Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
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([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (of order \(3\), 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 \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 74 x^{14} + 4007 x^{12} + 91050 x^{10} + 1502189 x^{8} + 12598332 x^{6} + 74261084 x^{4} + 22070000 x^{2} + 6250000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{8}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-3.40706 - 5.90120i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.361 |
Dual form | 441.4.e.z.226.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69995 | − | 4.67646i | −0.954578 | − | 1.65338i | −0.735332 | − | 0.677707i | \(-0.762974\pi\) |
−0.219246 | − | 0.975670i | \(-0.570360\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −10.5795 | + | 18.3242i | −1.32244 | + | 2.29053i | ||||
\(5\) | −7.78839 | − | 13.4899i | −0.696615 | − | 1.20657i | −0.969633 | − | 0.244563i | \(-0.921355\pi\) |
0.273019 | − | 0.962009i | \(-0.411978\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 71.0573 | 3.14032 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −42.0566 | + | 72.8441i | −1.32995 | + | 2.30353i | ||||
\(11\) | −15.9851 | + | 27.6870i | −0.438153 | + | 0.758904i | −0.997547 | − | 0.0699983i | \(-0.977701\pi\) |
0.559394 | + | 0.828902i | \(0.311034\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −72.5746 | −1.54835 | −0.774176 | − | 0.632971i | \(-0.781835\pi\) | ||||
−0.774176 | + | 0.632971i | \(0.781835\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −107.215 | − | 185.703i | −1.67524 | − | 2.90160i | ||||
\(17\) | 14.5144 | − | 25.1397i | 0.207074 | − | 0.358663i | −0.743717 | − | 0.668494i | \(-0.766939\pi\) |
0.950792 | + | 0.309831i | \(0.100273\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 54.4146 | + | 94.2489i | 0.657030 | + | 1.13801i | 0.981381 | + | 0.192073i | \(0.0615210\pi\) |
−0.324350 | + | 0.945937i | \(0.605146\pi\) | |||||||
\(20\) | 329.589 | 3.68492 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 172.636 | 1.67300 | ||||||||
\(23\) | 27.6434 | + | 47.8798i | 0.250611 | + | 0.434071i | 0.963694 | − | 0.267008i | \(-0.0860352\pi\) |
−0.713083 | + | 0.701079i | \(0.752702\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −58.8180 | + | 101.876i | −0.470544 | + | 0.815006i | ||||
\(26\) | 195.948 | + | 339.392i | 1.47802 | + | 2.56001i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17.7363 | 0.113570 | 0.0567852 | − | 0.998386i | \(-0.481915\pi\) | ||||
0.0567852 | + | 0.998386i | \(0.481915\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 28.0594 | − | 48.6004i | 0.162568 | − | 0.281577i | −0.773221 | − | 0.634137i | \(-0.781356\pi\) |
0.935789 | + | 0.352560i | \(0.114689\pi\) | |||||||
\(32\) | −294.724 | + | 510.477i | −1.62814 | + | 2.82001i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −156.753 | −0.790673 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 147.908 | + | 256.184i | 0.657187 | + | 1.13828i | 0.981341 | + | 0.192276i | \(0.0615870\pi\) |
−0.324154 | + | 0.946004i | \(0.605080\pi\) | |||||||
\(38\) | 293.834 | − | 508.935i | 1.25437 | − | 2.17264i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −553.422 | − | 958.555i | −2.18759 | − | 3.78902i | ||||
\(41\) | 238.605 | 0.908873 | 0.454437 | − | 0.890779i | \(-0.349841\pi\) | ||||
0.454437 | + | 0.890779i | \(0.349841\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16.8202 | 0.0596526 | 0.0298263 | − | 0.999555i | \(-0.490505\pi\) | ||||
0.0298263 | + | 0.999555i | \(0.490505\pi\) | |||||||
\(44\) | −338.228 | − | 585.829i | −1.15886 | − | 2.00720i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 149.272 | − | 258.547i | 0.478455 | − | 0.828709i | ||||
\(47\) | −255.954 | − | 443.326i | −0.794357 | − | 1.37587i | −0.923246 | − | 0.384208i | \(-0.874474\pi\) |
0.128889 | − | 0.991659i | \(-0.458859\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 635.223 | 1.79668 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 767.802 | − | 1329.87i | 2.04760 | − | 3.54654i | ||||
\(53\) | −132.603 | + | 229.674i | −0.343667 | + | 0.595249i | −0.985111 | − | 0.171921i | \(-0.945003\pi\) |
0.641443 | + | 0.767170i | \(0.278336\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 497.992 | 1.22090 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −47.8871 | − | 82.9429i | −0.108412 | − | 0.187775i | ||||
\(59\) | 127.091 | − | 220.128i | 0.280437 | − | 0.485732i | −0.691055 | − | 0.722802i | \(-0.742854\pi\) |
0.971493 | + | 0.237070i | \(0.0761872\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −36.4176 | − | 63.0771i | −0.0764392 | − | 0.132397i | 0.825272 | − | 0.564735i | \(-0.191022\pi\) |
−0.901711 | + | 0.432339i | \(0.857688\pi\) | |||||||
\(62\) | −303.037 | −0.620737 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1467.52 | 2.86625 | ||||||||
\(65\) | 565.239 | + | 979.023i | 1.07860 | + | 1.86820i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 253.180 | − | 438.520i | 0.461654 | − | 0.799609i | −0.537389 | − | 0.843334i | \(-0.680589\pi\) |
0.999044 | + | 0.0437257i | \(0.0139228\pi\) | |||||||
\(68\) | 307.110 | + | 531.930i | 0.547685 | + | 0.948618i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −827.722 | −1.38356 | −0.691779 | − | 0.722110i | \(-0.743173\pi\) | ||||
−0.691779 | + | 0.722110i | \(0.743173\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −186.288 | + | 322.661i | −0.298677 | + | 0.517324i | −0.975834 | − | 0.218515i | \(-0.929879\pi\) |
0.677157 | + | 0.735839i | \(0.263212\pi\) | |||||||
\(74\) | 798.689 | − | 1383.37i | 1.25467 | − | 2.17315i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2302.72 | −3.47552 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −514.226 | − | 890.665i | −0.732341 | − | 1.26845i | −0.955880 | − | 0.293757i | \(-0.905094\pi\) |
0.223539 | − | 0.974695i | \(-0.428239\pi\) | |||||||
\(80\) | −1670.07 | + | 2892.65i | −2.33400 | + | 4.04260i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −644.222 | − | 1115.82i | −0.867590 | − | 1.50271i | ||||
\(83\) | 453.148 | 0.599270 | 0.299635 | − | 0.954054i | \(-0.403135\pi\) | ||||
0.299635 | + | 0.954054i | \(0.403135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −452.175 | −0.577003 | ||||||||
\(86\) | −45.4138 | − | 78.6590i | −0.0569430 | − | 0.0986282i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1135.86 | + | 1967.36i | −1.37594 | + | 2.38320i | ||||
\(89\) | −166.033 | − | 287.577i | −0.197746 | − | 0.342507i | 0.750051 | − | 0.661380i | \(-0.230029\pi\) |
−0.947797 | + | 0.318873i | \(0.896696\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1169.81 | −1.32567 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1382.13 | + | 2393.92i | −1.51655 | + | 2.62674i | ||||
\(95\) | 847.605 | − | 1468.09i | 0.915394 | − | 1.58551i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1164.54 | 1.21898 | 0.609489 | − | 0.792795i | \(-0.291375\pi\) | ||||
0.609489 | + | 0.792795i | \(0.291375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1244.53 | − | 2155.59i | −1.24453 | − | 2.15559i | ||||
\(101\) | 931.771 | − | 1613.88i | 0.917967 | − | 1.58997i | 0.115470 | − | 0.993311i | \(-0.463163\pi\) |
0.802498 | − | 0.596655i | \(-0.203504\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 493.140 | + | 854.144i | 0.471753 | + | 0.817100i | 0.999478 | − | 0.0323154i | \(-0.0102881\pi\) |
−0.527725 | + | 0.849415i | \(0.676955\pi\) | |||||||
\(104\) | −5156.95 | −4.86232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1432.08 | 1.31223 | ||||||||
\(107\) | 347.843 | + | 602.481i | 0.314273 | + | 0.544337i | 0.979283 | − | 0.202498i | \(-0.0649059\pi\) |
−0.665010 | + | 0.746835i | \(0.731573\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −857.498 | + | 1485.23i | −0.753517 | + | 1.30513i | 0.192591 | + | 0.981279i | \(0.438311\pi\) |
−0.946108 | + | 0.323851i | \(0.895022\pi\) | |||||||
\(110\) | −1344.56 | − | 2328.84i | −1.16544 | − | 2.01860i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 877.721 | 0.730700 | 0.365350 | − | 0.930870i | \(-0.380949\pi\) | ||||
0.365350 | + | 0.930870i | \(0.380949\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 430.595 | − | 745.813i | 0.349159 | − | 0.604760i | ||||
\(116\) | −187.641 | + | 325.003i | −0.150190 | + | 0.260136i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1372.56 | −1.07080 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 154.454 | + | 267.522i | 0.116044 | + | 0.200993i | ||||
\(122\) | −196.652 | + | 340.610i | −0.145934 | + | 0.252766i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 593.709 | + | 1028.33i | 0.429973 | + | 0.744735i | ||||
\(125\) | −114.708 | −0.0820784 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 781.088 | 0.545751 | 0.272875 | − | 0.962049i | \(-0.412025\pi\) | ||||
0.272875 | + | 0.962049i | \(0.412025\pi\) | |||||||
\(128\) | −1604.44 | − | 2778.97i | −1.10792 | − | 1.91897i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3052.24 | − | 5286.63i | 2.05922 | − | 3.56668i | ||||
\(131\) | −980.619 | − | 1698.48i | −0.654024 | − | 1.13280i | −0.982138 | − | 0.188164i | \(-0.939746\pi\) |
0.328114 | − | 0.944638i | \(-0.393587\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2734.29 | −1.76274 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1031.35 | − | 1786.36i | 0.650279 | − | 1.12632i | ||||
\(137\) | 610.155 | − | 1056.82i | 0.380504 | − | 0.659053i | −0.610630 | − | 0.791916i | \(-0.709084\pi\) |
0.991134 | + | 0.132863i | \(0.0424171\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1068.10 | −0.651765 | −0.325882 | − | 0.945410i | \(-0.605661\pi\) | ||||
−0.325882 | + | 0.945410i | \(0.605661\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2234.81 | + | 3870.81i | 1.32071 | + | 2.28754i | ||||
\(143\) | 1160.11 | − | 2009.37i | 0.678415 | − | 1.17505i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −138.137 | − | 239.260i | −0.0791148 | − | 0.137031i | ||||
\(146\) | 2011.88 | 1.14044 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6259.16 | −3.47635 | ||||||||
\(149\) | 1295.41 | + | 2243.72i | 0.712243 | + | 1.23364i | 0.964013 | + | 0.265855i | \(0.0856541\pi\) |
−0.251770 | + | 0.967787i | \(0.581013\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −964.770 | + | 1671.03i | −0.519946 | + | 0.900573i | 0.479785 | + | 0.877386i | \(0.340715\pi\) |
−0.999731 | + | 0.0231868i | \(0.992619\pi\) | |||||||
\(152\) | 3866.56 | + | 6697.08i | 2.06328 | + | 3.57371i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −874.151 | −0.452990 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1312.87 | − | 2273.95i | 0.667377 | − | 1.15593i | −0.311259 | − | 0.950325i | \(-0.600751\pi\) |
0.978635 | − | 0.205605i | \(-0.0659162\pi\) | |||||||
\(158\) | −2776.77 | + | 4809.51i | −1.39815 | + | 2.42167i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9181.70 | 4.53673 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1550.08 | + | 2684.82i | 0.744858 | + | 1.29013i | 0.950261 | + | 0.311455i | \(0.100816\pi\) |
−0.205403 | + | 0.978678i | \(0.565850\pi\) | |||||||
\(164\) | −2524.32 | + | 4372.25i | −1.20193 | + | 2.08180i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1223.48 | − | 2119.13i | −0.572050 | − | 0.990819i | ||||
\(167\) | 3264.73 | 1.51277 | 0.756386 | − | 0.654126i | \(-0.226963\pi\) | ||||
0.756386 | + | 0.654126i | \(0.226963\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3070.07 | 1.39739 | ||||||||
\(170\) | 1220.85 | + | 2114.58i | 0.550795 | + | 0.954004i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −177.949 | + | 308.217i | −0.0788867 | + | 0.136636i | ||||
\(173\) | 1018.15 | + | 1763.49i | 0.447450 | + | 0.775006i | 0.998219 | − | 0.0596516i | \(-0.0189990\pi\) |
−0.550769 | + | 0.834657i | \(0.685666\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6855.39 | 2.93605 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −896.561 | + | 1552.89i | −0.377529 | + | 0.653899i | ||||
\(179\) | 1791.17 | − | 3102.40i | 0.747925 | − | 1.29544i | −0.200890 | − | 0.979614i | \(-0.564383\pi\) |
0.948816 | − | 0.315831i | \(-0.102283\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1637.35 | 0.672392 | 0.336196 | − | 0.941792i | \(-0.390860\pi\) | ||||
0.336196 | + | 0.941792i | \(0.390860\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1964.27 | + | 3402.21i | 0.786998 | + | 1.36312i | ||||
\(185\) | 2303.93 | − | 3990.52i | 0.915612 | − | 1.58589i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 464.028 | + | 803.720i | 0.181460 | + | 0.314299i | ||||
\(188\) | 10831.5 | 4.20195 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9153.97 | −3.49526 | ||||||||
\(191\) | −1412.39 | − | 2446.33i | −0.535063 | − | 0.926756i | −0.999160 | − | 0.0409717i | \(-0.986955\pi\) |
0.464098 | − | 0.885784i | \(-0.346379\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 828.765 | − | 1435.46i | 0.309098 | − | 0.535373i | −0.669068 | − | 0.743201i | \(-0.733306\pi\) |
0.978165 | + | 0.207829i | \(0.0666397\pi\) | |||||||
\(194\) | −3144.19 | − | 5445.90i | −1.16361 | − | 2.01543i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1890.78 | 0.683819 | 0.341909 | − | 0.939733i | \(-0.388926\pi\) | ||||
0.341909 | + | 0.939733i | \(0.388926\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −696.373 | + | 1206.15i | −0.248063 | + | 0.429658i | −0.962988 | − | 0.269543i | \(-0.913127\pi\) |
0.714925 | + | 0.699201i | \(0.246461\pi\) | |||||||
\(200\) | −4179.45 | + | 7239.01i | −1.47766 | + | 2.55938i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10063.0 | −3.50508 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1858.35 | − | 3218.75i | −0.633134 | − | 1.09662i | ||||
\(206\) | 2662.91 | − | 4612.30i | 0.900650 | − | 1.55997i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7781.12 | + | 13477.3i | 2.59386 | + | 4.49270i | ||||
\(209\) | −3479.29 | −1.15152 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3314.53 | 1.08143 | 0.540714 | − | 0.841206i | \(-0.318154\pi\) | ||||
0.540714 | + | 0.841206i | \(0.318154\pi\) | |||||||
\(212\) | −2805.74 | − | 4859.68i | −0.908957 | − | 1.57436i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1878.32 | − | 3253.34i | 0.599996 | − | 1.03922i | ||||
\(215\) | −131.002 | − | 226.903i | −0.0415548 | − | 0.0719751i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9260.82 | 2.87716 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5268.51 | + | 9125.32i | −1.61456 | + | 2.79650i | ||||
\(221\) | −1053.38 | + | 1824.50i | −0.320624 | + | 0.555336i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5576.50 | 1.67457 | 0.837287 | − | 0.546764i | \(-0.184140\pi\) | ||||
0.837287 | + | 0.546764i | \(0.184140\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2369.81 | − | 4104.63i | −0.697510 | − | 1.20812i | ||||
\(227\) | −723.961 | + | 1253.94i | −0.211678 | + | 0.366638i | −0.952240 | − | 0.305351i | \(-0.901226\pi\) |
0.740562 | + | 0.671989i | \(0.234560\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 808.774 | + | 1400.84i | 0.233385 | + | 0.404235i | 0.958802 | − | 0.284074i | \(-0.0916863\pi\) |
−0.725417 | + | 0.688310i | \(0.758353\pi\) | |||||||
\(230\) | −4650.35 | −1.33320 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1260.29 | 0.356647 | ||||||||
\(233\) | 3046.05 | + | 5275.92i | 0.856454 | + | 1.48342i | 0.875290 | + | 0.483598i | \(0.160670\pi\) |
−0.0188365 | + | 0.999823i | \(0.505996\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3986.94 | + | 6905.59i | −1.10672 | + | 1.91690i | ||||
\(236\) | 2689.11 | + | 4657.68i | 0.741721 | + | 1.28470i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1595.90 | −0.431927 | −0.215963 | − | 0.976401i | \(-0.569289\pi\) | ||||
−0.215963 | + | 0.976401i | \(0.569289\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1094.42 | − | 1895.58i | 0.292521 | − | 0.506661i | −0.681884 | − | 0.731460i | \(-0.738839\pi\) |
0.974405 | + | 0.224799i | \(0.0721726\pi\) | |||||||
\(242\) | 834.037 | − | 1444.59i | 0.221545 | − | 0.383727i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1541.12 | 0.404344 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3949.12 | − | 6840.08i | −1.01731 | − | 1.76204i | ||||
\(248\) | 1993.83 | − | 3453.41i | 0.510517 | − | 0.884241i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 309.706 | + | 536.427i | 0.0783502 | + | 0.135707i | ||||
\(251\) | 6203.07 | 1.55990 | 0.779949 | − | 0.625843i | \(-0.215245\pi\) | ||||
0.779949 | + | 0.625843i | \(0.215245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1767.53 | −0.439224 | ||||||||
\(254\) | −2108.90 | − | 3652.72i | −0.520961 | − | 0.902331i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2793.74 | + | 4838.90i | −0.682066 | + | 1.18137i | ||||
\(257\) | −134.162 | − | 232.375i | −0.0325633 | − | 0.0564013i | 0.849284 | − | 0.527935i | \(-0.177034\pi\) |
−0.881848 | + | 0.471534i | \(0.843700\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −23919.8 | −5.70554 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5295.25 | + | 9171.65i | −1.24863 | + | 2.16270i | ||||
\(263\) | −1862.48 | + | 3225.91i | −0.436675 | + | 0.756343i | −0.997431 | − | 0.0716384i | \(-0.977177\pi\) |
0.560756 | + | 0.827981i | \(0.310511\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4131.04 | 0.957615 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5357.03 | + | 9278.64i | 1.22102 | + | 2.11486i | ||||
\(269\) | −4278.63 | + | 7410.80i | −0.969786 | + | 1.67972i | −0.273619 | + | 0.961838i | \(0.588221\pi\) |
−0.696167 | + | 0.717880i | \(0.745112\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2639.83 | − | 4572.32i | −0.591728 | − | 1.02490i | −0.994000 | − | 0.109383i | \(-0.965112\pi\) |
0.402271 | − | 0.915521i | \(-0.368221\pi\) | |||||||
\(272\) | −6224.67 | −1.38760 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6589.56 | −1.45288 | ||||||||
\(275\) | −1880.42 | − | 3256.98i | −0.412341 | − | 0.714195i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 220.774 | − | 382.392i | 0.0478882 | − | 0.0829448i | −0.841088 | − | 0.540899i | \(-0.818084\pi\) |
0.888976 | + | 0.457954i | \(0.151418\pi\) | |||||||
\(278\) | 2883.83 | + | 4994.94i | 0.622160 | + | 1.07761i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3766.49 | −0.799609 | −0.399804 | − | 0.916601i | \(-0.630922\pi\) | ||||
−0.399804 | + | 0.916601i | \(0.630922\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 905.511 | − | 1568.39i | 0.190201 | − | 0.329439i | −0.755115 | − | 0.655592i | \(-0.772419\pi\) |
0.945317 | + | 0.326153i | \(0.105753\pi\) | |||||||
\(284\) | 8756.88 | − | 15167.4i | 1.82967 | − | 3.16908i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12529.0 | −2.59040 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2035.16 | + | 3525.01i | 0.414241 | + | 0.717486i | ||||
\(290\) | −745.926 | + | 1291.98i | −0.151042 | + | 0.261613i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3941.68 | − | 6827.18i | −0.789963 | − | 1.36826i | ||||
\(293\) | −5815.74 | −1.15959 | −0.579794 | − | 0.814763i | \(-0.696867\pi\) | ||||
−0.579794 | + | 0.814763i | \(0.696867\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3959.33 | −0.781427 | ||||||||
\(296\) | 10509.9 | + | 18203.7i | 2.06378 | + | 3.57456i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6995.10 | − | 12115.9i | 1.35978 | − | 2.35521i | ||||
\(299\) | −2006.21 | − | 3474.86i | −0.388034 | − | 0.672094i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10419.3 | 1.98532 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11668.2 | − | 20209.9i | 2.20137 | − | 3.81288i | ||||
\(305\) | −567.269 | + | 982.538i | −0.106497 | + | 0.184459i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1974.93 | 0.367150 | 0.183575 | − | 0.983006i | \(-0.441233\pi\) | ||||
0.183575 | + | 0.983006i | \(0.441233\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2360.17 | + | 4087.93i | 0.432414 | + | 0.748964i | ||||
\(311\) | −579.535 | + | 1003.78i | −0.105667 | + | 0.183020i | −0.914010 | − | 0.405691i | \(-0.867031\pi\) |
0.808344 | + | 0.588711i | \(0.200364\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2246.84 | + | 3891.64i | 0.405747 | + | 0.702774i | 0.994408 | − | 0.105606i | \(-0.0336781\pi\) |
−0.588661 | + | 0.808380i | \(0.700345\pi\) | |||||||
\(314\) | −14178.7 | −2.54825 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21761.0 | 3.87390 | ||||||||
\(317\) | −2338.75 | − | 4050.83i | −0.414376 | − | 0.717721i | 0.580987 | − | 0.813913i | \(-0.302667\pi\) |
−0.995363 | + | 0.0961925i | \(0.969334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −283.516 | + | 491.064i | −0.0497612 | + | 0.0861890i | ||||
\(320\) | −11429.6 | − | 19796.7i | −1.99667 | − | 3.45833i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3159.19 | 0.544216 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4268.69 | − | 7393.59i | 0.728567 | − | 1.26192i | ||||
\(326\) | 8370.30 | − | 14497.8i | 1.42205 | − | 2.46306i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16954.6 | 2.85415 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1491.36 | + | 2583.10i | 0.247650 | + | 0.428943i | 0.962873 | − | 0.269953i | \(-0.0870082\pi\) |
−0.715223 | + | 0.698896i | \(0.753675\pi\) | |||||||
\(332\) | −4794.07 | + | 8303.58i | −0.792497 | + | 1.37264i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8814.63 | − | 15267.4i | −1.44406 | − | 2.50118i | ||||
\(335\) | −7887.45 | −1.28638 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7328.53 | 1.18460 | 0.592301 | − | 0.805717i | \(-0.298220\pi\) | ||||
0.592301 | + | 0.805717i | \(0.298220\pi\) | |||||||
\(338\) | −8289.04 | − | 14357.0i | −1.33392 | − | 2.31042i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4783.79 | − | 8285.76i | 0.763051 | − | 1.32164i | ||||
\(341\) | 897.065 | + | 1553.76i | 0.142460 | + | 0.246748i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1195.20 | 0.187328 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5497.94 | − | 9522.71i | 0.854251 | − | 1.47961i | ||||
\(347\) | −4154.66 | + | 7196.09i | −0.642749 | + | 1.11327i | 0.342067 | + | 0.939676i | \(0.388873\pi\) |
−0.984816 | + | 0.173599i | \(0.944460\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −334.303 | −0.0512745 | −0.0256373 | − | 0.999671i | \(-0.508161\pi\) | ||||
−0.0256373 | + | 0.999671i | \(0.508161\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9422.38 | − | 16320.0i | −1.42675 | − | 2.47120i | ||||
\(353\) | −2729.09 | + | 4726.93i | −0.411487 | + | 0.712717i | −0.995053 | − | 0.0993491i | \(-0.968324\pi\) |
0.583565 | + | 0.812066i | \(0.301657\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6446.62 | + | 11165.9i | 0.963806 | + | 1.66936i | ||||
\(356\) | 7026.17 | 1.04603 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19344.3 | −2.85581 | ||||||||
\(359\) | −3598.45 | − | 6232.70i | −0.529022 | − | 0.916293i | −0.999427 | − | 0.0338425i | \(-0.989226\pi\) |
0.470405 | − | 0.882451i | \(-0.344108\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2492.41 | + | 4316.98i | −0.363378 | + | 0.629389i | ||||
\(362\) | −4420.76 | − | 7656.98i | −0.641851 | − | 1.11172i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5803.55 | 0.832251 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3162.21 | + | 5477.12i | −0.449772 | + | 0.779028i | −0.998371 | − | 0.0570579i | \(-0.981828\pi\) |
0.548599 | + | 0.836086i | \(0.315161\pi\) | |||||||
\(368\) | 5927.60 | − | 10266.9i | 0.839668 | − | 1.45435i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −24882.0 | −3.49609 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5465.88 | + | 9467.18i | 0.758746 | + | 1.31419i | 0.943490 | + | 0.331400i | \(0.107521\pi\) |
−0.184744 | + | 0.982787i | \(0.559146\pi\) | |||||||
\(374\) | 2505.71 | − | 4340.01i | 0.346436 | − | 0.600045i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18187.4 | − | 31501.6i | −2.49454 | − | 4.32066i | ||||
\(377\) | −1287.20 | −0.175847 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6024.02 | 0.816446 | 0.408223 | − | 0.912882i | \(-0.366149\pi\) | ||||
0.408223 | + | 0.912882i | \(0.366149\pi\) | |||||||
\(380\) | 17934.5 | + | 31063.4i | 2.42110 | + | 4.19347i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7626.78 | + | 13210.0i | −1.02152 | + | 1.76932i | ||||
\(383\) | 3424.05 | + | 5930.63i | 0.456816 | + | 0.791229i | 0.998791 | − | 0.0491658i | \(-0.0156563\pi\) |
−0.541974 | + | 0.840395i | \(0.682323\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8950.51 | −1.18023 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12320.2 | + | 21339.2i | −1.61202 | + | 2.79210i | ||||
\(389\) | −2580.94 | + | 4470.32i | −0.336398 | + | 0.582659i | −0.983752 | − | 0.179531i | \(-0.942542\pi\) |
0.647354 | + | 0.762189i | \(0.275875\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1604.91 | 0.207580 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5105.01 | − | 8842.14i | −0.652758 | − | 1.13061i | ||||
\(395\) | −8009.98 | + | 13873.7i | −1.02032 | + | 1.76724i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −172.384 | − | 298.578i | −0.0217927 | − | 0.0377461i | 0.854923 | − | 0.518754i | \(-0.173604\pi\) |
−0.876716 | + | 0.481008i | \(0.840271\pi\) | |||||||
\(398\) | 7520.70 | 0.947182 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 25224.8 | 3.15310 | ||||||||
\(401\) | −2549.42 | − | 4415.72i | −0.317486 | − | 0.549902i | 0.662477 | − | 0.749083i | \(-0.269505\pi\) |
−0.979963 | + | 0.199180i | \(0.936172\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2036.40 | + | 3527.15i | −0.251713 | + | 0.435980i | ||||
\(404\) | 19715.3 | + | 34148.0i | 2.42791 | + | 4.20526i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9457.28 | −1.15179 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 161.562 | − | 279.834i | 0.0195323 | − | 0.0338310i | −0.856094 | − | 0.516820i | \(-0.827116\pi\) |
0.875626 | + | 0.482989i | \(0.160449\pi\) | |||||||
\(410\) | −10034.9 | + | 17380.9i | −1.20875 | + | 2.09362i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20868.7 | −2.49545 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3529.29 | − | 6112.91i | −0.417460 | − | 0.723062i | ||||
\(416\) | 21389.5 | − | 37047.7i | 2.52093 | − | 4.36637i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9393.92 | + | 16270.8i | 1.09922 | + | 1.90390i | ||||
\(419\) | 4415.98 | 0.514880 | 0.257440 | − | 0.966294i | \(-0.417121\pi\) | ||||
0.257440 | + | 0.966294i | \(0.417121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1379.37 | 0.159683 | 0.0798415 | − | 0.996808i | \(-0.474559\pi\) | ||||
0.0798415 | + | 0.996808i | \(0.474559\pi\) | |||||||
\(422\) | −8949.06 | − | 15500.2i | −1.03231 | − | 1.78801i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9422.38 | + | 16320.0i | −1.07922 | + | 1.86927i | ||||
\(425\) | 1707.42 | + | 2957.33i | 0.194875 | + | 0.337533i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14720.0 | −1.66243 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −707.401 | + | 1225.25i | −0.0793346 | + | 0.137412i | ||||
\(431\) | −827.893 | + | 1433.95i | −0.0925248 | + | 0.160258i | −0.908573 | − | 0.417726i | \(-0.862827\pi\) |
0.816048 | + | 0.577984i | \(0.196160\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8612.65 | 0.955883 | 0.477942 | − | 0.878392i | \(-0.341383\pi\) | ||||
0.477942 | + | 0.878392i | \(0.341383\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18143.8 | − | 31426.0i | −1.99296 | − | 3.45190i | ||||
\(437\) | −3008.41 | + | 5210.73i | −0.329318 | + | 0.570396i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2987.69 | + | 5174.84i | 0.324817 | + | 0.562600i | 0.981475 | − | 0.191588i | \(-0.0613638\pi\) |
−0.656658 | + | 0.754188i | \(0.728031\pi\) | |||||||
\(440\) | 35386.0 | 3.83400 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11376.3 | 1.22424 | ||||||||
\(443\) | −403.266 | − | 698.477i | −0.0432500 | − | 0.0749112i | 0.843590 | − | 0.536988i | \(-0.180438\pi\) |
−0.886840 | + | 0.462077i | \(0.847105\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2586.25 | + | 4479.52i | −0.275506 | + | 0.477190i | ||||
\(446\) | −15056.3 | − | 26078.2i | −1.59851 | − | 2.76870i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6253.04 | 0.657237 | 0.328618 | − | 0.944463i | \(-0.393417\pi\) | ||||
0.328618 | + | 0.944463i | \(0.393417\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3814.12 | + | 6606.24i | −0.398226 | + | 0.689747i | ||||
\(452\) | −9285.85 | + | 16083.6i | −0.966304 | + | 1.67369i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7818.65 | 0.808254 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −80.1439 | − | 138.813i | −0.00820344 | − | 0.0142088i | 0.861895 | − | 0.507088i | \(-0.169278\pi\) |
−0.870098 | + | 0.492879i | \(0.835945\pi\) | |||||||
\(458\) | 4367.30 | − | 7564.39i | 0.445569 | − | 0.771748i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9110.96 | + | 15780.7i | 0.923480 | + | 1.59951i | ||||
\(461\) | −2408.80 | −0.243360 | −0.121680 | − | 0.992569i | \(-0.538828\pi\) | ||||
−0.121680 | + | 0.992569i | \(0.538828\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1092.89 | −0.109699 | −0.0548496 | − | 0.998495i | \(-0.517468\pi\) | ||||
−0.0548496 | + | 0.998495i | \(0.517468\pi\) | |||||||
\(464\) | −1901.60 | − | 3293.67i | −0.190258 | − | 0.329536i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16448.4 | − | 28489.5i | 1.63510 | − | 2.83208i | ||||
\(467\) | 7527.42 | + | 13037.9i | 0.745884 | + | 1.29191i | 0.949781 | + | 0.312916i | \(0.101306\pi\) |
−0.203897 | + | 0.978992i | \(0.565361\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 43058.3 | 4.22581 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9030.73 | − | 15641.7i | 0.880663 | − | 1.52535i | ||||
\(473\) | −268.873 | + | 465.701i | −0.0261370 | + | 0.0452705i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12802.2 | −1.23665 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4308.87 | + | 7463.18i | 0.412308 | + | 0.714138i | ||||
\(479\) | 5227.80 | − | 9054.82i | 0.498673 | − | 0.863727i | −0.501326 | − | 0.865259i | \(-0.667154\pi\) |
0.999999 | + | 0.00153157i | \(0.000487513\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10734.4 | − | 18592.4i | −1.01756 | − | 1.76246i | ||||
\(482\) | −11819.5 | −1.11693 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6536.18 | −0.613841 | ||||||||
\(485\) | −9069.86 | − | 15709.5i | −0.849157 | − | 1.47078i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6358.83 | − | 11013.8i | 0.591675 | − | 1.02481i | −0.402331 | − | 0.915494i | \(-0.631800\pi\) |
0.994007 | − | 0.109318i | \(-0.0348666\pi\) | |||||||
\(488\) | −2587.74 | − | 4482.09i | −0.240044 | − | 0.415768i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20983.1 | 1.92863 | 0.964313 | − | 0.264763i | \(-0.0852937\pi\) | ||||
0.964313 | + | 0.264763i | \(0.0852937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 257.431 | − | 445.884i | 0.0235175 | − | 0.0407335i | ||||
\(494\) | −21324.9 | + | 36935.8i | −1.94221 | + | 3.36401i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12033.6 | −1.08937 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6359.04 | − | 11014.2i | −0.570480 | − | 0.988101i | −0.996517 | − | 0.0833946i | \(-0.973424\pi\) |
0.426036 | − | 0.904706i | \(-0.359910\pi\) | |||||||
\(500\) | 1213.55 | − | 2101.94i | 0.108544 | − | 0.188003i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16748.0 | − | 29008.4i | −1.48904 | − | 2.57910i | ||||
\(503\) | −15675.9 | −1.38957 | −0.694785 | − | 0.719218i | \(-0.744500\pi\) | ||||
−0.694785 | + | 0.719218i | \(0.744500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29028.0 | −2.55788 | ||||||||
\(506\) | 4772.25 | + | 8265.78i | 0.419273 | + | 0.726203i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8263.51 | + | 14312.8i | −0.721721 | + | 1.25006i | ||||
\(509\) | 5109.15 | + | 8849.30i | 0.444910 | + | 0.770606i | 0.998046 | − | 0.0624847i | \(-0.0199025\pi\) |
−0.553136 | + | 0.833091i | \(0.686569\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4500.87 | 0.388501 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −724.460 | + | 1254.80i | −0.0621684 | + | 0.107679i | ||||
\(515\) | 7681.54 | − | 13304.8i | 0.657260 | − | 1.13841i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16365.8 | 1.39220 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 40164.4 | + | 69566.7i | 3.38716 | + | 5.86674i | ||||
\(521\) | 2404.07 | − | 4163.96i | 0.202157 | − | 0.350147i | −0.747066 | − | 0.664750i | \(-0.768538\pi\) |
0.949223 | + | 0.314603i | \(0.101871\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4968.09 | + | 8604.99i | 0.415372 | + | 0.719445i | 0.995467 | − | 0.0951032i | \(-0.0303181\pi\) |
−0.580095 | + | 0.814548i | \(0.696985\pi\) | |||||||
\(524\) | 41497.8 | 3.45962 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20114.4 | 1.66736 | ||||||||
\(527\) | −814.532 | − | 1410.81i | −0.0673274 | − | 0.116615i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4555.18 | − | 7889.81i | 0.374388 | − | 0.648459i | ||||
\(530\) | −11153.6 | − | 19318.6i | −0.914117 | − | 1.58330i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17316.6 | −1.40725 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5418.27 | − | 9384.72i | 0.437854 | − | 0.758386i | ||||
\(536\) | 17990.3 | − | 31160.1i | 1.44974 | − | 2.51103i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 46208.4 | 3.70294 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1024.33 | + | 1774.19i | 0.0814038 | + | 0.140995i | 0.903853 | − | 0.427843i | \(-0.140726\pi\) |
−0.822449 | + | 0.568838i | \(0.807393\pi\) | |||||||
\(542\) | −14254.8 | + | 24690.1i | −1.12970 | + | 1.95670i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8555.49 | + | 14818.5i | 0.674290 | + | 1.16790i | ||||
\(545\) | 26714.1 | 2.09964 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6154.72 | 0.481091 | 0.240546 | − | 0.970638i | \(-0.422674\pi\) | ||||
0.240546 | + | 0.970638i | \(0.422674\pi\) | |||||||
\(548\) | 12910.3 | + | 22361.2i | 1.00639 | + | 1.74311i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10154.1 | + | 17587.4i | −0.787222 | + | 1.36351i | ||||
\(551\) | 965.112 | + | 1671.62i | 0.0746192 | + | 0.129244i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2384.32 | −0.182852 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11300.0 | − | 19572.2i | 0.861918 | − | 1.49289i | ||||
\(557\) | 2223.38 | − | 3851.00i | 0.169134 | − | 0.292948i | −0.768982 | − | 0.639271i | \(-0.779236\pi\) |
0.938116 | + | 0.346322i | \(0.112570\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1220.72 | −0.0923631 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10169.3 | + | 17613.8i | 0.763288 | + | 1.32205i | ||||
\(563\) | −4843.29 | + | 8388.83i | −0.362559 | + | 0.627970i | −0.988381 | − | 0.151996i | \(-0.951430\pi\) |
0.625823 | + | 0.779965i | \(0.284763\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6836.04 | − | 11840.4i | −0.509016 | − | 0.881642i | ||||
\(566\) | −9779.35 | −0.726248 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −58815.7 | −4.34481 | ||||||||
\(569\) | −3653.46 | − | 6327.98i | −0.269176 | − | 0.466226i | 0.699473 | − | 0.714659i | \(-0.253418\pi\) |
−0.968649 | + | 0.248433i | \(0.920085\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4554.67 | + | 7888.92i | −0.333813 | + | 0.578180i | −0.983256 | − | 0.182230i | \(-0.941669\pi\) |
0.649443 | + | 0.760410i | \(0.275002\pi\) | |||||||
\(572\) | 24546.8 | + | 42516.3i | 1.79432 | + | 3.10786i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6503.72 | −0.471694 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9353.85 | − | 16201.3i | 0.674880 | − | 1.16893i | −0.301624 | − | 0.953427i | \(-0.597529\pi\) |
0.976504 | − | 0.215500i | \(-0.0691380\pi\) | |||||||
\(578\) | 10989.7 | − | 19034.7i | 0.790850 | − | 1.36979i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5845.67 | 0.418497 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4239.33 | − | 7342.73i | −0.301158 | − | 0.521621i | ||||
\(584\) | −13237.2 | + | 22927.4i | −0.937941 | + | 1.62456i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15702.2 | + | 27197.0i | 1.10692 | + | 1.91723i | ||||
\(587\) | −24610.4 | −1.73046 | −0.865230 | − | 0.501375i | \(-0.832828\pi\) | ||||
−0.865230 | + | 0.501375i | \(0.832828\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6107.38 | 0.427250 | ||||||||
\(590\) | 10690.0 | + | 18515.6i | 0.745933 | + | 1.29199i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 31716.0 | − | 54933.8i | 2.20189 | − | 3.81379i | ||||
\(593\) | −9420.00 | − | 16315.9i | −0.652332 | − | 1.12987i | −0.982555 | − | 0.185970i | \(-0.940457\pi\) |
0.330223 | − | 0.943903i | \(-0.392876\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −54819.2 | −3.76759 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10833.3 | + | 18763.9i | −0.740817 | + | 1.28313i | ||||
\(599\) | −10323.8 | + | 17881.4i | −0.704206 | + | 1.21972i | 0.262771 | + | 0.964858i | \(0.415363\pi\) |
−0.966977 | + | 0.254862i | \(0.917970\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15772.8 | −1.07053 | −0.535264 | − | 0.844685i | \(-0.679788\pi\) | ||||
−0.535264 | + | 0.844685i | \(0.679788\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20413.6 | − | 35357.3i | −1.37519 | − | 2.38190i | ||||
\(605\) | 2405.89 | − | 4167.13i | 0.161675 | − | 0.280030i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2591.32 | − | 4488.30i | −0.173276 | − | 0.300123i | 0.766287 | − | 0.642498i | \(-0.222102\pi\) |
−0.939563 | + | 0.342375i | \(0.888769\pi\) | |||||||
\(608\) | −64149.2 | −4.27894 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6126.39 | 0.406640 | ||||||||
\(611\) | 18575.8 | + | 32174.2i | 1.22994 | + | 2.13033i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14419.5 | − | 24975.4i | 0.950081 | − | 1.64559i | 0.204837 | − | 0.978796i | \(-0.434333\pi\) |
0.745244 | − | 0.666792i | \(-0.232333\pi\) | |||||||
\(614\) | −5332.21 | − | 9235.66i | −0.350473 | − | 0.607037i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5114.80 | 0.333734 | 0.166867 | − | 0.985979i | \(-0.446635\pi\) | ||||
0.166867 | + | 0.985979i | \(0.446635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14607.0 | + | 25300.0i | −0.948471 | + | 1.64280i | −0.199823 | + | 0.979832i | \(0.564037\pi\) |
−0.748648 | + | 0.662968i | \(0.769297\pi\) | |||||||
\(620\) | 9248.07 | − | 16018.1i | 0.599051 | − | 1.03759i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6258.87 | 0.403469 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8245.64 | + | 14281.9i | 0.527721 | + | 0.914039i | ||||
\(626\) | 12132.7 | − | 21014.5i | 0.774634 | − | 1.34170i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 27778.9 | + | 48114.5i | 1.76513 | + | 3.05729i | ||||
\(629\) | 8587.18 | 0.544345 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19557.5 | 1.23387 | 0.616934 | − | 0.787015i | \(-0.288374\pi\) | ||||
0.616934 | + | 0.787015i | \(0.288374\pi\) | |||||||
\(632\) | −36539.5 | − | 63288.3i | −2.29978 | − | 3.98334i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12629.0 | + | 21874.1i | −0.791108 | + | 1.37024i | ||||
\(635\) | −6083.41 | − | 10536.8i | −0.380178 | − | 0.658487i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3061.92 | 0.190004 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24992.0 | + | 43287.4i | −1.54359 | + | 2.67357i | ||||
\(641\) | 7316.15 | − | 12671.9i | 0.450812 | − | 0.780829i | −0.547625 | − | 0.836724i | \(-0.684468\pi\) |
0.998437 | + | 0.0558950i | \(0.0178012\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23808.1 | −1.46019 | −0.730094 | − | 0.683347i | \(-0.760524\pi\) | ||||
−0.730094 | + | 0.683347i | \(0.760524\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8529.65 | − | 14773.8i | −0.519496 | − | 0.899794i | ||||
\(647\) | 8661.08 | − | 15001.4i | 0.526279 | − | 0.911541i | −0.473253 | − | 0.880927i | \(-0.656920\pi\) |
0.999531 | − | 0.0306145i | \(-0.00974643\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4063.11 | + | 7037.52i | 0.245749 | + | 0.425650i | ||||
\(650\) | −46101.1 | −2.78190 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −65596.4 | −3.94011 | ||||||||
\(653\) | −1620.84 | − | 2807.38i | −0.0971338 | − | 0.168241i | 0.813363 | − | 0.581756i | \(-0.197634\pi\) |
−0.910497 | + | 0.413515i | \(0.864301\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15274.9 | + | 26456.9i | −0.911205 | + | 1.57825i | ||||
\(656\) | −25582.1 | − | 44309.5i | −1.52258 | − | 2.63719i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16358.2 | 0.966958 | 0.483479 | − | 0.875356i | \(-0.339373\pi\) | ||||
0.483479 | + | 0.875356i | \(0.339373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6286.30 | + | 10888.2i | −0.369907 | + | 0.640698i | −0.989551 | − | 0.144185i | \(-0.953944\pi\) |
0.619644 | + | 0.784883i | \(0.287277\pi\) | |||||||
\(662\) | 8053.18 | − | 13948.5i | 0.472803 | − | 0.818919i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 32199.5 | 1.88190 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 490.291 | + | 849.209i | 0.0284620 | + | 0.0492976i | ||||
\(668\) | −34539.2 | + | 59823.7i | −2.00054 | + | 3.46504i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 21295.7 | + | 36885.3i | 1.22795 | + | 2.12687i | ||||
\(671\) | 2328.55 | 0.133968 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13130.7 | 0.752082 | 0.376041 | − | 0.926603i | \(-0.377285\pi\) | ||||
0.376041 | + | 0.926603i | \(0.377285\pi\) | |||||||
\(674\) | −19786.7 | − | 34271.6i | −1.13079 | − | 1.95859i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −32479.8 | + | 56256.6i | −1.84796 | + | 3.20076i | ||||
\(677\) | −9312.08 | − | 16129.0i | −0.528644 | − | 0.915639i | −0.999442 | − | 0.0333977i | \(-0.989367\pi\) |
0.470798 | − | 0.882241i | \(-0.343966\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −32130.4 | −1.81198 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4844.07 | − | 8390.17i | 0.271978 | − | 0.471079i | ||||
\(683\) | 12688.5 | − | 21977.1i | 0.710852 | − | 1.23123i | −0.253685 | − | 0.967287i | \(-0.581643\pi\) |
0.964538 | − | 0.263946i | \(-0.0850240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19008.5 | −1.06026 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1803.39 | − | 3123.56i | −0.0999324 | − | 0.173088i | ||||
\(689\) | 9623.58 | − | 16668.5i | 0.532118 | − | 0.921655i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1067.71 | − | 1849.33i | −0.0587810 | − | 0.101812i | 0.835137 | − | 0.550041i | \(-0.185388\pi\) |
−0.893918 | + | 0.448230i | \(0.852055\pi\) | |||||||
\(692\) | −43086.2 | −2.36690 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 44869.6 | 2.45422 | ||||||||
\(695\) | 8318.80 | + | 14408.6i | 0.454029 | + | 0.786401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3463.21 | − | 5998.45i | 0.188204 | − | 0.325979i | ||||
\(698\) | 902.602 | + | 1563.35i | 0.0489455 | + | 0.0847761i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9679.27 | −0.521513 | −0.260757 | − | 0.965405i | \(-0.583972\pi\) | ||||
−0.260757 | + | 0.965405i | \(0.583972\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16096.7 | + | 27880.3i | −0.863583 | + | 1.49577i | ||||
\(704\) | −23458.4 | + | 40631.2i | −1.25586 | + | 2.17521i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29473.7 | 1.57119 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12871.6 | + | 22294.2i | 0.681809 | + | 1.18093i | 0.974428 | + | 0.224699i | \(0.0721399\pi\) |
−0.292619 | + | 0.956229i | \(0.594527\pi\) | |||||||
\(710\) | 34811.2 | − | 60294.7i | 1.84006 | − | 3.18707i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11797.8 | − | 20434.5i | −0.620987 | − | 1.07558i | ||||
\(713\) | 3102.63 | 0.162966 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36141.6 | −1.89038 | ||||||||
\(716\) | 37899.4 | + | 65643.7i | 1.97817 | + | 3.42629i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19431.3 | + | 33656.0i | −1.00999 | + | 1.74935i | ||||
\(719\) | −5254.26 | − | 9100.64i | −0.272532 | − | 0.472040i | 0.696977 | − | 0.717093i | \(-0.254528\pi\) |
−0.969510 | + | 0.245053i | \(0.921194\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 26917.5 | 1.38749 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17322.3 | + | 30003.1i | −0.889196 | + | 1.54013i | ||||
\(725\) | −1043.21 | + | 1806.89i | −0.0534398 | + | 0.0925605i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24259.4 | −1.23759 | −0.618797 | − | 0.785551i | \(-0.712380\pi\) | ||||
−0.618797 | + | 0.785551i | \(0.712380\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15669.3 | − | 27140.0i | −0.794448 | − | 1.37602i | ||||
\(731\) | 244.136 | − | 422.855i | 0.0123525 | − | 0.0213952i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9816.08 | − | 17001.9i | −0.494632 | − | 0.856727i | 0.505349 | − | 0.862915i | \(-0.331364\pi\) |
−0.999981 | + | 0.00618771i | \(0.998030\pi\) | |||||||
\(734\) | 34151.3 | 1.71737 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32588.7 | −1.63212 | ||||||||
\(737\) | 8094.20 | + | 14019.6i | 0.404551 | + | 0.700702i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13176.8 | − | 22822.9i | 0.655909 | − | 1.13607i | −0.325756 | − | 0.945454i | \(-0.605619\pi\) |
0.981665 | − | 0.190614i | \(-0.0610478\pi\) | |||||||
\(740\) | 48748.8 | + | 84435.4i | 2.42168 | + | 4.19447i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31464.6 | −1.55360 | −0.776799 | − | 0.629749i | \(-0.783158\pi\) | ||||
−0.776799 | + | 0.629749i | \(0.783158\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20178.3 | − | 34949.9i | 0.992318 | − | 1.71875i | ||||
\(746\) | 29515.2 | − | 51121.9i | 1.44856 | − | 2.50899i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −19636.7 | −0.959880 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2705.76 | − | 4686.51i | −0.131471 | − | 0.227714i | 0.792773 | − | 0.609517i | \(-0.208637\pi\) |
−0.924244 | + | 0.381803i | \(0.875303\pi\) | |||||||
\(752\) | −54884.5 | + | 95062.8i | −2.66148 | + | 4.60982i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3475.38 | + | 6019.54i | 0.167859 | + | 0.290741i | ||||
\(755\) | 30056.0 | 1.44881 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3607.94 | 0.173227 | 0.0866135 | − | 0.996242i | \(-0.472395\pi\) | ||||
0.0866135 | + | 0.996242i | \(0.472395\pi\) | |||||||
\(758\) | −16264.6 | − | 28171.1i | −0.779361 | − | 1.34989i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 60228.5 | − | 104319.i | 2.87463 | − | 4.97900i | ||||
\(761\) | 2331.85 | + | 4038.89i | 0.111077 | + | 0.192391i | 0.916205 | − | 0.400710i | \(-0.131237\pi\) |
−0.805128 | + | 0.593101i | \(0.797903\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 59769.5 | 2.83035 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18489.5 | − | 32024.8i | 0.872134 | − | 1.51058i | ||||
\(767\) | −9223.56 | + | 15975.7i | −0.434216 | + | 0.752083i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9725.21 | −0.456047 | −0.228023 | − | 0.973656i | \(-0.573226\pi\) | ||||
−0.228023 | + | 0.973656i | \(0.573226\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17535.8 | + | 30373.0i | 0.817524 | + | 1.41599i | ||||
\(773\) | −1546.40 | + | 2678.44i | −0.0719536 | + | 0.124627i | −0.899757 | − | 0.436390i | \(-0.856257\pi\) |
0.827804 | + | 0.561018i | \(0.189590\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3300.80 | + | 5717.15i | 0.152991 | + | 0.264988i | ||||
\(776\) | 82748.8 | 3.82798 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27873.7 | 1.28447 | ||||||||
\(779\) | 12983.6 | + | 22488.2i | 0.597157 | + | 1.03431i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13231.2 | − | 22917.1i | 0.606210 | − | 1.04999i | ||||
\(782\) | −4333.19 | − | 7505.30i | −0.198151 | − | 0.343208i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −40900.4 | −1.85962 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11406.4 | + | 19756.5i | −0.516640 | + | 0.894846i | 0.483174 | + | 0.875525i | \(0.339484\pi\) |
−0.999813 | + | 0.0193216i | \(0.993849\pi\) | |||||||
\(788\) | −20003.5 | + | 34647.0i | −0.904307 | + | 1.56631i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 86506.3 | 3.89589 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2642.99 | + | 4577.79i | 0.118355 | + | 0.204997i | ||||
\(794\) | −930.857 | + | 1612.29i | −0.0416056 | + | 0.0720631i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14734.5 | − | 25521.0i | −0.656096 | − | 1.13639i | ||||
\(797\) | 34305.4 | 1.52467 | 0.762334 | − | 0.647184i | \(-0.224053\pi\) | ||||
0.762334 | + | 0.647184i | \(0.224053\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14860.1 | −0.657963 | ||||||||
\(800\) | −34670.2 | − | 60050.5i | −1.53222 | − | 2.65388i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13766.6 | + | 23844.5i | −0.606130 | + | 1.04985i | ||||
\(803\) | −5955.68 | − | 10315.5i | −0.261733 | − | 0.453334i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21992.8 | 0.961119 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 66209.2 | − | 114678.i | 2.88271 | − | 4.99300i | ||||
\(809\) | −1632.40 | + | 2827.40i | −0.0709421 | + | 0.122875i | −0.899314 | − | 0.437303i | \(-0.855934\pi\) |
0.828372 | + | 0.560178i | \(0.189267\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27264.0 | 1.18048 | 0.590239 | − | 0.807228i | \(-0.299033\pi\) | ||||
0.590239 | + | 0.807228i | \(0.299033\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 25534.2 | + | 44226.6i | 1.09948 | + | 1.90435i | ||||
\(815\) | 24145.3 | − | 41820.9i | 1.03776 | − | 1.79745i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 915.266 | + | 1585.29i | 0.0391935 | + | 0.0678852i | ||||
\(818\) | −1744.84 | −0.0745805 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 78641.4 | 3.34912 | ||||||||
\(821\) | 18167.1 | + | 31466.3i | 0.772272 | + | 1.33761i | 0.936315 | + | 0.351161i | \(0.114213\pi\) |
−0.164043 | + | 0.986453i | \(0.552454\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3895.90 | + | 6747.90i | −0.165009 | + | 0.285804i | −0.936659 | − | 0.350244i | \(-0.886099\pi\) |
0.771649 | + | 0.636048i | \(0.219432\pi\) | |||||||
\(824\) | 35041.2 | + | 60693.2i | 1.48145 | + | 2.56595i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36082.7 | 1.51719 | 0.758596 | − | 0.651561i | \(-0.225886\pi\) | ||||
0.758596 | + | 0.651561i | \(0.225886\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21497.5 | − | 37234.8i | 0.900650 | − | 1.55997i | 0.0739984 | − | 0.997258i | \(-0.476424\pi\) |
0.826652 | − | 0.562714i | \(-0.190243\pi\) | |||||||
\(830\) | −19057.8 | + | 33009.1i | −0.796997 | + | 1.38044i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −106505. | −4.43796 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25427.0 | − | 44040.9i | −1.05382 | − | 1.82527i | ||||
\(836\) | 36809.1 | − | 63755.3i | 1.52281 | − | 2.63759i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11922.9 | − | 20651.1i | −0.491493 | − | 0.851291i | ||||
\(839\) | −28252.8 | −1.16257 | −0.581283 | − | 0.813701i | \(-0.697449\pi\) | ||||
−0.581283 | + | 0.813701i | \(0.697449\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24074.4 | −0.987102 | ||||||||
\(842\) | −3724.24 | − | 6450.58i | −0.152430 | − | 0.264016i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −35066.0 | + | 60736.1i | −1.43012 | + | 2.47704i | ||||
\(845\) | −23910.9 | − | 41414.9i | −0.973444 | − | 1.68605i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 56868.2 | 2.30290 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9219.89 | − | 15969.3i | 0.372046 | − | 0.644403i | ||||
\(851\) | −8177.36 | + | 14163.6i | −0.329396 | + | 0.570531i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28994.8 | 1.16385 | 0.581924 | − | 0.813243i | \(-0.302300\pi\) | ||||
0.581924 | + | 0.813243i | \(0.302300\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24716.8 | + | 42810.7i | 0.986918 | + | 1.70939i | ||||
\(857\) | −4316.44 | + | 7476.28i | −0.172050 | + | 0.297999i | −0.939136 | − | 0.343545i | \(-0.888372\pi\) |
0.767087 | + | 0.641544i | \(0.221706\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16973.5 | − | 29399.0i | −0.674191 | − | 1.16773i | −0.976705 | − | 0.214587i | \(-0.931159\pi\) |
0.302514 | − | 0.953145i | \(-0.402174\pi\) | |||||||
\(860\) | 5543.76 | 0.219815 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8941.09 | 0.353288 | ||||||||
\(863\) | 35.3306 | + | 61.1944i | 0.00139359 | + | 0.00241377i | 0.866721 | − | 0.498793i | \(-0.166223\pi\) |
−0.865328 | + | 0.501206i | \(0.832890\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15859.6 | − | 27469.6i | 0.623400 | − | 1.07976i | ||||
\(866\) | −23253.7 | − | 40276.7i | −0.912465 | − | 1.58044i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32879.8 | 1.28351 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18374.4 | + | 31825.4i | −0.714803 | + | 1.23807i | ||||
\(872\) | −60931.5 | + | 105536.i | −2.36628 | + | 4.09853i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32490.3 | 1.25744 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5587.66 | + | 9678.10i | 0.215144 | + | 0.372641i | 0.953317 | − | 0.301971i | \(-0.0976444\pi\) |
−0.738173 | + | 0.674612i | \(0.764311\pi\) | |||||||
\(878\) | 16133.3 | − | 27943.6i | 0.620127 | − | 1.07409i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −53392.5 | − | 92478.5i | −2.04530 | − | 3.54255i | ||||
\(881\) | −14341.3 | −0.548433 | −0.274216 | − | 0.961668i | \(-0.588418\pi\) | ||||
−0.274216 | + | 0.961668i | \(0.588418\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23559.2 | −0.897884 | −0.448942 | − | 0.893561i | \(-0.648199\pi\) | ||||
−0.448942 | + | 0.893561i | \(0.648199\pi\) | |||||||
\(884\) | −22288.4 | − | 38604.6i | −0.848009 | − | 1.46879i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2177.60 | + | 3771.71i | −0.0825710 | + | 0.143017i | ||||
\(887\) | 15872.2 | + | 27491.5i | 0.600831 | + | 1.04067i | 0.992696 | + | 0.120647i | \(0.0384968\pi\) |
−0.391865 | + | 0.920023i | \(0.628170\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 27931.1 | 1.05197 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −58996.5 | + | 102185.i | −2.21452 | + | 3.83566i | ||||
\(893\) | 27855.3 | − | 48246.9i | 1.04383 | − | 1.80797i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −55801.4 | −2.08406 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16882.9 | − | 29242.1i | −0.627384 | − | 1.08666i | ||||
\(899\) | 497.669 | − | 861.989i | 0.0184630 | − | 0.0319788i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3849.30 | + | 6667.18i | 0.142329 | + | 0.246521i | ||||
\(902\) | 41191.8 | 1.52055 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 62368.5 | 2.29463 | ||||||||
\(905\) | −12752.3 | − | 22087.6i | −0.468398 | − | 0.811290i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3031.33 | + | 5250.42i | −0.110974 | + | 0.192213i | −0.916163 | − | 0.400805i | \(-0.868730\pi\) |
0.805189 | + | 0.593018i | \(0.202064\pi\) | |||||||
\(908\) | −15318.3 | − | 26532.1i | −0.559863 | − | 0.969711i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25862.9 | −0.940589 | −0.470295 | − | 0.882509i | \(-0.655852\pi\) | ||||
−0.470295 | + | 0.882509i | \(0.655852\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7243.61 | + | 12546.3i | −0.262572 | + | 0.454788i | ||||
\(914\) | −432.769 | + | 749.579i | −0.0156616 | + | 0.0271268i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −34225.7 | −1.23455 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −727.570 | − | 1260.19i | −0.0261157 | − | 0.0452337i | 0.852672 | − | 0.522446i | \(-0.174980\pi\) |
−0.878788 | + | 0.477213i | \(0.841647\pi\) | |||||||
\(920\) | 30597.0 | − | 52995.5i | 1.09647 | − | 1.89914i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6503.65 | + | 11264.6i | 0.232306 | + | 0.402366i | ||||
\(923\) | 60071.6 | 2.14223 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34798.6 | −1.23694 | ||||||||
\(926\) | 2950.74 | + | 5110.83i | 0.104716 | + | 0.181374i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5227.30 | + | 9053.96i | −0.184908 | + | 0.320270i | ||||
\(929\) | −1538.87 | − | 2665.40i | −0.0543474 | − | 0.0941325i | 0.837572 | − | 0.546327i | \(-0.183975\pi\) |
−0.891919 | + | 0.452195i | \(0.850641\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −128903. | −4.53042 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 40647.4 | − | 70403.3i | 1.42401 | − | 2.46645i | ||||
\(935\) | 7228.06 | − | 12519.4i | 0.252816 | − | 0.437890i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5354.80 | 0.186695 | 0.0933477 | − | 0.995634i | \(-0.470243\pi\) | ||||
0.0933477 | + | 0.995634i | \(0.470243\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −84359.7 | − | 146115.i | −2.92714 | − | 5.06995i | ||||
\(941\) | 23898.9 | − | 41394.1i | 0.827930 | − | 1.43402i | −0.0717294 | − | 0.997424i | \(-0.522852\pi\) |
0.899659 | − | 0.436593i | \(-0.143815\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6595.85 | + | 11424.4i | 0.227774 | + | 0.394515i | ||||
\(944\) | −54504.4 | −1.87920 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2903.78 | 0.0997990 | ||||||||
\(947\) | −1245.85 | − | 2157.87i | −0.0427503 | − | 0.0740457i | 0.843859 | − | 0.536566i | \(-0.180279\pi\) |
−0.886609 | + | 0.462520i | \(0.846945\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13519.8 | − | 23417.0i | 0.462457 | − | 0.800999i | ||||
\(950\) | 34565.4 | + | 59869.1i | 1.18047 | + | 2.04464i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13130.4 | 0.446313 | 0.223156 | − | 0.974783i | \(-0.428364\pi\) | ||||
0.223156 | + | 0.974783i | \(0.428364\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22000.5 | + | 38106.0i | −0.745465 | + | 1.29118i | ||||
\(956\) | 16883.9 | − | 29243.7i | 0.571196 | − | 0.989340i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −56459.3 | −1.90409 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13320.8 | + | 23072.4i | 0.447143 | + | 0.774474i | ||||
\(962\) | −57964.5 | + | 100397.i | −1.94267 | + | 3.36481i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 23156.7 | + | 40108.6i | 0.773680 | + | 1.34005i | ||||
\(965\) | −25819.0 | −0.861287 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43314.8 | 1.44044 | 0.720222 | − | 0.693743i | \(-0.244040\pi\) | ||||
0.720222 | + | 0.693743i | \(0.244040\pi\) | |||||||
\(968\) | 10975.1 | + | 19009.4i | 0.364414 | + | 0.631183i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −48976.4 | + | 84829.6i | −1.62117 | + | 2.80795i | ||||
\(971\) | 9877.90 | + | 17109.0i | 0.326464 | + | 0.565453i | 0.981808 | − | 0.189878i | \(-0.0608094\pi\) |
−0.655343 | + | 0.755331i | \(0.727476\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −68674.1 | −2.25920 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7809.06 | + | 13525.7i | −0.256108 | + | 0.443593i | ||||
\(977\) | −5570.05 | + | 9647.61i | −0.182397 | + | 0.315921i | −0.942696 | − | 0.333652i | \(-0.891719\pi\) |
0.760299 | + | 0.649573i | \(0.225052\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10616.2 | 0.346573 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −56653.5 | − | 98126.7i | −1.84102 | − | 3.18875i | ||||
\(983\) | 1787.88 | − | 3096.70i | 0.0580107 | − | 0.100478i | −0.835562 | − | 0.549397i | \(-0.814858\pi\) |
0.893572 | + | 0.448919i | \(0.148191\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14726.1 | − | 25506.4i | −0.476358 | − | 0.825077i | ||||
\(986\) | −2780.21 | −0.0897971 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 167119. | 5.38133 | ||||||||
\(989\) | 464.969 | + | 805.349i | 0.0149496 | + | 0.0258934i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11195.9 | + | 19391.9i | −0.358880 | + | 0.621598i | −0.987774 | − | 0.155893i | \(-0.950175\pi\) |
0.628894 | + | 0.777491i | \(0.283508\pi\) | |||||||
\(992\) | 16539.6 | + | 28647.4i | 0.529367 | + | 0.916891i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21694.5 | 0.691218 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8733.25 | + | 15126.4i | −0.277417 | + | 0.480501i | −0.970742 | − | 0.240124i | \(-0.922812\pi\) |
0.693325 | + | 0.720625i | \(0.256145\pi\) | |||||||
\(998\) | −34338.2 | + | 59475.5i | −1.08914 | + | 1.88644i | ||||
\(999\) | 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.e.z.361.1 | 16 | ||
3.2 | odd | 2 | inner | 441.4.e.z.361.8 | 16 | ||
7.2 | even | 3 | inner | 441.4.e.z.226.1 | 16 | ||
7.3 | odd | 6 | 441.4.a.x.1.7 | yes | 8 | ||
7.4 | even | 3 | 441.4.a.x.1.8 | yes | 8 | ||
7.5 | odd | 6 | inner | 441.4.e.z.226.2 | 16 | ||
7.6 | odd | 2 | inner | 441.4.e.z.361.2 | 16 | ||
21.2 | odd | 6 | inner | 441.4.e.z.226.8 | 16 | ||
21.5 | even | 6 | inner | 441.4.e.z.226.7 | 16 | ||
21.11 | odd | 6 | 441.4.a.x.1.1 | ✓ | 8 | ||
21.17 | even | 6 | 441.4.a.x.1.2 | yes | 8 | ||
21.20 | even | 2 | inner | 441.4.e.z.361.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.4.a.x.1.1 | ✓ | 8 | 21.11 | odd | 6 | ||
441.4.a.x.1.2 | yes | 8 | 21.17 | even | 6 | ||
441.4.a.x.1.7 | yes | 8 | 7.3 | odd | 6 | ||
441.4.a.x.1.8 | yes | 8 | 7.4 | even | 3 | ||
441.4.e.z.226.1 | 16 | 7.2 | even | 3 | inner | ||
441.4.e.z.226.2 | 16 | 7.5 | odd | 6 | inner | ||
441.4.e.z.226.7 | 16 | 21.5 | even | 6 | inner | ||
441.4.e.z.226.8 | 16 | 21.2 | odd | 6 | inner | ||
441.4.e.z.361.1 | 16 | 1.1 | even | 1 | trivial | ||
441.4.e.z.361.2 | 16 | 7.6 | odd | 2 | inner | ||
441.4.e.z.361.7 | 16 | 21.20 | even | 2 | inner | ||
441.4.e.z.361.8 | 16 | 3.2 | odd | 2 | inner |