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 | 80.5 | ||
Root | \(0.648633 - 0.374489i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.80 |
Dual form | 441.4.p.c.215.5 |
$q$-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 | −0.380935 | − | 0.924602i | \(-0.624398\pi\) |
0.610261 | + | 0.792200i | \(0.291064\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.71952 | + | 6.44239i | −0.464940 | + | 0.805299i | ||||
\(5\) | −5.42768 | − | 9.40102i | −0.485466 | − | 0.840852i | 0.514394 | − | 0.857554i | \(-0.328017\pi\) |
−0.999861 | + | 0.0167014i | \(0.994684\pi\) | |||||||
\(6\) | 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 | 0.967254 | − | 0.253812i | \(-0.0816845\pi\) |
0.263819 | + | 0.964572i | \(0.415018\pi\) | |||||||
\(12\) | 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 | \(0.364053\pi\) |
−0.995347 | + | 0.0963575i | \(0.969281\pi\) | |||||||
\(18\) | 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 | −0.807750 | − | 0.589525i | \(-0.799315\pi\) |
0.106668 | + | 0.994295i | \(0.465982\pi\) | |||||||
\(24\) | 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 | \(-0.810388\pi\) | ||
0.827766 | − | 0.561074i | \(-0.189612\pi\) | |||||||
\(30\) | 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 | \(-0.786669\pi\) | ||||
−0.783698 | + | 0.621142i | \(0.786669\pi\) | |||||||
\(42\) | 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 | \(-0.728905\pi\) |
−0.322219 | − | 0.946665i | \(-0.604429\pi\) | |||||||
\(48\) | 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 | 0.767553 | − | 0.640985i | \(-0.221474\pi\) |
−0.171333 | + | 0.985213i | \(0.554807\pi\) | |||||||
\(54\) | 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 | −0.992088 | − | 0.125541i | \(-0.959933\pi\) |
0.604766 | + | 0.796403i | \(0.293267\pi\) | |||||||
\(60\) | 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 | \(0.0380349\pi\) | ||||
−0.992870 | + | 0.119206i | \(0.961965\pi\) | |||||||
\(72\) | 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 | \(-0.450311\pi\) | ||||
0.155470 | + | 0.987841i | \(0.450311\pi\) | |||||||
\(84\) | 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 | 0.993658 | − | 0.112441i | \(-0.0358669\pi\) |
−0.594206 | + | 0.804313i | \(0.702534\pi\) | |||||||
\(90\) | 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 | \(0.360888\pi\) |
−0.996256 | + | 0.0864572i | \(0.972445\pi\) | |||||||
\(102\) | 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 | −0.948377 | − | 0.317145i | \(-0.897276\pi\) |
−0.199532 | + | 0.979891i | \(0.563942\pi\) | |||||||
\(108\) | 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 | \(0.0383137\pi\) | ||||
−0.992765 | + | 0.120076i | \(0.961686\pi\) | |||||||
\(114\) | 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 | 0.793706 | − | 0.608302i | \(-0.208149\pi\) |
−0.923658 | + | 0.383218i | \(0.874816\pi\) | |||||||
\(132\) | 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 | 0.0478898 | − | 0.998853i | \(-0.484750\pi\) |
−0.841087 | + | 0.540900i | \(0.818084\pi\) | |||||||
\(138\) | 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 | −0.0675396 | − | 0.997717i | \(-0.521515\pi\) |
0.830278 | + | 0.557349i | \(0.188182\pi\) | |||||||
\(150\) | 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 | \(-0.404843\pi\) | ||||
0.294511 | + | 0.955648i | \(0.404843\pi\) | |||||||
\(168\) | 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 | \(0.261331\pi\) |
0.293032 | + | 0.956103i | \(0.405336\pi\) | |||||||
\(174\) | 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 | 0.290304 | − | 0.956935i | \(-0.406244\pi\) |
−0.683578 | + | 0.729878i | \(0.739577\pi\) | |||||||
\(180\) | 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 | 0.496017 | − | 0.868313i | \(-0.334796\pi\) |
0.999989 | + | 0.00459364i | \(0.00146221\pi\) | |||||||
\(192\) | 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 | \(0.118676\pi\) | ||||
−0.931300 | + | 0.364253i | \(0.881324\pi\) | |||||||
\(198\) | 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 | −0.827111 | − | 0.562039i | \(-0.810017\pi\) |
0.900295 | + | 0.435280i | \(0.143351\pi\) | |||||||
\(228\) | 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 | −0.0195676 | − | 0.999809i | \(-0.506229\pi\) |
0.856076 | + | 0.516850i | \(0.172896\pi\) | |||||||
\(234\) | 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 | \(0.0968537\pi\) | ||||
−0.954064 | + | 0.299602i | \(0.903146\pi\) | |||||||
\(240\) | 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 | \(-0.710776\pi\) | ||||
−0.614831 | + | 0.788659i | \(0.710776\pi\) | |||||||
\(252\) | 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 | 0.992169 | − | 0.124906i | \(-0.0398629\pi\) |
−0.604256 | + | 0.796790i | \(0.706530\pi\) | |||||||
\(258\) | 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 | 0.574058 | − | 0.818814i | \(-0.305368\pi\) |
−0.422085 | + | 0.906556i | \(0.638702\pi\) | |||||||
\(264\) | 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 | −0.782964 | − | 0.622067i | \(-0.786293\pi\) |
0.930208 | + | 0.367033i | \(0.119627\pi\) | |||||||
\(270\) | 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 | \(-0.993942\pi\) | ||
0.999819 | − | 0.0190311i | \(-0.00605816\pi\) | |||||||
\(282\) | 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 | \(-0.609721\pi\) | ||||
−0.337914 | + | 0.941177i | \(0.609721\pi\) | |||||||
\(294\) | 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 | \(0.345516\pi\) |
−0.999268 | + | 0.0382648i | \(0.987817\pi\) | |||||||
\(312\) | 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 | −0.889842 | − | 0.456270i | \(-0.849185\pi\) |
−0.0497796 | + | 0.998760i | \(0.515852\pi\) | |||||||
\(318\) | 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 | 0.617212 | − | 0.786797i | \(-0.288262\pi\) |
−0.372780 | + | 0.927920i | \(0.621595\pi\) | |||||||
\(348\) | 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 | −0.551324 | − | 0.834291i | \(-0.685877\pi\) |
0.998179 | + | 0.0603149i | \(0.0192105\pi\) | |||||||
\(354\) | 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 | −0.775370 | − | 0.631508i | \(-0.782436\pi\) |
0.159217 | + | 0.987244i | \(0.449103\pi\) | |||||||
\(360\) | 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 | 0.790366 | − | 0.612634i | \(-0.209890\pi\) |
−0.925740 | + | 0.378160i | \(0.876557\pi\) | |||||||
\(384\) | 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 | 0.817295 | − | 0.576219i | \(-0.195472\pi\) |
−0.0903727 | + | 0.995908i | \(0.528806\pi\) | |||||||
\(390\) | 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 | −0.974723 | − | 0.223417i | \(-0.928279\pi\) |
−0.293876 | + | 0.955843i | \(0.594945\pi\) | |||||||
\(402\) | 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 | \(-0.403847\pi\) | ||||
0.297502 | + | 0.954721i | \(0.403847\pi\) | |||||||
\(420\) | 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 | 0.597652 | − | 0.801756i | \(-0.296100\pi\) |
−0.395515 | + | 0.918460i | \(0.629434\pi\) | |||||||
\(432\) | 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 | −0.645561 | − | 0.763708i | \(-0.723377\pi\) |
0.338610 | + | 0.940927i | \(0.390043\pi\) | |||||||
\(444\) | 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 | \(-0.880938\pi\) | ||
0.930857 | − | 0.365384i | \(-0.119062\pi\) | |||||||
\(450\) | 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 | \(-0.590673\pi\) | ||||
−0.281021 | + | 0.959702i | \(0.590673\pi\) | |||||||
\(462\) | 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 | 0.976208 | − | 0.216837i | \(-0.0695739\pi\) |
−0.675890 | + | 0.737002i | \(0.736241\pi\) | |||||||
\(468\) | 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 | −0.992885 | − | 0.119077i | \(-0.962006\pi\) |
0.599566 | + | 0.800325i | \(0.295340\pi\) | |||||||
\(480\) | 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 | \(-0.910950\pi\) | ||
0.961122 | − | 0.276123i | \(-0.0890497\pi\) | |||||||
\(492\) | 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 | \(-0.430854\pi\) | ||||
0.215524 | + | 0.976499i | \(0.430854\pi\) | |||||||
\(504\) | 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 | \(-0.886097\pi\) |
0.165003 | − | 0.986293i | \(-0.447237\pi\) | |||||||
\(510\) | 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 | \(-0.637024\pi\) |
0.995667 | − | 0.0929909i | \(-0.0296427\pi\) | |||||||
\(522\) | 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 | 0.606461 | − | 0.795113i | \(-0.292589\pi\) |
−0.385357 | + | 0.922767i | \(0.625922\pi\) | |||||||
\(558\) | 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 | −0.791096 | − | 0.611692i | \(-0.790489\pi\) |
0.925289 | + | 0.379263i | \(0.123822\pi\) | |||||||
\(564\) | 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 | 0.213829 | − | 0.976871i | \(-0.431407\pi\) |
0.952910 | + | 0.303254i | \(0.0980732\pi\) | |||||||
\(570\) | 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 | \(-0.546973\pi\) | ||||
−0.147034 | + | 0.989131i | \(0.546973\pi\) | |||||||
\(588\) | 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 | \(0.0227445\pi\) |
−0.436896 | + | 0.899512i | \(0.643922\pi\) | |||||||
\(594\) | 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 | 0.827425 | − | 0.561576i | \(-0.189805\pi\) |
−0.0726267 | + | 0.997359i | \(0.523138\pi\) | |||||||
\(600\) | 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 | \(0.0809639\pi\) | ||||
−0.967826 | + | 0.251622i | \(0.919036\pi\) | |||||||
\(618\) | 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 | \(-0.972056\pi\) |
−0.574004 | − | 0.818852i | \(-0.694611\pi\) | |||||||
\(642\) | 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 | −0.961683 | − | 0.274164i | \(-0.911599\pi\) |
0.718275 | + | 0.695760i | \(0.244932\pi\) | |||||||
\(648\) | 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 | −0.0425886 | − | 0.999093i | \(-0.513560\pi\) |
0.843945 | + | 0.536429i | \(0.180227\pi\) | |||||||
\(654\) | 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 | \(-0.624261\pi\) | ||
0.380537 | − | 0.924766i | \(-0.375739\pi\) | |||||||
\(660\) | 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 | 0.758063 | − | 0.652181i | \(-0.226146\pi\) |
−0.943837 | + | 0.330411i | \(0.892813\pi\) | |||||||
\(678\) | 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 | \(0.0104401\pi\) |
0.528130 | + | 0.849163i | \(0.322893\pi\) | |||||||
\(684\) | 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 | \(-0.993412\pi\) | ||
0.999786 | − | 0.0206950i | \(-0.00658789\pi\) | |||||||
\(702\) | 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 | 0.978454 | − | 0.206465i | \(-0.0661958\pi\) |
−0.668031 | + | 0.744134i | \(0.732862\pi\) | |||||||
\(720\) | 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 | \(0.151899\pi\) | ||||
−0.888283 | + | 0.459297i | \(0.848101\pi\) | |||||||
\(744\) | 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 | 0.636563 | − | 0.771224i | \(-0.280355\pi\) |
−0.986182 | + | 0.165668i | \(0.947022\pi\) | |||||||
\(762\) | 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 | \(-0.656340\pi\) |
0.999474 | − | 0.0324367i | \(-0.0103267\pi\) | |||||||
\(774\) | 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 | \(-0.708323\pi\) | ||||
−0.608735 | + | 0.793373i | \(0.708323\pi\) | |||||||
\(798\) | 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 | −0.0980012 | − | 0.995186i | \(-0.531245\pi\) |
−0.910857 | + | 0.412722i | \(0.864578\pi\) | |||||||
\(810\) | 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 | −0.650358 | − | 0.759628i | \(-0.725381\pi\) |
0.332678 | + | 0.943041i | \(0.392048\pi\) | |||||||
\(822\) | 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 | \(0.0123523\pi\) | ||||
−0.999247 | + | 0.0387963i | \(0.987648\pi\) | |||||||
\(828\) | 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 | \(-0.306047\pi\) | ||||
0.572312 | + | 0.820036i | \(0.306047\pi\) | |||||||
\(840\) | 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 | \(0.407998\pi\) |
−0.972615 | + | 0.232420i | \(0.925336\pi\) | |||||||
\(858\) | 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 | −0.898586 | − | 0.438797i | \(-0.855405\pi\) |
−0.0692834 | + | 0.997597i | \(0.522071\pi\) | |||||||
\(864\) | 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 | \(-0.525859\pi\) | ||||
−0.0811504 | + | 0.996702i | \(0.525859\pi\) | |||||||
\(882\) | 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 | 0.928244 | − | 0.371972i | \(-0.121318\pi\) |
−0.786259 | + | 0.617896i | \(0.787985\pi\) | |||||||
\(888\) | 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 | \(0.0824189\pi\) | ||||
−0.966665 | + | 0.256043i | \(0.917581\pi\) | |||||||
\(912\) | 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 | \(-0.965366\pi\) |
0.403002 | − | 0.915199i | \(-0.367967\pi\) | |||||||
\(930\) | 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 | −0.842601 | − | 0.538538i | \(-0.818977\pi\) |
0.887688 | + | 0.460445i | \(0.152310\pi\) | |||||||
\(942\) | 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 | −0.940854 | − | 0.338813i | \(-0.889975\pi\) |
−0.177006 | + | 0.984210i | \(0.556641\pi\) | |||||||
\(948\) | 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 | \(-0.869549\pi\) | ||
0.917191 | − | 0.398448i | \(-0.130451\pi\) | |||||||
\(954\) | 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 | \(-0.883131\pi\) |
0.155808 | − | 0.987787i | \(-0.450202\pi\) | |||||||
\(972\) | 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 | 0.761256 | − | 0.648452i | \(-0.224583\pi\) |
−0.180948 | + | 0.983493i | \(0.557916\pi\) | |||||||
\(978\) | 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 | \(0.424380\pi\) |
−0.959372 | + | 0.282146i | \(0.908954\pi\) | |||||||
\(984\) | 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.80.5 | 16 | ||
3.2 | odd | 2 | inner | 441.4.p.c.80.4 | 16 | ||
7.2 | even | 3 | 63.4.p.a.26.4 | yes | 16 | ||
7.3 | odd | 6 | 441.4.c.a.440.9 | 16 | |||
7.4 | even | 3 | 441.4.c.a.440.10 | 16 | |||
7.5 | odd | 6 | inner | 441.4.p.c.215.4 | 16 | ||
7.6 | odd | 2 | 63.4.p.a.17.5 | yes | 16 | ||
21.2 | odd | 6 | 63.4.p.a.26.5 | yes | 16 | ||
21.5 | even | 6 | inner | 441.4.p.c.215.5 | 16 | ||
21.11 | odd | 6 | 441.4.c.a.440.7 | 16 | |||
21.17 | even | 6 | 441.4.c.a.440.8 | 16 | |||
21.20 | even | 2 | 63.4.p.a.17.4 | ✓ | 16 | ||
28.23 | odd | 6 | 1008.4.bt.a.593.3 | 16 | |||
28.27 | even | 2 | 1008.4.bt.a.17.6 | 16 | |||
84.23 | even | 6 | 1008.4.bt.a.593.6 | 16 | |||
84.83 | odd | 2 | 1008.4.bt.a.17.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.p.a.17.4 | ✓ | 16 | 21.20 | even | 2 | ||
63.4.p.a.17.5 | yes | 16 | 7.6 | odd | 2 | ||
63.4.p.a.26.4 | yes | 16 | 7.2 | even | 3 | ||
63.4.p.a.26.5 | yes | 16 | 21.2 | odd | 6 | ||
441.4.c.a.440.7 | 16 | 21.11 | odd | 6 | |||
441.4.c.a.440.8 | 16 | 21.17 | even | 6 | |||
441.4.c.a.440.9 | 16 | 7.3 | odd | 6 | |||
441.4.c.a.440.10 | 16 | 7.4 | even | 3 | |||
441.4.p.c.80.4 | 16 | 3.2 | odd | 2 | inner | ||
441.4.p.c.80.5 | 16 | 1.1 | even | 1 | trivial | ||
441.4.p.c.215.4 | 16 | 7.5 | odd | 6 | inner | ||
441.4.p.c.215.5 | 16 | 21.5 | even | 6 | inner | ||
1008.4.bt.a.17.3 | 16 | 84.83 | odd | 2 | |||
1008.4.bt.a.17.6 | 16 | 28.27 | even | 2 | |||
1008.4.bt.a.593.3 | 16 | 28.23 | odd | 6 | |||
1008.4.bt.a.593.6 | 16 | 84.23 | even | 6 |