Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,4,Mod(169,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.169");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.3904011012\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{21})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 11x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 169.2 | ||
Root | \(-1.79129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.169 |
Dual form | 210.4.g.b.169.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.00000i | − | 0.707107i | ||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 8.58258 | − | 7.16515i | 0.767649 | − | 0.640871i | ||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | −14.3303 | − | 17.1652i | −0.453164 | − | 0.542810i | ||||
\(11\) | 30.6606 | 0.840411 | 0.420205 | − | 0.907429i | \(-0.361958\pi\) | ||||
0.420205 | + | 0.907429i | \(0.361958\pi\) | |||||||
\(12\) | − | 12.0000i | − | 0.288675i | ||||||
\(13\) | − | 54.8348i | − | 1.16988i | −0.811076 | − | 0.584940i | \(-0.801118\pi\) | ||
0.811076 | − | 0.584940i | \(-0.198882\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 21.4955 | + | 25.7477i | 0.370007 | + | 0.443202i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 116.486i | 1.66189i | 0.556356 | + | 0.830944i | \(0.312199\pi\) | ||||
−0.556356 | + | 0.830944i | \(0.687801\pi\) | |||||||
\(18\) | 18.0000i | 0.235702i | ||||||||
\(19\) | 105.652 | 1.27569 | 0.637845 | − | 0.770165i | \(-0.279826\pi\) | ||||
0.637845 | + | 0.770165i | \(0.279826\pi\) | |||||||
\(20\) | −34.3303 | + | 28.6606i | −0.383824 | + | 0.320435i | ||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | − | 61.3212i | − | 0.594260i | ||||||
\(23\) | − | 195.652i | − | 1.77375i | −0.462013 | − | 0.886873i | \(-0.652873\pi\) | ||
0.462013 | − | 0.886873i | \(-0.347127\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 22.3212 | − | 122.991i | 0.178570 | − | 0.983927i | ||||
\(26\) | −109.670 | −0.827231 | ||||||||
\(27\) | − | 27.0000i | − | 0.192450i | ||||||
\(28\) | − | 28.0000i | − | 0.188982i | ||||||
\(29\) | 176.156 | 1.12798 | 0.563989 | − | 0.825782i | \(-0.309266\pi\) | ||||
0.563989 | + | 0.825782i | \(0.309266\pi\) | |||||||
\(30\) | 51.4955 | − | 42.9909i | 0.313391 | − | 0.261634i | ||||
\(31\) | 159.808 | 0.925880 | 0.462940 | − | 0.886390i | \(-0.346794\pi\) | ||||
0.462940 | + | 0.886390i | \(0.346794\pi\) | |||||||
\(32\) | − | 32.0000i | − | 0.176777i | ||||||
\(33\) | 91.9818i | 0.485211i | ||||||||
\(34\) | 232.973 | 1.17513 | ||||||||
\(35\) | 50.1561 | + | 60.0780i | 0.242226 | + | 0.290144i | ||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 47.5136i | 0.211113i | 0.994413 | + | 0.105557i | \(0.0336624\pi\) | ||||
−0.994413 | + | 0.105557i | \(0.966338\pi\) | |||||||
\(38\) | − | 211.303i | − | 0.902049i | ||||||
\(39\) | 164.505 | 0.675431 | ||||||||
\(40\) | 57.3212 | + | 68.6606i | 0.226582 | + | 0.271405i | ||||
\(41\) | 83.8076 | 0.319233 | 0.159616 | − | 0.987179i | \(-0.448974\pi\) | ||||
0.159616 | + | 0.987179i | \(0.448974\pi\) | |||||||
\(42\) | 42.0000i | 0.154303i | ||||||||
\(43\) | − | 280.835i | − | 0.995975i | −0.867184 | − | 0.497987i | \(-0.834073\pi\) | ||
0.867184 | − | 0.497987i | \(-0.165927\pi\) | |||||||
\(44\) | −122.642 | −0.420205 | ||||||||
\(45\) | −77.2432 | + | 64.4864i | −0.255883 | + | 0.213624i | ||||
\(46\) | −391.303 | −1.25423 | ||||||||
\(47\) | − | 538.744i | − | 1.67200i | −0.548731 | − | 0.835999i | \(-0.684889\pi\) | ||
0.548731 | − | 0.835999i | \(-0.315111\pi\) | |||||||
\(48\) | 48.0000i | 0.144338i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | −245.982 | − | 44.6424i | −0.695742 | − | 0.126268i | ||||
\(51\) | −349.459 | −0.959491 | ||||||||
\(52\) | 219.339i | 0.584940i | ||||||||
\(53\) | 555.633i | 1.44004i | 0.693953 | + | 0.720020i | \(0.255867\pi\) | ||||
−0.693953 | + | 0.720020i | \(0.744133\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 263.147 | − | 219.688i | 0.645141 | − | 0.538595i | ||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | 316.955i | 0.736520i | ||||||||
\(58\) | − | 352.312i | − | 0.797601i | ||||||
\(59\) | −494.606 | −1.09139 | −0.545697 | − | 0.837983i | \(-0.683735\pi\) | ||||
−0.545697 | + | 0.837983i | \(0.683735\pi\) | |||||||
\(60\) | −85.9818 | − | 102.991i | −0.185003 | − | 0.221601i | ||||
\(61\) | 312.744 | 0.656439 | 0.328219 | − | 0.944602i | \(-0.393551\pi\) | ||||
0.328219 | + | 0.944602i | \(0.393551\pi\) | |||||||
\(62\) | − | 319.615i | − | 0.654696i | ||||||
\(63\) | − | 63.0000i | − | 0.125988i | ||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | −392.900 | − | 470.624i | −0.749742 | − | 0.898058i | ||||
\(66\) | 183.964 | 0.343096 | ||||||||
\(67\) | 1061.39i | 1.93536i | 0.252185 | + | 0.967679i | \(0.418851\pi\) | ||||
−0.252185 | + | 0.967679i | \(0.581149\pi\) | |||||||
\(68\) | − | 465.945i | − | 0.830944i | ||||||
\(69\) | 586.955 | 1.02407 | ||||||||
\(70\) | 120.156 | − | 100.312i | 0.205163 | − | 0.171280i | ||||
\(71\) | −1106.07 | −1.84881 | −0.924407 | − | 0.381408i | \(-0.875439\pi\) | ||||
−0.924407 | + | 0.381408i | \(0.875439\pi\) | |||||||
\(72\) | − | 72.0000i | − | 0.117851i | ||||||
\(73\) | 279.808i | 0.448616i | 0.974518 | + | 0.224308i | \(0.0720122\pi\) | ||||
−0.974518 | + | 0.224308i | \(0.927988\pi\) | |||||||
\(74\) | 95.0273 | 0.149280 | ||||||||
\(75\) | 368.973 | + | 66.9636i | 0.568071 | + | 0.103097i | ||||
\(76\) | −422.606 | −0.637845 | ||||||||
\(77\) | 214.624i | 0.317645i | ||||||||
\(78\) | − | 329.009i | − | 0.477602i | ||||||
\(79\) | 643.579 | 0.916560 | 0.458280 | − | 0.888808i | \(-0.348466\pi\) | ||||
0.458280 | + | 0.888808i | \(0.348466\pi\) | |||||||
\(80\) | 137.321 | − | 114.642i | 0.191912 | − | 0.160218i | ||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | − | 167.615i | − | 0.225732i | ||||||
\(83\) | 578.367i | 0.764867i | 0.923983 | + | 0.382434i | \(0.124914\pi\) | ||||
−0.923983 | + | 0.382434i | \(0.875086\pi\) | |||||||
\(84\) | 84.0000 | 0.109109 | ||||||||
\(85\) | 834.642 | + | 999.753i | 1.06506 | + | 1.27575i | ||||
\(86\) | −561.670 | −0.704260 | ||||||||
\(87\) | 528.468i | 0.651238i | ||||||||
\(88\) | 245.285i | 0.297130i | ||||||||
\(89\) | 117.477 | 0.139916 | 0.0699582 | − | 0.997550i | \(-0.477713\pi\) | ||||
0.0699582 | + | 0.997550i | \(0.477713\pi\) | |||||||
\(90\) | 128.973 | + | 154.486i | 0.151055 | + | 0.180937i | ||||
\(91\) | 383.844 | 0.442173 | ||||||||
\(92\) | 782.606i | 0.886873i | ||||||||
\(93\) | 479.423i | 0.534557i | ||||||||
\(94\) | −1077.49 | −1.18228 | ||||||||
\(95\) | 906.762 | − | 757.009i | 0.979282 | − | 0.817553i | ||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | 648.635i | 0.678958i | 0.940614 | + | 0.339479i | \(0.110251\pi\) | ||||
−0.940614 | + | 0.339479i | \(0.889749\pi\) | |||||||
\(98\) | 98.0000i | 0.101015i | ||||||||
\(99\) | −275.945 | −0.280137 | ||||||||
\(100\) | −89.2848 | + | 491.964i | −0.0892848 | + | 0.491964i | ||||
\(101\) | −1465.96 | −1.44424 | −0.722119 | − | 0.691769i | \(-0.756832\pi\) | ||||
−0.722119 | + | 0.691769i | \(0.756832\pi\) | |||||||
\(102\) | 698.918i | 0.678463i | ||||||||
\(103\) | − | 681.670i | − | 0.652106i | −0.945352 | − | 0.326053i | \(-0.894281\pi\) | ||
0.945352 | − | 0.326053i | \(-0.105719\pi\) | |||||||
\(104\) | 438.679 | 0.413615 | ||||||||
\(105\) | −180.234 | + | 150.468i | −0.167515 | + | 0.139849i | ||||
\(106\) | 1111.27 | 1.01826 | ||||||||
\(107\) | 1401.05i | 1.26583i | 0.774220 | + | 0.632917i | \(0.218142\pi\) | ||||
−0.774220 | + | 0.632917i | \(0.781858\pi\) | |||||||
\(108\) | 108.000i | 0.0962250i | ||||||||
\(109\) | 161.761 | 0.142145 | 0.0710727 | − | 0.997471i | \(-0.477358\pi\) | ||||
0.0710727 | + | 0.997471i | \(0.477358\pi\) | |||||||
\(110\) | −439.376 | − | 526.294i | −0.380844 | − | 0.456183i | ||||
\(111\) | −142.541 | −0.121886 | ||||||||
\(112\) | 112.000i | 0.0944911i | ||||||||
\(113\) | 382.552i | 0.318473i | 0.987240 | + | 0.159236i | \(0.0509032\pi\) | ||||
−0.987240 | + | 0.159236i | \(0.949097\pi\) | |||||||
\(114\) | 633.909 | 0.520798 | ||||||||
\(115\) | −1401.87 | − | 1679.19i | −1.13674 | − | 1.36161i | ||||
\(116\) | −704.624 | −0.563989 | ||||||||
\(117\) | 493.514i | 0.389960i | ||||||||
\(118\) | 989.212i | 0.771732i | ||||||||
\(119\) | −815.405 | −0.628135 | ||||||||
\(120\) | −205.982 | + | 171.964i | −0.156696 | + | 0.130817i | ||||
\(121\) | −390.927 | −0.293709 | ||||||||
\(122\) | − | 625.488i | − | 0.464172i | ||||||
\(123\) | 251.423i | 0.184309i | ||||||||
\(124\) | −639.230 | −0.462940 | ||||||||
\(125\) | −689.675 | − | 1215.51i | −0.493491 | − | 0.869751i | ||||
\(126\) | −126.000 | −0.0890871 | ||||||||
\(127\) | − | 144.515i | − | 0.100974i | −0.998725 | − | 0.0504868i | \(-0.983923\pi\) | ||
0.998725 | − | 0.0504868i | \(-0.0160773\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 842.505 | 0.575026 | ||||||||
\(130\) | −941.248 | + | 785.800i | −0.635023 | + | 0.530148i | ||||
\(131\) | 767.194 | 0.511680 | 0.255840 | − | 0.966719i | \(-0.417648\pi\) | ||||
0.255840 | + | 0.966719i | \(0.417648\pi\) | |||||||
\(132\) | − | 367.927i | − | 0.242606i | ||||||
\(133\) | 739.561i | 0.482166i | ||||||||
\(134\) | 2122.77 | 1.36850 | ||||||||
\(135\) | −193.459 | − | 231.730i | −0.123336 | − | 0.147734i | ||||
\(136\) | −931.891 | −0.587566 | ||||||||
\(137\) | 17.7606i | 0.0110759i | 0.999985 | + | 0.00553793i | \(0.00176279\pi\) | ||||
−0.999985 | + | 0.00553793i | \(0.998237\pi\) | |||||||
\(138\) | − | 1173.91i | − | 0.724129i | ||||||
\(139\) | −1217.48 | −0.742919 | −0.371459 | − | 0.928449i | \(-0.621143\pi\) | ||||
−0.371459 | + | 0.928449i | \(0.621143\pi\) | |||||||
\(140\) | −200.624 | − | 240.312i | −0.121113 | − | 0.145072i | ||||
\(141\) | 1616.23 | 0.965328 | ||||||||
\(142\) | 2212.13i | 1.30731i | ||||||||
\(143\) | − | 1681.27i | − | 0.983181i | ||||||
\(144\) | −144.000 | −0.0833333 | ||||||||
\(145\) | 1511.87 | − | 1262.18i | 0.865891 | − | 0.722888i | ||||
\(146\) | 559.615 | 0.317220 | ||||||||
\(147\) | − | 147.000i | − | 0.0824786i | ||||||
\(148\) | − | 190.055i | − | 0.105557i | ||||||
\(149\) | −3485.64 | −1.91648 | −0.958239 | − | 0.285970i | \(-0.907684\pi\) | ||||
−0.958239 | + | 0.285970i | \(0.907684\pi\) | |||||||
\(150\) | 133.927 | − | 737.945i | 0.0729008 | − | 0.401687i | ||||
\(151\) | 665.394 | 0.358603 | 0.179301 | − | 0.983794i | \(-0.442616\pi\) | ||||
0.179301 | + | 0.983794i | \(0.442616\pi\) | |||||||
\(152\) | 845.212i | 0.451025i | ||||||||
\(153\) | − | 1048.38i | − | 0.553963i | ||||||
\(154\) | 429.248 | 0.224609 | ||||||||
\(155\) | 1371.56 | − | 1145.05i | 0.710751 | − | 0.593369i | ||||
\(156\) | −658.018 | −0.337716 | ||||||||
\(157\) | − | 1905.39i | − | 0.968577i | −0.874908 | − | 0.484289i | \(-0.839078\pi\) | ||
0.874908 | − | 0.484289i | \(-0.160922\pi\) | |||||||
\(158\) | − | 1287.16i | − | 0.648106i | ||||||
\(159\) | −1666.90 | −0.831407 | ||||||||
\(160\) | −229.285 | − | 274.642i | −0.113291 | − | 0.135702i | ||||
\(161\) | 1369.56 | 0.670413 | ||||||||
\(162\) | − | 162.000i | − | 0.0785674i | ||||||
\(163\) | − | 1389.83i | − | 0.667851i | −0.942599 | − | 0.333926i | \(-0.891627\pi\) | ||
0.942599 | − | 0.333926i | \(-0.108373\pi\) | |||||||
\(164\) | −335.230 | −0.159616 | ||||||||
\(165\) | 659.064 | + | 789.441i | 0.310958 | + | 0.372472i | ||||
\(166\) | 1156.73 | 0.540843 | ||||||||
\(167\) | 216.080i | 0.100125i | 0.998746 | + | 0.0500623i | \(0.0159420\pi\) | ||||
−0.998746 | + | 0.0500623i | \(0.984058\pi\) | |||||||
\(168\) | − | 168.000i | − | 0.0771517i | ||||||
\(169\) | −809.861 | −0.368621 | ||||||||
\(170\) | 1999.51 | − | 1669.28i | 0.902089 | − | 0.753108i | ||||
\(171\) | −950.864 | −0.425230 | ||||||||
\(172\) | 1123.34i | 0.497987i | ||||||||
\(173\) | − | 3128.09i | − | 1.37471i | −0.726322 | − | 0.687354i | \(-0.758772\pi\) | ||
0.726322 | − | 0.687354i | \(-0.241228\pi\) | |||||||
\(174\) | 1056.94 | 0.460495 | ||||||||
\(175\) | 860.936 | + | 156.248i | 0.371890 | + | 0.0674930i | ||||
\(176\) | 490.570 | 0.210103 | ||||||||
\(177\) | − | 1483.82i | − | 0.630116i | ||||||
\(178\) | − | 234.955i | − | 0.0989359i | ||||||
\(179\) | −449.870 | −0.187848 | −0.0939241 | − | 0.995579i | \(-0.529941\pi\) | ||||
−0.0939241 | + | 0.995579i | \(0.529941\pi\) | |||||||
\(180\) | 308.973 | − | 257.945i | 0.127941 | − | 0.106812i | ||||
\(181\) | 2647.87 | 1.08737 | 0.543686 | − | 0.839289i | \(-0.317028\pi\) | ||||
0.543686 | + | 0.839289i | \(0.317028\pi\) | |||||||
\(182\) | − | 767.688i | − | 0.312664i | ||||||
\(183\) | 938.232i | 0.378995i | ||||||||
\(184\) | 1565.21 | 0.627114 | ||||||||
\(185\) | 340.442 | + | 407.789i | 0.135296 | + | 0.162061i | ||||
\(186\) | 958.845 | 0.377989 | ||||||||
\(187\) | 3571.54i | 1.39667i | ||||||||
\(188\) | 2154.98i | 0.835999i | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | −1514.02 | − | 1813.52i | −0.578097 | − | 0.692457i | ||||
\(191\) | −2809.04 | −1.06416 | −0.532081 | − | 0.846693i | \(-0.678590\pi\) | ||||
−0.532081 | + | 0.846693i | \(0.678590\pi\) | |||||||
\(192\) | − | 192.000i | − | 0.0721688i | ||||||
\(193\) | − | 342.621i | − | 0.127785i | −0.997957 | − | 0.0638923i | \(-0.979649\pi\) | ||
0.997957 | − | 0.0638923i | \(-0.0203514\pi\) | |||||||
\(194\) | 1297.27 | 0.480096 | ||||||||
\(195\) | 1411.87 | − | 1178.70i | 0.518494 | − | 0.432864i | ||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 3653.00i | 1.32114i | 0.750763 | + | 0.660572i | \(0.229686\pi\) | ||||
−0.750763 | + | 0.660572i | \(0.770314\pi\) | |||||||
\(198\) | 551.891i | 0.198087i | ||||||||
\(199\) | −5024.78 | −1.78994 | −0.894968 | − | 0.446131i | \(-0.852802\pi\) | ||||
−0.894968 | + | 0.446131i | \(0.852802\pi\) | |||||||
\(200\) | 983.927 | + | 178.570i | 0.347871 | + | 0.0631339i | ||||
\(201\) | −3184.16 | −1.11738 | ||||||||
\(202\) | 2931.91i | 1.02123i | ||||||||
\(203\) | 1233.09i | 0.426336i | ||||||||
\(204\) | 1397.84 | 0.479746 | ||||||||
\(205\) | 719.285 | − | 600.494i | 0.245059 | − | 0.204587i | ||||
\(206\) | −1363.34 | −0.461109 | ||||||||
\(207\) | 1760.86i | 0.591249i | ||||||||
\(208\) | − | 877.358i | − | 0.292470i | ||||||
\(209\) | 3239.34 | 1.07210 | ||||||||
\(210\) | 300.936 | + | 360.468i | 0.0988885 | + | 0.118451i | ||||
\(211\) | 4033.65 | 1.31606 | 0.658029 | − | 0.752993i | \(-0.271390\pi\) | ||||
0.658029 | + | 0.752993i | \(0.271390\pi\) | |||||||
\(212\) | − | 2222.53i | − | 0.720020i | ||||||
\(213\) | − | 3318.20i | − | 1.06741i | ||||||
\(214\) | 2802.09 | 0.895079 | ||||||||
\(215\) | −2012.22 | − | 2410.29i | −0.638291 | − | 0.764559i | ||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 1118.65i | 0.349950i | ||||||||
\(218\) | − | 323.521i | − | 0.100512i | ||||||
\(219\) | −839.423 | −0.259009 | ||||||||
\(220\) | −1052.59 | + | 878.752i | −0.322570 | + | 0.269297i | ||||
\(221\) | 6387.51 | 1.94421 | ||||||||
\(222\) | 285.082i | 0.0861867i | ||||||||
\(223\) | − | 4000.83i | − | 1.20141i | −0.799469 | − | 0.600707i | \(-0.794886\pi\) | ||
0.799469 | − | 0.600707i | \(-0.205114\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | −200.891 | + | 1106.92i | −0.0595232 | + | 0.327976i | ||||
\(226\) | 765.103 | 0.225194 | ||||||||
\(227\) | − | 2755.60i | − | 0.805707i | −0.915264 | − | 0.402854i | \(-0.868018\pi\) | ||
0.915264 | − | 0.402854i | \(-0.131982\pi\) | |||||||
\(228\) | − | 1267.82i | − | 0.368260i | ||||||
\(229\) | −333.971 | −0.0963731 | −0.0481865 | − | 0.998838i | \(-0.515344\pi\) | ||||
−0.0481865 | + | 0.998838i | \(0.515344\pi\) | |||||||
\(230\) | −3358.39 | + | 2803.75i | −0.962807 | + | 0.803798i | ||||
\(231\) | −643.873 | −0.183393 | ||||||||
\(232\) | 1409.25i | 0.398800i | ||||||||
\(233\) | 5518.48i | 1.55162i | 0.630966 | + | 0.775810i | \(0.282659\pi\) | ||||
−0.630966 | + | 0.775810i | \(0.717341\pi\) | |||||||
\(234\) | 987.027 | 0.275744 | ||||||||
\(235\) | −3860.18 | − | 4623.81i | −1.07153 | − | 1.28351i | ||||
\(236\) | 1978.42 | 0.545697 | ||||||||
\(237\) | 1930.74i | 0.529176i | ||||||||
\(238\) | 1630.81i | 0.444158i | ||||||||
\(239\) | 3933.97 | 1.06472 | 0.532359 | − | 0.846519i | \(-0.321306\pi\) | ||||
0.532359 | + | 0.846519i | \(0.321306\pi\) | |||||||
\(240\) | 343.927 | + | 411.964i | 0.0925017 | + | 0.110801i | ||||
\(241\) | 3910.07 | 1.04510 | 0.522552 | − | 0.852608i | \(-0.324980\pi\) | ||||
0.522552 | + | 0.852608i | \(0.324980\pi\) | |||||||
\(242\) | 781.855i | 0.207684i | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | −1250.98 | −0.328219 | ||||||||
\(245\) | −420.546 | + | 351.092i | −0.109664 | + | 0.0915529i | ||||
\(246\) | 502.845 | 0.130326 | ||||||||
\(247\) | − | 5793.38i | − | 1.49241i | ||||||
\(248\) | 1278.46i | 0.327348i | ||||||||
\(249\) | −1735.10 | −0.441596 | ||||||||
\(250\) | −2431.03 | + | 1379.35i | −0.615007 | + | 0.348951i | ||||
\(251\) | −1950.53 | −0.490504 | −0.245252 | − | 0.969459i | \(-0.578871\pi\) | ||||
−0.245252 | + | 0.969459i | \(0.578871\pi\) | |||||||
\(252\) | 252.000i | 0.0629941i | ||||||||
\(253\) | − | 5998.79i | − | 1.49068i | ||||||
\(254\) | −289.030 | −0.0713991 | ||||||||
\(255\) | −2999.26 | + | 2503.93i | −0.736553 | + | 0.614910i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 4481.31i | 1.08769i | 0.839185 | + | 0.543846i | \(0.183032\pi\) | ||||
−0.839185 | + | 0.543846i | \(0.816968\pi\) | |||||||
\(258\) | − | 1685.01i | − | 0.406605i | ||||||
\(259\) | −332.595 | −0.0797933 | ||||||||
\(260\) | 1571.60 | + | 1882.50i | 0.374871 | + | 0.449029i | ||||
\(261\) | −1585.40 | −0.375993 | ||||||||
\(262\) | − | 1534.39i | − | 0.361812i | ||||||
\(263\) | 4266.78i | 1.00038i | 0.865915 | + | 0.500192i | \(0.166737\pi\) | ||||
−0.865915 | + | 0.500192i | \(0.833263\pi\) | |||||||
\(264\) | −735.855 | −0.171548 | ||||||||
\(265\) | 3981.20 | + | 4768.77i | 0.922879 | + | 1.10544i | ||||
\(266\) | 1479.12 | 0.340943 | ||||||||
\(267\) | 352.432i | 0.0807808i | ||||||||
\(268\) | − | 4245.55i | − | 0.967679i | ||||||
\(269\) | 500.380 | 0.113415 | 0.0567077 | − | 0.998391i | \(-0.481940\pi\) | ||||
0.0567077 | + | 0.998391i | \(0.481940\pi\) | |||||||
\(270\) | −463.459 | + | 386.918i | −0.104464 | + | 0.0872114i | ||||
\(271\) | −1133.76 | −0.254136 | −0.127068 | − | 0.991894i | \(-0.540557\pi\) | ||||
−0.127068 | + | 0.991894i | \(0.540557\pi\) | |||||||
\(272\) | 1863.78i | 0.415472i | ||||||||
\(273\) | 1151.53i | 0.255289i | ||||||||
\(274\) | 35.5212 | 0.00783181 | ||||||||
\(275\) | 684.382 | − | 3770.98i | 0.150072 | − | 0.826903i | ||||
\(276\) | −2347.82 | −0.512036 | ||||||||
\(277\) | 2315.90i | 0.502342i | 0.967943 | + | 0.251171i | \(0.0808157\pi\) | ||||
−0.967943 | + | 0.251171i | \(0.919184\pi\) | |||||||
\(278\) | 2434.97i | 0.525323i | ||||||||
\(279\) | −1438.27 | −0.308627 | ||||||||
\(280\) | −480.624 | + | 401.248i | −0.102581 | + | 0.0856399i | ||||
\(281\) | −3792.45 | −0.805119 | −0.402559 | − | 0.915394i | \(-0.631879\pi\) | ||||
−0.402559 | + | 0.915394i | \(0.631879\pi\) | |||||||
\(282\) | − | 3232.46i | − | 0.682590i | ||||||
\(283\) | − | 4375.29i | − | 0.919026i | −0.888171 | − | 0.459513i | \(-0.848024\pi\) | ||
0.888171 | − | 0.459513i | \(-0.151976\pi\) | |||||||
\(284\) | 4424.26 | 0.924407 | ||||||||
\(285\) | 2271.03 | + | 2720.29i | 0.472014 | + | 0.565389i | ||||
\(286\) | −3362.54 | −0.695214 | ||||||||
\(287\) | 586.653i | 0.120659i | ||||||||
\(288\) | 288.000i | 0.0589256i | ||||||||
\(289\) | −8656.07 | −1.76187 | ||||||||
\(290\) | −2524.37 | − | 3023.75i | −0.511159 | − | 0.612277i | ||||
\(291\) | −1945.90 | −0.391996 | ||||||||
\(292\) | − | 1119.23i | − | 0.224308i | ||||||
\(293\) | − | 1703.22i | − | 0.339602i | −0.985478 | − | 0.169801i | \(-0.945687\pi\) | ||
0.985478 | − | 0.169801i | \(-0.0543125\pi\) | |||||||
\(294\) | −294.000 | −0.0583212 | ||||||||
\(295\) | −4244.99 | + | 3543.93i | −0.837807 | + | 0.699442i | ||||
\(296\) | −380.109 | −0.0746398 | ||||||||
\(297\) | − | 827.836i | − | 0.161737i | ||||||
\(298\) | 6971.29i | 1.35515i | ||||||||
\(299\) | −10728.5 | −2.07507 | ||||||||
\(300\) | −1475.89 | − | 267.855i | −0.284035 | − | 0.0515486i | ||||
\(301\) | 1965.84 | 0.376443 | ||||||||
\(302\) | − | 1330.79i | − | 0.253570i | ||||||
\(303\) | − | 4397.87i | − | 0.833831i | ||||||
\(304\) | 1690.42 | 0.318923 | ||||||||
\(305\) | 2684.15 | − | 2240.86i | 0.503914 | − | 0.420692i | ||||
\(306\) | −2096.75 | −0.391711 | ||||||||
\(307\) | − | 4284.48i | − | 0.796509i | −0.917275 | − | 0.398254i | \(-0.869616\pi\) | ||
0.917275 | − | 0.398254i | \(-0.130384\pi\) | |||||||
\(308\) | − | 858.497i | − | 0.158823i | ||||||
\(309\) | 2045.01 | 0.376494 | ||||||||
\(310\) | −2290.09 | − | 2743.12i | −0.419576 | − | 0.502577i | ||||
\(311\) | 2637.47 | 0.480892 | 0.240446 | − | 0.970663i | \(-0.422706\pi\) | ||||
0.240446 | + | 0.970663i | \(0.422706\pi\) | |||||||
\(312\) | 1316.04i | 0.238801i | ||||||||
\(313\) | 6610.92i | 1.19384i | 0.802302 | + | 0.596919i | \(0.203609\pi\) | ||||
−0.802302 | + | 0.596919i | \(0.796391\pi\) | |||||||
\(314\) | −3810.78 | −0.684888 | ||||||||
\(315\) | −451.405 | − | 540.702i | −0.0807421 | − | 0.0967147i | ||||
\(316\) | −2574.32 | −0.458280 | ||||||||
\(317\) | 8959.15i | 1.58737i | 0.608329 | + | 0.793685i | \(0.291840\pi\) | ||||
−0.608329 | + | 0.793685i | \(0.708160\pi\) | |||||||
\(318\) | 3333.80i | 0.587894i | ||||||||
\(319\) | 5401.05 | 0.947965 | ||||||||
\(320\) | −549.285 | + | 458.570i | −0.0959561 | + | 0.0801088i | ||||
\(321\) | −4203.14 | −0.730829 | ||||||||
\(322\) | − | 2739.12i | − | 0.474054i | ||||||
\(323\) | 12307.0i | 2.12005i | ||||||||
\(324\) | −324.000 | −0.0555556 | ||||||||
\(325\) | −6744.19 | − | 1223.98i | −1.15108 | − | 0.208905i | ||||
\(326\) | −2779.66 | −0.472242 | ||||||||
\(327\) | 485.282i | 0.0820677i | ||||||||
\(328\) | 670.461i | 0.112866i | ||||||||
\(329\) | 3771.21 | 0.631956 | ||||||||
\(330\) | 1578.88 | − | 1318.13i | 0.263378 | − | 0.219880i | ||||
\(331\) | 3741.55 | 0.621311 | 0.310655 | − | 0.950523i | \(-0.399451\pi\) | ||||
0.310655 | + | 0.950523i | \(0.399451\pi\) | |||||||
\(332\) | − | 2313.47i | − | 0.382434i | ||||||
\(333\) | − | 427.623i | − | 0.0703711i | ||||||
\(334\) | 432.161 | 0.0707987 | ||||||||
\(335\) | 7604.99 | + | 9109.43i | 1.24031 | + | 1.48568i | ||||
\(336\) | −336.000 | −0.0545545 | ||||||||
\(337\) | − | 738.512i | − | 0.119375i | −0.998217 | − | 0.0596874i | \(-0.980990\pi\) | ||
0.998217 | − | 0.0596874i | \(-0.0190104\pi\) | |||||||
\(338\) | 1619.72i | 0.260655i | ||||||||
\(339\) | −1147.65 | −0.183870 | ||||||||
\(340\) | −3338.57 | − | 3999.01i | −0.532528 | − | 0.637873i | ||||
\(341\) | 4899.80 | 0.778120 | ||||||||
\(342\) | 1901.73i | 0.300683i | ||||||||
\(343\) | − | 343.000i | − | 0.0539949i | ||||||
\(344\) | 2246.68 | 0.352130 | ||||||||
\(345\) | 5037.58 | − | 4205.62i | 0.786128 | − | 0.656298i | ||||
\(346\) | −6256.19 | −0.972066 | ||||||||
\(347\) | 3194.42i | 0.494195i | 0.968991 | + | 0.247098i | \(0.0794768\pi\) | ||||
−0.968991 | + | 0.247098i | \(0.920523\pi\) | |||||||
\(348\) | − | 2113.87i | − | 0.325619i | ||||||
\(349\) | 7646.63 | 1.17282 | 0.586411 | − | 0.810014i | \(-0.300540\pi\) | ||||
0.586411 | + | 0.810014i | \(0.300540\pi\) | |||||||
\(350\) | 312.497 | − | 1721.87i | 0.0477248 | − | 0.262966i | ||||
\(351\) | −1480.54 | −0.225144 | ||||||||
\(352\) | − | 981.139i | − | 0.148565i | ||||||
\(353\) | 4009.84i | 0.604596i | 0.953213 | + | 0.302298i | \(0.0977538\pi\) | ||||
−0.953213 | + | 0.302298i | \(0.902246\pi\) | |||||||
\(354\) | −2967.64 | −0.445560 | ||||||||
\(355\) | −9492.89 | + | 7925.12i | −1.41924 | + | 1.18485i | ||||
\(356\) | −469.909 | −0.0699582 | ||||||||
\(357\) | − | 2446.21i | − | 0.362654i | ||||||
\(358\) | 899.739i | 0.132829i | ||||||||
\(359\) | −3743.25 | −0.550309 | −0.275155 | − | 0.961400i | \(-0.588729\pi\) | ||||
−0.275155 | + | 0.961400i | \(0.588729\pi\) | |||||||
\(360\) | −515.891 | − | 617.945i | −0.0755273 | − | 0.0904683i | ||||
\(361\) | 4303.24 | 0.627386 | ||||||||
\(362\) | − | 5295.73i | − | 0.768888i | ||||||
\(363\) | − | 1172.78i | − | 0.169573i | ||||||
\(364\) | −1535.38 | −0.221087 | ||||||||
\(365\) | 2004.86 | + | 2401.47i | 0.287505 | + | 0.344380i | ||||
\(366\) | 1876.46 | 0.267990 | ||||||||
\(367\) | − | 3886.64i | − | 0.552809i | −0.961041 | − | 0.276404i | \(-0.910857\pi\) | ||
0.961041 | − | 0.276404i | \(-0.0891429\pi\) | |||||||
\(368\) | − | 3130.42i | − | 0.443437i | ||||||
\(369\) | −754.268 | −0.106411 | ||||||||
\(370\) | 815.579 | − | 680.885i | 0.114594 | − | 0.0956690i | ||||
\(371\) | −3889.43 | −0.544284 | ||||||||
\(372\) | − | 1917.69i | − | 0.267279i | ||||||
\(373\) | 5980.37i | 0.830165i | 0.909784 | + | 0.415083i | \(0.136247\pi\) | ||||
−0.909784 | + | 0.415083i | \(0.863753\pi\) | |||||||
\(374\) | 7143.08 | 0.987594 | ||||||||
\(375\) | 3646.54 | − | 2069.02i | 0.502151 | − | 0.284917i | ||||
\(376\) | 4309.95 | 0.591140 | ||||||||
\(377\) | − | 9659.49i | − | 1.31960i | ||||||
\(378\) | − | 378.000i | − | 0.0514344i | ||||||
\(379\) | −3455.16 | −0.468285 | −0.234142 | − | 0.972202i | \(-0.575228\pi\) | ||||
−0.234142 | + | 0.972202i | \(0.575228\pi\) | |||||||
\(380\) | −3627.05 | + | 3028.04i | −0.489641 | + | 0.408776i | ||||
\(381\) | 433.545 | 0.0582971 | ||||||||
\(382\) | 5618.08i | 0.752477i | ||||||||
\(383\) | − | 11859.9i | − | 1.58228i | −0.611638 | − | 0.791138i | \(-0.709489\pi\) | ||
0.611638 | − | 0.791138i | \(-0.290511\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 1537.82 | + | 1842.03i | 0.203570 | + | 0.243840i | ||||
\(386\) | −685.242 | −0.0903573 | ||||||||
\(387\) | 2527.51i | 0.331992i | ||||||||
\(388\) | − | 2594.54i | − | 0.339479i | ||||||
\(389\) | 11427.4 | 1.48944 | 0.744720 | − | 0.667377i | \(-0.232583\pi\) | ||||
0.744720 | + | 0.667377i | \(0.232583\pi\) | |||||||
\(390\) | −2357.40 | − | 2823.75i | −0.306081 | − | 0.366631i | ||||
\(391\) | 22790.7 | 2.94777 | ||||||||
\(392\) | − | 392.000i | − | 0.0505076i | ||||||
\(393\) | 2301.58i | 0.295418i | ||||||||
\(394\) | 7305.99 | 0.934189 | ||||||||
\(395\) | 5523.56 | − | 4611.34i | 0.703597 | − | 0.587397i | ||||
\(396\) | 1103.78 | 0.140068 | ||||||||
\(397\) | 794.377i | 0.100425i | 0.998739 | + | 0.0502124i | \(0.0159898\pi\) | ||||
−0.998739 | + | 0.0502124i | \(0.984010\pi\) | |||||||
\(398\) | 10049.6i | 1.26568i | ||||||||
\(399\) | −2218.68 | −0.278378 | ||||||||
\(400\) | 357.139 | − | 1967.85i | 0.0446424 | − | 0.245982i | ||||
\(401\) | −4513.82 | −0.562118 | −0.281059 | − | 0.959690i | \(-0.590686\pi\) | ||||
−0.281059 | + | 0.959690i | \(0.590686\pi\) | |||||||
\(402\) | 6368.32i | 0.790107i | ||||||||
\(403\) | − | 8763.02i | − | 1.08317i | ||||||
\(404\) | 5863.82 | 0.722119 | ||||||||
\(405\) | 695.189 | − | 580.377i | 0.0852943 | − | 0.0712078i | ||||
\(406\) | 2466.18 | 0.301465 | ||||||||
\(407\) | 1456.80i | 0.177422i | ||||||||
\(408\) | − | 2795.67i | − | 0.339231i | ||||||
\(409\) | −4671.30 | −0.564745 | −0.282373 | − | 0.959305i | \(-0.591121\pi\) | ||||
−0.282373 | + | 0.959305i | \(0.591121\pi\) | |||||||
\(410\) | −1200.99 | − | 1438.57i | −0.144665 | − | 0.173283i | ||||
\(411\) | −53.2818 | −0.00639465 | ||||||||
\(412\) | 2726.68i | 0.326053i | ||||||||
\(413\) | − | 3462.24i | − | 0.412508i | ||||||
\(414\) | 3521.73 | 0.418076 | ||||||||
\(415\) | 4144.08 | + | 4963.88i | 0.490181 | + | 0.587150i | ||||
\(416\) | −1754.72 | −0.206808 | ||||||||
\(417\) | − | 3652.45i | − | 0.428924i | ||||||
\(418\) | − | 6478.68i | − | 0.758092i | ||||||
\(419\) | −11816.9 | −1.37779 | −0.688893 | − | 0.724863i | \(-0.741903\pi\) | ||||
−0.688893 | + | 0.724863i | \(0.741903\pi\) | |||||||
\(420\) | 720.936 | − | 601.873i | 0.0837574 | − | 0.0699247i | ||||
\(421\) | −14992.7 | −1.73563 | −0.867815 | − | 0.496888i | \(-0.834476\pi\) | ||||
−0.867815 | + | 0.496888i | \(0.834476\pi\) | |||||||
\(422\) | − | 8067.31i | − | 0.930594i | ||||||
\(423\) | 4848.70i | 0.557332i | ||||||||
\(424\) | −4445.07 | −0.509131 | ||||||||
\(425\) | 14326.8 | + | 2600.12i | 1.63518 | + | 0.296763i | ||||
\(426\) | −6636.39 | −0.754775 | ||||||||
\(427\) | 2189.21i | 0.248110i | ||||||||
\(428\) | − | 5604.18i | − | 0.632917i | ||||||
\(429\) | 5043.81 | 0.567640 | ||||||||
\(430\) | −4820.57 | + | 4024.45i | −0.540625 | + | 0.451340i | ||||
\(431\) | −8068.52 | −0.901733 | −0.450866 | − | 0.892591i | \(-0.648885\pi\) | ||||
−0.450866 | + | 0.892591i | \(0.648885\pi\) | |||||||
\(432\) | − | 432.000i | − | 0.0481125i | ||||||
\(433\) | 12399.1i | 1.37612i | 0.725652 | + | 0.688062i | \(0.241538\pi\) | ||||
−0.725652 | + | 0.688062i | \(0.758462\pi\) | |||||||
\(434\) | 2237.31 | 0.247452 | ||||||||
\(435\) | 3786.55 | + | 4535.62i | 0.417360 | + | 0.499922i | ||||
\(436\) | −647.042 | −0.0710727 | ||||||||
\(437\) | − | 20670.9i | − | 2.26275i | ||||||
\(438\) | 1678.85i | 0.183147i | ||||||||
\(439\) | −4110.70 | −0.446909 | −0.223455 | − | 0.974714i | \(-0.571733\pi\) | ||||
−0.223455 | + | 0.974714i | \(0.571733\pi\) | |||||||
\(440\) | 1757.50 | + | 2105.18i | 0.190422 | + | 0.228092i | ||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | − | 12775.0i | − | 1.37476i | ||||||
\(443\) | 2734.90i | 0.293316i | 0.989187 | + | 0.146658i | \(0.0468516\pi\) | ||||
−0.989187 | + | 0.146658i | \(0.953148\pi\) | |||||||
\(444\) | 570.164 | 0.0609432 | ||||||||
\(445\) | 1008.26 | − | 841.742i | 0.107407 | − | 0.0896684i | ||||
\(446\) | −8001.65 | −0.849528 | ||||||||
\(447\) | − | 10456.9i | − | 1.10648i | ||||||
\(448\) | − | 448.000i | − | 0.0472456i | ||||||
\(449\) | 5943.34 | 0.624685 | 0.312342 | − | 0.949970i | \(-0.398886\pi\) | ||||
0.312342 | + | 0.949970i | \(0.398886\pi\) | |||||||
\(450\) | 2213.84 | + | 401.782i | 0.231914 | + | 0.0420893i | ||||
\(451\) | 2569.59 | 0.268287 | ||||||||
\(452\) | − | 1530.21i | − | 0.159236i | ||||||
\(453\) | 1996.18i | 0.207039i | ||||||||
\(454\) | −5511.20 | −0.569721 | ||||||||
\(455\) | 3294.37 | − | 2750.30i | 0.339434 | − | 0.283376i | ||||
\(456\) | −2535.64 | −0.260399 | ||||||||
\(457\) | − | 287.312i | − | 0.0294090i | −0.999892 | − | 0.0147045i | \(-0.995319\pi\) | ||
0.999892 | − | 0.0147045i | \(-0.00468075\pi\) | |||||||
\(458\) | 667.942i | 0.0681461i | ||||||||
\(459\) | 3145.13 | 0.319830 | ||||||||
\(460\) | 5607.49 | + | 6716.78i | 0.568371 | + | 0.680807i | ||||
\(461\) | −12184.2 | −1.23096 | −0.615481 | − | 0.788152i | \(-0.711038\pi\) | ||||
−0.615481 | + | 0.788152i | \(0.711038\pi\) | |||||||
\(462\) | 1287.75i | 0.129678i | ||||||||
\(463\) | 6900.69i | 0.692662i | 0.938112 | + | 0.346331i | \(0.112573\pi\) | ||||
−0.938112 | + | 0.346331i | \(0.887427\pi\) | |||||||
\(464\) | 2818.50 | 0.281994 | ||||||||
\(465\) | 3435.14 | + | 4114.68i | 0.342582 | + | 0.410352i | ||||
\(466\) | 11037.0 | 1.09716 | ||||||||
\(467\) | − | 4294.71i | − | 0.425557i | −0.977100 | − | 0.212779i | \(-0.931749\pi\) | ||
0.977100 | − | 0.212779i | \(-0.0682513\pi\) | |||||||
\(468\) | − | 1974.05i | − | 0.194980i | ||||||
\(469\) | −7429.70 | −0.731497 | ||||||||
\(470\) | −9247.62 | + | 7720.36i | −0.907577 | + | 0.757689i | ||||
\(471\) | 5716.17 | 0.559208 | ||||||||
\(472\) | − | 3956.85i | − | 0.385866i | ||||||
\(473\) | − | 8610.57i | − | 0.837028i | ||||||
\(474\) | 3861.47 | 0.374184 | ||||||||
\(475\) | 2358.27 | − | 12994.2i | 0.227800 | − | 1.25519i | ||||
\(476\) | 3261.62 | 0.314067 | ||||||||
\(477\) | − | 5000.70i | − | 0.480013i | ||||||
\(478\) | − | 7867.94i | − | 0.752869i | ||||||
\(479\) | 6568.42 | 0.626553 | 0.313276 | − | 0.949662i | \(-0.398573\pi\) | ||||
0.313276 | + | 0.949662i | \(0.398573\pi\) | |||||||
\(480\) | 823.927 | − | 687.855i | 0.0783478 | − | 0.0654086i | ||||
\(481\) | 2605.40 | 0.246977 | ||||||||
\(482\) | − | 7820.15i | − | 0.739000i | ||||||
\(483\) | 4108.68i | 0.387063i | ||||||||
\(484\) | 1563.71 | 0.146855 | ||||||||
\(485\) | 4647.57 | + | 5566.96i | 0.435124 | + | 0.521201i | ||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | − | 3832.82i | − | 0.356636i | −0.983973 | − | 0.178318i | \(-0.942934\pi\) | ||
0.983973 | − | 0.178318i | \(-0.0570655\pi\) | |||||||
\(488\) | 2501.95i | 0.232086i | ||||||||
\(489\) | 4169.49 | 0.385584 | ||||||||
\(490\) | 702.185 | + | 841.092i | 0.0647377 | + | 0.0775442i | ||||
\(491\) | −179.779 | −0.0165240 | −0.00826202 | − | 0.999966i | \(-0.502630\pi\) | ||||
−0.00826202 | + | 0.999966i | \(0.502630\pi\) | |||||||
\(492\) | − | 1005.69i | − | 0.0921546i | ||||||
\(493\) | 20519.8i | 1.87457i | ||||||||
\(494\) | −11586.8 | −1.05529 | ||||||||
\(495\) | −2368.32 | + | 1977.19i | −0.215047 | + | 0.179532i | ||||
\(496\) | 2556.92 | 0.231470 | ||||||||
\(497\) | − | 7742.46i | − | 0.698786i | ||||||
\(498\) | 3470.20i | 0.312256i | ||||||||
\(499\) | 9992.79 | 0.896470 | 0.448235 | − | 0.893916i | \(-0.352053\pi\) | ||||
0.448235 | + | 0.893916i | \(0.352053\pi\) | |||||||
\(500\) | 2758.70 | + | 4862.05i | 0.246746 | + | 0.434875i | ||||
\(501\) | −648.241 | −0.0578069 | ||||||||
\(502\) | 3901.07i | 0.346839i | ||||||||
\(503\) | − | 3949.67i | − | 0.350113i | −0.984558 | − | 0.175057i | \(-0.943989\pi\) | ||
0.984558 | − | 0.175057i | \(-0.0560109\pi\) | |||||||
\(504\) | 504.000 | 0.0445435 | ||||||||
\(505\) | −12581.7 | + | 10503.8i | −1.10867 | + | 0.925570i | ||||
\(506\) | −11997.6 | −1.05407 | ||||||||
\(507\) | − | 2429.58i | − | 0.212824i | ||||||
\(508\) | 578.061i | 0.0504868i | ||||||||
\(509\) | −10074.5 | −0.877301 | −0.438650 | − | 0.898658i | \(-0.644543\pi\) | ||||
−0.438650 | + | 0.898658i | \(0.644543\pi\) | |||||||
\(510\) | 5007.85 | + | 5998.52i | 0.434807 | + | 0.520821i | ||||
\(511\) | −1958.65 | −0.169561 | ||||||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | − | 2852.59i | − | 0.245507i | ||||||
\(514\) | 8962.63 | 0.769114 | ||||||||
\(515\) | −4884.27 | − | 5850.48i | −0.417916 | − | 0.500588i | ||||
\(516\) | −3370.02 | −0.287513 | ||||||||
\(517\) | − | 16518.2i | − | 1.40516i | ||||||
\(518\) | 665.191i | 0.0564224i | ||||||||
\(519\) | 9384.28 | 0.793688 | ||||||||
\(520\) | 3764.99 | − | 3143.20i | 0.317511 | − | 0.265074i | ||||
\(521\) | 414.977 | 0.0348954 | 0.0174477 | − | 0.999848i | \(-0.494446\pi\) | ||||
0.0174477 | + | 0.999848i | \(0.494446\pi\) | |||||||
\(522\) | 3170.81i | 0.265867i | ||||||||
\(523\) | − | 22461.1i | − | 1.87793i | −0.344013 | − | 0.938965i | \(-0.611787\pi\) | ||
0.344013 | − | 0.938965i | \(-0.388213\pi\) | |||||||
\(524\) | −3068.78 | −0.255840 | ||||||||
\(525\) | −468.745 | + | 2582.81i | −0.0389671 | + | 0.214711i | ||||
\(526\) | 8533.56 | 0.707378 | ||||||||
\(527\) | 18615.4i | 1.53871i | ||||||||
\(528\) | 1471.71i | 0.121303i | ||||||||
\(529\) | −26112.5 | −2.14618 | ||||||||
\(530\) | 9537.53 | − | 7962.39i | 0.781668 | − | 0.652574i | ||||
\(531\) | 4451.45 | 0.363798 | ||||||||
\(532\) | − | 2958.24i | − | 0.241083i | ||||||
\(533\) | − | 4595.58i | − | 0.373464i | ||||||
\(534\) | 704.864 | 0.0571207 | ||||||||
\(535\) | 10038.7 | + | 12024.6i | 0.811235 | + | 0.971716i | ||||
\(536\) | −8491.09 | −0.684252 | ||||||||
\(537\) | − | 1349.61i | − | 0.108454i | ||||||
\(538\) | − | 1000.76i | − | 0.0801967i | ||||||
\(539\) | −1502.37 | −0.120059 | ||||||||
\(540\) | 773.836 | + | 926.918i | 0.0616678 | + | 0.0738671i | ||||
\(541\) | 12212.8 | 0.970551 | 0.485275 | − | 0.874361i | \(-0.338719\pi\) | ||||
0.485275 | + | 0.874361i | \(0.338719\pi\) | |||||||
\(542\) | 2267.52i | 0.179702i | ||||||||
\(543\) | 7943.60i | 0.627794i | ||||||||
\(544\) | 3727.56 | 0.293783 | ||||||||
\(545\) | 1388.32 | − | 1159.04i | 0.109118 | − | 0.0910969i | ||||
\(546\) | 2303.06 | 0.180517 | ||||||||
\(547\) | − | 3849.74i | − | 0.300920i | −0.988616 | − | 0.150460i | \(-0.951925\pi\) | ||
0.988616 | − | 0.150460i | \(-0.0480754\pi\) | |||||||
\(548\) | − | 71.0425i | − | 0.00553793i | ||||||
\(549\) | −2814.70 | −0.218813 | ||||||||
\(550\) | −7541.95 | − | 1368.76i | −0.584709 | − | 0.106117i | ||||
\(551\) | 18611.2 | 1.43895 | ||||||||
\(552\) | 4695.64i | 0.362064i | ||||||||
\(553\) | 4505.05i | 0.346427i | ||||||||
\(554\) | 4631.80 | 0.355210 | ||||||||
\(555\) | −1223.37 | + | 1021.33i | −0.0935659 | + | 0.0781134i | ||||
\(556\) | 4869.94 | 0.371459 | ||||||||
\(557\) | − | 5257.65i | − | 0.399953i | −0.979801 | − | 0.199977i | \(-0.935913\pi\) | ||
0.979801 | − | 0.199977i | \(-0.0640866\pi\) | |||||||
\(558\) | 2876.54i | 0.218232i | ||||||||
\(559\) | −15399.5 | −1.16517 | ||||||||
\(560\) | 802.497 | + | 961.248i | 0.0605566 | + | 0.0725360i | ||||
\(561\) | −10714.6 | −0.806367 | ||||||||
\(562\) | 7584.89i | 0.569305i | ||||||||
\(563\) | − | 11261.0i | − | 0.842972i | −0.906835 | − | 0.421486i | \(-0.861509\pi\) | ||
0.906835 | − | 0.421486i | \(-0.138491\pi\) | |||||||
\(564\) | −6464.93 | −0.482664 | ||||||||
\(565\) | 2741.04 | + | 3283.28i | 0.204100 | + | 0.244475i | ||||
\(566\) | −8750.59 | −0.649849 | ||||||||
\(567\) | 567.000i | 0.0419961i | ||||||||
\(568\) | − | 8848.52i | − | 0.653654i | ||||||
\(569\) | −16824.1 | −1.23955 | −0.619773 | − | 0.784781i | \(-0.712775\pi\) | ||||
−0.619773 | + | 0.784781i | \(0.712775\pi\) | |||||||
\(570\) | 5440.57 | − | 4542.05i | 0.399790 | − | 0.333764i | ||||
\(571\) | −3359.28 | −0.246202 | −0.123101 | − | 0.992394i | \(-0.539284\pi\) | ||||
−0.123101 | + | 0.992394i | \(0.539284\pi\) | |||||||
\(572\) | 6725.08i | 0.491590i | ||||||||
\(573\) | − | 8427.12i | − | 0.614395i | ||||||
\(574\) | 1173.31 | 0.0853185 | ||||||||
\(575\) | −24063.4 | − | 4367.18i | −1.74524 | − | 0.316737i | ||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 5889.04i | 0.424894i | 0.977173 | + | 0.212447i | \(0.0681433\pi\) | ||||
−0.977173 | + | 0.212447i | \(0.931857\pi\) | |||||||
\(578\) | 17312.1i | 1.24583i | ||||||||
\(579\) | 1027.86 | 0.0737764 | ||||||||
\(580\) | −6047.49 | + | 5048.74i | −0.432946 | + | 0.361444i | ||||
\(581\) | −4048.57 | −0.289093 | ||||||||
\(582\) | 3891.81i | 0.277183i | ||||||||
\(583\) | 17036.1i | 1.21023i | ||||||||
\(584\) | −2238.46 | −0.158610 | ||||||||
\(585\) | 3536.10 | + | 4235.62i | 0.249914 | + | 0.299353i | ||||
\(586\) | −3406.45 | −0.240135 | ||||||||
\(587\) | − | 4350.31i | − | 0.305888i | −0.988235 | − | 0.152944i | \(-0.951125\pi\) | ||
0.988235 | − | 0.152944i | \(-0.0488754\pi\) | |||||||
\(588\) | 588.000i | 0.0412393i | ||||||||
\(589\) | 16883.9 | 1.18114 | ||||||||
\(590\) | 7087.85 | + | 8489.99i | 0.494580 | + | 0.592419i | ||||
\(591\) | −10959.0 | −0.762763 | ||||||||
\(592\) | 760.218i | 0.0527783i | ||||||||
\(593\) | − | 8538.13i | − | 0.591263i | −0.955302 | − | 0.295632i | \(-0.904470\pi\) | ||
0.955302 | − | 0.295632i | \(-0.0955301\pi\) | |||||||
\(594\) | −1655.67 | −0.114365 | ||||||||
\(595\) | −6998.27 | + | 5842.50i | −0.482187 | + | 0.402553i | ||||
\(596\) | 13942.6 | 0.958239 | ||||||||
\(597\) | − | 15074.3i | − | 1.03342i | ||||||
\(598\) | 21457.0i | 1.46730i | ||||||||
\(599\) | 7492.48 | 0.511076 | 0.255538 | − | 0.966799i | \(-0.417747\pi\) | ||||
0.255538 | + | 0.966799i | \(0.417747\pi\) | |||||||
\(600\) | −535.709 | + | 2951.78i | −0.0364504 | + | 0.200843i | ||||
\(601\) | −6589.31 | −0.447227 | −0.223614 | − | 0.974678i | \(-0.571785\pi\) | ||||
−0.223614 | + | 0.974678i | \(0.571785\pi\) | |||||||
\(602\) | − | 3931.69i | − | 0.266185i | ||||||
\(603\) | − | 9552.48i | − | 0.645119i | ||||||
\(604\) | −2661.58 | −0.179301 | ||||||||
\(605\) | −3355.16 | + | 2801.05i | −0.225466 | + | 0.188230i | ||||
\(606\) | −8795.74 | −0.589608 | ||||||||
\(607\) | 28667.8i | 1.91695i | 0.285169 | + | 0.958477i | \(0.407950\pi\) | ||||
−0.285169 | + | 0.958477i | \(0.592050\pi\) | |||||||
\(608\) | − | 3380.85i | − | 0.225512i | ||||||
\(609\) | −3699.28 | −0.246145 | ||||||||
\(610\) | −4481.72 | − | 5368.30i | −0.297474 | − | 0.356321i | ||||
\(611\) | −29541.9 | −1.95604 | ||||||||
\(612\) | 4193.51i | 0.276981i | ||||||||
\(613\) | − | 55.7559i | − | 0.00367367i | −0.999998 | − | 0.00183683i | \(-0.999415\pi\) | ||
0.999998 | − | 0.00183683i | \(-0.000584683\pi\) | |||||||
\(614\) | −8568.96 | −0.563217 | ||||||||
\(615\) | 1801.48 | + | 2157.85i | 0.118118 | + | 0.141485i | ||||
\(616\) | −1716.99 | −0.112305 | ||||||||
\(617\) | − | 18958.2i | − | 1.23700i | −0.785786 | − | 0.618499i | \(-0.787741\pi\) | ||
0.785786 | − | 0.618499i | \(-0.212259\pi\) | |||||||
\(618\) | − | 4090.02i | − | 0.266221i | ||||||
\(619\) | 12269.4 | 0.796684 | 0.398342 | − | 0.917237i | \(-0.369586\pi\) | ||||
0.398342 | + | 0.917237i | \(0.369586\pi\) | |||||||
\(620\) | −5486.24 | + | 4580.18i | −0.355375 | + | 0.296685i | ||||
\(621\) | −5282.59 | −0.341358 | ||||||||
\(622\) | − | 5274.95i | − | 0.340042i | ||||||
\(623\) | 822.341i | 0.0528835i | ||||||||
\(624\) | 2632.07 | 0.168858 | ||||||||
\(625\) | −14628.5 | − | 5490.61i | −0.936226 | − | 0.351399i | ||||
\(626\) | 13221.8 | 0.844171 | ||||||||
\(627\) | 9718.02i | 0.618980i | ||||||||
\(628\) | 7621.56i | 0.484289i | ||||||||
\(629\) | −5534.69 | −0.350847 | ||||||||
\(630\) | −1081.40 | + | 902.809i | −0.0683876 | + | 0.0570933i | ||||
\(631\) | −33.4151 | −0.00210814 | −0.00105407 | − | 0.999999i | \(-0.500336\pi\) | ||||
−0.00105407 | + | 0.999999i | \(0.500336\pi\) | |||||||
\(632\) | 5148.63i | 0.324053i | ||||||||
\(633\) | 12101.0i | 0.759826i | ||||||||
\(634\) | 17918.3 | 1.12244 | ||||||||
\(635\) | −1035.47 | − | 1240.31i | −0.0647110 | − | 0.0775123i | ||||
\(636\) | 6667.60 | 0.415704 | ||||||||
\(637\) | 2686.91i | 0.167126i | ||||||||
\(638\) | − | 10802.1i | − | 0.670312i | ||||||
\(639\) | 9954.59 | 0.616271 | ||||||||
\(640\) | 917.139 | + | 1098.57i | 0.0566455 | + | 0.0678512i | ||||
\(641\) | −12210.4 | −0.752389 | −0.376195 | − | 0.926541i | \(-0.622768\pi\) | ||||
−0.376195 | + | 0.926541i | \(0.622768\pi\) | |||||||
\(642\) | 8406.27i | 0.516774i | ||||||||
\(643\) | 22026.2i | 1.35090i | 0.737406 | + | 0.675450i | \(0.236050\pi\) | ||||
−0.737406 | + | 0.675450i | \(0.763950\pi\) | |||||||
\(644\) | −5478.24 | −0.335207 | ||||||||
\(645\) | 7230.86 | − | 6036.67i | 0.441418 | − | 0.368517i | ||||
\(646\) | 24613.9 | 1.49910 | ||||||||
\(647\) | 27688.0i | 1.68242i | 0.540706 | + | 0.841212i | \(0.318157\pi\) | ||||
−0.540706 | + | 0.841212i | \(0.681843\pi\) | |||||||
\(648\) | 648.000i | 0.0392837i | ||||||||
\(649\) | −15164.9 | −0.917219 | ||||||||
\(650\) | −2447.96 | + | 13488.4i | −0.147718 | + | 0.813935i | ||||
\(651\) | −3355.96 | −0.202044 | ||||||||
\(652\) | 5559.32i | 0.333926i | ||||||||
\(653\) | 23235.6i | 1.39246i | 0.717816 | + | 0.696232i | \(0.245142\pi\) | ||||
−0.717816 | + | 0.696232i | \(0.754858\pi\) | |||||||
\(654\) | 970.564 | 0.0580306 | ||||||||
\(655\) | 6584.50 | − | 5497.06i | 0.392790 | − | 0.327921i | ||||
\(656\) | 1340.92 | 0.0798082 | ||||||||
\(657\) | − | 2518.27i | − | 0.149539i | ||||||
\(658\) | − | 7542.42i | − | 0.446860i | ||||||
\(659\) | −7260.41 | −0.429174 | −0.214587 | − | 0.976705i | \(-0.568841\pi\) | ||||
−0.214587 | + | 0.976705i | \(0.568841\pi\) | |||||||
\(660\) | −2636.25 | − | 3157.76i | −0.155479 | − | 0.186236i | ||||
\(661\) | 2442.72 | 0.143738 | 0.0718690 | − | 0.997414i | \(-0.477104\pi\) | ||||
0.0718690 | + | 0.997414i | \(0.477104\pi\) | |||||||
\(662\) | − | 7483.09i | − | 0.439333i | ||||||
\(663\) | 19162.5i | 1.12249i | ||||||||
\(664\) | −4626.93 | −0.270421 | ||||||||
\(665\) | 5299.06 | + | 6347.33i | 0.309006 | + | 0.370134i | ||||
\(666\) | −855.245 | −0.0497599 | ||||||||
\(667\) | − | 34465.2i | − | 2.00075i | ||||||
\(668\) | − | 864.321i | − | 0.0500623i | ||||||
\(669\) | 12002.5 | 0.693636 | ||||||||
\(670\) | 18218.9 | − | 15210.0i | 1.05053 | − | 0.877034i | ||||
\(671\) | 9588.92 | 0.551678 | ||||||||
\(672\) | 672.000i | 0.0385758i | ||||||||
\(673\) | − | 12046.6i | − | 0.689986i | −0.938605 | − | 0.344993i | \(-0.887881\pi\) | ||
0.938605 | − | 0.344993i | \(-0.112119\pi\) | |||||||
\(674\) | −1477.02 | −0.0844108 | ||||||||
\(675\) | −3320.75 | − | 602.673i | −0.189357 | − | 0.0343658i | ||||
\(676\) | 3239.44 | 0.184311 | ||||||||
\(677\) | 8308.82i | 0.471689i | 0.971791 | + | 0.235845i | \(0.0757857\pi\) | ||||
−0.971791 | + | 0.235845i | \(0.924214\pi\) | |||||||
\(678\) | 2295.31i | 0.130016i | ||||||||
\(679\) | −4540.44 | −0.256622 | ||||||||
\(680\) | −7998.02 | + | 6677.14i | −0.451044 | + | 0.376554i | ||||
\(681\) | 8266.80 | 0.465175 | ||||||||
\(682\) | − | 9799.59i | − | 0.550214i | ||||||
\(683\) | − | 18537.2i | − | 1.03852i | −0.854617 | − | 0.519259i | \(-0.826208\pi\) | ||
0.854617 | − | 0.519259i | \(-0.173792\pi\) | |||||||
\(684\) | 3803.45 | 0.212615 | ||||||||
\(685\) | 127.257 | + | 152.432i | 0.00709819 | + | 0.00850237i | ||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | − | 1001.91i | − | 0.0556410i | ||||||
\(688\) | − | 4493.36i | − | 0.248994i | ||||||
\(689\) | 30468.1 | 1.68467 | ||||||||
\(690\) | −8411.24 | − | 10075.2i | −0.464073 | − | 0.555877i | ||||
\(691\) | 28357.0 | 1.56114 | 0.780572 | − | 0.625066i | \(-0.214928\pi\) | ||||
0.780572 | + | 0.625066i | \(0.214928\pi\) | |||||||
\(692\) | 12512.4i | 0.687354i | ||||||||
\(693\) | − | 1931.62i | − | 0.105882i | ||||||
\(694\) | 6388.85 | 0.349449 | ||||||||
\(695\) | −10449.2 | + | 8723.46i | −0.570301 | + | 0.476115i | ||||
\(696\) | −4227.75 | −0.230248 | ||||||||
\(697\) | 9762.44i | 0.530529i | ||||||||
\(698\) | − | 15293.3i | − | 0.829310i | ||||||
\(699\) | −16555.4 | −0.895828 | ||||||||
\(700\) | −3443.75 | − | 624.994i | −0.185945 | − | 0.0337465i | ||||
\(701\) | −28949.5 | −1.55978 | −0.779892 | − | 0.625915i | \(-0.784726\pi\) | ||||
−0.779892 | + | 0.625915i | \(0.784726\pi\) | |||||||
\(702\) | 2961.08i | 0.159201i | ||||||||
\(703\) | 5019.89i | 0.269315i | ||||||||
\(704\) | −1962.28 | −0.105051 | ||||||||
\(705\) | 13871.4 | − | 11580.5i | 0.741033 | − | 0.618650i | ||||
\(706\) | 8019.69 | 0.427514 | ||||||||
\(707\) | − | 10261.7i | − | 0.545871i | ||||||
\(708\) | 5935.27i | 0.315058i | ||||||||
\(709\) | −15702.9 | −0.831783 | −0.415891 | − | 0.909414i | \(-0.636530\pi\) | ||||
−0.415891 | + | 0.909414i | \(0.636530\pi\) | |||||||
\(710\) | 15850.2 | + | 18985.8i | 0.837816 | + | 1.00355i | ||||
\(711\) | −5792.21 | −0.305520 | ||||||||
\(712\) | 939.818i | 0.0494679i | ||||||||
\(713\) | − | 31266.6i | − | 1.64228i | ||||||
\(714\) | −4892.43 | −0.256435 | ||||||||
\(715\) | −12046.6 | − | 14429.6i | −0.630092 | − | 0.754738i | ||||
\(716\) | 1799.48 | 0.0939241 | ||||||||
\(717\) | 11801.9i | 0.614715i | ||||||||
\(718\) | 7486.49i | 0.389127i | ||||||||
\(719\) | 19148.5 | 0.993210 | 0.496605 | − | 0.867977i | \(-0.334580\pi\) | ||||
0.496605 | + | 0.867977i | \(0.334580\pi\) | |||||||
\(720\) | −1235.89 | + | 1031.78i | −0.0639707 | + | 0.0534059i | ||||
\(721\) | 4771.69 | 0.246473 | ||||||||
\(722\) | − | 8606.48i | − | 0.443629i | ||||||
\(723\) | 11730.2i | 0.603391i | ||||||||
\(724\) | −10591.5 | −0.543686 | ||||||||
\(725\) | 3932.02 | − | 21665.6i | 0.201423 | − | 1.10985i | ||||
\(726\) | −2345.56 | −0.119906 | ||||||||
\(727\) | − | 18535.5i | − | 0.945591i | −0.881172 | − | 0.472795i | \(-0.843245\pi\) | ||
0.881172 | − | 0.472795i | \(-0.156755\pi\) | |||||||
\(728\) | 3070.75i | 0.156332i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 4802.94 | − | 4009.73i | 0.243513 | − | 0.203297i | ||||
\(731\) | 32713.4 | 1.65520 | ||||||||
\(732\) | − | 3752.93i | − | 0.189498i | ||||||
\(733\) | 13310.0i | 0.670690i | 0.942095 | + | 0.335345i | \(0.108853\pi\) | ||||
−0.942095 | + | 0.335345i | \(0.891147\pi\) | |||||||
\(734\) | −7773.27 | −0.390895 | ||||||||
\(735\) | −1053.28 | − | 1261.64i | −0.0528581 | − | 0.0633146i | ||||
\(736\) | −6260.85 | −0.313557 | ||||||||
\(737\) | 32542.7i | 1.62650i | ||||||||
\(738\) | 1508.54i | 0.0752439i | ||||||||
\(739\) | −23801.7 | −1.18479 | −0.592394 | − | 0.805648i | \(-0.701817\pi\) | ||||
−0.592394 | + | 0.805648i | \(0.701817\pi\) | |||||||
\(740\) | −1361.77 | − | 1631.16i | −0.0676482 | − | 0.0810305i | ||||
\(741\) | 17380.2 | 0.861641 | ||||||||
\(742\) | 7778.87i | 0.384867i | ||||||||
\(743\) | 4631.89i | 0.228705i | 0.993440 | + | 0.114352i | \(0.0364793\pi\) | ||||
−0.993440 | + | 0.114352i | \(0.963521\pi\) | |||||||
\(744\) | −3835.38 | −0.188995 | ||||||||
\(745\) | −29915.8 | + | 24975.2i | −1.47118 | + | 1.22821i | ||||
\(746\) | 11960.7 | 0.587016 | ||||||||
\(747\) | − | 5205.30i | − | 0.254956i | ||||||
\(748\) | − | 14286.2i | − | 0.698334i | ||||||
\(749\) | −9807.32 | −0.478440 | ||||||||
\(750\) | −4138.05 | − | 7293.08i | −0.201467 | − | 0.355074i | ||||
\(751\) | 39632.9 | 1.92573 | 0.962867 | − | 0.269976i | \(-0.0870159\pi\) | ||||
0.962867 | + | 0.269976i | \(0.0870159\pi\) | |||||||
\(752\) | − | 8619.90i | − | 0.417999i | ||||||
\(753\) | − | 5851.60i | − | 0.283193i | ||||||
\(754\) | −19319.0 | −0.933098 | ||||||||
\(755\) | 5710.79 | − | 4767.65i | 0.275281 | − | 0.229818i | ||||
\(756\) | −756.000 | −0.0363696 | ||||||||
\(757\) | − | 9018.43i | − | 0.432999i | −0.976283 | − | 0.216500i | \(-0.930536\pi\) | ||
0.976283 | − | 0.216500i | \(-0.0694640\pi\) | |||||||
\(758\) | 6910.33i | 0.331127i | ||||||||
\(759\) | 17996.4 | 0.860642 | ||||||||
\(760\) | 6056.07 | + | 7254.10i | 0.289048 | + | 0.346229i | ||||
\(761\) | −8028.09 | −0.382415 | −0.191208 | − | 0.981550i | \(-0.561240\pi\) | ||||
−0.191208 | + | 0.981550i | \(0.561240\pi\) | |||||||
\(762\) | − | 867.091i | − | 0.0412223i | ||||||
\(763\) | 1132.32i | 0.0537259i | ||||||||
\(764\) | 11236.2 | 0.532081 | ||||||||
\(765\) | −7511.78 | − | 8997.78i | −0.355018 | − | 0.425249i | ||||
\(766\) | −23719.8 | −1.11884 | ||||||||
\(767\) | 27121.6i | 1.27680i | ||||||||
\(768\) | 768.000i | 0.0360844i | ||||||||
\(769\) | 2437.28 | 0.114292 | 0.0571461 | − | 0.998366i | \(-0.481800\pi\) | ||||
0.0571461 | + | 0.998366i | \(0.481800\pi\) | |||||||
\(770\) | 3684.06 | − | 3075.63i | 0.172421 | − | 0.143945i | ||||
\(771\) | −13443.9 | −0.627979 | ||||||||
\(772\) | 1370.48i | 0.0638923i | ||||||||
\(773\) | − | 20074.6i | − | 0.934065i | −0.884240 | − | 0.467032i | \(-0.845323\pi\) | ||
0.884240 | − | 0.467032i | \(-0.154677\pi\) | |||||||
\(774\) | 5055.03 | 0.234753 | ||||||||
\(775\) | 3567.10 | − | 19654.9i | 0.165334 | − | 0.910999i | ||||
\(776\) | −5189.08 | −0.240048 | ||||||||
\(777\) | − | 997.786i | − | 0.0460687i | ||||||
\(778\) | − | 22854.8i | − | 1.05319i | ||||||
\(779\) | 8854.40 | 0.407242 | ||||||||
\(780\) | −5647.49 | + | 4714.80i | −0.259247 | + | 0.216432i | ||||
\(781\) | −33912.6 | −1.55376 | ||||||||
\(782\) | − | 45581.5i | − | 2.08439i | ||||||
\(783\) | − | 4756.21i | − | 0.217079i | ||||||
\(784\) | −784.000 | −0.0357143 | ||||||||
\(785\) | −13652.4 | − | 16353.1i | −0.620733 | − | 0.743527i | ||||
\(786\) | 4603.16 | 0.208892 | ||||||||
\(787\) | − | 8697.12i | − | 0.393925i | −0.980411 | − | 0.196962i | \(-0.936892\pi\) | ||
0.980411 | − | 0.196962i | \(-0.0631077\pi\) | |||||||
\(788\) | − | 14612.0i | − | 0.660572i | ||||||
\(789\) | −12800.3 | −0.577572 | ||||||||
\(790\) | −9222.68 | − | 11047.1i | −0.415352 | − | 0.497518i | ||||
\(791\) | −2677.86 | −0.120371 | ||||||||
\(792\) | − | 2207.56i | − | 0.0990434i | ||||||
\(793\) | − | 17149.3i | − | 0.767955i | ||||||
\(794\) | 1588.75 | 0.0710111 | ||||||||
\(795\) | −14306.3 | + | 11943.6i | −0.638229 | + | 0.532825i | ||||
\(796\) | 20099.1 | 0.894968 | ||||||||
\(797\) | 35253.0i | 1.56678i | 0.621528 | + | 0.783392i | \(0.286512\pi\) | ||||
−0.621528 | + | 0.783392i | \(0.713488\pi\) | |||||||
\(798\) | 4437.36i | 0.196843i | ||||||||
\(799\) | 62756.3 | 2.77867 | ||||||||
\(800\) | −3935.71 | − | 714.279i | −0.173935 | − | 0.0315670i | ||||
\(801\) | −1057.30 | −0.0466388 | ||||||||
\(802\) | 9027.64i | 0.397477i | ||||||||
\(803\) | 8579.07i | 0.377022i | ||||||||
\(804\) | 12736.6 | 0.558690 | ||||||||
\(805\) | 11754.4 | − | 9813.11i | 0.514642 | − | 0.429648i | ||||
\(806\) | −17526.0 | −0.765917 | ||||||||
\(807\) | 1501.14i | 0.0654804i | ||||||||
\(808\) | − | 11727.6i | − | 0.510615i | ||||||
\(809\) | 31944.9 | 1.38828 | 0.694142 | − | 0.719838i | \(-0.255784\pi\) | ||||
0.694142 | + | 0.719838i | \(0.255784\pi\) | |||||||
\(810\) | −1160.75 | − | 1390.38i | −0.0503516 | − | 0.0603122i | ||||
\(811\) | −1254.44 | −0.0543150 | −0.0271575 | − | 0.999631i | \(-0.508646\pi\) | ||||
−0.0271575 | + | 0.999631i | \(0.508646\pi\) | |||||||
\(812\) | − | 4932.37i | − | 0.213168i | ||||||
\(813\) | − | 3401.28i | − | 0.146726i | ||||||
\(814\) | 2913.59 | 0.125456 | ||||||||
\(815\) | −9958.33 | − | 11928.3i | −0.428006 | − | 0.512675i | ||||
\(816\) | −5591.35 | −0.239873 | ||||||||
\(817\) | − | 29670.6i | − | 1.27056i | ||||||
\(818\) | 9342.59i | 0.399335i | ||||||||
\(819\) | −3454.60 | −0.147391 | ||||||||
\(820\) | −2877.14 | + | 2401.98i | −0.122529 | + | 0.102293i | ||||
\(821\) | 10557.8 | 0.448807 | 0.224404 | − | 0.974496i | \(-0.427957\pi\) | ||||
0.224404 | + | 0.974496i | \(0.427957\pi\) | |||||||
\(822\) | 106.564i | 0.00452170i | ||||||||
\(823\) | − | 3302.12i | − | 0.139860i | −0.997552 | − | 0.0699300i | \(-0.977722\pi\) | ||
0.997552 | − | 0.0699300i | \(-0.0222776\pi\) | |||||||
\(824\) | 5453.36 | 0.230554 | ||||||||
\(825\) | 11312.9 | + | 2053.15i | 0.477413 | + | 0.0866441i | ||||
\(826\) | −6924.48 | −0.291687 | ||||||||
\(827\) | 14906.3i | 0.626773i | 0.949626 | + | 0.313387i | \(0.101464\pi\) | ||||
−0.949626 | + | 0.313387i | \(0.898536\pi\) | |||||||
\(828\) | − | 7043.45i | − | 0.295624i | ||||||
\(829\) | 44271.0 | 1.85476 | 0.927380 | − | 0.374121i | \(-0.122055\pi\) | ||||
0.927380 | + | 0.374121i | \(0.122055\pi\) | |||||||
\(830\) | 9927.75 | − | 8288.17i | 0.415177 | − | 0.346610i | ||||
\(831\) | −6947.70 | −0.290028 | ||||||||
\(832\) | 3509.43i | 0.146235i | ||||||||
\(833\) | − | 5707.83i | − | 0.237413i | ||||||
\(834\) | −7304.91 | −0.303295 | ||||||||
\(835\) | 1548.25 | + | 1854.53i | 0.0641669 | + | 0.0768605i | ||||
\(836\) | −12957.4 | −0.536052 | ||||||||
\(837\) | − | 4314.80i | − | 0.178186i | ||||||
\(838\) | 23633.8i | 0.974242i | ||||||||
\(839\) | −20275.1 | −0.834294 | −0.417147 | − | 0.908839i | \(-0.636970\pi\) | ||||
−0.417147 | + | 0.908839i | \(0.636970\pi\) | |||||||
\(840\) | −1203.75 | − | 1441.87i | −0.0494442 | − | 0.0592254i | ||||
\(841\) | 6641.96 | 0.272334 | ||||||||
\(842\) | 29985.4i | 1.22728i | ||||||||
\(843\) | − | 11377.3i | − | 0.464835i | ||||||
\(844\) | −16134.6 | −0.658029 | ||||||||
\(845\) | −6950.69 | + | 5802.77i | −0.282972 | + | 0.236238i | ||||
\(846\) | 9697.39 | 0.394094 | ||||||||
\(847\) | − | 2736.49i | − | 0.111012i | ||||||
\(848\) | 8890.13i | 0.360010i | ||||||||
\(849\) | 13125.9 | 0.530600 | ||||||||
\(850\) | 5200.23 | − | 28653.5i | 0.209843 | − | 1.15624i | ||||
\(851\) | 9296.12 | 0.374461 | ||||||||
\(852\) | 13272.8i | 0.533707i | ||||||||
\(853\) | − | 5641.20i | − | 0.226437i | −0.993570 | − | 0.113219i | \(-0.963884\pi\) | ||
0.993570 | − | 0.113219i | \(-0.0361161\pi\) | |||||||
\(854\) | 4378.42 | 0.175441 | ||||||||
\(855\) | −8160.86 | + | 6813.08i | −0.326427 | + | 0.272518i | ||||
\(856\) | −11208.4 | −0.447540 | ||||||||
\(857\) | − | 10407.2i | − | 0.414823i | −0.978254 | − | 0.207412i | \(-0.933496\pi\) | ||
0.978254 | − | 0.207412i | \(-0.0665039\pi\) | |||||||
\(858\) | − | 10087.6i | − | 0.401382i | ||||||
\(859\) | −32492.8 | −1.29062 | −0.645308 | − | 0.763923i | \(-0.723271\pi\) | ||||
−0.645308 | + | 0.763923i | \(0.723271\pi\) | |||||||
\(860\) | 8048.90 | + | 9641.15i | 0.319145 | + | 0.382279i | ||||
\(861\) | −1759.96 | −0.0696623 | ||||||||
\(862\) | 16137.0i | 0.637622i | ||||||||
\(863\) | 13052.9i | 0.514862i | 0.966297 | + | 0.257431i | \(0.0828761\pi\) | ||||
−0.966297 | + | 0.257431i | \(0.917124\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | −22413.3 | − | 26847.1i | −0.881010 | − | 1.05529i | ||||
\(866\) | 24798.1 | 0.973066 | ||||||||
\(867\) | − | 25968.2i | − | 1.01722i | ||||||
\(868\) | − | 4474.61i | − | 0.174975i | ||||||
\(869\) | 19732.5 | 0.770287 | ||||||||
\(870\) | 9071.24 | − | 7573.11i | 0.353499 | − | 0.295118i | ||||
\(871\) | 58201.0 | 2.26414 | ||||||||
\(872\) | 1294.08i | 0.0502560i | ||||||||
\(873\) | − | 5837.71i | − | 0.226319i | ||||||
\(874\) | −41341.8 | −1.60001 | ||||||||
\(875\) | 8508.60 | − | 4827.72i | 0.328735 | − | 0.186522i | ||||
\(876\) | 3357.69 | 0.129504 | ||||||||
\(877\) | 40123.2i | 1.54488i | 0.635085 | + | 0.772442i | \(0.280965\pi\) | ||||
−0.635085 | + | 0.772442i | \(0.719035\pi\) | |||||||
\(878\) | 8221.41i | 0.316013i | ||||||||
\(879\) | 5109.67 | 0.196069 | ||||||||
\(880\) | 4210.35 | − | 3515.01i | 0.161285 | − | 0.134649i | ||||
\(881\) | 24173.9 | 0.924450 | 0.462225 | − | 0.886763i | \(-0.347051\pi\) | ||||
0.462225 | + | 0.886763i | \(0.347051\pi\) | |||||||
\(882\) | − | 882.000i | − | 0.0336718i | ||||||
\(883\) | 17236.7i | 0.656921i | 0.944518 | + | 0.328460i | \(0.106530\pi\) | ||||
−0.944518 | + | 0.328460i | \(0.893470\pi\) | |||||||
\(884\) | −25550.0 | −0.972105 | ||||||||
\(885\) | −10631.8 | − | 12735.0i | −0.403823 | − | 0.483708i | ||||
\(886\) | 5469.79 | 0.207406 | ||||||||
\(887\) | 20394.9i | 0.772033i | 0.922492 | + | 0.386017i | \(0.126149\pi\) | ||||
−0.922492 | + | 0.386017i | \(0.873851\pi\) | |||||||
\(888\) | − | 1140.33i | − | 0.0430933i | ||||||
\(889\) | 1011.61 | 0.0381644 | ||||||||
\(890\) | −1683.48 | − | 2016.52i | −0.0634051 | − | 0.0759480i | ||||
\(891\) | 2483.51 | 0.0933790 | ||||||||
\(892\) | 16003.3i | 0.600707i | ||||||||
\(893\) | − | 56919.1i | − | 2.13295i | ||||||
\(894\) | −20913.9 | −0.782398 | ||||||||
\(895\) | −3861.04 | + | 3223.38i | −0.144202 | + | 0.120386i | ||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | − | 32185.6i | − | 1.19804i | ||||||
\(898\) | − | 11886.7i | − | 0.441719i | ||||||
\(899\) | 28151.1 | 1.04437 | ||||||||
\(900\) | 803.564 | − | 4427.67i | 0.0297616 | − | 0.163988i | ||||
\(901\) | −64723.7 | −2.39318 | ||||||||
\(902\) | − | 5139.18i | − | 0.189707i | ||||||
\(903\) | 5897.53i | 0.217340i | ||||||||
\(904\) | −3060.41 | −0.112597 | ||||||||
\(905\) | 22725.5 | − | 18972.4i | 0.834720 | − | 0.696865i | ||||
\(906\) | 3992.36 | 0.146399 | ||||||||
\(907\) | 34733.2i | 1.27155i | 0.771875 | + | 0.635775i | \(0.219319\pi\) | ||||
−0.771875 | + | 0.635775i | \(0.780681\pi\) | |||||||
\(908\) | 11022.4i | 0.402854i | ||||||||
\(909\) | 13193.6 | 0.481413 | ||||||||
\(910\) | −5500.60 | − | 6588.74i | −0.200377 | − | 0.240016i | ||||
\(911\) | 26713.5 | 0.971524 | 0.485762 | − | 0.874091i | \(-0.338542\pi\) | ||||
0.485762 | + | 0.874091i | \(0.338542\pi\) | |||||||
\(912\) | 5071.27i | 0.184130i | ||||||||
\(913\) | 17733.1i | 0.642803i | ||||||||
\(914\) | −574.624 | −0.0207953 | ||||||||
\(915\) | 6722.57 | + | 8052.45i | 0.242887 | + | 0.290935i | ||||
\(916\) | 1335.88 | 0.0481865 | ||||||||
\(917\) | 5370.36i | 0.193397i | ||||||||
\(918\) | − | 6290.26i | − | 0.226154i | ||||||
\(919\) | −38603.5 | −1.38565 | −0.692825 | − | 0.721106i | \(-0.743634\pi\) | ||||
−0.692825 | + | 0.721106i | \(0.743634\pi\) | |||||||
\(920\) | 13433.6 | − | 11215.0i | 0.481403 | − | 0.401899i | ||||
\(921\) | 12853.4 | 0.459864 | ||||||||
\(922\) | 24368.4i | 0.870422i | ||||||||
\(923\) | 60650.9i | 2.16289i | ||||||||
\(924\) | 2575.49 | 0.0916964 | ||||||||
\(925\) | 5843.75 | + | 1060.56i | 0.207720 | + | 0.0376984i | ||||
\(926\) | 13801.4 | 0.489786 | ||||||||
\(927\) | 6135.03i | 0.217369i | ||||||||
\(928\) | − | 5636.99i | − | 0.199400i | ||||||
\(929\) | 54066.0 | 1.90942 | 0.954709 | − | 0.297541i | \(-0.0961665\pi\) | ||||
0.954709 | + | 0.297541i | \(0.0961665\pi\) | |||||||
\(930\) | 8229.36 | − | 6870.27i | 0.290163 | − | 0.242242i | ||||
\(931\) | −5176.92 | −0.182242 | ||||||||
\(932\) | − | 22073.9i | − | 0.775810i | ||||||
\(933\) | 7912.42i | 0.277643i | ||||||||
\(934\) | −8589.41 | −0.300915 | ||||||||
\(935\) | 25590.6 | + | 30653.0i | 0.895084 | + | 1.07215i | ||||
\(936\) | −3948.11 | −0.137872 | ||||||||
\(937\) | 1515.57i | 0.0528403i | 0.999651 | + | 0.0264202i | \(0.00841077\pi\) | ||||
−0.999651 | + | 0.0264202i | \(0.991589\pi\) | |||||||
\(938\) | 14859.4i | 0.517246i | ||||||||
\(939\) | −19832.8 | −0.689263 | ||||||||
\(940\) | 15440.7 | + | 18495.2i | 0.535767 | + | 0.641753i | ||||
\(941\) | −37134.9 | −1.28647 | −0.643233 | − | 0.765671i | \(-0.722407\pi\) | ||||
−0.643233 | + | 0.765671i | \(0.722407\pi\) | |||||||
\(942\) | − | 11432.3i | − | 0.395420i | ||||||
\(943\) | − | 16397.1i | − | 0.566238i | ||||||
\(944\) | −7913.70 | −0.272848 | ||||||||
\(945\) | 1622.11 | − | 1354.21i | 0.0558382 | − | 0.0466165i | ||||
\(946\) | −17221.1 | −0.591868 | ||||||||
\(947\) | − | 18402.2i | − | 0.631460i | −0.948849 | − | 0.315730i | \(-0.897751\pi\) | ||
0.948849 | − | 0.315730i | \(-0.102249\pi\) | |||||||
\(948\) | − | 7722.95i | − | 0.264588i | ||||||
\(949\) | 15343.2 | 0.524828 | ||||||||
\(950\) | −25988.4 | − | 4716.54i | −0.887551 | − | 0.161079i | ||||
\(951\) | −26877.5 | −0.916468 | ||||||||
\(952\) | − | 6523.24i | − | 0.222079i | ||||||
\(953\) | 22868.7i | 0.777325i | 0.921380 | + | 0.388663i | \(0.127063\pi\) | ||||
−0.921380 | + | 0.388663i | \(0.872937\pi\) | |||||||
\(954\) | −10001.4 | −0.339421 | ||||||||
\(955\) | −24108.8 | + | 20127.2i | −0.816903 | + | 0.681991i | ||||
\(956\) | −15735.9 | −0.532359 | ||||||||
\(957\) | 16203.2i | 0.547308i | ||||||||
\(958\) | − | 13136.8i | − | 0.443040i | ||||||
\(959\) | −124.324 | −0.00418628 | ||||||||
\(960\) | −1375.71 | − | 1647.85i | −0.0462509 | − | 0.0554003i | ||||
\(961\) | −4252.54 | −0.142746 | ||||||||
\(962\) | − | 5210.81i | − | 0.174639i | ||||||
\(963\) | − | 12609.4i | − | 0.421944i | ||||||
\(964\) | −15640.3 | −0.522552 | ||||||||
\(965\) | −2454.93 | − | 2940.57i | −0.0818934 | − | 0.0980937i | ||||
\(966\) | 8217.36 | 0.273695 | ||||||||
\(967\) | 40859.1i | 1.35878i | 0.733777 | + | 0.679391i | \(0.237756\pi\) | ||||
−0.733777 | + | 0.679391i | \(0.762244\pi\) | |||||||
\(968\) | − | 3127.42i | − | 0.103842i | ||||||
\(969\) | −36920.9 | −1.22401 | ||||||||
\(970\) | 11133.9 | − | 9295.13i | 0.368545 | − | 0.307679i | ||||
\(971\) | 45438.0 | 1.50172 | 0.750862 | − | 0.660460i | \(-0.229639\pi\) | ||||
0.750862 | + | 0.660460i | \(0.229639\pi\) | |||||||
\(972\) | − | 972.000i | − | 0.0320750i | ||||||
\(973\) | − | 8522.39i | − | 0.280797i | ||||||
\(974\) | −7665.64 | −0.252179 | ||||||||
\(975\) | 3671.94 | − | 20232.6i | 0.120612 | − | 0.664575i | ||||
\(976\) | 5003.90 | 0.164110 | ||||||||
\(977\) | 28110.1i | 0.920493i | 0.887791 | + | 0.460247i | \(0.152239\pi\) | ||||
−0.887791 | + | 0.460247i | \(0.847761\pi\) | |||||||
\(978\) | − | 8338.97i | − | 0.272649i | ||||||
\(979\) | 3601.92 | 0.117587 | ||||||||
\(980\) | 1682.18 | − | 1404.37i | 0.0548321 | − | 0.0457765i | ||||
\(981\) | −1455.85 | −0.0473818 | ||||||||
\(982\) | 359.558i | 0.0116843i | ||||||||
\(983\) | − | 22370.7i | − | 0.725853i | −0.931818 | − | 0.362927i | \(-0.881778\pi\) | ||
0.931818 | − | 0.362927i | \(-0.118222\pi\) | |||||||
\(984\) | −2011.38 | −0.0651631 | ||||||||
\(985\) | 26174.3 | + | 31352.1i | 0.846682 | + | 1.01417i | ||||
\(986\) | 41039.6 | 1.32552 | ||||||||
\(987\) | 11313.6i | 0.364860i | ||||||||
\(988\) | 23173.5i | 0.746203i | ||||||||
\(989\) | −54945.8 | −1.76661 | ||||||||
\(990\) | 3954.38 | + | 4736.65i | 0.126948 | + | 0.152061i | ||||
\(991\) | 3410.74 | 0.109330 | 0.0546648 | − | 0.998505i | \(-0.482591\pi\) | ||||
0.0546648 | + | 0.998505i | \(0.482591\pi\) | |||||||
\(992\) | − | 5113.84i | − | 0.163674i | ||||||
\(993\) | 11224.6i | 0.358714i | ||||||||
\(994\) | −15484.9 | −0.494116 | ||||||||
\(995\) | −43125.6 | + | 36003.3i | −1.37404 | + | 1.14712i | ||||
\(996\) | 6940.40 | 0.220798 | ||||||||
\(997\) | 45250.9i | 1.43742i | 0.695309 | + | 0.718711i | \(0.255267\pi\) | ||||
−0.695309 | + | 0.718711i | \(0.744733\pi\) | |||||||
\(998\) | − | 19985.6i | − | 0.633900i | ||||||
\(999\) | 1282.87 | 0.0406288 |
(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 | 210.4.g.b.169.2 | ✓ | 4 | |
3.2 | odd | 2 | 630.4.g.d.379.3 | 4 | |||
5.2 | odd | 4 | 1050.4.a.bh.1.2 | 2 | |||
5.3 | odd | 4 | 1050.4.a.ba.1.2 | 2 | |||
5.4 | even | 2 | inner | 210.4.g.b.169.4 | yes | 4 | |
15.14 | odd | 2 | 630.4.g.d.379.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.4.g.b.169.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
210.4.g.b.169.4 | yes | 4 | 5.4 | even | 2 | inner | |
630.4.g.d.379.1 | 4 | 15.14 | odd | 2 | |||
630.4.g.d.379.3 | 4 | 3.2 | odd | 2 | |||
1050.4.a.ba.1.2 | 2 | 5.3 | odd | 4 | |||
1050.4.a.bh.1.2 | 2 | 5.2 | odd | 4 |