Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(80,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.80");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.p (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} + \cdots + 810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 80.4 | ||
Root | \(-0.648633 + 0.374489i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.80 |
Dual form | 441.4.p.c.215.4 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.648633 | + | 0.374489i | −0.229326 | + | 0.132402i | −0.610261 | − | 0.792200i | \(-0.708936\pi\) |
0.380935 | + | 0.924602i | \(0.375602\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.71952 | + | 6.44239i | −0.464940 | + | 0.805299i | ||||
\(5\) | 5.42768 | + | 9.40102i | 0.485466 | + | 0.840852i | 0.999861 | − | 0.0167014i | \(-0.00531648\pi\) |
−0.514394 | + | 0.857554i | \(0.671983\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 11.5635i | − | 0.511039i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.04115 | − | 4.06521i | −0.222661 | − | 0.128553i | ||||
\(11\) | −44.9131 | − | 25.9306i | −1.23107 | − | 0.710760i | −0.263819 | − | 0.964572i | \(-0.584982\pi\) |
−0.967254 | + | 0.253812i | \(0.918315\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 32.1880i | − | 0.686719i | −0.939204 | − | 0.343360i | \(-0.888435\pi\) | ||
0.939204 | − | 0.343360i | \(-0.111565\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −25.4257 | − | 44.0387i | −0.397277 | − | 0.688104i | ||||
\(17\) | 40.7324 | − | 70.5506i | 0.581121 | − | 1.00653i | −0.414225 | − | 0.910174i | \(-0.635947\pi\) |
0.995347 | − | 0.0963575i | \(-0.0307192\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0420661 | − | 0.0242869i | 0.000507927 | − | 0.000293252i | −0.499746 | − | 0.866172i | \(-0.666573\pi\) |
0.500254 | + | 0.865879i | \(0.333240\pi\) | |||||||
\(20\) | −80.7534 | −0.902850 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 38.8428 | 0.376423 | ||||||||
\(23\) | 77.3322 | − | 44.6478i | 0.701082 | − | 0.404770i | −0.106668 | − | 0.994295i | \(-0.534018\pi\) |
0.807750 | + | 0.589525i | \(0.200685\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.58060 | − | 6.20178i | 0.0286448 | − | 0.0496142i | ||||
\(26\) | 12.0540 | + | 20.8782i | 0.0909228 | + | 0.157483i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 175.246i | 1.12215i | 0.827766 | + | 0.561074i | \(0.189612\pi\) | ||||
−0.827766 | + | 0.561074i | \(0.810388\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −186.238 | − | 107.524i | −1.07901 | − | 0.622966i | −0.148380 | − | 0.988930i | \(-0.547406\pi\) |
−0.930629 | + | 0.365964i | \(0.880739\pi\) | |||||||
\(32\) | 113.098 | + | 65.2972i | 0.624785 | + | 0.360720i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 61.0153i | 0.307766i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −32.2729 | − | 55.8983i | −0.143395 | − | 0.248368i | 0.785378 | − | 0.619017i | \(-0.212469\pi\) |
−0.928773 | + | 0.370649i | \(0.879135\pi\) | |||||||
\(38\) | −0.0181903 | + | 0.0315065i | −7.76541e−5 | + | 0.000134501i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 108.708 | − | 62.7629i | 0.429708 | − | 0.248092i | ||||
\(41\) | 411.485 | 1.56740 | 0.783698 | − | 0.621142i | \(-0.213331\pi\) | ||||
0.783698 | + | 0.621142i | \(0.213331\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −234.771 | −0.832611 | −0.416305 | − | 0.909225i | \(-0.636675\pi\) | ||||
−0.416305 | + | 0.909225i | \(0.636675\pi\) | |||||||
\(44\) | 334.110 | − | 192.898i | 1.14475 | − | 0.660921i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −33.4402 | + | 57.9201i | −0.107184 | + | 0.185649i | ||||
\(47\) | 316.076 | + | 547.460i | 0.980946 | + | 1.69905i | 0.658726 | + | 0.752382i | \(0.271095\pi\) |
0.322219 | + | 0.946665i | \(0.395571\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.36357i | 0.0151705i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 207.368 | + | 119.724i | 0.553014 | + | 0.319283i | ||||
\(53\) | −230.049 | − | 132.819i | −0.596220 | − | 0.344228i | 0.171333 | − | 0.985213i | \(-0.445193\pi\) |
−0.767553 | + | 0.640985i | \(0.778526\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 562.971i | − | 1.38020i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −65.6275 | − | 113.670i | −0.148574 | − | 0.257338i | ||||
\(59\) | 175.530 | − | 304.026i | 0.387322 | − | 0.670862i | −0.604766 | − | 0.796403i | \(-0.706733\pi\) |
0.992088 | + | 0.125541i | \(0.0400667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 673.827 | − | 389.034i | 1.41434 | − | 0.816569i | 0.418546 | − | 0.908196i | \(-0.362540\pi\) |
0.995793 | + | 0.0916261i | \(0.0292065\pi\) | |||||||
\(62\) | 161.067 | 0.329927 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 309.000 | 0.603515 | ||||||||
\(65\) | 302.600 | − | 174.706i | 0.577430 | − | 0.333379i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 98.0043 | − | 169.748i | 0.178703 | − | 0.309523i | −0.762733 | − | 0.646713i | \(-0.776143\pi\) |
0.941437 | + | 0.337190i | \(0.109476\pi\) | |||||||
\(68\) | 303.010 | + | 524.828i | 0.540373 | + | 0.935953i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 142.632i | − | 0.238412i | −0.992870 | − | 0.119206i | \(-0.961965\pi\) | ||
0.992870 | − | 0.119206i | \(-0.0380349\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −676.261 | − | 390.439i | −1.08425 | − | 0.625993i | −0.152211 | − | 0.988348i | \(-0.548639\pi\) |
−0.932040 | + | 0.362355i | \(0.881973\pi\) | |||||||
\(74\) | 41.8665 | + | 24.1716i | 0.0657687 | + | 0.0379716i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.361341i | 0.000545378i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −644.525 | − | 1116.35i | −0.917908 | − | 1.58986i | −0.802588 | − | 0.596534i | \(-0.796544\pi\) |
−0.115320 | − | 0.993328i | \(-0.536789\pi\) | |||||||
\(80\) | 276.006 | − | 478.056i | 0.385729 | − | 0.668103i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −266.903 | + | 154.097i | −0.359445 | + | 0.207526i | ||||
\(83\) | −235.123 | −0.310940 | −0.155470 | − | 0.987841i | \(-0.549689\pi\) | ||||
−0.155470 | + | 0.987841i | \(0.549689\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 884.330 | 1.12846 | ||||||||
\(86\) | 152.280 | − | 87.9191i | 0.190940 | − | 0.110239i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −299.848 | + | 519.351i | −0.363226 | + | 0.629125i | ||||
\(89\) | −335.390 | − | 580.913i | −0.399453 | − | 0.691872i | 0.594206 | − | 0.804313i | \(-0.297466\pi\) |
−0.993658 | + | 0.112441i | \(0.964133\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 664.273i | 0.752774i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −410.035 | − | 236.734i | −0.449914 | − | 0.259758i | ||||
\(95\) | 0.456642 | + | 0.263642i | 0.000493163 | + | 0.000284728i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 655.891i | 0.686553i | 0.939234 | + | 0.343276i | \(0.111537\pi\) | ||||
−0.939234 | + | 0.343276i | \(0.888463\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 26.6362 | + | 46.1352i | 0.0266362 | + | 0.0461352i | ||||
\(101\) | 581.618 | − | 1007.39i | 0.573002 | − | 0.992468i | −0.423254 | − | 0.906011i | \(-0.639112\pi\) |
0.996256 | − | 0.0864572i | \(-0.0275546\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −22.8802 | + | 13.2099i | −0.0218879 | + | 0.0126370i | −0.510904 | − | 0.859638i | \(-0.670689\pi\) |
0.489016 | + | 0.872275i | \(0.337356\pi\) | |||||||
\(104\) | −372.206 | −0.350940 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 198.957 | 0.182305 | ||||||||
\(107\) | 1270.53 | − | 733.538i | 1.14791 | − | 0.662746i | 0.199532 | − | 0.979891i | \(-0.436058\pi\) |
0.948377 | + | 0.317145i | \(0.102724\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 67.5343 | − | 116.973i | 0.0593450 | − | 0.102789i | −0.834827 | − | 0.550513i | \(-0.814432\pi\) |
0.894172 | + | 0.447724i | \(0.147765\pi\) | |||||||
\(110\) | 210.826 | + | 365.162i | 0.182741 | + | 0.316516i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 288.471i | − | 0.240151i | −0.992765 | − | 0.120076i | \(-0.961686\pi\) | ||
0.992765 | − | 0.120076i | \(-0.0383137\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 839.469 | + | 484.668i | 0.680703 | + | 0.393004i | ||||
\(116\) | −1129.00 | − | 651.829i | −0.903665 | − | 0.521731i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 262.935i | 0.205129i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 679.288 | + | 1176.56i | 0.510359 | + | 0.883969i | ||||
\(122\) | −291.378 | + | 504.681i | −0.216230 | + | 0.374522i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1385.43 | − | 799.877i | 1.00335 | − | 0.579283i | ||||
\(125\) | 1434.66 | 1.02656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2269.80 | −1.58592 | −0.792961 | − | 0.609273i | \(-0.791461\pi\) | ||||
−0.792961 | + | 0.609273i | \(0.791461\pi\) | |||||||
\(128\) | −1105.21 | + | 638.095i | −0.763187 | + | 0.440626i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −130.851 | + | 226.641i | −0.0882799 | + | 0.152905i | ||||
\(131\) | 194.846 | + | 337.483i | 0.129952 | + | 0.225084i | 0.923658 | − | 0.383218i | \(-0.125184\pi\) |
−0.793706 | + | 0.608302i | \(0.791851\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 146.806i | 0.0946425i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −815.811 | − | 471.009i | −0.514377 | − | 0.296975i | ||||
\(137\) | 1271.93 | + | 734.347i | 0.793197 | + | 0.457953i | 0.841087 | − | 0.540900i | \(-0.181916\pi\) |
−0.0478898 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 624.712i | − | 0.381204i | −0.981667 | − | 0.190602i | \(-0.938956\pi\) | ||
0.981667 | − | 0.190602i | \(-0.0610440\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 53.4139 | + | 92.5156i | 0.0315662 | + | 0.0546742i | ||||
\(143\) | −834.654 | + | 1445.66i | −0.488093 | + | 0.845401i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1647.49 | + | 951.177i | −0.943561 | + | 0.544765i | ||||
\(146\) | 584.860 | 0.331530 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 480.158 | 0.266681 | ||||||||
\(149\) | −1387.25 | + | 800.930i | −0.762739 | + | 0.440367i | −0.830278 | − | 0.557349i | \(-0.811818\pi\) |
0.0675396 | + | 0.997717i | \(0.478485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −202.188 | + | 350.200i | −0.108966 | + | 0.188734i | −0.915351 | − | 0.402656i | \(-0.868087\pi\) |
0.806386 | + | 0.591390i | \(0.201421\pi\) | |||||||
\(152\) | −0.280841 | − | 0.486430i | −0.000149863 | − | 0.000259570i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2334.43i | − | 1.20972i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2088.91 | + | 1206.04i | 1.06187 | + | 0.613071i | 0.925949 | − | 0.377649i | \(-0.123267\pi\) |
0.135921 | + | 0.990720i | \(0.456601\pi\) | |||||||
\(158\) | 836.120 | + | 482.734i | 0.421001 | + | 0.243065i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1417.65i | 0.700469i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 472.684 | + | 818.712i | 0.227138 | + | 0.393414i | 0.956959 | − | 0.290224i | \(-0.0937299\pi\) |
−0.729821 | + | 0.683638i | \(0.760397\pi\) | |||||||
\(164\) | −1530.53 | + | 2650.95i | −0.728744 | + | 1.26222i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 152.508 | − | 88.0507i | 0.0713069 | − | 0.0411690i | ||||
\(167\) | −1271.18 | −0.589022 | −0.294511 | − | 0.955648i | \(-0.595157\pi\) | ||||
−0.294511 | + | 0.955648i | \(0.595157\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1160.93 | 0.528417 | ||||||||
\(170\) | −573.606 | + | 331.172i | −0.258786 | + | 0.149410i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 873.235 | − | 1512.49i | 0.387114 | − | 0.670501i | ||||
\(173\) | −2217.49 | − | 3840.81i | −0.974525 | − | 1.68793i | −0.681493 | − | 0.731825i | \(-0.738669\pi\) |
−0.293032 | − | 0.956103i | \(-0.594664\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2637.22i | 1.12947i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 435.090 | + | 251.200i | 0.183210 | + | 0.105776i | ||||
\(179\) | 941.835 | + | 543.769i | 0.393274 | + | 0.227057i | 0.683578 | − | 0.729878i | \(-0.260423\pi\) |
−0.290304 | + | 0.956935i | \(0.593756\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2916.08i | − | 1.19752i | −0.800930 | − | 0.598758i | \(-0.795661\pi\) | ||
0.800930 | − | 0.598758i | \(-0.204339\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −516.284 | − | 894.230i | −0.206853 | − | 0.358280i | ||||
\(185\) | 350.334 | − | 606.796i | 0.139227 | − | 0.241149i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3658.84 | + | 2112.43i | −1.43081 | + | 0.826076i | ||||
\(188\) | −4702.60 | −1.82432 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.394924 | −0.000150794 | ||||||||
\(191\) | −3948.97 | + | 2279.94i | −1.49601 | + | 0.863719i | −0.999989 | − | 0.00459364i | \(-0.998538\pi\) |
−0.496017 | + | 0.868313i | \(0.665204\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1878.60 | − | 3253.83i | 0.700645 | − | 1.21355i | −0.267595 | − | 0.963531i | \(-0.586229\pi\) |
0.968240 | − | 0.250022i | \(-0.0804378\pi\) | |||||||
\(194\) | −245.624 | − | 425.433i | −0.0909008 | − | 0.157445i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2014.34i | − | 0.728507i | −0.931300 | − | 0.364253i | \(-0.881324\pi\) | ||
0.931300 | − | 0.364253i | \(-0.118676\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.8355 | − | 6.25590i | −0.00385986 | − | 0.00222849i | 0.498069 | − | 0.867137i | \(-0.334043\pi\) |
−0.501929 | + | 0.864909i | \(0.667376\pi\) | |||||||
\(200\) | −71.7141 | − | 41.4042i | −0.0253548 | − | 0.0146386i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 871.238i | 0.303466i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2233.41 | + | 3868.38i | 0.760918 | + | 1.31795i | ||||
\(206\) | 9.89391 | − | 17.1367i | 0.00334632 | − | 0.00579599i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1417.52 | + | 818.404i | −0.472534 | + | 0.272818i | ||||
\(209\) | −2.51909 | −0.000833727 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2915.84 | −0.951349 | −0.475675 | − | 0.879621i | \(-0.657796\pi\) | ||||
−0.475675 | + | 0.879621i | \(0.657796\pi\) | |||||||
\(212\) | 1711.34 | − | 988.044i | 0.554413 | − | 0.320090i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −549.403 | + | 951.594i | −0.175497 | + | 0.303970i | ||||
\(215\) | −1274.26 | − | 2207.09i | −0.404205 | − | 0.700103i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 101.163i | 0.0314295i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3626.88 | + | 2093.98i | 1.11147 | + | 0.641710i | ||||
\(221\) | −2270.88 | − | 1311.10i | −0.691205 | − | 0.399067i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1097.87i | 0.329681i | 0.986320 | + | 0.164841i | \(0.0527110\pi\) | ||||
−0.986320 | + | 0.164841i | \(0.947289\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 108.029 | + | 187.112i | 0.0317964 | + | 0.0550731i | ||||
\(227\) | −250.297 | + | 433.527i | −0.0731841 | + | 0.126759i | −0.900295 | − | 0.435280i | \(-0.856649\pi\) |
0.827111 | + | 0.562039i | \(0.189983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 981.664 | − | 566.764i | 0.283276 | − | 0.163549i | −0.351630 | − | 0.936139i | \(-0.614372\pi\) |
0.634906 | + | 0.772590i | \(0.281039\pi\) | |||||||
\(230\) | −726.010 | −0.208138 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2026.45 | 0.573461 | ||||||||
\(233\) | −2975.12 | + | 1717.68i | −0.836508 | + | 0.482958i | −0.856076 | − | 0.516850i | \(-0.827104\pi\) |
0.0195676 | + | 0.999809i | \(0.493771\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3431.12 | + | 5942.87i | −0.952432 | + | 1.64966i | ||||
\(236\) | 1305.77 | + | 2261.66i | 0.360163 | + | 0.623821i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2213.97i | − | 0.599203i | −0.954064 | − | 0.299602i | \(-0.903146\pi\) | ||
0.954064 | − | 0.299602i | \(-0.0968537\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5154.55 | − | 2975.98i | −1.37773 | − | 0.795435i | −0.385847 | − | 0.922563i | \(-0.626091\pi\) |
−0.991886 | + | 0.127128i | \(0.959424\pi\) | |||||||
\(242\) | −881.218 | − | 508.772i | −0.234078 | − | 0.135145i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5788.08i | 1.51862i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.781746 | − | 1.35402i | −0.000201382 | − | 0.000348803i | ||||
\(248\) | −1243.36 | + | 2153.56i | −0.318360 | + | 0.551415i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −930.566 | + | 537.263i | −0.235417 | + | 0.135918i | ||||
\(251\) | 4889.86 | 1.22966 | 0.614831 | − | 0.788659i | \(-0.289224\pi\) | ||||
0.614831 | + | 0.788659i | \(0.289224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4630.97 | −1.15078 | ||||||||
\(254\) | 1472.27 | − | 850.013i | 0.363694 | − | 0.209979i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −758.080 | + | 1313.03i | −0.185078 | + | 0.320565i | ||||
\(257\) | −1598.21 | − | 2768.18i | −0.387913 | − | 0.671884i | 0.604256 | − | 0.796790i | \(-0.293470\pi\) |
−0.992169 | + | 0.124906i | \(0.960137\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2599.29i | 0.620005i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −252.767 | − | 145.935i | −0.0596030 | − | 0.0344118i | ||||
\(263\) | −648.189 | − | 374.232i | −0.151973 | − | 0.0877419i | 0.422085 | − | 0.906556i | \(-0.361298\pi\) |
−0.574058 | + | 0.818814i | \(0.694632\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2883.59i | − | 0.668444i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 729.057 | + | 1262.76i | 0.166173 | + | 0.287819i | ||||
\(269\) | −649.628 | + | 1125.19i | −0.147244 | + | 0.255033i | −0.930208 | − | 0.367033i | \(-0.880373\pi\) |
0.782964 | + | 0.622067i | \(0.213707\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −72.3660 | + | 41.7806i | −0.0162211 | + | 0.00936527i | −0.508089 | − | 0.861305i | \(-0.669648\pi\) |
0.491868 | + | 0.870670i | \(0.336314\pi\) | |||||||
\(272\) | −4142.61 | −0.923465 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1100.02 | −0.242535 | ||||||||
\(275\) | −321.631 | + | 185.694i | −0.0705276 | + | 0.0407191i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2320.93 | − | 4019.97i | 0.503434 | − | 0.871973i | −0.496558 | − | 0.868003i | \(-0.665403\pi\) |
0.999992 | − | 0.00396948i | \(-0.00126353\pi\) | |||||||
\(278\) | 233.948 | + | 405.209i | 0.0504721 | + | 0.0874202i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 179.289i | 0.0380622i | 0.999819 | + | 0.0190311i | \(0.00605816\pi\) | ||||
−0.999819 | + | 0.0190311i | \(0.993942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3506.14 | + | 2024.27i | 0.736461 | + | 0.425196i | 0.820781 | − | 0.571243i | \(-0.193539\pi\) |
−0.0843205 | + | 0.996439i | \(0.526872\pi\) | |||||||
\(284\) | 918.889 | + | 530.521i | 0.191993 | + | 0.110847i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 1250.27i | − | 0.258497i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −861.761 | − | 1492.61i | −0.175404 | − | 0.303809i | ||||
\(290\) | 712.410 | − | 1233.93i | 0.144256 | − | 0.249858i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5030.73 | − | 2904.49i | 1.00822 | − | 0.582098i | ||||
\(293\) | 3389.52 | 0.675828 | 0.337914 | − | 0.941177i | \(-0.390279\pi\) | ||||
0.337914 | + | 0.941177i | \(0.390279\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3810.88 | 0.752128 | ||||||||
\(296\) | −646.379 | + | 373.187i | −0.126926 | + | 0.0732806i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 599.878 | − | 1039.02i | 0.116611 | − | 0.201976i | ||||
\(299\) | −1437.12 | − | 2489.17i | −0.277963 | − | 0.481446i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 302.868i | − | 0.0577089i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.13912 | − | 1.23502i | −0.000403576 | − | 0.000233005i | ||||
\(305\) | 7314.63 | + | 4223.11i | 1.37323 | + | 0.792834i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2014.64i | 0.374534i | 0.982309 | + | 0.187267i | \(0.0599629\pi\) | ||||
−0.982309 | + | 0.187267i | \(0.940037\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 874.218 | + | 1514.19i | 0.160169 | + | 0.277420i | ||||
\(311\) | 2922.01 | − | 5061.07i | 0.532772 | − | 0.922788i | −0.466496 | − | 0.884524i | \(-0.654484\pi\) |
0.999268 | − | 0.0382648i | \(-0.0121830\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2121.29 | + | 1224.73i | −0.383074 | + | 0.221168i | −0.679155 | − | 0.733995i | \(-0.737654\pi\) |
0.296081 | + | 0.955163i | \(0.404320\pi\) | |||||||
\(314\) | −1806.59 | −0.324686 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9589.28 | 1.70709 | ||||||||
\(317\) | 5303.24 | − | 3061.83i | 0.939621 | − | 0.542490i | 0.0497796 | − | 0.998760i | \(-0.484148\pi\) |
0.889842 | + | 0.456270i | \(0.150815\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4544.22 | − | 7870.82i | 0.797578 | − | 1.38145i | ||||
\(320\) | 1677.15 | + | 2904.91i | 0.292986 | + | 0.507467i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.95705i | − | 0.000681660i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −199.623 | − | 115.252i | −0.0340710 | − | 0.0196709i | ||||
\(326\) | −613.197 | − | 354.029i | −0.104177 | − | 0.0601468i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 4758.20i | − | 0.801000i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3798.52 | − | 6579.23i | −0.630772 | − | 1.09253i | −0.987394 | − | 0.158280i | \(-0.949405\pi\) |
0.356622 | − | 0.934249i | \(-0.383928\pi\) | |||||||
\(332\) | 874.542 | − | 1514.75i | 0.144568 | − | 0.250400i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 824.528 | − | 476.042i | 0.135078 | − | 0.0779875i | ||||
\(335\) | 2127.74 | 0.347018 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3863.22 | −0.624460 | −0.312230 | − | 0.950007i | \(-0.601076\pi\) | ||||
−0.312230 | + | 0.950007i | \(0.601076\pi\) | |||||||
\(338\) | −753.019 | + | 434.756i | −0.121180 | + | 0.0699633i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3289.28 | + | 5697.20i | −0.524666 | + | 0.908747i | ||||
\(341\) | 5576.34 | + | 9658.50i | 0.885559 | + | 1.53383i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2714.77i | 0.425496i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2876.68 | + | 1660.85i | 0.446969 | + | 0.258058i | ||||
\(347\) | −1579.98 | − | 912.204i | −0.244432 | − | 0.141123i | 0.372780 | − | 0.927920i | \(-0.378405\pi\) |
−0.617212 | + | 0.786797i | \(0.711738\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1537.52i | − | 0.235822i | −0.993024 | − | 0.117911i | \(-0.962380\pi\) | ||
0.993024 | − | 0.117911i | \(-0.0376197\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3386.39 | − | 5865.40i | −0.512770 | − | 0.888144i | ||||
\(353\) | −2963.66 | + | 5133.22i | −0.446855 | + | 0.773976i | −0.998179 | − | 0.0603149i | \(-0.980789\pi\) |
0.551324 | + | 0.834291i | \(0.314123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1340.88 | − | 774.159i | 0.200469 | − | 0.115741i | ||||
\(356\) | 4989.96 | 0.742885 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −814.541 | −0.120251 | ||||||||
\(359\) | 4191.12 | − | 2419.74i | 0.616153 | − | 0.355736i | −0.159217 | − | 0.987244i | \(-0.550897\pi\) |
0.775370 | + | 0.631508i | \(0.217564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3429.50 | + | 5940.07i | −0.500000 | + | 0.866025i | ||||
\(362\) | 1092.04 | + | 1891.46i | 0.158553 | + | 0.274622i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 8476.72i | − | 1.21559i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9967.21 | − | 5754.57i | −1.41767 | − | 0.818491i | −0.421575 | − | 0.906794i | \(-0.638522\pi\) |
−0.996094 | + | 0.0883026i | \(0.971856\pi\) | |||||||
\(368\) | −3932.46 | − | 2270.41i | −0.557048 | − | 0.321612i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 524.784i | 0.0737357i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −93.7487 | − | 162.378i | −0.0130137 | − | 0.0225405i | 0.859445 | − | 0.511228i | \(-0.170809\pi\) |
−0.872459 | + | 0.488687i | \(0.837476\pi\) | |||||||
\(374\) | 1582.16 | − | 2740.38i | 0.218748 | − | 0.378882i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6330.54 | − | 3654.94i | 0.868279 | − | 0.501301i | ||||
\(377\) | 5640.81 | 0.770601 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3515.82 | 0.476506 | 0.238253 | − | 0.971203i | \(-0.423425\pi\) | ||||
0.238253 | + | 0.971203i | \(0.423425\pi\) | |||||||
\(380\) | −3.39698 | + | 1.96125i | −0.000458582 | + | 0.000264763i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1707.62 | − | 2957.69i | 0.228716 | − | 0.396147i | ||||
\(383\) | 1014.69 | + | 1757.49i | 0.135374 | + | 0.234474i | 0.925740 | − | 0.378160i | \(-0.123443\pi\) |
−0.790366 | + | 0.612634i | \(0.790110\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2814.06i | 0.371067i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4225.51 | − | 2439.60i | −0.552880 | − | 0.319206i | ||||
\(389\) | −5577.15 | − | 3219.97i | −0.726923 | − | 0.419689i | 0.0903727 | − | 0.995908i | \(-0.471194\pi\) |
−0.817295 | + | 0.576219i | \(0.804528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7274.45i | − | 0.940882i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 754.348 | + | 1306.57i | 0.0964555 | + | 0.167066i | ||||
\(395\) | 6996.55 | − | 12118.4i | 0.891227 | − | 1.54365i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8369.80 | − | 4832.31i | 1.05811 | − | 0.610898i | 0.133199 | − | 0.991089i | \(-0.457475\pi\) |
0.924908 | + | 0.380191i | \(0.124142\pi\) | |||||||
\(398\) | 9.37106 | 0.00118022 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −364.157 | −0.0455197 | ||||||||
\(401\) | 10186.9 | − | 5881.40i | 1.26860 | − | 0.732426i | 0.293876 | − | 0.955843i | \(-0.405055\pi\) |
0.974723 | + | 0.223417i | \(0.0717212\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3461.00 | + | 5994.62i | −0.427803 | + | 0.740976i | ||||
\(404\) | 4326.68 | + | 7494.03i | 0.532823 | + | 0.922876i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3347.42i | 0.407679i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4565.71 | + | 2636.01i | 0.551980 | + | 0.318686i | 0.749920 | − | 0.661528i | \(-0.230092\pi\) |
−0.197940 | + | 0.980214i | \(0.563425\pi\) | |||||||
\(410\) | −2897.33 | − | 1672.77i | −0.348997 | − | 0.201494i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 196.538i | − | 0.0235017i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1276.17 | − | 2210.39i | −0.150951 | − | 0.261455i | ||||
\(416\) | 2101.79 | − | 3640.40i | 0.247713 | − | 0.429052i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.63396 | − | 0.943369i | 0.000191196 | − | 0.000110387i | ||||
\(419\) | −5103.18 | −0.595003 | −0.297502 | − | 0.954721i | \(-0.596153\pi\) | ||||
−0.297502 | + | 0.954721i | \(0.596153\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8395.31 | −0.971882 | −0.485941 | − | 0.873992i | \(-0.661523\pi\) | ||||
−0.485941 | + | 0.873992i | \(0.661523\pi\) | |||||||
\(422\) | 1891.31 | − | 1091.95i | 0.218170 | − | 0.125960i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1535.85 | + | 2660.17i | −0.175914 | + | 0.304691i | ||||
\(425\) | −291.693 | − | 505.227i | −0.0332922 | − | 0.0576638i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10913.6i | 1.23255i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1653.06 | + | 954.394i | 0.185390 | + | 0.107035i | ||||
\(431\) | −1808.68 | − | 1044.24i | −0.202137 | − | 0.116704i | 0.395515 | − | 0.918460i | \(-0.370566\pi\) |
−0.597652 | + | 0.801756i | \(0.703900\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11495.3i | 1.27582i | 0.770111 | + | 0.637910i | \(0.220201\pi\) | ||||
−0.770111 | + | 0.637910i | \(0.779799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 502.390 | + | 870.164i | 0.0551837 | + | 0.0955810i | ||||
\(437\) | 2.16871 | − | 3.75631i | 0.000237399 | − | 0.000411187i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3682.95 | + | 2126.35i | −0.400404 | + | 0.231173i | −0.686658 | − | 0.726980i | \(-0.740923\pi\) |
0.286254 | + | 0.958154i | \(0.407590\pi\) | |||||||
\(440\) | −6509.91 | −0.705336 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1963.96 | 0.211349 | ||||||||
\(443\) | 2862.03 | − | 1652.40i | 0.306951 | − | 0.177218i | −0.338610 | − | 0.940927i | \(-0.609957\pi\) |
0.645561 | + | 0.763708i | \(0.276623\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3640.78 | − | 6306.02i | 0.387842 | − | 0.671761i | ||||
\(446\) | −411.140 | − | 712.116i | −0.0436503 | − | 0.0756046i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6952.63i | 0.730768i | 0.930857 | + | 0.365384i | \(0.119062\pi\) | ||||
−0.930857 | + | 0.365384i | \(0.880938\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18481.1 | − | 10670.0i | −1.92958 | − | 1.11404i | ||||
\(452\) | 1858.45 | + | 1072.97i | 0.193394 | + | 0.111656i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 374.933i | − | 0.0387588i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4870.57 | − | 8436.08i | −0.498546 | − | 0.863508i | 0.501452 | − | 0.865185i | \(-0.332799\pi\) |
−0.999999 | + | 0.00167767i | \(0.999466\pi\) | |||||||
\(458\) | −424.493 | + | 735.244i | −0.0433085 | + | 0.0750124i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6244.84 | + | 3605.46i | −0.632972 | + | 0.365447i | ||||
\(461\) | 5563.15 | 0.562043 | 0.281021 | − | 0.959702i | \(-0.409327\pi\) | ||||
0.281021 | + | 0.959702i | \(0.409327\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4114.02 | 0.412948 | 0.206474 | − | 0.978452i | \(-0.433801\pi\) | ||||
0.206474 | + | 0.978452i | \(0.433801\pi\) | |||||||
\(464\) | 7717.59 | − | 4455.75i | 0.772155 | − | 0.445804i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1286.51 | − | 2228.29i | 0.127889 | − | 0.221510i | ||||
\(467\) | −3030.79 | − | 5249.49i | −0.300318 | − | 0.520166i | 0.675890 | − | 0.737002i | \(-0.263759\pi\) |
−0.976208 | + | 0.216837i | \(0.930426\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 5139.66i | − | 0.504415i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3515.60 | − | 2029.73i | −0.342836 | − | 0.197937i | ||||
\(473\) | 10544.3 | + | 6087.75i | 1.02500 | + | 0.591787i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.347846i | − | 3.36005e-5i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 829.105 | + | 1436.05i | 0.0793355 | + | 0.137413i | ||||
\(479\) | 4123.33 | − | 7141.82i | 0.393319 | − | 0.681248i | −0.599566 | − | 0.800325i | \(-0.704660\pi\) |
0.992885 | + | 0.119077i | \(0.0379935\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1799.25 | + | 1038.80i | −0.170559 | + | 0.0984724i | ||||
\(482\) | 4457.88 | 0.421268 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10106.5 | −0.949145 | ||||||||
\(485\) | −6166.04 | + | 3559.96i | −0.577290 | + | 0.333298i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5872.08 | + | 10170.7i | −0.546385 | + | 0.946366i | 0.452134 | + | 0.891950i | \(0.350663\pi\) |
−0.998518 | + | 0.0544159i | \(0.982670\pi\) | |||||||
\(488\) | −4498.59 | − | 7791.79i | −0.417298 | − | 0.722782i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6008.34i | 0.552246i | 0.961122 | + | 0.276123i | \(0.0890497\pi\) | ||||
−0.961122 | + | 0.276123i | \(0.910950\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12363.7 | + | 7138.18i | 1.12948 | + | 0.652104i | ||||
\(494\) | 1.01413 | + | 0.585510i | 9.23643e−5 | + | 5.33266e-5i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10935.5i | 0.989961i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6824.93 | + | 11821.1i | 0.612276 | + | 1.06049i | 0.990856 | + | 0.134925i | \(0.0430792\pi\) |
−0.378580 | + | 0.925569i | \(0.623587\pi\) | |||||||
\(500\) | −5336.23 | + | 9242.62i | −0.477287 | + | 0.826685i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3171.72 | + | 1831.20i | −0.281994 | + | 0.162809i | ||||
\(503\) | −4862.69 | −0.431047 | −0.215524 | − | 0.976499i | \(-0.569146\pi\) | ||||
−0.215524 | + | 0.976499i | \(0.569146\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12627.4 | 1.11269 | ||||||||
\(506\) | 3003.80 | − | 1734.25i | 0.263904 | − | 0.152365i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8442.55 | − | 14622.9i | 0.737358 | − | 1.27714i | ||||
\(509\) | 8861.33 | + | 15348.3i | 0.771653 | + | 1.33654i | 0.936656 | + | 0.350250i | \(0.113903\pi\) |
−0.165003 | + | 0.986293i | \(0.552763\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 11345.1i | − | 0.979271i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2073.30 | + | 1197.02i | 0.177917 | + | 0.102721i | ||||
\(515\) | −248.373 | − | 143.398i | −0.0212517 | − | 0.0122697i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 32784.1i | − | 2.78887i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2020.21 | − | 3499.11i | −0.170370 | − | 0.295089i | ||||
\(521\) | −6877.95 | + | 11913.0i | −0.578366 | + | 1.00176i | 0.417301 | + | 0.908768i | \(0.362976\pi\) |
−0.995667 | + | 0.0929909i | \(0.970357\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1136.17 | + | 655.971i | −0.0949932 | + | 0.0548443i | −0.546744 | − | 0.837300i | \(-0.684133\pi\) |
0.451751 | + | 0.892144i | \(0.350800\pi\) | |||||||
\(524\) | −2898.93 | −0.241680 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 560.582 | 0.0464687 | ||||||||
\(527\) | −15171.8 | + | 8759.46i | −1.25407 | + | 0.724038i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2096.65 | + | 3631.50i | −0.172323 | + | 0.298472i | ||||
\(530\) | 1079.87 | + | 1870.39i | 0.0885031 | + | 0.153292i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 13244.9i | − | 1.07636i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13792.0 | + | 7962.82i | 1.11454 | + | 0.643482i | ||||
\(536\) | −1962.88 | − | 1133.27i | −0.158178 | − | 0.0913243i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 973.114i | − | 0.0779812i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −597.954 | − | 1035.69i | −0.0475195 | − | 0.0823061i | 0.841287 | − | 0.540588i | \(-0.181798\pi\) |
−0.888807 | + | 0.458282i | \(0.848465\pi\) | |||||||
\(542\) | 31.2927 | − | 54.2005i | 0.00247996 | − | 0.00429541i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9213.52 | − | 5319.43i | 0.726152 | − | 0.419244i | ||||
\(545\) | 1466.22 | 0.115240 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6178.59 | −0.482957 | −0.241478 | − | 0.970406i | \(-0.577632\pi\) | ||||
−0.241478 | + | 0.970406i | \(0.577632\pi\) | |||||||
\(548\) | −9461.90 | + | 5462.83i | −0.737577 | + | 0.425841i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 139.080 | − | 240.894i | 0.0107826 | − | 0.0186759i | ||||
\(551\) | 4.25617 | + | 7.37189i | 0.000329072 | + | 0.000569970i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3476.65i | 0.266622i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4024.64 | + | 2323.63i | 0.306983 | + | 0.177237i | ||||
\(557\) | −2906.56 | − | 1678.10i | −0.221104 | − | 0.127654i | 0.385357 | − | 0.922767i | \(-0.374078\pi\) |
−0.606461 | + | 0.795113i | \(0.707411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7556.82i | 0.571770i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −67.1417 | − | 116.293i | −0.00503950 | − | 0.00872868i | ||||
\(563\) | −1792.64 | + | 3104.94i | −0.134193 | + | 0.232429i | −0.925289 | − | 0.379263i | \(-0.876178\pi\) |
0.791096 | + | 0.611692i | \(0.209511\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2711.92 | − | 1565.73i | 0.201932 | − | 0.116585i | ||||
\(566\) | −3032.26 | −0.225187 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1649.32 | −0.121838 | ||||||||
\(569\) | −15835.9 | + | 9142.84i | −1.16674 | + | 0.673617i | −0.952910 | − | 0.303254i | \(-0.901927\pi\) |
−0.213829 | + | 0.976871i | \(0.568593\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8181.51 | − | 14170.8i | 0.599624 | − | 1.03858i | −0.393252 | − | 0.919431i | \(-0.628650\pi\) |
0.992876 | − | 0.119149i | \(-0.0380165\pi\) | |||||||
\(572\) | −6209.02 | − | 10754.3i | −0.453867 | − | 0.786121i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 639.463i | − | 0.0463782i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6678.26 | + | 3855.69i | 0.481836 | + | 0.278188i | 0.721181 | − | 0.692746i | \(-0.243599\pi\) |
−0.239345 | + | 0.970935i | \(0.576933\pi\) | |||||||
\(578\) | 1117.93 | + | 645.439i | 0.0804497 | + | 0.0464476i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 14151.7i | − | 1.01313i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6888.14 | + | 11930.6i | 0.489327 | + | 0.847539i | ||||
\(584\) | −4514.84 | + | 7819.93i | −0.319906 | + | 0.554094i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2198.55 | + | 1269.34i | −0.154985 | + | 0.0894808i | ||||
\(587\) | 4182.21 | 0.294069 | 0.147034 | − | 0.989131i | \(-0.453027\pi\) | ||||
0.147034 | + | 0.989131i | \(0.453027\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.4457 | −0.000730744 | ||||||||
\(590\) | −2471.86 | + | 1427.13i | −0.172483 | + | 0.0995830i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1641.12 | + | 2842.51i | −0.113935 | + | 0.197342i | ||||
\(593\) | −8094.65 | − | 14020.4i | −0.560552 | − | 0.970905i | −0.997448 | − | 0.0713932i | \(-0.977256\pi\) |
0.436896 | − | 0.899512i | \(-0.356078\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 11916.3i | − | 0.818977i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1864.33 | + | 1076.37i | 0.127489 | + | 0.0736056i | ||||
\(599\) | −11065.5 | − | 6388.67i | −0.754798 | − | 0.435783i | 0.0726267 | − | 0.997359i | \(-0.476862\pi\) |
−0.827425 | + | 0.561576i | \(0.810195\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24022.7i | 1.63046i | 0.579137 | + | 0.815231i | \(0.303390\pi\) | ||||
−0.579137 | + | 0.815231i | \(0.696610\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1504.08 | − | 2605.15i | −0.101325 | − | 0.175500i | ||||
\(605\) | −7373.92 | + | 12772.0i | −0.495525 | + | 0.858274i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8371.72 | + | 4833.42i | −0.559798 | + | 0.323200i | −0.753065 | − | 0.657947i | \(-0.771425\pi\) |
0.193266 | + | 0.981146i | \(0.438092\pi\) | |||||||
\(608\) | 6.34346 | 0.000423127 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6326.02 | −0.419890 | ||||||||
\(611\) | 17621.7 | − | 10173.9i | 1.16677 | − | 0.673634i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7192.73 | + | 12458.2i | −0.473918 | + | 0.820850i | −0.999554 | − | 0.0298593i | \(-0.990494\pi\) |
0.525636 | + | 0.850710i | \(0.323827\pi\) | |||||||
\(614\) | −754.461 | − | 1306.77i | −0.0495889 | − | 0.0858905i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7712.69i | − | 0.503244i | −0.967826 | − | 0.251622i | \(-0.919036\pi\) | ||
0.967826 | − | 0.251622i | \(-0.0809639\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12398.9 | − | 7158.52i | −0.805096 | − | 0.464822i | 0.0401539 | − | 0.999194i | \(-0.487215\pi\) |
−0.845250 | + | 0.534371i | \(0.820549\pi\) | |||||||
\(620\) | 15039.3 | + | 8682.96i | 0.974183 | + | 0.562445i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4377.04i | 0.282160i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7339.28 | + | 12712.0i | 0.469714 | + | 0.813569i | ||||
\(626\) | 917.292 | − | 1588.80i | 0.0585661 | − | 0.101439i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15539.5 | + | 8971.73i | −0.987410 | + | 0.570082i | ||||
\(629\) | −5258.21 | −0.333320 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4971.96 | 0.313678 | 0.156839 | − | 0.987624i | \(-0.449870\pi\) | ||||
0.156839 | + | 0.987624i | \(0.449870\pi\) | |||||||
\(632\) | −12908.9 | + | 7452.95i | −0.812481 | + | 0.469086i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2293.24 | + | 3972.01i | −0.143653 | + | 0.248815i | ||||
\(635\) | −12319.7 | − | 21338.4i | −0.769911 | − | 1.33353i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6807.03i | 0.422403i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11997.5 | − | 6926.75i | −0.741003 | − | 0.427818i | ||||
\(641\) | 25481.7 | + | 14711.9i | 1.57015 | + | 0.906529i | 0.996149 | + | 0.0876763i | \(0.0279441\pi\) |
0.574004 | + | 0.818852i | \(0.305389\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31273.9i | 1.91807i | 0.283283 | + | 0.959036i | \(0.408576\pi\) | ||||
−0.283283 | + | 0.959036i | \(0.591424\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.48187 | + | 2.56667i | 9.02529e−5 | + | 0.000156323i | ||||
\(647\) | 4005.82 | − | 6938.29i | 0.243408 | − | 0.421595i | −0.718275 | − | 0.695760i | \(-0.755068\pi\) |
0.961683 | + | 0.274164i | \(0.0884012\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15767.2 | + | 9103.17i | −0.953644 | + | 0.550586i | ||||
\(650\) | 172.643 | 0.0104179 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7032.62 | −0.422421 | ||||||||
\(653\) | −13372.0 | + | 7720.32i | −0.801357 | + | 0.462664i | −0.843945 | − | 0.536429i | \(-0.819773\pi\) |
0.0425886 | + | 0.999093i | \(0.486440\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2115.12 | + | 3663.50i | −0.126175 | + | 0.218542i | ||||
\(656\) | −10462.3 | − | 18121.3i | −0.622691 | − | 1.07853i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31288.9i | 1.84953i | 0.380537 | + | 0.924766i | \(0.375739\pi\) | ||||
−0.380537 | + | 0.924766i | \(0.624261\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26263.2 | + | 15163.1i | 1.54541 | + | 0.892246i | 0.998483 | + | 0.0550690i | \(0.0175379\pi\) |
0.546932 | + | 0.837177i | \(0.315795\pi\) | |||||||
\(662\) | 4927.69 | + | 2845.00i | 0.289305 | + | 0.167031i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2718.84i | 0.158903i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7824.33 | + | 13552.1i | 0.454212 | + | 0.786718i | ||||
\(668\) | 4728.17 | − | 8189.42i | 0.273860 | − | 0.474339i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1380.12 | + | 796.815i | −0.0795804 | + | 0.0459458i | ||||
\(671\) | −40351.5 | −2.32154 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12067.9 | 0.691207 | 0.345604 | − | 0.938381i | \(-0.387674\pi\) | ||||
0.345604 | + | 0.938381i | \(0.387674\pi\) | |||||||
\(674\) | 2505.81 | − | 1446.73i | 0.143205 | − | 0.0826795i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4318.10 | + | 7479.18i | −0.245682 | + | 0.425533i | ||||
\(677\) | 3272.41 | + | 5667.98i | 0.185774 | + | 0.321770i | 0.943837 | − | 0.330411i | \(-0.107187\pi\) |
−0.758063 | + | 0.652181i | \(0.773854\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 10225.9i | − | 0.576686i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7233.99 | − | 4176.55i | −0.406164 | − | 0.234499i | ||||
\(683\) | −27267.1 | − | 15742.7i | −1.52759 | − | 0.881956i | −0.999462 | − | 0.0327927i | \(-0.989560\pi\) |
−0.528130 | − | 0.849163i | \(-0.677107\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15943.2i | 0.889282i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5969.23 | + | 10339.0i | 0.330777 | + | 0.572923i | ||||
\(689\) | −4275.18 | + | 7404.82i | −0.236388 | + | 0.409436i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8690.83 | − | 5017.66i | 0.478459 | − | 0.276238i | −0.241315 | − | 0.970447i | \(-0.577579\pi\) |
0.719774 | + | 0.694209i | \(0.244245\pi\) | |||||||
\(692\) | 32992.0 | 1.81238 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1366.44 | 0.0747397 | ||||||||
\(695\) | 5872.93 | − | 3390.74i | 0.320537 | − | 0.185062i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16760.8 | − | 29030.6i | 0.910847 | − | 1.57763i | ||||
\(698\) | 575.785 | + | 997.290i | 0.0312232 | + | 0.0540802i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 768.196i | 0.0413900i | 0.999786 | + | 0.0206950i | \(0.00658789\pi\) | ||||
−0.999786 | + | 0.0206950i | \(0.993412\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.71519 | − | 1.56761i | −0.000145669 | − | 8.41019e-5i | ||||
\(704\) | −13878.1 | − | 8012.53i | −0.742970 | − | 0.428954i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 4439.43i | − | 0.236658i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6984.30 | − | 12097.2i | −0.369959 | − | 0.640787i | 0.619600 | − | 0.784918i | \(-0.287295\pi\) |
−0.989559 | + | 0.144130i | \(0.953962\pi\) | |||||||
\(710\) | −579.827 | + | 1004.29i | −0.0306486 | + | 0.0530850i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6717.38 | + | 3878.28i | −0.353573 | + | 0.204136i | ||||
\(713\) | −19202.9 | −1.00863 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18120.9 | −0.947810 | ||||||||
\(716\) | −7006.34 | + | 4045.11i | −0.365697 | + | 0.211135i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1812.33 | + | 3139.05i | −0.0942001 | + | 0.163159i | ||||
\(719\) | −5984.78 | − | 10365.9i | −0.310424 | − | 0.537669i | 0.668031 | − | 0.744134i | \(-0.267138\pi\) |
−0.978454 | + | 0.206465i | \(0.933804\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 5137.23i | − | 0.264803i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18786.5 | + | 10846.4i | 0.964358 | + | 0.556772i | ||||
\(725\) | 1086.83 | + | 627.484i | 0.0556745 | + | 0.0321437i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12223.3i | − | 0.623575i | −0.950152 | − | 0.311787i | \(-0.899072\pi\) | ||
0.950152 | − | 0.311787i | \(-0.100928\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3174.43 | + | 5498.28i | 0.160947 | + | 0.278768i | ||||
\(731\) | −9562.80 | + | 16563.3i | −0.483848 | + | 0.838049i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20598.5 | − | 11892.5i | 1.03796 | − | 0.599264i | 0.118702 | − | 0.992930i | \(-0.462127\pi\) |
0.919253 | + | 0.393666i | \(0.128793\pi\) | |||||||
\(734\) | 8620.09 | 0.433478 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11661.5 | 0.584034 | ||||||||
\(737\) | −8803.34 | + | 5082.61i | −0.439994 | + | 0.254030i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5739.04 | + | 9940.31i | −0.285675 | + | 0.494804i | −0.972773 | − | 0.231761i | \(-0.925551\pi\) |
0.687097 | + | 0.726565i | \(0.258885\pi\) | |||||||
\(740\) | 2606.14 | + | 4513.97i | 0.129465 | + | 0.224239i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 18604.0i | − | 0.918593i | −0.888283 | − | 0.459297i | \(-0.848101\pi\) | ||
0.888283 | − | 0.459297i | \(-0.151899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15059.1 | − | 8694.38i | −0.740568 | − | 0.427567i | ||||
\(746\) | 121.617 | + | 70.2157i | 0.00596879 | + | 0.00344608i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 31428.9i | − | 1.53630i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15506.2 | − | 26857.6i | −0.753436 | − | 1.30499i | −0.946148 | − | 0.323734i | \(-0.895062\pi\) |
0.192713 | − | 0.981255i | \(-0.438272\pi\) | |||||||
\(752\) | 16072.9 | − | 27839.1i | 0.779415 | − | 1.34999i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3658.82 | + | 2112.42i | −0.176719 | + | 0.102029i | ||||
\(755\) | −4389.64 | −0.211597 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19065.9 | −0.915407 | −0.457703 | − | 0.889105i | \(-0.651328\pi\) | ||||
−0.457703 | + | 0.889105i | \(0.651328\pi\) | |||||||
\(758\) | −2280.48 | + | 1316.63i | −0.109275 | + | 0.0630901i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.04863 | − | 5.28037i | 0.000145507 | − | 0.000252025i | ||||
\(761\) | 7339.58 | + | 12712.5i | 0.349618 | + | 0.605556i | 0.986182 | − | 0.165668i | \(-0.0529780\pi\) |
−0.636563 | + | 0.771224i | \(0.719645\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 33921.0i | − | 1.60631i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1316.32 | − | 759.979i | −0.0620896 | − | 0.0358475i | ||||
\(767\) | −9786.01 | − | 5649.95i | −0.460694 | − | 0.265982i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 29972.5i | − | 1.40551i | −0.711434 | − | 0.702753i | \(-0.751954\pi\) | ||
0.711434 | − | 0.702753i | \(-0.248046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13975.0 | + | 24205.3i | 0.651515 | + | 1.12846i | ||||
\(773\) | −11343.9 | + | 19648.2i | −0.527828 | + | 0.914225i | 0.471646 | + | 0.881788i | \(0.343660\pi\) |
−0.999474 | + | 0.0324367i | \(0.989673\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1333.68 | + | 770.003i | −0.0618159 | + | 0.0356894i | ||||
\(776\) | 7584.38 | 0.350855 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4823.37 | 0.222270 | ||||||||
\(779\) | 17.3096 | − | 9.99369i | 0.000796123 | − | 0.000459642i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3698.52 | + | 6406.02i | −0.169454 | + | 0.293503i | ||||
\(782\) | 2724.20 | + | 4718.45i | 0.124574 | + | 0.215769i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26183.9i | 1.19050i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18132.8 | + | 10469.0i | 0.821301 | + | 0.474178i | 0.850865 | − | 0.525385i | \(-0.176079\pi\) |
−0.0295639 | + | 0.999563i | \(0.509412\pi\) | |||||||
\(788\) | 12977.2 | + | 7492.37i | 0.586666 | + | 0.338712i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10480.5i | 0.472000i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12522.2 | − | 21689.2i | −0.560754 | − | 0.971254i | ||||
\(794\) | −3619.29 | + | 6268.79i | −0.161768 | + | 0.280190i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 80.6060 | − | 46.5379i | 0.00358920 | − | 0.00207223i | ||||
\(797\) | 27393.4 | 1.21747 | 0.608735 | − | 0.793373i | \(-0.291677\pi\) | ||||
0.608735 | + | 0.793373i | \(0.291677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51498.2 | 2.28019 | ||||||||
\(800\) | 809.918 | − | 467.606i | 0.0357936 | − | 0.0206655i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4405.03 | + | 7629.74i | −0.193949 | + | 0.335929i | ||||
\(803\) | 20248.6 | + | 35071.7i | 0.889861 | + | 1.54128i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 5184.41i | − | 0.226567i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11649.0 | − | 6725.53i | −0.507190 | − | 0.292826i | ||||
\(809\) | 23214.2 | + | 13402.7i | 1.00886 | + | 0.582465i | 0.910857 | − | 0.412722i | \(-0.135422\pi\) |
0.0980012 | + | 0.995186i | \(0.468755\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17139.6i | 0.742113i | 0.928610 | + | 0.371056i | \(0.121004\pi\) | ||||
−0.928610 | + | 0.371056i | \(0.878996\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1253.57 | − | 2171.25i | −0.0539774 | − | 0.0934915i | ||||
\(815\) | −5131.15 | + | 8887.41i | −0.220535 | + | 0.381979i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.87590 | + | 5.70185i | −0.000422906 | + | 0.000244165i | ||||
\(818\) | −3948.63 | −0.168778 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −33228.8 | −1.41512 | ||||||||
\(821\) | 7473.17 | − | 4314.64i | 0.317680 | − | 0.183413i | −0.332678 | − | 0.943041i | \(-0.607952\pi\) |
0.650358 | + | 0.759628i | \(0.274619\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2642.48 | − | 4576.91i | 0.111921 | − | 0.193853i | −0.804624 | − | 0.593785i | \(-0.797633\pi\) |
0.916545 | + | 0.399932i | \(0.130966\pi\) | |||||||
\(824\) | 152.752 | + | 264.575i | 0.00645798 | + | 0.0111856i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1845.35i | − | 0.0775926i | −0.999247 | − | 0.0387963i | \(-0.987648\pi\) | ||
0.999247 | − | 0.0387963i | \(-0.0123523\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16881.6 | − | 9746.58i | −0.707263 | − | 0.408339i | 0.102784 | − | 0.994704i | \(-0.467225\pi\) |
−0.810047 | + | 0.586365i | \(0.800558\pi\) | |||||||
\(830\) | 1655.53 | + | 955.822i | 0.0692342 | + | 0.0399724i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 9946.08i | − | 0.414445i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6899.54 | − | 11950.4i | −0.285950 | − | 0.495281i | ||||
\(836\) | 9.36979 | − | 16.2289i | 0.000387633 | − | 0.000671399i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3310.09 | − | 1911.08i | 0.136450 | − | 0.0787795i | ||||
\(839\) | −27816.7 | −1.14462 | −0.572312 | − | 0.820036i | \(-0.693953\pi\) | ||||
−0.572312 | + | 0.820036i | \(0.693953\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6322.03 | −0.259217 | ||||||||
\(842\) | 5445.48 | − | 3143.95i | 0.222878 | − | 0.128679i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10845.5 | − | 18785.0i | 0.442320 | − | 0.766121i | ||||
\(845\) | 6301.16 | + | 10913.9i | 0.256529 | + | 0.444320i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 13508.1i | 0.547015i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 378.403 | + | 218.471i | 0.0152696 | + | 0.00881588i | ||||
\(851\) | −4991.47 | − | 2881.83i | −0.201064 | − | 0.116084i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 9210.41i | − | 0.369705i | −0.982766 | − | 0.184852i | \(-0.940819\pi\) | ||
0.982766 | − | 0.184852i | \(-0.0591807\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8482.25 | − | 14691.7i | −0.338689 | − | 0.586626i | ||||
\(857\) | 17250.5 | − | 29878.7i | 0.687589 | − | 1.19094i | −0.285026 | − | 0.958520i | \(-0.592002\pi\) |
0.972615 | − | 0.232420i | \(-0.0746644\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37843.6 | − | 21849.0i | 1.50315 | − | 0.867845i | 0.503158 | − | 0.864195i | \(-0.332171\pi\) |
0.999993 | − | 0.00365004i | \(-0.00116185\pi\) | |||||||
\(860\) | 18958.6 | 0.751723 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1564.23 | 0.0618072 | ||||||||
\(863\) | 24537.6 | − | 14166.8i | 0.967869 | − | 0.558800i | 0.0692834 | − | 0.997597i | \(-0.477929\pi\) |
0.898586 | + | 0.438797i | \(0.144595\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24071.7 | − | 41693.4i | 0.946199 | − | 1.63886i | ||||
\(866\) | −4304.86 | − | 7456.24i | −0.168921 | − | 0.292579i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 66851.6i | 2.60965i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5463.86 | − | 3154.56i | −0.212556 | − | 0.122719i | ||||
\(872\) | −1352.61 | − | 780.931i | −0.0525290 | − | 0.0303276i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.24863i | 0.000125728i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22562.9 | + | 39080.1i | 0.868751 | + | 1.50472i | 0.863274 | + | 0.504736i | \(0.168410\pi\) |
0.00547715 | + | 0.999985i | \(0.498257\pi\) | |||||||
\(878\) | 1592.59 | − | 2758.44i | 0.0612155 | − | 0.106028i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −24792.5 | + | 14314.0i | −0.949722 | + | 0.548322i | ||||
\(881\) | 4244.09 | 0.162301 | 0.0811504 | − | 0.996702i | \(-0.474141\pi\) | ||||
0.0811504 | + | 0.996702i | \(0.474141\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.9077 | −0.000834939 | −0.000417470 | − | 1.00000i | \(-0.500133\pi\) | ||||
−0.000417470 | 1.00000i | \(0.500133\pi\) | ||||||||
\(884\) | 16893.2 | − | 9753.29i | 0.642737 | − | 0.371084i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1237.61 | + | 2143.60i | −0.0469280 | + | 0.0812817i | ||||
\(887\) | −3750.82 | − | 6496.61i | −0.141984 | − | 0.245924i | 0.786259 | − | 0.617896i | \(-0.212015\pi\) |
−0.928244 | + | 0.371972i | \(0.878682\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5453.72i | 0.205404i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7072.92 | − | 4083.55i | −0.265492 | − | 0.153282i | ||||
\(893\) | 26.5922 | + | 15.3530i | 0.000996498 | + | 0.000575328i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11805.6i | 0.440914i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2603.68 | − | 4509.71i | −0.0967550 | − | 0.167584i | ||||
\(899\) | 18843.2 | − | 32637.3i | 0.699060 | − | 1.21081i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18740.9 | + | 10820.1i | −0.692952 | + | 0.400076i | ||||
\(902\) | 15983.2 | 0.590004 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3335.73 | −0.122727 | ||||||||
\(905\) | 27414.1 | − | 15827.5i | 1.00693 | − | 0.581354i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20568.7 | + | 35626.0i | −0.753001 | + | 1.30424i | 0.193362 | + | 0.981128i | \(0.438061\pi\) |
−0.946362 | + | 0.323108i | \(0.895272\pi\) | |||||||
\(908\) | −1861.97 | − | 3225.02i | −0.0680524 | − | 0.117870i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 14080.6i | − | 0.512086i | −0.966665 | − | 0.256043i | \(-0.917581\pi\) | ||
0.966665 | − | 0.256043i | \(-0.0824189\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10560.1 | + | 6096.86i | 0.382790 | + | 0.221004i | ||||
\(914\) | 6318.43 | + | 3647.95i | 0.228660 | + | 0.132017i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8432.35i | 0.304162i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6311.58 | − | 10932.0i | −0.226550 | − | 0.392397i | 0.730233 | − | 0.683198i | \(-0.239411\pi\) |
−0.956783 | + | 0.290801i | \(0.906078\pi\) | |||||||
\(920\) | 5604.45 | − | 9707.19i | 0.200840 | − | 0.347866i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3608.44 | + | 2083.34i | −0.128891 | + | 0.0744154i | ||||
\(923\) | −4591.03 | −0.163722 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −462.225 | −0.0164301 | ||||||||
\(926\) | −2668.49 | + | 1540.65i | −0.0946998 | + | 0.0546750i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −11443.1 | + | 19820.0i | −0.404781 | + | 0.701101i | ||||
\(929\) | 16736.8 | + | 28989.1i | 0.591085 | + | 1.02379i | 0.994087 | + | 0.108590i | \(0.0346336\pi\) |
−0.403002 | + | 0.915199i | \(0.632033\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 25555.8i | − | 0.898186i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3931.75 | + | 2270.00i | 0.137742 | + | 0.0795252i | ||||
\(935\) | −39718.0 | − | 22931.2i | −1.38922 | − | 0.802064i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 25652.3i | − | 0.894371i | −0.894441 | − | 0.447185i | \(-0.852426\pi\) | ||
0.894441 | − | 0.447185i | \(-0.147574\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −25524.2 | − | 44209.2i | −0.885647 | − | 1.53399i | ||||
\(941\) | −1301.48 | + | 2254.23i | −0.0450872 | + | 0.0780933i | −0.887688 | − | 0.460445i | \(-0.847690\pi\) |
0.842601 | + | 0.538538i | \(0.181023\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31821.1 | − | 18371.9i | 1.09887 | − | 0.634435i | ||||
\(944\) | −17851.9 | −0.615497 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9119.17 | −0.313414 | ||||||||
\(947\) | 32577.1 | − | 18808.4i | 1.11786 | − | 0.645397i | 0.177006 | − | 0.984210i | \(-0.443359\pi\) |
0.940854 | + | 0.338813i | \(0.110025\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12567.5 | + | 21767.5i | −0.429881 | + | 0.744576i | ||||
\(950\) | 0.130264 | + | 0.225624i | 4.44877e−6 | + | 7.70549e-6i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23444.5i | 0.796896i | 0.917191 | + | 0.398448i | \(0.130451\pi\) | ||||
−0.917191 | + | 0.398448i | \(0.869549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42867.4 | − | 24749.5i | −1.45252 | − | 0.838614i | ||||
\(956\) | 14263.2 | + | 8234.88i | 0.482538 | + | 0.278593i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6176.56i | 0.208304i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8227.49 | + | 14250.4i | 0.276174 | + | 0.478347i | ||||
\(962\) | 778.037 | − | 1347.60i | 0.0260758 | − | 0.0451646i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 38344.9 | − | 22138.4i | 1.28113 | − | 0.739658i | ||||
\(965\) | 40785.7 | 1.36056 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4312.24 | 0.143405 | 0.0717023 | − | 0.997426i | \(-0.477157\pi\) | ||||
0.0717023 | + | 0.997426i | \(0.477157\pi\) | |||||||
\(968\) | 13605.2 | − | 7854.94i | 0.451742 | − | 0.260813i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2666.33 | − | 4618.22i | 0.0882585 | − | 0.152868i | ||||
\(971\) | 23526.3 | + | 40748.8i | 0.777545 | + | 1.34675i | 0.933353 | + | 0.358960i | \(0.116869\pi\) |
−0.155808 | + | 0.987787i | \(0.549798\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 8796.11i | − | 0.289369i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34265.1 | − | 19783.0i | −1.12377 | − | 0.648809i | ||||
\(977\) | −17721.5 | − | 10231.5i | −0.580308 | − | 0.335041i | 0.180948 | − | 0.983493i | \(-0.442084\pi\) |
−0.761256 | + | 0.648452i | \(0.775417\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34787.4i | 1.13566i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2250.06 | − | 3897.21i | −0.0731183 | − | 0.126645i | ||||
\(983\) | 22314.5 | − | 38649.9i | 0.724031 | − | 1.25406i | −0.235340 | − | 0.971913i | \(-0.575620\pi\) |
0.959372 | − | 0.282146i | \(-0.0910462\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18936.9 | − | 10933.2i | 0.612567 | − | 0.353666i | ||||
\(986\) | −10692.7 | −0.345359 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.6309 | 0.000374521 | ||||||||
\(989\) | −18155.4 | + | 10482.0i | −0.583729 | + | 0.337016i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21565.5 | + | 37352.5i | −0.691272 | + | 1.19732i | 0.280149 | + | 0.959957i | \(0.409616\pi\) |
−0.971421 | + | 0.237362i | \(0.923717\pi\) | |||||||
\(992\) | −14042.1 | − | 24321.6i | −0.449432 | − | 0.778439i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 135.820i | − | 0.00432743i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3136.96 | − | 1811.13i | −0.0996475 | − | 0.0575315i | 0.449348 | − | 0.893357i | \(-0.351656\pi\) |
−0.548996 | + | 0.835825i | \(0.684990\pi\) | |||||||
\(998\) | −8853.75 | − | 5111.72i | −0.280822 | − | 0.162133i | ||||
\(999\) | 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 | 441.4.p.c.80.4 | 16 | ||
3.2 | odd | 2 | inner | 441.4.p.c.80.5 | 16 | ||
7.2 | even | 3 | 63.4.p.a.26.5 | yes | 16 | ||
7.3 | odd | 6 | 441.4.c.a.440.8 | 16 | |||
7.4 | even | 3 | 441.4.c.a.440.7 | 16 | |||
7.5 | odd | 6 | inner | 441.4.p.c.215.5 | 16 | ||
7.6 | odd | 2 | 63.4.p.a.17.4 | ✓ | 16 | ||
21.2 | odd | 6 | 63.4.p.a.26.4 | yes | 16 | ||
21.5 | even | 6 | inner | 441.4.p.c.215.4 | 16 | ||
21.11 | odd | 6 | 441.4.c.a.440.10 | 16 | |||
21.17 | even | 6 | 441.4.c.a.440.9 | 16 | |||
21.20 | even | 2 | 63.4.p.a.17.5 | yes | 16 | ||
28.23 | odd | 6 | 1008.4.bt.a.593.6 | 16 | |||
28.27 | even | 2 | 1008.4.bt.a.17.3 | 16 | |||
84.23 | even | 6 | 1008.4.bt.a.593.3 | 16 | |||
84.83 | odd | 2 | 1008.4.bt.a.17.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.p.a.17.4 | ✓ | 16 | 7.6 | odd | 2 | ||
63.4.p.a.17.5 | yes | 16 | 21.20 | even | 2 | ||
63.4.p.a.26.4 | yes | 16 | 21.2 | odd | 6 | ||
63.4.p.a.26.5 | yes | 16 | 7.2 | even | 3 | ||
441.4.c.a.440.7 | 16 | 7.4 | even | 3 | |||
441.4.c.a.440.8 | 16 | 7.3 | odd | 6 | |||
441.4.c.a.440.9 | 16 | 21.17 | even | 6 | |||
441.4.c.a.440.10 | 16 | 21.11 | odd | 6 | |||
441.4.p.c.80.4 | 16 | 1.1 | even | 1 | trivial | ||
441.4.p.c.80.5 | 16 | 3.2 | odd | 2 | inner | ||
441.4.p.c.215.4 | 16 | 21.5 | even | 6 | inner | ||
441.4.p.c.215.5 | 16 | 7.5 | odd | 6 | inner | ||
1008.4.bt.a.17.3 | 16 | 28.27 | even | 2 | |||
1008.4.bt.a.17.6 | 16 | 84.83 | odd | 2 | |||
1008.4.bt.a.593.3 | 16 | 84.23 | even | 6 | |||
1008.4.bt.a.593.6 | 16 | 28.23 | odd | 6 |