Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(25,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.q (of order \(3\), degree \(2\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 25.2 | ||
Character | \(\chi\) | \(=\) | 504.25 |
Dual form | 504.2.q.d.121.2 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | −1.56287 | + | 0.746620i | −0.902323 | + | 0.431061i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.71796 | − | 2.97559i | 0.768294 | − | 1.33072i | −0.170193 | − | 0.985411i | \(-0.554439\pi\) |
0.938487 | − | 0.345314i | \(-0.112227\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.727932 | + | 2.54364i | −0.275132 | + | 0.961406i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.88512 | − | 2.33374i | 0.628373 | − | 0.777913i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.20469 | − | 3.81863i | −0.664739 | − | 1.15136i | −0.979356 | − | 0.202143i | \(-0.935210\pi\) |
0.314618 | − | 0.949219i | \(-0.398124\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.49401 | + | 2.58771i | 0.414365 | + | 0.717701i | 0.995362 | − | 0.0962048i | \(-0.0306704\pi\) |
−0.580997 | + | 0.813906i | \(0.697337\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.463308 | + | 5.93312i | −0.119626 | + | 1.53192i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.542270 | − | 0.939239i | 0.131520 | − | 0.227799i | −0.792743 | − | 0.609556i | \(-0.791348\pi\) |
0.924263 | + | 0.381757i | \(0.124681\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.74273 | − | 6.48261i | −0.858642 | − | 1.48721i | −0.873225 | − | 0.487318i | \(-0.837975\pi\) |
0.0145824 | − | 0.999894i | \(-0.495358\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.761471 | − | 4.51887i | −0.166167 | − | 0.986098i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.16279 | − | 3.74606i | 0.450972 | − | 0.781107i | −0.547474 | − | 0.836823i | \(-0.684411\pi\) |
0.998447 | + | 0.0557153i | \(0.0177439\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.40276 | − | 5.89375i | −0.680552 | − | 1.17875i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.20378 | + | 5.05479i | −0.231667 | + | 0.972795i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.68485 | − | 2.91825i | 0.312870 | − | 0.541906i | −0.666113 | − | 0.745851i | \(-0.732043\pi\) |
0.978982 | + | 0.203945i | \(0.0653764\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.37469 | 1.68374 | 0.841872 | − | 0.539678i | \(-0.181454\pi\) | ||||
0.841872 | + | 0.539678i | \(0.181454\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.29671 | + | 4.32196i | 1.09612 | + | 0.752356i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.31828 | + | 6.53590i | 1.06798 | + | 1.10477i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.50767 | − | 4.34341i | −0.412258 | − | 0.714052i | 0.582878 | − | 0.812559i | \(-0.301926\pi\) |
−0.995136 | + | 0.0985079i | \(0.968593\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.26698 | − | 2.92879i | −0.683264 | − | 0.468981i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.20160 | − | 2.08122i | −0.187658 | − | 0.325033i | 0.756811 | − | 0.653634i | \(-0.226756\pi\) |
−0.944469 | + | 0.328601i | \(0.893423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.31412 | − | 5.74023i | 0.505399 | − | 0.875377i | −0.494581 | − | 0.869131i | \(-0.664679\pi\) |
0.999980 | − | 0.00624563i | \(-0.00198806\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.70569 | − | 9.61860i | −0.552412 | − | 1.43386i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00831 | 0.438807 | 0.219403 | − | 0.975634i | \(-0.429589\pi\) | ||||
0.219403 | + | 0.975634i | \(0.429589\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.94023 | − | 3.70320i | −0.848604 | − | 0.529028i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.146242 | + | 1.87278i | −0.0204780 | + | 0.262241i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.530699 | + | 0.919198i | −0.0728971 | + | 0.126262i | −0.900170 | − | 0.435539i | \(-0.856558\pi\) |
0.827273 | + | 0.561801i | \(0.189891\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.1502 | −2.04286 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.6894 | + | 7.33706i | 1.41585 | + | 0.971818i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.4094 | 1.61557 | 0.807783 | − | 0.589480i | \(-0.200668\pi\) | ||||
0.807783 | + | 0.589480i | \(0.200668\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.42668 | −0.694816 | −0.347408 | − | 0.937714i | \(-0.612938\pi\) | ||||
−0.347408 | + | 0.937714i | \(0.612938\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.56396 | + | 6.49387i | 0.575004 | + | 0.818150i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.2666 | 1.27342 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.33998 | 0.408043 | 0.204022 | − | 0.978966i | \(-0.434599\pi\) | ||||
0.204022 | + | 0.978966i | \(0.434599\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.583272 | + | 7.46938i | −0.0702177 | + | 0.899208i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.9064 | −1.53171 | −0.765857 | − | 0.643011i | \(-0.777685\pi\) | ||||
−0.765857 | + | 0.643011i | \(0.777685\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.21382 | + | 14.2267i | −0.961355 | + | 1.66511i | −0.242249 | + | 0.970214i | \(0.577885\pi\) |
−0.719106 | + | 0.694901i | \(0.755448\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.71846 | + | 6.67059i | 1.12219 | + | 0.770254i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.3181 | − | 2.82823i | 1.28982 | − | 0.322307i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.35031 | −0.264431 | −0.132216 | − | 0.991221i | \(-0.542209\pi\) | ||||
−0.132216 | + | 0.991221i | \(0.542209\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.89266 | − | 8.79874i | −0.210296 | − | 0.977638i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.60602 | + | 2.78171i | −0.176283 | + | 0.305332i | −0.940605 | − | 0.339504i | \(-0.889741\pi\) |
0.764321 | + | 0.644836i | \(0.223074\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.86319 | − | 3.22715i | −0.202092 | − | 0.350033i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.454380 | + | 5.81879i | −0.0487147 | + | 0.623840i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.67524 | + | 9.82981i | 0.601575 | + | 1.04196i | 0.992583 | + | 0.121570i | \(0.0387930\pi\) |
−0.391008 | + | 0.920387i | \(0.627874\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.66974 | + | 1.91656i | −0.804008 | + | 0.200910i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.6514 | + | 6.99933i | −1.51928 | + | 0.725796i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −25.7194 | −2.63876 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.40321 | + | 11.0907i | −0.650148 | + | 1.12609i | 0.332939 | + | 0.942948i | \(0.391960\pi\) |
−0.983087 | + | 0.183140i | \(0.941374\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.0678 | − | 2.05341i | −1.31336 | − | 0.206375i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.388110 | + | 0.672227i | 0.0386184 | + | 0.0668891i | 0.884689 | − | 0.466182i | \(-0.154371\pi\) |
−0.846070 | + | 0.533072i | \(0.821038\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.14131 | + | 1.97681i | −0.112457 | + | 0.194781i | −0.916760 | − | 0.399438i | \(-0.869205\pi\) |
0.804304 | + | 0.594219i | \(0.202539\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.7545 | − | 5.49740i | −1.43989 | − | 0.536491i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.27468 | − | 3.93986i | −0.219901 | − | 0.380880i | 0.734876 | − | 0.678201i | \(-0.237240\pi\) |
−0.954778 | + | 0.297321i | \(0.903907\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.36710 | − | 4.09994i | 0.226727 | − | 0.392703i | −0.730109 | − | 0.683331i | \(-0.760531\pi\) |
0.956836 | + | 0.290627i | \(0.0938640\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.16203 | + | 4.91590i | 0.679789 | + | 0.466597i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.175367 | + | 0.303745i | 0.0164972 | + | 0.0285740i | 0.874156 | − | 0.485645i | \(-0.161415\pi\) |
−0.857659 | + | 0.514219i | \(0.828082\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.43116 | − | 12.8711i | −0.692959 | − | 1.20024i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.85542 | + | 1.39150i | 0.818684 | + | 0.128644i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.99435 | + | 2.06304i | 0.182822 | + | 0.189119i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.22130 | + | 7.31151i | −0.383755 | + | 0.664683i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.43182 | + | 2.35554i | 0.309437 | + | 0.212392i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.20360 | −0.554867 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.4175 | 1.10187 | 0.550935 | − | 0.834548i | \(-0.314271\pi\) | ||||
0.550935 | + | 0.834548i | \(0.314271\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.893770 | + | 11.4456i | −0.0786921 | + | 1.00773i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.87152 | + | 13.6339i | −0.687738 | + | 1.19120i | 0.284830 | + | 0.958578i | \(0.408063\pi\) |
−0.972568 | + | 0.232619i | \(0.925270\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.2139 | − | 4.80128i | 1.66606 | − | 0.416324i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12.9730 | + | 12.2659i | 1.11653 | + | 1.05568i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.11510 | + | 3.66346i | 0.180705 | + | 0.312990i | 0.942121 | − | 0.335274i | \(-0.108829\pi\) |
−0.761416 | + | 0.648264i | \(0.775495\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.80367 | + | 16.9805i | 0.831537 | + | 1.44026i | 0.896819 | + | 0.442397i | \(0.145872\pi\) |
−0.0652824 | + | 0.997867i | \(0.520795\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.70159 | + | 2.24606i | −0.395945 | + | 0.189152i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.58767 | − | 11.4102i | 0.550889 | − | 0.954167i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.78902 | − | 10.0269i | −0.480752 | − | 0.832686i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.0487 | + | 1.35252i | 0.993758 | + | 0.111554i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.86326 | − | 8.42341i | 0.398414 | − | 0.690073i | −0.595117 | − | 0.803639i | \(-0.702894\pi\) |
0.993530 | + | 0.113567i | \(0.0362276\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.91074 | + | 8.50565i | 0.399630 | + | 0.692180i | 0.993680 | − | 0.112248i | \(-0.0358051\pi\) |
−0.594050 | + | 0.804428i | \(0.702472\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.16969 | − | 3.03609i | −0.0945642 | − | 0.245453i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.1053 | − | 27.8952i | 1.29361 | − | 2.24060i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0408 | −0.960962 | −0.480481 | − | 0.877005i | \(-0.659538\pi\) | ||||
−0.480481 | + | 0.877005i | \(0.659538\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.143122 | − | 1.83282i | 0.0113503 | − | 0.145352i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.95427 | + | 8.22824i | 0.626884 | + | 0.648476i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.885601 | + | 1.53391i | 0.0693656 | + | 0.120145i | 0.898622 | − | 0.438723i | \(-0.144569\pi\) |
−0.829257 | + | 0.558868i | \(0.811236\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 23.6778 | − | 11.3115i | 1.84332 | − | 0.880597i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.86350 | − | 13.6200i | −0.608496 | − | 1.05395i | −0.991489 | − | 0.130194i | \(-0.958440\pi\) |
0.382993 | − | 0.923751i | \(-0.374893\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.03584 | − | 3.52618i | 0.156603 | − | 0.271245i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22.1842 | − | 3.48591i | −1.69647 | − | 0.266575i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.8063 | 1.42981 | 0.714907 | − | 0.699220i | \(-0.246469\pi\) | ||||
0.714907 | + | 0.699220i | \(0.246469\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.4686 | − | 4.36515i | 1.32050 | − | 0.329974i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.3943 | + | 9.26510i | −1.45776 | + | 0.696407i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.34201 | − | 5.78853i | 0.249794 | − | 0.432655i | −0.713675 | − | 0.700477i | \(-0.752971\pi\) |
0.963468 | + | 0.267822i | \(0.0863039\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.73726 | 0.352117 | 0.176059 | − | 0.984380i | \(-0.443665\pi\) | ||||
0.176059 | + | 0.984380i | \(0.443665\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.48119 | − | 4.05167i | 0.626948 | − | 0.299508i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.2323 | −1.26694 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.78214 | −0.349705 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.9813 | − | 6.74152i | −0.871512 | − | 0.490374i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.0693 | −1.66924 | −0.834618 | − | 0.550829i | \(-0.814312\pi\) | ||||
−0.834618 | + | 0.550829i | \(0.814312\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.3070 | 1.31777 | 0.658885 | − | 0.752244i | \(-0.271028\pi\) | ||||
0.658885 | + | 0.752244i | \(0.271028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.0454 | + | 7.66526i | −1.14903 | + | 0.548920i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.5866 | 1.03925 | 0.519625 | − | 0.854395i | \(-0.326072\pi\) | ||||
0.519625 | + | 0.854395i | \(0.326072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.912102 | + | 1.57981i | −0.0646572 | + | 0.111990i | −0.896542 | − | 0.442959i | \(-0.853929\pi\) |
0.831885 | + | 0.554949i | \(0.187262\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.21995 | + | 2.49369i | −0.368187 | + | 0.175892i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.19653 | + | 6.40996i | 0.434911 | + | 0.449891i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.25716 | −0.576705 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.66521 | − | 12.1091i | −0.324254 | − | 0.841644i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.5031 | + | 28.5843i | −1.14155 | + | 1.97721i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.77359 | − | 4.80400i | −0.190942 | − | 0.330721i | 0.754621 | − | 0.656161i | \(-0.227821\pi\) |
−0.945563 | + | 0.325440i | \(0.894488\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.1711 | − | 9.63621i | 1.38210 | − | 0.660262i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.3870 | − | 19.7229i | −0.776590 | − | 1.34509i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.82413 | + | 23.8458i | −0.463252 | + | 1.61876i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.21515 | − | 28.3671i | 0.149686 | − | 1.91687i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.24064 | 0.217989 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.01726 | − | 10.4222i | 0.402946 | − | 0.697922i | −0.591134 | − | 0.806573i | \(-0.701320\pi\) |
0.994080 | + | 0.108651i | \(0.0346530\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −20.1691 | − | 3.16927i | −1.34460 | − | 0.211284i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.57834 | + | 11.3940i | 0.436620 | + | 0.756248i | 0.997426 | − | 0.0716991i | \(-0.0228421\pi\) |
−0.560806 | + | 0.827947i | \(0.689509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.24159 | + | 10.8108i | −0.412456 | + | 0.714395i | −0.995158 | − | 0.0982915i | \(-0.968662\pi\) |
0.582702 | + | 0.812686i | \(0.301996\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.5771 | + | 12.8705i | −1.02490 | + | 0.846815i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.01687 | − | 3.49332i | −0.132130 | − | 0.228855i | 0.792368 | − | 0.610044i | \(-0.208848\pi\) |
−0.924497 | + | 0.381189i | \(0.875515\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.16814 | − | 8.95149i | 0.337133 | − | 0.583931i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.67323 | − | 1.75479i | 0.238602 | − | 0.113986i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.8679 | + | 24.0200i | 0.897043 | + | 1.55372i | 0.831256 | + | 0.555890i | \(0.187623\pi\) |
0.0657873 | + | 0.997834i | \(0.479044\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.9567 | − | 20.7096i | −0.770199 | − | 1.33402i | −0.937453 | − | 0.348111i | \(-0.886823\pi\) |
0.167254 | − | 0.985914i | \(-0.446510\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.52730 | + | 12.3382i | 0.611176 | + | 0.791494i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −21.2243 | + | 11.3138i | −1.35597 | + | 0.722809i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.1834 | − | 19.3702i | 0.711582 | − | 1.23250i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.433119 | − | 5.54653i | 0.0274478 | − | 0.351497i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.33510 | −0.210509 | −0.105255 | − | 0.994445i | \(-0.533566\pi\) | ||||
−0.105255 | + | 0.994445i | \(0.533566\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.0731 | −1.19912 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.32138 | + | 3.65251i | 0.333238 | + | 0.228729i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.9345 | − | 18.9392i | 0.682078 | − | 1.18139i | −0.292268 | − | 0.956336i | \(-0.594410\pi\) |
0.974346 | − | 0.225057i | \(-0.0722567\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.8735 | − | 3.21690i | 0.799919 | − | 0.199889i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.63429 | − | 9.43326i | −0.224957 | − | 0.583904i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.75522 | − | 4.77218i | −0.169894 | − | 0.294265i | 0.768488 | − | 0.639864i | \(-0.221009\pi\) |
−0.938382 | + | 0.345599i | \(0.887676\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.82344 | + | 3.15829i | 0.112013 | + | 0.194012i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.2088 | − | 11.1255i | −0.991962 | − | 0.680867i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.37393 | − | 5.84382i | 0.205712 | − | 0.356304i | −0.744647 | − | 0.667458i | \(-0.767382\pi\) |
0.950359 | + | 0.311154i | \(0.100716\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.21944 | + | 10.7724i | 0.377804 | + | 0.654376i | 0.990742 | − | 0.135755i | \(-0.0433459\pi\) |
−0.612938 | + | 0.790131i | \(0.710013\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.5559 | − | 8.72172i | 0.638870 | − | 0.527862i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.0040 | + | 25.9878i | −0.904778 | + | 1.56712i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.85945 | + | 8.41681i | 0.291976 | + | 0.505717i | 0.974277 | − | 0.225354i | \(-0.0723539\pi\) |
−0.682301 | + | 0.731071i | \(0.739021\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.6724 | − | 21.8781i | 1.05802 | − | 1.30981i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.66772 | + | 16.7450i | −0.576728 | + | 0.998922i | 0.419124 | + | 0.907929i | \(0.362337\pi\) |
−0.995852 | + | 0.0909928i | \(0.970996\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.30900 | 0.493919 | 0.246959 | − | 0.969026i | \(-0.420569\pi\) | ||||
0.246959 | + | 0.969026i | \(0.420569\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 40.1961 | − | 19.2026i | 2.38101 | − | 1.13747i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.16857 | − | 1.54144i | 0.364119 | − | 0.0909882i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.91189 | + | 13.7038i | 0.465405 | + | 0.806105i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.72685 | − | 22.1141i | 0.101230 | − | 1.29635i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.97318 | − | 6.88175i | −0.232116 | − | 0.402036i | 0.726315 | − | 0.687362i | \(-0.241231\pi\) |
−0.958430 | + | 0.285326i | \(0.907898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.3188 | − | 36.9253i | 1.24123 | − | 2.14987i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.9563 | − | 6.54746i | 1.27404 | − | 0.379922i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.9249 | 0.747469 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.1886 | + | 12.6084i | 0.702541 | + | 0.726739i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.10846 | − | 0.760832i | −0.0636796 | − | 0.0437086i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.32281 | + | 16.1476i | −0.533823 | + | 0.924608i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.9180 | −1.53629 | −0.768145 | − | 0.640276i | \(-0.778820\pi\) | ||||
−0.768145 | + | 0.640276i | \(0.778820\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.307795 | − | 3.94162i | 0.0175098 | − | 0.224231i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.34917 | 0.530143 | 0.265071 | − | 0.964229i | \(-0.414604\pi\) | ||||
0.265071 | + | 0.964229i | \(0.414604\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.8380 | 0.895219 | 0.447610 | − | 0.894229i | \(-0.352275\pi\) | ||||
0.447610 | + | 0.894229i | \(0.352275\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 27.1638 | − | 2.42427i | 1.53051 | − | 0.136592i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.4591 | −1.59843 | −0.799213 | − | 0.601049i | \(-0.794750\pi\) | ||||
−0.799213 | + | 0.601049i | \(0.794750\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.8583 | −0.831906 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.49660 | + | 4.45916i | 0.362605 | + | 0.248886i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.11829 | −0.451714 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.1675 | − | 17.6107i | 0.563994 | − | 0.976865i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.638373 | + | 8.17500i | −0.0353021 | + | 0.452078i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.18984 | + | 7.65205i | −0.120730 | + | 0.421871i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.5904 | −1.07679 | −0.538393 | − | 0.842694i | \(-0.680968\pi\) | ||||
−0.538393 | + | 0.842694i | \(0.680968\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.8636 | − | 2.33559i | −0.814521 | − | 0.127990i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.73794 | − | 9.93841i | 0.313497 | − | 0.542993i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.73059 | + | 15.1218i | 0.475586 | + | 0.823739i | 0.999609 | − | 0.0279654i | \(-0.00890283\pi\) |
−0.524023 | + | 0.851704i | \(0.675569\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.500859 | − | 0.343781i | −0.0272029 | − | 0.0186716i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.6683 | − | 35.7985i | −1.11925 | − | 1.93860i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.7437 | − | 12.4141i | 0.742090 | − | 0.670301i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.2238 | + | 14.5677i | 1.14265 | + | 0.784296i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.4502 | −1.04414 | −0.522070 | − | 0.852903i | \(-0.674840\pi\) | ||||
−0.522070 | + | 0.852903i | \(0.674840\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.91419 | − | 11.9757i | 0.370108 | − | 0.641046i | −0.619474 | − | 0.785018i | \(-0.712654\pi\) |
0.989582 | + | 0.143971i | \(0.0459872\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.8788 | + | 4.43691i | −0.794171 | + | 0.236825i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.92295 | − | 10.2588i | −0.315247 | − | 0.546023i | 0.664243 | − | 0.747517i | \(-0.268754\pi\) |
−0.979490 | + | 0.201493i | \(0.935421\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.1727 | + | 38.4043i | −1.17681 | + | 2.03829i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.65722 | − | 1.73524i | −0.246486 | − | 0.0918388i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.628489 | − | 1.08858i | −0.0331704 | − | 0.0574528i | 0.848964 | − | 0.528451i | \(-0.177227\pi\) |
−0.882134 | + | 0.470998i | \(0.843894\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5161 | + | 32.0709i | −0.974533 | + | 1.68794i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.13842 | − | 14.5786i | 0.0597517 | − | 0.765180i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.2220 | + | 48.8819i | 1.47721 | + | 2.55860i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.61928 | + | 13.1970i | 0.397723 | + | 0.688877i | 0.993445 | − | 0.114314i | \(-0.0364671\pi\) |
−0.595721 | + | 0.803191i | \(0.703134\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.12218 | − | 1.11914i | −0.370766 | − | 0.0582603i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.95180 | − | 2.01902i | −0.101332 | − | 0.104822i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.66756 | + | 15.0127i | −0.448789 | + | 0.777326i | −0.998308 | − | 0.0581556i | \(-0.981478\pi\) |
0.549518 | + | 0.835482i | \(0.314811\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.69542 | − | 4.63173i | 0.500669 | − | 0.239182i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.0688 | 0.518569 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.6319 | 0.802955 | 0.401478 | − | 0.915869i | \(-0.368497\pi\) | ||||
0.401478 | + | 0.915869i | \(0.368497\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.4068 | + | 9.27112i | −0.994243 | + | 0.474974i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.90615 | − | 15.4259i | 0.455083 | − | 0.788227i | −0.543610 | − | 0.839338i | \(-0.682943\pi\) |
0.998693 | + | 0.0511113i | \(0.0162763\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.0284 | − | 38.5368i | 0.562057 | − | 1.96402i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.14868 | − | 18.5553i | −0.363388 | − | 0.943219i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.7074 | − | 25.4740i | −0.745695 | − | 1.29158i | −0.949869 | − | 0.312647i | \(-0.898784\pi\) |
0.204175 | − | 0.978934i | \(-0.434549\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.34563 | − | 4.06275i | −0.118624 | − | 0.205462i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.12283 | − | 27.1850i | 0.107083 | − | 1.37130i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.03774 | + | 6.99357i | −0.203161 | + | 0.351885i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.55930 | − | 2.70079i | −0.0782592 | − | 0.135549i | 0.824240 | − | 0.566241i | \(-0.191603\pi\) |
−0.902499 | + | 0.430692i | \(0.858270\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −26.4441 | + | 21.8492i | −1.32386 | + | 1.09383i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.8613 | − | 30.9367i | 0.891950 | − | 1.54490i | 0.0544157 | − | 0.998518i | \(-0.482670\pi\) |
0.837534 | − | 0.546385i | \(-0.183996\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.0059 | + | 24.2590i | 0.697684 | + | 1.20842i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −29.4330 | − | 9.48407i | −1.46254 | − | 0.471267i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.0572 | + | 19.1517i | −0.548087 | + | 0.949315i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.81652 | 0.485396 | 0.242698 | − | 0.970102i | \(-0.421968\pi\) | ||||
0.242698 | + | 0.970102i | \(0.421968\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.04083 | − | 4.14633i | −0.297972 | − | 0.204523i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.03320 | + | 31.5651i | −0.444494 | + | 1.55321i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.51814 | + | 9.55771i | 0.270875 | + | 0.469169i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27.9998 | − | 19.2186i | −1.37116 | − | 0.941140i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.09812 | + | 10.5623i | 0.297913 | + | 0.516000i | 0.975658 | − | 0.219297i | \(-0.0703762\pi\) |
−0.677746 | + | 0.735297i | \(0.737043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.10015 | + | 8.83373i | −0.248566 | + | 0.430529i | −0.963128 | − | 0.269043i | \(-0.913293\pi\) |
0.714562 | + | 0.699572i | \(0.246626\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.67101 | − | 7.02060i | 0.275734 | − | 0.341353i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.38085 | −0.358024 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.95026 | − | 13.8035i | 0.191166 | − | 0.668000i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.77660 | + | 22.7511i | −0.0857750 | + | 1.09843i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.70254 | + | 9.87710i | −0.274682 | + | 0.475763i | −0.970055 | − | 0.242886i | \(-0.921906\pi\) |
0.695373 | + | 0.718649i | \(0.255239\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.2391 | 1.26097 | 0.630486 | − | 0.776201i | \(-0.282856\pi\) | ||||
0.630486 | + | 0.776201i | \(0.282856\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.5337 | + | 11.3485i | 0.792732 | + | 0.544118i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.3790 | −1.54890 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.9554 | 1.09560 | 0.547801 | − | 0.836609i | \(-0.315465\pi\) | ||||
0.547801 | + | 0.836609i | \(0.315465\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.8403 | + | 6.88197i | −0.944777 | + | 0.327713i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.4025 | 1.06438 | 0.532188 | − | 0.846626i | \(-0.321370\pi\) | ||||
0.532188 | + | 0.846626i | \(0.321370\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 38.9993 | 1.84874 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.31155 | + | 16.7957i | −0.0620341 | + | 0.794409i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.0576 | 0.805000 | 0.402500 | − | 0.915420i | \(-0.368141\pi\) | ||||
0.402500 | + | 0.915420i | \(0.368141\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.29829 | + | 9.17690i | −0.249487 | + | 0.432123i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.0253 | − | 9.62676i | −0.658968 | − | 0.452305i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.47340 | + | 26.1146i | −0.350358 | + | 1.22427i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.54729 | 0.446604 | 0.223302 | − | 0.974749i | \(-0.428316\pi\) | ||||
0.223302 | + | 0.974749i | \(0.428316\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.09489 | + | 3.87170i | 0.191133 | + | 0.180715i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.1213 | − | 17.5305i | 0.471394 | − | 0.816478i | −0.528070 | − | 0.849201i | \(-0.677084\pi\) |
0.999464 | + | 0.0327222i | \(0.0104177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.81948 | − | 13.5437i | −0.363402 | − | 0.629431i | 0.625116 | − | 0.780532i | \(-0.285052\pi\) |
−0.988518 | + | 0.151101i | \(0.951718\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.34337 | + | 55.6211i | −0.201419 | + | 2.57937i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.96638 | − | 5.13793i | −0.137268 | − | 0.237755i | 0.789194 | − | 0.614144i | \(-0.210499\pi\) |
−0.926461 | + | 0.376390i | \(0.877165\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.43128 | + | 8.49571i | −0.112266 | + | 0.392295i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.8182 | − | 8.98992i | 0.867098 | − | 0.414234i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −29.2264 | −1.34383 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.4712 | + | 44.1175i | −1.16870 | + | 2.02425i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.14474 | + | 2.97131i | 0.0524139 | + | 0.136047i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.69708 | + | 15.0638i | 0.397380 | + | 0.688282i | 0.993402 | − | 0.114686i | \(-0.0365862\pi\) |
−0.596022 | + | 0.802968i | \(0.703253\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.49298 | − | 12.9782i | 0.341650 | − | 0.591756i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.5748 | − | 6.92084i | −0.845185 | − | 0.314909i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.0009 | + | 38.1067i | 0.999009 | + | 1.73033i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.76967 | + | 16.9216i | −0.442706 | + | 0.766790i | −0.997889 | − | 0.0649386i | \(-0.979315\pi\) |
0.555183 | + | 0.831728i | \(0.312648\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.52932 | − | 1.73609i | −0.114380 | − | 0.0785086i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.16702 | − | 10.6816i | −0.278314 | − | 0.482054i | 0.692652 | − | 0.721272i | \(-0.256442\pi\) |
−0.970966 | + | 0.239218i | \(0.923109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.82729 | − | 3.16496i | −0.0822971 | − | 0.142543i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −28.5600 | + | 35.3567i | −1.28368 | + | 1.58917i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.39502 | − | 32.8294i | 0.421424 | − | 1.47260i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.27308 | + | 16.0614i | −0.415120 | + | 0.719009i | −0.995441 | − | 0.0953788i | \(-0.969594\pi\) |
0.580321 | + | 0.814388i | \(0.302927\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.4586 | + | 15.4152i | 1.00337 | + | 0.688700i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.3264 | −0.638782 | −0.319391 | − | 0.947623i | \(-0.603478\pi\) | ||||
−0.319391 | + | 0.947623i | \(0.603478\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.66703 | 0.118681 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.549037 | + | 7.03097i | −0.0243836 | + | 0.312256i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.43056 | − | 14.6022i | 0.373678 | − | 0.647229i | −0.616450 | − | 0.787394i | \(-0.711430\pi\) |
0.990128 | + | 0.140165i | \(0.0447632\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.2087 | − | 31.2491i | −1.33635 | − | 1.38238i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 37.2736 | − | 11.1151i | 1.64567 | − | 0.490745i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.92145 | + | 6.79215i | 0.172800 | + | 0.299298i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.63238 | − | 11.4876i | −0.291692 | − | 0.505225i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.3917 | + | 14.0411i | −1.29015 | + | 0.616337i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.8132 | − | 18.7291i | 0.473737 | − | 0.820536i | −0.525811 | − | 0.850601i | \(-0.676238\pi\) |
0.999548 | + | 0.0300652i | \(0.00957151\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.27472 | + | 14.3322i | 0.361828 | + | 0.626705i | 0.988262 | − | 0.152770i | \(-0.0488193\pi\) |
−0.626433 | + | 0.779475i | \(0.715486\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −24.0420 | + | 19.8645i | −1.04928 | + | 0.866959i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.08361 | − | 8.80507i | 0.221446 | − | 0.383555i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.14470 | + | 3.71472i | 0.0932476 | + | 0.161510i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.3932 | − | 28.9603i | 1.01518 | − | 1.25677i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.59040 | − | 6.21876i | 0.155517 | − | 0.269364i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.6312 | −0.675796 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.901291 | + | 11.5419i | −0.0388936 | + | 0.498071i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.04479 | + | 30.8480i | −0.0450025 | + | 1.32872i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9542 | − | 20.7053i | −0.513952 | − | 0.890191i | −0.999869 | − | 0.0161861i | \(-0.994848\pi\) |
0.485917 | − | 0.874005i | \(-0.338486\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.40371 | + | 3.53693i | −0.317724 | + | 0.151784i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.13317 | − | 14.0871i | −0.348387 | − | 0.603423i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.8193 | + | 25.6678i | −0.633627 | + | 1.09747i | 0.353177 | + | 0.935556i | \(0.385101\pi\) |
−0.986804 | + | 0.161918i | \(0.948232\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.2299 | + | 12.6645i | −0.436603 | + | 0.540506i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.2238 | −1.07457 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.71087 | − | 5.97836i | 0.0727536 | − | 0.254226i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 26.9318 | − | 12.8659i | 1.14319 | − | 0.546129i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.8366 | + | 18.7695i | −0.459160 | + | 0.795288i | −0.998917 | − | 0.0465330i | \(-0.985183\pi\) |
0.539757 | + | 0.841821i | \(0.318516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.8054 | 0.837679 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.47387 | − | 3.57044i | 0.315547 | − | 0.150744i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.1556 | 0.596589 | 0.298294 | − | 0.954474i | \(-0.403582\pi\) | ||||
0.298294 | + | 0.954474i | \(0.403582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.20510 | 0.0506988 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.7586 | + | 1.59063i | 0.997766 | + | 0.0668001i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.0356 | −1.42684 | −0.713422 | − | 0.700734i | \(-0.752856\pi\) | ||||
−0.713422 | + | 0.700734i | \(0.752856\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.34970 | −0.223878 | −0.111939 | − | 0.993715i | \(-0.535706\pi\) | ||||
−0.111939 | + | 0.993715i | \(0.535706\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 36.0543 | − | 17.2240i | 1.50619 | − | 0.719543i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −29.4378 | −1.22764 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.1865 | − | 19.3756i | 0.465699 | − | 0.806615i | −0.533533 | − | 0.845779i | \(-0.679136\pi\) |
0.999233 | + | 0.0391640i | \(0.0124695\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.6115 | + | 13.6684i | −1.18905 | + | 0.568039i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.90659 | − | 6.11003i | −0.245047 | − | 0.253487i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.68011 | 0.193830 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.3538 | − | 23.9596i | 0.800180 | − | 0.990607i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.49899 | + | 4.32839i | −0.103145 | + | 0.178652i | −0.912979 | − | 0.408007i | \(-0.866224\pi\) |
0.809834 | + | 0.586659i | \(0.199557\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.0870 | − | 60.7724i | −1.44573 | − | 2.50408i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.7969 | + | 10.8906i | −0.937739 | + | 0.447980i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.1698 | + | 21.0788i | 0.499755 | + | 0.865601i | 1.00000 | 0.000282582i | \(-8.99487e-5\pi\) | |
−0.500245 | + | 0.865884i | \(0.666757\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.56498 | − | 2.39015i | 0.392126 | − | 0.0979868i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.245981 | − | 3.15003i | 0.0100673 | − | 0.128922i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.2145 | 1.88827 | 0.944137 | − | 0.329552i | \(-0.106898\pi\) | ||||
0.944137 | + | 0.329552i | \(0.106898\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.6163 | + | 28.7803i | −0.677792 | + | 1.17397i | 0.297852 | + | 0.954612i | \(0.403730\pi\) |
−0.975644 | + | 0.219359i | \(0.929603\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.29625 | − | 7.79463i | 0.256403 | − | 0.317422i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.5040 | + | 25.1217i | 0.589673 | + | 1.02134i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.9318 | + | 37.9869i | −0.890182 | + | 1.54184i | −0.0505262 | + | 0.998723i | \(0.516090\pi\) |
−0.839656 | + | 0.543118i | \(0.817244\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.4702 | − | 5.39147i | −0.586361 | − | 0.218473i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.49445 | + | 7.78462i | 0.181826 | + | 0.314932i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.81569 | − | 3.14487i | 0.0733351 | − | 0.127020i | −0.827026 | − | 0.562164i | \(-0.809969\pi\) |
0.900361 | + | 0.435144i | \(0.143302\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.9049 | − | 6.16496i | 0.520374 | − | 0.248595i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.4542 | + | 18.1073i | 0.420872 | + | 0.728971i | 0.996025 | − | 0.0890744i | \(-0.0283909\pi\) |
−0.575153 | + | 0.818046i | \(0.695058\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.9745 | − | 20.7405i | −0.481296 | − | 0.833629i | 0.518474 | − | 0.855094i | \(-0.326500\pi\) |
−0.999770 | + | 0.0214645i | \(0.993167\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.3320 | + | 15.4419i | 0.655382 | + | 0.619661i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.1347 | + | 7.28035i | −1.16726 | + | 0.291681i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.35626 | − | 11.0094i | 0.254251 | − | 0.440375i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.45065 | − | 56.9950i | 0.177742 | − | 2.27616i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.43933 | −0.216880 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.06918 | −0.241610 | −0.120805 | − | 0.992676i | \(-0.538548\pi\) | ||||
−0.120805 | + | 0.992676i | \(0.538548\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.92152 | + | 5.43720i | 0.314852 | + | 0.216109i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.3327 | − | 36.9492i | 0.846561 | − | 1.46629i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.708008 | − | 20.9042i | 0.0280523 | − | 0.828255i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.3302 | + | 30.1203i | −0.962487 | + | 1.19154i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.69407 | + | 15.0586i | 0.343395 | + | 0.594778i | 0.985061 | − | 0.172207i | \(-0.0550897\pi\) |
−0.641666 | + | 0.766984i | \(0.721756\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.66411 | + | 16.7387i | 0.381115 | + | 0.660111i | 0.991222 | − | 0.132208i | \(-0.0422068\pi\) |
−0.610107 | + | 0.792319i | \(0.708873\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 32.5220 | + | 22.3226i | 1.28055 | + | 0.878951i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.7041 | − | 22.0042i | 0.499451 | − | 0.865075i | −0.500549 | − | 0.865708i | \(-0.666868\pi\) |
1.00000 | 0.000633482i | \(0.000201644\pi\) | ||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.3588 | − | 47.3869i | −1.07393 | − | 1.86010i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.13855 | − | 42.3630i | −0.279782 | − | 1.66034i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.9064 | − | 22.3545i | 0.505065 | − | 0.874799i | −0.494917 | − | 0.868940i | \(-0.664802\pi\) |
0.999983 | − | 0.00585902i | \(-0.00186499\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.0459 | + | 46.8449i | 1.05677 | + | 1.83038i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.7175 | + | 45.9880i | 0.691225 | + | 1.79416i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.62598 | − | 14.9406i | 0.336020 | − | 0.582004i | −0.647660 | − | 0.761930i | \(-0.724252\pi\) |
0.983680 | + | 0.179925i | \(0.0575856\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.9635 | 0.504222 | 0.252111 | − | 0.967698i | \(-0.418875\pi\) | ||||
0.252111 | + | 0.967698i | \(0.418875\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.06469 | + | 2.41952i | −0.196696 | + | 0.0939665i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.7220 | − | 65.4210i | 0.726008 | − | 2.53692i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.28797 | − | 12.6231i | −0.282191 | − | 0.488769i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.62277 | + | 20.7811i | −0.0627398 | + | 0.803445i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.9641 | + | 20.7225i | 0.461871 | + | 0.799984i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.8060 | + | 36.0371i | −0.802013 | + | 1.38913i | 0.116277 | + | 0.993217i | \(0.462904\pi\) |
−0.918289 | + | 0.395910i | \(0.870429\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 33.8878 | − | 10.1055i | 1.30434 | − | 0.388960i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.1998 | −0.853209 | −0.426605 | − | 0.904438i | \(-0.640290\pi\) | ||||
−0.426605 | + | 0.904438i | \(0.640290\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.5496 | − | 24.3607i | −0.903752 | − | 0.934879i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.7881 | − | 12.8958i | −0.719961 | − | 0.494170i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.60315 | + | 7.97289i | −0.176135 | + | 0.305074i | −0.940553 | − | 0.339646i | \(-0.889693\pi\) |
0.764419 | + | 0.644720i | \(0.223026\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.5346 | 0.555338 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.68326 | − | 21.5559i | 0.0642206 | − | 0.822408i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.17149 | −0.120824 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.0585 | −1.52390 | −0.761949 | − | 0.647636i | \(-0.775758\pi\) | ||||
−0.761949 | + | 0.647636i | \(0.775758\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.7356 | − | 31.7450i | 0.559759 | − | 1.20589i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 67.3692 | 2.55546 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.60636 | −0.0987228 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.76029 | + | 3.95377i | 0.217874 | + | 0.149545i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.3868 | 1.29877 | 0.649385 | − | 0.760459i | \(-0.275026\pi\) | ||||
0.649385 | + | 0.760459i | \(0.275026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.7711 | + | 32.5124i | −0.707964 | + | 1.22623i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.39377 | + | 17.8486i | −0.0524925 | + | 0.672219i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.99242 | + | 0.497878i | −0.0749328 | + | 0.0187246i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.1840 | 0.795582 | 0.397791 | − | 0.917476i | \(-0.369777\pi\) | ||||
0.397791 | + | 0.917476i | \(0.369777\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.43062 | + | 5.48502i | −0.166161 | + | 0.205704i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.2755 | − | 35.1181i | 0.759322 | − | 1.31518i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.6347 | − | 39.2044i | −0.846489 | − | 1.46616i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −39.6076 | − | 27.1860i | −1.47917 | − | 1.01528i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.5994 | − | 37.4113i | −0.805523 | − | 1.39521i | −0.915937 | − | 0.401321i | \(-0.868551\pi\) |
0.110414 | − | 0.993886i | \(-0.464782\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.19750 | − | 4.34207i | −0.156323 | − | 0.161707i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.1490 | + | 23.4393i | 1.27001 | + | 0.871718i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.9326 | −0.851696 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.5571 | − | 35.6059i | 0.762420 | − | 1.32055i | −0.179180 | − | 0.983816i | \(-0.557344\pi\) |
0.941600 | − | 0.336734i | \(-0.109322\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.1018 | − | 12.1697i | −0.892661 | − | 0.450729i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.59430 | − | 6.22551i | −0.132940 | − | 0.230259i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.0425 | + | 45.1070i | −0.961903 | + | 1.66607i | −0.244189 | + | 0.969728i | \(0.578522\pi\) |
−0.717715 | + | 0.696337i | \(0.754812\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 24.7237 | − | 33.5284i | 0.911946 | − | 1.23671i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.36361 | − | 12.7541i | −0.271242 | − | 0.469805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.18624 | − | 12.4469i | 0.264350 | − | 0.457868i | −0.703043 | − | 0.711147i | \(-0.748176\pi\) |
0.967393 | + | 0.253279i | \(0.0815092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.01600 | + | 38.6228i | −0.110795 | + | 1.41885i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.3167 | − | 36.9216i | −0.782034 | − | 1.35452i | −0.930755 | − | 0.365643i | \(-0.880849\pi\) |
0.148721 | − | 0.988879i | \(-0.452484\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.7097 | − | 28.9421i | −0.612198 | − | 1.06036i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.46424 | + | 8.99187i | 0.126750 | + | 0.328995i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.6774 | − | 2.91802i | 0.426683 | − | 0.106622i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.9846 | − | 32.8823i | 0.692758 | − | 1.19989i | −0.278173 | − | 0.960531i | \(-0.589729\pi\) |
0.970931 | − | 0.239360i | \(-0.0769378\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.21232 | − | 2.49005i | 0.189947 | − | 0.0907424i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.7458 | 1.22813 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.6692 | 1.00565 | 0.502827 | − | 0.864387i | \(-0.332293\pi\) | ||||
0.502827 | + | 0.864387i | \(0.332293\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.8087 | − | 14.2404i | 1.08199 | − | 0.516892i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.97210 | + | 10.3440i | −0.216488 | + | 0.374969i | −0.953732 | − | 0.300658i | \(-0.902794\pi\) |
0.737244 | + | 0.675627i | \(0.236127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.70570 | + | 9.00554i | 0.315167 | + | 0.326023i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.0437 | − | 1.73534i | −0.399284 | − | 0.0627415i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.5398 | + | 32.1119i | 0.669434 | + | 1.15949i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.4026 | − | 30.1422i | −0.627554 | − | 1.08695i | −0.988041 | − | 0.154191i | \(-0.950723\pi\) |
0.360487 | − | 0.932764i | \(-0.382610\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.94888 | + | 37.7634i | −0.106201 | + | 1.36002i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.5014 | + | 23.3851i | −0.485611 | + | 0.841103i | −0.999863 | − | 0.0165363i | \(-0.994736\pi\) |
0.514253 | + | 0.857639i | \(0.328069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.8998 | − | 55.2521i | −1.14587 | − | 1.98471i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.7178 | + | 14.6392i | −0.635621 | + | 0.525178i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.99450 | + | 15.5789i | −0.322261 | + | 0.558173i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.4547 | + | 49.2850i | 1.01819 | + | 1.76356i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.7230 | + | 12.0295i | 0.454682 | + | 0.429900i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.6856 | + | 35.8286i | −0.738302 | + | 1.27878i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.2840 | 0.758693 | 0.379347 | − | 0.925255i | \(-0.376149\pi\) | ||||
0.379347 | + | 0.925255i | \(0.376149\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.86905 | + | 5.40119i | 0.280146 | + | 0.192287i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.900275 | + | 0.224966i | −0.0320101 | + | 0.00799887i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.10754 | − | 14.0427i | −0.287907 | − | 0.498670i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.20783 | − | 3.57457i | −0.184703 | − | 0.126777i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.3062 | − | 17.8508i | −0.365064 | − | 0.632309i | 0.623723 | − | 0.781646i | \(-0.285619\pi\) |
−0.988786 | + | 0.149337i | \(0.952286\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.63131 | − | 2.82552i | 0.0577117 | − | 0.0999597i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33.6387 | + | 5.28582i | 1.18856 | + | 0.186765i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 72.4356 | 2.55620 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38.1490 | − | 9.53289i | 1.34457 | − | 0.335990i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.909900 | + | 11.6522i | −0.0320300 | + | 0.410176i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.54223 | − | 4.40328i | 0.0893802 | − | 0.154811i | −0.817869 | − | 0.575404i | \(-0.804845\pi\) |
0.907249 | + | 0.420593i | \(0.138178\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.58775 | −0.266442 | −0.133221 | − | 0.991086i | \(-0.542532\pi\) | ||||
−0.133221 | + | 0.991086i | \(0.542532\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.7631 | − | 12.1923i | −0.622977 | − | 0.427602i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.08570 | 0.213173 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −49.6155 | −1.73583 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.98562 | + | 21.5121i | −0.348926 | + | 0.751694i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.2696 | 0.707413 | 0.353706 | − | 0.935357i | \(-0.384921\pi\) | ||||
0.353706 | + | 0.935357i | \(0.384921\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.7911 | 0.759588 | 0.379794 | − | 0.925071i | \(-0.375995\pi\) | ||||
0.379794 | + | 0.925071i | \(0.375995\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.04637 | − | 51.8178i | 0.140877 | − | 1.80406i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.3796 | 0.917307 | 0.458654 | − | 0.888615i | \(-0.348332\pi\) | ||||
0.458654 | + | 0.888615i | \(0.348332\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.33400 | − | 16.1670i | 0.324183 | − | 0.561502i | −0.657164 | − | 0.753748i | \(-0.728244\pi\) |
0.981347 | + | 0.192246i | \(0.0615773\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.8788 | − | 9.52621i | −0.481452 | − | 0.330461i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.69940 | + | 3.57116i | −0.232120 | + | 0.123733i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −54.0366 | −1.87001 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.2850 | + | 47.3871i | −0.390068 | + | 1.63794i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.5265 | − | 21.6966i | 0.432464 | − | 0.749050i | −0.564621 | − | 0.825351i | \(-0.690977\pi\) |
0.997085 | + | 0.0763004i | \(0.0243108\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.82253 | + | 15.2811i | 0.304225 | + | 0.526934i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.60724 | − | 33.3883i | 0.0897982 | − | 1.14995i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.99499 | − | 12.1157i | −0.240635 | − | 0.416792i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.5250 | − | 16.0598i | −0.533447 | − | 0.551820i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.9859 | + | 6.20367i | −0.445674 | + | 0.212909i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.6942 | −0.743668 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.2219 | + | 33.2933i | −0.658146 | + | 1.13994i | 0.322949 | + | 0.946416i | \(0.395326\pi\) |
−0.981095 | + | 0.193526i | \(0.938008\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −48.4842 | + | 60.0224i | −1.65812 | + | 2.05272i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.00299 | + | 10.3975i | 0.205058 | + | 0.355172i | 0.950151 | − | 0.311789i | \(-0.100928\pi\) |
−0.745093 | + | 0.666961i | \(0.767595\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.30154 | − | 10.9146i | 0.215006 | − | 0.372401i | −0.738269 | − | 0.674507i | \(-0.764356\pi\) |
0.953274 | + | 0.302106i | \(0.0976896\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.48979 | + | 7.01464i | −0.289331 | + | 0.239058i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.210643 | − | 0.364845i | −0.00717038 | − | 0.0124195i | 0.862418 | − | 0.506197i | \(-0.168949\pi\) |
−0.869588 | + | 0.493777i | \(0.835616\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.3084 | − | 55.9597i | 1.09852 | − | 1.90269i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.5968 | − | 15.5101i | −0.767426 | − | 0.526749i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.18171 | + | 8.97499i | 0.175778 | + | 0.304456i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.98997 | + | 8.64289i | 0.169079 | + | 0.292853i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.8119 | + | 35.8507i | 0.467464 | + | 1.21336i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.51580 | − | 15.7797i | 0.152662 | − | 0.533453i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.893424 | + | 1.54746i | −0.0301688 | + | 0.0522539i | −0.880716 | − | 0.473645i | \(-0.842938\pi\) |
0.850547 | + | 0.525899i | \(0.176271\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.3476 | + | 7.78881i | 0.382745 | + | 0.262710i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.8891 | −1.68081 | −0.840403 | − | 0.541962i | \(-0.817682\pi\) | ||||
−0.840403 | + | 0.541962i | \(0.817682\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.7935 | 1.17090 | 0.585448 | − | 0.810710i | \(-0.300919\pi\) | ||||
0.585448 | + | 0.810710i | \(0.300919\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.74937 | + | 73.6264i | −0.193263 | + | 2.47492i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.9040 | + | 20.6184i | −0.399698 | + | 0.692297i | −0.993688 | − | 0.112175i | \(-0.964218\pi\) |
0.593991 | + | 0.804472i | \(0.297552\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.03906 | + | 31.5855i | −0.303160 | + | 1.05935i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.4264 | + | 26.6259i | −0.985822 | + | 0.892000i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.2593 | − | 19.5017i | −0.376778 | − | 0.652598i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.4829 | − | 19.8889i | −0.383830 | − | 0.664813i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.2000 | + | 9.65002i | −0.674458 | + | 0.322205i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.7950 | − | 27.3577i | 0.526792 | − | 0.912431i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.575564 | + | 0.996907i | 0.0191748 | + | 0.0332118i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −28.4630 | − | 10.6051i | −0.947188 | − | 0.352914i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.13841 | − | 14.0961i | 0.270530 | − | 0.468571i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.1406 | − | 29.6885i | −0.569146 | − | 0.985789i | −0.996651 | − | 0.0817761i | \(-0.973941\pi\) |
0.427505 | − | 0.904013i | \(-0.359393\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.30044 | + | 0.361479i | 0.0763006 | + | 0.0119895i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.9839 | − | 25.9529i | 0.496438 | − | 0.859857i | −0.503553 | − | 0.863964i | \(-0.667974\pi\) |
0.999992 | + | 0.00410771i | \(0.00130753\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.1631 | 0.468730 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.51423 | − | 32.1972i | 0.0831177 | − | 1.06441i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.9498 | − | 29.9469i | −0.956006 | − | 0.988933i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.391037 | − | 0.677296i | −0.0128991 | − | 0.0223419i | 0.859504 | − | 0.511129i | \(-0.170773\pi\) |
−0.872403 | + | 0.488787i | \(0.837439\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.0693 | − | 20.0975i | 1.38623 | − | 0.662235i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19.2824 | − | 33.3981i | −0.634688 | − | 1.09931i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.0660 | + | 29.5591i | −0.561126 | + | 0.971898i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.46185 | + | 6.39004i | 0.0808577 | + | 0.209876i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.5324 | −0.443983 | −0.221992 | − | 0.975049i | \(-0.571256\pi\) | ||||
−0.221992 | + | 0.975049i | \(0.571256\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.77367 | + | 52.3683i | −0.0581297 | + | 1.71630i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.6115 | + | 6.98028i | −0.478360 | + | 0.228524i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.21552 | + | 14.2297i | −0.268676 | + | 0.465361i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.27674 | −0.0743777 | −0.0371889 | − | 0.999308i | \(-0.511840\pi\) | ||||
−0.0371889 | + | 0.999308i | \(0.511840\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.7528 | + | 11.8250i | −0.807776 | + | 0.385894i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.15440 | −0.265826 | −0.132913 | − | 0.991128i | \(-0.542433\pi\) | ||||
−0.132913 | + | 0.991128i | \(0.542433\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.3952 | −0.338514 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −40.6434 | + | 24.0698i | −1.32213 | + | 0.782992i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.87106 | 0.255775 | 0.127888 | − | 0.991789i | \(-0.459180\pi\) | ||||
0.127888 | + | 0.991789i | \(0.459180\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.0862 | −1.59341 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 44.4779 | − | 21.2482i | 1.44230 | − | 0.689019i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.1097 | 1.39646 | 0.698230 | − | 0.715873i | \(-0.253971\pi\) | ||||
0.698230 | + | 0.715873i | \(0.253971\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39.6321 | + | 68.6448i | −1.28246 | + | 2.22129i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.2216 | − | 11.0935i | 0.750648 | − | 0.358602i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.8582 | + | 2.71330i | −0.350629 | + | 0.0876172i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.8847 | 1.83499 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.4826 | − | 2.11859i | −0.434472 | − | 0.0682707i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31.4507 | − | 54.4742i | 1.01243 | − | 1.75359i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.9537 | + | 24.1684i | 0.448719 | + | 0.777205i | 0.998303 | − | 0.0582340i | \(-0.0185470\pi\) |
−0.549584 | + | 0.835439i | \(0.685214\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.6878 | − | 6.06128i | 0.407591 | − | 0.194716i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0705 | + | 36.4952i | 0.676185 | + | 1.17119i | 0.976121 | + | 0.217228i | \(0.0697015\pi\) |
−0.299936 | + | 0.953959i | \(0.596965\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50.3286 | + | 12.5764i | −1.61346 | + | 0.403181i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.74204 | + | 35.1145i | −0.0878154 | + | 1.12456i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.8549 | −0.443259 | −0.221629 | − | 0.975131i | \(-0.571137\pi\) | ||||
−0.221629 | + | 0.975131i | \(0.571137\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.0243 | − | 43.3433i | 0.799780 | − | 1.38526i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.10592 | − | 13.2531i | −0.163020 | − | 0.423138i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.97938 | − | 6.89249i | −0.126923 | − | 0.219836i | 0.795560 | − | 0.605874i | \(-0.207177\pi\) |
−0.922483 | + | 0.386038i | \(0.873843\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.0591 | − | 43.4036i | 0.798449 | − | 1.38296i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.29074 | − | 13.5941i | −0.0729150 | − | 0.432706i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.3355 | − | 24.8298i | −0.455842 | − | 0.789542i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.36428 | − | 7.55916i | 0.138636 | − | 0.240125i | −0.788345 | − | 0.615234i | \(-0.789062\pi\) |
0.926981 | + | 0.375109i | \(0.122395\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.6172 | − | 14.6266i | 0.971609 | − | 0.464161i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.13391 | + | 5.42809i | 0.0993515 | + | 0.172082i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.15190 | + | 1.99514i | 0.0364810 | + | 0.0631869i | 0.883689 | − | 0.468074i | \(-0.155052\pi\) |
−0.847208 | + | 0.531261i | \(0.821719\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.9737 | − | 7.44724i | 0.790132 | − | 0.235620i |
(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 | 504.2.q.d.25.2 | ✓ | 22 | |
3.2 | odd | 2 | 1512.2.q.c.1369.2 | 22 | |||
4.3 | odd | 2 | 1008.2.q.k.529.10 | 22 | |||
7.2 | even | 3 | 504.2.t.d.457.5 | yes | 22 | ||
9.4 | even | 3 | 504.2.t.d.193.5 | yes | 22 | ||
9.5 | odd | 6 | 1512.2.t.d.361.10 | 22 | |||
12.11 | even | 2 | 3024.2.q.k.2881.2 | 22 | |||
21.2 | odd | 6 | 1512.2.t.d.289.10 | 22 | |||
28.23 | odd | 6 | 1008.2.t.k.961.7 | 22 | |||
36.23 | even | 6 | 3024.2.t.l.1873.10 | 22 | |||
36.31 | odd | 6 | 1008.2.t.k.193.7 | 22 | |||
63.23 | odd | 6 | 1512.2.q.c.793.2 | 22 | |||
63.58 | even | 3 | inner | 504.2.q.d.121.2 | yes | 22 | |
84.23 | even | 6 | 3024.2.t.l.289.10 | 22 | |||
252.23 | even | 6 | 3024.2.q.k.2305.2 | 22 | |||
252.247 | odd | 6 | 1008.2.q.k.625.10 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.2 | ✓ | 22 | 1.1 | even | 1 | trivial | |
504.2.q.d.121.2 | yes | 22 | 63.58 | even | 3 | inner | |
504.2.t.d.193.5 | yes | 22 | 9.4 | even | 3 | ||
504.2.t.d.457.5 | yes | 22 | 7.2 | even | 3 | ||
1008.2.q.k.529.10 | 22 | 4.3 | odd | 2 | |||
1008.2.q.k.625.10 | 22 | 252.247 | odd | 6 | |||
1008.2.t.k.193.7 | 22 | 36.31 | odd | 6 | |||
1008.2.t.k.961.7 | 22 | 28.23 | odd | 6 | |||
1512.2.q.c.793.2 | 22 | 63.23 | odd | 6 | |||
1512.2.q.c.1369.2 | 22 | 3.2 | odd | 2 | |||
1512.2.t.d.289.10 | 22 | 21.2 | odd | 6 | |||
1512.2.t.d.361.10 | 22 | 9.5 | odd | 6 | |||
3024.2.q.k.2305.2 | 22 | 252.23 | even | 6 | |||
3024.2.q.k.2881.2 | 22 | 12.11 | even | 2 | |||
3024.2.t.l.289.10 | 22 | 84.23 | even | 6 | |||
3024.2.t.l.1873.10 | 22 | 36.23 | even | 6 |