Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(1,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.a (trivial) |
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: | yes |
Analytic conductor: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{129}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 32 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(6.17891\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −28.7156 | −1.84211 | −0.921054 | − | 0.389434i | \(-0.872671\pi\) | ||||
−0.921054 | + | 0.389434i | \(0.872671\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 42.1469 | 0.325103 | 0.162551 | − | 0.986700i | \(-0.448028\pi\) | ||||
0.162551 | + | 0.986700i | \(0.448028\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 581.588 | 2.39336 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 416.294 | 1.03733 | 0.518667 | − | 0.854977i | \(-0.326429\pi\) | ||||
0.518667 | + | 0.854977i | \(0.326429\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −966.588 | −1.58629 | −0.793145 | − | 0.609032i | \(-0.791558\pi\) | ||||
−0.793145 | + | 0.609032i | \(0.791558\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 717.891 | 0.823816 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1834.11 | −1.53923 | −0.769616 | − | 0.638508i | \(-0.779552\pi\) | ||||
−0.769616 | + | 0.638508i | \(0.779552\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | −1568.02 | −0.618063 | −0.309032 | − | 0.951052i | \(-0.600005\pi\) | ||||
−0.309032 | + | 0.951052i | \(0.600005\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9722.76 | −2.56673 | ||||||||
\(28\) | 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 | ||||||||
\(33\) | −11954.1 | −1.91088 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1053.67 | −0.145390 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1936.58 | −0.232558 | −0.116279 | − | 0.993217i | \(-0.537097\pi\) | ||||
−0.116279 | + | 0.993217i | \(0.537097\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 16542.6 | 1.36437 | 0.682186 | − | 0.731179i | \(-0.261030\pi\) | ||||
0.682186 | + | 0.731179i | \(0.261030\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14539.7 | −1.07035 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −18649.3 | −1.23146 | −0.615728 | − | 0.787959i | \(-0.711138\pi\) | ||||
−0.615728 | + | 0.787959i | \(0.711138\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15030.6 | −0.894308 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 52667.7 | 2.83543 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14972.4 | 0.732155 | 0.366077 | − | 0.930584i | \(-0.380701\pi\) | ||||
0.366077 | + | 0.930584i | \(0.380701\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10407.3 | −0.463909 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9124.76 | −0.371993 | ||||||||
\(58\) | 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 | \(-0.399638\pi\) | ||||
0.310097 | + | 0.950705i | \(0.399638\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 24512.1 | 0.778089 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 24164.7 | 0.709411 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −55040.6 | −1.49795 | −0.748973 | − | 0.662601i | \(-0.769453\pi\) | ||||
−0.748973 | + | 0.662601i | \(0.769453\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | −4013.95 | −0.0881587 | −0.0440793 | − | 0.999028i | \(-0.514035\pi\) | ||||
−0.0440793 | + | 0.999028i | \(0.514035\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17947.3 | −0.368422 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17545.5 | 0.337240 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −24018.8 | −0.432996 | −0.216498 | − | 0.976283i | \(-0.569463\pi\) | ||||
−0.216498 | + | 0.976283i | \(0.569463\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 137869. | 2.33483 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 70512.8 | 1.12350 | 0.561750 | − | 0.827307i | \(-0.310128\pi\) | ||||
0.561750 | + | 0.827307i | \(0.310128\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 45852.8 | 0.688365 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 222755. | 3.15522 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −60765.7 | −0.813174 | −0.406587 | − | 0.913612i | \(-0.633281\pi\) | ||||
−0.406587 | + | 0.913612i | \(0.633281\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −40738.7 | −0.515707 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2947.49 | 0.0353383 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7944.07 | −0.0903096 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −31112.2 | −0.335739 | −0.167869 | − | 0.985809i | \(-0.553689\pi\) | ||||
−0.167869 | + | 0.985809i | \(0.553689\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 242111. | 2.48272 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 49491.4 | 0.482755 | 0.241377 | − | 0.970431i | \(-0.422401\pi\) | ||||
0.241377 | + | 0.970431i | \(0.422401\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 95117.9 | 0.883424 | 0.441712 | − | 0.897157i | \(-0.354371\pi\) | ||||
0.441712 | + | 0.897157i | \(0.354371\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 30256.9 | 0.267825 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 88429.8 | 0.746688 | 0.373344 | − | 0.927693i | \(-0.378211\pi\) | ||||
0.373344 | + | 0.927693i | \(0.378211\pi\) | |||||||
\(108\) | 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. | 1.73221 | 0.866107 | − | 0.499859i | \(-0.166615\pi\) | ||||
0.866107 | + | 0.499859i | \(0.166615\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 39200.6 | 0.276406 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −562155. | −3.79657 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −77302.2 | −0.500408 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12249.5 | 0.0760599 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −229563. | −1.36817 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 102533. | 0.564098 | 0.282049 | − | 0.959400i | \(-0.408986\pi\) | ||||
0.282049 | + | 0.959400i | \(0.408986\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −475031. | −2.51332 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 50603.0 | 0.257631 | 0.128815 | − | 0.991669i | \(-0.458883\pi\) | ||||
0.128815 | + | 0.991669i | \(0.458883\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13392.7 | 0.0656507 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 243069. | 1.14788 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 47811.7 | 0.217637 | 0.108818 | − | 0.994062i | \(-0.465293\pi\) | ||||
0.108818 | + | 0.994062i | \(0.465293\pi\) | |||||||
\(138\) | 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. | −1.64551 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 193932. | 0.766001 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 431614. | 1.64741 | ||||||||
\(148\) | 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 | ||||||||
\(153\) | −1.06670e6 | −3.68394 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2566.11 | 0.00857917 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −361690. | −1.17108 | −0.585541 | − | 0.810643i | \(-0.699118\pi\) | ||||
−0.585541 | + | 0.810643i | \(0.699118\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −429943. | −1.34871 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −66087.3 | −0.200934 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 490843. | 1.44702 | 0.723508 | − | 0.690316i | \(-0.242528\pi\) | ||||
0.723508 | + | 0.690316i | \(0.242528\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 298854. | 0.854572 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 196273. | 0.544591 | 0.272295 | − | 0.962214i | \(-0.412217\pi\) | ||||
0.272295 | + | 0.962214i | \(0.412217\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 562999. | 1.51632 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 184807. | 0.483312 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −183395. | −0.465877 | −0.232938 | − | 0.972491i | \(-0.574834\pi\) | ||||
−0.232938 | + | 0.972491i | \(0.574834\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 26341.8 | 0.0650205 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −569814. | −1.36710 | ||||||||
\(178\) | 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 | \(-0.280285\pi\) | ||||
0.636735 | + | 0.771083i | \(0.280285\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −517572. | −1.14247 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 48414.4 | 0.104003 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −763530. | −1.59670 | ||||||||
\(188\) | 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. | 1.66798 | 0.833992 | − | 0.551776i | \(-0.186050\pi\) | ||||
0.833992 | + | 0.551776i | \(0.186050\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −693904. | −1.30681 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −281871. | −0.517469 | −0.258734 | − | 0.965949i | \(-0.583305\pi\) | ||||
−0.258734 | + | 0.965949i | \(0.583305\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 192798. | 0.345120 | 0.172560 | − | 0.984999i | \(-0.444796\pi\) | ||||
0.172560 | + | 0.984999i | \(0.444796\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.58053e6 | 2.75938 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −326945. | −0.556846 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −199859. | −0.332154 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −911943. | −1.47925 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 132283. | 0.209477 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 44631.4 | 0.0690136 | 0.0345068 | − | 0.999404i | \(-0.489014\pi\) | ||||
0.0345068 | + | 0.999404i | \(0.489014\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 321651. | 0.485776 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −413565. | −0.610165 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4326.13 | −0.00623664 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 115263. | 0.162398 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.77283e6 | 2.44167 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 904469. | 1.21796 | 0.608978 | − | 0.793187i | \(-0.291580\pi\) | ||||
0.608978 | + | 0.793187i | \(0.291580\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 363492. | 0.478673 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.02684e6 | −1.32263 | −0.661314 | − | 0.750109i | \(-0.730001\pi\) | ||||
−0.661314 | + | 0.750109i | \(0.730001\pi\) | |||||||
\(228\) | 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. | −0.378567 | −0.189283 | − | 0.981923i | \(-0.560616\pi\) | ||||
−0.189283 | + | 0.981923i | \(0.560616\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 466233. | 0.550724 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 689715. | 0.797625 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.53093e6 | 1.73365 | 0.866825 | − | 0.498612i | \(-0.166157\pi\) | ||||
0.866825 | + | 0.498612i | \(0.166157\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 506999. | 0.562296 | 0.281148 | − | 0.959664i | \(-0.409285\pi\) | ||||
0.281148 | + | 0.959664i | \(0.409285\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.59638e6 | −1.73428 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 375766. | 0.399947 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −307146. | −0.320333 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.02482e6 | −2.06961 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −511659. | −0.512621 | −0.256311 | − | 0.966594i | \(-0.582507\pi\) | ||||
−0.256311 | + | 0.966594i | \(0.582507\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −652758. | −0.641137 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.31669e6 | −1.26804 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −256082. | −0.241850 | −0.120925 | − | 0.992662i | \(-0.538586\pi\) | ||||
−0.120925 | + | 0.992662i | \(0.538586\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −81620.7 | −0.0756051 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.51154e6 | −4.09943 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.32451e6 | −1.18077 | −0.590386 | − | 0.807121i | \(-0.701024\pi\) | ||||
−0.590386 | + | 0.807121i | \(0.701024\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −374311. | −0.327430 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.74493e6 | 1.49795 | ||||||||
\(268\) | 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 | ||||||||
\(273\) | 1.16984e6 | 0.949989 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 260184. | 0.207467 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −314677. | −0.246414 | −0.123207 | − | 0.992381i | \(-0.539318\pi\) | ||||
−0.123207 | + | 0.992381i | \(0.539318\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −2.08248e6 | −1.54566 | −0.772831 | − | 0.634612i | \(-0.781160\pi\) | ||||
−0.772831 | + | 0.634612i | \(0.781160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 228119. | 0.166360 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 336938. | 0.241460 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.94411e6 | 1.36923 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 893407. | 0.618468 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −90716.3 | −0.0617329 | −0.0308664 | − | 0.999524i | \(-0.509827\pi\) | ||||
−0.0308664 | + | 0.999524i | \(0.509827\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −496083. | −0.331894 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.04752e6 | −2.66255 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.51563e6 | 0.980428 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 697219. | 0.443561 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.42118e6 | −0.889286 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −450601. | −0.277359 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −571699. | −0.346196 | −0.173098 | − | 0.984905i | \(-0.555378\pi\) | ||||
−0.173098 | + | 0.984905i | \(0.555378\pi\) | |||||||
\(308\) | 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. | −0.294625 | −0.147313 | − | 0.989090i | \(-0.547062\pi\) | ||||
−0.147313 | + | 0.989090i | \(0.547062\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −612803. | −0.347972 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.37030e6 | 1.88374 | 0.941868 | − | 0.335984i | \(-0.109069\pi\) | ||||
0.941868 | + | 0.335984i | \(0.109069\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.22931e6 | −1.77678 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.53932e6 | −1.37548 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −582813. | −0.310830 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −604117. | −0.317258 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −304354. | −0.157402 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −786012. | −0.400349 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.80172e6 | 1.90726 | 0.953632 | − | 0.300976i | \(-0.0973125\pi\) | ||||
0.953632 | + | 0.300976i | \(0.0973125\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.12629e6 | −0.556595 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.37601e6 | 0.669902 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.06627e6 | 0.991088 | 0.495544 | − | 0.868583i | \(-0.334969\pi\) | ||||
0.495544 | + | 0.868583i | \(0.334969\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.75174e6 | −3.19093 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −42730.1 | −0.0198998 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.34186e6 | −0.615845 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.12567e6 | −0.509170 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.35066e6 | 1.04801 | 0.524005 | − | 0.851715i | \(-0.324437\pi\) | ||||
0.524005 | + | 0.851715i | \(0.324437\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | 1.71355e6 | 0.731914 | 0.365957 | − | 0.930632i | \(-0.380742\pi\) | ||||
0.365957 | + | 0.930632i | \(0.380742\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 280032. | 0.117933 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.21978e6 | 0.921806 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.85773e6 | 1.57978 | 0.789888 | − | 0.613251i | \(-0.210139\pi\) | ||||
0.789888 | + | 0.613251i | \(0.210139\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.37513e6 | −0.959221 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −351753. | −0.140111 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 100349. | 0.0394258 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.18109e6 | 1.23285 | 0.616427 | − | 0.787412i | \(-0.288580\pi\) | ||||
0.616427 | + | 0.787412i | \(0.288580\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.64942e6 | 1.77760 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 631042. | 0.238026 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.79295e6 | 1.78374 | 0.891868 | − | 0.452295i | \(-0.149395\pi\) | ||||
0.891868 | + | 0.452295i | \(0.149395\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 448682. | 0.164763 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.49809e6 | 2.71705 | ||||||||
\(378\) | 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. | 0.241784 | 0.120892 | − | 0.992666i | \(-0.461424\pi\) | ||||
0.120892 | + | 0.992666i | \(0.461424\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −438637. | −0.150818 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.62097e6 | 3.26544 | ||||||||
\(388\) | 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 | ||||||||
\(393\) | −1.45310e6 | −0.474584 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 600470. | 0.193642 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −907937. | −0.289121 | −0.144560 | − | 0.989496i | \(-0.546177\pi\) | ||||
−0.144560 | + | 0.989496i | \(0.546177\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 99214.6 | 0.0304308 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.44673e6 | −1.04417 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −806185. | −0.241240 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.61814e6 | 1.66067 | 0.830337 | − | 0.557262i | \(-0.188148\pi\) | ||||
0.830337 | + | 0.557262i | \(0.188148\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.37294e6 | −0.400911 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 836334. | 0.241271 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.76282e6 | −0.502444 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.32288e6 | 1.78064 | ||||||||
\(418\) | 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 | \(-0.318954\pi\) | ||||
0.538597 | + | 0.842563i | \(0.318954\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.08462e7 | −2.94732 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.14632e6 | −0.307846 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 759658. | 0.201627 | ||||||||
\(428\) | 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 | ||||||||
\(433\) | −4.01914e6 | −1.03018 | −0.515090 | − | 0.857136i | \(-0.672242\pi\) | ||||
−0.515090 | + | 0.857136i | \(0.672242\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.56888e6 | −1.41106 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −498259. | −0.124811 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.41795e6 | 1.34176 | 0.670879 | − | 0.741567i | \(-0.265917\pi\) | ||||
0.670879 | + | 0.741567i | \(0.265917\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.74163e6 | −2.14041 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.21518e6 | −1.74678 | −0.873389 | − | 0.487023i | \(-0.838083\pi\) | ||||
−0.873389 | + | 0.487023i | \(0.838083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.51914e6 | 0.363662 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.43751e6 | 1.05044 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −203792. | −0.0477057 | −0.0238529 | − | 0.999715i | \(-0.507593\pi\) | ||||
−0.0238529 | + | 0.999715i | \(0.507593\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.32800e6 | 0.770446 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.30769e7 | −2.99406 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.01847e6 | 0.230631 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.45642e6 | −0.774169 | −0.387085 | − | 0.922044i | \(-0.626518\pi\) | ||||
−0.387085 | + | 0.922044i | \(0.626518\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.78326e7 | 3.95079 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.40596e6 | −1.40389 | −0.701944 | − | 0.712233i | \(-0.747684\pi\) | ||||
−0.701944 | + | 0.712233i | \(0.747684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.59550e6 | 1.64666 | 0.823330 | − | 0.567563i | \(-0.192113\pi\) | ||||
0.823330 | + | 0.567563i | \(0.192113\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −73687.3 | −0.0158038 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.58166e6 | −0.972145 | −0.486072 | − | 0.873919i | \(-0.661571\pi\) | ||||
−0.486072 | + | 0.873919i | \(0.661571\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.31979e6 | −0.486986 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.03862e7 | 2.15726 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.88658e6 | 1.41531 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 198602. | 0.0403877 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.70779e6 | 1.75231 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.01195e6 | −0.998085 | −0.499043 | − | 0.866577i | \(-0.666315\pi\) | ||||
−0.499043 | + | 0.866577i | \(0.666315\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.87187e6 | 0.368904 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.89774e6 | 0.370142 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 777806. | 0.150147 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.10670e6 | 0.402514 | 0.201257 | − | 0.979539i | \(-0.435497\pi\) | ||||
0.201257 | + | 0.979539i | \(0.435497\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.40949e7 | −2.66556 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.43322e6 | 1.01708 | 0.508538 | − | 0.861040i | \(-0.330186\pi\) | ||||
0.508538 | + | 0.861040i | \(0.330186\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.42277e7 | 2.63644 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.05278e6 | −1.11030 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −472099. | −0.0857318 | ||||||||
\(498\) | 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 | ||||||||
\(503\) | −1.33954e6 | −0.236067 | −0.118034 | − | 0.993010i | \(-0.537659\pi\) | ||||
−0.118034 | + | 0.993010i | \(0.537659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.23729e6 | −0.215894 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.61669e7 | −2.79322 | ||||||||
\(508\) | 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 | ||||||||
\(513\) | −3.08953e6 | −0.518321 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.37795e6 | −0.395079 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.76360e6 | −1.27743 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | −3.83877e6 | −0.613674 | −0.306837 | − | 0.951762i | \(-0.599271\pi\) | ||||
−0.306837 | + | 0.951762i | \(0.599271\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −756422. | −0.119775 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 188261. | 0.0295280 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.97765e6 | −0.617998 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.15406e7 | 1.77621 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.72725e6 | −1.17817 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.21075e6 | −0.333929 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.11015e6 | 0.166129 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.25716e6 | −0.927696 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.28830e6 | −0.923720 | −0.461860 | − | 0.886953i | \(-0.652818\pi\) | ||||
−0.461860 | + | 0.886953i | \(0.652818\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.61177e7 | −2.34587 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −264972. | −0.0382128 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.54365e6 | 0.649287 | 0.324644 | − | 0.945836i | \(-0.394756\pi\) | ||||
0.324644 | + | 0.945836i | \(0.394756\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.04826e7 | 1.48435 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.46497e6 | −0.345886 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.01232e6 | −0.140768 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.39025e6 | −0.191585 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.20198e7 | −1.64157 | −0.820783 | − | 0.571239i | \(-0.806463\pi\) | ||||
−0.820783 | + | 0.571239i | \(0.806463\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.59899e7 | −2.16429 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.19252e7 | 2.94129 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.65741e6 | 0.486298 | 0.243149 | − | 0.969989i | \(-0.421820\pi\) | ||||
0.243149 | + | 0.969989i | \(0.421820\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.87811e6 | −0.774670 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.81077e6 | 0.759059 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.80214e6 | −0.362835 | −0.181418 | − | 0.983406i | \(-0.558069\pi\) | ||||
−0.181418 | + | 0.983406i | \(0.558069\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.78472e6 | −0.870846 | −0.435423 | − | 0.900226i | \(-0.643401\pi\) | ||||
−0.435423 | + | 0.900226i | \(0.643401\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.62091e6 | 0.969662 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −980014. | −0.123613 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.25416e6 | −0.156825 | −0.0784123 | − | 0.996921i | \(-0.524985\pi\) | ||||
−0.0784123 | + | 0.996921i | \(0.524985\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.47858e7 | −3.07261 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.97190e6 | 0.365253 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.23293e6 | 0.759488 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.40539e7 | 1.69788 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 726476. | 0.0870213 | 0.0435107 | − | 0.999053i | \(-0.486146\pi\) | ||||
0.0435107 | + | 0.999053i | \(0.486146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32616.5 | −0.00387391 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.09409e6 | 0.953234 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 933494. | 0.109012 | 0.0545060 | − | 0.998513i | \(-0.482642\pi\) | ||||
0.0545060 | + | 0.998513i | \(0.482642\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.93255e6 | 0.223789 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.53632e6 | −0.635749 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.27354e7 | 1.45025 | 0.725127 | − | 0.688615i | \(-0.241781\pi\) | ||||
0.725127 | + | 0.688615i | \(0.241781\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.87190e6 | −0.776052 | −0.388026 | − | 0.921648i | \(-0.626843\pi\) | ||||
−0.388026 | + | 0.921648i | \(0.626843\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.20109e7 | −3.58513 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −306238. | −0.0340150 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.87130e6 | 0.426467 | 0.213233 | − | 0.977001i | \(-0.431601\pi\) | ||||
0.213233 | + | 0.977001i | \(0.431601\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.38844e6 | 1.02577 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.80262e7 | 1.95345 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.38824e6 | 0.256701 | 0.128350 | − | 0.991729i | \(-0.459032\pi\) | ||||
0.128350 | + | 0.991729i | \(0.459032\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.73908e6 | 0.611863 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.07299e6 | −0.324974 | −0.162487 | − | 0.986711i | \(-0.551952\pi\) | ||||
−0.162487 | + | 0.986711i | \(0.551952\pi\) | |||||||
\(618\) | 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 | ||||||||
\(623\) | −2.56109e6 | −0.264365 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.79858e6 | −0.385880 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | −1.28162e6 | −0.127131 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.56333e6 | −0.252272 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.45284e7 | 1.41863 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 1.40516e7 | 1.34029 | 0.670144 | − | 0.742231i | \(-0.266232\pi\) | ||||
0.670144 | + | 0.742231i | \(0.266232\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.18758e7 | 1.12399 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −962366. | −0.0903815 | −0.0451908 | − | 0.998978i | \(-0.514390\pi\) | ||||
−0.0451908 | + | 0.998978i | \(0.514390\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.26065e6 | 0.769844 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 124228. | 0.0114886 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 413989. | 0.0379932 | 0.0189966 | − | 0.999820i | \(-0.493953\pi\) | ||||
0.0189966 | + | 0.999820i | \(0.493953\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.26508e6 | −0.115216 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.33446e6 | −0.210996 | ||||||||
\(658\) | 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 | \(-0.135370\pi\) | ||||
0.910924 | + | 0.412574i | \(0.135370\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.09080e7 | −4.49782 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −334818. | −0.0293599 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.21636e7 | 1.05864 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.59724e7 | −2.24361 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.50330e6 | 0.643348 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.12086e6 | −0.776244 | −0.388122 | − | 0.921608i | \(-0.626876\pi\) | ||||
−0.388122 | + | 0.921608i | \(0.626876\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.07672e6 | −0.513346 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.29457e7 | 1.08556 | 0.542778 | − | 0.839876i | \(-0.317372\pi\) | ||||
0.542778 | + | 0.839876i | \(0.317372\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.31128e6 | −0.109150 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.94863e7 | 2.43642 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.56637e6 | −0.702660 | −0.351330 | − | 0.936252i | \(-0.614270\pi\) | ||||
−0.351330 | + | 0.936252i | \(0.614270\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.19529e6 | −0.0973302 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.91523e6 | −0.235658 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.44722e7 | −1.16141 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.01163e7 | −0.805984 | −0.402992 | − | 0.915204i | \(-0.632030\pi\) | ||||
−0.402992 | + | 0.915204i | \(0.632030\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.02042e7 | 0.807138 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.50474e6 | 0.432289 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.46626e7 | −1.14322 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.00846e6 | 0.697361 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.95732e7 | 1.50441 | 0.752207 | − | 0.658927i | \(-0.228989\pi\) | ||||
0.752207 | + | 0.658927i | \(0.228989\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −615372. | −0.0469623 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.33882e7 | −1.01449 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.08591e6 | 0.156945 | ||||||||
\(708\) | 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. | 0.0118567 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.00596e7 | 0.735895 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.39617e7 | −3.19357 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.44994e7 | −1.76740 | −0.883698 | − | 0.468058i | \(-0.844954\pi\) | ||||
−0.883698 | + | 0.468058i | \(0.844954\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00892e6 | 0.287204 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.45588e7 | −1.03581 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.84830e6 | −0.342566 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.75199e7 | 1.22941 | 0.614703 | − | 0.788759i | \(-0.289276\pi\) | ||||
0.614703 | + | 0.788759i | \(0.289276\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.23387e7 | 0.859904 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.03410e7 | −2.10008 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.29025e7 | −1.57443 | −0.787215 | − | 0.616679i | \(-0.788478\pi\) | ||||
−0.787215 | + | 0.616679i | \(0.788478\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.07904e7 | −0.736746 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.29131e7 | −1.55387 | ||||||||
\(738\) | 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 | ||||||||
\(743\) | 1.89399e6 | 0.125865 | 0.0629326 | − | 0.998018i | \(-0.479955\pi\) | ||||
0.0629326 | + | 0.998018i | \(0.479955\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.86332e6 | 0.255017 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.10094e7 | 2.68894 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 1.46926e7 | 0.944304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.13849e7 | −0.726876 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.02697e7 | −1.28561 | −0.642804 | − | 0.766031i | \(-0.722229\pi\) | ||||
−0.642804 | + | 0.766031i | \(0.722229\pi\) | |||||||
\(758\) | 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. | 0.0277789 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.66674e7 | 1.64751 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.91803e7 | −1.17725 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.48043e7 | −1.51256 | −0.756278 | − | 0.654251i | \(-0.772984\pi\) | ||||
−0.756278 | + | 0.654251i | \(0.772984\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.35357e6 | 0.445515 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.27616e7 | −1.37010 | −0.685052 | − | 0.728495i | \(-0.740220\pi\) | ||||
−0.685052 | + | 0.728495i | \(0.740220\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −64152.6 | −0.00383672 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.34379e6 | 0.139273 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.54031e6 | 0.149983 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.66302e6 | −0.273552 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.54221e7 | 4.39637 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.04225e6 | 0.523724 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.56494e7 | 0.900658 | 0.450329 | − | 0.892863i | \(-0.351307\pi\) | ||||
0.450329 | + | 0.892863i | \(0.351307\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.80341e7 | 2.17511 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.90976e6 | 0.563147 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.74218e7 | −0.983809 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.07486e7 | 0.603161 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.26205e7 | 1.26141 | 0.630704 | − | 0.776023i | \(-0.282766\pi\) | ||||
0.630704 | + | 0.776023i | \(0.282766\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.42050e7 | 1.89549 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.53406e7 | −1.94622 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.67098e6 | −0.0914499 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.65218e6 | 0.0898604 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.10602e7 | −2.21941 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.25367e7 | −1.21065 | −0.605326 | − | 0.795977i | \(-0.706957\pi\) | ||||
−0.605326 | + | 0.795977i | \(0.706957\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −410196. | −0.0218997 | −0.0109499 | − | 0.999940i | \(-0.503486\pi\) | ||||
−0.0109499 | + | 0.999940i | \(0.503486\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.02855e7 | −1.07636 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.22711e7 | −0.647126 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.25662e6 | 0.275519 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.36931e7 | −1.23428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.62749e7 | −0.842678 | −0.421339 | − | 0.906903i | \(-0.638440\pi\) | ||||
−0.421339 | + | 0.906903i | \(0.638440\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 628881. | 0.0323645 | 0.0161823 | − | 0.999869i | \(-0.494849\pi\) | ||||
0.0161823 | + | 0.999869i | \(0.494849\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.47134e6 | −0.382176 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.94403e7 | −0.988417 | −0.494209 | − | 0.869343i | \(-0.664542\pi\) | ||||
−0.494209 | + | 0.869343i | \(0.664542\pi\) | |||||||
\(828\) | 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 | ||||||||
\(833\) | 2.75679e7 | 1.37655 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.90683e6 | −0.243548 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 997985. | 0.0492391 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.84583e6 | −0.335754 | −0.167877 | − | 0.985808i | \(-0.553691\pi\) | ||||
−0.167877 | + | 0.985808i | \(0.553691\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.96642e7 | 1.93379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.25715e7 | 0.609282 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.40750e7 | −0.678118 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 516280. | 0.0247273 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.97997e7 | 2.84728 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.03660e6 | 0.143735 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.67852e7 | 1.26044 | 0.630221 | − | 0.776416i | \(-0.282964\pi\) | ||||
0.630221 | + | 0.776416i | \(0.282964\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.62017e6 | −0.216144 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.32339e6 | 0.433632 | 0.216816 | − | 0.976212i | \(-0.430433\pi\) | ||||
0.216816 | + | 0.976212i | \(0.430433\pi\) | |||||||
\(858\) | 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 | ||||||||
\(863\) | 5.18636e6 | 0.237048 | 0.118524 | − | 0.992951i | \(-0.462184\pi\) | ||||
0.118524 | + | 0.992951i | \(0.462184\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.58486e6 | 0.208346 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.58265e7 | −2.52228 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.99888e6 | −0.449161 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.32016e7 | 2.37618 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.80945e7 | −0.803546 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −658545. | −0.0290781 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.63396e6 | 0.247352 | 0.123676 | − | 0.992323i | \(-0.460532\pi\) | ||||
0.123676 | + | 0.992323i | \(0.460532\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 2.60630e7 | 1.12492 | 0.562462 | − | 0.826823i | \(-0.309854\pi\) | ||||
0.562462 | + | 0.826823i | \(0.309854\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.42453e7 | 0.611385 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.24889e7 | −1.38652 | −0.693259 | − | 0.720688i | \(-0.743826\pi\) | ||||
−0.693259 | + | 0.720688i | \(0.743826\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.32145e6 | 0.183390 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.73942e7 | 2.42200 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.92607e6 | −0.248678 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 966499. | 0.0403315 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.35223e7 | −1.80605 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 796240. | 0.0328583 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.74612e7 | −1.12696 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.00211e7 | −0.817087 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.40322e7 | −0.569513 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.11745e7 | −1.25829 | −0.629145 | − | 0.777288i | \(-0.716595\pi\) | ||||
−0.629145 | + | 0.777288i | \(0.716595\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | 2.93540e7 | 1.16544 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.29393e7 | 0.510926 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.13276e6 | 0.0837565 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.14710e7 | 1.22920 | 0.614598 | − | 0.788840i | \(-0.289318\pi\) | ||||
0.614598 | + | 0.788840i | \(0.289318\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.64167e7 | 0.637730 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.08270e7 | 0.418316 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.21036e6 | −0.0465115 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.53194e7 | 2.11436 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 532600. | 0.0202471 | 0.0101235 | − | 0.999949i | \(-0.496778\pi\) | ||||
0.0101235 | + | 0.999949i | \(0.496778\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.77618e6 | −0.180595 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.45215e7 | 2.80270 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.90882e7 | 0.714064 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.97320e7 | 0.734214 | 0.367107 | − | 0.930179i | \(-0.380348\pi\) | ||||
0.367107 | + | 0.930179i | \(0.380348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.46639e7 | 0.542732 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.12060e7 | 0.780702 | 0.390351 | − | 0.920666i | \(-0.372354\pi\) | ||||
0.390351 | + | 0.920666i | \(0.372354\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.25353e7 | −0.459047 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.02446e7 | 0.373178 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.60224e7 | 1.66761 | 0.833804 | − | 0.552060i | \(-0.186158\pi\) | ||||
0.833804 | + | 0.552060i | \(0.186158\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.87984e6 | 0.139845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.67802e7 | −3.47004 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.76525e7 | 1.69963 | 0.849813 | − | 0.527085i | \(-0.176715\pi\) | ||||
0.849813 | + | 0.527085i | \(0.176715\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.63481e6 | 0.235407 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.27316e7 | 3.27301 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.01511e6 | 0.0707543 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.86186e7 | −0.999632 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.14297e7 | 1.78710 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.15787e7 | −0.745946 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.29686e7 | 0.789893 | 0.394946 | − | 0.918704i | \(-0.370763\pi\) | ||||
0.394946 | + | 0.918704i | \(0.370763\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.67358e7 | 0.572583 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.22231e7 | 0.756408 | 0.378204 | − | 0.925722i | \(-0.376542\pi\) | ||||
0.378204 | + | 0.925722i | \(0.376542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.28031e6 | −0.314254 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.73476e7 | 0.584424 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.68581e7 | −1.23537 | −0.617684 | − | 0.786426i | \(-0.711929\pi\) | ||||
−0.617684 | + | 0.786426i | \(0.711929\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.52964e7 | −0.843532 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.16418e6 | 0.204504 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.53136e7 | 1.49570 | 0.747850 | − | 0.663868i | \(-0.231086\pi\) | ||||
0.747850 | + | 0.663868i | \(0.231086\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.04676e6 | 0.231419 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.25708e7 | 0.737487 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | −1.09169e8 | −3.51339 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.81995e6 | −0.154342 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.19245e7 | 1.33577 | 0.667883 | − | 0.744266i | \(-0.267201\pi\) | ||||
0.667883 | + | 0.744266i | \(0.267201\pi\) | |||||||
\(998\) | 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 | 320.6.a.q.1.1 | 2 | ||
4.3 | odd | 2 | 320.6.a.w.1.2 | 2 | |||
8.3 | odd | 2 | 40.6.a.d.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 80.6.a.i.1.2 | 2 | |||
24.5 | odd | 2 | 720.6.a.z.1.2 | 2 | |||
24.11 | even | 2 | 360.6.a.l.1.1 | 2 | |||
40.3 | even | 4 | 200.6.c.e.49.1 | 4 | |||
40.13 | odd | 4 | 400.6.c.l.49.4 | 4 | |||
40.19 | odd | 2 | 200.6.a.g.1.2 | 2 | |||
40.27 | even | 4 | 200.6.c.e.49.4 | 4 | |||
40.29 | even | 2 | 400.6.a.q.1.1 | 2 | |||
40.37 | odd | 4 | 400.6.c.l.49.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.a.d.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
80.6.a.i.1.2 | 2 | 8.5 | even | 2 | |||
200.6.a.g.1.2 | 2 | 40.19 | odd | 2 | |||
200.6.c.e.49.1 | 4 | 40.3 | even | 4 | |||
200.6.c.e.49.4 | 4 | 40.27 | even | 4 | |||
320.6.a.q.1.1 | 2 | 1.1 | even | 1 | trivial | ||
320.6.a.w.1.2 | 2 | 4.3 | odd | 2 | |||
360.6.a.l.1.1 | 2 | 24.11 | even | 2 | |||
400.6.a.q.1.1 | 2 | 40.29 | even | 2 | |||
400.6.c.l.49.1 | 4 | 40.37 | odd | 4 | |||
400.6.c.l.49.4 | 4 | 40.13 | odd | 4 | |||
720.6.a.z.1.2 | 2 | 24.5 | odd | 2 |