Properties

Label 197.12.a.b.1.15
Level $197$
Weight $12$
Character 197.1
Self dual yes
Analytic conductor $151.364$
Analytic rank $0$
Dimension $92$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [197,12,Mod(1,197)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(197, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.1");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 197.a (trivial)

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: yes
Analytic conductor: \(151.363606570\)
Analytic rank: \(0\)
Dimension: \(92\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 197.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-66.4070 q^{2} -356.598 q^{3} +2361.89 q^{4} -8882.65 q^{5} +23680.6 q^{6} -71949.2 q^{7} -20844.3 q^{8} -49984.8 q^{9} +O(q^{10})\) \(q-66.4070 q^{2} -356.598 q^{3} +2361.89 q^{4} -8882.65 q^{5} +23680.6 q^{6} -71949.2 q^{7} -20844.3 q^{8} -49984.8 q^{9} +589870. q^{10} +734093. q^{11} -842244. q^{12} -172292. q^{13} +4.77793e6 q^{14} +3.16754e6 q^{15} -3.45294e6 q^{16} +1.81711e6 q^{17} +3.31934e6 q^{18} +8.19267e6 q^{19} -2.09798e7 q^{20} +2.56569e7 q^{21} -4.87489e7 q^{22} +4.88503e7 q^{23} +7.43302e6 q^{24} +3.00734e7 q^{25} +1.14414e7 q^{26} +8.09948e7 q^{27} -1.69936e8 q^{28} -5.68080e7 q^{29} -2.10347e8 q^{30} -2.22367e8 q^{31} +2.71988e8 q^{32} -2.61776e8 q^{33} -1.20669e8 q^{34} +6.39100e8 q^{35} -1.18058e8 q^{36} -5.85250e8 q^{37} -5.44051e8 q^{38} +6.14392e7 q^{39} +1.85152e8 q^{40} +9.16053e8 q^{41} -1.70380e9 q^{42} +8.11149e8 q^{43} +1.73385e9 q^{44} +4.43998e8 q^{45} -3.24400e9 q^{46} +1.78873e9 q^{47} +1.23131e9 q^{48} +3.19936e9 q^{49} -1.99708e9 q^{50} -6.47977e8 q^{51} -4.06935e8 q^{52} +1.17129e9 q^{53} -5.37862e9 q^{54} -6.52070e9 q^{55} +1.49973e9 q^{56} -2.92149e9 q^{57} +3.77245e9 q^{58} +2.25620e8 q^{59} +7.48136e9 q^{60} +4.05728e9 q^{61} +1.47667e10 q^{62} +3.59637e9 q^{63} -1.09903e10 q^{64} +1.53041e9 q^{65} +1.73838e10 q^{66} -2.93192e9 q^{67} +4.29180e9 q^{68} -1.74199e10 q^{69} -4.24407e10 q^{70} -1.34111e10 q^{71} +1.04190e9 q^{72} -1.27365e10 q^{73} +3.88647e10 q^{74} -1.07241e10 q^{75} +1.93502e10 q^{76} -5.28174e10 q^{77} -4.07999e9 q^{78} -4.82571e10 q^{79} +3.06713e10 q^{80} -2.00279e10 q^{81} -6.08323e10 q^{82} -5.57621e10 q^{83} +6.05988e10 q^{84} -1.61407e10 q^{85} -5.38660e10 q^{86} +2.02576e10 q^{87} -1.53016e10 q^{88} +7.86518e9 q^{89} -2.94845e10 q^{90} +1.23963e10 q^{91} +1.15379e11 q^{92} +7.92956e10 q^{93} -1.18784e11 q^{94} -7.27727e10 q^{95} -9.69905e10 q^{96} +9.81092e10 q^{97} -2.12460e11 q^{98} -3.66935e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 92 q + 64 q^{2} + 2420 q^{3} + 98304 q^{4} + 16604 q^{5} + 46656 q^{6} + 305891 q^{7} + 234027 q^{8} + 5900444 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 92 q + 64 q^{2} + 2420 q^{3} + 98304 q^{4} + 16604 q^{5} + 46656 q^{6} + 305891 q^{7} + 234027 q^{8} + 5900444 q^{9} + 1074277 q^{10} + 595928 q^{11} + 4956160 q^{12} + 7463810 q^{13} + 4915769 q^{14} + 6749159 q^{15} + 109051904 q^{16} + 9869683 q^{17} + 15324721 q^{18} + 71500013 q^{19} + 79804779 q^{20} + 55741034 q^{21} + 120367289 q^{22} + 38597564 q^{23} + 104015637 q^{24} + 1039976880 q^{25} + 51802726 q^{26} + 665312351 q^{27} + 713160630 q^{28} - 2827541 q^{29} - 43013765 q^{30} + 939775728 q^{31} + 723479980 q^{32} + 978717002 q^{33} + 1063528738 q^{34} + 843197112 q^{35} + 6613742458 q^{36} + 2009031770 q^{37} + 918086794 q^{38} + 2279970607 q^{39} + 3093842646 q^{40} - 30014736 q^{41} + 3159549307 q^{42} + 6320365127 q^{43} + 3019176802 q^{44} + 5538230697 q^{45} + 4344764621 q^{46} + 2853606373 q^{47} + 15616060178 q^{48} + 31617715853 q^{49} - 28784136763 q^{50} - 7216660253 q^{51} + 19141188860 q^{52} + 3389732468 q^{53} + 14059623295 q^{54} + 23123173075 q^{55} + 75592019872 q^{56} + 27508365203 q^{57} + 42079603023 q^{58} + 40032802875 q^{59} + 99482549469 q^{60} + 31816702886 q^{61} + 35401555571 q^{62} + 79170604993 q^{63} + 168463042533 q^{64} + 50313809737 q^{65} + 93218912814 q^{66} + 129966589578 q^{67} + 73640879491 q^{68} - 9850635033 q^{69} + 62387700391 q^{70} + 32189826123 q^{71} + 47439469795 q^{72} + 60612500511 q^{73} - 110473527245 q^{74} + 48823210110 q^{75} + 48170982110 q^{76} - 9381499362 q^{77} - 251751253299 q^{78} + 40812909551 q^{79} - 36932560002 q^{80} + 294126355776 q^{81} + 29914326881 q^{82} + 112077199076 q^{83} - 242466547988 q^{84} - 65194167314 q^{85} - 384596985360 q^{86} + 30701235703 q^{87} + 102229734783 q^{88} - 47595308310 q^{89} - 957657692329 q^{90} + 217575098757 q^{91} - 762245602306 q^{92} - 47762776839 q^{93} - 251435906373 q^{94} - 84935429021 q^{95} - 1089429573223 q^{96} + 432665748880 q^{97} - 404245603446 q^{98} + 9542377031 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −66.4070 −1.46740 −0.733700 0.679473i \(-0.762208\pi\)
−0.733700 + 0.679473i \(0.762208\pi\)
\(3\) −356.598 −0.847251 −0.423626 0.905837i \(-0.639243\pi\)
−0.423626 + 0.905837i \(0.639243\pi\)
\(4\) 2361.89 1.15326
\(5\) −8882.65 −1.27118 −0.635591 0.772026i \(-0.719243\pi\)
−0.635591 + 0.772026i \(0.719243\pi\)
\(6\) 23680.6 1.24326
\(7\) −71949.2 −1.61803 −0.809015 0.587788i \(-0.799999\pi\)
−0.809015 + 0.587788i \(0.799999\pi\)
\(8\) −20844.3 −0.224901
\(9\) −49984.8 −0.282166
\(10\) 589870. 1.86533
\(11\) 734093. 1.37433 0.687166 0.726501i \(-0.258855\pi\)
0.687166 + 0.726501i \(0.258855\pi\)
\(12\) −842244. −0.977105
\(13\) −172292. −0.128700 −0.0643499 0.997927i \(-0.520497\pi\)
−0.0643499 + 0.997927i \(0.520497\pi\)
\(14\) 4.77793e6 2.37430
\(15\) 3.16754e6 1.07701
\(16\) −3.45294e6 −0.823245
\(17\) 1.81711e6 0.310393 0.155196 0.987884i \(-0.450399\pi\)
0.155196 + 0.987884i \(0.450399\pi\)
\(18\) 3.31934e6 0.414050
\(19\) 8.19267e6 0.759068 0.379534 0.925178i \(-0.376084\pi\)
0.379534 + 0.925178i \(0.376084\pi\)
\(20\) −2.09798e7 −1.46601
\(21\) 2.56569e7 1.37088
\(22\) −4.87489e7 −2.01670
\(23\) 4.88503e7 1.58258 0.791288 0.611444i \(-0.209411\pi\)
0.791288 + 0.611444i \(0.209411\pi\)
\(24\) 7.43302e6 0.190548
\(25\) 3.00734e7 0.615903
\(26\) 1.14414e7 0.188854
\(27\) 8.09948e7 1.08632
\(28\) −1.69936e8 −1.86602
\(29\) −5.68080e7 −0.514305 −0.257152 0.966371i \(-0.582784\pi\)
−0.257152 + 0.966371i \(0.582784\pi\)
\(30\) −2.10347e8 −1.58041
\(31\) −2.22367e8 −1.39502 −0.697510 0.716575i \(-0.745709\pi\)
−0.697510 + 0.716575i \(0.745709\pi\)
\(32\) 2.71988e8 1.43293
\(33\) −2.61776e8 −1.16440
\(34\) −1.20669e8 −0.455471
\(35\) 6.39100e8 2.05681
\(36\) −1.18058e8 −0.325412
\(37\) −5.85250e8 −1.38750 −0.693748 0.720218i \(-0.744042\pi\)
−0.693748 + 0.720218i \(0.744042\pi\)
\(38\) −5.44051e8 −1.11386
\(39\) 6.14392e7 0.109041
\(40\) 1.85152e8 0.285890
\(41\) 9.16053e8 1.23484 0.617418 0.786635i \(-0.288179\pi\)
0.617418 + 0.786635i \(0.288179\pi\)
\(42\) −1.70380e9 −2.01163
\(43\) 8.11149e8 0.841442 0.420721 0.907190i \(-0.361777\pi\)
0.420721 + 0.907190i \(0.361777\pi\)
\(44\) 1.73385e9 1.58497
\(45\) 4.43998e8 0.358684
\(46\) −3.24400e9 −2.32227
\(47\) 1.78873e9 1.13764 0.568821 0.822461i \(-0.307400\pi\)
0.568821 + 0.822461i \(0.307400\pi\)
\(48\) 1.23131e9 0.697495
\(49\) 3.19936e9 1.61802
\(50\) −1.99708e9 −0.903777
\(51\) −6.47977e8 −0.262981
\(52\) −4.06935e8 −0.148425
\(53\) 1.17129e9 0.384722 0.192361 0.981324i \(-0.438386\pi\)
0.192361 + 0.981324i \(0.438386\pi\)
\(54\) −5.37862e9 −1.59406
\(55\) −6.52070e9 −1.74703
\(56\) 1.49973e9 0.363897
\(57\) −2.92149e9 −0.643121
\(58\) 3.77245e9 0.754691
\(59\) 2.25620e8 0.0410859 0.0205429 0.999789i \(-0.493461\pi\)
0.0205429 + 0.999789i \(0.493461\pi\)
\(60\) 7.48136e9 1.24208
\(61\) 4.05728e9 0.615064 0.307532 0.951538i \(-0.400497\pi\)
0.307532 + 0.951538i \(0.400497\pi\)
\(62\) 1.47667e10 2.04705
\(63\) 3.59637e9 0.456553
\(64\) −1.09903e10 −1.27944
\(65\) 1.53041e9 0.163601
\(66\) 1.73838e10 1.70865
\(67\) −2.93192e9 −0.265302 −0.132651 0.991163i \(-0.542349\pi\)
−0.132651 + 0.991163i \(0.542349\pi\)
\(68\) 4.29180e9 0.357965
\(69\) −1.74199e10 −1.34084
\(70\) −4.24407e10 −3.01817
\(71\) −1.34111e10 −0.882150 −0.441075 0.897470i \(-0.645403\pi\)
−0.441075 + 0.897470i \(0.645403\pi\)
\(72\) 1.04190e9 0.0634594
\(73\) −1.27365e10 −0.719076 −0.359538 0.933130i \(-0.617066\pi\)
−0.359538 + 0.933130i \(0.617066\pi\)
\(74\) 3.88647e10 2.03601
\(75\) −1.07241e10 −0.521825
\(76\) 1.93502e10 0.875407
\(77\) −5.28174e10 −2.22371
\(78\) −4.07999e9 −0.160007
\(79\) −4.82571e10 −1.76446 −0.882230 0.470818i \(-0.843959\pi\)
−0.882230 + 0.470818i \(0.843959\pi\)
\(80\) 3.06713e10 1.04649
\(81\) −2.00279e10 −0.638217
\(82\) −6.08323e10 −1.81200
\(83\) −5.57621e10 −1.55385 −0.776926 0.629591i \(-0.783222\pi\)
−0.776926 + 0.629591i \(0.783222\pi\)
\(84\) 6.05988e10 1.58099
\(85\) −1.61407e10 −0.394566
\(86\) −5.38660e10 −1.23473
\(87\) 2.02576e10 0.435745
\(88\) −1.53016e10 −0.309089
\(89\) 7.86518e9 0.149301 0.0746506 0.997210i \(-0.476216\pi\)
0.0746506 + 0.997210i \(0.476216\pi\)
\(90\) −2.94845e10 −0.526333
\(91\) 1.23963e10 0.208240
\(92\) 1.15379e11 1.82513
\(93\) 7.92956e10 1.18193
\(94\) −1.18784e11 −1.66938
\(95\) −7.27727e10 −0.964914
\(96\) −9.69905e10 −1.21405
\(97\) 9.81092e10 1.16002 0.580009 0.814610i \(-0.303049\pi\)
0.580009 + 0.814610i \(0.303049\pi\)
\(98\) −2.12460e11 −2.37429
\(99\) −3.66935e10 −0.387789
\(100\) 7.10300e10 0.710300
\(101\) 5.20646e10 0.492918 0.246459 0.969153i \(-0.420733\pi\)
0.246459 + 0.969153i \(0.420733\pi\)
\(102\) 4.30302e10 0.385898
\(103\) −7.05612e10 −0.599737 −0.299869 0.953981i \(-0.596943\pi\)
−0.299869 + 0.953981i \(0.596943\pi\)
\(104\) 3.59131e9 0.0289447
\(105\) −2.27902e11 −1.74264
\(106\) −7.77818e10 −0.564541
\(107\) −1.52894e11 −1.05385 −0.526927 0.849910i \(-0.676656\pi\)
−0.526927 + 0.849910i \(0.676656\pi\)
\(108\) 1.91300e11 1.25281
\(109\) 5.35156e10 0.333146 0.166573 0.986029i \(-0.446730\pi\)
0.166573 + 0.986029i \(0.446730\pi\)
\(110\) 4.33020e11 2.56359
\(111\) 2.08699e11 1.17556
\(112\) 2.48436e11 1.33204
\(113\) −1.31645e11 −0.672163 −0.336081 0.941833i \(-0.609102\pi\)
−0.336081 + 0.941833i \(0.609102\pi\)
\(114\) 1.94007e11 0.943717
\(115\) −4.33921e11 −2.01174
\(116\) −1.34174e11 −0.593129
\(117\) 8.61201e9 0.0363147
\(118\) −1.49828e10 −0.0602894
\(119\) −1.30739e11 −0.502225
\(120\) −6.60250e10 −0.242221
\(121\) 2.53581e11 0.888787
\(122\) −2.69432e11 −0.902546
\(123\) −3.26663e11 −1.04622
\(124\) −5.25205e11 −1.60883
\(125\) 1.66592e11 0.488257
\(126\) −2.38824e11 −0.669946
\(127\) −5.31958e10 −0.142875 −0.0714376 0.997445i \(-0.522759\pi\)
−0.0714376 + 0.997445i \(0.522759\pi\)
\(128\) 1.72801e11 0.444519
\(129\) −2.89254e11 −0.712913
\(130\) −1.01630e11 −0.240068
\(131\) −6.83862e11 −1.54873 −0.774366 0.632737i \(-0.781931\pi\)
−0.774366 + 0.632737i \(0.781931\pi\)
\(132\) −6.18286e11 −1.34287
\(133\) −5.89456e11 −1.22820
\(134\) 1.94700e11 0.389305
\(135\) −7.19448e11 −1.38091
\(136\) −3.78763e10 −0.0698077
\(137\) −3.11681e9 −0.00551755 −0.00275878 0.999996i \(-0.500878\pi\)
−0.00275878 + 0.999996i \(0.500878\pi\)
\(138\) 1.15681e12 1.96755
\(139\) −3.81730e10 −0.0623985 −0.0311993 0.999513i \(-0.509933\pi\)
−0.0311993 + 0.999513i \(0.509933\pi\)
\(140\) 1.50948e12 2.37205
\(141\) −6.37856e11 −0.963868
\(142\) 8.90589e11 1.29447
\(143\) −1.26479e11 −0.176876
\(144\) 1.72594e11 0.232291
\(145\) 5.04606e11 0.653775
\(146\) 8.45794e11 1.05517
\(147\) −1.14089e12 −1.37087
\(148\) −1.38229e12 −1.60015
\(149\) 1.34519e12 1.50058 0.750289 0.661110i \(-0.229914\pi\)
0.750289 + 0.661110i \(0.229914\pi\)
\(150\) 7.12156e11 0.765726
\(151\) −4.77753e11 −0.495257 −0.247628 0.968855i \(-0.579651\pi\)
−0.247628 + 0.968855i \(0.579651\pi\)
\(152\) −1.70770e11 −0.170715
\(153\) −9.08278e10 −0.0875822
\(154\) 3.50745e12 3.26307
\(155\) 1.97521e12 1.77333
\(156\) 1.45112e11 0.125753
\(157\) 1.42016e12 1.18820 0.594098 0.804393i \(-0.297509\pi\)
0.594098 + 0.804393i \(0.297509\pi\)
\(158\) 3.20461e12 2.58917
\(159\) −4.17679e11 −0.325956
\(160\) −2.41598e12 −1.82152
\(161\) −3.51474e12 −2.56066
\(162\) 1.32999e12 0.936520
\(163\) 2.17044e12 1.47746 0.738730 0.674002i \(-0.235426\pi\)
0.738730 + 0.674002i \(0.235426\pi\)
\(164\) 2.16361e12 1.42409
\(165\) 2.32527e12 1.48017
\(166\) 3.70300e12 2.28013
\(167\) 1.30933e12 0.780027 0.390014 0.920809i \(-0.372470\pi\)
0.390014 + 0.920809i \(0.372470\pi\)
\(168\) −5.34800e11 −0.308312
\(169\) −1.76248e12 −0.983436
\(170\) 1.07186e12 0.578986
\(171\) −4.09509e11 −0.214183
\(172\) 1.91584e12 0.970406
\(173\) −8.80885e10 −0.0432181 −0.0216091 0.999766i \(-0.506879\pi\)
−0.0216091 + 0.999766i \(0.506879\pi\)
\(174\) −1.34525e12 −0.639413
\(175\) −2.16376e12 −0.996550
\(176\) −2.53478e12 −1.13141
\(177\) −8.04558e10 −0.0348100
\(178\) −5.22303e11 −0.219085
\(179\) 3.56060e12 1.44821 0.724105 0.689690i \(-0.242253\pi\)
0.724105 + 0.689690i \(0.242253\pi\)
\(180\) 1.04867e12 0.413658
\(181\) −3.46272e12 −1.32491 −0.662453 0.749104i \(-0.730485\pi\)
−0.662453 + 0.749104i \(0.730485\pi\)
\(182\) −8.23201e11 −0.305572
\(183\) −1.44682e12 −0.521114
\(184\) −1.01825e12 −0.355923
\(185\) 5.19857e12 1.76376
\(186\) −5.26578e12 −1.73437
\(187\) 1.33393e12 0.426583
\(188\) 4.22477e12 1.31200
\(189\) −5.82751e12 −1.75769
\(190\) 4.83261e12 1.41592
\(191\) 1.01997e11 0.0290337 0.0145169 0.999895i \(-0.495379\pi\)
0.0145169 + 0.999895i \(0.495379\pi\)
\(192\) 3.91912e12 1.08401
\(193\) 5.38994e11 0.144884 0.0724418 0.997373i \(-0.476921\pi\)
0.0724418 + 0.997373i \(0.476921\pi\)
\(194\) −6.51513e12 −1.70221
\(195\) −5.45743e11 −0.138611
\(196\) 7.55652e12 1.86601
\(197\) −2.96709e11 −0.0712470
\(198\) 2.43670e12 0.569042
\(199\) 1.42363e11 0.0323375 0.0161687 0.999869i \(-0.494853\pi\)
0.0161687 + 0.999869i \(0.494853\pi\)
\(200\) −6.26858e11 −0.138517
\(201\) 1.04552e12 0.224778
\(202\) −3.45745e12 −0.723308
\(203\) 4.08729e12 0.832160
\(204\) −1.53045e12 −0.303286
\(205\) −8.13698e12 −1.56970
\(206\) 4.68575e12 0.880055
\(207\) −2.44177e12 −0.446548
\(208\) 5.94916e11 0.105951
\(209\) 6.01419e12 1.04321
\(210\) 1.51343e13 2.55714
\(211\) 2.22628e12 0.366461 0.183230 0.983070i \(-0.441345\pi\)
0.183230 + 0.983070i \(0.441345\pi\)
\(212\) 2.76645e12 0.443686
\(213\) 4.78236e12 0.747403
\(214\) 1.01533e13 1.54643
\(215\) −7.20516e12 −1.06963
\(216\) −1.68828e12 −0.244314
\(217\) 1.59991e13 2.25719
\(218\) −3.55381e12 −0.488859
\(219\) 4.54182e12 0.609238
\(220\) −1.54011e13 −2.01478
\(221\) −3.13074e11 −0.0399475
\(222\) −1.38591e13 −1.72501
\(223\) −6.37378e11 −0.0773964 −0.0386982 0.999251i \(-0.512321\pi\)
−0.0386982 + 0.999251i \(0.512321\pi\)
\(224\) −1.95693e13 −2.31853
\(225\) −1.50321e12 −0.173787
\(226\) 8.74218e12 0.986332
\(227\) −1.20060e13 −1.32208 −0.661038 0.750353i \(-0.729884\pi\)
−0.661038 + 0.750353i \(0.729884\pi\)
\(228\) −6.90023e12 −0.741689
\(229\) −8.77847e12 −0.921136 −0.460568 0.887624i \(-0.652354\pi\)
−0.460568 + 0.887624i \(0.652354\pi\)
\(230\) 2.88154e13 2.95203
\(231\) 1.88346e13 1.88404
\(232\) 1.18412e12 0.115668
\(233\) 1.49151e13 1.42288 0.711440 0.702747i \(-0.248043\pi\)
0.711440 + 0.702747i \(0.248043\pi\)
\(234\) −5.71897e11 −0.0532882
\(235\) −1.58886e13 −1.44615
\(236\) 5.32890e11 0.0473829
\(237\) 1.72084e13 1.49494
\(238\) 8.68201e12 0.736965
\(239\) −6.38408e12 −0.529554 −0.264777 0.964310i \(-0.585298\pi\)
−0.264777 + 0.964310i \(0.585298\pi\)
\(240\) −1.09373e13 −0.886643
\(241\) −3.26533e12 −0.258722 −0.129361 0.991598i \(-0.541293\pi\)
−0.129361 + 0.991598i \(0.541293\pi\)
\(242\) −1.68396e13 −1.30421
\(243\) −7.20606e12 −0.545586
\(244\) 9.58283e12 0.709332
\(245\) −2.84188e13 −2.05680
\(246\) 2.16927e13 1.53522
\(247\) −1.41154e12 −0.0976919
\(248\) 4.63507e12 0.313742
\(249\) 1.98847e13 1.31650
\(250\) −1.10628e13 −0.716468
\(251\) −1.19506e13 −0.757154 −0.378577 0.925570i \(-0.623586\pi\)
−0.378577 + 0.925570i \(0.623586\pi\)
\(252\) 8.49421e12 0.526526
\(253\) 3.58607e13 2.17498
\(254\) 3.53257e12 0.209655
\(255\) 5.75576e12 0.334296
\(256\) 1.10330e13 0.627152
\(257\) 1.75239e13 0.974985 0.487492 0.873127i \(-0.337912\pi\)
0.487492 + 0.873127i \(0.337912\pi\)
\(258\) 1.92085e13 1.04613
\(259\) 4.21083e13 2.24501
\(260\) 3.61467e12 0.188675
\(261\) 2.83954e12 0.145119
\(262\) 4.54132e13 2.27261
\(263\) −1.51987e13 −0.744815 −0.372408 0.928069i \(-0.621468\pi\)
−0.372408 + 0.928069i \(0.621468\pi\)
\(264\) 5.45653e12 0.261876
\(265\) −1.04042e13 −0.489051
\(266\) 3.91440e13 1.80225
\(267\) −2.80471e12 −0.126496
\(268\) −6.92486e12 −0.305964
\(269\) 2.12488e12 0.0919808 0.0459904 0.998942i \(-0.485356\pi\)
0.0459904 + 0.998942i \(0.485356\pi\)
\(270\) 4.77764e13 2.02634
\(271\) 3.13855e12 0.130436 0.0652180 0.997871i \(-0.479226\pi\)
0.0652180 + 0.997871i \(0.479226\pi\)
\(272\) −6.27436e12 −0.255529
\(273\) −4.42050e12 −0.176432
\(274\) 2.06978e11 0.00809646
\(275\) 2.20767e13 0.846455
\(276\) −4.11439e13 −1.54634
\(277\) 3.38406e13 1.24681 0.623404 0.781900i \(-0.285749\pi\)
0.623404 + 0.781900i \(0.285749\pi\)
\(278\) 2.53495e12 0.0915637
\(279\) 1.11150e13 0.393627
\(280\) −1.33216e13 −0.462579
\(281\) 2.80480e13 0.955029 0.477515 0.878624i \(-0.341538\pi\)
0.477515 + 0.878624i \(0.341538\pi\)
\(282\) 4.23581e13 1.41438
\(283\) 1.83797e13 0.601883 0.300941 0.953643i \(-0.402699\pi\)
0.300941 + 0.953643i \(0.402699\pi\)
\(284\) −3.16754e13 −1.01735
\(285\) 2.59506e13 0.817524
\(286\) 8.39907e12 0.259548
\(287\) −6.59092e13 −1.99800
\(288\) −1.35953e13 −0.404324
\(289\) −3.09700e13 −0.903656
\(290\) −3.35093e13 −0.959349
\(291\) −3.49855e13 −0.982827
\(292\) −3.00822e13 −0.829285
\(293\) −4.97511e13 −1.34595 −0.672977 0.739663i \(-0.734985\pi\)
−0.672977 + 0.739663i \(0.734985\pi\)
\(294\) 7.57627e13 2.01162
\(295\) −2.00411e12 −0.0522276
\(296\) 1.21991e13 0.312050
\(297\) 5.94577e13 1.49296
\(298\) −8.93299e13 −2.20195
\(299\) −8.41655e12 −0.203677
\(300\) −2.53292e13 −0.601802
\(301\) −5.83615e13 −1.36148
\(302\) 3.17261e13 0.726740
\(303\) −1.85661e13 −0.417625
\(304\) −2.82888e13 −0.624899
\(305\) −3.60394e13 −0.781859
\(306\) 6.03160e12 0.128518
\(307\) 2.79635e13 0.585235 0.292617 0.956230i \(-0.405474\pi\)
0.292617 + 0.956230i \(0.405474\pi\)
\(308\) −1.24749e14 −2.56453
\(309\) 2.51620e13 0.508128
\(310\) −1.31168e14 −2.60218
\(311\) −1.43131e13 −0.278967 −0.139483 0.990224i \(-0.544544\pi\)
−0.139483 + 0.990224i \(0.544544\pi\)
\(312\) −1.28065e12 −0.0245235
\(313\) −7.01132e13 −1.31919 −0.659593 0.751623i \(-0.729271\pi\)
−0.659593 + 0.751623i \(0.729271\pi\)
\(314\) −9.43083e13 −1.74356
\(315\) −3.19453e13 −0.580361
\(316\) −1.13978e14 −2.03489
\(317\) 2.33871e13 0.410346 0.205173 0.978726i \(-0.434224\pi\)
0.205173 + 0.978726i \(0.434224\pi\)
\(318\) 2.77368e13 0.478308
\(319\) −4.17024e13 −0.706825
\(320\) 9.76230e13 1.62640
\(321\) 5.45218e13 0.892879
\(322\) 2.33403e14 3.75751
\(323\) 1.48870e13 0.235609
\(324\) −4.73037e13 −0.736033
\(325\) −5.18142e12 −0.0792666
\(326\) −1.44132e14 −2.16803
\(327\) −1.90836e13 −0.282258
\(328\) −1.90944e13 −0.277716
\(329\) −1.28697e14 −1.84074
\(330\) −1.54414e14 −2.17200
\(331\) −5.65661e13 −0.782532 −0.391266 0.920278i \(-0.627963\pi\)
−0.391266 + 0.920278i \(0.627963\pi\)
\(332\) −1.31704e14 −1.79200
\(333\) 2.92536e13 0.391504
\(334\) −8.69489e13 −1.14461
\(335\) 2.60432e13 0.337247
\(336\) −8.85919e13 −1.12857
\(337\) 8.25902e13 1.03506 0.517528 0.855666i \(-0.326852\pi\)
0.517528 + 0.855666i \(0.326852\pi\)
\(338\) 1.17041e14 1.44310
\(339\) 4.69445e13 0.569490
\(340\) −3.81226e13 −0.455039
\(341\) −1.63238e14 −1.91722
\(342\) 2.71943e13 0.314292
\(343\) −8.79242e13 −0.999979
\(344\) −1.69078e13 −0.189241
\(345\) 1.54735e14 1.70445
\(346\) 5.84969e12 0.0634183
\(347\) 9.88266e13 1.05454 0.527268 0.849699i \(-0.323216\pi\)
0.527268 + 0.849699i \(0.323216\pi\)
\(348\) 4.78462e13 0.502530
\(349\) 3.55192e13 0.367218 0.183609 0.982999i \(-0.441222\pi\)
0.183609 + 0.982999i \(0.441222\pi\)
\(350\) 1.43689e14 1.46234
\(351\) −1.39548e13 −0.139809
\(352\) 1.99665e14 1.96932
\(353\) −2.96980e13 −0.288381 −0.144190 0.989550i \(-0.546058\pi\)
−0.144190 + 0.989550i \(0.546058\pi\)
\(354\) 5.34283e12 0.0510803
\(355\) 1.19126e14 1.12137
\(356\) 1.85767e13 0.172184
\(357\) 4.66214e13 0.425511
\(358\) −2.36449e14 −2.12510
\(359\) −7.96347e13 −0.704827 −0.352414 0.935844i \(-0.614639\pi\)
−0.352414 + 0.935844i \(0.614639\pi\)
\(360\) −9.25480e12 −0.0806684
\(361\) −4.93704e13 −0.423815
\(362\) 2.29949e14 1.94417
\(363\) −9.04266e13 −0.753026
\(364\) 2.92787e13 0.240156
\(365\) 1.13134e14 0.914077
\(366\) 9.60788e13 0.764683
\(367\) 2.17763e14 1.70734 0.853672 0.520810i \(-0.174370\pi\)
0.853672 + 0.520810i \(0.174370\pi\)
\(368\) −1.68677e14 −1.30285
\(369\) −4.57887e13 −0.348428
\(370\) −3.45222e14 −2.58814
\(371\) −8.42733e13 −0.622492
\(372\) 1.87287e14 1.36308
\(373\) −8.76633e13 −0.628665 −0.314333 0.949313i \(-0.601781\pi\)
−0.314333 + 0.949313i \(0.601781\pi\)
\(374\) −8.85820e13 −0.625968
\(375\) −5.94063e13 −0.413676
\(376\) −3.72847e13 −0.255857
\(377\) 9.78759e12 0.0661909
\(378\) 3.86987e14 2.57924
\(379\) −3.46120e11 −0.00227359 −0.00113679 0.999999i \(-0.500362\pi\)
−0.00113679 + 0.999999i \(0.500362\pi\)
\(380\) −1.71881e14 −1.11280
\(381\) 1.89695e13 0.121051
\(382\) −6.77329e12 −0.0426041
\(383\) 3.19451e14 1.98067 0.990334 0.138704i \(-0.0442937\pi\)
0.990334 + 0.138704i \(0.0442937\pi\)
\(384\) −6.16204e13 −0.376619
\(385\) 4.69159e14 2.82674
\(386\) −3.57930e13 −0.212602
\(387\) −4.05451e13 −0.237426
\(388\) 2.31723e14 1.33781
\(389\) −1.34834e14 −0.767497 −0.383749 0.923438i \(-0.625367\pi\)
−0.383749 + 0.923438i \(0.625367\pi\)
\(390\) 3.62411e13 0.203398
\(391\) 8.87663e13 0.491220
\(392\) −6.66883e13 −0.363895
\(393\) 2.43864e14 1.31217
\(394\) 1.97036e13 0.104548
\(395\) 4.28651e14 2.24295
\(396\) −8.66659e13 −0.447224
\(397\) −3.35806e14 −1.70900 −0.854498 0.519454i \(-0.826135\pi\)
−0.854498 + 0.519454i \(0.826135\pi\)
\(398\) −9.45391e12 −0.0474520
\(399\) 2.10199e14 1.04059
\(400\) −1.03842e14 −0.507039
\(401\) 2.68768e14 1.29444 0.647222 0.762302i \(-0.275931\pi\)
0.647222 + 0.762302i \(0.275931\pi\)
\(402\) −6.94297e13 −0.329839
\(403\) 3.83121e13 0.179539
\(404\) 1.22971e14 0.568465
\(405\) 1.77901e14 0.811290
\(406\) −2.71424e14 −1.22111
\(407\) −4.29628e14 −1.90688
\(408\) 1.35066e13 0.0591446
\(409\) −2.43368e14 −1.05144 −0.525720 0.850657i \(-0.676204\pi\)
−0.525720 + 0.850657i \(0.676204\pi\)
\(410\) 5.40352e14 2.30338
\(411\) 1.11145e12 0.00467475
\(412\) −1.66657e14 −0.691656
\(413\) −1.62332e13 −0.0664782
\(414\) 1.62151e14 0.655266
\(415\) 4.95316e14 1.97523
\(416\) −4.68615e13 −0.184418
\(417\) 1.36124e13 0.0528672
\(418\) −3.99384e14 −1.53081
\(419\) −4.62562e14 −1.74982 −0.874909 0.484287i \(-0.839079\pi\)
−0.874909 + 0.484287i \(0.839079\pi\)
\(420\) −5.38278e14 −2.00972
\(421\) −2.85905e14 −1.05359 −0.526793 0.849993i \(-0.676606\pi\)
−0.526793 + 0.849993i \(0.676606\pi\)
\(422\) −1.47841e14 −0.537744
\(423\) −8.94091e13 −0.321003
\(424\) −2.44147e13 −0.0865244
\(425\) 5.46466e13 0.191172
\(426\) −3.17582e14 −1.09674
\(427\) −2.91918e14 −0.995193
\(428\) −3.61119e14 −1.21537
\(429\) 4.51021e13 0.149859
\(430\) 4.78473e14 1.56957
\(431\) 4.07553e14 1.31996 0.659978 0.751285i \(-0.270565\pi\)
0.659978 + 0.751285i \(0.270565\pi\)
\(432\) −2.79670e14 −0.894304
\(433\) −1.22761e13 −0.0387594 −0.0193797 0.999812i \(-0.506169\pi\)
−0.0193797 + 0.999812i \(0.506169\pi\)
\(434\) −1.06245e15 −3.31220
\(435\) −1.79941e14 −0.553911
\(436\) 1.26398e14 0.384206
\(437\) 4.00215e14 1.20128
\(438\) −3.01608e14 −0.893996
\(439\) 3.05170e14 0.893279 0.446640 0.894714i \(-0.352621\pi\)
0.446640 + 0.894714i \(0.352621\pi\)
\(440\) 1.35919e14 0.392908
\(441\) −1.59919e14 −0.456550
\(442\) 2.07903e13 0.0586190
\(443\) 6.65281e12 0.0185261 0.00926307 0.999957i \(-0.497051\pi\)
0.00926307 + 0.999957i \(0.497051\pi\)
\(444\) 4.92923e14 1.35573
\(445\) −6.98637e13 −0.189789
\(446\) 4.23264e13 0.113572
\(447\) −4.79692e14 −1.27137
\(448\) 7.90743e14 2.07017
\(449\) −2.05736e14 −0.532054 −0.266027 0.963966i \(-0.585711\pi\)
−0.266027 + 0.963966i \(0.585711\pi\)
\(450\) 9.98238e13 0.255015
\(451\) 6.72468e14 1.69707
\(452\) −3.10932e14 −0.775182
\(453\) 1.70366e14 0.419607
\(454\) 7.97282e14 1.94001
\(455\) −1.10112e14 −0.264711
\(456\) 6.08963e13 0.144639
\(457\) 7.22802e14 1.69621 0.848106 0.529826i \(-0.177743\pi\)
0.848106 + 0.529826i \(0.177743\pi\)
\(458\) 5.82952e14 1.35168
\(459\) 1.47176e14 0.337185
\(460\) −1.02487e15 −2.32007
\(461\) −7.93708e14 −1.77544 −0.887719 0.460385i \(-0.847711\pi\)
−0.887719 + 0.460385i \(0.847711\pi\)
\(462\) −1.25075e15 −2.76464
\(463\) −7.95113e14 −1.73673 −0.868367 0.495922i \(-0.834830\pi\)
−0.868367 + 0.495922i \(0.834830\pi\)
\(464\) 1.96155e14 0.423399
\(465\) −7.04355e14 −1.50245
\(466\) −9.90466e14 −2.08794
\(467\) −1.28045e14 −0.266759 −0.133379 0.991065i \(-0.542583\pi\)
−0.133379 + 0.991065i \(0.542583\pi\)
\(468\) 2.03406e13 0.0418804
\(469\) 2.10949e14 0.429267
\(470\) 1.05512e15 2.12208
\(471\) −5.06425e14 −1.00670
\(472\) −4.70289e12 −0.00924026
\(473\) 5.95459e14 1.15642
\(474\) −1.14276e15 −2.19368
\(475\) 2.46382e14 0.467513
\(476\) −3.08792e14 −0.579198
\(477\) −5.85467e13 −0.108555
\(478\) 4.23947e14 0.777067
\(479\) −5.78121e14 −1.04755 −0.523773 0.851858i \(-0.675476\pi\)
−0.523773 + 0.851858i \(0.675476\pi\)
\(480\) 8.61533e14 1.54328
\(481\) 1.00834e14 0.178571
\(482\) 2.16841e14 0.379649
\(483\) 1.25335e15 2.16952
\(484\) 5.98930e14 1.02501
\(485\) −8.71470e14 −1.47460
\(486\) 4.78533e14 0.800594
\(487\) 6.73661e14 1.11438 0.557189 0.830386i \(-0.311880\pi\)
0.557189 + 0.830386i \(0.311880\pi\)
\(488\) −8.45710e13 −0.138329
\(489\) −7.73974e14 −1.25178
\(490\) 1.88721e15 3.01815
\(491\) −1.01698e15 −1.60828 −0.804141 0.594439i \(-0.797374\pi\)
−0.804141 + 0.594439i \(0.797374\pi\)
\(492\) −7.71540e14 −1.20656
\(493\) −1.03226e14 −0.159636
\(494\) 9.37358e13 0.143353
\(495\) 3.25936e14 0.492951
\(496\) 7.67819e14 1.14844
\(497\) 9.64916e14 1.42735
\(498\) −1.32048e15 −1.93184
\(499\) 1.31409e15 1.90139 0.950694 0.310129i \(-0.100372\pi\)
0.950694 + 0.310129i \(0.100372\pi\)
\(500\) 3.93471e14 0.563089
\(501\) −4.66906e14 −0.660879
\(502\) 7.93603e14 1.11105
\(503\) −7.64595e14 −1.05878 −0.529392 0.848377i \(-0.677580\pi\)
−0.529392 + 0.848377i \(0.677580\pi\)
\(504\) −7.49636e13 −0.102679
\(505\) −4.62472e14 −0.626589
\(506\) −2.38140e15 −3.19157
\(507\) 6.28495e14 0.833217
\(508\) −1.25642e14 −0.164773
\(509\) −1.33935e15 −1.73759 −0.868793 0.495175i \(-0.835104\pi\)
−0.868793 + 0.495175i \(0.835104\pi\)
\(510\) −3.82222e14 −0.490547
\(511\) 9.16382e14 1.16349
\(512\) −1.08656e15 −1.36480
\(513\) 6.63564e14 0.824588
\(514\) −1.16371e15 −1.43069
\(515\) 6.26770e14 0.762375
\(516\) −6.83186e14 −0.822177
\(517\) 1.31309e15 1.56350
\(518\) −2.79628e15 −3.29433
\(519\) 3.14122e13 0.0366166
\(520\) −3.19004e13 −0.0367940
\(521\) 5.20356e13 0.0593873 0.0296936 0.999559i \(-0.490547\pi\)
0.0296936 + 0.999559i \(0.490547\pi\)
\(522\) −1.88565e14 −0.212948
\(523\) 1.09851e15 1.22756 0.613780 0.789477i \(-0.289648\pi\)
0.613780 + 0.789477i \(0.289648\pi\)
\(524\) −1.61521e15 −1.78610
\(525\) 7.71592e14 0.844328
\(526\) 1.00930e15 1.09294
\(527\) −4.04065e14 −0.433004
\(528\) 9.03898e14 0.958590
\(529\) 1.43355e15 1.50455
\(530\) 6.90909e14 0.717634
\(531\) −1.12776e13 −0.0115930
\(532\) −1.39223e15 −1.41643
\(533\) −1.57829e14 −0.158923
\(534\) 1.86252e14 0.185620
\(535\) 1.35811e15 1.33964
\(536\) 6.11137e13 0.0596668
\(537\) −1.26970e15 −1.22700
\(538\) −1.41107e14 −0.134973
\(539\) 2.34863e15 2.22370
\(540\) −1.69926e15 −1.59255
\(541\) −7.41170e14 −0.687595 −0.343798 0.939044i \(-0.611713\pi\)
−0.343798 + 0.939044i \(0.611713\pi\)
\(542\) −2.08421e14 −0.191402
\(543\) 1.23480e15 1.12253
\(544\) 4.94232e14 0.444772
\(545\) −4.75360e14 −0.423489
\(546\) 2.93552e14 0.258896
\(547\) −6.86045e13 −0.0598994 −0.0299497 0.999551i \(-0.509535\pi\)
−0.0299497 + 0.999551i \(0.509535\pi\)
\(548\) −7.36154e12 −0.00636320
\(549\) −2.02802e14 −0.173550
\(550\) −1.46605e15 −1.24209
\(551\) −4.65409e14 −0.390392
\(552\) 3.63106e14 0.301556
\(553\) 3.47206e15 2.85495
\(554\) −2.24725e15 −1.82957
\(555\) −1.85380e15 −1.49435
\(556\) −9.01602e13 −0.0719620
\(557\) 1.97526e15 1.56107 0.780533 0.625114i \(-0.214948\pi\)
0.780533 + 0.625114i \(0.214948\pi\)
\(558\) −7.38111e14 −0.577609
\(559\) −1.39755e14 −0.108293
\(560\) −2.20677e15 −1.69326
\(561\) −4.75676e14 −0.361423
\(562\) −1.86258e15 −1.40141
\(563\) −1.95018e15 −1.45304 −0.726521 0.687144i \(-0.758864\pi\)
−0.726521 + 0.687144i \(0.758864\pi\)
\(564\) −1.50654e15 −1.11160
\(565\) 1.16936e15 0.854441
\(566\) −1.22054e15 −0.883203
\(567\) 1.44099e15 1.03265
\(568\) 2.79544e14 0.198397
\(569\) 9.04698e13 0.0635896 0.0317948 0.999494i \(-0.489878\pi\)
0.0317948 + 0.999494i \(0.489878\pi\)
\(570\) −1.72330e15 −1.19964
\(571\) −1.35852e15 −0.936631 −0.468315 0.883561i \(-0.655139\pi\)
−0.468315 + 0.883561i \(0.655139\pi\)
\(572\) −2.98728e14 −0.203985
\(573\) −3.63718e13 −0.0245988
\(574\) 4.37683e15 2.93187
\(575\) 1.46910e15 0.974714
\(576\) 5.49348e14 0.361014
\(577\) −2.70905e15 −1.76340 −0.881699 0.471812i \(-0.843600\pi\)
−0.881699 + 0.471812i \(0.843600\pi\)
\(578\) 2.05663e15 1.32603
\(579\) −1.92204e14 −0.122753
\(580\) 1.19182e15 0.753975
\(581\) 4.01204e15 2.51418
\(582\) 2.32328e15 1.44220
\(583\) 8.59836e14 0.528735
\(584\) 2.65483e14 0.161721
\(585\) −7.64975e13 −0.0461625
\(586\) 3.30382e15 1.97505
\(587\) 2.40206e15 1.42257 0.711286 0.702903i \(-0.248113\pi\)
0.711286 + 0.702903i \(0.248113\pi\)
\(588\) −2.69464e15 −1.58098
\(589\) −1.82178e15 −1.05892
\(590\) 1.33087e14 0.0766388
\(591\) 1.05806e14 0.0603641
\(592\) 2.02083e15 1.14225
\(593\) 9.94972e14 0.557199 0.278599 0.960407i \(-0.410130\pi\)
0.278599 + 0.960407i \(0.410130\pi\)
\(594\) −3.94841e15 −2.19077
\(595\) 1.16131e15 0.638419
\(596\) 3.17718e15 1.73056
\(597\) −5.07665e13 −0.0273980
\(598\) 5.58917e14 0.298876
\(599\) 7.03886e14 0.372954 0.186477 0.982459i \(-0.440293\pi\)
0.186477 + 0.982459i \(0.440293\pi\)
\(600\) 2.23536e14 0.117359
\(601\) −6.08696e14 −0.316658 −0.158329 0.987386i \(-0.550611\pi\)
−0.158329 + 0.987386i \(0.550611\pi\)
\(602\) 3.87561e15 1.99784
\(603\) 1.46551e14 0.0748592
\(604\) −1.12840e15 −0.571162
\(605\) −2.25248e15 −1.12981
\(606\) 1.23292e15 0.612824
\(607\) 1.96266e15 0.966737 0.483368 0.875417i \(-0.339413\pi\)
0.483368 + 0.875417i \(0.339413\pi\)
\(608\) 2.22831e15 1.08769
\(609\) −1.45752e15 −0.705049
\(610\) 2.39327e15 1.14730
\(611\) −3.08184e14 −0.146414
\(612\) −2.14525e14 −0.101005
\(613\) −3.41572e15 −1.59386 −0.796928 0.604074i \(-0.793543\pi\)
−0.796928 + 0.604074i \(0.793543\pi\)
\(614\) −1.85697e15 −0.858774
\(615\) 2.90163e15 1.32993
\(616\) 1.10094e15 0.500115
\(617\) −1.86989e15 −0.841873 −0.420936 0.907090i \(-0.638298\pi\)
−0.420936 + 0.907090i \(0.638298\pi\)
\(618\) −1.67093e15 −0.745627
\(619\) −1.77723e15 −0.786042 −0.393021 0.919530i \(-0.628570\pi\)
−0.393021 + 0.919530i \(0.628570\pi\)
\(620\) 4.66522e15 2.04511
\(621\) 3.95662e15 1.71918
\(622\) 9.50492e14 0.409356
\(623\) −5.65893e14 −0.241574
\(624\) −2.12146e14 −0.0897675
\(625\) −2.94820e15 −1.23657
\(626\) 4.65601e15 1.93577
\(627\) −2.14465e15 −0.883862
\(628\) 3.35425e15 1.37030
\(629\) −1.06346e15 −0.430669
\(630\) 2.12139e15 0.851623
\(631\) −2.17086e14 −0.0863914 −0.0431957 0.999067i \(-0.513754\pi\)
−0.0431957 + 0.999067i \(0.513754\pi\)
\(632\) 1.00588e15 0.396829
\(633\) −7.93889e14 −0.310484
\(634\) −1.55307e15 −0.602142
\(635\) 4.72520e14 0.181620
\(636\) −9.86512e14 −0.375914
\(637\) −5.51225e14 −0.208239
\(638\) 2.76933e15 1.03720
\(639\) 6.70350e14 0.248913
\(640\) −1.53493e15 −0.565065
\(641\) 4.44521e15 1.62246 0.811229 0.584729i \(-0.198799\pi\)
0.811229 + 0.584729i \(0.198799\pi\)
\(642\) −3.62063e15 −1.31021
\(643\) 1.01635e15 0.364654 0.182327 0.983238i \(-0.441637\pi\)
0.182327 + 0.983238i \(0.441637\pi\)
\(644\) −8.30142e15 −2.95311
\(645\) 2.56935e15 0.906242
\(646\) −9.88599e14 −0.345733
\(647\) 1.97785e15 0.685834 0.342917 0.939366i \(-0.388585\pi\)
0.342917 + 0.939366i \(0.388585\pi\)
\(648\) 4.17467e14 0.143536
\(649\) 1.65626e14 0.0564656
\(650\) 3.44083e14 0.116316
\(651\) −5.70525e15 −1.91240
\(652\) 5.12633e15 1.70390
\(653\) −5.36920e14 −0.176965 −0.0884825 0.996078i \(-0.528202\pi\)
−0.0884825 + 0.996078i \(0.528202\pi\)
\(654\) 1.26728e15 0.414186
\(655\) 6.07451e15 1.96872
\(656\) −3.16307e15 −1.01657
\(657\) 6.36632e14 0.202899
\(658\) 8.54640e15 2.70110
\(659\) −5.49096e15 −1.72099 −0.860496 0.509457i \(-0.829846\pi\)
−0.860496 + 0.509457i \(0.829846\pi\)
\(660\) 5.49202e15 1.70703
\(661\) −1.02732e15 −0.316665 −0.158332 0.987386i \(-0.550612\pi\)
−0.158332 + 0.987386i \(0.550612\pi\)
\(662\) 3.75638e15 1.14829
\(663\) 1.11642e14 0.0338456
\(664\) 1.16232e15 0.349463
\(665\) 5.23593e15 1.56126
\(666\) −1.94264e15 −0.574493
\(667\) −2.77509e15 −0.813926
\(668\) 3.09250e15 0.899578
\(669\) 2.27288e14 0.0655742
\(670\) −1.72945e15 −0.494877
\(671\) 2.97842e15 0.845302
\(672\) 6.97839e15 1.96437
\(673\) −4.63405e15 −1.29383 −0.646916 0.762561i \(-0.723941\pi\)
−0.646916 + 0.762561i \(0.723941\pi\)
\(674\) −5.48456e15 −1.51884
\(675\) 2.43579e15 0.669066
\(676\) −4.16277e15 −1.13416
\(677\) 6.36284e15 1.71954 0.859772 0.510677i \(-0.170605\pi\)
0.859772 + 0.510677i \(0.170605\pi\)
\(678\) −3.11744e15 −0.835671
\(679\) −7.05888e15 −1.87695
\(680\) 3.36442e14 0.0887383
\(681\) 4.28132e15 1.12013
\(682\) 1.08401e16 2.81333
\(683\) 8.32427e14 0.214305 0.107153 0.994243i \(-0.465827\pi\)
0.107153 + 0.994243i \(0.465827\pi\)
\(684\) −9.67214e14 −0.247010
\(685\) 2.76855e13 0.00701381
\(686\) 5.83878e15 1.46737
\(687\) 3.13039e15 0.780434
\(688\) −2.80085e15 −0.692713
\(689\) −2.01804e14 −0.0495136
\(690\) −1.02755e16 −2.50111
\(691\) 8.61434e14 0.208014 0.104007 0.994577i \(-0.466834\pi\)
0.104007 + 0.994577i \(0.466834\pi\)
\(692\) −2.08055e14 −0.0498419
\(693\) 2.64007e15 0.627455
\(694\) −6.56277e15 −1.54743
\(695\) 3.39077e14 0.0793199
\(696\) −4.22255e14 −0.0979996
\(697\) 1.66457e15 0.383284
\(698\) −2.35872e15 −0.538855
\(699\) −5.31869e15 −1.20554
\(700\) −5.11055e15 −1.14929
\(701\) −6.61418e15 −1.47580 −0.737899 0.674911i \(-0.764182\pi\)
−0.737899 + 0.674911i \(0.764182\pi\)
\(702\) 9.26695e14 0.205155
\(703\) −4.79476e15 −1.05320
\(704\) −8.06791e15 −1.75837
\(705\) 5.66586e15 1.22525
\(706\) 1.97215e15 0.423170
\(707\) −3.74600e15 −0.797556
\(708\) −1.90028e14 −0.0401452
\(709\) 4.90188e15 1.02756 0.513781 0.857921i \(-0.328244\pi\)
0.513781 + 0.857921i \(0.328244\pi\)
\(710\) −7.91079e15 −1.64550
\(711\) 2.41212e15 0.497870
\(712\) −1.63944e14 −0.0335780
\(713\) −1.08627e16 −2.20773
\(714\) −3.09599e15 −0.624395
\(715\) 1.12347e15 0.224842
\(716\) 8.40973e15 1.67017
\(717\) 2.27655e15 0.448665
\(718\) 5.28830e15 1.03426
\(719\) −8.02162e15 −1.55687 −0.778436 0.627724i \(-0.783987\pi\)
−0.778436 + 0.627724i \(0.783987\pi\)
\(720\) −1.53310e15 −0.295285
\(721\) 5.07682e15 0.970393
\(722\) 3.27854e15 0.621907
\(723\) 1.16441e15 0.219202
\(724\) −8.17855e15 −1.52797
\(725\) −1.70841e15 −0.316762
\(726\) 6.00496e15 1.10499
\(727\) −7.48240e15 −1.36647 −0.683237 0.730196i \(-0.739429\pi\)
−0.683237 + 0.730196i \(0.739429\pi\)
\(728\) −2.58392e14 −0.0468334
\(729\) 6.11755e15 1.10047
\(730\) −7.51289e15 −1.34132
\(731\) 1.47395e15 0.261178
\(732\) −3.41722e15 −0.600983
\(733\) −3.43264e15 −0.599180 −0.299590 0.954068i \(-0.596850\pi\)
−0.299590 + 0.954068i \(0.596850\pi\)
\(734\) −1.44610e16 −2.50536
\(735\) 1.01341e16 1.74263
\(736\) 1.32867e16 2.26772
\(737\) −2.15230e15 −0.364613
\(738\) 3.04069e15 0.511284
\(739\) 3.78300e15 0.631381 0.315690 0.948862i \(-0.397764\pi\)
0.315690 + 0.948862i \(0.397764\pi\)
\(740\) 1.22784e16 2.03408
\(741\) 5.03351e14 0.0827696
\(742\) 5.59634e15 0.913445
\(743\) 3.18850e14 0.0516592 0.0258296 0.999666i \(-0.491777\pi\)
0.0258296 + 0.999666i \(0.491777\pi\)
\(744\) −1.65286e15 −0.265818
\(745\) −1.19488e16 −1.90751
\(746\) 5.82146e15 0.922504
\(747\) 2.78726e15 0.438444
\(748\) 3.15058e15 0.491963
\(749\) 1.10006e16 1.70517
\(750\) 3.94499e15 0.607028
\(751\) −1.92402e15 −0.293893 −0.146947 0.989144i \(-0.546945\pi\)
−0.146947 + 0.989144i \(0.546945\pi\)
\(752\) −6.17636e15 −0.936558
\(753\) 4.26156e15 0.641499
\(754\) −6.49964e14 −0.0971286
\(755\) 4.24372e15 0.629561
\(756\) −1.37639e16 −2.02709
\(757\) −6.83677e15 −0.999594 −0.499797 0.866142i \(-0.666592\pi\)
−0.499797 + 0.866142i \(0.666592\pi\)
\(758\) 2.29848e13 0.00333626
\(759\) −1.27879e16 −1.84276
\(760\) 1.51689e15 0.217010
\(761\) 1.15743e16 1.64391 0.821956 0.569550i \(-0.192883\pi\)
0.821956 + 0.569550i \(0.192883\pi\)
\(762\) −1.25971e15 −0.177630
\(763\) −3.85040e15 −0.539040
\(764\) 2.40905e14 0.0334836
\(765\) 8.06792e14 0.111333
\(766\) −2.12138e16 −2.90643
\(767\) −3.88727e13 −0.00528774
\(768\) −3.93434e15 −0.531355
\(769\) 2.61757e15 0.350997 0.175498 0.984480i \(-0.443846\pi\)
0.175498 + 0.984480i \(0.443846\pi\)
\(770\) −3.11554e16 −4.14796
\(771\) −6.24898e15 −0.826057
\(772\) 1.27304e15 0.167089
\(773\) 1.23256e16 1.60628 0.803140 0.595790i \(-0.203161\pi\)
0.803140 + 0.595790i \(0.203161\pi\)
\(774\) 2.69248e15 0.348399
\(775\) −6.68733e15 −0.859198
\(776\) −2.04501e15 −0.260890
\(777\) −1.50157e16 −1.90209
\(778\) 8.95392e15 1.12623
\(779\) 7.50492e15 0.937325
\(780\) −1.28898e15 −0.159855
\(781\) −9.84498e15 −1.21237
\(782\) −5.89470e15 −0.720817
\(783\) −4.60115e15 −0.558697
\(784\) −1.10472e16 −1.33203
\(785\) −1.26148e16 −1.51041
\(786\) −1.61943e16 −1.92547
\(787\) 9.78875e15 1.15576 0.577878 0.816123i \(-0.303881\pi\)
0.577878 + 0.816123i \(0.303881\pi\)
\(788\) −7.00794e14 −0.0821667
\(789\) 5.41981e15 0.631045
\(790\) −2.84654e16 −3.29131
\(791\) 9.47178e15 1.08758
\(792\) 7.64849e14 0.0872142
\(793\) −6.99038e14 −0.0791587
\(794\) 2.22999e16 2.50778
\(795\) 3.71010e15 0.414349
\(796\) 3.36246e14 0.0372937
\(797\) 4.21477e15 0.464251 0.232126 0.972686i \(-0.425432\pi\)
0.232126 + 0.972686i \(0.425432\pi\)
\(798\) −1.39587e16 −1.52696
\(799\) 3.25031e15 0.353116
\(800\) 8.17961e15 0.882547
\(801\) −3.93139e14 −0.0421277
\(802\) −1.78481e16 −1.89947
\(803\) −9.34979e15 −0.988249
\(804\) 2.46939e15 0.259228
\(805\) 3.12202e16 3.25506
\(806\) −2.54419e15 −0.263456
\(807\) −7.57728e14 −0.0779308
\(808\) −1.08525e15 −0.110858
\(809\) −1.55258e16 −1.57521 −0.787605 0.616181i \(-0.788679\pi\)
−0.787605 + 0.616181i \(0.788679\pi\)
\(810\) −1.18139e16 −1.19049
\(811\) 1.95871e16 1.96045 0.980226 0.197882i \(-0.0634064\pi\)
0.980226 + 0.197882i \(0.0634064\pi\)
\(812\) 9.65371e15 0.959702
\(813\) −1.11920e15 −0.110512
\(814\) 2.85303e16 2.79816
\(815\) −1.92793e16 −1.87812
\(816\) 2.23743e15 0.216497
\(817\) 6.64548e15 0.638712
\(818\) 1.61613e16 1.54289
\(819\) −6.19627e14 −0.0587582
\(820\) −1.92186e16 −1.81028
\(821\) −9.61396e15 −0.899528 −0.449764 0.893147i \(-0.648492\pi\)
−0.449764 + 0.893147i \(0.648492\pi\)
\(822\) −7.38078e13 −0.00685974
\(823\) −5.95315e15 −0.549601 −0.274801 0.961501i \(-0.588612\pi\)
−0.274801 + 0.961501i \(0.588612\pi\)
\(824\) 1.47080e15 0.134882
\(825\) −7.87250e15 −0.717160
\(826\) 1.07800e15 0.0975501
\(827\) −1.45871e16 −1.31126 −0.655628 0.755084i \(-0.727596\pi\)
−0.655628 + 0.755084i \(0.727596\pi\)
\(828\) −5.76719e15 −0.514989
\(829\) 5.22485e15 0.463472 0.231736 0.972779i \(-0.425559\pi\)
0.231736 + 0.972779i \(0.425559\pi\)
\(830\) −3.28924e16 −2.89845
\(831\) −1.20675e16 −1.05636
\(832\) 1.89355e15 0.164664
\(833\) 5.81358e15 0.502222
\(834\) −9.03959e14 −0.0775774
\(835\) −1.16304e16 −0.991557
\(836\) 1.42048e16 1.20310
\(837\) −1.80106e16 −1.51543
\(838\) 3.07173e16 2.56768
\(839\) 2.06112e16 1.71164 0.855820 0.517275i \(-0.173053\pi\)
0.855820 + 0.517275i \(0.173053\pi\)
\(840\) 4.75044e15 0.391921
\(841\) −8.97336e15 −0.735491
\(842\) 1.89861e16 1.54603
\(843\) −1.00019e16 −0.809150
\(844\) 5.25823e15 0.422626
\(845\) 1.56555e16 1.25013
\(846\) 5.93739e15 0.471041
\(847\) −1.82450e16 −1.43808
\(848\) −4.04439e15 −0.316720
\(849\) −6.55415e15 −0.509946
\(850\) −3.62892e15 −0.280526
\(851\) −2.85897e16 −2.19582
\(852\) 1.12954e16 0.861953
\(853\) −1.51561e16 −1.14913 −0.574565 0.818459i \(-0.694829\pi\)
−0.574565 + 0.818459i \(0.694829\pi\)
\(854\) 1.93854e16 1.46035
\(855\) 3.63753e15 0.272266
\(856\) 3.18697e15 0.237013
\(857\) −3.46162e15 −0.255791 −0.127895 0.991788i \(-0.540822\pi\)
−0.127895 + 0.991788i \(0.540822\pi\)
\(858\) −2.99509e15 −0.219903
\(859\) 4.22500e15 0.308223 0.154111 0.988053i \(-0.450749\pi\)
0.154111 + 0.988053i \(0.450749\pi\)
\(860\) −1.70178e16 −1.23356
\(861\) 2.35031e16 1.69281
\(862\) −2.70644e16 −1.93691
\(863\) −1.05088e15 −0.0747297 −0.0373649 0.999302i \(-0.511896\pi\)
−0.0373649 + 0.999302i \(0.511896\pi\)
\(864\) 2.20296e16 1.55662
\(865\) 7.82460e14 0.0549381
\(866\) 8.15218e14 0.0568755
\(867\) 1.10438e16 0.765624
\(868\) 3.77881e16 2.60313
\(869\) −3.54252e16 −2.42495
\(870\) 1.19494e16 0.812810
\(871\) 5.05148e14 0.0341443
\(872\) −1.11549e15 −0.0749249
\(873\) −4.90397e15 −0.327318
\(874\) −2.65771e16 −1.76276
\(875\) −1.19861e16 −0.790014
\(876\) 1.07273e16 0.702613
\(877\) −2.10513e16 −1.37019 −0.685096 0.728453i \(-0.740240\pi\)
−0.685096 + 0.728453i \(0.740240\pi\)
\(878\) −2.02654e16 −1.31080
\(879\) 1.77411e16 1.14036
\(880\) 2.25156e16 1.43823
\(881\) −1.47479e16 −0.936186 −0.468093 0.883679i \(-0.655059\pi\)
−0.468093 + 0.883679i \(0.655059\pi\)
\(882\) 1.06198e16 0.669942
\(883\) 6.44188e15 0.403858 0.201929 0.979400i \(-0.435279\pi\)
0.201929 + 0.979400i \(0.435279\pi\)
\(884\) −7.39445e14 −0.0460700
\(885\) 7.14661e14 0.0442499
\(886\) −4.41793e14 −0.0271853
\(887\) 2.27071e16 1.38861 0.694306 0.719680i \(-0.255711\pi\)
0.694306 + 0.719680i \(0.255711\pi\)
\(888\) −4.35018e15 −0.264384
\(889\) 3.82739e15 0.231176
\(890\) 4.63943e15 0.278497
\(891\) −1.47024e16 −0.877122
\(892\) −1.50542e15 −0.0892585
\(893\) 1.46544e16 0.863548
\(894\) 3.18549e16 1.86560
\(895\) −3.16276e16 −1.84094
\(896\) −1.24329e16 −0.719246
\(897\) 3.00132e15 0.172566
\(898\) 1.36623e16 0.780737
\(899\) 1.26322e16 0.717466
\(900\) −3.55042e15 −0.200422
\(901\) 2.12836e15 0.119415
\(902\) −4.46566e16 −2.49029
\(903\) 2.08116e16 1.15351
\(904\) 2.74405e15 0.151170
\(905\) 3.07581e16 1.68420
\(906\) −1.13135e16 −0.615731
\(907\) −8.91834e15 −0.482440 −0.241220 0.970470i \(-0.577548\pi\)
−0.241220 + 0.970470i \(0.577548\pi\)
\(908\) −2.83568e16 −1.52470
\(909\) −2.60244e15 −0.139085
\(910\) 7.31221e15 0.388437
\(911\) −4.70880e15 −0.248633 −0.124317 0.992243i \(-0.539674\pi\)
−0.124317 + 0.992243i \(0.539674\pi\)
\(912\) 1.00877e16 0.529446
\(913\) −4.09346e16 −2.13551
\(914\) −4.79991e16 −2.48902
\(915\) 1.28516e16 0.662431
\(916\) −2.07338e16 −1.06231
\(917\) 4.92033e16 2.50590
\(918\) −9.77353e15 −0.494785
\(919\) −1.36883e16 −0.688832 −0.344416 0.938817i \(-0.611923\pi\)
−0.344416 + 0.938817i \(0.611923\pi\)
\(920\) 9.04475e15 0.452443
\(921\) −9.97172e15 −0.495841
\(922\) 5.27078e16 2.60528
\(923\) 2.31063e15 0.113533
\(924\) 4.44852e16 2.17280
\(925\) −1.76005e16 −0.854564
\(926\) 5.28010e16 2.54848
\(927\) 3.52699e15 0.169225
\(928\) −1.54511e16 −0.736963
\(929\) 3.10992e16 1.47456 0.737282 0.675586i \(-0.236109\pi\)
0.737282 + 0.675586i \(0.236109\pi\)
\(930\) 4.67741e16 2.20470
\(931\) 2.62113e16 1.22819
\(932\) 3.52278e16 1.64096
\(933\) 5.10403e15 0.236355
\(934\) 8.50305e15 0.391442
\(935\) −1.18488e16 −0.542264
\(936\) −1.79511e14 −0.00816721
\(937\) −3.02952e15 −0.137027 −0.0685134 0.997650i \(-0.521826\pi\)
−0.0685134 + 0.997650i \(0.521826\pi\)
\(938\) −1.40085e16 −0.629907
\(939\) 2.50022e16 1.11768
\(940\) −3.75272e16 −1.66779
\(941\) −7.94534e15 −0.351050 −0.175525 0.984475i \(-0.556162\pi\)
−0.175525 + 0.984475i \(0.556162\pi\)
\(942\) 3.36302e16 1.47723
\(943\) 4.47495e16 1.95422
\(944\) −7.79054e14 −0.0338237
\(945\) 5.17637e16 2.23435
\(946\) −3.95426e16 −1.69693
\(947\) −7.96212e15 −0.339706 −0.169853 0.985469i \(-0.554329\pi\)
−0.169853 + 0.985469i \(0.554329\pi\)
\(948\) 4.06442e16 1.72406
\(949\) 2.19441e15 0.0925450
\(950\) −1.63615e16 −0.686028
\(951\) −8.33979e15 −0.347666
\(952\) 2.72517e15 0.112951
\(953\) 4.41331e16 1.81867 0.909334 0.416067i \(-0.136592\pi\)
0.909334 + 0.416067i \(0.136592\pi\)
\(954\) 3.88791e15 0.159294
\(955\) −9.06001e14 −0.0369071
\(956\) −1.50785e16 −0.610716
\(957\) 1.48710e16 0.598858
\(958\) 3.83913e16 1.53717
\(959\) 2.24252e14 0.00892757
\(960\) −3.48122e16 −1.37797
\(961\) 2.40385e16 0.946083
\(962\) −6.69609e15 −0.262035
\(963\) 7.64239e15 0.297362
\(964\) −7.71234e15 −0.298375
\(965\) −4.78770e15 −0.184173
\(966\) −8.32312e16 −3.18355
\(967\) −2.96400e16 −1.12728 −0.563640 0.826020i \(-0.690600\pi\)
−0.563640 + 0.826020i \(0.690600\pi\)
\(968\) −5.28572e15 −0.199889
\(969\) −5.30867e15 −0.199620
\(970\) 5.78717e16 2.16382
\(971\) −3.43704e16 −1.27785 −0.638924 0.769270i \(-0.720620\pi\)
−0.638924 + 0.769270i \(0.720620\pi\)
\(972\) −1.70199e16 −0.629206
\(973\) 2.74651e15 0.100963
\(974\) −4.47358e16 −1.63524
\(975\) 1.84769e15 0.0671587
\(976\) −1.40095e16 −0.506349
\(977\) −1.79823e16 −0.646285 −0.323142 0.946350i \(-0.604739\pi\)
−0.323142 + 0.946350i \(0.604739\pi\)
\(978\) 5.13973e16 1.83686
\(979\) 5.77378e15 0.205189
\(980\) −6.71220e16 −2.37204
\(981\) −2.67497e15 −0.0940024
\(982\) 6.75342e16 2.35999
\(983\) −2.24970e16 −0.781773 −0.390886 0.920439i \(-0.627831\pi\)
−0.390886 + 0.920439i \(0.627831\pi\)
\(984\) 6.80904e15 0.235295
\(985\) 2.63557e15 0.0905680
\(986\) 6.85494e15 0.234251
\(987\) 4.58932e16 1.55957
\(988\) −3.33389e15 −0.112665
\(989\) 3.96249e16 1.33165
\(990\) −2.16444e16 −0.723356
\(991\) 1.43578e16 0.477182 0.238591 0.971120i \(-0.423314\pi\)
0.238591 + 0.971120i \(0.423314\pi\)
\(992\) −6.04812e16 −1.99897
\(993\) 2.01713e16 0.663001
\(994\) −6.40771e16 −2.09449
\(995\) −1.26456e15 −0.0411068
\(996\) 4.69653e16 1.51828
\(997\) 1.14056e16 0.366687 0.183343 0.983049i \(-0.441308\pi\)
0.183343 + 0.983049i \(0.441308\pi\)
\(998\) −8.72645e16 −2.79010
\(999\) −4.74022e16 −1.50726
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 197.12.a.b.1.15 92
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.12.a.b.1.15 92 1.1 even 1 trivial