Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [90,6,Mod(19,90)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(90, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("90.19");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 90 = 2 \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 90.c (of order \(2\), degree \(1\), 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: | \(14.4345437832\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{1249})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 625x^{2} + 97344 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.3 | ||
Root | \(-17.1706i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 90.19 |
Dual form | 90.6.c.c.19.1 |
$q$-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 \(\left(\mathbb{Z}/90\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | −19.1706 | + | 52.5118i | −0.342934 | + | 0.939359i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 233.706i | − | 1.80271i | −0.433086 | − | 0.901353i | \(-0.642575\pi\) | ||
0.433086 | − | 0.901353i | \(-0.357425\pi\) | |||||||
\(8\) | − | 64.0000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −210.047 | − | 76.6824i | −0.664227 | − | 0.242491i | ||||
\(11\) | 89.7060 | 0.223532 | 0.111766 | − | 0.993735i | \(-0.464349\pi\) | ||||
0.111766 | + | 0.993735i | \(0.464349\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 209.118i | − | 0.343189i | −0.985168 | − | 0.171594i | \(-0.945108\pi\) | ||
0.985168 | − | 0.171594i | \(-0.0548918\pi\) | |||||||
\(14\) | 934.824 | 1.27471 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 226.882i | 0.190405i | 0.995458 | + | 0.0952024i | \(0.0303498\pi\) | ||||
−0.995458 | + | 0.0952024i | \(0.969650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2180.47 | 1.38569 | 0.692846 | − | 0.721086i | \(-0.256357\pi\) | ||||
0.692846 | + | 0.721086i | \(0.256357\pi\) | |||||||
\(20\) | 306.730 | − | 840.189i | 0.171467 | − | 0.469680i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 358.824i | 0.158061i | ||||||||
\(23\) | − | 4296.47i | − | 1.69353i | −0.531969 | − | 0.846764i | \(-0.678548\pi\) | ||
0.531969 | − | 0.846764i | \(-0.321452\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2389.98 | − | 2013.36i | −0.764792 | − | 0.644277i | ||||
\(26\) | 836.472 | 0.242671 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3739.30i | 0.901353i | ||||||||
\(29\) | 3556.06 | 0.785189 | 0.392595 | − | 0.919712i | \(-0.371578\pi\) | ||||
0.392595 | + | 0.919712i | \(0.371578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6902.24 | 1.28999 | 0.644994 | − | 0.764188i | \(-0.276860\pi\) | ||||
0.644994 | + | 0.764188i | \(0.276860\pi\) | |||||||
\(32\) | 1024.00i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −907.528 | −0.134637 | ||||||||
\(35\) | 12272.3 | + | 4480.28i | 1.69339 | + | 0.618209i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5435.59i | 0.652743i | 0.945242 | + | 0.326371i | \(0.105826\pi\) | ||||
−0.945242 | + | 0.326371i | \(0.894174\pi\) | |||||||
\(38\) | 8721.89i | 0.979832i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3360.75 | + | 1226.92i | 0.332114 | + | 0.121246i | ||||
\(41\) | −6484.00 | −0.602398 | −0.301199 | − | 0.953561i | \(-0.597387\pi\) | ||||
−0.301199 | + | 0.953561i | \(0.597387\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 21979.5i | − | 1.81279i | −0.422432 | − | 0.906395i | \(-0.638823\pi\) | ||
0.422432 | − | 0.906395i | \(-0.361177\pi\) | |||||||
\(44\) | −1435.30 | −0.111766 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17185.9 | 1.19751 | ||||||||
\(47\) | − | 7718.24i | − | 0.509652i | −0.966987 | − | 0.254826i | \(-0.917982\pi\) | ||
0.966987 | − | 0.254826i | \(-0.0820181\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −37811.5 | −2.24975 | ||||||||
\(50\) | 8053.46 | − | 9559.91i | 0.455572 | − | 0.540790i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3345.89i | 0.171594i | ||||||||
\(53\) | − | 12765.4i | − | 0.624228i | −0.950045 | − | 0.312114i | \(-0.898963\pi\) | ||
0.950045 | − | 0.312114i | \(-0.101037\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1719.72 | + | 4710.62i | −0.0766567 | + | 0.209977i | ||||
\(56\) | −14957.2 | −0.637353 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14224.2i | 0.555212i | ||||||||
\(59\) | −44555.6 | −1.66637 | −0.833187 | − | 0.552992i | \(-0.813486\pi\) | ||||
−0.833187 | + | 0.552992i | \(0.813486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11598.2 | 0.399086 | 0.199543 | − | 0.979889i | \(-0.436054\pi\) | ||||
0.199543 | + | 0.979889i | \(0.436054\pi\) | |||||||
\(62\) | 27608.9i | 0.912159i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 10981.2 | + | 4008.92i | 0.322377 | + | 0.117691i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3961.29i | 0.107808i | 0.998546 | + | 0.0539038i | \(0.0171664\pi\) | ||||
−0.998546 | + | 0.0539038i | \(0.982834\pi\) | |||||||
\(68\) | − | 3630.11i | − | 0.0952024i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −17921.1 | + | 49089.3i | −0.437140 | + | 1.19741i | ||||
\(71\) | −46413.6 | −1.09270 | −0.546348 | − | 0.837559i | \(-0.683982\pi\) | ||||
−0.546348 | + | 0.837559i | \(0.683982\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 61591.2i | − | 1.35273i | −0.736566 | − | 0.676365i | \(-0.763554\pi\) | ||
0.736566 | − | 0.676365i | \(-0.236446\pi\) | |||||||
\(74\) | −21742.3 | −0.461559 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −34887.5 | −0.692846 | ||||||||
\(77\) | − | 20964.8i | − | 0.402962i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 27877.8 | 0.502563 | 0.251281 | − | 0.967914i | \(-0.419148\pi\) | ||||
0.251281 | + | 0.967914i | \(0.419148\pi\) | |||||||
\(80\) | −4907.67 | + | 13443.0i | −0.0857335 | + | 0.234840i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 25936.0i | − | 0.425959i | ||||||
\(83\) | 50941.0i | 0.811656i | 0.913949 | + | 0.405828i | \(0.133017\pi\) | ||||
−0.913949 | + | 0.405828i | \(0.866983\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11914.0 | − | 4349.47i | −0.178859 | − | 0.0652963i | ||||
\(86\) | 87918.1 | 1.28184 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 5741.18i | − | 0.0790305i | ||||||
\(89\) | 5131.19 | 0.0686663 | 0.0343331 | − | 0.999410i | \(-0.489069\pi\) | ||||
0.0343331 | + | 0.999410i | \(0.489069\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −48872.1 | −0.618668 | ||||||||
\(92\) | 68743.5i | 0.846764i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 30872.9 | 0.360378 | ||||||||
\(95\) | −41800.9 | + | 114500.i | −0.475201 | + | 1.30166i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 88435.3i | 0.954325i | 0.878815 | + | 0.477162i | \(0.158335\pi\) | ||||
−0.878815 | + | 0.477162i | \(0.841665\pi\) | |||||||
\(98\) | − | 151246.i | − | 1.59081i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 38239.6 | + | 32213.8i | 0.382396 | + | 0.322138i | ||||
\(101\) | 116471. | 1.13609 | 0.568047 | − | 0.822996i | \(-0.307699\pi\) | ||||
0.568047 | + | 0.822996i | \(0.307699\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 22369.1i | 0.207756i | 0.994590 | + | 0.103878i | \(0.0331252\pi\) | ||||
−0.994590 | + | 0.103878i | \(0.966875\pi\) | |||||||
\(104\) | −13383.5 | −0.121335 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 51061.5 | 0.441396 | ||||||||
\(107\) | − | 130626.i | − | 1.10299i | −0.834178 | − | 0.551495i | \(-0.814058\pi\) | ||
0.834178 | − | 0.551495i | \(-0.185942\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 51443.5 | 0.414729 | 0.207365 | − | 0.978264i | \(-0.433511\pi\) | ||||
0.207365 | + | 0.978264i | \(0.433511\pi\) | |||||||
\(110\) | −18842.5 | − | 6878.87i | −0.148476 | − | 0.0542045i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 59828.7i | − | 0.450676i | ||||||
\(113\) | − | 138259.i | − | 1.01858i | −0.860594 | − | 0.509291i | \(-0.829908\pi\) | ||
0.860594 | − | 0.509291i | \(-0.170092\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 225615. | + | 82365.9i | 1.59083 | + | 0.580768i | ||||
\(116\) | −56897.0 | −0.392595 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 178222.i | − | 1.17830i | ||||||
\(119\) | 53023.7 | 0.343244 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −153004. | −0.950033 | ||||||||
\(122\) | 46392.9i | 0.282197i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −110436. | −0.644994 | ||||||||
\(125\) | 151543. | − | 86904.5i | 0.867481 | − | 0.497471i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 199662.i | 1.09847i | 0.835669 | + | 0.549233i | \(0.185080\pi\) | ||||
−0.835669 | + | 0.549233i | \(0.814920\pi\) | |||||||
\(128\) | − | 16384.0i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −16035.7 | + | 43924.6i | −0.0832201 | + | 0.227955i | ||||
\(131\) | 314223. | 1.59978 | 0.799889 | − | 0.600148i | \(-0.204891\pi\) | ||||
0.799889 | + | 0.600148i | \(0.204891\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 509589.i | − | 2.49799i | ||||||
\(134\) | −15845.1 | −0.0762315 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14520.5 | 0.0673183 | ||||||||
\(137\) | 256841.i | 1.16913i | 0.811348 | + | 0.584564i | \(0.198734\pi\) | ||||
−0.811348 | + | 0.584564i | \(0.801266\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10777.2 | 0.0473118 | 0.0236559 | − | 0.999720i | \(-0.492469\pi\) | ||||
0.0236559 | + | 0.999720i | \(0.492469\pi\) | |||||||
\(140\) | −196357. | − | 71684.5i | −0.846694 | − | 0.309105i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 185654.i | − | 0.772652i | ||||||
\(143\) | − | 18759.1i | − | 0.0767136i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −68171.8 | + | 186735.i | −0.269268 | + | 0.737575i | ||||
\(146\) | 246365. | 0.956525 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 86969.4i | − | 0.326371i | ||||||
\(149\) | 4103.27 | 0.0151413 | 0.00757067 | − | 0.999971i | \(-0.497590\pi\) | ||||
0.00757067 | + | 0.999971i | \(0.497590\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 107449. | 0.383495 | 0.191748 | − | 0.981444i | \(-0.438585\pi\) | ||||
0.191748 | + | 0.981444i | \(0.438585\pi\) | |||||||
\(152\) | − | 139550.i | − | 0.489916i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 83859.3 | 0.284937 | ||||||||
\(155\) | −132320. | + | 362449.i | −0.442381 | + | 1.21176i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 345824.i | 1.11971i | 0.828591 | + | 0.559855i | \(0.189143\pi\) | ||||
−0.828591 | + | 0.559855i | \(0.810857\pi\) | |||||||
\(158\) | 111511.i | 0.355366i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −53772.1 | − | 19630.7i | −0.166057 | − | 0.0606228i | ||||
\(161\) | −1.00411e6 | −3.05293 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 58776.3i | 0.173274i | 0.996240 | + | 0.0866370i | \(0.0276120\pi\) | ||||
−0.996240 | + | 0.0866370i | \(0.972388\pi\) | |||||||
\(164\) | 103744. | 0.301199 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −203764. | −0.573928 | ||||||||
\(167\) | 154654.i | 0.429111i | 0.976712 | + | 0.214556i | \(0.0688303\pi\) | ||||
−0.976712 | + | 0.214556i | \(0.931170\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 327563. | 0.882222 | ||||||||
\(170\) | 17397.9 | − | 47655.9i | 0.0461715 | − | 0.126472i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 351673.i | 0.906395i | ||||||||
\(173\) | − | 171600.i | − | 0.435916i | −0.975958 | − | 0.217958i | \(-0.930060\pi\) | ||
0.975958 | − | 0.217958i | \(-0.0699395\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −470535. | + | 558552.i | −1.16144 | + | 1.37870i | ||||
\(176\) | 22964.7 | 0.0558830 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 20524.8i | 0.0485544i | ||||||||
\(179\) | 595571. | 1.38932 | 0.694658 | − | 0.719340i | \(-0.255556\pi\) | ||||
0.694658 | + | 0.719340i | \(0.255556\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 144518. | 0.327889 | 0.163944 | − | 0.986470i | \(-0.447578\pi\) | ||||
0.163944 | + | 0.986470i | \(0.447578\pi\) | |||||||
\(182\) | − | 195488.i | − | 0.437464i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −274974. | −0.598753 | ||||||||
\(185\) | −285432. | − | 104203.i | −0.613160 | − | 0.223848i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20352.7i | 0.0425616i | ||||||||
\(188\) | 123492.i | 0.254826i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −458002. | − | 167204.i | −0.920414 | − | 0.336018i | ||||
\(191\) | −815918. | −1.61831 | −0.809157 | − | 0.587592i | \(-0.800076\pi\) | ||||
−0.809157 | + | 0.587592i | \(0.800076\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 665030.i | − | 1.28513i | −0.766230 | − | 0.642566i | \(-0.777870\pi\) | ||
0.766230 | − | 0.642566i | \(-0.222130\pi\) | |||||||
\(194\) | −353741. | −0.674810 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 604984. | 1.12487 | ||||||||
\(197\) | 332972.i | 0.611283i | 0.952147 | + | 0.305642i | \(0.0988709\pi\) | ||||
−0.952147 | + | 0.305642i | \(0.901129\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19565.3 | 0.0350231 | 0.0175115 | − | 0.999847i | \(-0.494426\pi\) | ||||
0.0175115 | + | 0.999847i | \(0.494426\pi\) | |||||||
\(200\) | −128855. | + | 152958.i | −0.227786 | + | 0.270395i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 465884.i | 0.803339i | ||||||||
\(203\) | − | 831073.i | − | 1.41546i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 124302. | − | 340486.i | 0.206583 | − | 0.565868i | ||||
\(206\) | −89476.2 | −0.146906 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 53534.2i | − | 0.0857971i | ||||||
\(209\) | 195601. | 0.309746 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −669474. | −1.03521 | −0.517604 | − | 0.855620i | \(-0.673176\pi\) | ||||
−0.517604 | + | 0.855620i | \(0.673176\pi\) | |||||||
\(212\) | 204246.i | 0.312114i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 522506. | 0.779932 | ||||||||
\(215\) | 1.15418e6 | + | 421361.i | 1.70286 | + | 0.621667i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.61309e6i | − | 2.32547i | ||||||
\(218\) | 205774.i | 0.293258i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 27515.5 | − | 75369.9i | 0.0383284 | − | 0.104988i | ||||
\(221\) | 47445.1 | 0.0653448 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 841915.i | 1.13372i | 0.823814 | + | 0.566860i | \(0.191842\pi\) | ||||
−0.823814 | + | 0.566860i | \(0.808158\pi\) | |||||||
\(224\) | 239315. | 0.318676 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 553034. | 0.720246 | ||||||||
\(227\) | − | 106296.i | − | 0.136916i | −0.997654 | − | 0.0684580i | \(-0.978192\pi\) | ||
0.997654 | − | 0.0684580i | \(-0.0218079\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.52931e6 | −1.92711 | −0.963553 | − | 0.267518i | \(-0.913797\pi\) | ||||
−0.963553 | + | 0.267518i | \(0.913797\pi\) | |||||||
\(230\) | −329464. | + | 902462.i | −0.410665 | + | 1.12489i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 227588.i | − | 0.277606i | ||||||
\(233\) | 362144.i | 0.437011i | 0.975836 | + | 0.218505i | \(0.0701181\pi\) | ||||
−0.975836 | + | 0.218505i | \(0.929882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 405298. | + | 147963.i | 0.478746 | + | 0.174777i | ||||
\(236\) | 712890. | 0.833187 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 212095.i | 0.242710i | ||||||||
\(239\) | 38495.6 | 0.0435929 | 0.0217965 | − | 0.999762i | \(-0.493061\pi\) | ||||
0.0217965 | + | 0.999762i | \(0.493061\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 567433. | 0.629320 | 0.314660 | − | 0.949204i | \(-0.398109\pi\) | ||||
0.314660 | + | 0.949204i | \(0.398109\pi\) | |||||||
\(242\) | − | 612015.i | − | 0.671775i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −185572. | −0.199543 | ||||||||
\(245\) | 724869. | − | 1.98555e6i | 0.771515 | − | 2.11332i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 455976.i | − | 0.475553i | ||||||
\(248\) | − | 441743.i | − | 0.456080i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 347618. | + | 606171.i | 0.351765 | + | 0.613402i | ||||
\(251\) | −19067.0 | −0.0191028 | −0.00955141 | − | 0.999954i | \(-0.503040\pi\) | ||||
−0.00955141 | + | 0.999954i | \(0.503040\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 385419.i | − | 0.378558i | ||||||
\(254\) | −798649. | −0.776733 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | − | 854054.i | − | 0.806589i | −0.915070 | − | 0.403295i | \(-0.867865\pi\) | ||
0.915070 | − | 0.403295i | \(-0.132135\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.27033e6 | 1.17670 | ||||||||
\(260\) | −175698. | − | 64142.6i | −0.161189 | − | 0.0588455i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.25689e6i | 1.13121i | ||||||||
\(263\) | 755220.i | 0.673262i | 0.941637 | + | 0.336631i | \(0.109288\pi\) | ||||
−0.941637 | + | 0.336631i | \(0.890712\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 670332. | + | 244720.i | 0.586375 | + | 0.214069i | ||||
\(266\) | 2.03836e6 | 1.76635 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 63380.6i | − | 0.0539038i | ||||||
\(269\) | −256615. | −0.216222 | −0.108111 | − | 0.994139i | \(-0.534480\pi\) | ||||
−0.108111 | + | 0.994139i | \(0.534480\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 598518. | 0.495056 | 0.247528 | − | 0.968881i | \(-0.420382\pi\) | ||||
0.247528 | + | 0.968881i | \(0.420382\pi\) | |||||||
\(272\) | 58081.8i | 0.0476012i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.02736e6 | −0.826698 | ||||||||
\(275\) | −214395. | − | 180611.i | −0.170956 | − | 0.144016i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 425045.i | 0.332840i | 0.986055 | + | 0.166420i | \(0.0532208\pi\) | ||||
−0.986055 | + | 0.166420i | \(0.946779\pi\) | |||||||
\(278\) | 43108.9i | 0.0334545i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 286738. | − | 785428.i | 0.218570 | − | 0.598703i | ||||
\(281\) | 949963. | 0.717696 | 0.358848 | − | 0.933396i | \(-0.383170\pi\) | ||||
0.358848 | + | 0.933396i | \(0.383170\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.12422e6i | 1.57664i | 0.615264 | + | 0.788321i | \(0.289050\pi\) | ||||
−0.615264 | + | 0.788321i | \(0.710950\pi\) | |||||||
\(284\) | 742617. | 0.546348 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 75036.5 | 0.0542447 | ||||||||
\(287\) | 1.51535e6i | 1.08595i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.36838e6 | 0.963746 | ||||||||
\(290\) | −746941. | − | 272687.i | −0.521544 | − | 0.190401i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 985459.i | 0.676365i | ||||||||
\(293\) | 1.17556e6i | 0.799977i | 0.916520 | + | 0.399988i | \(0.130986\pi\) | ||||
−0.916520 | + | 0.399988i | \(0.869014\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 854158. | − | 2.33969e6i | 0.571456 | − | 1.56532i | ||||
\(296\) | 347878. | 0.230779 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16413.1i | 0.0107065i | ||||||||
\(299\) | −898469. | −0.581199 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.13675e6 | −3.26792 | ||||||||
\(302\) | 429796.i | 0.271172i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 558201. | 0.346423 | ||||||||
\(305\) | −222345. | + | 609044.i | −0.136860 | + | 0.374886i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 588520.i | − | 0.356382i | −0.983996 | − | 0.178191i | \(-0.942976\pi\) | ||
0.983996 | − | 0.178191i | \(-0.0570244\pi\) | |||||||
\(308\) | 335437.i | 0.201481i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.44980e6 | − | 529280.i | −0.856845 | − | 0.312810i | ||||
\(311\) | −1.61863e6 | −0.948958 | −0.474479 | − | 0.880267i | \(-0.657363\pi\) | ||||
−0.474479 | + | 0.880267i | \(0.657363\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.58901e6i | − | 0.916783i | −0.888750 | − | 0.458392i | \(-0.848426\pi\) | ||
0.888750 | − | 0.458392i | \(-0.151574\pi\) | |||||||
\(314\) | −1.38329e6 | −0.791754 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −446045. | −0.251281 | ||||||||
\(317\) | − | 2.35137e6i | − | 1.31423i | −0.753789 | − | 0.657117i | \(-0.771776\pi\) | ||
0.753789 | − | 0.657117i | \(-0.228224\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 319000. | 0.175515 | ||||||||
\(320\) | 78522.8 | − | 215088.i | 0.0428668 | − | 0.117420i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 4.01644e6i | − | 2.15875i | ||||||
\(323\) | 494710.i | 0.263842i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −421031. | + | 499787.i | −0.221108 | + | 0.262468i | ||||
\(326\) | −235105. | −0.122523 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 414976.i | 0.212980i | ||||||||
\(329\) | −1.80380e6 | −0.918752 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 480922. | 0.241271 | 0.120635 | − | 0.992697i | \(-0.461507\pi\) | ||||
0.120635 | + | 0.992697i | \(0.461507\pi\) | |||||||
\(332\) | − | 815056.i | − | 0.405828i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −618616. | −0.303427 | ||||||||
\(335\) | −208014. | − | 75940.2i | −0.101270 | − | 0.0369709i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 981449.i | 0.470753i | 0.971904 | + | 0.235376i | \(0.0756323\pi\) | ||||
−0.971904 | + | 0.235376i | \(0.924368\pi\) | |||||||
\(338\) | 1.31025e6i | 0.623825i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 190624. | + | 69591.4i | 0.0894293 | + | 0.0326481i | ||||
\(341\) | 619172. | 0.288353 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.90887e6i | 2.25292i | ||||||||
\(344\) | −1.40669e6 | −0.640918 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 686400. | 0.308239 | ||||||||
\(347\) | 1.91647e6i | 0.854432i | 0.904150 | + | 0.427216i | \(0.140506\pi\) | ||||
−0.904150 | + | 0.427216i | \(0.859494\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.22795e6 | −0.539658 | −0.269829 | − | 0.962908i | \(-0.586967\pi\) | ||||
−0.269829 | + | 0.962908i | \(0.586967\pi\) | |||||||
\(350\) | −2.23421e6 | − | 1.88214e6i | −0.974885 | − | 0.821263i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 91858.9i | 0.0395152i | ||||||||
\(353\) | 547823.i | 0.233993i | 0.993132 | + | 0.116997i | \(0.0373267\pi\) | ||||
−0.993132 | + | 0.116997i | \(0.962673\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 889776. | − | 2.43726e6i | 0.374722 | − | 1.02643i | ||||
\(356\) | −82099.1 | −0.0343331 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.38228e6i | 0.982395i | ||||||||
\(359\) | 1.02314e6 | 0.418984 | 0.209492 | − | 0.977810i | \(-0.432819\pi\) | ||||
0.209492 | + | 0.977810i | \(0.432819\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.27836e6 | 0.920140 | ||||||||
\(362\) | 578073.i | 0.231852i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 781954. | 0.309334 | ||||||||
\(365\) | 3.23426e6 | + | 1.18074e6i | 1.27070 | + | 0.463898i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.05305e6i | 1.18323i | 0.806221 | + | 0.591614i | \(0.201509\pi\) | ||||
−0.806221 | + | 0.591614i | \(0.798491\pi\) | |||||||
\(368\) | − | 1.09990e6i | − | 0.423382i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 416814. | − | 1.14173e6i | 0.158284 | − | 0.433570i | ||||
\(371\) | −2.98334e6 | −1.12530 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.69411e6i | 1.37479i | 0.726282 | + | 0.687397i | \(0.241247\pi\) | ||||
−0.726282 | + | 0.687397i | \(0.758753\pi\) | |||||||
\(374\) | −81410.7 | −0.0300956 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −493967. | −0.180189 | ||||||||
\(377\) | − | 743636.i | − | 0.269468i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.48524e6 | −1.60394 | −0.801969 | − | 0.597365i | \(-0.796214\pi\) | ||||
−0.801969 | + | 0.597365i | \(0.796214\pi\) | |||||||
\(380\) | 668815. | − | 1.83201e6i | 0.237600 | − | 0.650831i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 3.26367e6i | − | 1.14432i | ||||||
\(383\) | − | 4.53062e6i | − | 1.57819i | −0.614269 | − | 0.789097i | \(-0.710549\pi\) | ||
0.614269 | − | 0.789097i | \(-0.289451\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.10090e6 | + | 401908.i | 0.378526 | + | 0.138189i | ||||
\(386\) | 2.66012e6 | 0.908726 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 1.41496e6i | − | 0.477162i | ||||||
\(389\) | 2.73557e6 | 0.916588 | 0.458294 | − | 0.888801i | \(-0.348461\pi\) | ||||
0.458294 | + | 0.888801i | \(0.348461\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 974792. | 0.322456 | ||||||||
\(392\) | 2.41993e6i | 0.795405i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.33189e6 | −0.432242 | ||||||||
\(395\) | −534434. | + | 1.46391e6i | −0.172346 | + | 0.472087i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.54948e6i | − | 0.493413i | −0.969090 | − | 0.246707i | \(-0.920652\pi\) | ||
0.969090 | − | 0.246707i | \(-0.0793484\pi\) | |||||||
\(398\) | 78261.3i | 0.0247651i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −611834. | − | 515421.i | −0.191198 | − | 0.161069i | ||||
\(401\) | −4.46136e6 | −1.38550 | −0.692749 | − | 0.721179i | \(-0.743601\pi\) | ||||
−0.692749 | + | 0.721179i | \(0.743601\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.44338e6i | − | 0.442709i | ||||||
\(404\) | −1.86353e6 | −0.568047 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.32429e6 | 1.00088 | ||||||||
\(407\) | 487605.i | 0.145909i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.36815e6 | 0.700003 | 0.350002 | − | 0.936749i | \(-0.386181\pi\) | ||||
0.350002 | + | 0.936749i | \(0.386181\pi\) | |||||||
\(410\) | 1.36195e6 | + | 497208.i | 0.400129 | + | 0.146076i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 357905.i | − | 0.103878i | ||||||
\(413\) | 1.04129e7i | 3.00398i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.67500e6 | − | 976569.i | −0.762437 | − | 0.278345i | ||||
\(416\) | 214137. | 0.0606677 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 782405.i | 0.219024i | ||||||||
\(419\) | 5.76363e6 | 1.60384 | 0.801920 | − | 0.597432i | \(-0.203812\pi\) | ||||
0.801920 | + | 0.597432i | \(0.203812\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.26572e6 | 0.897995 | 0.448998 | − | 0.893533i | \(-0.351781\pi\) | ||||
0.448998 | + | 0.893533i | \(0.351781\pi\) | |||||||
\(422\) | − | 2.67789e6i | − | 0.732002i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −816983. | −0.220698 | ||||||||
\(425\) | 456796. | − | 542243.i | 0.122673 | − | 0.145620i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2.71057e6i | − | 0.719435i | ||||||
\(428\) | 2.09002e6i | 0.551495i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.68544e6 | + | 4.61674e6i | −0.439585 | + | 1.20410i | ||||
\(431\) | 5.62110e6 | 1.45756 | 0.728782 | − | 0.684745i | \(-0.240087\pi\) | ||||
0.728782 | + | 0.684745i | \(0.240087\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.18656e6i | − | 0.816774i | −0.912809 | − | 0.408387i | \(-0.866091\pi\) | ||
0.912809 | − | 0.408387i | \(-0.133909\pi\) | |||||||
\(434\) | 6.45237e6 | 1.64435 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −823097. | −0.207365 | ||||||||
\(437\) | − | 9.36833e6i | − | 2.34671i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.41102e6 | 1.83534 | 0.917671 | − | 0.397342i | \(-0.130067\pi\) | ||||
0.917671 | + | 0.397342i | \(0.130067\pi\) | |||||||
\(440\) | 301480. | + | 110062.i | 0.0742380 | + | 0.0271022i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 189780.i | 0.0462057i | ||||||||
\(443\) | − | 2.62862e6i | − | 0.636382i | −0.948027 | − | 0.318191i | \(-0.896925\pi\) | ||
0.948027 | − | 0.318191i | \(-0.103075\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −98368.1 | + | 269448.i | −0.0235480 | + | 0.0645023i | ||||
\(446\) | −3.36766e6 | −0.801662 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 957260.i | 0.225338i | ||||||||
\(449\) | 71764.4 | 0.0167994 | 0.00839969 | − | 0.999965i | \(-0.497326\pi\) | ||||
0.00839969 | + | 0.999965i | \(0.497326\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −581653. | −0.134655 | ||||||||
\(452\) | 2.21214e6i | 0.509291i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 425186. | 0.0968142 | ||||||||
\(455\) | 936907. | − | 2.56636e6i | 0.212162 | − | 0.581152i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.51471e6i | 0.787225i | 0.919276 | + | 0.393613i | \(0.128775\pi\) | ||||
−0.919276 | + | 0.393613i | \(0.871225\pi\) | |||||||
\(458\) | − | 6.11722e6i | − | 1.36267i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.60985e6 | − | 1.31785e6i | −0.795416 | − | 0.290384i | ||||
\(461\) | −3.35569e6 | −0.735410 | −0.367705 | − | 0.929943i | \(-0.619856\pi\) | ||||
−0.367705 | + | 0.929943i | \(0.619856\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.47269e6i | − | 0.752860i | −0.926445 | − | 0.376430i | \(-0.877152\pi\) | ||
0.926445 | − | 0.376430i | \(-0.122848\pi\) | |||||||
\(464\) | 910352. | 0.196297 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.44858e6 | −0.309013 | ||||||||
\(467\) | − | 2.35495e6i | − | 0.499678i | −0.968287 | − | 0.249839i | \(-0.919622\pi\) | ||
0.968287 | − | 0.249839i | \(-0.0803777\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 925776. | 0.194345 | ||||||||
\(470\) | −591853. | + | 1.62119e6i | −0.123586 | + | 0.338525i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.85156e6i | 0.589152i | ||||||||
\(473\) | − | 1.97170e6i | − | 0.405216i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.21128e6 | − | 4.39008e6i | −1.05977 | − | 0.892769i | ||||
\(476\) | −848379. | −0.171622 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 153982.i | 0.0308249i | ||||||||
\(479\) | −187771. | −0.0373929 | −0.0186964 | − | 0.999825i | \(-0.505952\pi\) | ||||
−0.0186964 | + | 0.999825i | \(0.505952\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.13668e6 | 0.224014 | ||||||||
\(482\) | 2.26973e6i | 0.444997i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.44806e6 | 0.475017 | ||||||||
\(485\) | −4.64390e6 | − | 1.69536e6i | −0.896454 | − | 0.327271i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.01505e6i | − | 0.385002i | −0.981297 | − | 0.192501i | \(-0.938340\pi\) | ||
0.981297 | − | 0.192501i | \(-0.0616598\pi\) | |||||||
\(488\) | − | 742287.i | − | 0.141098i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.94219e6 | + | 2.89947e6i | 1.49434 | + | 0.545543i | ||||
\(491\) | −5.80814e6 | −1.08726 | −0.543630 | − | 0.839325i | \(-0.682951\pi\) | ||||
−0.543630 | + | 0.839325i | \(0.682951\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 806807.i | 0.149504i | ||||||||
\(494\) | 1.82390e6 | 0.336267 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.76697e6 | 0.322497 | ||||||||
\(497\) | 1.08471e7i | 1.96981i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −580611. | −0.104384 | −0.0521920 | − | 0.998637i | \(-0.516621\pi\) | ||||
−0.0521920 | + | 0.998637i | \(0.516621\pi\) | |||||||
\(500\) | −2.42468e6 | + | 1.39047e6i | −0.433740 | + | 0.248735i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 76267.9i | − | 0.0135077i | ||||||
\(503\) | − | 557751.i | − | 0.0982926i | −0.998792 | − | 0.0491463i | \(-0.984350\pi\) | ||
0.998792 | − | 0.0491463i | \(-0.0156501\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.23282e6 | + | 6.11610e6i | −0.389605 | + | 1.06720i | ||||
\(506\) | 1.54168e6 | 0.267681 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 3.19460e6i | − | 0.549233i | ||||||
\(509\) | −2.63318e6 | −0.450491 | −0.225246 | − | 0.974302i | \(-0.572318\pi\) | ||||
−0.225246 | + | 0.974302i | \(0.572318\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.43942e7 | −2.43858 | ||||||||
\(512\) | 262144.i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.41621e6 | 0.570345 | ||||||||
\(515\) | −1.17464e6 | − | 428828.i | −0.195158 | − | 0.0712468i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 692372.i | − | 0.113923i | ||||||
\(518\) | 5.08132e6i | 0.832055i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 256571. | − | 702794.i | 0.0416101 | − | 0.113978i | ||||
\(521\) | 6.78129e6 | 1.09451 | 0.547253 | − | 0.836967i | \(-0.315674\pi\) | ||||
0.547253 | + | 0.836967i | \(0.315674\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.55863e6i | − | 0.249166i | −0.992209 | − | 0.124583i | \(-0.960241\pi\) | ||
0.992209 | − | 0.124583i | \(-0.0397592\pi\) | |||||||
\(524\) | −5.02757e6 | −0.799889 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.02088e6 | −0.476068 | ||||||||
\(527\) | 1.56599e6i | 0.245620i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.20233e7 | −1.86804 | ||||||||
\(530\) | −978878. | + | 2.68133e6i | −0.151370 | + | 0.414630i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.15343e6i | 1.24900i | ||||||||
\(533\) | 1.35592e6i | 0.206736i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.85943e6 | + | 2.50419e6i | 1.03610 | + | 0.378253i | ||||
\(536\) | 253522. | 0.0381157 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 1.02646e6i | − | 0.152892i | ||||||
\(539\) | −3.39192e6 | −0.502890 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.29465e6 | 1.07155 | 0.535774 | − | 0.844362i | \(-0.320020\pi\) | ||||
0.535774 | + | 0.844362i | \(0.320020\pi\) | |||||||
\(542\) | 2.39407e6i | 0.350057i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −232327. | −0.0336591 | ||||||||
\(545\) | −986203. | + | 2.70139e6i | −0.142225 | + | 0.389580i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5.15944e6i | − | 0.737283i | −0.929572 | − | 0.368642i | \(-0.879823\pi\) | ||
0.929572 | − | 0.368642i | \(-0.120177\pi\) | |||||||
\(548\) | − | 4.10945e6i | − | 0.584564i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 722443. | − | 857581.i | 0.101835 | − | 0.120884i | ||||
\(551\) | 7.75389e6 | 1.08803 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.51520e6i | − | 0.905973i | ||||||
\(554\) | −1.70018e6 | −0.235353 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −172436. | −0.0236559 | ||||||||
\(557\) | 2.18378e6i | 0.298244i | 0.988819 | + | 0.149122i | \(0.0476447\pi\) | ||||
−0.988819 | + | 0.149122i | \(0.952355\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.59631e6 | −0.622129 | ||||||||
\(560\) | 3.14171e6 | + | 1.14695e6i | 0.423347 | + | 0.154552i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.79985e6i | 0.507488i | ||||||||
\(563\) | − | 1.13003e7i | − | 1.50252i | −0.660007 | − | 0.751259i | \(-0.729447\pi\) | ||
0.660007 | − | 0.751259i | \(-0.270553\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.26021e6 | + | 2.65050e6i | 0.956815 | + | 0.349306i | ||||
\(566\) | −8.49688e6 | −1.11485 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.97047e6i | 0.386326i | ||||||||
\(569\) | −1.01686e7 | −1.31669 | −0.658343 | − | 0.752718i | \(-0.728742\pi\) | ||||
−0.658343 | + | 0.752718i | \(0.728742\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −284871. | −0.0365644 | −0.0182822 | − | 0.999833i | \(-0.505820\pi\) | ||||
−0.0182822 | + | 0.999833i | \(0.505820\pi\) | |||||||
\(572\) | 300146.i | 0.0383568i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.06140e6 | −0.767879 | ||||||||
\(575\) | −8.65036e6 | + | 1.02685e7i | −1.09110 | + | 1.29520i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.14119e6i | 1.14304i | 0.820587 | + | 0.571522i | \(0.193647\pi\) | ||||
−0.820587 | + | 0.571522i | \(0.806353\pi\) | |||||||
\(578\) | 5.47353e6i | 0.681471i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.09075e6 | − | 2.98776e6i | 0.134634 | − | 0.368787i | ||||
\(581\) | 1.19052e7 | 1.46318 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.14513e6i | − | 0.139535i | ||||||
\(584\) | −3.94184e6 | −0.478263 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.70226e6 | −0.565669 | ||||||||
\(587\) | 1.85347e6i | 0.222019i | 0.993819 | + | 0.111010i | \(0.0354084\pi\) | ||||
−0.993819 | + | 0.111010i | \(0.964592\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.50501e7 | 1.78752 | ||||||||
\(590\) | 9.35878e6 | + | 3.41663e6i | 1.10685 | + | 0.404081i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.39151e6i | 0.163186i | ||||||||
\(593\) | − | 1.30967e7i | − | 1.52941i | −0.644380 | − | 0.764705i | \(-0.722884\pi\) | ||
0.644380 | − | 0.764705i | \(-0.277116\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.01650e6 | + | 2.78437e6i | −0.117710 | + | 0.322429i | ||||
\(596\) | −65652.3 | −0.00757067 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 3.59388e6i | − | 0.410970i | ||||||
\(599\) | −7.13874e6 | −0.812933 | −0.406466 | − | 0.913666i | \(-0.633239\pi\) | ||||
−0.406466 | + | 0.913666i | \(0.633239\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.27856e6 | −0.821976 | −0.410988 | − | 0.911641i | \(-0.634816\pi\) | ||||
−0.410988 | + | 0.911641i | \(0.634816\pi\) | |||||||
\(602\) | − | 2.05470e7i | − | 2.31077i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.71918e6 | −0.191748 | ||||||||
\(605\) | 2.93317e6 | − | 8.03451e6i | 0.325799 | − | 0.892423i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 466696.i | − | 0.0514117i | −0.999670 | − | 0.0257058i | \(-0.991817\pi\) | ||
0.999670 | − | 0.0257058i | \(-0.00818333\pi\) | |||||||
\(608\) | 2.23280e6i | 0.244958i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.43617e6 | − | 889380.i | −0.265084 | − | 0.0967749i | ||||
\(611\) | −1.61402e6 | −0.174907 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 9.21342e6i | − | 0.990307i | −0.868806 | − | 0.495153i | \(-0.835112\pi\) | ||
0.868806 | − | 0.495153i | \(-0.164888\pi\) | |||||||
\(614\) | 2.35408e6 | 0.252000 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.34175e6 | −0.142469 | ||||||||
\(617\) | 8.53638e6i | 0.902736i | 0.892338 | + | 0.451368i | \(0.149064\pi\) | ||||
−0.892338 | + | 0.451368i | \(0.850936\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.72476e6 | −0.810323 | −0.405162 | − | 0.914245i | \(-0.632785\pi\) | ||||
−0.405162 | + | 0.914245i | \(0.632785\pi\) | |||||||
\(620\) | 2.11712e6 | − | 5.79918e6i | 0.221190 | − | 0.605881i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 6.47452e6i | − | 0.671014i | ||||||
\(623\) | − | 1.19919e6i | − | 0.123785i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.65835e6 | + | 9.62379e6i | 0.169815 | + | 0.985476i | ||||
\(626\) | 6.35605e6 | 0.648264 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 5.53318e6i | − | 0.559855i | ||||||
\(629\) | −1.23324e6 | −0.124285 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.50119e7 | 1.50094 | 0.750470 | − | 0.660904i | \(-0.229827\pi\) | ||||
0.750470 | + | 0.660904i | \(0.229827\pi\) | |||||||
\(632\) | − | 1.78418e6i | − | 0.177683i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.40547e6 | 0.929303 | ||||||||
\(635\) | −1.04846e7 | − | 3.82765e6i | −1.03185 | − | 0.376702i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.90706e6i | 0.772087i | ||||||||
\(638\) | 1.27600e6i | 0.124108i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 860353. | + | 314091.i | 0.0830284 | + | 0.0303114i | ||||
\(641\) | 8.60718e6 | 0.827401 | 0.413700 | − | 0.910413i | \(-0.364236\pi\) | ||||
0.413700 | + | 0.910413i | \(0.364236\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.97196e7i | − | 1.88092i | −0.339904 | − | 0.940460i | \(-0.610395\pi\) | ||
0.339904 | − | 0.940460i | \(-0.389605\pi\) | |||||||
\(644\) | 1.60658e7 | 1.52647 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.97884e6 | −0.186565 | ||||||||
\(647\) | − | 541311.i | − | 0.0508378i | −0.999677 | − | 0.0254189i | \(-0.991908\pi\) | ||
0.999677 | − | 0.0254189i | \(-0.00809195\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.99690e6 | −0.372488 | ||||||||
\(650\) | −1.99915e6 | − | 1.68412e6i | −0.185593 | − | 0.156347i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 940421.i | − | 0.0866370i | ||||||
\(653\) | 9.28231e6i | 0.851870i | 0.904754 | + | 0.425935i | \(0.140055\pi\) | ||||
−0.904754 | + | 0.425935i | \(0.859945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.02384e6 | + | 1.65004e7i | −0.548619 | + | 1.50277i | ||||
\(656\) | −1.65990e6 | −0.150599 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 7.21519e6i | − | 0.649655i | ||||||
\(659\) | 1.79964e7 | 1.61425 | 0.807127 | − | 0.590378i | \(-0.201021\pi\) | ||||
0.807127 | + | 0.590378i | \(0.201021\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.78607e6 | 0.693130 | 0.346565 | − | 0.938026i | \(-0.387348\pi\) | ||||
0.346565 | + | 0.938026i | \(0.387348\pi\) | |||||||
\(662\) | 1.92369e6i | 0.170604i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.26022e6 | 0.286964 | ||||||||
\(665\) | 2.67594e7 | + | 9.76913e6i | 2.34651 | + | 0.856647i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.52785e7i | − | 1.32974i | ||||||
\(668\) | − | 2.47446e6i | − | 0.214556i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 303761. | − | 832057.i | 0.0261424 | − | 0.0716087i | ||||
\(671\) | 1.04043e6 | 0.0892086 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.35540e7i | 1.15353i | 0.816910 | + | 0.576766i | \(0.195685\pi\) | ||||
−0.816910 | + | 0.576766i | \(0.804315\pi\) | |||||||
\(674\) | −3.92579e6 | −0.332872 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.24100e6 | −0.441111 | ||||||||
\(677\) | 1.46008e7i | 1.22435i | 0.790724 | + | 0.612173i | \(0.209704\pi\) | ||||
−0.790724 | + | 0.612173i | \(0.790296\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.06679e7 | 1.72037 | ||||||||
\(680\) | −278366. | + | 762495.i | −0.0230857 | + | 0.0632361i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.47669e6i | 0.203897i | ||||||||
\(683\) | 9.71085e6i | 0.796536i | 0.917269 | + | 0.398268i | \(0.130389\pi\) | ||||
−0.917269 | + | 0.398268i | \(0.869611\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.34872e7 | − | 4.92379e6i | −1.09823 | − | 0.400934i | ||||
\(686\) | −1.96355e7 | −1.59306 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 5.62676e6i | − | 0.453197i | ||||||
\(689\) | −2.66947e6 | −0.214228 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.30382e7 | 1.03878 | 0.519389 | − | 0.854538i | \(-0.326159\pi\) | ||||
0.519389 | + | 0.854538i | \(0.326159\pi\) | |||||||
\(692\) | 2.74560e6i | 0.217958i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.66587e6 | −0.604175 | ||||||||
\(695\) | −206606. | + | 565931.i | −0.0162248 | + | 0.0444428i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.47110e6i | − | 0.114699i | ||||||
\(698\) | − | 4.91182e6i | − | 0.381596i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.52857e6 | − | 8.93683e6i | 0.580720 | − | 0.689348i | ||||
\(701\) | −4.65952e6 | −0.358134 | −0.179067 | − | 0.983837i | \(-0.557308\pi\) | ||||
−0.179067 | + | 0.983837i | \(0.557308\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.18521e7i | 0.904500i | ||||||||
\(704\) | −367436. | −0.0279415 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.19129e6 | −0.165458 | ||||||||
\(707\) | − | 2.72199e7i | − | 2.04804i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.94059e7 | −1.44983 | −0.724916 | − | 0.688837i | \(-0.758122\pi\) | ||||
−0.724916 | + | 0.688837i | \(0.758122\pi\) | |||||||
\(710\) | 9.74904e6 | + | 3.55910e6i | 0.725798 | + | 0.264969i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 328396.i | − | 0.0242772i | ||||||
\(713\) | − | 2.96553e7i | − | 2.18463i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 985075. | + | 359624.i | 0.0720617 | + | 0.0263077i | ||||
\(716\) | −9.52914e6 | −0.694658 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.09254e6i | 0.296266i | ||||||||
\(719\) | 1.20100e7 | 0.866405 | 0.433202 | − | 0.901297i | \(-0.357384\pi\) | ||||
0.433202 | + | 0.901297i | \(0.357384\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.22778e6 | 0.374524 | ||||||||
\(722\) | 9.11343e6i | 0.650637i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.31229e6 | −0.163944 | ||||||||
\(725\) | −8.49890e6 | − | 7.15965e6i | −0.600507 | − | 0.505879i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.14993e7i | 0.806927i | 0.914996 | + | 0.403463i | \(0.132194\pi\) | ||||
−0.914996 | + | 0.403463i | \(0.867806\pi\) | |||||||
\(728\) | 3.12781e6i | 0.218732i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.72296e6 | + | 1.29371e7i | −0.328025 | + | 0.898521i | ||||
\(731\) | 4.98676e6 | 0.345164 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.04473e7i | 1.40565i | 0.711364 | + | 0.702823i | \(0.248078\pi\) | ||||
−0.711364 | + | 0.702823i | \(0.751922\pi\) | |||||||
\(734\) | −1.22122e7 | −0.836668 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.39959e6 | 0.299376 | ||||||||
\(737\) | 355351.i | 0.0240984i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −220621. | −0.0148606 | −0.00743030 | − | 0.999972i | \(-0.502365\pi\) | ||||
−0.00743030 | + | 0.999972i | \(0.502365\pi\) | |||||||
\(740\) | 4.56692e6 | + | 1.66726e6i | 0.306580 | + | 0.111924i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 1.19334e7i | − | 0.795707i | ||||||
\(743\) | 2.51435e7i | 1.67091i | 0.549558 | + | 0.835456i | \(0.314796\pi\) | ||||
−0.549558 | + | 0.835456i | \(0.685204\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −78662.1 | + | 215470.i | −0.00519248 | + | 0.0142232i | ||||
\(746\) | −1.47764e7 | −0.972126 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 325643.i | − | 0.0212808i | ||||||
\(749\) | −3.05282e7 | −1.98837 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −667547. | −0.0431899 | −0.0215950 | − | 0.999767i | \(-0.506874\pi\) | ||||
−0.0215950 | + | 0.999767i | \(0.506874\pi\) | |||||||
\(752\) | − | 1.97587e6i | − | 0.127413i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.97454e6 | 0.190543 | ||||||||
\(755\) | −2.05986e6 | + | 5.64234e6i | −0.131514 | + | 0.360240i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.62490e7i | 1.03059i | 0.857012 | + | 0.515297i | \(0.172318\pi\) | ||||
−0.857012 | + | 0.515297i | \(0.827682\pi\) | |||||||
\(758\) | − | 1.79410e7i | − | 1.13416i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.32803e6 | + | 2.67526e6i | 0.460207 | + | 0.168009i | ||||
\(761\) | 1.43662e7 | 0.899253 | 0.449626 | − | 0.893217i | \(-0.351557\pi\) | ||||
0.449626 | + | 0.893217i | \(0.351557\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.20227e7i | − | 0.747634i | ||||||
\(764\) | 1.30547e7 | 0.809157 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.81225e7 | 1.11595 | ||||||||
\(767\) | 9.31737e6i | 0.571880i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.92705e7 | −1.17511 | −0.587553 | − | 0.809185i | \(-0.699909\pi\) | ||||
−0.587553 | + | 0.809185i | \(0.699909\pi\) | |||||||
\(770\) | −1.60763e6 | + | 4.40360e6i | −0.0977147 | + | 0.267659i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.06405e7i | 0.642566i | ||||||||
\(773\) | 2.40693e7i | 1.44882i | 0.689370 | + | 0.724410i | \(0.257888\pi\) | ||||
−0.689370 | + | 0.724410i | \(0.742112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.64962e7 | − | 1.38967e7i | −0.986573 | − | 0.831109i | ||||
\(776\) | 5.65986e6 | 0.337405 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.09423e7i | 0.648125i | ||||||||
\(779\) | −1.41382e7 | −0.834737 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.16357e6 | −0.244252 | ||||||||
\(782\) | 3.89917e6i | 0.228011i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.67974e6 | −0.562436 | ||||||||
\(785\) | −1.81598e7 | − | 6.62964e6i | −1.05181 | − | 0.383987i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.76223e6i | 0.216525i | 0.994122 | + | 0.108263i | \(0.0345288\pi\) | ||||
−0.994122 | + | 0.108263i | \(0.965471\pi\) | |||||||
\(788\) | − | 5.32756e6i | − | 0.305642i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.85565e6 | − | 2.13773e6i | −0.333816 | − | 0.121867i | ||||
\(791\) | −3.23119e7 | −1.83620 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.42540e6i | − | 0.136962i | ||||||
\(794\) | 6.19794e6 | 0.348896 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −313045. | −0.0175115 | ||||||||
\(797\) | − | 9.10423e6i | − | 0.507689i | −0.967245 | − | 0.253844i | \(-0.918305\pi\) | ||
0.967245 | − | 0.253844i | \(-0.0816951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.75113e6 | 0.0970401 | ||||||||
\(800\) | 2.06169e6 | − | 2.44734e6i | 0.113893 | − | 0.135197i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 1.78454e7i | − | 0.979695i | ||||||
\(803\) | − | 5.52510e6i | − | 0.302379i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.92494e7 | − | 5.27277e7i | 1.04695 | − | 2.86780i | ||||
\(806\) | 5.77352e6 | 0.313043 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 7.45414e6i | − | 0.401670i | ||||||
\(809\) | 1.20232e7 | 0.645877 | 0.322938 | − | 0.946420i | \(-0.395329\pi\) | ||||
0.322938 | + | 0.946420i | \(0.395329\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.50728e6 | −0.294026 | −0.147013 | − | 0.989135i | \(-0.546966\pi\) | ||||
−0.147013 | + | 0.989135i | \(0.546966\pi\) | |||||||
\(812\) | 1.32972e7i | 0.707732i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.95042e6 | −0.103173 | ||||||||
\(815\) | −3.08645e6 | − | 1.12678e6i | −0.162766 | − | 0.0594215i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.79258e7i | − | 2.51197i | ||||||
\(818\) | 9.47258e6i | 0.494977i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.98883e6 | + | 5.44778e6i | −0.103291 | + | 0.282934i | ||||
\(821\) | −1.33971e7 | −0.693672 | −0.346836 | − | 0.937926i | \(-0.612744\pi\) | ||||
−0.346836 | + | 0.937926i | \(0.612744\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.41005e7i | 0.725664i | 0.931855 | + | 0.362832i | \(0.118190\pi\) | ||||
−0.931855 | + | 0.362832i | \(0.881810\pi\) | |||||||
\(824\) | 1.43162e6 | 0.0734530 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.16516e7 | −2.12413 | ||||||||
\(827\) | − | 1.28958e7i | − | 0.655669i | −0.944735 | − | 0.327834i | \(-0.893681\pi\) | ||
0.944735 | − | 0.327834i | \(-0.106319\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 372726. | 0.0188366 | 0.00941831 | − | 0.999956i | \(-0.497002\pi\) | ||||
0.00941831 | + | 0.999956i | \(0.497002\pi\) | |||||||
\(830\) | 3.90628e6 | − | 1.07000e7i | 0.196819 | − | 0.539124i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 856547.i | 0.0428986i | ||||||||
\(833\) | − | 8.57875e6i | − | 0.428362i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.12115e6 | − | 2.96481e6i | −0.403089 | − | 0.147157i | ||||
\(836\) | −3.12962e6 | −0.154873 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.30545e7i | 1.13409i | ||||||||
\(839\) | 1.57724e7 | 0.773560 | 0.386780 | − | 0.922172i | \(-0.373587\pi\) | ||||
0.386780 | + | 0.922172i | \(0.373587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.86558e6 | −0.383478 | ||||||||
\(842\) | 1.30629e7i | 0.634978i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.07116e7 | 0.517604 | ||||||||
\(845\) | −6.27957e6 | + | 1.72009e7i | −0.302544 | + | 0.828723i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.57579e7i | 1.71263i | ||||||||
\(848\) | − | 3.26793e6i | − | 0.156057i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.16897e6 | + | 1.82719e6i | 0.102969 | + | 0.0867432i | ||||
\(851\) | 2.33538e7 | 1.10544 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.39555e6i | − | 0.159786i | −0.996803 | − | 0.0798928i | \(-0.974542\pi\) | ||
0.996803 | − | 0.0798928i | \(-0.0254578\pi\) | |||||||
\(854\) | 1.08423e7 | 0.508718 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.36009e6 | −0.389966 | ||||||||
\(857\) | 4.62981e6i | 0.215333i | 0.994187 | + | 0.107667i | \(0.0343379\pi\) | ||||
−0.994187 | + | 0.107667i | \(0.965662\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.57703e7 | 0.729218 | 0.364609 | − | 0.931161i | \(-0.381203\pi\) | ||||
0.364609 | + | 0.931161i | \(0.381203\pi\) | |||||||
\(860\) | −1.84670e7 | − | 6.74177e6i | −0.851430 | − | 0.310834i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.24844e7i | 1.03065i | ||||||||
\(863\) | 3.26217e7i | 1.49101i | 0.666502 | + | 0.745503i | \(0.267791\pi\) | ||||
−0.666502 | + | 0.745503i | \(0.732209\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.01103e6 | + | 3.28968e6i | 0.409481 | + | 0.149490i | ||||
\(866\) | 1.27462e7 | 0.577546 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.58095e7i | 1.16273i | ||||||||
\(869\) | 2.50080e6 | 0.112339 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 828376. | 0.0369983 | ||||||||
\(872\) | − | 3.29239e6i | − | 0.146629i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.74733e7 | 1.65937 | ||||||||
\(875\) | −2.03101e7 | − | 3.54164e7i | −0.896793 | − | 1.56381i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 3.88139e6i | − | 0.170407i | −0.996364 | − | 0.0852037i | \(-0.972846\pi\) | ||
0.996364 | − | 0.0852037i | \(-0.0271541\pi\) | |||||||
\(878\) | 2.96441e7i | 1.29778i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −440248. | + | 1.20592e6i | −0.0191642 | + | 0.0524942i | ||||
\(881\) | 2.11909e7 | 0.919834 | 0.459917 | − | 0.887962i | \(-0.347879\pi\) | ||||
0.459917 | + | 0.887962i | \(0.347879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 257162.i | 0.0110995i | 0.999985 | + | 0.00554976i | \(0.00176655\pi\) | ||||
−0.999985 | + | 0.00554976i | \(0.998233\pi\) | |||||||
\(884\) | −759122. | −0.0326724 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.05145e7 | 0.449990 | ||||||||
\(887\) | − | 1.02364e7i | − | 0.436856i | −0.975853 | − | 0.218428i | \(-0.929907\pi\) | ||
0.975853 | − | 0.218428i | \(-0.0700929\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.66623e7 | 1.98021 | ||||||||
\(890\) | −1.07779e6 | − | 393472.i | −0.0456100 | − | 0.0166510i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 1.34706e7i | − | 0.566860i | ||||||
\(893\) | − | 1.68294e7i | − | 0.706220i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.14175e7 | + | 3.12745e7i | −0.476444 | + | 1.30507i | ||||
\(896\) | −3.82904e6 | −0.159338 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 287058.i | 0.0118790i | ||||||||
\(899\) | 2.45448e7 | 1.01288 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.89623e6 | 0.118856 | ||||||||
\(902\) | − | 2.32661e6i | − | 0.0952155i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.84855e6 | −0.360123 | ||||||||
\(905\) | −2.77050e6 | + | 7.58891e6i | −0.112444 | + | 0.308005i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.30652e7i | − | 0.527350i | −0.964612 | − | 0.263675i | \(-0.915065\pi\) | ||
0.964612 | − | 0.263675i | \(-0.0849346\pi\) | |||||||
\(908\) | 1.70074e6i | 0.0684580i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.02654e7 | + | 3.74763e6i | 0.410936 | + | 0.150021i | ||||
\(911\) | 9.81608e6 | 0.391870 | 0.195935 | − | 0.980617i | \(-0.437226\pi\) | ||||
0.195935 | + | 0.980617i | \(0.437226\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.56971e6i | 0.181431i | ||||||||
\(914\) | −1.40588e7 | −0.556652 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.44689e7 | 0.963553 | ||||||||
\(917\) | − | 7.34358e7i | − | 2.88393i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.71414e6 | −0.106009 | −0.0530045 | − | 0.998594i | \(-0.516880\pi\) | ||||
−0.0530045 | + | 0.998594i | \(0.516880\pi\) | |||||||
\(920\) | 5.27142e6 | − | 1.44394e7i | 0.205333 | − | 0.562444i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 1.34228e7i | − | 0.520013i | ||||||
\(923\) | 9.70591e6i | 0.375000i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.09438e7 | − | 1.29909e7i | 0.420547 | − | 0.499213i | ||||
\(926\) | 1.38908e7 | 0.532352 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.64141e6i | 0.138803i | ||||||||
\(929\) | −4.31963e6 | −0.164213 | −0.0821064 | − | 0.996624i | \(-0.526165\pi\) | ||||
−0.0821064 | + | 0.996624i | \(0.526165\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.24469e7 | −3.11745 | ||||||||
\(932\) | − | 5.79431e6i | − | 0.218505i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.41981e6 | 0.353326 | ||||||||
\(935\) | −1.06876e6 | − | 390173.i | −0.0399806 | − | 0.0145958i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.17380e7i | − | 0.808854i | −0.914570 | − | 0.404427i | \(-0.867471\pi\) | ||
0.914570 | − | 0.404427i | \(-0.132529\pi\) | |||||||
\(938\) | 3.70311e6i | 0.137423i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.48477e6 | − | 2.36741e6i | −0.239373 | − | 0.0873884i | ||||
\(941\) | 2.17794e7 | 0.801811 | 0.400905 | − | 0.916119i | \(-0.368696\pi\) | ||||
0.400905 | + | 0.916119i | \(0.368696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.78583e7i | 1.02018i | ||||||||
\(944\) | −1.14062e7 | −0.416593 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.88678e6 | 0.286531 | ||||||||
\(947\) | 4.93262e7i | 1.78732i | 0.448745 | + | 0.893660i | \(0.351871\pi\) | ||||
−0.448745 | + | 0.893660i | \(0.648129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.28798e7 | −0.464242 | ||||||||
\(950\) | 1.75603e7 | − | 2.08451e7i | 0.631283 | − | 0.749368i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 3.39352e6i | − | 0.121355i | ||||||
\(953\) | − | 3.37247e7i | − | 1.20286i | −0.798924 | − | 0.601432i | \(-0.794597\pi\) | ||
0.798924 | − | 0.601432i | \(-0.205403\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.56416e7 | − | 4.28453e7i | 0.554975 | − | 1.52018i | ||||
\(956\) | −615929. | −0.0217965 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 751082.i | − | 0.0264407i | ||||||
\(959\) | 6.00252e7 | 2.10759 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.90117e7 | 0.664068 | ||||||||
\(962\) | 4.54671e6i | 0.158402i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.07892e6 | −0.314660 | ||||||||
\(965\) | 3.49219e7 | + | 1.27490e7i | 1.20720 | + | 0.440716i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.77310e7i | 0.953673i | 0.878992 | + | 0.476836i | \(0.158217\pi\) | ||||
−0.878992 | + | 0.476836i | \(0.841783\pi\) | |||||||
\(968\) | 9.79225e6i | 0.335888i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.78143e6 | − | 1.85756e7i | 0.231415 | − | 0.633889i | ||||
\(971\) | 6.67841e6 | 0.227314 | 0.113657 | − | 0.993520i | \(-0.463744\pi\) | ||||
0.113657 | + | 0.993520i | \(0.463744\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.51870e6i | − | 0.0852893i | ||||||
\(974\) | 8.06018e6 | 0.272237 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.96915e6 | 0.0997716 | ||||||||
\(977\) | 4.34946e7i | 1.45780i | 0.684618 | + | 0.728902i | \(0.259969\pi\) | ||||
−0.684618 | + | 0.728902i | \(0.740031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 460299. | 0.0153491 | ||||||||
\(980\) | −1.15979e7 | + | 3.17688e7i | −0.385757 | + | 1.05666i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 2.32326e7i | − | 0.768809i | ||||||
\(983\) | 1.24213e7i | 0.410000i | 0.978762 | + | 0.205000i | \(0.0657194\pi\) | ||||
−0.978762 | + | 0.205000i | \(0.934281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.74850e7 | − | 6.38328e6i | −0.574215 | − | 0.209630i | ||||
\(986\) | −3.22723e6 | −0.105715 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.29561e6i | 0.237777i | ||||||||
\(989\) | −9.44344e7 | −3.07001 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.93479e7 | 1.91965 | 0.959824 | − | 0.280604i | \(-0.0905348\pi\) | ||||
0.959824 | + | 0.280604i | \(0.0905348\pi\) | |||||||
\(992\) | 7.06789e6i | 0.228040i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.33885e7 | −1.39286 | ||||||||
\(995\) | −375079. | + | 1.02741e6i | −0.0120106 | + | 0.0328993i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 2.44456e7i | − | 0.778867i | −0.921055 | − | 0.389434i | \(-0.872671\pi\) | ||
0.921055 | − | 0.389434i | \(-0.127329\pi\) | |||||||
\(998\) | − | 2.32244e6i | − | 0.0738107i | ||||||
\(999\) | 0 | 0 |
(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 | 90.6.c.c.19.3 | 4 | ||
3.2 | odd | 2 | 30.6.c.b.19.2 | ✓ | 4 | ||
4.3 | odd | 2 | 720.6.f.i.289.2 | 4 | |||
5.2 | odd | 4 | 450.6.a.bb.1.2 | 2 | |||
5.3 | odd | 4 | 450.6.a.bc.1.1 | 2 | |||
5.4 | even | 2 | inner | 90.6.c.c.19.1 | 4 | ||
12.11 | even | 2 | 240.6.f.b.49.2 | 4 | |||
15.2 | even | 4 | 150.6.a.o.1.2 | 2 | |||
15.8 | even | 4 | 150.6.a.n.1.1 | 2 | |||
15.14 | odd | 2 | 30.6.c.b.19.4 | yes | 4 | ||
20.19 | odd | 2 | 720.6.f.i.289.1 | 4 | |||
60.59 | even | 2 | 240.6.f.b.49.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.6.c.b.19.2 | ✓ | 4 | 3.2 | odd | 2 | ||
30.6.c.b.19.4 | yes | 4 | 15.14 | odd | 2 | ||
90.6.c.c.19.1 | 4 | 5.4 | even | 2 | inner | ||
90.6.c.c.19.3 | 4 | 1.1 | even | 1 | trivial | ||
150.6.a.n.1.1 | 2 | 15.8 | even | 4 | |||
150.6.a.o.1.2 | 2 | 15.2 | even | 4 | |||
240.6.f.b.49.2 | 4 | 12.11 | even | 2 | |||
240.6.f.b.49.4 | 4 | 60.59 | even | 2 | |||
450.6.a.bb.1.2 | 2 | 5.2 | odd | 4 | |||
450.6.a.bc.1.1 | 2 | 5.3 | odd | 4 | |||
720.6.f.i.289.1 | 4 | 20.19 | odd | 2 | |||
720.6.f.i.289.2 | 4 | 4.3 | odd | 2 |