Properties

Label 197.14.a.a.1.8
Level $197$
Weight $14$
Character 197.1
Self dual yes
Analytic conductor $211.245$
Analytic rank $1$
Dimension $104$
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] = [197,14,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, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 14 \)
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: \(211.244930035\)
Analytic rank: \(1\)
Dimension: \(104\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
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)
 
\(f(q)\) \(=\) \(q-162.329 q^{2} -746.765 q^{3} +18158.7 q^{4} +42494.0 q^{5} +121222. q^{6} +350398. q^{7} -1.61789e6 q^{8} -1.03666e6 q^{9} +O(q^{10})\) \(q-162.329 q^{2} -746.765 q^{3} +18158.7 q^{4} +42494.0 q^{5} +121222. q^{6} +350398. q^{7} -1.61789e6 q^{8} -1.03666e6 q^{9} -6.89802e6 q^{10} -5.98873e6 q^{11} -1.35603e7 q^{12} -9.45844e6 q^{13} -5.68797e7 q^{14} -3.17331e7 q^{15} +1.13874e8 q^{16} -1.86331e7 q^{17} +1.68281e8 q^{18} +9.76912e7 q^{19} +7.71638e8 q^{20} -2.61665e8 q^{21} +9.72145e8 q^{22} +1.11174e9 q^{23} +1.20818e9 q^{24} +5.85041e8 q^{25} +1.53538e9 q^{26} +1.96473e9 q^{27} +6.36277e9 q^{28} -4.96957e9 q^{29} +5.15120e9 q^{30} -2.62498e9 q^{31} -5.23132e9 q^{32} +4.47218e9 q^{33} +3.02469e9 q^{34} +1.48898e10 q^{35} -1.88245e10 q^{36} -2.75230e9 q^{37} -1.58581e10 q^{38} +7.06324e9 q^{39} -6.87506e10 q^{40} -1.94142e10 q^{41} +4.24758e10 q^{42} +4.24240e10 q^{43} -1.08748e11 q^{44} -4.40521e10 q^{45} -1.80468e11 q^{46} +1.20787e11 q^{47} -8.50372e10 q^{48} +2.58895e10 q^{49} -9.49692e10 q^{50} +1.39145e10 q^{51} -1.71753e11 q^{52} +4.20067e10 q^{53} -3.18933e11 q^{54} -2.54486e11 q^{55} -5.66904e11 q^{56} -7.29524e10 q^{57} +8.06705e11 q^{58} +6.60516e10 q^{59} -5.76232e11 q^{60} -2.71752e11 q^{61} +4.26111e11 q^{62} -3.63245e11 q^{63} -8.36605e10 q^{64} -4.01928e11 q^{65} -7.25964e11 q^{66} +5.91218e10 q^{67} -3.38353e11 q^{68} -8.30212e11 q^{69} -2.41705e12 q^{70} +1.68901e10 q^{71} +1.67721e12 q^{72} +4.60459e11 q^{73} +4.46778e11 q^{74} -4.36888e11 q^{75} +1.77395e12 q^{76} -2.09844e12 q^{77} -1.14657e12 q^{78} +3.32303e11 q^{79} +4.83897e12 q^{80} +1.85586e11 q^{81} +3.15148e12 q^{82} +3.09461e12 q^{83} -4.75150e12 q^{84} -7.91795e11 q^{85} -6.88665e12 q^{86} +3.71110e12 q^{87} +9.68910e12 q^{88} -1.81559e12 q^{89} +7.15093e12 q^{90} -3.31422e12 q^{91} +2.01878e13 q^{92} +1.96025e12 q^{93} -1.96072e13 q^{94} +4.15129e12 q^{95} +3.90657e12 q^{96} -9.21227e12 q^{97} -4.20262e12 q^{98} +6.20831e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9} - 9626347 q^{10} - 10688800 q^{11} - 68157440 q^{12} - 94762650 q^{13} - 52465903 q^{14} - 186128761 q^{15} + 1543503872 q^{16} - 109572251 q^{17} - 449658263 q^{18} - 1495268031 q^{19} - 1194030741 q^{20} - 832275538 q^{21} - 2695120703 q^{22} - 2632554532 q^{23} - 190649667 q^{24} + 22696779124 q^{25} - 2460454754 q^{26} - 16267542277 q^{27} - 18137835250 q^{28} + 47556769 q^{29} - 9613748117 q^{30} - 24774628288 q^{31} - 29246249180 q^{32} - 42367036666 q^{33} - 39395206606 q^{34} - 26216433864 q^{35} + 190013501626 q^{36} - 82419664050 q^{37} - 34593622142 q^{38} - 39498281801 q^{39} - 150303128514 q^{40} - 25862853768 q^{41} - 138889965149 q^{42} - 258164897781 q^{43} - 197365738094 q^{44} - 240782892021 q^{45} - 218441397971 q^{46} - 208905762731 q^{47} - 664063830814 q^{48} + 1113758315863 q^{49} - 1516068087607 q^{50} - 1019253294393 q^{51} - 1162941441840 q^{52} + 161684855900 q^{53} + 1679137315823 q^{54} - 557952233701 q^{55} + 2842561845328 q^{56} + 801593765429 q^{57} - 7249760433 q^{58} - 775487110641 q^{59} - 57598844627 q^{60} - 36786715662 q^{61} + 681529132643 q^{62} - 4349115033663 q^{63} + 4600420238797 q^{64} - 2531819073161 q^{65} - 3958922748734 q^{66} - 7314072405766 q^{67} - 10297353950393 q^{68} - 2089200206275 q^{69} - 14268943913713 q^{70} - 6055724651085 q^{71} - 26860198563805 q^{72} - 7572811533391 q^{73} - 11175265675817 q^{74} - 24431657592434 q^{75} - 26425925198106 q^{76} - 9735327037686 q^{77} - 35310017230907 q^{78} - 8981210762721 q^{79} - 25913753436330 q^{80} + 15437375349812 q^{81} - 19721330628227 q^{82} - 22209909714532 q^{83} - 18837805278768 q^{84} - 5905005171430 q^{85} - 8913876797772 q^{86} - 7341562344401 q^{87} - 35154329886441 q^{88} - 4646484034146 q^{89} + 9564902968095 q^{90} - 22752431457047 q^{91} - 13601121953458 q^{92} - 9615114240293 q^{93} + 15352521272967 q^{94} + 5258551767043 q^{95} + 87277848810881 q^{96} - 42298840804040 q^{97} + 27000102375354 q^{98} - 8666459567773 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −162.329 −1.79350 −0.896750 0.442538i \(-0.854078\pi\)
−0.896750 + 0.442538i \(0.854078\pi\)
\(3\) −746.765 −0.591420 −0.295710 0.955278i \(-0.595556\pi\)
−0.295710 + 0.955278i \(0.595556\pi\)
\(4\) 18158.7 2.21664
\(5\) 42494.0 1.21625 0.608125 0.793841i \(-0.291922\pi\)
0.608125 + 0.793841i \(0.291922\pi\)
\(6\) 121222. 1.06071
\(7\) 350398. 1.12570 0.562852 0.826558i \(-0.309704\pi\)
0.562852 + 0.826558i \(0.309704\pi\)
\(8\) −1.61789e6 −2.18204
\(9\) −1.03666e6 −0.650222
\(10\) −6.89802e6 −2.18134
\(11\) −5.98873e6 −1.01925 −0.509627 0.860395i \(-0.670217\pi\)
−0.509627 + 0.860395i \(0.670217\pi\)
\(12\) −1.35603e7 −1.31097
\(13\) −9.45844e6 −0.543485 −0.271743 0.962370i \(-0.587600\pi\)
−0.271743 + 0.962370i \(0.587600\pi\)
\(14\) −5.68797e7 −2.01895
\(15\) −3.17331e7 −0.719315
\(16\) 1.13874e8 1.69686
\(17\) −1.86331e7 −0.187226 −0.0936131 0.995609i \(-0.529842\pi\)
−0.0936131 + 0.995609i \(0.529842\pi\)
\(18\) 1.68281e8 1.16617
\(19\) 9.76912e7 0.476384 0.238192 0.971218i \(-0.423445\pi\)
0.238192 + 0.971218i \(0.423445\pi\)
\(20\) 7.71638e8 2.69599
\(21\) −2.61665e8 −0.665763
\(22\) 9.72145e8 1.82803
\(23\) 1.11174e9 1.56594 0.782968 0.622062i \(-0.213705\pi\)
0.782968 + 0.622062i \(0.213705\pi\)
\(24\) 1.20818e9 1.29050
\(25\) 5.85041e8 0.479266
\(26\) 1.53538e9 0.974741
\(27\) 1.96473e9 0.975974
\(28\) 6.36277e9 2.49528
\(29\) −4.96957e9 −1.55143 −0.775714 0.631084i \(-0.782610\pi\)
−0.775714 + 0.631084i \(0.782610\pi\)
\(30\) 5.15120e9 1.29009
\(31\) −2.62498e9 −0.531221 −0.265611 0.964080i \(-0.585574\pi\)
−0.265611 + 0.964080i \(0.585574\pi\)
\(32\) −5.23132e9 −0.861265
\(33\) 4.47218e9 0.602807
\(34\) 3.02469e9 0.335790
\(35\) 1.48898e10 1.36914
\(36\) −1.88245e10 −1.44131
\(37\) −2.75230e9 −0.176354 −0.0881768 0.996105i \(-0.528104\pi\)
−0.0881768 + 0.996105i \(0.528104\pi\)
\(38\) −1.58581e10 −0.854394
\(39\) 7.06324e9 0.321428
\(40\) −6.87506e10 −2.65391
\(41\) −1.94142e10 −0.638298 −0.319149 0.947704i \(-0.603397\pi\)
−0.319149 + 0.947704i \(0.603397\pi\)
\(42\) 4.24758e10 1.19405
\(43\) 4.24240e10 1.02345 0.511725 0.859149i \(-0.329007\pi\)
0.511725 + 0.859149i \(0.329007\pi\)
\(44\) −1.08748e11 −2.25932
\(45\) −4.40521e10 −0.790833
\(46\) −1.80468e11 −2.80850
\(47\) 1.20787e11 1.63449 0.817246 0.576290i \(-0.195500\pi\)
0.817246 + 0.576290i \(0.195500\pi\)
\(48\) −8.50372e10 −1.00355
\(49\) 2.58895e10 0.267208
\(50\) −9.49692e10 −0.859563
\(51\) 1.39145e10 0.110729
\(52\) −1.71753e11 −1.20471
\(53\) 4.20067e10 0.260330 0.130165 0.991492i \(-0.458449\pi\)
0.130165 + 0.991492i \(0.458449\pi\)
\(54\) −3.18933e11 −1.75041
\(55\) −2.54486e11 −1.23967
\(56\) −5.66904e11 −2.45633
\(57\) −7.29524e10 −0.281743
\(58\) 8.06705e11 2.78249
\(59\) 6.60516e10 0.203866 0.101933 0.994791i \(-0.467497\pi\)
0.101933 + 0.994791i \(0.467497\pi\)
\(60\) −5.76232e11 −1.59446
\(61\) −2.71752e11 −0.675349 −0.337675 0.941263i \(-0.609640\pi\)
−0.337675 + 0.941263i \(0.609640\pi\)
\(62\) 4.26111e11 0.952745
\(63\) −3.63245e11 −0.731957
\(64\) −8.36605e10 −0.152177
\(65\) −4.01928e11 −0.661014
\(66\) −7.25964e11 −1.08113
\(67\) 5.91218e10 0.0798475 0.0399238 0.999203i \(-0.487288\pi\)
0.0399238 + 0.999203i \(0.487288\pi\)
\(68\) −3.38353e11 −0.415013
\(69\) −8.30212e11 −0.926125
\(70\) −2.41705e12 −2.45555
\(71\) 1.68901e10 0.0156478 0.00782390 0.999969i \(-0.497510\pi\)
0.00782390 + 0.999969i \(0.497510\pi\)
\(72\) 1.67721e12 1.41881
\(73\) 4.60459e11 0.356116 0.178058 0.984020i \(-0.443018\pi\)
0.178058 + 0.984020i \(0.443018\pi\)
\(74\) 4.46778e11 0.316290
\(75\) −4.36888e11 −0.283447
\(76\) 1.77395e12 1.05597
\(77\) −2.09844e12 −1.14738
\(78\) −1.14657e12 −0.576481
\(79\) 3.32303e11 0.153801 0.0769003 0.997039i \(-0.475498\pi\)
0.0769003 + 0.997039i \(0.475498\pi\)
\(80\) 4.83897e12 2.06380
\(81\) 1.85586e11 0.0730117
\(82\) 3.15148e12 1.14479
\(83\) 3.09461e12 1.03896 0.519480 0.854483i \(-0.326126\pi\)
0.519480 + 0.854483i \(0.326126\pi\)
\(84\) −4.75150e12 −1.47576
\(85\) −7.91795e11 −0.227714
\(86\) −6.88665e12 −1.83556
\(87\) 3.71110e12 0.917546
\(88\) 9.68910e12 2.22406
\(89\) −1.81559e12 −0.387242 −0.193621 0.981076i \(-0.562023\pi\)
−0.193621 + 0.981076i \(0.562023\pi\)
\(90\) 7.15093e12 1.41836
\(91\) −3.31422e12 −0.611803
\(92\) 2.01878e13 3.47112
\(93\) 1.96025e12 0.314175
\(94\) −1.96072e13 −2.93146
\(95\) 4.15129e12 0.579402
\(96\) 3.90657e12 0.509369
\(97\) −9.21227e12 −1.12292 −0.561462 0.827502i \(-0.689761\pi\)
−0.561462 + 0.827502i \(0.689761\pi\)
\(98\) −4.20262e12 −0.479237
\(99\) 6.20831e12 0.662742
\(100\) 1.06236e13 1.06236
\(101\) 9.07216e12 0.850398 0.425199 0.905100i \(-0.360204\pi\)
0.425199 + 0.905100i \(0.360204\pi\)
\(102\) −2.25873e12 −0.198593
\(103\) −3.75852e12 −0.310152 −0.155076 0.987903i \(-0.549562\pi\)
−0.155076 + 0.987903i \(0.549562\pi\)
\(104\) 1.53027e13 1.18591
\(105\) −1.11192e13 −0.809735
\(106\) −6.81890e12 −0.466903
\(107\) −2.15266e13 −1.38669 −0.693346 0.720605i \(-0.743864\pi\)
−0.693346 + 0.720605i \(0.743864\pi\)
\(108\) 3.56770e13 2.16338
\(109\) −2.52865e13 −1.44416 −0.722082 0.691808i \(-0.756815\pi\)
−0.722082 + 0.691808i \(0.756815\pi\)
\(110\) 4.13104e13 2.22335
\(111\) 2.05532e12 0.104299
\(112\) 3.99012e13 1.91016
\(113\) 4.73239e12 0.213831 0.106915 0.994268i \(-0.465903\pi\)
0.106915 + 0.994268i \(0.465903\pi\)
\(114\) 1.18423e13 0.505306
\(115\) 4.72425e13 1.90457
\(116\) −9.02410e13 −3.43896
\(117\) 9.80523e12 0.353386
\(118\) −1.07221e13 −0.365634
\(119\) −6.52899e12 −0.210761
\(120\) 5.13406e13 1.56958
\(121\) 1.34221e12 0.0388791
\(122\) 4.41132e13 1.21124
\(123\) 1.44978e13 0.377502
\(124\) −4.76663e13 −1.17753
\(125\) −2.70119e13 −0.633344
\(126\) 5.89652e13 1.31277
\(127\) −3.35833e13 −0.710229 −0.355115 0.934823i \(-0.615558\pi\)
−0.355115 + 0.934823i \(0.615558\pi\)
\(128\) 5.64355e13 1.13419
\(129\) −3.16808e13 −0.605289
\(130\) 6.52445e13 1.18553
\(131\) 8.92494e13 1.54291 0.771457 0.636281i \(-0.219528\pi\)
0.771457 + 0.636281i \(0.219528\pi\)
\(132\) 8.12090e13 1.33621
\(133\) 3.42308e13 0.536267
\(134\) −9.59718e12 −0.143206
\(135\) 8.34893e13 1.18703
\(136\) 3.01463e13 0.408536
\(137\) 1.03021e13 0.133119 0.0665597 0.997782i \(-0.478798\pi\)
0.0665597 + 0.997782i \(0.478798\pi\)
\(138\) 1.34767e14 1.66101
\(139\) 4.06661e13 0.478229 0.239115 0.970991i \(-0.423143\pi\)
0.239115 + 0.970991i \(0.423143\pi\)
\(140\) 2.70380e14 3.03489
\(141\) −9.01992e13 −0.966671
\(142\) −2.74176e12 −0.0280643
\(143\) 5.66441e13 0.553950
\(144\) −1.18049e14 −1.10333
\(145\) −2.11177e14 −1.88693
\(146\) −7.47458e13 −0.638695
\(147\) −1.93334e13 −0.158032
\(148\) −4.99782e13 −0.390913
\(149\) −1.13626e14 −0.850683 −0.425341 0.905033i \(-0.639846\pi\)
−0.425341 + 0.905033i \(0.639846\pi\)
\(150\) 7.09197e13 0.508362
\(151\) 1.75889e14 1.20750 0.603752 0.797172i \(-0.293672\pi\)
0.603752 + 0.797172i \(0.293672\pi\)
\(152\) −1.58053e14 −1.03949
\(153\) 1.93163e13 0.121739
\(154\) 3.40637e14 2.05782
\(155\) −1.11546e14 −0.646098
\(156\) 1.28259e14 0.712491
\(157\) 1.17561e14 0.626492 0.313246 0.949672i \(-0.398584\pi\)
0.313246 + 0.949672i \(0.398584\pi\)
\(158\) −5.39424e13 −0.275841
\(159\) −3.13691e13 −0.153965
\(160\) −2.22300e14 −1.04751
\(161\) 3.89552e14 1.76278
\(162\) −3.01260e13 −0.130946
\(163\) 4.03818e14 1.68642 0.843211 0.537583i \(-0.180663\pi\)
0.843211 + 0.537583i \(0.180663\pi\)
\(164\) −3.52536e14 −1.41488
\(165\) 1.90041e14 0.733165
\(166\) −5.02346e14 −1.86337
\(167\) 5.35696e12 0.0191100 0.00955501 0.999954i \(-0.496959\pi\)
0.00955501 + 0.999954i \(0.496959\pi\)
\(168\) 4.23344e14 1.45273
\(169\) −2.13413e14 −0.704624
\(170\) 1.28531e14 0.408405
\(171\) −1.01273e14 −0.309755
\(172\) 7.70366e14 2.26862
\(173\) −5.00040e13 −0.141809 −0.0709047 0.997483i \(-0.522589\pi\)
−0.0709047 + 0.997483i \(0.522589\pi\)
\(174\) −6.02420e14 −1.64562
\(175\) 2.04997e14 0.539511
\(176\) −6.81961e14 −1.72953
\(177\) −4.93250e13 −0.120571
\(178\) 2.94723e14 0.694518
\(179\) −2.96394e14 −0.673481 −0.336740 0.941597i \(-0.609325\pi\)
−0.336740 + 0.941597i \(0.609325\pi\)
\(180\) −7.99929e14 −1.75299
\(181\) −4.54526e14 −0.960833 −0.480417 0.877040i \(-0.659515\pi\)
−0.480417 + 0.877040i \(0.659515\pi\)
\(182\) 5.37993e14 1.09727
\(183\) 2.02935e14 0.399415
\(184\) −1.79868e15 −3.41694
\(185\) −1.16956e14 −0.214490
\(186\) −3.18205e14 −0.563472
\(187\) 1.11589e14 0.190831
\(188\) 2.19333e15 3.62308
\(189\) 6.88437e14 1.09866
\(190\) −6.73876e14 −1.03916
\(191\) −3.86368e14 −0.575816 −0.287908 0.957658i \(-0.592960\pi\)
−0.287908 + 0.957658i \(0.592960\pi\)
\(192\) 6.24747e13 0.0900008
\(193\) −1.06327e15 −1.48088 −0.740441 0.672121i \(-0.765383\pi\)
−0.740441 + 0.672121i \(0.765383\pi\)
\(194\) 1.49542e15 2.01396
\(195\) 3.00146e14 0.390937
\(196\) 4.70120e14 0.592303
\(197\) −5.84517e13 −0.0712470
\(198\) −1.00779e15 −1.18863
\(199\) −9.48385e14 −1.08253 −0.541265 0.840852i \(-0.682054\pi\)
−0.541265 + 0.840852i \(0.682054\pi\)
\(200\) −9.46531e14 −1.04578
\(201\) −4.41501e13 −0.0472234
\(202\) −1.47268e15 −1.52519
\(203\) −1.74133e15 −1.74645
\(204\) 2.52670e14 0.245447
\(205\) −8.24987e14 −0.776331
\(206\) 6.10117e14 0.556258
\(207\) −1.15251e15 −1.01821
\(208\) −1.07707e15 −0.922216
\(209\) −5.85046e14 −0.485556
\(210\) 1.80497e15 1.45226
\(211\) 3.33389e14 0.260085 0.130043 0.991508i \(-0.458489\pi\)
0.130043 + 0.991508i \(0.458489\pi\)
\(212\) 7.62787e14 0.577059
\(213\) −1.26130e13 −0.00925443
\(214\) 3.49439e15 2.48703
\(215\) 1.80277e15 1.24477
\(216\) −3.17871e15 −2.12962
\(217\) −9.19787e14 −0.597997
\(218\) 4.10473e15 2.59011
\(219\) −3.43854e14 −0.210614
\(220\) −4.62113e15 −2.74790
\(221\) 1.76240e14 0.101755
\(222\) −3.33638e14 −0.187060
\(223\) 2.27974e14 0.124138 0.0620690 0.998072i \(-0.480230\pi\)
0.0620690 + 0.998072i \(0.480230\pi\)
\(224\) −1.83304e15 −0.969528
\(225\) −6.06491e14 −0.311629
\(226\) −7.68204e14 −0.383506
\(227\) 1.70547e15 0.827326 0.413663 0.910430i \(-0.364249\pi\)
0.413663 + 0.910430i \(0.364249\pi\)
\(228\) −1.32472e15 −0.624523
\(229\) 1.27399e14 0.0583761 0.0291881 0.999574i \(-0.490708\pi\)
0.0291881 + 0.999574i \(0.490708\pi\)
\(230\) −7.66883e15 −3.41585
\(231\) 1.56704e15 0.678582
\(232\) 8.04021e15 3.38529
\(233\) 4.26980e15 1.74821 0.874105 0.485737i \(-0.161449\pi\)
0.874105 + 0.485737i \(0.161449\pi\)
\(234\) −1.59167e15 −0.633798
\(235\) 5.13271e15 1.98795
\(236\) 1.19941e15 0.451898
\(237\) −2.48152e14 −0.0909607
\(238\) 1.05984e15 0.378000
\(239\) 4.20711e15 1.46015 0.730075 0.683367i \(-0.239485\pi\)
0.730075 + 0.683367i \(0.239485\pi\)
\(240\) −3.61357e15 −1.22057
\(241\) 1.04381e15 0.343172 0.171586 0.985169i \(-0.445111\pi\)
0.171586 + 0.985169i \(0.445111\pi\)
\(242\) −2.17880e14 −0.0697297
\(243\) −3.27100e15 −1.01916
\(244\) −4.93466e15 −1.49701
\(245\) 1.10015e15 0.324991
\(246\) −2.35342e15 −0.677050
\(247\) −9.24006e14 −0.258908
\(248\) 4.24693e15 1.15915
\(249\) −2.31095e15 −0.614462
\(250\) 4.38481e15 1.13590
\(251\) −2.28174e15 −0.575952 −0.287976 0.957638i \(-0.592982\pi\)
−0.287976 + 0.957638i \(0.592982\pi\)
\(252\) −6.59606e15 −1.62249
\(253\) −6.65794e15 −1.59609
\(254\) 5.45154e15 1.27380
\(255\) 5.91285e14 0.134675
\(256\) −8.47578e15 −1.88200
\(257\) 1.65545e15 0.358385 0.179192 0.983814i \(-0.442652\pi\)
0.179192 + 0.983814i \(0.442652\pi\)
\(258\) 5.14271e15 1.08559
\(259\) −9.64399e14 −0.198522
\(260\) −7.29849e15 −1.46523
\(261\) 5.15178e15 1.00877
\(262\) −1.44878e16 −2.76722
\(263\) −7.60655e15 −1.41734 −0.708672 0.705538i \(-0.750705\pi\)
−0.708672 + 0.705538i \(0.750705\pi\)
\(264\) −7.23548e15 −1.31535
\(265\) 1.78503e15 0.316627
\(266\) −5.55665e15 −0.961794
\(267\) 1.35582e15 0.229022
\(268\) 1.07358e15 0.176993
\(269\) −1.69749e15 −0.273160 −0.136580 0.990629i \(-0.543611\pi\)
−0.136580 + 0.990629i \(0.543611\pi\)
\(270\) −1.35527e16 −2.12894
\(271\) 6.37386e15 0.977467 0.488733 0.872433i \(-0.337459\pi\)
0.488733 + 0.872433i \(0.337459\pi\)
\(272\) −2.12182e15 −0.317696
\(273\) 2.47494e15 0.361833
\(274\) −1.67233e15 −0.238750
\(275\) −3.50365e15 −0.488493
\(276\) −1.50756e16 −2.05289
\(277\) −6.40106e15 −0.851399 −0.425700 0.904865i \(-0.639972\pi\)
−0.425700 + 0.904865i \(0.639972\pi\)
\(278\) −6.60129e15 −0.857704
\(279\) 2.72123e15 0.345412
\(280\) −2.40901e16 −2.98752
\(281\) −1.29626e16 −1.57073 −0.785366 0.619032i \(-0.787525\pi\)
−0.785366 + 0.619032i \(0.787525\pi\)
\(282\) 1.46420e16 1.73372
\(283\) 9.27970e15 1.07380 0.536898 0.843647i \(-0.319596\pi\)
0.536898 + 0.843647i \(0.319596\pi\)
\(284\) 3.06703e14 0.0346856
\(285\) −3.10004e15 −0.342670
\(286\) −9.19498e15 −0.993509
\(287\) −6.80268e15 −0.718534
\(288\) 5.42313e15 0.560014
\(289\) −9.55739e15 −0.964946
\(290\) 3.42802e16 3.38420
\(291\) 6.87941e15 0.664120
\(292\) 8.36134e15 0.789382
\(293\) −3.31521e15 −0.306106 −0.153053 0.988218i \(-0.548910\pi\)
−0.153053 + 0.988218i \(0.548910\pi\)
\(294\) 3.13837e15 0.283430
\(295\) 2.80680e15 0.247952
\(296\) 4.45291e15 0.384811
\(297\) −1.17662e16 −0.994766
\(298\) 1.84448e16 1.52570
\(299\) −1.05154e16 −0.851063
\(300\) −7.93333e15 −0.628301
\(301\) 1.48653e16 1.15210
\(302\) −2.85519e16 −2.16566
\(303\) −6.77478e15 −0.502942
\(304\) 1.11245e16 0.808354
\(305\) −1.15478e16 −0.821394
\(306\) −3.13559e15 −0.218338
\(307\) −2.77278e16 −1.89023 −0.945117 0.326733i \(-0.894052\pi\)
−0.945117 + 0.326733i \(0.894052\pi\)
\(308\) −3.81049e16 −2.54332
\(309\) 2.80673e15 0.183430
\(310\) 1.81072e16 1.15878
\(311\) 6.46299e14 0.0405033 0.0202517 0.999795i \(-0.493553\pi\)
0.0202517 + 0.999795i \(0.493553\pi\)
\(312\) −1.14275e16 −0.701370
\(313\) 9.90931e15 0.595669 0.297835 0.954617i \(-0.403736\pi\)
0.297835 + 0.954617i \(0.403736\pi\)
\(314\) −1.90836e16 −1.12361
\(315\) −1.54357e16 −0.890244
\(316\) 6.03419e15 0.340920
\(317\) 1.24515e16 0.689188 0.344594 0.938752i \(-0.388017\pi\)
0.344594 + 0.938752i \(0.388017\pi\)
\(318\) 5.09212e15 0.276135
\(319\) 2.97614e16 1.58130
\(320\) −3.55507e15 −0.185086
\(321\) 1.60753e16 0.820117
\(322\) −6.32357e16 −3.16154
\(323\) −1.82029e15 −0.0891916
\(324\) 3.37000e15 0.161841
\(325\) −5.53358e15 −0.260474
\(326\) −6.55514e16 −3.02460
\(327\) 1.88831e16 0.854107
\(328\) 3.14100e16 1.39280
\(329\) 4.23233e16 1.83995
\(330\) −3.08492e16 −1.31493
\(331\) −4.07958e16 −1.70504 −0.852518 0.522698i \(-0.824925\pi\)
−0.852518 + 0.522698i \(0.824925\pi\)
\(332\) 5.61942e16 2.30300
\(333\) 2.85321e15 0.114669
\(334\) −8.69590e14 −0.0342738
\(335\) 2.51232e15 0.0971146
\(336\) −2.97968e16 −1.12970
\(337\) 3.12302e16 1.16139 0.580697 0.814120i \(-0.302780\pi\)
0.580697 + 0.814120i \(0.302780\pi\)
\(338\) 3.46431e16 1.26374
\(339\) −3.53398e15 −0.126464
\(340\) −1.43780e16 −0.504760
\(341\) 1.57203e16 0.541449
\(342\) 1.64396e16 0.555546
\(343\) −2.48781e16 −0.824907
\(344\) −6.86373e16 −2.23321
\(345\) −3.52791e16 −1.12640
\(346\) 8.11710e15 0.254335
\(347\) 3.05257e16 0.938693 0.469347 0.883014i \(-0.344489\pi\)
0.469347 + 0.883014i \(0.344489\pi\)
\(348\) 6.73889e16 2.03387
\(349\) 1.52268e16 0.451068 0.225534 0.974235i \(-0.427587\pi\)
0.225534 + 0.974235i \(0.427587\pi\)
\(350\) −3.32770e16 −0.967612
\(351\) −1.85833e16 −0.530428
\(352\) 3.13290e16 0.877848
\(353\) −3.41502e16 −0.939416 −0.469708 0.882822i \(-0.655641\pi\)
−0.469708 + 0.882822i \(0.655641\pi\)
\(354\) 8.00688e15 0.216243
\(355\) 7.17730e14 0.0190317
\(356\) −3.29687e16 −0.858376
\(357\) 4.87562e15 0.124648
\(358\) 4.81134e16 1.20789
\(359\) −3.06264e15 −0.0755060 −0.0377530 0.999287i \(-0.512020\pi\)
−0.0377530 + 0.999287i \(0.512020\pi\)
\(360\) 7.12713e16 1.72563
\(361\) −3.25094e16 −0.773058
\(362\) 7.37828e16 1.72325
\(363\) −1.00232e15 −0.0229939
\(364\) −6.01819e16 −1.35615
\(365\) 1.95667e16 0.433127
\(366\) −3.29422e16 −0.716350
\(367\) 3.05179e15 0.0651965 0.0325983 0.999469i \(-0.489622\pi\)
0.0325983 + 0.999469i \(0.489622\pi\)
\(368\) 1.26599e17 2.65717
\(369\) 2.01260e16 0.415036
\(370\) 1.89854e16 0.384688
\(371\) 1.47190e16 0.293055
\(372\) 3.55955e16 0.696413
\(373\) 5.72453e16 1.10061 0.550304 0.834965i \(-0.314512\pi\)
0.550304 + 0.834965i \(0.314512\pi\)
\(374\) −1.81141e16 −0.342256
\(375\) 2.01715e16 0.374572
\(376\) −1.95419e17 −3.56653
\(377\) 4.70044e16 0.843179
\(378\) −1.11753e17 −1.97044
\(379\) −3.63276e16 −0.629624 −0.314812 0.949154i \(-0.601941\pi\)
−0.314812 + 0.949154i \(0.601941\pi\)
\(380\) 7.53822e16 1.28433
\(381\) 2.50788e16 0.420044
\(382\) 6.27187e16 1.03273
\(383\) −1.50985e16 −0.244423 −0.122212 0.992504i \(-0.538999\pi\)
−0.122212 + 0.992504i \(0.538999\pi\)
\(384\) −4.21441e16 −0.670785
\(385\) −8.91711e16 −1.39550
\(386\) 1.72599e17 2.65596
\(387\) −4.39795e16 −0.665470
\(388\) −1.67283e17 −2.48912
\(389\) 7.25477e16 1.06158 0.530788 0.847505i \(-0.321896\pi\)
0.530788 + 0.847505i \(0.321896\pi\)
\(390\) −4.87223e16 −0.701145
\(391\) −2.07152e16 −0.293184
\(392\) −4.18863e16 −0.583059
\(393\) −6.66484e16 −0.912510
\(394\) 9.48841e15 0.127782
\(395\) 1.41209e16 0.187060
\(396\) 1.12735e17 1.46906
\(397\) −3.48870e16 −0.447224 −0.223612 0.974678i \(-0.571785\pi\)
−0.223612 + 0.974678i \(0.571785\pi\)
\(398\) 1.53950e17 1.94152
\(399\) −2.55623e16 −0.317159
\(400\) 6.66210e16 0.813244
\(401\) 8.74223e16 1.04999 0.524993 0.851106i \(-0.324068\pi\)
0.524993 + 0.851106i \(0.324068\pi\)
\(402\) 7.16684e15 0.0846952
\(403\) 2.48282e16 0.288711
\(404\) 1.64739e17 1.88503
\(405\) 7.88630e15 0.0888005
\(406\) 2.82668e17 3.13225
\(407\) 1.64828e16 0.179749
\(408\) −2.25122e16 −0.241616
\(409\) 9.48305e16 1.00172 0.500860 0.865528i \(-0.333017\pi\)
0.500860 + 0.865528i \(0.333017\pi\)
\(410\) 1.33919e17 1.39235
\(411\) −7.69324e15 −0.0787295
\(412\) −6.82499e16 −0.687496
\(413\) 2.31443e16 0.229493
\(414\) 1.87085e17 1.82615
\(415\) 1.31503e17 1.26364
\(416\) 4.94802e16 0.468085
\(417\) −3.03680e16 −0.282834
\(418\) 9.49700e16 0.870845
\(419\) 1.04698e17 0.945247 0.472623 0.881264i \(-0.343307\pi\)
0.472623 + 0.881264i \(0.343307\pi\)
\(420\) −2.01910e17 −1.79489
\(421\) 1.21829e17 1.06639 0.533197 0.845991i \(-0.320990\pi\)
0.533197 + 0.845991i \(0.320990\pi\)
\(422\) −5.41188e16 −0.466463
\(423\) −1.25215e17 −1.06278
\(424\) −6.79621e16 −0.568053
\(425\) −1.09011e16 −0.0897311
\(426\) 2.04745e15 0.0165978
\(427\) −9.52211e16 −0.760243
\(428\) −3.90895e17 −3.07380
\(429\) −4.22998e16 −0.327617
\(430\) −2.92642e17 −2.23250
\(431\) 9.93881e16 0.746848 0.373424 0.927661i \(-0.378184\pi\)
0.373424 + 0.927661i \(0.378184\pi\)
\(432\) 2.23732e17 1.65609
\(433\) −1.61579e17 −1.17818 −0.589092 0.808066i \(-0.700515\pi\)
−0.589092 + 0.808066i \(0.700515\pi\)
\(434\) 1.49308e17 1.07251
\(435\) 1.57700e17 1.11597
\(436\) −4.59170e17 −3.20119
\(437\) 1.08608e17 0.745986
\(438\) 5.58176e16 0.377737
\(439\) −1.15662e17 −0.771208 −0.385604 0.922664i \(-0.626007\pi\)
−0.385604 + 0.922664i \(0.626007\pi\)
\(440\) 4.11729e17 2.70501
\(441\) −2.68387e16 −0.173744
\(442\) −2.86089e16 −0.182497
\(443\) −4.96027e16 −0.311803 −0.155902 0.987773i \(-0.549828\pi\)
−0.155902 + 0.987773i \(0.549828\pi\)
\(444\) 3.73220e16 0.231193
\(445\) −7.71516e16 −0.470983
\(446\) −3.70069e16 −0.222641
\(447\) 8.48521e16 0.503111
\(448\) −2.93144e16 −0.171307
\(449\) −1.63273e17 −0.940404 −0.470202 0.882559i \(-0.655819\pi\)
−0.470202 + 0.882559i \(0.655819\pi\)
\(450\) 9.84512e16 0.558907
\(451\) 1.16266e17 0.650588
\(452\) 8.59341e16 0.473986
\(453\) −1.31348e17 −0.714142
\(454\) −2.76848e17 −1.48381
\(455\) −1.40834e17 −0.744106
\(456\) 1.18029e17 0.614776
\(457\) −1.29183e17 −0.663361 −0.331681 0.943392i \(-0.607616\pi\)
−0.331681 + 0.943392i \(0.607616\pi\)
\(458\) −2.06806e16 −0.104698
\(459\) −3.66090e16 −0.182728
\(460\) 8.57863e17 4.22175
\(461\) −3.53577e17 −1.71565 −0.857824 0.513944i \(-0.828184\pi\)
−0.857824 + 0.513944i \(0.828184\pi\)
\(462\) −2.54376e17 −1.21704
\(463\) 4.66410e16 0.220035 0.110017 0.993930i \(-0.464909\pi\)
0.110017 + 0.993930i \(0.464909\pi\)
\(464\) −5.65905e17 −2.63255
\(465\) 8.32988e16 0.382115
\(466\) −6.93112e17 −3.13541
\(467\) 5.02655e16 0.224238 0.112119 0.993695i \(-0.464236\pi\)
0.112119 + 0.993695i \(0.464236\pi\)
\(468\) 1.78050e17 0.783331
\(469\) 2.07161e16 0.0898846
\(470\) −8.33188e17 −3.56539
\(471\) −8.77904e16 −0.370520
\(472\) −1.06864e17 −0.444845
\(473\) −2.54066e17 −1.04316
\(474\) 4.02823e16 0.163138
\(475\) 5.71534e16 0.228314
\(476\) −1.18558e17 −0.467182
\(477\) −4.35468e16 −0.169273
\(478\) −6.82936e17 −2.61878
\(479\) 4.33037e17 1.63811 0.819056 0.573713i \(-0.194498\pi\)
0.819056 + 0.573713i \(0.194498\pi\)
\(480\) 1.66006e17 0.619520
\(481\) 2.60325e16 0.0958456
\(482\) −1.69441e17 −0.615479
\(483\) −2.90904e17 −1.04254
\(484\) 2.43729e16 0.0861811
\(485\) −3.91467e17 −1.36576
\(486\) 5.30979e17 1.82785
\(487\) −1.64726e17 −0.559532 −0.279766 0.960068i \(-0.590257\pi\)
−0.279766 + 0.960068i \(0.590257\pi\)
\(488\) 4.39664e17 1.47364
\(489\) −3.01557e17 −0.997383
\(490\) −1.78586e17 −0.582872
\(491\) −5.52532e17 −1.77962 −0.889811 0.456329i \(-0.849164\pi\)
−0.889811 + 0.456329i \(0.849164\pi\)
\(492\) 2.63262e17 0.836787
\(493\) 9.25984e16 0.290468
\(494\) 1.49993e17 0.464351
\(495\) 2.63816e17 0.806060
\(496\) −2.98917e17 −0.901405
\(497\) 5.91826e15 0.0176148
\(498\) 3.75134e17 1.10204
\(499\) −8.42351e16 −0.244253 −0.122126 0.992515i \(-0.538971\pi\)
−0.122126 + 0.992515i \(0.538971\pi\)
\(500\) −4.90501e17 −1.40390
\(501\) −4.00039e15 −0.0113020
\(502\) 3.70392e17 1.03297
\(503\) −4.11970e16 −0.113416 −0.0567079 0.998391i \(-0.518060\pi\)
−0.0567079 + 0.998391i \(0.518060\pi\)
\(504\) 5.87690e17 1.59716
\(505\) 3.85513e17 1.03430
\(506\) 1.08078e18 2.86258
\(507\) 1.59369e17 0.416729
\(508\) −6.09829e17 −1.57432
\(509\) 2.24293e17 0.571677 0.285839 0.958278i \(-0.407728\pi\)
0.285839 + 0.958278i \(0.407728\pi\)
\(510\) −9.59828e16 −0.241539
\(511\) 1.61344e17 0.400881
\(512\) 9.13545e17 2.24117
\(513\) 1.91937e17 0.464938
\(514\) −2.68727e17 −0.642763
\(515\) −1.59715e17 −0.377223
\(516\) −5.75282e17 −1.34171
\(517\) −7.23359e17 −1.66596
\(518\) 1.56550e17 0.356049
\(519\) 3.73412e16 0.0838689
\(520\) 6.50274e17 1.44236
\(521\) 1.17707e17 0.257843 0.128922 0.991655i \(-0.458848\pi\)
0.128922 + 0.991655i \(0.458848\pi\)
\(522\) −8.36283e17 −1.80924
\(523\) 5.82336e16 0.124426 0.0622132 0.998063i \(-0.480184\pi\)
0.0622132 + 0.998063i \(0.480184\pi\)
\(524\) 1.62065e18 3.42009
\(525\) −1.53085e17 −0.319077
\(526\) 1.23476e18 2.54200
\(527\) 4.89115e16 0.0994585
\(528\) 5.09265e17 1.02288
\(529\) 7.31938e17 1.45215
\(530\) −2.89763e17 −0.567871
\(531\) −6.84733e16 −0.132558
\(532\) 6.21587e17 1.18871
\(533\) 1.83628e17 0.346906
\(534\) −2.20089e17 −0.410752
\(535\) −9.14751e17 −1.68657
\(536\) −9.56525e16 −0.174231
\(537\) 2.21337e17 0.398310
\(538\) 2.75551e17 0.489912
\(539\) −1.55045e17 −0.272353
\(540\) 1.51606e18 2.63122
\(541\) −3.21741e17 −0.551726 −0.275863 0.961197i \(-0.588964\pi\)
−0.275863 + 0.961197i \(0.588964\pi\)
\(542\) −1.03466e18 −1.75309
\(543\) 3.39424e17 0.568256
\(544\) 9.74757e16 0.161251
\(545\) −1.07453e18 −1.75646
\(546\) −4.01755e17 −0.648947
\(547\) −7.83664e17 −1.25087 −0.625435 0.780276i \(-0.715078\pi\)
−0.625435 + 0.780276i \(0.715078\pi\)
\(548\) 1.87073e17 0.295078
\(549\) 2.81715e17 0.439127
\(550\) 5.68745e17 0.876113
\(551\) −4.85483e17 −0.739075
\(552\) 1.34319e18 2.02085
\(553\) 1.16438e17 0.173134
\(554\) 1.03908e18 1.52698
\(555\) 8.73389e16 0.126854
\(556\) 7.38444e17 1.06006
\(557\) −1.17598e18 −1.66856 −0.834281 0.551340i \(-0.814117\pi\)
−0.834281 + 0.551340i \(0.814117\pi\)
\(558\) −4.41734e17 −0.619496
\(559\) −4.01265e17 −0.556230
\(560\) 1.69556e18 2.32323
\(561\) −8.33305e16 −0.112861
\(562\) 2.10421e18 2.81711
\(563\) 9.32560e17 1.23416 0.617081 0.786899i \(-0.288315\pi\)
0.617081 + 0.786899i \(0.288315\pi\)
\(564\) −1.63790e18 −2.14276
\(565\) 2.01098e17 0.260072
\(566\) −1.50636e18 −1.92585
\(567\) 6.50289e16 0.0821895
\(568\) −2.73263e16 −0.0341442
\(569\) −1.17434e18 −1.45065 −0.725326 0.688405i \(-0.758311\pi\)
−0.725326 + 0.688405i \(0.758311\pi\)
\(570\) 5.03227e17 0.614578
\(571\) 2.00298e17 0.241847 0.120924 0.992662i \(-0.461414\pi\)
0.120924 + 0.992662i \(0.461414\pi\)
\(572\) 1.02858e18 1.22791
\(573\) 2.88526e17 0.340549
\(574\) 1.10427e18 1.28869
\(575\) 6.50416e17 0.750499
\(576\) 8.67278e16 0.0989492
\(577\) −8.49702e17 −0.958570 −0.479285 0.877659i \(-0.659104\pi\)
−0.479285 + 0.877659i \(0.659104\pi\)
\(578\) 1.55144e18 1.73063
\(579\) 7.94012e17 0.875823
\(580\) −3.83471e18 −4.18264
\(581\) 1.08435e18 1.16956
\(582\) −1.11673e18 −1.19110
\(583\) −2.51567e17 −0.265343
\(584\) −7.44971e17 −0.777062
\(585\) 4.16664e17 0.429806
\(586\) 5.38155e17 0.549000
\(587\) −1.87792e18 −1.89466 −0.947328 0.320265i \(-0.896228\pi\)
−0.947328 + 0.320265i \(0.896228\pi\)
\(588\) −3.51069e17 −0.350300
\(589\) −2.56438e17 −0.253065
\(590\) −4.55625e17 −0.444702
\(591\) 4.36497e16 0.0421369
\(592\) −3.13415e17 −0.299247
\(593\) −1.13216e18 −1.06918 −0.534590 0.845111i \(-0.679534\pi\)
−0.534590 + 0.845111i \(0.679534\pi\)
\(594\) 1.91000e18 1.78411
\(595\) −2.77443e17 −0.256338
\(596\) −2.06331e18 −1.88566
\(597\) 7.08221e17 0.640230
\(598\) 1.70695e18 1.52638
\(599\) 1.50059e18 1.32736 0.663681 0.748016i \(-0.268993\pi\)
0.663681 + 0.748016i \(0.268993\pi\)
\(600\) 7.06836e17 0.618494
\(601\) −1.25912e18 −1.08989 −0.544944 0.838472i \(-0.683449\pi\)
−0.544944 + 0.838472i \(0.683449\pi\)
\(602\) −2.41307e18 −2.06629
\(603\) −6.12895e16 −0.0519186
\(604\) 3.19392e18 2.67660
\(605\) 5.70361e16 0.0472868
\(606\) 1.09974e18 0.902026
\(607\) 1.68800e18 1.36976 0.684881 0.728655i \(-0.259854\pi\)
0.684881 + 0.728655i \(0.259854\pi\)
\(608\) −5.11054e17 −0.410293
\(609\) 1.30036e18 1.03288
\(610\) 1.87455e18 1.47317
\(611\) −1.14245e18 −0.888322
\(612\) 3.50759e17 0.269851
\(613\) −7.16924e17 −0.545733 −0.272866 0.962052i \(-0.587972\pi\)
−0.272866 + 0.962052i \(0.587972\pi\)
\(614\) 4.50102e18 3.39013
\(615\) 6.16071e17 0.459137
\(616\) 3.39504e18 2.50363
\(617\) −5.07239e16 −0.0370134 −0.0185067 0.999829i \(-0.505891\pi\)
−0.0185067 + 0.999829i \(0.505891\pi\)
\(618\) −4.55614e17 −0.328982
\(619\) −2.35708e17 −0.168417 −0.0842083 0.996448i \(-0.526836\pi\)
−0.0842083 + 0.996448i \(0.526836\pi\)
\(620\) −2.02553e18 −1.43217
\(621\) 2.18428e18 1.52831
\(622\) −1.04913e17 −0.0726427
\(623\) −6.36177e17 −0.435919
\(624\) 8.04319e17 0.545417
\(625\) −1.86200e18 −1.24957
\(626\) −1.60857e18 −1.06833
\(627\) 4.36892e17 0.287168
\(628\) 2.13476e18 1.38871
\(629\) 5.12838e16 0.0330180
\(630\) 2.50567e18 1.59665
\(631\) −1.20203e18 −0.758094 −0.379047 0.925377i \(-0.623748\pi\)
−0.379047 + 0.925377i \(0.623748\pi\)
\(632\) −5.37629e17 −0.335600
\(633\) −2.48964e17 −0.153820
\(634\) −2.02124e18 −1.23606
\(635\) −1.42709e18 −0.863817
\(636\) −5.69623e17 −0.341284
\(637\) −2.44874e17 −0.145223
\(638\) −4.83114e18 −2.83606
\(639\) −1.75094e16 −0.0101746
\(640\) 2.39817e18 1.37947
\(641\) −1.79680e18 −1.02311 −0.511556 0.859250i \(-0.670931\pi\)
−0.511556 + 0.859250i \(0.670931\pi\)
\(642\) −2.60949e18 −1.47088
\(643\) −2.49075e18 −1.38982 −0.694911 0.719095i \(-0.744556\pi\)
−0.694911 + 0.719095i \(0.744556\pi\)
\(644\) 7.07377e18 3.90745
\(645\) −1.34624e18 −0.736183
\(646\) 2.95486e17 0.159965
\(647\) 2.38898e18 1.28037 0.640183 0.768222i \(-0.278858\pi\)
0.640183 + 0.768222i \(0.278858\pi\)
\(648\) −3.00257e17 −0.159315
\(649\) −3.95565e17 −0.207791
\(650\) 8.98260e17 0.467160
\(651\) 6.86865e17 0.353668
\(652\) 7.33282e18 3.73819
\(653\) −3.08142e18 −1.55530 −0.777652 0.628695i \(-0.783589\pi\)
−0.777652 + 0.628695i \(0.783589\pi\)
\(654\) −3.06527e18 −1.53184
\(655\) 3.79257e18 1.87657
\(656\) −2.21077e18 −1.08310
\(657\) −4.77341e17 −0.231555
\(658\) −6.87031e18 −3.29995
\(659\) −2.86499e17 −0.136260 −0.0681299 0.997676i \(-0.521703\pi\)
−0.0681299 + 0.997676i \(0.521703\pi\)
\(660\) 3.45090e18 1.62516
\(661\) −2.61060e18 −1.21739 −0.608697 0.793403i \(-0.708308\pi\)
−0.608697 + 0.793403i \(0.708308\pi\)
\(662\) 6.62234e18 3.05798
\(663\) −1.31610e17 −0.0601798
\(664\) −5.00674e18 −2.26706
\(665\) 1.45460e18 0.652235
\(666\) −4.63159e17 −0.205659
\(667\) −5.52489e18 −2.42944
\(668\) 9.72755e16 0.0423600
\(669\) −1.70243e17 −0.0734176
\(670\) −4.07823e17 −0.174175
\(671\) 1.62745e18 0.688352
\(672\) 1.36885e18 0.573398
\(673\) −2.04496e18 −0.848373 −0.424186 0.905575i \(-0.639440\pi\)
−0.424186 + 0.905575i \(0.639440\pi\)
\(674\) −5.06956e18 −2.08296
\(675\) 1.14945e18 0.467751
\(676\) −3.87531e18 −1.56190
\(677\) −3.89797e17 −0.155601 −0.0778004 0.996969i \(-0.524790\pi\)
−0.0778004 + 0.996969i \(0.524790\pi\)
\(678\) 5.73668e17 0.226813
\(679\) −3.22796e18 −1.26408
\(680\) 1.28104e18 0.496882
\(681\) −1.27359e18 −0.489297
\(682\) −2.55186e18 −0.971089
\(683\) −1.91733e18 −0.722707 −0.361353 0.932429i \(-0.617685\pi\)
−0.361353 + 0.932429i \(0.617685\pi\)
\(684\) −1.83899e18 −0.686617
\(685\) 4.37777e17 0.161907
\(686\) 4.03843e18 1.47947
\(687\) −9.51371e16 −0.0345248
\(688\) 4.83099e18 1.73665
\(689\) −3.97318e17 −0.141486
\(690\) 5.72682e18 2.02020
\(691\) −1.63628e18 −0.571806 −0.285903 0.958259i \(-0.592294\pi\)
−0.285903 + 0.958259i \(0.592294\pi\)
\(692\) −9.08008e17 −0.314340
\(693\) 2.17538e18 0.746051
\(694\) −4.95520e18 −1.68355
\(695\) 1.72807e18 0.581647
\(696\) −6.00415e18 −2.00213
\(697\) 3.61746e17 0.119506
\(698\) −2.47175e18 −0.808991
\(699\) −3.18854e18 −1.03393
\(700\) 3.72248e18 1.19590
\(701\) −8.13845e17 −0.259045 −0.129522 0.991576i \(-0.541344\pi\)
−0.129522 + 0.991576i \(0.541344\pi\)
\(702\) 3.01661e18 0.951322
\(703\) −2.68875e17 −0.0840120
\(704\) 5.01020e17 0.155108
\(705\) −3.83293e18 −1.17571
\(706\) 5.54358e18 1.68484
\(707\) 3.17886e18 0.957295
\(708\) −8.95679e17 −0.267261
\(709\) 4.40859e18 1.30346 0.651732 0.758450i \(-0.274043\pi\)
0.651732 + 0.758450i \(0.274043\pi\)
\(710\) −1.16508e17 −0.0341333
\(711\) −3.44486e17 −0.100005
\(712\) 2.93742e18 0.844978
\(713\) −2.91831e18 −0.831858
\(714\) −7.91455e17 −0.223557
\(715\) 2.40704e18 0.673742
\(716\) −5.38214e18 −1.49287
\(717\) −3.14172e18 −0.863561
\(718\) 4.97155e17 0.135420
\(719\) −6.27952e18 −1.69508 −0.847538 0.530735i \(-0.821916\pi\)
−0.847538 + 0.530735i \(0.821916\pi\)
\(720\) −5.01639e18 −1.34193
\(721\) −1.31698e18 −0.349139
\(722\) 5.27722e18 1.38648
\(723\) −7.79483e17 −0.202959
\(724\) −8.25361e18 −2.12982
\(725\) −2.90740e18 −0.743546
\(726\) 1.62705e17 0.0412396
\(727\) −3.12809e18 −0.785789 −0.392895 0.919583i \(-0.628526\pi\)
−0.392895 + 0.919583i \(0.628526\pi\)
\(728\) 5.36203e18 1.33498
\(729\) 2.14679e18 0.529737
\(730\) −3.17625e18 −0.776813
\(731\) −7.90490e17 −0.191617
\(732\) 3.68503e18 0.885359
\(733\) 3.13690e18 0.747007 0.373503 0.927629i \(-0.378156\pi\)
0.373503 + 0.927629i \(0.378156\pi\)
\(734\) −4.95393e17 −0.116930
\(735\) −8.21553e17 −0.192206
\(736\) −5.81589e18 −1.34868
\(737\) −3.54065e17 −0.0813849
\(738\) −3.26703e18 −0.744367
\(739\) −6.09806e18 −1.37722 −0.688609 0.725132i \(-0.741779\pi\)
−0.688609 + 0.725132i \(0.741779\pi\)
\(740\) −2.12378e18 −0.475448
\(741\) 6.90016e17 0.153123
\(742\) −2.38933e18 −0.525594
\(743\) 1.84814e17 0.0403003 0.0201501 0.999797i \(-0.493586\pi\)
0.0201501 + 0.999797i \(0.493586\pi\)
\(744\) −3.17146e18 −0.685543
\(745\) −4.82843e18 −1.03464
\(746\) −9.29258e18 −1.97394
\(747\) −3.20808e18 −0.675555
\(748\) 2.02631e18 0.423004
\(749\) −7.54286e18 −1.56100
\(750\) −3.27442e18 −0.671795
\(751\) 4.88053e18 0.992675 0.496338 0.868130i \(-0.334678\pi\)
0.496338 + 0.868130i \(0.334678\pi\)
\(752\) 1.37545e19 2.77349
\(753\) 1.70392e18 0.340629
\(754\) −7.63018e18 −1.51224
\(755\) 7.47424e18 1.46863
\(756\) 1.25011e19 2.43533
\(757\) 7.33696e18 1.41708 0.708538 0.705673i \(-0.249355\pi\)
0.708538 + 0.705673i \(0.249355\pi\)
\(758\) 5.89702e18 1.12923
\(759\) 4.97192e18 0.943957
\(760\) −6.71633e18 −1.26428
\(761\) 5.30890e18 0.990841 0.495421 0.868653i \(-0.335014\pi\)
0.495421 + 0.868653i \(0.335014\pi\)
\(762\) −4.07102e18 −0.753348
\(763\) −8.86033e18 −1.62570
\(764\) −7.01594e18 −1.27638
\(765\) 8.20826e17 0.148065
\(766\) 2.45093e18 0.438373
\(767\) −6.24745e17 −0.110798
\(768\) 6.32942e18 1.11305
\(769\) −8.97182e18 −1.56444 −0.782221 0.623001i \(-0.785913\pi\)
−0.782221 + 0.623001i \(0.785913\pi\)
\(770\) 1.44751e19 2.50283
\(771\) −1.23623e18 −0.211956
\(772\) −1.93076e19 −3.28258
\(773\) 4.11811e18 0.694274 0.347137 0.937814i \(-0.387154\pi\)
0.347137 + 0.937814i \(0.387154\pi\)
\(774\) 7.13914e18 1.19352
\(775\) −1.53572e18 −0.254596
\(776\) 1.49044e19 2.45027
\(777\) 7.20180e17 0.117410
\(778\) −1.17766e19 −1.90394
\(779\) −1.89659e18 −0.304075
\(780\) 5.45026e18 0.866567
\(781\) −1.01150e17 −0.0159491
\(782\) 3.36268e18 0.525826
\(783\) −9.76386e18 −1.51415
\(784\) 2.94814e18 0.453413
\(785\) 4.99564e18 0.761971
\(786\) 1.08190e19 1.63659
\(787\) 5.69642e18 0.854606 0.427303 0.904108i \(-0.359464\pi\)
0.427303 + 0.904108i \(0.359464\pi\)
\(788\) −1.06141e18 −0.157929
\(789\) 5.68030e18 0.838245
\(790\) −2.29223e18 −0.335492
\(791\) 1.65822e18 0.240710
\(792\) −1.00443e19 −1.44613
\(793\) 2.57035e18 0.367042
\(794\) 5.66317e18 0.802096
\(795\) −1.33300e18 −0.187260
\(796\) −1.72215e19 −2.39958
\(797\) −1.05222e19 −1.45421 −0.727104 0.686527i \(-0.759134\pi\)
−0.727104 + 0.686527i \(0.759134\pi\)
\(798\) 4.14951e18 0.568824
\(799\) −2.25063e18 −0.306020
\(800\) −3.06054e18 −0.412775
\(801\) 1.88215e18 0.251793
\(802\) −1.41912e19 −1.88315
\(803\) −2.75756e18 −0.362973
\(804\) −8.01709e17 −0.104677
\(805\) 1.65537e19 2.14398
\(806\) −4.03034e18 −0.517803
\(807\) 1.26762e18 0.161552
\(808\) −1.46777e19 −1.85561
\(809\) 9.07498e18 1.13810 0.569050 0.822303i \(-0.307311\pi\)
0.569050 + 0.822303i \(0.307311\pi\)
\(810\) −1.28018e18 −0.159264
\(811\) 3.35438e18 0.413977 0.206989 0.978343i \(-0.433634\pi\)
0.206989 + 0.978343i \(0.433634\pi\)
\(812\) −3.16202e19 −3.87125
\(813\) −4.75978e18 −0.578093
\(814\) −2.67563e18 −0.322380
\(815\) 1.71599e19 2.05111
\(816\) 1.58450e18 0.187892
\(817\) 4.14445e18 0.487555
\(818\) −1.53937e19 −1.79658
\(819\) 3.43573e18 0.397808
\(820\) −1.49807e19 −1.72085
\(821\) −9.95459e18 −1.13447 −0.567235 0.823556i \(-0.691987\pi\)
−0.567235 + 0.823556i \(0.691987\pi\)
\(822\) 1.24884e18 0.141201
\(823\) −9.71689e18 −1.09000 −0.545002 0.838435i \(-0.683471\pi\)
−0.545002 + 0.838435i \(0.683471\pi\)
\(824\) 6.08086e18 0.676766
\(825\) 2.61641e18 0.288905
\(826\) −3.75699e18 −0.411595
\(827\) 1.41193e19 1.53472 0.767359 0.641218i \(-0.221570\pi\)
0.767359 + 0.641218i \(0.221570\pi\)
\(828\) −2.09280e19 −2.25700
\(829\) −9.41989e18 −1.00796 −0.503978 0.863717i \(-0.668131\pi\)
−0.503978 + 0.863717i \(0.668131\pi\)
\(830\) −2.13467e19 −2.26633
\(831\) 4.78009e18 0.503534
\(832\) 7.91298e17 0.0827062
\(833\) −4.82401e17 −0.0500283
\(834\) 4.92961e18 0.507263
\(835\) 2.27639e17 0.0232426
\(836\) −1.06237e19 −1.07630
\(837\) −5.15738e18 −0.518458
\(838\) −1.69955e19 −1.69530
\(839\) −2.59679e18 −0.257030 −0.128515 0.991708i \(-0.541021\pi\)
−0.128515 + 0.991708i \(0.541021\pi\)
\(840\) 1.79896e19 1.76688
\(841\) 1.44360e19 1.40693
\(842\) −1.97764e19 −1.91258
\(843\) 9.68004e18 0.928962
\(844\) 6.05392e18 0.576515
\(845\) −9.06878e18 −0.856999
\(846\) 2.03261e19 1.90610
\(847\) 4.70308e17 0.0437664
\(848\) 4.78347e18 0.441743
\(849\) −6.92976e18 −0.635065
\(850\) 1.76957e18 0.160933
\(851\) −3.05985e18 −0.276158
\(852\) −2.29035e17 −0.0205137
\(853\) −4.17360e18 −0.370973 −0.185486 0.982647i \(-0.559386\pi\)
−0.185486 + 0.982647i \(0.559386\pi\)
\(854\) 1.54572e19 1.36349
\(855\) −4.30350e18 −0.376740
\(856\) 3.48276e19 3.02582
\(857\) 3.62207e18 0.312307 0.156153 0.987733i \(-0.450091\pi\)
0.156153 + 0.987733i \(0.450091\pi\)
\(858\) 6.86649e18 0.587581
\(859\) −2.02485e19 −1.71964 −0.859818 0.510601i \(-0.829423\pi\)
−0.859818 + 0.510601i \(0.829423\pi\)
\(860\) 3.27360e19 2.75921
\(861\) 5.08000e18 0.424956
\(862\) −1.61336e19 −1.33947
\(863\) 3.99628e18 0.329295 0.164648 0.986352i \(-0.447351\pi\)
0.164648 + 0.986352i \(0.447351\pi\)
\(864\) −1.02781e19 −0.840572
\(865\) −2.12487e18 −0.172476
\(866\) 2.62289e19 2.11307
\(867\) 7.13712e18 0.570688
\(868\) −1.67022e19 −1.32555
\(869\) −1.99007e18 −0.156762
\(870\) −2.55992e19 −2.00148
\(871\) −5.59200e17 −0.0433960
\(872\) 4.09107e19 3.15123
\(873\) 9.55004e18 0.730151
\(874\) −1.76302e19 −1.33793
\(875\) −9.46489e18 −0.712957
\(876\) −6.24396e18 −0.466856
\(877\) 2.54327e19 1.88754 0.943769 0.330604i \(-0.107253\pi\)
0.943769 + 0.330604i \(0.107253\pi\)
\(878\) 1.87753e19 1.38316
\(879\) 2.47568e18 0.181037
\(880\) −2.89793e19 −2.10354
\(881\) 2.06368e19 1.48696 0.743479 0.668759i \(-0.233174\pi\)
0.743479 + 0.668759i \(0.233174\pi\)
\(882\) 4.35670e18 0.311611
\(883\) −1.35300e19 −0.960624 −0.480312 0.877098i \(-0.659477\pi\)
−0.480312 + 0.877098i \(0.659477\pi\)
\(884\) 3.20029e18 0.225554
\(885\) −2.09602e18 −0.146644
\(886\) 8.05195e18 0.559219
\(887\) 3.36990e18 0.232335 0.116167 0.993230i \(-0.462939\pi\)
0.116167 + 0.993230i \(0.462939\pi\)
\(888\) −3.32528e18 −0.227585
\(889\) −1.17675e19 −0.799508
\(890\) 1.25240e19 0.844708
\(891\) −1.11142e18 −0.0744175
\(892\) 4.13972e18 0.275169
\(893\) 1.17998e19 0.778645
\(894\) −1.37740e19 −0.902329
\(895\) −1.25950e19 −0.819122
\(896\) 1.97749e19 1.27677
\(897\) 7.85251e18 0.503336
\(898\) 2.65040e19 1.68661
\(899\) 1.30450e19 0.824152
\(900\) −1.10131e19 −0.690770
\(901\) −7.82714e17 −0.0487407
\(902\) −1.88734e19 −1.16683
\(903\) −1.11009e19 −0.681376
\(904\) −7.65647e18 −0.466589
\(905\) −1.93146e19 −1.16861
\(906\) 2.13216e19 1.28081
\(907\) 3.09059e19 1.84329 0.921647 0.388030i \(-0.126844\pi\)
0.921647 + 0.388030i \(0.126844\pi\)
\(908\) 3.09692e19 1.83388
\(909\) −9.40479e18 −0.552948
\(910\) 2.28615e19 1.33455
\(911\) 1.84380e19 1.06867 0.534335 0.845273i \(-0.320562\pi\)
0.534335 + 0.845273i \(0.320562\pi\)
\(912\) −8.30738e18 −0.478077
\(913\) −1.85328e19 −1.05896
\(914\) 2.09702e19 1.18974
\(915\) 8.62352e18 0.485789
\(916\) 2.31340e18 0.129399
\(917\) 3.12728e19 1.73686
\(918\) 5.94270e18 0.327723
\(919\) −2.32400e19 −1.27258 −0.636290 0.771450i \(-0.719532\pi\)
−0.636290 + 0.771450i \(0.719532\pi\)
\(920\) −7.64331e19 −4.15586
\(921\) 2.07061e19 1.11792
\(922\) 5.73958e19 3.07701
\(923\) −1.59754e17 −0.00850435
\(924\) 2.84555e19 1.50417
\(925\) −1.61021e18 −0.0845202
\(926\) −7.57119e18 −0.394633
\(927\) 3.89632e18 0.201668
\(928\) 2.59974e19 1.33619
\(929\) 1.90343e19 0.971482 0.485741 0.874103i \(-0.338550\pi\)
0.485741 + 0.874103i \(0.338550\pi\)
\(930\) −1.35218e19 −0.685324
\(931\) 2.52917e18 0.127293
\(932\) 7.75340e19 3.87515
\(933\) −4.82633e17 −0.0239545
\(934\) −8.15954e18 −0.402171
\(935\) 4.74185e18 0.232099
\(936\) −1.58638e19 −0.771105
\(937\) −1.97128e19 −0.951571 −0.475785 0.879561i \(-0.657836\pi\)
−0.475785 + 0.879561i \(0.657836\pi\)
\(938\) −3.36283e18 −0.161208
\(939\) −7.39993e18 −0.352291
\(940\) 9.32034e19 4.40657
\(941\) 3.14602e19 1.47717 0.738583 0.674163i \(-0.235496\pi\)
0.738583 + 0.674163i \(0.235496\pi\)
\(942\) 1.42509e19 0.664527
\(943\) −2.15836e19 −0.999534
\(944\) 7.52156e18 0.345931
\(945\) 2.92545e19 1.33624
\(946\) 4.12423e19 1.87090
\(947\) −2.53364e19 −1.14149 −0.570743 0.821129i \(-0.693345\pi\)
−0.570743 + 0.821129i \(0.693345\pi\)
\(948\) −4.50613e18 −0.201627
\(949\) −4.35522e18 −0.193544
\(950\) −9.27765e18 −0.409482
\(951\) −9.29837e18 −0.407599
\(952\) 1.05632e19 0.459890
\(953\) 2.67678e18 0.115747 0.0578734 0.998324i \(-0.481568\pi\)
0.0578734 + 0.998324i \(0.481568\pi\)
\(954\) 7.06891e18 0.303591
\(955\) −1.64183e19 −0.700337
\(956\) 7.63957e19 3.23663
\(957\) −2.22248e19 −0.935212
\(958\) −7.02944e19 −2.93795
\(959\) 3.60983e18 0.149853
\(960\) 2.65480e18 0.109464
\(961\) −1.75270e19 −0.717804
\(962\) −4.22582e18 −0.171899
\(963\) 2.23158e19 0.901658
\(964\) 1.89543e19 0.760689
\(965\) −4.51826e19 −1.80112
\(966\) 4.72222e19 1.86980
\(967\) 4.11667e19 1.61910 0.809551 0.587049i \(-0.199710\pi\)
0.809551 + 0.587049i \(0.199710\pi\)
\(968\) −2.17155e18 −0.0848360
\(969\) 1.35933e18 0.0527497
\(970\) 6.35464e19 2.44949
\(971\) −4.24821e19 −1.62660 −0.813301 0.581843i \(-0.802332\pi\)
−0.813301 + 0.581843i \(0.802332\pi\)
\(972\) −5.93972e19 −2.25910
\(973\) 1.42493e19 0.538344
\(974\) 2.67399e19 1.00352
\(975\) 4.13228e18 0.154049
\(976\) −3.09455e19 −1.14597
\(977\) 3.96415e19 1.45826 0.729131 0.684374i \(-0.239925\pi\)
0.729131 + 0.684374i \(0.239925\pi\)
\(978\) 4.89515e19 1.78881
\(979\) 1.08731e19 0.394698
\(980\) 1.99773e19 0.720389
\(981\) 2.62136e19 0.939027
\(982\) 8.96920e19 3.19175
\(983\) 5.12783e19 1.81274 0.906371 0.422482i \(-0.138841\pi\)
0.906371 + 0.422482i \(0.138841\pi\)
\(984\) −2.34559e19 −0.823727
\(985\) −2.48385e18 −0.0866543
\(986\) −1.50314e19 −0.520955
\(987\) −3.16056e19 −1.08818
\(988\) −1.67788e19 −0.573905
\(989\) 4.71646e19 1.60266
\(990\) −4.28250e19 −1.44567
\(991\) −3.75390e19 −1.25894 −0.629469 0.777026i \(-0.716727\pi\)
−0.629469 + 0.777026i \(0.716727\pi\)
\(992\) 1.37321e19 0.457522
\(993\) 3.04649e19 1.00839
\(994\) −9.60705e17 −0.0315921
\(995\) −4.03007e19 −1.31663
\(996\) −4.19639e19 −1.36204
\(997\) −3.80050e19 −1.22553 −0.612763 0.790266i \(-0.709942\pi\)
−0.612763 + 0.790266i \(0.709942\pi\)
\(998\) 1.36738e19 0.438067
\(999\) −5.40752e18 −0.172117
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 197.14.a.a.1.8 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.14.a.a.1.8 104 1.1 even 1 trivial