Properties

Label 1.24.a.a.1.2
Level $1$
Weight $24$
Character 1.1
Self dual yes
Analytic conductor $3.352$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.35204037345\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{144169}) \)
Defining polynomial: \(x^{2} - x - 36042\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{3}\cdot 3 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-189.348\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+5096.35 q^{2} -48964.9 q^{3} +1.75842e7 q^{4} -3.19930e7 q^{5} -2.49542e8 q^{6} -5.17135e9 q^{7} +4.68639e10 q^{8} -9.17456e10 q^{9} +O(q^{10})\) \(q+5096.35 q^{2} -48964.9 q^{3} +1.75842e7 q^{4} -3.19930e7 q^{5} -2.49542e8 q^{6} -5.17135e9 q^{7} +4.68639e10 q^{8} -9.17456e10 q^{9} -1.63048e11 q^{10} +6.04602e11 q^{11} -8.61007e11 q^{12} +7.96710e12 q^{13} -2.63550e13 q^{14} +1.56653e12 q^{15} +9.13280e13 q^{16} +1.98385e13 q^{17} -4.67568e14 q^{18} +6.27346e14 q^{19} -5.62571e14 q^{20} +2.53215e14 q^{21} +3.08127e15 q^{22} -4.55685e15 q^{23} -2.29468e15 q^{24} -1.08974e16 q^{25} +4.06032e16 q^{26} +9.10202e15 q^{27} -9.09340e16 q^{28} +4.14107e16 q^{29} +7.98360e15 q^{30} +1.35683e15 q^{31} +7.23169e16 q^{32} -2.96043e16 q^{33} +1.01104e17 q^{34} +1.65447e17 q^{35} -1.61327e18 q^{36} +3.41258e17 q^{37} +3.19718e18 q^{38} -3.90108e17 q^{39} -1.49932e18 q^{40} -3.69518e18 q^{41} +1.29047e18 q^{42} -1.96955e18 q^{43} +1.06314e19 q^{44} +2.93522e18 q^{45} -2.32233e19 q^{46} +2.44381e19 q^{47} -4.47186e18 q^{48} -6.25860e17 q^{49} -5.55369e19 q^{50} -9.71391e17 q^{51} +1.40095e20 q^{52} -6.39437e19 q^{53} +4.63871e19 q^{54} -1.93431e19 q^{55} -2.42350e20 q^{56} -3.07179e19 q^{57} +2.11044e20 q^{58} +2.81892e20 q^{59} +2.75462e19 q^{60} -4.67790e20 q^{61} +6.91488e18 q^{62} +4.74449e20 q^{63} -3.97563e20 q^{64} -2.54892e20 q^{65} -1.50874e20 q^{66} +2.77406e20 q^{67} +3.48844e20 q^{68} +2.23126e20 q^{69} +8.43177e20 q^{70} +2.29069e21 q^{71} -4.29956e21 q^{72} -4.56908e21 q^{73} +1.73917e21 q^{74} +5.33588e20 q^{75} +1.10314e22 q^{76} -3.12661e21 q^{77} -1.98813e21 q^{78} -3.99005e21 q^{79} -2.92186e21 q^{80} +8.19155e21 q^{81} -1.88319e22 q^{82} +1.45920e22 q^{83} +4.45257e21 q^{84} -6.34694e20 q^{85} -1.00375e22 q^{86} -2.02767e21 q^{87} +2.83340e22 q^{88} +1.80991e21 q^{89} +1.49589e22 q^{90} -4.12007e22 q^{91} -8.01285e22 q^{92} -6.64369e19 q^{93} +1.24545e23 q^{94} -2.00707e22 q^{95} -3.54099e21 q^{96} +8.25561e22 q^{97} -3.18960e21 q^{98} -5.54696e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 1080q^{2} + 339480q^{3} + 25326656q^{4} + 73069020q^{5} - 1809673056q^{6} - 1359184400q^{7} + 49459023360q^{8} - 34999394166q^{9} + O(q^{10}) \) \( 2q + 1080q^{2} + 339480q^{3} + 25326656q^{4} + 73069020q^{5} - 1809673056q^{6} - 1359184400q^{7} + 49459023360q^{8} - 34999394166q^{9} - 585013636080q^{10} + 856801968264q^{11} + 2146514952960q^{12} + 4376109322060q^{13} - 41666034529728q^{14} + 42377338985040q^{15} + 15956586401792q^{16} + 254028147597540q^{17} - 695480683916520q^{18} + 4260600979960q^{19} + 250868387468160q^{20} + 1734031637722944q^{21} + 2068343882177760q^{22} - 8144713079008560q^{23} - 1286622315141120q^{24} - 11780274628800850q^{25} + 55025854658735184q^{26} - 5424634982716560q^{27} - 61418438819709440q^{28} + 20818433601623340q^{29} - 155926924188644160q^{30} + 137714017177000384q^{31} + 353265663781601280q^{32} + 68361366766001760q^{33} - 839483655961325328q^{34} + 565961271250425120q^{35} - 1173916300077574848q^{36} - 897721264408967780q^{37} + 5699708971590961440q^{38} - 1785011473665029232q^{39} - 1226668524414336000q^{40} - 2294435477168314956q^{41} - 4657011326437397760q^{42} - 1750760768619855800q^{43} + 12584088840033038592q^{44} + 8897092690294206540q^{45} - 8813206018050221376q^{46} + 15759744217656780960q^{47} - 33749519399576616960q^{48} - 13461981704376200814q^{49} - 51990825483785316600q^{50} + 89998362845078292144q^{51} + 112291883783912022400q^{52} - 140287253401646796420q^{53} + 104731223417039799360q^{54} + 7153550955060182640q^{55} - 232456712054288117760q^{56} - 272752401448627175520q^{57} + 293749486923568689360q^{58} + 280872989971340771880q^{59} + 343522601114937592320q^{60} - 180452892516502223636q^{61} - 540743475843874103040q^{62} + 690775113933935014320q^{63} - 893690254469352914944q^{64} - 632168834809440380760q^{65} - 544338140913651883392q^{66} + 1754233163431557625240q^{67} + 2162050190142944330880q^{68} - 1170560672172404223552q^{69} - 765428657799921252480q^{70} + 3055033510194143328624q^{71} - 4152294352103038548480q^{72} - 8063408253877606149260q^{73} + 6715344283148807757072q^{74} + 190631089350520885800q^{75} + 6207154294513080590080q^{76} - 2165184764357449665600q^{77} + 3614293948840808587200q^{78} + 6244916814559639980640q^{79} - 10840537585501794017280q^{80} - 2793528580929833975598q^{81} - 24457792891615712450640q^{82} + 6875994082418498976120q^{83} + 15917751907190402476032q^{84} + 23969743087870314902520q^{85} - 10916288812918999243296q^{86} - 10026640653837674384880q^{87} + 28988514668199273707520q^{88} + 6395093086173070004820q^{89} - 8986073954327865866160q^{90} - 54890178162704560146016q^{91} - 107907439017191756981760q^{92} + 52900811441357852079360q^{93} + 159400518006534931827072q^{94} - 85533361066700858502000q^{95} + 105592121669584394256384q^{96} - 31147288846254030500540q^{97} + 48364767616374671003640q^{98} - 41158245132312135981912q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5096.35 1.75960 0.879801 0.475342i \(-0.157676\pi\)
0.879801 + 0.475342i \(0.157676\pi\)
\(3\) −48964.9 −0.159584 −0.0797921 0.996812i \(-0.525426\pi\)
−0.0797921 + 0.996812i \(0.525426\pi\)
\(4\) 1.75842e7 2.09620
\(5\) −3.19930e7 −0.293022 −0.146511 0.989209i \(-0.546804\pi\)
−0.146511 + 0.989209i \(0.546804\pi\)
\(6\) −2.49542e8 −0.280805
\(7\) −5.17135e9 −0.988500 −0.494250 0.869320i \(-0.664557\pi\)
−0.494250 + 0.869320i \(0.664557\pi\)
\(8\) 4.68639e10 1.92887
\(9\) −9.17456e10 −0.974533
\(10\) −1.63048e11 −0.515602
\(11\) 6.04602e11 0.638931 0.319466 0.947598i \(-0.396497\pi\)
0.319466 + 0.947598i \(0.396497\pi\)
\(12\) −8.61007e11 −0.334520
\(13\) 7.96710e12 1.23297 0.616484 0.787367i \(-0.288556\pi\)
0.616484 + 0.787367i \(0.288556\pi\)
\(14\) −2.63550e13 −1.73937
\(15\) 1.56653e12 0.0467617
\(16\) 9.13280e13 1.29785
\(17\) 1.98385e13 0.140393 0.0701967 0.997533i \(-0.477637\pi\)
0.0701967 + 0.997533i \(0.477637\pi\)
\(18\) −4.67568e14 −1.71479
\(19\) 6.27346e14 1.23550 0.617748 0.786377i \(-0.288045\pi\)
0.617748 + 0.786377i \(0.288045\pi\)
\(20\) −5.62571e14 −0.614232
\(21\) 2.53215e14 0.157749
\(22\) 3.08127e15 1.12426
\(23\) −4.55685e15 −0.997229 −0.498614 0.866824i \(-0.666158\pi\)
−0.498614 + 0.866824i \(0.666158\pi\)
\(24\) −2.29468e15 −0.307818
\(25\) −1.08974e16 −0.914138
\(26\) 4.06032e16 2.16953
\(27\) 9.10202e15 0.315104
\(28\) −9.09340e16 −2.07209
\(29\) 4.14107e16 0.630283 0.315142 0.949045i \(-0.397948\pi\)
0.315142 + 0.949045i \(0.397948\pi\)
\(30\) 7.98360e15 0.0822819
\(31\) 1.35683e15 0.00959104 0.00479552 0.999989i \(-0.498474\pi\)
0.00479552 + 0.999989i \(0.498474\pi\)
\(32\) 7.23169e16 0.354826
\(33\) −2.96043e16 −0.101963
\(34\) 1.01104e17 0.247037
\(35\) 1.65447e17 0.289652
\(36\) −1.61327e18 −2.04281
\(37\) 3.41258e17 0.315328 0.157664 0.987493i \(-0.449604\pi\)
0.157664 + 0.987493i \(0.449604\pi\)
\(38\) 3.19718e18 2.17398
\(39\) −3.90108e17 −0.196762
\(40\) −1.49932e18 −0.565202
\(41\) −3.69518e18 −1.04863 −0.524313 0.851525i \(-0.675678\pi\)
−0.524313 + 0.851525i \(0.675678\pi\)
\(42\) 1.29047e18 0.277576
\(43\) −1.96955e18 −0.323207 −0.161603 0.986856i \(-0.551667\pi\)
−0.161603 + 0.986856i \(0.551667\pi\)
\(44\) 1.06314e19 1.33933
\(45\) 2.93522e18 0.285559
\(46\) −2.32233e19 −1.75473
\(47\) 2.44381e19 1.44192 0.720962 0.692975i \(-0.243700\pi\)
0.720962 + 0.692975i \(0.243700\pi\)
\(48\) −4.47186e18 −0.207116
\(49\) −6.25860e17 −0.0228677
\(50\) −5.55369e19 −1.60852
\(51\) −9.71391e17 −0.0224046
\(52\) 1.40095e20 2.58455
\(53\) −6.39437e19 −0.947600 −0.473800 0.880632i \(-0.657118\pi\)
−0.473800 + 0.880632i \(0.657118\pi\)
\(54\) 4.63871e19 0.554458
\(55\) −1.93431e19 −0.187221
\(56\) −2.42350e20 −1.90669
\(57\) −3.07179e19 −0.197166
\(58\) 2.11044e20 1.10905
\(59\) 2.81892e20 1.21698 0.608491 0.793561i \(-0.291775\pi\)
0.608491 + 0.793561i \(0.291775\pi\)
\(60\) 2.75462e19 0.0980218
\(61\) −4.67790e20 −1.37644 −0.688221 0.725501i \(-0.741608\pi\)
−0.688221 + 0.725501i \(0.741608\pi\)
\(62\) 6.91488e18 0.0168764
\(63\) 4.74449e20 0.963326
\(64\) −3.97563e20 −0.673498
\(65\) −2.54892e20 −0.361287
\(66\) −1.50874e20 −0.179415
\(67\) 2.77406e20 0.277495 0.138747 0.990328i \(-0.455692\pi\)
0.138747 + 0.990328i \(0.455692\pi\)
\(68\) 3.48844e20 0.294293
\(69\) 2.23126e20 0.159142
\(70\) 8.43177e20 0.509672
\(71\) 2.29069e21 1.17624 0.588119 0.808775i \(-0.299869\pi\)
0.588119 + 0.808775i \(0.299869\pi\)
\(72\) −4.29956e21 −1.87975
\(73\) −4.56908e21 −1.70457 −0.852286 0.523075i \(-0.824785\pi\)
−0.852286 + 0.523075i \(0.824785\pi\)
\(74\) 1.73917e21 0.554852
\(75\) 5.33588e20 0.145882
\(76\) 1.10314e22 2.58984
\(77\) −3.12661e21 −0.631583
\(78\) −1.98813e21 −0.346223
\(79\) −3.99005e21 −0.600160 −0.300080 0.953914i \(-0.597013\pi\)
−0.300080 + 0.953914i \(0.597013\pi\)
\(80\) −2.92186e21 −0.380298
\(81\) 8.19155e21 0.924247
\(82\) −1.88319e22 −1.84517
\(83\) 1.45920e22 1.24370 0.621850 0.783136i \(-0.286381\pi\)
0.621850 + 0.783136i \(0.286381\pi\)
\(84\) 4.45257e21 0.330673
\(85\) −6.34694e20 −0.0411384
\(86\) −1.00375e22 −0.568715
\(87\) −2.02767e21 −0.100583
\(88\) 2.83340e22 1.23242
\(89\) 1.80991e21 0.0691310 0.0345655 0.999402i \(-0.488995\pi\)
0.0345655 + 0.999402i \(0.488995\pi\)
\(90\) 1.49589e22 0.502471
\(91\) −4.12007e22 −1.21879
\(92\) −8.01285e22 −2.09039
\(93\) −6.64369e19 −0.00153058
\(94\) 1.24545e23 2.53721
\(95\) −2.00707e22 −0.362027
\(96\) −3.54099e21 −0.0566246
\(97\) 8.25561e22 1.17186 0.585928 0.810363i \(-0.300730\pi\)
0.585928 + 0.810363i \(0.300730\pi\)
\(98\) −3.18960e21 −0.0402380
\(99\) −5.54696e22 −0.622659
\(100\) −1.91622e23 −1.91622
\(101\) 4.84234e22 0.431877 0.215938 0.976407i \(-0.430719\pi\)
0.215938 + 0.976407i \(0.430719\pi\)
\(102\) −4.95055e21 −0.0394231
\(103\) −3.23687e22 −0.230408 −0.115204 0.993342i \(-0.536752\pi\)
−0.115204 + 0.993342i \(0.536752\pi\)
\(104\) 3.73370e23 2.37824
\(105\) −8.10110e21 −0.0462239
\(106\) −3.25880e23 −1.66740
\(107\) −5.92757e22 −0.272247 −0.136124 0.990692i \(-0.543464\pi\)
−0.136124 + 0.990692i \(0.543464\pi\)
\(108\) 1.60052e23 0.660521
\(109\) 2.86887e23 1.06490 0.532448 0.846463i \(-0.321272\pi\)
0.532448 + 0.846463i \(0.321272\pi\)
\(110\) −9.85790e22 −0.329434
\(111\) −1.67096e22 −0.0503214
\(112\) −4.72290e23 −1.28292
\(113\) −4.87844e22 −0.119641 −0.0598204 0.998209i \(-0.519053\pi\)
−0.0598204 + 0.998209i \(0.519053\pi\)
\(114\) −1.56549e23 −0.346933
\(115\) 1.45787e23 0.292210
\(116\) 7.28174e23 1.32120
\(117\) −7.30947e23 −1.20157
\(118\) 1.43662e24 2.14140
\(119\) −1.02592e23 −0.138779
\(120\) 7.34139e22 0.0901973
\(121\) −5.29886e23 −0.591767
\(122\) −2.38402e24 −2.42199
\(123\) 1.80934e23 0.167344
\(124\) 2.38587e22 0.0201047
\(125\) 7.30026e23 0.560884
\(126\) 2.41796e24 1.69507
\(127\) 1.36871e24 0.876131 0.438065 0.898943i \(-0.355664\pi\)
0.438065 + 0.898943i \(0.355664\pi\)
\(128\) −2.63276e24 −1.53991
\(129\) 9.64389e22 0.0515787
\(130\) −1.29902e24 −0.635721
\(131\) 2.63272e24 1.17974 0.589869 0.807499i \(-0.299180\pi\)
0.589869 + 0.807499i \(0.299180\pi\)
\(132\) −5.20567e23 −0.213735
\(133\) −3.24423e24 −1.22129
\(134\) 1.41376e24 0.488280
\(135\) −2.91201e23 −0.0923325
\(136\) 9.29711e23 0.270801
\(137\) −1.21837e24 −0.326207 −0.163103 0.986609i \(-0.552150\pi\)
−0.163103 + 0.986609i \(0.552150\pi\)
\(138\) 1.13713e24 0.280027
\(139\) −3.72223e24 −0.843593 −0.421797 0.906690i \(-0.638600\pi\)
−0.421797 + 0.906690i \(0.638600\pi\)
\(140\) 2.90925e24 0.607168
\(141\) −1.19661e24 −0.230108
\(142\) 1.16741e25 2.06971
\(143\) 4.81693e24 0.787782
\(144\) −8.37895e24 −1.26480
\(145\) −1.32485e24 −0.184687
\(146\) −2.32856e25 −2.99937
\(147\) 3.06452e22 0.00364932
\(148\) 6.00074e24 0.660990
\(149\) 1.53044e25 1.56018 0.780088 0.625670i \(-0.215174\pi\)
0.780088 + 0.625670i \(0.215174\pi\)
\(150\) 2.71935e24 0.256694
\(151\) −1.25232e25 −1.09516 −0.547582 0.836752i \(-0.684452\pi\)
−0.547582 + 0.836752i \(0.684452\pi\)
\(152\) 2.93999e25 2.38311
\(153\) −1.82010e24 −0.136818
\(154\) −1.59343e25 −1.11134
\(155\) −4.34090e22 −0.00281038
\(156\) −6.85973e24 −0.412453
\(157\) 1.92166e23 0.0107357 0.00536785 0.999986i \(-0.498291\pi\)
0.00536785 + 0.999986i \(0.498291\pi\)
\(158\) −2.03347e25 −1.05604
\(159\) 3.13099e24 0.151222
\(160\) −2.31363e24 −0.103972
\(161\) 2.35651e25 0.985761
\(162\) 4.17470e25 1.62631
\(163\) −2.27639e25 −0.826206 −0.413103 0.910684i \(-0.635555\pi\)
−0.413103 + 0.910684i \(0.635555\pi\)
\(164\) −6.49767e25 −2.19813
\(165\) 9.47130e23 0.0298775
\(166\) 7.43657e25 2.18842
\(167\) −1.17984e25 −0.324029 −0.162015 0.986788i \(-0.551799\pi\)
−0.162015 + 0.986788i \(0.551799\pi\)
\(168\) 1.18666e25 0.304278
\(169\) 2.17208e25 0.520211
\(170\) −3.23462e24 −0.0723871
\(171\) −5.75563e25 −1.20403
\(172\) −3.46330e25 −0.677506
\(173\) −4.75865e25 −0.870871 −0.435435 0.900220i \(-0.643406\pi\)
−0.435435 + 0.900220i \(0.643406\pi\)
\(174\) −1.03337e25 −0.176987
\(175\) 5.63542e25 0.903626
\(176\) 5.52172e25 0.829236
\(177\) −1.38028e25 −0.194211
\(178\) 9.22395e24 0.121643
\(179\) 9.84804e25 1.21770 0.608850 0.793286i \(-0.291631\pi\)
0.608850 + 0.793286i \(0.291631\pi\)
\(180\) 5.16134e25 0.598589
\(181\) 4.76456e25 0.518465 0.259233 0.965815i \(-0.416530\pi\)
0.259233 + 0.965815i \(0.416530\pi\)
\(182\) −2.09973e26 −2.14458
\(183\) 2.29053e25 0.219659
\(184\) −2.13552e26 −1.92353
\(185\) −1.09179e25 −0.0923980
\(186\) −3.38586e23 −0.00269321
\(187\) 1.19944e25 0.0897017
\(188\) 4.29724e26 3.02256
\(189\) −4.70697e25 −0.311481
\(190\) −1.02287e26 −0.637024
\(191\) −8.54117e25 −0.500765 −0.250382 0.968147i \(-0.580556\pi\)
−0.250382 + 0.968147i \(0.580556\pi\)
\(192\) 1.94666e25 0.107480
\(193\) −2.66797e26 −1.38762 −0.693812 0.720156i \(-0.744070\pi\)
−0.693812 + 0.720156i \(0.744070\pi\)
\(194\) 4.20735e26 2.06200
\(195\) 1.24807e25 0.0576557
\(196\) −1.10052e25 −0.0479352
\(197\) −1.00070e26 −0.411095 −0.205547 0.978647i \(-0.565897\pi\)
−0.205547 + 0.978647i \(0.565897\pi\)
\(198\) −2.82693e26 −1.09563
\(199\) 4.46897e26 1.63454 0.817272 0.576251i \(-0.195485\pi\)
0.817272 + 0.576251i \(0.195485\pi\)
\(200\) −5.10694e26 −1.76326
\(201\) −1.35831e25 −0.0442838
\(202\) 2.46783e26 0.759931
\(203\) −2.14149e26 −0.623035
\(204\) −1.70811e25 −0.0469645
\(205\) 1.18220e26 0.307271
\(206\) −1.64962e26 −0.405426
\(207\) 4.18071e26 0.971832
\(208\) 7.27620e26 1.60021
\(209\) 3.79295e26 0.789396
\(210\) −4.12860e25 −0.0813357
\(211\) −7.96987e26 −1.48663 −0.743315 0.668941i \(-0.766748\pi\)
−0.743315 + 0.668941i \(0.766748\pi\)
\(212\) −1.12440e27 −1.98636
\(213\) −1.12163e26 −0.187709
\(214\) −3.02090e26 −0.479047
\(215\) 6.30120e25 0.0947067
\(216\) 4.26556e26 0.607796
\(217\) −7.01664e24 −0.00948074
\(218\) 1.46208e27 1.87379
\(219\) 2.23724e26 0.272023
\(220\) −3.40132e26 −0.392452
\(221\) 1.58056e26 0.173101
\(222\) −8.51582e25 −0.0885456
\(223\) −5.69004e26 −0.561836 −0.280918 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(224\) −3.73976e26 −0.350745
\(225\) 9.99787e26 0.890858
\(226\) −2.48623e26 −0.210520
\(227\) −1.82165e27 −1.46611 −0.733056 0.680168i \(-0.761907\pi\)
−0.733056 + 0.680168i \(0.761907\pi\)
\(228\) −5.40150e26 −0.413298
\(229\) 1.11330e27 0.810032 0.405016 0.914310i \(-0.367266\pi\)
0.405016 + 0.914310i \(0.367266\pi\)
\(230\) 7.42984e26 0.514173
\(231\) 1.53094e26 0.100791
\(232\) 1.94067e27 1.21574
\(233\) −1.63214e27 −0.973118 −0.486559 0.873648i \(-0.661748\pi\)
−0.486559 + 0.873648i \(0.661748\pi\)
\(234\) −3.72516e27 −2.11428
\(235\) −7.81849e26 −0.422515
\(236\) 4.95683e27 2.55104
\(237\) 1.95372e26 0.0957761
\(238\) −5.22845e26 −0.244196
\(239\) 2.58550e27 1.15072 0.575358 0.817902i \(-0.304863\pi\)
0.575358 + 0.817902i \(0.304863\pi\)
\(240\) 1.43068e26 0.0606896
\(241\) 1.86784e27 0.755340 0.377670 0.925940i \(-0.376725\pi\)
0.377670 + 0.925940i \(0.376725\pi\)
\(242\) −2.70049e27 −1.04127
\(243\) −1.25799e27 −0.462600
\(244\) −8.22571e27 −2.88530
\(245\) 2.00232e25 0.00670074
\(246\) 9.22102e26 0.294459
\(247\) 4.99813e27 1.52333
\(248\) 6.35863e25 0.0184999
\(249\) −7.14493e26 −0.198475
\(250\) 3.72047e27 0.986933
\(251\) −4.11170e27 −1.04177 −0.520887 0.853626i \(-0.674399\pi\)
−0.520887 + 0.853626i \(0.674399\pi\)
\(252\) 8.34280e27 2.01932
\(253\) −2.75508e27 −0.637160
\(254\) 6.97543e27 1.54164
\(255\) 3.10777e25 0.00656503
\(256\) −1.00825e28 −2.03614
\(257\) −5.10426e27 −0.985603 −0.492802 0.870142i \(-0.664027\pi\)
−0.492802 + 0.870142i \(0.664027\pi\)
\(258\) 4.91487e26 0.0907580
\(259\) −1.76476e27 −0.311702
\(260\) −4.48206e27 −0.757329
\(261\) −3.79925e27 −0.614232
\(262\) 1.34173e28 2.07587
\(263\) 9.95433e27 1.47408 0.737040 0.675849i \(-0.236223\pi\)
0.737040 + 0.675849i \(0.236223\pi\)
\(264\) −1.38737e27 −0.196674
\(265\) 2.04575e27 0.277668
\(266\) −1.65337e28 −2.14898
\(267\) −8.86222e25 −0.0110322
\(268\) 4.87795e27 0.581684
\(269\) 6.42524e26 0.0734071 0.0367036 0.999326i \(-0.488314\pi\)
0.0367036 + 0.999326i \(0.488314\pi\)
\(270\) −1.48406e27 −0.162468
\(271\) 1.19246e28 1.25111 0.625557 0.780178i \(-0.284872\pi\)
0.625557 + 0.780178i \(0.284872\pi\)
\(272\) 1.81181e27 0.182210
\(273\) 2.01739e27 0.194500
\(274\) −6.20925e27 −0.573994
\(275\) −6.58858e27 −0.584071
\(276\) 3.92348e27 0.333593
\(277\) −5.29510e27 −0.431874 −0.215937 0.976407i \(-0.569281\pi\)
−0.215937 + 0.976407i \(0.569281\pi\)
\(278\) −1.89698e28 −1.48439
\(279\) −1.24483e26 −0.00934678
\(280\) 7.75350e27 0.558702
\(281\) 9.67433e27 0.669111 0.334556 0.942376i \(-0.391414\pi\)
0.334556 + 0.942376i \(0.391414\pi\)
\(282\) −6.09834e27 −0.404899
\(283\) −2.62436e28 −1.67294 −0.836468 0.548016i \(-0.815383\pi\)
−0.836468 + 0.548016i \(0.815383\pi\)
\(284\) 4.02799e28 2.46563
\(285\) 9.82759e26 0.0577738
\(286\) 2.45488e28 1.38618
\(287\) 1.91091e28 1.03657
\(288\) −6.63476e27 −0.345789
\(289\) −1.95740e28 −0.980290
\(290\) −6.75192e27 −0.324975
\(291\) −4.04235e27 −0.187010
\(292\) −8.03435e28 −3.57312
\(293\) 3.20151e28 1.36892 0.684458 0.729052i \(-0.260039\pi\)
0.684458 + 0.729052i \(0.260039\pi\)
\(294\) 1.56178e26 0.00642136
\(295\) −9.01856e27 −0.356602
\(296\) 1.59927e28 0.608228
\(297\) 5.50310e27 0.201330
\(298\) 7.79965e28 2.74529
\(299\) −3.63049e28 −1.22955
\(300\) 9.38272e27 0.305798
\(301\) 1.01853e28 0.319490
\(302\) −6.38225e28 −1.92705
\(303\) −2.37105e27 −0.0689207
\(304\) 5.72943e28 1.60349
\(305\) 1.49660e28 0.403328
\(306\) −9.27586e27 −0.240745
\(307\) −1.15407e28 −0.288496 −0.144248 0.989542i \(-0.546076\pi\)
−0.144248 + 0.989542i \(0.546076\pi\)
\(308\) −5.49789e28 −1.32392
\(309\) 1.58493e27 0.0367695
\(310\) −2.21228e26 −0.00494516
\(311\) 3.62817e28 0.781525 0.390763 0.920491i \(-0.372211\pi\)
0.390763 + 0.920491i \(0.372211\pi\)
\(312\) −1.82820e28 −0.379530
\(313\) 2.56117e28 0.512481 0.256241 0.966613i \(-0.417516\pi\)
0.256241 + 0.966613i \(0.417516\pi\)
\(314\) 9.79346e26 0.0188906
\(315\) −1.51791e28 −0.282276
\(316\) −7.01618e28 −1.25805
\(317\) −2.91424e27 −0.0503899 −0.0251950 0.999683i \(-0.508021\pi\)
−0.0251950 + 0.999683i \(0.508021\pi\)
\(318\) 1.59566e28 0.266091
\(319\) 2.50370e28 0.402708
\(320\) 1.27192e28 0.197350
\(321\) 2.90243e27 0.0434464
\(322\) 1.20096e29 1.73455
\(323\) 1.24456e28 0.173455
\(324\) 1.44042e29 1.93741
\(325\) −8.68205e28 −1.12710
\(326\) −1.16013e29 −1.45379
\(327\) −1.40474e28 −0.169940
\(328\) −1.73170e29 −2.02267
\(329\) −1.26378e29 −1.42534
\(330\) 4.82691e27 0.0525725
\(331\) 4.00537e28 0.421328 0.210664 0.977558i \(-0.432437\pi\)
0.210664 + 0.977558i \(0.432437\pi\)
\(332\) 2.56588e29 2.60704
\(333\) −3.13089e28 −0.307298
\(334\) −6.01289e28 −0.570163
\(335\) −8.87504e27 −0.0813121
\(336\) 2.31256e28 0.204735
\(337\) 1.31131e29 1.12192 0.560959 0.827843i \(-0.310432\pi\)
0.560959 + 0.827843i \(0.310432\pi\)
\(338\) 1.10697e29 0.915364
\(339\) 2.38872e27 0.0190928
\(340\) −1.11606e28 −0.0862342
\(341\) 8.20342e26 0.00612801
\(342\) −2.93327e29 −2.11861
\(343\) 1.44770e29 1.01110
\(344\) −9.23010e28 −0.623425
\(345\) −7.13846e27 −0.0466321
\(346\) −2.42518e29 −1.53239
\(347\) 1.14051e29 0.697126 0.348563 0.937285i \(-0.386670\pi\)
0.348563 + 0.937285i \(0.386670\pi\)
\(348\) −3.56549e28 −0.210843
\(349\) 7.28518e28 0.416820 0.208410 0.978042i \(-0.433171\pi\)
0.208410 + 0.978042i \(0.433171\pi\)
\(350\) 2.87201e29 1.59002
\(351\) 7.25167e28 0.388514
\(352\) 4.37230e28 0.226709
\(353\) −3.68425e29 −1.84902 −0.924508 0.381164i \(-0.875523\pi\)
−0.924508 + 0.381164i \(0.875523\pi\)
\(354\) −7.03438e28 −0.341734
\(355\) −7.32860e28 −0.344663
\(356\) 3.18259e28 0.144912
\(357\) 5.02340e27 0.0221469
\(358\) 5.01891e29 2.14267
\(359\) −2.45802e29 −1.01625 −0.508123 0.861284i \(-0.669661\pi\)
−0.508123 + 0.861284i \(0.669661\pi\)
\(360\) 1.37556e29 0.550808
\(361\) 1.35734e29 0.526448
\(362\) 2.42819e29 0.912292
\(363\) 2.59458e28 0.0944367
\(364\) −7.24481e29 −2.55482
\(365\) 1.46179e29 0.499477
\(366\) 1.16733e29 0.386512
\(367\) −4.73025e29 −1.51783 −0.758917 0.651187i \(-0.774271\pi\)
−0.758917 + 0.651187i \(0.774271\pi\)
\(368\) −4.16168e29 −1.29425
\(369\) 3.39016e29 1.02192
\(370\) −5.56413e28 −0.162584
\(371\) 3.30675e29 0.936703
\(372\) −1.16824e27 −0.00320840
\(373\) −2.90241e29 −0.772872 −0.386436 0.922316i \(-0.626294\pi\)
−0.386436 + 0.922316i \(0.626294\pi\)
\(374\) 6.11278e28 0.157839
\(375\) −3.57456e28 −0.0895083
\(376\) 1.14526e30 2.78129
\(377\) 3.29924e29 0.777120
\(378\) −2.39884e29 −0.548082
\(379\) 2.72591e29 0.604172 0.302086 0.953281i \(-0.402317\pi\)
0.302086 + 0.953281i \(0.402317\pi\)
\(380\) −3.52927e29 −0.758881
\(381\) −6.70187e28 −0.139817
\(382\) −4.35288e29 −0.881147
\(383\) −9.91721e29 −1.94806 −0.974032 0.226408i \(-0.927302\pi\)
−0.974032 + 0.226408i \(0.927302\pi\)
\(384\) 1.28913e29 0.245746
\(385\) 1.00030e29 0.185068
\(386\) −1.35969e30 −2.44166
\(387\) 1.80698e29 0.314976
\(388\) 1.45168e30 2.45644
\(389\) 8.39840e29 1.37967 0.689836 0.723966i \(-0.257683\pi\)
0.689836 + 0.723966i \(0.257683\pi\)
\(390\) 6.36062e28 0.101451
\(391\) −9.04012e28 −0.140004
\(392\) −2.93303e28 −0.0441089
\(393\) −1.28911e29 −0.188268
\(394\) −5.09992e29 −0.723363
\(395\) 1.27654e29 0.175860
\(396\) −9.75388e29 −1.30522
\(397\) 9.94808e27 0.0129315 0.00646574 0.999979i \(-0.497942\pi\)
0.00646574 + 0.999979i \(0.497942\pi\)
\(398\) 2.27754e30 2.87615
\(399\) 1.58853e29 0.194898
\(400\) −9.95236e29 −1.18641
\(401\) −4.81480e29 −0.557723 −0.278861 0.960331i \(-0.589957\pi\)
−0.278861 + 0.960331i \(0.589957\pi\)
\(402\) −6.92244e28 −0.0779219
\(403\) 1.08100e28 0.0118254
\(404\) 8.51487e29 0.905299
\(405\) −2.62072e29 −0.270825
\(406\) −1.09138e30 −1.09629
\(407\) 2.06325e29 0.201473
\(408\) −4.55232e28 −0.0432156
\(409\) −8.22531e29 −0.759162 −0.379581 0.925159i \(-0.623932\pi\)
−0.379581 + 0.925159i \(0.623932\pi\)
\(410\) 6.02490e29 0.540674
\(411\) 5.96573e28 0.0520575
\(412\) −5.69178e29 −0.482981
\(413\) −1.45776e30 −1.20299
\(414\) 2.13064e30 1.71004
\(415\) −4.66841e29 −0.364431
\(416\) 5.76156e29 0.437489
\(417\) 1.82259e29 0.134624
\(418\) 1.93302e30 1.38902
\(419\) 2.72055e30 1.90194 0.950969 0.309287i \(-0.100090\pi\)
0.950969 + 0.309287i \(0.100090\pi\)
\(420\) −1.42451e29 −0.0968945
\(421\) 1.73534e30 1.14852 0.574261 0.818672i \(-0.305289\pi\)
0.574261 + 0.818672i \(0.305289\pi\)
\(422\) −4.06173e30 −2.61588
\(423\) −2.24209e30 −1.40520
\(424\) −2.99665e30 −1.82780
\(425\) −2.16188e29 −0.128339
\(426\) −5.71623e29 −0.330293
\(427\) 2.41911e30 1.36061
\(428\) −1.04232e30 −0.570684
\(429\) −2.35860e29 −0.125718
\(430\) 3.21131e29 0.166646
\(431\) 2.30954e30 1.16691 0.583455 0.812146i \(-0.301701\pi\)
0.583455 + 0.812146i \(0.301701\pi\)
\(432\) 8.31270e29 0.408958
\(433\) −4.49441e29 −0.215309 −0.107655 0.994188i \(-0.534334\pi\)
−0.107655 + 0.994188i \(0.534334\pi\)
\(434\) −3.57593e28 −0.0166823
\(435\) 6.48713e28 0.0294731
\(436\) 5.04468e30 2.23223
\(437\) −2.85872e30 −1.23207
\(438\) 1.14018e30 0.478652
\(439\) −1.98640e30 −0.812315 −0.406157 0.913803i \(-0.633132\pi\)
−0.406157 + 0.913803i \(0.633132\pi\)
\(440\) −9.06491e29 −0.361125
\(441\) 5.74199e28 0.0222853
\(442\) 8.05507e29 0.304588
\(443\) −2.09074e30 −0.770294 −0.385147 0.922855i \(-0.625849\pi\)
−0.385147 + 0.922855i \(0.625849\pi\)
\(444\) −2.93825e29 −0.105484
\(445\) −5.79046e28 −0.0202569
\(446\) −2.89984e30 −0.988607
\(447\) −7.49376e29 −0.248979
\(448\) 2.05594e30 0.665753
\(449\) 2.38796e30 0.753694 0.376847 0.926276i \(-0.377008\pi\)
0.376847 + 0.926276i \(0.377008\pi\)
\(450\) 5.09526e30 1.56755
\(451\) −2.23411e30 −0.670000
\(452\) −8.57834e29 −0.250791
\(453\) 6.13195e29 0.174771
\(454\) −9.28376e30 −2.57977
\(455\) 1.31813e30 0.357132
\(456\) −1.43956e30 −0.380307
\(457\) 1.54921e30 0.399093 0.199547 0.979888i \(-0.436053\pi\)
0.199547 + 0.979888i \(0.436053\pi\)
\(458\) 5.67374e30 1.42533
\(459\) 1.80571e29 0.0442386
\(460\) 2.56355e30 0.612530
\(461\) 4.06665e30 0.947711 0.473855 0.880603i \(-0.342862\pi\)
0.473855 + 0.880603i \(0.342862\pi\)
\(462\) 7.80221e29 0.177352
\(463\) −6.37975e29 −0.141456 −0.0707282 0.997496i \(-0.522532\pi\)
−0.0707282 + 0.997496i \(0.522532\pi\)
\(464\) 3.78196e30 0.818013
\(465\) 2.12552e27 0.000448493 0
\(466\) −8.31798e30 −1.71230
\(467\) 1.15365e30 0.231701 0.115851 0.993267i \(-0.463041\pi\)
0.115851 + 0.993267i \(0.463041\pi\)
\(468\) −1.28531e31 −2.51873
\(469\) −1.43456e30 −0.274304
\(470\) −3.98458e30 −0.743458
\(471\) −9.40938e27 −0.00171325
\(472\) 1.32105e31 2.34740
\(473\) −1.19080e30 −0.206507
\(474\) 9.95686e29 0.168528
\(475\) −6.83643e30 −1.12941
\(476\) −1.80400e30 −0.290908
\(477\) 5.86655e30 0.923468
\(478\) 1.31766e31 2.02480
\(479\) −2.12936e30 −0.319441 −0.159721 0.987162i \(-0.551059\pi\)
−0.159721 + 0.987162i \(0.551059\pi\)
\(480\) 1.13287e29 0.0165922
\(481\) 2.71884e30 0.388790
\(482\) 9.51914e30 1.32910
\(483\) −1.15386e30 −0.157312
\(484\) −9.31762e30 −1.24046
\(485\) −2.64122e30 −0.343380
\(486\) −6.41116e30 −0.813991
\(487\) 4.84200e30 0.600401 0.300201 0.953876i \(-0.402946\pi\)
0.300201 + 0.953876i \(0.402946\pi\)
\(488\) −2.19225e31 −2.65498
\(489\) 1.11463e30 0.131849
\(490\) 1.02045e29 0.0117906
\(491\) −3.44338e29 −0.0388640 −0.0194320 0.999811i \(-0.506186\pi\)
−0.0194320 + 0.999811i \(0.506186\pi\)
\(492\) 3.18157e30 0.350787
\(493\) 8.21528e29 0.0884877
\(494\) 2.54722e31 2.68045
\(495\) 1.77464e30 0.182453
\(496\) 1.23917e29 0.0124477
\(497\) −1.18460e31 −1.16271
\(498\) −3.64131e30 −0.349237
\(499\) −1.27549e31 −1.19542 −0.597711 0.801711i \(-0.703923\pi\)
−0.597711 + 0.801711i \(0.703923\pi\)
\(500\) 1.28369e31 1.17573
\(501\) 5.77708e29 0.0517100
\(502\) −2.09546e31 −1.83311
\(503\) 1.67840e31 1.43504 0.717520 0.696538i \(-0.245277\pi\)
0.717520 + 0.696538i \(0.245277\pi\)
\(504\) 2.22345e31 1.85813
\(505\) −1.54921e30 −0.126549
\(506\) −1.40409e31 −1.12115
\(507\) −1.06356e30 −0.0830175
\(508\) 2.40677e31 1.83654
\(509\) −2.11935e31 −1.58106 −0.790529 0.612425i \(-0.790194\pi\)
−0.790529 + 0.612425i \(0.790194\pi\)
\(510\) 1.58383e29 0.0115518
\(511\) 2.36283e31 1.68497
\(512\) −2.92986e31 −2.04288
\(513\) 5.71012e30 0.389310
\(514\) −2.60131e31 −1.73427
\(515\) 1.03557e30 0.0675146
\(516\) 1.69580e30 0.108119
\(517\) 1.47753e31 0.921290
\(518\) −8.99386e30 −0.548471
\(519\) 2.33007e30 0.138977
\(520\) −1.19452e31 −0.696876
\(521\) −1.22820e30 −0.0700869 −0.0350434 0.999386i \(-0.511157\pi\)
−0.0350434 + 0.999386i \(0.511157\pi\)
\(522\) −1.93623e31 −1.08080
\(523\) 7.24558e30 0.395643 0.197821 0.980238i \(-0.436613\pi\)
0.197821 + 0.980238i \(0.436613\pi\)
\(524\) 4.62943e31 2.47296
\(525\) −2.75937e30 −0.144204
\(526\) 5.07308e31 2.59379
\(527\) 2.69175e28 0.00134652
\(528\) −2.70370e30 −0.132333
\(529\) −1.15570e29 −0.00553483
\(530\) 1.04259e31 0.488585
\(531\) −2.58623e31 −1.18599
\(532\) −5.70471e31 −2.56006
\(533\) −2.94399e31 −1.29292
\(534\) −4.51650e29 −0.0194123
\(535\) 1.89641e30 0.0797744
\(536\) 1.30003e31 0.535252
\(537\) −4.82208e30 −0.194326
\(538\) 3.27453e30 0.129167
\(539\) −3.78397e29 −0.0146109
\(540\) −5.12053e30 −0.193547
\(541\) 9.30820e30 0.344427 0.172214 0.985060i \(-0.444908\pi\)
0.172214 + 0.985060i \(0.444908\pi\)
\(542\) 6.07719e31 2.20146
\(543\) −2.33296e30 −0.0827389
\(544\) 1.43466e30 0.0498152
\(545\) −9.17839e30 −0.312038
\(546\) 1.02813e31 0.342242
\(547\) −2.67466e31 −0.871796 −0.435898 0.899996i \(-0.643569\pi\)
−0.435898 + 0.899996i \(0.643569\pi\)
\(548\) −2.14241e31 −0.683794
\(549\) 4.29177e31 1.34139
\(550\) −3.35777e31 −1.02773
\(551\) 2.59789e31 0.778712
\(552\) 1.04565e31 0.306965
\(553\) 2.06340e31 0.593258
\(554\) −2.69857e31 −0.759926
\(555\) 5.34592e29 0.0147453
\(556\) −6.54524e31 −1.76834
\(557\) 2.40510e31 0.636501 0.318250 0.948007i \(-0.396905\pi\)
0.318250 + 0.948007i \(0.396905\pi\)
\(558\) −6.34410e29 −0.0164466
\(559\) −1.56916e31 −0.398504
\(560\) 1.51100e31 0.375925
\(561\) −5.87305e29 −0.0143150
\(562\) 4.93038e31 1.17737
\(563\) 2.15437e31 0.504049 0.252025 0.967721i \(-0.418904\pi\)
0.252025 + 0.967721i \(0.418904\pi\)
\(564\) −2.10414e31 −0.482353
\(565\) 1.56076e30 0.0350574
\(566\) −1.33747e32 −2.94370
\(567\) −4.23614e31 −0.913618
\(568\) 1.07351e32 2.26881
\(569\) 1.70978e31 0.354120 0.177060 0.984200i \(-0.443341\pi\)
0.177060 + 0.984200i \(0.443341\pi\)
\(570\) 5.00848e30 0.101659
\(571\) −8.69138e31 −1.72891 −0.864457 0.502707i \(-0.832337\pi\)
−0.864457 + 0.502707i \(0.832337\pi\)
\(572\) 8.47018e31 1.65135
\(573\) 4.18217e30 0.0799142
\(574\) 9.73865e31 1.82395
\(575\) 4.96577e31 0.911605
\(576\) 3.64747e31 0.656346
\(577\) 1.59167e31 0.280757 0.140378 0.990098i \(-0.455168\pi\)
0.140378 + 0.990098i \(0.455168\pi\)
\(578\) −9.97560e31 −1.72492
\(579\) 1.30637e31 0.221443
\(580\) −2.32965e31 −0.387140
\(581\) −7.54602e31 −1.22940
\(582\) −2.06012e31 −0.329063
\(583\) −3.86605e31 −0.605451
\(584\) −2.14125e32 −3.28790
\(585\) 2.33852e31 0.352086
\(586\) 1.63160e32 2.40875
\(587\) 5.71080e31 0.826721 0.413361 0.910567i \(-0.364355\pi\)
0.413361 + 0.910567i \(0.364355\pi\)
\(588\) 5.38870e29 0.00764971
\(589\) 8.51202e29 0.0118497
\(590\) −4.59618e31 −0.627478
\(591\) 4.89991e30 0.0656043
\(592\) 3.11664e31 0.409248
\(593\) 2.68653e31 0.345989 0.172995 0.984923i \(-0.444656\pi\)
0.172995 + 0.984923i \(0.444656\pi\)
\(594\) 2.80457e31 0.354261
\(595\) 3.28223e30 0.0406653
\(596\) 2.69115e32 3.27044
\(597\) −2.18822e31 −0.260848
\(598\) −1.85023e32 −2.16352
\(599\) 1.35452e30 0.0155373 0.00776867 0.999970i \(-0.497527\pi\)
0.00776867 + 0.999970i \(0.497527\pi\)
\(600\) 2.50060e31 0.281388
\(601\) −7.37959e31 −0.814659 −0.407329 0.913281i \(-0.633540\pi\)
−0.407329 + 0.913281i \(0.633540\pi\)
\(602\) 5.19077e31 0.562175
\(603\) −2.54507e31 −0.270428
\(604\) −2.20210e32 −2.29568
\(605\) 1.69527e31 0.173401
\(606\) −1.20837e31 −0.121273
\(607\) −3.23323e31 −0.318395 −0.159198 0.987247i \(-0.550891\pi\)
−0.159198 + 0.987247i \(0.550891\pi\)
\(608\) 4.53677e31 0.438385
\(609\) 1.04858e31 0.0994266
\(610\) 7.62721e31 0.709696
\(611\) 1.94701e32 1.77785
\(612\) −3.20049e31 −0.286798
\(613\) 4.35574e31 0.383059 0.191530 0.981487i \(-0.438655\pi\)
0.191530 + 0.981487i \(0.438655\pi\)
\(614\) −5.88154e31 −0.507639
\(615\) −5.78862e30 −0.0490356
\(616\) −1.46525e32 −1.21824
\(617\) −2.29127e32 −1.86981 −0.934904 0.354902i \(-0.884514\pi\)
−0.934904 + 0.354902i \(0.884514\pi\)
\(618\) 8.07736e30 0.0646997
\(619\) 2.32366e32 1.82697 0.913484 0.406875i \(-0.133382\pi\)
0.913484 + 0.406875i \(0.133382\pi\)
\(620\) −7.63313e29 −0.00589112
\(621\) −4.14765e31 −0.314231
\(622\) 1.84904e32 1.37517
\(623\) −9.35970e30 −0.0683360
\(624\) −3.56278e31 −0.255368
\(625\) 1.06551e32 0.749787
\(626\) 1.30526e32 0.901763
\(627\) −1.85721e31 −0.125975
\(628\) 3.37908e30 0.0225042
\(629\) 6.77005e30 0.0442700
\(630\) −7.73578e31 −0.496693
\(631\) −2.22944e32 −1.40559 −0.702793 0.711394i \(-0.748064\pi\)
−0.702793 + 0.711394i \(0.748064\pi\)
\(632\) −1.86989e32 −1.15763
\(633\) 3.90244e31 0.237243
\(634\) −1.48520e31 −0.0886662
\(635\) −4.37892e31 −0.256726
\(636\) 5.50560e31 0.316992
\(637\) −4.98629e30 −0.0281951
\(638\) 1.27597e32 0.708605
\(639\) −2.10161e32 −1.14628
\(640\) 8.42299e31 0.451228
\(641\) −2.75021e32 −1.44710 −0.723550 0.690272i \(-0.757491\pi\)
−0.723550 + 0.690272i \(0.757491\pi\)
\(642\) 1.47918e31 0.0764483
\(643\) 1.47614e32 0.749377 0.374689 0.927151i \(-0.377750\pi\)
0.374689 + 0.927151i \(0.377750\pi\)
\(644\) 4.14373e32 2.06635
\(645\) −3.08537e30 −0.0151137
\(646\) 6.34273e31 0.305212
\(647\) 1.82358e32 0.862036 0.431018 0.902343i \(-0.358154\pi\)
0.431018 + 0.902343i \(0.358154\pi\)
\(648\) 3.83888e32 1.78276
\(649\) 1.70432e32 0.777567
\(650\) −4.42468e32 −1.98325
\(651\) 3.43569e29 0.00151298
\(652\) −4.00284e32 −1.73189
\(653\) −4.35899e31 −0.185304 −0.0926519 0.995699i \(-0.529534\pi\)
−0.0926519 + 0.995699i \(0.529534\pi\)
\(654\) −7.15905e31 −0.299028
\(655\) −8.42287e31 −0.345689
\(656\) −3.37473e32 −1.36096
\(657\) 4.19193e32 1.66116
\(658\) −6.44067e32 −2.50803
\(659\) −3.58880e31 −0.137331 −0.0686653 0.997640i \(-0.521874\pi\)
−0.0686653 + 0.997640i \(0.521874\pi\)
\(660\) 1.66545e31 0.0626291
\(661\) 2.78803e32 1.03034 0.515171 0.857088i \(-0.327729\pi\)
0.515171 + 0.857088i \(0.327729\pi\)
\(662\) 2.04128e32 0.741370
\(663\) −7.73917e30 −0.0276241
\(664\) 6.83836e32 2.39894
\(665\) 1.03793e32 0.357864
\(666\) −1.59561e32 −0.540721
\(667\) −1.88703e32 −0.628537
\(668\) −2.07466e32 −0.679230
\(669\) 2.78612e31 0.0896601
\(670\) −4.52303e31 −0.143077
\(671\) −2.82827e32 −0.879452
\(672\) 1.83117e31 0.0559734
\(673\) 1.90131e31 0.0571320 0.0285660 0.999592i \(-0.490906\pi\)
0.0285660 + 0.999592i \(0.490906\pi\)
\(674\) 6.68289e32 1.97413
\(675\) −9.91881e31 −0.288049
\(676\) 3.81943e32 1.09047
\(677\) −3.87840e32 −1.08864 −0.544318 0.838879i \(-0.683212\pi\)
−0.544318 + 0.838879i \(0.683212\pi\)
\(678\) 1.21738e31 0.0335957
\(679\) −4.26927e32 −1.15838
\(680\) −2.97442e31 −0.0793507
\(681\) 8.91968e31 0.233969
\(682\) 4.18075e30 0.0107829
\(683\) 6.51681e32 1.65271 0.826356 0.563148i \(-0.190410\pi\)
0.826356 + 0.563148i \(0.190410\pi\)
\(684\) −1.01208e33 −2.52389
\(685\) 3.89794e31 0.0955857
\(686\) 7.37799e32 1.77914
\(687\) −5.45123e31 −0.129268
\(688\) −1.79876e32 −0.419474
\(689\) −5.09446e32 −1.16836
\(690\) −3.63801e31 −0.0820539
\(691\) −6.18205e31 −0.137131 −0.0685654 0.997647i \(-0.521842\pi\)
−0.0685654 + 0.997647i \(0.521842\pi\)
\(692\) −8.36770e32 −1.82552
\(693\) 2.86853e32 0.615499
\(694\) 5.81246e32 1.22666
\(695\) 1.19085e32 0.247191
\(696\) −9.50245e31 −0.194012
\(697\) −7.33069e31 −0.147220
\(698\) 3.71278e32 0.733436
\(699\) 7.99177e31 0.155294
\(700\) 9.90942e32 1.89418
\(701\) 5.26483e32 0.989982 0.494991 0.868898i \(-0.335171\pi\)
0.494991 + 0.868898i \(0.335171\pi\)
\(702\) 3.69571e32 0.683629
\(703\) 2.14087e32 0.389586
\(704\) −2.40367e32 −0.430319
\(705\) 3.82831e31 0.0674268
\(706\) −1.87763e33 −3.25353
\(707\) −2.50415e32 −0.426910
\(708\) −2.42711e32 −0.407105
\(709\) −7.09958e32 −1.17166 −0.585829 0.810435i \(-0.699231\pi\)
−0.585829 + 0.810435i \(0.699231\pi\)
\(710\) −3.73491e32 −0.606470
\(711\) 3.66070e32 0.584876
\(712\) 8.48196e31 0.133345
\(713\) −6.18287e30 −0.00956446
\(714\) 2.56010e31 0.0389698
\(715\) −1.54108e32 −0.230837
\(716\) 1.73170e33 2.55254
\(717\) −1.26598e32 −0.183636
\(718\) −1.25269e33 −1.78819
\(719\) 4.58875e32 0.644633 0.322316 0.946632i \(-0.395539\pi\)
0.322316 + 0.946632i \(0.395539\pi\)
\(720\) 2.68068e32 0.370613
\(721\) 1.67390e32 0.227758
\(722\) 6.91748e32 0.926339
\(723\) −9.14583e31 −0.120540
\(724\) 8.37810e32 1.08681
\(725\) −4.51268e32 −0.576166
\(726\) 1.32229e32 0.166171
\(727\) 1.25284e33 1.54970 0.774851 0.632144i \(-0.217825\pi\)
0.774851 + 0.632144i \(0.217825\pi\)
\(728\) −1.93083e33 −2.35089
\(729\) −7.09581e32 −0.850424
\(730\) 7.44977e32 0.878881
\(731\) −3.90730e31 −0.0453761
\(732\) 4.02771e32 0.460448
\(733\) −1.67809e30 −0.00188852 −0.000944258 1.00000i \(-0.500301\pi\)
−0.000944258 1.00000i \(0.500301\pi\)
\(734\) −2.41070e33 −2.67078
\(735\) −9.80431e29 −0.00106933
\(736\) −3.29537e32 −0.353842
\(737\) 1.67720e32 0.177300
\(738\) 1.72775e33 1.79817
\(739\) 2.96573e32 0.303893 0.151946 0.988389i \(-0.451446\pi\)
0.151946 + 0.988389i \(0.451446\pi\)
\(740\) −1.91982e32 −0.193685
\(741\) −2.44733e32 −0.243099
\(742\) 1.68524e33 1.64822
\(743\) −4.48312e32 −0.431727 −0.215863 0.976424i \(-0.569257\pi\)
−0.215863 + 0.976424i \(0.569257\pi\)
\(744\) −3.11349e30 −0.00295229
\(745\) −4.89633e32 −0.457166
\(746\) −1.47917e33 −1.35995
\(747\) −1.33875e33 −1.21203
\(748\) 2.10912e32 0.188033
\(749\) 3.06536e32 0.269116
\(750\) −1.82172e32 −0.157499
\(751\) −3.50465e32 −0.298391 −0.149195 0.988808i \(-0.547668\pi\)
−0.149195 + 0.988808i \(0.547668\pi\)
\(752\) 2.23188e33 1.87140
\(753\) 2.01329e32 0.166251
\(754\) 1.68141e33 1.36742
\(755\) 4.00654e32 0.320907
\(756\) −8.27683e32 −0.652925
\(757\) 4.37490e32 0.339911 0.169956 0.985452i \(-0.445638\pi\)
0.169956 + 0.985452i \(0.445638\pi\)
\(758\) 1.38922e33 1.06310
\(759\) 1.34902e32 0.101681
\(760\) −9.40591e32 −0.698304
\(761\) −1.53089e31 −0.0111949 −0.00559744 0.999984i \(-0.501782\pi\)
−0.00559744 + 0.999984i \(0.501782\pi\)
\(762\) −3.41551e32 −0.246022
\(763\) −1.48360e33 −1.05265
\(764\) −1.50190e33 −1.04970
\(765\) 5.82304e31 0.0400907
\(766\) −5.05416e33 −3.42782
\(767\) 2.24586e33 1.50050
\(768\) 4.93686e32 0.324935
\(769\) 2.67481e33 1.73436 0.867180 0.497995i \(-0.165930\pi\)
0.867180 + 0.497995i \(0.165930\pi\)
\(770\) 5.09787e32 0.325646
\(771\) 2.49929e32 0.157287
\(772\) −4.69141e33 −2.90873
\(773\) 8.38808e31 0.0512387 0.0256194 0.999672i \(-0.491844\pi\)
0.0256194 + 0.999672i \(0.491844\pi\)
\(774\) 9.20900e32 0.554232
\(775\) −1.47859e31 −0.00876753
\(776\) 3.86890e33 2.26036
\(777\) 8.64114e31 0.0497427
\(778\) 4.28012e33 2.42767
\(779\) −2.31816e33 −1.29557
\(780\) 2.19464e32 0.120858
\(781\) 1.38496e33 0.751534
\(782\) −4.60716e32 −0.246352
\(783\) 3.76921e32 0.198605
\(784\) −5.71586e31 −0.0296788
\(785\) −6.14797e30 −0.00314580
\(786\) −6.56975e32 −0.331276
\(787\) −3.07440e33 −1.52775 −0.763874 0.645366i \(-0.776705\pi\)
−0.763874 + 0.645366i \(0.776705\pi\)
\(788\) −1.75965e33 −0.861737
\(789\) −4.87412e32 −0.235240
\(790\) 6.50569e32 0.309444
\(791\) 2.52281e32 0.118265
\(792\) −2.59952e33 −1.20103
\(793\) −3.72693e33 −1.69711
\(794\) 5.06989e31 0.0227543
\(795\) −1.00170e32 −0.0443114
\(796\) 7.85832e33 3.42633
\(797\) 2.31415e33 0.994535 0.497268 0.867597i \(-0.334337\pi\)
0.497268 + 0.867597i \(0.334337\pi\)
\(798\) 8.09572e32 0.342943
\(799\) 4.84816e32 0.202437
\(800\) −7.88064e32 −0.324360
\(801\) −1.66052e32 −0.0673704
\(802\) −2.45379e33 −0.981370
\(803\) −2.76247e33 −1.08910
\(804\) −2.38848e32 −0.0928276
\(805\) −7.53918e32 −0.288849
\(806\) 5.50915e31 0.0208081
\(807\) −3.14611e31 −0.0117146
\(808\) 2.26931e33 0.833035
\(809\) 3.80662e33 1.37763 0.688814 0.724938i \(-0.258132\pi\)
0.688814 + 0.724938i \(0.258132\pi\)
\(810\) −1.33561e33 −0.476544
\(811\) 4.24454e33 1.49311 0.746554 0.665325i \(-0.231707\pi\)
0.746554 + 0.665325i \(0.231707\pi\)
\(812\) −3.76564e33 −1.30601
\(813\) −5.83886e32 −0.199658
\(814\) 1.05151e33 0.354512
\(815\) 7.28284e32 0.242096
\(816\) −8.87152e31 −0.0290778
\(817\) −1.23559e33 −0.399321
\(818\) −4.19191e33 −1.33582
\(819\) 3.77998e33 1.18775
\(820\) 2.07880e33 0.644100
\(821\) −2.99736e33 −0.915784 −0.457892 0.889008i \(-0.651395\pi\)
−0.457892 + 0.889008i \(0.651395\pi\)
\(822\) 3.04035e32 0.0916004
\(823\) −5.19319e32 −0.154289 −0.0771447 0.997020i \(-0.524580\pi\)
−0.0771447 + 0.997020i \(0.524580\pi\)
\(824\) −1.51692e33 −0.444428
\(825\) 3.22609e32 0.0932086
\(826\) −7.42926e33 −2.11678
\(827\) 4.81781e32 0.135374 0.0676872 0.997707i \(-0.478438\pi\)
0.0676872 + 0.997707i \(0.478438\pi\)
\(828\) 7.35144e33 2.03715
\(829\) −2.15627e33 −0.589287 −0.294644 0.955607i \(-0.595201\pi\)
−0.294644 + 0.955607i \(0.595201\pi\)
\(830\) −2.37918e33 −0.641254
\(831\) 2.59274e32 0.0689202
\(832\) −3.16743e33 −0.830401
\(833\) −1.24161e31 −0.00321048
\(834\) 9.28853e32 0.236885
\(835\) 3.77467e32 0.0949477
\(836\) 6.66960e33 1.65473
\(837\) 1.23499e31 0.00302218
\(838\) 1.38649e34 3.34665
\(839\) −2.38371e32 −0.0567532 −0.0283766 0.999597i \(-0.509034\pi\)
−0.0283766 + 0.999597i \(0.509034\pi\)
\(840\) −3.79649e32 −0.0891601
\(841\) −2.60187e33 −0.602743
\(842\) 8.84388e33 2.02094
\(843\) −4.73702e32 −0.106780
\(844\) −1.40144e34 −3.11627
\(845\) −6.94915e32 −0.152433
\(846\) −1.14265e34 −2.47260
\(847\) 2.74023e33 0.584962
\(848\) −5.83985e33 −1.22984
\(849\) 1.28501e33 0.266974
\(850\) −1.10177e33 −0.225826
\(851\) −1.55506e33 −0.314454
\(852\) −1.97230e33 −0.393475
\(853\) −1.94872e32 −0.0383563 −0.0191781 0.999816i \(-0.506105\pi\)
−0.0191781 + 0.999816i \(0.506105\pi\)
\(854\) 1.23286e34 2.39414
\(855\) 1.84140e33 0.352807
\(856\) −2.77789e33 −0.525130
\(857\) −1.87495e33 −0.349711 −0.174855 0.984594i \(-0.555946\pi\)
−0.174855 + 0.984594i \(0.555946\pi\)
\(858\) −1.20203e33 −0.221213
\(859\) 6.46779e33 1.17445 0.587225 0.809424i \(-0.300220\pi\)
0.587225 + 0.809424i \(0.300220\pi\)
\(860\) 1.10801e33 0.198524
\(861\) −9.35673e32 −0.165420
\(862\) 1.17702e34 2.05330
\(863\) −1.04050e34 −1.79110 −0.895550 0.444961i \(-0.853218\pi\)
−0.895550 + 0.444961i \(0.853218\pi\)
\(864\) 6.58230e32 0.111807
\(865\) 1.52244e33 0.255184
\(866\) −2.29051e33 −0.378858
\(867\) 9.58438e32 0.156439
\(868\) −1.23382e32 −0.0198735
\(869\) −2.41239e33 −0.383461
\(870\) 3.30607e32 0.0518609
\(871\) 2.21012e33 0.342142
\(872\) 1.34447e34 2.05405
\(873\) −7.57417e33 −1.14201
\(874\) −1.45691e34 −2.16795
\(875\) −3.77522e33 −0.554434
\(876\) 3.93401e33 0.570214
\(877\) 8.52438e33 1.21946 0.609730 0.792609i \(-0.291278\pi\)
0.609730 + 0.792609i \(0.291278\pi\)
\(878\) −1.01234e34 −1.42935
\(879\) −1.56761e33 −0.218457
\(880\) −1.76656e33 −0.242984
\(881\) 1.20706e34 1.63872 0.819362 0.573276i \(-0.194328\pi\)
0.819362 + 0.573276i \(0.194328\pi\)
\(882\) 2.92632e32 0.0392133
\(883\) 4.60310e33 0.608839 0.304420 0.952538i \(-0.401538\pi\)
0.304420 + 0.952538i \(0.401538\pi\)
\(884\) 2.77928e33 0.362853
\(885\) 4.41593e32 0.0569081
\(886\) −1.06551e34 −1.35541
\(887\) −7.25037e33 −0.910413 −0.455207 0.890386i \(-0.650435\pi\)
−0.455207 + 0.890386i \(0.650435\pi\)
\(888\) −7.83079e32 −0.0970636
\(889\) −7.07809e33 −0.866055
\(890\) −2.95102e32 −0.0356441
\(891\) 4.95263e33 0.590530
\(892\) −1.00055e34 −1.17772
\(893\) 1.53312e34 1.78149
\(894\) −3.81909e33 −0.438105
\(895\) −3.15069e33 −0.356813
\(896\) 1.36149e34 1.52220
\(897\) 1.77766e33 0.196217
\(898\) 1.21699e34 1.32620
\(899\) 5.61873e31 0.00604507
\(900\) 1.75804e34 1.86741
\(901\) −1.26855e33 −0.133037
\(902\) −1.13858e34 −1.17893
\(903\) −4.98720e32 −0.0509856
\(904\) −2.28623e33 −0.230772
\(905\) −1.52433e33 −0.151922
\(906\) 3.12506e33 0.307528
\(907\) −3.03876e33 −0.295266 −0.147633 0.989042i \(-0.547165\pi\)
−0.147633 + 0.989042i \(0.547165\pi\)
\(908\) −3.20322e34 −3.07326
\(909\) −4.44264e33 −0.420878
\(910\) 6.71768e33 0.628410
\(911\) −1.60065e34 −1.47855 −0.739273 0.673406i \(-0.764831\pi\)
−0.739273 + 0.673406i \(0.764831\pi\)
\(912\) −2.80541e33 −0.255891
\(913\) 8.82233e33 0.794638
\(914\) 7.89533e33 0.702245
\(915\) −7.32809e32 −0.0643648
\(916\) 1.95764e34 1.69799
\(917\) −1.36147e34 −1.16617
\(918\) 9.20251e32 0.0778423
\(919\) −1.54454e34 −1.29024 −0.645120 0.764081i \(-0.723193\pi\)
−0.645120 + 0.764081i \(0.723193\pi\)
\(920\) 6.83217e33 0.563636
\(921\) 5.65088e32 0.0460395
\(922\) 2.07251e34 1.66759
\(923\) 1.82501e34 1.45026
\(924\) 2.69204e33 0.211277
\(925\) −3.71881e33 −0.288253
\(926\) −3.25135e33 −0.248907
\(927\) 2.96969e33 0.224540
\(928\) 2.99469e33 0.223641
\(929\) 1.19786e34 0.883535 0.441768 0.897129i \(-0.354352\pi\)
0.441768 + 0.897129i \(0.354352\pi\)
\(930\) 1.08324e31 0.000789169 0
\(931\) −3.92631e32 −0.0282529
\(932\) −2.86999e34 −2.03985
\(933\) −1.77653e33 −0.124719
\(934\) 5.87939e33 0.407702
\(935\) −3.83738e32 −0.0262846
\(936\) −3.42550e34 −2.31767
\(937\) −2.83646e33 −0.189570 −0.0947852 0.995498i \(-0.530216\pi\)
−0.0947852 + 0.995498i \(0.530216\pi\)
\(938\) −7.31103e33 −0.482665
\(939\) −1.25407e33 −0.0817839
\(940\) −1.37482e34 −0.885676
\(941\) 2.88589e34 1.83653 0.918267 0.395961i \(-0.129588\pi\)
0.918267 + 0.395961i \(0.129588\pi\)
\(942\) −4.79535e31 −0.00301464
\(943\) 1.68384e34 1.04572
\(944\) 2.57446e34 1.57946
\(945\) 1.50590e33 0.0912707
\(946\) −6.06872e33 −0.363370
\(947\) 2.29990e34 1.36045 0.680226 0.733002i \(-0.261882\pi\)
0.680226 + 0.733002i \(0.261882\pi\)
\(948\) 3.43546e33 0.200766
\(949\) −3.64023e34 −2.10168
\(950\) −3.48408e34 −1.98732
\(951\) 1.42695e32 0.00804144
\(952\) −4.80786e33 −0.267687
\(953\) −2.39769e34 −1.31894 −0.659470 0.751731i \(-0.729219\pi\)
−0.659470 + 0.751731i \(0.729219\pi\)
\(954\) 2.98980e34 1.62494
\(955\) 2.73258e33 0.146735
\(956\) 4.54638e34 2.41213
\(957\) −1.22593e33 −0.0642658
\(958\) −1.08520e34 −0.562090
\(959\) 6.30062e33 0.322455
\(960\) −6.22796e32 −0.0314939
\(961\) −2.00115e34 −0.999908
\(962\) 1.38561e34 0.684115
\(963\) 5.43829e33 0.265314
\(964\) 3.28444e34 1.58334
\(965\) 8.53563e33 0.406604
\(966\) −5.88048e33 −0.276806
\(967\) −6.66196e33 −0.309883 −0.154942 0.987924i \(-0.549519\pi\)
−0.154942 + 0.987924i \(0.549519\pi\)
\(968\) −2.48325e34 −1.14144
\(969\) −6.09398e32 −0.0276808
\(970\) −1.34606e34 −0.604211
\(971\) −3.35172e34 −1.48678 −0.743390 0.668858i \(-0.766783\pi\)
−0.743390 + 0.668858i \(0.766783\pi\)
\(972\) −2.21207e34 −0.969701
\(973\) 1.92490e34 0.833892
\(974\) 2.46765e34 1.05647
\(975\) 4.25115e33 0.179868
\(976\) −4.27224e34 −1.78642
\(977\) 1.17263e34 0.484590 0.242295 0.970203i \(-0.422100\pi\)
0.242295 + 0.970203i \(0.422100\pi\)
\(978\) 5.68054e33 0.232003
\(979\) 1.09428e33 0.0441699
\(980\) 3.52091e32 0.0140461
\(981\) −2.63207e34 −1.03778
\(982\) −1.75487e33 −0.0683851
\(983\) 1.51439e34 0.583274 0.291637 0.956529i \(-0.405800\pi\)
0.291637 + 0.956529i \(0.405800\pi\)
\(984\) 8.47927e33 0.322786
\(985\) 3.20154e33 0.120460
\(986\) 4.18679e33 0.155703
\(987\) 6.18808e33 0.227462
\(988\) 8.78881e34 3.19319
\(989\) 8.97497e33 0.322311
\(990\) 9.04419e33 0.321044
\(991\) 2.60260e34 0.913187 0.456593 0.889675i \(-0.349069\pi\)
0.456593 + 0.889675i \(0.349069\pi\)
\(992\) 9.81216e31 0.00340315
\(993\) −1.96122e33 −0.0672374
\(994\) −6.03711e34 −2.04591
\(995\) −1.42976e34 −0.478957
\(996\) −1.25638e34 −0.416043
\(997\) −1.96863e34 −0.644422 −0.322211 0.946668i \(-0.604426\pi\)
−0.322211 + 0.946668i \(0.604426\pi\)
\(998\) −6.50036e34 −2.10347
\(999\) 3.10613e33 0.0993613
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 1.24.a.a.1.2 2
3.2 odd 2 9.24.a.b.1.1 2
4.3 odd 2 16.24.a.b.1.2 2
5.2 odd 4 25.24.b.a.24.4 4
5.3 odd 4 25.24.b.a.24.1 4
5.4 even 2 25.24.a.a.1.1 2
7.6 odd 2 49.24.a.b.1.2 2
8.3 odd 2 64.24.a.g.1.1 2
8.5 even 2 64.24.a.d.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.24.a.a.1.2 2 1.1 even 1 trivial
9.24.a.b.1.1 2 3.2 odd 2
16.24.a.b.1.2 2 4.3 odd 2
25.24.a.a.1.1 2 5.4 even 2
25.24.b.a.24.1 4 5.3 odd 4
25.24.b.a.24.4 4 5.2 odd 4
49.24.a.b.1.2 2 7.6 odd 2
64.24.a.d.1.2 2 8.5 even 2
64.24.a.g.1.1 2 8.3 odd 2