Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(361,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.h (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 882) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.3 | ||
Root | \(1.72286 + 0.178197i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.361 |
Dual form | 2646.2.h.s.667.3 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.03151 | 0.908517 | 0.454259 | − | 0.890870i | \(-0.349904\pi\) | ||||
0.454259 | + | 0.890870i | \(0.349904\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.01575 | − | 1.75934i | 0.321209 | − | 0.556351i | ||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.12132 | + | 3.67423i | −0.588348 | + | 1.01905i | 0.406100 | + | 0.913828i | \(0.366888\pi\) |
−0.994449 | + | 0.105221i | \(0.966445\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.707107 | + | 1.22474i | −0.171499 | + | 0.297044i | −0.938944 | − | 0.344070i | \(-0.888194\pi\) |
0.767445 | + | 0.641114i | \(0.221528\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.398461 | − | 0.690154i | −0.0914131 | − | 0.158332i | 0.816693 | − | 0.577073i | \(-0.195805\pi\) |
−0.908106 | + | 0.418740i | \(0.862472\pi\) | |||||||
\(20\) | −1.01575 | − | 1.75934i | −0.227129 | − | 0.393399i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | + | 3.46410i | −0.426401 | + | 0.738549i | ||||
\(23\) | −6.74597 | −1.40663 | −0.703316 | − | 0.710878i | \(-0.748298\pi\) | ||||
−0.703316 | + | 0.710878i | \(0.748298\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.872983 | −0.174597 | ||||||||
\(26\) | 2.12132 | + | 3.67423i | 0.416025 | + | 0.720577i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.43649 | + | 7.68423i | 0.823836 | + | 1.42693i | 0.902806 | + | 0.430049i | \(0.141504\pi\) |
−0.0789700 | + | 0.996877i | \(0.525163\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.73861 | − | 4.74342i | −0.491869 | − | 0.851943i | 0.508087 | − | 0.861306i | \(-0.330353\pi\) |
−0.999956 | + | 0.00936313i | \(0.997020\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.707107 | + | 1.22474i | 0.121268 | + | 0.210042i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.87298 | + | 8.44025i | 0.801114 | + | 1.38757i | 0.918884 | + | 0.394528i | \(0.129092\pi\) |
−0.117770 | + | 0.993041i | \(0.537575\pi\) | |||||||
\(38\) | −0.796921 | −0.129278 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.03151 | −0.321209 | ||||||||
\(41\) | −2.82843 | + | 4.89898i | −0.441726 | + | 0.765092i | −0.997818 | − | 0.0660290i | \(-0.978967\pi\) |
0.556092 | + | 0.831121i | \(0.312300\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.43649 | − | 7.68423i | −0.676559 | − | 1.17183i | −0.976011 | − | 0.217723i | \(-0.930137\pi\) |
0.299452 | − | 0.954111i | \(-0.403196\pi\) | |||||||
\(44\) | 2.00000 | + | 3.46410i | 0.301511 | + | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.37298 | + | 5.84218i | −0.497319 | + | 0.861382i | ||||
\(47\) | −3.44572 | + | 5.96816i | −0.502610 | + | 0.870546i | 0.497386 | + | 0.867530i | \(0.334293\pi\) |
−0.999995 | + | 0.00301623i | \(0.999040\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.436492 | + | 0.756026i | −0.0617292 | + | 0.106918i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.24264 | 0.588348 | ||||||||
\(53\) | −5.30948 | + | 9.19628i | −0.729312 | + | 1.26321i | 0.227862 | + | 0.973694i | \(0.426827\pi\) |
−0.957174 | + | 0.289513i | \(0.906507\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.12602 | −1.09571 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.87298 | 1.16508 | ||||||||
\(59\) | −1.32440 | − | 2.29393i | −0.172422 | − | 0.298644i | 0.766844 | − | 0.641833i | \(-0.221826\pi\) |
−0.939266 | + | 0.343190i | \(0.888493\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.398461 | − | 0.690154i | 0.0510176 | − | 0.0883652i | −0.839389 | − | 0.543531i | \(-0.817087\pi\) |
0.890406 | + | 0.455166i | \(0.150420\pi\) | |||||||
\(62\) | −5.47723 | −0.695608 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.30948 | + | 7.46423i | −0.534525 | + | 0.925824i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.436492 | − | 0.756026i | −0.0533259 | − | 0.0923632i | 0.838130 | − | 0.545470i | \(-0.183649\pi\) |
−0.891456 | + | 0.453107i | \(0.850316\pi\) | |||||||
\(68\) | 1.41421 | 0.171499 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.12702 | 0.252430 | 0.126215 | − | 0.992003i | \(-0.459717\pi\) | ||||
0.126215 | + | 0.992003i | \(0.459717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.68836 | − | 13.3166i | 0.899855 | − | 1.55859i | 0.0721755 | − | 0.997392i | \(-0.477006\pi\) |
0.827679 | − | 0.561202i | \(-0.189661\pi\) | |||||||
\(74\) | 9.74597 | 1.13295 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.398461 | + | 0.690154i | −0.0457066 | + | 0.0791661i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.93649 | + | 5.08615i | −0.330381 | + | 0.572237i | −0.982587 | − | 0.185805i | \(-0.940511\pi\) |
0.652205 | + | 0.758042i | \(0.273844\pi\) | |||||||
\(80\) | −1.01575 | + | 1.75934i | −0.113565 | + | 0.196700i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.82843 | + | 4.89898i | 0.312348 | + | 0.541002i | ||||
\(83\) | −4.15283 | − | 7.19291i | −0.455832 | − | 0.789524i | 0.542904 | − | 0.839795i | \(-0.317325\pi\) |
−0.998736 | + | 0.0502709i | \(0.983992\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.43649 | + | 2.48808i | −0.155809 | + | 0.269870i | ||||
\(86\) | −8.87298 | −0.956798 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.00000 | 0.426401 | ||||||||
\(89\) | −3.53553 | − | 6.12372i | −0.374766 | − | 0.649113i | 0.615526 | − | 0.788116i | \(-0.288944\pi\) |
−0.990292 | + | 0.139003i | \(0.955610\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.37298 | + | 5.84218i | 0.351658 | + | 0.609089i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.44572 | + | 5.96816i | 0.355399 | + | 0.615569i | ||||
\(95\) | −0.809475 | − | 1.40205i | −0.0830504 | − | 0.143847i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.92295 | − | 15.4550i | −0.905988 | − | 1.56922i | −0.819586 | − | 0.572957i | \(-0.805796\pi\) |
−0.0864021 | − | 0.996260i | \(-0.527537\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.436492 | + | 0.756026i | 0.0436492 | + | 0.0756026i | ||||
\(101\) | −7.86799 | −0.782894 | −0.391447 | − | 0.920201i | \(-0.628025\pi\) | ||||
−0.391447 | + | 0.920201i | \(0.628025\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.0255 | 1.77611 | 0.888054 | − | 0.459740i | \(-0.152057\pi\) | ||||
0.888054 | + | 0.459740i | \(0.152057\pi\) | |||||||
\(104\) | 2.12132 | − | 3.67423i | 0.208013 | − | 0.360288i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.30948 | + | 9.19628i | 0.515702 | + | 0.893222i | ||||
\(107\) | 7.87298 | + | 13.6364i | 0.761110 | + | 1.31828i | 0.942279 | + | 0.334829i | \(0.108679\pi\) |
−0.181169 | + | 0.983452i | \(0.557988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.56351 | + | 7.90423i | −0.437105 | + | 0.757088i | −0.997465 | − | 0.0711614i | \(-0.977329\pi\) |
0.560360 | + | 0.828249i | \(0.310663\pi\) | |||||||
\(110\) | −4.06301 | + | 7.03734i | −0.387393 | + | 0.670984i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.93649 | + | 3.35410i | −0.182170 | + | 0.315527i | −0.942619 | − | 0.333870i | \(-0.891645\pi\) |
0.760449 | + | 0.649397i | \(0.224979\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.7045 | −1.27795 | ||||||||
\(116\) | 4.43649 | − | 7.68423i | 0.411918 | − | 0.713463i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.64880 | −0.243842 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | −0.398461 | − | 0.690154i | −0.0360749 | − | 0.0624836i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.73861 | + | 4.74342i | −0.245935 | + | 0.425971i | ||||
\(125\) | −11.9310 | −1.06714 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.7460 | 1.30849 | 0.654246 | − | 0.756281i | \(-0.272986\pi\) | ||||
0.654246 | + | 0.756281i | \(0.272986\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.30948 | + | 7.46423i | 0.377966 | + | 0.654656i | ||||
\(131\) | 7.86799 | 0.687429 | 0.343715 | − | 0.939074i | \(-0.388315\pi\) | ||||
0.343715 | + | 0.939074i | \(0.388315\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.872983 | −0.0754143 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.707107 | − | 1.22474i | 0.0606339 | − | 0.105021i | ||||
\(137\) | −15.4919 | −1.32357 | −0.661783 | − | 0.749696i | \(-0.730200\pi\) | ||||
−0.661783 | + | 0.749696i | \(0.730200\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.23159 | + | 15.9896i | −0.783013 | + | 1.35622i | 0.147165 | + | 0.989112i | \(0.452985\pi\) |
−0.930179 | + | 0.367107i | \(0.880348\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.06351 | − | 1.84205i | 0.0892476 | − | 0.154581i | ||||
\(143\) | 8.48528 | − | 14.6969i | 0.709575 | − | 1.22902i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.01276 | + | 15.6106i | 0.748469 | + | 1.29639i | ||||
\(146\) | −7.68836 | − | 13.3166i | −0.636293 | − | 1.10209i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.87298 | − | 8.44025i | 0.400557 | − | 0.693785i | ||||
\(149\) | 0.254033 | 0.0208112 | 0.0104056 | − | 0.999946i | \(-0.496688\pi\) | ||||
0.0104056 | + | 0.999946i | \(0.496688\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0000 | 0.895167 | 0.447584 | − | 0.894242i | \(-0.352285\pi\) | ||||
0.447584 | + | 0.894242i | \(0.352285\pi\) | |||||||
\(152\) | 0.398461 | + | 0.690154i | 0.0323194 | + | 0.0559789i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.56351 | − | 9.63628i | −0.446872 | − | 0.774005i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.22689 | + | 5.58913i | 0.257534 | + | 0.446061i | 0.965581 | − | 0.260104i | \(-0.0837568\pi\) |
−0.708047 | + | 0.706165i | \(0.750424\pi\) | |||||||
\(158\) | 2.93649 | + | 5.08615i | 0.233615 | + | 0.404633i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.01575 | + | 1.75934i | 0.0803023 | + | 0.139088i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.00000 | − | 8.66025i | −0.391630 | − | 0.678323i | 0.601035 | − | 0.799223i | \(-0.294755\pi\) |
−0.992665 | + | 0.120900i | \(0.961422\pi\) | |||||||
\(164\) | 5.65685 | 0.441726 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.30565 | −0.644644 | ||||||||
\(167\) | 6.18433 | − | 10.7116i | 0.478558 | − | 0.828887i | −0.521140 | − | 0.853471i | \(-0.674493\pi\) |
0.999698 | + | 0.0245846i | \(0.00782630\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.50000 | − | 4.33013i | −0.192308 | − | 0.333087i | ||||
\(170\) | 1.43649 | + | 2.48808i | 0.110174 | + | 0.190827i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.43649 | + | 7.68423i | −0.338279 | + | 0.585917i | ||||
\(173\) | −6.36396 | + | 11.0227i | −0.483843 | + | 0.838041i | −0.999828 | − | 0.0185571i | \(-0.994093\pi\) |
0.515985 | + | 0.856598i | \(0.327426\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | − | 3.46410i | 0.150756 | − | 0.261116i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.07107 | −0.529999 | ||||||||
\(179\) | 0.436492 | − | 0.756026i | 0.0326249 | − | 0.0565080i | −0.849252 | − | 0.527988i | \(-0.822947\pi\) |
0.881877 | + | 0.471480i | \(0.156280\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.86799 | 0.584823 | 0.292412 | − | 0.956293i | \(-0.405542\pi\) | ||||
0.292412 | + | 0.956293i | \(0.405542\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.74597 | 0.497319 | ||||||||
\(185\) | 9.89949 | + | 17.1464i | 0.727825 | + | 1.26063i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.82843 | − | 4.89898i | 0.206835 | − | 0.358249i | ||||
\(188\) | 6.89144 | 0.502610 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.61895 | −0.117451 | ||||||||
\(191\) | −6.93649 | + | 12.0144i | −0.501907 | + | 0.869328i | 0.498091 | + | 0.867125i | \(0.334035\pi\) |
−0.999998 | + | 0.00220333i | \(0.999299\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.06351 | − | 13.9664i | −0.580424 | − | 1.00532i | −0.995429 | − | 0.0955048i | \(-0.969553\pi\) |
0.415005 | − | 0.909819i | \(-0.363780\pi\) | |||||||
\(194\) | −17.8459 | −1.28126 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.61895 | 0.471581 | 0.235790 | − | 0.971804i | \(-0.424232\pi\) | ||||
0.235790 | + | 0.971804i | \(0.424232\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3372 | + | 17.9045i | −0.732782 | + | 1.26922i | 0.222908 | + | 0.974839i | \(0.428445\pi\) |
−0.955690 | + | 0.294376i | \(0.904888\pi\) | |||||||
\(200\) | 0.872983 | 0.0617292 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.93399 | + | 6.81388i | −0.276795 | + | 0.479423i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.74597 | + | 9.95231i | −0.401316 | + | 0.695099i | ||||
\(206\) | 9.01276 | − | 15.6106i | 0.627949 | − | 1.08764i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.12132 | − | 3.67423i | −0.147087 | − | 0.254762i | ||||
\(209\) | 1.59384 | + | 2.76062i | 0.110248 | + | 0.190956i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.30948 | − | 2.26808i | 0.0901480 | − | 0.156141i | −0.817425 | − | 0.576035i | \(-0.804599\pi\) |
0.907573 | + | 0.419894i | \(0.137933\pi\) | |||||||
\(212\) | 10.6190 | 0.729312 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.7460 | 1.07637 | ||||||||
\(215\) | −9.01276 | − | 15.6106i | −0.614665 | − | 1.06463i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.56351 | + | 7.90423i | 0.309080 | + | 0.535342i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.06301 | + | 7.03734i | 0.273928 | + | 0.474458i | ||||
\(221\) | −3.00000 | − | 5.19615i | −0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.74667 | − | 9.95352i | −0.384825 | − | 0.666537i | 0.606920 | − | 0.794763i | \(-0.292405\pi\) |
−0.991745 | + | 0.128226i | \(0.959072\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.93649 | + | 3.35410i | 0.128814 | + | 0.223112i | ||||
\(227\) | −6.09452 | −0.404507 | −0.202254 | − | 0.979333i | \(-0.564827\pi\) | ||||
−0.202254 | + | 0.979333i | \(0.564827\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.86799 | −0.519931 | −0.259966 | − | 0.965618i | \(-0.583711\pi\) | ||||
−0.259966 | + | 0.965618i | \(0.583711\pi\) | |||||||
\(230\) | −6.85224 | + | 11.8684i | −0.451823 | + | 0.782580i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.43649 | − | 7.68423i | −0.291270 | − | 0.504494i | ||||
\(233\) | 11.3730 | + | 19.6986i | 0.745069 | + | 1.29050i | 0.950163 | + | 0.311755i | \(0.100917\pi\) |
−0.205094 | + | 0.978742i | \(0.565750\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.00000 | + | 12.1244i | −0.456630 | + | 0.790906i | ||||
\(236\) | −1.32440 | + | 2.29393i | −0.0862110 | + | 0.149322i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.50000 | + | 12.9904i | −0.485135 | + | 0.840278i | −0.999854 | − | 0.0170808i | \(-0.994563\pi\) |
0.514719 | + | 0.857359i | \(0.327896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.77347 | 0.114239 | 0.0571197 | − | 0.998367i | \(-0.481808\pi\) | ||||
0.0571197 | + | 0.998367i | \(0.481808\pi\) | |||||||
\(242\) | 2.50000 | − | 4.33013i | 0.160706 | − | 0.278351i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.796921 | −0.0510176 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.38105 | 0.215131 | ||||||||
\(248\) | 2.73861 | + | 4.74342i | 0.173902 | + | 0.301207i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.96550 | + | 10.3325i | −0.377291 | + | 0.653488i | ||||
\(251\) | 25.8935 | 1.63438 | 0.817192 | − | 0.576366i | \(-0.195530\pi\) | ||||
0.817192 | + | 0.576366i | \(0.195530\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.9839 | 1.69646 | ||||||||
\(254\) | 7.37298 | − | 12.7704i | 0.462622 | − | 0.801285i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 13.9625 | 0.870957 | 0.435479 | − | 0.900199i | \(-0.356579\pi\) | ||||
0.435479 | + | 0.900199i | \(0.356579\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.61895 | 0.534525 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.93399 | − | 6.81388i | 0.243043 | − | 0.420963i | ||||
\(263\) | −5.61895 | −0.346479 | −0.173240 | − | 0.984880i | \(-0.555424\pi\) | ||||
−0.173240 | + | 0.984880i | \(0.555424\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.7862 | + | 18.6823i | −0.662593 | + | 1.14764i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.436492 | + | 0.756026i | −0.0266630 | + | 0.0461816i | ||||
\(269\) | −1.72286 | + | 2.98408i | −0.105045 | + | 0.181943i | −0.913756 | − | 0.406262i | \(-0.866832\pi\) |
0.808712 | + | 0.588205i | \(0.200165\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.53553 | + | 6.12372i | 0.214768 | + | 0.371990i | 0.953201 | − | 0.302338i | \(-0.0977670\pi\) |
−0.738433 | + | 0.674327i | \(0.764434\pi\) | |||||||
\(272\) | −0.707107 | − | 1.22474i | −0.0428746 | − | 0.0742611i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.74597 | + | 13.4164i | −0.467951 | + | 0.810515i | ||||
\(275\) | 3.49193 | 0.210572 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.3649 | −1.46395 | −0.731973 | − | 0.681334i | \(-0.761400\pi\) | ||||
−0.731973 | + | 0.681334i | \(0.761400\pi\) | |||||||
\(278\) | 9.23159 | + | 15.9896i | 0.553674 | + | 0.958992i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.37298 | − | 5.84218i | −0.201215 | − | 0.348515i | 0.747705 | − | 0.664031i | \(-0.231156\pi\) |
−0.948920 | + | 0.315516i | \(0.897822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.25839 | + | 9.10781i | 0.312579 | + | 0.541403i | 0.978920 | − | 0.204244i | \(-0.0654737\pi\) |
−0.666341 | + | 0.745647i | \(0.732140\pi\) | |||||||
\(284\) | −1.06351 | − | 1.84205i | −0.0631076 | − | 0.109306i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.48528 | − | 14.6969i | −0.501745 | − | 0.869048i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.50000 | + | 12.9904i | 0.441176 | + | 0.764140i | ||||
\(290\) | 18.0255 | 1.05849 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −15.3767 | −0.899855 | ||||||||
\(293\) | 3.13707 | − | 5.43357i | 0.183270 | − | 0.317433i | −0.759722 | − | 0.650248i | \(-0.774665\pi\) |
0.942992 | + | 0.332815i | \(0.107998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.69052 | − | 4.66013i | −0.156648 | − | 0.271323i | ||||
\(296\) | −4.87298 | − | 8.44025i | −0.283236 | − | 0.490580i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.127017 | − | 0.219999i | 0.00735788 | − | 0.0127442i | ||||
\(299\) | 14.3104 | − | 24.7863i | 0.827589 | − | 1.43343i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.50000 | − | 9.52628i | 0.316489 | − | 0.548176i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.796921 | 0.0457066 | ||||||||
\(305\) | 0.809475 | − | 1.40205i | 0.0463504 | − | 0.0802813i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.1200 | 1.37660 | 0.688302 | − | 0.725425i | \(-0.258357\pi\) | ||||
0.688302 | + | 0.725425i | \(0.258357\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11.1270 | −0.631972 | ||||||||
\(311\) | 0.707107 | + | 1.22474i | 0.0400963 | + | 0.0694489i | 0.885377 | − | 0.464873i | \(-0.153900\pi\) |
−0.845281 | + | 0.534322i | \(0.820567\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.3452 | − | 23.1146i | 0.754316 | − | 1.30651i | −0.191397 | − | 0.981513i | \(-0.561302\pi\) |
0.945714 | − | 0.325001i | \(-0.105365\pi\) | |||||||
\(314\) | 6.45378 | 0.364208 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.87298 | 0.330381 | ||||||||
\(317\) | 0.690525 | − | 1.19602i | 0.0387837 | − | 0.0671754i | −0.845982 | − | 0.533212i | \(-0.820985\pi\) |
0.884766 | + | 0.466036i | \(0.154318\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.7460 | − | 30.7369i | −0.993583 | − | 1.72094i | ||||
\(320\) | 2.03151 | 0.113565 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.12702 | 0.0627089 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.85188 | − | 3.20755i | 0.102724 | − | 0.177923i | ||||
\(326\) | −10.0000 | −0.553849 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.82843 | − | 4.89898i | 0.156174 | − | 0.270501i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.18246 | − | 15.9045i | 0.504714 | − | 0.874190i | −0.495272 | − | 0.868738i | \(-0.664931\pi\) |
0.999985 | − | 0.00545133i | \(-0.00173522\pi\) | |||||||
\(332\) | −4.15283 | + | 7.19291i | −0.227916 | + | 0.394762i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.18433 | − | 10.7116i | −0.338392 | − | 0.586111i | ||||
\(335\) | −0.886735 | − | 1.53587i | −0.0484475 | − | 0.0839136i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.127017 | + | 0.219999i | −0.00691904 | + | 0.0119841i | −0.869464 | − | 0.493996i | \(-0.835536\pi\) |
0.862545 | + | 0.505980i | \(0.168869\pi\) | |||||||
\(338\) | −5.00000 | −0.271964 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.87298 | 0.155809 | ||||||||
\(341\) | 10.9545 | + | 18.9737i | 0.593217 | + | 1.02748i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.43649 | + | 7.68423i | 0.239200 | + | 0.414306i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.36396 | + | 11.0227i | 0.342129 | + | 0.592584i | ||||
\(347\) | −3.87298 | − | 6.70820i | −0.207913 | − | 0.360115i | 0.743144 | − | 0.669131i | \(-0.233334\pi\) |
−0.951057 | + | 0.309016i | \(0.900000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.21584 | + | 14.2302i | 0.439784 | + | 0.761728i | 0.997672 | − | 0.0681880i | \(-0.0217218\pi\) |
−0.557889 | + | 0.829916i | \(0.688388\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.00000 | − | 3.46410i | −0.106600 | − | 0.184637i | ||||
\(353\) | −18.0255 | −0.959402 | −0.479701 | − | 0.877432i | \(-0.659255\pi\) | ||||
−0.479701 | + | 0.877432i | \(0.659255\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.32105 | 0.229337 | ||||||||
\(356\) | −3.53553 | + | 6.12372i | −0.187383 | + | 0.324557i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.436492 | − | 0.756026i | −0.0230693 | − | 0.0399572i | ||||
\(359\) | −14.1190 | − | 24.4547i | −0.745170 | − | 1.29067i | −0.950115 | − | 0.311898i | \(-0.899035\pi\) |
0.204946 | − | 0.978773i | \(-0.434298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.18246 | − | 15.9045i | 0.483287 | − | 0.837078i | ||||
\(362\) | 3.93399 | − | 6.81388i | 0.206766 | − | 0.358129i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.6190 | − | 27.0528i | 0.817533 | − | 1.41601i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.06301 | 0.212088 | 0.106044 | − | 0.994361i | \(-0.466182\pi\) | ||||
0.106044 | + | 0.994361i | \(0.466182\pi\) | |||||||
\(368\) | 3.37298 | − | 5.84218i | 0.175829 | − | 0.304545i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 19.7990 | 1.02930 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.87298 | −0.459426 | −0.229713 | − | 0.973258i | \(-0.573779\pi\) | ||||
−0.229713 | + | 0.973258i | \(0.573779\pi\) | |||||||
\(374\) | −2.82843 | − | 4.89898i | −0.146254 | − | 0.253320i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.44572 | − | 5.96816i | 0.177699 | − | 0.307784i | ||||
\(377\) | −37.6449 | −1.93881 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.3649 | −0.635143 | −0.317572 | − | 0.948234i | \(-0.602867\pi\) | ||||
−0.317572 | + | 0.948234i | \(0.602867\pi\) | |||||||
\(380\) | −0.809475 | + | 1.40205i | −0.0415252 | + | 0.0719237i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.93649 | + | 12.0144i | 0.354902 | + | 0.614708i | ||||
\(383\) | −23.8620 | −1.21929 | −0.609646 | − | 0.792674i | \(-0.708688\pi\) | ||||
−0.609646 | + | 0.792674i | \(0.708688\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.1270 | −0.820844 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.92295 | + | 15.4550i | −0.452994 | + | 0.784608i | ||||
\(389\) | −20.8730 | −1.05830 | −0.529151 | − | 0.848528i | \(-0.677490\pi\) | ||||
−0.529151 | + | 0.848528i | \(0.677490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.77012 | − | 8.26209i | 0.241235 | − | 0.417832i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.30948 | − | 5.73218i | 0.166729 | − | 0.288783i | ||||
\(395\) | −5.96550 | + | 10.3325i | −0.300157 | + | 0.519887i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.53553 | + | 6.12372i | 0.177443 | + | 0.307341i | 0.941004 | − | 0.338395i | \(-0.109884\pi\) |
−0.763561 | + | 0.645736i | \(0.776551\pi\) | |||||||
\(398\) | 10.3372 | + | 17.9045i | 0.518155 | + | 0.897471i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.436492 | − | 0.756026i | 0.0218246 | − | 0.0378013i | ||||
\(401\) | −3.87298 | −0.193408 | −0.0967038 | − | 0.995313i | \(-0.530830\pi\) | ||||
−0.0967038 | + | 0.995313i | \(0.530830\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.2379 | 1.15756 | ||||||||
\(404\) | 3.93399 | + | 6.81388i | 0.195724 | + | 0.339003i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.4919 | − | 33.7610i | −0.966179 | − | 1.67347i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.8144 | − | 27.3913i | −0.781971 | − | 1.35441i | −0.930792 | − | 0.365549i | \(-0.880881\pi\) |
0.148821 | − | 0.988864i | \(-0.452452\pi\) | |||||||
\(410\) | 5.74597 | + | 9.95231i | 0.283773 | + | 0.491509i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.01276 | − | 15.6106i | −0.444027 | − | 0.769077i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.43649 | − | 14.6124i | −0.414131 | − | 0.717296i | ||||
\(416\) | −4.24264 | −0.208013 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.18768 | 0.155915 | ||||||||
\(419\) | 1.99230 | − | 3.45077i | 0.0973304 | − | 0.168581i | −0.813248 | − | 0.581917i | \(-0.802303\pi\) |
0.910579 | + | 0.413335i | \(0.135636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.56351 | + | 4.44013i | 0.124938 | + | 0.216399i | 0.921709 | − | 0.387883i | \(-0.126794\pi\) |
−0.796771 | + | 0.604282i | \(0.793460\pi\) | |||||||
\(422\) | −1.30948 | − | 2.26808i | −0.0637442 | − | 0.110408i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.30948 | − | 9.19628i | 0.257851 | − | 0.446611i | ||||
\(425\) | 0.617292 | − | 1.06918i | 0.0299431 | − | 0.0518629i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.87298 | − | 13.6364i | 0.380555 | − | 0.659141i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.0255 | −0.869268 | ||||||||
\(431\) | 4.74597 | − | 8.22026i | 0.228605 | − | 0.395956i | −0.728790 | − | 0.684737i | \(-0.759917\pi\) |
0.957395 | + | 0.288782i | \(0.0932502\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.6985 | 1.42722 | 0.713609 | − | 0.700544i | \(-0.247059\pi\) | ||||
0.713609 | + | 0.700544i | \(0.247059\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.12702 | 0.437105 | ||||||||
\(437\) | 2.68800 | + | 4.65576i | 0.128585 | + | 0.222715i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.47723 | − | 9.48683i | 0.261414 | − | 0.452782i | −0.705204 | − | 0.709004i | \(-0.749145\pi\) |
0.966618 | + | 0.256223i | \(0.0824780\pi\) | |||||||
\(440\) | 8.12602 | 0.387393 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | 12.1825 | − | 21.1006i | 0.578806 | − | 1.00252i | −0.416811 | − | 0.908993i | \(-0.636852\pi\) |
0.995617 | − | 0.0935281i | \(-0.0298145\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.18246 | − | 12.4404i | −0.340481 | − | 0.589731i | ||||
\(446\) | −11.4933 | −0.544225 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.00000 | −0.424736 | −0.212368 | − | 0.977190i | \(-0.568118\pi\) | ||||
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3137 | − | 19.5959i | 0.532742 | − | 0.922736i | ||||
\(452\) | 3.87298 | 0.182170 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.04726 | + | 5.27801i | −0.143015 | + | 0.247709i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.9365 | + | 29.3349i | −0.792256 | + | 1.37223i | 0.132312 | + | 0.991208i | \(0.457760\pi\) |
−0.924567 | + | 0.381019i | \(0.875573\pi\) | |||||||
\(458\) | −3.93399 | + | 6.81388i | −0.183823 | + | 0.318392i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.85224 | + | 11.8684i | 0.319487 | + | 0.553368i | ||||
\(461\) | 4.98895 | + | 8.64112i | 0.232359 | + | 0.402457i | 0.958502 | − | 0.285087i | \(-0.0920224\pi\) |
−0.726143 | + | 0.687544i | \(0.758689\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.8095 | + | 18.7226i | −0.502359 | + | 0.870111i | 0.497637 | + | 0.867385i | \(0.334201\pi\) |
−0.999996 | + | 0.00272598i | \(0.999132\pi\) | |||||||
\(464\) | −8.87298 | −0.411918 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.7460 | 1.05369 | ||||||||
\(467\) | −19.5295 | − | 33.8262i | −0.903720 | − | 1.56529i | −0.822627 | − | 0.568582i | \(-0.807492\pi\) |
−0.0810929 | − | 0.996707i | \(-0.525841\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.00000 | + | 12.1244i | 0.322886 | + | 0.559255i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.32440 | + | 2.29393i | 0.0609604 | + | 0.105587i | ||||
\(473\) | 17.7460 | + | 30.7369i | 0.815960 | + | 1.41328i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.347849 | + | 0.602493i | 0.0159604 | + | 0.0276443i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.50000 | + | 12.9904i | 0.343042 | + | 0.594166i | ||||
\(479\) | −18.0255 | −0.823607 | −0.411803 | − | 0.911273i | \(-0.635101\pi\) | ||||
−0.411803 | + | 0.911273i | \(0.635101\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.3486 | −1.88534 | ||||||||
\(482\) | 0.886735 | − | 1.53587i | 0.0403897 | − | 0.0699570i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.50000 | − | 4.33013i | −0.113636 | − | 0.196824i | ||||
\(485\) | −18.1270 | − | 31.3969i | −0.823105 | − | 1.42566i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.2460 | + | 26.4068i | −0.690861 | + | 1.19661i | 0.280696 | + | 0.959797i | \(0.409435\pi\) |
−0.971556 | + | 0.236809i | \(0.923898\pi\) | |||||||
\(488\) | −0.398461 | + | 0.690154i | −0.0180375 | + | 0.0312418i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.87298 | + | 11.9044i | −0.310173 | + | 0.537236i | −0.978400 | − | 0.206722i | \(-0.933720\pi\) |
0.668226 | + | 0.743958i | \(0.267054\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.5483 | −0.565147 | ||||||||
\(494\) | 1.69052 | − | 2.92808i | 0.0760603 | − | 0.131740i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.47723 | 0.245935 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.2540 | −0.638098 | −0.319049 | − | 0.947738i | \(-0.603363\pi\) | ||||
−0.319049 | + | 0.947738i | \(0.603363\pi\) | |||||||
\(500\) | 5.96550 | + | 10.3325i | 0.266785 | + | 0.462086i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.9468 | − | 22.4244i | 0.577842 | − | 1.00085i | ||||
\(503\) | 18.0255 | 0.803718 | 0.401859 | − | 0.915702i | \(-0.368364\pi\) | ||||
0.401859 | + | 0.915702i | \(0.368364\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.9839 | −0.711273 | ||||||||
\(506\) | 13.4919 | − | 23.3687i | 0.599790 | − | 1.03887i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.37298 | − | 12.7704i | −0.327123 | − | 0.566594i | ||||
\(509\) | 33.7615 | 1.49645 | 0.748226 | − | 0.663444i | \(-0.230906\pi\) | ||||
0.748226 | + | 0.663444i | \(0.230906\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.98125 | − | 12.0919i | 0.307930 | − | 0.533350i | ||||
\(515\) | 36.6190 | 1.61362 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.7829 | − | 23.8726i | 0.606170 | − | 1.04992i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.30948 | − | 7.46423i | 0.188983 | − | 0.327328i | ||||
\(521\) | −0.707107 | + | 1.22474i | −0.0309789 | + | 0.0536570i | −0.881099 | − | 0.472931i | \(-0.843196\pi\) |
0.850120 | + | 0.526589i | \(0.176529\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5057 | − | 26.8567i | −0.678019 | − | 1.17436i | −0.975577 | − | 0.219659i | \(-0.929506\pi\) |
0.297558 | − | 0.954704i | \(-0.403828\pi\) | |||||||
\(524\) | −3.93399 | − | 6.81388i | −0.171857 | − | 0.297666i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.80948 | + | 4.86615i | −0.122499 | + | 0.212174i | ||||
\(527\) | 7.74597 | 0.337420 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.5081 | 0.978612 | ||||||||
\(530\) | 10.7862 | + | 18.6823i | 0.468524 | + | 0.811507i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0000 | − | 20.7846i | −0.519778 | − | 0.900281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.9940 | + | 27.7024i | 0.691481 | + | 1.19768i | ||||
\(536\) | 0.436492 | + | 0.756026i | 0.0188536 | + | 0.0326553i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.72286 | + | 2.98408i | 0.0742778 | + | 0.128653i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.05544 | − | 13.9524i | −0.346330 | − | 0.599862i | 0.639264 | − | 0.768987i | \(-0.279239\pi\) |
−0.985595 | + | 0.169125i | \(0.945906\pi\) | |||||||
\(542\) | 7.07107 | 0.303728 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.41421 | −0.0606339 | ||||||||
\(545\) | −9.27079 | + | 16.0575i | −0.397117 | + | 0.687827i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.4919 | − | 25.1008i | −0.619630 | − | 1.07323i | −0.989553 | − | 0.144169i | \(-0.953949\pi\) |
0.369923 | − | 0.929062i | \(-0.379384\pi\) | |||||||
\(548\) | 7.74597 | + | 13.4164i | 0.330891 | + | 0.573121i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.74597 | − | 3.02410i | 0.0744483 | − | 0.128948i | ||||
\(551\) | 3.53553 | − | 6.12372i | 0.150619 | − | 0.260879i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −12.1825 | + | 21.1006i | −0.517583 | + | 0.896480i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.4632 | 0.783013 | ||||||||
\(557\) | 1.69052 | − | 2.92808i | 0.0716298 | − | 0.124067i | −0.827986 | − | 0.560749i | \(-0.810513\pi\) |
0.899616 | + | 0.436682i | \(0.143847\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.6449 | 1.59221 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.74597 | −0.284561 | ||||||||
\(563\) | 2.60960 | + | 4.51995i | 0.109981 | + | 0.190493i | 0.915762 | − | 0.401720i | \(-0.131588\pi\) |
−0.805781 | + | 0.592213i | \(0.798254\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.93399 | + | 6.81388i | −0.165504 | + | 0.286662i | ||||
\(566\) | 10.5168 | 0.442054 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.12702 | −0.0892476 | ||||||||
\(569\) | 3.74597 | − | 6.48820i | 0.157039 | − | 0.272000i | −0.776761 | − | 0.629796i | \(-0.783138\pi\) |
0.933800 | + | 0.357796i | \(0.116472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.254033 | − | 0.439999i | −0.0106310 | − | 0.0184134i | 0.860661 | − | 0.509178i | \(-0.170051\pi\) |
−0.871292 | + | 0.490765i | \(0.836717\pi\) | |||||||
\(572\) | −16.9706 | −0.709575 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.88912 | 0.245593 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.5879 | − | 30.4631i | 0.732192 | − | 1.26819i | −0.223752 | − | 0.974646i | \(-0.571831\pi\) |
0.955944 | − | 0.293548i | \(-0.0948360\pi\) | |||||||
\(578\) | 15.0000 | 0.623918 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.01276 | − | 15.6106i | 0.374234 | − | 0.648193i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.2379 | − | 36.7851i | 0.879584 | − | 1.52348i | ||||
\(584\) | −7.68836 | + | 13.3166i | −0.318147 | + | 0.551046i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.13707 | − | 5.43357i | −0.129591 | − | 0.224459i | ||||
\(587\) | 14.8884 | + | 25.7875i | 0.614512 | + | 1.06437i | 0.990470 | + | 0.137729i | \(0.0439804\pi\) |
−0.375958 | + | 0.926637i | \(0.622686\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.18246 | + | 3.78013i | −0.0899266 | + | 0.155757i | ||||
\(590\) | −5.38105 | −0.221534 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.74597 | −0.400557 | ||||||||
\(593\) | −11.4035 | − | 19.7515i | −0.468287 | − | 0.811096i | 0.531057 | − | 0.847336i | \(-0.321795\pi\) |
−0.999343 | + | 0.0362403i | \(0.988462\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.127017 | − | 0.219999i | −0.00520280 | − | 0.00901152i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14.3104 | − | 24.7863i | −0.585194 | − | 1.01359i | ||||
\(599\) | 0.618950 | + | 1.07205i | 0.0252896 | + | 0.0438029i | 0.878393 | − | 0.477939i | \(-0.158616\pi\) |
−0.853104 | + | 0.521742i | \(0.825283\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.8224 | − | 32.6014i | −0.767783 | − | 1.32984i | −0.938762 | − | 0.344565i | \(-0.888026\pi\) |
0.170979 | − | 0.985275i | \(-0.445307\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.50000 | − | 9.52628i | −0.223792 | − | 0.387619i | ||||
\(605\) | 10.1575 | 0.412962 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.7360 | −0.638704 | −0.319352 | − | 0.947636i | \(-0.603465\pi\) | ||||
−0.319352 | + | 0.947636i | \(0.603465\pi\) | |||||||
\(608\) | 0.398461 | − | 0.690154i | 0.0161597 | − | 0.0279894i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.809475 | − | 1.40205i | −0.0327747 | − | 0.0567674i | ||||
\(611\) | −14.6190 | − | 25.3208i | −0.591419 | − | 1.02437i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.69052 | + | 2.92808i | −0.0682797 | + | 0.118264i | −0.898144 | − | 0.439701i | \(-0.855084\pi\) |
0.829864 | + | 0.557965i | \(0.188418\pi\) | |||||||
\(614\) | 12.0600 | − | 20.8886i | 0.486703 | − | 0.842994i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.8730 | + | 24.0287i | −0.558505 | + | 0.967360i | 0.439116 | + | 0.898430i | \(0.355292\pi\) |
−0.997622 | + | 0.0689293i | \(0.978042\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.3466 | −0.898184 | −0.449092 | − | 0.893485i | \(-0.648253\pi\) | ||||
−0.449092 | + | 0.893485i | \(0.648253\pi\) | |||||||
\(620\) | −5.56351 | + | 9.63628i | −0.223436 | + | 0.387002i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.41421 | 0.0567048 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.8730 | −0.794919 | ||||||||
\(626\) | −13.3452 | − | 23.1146i | −0.533382 | − | 0.923845i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.22689 | − | 5.58913i | 0.128767 | − | 0.223031i | ||||
\(629\) | −13.7829 | −0.549559 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.6190 | −1.09949 | −0.549747 | − | 0.835332i | \(-0.685276\pi\) | ||||
−0.549747 | + | 0.835332i | \(0.685276\pi\) | |||||||
\(632\) | 2.93649 | − | 5.08615i | 0.116807 | − | 0.202316i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.690525 | − | 1.19602i | −0.0274243 | − | 0.0475002i | ||||
\(635\) | 29.9565 | 1.18879 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −35.4919 | −1.40514 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.01575 | − | 1.75934i | 0.0401512 | − | 0.0695439i | ||||
\(641\) | 37.1109 | 1.46579 | 0.732896 | − | 0.680341i | \(-0.238168\pi\) | ||||
0.732896 | + | 0.680341i | \(0.238168\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.1468 | + | 34.8953i | −0.794514 | + | 1.37614i | 0.128634 | + | 0.991692i | \(0.458941\pi\) |
−0.923147 | + | 0.384446i | \(0.874392\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.563508 | − | 0.976025i | 0.0221709 | − | 0.0384012i | ||||
\(647\) | −2.73861 | + | 4.74342i | −0.107666 | + | 0.186483i | −0.914824 | − | 0.403852i | \(-0.867671\pi\) |
0.807158 | + | 0.590335i | \(0.201004\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.29760 | + | 9.17571i | 0.207949 | + | 0.360178i | ||||
\(650\) | −1.85188 | − | 3.20755i | −0.0726366 | − | 0.125810i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.00000 | + | 8.66025i | −0.195815 | + | 0.339162i | ||||
\(653\) | 45.4919 | 1.78024 | 0.890118 | − | 0.455729i | \(-0.150621\pi\) | ||||
0.890118 | + | 0.455729i | \(0.150621\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.9839 | 0.624541 | ||||||||
\(656\) | −2.82843 | − | 4.89898i | −0.110432 | − | 0.191273i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.4365 | + | 31.9329i | 0.718184 | + | 1.24393i | 0.961719 | + | 0.274039i | \(0.0883596\pi\) |
−0.243535 | + | 0.969892i | \(0.578307\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.4977 | + | 21.6466i | 0.486104 | + | 0.841956i | 0.999872 | − | 0.0159726i | \(-0.00508447\pi\) |
−0.513769 | + | 0.857929i | \(0.671751\pi\) | |||||||
\(662\) | −9.18246 | − | 15.9045i | −0.356886 | − | 0.618145i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.15283 | + | 7.19291i | 0.161161 | + | 0.279139i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.9284 | − | 51.8376i | −1.15883 | − | 2.00716i | ||||
\(668\) | −12.3687 | −0.478558 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.77347 | −0.0685152 | ||||||||
\(671\) | −1.59384 | + | 2.76062i | −0.0615296 | + | 0.106572i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.1190 | + | 27.9188i | 0.621340 | + | 1.07619i | 0.989236 | + | 0.146326i | \(0.0467447\pi\) |
−0.367897 | + | 0.929867i | \(0.619922\pi\) | |||||||
\(674\) | 0.127017 | + | 0.219999i | 0.00489250 | + | 0.00847406i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.50000 | + | 4.33013i | −0.0961538 | + | 0.166543i | ||||
\(677\) | −6.36396 | + | 11.0227i | −0.244587 | + | 0.423637i | −0.962015 | − | 0.272995i | \(-0.911986\pi\) |
0.717428 | + | 0.696632i | \(0.245319\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.43649 | − | 2.48808i | 0.0550869 | − | 0.0954134i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 21.9089 | 0.838935 | ||||||||
\(683\) | −3.87298 | + | 6.70820i | −0.148196 | + | 0.256682i | −0.930561 | − | 0.366138i | \(-0.880680\pi\) |
0.782365 | + | 0.622820i | \(0.214013\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.4720 | −1.20248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.87298 | 0.338279 | ||||||||
\(689\) | −22.5262 | − | 39.0165i | −0.858180 | − | 1.48641i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.6458 | + | 18.4391i | −0.404986 | + | 0.701455i | −0.994320 | − | 0.106434i | \(-0.966057\pi\) |
0.589334 | + | 0.807889i | \(0.299390\pi\) | |||||||
\(692\) | 12.7279 | 0.483843 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.74597 | −0.294033 | ||||||||
\(695\) | −18.7540 | + | 32.4829i | −0.711381 | + | 1.23215i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | − | 6.92820i | −0.151511 | − | 0.262424i | ||||
\(698\) | 16.4317 | 0.621948 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.7460 | 1.19903 | 0.599514 | − | 0.800364i | \(-0.295360\pi\) | ||||
0.599514 | + | 0.800364i | \(0.295360\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.88338 | − | 6.72622i | 0.146465 | − | 0.253684i | ||||
\(704\) | −4.00000 | −0.150756 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.01276 | + | 15.6106i | −0.339200 | + | 0.587511i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.3649 | + | 21.4167i | −0.464374 | + | 0.804320i | −0.999173 | − | 0.0406597i | \(-0.987054\pi\) |
0.534799 | + | 0.844979i | \(0.320387\pi\) | |||||||
\(710\) | 2.16052 | − | 3.74214i | 0.0810830 | − | 0.140440i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.53553 | + | 6.12372i | 0.132500 | + | 0.229496i | ||||
\(713\) | 18.4746 | + | 31.9989i | 0.691879 | + | 1.19837i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.2379 | − | 29.8569i | 0.644661 | − | 1.11659i | ||||
\(716\) | −0.872983 | −0.0326249 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.2379 | −1.05383 | ||||||||
\(719\) | −4.68030 | − | 8.10653i | −0.174546 | − | 0.302322i | 0.765458 | − | 0.643486i | \(-0.222512\pi\) |
−0.940004 | + | 0.341163i | \(0.889179\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −9.18246 | − | 15.9045i | −0.341736 | − | 0.591904i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.93399 | − | 6.81388i | −0.146206 | − | 0.253236i | ||||
\(725\) | −3.87298 | − | 6.70820i | −0.143839 | − | 0.249136i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.1153 | + | 31.3767i | 0.671861 | + | 1.16370i | 0.977376 | + | 0.211509i | \(0.0678379\pi\) |
−0.305515 | + | 0.952187i | \(0.598829\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15.6190 | − | 27.0528i | −0.578083 | − | 1.00127i | ||||
\(731\) | 12.5483 | 0.464115 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.64146 | 0.356115 | 0.178058 | − | 0.984020i | \(-0.443019\pi\) | ||||
0.178058 | + | 0.984020i | \(0.443019\pi\) | |||||||
\(734\) | 2.03151 | − | 3.51867i | 0.0749843 | − | 0.129877i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.37298 | − | 5.84218i | −0.124330 | − | 0.215346i | ||||
\(737\) | 1.74597 | + | 3.02410i | 0.0643135 | + | 0.111394i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.0000 | − | 25.9808i | 0.551784 | − | 0.955718i | −0.446362 | − | 0.894852i | \(-0.647281\pi\) |
0.998146 | − | 0.0608653i | \(-0.0193860\pi\) | |||||||
\(740\) | 9.89949 | − | 17.1464i | 0.363913 | − | 0.630315i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.8730 | + | 24.0287i | −0.508950 | + | 0.881528i | 0.490996 | + | 0.871162i | \(0.336633\pi\) |
−0.999946 | + | 0.0103660i | \(0.996700\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.516070 | 0.0189073 | ||||||||
\(746\) | −4.43649 | + | 7.68423i | −0.162432 | + | 0.281340i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.65685 | −0.206835 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0000 | −0.474377 | −0.237188 | − | 0.971464i | \(-0.576226\pi\) | ||||
−0.237188 | + | 0.971464i | \(0.576226\pi\) | |||||||
\(752\) | −3.44572 | − | 5.96816i | −0.125652 | − | 0.217636i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.8224 | + | 32.6014i | −0.685473 | + | 1.18727i | ||||
\(755\) | 22.3466 | 0.813275 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.2379 | −0.553831 | −0.276915 | − | 0.960894i | \(-0.589312\pi\) | ||||
−0.276915 | + | 0.960894i | \(0.589312\pi\) | |||||||
\(758\) | −6.18246 | + | 10.7083i | −0.224557 | + | 0.388944i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.809475 | + | 1.40205i | 0.0293627 | + | 0.0508578i | ||||
\(761\) | 2.28954 | 0.0829958 | 0.0414979 | − | 0.999139i | \(-0.486787\pi\) | ||||
0.0414979 | + | 0.999139i | \(0.486787\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.8730 | 0.501907 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.9310 | + | 20.6651i | −0.431085 | + | 0.746660i | ||||
\(767\) | 11.2379 | 0.405777 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.85993 | − | 8.41765i | 0.175254 | − | 0.303548i | −0.764995 | − | 0.644036i | \(-0.777259\pi\) |
0.940249 | + | 0.340488i | \(0.110592\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.06351 | + | 13.9664i | −0.290212 | + | 0.502662i | ||||
\(773\) | −1.72286 | + | 2.98408i | −0.0619670 | + | 0.107330i | −0.895345 | − | 0.445374i | \(-0.853071\pi\) |
0.833378 | + | 0.552704i | \(0.186404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.39076 | + | 4.14092i | 0.0858788 | + | 0.148746i | ||||
\(776\) | 8.92295 | + | 15.4550i | 0.320315 | + | 0.554802i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.4365 | + | 18.0765i | −0.374166 | + | 0.648075i | ||||
\(779\) | 4.50807 | 0.161518 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.50807 | −0.304443 | ||||||||
\(782\) | −4.77012 | − | 8.26209i | −0.170579 | − | 0.295452i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.55544 | + | 11.3544i | 0.233974 | + | 0.405254i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.77012 | − | 8.26209i | −0.170036 | − | 0.294512i | 0.768396 | − | 0.639975i | \(-0.221055\pi\) |
−0.938432 | + | 0.345463i | \(0.887722\pi\) | |||||||
\(788\) | −3.30948 | − | 5.73218i | −0.117895 | − | 0.204200i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.96550 | + | 10.3325i | 0.212243 | + | 0.367616i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.69052 | + | 2.92808i | 0.0600323 | + | 0.103979i | ||||
\(794\) | 7.07107 | 0.250943 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.6743 | 0.732782 | ||||||||
\(797\) | 13.0366 | − | 22.5800i | 0.461779 | − | 0.799825i | −0.537271 | − | 0.843410i | \(-0.680545\pi\) |
0.999050 | + | 0.0435852i | \(0.0138780\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.87298 | − | 8.44025i | −0.172394 | − | 0.298595i | ||||
\(800\) | −0.436492 | − | 0.756026i | −0.0154323 | − | 0.0267295i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.93649 | + | 3.35410i | −0.0683799 | + | 0.118437i | ||||
\(803\) | −30.7534 | + | 53.2665i | −1.08527 | + | 1.87973i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.6190 | − | 20.1246i | 0.409260 | − | 0.708859i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.86799 | 0.276795 | ||||||||
\(809\) | −15.3649 | + | 26.6128i | −0.540202 | + | 0.935657i | 0.458690 | + | 0.888596i | \(0.348319\pi\) |
−0.998892 | + | 0.0470606i | \(0.985015\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.9625 | 0.490290 | 0.245145 | − | 0.969486i | \(-0.421164\pi\) | ||||
0.245145 | + | 0.969486i | \(0.421164\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −38.9839 | −1.36638 | ||||||||
\(815\) | −10.1575 | − | 17.5934i | −0.355803 | − | 0.616268i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.53553 | + | 6.12372i | −0.123693 | + | 0.214242i | ||||
\(818\) | −31.6288 | −1.10587 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.4919 | 0.401316 | ||||||||
\(821\) | 10.7460 | − | 18.6126i | 0.375037 | − | 0.649583i | −0.615296 | − | 0.788296i | \(-0.710963\pi\) |
0.990333 | + | 0.138714i | \(0.0442967\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.8730 | + | 18.8326i | 0.379008 | + | 0.656462i | 0.990918 | − | 0.134466i | \(-0.0429318\pi\) |
−0.611910 | + | 0.790928i | \(0.709598\pi\) | |||||||
\(824\) | −18.0255 | −0.627949 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.1270 | −1.43013 | −0.715063 | − | 0.699060i | \(-0.753602\pi\) | ||||
−0.715063 | + | 0.699060i | \(0.753602\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.2179 | + | 47.1428i | −0.945317 | + | 1.63734i | −0.190202 | + | 0.981745i | \(0.560914\pi\) |
−0.755115 | + | 0.655592i | \(0.772419\pi\) | |||||||
\(830\) | −16.8730 | −0.585670 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.12132 | + | 3.67423i | −0.0735436 | + | 0.127381i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.5635 | − | 21.7606i | 0.434778 | − | 0.753058i | ||||
\(836\) | 1.59384 | − | 2.76062i | 0.0551242 | − | 0.0954779i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.99230 | − | 3.45077i | −0.0688230 | − | 0.119205i | ||||
\(839\) | 19.9672 | + | 34.5842i | 0.689345 | + | 1.19398i | 0.972050 | + | 0.234773i | \(0.0754348\pi\) |
−0.282706 | + | 0.959207i | \(0.591232\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.8649 | + | 43.0673i | −0.857411 | + | 1.48508i | ||||
\(842\) | 5.12702 | 0.176689 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.61895 | −0.0901480 | ||||||||
\(845\) | −5.07877 | − | 8.79668i | −0.174715 | − | 0.302615i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.30948 | − | 9.19628i | −0.182328 | − | 0.315802i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.617292 | − | 1.06918i | −0.0211730 | − | 0.0366726i | ||||
\(851\) | −32.8730 | − | 56.9377i | −1.12687 | − | 1.95180i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.7564 | − | 39.4153i | −0.779165 | − | 1.34955i | −0.932423 | − | 0.361368i | \(-0.882310\pi\) |
0.153258 | − | 0.988186i | \(-0.451024\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.87298 | − | 13.6364i | −0.269093 | − | 0.466083i | ||||
\(857\) | 47.7240 | 1.63022 | 0.815110 | − | 0.579306i | \(-0.196676\pi\) | ||||
0.815110 | + | 0.579306i | \(0.196676\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.28954 | 0.0781181 | 0.0390591 | − | 0.999237i | \(-0.487564\pi\) | ||||
0.0390591 | + | 0.999237i | \(0.487564\pi\) | |||||||
\(860\) | −9.01276 | + | 15.6106i | −0.307333 | + | 0.532316i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.74597 | − | 8.22026i | −0.161648 | − | 0.279983i | ||||
\(863\) | −18.0635 | − | 31.2869i | −0.614889 | − | 1.06502i | −0.990404 | − | 0.138203i | \(-0.955867\pi\) |
0.375515 | − | 0.926816i | \(-0.377466\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.9284 | + | 22.3927i | −0.439580 | + | 0.761374i | ||||
\(866\) | 14.8492 | − | 25.7196i | 0.504598 | − | 0.873989i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.7460 | − | 20.3446i | 0.398455 | − | 0.690144i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.70375 | 0.125497 | ||||||||
\(872\) | 4.56351 | − | 7.90423i | 0.154540 | − | 0.267671i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.37600 | 0.181846 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.8730 | 1.31265 | 0.656324 | − | 0.754479i | \(-0.272111\pi\) | ||||
0.656324 | + | 0.754479i | \(0.272111\pi\) | |||||||
\(878\) | −5.47723 | − | 9.48683i | −0.184847 | − | 0.320165i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.06301 | − | 7.03734i | 0.136964 | − | 0.237229i | ||||
\(881\) | 15.7360 | 0.530159 | 0.265079 | − | 0.964227i | \(-0.414602\pi\) | ||||
0.265079 | + | 0.964227i | \(0.414602\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.50807 | 0.151709 | 0.0758543 | − | 0.997119i | \(-0.475832\pi\) | ||||
0.0758543 | + | 0.997119i | \(0.475832\pi\) | |||||||
\(884\) | −3.00000 | + | 5.19615i | −0.100901 | + | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.1825 | − | 21.1006i | −0.409278 | − | 0.708890i | ||||
\(887\) | −36.0510 | −1.21048 | −0.605238 | − | 0.796045i | \(-0.706922\pi\) | ||||
−0.605238 | + | 0.796045i | \(0.706922\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.3649 | −0.481513 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.74667 | + | 9.95352i | −0.192413 | + | 0.333269i | ||||
\(893\) | 5.49193 | 0.183781 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.886735 | − | 1.53587i | 0.0296403 | − | 0.0513385i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.50000 | + | 7.79423i | −0.150167 | + | 0.260097i | ||||
\(899\) | 24.2997 | − | 42.0883i | 0.810439 | − | 1.40372i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.50873 | − | 13.0055i | −0.250152 | − | 0.433276i | ||||
\(902\) | −11.3137 | − | 19.5959i | −0.376705 | − | 0.652473i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.93649 | − | 3.35410i | 0.0644068 | − | 0.111556i | ||||
\(905\) | 15.9839 | 0.531322 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.61895 | −0.153370 | −0.0766849 | − | 0.997055i | \(-0.524434\pi\) | ||||
−0.0766849 | + | 0.997055i | \(0.524434\pi\) | |||||||
\(908\) | 3.04726 | + | 5.27801i | 0.101127 | + | 0.175157i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.6270 | − | 20.1386i | −0.385220 | − | 0.667221i | 0.606579 | − | 0.795023i | \(-0.292541\pi\) |
−0.991800 | + | 0.127802i | \(0.959208\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.6113 | + | 28.7716i | 0.549754 | + | 0.952202i | ||||
\(914\) | 16.9365 | + | 29.3349i | 0.560209 | + | 0.970311i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.93399 | + | 6.81388i | 0.129983 | + | 0.225137i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.6825 | + | 34.0910i | 0.649264 | + | 1.12456i | 0.983299 | + | 0.181998i | \(0.0582565\pi\) |
−0.334034 | + | 0.942561i | \(0.608410\pi\) | |||||||
\(920\) | 13.7045 | 0.451823 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.97790 | 0.328605 | ||||||||
\(923\) | −4.51208 | + | 7.81516i | −0.148517 | + | 0.257239i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.25403 | − | 7.36820i | −0.139872 | − | 0.242265i | ||||
\(926\) | 10.8095 | + | 18.7226i | 0.355221 | + | 0.615261i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.43649 | + | 7.68423i | −0.145635 | + | 0.252247i | ||||
\(929\) | 5.30900 | − | 9.19547i | 0.174183 | − | 0.301693i | −0.765695 | − | 0.643203i | \(-0.777605\pi\) |
0.939878 | + | 0.341510i | \(0.110938\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 11.3730 | − | 19.6986i | 0.372534 | − | 0.645249i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −39.0591 | −1.27805 | ||||||||
\(935\) | 5.74597 | − | 9.95231i | 0.187913 | − | 0.325475i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.4036 | −1.38526 | −0.692632 | − | 0.721291i | \(-0.743549\pi\) | ||||
−0.692632 | + | 0.721291i | \(0.743549\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 14.0000 | 0.456630 | ||||||||
\(941\) | 0.836124 | + | 1.44821i | 0.0272569 | + | 0.0472103i | 0.879332 | − | 0.476209i | \(-0.157989\pi\) |
−0.852075 | + | 0.523419i | \(0.824656\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.0805 | − | 33.0484i | 0.621346 | − | 1.07620i | ||||
\(944\) | 2.64880 | 0.0862110 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.4919 | 1.15394 | ||||||||
\(947\) | 13.8014 | − | 23.9047i | 0.448486 | − | 0.776800i | −0.549802 | − | 0.835295i | \(-0.685297\pi\) |
0.998288 | + | 0.0584952i | \(0.0186302\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.6190 | + | 56.4977i | 1.05886 | + | 1.83399i | ||||
\(950\) | 0.695699 | 0.0225715 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.5081 | 0.923467 | 0.461733 | − | 0.887019i | \(-0.347228\pi\) | ||||
0.461733 | + | 0.887019i | \(0.347228\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.0915 | + | 24.4072i | −0.455991 | + | 0.789800i | ||||
\(956\) | 15.0000 | 0.485135 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.01276 | + | 15.6106i | −0.291189 | + | 0.504354i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.500000 | − | 0.866025i | 0.0161290 | − | 0.0279363i | ||||
\(962\) | −20.6743 | + | 35.8090i | −0.666567 | + | 1.15453i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.886735 | − | 1.53587i | −0.0285598 | − | 0.0494671i | ||||
\(965\) | −16.3811 | − | 28.3728i | −0.527325 | − | 0.913354i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.7540 | + | 25.5547i | −0.474458 | + | 0.821785i | −0.999572 | − | 0.0292467i | \(-0.990689\pi\) |
0.525114 | + | 0.851032i | \(0.324022\pi\) | |||||||
\(968\) | −5.00000 | −0.160706 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −36.2540 | −1.16405 | ||||||||
\(971\) | 18.4240 | + | 31.9113i | 0.591254 | + | 1.02408i | 0.994064 | + | 0.108798i | \(0.0347001\pi\) |
−0.402810 | + | 0.915284i | \(0.631967\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 15.2460 | + | 26.4068i | 0.488512 | + | 0.846128i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.398461 | + | 0.690154i | 0.0127544 | + | 0.0220913i | ||||
\(977\) | 7.25403 | + | 12.5644i | 0.232077 | + | 0.401969i | 0.958419 | − | 0.285364i | \(-0.0921145\pi\) |
−0.726342 | + | 0.687333i | \(0.758781\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.1421 | + | 24.4949i | 0.451985 | + | 0.782860i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.87298 | + | 11.9044i | 0.219326 | + | 0.379883i | ||||
\(983\) | −9.89949 | −0.315745 | −0.157872 | − | 0.987460i | \(-0.550463\pi\) | ||||
−0.157872 | + | 0.987460i | \(0.550463\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.4464 | 0.428439 | ||||||||
\(986\) | −6.27415 | + | 10.8671i | −0.199810 | + | 0.346080i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.69052 | − | 2.92808i | −0.0537828 | − | 0.0931545i | ||||
\(989\) | 29.9284 | + | 51.8376i | 0.951669 | + | 1.64834i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.87298 | + | 3.24410i | −0.0594973 | + | 0.103052i | −0.894240 | − | 0.447588i | \(-0.852283\pi\) |
0.834743 | + | 0.550640i | \(0.185616\pi\) | |||||||
\(992\) | 2.73861 | − | 4.74342i | 0.0869510 | − | 0.150604i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.0000 | + | 36.3731i | −0.665745 | + | 1.15310i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.258035 | −0.00817205 | −0.00408603 | − | 0.999992i | \(-0.501301\pi\) | ||||
−0.00408603 | + | 0.999992i | \(0.501301\pi\) | |||||||
\(998\) | −7.12702 | + | 12.3444i | −0.225602 | + | 0.390754i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2646.2.h.s.361.3 | 8 | ||
3.2 | odd | 2 | 882.2.h.r.67.2 | 8 | |||
7.2 | even | 3 | 2646.2.e.r.1549.2 | 8 | |||
7.3 | odd | 6 | 2646.2.f.s.1765.3 | 8 | |||
7.4 | even | 3 | 2646.2.f.s.1765.2 | 8 | |||
7.5 | odd | 6 | 2646.2.e.r.1549.3 | 8 | |||
7.6 | odd | 2 | inner | 2646.2.h.s.361.2 | 8 | ||
9.2 | odd | 6 | 882.2.e.t.655.4 | 8 | |||
9.7 | even | 3 | 2646.2.e.r.2125.2 | 8 | |||
21.2 | odd | 6 | 882.2.e.t.373.4 | 8 | |||
21.5 | even | 6 | 882.2.e.t.373.1 | 8 | |||
21.11 | odd | 6 | 882.2.f.p.589.2 | yes | 8 | ||
21.17 | even | 6 | 882.2.f.p.589.3 | yes | 8 | ||
21.20 | even | 2 | 882.2.h.r.67.3 | 8 | |||
63.2 | odd | 6 | 882.2.h.r.79.2 | 8 | |||
63.4 | even | 3 | 7938.2.a.cd.1.3 | 4 | |||
63.11 | odd | 6 | 882.2.f.p.295.1 | ✓ | 8 | ||
63.16 | even | 3 | inner | 2646.2.h.s.667.3 | 8 | ||
63.20 | even | 6 | 882.2.e.t.655.1 | 8 | |||
63.25 | even | 3 | 2646.2.f.s.883.2 | 8 | |||
63.31 | odd | 6 | 7938.2.a.cd.1.2 | 4 | |||
63.32 | odd | 6 | 7938.2.a.cu.1.2 | 4 | |||
63.34 | odd | 6 | 2646.2.e.r.2125.3 | 8 | |||
63.38 | even | 6 | 882.2.f.p.295.4 | yes | 8 | ||
63.47 | even | 6 | 882.2.h.r.79.3 | 8 | |||
63.52 | odd | 6 | 2646.2.f.s.883.3 | 8 | |||
63.59 | even | 6 | 7938.2.a.cu.1.3 | 4 | |||
63.61 | odd | 6 | inner | 2646.2.h.s.667.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.e.t.373.1 | 8 | 21.5 | even | 6 | |||
882.2.e.t.373.4 | 8 | 21.2 | odd | 6 | |||
882.2.e.t.655.1 | 8 | 63.20 | even | 6 | |||
882.2.e.t.655.4 | 8 | 9.2 | odd | 6 | |||
882.2.f.p.295.1 | ✓ | 8 | 63.11 | odd | 6 | ||
882.2.f.p.295.4 | yes | 8 | 63.38 | even | 6 | ||
882.2.f.p.589.2 | yes | 8 | 21.11 | odd | 6 | ||
882.2.f.p.589.3 | yes | 8 | 21.17 | even | 6 | ||
882.2.h.r.67.2 | 8 | 3.2 | odd | 2 | |||
882.2.h.r.67.3 | 8 | 21.20 | even | 2 | |||
882.2.h.r.79.2 | 8 | 63.2 | odd | 6 | |||
882.2.h.r.79.3 | 8 | 63.47 | even | 6 | |||
2646.2.e.r.1549.2 | 8 | 7.2 | even | 3 | |||
2646.2.e.r.1549.3 | 8 | 7.5 | odd | 6 | |||
2646.2.e.r.2125.2 | 8 | 9.7 | even | 3 | |||
2646.2.e.r.2125.3 | 8 | 63.34 | odd | 6 | |||
2646.2.f.s.883.2 | 8 | 63.25 | even | 3 | |||
2646.2.f.s.883.3 | 8 | 63.52 | odd | 6 | |||
2646.2.f.s.1765.2 | 8 | 7.4 | even | 3 | |||
2646.2.f.s.1765.3 | 8 | 7.3 | odd | 6 | |||
2646.2.h.s.361.2 | 8 | 7.6 | odd | 2 | inner | ||
2646.2.h.s.361.3 | 8 | 1.1 | even | 1 | trivial | ||
2646.2.h.s.667.2 | 8 | 63.61 | odd | 6 | inner | ||
2646.2.h.s.667.3 | 8 | 63.16 | even | 3 | inner | ||
7938.2.a.cd.1.2 | 4 | 63.31 | odd | 6 | |||
7938.2.a.cd.1.3 | 4 | 63.4 | even | 3 | |||
7938.2.a.cu.1.2 | 4 | 63.32 | odd | 6 | |||
7938.2.a.cu.1.3 | 4 | 63.59 | even | 6 |