Properties

Label 920.2.bv.a.17.12
Level $920$
Weight $2$
Character 920.17
Analytic conductor $7.346$
Analytic rank $0$
Dimension $720$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [920,2,Mod(17,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("920.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bv (of order \(44\), degree \(20\), 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: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(720\)
Relative dimension: \(36\) over \(\Q(\zeta_{44})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label 17.12
Character \(\chi\) \(=\) 920.17
Dual form 920.2.bv.a.433.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.21475 + 0.663302i) q^{3} +(0.933470 - 2.03190i) q^{5} +(-0.205002 - 0.273851i) q^{7} +(-0.586283 + 0.912274i) q^{9} +(0.437876 - 0.199971i) q^{11} +(-1.45611 - 1.09003i) q^{13} +(0.213837 + 3.08742i) q^{15} +(-0.429113 - 5.99978i) q^{17} +(2.24436 + 2.59013i) q^{19} +(0.430671 + 0.196681i) q^{21} +(4.77197 + 0.477794i) q^{23} +(-3.25727 - 3.79344i) q^{25} +(0.403282 - 5.63862i) q^{27} +(-7.06351 - 6.12056i) q^{29} +(-8.81071 + 2.58706i) q^{31} +(-0.399267 + 0.533358i) q^{33} +(-0.747802 + 0.160913i) q^{35} +(4.51781 - 0.982790i) q^{37} +(2.49182 + 0.358270i) q^{39} +(-5.19934 + 3.34142i) q^{41} +(2.67559 + 4.89997i) q^{43} +(1.30638 + 2.04285i) q^{45} +(-6.66836 - 6.66836i) q^{47} +(1.93916 - 6.60417i) q^{49} +(4.50093 + 7.00358i) q^{51} +(10.8030 - 8.08702i) q^{53} +(0.00242150 - 1.07639i) q^{55} +(-4.44437 - 1.65766i) q^{57} +(-5.21327 + 0.749555i) q^{59} +(-4.23334 - 14.4174i) q^{61} +(0.370016 - 0.0264641i) q^{63} +(-3.57407 + 1.94117i) q^{65} +(-2.35479 - 6.31343i) q^{67} +(-6.11366 + 2.58486i) q^{69} +(5.71261 - 12.5089i) q^{71} +(3.25371 + 0.232710i) q^{73} +(6.47295 + 2.44752i) q^{75} +(-0.144528 - 0.0789181i) q^{77} +(-1.00791 - 7.01019i) q^{79} +(1.89876 + 4.15771i) q^{81} +(1.64364 + 7.55568i) q^{83} +(-12.5915 - 4.72870i) q^{85} +(12.6402 + 2.74970i) q^{87} +(0.505952 + 0.148561i) q^{89} +0.622215i q^{91} +(8.98678 - 8.98678i) q^{93} +(7.35795 - 2.14252i) q^{95} +(-0.554245 + 2.54782i) q^{97} +(-0.0742905 + 0.516702i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{22}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) −1.21475 + 0.663302i −0.701334 + 0.382957i −0.790002 0.613104i \(-0.789921\pi\)
0.0886682 + 0.996061i \(0.471739\pi\)
\(4\) 0 0
\(5\) 0.933470 2.03190i 0.417460 0.908695i
\(6\) 0 0
\(7\) −0.205002 0.273851i −0.0774835 0.103506i 0.760125 0.649777i \(-0.225138\pi\)
−0.837608 + 0.546271i \(0.816047\pi\)
\(8\) 0 0
\(9\) −0.586283 + 0.912274i −0.195428 + 0.304091i
\(10\) 0 0
\(11\) 0.437876 0.199971i 0.132024 0.0602935i −0.348307 0.937380i \(-0.613243\pi\)
0.480332 + 0.877087i \(0.340516\pi\)
\(12\) 0 0
\(13\) −1.45611 1.09003i −0.403852 0.302320i 0.377974 0.925816i \(-0.376621\pi\)
−0.781826 + 0.623496i \(0.785712\pi\)
\(14\) 0 0
\(15\) 0.213837 + 3.08742i 0.0552124 + 0.797169i
\(16\) 0 0
\(17\) −0.429113 5.99978i −0.104075 1.45516i −0.734341 0.678781i \(-0.762509\pi\)
0.630266 0.776379i \(-0.282946\pi\)
\(18\) 0 0
\(19\) 2.24436 + 2.59013i 0.514892 + 0.594217i 0.952345 0.305024i \(-0.0986646\pi\)
−0.437452 + 0.899242i \(0.644119\pi\)
\(20\) 0 0
\(21\) 0.430671 + 0.196681i 0.0939802 + 0.0429193i
\(22\) 0 0
\(23\) 4.77197 + 0.477794i 0.995025 + 0.0996270i
\(24\) 0 0
\(25\) −3.25727 3.79344i −0.651454 0.758688i
\(26\) 0 0
\(27\) 0.403282 5.63862i 0.0776116 1.08515i
\(28\) 0 0
\(29\) −7.06351 6.12056i −1.31166 1.13656i −0.981253 0.192722i \(-0.938268\pi\)
−0.330407 0.943838i \(-0.607186\pi\)
\(30\) 0 0
\(31\) −8.81071 + 2.58706i −1.58245 + 0.464649i −0.950594 0.310436i \(-0.899525\pi\)
−0.631856 + 0.775086i \(0.717707\pi\)
\(32\) 0 0
\(33\) −0.399267 + 0.533358i −0.0695034 + 0.0928457i
\(34\) 0 0
\(35\) −0.747802 + 0.160913i −0.126402 + 0.0271993i
\(36\) 0 0
\(37\) 4.51781 0.982790i 0.742724 0.161570i 0.174746 0.984614i \(-0.444090\pi\)
0.567978 + 0.823044i \(0.307726\pi\)
\(38\) 0 0
\(39\) 2.49182 + 0.358270i 0.399011 + 0.0573691i
\(40\) 0 0
\(41\) −5.19934 + 3.34142i −0.812001 + 0.521841i −0.879512 0.475877i \(-0.842131\pi\)
0.0675106 + 0.997719i \(0.478494\pi\)
\(42\) 0 0
\(43\) 2.67559 + 4.89997i 0.408023 + 0.747239i 0.998196 0.0600382i \(-0.0191223\pi\)
−0.590173 + 0.807277i \(0.700940\pi\)
\(44\) 0 0
\(45\) 1.30638 + 2.04285i 0.194743 + 0.304530i
\(46\) 0 0
\(47\) −6.66836 6.66836i −0.972680 0.972680i 0.0269569 0.999637i \(-0.491418\pi\)
−0.999637 + 0.0269569i \(0.991418\pi\)
\(48\) 0 0
\(49\) 1.93916 6.60417i 0.277023 0.943453i
\(50\) 0 0
\(51\) 4.50093 + 7.00358i 0.630256 + 0.980697i
\(52\) 0 0
\(53\) 10.8030 8.08702i 1.48390 1.11084i 0.516911 0.856039i \(-0.327082\pi\)
0.966994 0.254798i \(-0.0820089\pi\)
\(54\) 0 0
\(55\) 0.00242150 1.07639i 0.000326515 0.145140i
\(56\) 0 0
\(57\) −4.44437 1.65766i −0.588671 0.219563i
\(58\) 0 0
\(59\) −5.21327 + 0.749555i −0.678710 + 0.0975838i −0.473045 0.881039i \(-0.656845\pi\)
−0.205666 + 0.978622i \(0.565936\pi\)
\(60\) 0 0
\(61\) −4.23334 14.4174i −0.542024 1.84596i −0.533177 0.846004i \(-0.679002\pi\)
−0.00884702 0.999961i \(-0.502816\pi\)
\(62\) 0 0
\(63\) 0.370016 0.0264641i 0.0466177 0.00333416i
\(64\) 0 0
\(65\) −3.57407 + 1.94117i −0.443309 + 0.240772i
\(66\) 0 0
\(67\) −2.35479 6.31343i −0.287683 0.771308i −0.997742 0.0671659i \(-0.978604\pi\)
0.710059 0.704143i \(-0.248668\pi\)
\(68\) 0 0
\(69\) −6.11366 + 2.58486i −0.735998 + 0.311180i
\(70\) 0 0
\(71\) 5.71261 12.5089i 0.677962 1.48453i −0.186827 0.982393i \(-0.559820\pi\)
0.864789 0.502136i \(-0.167452\pi\)
\(72\) 0 0
\(73\) 3.25371 + 0.232710i 0.380818 + 0.0272367i 0.260436 0.965491i \(-0.416134\pi\)
0.120382 + 0.992728i \(0.461588\pi\)
\(74\) 0 0
\(75\) 6.47295 + 2.44752i 0.747432 + 0.282615i
\(76\) 0 0
\(77\) −0.144528 0.0789181i −0.0164705 0.00899355i
\(78\) 0 0
\(79\) −1.00791 7.01019i −0.113399 0.788708i −0.964571 0.263822i \(-0.915017\pi\)
0.851172 0.524886i \(-0.175892\pi\)
\(80\) 0 0
\(81\) 1.89876 + 4.15771i 0.210974 + 0.461968i
\(82\) 0 0
\(83\) 1.64364 + 7.55568i 0.180413 + 0.829344i 0.975002 + 0.222196i \(0.0713226\pi\)
−0.794589 + 0.607147i \(0.792314\pi\)
\(84\) 0 0
\(85\) −12.5915 4.72870i −1.36574 0.512899i
\(86\) 0 0
\(87\) 12.6402 + 2.74970i 1.35517 + 0.294798i
\(88\) 0 0
\(89\) 0.505952 + 0.148561i 0.0536308 + 0.0157474i 0.308438 0.951244i \(-0.400194\pi\)
−0.254807 + 0.966992i \(0.582012\pi\)
\(90\) 0 0
\(91\) 0.622215i 0.0652259i
\(92\) 0 0
\(93\) 8.98678 8.98678i 0.931885 0.931885i
\(94\) 0 0
\(95\) 7.35795 2.14252i 0.754909 0.219818i
\(96\) 0 0
\(97\) −0.554245 + 2.54782i −0.0562750 + 0.258692i −0.996686 0.0813487i \(-0.974077\pi\)
0.940411 + 0.340041i \(0.110441\pi\)
\(98\) 0 0
\(99\) −0.0742905 + 0.516702i −0.00746648 + 0.0519305i
\(100\) 0 0
\(101\) 13.8433 + 8.89658i 1.37746 + 0.885243i 0.999182 0.0404471i \(-0.0128782\pi\)
0.378283 + 0.925690i \(0.376515\pi\)
\(102\) 0 0
\(103\) −4.44225 + 11.9101i −0.437708 + 1.17354i 0.511609 + 0.859218i \(0.329050\pi\)
−0.949317 + 0.314321i \(0.898223\pi\)
\(104\) 0 0
\(105\) 0.801656 0.691487i 0.0782336 0.0674822i
\(106\) 0 0
\(107\) 6.07858 11.1321i 0.587638 1.07618i −0.399564 0.916705i \(-0.630838\pi\)
0.987202 0.159474i \(-0.0509798\pi\)
\(108\) 0 0
\(109\) −4.75520 + 5.48779i −0.455465 + 0.525635i −0.936312 0.351170i \(-0.885784\pi\)
0.480847 + 0.876805i \(0.340329\pi\)
\(110\) 0 0
\(111\) −4.83611 + 4.19051i −0.459023 + 0.397746i
\(112\) 0 0
\(113\) −10.5184 + 3.92314i −0.989483 + 0.369058i −0.791515 0.611150i \(-0.790707\pi\)
−0.197969 + 0.980208i \(0.563434\pi\)
\(114\) 0 0
\(115\) 5.42532 9.25018i 0.505914 0.862584i
\(116\) 0 0
\(117\) 1.84810 0.689305i 0.170857 0.0637262i
\(118\) 0 0
\(119\) −1.55508 + 1.34748i −0.142554 + 0.123523i
\(120\) 0 0
\(121\) −7.05172 + 8.13812i −0.641066 + 0.739829i
\(122\) 0 0
\(123\) 4.09952 7.50771i 0.369641 0.676947i
\(124\) 0 0
\(125\) −10.7485 + 3.07740i −0.961373 + 0.275251i
\(126\) 0 0
\(127\) 3.79731 10.1810i 0.336957 0.903417i −0.652396 0.757879i \(-0.726236\pi\)
0.989353 0.145538i \(-0.0464914\pi\)
\(128\) 0 0
\(129\) −6.50032 4.17750i −0.572321 0.367808i
\(130\) 0 0
\(131\) −0.730718 + 5.08226i −0.0638432 + 0.444039i 0.932679 + 0.360708i \(0.117465\pi\)
−0.996522 + 0.0833309i \(0.973444\pi\)
\(132\) 0 0
\(133\) 0.249211 1.14560i 0.0216093 0.0993364i
\(134\) 0 0
\(135\) −11.0807 6.08291i −0.953673 0.523533i
\(136\) 0 0
\(137\) 5.18289 5.18289i 0.442804 0.442804i −0.450149 0.892953i \(-0.648629\pi\)
0.892953 + 0.450149i \(0.148629\pi\)
\(138\) 0 0
\(139\) 20.3063i 1.72236i 0.508302 + 0.861179i \(0.330273\pi\)
−0.508302 + 0.861179i \(0.669727\pi\)
\(140\) 0 0
\(141\) 12.5235 + 3.67723i 1.05467 + 0.309679i
\(142\) 0 0
\(143\) −0.855569 0.186118i −0.0715463 0.0155639i
\(144\) 0 0
\(145\) −19.0300 + 8.63901i −1.58035 + 0.717431i
\(146\) 0 0
\(147\) 2.02497 + 9.30864i 0.167017 + 0.767764i
\(148\) 0 0
\(149\) 7.20474 + 15.7762i 0.590235 + 1.29243i 0.935300 + 0.353856i \(0.115130\pi\)
−0.345065 + 0.938579i \(0.612143\pi\)
\(150\) 0 0
\(151\) 1.43401 + 9.97378i 0.116698 + 0.811655i 0.961151 + 0.276024i \(0.0890170\pi\)
−0.844452 + 0.535631i \(0.820074\pi\)
\(152\) 0 0
\(153\) 5.72502 + 3.12610i 0.462841 + 0.252730i
\(154\) 0 0
\(155\) −2.96788 + 20.3175i −0.238386 + 1.63194i
\(156\) 0 0
\(157\) 13.7521 + 0.983567i 1.09753 + 0.0784972i 0.608339 0.793677i \(-0.291836\pi\)
0.489195 + 0.872174i \(0.337291\pi\)
\(158\) 0 0
\(159\) −7.75876 + 16.9893i −0.615310 + 1.34734i
\(160\) 0 0
\(161\) −0.847420 1.40476i −0.0667861 0.110710i
\(162\) 0 0
\(163\) −0.606290 1.62553i −0.0474883 0.127321i 0.911040 0.412317i \(-0.135280\pi\)
−0.958529 + 0.284996i \(0.908008\pi\)
\(164\) 0 0
\(165\) 0.711029 + 1.30914i 0.0553535 + 0.101917i
\(166\) 0 0
\(167\) −9.50157 + 0.679565i −0.735253 + 0.0525863i −0.433944 0.900940i \(-0.642878\pi\)
−0.301310 + 0.953526i \(0.597424\pi\)
\(168\) 0 0
\(169\) −2.73043 9.29900i −0.210033 0.715308i
\(170\) 0 0
\(171\) −3.67874 + 0.528923i −0.281320 + 0.0404478i
\(172\) 0 0
\(173\) 0.0778291 + 0.0290287i 0.00591723 + 0.00220701i 0.352421 0.935842i \(-0.385359\pi\)
−0.346504 + 0.938049i \(0.612631\pi\)
\(174\) 0 0
\(175\) −0.371090 + 1.66967i −0.0280518 + 0.126215i
\(176\) 0 0
\(177\) 5.83562 4.36849i 0.438632 0.328356i
\(178\) 0 0
\(179\) 4.07713 + 6.34413i 0.304739 + 0.474183i 0.959522 0.281634i \(-0.0908764\pi\)
−0.654783 + 0.755817i \(0.727240\pi\)
\(180\) 0 0
\(181\) 0.155884 0.530891i 0.0115867 0.0394608i −0.953497 0.301403i \(-0.902545\pi\)
0.965083 + 0.261943i \(0.0843631\pi\)
\(182\) 0 0
\(183\) 14.7056 + 14.7056i 1.08707 + 1.08707i
\(184\) 0 0
\(185\) 2.22031 10.0972i 0.163240 0.742359i
\(186\) 0 0
\(187\) −1.38768 2.54135i −0.101477 0.185842i
\(188\) 0 0
\(189\) −1.62681 + 1.04549i −0.118333 + 0.0760482i
\(190\) 0 0
\(191\) −6.89106 0.990785i −0.498619 0.0716907i −0.111583 0.993755i \(-0.535592\pi\)
−0.387036 + 0.922064i \(0.626501\pi\)
\(192\) 0 0
\(193\) −13.6814 + 2.97621i −0.984808 + 0.214232i −0.676007 0.736895i \(-0.736291\pi\)
−0.308801 + 0.951127i \(0.599928\pi\)
\(194\) 0 0
\(195\) 3.05401 4.72871i 0.218702 0.338630i
\(196\) 0 0
\(197\) −5.28101 + 7.05460i −0.376256 + 0.502619i −0.948200 0.317673i \(-0.897099\pi\)
0.571944 + 0.820293i \(0.306189\pi\)
\(198\) 0 0
\(199\) −16.6566 + 4.89080i −1.18075 + 0.346700i −0.812464 0.583012i \(-0.801874\pi\)
−0.368288 + 0.929712i \(0.620056\pi\)
\(200\) 0 0
\(201\) 7.04818 + 6.10728i 0.497140 + 0.430775i
\(202\) 0 0
\(203\) −0.228087 + 3.18908i −0.0160086 + 0.223829i
\(204\) 0 0
\(205\) 1.93601 + 13.6837i 0.135217 + 0.955710i
\(206\) 0 0
\(207\) −3.23360 + 4.07322i −0.224751 + 0.283109i
\(208\) 0 0
\(209\) 1.50070 + 0.685348i 0.103806 + 0.0474065i
\(210\) 0 0
\(211\) −4.14939 4.78865i −0.285656 0.329664i 0.594727 0.803927i \(-0.297260\pi\)
−0.880383 + 0.474263i \(0.842715\pi\)
\(212\) 0 0
\(213\) 1.35778 + 18.9843i 0.0930337 + 1.30078i
\(214\) 0 0
\(215\) 12.4539 0.862561i 0.849346 0.0588262i
\(216\) 0 0
\(217\) 2.51468 + 1.88247i 0.170708 + 0.127790i
\(218\) 0 0
\(219\) −4.10679 + 1.87551i −0.277511 + 0.126735i
\(220\) 0 0
\(221\) −5.91510 + 9.20408i −0.397893 + 0.619134i
\(222\) 0 0
\(223\) −8.42173 11.2501i −0.563961 0.753364i 0.424403 0.905474i \(-0.360484\pi\)
−0.988364 + 0.152110i \(0.951393\pi\)
\(224\) 0 0
\(225\) 5.37034 0.747492i 0.358023 0.0498328i
\(226\) 0 0
\(227\) 7.23215 3.94905i 0.480015 0.262108i −0.220975 0.975280i \(-0.570924\pi\)
0.700989 + 0.713172i \(0.252742\pi\)
\(228\) 0 0
\(229\) 12.9303 0.854461 0.427230 0.904143i \(-0.359489\pi\)
0.427230 + 0.904143i \(0.359489\pi\)
\(230\) 0 0
\(231\) 0.227911 0.0149954
\(232\) 0 0
\(233\) 1.05078 0.573767i 0.0688386 0.0375887i −0.444461 0.895798i \(-0.646605\pi\)
0.513300 + 0.858209i \(0.328423\pi\)
\(234\) 0 0
\(235\) −19.7742 + 7.32475i −1.28992 + 0.477814i
\(236\) 0 0
\(237\) 5.87423 + 7.84706i 0.381572 + 0.509721i
\(238\) 0 0
\(239\) 6.67177 10.3815i 0.431561 0.671522i −0.555564 0.831474i \(-0.687497\pi\)
0.987125 + 0.159952i \(0.0511338\pi\)
\(240\) 0 0
\(241\) 11.5578 5.27826i 0.744502 0.340003i −0.00678624 0.999977i \(-0.502160\pi\)
0.751288 + 0.659974i \(0.229433\pi\)
\(242\) 0 0
\(243\) 8.51209 + 6.37207i 0.546051 + 0.408769i
\(244\) 0 0
\(245\) −11.6089 10.1050i −0.741665 0.645583i
\(246\) 0 0
\(247\) −0.444716 6.21794i −0.0282966 0.395638i
\(248\) 0 0
\(249\) −7.00830 8.08801i −0.444133 0.512557i
\(250\) 0 0
\(251\) 22.1458 + 10.1136i 1.39783 + 0.638366i 0.964793 0.263011i \(-0.0847155\pi\)
0.433035 + 0.901377i \(0.357443\pi\)
\(252\) 0 0
\(253\) 2.18507 0.745042i 0.137374 0.0468404i
\(254\) 0 0
\(255\) 18.4321 2.60782i 1.15426 0.163308i
\(256\) 0 0
\(257\) −0.0525736 + 0.735075i −0.00327945 + 0.0458527i −0.998828 0.0483940i \(-0.984590\pi\)
0.995549 + 0.0942467i \(0.0300442\pi\)
\(258\) 0 0
\(259\) −1.19530 1.03573i −0.0742723 0.0643573i
\(260\) 0 0
\(261\) 9.72484 2.85547i 0.601953 0.176749i
\(262\) 0 0
\(263\) 10.9762 14.6624i 0.676820 0.904125i −0.322276 0.946646i \(-0.604448\pi\)
0.999096 + 0.0425205i \(0.0135388\pi\)
\(264\) 0 0
\(265\) −6.34778 29.4996i −0.389941 1.81215i
\(266\) 0 0
\(267\) −0.713144 + 0.155135i −0.0436437 + 0.00949410i
\(268\) 0 0
\(269\) 16.0708 + 2.31063i 0.979855 + 0.140882i 0.613586 0.789628i \(-0.289726\pi\)
0.366268 + 0.930509i \(0.380635\pi\)
\(270\) 0 0
\(271\) 2.55320 1.64084i 0.155096 0.0996740i −0.460791 0.887509i \(-0.652434\pi\)
0.615887 + 0.787835i \(0.288798\pi\)
\(272\) 0 0
\(273\) −0.412717 0.755834i −0.0249787 0.0457451i
\(274\) 0 0
\(275\) −2.18486 1.00970i −0.131752 0.0608870i
\(276\) 0 0
\(277\) 11.0723 + 11.0723i 0.665268 + 0.665268i 0.956617 0.291349i \(-0.0941041\pi\)
−0.291349 + 0.956617i \(0.594104\pi\)
\(278\) 0 0
\(279\) 2.80546 9.55453i 0.167959 0.572015i
\(280\) 0 0
\(281\) 2.41198 + 3.75311i 0.143887 + 0.223892i 0.905715 0.423887i \(-0.139335\pi\)
−0.761829 + 0.647779i \(0.775698\pi\)
\(282\) 0 0
\(283\) 1.71562 1.28430i 0.101983 0.0763435i −0.547069 0.837087i \(-0.684257\pi\)
0.649052 + 0.760744i \(0.275166\pi\)
\(284\) 0 0
\(285\) −7.51690 + 7.48316i −0.445263 + 0.443264i
\(286\) 0 0
\(287\) 1.98093 + 0.738847i 0.116930 + 0.0436128i
\(288\) 0 0
\(289\) −18.9863 + 2.72981i −1.11684 + 0.160577i
\(290\) 0 0
\(291\) −1.01671 3.46259i −0.0596005 0.202981i
\(292\) 0 0
\(293\) 13.5945 0.972299i 0.794200 0.0568023i 0.331658 0.943400i \(-0.392392\pi\)
0.462542 + 0.886597i \(0.346937\pi\)
\(294\) 0 0
\(295\) −3.34341 + 11.2926i −0.194661 + 0.657478i
\(296\) 0 0
\(297\) −0.950973 2.54966i −0.0551811 0.147946i
\(298\) 0 0
\(299\) −6.42770 5.89731i −0.371724 0.341050i
\(300\) 0 0
\(301\) 0.793360 1.73722i 0.0457285 0.100131i
\(302\) 0 0
\(303\) −22.7173 1.62477i −1.30507 0.0933407i
\(304\) 0 0
\(305\) −33.2466 4.85650i −1.90369 0.278082i
\(306\) 0 0
\(307\) −28.6713 15.6557i −1.63636 0.893519i −0.991631 0.129108i \(-0.958789\pi\)
−0.644728 0.764412i \(-0.723029\pi\)
\(308\) 0 0
\(309\) −2.50380 17.4143i −0.142436 0.990667i
\(310\) 0 0
\(311\) 14.3216 + 31.3600i 0.812105 + 1.77826i 0.598085 + 0.801433i \(0.295929\pi\)
0.214020 + 0.976829i \(0.431344\pi\)
\(312\) 0 0
\(313\) −0.401614 1.84619i −0.0227005 0.104353i 0.964403 0.264438i \(-0.0851866\pi\)
−0.987103 + 0.160086i \(0.948823\pi\)
\(314\) 0 0
\(315\) 0.291626 0.776541i 0.0164313 0.0437531i
\(316\) 0 0
\(317\) 29.6509 + 6.45016i 1.66536 + 0.362277i 0.943913 0.330193i \(-0.107114\pi\)
0.721446 + 0.692470i \(0.243478\pi\)
\(318\) 0 0
\(319\) −4.31687 1.26755i −0.241699 0.0709691i
\(320\) 0 0
\(321\) 17.5546i 0.979802i
\(322\) 0 0
\(323\) 14.5771 14.5771i 0.811094 0.811094i
\(324\) 0 0
\(325\) 0.607975 + 9.07419i 0.0337244 + 0.503345i
\(326\) 0 0
\(327\) 2.13630 9.82040i 0.118138 0.543069i
\(328\) 0 0
\(329\) −0.459107 + 3.19316i −0.0253114 + 0.176045i
\(330\) 0 0
\(331\) −11.0838 7.12312i −0.609220 0.391522i 0.199344 0.979930i \(-0.436119\pi\)
−0.808565 + 0.588407i \(0.799755\pi\)
\(332\) 0 0
\(333\) −1.75214 + 4.69768i −0.0960168 + 0.257431i
\(334\) 0 0
\(335\) −15.0264 1.10869i −0.820981 0.0605744i
\(336\) 0 0
\(337\) 13.9104 25.4751i 0.757750 1.38772i −0.158602 0.987343i \(-0.550699\pi\)
0.916352 0.400373i \(-0.131119\pi\)
\(338\) 0 0
\(339\) 10.1749 11.7425i 0.552625 0.637763i
\(340\) 0 0
\(341\) −3.34066 + 2.89470i −0.180907 + 0.156757i
\(342\) 0 0
\(343\) −4.44969 + 1.65965i −0.240260 + 0.0896125i
\(344\) 0 0
\(345\) −0.454729 + 14.8353i −0.0244818 + 0.798703i
\(346\) 0 0
\(347\) 20.6424 7.69921i 1.10814 0.413315i 0.272258 0.962224i \(-0.412229\pi\)
0.835882 + 0.548909i \(0.184957\pi\)
\(348\) 0 0
\(349\) 9.46026 8.19736i 0.506396 0.438795i −0.363817 0.931470i \(-0.618527\pi\)
0.870213 + 0.492676i \(0.163981\pi\)
\(350\) 0 0
\(351\) −6.73348 + 7.77085i −0.359407 + 0.414778i
\(352\) 0 0
\(353\) −14.6828 + 26.8895i −0.781485 + 1.43118i 0.117439 + 0.993080i \(0.462532\pi\)
−0.898924 + 0.438104i \(0.855650\pi\)
\(354\) 0 0
\(355\) −20.0843 23.2841i −1.06596 1.23579i
\(356\) 0 0
\(357\) 0.995236 2.66833i 0.0526735 0.141223i
\(358\) 0 0
\(359\) 27.5733 + 17.7203i 1.45526 + 0.935240i 0.998968 + 0.0454098i \(0.0144593\pi\)
0.456293 + 0.889830i \(0.349177\pi\)
\(360\) 0 0
\(361\) 1.03236 7.18021i 0.0543347 0.377906i
\(362\) 0 0
\(363\) 3.16802 14.5632i 0.166278 0.764368i
\(364\) 0 0
\(365\) 3.51009 6.39400i 0.183726 0.334677i
\(366\) 0 0
\(367\) −16.9996 + 16.9996i −0.887373 + 0.887373i −0.994270 0.106897i \(-0.965909\pi\)
0.106897 + 0.994270i \(0.465909\pi\)
\(368\) 0 0
\(369\) 6.70224i 0.348905i
\(370\) 0 0
\(371\) −4.42927 1.30055i −0.229956 0.0675213i
\(372\) 0 0
\(373\) 3.74434 + 0.814532i 0.193875 + 0.0421749i 0.308454 0.951239i \(-0.400188\pi\)
−0.114579 + 0.993414i \(0.536552\pi\)
\(374\) 0 0
\(375\) 11.0154 10.8677i 0.568834 0.561207i
\(376\) 0 0
\(377\) 3.61364 + 16.6116i 0.186112 + 0.855543i
\(378\) 0 0
\(379\) 3.26503 + 7.14942i 0.167713 + 0.367241i 0.974763 0.223243i \(-0.0716643\pi\)
−0.807050 + 0.590484i \(0.798937\pi\)
\(380\) 0 0
\(381\) 2.14030 + 14.8861i 0.109651 + 0.762637i
\(382\) 0 0
\(383\) −20.1566 11.0063i −1.02995 0.562398i −0.126896 0.991916i \(-0.540501\pi\)
−0.903058 + 0.429519i \(0.858683\pi\)
\(384\) 0 0
\(385\) −0.295266 + 0.219999i −0.0150482 + 0.0112122i
\(386\) 0 0
\(387\) −6.03877 0.431901i −0.306968 0.0219548i
\(388\) 0 0
\(389\) 9.91792 21.7172i 0.502859 1.10111i −0.472671 0.881239i \(-0.656710\pi\)
0.975530 0.219868i \(-0.0705626\pi\)
\(390\) 0 0
\(391\) 0.818945 28.8358i 0.0414159 1.45829i
\(392\) 0 0
\(393\) −2.48343 6.65834i −0.125273 0.335869i
\(394\) 0 0
\(395\) −15.1849 4.49582i −0.764035 0.226209i
\(396\) 0 0
\(397\) −29.9011 + 2.13857i −1.50069 + 0.107332i −0.797348 0.603519i \(-0.793765\pi\)
−0.703343 + 0.710851i \(0.748310\pi\)
\(398\) 0 0
\(399\) 0.457153 + 1.55692i 0.0228863 + 0.0779435i
\(400\) 0 0
\(401\) −18.2622 + 2.62571i −0.911971 + 0.131122i −0.582300 0.812974i \(-0.697847\pi\)
−0.329671 + 0.944096i \(0.606938\pi\)
\(402\) 0 0
\(403\) 15.6493 + 5.83690i 0.779549 + 0.290757i
\(404\) 0 0
\(405\) 10.2205 + 0.0229926i 0.507861 + 0.00114251i
\(406\) 0 0
\(407\) 1.78171 1.33377i 0.0883161 0.0661126i
\(408\) 0 0
\(409\) 3.32710 + 5.17708i 0.164515 + 0.255990i 0.913717 0.406352i \(-0.133199\pi\)
−0.749202 + 0.662341i \(0.769563\pi\)
\(410\) 0 0
\(411\) −2.85807 + 9.73371i −0.140978 + 0.480128i
\(412\) 0 0
\(413\) 1.27400 + 1.27400i 0.0626894 + 0.0626894i
\(414\) 0 0
\(415\) 16.8867 + 3.71328i 0.828936 + 0.182278i
\(416\) 0 0
\(417\) −13.4692 24.6670i −0.659590 1.20795i
\(418\) 0 0
\(419\) −16.3546 + 10.5104i −0.798973 + 0.513469i −0.875281 0.483615i \(-0.839323\pi\)
0.0763072 + 0.997084i \(0.475687\pi\)
\(420\) 0 0
\(421\) 22.8972 + 3.29212i 1.11594 + 0.160448i 0.675520 0.737342i \(-0.263919\pi\)
0.440423 + 0.897790i \(0.354829\pi\)
\(422\) 0 0
\(423\) 9.99291 2.17382i 0.485872 0.105695i
\(424\) 0 0
\(425\) −21.3621 + 21.1707i −1.03621 + 1.02693i
\(426\) 0 0
\(427\) −3.08038 + 4.11491i −0.149070 + 0.199135i
\(428\) 0 0
\(429\) 1.16275 0.341415i 0.0561382 0.0164837i
\(430\) 0 0
\(431\) −5.28791 4.58200i −0.254710 0.220707i 0.518141 0.855295i \(-0.326624\pi\)
−0.772851 + 0.634588i \(0.781170\pi\)
\(432\) 0 0
\(433\) −0.355679 + 4.97304i −0.0170928 + 0.238989i 0.981722 + 0.190320i \(0.0609525\pi\)
−0.998815 + 0.0486692i \(0.984502\pi\)
\(434\) 0 0
\(435\) 17.3863 23.1168i 0.833610 1.10837i
\(436\) 0 0
\(437\) 9.47249 + 13.4324i 0.453130 + 0.642558i
\(438\) 0 0
\(439\) −2.42656 1.10817i −0.115813 0.0528901i 0.356666 0.934232i \(-0.383913\pi\)
−0.472479 + 0.881342i \(0.656641\pi\)
\(440\) 0 0
\(441\) 4.88792 + 5.64096i 0.232758 + 0.268617i
\(442\) 0 0
\(443\) 1.09727 + 15.3419i 0.0521331 + 0.728916i 0.954550 + 0.298052i \(0.0963368\pi\)
−0.902417 + 0.430864i \(0.858209\pi\)
\(444\) 0 0
\(445\) 0.774152 0.889368i 0.0366983 0.0421601i
\(446\) 0 0
\(447\) −19.2163 14.3851i −0.908900 0.680394i
\(448\) 0 0
\(449\) 11.7182 5.35152i 0.553016 0.252554i −0.119249 0.992864i \(-0.538049\pi\)
0.672265 + 0.740311i \(0.265322\pi\)
\(450\) 0 0
\(451\) −1.60848 + 2.50284i −0.0757403 + 0.117854i
\(452\) 0 0
\(453\) −8.35759 11.1644i −0.392674 0.524551i
\(454\) 0 0
\(455\) 1.26428 + 0.580819i 0.0592705 + 0.0272292i
\(456\) 0 0
\(457\) −6.54577 + 3.57426i −0.306198 + 0.167197i −0.625000 0.780624i \(-0.714901\pi\)
0.318802 + 0.947821i \(0.396719\pi\)
\(458\) 0 0
\(459\) −34.0035 −1.58715
\(460\) 0 0
\(461\) 1.78272 0.0830295 0.0415147 0.999138i \(-0.486782\pi\)
0.0415147 + 0.999138i \(0.486782\pi\)
\(462\) 0 0
\(463\) 15.4286 8.42465i 0.717028 0.391527i −0.0789291 0.996880i \(-0.525150\pi\)
0.795957 + 0.605354i \(0.206968\pi\)
\(464\) 0 0
\(465\) −9.87139 26.6492i −0.457775 1.23583i
\(466\) 0 0
\(467\) −23.4916 31.3812i −1.08706 1.45215i −0.880702 0.473671i \(-0.842929\pi\)
−0.206362 0.978476i \(-0.566162\pi\)
\(468\) 0 0
\(469\) −1.24620 + 1.93913i −0.0575443 + 0.0895406i
\(470\) 0 0
\(471\) −17.3577 + 7.92699i −0.799800 + 0.365256i
\(472\) 0 0
\(473\) 2.15143 + 1.61054i 0.0989227 + 0.0740526i
\(474\) 0 0
\(475\) 2.51502 16.9506i 0.115397 0.777748i
\(476\) 0 0
\(477\) 1.04397 + 14.5966i 0.0478000 + 0.668331i
\(478\) 0 0
\(479\) 2.50775 + 2.89410i 0.114582 + 0.132235i 0.810143 0.586232i \(-0.199389\pi\)
−0.695561 + 0.718467i \(0.744844\pi\)
\(480\) 0 0
\(481\) −7.64970 3.49350i −0.348796 0.159290i
\(482\) 0 0
\(483\) 1.96118 + 1.14433i 0.0892367 + 0.0520688i
\(484\) 0 0
\(485\) 4.65956 + 3.50449i 0.211580 + 0.159131i
\(486\) 0 0
\(487\) 2.72669 38.1241i 0.123558 1.72757i −0.437006 0.899458i \(-0.643961\pi\)
0.560564 0.828111i \(-0.310584\pi\)
\(488\) 0 0
\(489\) 1.81470 + 1.57245i 0.0820638 + 0.0711087i
\(490\) 0 0
\(491\) −14.5271 + 4.26553i −0.655598 + 0.192501i −0.592580 0.805512i \(-0.701891\pi\)
−0.0630177 + 0.998012i \(0.520072\pi\)
\(492\) 0 0
\(493\) −33.6910 + 45.0059i −1.51737 + 2.02696i
\(494\) 0 0
\(495\) 0.980541 + 0.633277i 0.0440720 + 0.0284637i
\(496\) 0 0
\(497\) −4.59666 + 0.999942i −0.206188 + 0.0448535i
\(498\) 0 0
\(499\) −21.1033 3.03420i −0.944714 0.135829i −0.347293 0.937757i \(-0.612899\pi\)
−0.597422 + 0.801927i \(0.703808\pi\)
\(500\) 0 0
\(501\) 11.0912 7.12790i 0.495520 0.318451i
\(502\) 0 0
\(503\) 0.730270 + 1.33739i 0.0325611 + 0.0596312i 0.893453 0.449157i \(-0.148276\pi\)
−0.860892 + 0.508788i \(0.830094\pi\)
\(504\) 0 0
\(505\) 30.9993 19.8237i 1.37945 0.882142i
\(506\) 0 0
\(507\) 9.48483 + 9.48483i 0.421236 + 0.421236i
\(508\) 0 0
\(509\) 3.13431 10.6745i 0.138926 0.473138i −0.860409 0.509604i \(-0.829792\pi\)
0.999335 + 0.0364663i \(0.0116102\pi\)
\(510\) 0 0
\(511\) −0.603290 0.938738i −0.0266880 0.0415273i
\(512\) 0 0
\(513\) 15.5099 11.6105i 0.684778 0.512618i
\(514\) 0 0
\(515\) 20.0535 + 20.1440i 0.883664 + 0.887649i
\(516\) 0 0
\(517\) −4.25339 1.58643i −0.187064 0.0697712i
\(518\) 0 0
\(519\) −0.113797 + 0.0163616i −0.00499515 + 0.000718194i
\(520\) 0 0
\(521\) 1.21793 + 4.14789i 0.0533586 + 0.181723i 0.981860 0.189605i \(-0.0607208\pi\)
−0.928502 + 0.371328i \(0.878903\pi\)
\(522\) 0 0
\(523\) −14.0370 + 1.00394i −0.613793 + 0.0438994i −0.374775 0.927116i \(-0.622280\pi\)
−0.239018 + 0.971015i \(0.576826\pi\)
\(524\) 0 0
\(525\) −0.656715 2.27437i −0.0286614 0.0992616i
\(526\) 0 0
\(527\) 19.3026 + 51.7522i 0.840833 + 2.25436i
\(528\) 0 0
\(529\) 22.5434 + 4.56004i 0.980149 + 0.198263i
\(530\) 0 0
\(531\) 2.37265 5.19538i 0.102964 0.225460i
\(532\) 0 0
\(533\) 11.2131 + 0.801974i 0.485691 + 0.0347373i
\(534\) 0 0
\(535\) −16.9452 22.7426i −0.732603 0.983246i
\(536\) 0 0
\(537\) −9.16075 5.00215i −0.395315 0.215859i
\(538\) 0 0
\(539\) −0.471533 3.27958i −0.0203103 0.141262i
\(540\) 0 0
\(541\) −15.8761 34.7639i −0.682568 1.49462i −0.859899 0.510465i \(-0.829473\pi\)
0.177330 0.984151i \(-0.443254\pi\)
\(542\) 0 0
\(543\) 0.162782 + 0.748296i 0.00698564 + 0.0321125i
\(544\) 0 0
\(545\) 6.71183 + 14.7848i 0.287503 + 0.633311i
\(546\) 0 0
\(547\) 11.9966 + 2.60970i 0.512937 + 0.111583i 0.461581 0.887098i \(-0.347282\pi\)
0.0513554 + 0.998680i \(0.483646\pi\)
\(548\) 0 0
\(549\) 15.6346 + 4.59073i 0.667268 + 0.195928i
\(550\) 0 0
\(551\) 32.0322i 1.36462i
\(552\) 0 0
\(553\) −1.71312 + 1.71312i −0.0728494 + 0.0728494i
\(554\) 0 0
\(555\) 4.00036 + 13.7382i 0.169806 + 0.583155i
\(556\) 0 0
\(557\) 3.43979 15.8125i 0.145749 0.669995i −0.845054 0.534681i \(-0.820432\pi\)
0.990803 0.135315i \(-0.0432045\pi\)
\(558\) 0 0
\(559\) 1.44517 10.0514i 0.0611241 0.425127i
\(560\) 0 0
\(561\) 3.37136 + 2.16664i 0.142339 + 0.0914757i
\(562\) 0 0
\(563\) 15.8213 42.4186i 0.666789 1.78773i 0.0525413 0.998619i \(-0.483268\pi\)
0.614248 0.789113i \(-0.289459\pi\)
\(564\) 0 0
\(565\) −1.84711 + 25.0344i −0.0777086 + 1.05321i
\(566\) 0 0
\(567\) 0.749342 1.37232i 0.0314694 0.0576320i
\(568\) 0 0
\(569\) 14.6434 16.8994i 0.613883 0.708459i −0.360650 0.932701i \(-0.617445\pi\)
0.974533 + 0.224242i \(0.0719906\pi\)
\(570\) 0 0
\(571\) −3.23046 + 2.79921i −0.135190 + 0.117143i −0.719831 0.694149i \(-0.755781\pi\)
0.584641 + 0.811292i \(0.301235\pi\)
\(572\) 0 0
\(573\) 9.02808 3.36730i 0.377153 0.140671i
\(574\) 0 0
\(575\) −13.7311 19.6585i −0.572627 0.819816i
\(576\) 0 0
\(577\) 6.97385 2.60111i 0.290325 0.108286i −0.200082 0.979779i \(-0.564121\pi\)
0.490407 + 0.871493i \(0.336848\pi\)
\(578\) 0 0
\(579\) 14.6453 12.6902i 0.608638 0.527388i
\(580\) 0 0
\(581\) 1.73218 1.99904i 0.0718629 0.0829343i
\(582\) 0 0
\(583\) 3.11320 5.70139i 0.128935 0.236128i
\(584\) 0 0
\(585\) 0.324542 4.39860i 0.0134182 0.181860i
\(586\) 0 0
\(587\) 2.72897 7.31666i 0.112637 0.301991i −0.868384 0.495892i \(-0.834841\pi\)
0.981021 + 0.193901i \(0.0621140\pi\)
\(588\) 0 0
\(589\) −26.4753 17.0146i −1.09089 0.701075i
\(590\) 0 0
\(591\) 1.73576 12.0725i 0.0713995 0.496594i
\(592\) 0 0
\(593\) 0.731036 3.36052i 0.0300201 0.138000i −0.959698 0.281035i \(-0.909322\pi\)
0.989718 + 0.143035i \(0.0456860\pi\)
\(594\) 0 0
\(595\) 1.28634 + 4.41760i 0.0527346 + 0.181104i
\(596\) 0 0
\(597\) 16.9894 16.9894i 0.695330 0.695330i
\(598\) 0 0
\(599\) 9.17302i 0.374799i 0.982284 + 0.187400i \(0.0600060\pi\)
−0.982284 + 0.187400i \(0.939994\pi\)
\(600\) 0 0
\(601\) −1.24243 0.364811i −0.0506799 0.0148810i 0.256294 0.966599i \(-0.417498\pi\)
−0.306974 + 0.951718i \(0.599317\pi\)
\(602\) 0 0
\(603\) 7.14015 + 1.55324i 0.290769 + 0.0632530i
\(604\) 0 0
\(605\) 9.95331 + 21.9251i 0.404660 + 0.891382i
\(606\) 0 0
\(607\) 4.38250 + 20.1460i 0.177880 + 0.817702i 0.976440 + 0.215787i \(0.0692318\pi\)
−0.798560 + 0.601915i \(0.794405\pi\)
\(608\) 0 0
\(609\) −1.83825 4.02521i −0.0744897 0.163110i
\(610\) 0 0
\(611\) 2.44115 + 16.9786i 0.0987583 + 0.686879i
\(612\) 0 0
\(613\) 15.7353 + 8.59214i 0.635544 + 0.347033i 0.764506 0.644616i \(-0.222983\pi\)
−0.128962 + 0.991649i \(0.541165\pi\)
\(614\) 0 0
\(615\) −11.4282 15.3380i −0.460828 0.618490i
\(616\) 0 0
\(617\) −26.7290 1.91170i −1.07607 0.0769620i −0.477964 0.878379i \(-0.658625\pi\)
−0.598106 + 0.801417i \(0.704080\pi\)
\(618\) 0 0
\(619\) −7.48869 + 16.3979i −0.300996 + 0.659089i −0.998337 0.0576506i \(-0.981639\pi\)
0.697341 + 0.716740i \(0.254366\pi\)
\(620\) 0 0
\(621\) 4.61855 26.7146i 0.185336 1.07202i
\(622\) 0 0
\(623\) −0.0630377 0.169011i −0.00252555 0.00677127i
\(624\) 0 0
\(625\) −3.78040 + 24.7125i −0.151216 + 0.988501i
\(626\) 0 0
\(627\) −2.27757 + 0.162895i −0.0909573 + 0.00650539i
\(628\) 0 0
\(629\) −7.83518 26.6842i −0.312409 1.06397i
\(630\) 0 0
\(631\) −19.3844 + 2.78705i −0.771680 + 0.110951i −0.516897 0.856048i \(-0.672913\pi\)
−0.254783 + 0.966998i \(0.582004\pi\)
\(632\) 0 0
\(633\) 8.21678 + 3.06470i 0.326588 + 0.121811i
\(634\) 0 0
\(635\) −17.1421 17.2194i −0.680264 0.683332i
\(636\) 0 0
\(637\) −10.0224 + 7.50265i −0.397101 + 0.297266i
\(638\) 0 0
\(639\) 8.06230 + 12.5452i 0.318940 + 0.496280i
\(640\) 0 0
\(641\) −6.91160 + 23.5387i −0.272992 + 0.929724i 0.702867 + 0.711321i \(0.251903\pi\)
−0.975859 + 0.218403i \(0.929915\pi\)
\(642\) 0 0
\(643\) −22.6055 22.6055i −0.891474 0.891474i 0.103188 0.994662i \(-0.467096\pi\)
−0.994662 + 0.103188i \(0.967096\pi\)
\(644\) 0 0
\(645\) −14.5561 + 9.30845i −0.573147 + 0.366520i
\(646\) 0 0
\(647\) 17.2300 + 31.5544i 0.677381 + 1.24053i 0.959651 + 0.281195i \(0.0907309\pi\)
−0.282270 + 0.959335i \(0.591087\pi\)
\(648\) 0 0
\(649\) −2.13288 + 1.37072i −0.0837227 + 0.0538053i
\(650\) 0 0
\(651\) −4.30335 0.618728i −0.168661 0.0242499i
\(652\) 0 0
\(653\) 6.38617 1.38923i 0.249910 0.0543646i −0.0858650 0.996307i \(-0.527365\pi\)
0.335775 + 0.941942i \(0.391002\pi\)
\(654\) 0 0
\(655\) 9.64456 + 6.22888i 0.376844 + 0.243383i
\(656\) 0 0
\(657\) −2.11989 + 2.83184i −0.0827048 + 0.110481i
\(658\) 0 0
\(659\) 42.0499 12.3470i 1.63803 0.480970i 0.672250 0.740324i \(-0.265328\pi\)
0.965782 + 0.259355i \(0.0835099\pi\)
\(660\) 0 0
\(661\) 3.70631 + 3.21154i 0.144159 + 0.124914i 0.723955 0.689847i \(-0.242322\pi\)
−0.579796 + 0.814762i \(0.696868\pi\)
\(662\) 0 0
\(663\) 1.08027 15.1041i 0.0419541 0.586596i
\(664\) 0 0
\(665\) −2.09513 1.57576i −0.0812455 0.0611053i
\(666\) 0 0
\(667\) −30.7825 32.5821i −1.19190 1.26158i
\(668\) 0 0
\(669\) 17.6925 + 8.07989i 0.684031 + 0.312387i
\(670\) 0 0
\(671\) −4.73675 5.46650i −0.182860 0.211032i
\(672\) 0 0
\(673\) −1.74162 24.3510i −0.0671344 0.938661i −0.913703 0.406382i \(-0.866790\pi\)
0.846569 0.532279i \(-0.178664\pi\)
\(674\) 0 0
\(675\) −22.7034 + 16.8367i −0.873853 + 0.648044i
\(676\) 0 0
\(677\) −16.3048 12.2056i −0.626646 0.469101i 0.238148 0.971229i \(-0.423460\pi\)
−0.864793 + 0.502128i \(0.832551\pi\)
\(678\) 0 0
\(679\) 0.811345 0.370529i 0.0311366 0.0142196i
\(680\) 0 0
\(681\) −6.16581 + 9.59419i −0.236275 + 0.367650i
\(682\) 0 0
\(683\) 3.17237 + 4.23779i 0.121387 + 0.162155i 0.857119 0.515119i \(-0.172252\pi\)
−0.735731 + 0.677274i \(0.763161\pi\)
\(684\) 0 0
\(685\) −5.69306 15.3692i −0.217521 0.587227i
\(686\) 0 0
\(687\) −15.7071 + 8.57672i −0.599263 + 0.327222i
\(688\) 0 0
\(689\) −24.5454 −0.935106
\(690\) 0 0
\(691\) −19.3261 −0.735198 −0.367599 0.929984i \(-0.619820\pi\)
−0.367599 + 0.929984i \(0.619820\pi\)
\(692\) 0 0
\(693\) 0.156729 0.0855805i 0.00595364 0.00325094i
\(694\) 0 0
\(695\) 41.2605 + 18.9553i 1.56510 + 0.719016i
\(696\) 0 0
\(697\) 22.2789 + 29.7611i 0.843872 + 1.12728i
\(698\) 0 0
\(699\) −0.895845 + 1.39396i −0.0338840 + 0.0527245i
\(700\) 0 0
\(701\) −9.11833 + 4.16420i −0.344395 + 0.157280i −0.580101 0.814545i \(-0.696987\pi\)
0.235706 + 0.971824i \(0.424260\pi\)
\(702\) 0 0
\(703\) 12.6852 + 9.49600i 0.478430 + 0.358148i
\(704\) 0 0
\(705\) 19.1621 22.0140i 0.721686 0.829094i
\(706\) 0 0
\(707\) −0.401581 5.61483i −0.0151030 0.211167i
\(708\) 0 0
\(709\) −9.38474 10.8306i −0.352451 0.406750i 0.551645 0.834079i \(-0.314000\pi\)
−0.904096 + 0.427328i \(0.859455\pi\)
\(710\) 0 0
\(711\) 6.98614 + 3.19046i 0.262001 + 0.119652i
\(712\) 0 0
\(713\) −43.2805 + 8.13566i −1.62087 + 0.304683i
\(714\) 0 0
\(715\) −1.17682 + 1.56470i −0.0440106 + 0.0585164i
\(716\) 0 0
\(717\) −1.21846 + 17.0363i −0.0455041 + 0.636231i
\(718\) 0 0
\(719\) 16.3929 + 14.2045i 0.611352 + 0.529739i 0.904580 0.426303i \(-0.140184\pi\)
−0.293229 + 0.956042i \(0.594730\pi\)
\(720\) 0 0
\(721\) 4.17227 1.22509i 0.155383 0.0456247i
\(722\) 0 0
\(723\) −10.5387 + 14.0780i −0.391938 + 0.523568i
\(724\) 0 0
\(725\) −0.210259 + 46.7313i −0.00780884 + 1.73556i
\(726\) 0 0
\(727\) 12.1405 2.64100i 0.450266 0.0979494i 0.0182865 0.999833i \(-0.494179\pi\)
0.431980 + 0.901883i \(0.357815\pi\)
\(728\) 0 0
\(729\) −28.1394 4.04583i −1.04220 0.149846i
\(730\) 0 0
\(731\) 28.2506 18.1556i 1.04489 0.671508i
\(732\) 0 0
\(733\) 6.90727 + 12.6497i 0.255126 + 0.467228i 0.973580 0.228346i \(-0.0733318\pi\)
−0.718454 + 0.695574i \(0.755150\pi\)
\(734\) 0 0
\(735\) 20.8045 + 4.57479i 0.767386 + 0.168744i
\(736\) 0 0
\(737\) −2.29361 2.29361i −0.0844861 0.0844861i
\(738\) 0 0
\(739\) −9.19622 + 31.3194i −0.338288 + 1.15210i 0.598183 + 0.801360i \(0.295890\pi\)
−0.936471 + 0.350745i \(0.885929\pi\)
\(740\) 0 0
\(741\) 4.66459 + 7.25824i 0.171358 + 0.266638i
\(742\) 0 0
\(743\) 25.8905 19.3814i 0.949832 0.711035i −0.00751631 0.999972i \(-0.502393\pi\)
0.957348 + 0.288936i \(0.0933016\pi\)
\(744\) 0 0
\(745\) 38.7811 + 0.0872439i 1.42083 + 0.00319637i
\(746\) 0 0
\(747\) −7.85649 2.93032i −0.287454 0.107215i
\(748\) 0 0
\(749\) −4.29465 + 0.617478i −0.156923 + 0.0225622i
\(750\) 0 0
\(751\) −7.87817 26.8306i −0.287479 0.979062i −0.968958 0.247225i \(-0.920481\pi\)
0.681480 0.731837i \(-0.261337\pi\)
\(752\) 0 0
\(753\) −33.6099 + 2.40382i −1.22481 + 0.0876002i
\(754\) 0 0
\(755\) 21.6044 + 6.39645i 0.786264 + 0.232790i
\(756\) 0 0
\(757\) 8.74260 + 23.4398i 0.317755 + 0.851935i 0.993399 + 0.114707i \(0.0365929\pi\)
−0.675644 + 0.737228i \(0.736134\pi\)
\(758\) 0 0
\(759\) −2.16012 + 2.35440i −0.0784075 + 0.0854593i
\(760\) 0 0
\(761\) 14.0409 30.7452i 0.508981 1.11451i −0.464464 0.885592i \(-0.653753\pi\)
0.973445 0.228921i \(-0.0735198\pi\)
\(762\) 0 0
\(763\) 2.47766 + 0.177206i 0.0896974 + 0.00641528i
\(764\) 0 0
\(765\) 11.6961 8.71458i 0.422872 0.315076i
\(766\) 0 0
\(767\) 8.40813 + 4.59119i 0.303600 + 0.165778i
\(768\) 0 0
\(769\) 3.25665 + 22.6505i 0.117438 + 0.816798i 0.960360 + 0.278762i \(0.0899242\pi\)
−0.842922 + 0.538035i \(0.819167\pi\)
\(770\) 0 0
\(771\) −0.423713 0.927802i −0.0152597 0.0334140i
\(772\) 0 0
\(773\) −3.13807 14.4255i −0.112868 0.518848i −0.998514 0.0544868i \(-0.982648\pi\)
0.885646 0.464361i \(-0.153716\pi\)
\(774\) 0 0
\(775\) 38.5127 + 24.9962i 1.38342 + 0.897889i
\(776\) 0 0
\(777\) 2.13899 + 0.465309i 0.0767358 + 0.0166929i
\(778\) 0 0
\(779\) −20.3239 5.96764i −0.728180 0.213813i
\(780\) 0 0
\(781\) 6.61968i 0.236871i
\(782\) 0 0
\(783\) −37.3601 + 37.3601i −1.33514 + 1.33514i
\(784\) 0 0
\(785\) 14.8357 27.0248i 0.529507 0.964555i
\(786\) 0 0
\(787\) 0.460569 2.11720i 0.0164175 0.0754702i −0.968209 0.250142i \(-0.919523\pi\)
0.984627 + 0.174672i \(0.0558864\pi\)
\(788\) 0 0
\(789\) −3.60764 + 25.0917i −0.128435 + 0.893287i
\(790\) 0 0
\(791\) 3.23064 + 2.07621i 0.114868 + 0.0738214i
\(792\) 0 0
\(793\) −9.55123 + 25.6078i −0.339174 + 0.909361i
\(794\) 0 0
\(795\) 27.2781 + 31.6241i 0.967454 + 1.12159i
\(796\) 0 0
\(797\) 17.0460 31.2174i 0.603800 1.10578i −0.379741 0.925093i \(-0.623987\pi\)
0.983541 0.180684i \(-0.0578311\pi\)
\(798\) 0 0
\(799\) −37.1472 + 42.8701i −1.31417 + 1.51664i
\(800\) 0 0
\(801\) −0.432159 + 0.374468i −0.0152696 + 0.0132312i
\(802\) 0 0
\(803\) 1.47126 0.548750i 0.0519195 0.0193650i
\(804\) 0 0
\(805\) −3.64537 + 0.410578i −0.128483 + 0.0144710i
\(806\) 0 0
\(807\) −21.0546 + 7.85296i −0.741157 + 0.276437i
\(808\) 0 0
\(809\) 8.63341 7.48089i 0.303535 0.263014i −0.489753 0.871861i \(-0.662913\pi\)
0.793288 + 0.608847i \(0.208368\pi\)
\(810\) 0 0
\(811\) 5.12440 5.91387i 0.179942 0.207664i −0.658612 0.752483i \(-0.728856\pi\)
0.838554 + 0.544819i \(0.183402\pi\)
\(812\) 0 0
\(813\) −2.01312 + 3.68675i −0.0706031 + 0.129300i
\(814\) 0 0
\(815\) −3.86887 0.285457i −0.135521 0.00999911i
\(816\) 0 0
\(817\) −6.68659 + 17.9274i −0.233934 + 0.627202i
\(818\) 0 0
\(819\) −0.567631 0.364794i −0.0198346 0.0127469i
\(820\) 0 0
\(821\) 5.49638 38.2282i 0.191825 1.33417i −0.635349 0.772225i \(-0.719144\pi\)
0.827174 0.561946i \(-0.189947\pi\)
\(822\) 0 0
\(823\) −3.81542 + 17.5392i −0.132997 + 0.611377i 0.861602 + 0.507585i \(0.169462\pi\)
−0.994599 + 0.103793i \(0.966902\pi\)
\(824\) 0 0
\(825\) 3.32378 0.222695i 0.115719 0.00775325i
\(826\) 0 0
\(827\) −21.8354 + 21.8354i −0.759291 + 0.759291i −0.976193 0.216902i \(-0.930405\pi\)
0.216902 + 0.976193i \(0.430405\pi\)
\(828\) 0 0
\(829\) 37.2747i 1.29460i −0.762234 0.647302i \(-0.775897\pi\)
0.762234 0.647302i \(-0.224103\pi\)
\(830\) 0 0
\(831\) −20.7942 6.10574i −0.721344 0.211806i
\(832\) 0 0
\(833\) −40.4557 8.80060i −1.40171 0.304923i
\(834\) 0 0
\(835\) −7.48861 + 19.9406i −0.259154 + 0.690074i
\(836\) 0 0
\(837\) 11.0342 + 50.7235i 0.381399 + 1.75326i
\(838\) 0 0
\(839\) 3.22273 + 7.05680i 0.111261 + 0.243628i 0.957069 0.289859i \(-0.0936085\pi\)
−0.845808 + 0.533487i \(0.820881\pi\)
\(840\) 0 0
\(841\) 8.30471 + 57.7605i 0.286369 + 1.99174i
\(842\) 0 0
\(843\) −5.41939 2.95921i −0.186654 0.101921i
\(844\) 0 0
\(845\) −21.4435 3.13236i −0.737677 0.107756i
\(846\) 0 0
\(847\) 3.67425 + 0.262788i 0.126249 + 0.00902949i
\(848\) 0 0
\(849\) −1.23217 + 2.69807i −0.0422878 + 0.0925974i
\(850\) 0 0
\(851\) 22.0284 2.53126i 0.755126 0.0867706i
\(852\) 0 0
\(853\) −3.59897 9.64922i −0.123226 0.330383i 0.860659 0.509181i \(-0.170052\pi\)
−0.983886 + 0.178798i \(0.942779\pi\)
\(854\) 0 0
\(855\) −2.35927 + 7.96858i −0.0806854 + 0.272520i
\(856\) 0 0
\(857\) −34.4775 + 2.46588i −1.17773 + 0.0842329i −0.646445 0.762961i \(-0.723745\pi\)
−0.531284 + 0.847193i \(0.678290\pi\)
\(858\) 0 0
\(859\) 5.50305 + 18.7417i 0.187762 + 0.639458i 0.998536 + 0.0540983i \(0.0172284\pi\)
−0.810774 + 0.585360i \(0.800953\pi\)
\(860\) 0 0
\(861\) −2.89640 + 0.416440i −0.0987091 + 0.0141922i
\(862\) 0 0
\(863\) −0.968710 0.361310i −0.0329753 0.0122991i 0.332922 0.942954i \(-0.391965\pi\)
−0.365898 + 0.930655i \(0.619238\pi\)
\(864\) 0 0
\(865\) 0.131635 0.131044i 0.00447571 0.00445562i
\(866\) 0 0
\(867\) 21.2528 15.9096i 0.721783 0.540320i
\(868\) 0 0
\(869\) −1.84318 2.86804i −0.0625255 0.0972916i
\(870\) 0 0
\(871\) −3.45300 + 11.7598i −0.117000 + 0.398467i
\(872\) 0 0
\(873\) −1.99937 1.99937i −0.0676683 0.0676683i
\(874\) 0 0
\(875\) 3.04621 + 2.31261i 0.102981 + 0.0781803i
\(876\) 0 0
\(877\) 15.6553 + 28.6705i 0.528641 + 0.968134i 0.996440 + 0.0842994i \(0.0268652\pi\)
−0.467799 + 0.883835i \(0.654953\pi\)
\(878\) 0 0
\(879\) −15.8690 + 10.1984i −0.535247 + 0.343982i
\(880\) 0 0
\(881\) 16.4824 + 2.36981i 0.555306 + 0.0798410i 0.414254 0.910161i \(-0.364042\pi\)
0.141052 + 0.990002i \(0.454952\pi\)
\(882\) 0 0
\(883\) 25.8688 5.62741i 0.870554 0.189377i 0.244967 0.969532i \(-0.421223\pi\)
0.625587 + 0.780154i \(0.284859\pi\)
\(884\) 0 0
\(885\) −3.42898 15.9353i −0.115264 0.535659i
\(886\) 0 0
\(887\) 1.42395 1.90218i 0.0478116 0.0638688i −0.775998 0.630735i \(-0.782753\pi\)
0.823810 + 0.566866i \(0.191844\pi\)
\(888\) 0 0
\(889\) −3.56653 + 1.04723i −0.119618 + 0.0351229i
\(890\) 0 0
\(891\) 1.66284 + 1.44086i 0.0557074 + 0.0482707i
\(892\) 0 0
\(893\) 2.30572 32.2381i 0.0771579 1.07881i
\(894\) 0 0
\(895\) 16.6965 2.36227i 0.558104 0.0789621i
\(896\) 0 0
\(897\) 11.7197 + 2.90023i 0.391310 + 0.0968359i
\(898\) 0 0
\(899\) 78.0688 + 35.6528i 2.60374 + 1.18909i
\(900\) 0 0
\(901\) −53.1560 61.3453i −1.77088 2.04371i
\(902\) 0 0
\(903\) 0.188567 + 2.63651i 0.00627513 + 0.0877377i
\(904\) 0 0
\(905\) −0.933207 0.812312i −0.0310209 0.0270022i
\(906\) 0 0
\(907\) 11.1744 + 8.36505i 0.371040 + 0.277757i 0.768483 0.639870i \(-0.221012\pi\)
−0.397444 + 0.917627i \(0.630103\pi\)
\(908\) 0 0
\(909\) −16.2322 + 7.41301i −0.538389 + 0.245874i
\(910\) 0 0
\(911\) −4.12898 + 6.42481i −0.136799 + 0.212864i −0.902893 0.429865i \(-0.858561\pi\)
0.766094 + 0.642728i \(0.222198\pi\)
\(912\) 0 0
\(913\) 2.23063 + 2.97977i 0.0738230 + 0.0986159i
\(914\) 0 0
\(915\) 43.6075 16.1531i 1.44162 0.534005i
\(916\) 0 0
\(917\) 1.54158 0.841766i 0.0509074 0.0277976i
\(918\) 0 0
\(919\) 19.5874 0.646130 0.323065 0.946377i \(-0.395287\pi\)
0.323065 + 0.946377i \(0.395287\pi\)
\(920\) 0 0
\(921\) 45.2129 1.48981
\(922\) 0 0
\(923\) −21.9532 + 11.9874i −0.722599 + 0.394569i
\(924\) 0 0
\(925\) −18.4439 13.9368i −0.606431 0.458241i
\(926\) 0 0
\(927\) −8.26088 11.0352i −0.271323 0.362445i
\(928\) 0 0
\(929\) −17.0422 + 26.5181i −0.559135 + 0.870031i −0.999615 0.0277309i \(-0.991172\pi\)
0.440480 + 0.897762i \(0.354808\pi\)
\(930\) 0 0
\(931\) 21.4579 9.79947i 0.703253 0.321165i
\(932\) 0 0
\(933\) −38.1983 28.5949i −1.25056 0.936154i
\(934\) 0 0
\(935\) −6.45913 + 0.447363i −0.211236 + 0.0146303i
\(936\) 0 0
\(937\) −1.28410 17.9541i −0.0419498 0.586535i −0.974340 0.225081i \(-0.927735\pi\)
0.932390 0.361453i \(-0.117719\pi\)
\(938\) 0 0
\(939\) 1.71244 + 1.97626i 0.0558833 + 0.0644928i
\(940\) 0 0
\(941\) 45.7808 + 20.9074i 1.49241 + 0.681562i 0.983773 0.179418i \(-0.0574214\pi\)
0.508639 + 0.860980i \(0.330149\pi\)
\(942\) 0 0
\(943\) −26.4076 + 13.4609i −0.859951 + 0.438348i
\(944\) 0 0
\(945\) 0.605754 + 4.28146i 0.0197052 + 0.139276i
\(946\) 0 0
\(947\) −3.01599 + 42.1691i −0.0980065 + 1.37031i 0.675892 + 0.737001i \(0.263759\pi\)
−0.773898 + 0.633310i \(0.781696\pi\)
\(948\) 0 0
\(949\) −4.48410 3.88549i −0.145560 0.126128i
\(950\) 0 0
\(951\) −40.2967 + 11.8322i −1.30671 + 0.383685i
\(952\) 0 0
\(953\) −5.45650 + 7.28903i −0.176753 + 0.236115i −0.880165 0.474668i \(-0.842568\pi\)
0.703412 + 0.710783i \(0.251659\pi\)
\(954\) 0 0
\(955\) −8.44577 + 13.0771i −0.273299 + 0.423165i
\(956\) 0 0
\(957\) 6.08467 1.32364i 0.196690 0.0427872i
\(958\) 0 0
\(959\) −2.48184 0.356835i −0.0801428 0.0115228i
\(960\) 0 0
\(961\) 44.8569 28.8278i 1.44700 0.929928i
\(962\) 0 0
\(963\) 6.59174 + 12.0719i 0.212416 + 0.389011i
\(964\) 0 0
\(965\) −6.72380 + 30.5775i −0.216447 + 0.984324i
\(966\) 0 0
\(967\) 38.9774 + 38.9774i 1.25343 + 1.25343i 0.954174 + 0.299254i \(0.0967376\pi\)
0.299254 + 0.954174i \(0.403262\pi\)
\(968\) 0 0
\(969\) −8.03849 + 27.3766i −0.258233 + 0.879462i
\(970\) 0 0
\(971\) −26.1330 40.6638i −0.838649 1.30496i −0.950338 0.311219i \(-0.899263\pi\)
0.111689 0.993743i \(-0.464374\pi\)
\(972\) 0 0
\(973\) 5.56090 4.16284i 0.178274 0.133454i
\(974\) 0 0
\(975\) −6.75746 10.6196i −0.216412 0.340098i
\(976\) 0 0
\(977\) −8.30510 3.09764i −0.265704 0.0991023i 0.213082 0.977034i \(-0.431650\pi\)
−0.478785 + 0.877932i \(0.658923\pi\)
\(978\) 0 0
\(979\) 0.251252 0.0361245i 0.00803004 0.00115455i
\(980\) 0 0
\(981\) −2.21848 7.55544i −0.0708305 0.241227i
\(982\) 0 0
\(983\) 39.1545 2.80039i 1.24883 0.0893184i 0.568786 0.822486i \(-0.307413\pi\)
0.680049 + 0.733167i \(0.261959\pi\)
\(984\) 0 0
\(985\) 9.40461 + 17.3158i 0.299656 + 0.551726i
\(986\) 0 0
\(987\) −1.56033 4.18341i −0.0496659 0.133159i
\(988\) 0 0
\(989\) 10.4266 + 24.6609i 0.331548 + 0.784171i
\(990\) 0 0
\(991\) 16.1771 35.4229i 0.513883 1.12525i −0.457821 0.889044i \(-0.651370\pi\)
0.971704 0.236202i \(-0.0759028\pi\)
\(992\) 0 0
\(993\) 18.1888 + 1.30089i 0.577203 + 0.0412824i
\(994\) 0 0
\(995\) −5.61074 + 38.4099i −0.177872 + 1.21768i
\(996\) 0 0
\(997\) 29.1410 + 15.9122i 0.922905 + 0.503944i 0.869116 0.494608i \(-0.164688\pi\)
0.0537891 + 0.998552i \(0.482870\pi\)
\(998\) 0 0
\(999\) −3.71963 25.8706i −0.117684 0.818508i
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 920.2.bv.a.17.12 720
5.3 odd 4 inner 920.2.bv.a.753.12 yes 720
23.19 odd 22 inner 920.2.bv.a.617.12 yes 720
115.88 even 44 inner 920.2.bv.a.433.12 yes 720
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.bv.a.17.12 720 1.1 even 1 trivial
920.2.bv.a.433.12 yes 720 115.88 even 44 inner
920.2.bv.a.617.12 yes 720 23.19 odd 22 inner
920.2.bv.a.753.12 yes 720 5.3 odd 4 inner