Properties

Label 177.14.a.a.1.20
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $30$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(1\)
Dimension: \(30\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+43.5631 q^{2} +729.000 q^{3} -6294.26 q^{4} -53819.8 q^{5} +31757.5 q^{6} -600256. q^{7} -631066. q^{8} +531441. q^{9} +O(q^{10})\) \(q+43.5631 q^{2} +729.000 q^{3} -6294.26 q^{4} -53819.8 q^{5} +31757.5 q^{6} -600256. q^{7} -631066. q^{8} +531441. q^{9} -2.34456e6 q^{10} +4.53623e6 q^{11} -4.58851e6 q^{12} +1.89968e7 q^{13} -2.61490e7 q^{14} -3.92347e7 q^{15} +2.40714e7 q^{16} +5.77965e7 q^{17} +2.31512e7 q^{18} -1.29263e7 q^{19} +3.38756e8 q^{20} -4.37587e8 q^{21} +1.97612e8 q^{22} +5.60284e8 q^{23} -4.60047e8 q^{24} +1.67587e9 q^{25} +8.27558e8 q^{26} +3.87420e8 q^{27} +3.77817e9 q^{28} -4.37208e9 q^{29} -1.70918e9 q^{30} -7.07112e9 q^{31} +6.21832e9 q^{32} +3.30691e9 q^{33} +2.51780e9 q^{34} +3.23057e10 q^{35} -3.34503e9 q^{36} +1.95842e10 q^{37} -5.63110e8 q^{38} +1.38486e10 q^{39} +3.39639e10 q^{40} +1.43851e10 q^{41} -1.90626e10 q^{42} +1.26442e10 q^{43} -2.85522e10 q^{44} -2.86021e10 q^{45} +2.44077e10 q^{46} -2.13046e10 q^{47} +1.75480e10 q^{48} +2.63418e11 q^{49} +7.30062e10 q^{50} +4.21337e10 q^{51} -1.19570e11 q^{52} +1.08144e11 q^{53} +1.68772e10 q^{54} -2.44139e11 q^{55} +3.78801e11 q^{56} -9.42327e9 q^{57} -1.90462e11 q^{58} +4.21805e10 q^{59} +2.46953e11 q^{60} -6.15544e11 q^{61} -3.08040e11 q^{62} -3.19001e11 q^{63} +7.36966e10 q^{64} -1.02240e12 q^{65} +1.44059e11 q^{66} +2.30947e11 q^{67} -3.63786e11 q^{68} +4.08447e11 q^{69} +1.40734e12 q^{70} -4.88923e10 q^{71} -3.35374e11 q^{72} +2.23802e12 q^{73} +8.53146e11 q^{74} +1.22171e12 q^{75} +8.13615e10 q^{76} -2.72290e12 q^{77} +6.03290e11 q^{78} -3.41626e12 q^{79} -1.29552e12 q^{80} +2.82430e11 q^{81} +6.26658e11 q^{82} +2.93065e12 q^{83} +2.75428e12 q^{84} -3.11060e12 q^{85} +5.50822e11 q^{86} -3.18725e12 q^{87} -2.86266e12 q^{88} +4.55708e12 q^{89} -1.24599e12 q^{90} -1.14029e13 q^{91} -3.52657e12 q^{92} -5.15484e12 q^{93} -9.28094e11 q^{94} +6.95691e11 q^{95} +4.53315e12 q^{96} -8.26454e12 q^{97} +1.14753e13 q^{98} +2.41074e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 43.5631 0.481309 0.240654 0.970611i \(-0.422638\pi\)
0.240654 + 0.970611i \(0.422638\pi\)
\(3\) 729.000 0.577350
\(4\) −6294.26 −0.768342
\(5\) −53819.8 −1.54041 −0.770207 0.637794i \(-0.779847\pi\)
−0.770207 + 0.637794i \(0.779847\pi\)
\(6\) 31757.5 0.277884
\(7\) −600256. −1.92841 −0.964205 0.265158i \(-0.914576\pi\)
−0.964205 + 0.265158i \(0.914576\pi\)
\(8\) −631066. −0.851118
\(9\) 531441. 0.333333
\(10\) −2.34456e6 −0.741415
\(11\) 4.53623e6 0.772044 0.386022 0.922489i \(-0.373849\pi\)
0.386022 + 0.922489i \(0.373849\pi\)
\(12\) −4.58851e6 −0.443602
\(13\) 1.89968e7 1.09156 0.545780 0.837928i \(-0.316233\pi\)
0.545780 + 0.837928i \(0.316233\pi\)
\(14\) −2.61490e7 −0.928161
\(15\) −3.92347e7 −0.889358
\(16\) 2.40714e7 0.358691
\(17\) 5.77965e7 0.580743 0.290371 0.956914i \(-0.406221\pi\)
0.290371 + 0.956914i \(0.406221\pi\)
\(18\) 2.31512e7 0.160436
\(19\) −1.29263e7 −0.0630341 −0.0315171 0.999503i \(-0.510034\pi\)
−0.0315171 + 0.999503i \(0.510034\pi\)
\(20\) 3.38756e8 1.18356
\(21\) −4.37587e8 −1.11337
\(22\) 1.97612e8 0.371592
\(23\) 5.60284e8 0.789183 0.394591 0.918857i \(-0.370886\pi\)
0.394591 + 0.918857i \(0.370886\pi\)
\(24\) −4.60047e8 −0.491393
\(25\) 1.67587e9 1.37287
\(26\) 8.27558e8 0.525378
\(27\) 3.87420e8 0.192450
\(28\) 3.77817e9 1.48168
\(29\) −4.37208e9 −1.36490 −0.682451 0.730931i \(-0.739086\pi\)
−0.682451 + 0.730931i \(0.739086\pi\)
\(30\) −1.70918e9 −0.428056
\(31\) −7.07112e9 −1.43099 −0.715496 0.698617i \(-0.753799\pi\)
−0.715496 + 0.698617i \(0.753799\pi\)
\(32\) 6.21832e9 1.02376
\(33\) 3.30691e9 0.445740
\(34\) 2.51780e9 0.279516
\(35\) 3.23057e10 2.97055
\(36\) −3.34503e9 −0.256114
\(37\) 1.95842e10 1.25486 0.627428 0.778675i \(-0.284108\pi\)
0.627428 + 0.778675i \(0.284108\pi\)
\(38\) −5.63110e8 −0.0303389
\(39\) 1.38486e10 0.630213
\(40\) 3.39639e10 1.31107
\(41\) 1.43851e10 0.472952 0.236476 0.971637i \(-0.424008\pi\)
0.236476 + 0.971637i \(0.424008\pi\)
\(42\) −1.90626e10 −0.535874
\(43\) 1.26442e10 0.305033 0.152517 0.988301i \(-0.451262\pi\)
0.152517 + 0.988301i \(0.451262\pi\)
\(44\) −2.85522e10 −0.593194
\(45\) −2.86021e10 −0.513471
\(46\) 2.44077e10 0.379841
\(47\) −2.13046e10 −0.288295 −0.144148 0.989556i \(-0.546044\pi\)
−0.144148 + 0.989556i \(0.546044\pi\)
\(48\) 1.75480e10 0.207090
\(49\) 2.63418e11 2.71876
\(50\) 7.30062e10 0.660776
\(51\) 4.21337e10 0.335292
\(52\) −1.19570e11 −0.838692
\(53\) 1.08144e11 0.670205 0.335102 0.942182i \(-0.391229\pi\)
0.335102 + 0.942182i \(0.391229\pi\)
\(54\) 1.68772e10 0.0926279
\(55\) −2.44139e11 −1.18927
\(56\) 3.78801e11 1.64131
\(57\) −9.42327e9 −0.0363928
\(58\) −1.90462e11 −0.656939
\(59\) 4.21805e10 0.130189
\(60\) 2.46953e11 0.683331
\(61\) −6.15544e11 −1.52973 −0.764866 0.644190i \(-0.777195\pi\)
−0.764866 + 0.644190i \(0.777195\pi\)
\(62\) −3.08040e11 −0.688749
\(63\) −3.19001e11 −0.642803
\(64\) 7.36966e10 0.134053
\(65\) −1.02240e12 −1.68145
\(66\) 1.44059e11 0.214539
\(67\) 2.30947e11 0.311907 0.155954 0.987764i \(-0.450155\pi\)
0.155954 + 0.987764i \(0.450155\pi\)
\(68\) −3.63786e11 −0.446209
\(69\) 4.08447e11 0.455635
\(70\) 1.40734e12 1.42975
\(71\) −4.88923e10 −0.0452961 −0.0226481 0.999743i \(-0.507210\pi\)
−0.0226481 + 0.999743i \(0.507210\pi\)
\(72\) −3.35374e11 −0.283706
\(73\) 2.23802e12 1.73087 0.865435 0.501021i \(-0.167042\pi\)
0.865435 + 0.501021i \(0.167042\pi\)
\(74\) 8.53146e11 0.603973
\(75\) 1.22171e12 0.792629
\(76\) 8.13615e10 0.0484318
\(77\) −2.72290e12 −1.48882
\(78\) 6.03290e11 0.303327
\(79\) −3.41626e12 −1.58116 −0.790579 0.612361i \(-0.790220\pi\)
−0.790579 + 0.612361i \(0.790220\pi\)
\(80\) −1.29552e12 −0.552533
\(81\) 2.82430e11 0.111111
\(82\) 6.26658e11 0.227636
\(83\) 2.93065e12 0.983911 0.491955 0.870620i \(-0.336282\pi\)
0.491955 + 0.870620i \(0.336282\pi\)
\(84\) 2.75428e12 0.855447
\(85\) −3.11060e12 −0.894584
\(86\) 5.50822e11 0.146815
\(87\) −3.18725e12 −0.788027
\(88\) −2.86266e12 −0.657101
\(89\) 4.55708e12 0.971967 0.485984 0.873968i \(-0.338461\pi\)
0.485984 + 0.873968i \(0.338461\pi\)
\(90\) −1.24599e12 −0.247138
\(91\) −1.14029e13 −2.10498
\(92\) −3.52657e12 −0.606362
\(93\) −5.15484e12 −0.826183
\(94\) −9.28094e11 −0.138759
\(95\) 6.95691e11 0.0970987
\(96\) 4.53315e12 0.591068
\(97\) −8.26454e12 −1.00740 −0.503701 0.863878i \(-0.668028\pi\)
−0.503701 + 0.863878i \(0.668028\pi\)
\(98\) 1.14753e13 1.30857
\(99\) 2.41074e12 0.257348
\(100\) −1.05484e13 −1.05484
\(101\) 5.40578e12 0.506722 0.253361 0.967372i \(-0.418464\pi\)
0.253361 + 0.967372i \(0.418464\pi\)
\(102\) 1.83547e12 0.161379
\(103\) −6.54245e11 −0.0539881 −0.0269941 0.999636i \(-0.508594\pi\)
−0.0269941 + 0.999636i \(0.508594\pi\)
\(104\) −1.19882e13 −0.929047
\(105\) 2.35508e13 1.71505
\(106\) 4.71107e12 0.322575
\(107\) −2.01968e13 −1.30103 −0.650515 0.759494i \(-0.725447\pi\)
−0.650515 + 0.759494i \(0.725447\pi\)
\(108\) −2.43852e12 −0.147867
\(109\) −3.14736e13 −1.79752 −0.898762 0.438437i \(-0.855532\pi\)
−0.898762 + 0.438437i \(0.855532\pi\)
\(110\) −1.06354e13 −0.572405
\(111\) 1.42769e13 0.724491
\(112\) −1.44490e13 −0.691704
\(113\) −2.69712e13 −1.21868 −0.609341 0.792909i \(-0.708566\pi\)
−0.609341 + 0.792909i \(0.708566\pi\)
\(114\) −4.10507e11 −0.0175162
\(115\) −3.01544e13 −1.21567
\(116\) 2.75190e13 1.04871
\(117\) 1.00957e13 0.363853
\(118\) 1.83751e12 0.0626611
\(119\) −3.46927e13 −1.11991
\(120\) 2.47597e13 0.756949
\(121\) −1.39454e13 −0.403947
\(122\) −2.68150e13 −0.736273
\(123\) 1.04867e13 0.273059
\(124\) 4.45074e13 1.09949
\(125\) −2.44971e13 −0.574381
\(126\) −1.38967e13 −0.309387
\(127\) 6.52454e13 1.37983 0.689915 0.723890i \(-0.257648\pi\)
0.689915 + 0.723890i \(0.257648\pi\)
\(128\) −4.77300e13 −0.959239
\(129\) 9.21764e12 0.176111
\(130\) −4.45390e13 −0.809299
\(131\) 1.69094e13 0.292324 0.146162 0.989261i \(-0.453308\pi\)
0.146162 + 0.989261i \(0.453308\pi\)
\(132\) −2.08145e13 −0.342481
\(133\) 7.75909e12 0.121556
\(134\) 1.00608e13 0.150124
\(135\) −2.08509e13 −0.296453
\(136\) −3.64734e13 −0.494281
\(137\) −6.34715e13 −0.820154 −0.410077 0.912051i \(-0.634498\pi\)
−0.410077 + 0.912051i \(0.634498\pi\)
\(138\) 1.77932e13 0.219301
\(139\) 4.11242e13 0.483617 0.241809 0.970324i \(-0.422259\pi\)
0.241809 + 0.970324i \(0.422259\pi\)
\(140\) −2.03340e14 −2.28240
\(141\) −1.55311e13 −0.166447
\(142\) −2.12990e12 −0.0218014
\(143\) 8.61736e13 0.842733
\(144\) 1.27925e13 0.119564
\(145\) 2.35305e14 2.10251
\(146\) 9.74949e13 0.833083
\(147\) 1.92032e14 1.56968
\(148\) −1.23268e14 −0.964158
\(149\) 1.82687e14 1.36772 0.683859 0.729614i \(-0.260300\pi\)
0.683859 + 0.729614i \(0.260300\pi\)
\(150\) 5.32215e13 0.381499
\(151\) 3.11847e13 0.214087 0.107044 0.994254i \(-0.465862\pi\)
0.107044 + 0.994254i \(0.465862\pi\)
\(152\) 8.15735e12 0.0536495
\(153\) 3.07154e13 0.193581
\(154\) −1.18618e14 −0.716581
\(155\) 3.80566e14 2.20432
\(156\) −8.71669e13 −0.484219
\(157\) 1.19492e14 0.636784 0.318392 0.947959i \(-0.396857\pi\)
0.318392 + 0.947959i \(0.396857\pi\)
\(158\) −1.48823e14 −0.761025
\(159\) 7.88367e13 0.386943
\(160\) −3.34669e14 −1.57701
\(161\) −3.36314e14 −1.52187
\(162\) 1.23035e13 0.0534787
\(163\) 3.35984e14 1.40313 0.701566 0.712604i \(-0.252484\pi\)
0.701566 + 0.712604i \(0.252484\pi\)
\(164\) −9.05433e13 −0.363389
\(165\) −1.77977e14 −0.686624
\(166\) 1.27668e14 0.473565
\(167\) −1.48112e14 −0.528365 −0.264183 0.964473i \(-0.585102\pi\)
−0.264183 + 0.964473i \(0.585102\pi\)
\(168\) 2.76146e14 0.947608
\(169\) 5.80018e13 0.191504
\(170\) −1.35507e14 −0.430571
\(171\) −6.86957e12 −0.0210114
\(172\) −7.95860e13 −0.234370
\(173\) −4.96846e13 −0.140904 −0.0704518 0.997515i \(-0.522444\pi\)
−0.0704518 + 0.997515i \(0.522444\pi\)
\(174\) −1.38846e14 −0.379284
\(175\) −1.00595e15 −2.64746
\(176\) 1.09193e14 0.276925
\(177\) 3.07496e13 0.0751646
\(178\) 1.98521e14 0.467816
\(179\) −2.02867e14 −0.460963 −0.230481 0.973077i \(-0.574030\pi\)
−0.230481 + 0.973077i \(0.574030\pi\)
\(180\) 1.80029e14 0.394521
\(181\) 3.87973e14 0.820146 0.410073 0.912053i \(-0.365503\pi\)
0.410073 + 0.912053i \(0.365503\pi\)
\(182\) −4.96747e14 −1.01314
\(183\) −4.48732e14 −0.883191
\(184\) −3.53577e14 −0.671688
\(185\) −1.05402e15 −1.93300
\(186\) −2.24561e14 −0.397649
\(187\) 2.62178e14 0.448359
\(188\) 1.34097e14 0.221509
\(189\) −2.32552e14 −0.371123
\(190\) 3.03065e13 0.0467344
\(191\) 2.70789e14 0.403565 0.201782 0.979430i \(-0.435327\pi\)
0.201782 + 0.979430i \(0.435327\pi\)
\(192\) 5.37248e13 0.0773957
\(193\) 6.36613e14 0.886652 0.443326 0.896360i \(-0.353798\pi\)
0.443326 + 0.896360i \(0.353798\pi\)
\(194\) −3.60029e14 −0.484871
\(195\) −7.45332e14 −0.970788
\(196\) −1.65802e15 −2.08894
\(197\) 1.08435e15 1.32172 0.660858 0.750511i \(-0.270193\pi\)
0.660858 + 0.750511i \(0.270193\pi\)
\(198\) 1.05019e14 0.123864
\(199\) −1.40793e15 −1.60708 −0.803540 0.595251i \(-0.797053\pi\)
−0.803540 + 0.595251i \(0.797053\pi\)
\(200\) −1.05759e15 −1.16848
\(201\) 1.68360e14 0.180080
\(202\) 2.35493e14 0.243890
\(203\) 2.62437e15 2.63209
\(204\) −2.65200e14 −0.257619
\(205\) −7.74202e14 −0.728541
\(206\) −2.85009e13 −0.0259850
\(207\) 2.97758e14 0.263061
\(208\) 4.57278e14 0.391533
\(209\) −5.86366e13 −0.0486652
\(210\) 1.02595e15 0.825467
\(211\) −2.07296e15 −1.61717 −0.808583 0.588382i \(-0.799765\pi\)
−0.808583 + 0.588382i \(0.799765\pi\)
\(212\) −6.80684e14 −0.514947
\(213\) −3.56425e13 −0.0261517
\(214\) −8.79833e14 −0.626197
\(215\) −6.80510e14 −0.469878
\(216\) −2.44488e14 −0.163798
\(217\) 4.24448e15 2.75954
\(218\) −1.37109e15 −0.865164
\(219\) 1.63151e15 0.999318
\(220\) 1.53667e15 0.913764
\(221\) 1.09795e15 0.633916
\(222\) 6.21944e14 0.348704
\(223\) −7.10419e14 −0.386842 −0.193421 0.981116i \(-0.561958\pi\)
−0.193421 + 0.981116i \(0.561958\pi\)
\(224\) −3.73258e15 −1.97423
\(225\) 8.90627e14 0.457625
\(226\) −1.17495e15 −0.586562
\(227\) −1.65843e15 −0.804507 −0.402254 0.915528i \(-0.631773\pi\)
−0.402254 + 0.915528i \(0.631773\pi\)
\(228\) 5.93125e13 0.0279621
\(229\) −1.29550e15 −0.593617 −0.296808 0.954937i \(-0.595922\pi\)
−0.296808 + 0.954937i \(0.595922\pi\)
\(230\) −1.31362e15 −0.585112
\(231\) −1.98499e15 −0.859569
\(232\) 2.75907e15 1.16169
\(233\) 4.69091e15 1.92063 0.960315 0.278918i \(-0.0899758\pi\)
0.960315 + 0.278918i \(0.0899758\pi\)
\(234\) 4.39798e14 0.175126
\(235\) 1.14661e15 0.444094
\(236\) −2.65495e14 −0.100030
\(237\) −2.49045e15 −0.912882
\(238\) −1.51132e15 −0.539022
\(239\) 3.18696e15 1.10609 0.553044 0.833152i \(-0.313466\pi\)
0.553044 + 0.833152i \(0.313466\pi\)
\(240\) −9.44432e14 −0.319005
\(241\) −2.57566e15 −0.846794 −0.423397 0.905944i \(-0.639162\pi\)
−0.423397 + 0.905944i \(0.639162\pi\)
\(242\) −6.07503e14 −0.194423
\(243\) 2.05891e14 0.0641500
\(244\) 3.87439e15 1.17536
\(245\) −1.41771e16 −4.18802
\(246\) 4.56834e14 0.131426
\(247\) −2.45558e14 −0.0688056
\(248\) 4.46234e15 1.21794
\(249\) 2.13644e15 0.568061
\(250\) −1.06717e15 −0.276454
\(251\) −3.49703e15 −0.882714 −0.441357 0.897332i \(-0.645503\pi\)
−0.441357 + 0.897332i \(0.645503\pi\)
\(252\) 2.00787e15 0.493893
\(253\) 2.54158e15 0.609284
\(254\) 2.84229e15 0.664124
\(255\) −2.26763e15 −0.516488
\(256\) −2.68299e15 −0.595743
\(257\) 8.78471e15 1.90179 0.950895 0.309515i \(-0.100167\pi\)
0.950895 + 0.309515i \(0.100167\pi\)
\(258\) 4.01549e14 0.0847638
\(259\) −1.17555e16 −2.41988
\(260\) 6.43526e15 1.29193
\(261\) −2.32350e15 −0.454967
\(262\) 7.36625e14 0.140698
\(263\) −5.03607e15 −0.938382 −0.469191 0.883097i \(-0.655454\pi\)
−0.469191 + 0.883097i \(0.655454\pi\)
\(264\) −2.08688e15 −0.379378
\(265\) −5.82027e15 −1.03239
\(266\) 3.38010e14 0.0585058
\(267\) 3.32211e15 0.561166
\(268\) −1.45364e15 −0.239652
\(269\) −8.65542e15 −1.39283 −0.696415 0.717639i \(-0.745223\pi\)
−0.696415 + 0.717639i \(0.745223\pi\)
\(270\) −9.08330e14 −0.142685
\(271\) −8.30355e15 −1.27340 −0.636698 0.771113i \(-0.719700\pi\)
−0.636698 + 0.771113i \(0.719700\pi\)
\(272\) 1.39124e15 0.208307
\(273\) −8.31273e15 −1.21531
\(274\) −2.76502e15 −0.394747
\(275\) 7.60213e15 1.05992
\(276\) −2.57087e15 −0.350083
\(277\) 1.70303e15 0.226518 0.113259 0.993565i \(-0.463871\pi\)
0.113259 + 0.993565i \(0.463871\pi\)
\(278\) 1.79150e15 0.232769
\(279\) −3.75788e15 −0.476997
\(280\) −2.03870e16 −2.52829
\(281\) 3.42250e15 0.414717 0.207359 0.978265i \(-0.433513\pi\)
0.207359 + 0.978265i \(0.433513\pi\)
\(282\) −6.76581e14 −0.0801125
\(283\) 6.86754e15 0.794675 0.397338 0.917673i \(-0.369934\pi\)
0.397338 + 0.917673i \(0.369934\pi\)
\(284\) 3.07741e14 0.0348029
\(285\) 5.07159e14 0.0560599
\(286\) 3.75399e15 0.405615
\(287\) −8.63473e15 −0.912045
\(288\) 3.30467e15 0.341253
\(289\) −6.56414e15 −0.662738
\(290\) 1.02506e16 1.01196
\(291\) −6.02485e15 −0.581623
\(292\) −1.40866e16 −1.32990
\(293\) −1.51715e16 −1.40084 −0.700422 0.713729i \(-0.747005\pi\)
−0.700422 + 0.713729i \(0.747005\pi\)
\(294\) 8.36551e15 0.755501
\(295\) −2.27015e15 −0.200545
\(296\) −1.23589e16 −1.06803
\(297\) 1.75743e15 0.148580
\(298\) 7.95841e15 0.658295
\(299\) 1.06436e16 0.861441
\(300\) −7.68976e15 −0.609010
\(301\) −7.58977e15 −0.588229
\(302\) 1.35850e15 0.103042
\(303\) 3.94082e15 0.292556
\(304\) −3.11154e14 −0.0226098
\(305\) 3.31285e16 2.35642
\(306\) 1.33806e15 0.0931722
\(307\) −1.24999e16 −0.852132 −0.426066 0.904692i \(-0.640101\pi\)
−0.426066 + 0.904692i \(0.640101\pi\)
\(308\) 1.71386e16 1.14392
\(309\) −4.76944e14 −0.0311701
\(310\) 1.65786e16 1.06096
\(311\) 1.61408e16 1.01154 0.505770 0.862668i \(-0.331208\pi\)
0.505770 + 0.862668i \(0.331208\pi\)
\(312\) −8.73941e15 −0.536386
\(313\) −3.98009e15 −0.239252 −0.119626 0.992819i \(-0.538169\pi\)
−0.119626 + 0.992819i \(0.538169\pi\)
\(314\) 5.20545e15 0.306490
\(315\) 1.71686e16 0.990183
\(316\) 2.15028e16 1.21487
\(317\) −5.32616e15 −0.294801 −0.147400 0.989077i \(-0.547091\pi\)
−0.147400 + 0.989077i \(0.547091\pi\)
\(318\) 3.43437e15 0.186239
\(319\) −1.98328e16 −1.05377
\(320\) −3.96634e15 −0.206498
\(321\) −1.47234e16 −0.751150
\(322\) −1.46509e16 −0.732488
\(323\) −7.47095e14 −0.0366066
\(324\) −1.77768e15 −0.0853713
\(325\) 3.18361e16 1.49858
\(326\) 1.46365e16 0.675340
\(327\) −2.29443e16 −1.03780
\(328\) −9.07793e15 −0.402538
\(329\) 1.27882e16 0.555951
\(330\) −7.75324e15 −0.330478
\(331\) −2.46478e16 −1.03014 −0.515070 0.857148i \(-0.672234\pi\)
−0.515070 + 0.857148i \(0.672234\pi\)
\(332\) −1.84462e16 −0.755980
\(333\) 1.04078e16 0.418285
\(334\) −6.45223e15 −0.254307
\(335\) −1.24295e16 −0.480467
\(336\) −1.05333e16 −0.399355
\(337\) 3.07147e16 1.14223 0.571113 0.820871i \(-0.306512\pi\)
0.571113 + 0.820871i \(0.306512\pi\)
\(338\) 2.52674e15 0.0921726
\(339\) −1.96620e16 −0.703606
\(340\) 1.95789e16 0.687346
\(341\) −3.20762e16 −1.10479
\(342\) −2.99260e14 −0.0101130
\(343\) −9.99603e16 −3.31448
\(344\) −7.97934e15 −0.259619
\(345\) −2.19826e16 −0.701866
\(346\) −2.16441e15 −0.0678181
\(347\) −2.76500e16 −0.850263 −0.425132 0.905132i \(-0.639772\pi\)
−0.425132 + 0.905132i \(0.639772\pi\)
\(348\) 2.00614e16 0.605474
\(349\) 4.40754e16 1.30566 0.652831 0.757504i \(-0.273581\pi\)
0.652831 + 0.757504i \(0.273581\pi\)
\(350\) −4.38224e16 −1.27425
\(351\) 7.35973e15 0.210071
\(352\) 2.82077e16 0.790388
\(353\) 4.03066e16 1.10877 0.554384 0.832261i \(-0.312954\pi\)
0.554384 + 0.832261i \(0.312954\pi\)
\(354\) 1.33955e15 0.0361774
\(355\) 2.63137e15 0.0697748
\(356\) −2.86834e16 −0.746803
\(357\) −2.52910e16 −0.646580
\(358\) −8.83750e15 −0.221865
\(359\) −7.41685e15 −0.182854 −0.0914272 0.995812i \(-0.529143\pi\)
−0.0914272 + 0.995812i \(0.529143\pi\)
\(360\) 1.80498e16 0.437025
\(361\) −4.18859e16 −0.996027
\(362\) 1.69013e16 0.394743
\(363\) −1.01662e16 −0.233219
\(364\) 7.17729e16 1.61734
\(365\) −1.20450e17 −2.66626
\(366\) −1.95481e16 −0.425088
\(367\) 4.32762e16 0.924527 0.462263 0.886743i \(-0.347037\pi\)
0.462263 + 0.886743i \(0.347037\pi\)
\(368\) 1.34868e16 0.283073
\(369\) 7.64482e15 0.157651
\(370\) −4.59162e16 −0.930368
\(371\) −6.49139e16 −1.29243
\(372\) 3.24459e16 0.634791
\(373\) 4.41744e16 0.849303 0.424652 0.905357i \(-0.360397\pi\)
0.424652 + 0.905357i \(0.360397\pi\)
\(374\) 1.14213e16 0.215799
\(375\) −1.78584e16 −0.331619
\(376\) 1.34446e16 0.245373
\(377\) −8.30554e16 −1.48987
\(378\) −1.01307e16 −0.178625
\(379\) −6.14710e16 −1.06541 −0.532703 0.846302i \(-0.678824\pi\)
−0.532703 + 0.846302i \(0.678824\pi\)
\(380\) −4.37886e15 −0.0746050
\(381\) 4.75639e16 0.796645
\(382\) 1.17964e16 0.194239
\(383\) 3.73747e16 0.605043 0.302521 0.953143i \(-0.402172\pi\)
0.302521 + 0.953143i \(0.402172\pi\)
\(384\) −3.47952e16 −0.553817
\(385\) 1.46546e17 2.29340
\(386\) 2.77328e16 0.426753
\(387\) 6.71966e15 0.101678
\(388\) 5.20191e16 0.774028
\(389\) 4.71503e16 0.689942 0.344971 0.938613i \(-0.387889\pi\)
0.344971 + 0.938613i \(0.387889\pi\)
\(390\) −3.24689e16 −0.467249
\(391\) 3.23825e16 0.458312
\(392\) −1.66234e17 −2.31399
\(393\) 1.23269e16 0.168773
\(394\) 4.72375e16 0.636153
\(395\) 1.83863e17 2.43564
\(396\) −1.51738e16 −0.197731
\(397\) 4.60714e16 0.590600 0.295300 0.955405i \(-0.404580\pi\)
0.295300 + 0.955405i \(0.404580\pi\)
\(398\) −6.13340e16 −0.773502
\(399\) 5.65638e15 0.0701802
\(400\) 4.03405e16 0.492438
\(401\) −1.17360e17 −1.40956 −0.704779 0.709427i \(-0.748954\pi\)
−0.704779 + 0.709427i \(0.748954\pi\)
\(402\) 7.33429e15 0.0866740
\(403\) −1.34328e17 −1.56201
\(404\) −3.40254e16 −0.389336
\(405\) −1.52003e16 −0.171157
\(406\) 1.14326e17 1.26685
\(407\) 8.88382e16 0.968804
\(408\) −2.65891e16 −0.285373
\(409\) 1.18336e17 1.25001 0.625006 0.780620i \(-0.285097\pi\)
0.625006 + 0.780620i \(0.285097\pi\)
\(410\) −3.37266e16 −0.350653
\(411\) −4.62707e16 −0.473516
\(412\) 4.11798e15 0.0414813
\(413\) −2.53191e16 −0.251058
\(414\) 1.29713e16 0.126614
\(415\) −1.57727e17 −1.51563
\(416\) 1.18128e17 1.11750
\(417\) 2.99796e16 0.279216
\(418\) −2.55439e15 −0.0234230
\(419\) 9.40473e16 0.849093 0.424546 0.905406i \(-0.360434\pi\)
0.424546 + 0.905406i \(0.360434\pi\)
\(420\) −1.48235e17 −1.31774
\(421\) 1.34689e17 1.17896 0.589478 0.807784i \(-0.299333\pi\)
0.589478 + 0.807784i \(0.299333\pi\)
\(422\) −9.03045e16 −0.778356
\(423\) −1.13221e16 −0.0960984
\(424\) −6.82458e16 −0.570424
\(425\) 9.68596e16 0.797287
\(426\) −1.55270e15 −0.0125871
\(427\) 3.69484e17 2.94995
\(428\) 1.27124e17 0.999635
\(429\) 6.28206e16 0.486552
\(430\) −2.96451e16 −0.226156
\(431\) −8.81796e16 −0.662622 −0.331311 0.943522i \(-0.607491\pi\)
−0.331311 + 0.943522i \(0.607491\pi\)
\(432\) 9.32574e15 0.0690301
\(433\) −4.42402e15 −0.0322586 −0.0161293 0.999870i \(-0.505134\pi\)
−0.0161293 + 0.999870i \(0.505134\pi\)
\(434\) 1.84903e17 1.32819
\(435\) 1.71537e17 1.21389
\(436\) 1.98103e17 1.38111
\(437\) −7.24241e15 −0.0497455
\(438\) 7.10738e16 0.480981
\(439\) −2.17504e17 −1.45027 −0.725133 0.688609i \(-0.758222\pi\)
−0.725133 + 0.688609i \(0.758222\pi\)
\(440\) 1.54068e17 1.01221
\(441\) 1.39991e17 0.906255
\(442\) 4.78300e16 0.305109
\(443\) 2.88824e17 1.81555 0.907777 0.419454i \(-0.137778\pi\)
0.907777 + 0.419454i \(0.137778\pi\)
\(444\) −8.98622e16 −0.556657
\(445\) −2.45261e17 −1.49723
\(446\) −3.09481e16 −0.186190
\(447\) 1.33179e17 0.789653
\(448\) −4.42368e16 −0.258510
\(449\) 2.73967e16 0.157796 0.0788981 0.996883i \(-0.474860\pi\)
0.0788981 + 0.996883i \(0.474860\pi\)
\(450\) 3.87985e16 0.220259
\(451\) 6.52539e16 0.365140
\(452\) 1.69764e17 0.936364
\(453\) 2.27336e16 0.123603
\(454\) −7.22465e16 −0.387216
\(455\) 6.13703e17 3.24253
\(456\) 5.94671e15 0.0309746
\(457\) −1.46978e17 −0.754737 −0.377368 0.926063i \(-0.623171\pi\)
−0.377368 + 0.926063i \(0.623171\pi\)
\(458\) −5.64359e16 −0.285713
\(459\) 2.23916e16 0.111764
\(460\) 1.89800e17 0.934049
\(461\) −3.03380e17 −1.47208 −0.736038 0.676940i \(-0.763306\pi\)
−0.736038 + 0.676940i \(0.763306\pi\)
\(462\) −8.64724e16 −0.413718
\(463\) −1.61846e17 −0.763528 −0.381764 0.924260i \(-0.624683\pi\)
−0.381764 + 0.924260i \(0.624683\pi\)
\(464\) −1.05242e17 −0.489578
\(465\) 2.77433e17 1.27266
\(466\) 2.04351e17 0.924416
\(467\) 1.95192e17 0.870766 0.435383 0.900245i \(-0.356613\pi\)
0.435383 + 0.900245i \(0.356613\pi\)
\(468\) −6.35447e16 −0.279564
\(469\) −1.38627e17 −0.601485
\(470\) 4.99499e16 0.213746
\(471\) 8.71098e16 0.367647
\(472\) −2.66187e16 −0.110806
\(473\) 5.73571e16 0.235499
\(474\) −1.08492e17 −0.439378
\(475\) −2.16628e16 −0.0865380
\(476\) 2.18365e17 0.860474
\(477\) 5.74719e16 0.223402
\(478\) 1.38834e17 0.532370
\(479\) −1.50312e17 −0.568608 −0.284304 0.958734i \(-0.591763\pi\)
−0.284304 + 0.958734i \(0.591763\pi\)
\(480\) −2.43974e17 −0.910489
\(481\) 3.72036e17 1.36975
\(482\) −1.12204e17 −0.407569
\(483\) −2.45173e17 −0.878651
\(484\) 8.77757e16 0.310370
\(485\) 4.44796e17 1.55181
\(486\) 8.96925e15 0.0308760
\(487\) −5.73308e16 −0.194738 −0.0973688 0.995248i \(-0.531043\pi\)
−0.0973688 + 0.995248i \(0.531043\pi\)
\(488\) 3.88449e17 1.30198
\(489\) 2.44932e17 0.810099
\(490\) −6.17600e17 −2.01573
\(491\) −4.00825e17 −1.29100 −0.645498 0.763762i \(-0.723350\pi\)
−0.645498 + 0.763762i \(0.723350\pi\)
\(492\) −6.60061e16 −0.209803
\(493\) −2.52691e17 −0.792657
\(494\) −1.06973e16 −0.0331167
\(495\) −1.29745e17 −0.396423
\(496\) −1.70211e17 −0.513284
\(497\) 2.93479e16 0.0873495
\(498\) 9.30700e16 0.273413
\(499\) 6.00021e17 1.73985 0.869927 0.493181i \(-0.164166\pi\)
0.869927 + 0.493181i \(0.164166\pi\)
\(500\) 1.54191e17 0.441321
\(501\) −1.07974e17 −0.305052
\(502\) −1.52341e17 −0.424858
\(503\) −1.77486e17 −0.488620 −0.244310 0.969697i \(-0.578561\pi\)
−0.244310 + 0.969697i \(0.578561\pi\)
\(504\) 2.01311e17 0.547102
\(505\) −2.90938e17 −0.780561
\(506\) 1.10719e17 0.293254
\(507\) 4.22833e16 0.110565
\(508\) −4.10671e17 −1.06018
\(509\) −1.45247e17 −0.370204 −0.185102 0.982719i \(-0.559262\pi\)
−0.185102 + 0.982719i \(0.559262\pi\)
\(510\) −9.87848e16 −0.248590
\(511\) −1.34338e18 −3.33783
\(512\) 2.74125e17 0.672502
\(513\) −5.00791e15 −0.0121309
\(514\) 3.82689e17 0.915348
\(515\) 3.52113e16 0.0831641
\(516\) −5.80182e16 −0.135314
\(517\) −9.66425e16 −0.222577
\(518\) −5.12106e17 −1.16471
\(519\) −3.62201e16 −0.0813507
\(520\) 6.45204e17 1.43112
\(521\) −6.85604e17 −1.50186 −0.750928 0.660384i \(-0.770393\pi\)
−0.750928 + 0.660384i \(0.770393\pi\)
\(522\) −1.01219e17 −0.218980
\(523\) −4.89577e17 −1.04607 −0.523035 0.852311i \(-0.675200\pi\)
−0.523035 + 0.852311i \(0.675200\pi\)
\(524\) −1.06432e17 −0.224605
\(525\) −7.33339e17 −1.52851
\(526\) −2.19387e17 −0.451651
\(527\) −4.08686e17 −0.831038
\(528\) 7.96018e16 0.159883
\(529\) −1.90118e17 −0.377190
\(530\) −2.53549e17 −0.496900
\(531\) 2.24165e16 0.0433963
\(532\) −4.88377e16 −0.0933963
\(533\) 2.73270e17 0.516255
\(534\) 1.44721e17 0.270094
\(535\) 1.08699e18 2.00412
\(536\) −1.45743e17 −0.265470
\(537\) −1.47890e17 −0.266137
\(538\) −3.77057e17 −0.670382
\(539\) 1.19493e18 2.09901
\(540\) 1.31241e17 0.227777
\(541\) −2.74375e16 −0.0470503 −0.0235251 0.999723i \(-0.507489\pi\)
−0.0235251 + 0.999723i \(0.507489\pi\)
\(542\) −3.61728e17 −0.612897
\(543\) 2.82833e17 0.473511
\(544\) 3.59397e17 0.594541
\(545\) 1.69391e18 2.76893
\(546\) −3.62128e17 −0.584939
\(547\) −6.61230e16 −0.105544 −0.0527721 0.998607i \(-0.516806\pi\)
−0.0527721 + 0.998607i \(0.516806\pi\)
\(548\) 3.99506e17 0.630159
\(549\) −3.27125e17 −0.509911
\(550\) 3.31173e17 0.510149
\(551\) 5.65149e16 0.0860354
\(552\) −2.57757e17 −0.387799
\(553\) 2.05063e18 3.04912
\(554\) 7.41891e16 0.109025
\(555\) −7.68378e17 −1.11602
\(556\) −2.58847e17 −0.371583
\(557\) −6.62052e17 −0.939363 −0.469681 0.882836i \(-0.655631\pi\)
−0.469681 + 0.882836i \(0.655631\pi\)
\(558\) −1.63705e17 −0.229583
\(559\) 2.40199e17 0.332962
\(560\) 7.77642e17 1.06551
\(561\) 1.91128e17 0.258860
\(562\) 1.49095e17 0.199607
\(563\) 3.84925e17 0.509415 0.254708 0.967018i \(-0.418021\pi\)
0.254708 + 0.967018i \(0.418021\pi\)
\(564\) 9.77564e16 0.127888
\(565\) 1.45158e18 1.87727
\(566\) 2.99171e17 0.382484
\(567\) −1.69530e17 −0.214268
\(568\) 3.08543e16 0.0385524
\(569\) 1.27520e17 0.157525 0.0787624 0.996893i \(-0.474903\pi\)
0.0787624 + 0.996893i \(0.474903\pi\)
\(570\) 2.20934e16 0.0269821
\(571\) 9.82029e17 1.18574 0.592870 0.805298i \(-0.297995\pi\)
0.592870 + 0.805298i \(0.297995\pi\)
\(572\) −5.42399e17 −0.647507
\(573\) 1.97405e17 0.232998
\(574\) −3.76155e17 −0.438975
\(575\) 9.38965e17 1.08345
\(576\) 3.91654e16 0.0446844
\(577\) −9.32031e16 −0.105145 −0.0525724 0.998617i \(-0.516742\pi\)
−0.0525724 + 0.998617i \(0.516742\pi\)
\(578\) −2.85954e17 −0.318982
\(579\) 4.64091e17 0.511909
\(580\) −1.48107e18 −1.61545
\(581\) −1.75914e18 −1.89738
\(582\) −2.62461e17 −0.279940
\(583\) 4.90564e17 0.517428
\(584\) −1.41234e18 −1.47318
\(585\) −5.43347e17 −0.560485
\(586\) −6.60918e17 −0.674238
\(587\) −1.88941e18 −1.90625 −0.953124 0.302580i \(-0.902152\pi\)
−0.953124 + 0.302580i \(0.902152\pi\)
\(588\) −1.20870e18 −1.20605
\(589\) 9.14034e16 0.0902013
\(590\) −9.88947e16 −0.0965240
\(591\) 7.90489e17 0.763093
\(592\) 4.71417e17 0.450106
\(593\) 6.06244e16 0.0572521 0.0286261 0.999590i \(-0.490887\pi\)
0.0286261 + 0.999590i \(0.490887\pi\)
\(594\) 7.65590e16 0.0715129
\(595\) 1.86716e18 1.72512
\(596\) −1.14988e18 −1.05088
\(597\) −1.02638e18 −0.927848
\(598\) 4.63668e17 0.414619
\(599\) −1.04909e18 −0.927977 −0.463988 0.885841i \(-0.653582\pi\)
−0.463988 + 0.885841i \(0.653582\pi\)
\(600\) −7.70980e17 −0.674621
\(601\) −1.45304e18 −1.25775 −0.628874 0.777507i \(-0.716484\pi\)
−0.628874 + 0.777507i \(0.716484\pi\)
\(602\) −3.30634e17 −0.283120
\(603\) 1.22735e17 0.103969
\(604\) −1.96284e17 −0.164492
\(605\) 7.50537e17 0.622246
\(606\) 1.71674e17 0.140810
\(607\) −1.18656e18 −0.962863 −0.481432 0.876484i \(-0.659883\pi\)
−0.481432 + 0.876484i \(0.659883\pi\)
\(608\) −8.03798e16 −0.0645318
\(609\) 1.91317e18 1.51964
\(610\) 1.44318e18 1.13417
\(611\) −4.04718e17 −0.314692
\(612\) −1.93331e17 −0.148736
\(613\) 1.12742e16 0.00858211 0.00429105 0.999991i \(-0.498634\pi\)
0.00429105 + 0.999991i \(0.498634\pi\)
\(614\) −5.44534e17 −0.410138
\(615\) −5.64393e17 −0.420624
\(616\) 1.71833e18 1.26716
\(617\) −1.04678e18 −0.763838 −0.381919 0.924196i \(-0.624737\pi\)
−0.381919 + 0.924196i \(0.624737\pi\)
\(618\) −2.07772e16 −0.0150024
\(619\) 1.54959e17 0.110720 0.0553601 0.998466i \(-0.482369\pi\)
0.0553601 + 0.998466i \(0.482369\pi\)
\(620\) −2.39538e18 −1.69367
\(621\) 2.17066e17 0.151878
\(622\) 7.03144e17 0.486863
\(623\) −2.73542e18 −1.87435
\(624\) 3.33356e17 0.226052
\(625\) −7.27311e17 −0.488090
\(626\) −1.73385e17 −0.115154
\(627\) −4.27461e16 −0.0280968
\(628\) −7.52115e17 −0.489268
\(629\) 1.13190e18 0.728748
\(630\) 7.47916e17 0.476584
\(631\) −7.67258e17 −0.483894 −0.241947 0.970289i \(-0.577786\pi\)
−0.241947 + 0.970289i \(0.577786\pi\)
\(632\) 2.15589e18 1.34575
\(633\) −1.51119e18 −0.933672
\(634\) −2.32024e17 −0.141890
\(635\) −3.51150e18 −2.12551
\(636\) −4.96218e17 −0.297305
\(637\) 5.00410e18 2.96770
\(638\) −8.63977e17 −0.507186
\(639\) −2.59834e16 −0.0150987
\(640\) 2.56882e18 1.47762
\(641\) 1.31735e18 0.750110 0.375055 0.927003i \(-0.377624\pi\)
0.375055 + 0.927003i \(0.377624\pi\)
\(642\) −6.41399e17 −0.361535
\(643\) −1.05245e18 −0.587261 −0.293631 0.955919i \(-0.594864\pi\)
−0.293631 + 0.955919i \(0.594864\pi\)
\(644\) 2.11685e18 1.16932
\(645\) −4.96092e17 −0.271284
\(646\) −3.25458e16 −0.0176191
\(647\) −2.85595e18 −1.53064 −0.765319 0.643652i \(-0.777419\pi\)
−0.765319 + 0.643652i \(0.777419\pi\)
\(648\) −1.78232e17 −0.0945687
\(649\) 1.91340e17 0.100512
\(650\) 1.38688e18 0.721277
\(651\) 3.09423e18 1.59322
\(652\) −2.11477e18 −1.07809
\(653\) −3.54567e18 −1.78963 −0.894814 0.446439i \(-0.852692\pi\)
−0.894814 + 0.446439i \(0.852692\pi\)
\(654\) −9.99524e17 −0.499503
\(655\) −9.10060e17 −0.450299
\(656\) 3.46268e17 0.169644
\(657\) 1.18937e18 0.576957
\(658\) 5.57094e17 0.267584
\(659\) 1.44324e18 0.686412 0.343206 0.939260i \(-0.388487\pi\)
0.343206 + 0.939260i \(0.388487\pi\)
\(660\) 1.12023e18 0.527562
\(661\) −6.17628e17 −0.288017 −0.144008 0.989576i \(-0.545999\pi\)
−0.144008 + 0.989576i \(0.545999\pi\)
\(662\) −1.07374e18 −0.495816
\(663\) 8.00403e17 0.365991
\(664\) −1.84943e18 −0.837425
\(665\) −4.17593e17 −0.187246
\(666\) 4.53397e17 0.201324
\(667\) −2.44961e18 −1.07716
\(668\) 9.32257e17 0.405965
\(669\) −5.17896e17 −0.223343
\(670\) −5.41468e17 −0.231253
\(671\) −2.79225e18 −1.18102
\(672\) −2.72105e18 −1.13982
\(673\) 4.31364e18 1.78956 0.894780 0.446508i \(-0.147332\pi\)
0.894780 + 0.446508i \(0.147332\pi\)
\(674\) 1.33803e18 0.549763
\(675\) 6.49267e17 0.264210
\(676\) −3.65078e17 −0.147141
\(677\) −2.55818e18 −1.02119 −0.510593 0.859823i \(-0.670574\pi\)
−0.510593 + 0.859823i \(0.670574\pi\)
\(678\) −8.56537e17 −0.338652
\(679\) 4.96084e18 1.94268
\(680\) 1.96299e18 0.761397
\(681\) −1.20900e18 −0.464483
\(682\) −1.39734e18 −0.531744
\(683\) −9.84128e17 −0.370952 −0.185476 0.982649i \(-0.559383\pi\)
−0.185476 + 0.982649i \(0.559383\pi\)
\(684\) 4.32388e16 0.0161439
\(685\) 3.41603e18 1.26338
\(686\) −4.35458e18 −1.59529
\(687\) −9.44418e17 −0.342725
\(688\) 3.04364e17 0.109413
\(689\) 2.05438e18 0.731569
\(690\) −9.57629e17 −0.337814
\(691\) −2.51089e18 −0.877447 −0.438723 0.898622i \(-0.644569\pi\)
−0.438723 + 0.898622i \(0.644569\pi\)
\(692\) 3.12728e17 0.108262
\(693\) −1.44706e18 −0.496273
\(694\) −1.20452e18 −0.409239
\(695\) −2.21330e18 −0.744970
\(696\) 2.01137e18 0.670704
\(697\) 8.31407e17 0.274663
\(698\) 1.92006e18 0.628426
\(699\) 3.41967e18 1.10888
\(700\) 6.33172e18 2.03416
\(701\) −2.20623e18 −0.702238 −0.351119 0.936331i \(-0.614199\pi\)
−0.351119 + 0.936331i \(0.614199\pi\)
\(702\) 3.20613e17 0.101109
\(703\) −2.53151e17 −0.0790987
\(704\) 3.34304e17 0.103495
\(705\) 8.35879e17 0.256398
\(706\) 1.75588e18 0.533659
\(707\) −3.24485e18 −0.977167
\(708\) −1.93546e17 −0.0577521
\(709\) 3.00415e18 0.888222 0.444111 0.895972i \(-0.353520\pi\)
0.444111 + 0.895972i \(0.353520\pi\)
\(710\) 1.14631e17 0.0335832
\(711\) −1.81554e18 −0.527052
\(712\) −2.87582e18 −0.827259
\(713\) −3.96184e18 −1.12931
\(714\) −1.10175e18 −0.311205
\(715\) −4.63785e18 −1.29816
\(716\) 1.27689e18 0.354177
\(717\) 2.32329e18 0.638600
\(718\) −3.23101e17 −0.0880095
\(719\) −4.12082e18 −1.11236 −0.556181 0.831061i \(-0.687734\pi\)
−0.556181 + 0.831061i \(0.687734\pi\)
\(720\) −6.88491e17 −0.184178
\(721\) 3.92714e17 0.104111
\(722\) −1.82468e18 −0.479396
\(723\) −1.87766e18 −0.488897
\(724\) −2.44200e18 −0.630153
\(725\) −7.32705e18 −1.87384
\(726\) −4.42870e17 −0.112250
\(727\) 6.30968e18 1.58502 0.792508 0.609862i \(-0.208775\pi\)
0.792508 + 0.609862i \(0.208775\pi\)
\(728\) 7.19600e18 1.79158
\(729\) 1.50095e17 0.0370370
\(730\) −5.24716e18 −1.28329
\(731\) 7.30792e17 0.177146
\(732\) 2.82443e18 0.678593
\(733\) 1.02753e18 0.244691 0.122346 0.992488i \(-0.460958\pi\)
0.122346 + 0.992488i \(0.460958\pi\)
\(734\) 1.88524e18 0.444983
\(735\) −1.03351e19 −2.41796
\(736\) 3.48403e18 0.807934
\(737\) 1.04763e18 0.240806
\(738\) 3.33032e17 0.0758786
\(739\) −3.32865e18 −0.751760 −0.375880 0.926668i \(-0.622660\pi\)
−0.375880 + 0.926668i \(0.622660\pi\)
\(740\) 6.63425e18 1.48520
\(741\) −1.79012e17 −0.0397249
\(742\) −2.82785e18 −0.622058
\(743\) −6.32750e18 −1.37976 −0.689882 0.723922i \(-0.742338\pi\)
−0.689882 + 0.723922i \(0.742338\pi\)
\(744\) 3.25305e18 0.703180
\(745\) −9.83218e18 −2.10685
\(746\) 1.92437e18 0.408777
\(747\) 1.55747e18 0.327970
\(748\) −1.65022e18 −0.344493
\(749\) 1.21232e19 2.50892
\(750\) −7.77967e17 −0.159611
\(751\) 9.28701e18 1.88893 0.944466 0.328608i \(-0.106579\pi\)
0.944466 + 0.328608i \(0.106579\pi\)
\(752\) −5.12831e17 −0.103409
\(753\) −2.54933e18 −0.509635
\(754\) −3.61815e18 −0.717089
\(755\) −1.67835e18 −0.329783
\(756\) 1.46374e18 0.285149
\(757\) 2.46880e17 0.0476829 0.0238415 0.999716i \(-0.492410\pi\)
0.0238415 + 0.999716i \(0.492410\pi\)
\(758\) −2.67786e18 −0.512789
\(759\) 1.85281e18 0.351770
\(760\) −4.39027e17 −0.0826425
\(761\) −1.27339e18 −0.237663 −0.118832 0.992914i \(-0.537915\pi\)
−0.118832 + 0.992914i \(0.537915\pi\)
\(762\) 2.07203e18 0.383432
\(763\) 1.88922e19 3.46636
\(764\) −1.70441e18 −0.310076
\(765\) −1.65310e18 −0.298195
\(766\) 1.62816e18 0.291212
\(767\) 8.01294e17 0.142109
\(768\) −1.95590e18 −0.343953
\(769\) 1.14083e18 0.198930 0.0994649 0.995041i \(-0.468287\pi\)
0.0994649 + 0.995041i \(0.468287\pi\)
\(770\) 6.38399e18 1.10383
\(771\) 6.40406e18 1.09800
\(772\) −4.00701e18 −0.681252
\(773\) −2.80195e18 −0.472382 −0.236191 0.971707i \(-0.575899\pi\)
−0.236191 + 0.971707i \(0.575899\pi\)
\(774\) 2.92729e17 0.0489384
\(775\) −1.18503e19 −1.96457
\(776\) 5.21547e18 0.857418
\(777\) −8.56977e18 −1.39712
\(778\) 2.05401e18 0.332075
\(779\) −1.85946e17 −0.0298121
\(780\) 4.69131e18 0.745897
\(781\) −2.21786e17 −0.0349706
\(782\) 1.41068e18 0.220590
\(783\) −1.69383e18 −0.262676
\(784\) 6.34084e18 0.975197
\(785\) −6.43105e18 −0.980910
\(786\) 5.36999e17 0.0812320
\(787\) 1.01329e19 1.52019 0.760097 0.649810i \(-0.225152\pi\)
0.760097 + 0.649810i \(0.225152\pi\)
\(788\) −6.82516e18 −1.01553
\(789\) −3.67130e18 −0.541775
\(790\) 8.00963e18 1.17229
\(791\) 1.61896e19 2.35012
\(792\) −1.52133e18 −0.219034
\(793\) −1.16933e19 −1.66979
\(794\) 2.00701e18 0.284261
\(795\) −4.24298e18 −0.596052
\(796\) 8.86190e18 1.23479
\(797\) −5.39744e18 −0.745948 −0.372974 0.927842i \(-0.621662\pi\)
−0.372974 + 0.927842i \(0.621662\pi\)
\(798\) 2.46409e17 0.0337783
\(799\) −1.23133e18 −0.167425
\(800\) 1.04211e19 1.40549
\(801\) 2.42182e18 0.323989
\(802\) −5.11258e18 −0.678432
\(803\) 1.01521e19 1.33631
\(804\) −1.05970e18 −0.138363
\(805\) 1.81004e19 2.34431
\(806\) −5.85176e18 −0.751811
\(807\) −6.30980e18 −0.804151
\(808\) −3.41141e18 −0.431280
\(809\) −1.37848e19 −1.72876 −0.864379 0.502841i \(-0.832288\pi\)
−0.864379 + 0.502841i \(0.832288\pi\)
\(810\) −6.62173e17 −0.0823794
\(811\) 7.86660e18 0.970849 0.485424 0.874279i \(-0.338665\pi\)
0.485424 + 0.874279i \(0.338665\pi\)
\(812\) −1.65185e19 −2.02235
\(813\) −6.05329e18 −0.735196
\(814\) 3.87007e18 0.466294
\(815\) −1.80826e19 −2.16140
\(816\) 1.01421e18 0.120266
\(817\) −1.63443e17 −0.0192275
\(818\) 5.15507e18 0.601642
\(819\) −6.05998e18 −0.701659
\(820\) 4.87303e18 0.559769
\(821\) −1.12256e18 −0.127932 −0.0639661 0.997952i \(-0.520375\pi\)
−0.0639661 + 0.997952i \(0.520375\pi\)
\(822\) −2.01570e18 −0.227907
\(823\) −5.31478e18 −0.596193 −0.298096 0.954536i \(-0.596352\pi\)
−0.298096 + 0.954536i \(0.596352\pi\)
\(824\) 4.12872e17 0.0459503
\(825\) 5.54196e18 0.611945
\(826\) −1.10298e18 −0.120836
\(827\) −1.51535e19 −1.64712 −0.823562 0.567226i \(-0.808017\pi\)
−0.823562 + 0.567226i \(0.808017\pi\)
\(828\) −1.87417e18 −0.202121
\(829\) −1.13320e19 −1.21256 −0.606280 0.795251i \(-0.707339\pi\)
−0.606280 + 0.795251i \(0.707339\pi\)
\(830\) −6.87107e18 −0.729486
\(831\) 1.24151e18 0.130780
\(832\) 1.40000e18 0.146327
\(833\) 1.52247e19 1.57890
\(834\) 1.30600e18 0.134389
\(835\) 7.97138e18 0.813901
\(836\) 3.69074e17 0.0373915
\(837\) −2.73950e18 −0.275394
\(838\) 4.09699e18 0.408676
\(839\) −5.77180e18 −0.571292 −0.285646 0.958335i \(-0.592208\pi\)
−0.285646 + 0.958335i \(0.592208\pi\)
\(840\) −1.48621e19 −1.45971
\(841\) 8.85449e18 0.862958
\(842\) 5.86746e18 0.567442
\(843\) 2.49500e18 0.239437
\(844\) 1.30477e19 1.24254
\(845\) −3.12165e18 −0.294995
\(846\) −4.93227e17 −0.0462530
\(847\) 8.37079e18 0.778976
\(848\) 2.60316e18 0.240397
\(849\) 5.00644e18 0.458806
\(850\) 4.21950e18 0.383741
\(851\) 1.09727e19 0.990310
\(852\) 2.24343e17 0.0200935
\(853\) −1.09086e18 −0.0969615 −0.0484807 0.998824i \(-0.515438\pi\)
−0.0484807 + 0.998824i \(0.515438\pi\)
\(854\) 1.60959e19 1.41984
\(855\) 3.69719e17 0.0323662
\(856\) 1.27455e19 1.10733
\(857\) 1.02647e19 0.885059 0.442530 0.896754i \(-0.354081\pi\)
0.442530 + 0.896754i \(0.354081\pi\)
\(858\) 2.73666e18 0.234182
\(859\) −7.39090e18 −0.627685 −0.313842 0.949475i \(-0.601616\pi\)
−0.313842 + 0.949475i \(0.601616\pi\)
\(860\) 4.28331e18 0.361027
\(861\) −6.29472e18 −0.526569
\(862\) −3.84138e18 −0.318926
\(863\) 5.38961e18 0.444107 0.222053 0.975034i \(-0.428724\pi\)
0.222053 + 0.975034i \(0.428724\pi\)
\(864\) 2.40910e18 0.197023
\(865\) 2.67402e18 0.217050
\(866\) −1.92724e17 −0.0155264
\(867\) −4.78526e18 −0.382632
\(868\) −2.67159e19 −2.12027
\(869\) −1.54969e19 −1.22072
\(870\) 7.47269e18 0.584254
\(871\) 4.38724e18 0.340466
\(872\) 1.98620e19 1.52991
\(873\) −4.39212e18 −0.335800
\(874\) −3.15502e17 −0.0239429
\(875\) 1.47045e19 1.10764
\(876\) −1.02692e19 −0.767818
\(877\) −1.44805e19 −1.07470 −0.537348 0.843361i \(-0.680574\pi\)
−0.537348 + 0.843361i \(0.680574\pi\)
\(878\) −9.47514e18 −0.698025
\(879\) −1.10600e19 −0.808777
\(880\) −5.87676e18 −0.426580
\(881\) −1.69980e19 −1.22477 −0.612385 0.790560i \(-0.709790\pi\)
−0.612385 + 0.790560i \(0.709790\pi\)
\(882\) 6.09846e18 0.436188
\(883\) 7.63222e18 0.541884 0.270942 0.962596i \(-0.412665\pi\)
0.270942 + 0.962596i \(0.412665\pi\)
\(884\) −6.91076e18 −0.487064
\(885\) −1.65494e18 −0.115785
\(886\) 1.25821e19 0.873842
\(887\) −5.94311e18 −0.409741 −0.204871 0.978789i \(-0.565677\pi\)
−0.204871 + 0.978789i \(0.565677\pi\)
\(888\) −9.00964e18 −0.616628
\(889\) −3.91639e19 −2.66088
\(890\) −1.06843e19 −0.720631
\(891\) 1.28116e18 0.0857827
\(892\) 4.47156e18 0.297227
\(893\) 2.75390e17 0.0181724
\(894\) 5.80168e18 0.380067
\(895\) 1.09183e19 0.710074
\(896\) 2.86502e19 1.84981
\(897\) 7.75918e18 0.497353
\(898\) 1.19348e18 0.0759486
\(899\) 3.09155e19 1.95316
\(900\) −5.60584e18 −0.351612
\(901\) 6.25032e18 0.389217
\(902\) 2.84266e18 0.175745
\(903\) −5.53295e18 −0.339614
\(904\) 1.70206e19 1.03724
\(905\) −2.08807e19 −1.26336
\(906\) 9.90347e17 0.0594914
\(907\) 1.52905e19 0.911957 0.455978 0.889991i \(-0.349289\pi\)
0.455978 + 0.889991i \(0.349289\pi\)
\(908\) 1.04386e19 0.618137
\(909\) 2.87285e18 0.168907
\(910\) 2.67348e19 1.56066
\(911\) 1.71685e19 0.995092 0.497546 0.867438i \(-0.334235\pi\)
0.497546 + 0.867438i \(0.334235\pi\)
\(912\) −2.26831e17 −0.0130538
\(913\) 1.32941e19 0.759623
\(914\) −6.40280e18 −0.363262
\(915\) 2.41507e19 1.36048
\(916\) 8.15420e18 0.456101
\(917\) −1.01500e19 −0.563720
\(918\) 9.75445e17 0.0537930
\(919\) 2.99876e19 1.64207 0.821034 0.570879i \(-0.193397\pi\)
0.821034 + 0.570879i \(0.193397\pi\)
\(920\) 1.90294e19 1.03468
\(921\) −9.11242e18 −0.491978
\(922\) −1.32162e19 −0.708523
\(923\) −9.28795e17 −0.0494434
\(924\) 1.24941e19 0.660443
\(925\) 3.28205e19 1.72276
\(926\) −7.05050e18 −0.367493
\(927\) −3.47692e17 −0.0179960
\(928\) −2.71870e19 −1.39733
\(929\) −2.16193e19 −1.10342 −0.551710 0.834036i \(-0.686024\pi\)
−0.551710 + 0.834036i \(0.686024\pi\)
\(930\) 1.20858e19 0.612544
\(931\) −3.40503e18 −0.171375
\(932\) −2.95258e19 −1.47570
\(933\) 1.17667e19 0.584013
\(934\) 8.50315e18 0.419107
\(935\) −1.41104e19 −0.690658
\(936\) −6.37103e18 −0.309682
\(937\) −1.19127e19 −0.575045 −0.287523 0.957774i \(-0.592832\pi\)
−0.287523 + 0.957774i \(0.592832\pi\)
\(938\) −6.03903e18 −0.289500
\(939\) −2.90149e18 −0.138132
\(940\) −7.21706e18 −0.341216
\(941\) −2.08670e19 −0.979776 −0.489888 0.871785i \(-0.662962\pi\)
−0.489888 + 0.871785i \(0.662962\pi\)
\(942\) 3.79477e18 0.176952
\(943\) 8.05973e18 0.373245
\(944\) 1.01534e18 0.0466976
\(945\) 1.25159e19 0.571682
\(946\) 2.49865e18 0.113348
\(947\) 2.59334e19 1.16838 0.584190 0.811617i \(-0.301412\pi\)
0.584190 + 0.811617i \(0.301412\pi\)
\(948\) 1.56756e19 0.701405
\(949\) 4.25150e19 1.88935
\(950\) −9.43700e17 −0.0416515
\(951\) −3.88277e18 −0.170203
\(952\) 2.18934e19 0.953176
\(953\) 2.69420e19 1.16500 0.582501 0.812830i \(-0.302074\pi\)
0.582501 + 0.812830i \(0.302074\pi\)
\(954\) 2.50366e18 0.107525
\(955\) −1.45738e19 −0.621657
\(956\) −2.00595e19 −0.849854
\(957\) −1.44581e19 −0.608392
\(958\) −6.54806e18 −0.273676
\(959\) 3.80992e19 1.58159
\(960\) −2.89146e18 −0.119221
\(961\) 2.55831e19 1.04774
\(962\) 1.62070e19 0.659273
\(963\) −1.07334e19 −0.433676
\(964\) 1.62119e19 0.650627
\(965\) −3.42624e19 −1.36581
\(966\) −1.06805e19 −0.422902
\(967\) 2.00944e19 0.790320 0.395160 0.918612i \(-0.370689\pi\)
0.395160 + 0.918612i \(0.370689\pi\)
\(968\) 8.80045e18 0.343807
\(969\) −5.44632e17 −0.0211348
\(970\) 1.93767e19 0.746902
\(971\) 1.08762e19 0.416441 0.208221 0.978082i \(-0.433233\pi\)
0.208221 + 0.978082i \(0.433233\pi\)
\(972\) −1.29593e18 −0.0492892
\(973\) −2.46851e19 −0.932612
\(974\) −2.49751e18 −0.0937289
\(975\) 2.32085e19 0.865203
\(976\) −1.48170e19 −0.548701
\(977\) −1.60956e19 −0.592098 −0.296049 0.955173i \(-0.595669\pi\)
−0.296049 + 0.955173i \(0.595669\pi\)
\(978\) 1.06700e19 0.389908
\(979\) 2.06719e19 0.750402
\(980\) 8.92345e19 3.21783
\(981\) −1.67264e19 −0.599175
\(982\) −1.74612e19 −0.621368
\(983\) 1.76692e19 0.624623 0.312312 0.949980i \(-0.398897\pi\)
0.312312 + 0.949980i \(0.398897\pi\)
\(984\) −6.61781e18 −0.232405
\(985\) −5.83594e19 −2.03599
\(986\) −1.10080e19 −0.381513
\(987\) 9.32261e18 0.320979
\(988\) 1.54560e18 0.0528662
\(989\) 7.08436e18 0.240727
\(990\) −5.65211e18 −0.190802
\(991\) −3.77816e19 −1.26707 −0.633536 0.773713i \(-0.718397\pi\)
−0.633536 + 0.773713i \(0.718397\pi\)
\(992\) −4.39704e19 −1.46499
\(993\) −1.79683e19 −0.594752
\(994\) 1.27848e18 0.0420421
\(995\) 7.57748e19 2.47557
\(996\) −1.34473e19 −0.436465
\(997\) 4.25387e19 1.37172 0.685860 0.727733i \(-0.259426\pi\)
0.685860 + 0.727733i \(0.259426\pi\)
\(998\) 2.61388e19 0.837407
\(999\) 7.58730e18 0.241497
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 177.14.a.a.1.20 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.20 30 1.1 even 1 trivial