Properties

Label 460.2.x.a.337.1
Level $460$
Weight $2$
Character 460.337
Analytic conductor $3.673$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(17,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([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("460.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.x (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: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(12\) over \(\Q(\zeta_{44})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label 337.1
Character \(\chi\) \(=\) 460.337
Dual form 460.2.x.a.273.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.04222 - 1.13469i) q^{3} +(2.23290 + 0.118951i) q^{5} +(-1.19659 + 0.260302i) q^{7} +(5.70035 + 4.93938i) q^{9} +O(q^{10})\) \(q+(-3.04222 - 1.13469i) q^{3} +(2.23290 + 0.118951i) q^{5} +(-1.19659 + 0.260302i) q^{7} +(5.70035 + 4.93938i) q^{9} +(0.536277 - 0.0771049i) q^{11} +(0.502683 - 2.31080i) q^{13} +(-6.65801 - 2.89553i) q^{15} +(-0.786784 + 1.44089i) q^{17} +(2.75454 + 0.808805i) q^{19} +(3.93565 + 0.565862i) q^{21} +(2.33216 - 4.19059i) q^{23} +(4.97170 + 0.531212i) q^{25} +(-7.06879 - 12.9455i) q^{27} +(-2.81361 - 9.58226i) q^{29} +(3.27302 - 7.16691i) q^{31} +(-1.71896 - 0.373938i) q^{33} +(-2.70283 + 0.438893i) q^{35} +(-0.814884 - 11.3936i) q^{37} +(-4.15131 + 6.45957i) q^{39} +(3.13912 + 3.62274i) q^{41} +(-0.300335 + 0.805229i) q^{43} +(12.1408 + 11.7072i) q^{45} +(3.65709 + 3.65709i) q^{47} +(-5.00335 + 2.28496i) q^{49} +(4.02854 - 3.49075i) q^{51} +(0.621826 + 2.85849i) q^{53} +(1.20662 - 0.108377i) q^{55} +(-7.46217 - 5.58611i) q^{57} +(3.16138 + 4.91920i) q^{59} +(6.42922 + 2.93613i) q^{61} +(-8.10671 - 4.42660i) q^{63} +(1.39731 - 5.09999i) q^{65} +(5.11047 + 6.82679i) q^{67} +(-11.8500 + 10.1024i) q^{69} +(1.26801 - 8.81920i) q^{71} +(1.23424 - 0.673947i) q^{73} +(-14.5223 - 7.25741i) q^{75} +(-0.621632 + 0.231857i) q^{77} +(-10.9404 + 7.03094i) q^{79} +(3.59538 + 25.0064i) q^{81} +(12.7562 - 0.912343i) q^{83} +(-1.92821 + 3.12377i) q^{85} +(-2.31328 + 32.3439i) q^{87} +(-1.53890 - 3.36972i) q^{89} +2.89592i q^{91} +(-18.0895 + 18.0895i) q^{93} +(6.05440 + 2.13364i) q^{95} +(-3.65804 - 0.261628i) q^{97} +(3.43782 + 2.20935i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q + 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{22}\right)\)

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
\(3\) −3.04222 1.13469i −1.75643 0.655114i −0.999999 0.00103813i \(-0.999670\pi\)
−0.756429 0.654076i \(-0.773058\pi\)
\(4\) 0 0
\(5\) 2.23290 + 0.118951i 0.998584 + 0.0531965i
\(6\) 0 0
\(7\) −1.19659 + 0.260302i −0.452268 + 0.0983849i −0.432929 0.901428i \(-0.642520\pi\)
−0.0193393 + 0.999813i \(0.506156\pi\)
\(8\) 0 0
\(9\) 5.70035 + 4.93938i 1.90012 + 1.64646i
\(10\) 0 0
\(11\) 0.536277 0.0771049i 0.161694 0.0232480i −0.0609926 0.998138i \(-0.519427\pi\)
0.222686 + 0.974890i \(0.428518\pi\)
\(12\) 0 0
\(13\) 0.502683 2.31080i 0.139419 0.640900i −0.853398 0.521260i \(-0.825462\pi\)
0.992817 0.119640i \(-0.0381741\pi\)
\(14\) 0 0
\(15\) −6.65801 2.89553i −1.71909 0.747622i
\(16\) 0 0
\(17\) −0.786784 + 1.44089i −0.190823 + 0.349467i −0.955521 0.294922i \(-0.904706\pi\)
0.764698 + 0.644389i \(0.222888\pi\)
\(18\) 0 0
\(19\) 2.75454 + 0.808805i 0.631934 + 0.185553i 0.581985 0.813199i \(-0.302276\pi\)
0.0499485 + 0.998752i \(0.484094\pi\)
\(20\) 0 0
\(21\) 3.93565 + 0.565862i 0.858830 + 0.123481i
\(22\) 0 0
\(23\) 2.33216 4.19059i 0.486289 0.873798i
\(24\) 0 0
\(25\) 4.97170 + 0.531212i 0.994340 + 0.106242i
\(26\) 0 0
\(27\) −7.06879 12.9455i −1.36039 2.49137i
\(28\) 0 0
\(29\) −2.81361 9.58226i −0.522473 1.77938i −0.620510 0.784198i \(-0.713074\pi\)
0.0980369 0.995183i \(-0.468744\pi\)
\(30\) 0 0
\(31\) 3.27302 7.16691i 0.587852 1.28722i −0.348880 0.937167i \(-0.613438\pi\)
0.936732 0.350048i \(-0.113835\pi\)
\(32\) 0 0
\(33\) −1.71896 0.373938i −0.299233 0.0650942i
\(34\) 0 0
\(35\) −2.70283 + 0.438893i −0.456862 + 0.0741865i
\(36\) 0 0
\(37\) −0.814884 11.3936i −0.133966 1.87309i −0.410195 0.911998i \(-0.634539\pi\)
0.276229 0.961092i \(-0.410915\pi\)
\(38\) 0 0
\(39\) −4.15131 + 6.45957i −0.664742 + 1.03436i
\(40\) 0 0
\(41\) 3.13912 + 3.62274i 0.490248 + 0.565777i 0.945932 0.324365i \(-0.105151\pi\)
−0.455684 + 0.890142i \(0.650605\pi\)
\(42\) 0 0
\(43\) −0.300335 + 0.805229i −0.0458006 + 0.122796i −0.957836 0.287315i \(-0.907237\pi\)
0.912036 + 0.410111i \(0.134510\pi\)
\(44\) 0 0
\(45\) 12.1408 + 11.7072i 1.80984 + 1.74521i
\(46\) 0 0
\(47\) 3.65709 + 3.65709i 0.533442 + 0.533442i 0.921595 0.388153i \(-0.126887\pi\)
−0.388153 + 0.921595i \(0.626887\pi\)
\(48\) 0 0
\(49\) −5.00335 + 2.28496i −0.714765 + 0.326422i
\(50\) 0 0
\(51\) 4.02854 3.49075i 0.564108 0.488802i
\(52\) 0 0
\(53\) 0.621826 + 2.85849i 0.0854144 + 0.392643i 0.999929 0.0119092i \(-0.00379089\pi\)
−0.914515 + 0.404553i \(0.867427\pi\)
\(54\) 0 0
\(55\) 1.20662 0.108377i 0.162701 0.0146136i
\(56\) 0 0
\(57\) −7.46217 5.58611i −0.988389 0.739898i
\(58\) 0 0
\(59\) 3.16138 + 4.91920i 0.411576 + 0.640425i 0.983716 0.179731i \(-0.0575227\pi\)
−0.572139 + 0.820156i \(0.693886\pi\)
\(60\) 0 0
\(61\) 6.42922 + 2.93613i 0.823177 + 0.375932i 0.782046 0.623221i \(-0.214176\pi\)
0.0411317 + 0.999154i \(0.486904\pi\)
\(62\) 0 0
\(63\) −8.10671 4.42660i −1.02135 0.557699i
\(64\) 0 0
\(65\) 1.39731 5.09999i 0.173315 0.632576i
\(66\) 0 0
\(67\) 5.11047 + 6.82679i 0.624343 + 0.834025i 0.995521 0.0945369i \(-0.0301370\pi\)
−0.371178 + 0.928562i \(0.621046\pi\)
\(68\) 0 0
\(69\) −11.8500 + 10.1024i −1.42657 + 1.21619i
\(70\) 0 0
\(71\) 1.26801 8.81920i 0.150485 1.04665i −0.764924 0.644121i \(-0.777223\pi\)
0.915409 0.402525i \(-0.131867\pi\)
\(72\) 0 0
\(73\) 1.23424 0.673947i 0.144457 0.0788796i −0.405395 0.914142i \(-0.632866\pi\)
0.549852 + 0.835262i \(0.314684\pi\)
\(74\) 0 0
\(75\) −14.5223 7.25741i −1.67689 0.838013i
\(76\) 0 0
\(77\) −0.621632 + 0.231857i −0.0708416 + 0.0264225i
\(78\) 0 0
\(79\) −10.9404 + 7.03094i −1.23089 + 0.791043i −0.984029 0.178009i \(-0.943034\pi\)
−0.246857 + 0.969052i \(0.579398\pi\)
\(80\) 0 0
\(81\) 3.59538 + 25.0064i 0.399487 + 2.77849i
\(82\) 0 0
\(83\) 12.7562 0.912343i 1.40018 0.100143i 0.649274 0.760555i \(-0.275073\pi\)
0.750903 + 0.660412i \(0.229618\pi\)
\(84\) 0 0
\(85\) −1.92821 + 3.12377i −0.209143 + 0.338821i
\(86\) 0 0
\(87\) −2.31328 + 32.3439i −0.248010 + 3.46764i
\(88\) 0 0
\(89\) −1.53890 3.36972i −0.163123 0.357189i 0.810366 0.585924i \(-0.199268\pi\)
−0.973489 + 0.228735i \(0.926541\pi\)
\(90\) 0 0
\(91\) 2.89592i 0.303575i
\(92\) 0 0
\(93\) −18.0895 + 18.0895i −1.87579 + 1.87579i
\(94\) 0 0
\(95\) 6.05440 + 2.13364i 0.621168 + 0.218906i
\(96\) 0 0
\(97\) −3.65804 0.261628i −0.371418 0.0265643i −0.115617 0.993294i \(-0.536885\pi\)
−0.255801 + 0.966730i \(0.582339\pi\)
\(98\) 0 0
\(99\) 3.43782 + 2.20935i 0.345514 + 0.222048i
\(100\) 0 0
\(101\) 8.97673 10.3597i 0.893219 1.03083i −0.106116 0.994354i \(-0.533842\pi\)
0.999335 0.0364754i \(-0.0116130\pi\)
\(102\) 0 0
\(103\) −5.30140 + 7.08185i −0.522363 + 0.697795i −0.981693 0.190471i \(-0.938999\pi\)
0.459330 + 0.888266i \(0.348090\pi\)
\(104\) 0 0
\(105\) 8.72062 + 1.73166i 0.851045 + 0.168993i
\(106\) 0 0
\(107\) −6.29832 16.8864i −0.608881 1.63247i −0.764475 0.644653i \(-0.777002\pi\)
0.155594 0.987821i \(-0.450271\pi\)
\(108\) 0 0
\(109\) 4.21350 1.23720i 0.403580 0.118502i −0.0736414 0.997285i \(-0.523462\pi\)
0.477222 + 0.878783i \(0.341644\pi\)
\(110\) 0 0
\(111\) −10.4491 + 35.5864i −0.991786 + 3.37771i
\(112\) 0 0
\(113\) 0.0708662 0.0530498i 0.00666653 0.00499050i −0.595939 0.803030i \(-0.703220\pi\)
0.602606 + 0.798039i \(0.294129\pi\)
\(114\) 0 0
\(115\) 5.70596 9.07976i 0.532083 0.846692i
\(116\) 0 0
\(117\) 14.2794 10.6894i 1.32013 0.988236i
\(118\) 0 0
\(119\) 0.566392 1.92895i 0.0519210 0.176827i
\(120\) 0 0
\(121\) −10.2728 + 3.01636i −0.933889 + 0.274214i
\(122\) 0 0
\(123\) −5.43922 14.5831i −0.490438 1.31491i
\(124\) 0 0
\(125\) 11.0381 + 1.77753i 0.987281 + 0.158987i
\(126\) 0 0
\(127\) −2.44681 + 3.26856i −0.217119 + 0.290038i −0.895856 0.444344i \(-0.853437\pi\)
0.678737 + 0.734382i \(0.262528\pi\)
\(128\) 0 0
\(129\) 1.82737 2.10890i 0.160891 0.185678i
\(130\) 0 0
\(131\) 13.6420 + 8.76715i 1.19190 + 0.765990i 0.977537 0.210764i \(-0.0675950\pi\)
0.214366 + 0.976753i \(0.431231\pi\)
\(132\) 0 0
\(133\) −3.50658 0.250796i −0.304059 0.0217467i
\(134\) 0 0
\(135\) −14.2440 29.7469i −1.22593 2.56021i
\(136\) 0 0
\(137\) −9.70149 + 9.70149i −0.828854 + 0.828854i −0.987358 0.158504i \(-0.949333\pi\)
0.158504 + 0.987358i \(0.449333\pi\)
\(138\) 0 0
\(139\) 12.4933i 1.05966i −0.848102 0.529832i \(-0.822255\pi\)
0.848102 0.529832i \(-0.177745\pi\)
\(140\) 0 0
\(141\) −6.97602 15.2754i −0.587487 1.28642i
\(142\) 0 0
\(143\) 0.0914034 1.27799i 0.00764353 0.106871i
\(144\) 0 0
\(145\) −5.14268 21.7309i −0.427077 1.80466i
\(146\) 0 0
\(147\) 17.8140 1.27409i 1.46928 0.105085i
\(148\) 0 0
\(149\) −1.54384 10.7376i −0.126476 0.879661i −0.949971 0.312338i \(-0.898888\pi\)
0.823495 0.567324i \(-0.192021\pi\)
\(150\) 0 0
\(151\) 4.41885 2.83983i 0.359601 0.231102i −0.348348 0.937365i \(-0.613257\pi\)
0.707949 + 0.706264i \(0.249621\pi\)
\(152\) 0 0
\(153\) −11.6020 + 4.32734i −0.937970 + 0.349845i
\(154\) 0 0
\(155\) 8.16084 15.6137i 0.655495 1.25412i
\(156\) 0 0
\(157\) −7.04208 + 3.84526i −0.562019 + 0.306886i −0.735030 0.678034i \(-0.762832\pi\)
0.173011 + 0.984920i \(0.444650\pi\)
\(158\) 0 0
\(159\) 1.35177 9.40174i 0.107202 0.745606i
\(160\) 0 0
\(161\) −1.69982 + 5.62148i −0.133964 + 0.443035i
\(162\) 0 0
\(163\) −3.45843 4.61992i −0.270885 0.361860i 0.644385 0.764701i \(-0.277114\pi\)
−0.915270 + 0.402841i \(0.868023\pi\)
\(164\) 0 0
\(165\) −3.79380 1.03944i −0.295347 0.0809202i
\(166\) 0 0
\(167\) 15.4583 + 8.44089i 1.19620 + 0.653176i 0.948843 0.315748i \(-0.102255\pi\)
0.247359 + 0.968924i \(0.420437\pi\)
\(168\) 0 0
\(169\) 6.73812 + 3.07720i 0.518317 + 0.236708i
\(170\) 0 0
\(171\) 11.7068 + 18.2162i 0.895243 + 1.39303i
\(172\) 0 0
\(173\) 18.6082 + 13.9299i 1.41475 + 1.05907i 0.987958 + 0.154724i \(0.0494488\pi\)
0.426796 + 0.904348i \(0.359642\pi\)
\(174\) 0 0
\(175\) −6.08736 + 0.658501i −0.460161 + 0.0497780i
\(176\) 0 0
\(177\) −4.03585 18.5525i −0.303353 1.39449i
\(178\) 0 0
\(179\) 3.88319 3.36481i 0.290243 0.251497i −0.497552 0.867434i \(-0.665768\pi\)
0.787796 + 0.615937i \(0.211222\pi\)
\(180\) 0 0
\(181\) −15.6672 + 7.15495i −1.16453 + 0.531823i −0.901421 0.432943i \(-0.857475\pi\)
−0.263109 + 0.964766i \(0.584748\pi\)
\(182\) 0 0
\(183\) −16.2275 16.2275i −1.19957 1.19957i
\(184\) 0 0
\(185\) −0.464279 25.5376i −0.0341345 1.87756i
\(186\) 0 0
\(187\) −0.310834 + 0.833379i −0.0227305 + 0.0609427i
\(188\) 0 0
\(189\) 11.8282 + 13.6504i 0.860374 + 0.992924i
\(190\) 0 0
\(191\) −5.39070 + 8.38809i −0.390057 + 0.606941i −0.979639 0.200768i \(-0.935656\pi\)
0.589581 + 0.807709i \(0.299293\pi\)
\(192\) 0 0
\(193\) 1.27599 + 17.8407i 0.0918481 + 1.28420i 0.809217 + 0.587510i \(0.199892\pi\)
−0.717368 + 0.696694i \(0.754654\pi\)
\(194\) 0 0
\(195\) −10.0378 + 13.9298i −0.718825 + 0.997532i
\(196\) 0 0
\(197\) 12.2194 + 2.65816i 0.870595 + 0.189386i 0.625605 0.780140i \(-0.284852\pi\)
0.244989 + 0.969526i \(0.421216\pi\)
\(198\) 0 0
\(199\) −9.97928 + 21.8516i −0.707413 + 1.54902i 0.123333 + 0.992365i \(0.460642\pi\)
−0.830746 + 0.556652i \(0.812086\pi\)
\(200\) 0 0
\(201\) −7.80090 26.5674i −0.550233 1.87392i
\(202\) 0 0
\(203\) 5.86101 + 10.7336i 0.411362 + 0.753354i
\(204\) 0 0
\(205\) 6.57842 + 8.46262i 0.459457 + 0.591055i
\(206\) 0 0
\(207\) 33.9930 12.3684i 2.36268 0.859664i
\(208\) 0 0
\(209\) 1.53956 + 0.221355i 0.106493 + 0.0153114i
\(210\) 0 0
\(211\) −14.4701 4.24882i −0.996166 0.292501i −0.257284 0.966336i \(-0.582828\pi\)
−0.738882 + 0.673835i \(0.764646\pi\)
\(212\) 0 0
\(213\) −13.8646 + 25.3912i −0.949989 + 1.73977i
\(214\) 0 0
\(215\) −0.766401 + 1.76227i −0.0522681 + 0.120186i
\(216\) 0 0
\(217\) −2.05090 + 9.42783i −0.139224 + 0.640002i
\(218\) 0 0
\(219\) −4.51956 + 0.649815i −0.305404 + 0.0439104i
\(220\) 0 0
\(221\) 2.93410 + 2.54241i 0.197369 + 0.171021i
\(222\) 0 0
\(223\) 7.13250 1.55158i 0.477628 0.103902i 0.0326947 0.999465i \(-0.489591\pi\)
0.444933 + 0.895564i \(0.353227\pi\)
\(224\) 0 0
\(225\) 25.7166 + 27.5852i 1.71444 + 1.83902i
\(226\) 0 0
\(227\) −9.98999 3.72607i −0.663059 0.247308i −0.00467325 0.999989i \(-0.501488\pi\)
−0.658385 + 0.752681i \(0.728760\pi\)
\(228\) 0 0
\(229\) −27.1983 −1.79731 −0.898657 0.438652i \(-0.855456\pi\)
−0.898657 + 0.438652i \(0.855456\pi\)
\(230\) 0 0
\(231\) 2.15423 0.141738
\(232\) 0 0
\(233\) −3.28512 1.22529i −0.215215 0.0802711i 0.239544 0.970885i \(-0.423002\pi\)
−0.454759 + 0.890614i \(0.650275\pi\)
\(234\) 0 0
\(235\) 7.73091 + 8.60094i 0.504309 + 0.561064i
\(236\) 0 0
\(237\) 41.2610 8.97577i 2.68019 0.583039i
\(238\) 0 0
\(239\) −3.02950 2.62508i −0.195962 0.169802i 0.551353 0.834272i \(-0.314112\pi\)
−0.747315 + 0.664470i \(0.768657\pi\)
\(240\) 0 0
\(241\) 6.31988 0.908661i 0.407099 0.0585320i 0.0642764 0.997932i \(-0.479526\pi\)
0.342823 + 0.939400i \(0.388617\pi\)
\(242\) 0 0
\(243\) 8.03077 36.9168i 0.515174 2.36822i
\(244\) 0 0
\(245\) −11.4438 + 4.50693i −0.731117 + 0.287937i
\(246\) 0 0
\(247\) 3.25364 5.95860i 0.207024 0.379137i
\(248\) 0 0
\(249\) −39.8425 11.6988i −2.52492 0.741382i
\(250\) 0 0
\(251\) −15.6701 2.25302i −0.989090 0.142210i −0.371266 0.928526i \(-0.621076\pi\)
−0.617823 + 0.786317i \(0.711985\pi\)
\(252\) 0 0
\(253\) 0.927567 2.42714i 0.0583156 0.152593i
\(254\) 0 0
\(255\) 9.41055 7.31529i 0.589312 0.458101i
\(256\) 0 0
\(257\) −4.96586 9.09430i −0.309762 0.567287i 0.675701 0.737176i \(-0.263841\pi\)
−0.985463 + 0.169889i \(0.945659\pi\)
\(258\) 0 0
\(259\) 3.94085 + 13.4213i 0.244872 + 0.833959i
\(260\) 0 0
\(261\) 31.2919 68.5197i 1.93692 4.24126i
\(262\) 0 0
\(263\) −8.59573 1.86989i −0.530035 0.115302i −0.0604197 0.998173i \(-0.519244\pi\)
−0.469616 + 0.882871i \(0.655608\pi\)
\(264\) 0 0
\(265\) 1.04846 + 6.45669i 0.0644061 + 0.396631i
\(266\) 0 0
\(267\) 0.858086 + 11.9976i 0.0525140 + 0.734241i
\(268\) 0 0
\(269\) −1.09032 + 1.69657i −0.0664778 + 0.103442i −0.872901 0.487897i \(-0.837764\pi\)
0.806423 + 0.591339i \(0.201400\pi\)
\(270\) 0 0
\(271\) −12.9267 14.9182i −0.785243 0.906218i 0.212234 0.977219i \(-0.431926\pi\)
−0.997476 + 0.0710006i \(0.977381\pi\)
\(272\) 0 0
\(273\) 3.28598 8.81005i 0.198876 0.533208i
\(274\) 0 0
\(275\) 2.70717 0.0984661i 0.163248 0.00593773i
\(276\) 0 0
\(277\) −11.4890 11.4890i −0.690309 0.690309i 0.271991 0.962300i \(-0.412318\pi\)
−0.962300 + 0.271991i \(0.912318\pi\)
\(278\) 0 0
\(279\) 54.0575 24.6872i 3.23634 1.47799i
\(280\) 0 0
\(281\) 1.57071 1.36103i 0.0937006 0.0811920i −0.606751 0.794892i \(-0.707527\pi\)
0.700452 + 0.713700i \(0.252982\pi\)
\(282\) 0 0
\(283\) 6.37471 + 29.3040i 0.378937 + 1.74194i 0.632439 + 0.774610i \(0.282054\pi\)
−0.253502 + 0.967335i \(0.581583\pi\)
\(284\) 0 0
\(285\) −15.9978 13.3609i −0.947629 0.791430i
\(286\) 0 0
\(287\) −4.69925 3.51781i −0.277388 0.207650i
\(288\) 0 0
\(289\) 7.73377 + 12.0340i 0.454927 + 0.707881i
\(290\) 0 0
\(291\) 10.8317 + 4.94667i 0.634966 + 0.289979i
\(292\) 0 0
\(293\) 8.98986 + 4.90883i 0.525193 + 0.286777i 0.719892 0.694086i \(-0.244191\pi\)
−0.194699 + 0.980863i \(0.562373\pi\)
\(294\) 0 0
\(295\) 6.47390 + 11.3601i 0.376925 + 0.661413i
\(296\) 0 0
\(297\) −4.78899 6.39734i −0.277885 0.371211i
\(298\) 0 0
\(299\) −8.51126 7.49568i −0.492219 0.433487i
\(300\) 0 0
\(301\) 0.149775 1.04171i 0.00863287 0.0600430i
\(302\) 0 0
\(303\) −39.0643 + 21.3307i −2.24418 + 1.22542i
\(304\) 0 0
\(305\) 14.0066 + 7.32084i 0.802013 + 0.419190i
\(306\) 0 0
\(307\) −26.5478 + 9.90183i −1.51516 + 0.565127i −0.963211 0.268747i \(-0.913390\pi\)
−0.551954 + 0.833875i \(0.686118\pi\)
\(308\) 0 0
\(309\) 24.1638 15.5291i 1.37463 0.883420i
\(310\) 0 0
\(311\) −1.59238 11.0753i −0.0902958 0.628021i −0.983841 0.179047i \(-0.942699\pi\)
0.893545 0.448974i \(-0.148210\pi\)
\(312\) 0 0
\(313\) 8.93566 0.639091i 0.505074 0.0361236i 0.183522 0.983016i \(-0.441250\pi\)
0.321552 + 0.946892i \(0.395796\pi\)
\(314\) 0 0
\(315\) −17.5749 10.8485i −0.990236 0.611242i
\(316\) 0 0
\(317\) −1.60828 + 22.4867i −0.0903300 + 1.26298i 0.726931 + 0.686711i \(0.240946\pi\)
−0.817261 + 0.576268i \(0.804509\pi\)
\(318\) 0 0
\(319\) −2.24771 4.92180i −0.125848 0.275568i
\(320\) 0 0
\(321\) 58.5190i 3.26621i
\(322\) 0 0
\(323\) −3.33262 + 3.33262i −0.185432 + 0.185432i
\(324\) 0 0
\(325\) 3.72671 11.2216i 0.206721 0.622460i
\(326\) 0 0
\(327\) −14.2222 1.01720i −0.786492 0.0562510i
\(328\) 0 0
\(329\) −5.32799 3.42409i −0.293741 0.188776i
\(330\) 0 0
\(331\) 4.37112 5.04454i 0.240259 0.277273i −0.622796 0.782385i \(-0.714003\pi\)
0.863054 + 0.505111i \(0.168549\pi\)
\(332\) 0 0
\(333\) 51.6320 68.9723i 2.82942 3.77966i
\(334\) 0 0
\(335\) 10.5991 + 15.8514i 0.579092 + 0.866057i
\(336\) 0 0
\(337\) −11.0044 29.5038i −0.599446 1.60718i −0.781512 0.623890i \(-0.785551\pi\)
0.182066 0.983286i \(-0.441722\pi\)
\(338\) 0 0
\(339\) −0.275786 + 0.0809781i −0.0149786 + 0.00439812i
\(340\) 0 0
\(341\) 1.20264 4.09581i 0.0651266 0.221801i
\(342\) 0 0
\(343\) 12.2544 9.17356i 0.661678 0.495326i
\(344\) 0 0
\(345\) −27.6615 + 21.1482i −1.48925 + 1.13858i
\(346\) 0 0
\(347\) −15.1194 + 11.3183i −0.811654 + 0.607596i −0.922393 0.386253i \(-0.873769\pi\)
0.110739 + 0.993850i \(0.464678\pi\)
\(348\) 0 0
\(349\) −3.38232 + 11.5191i −0.181051 + 0.616604i 0.818087 + 0.575095i \(0.195035\pi\)
−0.999138 + 0.0415093i \(0.986783\pi\)
\(350\) 0 0
\(351\) −33.4678 + 9.82704i −1.78638 + 0.524528i
\(352\) 0 0
\(353\) 6.71023 + 17.9908i 0.357150 + 0.957555i 0.983961 + 0.178384i \(0.0570870\pi\)
−0.626811 + 0.779171i \(0.715640\pi\)
\(354\) 0 0
\(355\) 3.88039 19.5416i 0.205950 1.03716i
\(356\) 0 0
\(357\) −3.91185 + 5.22563i −0.207037 + 0.276569i
\(358\) 0 0
\(359\) 19.3209 22.2975i 1.01972 1.17682i 0.0355904 0.999366i \(-0.488669\pi\)
0.984129 0.177453i \(-0.0567857\pi\)
\(360\) 0 0
\(361\) −9.05051 5.81641i −0.476343 0.306127i
\(362\) 0 0
\(363\) 34.6747 + 2.47998i 1.81995 + 0.130165i
\(364\) 0 0
\(365\) 2.83611 1.35804i 0.148449 0.0710833i
\(366\) 0 0
\(367\) −8.70758 + 8.70758i −0.454532 + 0.454532i −0.896856 0.442324i \(-0.854154\pi\)
0.442324 + 0.896856i \(0.354154\pi\)
\(368\) 0 0
\(369\) 36.1562i 1.88222i
\(370\) 0 0
\(371\) −1.48814 3.25857i −0.0772604 0.169177i
\(372\) 0 0
\(373\) 1.06533 14.8952i 0.0551607 0.771247i −0.892314 0.451416i \(-0.850919\pi\)
0.947475 0.319831i \(-0.103626\pi\)
\(374\) 0 0
\(375\) −31.5635 17.9325i −1.62993 0.926031i
\(376\) 0 0
\(377\) −23.5570 + 1.68483i −1.21325 + 0.0867732i
\(378\) 0 0
\(379\) 4.09836 + 28.5047i 0.210518 + 1.46419i 0.771431 + 0.636313i \(0.219541\pi\)
−0.560912 + 0.827875i \(0.689550\pi\)
\(380\) 0 0
\(381\) 11.1526 7.16731i 0.571363 0.367192i
\(382\) 0 0
\(383\) 12.2195 4.55763i 0.624387 0.232884i −0.0173009 0.999850i \(-0.505507\pi\)
0.641688 + 0.766966i \(0.278235\pi\)
\(384\) 0 0
\(385\) −1.41562 + 0.443770i −0.0721469 + 0.0226166i
\(386\) 0 0
\(387\) −5.68935 + 3.10662i −0.289206 + 0.157918i
\(388\) 0 0
\(389\) 3.72443 25.9040i 0.188836 1.31338i −0.646192 0.763175i \(-0.723639\pi\)
0.835028 0.550208i \(-0.185452\pi\)
\(390\) 0 0
\(391\) 4.20326 + 6.65747i 0.212568 + 0.336683i
\(392\) 0 0
\(393\) −31.5539 42.1510i −1.59168 2.12624i
\(394\) 0 0
\(395\) −25.2651 + 14.3980i −1.27122 + 0.724444i
\(396\) 0 0
\(397\) −17.9279 9.78936i −0.899774 0.491314i −0.0383870 0.999263i \(-0.512222\pi\)
−0.861387 + 0.507949i \(0.830404\pi\)
\(398\) 0 0
\(399\) 10.3832 + 4.74186i 0.519812 + 0.237390i
\(400\) 0 0
\(401\) 13.9500 + 21.7066i 0.696630 + 1.08398i 0.991709 + 0.128504i \(0.0410176\pi\)
−0.295079 + 0.955473i \(0.595346\pi\)
\(402\) 0 0
\(403\) −14.9160 11.1660i −0.743018 0.556216i
\(404\) 0 0
\(405\) 5.05359 + 56.2646i 0.251115 + 2.79581i
\(406\) 0 0
\(407\) −1.31550 6.04727i −0.0652071 0.299752i
\(408\) 0 0
\(409\) 7.81110 6.76835i 0.386234 0.334674i −0.440003 0.897996i \(-0.645023\pi\)
0.826237 + 0.563323i \(0.190477\pi\)
\(410\) 0 0
\(411\) 40.5223 18.5059i 1.99882 0.912829i
\(412\) 0 0
\(413\) −5.06335 5.06335i −0.249151 0.249151i
\(414\) 0 0
\(415\) 28.5919 0.519806i 1.40352 0.0255163i
\(416\) 0 0
\(417\) −14.1760 + 38.0073i −0.694201 + 1.86123i
\(418\) 0 0
\(419\) −4.93799 5.69875i −0.241237 0.278402i 0.622201 0.782858i \(-0.286239\pi\)
−0.863438 + 0.504456i \(0.831693\pi\)
\(420\) 0 0
\(421\) −4.50378 + 7.00802i −0.219501 + 0.341550i −0.933488 0.358609i \(-0.883251\pi\)
0.713987 + 0.700159i \(0.246888\pi\)
\(422\) 0 0
\(423\) 2.78293 + 38.9105i 0.135311 + 1.89189i
\(424\) 0 0
\(425\) −4.67707 + 6.74571i −0.226871 + 0.327215i
\(426\) 0 0
\(427\) −8.45742 1.83980i −0.409283 0.0890341i
\(428\) 0 0
\(429\) −1.72819 + 3.78420i −0.0834377 + 0.182703i
\(430\) 0 0
\(431\) 4.67342 + 15.9162i 0.225111 + 0.766656i 0.992150 + 0.125056i \(0.0399110\pi\)
−0.767039 + 0.641600i \(0.778271\pi\)
\(432\) 0 0
\(433\) 10.5904 + 19.3948i 0.508940 + 0.932055i 0.998203 + 0.0599182i \(0.0190840\pi\)
−0.489263 + 0.872136i \(0.662734\pi\)
\(434\) 0 0
\(435\) −9.01269 + 71.9457i −0.432125 + 3.44953i
\(436\) 0 0
\(437\) 9.81338 9.65687i 0.469438 0.461951i
\(438\) 0 0
\(439\) 21.3893 + 3.07532i 1.02086 + 0.146777i 0.632361 0.774674i \(-0.282086\pi\)
0.388495 + 0.921451i \(0.372995\pi\)
\(440\) 0 0
\(441\) −39.8071 11.6884i −1.89558 0.556592i
\(442\) 0 0
\(443\) 2.47469 4.53206i 0.117576 0.215325i −0.812263 0.583292i \(-0.801764\pi\)
0.929839 + 0.367967i \(0.119946\pi\)
\(444\) 0 0
\(445\) −3.03538 7.70730i −0.143891 0.365361i
\(446\) 0 0
\(447\) −7.48719 + 34.4181i −0.354132 + 1.62792i
\(448\) 0 0
\(449\) −29.4190 + 4.22981i −1.38837 + 0.199617i −0.795632 0.605780i \(-0.792861\pi\)
−0.592736 + 0.805397i \(0.701952\pi\)
\(450\) 0 0
\(451\) 1.96277 + 1.70075i 0.0924232 + 0.0800851i
\(452\) 0 0
\(453\) −16.6655 + 3.62535i −0.783012 + 0.170334i
\(454\) 0 0
\(455\) −0.344473 + 6.46632i −0.0161492 + 0.303146i
\(456\) 0 0
\(457\) 29.3391 + 10.9429i 1.37243 + 0.511888i 0.924158 0.382011i \(-0.124769\pi\)
0.448267 + 0.893899i \(0.352041\pi\)
\(458\) 0 0
\(459\) 24.2146 1.13024
\(460\) 0 0
\(461\) 7.39116 0.344241 0.172120 0.985076i \(-0.444938\pi\)
0.172120 + 0.985076i \(0.444938\pi\)
\(462\) 0 0
\(463\) 11.6270 + 4.33663i 0.540350 + 0.201540i 0.604795 0.796381i \(-0.293255\pi\)
−0.0644449 + 0.997921i \(0.520528\pi\)
\(464\) 0 0
\(465\) −42.5438 + 38.2403i −1.97292 + 1.77335i
\(466\) 0 0
\(467\) 4.30979 0.937538i 0.199433 0.0433841i −0.111739 0.993738i \(-0.535642\pi\)
0.311172 + 0.950354i \(0.399278\pi\)
\(468\) 0 0
\(469\) −7.89216 6.83860i −0.364426 0.315777i
\(470\) 0 0
\(471\) 25.7868 3.70758i 1.18819 0.170836i
\(472\) 0 0
\(473\) −0.0989755 + 0.454983i −0.00455090 + 0.0209201i
\(474\) 0 0
\(475\) 13.2651 + 5.48438i 0.608644 + 0.251641i
\(476\) 0 0
\(477\) −10.5745 + 19.3658i −0.484175 + 0.886700i
\(478\) 0 0
\(479\) 23.9641 + 7.03650i 1.09495 + 0.321506i 0.778843 0.627219i \(-0.215807\pi\)
0.316105 + 0.948724i \(0.397625\pi\)
\(480\) 0 0
\(481\) −26.7378 3.84432i −1.21914 0.175286i
\(482\) 0 0
\(483\) 11.5499 15.1730i 0.525537 0.690397i
\(484\) 0 0
\(485\) −8.13692 1.01932i −0.369479 0.0462848i
\(486\) 0 0
\(487\) 8.55032 + 15.6587i 0.387452 + 0.709565i 0.996502 0.0835664i \(-0.0266311\pi\)
−0.609050 + 0.793132i \(0.708449\pi\)
\(488\) 0 0
\(489\) 5.27913 + 17.9791i 0.238731 + 0.813042i
\(490\) 0 0
\(491\) 16.4315 35.9800i 0.741545 1.62376i −0.0394519 0.999221i \(-0.512561\pi\)
0.780997 0.624535i \(-0.214712\pi\)
\(492\) 0 0
\(493\) 16.0207 + 3.48508i 0.721534 + 0.156960i
\(494\) 0 0
\(495\) 7.41350 + 5.34219i 0.333212 + 0.240114i
\(496\) 0 0
\(497\) 0.778369 + 10.8830i 0.0349146 + 0.488170i
\(498\) 0 0
\(499\) −15.4214 + 23.9962i −0.690358 + 1.07422i 0.302294 + 0.953215i \(0.402248\pi\)
−0.992652 + 0.121004i \(0.961389\pi\)
\(500\) 0 0
\(501\) −37.4499 43.2195i −1.67314 1.93091i
\(502\) 0 0
\(503\) −8.90792 + 23.8831i −0.397185 + 1.06489i 0.572365 + 0.819999i \(0.306026\pi\)
−0.969550 + 0.244894i \(0.921247\pi\)
\(504\) 0 0
\(505\) 21.2765 22.0644i 0.946790 0.981853i
\(506\) 0 0
\(507\) −17.0072 17.0072i −0.755317 0.755317i
\(508\) 0 0
\(509\) −18.4818 + 8.44037i −0.819193 + 0.374113i −0.780514 0.625139i \(-0.785042\pi\)
−0.0386794 + 0.999252i \(0.512315\pi\)
\(510\) 0 0
\(511\) −1.30145 + 1.12771i −0.0575728 + 0.0498871i
\(512\) 0 0
\(513\) −9.00083 41.3762i −0.397396 1.82680i
\(514\) 0 0
\(515\) −12.6799 + 15.1825i −0.558744 + 0.669019i
\(516\) 0 0
\(517\) 2.24319 + 1.67923i 0.0986555 + 0.0738526i
\(518\) 0 0
\(519\) −40.8041 63.4924i −1.79110 2.78701i
\(520\) 0 0
\(521\) −0.793528 0.362392i −0.0347651 0.0158767i 0.397957 0.917404i \(-0.369719\pi\)
−0.432722 + 0.901528i \(0.642447\pi\)
\(522\) 0 0
\(523\) 0.0507598 + 0.0277169i 0.00221957 + 0.00121198i 0.480358 0.877072i \(-0.340507\pi\)
−0.478139 + 0.878284i \(0.658688\pi\)
\(524\) 0 0
\(525\) 19.2663 + 4.90396i 0.840851 + 0.214026i
\(526\) 0 0
\(527\) 7.75156 + 10.3549i 0.337663 + 0.451065i
\(528\) 0 0
\(529\) −12.1221 19.5462i −0.527047 0.849836i
\(530\) 0 0
\(531\) −6.27685 + 43.6564i −0.272392 + 1.89453i
\(532\) 0 0
\(533\) 9.94940 5.43278i 0.430956 0.235320i
\(534\) 0 0
\(535\) −12.0549 38.4550i −0.521177 1.66255i
\(536\) 0 0
\(537\) −15.6316 + 5.83027i −0.674551 + 0.251595i
\(538\) 0 0
\(539\) −2.50700 + 1.61115i −0.107984 + 0.0693972i
\(540\) 0 0
\(541\) −1.48632 10.3376i −0.0639020 0.444448i −0.996504 0.0835421i \(-0.973377\pi\)
0.932602 0.360906i \(-0.117532\pi\)
\(542\) 0 0
\(543\) 55.7817 3.98958i 2.39382 0.171209i
\(544\) 0 0
\(545\) 9.55550 2.26134i 0.409313 0.0968650i
\(546\) 0 0
\(547\) 0.939925 13.1419i 0.0401883 0.561906i −0.936972 0.349404i \(-0.886384\pi\)
0.977161 0.212502i \(-0.0681612\pi\)
\(548\) 0 0
\(549\) 22.1462 + 48.4933i 0.945175 + 2.06964i
\(550\) 0 0
\(551\) 28.6703i 1.22140i
\(552\) 0 0
\(553\) 11.2609 11.2609i 0.478864 0.478864i
\(554\) 0 0
\(555\) −27.5649 + 78.2180i −1.17006 + 3.32017i
\(556\) 0 0
\(557\) 12.6019 + 0.901309i 0.533961 + 0.0381897i 0.335717 0.941963i \(-0.391021\pi\)
0.198245 + 0.980153i \(0.436476\pi\)
\(558\) 0 0
\(559\) 1.70975 + 1.09879i 0.0723146 + 0.0464738i
\(560\) 0 0
\(561\) 1.89126 2.18263i 0.0798489 0.0921505i
\(562\) 0 0
\(563\) −11.5652 + 15.4493i −0.487414 + 0.651109i −0.975062 0.221931i \(-0.928764\pi\)
0.487648 + 0.873040i \(0.337855\pi\)
\(564\) 0 0
\(565\) 0.164548 0.110025i 0.00692257 0.00462880i
\(566\) 0 0
\(567\) −10.8114 28.9865i −0.454037 1.21732i
\(568\) 0 0
\(569\) −42.3196 + 12.4262i −1.77413 + 0.520932i −0.994447 0.105241i \(-0.966439\pi\)
−0.779684 + 0.626173i \(0.784620\pi\)
\(570\) 0 0
\(571\) −7.33058 + 24.9657i −0.306775 + 1.04478i 0.651432 + 0.758707i \(0.274168\pi\)
−0.958208 + 0.286074i \(0.907650\pi\)
\(572\) 0 0
\(573\) 25.9176 19.4017i 1.08272 0.810517i
\(574\) 0 0
\(575\) 13.8209 19.5955i 0.576371 0.817188i
\(576\) 0 0
\(577\) 18.6948 13.9948i 0.778277 0.582611i −0.134574 0.990904i \(-0.542967\pi\)
0.912851 + 0.408293i \(0.133876\pi\)
\(578\) 0 0
\(579\) 16.3619 55.7234i 0.679976 2.31578i
\(580\) 0 0
\(581\) −15.0265 + 4.41217i −0.623403 + 0.183048i
\(582\) 0 0
\(583\) 0.553874 + 1.48499i 0.0229391 + 0.0615022i
\(584\) 0 0
\(585\) 33.1560 22.1699i 1.37083 0.916611i
\(586\) 0 0
\(587\) 3.38650 4.52383i 0.139776 0.186718i −0.725191 0.688548i \(-0.758249\pi\)
0.864967 + 0.501829i \(0.167339\pi\)
\(588\) 0 0
\(589\) 14.8123 17.0943i 0.610329 0.704358i
\(590\) 0 0
\(591\) −34.1579 21.9519i −1.40507 0.902982i
\(592\) 0 0
\(593\) −24.5464 1.75559i −1.00800 0.0720936i −0.442438 0.896799i \(-0.645886\pi\)
−0.565562 + 0.824706i \(0.691341\pi\)
\(594\) 0 0
\(595\) 1.49415 4.23979i 0.0612541 0.173814i
\(596\) 0 0
\(597\) 55.1540 55.1540i 2.25730 2.25730i
\(598\) 0 0
\(599\) 10.9263i 0.446435i −0.974769 0.223217i \(-0.928344\pi\)
0.974769 0.223217i \(-0.0716560\pi\)
\(600\) 0 0
\(601\) −9.96303 21.8160i −0.406401 0.889893i −0.996581 0.0826218i \(-0.973671\pi\)
0.590180 0.807271i \(-0.299057\pi\)
\(602\) 0 0
\(603\) −4.58864 + 64.1576i −0.186864 + 2.61270i
\(604\) 0 0
\(605\) −23.2969 + 5.51328i −0.947154 + 0.224147i
\(606\) 0 0
\(607\) −3.84185 + 0.274774i −0.155936 + 0.0111527i −0.149089 0.988824i \(-0.547634\pi\)
−0.00684697 + 0.999977i \(0.502179\pi\)
\(608\) 0 0
\(609\) −5.65115 39.3046i −0.228996 1.59270i
\(610\) 0 0
\(611\) 10.2892 6.61244i 0.416255 0.267511i
\(612\) 0 0
\(613\) −21.3110 + 7.94860i −0.860744 + 0.321041i −0.740789 0.671738i \(-0.765548\pi\)
−0.119956 + 0.992779i \(0.538275\pi\)
\(614\) 0 0
\(615\) −10.4106 33.2097i −0.419795 1.33914i
\(616\) 0 0
\(617\) 28.1469 15.3694i 1.13315 0.618748i 0.200561 0.979681i \(-0.435723\pi\)
0.932592 + 0.360933i \(0.117542\pi\)
\(618\) 0 0
\(619\) −2.67746 + 18.6222i −0.107616 + 0.748488i 0.862537 + 0.505995i \(0.168874\pi\)
−0.970153 + 0.242494i \(0.922035\pi\)
\(620\) 0 0
\(621\) −70.7349 0.568617i −2.83849 0.0228178i
\(622\) 0 0
\(623\) 2.71857 + 3.63159i 0.108917 + 0.145497i
\(624\) 0 0
\(625\) 24.4356 + 5.28206i 0.977425 + 0.211282i
\(626\) 0 0
\(627\) −4.43250 2.42033i −0.177017 0.0966587i
\(628\) 0 0
\(629\) 17.0580 + 7.79012i 0.680146 + 0.310612i
\(630\) 0 0
\(631\) 11.4483 + 17.8138i 0.455748 + 0.709158i 0.990751 0.135692i \(-0.0433258\pi\)
−0.535003 + 0.844850i \(0.679689\pi\)
\(632\) 0 0
\(633\) 39.2003 + 29.3450i 1.55807 + 1.16636i
\(634\) 0 0
\(635\) −5.85229 + 7.00732i −0.232241 + 0.278077i
\(636\) 0 0
\(637\) 2.76497 + 12.7103i 0.109552 + 0.503602i
\(638\) 0 0
\(639\) 50.7895 44.0093i 2.00920 1.74098i
\(640\) 0 0
\(641\) 30.7323 14.0350i 1.21385 0.554349i 0.297502 0.954721i \(-0.403846\pi\)
0.916353 + 0.400372i \(0.131119\pi\)
\(642\) 0 0
\(643\) −13.6936 13.6936i −0.540022 0.540022i 0.383513 0.923535i \(-0.374714\pi\)
−0.923535 + 0.383513i \(0.874714\pi\)
\(644\) 0 0
\(645\) 4.33120 4.49160i 0.170541 0.176856i
\(646\) 0 0
\(647\) −0.667376 + 1.78930i −0.0262372 + 0.0703448i −0.949408 0.314045i \(-0.898316\pi\)
0.923171 + 0.384390i \(0.125588\pi\)
\(648\) 0 0
\(649\) 2.07467 + 2.39429i 0.0814378 + 0.0939843i
\(650\) 0 0
\(651\) 16.9370 26.3544i 0.663812 1.03291i
\(652\) 0 0
\(653\) 2.64960 + 37.0463i 0.103687 + 1.44973i 0.737029 + 0.675861i \(0.236228\pi\)
−0.633342 + 0.773872i \(0.718317\pi\)
\(654\) 0 0
\(655\) 29.4183 + 21.1989i 1.14947 + 0.828310i
\(656\) 0 0
\(657\) 10.3645 + 2.25466i 0.404358 + 0.0879626i
\(658\) 0 0
\(659\) 6.91386 15.1392i 0.269326 0.589741i −0.725850 0.687854i \(-0.758553\pi\)
0.995175 + 0.0981122i \(0.0312804\pi\)
\(660\) 0 0
\(661\) −3.11639 10.6134i −0.121213 0.412815i 0.876422 0.481544i \(-0.159924\pi\)
−0.997635 + 0.0687289i \(0.978106\pi\)
\(662\) 0 0
\(663\) −6.04133 11.0639i −0.234626 0.429685i
\(664\) 0 0
\(665\) −7.80002 0.977114i −0.302472 0.0378909i
\(666\) 0 0
\(667\) −46.7171 10.5567i −1.80889 0.408757i
\(668\) 0 0
\(669\) −23.4592 3.37293i −0.906987 0.130405i
\(670\) 0 0
\(671\) 3.67423 + 1.07885i 0.141842 + 0.0416486i
\(672\) 0 0
\(673\) 3.08676 5.65298i 0.118986 0.217906i −0.811397 0.584495i \(-0.801293\pi\)
0.930383 + 0.366589i \(0.119474\pi\)
\(674\) 0 0
\(675\) −28.2671 68.1163i −1.08800 2.62180i
\(676\) 0 0
\(677\) 1.46221 6.72166i 0.0561972 0.258334i −0.940473 0.339867i \(-0.889618\pi\)
0.996671 + 0.0815328i \(0.0259815\pi\)
\(678\) 0 0
\(679\) 4.44527 0.639134i 0.170594 0.0245277i
\(680\) 0 0
\(681\) 26.1638 + 22.6711i 1.00260 + 0.868758i
\(682\) 0 0
\(683\) −17.9805 + 3.91141i −0.688004 + 0.149666i −0.542959 0.839759i \(-0.682696\pi\)
−0.145044 + 0.989425i \(0.546333\pi\)
\(684\) 0 0
\(685\) −22.8165 + 20.5085i −0.871772 + 0.783588i
\(686\) 0 0
\(687\) 82.7433 + 30.8617i 3.15685 + 1.17745i
\(688\) 0 0
\(689\) 6.91797 0.263553
\(690\) 0 0
\(691\) 26.8651 1.02200 0.510998 0.859582i \(-0.329276\pi\)
0.510998 + 0.859582i \(0.329276\pi\)
\(692\) 0 0
\(693\) −4.68875 1.74881i −0.178111 0.0664320i
\(694\) 0 0
\(695\) 1.48609 27.8962i 0.0563705 1.05816i
\(696\) 0 0
\(697\) −7.68977 + 1.67281i −0.291271 + 0.0633621i
\(698\) 0 0
\(699\) 8.60374 + 7.45519i 0.325423 + 0.281981i
\(700\) 0 0
\(701\) −33.8366 + 4.86497i −1.27799 + 0.183747i −0.747682 0.664057i \(-0.768833\pi\)
−0.530309 + 0.847804i \(0.677924\pi\)
\(702\) 0 0
\(703\) 6.97054 32.0431i 0.262899 1.20853i
\(704\) 0 0
\(705\) −13.7598 34.9382i −0.518222 1.31585i
\(706\) 0 0
\(707\) −8.04481 + 14.7330i −0.302556 + 0.554091i
\(708\) 0 0
\(709\) 9.40893 + 2.76271i 0.353360 + 0.103756i 0.453595 0.891208i \(-0.350141\pi\)
−0.100235 + 0.994964i \(0.531960\pi\)
\(710\) 0 0
\(711\) −97.0924 13.9598i −3.64125 0.523533i
\(712\) 0 0
\(713\) −22.4004 30.4303i −0.838901 1.13962i
\(714\) 0 0
\(715\) 0.356112 2.84274i 0.0133179 0.106313i
\(716\) 0 0
\(717\) 6.23777 + 11.4236i 0.232954 + 0.426623i
\(718\) 0 0
\(719\) −5.28046 17.9836i −0.196928 0.670676i −0.997450 0.0713717i \(-0.977262\pi\)
0.800522 0.599304i \(-0.204556\pi\)
\(720\) 0 0
\(721\) 4.50018 9.85403i 0.167596 0.366983i
\(722\) 0 0
\(723\) −20.2575 4.40676i −0.753386 0.163889i
\(724\) 0 0
\(725\) −8.89819 49.1348i −0.330471 1.82482i
\(726\) 0 0
\(727\) 2.32392 + 32.4927i 0.0861896 + 1.20509i 0.837986 + 0.545692i \(0.183733\pi\)
−0.751796 + 0.659396i \(0.770812\pi\)
\(728\) 0 0
\(729\) −25.3450 + 39.4376i −0.938705 + 1.46065i
\(730\) 0 0
\(731\) −0.923946 1.06629i −0.0341734 0.0394382i
\(732\) 0 0
\(733\) 5.83359 15.6405i 0.215469 0.577694i −0.783581 0.621290i \(-0.786609\pi\)
0.999049 + 0.0435964i \(0.0138816\pi\)
\(734\) 0 0
\(735\) 39.9286 0.725908i 1.47279 0.0267755i
\(736\) 0 0
\(737\) 3.26700 + 3.26700i 0.120342 + 0.120342i
\(738\) 0 0
\(739\) 18.1689 8.29744i 0.668352 0.305226i −0.0521901 0.998637i \(-0.516620\pi\)
0.720542 + 0.693411i \(0.243893\pi\)
\(740\) 0 0
\(741\) −16.6595 + 14.4355i −0.612001 + 0.530302i
\(742\) 0 0
\(743\) −3.93767 18.1012i −0.144459 0.664067i −0.991234 0.132116i \(-0.957823\pi\)
0.846775 0.531951i \(-0.178541\pi\)
\(744\) 0 0
\(745\) −2.16999 24.1597i −0.0795022 0.885144i
\(746\) 0 0
\(747\) 77.2213 + 57.8072i 2.82538 + 2.11505i
\(748\) 0 0
\(749\) 11.9321 + 18.5667i 0.435989 + 0.678412i
\(750\) 0 0
\(751\) −1.21595 0.555304i −0.0443705 0.0202633i 0.393106 0.919493i \(-0.371400\pi\)
−0.437477 + 0.899230i \(0.644128\pi\)
\(752\) 0 0
\(753\) 45.1155 + 24.6349i 1.64410 + 0.897747i
\(754\) 0 0
\(755\) 10.2047 5.81542i 0.371386 0.211645i
\(756\) 0 0
\(757\) 11.0478 + 14.7581i 0.401539 + 0.536394i 0.955049 0.296449i \(-0.0958026\pi\)
−0.553509 + 0.832843i \(0.686712\pi\)
\(758\) 0 0
\(759\) −5.57592 + 6.33139i −0.202393 + 0.229815i
\(760\) 0 0
\(761\) −2.92035 + 20.3115i −0.105862 + 0.736290i 0.865881 + 0.500250i \(0.166759\pi\)
−0.971743 + 0.236040i \(0.924151\pi\)
\(762\) 0 0
\(763\) −4.71979 + 2.57720i −0.170868 + 0.0933009i
\(764\) 0 0
\(765\) −26.4210 + 8.28245i −0.955252 + 0.299452i
\(766\) 0 0
\(767\) 12.9564 4.83250i 0.467830 0.174492i
\(768\) 0 0
\(769\) 8.24625 5.29955i 0.297368 0.191106i −0.383446 0.923563i \(-0.625263\pi\)
0.680814 + 0.732457i \(0.261626\pi\)
\(770\) 0 0
\(771\) 4.78805 + 33.3016i 0.172437 + 1.19933i
\(772\) 0 0
\(773\) 19.1342 1.36850i 0.688209 0.0492217i 0.277145 0.960828i \(-0.410612\pi\)
0.411064 + 0.911606i \(0.365157\pi\)
\(774\) 0 0
\(775\) 20.0796 33.8931i 0.721281 1.21748i
\(776\) 0 0
\(777\) 3.24008 45.3022i 0.116237 1.62521i
\(778\) 0 0
\(779\) 5.71673 + 12.5179i 0.204823 + 0.448500i
\(780\) 0 0
\(781\) 4.82730i 0.172734i
\(782\) 0 0
\(783\) −104.159 + 104.159i −3.72232 + 3.72232i
\(784\) 0 0
\(785\) −16.1817 + 7.74844i −0.577548 + 0.276554i
\(786\) 0 0
\(787\) −39.5768 2.83059i −1.41076 0.100900i −0.654942 0.755680i \(-0.727307\pi\)
−0.755820 + 0.654780i \(0.772761\pi\)
\(788\) 0 0
\(789\) 24.0284 + 15.4421i 0.855433 + 0.549754i
\(790\) 0 0
\(791\) −0.0709888 + 0.0819254i −0.00252407 + 0.00291293i
\(792\) 0 0
\(793\) 10.0167 13.3807i 0.355702 0.475162i
\(794\) 0 0
\(795\) 4.13671 20.8324i 0.146714 0.738848i
\(796\) 0 0
\(797\) 18.1364 + 48.6257i 0.642426 + 1.72241i 0.690267 + 0.723555i \(0.257493\pi\)
−0.0478411 + 0.998855i \(0.515234\pi\)
\(798\) 0 0
\(799\) −8.14680 + 2.39212i −0.288213 + 0.0846270i
\(800\) 0 0
\(801\) 7.87206 26.8098i 0.278146 0.947277i
\(802\) 0 0
\(803\) 0.609931 0.456588i 0.0215240 0.0161127i
\(804\) 0 0
\(805\) −4.46421 + 12.3500i −0.157343 + 0.435281i
\(806\) 0 0
\(807\) 5.24207 3.92416i 0.184530 0.138137i
\(808\) 0 0
\(809\) −9.95761 + 33.9125i −0.350091 + 1.19230i 0.576773 + 0.816904i \(0.304312\pi\)
−0.926864 + 0.375396i \(0.877507\pi\)
\(810\) 0 0
\(811\) 34.1108 10.0158i 1.19779 0.351703i 0.378783 0.925485i \(-0.376343\pi\)
0.819008 + 0.573782i \(0.194524\pi\)
\(812\) 0 0
\(813\) 22.3984 + 60.0524i 0.785546 + 2.10613i
\(814\) 0 0
\(815\) −7.17279 10.7272i −0.251252 0.375758i
\(816\) 0 0
\(817\) −1.47856 + 1.97512i −0.0517281 + 0.0691007i
\(818\) 0 0
\(819\) −14.3041 + 16.5078i −0.499825 + 0.576829i
\(820\) 0 0
\(821\) 40.7858 + 26.2115i 1.42344 + 0.914786i 0.999961 + 0.00887811i \(0.00282603\pi\)
0.423474 + 0.905908i \(0.360810\pi\)
\(822\) 0 0
\(823\) 13.6464 + 0.976007i 0.475682 + 0.0340215i 0.307123 0.951670i \(-0.400634\pi\)
0.168560 + 0.985691i \(0.446088\pi\)
\(824\) 0 0
\(825\) −8.34753 2.77224i −0.290624 0.0965170i
\(826\) 0 0
\(827\) 22.5217 22.5217i 0.783157 0.783157i −0.197205 0.980362i \(-0.563187\pi\)
0.980362 + 0.197205i \(0.0631866\pi\)
\(828\) 0 0
\(829\) 21.4688i 0.745641i 0.927903 + 0.372821i \(0.121609\pi\)
−0.927903 + 0.372821i \(0.878391\pi\)
\(830\) 0 0
\(831\) 21.9157 + 47.9887i 0.760248 + 1.66471i
\(832\) 0 0
\(833\) 0.644196 9.00704i 0.0223201 0.312075i
\(834\) 0 0
\(835\) 33.5129 + 20.6865i 1.15976 + 0.715885i
\(836\) 0 0
\(837\) −115.916 + 8.29045i −4.00663 + 0.286560i
\(838\) 0 0
\(839\) 0.166345 + 1.15696i 0.00574287 + 0.0399425i 0.992491 0.122315i \(-0.0390317\pi\)
−0.986749 + 0.162257i \(0.948123\pi\)
\(840\) 0 0
\(841\) −59.5070 + 38.2428i −2.05197 + 1.31872i
\(842\) 0 0
\(843\) −6.32279 + 2.35828i −0.217768 + 0.0812234i
\(844\) 0 0
\(845\) 14.6795 + 7.67259i 0.504991 + 0.263945i
\(846\) 0 0
\(847\) 11.5071 6.28337i 0.395390 0.215899i
\(848\) 0 0
\(849\) 13.8578 96.3828i 0.475597 3.30785i
\(850\) 0 0
\(851\) −49.6462 23.1567i −1.70185 0.793803i
\(852\) 0 0
\(853\) −20.5486 27.4497i −0.703570 0.939860i 0.296314 0.955091i \(-0.404243\pi\)
−0.999884 + 0.0152310i \(0.995152\pi\)
\(854\) 0 0
\(855\) 23.9734 + 42.0675i 0.819872 + 1.43868i
\(856\) 0 0
\(857\) 37.2527 + 20.3415i 1.27253 + 0.694853i 0.966377 0.257130i \(-0.0827768\pi\)
0.306151 + 0.951983i \(0.400959\pi\)
\(858\) 0 0
\(859\) −0.268623 0.122676i −0.00916530 0.00418565i 0.410827 0.911713i \(-0.365240\pi\)
−0.419992 + 0.907528i \(0.637967\pi\)
\(860\) 0 0
\(861\) 10.3045 + 16.0342i 0.351177 + 0.546443i
\(862\) 0 0
\(863\) −27.3931 20.5062i −0.932472 0.698040i 0.0209179 0.999781i \(-0.493341\pi\)
−0.953390 + 0.301742i \(0.902432\pi\)
\(864\) 0 0
\(865\) 39.8933 + 33.3176i 1.35641 + 1.13283i
\(866\) 0 0
\(867\) −9.87300 45.3855i −0.335305 1.54137i
\(868\) 0 0
\(869\) −5.32494 + 4.61409i −0.180636 + 0.156522i
\(870\) 0 0
\(871\) 18.3443 8.37754i 0.621572 0.283862i
\(872\) 0 0
\(873\) −19.5598 19.5598i −0.662000 0.662000i
\(874\) 0 0
\(875\) −13.6708 + 0.746271i −0.462158 + 0.0252286i
\(876\) 0 0
\(877\) 3.93016 10.5372i 0.132712 0.355815i −0.853548 0.521014i \(-0.825554\pi\)
0.986260 + 0.165199i \(0.0528267\pi\)
\(878\) 0 0
\(879\) −21.7791 25.1345i −0.734592 0.847765i
\(880\) 0 0
\(881\) 2.12517 3.30683i 0.0715989 0.111410i −0.803608 0.595159i \(-0.797089\pi\)
0.875207 + 0.483749i \(0.160725\pi\)
\(882\) 0 0
\(883\) 0.0374756 + 0.523977i 0.00126115 + 0.0176332i 0.998044 0.0625198i \(-0.0199137\pi\)
−0.996783 + 0.0801530i \(0.974459\pi\)
\(884\) 0 0
\(885\) −6.80481 41.9060i −0.228741 1.40865i
\(886\) 0 0
\(887\) −19.4953 4.24094i −0.654587 0.142397i −0.127007 0.991902i \(-0.540537\pi\)
−0.527580 + 0.849505i \(0.676901\pi\)
\(888\) 0 0
\(889\) 2.07702 4.54803i 0.0696609 0.152536i
\(890\) 0 0
\(891\) 3.85624 + 13.1331i 0.129189 + 0.439977i
\(892\) 0 0
\(893\) 7.11572 + 13.0315i 0.238118 + 0.436081i
\(894\) 0 0
\(895\) 9.07103 7.05137i 0.303211 0.235701i
\(896\) 0 0
\(897\) 17.3879 + 32.4612i 0.580564 + 1.08385i
\(898\) 0 0
\(899\) −77.8842 11.1981i −2.59758 0.373476i
\(900\) 0 0
\(901\) −4.60800 1.35303i −0.153515 0.0450760i
\(902\) 0 0
\(903\) −1.63766 + 2.99916i −0.0544980 + 0.0998056i
\(904\) 0 0
\(905\) −35.8343 + 14.1127i −1.19117 + 0.469121i
\(906\) 0 0
\(907\) 7.32730 33.6831i 0.243299 1.11843i −0.679659 0.733528i \(-0.737872\pi\)
0.922958 0.384900i \(-0.125764\pi\)
\(908\) 0 0
\(909\) 102.341 14.7144i 3.39444 0.488047i
\(910\) 0 0
\(911\) −11.7709 10.1995i −0.389986 0.337925i 0.437695 0.899124i \(-0.355795\pi\)
−0.827681 + 0.561198i \(0.810340\pi\)
\(912\) 0 0
\(913\) 6.77052 1.47284i 0.224071 0.0487437i
\(914\) 0 0
\(915\) −34.3042 38.1648i −1.13406 1.26169i
\(916\) 0 0
\(917\) −18.6059 6.93965i −0.614422 0.229168i
\(918\) 0 0
\(919\) −22.3932 −0.738683 −0.369342 0.929294i \(-0.620417\pi\)
−0.369342 + 0.929294i \(0.620417\pi\)
\(920\) 0 0
\(921\) 91.9999 3.03150
\(922\) 0 0
\(923\) −19.7420 7.36337i −0.649815 0.242368i
\(924\) 0 0
\(925\) 2.00104 57.0783i 0.0657938 1.87672i
\(926\) 0 0
\(927\) −65.1998 + 14.1834i −2.14144 + 0.465842i
\(928\) 0 0
\(929\) −2.42400 2.10041i −0.0795289 0.0689122i 0.614189 0.789159i \(-0.289483\pi\)
−0.693718 + 0.720247i \(0.744029\pi\)
\(930\) 0 0
\(931\) −15.6300 + 2.24726i −0.512253 + 0.0736508i
\(932\) 0 0
\(933\) −7.72262 + 35.5003i −0.252827 + 1.16223i
\(934\) 0 0
\(935\) −0.793194 + 1.82388i −0.0259402 + 0.0596473i
\(936\) 0 0
\(937\) 19.1562 35.0820i 0.625806 1.14608i −0.351887 0.936042i \(-0.614460\pi\)
0.977694 0.210036i \(-0.0673582\pi\)
\(938\) 0 0
\(939\) −27.9095 8.19496i −0.910791 0.267432i
\(940\) 0 0
\(941\) 0.742500 + 0.106755i 0.0242048 + 0.00348013i 0.154407 0.988007i \(-0.450653\pi\)
−0.130202 + 0.991488i \(0.541563\pi\)
\(942\) 0 0
\(943\) 22.5023 4.70596i 0.732777 0.153247i
\(944\) 0 0
\(945\) 24.7874 + 31.8871i 0.806335 + 1.03729i
\(946\) 0 0
\(947\) −26.2393 48.0537i −0.852662 1.56153i −0.827234 0.561858i \(-0.810087\pi\)
−0.0254281 0.999677i \(-0.508095\pi\)
\(948\) 0 0
\(949\) −0.936923 3.19087i −0.0304138 0.103580i
\(950\) 0 0
\(951\) 30.4082 66.5846i 0.986053 2.15915i
\(952\) 0 0
\(953\) 40.7535 + 8.86538i 1.32014 + 0.287178i 0.816804 0.576916i \(-0.195744\pi\)
0.503331 + 0.864093i \(0.332107\pi\)
\(954\) 0 0
\(955\) −13.0347 + 18.0886i −0.421792 + 0.585332i
\(956\) 0 0
\(957\) 1.25332 + 17.5237i 0.0405140 + 0.566460i
\(958\) 0 0
\(959\) 9.08338 14.1340i 0.293318 0.456411i
\(960\) 0 0
\(961\) −20.3513 23.4866i −0.656493 0.757634i
\(962\) 0 0
\(963\) 47.5060 127.368i 1.53086 4.10439i
\(964\) 0 0
\(965\) 0.726996 + 39.9884i 0.0234028 + 1.28727i
\(966\) 0 0
\(967\) −39.7040 39.7040i −1.27679 1.27679i −0.942452 0.334342i \(-0.891486\pi\)
−0.334342 0.942452i \(-0.608514\pi\)
\(968\) 0 0
\(969\) 13.9201 6.35709i 0.447177 0.204219i
\(970\) 0 0
\(971\) −3.35197 + 2.90449i −0.107570 + 0.0932097i −0.706985 0.707228i \(-0.749945\pi\)
0.599415 + 0.800438i \(0.295400\pi\)
\(972\) 0 0
\(973\) 3.25202 + 14.9493i 0.104255 + 0.479253i
\(974\) 0 0
\(975\) −24.0705 + 29.9098i −0.770873 + 0.957881i
\(976\) 0 0
\(977\) 32.3696 + 24.2316i 1.03560 + 0.775237i 0.974838 0.222915i \(-0.0715574\pi\)
0.0607578 + 0.998153i \(0.480648\pi\)
\(978\) 0 0
\(979\) −1.08510 1.68844i −0.0346799 0.0539629i
\(980\) 0 0
\(981\) 30.1294 + 13.7596i 0.961959 + 0.439312i
\(982\) 0 0
\(983\) −17.7837 9.71066i −0.567213 0.309722i 0.169932 0.985456i \(-0.445645\pi\)
−0.737146 + 0.675734i \(0.763827\pi\)
\(984\) 0 0
\(985\) 26.9685 + 7.38892i 0.859287 + 0.235431i
\(986\) 0 0
\(987\) 12.3236 + 16.4625i 0.392266 + 0.524006i
\(988\) 0 0
\(989\) 2.67396 + 3.13650i 0.0850268 + 0.0997350i
\(990\) 0 0
\(991\) −4.14927 + 28.8588i −0.131806 + 0.916731i 0.811393 + 0.584502i \(0.198710\pi\)
−0.943199 + 0.332230i \(0.892199\pi\)
\(992\) 0 0
\(993\) −19.0219 + 10.3868i −0.603643 + 0.329614i
\(994\) 0 0
\(995\) −24.8820 + 47.6054i −0.788813 + 1.50919i
\(996\) 0 0
\(997\) 14.4698 5.39694i 0.458262 0.170923i −0.109722 0.993962i \(-0.534996\pi\)
0.567984 + 0.823039i \(0.307723\pi\)
\(998\) 0 0
\(999\) −141.735 + 91.0877i −4.48431 + 2.88189i
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.x.a.337.1 yes 240
5.3 odd 4 inner 460.2.x.a.153.12 240
23.20 odd 22 inner 460.2.x.a.457.12 yes 240
115.43 even 44 inner 460.2.x.a.273.1 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.x.a.153.12 240 5.3 odd 4 inner
460.2.x.a.273.1 yes 240 115.43 even 44 inner
460.2.x.a.337.1 yes 240 1.1 even 1 trivial
460.2.x.a.457.12 yes 240 23.20 odd 22 inner