Properties

Label 177.14.a.a.1.5
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 1.5
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-150.711 q^{2} +729.000 q^{3} +14521.7 q^{4} +40403.2 q^{5} -109868. q^{6} -111720. q^{7} -953949. q^{8} +531441. q^{9} +O(q^{10})\) \(q-150.711 q^{2} +729.000 q^{3} +14521.7 q^{4} +40403.2 q^{5} -109868. q^{6} -111720. q^{7} -953949. q^{8} +531441. q^{9} -6.08919e6 q^{10} +1.14493e7 q^{11} +1.05863e7 q^{12} -2.30492e7 q^{13} +1.68373e7 q^{14} +2.94539e7 q^{15} +2.48086e7 q^{16} -3.16046e7 q^{17} -8.00938e7 q^{18} -1.79039e8 q^{19} +5.86722e8 q^{20} -8.14436e7 q^{21} -1.72553e9 q^{22} +2.82674e8 q^{23} -6.95429e8 q^{24} +4.11716e8 q^{25} +3.47376e9 q^{26} +3.87420e8 q^{27} -1.62236e9 q^{28} +4.89072e9 q^{29} -4.43902e9 q^{30} +6.10633e9 q^{31} +4.07583e9 q^{32} +8.34656e9 q^{33} +4.76315e9 q^{34} -4.51383e9 q^{35} +7.71741e9 q^{36} -2.53180e10 q^{37} +2.69831e10 q^{38} -1.68029e10 q^{39} -3.85426e10 q^{40} -8.94314e8 q^{41} +1.22744e10 q^{42} -5.19863e10 q^{43} +1.66263e11 q^{44} +2.14719e10 q^{45} -4.26020e10 q^{46} -8.00138e10 q^{47} +1.80855e10 q^{48} -8.44078e10 q^{49} -6.20499e10 q^{50} -2.30398e10 q^{51} -3.34713e11 q^{52} -3.21867e11 q^{53} -5.83884e10 q^{54} +4.62590e11 q^{55} +1.06575e11 q^{56} -1.30520e11 q^{57} -7.37084e11 q^{58} +4.21805e10 q^{59} +4.27721e11 q^{60} +9.93954e10 q^{61} -9.20288e11 q^{62} -5.93724e10 q^{63} -8.17503e11 q^{64} -9.31261e11 q^{65} -1.25791e12 q^{66} -3.29871e11 q^{67} -4.58952e11 q^{68} +2.06069e11 q^{69} +6.80282e11 q^{70} +1.94331e12 q^{71} -5.06968e11 q^{72} -4.35977e11 q^{73} +3.81569e12 q^{74} +3.00141e11 q^{75} -2.59995e12 q^{76} -1.27911e12 q^{77} +2.53237e12 q^{78} -3.67817e12 q^{79} +1.00235e12 q^{80} +2.82430e11 q^{81} +1.34783e11 q^{82} -3.03973e12 q^{83} -1.18270e12 q^{84} -1.27693e12 q^{85} +7.83488e12 q^{86} +3.56534e12 q^{87} -1.09221e13 q^{88} -6.66725e11 q^{89} -3.23605e12 q^{90} +2.57505e12 q^{91} +4.10490e12 q^{92} +4.45151e12 q^{93} +1.20589e13 q^{94} -7.23376e12 q^{95} +2.97128e12 q^{96} +1.40882e12 q^{97} +1.27211e13 q^{98} +6.08464e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −150.711 −1.66513 −0.832566 0.553926i \(-0.813129\pi\)
−0.832566 + 0.553926i \(0.813129\pi\)
\(3\) 729.000 0.577350
\(4\) 14521.7 1.77267
\(5\) 40403.2 1.15641 0.578204 0.815893i \(-0.303754\pi\)
0.578204 + 0.815893i \(0.303754\pi\)
\(6\) −109868. −0.961365
\(7\) −111720. −0.358915 −0.179458 0.983766i \(-0.557434\pi\)
−0.179458 + 0.983766i \(0.557434\pi\)
\(8\) −953949. −1.28659
\(9\) 531441. 0.333333
\(10\) −6.08919e6 −1.92557
\(11\) 1.14493e7 1.94862 0.974311 0.225207i \(-0.0723059\pi\)
0.974311 + 0.225207i \(0.0723059\pi\)
\(12\) 1.05863e7 1.02345
\(13\) −2.30492e7 −1.32441 −0.662207 0.749321i \(-0.730380\pi\)
−0.662207 + 0.749321i \(0.730380\pi\)
\(14\) 1.68373e7 0.597641
\(15\) 2.94539e7 0.667652
\(16\) 2.48086e7 0.369678
\(17\) −3.16046e7 −0.317565 −0.158783 0.987314i \(-0.550757\pi\)
−0.158783 + 0.987314i \(0.550757\pi\)
\(18\) −8.00938e7 −0.555044
\(19\) −1.79039e8 −0.873071 −0.436536 0.899687i \(-0.643795\pi\)
−0.436536 + 0.899687i \(0.643795\pi\)
\(20\) 5.86722e8 2.04992
\(21\) −8.14436e7 −0.207220
\(22\) −1.72553e9 −3.24471
\(23\) 2.82674e8 0.398158 0.199079 0.979983i \(-0.436205\pi\)
0.199079 + 0.979983i \(0.436205\pi\)
\(24\) −6.95429e8 −0.742813
\(25\) 4.11716e8 0.337278
\(26\) 3.47376e9 2.20533
\(27\) 3.87420e8 0.192450
\(28\) −1.62236e9 −0.636237
\(29\) 4.89072e9 1.52681 0.763407 0.645918i \(-0.223525\pi\)
0.763407 + 0.645918i \(0.223525\pi\)
\(30\) −4.43902e9 −1.11173
\(31\) 6.10633e9 1.23575 0.617873 0.786278i \(-0.287995\pi\)
0.617873 + 0.786278i \(0.287995\pi\)
\(32\) 4.07583e9 0.671028
\(33\) 8.34656e9 1.12504
\(34\) 4.76315e9 0.528788
\(35\) −4.51383e9 −0.415052
\(36\) 7.71741e9 0.590889
\(37\) −2.53180e10 −1.62225 −0.811126 0.584872i \(-0.801145\pi\)
−0.811126 + 0.584872i \(0.801145\pi\)
\(38\) 2.69831e10 1.45378
\(39\) −1.68029e10 −0.764651
\(40\) −3.85426e10 −1.48782
\(41\) −8.94314e8 −0.0294032 −0.0147016 0.999892i \(-0.504680\pi\)
−0.0147016 + 0.999892i \(0.504680\pi\)
\(42\) 1.22744e10 0.345048
\(43\) −5.19863e10 −1.25413 −0.627067 0.778965i \(-0.715745\pi\)
−0.627067 + 0.778965i \(0.715745\pi\)
\(44\) 1.66263e11 3.45425
\(45\) 2.14719e10 0.385469
\(46\) −4.26020e10 −0.662985
\(47\) −8.00138e10 −1.08275 −0.541376 0.840781i \(-0.682096\pi\)
−0.541376 + 0.840781i \(0.682096\pi\)
\(48\) 1.80855e10 0.213433
\(49\) −8.44078e10 −0.871180
\(50\) −6.20499e10 −0.561612
\(51\) −2.30398e10 −0.183346
\(52\) −3.34713e11 −2.34774
\(53\) −3.21867e11 −1.99473 −0.997363 0.0725690i \(-0.976880\pi\)
−0.997363 + 0.0725690i \(0.976880\pi\)
\(54\) −5.83884e10 −0.320455
\(55\) 4.62590e11 2.25340
\(56\) 1.06575e11 0.461777
\(57\) −1.30520e11 −0.504068
\(58\) −7.37084e11 −2.54235
\(59\) 4.21805e10 0.130189
\(60\) 4.27721e11 1.18352
\(61\) 9.93954e10 0.247014 0.123507 0.992344i \(-0.460586\pi\)
0.123507 + 0.992344i \(0.460586\pi\)
\(62\) −9.20288e11 −2.05768
\(63\) −5.93724e10 −0.119638
\(64\) −8.17503e11 −1.48703
\(65\) −9.31261e11 −1.53156
\(66\) −1.25791e12 −1.87334
\(67\) −3.29871e11 −0.445511 −0.222755 0.974874i \(-0.571505\pi\)
−0.222755 + 0.974874i \(0.571505\pi\)
\(68\) −4.58952e11 −0.562937
\(69\) 2.06069e11 0.229877
\(70\) 6.80282e11 0.691117
\(71\) 1.94331e12 1.80038 0.900188 0.435502i \(-0.143429\pi\)
0.900188 + 0.435502i \(0.143429\pi\)
\(72\) −5.06968e11 −0.428863
\(73\) −4.35977e11 −0.337182 −0.168591 0.985686i \(-0.553922\pi\)
−0.168591 + 0.985686i \(0.553922\pi\)
\(74\) 3.81569e12 2.70126
\(75\) 3.00141e11 0.194727
\(76\) −2.59995e12 −1.54766
\(77\) −1.27911e12 −0.699390
\(78\) 2.53237e12 1.27325
\(79\) −3.67817e12 −1.70238 −0.851189 0.524859i \(-0.824118\pi\)
−0.851189 + 0.524859i \(0.824118\pi\)
\(80\) 1.00235e12 0.427498
\(81\) 2.82430e11 0.111111
\(82\) 1.34783e11 0.0489603
\(83\) −3.03973e12 −1.02053 −0.510267 0.860016i \(-0.670454\pi\)
−0.510267 + 0.860016i \(0.670454\pi\)
\(84\) −1.18270e12 −0.367331
\(85\) −1.27693e12 −0.367235
\(86\) 7.83488e12 2.08830
\(87\) 3.56534e12 0.881506
\(88\) −1.09221e13 −2.50708
\(89\) −6.66725e11 −0.142204 −0.0711020 0.997469i \(-0.522652\pi\)
−0.0711020 + 0.997469i \(0.522652\pi\)
\(90\) −3.23605e12 −0.641857
\(91\) 2.57505e12 0.475353
\(92\) 4.10490e12 0.705801
\(93\) 4.45151e12 0.713458
\(94\) 1.20589e13 1.80293
\(95\) −7.23376e12 −1.00963
\(96\) 2.97128e12 0.387418
\(97\) 1.40882e12 0.171727 0.0858636 0.996307i \(-0.472635\pi\)
0.0858636 + 0.996307i \(0.472635\pi\)
\(98\) 1.27211e13 1.45063
\(99\) 6.08464e12 0.649541
\(100\) 5.97880e12 0.597880
\(101\) −1.36581e13 −1.28027 −0.640136 0.768262i \(-0.721122\pi\)
−0.640136 + 0.768262i \(0.721122\pi\)
\(102\) 3.47234e12 0.305296
\(103\) −3.36418e12 −0.277611 −0.138806 0.990320i \(-0.544326\pi\)
−0.138806 + 0.990320i \(0.544326\pi\)
\(104\) 2.19878e13 1.70398
\(105\) −3.29058e12 −0.239630
\(106\) 4.85088e13 3.32148
\(107\) −6.30309e12 −0.406030 −0.203015 0.979176i \(-0.565074\pi\)
−0.203015 + 0.979176i \(0.565074\pi\)
\(108\) 5.62599e12 0.341150
\(109\) −1.06086e12 −0.0605881 −0.0302940 0.999541i \(-0.509644\pi\)
−0.0302940 + 0.999541i \(0.509644\pi\)
\(110\) −6.97171e13 −3.75221
\(111\) −1.84568e13 −0.936607
\(112\) −2.77161e12 −0.132683
\(113\) 4.33645e13 1.95941 0.979703 0.200456i \(-0.0642425\pi\)
0.979703 + 0.200456i \(0.0642425\pi\)
\(114\) 1.96707e13 0.839340
\(115\) 1.14209e13 0.460433
\(116\) 7.10215e13 2.70653
\(117\) −1.22493e13 −0.441471
\(118\) −6.35705e12 −0.216782
\(119\) 3.53086e12 0.113979
\(120\) −2.80976e13 −0.858995
\(121\) 9.65644e13 2.79713
\(122\) −1.49799e13 −0.411312
\(123\) −6.51955e11 −0.0169760
\(124\) 8.86741e13 2.19056
\(125\) −3.26857e13 −0.766377
\(126\) 8.94804e12 0.199214
\(127\) −6.17167e13 −1.30521 −0.652603 0.757700i \(-0.726323\pi\)
−0.652603 + 0.757700i \(0.726323\pi\)
\(128\) 8.98171e13 1.80507
\(129\) −3.78980e13 −0.724075
\(130\) 1.40351e14 2.55025
\(131\) −4.55967e13 −0.788262 −0.394131 0.919054i \(-0.628954\pi\)
−0.394131 + 0.919054i \(0.628954\pi\)
\(132\) 1.21206e14 1.99431
\(133\) 2.00022e13 0.313359
\(134\) 4.97151e13 0.741834
\(135\) 1.56530e13 0.222551
\(136\) 3.01492e13 0.408576
\(137\) −6.74061e13 −0.870995 −0.435497 0.900190i \(-0.643427\pi\)
−0.435497 + 0.900190i \(0.643427\pi\)
\(138\) −3.10569e13 −0.382775
\(139\) 1.49487e14 1.75795 0.878976 0.476865i \(-0.158227\pi\)
0.878976 + 0.476865i \(0.158227\pi\)
\(140\) −6.55483e13 −0.735749
\(141\) −5.83301e13 −0.625127
\(142\) −2.92878e14 −2.99786
\(143\) −2.63898e14 −2.58078
\(144\) 1.31843e13 0.123226
\(145\) 1.97601e14 1.76562
\(146\) 6.57063e13 0.561453
\(147\) −6.15333e13 −0.502976
\(148\) −3.67660e14 −2.87571
\(149\) −2.71532e13 −0.203287 −0.101644 0.994821i \(-0.532410\pi\)
−0.101644 + 0.994821i \(0.532410\pi\)
\(150\) −4.52344e13 −0.324247
\(151\) −8.33497e13 −0.572208 −0.286104 0.958199i \(-0.592360\pi\)
−0.286104 + 0.958199i \(0.592360\pi\)
\(152\) 1.70794e14 1.12328
\(153\) −1.67960e13 −0.105855
\(154\) 1.92776e14 1.16458
\(155\) 2.46715e14 1.42903
\(156\) −2.44006e14 −1.35547
\(157\) −3.06635e14 −1.63408 −0.817042 0.576579i \(-0.804387\pi\)
−0.817042 + 0.576579i \(0.804387\pi\)
\(158\) 5.54339e14 2.83468
\(159\) −2.34641e14 −1.15166
\(160\) 1.64676e14 0.775982
\(161\) −3.15802e13 −0.142905
\(162\) −4.25651e13 −0.185015
\(163\) 3.46201e14 1.44580 0.722902 0.690951i \(-0.242808\pi\)
0.722902 + 0.690951i \(0.242808\pi\)
\(164\) −1.29869e13 −0.0521221
\(165\) 3.37228e14 1.30100
\(166\) 4.58120e14 1.69933
\(167\) 4.52597e14 1.61456 0.807280 0.590168i \(-0.200939\pi\)
0.807280 + 0.590168i \(0.200939\pi\)
\(168\) 7.76930e13 0.266607
\(169\) 2.28390e14 0.754074
\(170\) 1.92447e14 0.611494
\(171\) −9.51488e13 −0.291024
\(172\) −7.54928e14 −2.22316
\(173\) 2.74297e13 0.0777895 0.0388947 0.999243i \(-0.487616\pi\)
0.0388947 + 0.999243i \(0.487616\pi\)
\(174\) −5.37334e14 −1.46782
\(175\) −4.59967e13 −0.121054
\(176\) 2.84042e14 0.720362
\(177\) 3.07496e13 0.0751646
\(178\) 1.00483e14 0.236789
\(179\) 4.68788e14 1.06520 0.532600 0.846367i \(-0.321215\pi\)
0.532600 + 0.846367i \(0.321215\pi\)
\(180\) 3.11808e14 0.683308
\(181\) −1.71757e14 −0.363080 −0.181540 0.983384i \(-0.558108\pi\)
−0.181540 + 0.983384i \(0.558108\pi\)
\(182\) −3.88087e14 −0.791525
\(183\) 7.24593e13 0.142614
\(184\) −2.69657e14 −0.512266
\(185\) −1.02293e15 −1.87598
\(186\) −6.70890e14 −1.18800
\(187\) −3.61852e14 −0.618814
\(188\) −1.16193e15 −1.91936
\(189\) −4.32824e13 −0.0690733
\(190\) 1.09020e15 1.68116
\(191\) 8.15534e14 1.21542 0.607708 0.794160i \(-0.292089\pi\)
0.607708 + 0.794160i \(0.292089\pi\)
\(192\) −5.95959e14 −0.858536
\(193\) −8.65127e14 −1.20492 −0.602459 0.798150i \(-0.705812\pi\)
−0.602459 + 0.798150i \(0.705812\pi\)
\(194\) −2.12324e14 −0.285949
\(195\) −6.78889e14 −0.884248
\(196\) −1.22574e15 −1.54431
\(197\) 3.32229e14 0.404955 0.202477 0.979287i \(-0.435101\pi\)
0.202477 + 0.979287i \(0.435101\pi\)
\(198\) −9.17020e14 −1.08157
\(199\) 1.08216e15 1.23522 0.617611 0.786484i \(-0.288101\pi\)
0.617611 + 0.786484i \(0.288101\pi\)
\(200\) −3.92756e14 −0.433938
\(201\) −2.40476e14 −0.257216
\(202\) 2.05842e15 2.13182
\(203\) −5.46389e14 −0.547997
\(204\) −3.34576e14 −0.325012
\(205\) −3.61331e13 −0.0340021
\(206\) 5.07018e14 0.462260
\(207\) 1.50225e14 0.132719
\(208\) −5.71819e14 −0.489606
\(209\) −2.04988e15 −1.70129
\(210\) 4.95925e14 0.399016
\(211\) −8.38734e14 −0.654317 −0.327159 0.944969i \(-0.606091\pi\)
−0.327159 + 0.944969i \(0.606091\pi\)
\(212\) −4.67405e15 −3.53598
\(213\) 1.41667e15 1.03945
\(214\) 9.49942e14 0.676094
\(215\) −2.10041e15 −1.45029
\(216\) −3.69579e14 −0.247604
\(217\) −6.82196e14 −0.443528
\(218\) 1.59883e14 0.100887
\(219\) −3.17827e14 −0.194672
\(220\) 6.71758e15 3.99452
\(221\) 7.28461e14 0.420588
\(222\) 2.78164e15 1.55957
\(223\) 3.09576e14 0.168572 0.0842861 0.996442i \(-0.473139\pi\)
0.0842861 + 0.996442i \(0.473139\pi\)
\(224\) −4.55350e14 −0.240842
\(225\) 2.18803e14 0.112426
\(226\) −6.53549e15 −3.26267
\(227\) −1.37548e14 −0.0667248 −0.0333624 0.999443i \(-0.510622\pi\)
−0.0333624 + 0.999443i \(0.510622\pi\)
\(228\) −1.89536e15 −0.893544
\(229\) 1.02345e15 0.468962 0.234481 0.972121i \(-0.424661\pi\)
0.234481 + 0.972121i \(0.424661\pi\)
\(230\) −1.72126e15 −0.766681
\(231\) −9.32474e14 −0.403793
\(232\) −4.66550e15 −1.96438
\(233\) 2.48929e14 0.101921 0.0509603 0.998701i \(-0.483772\pi\)
0.0509603 + 0.998701i \(0.483772\pi\)
\(234\) 1.84610e15 0.735108
\(235\) −3.23281e15 −1.25210
\(236\) 6.12532e14 0.230781
\(237\) −2.68139e15 −0.982868
\(238\) −5.32137e14 −0.189790
\(239\) 3.22328e15 1.11870 0.559348 0.828933i \(-0.311052\pi\)
0.559348 + 0.828933i \(0.311052\pi\)
\(240\) 7.30712e14 0.246816
\(241\) −3.46004e15 −1.13755 −0.568774 0.822494i \(-0.692582\pi\)
−0.568774 + 0.822494i \(0.692582\pi\)
\(242\) −1.45533e16 −4.65759
\(243\) 2.05891e14 0.0641500
\(244\) 1.44339e15 0.437874
\(245\) −3.41034e15 −1.00744
\(246\) 9.82565e13 0.0282672
\(247\) 4.12671e15 1.15631
\(248\) −5.82512e15 −1.58990
\(249\) −2.21596e15 −0.589206
\(250\) 4.92608e15 1.27612
\(251\) −6.28189e15 −1.58566 −0.792832 0.609440i \(-0.791394\pi\)
−0.792832 + 0.609440i \(0.791394\pi\)
\(252\) −8.62186e14 −0.212079
\(253\) 3.23643e15 0.775859
\(254\) 9.30136e15 2.17334
\(255\) −9.30881e14 −0.212023
\(256\) −6.83941e15 −1.51865
\(257\) 1.92923e15 0.417655 0.208828 0.977952i \(-0.433035\pi\)
0.208828 + 0.977952i \(0.433035\pi\)
\(258\) 5.71163e15 1.20568
\(259\) 2.82851e15 0.582251
\(260\) −1.35235e16 −2.71495
\(261\) 2.59913e15 0.508938
\(262\) 6.87191e15 1.31256
\(263\) −6.59134e15 −1.22818 −0.614089 0.789237i \(-0.710476\pi\)
−0.614089 + 0.789237i \(0.710476\pi\)
\(264\) −7.96219e15 −1.44746
\(265\) −1.30045e16 −2.30672
\(266\) −3.01454e15 −0.521783
\(267\) −4.86043e14 −0.0821015
\(268\) −4.79028e15 −0.789741
\(269\) −1.00825e16 −1.62248 −0.811238 0.584716i \(-0.801206\pi\)
−0.811238 + 0.584716i \(0.801206\pi\)
\(270\) −2.35908e15 −0.370576
\(271\) −6.94649e15 −1.06528 −0.532642 0.846341i \(-0.678801\pi\)
−0.532642 + 0.846341i \(0.678801\pi\)
\(272\) −7.84068e14 −0.117397
\(273\) 1.87721e15 0.274445
\(274\) 1.01588e16 1.45032
\(275\) 4.71387e15 0.657226
\(276\) 2.99247e15 0.407494
\(277\) −5.61042e15 −0.746237 −0.373119 0.927784i \(-0.621712\pi\)
−0.373119 + 0.927784i \(0.621712\pi\)
\(278\) −2.25293e16 −2.92722
\(279\) 3.24515e15 0.411915
\(280\) 4.30596e15 0.534002
\(281\) −2.01691e15 −0.244397 −0.122199 0.992506i \(-0.538994\pi\)
−0.122199 + 0.992506i \(0.538994\pi\)
\(282\) 8.79096e15 1.04092
\(283\) 9.97297e15 1.15402 0.577009 0.816738i \(-0.304220\pi\)
0.577009 + 0.816738i \(0.304220\pi\)
\(284\) 2.82201e16 3.19146
\(285\) −5.27341e15 −0.582908
\(286\) 3.97722e16 4.29734
\(287\) 9.99124e13 0.0105533
\(288\) 2.16606e15 0.223676
\(289\) −8.90573e15 −0.899152
\(290\) −2.97805e16 −2.93999
\(291\) 1.02703e15 0.0991468
\(292\) −6.33111e15 −0.597712
\(293\) −5.67845e15 −0.524312 −0.262156 0.965025i \(-0.584434\pi\)
−0.262156 + 0.965025i \(0.584434\pi\)
\(294\) 9.27371e15 0.837521
\(295\) 1.70423e15 0.150551
\(296\) 2.41521e16 2.08717
\(297\) 4.43570e15 0.375012
\(298\) 4.09227e15 0.338500
\(299\) −6.51541e15 −0.527326
\(300\) 4.35855e15 0.345186
\(301\) 5.80789e15 0.450128
\(302\) 1.25617e16 0.952802
\(303\) −9.95677e15 −0.739165
\(304\) −4.44172e15 −0.322755
\(305\) 4.01589e15 0.285649
\(306\) 2.53133e15 0.176263
\(307\) −3.03492e15 −0.206894 −0.103447 0.994635i \(-0.532987\pi\)
−0.103447 + 0.994635i \(0.532987\pi\)
\(308\) −1.85749e16 −1.23978
\(309\) −2.45249e15 −0.160279
\(310\) −3.71826e16 −2.37952
\(311\) 2.74950e16 1.72310 0.861552 0.507670i \(-0.169493\pi\)
0.861552 + 0.507670i \(0.169493\pi\)
\(312\) 1.60291e16 0.983793
\(313\) −2.22356e16 −1.33663 −0.668315 0.743879i \(-0.732984\pi\)
−0.668315 + 0.743879i \(0.732984\pi\)
\(314\) 4.62132e16 2.72097
\(315\) −2.39883e15 −0.138351
\(316\) −5.34132e16 −3.01775
\(317\) 8.61319e15 0.476737 0.238368 0.971175i \(-0.423387\pi\)
0.238368 + 0.971175i \(0.423387\pi\)
\(318\) 3.53629e16 1.91766
\(319\) 5.59955e16 2.97518
\(320\) −3.30297e16 −1.71961
\(321\) −4.59495e15 −0.234422
\(322\) 4.75948e15 0.237956
\(323\) 5.65847e15 0.277257
\(324\) 4.10135e15 0.196963
\(325\) −9.48972e15 −0.446695
\(326\) −5.21762e16 −2.40745
\(327\) −7.73369e14 −0.0349805
\(328\) 8.53130e14 0.0378299
\(329\) 8.93911e15 0.388616
\(330\) −5.08238e16 −2.16634
\(331\) 1.78462e16 0.745870 0.372935 0.927858i \(-0.378351\pi\)
0.372935 + 0.927858i \(0.378351\pi\)
\(332\) −4.41420e16 −1.80907
\(333\) −1.34550e16 −0.540750
\(334\) −6.82111e16 −2.68846
\(335\) −1.33278e16 −0.515192
\(336\) −2.02050e15 −0.0766045
\(337\) −4.78621e16 −1.77991 −0.889953 0.456052i \(-0.849263\pi\)
−0.889953 + 0.456052i \(0.849263\pi\)
\(338\) −3.44208e16 −1.25563
\(339\) 3.16127e16 1.13126
\(340\) −1.85431e16 −0.650984
\(341\) 6.99133e16 2.40800
\(342\) 1.43399e16 0.484593
\(343\) 2.02544e16 0.671595
\(344\) 4.95923e16 1.61356
\(345\) 8.32587e15 0.265831
\(346\) −4.13394e15 −0.129530
\(347\) 3.10821e16 0.955805 0.477903 0.878413i \(-0.341397\pi\)
0.477903 + 0.878413i \(0.341397\pi\)
\(348\) 5.17747e16 1.56262
\(349\) 3.35603e16 0.994170 0.497085 0.867702i \(-0.334404\pi\)
0.497085 + 0.867702i \(0.334404\pi\)
\(350\) 6.93219e15 0.201571
\(351\) −8.92973e15 −0.254884
\(352\) 4.66655e16 1.30758
\(353\) 2.96364e16 0.815247 0.407624 0.913150i \(-0.366358\pi\)
0.407624 + 0.913150i \(0.366358\pi\)
\(354\) −4.63429e15 −0.125159
\(355\) 7.85160e16 2.08197
\(356\) −9.68197e15 −0.252080
\(357\) 2.57399e15 0.0658058
\(358\) −7.06512e16 −1.77370
\(359\) −4.54894e16 −1.12149 −0.560747 0.827987i \(-0.689486\pi\)
−0.560747 + 0.827987i \(0.689486\pi\)
\(360\) −2.04831e16 −0.495941
\(361\) −9.99796e15 −0.237747
\(362\) 2.58855e16 0.604577
\(363\) 7.03955e16 1.61492
\(364\) 3.73940e16 0.842641
\(365\) −1.76149e16 −0.389920
\(366\) −1.09204e16 −0.237471
\(367\) 4.75684e16 1.01622 0.508111 0.861291i \(-0.330344\pi\)
0.508111 + 0.861291i \(0.330344\pi\)
\(368\) 7.01276e15 0.147190
\(369\) −4.75275e14 −0.00980107
\(370\) 1.54166e17 3.12376
\(371\) 3.59588e16 0.715938
\(372\) 6.46434e16 1.26472
\(373\) 6.36227e16 1.22322 0.611610 0.791160i \(-0.290522\pi\)
0.611610 + 0.791160i \(0.290522\pi\)
\(374\) 5.45349e16 1.03041
\(375\) −2.38279e16 −0.442468
\(376\) 7.63291e16 1.39306
\(377\) −1.12727e17 −2.02213
\(378\) 6.52312e15 0.115016
\(379\) −5.95563e16 −1.03222 −0.516110 0.856522i \(-0.672621\pi\)
−0.516110 + 0.856522i \(0.672621\pi\)
\(380\) −1.05046e17 −1.78973
\(381\) −4.49915e16 −0.753560
\(382\) −1.22910e17 −2.02383
\(383\) 4.03567e16 0.653317 0.326659 0.945142i \(-0.394077\pi\)
0.326659 + 0.945142i \(0.394077\pi\)
\(384\) 6.54767e16 1.04216
\(385\) −5.16803e16 −0.808780
\(386\) 1.30384e17 2.00635
\(387\) −2.76276e16 −0.418045
\(388\) 2.04584e16 0.304415
\(389\) −1.12817e17 −1.65082 −0.825412 0.564531i \(-0.809057\pi\)
−0.825412 + 0.564531i \(0.809057\pi\)
\(390\) 1.02316e17 1.47239
\(391\) −8.93382e15 −0.126441
\(392\) 8.05207e16 1.12085
\(393\) −3.32400e16 −0.455103
\(394\) −5.00704e16 −0.674304
\(395\) −1.48610e17 −1.96864
\(396\) 8.83592e16 1.15142
\(397\) −6.92426e16 −0.887637 −0.443818 0.896117i \(-0.646376\pi\)
−0.443818 + 0.896117i \(0.646376\pi\)
\(398\) −1.63092e17 −2.05681
\(399\) 1.45816e16 0.180918
\(400\) 1.02141e16 0.124684
\(401\) 6.44868e16 0.774519 0.387260 0.921971i \(-0.373422\pi\)
0.387260 + 0.921971i \(0.373422\pi\)
\(402\) 3.62423e16 0.428298
\(403\) −1.40746e17 −1.63664
\(404\) −1.98339e17 −2.26949
\(405\) 1.14111e16 0.128490
\(406\) 8.23467e16 0.912487
\(407\) −2.89874e17 −3.16115
\(408\) 2.19788e16 0.235892
\(409\) −1.89160e16 −0.199815 −0.0999077 0.994997i \(-0.531855\pi\)
−0.0999077 + 0.994997i \(0.531855\pi\)
\(410\) 5.44565e15 0.0566180
\(411\) −4.91390e16 −0.502869
\(412\) −4.88535e16 −0.492112
\(413\) −4.71239e15 −0.0467268
\(414\) −2.26404e16 −0.220995
\(415\) −1.22815e17 −1.18015
\(416\) −9.39445e16 −0.888720
\(417\) 1.08976e17 1.01495
\(418\) 3.08938e17 2.83287
\(419\) 3.70729e16 0.334708 0.167354 0.985897i \(-0.446478\pi\)
0.167354 + 0.985897i \(0.446478\pi\)
\(420\) −4.77847e16 −0.424785
\(421\) −1.28568e16 −0.112538 −0.0562689 0.998416i \(-0.517920\pi\)
−0.0562689 + 0.998416i \(0.517920\pi\)
\(422\) 1.26406e17 1.08953
\(423\) −4.25226e16 −0.360917
\(424\) 3.07045e17 2.56640
\(425\) −1.30121e16 −0.107108
\(426\) −2.13508e17 −1.73082
\(427\) −1.11044e16 −0.0886573
\(428\) −9.15314e16 −0.719756
\(429\) −1.92381e17 −1.49002
\(430\) 3.16554e17 2.41492
\(431\) −1.54117e17 −1.15810 −0.579052 0.815291i \(-0.696577\pi\)
−0.579052 + 0.815291i \(0.696577\pi\)
\(432\) 9.61137e15 0.0711445
\(433\) −1.90601e17 −1.38981 −0.694903 0.719104i \(-0.744553\pi\)
−0.694903 + 0.719104i \(0.744553\pi\)
\(434\) 1.02814e17 0.738533
\(435\) 1.44051e17 1.01938
\(436\) −1.54055e16 −0.107402
\(437\) −5.06098e16 −0.347620
\(438\) 4.78999e16 0.324155
\(439\) −9.76834e16 −0.651331 −0.325665 0.945485i \(-0.605588\pi\)
−0.325665 + 0.945485i \(0.605588\pi\)
\(440\) −4.41287e17 −2.89920
\(441\) −4.48577e16 −0.290393
\(442\) −1.09787e17 −0.700334
\(443\) 9.51248e16 0.597956 0.298978 0.954260i \(-0.403354\pi\)
0.298978 + 0.954260i \(0.403354\pi\)
\(444\) −2.68024e17 −1.66029
\(445\) −2.69378e16 −0.164446
\(446\) −4.66564e16 −0.280695
\(447\) −1.97947e16 −0.117368
\(448\) 9.13310e16 0.533717
\(449\) −3.18756e17 −1.83593 −0.917967 0.396656i \(-0.870171\pi\)
−0.917967 + 0.396656i \(0.870171\pi\)
\(450\) −3.29759e16 −0.187204
\(451\) −1.02393e16 −0.0572958
\(452\) 6.29725e17 3.47337
\(453\) −6.07620e16 −0.330365
\(454\) 2.07300e16 0.111106
\(455\) 1.04040e17 0.549701
\(456\) 1.24509e17 0.648529
\(457\) 2.06050e17 1.05808 0.529039 0.848598i \(-0.322553\pi\)
0.529039 + 0.848598i \(0.322553\pi\)
\(458\) −1.54245e17 −0.780884
\(459\) −1.22443e16 −0.0611154
\(460\) 1.65851e17 0.816193
\(461\) 7.19050e16 0.348901 0.174451 0.984666i \(-0.444185\pi\)
0.174451 + 0.984666i \(0.444185\pi\)
\(462\) 1.40534e17 0.672369
\(463\) 3.53434e17 1.66737 0.833685 0.552240i \(-0.186227\pi\)
0.833685 + 0.552240i \(0.186227\pi\)
\(464\) 1.21332e17 0.564429
\(465\) 1.79855e17 0.825048
\(466\) −3.75162e16 −0.169711
\(467\) 2.16580e17 0.966181 0.483091 0.875570i \(-0.339514\pi\)
0.483091 + 0.875570i \(0.339514\pi\)
\(468\) −1.77880e17 −0.782581
\(469\) 3.68531e16 0.159901
\(470\) 4.87219e17 2.08492
\(471\) −2.23537e17 −0.943438
\(472\) −4.02381e16 −0.167500
\(473\) −5.95208e17 −2.44383
\(474\) 4.04113e17 1.63661
\(475\) −7.37133e16 −0.294467
\(476\) 5.12739e16 0.202047
\(477\) −1.71053e17 −0.664909
\(478\) −4.85783e17 −1.86278
\(479\) 2.37808e17 0.899592 0.449796 0.893131i \(-0.351497\pi\)
0.449796 + 0.893131i \(0.351497\pi\)
\(480\) 1.20049e17 0.448013
\(481\) 5.83559e17 2.14853
\(482\) 5.21464e17 1.89417
\(483\) −2.30220e16 −0.0825062
\(484\) 1.40228e18 4.95837
\(485\) 5.69209e16 0.198587
\(486\) −3.10300e16 −0.106818
\(487\) −1.27813e17 −0.434148 −0.217074 0.976155i \(-0.569651\pi\)
−0.217074 + 0.976155i \(0.569651\pi\)
\(488\) −9.48182e16 −0.317806
\(489\) 2.52381e17 0.834735
\(490\) 5.13975e17 1.67752
\(491\) 1.02449e17 0.329973 0.164986 0.986296i \(-0.447242\pi\)
0.164986 + 0.986296i \(0.447242\pi\)
\(492\) −9.46748e15 −0.0300927
\(493\) −1.54570e17 −0.484863
\(494\) −6.21939e17 −1.92541
\(495\) 2.45839e17 0.751133
\(496\) 1.51490e17 0.456827
\(497\) −2.17106e17 −0.646182
\(498\) 3.33969e17 0.981106
\(499\) 7.06516e15 0.0204865 0.0102433 0.999948i \(-0.496739\pi\)
0.0102433 + 0.999948i \(0.496739\pi\)
\(500\) −4.74651e17 −1.35853
\(501\) 3.29943e17 0.932167
\(502\) 9.46747e17 2.64034
\(503\) −5.30401e17 −1.46020 −0.730100 0.683341i \(-0.760526\pi\)
−0.730100 + 0.683341i \(0.760526\pi\)
\(504\) 5.66382e16 0.153926
\(505\) −5.51832e17 −1.48051
\(506\) −4.87764e17 −1.29191
\(507\) 1.66496e17 0.435365
\(508\) −8.96230e17 −2.31369
\(509\) 2.76867e17 0.705678 0.352839 0.935684i \(-0.385216\pi\)
0.352839 + 0.935684i \(0.385216\pi\)
\(510\) 1.40294e17 0.353046
\(511\) 4.87071e16 0.121020
\(512\) 2.94989e17 0.723688
\(513\) −6.93634e16 −0.168023
\(514\) −2.90755e17 −0.695451
\(515\) −1.35924e17 −0.321032
\(516\) −5.50343e17 −1.28354
\(517\) −9.16104e17 −2.10987
\(518\) −4.26287e17 −0.969524
\(519\) 1.99962e16 0.0449118
\(520\) 8.88376e17 1.97049
\(521\) 8.57153e17 1.87764 0.938822 0.344403i \(-0.111919\pi\)
0.938822 + 0.344403i \(0.111919\pi\)
\(522\) −3.91716e17 −0.847449
\(523\) −4.76424e17 −1.01796 −0.508982 0.860777i \(-0.669978\pi\)
−0.508982 + 0.860777i \(0.669978\pi\)
\(524\) −6.62141e17 −1.39732
\(525\) −3.35316e16 −0.0698906
\(526\) 9.93384e17 2.04508
\(527\) −1.92988e17 −0.392430
\(528\) 2.07067e17 0.415901
\(529\) −4.24132e17 −0.841470
\(530\) 1.95991e18 3.84099
\(531\) 2.24165e16 0.0433963
\(532\) 2.90465e17 0.555480
\(533\) 2.06132e16 0.0389421
\(534\) 7.32518e16 0.136710
\(535\) −2.54665e17 −0.469537
\(536\) 3.14680e17 0.573190
\(537\) 3.41746e17 0.614994
\(538\) 1.51954e18 2.70164
\(539\) −9.66412e17 −1.69760
\(540\) 2.27308e17 0.394508
\(541\) 1.29060e17 0.221314 0.110657 0.993859i \(-0.464704\pi\)
0.110657 + 0.993859i \(0.464704\pi\)
\(542\) 1.04691e18 1.77384
\(543\) −1.25211e17 −0.209624
\(544\) −1.28815e17 −0.213095
\(545\) −4.28623e16 −0.0700645
\(546\) −2.82915e17 −0.456987
\(547\) 8.79234e16 0.140342 0.0701708 0.997535i \(-0.477646\pi\)
0.0701708 + 0.997535i \(0.477646\pi\)
\(548\) −9.78849e17 −1.54398
\(549\) 5.28228e16 0.0823382
\(550\) −7.10430e17 −1.09437
\(551\) −8.75631e17 −1.33302
\(552\) −1.96580e17 −0.295757
\(553\) 4.10924e17 0.611009
\(554\) 8.45549e17 1.24258
\(555\) −7.45715e17 −1.08310
\(556\) 2.17080e18 3.11626
\(557\) 4.44967e17 0.631348 0.315674 0.948868i \(-0.397769\pi\)
0.315674 + 0.948868i \(0.397769\pi\)
\(558\) −4.89079e17 −0.685893
\(559\) 1.19824e18 1.66099
\(560\) −1.11982e17 −0.153435
\(561\) −2.63790e17 −0.357273
\(562\) 3.03970e17 0.406954
\(563\) −6.06771e16 −0.0803008 −0.0401504 0.999194i \(-0.512784\pi\)
−0.0401504 + 0.999194i \(0.512784\pi\)
\(564\) −8.47050e17 −1.10814
\(565\) 1.75206e18 2.26587
\(566\) −1.50303e18 −1.92159
\(567\) −3.15529e16 −0.0398795
\(568\) −1.85382e18 −2.31635
\(569\) −8.63262e17 −1.06638 −0.533191 0.845995i \(-0.679007\pi\)
−0.533191 + 0.845995i \(0.679007\pi\)
\(570\) 7.94758e17 0.970618
\(571\) −6.10409e17 −0.737032 −0.368516 0.929621i \(-0.620134\pi\)
−0.368516 + 0.929621i \(0.620134\pi\)
\(572\) −3.83224e18 −4.57486
\(573\) 5.94524e17 0.701721
\(574\) −1.50578e16 −0.0175726
\(575\) 1.16381e17 0.134290
\(576\) −4.34454e17 −0.495676
\(577\) 1.33145e18 1.50204 0.751020 0.660280i \(-0.229562\pi\)
0.751020 + 0.660280i \(0.229562\pi\)
\(578\) 1.34219e18 1.49721
\(579\) −6.30678e17 −0.695660
\(580\) 2.86950e18 3.12985
\(581\) 3.39598e17 0.366285
\(582\) −1.54784e17 −0.165093
\(583\) −3.68516e18 −3.88697
\(584\) 4.15900e17 0.433816
\(585\) −4.94910e17 −0.510521
\(586\) 8.55802e17 0.873049
\(587\) −2.90660e14 −0.000293250 0 −0.000146625 1.00000i \(-0.500047\pi\)
−0.000146625 1.00000i \(0.500047\pi\)
\(588\) −8.93566e17 −0.891608
\(589\) −1.09327e18 −1.07889
\(590\) −2.56845e17 −0.250688
\(591\) 2.42195e17 0.233801
\(592\) −6.28105e17 −0.599710
\(593\) −1.26913e18 −1.19853 −0.599267 0.800549i \(-0.704541\pi\)
−0.599267 + 0.800549i \(0.704541\pi\)
\(594\) −6.68508e17 −0.624445
\(595\) 1.42658e17 0.131806
\(596\) −3.94310e17 −0.360360
\(597\) 7.88892e17 0.713156
\(598\) 9.81941e17 0.878068
\(599\) −6.45916e17 −0.571349 −0.285674 0.958327i \(-0.592218\pi\)
−0.285674 + 0.958327i \(0.592218\pi\)
\(600\) −2.86319e17 −0.250534
\(601\) 4.89938e17 0.424089 0.212045 0.977260i \(-0.431988\pi\)
0.212045 + 0.977260i \(0.431988\pi\)
\(602\) −8.75310e17 −0.749522
\(603\) −1.75307e17 −0.148504
\(604\) −1.21038e18 −1.01433
\(605\) 3.90151e18 3.23462
\(606\) 1.50059e18 1.23081
\(607\) −8.34286e17 −0.676999 −0.338500 0.940966i \(-0.609919\pi\)
−0.338500 + 0.940966i \(0.609919\pi\)
\(608\) −7.29733e17 −0.585855
\(609\) −3.98318e17 −0.316386
\(610\) −6.05238e17 −0.475644
\(611\) 1.84425e18 1.43401
\(612\) −2.43906e17 −0.187646
\(613\) 1.38696e18 1.05577 0.527887 0.849315i \(-0.322985\pi\)
0.527887 + 0.849315i \(0.322985\pi\)
\(614\) 4.57395e17 0.344506
\(615\) −2.63411e16 −0.0196311
\(616\) 1.22021e18 0.899829
\(617\) 1.97534e18 1.44141 0.720707 0.693240i \(-0.243818\pi\)
0.720707 + 0.693240i \(0.243818\pi\)
\(618\) 3.69616e17 0.266886
\(619\) −1.11041e18 −0.793405 −0.396702 0.917947i \(-0.629846\pi\)
−0.396702 + 0.917947i \(0.629846\pi\)
\(620\) 3.58272e18 2.53318
\(621\) 1.09514e17 0.0766255
\(622\) −4.14379e18 −2.86919
\(623\) 7.44863e16 0.0510392
\(624\) −4.16856e17 −0.282674
\(625\) −1.82319e18 −1.22352
\(626\) 3.35114e18 2.22566
\(627\) −1.49436e18 −0.982238
\(628\) −4.45286e18 −2.89668
\(629\) 8.00166e17 0.515170
\(630\) 3.61530e17 0.230372
\(631\) −2.78757e18 −1.75806 −0.879032 0.476762i \(-0.841810\pi\)
−0.879032 + 0.476762i \(0.841810\pi\)
\(632\) 3.50879e18 2.19026
\(633\) −6.11437e17 −0.377770
\(634\) −1.29810e18 −0.793830
\(635\) −2.49355e18 −1.50935
\(636\) −3.40738e18 −2.04150
\(637\) 1.94553e18 1.15380
\(638\) −8.43911e18 −4.95407
\(639\) 1.03276e18 0.600125
\(640\) 3.62890e18 2.08740
\(641\) −1.24946e18 −0.711454 −0.355727 0.934590i \(-0.615767\pi\)
−0.355727 + 0.934590i \(0.615767\pi\)
\(642\) 6.92507e17 0.390343
\(643\) −1.24735e18 −0.696011 −0.348005 0.937493i \(-0.613141\pi\)
−0.348005 + 0.937493i \(0.613141\pi\)
\(644\) −4.58598e17 −0.253323
\(645\) −1.53120e18 −0.837325
\(646\) −8.52791e17 −0.461669
\(647\) 1.84305e17 0.0987778 0.0493889 0.998780i \(-0.484273\pi\)
0.0493889 + 0.998780i \(0.484273\pi\)
\(648\) −2.69423e17 −0.142954
\(649\) 4.82939e17 0.253689
\(650\) 1.43020e18 0.743807
\(651\) −4.97321e17 −0.256071
\(652\) 5.02742e18 2.56293
\(653\) −2.71262e18 −1.36916 −0.684578 0.728940i \(-0.740014\pi\)
−0.684578 + 0.728940i \(0.740014\pi\)
\(654\) 1.16555e17 0.0582472
\(655\) −1.84225e18 −0.911551
\(656\) −2.21867e16 −0.0108697
\(657\) −2.31696e17 −0.112394
\(658\) −1.34722e18 −0.647097
\(659\) 2.55377e18 1.21458 0.607290 0.794480i \(-0.292257\pi\)
0.607290 + 0.794480i \(0.292257\pi\)
\(660\) 4.89711e18 2.30624
\(661\) −1.99227e18 −0.929051 −0.464526 0.885560i \(-0.653775\pi\)
−0.464526 + 0.885560i \(0.653775\pi\)
\(662\) −2.68961e18 −1.24197
\(663\) 5.31048e17 0.242827
\(664\) 2.89975e18 1.31301
\(665\) 8.08152e17 0.362370
\(666\) 2.02781e18 0.900421
\(667\) 1.38248e18 0.607913
\(668\) 6.57246e18 2.86208
\(669\) 2.25681e17 0.0973252
\(670\) 2.00865e18 0.857862
\(671\) 1.13801e18 0.481338
\(672\) −3.31950e17 −0.139050
\(673\) −1.71370e18 −0.710945 −0.355472 0.934687i \(-0.615680\pi\)
−0.355472 + 0.934687i \(0.615680\pi\)
\(674\) 7.21332e18 2.96378
\(675\) 1.59507e17 0.0649091
\(676\) 3.31661e18 1.33672
\(677\) −4.47301e18 −1.78556 −0.892778 0.450497i \(-0.851247\pi\)
−0.892778 + 0.450497i \(0.851247\pi\)
\(678\) −4.76437e18 −1.88370
\(679\) −1.57393e17 −0.0616355
\(680\) 1.21812e18 0.472480
\(681\) −1.00273e17 −0.0385236
\(682\) −1.05367e19 −4.00964
\(683\) 2.92426e18 1.10225 0.551126 0.834422i \(-0.314198\pi\)
0.551126 + 0.834422i \(0.314198\pi\)
\(684\) −1.38172e18 −0.515888
\(685\) −2.72342e18 −1.00722
\(686\) −3.05255e18 −1.11829
\(687\) 7.46098e17 0.270756
\(688\) −1.28971e18 −0.463625
\(689\) 7.41878e18 2.64185
\(690\) −1.25480e18 −0.442644
\(691\) −1.01726e18 −0.355488 −0.177744 0.984077i \(-0.556880\pi\)
−0.177744 + 0.984077i \(0.556880\pi\)
\(692\) 3.98325e17 0.137895
\(693\) −6.79774e17 −0.233130
\(694\) −4.68441e18 −1.59154
\(695\) 6.03975e18 2.03291
\(696\) −3.40115e18 −1.13414
\(697\) 2.82645e16 0.00933744
\(698\) −5.05789e18 −1.65542
\(699\) 1.81469e17 0.0588439
\(700\) −6.67949e17 −0.214588
\(701\) 1.04531e18 0.332719 0.166359 0.986065i \(-0.446799\pi\)
0.166359 + 0.986065i \(0.446799\pi\)
\(702\) 1.34580e18 0.424415
\(703\) 4.53291e18 1.41634
\(704\) −9.35985e18 −2.89766
\(705\) −2.35672e18 −0.722901
\(706\) −4.46651e18 −1.35749
\(707\) 1.52588e18 0.459509
\(708\) 4.46536e17 0.133242
\(709\) −2.81009e16 −0.00830846 −0.00415423 0.999991i \(-0.501322\pi\)
−0.00415423 + 0.999991i \(0.501322\pi\)
\(710\) −1.18332e19 −3.46675
\(711\) −1.95473e18 −0.567459
\(712\) 6.36022e17 0.182958
\(713\) 1.72610e18 0.492022
\(714\) −3.87928e17 −0.109575
\(715\) −1.06623e19 −2.98444
\(716\) 6.80758e18 1.88824
\(717\) 2.34977e18 0.645879
\(718\) 6.85574e18 1.86743
\(719\) −3.07806e18 −0.830882 −0.415441 0.909620i \(-0.636373\pi\)
−0.415441 + 0.909620i \(0.636373\pi\)
\(720\) 5.32689e17 0.142499
\(721\) 3.75845e17 0.0996390
\(722\) 1.50680e18 0.395880
\(723\) −2.52237e18 −0.656764
\(724\) −2.49419e18 −0.643620
\(725\) 2.01359e18 0.514960
\(726\) −1.06093e19 −2.68906
\(727\) −4.87636e18 −1.22496 −0.612480 0.790486i \(-0.709828\pi\)
−0.612480 + 0.790486i \(0.709828\pi\)
\(728\) −2.45646e18 −0.611584
\(729\) 1.50095e17 0.0370370
\(730\) 2.65475e18 0.649269
\(731\) 1.64301e18 0.398269
\(732\) 1.05223e18 0.252807
\(733\) 1.13200e18 0.269570 0.134785 0.990875i \(-0.456966\pi\)
0.134785 + 0.990875i \(0.456966\pi\)
\(734\) −7.16906e18 −1.69215
\(735\) −2.48614e18 −0.581645
\(736\) 1.15213e18 0.267175
\(737\) −3.77680e18 −0.868132
\(738\) 7.16290e16 0.0163201
\(739\) −2.49969e18 −0.564544 −0.282272 0.959334i \(-0.591088\pi\)
−0.282272 + 0.959334i \(0.591088\pi\)
\(740\) −1.48546e19 −3.32549
\(741\) 3.00837e18 0.667595
\(742\) −5.41938e18 −1.19213
\(743\) 5.47842e18 1.19461 0.597307 0.802013i \(-0.296237\pi\)
0.597307 + 0.802013i \(0.296237\pi\)
\(744\) −4.24652e18 −0.917928
\(745\) −1.09708e18 −0.235083
\(746\) −9.58861e18 −2.03682
\(747\) −1.61544e18 −0.340178
\(748\) −5.25470e18 −1.09695
\(749\) 7.04178e17 0.145731
\(750\) 3.59111e18 0.736768
\(751\) −2.91220e18 −0.592327 −0.296163 0.955137i \(-0.595707\pi\)
−0.296163 + 0.955137i \(0.595707\pi\)
\(752\) −1.98503e18 −0.400269
\(753\) −4.57950e18 −0.915484
\(754\) 1.69892e19 3.36712
\(755\) −3.36760e18 −0.661706
\(756\) −6.28534e17 −0.122444
\(757\) 7.98882e17 0.154298 0.0771488 0.997020i \(-0.475418\pi\)
0.0771488 + 0.997020i \(0.475418\pi\)
\(758\) 8.97576e18 1.71878
\(759\) 2.35936e18 0.447942
\(760\) 6.90063e18 1.29897
\(761\) −7.16912e18 −1.33803 −0.669014 0.743250i \(-0.733284\pi\)
−0.669014 + 0.743250i \(0.733284\pi\)
\(762\) 6.78069e18 1.25478
\(763\) 1.18519e17 0.0217460
\(764\) 1.18429e19 2.15453
\(765\) −6.78612e17 −0.122412
\(766\) −6.08219e18 −1.08786
\(767\) −9.72227e17 −0.172424
\(768\) −4.98593e18 −0.876795
\(769\) 2.08585e18 0.363715 0.181858 0.983325i \(-0.441789\pi\)
0.181858 + 0.983325i \(0.441789\pi\)
\(770\) 7.78877e18 1.34673
\(771\) 1.40641e18 0.241133
\(772\) −1.25631e19 −2.13592
\(773\) 7.68583e18 1.29576 0.647879 0.761743i \(-0.275656\pi\)
0.647879 + 0.761743i \(0.275656\pi\)
\(774\) 4.16378e18 0.696100
\(775\) 2.51407e18 0.416789
\(776\) −1.34394e18 −0.220943
\(777\) 2.06199e18 0.336163
\(778\) 1.70027e19 2.74884
\(779\) 1.60117e17 0.0256711
\(780\) −9.85861e18 −1.56748
\(781\) 2.22496e19 3.50825
\(782\) 1.34642e18 0.210541
\(783\) 1.89477e18 0.293835
\(784\) −2.09404e18 −0.322056
\(785\) −1.23890e19 −1.88967
\(786\) 5.00962e18 0.757807
\(787\) 4.09465e18 0.614301 0.307151 0.951661i \(-0.400624\pi\)
0.307151 + 0.951661i \(0.400624\pi\)
\(788\) 4.82452e18 0.717850
\(789\) −4.80508e18 −0.709088
\(790\) 2.23971e19 3.27805
\(791\) −4.84466e18 −0.703260
\(792\) −5.80444e18 −0.835693
\(793\) −2.29098e18 −0.327150
\(794\) 1.04356e19 1.47803
\(795\) −9.48025e18 −1.33178
\(796\) 1.57147e19 2.18964
\(797\) 1.43283e17 0.0198022 0.00990112 0.999951i \(-0.496848\pi\)
0.00990112 + 0.999951i \(0.496848\pi\)
\(798\) −2.19760e18 −0.301252
\(799\) 2.52881e18 0.343844
\(800\) 1.67808e18 0.226323
\(801\) −3.54325e17 −0.0474013
\(802\) −9.71884e18 −1.28968
\(803\) −4.99164e18 −0.657041
\(804\) −3.49211e18 −0.455957
\(805\) −1.27594e18 −0.165256
\(806\) 2.12119e19 2.72522
\(807\) −7.35014e18 −0.936737
\(808\) 1.30291e19 1.64718
\(809\) −3.32883e18 −0.417472 −0.208736 0.977972i \(-0.566935\pi\)
−0.208736 + 0.977972i \(0.566935\pi\)
\(810\) −1.71977e18 −0.213952
\(811\) 8.14268e17 0.100492 0.0502460 0.998737i \(-0.483999\pi\)
0.0502460 + 0.998737i \(0.483999\pi\)
\(812\) −7.93449e18 −0.971415
\(813\) −5.06399e18 −0.615042
\(814\) 4.36871e19 5.26374
\(815\) 1.39876e19 1.67194
\(816\) −5.71586e17 −0.0677790
\(817\) 9.30758e18 1.09495
\(818\) 2.85085e18 0.332719
\(819\) 1.36848e18 0.158451
\(820\) −5.24714e17 −0.0602743
\(821\) −5.36875e18 −0.611846 −0.305923 0.952056i \(-0.598965\pi\)
−0.305923 + 0.952056i \(0.598965\pi\)
\(822\) 7.40577e18 0.837343
\(823\) 3.09246e18 0.346901 0.173450 0.984843i \(-0.444508\pi\)
0.173450 + 0.984843i \(0.444508\pi\)
\(824\) 3.20926e18 0.357172
\(825\) 3.43641e18 0.379450
\(826\) 7.10207e17 0.0778063
\(827\) 4.60428e18 0.500467 0.250234 0.968185i \(-0.419493\pi\)
0.250234 + 0.968185i \(0.419493\pi\)
\(828\) 2.18151e18 0.235267
\(829\) −8.37747e18 −0.896414 −0.448207 0.893930i \(-0.647937\pi\)
−0.448207 + 0.893930i \(0.647937\pi\)
\(830\) 1.85095e19 1.96511
\(831\) −4.09000e18 −0.430840
\(832\) 1.88428e19 1.96944
\(833\) 2.66768e18 0.276656
\(834\) −1.64238e19 −1.69003
\(835\) 1.82864e19 1.86709
\(836\) −2.97677e19 −3.01581
\(837\) 2.36572e18 0.237819
\(838\) −5.58728e18 −0.557333
\(839\) −4.66599e18 −0.461840 −0.230920 0.972973i \(-0.574173\pi\)
−0.230920 + 0.972973i \(0.574173\pi\)
\(840\) 3.13905e18 0.308306
\(841\) 1.36585e19 1.33116
\(842\) 1.93765e18 0.187390
\(843\) −1.47033e18 −0.141103
\(844\) −1.21798e19 −1.15989
\(845\) 9.22769e18 0.872016
\(846\) 6.40861e18 0.600975
\(847\) −1.07881e19 −1.00393
\(848\) −7.98508e18 −0.737406
\(849\) 7.27029e18 0.666273
\(850\) 1.96107e18 0.178348
\(851\) −7.15674e18 −0.645912
\(852\) 2.05725e19 1.84259
\(853\) −8.23919e18 −0.732345 −0.366172 0.930547i \(-0.619332\pi\)
−0.366172 + 0.930547i \(0.619332\pi\)
\(854\) 1.67355e18 0.147626
\(855\) −3.84431e18 −0.336542
\(856\) 6.01282e18 0.522395
\(857\) −1.56428e18 −0.134877 −0.0674385 0.997723i \(-0.521483\pi\)
−0.0674385 + 0.997723i \(0.521483\pi\)
\(858\) 2.89939e19 2.48107
\(859\) 7.44884e18 0.632606 0.316303 0.948658i \(-0.397558\pi\)
0.316303 + 0.948658i \(0.397558\pi\)
\(860\) −3.05015e19 −2.57088
\(861\) 7.28361e16 0.00609293
\(862\) 2.32270e19 1.92840
\(863\) 1.96442e18 0.161870 0.0809348 0.996719i \(-0.474209\pi\)
0.0809348 + 0.996719i \(0.474209\pi\)
\(864\) 1.57906e18 0.129139
\(865\) 1.10825e18 0.0899563
\(866\) 2.87256e19 2.31421
\(867\) −6.49227e18 −0.519126
\(868\) −9.90663e18 −0.786227
\(869\) −4.21126e19 −3.31729
\(870\) −2.17100e19 −1.69740
\(871\) 7.60326e18 0.590041
\(872\) 1.01201e18 0.0779520
\(873\) 7.48705e17 0.0572424
\(874\) 7.62742e18 0.578833
\(875\) 3.65163e18 0.275064
\(876\) −4.61538e18 −0.345089
\(877\) 5.27261e17 0.0391316 0.0195658 0.999809i \(-0.493772\pi\)
0.0195658 + 0.999809i \(0.493772\pi\)
\(878\) 1.47219e19 1.08455
\(879\) −4.13959e18 −0.302712
\(880\) 1.14762e19 0.833031
\(881\) −2.94286e17 −0.0212044 −0.0106022 0.999944i \(-0.503375\pi\)
−0.0106022 + 0.999944i \(0.503375\pi\)
\(882\) 6.76054e18 0.483543
\(883\) 8.23829e18 0.584915 0.292457 0.956279i \(-0.405527\pi\)
0.292457 + 0.956279i \(0.405527\pi\)
\(884\) 1.05785e19 0.745562
\(885\) 1.24238e18 0.0869209
\(886\) −1.43363e19 −0.995676
\(887\) −2.09541e19 −1.44466 −0.722331 0.691547i \(-0.756929\pi\)
−0.722331 + 0.691547i \(0.756929\pi\)
\(888\) 1.76069e19 1.20503
\(889\) 6.89497e18 0.468458
\(890\) 4.05982e18 0.273824
\(891\) 3.23363e18 0.216514
\(892\) 4.49557e18 0.298822
\(893\) 1.43256e19 0.945319
\(894\) 2.98327e18 0.195433
\(895\) 1.89405e19 1.23181
\(896\) −1.00343e19 −0.647867
\(897\) −4.74974e18 −0.304452
\(898\) 4.80399e19 3.05707
\(899\) 2.98644e19 1.88675
\(900\) 3.17738e18 0.199293
\(901\) 1.01725e19 0.633456
\(902\) 1.54317e18 0.0954050
\(903\) 4.23395e18 0.259881
\(904\) −4.13675e19 −2.52095
\(905\) −6.93952e18 −0.419869
\(906\) 9.15747e18 0.550101
\(907\) 1.33688e19 0.797345 0.398673 0.917093i \(-0.369471\pi\)
0.398673 + 0.917093i \(0.369471\pi\)
\(908\) −1.99743e18 −0.118281
\(909\) −7.25848e18 −0.426757
\(910\) −1.56799e19 −0.915325
\(911\) 1.62023e19 0.939093 0.469546 0.882908i \(-0.344417\pi\)
0.469546 + 0.882908i \(0.344417\pi\)
\(912\) −3.23801e18 −0.186343
\(913\) −3.48029e19 −1.98864
\(914\) −3.10539e19 −1.76184
\(915\) 2.92759e18 0.164920
\(916\) 1.48623e19 0.831313
\(917\) 5.09405e18 0.282919
\(918\) 1.84534e18 0.101765
\(919\) −2.50626e19 −1.37238 −0.686191 0.727422i \(-0.740718\pi\)
−0.686191 + 0.727422i \(0.740718\pi\)
\(920\) −1.08950e19 −0.592388
\(921\) −2.21246e18 −0.119450
\(922\) −1.08368e19 −0.580967
\(923\) −4.47918e19 −2.38444
\(924\) −1.35411e19 −0.715790
\(925\) −1.04238e19 −0.547149
\(926\) −5.32663e19 −2.77639
\(927\) −1.78786e18 −0.0925372
\(928\) 1.99337e19 1.02454
\(929\) 6.96456e18 0.355460 0.177730 0.984079i \(-0.443125\pi\)
0.177730 + 0.984079i \(0.443125\pi\)
\(930\) −2.71061e19 −1.37381
\(931\) 1.51123e19 0.760602
\(932\) 3.61487e18 0.180671
\(933\) 2.00439e19 0.994834
\(934\) −3.26409e19 −1.60882
\(935\) −1.46200e19 −0.715601
\(936\) 1.16852e19 0.567993
\(937\) −3.69180e19 −1.78209 −0.891047 0.453911i \(-0.850028\pi\)
−0.891047 + 0.453911i \(0.850028\pi\)
\(938\) −5.55414e18 −0.266256
\(939\) −1.62098e19 −0.771703
\(940\) −4.69459e19 −2.21956
\(941\) 1.49546e19 0.702169 0.351085 0.936344i \(-0.385813\pi\)
0.351085 + 0.936344i \(0.385813\pi\)
\(942\) 3.36894e19 1.57095
\(943\) −2.52799e17 −0.0117071
\(944\) 1.04644e18 0.0481279
\(945\) −1.74875e18 −0.0798768
\(946\) 8.97042e19 4.06930
\(947\) −1.48585e19 −0.669424 −0.334712 0.942320i \(-0.608639\pi\)
−0.334712 + 0.942320i \(0.608639\pi\)
\(948\) −3.89382e19 −1.74230
\(949\) 1.00489e19 0.446569
\(950\) 1.11094e19 0.490327
\(951\) 6.27902e18 0.275244
\(952\) −3.36826e18 −0.146644
\(953\) 3.06528e19 1.32546 0.662729 0.748859i \(-0.269398\pi\)
0.662729 + 0.748859i \(0.269398\pi\)
\(954\) 2.57796e19 1.10716
\(955\) 3.29502e19 1.40552
\(956\) 4.68075e19 1.98307
\(957\) 4.08207e19 1.71772
\(958\) −3.58402e19 −1.49794
\(959\) 7.53058e18 0.312613
\(960\) −2.40787e19 −0.992818
\(961\) 1.28697e19 0.527067
\(962\) −8.79486e19 −3.57759
\(963\) −3.34972e18 −0.135343
\(964\) −5.02455e19 −2.01649
\(965\) −3.49539e19 −1.39338
\(966\) 3.46966e18 0.137384
\(967\) −3.54748e19 −1.39524 −0.697618 0.716470i \(-0.745757\pi\)
−0.697618 + 0.716470i \(0.745757\pi\)
\(968\) −9.21175e19 −3.59876
\(969\) 4.12502e18 0.160074
\(970\) −8.57857e18 −0.330673
\(971\) −2.77192e19 −1.06134 −0.530672 0.847577i \(-0.678060\pi\)
−0.530672 + 0.847577i \(0.678060\pi\)
\(972\) 2.98988e18 0.113717
\(973\) −1.67006e19 −0.630956
\(974\) 1.92628e19 0.722914
\(975\) −6.91800e18 −0.257900
\(976\) 2.46586e18 0.0913157
\(977\) 7.89659e18 0.290486 0.145243 0.989396i \(-0.453604\pi\)
0.145243 + 0.989396i \(0.453604\pi\)
\(978\) −3.80365e19 −1.38994
\(979\) −7.63356e18 −0.277102
\(980\) −4.95239e19 −1.78585
\(981\) −5.63786e17 −0.0201960
\(982\) −1.54402e19 −0.549448
\(983\) −1.08534e19 −0.383678 −0.191839 0.981426i \(-0.561445\pi\)
−0.191839 + 0.981426i \(0.561445\pi\)
\(984\) 6.21932e17 0.0218411
\(985\) 1.34231e19 0.468293
\(986\) 2.32953e19 0.807361
\(987\) 6.51661e18 0.224368
\(988\) 5.99267e19 2.04975
\(989\) −1.46952e19 −0.499343
\(990\) −3.70505e19 −1.25074
\(991\) −2.68278e19 −0.899717 −0.449859 0.893100i \(-0.648526\pi\)
−0.449859 + 0.893100i \(0.648526\pi\)
\(992\) 2.48883e19 0.829220
\(993\) 1.30099e19 0.430628
\(994\) 3.27202e19 1.07598
\(995\) 4.37226e19 1.42842
\(996\) −3.21795e19 −1.04446
\(997\) −5.47883e18 −0.176673 −0.0883364 0.996091i \(-0.528155\pi\)
−0.0883364 + 0.996091i \(0.528155\pi\)
\(998\) −1.06480e18 −0.0341128
\(999\) −9.80871e18 −0.312202
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.1.5 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.5 30 1.1 even 1 trivial