Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,6,Mod(49,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.c (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: | \(64.1535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{129})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 65x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.3 | ||
Root | \(5.17891i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.49 |
Dual form | 400.6.c.l.49.2 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 16.7156i | 1.07231i | 0.844120 | + | 0.536154i | \(0.180123\pi\) | ||||
−0.844120 | + | 0.536154i | \(0.819877\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 94.1469i | − 0.726208i | −0.931749 | − | 0.363104i | \(-0.881717\pi\) | ||||
0.931749 | − | 0.363104i | \(-0.118283\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −36.4124 | −0.149845 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −143.706 | −0.358091 | −0.179046 | − | 0.983841i | \(-0.557301\pi\) | ||||
−0.179046 | + | 0.983841i | \(0.557301\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 421.412i | − 0.691590i | −0.938310 | − | 0.345795i | \(-0.887609\pi\) | ||||
0.938310 | − | 0.345795i | \(-0.112391\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1982.11i | 1.66344i | 0.555198 | + | 0.831718i | \(0.312642\pi\) | ||||
−0.555198 | + | 0.831718i | \(0.687358\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1317.76 | −0.837439 | −0.418720 | − | 0.908116i | \(-0.637521\pi\) | ||||
−0.418720 | + | 0.908116i | \(0.637521\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1573.73 | 0.778719 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 4020.02i | − 1.58456i | −0.610157 | − | 0.792280i | \(-0.708894\pi\) | ||||
0.610157 | − | 0.792280i | \(-0.291106\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3453.24i | 0.911628i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6417.28 | 1.41695 | 0.708477 | − | 0.705734i | \(-0.249383\pi\) | ||||
0.708477 | + | 0.705734i | \(0.249383\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2350.64 | 0.439322 | 0.219661 | − | 0.975576i | \(-0.429505\pi\) | ||||
0.219661 | + | 0.975576i | \(0.429505\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 2402.14i | − 0.383984i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 7876.58i | − 0.945874i | −0.881096 | − | 0.472937i | \(-0.843194\pi\) | ||||
0.881096 | − | 0.472937i | \(-0.156806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7044.18 | 0.741598 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15081.6 | 1.40116 | 0.700582 | − | 0.713572i | \(-0.252924\pi\) | ||||
0.700582 | + | 0.713572i | \(0.252924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1141.40i | 0.0941384i | 0.998892 | + | 0.0470692i | \(0.0149881\pi\) | ||||
−0.998892 | + | 0.0470692i | \(0.985012\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 21557.3i | 1.42348i | 0.702445 | + | 0.711738i | \(0.252092\pi\) | ||||
−0.702445 | + | 0.711738i | \(0.747908\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7943.36 | 0.472622 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −33132.3 | −1.78372 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9560.44i | − 0.467507i | −0.972296 | − | 0.233754i | \(-0.924899\pi\) | ||||
0.972296 | − | 0.233754i | \(-0.0751009\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 22027.2i | − 0.897993i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 42740.7 | 1.59850 | 0.799248 | − | 0.601002i | \(-0.205232\pi\) | ||||
0.799248 | + | 0.601002i | \(0.205232\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 32132.1 | 1.10564 | 0.552820 | − | 0.833301i | \(-0.313552\pi\) | ||||
0.552820 | + | 0.833301i | \(0.313552\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3428.11i | 0.108819i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 30371.4i | 0.826567i | 0.910602 | + | 0.413283i | \(0.135618\pi\) | ||||
−0.910602 | + | 0.413283i | \(0.864382\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 67197.2 | 1.69914 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −36006.7 | −0.847692 | −0.423846 | − | 0.905734i | \(-0.639320\pi\) | ||||
−0.423846 | + | 0.905734i | \(0.639320\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 63438.0i | 1.39329i | 0.717414 | + | 0.696647i | \(0.245326\pi\) | ||||
−0.717414 | + | 0.696647i | \(0.754674\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13529.5i | 0.260049i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −89922.8 | −1.62107 | −0.810536 | − | 0.585689i | \(-0.800824\pi\) | ||||
−0.810536 | + | 0.585689i | \(0.800824\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −66571.4 | −1.12739 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 38211.2i | 0.608829i | 0.952540 | + | 0.304414i | \(0.0984608\pi\) | ||||
−0.952540 | + | 0.304414i | \(0.901539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 107269.i | 1.51941i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5745.69 | −0.0768895 | −0.0384447 | − | 0.999261i | \(-0.512240\pi\) | ||||
−0.0384447 | + | 0.999261i | \(0.512240\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −39674.7 | −0.502238 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 39292.5i | 0.471088i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 178780.i | 1.92926i | 0.263613 | + | 0.964629i | \(0.415086\pi\) | ||||
−0.263613 | + | 0.964629i | \(0.584914\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5232.69 | 0.0536583 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 152223. | 1.48483 | 0.742417 | − | 0.669938i | \(-0.233679\pi\) | ||||
0.742417 | + | 0.669938i | \(0.233679\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 35830.1i | − 0.332778i | −0.986060 | − | 0.166389i | \(-0.946789\pi\) | ||||
0.986060 | − | 0.166389i | \(-0.0532108\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 70030.2i | − 0.591324i | −0.955293 | − | 0.295662i | \(-0.904460\pi\) | ||||
0.955293 | − | 0.295662i | \(-0.0955403\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −38466.9 | −0.310114 | −0.155057 | − | 0.987906i | \(-0.549556\pi\) | ||||
−0.155057 | + | 0.987906i | \(0.549556\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 131662. | 1.01427 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 39951.6i | − 0.294333i | −0.989112 | − | 0.147166i | \(-0.952985\pi\) | ||||
0.989112 | − | 0.147166i | \(-0.0470153\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15344.6i | 0.103632i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 186610. | 1.20800 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −140400. | −0.871771 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 252099.i | 1.50248i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 233239.i | 1.28319i | 0.767043 | + | 0.641596i | \(0.221727\pi\) | ||||
−0.767043 | + | 0.641596i | \(0.778273\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −19079.2 | −0.100945 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −55237.0 | −0.281224 | −0.140612 | − | 0.990065i | \(-0.544907\pi\) | ||||
−0.140612 | + | 0.990065i | \(0.544907\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 124063.i | 0.608155i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 261520.i | 1.19043i | 0.803566 | + | 0.595215i | \(0.202933\pi\) | ||||
−0.803566 | + | 0.595215i | \(0.797067\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 293366. | 1.28787 | 0.643935 | − | 0.765080i | \(-0.277301\pi\) | ||||
0.643935 | + | 0.765080i | \(0.277301\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −360345. | −1.52641 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 60559.6i | 0.247653i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 132778.i | 0.506797i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 304505. | 1.12364 | 0.561822 | − | 0.827258i | \(-0.310101\pi\) | ||||
0.561822 | + | 0.827258i | \(0.310101\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 337909. | 1.20603 | 0.603015 | − | 0.797730i | \(-0.293966\pi\) | ||||
0.603015 | + | 0.797730i | \(0.293966\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 72173.5i | − 0.249258i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 68385.9i | 0.221420i | 0.993853 | + | 0.110710i | \(0.0353125\pi\) | ||||
−0.993853 | + | 0.110710i | \(0.964687\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 159809. | 0.501312 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −378473. | −1.15072 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 404471.i | − 1.19239i | −0.802840 | − | 0.596195i | \(-0.796678\pi\) | ||||
0.802840 | − | 0.596195i | \(-0.203322\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 411733.i | − 1.14242i | −0.820805 | − | 0.571209i | \(-0.806475\pi\) | ||||
0.820805 | − | 0.571209i | \(-0.193525\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 193705. | 0.521703 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 47982.9 | 0.125486 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 162247.i | 0.412155i | 0.978536 | + | 0.206077i | \(0.0660698\pi\) | ||||
−0.978536 | + | 0.206077i | \(0.933930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 714438.i | 1.71408i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 384396. | 0.896698 | 0.448349 | − | 0.893859i | \(-0.352012\pi\) | ||||
0.448349 | + | 0.893859i | \(0.352012\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 579219. | 1.31415 | 0.657077 | − | 0.753823i | \(-0.271792\pi\) | ||||
0.657077 | + | 0.753823i | \(0.271792\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 537108.i | 1.18559i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 284842.i | − 0.595662i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 325112. | 0.662031 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −142455. | −0.282550 | −0.141275 | − | 0.989970i | \(-0.545120\pi\) | ||||
−0.141275 | + | 0.989970i | \(0.545120\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 267272.i | − 0.516487i | −0.966080 | − | 0.258244i | \(-0.916856\pi\) | ||||
0.966080 | − | 0.258244i | \(-0.0831438\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14189.5i | 0.0260496i | 0.999915 | + | 0.0130248i | \(0.00414604\pi\) | ||||
−0.999915 | + | 0.0130248i | \(0.995854\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 169198. | 0.302875 | 0.151437 | − | 0.988467i | \(-0.451610\pi\) | ||||
0.151437 | + | 0.988467i | \(0.451610\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −507677. | −0.886335 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 604167.i | − 1.02900i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 146379.i | 0.237439i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 189371. | 0.299880 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 407591. | 0.630259 | 0.315129 | − | 0.949049i | \(-0.397952\pi\) | ||||
0.315129 | + | 0.949049i | \(0.397952\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 601875.i | − 0.908987i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 221306.i | − 0.319039i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.06041e6 | −1.49404 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 835287. | 1.15042 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 103743.i | − 0.139700i | −0.997558 | − | 0.0698500i | \(-0.977748\pi\) | ||||
0.997558 | − | 0.0698500i | \(-0.0222521\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 803726.i | 1.03524i | 0.855609 | + | 0.517622i | \(0.173183\pi\) | ||||
−0.855609 | + | 0.517622i | \(0.826817\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.35955e6 | −1.71319 | −0.856596 | − | 0.515988i | \(-0.827425\pi\) | ||||
−0.856596 | + | 0.515988i | \(0.827425\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −226154. | −0.278852 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 622827.i | 0.751584i | 0.926704 | + | 0.375792i | \(0.122629\pi\) | ||||
−0.926704 | + | 0.375792i | \(0.877371\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.50312e6i | − 1.73829i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −642843. | −0.727964 | −0.363982 | − | 0.931406i | \(-0.618583\pi\) | ||||
−0.363982 | + | 0.931406i | \(0.618583\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.11814e6 | 1.24009 | 0.620046 | − | 0.784566i | \(-0.287114\pi\) | ||||
0.620046 | + | 0.784566i | \(0.287114\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 273644.i | − 0.297283i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 555322.i | 0.579165i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −638724. | −0.652852 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −731067. | −0.732442 | −0.366221 | − | 0.930528i | \(-0.619349\pi\) | ||||
−0.366221 | + | 0.930528i | \(0.619349\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 577702.i | 0.567418i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 1.76622e6i | − 1.66806i | −0.551720 | − | 0.834030i | \(-0.686028\pi\) | ||||
0.551720 | − | 0.834030i | \(-0.313972\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −741555. | −0.686901 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −233668. | −0.212324 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.00926e6i | 0.899735i | 0.893095 | + | 0.449868i | \(0.148529\pi\) | ||||
−0.893095 | + | 0.449868i | \(0.851471\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 96042.8i | − 0.0824492i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 775681. | 0.653585 | 0.326793 | − | 0.945096i | \(-0.394032\pi\) | ||||
0.326793 | + | 0.945096i | \(0.394032\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.21395e6 | −1.00410 | −0.502052 | − | 0.864837i | \(-0.667422\pi\) | ||||
−0.502052 | + | 0.864837i | \(0.667422\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 663187.i | − 0.538554i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 218505.i | − 0.171104i | −0.996334 | − | 0.0855522i | \(-0.972735\pi\) | ||||
0.996334 | − | 0.0855522i | \(-0.0272654\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −85592.6 | −0.0658303 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −316219. | −0.238903 | −0.119452 | − | 0.992840i | \(-0.538114\pi\) | ||||
−0.119452 | + | 0.992840i | \(0.538114\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 927934.i | − 0.688733i | −0.938835 | − | 0.344366i | \(-0.888094\pi\) | ||||
0.938835 | − | 0.344366i | \(-0.111906\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1.41989e6i | − 1.01754i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.50892e6 | −1.76702 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.98842e6 | −2.06876 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 262992.i | − 0.178967i | −0.995988 | − | 0.0894835i | \(-0.971478\pi\) | ||||
0.995988 | − | 0.0894835i | \(-0.0285216\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 496252.i | − 0.326446i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.69409e6 | −1.09587 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 107459. | 0.0683640 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.54451e6i | 1.59220i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.15704e6i | − 1.30621i | −0.757269 | − | 0.653104i | \(-0.773467\pi\) | ||||
0.757269 | − | 0.653104i | \(-0.226533\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 598923. | 0.356841 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.33078e6 | 1.36647 | 0.683235 | − | 0.730199i | \(-0.260573\pi\) | ||||
0.683235 | + | 0.730199i | \(0.260573\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.12235e6i | 0.647539i | 0.946136 | + | 0.323769i | \(0.104950\pi\) | ||||
−0.946136 | + | 0.323769i | \(0.895050\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.27955e6i | − 0.715169i | −0.933881 | − | 0.357584i | \(-0.883600\pi\) | ||||
0.933881 | − | 0.357584i | \(-0.116400\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −922203. | −0.507399 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.17060e6 | 0.634082 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.61196e6i | − 1.39303i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 642998.i | − 0.332537i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.02956e6 | 1.03374 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.09571e6 | 1.05138 | 0.525691 | − | 0.850675i | \(-0.323807\pi\) | ||||
0.525691 | + | 0.850675i | \(0.323807\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 286805.i | 0.141735i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 571289.i | − 0.274019i | −0.990570 | − | 0.137010i | \(-0.956251\pi\) | ||||
0.990570 | − | 0.137010i | \(-0.0437491\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 667817. | 0.315615 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −337802. | −0.157317 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 2.33017e6i | − 1.06943i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.24067e6i | − 0.998973i | −0.866322 | − | 0.499486i | \(-0.833522\pi\) | ||||
0.866322 | − | 0.499486i | \(-0.166478\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −130448. | −0.0573290 | −0.0286645 | − | 0.999589i | \(-0.509125\pi\) | ||||
−0.0286645 | + | 0.999589i | \(0.509125\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.45524e6 | 0.630473 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1.95452e6i | − 0.834839i | −0.908714 | − | 0.417420i | \(-0.862935\pi\) | ||||
0.908714 | − | 0.417420i | \(-0.137065\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.11930e6i | 1.29535i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −850543. | −0.348305 | −0.174153 | − | 0.984719i | \(-0.555719\pi\) | ||||
−0.174153 | + | 0.984719i | \(0.555719\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −739600. | −0.298696 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.34687e6i | − 0.934807i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.50673e6i | 0.583941i | 0.956427 | + | 0.291970i | \(0.0943109\pi\) | ||||
−0.956427 | + | 0.291970i | \(0.905689\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −549159. | −0.209958 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −900086. | −0.339507 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 2.90602e6i | − 1.08150i | −0.841184 | − | 0.540749i | \(-0.818141\pi\) | ||||
0.841184 | − | 0.540749i | \(-0.181859\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2.70432e6i | − 0.979952i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.16710e6 | 1.84777 | 0.923887 | − | 0.382665i | \(-0.124994\pi\) | ||||
0.923887 | + | 0.382665i | \(0.124994\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.89874e6 | −1.37598 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.85088e6i | 1.34142i | 0.741721 | + | 0.670708i | \(0.234010\pi\) | ||||
−0.741721 | + | 0.670708i | \(0.765990\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 41561.1i | − 0.0141062i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.49855e6 | −1.84236 | −0.921179 | − | 0.389138i | \(-0.872773\pi\) | ||||
−0.921179 | + | 0.389138i | \(0.872773\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.96814e6 | 2.63582 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 923321.i | − 0.301558i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.71425e6i | 0.545881i | 0.962031 | + | 0.272941i | \(0.0879963\pi\) | ||||
−0.962031 | + | 0.272941i | \(0.912004\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.07380e6 | −0.652130 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.63329e6 | 1.12834 | 0.564169 | − | 0.825660i | \(-0.309197\pi\) | ||||
0.564169 | + | 0.825660i | \(0.309197\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 990591.i | − 0.303831i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.13191e6i | 0.338709i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.38246e6 | 0.408642 | 0.204321 | − | 0.978904i | \(-0.434501\pi\) | ||||
0.204321 | + | 0.978904i | \(0.434501\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.37148e6 | −1.27651 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.02390e6i | − 1.16084i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.90379e6i | 1.38099i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.55435e6 | 0.710795 | 0.355398 | − | 0.934715i | \(-0.384345\pi\) | ||||
0.355398 | + | 0.934715i | \(0.384345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.68110e6 | −0.462263 | −0.231132 | − | 0.972923i | \(-0.574243\pi\) | ||||
−0.231132 | + | 0.972923i | \(0.574243\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 784954.i | − 0.213301i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3.02513e6i | − 0.802925i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.01229e6 | −0.265560 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.32369e6 | 0.602539 | 0.301269 | − | 0.953539i | \(-0.402590\pi\) | ||||
0.301269 | + | 0.953539i | \(0.402590\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.06439e6i | 1.04178i | 0.853624 | + | 0.520890i | \(0.174400\pi\) | ||||
−0.853624 | + | 0.520890i | \(0.825600\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.29744e6i | 1.32697i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.39272e6 | 1.58316 | 0.791579 | − | 0.611066i | \(-0.209259\pi\) | ||||
0.791579 | + | 0.611066i | \(0.209259\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −289237. | −0.0708202 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.23515e6i | 0.783222i | 0.920131 | + | 0.391611i | \(0.128082\pi\) | ||||
−0.920131 | + | 0.391611i | \(0.871918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.08999e6i | 1.20489i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.74812e6 | 0.643310 | 0.321655 | − | 0.946857i | \(-0.395761\pi\) | ||||
0.321655 | + | 0.946857i | \(0.395761\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.16732e6 | −0.501745 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.64837e6i | 1.29324i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 5.37326e6i | − 1.20350i | −0.798684 | − | 0.601751i | \(-0.794470\pi\) | ||||
0.798684 | − | 0.601751i | \(-0.205530\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.84472e6 | −1.51644 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.19928e6 | −1.79690 | −0.898449 | − | 0.439078i | \(-0.855305\pi\) | ||||
−0.898449 | + | 0.439078i | \(0.855305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.76963e6i | 0.817233i | 0.912706 | + | 0.408617i | \(0.133989\pi\) | ||||
−0.912706 | + | 0.408617i | \(0.866011\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 6.03412e6i | − 1.28033i | −0.768237 | − | 0.640165i | \(-0.778866\pi\) | ||||
0.768237 | − | 0.640165i | \(-0.221134\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.85937e6 | 0.600259 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.14311e6 | −0.237431 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 164026.i | − 0.0337101i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 348119.i | 0.0700537i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.26406e6 | −1.04829 | −0.524146 | − | 0.851629i | \(-0.675615\pi\) | ||||
−0.524146 | + | 0.851629i | \(0.675615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.31929e6 | −0.654157 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 6.32641e6i | − 1.23393i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.19979e6i | 0.420300i | 0.977669 | + | 0.210150i | \(0.0673952\pi\) | ||||
−0.977669 | + | 0.210150i | \(0.932605\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.76099e6 | 1.27861 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.47314e6 | −1.21174 | −0.605872 | − | 0.795562i | \(-0.707176\pi\) | ||||
−0.605872 | + | 0.795562i | \(0.707176\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.27198e7i | 2.35701i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.38992e6i | 0.615600i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.62090e6 | 1.54989 | 0.774946 | − | 0.632028i | \(-0.217777\pi\) | ||||
0.774946 | + | 0.632028i | \(0.217777\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.88238e6 | 1.22502 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.10557e6i | 1.42845i | 0.699918 | + | 0.714223i | \(0.253220\pi\) | ||||
−0.699918 | + | 0.714223i | \(0.746780\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.23789e6i | 0.559426i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.39610e6 | 1.09426 | 0.547131 | − | 0.837047i | \(-0.315720\pi\) | ||||
0.547131 | + | 0.837047i | \(0.315720\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.97250e6 | 1.01182 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 4.55055e6i | − 0.763433i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 3.09792e6i | − 0.509735i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.71205e6 | −0.441957 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.53647e6 | 1.21639 | 0.608197 | − | 0.793786i | \(-0.291893\pi\) | ||||
0.608197 | + | 0.793786i | \(0.291893\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.87780e6i | 0.300189i | 0.988672 | + | 0.150095i | \(0.0479578\pi\) | ||||
−0.988672 | + | 0.150095i | \(0.952042\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.65924e6i | 0.730784i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.72424e6 | −1.51083 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.55629e6 | −0.239527 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 6.35559e6i | − 0.969031i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.42542e6i | 0.961537i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.14151e6 | −0.169242 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.44482e6 | 0.359131 | 0.179566 | − | 0.983746i | \(-0.442531\pi\) | ||||
0.179566 | + | 0.983746i | \(0.442531\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.68202e6i | 1.40918i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.09485e7i | 1.56453i | 0.622944 | + | 0.782266i | \(0.285936\pi\) | ||||
−0.622944 | + | 0.782266i | \(0.714064\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.17001e6 | −0.165675 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.45645e6 | −1.18661 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.46595e6i | 1.17723i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 768938.i | − 0.105015i | −0.998621 | − | 0.0525077i | \(-0.983279\pi\) | ||||
0.998621 | − | 0.0525077i | \(-0.0167214\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 481000. | 0.0651052 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.76131e6 | 0.638733 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.47386e7i | − 1.95968i | −0.199792 | − | 0.979838i | \(-0.564026\pi\) | ||||
0.199792 | − | 0.979838i | \(-0.435974\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.26749e6i | 0.818721i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.33696e6 | 0.432086 | 0.216043 | − | 0.976384i | \(-0.430685\pi\) | ||||
0.216043 | + | 0.976384i | \(0.430685\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.54413e7 | −1.98195 | −0.990974 | − | 0.134051i | \(-0.957201\pi\) | ||||
−0.990974 | + | 0.134051i | \(0.957201\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 2.38123e6i | − 0.302981i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 4.05636e6i | − 0.507221i | −0.967306 | − | 0.253610i | \(-0.918382\pi\) | ||||
0.967306 | − | 0.253610i | \(-0.0816181\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.46762e6 | 0.553834 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.59746e6 | 0.442136 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.37389e6i | 0.167410i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.22567e7i | 1.46818i | 0.679052 | + | 0.734090i | \(0.262391\pi\) | ||||
−0.679052 | + | 0.734090i | \(0.737609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.09759e6 | −0.367905 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −237186. | −0.0279332 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 8.58993e6i | − 1.00312i | −0.865123 | − | 0.501560i | \(-0.832760\pi\) | ||||
0.865123 | − | 0.501560i | \(-0.167240\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.82825e6i | 0.324775i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.85849e6 | 1.00877 | 0.504386 | − | 0.863479i | \(-0.331719\pi\) | ||||
0.504386 | + | 0.863479i | \(0.331719\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.50579e6 | −0.960569 | −0.480284 | − | 0.877113i | \(-0.659467\pi\) | ||||
−0.480284 | + | 0.877113i | \(0.659467\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.10590e6i | − 0.123857i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.15481e6i | 0.347537i | 0.984787 | + | 0.173768i | \(0.0555944\pi\) | ||||
−0.984787 | + | 0.173768i | \(0.944406\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.00990e7 | 1.10341 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.08453e6 | 0.984463 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 3.20689e6i | − 0.344694i | −0.985036 | − | 0.172347i | \(-0.944865\pi\) | ||||
0.985036 | − | 0.172347i | \(-0.0551350\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 1.31916e6i | − 0.139504i | −0.997564 | − | 0.0697519i | \(-0.977779\pi\) | ||||
0.997564 | − | 0.0697519i | \(-0.0222207\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.36061e6 | −0.352526 | −0.176263 | − | 0.984343i | \(-0.556401\pi\) | ||||
−0.176263 | + | 0.984343i | \(0.556401\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.38821e7 | 1.44453 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 540939.i | 0.0558377i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.16545e6i | 0.321563i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.56123e7 | 1.57340 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.46547e7 | 1.46522 | 0.732610 | − | 0.680648i | \(-0.238302\pi\) | ||||
0.732610 | + | 0.680648i | \(0.238302\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.81315e6i | 0.675832i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.34743e6i | − 0.326861i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.31109e6 | 0.127023 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.67545e6 | −0.545576 | −0.272788 | − | 0.962074i | \(-0.587946\pi\) | ||||
−0.272788 | + | 0.962074i | \(0.587946\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.81422e7i | − 1.73047i | −0.501370 | − | 0.865233i | \(-0.667170\pi\) | ||||
0.501370 | − | 0.865233i | \(-0.332830\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 472390.i | − 0.0443649i | −0.999754 | − | 0.0221825i | \(-0.992939\pi\) | ||||
0.999754 | − | 0.0221825i | \(-0.00706148\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.14210e6 | −0.572407 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.69927e6 | 0.342108 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 9.79442e6i | − 0.898867i | −0.893314 | − | 0.449434i | \(-0.851626\pi\) | ||||
0.893314 | − | 0.449434i | \(-0.148374\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 2.30993e6i | − 0.208778i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.83251e6 | −0.881964 | −0.440982 | − | 0.897516i | \(-0.645370\pi\) | ||||
−0.440982 | + | 0.897516i | \(0.645370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.84120e6 | 0.163907 | 0.0819535 | − | 0.996636i | \(-0.473884\pi\) | ||||
0.0819535 | + | 0.996636i | \(0.473884\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.39624e7i | 1.23360i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.57976e7i | − 2.24525i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.73413e6 | 0.149802 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.61758e6 | −0.395920 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.02990e7i | 0.876510i | 0.898851 | + | 0.438255i | \(0.144403\pi\) | ||||
−0.898851 | + | 0.438255i | \(0.855597\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 3.63461e6i | − 0.304779i | −0.988320 | − | 0.152390i | \(-0.951303\pi\) | ||||
0.988320 | − | 0.152390i | \(-0.0486969\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.68316e7 | 1.40104 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.34348e7 | −1.11010 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 9.78443e6i | − 0.802571i | −0.915953 | − | 0.401286i | \(-0.868563\pi\) | ||||
0.915953 | − | 0.401286i | \(-0.131437\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 2.27257e7i | − 1.83707i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.02889e6 | −0.323323 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.67949e6 | −0.372824 | −0.186412 | − | 0.982472i | \(-0.559686\pi\) | ||||
−0.186412 | + | 0.982472i | \(0.559686\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 492641.i | − 0.0389671i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.98935e7i | 2.33075i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.04110e7 | −0.805930 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −565147. | −0.0434376 | −0.0217188 | − | 0.999764i | \(-0.506914\pi\) | ||||
−0.0217188 | + | 0.999764i | \(0.506914\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.03795e7i | 0.792112i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.43314e7i | − 1.07830i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.00907e6 | 0.0753889 | 0.0376944 | − | 0.999289i | \(-0.487999\pi\) | ||||
0.0376944 | + | 0.999289i | \(0.487999\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.27431e6 | 0.242910 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 9.44964e6i | − 0.696132i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.07455e7i | − 0.780602i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.02329e6 | −0.434522 | −0.217261 | − | 0.976114i | \(-0.569712\pi\) | ||||
−0.217261 | + | 0.976114i | \(0.569712\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.37329e6 | −0.241666 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.86904e7i | 1.32976i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.30828e6i | 0.161977i | 0.996715 | + | 0.0809883i | \(0.0258076\pi\) | ||||
−0.996715 | + | 0.0809883i | \(0.974192\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.16027e7 | −0.808612 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.26238e6 | −0.156593 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.65224e7i | 1.13583i | 0.823088 | + | 0.567914i | \(0.192249\pi\) | ||||
−0.823088 | + | 0.567914i | \(0.807751\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 4.36456e6i | − 0.295986i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.41051e7 | 1.62367 | 0.811834 | − | 0.583888i | \(-0.198469\pi\) | ||||
0.811834 | + | 0.583888i | \(0.198469\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.28255e6 | −0.621043 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 2.54593e7i | − 1.69190i | −0.533262 | − | 0.845950i | \(-0.679034\pi\) | ||||
0.533262 | − | 0.845950i | \(-0.320966\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.39136e6i | − 0.0912301i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.59312e6 | −0.429424 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.25073e7 | 0.809215 | 0.404608 | − | 0.914490i | \(-0.367408\pi\) | ||||
0.404608 | + | 0.914490i | \(0.367408\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 1.22203e7i | − 0.785404i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 5.34914e6i | − 0.339269i | −0.985507 | − | 0.169635i | \(-0.945741\pi\) | ||||
0.985507 | − | 0.169635i | \(-0.0542588\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.65666e6 | −0.608447 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.80369e7 | −1.12901 | −0.564507 | − | 0.825428i | \(-0.690934\pi\) | ||||
−0.564507 | + | 0.825428i | \(0.690934\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.62154e6i | 0.225207i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1.80115e7i | − 1.10550i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.41928e7 | −1.47526 | −0.737632 | − | 0.675203i | \(-0.764056\pi\) | ||||
−0.737632 | + | 0.675203i | \(0.764056\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.95234e7 | 1.78867 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.22531e6i | 0.194143i | 0.995277 | + | 0.0970716i | \(0.0309476\pi\) | ||||
−0.995277 | + | 0.0970716i | \(0.969052\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 1.23956e7i | − 0.736570i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.98740e7 | −1.17339 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.17439e6 | 0.303551 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.21604e7i | 1.29174i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.12227e6i | 0.0645896i | 0.999478 | + | 0.0322948i | \(0.0102815\pi\) | ||||
−0.999478 | + | 0.0322948i | \(0.989718\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.68705e7 | −0.964793 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.76132e6 | −0.213747 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 1.35408e7i | − 0.764650i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.48763e7i | − 0.829560i | −0.909922 | − | 0.414780i | \(-0.863859\pi\) | ||||
0.909922 | − | 0.414780i | \(-0.136141\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.27291e7 | −2.36786 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 209214. | 0.0115215 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 9.11644e6i | − 0.498926i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.29660e7i | 0.700845i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.86436e7 | −1.00152 | −0.500759 | − | 0.865587i | \(-0.666946\pi\) | ||||
−0.500759 | + | 0.865587i | \(0.666946\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.50701e6 | −0.240623 | −0.120311 | − | 0.992736i | \(-0.538389\pi\) | ||||
−0.120311 | + | 0.992736i | \(0.538389\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.02920e7i | − 1.07671i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1.50409e6i | − 0.0788352i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.44465e6 | 0.0752580 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.26560e7 | −1.17307 | −0.586537 | − | 0.809922i | \(-0.699509\pi\) | ||||
−0.586537 | + | 0.809922i | \(0.699509\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 2.76806e7i | − 1.42454i | −0.701903 | − | 0.712272i | \(-0.747666\pi\) | ||||
0.701903 | − | 0.712272i | \(-0.252334\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.42673e6i | 0.377602i | 0.982015 | + | 0.188801i | \(0.0604600\pi\) | ||||
−0.982015 | + | 0.188801i | \(0.939540\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.41770e7 | −1.72722 | −0.863610 | − | 0.504160i | \(-0.831802\pi\) | ||||
−0.863610 | + | 0.504160i | \(0.831802\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.65244e6 | 0.183477 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.57446e7i | 0.786177i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.11734e6i | 0.400498i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 155990. | 0.00765051 | 0.00382526 | − | 0.999993i | \(-0.498782\pi\) | ||||
0.00382526 | + | 0.999993i | \(0.498782\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.06703e7 | 1.00776 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 5.28580e6i | − 0.256178i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.32182e7i | 0.633087i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.55110e7 | 0.738534 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.16640e7 | −1.49879 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.52778e7i | 1.18951i | 0.803908 | + | 0.594754i | \(0.202750\pi\) | ||||
−0.803908 | + | 0.594754i | \(0.797250\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.40854e6i | 0.0655112i | 0.999463 | + | 0.0327556i | \(0.0104283\pi\) | ||||
−0.999463 | + | 0.0327556i | \(0.989572\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −246158. | −0.0113823 | −0.00569116 | − | 0.999984i | \(-0.501812\pi\) | ||||
−0.00569116 | + | 0.999984i | \(0.501812\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.37344e7 | 1.09111 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.17019e7i | 0.534849i | 0.963579 | + | 0.267424i | \(0.0861725\pi\) | ||||
−0.963579 | + | 0.267424i | \(0.913827\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 4.19381e7i | − 1.89479i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.29225e7 | 0.580492 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.27989e7 | 0.571646 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 6.50982e6i | − 0.289090i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 7.85174e6i | − 0.344720i | −0.985034 | − | 0.172360i | \(-0.944861\pi\) | ||||
0.985034 | − | 0.172360i | \(-0.0551393\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.39607e6 | 0.191908 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 105461. | 0.00457777 | 0.00228888 | − | 0.999997i | \(-0.499271\pi\) | ||||
0.00228888 | + | 0.999997i | \(0.499271\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.43760e7i | 0.620491i | 0.950656 | + | 0.310245i | \(0.100411\pi\) | ||||
−0.950656 | + | 0.310245i | \(0.899589\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 2.71725e7i | − 1.15963i | −0.814748 | − | 0.579816i | \(-0.803125\pi\) | ||||
0.814748 | − | 0.579816i | \(-0.196875\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.19587e7 | 0.931864 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.56672e6 | 0.403709 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 2.84075e7i | − 1.19208i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 2.83177e7i | − 1.17511i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.50847e7 | 0.622499 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.89499e7 | 0.777668 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.79625e6i | 0.0733073i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.25290e6i | 0.212022i | 0.994365 | + | 0.106011i | \(0.0338079\pi\) | ||||
−0.994365 | + | 0.106011i | \(0.966192\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.54282e6 | −0.222495 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.68057e7 | −1.07012 | −0.535059 | − | 0.844815i | \(-0.679711\pi\) | ||||
−0.535059 | + | 0.844815i | \(0.679711\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 5.49118e6i | − 0.218016i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.20039e6i | 0.204227i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.25954e7 | −0.491951 | −0.245976 | − | 0.969276i | \(-0.579108\pi\) | ||||
−0.245976 | + | 0.969276i | \(0.579108\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.60563e7 | 1.40066 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.51737e7i | 0.586255i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.30466e6i | 0.0498652i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.23322e7 | 1.22912 | 0.614562 | − | 0.788868i | \(-0.289333\pi\) | ||||
0.614562 | + | 0.788868i | \(0.289333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.04675e7 | −0.395792 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.89604e7i | 1.46528i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.04882e7i | 0.762350i | 0.924503 | + | 0.381175i | \(0.124481\pi\) | ||||
−0.924503 | + | 0.381175i | \(0.875519\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.87607e7 | −0.694361 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.87135e6 | −0.216154 | −0.108077 | − | 0.994143i | \(-0.534469\pi\) | ||||
−0.108077 | + | 0.994143i | \(0.534469\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 6.06285e7i | − 2.22023i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.86718e7i | 0.676567i | 0.941044 | + | 0.338284i | \(0.109846\pi\) | ||||
−0.941044 | + | 0.338284i | \(0.890154\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.67336e7 | 0.963588 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.13885e7 | 0.766882 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 1.55896e7i | − 0.556037i | −0.960576 | − | 0.278018i | \(-0.910322\pi\) | ||||
0.960576 | − | 0.278018i | \(-0.0896776\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.54152e7i | − 0.544088i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.46213e7 | 0.864500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.31036e7 | −0.806996 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.54997e6i | 0.0886071i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.24491e7i | 1.11593i | 0.829865 | + | 0.557964i | \(0.188417\pi\) | ||||
−0.829865 | + | 0.557964i | \(0.811583\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.36605e7 | 1.49375 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.73661e7 | −1.27183 | −0.635916 | − | 0.771758i | \(-0.719378\pi\) | ||||
−0.635916 | + | 0.771758i | \(0.719378\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.76195e7i | − 0.935261i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 5.23874e7i | − 1.75586i | −0.478787 | − | 0.877931i | \(-0.658923\pi\) | ||||
0.478787 | − | 0.877931i | \(-0.341077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 825691. | 0.0275335 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.40067e6 | 0.0464690 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 4.75140e7i | − 1.56833i | −0.620551 | − | 0.784166i | \(-0.713091\pi\) | ||||
0.620551 | − | 0.784166i | \(-0.286909\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.39253e7i | 1.10849i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.58846e6 | 0.149168 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.47278e7 | −0.799835 | −0.399918 | − | 0.916551i | \(-0.630961\pi\) | ||||
−0.399918 | + | 0.916551i | \(0.630961\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.50311e7i | 1.12741i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.25139e7i | 0.398709i | 0.979927 | + | 0.199355i | \(0.0638845\pi\) | ||||
−0.979927 | + | 0.199355i | \(0.936115\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.71997e7 | 0.862285 |
(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 | 400.6.c.l.49.3 | 4 | ||
4.3 | odd | 2 | 200.6.c.e.49.2 | 4 | |||
5.2 | odd | 4 | 400.6.a.q.1.2 | 2 | |||
5.3 | odd | 4 | 80.6.a.i.1.1 | 2 | |||
5.4 | even | 2 | inner | 400.6.c.l.49.2 | 4 | ||
15.8 | even | 4 | 720.6.a.z.1.1 | 2 | |||
20.3 | even | 4 | 40.6.a.d.1.2 | ✓ | 2 | ||
20.7 | even | 4 | 200.6.a.g.1.1 | 2 | |||
20.19 | odd | 2 | 200.6.c.e.49.3 | 4 | |||
40.3 | even | 4 | 320.6.a.w.1.1 | 2 | |||
40.13 | odd | 4 | 320.6.a.q.1.2 | 2 | |||
60.23 | odd | 4 | 360.6.a.l.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.a.d.1.2 | ✓ | 2 | 20.3 | even | 4 | ||
80.6.a.i.1.1 | 2 | 5.3 | odd | 4 | |||
200.6.a.g.1.1 | 2 | 20.7 | even | 4 | |||
200.6.c.e.49.2 | 4 | 4.3 | odd | 2 | |||
200.6.c.e.49.3 | 4 | 20.19 | odd | 2 | |||
320.6.a.q.1.2 | 2 | 40.13 | odd | 4 | |||
320.6.a.w.1.1 | 2 | 40.3 | even | 4 | |||
360.6.a.l.1.2 | 2 | 60.23 | odd | 4 | |||
400.6.a.q.1.2 | 2 | 5.2 | odd | 4 | |||
400.6.c.l.49.2 | 4 | 5.4 | even | 2 | inner | ||
400.6.c.l.49.3 | 4 | 1.1 | even | 1 | trivial | ||
720.6.a.z.1.1 | 2 | 15.8 | even | 4 |