Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(49,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.f (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: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.10 | ||
Character | \(\chi\) | \(=\) | 160.49 |
Dual form | 160.6.f.a.49.9 |
$q$-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 \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −10.5561 | −0.677176 | −0.338588 | − | 0.940935i | \(-0.609949\pi\) | ||||
−0.338588 | + | 0.940935i | \(0.609949\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −52.7686 | + | 18.4521i | −0.943953 | + | 0.330081i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 47.9937i | 0.370203i | 0.982719 | + | 0.185101i | \(0.0592613\pi\) | ||||
−0.982719 | + | 0.185101i | \(0.940739\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −131.568 | −0.541432 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 690.713i | − | 1.72114i | −0.509332 | − | 0.860570i | \(-0.670108\pi\) | ||
0.509332 | − | 0.860570i | \(-0.329892\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −743.139 | −1.21958 | −0.609792 | − | 0.792562i | \(-0.708747\pi\) | ||||
−0.609792 | + | 0.792562i | \(0.708747\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 557.032 | − | 194.783i | 0.639222 | − | 0.223523i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2042.04i | 1.71373i | 0.515542 | + | 0.856864i | \(0.327591\pi\) | ||||
−0.515542 | + | 0.856864i | \(0.672409\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1446.84i | 0.919470i | 0.888056 | + | 0.459735i | \(0.152056\pi\) | ||||
−0.888056 | + | 0.459735i | \(0.847944\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 506.628i | − | 0.250692i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1433.47i | − | 0.565026i | −0.959263 | − | 0.282513i | \(-0.908832\pi\) | ||
0.959263 | − | 0.282513i | \(-0.0911680\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2444.04 | − | 1947.38i | 0.782093 | − | 0.623161i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3953.99 | 1.04382 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4388.18i | − | 0.968923i | −0.874813 | − | 0.484462i | \(-0.839016\pi\) | ||
0.874813 | − | 0.484462i | \(-0.160984\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5825.62 | 1.08877 | 0.544387 | − | 0.838834i | \(-0.316762\pi\) | ||||
0.544387 | + | 0.838834i | \(0.316762\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7291.26i | 1.16552i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −885.584 | − | 2532.56i | −0.122197 | − | 0.349454i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −632.966 | −0.0760110 | −0.0380055 | − | 0.999278i | \(-0.512100\pi\) | ||||
−0.0380055 | + | 0.999278i | \(0.512100\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7844.67 | 0.825873 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9131.48 | 0.848363 | 0.424182 | − | 0.905577i | \(-0.360562\pi\) | ||||
0.424182 | + | 0.905577i | \(0.360562\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1992.47 | 0.164332 | 0.0821658 | − | 0.996619i | \(-0.473816\pi\) | ||||
0.0821658 | + | 0.996619i | \(0.473816\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6942.65 | − | 2427.70i | 0.511086 | − | 0.178716i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1291.21i | 0.0852616i | 0.999091 | + | 0.0426308i | \(0.0135739\pi\) | ||||
−0.999091 | + | 0.0426308i | \(0.986426\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14503.6 | 0.862950 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 21556.1i | − | 1.16050i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7767.93 | 0.379853 | 0.189927 | − | 0.981798i | \(-0.439175\pi\) | ||||
0.189927 | + | 0.981798i | \(0.439175\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12745.1 | + | 36447.9i | 0.568115 | + | 1.62467i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 15273.1i | − | 0.622644i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 7014.55i | − | 0.262343i | −0.991360 | − | 0.131172i | \(-0.958126\pi\) | ||
0.991360 | − | 0.131172i | \(-0.0418739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5005.26i | − | 0.172227i | −0.996285 | − | 0.0861137i | \(-0.972555\pi\) | ||
0.996285 | − | 0.0861137i | \(-0.0274448\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 6314.44i | − | 0.200440i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 39214.4 | − | 13712.5i | 1.15123 | − | 0.402561i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14569.6 | −0.396516 | −0.198258 | − | 0.980150i | \(-0.563528\pi\) | ||||
−0.198258 | + | 0.980150i | \(0.563528\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15131.9i | 0.382622i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 59737.3 | 1.40637 | 0.703186 | − | 0.711006i | \(-0.251760\pi\) | ||||
0.703186 | + | 0.711006i | \(0.251760\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 37773.3i | 0.829616i | 0.909909 | + | 0.414808i | \(0.136151\pi\) | ||||
−0.909909 | + | 0.414808i | \(0.863849\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −25799.6 | + | 20556.8i | −0.529615 | + | 0.421990i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 33149.9 | 0.637170 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −78197.2 | −1.40969 | −0.704844 | − | 0.709362i | \(-0.748983\pi\) | ||||
−0.704844 | + | 0.709362i | \(0.748983\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9767.83 | −0.165419 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8704.60 | 0.138693 | 0.0693463 | − | 0.997593i | \(-0.477909\pi\) | ||||
0.0693463 | + | 0.997593i | \(0.477909\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −37679.9 | − | 107756.i | −0.565669 | − | 1.61768i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 46322.2i | 0.656132i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −78835.9 | −1.05499 | −0.527496 | − | 0.849558i | \(-0.676869\pi\) | ||||
−0.527496 | + | 0.849558i | \(0.676869\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 35666.0i | − | 0.451493i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −61496.0 | −0.737292 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −26697.3 | − | 76347.9i | −0.303500 | − | 0.867937i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5863.79i | − | 0.0632775i | −0.999499 | − | 0.0316387i | \(-0.989927\pi\) | ||
0.999499 | − | 0.0316387i | \(-0.0100726\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 90875.8i | 0.931880i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 189963.i | 1.85296i | 0.376343 | + | 0.926481i | \(0.377182\pi\) | ||||
−0.376343 | + | 0.926481i | \(0.622818\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 115497.i | − | 1.07270i | −0.843996 | − | 0.536349i | \(-0.819803\pi\) | ||
0.843996 | − | 0.536349i | \(-0.180197\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9348.35 | + | 26734.0i | 0.0827488 | + | 0.236642i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 167020. | 1.41030 | 0.705148 | − | 0.709060i | \(-0.250881\pi\) | ||||
0.705148 | + | 0.709060i | \(0.250881\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 18122.4i | − | 0.146100i | −0.997328 | − | 0.0730499i | \(-0.976727\pi\) | ||
0.997328 | − | 0.0730499i | \(-0.0232732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6681.68 | 0.0514728 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 24447.2i | − | 0.180108i | −0.995937 | − | 0.0900541i | \(-0.971296\pi\) | ||
0.995937 | − | 0.0900541i | \(-0.0287040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26450.5 | + | 75642.0i | 0.186504 | + | 0.533358i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 97773.3 | 0.660322 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −98005.2 | −0.634427 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −316034. | −1.96232 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −96393.2 | −0.574491 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −93035.3 | + | 147858.i | −0.532565 | + | 0.846389i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 274865.i | − | 1.51220i | −0.654456 | − | 0.756101i | \(-0.727102\pi\) | ||
0.654456 | − | 0.756101i | \(-0.272898\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21032.8 | −0.111281 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 171066.i | − | 0.870934i | −0.900205 | − | 0.435467i | \(-0.856583\pi\) | ||
0.900205 | − | 0.435467i | \(-0.143417\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −69439.5 | −0.340390 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −208646. | + | 72959.4i | −0.985318 | + | 0.344546i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 208744.i | − | 0.950194i | −0.879934 | − | 0.475097i | \(-0.842413\pi\) | ||
0.879934 | − | 0.475097i | \(-0.157587\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 236729.i | 1.03924i | 0.854399 | + | 0.519618i | \(0.173926\pi\) | ||||
−0.854399 | + | 0.519618i | \(0.826074\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 13630.2i | − | 0.0577372i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 513296.i | 2.09907i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 80971.0 | + | 231558.i | 0.319823 | + | 0.914618i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −153102. | −0.584369 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 157593.i | − | 0.581530i | −0.956794 | − | 0.290765i | \(-0.906090\pi\) | ||
0.956794 | − | 0.290765i | \(-0.0939098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −59264.9 | −0.211522 | −0.105761 | − | 0.994392i | \(-0.533728\pi\) | ||||
−0.105761 | + | 0.994392i | \(0.533728\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 268667.i | − | 0.927868i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −307410. | + | 107495.i | −1.02775 | + | 0.359384i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 152525. | 0.493845 | 0.246923 | − | 0.969035i | \(-0.420581\pi\) | ||||
0.246923 | + | 0.969035i | \(0.420581\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −81999.3 | −0.257228 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 68797.5 | 0.209174 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −272338. | −0.802859 | −0.401430 | − | 0.915890i | \(-0.631487\pi\) | ||||
−0.401430 | + | 0.915890i | \(0.631487\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −134539. | − | 384749.i | −0.384714 | − | 1.10019i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 195117.i | − | 0.541383i | −0.962666 | − | 0.270692i | \(-0.912748\pi\) | ||
0.962666 | − | 0.270692i | \(-0.0872524\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 180962. | 0.487383 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 190358.i | − | 0.497831i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 213434. | 0.542185 | 0.271093 | − | 0.962553i | \(-0.412615\pi\) | ||||
0.271093 | + | 0.962553i | \(0.412615\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 93462.0 | + | 117299.i | 0.230696 | + | 0.289533i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 74046.5i | 0.177653i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 464341.i | − | 1.08319i | −0.840640 | − | 0.541595i | \(-0.817821\pi\) | ||
0.840640 | − | 0.541595i | \(-0.182179\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 601344.i | 1.36435i | 0.731188 | + | 0.682176i | \(0.238966\pi\) | ||||
−0.731188 | + | 0.682176i | \(0.761034\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 52836.2i | 0.116628i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 33400.7 | − | 11679.5i | 0.0717507 | − | 0.0250898i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.41046e6 | 2.94957 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189767.i | 0.386425i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 618397. | 1.22655 | 0.613273 | − | 0.789871i | \(-0.289852\pi\) | ||||
0.613273 | + | 0.789871i | \(0.289852\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 24646.1i | − | 0.0476271i | −0.999716 | − | 0.0238136i | \(-0.992419\pi\) | ||
0.999716 | − | 0.0238136i | \(-0.00758081\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −413952. | + | 144751.i | −0.779585 | + | 0.272605i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 791174. | 1.45247 | 0.726233 | − | 0.687448i | \(-0.241269\pi\) | ||||
0.726233 | + | 0.687448i | \(0.241269\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 787051. | 1.40887 | 0.704434 | − | 0.709770i | \(-0.251201\pi\) | ||||
0.704434 | + | 0.709770i | \(0.251201\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 153799. | 0.268511 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 210605. | 0.358698 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −481855. | + | 168495.i | −0.800815 | + | 0.280028i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 188598.i | 0.305923i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 999355. | 1.58254 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 100172.i | 0.154896i | 0.996996 | + | 0.0774482i | \(0.0246772\pi\) | ||||
−0.996996 | + | 0.0774482i | \(0.975323\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −630596. | −0.952362 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −105140. | + | 36765.2i | −0.155121 | + | 0.0542427i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 279593.i | 0.403067i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 398740.i | − | 0.561797i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.51752e6i | − | 2.09004i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 641949.i | − | 0.864447i | −0.901766 | − | 0.432224i | \(-0.857729\pi\) | ||
0.901766 | − | 0.432224i | \(-0.142271\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −321558. | + | 256213.i | −0.423450 | + | 0.337400i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 168375. | 0.216876 | 0.108438 | − | 0.994103i | \(-0.465415\pi\) | ||||
0.108438 | + | 0.994103i | \(0.465415\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 847070.i | − | 1.06741i | −0.845671 | − | 0.533704i | \(-0.820800\pi\) | ||
0.845671 | − | 0.533704i | \(-0.179200\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −349935. | −0.431477 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.62230e6i | 1.95768i | 0.204623 | + | 0.978841i | \(0.434403\pi\) | ||||
−0.204623 | + | 0.978841i | \(0.565597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23825.6 | − | 68135.5i | −0.0281432 | − | 0.0804829i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 825460. | 0.954608 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 755195. | 0.855193 | 0.427597 | − | 0.903970i | \(-0.359360\pi\) | ||||
0.427597 | + | 0.903970i | \(0.359360\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 203535. | 0.225734 | 0.112867 | − | 0.993610i | \(-0.463997\pi\) | ||||
0.112867 | + | 0.993610i | \(0.463997\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −857709. | −0.931804 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −765334. | + | 267622.i | −0.814584 | + | 0.284843i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.07521e6i | − | 1.12137i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −91886.9 | −0.0939194 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.07763e6i | 1.07966i | 0.841775 | + | 0.539829i | \(0.181511\pi\) | ||||
−0.841775 | + | 0.539829i | \(0.818489\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −990115. | −0.972488 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 397754. | + | 1.13748e6i | 0.383058 | + | 1.09545i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.85261e6i | − | 1.74965i | −0.484439 | − | 0.874825i | \(-0.660976\pi\) | ||
0.484439 | − | 0.874825i | \(-0.339024\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 30378.4i | − | 0.0281394i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 577344.i | 0.524606i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 914131.i | 0.814927i | 0.913221 | + | 0.407464i | \(0.133587\pi\) | ||||
−0.913221 | + | 0.407464i | \(0.866413\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −409903. | + | 143335.i | −0.358563 | + | 0.125382i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 832202. | 0.714415 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 767239.i | 0.646473i | 0.946318 | + | 0.323236i | \(0.104771\pi\) | ||||
−0.946318 | + | 0.323236i | \(0.895229\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.13627e6 | −0.939848 | −0.469924 | − | 0.882707i | \(-0.655719\pi\) | ||||
−0.469924 | + | 0.882707i | \(0.655719\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 376495.i | 0.305740i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.34508e6 | − | 1.68813e6i | −1.07255 | − | 1.34609i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.36392e6 | 1.06805 | 0.534024 | − | 0.845469i | \(-0.320679\pi\) | ||||
0.534024 | + | 0.845469i | \(0.320679\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −766465. | −0.589498 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.48233e6 | 1.11990 | 0.559951 | − | 0.828526i | \(-0.310820\pi\) | ||||
0.559951 | + | 0.828526i | \(0.310820\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 767342. | 0.569538 | 0.284769 | − | 0.958596i | \(-0.408083\pi\) | ||||
0.284769 | + | 0.958596i | \(0.408083\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 281820. | + | 805939.i | 0.205523 | + | 0.587746i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 438254.i | 0.314066i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.75007e6 | −1.93687 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 61899.0i | 0.0428500i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 318861. | 0.216986 | 0.108493 | − | 0.994097i | \(-0.465397\pi\) | ||||
0.108493 | + | 0.994097i | \(0.465397\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 129433. | + | 370147.i | 0.0865944 | + | 0.247639i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.73107e6i | − | 1.79656i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.06527e6i | 0.689096i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 95626.1i | 0.0608359i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.00528e6i | − | 1.25478i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 92357.6 | + | 264121.i | 0.0568490 | + | 0.162575i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 209398. | 0.126802 | 0.0634010 | − | 0.997988i | \(-0.479805\pi\) | ||||
0.0634010 | + | 0.997988i | \(0.479805\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.21920e6i | 0.726406i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −663890. | −0.389220 | −0.194610 | − | 0.980881i | \(-0.562344\pi\) | ||||
−0.194610 | + | 0.980881i | \(0.562344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 960429.i | − | 0.554121i | −0.960853 | − | 0.277060i | \(-0.910640\pi\) | ||
0.960853 | − | 0.277060i | \(-0.0893602\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 116515. | + | 333204.i | 0.0661613 | + | 0.189205i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.05328e6 | 0.588704 | 0.294352 | − | 0.955697i | \(-0.404896\pi\) | ||||
0.294352 | + | 0.955697i | \(0.404896\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.03097e6 | −1.66765 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.76309e6 | −0.955019 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.95451e6 | −1.57572 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.81626e6 | + | 1.44717e6i | −0.953828 | + | 0.759997i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 191303.i | 0.0989353i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −61970.2 | −0.0315641 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.28525e6i | 0.644788i | 0.946606 | + | 0.322394i | \(0.104488\pi\) | ||||
−0.946606 | + | 0.322394i | \(0.895512\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 83278.1 | 0.0411548 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 768817. | − | 268840.i | 0.374292 | − | 0.130882i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.75075e6i | 1.31940i | 0.751529 | + | 0.659700i | \(0.229317\pi\) | ||||
−0.751529 | + | 0.659700i | \(0.770683\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 258068.i | 0.121965i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.02383e6i | − | 1.87393i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.50271e6i | 0.689669i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −279215. | − | 798487.i | −0.126296 | − | 0.361177i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.93898e6 | 1.31031 | 0.655153 | − | 0.755496i | \(-0.272604\pi\) | ||||
0.655153 | + | 0.755496i | \(0.272604\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 817288.i | 0.359179i | 0.983742 | + | 0.179590i | \(0.0574770\pi\) | ||||
−0.983742 | + | 0.179590i | \(0.942523\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.93836e6 | −1.27303 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.83106e6i | − | 0.782106i | −0.920368 | − | 0.391053i | \(-0.872111\pi\) | ||
0.920368 | − | 0.391053i | \(-0.127889\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.15225e6 | + | 1.10228e6i | −1.32755 | + | 0.464216i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.03456e6 | 0.429619 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.94811e6 | 0.797768 | 0.398884 | − | 0.917001i | \(-0.369398\pi\) | ||||
0.398884 | + | 0.917001i | \(0.369398\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 382741. | 0.154574 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.33610e6 | 1.32884 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −696995. | − | 1.99324e6i | −0.273841 | − | 0.783119i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.04360e6i | − | 1.56712i | −0.621314 | − | 0.783562i | \(-0.713401\pi\) | ||
0.621314 | − | 0.783562i | \(-0.286599\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.20141e6 | −0.459331 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 372812.i | 0.140623i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.18472e6 | −0.440903 | −0.220451 | − | 0.975398i | \(-0.570753\pi\) | ||||
−0.220451 | + | 0.975398i | \(0.570753\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 982093. | − | 1.56081e6i | 0.360641 | − | 0.573155i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.26103e6i | 1.18168i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 983110.i | − | 0.351564i | −0.984429 | − | 0.175782i | \(-0.943755\pi\) | ||
0.984429 | − | 0.175782i | \(-0.0562453\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.90151e6i | 1.02403i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.10213e6i | 0.732256i | 0.930564 | + | 0.366128i | \(0.119317\pi\) | ||||
−0.930564 | + | 0.366128i | \(0.880683\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.74927e6 | + | 611685.i | −0.601459 | + | 0.210318i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −262145. | −0.0889744 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.32916e6i | 0.780414i | 0.920727 | + | 0.390207i | \(0.127596\pi\) | ||||
−0.920727 | + | 0.390207i | \(0.872404\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.92720e6 | 0.968301 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.80579e6i | 0.589776i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.12635e6 | − | 1.44290e6i | 1.33068 | − | 0.465311i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.36029e6 | −1.38848 | −0.694239 | − | 0.719745i | \(-0.744259\pi\) | ||||
−0.694239 | + | 0.719745i | \(0.744259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 733012. | 0.230504 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.73757e6 | 1.16072 | 0.580361 | − | 0.814359i | \(-0.302911\pi\) | ||||
0.580361 | + | 0.814359i | \(0.302911\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.32924e6 | −1.32785 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 515434. | − | 180237.i | 0.156148 | − | 0.0546017i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 437198.i | 0.130825i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 90602.1 | 0.0267812 | 0.0133906 | − | 0.999910i | \(-0.495738\pi\) | ||||
0.0133906 | + | 0.999910i | \(0.495738\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.20353e6i | 0.643449i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 336654. | 0.0971201 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −459329. | + | 160618.i | −0.130919 | + | 0.0457798i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 2.49894e6i | − | 0.703746i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 4.75171e6i | − | 1.32225i | −0.750274 | − | 0.661127i | \(-0.770078\pi\) | ||
0.750274 | − | 0.661127i | \(-0.229922\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.47064e6i | − | 0.679367i | −0.940540 | − | 0.339684i | \(-0.889680\pi\) | ||
0.940540 | − | 0.339684i | \(-0.110320\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 169882.i | − | 0.0461634i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.97663e6 | + | 4.99083e6i | 1.06793 | + | 1.34030i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 240221. | 0.0637591 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 5.41842e6i | − | 1.42144i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.40187e6 | 1.66002 | 0.830010 | − | 0.557748i | \(-0.188334\pi\) | ||||
0.830010 | + | 0.557748i | \(0.188334\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.21518e6i | − | 0.567792i | −0.958855 | − | 0.283896i | \(-0.908373\pi\) | ||
0.958855 | − | 0.283896i | \(-0.0916271\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −854741. | − | 2.44436e6i | −0.216577 | − | 0.619357i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.07400e6 | 0.519525 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.50374e6 | −0.867702 | −0.433851 | − | 0.900985i | \(-0.642845\pi\) | ||||
−0.433851 | + | 0.900985i | \(0.642845\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.90821e6 | −0.467229 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.78808e6 | 0.917085 | 0.458543 | − | 0.888672i | \(-0.348372\pi\) | ||||
0.458543 | + | 0.888672i | \(0.348372\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.16006e6 | − | 1.45469e6i | 0.995862 | − | 0.348233i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.66358e6i | 0.393799i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.77118e6 | 1.11689 | 0.558444 | − | 0.829542i | \(-0.311398\pi\) | ||||
0.558444 | + | 0.829542i | \(0.311398\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6.30724e6i | − | 1.46015i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 625609. | 0.143238 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 658112. | + | 1.88204e6i | 0.149029 | + | 0.426188i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.15919e6i | − | 0.483617i | −0.970324 | − | 0.241808i | \(-0.922259\pi\) | ||
0.970324 | − | 0.241808i | \(-0.0777405\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.07421e6i | 1.78883i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.80473e6i | 1.05297i | 0.850184 | + | 0.526486i | \(0.176491\pi\) | ||||
−0.850184 | + | 0.526486i | \(0.823509\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.27794e6i | 1.57781i | 0.614512 | + | 0.788907i | \(0.289353\pi\) | ||||
−0.614512 | + | 0.788907i | \(0.710647\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.24506e6 | − | 1.13473e6i | 0.695969 | − | 0.243366i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.04375e6 | −1.28237 | −0.641186 | − | 0.767385i | \(-0.721557\pi\) | ||||
−0.641186 | + | 0.767385i | \(0.721557\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 699250.i | − | 0.146791i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.61007e6 | −0.334420 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.37623e6i | − | 0.282838i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.81756e6 | + | 3.53615e6i | 0.572979 | + | 0.719112i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.02201e6 | −0.205665 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.37213e6 | 1.86638 | 0.933188 | − | 0.359388i | \(-0.117014\pi\) | ||||
0.933188 | + | 0.359388i | \(0.117014\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 470382. | 0.0927017 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −726235. | −0.141648 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 108199. | + | 309424.i | 0.0208867 | + | 0.0597310i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.12157e6i | 0.596418i | 0.954501 | + | 0.298209i | \(0.0963892\pi\) | ||||
−0.954501 | + | 0.298209i | \(0.903611\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.87484e6 | 0.543677 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.79083e6i | − | 1.45841i | −0.684294 | − | 0.729206i | \(-0.739890\pi\) | ||
0.684294 | − | 0.729206i | \(-0.260110\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.96084e6 | 1.66047 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.67685e6 | − | 4.79538e6i | −0.307596 | − | 0.879651i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.86702e6i | 0.520642i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.49895e6i | 0.449268i | 0.974443 | + | 0.224634i | \(0.0721187\pi\) | ||||
−0.974443 | + | 0.224634i | \(0.927881\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.05969e6i | 0.366612i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.06363e7i | − | 1.87444i | −0.348734 | − | 0.937222i | \(-0.613388\pi\) | ||
0.348734 | − | 0.937222i | \(-0.386612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.50522e6 | − | 1.00241e7i | −0.611627 | − | 1.74911i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.91026e6 | −0.330045 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 5.62277e6i | − | 0.961958i | −0.876732 | − | 0.480979i | \(-0.840281\pi\) | ||
0.876732 | − | 0.480979i | \(-0.159719\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.81288e6 | −0.307126 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.72081e6i | 0.959763i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.13116e6 | + | 6.09461e6i | 0.354077 | + | 1.01258i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 891859. | 0.146747 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.25304e6 | −0.367155 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.57801e6 | −0.416093 | −0.208047 | − | 0.978119i | \(-0.566711\pi\) | ||||
−0.208047 | + | 0.978119i | \(0.566711\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.31533e6 | 0.689859 | 0.344929 | − | 0.938629i | \(-0.387903\pi\) | ||||
0.344929 | + | 0.938629i | \(0.387903\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −986598. | − | 1.23822e6i | −0.156222 | − | 0.196065i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.18962e7i | 1.86586i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.38151e6 | 0.680746 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 922890.i | 0.142041i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.78596e6 | −1.03465 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.81343e6 | + | 3.08188e6i | −1.33125 | + | 0.465512i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.90165e6i | 0.733511i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.00178e7i | − | 1.48526i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.44548e6i | 0.946808i | 0.880845 | + | 0.473404i | \(0.156975\pi\) | ||||
−0.880845 | + | 0.473404i | \(0.843025\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 6.34787e6i | − | 0.923907i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 334396. | + | 956293.i | 0.0482247 | + | 0.137911i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.12757e7 | −1.61130 | −0.805650 | − | 0.592392i | \(-0.798184\pi\) | ||||
−0.805650 | + | 0.592392i | \(0.798184\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 658533.i | 0.0932495i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.34901e6 | 0.890896 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.75297e6i | − | 0.521870i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −352582. | + | 123291.i | −0.0485879 | + | 0.0169902i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.41719e7 | −1.93549 | −0.967743 | − | 0.251938i | \(-0.918932\pi\) | ||||
−0.967743 | + | 0.251938i | \(0.918932\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.48068e6 | −0.200416 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.48891e7 | −1.99738 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.87590e6 | 0.382387 | 0.191194 | − | 0.981552i | \(-0.438764\pi\) | ||||
0.191194 | + | 0.981552i | \(0.438764\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 451102. | + | 1.29004e6i | 0.0594503 | + | 0.170014i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 468795.i | − | 0.0612386i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.05148e6 | −0.654091 | −0.327046 | − | 0.945009i | \(-0.606053\pi\) | ||||
−0.327046 | + | 0.945009i | \(0.606053\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.13766e6i | 0.916148i | 0.888914 | + | 0.458074i | \(0.151461\pi\) | ||||
−0.888914 | + | 0.458074i | \(0.848539\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.52788e6 | −0.830588 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.79151e6 | − | 3.50345e6i | −0.352102 | − | 0.441903i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.58999e6i | 0.448904i | 0.974485 | + | 0.224452i | \(0.0720591\pi\) | ||||
−0.974485 | + | 0.224452i | \(0.927941\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 260167.i | 0.0322520i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 417766.i | 0.0513444i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5.36542e6i | − | 0.653780i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.15935e6 | + | 1.80412e6i | −0.623312 | + | 0.217960i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.54658e6 | 0.544615 | 0.272307 | − | 0.962210i | \(-0.412213\pi\) | ||||
0.272307 | + | 0.962210i | \(0.412213\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.42877e6i | 1.00110i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.35173e6 | −0.983576 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.35478e6i | 0.742102i | 0.928613 | + | 0.371051i | \(0.121002\pi\) | ||||
−0.928613 | + | 0.371051i | \(0.878998\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.17159e6 | − | 1.80840e6i | 0.598869 | − | 0.209412i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.30822e6 | −0.954052 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.19156e6 | −0.591195 | −0.295597 | − | 0.955313i | \(-0.595519\pi\) | ||||
−0.295597 | + | 0.955313i | \(0.595519\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.30782e6 | −0.712349 | −0.356174 | − | 0.934419i | \(-0.615919\pi\) | ||||
−0.356174 | + | 0.934419i | \(0.615919\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.91689e6 | 0.214687 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.66767e7 | − | 5.83149e6i | 1.85234 | − | 0.647725i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.24819e7i | − | 1.37502i | −0.726176 | − | 0.687509i | \(-0.758704\pi\) | ||
0.726176 | − | 0.687509i | \(-0.241296\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.22318e6 | −0.242902 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 959551.i | − | 0.103984i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.20806e7 | 1.29848 | 0.649241 | − | 0.760583i | \(-0.275087\pi\) | ||||
0.649241 | + | 0.760583i | \(0.275087\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.08653e6 | − | 1.77866e6i | 0.542293 | − | 0.189629i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 4.45314e6i | − | 0.470927i | −0.971883 | − | 0.235464i | \(-0.924339\pi\) | ||
0.971883 | − | 0.235464i | \(-0.0756608\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.30525e7i | 1.36920i | 0.728920 | + | 0.684599i | \(0.240023\pi\) | ||||
−0.728920 | + | 0.684599i | \(0.759977\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 5.66792e6i | − | 0.589786i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 3.78363e6i | − | 0.390561i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.18105e6 | − | 9.51895e6i | 0.223340 | − | 0.974741i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.05493e7 | −1.07166 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.29254e6i | − | 0.130262i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −134264. | −0.0134242 | −0.00671208 | − | 0.999977i | \(-0.502137\pi\) | ||||
−0.00671208 | + | 0.999977i | \(0.502137\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.05743e6i | − | 0.104892i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.07182e6 | + | 1.45042e7i | 0.499149 | + | 1.42745i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.07782e7 | −1.05244 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.85952e6 | −0.761455 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.52563e7 | 1.46657 | 0.733286 | − | 0.679921i | \(-0.237986\pi\) | ||||
0.733286 | + | 0.679921i | \(0.237986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.40110e6 | 0.419792 | 0.209896 | − | 0.977724i | \(-0.432688\pi\) | ||||
0.209896 | + | 0.977724i | \(0.432688\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.10987e6 | − | 388099.i | 0.105044 | − | 0.0367319i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 157813.i | − | 0.0148211i | −0.999973 | − | 0.00741057i | \(-0.997641\pi\) | ||
0.999973 | − | 0.00741057i | \(-0.00235888\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.84504e6 | −0.451529 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 2.95142e6i | − | 0.272948i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.08352e6 | 0.741853 | 0.370926 | − | 0.928662i | \(-0.379040\pi\) | ||||
0.370926 | + | 0.928662i | \(0.379040\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.15652e6 | + | 9.02690e6i | 0.287479 | + | 0.822120i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4.96975e6i | − | 0.449181i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.03509e6i | 0.272244i | 0.990692 | + | 0.136122i | \(0.0434639\pi\) | ||||
−0.990692 | + | 0.136122i | \(0.956536\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.53992e6i | 0.849261i | 0.905367 | + | 0.424630i | \(0.139596\pi\) | ||||
−0.905367 | + | 0.424630i | \(0.860404\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.60191e7i | 1.41532i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.66422e6 | − | 1.28130e6i | 0.321312 | − | 0.112356i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.29031e6 | −0.547467 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.77650e6i | 0.585383i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.45720e6 | −0.296428 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.03245e7i | − | 0.878680i | −0.898321 | − | 0.439340i | \(-0.855212\pi\) | ||
0.898321 | − | 0.439340i | \(-0.144788\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.66372e6 | − | 7.69992e6i | 0.816366 | − | 0.650469i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.69059e6 | 0.644893 | 0.322447 | − | 0.946588i | \(-0.395495\pi\) | ||||
0.322447 | + | 0.946588i | \(0.395495\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 281425. | 0.0234255 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.77739e6 | −0.146864 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.58453e6 | −0.622124 | −0.311062 | − | 0.950390i | \(-0.600685\pi\) | ||||
−0.311062 | + | 0.950390i | \(0.600685\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.85176e6 | + | 1.10151e7i | 0.313641 | + | 0.896938i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.94178e6i | 0.722823i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.77265e6 | −0.463263 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.18130e6i | − | 0.173788i | −0.996218 | − | 0.0868942i | \(-0.972306\pi\) | ||
0.996218 | − | 0.0868942i | \(-0.0276942\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.36147e6 | −0.344985 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.36814e6 | − | 1.24918e7i | −0.343032 | − | 0.980990i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.86469e7i | 1.45386i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1.71252e7i | − | 1.32570i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.10413e7i | − | 0.848640i | −0.905512 | − | 0.424320i | \(-0.860513\pi\) | ||
0.905512 | − | 0.424320i | \(-0.139487\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 915803.i | − | 0.0698898i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 251506. | + | 719248.i | 0.0190579 | + | 0.0545011i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.11705e6 | −0.685971 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.52020e7i | − | 1.13575i | −0.823114 | − | 0.567876i | \(-0.807765\pi\) | ||
0.823114 | − | 0.567876i | \(-0.192235\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.02882e7 | 0.763251 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 8.35084e6i | − | 0.615186i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.47138e6 | − | 2.70859e7i | −0.692864 | − | 1.98143i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.97194e6 | −0.579117 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.01762e7 | 0.734115 | 0.367058 | − | 0.930198i | \(-0.380365\pi\) | ||||
0.367058 | + | 0.930198i | \(0.380365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.54313e6 | 0.397116 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.14855e6 | −0.152862 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.54545e6 | − | 1.07249e7i | −0.603796 | − | 0.757788i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.61142e7i | 1.13077i | 0.824828 | + | 0.565384i | \(0.191272\pi\) | ||||
−0.824828 | + | 0.565384i | \(0.808728\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.14277e7 | 0.796414 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.06871e6i | 0.281620i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 205074. | 0.0140978 | 0.00704888 | − | 0.999975i | \(-0.497756\pi\) | ||||
0.00704888 | + | 0.999975i | \(0.497756\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.07897e6 | − | 2.82505e6i | 0.551617 | − | 0.192889i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.00634e7i | 0.682460i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.90886e6i | − | 0.195935i | −0.995190 | − | 0.0979673i | \(-0.968766\pi\) | ||
0.995190 | − | 0.0979673i | \(-0.0312341\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.13500e7i | 0.759366i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.95734e7i | 1.30075i | 0.759612 | + | 0.650376i | \(0.225389\pi\) | ||||
−0.759612 | + | 0.650376i | \(0.774611\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.90793e6 | + | 8.31598e6i | 0.191952 | + | 0.548937i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.14525e6 | −0.0750927 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.01594e6i | 0.522095i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.78300e6 | −0.115359 | −0.0576795 | − | 0.998335i | \(-0.518370\pi\) | ||||
−0.0576795 | + | 0.998335i | \(0.518370\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.13756e7i | − | 0.731119i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.12733e6 | − | 1.09356e6i | 0.199667 | − | 0.0698194i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −201802. | −0.0127993 | −0.00639965 | − | 0.999980i | \(-0.502037\pi\) | ||||
−0.00639965 | + | 0.999980i | \(0.502037\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.04518e7 | 0.658546 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.89830e7 | 1.81419 | 0.907093 | − | 0.420929i | \(-0.138296\pi\) | ||||
0.907093 | + | 0.420929i | \(0.138296\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 869762. | 0.0540865 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.95747e6 | + | 1.41772e7i | 0.306271 | + | 0.875863i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.21278e6i | 0.319949i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.39742e6 | 0.0852140 | 0.0426070 | − | 0.999092i | \(-0.486434\pi\) | ||||
0.0426070 | + | 0.999092i | \(0.486434\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.95564e7i | 1.18482i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.09015e6 | 0.426783 | 0.213391 | − | 0.976967i | \(-0.431549\pi\) | ||||
0.213391 | + | 0.976967i | \(0.431549\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.42381e7 | − | 1.13447e7i | 0.851523 | − | 0.678482i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 320679.i | 0.0190554i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.32118e7i | 0.780045i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 4.12614e7i | − | 2.42056i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.73508e7i | − | 1.01138i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.04851e6 | + | 2.81440e6i | −0.466167 | + | 0.163009i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.17815e7 | 1.25358 | 0.626790 | − | 0.779188i | \(-0.284368\pi\) | ||||
0.626790 | + | 0.779188i | \(0.284368\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 9.64969e6i | − | 0.551850i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.17331e6 | 0.0666765 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.71961e6i | 0.210046i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.32699e6 | − | 1.51306e6i | 0.242811 | − | 0.0849059i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −619753. | −0.0345599 | −0.0172800 | − | 0.999851i | \(-0.505501\pi\) | ||||
−0.0172800 | + | 0.999851i | \(0.505501\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.63671e6 | −0.146115 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.03723e7 | 0.571206 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.60905e7 | 1.42789 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.63034e6 | + | 1.26946e6i | −0.197450 | + | 0.0690443i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 8.09908e6i | − | 0.437776i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.35484e7 | −0.727807 | −0.363904 | − | 0.931437i | \(-0.618556\pi\) | ||||
−0.363904 | + | 0.931437i | \(0.618556\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6.84579e6i | − | 0.365486i | −0.983161 | − | 0.182743i | \(-0.941502\pi\) | ||
0.983161 | − | 0.182743i | \(-0.0584977\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.19946e7 | 0.636443 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.43709e7 | − | 5.02520e6i | 0.757861 | − | 0.265008i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.88280e6i | 0.151098i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.69250e6i | 0.244453i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.82656e7i | − | 0.945748i | −0.881130 | − | 0.472874i | \(-0.843217\pi\) | ||
0.881130 | − | 0.472874i | \(-0.156783\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 7.70732e6i | − | 0.396647i | −0.980137 | − | 0.198323i | \(-0.936450\pi\) | ||
0.980137 | − | 0.198323i | \(-0.0635496\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.41989e7 | + | 1.78201e7i | 0.726304 | + | 0.911542i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.91726e7 | −0.974804 | −0.487402 | − | 0.873178i | \(-0.662055\pi\) | ||||
−0.487402 | + | 0.873178i | \(0.662055\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.76259e6i | 0.442839i | 0.975179 | + | 0.221420i | \(0.0710690\pi\) | ||||
−0.975179 | + | 0.221420i | \(0.928931\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.43978e7 | −0.723257 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.96169e7i | 1.47886i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.60032e6 | + | 1.02961e7i | 0.178700 | + | 0.511040i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.30344e7 | 1.13649 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.21316e6 | −0.0594992 | −0.0297496 | − | 0.999557i | \(-0.509471\pi\) | ||||
−0.0297496 | + | 0.999557i | \(0.509471\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.25504e6 | 0.0611880 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.56477e7 | −0.758371 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.54911e6 | + | 3.33913e6i | −0.460067 | + | 0.160876i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.51676e7i | − | 0.726457i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.10016e6 | −0.385678 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 907336.i | 0.0429481i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.29210e7 | −1.54917 | −0.774586 | − | 0.632468i | \(-0.782042\pi\) | ||||
−0.774586 | + | 0.632468i | \(0.782042\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.51251e6 | + | 1.00449e7i | 0.164324 | + | 0.469929i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 3.37640e7i | − | 1.57037i | −0.619261 | − | 0.785185i | \(-0.712568\pi\) | ||
0.619261 | − | 0.785185i | \(-0.287432\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.06943e7i | − | 0.956905i | −0.878114 | − | 0.478452i | \(-0.841198\pi\) | ||
0.878114 | − | 0.478452i | \(-0.158802\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 4.62627e6i | − | 0.212678i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.64284e7i | 0.750878i | 0.926847 | + | 0.375439i | \(0.122508\pi\) | ||||
−0.926847 | + | 0.375439i | \(0.877492\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.12626e7 | + | 3.93830e6i | −0.511797 | + | 0.178965i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.90301e7 | 1.31160 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.40118e7i | 2.42627i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.08272e7 | 0.483585 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 771488.i | 0.0342605i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.09626e6 | − | 4.46511e6i | −0.313335 | − | 0.197157i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.39642e7 | −0.613080 | −0.306540 | − | 0.951858i | \(-0.599171\pi\) | ||||
−0.306540 | + | 0.951858i | \(0.599171\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.36594e6 | −0.146938 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.00733e7 | −1.30540 | −0.652698 | − | 0.757619i | \(-0.726363\pi\) | ||||
−0.652698 | + | 0.757619i | \(0.726363\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.25984e7 | 0.543768 | 0.271884 | − | 0.962330i | \(-0.412353\pi\) | ||||
0.271884 | + | 0.962330i | \(0.412353\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.36631e6 | − | 3.90733e6i | −0.0586397 | − | 0.167696i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 3.03915e7i | − | 1.29701i | −0.761210 | − | 0.648505i | \(-0.775394\pi\) | ||
0.761210 | − | 0.648505i | \(-0.224606\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.31918e7 | 0.559821 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.74677e6i | 0.284709i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.86819e6 | −0.0783955 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.56806e6 | + | 2.45026e7i | 0.357540 | + | 1.02248i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1.12451e7i | − | 0.466640i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2.55639e7i | − | 1.05494i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.58624e7i | 0.650965i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.00944e6i | − | 0.0411967i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.10961e7 | − | 3.17321e7i | −0.450347 | − | 1.28788i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.34696e7 | −0.947302 | −0.473651 | − | 0.880713i | \(-0.657064\pi\) | ||||
−0.473651 | + | 0.880713i | \(0.657064\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2.49931e7i | − | 1.00325i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.87754e7 | −1.14875 | −0.574375 | − | 0.818592i | \(-0.694755\pi\) | ||||
−0.574375 | + | 0.818592i | \(0.694755\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 6.01238e6i | − | 0.238709i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −974939. | − | 2.78809e6i | −0.0384968 | − | 0.110092i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.21009e6 | 0.322422 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.30665e7 | −0.510352 | −0.255176 | − | 0.966895i | \(-0.582133\pi\) | ||||
−0.255176 | + | 0.966895i | \(0.582133\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.21043e6 | −0.0858673 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.43931e7 | −1.71519 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.54700e6 | + | 1.23263e6i | −0.0594476 | + | 0.0473671i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.51957e7i | 0.580793i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.53760e7 | −0.964682 | −0.482341 | − | 0.875984i | \(-0.660213\pi\) | ||||
−0.482341 | + | 0.875984i | \(0.660213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.09845e7i | 0.793457i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.00811e6 | 0.263570 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.44282e7 | + | 2.60260e7i | −2.78425 | + | 0.973596i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.55239e7i | 0.577634i | 0.957384 | + | 0.288817i | \(0.0932619\pi\) | ||||
−0.957384 | + | 0.288817i | \(0.906738\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.01384e7i | 0.375237i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.21463e7i | 1.55162i | 0.630967 | + | 0.775810i | \(0.282658\pi\) | ||||
−0.630967 | + | 0.775810i | \(0.717342\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.30897e7i | − | 0.479347i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.50159e6 | − | 1.00137e7i | −0.127552 | − | 0.364767i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.64274e7 | 1.68228 | 0.841142 | − | 0.540815i | \(-0.181884\pi\) | ||||
0.841142 | + | 0.540815i | \(0.181884\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2.80708e7i | − | 1.01179i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.11186e7 | −0.398656 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.05749e6i | 0.287387i | 0.989622 | + | 0.143694i | \(0.0458980\pi\) | ||||
−0.989622 | + | 0.143694i | \(0.954102\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.26319e7 | + | 1.14107e7i | −1.15780 | + | 0.404860i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.19954e7 | 1.12929 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.00184e7 | 0.351764 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.30870e6 | 0.185430 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.19746e7 | −0.763580 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 454771. | + | 1.30054e6i | 0.0157208 | + | 0.0449577i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.92356e6i | 0.272492i | 0.990675 | + | 0.136246i | \(0.0435038\pi\) | ||||
−0.990675 | + | 0.136246i | \(0.956496\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.11883e7 | 1.06704 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.11594e7i | 0.379831i | 0.981800 | + | 0.189916i | \(0.0608215\pi\) | ||||
−0.981800 | + | 0.189916i | \(0.939179\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.13615e7 | −0.384728 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.91727e7 | − | 1.52766e7i | 0.645910 | − | 0.514652i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 3.69540e7i | − | 1.23858i | −0.785162 | − | 0.619291i | \(-0.787420\pi\) | ||
0.785162 | − | 0.619291i | \(-0.212580\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.44530e7i | 1.81579i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.38433e6i | 0.0791031i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 3.73269e7i | − | 1.23208i | −0.787716 | − | 0.616038i | \(-0.788737\pi\) | ||
0.787716 | − | 0.616038i | \(-0.211263\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.17491e7 | + | 1.45988e7i | −1.37106 | + | 0.479432i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 654166. | 0.0213744 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2.85614e6i | − | 0.0928515i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.74561e6 | 0.0888084 | 0.0444042 | − | 0.999014i | \(-0.485861\pi\) | ||||
0.0444042 | + | 0.999014i | \(0.485861\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1.35672e7i | − | 0.436635i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.15316e7 | + | 1.45227e7i | −1.32990 | + | 0.465040i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.93328e7 | 1.25319 | 0.626595 | − | 0.779345i | \(-0.284448\pi\) | ||||
0.626595 | + | 0.779345i | \(0.284448\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.50274e6 | −0.0793419 |
(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 | 160.6.f.a.49.10 | 28 | ||
4.3 | odd | 2 | 40.6.f.a.29.5 | ✓ | 28 | ||
5.2 | odd | 4 | 800.6.d.e.401.10 | 28 | |||
5.3 | odd | 4 | 800.6.d.e.401.19 | 28 | |||
5.4 | even | 2 | inner | 160.6.f.a.49.19 | 28 | ||
8.3 | odd | 2 | 40.6.f.a.29.23 | yes | 28 | ||
8.5 | even | 2 | inner | 160.6.f.a.49.20 | 28 | ||
20.3 | even | 4 | 200.6.d.e.101.10 | 28 | |||
20.7 | even | 4 | 200.6.d.e.101.19 | 28 | |||
20.19 | odd | 2 | 40.6.f.a.29.24 | yes | 28 | ||
40.3 | even | 4 | 200.6.d.e.101.9 | 28 | |||
40.13 | odd | 4 | 800.6.d.e.401.20 | 28 | |||
40.19 | odd | 2 | 40.6.f.a.29.6 | yes | 28 | ||
40.27 | even | 4 | 200.6.d.e.101.20 | 28 | |||
40.29 | even | 2 | inner | 160.6.f.a.49.9 | 28 | ||
40.37 | odd | 4 | 800.6.d.e.401.9 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.f.a.29.5 | ✓ | 28 | 4.3 | odd | 2 | ||
40.6.f.a.29.6 | yes | 28 | 40.19 | odd | 2 | ||
40.6.f.a.29.23 | yes | 28 | 8.3 | odd | 2 | ||
40.6.f.a.29.24 | yes | 28 | 20.19 | odd | 2 | ||
160.6.f.a.49.9 | 28 | 40.29 | even | 2 | inner | ||
160.6.f.a.49.10 | 28 | 1.1 | even | 1 | trivial | ||
160.6.f.a.49.19 | 28 | 5.4 | even | 2 | inner | ||
160.6.f.a.49.20 | 28 | 8.5 | even | 2 | inner | ||
200.6.d.e.101.9 | 28 | 40.3 | even | 4 | |||
200.6.d.e.101.10 | 28 | 20.3 | even | 4 | |||
200.6.d.e.101.19 | 28 | 20.7 | even | 4 | |||
200.6.d.e.101.20 | 28 | 40.27 | even | 4 | |||
800.6.d.e.401.9 | 28 | 40.37 | odd | 4 | |||
800.6.d.e.401.10 | 28 | 5.2 | odd | 4 | |||
800.6.d.e.401.19 | 28 | 5.3 | odd | 4 | |||
800.6.d.e.401.20 | 28 | 40.13 | odd | 4 |