Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [200,2,Mod(41,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("200.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.m (of order \(5\), degree \(4\), 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: | \(1.59700804043\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 81.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 200.81 |
Dual form | 200.2.m.a.121.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/200\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 | 0 | ||||||||
\(3\) | 1.80902 | − | 1.31433i | 1.04444 | − | 0.758827i | 0.0732898 | − | 0.997311i | \(-0.476650\pi\) |
0.971147 | + | 0.238483i | \(0.0766502\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.690983 | + | 2.12663i | −0.309017 | + | 0.951057i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.61803 | 0.989524 | 0.494762 | − | 0.869029i | \(-0.335255\pi\) | ||||
0.494762 | + | 0.869029i | \(0.335255\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.618034 | − | 1.90211i | 0.206011 | − | 0.634038i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.381966 | + | 1.17557i | 0.115167 | + | 0.354448i | 0.991982 | − | 0.126380i | \(-0.0403360\pi\) |
−0.876815 | + | 0.480828i | \(0.840336\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.04508 | − | 3.21644i | 0.289854 | − | 0.892080i | −0.695047 | − | 0.718964i | \(-0.744616\pi\) |
0.984901 | − | 0.173116i | \(-0.0553835\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.54508 | + | 4.75528i | 0.398939 | + | 1.22781i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.23607 | − | 3.07768i | −1.02740 | − | 0.746448i | −0.0596113 | − | 0.998222i | \(-0.518986\pi\) |
−0.967786 | + | 0.251774i | \(0.918986\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.16312 | − | 4.47777i | −1.41392 | − | 1.02727i | −0.992739 | − | 0.120292i | \(-0.961617\pi\) |
−0.421178 | − | 0.906978i | \(-0.638383\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.73607 | − | 3.44095i | 1.03349 | − | 0.750878i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.69098 | + | 5.20431i | 0.352594 | + | 1.08517i | 0.957391 | + | 0.288794i | \(0.0932543\pi\) |
−0.604797 | + | 0.796380i | \(0.706746\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04508 | − | 2.93893i | −0.809017 | − | 0.587785i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.690983 | + | 2.12663i | 0.132980 | + | 0.409270i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.54508 | + | 2.57565i | −0.658306 | + | 0.478287i | −0.866090 | − | 0.499887i | \(-0.833375\pi\) |
0.207785 | + | 0.978175i | \(0.433375\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.80902 | + | 2.76741i | 0.684120 | + | 0.497042i | 0.874722 | − | 0.484625i | \(-0.161044\pi\) |
−0.190602 | + | 0.981667i | \(0.561044\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.23607 | + | 1.62460i | 0.389249 | + | 0.282806i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.80902 | + | 5.56758i | −0.305780 | + | 0.941093i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.54508 | + | 7.83297i | −0.418409 | + | 1.28773i | 0.490756 | + | 0.871297i | \(0.336721\pi\) |
−0.909166 | + | 0.416435i | \(0.863279\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.33688 | − | 7.19218i | −0.374200 | − | 1.15167i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.76393 | − | 5.42882i | 0.275480 | − | 0.847840i | −0.713612 | − | 0.700541i | \(-0.752942\pi\) |
0.989092 | − | 0.147299i | \(-0.0470579\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.38197 | 0.668244 | 0.334122 | − | 0.942530i | \(-0.391560\pi\) | ||||
0.334122 | + | 0.942530i | \(0.391560\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.61803 | + | 2.62866i | 0.539345 | + | 0.391857i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.118034 | + | 0.0857567i | −0.0172170 | + | 0.0125089i | −0.596360 | − | 0.802717i | \(-0.703387\pi\) |
0.579143 | + | 0.815226i | \(0.303387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.145898 | −0.0208426 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.7082 | −1.63948 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.42705 | + | 4.66953i | −0.882823 | + | 0.641409i | −0.933997 | − | 0.357281i | \(-0.883704\pi\) |
0.0511736 | + | 0.998690i | \(0.483704\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.76393 | −0.372689 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.0344 | −2.25627 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.736068 | − | 2.26538i | 0.0958279 | − | 0.294928i | −0.891641 | − | 0.452744i | \(-0.850445\pi\) |
0.987469 | + | 0.157816i | \(0.0504452\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.07295 | − | 12.5352i | −0.521488 | − | 1.60497i | −0.771158 | − | 0.636643i | \(-0.780322\pi\) |
0.249671 | − | 0.968331i | \(-0.419678\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.61803 | − | 4.97980i | 0.203853 | − | 0.627395i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.11803 | + | 4.44501i | 0.758849 | + | 0.551336i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.0902 | − | 8.05748i | −1.35488 | − | 0.984378i | −0.998752 | − | 0.0499406i | \(-0.984097\pi\) |
−0.356128 | − | 0.934437i | \(-0.615903\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.89919 | + | 7.19218i | 1.19172 | + | 0.865837i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.97214 | − | 5.06555i | 0.827440 | − | 0.601171i | −0.0913937 | − | 0.995815i | \(-0.529132\pi\) |
0.918834 | + | 0.394644i | \(0.129132\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.39919 | + | 10.4616i | 0.397845 | + | 1.22444i | 0.926724 | + | 0.375743i | \(0.122612\pi\) |
−0.528879 | + | 0.848697i | \(0.677388\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.1803 | −1.29099 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | + | 3.07768i | 0.113961 | + | 0.350735i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.30902 | − | 3.13068i | 0.484802 | − | 0.352229i | −0.318380 | − | 0.947963i | \(-0.603139\pi\) |
0.803182 | + | 0.595734i | \(0.203139\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.89919 | + | 6.46564i | 0.988799 | + | 0.718404i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.66312 | + | 2.66141i | 0.402080 | + | 0.292128i | 0.770387 | − | 0.637576i | \(-0.220063\pi\) |
−0.368308 | + | 0.929704i | \(0.620063\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.47214 | − | 6.88191i | 1.02740 | − | 0.746448i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.02786 | + | 9.31881i | −0.324621 | + | 0.999081i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.23607 | + | 3.80423i | 0.131023 | + | 0.403247i | 0.994950 | − | 0.100369i | \(-0.0320025\pi\) |
−0.863927 | + | 0.503617i | \(0.832002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.73607 | − | 8.42075i | 0.286818 | − | 0.882735i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.5279 | 1.09169 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.7812 | − | 10.0126i | 1.41392 | − | 1.02727i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3541 | − | 8.97578i | 1.25437 | − | 0.911352i | 0.255902 | − | 0.966703i | \(-0.417628\pi\) |
0.998467 | + | 0.0553503i | \(0.0176276\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.47214 | 0.248459 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.9443 | −1.78552 | −0.892761 | − | 0.450531i | \(-0.851235\pi\) | ||||
−0.892761 | + | 0.450531i | \(0.851235\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.54508 | − | 1.84911i | 0.250775 | − | 0.182198i | −0.455295 | − | 0.890340i | \(-0.650466\pi\) |
0.706070 | + | 0.708142i | \(0.250466\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.04508 | + | 12.4495i | 0.394760 | + | 1.21495i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.7082 | 1.61524 | 0.807622 | − | 0.589701i | \(-0.200754\pi\) | ||||
0.807622 | + | 0.589701i | \(0.200754\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.909830 | − | 2.80017i | 0.0871459 | − | 0.268208i | −0.897981 | − | 0.440033i | \(-0.854967\pi\) |
0.985127 | + | 0.171826i | \(0.0549666\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.69098 | + | 17.5150i | 0.540164 | + | 1.66245i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.26393 | + | 10.0453i | −0.307045 | + | 0.944987i | 0.671861 | + | 0.740677i | \(0.265495\pi\) |
−0.978906 | + | 0.204310i | \(0.934505\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.2361 | −1.14102 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.47214 | − | 3.97574i | −0.505899 | − | 0.367557i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.0902 | − | 8.05748i | −1.01663 | − | 0.738628i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.66312 | − | 5.56758i | 0.696647 | − | 0.506144i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.94427 | − | 12.1392i | −0.355643 | − | 1.09456i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.04508 | − | 6.57164i | 0.809017 | − | 0.587785i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.32624 | + | 7.15942i | 0.206420 | + | 0.635296i | 0.999652 | + | 0.0263764i | \(0.00839685\pi\) |
−0.793232 | + | 0.608920i | \(0.791603\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.92705 | − | 5.75934i | 0.697938 | − | 0.507082i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.881966 | + | 0.640786i | 0.0770577 | + | 0.0559857i | 0.625647 | − | 0.780106i | \(-0.284835\pi\) |
−0.548589 | + | 0.836092i | \(0.684835\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.1353 | − | 11.7229i | −1.39910 | − | 1.01651i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.00000 | −0.430331 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.54508 | − | 4.75528i | 0.132006 | − | 0.406271i | −0.863107 | − | 0.505022i | \(-0.831485\pi\) |
0.995112 | + | 0.0987504i | \(0.0314845\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.01722 | + | 9.28605i | 0.255917 | + | 0.787633i | 0.993648 | + | 0.112537i | \(0.0358977\pi\) |
−0.737730 | + | 0.675096i | \(0.764102\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.100813 | + | 0.310271i | −0.00848999 | + | 0.0261295i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.18034 | 0.349578 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.02786 | − | 9.31881i | −0.251450 | − | 0.773885i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.263932 | + | 0.191758i | −0.0217687 | + | 0.0158159i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.4164 | −1.50873 | −0.754365 | − | 0.656455i | \(-0.772055\pi\) | ||||
−0.754365 | + | 0.656455i | \(0.772055\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.381966 | 0.0310840 | 0.0155420 | − | 0.999879i | \(-0.495053\pi\) | ||||
0.0155420 | + | 0.999879i | \(0.495053\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.47214 | + | 6.15537i | −0.684932 | + | 0.497632i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.51722 | + | 6.18812i | −0.684120 | + | 0.497042i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.23607 | 0.338075 | 0.169038 | − | 0.985610i | \(-0.445934\pi\) | ||||
0.169038 | + | 0.985610i | \(0.445934\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.48936 | + | 16.8945i | −0.435334 | + | 1.33982i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.42705 | + | 13.6251i | 0.348900 | + | 1.07381i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.69098 | − | 14.4374i | 0.367426 | − | 1.13082i | −0.581022 | − | 0.813888i | \(-0.697347\pi\) |
0.948448 | − | 0.316933i | \(-0.102653\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.00000 | + | 3.63271i | −0.389249 | + | 0.282806i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.3992 | + | 11.1882i | 1.19162 | + | 0.865766i | 0.993435 | − | 0.114398i | \(-0.0364938\pi\) |
0.198190 | + | 0.980164i | \(0.436494\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.26393 | + | 0.918300i | 0.0972255 | + | 0.0706385i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.3262 | + | 8.95554i | −0.942611 | + | 0.684847i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.01722 | + | 6.20837i | 0.153366 | + | 0.472013i | 0.997992 | − | 0.0633445i | \(-0.0201767\pi\) |
−0.844625 | + | 0.535358i | \(0.820177\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.5902 | − | 7.69421i | −0.800542 | − | 0.581628i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.64590 | − | 5.06555i | −0.123713 | − | 0.380750i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.66312 | + | 1.93487i | −0.199051 | + | 0.144619i | −0.682846 | − | 0.730562i | \(-0.739258\pi\) |
0.483795 | + | 0.875181i | \(0.339258\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.70820 | + | 4.87380i | 0.498617 | + | 0.362266i | 0.808488 | − | 0.588512i | \(-0.200286\pi\) |
−0.309872 | + | 0.950778i | \(0.600286\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.8435 | − | 17.3233i | −1.76256 | − | 1.28057i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.8992 | − | 10.8249i | −1.09541 | − | 0.795862i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | − | 6.15537i | 0.146254 | − | 0.450125i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.80902 | + | 5.56758i | 0.131587 | + | 0.404982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.0901699 | + | 0.277515i | −0.00652447 | + | 0.0200802i | −0.954266 | − | 0.298960i | \(-0.903360\pi\) |
0.947741 | + | 0.319040i | \(0.103360\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.70820 | −0.554849 | −0.277424 | − | 0.960747i | \(-0.589481\pi\) | ||||
−0.277424 | + | 0.960747i | \(0.589481\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.9098 | 1.21094 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.9443 | − | 8.67802i | 0.850994 | − | 0.618283i | −0.0744258 | − | 0.997227i | \(-0.523712\pi\) |
0.925420 | + | 0.378943i | \(0.123712\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.38197 | 0.665070 | 0.332535 | − | 0.943091i | \(-0.392096\pi\) | ||||
0.332535 | + | 0.943091i | \(0.392096\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −30.6525 | −2.16206 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.28115 | + | 6.74315i | −0.651409 | + | 0.473277i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.3262 | + | 7.50245i | 0.721216 | + | 0.523994i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.9443 | 0.760679 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.90983 | − | 8.95554i | 0.201277 | − | 0.619467i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.16312 | + | 18.9681i | 0.424287 | + | 1.30582i | 0.903676 | + | 0.428217i | \(0.140858\pi\) |
−0.479389 | + | 0.877602i | \(0.659142\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.95492 | − | 18.3273i | 0.408024 | − | 1.25577i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.02786 | + | 9.31881i | −0.206499 | + | 0.635537i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.97214 | + | 7.24518i | 0.676953 | + | 0.491835i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.8992 | + | 14.4576i | 1.34466 | + | 0.976954i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.3262 | + | 10.4086i | −0.963687 | + | 0.700160i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.76393 | + | 5.42882i | 0.118122 | + | 0.363541i | 0.992585 | − | 0.121550i | \(-0.0387865\pi\) |
−0.874464 | + | 0.485091i | \(0.838786\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.09017 | + | 5.87785i | −0.539345 | + | 0.391857i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.90983 | − | 24.3440i | −0.524994 | − | 1.61576i | −0.764328 | − | 0.644828i | \(-0.776929\pi\) |
0.239334 | − | 0.970937i | \(-0.423071\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.3262 | + | 11.8617i | −1.07887 | + | 0.783844i | −0.977485 | − | 0.211004i | \(-0.932327\pi\) |
−0.101383 | + | 0.994847i | \(0.532327\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.85410 | + | 4.25325i | 0.385172 | + | 0.279844i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.85410 | − | 3.52671i | −0.318003 | − | 0.231043i | 0.417320 | − | 0.908760i | \(-0.362969\pi\) |
−0.735323 | + | 0.677717i | \(0.762969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.100813 | − | 0.310271i | −0.00657632 | − | 0.0202398i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.68034 | − | 11.3269i | 0.239064 | − | 0.735763i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.87132 | − | 21.1478i | −0.444469 | − | 1.36793i | −0.883065 | − | 0.469250i | \(-0.844524\pi\) |
0.438596 | − | 0.898684i | \(-0.355476\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.54508 | − | 10.9106i | 0.228359 | − | 0.702817i | −0.769574 | − | 0.638557i | \(-0.779532\pi\) |
0.997933 | − | 0.0642594i | \(-0.0204685\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.8885 | 1.14755 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.100813 | − | 0.310271i | 0.00644071 | − | 0.0198225i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.8435 | + | 15.1437i | −1.32624 | + | 0.963568i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.1246 | 0.641621 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.05573 | −0.508473 | −0.254237 | − | 0.967142i | \(-0.581824\pi\) | ||||
−0.254237 | + | 0.967142i | \(0.581824\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.47214 | + | 3.97574i | −0.344030 | + | 0.249953i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.09017 | − | 24.8990i | 0.506626 | − | 1.55923i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.61803 | −0.225687 | −0.112843 | − | 0.993613i | \(-0.535996\pi\) | ||||
−0.112843 | + | 0.993613i | \(0.535996\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.66312 | + | 20.5070i | −0.414026 | + | 1.27424i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.70820 | + | 8.33499i | 0.167634 | + | 0.515923i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.28115 | + | 13.1760i | −0.263987 | + | 0.812469i | 0.727938 | + | 0.685643i | \(0.240479\pi\) |
−0.991925 | + | 0.126826i | \(0.959521\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.48936 | − | 16.8945i | −0.337209 | − | 1.03782i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.23607 | + | 5.25731i | 0.442840 | + | 0.321742i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.5623 | + | 8.40051i | 0.704966 | + | 0.512188i | 0.881546 | − | 0.472098i | \(-0.156503\pi\) |
−0.176580 | + | 0.984286i | \(0.556503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4721 | + | 7.60845i | −0.636137 | + | 0.462181i | −0.858521 | − | 0.512779i | \(-0.828616\pi\) |
0.222384 | + | 0.974959i | \(0.428616\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.11803 | − | 18.8294i | −0.370280 | − | 1.13961i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.90983 | − | 5.87785i | 0.115167 | − | 0.354448i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.54508 | + | 20.1437i | 0.393256 | + | 1.21032i | 0.930311 | + | 0.366771i | \(0.119537\pi\) |
−0.537055 | + | 0.843547i | \(0.680463\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.61803 | − | 5.53483i | 0.456080 | − | 0.331361i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.39919 | − | 5.37582i | −0.441398 | − | 0.320695i | 0.344792 | − | 0.938679i | \(-0.387949\pi\) |
−0.786190 | + | 0.617984i | \(0.787949\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.88197 | + | 4.27350i | 0.349647 | + | 0.254033i | 0.748721 | − | 0.662886i | \(-0.230668\pi\) |
−0.399074 | + | 0.916919i | \(0.630668\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.7705 | − | 36.2259i | 0.697225 | − | 2.14584i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.61803 | − | 14.2128i | 0.272594 | − | 0.838958i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.21885 | + | 9.90659i | 0.189344 | + | 0.582741i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.5517 | − | 32.4747i | 0.618549 | − | 1.90370i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.472136 | 0.0275825 | 0.0137912 | − | 0.999905i | \(-0.495610\pi\) | ||||
0.0137912 | + | 0.999905i | \(0.495610\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.30902 | + | 3.13068i | 0.250881 | + | 0.182275i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.23607 | + | 1.62460i | −0.129750 | + | 0.0942688i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.5066 | 1.07026 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.4721 | 0.661243 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −32.4615 | + | 23.5847i | −1.86486 | + | 1.35490i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 29.4721 | 1.68757 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.7639 | 0.614330 | 0.307165 | − | 0.951656i | \(-0.400620\pi\) | ||||
0.307165 | + | 0.951656i | \(0.400620\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.17376 | − | 6.69015i | 0.123661 | − | 0.380589i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.51722 | − | 4.66953i | −0.0860337 | − | 0.264785i | 0.898780 | − | 0.438401i | \(-0.144455\pi\) |
−0.984813 | + | 0.173616i | \(0.944455\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.76393 | − | 5.42882i | 0.0997033 | − | 0.306855i | −0.888748 | − | 0.458397i | \(-0.848424\pi\) |
0.988451 | + | 0.151542i | \(0.0484238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.47214 | + | 6.88191i | 0.533694 | + | 0.387752i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.5172 | + | 8.36775i | 0.646872 | + | 0.469980i | 0.862204 | − | 0.506561i | \(-0.169084\pi\) |
−0.215333 | + | 0.976541i | \(0.569084\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.38197 | − | 3.18368i | −0.245343 | − | 0.178252i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.2254 | − | 21.9601i | 1.68702 | − | 1.22569i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.3262 | + | 37.9363i | 0.685850 | + | 2.11083i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.6803 | + | 9.93935i | −0.758849 | + | 0.551336i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.03444 | − | 6.26137i | −0.112505 | − | 0.346254i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.309017 | + | 0.224514i | −0.0170367 | + | 0.0123779i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.9443 | − | 18.8496i | −1.42603 | − | 1.03607i | −0.990739 | − | 0.135777i | \(-0.956647\pi\) |
−0.435287 | − | 0.900292i | \(-0.643353\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.3262 | + | 9.68208i | 0.730273 | + | 0.530575i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.7984 | − | 18.0171i | 1.35488 | − | 0.984378i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.80902 | + | 8.64527i | −0.153017 | + | 0.470938i | −0.997955 | − | 0.0639272i | \(-0.979637\pi\) |
0.844938 | + | 0.534865i | \(0.179637\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.29837 | + | 22.4621i | 0.396393 | + | 1.21997i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.79837 | + | 5.53483i | −0.0973874 | + | 0.299728i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.7082 | −1.01015 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −22.1353 | + | 16.0822i | −1.19172 | + | 0.865837i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.54508 | + | 4.02874i | −0.297676 | + | 0.216274i | −0.726590 | − | 0.687071i | \(-0.758896\pi\) |
0.428915 | + | 0.903345i | \(0.358896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.1246 | 1.34489 | 0.672445 | − | 0.740147i | \(-0.265244\pi\) | ||||
0.672445 | + | 0.740147i | \(0.265244\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.56231 | 0.403646 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.9164 | − | 17.3763i | 1.27294 | − | 0.924846i | 0.273626 | − | 0.961836i | \(-0.411777\pi\) |
0.999316 | + | 0.0369896i | \(0.0117768\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.95492 | + | 18.3273i | 0.316054 | + | 0.972714i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −30.6525 | −1.62230 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.80902 | − | 24.0337i | 0.412144 | − | 1.26845i | −0.502636 | − | 0.864498i | \(-0.667637\pi\) |
0.914780 | − | 0.403951i | \(-0.132363\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.0623 | + | 37.1240i | 0.634858 | + | 1.95389i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.54508 | − | 20.1437i | 0.343528 | − | 1.05727i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −24.5967 | −1.28745 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.5902 | − | 11.3269i | −0.813800 | − | 0.591260i | 0.101130 | − | 0.994873i | \(-0.467754\pi\) |
−0.914930 | + | 0.403613i | \(0.867754\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.23607 | − | 6.71040i | −0.480810 | − | 0.349329i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.8262 | + | 12.2250i | −0.873575 | + | 0.634689i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.97214 | + | 15.3027i | 0.257447 | + | 0.792342i | 0.993338 | + | 0.115241i | \(0.0367640\pi\) |
−0.735890 | + | 0.677101i | \(0.763236\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.72542 | − | 23.7764i | 0.398939 | − | 1.22781i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.57953 | + | 14.0943i | 0.235858 | + | 0.725895i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.04508 | − | 2.93893i | 0.207782 | − | 0.150963i | −0.479028 | − | 0.877800i | \(-0.659011\pi\) |
0.686810 | + | 0.726837i | \(0.259011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.6180 | + | 9.89408i | 0.697673 | + | 0.506889i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.1353 | − | 8.09024i | −0.568985 | − | 0.413392i | 0.265751 | − | 0.964042i | \(-0.414380\pi\) |
−0.834736 | + | 0.550650i | \(0.814380\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.23607 | −0.368784 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.70820 | − | 8.33499i | 0.137666 | − | 0.423692i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.83688 | − | 11.8087i | −0.194538 | − | 0.598725i | −0.999982 | − | 0.00605338i | \(-0.998073\pi\) |
0.805444 | − | 0.592672i | \(-0.201927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.85410 | − | 27.2501i | 0.447771 | − | 1.37810i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.43769 | 0.122965 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.68034 | + | 11.3269i | 0.185178 | + | 0.569919i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.2533 | + | 11.8087i | −0.815729 | + | 0.592662i | −0.915486 | − | 0.402350i | \(-0.868194\pi\) |
0.0997568 | + | 0.995012i | \(0.468194\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −44.5967 | −2.23263 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.5967 | −1.82755 | −0.913777 | − | 0.406216i | \(-0.866848\pi\) | ||||
−0.913777 | + | 0.406216i | \(0.866848\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.8820 | − | 9.35930i | 0.641696 | − | 0.466220i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.8992 | + | 14.4576i | −0.988799 | + | 0.718404i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.1803 | −0.504621 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.34346 | + | 19.5232i | −0.313664 | + | 0.965358i | 0.662637 | + | 0.748941i | \(0.269437\pi\) |
−0.976301 | + | 0.216417i | \(0.930563\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.45492 | − | 10.6331i | −0.170418 | − | 0.524494i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.92705 | − | 5.93085i | 0.0948240 | − | 0.291838i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.19098 | + | 5.95110i | −0.402080 | + | 0.292128i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.6631 | + | 12.8330i | 0.864967 | + | 0.628435i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.1353 | − | 15.3557i | −1.03252 | − | 0.750173i | −0.0637123 | − | 0.997968i | \(-0.520294\pi\) |
−0.968812 | + | 0.247795i | \(0.920294\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | + | 2.90617i | −0.194948 | + | 0.141638i | −0.680977 | − | 0.732304i | \(-0.738445\pi\) |
0.486029 | + | 0.873943i | \(0.338445\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.0901699 | + | 0.277515i | 0.00438421 | + | 0.0134932i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.09017 | + | 24.8990i | 0.392431 | + | 1.20778i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.6631 | − | 32.8177i | −0.516024 | − | 1.58816i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.56231 | − | 5.49434i | 0.365112 | − | 0.265269i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.66312 | − | 1.93487i | −0.128278 | − | 0.0931994i | 0.521796 | − | 0.853070i | \(-0.325262\pi\) |
−0.650074 | + | 0.759871i | \(0.725262\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.83688 | − | 1.33457i | −0.0882749 | − | 0.0641354i | 0.542772 | − | 0.839880i | \(-0.317375\pi\) |
−0.631047 | + | 0.775744i | \(0.717375\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.7254 | − | 12.8783i | −0.849869 | − | 0.617466i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.8820 | − | 39.6466i | 0.616228 | − | 1.89655i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.19098 | + | 15.9762i | 0.247752 | + | 0.762503i | 0.995172 | + | 0.0981502i | \(0.0312926\pi\) |
−0.747420 | + | 0.664352i | \(0.768707\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0901699 | + | 0.277515i | −0.00429381 | + | 0.0132150i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.34752 | −0.396603 | −0.198301 | − | 0.980141i | \(-0.563542\pi\) | ||||
−0.198301 | + | 0.980141i | \(0.563542\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.94427 | −0.423999 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −33.3156 | + | 24.2052i | −1.57577 | + | 1.14487i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.9098 | −1.12837 | −0.564187 | − | 0.825647i | \(-0.690810\pi\) | ||||
−0.564187 | + | 0.825647i | \(0.690810\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.05573 | 0.332241 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.690983 | − | 0.502029i | 0.0324652 | − | 0.0235874i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.0172 | + | 11.6372i | 0.750899 | + | 0.545560i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.47214 | −0.209198 | −0.104599 | − | 0.994514i | \(-0.533356\pi\) | ||||
−0.104599 | + | 0.994514i | \(0.533356\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.61803 | − | 11.1352i | 0.168875 | − | 0.519745i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.57953 | − | 20.2497i | −0.306439 | − | 0.943123i | −0.979136 | − | 0.203205i | \(-0.934864\pi\) |
0.672697 | − | 0.739918i | \(-0.265136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.92705 | + | 15.1639i | −0.228979 | + | 0.704726i | 0.768884 | + | 0.639389i | \(0.220812\pi\) |
−0.997863 | + | 0.0653377i | \(0.979188\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.27458 | + | 22.3888i | −0.337350 | + | 1.03826i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.88197 | + | 4.27350i | 0.272185 | + | 0.197754i | 0.715502 | − | 0.698611i | \(-0.246198\pi\) |
−0.443317 | + | 0.896365i | \(0.646198\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.0344 | − | 21.0948i | −1.34069 | − | 0.974065i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.66312 | − | 5.56758i | 0.353098 | − | 0.256541i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.67376 | + | 5.15131i | 0.0769597 | + | 0.236857i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.7705 | + | 36.2259i | 0.540068 | + | 1.66216i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.90983 | + | 15.1109i | 0.224806 | + | 0.691881i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.1074 | + | 13.1558i | −0.827348 | + | 0.601103i | −0.918808 | − | 0.394705i | \(-0.870847\pi\) |
0.0914599 | + | 0.995809i | \(0.470847\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.5344 | + | 16.3722i | 1.02748 | + | 0.746509i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 25.9164 | + | 18.8294i | 1.17924 | + | 0.856766i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.5517 | + | 32.4747i | 0.479126 | + | 1.47460i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.25329 | + | 25.4010i | −0.373992 | + | 1.15103i | 0.570164 | + | 0.821531i | \(0.306880\pi\) |
−0.944156 | + | 0.329499i | \(0.893120\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.4894 | − | 32.2829i | −0.474345 | − | 1.45988i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.16312 | − | 3.57971i | 0.0524908 | − | 0.161550i | −0.921375 | − | 0.388676i | \(-0.872933\pi\) |
0.973866 | + | 0.227125i | \(0.0729327\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.9443 | 1.03336 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.70820 | + | 5.25731i | −0.0767781 | + | 0.236299i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.2533 | − | 13.2618i | 0.818772 | − | 0.594873i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.5623 | 1.32339 | 0.661695 | − | 0.749773i | \(-0.269837\pi\) | ||||
0.661695 | + | 0.749773i | \(0.269837\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.5623 | 1.90154 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.8541 | − | 9.33905i | 0.573136 | − | 0.416408i | −0.263107 | − | 0.964767i | \(-0.584747\pi\) |
0.836243 | + | 0.548359i | \(0.184747\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.3992 | − | 38.1608i | 0.551757 | − | 1.69813i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.49342 | 0.155148 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.60739 | − | 29.5685i | 0.425840 | − | 1.31060i | −0.476347 | − | 0.879257i | \(-0.658040\pi\) |
0.902188 | − | 0.431344i | \(-0.141960\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.89919 | + | 27.3889i | 0.393677 | + | 1.21161i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.26393 | − | 16.2007i | 0.232408 | − | 0.715279i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.17376 | + | 6.69015i | 0.0957874 | + | 0.294803i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.145898 | − | 0.106001i | −0.00641659 | − | 0.00466192i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.8090 | + | 8.57975i | 0.518358 | + | 0.376609i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.80902 | + | 4.94704i | −0.298308 | + | 0.216734i | −0.726864 | − | 0.686782i | \(-0.759023\pi\) |
0.428555 | + | 0.903516i | \(0.359023\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.68034 | − | 17.4823i | −0.248384 | − | 0.764447i | −0.995061 | − | 0.0992609i | \(-0.968352\pi\) |
0.746678 | − | 0.665186i | \(-0.231648\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −29.2705 | −1.27747 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.61803 | − | 23.4459i | −0.331847 | − | 1.02132i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.61803 | + | 4.08174i | −0.244262 | + | 0.177467i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.85410 | − | 2.80017i | −0.167254 | − | 0.121517i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.6180 | − | 11.3472i | −0.676492 | − | 0.491500i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.5451 | + | 35.5321i | −0.499138 | + | 1.53619i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.27458 | + | 7.00042i | −0.0981552 | + | 0.302091i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.0557281 | − | 0.171513i | −0.00240038 | − | 0.00738761i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.67376 | − | 8.22899i | 0.114954 | − | 0.353792i | −0.876983 | − | 0.480521i | \(-0.840448\pi\) |
0.991937 | + | 0.126729i | \(0.0404477\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.5410 | 0.795671 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.32624 | + | 3.86974i | 0.228151 | + | 0.165761i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.57295 | + | 5.50207i | −0.323796 | + | 0.235252i | −0.737794 | − | 0.675026i | \(-0.764132\pi\) |
0.413998 | + | 0.910278i | \(0.364132\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −26.3607 | −1.12505 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.3820 | 1.42212 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.2812 | − | 8.19624i | 0.479723 | − | 0.348539i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −41.1803 | −1.74801 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.81966 | −0.331330 | −0.165665 | − | 0.986182i | \(-0.552977\pi\) | ||||
−0.165665 | + | 0.986182i | \(0.552977\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.57953 | − | 14.0943i | 0.193693 | − | 0.596127i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.47214 | − | 13.7638i | −0.188814 | − | 0.581109i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.607391 | − | 1.86936i | 0.0255985 | − | 0.0787840i | −0.937441 | − | 0.348144i | \(-0.886812\pi\) |
0.963040 | + | 0.269360i | \(0.0868121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.1074 | − | 13.8823i | −0.803854 | − | 0.584034i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.2984 | + | 16.9273i | 0.978440 | + | 0.710878i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.1353 | − | 10.2699i | −0.592581 | − | 0.430535i | 0.250657 | − | 0.968076i | \(-0.419353\pi\) |
−0.843238 | + | 0.537541i | \(0.819353\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.1353 | − | 18.9884i | 1.09373 | − | 0.794639i | 0.113702 | − | 0.993515i | \(-0.463729\pi\) |
0.980025 | + | 0.198876i | \(0.0637292\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.201626 | + | 0.620541i | 0.00842305 | + | 0.0259235i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.45492 | − | 26.0216i | 0.352594 | − | 1.08517i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.90983 | + | 15.1109i | 0.204399 | + | 0.629075i | 0.999738 | + | 0.0229098i | \(0.00729304\pi\) |
−0.795339 | + | 0.606165i | \(0.792707\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.9443 | + | 10.1311i | −0.579504 | + | 0.421034i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.59017 | + | 6.96767i | 0.397867 | + | 0.289068i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.94427 | − | 5.77185i | −0.329018 | − | 0.239046i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.2361 | − | 8.89002i | 0.505899 | − | 0.367557i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.72542 | + | 29.9318i | −0.401411 | + | 1.23542i | 0.522444 | + | 0.852674i | \(0.325021\pi\) |
−0.923855 | + | 0.382743i | \(0.874979\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.0836 | − | 34.1118i | −0.456691 | − | 1.40555i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.2016 | − | 31.3974i | 0.419639 | − | 1.29152i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.5623 | 0.803328 | 0.401664 | − | 0.915787i | \(-0.368432\pi\) | ||||
0.401664 | + | 0.915787i | \(0.368432\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.7984 | − | 18.0171i | 1.01663 | − | 0.738628i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.9721 | − | 12.3310i | 0.694623 | − | 0.504673i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.1803 | −0.620252 | −0.310126 | − | 0.950695i | \(-0.600371\pi\) | ||||
−0.310126 | + | 0.950695i | \(0.600371\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.4377 | −0.915253 | −0.457626 | − | 0.889145i | \(-0.651300\pi\) | ||||
−0.457626 | + | 0.889145i | \(0.651300\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.1803 | + | 16.1150i | −0.903253 | + | 0.656252i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.54508 | + | 20.1437i | 0.266096 | + | 0.818958i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.27051 | 0.0515684 | 0.0257842 | − | 0.999668i | \(-0.491792\pi\) | ||||
0.0257842 | + | 0.999668i | \(0.491792\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.92705 | + | 24.3970i | −0.321220 | + | 0.988614i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.152476 | + | 0.469272i | 0.00616851 | + | 0.0189847i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.10081 | + | 9.54332i | −0.125241 | + | 0.385451i | −0.993945 | − | 0.109880i | \(-0.964953\pi\) |
0.868704 | + | 0.495331i | \(0.164953\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.5410 | 1.15088 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.7533 | − | 17.9843i | −0.996530 | − | 0.724021i | −0.0351885 | − | 0.999381i | \(-0.511203\pi\) |
−0.961341 | + | 0.275359i | \(0.911203\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.9336 | + | 23.9277i | 1.32371 | + | 0.961735i | 0.999878 | + | 0.0156216i | \(0.00497272\pi\) |
0.323836 | + | 0.946113i | \(0.395027\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.89919 | + | 7.19218i | −0.397241 | + | 0.288612i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.23607 | + | 9.95959i | 0.129650 | + | 0.399023i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.72542 | + | 23.7764i | 0.309017 | + | 0.951057i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.50658 | − | 20.0252i | −0.259848 | − | 0.799729i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.8885 | − | 25.3480i | 1.39110 | − | 1.01069i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.33688 | − | 4.60401i | −0.252267 | − | 0.183283i | 0.454464 | − | 0.890765i | \(-0.349831\pi\) |
−0.706731 | + | 0.707482i | \(0.749831\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 36.0795 | + | 26.2133i | 1.43403 | + | 1.04189i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.8328 | −0.667990 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.152476 | + | 0.469272i | −0.00604131 | + | 0.0185932i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.32624 | − | 16.3925i | −0.210703 | − | 0.648476i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.39261 | + | 16.5967i | −0.212995 | + | 0.655532i | 0.786295 | + | 0.617852i | \(0.211997\pi\) |
−0.999290 | + | 0.0376802i | \(0.988003\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.0557 | 0.751485 | 0.375742 | − | 0.926724i | \(-0.377388\pi\) | ||||
0.375742 | + | 0.926724i | \(0.377388\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.77051 | + | 20.8375i | 0.266589 | + | 0.820475i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.3262 | − | 13.3148i | 0.720479 | − | 0.523458i | −0.166058 | − | 0.986116i | \(-0.553104\pi\) |
0.886537 | + | 0.462657i | \(0.153104\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.94427 | 0.115573 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.5623 | 1.08025 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.6803 | + | 17.9313i | −0.965816 | + | 0.701707i | −0.954494 | − | 0.298229i | \(-0.903604\pi\) |
−0.0113221 | + | 0.999936i | \(0.503604\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.97214 | + | 1.43284i | −0.0770577 | + | 0.0559857i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.0000 | 0.858302 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.0344419 | − | 0.106001i | 0.00134166 | − | 0.00412922i | −0.950383 | − | 0.311081i | \(-0.899309\pi\) |
0.951725 | + | 0.306952i | \(0.0993090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.6803 | − | 32.8707i | −0.415417 | − | 1.27852i | −0.911877 | − | 0.410463i | \(-0.865367\pi\) |
0.496460 | − | 0.868059i | \(-0.334633\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.2361 | + | 37.6587i | −0.475210 | + | 1.46254i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 36.0795 | − | 26.2133i | 1.39910 | − | 1.01651i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.3992 | − | 14.0943i | −0.751140 | − | 0.545735i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.3262 | + | 7.50245i | 0.399235 | + | 0.290062i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.1803 | − | 9.57608i | 0.508821 | − | 0.369680i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.2361 | − | 31.5034i | −0.394571 | − | 1.21437i | −0.929295 | − | 0.369339i | \(-0.879584\pi\) |
0.534723 | − | 0.845027i | \(-0.320416\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.45492 | − | 10.6331i | 0.132980 | − | 0.409270i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.42705 | − | 7.46969i | −0.0932791 | − | 0.287084i | 0.893522 | − | 0.449019i | \(-0.148226\pi\) |
−0.986801 | + | 0.161935i | \(0.948226\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.3435 | − | 23.4989i | 1.24123 | − | 0.901805i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −46.3050 | − | 33.6425i | −1.77441 | − | 1.28918i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.7533 | + | 12.1720i | 0.641047 | + | 0.465748i | 0.860210 | − | 0.509941i | \(-0.170333\pi\) |
−0.219163 | + | 0.975688i | \(0.570333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.04508 | + | 6.57164i | 0.345595 | + | 0.251089i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.9443 | + | 42.9161i | −0.532007 | + | 1.63735i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.30244 | + | 25.5523i | 0.316298 | + | 0.973464i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.4787 | + | 44.5609i | −0.550796 | + | 1.69518i | 0.155998 | + | 0.987757i | \(0.450141\pi\) |
−0.706794 | + | 0.707419i | \(0.749859\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.47214 | 0.245856 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.8328 | −0.828166 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.1803 | + | 17.5680i | −0.915896 | + | 0.665437i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.4164 | −0.507455 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.18034 | 0.0823503 | 0.0411752 | − | 0.999152i | \(-0.486890\pi\) | ||||
0.0411752 | + | 0.999152i | \(0.486890\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.7599 | − | 36.8792i | 1.91444 | − | 1.39093i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.590170 | − | 0.428784i | −0.0222271 | − | 0.0161489i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −46.9787 | −1.76682 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.3090 | + | 34.8056i | −0.424719 | + | 1.30715i | 0.478544 | + | 0.878064i | \(0.341165\pi\) |
−0.903263 | + | 0.429087i | \(0.858835\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.29180 | − | 10.1311i | −0.123452 | − | 0.379946i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.96149 | + | 24.5030i | −0.298160 | + | 0.917643i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.88854 | + | 8.89002i | −0.108025 | + | 0.332468i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −40.2254 | − | 29.2255i | −1.50225 | − | 1.09145i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.9894 | + | 22.5151i | 1.15571 | + | 0.839671i | 0.989229 | − | 0.146374i | \(-0.0467603\pi\) |
0.166479 | + | 0.986045i | \(0.446760\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.66312 | − | 4.84104i | 0.248148 | − | 0.180290i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.92705 | − | 24.3970i | −0.294810 | − | 0.907332i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.9098 | 0.813711 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.50000 | + | 10.7719i | 0.129808 | + | 0.399507i | 0.994746 | − | 0.102370i | \(-0.0326427\pi\) |
−0.864939 | + | 0.501878i | \(0.832643\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.66312 | − | 4.11450i | 0.209745 | − | 0.152389i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.5623 | − | 13.4863i | −0.686552 | − | 0.498809i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.78115 | − | 6.37988i | −0.324339 | − | 0.235646i | 0.413686 | − | 0.910420i | \(-0.364241\pi\) |
−0.738025 | + | 0.674774i | \(0.764241\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.225425 | − | 0.693786i | −0.00831492 | − | 0.0255907i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.23607 | − | 16.1150i | 0.192873 | − | 0.593602i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.50000 | + | 10.7719i | 0.128750 | + | 0.396250i | 0.994566 | − | 0.104112i | \(-0.0332001\pi\) |
−0.865816 | + | 0.500363i | \(0.833200\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.8024 | + | 54.7903i | −0.653989 | + | 2.01277i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.2492 | −1.69672 | −0.848360 | − | 0.529420i | \(-0.822409\pi\) | ||||
−0.848360 | + | 0.529420i | \(0.822409\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.7254 | − | 39.1648i | 0.466223 | − | 1.43489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.32624 | − | 5.32282i | 0.268053 | − | 0.194752i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43.7426 | 1.59832 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.7639 | −1.15908 | −0.579541 | − | 0.814943i | \(-0.696768\pi\) | ||||
−0.579541 | + | 0.814943i | \(0.696768\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.5729 | + | 10.5879i | −0.531068 | + | 0.385843i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.263932 | + | 0.812299i | −0.00960547 | + | 0.0295626i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0000 | 0.545184 | 0.272592 | − | 0.962130i | \(-0.412119\pi\) | ||||
0.272592 | + | 0.962130i | \(0.412119\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.67376 | + | 14.3844i | −0.169647 | + | 0.522119i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.77051 | − | 23.9152i | −0.281681 | − | 0.866924i | −0.987374 | − | 0.158407i | \(-0.949364\pi\) |
0.705693 | − | 0.708518i | \(-0.250636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.38197 | − | 7.33094i | 0.0862330 | − | 0.265398i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.23607 | − | 22.2703i | −0.261621 | − | 0.805185i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.51722 | − | 4.73504i | −0.235323 | − | 0.170972i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.9787 | − | 23.2339i | −1.15318 | − | 0.837836i | −0.164281 | − | 0.986414i | \(-0.552530\pi\) |
−0.988901 | + | 0.148578i | \(0.952530\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.54508 | + | 4.75528i | −0.235715 | + | 0.171257i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.24265 | + | 25.3683i | 0.296467 | + | 0.912433i | 0.982725 | + | 0.185074i | \(0.0592524\pi\) |
−0.686257 | + | 0.727359i | \(0.740748\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.27458 | − | 22.3888i | −0.261310 | − | 0.804231i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.8992 | + | 45.8550i | 0.534505 | + | 1.64504i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −35.1803 | + | 25.5600i | −1.26047 | + | 0.915783i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.61803 | + | 6.26137i | 0.308378 | + | 0.224049i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.92705 | − | 5.75934i | −0.283290 | − | 0.205822i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.92705 | + | 9.00854i | −0.104471 | + | 0.321528i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.36068 | − | 28.8092i | 0.333672 | − | 1.02694i | −0.633700 | − | 0.773579i | \(-0.718465\pi\) |
0.967372 | − | 0.253359i | \(-0.0815353\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.57295 | + | 29.4625i | 0.340806 | + | 1.04889i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.54508 | + | 26.2991i | −0.303828 | + | 0.935087i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −44.5755 | −1.58292 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −32.1353 | − | 23.3476i | −1.13972 | − | 0.828055i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.28115 | − | 3.11044i | 0.151646 | − | 0.110177i | −0.509375 | − | 0.860545i | \(-0.670123\pi\) |
0.661021 | + | 0.750367i | \(0.270123\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.763932 | 0.0270260 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.00000 | 0.282666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.0000 | + | 7.99197i | −0.388182 | + | 0.282030i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32.0344 | −1.12907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.9574 | 1.12495 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.22542 | − | 6.84915i | 0.0782418 | − | 0.240803i | −0.904284 | − | 0.426932i | \(-0.859594\pi\) |
0.982525 | + | 0.186129i | \(0.0595942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.0172 | − | 43.1406i | −0.492211 | − | 1.51487i | −0.821258 | − | 0.570557i | \(-0.806727\pi\) |
0.329047 | − | 0.944314i | \(-0.393273\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.94427 | + | 27.5276i | −0.313689 | + | 0.965436i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.4615 | + | 19.9519i | 0.961934 | + | 0.698886i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.0066 | − | 19.6214i | −0.944841 | − | 0.686467i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.3262 | − | 10.4086i | −0.500599 | − | 0.363707i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.2082 | − | 8.14324i | 0.391169 | − | 0.284201i | −0.374765 | − | 0.927120i | \(-0.622277\pi\) |
0.765934 | + | 0.642919i | \(0.222277\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.20163 | − | 12.9313i | −0.146459 | − | 0.450756i | 0.850736 | − | 0.525593i | \(-0.176156\pi\) |
−0.997196 | + | 0.0748368i | \(0.976156\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.27051 | − | 13.1433i | −0.148680 | − | 0.457590i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.1525 | + | 31.2461i | 0.353036 | + | 1.08653i | 0.957139 | + | 0.289628i | \(0.0935314\pi\) |
−0.604103 | + | 0.796906i | \(0.706469\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.59017 | − | 2.60841i | 0.124692 | − | 0.0905939i | −0.523691 | − | 0.851908i | \(-0.675446\pi\) |
0.648383 | + | 0.761314i | \(0.275446\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 38.3156 | + | 27.8379i | 1.32915 | + | 0.965686i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.618034 | + | 0.449028i | 0.0214136 | + | 0.0155579i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.4336 | + | 25.0175i | −1.19162 | + | 0.865766i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.25329 | + | 10.0126i | −0.112450 | + | 0.346086i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.02786 | − | 9.31881i | −0.104533 | − | 0.321721i | 0.885087 | − | 0.465425i | \(-0.154099\pi\) |
−0.989621 | + | 0.143704i | \(0.954099\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.02786 | + | 9.31881i | −0.104409 | + | 0.321338i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.4508 | −0.704365 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.82624 | + | 2.05338i | −0.0972255 | + | 0.0706385i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.0623 | − | 14.5761i | 0.689349 | − | 0.500841i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.2574 | 0.557951 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −45.0689 | −1.54494 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.38197 | + | 3.18368i | −0.150036 | + | 0.109007i | −0.660271 | − | 0.751028i | \(-0.729558\pi\) |
0.510235 | + | 0.860035i | \(0.329558\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.5279 | − | 32.4014i | −0.360045 | − | 1.10811i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.14590 | −0.107462 | −0.0537309 | − | 0.998555i | \(-0.517111\pi\) | ||||
−0.0537309 | + | 0.998555i | \(0.517111\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.45492 | − | 29.0992i | 0.322598 | − | 0.992853i | −0.649916 | − | 0.760006i | \(-0.725196\pi\) |
0.972513 | − | 0.232847i | \(-0.0748041\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.3262 | − | 31.7809i | −0.351917 | − | 1.08309i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.17376 | + | 12.8455i | −0.142077 | + | 0.437267i | −0.996623 | − | 0.0821076i | \(-0.973835\pi\) |
0.854547 | + | 0.519374i | \(0.173835\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.5967 | −0.496304 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.8435 | + | 13.6906i | 0.639957 | + | 0.464956i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.32624 | + | 3.86974i | 0.180680 | + | 0.131272i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.5066 | + | 27.2501i | −1.27086 | + | 0.923335i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.43769 | − | 29.0462i | −0.319418 | − | 0.983066i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23.6803 | − | 17.2048i | 0.800542 | − | 0.581628i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.7082 | + | 32.9565i | 0.361590 | + | 1.11286i | 0.952089 | + | 0.305822i | \(0.0989312\pi\) |
−0.590498 | + | 0.807039i | \(0.701069\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.854102 | − | 0.620541i | 0.0288081 | − | 0.0209303i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.1246 | + | 25.5195i | 1.18338 | + | 0.859775i | 0.992549 | − | 0.121849i | \(-0.0388822\pi\) |
0.190830 | + | 0.981623i | \(0.438882\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.6525 | − | 17.9111i | −0.829622 | − | 0.602756i | 0.0898305 | − | 0.995957i | \(-0.471367\pi\) |
−0.919452 | + | 0.393202i | \(0.871367\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.9098 | 0.400345 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.652476 | + | 2.00811i | −0.0219080 | + | 0.0674259i | −0.961413 | − | 0.275110i | \(-0.911286\pi\) |
0.939505 | + | 0.342536i | \(0.111286\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.09017 | + | 18.7436i | 0.204258 | + | 0.628641i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.20163 | + | 12.9313i | −0.140760 | + | 0.433214i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.11146 | 0.0371935 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.27458 | − | 7.00042i | −0.0760307 | − | 0.233998i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.4787 | − | 24.3237i | 1.11782 | − | 0.812145i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.6312 | −0.688089 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.5967 | 1.38579 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.7533 | − | 15.0781i | 0.690626 | − | 0.501769i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.0000 | + | 10.8981i | −0.498617 | + | 0.362266i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.1803 | 1.10174 | 0.550868 | − | 0.834593i | \(-0.314297\pi\) | ||||
0.550868 | + | 0.834593i | \(0.314297\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.0902 | + | 34.1320i | −0.367838 | + | 1.13209i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.45492 | + | 26.0216i | 0.280124 | + | 0.862133i | 0.987818 | + | 0.155614i | \(0.0497355\pi\) |
−0.707694 | + | 0.706519i | \(0.750265\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.72949 | + | 5.32282i | −0.0572378 | + | 0.176160i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 53.3156 | − | 38.7360i | 1.76256 | − | 1.28057i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.30902 | + | 1.67760i | 0.0762505 | + | 0.0553992i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.69098 | + | 2.68166i | 0.121754 | + | 0.0884597i | 0.646996 | − | 0.762493i | \(-0.276025\pi\) |
−0.525242 | + | 0.850953i | \(0.676025\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.4721 | − | 14.1473i | 0.641629 | − | 0.466171i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.00658 | − | 27.7194i | −0.296455 | − | 0.912395i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.3156 | − | 24.2052i | 1.09541 | − | 0.795862i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.94427 | − | 5.98385i | −0.0638583 | − | 0.196536i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.0967 | + | 22.5931i | −1.02025 | + | 0.741256i | −0.966334 | − | 0.257290i | \(-0.917171\pi\) |
−0.0539168 | + | 0.998545i | \(0.517171\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.899187 | + | 0.653298i | 0.0294697 | + | 0.0214110i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.88197 | − | 6.45313i | −0.290783 | − | 0.211266i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.7082 | + | 8.50651i | 0.382899 | + | 0.278193i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.35410 | − | 19.5559i | 0.207579 | − | 0.638864i | −0.792018 | − | 0.610498i | \(-0.790970\pi\) |
0.999598 | − | 0.0283663i | \(-0.00903049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.94427 | − | 12.1392i | −0.128716 | − | 0.396148i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.8156 | + | 45.5977i | −0.482975 | + | 1.48644i | 0.351918 | + | 0.936031i | \(0.385529\pi\) |
−0.834893 | + | 0.550412i | \(0.814471\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.2361 | 1.01719 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.0902 | −0.425823 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.5066 | − | 32.3359i | 1.44627 | − | 1.05078i | 0.459584 | − | 0.888134i | \(-0.347998\pi\) |
0.986685 | − | 0.162642i | \(-0.0520016\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37.2016 | 1.20762 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.8328 | 1.03225 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.1525 | − | 24.8132i | 1.10631 | − | 0.803779i | 0.124229 | − | 0.992254i | \(-0.460354\pi\) |
0.982078 | + | 0.188474i | \(0.0603542\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.527864 | − | 0.383516i | −0.0170813 | − | 0.0124103i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.1115 | −0.391508 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.04508 | − | 12.4495i | 0.130623 | − | 0.402015i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.72949 | − | 8.40051i | −0.0880481 | − | 0.270984i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.3262 | − | 31.7809i | 0.332758 | − | 1.02412i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.32624 | − | 16.3925i | 0.171458 | − | 0.527692i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.381966 | − | 0.277515i | −0.0122832 | − | 0.00892427i | 0.581627 | − | 0.813456i | \(-0.302416\pi\) |
−0.593910 | + | 0.804532i | \(0.702416\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 72.1591 | + | 52.4266i | 2.31808 | + | 1.68419i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.1976 | + | 16.1275i | −0.712354 | + | 0.517555i | −0.883932 | − | 0.467615i | \(-0.845113\pi\) |
0.171578 | + | 0.985170i | \(0.445113\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.89919 | + | 24.3112i | 0.253236 | + | 0.779381i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.6844 | + | 35.9609i | −0.374200 | + | 1.15167i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.78115 | − | 17.7926i | −0.184955 | − | 0.569234i | 0.814992 | − | 0.579472i | \(-0.196741\pi\) |
−0.999948 | + | 0.0102376i | \(0.996741\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.00000 | + | 2.90617i | −0.127841 | + | 0.0928816i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.76393 | − | 3.46120i | −0.152101 | − | 0.110508i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.07295 | − | 2.23263i | −0.0980119 | − | 0.0712098i | 0.537700 | − | 0.843136i | \(-0.319293\pi\) |
−0.635712 | + | 0.771926i | \(0.719293\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.2016 | + | 31.3974i | 0.325051 | + | 1.00040i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.263932 | + | 0.812299i | −0.00840105 | + | 0.0258558i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.40983 | + | 22.8051i | 0.235619 | + | 0.725160i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.8156 | + | 48.6754i | −0.502399 | + | 1.54622i | 0.302701 | + | 0.953086i | \(0.402112\pi\) |
−0.805100 | + | 0.593139i | \(0.797888\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −71.7082 | −2.27559 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.48278 | + | 19.9519i | −0.205518 | + | 0.632519i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.1697 | − | 22.6461i | 0.987154 | − | 0.717210i | 0.0278582 | − | 0.999612i | \(-0.491131\pi\) |
0.959296 | + | 0.282402i | \(0.0911313\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.4164 | −0.582669 |
(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 | 200.2.m.a.81.1 | ✓ | 4 | |
4.3 | odd | 2 | 400.2.u.a.81.1 | 4 | |||
5.2 | odd | 4 | 1000.2.q.a.849.1 | 8 | |||
5.3 | odd | 4 | 1000.2.q.a.849.2 | 8 | |||
5.4 | even | 2 | 1000.2.m.a.401.1 | 4 | |||
25.3 | odd | 20 | 1000.2.q.a.649.1 | 8 | |||
25.4 | even | 10 | 1000.2.m.a.601.1 | 4 | |||
25.11 | even | 5 | 5000.2.a.c.1.1 | 2 | |||
25.14 | even | 10 | 5000.2.a.a.1.2 | 2 | |||
25.21 | even | 5 | inner | 200.2.m.a.121.1 | yes | 4 | |
25.22 | odd | 20 | 1000.2.q.a.649.2 | 8 | |||
100.11 | odd | 10 | 10000.2.a.g.1.2 | 2 | |||
100.39 | odd | 10 | 10000.2.a.i.1.1 | 2 | |||
100.71 | odd | 10 | 400.2.u.a.321.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.2.m.a.81.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
200.2.m.a.121.1 | yes | 4 | 25.21 | even | 5 | inner | |
400.2.u.a.81.1 | 4 | 4.3 | odd | 2 | |||
400.2.u.a.321.1 | 4 | 100.71 | odd | 10 | |||
1000.2.m.a.401.1 | 4 | 5.4 | even | 2 | |||
1000.2.m.a.601.1 | 4 | 25.4 | even | 10 | |||
1000.2.q.a.649.1 | 8 | 25.3 | odd | 20 | |||
1000.2.q.a.649.2 | 8 | 25.22 | odd | 20 | |||
1000.2.q.a.849.1 | 8 | 5.2 | odd | 4 | |||
1000.2.q.a.849.2 | 8 | 5.3 | odd | 4 | |||
5000.2.a.a.1.2 | 2 | 25.14 | even | 10 | |||
5000.2.a.c.1.1 | 2 | 25.11 | even | 5 | |||
10000.2.a.g.1.2 | 2 | 100.11 | odd | 10 | |||
10000.2.a.i.1.1 | 2 | 100.39 | odd | 10 |