Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,6,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (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: | \(4.00959549532\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.6.b.a.24.2 |
$q$-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 \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.00000i | − 0.353553i | −0.984251 | − | 0.176777i | \(-0.943433\pi\) | ||||
0.984251 | − | 0.176777i | \(-0.0565670\pi\) | |||||||
\(3\) | − 4.00000i | − 0.256600i | −0.991735 | − | 0.128300i | \(-0.959048\pi\) | ||||
0.991735 | − | 0.128300i | \(-0.0409521\pi\) | |||||||
\(4\) | 28.0000 | 0.875000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −8.00000 | −0.0907218 | ||||||||
\(7\) | − 192.000i | − 1.48100i | −0.672054 | − | 0.740502i | \(-0.734588\pi\) | ||||
0.672054 | − | 0.740502i | \(-0.265412\pi\) | |||||||
\(8\) | − 120.000i | − 0.662913i | ||||||||
\(9\) | 227.000 | 0.934156 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −148.000 | −0.368791 | −0.184395 | − | 0.982852i | \(-0.559033\pi\) | ||||
−0.184395 | + | 0.982852i | \(0.559033\pi\) | |||||||
\(12\) | − 112.000i | − 0.224525i | ||||||||
\(13\) | 286.000i | 0.469362i | 0.972072 | + | 0.234681i | \(0.0754045\pi\) | ||||
−0.972072 | + | 0.234681i | \(0.924595\pi\) | |||||||
\(14\) | −384.000 | −0.523614 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 656.000 | 0.640625 | ||||||||
\(17\) | 1678.00i | 1.40822i | 0.710092 | + | 0.704109i | \(0.248653\pi\) | ||||
−0.710092 | + | 0.704109i | \(0.751347\pi\) | |||||||
\(18\) | − 454.000i | − 0.330274i | ||||||||
\(19\) | −1060.00 | −0.673631 | −0.336815 | − | 0.941571i | \(-0.609350\pi\) | ||||
−0.336815 | + | 0.941571i | \(0.609350\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −768.000 | −0.380026 | ||||||||
\(22\) | 296.000i | 0.130387i | ||||||||
\(23\) | 2976.00i | 1.17304i | 0.809934 | + | 0.586521i | \(0.199503\pi\) | ||||
−0.809934 | + | 0.586521i | \(0.800497\pi\) | |||||||
\(24\) | −480.000 | −0.170103 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 572.000 | 0.165944 | ||||||||
\(27\) | − 1880.00i | − 0.496305i | ||||||||
\(28\) | − 5376.00i | − 1.29588i | ||||||||
\(29\) | 3410.00 | 0.752938 | 0.376469 | − | 0.926429i | \(-0.377138\pi\) | ||||
0.376469 | + | 0.926429i | \(0.377138\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2448.00 | −0.457517 | −0.228758 | − | 0.973483i | \(-0.573467\pi\) | ||||
−0.228758 | + | 0.973483i | \(0.573467\pi\) | |||||||
\(32\) | − 5152.00i | − 0.889408i | ||||||||
\(33\) | 592.000i | 0.0946317i | ||||||||
\(34\) | 3356.00 | 0.497880 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6356.00 | 0.817387 | ||||||||
\(37\) | − 182.000i | − 0.0218558i | −0.999940 | − | 0.0109279i | \(-0.996521\pi\) | ||||
0.999940 | − | 0.0109279i | \(-0.00347853\pi\) | |||||||
\(38\) | 2120.00i | 0.238164i | ||||||||
\(39\) | 1144.00 | 0.120438 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9398.00 | −0.873124 | −0.436562 | − | 0.899674i | \(-0.643804\pi\) | ||||
−0.436562 | + | 0.899674i | \(0.643804\pi\) | |||||||
\(42\) | 1536.00i | 0.134359i | ||||||||
\(43\) | − 1244.00i | − 0.102600i | −0.998683 | − | 0.0513002i | \(-0.983663\pi\) | ||||
0.998683 | − | 0.0513002i | \(-0.0163365\pi\) | |||||||
\(44\) | −4144.00 | −0.322692 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5952.00 | 0.414733 | ||||||||
\(47\) | 12088.0i | 0.798196i | 0.916908 | + | 0.399098i | \(0.130677\pi\) | ||||
−0.916908 | + | 0.399098i | \(0.869323\pi\) | |||||||
\(48\) | − 2624.00i | − 0.164384i | ||||||||
\(49\) | −20057.0 | −1.19337 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6712.00 | 0.361349 | ||||||||
\(52\) | 8008.00i | 0.410691i | ||||||||
\(53\) | 23846.0i | 1.16607i | 0.812446 | + | 0.583037i | \(0.198136\pi\) | ||||
−0.812446 | + | 0.583037i | \(0.801864\pi\) | |||||||
\(54\) | −3760.00 | −0.175470 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −23040.0 | −0.981776 | ||||||||
\(57\) | 4240.00i | 0.172854i | ||||||||
\(58\) | − 6820.00i | − 0.266204i | ||||||||
\(59\) | 20020.0 | 0.748745 | 0.374373 | − | 0.927278i | \(-0.377858\pi\) | ||||
0.374373 | + | 0.927278i | \(0.377858\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 32302.0 | 1.11149 | 0.555744 | − | 0.831353i | \(-0.312433\pi\) | ||||
0.555744 | + | 0.831353i | \(0.312433\pi\) | |||||||
\(62\) | 4896.00i | 0.161757i | ||||||||
\(63\) | − 43584.0i | − 1.38349i | ||||||||
\(64\) | 10688.0 | 0.326172 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1184.00 | 0.0334574 | ||||||||
\(67\) | − 60972.0i | − 1.65937i | −0.558231 | − | 0.829685i | \(-0.688520\pi\) | ||||
0.558231 | − | 0.829685i | \(-0.311480\pi\) | |||||||
\(68\) | 46984.0i | 1.23219i | ||||||||
\(69\) | 11904.0 | 0.301003 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −32648.0 | −0.768618 | −0.384309 | − | 0.923204i | \(-0.625560\pi\) | ||||
−0.384309 | + | 0.923204i | \(0.625560\pi\) | |||||||
\(72\) | − 27240.0i | − 0.619264i | ||||||||
\(73\) | − 38774.0i | − 0.851596i | −0.904818 | − | 0.425798i | \(-0.859993\pi\) | ||||
0.904818 | − | 0.425798i | \(-0.140007\pi\) | |||||||
\(74\) | −364.000 | −0.00772720 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −29680.0 | −0.589427 | ||||||||
\(77\) | 28416.0i | 0.546180i | ||||||||
\(78\) | − 2288.00i | − 0.0425814i | ||||||||
\(79\) | 33360.0 | 0.601393 | 0.300696 | − | 0.953720i | \(-0.402781\pi\) | ||||
0.300696 | + | 0.953720i | \(0.402781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 47641.0 | 0.806805 | ||||||||
\(82\) | 18796.0i | 0.308696i | ||||||||
\(83\) | 16716.0i | 0.266340i | 0.991093 | + | 0.133170i | \(0.0425157\pi\) | ||||
−0.991093 | + | 0.133170i | \(0.957484\pi\) | |||||||
\(84\) | −21504.0 | −0.332522 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2488.00 | −0.0362747 | ||||||||
\(87\) | − 13640.0i | − 0.193204i | ||||||||
\(88\) | 17760.0i | 0.244476i | ||||||||
\(89\) | −101370. | −1.35655 | −0.678273 | − | 0.734810i | \(-0.737271\pi\) | ||||
−0.678273 | + | 0.734810i | \(0.737271\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 54912.0 | 0.695126 | ||||||||
\(92\) | 83328.0i | 1.02641i | ||||||||
\(93\) | 9792.00i | 0.117399i | ||||||||
\(94\) | 24176.0 | 0.282205 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −20608.0 | −0.228222 | ||||||||
\(97\) | 119038.i | 1.28457i | 0.766468 | + | 0.642283i | \(0.222013\pi\) | ||||
−0.766468 | + | 0.642283i | \(0.777987\pi\) | |||||||
\(98\) | 40114.0i | 0.421921i | ||||||||
\(99\) | −33596.0 | −0.344508 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −89898.0 | −0.876893 | −0.438446 | − | 0.898757i | \(-0.644471\pi\) | ||||
−0.438446 | + | 0.898757i | \(0.644471\pi\) | |||||||
\(102\) | − 13424.0i | − 0.127756i | ||||||||
\(103\) | − 19504.0i | − 0.181147i | −0.995890 | − | 0.0905734i | \(-0.971130\pi\) | ||||
0.995890 | − | 0.0905734i | \(-0.0288700\pi\) | |||||||
\(104\) | 34320.0 | 0.311146 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 47692.0 | 0.412269 | ||||||||
\(107\) | − 158292.i | − 1.33659i | −0.743895 | − | 0.668297i | \(-0.767024\pi\) | ||||
0.743895 | − | 0.668297i | \(-0.232976\pi\) | |||||||
\(108\) | − 52640.0i | − 0.434267i | ||||||||
\(109\) | −36830.0 | −0.296917 | −0.148459 | − | 0.988919i | \(-0.547431\pi\) | ||||
−0.148459 | + | 0.988919i | \(0.547431\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −728.000 | −0.00560821 | ||||||||
\(112\) | − 125952.i | − 0.948768i | ||||||||
\(113\) | 11186.0i | 0.0824098i | 0.999151 | + | 0.0412049i | \(0.0131196\pi\) | ||||
−0.999151 | + | 0.0412049i | \(0.986880\pi\) | |||||||
\(114\) | 8480.00 | 0.0611130 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 95480.0 | 0.658821 | ||||||||
\(117\) | 64922.0i | 0.438457i | ||||||||
\(118\) | − 40040.0i | − 0.264721i | ||||||||
\(119\) | 322176. | 2.08557 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −139147. | −0.863993 | ||||||||
\(122\) | − 64604.0i | − 0.392970i | ||||||||
\(123\) | 37592.0i | 0.224044i | ||||||||
\(124\) | −68544.0 | −0.400327 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −87168.0 | −0.489137 | ||||||||
\(127\) | − 70552.0i | − 0.388150i | −0.980987 | − | 0.194075i | \(-0.937829\pi\) | ||||
0.980987 | − | 0.194075i | \(-0.0621706\pi\) | |||||||
\(128\) | − 186240.i | − 1.00473i | ||||||||
\(129\) | −4976.00 | −0.0263273 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 76452.0 | 0.389234 | 0.194617 | − | 0.980879i | \(-0.437654\pi\) | ||||
0.194617 | + | 0.980879i | \(0.437654\pi\) | |||||||
\(132\) | 16576.0i | 0.0828028i | ||||||||
\(133\) | 203520.i | 0.997650i | ||||||||
\(134\) | −121944. | −0.586676 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 201360. | 0.933525 | ||||||||
\(137\) | 144918.i | 0.659661i | 0.944040 | + | 0.329831i | \(0.106992\pi\) | ||||
−0.944040 | + | 0.329831i | \(0.893008\pi\) | |||||||
\(138\) | − 23808.0i | − 0.106420i | ||||||||
\(139\) | −112220. | −0.492644 | −0.246322 | − | 0.969188i | \(-0.579222\pi\) | ||||
−0.246322 | + | 0.969188i | \(0.579222\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 48352.0 | 0.204817 | ||||||||
\(142\) | 65296.0i | 0.271748i | ||||||||
\(143\) | − 42328.0i | − 0.173096i | ||||||||
\(144\) | 148912. | 0.598444 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −77548.0 | −0.301085 | ||||||||
\(147\) | 80228.0i | 0.306219i | ||||||||
\(148\) | − 5096.00i | − 0.0191238i | ||||||||
\(149\) | −403750. | −1.48986 | −0.744932 | − | 0.667140i | \(-0.767518\pi\) | ||||
−0.744932 | + | 0.667140i | \(0.767518\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −446648. | −1.59413 | −0.797064 | − | 0.603895i | \(-0.793615\pi\) | ||||
−0.797064 | + | 0.603895i | \(0.793615\pi\) | |||||||
\(152\) | 127200.i | 0.446558i | ||||||||
\(153\) | 380906.i | 1.31550i | ||||||||
\(154\) | 56832.0 | 0.193104 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 32032.0 | 0.105383 | ||||||||
\(157\) | 262258.i | 0.849141i | 0.905395 | + | 0.424570i | \(0.139575\pi\) | ||||
−0.905395 | + | 0.424570i | \(0.860425\pi\) | |||||||
\(158\) | − 66720.0i | − 0.212625i | ||||||||
\(159\) | 95384.0 | 0.299215 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 571392. | 1.73728 | ||||||||
\(162\) | − 95282.0i | − 0.285248i | ||||||||
\(163\) | − 154564.i | − 0.455658i | −0.973701 | − | 0.227829i | \(-0.926837\pi\) | ||||
0.973701 | − | 0.227829i | \(-0.0731628\pi\) | |||||||
\(164\) | −263144. | −0.763983 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 33432.0 | 0.0941656 | ||||||||
\(167\) | − 396672.i | − 1.10063i | −0.834958 | − | 0.550314i | \(-0.814508\pi\) | ||||
0.834958 | − | 0.550314i | \(-0.185492\pi\) | |||||||
\(168\) | 92160.0i | 0.251924i | ||||||||
\(169\) | 289497. | 0.779700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −240620. | −0.629276 | ||||||||
\(172\) | − 34832.0i | − 0.0897754i | ||||||||
\(173\) | − 573474.i | − 1.45680i | −0.685155 | − | 0.728398i | \(-0.740265\pi\) | ||||
0.685155 | − | 0.728398i | \(-0.259735\pi\) | |||||||
\(174\) | −27280.0 | −0.0683079 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −97088.0 | −0.236257 | ||||||||
\(177\) | − 80080.0i | − 0.192128i | ||||||||
\(178\) | 202740.i | 0.479611i | ||||||||
\(179\) | 594460. | 1.38672 | 0.693362 | − | 0.720589i | \(-0.256129\pi\) | ||||
0.693362 | + | 0.720589i | \(0.256129\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −107098. | −0.242988 | −0.121494 | − | 0.992592i | \(-0.538769\pi\) | ||||
−0.121494 | + | 0.992592i | \(0.538769\pi\) | |||||||
\(182\) | − 109824.i | − 0.245764i | ||||||||
\(183\) | − 129208.i | − 0.285208i | ||||||||
\(184\) | 357120. | 0.777624 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 19584.0 | 0.0415068 | ||||||||
\(187\) | − 248344.i | − 0.519337i | ||||||||
\(188\) | 338464.i | 0.698422i | ||||||||
\(189\) | −360960. | −0.735029 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 469552. | 0.931323 | 0.465661 | − | 0.884963i | \(-0.345816\pi\) | ||||
0.465661 | + | 0.884963i | \(0.345816\pi\) | |||||||
\(192\) | − 42752.0i | − 0.0836957i | ||||||||
\(193\) | 52706.0i | 0.101851i | 0.998702 | + | 0.0509257i | \(0.0162172\pi\) | ||||
−0.998702 | + | 0.0509257i | \(0.983783\pi\) | |||||||
\(194\) | 238076. | 0.454163 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −561596. | −1.04420 | ||||||||
\(197\) | − 455862.i | − 0.836889i | −0.908242 | − | 0.418444i | \(-0.862575\pi\) | ||||
0.908242 | − | 0.418444i | \(-0.137425\pi\) | |||||||
\(198\) | 67192.0i | 0.121802i | ||||||||
\(199\) | −865000. | −1.54840 | −0.774200 | − | 0.632940i | \(-0.781848\pi\) | ||||
−0.774200 | + | 0.632940i | \(0.781848\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −243888. | −0.425795 | ||||||||
\(202\) | 179796.i | 0.310028i | ||||||||
\(203\) | − 654720.i | − 1.11510i | ||||||||
\(204\) | 187936. | 0.316180 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −39008.0 | −0.0640451 | ||||||||
\(207\) | 675552.i | 1.09580i | ||||||||
\(208\) | 187616.i | 0.300685i | ||||||||
\(209\) | 156880. | 0.248429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.10565e6 | 1.70967 | 0.854835 | − | 0.518900i | \(-0.173658\pi\) | ||||
0.854835 | + | 0.518900i | \(0.173658\pi\) | |||||||
\(212\) | 667688.i | 1.02031i | ||||||||
\(213\) | 130592.i | 0.197228i | ||||||||
\(214\) | −316584. | −0.472557 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −225600. | −0.329007 | ||||||||
\(217\) | 470016.i | 0.677584i | ||||||||
\(218\) | 73660.0i | 0.104976i | ||||||||
\(219\) | −155096. | −0.218520 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −479908. | −0.660963 | ||||||||
\(222\) | 1456.00i | 0.00198280i | ||||||||
\(223\) | 1.12158e6i | 1.51031i | 0.655545 | + | 0.755156i | \(0.272439\pi\) | ||||
−0.655545 | + | 0.755156i | \(0.727561\pi\) | |||||||
\(224\) | −989184. | −1.31722 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 22372.0 | 0.0291363 | ||||||||
\(227\) | 23348.0i | 0.0300736i | 0.999887 | + | 0.0150368i | \(0.00478654\pi\) | ||||
−0.999887 | + | 0.0150368i | \(0.995213\pi\) | |||||||
\(228\) | 118720.i | 0.151247i | ||||||||
\(229\) | 596010. | 0.751043 | 0.375522 | − | 0.926814i | \(-0.377464\pi\) | ||||
0.375522 | + | 0.926814i | \(0.377464\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 113664. | 0.140150 | ||||||||
\(232\) | − 409200.i | − 0.499132i | ||||||||
\(233\) | − 485334.i | − 0.585667i | −0.956163 | − | 0.292834i | \(-0.905402\pi\) | ||||
0.956163 | − | 0.292834i | \(-0.0945982\pi\) | |||||||
\(234\) | 129844. | 0.155018 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 560560. | 0.655152 | ||||||||
\(237\) | − 133440.i | − 0.154317i | ||||||||
\(238\) | − 644352.i | − 0.737362i | ||||||||
\(239\) | 48880.0 | 0.0553524 | 0.0276762 | − | 0.999617i | \(-0.491189\pi\) | ||||
0.0276762 | + | 0.999617i | \(0.491189\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −110798. | −0.122882 | −0.0614411 | − | 0.998111i | \(-0.519570\pi\) | ||||
−0.0614411 | + | 0.998111i | \(0.519570\pi\) | |||||||
\(242\) | 278294.i | 0.305468i | ||||||||
\(243\) | − 647404.i | − 0.703331i | ||||||||
\(244\) | 904456. | 0.972552 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 75184.0 | 0.0792114 | ||||||||
\(247\) | − 303160.i | − 0.316176i | ||||||||
\(248\) | 293760.i | 0.303294i | ||||||||
\(249\) | 66864.0 | 0.0683430 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.64375e6 | −1.64684 | −0.823419 | − | 0.567434i | \(-0.807936\pi\) | ||||
−0.823419 | + | 0.567434i | \(0.807936\pi\) | |||||||
\(252\) | − 1.22035e6i | − 1.21055i | ||||||||
\(253\) | − 440448.i | − 0.432607i | ||||||||
\(254\) | −141104. | −0.137232 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −30464.0 | −0.0290527 | ||||||||
\(257\) | − 1.30624e6i | − 1.23365i | −0.787102 | − | 0.616823i | \(-0.788419\pi\) | ||||
0.787102 | − | 0.616823i | \(-0.211581\pi\) | |||||||
\(258\) | 9952.00i | 0.00930810i | ||||||||
\(259\) | −34944.0 | −0.0323685 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 774070. | 0.703362 | ||||||||
\(262\) | − 152904.i | − 0.137615i | ||||||||
\(263\) | 2.12834e6i | 1.89736i | 0.316231 | + | 0.948682i | \(0.397583\pi\) | ||||
−0.316231 | + | 0.948682i | \(0.602417\pi\) | |||||||
\(264\) | 71040.0 | 0.0627326 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 407040. | 0.352722 | ||||||||
\(267\) | 405480.i | 0.348090i | ||||||||
\(268\) | − 1.70722e6i | − 1.45195i | ||||||||
\(269\) | 1.44109e6 | 1.21426 | 0.607128 | − | 0.794604i | \(-0.292321\pi\) | ||||
0.607128 | + | 0.794604i | \(0.292321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −93248.0 | −0.0771288 | −0.0385644 | − | 0.999256i | \(-0.512278\pi\) | ||||
−0.0385644 | + | 0.999256i | \(0.512278\pi\) | |||||||
\(272\) | 1.10077e6i | 0.902139i | ||||||||
\(273\) | − 219648.i | − 0.178370i | ||||||||
\(274\) | 289836. | 0.233225 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 333312. | 0.263377 | ||||||||
\(277\) | 110298.i | 0.0863711i | 0.999067 | + | 0.0431855i | \(0.0137507\pi\) | ||||
−0.999067 | + | 0.0431855i | \(0.986249\pi\) | |||||||
\(278\) | 224440.i | 0.174176i | ||||||||
\(279\) | −555696. | −0.427392 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −192198. | −0.145205 | −0.0726027 | − | 0.997361i | \(-0.523131\pi\) | ||||
−0.0726027 | + | 0.997361i | \(0.523131\pi\) | |||||||
\(282\) | − 96704.0i | − 0.0724139i | ||||||||
\(283\) | − 331884.i | − 0.246332i | −0.992386 | − | 0.123166i | \(-0.960695\pi\) | ||||
0.992386 | − | 0.123166i | \(-0.0393047\pi\) | |||||||
\(284\) | −914144. | −0.672541 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −84656.0 | −0.0611988 | ||||||||
\(287\) | 1.80442e6i | 1.29310i | ||||||||
\(288\) | − 1.16950e6i | − 0.830846i | ||||||||
\(289\) | −1.39583e6 | −0.983076 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 476152. | 0.329620 | ||||||||
\(292\) | − 1.08567e6i | − 0.745146i | ||||||||
\(293\) | 2.19481e6i | 1.49358i | 0.665063 | + | 0.746788i | \(0.268405\pi\) | ||||
−0.665063 | + | 0.746788i | \(0.731595\pi\) | |||||||
\(294\) | 160456. | 0.108265 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −21840.0 | −0.0144885 | ||||||||
\(297\) | 278240.i | 0.183033i | ||||||||
\(298\) | 807500.i | 0.526747i | ||||||||
\(299\) | −851136. | −0.550581 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −238848. | −0.151952 | ||||||||
\(302\) | 893296.i | 0.563609i | ||||||||
\(303\) | 359592.i | 0.225011i | ||||||||
\(304\) | −695360. | −0.431545 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 761812. | 0.465098 | ||||||||
\(307\) | 2.37751e6i | 1.43971i | 0.694123 | + | 0.719857i | \(0.255793\pi\) | ||||
−0.694123 | + | 0.719857i | \(0.744207\pi\) | |||||||
\(308\) | 795648.i | 0.477908i | ||||||||
\(309\) | −78016.0 | −0.0464823 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.37305e6 | −1.39125 | −0.695626 | − | 0.718405i | \(-0.744873\pi\) | ||||
−0.695626 | + | 0.718405i | \(0.744873\pi\) | |||||||
\(312\) | − 137280.i | − 0.0798400i | ||||||||
\(313\) | − 1.42941e6i | − 0.824702i | −0.911025 | − | 0.412351i | \(-0.864708\pi\) | ||||
0.911025 | − | 0.412351i | \(-0.135292\pi\) | |||||||
\(314\) | 524516. | 0.300217 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 934080. | 0.526219 | ||||||||
\(317\) | − 2.12462e6i | − 1.18750i | −0.804650 | − | 0.593750i | \(-0.797647\pi\) | ||||
0.804650 | − | 0.593750i | \(-0.202353\pi\) | |||||||
\(318\) | − 190768.i | − 0.105788i | ||||||||
\(319\) | −504680. | −0.277677 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −633168. | −0.342970 | ||||||||
\(322\) | − 1.14278e6i | − 0.614221i | ||||||||
\(323\) | − 1.77868e6i | − 0.948618i | ||||||||
\(324\) | 1.33395e6 | 0.705954 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −309128. | −0.161100 | ||||||||
\(327\) | 147320.i | 0.0761890i | ||||||||
\(328\) | 1.12776e6i | 0.578805i | ||||||||
\(329\) | 2.32090e6 | 1.18213 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.09985e6 | 1.55515 | 0.777573 | − | 0.628793i | \(-0.216451\pi\) | ||||
0.777573 | + | 0.628793i | \(0.216451\pi\) | |||||||
\(332\) | 468048.i | 0.233048i | ||||||||
\(333\) | − 41314.0i | − 0.0204168i | ||||||||
\(334\) | −793344. | −0.389131 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −503808. | −0.243454 | ||||||||
\(337\) | − 2.40008e6i | − 1.15120i | −0.817731 | − | 0.575601i | \(-0.804768\pi\) | ||||
0.817731 | − | 0.575601i | \(-0.195232\pi\) | |||||||
\(338\) | − 578994.i | − 0.275665i | ||||||||
\(339\) | 44744.0 | 0.0211464 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 362304. | 0.168728 | ||||||||
\(342\) | 481240.i | 0.222483i | ||||||||
\(343\) | 624000.i | 0.286384i | ||||||||
\(344\) | −149280. | −0.0680151 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.14695e6 | −0.515055 | ||||||||
\(347\) | − 1.77741e6i | − 0.792436i | −0.918156 | − | 0.396218i | \(-0.870322\pi\) | ||||
0.918156 | − | 0.396218i | \(-0.129678\pi\) | |||||||
\(348\) | − 381920.i | − 0.169054i | ||||||||
\(349\) | 2.14805e6 | 0.944019 | 0.472010 | − | 0.881593i | \(-0.343529\pi\) | ||||
0.472010 | + | 0.881593i | \(0.343529\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 537680. | 0.232946 | ||||||||
\(352\) | 762496.i | 0.328005i | ||||||||
\(353\) | − 661854.i | − 0.282700i | −0.989960 | − | 0.141350i | \(-0.954856\pi\) | ||||
0.989960 | − | 0.141350i | \(-0.0451443\pi\) | |||||||
\(354\) | −160160. | −0.0679275 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.83836e6 | −1.18698 | ||||||||
\(357\) | − 1.28870e6i | − 0.535159i | ||||||||
\(358\) | − 1.18892e6i | − 0.490281i | ||||||||
\(359\) | 259320. | 0.106194 | 0.0530970 | − | 0.998589i | \(-0.483091\pi\) | ||||
0.0530970 | + | 0.998589i | \(0.483091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.35250e6 | −0.546222 | ||||||||
\(362\) | 214196.i | 0.0859093i | ||||||||
\(363\) | 556588.i | 0.221701i | ||||||||
\(364\) | 1.53754e6 | 0.608236 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −258416. | −0.100836 | ||||||||
\(367\) | 1.49993e6i | 0.581307i | 0.956828 | + | 0.290653i | \(0.0938726\pi\) | ||||
−0.956828 | + | 0.290653i | \(0.906127\pi\) | |||||||
\(368\) | 1.95226e6i | 0.751480i | ||||||||
\(369\) | −2.13335e6 | −0.815634 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.57843e6 | 1.72696 | ||||||||
\(372\) | 274176.i | 0.102724i | ||||||||
\(373\) | − 2.23807e6i | − 0.832918i | −0.909154 | − | 0.416459i | \(-0.863271\pi\) | ||||
0.909154 | − | 0.416459i | \(-0.136729\pi\) | |||||||
\(374\) | −496688. | −0.183614 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.45056e6 | 0.529135 | ||||||||
\(377\) | 975260.i | 0.353400i | ||||||||
\(378\) | 721920.i | 0.259872i | ||||||||
\(379\) | −3.15934e6 | −1.12979 | −0.564896 | − | 0.825162i | \(-0.691084\pi\) | ||||
−0.564896 | + | 0.825162i | \(0.691084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −282208. | −0.0995994 | ||||||||
\(382\) | − 939104.i | − 0.329272i | ||||||||
\(383\) | 342216.i | 0.119207i | 0.998222 | + | 0.0596037i | \(0.0189837\pi\) | ||||
−0.998222 | + | 0.0596037i | \(0.981016\pi\) | |||||||
\(384\) | −744960. | −0.257813 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 105412. | 0.0360099 | ||||||||
\(387\) | − 282388.i | − 0.0958449i | ||||||||
\(388\) | 3.33306e6i | 1.12399i | ||||||||
\(389\) | −88470.0 | −0.0296430 | −0.0148215 | − | 0.999890i | \(-0.504718\pi\) | ||||
−0.0148215 | + | 0.999890i | \(0.504718\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.99373e6 | −1.65190 | ||||||||
\(392\) | 2.40684e6i | 0.791101i | ||||||||
\(393\) | − 305808.i | − 0.0998775i | ||||||||
\(394\) | −911724. | −0.295885 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −940688. | −0.301445 | ||||||||
\(397\) | 5.45674e6i | 1.73763i | 0.495138 | + | 0.868814i | \(0.335117\pi\) | ||||
−0.495138 | + | 0.868814i | \(0.664883\pi\) | |||||||
\(398\) | 1.73000e6i | 0.547442i | ||||||||
\(399\) | 814080. | 0.255997 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.04680e6 | 1.25676 | 0.628378 | − | 0.777908i | \(-0.283719\pi\) | ||||
0.628378 | + | 0.777908i | \(0.283719\pi\) | |||||||
\(402\) | 487776.i | 0.150541i | ||||||||
\(403\) | − 700128.i | − 0.214741i | ||||||||
\(404\) | −2.51714e6 | −0.767281 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.30944e6 | −0.394249 | ||||||||
\(407\) | 26936.0i | 0.00806022i | ||||||||
\(408\) | − 805440.i | − 0.239543i | ||||||||
\(409\) | 2.71207e6 | 0.801664 | 0.400832 | − | 0.916151i | \(-0.368721\pi\) | ||||
0.400832 | + | 0.916151i | \(0.368721\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 579672. | 0.169269 | ||||||||
\(412\) | − 546112.i | − 0.158503i | ||||||||
\(413\) | − 3.84384e6i | − 1.10889i | ||||||||
\(414\) | 1.35110e6 | 0.387425 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.47347e6 | 0.417454 | ||||||||
\(417\) | 448880.i | 0.126413i | ||||||||
\(418\) | − 313760.i | − 0.0878328i | ||||||||
\(419\) | −3.71746e6 | −1.03445 | −0.517227 | − | 0.855848i | \(-0.673036\pi\) | ||||
−0.517227 | + | 0.855848i | \(0.673036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.55250e6 | 0.976853 | 0.488426 | − | 0.872605i | \(-0.337571\pi\) | ||||
0.488426 | + | 0.872605i | \(0.337571\pi\) | |||||||
\(422\) | − 2.21130e6i | − 0.604460i | ||||||||
\(423\) | 2.74398e6i | 0.745640i | ||||||||
\(424\) | 2.86152e6 | 0.773005 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 261184. | 0.0697305 | ||||||||
\(427\) | − 6.20198e6i | − 1.64612i | ||||||||
\(428\) | − 4.43218e6i | − 1.16952i | ||||||||
\(429\) | −169312. | −0.0444165 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.06205e6 | −1.05330 | −0.526650 | − | 0.850082i | \(-0.676552\pi\) | ||||
−0.526650 | + | 0.850082i | \(0.676552\pi\) | |||||||
\(432\) | − 1.23328e6i | − 0.317945i | ||||||||
\(433\) | 7.26287e6i | 1.86161i | 0.365518 | + | 0.930804i | \(0.380892\pi\) | ||||
−0.365518 | + | 0.930804i | \(0.619108\pi\) | |||||||
\(434\) | 940032. | 0.239562 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.03124e6 | −0.259803 | ||||||||
\(437\) | − 3.15456e6i | − 0.790197i | ||||||||
\(438\) | 310192.i | 0.0772583i | ||||||||
\(439\) | 5.41028e6 | 1.33986 | 0.669928 | − | 0.742426i | \(-0.266325\pi\) | ||||
0.669928 | + | 0.742426i | \(0.266325\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.55294e6 | −1.11480 | ||||||||
\(442\) | 959816.i | 0.233686i | ||||||||
\(443\) | − 6.51524e6i | − 1.57733i | −0.614826 | − | 0.788663i | \(-0.710774\pi\) | ||||
0.614826 | − | 0.788663i | \(-0.289226\pi\) | |||||||
\(444\) | −20384.0 | −0.00490718 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.24315e6 | 0.533976 | ||||||||
\(447\) | 1.61500e6i | 0.382299i | ||||||||
\(448\) | − 2.05210e6i | − 0.483062i | ||||||||
\(449\) | 509950. | 0.119375 | 0.0596873 | − | 0.998217i | \(-0.480990\pi\) | ||||
0.0596873 | + | 0.998217i | \(0.480990\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.39090e6 | 0.322000 | ||||||||
\(452\) | 313208.i | 0.0721085i | ||||||||
\(453\) | 1.78659e6i | 0.409053i | ||||||||
\(454\) | 46696.0 | 0.0106326 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 508800. | 0.114587 | ||||||||
\(457\) | − 1.22084e6i | − 0.273444i | −0.990609 | − | 0.136722i | \(-0.956343\pi\) | ||||
0.990609 | − | 0.136722i | \(-0.0436568\pi\) | |||||||
\(458\) | − 1.19202e6i | − 0.265534i | ||||||||
\(459\) | 3.15464e6 | 0.698905 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.07210e6 | −0.892413 | −0.446207 | − | 0.894930i | \(-0.647225\pi\) | ||||
−0.446207 | + | 0.894930i | \(0.647225\pi\) | |||||||
\(462\) | − 227328.i | − 0.0495505i | ||||||||
\(463\) | 2.02294e6i | 0.438561i | 0.975662 | + | 0.219280i | \(0.0703709\pi\) | ||||
−0.975662 | + | 0.219280i | \(0.929629\pi\) | |||||||
\(464\) | 2.23696e6 | 0.482351 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −970668. | −0.207065 | ||||||||
\(467\) | − 3.25097e6i | − 0.689797i | −0.938640 | − | 0.344898i | \(-0.887913\pi\) | ||||
0.938640 | − | 0.344898i | \(-0.112087\pi\) | |||||||
\(468\) | 1.81782e6i | 0.383650i | ||||||||
\(469\) | −1.17066e7 | −2.45753 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.04903e6 | 0.217890 | ||||||||
\(472\) | − 2.40240e6i | − 0.496353i | ||||||||
\(473\) | 184112.i | 0.0378381i | ||||||||
\(474\) | −266880. | −0.0545595 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.02093e6 | 1.82488 | ||||||||
\(477\) | 5.41304e6i | 1.08929i | ||||||||
\(478\) | − 97760.0i | − 0.0195700i | ||||||||
\(479\) | 3.27936e6 | 0.653056 | 0.326528 | − | 0.945188i | \(-0.394121\pi\) | ||||
0.326528 | + | 0.945188i | \(0.394121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 52052.0 | 0.0102583 | ||||||||
\(482\) | 221596.i | 0.0434455i | ||||||||
\(483\) | − 2.28557e6i | − 0.445786i | ||||||||
\(484\) | −3.89612e6 | −0.755994 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.29481e6 | −0.248665 | ||||||||
\(487\) | 8.53197e6i | 1.63015i | 0.579357 | + | 0.815074i | \(0.303304\pi\) | ||||
−0.579357 | + | 0.815074i | \(0.696696\pi\) | |||||||
\(488\) | − 3.87624e6i | − 0.736819i | ||||||||
\(489\) | −618256. | −0.116922 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.51265e6 | 0.283162 | 0.141581 | − | 0.989927i | \(-0.454781\pi\) | ||||
0.141581 | + | 0.989927i | \(0.454781\pi\) | |||||||
\(492\) | 1.05258e6i | 0.196038i | ||||||||
\(493\) | 5.72198e6i | 1.06030i | ||||||||
\(494\) | −606320. | −0.111785 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.60589e6 | −0.293097 | ||||||||
\(497\) | 6.26842e6i | 1.13833i | ||||||||
\(498\) | − 133728.i | − 0.0241629i | ||||||||
\(499\) | 6.49190e6 | 1.16713 | 0.583567 | − | 0.812065i | \(-0.301657\pi\) | ||||
0.583567 | + | 0.812065i | \(0.301657\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.58669e6 | −0.282421 | ||||||||
\(502\) | 3.28750e6i | 0.582245i | ||||||||
\(503\) | 8.61770e6i | 1.51870i | 0.650684 | + | 0.759349i | \(0.274482\pi\) | ||||
−0.650684 | + | 0.759349i | \(0.725518\pi\) | |||||||
\(504\) | −5.23008e6 | −0.917132 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −880896. | −0.152950 | ||||||||
\(507\) | − 1.15799e6i | − 0.200071i | ||||||||
\(508\) | − 1.97546e6i | − 0.339632i | ||||||||
\(509\) | −2.67323e6 | −0.457343 | −0.228671 | − | 0.973504i | \(-0.573438\pi\) | ||||
−0.228671 | + | 0.973504i | \(0.573438\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.44461e6 | −1.26122 | ||||||||
\(512\) | − 5.89875e6i | − 0.994455i | ||||||||
\(513\) | 1.99280e6i | 0.334326i | ||||||||
\(514\) | −2.61248e6 | −0.436160 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −139328. | −0.0230364 | ||||||||
\(517\) | − 1.78902e6i | − 0.294367i | ||||||||
\(518\) | 69888.0i | 0.0114440i | ||||||||
\(519\) | −2.29390e6 | −0.373814 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.18500e6 | 0.998264 | 0.499132 | − | 0.866526i | \(-0.333652\pi\) | ||||
0.499132 | + | 0.866526i | \(0.333652\pi\) | |||||||
\(522\) | − 1.54814e6i | − 0.248676i | ||||||||
\(523\) | − 6.89452e6i | − 1.10217i | −0.834448 | − | 0.551087i | \(-0.814213\pi\) | ||||
0.834448 | − | 0.551087i | \(-0.185787\pi\) | |||||||
\(524\) | 2.14066e6 | 0.340580 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.25667e6 | 0.670820 | ||||||||
\(527\) | − 4.10774e6i | − 0.644283i | ||||||||
\(528\) | 388352.i | 0.0606235i | ||||||||
\(529\) | −2.42023e6 | −0.376026 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.54454e6 | 0.699445 | ||||||||
\(532\) | 5.69856e6i | 0.872943i | ||||||||
\(533\) | − 2.68783e6i | − 0.409811i | ||||||||
\(534\) | 810960. | 0.123068 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.31664e6 | −1.10002 | ||||||||
\(537\) | − 2.37784e6i | − 0.355834i | ||||||||
\(538\) | − 2.88218e6i | − 0.429304i | ||||||||
\(539\) | 2.96844e6 | 0.440104 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 155502. | 0.0228425 | 0.0114212 | − | 0.999935i | \(-0.496364\pi\) | ||||
0.0114212 | + | 0.999935i | \(0.496364\pi\) | |||||||
\(542\) | 186496.i | 0.0272691i | ||||||||
\(543\) | 428392.i | 0.0623508i | ||||||||
\(544\) | 8.64506e6 | 1.25248 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −439296. | −0.0630631 | ||||||||
\(547\) | − 1.26544e7i | − 1.80831i | −0.427201 | − | 0.904157i | \(-0.640500\pi\) | ||||
0.427201 | − | 0.904157i | \(-0.359500\pi\) | |||||||
\(548\) | 4.05770e6i | 0.577204i | ||||||||
\(549\) | 7.33255e6 | 1.03830 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.61460e6 | −0.507202 | ||||||||
\(552\) | − 1.42848e6i | − 0.199538i | ||||||||
\(553\) | − 6.40512e6i | − 0.890665i | ||||||||
\(554\) | 220596. | 0.0305368 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.14216e6 | −0.431064 | ||||||||
\(557\) | 7.07786e6i | 0.966638i | 0.875444 | + | 0.483319i | \(0.160569\pi\) | ||||
−0.875444 | + | 0.483319i | \(0.839431\pi\) | |||||||
\(558\) | 1.11139e6i | 0.151106i | ||||||||
\(559\) | 355784. | 0.0481567 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −993376. | −0.133262 | ||||||||
\(562\) | 384396.i | 0.0513379i | ||||||||
\(563\) | 846636.i | 0.112571i | 0.998415 | + | 0.0562854i | \(0.0179257\pi\) | ||||
−0.998415 | + | 0.0562854i | \(0.982074\pi\) | |||||||
\(564\) | 1.35386e6 | 0.179215 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −663768. | −0.0870914 | ||||||||
\(567\) | − 9.14707e6i | − 1.19488i | ||||||||
\(568\) | 3.91776e6i | 0.509527i | ||||||||
\(569\) | −4.96041e6 | −0.642299 | −0.321149 | − | 0.947029i | \(-0.604069\pi\) | ||||
−0.321149 | + | 0.947029i | \(0.604069\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.96505e6 | 1.15070 | 0.575351 | − | 0.817907i | \(-0.304866\pi\) | ||||
0.575351 | + | 0.817907i | \(0.304866\pi\) | |||||||
\(572\) | − 1.18518e6i | − 0.151459i | ||||||||
\(573\) | − 1.87821e6i | − 0.238978i | ||||||||
\(574\) | 3.60883e6 | 0.457180 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.42618e6 | 0.304696 | ||||||||
\(577\) | 2.86080e6i | 0.357724i | 0.983874 | + | 0.178862i | \(0.0572415\pi\) | ||||
−0.983874 | + | 0.178862i | \(0.942758\pi\) | |||||||
\(578\) | 2.79165e6i | 0.347570i | ||||||||
\(579\) | 210824. | 0.0261351 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.20947e6 | 0.394451 | ||||||||
\(582\) | − 952304.i | − 0.116538i | ||||||||
\(583\) | − 3.52921e6i | − 0.430037i | ||||||||
\(584\) | −4.65288e6 | −0.564534 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.38961e6 | 0.528059 | ||||||||
\(587\) | 6.74027e6i | 0.807387i | 0.914894 | + | 0.403694i | \(0.132274\pi\) | ||||
−0.914894 | + | 0.403694i | \(0.867726\pi\) | |||||||
\(588\) | 2.24638e6i | 0.267942i | ||||||||
\(589\) | 2.59488e6 | 0.308197 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.82345e6 | −0.214746 | ||||||||
\(592\) | − 119392.i | − 0.0140014i | ||||||||
\(593\) | − 1.78609e6i | − 0.208578i | −0.994547 | − | 0.104289i | \(-0.966743\pi\) | ||||
0.994547 | − | 0.104289i | \(-0.0332566\pi\) | |||||||
\(594\) | 556480. | 0.0647118 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.13050e7 | −1.30363 | ||||||||
\(597\) | 3.46000e6i | 0.397320i | ||||||||
\(598\) | 1.70227e6i | 0.194660i | ||||||||
\(599\) | −4.94620e6 | −0.563254 | −0.281627 | − | 0.959524i | \(-0.590874\pi\) | ||||
−0.281627 | + | 0.959524i | \(0.590874\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.58100e6 | −0.517337 | −0.258669 | − | 0.965966i | \(-0.583284\pi\) | ||||
−0.258669 | + | 0.965966i | \(0.583284\pi\) | |||||||
\(602\) | 477696.i | 0.0537230i | ||||||||
\(603\) | − 1.38406e7i | − 1.55011i | ||||||||
\(604\) | −1.25061e7 | −1.39486 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 719184. | 0.0795533 | ||||||||
\(607\) | − 7.07999e6i | − 0.779940i | −0.920828 | − | 0.389970i | \(-0.872485\pi\) | ||||
0.920828 | − | 0.389970i | \(-0.127515\pi\) | |||||||
\(608\) | 5.46112e6i | 0.599132i | ||||||||
\(609\) | −2.61888e6 | −0.286136 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.45717e6 | −0.374643 | ||||||||
\(612\) | 1.06654e7i | 1.15106i | ||||||||
\(613\) | 5.09609e6i | 0.547754i | 0.961765 | + | 0.273877i | \(0.0883061\pi\) | ||||
−0.961765 | + | 0.273877i | \(0.911694\pi\) | |||||||
\(614\) | 4.75502e6 | 0.509016 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.40992e6 | 0.362070 | ||||||||
\(617\) | 1.30003e7i | 1.37480i | 0.726279 | + | 0.687400i | \(0.241248\pi\) | ||||
−0.726279 | + | 0.687400i | \(0.758752\pi\) | |||||||
\(618\) | 156032.i | 0.0164340i | ||||||||
\(619\) | −4.84406e6 | −0.508139 | −0.254070 | − | 0.967186i | \(-0.581769\pi\) | ||||
−0.254070 | + | 0.967186i | \(0.581769\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.59488e6 | 0.582186 | ||||||||
\(622\) | 4.74610e6i | 0.491882i | ||||||||
\(623\) | 1.94630e7i | 2.00905i | ||||||||
\(624\) | 750464. | 0.0771558 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.85883e6 | −0.291576 | ||||||||
\(627\) | − 627520.i | − 0.0637468i | ||||||||
\(628\) | 7.34322e6i | 0.742998i | ||||||||
\(629\) | 305396. | 0.0307777 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.22775e6 | 0.622670 | 0.311335 | − | 0.950300i | \(-0.399224\pi\) | ||||
0.311335 | + | 0.950300i | \(0.399224\pi\) | |||||||
\(632\) | − 4.00320e6i | − 0.398671i | ||||||||
\(633\) | − 4.42261e6i | − 0.438702i | ||||||||
\(634\) | −4.24924e6 | −0.419845 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.67075e6 | 0.261813 | ||||||||
\(637\) | − 5.73630e6i | − 0.560123i | ||||||||
\(638\) | 1.00936e6i | 0.0981735i | ||||||||
\(639\) | −7.41110e6 | −0.718010 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.53280e6 | 0.147347 | 0.0736734 | − | 0.997282i | \(-0.476528\pi\) | ||||
0.0736734 | + | 0.997282i | \(0.476528\pi\) | |||||||
\(642\) | 1.26634e6i | 0.121258i | ||||||||
\(643\) | − 1.74382e7i | − 1.66332i | −0.555287 | − | 0.831659i | \(-0.687391\pi\) | ||||
0.555287 | − | 0.831659i | \(-0.312609\pi\) | |||||||
\(644\) | 1.59990e7 | 1.52012 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.55736e6 | −0.335387 | ||||||||
\(647\) | 4.25469e6i | 0.399583i | 0.979838 | + | 0.199792i | \(0.0640265\pi\) | ||||
−0.979838 | + | 0.199792i | \(0.935974\pi\) | |||||||
\(648\) | − 5.71692e6i | − 0.534841i | ||||||||
\(649\) | −2.96296e6 | −0.276130 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.88006e6 | 0.173868 | ||||||||
\(652\) | − 4.32779e6i | − 0.398701i | ||||||||
\(653\) | 3.01085e6i | 0.276316i | 0.990410 | + | 0.138158i | \(0.0441181\pi\) | ||||
−0.990410 | + | 0.138158i | \(0.955882\pi\) | |||||||
\(654\) | 294640. | 0.0269369 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.16509e6 | −0.559345 | ||||||||
\(657\) | − 8.80170e6i | − 0.795524i | ||||||||
\(658\) | − 4.64179e6i | − 0.417947i | ||||||||
\(659\) | 8.11462e6 | 0.727871 | 0.363936 | − | 0.931424i | \(-0.381433\pi\) | ||||
0.363936 | + | 0.931424i | \(0.381433\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.47370e6 | 0.220213 | 0.110107 | − | 0.993920i | \(-0.464881\pi\) | ||||
0.110107 | + | 0.993920i | \(0.464881\pi\) | |||||||
\(662\) | − 6.19970e6i | − 0.549827i | ||||||||
\(663\) | 1.91963e6i | 0.169603i | ||||||||
\(664\) | 2.00592e6 | 0.176560 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −82628.0 | −0.00721841 | ||||||||
\(667\) | 1.01482e7i | 0.883228i | ||||||||
\(668\) | − 1.11068e7i | − 0.963049i | ||||||||
\(669\) | 4.48630e6 | 0.387546 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.78070e6 | −0.409907 | ||||||||
\(672\) | 3.95674e6i | 0.337998i | ||||||||
\(673\) | 5.77063e6i | 0.491117i | 0.969382 | + | 0.245559i | \(0.0789714\pi\) | ||||
−0.969382 | + | 0.245559i | \(0.921029\pi\) | |||||||
\(674\) | −4.80016e6 | −0.407011 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.10592e6 | 0.682237 | ||||||||
\(677\) | − 1.67197e7i | − 1.40203i | −0.713147 | − | 0.701014i | \(-0.752731\pi\) | ||||
0.713147 | − | 0.701014i | \(-0.247269\pi\) | |||||||
\(678\) | − 89488.0i | − 0.00747637i | ||||||||
\(679\) | 2.28553e7 | 1.90245 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 93392.0 | 0.00771688 | ||||||||
\(682\) | − 724608.i | − 0.0596544i | ||||||||
\(683\) | 7.14532e6i | 0.586097i | 0.956098 | + | 0.293049i | \(0.0946698\pi\) | ||||
−0.956098 | + | 0.293049i | \(0.905330\pi\) | |||||||
\(684\) | −6.73736e6 | −0.550617 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.24800e6 | 0.101252 | ||||||||
\(687\) | − 2.38404e6i | − 0.192718i | ||||||||
\(688\) | − 816064.i | − 0.0657284i | ||||||||
\(689\) | −6.81996e6 | −0.547310 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.78395e6 | −0.699833 | −0.349917 | − | 0.936781i | \(-0.613790\pi\) | ||||
−0.349917 | + | 0.936781i | \(0.613790\pi\) | |||||||
\(692\) | − 1.60573e7i | − 1.27470i | ||||||||
\(693\) | 6.45043e6i | 0.510218i | ||||||||
\(694\) | −3.55482e6 | −0.280169 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.63680e6 | −0.128077 | ||||||||
\(697\) | − 1.57698e7i | − 1.22955i | ||||||||
\(698\) | − 4.29610e6i | − 0.333761i | ||||||||
\(699\) | −1.94134e6 | −0.150282 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.60141e7 | −1.23086 | −0.615428 | − | 0.788193i | \(-0.711017\pi\) | ||||
−0.615428 | + | 0.788193i | \(0.711017\pi\) | |||||||
\(702\) | − 1.07536e6i | − 0.0823590i | ||||||||
\(703\) | 192920.i | 0.0147228i | ||||||||
\(704\) | −1.58182e6 | −0.120289 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.32371e6 | −0.0999495 | ||||||||
\(707\) | 1.72604e7i | 1.29868i | ||||||||
\(708\) | − 2.24224e6i | − 0.168112i | ||||||||
\(709\) | 1.91354e7 | 1.42962 | 0.714811 | − | 0.699318i | \(-0.246513\pi\) | ||||
0.714811 | + | 0.699318i | \(0.246513\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.57272e6 | 0.561795 | ||||||||
\(712\) | 1.21644e7i | 0.899271i | ||||||||
\(713\) | − 7.28525e6i | − 0.536686i | ||||||||
\(714\) | −2.57741e6 | −0.189207 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.66449e7 | 1.21338 | ||||||||
\(717\) | − 195520.i | − 0.0142034i | ||||||||
\(718\) | − 518640.i | − 0.0375452i | ||||||||
\(719\) | −1.02934e7 | −0.742566 | −0.371283 | − | 0.928520i | \(-0.621082\pi\) | ||||
−0.371283 | + | 0.928520i | \(0.621082\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.74477e6 | −0.268279 | ||||||||
\(722\) | 2.70500e6i | 0.193119i | ||||||||
\(723\) | 443192.i | 0.0315316i | ||||||||
\(724\) | −2.99874e6 | −0.212615 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.11318e6 | 0.0783831 | ||||||||
\(727\) | 1.93264e7i | 1.35618i | 0.734981 | + | 0.678088i | \(0.237191\pi\) | ||||
−0.734981 | + | 0.678088i | \(0.762809\pi\) | |||||||
\(728\) | − 6.58944e6i | − 0.460808i | ||||||||
\(729\) | 8.98715e6 | 0.626330 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.08743e6 | 0.144484 | ||||||||
\(732\) | − 3.61782e6i | − 0.249557i | ||||||||
\(733\) | 5.26197e6i | 0.361733i | 0.983508 | + | 0.180866i | \(0.0578902\pi\) | ||||
−0.983508 | + | 0.180866i | \(0.942110\pi\) | |||||||
\(734\) | 2.99986e6 | 0.205523 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.53324e7 | 1.04331 | ||||||||
\(737\) | 9.02386e6i | 0.611961i | ||||||||
\(738\) | 4.26669e6i | 0.288370i | ||||||||
\(739\) | −2.82944e7 | −1.90585 | −0.952927 | − | 0.303199i | \(-0.901945\pi\) | ||||
−0.952927 | + | 0.303199i | \(0.901945\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.21264e6 | −0.0811309 | ||||||||
\(742\) | − 9.15686e6i | − 0.610572i | ||||||||
\(743\) | 2.09863e7i | 1.39464i | 0.716759 | + | 0.697321i | \(0.245625\pi\) | ||||
−0.716759 | + | 0.697321i | \(0.754375\pi\) | |||||||
\(744\) | 1.17504e6 | 0.0778252 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.47615e6 | −0.294481 | ||||||||
\(747\) | 3.79453e6i | 0.248804i | ||||||||
\(748\) | − 6.95363e6i | − 0.454420i | ||||||||
\(749\) | −3.03921e7 | −1.97950 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.89668e7 | −1.22714 | −0.613572 | − | 0.789639i | \(-0.710268\pi\) | ||||
−0.613572 | + | 0.789639i | \(0.710268\pi\) | |||||||
\(752\) | 7.92973e6i | 0.511345i | ||||||||
\(753\) | 6.57499e6i | 0.422579i | ||||||||
\(754\) | 1.95052e6 | 0.124946 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.01069e7 | −0.643151 | ||||||||
\(757\) | 1.08257e7i | 0.686617i | 0.939223 | + | 0.343309i | \(0.111548\pi\) | ||||
−0.939223 | + | 0.343309i | \(0.888452\pi\) | |||||||
\(758\) | 6.31868e6i | 0.399442i | ||||||||
\(759\) | −1.76179e6 | −0.111007 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.90534e7 | 1.19264 | 0.596322 | − | 0.802745i | \(-0.296628\pi\) | ||||
0.596322 | + | 0.802745i | \(0.296628\pi\) | |||||||
\(762\) | 564416.i | 0.0352137i | ||||||||
\(763\) | 7.07136e6i | 0.439736i | ||||||||
\(764\) | 1.31475e7 | 0.814908 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 684432. | 0.0421462 | ||||||||
\(767\) | 5.72572e6i | 0.351432i | ||||||||
\(768\) | 121856.i | 0.00745494i | ||||||||
\(769\) | 1.57826e7 | 0.962415 | 0.481208 | − | 0.876607i | \(-0.340198\pi\) | ||||
0.481208 | + | 0.876607i | \(0.340198\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.22497e6 | −0.316554 | ||||||||
\(772\) | 1.47577e6i | 0.0891199i | ||||||||
\(773\) | − 2.44049e7i | − 1.46902i | −0.678598 | − | 0.734510i | \(-0.737412\pi\) | ||||
0.678598 | − | 0.734510i | \(-0.262588\pi\) | |||||||
\(774\) | −564776. | −0.0338863 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.42846e7 | 0.851555 | ||||||||
\(777\) | 139776.i | 0.00830577i | ||||||||
\(778\) | 176940.i | 0.0104804i | ||||||||
\(779\) | 9.96188e6 | 0.588163 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.83190e6 | 0.283459 | ||||||||
\(782\) | 9.98746e6i | 0.584034i | ||||||||
\(783\) | − 6.41080e6i | − 0.373687i | ||||||||
\(784\) | −1.31574e7 | −0.764504 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −611616. | −0.0353120 | ||||||||
\(787\) | − 3.37607e7i | − 1.94301i | −0.237019 | − | 0.971505i | \(-0.576170\pi\) | ||||
0.237019 | − | 0.971505i | \(-0.423830\pi\) | |||||||
\(788\) | − 1.27641e7i | − 0.732278i | ||||||||
\(789\) | 8.51334e6 | 0.486864 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.14771e6 | 0.122049 | ||||||||
\(792\) | 4.03152e6i | 0.228379i | ||||||||
\(793\) | 9.23837e6i | 0.521690i | ||||||||
\(794\) | 1.09135e7 | 0.614344 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.42200e7 | −1.35485 | ||||||||
\(797\) | − 2.19885e7i | − 1.22617i | −0.790019 | − | 0.613083i | \(-0.789929\pi\) | ||||
0.790019 | − | 0.613083i | \(-0.210071\pi\) | |||||||
\(798\) | − 1.62816e6i | − 0.0905086i | ||||||||
\(799\) | −2.02837e7 | −1.12403 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.30110e7 | −1.26723 | ||||||||
\(802\) | − 8.09360e6i | − 0.444330i | ||||||||
\(803\) | 5.73855e6i | 0.314061i | ||||||||
\(804\) | −6.82886e6 | −0.372570 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.40026e6 | −0.0759224 | ||||||||
\(807\) | − 5.76436e6i | − 0.311578i | ||||||||
\(808\) | 1.07878e7i | 0.581303i | ||||||||
\(809\) | 2.93597e7 | 1.57717 | 0.788587 | − | 0.614923i | \(-0.210813\pi\) | ||||
0.788587 | + | 0.614923i | \(0.210813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.17703e7 | 1.69617 | 0.848083 | − | 0.529863i | \(-0.177757\pi\) | ||||
0.848083 | + | 0.529863i | \(0.177757\pi\) | |||||||
\(812\) | − 1.83322e7i | − 0.975716i | ||||||||
\(813\) | 372992.i | 0.0197912i | ||||||||
\(814\) | 53872.0 | 0.00284972 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.40307e6 | 0.231489 | ||||||||
\(817\) | 1.31864e6i | 0.0691148i | ||||||||
\(818\) | − 5.42414e6i | − 0.283431i | ||||||||
\(819\) | 1.24650e7 | 0.649357 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.71430e6 | −0.140540 | −0.0702699 | − | 0.997528i | \(-0.522386\pi\) | ||||
−0.0702699 | + | 0.997528i | \(0.522386\pi\) | |||||||
\(822\) | − 1.15934e6i | − 0.0598457i | ||||||||
\(823\) | − 1.25866e7i | − 0.647753i | −0.946099 | − | 0.323877i | \(-0.895014\pi\) | ||||
0.946099 | − | 0.323877i | \(-0.104986\pi\) | |||||||
\(824\) | −2.34048e6 | −0.120084 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.68768e6 | −0.392053 | ||||||||
\(827\) | 8.72355e6i | 0.443537i | 0.975099 | + | 0.221768i | \(0.0711828\pi\) | ||||
−0.975099 | + | 0.221768i | \(0.928817\pi\) | |||||||
\(828\) | 1.89155e7i | 0.958829i | ||||||||
\(829\) | 1.06178e7 | 0.536597 | 0.268299 | − | 0.963336i | \(-0.413539\pi\) | ||||
0.268299 | + | 0.963336i | \(0.413539\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 441192. | 0.0221628 | ||||||||
\(832\) | 3.05677e6i | 0.153093i | ||||||||
\(833\) | − 3.36556e7i | − 1.68053i | ||||||||
\(834\) | 897760. | 0.0446936 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.39264e6 | 0.217375 | ||||||||
\(837\) | 4.60224e6i | 0.227068i | ||||||||
\(838\) | 7.43492e6i | 0.365735i | ||||||||
\(839\) | −1.67765e7 | −0.822805 | −0.411403 | − | 0.911454i | \(-0.634961\pi\) | ||||
−0.411403 | + | 0.911454i | \(0.634961\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.88305e6 | −0.433084 | ||||||||
\(842\) | − 7.10500e6i | − 0.345370i | ||||||||
\(843\) | 768792.i | 0.0372597i | ||||||||
\(844\) | 3.09583e7 | 1.49596 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.48795e6 | 0.263624 | ||||||||
\(847\) | 2.67162e7i | 1.27958i | ||||||||
\(848\) | 1.56430e7i | 0.747016i | ||||||||
\(849\) | −1.32754e6 | −0.0632087 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 541632. | 0.0256378 | ||||||||
\(852\) | 3.65658e6i | 0.172574i | ||||||||
\(853\) | − 2.20186e7i | − 1.03613i | −0.855340 | − | 0.518067i | \(-0.826652\pi\) | ||||
0.855340 | − | 0.518067i | \(-0.173348\pi\) | |||||||
\(854\) | −1.24040e7 | −0.581991 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.89950e7 | −0.886045 | ||||||||
\(857\) | − 3.16676e7i | − 1.47287i | −0.676510 | − | 0.736434i | \(-0.736508\pi\) | ||||
0.676510 | − | 0.736434i | \(-0.263492\pi\) | |||||||
\(858\) | 338624.i | 0.0157036i | ||||||||
\(859\) | −1.58064e7 | −0.730886 | −0.365443 | − | 0.930834i | \(-0.619082\pi\) | ||||
−0.365443 | + | 0.930834i | \(0.619082\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.21766e6 | 0.331809 | ||||||||
\(862\) | 8.12410e6i | 0.372398i | ||||||||
\(863\) | − 1.44287e7i | − 0.659476i | −0.944072 | − | 0.329738i | \(-0.893040\pi\) | ||||
0.944072 | − | 0.329738i | \(-0.106960\pi\) | |||||||
\(864\) | −9.68576e6 | −0.441417 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.45257e7 | 0.658178 | ||||||||
\(867\) | 5.58331e6i | 0.252257i | ||||||||
\(868\) | 1.31604e7i | 0.592886i | ||||||||
\(869\) | −4.93728e6 | −0.221788 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.74380e7 | 0.778845 | ||||||||
\(872\) | 4.41960e6i | 0.196830i | ||||||||
\(873\) | 2.70216e7i | 1.19999i | ||||||||
\(874\) | −6.30912e6 | −0.279377 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.34269e6 | −0.191205 | ||||||||
\(877\) | − 247902.i | − 0.0108838i | −0.999985 | − | 0.00544191i | \(-0.998268\pi\) | ||||
0.999985 | − | 0.00544191i | \(-0.00173222\pi\) | |||||||
\(878\) | − 1.08206e7i | − 0.473711i | ||||||||
\(879\) | 8.77922e6 | 0.383252 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.10268e7 | 1.78085 | 0.890426 | − | 0.455128i | \(-0.150406\pi\) | ||||
0.890426 | + | 0.455128i | \(0.150406\pi\) | |||||||
\(882\) | 9.10588e6i | 0.394140i | ||||||||
\(883\) | 4.18015e7i | 1.80422i | 0.431503 | + | 0.902112i | \(0.357984\pi\) | ||||
−0.431503 | + | 0.902112i | \(0.642016\pi\) | |||||||
\(884\) | −1.34374e7 | −0.578343 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.30305e7 | −0.557669 | ||||||||
\(887\) | 2.10476e7i | 0.898241i | 0.893471 | + | 0.449120i | \(0.148263\pi\) | ||||
−0.893471 | + | 0.449120i | \(0.851737\pi\) | |||||||
\(888\) | 87360.0i | 0.00371775i | ||||||||
\(889\) | −1.35460e7 | −0.574852 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.05087e6 | −0.297542 | ||||||||
\(892\) | 3.14041e7i | 1.32152i | ||||||||
\(893\) | − 1.28133e7i | − 0.537690i | ||||||||
\(894\) | 3.23000e6 | 0.135163 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.57581e7 | −1.48800 | ||||||||
\(897\) | 3.40454e6i | 0.141279i | ||||||||
\(898\) | − 1.01990e6i | − 0.0422053i | ||||||||
\(899\) | −8.34768e6 | −0.344482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00136e7 | −1.64208 | ||||||||
\(902\) | − 2.78181e6i | − 0.113844i | ||||||||
\(903\) | 955392.i | 0.0389908i | ||||||||
\(904\) | 1.34232e6 | 0.0546305 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.57318e6 | 0.144622 | ||||||||
\(907\) | − 7.48309e6i | − 0.302039i | −0.988531 | − | 0.151019i | \(-0.951744\pi\) | ||||
0.988531 | − | 0.151019i | \(-0.0482556\pi\) | |||||||
\(908\) | 653744.i | 0.0263144i | ||||||||
\(909\) | −2.04068e7 | −0.819155 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.63165e6 | −0.264744 | −0.132372 | − | 0.991200i | \(-0.542259\pi\) | ||||
−0.132372 | + | 0.991200i | \(0.542259\pi\) | |||||||
\(912\) | 2.78144e6i | 0.110734i | ||||||||
\(913\) | − 2.47397e6i | − 0.0982239i | ||||||||
\(914\) | −2.44168e6 | −0.0966772 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.66883e7 | 0.657163 | ||||||||
\(917\) | − 1.46788e7i | − 0.576457i | ||||||||
\(918\) | − 6.30928e6i | − 0.247100i | ||||||||
\(919\) | 1.68976e7 | 0.659990 | 0.329995 | − | 0.943983i | \(-0.392953\pi\) | ||||
0.329995 | + | 0.943983i | \(0.392953\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.51003e6 | 0.369431 | ||||||||
\(922\) | 8.14420e6i | 0.315516i | ||||||||
\(923\) | − 9.33733e6i | − 0.360760i | ||||||||
\(924\) | 3.18259e6 | 0.122631 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.04587e6 | 0.155055 | ||||||||
\(927\) | − 4.42741e6i | − 0.169219i | ||||||||
\(928\) | − 1.75683e7i | − 0.669669i | ||||||||
\(929\) | 1.28653e7 | 0.489081 | 0.244541 | − | 0.969639i | \(-0.421363\pi\) | ||||
0.244541 | + | 0.969639i | \(0.421363\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.12604e7 | 0.803892 | ||||||||
\(932\) | − 1.35894e7i | − 0.512459i | ||||||||
\(933\) | 9.49219e6i | 0.356995i | ||||||||
\(934\) | −6.50194e6 | −0.243880 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.79064e6 | 0.290659 | ||||||||
\(937\) | − 1.06887e7i | − 0.397718i | −0.980028 | − | 0.198859i | \(-0.936276\pi\) | ||||
0.980028 | − | 0.198859i | \(-0.0637236\pi\) | |||||||
\(938\) | 2.34132e7i | 0.868870i | ||||||||
\(939\) | −5.71766e6 | −0.211619 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.82455e7 | 1.03986 | 0.519930 | − | 0.854209i | \(-0.325958\pi\) | ||||
0.519930 | + | 0.854209i | \(0.325958\pi\) | |||||||
\(942\) | − 2.09806e6i | − 0.0770356i | ||||||||
\(943\) | − 2.79684e7i | − 1.02421i | ||||||||
\(944\) | 1.31331e7 | 0.479665 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 368224. | 0.0133778 | ||||||||
\(947\) | 1.70892e7i | 0.619222i | 0.950863 | + | 0.309611i | \(0.100199\pi\) | ||||
−0.950863 | + | 0.309611i | \(0.899801\pi\) | |||||||
\(948\) | − 3.73632e6i | − 0.135028i | ||||||||
\(949\) | 1.10894e7 | 0.399706 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.49849e6 | −0.304713 | ||||||||
\(952\) | − 3.86611e7i | − 1.38255i | ||||||||
\(953\) | 2.22259e7i | 0.792735i | 0.918092 | + | 0.396367i | \(0.129729\pi\) | ||||
−0.918092 | + | 0.396367i | \(0.870271\pi\) | |||||||
\(954\) | 1.08261e7 | 0.385124 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.36864e6 | 0.0484333 | ||||||||
\(957\) | 2.01872e6i | 0.0712519i | ||||||||
\(958\) | − 6.55872e6i | − 0.230890i | ||||||||
\(959\) | 2.78243e7 | 0.976961 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.26364e7 | −0.790678 | ||||||||
\(962\) | − 104104.i | − 0.00362685i | ||||||||
\(963\) | − 3.59323e7i | − 1.24859i | ||||||||
\(964\) | −3.10234e6 | −0.107522 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.57114e6 | −0.157609 | ||||||||
\(967\) | − 2.41551e7i | − 0.830696i | −0.909663 | − | 0.415348i | \(-0.863660\pi\) | ||||
0.909663 | − | 0.415348i | \(-0.136340\pi\) | |||||||
\(968\) | 1.66976e7i | 0.572752i | ||||||||
\(969\) | −7.11472e6 | −0.243416 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.48313e7 | −1.86630 | −0.933149 | − | 0.359491i | \(-0.882950\pi\) | ||||
−0.933149 | + | 0.359491i | \(0.882950\pi\) | |||||||
\(972\) | − 1.81273e7i | − 0.615415i | ||||||||
\(973\) | 2.15462e7i | 0.729608i | ||||||||
\(974\) | 1.70639e7 | 0.576344 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.11901e7 | 0.712047 | ||||||||
\(977\) | 1.56612e7i | 0.524915i | 0.964944 | + | 0.262457i | \(0.0845329\pi\) | ||||
−0.964944 | + | 0.262457i | \(0.915467\pi\) | |||||||
\(978\) | 1.23651e6i | 0.0413382i | ||||||||
\(979\) | 1.50028e7 | 0.500281 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.36041e6 | −0.277367 | ||||||||
\(982\) | − 3.02530e6i | − 0.100113i | ||||||||
\(983\) | − 1.63420e7i | − 0.539412i | −0.962943 | − | 0.269706i | \(-0.913073\pi\) | ||||
0.962943 | − | 0.269706i | \(-0.0869266\pi\) | |||||||
\(984\) | 4.51104e6 | 0.148521 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.14440e7 | 0.374873 | ||||||||
\(987\) | − 9.28358e6i | − 0.303335i | ||||||||
\(988\) | − 8.48848e6i | − 0.276654i | ||||||||
\(989\) | 3.70214e6 | 0.120355 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.37576e7 | 0.444997 | 0.222498 | − | 0.974933i | \(-0.428579\pi\) | ||||
0.222498 | + | 0.974933i | \(0.428579\pi\) | |||||||
\(992\) | 1.26121e7i | 0.406919i | ||||||||
\(993\) | − 1.23994e7i | − 0.399050i | ||||||||
\(994\) | 1.25368e7 | 0.402459 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.87219e6 | 0.0598001 | ||||||||
\(997\) | 1.29097e7i | 0.411320i | 0.978624 | + | 0.205660i | \(0.0659341\pi\) | ||||
−0.978624 | + | 0.205660i | \(0.934066\pi\) | |||||||
\(998\) | − 1.29838e7i | − 0.412644i | ||||||||
\(999\) | −342160. | −0.0108471 |
(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 | 25.6.b.a.24.1 | 2 | ||
3.2 | odd | 2 | 225.6.b.e.199.2 | 2 | |||
4.3 | odd | 2 | 400.6.c.j.49.2 | 2 | |||
5.2 | odd | 4 | 5.6.a.a.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 25.6.a.a.1.1 | 1 | |||
5.4 | even | 2 | inner | 25.6.b.a.24.2 | 2 | ||
15.2 | even | 4 | 45.6.a.b.1.1 | 1 | |||
15.8 | even | 4 | 225.6.a.f.1.1 | 1 | |||
15.14 | odd | 2 | 225.6.b.e.199.1 | 2 | |||
20.3 | even | 4 | 400.6.a.g.1.1 | 1 | |||
20.7 | even | 4 | 80.6.a.e.1.1 | 1 | |||
20.19 | odd | 2 | 400.6.c.j.49.1 | 2 | |||
35.27 | even | 4 | 245.6.a.b.1.1 | 1 | |||
40.27 | even | 4 | 320.6.a.g.1.1 | 1 | |||
40.37 | odd | 4 | 320.6.a.j.1.1 | 1 | |||
55.32 | even | 4 | 605.6.a.a.1.1 | 1 | |||
60.47 | odd | 4 | 720.6.a.a.1.1 | 1 | |||
65.12 | odd | 4 | 845.6.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.6.a.a.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
25.6.a.a.1.1 | 1 | 5.3 | odd | 4 | |||
25.6.b.a.24.1 | 2 | 1.1 | even | 1 | trivial | ||
25.6.b.a.24.2 | 2 | 5.4 | even | 2 | inner | ||
45.6.a.b.1.1 | 1 | 15.2 | even | 4 | |||
80.6.a.e.1.1 | 1 | 20.7 | even | 4 | |||
225.6.a.f.1.1 | 1 | 15.8 | even | 4 | |||
225.6.b.e.199.1 | 2 | 15.14 | odd | 2 | |||
225.6.b.e.199.2 | 2 | 3.2 | odd | 2 | |||
245.6.a.b.1.1 | 1 | 35.27 | even | 4 | |||
320.6.a.g.1.1 | 1 | 40.27 | even | 4 | |||
320.6.a.j.1.1 | 1 | 40.37 | odd | 4 | |||
400.6.a.g.1.1 | 1 | 20.3 | even | 4 | |||
400.6.c.j.49.1 | 2 | 20.19 | odd | 2 | |||
400.6.c.j.49.2 | 2 | 4.3 | odd | 2 | |||
605.6.a.a.1.1 | 1 | 55.32 | even | 4 | |||
720.6.a.a.1.1 | 1 | 60.47 | odd | 4 | |||
845.6.a.b.1.1 | 1 | 65.12 | odd | 4 |