Properties

Label 197.12.a.b.1.6
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 1.6
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)
 
\(f(q)\) \(=\) \(q-79.8918 q^{2} +101.497 q^{3} +4334.69 q^{4} +1864.60 q^{5} -8108.77 q^{6} +52018.3 q^{7} -182688. q^{8} -166845. q^{9} +O(q^{10})\) \(q-79.8918 q^{2} +101.497 q^{3} +4334.69 q^{4} +1864.60 q^{5} -8108.77 q^{6} +52018.3 q^{7} -182688. q^{8} -166845. q^{9} -148966. q^{10} -81826.4 q^{11} +439958. q^{12} +1.50884e6 q^{13} -4.15583e6 q^{14} +189251. q^{15} +5.71780e6 q^{16} -9.93022e6 q^{17} +1.33296e7 q^{18} -1.66012e7 q^{19} +8.08246e6 q^{20} +5.27970e6 q^{21} +6.53725e6 q^{22} -4.11960e7 q^{23} -1.85423e7 q^{24} -4.53514e7 q^{25} -1.20544e8 q^{26} -3.49142e7 q^{27} +2.25483e8 q^{28} -2.29850e7 q^{29} -1.51196e7 q^{30} +1.81442e7 q^{31} -8.26606e7 q^{32} -8.30513e6 q^{33} +7.93343e8 q^{34} +9.69932e7 q^{35} -7.23223e8 q^{36} -5.49903e8 q^{37} +1.32630e9 q^{38} +1.53143e8 q^{39} -3.40640e8 q^{40} +8.19172e7 q^{41} -4.21805e8 q^{42} +1.43469e9 q^{43} -3.54692e8 q^{44} -3.11100e8 q^{45} +3.29122e9 q^{46} -5.29515e8 q^{47} +5.80340e8 q^{48} +7.28575e8 q^{49} +3.62320e9 q^{50} -1.00789e9 q^{51} +6.54037e9 q^{52} +1.88546e9 q^{53} +2.78936e9 q^{54} -1.52573e8 q^{55} -9.50311e9 q^{56} -1.68497e9 q^{57} +1.83631e9 q^{58} +9.68096e9 q^{59} +8.20346e8 q^{60} +2.66854e9 q^{61} -1.44957e9 q^{62} -8.67901e9 q^{63} -5.10616e9 q^{64} +2.81339e9 q^{65} +6.63512e8 q^{66} +1.03086e10 q^{67} -4.30445e10 q^{68} -4.18127e9 q^{69} -7.74896e9 q^{70} -2.60268e10 q^{71} +3.04806e10 q^{72} +3.05024e10 q^{73} +4.39327e10 q^{74} -4.60303e9 q^{75} -7.19610e10 q^{76} -4.25647e9 q^{77} -1.22349e10 q^{78} +3.22798e10 q^{79} +1.06614e10 q^{80} +2.60125e10 q^{81} -6.54451e9 q^{82} -5.02186e10 q^{83} +2.28859e10 q^{84} -1.85159e10 q^{85} -1.14620e11 q^{86} -2.33291e9 q^{87} +1.49487e10 q^{88} +2.94603e10 q^{89} +2.48543e10 q^{90} +7.84874e10 q^{91} -1.78572e11 q^{92} +1.84158e9 q^{93} +4.23039e10 q^{94} -3.09545e10 q^{95} -8.38980e9 q^{96} +4.41143e10 q^{97} -5.82071e10 q^{98} +1.36524e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 92 q + 64 q^{2} + 2420 q^{3} + 98304 q^{4} + 16604 q^{5} + 46656 q^{6} + 305891 q^{7} + 234027 q^{8} + 5900444 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −79.8918 −1.76537 −0.882687 0.469960i \(-0.844268\pi\)
−0.882687 + 0.469960i \(0.844268\pi\)
\(3\) 101.497 0.241150 0.120575 0.992704i \(-0.461526\pi\)
0.120575 + 0.992704i \(0.461526\pi\)
\(4\) 4334.69 2.11655
\(5\) 1864.60 0.266840 0.133420 0.991060i \(-0.457404\pi\)
0.133420 + 0.991060i \(0.457404\pi\)
\(6\) −8108.77 −0.425719
\(7\) 52018.3 1.16981 0.584907 0.811100i \(-0.301131\pi\)
0.584907 + 0.811100i \(0.301131\pi\)
\(8\) −182688. −1.97113
\(9\) −166845. −0.941847
\(10\) −148966. −0.471072
\(11\) −81826.4 −0.153191 −0.0765956 0.997062i \(-0.524405\pi\)
−0.0765956 + 0.997062i \(0.524405\pi\)
\(12\) 439958. 0.510405
\(13\) 1.50884e6 1.12708 0.563541 0.826088i \(-0.309439\pi\)
0.563541 + 0.826088i \(0.309439\pi\)
\(14\) −4.15583e6 −2.06516
\(15\) 189251. 0.0643483
\(16\) 5.71780e6 1.36323
\(17\) −9.93022e6 −1.69625 −0.848125 0.529796i \(-0.822268\pi\)
−0.848125 + 0.529796i \(0.822268\pi\)
\(18\) 1.33296e7 1.66271
\(19\) −1.66012e7 −1.53813 −0.769067 0.639168i \(-0.779279\pi\)
−0.769067 + 0.639168i \(0.779279\pi\)
\(20\) 8.08246e6 0.564779
\(21\) 5.27970e6 0.282100
\(22\) 6.53725e6 0.270440
\(23\) −4.11960e7 −1.33460 −0.667302 0.744788i \(-0.732551\pi\)
−0.667302 + 0.744788i \(0.732551\pi\)
\(24\) −1.85423e7 −0.475336
\(25\) −4.53514e7 −0.928797
\(26\) −1.20544e8 −1.98972
\(27\) −3.49142e7 −0.468275
\(28\) 2.25483e8 2.47597
\(29\) −2.29850e7 −0.208092 −0.104046 0.994573i \(-0.533179\pi\)
−0.104046 + 0.994573i \(0.533179\pi\)
\(30\) −1.51196e7 −0.113599
\(31\) 1.81442e7 0.113828 0.0569138 0.998379i \(-0.481874\pi\)
0.0569138 + 0.998379i \(0.481874\pi\)
\(32\) −8.26606e7 −0.435485
\(33\) −8.30513e6 −0.0369420
\(34\) 7.93343e8 2.99452
\(35\) 9.69932e7 0.312153
\(36\) −7.23223e8 −1.99347
\(37\) −5.49903e8 −1.30370 −0.651849 0.758349i \(-0.726006\pi\)
−0.651849 + 0.758349i \(0.726006\pi\)
\(38\) 1.32630e9 2.71538
\(39\) 1.53143e8 0.271795
\(40\) −3.40640e8 −0.525975
\(41\) 8.19172e7 0.110424 0.0552121 0.998475i \(-0.482417\pi\)
0.0552121 + 0.998475i \(0.482417\pi\)
\(42\) −4.21805e8 −0.498012
\(43\) 1.43469e9 1.48827 0.744134 0.668030i \(-0.232862\pi\)
0.744134 + 0.668030i \(0.232862\pi\)
\(44\) −3.54692e8 −0.324236
\(45\) −3.11100e8 −0.251322
\(46\) 3.29122e9 2.35607
\(47\) −5.29515e8 −0.336775 −0.168388 0.985721i \(-0.553856\pi\)
−0.168388 + 0.985721i \(0.553856\pi\)
\(48\) 5.80340e8 0.328742
\(49\) 7.28575e8 0.368464
\(50\) 3.62320e9 1.63967
\(51\) −1.00789e9 −0.409050
\(52\) 6.54037e9 2.38552
\(53\) 1.88546e9 0.619297 0.309648 0.950851i \(-0.399789\pi\)
0.309648 + 0.950851i \(0.399789\pi\)
\(54\) 2.78936e9 0.826682
\(55\) −1.52573e8 −0.0408775
\(56\) −9.50311e9 −2.30585
\(57\) −1.68497e9 −0.370920
\(58\) 1.83631e9 0.367360
\(59\) 9.68096e9 1.76292 0.881460 0.472259i \(-0.156561\pi\)
0.881460 + 0.472259i \(0.156561\pi\)
\(60\) 8.20346e8 0.136196
\(61\) 2.66854e9 0.404539 0.202269 0.979330i \(-0.435168\pi\)
0.202269 + 0.979330i \(0.435168\pi\)
\(62\) −1.44957e9 −0.200948
\(63\) −8.67901e9 −1.10179
\(64\) −5.10616e9 −0.594436
\(65\) 2.81339e9 0.300750
\(66\) 6.63512e8 0.0652164
\(67\) 1.03086e10 0.932804 0.466402 0.884573i \(-0.345550\pi\)
0.466402 + 0.884573i \(0.345550\pi\)
\(68\) −4.30445e10 −3.59020
\(69\) −4.18127e9 −0.321839
\(70\) −7.74896e9 −0.551067
\(71\) −2.60268e10 −1.71199 −0.855993 0.516988i \(-0.827053\pi\)
−0.855993 + 0.516988i \(0.827053\pi\)
\(72\) 3.04806e10 1.85650
\(73\) 3.05024e10 1.72210 0.861051 0.508518i \(-0.169807\pi\)
0.861051 + 0.508518i \(0.169807\pi\)
\(74\) 4.39327e10 2.30152
\(75\) −4.60303e9 −0.223979
\(76\) −7.19610e10 −3.25554
\(77\) −4.25647e9 −0.179205
\(78\) −1.22349e10 −0.479821
\(79\) 3.22798e10 1.18027 0.590135 0.807305i \(-0.299074\pi\)
0.590135 + 0.807305i \(0.299074\pi\)
\(80\) 1.06614e10 0.363764
\(81\) 2.60125e10 0.828923
\(82\) −6.54451e9 −0.194940
\(83\) −5.02186e10 −1.39938 −0.699690 0.714447i \(-0.746678\pi\)
−0.699690 + 0.714447i \(0.746678\pi\)
\(84\) 2.28859e10 0.597079
\(85\) −1.85159e10 −0.452627
\(86\) −1.14620e11 −2.62735
\(87\) −2.33291e9 −0.0501812
\(88\) 1.49487e10 0.301959
\(89\) 2.94603e10 0.559232 0.279616 0.960112i \(-0.409793\pi\)
0.279616 + 0.960112i \(0.409793\pi\)
\(90\) 2.48543e10 0.443678
\(91\) 7.84874e10 1.31848
\(92\) −1.78572e11 −2.82475
\(93\) 1.84158e9 0.0274495
\(94\) 4.23039e10 0.594534
\(95\) −3.09545e10 −0.410435
\(96\) −8.38980e9 −0.105017
\(97\) 4.41143e10 0.521597 0.260798 0.965393i \(-0.416014\pi\)
0.260798 + 0.965393i \(0.416014\pi\)
\(98\) −5.82071e10 −0.650478
\(99\) 1.36524e10 0.144283
\(100\) −1.96584e11 −1.96584
\(101\) 1.99545e10 0.188918 0.0944591 0.995529i \(-0.469888\pi\)
0.0944591 + 0.995529i \(0.469888\pi\)
\(102\) 8.05219e10 0.722126
\(103\) −2.97252e9 −0.0252650 −0.0126325 0.999920i \(-0.504021\pi\)
−0.0126325 + 0.999920i \(0.504021\pi\)
\(104\) −2.75647e11 −2.22162
\(105\) 9.84452e9 0.0752755
\(106\) −1.50632e11 −1.09329
\(107\) −1.57952e11 −1.08872 −0.544359 0.838852i \(-0.683227\pi\)
−0.544359 + 0.838852i \(0.683227\pi\)
\(108\) −1.51342e11 −0.991128
\(109\) 4.62875e10 0.288150 0.144075 0.989567i \(-0.453979\pi\)
0.144075 + 0.989567i \(0.453979\pi\)
\(110\) 1.21894e10 0.0721641
\(111\) −5.58135e10 −0.314386
\(112\) 2.97430e11 1.59473
\(113\) −1.93933e11 −0.990196 −0.495098 0.868837i \(-0.664868\pi\)
−0.495098 + 0.868837i \(0.664868\pi\)
\(114\) 1.34615e11 0.654813
\(115\) −7.68141e10 −0.356125
\(116\) −9.96327e10 −0.440436
\(117\) −2.51743e11 −1.06154
\(118\) −7.73429e11 −3.11221
\(119\) −5.16553e11 −1.98430
\(120\) −3.45739e10 −0.126839
\(121\) −2.78616e11 −0.976532
\(122\) −2.13195e11 −0.714163
\(123\) 8.31436e9 0.0266287
\(124\) 7.86494e10 0.240922
\(125\) −1.75607e11 −0.514680
\(126\) 6.93381e11 1.94506
\(127\) −6.97597e10 −0.187363 −0.0936816 0.995602i \(-0.529864\pi\)
−0.0936816 + 0.995602i \(0.529864\pi\)
\(128\) 5.77229e11 1.48489
\(129\) 1.45617e11 0.358895
\(130\) −2.24766e11 −0.530937
\(131\) 6.20880e11 1.40610 0.703049 0.711141i \(-0.251821\pi\)
0.703049 + 0.711141i \(0.251821\pi\)
\(132\) −3.60002e10 −0.0781895
\(133\) −8.63565e11 −1.79933
\(134\) −8.23576e11 −1.64675
\(135\) −6.51010e10 −0.124954
\(136\) 1.81413e12 3.34353
\(137\) 8.34982e11 1.47813 0.739067 0.673632i \(-0.235267\pi\)
0.739067 + 0.673632i \(0.235267\pi\)
\(138\) 3.34049e11 0.568166
\(139\) 6.64732e11 1.08659 0.543294 0.839543i \(-0.317177\pi\)
0.543294 + 0.839543i \(0.317177\pi\)
\(140\) 4.20436e11 0.660687
\(141\) −5.37442e10 −0.0812132
\(142\) 2.07933e12 3.02230
\(143\) −1.23463e11 −0.172659
\(144\) −9.53989e11 −1.28395
\(145\) −4.28577e10 −0.0555271
\(146\) −2.43689e12 −3.04016
\(147\) 7.39482e10 0.0888550
\(148\) −2.38366e12 −2.75934
\(149\) 4.71677e11 0.526163 0.263082 0.964774i \(-0.415261\pi\)
0.263082 + 0.964774i \(0.415261\pi\)
\(150\) 3.67744e11 0.395407
\(151\) 1.52329e12 1.57910 0.789552 0.613684i \(-0.210313\pi\)
0.789552 + 0.613684i \(0.210313\pi\)
\(152\) 3.03283e12 3.03186
\(153\) 1.65681e12 1.59761
\(154\) 3.40057e11 0.316364
\(155\) 3.38316e10 0.0303737
\(156\) 6.63828e11 0.575268
\(157\) 5.90539e11 0.494083 0.247042 0.969005i \(-0.420542\pi\)
0.247042 + 0.969005i \(0.420542\pi\)
\(158\) −2.57889e12 −2.08362
\(159\) 1.91368e11 0.149343
\(160\) −1.54129e11 −0.116205
\(161\) −2.14295e12 −1.56124
\(162\) −2.07818e12 −1.46336
\(163\) 1.00470e11 0.0683919 0.0341960 0.999415i \(-0.489113\pi\)
0.0341960 + 0.999415i \(0.489113\pi\)
\(164\) 3.55086e11 0.233718
\(165\) −1.54857e10 −0.00985758
\(166\) 4.01206e12 2.47043
\(167\) 2.72062e12 1.62079 0.810396 0.585883i \(-0.199252\pi\)
0.810396 + 0.585883i \(0.199252\pi\)
\(168\) −9.64537e11 −0.556055
\(169\) 4.84445e11 0.270313
\(170\) 1.47927e12 0.799056
\(171\) 2.76983e12 1.44869
\(172\) 6.21894e12 3.14999
\(173\) −6.77593e11 −0.332442 −0.166221 0.986089i \(-0.553156\pi\)
−0.166221 + 0.986089i \(0.553156\pi\)
\(174\) 1.86380e11 0.0885887
\(175\) −2.35910e12 −1.08652
\(176\) −4.67867e11 −0.208835
\(177\) 9.82589e11 0.425127
\(178\) −2.35363e12 −0.987254
\(179\) 3.55100e12 1.44431 0.722153 0.691734i \(-0.243153\pi\)
0.722153 + 0.691734i \(0.243153\pi\)
\(180\) −1.34852e12 −0.531936
\(181\) 1.88616e12 0.721684 0.360842 0.932627i \(-0.382489\pi\)
0.360842 + 0.932627i \(0.382489\pi\)
\(182\) −6.27049e12 −2.32760
\(183\) 2.70849e11 0.0975544
\(184\) 7.52601e12 2.63067
\(185\) −1.02535e12 −0.347878
\(186\) −1.47127e11 −0.0484586
\(187\) 8.12554e11 0.259850
\(188\) −2.29528e12 −0.712801
\(189\) −1.81618e12 −0.547795
\(190\) 2.47301e12 0.724572
\(191\) −5.40642e12 −1.53896 −0.769478 0.638673i \(-0.779484\pi\)
−0.769478 + 0.638673i \(0.779484\pi\)
\(192\) −5.18260e11 −0.143348
\(193\) 1.98890e12 0.534624 0.267312 0.963610i \(-0.413865\pi\)
0.267312 + 0.963610i \(0.413865\pi\)
\(194\) −3.52437e12 −0.920814
\(195\) 2.85550e11 0.0725258
\(196\) 3.15815e12 0.779873
\(197\) −2.96709e11 −0.0712470
\(198\) −1.09071e12 −0.254713
\(199\) 2.02691e11 0.0460408 0.0230204 0.999735i \(-0.492672\pi\)
0.0230204 + 0.999735i \(0.492672\pi\)
\(200\) 8.28515e12 1.83078
\(201\) 1.04630e12 0.224945
\(202\) −1.59420e12 −0.333512
\(203\) −1.19564e12 −0.243429
\(204\) −4.36888e12 −0.865774
\(205\) 1.52743e11 0.0294656
\(206\) 2.37479e11 0.0446022
\(207\) 6.87336e12 1.25699
\(208\) 8.62726e12 1.53647
\(209\) 1.35841e12 0.235628
\(210\) −7.86496e11 −0.132889
\(211\) −1.23239e12 −0.202860 −0.101430 0.994843i \(-0.532342\pi\)
−0.101430 + 0.994843i \(0.532342\pi\)
\(212\) 8.17287e12 1.31077
\(213\) −2.64164e12 −0.412844
\(214\) 1.26191e13 1.92200
\(215\) 2.67512e12 0.397129
\(216\) 6.37840e12 0.923031
\(217\) 9.43828e11 0.133157
\(218\) −3.69799e12 −0.508693
\(219\) 3.09591e12 0.415284
\(220\) −6.61359e11 −0.0865192
\(221\) −1.49831e13 −1.91181
\(222\) 4.45904e12 0.555009
\(223\) −9.78719e12 −1.18845 −0.594226 0.804298i \(-0.702541\pi\)
−0.594226 + 0.804298i \(0.702541\pi\)
\(224\) −4.29986e12 −0.509437
\(225\) 7.56667e12 0.874784
\(226\) 1.54937e13 1.74807
\(227\) −9.47252e12 −1.04309 −0.521547 0.853223i \(-0.674645\pi\)
−0.521547 + 0.853223i \(0.674645\pi\)
\(228\) −7.30383e12 −0.785071
\(229\) −1.05546e13 −1.10751 −0.553753 0.832681i \(-0.686805\pi\)
−0.553753 + 0.832681i \(0.686805\pi\)
\(230\) 6.13681e12 0.628694
\(231\) −4.32019e11 −0.0432152
\(232\) 4.19907e12 0.410175
\(233\) 1.58697e13 1.51395 0.756973 0.653447i \(-0.226678\pi\)
0.756973 + 0.653447i \(0.226678\pi\)
\(234\) 2.01122e13 1.87401
\(235\) −9.87333e11 −0.0898650
\(236\) 4.19640e13 3.73131
\(237\) 3.27630e12 0.284622
\(238\) 4.12683e13 3.50303
\(239\) 1.88903e13 1.56694 0.783468 0.621432i \(-0.213449\pi\)
0.783468 + 0.621432i \(0.213449\pi\)
\(240\) 1.08210e12 0.0877215
\(241\) −8.31011e12 −0.658435 −0.329218 0.944254i \(-0.606785\pi\)
−0.329218 + 0.944254i \(0.606785\pi\)
\(242\) 2.22591e13 1.72395
\(243\) 8.82513e12 0.668170
\(244\) 1.15673e13 0.856226
\(245\) 1.35850e12 0.0983210
\(246\) −6.64248e11 −0.0470097
\(247\) −2.50486e13 −1.73360
\(248\) −3.31472e12 −0.224369
\(249\) −5.09704e12 −0.337460
\(250\) 1.40296e13 0.908602
\(251\) 7.87031e12 0.498639 0.249320 0.968421i \(-0.419793\pi\)
0.249320 + 0.968421i \(0.419793\pi\)
\(252\) −3.76208e13 −2.33198
\(253\) 3.37092e12 0.204449
\(254\) 5.57323e12 0.330766
\(255\) −1.87931e12 −0.109151
\(256\) −3.56584e13 −2.02695
\(257\) −1.12626e13 −0.626625 −0.313313 0.949650i \(-0.601439\pi\)
−0.313313 + 0.949650i \(0.601439\pi\)
\(258\) −1.16336e13 −0.633585
\(259\) −2.86050e13 −1.52508
\(260\) 1.21952e13 0.636552
\(261\) 3.83493e12 0.195991
\(262\) −4.96032e13 −2.48229
\(263\) −2.15206e13 −1.05462 −0.527311 0.849672i \(-0.676800\pi\)
−0.527311 + 0.849672i \(0.676800\pi\)
\(264\) 1.51725e12 0.0728173
\(265\) 3.51562e12 0.165253
\(266\) 6.89917e13 3.17649
\(267\) 2.99013e12 0.134858
\(268\) 4.46848e13 1.97432
\(269\) 1.15303e13 0.499117 0.249559 0.968360i \(-0.419714\pi\)
0.249559 + 0.968360i \(0.419714\pi\)
\(270\) 5.20103e12 0.220592
\(271\) 5.46846e11 0.0227266 0.0113633 0.999935i \(-0.496383\pi\)
0.0113633 + 0.999935i \(0.496383\pi\)
\(272\) −5.67790e13 −2.31238
\(273\) 7.96624e12 0.317950
\(274\) −6.67082e13 −2.60946
\(275\) 3.71094e12 0.142283
\(276\) −1.81245e13 −0.681188
\(277\) 1.85877e13 0.684836 0.342418 0.939548i \(-0.388754\pi\)
0.342418 + 0.939548i \(0.388754\pi\)
\(278\) −5.31066e13 −1.91824
\(279\) −3.02727e12 −0.107208
\(280\) −1.77195e13 −0.615293
\(281\) 5.53087e13 1.88325 0.941626 0.336661i \(-0.109298\pi\)
0.941626 + 0.336661i \(0.109298\pi\)
\(282\) 4.29372e12 0.143372
\(283\) −7.89731e12 −0.258615 −0.129308 0.991605i \(-0.541275\pi\)
−0.129308 + 0.991605i \(0.541275\pi\)
\(284\) −1.12818e14 −3.62350
\(285\) −3.14179e12 −0.0989762
\(286\) 9.86368e12 0.304808
\(287\) 4.26119e12 0.129176
\(288\) 1.37915e13 0.410160
\(289\) 6.43374e13 1.87726
\(290\) 3.42398e12 0.0980262
\(291\) 4.47747e12 0.125783
\(292\) 1.32219e14 3.64491
\(293\) −6.80152e13 −1.84007 −0.920034 0.391838i \(-0.871839\pi\)
−0.920034 + 0.391838i \(0.871839\pi\)
\(294\) −5.90785e12 −0.156862
\(295\) 1.80511e13 0.470417
\(296\) 1.00461e14 2.56975
\(297\) 2.85690e12 0.0717356
\(298\) −3.76831e13 −0.928876
\(299\) −6.21583e13 −1.50421
\(300\) −1.99527e13 −0.474062
\(301\) 7.46301e13 1.74100
\(302\) −1.21699e14 −2.78771
\(303\) 2.02532e12 0.0455575
\(304\) −9.49223e13 −2.09683
\(305\) 4.97577e12 0.107947
\(306\) −1.32366e14 −2.82038
\(307\) 6.64088e13 1.38984 0.694920 0.719087i \(-0.255440\pi\)
0.694920 + 0.719087i \(0.255440\pi\)
\(308\) −1.84505e13 −0.379296
\(309\) −3.01701e11 −0.00609264
\(310\) −2.70286e12 −0.0536210
\(311\) 9.69704e12 0.188998 0.0944989 0.995525i \(-0.469875\pi\)
0.0944989 + 0.995525i \(0.469875\pi\)
\(312\) −2.79774e13 −0.535743
\(313\) 3.17670e13 0.597698 0.298849 0.954300i \(-0.403397\pi\)
0.298849 + 0.954300i \(0.403397\pi\)
\(314\) −4.71792e13 −0.872242
\(315\) −1.61829e13 −0.294000
\(316\) 1.39923e14 2.49810
\(317\) −9.96377e13 −1.74823 −0.874113 0.485722i \(-0.838557\pi\)
−0.874113 + 0.485722i \(0.838557\pi\)
\(318\) −1.52887e13 −0.263647
\(319\) 1.88078e12 0.0318778
\(320\) −9.52095e12 −0.158619
\(321\) −1.60317e13 −0.262544
\(322\) 1.71204e14 2.75617
\(323\) 1.64853e14 2.60906
\(324\) 1.12756e14 1.75446
\(325\) −6.84281e13 −1.04683
\(326\) −8.02673e12 −0.120737
\(327\) 4.69805e12 0.0694872
\(328\) −1.49653e13 −0.217660
\(329\) −2.75445e13 −0.393964
\(330\) 1.23718e12 0.0174023
\(331\) −1.85492e13 −0.256608 −0.128304 0.991735i \(-0.540953\pi\)
−0.128304 + 0.991735i \(0.540953\pi\)
\(332\) −2.17682e14 −2.96185
\(333\) 9.17488e13 1.22788
\(334\) −2.17355e14 −2.86130
\(335\) 1.92215e13 0.248909
\(336\) 3.01883e13 0.384567
\(337\) 3.17248e13 0.397589 0.198794 0.980041i \(-0.436297\pi\)
0.198794 + 0.980041i \(0.436297\pi\)
\(338\) −3.87032e13 −0.477205
\(339\) −1.96837e13 −0.238785
\(340\) −8.02606e13 −0.958007
\(341\) −1.48467e12 −0.0174374
\(342\) −2.21287e14 −2.55748
\(343\) −6.49579e13 −0.738779
\(344\) −2.62100e14 −2.93357
\(345\) −7.79640e12 −0.0858794
\(346\) 5.41341e13 0.586884
\(347\) −2.83475e13 −0.302484 −0.151242 0.988497i \(-0.548327\pi\)
−0.151242 + 0.988497i \(0.548327\pi\)
\(348\) −1.01124e13 −0.106211
\(349\) 3.64436e13 0.376774 0.188387 0.982095i \(-0.439674\pi\)
0.188387 + 0.982095i \(0.439674\pi\)
\(350\) 1.88473e14 1.91811
\(351\) −5.26800e13 −0.527785
\(352\) 6.76381e12 0.0667125
\(353\) −4.91177e13 −0.476955 −0.238478 0.971148i \(-0.576648\pi\)
−0.238478 + 0.971148i \(0.576648\pi\)
\(354\) −7.85007e13 −0.750509
\(355\) −4.85296e13 −0.456826
\(356\) 1.27701e14 1.18364
\(357\) −5.24286e13 −0.478512
\(358\) −2.83696e14 −2.54974
\(359\) 1.78482e14 1.57970 0.789850 0.613300i \(-0.210158\pi\)
0.789850 + 0.613300i \(0.210158\pi\)
\(360\) 5.68341e13 0.495388
\(361\) 1.59109e14 1.36586
\(362\) −1.50689e14 −1.27404
\(363\) −2.82787e13 −0.235490
\(364\) 3.40219e14 2.79062
\(365\) 5.68748e13 0.459525
\(366\) −2.16386e13 −0.172220
\(367\) 1.53021e14 1.19974 0.599871 0.800097i \(-0.295218\pi\)
0.599871 + 0.800097i \(0.295218\pi\)
\(368\) −2.35551e14 −1.81937
\(369\) −1.36675e13 −0.104003
\(370\) 8.19169e13 0.614136
\(371\) 9.80781e13 0.724462
\(372\) 7.98267e12 0.0580981
\(373\) 1.58375e14 1.13576 0.567880 0.823111i \(-0.307764\pi\)
0.567880 + 0.823111i \(0.307764\pi\)
\(374\) −6.49164e13 −0.458733
\(375\) −1.78236e13 −0.124115
\(376\) 9.67360e13 0.663827
\(377\) −3.46807e13 −0.234536
\(378\) 1.45098e14 0.967064
\(379\) −2.62873e14 −1.72675 −0.863377 0.504559i \(-0.831655\pi\)
−0.863377 + 0.504559i \(0.831655\pi\)
\(380\) −1.34178e14 −0.868706
\(381\) −7.08040e12 −0.0451825
\(382\) 4.31928e14 2.71683
\(383\) −2.35961e13 −0.146301 −0.0731504 0.997321i \(-0.523305\pi\)
−0.0731504 + 0.997321i \(0.523305\pi\)
\(384\) 5.85870e13 0.358080
\(385\) −7.93661e12 −0.0478190
\(386\) −1.58897e14 −0.943811
\(387\) −2.39371e14 −1.40172
\(388\) 1.91222e14 1.10399
\(389\) 3.02235e13 0.172037 0.0860185 0.996294i \(-0.472586\pi\)
0.0860185 + 0.996294i \(0.472586\pi\)
\(390\) −2.28131e13 −0.128035
\(391\) 4.09086e14 2.26382
\(392\) −1.33102e14 −0.726290
\(393\) 6.30175e13 0.339080
\(394\) 2.37046e13 0.125778
\(395\) 6.01888e13 0.314943
\(396\) 5.91787e13 0.305381
\(397\) 1.16590e14 0.593352 0.296676 0.954978i \(-0.404122\pi\)
0.296676 + 0.954978i \(0.404122\pi\)
\(398\) −1.61933e13 −0.0812792
\(399\) −8.76492e13 −0.433908
\(400\) −2.59310e14 −1.26616
\(401\) 8.37630e13 0.403421 0.201710 0.979445i \(-0.435350\pi\)
0.201710 + 0.979445i \(0.435350\pi\)
\(402\) −8.35905e13 −0.397113
\(403\) 2.73767e13 0.128293
\(404\) 8.64967e13 0.399855
\(405\) 4.85028e13 0.221189
\(406\) 9.55216e13 0.429743
\(407\) 4.49966e13 0.199715
\(408\) 1.84129e14 0.806289
\(409\) −2.31783e14 −1.00139 −0.500695 0.865624i \(-0.666922\pi\)
−0.500695 + 0.865624i \(0.666922\pi\)
\(410\) −1.22029e13 −0.0520177
\(411\) 8.47482e13 0.356451
\(412\) −1.28849e13 −0.0534746
\(413\) 5.03587e14 2.06229
\(414\) −5.49125e14 −2.21906
\(415\) −9.36376e13 −0.373410
\(416\) −1.24722e14 −0.490827
\(417\) 6.74683e13 0.262030
\(418\) −1.08526e14 −0.415973
\(419\) 4.51676e14 1.70864 0.854318 0.519750i \(-0.173975\pi\)
0.854318 + 0.519750i \(0.173975\pi\)
\(420\) 4.26730e13 0.159324
\(421\) 1.04417e14 0.384786 0.192393 0.981318i \(-0.438375\pi\)
0.192393 + 0.981318i \(0.438375\pi\)
\(422\) 9.84582e13 0.358124
\(423\) 8.83471e13 0.317191
\(424\) −3.44450e14 −1.22071
\(425\) 4.50349e14 1.57547
\(426\) 2.11046e14 0.728825
\(427\) 1.38813e14 0.473235
\(428\) −6.84675e14 −2.30432
\(429\) −1.25311e13 −0.0416366
\(430\) −2.13720e14 −0.701082
\(431\) −3.92866e14 −1.27239 −0.636194 0.771529i \(-0.719492\pi\)
−0.636194 + 0.771529i \(0.719492\pi\)
\(432\) −1.99632e14 −0.638367
\(433\) 1.57318e14 0.496702 0.248351 0.968670i \(-0.420111\pi\)
0.248351 + 0.968670i \(0.420111\pi\)
\(434\) −7.54041e13 −0.235072
\(435\) −4.34993e12 −0.0133903
\(436\) 2.00642e14 0.609883
\(437\) 6.83902e14 2.05280
\(438\) −2.47337e14 −0.733132
\(439\) −3.44490e13 −0.100837 −0.0504187 0.998728i \(-0.516056\pi\)
−0.0504187 + 0.998728i \(0.516056\pi\)
\(440\) 2.78733e13 0.0805747
\(441\) −1.21559e14 −0.347037
\(442\) 1.19703e15 3.37507
\(443\) 6.48442e13 0.180572 0.0902860 0.995916i \(-0.471222\pi\)
0.0902860 + 0.995916i \(0.471222\pi\)
\(444\) −2.41935e14 −0.665413
\(445\) 5.49316e13 0.149225
\(446\) 7.81916e14 2.09806
\(447\) 4.78739e13 0.126884
\(448\) −2.65614e14 −0.695379
\(449\) −4.44984e14 −1.15077 −0.575386 0.817882i \(-0.695148\pi\)
−0.575386 + 0.817882i \(0.695148\pi\)
\(450\) −6.04514e14 −1.54432
\(451\) −6.70299e12 −0.0169160
\(452\) −8.40641e14 −2.09580
\(453\) 1.54610e14 0.380800
\(454\) 7.56776e14 1.84145
\(455\) 1.46348e14 0.351822
\(456\) 3.07824e14 0.731131
\(457\) 6.04598e14 1.41882 0.709410 0.704796i \(-0.248961\pi\)
0.709410 + 0.704796i \(0.248961\pi\)
\(458\) 8.43225e14 1.95516
\(459\) 3.46706e14 0.794312
\(460\) −3.32965e14 −0.753756
\(461\) −2.44475e14 −0.546864 −0.273432 0.961891i \(-0.588159\pi\)
−0.273432 + 0.961891i \(0.588159\pi\)
\(462\) 3.45147e13 0.0762911
\(463\) −3.72317e14 −0.813239 −0.406619 0.913598i \(-0.633292\pi\)
−0.406619 + 0.913598i \(0.633292\pi\)
\(464\) −1.31423e14 −0.283677
\(465\) 3.43381e12 0.00732461
\(466\) −1.26786e15 −2.67268
\(467\) −5.42981e14 −1.13121 −0.565603 0.824678i \(-0.691357\pi\)
−0.565603 + 0.824678i \(0.691357\pi\)
\(468\) −1.09123e15 −2.24680
\(469\) 5.36238e14 1.09121
\(470\) 7.88798e13 0.158645
\(471\) 5.99379e13 0.119148
\(472\) −1.76859e15 −3.47494
\(473\) −1.17395e14 −0.227990
\(474\) −2.61749e14 −0.502464
\(475\) 7.52887e14 1.42861
\(476\) −2.23910e15 −4.19986
\(477\) −3.14579e14 −0.583283
\(478\) −1.50918e15 −2.76623
\(479\) −1.96268e14 −0.355635 −0.177817 0.984063i \(-0.556904\pi\)
−0.177817 + 0.984063i \(0.556904\pi\)
\(480\) −1.56436e13 −0.0280227
\(481\) −8.29717e14 −1.46937
\(482\) 6.63909e14 1.16239
\(483\) −2.17503e14 −0.376492
\(484\) −1.20772e15 −2.06688
\(485\) 8.22555e13 0.139183
\(486\) −7.05055e14 −1.17957
\(487\) −1.06344e15 −1.75915 −0.879576 0.475758i \(-0.842174\pi\)
−0.879576 + 0.475758i \(0.842174\pi\)
\(488\) −4.87511e14 −0.797398
\(489\) 1.01974e13 0.0164927
\(490\) −1.08533e14 −0.173573
\(491\) −2.56729e14 −0.406000 −0.203000 0.979179i \(-0.565069\pi\)
−0.203000 + 0.979179i \(0.565069\pi\)
\(492\) 3.60402e13 0.0563610
\(493\) 2.28246e14 0.352976
\(494\) 2.00117e15 3.06046
\(495\) 2.54562e13 0.0385003
\(496\) 1.03745e14 0.155173
\(497\) −1.35387e15 −2.00270
\(498\) 4.07212e14 0.595743
\(499\) 6.69840e14 0.969210 0.484605 0.874733i \(-0.338963\pi\)
0.484605 + 0.874733i \(0.338963\pi\)
\(500\) −7.61203e14 −1.08934
\(501\) 2.76135e14 0.390853
\(502\) −6.28773e14 −0.880285
\(503\) −1.36310e15 −1.88757 −0.943784 0.330563i \(-0.892762\pi\)
−0.943784 + 0.330563i \(0.892762\pi\)
\(504\) 1.58555e15 2.17176
\(505\) 3.72072e13 0.0504109
\(506\) −2.69309e14 −0.360930
\(507\) 4.91697e13 0.0651859
\(508\) −3.02387e14 −0.396563
\(509\) −1.04561e15 −1.35651 −0.678254 0.734827i \(-0.737263\pi\)
−0.678254 + 0.734827i \(0.737263\pi\)
\(510\) 1.50141e14 0.192692
\(511\) 1.58668e15 2.01454
\(512\) 1.66665e15 2.09343
\(513\) 5.79617e14 0.720270
\(514\) 8.99792e14 1.10623
\(515\) −5.54255e12 −0.00674171
\(516\) 6.31204e14 0.759619
\(517\) 4.33283e13 0.0515910
\(518\) 2.28531e15 2.69234
\(519\) −6.87737e13 −0.0801681
\(520\) −5.13971e14 −0.592817
\(521\) 1.08874e15 1.24256 0.621280 0.783589i \(-0.286613\pi\)
0.621280 + 0.783589i \(0.286613\pi\)
\(522\) −3.06380e14 −0.345997
\(523\) 9.45122e14 1.05616 0.528078 0.849196i \(-0.322913\pi\)
0.528078 + 0.849196i \(0.322913\pi\)
\(524\) 2.69132e15 2.97608
\(525\) −2.39442e14 −0.262014
\(526\) 1.71931e15 1.86180
\(527\) −1.80176e14 −0.193080
\(528\) −4.74871e13 −0.0503604
\(529\) 7.44302e14 0.781165
\(530\) −2.80869e14 −0.291734
\(531\) −1.61522e15 −1.66040
\(532\) −3.74329e15 −3.80837
\(533\) 1.23600e14 0.124457
\(534\) −2.38887e14 −0.238076
\(535\) −2.94518e14 −0.290513
\(536\) −1.88326e15 −1.83867
\(537\) 3.60416e14 0.348294
\(538\) −9.21175e14 −0.881129
\(539\) −5.96166e13 −0.0564455
\(540\) −2.82193e14 −0.264472
\(541\) 1.11380e15 1.03329 0.516646 0.856199i \(-0.327180\pi\)
0.516646 + 0.856199i \(0.327180\pi\)
\(542\) −4.36885e13 −0.0401209
\(543\) 1.91440e14 0.174034
\(544\) 8.20838e14 0.738692
\(545\) 8.63077e13 0.0768898
\(546\) −6.36437e14 −0.561301
\(547\) −1.97274e15 −1.72242 −0.861212 0.508245i \(-0.830294\pi\)
−0.861212 + 0.508245i \(0.830294\pi\)
\(548\) 3.61939e15 3.12854
\(549\) −4.45234e14 −0.381014
\(550\) −2.96474e14 −0.251184
\(551\) 3.81577e14 0.320073
\(552\) 7.63868e14 0.634385
\(553\) 1.67914e15 1.38070
\(554\) −1.48500e15 −1.20899
\(555\) −1.04070e14 −0.0838907
\(556\) 2.88141e15 2.29982
\(557\) 2.40646e15 1.90184 0.950921 0.309433i \(-0.100139\pi\)
0.950921 + 0.309433i \(0.100139\pi\)
\(558\) 2.41854e14 0.189263
\(559\) 2.16472e15 1.67740
\(560\) 5.54588e14 0.425536
\(561\) 8.24718e13 0.0626628
\(562\) −4.41871e15 −3.32465
\(563\) 2.55477e14 0.190351 0.0951757 0.995460i \(-0.469659\pi\)
0.0951757 + 0.995460i \(0.469659\pi\)
\(564\) −2.32965e14 −0.171892
\(565\) −3.61608e14 −0.264223
\(566\) 6.30930e14 0.456553
\(567\) 1.35312e15 0.969685
\(568\) 4.75478e15 3.37454
\(569\) 1.06022e15 0.745207 0.372603 0.927991i \(-0.378465\pi\)
0.372603 + 0.927991i \(0.378465\pi\)
\(570\) 2.51003e14 0.174730
\(571\) −1.82875e15 −1.26083 −0.630413 0.776260i \(-0.717114\pi\)
−0.630413 + 0.776260i \(0.717114\pi\)
\(572\) −5.35175e14 −0.365441
\(573\) −5.48735e14 −0.371119
\(574\) −3.40434e14 −0.228044
\(575\) 1.86830e15 1.23957
\(576\) 8.51940e14 0.559867
\(577\) 2.95605e15 1.92418 0.962089 0.272737i \(-0.0879290\pi\)
0.962089 + 0.272737i \(0.0879290\pi\)
\(578\) −5.14003e15 −3.31408
\(579\) 2.01868e14 0.128924
\(580\) −1.85775e14 −0.117526
\(581\) −2.61229e15 −1.63701
\(582\) −3.57713e14 −0.222054
\(583\) −1.54280e14 −0.0948708
\(584\) −5.57243e15 −3.39448
\(585\) −4.69400e14 −0.283261
\(586\) 5.43385e15 3.24841
\(587\) −1.26309e15 −0.748038 −0.374019 0.927421i \(-0.622021\pi\)
−0.374019 + 0.927421i \(0.622021\pi\)
\(588\) 3.20543e14 0.188066
\(589\) −3.01214e14 −0.175082
\(590\) −1.44214e15 −0.830462
\(591\) −3.01151e13 −0.0171812
\(592\) −3.14424e15 −1.77724
\(593\) 2.38619e15 1.33630 0.668150 0.744027i \(-0.267087\pi\)
0.668150 + 0.744027i \(0.267087\pi\)
\(594\) −2.28243e14 −0.126640
\(595\) −9.63164e14 −0.529489
\(596\) 2.04458e15 1.11365
\(597\) 2.05725e13 0.0111027
\(598\) 4.96594e15 2.65549
\(599\) −2.33823e15 −1.23891 −0.619454 0.785033i \(-0.712646\pi\)
−0.619454 + 0.785033i \(0.712646\pi\)
\(600\) 8.40918e14 0.441491
\(601\) 1.24352e14 0.0646909 0.0323454 0.999477i \(-0.489702\pi\)
0.0323454 + 0.999477i \(0.489702\pi\)
\(602\) −5.96233e15 −3.07351
\(603\) −1.71995e15 −0.878558
\(604\) 6.60301e15 3.34225
\(605\) −5.19507e14 −0.260578
\(606\) −1.61807e14 −0.0804261
\(607\) 2.17760e15 1.07261 0.536304 0.844025i \(-0.319820\pi\)
0.536304 + 0.844025i \(0.319820\pi\)
\(608\) 1.37226e15 0.669835
\(609\) −1.21354e14 −0.0587027
\(610\) −3.97523e14 −0.190567
\(611\) −7.98955e14 −0.379573
\(612\) 7.18177e15 3.38142
\(613\) 2.76949e15 1.29231 0.646157 0.763205i \(-0.276375\pi\)
0.646157 + 0.763205i \(0.276375\pi\)
\(614\) −5.30552e15 −2.45359
\(615\) 1.55029e13 0.00710560
\(616\) 7.77605e14 0.353236
\(617\) −6.64877e14 −0.299346 −0.149673 0.988736i \(-0.547822\pi\)
−0.149673 + 0.988736i \(0.547822\pi\)
\(618\) 2.41035e13 0.0107558
\(619\) −1.19536e15 −0.528689 −0.264345 0.964428i \(-0.585156\pi\)
−0.264345 + 0.964428i \(0.585156\pi\)
\(620\) 1.46650e14 0.0642875
\(621\) 1.43833e15 0.624962
\(622\) −7.74713e14 −0.333652
\(623\) 1.53247e15 0.654197
\(624\) 8.75641e14 0.370520
\(625\) 1.88699e15 0.791460
\(626\) −2.53792e15 −1.05516
\(627\) 1.37875e14 0.0568217
\(628\) 2.55980e15 1.04575
\(629\) 5.46066e15 2.21140
\(630\) 1.29288e15 0.519020
\(631\) −1.02104e15 −0.406334 −0.203167 0.979144i \(-0.565123\pi\)
−0.203167 + 0.979144i \(0.565123\pi\)
\(632\) −5.89712e15 −2.32646
\(633\) −1.25084e14 −0.0489196
\(634\) 7.96023e15 3.08628
\(635\) −1.30074e14 −0.0499959
\(636\) 8.29522e14 0.316092
\(637\) 1.09930e15 0.415290
\(638\) −1.50258e14 −0.0562763
\(639\) 4.34245e15 1.61243
\(640\) 1.07630e15 0.396227
\(641\) −3.93885e15 −1.43764 −0.718820 0.695197i \(-0.755317\pi\)
−0.718820 + 0.695197i \(0.755317\pi\)
\(642\) 1.28080e15 0.463488
\(643\) −2.41123e15 −0.865123 −0.432561 0.901604i \(-0.642390\pi\)
−0.432561 + 0.901604i \(0.642390\pi\)
\(644\) −9.28901e15 −3.30443
\(645\) 2.71517e14 0.0957675
\(646\) −1.31704e16 −4.60597
\(647\) 2.50673e15 0.869230 0.434615 0.900616i \(-0.356884\pi\)
0.434615 + 0.900616i \(0.356884\pi\)
\(648\) −4.75216e15 −1.63391
\(649\) −7.92158e14 −0.270064
\(650\) 5.46684e15 1.84805
\(651\) 9.57957e13 0.0321108
\(652\) 4.35507e14 0.144755
\(653\) 8.01060e14 0.264023 0.132012 0.991248i \(-0.457856\pi\)
0.132012 + 0.991248i \(0.457856\pi\)
\(654\) −3.75335e14 −0.122671
\(655\) 1.15769e15 0.375203
\(656\) 4.68387e14 0.150534
\(657\) −5.08919e15 −1.62196
\(658\) 2.20058e15 0.695495
\(659\) 1.23234e13 0.00386243 0.00193122 0.999998i \(-0.499385\pi\)
0.00193122 + 0.999998i \(0.499385\pi\)
\(660\) −6.71259e13 −0.0208641
\(661\) 3.29931e14 0.101699 0.0508493 0.998706i \(-0.483807\pi\)
0.0508493 + 0.998706i \(0.483807\pi\)
\(662\) 1.48193e15 0.453010
\(663\) −1.52074e15 −0.461033
\(664\) 9.17434e15 2.75836
\(665\) −1.61020e15 −0.480133
\(666\) −7.32997e15 −2.16767
\(667\) 9.46889e14 0.277720
\(668\) 1.17930e16 3.43048
\(669\) −9.93371e14 −0.286594
\(670\) −1.53564e15 −0.439418
\(671\) −2.18357e14 −0.0619718
\(672\) −4.36423e14 −0.122850
\(673\) −8.60530e14 −0.240261 −0.120131 0.992758i \(-0.538331\pi\)
−0.120131 + 0.992758i \(0.538331\pi\)
\(674\) −2.53455e15 −0.701893
\(675\) 1.58341e15 0.434933
\(676\) 2.09992e15 0.572132
\(677\) 2.19254e14 0.0592530 0.0296265 0.999561i \(-0.490568\pi\)
0.0296265 + 0.999561i \(0.490568\pi\)
\(678\) 1.57256e15 0.421545
\(679\) 2.29475e15 0.610171
\(680\) 3.38263e15 0.892185
\(681\) −9.61433e14 −0.251542
\(682\) 1.18613e14 0.0307835
\(683\) −4.08440e15 −1.05151 −0.525756 0.850635i \(-0.676217\pi\)
−0.525756 + 0.850635i \(0.676217\pi\)
\(684\) 1.20064e16 3.06622
\(685\) 1.55691e15 0.394425
\(686\) 5.18960e15 1.30422
\(687\) −1.07126e15 −0.267075
\(688\) 8.20327e15 2.02885
\(689\) 2.84485e15 0.697998
\(690\) 6.22868e14 0.151609
\(691\) −5.97418e15 −1.44261 −0.721305 0.692618i \(-0.756457\pi\)
−0.721305 + 0.692618i \(0.756457\pi\)
\(692\) −2.93716e15 −0.703629
\(693\) 7.10172e14 0.168784
\(694\) 2.26473e15 0.533998
\(695\) 1.23946e15 0.289945
\(696\) 4.26193e14 0.0989136
\(697\) −8.13456e14 −0.187307
\(698\) −2.91154e15 −0.665148
\(699\) 1.61072e15 0.365087
\(700\) −1.02260e16 −2.29967
\(701\) −6.07856e15 −1.35629 −0.678144 0.734929i \(-0.737215\pi\)
−0.678144 + 0.734929i \(0.737215\pi\)
\(702\) 4.20870e15 0.931738
\(703\) 9.12904e15 2.00526
\(704\) 4.17819e14 0.0910622
\(705\) −1.00211e14 −0.0216709
\(706\) 3.92410e15 0.842005
\(707\) 1.03800e15 0.220999
\(708\) 4.25922e15 0.899802
\(709\) −3.49835e15 −0.733345 −0.366673 0.930350i \(-0.619503\pi\)
−0.366673 + 0.930350i \(0.619503\pi\)
\(710\) 3.87711e15 0.806469
\(711\) −5.38573e15 −1.11163
\(712\) −5.38204e15 −1.10232
\(713\) −7.47467e14 −0.151915
\(714\) 4.18861e15 0.844754
\(715\) −2.30209e14 −0.0460723
\(716\) 1.53925e16 3.05694
\(717\) 1.91731e15 0.377866
\(718\) −1.42592e16 −2.78876
\(719\) 1.02063e16 1.98088 0.990441 0.137939i \(-0.0440479\pi\)
0.990441 + 0.137939i \(0.0440479\pi\)
\(720\) −1.77881e15 −0.342610
\(721\) −1.54625e14 −0.0295553
\(722\) −1.27115e16 −2.41125
\(723\) −8.43452e14 −0.158781
\(724\) 8.17593e15 1.52748
\(725\) 1.04240e15 0.193275
\(726\) 2.25924e15 0.415729
\(727\) 8.11473e15 1.48195 0.740977 0.671531i \(-0.234363\pi\)
0.740977 + 0.671531i \(0.234363\pi\)
\(728\) −1.43387e16 −2.59888
\(729\) −3.71231e15 −0.667794
\(730\) −4.54383e15 −0.811234
\(731\) −1.42468e16 −2.52448
\(732\) 1.17405e15 0.206479
\(733\) −1.00244e16 −1.74980 −0.874898 0.484307i \(-0.839072\pi\)
−0.874898 + 0.484307i \(0.839072\pi\)
\(734\) −1.22251e16 −2.11800
\(735\) 1.37884e14 0.0237101
\(736\) 3.40529e15 0.581200
\(737\) −8.43519e14 −0.142897
\(738\) 1.09192e15 0.183604
\(739\) 5.65116e15 0.943176 0.471588 0.881819i \(-0.343681\pi\)
0.471588 + 0.881819i \(0.343681\pi\)
\(740\) −4.44457e15 −0.736301
\(741\) −2.54235e15 −0.418057
\(742\) −7.83563e15 −1.27895
\(743\) 8.50764e15 1.37839 0.689193 0.724578i \(-0.257965\pi\)
0.689193 + 0.724578i \(0.257965\pi\)
\(744\) −3.36434e14 −0.0541064
\(745\) 8.79489e14 0.140401
\(746\) −1.26528e16 −2.00504
\(747\) 8.37875e15 1.31800
\(748\) 3.52217e15 0.549986
\(749\) −8.21641e15 −1.27360
\(750\) 1.42396e15 0.219109
\(751\) −1.00126e16 −1.52942 −0.764712 0.644372i \(-0.777119\pi\)
−0.764712 + 0.644372i \(0.777119\pi\)
\(752\) −3.02766e15 −0.459102
\(753\) 7.98813e14 0.120247
\(754\) 2.77070e15 0.414045
\(755\) 2.84033e15 0.421367
\(756\) −7.87257e15 −1.15944
\(757\) 8.17216e15 1.19484 0.597420 0.801929i \(-0.296193\pi\)
0.597420 + 0.801929i \(0.296193\pi\)
\(758\) 2.10014e16 3.04837
\(759\) 3.42138e14 0.0493029
\(760\) 5.65502e15 0.809020
\(761\) −9.13630e15 −1.29764 −0.648820 0.760942i \(-0.724737\pi\)
−0.648820 + 0.760942i \(0.724737\pi\)
\(762\) 5.65666e14 0.0797641
\(763\) 2.40780e15 0.337082
\(764\) −2.34352e16 −3.25728
\(765\) 3.08929e15 0.426305
\(766\) 1.88513e15 0.258276
\(767\) 1.46070e16 1.98695
\(768\) −3.61922e15 −0.488797
\(769\) 7.92063e15 1.06210 0.531049 0.847341i \(-0.321798\pi\)
0.531049 + 0.847341i \(0.321798\pi\)
\(770\) 6.34069e14 0.0844185
\(771\) −1.14312e15 −0.151110
\(772\) 8.62128e15 1.13156
\(773\) −1.11311e16 −1.45061 −0.725306 0.688426i \(-0.758302\pi\)
−0.725306 + 0.688426i \(0.758302\pi\)
\(774\) 1.91238e16 2.47456
\(775\) −8.22863e14 −0.105723
\(776\) −8.05915e15 −1.02813
\(777\) −2.90332e15 −0.367773
\(778\) −2.41461e15 −0.303710
\(779\) −1.35992e15 −0.169847
\(780\) 1.23777e15 0.153504
\(781\) 2.12968e15 0.262261
\(782\) −3.26826e16 −3.99649
\(783\) 8.02502e14 0.0974442
\(784\) 4.16585e15 0.502302
\(785\) 1.10112e15 0.131841
\(786\) −5.03458e15 −0.598603
\(787\) −1.89021e14 −0.0223177 −0.0111588 0.999938i \(-0.503552\pi\)
−0.0111588 + 0.999938i \(0.503552\pi\)
\(788\) −1.28614e15 −0.150798
\(789\) −2.18427e15 −0.254322
\(790\) −4.80859e15 −0.555992
\(791\) −1.00881e16 −1.15834
\(792\) −2.49412e15 −0.284399
\(793\) 4.02641e15 0.455949
\(794\) −9.31456e15 −1.04749
\(795\) 3.56825e14 0.0398507
\(796\) 8.78603e14 0.0974475
\(797\) 8.56639e15 0.943576 0.471788 0.881712i \(-0.343609\pi\)
0.471788 + 0.881712i \(0.343609\pi\)
\(798\) 7.00245e15 0.766010
\(799\) 5.25820e15 0.571255
\(800\) 3.74877e15 0.404477
\(801\) −4.91531e15 −0.526711
\(802\) −6.69197e15 −0.712189
\(803\) −2.49590e15 −0.263811
\(804\) 4.53538e15 0.476107
\(805\) −3.99574e15 −0.416600
\(806\) −2.18717e15 −0.226485
\(807\) 1.17029e15 0.120362
\(808\) −3.64545e15 −0.372382
\(809\) −9.97290e15 −1.01182 −0.505911 0.862585i \(-0.668844\pi\)
−0.505911 + 0.862585i \(0.668844\pi\)
\(810\) −3.87498e15 −0.390482
\(811\) −6.57801e15 −0.658384 −0.329192 0.944263i \(-0.606776\pi\)
−0.329192 + 0.944263i \(0.606776\pi\)
\(812\) −5.18272e15 −0.515228
\(813\) 5.55032e13 0.00548050
\(814\) −3.59486e15 −0.352572
\(815\) 1.87336e14 0.0182497
\(816\) −5.76290e15 −0.557629
\(817\) −2.38175e16 −2.28916
\(818\) 1.85176e16 1.76783
\(819\) −1.30953e16 −1.24180
\(820\) 6.62093e14 0.0623653
\(821\) 8.28416e14 0.0775106 0.0387553 0.999249i \(-0.487661\pi\)
0.0387553 + 0.999249i \(0.487661\pi\)
\(822\) −6.77068e15 −0.629270
\(823\) 9.26342e15 0.855209 0.427604 0.903966i \(-0.359358\pi\)
0.427604 + 0.903966i \(0.359358\pi\)
\(824\) 5.43042e14 0.0498005
\(825\) 3.76649e14 0.0343116
\(826\) −4.02324e16 −3.64071
\(827\) −3.87100e14 −0.0347971 −0.0173986 0.999849i \(-0.505538\pi\)
−0.0173986 + 0.999849i \(0.505538\pi\)
\(828\) 2.97939e16 2.66048
\(829\) 2.75678e15 0.244541 0.122271 0.992497i \(-0.460982\pi\)
0.122271 + 0.992497i \(0.460982\pi\)
\(830\) 7.48087e15 0.659209
\(831\) 1.88660e15 0.165148
\(832\) −7.70440e15 −0.669978
\(833\) −7.23491e15 −0.625008
\(834\) −5.39016e15 −0.462581
\(835\) 5.07286e15 0.432491
\(836\) 5.88831e15 0.498719
\(837\) −6.33489e14 −0.0533027
\(838\) −3.60852e16 −3.01638
\(839\) −1.04464e16 −0.867510 −0.433755 0.901031i \(-0.642812\pi\)
−0.433755 + 0.901031i \(0.642812\pi\)
\(840\) −1.79847e15 −0.148378
\(841\) −1.16722e16 −0.956698
\(842\) −8.34205e15 −0.679292
\(843\) 5.61366e15 0.454145
\(844\) −5.34205e15 −0.429363
\(845\) 9.03296e14 0.0721304
\(846\) −7.05821e15 −0.559960
\(847\) −1.44931e16 −1.14236
\(848\) 1.07807e16 0.844244
\(849\) −8.01554e14 −0.0623649
\(850\) −3.59792e16 −2.78130
\(851\) 2.26538e16 1.73992
\(852\) −1.14507e16 −0.873806
\(853\) 8.43783e14 0.0639751 0.0319875 0.999488i \(-0.489816\pi\)
0.0319875 + 0.999488i \(0.489816\pi\)
\(854\) −1.10900e16 −0.835438
\(855\) 5.16462e15 0.386567
\(856\) 2.88560e16 2.14600
\(857\) −5.87956e14 −0.0434460 −0.0217230 0.999764i \(-0.506915\pi\)
−0.0217230 + 0.999764i \(0.506915\pi\)
\(858\) 1.00113e15 0.0735042
\(859\) −9.88023e15 −0.720783 −0.360392 0.932801i \(-0.617357\pi\)
−0.360392 + 0.932801i \(0.617357\pi\)
\(860\) 1.15958e16 0.840543
\(861\) 4.32499e14 0.0311507
\(862\) 3.13868e16 2.24624
\(863\) 2.99589e15 0.213042 0.106521 0.994310i \(-0.466029\pi\)
0.106521 + 0.994310i \(0.466029\pi\)
\(864\) 2.88603e15 0.203927
\(865\) −1.26344e15 −0.0887086
\(866\) −1.25684e16 −0.876864
\(867\) 6.53005e15 0.452701
\(868\) 4.09120e15 0.281834
\(869\) −2.64134e15 −0.180807
\(870\) 3.47524e14 0.0236390
\(871\) 1.55541e16 1.05135
\(872\) −8.45617e15 −0.567980
\(873\) −7.36027e15 −0.491264
\(874\) −5.46382e16 −3.62396
\(875\) −9.13478e15 −0.602079
\(876\) 1.34198e16 0.878969
\(877\) 2.29142e16 1.49144 0.745721 0.666258i \(-0.232105\pi\)
0.745721 + 0.666258i \(0.232105\pi\)
\(878\) 2.75219e15 0.178016
\(879\) −6.90334e15 −0.443732
\(880\) −8.72384e14 −0.0557254
\(881\) 2.25902e16 1.43401 0.717007 0.697066i \(-0.245511\pi\)
0.717007 + 0.697066i \(0.245511\pi\)
\(882\) 9.71159e15 0.612651
\(883\) 1.66067e16 1.04111 0.520557 0.853827i \(-0.325724\pi\)
0.520557 + 0.853827i \(0.325724\pi\)
\(884\) −6.49473e16 −4.04644
\(885\) 1.83213e15 0.113441
\(886\) −5.18051e15 −0.318777
\(887\) 2.34470e16 1.43386 0.716932 0.697143i \(-0.245546\pi\)
0.716932 + 0.697143i \(0.245546\pi\)
\(888\) 1.01965e16 0.619695
\(889\) −3.62878e15 −0.219180
\(890\) −4.38858e15 −0.263439
\(891\) −2.12851e15 −0.126984
\(892\) −4.24245e16 −2.51542
\(893\) 8.79057e15 0.518005
\(894\) −3.82473e15 −0.223998
\(895\) 6.62119e15 0.385398
\(896\) 3.00265e16 1.73704
\(897\) −6.30888e15 −0.362739
\(898\) 3.55505e16 2.03154
\(899\) −4.17043e14 −0.0236866
\(900\) 3.27992e16 1.85152
\(901\) −1.87230e16 −1.05048
\(902\) 5.35514e14 0.0298631
\(903\) 7.57473e15 0.419841
\(904\) 3.54293e16 1.95180
\(905\) 3.51694e15 0.192574
\(906\) −1.23520e16 −0.672255
\(907\) 1.82286e16 0.986083 0.493041 0.870006i \(-0.335885\pi\)
0.493041 + 0.870006i \(0.335885\pi\)
\(908\) −4.10605e16 −2.20776
\(909\) −3.32932e15 −0.177932
\(910\) −1.16920e16 −0.621097
\(911\) 3.20443e16 1.69200 0.845999 0.533184i \(-0.179005\pi\)
0.845999 + 0.533184i \(0.179005\pi\)
\(912\) −9.63433e15 −0.505650
\(913\) 4.10921e15 0.214372
\(914\) −4.83024e16 −2.50475
\(915\) 5.05025e14 0.0260314
\(916\) −4.57509e16 −2.34409
\(917\) 3.22971e16 1.64487
\(918\) −2.76989e16 −1.40226
\(919\) 1.73607e16 0.873641 0.436820 0.899549i \(-0.356105\pi\)
0.436820 + 0.899549i \(0.356105\pi\)
\(920\) 1.40330e16 0.701968
\(921\) 6.74030e15 0.335159
\(922\) 1.95316e16 0.965421
\(923\) −3.92704e16 −1.92955
\(924\) −1.87267e15 −0.0914671
\(925\) 2.49389e16 1.21087
\(926\) 2.97451e16 1.43567
\(927\) 4.95950e14 0.0237958
\(928\) 1.89995e15 0.0906209
\(929\) 1.50305e15 0.0712670 0.0356335 0.999365i \(-0.488655\pi\)
0.0356335 + 0.999365i \(0.488655\pi\)
\(930\) −2.74333e14 −0.0129307
\(931\) −1.20952e16 −0.566748
\(932\) 6.87901e16 3.20434
\(933\) 9.84220e14 0.0455767
\(934\) 4.33797e16 1.99700
\(935\) 1.51509e15 0.0693384
\(936\) 4.59904e16 2.09243
\(937\) −3.61465e13 −0.00163493 −0.000817463 1.00000i \(-0.500260\pi\)
−0.000817463 1.00000i \(0.500260\pi\)
\(938\) −4.28410e16 −1.92639
\(939\) 3.22425e15 0.144135
\(940\) −4.27979e15 −0.190204
\(941\) −1.70143e16 −0.751747 −0.375873 0.926671i \(-0.622657\pi\)
−0.375873 + 0.926671i \(0.622657\pi\)
\(942\) −4.78854e15 −0.210341
\(943\) −3.37466e15 −0.147372
\(944\) 5.53538e16 2.40327
\(945\) −3.38644e15 −0.146173
\(946\) 9.37893e15 0.402487
\(947\) −3.45643e16 −1.47470 −0.737350 0.675511i \(-0.763923\pi\)
−0.737350 + 0.675511i \(0.763923\pi\)
\(948\) 1.42018e16 0.602416
\(949\) 4.60234e16 1.94095
\(950\) −6.01494e16 −2.52204
\(951\) −1.01129e16 −0.421584
\(952\) 9.43680e16 3.91130
\(953\) 5.69537e15 0.234699 0.117350 0.993091i \(-0.462560\pi\)
0.117350 + 0.993091i \(0.462560\pi\)
\(954\) 2.51323e16 1.02971
\(955\) −1.00808e16 −0.410655
\(956\) 8.18838e16 3.31650
\(957\) 1.90893e14 0.00768732
\(958\) 1.56802e16 0.627829
\(959\) 4.34343e16 1.72914
\(960\) −9.66348e14 −0.0382509
\(961\) −2.50793e16 −0.987043
\(962\) 6.62876e16 2.59400
\(963\) 2.63536e16 1.02541
\(964\) −3.60218e16 −1.39361
\(965\) 3.70850e15 0.142659
\(966\) 1.73767e16 0.664649
\(967\) −2.15504e16 −0.819616 −0.409808 0.912172i \(-0.634404\pi\)
−0.409808 + 0.912172i \(0.634404\pi\)
\(968\) 5.08998e16 1.92487
\(969\) 1.67321e16 0.629173
\(970\) −6.57154e15 −0.245710
\(971\) −2.48494e15 −0.0923869 −0.0461934 0.998933i \(-0.514709\pi\)
−0.0461934 + 0.998933i \(0.514709\pi\)
\(972\) 3.82542e16 1.41421
\(973\) 3.45782e16 1.27111
\(974\) 8.49600e16 3.10556
\(975\) −6.94525e15 −0.252442
\(976\) 1.52582e16 0.551480
\(977\) 1.81086e16 0.650827 0.325414 0.945572i \(-0.394496\pi\)
0.325414 + 0.945572i \(0.394496\pi\)
\(978\) −8.14689e14 −0.0291158
\(979\) −2.41063e15 −0.0856693
\(980\) 5.88868e15 0.208101
\(981\) −7.72286e15 −0.271393
\(982\) 2.05105e16 0.716743
\(983\) −1.41651e16 −0.492240 −0.246120 0.969239i \(-0.579156\pi\)
−0.246120 + 0.969239i \(0.579156\pi\)
\(984\) −1.51893e15 −0.0524886
\(985\) −5.53244e14 −0.0190115
\(986\) −1.82350e16 −0.623134
\(987\) −2.79568e15 −0.0950043
\(988\) −1.08578e17 −3.66925
\(989\) −5.91035e16 −1.98625
\(990\) −2.03374e15 −0.0679675
\(991\) −2.72321e16 −0.905058 −0.452529 0.891750i \(-0.649478\pi\)
−0.452529 + 0.891750i \(0.649478\pi\)
\(992\) −1.49981e15 −0.0495702
\(993\) −1.88269e15 −0.0618810
\(994\) 1.08163e17 3.53552
\(995\) 3.77937e14 0.0122855
\(996\) −2.20941e16 −0.714250
\(997\) −1.09742e16 −0.352817 −0.176408 0.984317i \(-0.556448\pi\)
−0.176408 + 0.984317i \(0.556448\pi\)
\(998\) −5.35147e16 −1.71102
\(999\) 1.91994e16 0.610490
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.1.6 92
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.12.a.b.1.6 92 1.1 even 1 trivial