Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(129,320)]
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, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.129");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.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: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 165x^{10} + 9528x^{8} + 254984x^{6} + 3245664x^{4} + 15975501x^{2} + 588289 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{44}\cdot 5^{4} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.11 | ||
Root | \(4.23250i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.129 |
Dual form | 320.6.c.k.129.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 26.2718i | 1.68534i | 0.538434 | + | 0.842668i | \(0.319016\pi\) | ||||
−0.538434 | + | 0.842668i | \(0.680984\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −48.8634 | − | 27.1545i | −0.874095 | − | 0.485754i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 23.9306i | 0.184590i | 0.995732 | + | 0.0922952i | \(0.0294203\pi\) | ||||
−0.995732 | + | 0.0922952i | \(0.970580\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −447.206 | −1.84035 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −704.032 | −1.75433 | −0.877164 | − | 0.480191i | \(-0.840567\pi\) | ||||
−0.877164 | + | 0.480191i | \(0.840567\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1037.56i | 1.70276i | 0.524549 | + | 0.851380i | \(0.324234\pi\) | ||||
−0.524549 | + | 0.851380i | \(0.675766\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 713.397 | − | 1283.73i | 0.818659 | − | 1.47314i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 217.433i | 0.182475i | 0.995829 | + | 0.0912375i | \(0.0290823\pi\) | ||||
−0.995829 | + | 0.0912375i | \(0.970918\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1290.13 | −0.819878 | −0.409939 | − | 0.912113i | \(-0.634450\pi\) | ||||
−0.409939 | + | 0.912113i | \(0.634450\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −628.700 | −0.311097 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2806.24i | − | 1.10613i | −0.833138 | − | 0.553065i | \(-0.813458\pi\) | ||
0.833138 | − | 0.553065i | \(-0.186542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1650.27 | + | 2653.72i | 0.528086 | + | 0.849191i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5364.86i | − | 1.41628i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4905.42 | 1.08313 | 0.541566 | − | 0.840658i | \(-0.317832\pi\) | ||||
0.541566 | + | 0.840658i | \(0.317832\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 415.555 | 0.0776648 | 0.0388324 | − | 0.999246i | \(-0.487636\pi\) | ||||
0.0388324 | + | 0.999246i | \(0.487636\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 18496.2i | − | 2.95663i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 649.824 | − | 1169.33i | 0.0896656 | − | 0.161350i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6450.71i | 0.774646i | 0.921944 | + | 0.387323i | \(0.126600\pi\) | ||||
−0.921944 | + | 0.387323i | \(0.873400\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −27258.5 | −2.86972 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −16402.5 | −1.52388 | −0.761940 | − | 0.647648i | \(-0.775753\pi\) | ||||
−0.761940 | + | 0.647648i | \(0.775753\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 13772.3i | − | 1.13589i | −0.823067 | − | 0.567944i | \(-0.807739\pi\) | ||
0.823067 | − | 0.567944i | \(-0.192261\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 21852.0 | + | 12143.7i | 1.60865 | + | 0.893960i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 12942.4i | − | 0.854612i | −0.904107 | − | 0.427306i | \(-0.859463\pi\) | ||
0.904107 | − | 0.427306i | \(-0.140537\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16234.3 | 0.965926 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5712.36 | −0.307532 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5239.24i | − | 0.256200i | −0.991761 | − | 0.128100i | \(-0.959112\pi\) | ||
0.991761 | − | 0.128100i | \(-0.0408878\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 34401.4 | + | 19117.6i | 1.53345 | + | 0.852172i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 33894.0i | − | 1.38177i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 24042.4 | 0.899182 | 0.449591 | − | 0.893234i | \(-0.351570\pi\) | ||||
0.449591 | + | 0.893234i | \(0.351570\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1037.24 | 0.0356908 | 0.0178454 | − | 0.999841i | \(-0.494319\pi\) | ||||
0.0178454 | + | 0.999841i | \(0.494319\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 10701.9i | − | 0.339712i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 28174.3 | − | 50698.6i | 0.827123 | − | 1.48838i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 47902.5i | 1.30368i | 0.758357 | + | 0.651840i | \(0.226002\pi\) | ||||
−0.758357 | + | 0.651840i | \(0.773998\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 73725.0 | 1.86420 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 74761.8 | 1.76009 | 0.880043 | − | 0.474893i | \(-0.157513\pi\) | ||||
0.880043 | + | 0.474893i | \(0.157513\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 22746.5i | 0.499582i | 0.968300 | + | 0.249791i | \(0.0803619\pi\) | ||||
−0.968300 | + | 0.249791i | \(0.919638\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −69718.0 | + | 43355.5i | −1.43117 | + | 0.890001i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 16847.9i | − | 0.323832i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −64213.8 | −1.15761 | −0.578803 | − | 0.815468i | \(-0.696480\pi\) | ||||
−0.578803 | + | 0.815468i | \(0.696480\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 32273.2 | 0.546550 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 22523.0i | 0.358865i | 0.983770 | + | 0.179432i | \(0.0574261\pi\) | ||||
−0.983770 | + | 0.179432i | \(0.942574\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5904.29 | − | 10624.5i | 0.0886381 | − | 0.159501i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 128874.i | 1.82544i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 37886.4 | 0.507000 | 0.253500 | − | 0.967335i | \(-0.418418\pi\) | ||||
0.253500 | + | 0.967335i | \(0.418418\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −24829.4 | −0.314313 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10917.4i | 0.130891i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 63040.1 | + | 35032.8i | 0.716651 | + | 0.398259i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 84119.7i | 0.907755i | 0.891064 | + | 0.453877i | \(0.149960\pi\) | ||||
−0.891064 | + | 0.453877i | \(0.850040\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 314847. | 3.22858 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 77492.2 | 0.755883 | 0.377941 | − | 0.925830i | \(-0.376632\pi\) | ||||
0.377941 | + | 0.925830i | \(0.376632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 68641.0i | − | 0.637516i | −0.947836 | − | 0.318758i | \(-0.896734\pi\) | ||
0.947836 | − | 0.318758i | \(-0.103266\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 30720.4 | + | 17072.0i | 0.271928 | + | 0.151117i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 84264.9i | − | 0.711520i | −0.934577 | − | 0.355760i | \(-0.884222\pi\) | ||
0.934577 | − | 0.355760i | \(-0.115778\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −51640.6 | −0.416318 | −0.208159 | − | 0.978095i | \(-0.566747\pi\) | ||||
−0.208159 | + | 0.978095i | \(0.566747\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −169472. | −1.30554 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 88744.4i | − | 0.653800i | −0.945059 | − | 0.326900i | \(-0.893996\pi\) | ||
0.945059 | − | 0.326900i | \(-0.106004\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −76202.1 | + | 137123.i | −0.537307 | + | 0.966863i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 464002.i | − | 3.13368i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5203.31 | −0.0336832 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 334610. | 2.07767 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 430923.i | − | 2.56825i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8577.22 | − | 174482.i | −0.0490989 | − | 0.998794i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 178878.i | − | 0.984121i | −0.870561 | − | 0.492061i | \(-0.836244\pi\) | ||
0.870561 | − | 0.492061i | \(-0.163756\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 361823. | 1.91435 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −235194. | −1.19742 | −0.598711 | − | 0.800965i | \(-0.704320\pi\) | ||||
−0.598711 | + | 0.800965i | \(0.704320\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 30873.6i | − | 0.151342i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −145680. | + | 262145.i | −0.687963 | + | 1.23796i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 216936.i | 0.987486i | 0.869608 | + | 0.493743i | \(0.164372\pi\) | ||||
−0.869608 | + | 0.493743i | \(0.835628\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −347938. | −1.52744 | −0.763721 | − | 0.645546i | \(-0.776630\pi\) | ||||
−0.763721 | + | 0.645546i | \(0.776630\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 340019. | 1.44031 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 730473.i | − | 2.98720i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −239696. | − | 133204.i | −0.946760 | − | 0.526136i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 426505.i | 1.62791i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 136495. | 0.503677 | 0.251839 | − | 0.967769i | \(-0.418965\pi\) | ||||
0.251839 | + | 0.967769i | \(0.418965\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 318940. | 1.13833 | 0.569163 | − | 0.822225i | \(-0.307267\pi\) | ||||
0.569163 | + | 0.822225i | \(0.307267\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 97237.5i | − | 0.335819i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20305.4 | − | 11284.2i | −0.0678864 | − | 0.0377260i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 54247.3i | 0.175642i | 0.996136 | + | 0.0878211i | \(0.0279904\pi\) | ||||
−0.996136 | + | 0.0878211i | \(0.972010\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 137644. | 0.431783 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 67155.2 | 0.204181 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 504961.i | − | 1.48864i | −0.667825 | − | 0.744318i | \(-0.732775\pi\) | ||
0.667825 | − | 0.744318i | \(-0.267225\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −502254. | + | 903786.i | −1.43620 | + | 2.58438i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 264305.i | 0.733355i | 0.930348 | + | 0.366677i | \(0.119505\pi\) | ||||
−0.930348 | + | 0.366677i | \(0.880495\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −705231. | −1.89939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 576953. | 1.50887 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 449650.i | − | 1.14225i | −0.820865 | − | 0.571123i | \(-0.806508\pi\) | ||
0.820865 | − | 0.571123i | \(-0.193492\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −63505.3 | + | 39491.9i | −0.156753 | + | 0.0974795i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 631636.i | 1.51542i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −657282. | −1.53327 | −0.766636 | − | 0.642082i | \(-0.778071\pi\) | ||||
−0.766636 | + | 0.642082i | \(0.778071\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −640421. | −1.45301 | −0.726506 | − | 0.687160i | \(-0.758857\pi\) | ||||
−0.726506 | + | 0.687160i | \(0.758857\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 27250.2i | 0.0601510i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 175166. | − | 315204.i | 0.376288 | − | 0.677115i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 153080.i | − | 0.320121i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 128384. | 0.261431 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −689612. | −1.36780 | −0.683898 | − | 0.729578i | \(-0.739717\pi\) | ||||
−0.683898 | + | 0.729578i | \(0.739717\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 398342.i | − | 0.769773i | −0.922964 | − | 0.384887i | \(-0.874241\pi\) | ||
0.922964 | − | 0.384887i | \(-0.125759\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.33194e6 | + | 740190.i | 2.50841 | + | 1.39398i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19330.2i | 0.0354870i | 0.999843 | + | 0.0177435i | \(0.00564823\pi\) | ||||
−0.999843 | + | 0.0177435i | \(0.994352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 314706. | 0.563342 | 0.281671 | − | 0.959511i | \(-0.409111\pi\) | ||||
0.281671 | + | 0.959511i | \(0.409111\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.25848e6 | −2.19714 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 117390.i | 0.199936i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 801482. | + | 445402.i | 1.33202 | + | 0.740231i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.25497e6i | 2.03567i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 908292. | 1.43833 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 478488. | 0.739885 | 0.369943 | − | 0.929055i | \(-0.379377\pi\) | ||||
0.369943 | + | 0.929055i | \(0.379377\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.96413e6i | 2.96634i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −373980. | + | 672962.i | −0.551762 | + | 0.992874i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9944.49i | 0.0143362i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −597590. | −0.841963 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −225599. | −0.310711 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 205163.i | − | 0.276273i | −0.990413 | − | 0.138136i | \(-0.955889\pi\) | ||
0.990413 | − | 0.138136i | \(-0.0441112\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −738010. | − | 1.18676e6i | −0.971865 | − | 1.56281i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 409093.i | 0.526936i | 0.964668 | + | 0.263468i | \(0.0848663\pi\) | ||||
−0.964668 | + | 0.263468i | \(0.915134\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 405619. | 0.511128 | 0.255564 | − | 0.966792i | \(-0.417739\pi\) | ||||
0.255564 | + | 0.966792i | \(0.417739\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 442625. | 0.545766 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 64192.9i | − | 0.0774635i | −0.999250 | − | 0.0387318i | \(-0.987668\pi\) | ||
0.999250 | − | 0.0387318i | \(-0.0123318\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −351443. | + | 632408.i | −0.415131 | + | 0.747012i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.68701e6i | − | 1.95095i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.36063e6 | 1.54080 | 0.770401 | − | 0.637560i | \(-0.220056\pi\) | ||||
0.770401 | + | 0.637560i | \(0.220056\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.34482e6 | −1.49149 | −0.745745 | − | 0.666231i | \(-0.767906\pi\) | ||||
−0.745745 | + | 0.666231i | \(0.767906\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 455786.i | − | 0.495159i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −793265. | − | 440835.i | −0.844312 | − | 0.469203i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.33858e6i | − | 1.39605i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −591719. | −0.604808 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −171857. | −0.172180 | −0.0860898 | − | 0.996287i | \(-0.527437\pi\) | ||||
−0.0860898 | + | 0.996287i | \(0.527437\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.97569e6i | 1.94051i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 279125. | + | 155116.i | 0.268812 | + | 0.149385i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.78486e6i | 1.68567i | 0.538173 | + | 0.842834i | \(0.319115\pi\) | ||||
−0.538173 | + | 0.842834i | \(0.680885\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −154370. | −0.142992 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.19373e6 | −1.99335 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.23207e6i | − | 1.09836i | −0.835703 | − | 0.549182i | \(-0.814940\pi\) | ||
0.835703 | − | 0.549182i | \(-0.185060\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −142269. | + | 256007.i | −0.124450 | + | 0.223943i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 995343.i | 0.854466i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −309231. | −0.260557 | −0.130278 | − | 0.991477i | \(-0.541587\pi\) | ||||
−0.130278 | + | 0.991477i | \(0.541587\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −143525. | −0.118714 | −0.0593572 | − | 0.998237i | \(-0.518905\pi\) | ||||
−0.0593572 | + | 0.998237i | \(0.518905\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 652312.i | − | 0.529723i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.16184e6 | − | 1.86831e6i | −0.926435 | − | 1.48976i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 635705.i | − | 0.497802i | −0.968529 | − | 0.248901i | \(-0.919931\pi\) | ||
0.968529 | − | 0.248901i | \(-0.0800693\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −185839. | −0.142931 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −240440. | −0.181652 | −0.0908262 | − | 0.995867i | \(-0.528951\pi\) | ||||
−0.0908262 | + | 0.995867i | \(0.528951\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 442548.i | − | 0.328469i | −0.986421 | − | 0.164234i | \(-0.947485\pi\) | ||
0.986421 | − | 0.164234i | \(-0.0525153\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −920373. | + | 1.65618e6i | −0.671200 | + | 1.20780i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 392522.i | − | 0.281293i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.37258e6 | 0.966703 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.20997e6 | −1.52987 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.02835e6i | − | 1.38030i | −0.723667 | − | 0.690149i | \(-0.757545\pi\) | ||
0.723667 | − | 0.690149i | \(-0.242455\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.17479e6 | − | 652859.i | −0.785971 | − | 0.436782i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.77703e6i | 2.48462i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.91164e6 | 1.88347 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 329580. | 0.209674 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.03586e6i | 1.27392i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −50683.3 | − | 28165.8i | −0.0311972 | − | 0.0173370i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.31899e6i | − | 1.40427i | −0.712042 | − | 0.702137i | \(-0.752229\pi\) | ||
0.712042 | − | 0.702137i | \(-0.247771\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.80332e6 | 1.07443 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.17253e6 | −1.27369 | −0.636846 | − | 0.770991i | \(-0.719761\pi\) | ||||
−0.636846 | + | 0.770991i | \(0.719761\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.93017e6i | 1.11362i | 0.830641 | + | 0.556808i | \(0.187974\pi\) | ||||
−0.830641 | + | 0.556808i | \(0.812026\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −290605. | + | 522933.i | −0.165016 | + | 0.296940i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2.16542e6i | − | 1.21030i | −0.796111 | − | 0.605151i | \(-0.793113\pi\) | ||
0.796111 | − | 0.605151i | \(-0.206887\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.45357e6 | −1.90017 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.21379e6 | 1.19915 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 280517.i | − | 0.149607i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.75339e6 | + | 1.71225e6i | −1.44597 | + | 0.899203i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.35669e6i | − | 0.701635i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 309719. | 0.157753 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.27143e6 | 0.637857 | 0.318929 | − | 0.947779i | \(-0.396677\pi\) | ||||
0.318929 | + | 0.947779i | \(0.396677\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.88480e6i | − | 1.42562i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.30077e6 | − | 2.34068e6i | 0.633268 | − | 1.13954i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.23785e6i | − | 1.07338i | −0.843778 | − | 0.536692i | \(-0.819674\pi\) | ||
0.843778 | − | 0.536692i | \(-0.180326\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.33147e6 | 1.10187 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −292564. | −0.136250 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 790700.i | 0.362891i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.60246e6 | − | 2.00197e6i | −1.62949 | − | 0.905542i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 4.29048e6i | − | 1.91285i | −0.291971 | − | 0.956427i | \(-0.594311\pi\) | ||
0.291971 | − | 0.956427i | \(-0.405689\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 907418. | 0.398790 | 0.199395 | − | 0.979919i | \(-0.436102\pi\) | ||||
0.199395 | + | 0.979919i | \(0.436102\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.56634e6 | 2.41158 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 383963.i | 0.164003i | 0.996632 | + | 0.0820017i | \(0.0261313\pi\) | ||||
−0.996632 | + | 0.0820017i | \(0.973869\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.65312e6 | − | 2.03012e6i | −1.53848 | − | 0.854970i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 136700.i | − | 0.0567674i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.38837e6 | −0.978060 | −0.489030 | − | 0.872267i | \(-0.662649\pi\) | ||||
−0.489030 | + | 0.872267i | \(0.662649\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −811667. | −0.327801 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.79080e6i | 3.50156i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 617668. | − | 1.11147e6i | 0.242674 | − | 0.436682i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.80989e6i | 1.08899i | 0.838764 | + | 0.544495i | \(0.183279\pi\) | ||||
−0.838764 | + | 0.544495i | \(0.816721\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.33530e6 | 2.80448 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 125378. | 0.0472920 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 602108.i | 0.224080i | 0.993704 | + | 0.112040i | \(0.0357384\pi\) | ||||
−0.993704 | + | 0.112040i | \(0.964262\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.58395e6 | − | 225339.i | 1.68330 | − | 0.0827481i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.08965e6i | 1.84431i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −153274. | −0.0548115 | −0.0274057 | − | 0.999624i | \(-0.508725\pi\) | ||||
−0.0274057 | + | 0.999624i | \(0.508725\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.69945e6 | 1.65857 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.29677e6i | 1.49673i | 0.663285 | + | 0.748367i | \(0.269162\pi\) | ||||
−0.663285 | + | 0.748367i | \(0.730838\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −457497. | + | 823248.i | −0.157303 | + | 0.283060i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.15906e6i | 2.09044i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.29468e6 | −0.433800 | −0.216900 | − | 0.976194i | \(-0.569595\pi\) | ||||
−0.216900 | + | 0.976194i | \(0.569595\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 610171. | 0.201841 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.17895e6i | − | 2.01806i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.13771e6 | + | 1.74369e6i | 1.01186 | + | 0.562312i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.41262e6i | − | 0.768266i | −0.923278 | − | 0.384133i | \(-0.874500\pi\) | ||
0.923278 | − | 0.384133i | \(-0.125500\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 811104. | 0.255061 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.88260e6 | 1.82687 | 0.913437 | − | 0.406980i | \(-0.133418\pi\) | ||||
0.913437 | + | 0.406980i | \(0.133418\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 431162.i | 0.132245i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.57698e6 | − | 876363.i | −0.477737 | − | 0.265489i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4.54151e6i | − | 1.35898i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −166944. | −0.0493473 | −0.0246737 | − | 0.999696i | \(-0.507855\pi\) | ||||
−0.0246737 | + | 0.999696i | \(0.507855\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.69930e6 | −1.66424 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 575350.i | 0.165980i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 611601. | − | 1.10055e6i | 0.174320 | − | 0.313682i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 9.14095e6i | − | 2.57425i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.19513e6 | −0.610838 | −0.305419 | − | 0.952218i | \(-0.598796\pi\) | ||||
−0.305419 | + | 0.952218i | \(0.598796\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.54531e6 | 0.424924 | 0.212462 | − | 0.977169i | \(-0.431852\pi\) | ||||
0.212462 | + | 0.977169i | \(0.431852\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.78790e6i | 1.57279i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −577007. | + | 358823.i | −0.154956 | + | 0.0963625i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24821.9i | 0.00658818i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.91908e7 | 5.03443 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.05590e6 | −0.792402 | −0.396201 | − | 0.918164i | \(-0.629672\pi\) | ||||
−0.396201 | + | 0.918164i | \(0.629672\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.34883e6i | − | 1.37100i | −0.728071 | − | 0.685502i | \(-0.759583\pi\) | ||
0.728071 | − | 0.685502i | \(-0.240417\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.49951e6 | − | 6.29723e6i | 0.886715 | − | 1.59561i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.62042e6i | 0.906891i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.65736e6 | −0.410446 | −0.205223 | − | 0.978715i | \(-0.565792\pi\) | ||||
−0.205223 | + | 0.978715i | \(0.565792\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.26009e6 | −1.77765 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 1.02478e6i | − | 0.248098i | −0.992276 | − | 0.124049i | \(-0.960412\pi\) | ||
0.992276 | − | 0.124049i | \(-0.0395880\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.85126e6 | − | 1.02879e6i | −0.443167 | − | 0.246278i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.58598e6i | 0.848865i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.87947e6 | 0.439966 | 0.219983 | − | 0.975504i | \(-0.429400\pi\) | ||||
0.219983 | + | 0.975504i | \(0.429400\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.15479e7 | 2.67338 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.37912e6i | 1.91846i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.21325e6 | + | 674230.i | 0.274740 | + | 0.152679i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.51688e6i | − | 1.01169i | −0.862624 | − | 0.505846i | \(-0.831180\pi\) | ||
0.862624 | − | 0.505846i | \(-0.168820\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.16650e6 | 0.258436 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.74712e6 | −1.47865 | −0.739326 | − | 0.673348i | \(-0.764856\pi\) | ||||
−0.739326 | + | 0.673348i | \(0.764856\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.43370e6i | − | 0.744407i | −0.928151 | − | 0.372203i | \(-0.878602\pi\) | ||
0.928151 | − | 0.372203i | \(-0.121398\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 296456. | − | 533460.i | 0.0635810 | − | 0.114411i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 791564.i | 0.167955i | 0.996468 | + | 0.0839777i | \(0.0267625\pi\) | ||||
−0.996468 | + | 0.0839777i | \(0.973238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.14634e6 | −0.240647 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.42517e6 | −0.296016 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.69614e6i | 1.99272i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.12906e6 | − | 3.42364e6i | −0.432965 | − | 0.696233i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.34302e6i | 0.471499i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 799322. | 0.159178 | 0.0795890 | − | 0.996828i | \(-0.474639\pi\) | ||||
0.0795890 | + | 0.996828i | \(0.474639\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.69298e6 | −1.31904 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.76429e6i | 0.344113i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.28423e6 | − | 4.11038e6i | 0.440946 | − | 0.793464i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.68591e6i | − | 1.27743i | −0.769442 | − | 0.638717i | \(-0.779466\pi\) | ||
0.769442 | − | 0.638717i | \(-0.220534\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.32662e7 | 2.50885 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −235143. | −0.0440179 | −0.0220089 | − | 0.999758i | \(-0.507006\pi\) | ||||
−0.0220089 | + | 0.999758i | \(0.507006\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.06660e6i | 0.197644i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.53845e7 | − | 8.54952e6i | −2.82209 | − | 1.56830i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.78910e6i | 0.324895i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.20861e6 | −1.29599 | −0.647993 | − | 0.761646i | \(-0.724391\pi\) | ||||
−0.647993 | + | 0.761646i | \(0.724391\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.94376e6 | −1.23595 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.24297e6i | 1.27643i | 0.769858 | + | 0.638215i | \(0.220327\pi\) | ||||
−0.769858 | + | 0.638215i | \(0.779673\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.78653e6 | − | 2.10426e6i | −0.660714 | − | 0.367173i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.85277e7i | − | 3.20111i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.34344e6 | 0.914169 | 0.457085 | − | 0.889423i | \(-0.348894\pi\) | ||||
0.457085 | + | 0.889423i | \(0.348894\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −544337. | −0.0922180 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.92135e6i | 1.16118i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.86391e6 | + | 3.35404e6i | −0.309676 | + | 0.557249i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.11184e6i | 1.49927i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.18131e7 | 1.92507 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.91899e6 | −0.632529 | −0.316264 | − | 0.948671i | \(-0.602429\pi\) | ||||
−0.316264 | + | 0.948671i | \(0.602429\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.74591e6i | 0.598829i | 0.954123 | + | 0.299414i | \(0.0967913\pi\) | ||||
−0.954123 | + | 0.299414i | \(0.903209\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.03752e6 | − | 1.66840e6i | −0.164286 | − | 0.264181i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 90355.5i | 0.0141719i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.43866e6 | −0.223522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.07519e7 | −1.65481 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.70185e7i | − | 2.59480i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.28817e6 | + | 4.11747e6i | −0.345624 | + | 0.621937i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1.72680e7i | − | 2.58408i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.14295e7 | −1.69455 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.32207e6 | 0.194206 | 0.0971031 | − | 0.995274i | \(-0.469042\pi\) | ||||
0.0971031 | + | 0.995274i | \(0.469042\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1.68250e7i | − | 2.44881i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.52334e6 | + | 1.40227e6i | 0.363901 | + | 0.202228i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.82591e6i | 1.26122i | 0.776100 | + | 0.630610i | \(0.217195\pi\) | ||||
−0.776100 | + | 0.630610i | \(0.782805\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −463862. | −0.0656837 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.32862e6 | −0.888035 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.53668e6i | − | 0.213683i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.28097e6 | + | 4.60192e6i | 1.14117 | + | 0.634171i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 446795.i | − | 0.0610197i | −0.999534 | − | 0.0305099i | \(-0.990287\pi\) | ||
0.999534 | − | 0.0305099i | \(-0.00971310\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.42895e7 | 1.93414 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.02168e6 | 0.539511 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.61652e6i | − | 0.214937i | −0.994208 | − | 0.107468i | \(-0.965726\pi\) | ||
0.994208 | − | 0.107468i | \(-0.0342745\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.40981e6 | + | 4.33636e6i | −0.317586 | + | 0.571484i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 772318.i | 0.100888i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.25416e7 | 1.62395 | 0.811974 | − | 0.583693i | \(-0.198393\pi\) | ||||
0.811974 | + | 0.583693i | \(0.198393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.19556e6 | 0.153455 | 0.0767276 | − | 0.997052i | \(-0.475553\pi\) | ||||
0.0767276 | + | 0.997052i | \(0.475553\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.81173e7i | − | 2.30519i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.44699e6 | − | 4.63105e6i | 0.939315 | − | 0.584131i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.15431e7i | 1.44339i | 0.692211 | + | 0.721695i | \(0.256637\pi\) | ||||
−0.692211 | + | 0.721695i | \(0.743363\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.04652e7 | 1.29733 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −538990. | −0.0662430 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.68860e6i | 0.449459i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.25997e7 | + | 2.26727e7i | −1.52220 | + | 2.73914i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.96527e6i | 0.594768i | 0.954758 | + | 0.297384i | \(0.0961142\pi\) | ||||
−0.954758 | + | 0.297384i | \(0.903886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −536119. | −0.0636756 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −507837. | −0.0598076 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 3.44208e6i | − | 0.401962i | −0.979595 | − | 0.200981i | \(-0.935587\pi\) | ||
0.979595 | − | 0.200981i | \(-0.0644129\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 254252. | + | 141293.i | 0.0294423 | + | 0.0163617i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.26787e6i | 0.949419i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.32967e6 | 0.834675 | 0.417338 | − | 0.908752i | \(-0.362963\pi\) | ||||
0.417338 | + | 0.908752i | \(0.362963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.96589e6 | −0.673735 | −0.336868 | − | 0.941552i | \(-0.609368\pi\) | ||||
−0.336868 | + | 0.941552i | \(0.609368\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2.14223e7i | − | 2.39923i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.63502e7 | − | 9.08617e6i | −1.81608 | − | 1.00924i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.35750e7i | 1.49543i | 0.664018 | + | 0.747716i | \(0.268850\pi\) | ||||
−0.664018 | + | 0.747716i | \(0.731150\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.08404e6 | −0.336959 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.34284e7 | 1.45520 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.11070e7i | 1.19384i | 0.802302 | + | 0.596918i | \(0.203608\pi\) | ||||
−0.802302 | + | 0.596918i | \(0.796392\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.17015e7 | + | 2.10564e7i | −1.24754 | + | 2.24489i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.62274e6i | 0.594614i | 0.954782 | + | 0.297307i | \(0.0960884\pi\) | ||||
−0.954782 | + | 0.297307i | \(0.903912\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.37545e6 | 0.249184 | 0.124592 | − | 0.992208i | \(-0.460238\pi\) | ||||
0.124592 | + | 0.992208i | \(0.460238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.50551e7 | −1.56659 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 906646.i | 0.0935874i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.31886e6 | + | 8.75870e6i | −0.442251 | + | 0.896891i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.38624e7i | 2.42407i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.40260e6 | −0.141354 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.70995e6 | 0.370932 | 0.185466 | − | 0.982651i | \(-0.440621\pi\) | ||||
0.185466 | + | 0.982651i | \(0.440621\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.25707e7i | 1.24695i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.85735e6 | + | 8.74061e6i | −0.478041 | + | 0.860216i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.68440e7i | 1.64474i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.34340e7 | −3.23918 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.35252e6 | 0.706791 | 0.353396 | − | 0.935474i | \(-0.385027\pi\) | ||||
0.353396 | + | 0.935474i | \(0.385027\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.03451e6i | 0.289442i | 0.989473 | + | 0.144721i | \(0.0462284\pi\) | ||||
−0.989473 | + | 0.144721i | \(0.953772\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.76799e7 | − | 9.82511e6i | −1.67333 | − | 0.929904i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 4.69808e6i | − | 0.441224i | −0.975362 | − | 0.220612i | \(-0.929194\pi\) | ||
0.975362 | − | 0.220612i | \(-0.0708055\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.69266e7 | −1.57746 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −261259. | −0.0241613 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.29779e7i | 1.19103i | 0.803346 | + | 0.595513i | \(0.203051\pi\) | ||||
−0.803346 | + | 0.595513i | \(0.796949\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.14924e7 | + | 6.38656e6i | 1.04666 | + | 0.581653i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.01724e7i | − | 0.919407i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.46461e6 | 0.131374 | 0.0656868 | − | 0.997840i | \(-0.479076\pi\) | ||||
0.0656868 | + | 0.997840i | \(0.479076\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.06947e7 | −0.952061 | −0.476031 | − | 0.879429i | \(-0.657925\pi\) | ||||
−0.476031 | + | 0.879429i | \(0.657925\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 5.92689e6i | − | 0.523653i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −838357. | + | 1.50859e6i | −0.0735148 | + | 0.132287i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.37658e7i | − | 1.19808i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.39001e6 | 0.465612 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −730253. | −0.0626134 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.91777e6i | 0.758959i | 0.925200 | + | 0.379480i | \(0.123897\pi\) | ||||
−0.925200 | + | 0.379480i | \(0.876103\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.42368e7 | − | 8.85345e6i | 1.20269 | − | 0.747916i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.93032e7i | − | 1.61867i | −0.587349 | − | 0.809334i | \(-0.699828\pi\) | ||
0.587349 | − | 0.809334i | \(-0.300172\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.01304e6 | −0.167563 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.07476e7 | −0.888063 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.15277e7i | 0.945565i | 0.881179 | + | 0.472783i | \(0.156750\pi\) | ||||
−0.881179 | + | 0.472783i | \(0.843250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.89079e6 | − | 1.06002e7i | 0.479675 | − | 0.863157i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.06563e7i | 0.861421i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.43601e6 | 0.436247 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.95573e6 | −0.315160 | −0.157580 | − | 0.987506i | \(-0.550369\pi\) | ||||
−0.157580 | + | 0.987506i | \(0.550369\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.53450e6i | 0.595966i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.70014e7 | + | 9.44808e6i | 1.33513 | + | 0.741962i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.56645e6i | − | 0.278070i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.68646e6 | 0.130552 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.05492e7 | 1.57943 | 0.789715 | − | 0.613474i | \(-0.210229\pi\) | ||||
0.789715 | + | 0.613474i | \(0.210229\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 8.32225e6i | − | 0.635115i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.66145e7 | − | 9.23304e6i | −1.25897 | − | 0.699636i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.85444e6i | 0.139529i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.07226e7 | −0.801100 | −0.400550 | − | 0.916275i | \(-0.631181\pi\) | ||||
−0.400550 | + | 0.916275i | \(0.631181\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.87168e7 | 2.13040 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.16615e6i | − | 0.0859073i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.98356e7 | + | 3.56934e7i | −1.45105 | + | 2.61110i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.57463e7i | 2.59677i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.12405e6 | 0.586071 | 0.293035 | − | 0.956102i | \(-0.405335\pi\) | ||||
0.293035 | + | 0.956102i | \(0.405335\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.64262e6 | 0.117679 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 3.53307e7i | − | 2.51366i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.09525e6 | + | 1.30176e7i | 0.571986 | + | 0.919786i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.87419e7i | − | 1.31516i | −0.753386 | − | 0.657578i | \(-0.771581\pi\) | ||
0.753386 | − | 0.657578i | \(-0.228419\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.98167e7 | 1.38106 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.99456e6 | 0.207271 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.43325e6i | 0.0985284i | 0.998786 | + | 0.0492642i | \(0.0156876\pi\) | ||||
−0.998786 | + | 0.0492642i | \(0.984312\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.15815e7 | − | 2.08405e7i | 0.790764 | − | 1.42295i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.37249e7i | − | 2.28708i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.87933e6 | −0.261304 | −0.130652 | − | 0.991428i | \(-0.541707\pi\) | ||||
−0.130652 | + | 0.991428i | \(0.541707\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.51669e7 | 2.35282 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.51128e7i | − | 1.66887i | −0.551104 | − | 0.834437i | \(-0.685793\pi\) | ||
0.551104 | − | 0.834437i | \(-0.314207\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.66963e6 | − | 3.70646e6i | −0.440262 | − | 0.244663i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1.00724e7i | − | 0.660439i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.01651e6 | 0.131340 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.68579e7 | −1.09070 | −0.545349 | − | 0.838209i | \(-0.683603\pi\) | ||||
−0.545349 | + | 0.838209i | \(0.683603\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 4.51498e6i | − | 0.290180i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.55845e7 | − | 8.66065e6i | −0.995005 | − | 0.552946i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.64597e6i | 0.167821i | 0.996473 | + | 0.0839104i | \(0.0267410\pi\) | ||||
−0.996473 | + | 0.0839104i | \(0.973259\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.19048e7 | −3.27042 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 778479. | 0.0487288 | 0.0243644 | − | 0.999703i | \(-0.492244\pi\) | ||||
0.0243644 | + | 0.999703i | \(0.492244\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.23579e6i | − | 0.0768483i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.64043e6 | + | 4.75135e6i | −0.163125 | + | 0.293538i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.49454e7i | 1.53109i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.11827e7 | −0.681919 | −0.340959 | − | 0.940078i | \(-0.610752\pi\) | ||||
−0.340959 | + | 0.940078i | \(0.610752\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.68915e7 | −2.84092 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 2.00821e7i | − | 1.20882i | −0.796675 | − | 0.604408i | \(-0.793410\pi\) | ||
0.796675 | − | 0.604408i | \(-0.206590\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 685777. | + | 1.10277e6i | 0.0410137 | + | 0.0659523i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 4.05556e6i | − | 0.240990i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.11613e7 | 1.24939 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.26347e7 | −3.08777 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.63169e7i | − | 1.53402i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.47306e6 | − | 2.65071e6i | 0.0853190 | − | 0.153528i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.62920e6i | 0.151317i | 0.997134 | + | 0.0756584i | \(0.0241059\pi\) | ||||
−0.997134 | + | 0.0756584i | \(0.975894\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.23687e7 | 1.85111 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.12371e6 | 0.120685 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.07620e6i | 0.0607729i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.72577e6 | − | 3.73766e6i | −0.377419 | − | 0.209740i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 6.44461e6i | − | 0.359377i | −0.983724 | − | 0.179689i | \(-0.942491\pi\) | ||
0.983724 | − | 0.179689i | \(-0.0575090\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.81410e6 | 0.155945 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.69430e7 | −0.933061 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.60142e7i | − | 0.876430i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.28143e6 | − | 1.82357e6i | −0.178474 | − | 0.0991817i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 8.12405e6i | − | 0.439126i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.59388e6 | −0.193060 | −0.0965299 | − | 0.995330i | \(-0.530774\pi\) | ||||
−0.0965299 | + | 0.995330i | \(0.530774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.79497e7 | 1.49220 | 0.746098 | − | 0.665837i | \(-0.231925\pi\) | ||||
0.746098 | + | 0.665837i | \(0.231925\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 3.77065e6i | − | 0.200074i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.37120e7 | + | 2.46741e7i | −0.723111 | + | 1.30121i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.77680e7i | 0.931289i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.11039e7 | 0.578448 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.41956e6 | 0.435945 | 0.217972 | − | 0.975955i | \(-0.430056\pi\) | ||||
0.217972 | + | 0.975955i | \(0.430056\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.51378e7i | 0.779048i | 0.921016 | + | 0.389524i | \(0.127360\pi\) | ||||
−0.921016 | + | 0.389524i | \(0.872640\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.90837e7 | − | 3.05236e7i | 2.51074 | − | 1.56135i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5.14412e6i | − | 0.261545i | −0.991412 | − | 0.130773i | \(-0.958254\pi\) | ||
0.991412 | − | 0.130773i | \(-0.0417458\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.00711e7 | −0.508970 | −0.254485 | − | 0.967077i | \(-0.581906\pi\) | ||||
−0.254485 | + | 0.967077i | \(0.581906\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.67011e7 | 0.838963 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.52988e6i | 0.176258i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.17706e6 | − | 1.29148e7i | 0.356230 | − | 0.641022i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 2.22939e6i | − | 0.109995i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −933470. | −0.0457821 | −0.0228910 | − | 0.999738i | \(-0.507287\pi\) | ||||
−0.0228910 | + | 0.999738i | \(0.507287\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.55199e6 | 0.173173 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 6.31679e6i | − | 0.306145i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.44600e7 | + | 1.91502e7i | 1.66025 | + | 0.922638i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.00743e6i | 0.383517i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.16265e7 | 0.553580 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.81023e7 | 0.856859 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.96289e7i | 0.923682i | 0.886963 | + | 0.461841i | \(0.152811\pi\) | ||||
−0.886963 | + | 0.461841i | \(0.847189\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.81919e7 | − | 1.56669e7i | −1.31889 | − | 0.732938i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2.93615e7i | − | 1.36561i | −0.730601 | − | 0.682805i | \(-0.760760\pi\) | ||
0.730601 | − | 0.682805i | \(-0.239240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.22206e7 | 1.02748 | 0.513739 | − | 0.857947i | \(-0.328260\pi\) | ||||
0.513739 | + | 0.857947i | \(0.328260\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.03123e7 | 0.474074 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.40411e7i | 0.641763i | 0.947119 | + | 0.320881i | \(0.103979\pi\) | ||||
−0.947119 | + | 0.320881i | \(0.896021\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.22100e7 | + | 2.19714e7i | −0.554851 | + | 0.998432i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.60601e7i | 1.62922i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.52086e7 | 2.03082 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.97015e7 | −2.21985 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3.76189e7i | − | 1.67059i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.17547e6 | − | 205258.i | 0.184368 | − | 0.00906318i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 3.11419e7i | − | 1.36724i | −0.729836 | − | 0.683622i | \(-0.760404\pi\) | ||
0.729836 | − | 0.683622i | \(-0.239596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.32882e7 | 2.32626 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.80425e6 | −0.295352 | −0.147676 | − | 0.989036i | \(-0.547179\pi\) | ||||
−0.147676 | + | 0.989036i | \(0.547179\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.02459e7i | − | 0.442230i | −0.975248 | − | 0.221115i | \(-0.929030\pi\) | ||
0.975248 | − | 0.221115i | \(-0.0709697\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.71518e7 | − | 3.08639e7i | 0.736123 | − | 1.32462i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 3.03507e7i | − | 1.29527i | −0.761951 | − | 0.647635i | \(-0.775758\pi\) | ||
0.761951 | − | 0.647635i | \(-0.224242\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.28067e6 | 0.181659 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.27214e7 | −0.958827 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.66973e7i | 0.700677i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.21171e7 | + | 1.78482e7i | 1.34023 | + | 0.744794i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.64939e7i | 3.17428i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.03847e6 | 0.0841212 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.13919e6 | 0.0467501 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.65865e6i | 0.353371i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.12932e7 | + | 1.73903e7i | 1.27007 | + | 0.705807i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.03000e6i | 0.203025i | 0.994834 | + | 0.101513i | \(0.0323682\pi\) | ||||
−0.994834 | + | 0.101513i | \(0.967632\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.46550e7 | −1.39109 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.17959e6 | −0.246697 | −0.123348 | − | 0.992363i | \(-0.539363\pi\) | ||||
−0.123348 | + | 0.992363i | \(0.539363\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.58569e7i | − | 0.629567i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 739966. | − | 1.33154e6i | 0.0292186 | − | 0.0525777i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 5.62833e6i | − | 0.221033i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.27546e7 | 1.66992 | 0.834958 | − | 0.550314i | \(-0.185492\pi\) | ||||
0.834958 | + | 0.550314i | \(0.185492\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.09239e7 | 2.36667 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.75697e7i | 2.99701i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.71184e7 | + | 1.06454e7i | −0.657823 | + | 0.409080i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.06967e7i | 1.17325i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.75757e7 | 0.668151 | 0.334075 | − | 0.942546i | \(-0.391576\pi\) | ||||
0.334075 | + | 0.942546i | \(0.391576\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.09444e7 | −0.791941 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 5.70761e7i | − | 2.14660i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.15681e6 | + | 7.48001e6i | −0.155500 | + | 0.279816i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.25313e7i | 1.58256i | 0.611455 | + | 0.791279i | \(0.290585\pi\) | ||||
−0.611455 | + | 0.791279i | \(0.709415\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.07091e7 | −1.87682 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.23345e7 | −0.454095 | −0.227047 | − | 0.973884i | \(-0.572907\pi\) | ||||
−0.227047 | + | 0.973884i | \(0.572907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.60294e7i | 1.68561i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.27330e6 | − | 3.48621e6i | −0.228516 | − | 0.126991i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 2.28532e7i | − | 0.828081i | −0.910259 | − | 0.414040i | \(-0.864117\pi\) | ||
0.910259 | − | 0.414040i | \(-0.135883\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.36007e7 | −0.850668 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.68894e7 | 2.03976 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.08757e7i | − | 1.10125i | −0.834754 | − | 0.550623i | \(-0.814390\pi\) | ||
0.834754 | − | 0.550623i | \(-0.185610\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.36968e7 | + | 1.87261e7i | 1.19558 | + | 0.664413i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 9.07315e7i | − | 3.20242i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.19142e6 | −0.182280 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.84565e7 | −0.993968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.76838e7i | 1.30945i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.08168e7 | + | 1.94644e7i | −0.373921 | + | 0.672855i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.99276e7i | − | 0.685313i | −0.939461 | − | 0.342657i | \(-0.888673\pi\) | ||
0.939461 | − | 0.342657i | \(-0.111327\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.36967e6 | 0.252138 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.53795e7 | 1.20421 | 0.602107 | − | 0.798415i | \(-0.294328\pi\) | ||||
0.602107 | + | 0.798415i | \(0.294328\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 8.32638e6i | − | 0.281951i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.49837e7 | − | 7.23364e7i | −1.51546 | − | 2.43694i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 3.28357e7i | − | 1.10055i | −0.834983 | − | 0.550275i | \(-0.814523\pi\) | ||
0.834983 | − | 0.550275i | \(-0.185477\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.66732e7 | −0.889445 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.30940e7 | 0.766172 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.83290e7i | 0.935077i | 0.883973 | + | 0.467539i | \(0.154859\pi\) | ||||
−0.883973 | + | 0.467539i | \(0.845141\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 524900. | − | 944537.i | 0.0172380 | − | 0.0310191i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.13687e6i | 0.265867i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.86484e7 | −1.25644 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.98087e6 | −0.193455 | −0.0967276 | − | 0.995311i | \(-0.530838\pi\) | ||||
−0.0967276 | + | 0.995311i | \(0.530838\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.34028e7i | 1.07500i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.53776e7 | − | 8.54567e6i | −0.492414 | − | 0.273646i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.87665e6i | 0.0597922i | 0.999553 | + | 0.0298961i | \(0.00951764\pi\) | ||||
−0.999553 | + | 0.0298961i | \(0.990482\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.46072e7 | 1.09711 |
(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.c.k.129.11 | 12 | ||
4.3 | odd | 2 | inner | 320.6.c.k.129.1 | 12 | ||
5.4 | even | 2 | inner | 320.6.c.k.129.2 | 12 | ||
8.3 | odd | 2 | 160.6.c.c.129.12 | yes | 12 | ||
8.5 | even | 2 | 160.6.c.c.129.2 | yes | 12 | ||
20.19 | odd | 2 | inner | 320.6.c.k.129.12 | 12 | ||
40.3 | even | 4 | 800.6.a.ba.1.1 | 6 | |||
40.13 | odd | 4 | 800.6.a.ba.1.6 | 6 | |||
40.19 | odd | 2 | 160.6.c.c.129.1 | ✓ | 12 | ||
40.27 | even | 4 | 800.6.a.z.1.6 | 6 | |||
40.29 | even | 2 | 160.6.c.c.129.11 | yes | 12 | ||
40.37 | odd | 4 | 800.6.a.z.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.c.c.129.1 | ✓ | 12 | 40.19 | odd | 2 | ||
160.6.c.c.129.2 | yes | 12 | 8.5 | even | 2 | ||
160.6.c.c.129.11 | yes | 12 | 40.29 | even | 2 | ||
160.6.c.c.129.12 | yes | 12 | 8.3 | odd | 2 | ||
320.6.c.k.129.1 | 12 | 4.3 | odd | 2 | inner | ||
320.6.c.k.129.2 | 12 | 5.4 | even | 2 | inner | ||
320.6.c.k.129.11 | 12 | 1.1 | even | 1 | trivial | ||
320.6.c.k.129.12 | 12 | 20.19 | odd | 2 | inner | ||
800.6.a.z.1.1 | 6 | 40.37 | odd | 4 | |||
800.6.a.z.1.6 | 6 | 40.27 | even | 4 | |||
800.6.a.ba.1.1 | 6 | 40.3 | even | 4 | |||
800.6.a.ba.1.6 | 6 | 40.13 | odd | 4 |