Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,5,Mod(163,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.163");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.d (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: | \(33.4918680392\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 163.11 | ||
Character | \(\chi\) | \(=\) | 324.163 |
Dual form | 324.5.d.f.163.12 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.328300 | − | 3.98650i | −0.0820750 | − | 0.996626i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −15.7844 | + | 2.61754i | −0.986527 | + | 0.163596i | ||||
\(5\) | 5.66182 | 0.226473 | 0.113236 | − | 0.993568i | \(-0.463878\pi\) | ||||
0.113236 | + | 0.993568i | \(0.463878\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 52.1456i | 1.06420i | 0.846683 | + | 0.532098i | \(0.178596\pi\) | ||||
−0.846683 | + | 0.532098i | \(0.821404\pi\) | |||||||
\(8\) | 15.6169 | + | 62.0654i | 0.244014 | + | 0.969772i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.85878 | − | 22.5709i | −0.0185878 | − | 0.225709i | ||||
\(11\) | 106.664i | 0.881519i | 0.897625 | + | 0.440760i | \(0.145291\pi\) | ||||
−0.897625 | + | 0.440760i | \(0.854709\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −122.137 | −0.722705 | −0.361352 | − | 0.932429i | \(-0.617685\pi\) | ||||
−0.361352 | + | 0.932429i | \(0.617685\pi\) | |||||||
\(14\) | 207.879 | − | 17.1194i | 1.06061 | − | 0.0873440i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 242.297 | − | 82.6328i | 0.946473 | − | 0.322784i | ||||
\(17\) | −122.675 | −0.424481 | −0.212240 | − | 0.977217i | \(-0.568076\pi\) | ||||
−0.212240 | + | 0.977217i | \(0.568076\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 593.624i | − | 1.64439i | −0.569207 | − | 0.822194i | \(-0.692750\pi\) | ||
0.569207 | − | 0.822194i | \(-0.307250\pi\) | |||||||
\(20\) | −89.3686 | + | 14.8200i | −0.223422 | + | 0.0370501i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 425.216 | − | 35.0178i | 0.878545 | − | 0.0723507i | ||||
\(23\) | − | 546.922i | − | 1.03388i | −0.856022 | − | 0.516940i | \(-0.827071\pi\) | ||
0.856022 | − | 0.516940i | \(-0.172929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −592.944 | −0.948710 | ||||||||
\(26\) | 40.0976 | + | 486.900i | 0.0593160 | + | 0.720266i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −136.493 | − | 823.090i | −0.174099 | − | 1.04986i | ||||
\(29\) | 735.866 | 0.874989 | 0.437495 | − | 0.899221i | \(-0.355866\pi\) | ||||
0.437495 | + | 0.899221i | \(0.355866\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 585.927i | − | 0.609705i | −0.952400 | − | 0.304853i | \(-0.901393\pi\) | ||
0.952400 | − | 0.304853i | \(-0.0986072\pi\) | |||||||
\(32\) | −408.962 | − | 938.790i | −0.399377 | − | 0.916787i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 40.2742 | + | 489.044i | 0.0348393 | + | 0.423049i | ||||
\(35\) | 295.239i | 0.241012i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2289.29 | 1.67223 | 0.836117 | − | 0.548551i | \(-0.184820\pi\) | ||||
0.836117 | + | 0.548551i | \(0.184820\pi\) | |||||||
\(38\) | −2366.49 | + | 194.887i | −1.63884 | + | 0.134963i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 88.4199 | + | 351.403i | 0.0552624 | + | 0.219627i | ||||
\(41\) | −2868.26 | −1.70628 | −0.853142 | − | 0.521678i | \(-0.825306\pi\) | ||||
−0.853142 | + | 0.521678i | \(0.825306\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2244.52i | − | 1.21391i | −0.794736 | − | 0.606955i | \(-0.792391\pi\) | ||
0.794736 | − | 0.606955i | \(-0.207609\pi\) | |||||||
\(44\) | −279.197 | − | 1683.63i | −0.144213 | − | 0.869643i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2180.31 | + | 179.555i | −1.03039 | + | 0.0848557i | ||||
\(47\) | − | 1054.85i | − | 0.477526i | −0.971078 | − | 0.238763i | \(-0.923258\pi\) | ||
0.971078 | − | 0.238763i | \(-0.0767419\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −318.168 | −0.132515 | ||||||||
\(50\) | 194.664 | + | 2363.77i | 0.0778654 | + | 0.945509i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1927.87 | − | 319.699i | 0.712968 | − | 0.118232i | ||||
\(53\) | −4752.60 | −1.69192 | −0.845960 | − | 0.533246i | \(-0.820972\pi\) | ||||
−0.845960 | + | 0.533246i | \(0.820972\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 603.911i | 0.199640i | ||||||||
\(56\) | −3236.44 | + | 814.352i | −1.03203 | + | 0.259678i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −241.585 | − | 2933.53i | −0.0718148 | − | 0.872037i | ||||
\(59\) | 2152.65i | 0.618399i | 0.950997 | + | 0.309200i | \(0.100061\pi\) | ||||
−0.950997 | + | 0.309200i | \(0.899939\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −66.3319 | −0.0178264 | −0.00891319 | − | 0.999960i | \(-0.502837\pi\) | ||||
−0.00891319 | + | 0.999960i | \(0.502837\pi\) | |||||||
\(62\) | −2335.80 | + | 192.360i | −0.607648 | + | 0.0500416i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3608.23 | + | 1938.53i | −0.880915 | + | 0.473275i | ||||
\(65\) | −691.518 | −0.163673 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4104.76i | − | 0.914404i | −0.889363 | − | 0.457202i | \(-0.848852\pi\) | ||
0.889363 | − | 0.457202i | \(-0.151148\pi\) | |||||||
\(68\) | 1936.36 | − | 321.107i | 0.418762 | − | 0.0694435i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1176.97 | − | 96.9271i | 0.240198 | − | 0.0197810i | ||||
\(71\) | − | 5031.65i | − | 0.998145i | −0.866560 | − | 0.499072i | \(-0.833674\pi\) | ||
0.866560 | − | 0.499072i | \(-0.166326\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2705.16 | 0.507631 | 0.253815 | − | 0.967253i | \(-0.418314\pi\) | ||||
0.253815 | + | 0.967253i | \(0.418314\pi\) | |||||||
\(74\) | −751.574 | − | 9126.26i | −0.137249 | − | 1.66659i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1553.84 | + | 9370.03i | 0.269016 | + | 1.62223i | ||||
\(77\) | −5562.06 | −0.938110 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1381.05i | − | 0.221286i | −0.993860 | − | 0.110643i | \(-0.964709\pi\) | ||
0.993860 | − | 0.110643i | \(-0.0352911\pi\) | |||||||
\(80\) | 1371.84 | − | 467.852i | 0.214350 | − | 0.0731019i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 941.652 | + | 11434.4i | 0.140043 | + | 1.70053i | ||||
\(83\) | 3008.36i | 0.436690i | 0.975872 | + | 0.218345i | \(0.0700658\pi\) | ||||
−0.975872 | + | 0.218345i | \(0.929934\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −694.563 | −0.0961333 | ||||||||
\(86\) | −8947.79 | + | 736.876i | −1.20981 | + | 0.0996317i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6620.13 | + | 1665.76i | −0.854873 | + | 0.215103i | ||||
\(89\) | 3186.35 | 0.402267 | 0.201133 | − | 0.979564i | \(-0.435538\pi\) | ||||
0.201133 | + | 0.979564i | \(0.435538\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6368.92i | − | 0.769100i | ||||||
\(92\) | 1431.59 | + | 8632.86i | 0.169139 | + | 1.01995i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4205.18 | + | 346.309i | −0.475915 | + | 0.0391930i | ||||
\(95\) | − | 3360.99i | − | 0.372409i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4814.06 | −0.511644 | −0.255822 | − | 0.966724i | \(-0.582346\pi\) | ||||
−0.255822 | + | 0.966724i | \(0.582346\pi\) | |||||||
\(98\) | 104.455 | + | 1268.38i | 0.0108762 | + | 0.132068i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9359.28 | − | 1552.05i | 0.935928 | − | 0.155205i | ||||
\(101\) | −7020.93 | −0.688259 | −0.344130 | − | 0.938922i | \(-0.611826\pi\) | ||||
−0.344130 | + | 0.938922i | \(0.611826\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2146.41i | 0.202320i | 0.994870 | + | 0.101160i | \(0.0322554\pi\) | ||||
−0.994870 | + | 0.101160i | \(0.967745\pi\) | |||||||
\(104\) | −1907.40 | − | 7580.49i | −0.176350 | − | 0.700859i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1560.28 | + | 18946.3i | 0.138864 | + | 1.68621i | ||||
\(107\) | 13846.7i | 1.20943i | 0.796443 | + | 0.604713i | \(0.206712\pi\) | ||||
−0.796443 | + | 0.604713i | \(0.793288\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19384.9 | −1.63159 | −0.815793 | − | 0.578344i | \(-0.803699\pi\) | ||||
−0.815793 | + | 0.578344i | \(0.803699\pi\) | |||||||
\(110\) | 2407.50 | − | 198.264i | 0.198967 | − | 0.0163855i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4308.94 | + | 12634.7i | 0.343506 | + | 1.00723i | ||||
\(113\) | 13634.4 | 1.06777 | 0.533887 | − | 0.845556i | \(-0.320731\pi\) | ||||
0.533887 | + | 0.845556i | \(0.320731\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 3096.57i | − | 0.234145i | ||||||
\(116\) | −11615.2 | + | 1926.16i | −0.863201 | + | 0.143145i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8581.54 | − | 706.715i | 0.616313 | − | 0.0507551i | ||||
\(119\) | − | 6396.96i | − | 0.451731i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3263.82 | 0.222923 | ||||||||
\(122\) | 21.7768 | + | 264.433i | 0.00146310 | + | 0.0177662i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1533.69 | + | 9248.52i | 0.0997455 | + | 0.601491i | ||||
\(125\) | −6895.78 | −0.441330 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15689.6i | − | 0.972754i | −0.873749 | − | 0.486377i | \(-0.838318\pi\) | ||
0.873749 | − | 0.486377i | \(-0.161682\pi\) | |||||||
\(128\) | 8912.56 | + | 13747.8i | 0.543979 | + | 0.839099i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 227.025 | + | 2756.74i | 0.0134335 | + | 0.163121i | ||||
\(131\) | − | 8371.86i | − | 0.487842i | −0.969795 | − | 0.243921i | \(-0.921566\pi\) | ||
0.969795 | − | 0.243921i | \(-0.0784338\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 30954.9 | 1.74995 | ||||||||
\(134\) | −16363.6 | + | 1347.59i | −0.911319 | + | 0.0750497i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1915.80 | − | 7613.87i | −0.103579 | − | 0.411650i | ||||
\(137\) | −29930.3 | −1.59467 | −0.797333 | − | 0.603540i | \(-0.793756\pi\) | ||||
−0.797333 | + | 0.603540i | \(0.793756\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 23846.7i | − | 1.23424i | −0.786871 | − | 0.617118i | \(-0.788300\pi\) | ||
0.786871 | − | 0.617118i | \(-0.211700\pi\) | |||||||
\(140\) | −772.800 | − | 4660.18i | −0.0394286 | − | 0.237764i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −20058.7 | + | 1651.89i | −0.994777 | + | 0.0819228i | ||||
\(143\) | − | 13027.6i | − | 0.637078i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4166.34 | 0.198161 | ||||||||
\(146\) | −888.106 | − | 10784.2i | −0.0416638 | − | 0.505918i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −36135.1 | + | 5992.30i | −1.64970 | + | 0.273571i | ||||
\(149\) | 5273.96 | 0.237555 | 0.118778 | − | 0.992921i | \(-0.462102\pi\) | ||||
0.118778 | + | 0.992921i | \(0.462102\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 33424.0i | − | 1.46590i | −0.680281 | − | 0.732951i | \(-0.738142\pi\) | ||
0.680281 | − | 0.732951i | \(-0.261858\pi\) | |||||||
\(152\) | 36843.5 | − | 9270.55i | 1.59468 | − | 0.401253i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1826.02 | + | 22173.2i | 0.0769954 | + | 0.934945i | ||||
\(155\) | − | 3317.41i | − | 0.138082i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17001.5 | 0.689742 | 0.344871 | − | 0.938650i | \(-0.387923\pi\) | ||||
0.344871 | + | 0.938650i | \(0.387923\pi\) | |||||||
\(158\) | −5505.55 | + | 453.398i | −0.220540 | + | 0.0181621i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2315.47 | − | 5315.26i | −0.0904480 | − | 0.207627i | ||||
\(161\) | 28519.6 | 1.10025 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 30843.8i | − | 1.16089i | −0.814298 | − | 0.580447i | \(-0.802878\pi\) | ||
0.814298 | − | 0.580447i | \(-0.197122\pi\) | |||||||
\(164\) | 45273.9 | − | 7507.80i | 1.68330 | − | 0.279142i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11992.8 | − | 987.644i | 0.435216 | − | 0.0358413i | ||||
\(167\) | 15798.7i | 0.566485i | 0.959048 | + | 0.283243i | \(0.0914102\pi\) | ||||
−0.959048 | + | 0.283243i | \(0.908590\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13643.5 | −0.477698 | ||||||||
\(170\) | 228.025 | + | 2768.88i | 0.00789015 | + | 0.0958090i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5875.12 | + | 35428.5i | 0.198591 | + | 1.19756i | ||||
\(173\) | 47062.8 | 1.57248 | 0.786241 | − | 0.617921i | \(-0.212025\pi\) | ||||
0.786241 | + | 0.617921i | \(0.212025\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 30919.4i | − | 1.00961i | ||||||
\(176\) | 8813.93 | + | 25844.3i | 0.284541 | + | 0.834334i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1046.08 | − | 12702.4i | −0.0330161 | − | 0.400909i | ||||
\(179\) | − | 2545.69i | − | 0.0794511i | −0.999211 | − | 0.0397256i | \(-0.987352\pi\) | ||
0.999211 | − | 0.0397256i | \(-0.0126484\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5676.58 | 0.173272 | 0.0866362 | − | 0.996240i | \(-0.472388\pi\) | ||||
0.0866362 | + | 0.996240i | \(0.472388\pi\) | |||||||
\(182\) | −25389.7 | + | 2090.92i | −0.766505 | + | 0.0631239i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 33944.9 | − | 8541.21i | 1.00263 | − | 0.252281i | ||||
\(185\) | 12961.5 | 0.378715 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 13085.0i | − | 0.374188i | ||||||
\(188\) | 2761.12 | + | 16650.3i | 0.0781214 | + | 0.471092i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13398.6 | + | 1103.41i | −0.371153 | + | 0.0305655i | ||||
\(191\) | 32478.5i | 0.890284i | 0.895460 | + | 0.445142i | \(0.146847\pi\) | ||||
−0.895460 | + | 0.445142i | \(0.853153\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 787.434 | 0.0211397 | 0.0105699 | − | 0.999944i | \(-0.496635\pi\) | ||||
0.0105699 | + | 0.999944i | \(0.496635\pi\) | |||||||
\(194\) | 1580.46 | + | 19191.3i | 0.0419932 | + | 0.509918i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5022.11 | − | 832.818i | 0.130730 | − | 0.0216789i | ||||
\(197\) | 24825.9 | 0.639694 | 0.319847 | − | 0.947469i | \(-0.396368\pi\) | ||||
0.319847 | + | 0.947469i | \(0.396368\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12008.5i | 0.303237i | 0.988439 | + | 0.151619i | \(0.0484485\pi\) | ||||
−0.988439 | + | 0.151619i | \(0.951551\pi\) | |||||||
\(200\) | −9259.93 | − | 36801.3i | −0.231498 | − | 0.920032i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2304.97 | + | 27989.0i | 0.0564889 | + | 0.685937i | ||||
\(203\) | 38372.2i | 0.931161i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16239.6 | −0.386427 | ||||||||
\(206\) | 8556.69 | − | 704.668i | 0.201638 | − | 0.0166054i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −29593.5 | + | 10092.5i | −0.684020 | + | 0.233278i | ||||
\(209\) | 63318.3 | 1.44956 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 29750.5i | − | 0.668235i | −0.942532 | − | 0.334117i | \(-0.891562\pi\) | ||
0.942532 | − | 0.334117i | \(-0.108438\pi\) | |||||||
\(212\) | 75017.2 | − | 12440.1i | 1.66913 | − | 0.276792i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 55200.0 | − | 4545.88i | 1.20535 | − | 0.0992637i | ||||
\(215\) | − | 12708.1i | − | 0.274917i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30553.5 | 0.648846 | ||||||||
\(218\) | 6364.06 | + | 77277.9i | 0.133912 | + | 1.62608i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1580.76 | − | 9532.40i | −0.0326604 | − | 0.196950i | ||||
\(221\) | 14983.2 | 0.306774 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 52948.5i | − | 1.06474i | −0.846511 | − | 0.532371i | \(-0.821301\pi\) | ||
0.846511 | − | 0.532371i | \(-0.178699\pi\) | |||||||
\(224\) | 48953.8 | − | 21325.6i | 0.975642 | − | 0.425016i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4476.18 | − | 54353.6i | −0.0876376 | − | 1.06417i | ||||
\(227\) | − | 37635.8i | − | 0.730380i | −0.930933 | − | 0.365190i | \(-0.881004\pi\) | ||
0.930933 | − | 0.365190i | \(-0.118996\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −57238.4 | −1.09148 | −0.545741 | − | 0.837954i | \(-0.683752\pi\) | ||||
−0.545741 | + | 0.837954i | \(0.683752\pi\) | |||||||
\(230\) | −12344.5 | + | 1016.61i | −0.233356 | + | 0.0192175i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11491.9 | + | 45671.8i | 0.213509 | + | 0.848540i | ||||
\(233\) | −36468.7 | −0.671751 | −0.335876 | − | 0.941906i | \(-0.609032\pi\) | ||||
−0.335876 | + | 0.941906i | \(0.609032\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 5972.39i | − | 0.108147i | ||||||
\(236\) | −5634.64 | − | 33978.3i | −0.101168 | − | 0.610068i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −25501.5 | + | 2100.12i | −0.450207 | + | 0.0370759i | ||||
\(239\) | − | 52357.1i | − | 0.916600i | −0.888798 | − | 0.458300i | \(-0.848459\pi\) | ||
0.888798 | − | 0.458300i | \(-0.151541\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13511.1 | −0.232625 | −0.116313 | − | 0.993213i | \(-0.537107\pi\) | ||||
−0.116313 | + | 0.993213i | \(0.537107\pi\) | |||||||
\(242\) | −1071.51 | − | 13011.2i | −0.0182964 | − | 0.222171i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1047.01 | − | 173.627i | 0.0175862 | − | 0.00291633i | ||||
\(245\) | −1801.41 | −0.0300110 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 72503.6i | 1.18841i | ||||||||
\(248\) | 36365.8 | − | 9150.34i | 0.591275 | − | 0.148776i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2263.88 | + | 27490.0i | 0.0362221 | + | 0.439841i | ||||
\(251\) | 111309.i | 1.76678i | 0.468635 | + | 0.883392i | \(0.344746\pi\) | ||||
−0.468635 | + | 0.883392i | \(0.655254\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 58336.8 | 0.911385 | ||||||||
\(254\) | −62546.5 | + | 5150.88i | −0.969472 | + | 0.0798388i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 51879.6 | − | 40043.4i | 0.791620 | − | 0.611013i | ||||
\(257\) | −73913.1 | −1.11906 | −0.559532 | − | 0.828809i | \(-0.689019\pi\) | ||||
−0.559532 | + | 0.828809i | \(0.689019\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 119376.i | 1.77959i | ||||||||
\(260\) | 10915.2 | − | 1810.08i | 0.161468 | − | 0.0267763i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −33374.5 | + | 2748.48i | −0.486197 | + | 0.0400397i | ||||
\(263\) | 7367.96i | 0.106521i | 0.998581 | + | 0.0532606i | \(0.0169614\pi\) | ||||
−0.998581 | + | 0.0532606i | \(0.983039\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −26908.4 | −0.383174 | ||||||||
\(266\) | −10162.5 | − | 123402.i | −0.143627 | − | 1.74405i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10744.4 | + | 64791.3i | 0.149593 | + | 0.902084i | ||||
\(269\) | −38604.8 | −0.533502 | −0.266751 | − | 0.963765i | \(-0.585950\pi\) | ||||
−0.266751 | + | 0.963765i | \(0.585950\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12540.3i | 0.170753i | 0.996349 | + | 0.0853767i | \(0.0272094\pi\) | ||||
−0.996349 | + | 0.0853767i | \(0.972791\pi\) | |||||||
\(272\) | −29723.8 | + | 10137.0i | −0.401759 | + | 0.137016i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9826.12 | + | 119317.i | 0.130882 | + | 1.58929i | ||||
\(275\) | − | 63245.7i | − | 0.836306i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −92104.7 | −1.20039 | −0.600195 | − | 0.799854i | \(-0.704910\pi\) | ||||
−0.600195 | + | 0.799854i | \(0.704910\pi\) | |||||||
\(278\) | −95064.9 | + | 7828.87i | −1.23007 | + | 0.101300i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −18324.1 | + | 4610.71i | −0.233726 | + | 0.0588101i | ||||
\(281\) | 22295.9 | 0.282366 | 0.141183 | − | 0.989983i | \(-0.454909\pi\) | ||||
0.141183 | + | 0.989983i | \(0.454909\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24997.7i | 0.312123i | 0.987747 | + | 0.156062i | \(0.0498799\pi\) | ||||
−0.987747 | + | 0.156062i | \(0.950120\pi\) | |||||||
\(284\) | 13170.5 | + | 79421.7i | 0.163293 | + | 0.984697i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −51934.6 | + | 4276.97i | −0.634929 | + | 0.0522882i | ||||
\(287\) | − | 149568.i | − | 1.81582i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −68471.9 | −0.819816 | ||||||||
\(290\) | −1367.81 | − | 16609.1i | −0.0162641 | − | 0.197493i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −42699.5 | + | 7080.88i | −0.500792 | + | 0.0830465i | ||||
\(293\) | −23497.1 | −0.273703 | −0.136852 | − | 0.990592i | \(-0.543698\pi\) | ||||
−0.136852 | + | 0.990592i | \(0.543698\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12187.9i | 0.140051i | ||||||||
\(296\) | 35751.5 | + | 142086.i | 0.408048 | + | 1.62169i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1731.44 | − | 21024.7i | −0.0194974 | − | 0.236754i | ||||
\(299\) | 66799.5i | 0.747190i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 117042. | 1.29184 | ||||||||
\(302\) | −133245. | + | 10973.1i | −1.46096 | + | 0.120314i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −49052.8 | − | 143833.i | −0.530783 | − | 1.55637i | ||||
\(305\) | −375.559 | −0.00403719 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32060.0i | 0.340163i | 0.985430 | + | 0.170082i | \(0.0544031\pi\) | ||||
−0.985430 | + | 0.170082i | \(0.945597\pi\) | |||||||
\(308\) | 87793.9 | − | 14558.9i | 0.925471 | − | 0.153471i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13224.9 | + | 1089.11i | −0.137616 | + | 0.0113331i | ||||
\(311\) | 70946.4i | 0.733516i | 0.930316 | + | 0.366758i | \(0.119532\pi\) | ||||
−0.930316 | + | 0.366758i | \(0.880468\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 118519. | 1.20976 | 0.604882 | − | 0.796315i | \(-0.293220\pi\) | ||||
0.604882 | + | 0.796315i | \(0.293220\pi\) | |||||||
\(314\) | −5581.58 | − | 67776.4i | −0.0566106 | − | 0.687415i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3614.95 | + | 21799.1i | 0.0362016 | + | 0.218305i | ||||
\(317\) | −134781. | −1.34125 | −0.670626 | − | 0.741795i | \(-0.733975\pi\) | ||||
−0.670626 | + | 0.741795i | \(0.733975\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 78490.3i | 0.771320i | ||||||||
\(320\) | −20429.1 | + | 10975.6i | −0.199503 | + | 0.107184i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9362.99 | − | 113694.i | −0.0903032 | − | 1.09654i | ||||
\(323\) | 72822.8i | 0.698011i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 72420.4 | 0.685637 | ||||||||
\(326\) | −122959. | + | 10126.0i | −1.15698 | + | 0.0952804i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −44793.3 | − | 178020.i | −0.416357 | − | 1.65471i | ||||
\(329\) | 55006.1 | 0.508181 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 153740.i | 1.40324i | 0.712552 | + | 0.701620i | \(0.247539\pi\) | ||||
−0.712552 | + | 0.701620i | \(0.752461\pi\) | |||||||
\(332\) | −7874.49 | − | 47485.2i | −0.0714408 | − | 0.430806i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 62981.6 | − | 5186.72i | 0.564574 | − | 0.0464943i | ||||
\(335\) | − | 23240.4i | − | 0.207087i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22943.7 | −0.202024 | −0.101012 | − | 0.994885i | \(-0.532208\pi\) | ||||
−0.101012 | + | 0.994885i | \(0.532208\pi\) | |||||||
\(338\) | 4479.17 | + | 54390.0i | 0.0392071 | + | 0.476086i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10963.3 | − | 1818.05i | 0.0948382 | − | 0.0157271i | ||||
\(341\) | 62497.2 | 0.537467 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 108611.i | 0.923175i | ||||||||
\(344\) | 139307. | − | 35052.4i | 1.17722 | − | 0.296211i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15450.7 | − | 187616.i | −0.129061 | − | 1.56718i | ||||
\(347\) | − | 7229.43i | − | 0.0600406i | −0.999549 | − | 0.0300203i | \(-0.990443\pi\) | ||
0.999549 | − | 0.0300203i | \(-0.00955720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 110565. | 0.907753 | 0.453877 | − | 0.891065i | \(-0.350041\pi\) | ||||
0.453877 | + | 0.891065i | \(0.350041\pi\) | |||||||
\(350\) | −123260. | + | 10150.9i | −1.00621 | + | 0.0828641i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 100135. | − | 43621.5i | 0.808165 | − | 0.352059i | ||||
\(353\) | −61603.4 | −0.494374 | −0.247187 | − | 0.968968i | \(-0.579506\pi\) | ||||
−0.247187 | + | 0.968968i | \(0.579506\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 28488.3i | − | 0.226053i | ||||||
\(356\) | −50294.8 | + | 8340.41i | −0.396847 | + | 0.0658093i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10148.4 | + | 835.752i | −0.0791831 | + | 0.00652095i | ||||
\(359\) | − | 84462.7i | − | 0.655354i | −0.944790 | − | 0.327677i | \(-0.893734\pi\) | ||
0.944790 | − | 0.327677i | \(-0.106266\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −222069. | −1.70401 | ||||||||
\(362\) | −1863.62 | − | 22629.7i | −0.0142213 | − | 0.172688i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 16670.9 | + | 100530.i | 0.125822 | + | 0.758738i | ||||
\(365\) | 15316.1 | 0.114965 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 185928.i | − | 1.38042i | −0.723607 | − | 0.690212i | \(-0.757517\pi\) | ||
0.723607 | − | 0.690212i | \(-0.242483\pi\) | |||||||
\(368\) | −45193.7 | − | 132518.i | −0.333720 | − | 0.978538i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4255.27 | − | 51671.2i | −0.0310831 | − | 0.377438i | ||||
\(371\) | − | 247828.i | − | 1.80054i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −85091.3 | −0.611600 | −0.305800 | − | 0.952096i | \(-0.598924\pi\) | ||||
−0.305800 | + | 0.952096i | \(0.598924\pi\) | |||||||
\(374\) | −52163.3 | + | 4295.80i | −0.372926 | + | 0.0307115i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 65470.0 | − | 16473.5i | 0.463091 | − | 0.116523i | ||||
\(377\) | −89876.5 | −0.632359 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 146982.i | 1.02326i | 0.859206 | + | 0.511630i | \(0.170958\pi\) | ||||
−0.859206 | + | 0.511630i | \(0.829042\pi\) | |||||||
\(380\) | 8797.53 | + | 53051.4i | 0.0609247 | + | 0.367392i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 129475. | − | 10662.7i | 0.887280 | − | 0.0730701i | ||||
\(383\) | 186199.i | 1.26935i | 0.772780 | + | 0.634674i | \(0.218866\pi\) | ||||
−0.772780 | + | 0.634674i | \(0.781134\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31491.3 | −0.212456 | ||||||||
\(386\) | −258.515 | − | 3139.11i | −0.00173504 | − | 0.0210684i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 75987.2 | − | 12601.0i | 0.504751 | − | 0.0837030i | ||||
\(389\) | −256004. | −1.69179 | −0.845897 | − | 0.533347i | \(-0.820934\pi\) | ||||
−0.845897 | + | 0.533347i | \(0.820934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 67093.7i | 0.438862i | ||||||||
\(392\) | −4968.79 | − | 19747.2i | −0.0323354 | − | 0.128509i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8150.35 | − | 98968.5i | −0.0525029 | − | 0.637536i | ||||
\(395\) | − | 7819.24i | − | 0.0501153i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −260735. | −1.65432 | −0.827159 | − | 0.561968i | \(-0.810044\pi\) | ||||
−0.827159 | + | 0.561968i | \(0.810044\pi\) | |||||||
\(398\) | 47871.9 | − | 3942.39i | 0.302214 | − | 0.0248882i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −143668. | + | 48996.6i | −0.897928 | + | 0.306229i | ||||
\(401\) | 53014.0 | 0.329687 | 0.164843 | − | 0.986320i | \(-0.447288\pi\) | ||||
0.164843 | + | 0.986320i | \(0.447288\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 71563.4i | 0.440637i | ||||||||
\(404\) | 110821. | − | 18377.6i | 0.678986 | − | 0.112597i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 152971. | − | 12597.6i | 0.928019 | − | 0.0764251i | ||||
\(407\) | 244184.i | 1.47411i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 147396. | 0.881126 | 0.440563 | − | 0.897722i | \(-0.354779\pi\) | ||||
0.440563 | + | 0.897722i | \(0.354779\pi\) | |||||||
\(410\) | 5331.46 | + | 64739.2i | 0.0317160 | + | 0.385123i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5618.33 | − | 33879.9i | −0.0330988 | − | 0.199594i | ||||
\(413\) | −112251. | −0.658099 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17032.8i | 0.0988983i | ||||||||
\(416\) | 49949.5 | + | 114661.i | 0.288632 | + | 0.662566i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −20787.4 | − | 252419.i | −0.118973 | − | 1.44467i | ||||
\(419\) | − | 232592.i | − | 1.32485i | −0.749127 | − | 0.662426i | \(-0.769527\pi\) | ||
0.749127 | − | 0.662426i | \(-0.230473\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −69801.5 | −0.393823 | −0.196911 | − | 0.980421i | \(-0.563091\pi\) | ||||
−0.196911 | + | 0.980421i | \(0.563091\pi\) | |||||||
\(422\) | −118600. | + | 9767.08i | −0.665980 | + | 0.0548454i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −74220.8 | − | 294972.i | −0.412852 | − | 1.64078i | ||||
\(425\) | 72739.4 | 0.402709 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3458.92i | − | 0.0189708i | ||||||
\(428\) | −36244.4 | − | 218563.i | −0.197858 | − | 1.19313i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −50660.7 | + | 4172.06i | −0.273990 | + | 0.0225639i | ||||
\(431\) | 147873.i | 0.796037i | 0.917377 | + | 0.398019i | \(0.130302\pi\) | ||||
−0.917377 | + | 0.398019i | \(0.869698\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 294850. | 1.57262 | 0.786312 | − | 0.617830i | \(-0.211988\pi\) | ||||
0.786312 | + | 0.617830i | \(0.211988\pi\) | |||||||
\(434\) | −10030.7 | − | 121802.i | −0.0532541 | − | 0.646657i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 305979. | − | 50740.7i | 1.60960 | − | 0.266921i | ||||
\(437\) | −324666. | −1.70010 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 72131.8i | 0.374281i | 0.982333 | + | 0.187140i | \(0.0599220\pi\) | ||||
−0.982333 | + | 0.187140i | \(0.940078\pi\) | |||||||
\(440\) | −37482.0 | + | 9431.20i | −0.193605 | + | 0.0487149i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4918.98 | − | 59730.5i | −0.0251785 | − | 0.305739i | ||||
\(443\) | − | 190907.i | − | 0.972781i | −0.873741 | − | 0.486391i | \(-0.838313\pi\) | ||
0.873741 | − | 0.486391i | \(-0.161687\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18040.6 | 0.0911024 | ||||||||
\(446\) | −211080. | + | 17383.0i | −1.06115 | + | 0.0873887i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −101086. | − | 188153.i | −0.503658 | − | 0.937467i | ||||
\(449\) | 192859. | 0.956639 | 0.478319 | − | 0.878186i | \(-0.341246\pi\) | ||||
0.478319 | + | 0.878186i | \(0.341246\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 305940.i | − | 1.50412i | ||||||
\(452\) | −215211. | + | 35688.6i | −1.05339 | + | 0.174684i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −150035. | + | 12355.8i | −0.727916 | + | 0.0599460i | ||||
\(455\) | − | 36059.7i | − | 0.174180i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5925.33 | −0.0283713 | −0.0141857 | − | 0.999899i | \(-0.504516\pi\) | ||||
−0.0141857 | + | 0.999899i | \(0.504516\pi\) | |||||||
\(458\) | 18791.4 | + | 228181.i | 0.0895834 | + | 1.08780i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8105.41 | + | 48877.7i | 0.0383053 | + | 0.230991i | ||||
\(461\) | 126684. | 0.596100 | 0.298050 | − | 0.954550i | \(-0.403664\pi\) | ||||
0.298050 | + | 0.954550i | \(0.403664\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 235572.i | 1.09891i | 0.835524 | + | 0.549454i | \(0.185164\pi\) | ||||
−0.835524 | + | 0.549454i | \(0.814836\pi\) | |||||||
\(464\) | 178298. | − | 60806.7i | 0.828153 | − | 0.282433i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11972.7 | + | 145383.i | 0.0551340 | + | 0.669485i | ||||
\(467\) | 97776.2i | 0.448332i | 0.974551 | + | 0.224166i | \(0.0719658\pi\) | ||||
−0.974551 | + | 0.224166i | \(0.928034\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 214045. | 0.973105 | ||||||||
\(470\) | −23809.0 | + | 1960.74i | −0.107782 | + | 0.00887613i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −133605. | + | 33617.6i | −0.599706 | + | 0.150898i | ||||
\(473\) | 239409. | 1.07009 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 351986.i | 1.56005i | ||||||||
\(476\) | 16744.3 | + | 100972.i | 0.0739015 | + | 0.445645i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −208722. | + | 17188.8i | −0.913508 | + | 0.0752300i | ||||
\(479\) | 403178.i | 1.75722i | 0.477543 | + | 0.878608i | \(0.341527\pi\) | ||||
−0.477543 | + | 0.878608i | \(0.658473\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −279607. | −1.20853 | ||||||||
\(482\) | 4435.70 | + | 53862.1i | 0.0190927 | + | 0.231841i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −51517.6 | + | 8543.18i | −0.219920 | + | 0.0364694i | ||||
\(485\) | −27256.3 | −0.115873 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 195207.i | 0.823071i | 0.911394 | + | 0.411536i | \(0.135007\pi\) | ||||
−0.911394 | + | 0.411536i | \(0.864993\pi\) | |||||||
\(488\) | −1035.90 | − | 4116.92i | −0.00434988 | − | 0.0172875i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 591.403 | + | 7181.33i | 0.00246315 | + | 0.0299097i | ||||
\(491\) | − | 76137.6i | − | 0.315818i | −0.987454 | − | 0.157909i | \(-0.949525\pi\) | ||
0.987454 | − | 0.157909i | \(-0.0504752\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −90272.3 | −0.371416 | ||||||||
\(494\) | 289036. | − | 23802.9i | 1.18440 | − | 0.0975386i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −48416.8 | − | 141968.i | −0.196803 | − | 0.577069i | ||||
\(497\) | 262379. | 1.06222 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 14570.3i | − | 0.0585152i | −0.999572 | − | 0.0292576i | \(-0.990686\pi\) | ||
0.999572 | − | 0.0292576i | \(-0.00931431\pi\) | |||||||
\(500\) | 108846. | − | 18050.0i | 0.435384 | − | 0.0721999i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 443735. | − | 36542.8i | 1.76082 | − | 0.145009i | ||||
\(503\) | − | 280154.i | − | 1.10729i | −0.832753 | − | 0.553645i | \(-0.813236\pi\) | ||
0.832753 | − | 0.553645i | \(-0.186764\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39751.2 | −0.155872 | ||||||||
\(506\) | −19152.0 | − | 232560.i | −0.0748019 | − | 0.908310i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 41068.0 | + | 247651.i | 0.159139 | + | 0.959649i | ||||
\(509\) | 203009. | 0.783573 | 0.391787 | − | 0.920056i | \(-0.371857\pi\) | ||||
0.391787 | + | 0.920056i | \(0.371857\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 141063.i | 0.540219i | ||||||||
\(512\) | −176665. | − | 193672.i | −0.673924 | − | 0.738801i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24265.7 | + | 294655.i | 0.0918472 | + | 1.11529i | ||||
\(515\) | 12152.6i | 0.0458200i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 112515. | 0.420948 | ||||||||
\(518\) | 475895. | − | 39191.3i | 1.77358 | − | 0.146060i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10799.3 | − | 42919.3i | −0.0399384 | − | 0.158725i | ||||
\(521\) | −30822.1 | −0.113550 | −0.0567749 | − | 0.998387i | \(-0.518082\pi\) | ||||
−0.0567749 | + | 0.998387i | \(0.518082\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 94412.3i | 0.345164i | 0.984995 | + | 0.172582i | \(0.0552109\pi\) | ||||
−0.984995 | + | 0.172582i | \(0.944789\pi\) | |||||||
\(524\) | 21913.7 | + | 132145.i | 0.0798092 | + | 0.481270i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29372.4 | − | 2418.90i | 0.106162 | − | 0.00874273i | ||||
\(527\) | 71878.5i | 0.258808i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19282.9 | −0.0689066 | ||||||||
\(530\) | 8834.03 | + | 107270.i | 0.0314490 | + | 0.381881i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −488606. | + | 81025.8i | −1.72638 | + | 0.286286i | ||||
\(533\) | 350322. | 1.23314 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 78397.6i | 0.273902i | ||||||||
\(536\) | 254763. | − | 64103.5i | 0.886763 | − | 0.223127i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12673.9 | + | 153898.i | 0.0437872 | + | 0.531702i | ||||
\(539\) | − | 33937.0i | − | 0.116814i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 166561. | 0.569087 | 0.284544 | − | 0.958663i | \(-0.408158\pi\) | ||||
0.284544 | + | 0.958663i | \(0.408158\pi\) | |||||||
\(542\) | 49992.0 | − | 4116.98i | 0.170177 | − | 0.0140146i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 50169.4 | + | 115166.i | 0.169528 | + | 0.389158i | ||||
\(545\) | −109754. | −0.369510 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 295887.i | − | 0.988897i | −0.869207 | − | 0.494448i | \(-0.835370\pi\) | ||
0.869207 | − | 0.494448i | \(-0.164630\pi\) | |||||||
\(548\) | 472433. | − | 78343.7i | 1.57318 | − | 0.260881i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −252129. | + | 20763.6i | −0.833485 | + | 0.0686399i | ||||
\(551\) | − | 436828.i | − | 1.43882i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 72015.6 | 0.235492 | ||||||||
\(554\) | 30238.0 | + | 367176.i | 0.0985220 | + | 1.19634i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 62419.6 | + | 376406.i | 0.201916 | + | 1.21761i | ||||
\(557\) | −30600.2 | −0.0986312 | −0.0493156 | − | 0.998783i | \(-0.515704\pi\) | ||||
−0.0493156 | + | 0.998783i | \(0.515704\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 274139.i | 0.877298i | ||||||||
\(560\) | 24396.4 | + | 71535.5i | 0.0777948 | + | 0.228111i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7319.76 | − | 88882.9i | −0.0231752 | − | 0.281414i | ||||
\(563\) | 242796.i | 0.765992i | 0.923750 | + | 0.382996i | \(0.125108\pi\) | ||||
−0.923750 | + | 0.382996i | \(0.874892\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 77195.5 | 0.241822 | ||||||||
\(566\) | 99653.3 | − | 8206.73i | 0.311070 | − | 0.0256175i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 312291. | − | 78578.6i | 0.967973 | − | 0.243561i | ||||
\(569\) | 296918. | 0.917090 | 0.458545 | − | 0.888671i | \(-0.348371\pi\) | ||||
0.458545 | + | 0.888671i | \(0.348371\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 263786.i | − | 0.809058i | −0.914525 | − | 0.404529i | \(-0.867435\pi\) | ||
0.914525 | − | 0.404529i | \(-0.132565\pi\) | |||||||
\(572\) | 34100.3 | + | 205634.i | 0.104224 | + | 0.628495i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −596252. | + | 49103.0i | −1.80970 | + | 0.149034i | ||||
\(575\) | 324294.i | 0.980852i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 350367. | 1.05238 | 0.526188 | − | 0.850368i | \(-0.323621\pi\) | ||||
0.526188 | + | 0.850368i | \(0.323621\pi\) | |||||||
\(578\) | 22479.3 | + | 272963.i | 0.0672864 | + | 0.817050i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −65763.3 | + | 10905.6i | −0.195491 | + | 0.0324184i | ||||
\(581\) | −156873. | −0.464724 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 506931.i | − | 1.49146i | ||||||
\(584\) | 42246.2 | + | 167897.i | 0.123869 | + | 0.492286i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7714.12 | + | 93671.5i | 0.0224642 | + | 0.272780i | ||||
\(587\) | − | 6888.66i | − | 0.0199921i | −0.999950 | − | 0.00999606i | \(-0.996818\pi\) | ||
0.999950 | − | 0.00999606i | \(-0.00318190\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −347820. | −1.00259 | ||||||||
\(590\) | 48587.1 | − | 4001.29i | 0.139578 | − | 0.0114947i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 554688. | − | 189170.i | 1.58272 | − | 0.539771i | ||||
\(593\) | 544416. | 1.54818 | 0.774090 | − | 0.633076i | \(-0.218208\pi\) | ||||
0.774090 | + | 0.633076i | \(0.218208\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 36218.4i | − | 0.102305i | ||||||
\(596\) | −83246.5 | + | 13804.8i | −0.234355 | + | 0.0388631i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 266296. | − | 21930.3i | 0.744669 | − | 0.0613256i | ||||
\(599\) | 141764.i | 0.395104i | 0.980292 | + | 0.197552i | \(0.0632992\pi\) | ||||
−0.980292 | + | 0.197552i | \(0.936701\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −530760. | −1.46943 | −0.734715 | − | 0.678376i | \(-0.762684\pi\) | ||||
−0.734715 | + | 0.678376i | \(0.762684\pi\) | |||||||
\(602\) | −38424.9 | − | 466588.i | −0.106028 | − | 1.28748i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 87488.8 | + | 527580.i | 0.239816 | + | 1.44615i | ||||
\(605\) | 18479.2 | 0.0504861 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 40663.6i | − | 0.110364i | −0.998476 | − | 0.0551821i | \(-0.982426\pi\) | ||
0.998476 | − | 0.0551821i | \(-0.0175739\pi\) | |||||||
\(608\) | −557288. | + | 242770.i | −1.50755 | + | 0.656731i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 123.296 | + | 1497.17i | 0.000331352 | + | 0.00402357i | ||||
\(611\) | 128837.i | 0.345110i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −498556. | −1.32676 | −0.663382 | − | 0.748281i | \(-0.730879\pi\) | ||||
−0.663382 | + | 0.748281i | \(0.730879\pi\) | |||||||
\(614\) | 127807. | − | 10525.3i | 0.339015 | − | 0.0279189i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −86861.9 | − | 345211.i | −0.228912 | − | 0.909753i | ||||
\(617\) | −90060.9 | −0.236573 | −0.118287 | − | 0.992979i | \(-0.537740\pi\) | ||||
−0.118287 | + | 0.992979i | \(0.537740\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 172488.i | − | 0.450171i | −0.974339 | − | 0.225086i | \(-0.927734\pi\) | ||
0.974339 | − | 0.225086i | \(-0.0722662\pi\) | |||||||
\(620\) | 8683.45 | + | 52363.5i | 0.0225896 | + | 0.136221i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 282828. | − | 23291.7i | 0.731042 | − | 0.0602034i | ||||
\(623\) | 166154.i | 0.428091i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 331547. | 0.848761 | ||||||||
\(626\) | −38909.9 | − | 472478.i | −0.0992914 | − | 1.20568i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −268358. | + | 44502.0i | −0.680449 | + | 0.112839i | ||||
\(629\) | −280838. | −0.709831 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 210621.i | − | 0.528985i | −0.964388 | − | 0.264492i | \(-0.914796\pi\) | ||
0.964388 | − | 0.264492i | \(-0.0852044\pi\) | |||||||
\(632\) | 85715.2 | − | 21567.6i | 0.214597 | − | 0.0539968i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 44248.7 | + | 537306.i | 0.110083 | + | 1.33673i | ||||
\(635\) | − | 88831.4i | − | 0.220302i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38860.1 | 0.0957691 | ||||||||
\(638\) | 312902. | − | 25768.4i | 0.768718 | − | 0.0633061i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 50461.3 | + | 77837.5i | 0.123196 | + | 0.190033i | ||||
\(641\) | −464524. | −1.13056 | −0.565278 | − | 0.824901i | \(-0.691231\pi\) | ||||
−0.565278 | + | 0.824901i | \(0.691231\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 417977.i | − | 1.01095i | −0.862841 | − | 0.505476i | \(-0.831317\pi\) | ||
0.862841 | − | 0.505476i | \(-0.168683\pi\) | |||||||
\(644\) | −450166. | + | 74651.2i | −1.08543 | + | 0.179997i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 290309. | − | 23907.7i | 0.695656 | − | 0.0572893i | ||||
\(647\) | − | 825841.i | − | 1.97282i | −0.164299 | − | 0.986411i | \(-0.552536\pi\) | ||
0.164299 | − | 0.986411i | \(-0.447464\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −229610. | −0.545131 | ||||||||
\(650\) | −23775.6 | − | 288704.i | −0.0562737 | − | 0.683324i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 80734.8 | + | 486852.i | 0.189918 | + | 1.14525i | ||||
\(653\) | 328545. | 0.770493 | 0.385247 | − | 0.922814i | \(-0.374116\pi\) | ||||
0.385247 | + | 0.922814i | \(0.374116\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 47400.0i | − | 0.110483i | ||||||
\(656\) | −694972. | + | 237013.i | −1.61495 | + | 0.550762i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18058.5 | − | 219282.i | −0.0417090 | − | 0.506467i | ||||
\(659\) | 167361.i | 0.385374i | 0.981260 | + | 0.192687i | \(0.0617202\pi\) | ||||
−0.981260 | + | 0.192687i | \(0.938280\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −305233. | −0.698599 | −0.349300 | − | 0.937011i | \(-0.613580\pi\) | ||||
−0.349300 | + | 0.937011i | \(0.613580\pi\) | |||||||
\(662\) | 612886. | − | 50473.0i | 1.39851 | − | 0.115171i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −186715. | + | 46981.1i | −0.423489 | + | 0.106558i | ||||
\(665\) | 175261. | 0.396317 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 402461.i | − | 0.904633i | ||||||
\(668\) | −41353.7 | − | 249374.i | −0.0926749 | − | 0.558853i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −92647.9 | + | 7629.82i | −0.206389 | + | 0.0169967i | ||||
\(671\) | − | 7075.22i | − | 0.0157143i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 806065. | 1.77967 | 0.889836 | − | 0.456281i | \(-0.150819\pi\) | ||||
0.889836 | + | 0.456281i | \(0.150819\pi\) | |||||||
\(674\) | 7532.41 | + | 91465.0i | 0.0165811 | + | 0.201342i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 215355. | − | 35712.5i | 0.471262 | − | 0.0781496i | ||||
\(677\) | −366235. | −0.799065 | −0.399533 | − | 0.916719i | \(-0.630828\pi\) | ||||
−0.399533 | + | 0.916719i | \(0.630828\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 251032.i | − | 0.544490i | ||||||
\(680\) | −10846.9 | − | 43108.3i | −0.0234578 | − | 0.0932274i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −20517.8 | − | 249145.i | −0.0441126 | − | 0.535654i | ||||
\(683\) | 398332.i | 0.853894i | 0.904277 | + | 0.426947i | \(0.140411\pi\) | ||||
−0.904277 | + | 0.426947i | \(0.859589\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −169460. | −0.361148 | ||||||||
\(686\) | 432977. | − | 35656.9i | 0.920060 | − | 0.0757696i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −185471. | − | 543840.i | −0.391831 | − | 1.14893i | ||||
\(689\) | 580469. | 1.22276 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 351812.i | 0.736809i | 0.929666 | + | 0.368405i | \(0.120096\pi\) | ||||
−0.929666 | + | 0.368405i | \(0.879904\pi\) | |||||||
\(692\) | −742860. | + | 123189.i | −1.55130 | + | 0.257252i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28820.2 | + | 2373.42i | −0.0598381 | + | 0.00492784i | ||||
\(695\) | − | 135016.i | − | 0.279521i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 351864. | 0.724285 | ||||||||
\(698\) | −36298.6 | − | 440769.i | −0.0745039 | − | 0.904691i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 80932.9 | + | 488046.i | 0.165169 | + | 0.996012i | ||||
\(701\) | −620142. | −1.26199 | −0.630994 | − | 0.775788i | \(-0.717353\pi\) | ||||
−0.630994 | + | 0.775788i | \(0.717353\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.35898e6i | − | 2.74980i | ||||||
\(704\) | −206772. | − | 384867.i | −0.417201 | − | 0.776543i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20224.4 | + | 245582.i | 0.0405758 | + | 0.492706i | ||||
\(707\) | − | 366111.i | − | 0.732443i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 314897. | 0.626434 | 0.313217 | − | 0.949682i | \(-0.398593\pi\) | ||||
0.313217 | + | 0.949682i | \(0.398593\pi\) | |||||||
\(710\) | −113569. | + | 9352.70i | −0.225290 | + | 0.0185533i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 49760.9 | + | 197762.i | 0.0981585 | + | 0.390107i | ||||
\(713\) | −320456. | −0.630362 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 73760.0i | − | 0.144281i | ||||||
\(716\) | 6663.45 | + | 40182.3i | 0.0129979 | + | 0.0783807i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −336711. | + | 27729.1i | −0.653143 | + | 0.0537882i | ||||
\(719\) | 361941.i | 0.700132i | 0.936725 | + | 0.350066i | \(0.113841\pi\) | ||||
−0.936725 | + | 0.350066i | \(0.886159\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −111926. | −0.215308 | ||||||||
\(722\) | 72905.2 | + | 885278.i | 0.139857 | + | 1.69826i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −89601.6 | + | 14858.7i | −0.170938 | + | 0.0283467i | ||||
\(725\) | −436327. | −0.830111 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 308930.i | − | 0.584510i | −0.956340 | − | 0.292255i | \(-0.905594\pi\) | ||
0.956340 | − | 0.292255i | \(-0.0944056\pi\) | |||||||
\(728\) | 395289. | − | 99462.6i | 0.745852 | − | 0.187671i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5028.29 | − | 61057.9i | −0.00943572 | − | 0.114577i | ||||
\(731\) | 275346.i | 0.515281i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 882544. | 1.64259 | 0.821293 | − | 0.570506i | \(-0.193253\pi\) | ||||
0.821293 | + | 0.570506i | \(0.193253\pi\) | |||||||
\(734\) | −741202. | + | 61040.2i | −1.37577 | + | 0.113298i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −513445. | + | 223670.i | −0.947847 | + | 0.412908i | ||||
\(737\) | 437829. | 0.806065 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 396910.i | − | 0.726781i | −0.931637 | − | 0.363390i | \(-0.881619\pi\) | ||
0.931637 | − | 0.363390i | \(-0.118381\pi\) | |||||||
\(740\) | −204590. | + | 33927.3i | −0.373613 | + | 0.0619564i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −987966. | + | 81361.8i | −1.79446 | + | 0.147779i | ||||
\(743\) | − | 959979.i | − | 1.73894i | −0.493988 | − | 0.869469i | \(-0.664461\pi\) | ||
0.493988 | − | 0.869469i | \(-0.335539\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29860.2 | 0.0537998 | ||||||||
\(746\) | 27935.5 | + | 339217.i | 0.0501971 | + | 0.609536i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 34250.5 | + | 206539.i | 0.0612158 | + | 0.369147i | ||||
\(749\) | −722046. | −1.28707 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 660734.i | − | 1.17151i | −0.810488 | − | 0.585756i | \(-0.800798\pi\) | ||
0.810488 | − | 0.585756i | \(-0.199202\pi\) | |||||||
\(752\) | −87165.6 | − | 255588.i | −0.154138 | − | 0.451965i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 29506.5 | + | 358293.i | 0.0519009 | + | 0.630225i | ||||
\(755\) | − | 189241.i | − | 0.331987i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 326842. | 0.570356 | 0.285178 | − | 0.958475i | \(-0.407947\pi\) | ||||
0.285178 | + | 0.958475i | \(0.407947\pi\) | |||||||
\(758\) | 585945. | − | 48254.2i | 1.01981 | − | 0.0839841i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 208601. | − | 52488.2i | 0.361152 | − | 0.0908729i | ||||
\(761\) | 329626. | 0.569183 | 0.284591 | − | 0.958649i | \(-0.408142\pi\) | ||||
0.284591 | + | 0.958649i | \(0.408142\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.01084e6i | − | 1.73633i | ||||||
\(764\) | −85013.7 | − | 512654.i | −0.145647 | − | 0.878290i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 742285. | − | 61129.3i | 1.26507 | − | 0.104182i | ||||
\(767\) | − | 262918.i | − | 0.446920i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −599476. | −1.01372 | −0.506862 | − | 0.862027i | \(-0.669194\pi\) | ||||
−0.506862 | + | 0.862027i | \(0.669194\pi\) | |||||||
\(770\) | 10338.6 | + | 125540.i | 0.0174374 | + | 0.211740i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12429.2 | + | 2061.14i | −0.0208549 | + | 0.00345838i | ||||
\(773\) | −58555.0 | −0.0979952 | −0.0489976 | − | 0.998799i | \(-0.515603\pi\) | ||||
−0.0489976 | + | 0.998799i | \(0.515603\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 347422.i | 0.578433i | ||||||||
\(776\) | −75180.5 | − | 298786.i | −0.124848 | − | 0.496178i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 84046.1 | + | 1.02056e6i | 0.138854 | + | 1.68609i | ||||
\(779\) | 1.70267e6i | 2.80580i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 536695. | 0.879884 | ||||||||
\(782\) | 267469. | − | 22026.9i | 0.437381 | − | 0.0360196i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −77091.2 | + | 26291.1i | −0.125422 | + | 0.0427737i | ||||
\(785\) | 96259.1 | 0.156208 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 638842.i | 1.03144i | 0.856757 | + | 0.515720i | \(0.172476\pi\) | ||||
−0.856757 | + | 0.515720i | \(0.827524\pi\) | |||||||
\(788\) | −391863. | + | 64982.8i | −0.631076 | + | 0.104652i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −31171.4 | + | 2567.06i | −0.0499462 | + | 0.00411321i | ||||
\(791\) | 710975.i | 1.13632i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8101.59 | 0.0128832 | ||||||||
\(794\) | 85599.4 | + | 1.03942e6i | 0.135778 | + | 1.64874i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31432.7 | − | 189547.i | −0.0496085 | − | 0.299152i | ||||
\(797\) | −1.17526e6 | −1.85019 | −0.925095 | − | 0.379737i | \(-0.876015\pi\) | ||||
−0.925095 | + | 0.379737i | \(0.876015\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 129404.i | 0.202701i | ||||||||
\(800\) | 242492. | + | 556649.i | 0.378893 | + | 0.869765i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17404.5 | − | 211340.i | −0.0270591 | − | 0.328574i | ||||
\(803\) | 288543.i | 0.447486i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 161473. | 0.249177 | ||||||||
\(806\) | 285288. | − | 23494.3i | 0.439150 | − | 0.0361653i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −109645. | − | 435757.i | −0.167945 | − | 0.667454i | ||||
\(809\) | −215543. | −0.329334 | −0.164667 | − | 0.986349i | \(-0.552655\pi\) | ||||
−0.164667 | + | 0.986349i | \(0.552655\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.05773e6i | 1.60817i | 0.594512 | + | 0.804087i | \(0.297345\pi\) | ||||
−0.594512 | + | 0.804087i | \(0.702655\pi\) | |||||||
\(812\) | −100441. | − | 605684.i | −0.152334 | − | 0.918616i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 973442. | − | 80165.7i | 1.46913 | − | 0.120987i | ||||
\(815\) | − | 174632.i | − | 0.262911i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.33240e6 | −1.99614 | ||||||||
\(818\) | −48390.0 | − | 587594.i | −0.0723185 | − | 0.878153i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 256333. | − | 42507.8i | 0.381221 | − | 0.0632180i | ||||
\(821\) | −75851.4 | −0.112532 | −0.0562662 | − | 0.998416i | \(-0.517920\pi\) | ||||
−0.0562662 | + | 0.998416i | \(0.517920\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 657611.i | − | 0.970889i | −0.874267 | − | 0.485445i | \(-0.838658\pi\) | ||
0.874267 | − | 0.485445i | \(-0.161342\pi\) | |||||||
\(824\) | −133218. | + | 33520.3i | −0.196204 | + | 0.0493689i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 36852.1 | + | 447490.i | 0.0540135 | + | 0.655878i | ||||
\(827\) | − | 669017.i | − | 0.978196i | −0.872229 | − | 0.489098i | \(-0.837326\pi\) | ||
0.872229 | − | 0.489098i | \(-0.162674\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −637042. | −0.926955 | −0.463478 | − | 0.886109i | \(-0.653399\pi\) | ||||
−0.463478 | + | 0.886109i | \(0.653399\pi\) | |||||||
\(830\) | 67901.2 | − | 5591.86i | 0.0985647 | − | 0.00811708i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 440698. | − | 236767.i | 0.636641 | − | 0.342038i | ||||
\(833\) | 39031.3 | 0.0562500 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 89449.4i | 0.128293i | ||||||||
\(836\) | −999443. | + | 165738.i | −1.43003 | + | 0.237143i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −927231. | + | 76360.1i | −1.32038 | + | 0.108737i | ||||
\(839\) | − | 1.00773e6i | − | 1.43159i | −0.698311 | − | 0.715795i | \(-0.746065\pi\) | ||
0.698311 | − | 0.715795i | \(-0.253935\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −165782. | −0.234394 | ||||||||
\(842\) | 22915.9 | + | 278264.i | 0.0323230 | + | 0.392494i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 77873.0 | + | 469594.i | 0.109321 | + | 0.659232i | ||||
\(845\) | −77247.2 | −0.108186 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 170194.i | 0.237234i | ||||||||
\(848\) | −1.15154e6 | + | 392721.i | −1.60136 | + | 0.546125i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −23880.3 | − | 289976.i | −0.0330524 | − | 0.401351i | ||||
\(851\) | − | 1.25206e6i | − | 1.72889i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −193580. | −0.266050 | −0.133025 | − | 0.991113i | \(-0.542469\pi\) | ||||
−0.133025 | + | 0.991113i | \(0.542469\pi\) | |||||||
\(854\) | −13789.0 | + | 1135.56i | −0.0189068 | + | 0.00155703i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −859402. | + | 216242.i | −1.17287 | + | 0.295116i | ||||
\(857\) | 923728. | 1.25772 | 0.628858 | − | 0.777520i | \(-0.283523\pi\) | ||||
0.628858 | + | 0.777520i | \(0.283523\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 725649.i | 0.983423i | 0.870758 | + | 0.491712i | \(0.163629\pi\) | ||||
−0.870758 | + | 0.491712i | \(0.836371\pi\) | |||||||
\(860\) | 33263.9 | + | 200590.i | 0.0449755 | + | 0.271214i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 589495. | − | 48546.6i | 0.793351 | − | 0.0653348i | ||||
\(863\) | − | 444700.i | − | 0.597097i | −0.954394 | − | 0.298549i | \(-0.903497\pi\) | ||
0.954394 | − | 0.298549i | \(-0.0965025\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 266461. | 0.356124 | ||||||||
\(866\) | −96799.2 | − | 1.17542e6i | −0.129073 | − | 1.56732i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −482270. | + | 79975.1i | −0.640105 | + | 0.106149i | ||||
\(869\) | 147308. | 0.195068 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 501343.i | 0.660844i | ||||||||
\(872\) | −302731. | − | 1.20313e6i | −0.398129 | − | 1.58227i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 106588. | + | 1.29428e6i | 0.139536 | + | 1.69436i | ||||
\(875\) | − | 359585.i | − | 0.469662i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −576603. | −0.749683 | −0.374841 | − | 0.927089i | \(-0.622303\pi\) | ||||
−0.374841 | + | 0.927089i | \(0.622303\pi\) | |||||||
\(878\) | 287554. | − | 23680.9i | 0.373018 | − | 0.0307191i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 49902.9 | + | 146326.i | 0.0644407 | + | 0.188954i | ||||
\(881\) | −1.16458e6 | −1.50044 | −0.750219 | − | 0.661190i | \(-0.770052\pi\) | ||||
−0.750219 | + | 0.661190i | \(0.770052\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12142.2i | 0.0155731i | 0.999970 | + | 0.00778655i | \(0.00247856\pi\) | ||||
−0.999970 | + | 0.00778655i | \(0.997521\pi\) | |||||||
\(884\) | −236501. | + | 39219.0i | −0.302641 | + | 0.0501871i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −761053. | + | 62674.9i | −0.969499 | + | 0.0798411i | ||||
\(887\) | 1.29477e6i | 1.64568i | 0.568273 | + | 0.822840i | \(0.307612\pi\) | ||||
−0.568273 | + | 0.822840i | \(0.692388\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 818142. | 1.03520 | ||||||||
\(890\) | −5922.72 | − | 71918.8i | −0.00747723 | − | 0.0907951i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 138595. | + | 835763.i | 0.174188 | + | 1.05040i | ||||
\(893\) | −626187. | −0.785238 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 14413.3i | − | 0.0179935i | ||||||
\(896\) | −716887. | + | 464751.i | −0.892966 | + | 0.578901i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −63315.8 | − | 768835.i | −0.0785162 | − | 0.953411i | ||||
\(899\) | − | 431164.i | − | 0.533485i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 583026. | 0.718188 | ||||||||
\(902\) | −1.21963e6 | + | 100440.i | −1.49905 | + | 0.123451i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 212927. | + | 846225.i | 0.260551 | + | 1.03550i | ||||
\(905\) | 32139.8 | 0.0392415 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 684812.i | − | 0.832448i | −0.909262 | − | 0.416224i | \(-0.863353\pi\) | ||
0.909262 | − | 0.416224i | \(-0.136647\pi\) | |||||||
\(908\) | 98513.1 | + | 594059.i | 0.119487 | + | 0.720540i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −143752. | + | 11838.4i | −0.173593 | + | 0.0142958i | ||||
\(911\) | 717669.i | 0.864743i | 0.901695 | + | 0.432372i | \(0.142323\pi\) | ||||
−0.901695 | + | 0.432372i | \(0.857677\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −320883. | −0.384951 | ||||||||
\(914\) | 1945.29 | + | 23621.3i | 0.00232858 | + | 0.0282756i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 903476. | − | 149824.i | 1.07678 | − | 0.178562i | ||||
\(917\) | 436556. | 0.519160 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 441444.i | 0.522691i | 0.965245 | + | 0.261345i | \(0.0841661\pi\) | ||||
−0.965245 | + | 0.261345i | \(0.915834\pi\) | |||||||
\(920\) | 192190. | − | 48358.8i | 0.227068 | − | 0.0571347i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −41590.3 | − | 505026.i | −0.0489249 | − | 0.594089i | ||||
\(923\) | 614551.i | 0.721364i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.35742e6 | −1.58646 | ||||||||
\(926\) | 939108. | − | 77338.2i | 1.09520 | − | 0.0901929i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −300941. | − | 690823.i | −0.349451 | − | 0.802179i | ||||
\(929\) | 1.26657e6 | 1.46757 | 0.733783 | − | 0.679384i | \(-0.237753\pi\) | ||||
0.733783 | + | 0.679384i | \(0.237753\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 188872.i | 0.217906i | ||||||||
\(932\) | 575638. | − | 95458.3i | 0.662701 | − | 0.109896i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 389785. | − | 32100.0i | 0.446819 | − | 0.0367969i | ||||
\(935\) | − | 74084.8i | − | 0.0847434i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 377258. | 0.429694 | 0.214847 | − | 0.976648i | \(-0.431075\pi\) | ||||
0.214847 | + | 0.976648i | \(0.431075\pi\) | |||||||
\(938\) | −70271.1 | − | 853292.i | −0.0798677 | − | 0.969822i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15633.0 | + | 94270.9i | 0.0176924 | + | 0.106690i | ||||
\(941\) | −1.29154e6 | −1.45858 | −0.729288 | − | 0.684207i | \(-0.760148\pi\) | ||||
−0.729288 | + | 0.684207i | \(0.760148\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.56872e6i | 1.76409i | ||||||||
\(944\) | 177879. | + | 521580.i | 0.199610 | + | 0.585298i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −78598.0 | − | 954405.i | −0.0878273 | − | 1.06647i | ||||
\(947\) | 1.17881e6i | 1.31444i | 0.753697 | + | 0.657222i | \(0.228269\pi\) | ||||
−0.753697 | + | 0.657222i | \(0.771731\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −330401. | −0.366867 | ||||||||
\(950\) | 1.40319e6 | − | 115557.i | 1.55478 | − | 0.128041i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 397030. | − | 99900.6i | 0.438076 | − | 0.110229i | ||||
\(953\) | 613396. | 0.675391 | 0.337695 | − | 0.941255i | \(-0.390353\pi\) | ||||
0.337695 | + | 0.941255i | \(0.390353\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 183887.i | 0.201625i | ||||||||
\(956\) | 137047. | + | 826428.i | 0.149952 | + | 0.904251i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.60727e6 | − | 132363.i | 1.75129 | − | 0.144224i | ||||
\(959\) | − | 1.56073e6i | − | 1.69704i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 580211. | 0.628260 | ||||||||
\(962\) | 91795.0 | + | 1.11465e6i | 0.0991903 | + | 1.20445i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 213265. | − | 35365.9i | 0.229491 | − | 0.0380567i | ||||
\(965\) | 4458.31 | 0.00478757 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47416.0i | 0.0507075i | 0.999679 | + | 0.0253537i | \(0.00807121\pi\) | ||||
−0.999679 | + | 0.0253537i | \(0.991929\pi\) | |||||||
\(968\) | 50970.7 | + | 202570.i | 0.0543963 | + | 0.216185i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8948.25 | + | 108657.i | 0.00951031 | + | 0.115482i | ||||
\(971\) | − | 746340.i | − | 0.791586i | −0.918340 | − | 0.395793i | \(-0.870470\pi\) | ||
0.918340 | − | 0.395793i | \(-0.129530\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.24350e6 | 1.31347 | ||||||||
\(974\) | 778193. | − | 64086.5i | 0.820294 | − | 0.0675536i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16072.0 | + | 5481.19i | −0.0168722 | + | 0.00575408i | ||||
\(977\) | −286711. | −0.300369 | −0.150185 | − | 0.988658i | \(-0.547987\pi\) | ||||
−0.150185 | + | 0.988658i | \(0.547987\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 339869.i | 0.354606i | ||||||||
\(980\) | 28434.2 | − | 4715.26i | 0.0296067 | − | 0.00490969i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −303523. | + | 24996.0i | −0.314752 | + | 0.0259208i | ||||
\(983\) | − | 582712.i | − | 0.603041i | −0.953460 | − | 0.301521i | \(-0.902506\pi\) | ||
0.953460 | − | 0.301521i | \(-0.0974942\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 140560. | 0.144873 | ||||||||
\(986\) | 29636.4 | + | 359871.i | 0.0304840 | + | 0.370163i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −189781. | − | 1.14443e6i | −0.194419 | − | 1.17240i | ||||
\(989\) | −1.22758e6 | −1.25504 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 918794.i | − | 0.935558i | −0.883845 | − | 0.467779i | \(-0.845054\pi\) | ||
0.883845 | − | 0.467779i | \(-0.154946\pi\) | |||||||
\(992\) | −550062. | + | 239622.i | −0.558970 | + | 0.243502i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −86138.9 | − | 1.04597e6i | −0.0871820 | − | 1.05864i | ||||
\(995\) | 67989.9i | 0.0686749i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.39525e6 | −1.40366 | −0.701830 | − | 0.712344i | \(-0.747633\pi\) | ||||
−0.701830 | + | 0.712344i | \(0.747633\pi\) | |||||||
\(998\) | −58084.7 | + | 4783.45i | −0.0583178 | + | 0.00480264i | ||||
\(999\) | 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 | 324.5.d.f.163.11 | 22 | ||
3.2 | odd | 2 | 324.5.d.e.163.12 | 22 | |||
4.3 | odd | 2 | inner | 324.5.d.f.163.12 | 22 | ||
9.2 | odd | 6 | 108.5.f.a.91.19 | 44 | |||
9.4 | even | 3 | 36.5.f.a.7.19 | yes | 44 | ||
9.5 | odd | 6 | 108.5.f.a.19.4 | 44 | |||
9.7 | even | 3 | 36.5.f.a.31.4 | yes | 44 | ||
12.11 | even | 2 | 324.5.d.e.163.11 | 22 | |||
36.7 | odd | 6 | 36.5.f.a.31.19 | yes | 44 | ||
36.11 | even | 6 | 108.5.f.a.91.4 | 44 | |||
36.23 | even | 6 | 108.5.f.a.19.19 | 44 | |||
36.31 | odd | 6 | 36.5.f.a.7.4 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.4 | ✓ | 44 | 36.31 | odd | 6 | ||
36.5.f.a.7.19 | yes | 44 | 9.4 | even | 3 | ||
36.5.f.a.31.4 | yes | 44 | 9.7 | even | 3 | ||
36.5.f.a.31.19 | yes | 44 | 36.7 | odd | 6 | ||
108.5.f.a.19.4 | 44 | 9.5 | odd | 6 | |||
108.5.f.a.19.19 | 44 | 36.23 | even | 6 | |||
108.5.f.a.91.4 | 44 | 36.11 | even | 6 | |||
108.5.f.a.91.19 | 44 | 9.2 | odd | 6 | |||
324.5.d.e.163.11 | 22 | 12.11 | even | 2 | |||
324.5.d.e.163.12 | 22 | 3.2 | odd | 2 | |||
324.5.d.f.163.11 | 22 | 1.1 | even | 1 | trivial | ||
324.5.d.f.163.12 | 22 | 4.3 | odd | 2 | inner |