Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,2,Mod(137,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.137");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.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: | \(2.20387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.14453810176.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 15x^{4} - 30x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 137.8 | ||
Root | \(1.06789 - 0.545948i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 276.137 |
Dual form | 276.2.g.a.137.6 |
$q$-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 \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(139\) | \(185\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.28078 | + | 1.16602i | 0.739457 | + | 0.673204i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.936426 | 0.418783 | 0.209391 | − | 0.977832i | \(-0.432852\pi\) | ||||
0.209391 | + | 0.977832i | \(0.432852\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.88884i | − | 1.46984i | −0.678151 | − | 0.734922i | \(-0.737219\pi\) | ||
0.678151 | − | 0.734922i | \(-0.262781\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.280776 | + | 2.98683i | 0.0935921 | + | 0.995611i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.27156 | 1.28792 | 0.643962 | − | 0.765058i | \(-0.277290\pi\) | ||||
0.643962 | + | 0.765058i | \(0.277290\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.56155 | 0.710447 | 0.355223 | − | 0.934781i | \(-0.384405\pi\) | ||||
0.355223 | + | 0.934781i | \(0.384405\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.19935 | + | 1.09190i | 0.309672 | + | 0.281926i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.60669 | −1.84489 | −0.922447 | − | 0.386124i | \(-0.873814\pi\) | ||||
−0.922447 | + | 0.386124i | \(0.873814\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.07263i | 1.39316i | 0.717480 | + | 0.696579i | \(0.245295\pi\) | ||||
−0.717480 | + | 0.696579i | \(0.754705\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.53448 | − | 4.98074i | 0.989506 | − | 1.08689i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.39871 | + | 4.15286i | −0.500165 | + | 0.865930i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.12311 | −0.824621 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.12311 | + | 4.15286i | −0.601042 | + | 0.799217i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.97366i | − | 1.10928i | −0.832090 | − | 0.554641i | \(-0.812856\pi\) | ||
0.832090 | − | 0.554641i | \(-0.187144\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.68466 | 0.661784 | 0.330892 | − | 0.943669i | \(-0.392650\pi\) | ||||
0.330892 | + | 0.943669i | \(0.392650\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.47091 | + | 4.98074i | 0.952363 | + | 0.867035i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 3.64162i | − | 0.615545i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.18379i | − | 0.359013i | −0.983757 | − | 0.179507i | \(-0.942550\pi\) | ||
0.983757 | − | 0.179507i | \(-0.0574501\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.28078 | + | 2.98683i | 0.525345 | + | 0.478276i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.6378i | − | 1.66134i | −0.556766 | − | 0.830669i | \(-0.687958\pi\) | ||
0.556766 | − | 0.830669i | \(-0.312042\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.07263i | − | 0.926068i | −0.886340 | − | 0.463034i | \(-0.846761\pi\) | ||
0.886340 | − | 0.463034i | \(-0.153239\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.262926 | + | 2.79695i | 0.0391948 | + | 0.416944i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.30957i | 0.191020i | 0.995428 | + | 0.0955101i | \(0.0304482\pi\) | ||||
−0.995428 | + | 0.0955101i | \(0.969552\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.12311 | −1.16044 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.74247 | − | 8.86958i | −1.36422 | − | 1.24199i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.13254 | −1.11709 | −0.558545 | − | 0.829474i | \(-0.688640\pi\) | ||||
−0.558545 | + | 0.829474i | \(0.688640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.08084 | + | 7.77769i | −0.937880 | + | 1.03018i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 4.66410i | − | 0.607214i | −0.952797 | − | 0.303607i | \(-0.901809\pi\) | ||
0.952797 | − | 0.303607i | \(-0.0981909\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.77769i | 0.995831i | 0.867226 | + | 0.497915i | \(0.165901\pi\) | ||||
−0.867226 | + | 0.497915i | \(0.834099\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.6153 | − | 1.09190i | 1.46339 | − | 0.137566i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.39871 | 0.297523 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6665i | 1.42529i | 0.701523 | + | 0.712647i | \(0.252504\pi\) | ||||
−0.701523 | + | 0.712647i | \(0.747496\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.91453 | + | 2.52193i | −0.952798 | + | 0.303605i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.33205i | 0.276763i | 0.990379 | + | 0.138382i | \(0.0441900\pi\) | ||||
−0.990379 | + | 0.138382i | \(0.955810\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.68466 | −0.665339 | −0.332669 | − | 0.943043i | \(-0.607949\pi\) | ||||
−0.332669 | + | 0.943043i | \(0.607949\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.28078 | − | 4.80764i | −0.609772 | − | 0.555138i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 16.6114i | − | 1.89305i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.70505i | − | 0.191833i | −0.995389 | − | 0.0959167i | \(-0.969422\pi\) | ||
0.995389 | − | 0.0959167i | \(-0.0305782\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.84233 | + | 1.67726i | −0.982481 | + | 0.186363i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.525853 | 0.0577199 | 0.0288599 | − | 0.999583i | \(-0.490812\pi\) | ||||
0.0288599 | + | 0.999583i | \(0.490812\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.12311 | −0.772609 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.96543 | − | 7.65093i | 0.746773 | − | 0.820266i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.46228 | 0.155001 | 0.0775006 | − | 0.996992i | \(-0.475306\pi\) | ||||
0.0775006 | + | 0.996992i | \(0.475306\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 9.96148i | − | 1.04425i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.71922 | + | 4.29640i | 0.489361 | + | 0.445516i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.68658i | 0.583430i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.96148i | 1.01143i | 0.862699 | + | 0.505717i | \(0.168772\pi\) | ||||
−0.862699 | + | 0.505717i | \(0.831228\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.19935 | + | 12.7584i | 0.120539 | + | 1.28227i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.28323i | 0.724709i | 0.932040 | + | 0.362354i | \(0.118027\pi\) | ||||
−0.932040 | + | 0.362354i | \(0.881973\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.6665i | − | 1.14954i | −0.818316 | − | 0.574769i | \(-0.805092\pi\) | ||
0.818316 | − | 0.574769i | \(-0.194908\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.24621 | − | 4.66410i | 0.414388 | − | 0.455169i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.87285 | 0.181056 | 0.0905278 | − | 0.995894i | \(-0.471145\pi\) | ||||
0.0905278 | + | 0.995894i | \(0.471145\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.77769i | − | 0.744967i | −0.928039 | − | 0.372484i | \(-0.878506\pi\) | ||
0.928039 | − | 0.372484i | \(-0.121494\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.54635 | − | 2.79695i | 0.241689 | − | 0.265475i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.73384 | −0.539394 | −0.269697 | − | 0.962945i | \(-0.586924\pi\) | ||||
−0.269697 | + | 0.962945i | \(0.586924\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.24621 | + | 3.88884i | −0.209460 | + | 0.362637i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.719224 | + | 7.65093i | 0.0664922 | + | 0.707329i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 29.5812i | 2.71171i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.24621 | 0.658746 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.4039 | − | 13.6246i | 1.11842 | − | 1.22849i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.54312 | −0.764120 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.68466 | −0.681903 | −0.340952 | − | 0.940081i | \(-0.610749\pi\) | ||||
−0.340952 | + | 0.940081i | \(0.610749\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.08084 | − | 7.77769i | 0.623433 | − | 0.684787i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.61528i | 0.840091i | 0.907503 | + | 0.420045i | \(0.137986\pi\) | ||||
−0.907503 | + | 0.420045i | \(0.862014\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.6155 | 2.04773 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.92456 | + | 3.88884i | −0.251706 | + | 0.334698i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.8782 | 1.01483 | 0.507414 | − | 0.861703i | \(-0.330602\pi\) | ||||
0.507414 | + | 0.861703i | \(0.330602\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.9309 | 1.18160 | 0.590800 | − | 0.806818i | \(-0.298812\pi\) | ||||
0.590800 | + | 0.806818i | \(0.298812\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.52699 | + | 1.67726i | −0.128596 | + | 0.141251i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.9418 | 0.915001 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 5.59390i | − | 0.464548i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.4039 | − | 9.47174i | −0.858098 | − | 0.781216i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.95369 | 0.733515 | 0.366757 | − | 0.930317i | \(-0.380468\pi\) | ||||
0.366757 | + | 0.930317i | \(0.380468\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5616 | 1.18500 | 0.592501 | − | 0.805570i | \(-0.298141\pi\) | ||||
0.592501 | + | 0.805570i | \(0.298141\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.13578 | − | 22.7199i | −0.172668 | − | 1.83680i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.45041 | 0.277144 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.1453i | − | 0.969298i | −0.874709 | − | 0.484649i | \(-0.838947\pi\) | ||
0.874709 | − | 0.484649i | \(-0.161053\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.4160 | − | 9.48274i | −0.826040 | − | 0.752030i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.1498 | + | 9.32819i | 1.27278 | + | 0.735164i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.43845 | −0.112668 | −0.0563339 | − | 0.998412i | \(-0.517941\pi\) | ||||
−0.0563339 | + | 0.998412i | \(0.517941\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.12311 | + | 4.66410i | 0.398833 | + | 0.363099i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.02248i | 0.0791219i | 0.999217 | + | 0.0395609i | \(0.0125959\pi\) | ||||
−0.999217 | + | 0.0395609i | \(0.987404\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.43845 | −0.495265 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.1379 | + | 1.70505i | −1.38704 | + | 0.130389i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.6564i | 1.41842i | 0.704998 | + | 0.709209i | \(0.250948\pi\) | ||||
−0.704998 | + | 0.709209i | \(0.749052\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.0341i | 1.21207i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.43845 | − | 5.97366i | 0.408779 | − | 0.449008i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 8.01862i | − | 0.599340i | −0.954043 | − | 0.299670i | \(-0.903123\pi\) | ||
0.954043 | − | 0.299670i | \(-0.0968766\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.1067i | 1.64318i | 0.570078 | + | 0.821591i | \(0.306913\pi\) | ||||
−0.570078 | + | 0.821591i | \(0.693087\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.06897 | + | 9.96148i | −0.670398 | + | 0.736374i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2.04496i | − | 0.150348i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −32.4924 | −2.37608 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.1498 | + | 12.1453i | 1.17473 | + | 0.883438i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.5366 | 1.48598 | 0.742990 | − | 0.669303i | \(-0.233407\pi\) | ||||
0.742990 | + | 0.669303i | \(0.233407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.5616 | 1.33609 | 0.668045 | − | 0.744121i | \(-0.267131\pi\) | ||||
0.668045 | + | 0.744121i | \(0.267131\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.07221 | + | 2.79695i | 0.220005 | + | 0.200294i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 19.9660i | − | 1.42252i | −0.702932 | − | 0.711258i | \(-0.748126\pi\) | ||
0.702932 | − | 0.711258i | \(-0.251874\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.88884i | − | 0.275673i | −0.990455 | − | 0.137836i | \(-0.955985\pi\) | ||
0.990455 | − | 0.137836i | \(-0.0440148\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.6035 | + | 14.9422i | −0.959514 | + | 1.05394i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.2306 | −1.63047 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 9.96148i | − | 0.695740i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.0774 | − | 5.99851i | −0.908941 | − | 0.416925i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.9396i | 1.79428i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.4924 | −1.68613 | −0.843064 | − | 0.537813i | \(-0.819251\pi\) | ||||
−0.843064 | + | 0.537813i | \(0.819251\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.71922 | + | 2.98683i | −0.186318 | + | 0.204654i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 5.68658i | − | 0.387821i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 14.3291i | − | 0.972720i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.28078 | − | 6.62845i | −0.491989 | − | 0.447909i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.4849 | −1.31070 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.24621 | 0.150417 | 0.0752087 | − | 0.997168i | \(-0.476038\pi\) | ||||
0.0752087 | + | 0.997168i | \(0.476038\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.15767 | − | 12.3150i | −0.0771781 | − | 0.821002i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.21985 | −0.213709 | −0.106855 | − | 0.994275i | \(-0.534078\pi\) | ||||
−0.106855 | + | 0.994275i | \(0.534078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.41011i | − | 0.225346i | −0.993632 | − | 0.112673i | \(-0.964059\pi\) | ||
0.993632 | − | 0.112673i | \(-0.0359413\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.3693 | − | 21.2755i | 1.27441 | − | 1.39983i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.3019i | 1.00246i | 0.865315 | + | 0.501229i | \(0.167119\pi\) | ||||
−0.865315 | + | 0.501229i | \(0.832881\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.22631i | 0.0799959i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.98813 | − | 2.18379i | 0.129143 | − | 0.141852i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 14.2794i | − | 0.923656i | −0.886970 | − | 0.461828i | \(-0.847194\pi\) | ||
0.886970 | − | 0.461828i | \(-0.152806\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9.96148i | − | 0.641675i | −0.947134 | − | 0.320838i | \(-0.896036\pi\) | ||
0.947134 | − | 0.320838i | \(-0.103964\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.2808 | − | 8.16217i | −0.851962 | − | 0.523603i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.60669 | −0.485974 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.5554i | 0.989765i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.673500 | + | 0.613157i | 0.0426813 | + | 0.0388572i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.1035 | 1.58452 | 0.792259 | − | 0.610184i | \(-0.208905\pi\) | ||||
0.792259 | + | 0.610184i | \(0.208905\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.2462 | + | 17.7392i | −0.644174 | + | 1.11525i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.12311 | − | 8.30571i | −0.571311 | − | 0.520124i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.2569i | − | 0.826942i | −0.910517 | − | 0.413471i | \(-0.864316\pi\) | ||
0.910517 | − | 0.413471i | \(-0.135684\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.49242 | −0.527693 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.8423 | − | 1.67726i | 1.10441 | − | 0.103820i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.8836 | 1.34940 | 0.674702 | − | 0.738091i | \(-0.264272\pi\) | ||||
0.674702 | + | 0.738091i | \(0.264272\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.61553 | −0.467818 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.87285 | + | 1.70505i | 0.114617 | + | 0.104348i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 13.2569i | − | 0.808287i | −0.914696 | − | 0.404144i | \(-0.867570\pi\) | ||
0.914696 | − | 0.404144i | \(-0.132430\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.2462 | 0.865396 | 0.432698 | − | 0.901539i | \(-0.357562\pi\) | ||||
0.432698 | + | 0.901539i | \(0.357562\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.6153 | − | 12.7584i | 0.702991 | − | 0.772175i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.6121 | −1.06205 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.43845 | −0.206596 | −0.103298 | − | 0.994650i | \(-0.532940\pi\) | ||||
−0.103298 | + | 0.994650i | \(0.532940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.03457 | + | 11.0055i | 0.0619378 | + | 0.658879i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.6412 | −1.41032 | −0.705158 | − | 0.709050i | \(-0.749124\pi\) | ||||
−0.705158 | + | 0.709050i | \(0.749124\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.29895i | 0.433877i | 0.976185 | + | 0.216939i | \(0.0696072\pi\) | ||||
−0.976185 | + | 0.216939i | \(0.930393\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.63068 | + | 7.28323i | −0.392768 | + | 0.431421i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −41.3686 | −2.44191 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.8617 | 2.40363 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.6153 | + | 12.7584i | −0.680902 | + | 0.747912i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.1671 | 1.41186 | 0.705928 | − | 0.708284i | \(-0.250530\pi\) | ||||
0.705928 | + | 0.708284i | \(0.250530\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.36758i | − | 0.254290i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.3405 | + | 17.7392i | −0.774096 | + | 1.02933i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.14441 | + | 10.6378i | −0.355340 | + | 0.615198i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.6155 | −1.36118 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.49242 | + | 9.32819i | −0.487877 | + | 0.535891i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.28323i | 0.417037i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.75379 | −0.328386 | −0.164193 | − | 0.986428i | \(-0.552502\pi\) | ||||
−0.164193 | + | 0.986428i | \(0.552502\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.6035 | − | 14.9422i | 0.773873 | − | 0.850033i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.6378i | 0.603212i | 0.953433 | + | 0.301606i | \(0.0975227\pi\) | ||||
−0.953433 | + | 0.301606i | \(0.902477\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.36758i | 0.246870i | 0.992353 | + | 0.123435i | \(0.0393911\pi\) | ||||
−0.992353 | + | 0.123435i | \(0.960609\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.8769 | − | 1.02248i | 0.612844 | − | 0.0576102i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 18.6564i | − | 1.04785i | −0.851765 | − | 0.523923i | \(-0.824468\pi\) | ||
0.851765 | − | 0.523923i | \(-0.175532\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 25.5169i | − | 1.42867i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.39871 | + | 2.18379i | 0.133883 | + | 0.121887i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 46.1927i | − | 2.57023i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.5616 | −0.585850 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.06897 | − | 9.96148i | 0.501515 | − | 0.550871i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.09271 | 0.280770 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.8078 | 0.703978 | 0.351989 | − | 0.936004i | \(-0.385505\pi\) | ||||
0.351989 | + | 0.936004i | \(0.385505\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.52262 | − | 0.613157i | 0.357437 | − | 0.0336008i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.9248i | 0.596888i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.5554i | 0.847355i | 0.905813 | + | 0.423678i | \(0.139261\pi\) | ||||
−0.905813 | + | 0.423678i | \(0.860739\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.34376 | − | 6.68579i | −0.398859 | − | 0.363122i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.7392 | 0.852327 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.36758i | 0.235827i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.41138 | + | 2.36160i | −0.399015 | + | 0.127144i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 28.5588i | − | 1.53311i | −0.642176 | − | 0.766557i | \(-0.721968\pi\) | ||
0.642176 | − | 0.766557i | \(-0.278032\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.19224 | −0.170876 | −0.0854382 | − | 0.996343i | \(-0.527229\pi\) | ||||
−0.0854382 | + | 0.996343i | \(0.527229\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00000 | + | 10.6378i | −0.427008 | + | 0.567802i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.9210i | 0.953838i | 0.878947 | + | 0.476919i | \(0.158247\pi\) | ||||
−0.878947 | + | 0.476919i | \(0.841753\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.18379i | 0.115904i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −34.4924 | + | 37.8869i | −1.82553 | + | 2.00519i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.8319 | 1.09947 | 0.549734 | − | 0.835340i | \(-0.314729\pi\) | ||||
0.549734 | + | 0.835340i | \(0.314729\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8769 | −0.940889 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.28078 | + | 8.44926i | 0.487114 | + | 0.443471i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.32326 | −0.278632 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.8118i | 1.24297i | 0.783428 | + | 0.621483i | \(0.213469\pi\) | ||||
−0.783428 | + | 0.621483i | \(0.786531\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 31.7732 | − | 2.98683i | 1.65405 | − | 0.155488i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 31.6262i | 1.64195i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 28.9270i | − | 1.49778i | −0.662694 | − | 0.748891i | \(-0.730587\pi\) | ||
0.662694 | − | 0.748891i | \(-0.269413\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.9418 | − | 9.96148i | −0.565033 | − | 0.514409i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 15.3019i | − | 0.788086i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.7733i | 1.73482i | 0.497597 | + | 0.867408i | \(0.334216\pi\) | ||||
−0.497597 | + | 0.867408i | \(0.665784\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.84233 | − | 8.96050i | −0.504238 | − | 0.459060i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.2888 | 0.627929 | 0.313965 | − | 0.949435i | \(-0.398343\pi\) | ||||
0.313965 | + | 0.949435i | \(0.398343\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 15.5554i | − | 0.792775i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.1379 | − | 1.70505i | 0.922003 | − | 0.0866727i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.20798 | −0.264055 | −0.132028 | − | 0.991246i | \(-0.542149\pi\) | ||||
−0.132028 | + | 0.991246i | \(0.542149\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.2462 | − | 31.5895i | 0.922751 | − | 1.59755i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.2116 | + | 12.3150i | −0.565553 | + | 0.621211i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.59666i | − | 0.0803365i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.0691303 | 0.00346955 | 0.00173478 | − | 0.999998i | \(-0.499448\pi\) | ||||
0.00173478 | + | 0.999998i | \(0.499448\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 30.2462 | + | 27.5363i | 1.51420 | + | 1.37854i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.80928 | −0.140289 | −0.0701444 | − | 0.997537i | \(-0.522346\pi\) | ||||
−0.0701444 | + | 0.997537i | \(0.522346\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.43845 | 0.470163 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.28019 | + | 1.57063i | −0.411446 | + | 0.0780454i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9.32819i | − | 0.462381i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.31534 | 0.411167 | 0.205584 | − | 0.978640i | \(-0.434091\pi\) | ||||
0.205584 | + | 0.978640i | \(0.434091\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.2134 | + | 13.8503i | 0.750421 | + | 0.683186i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.1379 | −0.892510 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.492423 | 0.0241721 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.8423 | + | 16.2437i | 0.873743 | + | 0.795459i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.97626 | −0.194253 | −0.0971266 | − | 0.995272i | \(-0.530965\pi\) | ||||
−0.0971266 | + | 0.995272i | \(0.530965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.18379i | − | 0.106431i | −0.998583 | − | 0.0532157i | \(-0.983053\pi\) | ||
0.998583 | − | 0.0532157i | \(-0.0169471\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.91146 | + | 0.367696i | −0.190182 | + | 0.0178780i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 31.3632 | 1.52134 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 30.2462 | 1.46372 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.0140 | + | 12.7584i | 0.676604 | + | 0.615983i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.6811 | −1.28518 | −0.642591 | − | 0.766210i | \(-0.722140\pi\) | ||||
−0.642591 | + | 0.766210i | \(0.722140\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.3291i | 0.688611i | 0.938858 | + | 0.344305i | \(0.111886\pi\) | ||||
−0.938858 | + | 0.344305i | \(0.888114\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.52262 | − | 7.16453i | 0.312736 | − | 0.343513i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.2188 | − | 14.5665i | −1.20638 | − | 0.696808i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.9309 | 1.23761 | 0.618806 | − | 0.785543i | \(-0.287617\pi\) | ||||
0.618806 | + | 0.785543i | \(0.287617\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.28078 | − | 24.2624i | −0.108608 | − | 1.15535i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.5549i | 1.68926i | 0.535347 | + | 0.844632i | \(0.320181\pi\) | ||||
−0.535347 | + | 0.844632i | \(0.679819\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.36932 | 0.0649118 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.4677 | + | 10.4402i | 0.542402 | + | 0.493805i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.9396i | 1.22417i | 0.790793 | + | 0.612083i | \(0.209668\pi\) | ||||
−0.790793 | + | 0.612083i | \(0.790332\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 45.4398i | − | 2.13968i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.6501 | + | 16.9791i | 0.876258 | + | 0.797749i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 9.32819i | − | 0.437312i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.22631i | 0.0573646i | 0.999589 | + | 0.0286823i | \(0.00913110\pi\) | ||||
−0.999589 | + | 0.0286823i | \(0.990869\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23.7565 | − | 31.5895i | 1.10886 | − | 1.47447i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 10.6378i | − | 0.495450i | −0.968830 | − | 0.247725i | \(-0.920317\pi\) | ||
0.968830 | − | 0.247725i | \(-0.0796829\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.4924 | −1.88184 | −0.940921 | − | 0.338626i | \(-0.890038\pi\) | ||||
−0.940921 | + | 0.338626i | \(0.890038\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.41921 | + | 4.02326i | 0.204936 | + | 0.186574i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.0108 | −0.925989 | −0.462995 | − | 0.886361i | \(-0.653225\pi\) | ||||
−0.462995 | + | 0.886361i | \(0.653225\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 45.3693 | 2.09496 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.1617 | − | 15.5554i | 0.652536 | − | 0.716754i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 25.9396i | − | 1.19270i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 25.0381i | − | 1.14883i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.28343 | − | 24.2905i | −0.104551 | − | 1.11219i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.9764 | 1.23258 | 0.616290 | − | 0.787519i | \(-0.288635\pi\) | ||||
0.616290 | + | 0.787519i | \(0.288635\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 5.59390i | − | 0.255060i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.80740 | + | 30.7784i | 0.446252 | + | 1.40047i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.32819i | 0.423571i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.0540 | −1.04468 | −0.522338 | − | 0.852739i | \(-0.674940\pi\) | ||||
−0.522338 | + | 0.852739i | \(0.674940\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.84233 | − | 1.67726i | −0.0833130 | − | 0.0758485i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8.01862i | − | 0.361875i | −0.983495 | − | 0.180938i | \(-0.942087\pi\) | ||
0.983495 | − | 0.180938i | \(-0.0579132\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 45.4398i | 2.04651i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.12311 | + | 11.9473i | 0.0504798 | + | 0.536992i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.06897 | 0.406799 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.5616 | −0.651865 | −0.325932 | − | 0.945393i | \(-0.605678\pi\) | ||||
−0.325932 | + | 0.945393i | \(0.605678\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.19224 | + | 1.30957i | −0.0532652 | + | 0.0585072i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.4785 | −1.40356 | −0.701778 | − | 0.712396i | \(-0.747610\pi\) | ||||
−0.701778 | + | 0.712396i | \(0.747610\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.82021i | 0.303495i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.24621 | − | 7.50738i | −0.366227 | − | 0.333415i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 3.35453i | − | 0.148687i | −0.997233 | − | 0.0743434i | \(-0.976314\pi\) | ||
0.997233 | − | 0.0743434i | \(-0.0236861\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.1067i | 0.977945i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −25.2188 | − | 18.9655i | −1.11344 | − | 0.837346i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 10.9248i | − | 0.481406i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.59390i | 0.246019i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.7538 | + | 23.8947i | −0.954885 | + | 1.04886i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.8545 | 0.694599 | 0.347299 | − | 0.937754i | \(-0.387099\pi\) | ||||
0.347299 | + | 0.937754i | \(0.387099\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3.88884i | − | 0.170047i | −0.996379 | − | 0.0850236i | \(-0.972903\pi\) | ||
0.996379 | − | 0.0850236i | \(-0.0270966\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.6962 | + | 20.5361i | −0.815967 | + | 0.896270i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.0281 | −1.22092 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4924 | − | 19.9230i | −0.499671 | − | 0.866216i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.9309 | − | 1.30957i | 0.604548 | − | 0.0568304i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 27.2492i | − | 1.18029i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.75379 | 0.0758229 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.34991 | − | 10.2701i | 0.403478 | − | 0.443186i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34.6983 | −1.49456 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.1771 | −0.523534 | −0.261767 | − | 0.965131i | \(-0.584305\pi\) | ||||
−0.261767 | + | 0.965131i | \(0.584305\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.7770 | + | 28.3138i | −1.10620 | + | 1.21506i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 7.28323i | − | 0.311979i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.8078 | 0.547620 | 0.273810 | − | 0.961784i | \(-0.411716\pi\) | ||||
0.273810 | + | 0.961784i | \(0.411716\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.2306 | + | 2.18379i | −0.991460 | + | 0.0932019i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.2759 | 1.54540 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.63068 | −0.281965 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.38447 | − | 2.61914i | 0.101215 | − | 0.111176i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.25969 | −0.265232 | −0.132616 | − | 0.991168i | \(-0.542338\pi\) | ||||
−0.132616 | + | 0.991168i | \(0.542338\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.5554i | − | 0.657922i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −41.6155 | − | 37.8869i | −1.75701 | − | 1.59959i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.4030 | 1.44991 | 0.724957 | − | 0.688794i | \(-0.241859\pi\) | ||||
0.724957 | + | 0.688794i | \(0.241859\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.36932 | −0.225889 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.52262 | + | 34.3864i | 0.273924 | + | 1.44409i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.47954 | −0.397403 | −0.198702 | − | 0.980060i | \(-0.563672\pi\) | ||||
−0.198702 | + | 0.980060i | \(0.563672\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.1794i | 1.17927i | 0.807670 | + | 0.589635i | \(0.200728\pi\) | ||||
−0.807670 | + | 0.589635i | \(0.799272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.3029 | + | 23.9462i | 1.09882 | + | 1.00037i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.89012 | − | 17.1227i | 0.412446 | − | 0.714064i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.6847 | −1.31905 | −0.659525 | − | 0.751683i | \(-0.729242\pi\) | ||||
−0.659525 | + | 0.751683i | \(0.729242\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 23.7732 | + | 21.6432i | 0.987980 | + | 0.899461i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.04496i | − | 0.0848392i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.7386 | −1.43873 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.673500 | + | 7.16453i | 0.0278458 | + | 0.296217i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.287088i | 0.0118494i | 0.999982 | + | 0.00592470i | \(0.00188590\pi\) | ||||
−0.999982 | + | 0.00592470i | \(0.998114\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.3756i | 0.921970i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.2808 | − | 25.5719i | 0.957643 | − | 1.05189i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.6114i | 0.682149i | 0.940036 | + | 0.341075i | \(0.110791\pi\) | ||||
−0.940036 | + | 0.341075i | \(0.889209\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.7006i | 1.13562i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.53448 | − | 4.98074i | 0.185584 | − | 0.203848i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 32.2004i | − | 1.31567i | −0.753162 | − | 0.657836i | \(-0.771472\pi\) | ||
0.753162 | − | 0.657836i | \(-0.228528\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.4384 | −0.874493 | −0.437246 | − | 0.899342i | \(-0.644046\pi\) | ||||
−0.437246 | + | 0.899342i | \(0.644046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −34.8460 | + | 3.27569i | −1.41904 | + | 0.133396i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.78554 | 0.275872 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −29.7533 | − | 27.0875i | −1.20566 | − | 1.09764i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.35453i | 0.135710i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 37.6621i | − | 1.52116i | −0.649245 | − | 0.760579i | \(-0.724915\pi\) | ||
0.649245 | − | 0.760579i | \(-0.275085\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.6153 | − | 12.7584i | 0.468375 | − | 0.514469i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.4214 | −0.822133 | −0.411067 | − | 0.911605i | \(-0.634844\pi\) | ||||
−0.411067 | + | 0.911605i | \(0.634844\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.07263i | − | 0.244080i | −0.992525 | − | 0.122040i | \(-0.961056\pi\) | ||
0.992525 | − | 0.122040i | \(-0.0389436\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.75480 | − | 22.9313i | −0.391447 | − | 0.920201i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 5.68658i | − | 0.227828i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.6155 | 0.504621 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −30.2462 | + | 33.2228i | −1.20792 | + | 1.32679i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.6114i | 0.662341i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.70505i | 0.0678771i | 0.999424 | + | 0.0339385i | \(0.0108050\pi\) | ||||
−0.999424 | + | 0.0339385i | \(0.989195\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −31.3693 | − | 28.5588i | −1.24682 | − | 1.13511i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.19612 | −0.285569 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.8078 | −0.824434 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.96543 | + | 0.654784i | −0.275548 | + | 0.0259029i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.9300 | 0.510703 | 0.255351 | − | 0.966848i | \(-0.417809\pi\) | ||||
0.255351 | + | 0.966848i | \(0.417809\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 16.0341i | − | 0.632324i | −0.948705 | − | 0.316162i | \(-0.897606\pi\) | ||
0.948705 | − | 0.316162i | \(-0.102394\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.63068 | − | 7.28323i | 0.261083 | − | 0.286777i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 13.2569i | − | 0.521182i | −0.965449 | − | 0.260591i | \(-0.916083\pi\) | ||
0.965449 | − | 0.260591i | \(-0.0839175\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 19.9230i | − | 0.782044i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.7080 | − | 18.3523i | 0.654839 | − | 0.719284i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 8.01862i | − | 0.313793i | −0.987615 | − | 0.156896i | \(-0.949851\pi\) | ||
0.987615 | − | 0.156896i | \(-0.0501489\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.00400i | 0.351815i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.59612 | − | 16.9791i | −0.0622705 | − | 0.662419i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.8664 | −0.540158 | −0.270079 | − | 0.962838i | \(-0.587050\pi\) | ||||
−0.270079 | + | 0.962838i | \(0.587050\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.8884i | 1.51258i | 0.654234 | + | 0.756292i | \(0.272991\pi\) | ||||
−0.654234 | + | 0.756292i | \(0.727009\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24.9559 | − | 22.7199i | −0.969205 | − | 0.882368i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.1142 | 0.857552 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.8078 | + | 14.3291i | 0.960560 | + | 0.554823i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.87689 | + | 2.61914i | 0.111227 | + | 0.101262i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.2228i | 1.28255i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.5464 | 1.37021 | 0.685106 | − | 0.728443i | \(-0.259756\pi\) | ||||
0.685106 | + | 0.728443i | \(0.259756\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.8769 | − | 17.1227i | 0.495632 | − | 0.659052i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.6477 | 0.447657 | 0.223829 | − | 0.974629i | \(-0.428144\pi\) | ||||
0.223829 | + | 0.974629i | \(0.428144\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.7386 | 1.48665 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.12391 | − | 3.75443i | −0.158029 | − | 0.143870i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.287088i | 0.0109851i | 0.999985 | + | 0.00549256i | \(0.00174835\pi\) | ||||
−0.999985 | + | 0.00549256i | \(0.998252\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.1231 | 0.424992 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.97626 | − | 4.36758i | 0.151704 | − | 0.166634i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.8319 | −0.793634 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.4924 | 0.627401 | 0.313701 | − | 0.949522i | \(-0.398431\pi\) | ||||
0.313701 | + | 0.949522i | \(0.398431\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 49.6155 | − | 4.66410i | 1.88474 | − | 0.177174i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.0452 | 0.494834 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 80.9181i | 3.06499i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.8423 | + | 19.5983i | −0.674859 | + | 0.741274i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.7792 | −1.57798 | −0.788989 | − | 0.614408i | \(-0.789395\pi\) | ||||
−0.788989 | + | 0.614408i | \(0.789395\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.2614 | 0.500162 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.42991 | + | 1.57063i | −0.0538536 | + | 0.0591535i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.3234 | 1.06521 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 28.9270i | − | 1.08637i | −0.839612 | − | 0.543187i | \(-0.817217\pi\) | ||
0.839612 | − | 0.543187i | \(-0.182783\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.09271 | − | 0.478739i | 0.190991 | − | 0.0179541i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.83841 | + | 15.3019i | −0.331001 | + | 0.573059i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.2462 | 0.383187 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.6501 | − | 18.2887i | 0.621809 | − | 0.683004i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 9.90237i | − | 0.369296i | −0.982805 | − | 0.184648i | \(-0.940885\pi\) | ||
0.982805 | − | 0.184648i | \(-0.0591145\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45.3693 | −1.68964 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.6153 | − | 12.7584i | 0.431978 | − | 0.474491i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.6300i | 0.914737i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 31.5895i | − | 1.17159i | −0.810460 | − | 0.585795i | \(-0.800783\pi\) | ||
0.810460 | − | 0.585795i | \(-0.199217\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.49242 | − | 25.9396i | −0.277497 | − | 0.960726i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.1927i | 1.70850i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 53.2175i | − | 1.96563i | −0.184585 | − | 0.982817i | \(-0.559094\pi\) | ||
0.184585 | − | 0.982817i | \(-0.440906\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.74247 | − | 8.86958i | −0.359356 | − | 0.327159i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 49.8343i | 1.83567i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.8078 | −0.471141 | −0.235571 | − | 0.971857i | \(-0.575696\pi\) | ||||
−0.235571 | + | 0.971857i | \(0.575696\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.1379 | + | 19.9230i | −0.666314 | + | 0.731888i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.4849 | −0.714833 | −0.357417 | − | 0.933945i | \(-0.616342\pi\) | ||||
−0.357417 | + | 0.933945i | \(0.616342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.38447 | 0.307183 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.147647 | + | 1.57063i | 0.00540212 | + | 0.0574665i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 7.28323i | − | 0.266123i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.07263i | 0.221594i | 0.993843 | + | 0.110797i | \(0.0353403\pi\) | ||||
−0.993843 | + | 0.110797i | \(0.964660\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 32.1520 | + | 29.2713i | 1.17168 | + | 1.06670i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.6358 | 0.496258 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 33.2945i | − | 1.21011i | −0.796183 | − | 0.605055i | \(-0.793151\pi\) | ||
0.796183 | − | 0.605055i | \(-0.206849\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −33.8074 | + | 10.7726i | −1.22713 | + | 0.391020i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.9056i | 1.66408i | 0.554719 | + | 0.832038i | \(0.312826\pi\) | ||||
−0.554719 | + | 0.832038i | \(0.687174\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.2462 | −1.09499 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.00000 | − | 21.2755i | −0.0723102 | − | 0.769218i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 11.9473i | − | 0.431393i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 21.1493i | − | 0.762662i | −0.924439 | − | 0.381331i | \(-0.875466\pi\) | ||
0.924439 | − | 0.381331i | \(-0.124534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.4579 | − | 16.9791i | 0.556701 | − | 0.611488i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 50.0270 | 1.79935 | 0.899673 | − | 0.436565i | \(-0.143805\pi\) | ||||
0.899673 | + | 0.436565i | \(0.143805\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.1922 | −0.545721 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.8769 | − | 9.90237i | −0.390206 | − | 0.355245i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 64.5992 | 2.31451 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.96148i | 0.356450i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.8078 | + | 18.6564i | 0.886557 | + | 0.666725i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 11.3732i | − | 0.405925i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 12.8928i | − | 0.459580i | −0.973240 | − | 0.229790i | \(-0.926196\pi\) | ||
0.973240 | − | 0.229790i | \(-0.0738040\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.0281 | + | 25.5169i | 0.997825 | + | 0.908424i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.2980i | 0.792826i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.9230i | 0.707485i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.75379 | − | 8.87989i | −0.345931 | − | 0.314937i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.3697 | −0.686109 | −0.343054 | − | 0.939316i | \(-0.611461\pi\) | ||||
−0.343054 | + | 0.939316i | \(0.611461\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9.96148i | − | 0.352412i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.410574 | + | 4.36758i | 0.0145069 | + | 0.154321i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.2824 | −0.856906 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.1231 | + | 8.73516i | 0.533019 | + | 0.307874i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.4579 | − | 16.9791i | 0.544142 | − | 0.597693i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.23827i | 0.184168i | 0.995751 | + | 0.0920839i | \(0.0293528\pi\) | ||||
−0.995751 | + | 0.0920839i | \(0.970647\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.6847 | 1.39352 | 0.696758 | − | 0.717306i | \(-0.254625\pi\) | ||||
0.696758 | + | 0.717306i | \(0.254625\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.2462 | + | 16.6114i | 0.639923 | + | 0.582588i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.34700 | −0.0471833 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.8769 | 1.29016 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 29.7533 | − | 2.79695i | 1.03966 | − | 0.0977333i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.5960i | 1.55641i | 0.628010 | + | 0.778206i | \(0.283870\pi\) | ||||
−0.628010 | + | 0.778206i | \(0.716130\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.5616 | −0.786446 | −0.393223 | − | 0.919443i | \(-0.628640\pi\) | ||||
−0.393223 | + | 0.919443i | \(0.628640\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.5571 | − | 20.5361i | −0.785339 | − | 0.714976i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.67026 | 0.231948 | 0.115974 | − | 0.993252i | \(-0.463001\pi\) | ||||
0.115974 | + | 0.993252i | \(0.463001\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.8617 | −1.66231 | −0.831153 | − | 0.556043i | \(-0.812319\pi\) | ||||
−0.831153 | + | 0.556043i | \(0.812319\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.40388 | − | 4.00931i | −0.152769 | − | 0.139081i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 61.7899 | 2.14089 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.957477i | 0.0331349i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.5076 | + | 15.3019i | −0.397760 | + | 0.528909i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.14441 | −0.212129 | −0.106064 | − | 0.994359i | \(-0.533825\pi\) | ||||
−0.106064 | + | 0.994359i | \(0.533825\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.68466 | −0.230505 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30.2791 | − | 27.5662i | −1.04287 | − | 0.949431i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.02913 | −0.207408 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 28.1794i | − | 0.968255i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.51075 | + | 9.34832i | −0.292088 | + | 0.320834i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.06897 | + | 5.23827i | 0.310880 | + | 0.179566i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.0000 | 0.342393 | 0.171197 | − | 0.985237i | \(-0.445237\pi\) | ||||
0.171197 | + | 0.985237i | \(0.445237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.9848 | + | 1.59666i | −0.580869 | + | 0.0546045i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 15.3019i | − | 0.522701i | −0.965244 | − | 0.261351i | \(-0.915832\pi\) | ||
0.965244 | − | 0.261351i | \(-0.0841679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.946025 | −0.0322779 | −0.0161390 | − | 0.999870i | \(-0.505137\pi\) | ||||
−0.0161390 | + | 0.999870i | \(0.505137\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −52.9839 | − | 48.2368i | −1.80569 | − | 1.64390i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 50.5697i | − | 1.72141i | −0.509103 | − | 0.860706i | \(-0.670023\pi\) | ||
0.509103 | − | 0.860706i | \(-0.329977\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.4703i | 0.594009i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 52.3348 | + | 47.6458i | 1.77738 | + | 1.61814i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 7.28323i | − | 0.247067i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.8844i | 1.01260i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29.7533 | + | 2.79695i | −1.00700 | + | 0.0946624i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.2228i | 1.12314i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.9848 | 0.370932 | 0.185466 | − | 0.982651i | \(-0.440621\pi\) | ||||
0.185466 | + | 0.982651i | \(0.440621\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.9526 | + | 28.1794i | 1.04401 | + | 0.950467i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.6692 | 0.965889 | 0.482945 | − | 0.875651i | \(-0.339567\pi\) | ||||
0.482945 | + | 0.875651i | \(0.339567\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.50758 | 0.252650 | 0.126325 | − | 0.991989i | \(-0.459682\pi\) | ||||
0.126325 | + | 0.991989i | \(0.459682\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.09271 | − | 5.59390i | 0.171189 | − | 0.188037i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43.8606i | 1.47270i | 0.676604 | + | 0.736348i | \(0.263451\pi\) | ||||
−0.676604 | + | 0.736348i | \(0.736549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.8844i | 1.00229i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −37.7705 | + | 7.16453i | −1.26536 | + | 0.240021i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.95253 | −0.266121 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 7.50885i | − | 0.250993i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.2735 | + | 6.46006i | −0.676912 | + | 0.215695i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 22.0109i | − | 0.734105i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 61.8617 | 2.06091 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.2462 | − | 27.5363i | −1.00653 | − | 0.916350i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.7013i | 0.688136i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 38.1409i | − | 1.26645i | −0.773969 | − | 0.633223i | \(-0.781731\pi\) | ||
0.773969 | − | 0.633223i | \(-0.218269\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21.7538 | + | 2.04496i | −0.721528 | + | 0.0678270i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.2242 | −1.16703 | −0.583514 | − | 0.812103i | \(-0.698323\pi\) | ||||
−0.583514 | + | 0.812103i | \(0.698323\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.24621 | 0.0743387 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.49242 | + | 9.32819i | −0.280751 | + | 0.308380i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37.3923 | 1.23480 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.1449i | 1.55517i | 0.628781 | + | 0.777583i | \(0.283554\pi\) | ||||
−0.628781 | + | 0.777583i | \(0.716446\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.36932 | − | 6.70906i | −0.242827 | − | 0.221071i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.97366i | 0.196626i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.00400i | 0.296050i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.8460 | − | 3.27569i | 1.14449 | − | 0.107588i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.5851i | 0.740993i | 0.928834 | + | 0.370496i | \(0.120812\pi\) | ||||
−0.928834 | + | 0.370496i | \(0.879188\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 49.3287i | − | 1.61668i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.4039 | + | 13.6246i | −0.406085 | + | 0.446049i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −30.4268 | −0.995062 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 16.7817i | − | 0.548234i | −0.961696 | − | 0.274117i | \(-0.911614\pi\) | ||
0.961696 | − | 0.274117i | \(-0.0883855\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.09271 | + | 5.59390i | −0.166194 | + | 0.182550i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.50328 | −0.179402 | −0.0897009 | − | 0.995969i | \(-0.528591\pi\) | ||||
−0.0897009 | + | 0.995969i | \(0.528591\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.1771 | + | 25.5169i | 1.43860 | + | 0.830943i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.1231 | + | 11.3732i | 0.491955 | + | 0.369969i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 13.2569i | − | 0.430791i | −0.976527 | − | 0.215396i | \(-0.930896\pi\) | ||
0.976527 | − | 0.215396i | \(-0.0691041\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.5616 | −0.472688 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.7538 | − | 23.8947i | 0.705415 | − | 0.774837i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.3459 | 0.756249 | 0.378124 | − | 0.925755i | \(-0.376569\pi\) | ||||
0.378124 | + | 0.925755i | \(0.376569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.2311 | 0.622302 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29.7533 | − | 32.6814i | 0.961786 | − | 1.05644i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 46.1927i | − | 1.49164i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.4233 | −0.562042 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.525853 | + | 5.59390i | 0.0169454 | + | 0.180261i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.3815 | 0.559531 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −57.1619 | −1.83820 | −0.919102 | − | 0.394020i | \(-0.871084\pi\) | ||||
−0.919102 | + | 0.394020i | \(0.871084\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 53.8617 | − | 59.1625i | 1.73029 | − | 1.90057i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.36426 | 0.300514 | 0.150257 | − | 0.988647i | \(-0.451990\pi\) | ||||
0.150257 | + | 0.988647i | \(0.451990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 54.1750i | − | 1.73677i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.5270 | − | 12.3150i | −0.433210 | − | 0.394396i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.73384 | −0.183442 | −0.0917209 | − | 0.995785i | \(-0.529237\pi\) | ||||
−0.0917209 | + | 0.995785i | \(0.529237\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.24621 | 0.199630 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.2306 | − | 2.18379i | 0.741697 | − | 0.0697231i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.5776 | −0.783905 | −0.391953 | − | 0.919985i | \(-0.628200\pi\) | ||||
−0.391953 | + | 0.919985i | \(0.628200\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 18.6966i | − | 0.595725i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.52262 | + | 5.93822i | 0.207617 | + | 0.189016i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.2188 | + | 14.5665i | 0.801910 | + | 0.463187i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.4924 | −0.396835 | −0.198417 | − | 0.980118i | \(-0.563580\pi\) | ||||
−0.198417 | + | 0.980118i | \(0.563580\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.4039 | + | 14.9342i | 0.520561 | + | 0.473921i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 3.64162i | − | 0.115447i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.8769 | −0.724519 | −0.362259 | − | 0.932077i | \(-0.617994\pi\) | ||||
−0.362259 | + | 0.932077i | \(0.617994\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.06897 | + | 6.82021i | 0.286930 | + | 0.215782i |
(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 | 276.2.g.a.137.8 | yes | 8 | |
3.2 | odd | 2 | inner | 276.2.g.a.137.5 | ✓ | 8 | |
4.3 | odd | 2 | 1104.2.m.b.689.2 | 8 | |||
12.11 | even | 2 | 1104.2.m.b.689.3 | 8 | |||
23.22 | odd | 2 | inner | 276.2.g.a.137.7 | yes | 8 | |
69.68 | even | 2 | inner | 276.2.g.a.137.6 | yes | 8 | |
92.91 | even | 2 | 1104.2.m.b.689.1 | 8 | |||
276.275 | odd | 2 | 1104.2.m.b.689.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.g.a.137.5 | ✓ | 8 | 3.2 | odd | 2 | inner | |
276.2.g.a.137.6 | yes | 8 | 69.68 | even | 2 | inner | |
276.2.g.a.137.7 | yes | 8 | 23.22 | odd | 2 | inner | |
276.2.g.a.137.8 | yes | 8 | 1.1 | even | 1 | trivial | |
1104.2.m.b.689.1 | 8 | 92.91 | even | 2 | |||
1104.2.m.b.689.2 | 8 | 4.3 | odd | 2 | |||
1104.2.m.b.689.3 | 8 | 12.11 | even | 2 | |||
1104.2.m.b.689.4 | 8 | 276.275 | odd | 2 |