Properties

Label 177.14.a.a.1.4
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 1.4
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-152.210 q^{2} +729.000 q^{3} +14976.0 q^{4} -42581.4 q^{5} -110961. q^{6} -571520. q^{7} -1.03259e6 q^{8} +531441. q^{9} +O(q^{10})\) \(q-152.210 q^{2} +729.000 q^{3} +14976.0 q^{4} -42581.4 q^{5} -110961. q^{6} -571520. q^{7} -1.03259e6 q^{8} +531441. q^{9} +6.48132e6 q^{10} -6.58581e6 q^{11} +1.09175e7 q^{12} +4.28374e6 q^{13} +8.69912e7 q^{14} -3.10418e7 q^{15} +3.44876e7 q^{16} -1.87480e8 q^{17} -8.08908e7 q^{18} -2.31872e8 q^{19} -6.37697e8 q^{20} -4.16638e8 q^{21} +1.00243e9 q^{22} +1.28925e9 q^{23} -7.52758e8 q^{24} +5.92471e8 q^{25} -6.52029e8 q^{26} +3.87420e8 q^{27} -8.55907e9 q^{28} +2.90122e9 q^{29} +4.72489e9 q^{30} -1.60330e9 q^{31} +3.20961e9 q^{32} -4.80106e9 q^{33} +2.85364e10 q^{34} +2.43361e10 q^{35} +7.95884e9 q^{36} +2.91197e10 q^{37} +3.52933e10 q^{38} +3.12285e9 q^{39} +4.39691e10 q^{40} -3.68274e10 q^{41} +6.34166e10 q^{42} +2.91441e10 q^{43} -9.86289e10 q^{44} -2.26295e10 q^{45} -1.96237e11 q^{46} -2.29465e10 q^{47} +2.51415e10 q^{48} +2.29746e11 q^{49} -9.01802e10 q^{50} -1.36673e11 q^{51} +6.41532e10 q^{52} -1.99989e11 q^{53} -5.89694e10 q^{54} +2.80433e11 q^{55} +5.90146e11 q^{56} -1.69035e11 q^{57} -4.41595e11 q^{58} +4.21805e10 q^{59} -4.64881e11 q^{60} +4.98973e11 q^{61} +2.44039e11 q^{62} -3.03729e11 q^{63} -7.71057e11 q^{64} -1.82408e11 q^{65} +7.30770e11 q^{66} +3.43120e11 q^{67} -2.80770e12 q^{68} +9.39864e11 q^{69} -3.70421e12 q^{70} +1.13561e12 q^{71} -5.48760e11 q^{72} -1.48911e12 q^{73} -4.43232e12 q^{74} +4.31911e11 q^{75} -3.47250e12 q^{76} +3.76393e12 q^{77} -4.75330e11 q^{78} +2.64540e12 q^{79} -1.46853e12 q^{80} +2.82430e11 q^{81} +5.60551e12 q^{82} -3.22063e12 q^{83} -6.23956e12 q^{84} +7.98316e12 q^{85} -4.43604e12 q^{86} +2.11499e12 q^{87} +6.80044e12 q^{88} -6.12635e12 q^{89} +3.44444e12 q^{90} -2.44824e12 q^{91} +1.93078e13 q^{92} -1.16881e12 q^{93} +3.49270e12 q^{94} +9.87342e12 q^{95} +2.33980e12 q^{96} +7.26379e11 q^{97} -3.49697e13 q^{98} -3.49997e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −152.210 −1.68170 −0.840851 0.541267i \(-0.817945\pi\)
−0.840851 + 0.541267i \(0.817945\pi\)
\(3\) 729.000 0.577350
\(4\) 14976.0 1.82812
\(5\) −42581.4 −1.21875 −0.609375 0.792882i \(-0.708580\pi\)
−0.609375 + 0.792882i \(0.708580\pi\)
\(6\) −110961. −0.970931
\(7\) −571520. −1.83609 −0.918046 0.396475i \(-0.870233\pi\)
−0.918046 + 0.396475i \(0.870233\pi\)
\(8\) −1.03259e6 −1.39265
\(9\) 531441. 0.333333
\(10\) 6.48132e6 2.04957
\(11\) −6.58581e6 −1.12087 −0.560437 0.828197i \(-0.689367\pi\)
−0.560437 + 0.828197i \(0.689367\pi\)
\(12\) 1.09175e7 1.05547
\(13\) 4.28374e6 0.246145 0.123073 0.992398i \(-0.460725\pi\)
0.123073 + 0.992398i \(0.460725\pi\)
\(14\) 8.69912e7 3.08776
\(15\) −3.10418e7 −0.703646
\(16\) 3.44876e7 0.513905
\(17\) −1.87480e8 −1.88381 −0.941905 0.335879i \(-0.890967\pi\)
−0.941905 + 0.335879i \(0.890967\pi\)
\(18\) −8.08908e7 −0.560567
\(19\) −2.31872e8 −1.13071 −0.565353 0.824849i \(-0.691260\pi\)
−0.565353 + 0.824849i \(0.691260\pi\)
\(20\) −6.37697e8 −2.22802
\(21\) −4.16638e8 −1.06007
\(22\) 1.00243e9 1.88498
\(23\) 1.28925e9 1.81596 0.907981 0.419012i \(-0.137624\pi\)
0.907981 + 0.419012i \(0.137624\pi\)
\(24\) −7.52758e8 −0.804048
\(25\) 5.92471e8 0.485352
\(26\) −6.52029e8 −0.413943
\(27\) 3.87420e8 0.192450
\(28\) −8.55907e9 −3.35660
\(29\) 2.90122e9 0.905719 0.452860 0.891582i \(-0.350404\pi\)
0.452860 + 0.891582i \(0.350404\pi\)
\(30\) 4.72489e9 1.18332
\(31\) −1.60330e9 −0.324463 −0.162231 0.986753i \(-0.551869\pi\)
−0.162231 + 0.986753i \(0.551869\pi\)
\(32\) 3.20961e9 0.528417
\(33\) −4.80106e9 −0.647137
\(34\) 2.85364e10 3.16801
\(35\) 2.43361e10 2.23774
\(36\) 7.95884e9 0.609374
\(37\) 2.91197e10 1.86585 0.932924 0.360073i \(-0.117248\pi\)
0.932924 + 0.360073i \(0.117248\pi\)
\(38\) 3.52933e10 1.90151
\(39\) 3.12285e9 0.142112
\(40\) 4.39691e10 1.69730
\(41\) −3.68274e10 −1.21081 −0.605405 0.795917i \(-0.706989\pi\)
−0.605405 + 0.795917i \(0.706989\pi\)
\(42\) 6.34166e10 1.78272
\(43\) 2.91441e10 0.703082 0.351541 0.936172i \(-0.385658\pi\)
0.351541 + 0.936172i \(0.385658\pi\)
\(44\) −9.86289e10 −2.04909
\(45\) −2.26295e10 −0.406250
\(46\) −1.96237e11 −3.05391
\(47\) −2.29465e10 −0.310514 −0.155257 0.987874i \(-0.549621\pi\)
−0.155257 + 0.987874i \(0.549621\pi\)
\(48\) 2.51415e10 0.296703
\(49\) 2.29746e11 2.37123
\(50\) −9.01802e10 −0.816218
\(51\) −1.36673e11 −1.08762
\(52\) 6.41532e10 0.449983
\(53\) −1.99989e11 −1.23941 −0.619703 0.784836i \(-0.712747\pi\)
−0.619703 + 0.784836i \(0.712747\pi\)
\(54\) −5.89694e10 −0.323644
\(55\) 2.80433e11 1.36607
\(56\) 5.90146e11 2.55704
\(57\) −1.69035e11 −0.652813
\(58\) −4.41595e11 −1.52315
\(59\) 4.21805e10 0.130189
\(60\) −4.64881e11 −1.28635
\(61\) 4.98973e11 1.24003 0.620016 0.784589i \(-0.287126\pi\)
0.620016 + 0.784589i \(0.287126\pi\)
\(62\) 2.44039e11 0.545650
\(63\) −3.03729e11 −0.612030
\(64\) −7.71057e11 −1.40255
\(65\) −1.82408e11 −0.299990
\(66\) 7.30770e11 1.08829
\(67\) 3.43120e11 0.463404 0.231702 0.972787i \(-0.425571\pi\)
0.231702 + 0.972787i \(0.425571\pi\)
\(68\) −2.80770e12 −3.44383
\(69\) 9.39864e11 1.04845
\(70\) −3.70421e12 −3.76321
\(71\) 1.13561e12 1.05208 0.526041 0.850459i \(-0.323676\pi\)
0.526041 + 0.850459i \(0.323676\pi\)
\(72\) −5.48760e11 −0.464218
\(73\) −1.48911e12 −1.15167 −0.575834 0.817567i \(-0.695322\pi\)
−0.575834 + 0.817567i \(0.695322\pi\)
\(74\) −4.43232e12 −3.13780
\(75\) 4.31911e11 0.280218
\(76\) −3.47250e12 −2.06707
\(77\) 3.76393e12 2.05803
\(78\) −4.75330e11 −0.238990
\(79\) 2.64540e12 1.22438 0.612188 0.790712i \(-0.290289\pi\)
0.612188 + 0.790712i \(0.290289\pi\)
\(80\) −1.46853e12 −0.626322
\(81\) 2.82430e11 0.111111
\(82\) 5.60551e12 2.03622
\(83\) −3.22063e12 −1.08127 −0.540633 0.841258i \(-0.681815\pi\)
−0.540633 + 0.841258i \(0.681815\pi\)
\(84\) −6.23956e12 −1.93793
\(85\) 7.98316e12 2.29589
\(86\) −4.43604e12 −1.18237
\(87\) 2.11499e12 0.522917
\(88\) 6.80044e12 1.56099
\(89\) −6.12635e12 −1.30667 −0.653336 0.757068i \(-0.726631\pi\)
−0.653336 + 0.757068i \(0.726631\pi\)
\(90\) 3.44444e12 0.683192
\(91\) −2.44824e12 −0.451945
\(92\) 1.93078e13 3.31980
\(93\) −1.16881e12 −0.187329
\(94\) 3.49270e12 0.522192
\(95\) 9.87342e12 1.37805
\(96\) 2.33980e12 0.305082
\(97\) 7.26379e11 0.0885416 0.0442708 0.999020i \(-0.485904\pi\)
0.0442708 + 0.999020i \(0.485904\pi\)
\(98\) −3.49697e13 −3.98770
\(99\) −3.49997e12 −0.373625
\(100\) 8.87283e12 0.887283
\(101\) −1.29660e13 −1.21539 −0.607697 0.794169i \(-0.707906\pi\)
−0.607697 + 0.794169i \(0.707906\pi\)
\(102\) 2.08030e13 1.82905
\(103\) 1.56871e13 1.29450 0.647249 0.762279i \(-0.275920\pi\)
0.647249 + 0.762279i \(0.275920\pi\)
\(104\) −4.42335e12 −0.342795
\(105\) 1.77410e13 1.29196
\(106\) 3.04404e13 2.08431
\(107\) 2.39164e13 1.54064 0.770322 0.637656i \(-0.220096\pi\)
0.770322 + 0.637656i \(0.220096\pi\)
\(108\) 5.80200e12 0.351822
\(109\) −1.28871e13 −0.736008 −0.368004 0.929824i \(-0.619959\pi\)
−0.368004 + 0.929824i \(0.619959\pi\)
\(110\) −4.26848e13 −2.29732
\(111\) 2.12283e13 1.07725
\(112\) −1.97104e13 −0.943577
\(113\) −6.32178e12 −0.285647 −0.142823 0.989748i \(-0.545618\pi\)
−0.142823 + 0.989748i \(0.545618\pi\)
\(114\) 2.57288e13 1.09784
\(115\) −5.48981e13 −2.21320
\(116\) 4.34486e13 1.65576
\(117\) 2.27656e12 0.0820484
\(118\) −6.42031e12 −0.218939
\(119\) 1.07149e14 3.45885
\(120\) 3.20535e13 0.979934
\(121\) 8.85024e12 0.256360
\(122\) −7.59488e13 −2.08536
\(123\) −2.68472e13 −0.699062
\(124\) −2.40110e13 −0.593157
\(125\) 2.67510e13 0.627227
\(126\) 4.62307e13 1.02925
\(127\) −3.67988e13 −0.778234 −0.389117 0.921188i \(-0.627220\pi\)
−0.389117 + 0.921188i \(0.627220\pi\)
\(128\) 9.10698e13 1.83025
\(129\) 2.12461e13 0.405925
\(130\) 2.77643e13 0.504493
\(131\) −4.29974e13 −0.743326 −0.371663 0.928368i \(-0.621212\pi\)
−0.371663 + 0.928368i \(0.621212\pi\)
\(132\) −7.19005e13 −1.18305
\(133\) 1.32519e14 2.07608
\(134\) −5.22264e13 −0.779307
\(135\) −1.64969e13 −0.234549
\(136\) 1.93590e14 2.62349
\(137\) 5.42287e13 0.700722 0.350361 0.936615i \(-0.386059\pi\)
0.350361 + 0.936615i \(0.386059\pi\)
\(138\) −1.43057e14 −1.76317
\(139\) 1.53326e14 1.80310 0.901548 0.432679i \(-0.142432\pi\)
0.901548 + 0.432679i \(0.142432\pi\)
\(140\) 3.64457e14 4.09085
\(141\) −1.67280e13 −0.179275
\(142\) −1.72852e14 −1.76929
\(143\) −2.82119e13 −0.275898
\(144\) 1.83281e13 0.171302
\(145\) −1.23538e14 −1.10385
\(146\) 2.26657e14 1.93676
\(147\) 1.67485e14 1.36903
\(148\) 4.36096e14 3.41100
\(149\) 9.07270e13 0.679244 0.339622 0.940562i \(-0.389701\pi\)
0.339622 + 0.940562i \(0.389701\pi\)
\(150\) −6.57414e13 −0.471244
\(151\) 1.05410e14 0.723658 0.361829 0.932244i \(-0.382152\pi\)
0.361829 + 0.932244i \(0.382152\pi\)
\(152\) 2.39428e14 1.57468
\(153\) −9.96346e13 −0.627937
\(154\) −5.72908e14 −3.46099
\(155\) 6.82709e13 0.395439
\(156\) 4.67677e13 0.259798
\(157\) 5.16344e13 0.275164 0.137582 0.990490i \(-0.456067\pi\)
0.137582 + 0.990490i \(0.456067\pi\)
\(158\) −4.02657e14 −2.05904
\(159\) −1.45792e14 −0.715572
\(160\) −1.36669e14 −0.644008
\(161\) −7.36833e14 −3.33427
\(162\) −4.29887e13 −0.186856
\(163\) −3.75621e13 −0.156867 −0.0784334 0.996919i \(-0.524992\pi\)
−0.0784334 + 0.996919i \(0.524992\pi\)
\(164\) −5.51526e14 −2.21351
\(165\) 2.04436e14 0.788699
\(166\) 4.90213e14 1.81837
\(167\) 2.16665e14 0.772916 0.386458 0.922307i \(-0.373698\pi\)
0.386458 + 0.922307i \(0.373698\pi\)
\(168\) 4.30216e14 1.47631
\(169\) −2.84525e14 −0.939413
\(170\) −1.21512e15 −3.86101
\(171\) −1.23226e14 −0.376902
\(172\) 4.36462e14 1.28532
\(173\) 4.17054e14 1.18275 0.591374 0.806397i \(-0.298586\pi\)
0.591374 + 0.806397i \(0.298586\pi\)
\(174\) −3.21923e14 −0.879391
\(175\) −3.38609e14 −0.891151
\(176\) −2.27129e14 −0.576023
\(177\) 3.07496e13 0.0751646
\(178\) 9.32493e14 2.19743
\(179\) −4.23921e14 −0.963254 −0.481627 0.876376i \(-0.659954\pi\)
−0.481627 + 0.876376i \(0.659954\pi\)
\(180\) −3.38899e14 −0.742674
\(181\) 3.73841e14 0.790271 0.395136 0.918623i \(-0.370698\pi\)
0.395136 + 0.918623i \(0.370698\pi\)
\(182\) 3.72648e14 0.760037
\(183\) 3.63751e14 0.715933
\(184\) −1.33127e15 −2.52900
\(185\) −1.23996e15 −2.27400
\(186\) 1.77905e14 0.315031
\(187\) 1.23471e15 2.11152
\(188\) −3.43646e14 −0.567657
\(189\) −2.21419e14 −0.353356
\(190\) −1.50284e15 −2.31746
\(191\) −1.83012e14 −0.272749 −0.136375 0.990657i \(-0.543545\pi\)
−0.136375 + 0.990657i \(0.543545\pi\)
\(192\) −5.62101e14 −0.809760
\(193\) 1.82454e14 0.254115 0.127058 0.991895i \(-0.459447\pi\)
0.127058 + 0.991895i \(0.459447\pi\)
\(194\) −1.10562e14 −0.148901
\(195\) −1.32975e14 −0.173199
\(196\) 3.44067e15 4.33490
\(197\) −3.29248e14 −0.401321 −0.200661 0.979661i \(-0.564309\pi\)
−0.200661 + 0.979661i \(0.564309\pi\)
\(198\) 5.32732e14 0.628326
\(199\) 1.39933e15 1.59726 0.798628 0.601825i \(-0.205559\pi\)
0.798628 + 0.601825i \(0.205559\pi\)
\(200\) −6.11779e14 −0.675927
\(201\) 2.50134e14 0.267546
\(202\) 1.97356e15 2.04393
\(203\) −1.65811e15 −1.66298
\(204\) −2.04681e15 −1.98830
\(205\) 1.56816e15 1.47568
\(206\) −2.38774e15 −2.17696
\(207\) 6.85161e14 0.605320
\(208\) 1.47736e14 0.126495
\(209\) 1.52706e15 1.26738
\(210\) −2.70037e15 −2.17269
\(211\) −1.16737e15 −0.910691 −0.455346 0.890315i \(-0.650484\pi\)
−0.455346 + 0.890315i \(0.650484\pi\)
\(212\) −2.99503e15 −2.26579
\(213\) 8.27860e14 0.607420
\(214\) −3.64033e15 −2.59090
\(215\) −1.24100e15 −0.856882
\(216\) −4.00046e14 −0.268016
\(217\) 9.16321e14 0.595743
\(218\) 1.96155e15 1.23775
\(219\) −1.08556e15 −0.664915
\(220\) 4.19976e15 2.49733
\(221\) −8.03116e14 −0.463691
\(222\) −3.23116e15 −1.81161
\(223\) 3.86468e14 0.210442 0.105221 0.994449i \(-0.466445\pi\)
0.105221 + 0.994449i \(0.466445\pi\)
\(224\) −1.83435e15 −0.970222
\(225\) 3.14863e14 0.161784
\(226\) 9.62240e14 0.480373
\(227\) −1.09793e15 −0.532607 −0.266303 0.963889i \(-0.585802\pi\)
−0.266303 + 0.963889i \(0.585802\pi\)
\(228\) −2.53146e15 −1.19342
\(229\) 1.86090e15 0.852694 0.426347 0.904560i \(-0.359800\pi\)
0.426347 + 0.904560i \(0.359800\pi\)
\(230\) 8.35605e15 3.72195
\(231\) 2.74390e15 1.18820
\(232\) −2.99577e15 −1.26135
\(233\) −3.86130e15 −1.58096 −0.790479 0.612489i \(-0.790168\pi\)
−0.790479 + 0.612489i \(0.790168\pi\)
\(234\) −3.46515e14 −0.137981
\(235\) 9.77095e14 0.378439
\(236\) 6.31694e14 0.238001
\(237\) 1.92850e15 0.706894
\(238\) −1.63091e16 −5.81675
\(239\) 1.74556e15 0.605826 0.302913 0.953018i \(-0.402041\pi\)
0.302913 + 0.953018i \(0.402041\pi\)
\(240\) −1.07056e15 −0.361607
\(241\) −3.64739e15 −1.19914 −0.599572 0.800321i \(-0.704663\pi\)
−0.599572 + 0.800321i \(0.704663\pi\)
\(242\) −1.34710e15 −0.431121
\(243\) 2.05891e14 0.0641500
\(244\) 7.47260e15 2.26693
\(245\) −9.78291e15 −2.88994
\(246\) 4.08642e15 1.17561
\(247\) −9.93279e14 −0.278318
\(248\) 1.65556e15 0.451864
\(249\) −2.34784e15 −0.624270
\(250\) −4.07178e15 −1.05481
\(251\) 3.03593e15 0.766325 0.383163 0.923681i \(-0.374835\pi\)
0.383163 + 0.923681i \(0.374835\pi\)
\(252\) −4.54864e15 −1.11887
\(253\) −8.49077e15 −2.03546
\(254\) 5.60116e15 1.30876
\(255\) 5.81973e15 1.32554
\(256\) −7.54525e15 −1.67538
\(257\) −2.33106e15 −0.504648 −0.252324 0.967643i \(-0.581195\pi\)
−0.252324 + 0.967643i \(0.581195\pi\)
\(258\) −3.23387e15 −0.682644
\(259\) −1.66425e16 −3.42587
\(260\) −2.73173e15 −0.548417
\(261\) 1.54183e15 0.301906
\(262\) 6.54465e15 1.25005
\(263\) −4.83143e15 −0.900250 −0.450125 0.892966i \(-0.648621\pi\)
−0.450125 + 0.892966i \(0.648621\pi\)
\(264\) 4.95752e15 0.901237
\(265\) 8.51582e15 1.51053
\(266\) −2.01708e16 −3.49134
\(267\) −4.46611e15 −0.754407
\(268\) 5.13855e15 0.847158
\(269\) −6.27431e14 −0.100966 −0.0504831 0.998725i \(-0.516076\pi\)
−0.0504831 + 0.998725i \(0.516076\pi\)
\(270\) 2.51100e15 0.394441
\(271\) 1.05451e16 1.61715 0.808576 0.588392i \(-0.200239\pi\)
0.808576 + 0.588392i \(0.200239\pi\)
\(272\) −6.46574e15 −0.968100
\(273\) −1.78477e15 −0.260931
\(274\) −8.25416e15 −1.17840
\(275\) −3.90190e15 −0.544019
\(276\) 1.40754e16 1.91669
\(277\) 1.23864e16 1.64750 0.823750 0.566954i \(-0.191878\pi\)
0.823750 + 0.566954i \(0.191878\pi\)
\(278\) −2.33378e16 −3.03227
\(279\) −8.52062e14 −0.108154
\(280\) −2.51292e16 −3.11639
\(281\) 6.73357e15 0.815933 0.407966 0.912997i \(-0.366238\pi\)
0.407966 + 0.912997i \(0.366238\pi\)
\(282\) 2.54618e15 0.301487
\(283\) −6.19163e15 −0.716462 −0.358231 0.933633i \(-0.616620\pi\)
−0.358231 + 0.933633i \(0.616620\pi\)
\(284\) 1.70069e16 1.92333
\(285\) 7.19772e15 0.795616
\(286\) 4.29415e15 0.463978
\(287\) 2.10476e16 2.22316
\(288\) 1.70572e15 0.176139
\(289\) 2.52442e16 2.54874
\(290\) 1.88037e16 1.85634
\(291\) 5.29531e14 0.0511195
\(292\) −2.23008e16 −2.10539
\(293\) −1.57340e16 −1.45278 −0.726390 0.687283i \(-0.758803\pi\)
−0.726390 + 0.687283i \(0.758803\pi\)
\(294\) −2.54929e16 −2.30230
\(295\) −1.79611e15 −0.158668
\(296\) −3.00687e16 −2.59848
\(297\) −2.55148e15 −0.215712
\(298\) −1.38096e16 −1.14229
\(299\) 5.52282e15 0.446990
\(300\) 6.46829e15 0.512273
\(301\) −1.66565e16 −1.29092
\(302\) −1.60446e16 −1.21698
\(303\) −9.45221e15 −0.701708
\(304\) −7.99670e15 −0.581076
\(305\) −2.12470e16 −1.51129
\(306\) 1.51654e16 1.05600
\(307\) −2.54581e16 −1.73551 −0.867753 0.496996i \(-0.834436\pi\)
−0.867753 + 0.496996i \(0.834436\pi\)
\(308\) 5.63684e16 3.76232
\(309\) 1.14359e16 0.747378
\(310\) −1.03915e16 −0.665011
\(311\) −1.31612e16 −0.824806 −0.412403 0.911002i \(-0.635310\pi\)
−0.412403 + 0.911002i \(0.635310\pi\)
\(312\) −3.22462e15 −0.197913
\(313\) 8.71316e15 0.523766 0.261883 0.965100i \(-0.415656\pi\)
0.261883 + 0.965100i \(0.415656\pi\)
\(314\) −7.85929e15 −0.462744
\(315\) 1.29332e16 0.745912
\(316\) 3.96174e16 2.23831
\(317\) −2.88553e16 −1.59713 −0.798564 0.601910i \(-0.794407\pi\)
−0.798564 + 0.601910i \(0.794407\pi\)
\(318\) 2.21911e16 1.20338
\(319\) −1.91069e16 −1.01520
\(320\) 3.28327e16 1.70935
\(321\) 1.74351e16 0.889491
\(322\) 1.12154e17 5.60725
\(323\) 4.34713e16 2.13003
\(324\) 4.22966e15 0.203125
\(325\) 2.53799e15 0.119467
\(326\) 5.71734e15 0.263803
\(327\) −9.39469e15 −0.424935
\(328\) 3.80276e16 1.68624
\(329\) 1.31144e16 0.570132
\(330\) −3.11172e16 −1.32636
\(331\) −1.40302e15 −0.0586385 −0.0293193 0.999570i \(-0.509334\pi\)
−0.0293193 + 0.999570i \(0.509334\pi\)
\(332\) −4.82320e16 −1.97669
\(333\) 1.54754e16 0.621949
\(334\) −3.29787e16 −1.29981
\(335\) −1.46105e16 −0.564773
\(336\) −1.43689e16 −0.544774
\(337\) 1.32900e16 0.494233 0.247117 0.968986i \(-0.420517\pi\)
0.247117 + 0.968986i \(0.420517\pi\)
\(338\) 4.33076e16 1.57981
\(339\) −4.60858e15 −0.164918
\(340\) 1.19556e17 4.19717
\(341\) 1.05591e16 0.363682
\(342\) 1.87563e16 0.633836
\(343\) −7.59306e16 −2.51771
\(344\) −3.00939e16 −0.979149
\(345\) −4.00207e16 −1.27779
\(346\) −6.34799e16 −1.98903
\(347\) −1.46139e16 −0.449391 −0.224696 0.974429i \(-0.572139\pi\)
−0.224696 + 0.974429i \(0.572139\pi\)
\(348\) 3.16740e16 0.955956
\(349\) 2.46782e16 0.731053 0.365526 0.930801i \(-0.380889\pi\)
0.365526 + 0.930801i \(0.380889\pi\)
\(350\) 5.15398e16 1.49865
\(351\) 1.65961e15 0.0473707
\(352\) −2.11379e16 −0.592289
\(353\) 6.52067e16 1.79373 0.896864 0.442307i \(-0.145840\pi\)
0.896864 + 0.442307i \(0.145840\pi\)
\(354\) −4.68041e15 −0.126404
\(355\) −4.83559e16 −1.28223
\(356\) −9.17480e16 −2.38875
\(357\) 7.81114e16 1.99697
\(358\) 6.45252e16 1.61991
\(359\) −2.21586e16 −0.546296 −0.273148 0.961972i \(-0.588065\pi\)
−0.273148 + 0.961972i \(0.588065\pi\)
\(360\) 2.33670e16 0.565765
\(361\) 1.17115e16 0.278495
\(362\) −5.69024e16 −1.32900
\(363\) 6.45183e15 0.148010
\(364\) −3.66648e16 −0.826210
\(365\) 6.34082e16 1.40359
\(366\) −5.53667e16 −1.20399
\(367\) −2.84583e16 −0.607967 −0.303983 0.952677i \(-0.598317\pi\)
−0.303983 + 0.952677i \(0.598317\pi\)
\(368\) 4.44632e16 0.933232
\(369\) −1.95716e16 −0.403604
\(370\) 1.88735e17 3.82420
\(371\) 1.14298e17 2.27566
\(372\) −1.75040e16 −0.342460
\(373\) −7.18716e16 −1.38181 −0.690907 0.722943i \(-0.742789\pi\)
−0.690907 + 0.722943i \(0.742789\pi\)
\(374\) −1.87935e17 −3.55094
\(375\) 1.95015e16 0.362130
\(376\) 2.36943e16 0.432438
\(377\) 1.24281e16 0.222938
\(378\) 3.37022e16 0.594239
\(379\) −4.67445e16 −0.810170 −0.405085 0.914279i \(-0.632758\pi\)
−0.405085 + 0.914279i \(0.632758\pi\)
\(380\) 1.47864e17 2.51924
\(381\) −2.68264e16 −0.449313
\(382\) 2.78564e16 0.458683
\(383\) −7.65345e16 −1.23898 −0.619491 0.785004i \(-0.712661\pi\)
−0.619491 + 0.785004i \(0.712661\pi\)
\(384\) 6.63899e16 1.05669
\(385\) −1.60273e17 −2.50822
\(386\) −2.77713e16 −0.427346
\(387\) 1.54884e16 0.234361
\(388\) 1.08782e16 0.161865
\(389\) 2.48310e16 0.363347 0.181674 0.983359i \(-0.441849\pi\)
0.181674 + 0.983359i \(0.441849\pi\)
\(390\) 2.02402e16 0.291269
\(391\) −2.41709e17 −3.42093
\(392\) −2.37234e17 −3.30230
\(393\) −3.13451e16 −0.429159
\(394\) 5.01149e16 0.674903
\(395\) −1.12645e17 −1.49221
\(396\) −5.24155e16 −0.683032
\(397\) 3.49176e16 0.447617 0.223808 0.974633i \(-0.428151\pi\)
0.223808 + 0.974633i \(0.428151\pi\)
\(398\) −2.12992e17 −2.68611
\(399\) 9.66066e16 1.19862
\(400\) 2.04329e16 0.249425
\(401\) 7.57544e15 0.0909849 0.0454925 0.998965i \(-0.485514\pi\)
0.0454925 + 0.998965i \(0.485514\pi\)
\(402\) −3.80730e16 −0.449933
\(403\) −6.86814e15 −0.0798650
\(404\) −1.94178e17 −2.22189
\(405\) −1.20262e16 −0.135417
\(406\) 2.52381e17 2.79664
\(407\) −1.91777e17 −2.09138
\(408\) 1.41127e17 1.51467
\(409\) 1.08789e17 1.14917 0.574583 0.818446i \(-0.305164\pi\)
0.574583 + 0.818446i \(0.305164\pi\)
\(410\) −2.38690e17 −2.48165
\(411\) 3.95327e16 0.404562
\(412\) 2.34930e17 2.36650
\(413\) −2.41070e16 −0.239039
\(414\) −1.04289e17 −1.01797
\(415\) 1.37139e17 1.31779
\(416\) 1.37491e16 0.130067
\(417\) 1.11774e17 1.04102
\(418\) −2.32435e17 −2.13135
\(419\) −1.04836e17 −0.946496 −0.473248 0.880929i \(-0.656919\pi\)
−0.473248 + 0.880929i \(0.656919\pi\)
\(420\) 2.65689e17 2.36186
\(421\) −4.22342e16 −0.369684 −0.184842 0.982768i \(-0.559177\pi\)
−0.184842 + 0.982768i \(0.559177\pi\)
\(422\) 1.77685e17 1.53151
\(423\) −1.21947e16 −0.103505
\(424\) 2.06507e17 1.72606
\(425\) −1.11077e17 −0.914312
\(426\) −1.26009e17 −1.02150
\(427\) −2.85173e17 −2.27681
\(428\) 3.58172e17 2.81648
\(429\) −2.05665e16 −0.159290
\(430\) 1.88893e17 1.44102
\(431\) 2.02917e15 0.0152481 0.00762406 0.999971i \(-0.497573\pi\)
0.00762406 + 0.999971i \(0.497573\pi\)
\(432\) 1.33612e16 0.0989011
\(433\) 7.28398e16 0.531126 0.265563 0.964094i \(-0.414442\pi\)
0.265563 + 0.964094i \(0.414442\pi\)
\(434\) −1.39473e17 −1.00186
\(435\) −9.00591e16 −0.637306
\(436\) −1.92997e17 −1.34551
\(437\) −2.98941e17 −2.05332
\(438\) 1.65233e17 1.11819
\(439\) 1.64714e16 0.109827 0.0549136 0.998491i \(-0.482512\pi\)
0.0549136 + 0.998491i \(0.482512\pi\)
\(440\) −2.89572e17 −1.90246
\(441\) 1.22097e17 0.790410
\(442\) 1.22243e17 0.779790
\(443\) 1.07069e17 0.673039 0.336520 0.941676i \(-0.390750\pi\)
0.336520 + 0.941676i \(0.390750\pi\)
\(444\) 3.17914e17 1.96934
\(445\) 2.60868e17 1.59251
\(446\) −5.88244e16 −0.353900
\(447\) 6.61400e16 0.392162
\(448\) 4.40675e17 2.57520
\(449\) 1.87302e17 1.07880 0.539399 0.842050i \(-0.318651\pi\)
0.539399 + 0.842050i \(0.318651\pi\)
\(450\) −4.79254e16 −0.272073
\(451\) 2.42539e17 1.35717
\(452\) −9.46748e16 −0.522197
\(453\) 7.68442e16 0.417804
\(454\) 1.67116e17 0.895686
\(455\) 1.04250e17 0.550808
\(456\) 1.74543e17 0.909142
\(457\) 2.59517e16 0.133263 0.0666315 0.997778i \(-0.478775\pi\)
0.0666315 + 0.997778i \(0.478775\pi\)
\(458\) −2.83249e17 −1.43398
\(459\) −7.26336e16 −0.362540
\(460\) −8.22152e17 −4.04600
\(461\) −3.19776e17 −1.55164 −0.775819 0.630956i \(-0.782663\pi\)
−0.775819 + 0.630956i \(0.782663\pi\)
\(462\) −4.17650e17 −1.99820
\(463\) −1.91330e17 −0.902622 −0.451311 0.892367i \(-0.649044\pi\)
−0.451311 + 0.892367i \(0.649044\pi\)
\(464\) 1.00056e17 0.465454
\(465\) 4.97695e16 0.228307
\(466\) 5.87730e17 2.65870
\(467\) −1.59663e16 −0.0712271 −0.0356136 0.999366i \(-0.511339\pi\)
−0.0356136 + 0.999366i \(0.511339\pi\)
\(468\) 3.40936e16 0.149994
\(469\) −1.96100e17 −0.850852
\(470\) −1.48724e17 −0.636421
\(471\) 3.76415e16 0.158866
\(472\) −4.35552e16 −0.181308
\(473\) −1.91938e17 −0.788067
\(474\) −2.93537e17 −1.18879
\(475\) −1.37377e17 −0.548790
\(476\) 1.60465e18 6.32319
\(477\) −1.06283e17 −0.413136
\(478\) −2.65692e17 −1.01882
\(479\) 3.47734e17 1.31542 0.657712 0.753269i \(-0.271524\pi\)
0.657712 + 0.753269i \(0.271524\pi\)
\(480\) −9.96320e16 −0.371818
\(481\) 1.24741e17 0.459270
\(482\) 5.55170e17 2.01660
\(483\) −5.37151e17 −1.92504
\(484\) 1.32541e17 0.468657
\(485\) −3.09302e16 −0.107910
\(486\) −3.13387e16 −0.107881
\(487\) −2.06116e17 −0.700120 −0.350060 0.936727i \(-0.613839\pi\)
−0.350060 + 0.936727i \(0.613839\pi\)
\(488\) −5.15234e17 −1.72693
\(489\) −2.73828e16 −0.0905671
\(490\) 1.48906e18 4.86001
\(491\) −1.42640e17 −0.459423 −0.229712 0.973259i \(-0.573778\pi\)
−0.229712 + 0.973259i \(0.573778\pi\)
\(492\) −4.02063e17 −1.27797
\(493\) −5.43921e17 −1.70620
\(494\) 1.51187e17 0.468047
\(495\) 1.49034e17 0.455355
\(496\) −5.52941e16 −0.166743
\(497\) −6.49024e17 −1.93172
\(498\) 3.57365e17 1.04984
\(499\) 3.53103e17 1.02388 0.511939 0.859022i \(-0.328927\pi\)
0.511939 + 0.859022i \(0.328927\pi\)
\(500\) 4.00622e17 1.14665
\(501\) 1.57949e17 0.446243
\(502\) −4.62100e17 −1.28873
\(503\) 4.75636e16 0.130943 0.0654716 0.997854i \(-0.479145\pi\)
0.0654716 + 0.997854i \(0.479145\pi\)
\(504\) 3.13628e17 0.852346
\(505\) 5.52110e17 1.48126
\(506\) 1.29238e18 3.42305
\(507\) −2.07418e17 −0.542370
\(508\) −5.51098e17 −1.42271
\(509\) 7.86117e15 0.0200365 0.0100182 0.999950i \(-0.496811\pi\)
0.0100182 + 0.999950i \(0.496811\pi\)
\(510\) −8.85822e17 −2.22916
\(511\) 8.51054e17 2.11457
\(512\) 4.02421e17 0.987248
\(513\) −8.98319e16 −0.217604
\(514\) 3.54811e17 0.848667
\(515\) −6.67979e17 −1.57767
\(516\) 3.18181e17 0.742080
\(517\) 1.51122e17 0.348047
\(518\) 2.53316e18 5.76129
\(519\) 3.04032e17 0.682860
\(520\) 1.88352e17 0.417781
\(521\) −5.55593e17 −1.21706 −0.608530 0.793531i \(-0.708240\pi\)
−0.608530 + 0.793531i \(0.708240\pi\)
\(522\) −2.34682e17 −0.507717
\(523\) −2.93225e17 −0.626528 −0.313264 0.949666i \(-0.601422\pi\)
−0.313264 + 0.949666i \(0.601422\pi\)
\(524\) −6.43928e17 −1.35889
\(525\) −2.46846e17 −0.514506
\(526\) 7.35393e17 1.51395
\(527\) 3.00588e17 0.611227
\(528\) −1.65577e17 −0.332567
\(529\) 1.15813e18 2.29772
\(530\) −1.29620e18 −2.54026
\(531\) 2.24165e16 0.0433963
\(532\) 1.98461e18 3.79532
\(533\) −1.57759e17 −0.298035
\(534\) 6.79787e17 1.26869
\(535\) −1.01840e18 −1.87766
\(536\) −3.54302e17 −0.645360
\(537\) −3.09039e17 −0.556135
\(538\) 9.55014e16 0.169795
\(539\) −1.51307e18 −2.65785
\(540\) −2.47057e17 −0.428783
\(541\) 1.44892e16 0.0248463 0.0124231 0.999923i \(-0.496045\pi\)
0.0124231 + 0.999923i \(0.496045\pi\)
\(542\) −1.60507e18 −2.71957
\(543\) 2.72530e17 0.456263
\(544\) −6.01737e17 −0.995438
\(545\) 5.48750e17 0.897011
\(546\) 2.71660e17 0.438808
\(547\) −7.50787e17 −1.19839 −0.599196 0.800602i \(-0.704513\pi\)
−0.599196 + 0.800602i \(0.704513\pi\)
\(548\) 8.12127e17 1.28100
\(549\) 2.65175e17 0.413344
\(550\) 5.93910e17 0.914878
\(551\) −6.72711e17 −1.02410
\(552\) −9.70494e17 −1.46012
\(553\) −1.51190e18 −2.24807
\(554\) −1.88533e18 −2.77060
\(555\) −9.03930e17 −1.31290
\(556\) 2.29620e18 3.29628
\(557\) −1.31115e17 −0.186034 −0.0930172 0.995665i \(-0.529651\pi\)
−0.0930172 + 0.995665i \(0.529651\pi\)
\(558\) 1.29693e17 0.181883
\(559\) 1.24846e17 0.173060
\(560\) 8.39294e17 1.14998
\(561\) 9.00103e17 1.21908
\(562\) −1.02492e18 −1.37216
\(563\) 2.43724e17 0.322548 0.161274 0.986910i \(-0.448440\pi\)
0.161274 + 0.986910i \(0.448440\pi\)
\(564\) −2.50518e17 −0.327737
\(565\) 2.69190e17 0.348132
\(566\) 9.42430e17 1.20488
\(567\) −1.61414e17 −0.204010
\(568\) −1.17262e18 −1.46519
\(569\) −6.65466e17 −0.822046 −0.411023 0.911625i \(-0.634828\pi\)
−0.411023 + 0.911625i \(0.634828\pi\)
\(570\) −1.09557e18 −1.33799
\(571\) 1.37419e18 1.65925 0.829626 0.558320i \(-0.188554\pi\)
0.829626 + 0.558320i \(0.188554\pi\)
\(572\) −4.22501e17 −0.504375
\(573\) −1.33416e17 −0.157472
\(574\) −3.20366e18 −3.73869
\(575\) 7.63844e17 0.881381
\(576\) −4.09771e17 −0.467515
\(577\) 8.93806e17 1.00833 0.504163 0.863609i \(-0.331801\pi\)
0.504163 + 0.863609i \(0.331801\pi\)
\(578\) −3.84243e18 −4.28622
\(579\) 1.33009e17 0.146713
\(580\) −1.85010e18 −2.01796
\(581\) 1.84065e18 1.98530
\(582\) −8.06000e16 −0.0859678
\(583\) 1.31709e18 1.38922
\(584\) 1.53764e18 1.60387
\(585\) −9.69389e16 −0.0999965
\(586\) 2.39488e18 2.44314
\(587\) 4.31503e17 0.435347 0.217674 0.976022i \(-0.430153\pi\)
0.217674 + 0.976022i \(0.430153\pi\)
\(588\) 2.50825e18 2.50275
\(589\) 3.71761e17 0.366872
\(590\) 2.73386e17 0.266832
\(591\) −2.40022e17 −0.231703
\(592\) 1.00427e18 0.958869
\(593\) −1.47166e17 −0.138980 −0.0694902 0.997583i \(-0.522137\pi\)
−0.0694902 + 0.997583i \(0.522137\pi\)
\(594\) 3.88361e17 0.362764
\(595\) −4.56254e18 −4.21547
\(596\) 1.35873e18 1.24174
\(597\) 1.02011e18 0.922176
\(598\) −8.40630e17 −0.751704
\(599\) 1.90569e17 0.168569 0.0842847 0.996442i \(-0.473139\pi\)
0.0842847 + 0.996442i \(0.473139\pi\)
\(600\) −4.45987e17 −0.390247
\(601\) 1.95341e18 1.69087 0.845435 0.534078i \(-0.179341\pi\)
0.845435 + 0.534078i \(0.179341\pi\)
\(602\) 2.53528e18 2.17095
\(603\) 1.82348e17 0.154468
\(604\) 1.57862e18 1.32293
\(605\) −3.76856e17 −0.312439
\(606\) 1.43872e18 1.18006
\(607\) −4.76753e17 −0.386872 −0.193436 0.981113i \(-0.561963\pi\)
−0.193436 + 0.981113i \(0.561963\pi\)
\(608\) −7.44217e17 −0.597484
\(609\) −1.20876e18 −0.960124
\(610\) 3.23400e18 2.54154
\(611\) −9.82970e16 −0.0764315
\(612\) −1.49212e18 −1.14794
\(613\) −5.08493e17 −0.387072 −0.193536 0.981093i \(-0.561996\pi\)
−0.193536 + 0.981093i \(0.561996\pi\)
\(614\) 3.87498e18 2.91860
\(615\) 1.14319e18 0.851982
\(616\) −3.88659e18 −2.86612
\(617\) 1.48244e18 1.08174 0.540870 0.841106i \(-0.318095\pi\)
0.540870 + 0.841106i \(0.318095\pi\)
\(618\) −1.74066e18 −1.25687
\(619\) −1.06056e18 −0.757783 −0.378891 0.925441i \(-0.623695\pi\)
−0.378891 + 0.925441i \(0.623695\pi\)
\(620\) 1.02242e18 0.722911
\(621\) 4.99482e17 0.349482
\(622\) 2.00326e18 1.38708
\(623\) 3.50133e18 2.39917
\(624\) 1.07700e17 0.0730321
\(625\) −1.86233e18 −1.24979
\(626\) −1.32623e18 −0.880819
\(627\) 1.11323e18 0.731722
\(628\) 7.73275e17 0.503033
\(629\) −5.45937e18 −3.51491
\(630\) −1.96857e18 −1.25440
\(631\) −1.24574e18 −0.785664 −0.392832 0.919610i \(-0.628505\pi\)
−0.392832 + 0.919610i \(0.628505\pi\)
\(632\) −2.73161e18 −1.70513
\(633\) −8.51010e17 −0.525788
\(634\) 4.39207e18 2.68589
\(635\) 1.56695e18 0.948472
\(636\) −2.18338e18 −1.30815
\(637\) 9.84174e17 0.583667
\(638\) 2.90827e18 1.70726
\(639\) 6.03510e17 0.350694
\(640\) −3.87788e18 −2.23061
\(641\) 1.82273e18 1.03788 0.518938 0.854812i \(-0.326328\pi\)
0.518938 + 0.854812i \(0.326328\pi\)
\(642\) −2.65380e18 −1.49586
\(643\) 7.68443e17 0.428786 0.214393 0.976748i \(-0.431223\pi\)
0.214393 + 0.976748i \(0.431223\pi\)
\(644\) −1.10348e19 −6.09545
\(645\) −9.04687e17 −0.494721
\(646\) −6.61679e18 −3.58208
\(647\) 7.15651e17 0.383551 0.191776 0.981439i \(-0.438575\pi\)
0.191776 + 0.981439i \(0.438575\pi\)
\(648\) −2.91634e17 −0.154739
\(649\) −2.77793e17 −0.145925
\(650\) −3.86309e17 −0.200908
\(651\) 6.67998e17 0.343953
\(652\) −5.62529e17 −0.286771
\(653\) 3.77084e18 1.90328 0.951640 0.307214i \(-0.0993968\pi\)
0.951640 + 0.307214i \(0.0993968\pi\)
\(654\) 1.42997e18 0.714613
\(655\) 1.83089e18 0.905928
\(656\) −1.27009e18 −0.622242
\(657\) −7.91372e17 −0.383889
\(658\) −1.99615e18 −0.958791
\(659\) −2.72591e18 −1.29645 −0.648227 0.761447i \(-0.724489\pi\)
−0.648227 + 0.761447i \(0.724489\pi\)
\(660\) 3.06162e18 1.44184
\(661\) 2.79637e18 1.30402 0.652012 0.758209i \(-0.273925\pi\)
0.652012 + 0.758209i \(0.273925\pi\)
\(662\) 2.13555e17 0.0986125
\(663\) −5.85472e17 −0.267712
\(664\) 3.32559e18 1.50583
\(665\) −5.64286e18 −2.53022
\(666\) −2.35552e18 −1.04593
\(667\) 3.74040e18 1.64475
\(668\) 3.24477e18 1.41298
\(669\) 2.81735e17 0.121499
\(670\) 2.22387e18 0.949781
\(671\) −3.28614e18 −1.38992
\(672\) −1.33724e18 −0.560158
\(673\) −2.50350e18 −1.03860 −0.519302 0.854591i \(-0.673808\pi\)
−0.519302 + 0.854591i \(0.673808\pi\)
\(674\) −2.02288e18 −0.831153
\(675\) 2.29535e17 0.0934061
\(676\) −4.26103e18 −1.71736
\(677\) −3.17013e18 −1.26547 −0.632733 0.774370i \(-0.718067\pi\)
−0.632733 + 0.774370i \(0.718067\pi\)
\(678\) 7.01473e17 0.277343
\(679\) −4.15140e17 −0.162570
\(680\) −8.24333e18 −3.19738
\(681\) −8.00391e17 −0.307501
\(682\) −1.60720e18 −0.611605
\(683\) 2.34851e18 0.885233 0.442617 0.896711i \(-0.354050\pi\)
0.442617 + 0.896711i \(0.354050\pi\)
\(684\) −1.84543e18 −0.689022
\(685\) −2.30913e18 −0.854005
\(686\) 1.15574e19 4.23403
\(687\) 1.35660e18 0.492303
\(688\) 1.00511e18 0.361318
\(689\) −8.56703e17 −0.305074
\(690\) 6.09156e18 2.14887
\(691\) −3.90699e18 −1.36532 −0.682661 0.730735i \(-0.739177\pi\)
−0.682661 + 0.730735i \(0.739177\pi\)
\(692\) 6.24578e18 2.16221
\(693\) 2.00030e18 0.686009
\(694\) 2.22439e18 0.755742
\(695\) −6.52882e18 −2.19752
\(696\) −2.18392e18 −0.728242
\(697\) 6.90441e18 2.28094
\(698\) −3.75628e18 −1.22941
\(699\) −2.81489e18 −0.912767
\(700\) −5.07100e18 −1.62913
\(701\) 4.66427e18 1.48462 0.742312 0.670054i \(-0.233729\pi\)
0.742312 + 0.670054i \(0.233729\pi\)
\(702\) −2.52610e17 −0.0796634
\(703\) −6.75205e18 −2.10972
\(704\) 5.07804e18 1.57208
\(705\) 7.12302e17 0.218492
\(706\) −9.92513e18 −3.01652
\(707\) 7.41032e18 2.23157
\(708\) 4.60505e17 0.137410
\(709\) 3.06020e18 0.904792 0.452396 0.891817i \(-0.350569\pi\)
0.452396 + 0.891817i \(0.350569\pi\)
\(710\) 7.36026e18 2.15632
\(711\) 1.40587e18 0.408126
\(712\) 6.32600e18 1.81974
\(713\) −2.06706e18 −0.589212
\(714\) −1.18894e19 −3.35830
\(715\) 1.20130e18 0.336251
\(716\) −6.34863e18 −1.76094
\(717\) 1.27251e18 0.349774
\(718\) 3.37276e18 0.918707
\(719\) 2.03325e18 0.548848 0.274424 0.961609i \(-0.411513\pi\)
0.274424 + 0.961609i \(0.411513\pi\)
\(720\) −7.80437e17 −0.208774
\(721\) −8.96550e18 −2.37681
\(722\) −1.78261e18 −0.468345
\(723\) −2.65895e18 −0.692327
\(724\) 5.59863e18 1.44471
\(725\) 1.71889e18 0.439593
\(726\) −9.82035e17 −0.248908
\(727\) −2.88259e18 −0.724118 −0.362059 0.932155i \(-0.617926\pi\)
−0.362059 + 0.932155i \(0.617926\pi\)
\(728\) 2.52803e18 0.629403
\(729\) 1.50095e17 0.0370370
\(730\) −9.65138e18 −2.36043
\(731\) −5.46395e18 −1.32447
\(732\) 5.44753e18 1.30881
\(733\) −5.56719e18 −1.32575 −0.662873 0.748732i \(-0.730663\pi\)
−0.662873 + 0.748732i \(0.730663\pi\)
\(734\) 4.33165e18 1.02242
\(735\) −7.13174e18 −1.66851
\(736\) 4.13799e18 0.959585
\(737\) −2.25972e18 −0.519418
\(738\) 2.97900e18 0.678741
\(739\) 2.39026e18 0.539829 0.269915 0.962884i \(-0.413004\pi\)
0.269915 + 0.962884i \(0.413004\pi\)
\(740\) −1.85696e19 −4.15715
\(741\) −7.24100e17 −0.160687
\(742\) −1.73973e19 −3.82699
\(743\) −2.73176e18 −0.595683 −0.297841 0.954615i \(-0.596267\pi\)
−0.297841 + 0.954615i \(0.596267\pi\)
\(744\) 1.20690e18 0.260884
\(745\) −3.86328e18 −0.827829
\(746\) 1.09396e19 2.32380
\(747\) −1.71157e18 −0.360422
\(748\) 1.84910e19 3.86011
\(749\) −1.36687e19 −2.82876
\(750\) −2.96832e18 −0.608994
\(751\) −5.28293e18 −1.07452 −0.537261 0.843416i \(-0.680541\pi\)
−0.537261 + 0.843416i \(0.680541\pi\)
\(752\) −7.91371e17 −0.159575
\(753\) 2.21320e18 0.442438
\(754\) −1.89168e18 −0.374916
\(755\) −4.48852e18 −0.881959
\(756\) −3.31596e18 −0.645977
\(757\) −3.79811e18 −0.733575 −0.366788 0.930305i \(-0.619542\pi\)
−0.366788 + 0.930305i \(0.619542\pi\)
\(758\) 7.11500e18 1.36246
\(759\) −6.18977e18 −1.17518
\(760\) −1.01952e19 −1.91914
\(761\) 3.86359e18 0.721092 0.360546 0.932741i \(-0.382590\pi\)
0.360546 + 0.932741i \(0.382590\pi\)
\(762\) 4.08325e18 0.755611
\(763\) 7.36523e18 1.35138
\(764\) −2.74079e18 −0.498618
\(765\) 4.24258e18 0.765298
\(766\) 1.16493e19 2.08360
\(767\) 1.80691e17 0.0320454
\(768\) −5.50049e18 −0.967283
\(769\) −3.11599e18 −0.543345 −0.271672 0.962390i \(-0.587577\pi\)
−0.271672 + 0.962390i \(0.587577\pi\)
\(770\) 2.43952e19 4.21808
\(771\) −1.69934e18 −0.291359
\(772\) 2.73242e18 0.464553
\(773\) −4.00105e18 −0.674540 −0.337270 0.941408i \(-0.609503\pi\)
−0.337270 + 0.941408i \(0.609503\pi\)
\(774\) −2.35749e18 −0.394125
\(775\) −9.49911e17 −0.157479
\(776\) −7.50052e17 −0.123308
\(777\) −1.21324e19 −1.97793
\(778\) −3.77953e18 −0.611042
\(779\) 8.53924e18 1.36907
\(780\) −1.99143e18 −0.316629
\(781\) −7.47892e18 −1.17925
\(782\) 3.67906e19 5.75298
\(783\) 1.12399e18 0.174306
\(784\) 7.92340e18 1.21859
\(785\) −2.19866e18 −0.335356
\(786\) 4.77105e18 0.721718
\(787\) 1.67609e18 0.251456 0.125728 0.992065i \(-0.459873\pi\)
0.125728 + 0.992065i \(0.459873\pi\)
\(788\) −4.93080e18 −0.733664
\(789\) −3.52211e18 −0.519759
\(790\) 1.71457e19 2.50945
\(791\) 3.61302e18 0.524474
\(792\) 3.61403e18 0.520330
\(793\) 2.13747e18 0.305228
\(794\) −5.31482e18 −0.752758
\(795\) 6.20804e18 0.872103
\(796\) 2.09563e19 2.91998
\(797\) −5.73881e18 −0.793127 −0.396563 0.918007i \(-0.629797\pi\)
−0.396563 + 0.918007i \(0.629797\pi\)
\(798\) −1.47045e19 −2.01573
\(799\) 4.30202e18 0.584949
\(800\) 1.90160e18 0.256468
\(801\) −3.25579e18 −0.435557
\(802\) −1.15306e18 −0.153010
\(803\) 9.80698e18 1.29087
\(804\) 3.74600e18 0.489107
\(805\) 3.13754e19 4.06364
\(806\) 1.04540e18 0.134309
\(807\) −4.57397e17 −0.0582929
\(808\) 1.33885e19 1.69262
\(809\) 1.49923e19 1.88020 0.940100 0.340900i \(-0.110732\pi\)
0.940100 + 0.340900i \(0.110732\pi\)
\(810\) 1.83052e18 0.227731
\(811\) 1.98826e18 0.245379 0.122690 0.992445i \(-0.460848\pi\)
0.122690 + 0.992445i \(0.460848\pi\)
\(812\) −2.48317e19 −3.04013
\(813\) 7.68739e18 0.933663
\(814\) 2.91905e19 3.51708
\(815\) 1.59945e18 0.191181
\(816\) −4.71352e18 −0.558933
\(817\) −6.75770e18 −0.794979
\(818\) −1.65588e19 −1.93255
\(819\) −1.30110e18 −0.150648
\(820\) 2.34847e19 2.69771
\(821\) 1.39607e19 1.59103 0.795514 0.605936i \(-0.207201\pi\)
0.795514 + 0.605936i \(0.207201\pi\)
\(822\) −6.01729e18 −0.680352
\(823\) 9.75233e18 1.09398 0.546990 0.837139i \(-0.315773\pi\)
0.546990 + 0.837139i \(0.315773\pi\)
\(824\) −1.61983e19 −1.80278
\(825\) −2.84449e18 −0.314090
\(826\) 3.66934e18 0.401992
\(827\) −7.70194e18 −0.837171 −0.418585 0.908177i \(-0.637474\pi\)
−0.418585 + 0.908177i \(0.637474\pi\)
\(828\) 1.02609e19 1.10660
\(829\) 2.84102e18 0.303997 0.151999 0.988381i \(-0.451429\pi\)
0.151999 + 0.988381i \(0.451429\pi\)
\(830\) −2.08739e19 −2.21614
\(831\) 9.02966e18 0.951184
\(832\) −3.30301e18 −0.345230
\(833\) −4.30729e19 −4.46695
\(834\) −1.70132e19 −1.75068
\(835\) −9.22590e18 −0.941991
\(836\) 2.28693e19 2.31692
\(837\) −6.21153e17 −0.0624429
\(838\) 1.59571e19 1.59172
\(839\) 1.30494e19 1.29163 0.645817 0.763493i \(-0.276517\pi\)
0.645817 + 0.763493i \(0.276517\pi\)
\(840\) −1.83192e19 −1.79925
\(841\) −1.84356e18 −0.179673
\(842\) 6.42848e18 0.621698
\(843\) 4.90877e18 0.471079
\(844\) −1.74824e19 −1.66485
\(845\) 1.21155e19 1.14491
\(846\) 1.85616e18 0.174064
\(847\) −5.05809e18 −0.470700
\(848\) −6.89715e18 −0.636938
\(849\) −4.51370e18 −0.413650
\(850\) 1.69070e19 1.53760
\(851\) 3.75427e19 3.38831
\(852\) 1.23980e19 1.11044
\(853\) 1.54188e19 1.37051 0.685254 0.728304i \(-0.259691\pi\)
0.685254 + 0.728304i \(0.259691\pi\)
\(854\) 4.34063e19 3.82892
\(855\) 5.24714e18 0.459349
\(856\) −2.46959e19 −2.14558
\(857\) −7.58947e18 −0.654389 −0.327195 0.944957i \(-0.606103\pi\)
−0.327195 + 0.944957i \(0.606103\pi\)
\(858\) 3.13043e18 0.267878
\(859\) 2.10137e18 0.178463 0.0892313 0.996011i \(-0.471559\pi\)
0.0892313 + 0.996011i \(0.471559\pi\)
\(860\) −1.85851e19 −1.56648
\(861\) 1.53437e19 1.28354
\(862\) −3.08860e17 −0.0256428
\(863\) 1.95772e19 1.61317 0.806584 0.591119i \(-0.201314\pi\)
0.806584 + 0.591119i \(0.201314\pi\)
\(864\) 1.24347e18 0.101694
\(865\) −1.77587e19 −1.44148
\(866\) −1.10870e19 −0.893195
\(867\) 1.84030e19 1.47152
\(868\) 1.37228e19 1.08909
\(869\) −1.74221e19 −1.37237
\(870\) 1.37079e19 1.07176
\(871\) 1.46984e18 0.114065
\(872\) 1.33071e19 1.02500
\(873\) 3.86028e17 0.0295139
\(874\) 4.55019e19 3.45307
\(875\) −1.52887e19 −1.15165
\(876\) −1.62573e19 −1.21555
\(877\) −1.64212e18 −0.121873 −0.0609367 0.998142i \(-0.519409\pi\)
−0.0609367 + 0.998142i \(0.519409\pi\)
\(878\) −2.50711e18 −0.184697
\(879\) −1.14701e19 −0.838762
\(880\) 9.67147e18 0.702029
\(881\) −1.55048e19 −1.11718 −0.558590 0.829444i \(-0.688657\pi\)
−0.558590 + 0.829444i \(0.688657\pi\)
\(882\) −1.85844e19 −1.32923
\(883\) 1.93639e19 1.37483 0.687414 0.726266i \(-0.258746\pi\)
0.687414 + 0.726266i \(0.258746\pi\)
\(884\) −1.20274e19 −0.847683
\(885\) −1.30936e18 −0.0916069
\(886\) −1.62970e19 −1.13185
\(887\) −3.71331e18 −0.256011 −0.128005 0.991773i \(-0.540857\pi\)
−0.128005 + 0.991773i \(0.540857\pi\)
\(888\) −2.19201e19 −1.50023
\(889\) 2.10313e19 1.42891
\(890\) −3.97068e19 −2.67812
\(891\) −1.86003e18 −0.124542
\(892\) 5.78773e18 0.384713
\(893\) 5.32065e18 0.351100
\(894\) −1.00672e19 −0.659499
\(895\) 1.80512e19 1.17397
\(896\) −5.20482e19 −3.36050
\(897\) 4.02613e18 0.258070
\(898\) −2.85092e19 −1.81422
\(899\) −4.65154e18 −0.293872
\(900\) 4.71538e18 0.295761
\(901\) 3.74940e19 2.33481
\(902\) −3.69169e19 −2.28235
\(903\) −1.21426e19 −0.745315
\(904\) 6.52780e18 0.397807
\(905\) −1.59187e19 −0.963143
\(906\) −1.16965e19 −0.702622
\(907\) 4.46231e18 0.266142 0.133071 0.991107i \(-0.457516\pi\)
0.133071 + 0.991107i \(0.457516\pi\)
\(908\) −1.64426e19 −0.973670
\(909\) −6.89066e18 −0.405131
\(910\) −1.58679e19 −0.926295
\(911\) 2.68282e19 1.55497 0.777486 0.628900i \(-0.216495\pi\)
0.777486 + 0.628900i \(0.216495\pi\)
\(912\) −5.82960e18 −0.335484
\(913\) 2.12105e19 1.21196
\(914\) −3.95011e18 −0.224109
\(915\) −1.54890e19 −0.872544
\(916\) 2.78688e19 1.55883
\(917\) 2.45739e19 1.36481
\(918\) 1.10556e19 0.609683
\(919\) −3.80892e17 −0.0208570 −0.0104285 0.999946i \(-0.503320\pi\)
−0.0104285 + 0.999946i \(0.503320\pi\)
\(920\) 5.66872e19 3.08222
\(921\) −1.85589e19 −1.00199
\(922\) 4.86732e19 2.60939
\(923\) 4.86466e18 0.258965
\(924\) 4.10926e19 2.17218
\(925\) 1.72526e19 0.905594
\(926\) 2.91223e19 1.51794
\(927\) 8.33678e18 0.431499
\(928\) 9.31177e18 0.478597
\(929\) −1.39725e19 −0.713133 −0.356567 0.934270i \(-0.616053\pi\)
−0.356567 + 0.934270i \(0.616053\pi\)
\(930\) −7.57543e18 −0.383944
\(931\) −5.32717e19 −2.68116
\(932\) −5.78267e19 −2.89018
\(933\) −9.59449e18 −0.476202
\(934\) 2.43024e18 0.119783
\(935\) −5.25756e19 −2.57341
\(936\) −2.35075e18 −0.114265
\(937\) 5.23457e18 0.252682 0.126341 0.991987i \(-0.459677\pi\)
0.126341 + 0.991987i \(0.459677\pi\)
\(938\) 2.98484e19 1.43088
\(939\) 6.35190e18 0.302397
\(940\) 1.46329e19 0.691832
\(941\) 3.00658e19 1.41169 0.705845 0.708366i \(-0.250567\pi\)
0.705845 + 0.708366i \(0.250567\pi\)
\(942\) −5.72942e18 −0.267165
\(943\) −4.74798e19 −2.19878
\(944\) 1.45471e18 0.0669048
\(945\) 9.42831e18 0.430653
\(946\) 2.92149e19 1.32529
\(947\) 1.61344e19 0.726906 0.363453 0.931613i \(-0.381598\pi\)
0.363453 + 0.931613i \(0.381598\pi\)
\(948\) 2.88811e19 1.29229
\(949\) −6.37895e18 −0.283477
\(950\) 2.09102e19 0.922902
\(951\) −2.10355e19 −0.922102
\(952\) −1.10641e20 −4.81697
\(953\) −7.86102e17 −0.0339919 −0.0169959 0.999856i \(-0.505410\pi\)
−0.0169959 + 0.999856i \(0.505410\pi\)
\(954\) 1.61773e19 0.694771
\(955\) 7.79292e18 0.332413
\(956\) 2.61414e19 1.10752
\(957\) −1.39289e19 −0.586125
\(958\) −5.29286e19 −2.21215
\(959\) −3.09928e19 −1.28659
\(960\) 2.39350e19 0.986895
\(961\) −2.18470e19 −0.894724
\(962\) −1.89869e19 −0.772355
\(963\) 1.27102e19 0.513548
\(964\) −5.46232e19 −2.19218
\(965\) −7.76914e18 −0.309703
\(966\) 8.17599e19 3.23735
\(967\) 3.74423e17 0.0147262 0.00736309 0.999973i \(-0.497656\pi\)
0.00736309 + 0.999973i \(0.497656\pi\)
\(968\) −9.13867e18 −0.357020
\(969\) 3.16906e19 1.22978
\(970\) 4.70790e18 0.181473
\(971\) −2.13260e19 −0.816553 −0.408277 0.912858i \(-0.633870\pi\)
−0.408277 + 0.912858i \(0.633870\pi\)
\(972\) 3.08342e18 0.117274
\(973\) −8.76287e19 −3.31065
\(974\) 3.13729e19 1.17739
\(975\) 1.85020e18 0.0689744
\(976\) 1.72084e19 0.637259
\(977\) 1.93222e19 0.710789 0.355395 0.934716i \(-0.384346\pi\)
0.355395 + 0.934716i \(0.384346\pi\)
\(978\) 4.16794e18 0.152307
\(979\) 4.03470e19 1.46462
\(980\) −1.46509e20 −5.28316
\(981\) −6.84873e18 −0.245336
\(982\) 2.17113e19 0.772613
\(983\) 3.48169e18 0.123081 0.0615407 0.998105i \(-0.480399\pi\)
0.0615407 + 0.998105i \(0.480399\pi\)
\(984\) 2.77221e19 0.973550
\(985\) 1.40198e19 0.489111
\(986\) 8.27904e19 2.86933
\(987\) 9.56040e18 0.329166
\(988\) −1.48753e19 −0.508799
\(989\) 3.75741e19 1.27677
\(990\) −2.26845e19 −0.765772
\(991\) 9.31452e18 0.312379 0.156189 0.987727i \(-0.450079\pi\)
0.156189 + 0.987727i \(0.450079\pi\)
\(992\) −5.14597e18 −0.171452
\(993\) −1.02280e18 −0.0338550
\(994\) 9.87881e19 3.24858
\(995\) −5.95853e19 −1.94666
\(996\) −3.51611e19 −1.14124
\(997\) −6.79851e18 −0.219227 −0.109614 0.993974i \(-0.534961\pi\)
−0.109614 + 0.993974i \(0.534961\pi\)
\(998\) −5.37459e19 −1.72186
\(999\) 1.12816e19 0.359083
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.1.4 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.4 30 1.1 even 1 trivial