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 | 49.4 | ||
Root | \(6.17891i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.49 |
Dual form | 400.6.c.l.49.1 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 28.7156i | 1.84211i | 0.389434 | + | 0.921054i | \(0.372671\pi\) | ||||
−0.389434 | + | 0.921054i | \(0.627329\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 42.1469i | − 0.325103i | −0.986700 | − | 0.162551i | \(-0.948028\pi\) | ||||
0.986700 | − | 0.162551i | \(-0.0519723\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −581.588 | −2.39336 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −416.294 | −1.03733 | −0.518667 | − | 0.854977i | \(-0.673571\pi\) | ||||
−0.518667 | + | 0.854977i | \(0.673571\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 966.588i | 1.58629i | 0.609032 | + | 0.793145i | \(0.291558\pi\) | ||||
−0.609032 | + | 0.793145i | \(0.708442\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1834.11i | 1.53923i | 0.638508 | + | 0.769616i | \(0.279552\pi\) | ||||
−0.638508 | + | 0.769616i | \(0.720448\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 317.763 | 0.201938 | 0.100969 | − | 0.994890i | \(-0.467806\pi\) | ||||
0.100969 | + | 0.994890i | \(0.467806\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1210.27 | 0.598874 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1568.02i | − 0.618063i | −0.951052 | − | 0.309032i | \(-0.899995\pi\) | ||||
0.951052 | − | 0.309032i | \(-0.100005\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 9722.76i | − 2.56673i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7757.28 | −1.71283 | −0.856415 | − | 0.516288i | \(-0.827313\pi\) | ||||
−0.856415 | + | 0.516288i | \(0.827313\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −102.644 | −0.0191836 | −0.00959180 | − | 0.999954i | \(-0.503053\pi\) | ||||
−0.00959180 | + | 0.999954i | \(0.503053\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 11954.1i | − 1.91088i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1936.58i | − 0.232558i | −0.993217 | − | 0.116279i | \(-0.962903\pi\) | ||||
0.993217 | − | 0.116279i | \(-0.0370966\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −27756.2 | −2.92212 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7994.36 | 0.742718 | 0.371359 | − | 0.928489i | \(-0.378892\pi\) | ||||
0.371359 | + | 0.928489i | \(0.378892\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 16542.6i | − 1.36437i | −0.731179 | − | 0.682186i | \(-0.761030\pi\) | ||||
0.731179 | − | 0.682186i | \(-0.238970\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 18649.3i | 1.23146i | 0.787959 | + | 0.615728i | \(0.211138\pi\) | ||||
−0.787959 | + | 0.615728i | \(0.788862\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15030.6 | 0.894308 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −52667.7 | −2.83543 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 14972.4i | − 0.732155i | −0.930584 | − | 0.366077i | \(-0.880701\pi\) | ||||
0.930584 | − | 0.366077i | \(-0.119299\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9124.76i | 0.371993i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 19843.3 | 0.742137 | 0.371069 | − | 0.928605i | \(-0.378991\pi\) | ||||
0.371069 | + | 0.928605i | \(0.378991\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −18024.1 | −0.620195 | −0.310097 | − | 0.950705i | \(-0.600362\pi\) | ||||
−0.310097 | + | 0.950705i | \(0.600362\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 24512.1i | 0.778089i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 55040.6i | − 1.49795i | −0.662601 | − | 0.748973i | \(-0.730547\pi\) | ||||
0.662601 | − | 0.748973i | \(-0.269453\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 45026.8 | 1.13854 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11201.3 | −0.263707 | −0.131853 | − | 0.991269i | \(-0.542093\pi\) | ||||
−0.131853 | + | 0.991269i | \(0.542093\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 4013.95i | − 0.0881587i | −0.999028 | − | 0.0440793i | \(-0.985965\pi\) | ||||
0.999028 | − | 0.0440793i | \(-0.0140354\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17545.5i | 0.337240i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 24018.8 | 0.432996 | 0.216498 | − | 0.976283i | \(-0.430537\pi\) | ||||
0.216498 | + | 0.976283i | \(0.430537\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 137869. | 2.33483 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 70512.8i | − 1.12350i | −0.827307 | − | 0.561750i | \(-0.810128\pi\) | ||||
0.827307 | − | 0.561750i | \(-0.189872\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 222755.i | − 3.15522i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 60765.7 | 0.813174 | 0.406587 | − | 0.913612i | \(-0.366719\pi\) | ||||
0.406587 | + | 0.913612i | \(0.366719\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 40738.7 | 0.515707 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 2947.49i | − 0.0353383i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 31112.2i | 0.335739i | 0.985809 | + | 0.167869i | \(0.0536887\pi\) | ||||
−0.985809 | + | 0.167869i | \(0.946311\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 242111. | 2.48272 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −49491.4 | −0.482755 | −0.241377 | − | 0.970431i | \(-0.577599\pi\) | ||||
−0.241377 | + | 0.970431i | \(0.577599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 95117.9i | 0.883424i | 0.897157 | + | 0.441712i | \(0.145629\pi\) | ||||
−0.897157 | + | 0.441712i | \(0.854371\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 88429.8i | 0.746688i | 0.927693 | + | 0.373344i | \(0.121789\pi\) | ||||
−0.927693 | + | 0.373344i | \(0.878211\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10598.9 | 0.0854464 | 0.0427232 | − | 0.999087i | \(-0.486397\pi\) | ||||
0.0427232 | + | 0.999087i | \(0.486397\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 55610.0 | 0.428396 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 235124.i | 1.73221i | 0.499859 | + | 0.866107i | \(0.333385\pi\) | ||||
−0.499859 | + | 0.866107i | \(0.666615\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 562155.i | − 3.79657i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 77302.2 | 0.500408 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12249.5 | 0.0760599 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 229563.i | 1.36817i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 102533.i | − 0.564098i | −0.959400 | − | 0.282049i | \(-0.908986\pi\) | ||||
0.959400 | − | 0.282049i | \(-0.0910141\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 475031. | 2.51332 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −50603.0 | −0.257631 | −0.128815 | − | 0.991669i | \(-0.541117\pi\) | ||||
−0.128815 | + | 0.991669i | \(0.541117\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 13392.7i | − 0.0656507i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 47811.7i | − 0.217637i | −0.994062 | − | 0.108818i | \(-0.965293\pi\) | ||||
0.994062 | − | 0.108818i | \(-0.0347067\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −220190. | −0.966629 | −0.483314 | − | 0.875447i | \(-0.660567\pi\) | ||||
−0.483314 | + | 0.875447i | \(0.660567\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −535527. | −2.26847 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 402384.i | − 1.64551i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 431614.i | 1.64741i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −154533. | −0.570236 | −0.285118 | − | 0.958492i | \(-0.592033\pi\) | ||||
−0.285118 | + | 0.958492i | \(0.592033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 455395. | 1.62534 | 0.812672 | − | 0.582721i | \(-0.198012\pi\) | ||||
0.812672 | + | 0.582721i | \(0.198012\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 1.06670e6i | − 3.68394i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 361690.i | − 1.17108i | −0.810643 | − | 0.585541i | \(-0.800882\pi\) | ||||
0.810643 | − | 0.585541i | \(-0.199118\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 429943. | 1.34871 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −66087.3 | −0.200934 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 490843.i | − 1.44702i | −0.690316 | − | 0.723508i | \(-0.742528\pi\) | ||||
0.690316 | − | 0.723508i | \(-0.257472\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 196273.i | − 0.544591i | −0.962214 | − | 0.272295i | \(-0.912217\pi\) | ||||
0.962214 | − | 0.272295i | \(-0.0877827\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −562999. | −1.51632 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −184807. | −0.483312 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 183395.i | 0.465877i | 0.972491 | + | 0.232938i | \(0.0748341\pi\) | ||||
−0.972491 | + | 0.232938i | \(0.925166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 569814.i | 1.36710i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −38660.0 | −0.0901839 | −0.0450920 | − | 0.998983i | \(-0.514358\pi\) | ||||
−0.0450920 | + | 0.998983i | \(0.514358\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −561287. | −1.27347 | −0.636735 | − | 0.771083i | \(-0.719715\pi\) | ||||
−0.636735 | + | 0.771083i | \(0.719715\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 517572.i | − 1.14247i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 763530.i | − 1.59670i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −409784. | −0.834450 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −265393. | −0.526387 | −0.263194 | − | 0.964743i | \(-0.584776\pi\) | ||||
−0.263194 | + | 0.964743i | \(0.584776\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 863148.i | 1.66798i | 0.551776 | + | 0.833992i | \(0.313950\pi\) | ||||
−0.551776 | + | 0.833992i | \(0.686050\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 281871.i | − 0.517469i | −0.965949 | − | 0.258734i | \(-0.916695\pi\) | ||||
0.965949 | − | 0.258734i | \(-0.0833054\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −192798. | −0.345120 | −0.172560 | − | 0.984999i | \(-0.555204\pi\) | ||||
−0.172560 | + | 0.984999i | \(0.555204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.58053e6 | 2.75938 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 326945.i | 0.556846i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 911943.i | 1.47925i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −132283. | −0.209477 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −44631.4 | −0.0690136 | −0.0345068 | − | 0.999404i | \(-0.510986\pi\) | ||||
−0.0345068 | + | 0.999404i | \(0.510986\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 321651.i | − 0.485776i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4326.13i | 0.00623664i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 115263. | 0.162398 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.77283e6 | −2.44167 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 904469.i | 1.21796i | 0.793187 | + | 0.608978i | \(0.208420\pi\) | ||||
−0.793187 | + | 0.608978i | \(0.791580\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1.02684e6i | − 1.32263i | −0.750109 | − | 0.661314i | \(-0.769999\pi\) | ||||
0.750109 | − | 0.661314i | \(-0.230001\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 101521. | 0.127928 | 0.0639641 | − | 0.997952i | \(-0.479626\pi\) | ||||
0.0639641 | + | 0.997952i | \(0.479626\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −503830. | −0.621232 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 313713.i | − 0.378567i | −0.981923 | − | 0.189283i | \(-0.939384\pi\) | ||||
0.981923 | − | 0.189283i | \(-0.0606165\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 689715.i | 0.797625i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.53093e6 | −1.73365 | −0.866825 | − | 0.498612i | \(-0.833843\pi\) | ||||
−0.866825 | + | 0.498612i | \(0.833843\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 506999. | 0.562296 | 0.281148 | − | 0.959664i | \(-0.409285\pi\) | ||||
0.281148 | + | 0.959664i | \(0.409285\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.59638e6i | 1.73428i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 307146.i | 0.320333i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.02482e6 | 2.06961 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 511659. | 0.512621 | 0.256311 | − | 0.966594i | \(-0.417493\pi\) | ||||
0.256311 | + | 0.966594i | \(0.417493\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 652758.i | 0.641137i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 256082.i | 0.241850i | 0.992662 | + | 0.120925i | \(0.0385861\pi\) | ||||
−0.992662 | + | 0.120925i | \(0.961414\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −81620.7 | −0.0756051 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.51154e6 | 4.09943 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 1.32451e6i | − 1.18077i | −0.807121 | − | 0.590386i | \(-0.798976\pi\) | ||||
0.807121 | − | 0.590386i | \(-0.201024\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.74493e6i | 1.49795i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.42989e6 | 1.20482 | 0.602410 | − | 0.798187i | \(-0.294207\pi\) | ||||
0.602410 | + | 0.798187i | \(0.294207\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 706426. | 0.584310 | 0.292155 | − | 0.956371i | \(-0.405628\pi\) | ||||
0.292155 | + | 0.956371i | \(0.405628\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.16984e6i | 0.949989i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 314677.i | − 0.246414i | −0.992381 | − | 0.123207i | \(-0.960682\pi\) | ||||
0.992381 | − | 0.123207i | \(-0.0393179\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 59696.6 | 0.0459134 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −437793. | −0.330752 | −0.165376 | − | 0.986231i | \(-0.552884\pi\) | ||||
−0.165376 | + | 0.986231i | \(0.552884\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.08248e6i | 1.54566i | 0.634612 | + | 0.772831i | \(0.281160\pi\) | ||||
−0.634612 | + | 0.772831i | \(0.718840\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 336938.i | − 0.241460i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.94411e6 | −1.36923 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −893407. | −0.618468 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 90716.3i | 0.0617329i | 0.999524 | + | 0.0308664i | \(0.00982665\pi\) | ||||
−0.999524 | + | 0.0308664i | \(0.990173\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.04752e6i | 2.66255i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.51563e6 | 0.980428 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −697219. | −0.443561 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 1.42118e6i | − 0.889286i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 571699.i | − 0.346196i | −0.984905 | − | 0.173098i | \(-0.944622\pi\) | ||||
0.984905 | − | 0.173098i | \(-0.0553777\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.73137e6 | −1.62736 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.59515e6 | −1.52147 | −0.760733 | − | 0.649065i | \(-0.775160\pi\) | ||||
−0.760733 | + | 0.649065i | \(0.775160\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 510659.i | − 0.294625i | −0.989090 | − | 0.147313i | \(-0.952938\pi\) | ||||
0.989090 | − | 0.147313i | \(-0.0470623\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.37030e6i | 1.88374i | 0.335984 | + | 0.941868i | \(0.390931\pi\) | ||||
−0.335984 | + | 0.941868i | \(0.609069\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.22931e6 | 1.77678 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.53932e6 | −1.37548 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 582813.i | 0.310830i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 304354.i | 0.157402i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 786012. | 0.400349 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.80172e6 | −1.90726 | −0.953632 | − | 0.300976i | \(-0.902688\pi\) | ||||
−0.953632 | + | 0.300976i | \(0.902688\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.12629e6i | 0.556595i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 2.06627e6i | − 0.991088i | −0.868583 | − | 0.495544i | \(-0.834969\pi\) | ||||
0.868583 | − | 0.495544i | \(-0.165031\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.75174e6 | −3.19093 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 42730.1 | 0.0198998 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.34186e6i | − 0.615845i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.35066e6i | 1.04801i | 0.851715 | + | 0.524005i | \(0.175563\pi\) | ||||
−0.851715 | + | 0.524005i | \(0.824437\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.67220e6 | −0.734896 | −0.367448 | − | 0.930044i | \(-0.619768\pi\) | ||||
−0.367448 | + | 0.930044i | \(0.619768\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.39790e6 | 4.07158 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.71355e6i | 0.731914i | 0.930632 | + | 0.365957i | \(0.119258\pi\) | ||||
−0.930632 | + | 0.365957i | \(0.880742\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.21978e6i | 0.921806i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.85773e6 | −1.57978 | −0.789888 | − | 0.613251i | \(-0.789861\pi\) | ||||
−0.789888 | + | 0.613251i | \(0.789861\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.37513e6 | −0.959221 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 351753.i | 0.140111i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3.18109e6i | − 1.23285i | −0.787412 | − | 0.616427i | \(-0.788580\pi\) | ||||
0.787412 | − | 0.616427i | \(-0.211420\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.64942e6 | −1.77760 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −631042. | −0.238026 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 4.79295e6i | − 1.78374i | −0.452295 | − | 0.891868i | \(-0.649395\pi\) | ||||
0.452295 | − | 0.891868i | \(-0.350605\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 7.49809e6i | − 2.71705i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7018.36 | 0.00250979 | 0.00125490 | − | 0.999999i | \(-0.499601\pi\) | ||||
0.00125490 | + | 0.999999i | \(0.499601\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.94430e6 | 1.03913 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 694105.i | 0.241784i | 0.992666 | + | 0.120892i | \(0.0385755\pi\) | ||||
−0.992666 | + | 0.120892i | \(0.961424\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.62097e6i | 3.26544i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 53514.1 | 0.0179306 | 0.00896529 | − | 0.999960i | \(-0.497146\pi\) | ||||
0.00896529 | + | 0.999960i | \(0.497146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.87593e6 | 0.951342 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 1.45310e6i | − 0.474584i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 907937.i | − 0.289121i | −0.989496 | − | 0.144560i | \(-0.953823\pi\) | ||||
0.989496 | − | 0.144560i | \(-0.0461768\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 384580. | 0.120936 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −514404. | −0.159751 | −0.0798755 | − | 0.996805i | \(-0.525452\pi\) | ||||
−0.0798755 | + | 0.996805i | \(0.525452\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 99214.6i | − 0.0304308i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 806185.i | 0.241240i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.61814e6 | −1.66067 | −0.830337 | − | 0.557262i | \(-0.811852\pi\) | ||||
−0.830337 | + | 0.557262i | \(0.811852\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.37294e6 | 0.400911 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 836334.i | − 0.241271i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 6.32288e6i | − 1.78064i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 708382. | 0.197121 | 0.0985605 | − | 0.995131i | \(-0.468576\pi\) | ||||
0.0985605 | + | 0.995131i | \(0.468576\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.91741e6 | −1.07719 | −0.538597 | − | 0.842563i | \(-0.681046\pi\) | ||||
−0.538597 | + | 0.842563i | \(0.681046\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 1.08462e7i | − 2.94732i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 759658.i | 0.201627i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.15547e7 | 3.03121 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.42095e6 | −1.14636 | −0.573181 | − | 0.819429i | \(-0.694291\pi\) | ||||
−0.573181 | + | 0.819429i | \(0.694291\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 4.01914e6i | − 1.03018i | −0.857136 | − | 0.515090i | \(-0.827758\pi\) | ||||
0.857136 | − | 0.515090i | \(-0.172242\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 498259.i | − 0.124811i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.41795e6 | −1.34176 | −0.670879 | − | 0.741567i | \(-0.734083\pi\) | ||||
−0.670879 | + | 0.741567i | \(0.734083\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.74163e6 | −2.14041 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.21518e6i | 1.74678i | 0.487023 | + | 0.873389i | \(0.338083\pi\) | ||||
−0.487023 | + | 0.873389i | \(0.661917\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 4.43751e6i | − 1.05044i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 203792. | 0.0477057 | 0.0238529 | − | 0.999715i | \(-0.492407\pi\) | ||||
0.0238529 | + | 0.999715i | \(0.492407\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.32800e6 | −0.770446 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.30769e7i | 2.99406i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.45642e6i | 0.774169i | 0.922044 | + | 0.387085i | \(0.126518\pi\) | ||||
−0.922044 | + | 0.387085i | \(0.873482\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.78326e7 | 3.95079 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.40596e6 | 1.40389 | 0.701944 | − | 0.712233i | \(-0.252316\pi\) | ||||
0.701944 | + | 0.712233i | \(0.252316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.59550e6i | 1.64666i | 0.567563 | + | 0.823330i | \(0.307887\pi\) | ||||
−0.567563 | + | 0.823330i | \(0.692113\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 4.58166e6i | − 0.972145i | −0.873919 | − | 0.486072i | \(-0.838429\pi\) | ||||
0.873919 | − | 0.486072i | \(-0.161571\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.31979e6 | −0.486986 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.03862e7 | 2.15726 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.88658e6i | 1.41531i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.70779e6i | 1.75231i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.01195e6 | 0.998085 | 0.499043 | − | 0.866577i | \(-0.333685\pi\) | ||||
0.499043 | + | 0.866577i | \(0.333685\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.87187e6 | 0.368904 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.89774e6i | − 0.370142i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 2.10670e6i | − 0.402514i | −0.979539 | − | 0.201257i | \(-0.935497\pi\) | ||||
0.979539 | − | 0.201257i | \(-0.0645026\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.40949e7 | 2.66556 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.43322e6 | −1.01708 | −0.508538 | − | 0.861040i | \(-0.669814\pi\) | ||||
−0.508538 | + | 0.861040i | \(0.669814\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.42277e7i | − 2.63644i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 472099.i | 0.0857318i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.65183e6 | 1.73523 | 0.867617 | − | 0.497233i | \(-0.165650\pi\) | ||||
0.867617 | + | 0.497233i | \(0.165650\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.63611e6 | 1.00319 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 1.33954e6i | − 0.236067i | −0.993010 | − | 0.118034i | \(-0.962341\pi\) | ||||
0.993010 | − | 0.118034i | \(-0.0376591\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1.61669e7i | − 2.79322i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.60771e6 | −0.788299 | −0.394150 | − | 0.919046i | \(-0.628961\pi\) | ||||
−0.394150 | + | 0.919046i | \(0.628961\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −169176. | −0.0286606 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 3.08953e6i | − 0.518321i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 7.76360e6i | − 1.27743i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.26629e6 | −0.858196 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.80941e6 | −0.937644 | −0.468822 | − | 0.883293i | \(-0.655321\pi\) | ||||
−0.468822 | + | 0.883293i | \(0.655321\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.83877e6i | 0.613674i | 0.951762 | + | 0.306837i | \(0.0992707\pi\) | ||||
−0.951762 | + | 0.306837i | \(0.900729\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 188261.i | − 0.0295280i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.97765e6 | 0.617998 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.15406e7 | −1.77621 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.72725e6i | 1.17817i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 1.11015e6i | − 0.166129i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.25716e6 | −0.927696 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.28830e6 | 0.923720 | 0.461860 | − | 0.886953i | \(-0.347182\pi\) | ||||
0.461860 | + | 0.886953i | \(0.347182\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1.61177e7i | − 2.34587i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.54365e6i | 0.649287i | 0.945836 | + | 0.324644i | \(0.105244\pi\) | ||||
−0.945836 | + | 0.324644i | \(0.894756\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.04826e7 | 1.48435 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.46497e6 | −0.345886 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1.01232e6i | − 0.140768i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 1.20198e7i | − 1.64157i | −0.571239 | − | 0.820783i | \(-0.693537\pi\) | ||||
0.571239 | − | 0.820783i | \(-0.306463\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.59899e7 | 2.16429 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.19252e7 | 2.94129 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 3.65741e6i | − 0.486298i | −0.969989 | − | 0.243149i | \(-0.921820\pi\) | ||||
0.969989 | − | 0.243149i | \(-0.0781804\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 5.81077e6i | − 0.759059i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.80214e6 | 0.362835 | 0.181418 | − | 0.983406i | \(-0.441931\pi\) | ||||
0.181418 | + | 0.983406i | \(0.441931\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.78472e6 | 0.870846 | 0.435423 | − | 0.900226i | \(-0.356599\pi\) | ||||
0.435423 | + | 0.900226i | \(0.356599\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 7.62091e6i | − 0.969662i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.25416e6i | 0.156825i | 0.996921 | + | 0.0784123i | \(0.0249850\pi\) | ||||
−0.996921 | + | 0.0784123i | \(0.975015\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.47858e7 | −3.07261 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.97190e6 | −0.365253 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.23293e6i | 0.759488i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 726476.i | 0.0870213i | 0.999053 | + | 0.0435107i | \(0.0138542\pi\) | ||||
−0.999053 | + | 0.0435107i | \(0.986146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32616.5 | −0.00387391 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.09409e6 | 0.953234 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 933494.i | 0.109012i | 0.998513 | + | 0.0545060i | \(0.0173584\pi\) | ||||
−0.998513 | + | 0.0545060i | \(0.982642\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 5.53632e6i | − 0.635749i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.27354e7 | −1.45025 | −0.725127 | − | 0.688615i | \(-0.758219\pi\) | ||||
−0.725127 | + | 0.688615i | \(0.758219\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.87190e6 | −0.776052 | −0.388026 | − | 0.921648i | \(-0.626843\pi\) | ||||
−0.388026 | + | 0.921648i | \(0.626843\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.20109e7i | 3.58513i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 3.87130e6i | − 0.426467i | −0.977001 | − | 0.213233i | \(-0.931601\pi\) | ||||
0.977001 | − | 0.213233i | \(-0.0683995\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.38844e6 | −1.02577 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.80262e7 | −1.95345 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 2.38824e6i | − 0.256701i | −0.991729 | − | 0.128350i | \(-0.959032\pi\) | ||||
0.991729 | − | 0.128350i | \(-0.0409682\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.07299e6i | 0.324974i | 0.986711 | + | 0.162487i | \(0.0519516\pi\) | ||||
−0.986711 | + | 0.162487i | \(0.948048\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.52257e6 | 0.894013 | 0.447007 | − | 0.894531i | \(-0.352490\pi\) | ||||
0.447007 | + | 0.894531i | \(0.352490\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.52455e7 | −1.58640 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2.56109e6i | − 0.264365i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 3.79858e6i | − 0.385880i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.55190e6 | 0.357960 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.54170e6 | −0.854026 | −0.427013 | − | 0.904246i | \(-0.640434\pi\) | ||||
−0.427013 | + | 0.904246i | \(0.640434\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 1.28162e6i | − 0.127131i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.45284e7i | 1.41863i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.51452e6 | 0.631146 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.81006e6 | 0.366257 | 0.183129 | − | 0.983089i | \(-0.441377\pi\) | ||||
0.183129 | + | 0.983089i | \(0.441377\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.40516e7i | − 1.34029i | −0.742231 | − | 0.670144i | \(-0.766232\pi\) | ||||
0.742231 | − | 0.670144i | \(-0.233768\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 962366.i | 0.0903815i | 0.998978 | + | 0.0451908i | \(0.0143896\pi\) | ||||
−0.998978 | + | 0.0451908i | \(0.985610\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.26065e6 | −0.769844 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −124228. | −0.0114886 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 413989.i | − 0.0379932i | −0.999820 | − | 0.0189966i | \(-0.993953\pi\) | ||||
0.999820 | − | 0.0189966i | \(-0.00604717\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.33446e6i | 0.210996i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.92401e7 | −1.72581 | −0.862905 | − | 0.505367i | \(-0.831357\pi\) | ||||
−0.862905 | + | 0.505367i | \(0.831357\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.04652e7 | −1.82185 | −0.910924 | − | 0.412574i | \(-0.864630\pi\) | ||||
−0.910924 | + | 0.412574i | \(0.864630\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 5.09080e7i | − 4.49782i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.21636e7i | 1.05864i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.59724e7 | −2.24361 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.50330e6 | 0.643348 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 9.12086e6i | − 0.776244i | −0.921608 | − | 0.388122i | \(-0.873124\pi\) | ||||
0.921608 | − | 0.388122i | \(-0.126876\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.29457e7i | 1.08556i | 0.839876 | + | 0.542778i | \(0.182628\pi\) | ||||
−0.839876 | + | 0.542778i | \(0.817372\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.31128e6 | 0.109150 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.94863e7 | 2.43642 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.56637e6i | 0.702660i | 0.936252 | + | 0.351330i | \(0.114270\pi\) | ||||
−0.936252 | + | 0.351330i | \(0.885730\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.91523e6i | 0.235658i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.44722e7 | 1.16141 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.01163e7 | 0.805984 | 0.402992 | − | 0.915204i | \(-0.367970\pi\) | ||||
0.402992 | + | 0.915204i | \(0.367970\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.02042e7i | − 0.807138i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.46626e7i | 1.14322i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.00846e6 | 0.697361 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.95732e7 | −1.50441 | −0.752207 | − | 0.658927i | \(-0.771011\pi\) | ||||
−0.752207 | + | 0.658927i | \(0.771011\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 615372.i | − 0.0469623i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.08591e6i | 0.156945i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.36252e7 | −1.76506 | −0.882531 | − | 0.470254i | \(-0.844162\pi\) | ||||
−0.882531 | + | 0.470254i | \(0.844162\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.39690e7 | −1.03632 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 160948.i | 0.0118567i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 4.39617e7i | − 3.19357i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.44994e7 | 1.76740 | 0.883698 | − | 0.468058i | \(-0.155046\pi\) | ||||
0.883698 | + | 0.468058i | \(0.155046\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00892e6 | 0.287204 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.45588e7i | 1.03581i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1.75199e7i | − 1.22941i | −0.788759 | − | 0.614703i | \(-0.789276\pi\) | ||||
0.788759 | − | 0.614703i | \(-0.210724\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.23387e7 | −0.859904 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.03410e7 | 2.10008 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.29025e7i | 1.57443i | 0.616679 | + | 0.787215i | \(0.288478\pi\) | ||||
−0.616679 | + | 0.787215i | \(0.711522\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.29131e7i | 1.55387i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.31983e7 | 0.889010 | 0.444505 | − | 0.895776i | \(-0.353380\pi\) | ||||
0.444505 | + | 0.895776i | \(0.353380\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.81988e6 | −0.590089 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.89399e6i | 0.125865i | 0.998018 | + | 0.0629326i | \(0.0200453\pi\) | ||||
−0.998018 | + | 0.0629326i | \(0.979955\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.10094e7i | 2.68894i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.72704e6 | 0.242750 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.71988e7 | 1.11275 | 0.556376 | − | 0.830930i | \(-0.312191\pi\) | ||||
0.556376 | + | 0.830930i | \(0.312191\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.46926e7i | 0.944304i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 2.02697e7i | − 1.28561i | −0.766031 | − | 0.642804i | \(-0.777771\pi\) | ||||
0.766031 | − | 0.642804i | \(-0.222229\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.87444e7 | −1.18104 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.54894e6 | −0.409929 | −0.204965 | − | 0.978769i | \(-0.565708\pi\) | ||||
−0.204965 | + | 0.978769i | \(0.565708\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 446710.i | − 0.0277789i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.91803e7i | 1.17725i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.48043e7 | 1.51256 | 0.756278 | − | 0.654251i | \(-0.227016\pi\) | ||||
0.756278 | + | 0.654251i | \(0.227016\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.35357e6 | −0.445515 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.27616e7i | 1.37010i | 0.728495 | + | 0.685052i | \(0.240220\pi\) | ||||
−0.728495 | + | 0.685052i | \(0.759780\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 2.34379e6i | − 0.139273i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.54031e6 | 0.149983 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.66302e6 | 0.273552 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.54221e7i | 4.39637i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.56494e7i | 0.900658i | 0.892863 | + | 0.450329i | \(0.148693\pi\) | ||||
−0.892863 | + | 0.450329i | \(0.851307\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.80341e7 | 2.17511 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.90976e6 | 0.563147 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 1.74218e7i | − 0.983809i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.26205e7i | 1.26141i | 0.776023 | + | 0.630704i | \(0.217234\pi\) | ||||
−0.776023 | + | 0.630704i | \(0.782766\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.42050e7 | −1.89549 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.53406e7 | −1.94622 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.67098e6i | 0.0914499i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.10602e7i | 2.21941i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.25367e7 | 1.21065 | 0.605326 | − | 0.795977i | \(-0.293043\pi\) | ||||
0.605326 | + | 0.795977i | \(0.293043\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 410196. | 0.0218997 | 0.0109499 | − | 0.999940i | \(-0.496514\pi\) | ||||
0.0109499 | + | 0.999940i | \(0.496514\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.02855e7i | 1.07636i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 5.25662e6i | − 0.275519i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.36931e7 | −1.23428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.62749e7 | 0.842678 | 0.421339 | − | 0.906903i | \(-0.361560\pi\) | ||||
0.421339 | + | 0.906903i | \(0.361560\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 628881.i | 0.0323645i | 0.999869 | + | 0.0161823i | \(0.00515120\pi\) | ||||
−0.999869 | + | 0.0161823i | \(0.994849\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1.94403e7i | − 0.988417i | −0.869343 | − | 0.494209i | \(-0.835458\pi\) | ||||
0.869343 | − | 0.494209i | \(-0.164542\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.39088e7 | −1.71366 | −0.856832 | − | 0.515595i | \(-0.827571\pi\) | ||||
−0.856832 | + | 0.515595i | \(0.827571\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.03614e6 | 0.453921 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.75679e7i | 1.37655i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 997985.i | 0.0492391i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.84583e6 | 0.335754 | 0.167877 | − | 0.985808i | \(-0.446309\pi\) | ||||
0.167877 | + | 0.985808i | \(0.446309\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.96642e7 | 1.93379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 1.25715e7i | − 0.609282i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 516280.i | − 0.0247273i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.97997e7 | −2.84728 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.03660e6 | −0.143735 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.67852e7i | − 1.26044i | −0.776416 | − | 0.630221i | \(-0.782964\pi\) | ||||
0.776416 | − | 0.630221i | \(-0.217036\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 9.32339e6i | − 0.433632i | −0.976212 | − | 0.216816i | \(-0.930433\pi\) | ||||
0.976212 | − | 0.216816i | \(-0.0695672\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.73055e7 | 1.72500 | 0.862502 | − | 0.506054i | \(-0.168896\pi\) | ||||
0.862502 | + | 0.506054i | \(0.168896\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.67537e6 | 0.444795 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.18636e6i | 0.237048i | 0.992951 | + | 0.118524i | \(0.0378162\pi\) | ||||
−0.992951 | + | 0.118524i | \(0.962184\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 5.58265e7i | − 2.52228i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.99888e6 | −0.449161 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.32016e7 | 2.37618 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 1.80945e7i | − 0.803546i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.63396e6i | 0.247352i | 0.992323 | + | 0.123676i | \(0.0394683\pi\) | ||||
−0.992323 | + | 0.123676i | \(0.960532\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.60498e6 | −0.113719 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.76880e6 | −0.250407 | −0.125203 | − | 0.992131i | \(-0.539958\pi\) | ||||
−0.125203 | + | 0.992131i | \(0.539958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.60630e7i | − 1.12492i | −0.826823 | − | 0.562462i | \(-0.809854\pi\) | ||||
0.826823 | − | 0.562462i | \(-0.190146\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.24889e7i | 1.38652i | 0.720688 | + | 0.693259i | \(0.243826\pi\) | ||||
−0.720688 | + | 0.693259i | \(0.756174\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.32145e6 | −0.183390 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.73942e7 | −2.42200 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.92607e6i | 0.248678i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.35223e7i | 1.80605i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 796240. | 0.0328583 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.74612e7 | 1.12696 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 2.00211e7i | − 0.817087i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 3.11745e7i | − 1.25829i | −0.777288 | − | 0.629145i | \(-0.783405\pi\) | ||||
0.777288 | − | 0.629145i | \(-0.216595\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.87836e7 | 1.15541 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.58254e7 | −1.43019 | −0.715097 | − | 0.699025i | \(-0.753618\pi\) | ||||
−0.715097 | + | 0.699025i | \(0.753618\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.93540e7i | 1.16544i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.13276e6i | 0.0837565i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.14710e7 | −1.22920 | −0.614598 | − | 0.788840i | \(-0.710682\pi\) | ||||
−0.614598 | + | 0.788840i | \(0.710682\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.64167e7 | 0.637730 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1.08270e7i | − 0.418316i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 5.53194e7i | − 2.11436i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −532600. | −0.0202471 | −0.0101235 | − | 0.999949i | \(-0.503222\pi\) | ||||
−0.0101235 | + | 0.999949i | \(0.503222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.77618e6 | 0.180595 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 7.45215e7i | − 2.80270i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1.97320e7i | − 0.734214i | −0.930179 | − | 0.367107i | \(-0.880348\pi\) | ||||
0.930179 | − | 0.367107i | \(-0.119652\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.46639e7 | 0.542732 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.12060e7 | −0.780702 | −0.390351 | − | 0.920666i | \(-0.627646\pi\) | ||||
−0.390351 | + | 0.920666i | \(0.627646\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.25353e7i | − 0.459047i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.60224e7i | 1.66761i | 0.552060 | + | 0.833804i | \(0.313842\pi\) | ||||
−0.552060 | + | 0.833804i | \(0.686158\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.87984e6 | 0.139845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.67802e7 | −3.47004 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.76525e7i | 1.69963i | 0.527085 | + | 0.849813i | \(0.323285\pi\) | ||||
−0.527085 | + | 0.849813i | \(0.676715\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.27316e7i | 3.27301i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.01511e6 | −0.0707543 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.86186e7 | −0.999632 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 5.14297e7i | − 1.78710i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 2.29686e7i | − 0.789893i | −0.918704 | − | 0.394946i | \(-0.870763\pi\) | ||||
0.918704 | − | 0.394946i | \(-0.129237\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.67358e7 | −0.572583 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.22231e7 | −0.756408 | −0.378204 | − | 0.925722i | \(-0.623458\pi\) | ||||
−0.378204 | + | 0.925722i | \(0.623458\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.28031e6i | 0.314254i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.68581e7i | 1.23537i | 0.786426 | + | 0.617684i | \(0.211929\pi\) | ||||
−0.786426 | + | 0.617684i | \(0.788071\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.52964e7 | −0.843532 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.16418e6 | −0.204504 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.53136e7i | 1.49570i | 0.663868 | + | 0.747850i | \(0.268914\pi\) | ||||
−0.663868 | + | 0.747850i | \(0.731086\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.25708e7i | 0.737487i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.59392e7 | −0.843268 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.68582e7 | 1.19220 | 0.596102 | − | 0.802909i | \(-0.296716\pi\) | ||||
0.596102 | + | 0.802909i | \(0.296716\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 1.09169e8i | − 3.51339i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.19245e7i | 1.33577i | 0.744266 | + | 0.667883i | \(0.232799\pi\) | ||||
−0.744266 | + | 0.667883i | \(0.767201\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.88289e7 | −0.596912 |
(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.49.4 | 4 | ||
4.3 | odd | 2 | 200.6.c.e.49.1 | 4 | |||
5.2 | odd | 4 | 80.6.a.i.1.2 | 2 | |||
5.3 | odd | 4 | 400.6.a.q.1.1 | 2 | |||
5.4 | even | 2 | inner | 400.6.c.l.49.1 | 4 | ||
15.2 | even | 4 | 720.6.a.z.1.2 | 2 | |||
20.3 | even | 4 | 200.6.a.g.1.2 | 2 | |||
20.7 | even | 4 | 40.6.a.d.1.1 | ✓ | 2 | ||
20.19 | odd | 2 | 200.6.c.e.49.4 | 4 | |||
40.27 | even | 4 | 320.6.a.w.1.2 | 2 | |||
40.37 | odd | 4 | 320.6.a.q.1.1 | 2 | |||
60.47 | odd | 4 | 360.6.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.a.d.1.1 | ✓ | 2 | 20.7 | even | 4 | ||
80.6.a.i.1.2 | 2 | 5.2 | odd | 4 | |||
200.6.a.g.1.2 | 2 | 20.3 | even | 4 | |||
200.6.c.e.49.1 | 4 | 4.3 | odd | 2 | |||
200.6.c.e.49.4 | 4 | 20.19 | odd | 2 | |||
320.6.a.q.1.1 | 2 | 40.37 | odd | 4 | |||
320.6.a.w.1.2 | 2 | 40.27 | even | 4 | |||
360.6.a.l.1.1 | 2 | 60.47 | odd | 4 | |||
400.6.a.q.1.1 | 2 | 5.3 | odd | 4 | |||
400.6.c.l.49.1 | 4 | 5.4 | even | 2 | inner | ||
400.6.c.l.49.4 | 4 | 1.1 | even | 1 | trivial | ||
720.6.a.z.1.2 | 2 | 15.2 | even | 4 |