Properties

Label 460.2.m.b.41.4
Level $460$
Weight $2$
Character 460.41
Analytic conductor $3.673$
Analytic rank $0$
Dimension $50$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(41,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.m (of order \(11\), degree \(10\), 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: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(50\)
Relative dimension: \(5\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 41.4
Character \(\chi\) \(=\) 460.41
Dual form 460.2.m.b.101.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.10811 - 1.27883i) q^{3} +(0.142315 - 0.989821i) q^{5} +(-1.08165 - 2.36848i) q^{7} +(0.0194536 + 0.135303i) q^{9} +O(q^{10})\) \(q+(1.10811 - 1.27883i) q^{3} +(0.142315 - 0.989821i) q^{5} +(-1.08165 - 2.36848i) q^{7} +(0.0194536 + 0.135303i) q^{9} +(2.24629 - 0.659569i) q^{11} +(-0.0828187 + 0.181348i) q^{13} +(-1.10811 - 1.27883i) q^{15} +(4.73736 - 3.04452i) q^{17} +(-6.46583 - 4.15533i) q^{19} +(-4.22747 - 1.24130i) q^{21} +(-3.17241 - 3.59664i) q^{23} +(-0.959493 - 0.281733i) q^{25} +(4.46512 + 2.86956i) q^{27} +(-2.94239 + 1.89096i) q^{29} +(5.81264 + 6.70814i) q^{31} +(1.64566 - 3.60349i) q^{33} +(-2.49831 + 0.733570i) q^{35} +(0.334267 + 2.32488i) q^{37} +(0.140140 + 0.306864i) q^{39} +(-0.441676 + 3.07192i) q^{41} +(4.84355 - 5.58976i) q^{43} +0.136694 q^{45} -7.38769 q^{47} +(0.144279 - 0.166507i) q^{49} +(1.35611 - 9.43193i) q^{51} +(2.03449 + 4.45492i) q^{53} +(-0.333176 - 2.31729i) q^{55} +(-12.4788 + 3.66411i) q^{57} +(0.971960 - 2.12830i) q^{59} +(8.18748 + 9.44886i) q^{61} +(0.299420 - 0.192426i) q^{63} +(0.167716 + 0.107784i) q^{65} +(15.5896 + 4.57753i) q^{67} +(-8.11486 + 0.0714895i) q^{69} +(-4.37919 - 1.28585i) q^{71} +(0.560221 + 0.360032i) q^{73} +(-1.42351 + 0.914835i) q^{75} +(-3.99187 - 4.60687i) q^{77} +(2.95253 - 6.46514i) q^{79} +(8.22404 - 2.41480i) q^{81} +(1.68937 + 11.7498i) q^{83} +(-2.33933 - 5.12243i) q^{85} +(-0.842281 + 5.85819i) q^{87} +(-6.64231 + 7.66564i) q^{89} +0.519100 q^{91} +15.0196 q^{93} +(-5.03322 + 5.80865i) q^{95} +(-0.0541899 + 0.376899i) q^{97} +(0.132940 + 0.291097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{6}{11}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.10811 1.27883i 0.639768 0.738331i −0.339566 0.940582i \(-0.610280\pi\)
0.979334 + 0.202251i \(0.0648257\pi\)
\(4\) 0 0
\(5\) 0.142315 0.989821i 0.0636451 0.442662i
\(6\) 0 0
\(7\) −1.08165 2.36848i −0.408825 0.895202i −0.996299 0.0859590i \(-0.972605\pi\)
0.587473 0.809243i \(-0.300123\pi\)
\(8\) 0 0
\(9\) 0.0194536 + 0.135303i 0.00648452 + 0.0451009i
\(10\) 0 0
\(11\) 2.24629 0.659569i 0.677281 0.198868i 0.0750382 0.997181i \(-0.476092\pi\)
0.602243 + 0.798313i \(0.294274\pi\)
\(12\) 0 0
\(13\) −0.0828187 + 0.181348i −0.0229698 + 0.0502968i −0.920769 0.390108i \(-0.872438\pi\)
0.897799 + 0.440405i \(0.145165\pi\)
\(14\) 0 0
\(15\) −1.10811 1.27883i −0.286113 0.330192i
\(16\) 0 0
\(17\) 4.73736 3.04452i 1.14898 0.738404i 0.179544 0.983750i \(-0.442538\pi\)
0.969436 + 0.245345i \(0.0789014\pi\)
\(18\) 0 0
\(19\) −6.46583 4.15533i −1.48336 0.953299i −0.996824 0.0796402i \(-0.974623\pi\)
−0.486539 0.873659i \(-0.661741\pi\)
\(20\) 0 0
\(21\) −4.22747 1.24130i −0.922509 0.270873i
\(22\) 0 0
\(23\) −3.17241 3.59664i −0.661493 0.749951i
\(24\) 0 0
\(25\) −0.959493 0.281733i −0.191899 0.0563465i
\(26\) 0 0
\(27\) 4.46512 + 2.86956i 0.859312 + 0.552247i
\(28\) 0 0
\(29\) −2.94239 + 1.89096i −0.546388 + 0.351142i −0.784533 0.620088i \(-0.787097\pi\)
0.238145 + 0.971230i \(0.423461\pi\)
\(30\) 0 0
\(31\) 5.81264 + 6.70814i 1.04398 + 1.20482i 0.978346 + 0.206974i \(0.0663616\pi\)
0.0656341 + 0.997844i \(0.479093\pi\)
\(32\) 0 0
\(33\) 1.64566 3.60349i 0.286472 0.627287i
\(34\) 0 0
\(35\) −2.49831 + 0.733570i −0.422292 + 0.123996i
\(36\) 0 0
\(37\) 0.334267 + 2.32488i 0.0549531 + 0.382208i 0.998675 + 0.0514666i \(0.0163896\pi\)
−0.943722 + 0.330741i \(0.892701\pi\)
\(38\) 0 0
\(39\) 0.140140 + 0.306864i 0.0224404 + 0.0491376i
\(40\) 0 0
\(41\) −0.441676 + 3.07192i −0.0689782 + 0.479754i 0.925826 + 0.377949i \(0.123371\pi\)
−0.994804 + 0.101804i \(0.967538\pi\)
\(42\) 0 0
\(43\) 4.84355 5.58976i 0.738635 0.852430i −0.254780 0.966999i \(-0.582003\pi\)
0.993415 + 0.114569i \(0.0365486\pi\)
\(44\) 0 0
\(45\) 0.136694 0.0203771
\(46\) 0 0
\(47\) −7.38769 −1.07761 −0.538803 0.842432i \(-0.681123\pi\)
−0.538803 + 0.842432i \(0.681123\pi\)
\(48\) 0 0
\(49\) 0.144279 0.166507i 0.0206113 0.0237868i
\(50\) 0 0
\(51\) 1.35611 9.43193i 0.189893 1.32073i
\(52\) 0 0
\(53\) 2.03449 + 4.45492i 0.279459 + 0.611930i 0.996360 0.0852449i \(-0.0271673\pi\)
−0.716901 + 0.697175i \(0.754440\pi\)
\(54\) 0 0
\(55\) −0.333176 2.31729i −0.0449254 0.312463i
\(56\) 0 0
\(57\) −12.4788 + 3.66411i −1.65286 + 0.485323i
\(58\) 0 0
\(59\) 0.971960 2.12830i 0.126538 0.277081i −0.835751 0.549109i \(-0.814967\pi\)
0.962289 + 0.272028i \(0.0876945\pi\)
\(60\) 0 0
\(61\) 8.18748 + 9.44886i 1.04830 + 1.20980i 0.977197 + 0.212333i \(0.0681063\pi\)
0.0711024 + 0.997469i \(0.477348\pi\)
\(62\) 0 0
\(63\) 0.299420 0.192426i 0.0377234 0.0242433i
\(64\) 0 0
\(65\) 0.167716 + 0.107784i 0.0208026 + 0.0133690i
\(66\) 0 0
\(67\) 15.5896 + 4.57753i 1.90458 + 0.559235i 0.986748 + 0.162261i \(0.0518787\pi\)
0.917830 + 0.396974i \(0.129940\pi\)
\(68\) 0 0
\(69\) −8.11486 + 0.0714895i −0.976914 + 0.00860633i
\(70\) 0 0
\(71\) −4.37919 1.28585i −0.519714 0.152602i 0.0113465 0.999936i \(-0.496388\pi\)
−0.531061 + 0.847334i \(0.678206\pi\)
\(72\) 0 0
\(73\) 0.560221 + 0.360032i 0.0655690 + 0.0421386i 0.573015 0.819545i \(-0.305774\pi\)
−0.507446 + 0.861684i \(0.669410\pi\)
\(74\) 0 0
\(75\) −1.42351 + 0.914835i −0.164373 + 0.105636i
\(76\) 0 0
\(77\) −3.99187 4.60687i −0.454916 0.525001i
\(78\) 0 0
\(79\) 2.95253 6.46514i 0.332186 0.727385i −0.667668 0.744459i \(-0.732708\pi\)
0.999854 + 0.0170734i \(0.00543489\pi\)
\(80\) 0 0
\(81\) 8.22404 2.41480i 0.913782 0.268311i
\(82\) 0 0
\(83\) 1.68937 + 11.7498i 0.185433 + 1.28971i 0.843653 + 0.536888i \(0.180400\pi\)
−0.658221 + 0.752825i \(0.728691\pi\)
\(84\) 0 0
\(85\) −2.33933 5.12243i −0.253736 0.555605i
\(86\) 0 0
\(87\) −0.842281 + 5.85819i −0.0903020 + 0.628064i
\(88\) 0 0
\(89\) −6.64231 + 7.66564i −0.704084 + 0.812556i −0.989298 0.145908i \(-0.953390\pi\)
0.285215 + 0.958464i \(0.407935\pi\)
\(90\) 0 0
\(91\) 0.519100 0.0544165
\(92\) 0 0
\(93\) 15.0196 1.55746
\(94\) 0 0
\(95\) −5.03322 + 5.80865i −0.516398 + 0.595955i
\(96\) 0 0
\(97\) −0.0541899 + 0.376899i −0.00550215 + 0.0382683i −0.992388 0.123154i \(-0.960699\pi\)
0.986885 + 0.161422i \(0.0516082\pi\)
\(98\) 0 0
\(99\) 0.132940 + 0.291097i 0.0133609 + 0.0292564i
\(100\) 0 0
\(101\) 1.32330 + 9.20375i 0.131673 + 0.915807i 0.943373 + 0.331733i \(0.107633\pi\)
−0.811700 + 0.584074i \(0.801458\pi\)
\(102\) 0 0
\(103\) 6.81119 1.99995i 0.671127 0.197061i 0.0716221 0.997432i \(-0.477182\pi\)
0.599505 + 0.800371i \(0.295364\pi\)
\(104\) 0 0
\(105\) −1.83029 + 4.00778i −0.178618 + 0.391120i
\(106\) 0 0
\(107\) 4.50448 + 5.19844i 0.435464 + 0.502552i 0.930486 0.366328i \(-0.119385\pi\)
−0.495022 + 0.868881i \(0.664840\pi\)
\(108\) 0 0
\(109\) −15.7820 + 10.1425i −1.51164 + 0.971471i −0.518431 + 0.855120i \(0.673484\pi\)
−0.993208 + 0.116352i \(0.962880\pi\)
\(110\) 0 0
\(111\) 3.34352 + 2.14875i 0.317353 + 0.203950i
\(112\) 0 0
\(113\) 9.69936 + 2.84799i 0.912439 + 0.267916i 0.704067 0.710133i \(-0.251365\pi\)
0.208372 + 0.978050i \(0.433184\pi\)
\(114\) 0 0
\(115\) −4.01151 + 2.62826i −0.374075 + 0.245087i
\(116\) 0 0
\(117\) −0.0261479 0.00767773i −0.00241738 0.000709806i
\(118\) 0 0
\(119\) −12.3351 7.92726i −1.13075 0.726691i
\(120\) 0 0
\(121\) −4.64302 + 2.98389i −0.422092 + 0.271262i
\(122\) 0 0
\(123\) 3.43903 + 3.96886i 0.310087 + 0.357860i
\(124\) 0 0
\(125\) −0.415415 + 0.909632i −0.0371558 + 0.0813600i
\(126\) 0 0
\(127\) 9.01293 2.64644i 0.799769 0.234833i 0.143786 0.989609i \(-0.454072\pi\)
0.655983 + 0.754776i \(0.272254\pi\)
\(128\) 0 0
\(129\) −1.78114 12.3881i −0.156821 1.09071i
\(130\) 0 0
\(131\) −6.67779 14.6223i −0.583441 1.27756i −0.939325 0.343028i \(-0.888547\pi\)
0.355884 0.934530i \(-0.384180\pi\)
\(132\) 0 0
\(133\) −2.84808 + 19.8088i −0.246960 + 1.71764i
\(134\) 0 0
\(135\) 3.47580 4.01129i 0.299149 0.345237i
\(136\) 0 0
\(137\) 4.91048 0.419531 0.209765 0.977752i \(-0.432730\pi\)
0.209765 + 0.977752i \(0.432730\pi\)
\(138\) 0 0
\(139\) −0.895703 −0.0759725 −0.0379863 0.999278i \(-0.512094\pi\)
−0.0379863 + 0.999278i \(0.512094\pi\)
\(140\) 0 0
\(141\) −8.18638 + 9.44758i −0.689417 + 0.795630i
\(142\) 0 0
\(143\) −0.0664232 + 0.461984i −0.00555459 + 0.0386330i
\(144\) 0 0
\(145\) 1.45296 + 3.18155i 0.120662 + 0.264213i
\(146\) 0 0
\(147\) −0.0530566 0.369017i −0.00437604 0.0304360i
\(148\) 0 0
\(149\) −14.7346 + 4.32648i −1.20711 + 0.354439i −0.822567 0.568668i \(-0.807459\pi\)
−0.384542 + 0.923108i \(0.625641\pi\)
\(150\) 0 0
\(151\) 4.04645 8.86048i 0.329295 0.721056i −0.670487 0.741921i \(-0.733915\pi\)
0.999782 + 0.0208654i \(0.00664214\pi\)
\(152\) 0 0
\(153\) 0.504090 + 0.581751i 0.0407533 + 0.0470318i
\(154\) 0 0
\(155\) 7.46709 4.79881i 0.599771 0.385449i
\(156\) 0 0
\(157\) −13.9041 8.93559i −1.10966 0.713138i −0.148444 0.988921i \(-0.547427\pi\)
−0.961220 + 0.275783i \(0.911063\pi\)
\(158\) 0 0
\(159\) 7.95151 + 2.33478i 0.630596 + 0.185160i
\(160\) 0 0
\(161\) −5.08715 + 11.4041i −0.400923 + 0.898769i
\(162\) 0 0
\(163\) 0.948713 + 0.278567i 0.0743090 + 0.0218191i 0.318676 0.947864i \(-0.396762\pi\)
−0.244367 + 0.969683i \(0.578580\pi\)
\(164\) 0 0
\(165\) −3.33261 2.14174i −0.259443 0.166734i
\(166\) 0 0
\(167\) −12.1537 + 7.81069i −0.940480 + 0.604410i −0.918531 0.395349i \(-0.870624\pi\)
−0.0219490 + 0.999759i \(0.506987\pi\)
\(168\) 0 0
\(169\) 8.48716 + 9.79471i 0.652859 + 0.753439i
\(170\) 0 0
\(171\) 0.436444 0.955679i 0.0333757 0.0730826i
\(172\) 0 0
\(173\) −16.2191 + 4.76235i −1.23311 + 0.362075i −0.832424 0.554139i \(-0.813048\pi\)
−0.400690 + 0.916214i \(0.631229\pi\)
\(174\) 0 0
\(175\) 0.370557 + 2.57728i 0.0280115 + 0.194824i
\(176\) 0 0
\(177\) −1.64468 3.60135i −0.123622 0.270694i
\(178\) 0 0
\(179\) −2.45633 + 17.0841i −0.183594 + 1.27693i 0.664583 + 0.747215i \(0.268609\pi\)
−0.848177 + 0.529713i \(0.822300\pi\)
\(180\) 0 0
\(181\) 7.02669 8.10924i 0.522290 0.602755i −0.431913 0.901915i \(-0.642161\pi\)
0.954203 + 0.299161i \(0.0967066\pi\)
\(182\) 0 0
\(183\) 21.1561 1.56390
\(184\) 0 0
\(185\) 2.34878 0.172686
\(186\) 0 0
\(187\) 8.63341 9.96348i 0.631337 0.728602i
\(188\) 0 0
\(189\) 1.96680 13.6794i 0.143064 0.995031i
\(190\) 0 0
\(191\) −8.26311 18.0937i −0.597898 1.30921i −0.930550 0.366164i \(-0.880671\pi\)
0.332653 0.943049i \(-0.392056\pi\)
\(192\) 0 0
\(193\) −1.31286 9.13113i −0.0945016 0.657273i −0.980923 0.194395i \(-0.937726\pi\)
0.886422 0.462878i \(-0.153183\pi\)
\(194\) 0 0
\(195\) 0.323685 0.0950424i 0.0231795 0.00680613i
\(196\) 0 0
\(197\) 5.93449 12.9947i 0.422815 0.925835i −0.571624 0.820516i \(-0.693686\pi\)
0.994438 0.105319i \(-0.0335864\pi\)
\(198\) 0 0
\(199\) −3.30993 3.81986i −0.234635 0.270783i 0.626206 0.779658i \(-0.284607\pi\)
−0.860840 + 0.508875i \(0.830062\pi\)
\(200\) 0 0
\(201\) 23.1289 14.8640i 1.63139 1.04843i
\(202\) 0 0
\(203\) 7.66133 + 4.92364i 0.537720 + 0.345572i
\(204\) 0 0
\(205\) 2.97780 + 0.874361i 0.207979 + 0.0610680i
\(206\) 0 0
\(207\) 0.424920 0.499203i 0.0295340 0.0346970i
\(208\) 0 0
\(209\) −17.2648 5.06941i −1.19423 0.350659i
\(210\) 0 0
\(211\) −1.19683 0.769153i −0.0823929 0.0529507i 0.498796 0.866720i \(-0.333776\pi\)
−0.581189 + 0.813769i \(0.697412\pi\)
\(212\) 0 0
\(213\) −6.49700 + 4.17537i −0.445167 + 0.286091i
\(214\) 0 0
\(215\) −4.84355 5.58976i −0.330328 0.381218i
\(216\) 0 0
\(217\) 9.60088 21.0230i 0.651750 1.42713i
\(218\) 0 0
\(219\) 1.08121 0.317471i 0.0730611 0.0214527i
\(220\) 0 0
\(221\) 0.159774 + 1.11125i 0.0107476 + 0.0747510i
\(222\) 0 0
\(223\) 2.12299 + 4.64871i 0.142166 + 0.311300i 0.967299 0.253638i \(-0.0816272\pi\)
−0.825133 + 0.564938i \(0.808900\pi\)
\(224\) 0 0
\(225\) 0.0194536 0.135303i 0.00129690 0.00902017i
\(226\) 0 0
\(227\) −7.80344 + 9.00565i −0.517933 + 0.597726i −0.953112 0.302618i \(-0.902139\pi\)
0.435180 + 0.900344i \(0.356685\pi\)
\(228\) 0 0
\(229\) 15.4444 1.02060 0.510298 0.859998i \(-0.329535\pi\)
0.510298 + 0.859998i \(0.329535\pi\)
\(230\) 0 0
\(231\) −10.3148 −0.678666
\(232\) 0 0
\(233\) 10.8904 12.5682i 0.713456 0.823372i −0.277048 0.960856i \(-0.589356\pi\)
0.990504 + 0.137484i \(0.0439015\pi\)
\(234\) 0 0
\(235\) −1.05138 + 7.31250i −0.0685844 + 0.477015i
\(236\) 0 0
\(237\) −4.99607 10.9399i −0.324530 0.710621i
\(238\) 0 0
\(239\) −2.76071 19.2012i −0.178576 1.24202i −0.860062 0.510190i \(-0.829575\pi\)
0.681486 0.731831i \(-0.261334\pi\)
\(240\) 0 0
\(241\) 9.16055 2.68978i 0.590083 0.173264i 0.0269590 0.999637i \(-0.491418\pi\)
0.563124 + 0.826373i \(0.309599\pi\)
\(242\) 0 0
\(243\) −0.589657 + 1.29117i −0.0378265 + 0.0828286i
\(244\) 0 0
\(245\) −0.144279 0.166507i −0.00921767 0.0106378i
\(246\) 0 0
\(247\) 1.28905 0.828424i 0.0820204 0.0527113i
\(248\) 0 0
\(249\) 16.8980 + 10.8597i 1.07087 + 0.688206i
\(250\) 0 0
\(251\) −10.6191 3.11805i −0.670272 0.196810i −0.0711479 0.997466i \(-0.522666\pi\)
−0.599124 + 0.800656i \(0.704484\pi\)
\(252\) 0 0
\(253\) −9.49837 5.98666i −0.597158 0.376378i
\(254\) 0 0
\(255\) −9.14293 2.68461i −0.572553 0.168117i
\(256\) 0 0
\(257\) −3.45113 2.21790i −0.215275 0.138349i 0.428559 0.903514i \(-0.359021\pi\)
−0.643835 + 0.765164i \(0.722658\pi\)
\(258\) 0 0
\(259\) 5.14487 3.30641i 0.319687 0.205450i
\(260\) 0 0
\(261\) −0.313091 0.361327i −0.0193799 0.0223656i
\(262\) 0 0
\(263\) 8.24902 18.0628i 0.508657 1.11380i −0.464901 0.885363i \(-0.653910\pi\)
0.973558 0.228440i \(-0.0733625\pi\)
\(264\) 0 0
\(265\) 4.69911 1.37978i 0.288664 0.0847595i
\(266\) 0 0
\(267\) 2.44261 + 16.9887i 0.149485 + 1.03969i
\(268\) 0 0
\(269\) −7.43692 16.2846i −0.453437 0.992889i −0.988935 0.148352i \(-0.952603\pi\)
0.535497 0.844537i \(-0.320124\pi\)
\(270\) 0 0
\(271\) −2.91222 + 20.2550i −0.176905 + 1.23040i 0.686967 + 0.726689i \(0.258942\pi\)
−0.863872 + 0.503712i \(0.831967\pi\)
\(272\) 0 0
\(273\) 0.575220 0.663839i 0.0348139 0.0401774i
\(274\) 0 0
\(275\) −2.34112 −0.141175
\(276\) 0 0
\(277\) −5.07429 −0.304885 −0.152442 0.988312i \(-0.548714\pi\)
−0.152442 + 0.988312i \(0.548714\pi\)
\(278\) 0 0
\(279\) −0.794552 + 0.916962i −0.0475686 + 0.0548971i
\(280\) 0 0
\(281\) 2.43267 16.9196i 0.145121 1.00934i −0.778942 0.627097i \(-0.784243\pi\)
0.924062 0.382242i \(-0.124848\pi\)
\(282\) 0 0
\(283\) −10.6238 23.2628i −0.631518 1.38283i −0.906838 0.421479i \(-0.861511\pi\)
0.275320 0.961353i \(-0.411216\pi\)
\(284\) 0 0
\(285\) 1.85089 + 12.8732i 0.109637 + 0.762545i
\(286\) 0 0
\(287\) 7.75354 2.27664i 0.457677 0.134386i
\(288\) 0 0
\(289\) 6.11147 13.3823i 0.359498 0.787192i
\(290\) 0 0
\(291\) 0.421940 + 0.486945i 0.0247346 + 0.0285452i
\(292\) 0 0
\(293\) −2.51292 + 1.61496i −0.146807 + 0.0943468i −0.611982 0.790872i \(-0.709628\pi\)
0.465176 + 0.885218i \(0.345991\pi\)
\(294\) 0 0
\(295\) −1.96831 1.26496i −0.114599 0.0736485i
\(296\) 0 0
\(297\) 11.9226 + 3.50079i 0.691820 + 0.203137i
\(298\) 0 0
\(299\) 0.914978 0.277440i 0.0529145 0.0160448i
\(300\) 0 0
\(301\) −18.4783 5.42571i −1.06507 0.312733i
\(302\) 0 0
\(303\) 13.2364 + 8.50649i 0.760409 + 0.488685i
\(304\) 0 0
\(305\) 10.5179 6.75943i 0.602252 0.387044i
\(306\) 0 0
\(307\) 10.0835 + 11.6370i 0.575497 + 0.664159i 0.966631 0.256175i \(-0.0824622\pi\)
−0.391133 + 0.920334i \(0.627917\pi\)
\(308\) 0 0
\(309\) 4.98997 10.9265i 0.283869 0.621587i
\(310\) 0 0
\(311\) −18.5008 + 5.43232i −1.04908 + 0.308039i −0.760447 0.649400i \(-0.775020\pi\)
−0.288637 + 0.957439i \(0.593202\pi\)
\(312\) 0 0
\(313\) 1.57363 + 10.9448i 0.0889468 + 0.618639i 0.984722 + 0.174132i \(0.0557120\pi\)
−0.895775 + 0.444507i \(0.853379\pi\)
\(314\) 0 0
\(315\) −0.147855 0.323757i −0.00833069 0.0182417i
\(316\) 0 0
\(317\) −2.03471 + 14.1517i −0.114281 + 0.794839i 0.849394 + 0.527760i \(0.176968\pi\)
−0.963674 + 0.267080i \(0.913941\pi\)
\(318\) 0 0
\(319\) −5.36223 + 6.18834i −0.300227 + 0.346481i
\(320\) 0 0
\(321\) 11.6394 0.649646
\(322\) 0 0
\(323\) −43.2820 −2.40827
\(324\) 0 0
\(325\) 0.130556 0.150669i 0.00724192 0.00835762i
\(326\) 0 0
\(327\) −4.51771 + 31.4214i −0.249830 + 1.73761i
\(328\) 0 0
\(329\) 7.99090 + 17.4976i 0.440552 + 0.964675i
\(330\) 0 0
\(331\) 2.05848 + 14.3170i 0.113144 + 0.786935i 0.964829 + 0.262880i \(0.0846722\pi\)
−0.851684 + 0.524055i \(0.824419\pi\)
\(332\) 0 0
\(333\) −0.308059 + 0.0904544i −0.0168815 + 0.00495687i
\(334\) 0 0
\(335\) 6.74958 14.7795i 0.368769 0.807491i
\(336\) 0 0
\(337\) −12.6829 14.6369i −0.690883 0.797321i 0.296608 0.954999i \(-0.404145\pi\)
−0.987491 + 0.157678i \(0.949599\pi\)
\(338\) 0 0
\(339\) 14.3900 9.24792i 0.781560 0.502278i
\(340\) 0 0
\(341\) 17.4813 + 11.2346i 0.946667 + 0.608386i
\(342\) 0 0
\(343\) −18.0386 5.29661i −0.973993 0.285990i
\(344\) 0 0
\(345\) −1.08410 + 8.04243i −0.0583661 + 0.432990i
\(346\) 0 0
\(347\) −5.29642 1.55517i −0.284327 0.0834858i 0.136460 0.990646i \(-0.456428\pi\)
−0.420786 + 0.907160i \(0.638246\pi\)
\(348\) 0 0
\(349\) 6.19680 + 3.98244i 0.331707 + 0.213175i 0.695883 0.718155i \(-0.255013\pi\)
−0.364176 + 0.931330i \(0.618649\pi\)
\(350\) 0 0
\(351\) −0.890183 + 0.572086i −0.0475145 + 0.0305357i
\(352\) 0 0
\(353\) 2.24659 + 2.59271i 0.119574 + 0.137996i 0.812380 0.583128i \(-0.198171\pi\)
−0.692806 + 0.721124i \(0.743626\pi\)
\(354\) 0 0
\(355\) −1.89598 + 4.15162i −0.100628 + 0.220345i
\(356\) 0 0
\(357\) −23.8062 + 6.99013i −1.25996 + 0.369957i
\(358\) 0 0
\(359\) 2.24244 + 15.5965i 0.118351 + 0.823152i 0.959371 + 0.282147i \(0.0910467\pi\)
−0.841020 + 0.541004i \(0.818044\pi\)
\(360\) 0 0
\(361\) 16.6472 + 36.4523i 0.876170 + 1.91854i
\(362\) 0 0
\(363\) −1.32910 + 9.24409i −0.0697596 + 0.485189i
\(364\) 0 0
\(365\) 0.436096 0.503281i 0.0228263 0.0263429i
\(366\) 0 0
\(367\) −13.2711 −0.692748 −0.346374 0.938097i \(-0.612587\pi\)
−0.346374 + 0.938097i \(0.612587\pi\)
\(368\) 0 0
\(369\) −0.424231 −0.0220846
\(370\) 0 0
\(371\) 8.35079 9.63733i 0.433552 0.500345i
\(372\) 0 0
\(373\) 3.45507 24.0305i 0.178897 1.24425i −0.680425 0.732818i \(-0.738205\pi\)
0.859322 0.511435i \(-0.170886\pi\)
\(374\) 0 0
\(375\) 0.702936 + 1.53922i 0.0362995 + 0.0794848i
\(376\) 0 0
\(377\) −0.0992361 0.690202i −0.00511092 0.0355472i
\(378\) 0 0
\(379\) −30.1545 + 8.85417i −1.54893 + 0.454808i −0.940782 0.339012i \(-0.889907\pi\)
−0.608152 + 0.793820i \(0.708089\pi\)
\(380\) 0 0
\(381\) 6.60299 14.4585i 0.338281 0.740733i
\(382\) 0 0
\(383\) −4.97646 5.74314i −0.254285 0.293461i 0.614226 0.789130i \(-0.289468\pi\)
−0.868511 + 0.495669i \(0.834923\pi\)
\(384\) 0 0
\(385\) −5.12808 + 3.29562i −0.261351 + 0.167960i
\(386\) 0 0
\(387\) 0.850533 + 0.546605i 0.0432350 + 0.0277855i
\(388\) 0 0
\(389\) 16.9810 + 4.98608i 0.860973 + 0.252804i 0.682271 0.731099i \(-0.260992\pi\)
0.178701 + 0.983903i \(0.442810\pi\)
\(390\) 0 0
\(391\) −25.9789 7.38014i −1.31381 0.373230i
\(392\) 0 0
\(393\) −26.0991 7.66340i −1.31653 0.386567i
\(394\) 0 0
\(395\) −5.97915 3.84256i −0.300844 0.193340i
\(396\) 0 0
\(397\) 9.05037 5.81632i 0.454225 0.291913i −0.293454 0.955973i \(-0.594805\pi\)
0.747679 + 0.664061i \(0.231168\pi\)
\(398\) 0 0
\(399\) 22.1761 + 25.5925i 1.11019 + 1.28123i
\(400\) 0 0
\(401\) 0.464661 1.01747i 0.0232041 0.0508098i −0.897675 0.440658i \(-0.854745\pi\)
0.920879 + 0.389848i \(0.127472\pi\)
\(402\) 0 0
\(403\) −1.69790 + 0.498549i −0.0845785 + 0.0248345i
\(404\) 0 0
\(405\) −1.21981 8.48399i −0.0606130 0.421573i
\(406\) 0 0
\(407\) 2.28428 + 5.00187i 0.113227 + 0.247933i
\(408\) 0 0
\(409\) −0.533583 + 3.71115i −0.0263840 + 0.183505i −0.998752 0.0499497i \(-0.984094\pi\)
0.972368 + 0.233454i \(0.0750030\pi\)
\(410\) 0 0
\(411\) 5.44135 6.27966i 0.268402 0.309753i
\(412\) 0 0
\(413\) −6.09215 −0.299775
\(414\) 0 0
\(415\) 11.8707 0.582708
\(416\) 0 0
\(417\) −0.992537 + 1.14545i −0.0486048 + 0.0560929i
\(418\) 0 0
\(419\) −2.51237 + 17.4739i −0.122737 + 0.853658i 0.831695 + 0.555232i \(0.187371\pi\)
−0.954433 + 0.298426i \(0.903539\pi\)
\(420\) 0 0
\(421\) 14.1461 + 30.9756i 0.689438 + 1.50966i 0.852324 + 0.523013i \(0.175192\pi\)
−0.162887 + 0.986645i \(0.552080\pi\)
\(422\) 0 0
\(423\) −0.143717 0.999574i −0.00698776 0.0486009i
\(424\) 0 0
\(425\) −5.40321 + 1.58653i −0.262094 + 0.0769578i
\(426\) 0 0
\(427\) 13.5235 29.6123i 0.654447 1.43304i
\(428\) 0 0
\(429\) 0.517193 + 0.596873i 0.0249703 + 0.0288173i
\(430\) 0 0
\(431\) −18.5009 + 11.8898i −0.891158 + 0.572713i −0.904156 0.427203i \(-0.859499\pi\)
0.0129975 + 0.999916i \(0.495863\pi\)
\(432\) 0 0
\(433\) 7.18622 + 4.61830i 0.345348 + 0.221941i 0.701803 0.712371i \(-0.252379\pi\)
−0.356456 + 0.934312i \(0.616015\pi\)
\(434\) 0 0
\(435\) 5.67870 + 1.66742i 0.272273 + 0.0799465i
\(436\) 0 0
\(437\) 5.56700 + 36.4377i 0.266306 + 1.74305i
\(438\) 0 0
\(439\) 31.7804 + 9.33157i 1.51680 + 0.445371i 0.930979 0.365072i \(-0.118956\pi\)
0.585817 + 0.810444i \(0.300774\pi\)
\(440\) 0 0
\(441\) 0.0253356 + 0.0162822i 0.00120646 + 0.000775344i
\(442\) 0 0
\(443\) −29.1613 + 18.7409i −1.38550 + 0.890405i −0.999485 0.0320889i \(-0.989784\pi\)
−0.386012 + 0.922494i \(0.626148\pi\)
\(444\) 0 0
\(445\) 6.64231 + 7.66564i 0.314876 + 0.363386i
\(446\) 0 0
\(447\) −10.7948 + 23.6373i −0.510576 + 1.11800i
\(448\) 0 0
\(449\) 38.2267 11.2244i 1.80403 0.529710i 0.805967 0.591960i \(-0.201646\pi\)
0.998061 + 0.0622499i \(0.0198276\pi\)
\(450\) 0 0
\(451\) 1.03402 + 7.19174i 0.0486899 + 0.338646i
\(452\) 0 0
\(453\) −6.84712 14.9931i −0.321706 0.704437i
\(454\) 0 0
\(455\) 0.0738756 0.513816i 0.00346334 0.0240881i
\(456\) 0 0
\(457\) 27.2211 31.4148i 1.27335 1.46952i 0.459802 0.888021i \(-0.347920\pi\)
0.813546 0.581501i \(-0.197534\pi\)
\(458\) 0 0
\(459\) 29.8893 1.39511
\(460\) 0 0
\(461\) 3.28790 0.153133 0.0765664 0.997064i \(-0.475604\pi\)
0.0765664 + 0.997064i \(0.475604\pi\)
\(462\) 0 0
\(463\) −5.64323 + 6.51264i −0.262263 + 0.302668i −0.871574 0.490263i \(-0.836901\pi\)
0.609311 + 0.792931i \(0.291446\pi\)
\(464\) 0 0
\(465\) 2.13751 14.8667i 0.0991247 0.689427i
\(466\) 0 0
\(467\) −12.8170 28.0654i −0.593102 1.29871i −0.933550 0.358448i \(-0.883306\pi\)
0.340448 0.940263i \(-0.389421\pi\)
\(468\) 0 0
\(469\) −6.02073 41.8751i −0.278011 1.93361i
\(470\) 0 0
\(471\) −26.8343 + 7.87926i −1.23646 + 0.363057i
\(472\) 0 0
\(473\) 7.19318 15.7509i 0.330743 0.724225i
\(474\) 0 0
\(475\) 5.03322 + 5.80865i 0.230940 + 0.266519i
\(476\) 0 0
\(477\) −0.563184 + 0.361936i −0.0257864 + 0.0165719i
\(478\) 0 0
\(479\) 28.7095 + 18.4505i 1.31177 + 0.843025i 0.994442 0.105290i \(-0.0335770\pi\)
0.317331 + 0.948315i \(0.397213\pi\)
\(480\) 0 0
\(481\) −0.449295 0.131925i −0.0204861 0.00601526i
\(482\) 0 0
\(483\) 8.94676 + 19.1426i 0.407092 + 0.871018i
\(484\) 0 0
\(485\) 0.365351 + 0.107277i 0.0165897 + 0.00487118i
\(486\) 0 0
\(487\) 7.40852 + 4.76117i 0.335712 + 0.215749i 0.697625 0.716463i \(-0.254240\pi\)
−0.361913 + 0.932212i \(0.617876\pi\)
\(488\) 0 0
\(489\) 1.40752 0.904557i 0.0636502 0.0409055i
\(490\) 0 0
\(491\) −14.2720 16.4707i −0.644085 0.743314i 0.336007 0.941860i \(-0.390924\pi\)
−0.980092 + 0.198546i \(0.936378\pi\)
\(492\) 0 0
\(493\) −8.18210 + 17.9163i −0.368503 + 0.806910i
\(494\) 0 0
\(495\) 0.307054 0.0901591i 0.0138010 0.00405235i
\(496\) 0 0
\(497\) 1.69125 + 11.7629i 0.0758627 + 0.527637i
\(498\) 0 0
\(499\) −4.27590 9.36292i −0.191416 0.419142i 0.789453 0.613811i \(-0.210364\pi\)
−0.980869 + 0.194669i \(0.937637\pi\)
\(500\) 0 0
\(501\) −3.47908 + 24.1976i −0.155434 + 1.08107i
\(502\) 0 0
\(503\) −1.28717 + 1.48547i −0.0573921 + 0.0662340i −0.783720 0.621115i \(-0.786680\pi\)
0.726328 + 0.687349i \(0.241226\pi\)
\(504\) 0 0
\(505\) 9.29839 0.413773
\(506\) 0 0
\(507\) 21.9304 0.973965
\(508\) 0 0
\(509\) −27.7588 + 32.0353i −1.23039 + 1.41994i −0.356158 + 0.934426i \(0.615913\pi\)
−0.874228 + 0.485515i \(0.838632\pi\)
\(510\) 0 0
\(511\) 0.246767 1.71630i 0.0109163 0.0759248i
\(512\) 0 0
\(513\) −16.9467 37.1081i −0.748216 1.63836i
\(514\) 0 0
\(515\) −1.01026 7.02649i −0.0445172 0.309624i
\(516\) 0 0
\(517\) −16.5949 + 4.87270i −0.729842 + 0.214301i
\(518\) 0 0
\(519\) −11.8823 + 26.0186i −0.521575 + 1.14209i
\(520\) 0 0
\(521\) −7.16119 8.26445i −0.313737 0.362072i 0.576877 0.816831i \(-0.304271\pi\)
−0.890615 + 0.454758i \(0.849726\pi\)
\(522\) 0 0
\(523\) 0.319343 0.205229i 0.0139639 0.00897404i −0.533640 0.845712i \(-0.679176\pi\)
0.547604 + 0.836738i \(0.315540\pi\)
\(524\) 0 0
\(525\) 3.70651 + 2.38203i 0.161765 + 0.103960i
\(526\) 0 0
\(527\) 47.9597 + 14.0822i 2.08916 + 0.613431i
\(528\) 0 0
\(529\) −2.87164 + 22.8200i −0.124854 + 0.992175i
\(530\) 0 0
\(531\) 0.306872 + 0.0901058i 0.0133171 + 0.00391026i
\(532\) 0 0
\(533\) −0.520507 0.334510i −0.0225457 0.0144892i
\(534\) 0 0
\(535\) 5.78658 3.71881i 0.250176 0.160778i
\(536\) 0 0
\(537\) 19.1258 + 22.0723i 0.825337 + 0.952490i
\(538\) 0 0
\(539\) 0.214270 0.469185i 0.00922925 0.0202092i
\(540\) 0 0
\(541\) −39.2338 + 11.5201i −1.68679 + 0.495287i −0.977731 0.209861i \(-0.932699\pi\)
−0.709060 + 0.705148i \(0.750881\pi\)
\(542\) 0 0
\(543\) −2.58396 17.9719i −0.110888 0.771246i
\(544\) 0 0
\(545\) 7.79321 + 17.0648i 0.333825 + 0.730974i
\(546\) 0 0
\(547\) 1.00520 6.99134i 0.0429794 0.298928i −0.956982 0.290147i \(-0.906296\pi\)
0.999961 0.00878105i \(-0.00279513\pi\)
\(548\) 0 0
\(549\) −1.11918 + 1.29160i −0.0477654 + 0.0551242i
\(550\) 0 0
\(551\) 26.8825 1.14523
\(552\) 0 0
\(553\) −18.5062 −0.786963
\(554\) 0 0
\(555\) 2.60271 3.00369i 0.110479 0.127500i
\(556\) 0 0
\(557\) 2.53877 17.6575i 0.107571 0.748173i −0.862624 0.505846i \(-0.831180\pi\)
0.970195 0.242327i \(-0.0779106\pi\)
\(558\) 0 0
\(559\) 0.612553 + 1.34130i 0.0259082 + 0.0567311i
\(560\) 0 0
\(561\) −3.17481 22.0813i −0.134040 0.932272i
\(562\) 0 0
\(563\) −28.5341 + 8.37836i −1.20257 + 0.353106i −0.820834 0.571166i \(-0.806491\pi\)
−0.381734 + 0.924272i \(0.624673\pi\)
\(564\) 0 0
\(565\) 4.19936 9.19532i 0.176669 0.386850i
\(566\) 0 0
\(567\) −14.6149 16.8665i −0.613769 0.708328i
\(568\) 0 0
\(569\) −7.07603 + 4.54749i −0.296643 + 0.190641i −0.680493 0.732755i \(-0.738234\pi\)
0.383850 + 0.923395i \(0.374598\pi\)
\(570\) 0 0
\(571\) 15.9857 + 10.2734i 0.668979 + 0.429927i 0.830557 0.556933i \(-0.188022\pi\)
−0.161578 + 0.986860i \(0.551658\pi\)
\(572\) 0 0
\(573\) −32.2951 9.48270i −1.34915 0.396146i
\(574\) 0 0
\(575\) 2.03061 + 4.34472i 0.0846824 + 0.181187i
\(576\) 0 0
\(577\) −45.9117 13.4809i −1.91133 0.561216i −0.980809 0.194970i \(-0.937539\pi\)
−0.930518 0.366246i \(-0.880643\pi\)
\(578\) 0 0
\(579\) −13.1319 8.43938i −0.545744 0.350729i
\(580\) 0 0
\(581\) 26.0020 16.7105i 1.07875 0.693267i
\(582\) 0 0
\(583\) 7.50838 + 8.66514i 0.310965 + 0.358873i
\(584\) 0 0
\(585\) −0.0113208 + 0.0247891i −0.000468058 + 0.00102490i
\(586\) 0 0
\(587\) −40.1871 + 11.8000i −1.65870 + 0.487038i −0.971025 0.238980i \(-0.923187\pi\)
−0.687676 + 0.726018i \(0.741369\pi\)
\(588\) 0 0
\(589\) −9.70894 67.5271i −0.400050 2.78241i
\(590\) 0 0
\(591\) −10.0419 21.9888i −0.413070 0.904496i
\(592\) 0 0
\(593\) −0.710815 + 4.94382i −0.0291897 + 0.203019i −0.999197 0.0400552i \(-0.987247\pi\)
0.970008 + 0.243074i \(0.0781557\pi\)
\(594\) 0 0
\(595\) −9.60204 + 11.0813i −0.393645 + 0.454291i
\(596\) 0 0
\(597\) −8.55271 −0.350039
\(598\) 0 0
\(599\) 21.4500 0.876422 0.438211 0.898872i \(-0.355612\pi\)
0.438211 + 0.898872i \(0.355612\pi\)
\(600\) 0 0
\(601\) −14.2482 + 16.4433i −0.581196 + 0.670736i −0.967861 0.251484i \(-0.919081\pi\)
0.386666 + 0.922220i \(0.373627\pi\)
\(602\) 0 0
\(603\) −0.316078 + 2.19837i −0.0128717 + 0.0895245i
\(604\) 0 0
\(605\) 2.29274 + 5.02041i 0.0932133 + 0.204109i
\(606\) 0 0
\(607\) −0.801196 5.57244i −0.0325195 0.226178i 0.967080 0.254472i \(-0.0819017\pi\)
−0.999600 + 0.0282938i \(0.990993\pi\)
\(608\) 0 0
\(609\) 14.7861 4.34159i 0.599162 0.175930i
\(610\) 0 0
\(611\) 0.611839 1.33974i 0.0247524 0.0542001i
\(612\) 0 0
\(613\) 27.7501 + 32.0253i 1.12082 + 1.29349i 0.951404 + 0.307946i \(0.0996417\pi\)
0.169413 + 0.985545i \(0.445813\pi\)
\(614\) 0 0
\(615\) 4.41788 2.83920i 0.178146 0.114488i
\(616\) 0 0
\(617\) −26.1711 16.8191i −1.05361 0.677113i −0.105293 0.994441i \(-0.533578\pi\)
−0.948316 + 0.317328i \(0.897214\pi\)
\(618\) 0 0
\(619\) 31.9525 + 9.38211i 1.28428 + 0.377099i 0.851478 0.524390i \(-0.175707\pi\)
0.432802 + 0.901489i \(0.357525\pi\)
\(620\) 0 0
\(621\) −3.84442 25.1628i −0.154271 1.00975i
\(622\) 0 0
\(623\) 25.3406 + 7.44067i 1.01525 + 0.298104i
\(624\) 0 0
\(625\) 0.841254 + 0.540641i 0.0336501 + 0.0216256i
\(626\) 0 0
\(627\) −25.6142 + 16.4613i −1.02293 + 0.657400i
\(628\) 0 0
\(629\) 8.66168 + 9.99611i 0.345364 + 0.398571i
\(630\) 0 0
\(631\) 5.49910 12.0413i 0.218916 0.479358i −0.768030 0.640414i \(-0.778763\pi\)
0.986945 + 0.161056i \(0.0514899\pi\)
\(632\) 0 0
\(633\) −2.30983 + 0.678227i −0.0918075 + 0.0269571i
\(634\) 0 0
\(635\) −1.33683 9.29782i −0.0530503 0.368973i
\(636\) 0 0
\(637\) 0.0182467 + 0.0399547i 0.000722960 + 0.00158306i
\(638\) 0 0
\(639\) 0.0887874 0.617530i 0.00351238 0.0244291i
\(640\) 0 0
\(641\) 20.5288 23.6915i 0.810840 0.935759i −0.188083 0.982153i \(-0.560228\pi\)
0.998923 + 0.0463941i \(0.0147730\pi\)
\(642\) 0 0
\(643\) −15.4669 −0.609954 −0.304977 0.952360i \(-0.598649\pi\)
−0.304977 + 0.952360i \(0.598649\pi\)
\(644\) 0 0
\(645\) −12.5155 −0.492798
\(646\) 0 0
\(647\) 14.7374 17.0078i 0.579386 0.668647i −0.388087 0.921623i \(-0.626864\pi\)
0.967473 + 0.252976i \(0.0814093\pi\)
\(648\) 0 0
\(649\) 0.779543 5.42184i 0.0305997 0.212826i
\(650\) 0 0
\(651\) −16.2459 35.5737i −0.636729 1.39424i
\(652\) 0 0
\(653\) 2.63752 + 18.3443i 0.103214 + 0.717870i 0.974056 + 0.226307i \(0.0726652\pi\)
−0.870842 + 0.491563i \(0.836426\pi\)
\(654\) 0 0
\(655\) −15.4238 + 4.52885i −0.602659 + 0.176957i
\(656\) 0 0
\(657\) −0.0378150 + 0.0828033i −0.00147530 + 0.00323047i
\(658\) 0 0
\(659\) −13.6221 15.7207i −0.530640 0.612391i 0.425623 0.904901i \(-0.360055\pi\)
−0.956263 + 0.292510i \(0.905510\pi\)
\(660\) 0 0
\(661\) −21.3773 + 13.7383i −0.831479 + 0.534359i −0.885747 0.464167i \(-0.846354\pi\)
0.0542688 + 0.998526i \(0.482717\pi\)
\(662\) 0 0
\(663\) 1.59815 + 1.02707i 0.0620670 + 0.0398880i
\(664\) 0 0
\(665\) 19.2019 + 5.63818i 0.744617 + 0.218639i
\(666\) 0 0
\(667\) 16.1355 + 4.58382i 0.624771 + 0.177486i
\(668\) 0 0
\(669\) 8.29740 + 2.43634i 0.320796 + 0.0941942i
\(670\) 0 0
\(671\) 24.6236 + 15.8246i 0.950584 + 0.610903i
\(672\) 0 0
\(673\) 24.1297 15.5072i 0.930130 0.597758i 0.0145502 0.999894i \(-0.495368\pi\)
0.915580 + 0.402136i \(0.131732\pi\)
\(674\) 0 0
\(675\) −3.47580 4.01129i −0.133784 0.154395i
\(676\) 0 0
\(677\) −4.96598 + 10.8740i −0.190858 + 0.417921i −0.980735 0.195345i \(-0.937417\pi\)
0.789876 + 0.613266i \(0.210145\pi\)
\(678\) 0 0
\(679\) 0.951294 0.279325i 0.0365073 0.0107195i
\(680\) 0 0
\(681\) 2.86960 + 19.9585i 0.109963 + 0.764811i
\(682\) 0 0
\(683\) 15.6880 + 34.3520i 0.600286 + 1.31444i 0.929023 + 0.370022i \(0.120650\pi\)
−0.328737 + 0.944421i \(0.606623\pi\)
\(684\) 0 0
\(685\) 0.698834 4.86050i 0.0267011 0.185710i
\(686\) 0 0
\(687\) 17.1141 19.7507i 0.652944 0.753537i
\(688\) 0 0
\(689\) −0.976384 −0.0371973
\(690\) 0 0
\(691\) −33.4709 −1.27329 −0.636646 0.771156i \(-0.719679\pi\)
−0.636646 + 0.771156i \(0.719679\pi\)
\(692\) 0 0
\(693\) 0.545665 0.629731i 0.0207281 0.0239215i
\(694\) 0 0
\(695\) −0.127472 + 0.886586i −0.00483528 + 0.0336301i
\(696\) 0 0
\(697\) 7.26015 + 15.8975i 0.274998 + 0.602161i
\(698\) 0 0
\(699\) −4.00480 27.8540i −0.151475 1.05353i
\(700\) 0 0
\(701\) −1.99992 + 0.587228i −0.0755358 + 0.0221793i −0.319282 0.947660i \(-0.603442\pi\)
0.243746 + 0.969839i \(0.421624\pi\)
\(702\) 0 0
\(703\) 7.49933 16.4212i 0.282843 0.619339i
\(704\) 0 0
\(705\) 8.18638 + 9.44758i 0.308317 + 0.355816i
\(706\) 0 0
\(707\) 20.3676 13.0894i 0.766001 0.492279i
\(708\) 0 0
\(709\) 0.871848 + 0.560302i 0.0327429 + 0.0210426i 0.556910 0.830573i \(-0.311987\pi\)
−0.524167 + 0.851616i \(0.675623\pi\)
\(710\) 0 0
\(711\) 0.932188 + 0.273715i 0.0349598 + 0.0102651i
\(712\) 0 0
\(713\) 5.68671 42.1869i 0.212969 1.57991i
\(714\) 0 0
\(715\) 0.447828 + 0.131494i 0.0167478 + 0.00491761i
\(716\) 0 0
\(717\) −27.6142 17.7465i −1.03127 0.662757i
\(718\) 0 0
\(719\) 38.6160 24.8170i 1.44013 0.925518i 0.440520 0.897743i \(-0.354794\pi\)
0.999614 0.0277750i \(-0.00884219\pi\)
\(720\) 0 0
\(721\) −12.1042 13.9690i −0.450783 0.520231i
\(722\) 0 0
\(723\) 6.71113 14.6953i 0.249590 0.546525i
\(724\) 0 0
\(725\) 3.35594 0.985394i 0.124637 0.0365966i
\(726\) 0 0
\(727\) −0.645510 4.48962i −0.0239406 0.166511i 0.974344 0.225066i \(-0.0722597\pi\)
−0.998284 + 0.0585552i \(0.981351\pi\)
\(728\) 0 0
\(729\) 11.6796 + 25.5748i 0.432579 + 0.947216i
\(730\) 0 0
\(731\) 5.92755 41.2270i 0.219238 1.52484i
\(732\) 0 0
\(733\) 16.9580 19.5706i 0.626357 0.722855i −0.350544 0.936546i \(-0.614003\pi\)
0.976901 + 0.213691i \(0.0685487\pi\)
\(734\) 0 0
\(735\) −0.372811 −0.0137514
\(736\) 0 0
\(737\) 38.0380 1.40115
\(738\) 0 0
\(739\) −9.43763 + 10.8916i −0.347169 + 0.400654i −0.902300 0.431109i \(-0.858123\pi\)
0.555131 + 0.831763i \(0.312668\pi\)
\(740\) 0 0
\(741\) 0.369001 2.56646i 0.0135556 0.0942812i
\(742\) 0 0
\(743\) −21.9683 48.1040i −0.805940 1.76476i −0.623953 0.781462i \(-0.714474\pi\)
−0.181987 0.983301i \(-0.558253\pi\)
\(744\) 0 0
\(745\) 2.18549 + 15.2004i 0.0800700 + 0.556899i
\(746\) 0 0
\(747\) −1.55692 + 0.457153i −0.0569647 + 0.0167264i
\(748\) 0 0
\(749\) 7.44016 16.2917i 0.271857 0.595285i
\(750\) 0 0
\(751\) 2.04273 + 2.35744i 0.0745404 + 0.0860242i 0.791795 0.610787i \(-0.209147\pi\)
−0.717254 + 0.696811i \(0.754601\pi\)
\(752\) 0 0
\(753\) −15.7546 + 10.1249i −0.574129 + 0.368970i
\(754\) 0 0
\(755\) −8.19442 5.26624i −0.298226 0.191658i
\(756\) 0 0
\(757\) −20.5639 6.03811i −0.747408 0.219459i −0.114218 0.993456i \(-0.536436\pi\)
−0.633189 + 0.773997i \(0.718255\pi\)
\(758\) 0 0
\(759\) −18.1811 + 5.51290i −0.659934 + 0.200106i
\(760\) 0 0
\(761\) −21.8145 6.40533i −0.790777 0.232193i −0.138688 0.990336i \(-0.544289\pi\)
−0.652088 + 0.758143i \(0.726107\pi\)
\(762\) 0 0
\(763\) 41.0928 + 26.4087i 1.48766 + 0.956061i
\(764\) 0 0
\(765\) 0.647569 0.416167i 0.0234129 0.0150466i
\(766\) 0 0
\(767\) 0.305465 + 0.352526i 0.0110297 + 0.0127290i
\(768\) 0 0
\(769\) 9.80845 21.4775i 0.353702 0.774498i −0.646234 0.763139i \(-0.723657\pi\)
0.999935 0.0113591i \(-0.00361578\pi\)
\(770\) 0 0
\(771\) −6.66054 + 1.95571i −0.239874 + 0.0704333i
\(772\) 0 0
\(773\) 3.05022 + 21.2147i 0.109709 + 0.763040i 0.968194 + 0.250202i \(0.0804970\pi\)
−0.858485 + 0.512839i \(0.828594\pi\)
\(774\) 0 0
\(775\) −3.68728 8.07402i −0.132451 0.290028i
\(776\) 0 0
\(777\) 1.47276 10.2433i 0.0528350 0.367475i
\(778\) 0 0
\(779\) 15.6207 18.0272i 0.559669 0.645892i
\(780\) 0 0
\(781\) −10.6850 −0.382340
\(782\) 0 0
\(783\) −18.5643 −0.663435
\(784\) 0 0
\(785\) −10.8234 + 12.4909i −0.386304 + 0.445818i
\(786\) 0 0
\(787\) 5.68359 39.5303i 0.202598 1.40910i −0.593938 0.804511i \(-0.702428\pi\)
0.796536 0.604591i \(-0.206663\pi\)
\(788\) 0 0
\(789\) −13.9584 30.5647i −0.496933 1.08813i
\(790\) 0 0
\(791\) −3.74590 26.0533i −0.133189 0.926348i
\(792\) 0 0
\(793\) −2.39161 + 0.702239i −0.0849284 + 0.0249372i
\(794\) 0 0
\(795\) 3.44263 7.53831i 0.122097 0.267356i
\(796\) 0 0
\(797\) 20.3637 + 23.5009i 0.721318 + 0.832445i 0.991465 0.130374i \(-0.0416179\pi\)
−0.270147 + 0.962819i \(0.587072\pi\)
\(798\) 0 0
\(799\) −34.9982 + 22.4920i −1.23815 + 0.795709i
\(800\) 0 0
\(801\) −1.16640 0.749598i −0.0412126 0.0264857i
\(802\) 0 0
\(803\) 1.49588 + 0.439231i 0.0527886 + 0.0155001i
\(804\) 0 0
\(805\) 10.5640 + 6.65834i 0.372334 + 0.234676i
\(806\) 0 0
\(807\) −29.0661 8.53458i −1.02318 0.300431i
\(808\) 0 0
\(809\) 31.7897 + 20.4300i 1.11767 + 0.718280i 0.962950 0.269679i \(-0.0869176\pi\)
0.154715 + 0.987959i \(0.450554\pi\)
\(810\) 0 0
\(811\) 10.4868 6.73948i 0.368243 0.236655i −0.343412 0.939185i \(-0.611583\pi\)
0.711654 + 0.702530i \(0.247946\pi\)
\(812\) 0 0
\(813\) 22.6755 + 26.1690i 0.795265 + 0.917785i
\(814\) 0 0
\(815\) 0.410748 0.899413i 0.0143879 0.0315050i
\(816\) 0 0
\(817\) −54.5449 + 16.0158i −1.90828 + 0.560323i
\(818\) 0 0
\(819\) 0.0100984 + 0.0702356i 0.000352865 + 0.00245423i
\(820\) 0 0
\(821\) 15.9328 + 34.8880i 0.556060 + 1.21760i 0.953894 + 0.300144i \(0.0970347\pi\)
−0.397834 + 0.917457i \(0.630238\pi\)
\(822\) 0 0
\(823\) −3.81064 + 26.5036i −0.132830 + 0.923856i 0.809010 + 0.587795i \(0.200004\pi\)
−0.941840 + 0.336061i \(0.890905\pi\)
\(824\) 0 0
\(825\) −2.59422 + 2.99389i −0.0903190 + 0.104234i
\(826\) 0 0
\(827\) 41.5456 1.44468 0.722341 0.691537i \(-0.243066\pi\)
0.722341 + 0.691537i \(0.243066\pi\)
\(828\) 0 0
\(829\) 20.2897 0.704691 0.352346 0.935870i \(-0.385384\pi\)
0.352346 + 0.935870i \(0.385384\pi\)
\(830\) 0 0
\(831\) −5.62287 + 6.48914i −0.195055 + 0.225106i
\(832\) 0 0
\(833\) 0.176569 1.22807i 0.00611777 0.0425500i
\(834\) 0 0
\(835\) 6.00154 + 13.1415i 0.207692 + 0.454782i
\(836\) 0 0
\(837\) 6.70472 + 46.6323i 0.231749 + 1.61185i
\(838\) 0 0
\(839\) −44.2738 + 13.0000i −1.52850 + 0.448809i −0.934592 0.355723i \(-0.884235\pi\)
−0.593910 + 0.804531i \(0.702417\pi\)
\(840\) 0 0
\(841\) −6.96511 + 15.2515i −0.240176 + 0.525913i
\(842\) 0 0
\(843\) −18.9416 21.8597i −0.652382 0.752889i
\(844\) 0 0
\(845\) 10.9029 7.00684i 0.375070 0.241043i
\(846\) 0 0
\(847\) 12.0894 + 7.76939i 0.415397 + 0.266959i
\(848\) 0 0
\(849\) −41.5214 12.1918i −1.42501 0.418421i
\(850\) 0 0
\(851\) 7.30132 8.57770i 0.250286 0.294040i
\(852\) 0 0
\(853\) −37.0059 10.8659i −1.26706 0.372042i −0.421941 0.906623i \(-0.638651\pi\)
−0.845117 + 0.534581i \(0.820469\pi\)
\(854\) 0 0
\(855\) −0.883839 0.568009i −0.0302267 0.0194255i
\(856\) 0 0
\(857\) −10.1876 + 6.54717i −0.348001 + 0.223647i −0.702951 0.711239i \(-0.748135\pi\)
0.354949 + 0.934886i \(0.384498\pi\)
\(858\) 0 0
\(859\) 20.3735 + 23.5123i 0.695135 + 0.802228i 0.988087 0.153899i \(-0.0491831\pi\)
−0.292952 + 0.956127i \(0.594638\pi\)
\(860\) 0 0
\(861\) 5.68034 12.4382i 0.193585 0.423893i
\(862\) 0 0
\(863\) −0.222969 + 0.0654695i −0.00758994 + 0.00222861i −0.285525 0.958371i \(-0.592168\pi\)
0.277935 + 0.960600i \(0.410350\pi\)
\(864\) 0 0
\(865\) 2.40566 + 16.7317i 0.0817950 + 0.568896i
\(866\) 0 0
\(867\) −10.3414 22.6445i −0.351213 0.769048i
\(868\) 0 0
\(869\) 2.36802 16.4700i 0.0803297 0.558705i
\(870\) 0 0
\(871\) −2.12124 + 2.44804i −0.0718755 + 0.0829487i
\(872\) 0 0
\(873\) −0.0520496 −0.00176161
\(874\) 0 0
\(875\) 2.60378 0.0880239
\(876\) 0 0
\(877\) 38.1226 43.9959i 1.28731 1.48564i 0.504445 0.863444i \(-0.331697\pi\)
0.782865 0.622191i \(-0.213757\pi\)
\(878\) 0 0
\(879\) −0.719343 + 5.00314i −0.0242629 + 0.168752i
\(880\) 0 0
\(881\) −18.9074 41.4014i −0.637007 1.39485i −0.902480 0.430732i \(-0.858255\pi\)
0.265473 0.964118i \(-0.414472\pi\)
\(882\) 0 0
\(883\) 0.912476 + 6.34641i 0.0307073 + 0.213574i 0.999398 0.0346973i \(-0.0110467\pi\)
−0.968691 + 0.248271i \(0.920138\pi\)
\(884\) 0 0
\(885\) −3.79876 + 1.11542i −0.127694 + 0.0374943i
\(886\) 0 0
\(887\) −9.66152 + 21.1558i −0.324402 + 0.710342i −0.999628 0.0272693i \(-0.991319\pi\)
0.675226 + 0.737611i \(0.264046\pi\)
\(888\) 0 0
\(889\) −16.0169 18.4845i −0.537189 0.619949i
\(890\) 0 0
\(891\) 16.8808 10.8486i 0.565529 0.363443i
\(892\) 0 0
\(893\) 47.7675 + 30.6983i 1.59848 + 1.02728i
\(894\) 0 0
\(895\) 16.5607 + 4.86265i 0.553562 + 0.162540i
\(896\) 0 0
\(897\) 0.659098 1.47753i 0.0220066 0.0493334i
\(898\) 0 0
\(899\) −29.7878 8.74650i −0.993480 0.291712i
\(900\) 0 0
\(901\) 23.2012 + 14.9105i 0.772945 + 0.496742i
\(902\) 0 0
\(903\) −27.4145 + 17.6182i −0.912298 + 0.586298i
\(904\) 0 0
\(905\) −7.02669 8.10924i −0.233575 0.269560i
\(906\) 0 0
\(907\) −21.9150 + 47.9872i −0.727677 + 1.59339i 0.0751457 + 0.997173i \(0.476058\pi\)
−0.802823 + 0.596218i \(0.796669\pi\)
\(908\) 0 0
\(909\) −1.21955 + 0.358092i −0.0404498 + 0.0118771i
\(910\) 0 0
\(911\) 3.66707 + 25.5050i 0.121495 + 0.845019i 0.955864 + 0.293811i \(0.0949237\pi\)
−0.834368 + 0.551208i \(0.814167\pi\)
\(912\) 0 0
\(913\) 11.5447 + 25.2793i 0.382072 + 0.836622i
\(914\) 0 0
\(915\) 3.01082 20.9407i 0.0995348 0.692280i
\(916\) 0 0
\(917\) −27.4097 + 31.6325i −0.905148 + 1.04460i
\(918\) 0 0
\(919\) 6.92575 0.228459 0.114230 0.993454i \(-0.463560\pi\)
0.114230 + 0.993454i \(0.463560\pi\)
\(920\) 0 0
\(921\) 26.0554 0.858554
\(922\) 0 0
\(923\) 0.595864 0.687664i 0.0196131 0.0226347i
\(924\) 0 0
\(925\) 0.334267 2.32488i 0.0109906 0.0764415i
\(926\) 0 0
\(927\) 0.403100 + 0.882666i 0.0132395 + 0.0289906i
\(928\) 0 0
\(929\) 7.31024 + 50.8438i 0.239841 + 1.66813i 0.652913 + 0.757433i \(0.273547\pi\)
−0.413072 + 0.910699i \(0.635544\pi\)
\(930\) 0 0
\(931\) −1.62478 + 0.477078i −0.0532500 + 0.0156356i
\(932\) 0 0
\(933\) −13.5539 + 29.6789i −0.443735 + 0.971645i
\(934\) 0 0
\(935\) −8.63341 9.96348i −0.282343 0.325841i
\(936\) 0 0
\(937\) 36.5895 23.5147i 1.19533 0.768191i 0.217186 0.976130i \(-0.430312\pi\)
0.978142 + 0.207939i \(0.0666757\pi\)
\(938\) 0 0
\(939\) 15.7403 + 10.1157i 0.513666 + 0.330113i
\(940\) 0 0
\(941\) 32.1318 + 9.43474i 1.04747 + 0.307564i 0.759793 0.650165i \(-0.225300\pi\)
0.287673 + 0.957729i \(0.407118\pi\)
\(942\) 0 0
\(943\) 12.4498 8.15685i 0.405421 0.265624i
\(944\) 0 0
\(945\) −13.2603 3.89357i −0.431357 0.126658i
\(946\) 0 0
\(947\) 0.901818 + 0.579563i 0.0293051 + 0.0188333i 0.555211 0.831709i \(-0.312637\pi\)
−0.525906 + 0.850543i \(0.676274\pi\)
\(948\) 0 0
\(949\) −0.111688 + 0.0717775i −0.00362554 + 0.00232999i
\(950\) 0 0
\(951\) 15.8429 + 18.2837i 0.513742 + 0.592889i
\(952\) 0 0
\(953\) 4.49030 9.83239i 0.145455 0.318502i −0.822856 0.568250i \(-0.807620\pi\)
0.968311 + 0.249748i \(0.0803478\pi\)
\(954\) 0 0
\(955\) −19.0855 + 5.60400i −0.617592 + 0.181341i
\(956\) 0 0
\(957\) 1.97188 + 13.7147i 0.0637418 + 0.443334i
\(958\) 0 0
\(959\) −5.31142 11.6304i −0.171515 0.375565i
\(960\) 0 0
\(961\) −6.80065 + 47.2995i −0.219376 + 1.52579i
\(962\) 0 0
\(963\) −0.615735 + 0.710596i −0.0198418 + 0.0228986i
\(964\) 0 0
\(965\) −9.22503 −0.296964
\(966\) 0 0
\(967\) −18.5042 −0.595054 −0.297527 0.954713i \(-0.596162\pi\)
−0.297527 + 0.954713i \(0.596162\pi\)
\(968\) 0 0
\(969\) −47.9612 + 55.3502i −1.54074 + 1.77810i
\(970\) 0 0
\(971\) −5.13949 + 35.7460i −0.164934 + 1.14714i 0.724232 + 0.689557i \(0.242195\pi\)
−0.889166 + 0.457585i \(0.848714\pi\)
\(972\) 0 0
\(973\) 0.968837 + 2.12146i 0.0310595 + 0.0680108i
\(974\) 0 0
\(975\) −0.0480099 0.333916i −0.00153755 0.0106939i
\(976\) 0 0
\(977\) −11.9236 + 3.50108i −0.381469 + 0.112009i −0.466844 0.884339i \(-0.654609\pi\)
0.0853754 + 0.996349i \(0.472791\pi\)
\(978\) 0 0
\(979\) −9.86452 + 21.6003i −0.315271 + 0.690348i
\(980\) 0 0
\(981\) −1.67932 1.93803i −0.0536165 0.0618767i
\(982\) 0 0
\(983\) 18.4731 11.8719i 0.589200 0.378656i −0.211806 0.977312i \(-0.567935\pi\)
0.801006 + 0.598656i \(0.204298\pi\)
\(984\) 0 0
\(985\) −12.0179 7.72342i −0.382922 0.246089i
\(986\) 0 0
\(987\) 31.2312 + 9.17032i 0.994101 + 0.291894i
\(988\) 0 0
\(989\) −35.4701 + 0.312481i −1.12788 + 0.00993632i
\(990\) 0 0
\(991\) 8.73337 + 2.56435i 0.277425 + 0.0814592i 0.417485 0.908684i \(-0.362912\pi\)
−0.140061 + 0.990143i \(0.544730\pi\)
\(992\) 0 0
\(993\) 20.5900 + 13.2324i 0.653404 + 0.419917i
\(994\) 0 0
\(995\) −4.25203 + 2.73262i −0.134798 + 0.0866297i
\(996\) 0 0
\(997\) −30.4558 35.1479i −0.964546 1.11315i −0.993531 0.113565i \(-0.963773\pi\)
0.0289846 0.999580i \(-0.490773\pi\)
\(998\) 0 0
\(999\) −5.17883 + 11.3401i −0.163851 + 0.358783i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 460.2.m.b.41.4 50
23.9 even 11 inner 460.2.m.b.101.4 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.m.b.41.4 50 1.1 even 1 trivial
460.2.m.b.101.4 yes 50 23.9 even 11 inner