302i | \(0.322375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.14617e7 | 1.29438 | 0.647192 | − | 0.762327i | \(-0.275943\pi\) | ||||
0.647192 | + | 0.762327i | \(0.275943\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.36112e6i | − 0.152442i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 1.03918e7i | − 1.15425i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.12784e7 | 1.24244 | 0.621219 | − | 0.783637i | \(-0.286638\pi\) | ||||
0.621219 | + | 0.783637i | \(0.286638\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.82922e6 | −0.964670 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1.29494e7i | − 1.40329i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 93782.0i | 0.0100802i | 0.999987 | + | 0.00504009i | \(0.00160432\pi\) | ||||
−0.999987 | + | 0.00504009i | \(0.998396\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.14012e7 | −1.21553 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.49642e7 | 1.58248 | 0.791242 | − | 0.611504i | \(-0.209435\pi\) | ||||
0.791242 | + | 0.611504i | \(0.209435\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 5.06888e6i | − 0.531723i | −0.964011 | − | 0.265861i | \(-0.914344\pi\) | ||||
0.964011 | − | 0.265861i | \(-0.0856563\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 437400.i | 0.0455145i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.76259e6 | −0.594837 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.20971e7 | −1.23875 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 516240.i | − 0.0524424i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.50161e6i | 0.352892i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.55919e7 | −1.55892 | −0.779462 | − | 0.626450i | \(-0.784507\pi\) | ||||
−0.779462 | + | 0.626450i | \(0.784507\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.03235e7 | −1.02405 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.14180e7i | − 1.12371i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.32320e6i | 0.910367i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 495720. | 0.0480269 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.09701e7 | 1.05455 | 0.527274 | − | 0.849695i | \(-0.323214\pi\) | ||||
0.527274 | + | 0.849695i | \(0.323214\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.83704e6i | 0.270607i | 0.990804 | + | 0.135303i | \(0.0432009\pi\) | ||||
−0.990804 | + | 0.135303i | \(0.956799\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.90970e6i | 0.748619i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.05686e6 | 0.568835 | 0.284418 | − | 0.958700i | \(-0.408200\pi\) | ||||
0.284418 | + | 0.958700i | \(0.408200\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.58040e6 | 0.147284 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.68973e6i | 0.526186i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.08892e6i | 0.0999341i | 0.998751 | + | 0.0499671i | \(0.0159116\pi\) | ||||
−0.998751 | + | 0.0499671i | \(0.984088\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.98316e6 | −0.909211 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.07020e6 | −0.187111 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 7.41803e6i | − 0.665388i | −0.943035 | − | 0.332694i | \(-0.892042\pi\) | ||||
0.943035 | − | 0.332694i | \(-0.107958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 767654.i | 0.0683379i | 0.999416 | + | 0.0341690i | \(0.0108784\pi\) | ||||
−0.999416 | + | 0.0341690i | \(0.989122\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.45171e6 | 0.216613 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.11049e7 | 0.973779 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.34440e6i | 0.291074i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.31764e6i | 0.545745i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.86540e6 | 0.159943 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.42263e6 | 0.121075 | 0.0605373 | − | 0.998166i | \(-0.480719\pi\) | ||||
0.0605373 | + | 0.998166i | \(0.480719\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 897399.i | 0.0758099i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 6.16231e6i | − 0.516739i | −0.966046 | − | 0.258370i | \(-0.916815\pi\) | ||||
0.966046 | − | 0.258370i | \(-0.0831853\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.92304e7 | −2.43310 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.11250e7 | 0.919245 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.50621e7i | 1.23548i | 0.786383 | + | 0.617739i | \(0.211951\pi\) | ||||
−0.786383 | + | 0.617739i | \(0.788049\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 8.47796e6i | − 0.690343i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −952470. | −0.0769945 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.05730e7 | 1.65101 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.87636e6i | 0.468180i | 0.972215 | + | 0.234090i | \(0.0752111\pi\) | ||||
−0.972215 | + | 0.234090i | \(0.924789\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 855360.i | − 0.0676575i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.01769e7 | 0.799199 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.94632e6 | 0.619561 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.94810e6i | 0.305630i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 3.60077e6i | − 0.276758i | −0.990379 | − | 0.138379i | \(-0.955811\pi\) | ||||
0.990379 | − | 0.138379i | \(-0.0441893\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.08585e6 | −0.617074 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.16899e7 | −0.885806 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.87235e6i | 0.291358i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.22516e6i | 0.689221i | 0.938746 | + | 0.344610i | \(0.111989\pi\) | ||||
−0.938746 | + | 0.344610i | \(0.888011\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.02705e6 | −0.447127 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.15520e6 | 0.158768 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2.60568e6i | − 0.190615i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 256176.i | 0.0186098i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.63923e7 | −1.90395 | −0.951975 | − | 0.306177i | \(-0.900950\pi\) | ||||
−0.951975 | + | 0.306177i | \(0.900950\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.39505e7 | −0.999426 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.03306e6i | 0.571525i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.86159e6i | 0.484819i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.79485e6 | 0.687324 | 0.343662 | − | 0.939093i | \(-0.388333\pi\) | ||||
0.343662 | + | 0.939093i | \(0.388333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 5.51282e6i | − 0.381576i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 4.07584e6i | − 0.280193i | −0.990138 | − | 0.140096i | \(-0.955259\pi\) | ||||
0.990138 | − | 0.140096i | \(-0.0447412\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.41639e6 | 0.574655 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.00824e6 | 0.0683747 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.65709e7i | 1.11618i | 0.829781 | + | 0.558089i | \(0.188465\pi\) | ||||
−0.829781 | + | 0.558089i | \(0.811535\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.66143e6i | 0.378775i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.44141e7 | −0.957892 | −0.478946 | − | 0.877844i | \(-0.658981\pi\) | ||||
−0.478946 | + | 0.877844i | \(0.658981\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.94396e6 | 0.128321 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 523908.i | − 0.0343521i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 4.01259e7i | − 2.61349i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.67944e7 | 1.08659 | 0.543295 | − | 0.839542i | \(-0.317177\pi\) | ||||
0.543295 | + | 0.839542i | \(0.317177\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 991116. | 0.0636997 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1.34556e7i | − 0.859081i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.32943e7i | 0.843188i | 0.906785 | + | 0.421594i | \(0.138529\pi\) | ||||
−0.906785 | + | 0.421594i | \(0.861471\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −324000. | −0.0204146 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.14786e6 | 0.134445 | 0.0672225 | − | 0.997738i | \(-0.478586\pi\) | ||||
0.0672225 | + | 0.997738i | \(0.478586\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.50128e6i | − 0.0933577i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 2.21324e6i | − 0.136734i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.73317e7 | −1.06378 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.31059e7 | −0.799193 | −0.399596 | − | 0.916691i | \(-0.630850\pi\) | ||||
−0.399596 | + | 0.916691i | \(0.630850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.26722e6i | 0.0767742i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 2.37154e7i | − 1.42752i | −0.700392 | − | 0.713759i | \(-0.746991\pi\) | ||||
0.700392 | − | 0.713759i | \(-0.253009\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.42175e6 | 0.264448 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.33975e7 | −0.796105 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.83495e7i | 1.08338i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 367200.i | 0.0215415i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.06345e6 | −0.236859 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.98537e6 | −0.520430 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.40048e6i | 0.483468i | 0.970343 | + | 0.241734i | \(0.0777161\pi\) | ||||
−0.970343 | + | 0.241734i | \(0.922284\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.44884e6i | 0.483175i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.43971e7 | 1.95470 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.04572e7 | −1.15522 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1.85720e7i | − 1.04218i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 5.41023e6i | − 0.301696i | −0.988557 | − | 0.150848i | \(-0.951800\pi\) | ||||
0.988557 | − | 0.150848i | \(-0.0482004\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.14752e6 | 0.451501 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.65210e6 | −0.146052 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.53348e6i | − 0.0839246i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 6.96960e6i | − 0.379069i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.00306e7 | −0.542177 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.60777e7 | 1.40087 | 0.700436 | − | 0.713715i | \(-0.252989\pi\) | ||||
0.700436 | + | 0.713715i | \(0.252989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.90021e7i | 1.01449i | 0.861800 | + | 0.507247i | \(0.169337\pi\) | ||||
−0.861800 | + | 0.507247i | \(0.830663\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.10934e6i | 0.271105i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.12942e7 | 0.595608 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.27301e7 | 0.667231 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.38045e6i | 0.488668i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 3.10173e7i | − 1.60600i | −0.595978 | − | 0.803001i | \(-0.703236\pi\) | ||||
0.595978 | − | 0.803001i | \(-0.296764\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.56290e7 | 0.804323 | 0.402162 | − | 0.915569i | \(-0.368259\pi\) | ||||
0.402162 | + | 0.915569i | \(0.368259\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −664740. | −0.0340030 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.58421e7i | 0.805467i | 0.915317 | + | 0.402733i | \(0.131940\pi\) | ||||
−0.915317 | + | 0.402733i | \(0.868060\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 2.06176e6i | − 0.104196i | −0.998642 | − | 0.0520980i | \(-0.983409\pi\) | ||||
0.998642 | − | 0.0520980i | \(-0.0165908\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.09193e7 | 0.548521 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.86597e6 | −0.292905 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 4.46292e7i | − 2.21515i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.61857e6i | 0.129196i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.03900e7 | −1.49048 | −0.745240 | − | 0.666796i | \(-0.767665\pi\) | ||||
−0.745240 | + | 0.666796i | \(0.767665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.05583e7 | −0.514760 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 6.18964e6i | − 0.299983i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.07029e6i | 0.196103i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.77114e7 | −1.32724 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.47817e6 | 0.356062 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.07480e6i | 0.240212i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.97738e7i | − 1.40108i | −0.713615 | − | 0.700538i | \(-0.752944\pi\) | ||||
0.713615 | − | 0.700538i | \(-0.247056\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.11078e6 | 0.239096 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.64100e6 | −0.401894 | −0.200947 | − | 0.979602i | \(-0.564402\pi\) | ||||
−0.200947 | + | 0.979602i | \(0.564402\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 3.35663e7i | − 1.55210i | −0.630670 | − | 0.776051i | \(-0.717220\pi\) | ||||
0.630670 | − | 0.776051i | \(-0.282780\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.04033e7i | 1.39770i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.90191e7 | 1.78341 | 0.891703 | − | 0.452621i | \(-0.149511\pi\) | ||||
0.891703 | + | 0.452621i | \(0.149511\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.78843e6 | −0.399366 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1.12361e7i | − 0.507656i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 4.46448e6i | − 0.200549i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.10570e7 | −0.493848 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.34526e7 | −0.597409 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.20007e7i | 0.971441i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.81382e7i | 0.796333i | 0.917313 | + | 0.398166i | \(0.130353\pi\) | ||||
−0.917313 | + | 0.398166i | \(0.869647\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.18136e7 | 0.515717 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.05312e7 | 1.32527 | 0.662634 | − | 0.748943i | \(-0.269438\pi\) | ||||
0.662634 | + | 0.748943i | \(0.269438\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.35533e7i | 1.87983i | 0.341405 | + | 0.939916i | \(0.389097\pi\) | ||||
−0.341405 | + | 0.939916i | \(0.610903\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.56460e7i | 0.671497i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.34152e7 | 0.572515 | 0.286257 | − | 0.958153i | \(-0.407589\pi\) | ||||
0.286257 | + | 0.958153i | \(0.407589\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.04480e7 | −1.29212 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 393660.i | − 0.0166122i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.88141e7i | 0.789504i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.57641e7 | 1.90971 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.55320e6 | 0.147448 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.00218e7i | 0.826236i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.29441e7i | 0.531203i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.10925e7 | 0.860815 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.48935e7 | 1.01033 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.10816e6i | 0.125454i | 0.998031 | + | 0.0627272i | \(0.0199798\pi\) | ||||
−0.998031 | + | 0.0627272i | \(0.980020\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.78216e6i | 0.0715381i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.19035e6 | 0.0475203 | 0.0237602 | − | 0.999718i | \(-0.492436\pi\) | ||||
0.0237602 | + | 0.999718i | \(0.492436\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 388080. | 0.0154079 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.84675e7i | 0.729213i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.66218e7i | 1.04547i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.71996e7 | 1.84353 | 0.921764 | − | 0.387752i | \(-0.126748\pi\) | ||||
0.921764 | + | 0.387752i | \(0.126748\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.52120e7 | 0.590931 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 4.02696e6i | − 0.155587i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.04118e7i | 0.400103i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.42038e6 | −0.245393 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.33595e6 | 0.0507870 | 0.0253935 | − | 0.999678i | \(-0.491916\pi\) | ||||
0.0253935 | + | 0.999678i | \(0.491916\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.35456e7i | − 0.512180i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.35184e7i | 0.508417i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.63944e6 | 0.0613291 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.47238e7 | −0.547861 | −0.273931 | − | 0.961749i | \(-0.588324\pi\) | ||||
−0.273931 | + | 0.961749i | \(0.588324\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 7.29758e6i | − 0.270094i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.69196e7i | 0.991049i | 0.868594 | + | 0.495525i | \(0.165024\pi\) | ||||
−0.868594 | + | 0.495525i | \(0.834976\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.15164e7 | 0.421733 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.46806e6 | 0.308464 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.73160e6i | 0.135214i | 0.997712 | + | 0.0676068i | \(0.0215364\pi\) | ||||
−0.997712 | + | 0.0676068i | \(0.978464\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.68172e7i | 0.606160i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.13202e6 | 0.291573 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.18735e7 | −0.780166 | −0.390083 | − | 0.920780i | \(-0.627554\pi\) | ||||
−0.390083 | + | 0.920780i | \(0.627554\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.75127e7i | 0.621362i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 3.00996e6i | − 0.106238i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.26079e7 | −0.793805 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.57267e7 | −0.549324 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.84670e7i | − 0.641699i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1.94897e7i | − 0.673730i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.76025e7 | −0.605352 | −0.302676 | − | 0.953093i | \(-0.597880\pi\) | ||||
−0.302676 | + | 0.953093i | \(0.597880\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.56206e6 | −0.121868 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.67317e7i | 0.569497i | 0.958602 | + | 0.284749i | \(0.0919101\pi\) | ||||
−0.958602 | + | 0.284749i | \(0.908090\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.71385e7i | − 0.918975i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.28998e6 | 0.245592 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.55382e7 | 1.86147 | 0.930733 | − | 0.365699i | \(-0.119170\pi\) | ||||
0.930733 | + | 0.365699i | \(0.119170\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.96452e6i | − 0.0655088i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 690930.i | − 0.0229225i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.86784e7 | 1.27669 | 0.638344 | − | 0.769751i | \(-0.279620\pi\) | ||||
0.638344 | + | 0.769751i | \(0.279620\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.32854e7 | 0.436299 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.11731e7i | 1.01856i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 7.98960e6i | − 0.259737i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.58498e6 | 0.310033 | 0.155016 | − | 0.987912i | \(-0.450457\pi\) | ||||
0.155016 | + | 0.987912i | \(0.450457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.00977e7 | −0.324976 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.30616e7i | 1.37890i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.03650e7i | − 0.330242i | −0.986273 | − | 0.165121i | \(-0.947198\pi\) | ||||
0.986273 | − | 0.165121i | \(-0.0528015\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.16588e6 | −0.195471 |
(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 | 768.6.d.c.385.2 | 2 | ||
4.3 | odd | 2 | 768.6.d.p.385.1 | 2 | |||
8.3 | odd | 2 | 768.6.d.p.385.2 | 2 | |||
8.5 | even | 2 | inner | 768.6.d.c.385.1 | 2 | ||
16.3 | odd | 4 | 48.6.a.c.1.1 | 1 | |||
16.5 | even | 4 | 192.6.a.o.1.1 | 1 | |||
16.11 | odd | 4 | 192.6.a.g.1.1 | 1 | |||
16.13 | even | 4 | 6.6.a.a.1.1 | ✓ | 1 | ||
48.5 | odd | 4 | 576.6.a.j.1.1 | 1 | |||
48.11 | even | 4 | 576.6.a.i.1.1 | 1 | |||
48.29 | odd | 4 | 18.6.a.b.1.1 | 1 | |||
48.35 | even | 4 | 144.6.a.j.1.1 | 1 | |||
80.13 | odd | 4 | 150.6.c.b.49.1 | 2 | |||
80.29 | even | 4 | 150.6.a.d.1.1 | 1 | |||
80.77 | odd | 4 | 150.6.c.b.49.2 | 2 | |||
112.13 | odd | 4 | 294.6.a.m.1.1 | 1 | |||
112.45 | odd | 12 | 294.6.e.a.79.1 | 2 | |||
112.61 | odd | 12 | 294.6.e.a.67.1 | 2 | |||
112.93 | even | 12 | 294.6.e.g.67.1 | 2 | |||
112.109 | even | 12 | 294.6.e.g.79.1 | 2 | |||
144.13 | even | 12 | 162.6.c.e.55.1 | 2 | |||
144.29 | odd | 12 | 162.6.c.h.109.1 | 2 | |||
144.61 | even | 12 | 162.6.c.e.109.1 | 2 | |||
144.77 | odd | 12 | 162.6.c.h.55.1 | 2 | |||
176.109 | odd | 4 | 726.6.a.a.1.1 | 1 | |||
208.77 | even | 4 | 1014.6.a.c.1.1 | 1 | |||
240.29 | odd | 4 | 450.6.a.m.1.1 | 1 | |||
240.77 | even | 4 | 450.6.c.j.199.1 | 2 | |||
240.173 | even | 4 | 450.6.c.j.199.2 | 2 | |||
336.125 | even | 4 | 882.6.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.6.a.a.1.1 | ✓ | 1 | 16.13 | even | 4 | ||
18.6.a.b.1.1 | 1 | 48.29 | odd | 4 | |||
48.6.a.c.1.1 | 1 | 16.3 | odd | 4 | |||
144.6.a.j.1.1 | 1 | 48.35 | even | 4 | |||
150.6.a.d.1.1 | 1 | 80.29 | even | 4 | |||
150.6.c.b.49.1 | 2 | 80.13 | odd | 4 | |||
150.6.c.b.49.2 | 2 | 80.77 | odd | 4 | |||
162.6.c.e.55.1 | 2 | 144.13 | even | 12 | |||
162.6.c.e.109.1 | 2 | 144.61 | even | 12 | |||
162.6.c.h.55.1 | 2 | 144.77 | odd | 12 | |||
162.6.c.h.109.1 | 2 | 144.29 | odd | 12 | |||
192.6.a.g.1.1 | 1 | 16.11 | odd | 4 | |||
192.6.a.o.1.1 | 1 | 16.5 | even | 4 | |||
294.6.a.m.1.1 | 1 | 112.13 | odd | 4 | |||
294.6.e.a.67.1 | 2 | 112.61 | odd | 12 | |||
294.6.e.a.79.1 | 2 | 112.45 | odd | 12 | |||
294.6.e.g.67.1 | 2 | 112.93 | even | 12 | |||
294.6.e.g.79.1 | 2 | 112.109 | even | 12 | |||
450.6.a.m.1.1 | 1 | 240.29 | odd | 4 | |||
450.6.c.j.199.1 | 2 | 240.77 | even | 4 | |||
450.6.c.j.199.2 | 2 | 240.173 | even | 4 | |||
576.6.a.i.1.1 | 1 | 48.11 | even | 4 | |||
576.6.a.j.1.1 | 1 | 48.5 | odd | 4 | |||
726.6.a.a.1.1 | 1 | 176.109 | odd | 4 | |||
768.6.d.c.385.1 | 2 | 8.5 | even | 2 | inner | ||
768.6.d.c.385.2 | 2 | 1.1 | even | 1 | trivial | ||
768.6.d.p.385.1 | 2 | 4.3 | odd | 2 | |||
768.6.d.p.385.2 | 2 | 8.3 | odd | 2 | |||
882.6.a.a.1.1 | 1 | 336.125 | even | 4 | |||
1014.6.a.c.1.1 | 1 | 208.77 | even | 4 |