Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,6,Mod(49,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(64.1535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.49 |
Dual form | 400.6.c.b.49.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 24.0000i | − 1.53960i | −0.638285 | − | 0.769800i | \(-0.720356\pi\) | ||||
0.638285 | − | 0.769800i | \(-0.279644\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 172.000i | − 1.32673i | −0.748295 | − | 0.663366i | \(-0.769127\pi\) | ||||
0.748295 | − | 0.663366i | \(-0.230873\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −333.000 | −1.37037 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −132.000 | −0.328921 | −0.164461 | − | 0.986384i | \(-0.552588\pi\) | ||||
−0.164461 | + | 0.986384i | \(0.552588\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 946.000i | − 1.55250i | −0.630423 | − | 0.776252i | \(-0.717118\pi\) | ||||
0.630423 | − | 0.776252i | \(-0.282882\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 222.000i | 0.186308i | 0.995652 | + | 0.0931538i | \(0.0296948\pi\) | ||||
−0.995652 | + | 0.0931538i | \(0.970305\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 500.000 | 0.317750 | 0.158875 | − | 0.987299i | \(-0.449213\pi\) | ||||
0.158875 | + | 0.987299i | \(0.449213\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4128.00 | −2.04264 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 3564.00i | − 1.40481i | −0.711777 | − | 0.702406i | \(-0.752109\pi\) | ||||
0.711777 | − | 0.702406i | \(-0.247891\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2160.00i | 0.570222i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2190.00 | −0.483559 | −0.241779 | − | 0.970331i | \(-0.577731\pi\) | ||||
−0.241779 | + | 0.970331i | \(0.577731\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2312.00 | −0.432099 | −0.216050 | − | 0.976382i | \(-0.569317\pi\) | ||||
−0.216050 | + | 0.976382i | \(0.569317\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3168.00i | 0.506408i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11242.0i | 1.35002i | 0.737810 | + | 0.675009i | \(0.235860\pi\) | ||||
−0.737810 | + | 0.675009i | \(0.764140\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −22704.0 | −2.39024 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1242.00 | 0.115388 | 0.0576942 | − | 0.998334i | \(-0.481625\pi\) | ||||
0.0576942 | + | 0.998334i | \(0.481625\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 20624.0i | − 1.70099i | −0.525983 | − | 0.850495i | \(-0.676303\pi\) | ||||
0.525983 | − | 0.850495i | \(-0.323697\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6588.00i | 0.435020i | 0.976058 | + | 0.217510i | \(0.0697934\pi\) | ||||
−0.976058 | + | 0.217510i | \(0.930207\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12777.0 | −0.760219 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5328.00 | 0.286839 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 21066.0i | − 1.03013i | −0.857151 | − | 0.515065i | \(-0.827768\pi\) | ||||
0.857151 | − | 0.515065i | \(-0.172232\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 12000.0i | − 0.489209i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7980.00 | 0.298451 | 0.149225 | − | 0.988803i | \(-0.452322\pi\) | ||||
0.149225 | + | 0.988803i | \(0.452322\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 16622.0 | 0.571951 | 0.285975 | − | 0.958237i | \(-0.407682\pi\) | ||||
0.285975 | + | 0.958237i | \(0.407682\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 57276.0i | 1.81811i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1808.00i | 0.0492052i | 0.999697 | + | 0.0246026i | \(0.00783205\pi\) | ||||
−0.999697 | + | 0.0246026i | \(0.992168\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −85536.0 | −2.16285 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 24528.0 | 0.577452 | 0.288726 | − | 0.957412i | \(-0.406768\pi\) | ||||
0.288726 | + | 0.957412i | \(0.406768\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 20474.0i | 0.449672i | 0.974397 | + | 0.224836i | \(0.0721846\pi\) | ||||
−0.974397 | + | 0.224836i | \(0.927815\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22704.0i | 0.436391i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −46240.0 | −0.833585 | −0.416793 | − | 0.909002i | \(-0.636846\pi\) | ||||
−0.416793 | + | 0.909002i | \(0.636846\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −29079.0 | −0.492455 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 51576.0i | 0.821774i | 0.911686 | + | 0.410887i | \(0.134781\pi\) | ||||
−0.911686 | + | 0.410887i | \(0.865219\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 52560.0i | 0.744487i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 110310. | 1.47618 | 0.738091 | − | 0.674701i | \(-0.235728\pi\) | ||||
0.738091 | + | 0.674701i | \(0.235728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −162712. | −2.05976 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 55488.0i | 0.665260i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 78382.0i | 0.845838i | 0.906168 | + | 0.422919i | \(0.138994\pi\) | ||||
−0.906168 | + | 0.422919i | \(0.861006\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 43956.0 | 0.450744 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 141942. | 1.38455 | 0.692273 | − | 0.721636i | \(-0.256609\pi\) | ||||
0.692273 | + | 0.721636i | \(0.256609\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 436.000i | 0.00404943i | 0.999998 | + | 0.00202471i | \(0.000644487\pi\) | ||||
−0.999998 | + | 0.00202471i | \(0.999356\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 232968.i | 1.96715i | 0.180508 | + | 0.983574i | \(0.442226\pi\) | ||||
−0.180508 | + | 0.983574i | \(0.557774\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 174850. | 1.40961 | 0.704806 | − | 0.709400i | \(-0.251034\pi\) | ||||
0.704806 | + | 0.709400i | \(0.251034\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 269808. | 2.07849 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 182994.i | 1.34816i | 0.738659 | + | 0.674079i | \(0.235459\pi\) | ||||
−0.738659 | + | 0.674079i | \(0.764541\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 315018.i | 2.12751i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 38184.0 | 0.247180 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −143627. | −0.891811 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 29808.0i | − 0.177652i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 122452.i | − 0.673685i | −0.941561 | − | 0.336842i | \(-0.890641\pi\) | ||||
0.941561 | − | 0.336842i | \(-0.109359\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −494976. | −2.61885 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 241908. | 1.23161 | 0.615803 | − | 0.787900i | \(-0.288832\pi\) | ||||
0.615803 | + | 0.787900i | \(0.288832\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 86000.0i | − 0.421570i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 277098.i | − 1.26134i | −0.776051 | − | 0.630670i | \(-0.782780\pi\) | ||||
0.776051 | − | 0.630670i | \(-0.217220\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −193540. | −0.849638 | −0.424819 | − | 0.905278i | \(-0.639662\pi\) | ||||
−0.424819 | + | 0.905278i | \(0.639662\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 158112. | 0.669757 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 124872.i | 0.510652i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 306648.i | 1.17043i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −140550. | −0.518639 | −0.259320 | − | 0.965792i | \(-0.583498\pi\) | ||||
−0.259320 | + | 0.965792i | \(0.583498\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −433952. | −1.54881 | −0.774407 | − | 0.632688i | \(-0.781952\pi\) | ||||
−0.774407 | + | 0.632688i | \(0.781952\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 73926.0i | − 0.255310i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 555922.i | 1.79997i | 0.435923 | + | 0.899984i | \(0.356422\pi\) | ||||
−0.435923 | + | 0.899984i | \(0.643578\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −505584. | −1.58599 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −613008. | −1.86381 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 66616.0i | 0.196386i | 0.995167 | + | 0.0981928i | \(0.0313062\pi\) | ||||
−0.995167 | + | 0.0981928i | \(0.968694\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 205692.i | − 0.570724i | −0.958420 | − | 0.285362i | \(-0.907886\pi\) | ||||
0.958420 | − | 0.285362i | \(-0.0921138\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −523623. | −1.41027 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −166500. | −0.435436 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 433854.i | 1.10212i | 0.834466 | + | 0.551059i | \(0.185776\pi\) | ||||
−0.834466 | + | 0.551059i | \(0.814224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 191520.i | − 0.459495i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −489180. | −1.14113 | −0.570566 | − | 0.821252i | \(-0.693276\pi\) | ||||
−0.570566 | + | 0.821252i | \(0.693276\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 719462. | 1.63234 | 0.816172 | − | 0.577810i | \(-0.196092\pi\) | ||||
0.816172 | + | 0.577810i | \(0.196092\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 398928.i | − 0.880576i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 29304.0i | − 0.0612806i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 371520. | 0.756533 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 185928. | 0.368775 | 0.184387 | − | 0.982854i | \(-0.440970\pi\) | ||||
0.184387 | + | 0.982854i | \(0.440970\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 591406.i | − 1.14286i | −0.820651 | − | 0.571429i | \(-0.806389\pi\) | ||||
0.820651 | − | 0.571429i | \(-0.193611\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 449478.i | − 0.825169i | −0.910919 | − | 0.412584i | \(-0.864626\pi\) | ||||
0.910919 | − | 0.412584i | \(-0.135374\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 157160. | 0.281326 | 0.140663 | − | 0.990058i | \(-0.455077\pi\) | ||||
0.140663 | + | 0.990058i | \(0.455077\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 43392.0 | 0.0757564 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 376680.i | 0.641553i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.18681e6i | 1.92511i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −66000.0 | −0.104515 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −253052. | −0.391294 | −0.195647 | − | 0.980674i | \(-0.562681\pi\) | ||||
−0.195647 | + | 0.980674i | \(0.562681\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 588672.i | − 0.889046i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 397664.i | 0.573280i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 491376. | 0.692315 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 210012. | 0.289243 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.07344e6i | − 1.44550i | −0.691111 | − | 0.722749i | \(-0.742878\pi\) | ||||
0.691111 | − | 0.722749i | \(-0.257122\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 626832.i | − 0.807396i | −0.914892 | − | 0.403698i | \(-0.867725\pi\) | ||||
0.914892 | − | 0.403698i | \(-0.132275\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 116650. | 0.146993 | 0.0734964 | − | 0.997295i | \(-0.476584\pi\) | ||||
0.0734964 | + | 0.997295i | \(0.476584\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 544896. | 0.671868 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 743046.i | − 0.896656i | −0.893869 | − | 0.448328i | \(-0.852020\pi\) | ||||
0.893869 | − | 0.448328i | \(-0.147980\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.10976e6i | 1.28339i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 978720. | 1.10832 | 0.554158 | − | 0.832411i | \(-0.313040\pi\) | ||||
0.554158 | + | 0.832411i | \(0.313040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.13280e6 | −1.25635 | −0.628174 | − | 0.778073i | \(-0.716197\pi\) | ||||
−0.628174 | + | 0.778073i | \(0.716197\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.22278e6i | 1.32841i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 473000.i | − 0.493309i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.23782e6 | 1.26520 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −905652. | −0.907355 | −0.453677 | − | 0.891166i | \(-0.649888\pi\) | ||||
−0.453677 | + | 0.891166i | \(0.649888\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 470448.i | 0.462073i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 1.93994e6i | − 1.83212i | −0.401036 | − | 0.916062i | \(-0.631350\pi\) | ||||
0.401036 | − | 0.916062i | \(-0.368650\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.93362e6 | 1.79111 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 729270. | 0.662654 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 805476.i | 0.718064i | 0.933325 | + | 0.359032i | \(0.116893\pi\) | ||||
−0.933325 | + | 0.359032i | \(0.883107\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 2.64744e6i | − 2.27273i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 858690. | 0.723529 | 0.361764 | − | 0.932270i | \(-0.382175\pi\) | ||||
0.361764 | + | 0.932270i | \(0.382175\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 383608. | 0.317296 | 0.158648 | − | 0.987335i | \(-0.449287\pi\) | ||||
0.158648 | + | 0.987335i | \(0.449287\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.90509e6i | 3.17120i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2.01076e6i | − 1.57456i | −0.616593 | − | 0.787282i | \(-0.711488\pi\) | ||||
0.616593 | − | 0.787282i | \(-0.288512\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 769896. | 0.592136 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 202602. | 0.153066 | 0.0765329 | − | 0.997067i | \(-0.475615\pi\) | ||||
0.0765329 | + | 0.997067i | \(0.475615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 221536.i | 0.164429i | 0.996615 | + | 0.0822145i | \(0.0261992\pi\) | ||||
−0.996615 | + | 0.0822145i | \(0.973801\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 213624.i | − 0.153089i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.37057e6 | 0.965289 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.88117e6 | 1.30225 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 322506.i | − 0.219467i | −0.993961 | − | 0.109733i | \(-0.965000\pi\) | ||||
0.993961 | − | 0.109733i | \(-0.0349997\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 285120.i | − 0.187558i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.37154e6 | −2.18098 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.54733e6 | −2.25676 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 3.40661e6i | − 2.13165i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.44301e6i | 0.873822i | 0.899505 | + | 0.436911i | \(0.143927\pi\) | ||||
−0.899505 | + | 0.436911i | \(0.856073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10464.0 | 0.00623450 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −171312. | −0.100435 | −0.0502177 | − | 0.998738i | \(-0.515992\pi\) | ||||
−0.0502177 | + | 0.998738i | \(0.515992\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1.02689e6i | − 0.592463i | −0.955116 | − | 0.296232i | \(-0.904270\pi\) | ||||
0.955116 | − | 0.296232i | \(-0.0957300\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 752958.i | − 0.420845i | −0.977610 | − | 0.210423i | \(-0.932516\pi\) | ||||
0.977610 | − | 0.210423i | \(-0.0674840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 289080. | 0.159053 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.59123e6 | 3.02862 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 111000.i | 0.0591993i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 4.19640e6i | − 2.17024i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.13314e6 | 0.577155 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.99413e6 | −1.00042 | −0.500212 | − | 0.865903i | \(-0.666745\pi\) | ||||
−0.500212 | + | 0.865903i | \(0.666745\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 3.74359e6i | − 1.85002i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 987022.i | 0.473426i | 0.971580 | + | 0.236713i | \(0.0760701\pi\) | ||||
−0.971580 | + | 0.236713i | \(0.923930\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.39186e6 | 2.07562 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 305184. | 0.142127 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 693160.i | − 0.318125i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.20601e6i | 0.983520i | 0.870731 | + | 0.491760i | \(0.163646\pi\) | ||||
−0.870731 | + | 0.491760i | \(0.836354\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.74187e6 | −1.20499 | −0.602495 | − | 0.798123i | \(-0.705827\pi\) | ||||
−0.602495 | + | 0.798123i | \(0.705827\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.04336e6 | 0.885273 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 2.38957e6i | − 1.02066i | −0.859978 | − | 0.510331i | \(-0.829523\pi\) | ||||
0.859978 | − | 0.510331i | \(-0.170477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 916416.i | − 0.380559i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −279480. | −0.114450 | −0.0572248 | − | 0.998361i | \(-0.518225\pi\) | ||||
−0.0572248 | + | 0.998361i | \(0.518225\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.22610e6 | −0.899035 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.44705e6i | 1.37303i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 2.47637e6i | − 0.959734i | −0.877341 | − | 0.479867i | \(-0.840685\pi\) | ||||
0.877341 | − | 0.479867i | \(-0.159315\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −413586. | −0.158125 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.62335e6 | −1.36671 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.74525e6i | 1.02167i | 0.859679 | + | 0.510835i | \(0.170664\pi\) | ||||
−0.859679 | + | 0.510835i | \(0.829336\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.07174e6i | 0.750727i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.18906e6 | −0.425212 | −0.212606 | − | 0.977138i | \(-0.568195\pi\) | ||||
−0.212606 | + | 0.977138i | \(0.568195\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.93885e6 | −1.03721 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 3.25760e6i | − 1.13475i | −0.823458 | − | 0.567377i | \(-0.807958\pi\) | ||||
0.823458 | − | 0.567377i | \(-0.192042\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.86779e6i | 2.33099i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.98351e6 | −0.664600 | −0.332300 | − | 0.943174i | \(-0.607825\pi\) | ||||
−0.332300 | + | 0.943174i | \(0.607825\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 791208. | 0.261727 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 5.80579e6i | − 1.89618i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.97416e6i | − 1.58396i | −0.610549 | − | 0.791978i | \(-0.709051\pi\) | ||||
0.610549 | − | 0.791978i | \(-0.290949\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.06400e6 | −0.649049 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.34264e6 | −0.416963 | −0.208482 | − | 0.978026i | \(-0.566852\pi\) | ||||
−0.208482 | + | 0.978026i | \(0.566852\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.18715e6i | 0.670836i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.48394e6i | − 0.444050i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.09423e6 | 0.323445 | 0.161722 | − | 0.986836i | \(-0.448295\pi\) | ||||
0.161722 | + | 0.986836i | \(0.448295\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.65035e6 | −1.94196 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.37256e6i | − 0.395964i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.64496e6i | 1.30810i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −954060. | −0.265485 | −0.132743 | − | 0.991151i | \(-0.542378\pi\) | ||||
−0.132743 | + | 0.991151i | \(0.542378\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.59390e6 | −0.438284 | −0.219142 | − | 0.975693i | \(-0.570326\pi\) | ||||
−0.219142 | + | 0.975693i | \(0.570326\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 2.19380e6i | − 0.596138i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.85898e6i | − 0.758826i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.99693e6 | 0.786200 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.64665e6 | 0.686283 | 0.343141 | − | 0.939284i | \(-0.388509\pi\) | ||||
0.343141 | + | 0.939284i | \(0.388509\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.72355e6i | 0.954416i | 0.878790 | + | 0.477208i | \(0.158351\pi\) | ||||
−0.878790 | + | 0.477208i | \(0.841649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.78200e6i | − 0.446379i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.58340e6 | −0.639780 | −0.319890 | − | 0.947455i | \(-0.603646\pi\) | ||||
−0.319890 | + | 0.947455i | \(0.603646\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.25474e6 | 1.04178 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 7.56206e6i | − 1.83076i | −0.402593 | − | 0.915379i | \(-0.631891\pi\) | ||||
0.402593 | − | 0.915379i | \(-0.368109\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.37320e6i | 0.798497i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.30773e6 | −1.00840 | −0.504200 | − | 0.863587i | \(-0.668212\pi\) | ||||
−0.504200 | + | 0.863587i | \(0.668212\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −163944. | −0.0379537 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.04148e7i | 2.38456i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.24354e6i | 0.502509i | 0.967921 | + | 0.251254i | \(0.0808431\pi\) | ||||
−0.967921 | + | 0.251254i | \(0.919157\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −479520. | −0.106237 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.65670e6 | 0.363071 | 0.181536 | − | 0.983384i | \(-0.441893\pi\) | ||||
0.181536 | + | 0.983384i | \(0.441893\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.89160e6i | 0.626881i | 0.949608 | + | 0.313441i | \(0.101482\pi\) | ||||
−0.949608 | + | 0.313441i | \(0.898518\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 6.52699e6i | − 1.38491i | −0.721462 | − | 0.692454i | \(-0.756530\pi\) | ||||
0.721462 | − | 0.692454i | \(-0.243470\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 310976. | 0.0652822 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.33421e7 | 2.77123 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.72237e6i | 0.559492i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.01498e6i | 1.41166i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.96232e6 | −1.18734 | −0.593672 | − | 0.804707i | \(-0.702322\pi\) | ||||
−0.593672 | + | 0.804707i | \(0.702322\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.06349e7 | 2.09591 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.47122e7i | 2.86952i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.99191e6i | 0.571644i | 0.958283 | + | 0.285822i | \(0.0922666\pi\) | ||||
−0.958283 | + | 0.285822i | \(0.907733\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.59878e6 | 0.302355 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.20419e6 | 0.225419 | 0.112710 | − | 0.993628i | \(-0.464047\pi\) | ||||
0.112710 | + | 0.993628i | \(0.464047\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 486180.i | − 0.0900907i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 4.21882e6i | − 0.766125i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.20546e6 | 1.65499 | 0.827493 | − | 0.561477i | \(-0.189767\pi\) | ||||
0.827493 | + | 0.561477i | \(0.189767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.93661e6 | −0.878687 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.35956e6i | 0.592055i | 0.955179 | + | 0.296027i | \(0.0956620\pi\) | ||||
−0.955179 | + | 0.296027i | \(0.904338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.25670e7i | 2.17125i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.53701e6 | 0.434038 | 0.217019 | − | 0.976167i | \(-0.430367\pi\) | ||||
0.217019 | + | 0.976167i | \(0.430367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.52153e6 | 0.596594 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.08000e6i | 0.181188i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 869616.i | − 0.143087i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.04125e7 | 1.69682 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.31580e6 | −1.50358 | −0.751789 | − | 0.659404i | \(-0.770809\pi\) | ||||
−0.751789 | + | 0.659404i | \(0.770809\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.02802e6i | 0.803790i | 0.915686 | + | 0.401895i | \(0.131648\pi\) | ||||
−0.915686 | + | 0.401895i | \(0.868352\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 513264.i | − 0.0805034i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.26575e6 | −0.973496 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.65734e6 | −0.408988 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.17493e6i | − 0.179141i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.17403e7i | 1.75689i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.68656e6 | 0.250052 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 134222. | 0.0197165 | 0.00985827 | − | 0.999951i | \(-0.496862\pi\) | ||||
0.00985827 | + | 0.999951i | \(0.496862\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1.72671e7i | − 2.51316i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 605648.i | 0.0865470i | 0.999063 | + | 0.0432735i | \(0.0137787\pi\) | ||||
−0.999063 | + | 0.0432735i | \(0.986221\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.53513e6 | −0.783784 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.09500e6 | −0.153651 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.95328e6i | 1.10594i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.06240e6i | 0.964527i | 0.876026 | + | 0.482264i | \(0.160185\pi\) | ||||
−0.876026 | + | 0.482264i | \(0.839815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.95103e7 | −2.64079 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −703296. | −0.0943476 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.03029e7i | 1.36990i | 0.728588 | + | 0.684952i | \(0.240177\pi\) | ||||
−0.728588 | + | 0.684952i | \(0.759823\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.00159e6i | 0.653357i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.04769e6 | −0.135660 | −0.0678300 | − | 0.997697i | \(-0.521608\pi\) | ||||
−0.0678300 | + | 0.997697i | \(0.521608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.40765e7 | −1.80677 | −0.903385 | − | 0.428830i | \(-0.858926\pi\) | ||||
−0.903385 | + | 0.428830i | \(0.858926\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 4.46227e6i | − 0.567766i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 1.62682e6i | − 0.203423i | −0.994814 | − | 0.101711i | \(-0.967568\pi\) | ||||
0.994814 | − | 0.101711i | \(-0.0324318\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.41937e7 | −1.75955 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.87107e6 | 1.09027 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.78071e6i | 0.338832i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.96089e6i | 0.833814i | 0.908949 | + | 0.416907i | \(0.136886\pi\) | ||||
−0.908949 | + | 0.416907i | \(0.863114\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.15600e6 | −0.137300 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.07875e7 | −1.27043 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.13639e7i | − 1.32706i | −0.748150 | − | 0.663529i | \(-0.769058\pi\) | ||||
0.748150 | − | 0.663529i | \(-0.230942\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 3.77184e6i | − 0.433129i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.48688e7 | 1.69321 | 0.846603 | − | 0.532224i | \(-0.178644\pi\) | ||||
0.846603 | + | 0.532224i | \(0.178644\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.23612e6 | −0.139596 | −0.0697981 | − | 0.997561i | \(-0.522236\pi\) | ||||
−0.0697981 | + | 0.997561i | \(0.522236\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 602064.i | − 0.0674294i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1.24498e7i | − 1.37149i | −0.727844 | − | 0.685743i | \(-0.759478\pi\) | ||||
0.727844 | − | 0.685743i | \(-0.240522\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.04032e6 | 0.987735 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.23225e6 | 0.675370 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 8.73491e6i | − 0.938873i | −0.882966 | − | 0.469437i | \(-0.844457\pi\) | ||||
0.882966 | − | 0.469437i | \(-0.155543\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 1.25495e7i | − 1.32713i | −0.748119 | − | 0.663565i | \(-0.769043\pi\) | ||||
0.748119 | − | 0.663565i | \(-0.230957\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.46658e7 | −1.53843 | −0.769216 | − | 0.638988i | \(-0.779353\pi\) | ||||
−0.769216 | + | 0.638988i | \(0.779353\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.69824e6 | 0.801055 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1.89733e7i | − 1.95850i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.58400e6i | 0.160911i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.49572e6 | −0.251519 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 196288. | 0.0196255 | 0.00981274 | − | 0.999952i | \(-0.496876\pi\) | ||||
0.00981274 | + | 0.999952i | \(0.496876\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.07325e6i | 0.602437i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.20870e7i | 1.18024i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.16782e6 | −0.791324 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.11596e7 | −1.07276 | −0.536381 | − | 0.843976i | \(-0.680209\pi\) | ||||
−0.536381 | + | 0.843976i | \(0.680209\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.25158e6i | 0.214763i | 0.994218 | + | 0.107381i | \(0.0342466\pi\) | ||||
−0.994218 | + | 0.107381i | \(0.965753\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.05319e6i | 0.756323i | 0.925740 | + | 0.378161i | \(0.123444\pi\) | ||||
−0.925740 | + | 0.378161i | \(0.876556\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.05336e6 | −0.0981669 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.54394e6 | 0.882623 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 416466.i | − 0.0382205i | −0.999817 | − | 0.0191103i | \(-0.993917\pi\) | ||||
0.999817 | − | 0.0191103i | \(-0.00608336\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 6.81784e6i | − 0.616217i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.31721e7 | 1.18152 | 0.590761 | − | 0.806847i | \(-0.298828\pi\) | ||||
0.590761 | + | 0.806847i | \(0.298828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.69494e6 | −0.150886 | −0.0754432 | − | 0.997150i | \(-0.524037\pi\) | ||||
−0.0754432 | + | 0.997150i | \(0.524037\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 5.04029e6i | − 0.445319i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.80516e6i | 0.679309i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.57627e7 | −2.22549 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.19410e6 | −0.188127 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 8.91605e6i | − 0.758813i | −0.925230 | − | 0.379406i | \(-0.876128\pi\) | ||||
0.925230 | − | 0.379406i | \(-0.123872\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.42894e7i | 1.19824i | 0.800661 | + | 0.599118i | \(0.204482\pi\) | ||||
−0.800661 | + | 0.599118i | \(0.795518\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.34817e7 | 1.12220 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.50440e7 | −1.24307 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.33314e6i | 0.437452i | 0.975786 | + | 0.218726i | \(0.0701902\pi\) | ||||
−0.975786 | + | 0.218726i | \(0.929810\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 2.79960e6i | − 0.226310i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.99284e7 | −1.59928 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −698252. | −0.0556310 | −0.0278155 | − | 0.999613i | \(-0.508855\pi\) | ||||
−0.0278155 | + | 0.999613i | \(0.508855\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 7.56043e6i | − 0.598017i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 275724.i | 0.0214977i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.78331e7 | −1.38049 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.79880e7 | 1.38257 | 0.691285 | − | 0.722582i | \(-0.257045\pi\) | ||||
0.691285 | + | 0.722582i | \(0.257045\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.62100e6i | 0.428968i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.44140e7i | − 1.83692i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.39464e7 | 1.04195 | 0.520975 | − | 0.853572i | \(-0.325568\pi\) | ||||
0.520975 | + | 0.853572i | \(0.325568\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.53979e7 | 1.14232 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.23997e6i | 0.607018i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.34893e7i | − 1.70636i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.22272e6 | 0.448909 | 0.224454 | − | 0.974485i | \(-0.427940\pi\) | ||||
0.224454 | + | 0.974485i | \(0.427940\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 74992.0 | 0.00537250 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.71872e7i | 1.93427i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 7.76729e6i | − 0.545047i | −0.962149 | − | 0.272523i | \(-0.912142\pi\) | ||||
0.962149 | − | 0.272523i | \(-0.0878582\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.22804e7 | 1.55276 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.57853e6 | 0.316907 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.42083e7i | 1.66420i | 0.554627 | + | 0.832099i | \(0.312861\pi\) | ||||
−0.554627 | + | 0.832099i | \(0.687139\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 238656.i | − 0.0161847i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.26850e7 | 0.854434 | 0.427217 | − | 0.904149i | \(-0.359494\pi\) | ||||
0.427217 | + | 0.904149i | \(0.359494\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.13520e7 | −0.759498 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1.97632e7i | − 1.31337i | −0.754166 | − | 0.656684i | \(-0.771959\pi\) | ||||
0.754166 | − | 0.656684i | \(-0.228041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.71748e7i | − 1.12613i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.00705e7 | 2.60988 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.01761e6 | 0.583434 | 0.291717 | − | 0.956505i | \(-0.405774\pi\) | ||||
0.291717 | + | 0.956505i | \(0.405774\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.17356e7i | 1.39696i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.12556e6i | 0.0713887i | 0.999363 | + | 0.0356944i | \(0.0113643\pi\) | ||||
−0.999363 | + | 0.0356944i | \(0.988636\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.12908e7 | 0.711407 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.25747e7 | 1.41306 | 0.706529 | − | 0.707684i | \(-0.250260\pi\) | ||||
0.706529 | + | 0.707684i | \(0.250260\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 3.00742e7i | − 1.87018i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 7.54908e6i | − 0.463346i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 632350. | 0.0385604 | 0.0192802 | − | 0.999814i | \(-0.493863\pi\) | ||||
0.0192802 | + | 0.999814i | \(0.493863\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.65585e7 | −2.82074 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.25867e7i | − 0.757643i | −0.925470 | − | 0.378822i | \(-0.876329\pi\) | ||||
0.925470 | − | 0.378822i | \(-0.123671\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 4.64070e7i | − 2.75760i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 621000. | 0.0366647 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.23770e6 | −0.189937 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 4.73040e6i | − 0.275736i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.15792e7i | 1.24194i | 0.783836 | + | 0.620968i | \(0.213260\pi\) | ||||
−0.783836 | + | 0.620968i | \(0.786740\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.93314e7 | 1.10553 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.14750e7 | 1.78864 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 1.57244e7i | − 0.887956i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.09760e7i | 1.72735i | 0.504052 | + | 0.863673i | \(0.331842\pi\) | ||||
−0.504052 | + | 0.863673i | \(0.668158\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.46254e6 | −0.0810475 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.67332e7 | −2.02292 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.70257e6i | − 0.147907i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 2.06086e7i | − 1.11395i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.24929e6 | −0.228268 | −0.114134 | − | 0.993465i | \(-0.536409\pi\) | ||||
−0.114134 | + | 0.993465i | \(0.536409\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.42333e6 | −0.182767 | −0.0913833 | − | 0.995816i | \(-0.529129\pi\) | ||||
−0.0913833 | + | 0.995816i | \(0.529129\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 9.20659e6i | − 0.488509i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1.03120e7i | − 0.540490i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.41831e7 | 2.82263 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.10571e7 | 1.60806 | 0.804030 | − | 0.594588i | \(-0.202685\pi\) | ||||
0.804030 | + | 0.594588i | \(0.202685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.11904e7i | 1.60517i | 0.596538 | + | 0.802584i | \(0.296542\pi\) | ||||
−0.596538 | + | 0.802584i | \(0.703458\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 8.28487e6i | − 0.421233i | −0.977569 | − | 0.210616i | \(-0.932453\pi\) | ||||
0.977569 | − | 0.210616i | \(-0.0675471\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.81688e7 | 0.918208 | 0.459104 | − | 0.888383i | \(-0.348171\pi\) | ||||
0.459104 | + | 0.888383i | \(0.348171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.82582e7 | −2.42420 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 2.83649e6i | − 0.141635i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 4.99392e6i | − 0.246393i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.02743e7 | −0.503902 | −0.251951 | − | 0.967740i | \(-0.581072\pi\) | ||||
−0.251951 | + | 0.967740i | \(0.581072\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.57150e7 | −0.766171 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 4.86245e6i | − 0.235660i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.47038e7i | 1.18319i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.31686e6 | 0.253155 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00665e7 | 1.89652 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.28597e6i | 0.295801i | 0.989002 | + | 0.147901i | \(0.0472516\pi\) | ||||
−0.989002 | + | 0.147901i | \(0.952748\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1.54050e7i | − 0.716490i | −0.933628 | − | 0.358245i | \(-0.883375\pi\) | ||||
0.933628 | − | 0.358245i | \(-0.116625\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.43526e7 | 0.663664 | 0.331832 | − | 0.943338i | \(-0.392333\pi\) | ||||
0.331832 | + | 0.943338i | \(0.392333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.12698e6 | −0.235697 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1.33278e7i | − 0.609158i | −0.952487 | − | 0.304579i | \(-0.901484\pi\) | ||||
0.952487 | − | 0.304579i | \(-0.0985158\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 3.28938e7i | − 1.48616i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.10368e6 | 0.274184 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.71037e6 | 0.0763913 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 2.61012e7i | − 1.15911i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3.24846e7i | − 1.42620i | −0.701065 | − | 0.713098i | \(-0.747292\pi\) | ||||
0.701065 | − | 0.713098i | \(-0.252708\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.74014e6 | −0.337891 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.54600e7 | 0.671073 | 0.335537 | − | 0.942027i | \(-0.391082\pi\) | ||||
0.335537 | + | 0.942027i | \(0.391082\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.69478e6i | 0.0731494i | 0.999331 | + | 0.0365747i | \(0.0116447\pi\) | ||||
−0.999331 | + | 0.0365747i | \(0.988355\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 2.87257e6i | − 0.122592i | −0.998120 | − | 0.0612960i | \(-0.980477\pi\) | ||||
0.998120 | − | 0.0612960i | \(-0.0195233\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.10617e7 | −0.893799 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.83843e6 | 0.161979 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.29400e6i | 0.138228i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.09171e7i | 3.35783i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.06328e6 | 0.208945 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.67665e6 | 0.191921 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.51359e7i | 3.47451i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.95422e7i | 1.59603i | 0.602635 | + | 0.798017i | \(0.294118\pi\) | ||||
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.72667e7 | −1.89734 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.13178e7 | −0.451819 | −0.225909 | − | 0.974148i | \(-0.572535\pi\) | ||||
−0.225909 | + | 0.974148i | \(0.572535\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 6.80803e6i | − 0.270299i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.16082e7i | − 1.63401i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.51348e6 | 0.332520 | 0.166260 | − | 0.986082i | \(-0.446831\pi\) | ||||
0.166260 | + | 0.986082i | \(0.446831\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.46322e7 | 1.34534 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 2.32035e7i | − 0.896497i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 145188.i | − 0.00554921i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.54587e6 | 0.286860 | 0.143430 | − | 0.989660i | \(-0.454187\pi\) | ||||
0.143430 | + | 0.989660i | \(0.454187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.38850e6 | −0.241560 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.11149e6i | 0.154630i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.84500e7i | 0.686512i | 0.939242 | + | 0.343256i | \(0.111530\pi\) | ||||
−0.939242 | + | 0.343256i | \(0.888470\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.46453e7 | −0.912157 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.75046e6 | 0.248519 | 0.124259 | − | 0.992250i | \(-0.460344\pi\) | ||||
0.124259 | + | 0.992250i | \(0.460344\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 4.42649e6i | − 0.162099i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.45677e6i | 0.233959i | 0.993134 | + | 0.116980i | \(0.0373212\pi\) | ||||
−0.993134 | + | 0.116980i | \(0.962679\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.93684e7 | 0.698117 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.80710e7 | −0.647934 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 3.96648e7i | − 1.41473i | −0.706849 | − | 0.707364i | \(-0.749884\pi\) | ||||
0.706849 | − | 0.707364i | \(-0.250116\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 6.93792e6i | − 0.244878i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.76609e7 | −1.67346 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.32838e7 | −0.813290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 7.75783e7i | − 2.69572i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 3.43015e7i | − 1.17963i | −0.807538 | − | 0.589816i | \(-0.799200\pi\) | ||||
0.807538 | − | 0.589816i | \(-0.200800\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.66400e6 | 0.0911433 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.77115e6 | 0.196433 | 0.0982164 | − | 0.995165i | \(-0.468686\pi\) | ||||
0.0982164 | + | 0.995165i | \(0.468686\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.32889e7i | 1.12724i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 7.08746e6i | − 0.237549i | −0.992921 | − | 0.118775i | \(-0.962103\pi\) | ||||
0.992921 | − | 0.118775i | \(-0.0378966\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.45609e7 | −0.485548 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.82250e7 | −1.93169 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 4.59362e7i | − 1.51625i | −0.652108 | − | 0.758126i | \(-0.726115\pi\) | ||||
0.652108 | − | 0.758126i | \(-0.273885\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.71953e7i | − 0.888588i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.35039e7 | −2.38957 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.50298e7 | 1.45652 | 0.728260 | − | 0.685301i | \(-0.240329\pi\) | ||||
0.728260 | + | 0.685301i | \(0.240329\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.78592e7i | 1.54025i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.37364e7i | 0.756271i | 0.925750 | + | 0.378136i | \(0.123435\pi\) | ||||
−0.925750 | + | 0.378136i | \(0.876565\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.42827e7 | −0.769810 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 400.6.c.b.49.1 | 2 | ||
4.3 | odd | 2 | 50.6.b.a.49.2 | 2 | |||
5.2 | odd | 4 | 80.6.a.a.1.1 | 1 | |||
5.3 | odd | 4 | 400.6.a.n.1.1 | 1 | |||
5.4 | even | 2 | inner | 400.6.c.b.49.2 | 2 | ||
12.11 | even | 2 | 450.6.c.h.199.1 | 2 | |||
15.2 | even | 4 | 720.6.a.j.1.1 | 1 | |||
20.3 | even | 4 | 50.6.a.d.1.1 | 1 | |||
20.7 | even | 4 | 10.6.a.b.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 50.6.b.a.49.1 | 2 | |||
40.27 | even | 4 | 320.6.a.b.1.1 | 1 | |||
40.37 | odd | 4 | 320.6.a.o.1.1 | 1 | |||
60.23 | odd | 4 | 450.6.a.l.1.1 | 1 | |||
60.47 | odd | 4 | 90.6.a.d.1.1 | 1 | |||
60.59 | even | 2 | 450.6.c.h.199.2 | 2 | |||
140.27 | odd | 4 | 490.6.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.6.a.b.1.1 | ✓ | 1 | 20.7 | even | 4 | ||
50.6.a.d.1.1 | 1 | 20.3 | even | 4 | |||
50.6.b.a.49.1 | 2 | 20.19 | odd | 2 | |||
50.6.b.a.49.2 | 2 | 4.3 | odd | 2 | |||
80.6.a.a.1.1 | 1 | 5.2 | odd | 4 | |||
90.6.a.d.1.1 | 1 | 60.47 | odd | 4 | |||
320.6.a.b.1.1 | 1 | 40.27 | even | 4 | |||
320.6.a.o.1.1 | 1 | 40.37 | odd | 4 | |||
400.6.a.n.1.1 | 1 | 5.3 | odd | 4 | |||
400.6.c.b.49.1 | 2 | 1.1 | even | 1 | trivial | ||
400.6.c.b.49.2 | 2 | 5.4 | even | 2 | inner | ||
450.6.a.l.1.1 | 1 | 60.23 | odd | 4 | |||
450.6.c.h.199.1 | 2 | 12.11 | even | 2 | |||
450.6.c.h.199.2 | 2 | 60.59 | even | 2 | |||
490.6.a.a.1.1 | 1 | 140.27 | odd | 4 | |||
720.6.a.j.1.1 | 1 | 15.2 | even | 4 |