Properties

Label 845.2.d.b.844.5
Level $845$
Weight $2$
Character 845.844
Analytic conductor $6.747$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [845,2,Mod(844,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.844");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.d (of order \(2\), degree \(1\), not 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: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 844.5
Root \(0.403032 + 0.403032i\) of defining polynomial
Character \(\chi\) \(=\) 845.844
Dual form 845.2.d.b.844.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.67513 q^{2} -0.481194i q^{3} +5.15633 q^{4} +(-1.48119 + 1.67513i) q^{5} -1.28726i q^{6} -0.806063 q^{7} +8.44358 q^{8} +2.76845 q^{9} +(-3.96239 + 4.48119i) q^{10} +3.67513i q^{11} -2.48119i q^{12} -2.15633 q^{14} +(0.806063 + 0.712742i) q^{15} +12.2750 q^{16} -1.35026i q^{17} +7.40597 q^{18} +1.67513i q^{19} +(-7.63752 + 8.63752i) q^{20} +0.387873i q^{21} +9.83146i q^{22} -6.48119i q^{23} -4.06300i q^{24} +(-0.612127 - 4.96239i) q^{25} -2.77575i q^{27} -4.15633 q^{28} -2.41819 q^{29} +(2.15633 + 1.90668i) q^{30} -5.28726i q^{31} +15.9502 q^{32} +1.76845 q^{33} -3.61213i q^{34} +(1.19394 - 1.35026i) q^{35} +14.2750 q^{36} -3.76845 q^{37} +4.48119i q^{38} +(-12.5066 + 14.1441i) q^{40} -8.31265i q^{41} +1.03761i q^{42} +6.79384i q^{43} +18.9502i q^{44} +(-4.10062 + 4.63752i) q^{45} -17.3380i q^{46} -3.19394 q^{47} -5.90668i q^{48} -6.35026 q^{49} +(-1.63752 - 13.2750i) q^{50} -0.649738 q^{51} +5.73813i q^{53} -7.42548i q^{54} +(-6.15633 - 5.44358i) q^{55} -6.80606 q^{56} +0.806063 q^{57} -6.46898 q^{58} +5.98778i q^{59} +(4.15633 + 3.67513i) q^{60} -1.76845 q^{61} -14.1441i q^{62} -2.23155 q^{63} +18.1187 q^{64} +4.73084 q^{66} +9.89446 q^{67} -6.96239i q^{68} -3.11871 q^{69} +(3.19394 - 3.61213i) q^{70} +8.56230i q^{71} +23.3757 q^{72} -11.7685 q^{73} -10.0811 q^{74} +(-2.38787 + 0.294552i) q^{75} +8.63752i q^{76} -2.96239i q^{77} +2.26187 q^{79} +(-18.1817 + 20.5623i) q^{80} +6.96968 q^{81} -22.2374i q^{82} -3.84367 q^{83} +2.00000i q^{84} +(2.26187 + 2.00000i) q^{85} +18.1744i q^{86} +1.16362i q^{87} +31.0313i q^{88} +2.77575i q^{89} +(-10.9697 + 12.4060i) q^{90} -33.4191i q^{92} -2.54420 q^{93} -8.54420 q^{94} +(-2.80606 - 2.48119i) q^{95} -7.67513i q^{96} -1.87399 q^{97} -16.9878 q^{98} +10.1744i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} + 10 q^{4} + 2 q^{5} - 4 q^{7} + 18 q^{8} - 6 q^{9} - 2 q^{10} + 8 q^{14} + 4 q^{15} + 10 q^{16} - 10 q^{18} - 14 q^{20} - 2 q^{25} - 4 q^{28} - 12 q^{29} - 8 q^{30} + 22 q^{32} - 12 q^{33}+ \cdots - 50 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.67513 1.89160 0.945802 0.324745i \(-0.105279\pi\)
0.945802 + 0.324745i \(0.105279\pi\)
\(3\) 0.481194i 0.277818i −0.990305 0.138909i \(-0.955641\pi\)
0.990305 0.138909i \(-0.0443595\pi\)
\(4\) 5.15633 2.57816
\(5\) −1.48119 + 1.67513i −0.662410 + 0.749141i
\(6\) 1.28726i 0.525521i
\(7\) −0.806063 −0.304663 −0.152332 0.988329i \(-0.548678\pi\)
−0.152332 + 0.988329i \(0.548678\pi\)
\(8\) 8.44358 2.98526
\(9\) 2.76845 0.922817
\(10\) −3.96239 + 4.48119i −1.25302 + 1.41708i
\(11\) 3.67513i 1.10809i 0.832486 + 0.554047i \(0.186917\pi\)
−0.832486 + 0.554047i \(0.813083\pi\)
\(12\) 2.48119i 0.716259i
\(13\) 0 0
\(14\) −2.15633 −0.576302
\(15\) 0.806063 + 0.712742i 0.208125 + 0.184029i
\(16\) 12.2750 3.06876
\(17\) 1.35026i 0.327487i −0.986503 0.163743i \(-0.947643\pi\)
0.986503 0.163743i \(-0.0523569\pi\)
\(18\) 7.40597 1.74560
\(19\) 1.67513i 0.384301i 0.981365 + 0.192151i \(0.0615462\pi\)
−0.981365 + 0.192151i \(0.938454\pi\)
\(20\) −7.63752 + 8.63752i −1.70780 + 1.93141i
\(21\) 0.387873i 0.0846409i
\(22\) 9.83146i 2.09607i
\(23\) 6.48119i 1.35142i −0.737166 0.675711i \(-0.763837\pi\)
0.737166 0.675711i \(-0.236163\pi\)
\(24\) 4.06300i 0.829357i
\(25\) −0.612127 4.96239i −0.122425 0.992478i
\(26\) 0 0
\(27\) 2.77575i 0.534193i
\(28\) −4.15633 −0.785472
\(29\) −2.41819 −0.449047 −0.224523 0.974469i \(-0.572083\pi\)
−0.224523 + 0.974469i \(0.572083\pi\)
\(30\) 2.15633 + 1.90668i 0.393689 + 0.348110i
\(31\) 5.28726i 0.949620i −0.880088 0.474810i \(-0.842517\pi\)
0.880088 0.474810i \(-0.157483\pi\)
\(32\) 15.9502 2.81962
\(33\) 1.76845 0.307848
\(34\) 3.61213i 0.619475i
\(35\) 1.19394 1.35026i 0.201812 0.228236i
\(36\) 14.2750 2.37917
\(37\) −3.76845 −0.619530 −0.309765 0.950813i \(-0.600250\pi\)
−0.309765 + 0.950813i \(0.600250\pi\)
\(38\) 4.48119i 0.726946i
\(39\) 0 0
\(40\) −12.5066 + 14.1441i −1.97747 + 2.23638i
\(41\) 8.31265i 1.29822i −0.760695 0.649109i \(-0.775142\pi\)
0.760695 0.649109i \(-0.224858\pi\)
\(42\) 1.03761i 0.160107i
\(43\) 6.79384i 1.03605i 0.855365 + 0.518026i \(0.173333\pi\)
−0.855365 + 0.518026i \(0.826667\pi\)
\(44\) 18.9502i 2.85685i
\(45\) −4.10062 + 4.63752i −0.611284 + 0.691321i
\(46\) 17.3380i 2.55635i
\(47\) −3.19394 −0.465884 −0.232942 0.972491i \(-0.574835\pi\)
−0.232942 + 0.972491i \(0.574835\pi\)
\(48\) 5.90668i 0.852556i
\(49\) −6.35026 −0.907180
\(50\) −1.63752 13.2750i −0.231580 1.87737i
\(51\) −0.649738 −0.0909816
\(52\) 0 0
\(53\) 5.73813i 0.788193i 0.919069 + 0.394097i \(0.128943\pi\)
−0.919069 + 0.394097i \(0.871057\pi\)
\(54\) 7.42548i 1.01048i
\(55\) −6.15633 5.44358i −0.830119 0.734013i
\(56\) −6.80606 −0.909498
\(57\) 0.806063 0.106766
\(58\) −6.46898 −0.849418
\(59\) 5.98778i 0.779543i 0.920912 + 0.389771i \(0.127446\pi\)
−0.920912 + 0.389771i \(0.872554\pi\)
\(60\) 4.15633 + 3.67513i 0.536579 + 0.474457i
\(61\) −1.76845 −0.226427 −0.113214 0.993571i \(-0.536114\pi\)
−0.113214 + 0.993571i \(0.536114\pi\)
\(62\) 14.1441i 1.79630i
\(63\) −2.23155 −0.281149
\(64\) 18.1187 2.26484
\(65\) 0 0
\(66\) 4.73084 0.582326
\(67\) 9.89446 1.20880 0.604400 0.796681i \(-0.293413\pi\)
0.604400 + 0.796681i \(0.293413\pi\)
\(68\) 6.96239i 0.844314i
\(69\) −3.11871 −0.375449
\(70\) 3.19394 3.61213i 0.381748 0.431732i
\(71\) 8.56230i 1.01616i 0.861311 + 0.508079i \(0.169644\pi\)
−0.861311 + 0.508079i \(0.830356\pi\)
\(72\) 23.3757 2.75485
\(73\) −11.7685 −1.37739 −0.688697 0.725050i \(-0.741817\pi\)
−0.688697 + 0.725050i \(0.741817\pi\)
\(74\) −10.0811 −1.17190
\(75\) −2.38787 + 0.294552i −0.275728 + 0.0340119i
\(76\) 8.63752i 0.990791i
\(77\) 2.96239i 0.337596i
\(78\) 0 0
\(79\) 2.26187 0.254480 0.127240 0.991872i \(-0.459388\pi\)
0.127240 + 0.991872i \(0.459388\pi\)
\(80\) −18.1817 + 20.5623i −2.03278 + 2.29893i
\(81\) 6.96968 0.774409
\(82\) 22.2374i 2.45571i
\(83\) −3.84367 −0.421898 −0.210949 0.977497i \(-0.567655\pi\)
−0.210949 + 0.977497i \(0.567655\pi\)
\(84\) 2.00000i 0.218218i
\(85\) 2.26187 + 2.00000i 0.245334 + 0.216930i
\(86\) 18.1744i 1.95980i
\(87\) 1.16362i 0.124753i
\(88\) 31.0313i 3.30794i
\(89\) 2.77575i 0.294229i 0.989120 + 0.147114i \(0.0469985\pi\)
−0.989120 + 0.147114i \(0.953001\pi\)
\(90\) −10.9697 + 12.4060i −1.15631 + 1.30770i
\(91\) 0 0
\(92\) 33.4191i 3.48419i
\(93\) −2.54420 −0.263821
\(94\) −8.54420 −0.881267
\(95\) −2.80606 2.48119i −0.287896 0.254565i
\(96\) 7.67513i 0.783340i
\(97\) −1.87399 −0.190275 −0.0951375 0.995464i \(-0.530329\pi\)
−0.0951375 + 0.995464i \(0.530329\pi\)
\(98\) −16.9878 −1.71603
\(99\) 10.1744i 1.02257i
\(100\) −3.15633 25.5877i −0.315633 2.55877i
\(101\) −10.4993 −1.04472 −0.522359 0.852725i \(-0.674948\pi\)
−0.522359 + 0.852725i \(0.674948\pi\)
\(102\) −1.73813 −0.172101
\(103\) 15.3684i 1.51429i −0.653247 0.757145i \(-0.726594\pi\)
0.653247 0.757145i \(-0.273406\pi\)
\(104\) 0 0
\(105\) −0.649738 0.574515i −0.0634080 0.0560670i
\(106\) 15.3503i 1.49095i
\(107\) 11.1309i 1.07607i −0.842923 0.538034i \(-0.819167\pi\)
0.842923 0.538034i \(-0.180833\pi\)
\(108\) 14.3127i 1.37724i
\(109\) 9.58769i 0.918334i −0.888350 0.459167i \(-0.848148\pi\)
0.888350 0.459167i \(-0.151852\pi\)
\(110\) −16.4690 14.5623i −1.57026 1.38846i
\(111\) 1.81336i 0.172116i
\(112\) −9.89446 −0.934939
\(113\) 0.574515i 0.0540459i 0.999635 + 0.0270229i \(0.00860271\pi\)
−0.999635 + 0.0270229i \(0.991397\pi\)
\(114\) 2.15633 0.201958
\(115\) 10.8568 + 9.59991i 1.01241 + 0.895196i
\(116\) −12.4690 −1.15772
\(117\) 0 0
\(118\) 16.0181i 1.47459i
\(119\) 1.08840i 0.0997732i
\(120\) 6.80606 + 6.01810i 0.621306 + 0.549375i
\(121\) −2.50659 −0.227872
\(122\) −4.73084 −0.428310
\(123\) −4.00000 −0.360668
\(124\) 27.2628i 2.44827i
\(125\) 9.21933 + 6.32487i 0.824602 + 0.565713i
\(126\) −5.96968 −0.531822
\(127\) 4.29455i 0.381080i −0.981679 0.190540i \(-0.938976\pi\)
0.981679 0.190540i \(-0.0610239\pi\)
\(128\) 16.5696 1.46456
\(129\) 3.26916 0.287833
\(130\) 0 0
\(131\) −0.836381 −0.0730749 −0.0365375 0.999332i \(-0.511633\pi\)
−0.0365375 + 0.999332i \(0.511633\pi\)
\(132\) 9.11871 0.793682
\(133\) 1.35026i 0.117083i
\(134\) 26.4690 2.28657
\(135\) 4.64974 + 4.11142i 0.400186 + 0.353855i
\(136\) 11.4010i 0.977632i
\(137\) 14.9380 1.27624 0.638118 0.769939i \(-0.279713\pi\)
0.638118 + 0.769939i \(0.279713\pi\)
\(138\) −8.34297 −0.710201
\(139\) 8.43866 0.715758 0.357879 0.933768i \(-0.383500\pi\)
0.357879 + 0.933768i \(0.383500\pi\)
\(140\) 6.15633 6.96239i 0.520304 0.588429i
\(141\) 1.53690i 0.129431i
\(142\) 22.9053i 1.92217i
\(143\) 0 0
\(144\) 33.9829 2.83190
\(145\) 3.58181 4.05079i 0.297453 0.336399i
\(146\) −31.4821 −2.60548
\(147\) 3.05571i 0.252031i
\(148\) −19.4314 −1.59725
\(149\) 11.3503i 0.929850i 0.885350 + 0.464925i \(0.153919\pi\)
−0.885350 + 0.464925i \(0.846081\pi\)
\(150\) −6.38787 + 0.787965i −0.521568 + 0.0643371i
\(151\) 13.9878i 1.13831i −0.822230 0.569155i \(-0.807271\pi\)
0.822230 0.569155i \(-0.192729\pi\)
\(152\) 14.1441i 1.14724i
\(153\) 3.73813i 0.302210i
\(154\) 7.92478i 0.638597i
\(155\) 8.85685 + 7.83146i 0.711399 + 0.629038i
\(156\) 0 0
\(157\) 2.77575i 0.221529i −0.993847 0.110764i \(-0.964670\pi\)
0.993847 0.110764i \(-0.0353299\pi\)
\(158\) 6.05079 0.481375
\(159\) 2.76116 0.218974
\(160\) −23.6253 + 26.7186i −1.86774 + 2.11229i
\(161\) 5.22425i 0.411729i
\(162\) 18.6448 1.46487
\(163\) 2.23155 0.174788 0.0873942 0.996174i \(-0.472146\pi\)
0.0873942 + 0.996174i \(0.472146\pi\)
\(164\) 42.8627i 3.34702i
\(165\) −2.61942 + 2.96239i −0.203922 + 0.230622i
\(166\) −10.2823 −0.798064
\(167\) 15.6932 1.21438 0.607189 0.794557i \(-0.292297\pi\)
0.607189 + 0.794557i \(0.292297\pi\)
\(168\) 3.27504i 0.252675i
\(169\) 0 0
\(170\) 6.05079 + 5.35026i 0.464074 + 0.410346i
\(171\) 4.63752i 0.354640i
\(172\) 35.0313i 2.67111i
\(173\) 25.5877i 1.94540i 0.232075 + 0.972698i \(0.425449\pi\)
−0.232075 + 0.972698i \(0.574551\pi\)
\(174\) 3.11283i 0.235983i
\(175\) 0.493413 + 4.00000i 0.0372985 + 0.302372i
\(176\) 45.1124i 3.40047i
\(177\) 2.88129 0.216571
\(178\) 7.42548i 0.556564i
\(179\) 12.1260 0.906340 0.453170 0.891424i \(-0.350293\pi\)
0.453170 + 0.891424i \(0.350293\pi\)
\(180\) −21.1441 + 23.9126i −1.57599 + 1.78234i
\(181\) 2.73084 0.202982 0.101491 0.994836i \(-0.467639\pi\)
0.101491 + 0.994836i \(0.467639\pi\)
\(182\) 0 0
\(183\) 0.850969i 0.0629054i
\(184\) 54.7245i 4.03434i
\(185\) 5.58181 6.31265i 0.410383 0.464115i
\(186\) −6.80606 −0.499045
\(187\) 4.96239 0.362886
\(188\) −16.4690 −1.20112
\(189\) 2.23743i 0.162749i
\(190\) −7.50659 6.63752i −0.544585 0.481536i
\(191\) 20.6253 1.49239 0.746197 0.665725i \(-0.231878\pi\)
0.746197 + 0.665725i \(0.231878\pi\)
\(192\) 8.71862i 0.629212i
\(193\) −21.7889 −1.56840 −0.784200 0.620508i \(-0.786927\pi\)
−0.784200 + 0.620508i \(0.786927\pi\)
\(194\) −5.01317 −0.359925
\(195\) 0 0
\(196\) −32.7440 −2.33886
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 27.2179i 1.93429i
\(199\) −16.7513 −1.18747 −0.593734 0.804661i \(-0.702347\pi\)
−0.593734 + 0.804661i \(0.702347\pi\)
\(200\) −5.16854 41.9003i −0.365471 2.96280i
\(201\) 4.76116i 0.335826i
\(202\) −28.0870 −1.97619
\(203\) 1.94921 0.136808
\(204\) −3.35026 −0.234565
\(205\) 13.9248 + 12.3127i 0.972549 + 0.859953i
\(206\) 41.1124i 2.86443i
\(207\) 17.9429i 1.24712i
\(208\) 0 0
\(209\) −6.15633 −0.425842
\(210\) −1.73813 1.53690i −0.119943 0.106056i
\(211\) −4.90175 −0.337451 −0.168725 0.985663i \(-0.553965\pi\)
−0.168725 + 0.985663i \(0.553965\pi\)
\(212\) 29.5877i 2.03209i
\(213\) 4.12013 0.282307
\(214\) 29.7767i 2.03549i
\(215\) −11.3806 10.0630i −0.776149 0.686291i
\(216\) 23.4372i 1.59470i
\(217\) 4.26187i 0.289314i
\(218\) 25.6483i 1.73712i
\(219\) 5.66291i 0.382664i
\(220\) −31.7440 28.0689i −2.14018 1.89240i
\(221\) 0 0
\(222\) 4.85097i 0.325576i
\(223\) −24.9076 −1.66794 −0.833969 0.551811i \(-0.813937\pi\)
−0.833969 + 0.551811i \(0.813937\pi\)
\(224\) −12.8568 −0.859034
\(225\) −1.69464 13.7381i −0.112976 0.915876i
\(226\) 1.53690i 0.102233i
\(227\) 9.95509 0.660743 0.330371 0.943851i \(-0.392826\pi\)
0.330371 + 0.943851i \(0.392826\pi\)
\(228\) 4.15633 0.275259
\(229\) 5.35026i 0.353555i 0.984251 + 0.176778i \(0.0565673\pi\)
−0.984251 + 0.176778i \(0.943433\pi\)
\(230\) 29.0435 + 25.6810i 1.91507 + 1.69336i
\(231\) −1.42548 −0.0937900
\(232\) −20.4182 −1.34052
\(233\) 10.7612i 0.704987i 0.935814 + 0.352493i \(0.114666\pi\)
−0.935814 + 0.352493i \(0.885334\pi\)
\(234\) 0 0
\(235\) 4.73084 5.35026i 0.308606 0.349013i
\(236\) 30.8749i 2.00979i
\(237\) 1.08840i 0.0706990i
\(238\) 2.91160i 0.188731i
\(239\) 11.8618i 0.767274i 0.923484 + 0.383637i \(0.125329\pi\)
−0.923484 + 0.383637i \(0.874671\pi\)
\(240\) 9.89446 + 8.74894i 0.638685 + 0.564742i
\(241\) 28.6253i 1.84392i 0.387288 + 0.921959i \(0.373412\pi\)
−0.387288 + 0.921959i \(0.626588\pi\)
\(242\) −6.70545 −0.431043
\(243\) 11.6810i 0.749337i
\(244\) −9.11871 −0.583766
\(245\) 9.40597 10.6375i 0.600925 0.679606i
\(246\) −10.7005 −0.682240
\(247\) 0 0
\(248\) 44.6434i 2.83486i
\(249\) 1.84955i 0.117211i
\(250\) 24.6629 + 16.9199i 1.55982 + 1.07011i
\(251\) 19.3865 1.22366 0.611831 0.790988i \(-0.290433\pi\)
0.611831 + 0.790988i \(0.290433\pi\)
\(252\) −11.5066 −0.724847
\(253\) 23.8192 1.49750
\(254\) 11.4885i 0.720852i
\(255\) 0.962389 1.08840i 0.0602671 0.0681580i
\(256\) 8.08840 0.505525
\(257\) 22.8627i 1.42614i 0.701094 + 0.713069i \(0.252695\pi\)
−0.701094 + 0.713069i \(0.747305\pi\)
\(258\) 8.74543 0.544467
\(259\) 3.03761 0.188748
\(260\) 0 0
\(261\) −6.69464 −0.414388
\(262\) −2.23743 −0.138229
\(263\) 21.8822i 1.34932i 0.738130 + 0.674658i \(0.235709\pi\)
−0.738130 + 0.674658i \(0.764291\pi\)
\(264\) 14.9321 0.919005
\(265\) −9.61213 8.49929i −0.590468 0.522107i
\(266\) 3.61213i 0.221474i
\(267\) 1.33567 0.0817419
\(268\) 51.0191 3.11648
\(269\) −22.7513 −1.38717 −0.693586 0.720374i \(-0.743970\pi\)
−0.693586 + 0.720374i \(0.743970\pi\)
\(270\) 12.4387 + 10.9986i 0.756993 + 0.669353i
\(271\) 0.123638i 0.00751049i −0.999993 0.00375525i \(-0.998805\pi\)
0.999993 0.00375525i \(-0.00119534\pi\)
\(272\) 16.5745i 1.00498i
\(273\) 0 0
\(274\) 39.9610 2.41413
\(275\) 18.2374 2.24965i 1.09976 0.135659i
\(276\) −16.0811 −0.967969
\(277\) 15.3503i 0.922308i −0.887320 0.461154i \(-0.847436\pi\)
0.887320 0.461154i \(-0.152564\pi\)
\(278\) 22.5745 1.35393
\(279\) 14.6375i 0.876325i
\(280\) 10.0811 11.4010i 0.602461 0.681343i
\(281\) 13.9248i 0.830683i −0.909666 0.415341i \(-0.863662\pi\)
0.909666 0.415341i \(-0.136338\pi\)
\(282\) 4.11142i 0.244831i
\(283\) 20.3815i 1.21156i −0.795634 0.605778i \(-0.792862\pi\)
0.795634 0.605778i \(-0.207138\pi\)
\(284\) 44.1500i 2.61982i
\(285\) −1.19394 + 1.35026i −0.0707227 + 0.0799826i
\(286\) 0 0
\(287\) 6.70052i 0.395519i
\(288\) 44.1573 2.60199
\(289\) 15.1768 0.892753
\(290\) 9.58181 10.8364i 0.562663 0.636334i
\(291\) 0.901754i 0.0528618i
\(292\) −60.6820 −3.55114
\(293\) 5.38058 0.314337 0.157168 0.987572i \(-0.449763\pi\)
0.157168 + 0.987572i \(0.449763\pi\)
\(294\) 8.17442i 0.476742i
\(295\) −10.0303 8.86907i −0.583988 0.516377i
\(296\) −31.8192 −1.84946
\(297\) 10.2012 0.591935
\(298\) 30.3634i 1.75891i
\(299\) 0 0
\(300\) −12.3127 + 1.51881i −0.710871 + 0.0876883i
\(301\) 5.47627i 0.315647i
\(302\) 37.4191i 2.15323i
\(303\) 5.05220i 0.290241i
\(304\) 20.5623i 1.17933i
\(305\) 2.61942 2.96239i 0.149988 0.169626i
\(306\) 10.0000i 0.571662i
\(307\) 19.1695 1.09406 0.547031 0.837113i \(-0.315758\pi\)
0.547031 + 0.837113i \(0.315758\pi\)
\(308\) 15.2750i 0.870376i
\(309\) −7.39517 −0.420696
\(310\) 23.6932 + 20.9502i 1.34568 + 1.18989i
\(311\) 25.2506 1.43183 0.715915 0.698187i \(-0.246010\pi\)
0.715915 + 0.698187i \(0.246010\pi\)
\(312\) 0 0
\(313\) 2.81194i 0.158940i 0.996837 + 0.0794702i \(0.0253229\pi\)
−0.996837 + 0.0794702i \(0.974677\pi\)
\(314\) 7.42548i 0.419044i
\(315\) 3.30536 3.73813i 0.186236 0.210620i
\(316\) 11.6629 0.656090
\(317\) −23.7685 −1.33497 −0.667485 0.744624i \(-0.732629\pi\)
−0.667485 + 0.744624i \(0.732629\pi\)
\(318\) 7.38646 0.414212
\(319\) 8.88717i 0.497586i
\(320\) −26.8373 + 30.3512i −1.50025 + 1.69668i
\(321\) −5.35614 −0.298951
\(322\) 13.9756i 0.778828i
\(323\) 2.26187 0.125854
\(324\) 35.9380 1.99655
\(325\) 0 0
\(326\) 5.96968 0.330630
\(327\) −4.61354 −0.255129
\(328\) 70.1886i 3.87551i
\(329\) 2.57452 0.141938
\(330\) −7.00729 + 7.92478i −0.385739 + 0.436245i
\(331\) 11.8011i 0.648649i −0.945946 0.324325i \(-0.894863\pi\)
0.945946 0.324325i \(-0.105137\pi\)
\(332\) −19.8192 −1.08772
\(333\) −10.4328 −0.571713
\(334\) 41.9814 2.29712
\(335\) −14.6556 + 16.5745i −0.800722 + 0.905563i
\(336\) 4.76116i 0.259742i
\(337\) 16.1114i 0.877645i 0.898574 + 0.438822i \(0.144604\pi\)
−0.898574 + 0.438822i \(0.855396\pi\)
\(338\) 0 0
\(339\) 0.276454 0.0150149
\(340\) 11.6629 + 10.3127i 0.632510 + 0.559282i
\(341\) 19.4314 1.05227
\(342\) 12.4060i 0.670838i
\(343\) 10.7612 0.581048
\(344\) 57.3644i 3.09288i
\(345\) 4.61942 5.22425i 0.248701 0.281264i
\(346\) 68.4504i 3.67992i
\(347\) 27.4944i 1.47598i −0.674814 0.737988i \(-0.735776\pi\)
0.674814 0.737988i \(-0.264224\pi\)
\(348\) 6.00000i 0.321634i
\(349\) 17.6023i 0.942228i −0.882072 0.471114i \(-0.843852\pi\)
0.882072 0.471114i \(-0.156148\pi\)
\(350\) 1.31994 + 10.7005i 0.0705540 + 0.571967i
\(351\) 0 0
\(352\) 58.6190i 3.12440i
\(353\) −15.7685 −0.839270 −0.419635 0.907693i \(-0.637842\pi\)
−0.419635 + 0.907693i \(0.637842\pi\)
\(354\) 7.70782 0.409666
\(355\) −14.3430 12.6824i −0.761246 0.673113i
\(356\) 14.3127i 0.758569i
\(357\) 0.523730 0.0277187
\(358\) 32.4387 1.71444
\(359\) 14.8242i 0.782389i −0.920308 0.391195i \(-0.872062\pi\)
0.920308 0.391195i \(-0.127938\pi\)
\(360\) −34.6239 + 39.1573i −1.82484 + 2.06377i
\(361\) 16.1939 0.852312
\(362\) 7.30536 0.383961
\(363\) 1.20616i 0.0633067i
\(364\) 0 0
\(365\) 17.4314 19.7137i 0.912399 1.03186i
\(366\) 2.27645i 0.118992i
\(367\) 27.0313i 1.41102i 0.708700 + 0.705510i \(0.249282\pi\)
−0.708700 + 0.705510i \(0.750718\pi\)
\(368\) 79.5569i 4.14719i
\(369\) 23.0132i 1.19802i
\(370\) 14.9321 16.8872i 0.776281 0.877922i
\(371\) 4.62530i 0.240134i
\(372\) −13.1187 −0.680174
\(373\) 12.9525i 0.670657i 0.942101 + 0.335329i \(0.108847\pi\)
−0.942101 + 0.335329i \(0.891153\pi\)
\(374\) 13.2750 0.686436
\(375\) 3.04349 4.43629i 0.157165 0.229089i
\(376\) −26.9683 −1.39078
\(377\) 0 0
\(378\) 5.98541i 0.307856i
\(379\) 30.2858i 1.55568i 0.628463 + 0.777840i \(0.283684\pi\)
−0.628463 + 0.777840i \(0.716316\pi\)
\(380\) −14.4690 12.7938i −0.742243 0.656310i
\(381\) −2.06651 −0.105871
\(382\) 55.1754 2.82302
\(383\) 21.0943 1.07787 0.538934 0.842348i \(-0.318827\pi\)
0.538934 + 0.842348i \(0.318827\pi\)
\(384\) 7.97319i 0.406880i
\(385\) 4.96239 + 4.38787i 0.252907 + 0.223627i
\(386\) −58.2882 −2.96679
\(387\) 18.8084i 0.956086i
\(388\) −9.66291 −0.490560
\(389\) −6.77575 −0.343544 −0.171772 0.985137i \(-0.554949\pi\)
−0.171772 + 0.985137i \(0.554949\pi\)
\(390\) 0 0
\(391\) −8.75131 −0.442573
\(392\) −53.6190 −2.70817
\(393\) 0.402462i 0.0203015i
\(394\) 5.35026 0.269542
\(395\) −3.35026 + 3.78892i −0.168570 + 0.190641i
\(396\) 52.4626i 2.63635i
\(397\) −10.4690 −0.525423 −0.262711 0.964874i \(-0.584617\pi\)
−0.262711 + 0.964874i \(0.584617\pi\)
\(398\) −44.8119 −2.24622
\(399\) −0.649738 −0.0325276
\(400\) −7.51388 60.9135i −0.375694 3.04568i
\(401\) 5.01317i 0.250346i −0.992135 0.125173i \(-0.960051\pi\)
0.992135 0.125173i \(-0.0399486\pi\)
\(402\) 12.7367i 0.635250i
\(403\) 0 0
\(404\) −54.1378 −2.69345
\(405\) −10.3235 + 11.6751i −0.512977 + 0.580142i
\(406\) 5.21440 0.258787
\(407\) 13.8496i 0.686497i
\(408\) −5.48612 −0.271603
\(409\) 14.3879i 0.711435i 0.934594 + 0.355717i \(0.115763\pi\)
−0.934594 + 0.355717i \(0.884237\pi\)
\(410\) 37.2506 + 32.9380i 1.83968 + 1.62669i
\(411\) 7.18806i 0.354561i
\(412\) 79.2443i 3.90408i
\(413\) 4.82653i 0.237498i
\(414\) 47.9995i 2.35905i
\(415\) 5.69323 6.43866i 0.279470 0.316061i
\(416\) 0 0
\(417\) 4.06063i 0.198850i
\(418\) −16.4690 −0.805524
\(419\) −17.4617 −0.853059 −0.426529 0.904474i \(-0.640264\pi\)
−0.426529 + 0.904474i \(0.640264\pi\)
\(420\) −3.35026 2.96239i −0.163476 0.144550i
\(421\) 2.88717i 0.140712i 0.997522 + 0.0703559i \(0.0224135\pi\)
−0.997522 + 0.0703559i \(0.977586\pi\)
\(422\) −13.1128 −0.638323
\(423\) −8.84226 −0.429925
\(424\) 48.4504i 2.35296i
\(425\) −6.70052 + 0.826531i −0.325023 + 0.0400927i
\(426\) 11.0219 0.534012
\(427\) 1.42548 0.0689840
\(428\) 57.3947i 2.77428i
\(429\) 0 0
\(430\) −30.4445 26.9199i −1.46817 1.29819i
\(431\) 0.889535i 0.0428474i 0.999770 + 0.0214237i \(0.00681990\pi\)
−0.999770 + 0.0214237i \(0.993180\pi\)
\(432\) 34.0724i 1.63931i
\(433\) 25.2506i 1.21347i 0.794906 + 0.606733i \(0.207520\pi\)
−0.794906 + 0.606733i \(0.792480\pi\)
\(434\) 11.4010i 0.547268i
\(435\) −1.94921 1.72355i −0.0934577 0.0826377i
\(436\) 49.4372i 2.36761i
\(437\) 10.8568 0.519354
\(438\) 15.1490i 0.723849i
\(439\) 28.8119 1.37512 0.687560 0.726128i \(-0.258682\pi\)
0.687560 + 0.726128i \(0.258682\pi\)
\(440\) −51.9814 45.9633i −2.47812 2.19122i
\(441\) −17.5804 −0.837162
\(442\) 0 0
\(443\) 36.9805i 1.75700i 0.477746 + 0.878498i \(0.341454\pi\)
−0.477746 + 0.878498i \(0.658546\pi\)
\(444\) 9.35026i 0.443744i
\(445\) −4.64974 4.11142i −0.220419 0.194900i
\(446\) −66.6312 −3.15508
\(447\) 5.46168 0.258329
\(448\) −14.6048 −0.690013
\(449\) 12.6859i 0.598686i −0.954146 0.299343i \(-0.903232\pi\)
0.954146 0.299343i \(-0.0967675\pi\)
\(450\) −4.53339 36.7513i −0.213706 1.73247i
\(451\) 30.5501 1.43855
\(452\) 2.96239i 0.139339i
\(453\) −6.73084 −0.316242
\(454\) 26.6312 1.24986
\(455\) 0 0
\(456\) 6.80606 0.318723
\(457\) −25.0494 −1.17176 −0.585880 0.810398i \(-0.699251\pi\)
−0.585880 + 0.810398i \(0.699251\pi\)
\(458\) 14.3127i 0.668786i
\(459\) −3.74798 −0.174941
\(460\) 55.9814 + 49.5002i 2.61015 + 2.30796i
\(461\) 36.8872i 1.71801i −0.511970 0.859003i \(-0.671084\pi\)
0.511970 0.859003i \(-0.328916\pi\)
\(462\) −3.81336 −0.177413
\(463\) −39.0191 −1.81337 −0.906685 0.421809i \(-0.861395\pi\)
−0.906685 + 0.421809i \(0.861395\pi\)
\(464\) −29.6834 −1.37802
\(465\) 3.76845 4.26187i 0.174758 0.197639i
\(466\) 28.7875i 1.33356i
\(467\) 32.7694i 1.51639i 0.652029 + 0.758194i \(0.273918\pi\)
−0.652029 + 0.758194i \(0.726082\pi\)
\(468\) 0 0
\(469\) −7.97556 −0.368277
\(470\) 12.6556 14.3127i 0.583760 0.660193i
\(471\) −1.33567 −0.0615446
\(472\) 50.5583i 2.32714i
\(473\) −24.9683 −1.14804
\(474\) 2.91160i 0.133734i
\(475\) 8.31265 1.02539i 0.381411 0.0470482i
\(476\) 5.61213i 0.257231i
\(477\) 15.8858i 0.727359i
\(478\) 31.7318i 1.45138i
\(479\) 16.8749i 0.771036i 0.922700 + 0.385518i \(0.125977\pi\)
−0.922700 + 0.385518i \(0.874023\pi\)
\(480\) 12.8568 + 11.3684i 0.586832 + 0.518892i
\(481\) 0 0
\(482\) 76.5764i 3.48796i
\(483\) 2.51388 0.114386
\(484\) −12.9248 −0.587490
\(485\) 2.77575 3.13918i 0.126040 0.142543i
\(486\) 31.2482i 1.41745i
\(487\) −9.24472 −0.418918 −0.209459 0.977817i \(-0.567170\pi\)
−0.209459 + 0.977817i \(0.567170\pi\)
\(488\) −14.9321 −0.675943
\(489\) 1.07381i 0.0485593i
\(490\) 25.1622 28.4568i 1.13671 1.28555i
\(491\) 25.7499 1.16208 0.581038 0.813876i \(-0.302647\pi\)
0.581038 + 0.813876i \(0.302647\pi\)
\(492\) −20.6253 −0.929860
\(493\) 3.26519i 0.147057i
\(494\) 0 0
\(495\) −17.0435 15.0703i −0.766048 0.677360i
\(496\) 64.9013i 2.91415i
\(497\) 6.90175i 0.309586i
\(498\) 4.94780i 0.221716i
\(499\) 27.7015i 1.24009i 0.784567 + 0.620044i \(0.212885\pi\)
−0.784567 + 0.620044i \(0.787115\pi\)
\(500\) 47.5379 + 32.6131i 2.12596 + 1.45850i
\(501\) 7.55149i 0.337376i
\(502\) 51.8613 2.31468
\(503\) 2.35519i 0.105013i 0.998621 + 0.0525063i \(0.0167210\pi\)
−0.998621 + 0.0525063i \(0.983279\pi\)
\(504\) −18.8423 −0.839301
\(505\) 15.5515 17.5877i 0.692032 0.782642i
\(506\) 63.7196 2.83268
\(507\) 0 0
\(508\) 22.1441i 0.982486i
\(509\) 21.5125i 0.953523i −0.879033 0.476762i \(-0.841810\pi\)
0.879033 0.476762i \(-0.158190\pi\)
\(510\) 2.57452 2.91160i 0.114001 0.128928i
\(511\) 9.48612 0.419641
\(512\) −11.5017 −0.508306
\(513\) 4.64974 0.205291
\(514\) 61.1608i 2.69769i
\(515\) 25.7440 + 22.7635i 1.13442 + 1.00308i
\(516\) 16.8568 0.742081
\(517\) 11.7381i 0.516243i
\(518\) 8.12601 0.357036
\(519\) 12.3127 0.540465
\(520\) 0 0
\(521\) 37.7440 1.65360 0.826798 0.562499i \(-0.190160\pi\)
0.826798 + 0.562499i \(0.190160\pi\)
\(522\) −17.9090 −0.783858
\(523\) 23.7416i 1.03815i 0.854729 + 0.519075i \(0.173723\pi\)
−0.854729 + 0.519075i \(0.826277\pi\)
\(524\) −4.31265 −0.188399
\(525\) 1.92478 0.237428i 0.0840042 0.0103622i
\(526\) 58.5379i 2.55237i
\(527\) −7.13918 −0.310988
\(528\) 21.7078 0.944712
\(529\) −19.0059 −0.826343
\(530\) −25.7137 22.7367i −1.11693 0.987620i
\(531\) 16.5769i 0.719376i
\(532\) 6.96239i 0.301858i
\(533\) 0 0
\(534\) 3.57310 0.154623
\(535\) 18.6458 + 16.4871i 0.806127 + 0.712798i
\(536\) 83.5447 3.60858
\(537\) 5.83497i 0.251797i
\(538\) −60.8627 −2.62398
\(539\) 23.3380i 1.00524i
\(540\) 23.9756 + 21.1998i 1.03174 + 0.912295i
\(541\) 13.0376i 0.560531i −0.959923 0.280265i \(-0.909578\pi\)
0.959923 0.280265i \(-0.0904225\pi\)
\(542\) 0.330749i 0.0142069i
\(543\) 1.31406i 0.0563919i
\(544\) 21.5369i 0.923387i
\(545\) 16.0606 + 14.2012i 0.687962 + 0.608314i
\(546\) 0 0
\(547\) 8.43041i 0.360458i −0.983625 0.180229i \(-0.942316\pi\)
0.983625 0.180229i \(-0.0576839\pi\)
\(548\) 77.0249 3.29034
\(549\) −4.89587 −0.208951
\(550\) 48.7875 6.01810i 2.08031 0.256613i
\(551\) 4.05079i 0.172569i
\(552\) −26.3331 −1.12081
\(553\) −1.82321 −0.0775306
\(554\) 41.0640i 1.74464i
\(555\) −3.03761 2.68594i −0.128939 0.114012i
\(556\) 43.5125 1.84534
\(557\) −13.6932 −0.580201 −0.290100 0.956996i \(-0.593689\pi\)
−0.290100 + 0.956996i \(0.593689\pi\)
\(558\) 39.1573i 1.65766i
\(559\) 0 0
\(560\) 14.6556 16.5745i 0.619313 0.700401i
\(561\) 2.38787i 0.100816i
\(562\) 37.2506i 1.57132i
\(563\) 8.86907i 0.373787i 0.982380 + 0.186893i \(0.0598419\pi\)
−0.982380 + 0.186893i \(0.940158\pi\)
\(564\) 7.92478i 0.333693i
\(565\) −0.962389 0.850969i −0.0404880 0.0358005i
\(566\) 54.5233i 2.29178i
\(567\) −5.61801 −0.235934
\(568\) 72.2965i 3.03349i
\(569\) −32.7816 −1.37428 −0.687139 0.726526i \(-0.741134\pi\)
−0.687139 + 0.726526i \(0.741134\pi\)
\(570\) −3.19394 + 3.61213i −0.133779 + 0.151295i
\(571\) −40.2882 −1.68601 −0.843005 0.537906i \(-0.819215\pi\)
−0.843005 + 0.537906i \(0.819215\pi\)
\(572\) 0 0
\(573\) 9.92478i 0.414614i
\(574\) 17.9248i 0.748166i
\(575\) −32.1622 + 3.96731i −1.34126 + 0.165448i
\(576\) 50.1608 2.09003
\(577\) 28.8568 1.20133 0.600663 0.799502i \(-0.294903\pi\)
0.600663 + 0.799502i \(0.294903\pi\)
\(578\) 40.5999 1.68873
\(579\) 10.4847i 0.435729i
\(580\) 18.4690 20.8872i 0.766882 0.867292i
\(581\) 3.09825 0.128537
\(582\) 2.41231i 0.0999935i
\(583\) −21.0884 −0.873392
\(584\) −99.3679 −4.11187
\(585\) 0 0
\(586\) 14.3938 0.594600
\(587\) 41.6786 1.72026 0.860131 0.510074i \(-0.170382\pi\)
0.860131 + 0.510074i \(0.170382\pi\)
\(588\) 15.7562i 0.649776i
\(589\) 8.85685 0.364940
\(590\) −26.8324 23.7259i −1.10467 0.976781i
\(591\) 0.962389i 0.0395874i
\(592\) −46.2579 −1.90119
\(593\) 22.4993 0.923935 0.461968 0.886897i \(-0.347144\pi\)
0.461968 + 0.886897i \(0.347144\pi\)
\(594\) 27.2896 1.11971
\(595\) −1.82321 1.61213i −0.0747442 0.0660908i
\(596\) 58.5256i 2.39730i
\(597\) 8.06063i 0.329900i
\(598\) 0 0
\(599\) −4.15045 −0.169583 −0.0847913 0.996399i \(-0.527022\pi\)
−0.0847913 + 0.996399i \(0.527022\pi\)
\(600\) −20.1622 + 2.48707i −0.823119 + 0.101534i
\(601\) 27.9248 1.13908 0.569538 0.821965i \(-0.307122\pi\)
0.569538 + 0.821965i \(0.307122\pi\)
\(602\) 14.6497i 0.597079i
\(603\) 27.3923 1.11550
\(604\) 72.1255i 2.93475i
\(605\) 3.71274 4.19886i 0.150944 0.170708i
\(606\) 13.5153i 0.549021i
\(607\) 8.19489i 0.332620i −0.986073 0.166310i \(-0.946815\pi\)
0.986073 0.166310i \(-0.0531853\pi\)
\(608\) 26.7186i 1.08358i
\(609\) 0.937951i 0.0380077i
\(610\) 7.00729 7.92478i 0.283717 0.320865i
\(611\) 0 0
\(612\) 19.2750i 0.779147i
\(613\) −33.1392 −1.33848 −0.669239 0.743047i \(-0.733380\pi\)
−0.669239 + 0.743047i \(0.733380\pi\)
\(614\) 51.2809 2.06953
\(615\) 5.92478 6.70052i 0.238910 0.270191i
\(616\) 25.0132i 1.00781i
\(617\) −29.0132 −1.16803 −0.584013 0.811744i \(-0.698518\pi\)
−0.584013 + 0.811744i \(0.698518\pi\)
\(618\) −19.7830 −0.795791
\(619\) 12.2134i 0.490900i 0.969409 + 0.245450i \(0.0789357\pi\)
−0.969409 + 0.245450i \(0.921064\pi\)
\(620\) 45.6688 + 40.3815i 1.83410 + 1.62176i
\(621\) −17.9902 −0.721920
\(622\) 67.5487 2.70845
\(623\) 2.23743i 0.0896406i
\(624\) 0 0
\(625\) −24.2506 + 6.07522i −0.970024 + 0.243009i
\(626\) 7.52232i 0.300652i
\(627\) 2.96239i 0.118306i
\(628\) 14.3127i 0.571137i
\(629\) 5.08840i 0.202888i
\(630\) 8.84226 10.0000i 0.352284 0.398410i
\(631\) 1.22188i 0.0486424i 0.999704 + 0.0243212i \(0.00774245\pi\)
−0.999704 + 0.0243212i \(0.992258\pi\)
\(632\) 19.0982 0.759687
\(633\) 2.35870i 0.0937498i
\(634\) −63.5837 −2.52523
\(635\) 7.19394 + 6.36107i 0.285483 + 0.252431i
\(636\) 14.2374 0.564551
\(637\) 0 0
\(638\) 23.7743i 0.941235i
\(639\) 23.7043i 0.937728i
\(640\) −24.5428 + 27.7562i −0.970139 + 1.09716i
\(641\) 22.1016 0.872960 0.436480 0.899714i \(-0.356225\pi\)
0.436480 + 0.899714i \(0.356225\pi\)
\(642\) −14.3284 −0.565496
\(643\) −11.6688 −0.460172 −0.230086 0.973170i \(-0.573901\pi\)
−0.230086 + 0.973170i \(0.573901\pi\)
\(644\) 26.9380i 1.06150i
\(645\) −4.84226 + 5.47627i −0.190664 + 0.215628i
\(646\) 6.05079 0.238065
\(647\) 11.9575i 0.470096i 0.971984 + 0.235048i \(0.0755248\pi\)
−0.971984 + 0.235048i \(0.924475\pi\)
\(648\) 58.8491 2.31181
\(649\) −22.0059 −0.863806
\(650\) 0 0
\(651\) 2.05079 0.0803766
\(652\) 11.5066 0.450633
\(653\) 10.9986i 0.430408i −0.976569 0.215204i \(-0.930958\pi\)
0.976569 0.215204i \(-0.0690416\pi\)
\(654\) −12.3418 −0.482604
\(655\) 1.23884 1.40105i 0.0484056 0.0547434i
\(656\) 102.038i 3.98392i
\(657\) −32.5804 −1.27108
\(658\) 6.88717 0.268490
\(659\) 2.63989 0.102835 0.0514177 0.998677i \(-0.483626\pi\)
0.0514177 + 0.998677i \(0.483626\pi\)
\(660\) −13.5066 + 15.2750i −0.525743 + 0.594580i
\(661\) 18.3028i 0.711896i −0.934506 0.355948i \(-0.884158\pi\)
0.934506 0.355948i \(-0.115842\pi\)
\(662\) 31.5696i 1.22699i
\(663\) 0 0
\(664\) −32.4544 −1.25947
\(665\) 2.26187 + 2.00000i 0.0877114 + 0.0775567i
\(666\) −27.9090 −1.08145
\(667\) 15.6728i 0.606852i
\(668\) 80.9194 3.13087
\(669\) 11.9854i 0.463383i
\(670\) −39.2057 + 44.3390i −1.51465 + 1.71296i
\(671\) 6.49929i 0.250902i
\(672\) 6.18664i 0.238655i
\(673\) 6.71037i 0.258666i −0.991601 0.129333i \(-0.958716\pi\)
0.991601 0.129333i \(-0.0412836\pi\)
\(674\) 43.1002i 1.66016i
\(675\) −13.7743 + 1.69911i −0.530174 + 0.0653987i
\(676\) 0 0
\(677\) 1.57593i 0.0605679i 0.999541 + 0.0302840i \(0.00964116\pi\)
−0.999541 + 0.0302840i \(0.990359\pi\)
\(678\) 0.739549 0.0284022
\(679\) 1.51056 0.0579698
\(680\) 19.0982 + 16.8872i 0.732384 + 0.647593i
\(681\) 4.79033i 0.183566i
\(682\) 51.9814 1.99047
\(683\) 15.1939 0.581380 0.290690 0.956817i \(-0.406115\pi\)
0.290690 + 0.956817i \(0.406115\pi\)
\(684\) 23.9126i 0.914320i
\(685\) −22.1260 + 25.0230i −0.845391 + 0.956081i
\(686\) 28.7875 1.09911
\(687\) 2.57452 0.0982239
\(688\) 83.3947i 3.17939i
\(689\) 0 0
\(690\) 12.3576 13.9756i 0.470444 0.532041i
\(691\) 18.7127i 0.711866i −0.934511 0.355933i \(-0.884163\pi\)
0.934511 0.355933i \(-0.115837\pi\)
\(692\) 131.938i 5.01555i
\(693\) 8.20123i 0.311539i
\(694\) 73.5510i 2.79196i
\(695\) −12.4993 + 14.1359i −0.474125 + 0.536204i
\(696\) 9.82512i 0.372420i
\(697\) −11.2243 −0.425149
\(698\) 47.0884i 1.78232i
\(699\) 5.17821 0.195858
\(700\) 2.54420 + 20.6253i 0.0961617 + 0.779563i
\(701\) −24.3028 −0.917904 −0.458952 0.888461i \(-0.651775\pi\)
−0.458952 + 0.888461i \(0.651775\pi\)
\(702\) 0 0
\(703\) 6.31265i 0.238086i
\(704\) 66.5886i 2.50965i
\(705\) −2.57452 2.27645i −0.0969619 0.0857362i
\(706\) −42.1827 −1.58757
\(707\) 8.46310 0.318287
\(708\) 14.8568 0.558355
\(709\) 9.66291i 0.362898i −0.983400 0.181449i \(-0.941921\pi\)
0.983400 0.181449i \(-0.0580788\pi\)
\(710\) −38.3693 33.9271i −1.43997 1.27326i
\(711\) 6.26187 0.234838
\(712\) 23.4372i 0.878348i
\(713\) −34.2677 −1.28334
\(714\) 1.40105 0.0524329
\(715\) 0 0
\(716\) 62.5256 2.33669
\(717\) 5.70782 0.213162
\(718\) 39.6566i 1.47997i
\(719\) 28.4142 1.05967 0.529836 0.848100i \(-0.322254\pi\)
0.529836 + 0.848100i \(0.322254\pi\)
\(720\) −50.3352 + 56.9257i −1.87588 + 2.12150i
\(721\) 12.3879i 0.461349i
\(722\) 43.3209 1.61224
\(723\) 13.7743 0.512273
\(724\) 14.0811 0.523320
\(725\) 1.48024 + 12.0000i 0.0549747 + 0.445669i
\(726\) 3.22662i 0.119751i
\(727\) 34.8545i 1.29268i −0.763049 0.646341i \(-0.776299\pi\)
0.763049 0.646341i \(-0.223701\pi\)
\(728\) 0 0
\(729\) 15.2882 0.566230
\(730\) 46.6312 52.7367i 1.72590 1.95187i
\(731\) 9.17347 0.339293
\(732\) 4.38787i 0.162180i
\(733\) −6.25202 −0.230923 −0.115462 0.993312i \(-0.536835\pi\)
−0.115462 + 0.993312i \(0.536835\pi\)
\(734\) 72.3122i 2.66909i
\(735\) −5.11871 4.52610i −0.188807 0.166948i
\(736\) 103.376i 3.81050i
\(737\) 36.3634i 1.33946i
\(738\) 61.5633i 2.26617i
\(739\) 32.0846i 1.18025i −0.807311 0.590126i \(-0.799078\pi\)
0.807311 0.590126i \(-0.200922\pi\)
\(740\) 28.7816 32.5501i 1.05803 1.19656i
\(741\) 0 0
\(742\) 12.3733i 0.454238i
\(743\) 30.5442 1.12056 0.560279 0.828304i \(-0.310694\pi\)
0.560279 + 0.828304i \(0.310694\pi\)
\(744\) −21.4821 −0.787574
\(745\) −19.0132 16.8119i −0.696589 0.615942i
\(746\) 34.6497i 1.26862i
\(747\) −10.6410 −0.389335
\(748\) 25.5877 0.935579
\(749\) 8.97224i 0.327838i
\(750\) 8.14174 11.8677i 0.297294 0.433345i
\(751\) −28.1622 −1.02765 −0.513827 0.857894i \(-0.671773\pi\)
−0.513827 + 0.857894i \(0.671773\pi\)
\(752\) −39.2057 −1.42968
\(753\) 9.32865i 0.339955i
\(754\) 0 0
\(755\) 23.4314 + 20.7186i 0.852755 + 0.754028i
\(756\) 11.5369i 0.419593i
\(757\) 35.4109i 1.28703i −0.765433 0.643515i \(-0.777475\pi\)
0.765433 0.643515i \(-0.222525\pi\)
\(758\) 81.0186i 2.94273i
\(759\) 11.4617i 0.416033i
\(760\) −23.6932 20.9502i −0.859444 0.759943i
\(761\) 19.2388i 0.697407i 0.937233 + 0.348704i \(0.113378\pi\)
−0.937233 + 0.348704i \(0.886622\pi\)
\(762\) −5.52820 −0.200265
\(763\) 7.72829i 0.279783i
\(764\) 106.351 3.84764
\(765\) 6.26187 + 5.53690i 0.226398 + 0.200187i
\(766\) 56.4299 2.03890
\(767\) 0 0
\(768\) 3.89209i 0.140444i
\(769\) 48.9643i 1.76570i −0.469657 0.882849i \(-0.655622\pi\)
0.469657 0.882849i \(-0.344378\pi\)
\(770\) 13.2750 + 11.7381i 0.478399 + 0.423013i
\(771\) 11.0014 0.396206
\(772\) −112.351 −4.04359
\(773\) −46.1681 −1.66055 −0.830275 0.557354i \(-0.811817\pi\)
−0.830275 + 0.557354i \(0.811817\pi\)
\(774\) 50.3150i 1.80854i
\(775\) −26.2374 + 3.23647i −0.942476 + 0.116258i
\(776\) −15.8232 −0.568020
\(777\) 1.46168i 0.0524375i
\(778\) −18.1260 −0.649849
\(779\) 13.9248 0.498907
\(780\) 0 0
\(781\) −31.4676 −1.12600
\(782\) −23.4109 −0.837172
\(783\) 6.71228i 0.239877i
\(784\) −77.9497 −2.78392
\(785\) 4.64974 + 4.11142i 0.165956 + 0.146743i
\(786\) 1.07664i 0.0384024i
\(787\) 22.6458 0.807234 0.403617 0.914928i \(-0.367753\pi\)
0.403617 + 0.914928i \(0.367753\pi\)
\(788\) 10.3127 0.367373
\(789\) 10.5296 0.374864
\(790\) −8.96239 + 10.1359i −0.318867 + 0.360618i
\(791\) 0.463096i 0.0164658i
\(792\) 85.9086i 3.05263i
\(793\) 0 0
\(794\) −28.0059 −0.993891
\(795\) −4.08981 + 4.62530i −0.145051 + 0.164043i
\(796\) −86.3752 −3.06149
\(797\) 8.23743i 0.291785i 0.989300 + 0.145892i \(0.0466053\pi\)
−0.989300 + 0.145892i \(0.953395\pi\)
\(798\) −1.73813 −0.0615293
\(799\) 4.31265i 0.152571i
\(800\) −9.76353 79.1509i −0.345193 2.79841i
\(801\) 7.68452i 0.271519i
\(802\) 13.4109i 0.473555i
\(803\) 43.2506i 1.52628i
\(804\) 24.5501i 0.865814i
\(805\) −8.75131 7.73813i −0.308443 0.272733i
\(806\) 0 0
\(807\) 10.9478i 0.385381i
\(808\) −88.6516 −3.11875
\(809\) −44.1319 −1.55159 −0.775797 0.630982i \(-0.782652\pi\)
−0.775797 + 0.630982i \(0.782652\pi\)
\(810\) −27.6166 + 31.2325i −0.970348 + 1.09740i
\(811\) 22.6883i 0.796694i 0.917235 + 0.398347i \(0.130416\pi\)
−0.917235 + 0.398347i \(0.869584\pi\)
\(812\) 10.0508 0.352713
\(813\) −0.0594941 −0.00208655
\(814\) 37.0494i 1.29858i
\(815\) −3.30536 + 3.73813i −0.115782 + 0.130941i
\(816\) −7.97556 −0.279201
\(817\) −11.3806 −0.398156
\(818\) 38.4894i 1.34575i
\(819\) 0 0
\(820\) 71.8007 + 63.4880i 2.50739 + 2.21710i
\(821\) 50.2736i 1.75456i −0.479978 0.877281i \(-0.659355\pi\)
0.479978 0.877281i \(-0.340645\pi\)
\(822\) 19.2290i 0.670688i
\(823\) 5.13093i 0.178853i −0.995993 0.0894265i \(-0.971497\pi\)
0.995993 0.0894265i \(-0.0285034\pi\)
\(824\) 129.764i 4.52054i
\(825\) −1.08252 8.77575i −0.0376884 0.305532i
\(826\) 12.9116i 0.449252i
\(827\) −18.6946 −0.650076 −0.325038 0.945701i \(-0.605377\pi\)
−0.325038 + 0.945701i \(0.605377\pi\)
\(828\) 92.5193i 3.21527i
\(829\) −3.44121 −0.119518 −0.0597591 0.998213i \(-0.519033\pi\)
−0.0597591 + 0.998213i \(0.519033\pi\)
\(830\) 15.2301 17.2243i 0.528646 0.597863i
\(831\) −7.38646 −0.256233
\(832\) 0 0
\(833\) 8.57452i 0.297089i
\(834\) 10.8627i 0.376146i
\(835\) −23.2447 + 26.2882i −0.804417 + 0.909741i
\(836\) −31.7440 −1.09789
\(837\) −14.6761 −0.507280
\(838\) −46.7123 −1.61365
\(839\) 52.6248i 1.81681i −0.418090 0.908406i \(-0.637300\pi\)
0.418090 0.908406i \(-0.362700\pi\)
\(840\) −5.48612 4.85097i −0.189289 0.167374i
\(841\) −23.1524 −0.798357
\(842\) 7.72355i 0.266171i
\(843\) −6.70052 −0.230778
\(844\) −25.2750 −0.870003
\(845\) 0 0
\(846\) −23.6542 −0.813248
\(847\) 2.02047 0.0694241
\(848\) 70.4358i 2.41878i
\(849\) −9.80748 −0.336592
\(850\) −17.9248 + 2.21108i −0.614815 + 0.0758394i
\(851\) 24.4241i 0.837246i
\(852\) 21.2447 0.727832
\(853\) −6.31853 −0.216342 −0.108171 0.994132i \(-0.534499\pi\)
−0.108171 + 0.994132i \(0.534499\pi\)
\(854\) 3.81336 0.130490
\(855\) −7.76845 6.86907i −0.265675 0.234917i
\(856\) 93.9850i 3.21234i
\(857\) 0.775746i 0.0264990i −0.999912 0.0132495i \(-0.995782\pi\)
0.999912 0.0132495i \(-0.00421757\pi\)
\(858\) 0 0
\(859\) −3.24869 −0.110844 −0.0554220 0.998463i \(-0.517650\pi\)
−0.0554220 + 0.998463i \(0.517650\pi\)
\(860\) −58.6820 51.8881i −2.00104 1.76937i
\(861\) 3.22425 0.109882
\(862\) 2.37962i 0.0810503i
\(863\) 19.9208 0.678112 0.339056 0.940766i \(-0.389892\pi\)
0.339056 + 0.940766i \(0.389892\pi\)
\(864\) 44.2736i 1.50622i
\(865\) −42.8627 37.9003i −1.45738 1.28865i
\(866\) 67.5487i 2.29540i
\(867\) 7.30299i 0.248022i
\(868\) 21.9756i 0.745899i
\(869\) 8.31265i 0.281987i
\(870\) −5.21440 4.61071i −0.176785 0.156318i
\(871\) 0 0
\(872\) 80.9544i 2.74146i
\(873\) −5.18806 −0.175589
\(874\) 29.0435 0.982411
\(875\) −7.43136 5.09825i −0.251226 0.172352i
\(876\) 29.1998i 0.986570i
\(877\) 22.1378 0.747539 0.373770 0.927522i \(-0.378065\pi\)
0.373770 + 0.927522i \(0.378065\pi\)
\(878\) 77.0757 2.60118
\(879\) 2.58910i 0.0873283i
\(880\) −75.5691 66.8202i −2.54743 2.25251i
\(881\) −2.23155 −0.0751828 −0.0375914 0.999293i \(-0.511969\pi\)
−0.0375914 + 0.999293i \(0.511969\pi\)
\(882\) −47.0299 −1.58358
\(883\) 4.30440i 0.144855i 0.997374 + 0.0724273i \(0.0230745\pi\)
−0.997374 + 0.0724273i \(0.976925\pi\)
\(884\) 0 0
\(885\) −4.26774 + 4.82653i −0.143459 + 0.162242i
\(886\) 98.9276i 3.32354i
\(887\) 15.9330i 0.534979i −0.963561 0.267489i \(-0.913806\pi\)
0.963561 0.267489i \(-0.0861940\pi\)
\(888\) 15.3112i 0.513811i
\(889\) 3.46168i 0.116101i
\(890\) −12.4387 10.9986i −0.416945 0.368673i
\(891\) 25.6145i 0.858118i
\(892\) −128.432 −4.30022
\(893\) 5.35026i 0.179040i
\(894\) 14.6107 0.488655
\(895\) −17.9610 + 20.3127i −0.600369 + 0.678977i
\(896\) −13.3561 −0.446197
\(897\) 0 0
\(898\) 33.9365i 1.13248i
\(899\) 12.7856i 0.426423i
\(900\) −8.73813 70.8383i −0.291271 2.36128i
\(901\) 7.74798 0.258123
\(902\) 81.7255 2.72116
\(903\) −2.63515 −0.0876923
\(904\) 4.85097i 0.161341i
\(905\) −4.04491 + 4.57452i −0.134457 + 0.152062i
\(906\) −18.0059 −0.598205
\(907\) 51.9086i 1.72360i −0.507251 0.861798i \(-0.669338\pi\)
0.507251 0.861798i \(-0.330662\pi\)
\(908\) 51.3317 1.70350
\(909\) −29.0668 −0.964085
\(910\) 0 0
\(911\) −9.67750 −0.320630 −0.160315 0.987066i \(-0.551251\pi\)
−0.160315 + 0.987066i \(0.551251\pi\)
\(912\) 9.89446 0.327638
\(913\) 14.1260i 0.467503i
\(914\) −67.0103 −2.21651
\(915\) −1.42548 1.26045i −0.0471251 0.0416692i
\(916\) 27.5877i 0.911523i
\(917\) 0.674176 0.0222632
\(918\) −10.0263 −0.330919
\(919\) −13.5515 −0.447022 −0.223511 0.974701i \(-0.571752\pi\)
−0.223511 + 0.974701i \(0.571752\pi\)
\(920\) 91.6707 + 81.0576i 3.02229 + 2.67239i
\(921\) 9.22425i 0.303949i
\(922\) 98.6780i 3.24979i
\(923\) 0 0
\(924\) −7.35026 −0.241806
\(925\) 2.30677 + 18.7005i 0.0758462 + 0.614869i
\(926\) −104.381 −3.43017
\(927\) 42.5466i 1.39741i
\(928\) −38.5705 −1.26614
\(929\) 9.44992i 0.310042i 0.987911 + 0.155021i \(0.0495445\pi\)
−0.987911 + 0.155021i \(0.950455\pi\)
\(930\) 10.0811 11.4010i 0.330572 0.373855i
\(931\) 10.6375i 0.348631i
\(932\) 55.4880i 1.81757i
\(933\) 12.1504i 0.397788i
\(934\) 87.6625i 2.86840i
\(935\) −7.35026 + 8.31265i −0.240379 + 0.271853i
\(936\) 0 0
\(937\) 16.0409i 0.524035i −0.965063 0.262017i \(-0.915612\pi\)
0.965063 0.262017i \(-0.0843877\pi\)
\(938\) −21.3357 −0.696634
\(939\) 1.35309 0.0441565
\(940\) 24.3938 27.5877i 0.795636 0.899811i
\(941\) 21.6747i 0.706574i −0.935515 0.353287i \(-0.885064\pi\)
0.935515 0.353287i \(-0.114936\pi\)
\(942\) −3.57310 −0.116418
\(943\) −53.8759 −1.75444
\(944\) 73.5002i 2.39223i
\(945\) −3.74798 3.31406i −0.121922 0.107807i
\(946\) −66.7934 −2.17164
\(947\) 4.63118 0.150493 0.0752466 0.997165i \(-0.476026\pi\)
0.0752466 + 0.997165i \(0.476026\pi\)
\(948\) 5.61213i 0.182273i
\(949\) 0 0
\(950\) 22.2374 2.74306i 0.721477 0.0889966i
\(951\) 11.4372i 0.370878i
\(952\) 9.18997i 0.297849i
\(953\) 26.2981i 0.851878i −0.904752 0.425939i \(-0.859944\pi\)
0.904752 0.425939i \(-0.140056\pi\)
\(954\) 42.4965i 1.37587i
\(955\) −30.5501 + 34.5501i −0.988577 + 1.11801i
\(956\) 61.1632i 1.97816i
\(957\) −4.27645 −0.138238
\(958\) 45.1427i 1.45849i
\(959\) −12.0409 −0.388822
\(960\) 14.6048 + 12.9140i 0.471369 + 0.416797i
\(961\) 3.04491 0.0982228
\(962\) 0 0
\(963\) 30.8155i 0.993014i
\(964\) 147.601i 4.75392i
\(965\) 32.2736 36.4993i 1.03892 1.17495i
\(966\) 6.72496 0.216372
\(967\) −11.9405 −0.383981 −0.191990 0.981397i \(-0.561494\pi\)
−0.191990 + 0.981397i \(0.561494\pi\)
\(968\) −21.1646 −0.680255
\(969\) 1.08840i 0.0349643i
\(970\) 7.42548 8.39772i 0.238418 0.269635i
\(971\) 30.1524 0.967635 0.483818 0.875169i \(-0.339250\pi\)
0.483818 + 0.875169i \(0.339250\pi\)
\(972\) 60.2311i 1.93191i
\(973\) −6.80209 −0.218065
\(974\) −24.7308 −0.792427
\(975\) 0 0
\(976\) −21.7078 −0.694850
\(977\) 26.9321 0.861633 0.430817 0.902439i \(-0.358226\pi\)
0.430817 + 0.902439i \(0.358226\pi\)
\(978\) 2.87258i 0.0918549i
\(979\) −10.2012 −0.326033
\(980\) 48.5002 54.8505i 1.54928 1.75214i
\(981\) 26.5431i 0.847455i
\(982\) 68.8843 2.19819
\(983\) −20.5902 −0.656727 −0.328363 0.944551i \(-0.606497\pi\)
−0.328363 + 0.944551i \(0.606497\pi\)
\(984\) −33.7743 −1.07669
\(985\) −2.96239 + 3.35026i −0.0943895 + 0.106748i
\(986\) 8.73481i 0.278173i
\(987\) 1.23884i 0.0394328i
\(988\) 0 0
\(989\) 44.0322 1.40014
\(990\) −45.5936 40.3150i −1.44906 1.28130i
\(991\) −48.1378 −1.52915 −0.764573 0.644537i \(-0.777050\pi\)
−0.764573 + 0.644537i \(0.777050\pi\)
\(992\) 84.3327i 2.67756i
\(993\) −5.67864 −0.180206
\(994\) 18.4631i 0.585614i
\(995\) 24.8119 28.0606i 0.786591 0.889582i
\(996\) 9.53690i 0.302188i
\(997\) 33.4255i 1.05860i −0.848436 0.529298i \(-0.822455\pi\)
0.848436 0.529298i \(-0.177545\pi\)
\(998\) 74.1051i 2.34576i
\(999\) 10.4603i 0.330948i
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 845.2.d.b.844.5 6
5.4 even 2 845.2.d.a.844.2 6
13.2 odd 12 845.2.n.f.529.6 12
13.3 even 3 845.2.l.d.654.2 12
13.4 even 6 845.2.l.e.699.5 12
13.5 odd 4 65.2.b.a.14.1 6
13.6 odd 12 845.2.n.f.484.1 12
13.7 odd 12 845.2.n.g.484.6 12
13.8 odd 4 845.2.b.c.339.6 6
13.9 even 3 845.2.l.d.699.1 12
13.10 even 6 845.2.l.e.654.6 12
13.11 odd 12 845.2.n.g.529.1 12
13.12 even 2 845.2.d.a.844.1 6
39.5 even 4 585.2.c.b.469.6 6
52.31 even 4 1040.2.d.c.209.4 6
65.4 even 6 845.2.l.d.699.2 12
65.8 even 4 4225.2.a.bh.1.3 3
65.9 even 6 845.2.l.e.699.6 12
65.18 even 4 325.2.a.j.1.1 3
65.19 odd 12 845.2.n.f.484.6 12
65.24 odd 12 845.2.n.g.529.6 12
65.29 even 6 845.2.l.e.654.5 12
65.34 odd 4 845.2.b.c.339.1 6
65.44 odd 4 65.2.b.a.14.6 yes 6
65.47 even 4 4225.2.a.ba.1.1 3
65.49 even 6 845.2.l.d.654.1 12
65.54 odd 12 845.2.n.f.529.1 12
65.57 even 4 325.2.a.k.1.3 3
65.59 odd 12 845.2.n.g.484.1 12
65.64 even 2 inner 845.2.d.b.844.6 6
195.44 even 4 585.2.c.b.469.1 6
195.83 odd 4 2925.2.a.bj.1.3 3
195.122 odd 4 2925.2.a.bf.1.1 3
260.83 odd 4 5200.2.a.cj.1.1 3
260.187 odd 4 5200.2.a.cb.1.3 3
260.239 even 4 1040.2.d.c.209.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.b.a.14.1 6 13.5 odd 4
65.2.b.a.14.6 yes 6 65.44 odd 4
325.2.a.j.1.1 3 65.18 even 4
325.2.a.k.1.3 3 65.57 even 4
585.2.c.b.469.1 6 195.44 even 4
585.2.c.b.469.6 6 39.5 even 4
845.2.b.c.339.1 6 65.34 odd 4
845.2.b.c.339.6 6 13.8 odd 4
845.2.d.a.844.1 6 13.12 even 2
845.2.d.a.844.2 6 5.4 even 2
845.2.d.b.844.5 6 1.1 even 1 trivial
845.2.d.b.844.6 6 65.64 even 2 inner
845.2.l.d.654.1 12 65.49 even 6
845.2.l.d.654.2 12 13.3 even 3
845.2.l.d.699.1 12 13.9 even 3
845.2.l.d.699.2 12 65.4 even 6
845.2.l.e.654.5 12 65.29 even 6
845.2.l.e.654.6 12 13.10 even 6
845.2.l.e.699.5 12 13.4 even 6
845.2.l.e.699.6 12 65.9 even 6
845.2.n.f.484.1 12 13.6 odd 12
845.2.n.f.484.6 12 65.19 odd 12
845.2.n.f.529.1 12 65.54 odd 12
845.2.n.f.529.6 12 13.2 odd 12
845.2.n.g.484.1 12 65.59 odd 12
845.2.n.g.484.6 12 13.7 odd 12
845.2.n.g.529.1 12 13.11 odd 12
845.2.n.g.529.6 12 65.24 odd 12
1040.2.d.c.209.3 6 260.239 even 4
1040.2.d.c.209.4 6 52.31 even 4
2925.2.a.bf.1.1 3 195.122 odd 4
2925.2.a.bj.1.3 3 195.83 odd 4
4225.2.a.ba.1.1 3 65.47 even 4
4225.2.a.bh.1.3 3 65.8 even 4
5200.2.a.cb.1.3 3 260.187 odd 4
5200.2.a.cj.1.1 3 260.83 odd 4