Properties

Label 177.14.a.a.1.16
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 1.16
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+9.64157 q^{2} +729.000 q^{3} -8099.04 q^{4} -58650.0 q^{5} +7028.71 q^{6} -68208.9 q^{7} -157071. q^{8} +531441. q^{9} +O(q^{10})\) \(q+9.64157 q^{2} +729.000 q^{3} -8099.04 q^{4} -58650.0 q^{5} +7028.71 q^{6} -68208.9 q^{7} -157071. q^{8} +531441. q^{9} -565478. q^{10} -8.19627e6 q^{11} -5.90420e6 q^{12} -4.22126e6 q^{13} -657641. q^{14} -4.27558e7 q^{15} +6.48329e7 q^{16} +1.28115e8 q^{17} +5.12393e6 q^{18} -5.29427e7 q^{19} +4.75009e8 q^{20} -4.97243e7 q^{21} -7.90250e7 q^{22} -8.07458e7 q^{23} -1.14505e8 q^{24} +2.21912e9 q^{25} -4.06996e7 q^{26} +3.87420e8 q^{27} +5.52427e8 q^{28} +1.70394e9 q^{29} -4.12233e8 q^{30} +5.22860e9 q^{31} +1.91182e9 q^{32} -5.97508e9 q^{33} +1.23523e9 q^{34} +4.00045e9 q^{35} -4.30416e9 q^{36} -2.22190e10 q^{37} -5.10450e8 q^{38} -3.07730e9 q^{39} +9.21223e9 q^{40} -1.90946e10 q^{41} -4.79421e8 q^{42} +5.00370e10 q^{43} +6.63820e10 q^{44} -3.11690e10 q^{45} -7.78517e8 q^{46} +1.40679e11 q^{47} +4.72632e10 q^{48} -9.22366e10 q^{49} +2.13958e10 q^{50} +9.33956e10 q^{51} +3.41881e10 q^{52} +2.75197e10 q^{53} +3.73534e9 q^{54} +4.80711e11 q^{55} +1.07137e10 q^{56} -3.85952e10 q^{57} +1.64287e10 q^{58} +4.21805e10 q^{59} +3.46281e11 q^{60} +8.31120e10 q^{61} +5.04119e10 q^{62} -3.62490e10 q^{63} -5.12678e11 q^{64} +2.47577e11 q^{65} -5.76092e10 q^{66} +1.44720e12 q^{67} -1.03761e12 q^{68} -5.88637e10 q^{69} +3.85707e10 q^{70} -8.00672e11 q^{71} -8.34741e10 q^{72} -1.15447e12 q^{73} -2.14226e11 q^{74} +1.61774e12 q^{75} +4.28785e11 q^{76} +5.59059e11 q^{77} -2.96700e10 q^{78} +3.68729e12 q^{79} -3.80245e12 q^{80} +2.82430e11 q^{81} -1.84102e11 q^{82} -2.67410e12 q^{83} +4.02719e11 q^{84} -7.51393e12 q^{85} +4.82435e11 q^{86} +1.24218e12 q^{87} +1.28740e12 q^{88} -7.91226e12 q^{89} -3.00518e11 q^{90} +2.87927e11 q^{91} +6.53964e11 q^{92} +3.81165e12 q^{93} +1.35636e12 q^{94} +3.10509e12 q^{95} +1.39372e12 q^{96} -1.18233e13 q^{97} -8.89305e11 q^{98} -4.35584e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.64157 0.106525 0.0532627 0.998581i \(-0.483038\pi\)
0.0532627 + 0.998581i \(0.483038\pi\)
\(3\) 729.000 0.577350
\(4\) −8099.04 −0.988652
\(5\) −58650.0 −1.67866 −0.839330 0.543622i \(-0.817053\pi\)
−0.839330 + 0.543622i \(0.817053\pi\)
\(6\) 7028.71 0.0615024
\(7\) −68208.9 −0.219131 −0.109566 0.993980i \(-0.534946\pi\)
−0.109566 + 0.993980i \(0.534946\pi\)
\(8\) −157071. −0.211842
\(9\) 531441. 0.333333
\(10\) −565478. −0.178820
\(11\) −8.19627e6 −1.39497 −0.697484 0.716601i \(-0.745697\pi\)
−0.697484 + 0.716601i \(0.745697\pi\)
\(12\) −5.90420e6 −0.570799
\(13\) −4.22126e6 −0.242555 −0.121277 0.992619i \(-0.538699\pi\)
−0.121277 + 0.992619i \(0.538699\pi\)
\(14\) −657641. −0.0233430
\(15\) −4.27558e7 −0.969175
\(16\) 6.48329e7 0.966086
\(17\) 1.28115e8 1.28730 0.643652 0.765318i \(-0.277418\pi\)
0.643652 + 0.765318i \(0.277418\pi\)
\(18\) 5.12393e6 0.0355084
\(19\) −5.29427e7 −0.258171 −0.129085 0.991633i \(-0.541204\pi\)
−0.129085 + 0.991633i \(0.541204\pi\)
\(20\) 4.75009e8 1.65961
\(21\) −4.97243e7 −0.126515
\(22\) −7.90250e7 −0.148599
\(23\) −8.07458e7 −0.113734 −0.0568669 0.998382i \(-0.518111\pi\)
−0.0568669 + 0.998382i \(0.518111\pi\)
\(24\) −1.14505e8 −0.122307
\(25\) 2.21912e9 1.81790
\(26\) −4.06996e7 −0.0258382
\(27\) 3.87420e8 0.192450
\(28\) 5.52427e8 0.216644
\(29\) 1.70394e9 0.531947 0.265974 0.963980i \(-0.414307\pi\)
0.265974 + 0.963980i \(0.414307\pi\)
\(30\) −4.12233e8 −0.103242
\(31\) 5.22860e9 1.05812 0.529059 0.848585i \(-0.322545\pi\)
0.529059 + 0.848585i \(0.322545\pi\)
\(32\) 1.91182e9 0.314754
\(33\) −5.97508e9 −0.805385
\(34\) 1.23523e9 0.137130
\(35\) 4.00045e9 0.367847
\(36\) −4.30416e9 −0.329551
\(37\) −2.22190e10 −1.42368 −0.711841 0.702341i \(-0.752138\pi\)
−0.711841 + 0.702341i \(0.752138\pi\)
\(38\) −5.10450e8 −0.0275017
\(39\) −3.07730e9 −0.140039
\(40\) 9.21223e9 0.355611
\(41\) −1.90946e10 −0.627791 −0.313895 0.949458i \(-0.601634\pi\)
−0.313895 + 0.949458i \(0.601634\pi\)
\(42\) −4.79421e8 −0.0134771
\(43\) 5.00370e10 1.20711 0.603554 0.797322i \(-0.293751\pi\)
0.603554 + 0.797322i \(0.293751\pi\)
\(44\) 6.63820e10 1.37914
\(45\) −3.11690e10 −0.559553
\(46\) −7.78517e8 −0.0121155
\(47\) 1.40679e11 1.90367 0.951837 0.306606i \(-0.0991934\pi\)
0.951837 + 0.306606i \(0.0991934\pi\)
\(48\) 4.72632e10 0.557770
\(49\) −9.22366e10 −0.951982
\(50\) 2.13958e10 0.193652
\(51\) 9.33956e10 0.743225
\(52\) 3.41881e10 0.239802
\(53\) 2.75197e10 0.170549 0.0852747 0.996357i \(-0.472823\pi\)
0.0852747 + 0.996357i \(0.472823\pi\)
\(54\) 3.73534e9 0.0205008
\(55\) 4.80711e11 2.34168
\(56\) 1.07137e10 0.0464211
\(57\) −3.85952e10 −0.149055
\(58\) 1.64287e10 0.0566658
\(59\) 4.21805e10 0.130189
\(60\) 3.46281e11 0.958177
\(61\) 8.31120e10 0.206547 0.103274 0.994653i \(-0.467068\pi\)
0.103274 + 0.994653i \(0.467068\pi\)
\(62\) 5.04119e10 0.112716
\(63\) −3.62490e10 −0.0730437
\(64\) −5.12678e11 −0.932557
\(65\) 2.47577e11 0.407167
\(66\) −5.76092e10 −0.0857939
\(67\) 1.44720e12 1.95453 0.977263 0.212029i \(-0.0680070\pi\)
0.977263 + 0.212029i \(0.0680070\pi\)
\(68\) −1.03761e12 −1.27270
\(69\) −5.88637e10 −0.0656642
\(70\) 3.85707e10 0.0391850
\(71\) −8.00672e11 −0.741781 −0.370890 0.928677i \(-0.620947\pi\)
−0.370890 + 0.928677i \(0.620947\pi\)
\(72\) −8.34741e10 −0.0706139
\(73\) −1.15447e12 −0.892859 −0.446430 0.894819i \(-0.647305\pi\)
−0.446430 + 0.894819i \(0.647305\pi\)
\(74\) −2.14226e11 −0.151658
\(75\) 1.61774e12 1.04957
\(76\) 4.28785e11 0.255241
\(77\) 5.59059e11 0.305681
\(78\) −2.96700e10 −0.0149177
\(79\) 3.68729e12 1.70660 0.853299 0.521421i \(-0.174598\pi\)
0.853299 + 0.521421i \(0.174598\pi\)
\(80\) −3.80245e12 −1.62173
\(81\) 2.82430e11 0.111111
\(82\) −1.84102e11 −0.0668756
\(83\) −2.67410e12 −0.897781 −0.448890 0.893587i \(-0.648181\pi\)
−0.448890 + 0.893587i \(0.648181\pi\)
\(84\) 4.02719e11 0.125080
\(85\) −7.51393e12 −2.16095
\(86\) 4.82435e11 0.128588
\(87\) 1.24218e12 0.307120
\(88\) 1.28740e12 0.295512
\(89\) −7.91226e12 −1.68759 −0.843793 0.536669i \(-0.819682\pi\)
−0.843793 + 0.536669i \(0.819682\pi\)
\(90\) −3.00518e11 −0.0596066
\(91\) 2.87927e11 0.0531513
\(92\) 6.53964e11 0.112443
\(93\) 3.81165e12 0.610905
\(94\) 1.35636e12 0.202789
\(95\) 3.10509e12 0.433381
\(96\) 1.39372e12 0.181724
\(97\) −1.18233e13 −1.44119 −0.720596 0.693355i \(-0.756132\pi\)
−0.720596 + 0.693355i \(0.756132\pi\)
\(98\) −8.89305e11 −0.101410
\(99\) −4.35584e12 −0.464989
\(100\) −1.79727e13 −1.79727
\(101\) −1.94509e11 −0.0182327 −0.00911634 0.999958i \(-0.502902\pi\)
−0.00911634 + 0.999958i \(0.502902\pi\)
\(102\) 9.00481e11 0.0791723
\(103\) 6.43127e12 0.530707 0.265354 0.964151i \(-0.414511\pi\)
0.265354 + 0.964151i \(0.414511\pi\)
\(104\) 6.63038e11 0.0513833
\(105\) 2.91633e12 0.212376
\(106\) 2.65333e11 0.0181678
\(107\) 1.47405e13 0.949553 0.474776 0.880106i \(-0.342529\pi\)
0.474776 + 0.880106i \(0.342529\pi\)
\(108\) −3.13773e12 −0.190266
\(109\) −1.33568e13 −0.762835 −0.381418 0.924403i \(-0.624564\pi\)
−0.381418 + 0.924403i \(0.624564\pi\)
\(110\) 4.63481e12 0.249448
\(111\) −1.61976e13 −0.821963
\(112\) −4.42218e12 −0.211699
\(113\) −2.20014e13 −0.994125 −0.497063 0.867715i \(-0.665588\pi\)
−0.497063 + 0.867715i \(0.665588\pi\)
\(114\) −3.72118e11 −0.0158781
\(115\) 4.73574e12 0.190920
\(116\) −1.38003e13 −0.525911
\(117\) −2.24335e12 −0.0808516
\(118\) 4.06687e11 0.0138684
\(119\) −8.73857e12 −0.282088
\(120\) 6.71571e12 0.205312
\(121\) 3.26562e13 0.945934
\(122\) 8.01330e11 0.0220025
\(123\) −1.39199e13 −0.362455
\(124\) −4.23466e13 −1.04611
\(125\) −5.85570e13 −1.37298
\(126\) −3.49498e11 −0.00778100
\(127\) 7.50480e13 1.58714 0.793569 0.608480i \(-0.208221\pi\)
0.793569 + 0.608480i \(0.208221\pi\)
\(128\) −2.06046e13 −0.414095
\(129\) 3.64769e13 0.696924
\(130\) 2.38703e12 0.0433736
\(131\) 3.13397e12 0.0541791 0.0270895 0.999633i \(-0.491376\pi\)
0.0270895 + 0.999633i \(0.491376\pi\)
\(132\) 4.83924e13 0.796246
\(133\) 3.61116e12 0.0565733
\(134\) 1.39533e13 0.208207
\(135\) −2.27222e13 −0.323058
\(136\) −2.01231e13 −0.272705
\(137\) 3.73904e13 0.483143 0.241572 0.970383i \(-0.422337\pi\)
0.241572 + 0.970383i \(0.422337\pi\)
\(138\) −5.67539e11 −0.00699490
\(139\) 9.33477e12 0.109776 0.0548880 0.998493i \(-0.482520\pi\)
0.0548880 + 0.998493i \(0.482520\pi\)
\(140\) −3.23998e13 −0.363672
\(141\) 1.02555e14 1.09909
\(142\) −7.71974e12 −0.0790185
\(143\) 3.45986e13 0.338356
\(144\) 3.44549e13 0.322029
\(145\) −9.99363e13 −0.892959
\(146\) −1.11309e13 −0.0951121
\(147\) −6.72404e13 −0.549627
\(148\) 1.79952e14 1.40753
\(149\) 1.77393e14 1.32809 0.664043 0.747695i \(-0.268839\pi\)
0.664043 + 0.747695i \(0.268839\pi\)
\(150\) 1.55975e13 0.111805
\(151\) −3.83684e13 −0.263405 −0.131702 0.991289i \(-0.542044\pi\)
−0.131702 + 0.991289i \(0.542044\pi\)
\(152\) 8.31577e12 0.0546914
\(153\) 6.80854e13 0.429101
\(154\) 5.39021e12 0.0325627
\(155\) −3.06657e14 −1.77622
\(156\) 2.49232e13 0.138450
\(157\) 1.79121e14 0.954550 0.477275 0.878754i \(-0.341625\pi\)
0.477275 + 0.878754i \(0.341625\pi\)
\(158\) 3.55513e13 0.181796
\(159\) 2.00619e13 0.0984668
\(160\) −1.12128e14 −0.528366
\(161\) 5.50759e12 0.0249226
\(162\) 2.72306e12 0.0118361
\(163\) 3.30232e14 1.37911 0.689557 0.724231i \(-0.257805\pi\)
0.689557 + 0.724231i \(0.257805\pi\)
\(164\) 1.54648e14 0.620667
\(165\) 3.50439e14 1.35197
\(166\) −2.57825e13 −0.0956364
\(167\) −5.52806e14 −1.97204 −0.986020 0.166627i \(-0.946712\pi\)
−0.986020 + 0.166627i \(0.946712\pi\)
\(168\) 7.81026e12 0.0268013
\(169\) −2.85056e14 −0.941167
\(170\) −7.24461e13 −0.230196
\(171\) −2.81359e13 −0.0860570
\(172\) −4.05251e14 −1.19341
\(173\) 2.12008e14 0.601246 0.300623 0.953743i \(-0.402805\pi\)
0.300623 + 0.953743i \(0.402805\pi\)
\(174\) 1.19765e13 0.0327160
\(175\) −1.51364e14 −0.398359
\(176\) −5.31388e14 −1.34766
\(177\) 3.07496e13 0.0751646
\(178\) −7.62867e13 −0.179771
\(179\) −7.03233e14 −1.59792 −0.798959 0.601385i \(-0.794616\pi\)
−0.798959 + 0.601385i \(0.794616\pi\)
\(180\) 2.52439e14 0.553204
\(181\) −7.40089e14 −1.56449 −0.782246 0.622970i \(-0.785926\pi\)
−0.782246 + 0.622970i \(0.785926\pi\)
\(182\) 2.77607e12 0.00566196
\(183\) 6.05886e13 0.119250
\(184\) 1.26828e13 0.0240936
\(185\) 1.30314e15 2.38988
\(186\) 3.67503e13 0.0650768
\(187\) −1.05006e15 −1.79575
\(188\) −1.13936e15 −1.88207
\(189\) −2.64255e13 −0.0421718
\(190\) 2.99379e13 0.0461661
\(191\) −3.02452e14 −0.450754 −0.225377 0.974272i \(-0.572361\pi\)
−0.225377 + 0.974272i \(0.572361\pi\)
\(192\) −3.73743e14 −0.538412
\(193\) −6.36959e14 −0.887134 −0.443567 0.896241i \(-0.646287\pi\)
−0.443567 + 0.896241i \(0.646287\pi\)
\(194\) −1.13995e14 −0.153524
\(195\) 1.80483e14 0.235078
\(196\) 7.47028e14 0.941179
\(197\) 4.40983e13 0.0537517 0.0268758 0.999639i \(-0.491444\pi\)
0.0268758 + 0.999639i \(0.491444\pi\)
\(198\) −4.19971e13 −0.0495331
\(199\) 1.34227e15 1.53212 0.766062 0.642767i \(-0.222213\pi\)
0.766062 + 0.642767i \(0.222213\pi\)
\(200\) −3.48559e14 −0.385107
\(201\) 1.05501e15 1.12845
\(202\) −1.87537e12 −0.00194224
\(203\) −1.16224e14 −0.116566
\(204\) −7.56415e14 −0.734791
\(205\) 1.11990e15 1.05385
\(206\) 6.20076e13 0.0565337
\(207\) −4.29116e13 −0.0379112
\(208\) −2.73676e14 −0.234329
\(209\) 4.33933e14 0.360140
\(210\) 2.81180e13 0.0226235
\(211\) 2.47246e15 1.92883 0.964415 0.264392i \(-0.0851711\pi\)
0.964415 + 0.264392i \(0.0851711\pi\)
\(212\) −2.22883e14 −0.168614
\(213\) −5.83690e14 −0.428267
\(214\) 1.42122e14 0.101151
\(215\) −2.93467e15 −2.02632
\(216\) −6.08526e13 −0.0407690
\(217\) −3.56637e14 −0.231867
\(218\) −1.28781e14 −0.0812613
\(219\) −8.41607e14 −0.515493
\(220\) −3.89330e15 −2.31510
\(221\) −5.40805e14 −0.312242
\(222\) −1.56171e14 −0.0875599
\(223\) −2.32661e15 −1.26690 −0.633450 0.773784i \(-0.718362\pi\)
−0.633450 + 0.773784i \(0.718362\pi\)
\(224\) −1.30403e14 −0.0689725
\(225\) 1.17933e15 0.605967
\(226\) −2.12128e14 −0.105900
\(227\) 2.41884e15 1.17338 0.586690 0.809812i \(-0.300431\pi\)
0.586690 + 0.809812i \(0.300431\pi\)
\(228\) 3.12584e14 0.147364
\(229\) −3.06398e15 −1.40396 −0.701980 0.712197i \(-0.747700\pi\)
−0.701980 + 0.712197i \(0.747700\pi\)
\(230\) 4.56600e13 0.0203378
\(231\) 4.07554e14 0.176485
\(232\) −2.67641e14 −0.112689
\(233\) −8.83877e14 −0.361892 −0.180946 0.983493i \(-0.557916\pi\)
−0.180946 + 0.983493i \(0.557916\pi\)
\(234\) −2.16294e13 −0.00861275
\(235\) −8.25080e15 −3.19562
\(236\) −3.41622e14 −0.128712
\(237\) 2.68804e15 0.985305
\(238\) −8.42536e13 −0.0300496
\(239\) 3.76341e15 1.30616 0.653078 0.757290i \(-0.273477\pi\)
0.653078 + 0.757290i \(0.273477\pi\)
\(240\) −2.77199e15 −0.936306
\(241\) −7.53466e14 −0.247715 −0.123858 0.992300i \(-0.539527\pi\)
−0.123858 + 0.992300i \(0.539527\pi\)
\(242\) 3.14857e14 0.100766
\(243\) 2.05891e14 0.0641500
\(244\) −6.73127e14 −0.204204
\(245\) 5.40967e15 1.59805
\(246\) −1.34210e14 −0.0386107
\(247\) 2.23485e14 0.0626206
\(248\) −8.21262e14 −0.224154
\(249\) −1.94942e15 −0.518334
\(250\) −5.64581e14 −0.146257
\(251\) −1.71704e15 −0.433412 −0.216706 0.976237i \(-0.569531\pi\)
−0.216706 + 0.976237i \(0.569531\pi\)
\(252\) 2.93582e14 0.0722148
\(253\) 6.61815e14 0.158655
\(254\) 7.23580e14 0.169070
\(255\) −5.47765e15 −1.24762
\(256\) 4.00120e15 0.888445
\(257\) −1.48391e15 −0.321250 −0.160625 0.987016i \(-0.551351\pi\)
−0.160625 + 0.987016i \(0.551351\pi\)
\(258\) 3.51695e14 0.0742400
\(259\) 1.51553e15 0.311973
\(260\) −2.00513e15 −0.402547
\(261\) 9.05546e14 0.177316
\(262\) 3.02164e13 0.00577144
\(263\) 4.26432e15 0.794579 0.397290 0.917693i \(-0.369951\pi\)
0.397290 + 0.917693i \(0.369951\pi\)
\(264\) 9.38514e14 0.170614
\(265\) −1.61403e15 −0.286295
\(266\) 3.48173e13 0.00602649
\(267\) −5.76804e15 −0.974328
\(268\) −1.17209e16 −1.93235
\(269\) −1.93843e15 −0.311932 −0.155966 0.987762i \(-0.549849\pi\)
−0.155966 + 0.987762i \(0.549849\pi\)
\(270\) −2.19078e14 −0.0344139
\(271\) −5.34540e15 −0.819747 −0.409874 0.912142i \(-0.634427\pi\)
−0.409874 + 0.912142i \(0.634427\pi\)
\(272\) 8.30605e15 1.24365
\(273\) 2.09899e14 0.0306869
\(274\) 3.60502e14 0.0514670
\(275\) −1.81885e16 −2.53591
\(276\) 4.76740e14 0.0649191
\(277\) −4.81951e15 −0.641039 −0.320519 0.947242i \(-0.603857\pi\)
−0.320519 + 0.947242i \(0.603857\pi\)
\(278\) 9.00018e13 0.0116939
\(279\) 2.77869e15 0.352706
\(280\) −6.28356e14 −0.0779253
\(281\) −6.76285e15 −0.819480 −0.409740 0.912202i \(-0.634381\pi\)
−0.409740 + 0.912202i \(0.634381\pi\)
\(282\) 9.88789e14 0.117081
\(283\) −1.07639e15 −0.124554 −0.0622772 0.998059i \(-0.519836\pi\)
−0.0622772 + 0.998059i \(0.519836\pi\)
\(284\) 6.48468e15 0.733363
\(285\) 2.26361e15 0.250213
\(286\) 3.33585e14 0.0360435
\(287\) 1.30242e15 0.137568
\(288\) 1.01602e15 0.104918
\(289\) 6.50881e15 0.657152
\(290\) −9.63543e14 −0.0951227
\(291\) −8.61918e15 −0.832073
\(292\) 9.35008e15 0.882728
\(293\) −2.35706e15 −0.217637 −0.108818 0.994062i \(-0.534707\pi\)
−0.108818 + 0.994062i \(0.534707\pi\)
\(294\) −6.48304e14 −0.0585492
\(295\) −2.47389e15 −0.218543
\(296\) 3.48996e15 0.301595
\(297\) −3.17540e15 −0.268462
\(298\) 1.71035e15 0.141475
\(299\) 3.40849e14 0.0275867
\(300\) −1.31021e16 −1.03766
\(301\) −3.41297e15 −0.264515
\(302\) −3.69932e14 −0.0280593
\(303\) −1.41797e14 −0.0105266
\(304\) −3.43243e15 −0.249415
\(305\) −4.87452e15 −0.346723
\(306\) 6.56451e14 0.0457102
\(307\) 1.61698e16 1.10231 0.551155 0.834403i \(-0.314187\pi\)
0.551155 + 0.834403i \(0.314187\pi\)
\(308\) −4.52784e15 −0.302212
\(309\) 4.68840e15 0.306404
\(310\) −2.95666e15 −0.189212
\(311\) 1.16381e16 0.729353 0.364677 0.931134i \(-0.381180\pi\)
0.364677 + 0.931134i \(0.381180\pi\)
\(312\) 4.83355e14 0.0296662
\(313\) 1.98768e16 1.19484 0.597419 0.801929i \(-0.296193\pi\)
0.597419 + 0.801929i \(0.296193\pi\)
\(314\) 1.72701e15 0.101684
\(315\) 2.12600e15 0.122616
\(316\) −2.98635e16 −1.68723
\(317\) −1.50701e15 −0.0834124 −0.0417062 0.999130i \(-0.513279\pi\)
−0.0417062 + 0.999130i \(0.513279\pi\)
\(318\) 1.93428e14 0.0104892
\(319\) −1.39660e16 −0.742049
\(320\) 3.00686e16 1.56545
\(321\) 1.07459e16 0.548225
\(322\) 5.31018e13 0.00265489
\(323\) −6.78274e15 −0.332344
\(324\) −2.28741e15 −0.109850
\(325\) −9.36746e15 −0.440941
\(326\) 3.18396e15 0.146911
\(327\) −9.73712e15 −0.440423
\(328\) 2.99921e15 0.132992
\(329\) −9.59555e15 −0.417154
\(330\) 3.37878e15 0.144019
\(331\) −1.09728e16 −0.458602 −0.229301 0.973356i \(-0.573644\pi\)
−0.229301 + 0.973356i \(0.573644\pi\)
\(332\) 2.16577e16 0.887593
\(333\) −1.18081e16 −0.474561
\(334\) −5.32992e15 −0.210072
\(335\) −8.48781e16 −3.28099
\(336\) −3.22377e15 −0.122225
\(337\) 8.21434e15 0.305477 0.152738 0.988267i \(-0.451191\pi\)
0.152738 + 0.988267i \(0.451191\pi\)
\(338\) −2.74839e15 −0.100258
\(339\) −1.60390e16 −0.573959
\(340\) 6.08556e16 2.13642
\(341\) −4.28550e16 −1.47604
\(342\) −2.71274e14 −0.00916725
\(343\) 1.29001e16 0.427740
\(344\) −7.85937e15 −0.255716
\(345\) 3.45236e15 0.110228
\(346\) 2.04409e15 0.0640480
\(347\) 2.78219e16 0.855550 0.427775 0.903885i \(-0.359298\pi\)
0.427775 + 0.903885i \(0.359298\pi\)
\(348\) −1.00604e16 −0.303635
\(349\) −5.73304e15 −0.169832 −0.0849161 0.996388i \(-0.527062\pi\)
−0.0849161 + 0.996388i \(0.527062\pi\)
\(350\) −1.45938e15 −0.0424353
\(351\) −1.63540e15 −0.0466797
\(352\) −1.56698e16 −0.439072
\(353\) −6.74015e16 −1.85410 −0.927052 0.374932i \(-0.877666\pi\)
−0.927052 + 0.374932i \(0.877666\pi\)
\(354\) 2.96475e14 0.00800693
\(355\) 4.69594e16 1.24520
\(356\) 6.40817e16 1.66844
\(357\) −6.37042e15 −0.162864
\(358\) −6.78027e15 −0.170219
\(359\) −1.09186e16 −0.269186 −0.134593 0.990901i \(-0.542973\pi\)
−0.134593 + 0.990901i \(0.542973\pi\)
\(360\) 4.89575e15 0.118537
\(361\) −3.92501e16 −0.933348
\(362\) −7.13562e15 −0.166658
\(363\) 2.38064e16 0.546135
\(364\) −2.33194e15 −0.0525482
\(365\) 6.77095e16 1.49881
\(366\) 5.84170e14 0.0127032
\(367\) −4.53053e16 −0.967876 −0.483938 0.875102i \(-0.660794\pi\)
−0.483938 + 0.875102i \(0.660794\pi\)
\(368\) −5.23499e15 −0.109877
\(369\) −1.01476e16 −0.209264
\(370\) 1.25643e16 0.254583
\(371\) −1.87709e15 −0.0373727
\(372\) −3.08707e16 −0.603972
\(373\) 4.49231e16 0.863699 0.431849 0.901946i \(-0.357861\pi\)
0.431849 + 0.901946i \(0.357861\pi\)
\(374\) −1.01243e16 −0.191293
\(375\) −4.26880e16 −0.792689
\(376\) −2.20966e16 −0.403278
\(377\) −7.19279e15 −0.129026
\(378\) −2.54784e14 −0.00449236
\(379\) −4.51749e16 −0.782965 −0.391483 0.920185i \(-0.628038\pi\)
−0.391483 + 0.920185i \(0.628038\pi\)
\(380\) −2.51482e16 −0.428463
\(381\) 5.47100e16 0.916335
\(382\) −2.91612e15 −0.0480168
\(383\) −5.58141e16 −0.903550 −0.451775 0.892132i \(-0.649209\pi\)
−0.451775 + 0.892132i \(0.649209\pi\)
\(384\) −1.50208e16 −0.239078
\(385\) −3.27888e16 −0.513134
\(386\) −6.14129e15 −0.0945022
\(387\) 2.65917e16 0.402369
\(388\) 9.57573e16 1.42484
\(389\) −5.09688e16 −0.745817 −0.372908 0.927868i \(-0.621639\pi\)
−0.372908 + 0.927868i \(0.621639\pi\)
\(390\) 1.74014e15 0.0250418
\(391\) −1.03447e16 −0.146410
\(392\) 1.44877e16 0.201670
\(393\) 2.28466e15 0.0312803
\(394\) 4.25177e14 0.00572591
\(395\) −2.16260e17 −2.86480
\(396\) 3.52781e16 0.459713
\(397\) 2.51770e16 0.322749 0.161375 0.986893i \(-0.448407\pi\)
0.161375 + 0.986893i \(0.448407\pi\)
\(398\) 1.29416e16 0.163210
\(399\) 2.63254e15 0.0326626
\(400\) 1.43872e17 1.75625
\(401\) 5.25786e16 0.631496 0.315748 0.948843i \(-0.397745\pi\)
0.315748 + 0.948843i \(0.397745\pi\)
\(402\) 1.01719e16 0.120208
\(403\) −2.20712e16 −0.256652
\(404\) 1.57533e15 0.0180258
\(405\) −1.65645e16 −0.186518
\(406\) −1.12058e15 −0.0124172
\(407\) 1.82113e17 1.98599
\(408\) −1.46698e16 −0.157446
\(409\) −4.41135e16 −0.465983 −0.232991 0.972479i \(-0.574851\pi\)
−0.232991 + 0.972479i \(0.574851\pi\)
\(410\) 1.07976e16 0.112261
\(411\) 2.72576e16 0.278943
\(412\) −5.20871e16 −0.524685
\(413\) −2.87709e15 −0.0285284
\(414\) −4.13736e14 −0.00403851
\(415\) 1.56836e17 1.50707
\(416\) −8.07028e15 −0.0763452
\(417\) 6.80505e15 0.0633792
\(418\) 4.18379e15 0.0383640
\(419\) −1.19723e16 −0.108090 −0.0540452 0.998538i \(-0.517212\pi\)
−0.0540452 + 0.998538i \(0.517212\pi\)
\(420\) −2.36195e16 −0.209966
\(421\) 5.96941e16 0.522513 0.261257 0.965269i \(-0.415863\pi\)
0.261257 + 0.965269i \(0.415863\pi\)
\(422\) 2.38384e16 0.205469
\(423\) 7.47624e16 0.634558
\(424\) −4.32255e15 −0.0361295
\(425\) 2.84302e17 2.34019
\(426\) −5.62769e15 −0.0456213
\(427\) −5.66898e15 −0.0452610
\(428\) −1.19384e17 −0.938778
\(429\) 2.52224e16 0.195350
\(430\) −2.82948e16 −0.215855
\(431\) −2.08470e17 −1.56654 −0.783271 0.621680i \(-0.786450\pi\)
−0.783271 + 0.621680i \(0.786450\pi\)
\(432\) 2.51176e16 0.185923
\(433\) 2.48092e17 1.80901 0.904506 0.426461i \(-0.140240\pi\)
0.904506 + 0.426461i \(0.140240\pi\)
\(434\) −3.43854e15 −0.0246997
\(435\) −7.28536e16 −0.515550
\(436\) 1.08177e17 0.754179
\(437\) 4.27490e15 0.0293627
\(438\) −8.11441e15 −0.0549130
\(439\) 1.78467e17 1.18997 0.594987 0.803735i \(-0.297157\pi\)
0.594987 + 0.803735i \(0.297157\pi\)
\(440\) −7.55059e16 −0.496065
\(441\) −4.90183e16 −0.317327
\(442\) −5.21421e15 −0.0332617
\(443\) 2.84466e17 1.78816 0.894080 0.447907i \(-0.147831\pi\)
0.894080 + 0.447907i \(0.147831\pi\)
\(444\) 1.31185e17 0.812636
\(445\) 4.64054e17 2.83288
\(446\) −2.24322e16 −0.134957
\(447\) 1.29320e17 0.766770
\(448\) 3.49692e16 0.204352
\(449\) 2.60812e17 1.50219 0.751096 0.660193i \(-0.229525\pi\)
0.751096 + 0.660193i \(0.229525\pi\)
\(450\) 1.13706e16 0.0645508
\(451\) 1.56504e17 0.875748
\(452\) 1.78191e17 0.982844
\(453\) −2.79706e16 −0.152077
\(454\) 2.33214e16 0.124995
\(455\) −1.68869e16 −0.0892230
\(456\) 6.06220e15 0.0315761
\(457\) −3.35212e17 −1.72133 −0.860664 0.509173i \(-0.829951\pi\)
−0.860664 + 0.509173i \(0.829951\pi\)
\(458\) −2.95416e16 −0.149557
\(459\) 4.96343e16 0.247742
\(460\) −3.83550e16 −0.188754
\(461\) −1.13139e17 −0.548978 −0.274489 0.961590i \(-0.588509\pi\)
−0.274489 + 0.961590i \(0.588509\pi\)
\(462\) 3.92946e15 0.0188001
\(463\) −2.11615e17 −0.998320 −0.499160 0.866510i \(-0.666358\pi\)
−0.499160 + 0.866510i \(0.666358\pi\)
\(464\) 1.10472e17 0.513907
\(465\) −2.23553e17 −1.02550
\(466\) −8.52197e15 −0.0385506
\(467\) −2.87406e16 −0.128214 −0.0641071 0.997943i \(-0.520420\pi\)
−0.0641071 + 0.997943i \(0.520420\pi\)
\(468\) 1.81690e16 0.0799342
\(469\) −9.87118e16 −0.428298
\(470\) −7.95507e16 −0.340415
\(471\) 1.30579e17 0.551110
\(472\) −6.62535e15 −0.0275795
\(473\) −4.10117e17 −1.68388
\(474\) 2.59169e16 0.104960
\(475\) −1.17486e17 −0.469329
\(476\) 7.07740e16 0.278887
\(477\) 1.46251e16 0.0568498
\(478\) 3.62852e16 0.139139
\(479\) 8.32682e16 0.314991 0.157496 0.987520i \(-0.449658\pi\)
0.157496 + 0.987520i \(0.449658\pi\)
\(480\) −8.17414e16 −0.305052
\(481\) 9.37920e16 0.345321
\(482\) −7.26460e15 −0.0263880
\(483\) 4.01503e15 0.0143891
\(484\) −2.64484e17 −0.935200
\(485\) 6.93436e17 2.41927
\(486\) 1.98511e15 0.00683360
\(487\) −1.73796e17 −0.590341 −0.295170 0.955445i \(-0.595376\pi\)
−0.295170 + 0.955445i \(0.595376\pi\)
\(488\) −1.30545e16 −0.0437554
\(489\) 2.40739e17 0.796232
\(490\) 5.21577e16 0.170233
\(491\) 2.48205e17 0.799430 0.399715 0.916640i \(-0.369109\pi\)
0.399715 + 0.916640i \(0.369109\pi\)
\(492\) 1.12738e17 0.358342
\(493\) 2.18300e17 0.684778
\(494\) 2.15474e15 0.00667068
\(495\) 2.55470e17 0.780559
\(496\) 3.38985e17 1.02223
\(497\) 5.46130e16 0.162547
\(498\) −1.87955e16 −0.0552157
\(499\) −3.12341e17 −0.905682 −0.452841 0.891591i \(-0.649589\pi\)
−0.452841 + 0.891591i \(0.649589\pi\)
\(500\) 4.74255e17 1.35740
\(501\) −4.02996e17 −1.13856
\(502\) −1.65550e16 −0.0461694
\(503\) −1.11461e17 −0.306853 −0.153426 0.988160i \(-0.549031\pi\)
−0.153426 + 0.988160i \(0.549031\pi\)
\(504\) 5.69368e15 0.0154737
\(505\) 1.14079e16 0.0306065
\(506\) 6.38094e15 0.0169008
\(507\) −2.07806e17 −0.543383
\(508\) −6.07816e17 −1.56913
\(509\) −3.12980e17 −0.797721 −0.398860 0.917012i \(-0.630594\pi\)
−0.398860 + 0.917012i \(0.630594\pi\)
\(510\) −5.28132e16 −0.132903
\(511\) 7.87450e16 0.195653
\(512\) 2.07371e17 0.508737
\(513\) −2.05111e16 −0.0496850
\(514\) −1.43072e16 −0.0342212
\(515\) −3.77194e17 −0.890877
\(516\) −2.95428e17 −0.689015
\(517\) −1.15304e18 −2.65556
\(518\) 1.46121e16 0.0332330
\(519\) 1.54554e17 0.347130
\(520\) −3.88872e16 −0.0862551
\(521\) 1.61559e17 0.353905 0.176953 0.984219i \(-0.443376\pi\)
0.176953 + 0.984219i \(0.443376\pi\)
\(522\) 8.73089e15 0.0188886
\(523\) 8.32128e17 1.77799 0.888994 0.457918i \(-0.151405\pi\)
0.888994 + 0.457918i \(0.151405\pi\)
\(524\) −2.53822e16 −0.0535643
\(525\) −1.10344e17 −0.229992
\(526\) 4.11147e16 0.0846428
\(527\) 6.69860e17 1.36212
\(528\) −3.87382e17 −0.778071
\(529\) −4.97516e17 −0.987065
\(530\) −1.55618e16 −0.0304976
\(531\) 2.24165e16 0.0433963
\(532\) −2.92469e16 −0.0559313
\(533\) 8.06031e16 0.152274
\(534\) −5.56130e16 −0.103791
\(535\) −8.64533e17 −1.59398
\(536\) −2.27313e17 −0.414051
\(537\) −5.12657e17 −0.922558
\(538\) −1.86895e16 −0.0332286
\(539\) 7.55996e17 1.32798
\(540\) 1.84028e17 0.319392
\(541\) 6.73090e17 1.15423 0.577113 0.816664i \(-0.304179\pi\)
0.577113 + 0.816664i \(0.304179\pi\)
\(542\) −5.15381e16 −0.0873238
\(543\) −5.39525e17 −0.903260
\(544\) 2.44932e17 0.405185
\(545\) 7.83377e17 1.28054
\(546\) 2.02376e15 0.00326894
\(547\) 7.45578e17 1.19008 0.595039 0.803697i \(-0.297137\pi\)
0.595039 + 0.803697i \(0.297137\pi\)
\(548\) −3.02826e17 −0.477661
\(549\) 4.41691e16 0.0688491
\(550\) −1.75366e17 −0.270139
\(551\) −9.02114e16 −0.137333
\(552\) 9.24580e15 0.0139104
\(553\) −2.51506e17 −0.373969
\(554\) −4.64676e16 −0.0682868
\(555\) 9.49991e17 1.37980
\(556\) −7.56027e16 −0.108530
\(557\) −8.10150e17 −1.14949 −0.574747 0.818331i \(-0.694899\pi\)
−0.574747 + 0.818331i \(0.694899\pi\)
\(558\) 2.67909e16 0.0375721
\(559\) −2.11219e17 −0.292790
\(560\) 2.59361e17 0.355371
\(561\) −7.65496e17 −1.03678
\(562\) −6.52045e16 −0.0872954
\(563\) 1.05610e17 0.139766 0.0698829 0.997555i \(-0.477737\pi\)
0.0698829 + 0.997555i \(0.477737\pi\)
\(564\) −8.30595e17 −1.08661
\(565\) 1.29038e18 1.66880
\(566\) −1.03781e16 −0.0132682
\(567\) −1.92642e16 −0.0243479
\(568\) 1.25763e17 0.157140
\(569\) −3.06846e17 −0.379045 −0.189522 0.981876i \(-0.560694\pi\)
−0.189522 + 0.981876i \(0.560694\pi\)
\(570\) 2.18247e16 0.0266540
\(571\) 1.14639e18 1.38420 0.692098 0.721803i \(-0.256686\pi\)
0.692098 + 0.721803i \(0.256686\pi\)
\(572\) −2.80215e17 −0.334517
\(573\) −2.20488e17 −0.260243
\(574\) 1.25574e16 0.0146545
\(575\) −1.79184e17 −0.206757
\(576\) −2.72458e17 −0.310852
\(577\) 1.19316e18 1.34604 0.673018 0.739626i \(-0.264998\pi\)
0.673018 + 0.739626i \(0.264998\pi\)
\(578\) 6.27552e16 0.0700033
\(579\) −4.64343e17 −0.512187
\(580\) 8.09388e17 0.882826
\(581\) 1.82398e17 0.196732
\(582\) −8.31024e16 −0.0886368
\(583\) −2.25559e17 −0.237911
\(584\) 1.81334e17 0.189145
\(585\) 1.31572e17 0.135722
\(586\) −2.27258e16 −0.0231838
\(587\) 9.85683e17 0.994466 0.497233 0.867617i \(-0.334349\pi\)
0.497233 + 0.867617i \(0.334349\pi\)
\(588\) 5.44583e17 0.543390
\(589\) −2.76816e17 −0.273175
\(590\) −2.38522e16 −0.0232804
\(591\) 3.21477e16 0.0310335
\(592\) −1.44052e18 −1.37540
\(593\) −1.79969e17 −0.169958 −0.0849791 0.996383i \(-0.527082\pi\)
−0.0849791 + 0.996383i \(0.527082\pi\)
\(594\) −3.06159e16 −0.0285980
\(595\) 5.12517e17 0.473530
\(596\) −1.43671e18 −1.31301
\(597\) 9.78513e17 0.884572
\(598\) 3.28632e15 0.00293868
\(599\) −2.00606e18 −1.77447 −0.887237 0.461314i \(-0.847378\pi\)
−0.887237 + 0.461314i \(0.847378\pi\)
\(600\) −2.54100e17 −0.222342
\(601\) 1.45050e18 1.25555 0.627773 0.778397i \(-0.283967\pi\)
0.627773 + 0.778397i \(0.283967\pi\)
\(602\) −3.29064e16 −0.0281775
\(603\) 7.69100e17 0.651509
\(604\) 3.10747e17 0.260416
\(605\) −1.91529e18 −1.58790
\(606\) −1.36715e15 −0.00112135
\(607\) −1.28727e17 −0.104459 −0.0522293 0.998635i \(-0.516633\pi\)
−0.0522293 + 0.998635i \(0.516633\pi\)
\(608\) −1.01217e17 −0.0812604
\(609\) −8.47275e16 −0.0672995
\(610\) −4.69980e16 −0.0369348
\(611\) −5.93841e17 −0.461745
\(612\) −5.51427e17 −0.424232
\(613\) 6.07943e17 0.462775 0.231387 0.972862i \(-0.425674\pi\)
0.231387 + 0.972862i \(0.425674\pi\)
\(614\) 1.55902e17 0.117424
\(615\) 8.16405e17 0.608439
\(616\) −8.78121e16 −0.0647560
\(617\) 1.43747e17 0.104892 0.0524462 0.998624i \(-0.483298\pi\)
0.0524462 + 0.998624i \(0.483298\pi\)
\(618\) 4.52035e16 0.0326398
\(619\) 1.14313e18 0.816782 0.408391 0.912807i \(-0.366090\pi\)
0.408391 + 0.912807i \(0.366090\pi\)
\(620\) 2.48363e18 1.75606
\(621\) −3.12826e16 −0.0218881
\(622\) 1.12209e17 0.0776946
\(623\) 5.39687e17 0.369802
\(624\) −1.99510e17 −0.135290
\(625\) 7.25481e17 0.486862
\(626\) 1.91644e17 0.127281
\(627\) 3.16337e17 0.207927
\(628\) −1.45071e18 −0.943718
\(629\) −2.84658e18 −1.83271
\(630\) 2.04980e16 0.0130617
\(631\) 1.01303e18 0.638899 0.319449 0.947603i \(-0.396502\pi\)
0.319449 + 0.947603i \(0.396502\pi\)
\(632\) −5.79168e17 −0.361529
\(633\) 1.80243e18 1.11361
\(634\) −1.45299e16 −0.00888553
\(635\) −4.40156e18 −2.66427
\(636\) −1.62482e17 −0.0973494
\(637\) 3.89354e17 0.230908
\(638\) −1.34654e17 −0.0790470
\(639\) −4.25510e17 −0.247260
\(640\) 1.20846e18 0.695125
\(641\) −2.11979e18 −1.20702 −0.603512 0.797354i \(-0.706233\pi\)
−0.603512 + 0.797354i \(0.706233\pi\)
\(642\) 1.03607e17 0.0583998
\(643\) 3.23198e17 0.180342 0.0901712 0.995926i \(-0.471259\pi\)
0.0901712 + 0.995926i \(0.471259\pi\)
\(644\) −4.46062e16 −0.0246398
\(645\) −2.13937e18 −1.16990
\(646\) −6.53962e16 −0.0354031
\(647\) −1.95948e18 −1.05018 −0.525089 0.851047i \(-0.675968\pi\)
−0.525089 + 0.851047i \(0.675968\pi\)
\(648\) −4.43616e16 −0.0235380
\(649\) −3.45723e17 −0.181609
\(650\) −9.03171e16 −0.0469714
\(651\) −2.59988e17 −0.133868
\(652\) −2.67456e18 −1.36346
\(653\) −2.43779e18 −1.23044 −0.615219 0.788356i \(-0.710933\pi\)
−0.615219 + 0.788356i \(0.710933\pi\)
\(654\) −9.38811e16 −0.0469162
\(655\) −1.83807e17 −0.0909483
\(656\) −1.23796e18 −0.606500
\(657\) −6.13531e17 −0.297620
\(658\) −9.25161e16 −0.0444375
\(659\) −4.07046e18 −1.93592 −0.967962 0.251098i \(-0.919208\pi\)
−0.967962 + 0.251098i \(0.919208\pi\)
\(660\) −2.83822e18 −1.33663
\(661\) −5.99794e17 −0.279700 −0.139850 0.990173i \(-0.544662\pi\)
−0.139850 + 0.990173i \(0.544662\pi\)
\(662\) −1.05795e17 −0.0488528
\(663\) −3.94247e17 −0.180273
\(664\) 4.20025e17 0.190188
\(665\) −2.11795e17 −0.0949673
\(666\) −1.13848e17 −0.0505527
\(667\) −1.37586e17 −0.0605003
\(668\) 4.47720e18 1.94966
\(669\) −1.69610e18 −0.731445
\(670\) −8.18359e17 −0.349508
\(671\) −6.81209e17 −0.288127
\(672\) −9.50639e16 −0.0398213
\(673\) 3.61261e18 1.49873 0.749364 0.662158i \(-0.230359\pi\)
0.749364 + 0.662158i \(0.230359\pi\)
\(674\) 7.91992e16 0.0325410
\(675\) 8.59731e17 0.349855
\(676\) 2.30868e18 0.930487
\(677\) −3.17569e18 −1.26769 −0.633843 0.773462i \(-0.718523\pi\)
−0.633843 + 0.773462i \(0.718523\pi\)
\(678\) −1.54642e17 −0.0611411
\(679\) 8.06454e17 0.315810
\(680\) 1.18022e18 0.457779
\(681\) 1.76333e18 0.677451
\(682\) −4.13190e17 −0.157236
\(683\) −7.70288e17 −0.290348 −0.145174 0.989406i \(-0.546374\pi\)
−0.145174 + 0.989406i \(0.546374\pi\)
\(684\) 2.27874e17 0.0850804
\(685\) −2.19294e18 −0.811034
\(686\) 1.24377e17 0.0455651
\(687\) −2.23364e18 −0.810577
\(688\) 3.24404e18 1.16617
\(689\) −1.16168e17 −0.0413676
\(690\) 3.32861e16 0.0117421
\(691\) 2.10103e18 0.734218 0.367109 0.930178i \(-0.380348\pi\)
0.367109 + 0.930178i \(0.380348\pi\)
\(692\) −1.71706e18 −0.594424
\(693\) 2.97107e17 0.101894
\(694\) 2.68247e17 0.0911378
\(695\) −5.47484e17 −0.184277
\(696\) −1.95110e17 −0.0650608
\(697\) −2.44630e18 −0.808158
\(698\) −5.52755e16 −0.0180914
\(699\) −6.44347e17 −0.208938
\(700\) 1.22590e18 0.393838
\(701\) −8.89194e16 −0.0283028 −0.0141514 0.999900i \(-0.504505\pi\)
−0.0141514 + 0.999900i \(0.504505\pi\)
\(702\) −1.57678e16 −0.00497257
\(703\) 1.17633e18 0.367553
\(704\) 4.20205e18 1.30089
\(705\) −6.01484e18 −1.84499
\(706\) −6.49857e17 −0.197509
\(707\) 1.32672e16 0.00399535
\(708\) −2.49042e17 −0.0743117
\(709\) −1.89281e18 −0.559636 −0.279818 0.960053i \(-0.590274\pi\)
−0.279818 + 0.960053i \(0.590274\pi\)
\(710\) 4.52763e17 0.132645
\(711\) 1.95958e18 0.568866
\(712\) 1.24279e18 0.357501
\(713\) −4.22187e17 −0.120344
\(714\) −6.14208e16 −0.0173491
\(715\) −2.02921e18 −0.567985
\(716\) 5.69551e18 1.57979
\(717\) 2.74353e18 0.754110
\(718\) −1.05272e17 −0.0286751
\(719\) −3.76891e18 −1.01737 −0.508684 0.860954i \(-0.669868\pi\)
−0.508684 + 0.860954i \(0.669868\pi\)
\(720\) −2.02078e18 −0.540577
\(721\) −4.38670e17 −0.116294
\(722\) −3.78432e17 −0.0994252
\(723\) −5.49277e17 −0.143019
\(724\) 5.99401e18 1.54674
\(725\) 3.78125e18 0.967027
\(726\) 2.29531e17 0.0581772
\(727\) 6.27024e17 0.157511 0.0787555 0.996894i \(-0.474905\pi\)
0.0787555 + 0.996894i \(0.474905\pi\)
\(728\) −4.52251e16 −0.0112597
\(729\) 1.50095e17 0.0370370
\(730\) 6.52826e17 0.159661
\(731\) 6.41047e18 1.55391
\(732\) −4.90710e17 −0.117897
\(733\) 5.32014e18 1.26691 0.633457 0.773778i \(-0.281635\pi\)
0.633457 + 0.773778i \(0.281635\pi\)
\(734\) −4.36814e17 −0.103103
\(735\) 3.94365e18 0.922637
\(736\) −1.54371e17 −0.0357982
\(737\) −1.18616e19 −2.72650
\(738\) −9.78392e16 −0.0222919
\(739\) 2.25320e18 0.508875 0.254437 0.967089i \(-0.418110\pi\)
0.254437 + 0.967089i \(0.418110\pi\)
\(740\) −1.05542e19 −2.36276
\(741\) 1.62920e17 0.0361540
\(742\) −1.80981e16 −0.00398114
\(743\) −6.81639e18 −1.48637 −0.743186 0.669085i \(-0.766686\pi\)
−0.743186 + 0.669085i \(0.766686\pi\)
\(744\) −5.98700e17 −0.129415
\(745\) −1.04041e19 −2.22940
\(746\) 4.33129e17 0.0920058
\(747\) −1.42113e18 −0.299260
\(748\) 8.50451e18 1.77537
\(749\) −1.00544e18 −0.208077
\(750\) −4.11580e17 −0.0844415
\(751\) −2.67406e18 −0.543890 −0.271945 0.962313i \(-0.587667\pi\)
−0.271945 + 0.962313i \(0.587667\pi\)
\(752\) 9.12061e18 1.83911
\(753\) −1.25172e18 −0.250231
\(754\) −6.93498e16 −0.0137446
\(755\) 2.25031e18 0.442167
\(756\) 2.14021e17 0.0416932
\(757\) −2.22413e18 −0.429573 −0.214786 0.976661i \(-0.568906\pi\)
−0.214786 + 0.976661i \(0.568906\pi\)
\(758\) −4.35557e17 −0.0834056
\(759\) 4.82463e17 0.0915994
\(760\) −4.87720e17 −0.0918083
\(761\) 8.42640e17 0.157269 0.0786343 0.996904i \(-0.474944\pi\)
0.0786343 + 0.996904i \(0.474944\pi\)
\(762\) 5.27490e17 0.0976128
\(763\) 9.11054e17 0.167161
\(764\) 2.44957e18 0.445639
\(765\) −3.99321e18 −0.720315
\(766\) −5.38136e17 −0.0962510
\(767\) −1.78055e17 −0.0315780
\(768\) 2.91687e18 0.512944
\(769\) 4.49983e18 0.784648 0.392324 0.919827i \(-0.371671\pi\)
0.392324 + 0.919827i \(0.371671\pi\)
\(770\) −3.16136e17 −0.0546618
\(771\) −1.08177e18 −0.185474
\(772\) 5.15876e18 0.877067
\(773\) 5.85877e18 0.987734 0.493867 0.869537i \(-0.335583\pi\)
0.493867 + 0.869537i \(0.335583\pi\)
\(774\) 2.56386e17 0.0428625
\(775\) 1.16029e19 1.92355
\(776\) 1.85710e18 0.305305
\(777\) 1.10482e18 0.180118
\(778\) −4.91420e17 −0.0794484
\(779\) 1.01092e18 0.162077
\(780\) −1.46174e18 −0.232411
\(781\) 6.56253e18 1.03476
\(782\) −9.97395e16 −0.0155964
\(783\) 6.60143e17 0.102373
\(784\) −5.97997e18 −0.919696
\(785\) −1.05054e19 −1.60237
\(786\) 2.20278e16 0.00333214
\(787\) −4.70812e18 −0.706336 −0.353168 0.935560i \(-0.614896\pi\)
−0.353168 + 0.935560i \(0.614896\pi\)
\(788\) −3.57154e17 −0.0531417
\(789\) 3.10869e18 0.458751
\(790\) −2.08508e18 −0.305174
\(791\) 1.50069e18 0.217844
\(792\) 6.84177e17 0.0985042
\(793\) −3.50837e17 −0.0500991
\(794\) 2.42745e17 0.0343809
\(795\) −1.17663e18 −0.165292
\(796\) −1.08711e19 −1.51474
\(797\) 5.53101e18 0.764408 0.382204 0.924078i \(-0.375165\pi\)
0.382204 + 0.924078i \(0.375165\pi\)
\(798\) 2.53818e16 0.00347939
\(799\) 1.80230e19 2.45061
\(800\) 4.24255e18 0.572192
\(801\) −4.20490e18 −0.562528
\(802\) 5.06940e17 0.0672703
\(803\) 9.46233e18 1.24551
\(804\) −8.54455e18 −1.11564
\(805\) −3.23020e17 −0.0418366
\(806\) −2.12802e17 −0.0273399
\(807\) −1.41311e18 −0.180094
\(808\) 3.05517e16 0.00386244
\(809\) 2.45656e18 0.308078 0.154039 0.988065i \(-0.450772\pi\)
0.154039 + 0.988065i \(0.450772\pi\)
\(810\) −1.59708e17 −0.0198689
\(811\) 1.09964e19 1.35711 0.678557 0.734548i \(-0.262606\pi\)
0.678557 + 0.734548i \(0.262606\pi\)
\(812\) 9.41305e17 0.115243
\(813\) −3.89680e18 −0.473281
\(814\) 1.75585e18 0.211558
\(815\) −1.93681e19 −2.31506
\(816\) 6.05511e18 0.718019
\(817\) −2.64909e18 −0.311640
\(818\) −4.25323e17 −0.0496390
\(819\) 1.53016e17 0.0177171
\(820\) −9.07009e18 −1.04189
\(821\) −9.81346e18 −1.11839 −0.559193 0.829038i \(-0.688889\pi\)
−0.559193 + 0.829038i \(0.688889\pi\)
\(822\) 2.62806e17 0.0297145
\(823\) −6.00216e18 −0.673300 −0.336650 0.941630i \(-0.609294\pi\)
−0.336650 + 0.941630i \(0.609294\pi\)
\(824\) −1.01017e18 −0.112426
\(825\) −1.32594e19 −1.46411
\(826\) −2.77397e16 −0.00303900
\(827\) 1.52307e19 1.65552 0.827760 0.561082i \(-0.189615\pi\)
0.827760 + 0.561082i \(0.189615\pi\)
\(828\) 3.47543e17 0.0374810
\(829\) −5.90352e18 −0.631694 −0.315847 0.948810i \(-0.602289\pi\)
−0.315847 + 0.948810i \(0.602289\pi\)
\(830\) 1.51215e18 0.160541
\(831\) −3.51342e18 −0.370104
\(832\) 2.16415e18 0.226196
\(833\) −1.18169e19 −1.22549
\(834\) 6.56113e16 0.00675149
\(835\) 3.24221e19 3.31039
\(836\) −3.51444e18 −0.356053
\(837\) 2.02566e18 0.203635
\(838\) −1.15432e17 −0.0115144
\(839\) 8.92085e18 0.882985 0.441492 0.897265i \(-0.354449\pi\)
0.441492 + 0.897265i \(0.354449\pi\)
\(840\) −4.58072e17 −0.0449902
\(841\) −7.35720e18 −0.717032
\(842\) 5.75545e17 0.0556609
\(843\) −4.93012e18 −0.473127
\(844\) −2.00246e19 −1.90694
\(845\) 1.67185e19 1.57990
\(846\) 7.20828e17 0.0675965
\(847\) −2.22745e18 −0.207284
\(848\) 1.78418e18 0.164765
\(849\) −7.84690e17 −0.0719115
\(850\) 2.74111e18 0.249290
\(851\) 1.79409e18 0.161921
\(852\) 4.72733e18 0.423408
\(853\) −1.92943e19 −1.71499 −0.857495 0.514493i \(-0.827980\pi\)
−0.857495 + 0.514493i \(0.827980\pi\)
\(854\) −5.46579e16 −0.00482144
\(855\) 1.65017e18 0.144460
\(856\) −2.31532e18 −0.201155
\(857\) 1.88539e19 1.62565 0.812825 0.582508i \(-0.197929\pi\)
0.812825 + 0.582508i \(0.197929\pi\)
\(858\) 2.43183e17 0.0208097
\(859\) 1.17967e19 1.00185 0.500927 0.865490i \(-0.332993\pi\)
0.500927 + 0.865490i \(0.332993\pi\)
\(860\) 2.37680e19 2.00333
\(861\) 9.49465e17 0.0794252
\(862\) −2.00998e18 −0.166876
\(863\) −1.91621e18 −0.157896 −0.0789482 0.996879i \(-0.525156\pi\)
−0.0789482 + 0.996879i \(0.525156\pi\)
\(864\) 7.40678e17 0.0605745
\(865\) −1.24343e19 −1.00929
\(866\) 2.39200e18 0.192706
\(867\) 4.74492e18 0.379407
\(868\) 2.88842e18 0.229235
\(869\) −3.02221e19 −2.38065
\(870\) −7.02423e17 −0.0549191
\(871\) −6.10899e18 −0.474080
\(872\) 2.09797e18 0.161600
\(873\) −6.28338e18 −0.480398
\(874\) 4.12167e16 0.00312788
\(875\) 3.99411e18 0.300862
\(876\) 6.81621e18 0.509643
\(877\) 2.28743e19 1.69766 0.848828 0.528669i \(-0.177309\pi\)
0.848828 + 0.528669i \(0.177309\pi\)
\(878\) 1.72070e18 0.126762
\(879\) −1.71830e18 −0.125653
\(880\) 3.11659e19 2.26226
\(881\) −1.62894e19 −1.17371 −0.586855 0.809692i \(-0.699634\pi\)
−0.586855 + 0.809692i \(0.699634\pi\)
\(882\) −4.72613e17 −0.0338034
\(883\) −1.24079e19 −0.880956 −0.440478 0.897763i \(-0.645191\pi\)
−0.440478 + 0.897763i \(0.645191\pi\)
\(884\) 4.38000e18 0.308699
\(885\) −1.80346e18 −0.126176
\(886\) 2.74270e18 0.190484
\(887\) −2.85771e19 −1.97022 −0.985110 0.171926i \(-0.945001\pi\)
−0.985110 + 0.171926i \(0.945001\pi\)
\(888\) 2.54418e18 0.174126
\(889\) −5.11894e18 −0.347791
\(890\) 4.47421e18 0.301774
\(891\) −2.31487e18 −0.154996
\(892\) 1.88433e19 1.25252
\(893\) −7.44791e18 −0.491473
\(894\) 1.24684e18 0.0816805
\(895\) 4.12446e19 2.68236
\(896\) 1.40542e18 0.0907412
\(897\) 2.48479e17 0.0159272
\(898\) 2.51463e18 0.160022
\(899\) 8.90924e18 0.562863
\(900\) −9.55144e18 −0.599091
\(901\) 3.52568e18 0.219549
\(902\) 1.50895e18 0.0932893
\(903\) −2.48805e18 −0.152718
\(904\) 3.45579e18 0.210597
\(905\) 4.34062e19 2.62625
\(906\) −2.69680e17 −0.0162000
\(907\) 6.87747e18 0.410186 0.205093 0.978742i \(-0.434250\pi\)
0.205093 + 0.978742i \(0.434250\pi\)
\(908\) −1.95903e19 −1.16007
\(909\) −1.03370e17 −0.00607756
\(910\) −1.62817e17 −0.00950451
\(911\) −7.71382e18 −0.447095 −0.223548 0.974693i \(-0.571764\pi\)
−0.223548 + 0.974693i \(0.571764\pi\)
\(912\) −2.50224e18 −0.144000
\(913\) 2.19177e19 1.25238
\(914\) −3.23197e18 −0.183365
\(915\) −3.55352e18 −0.200181
\(916\) 2.48153e19 1.38803
\(917\) −2.13765e17 −0.0118723
\(918\) 4.78552e17 0.0263908
\(919\) −9.11680e18 −0.499220 −0.249610 0.968347i \(-0.580302\pi\)
−0.249610 + 0.968347i \(0.580302\pi\)
\(920\) −7.43849e17 −0.0404449
\(921\) 1.17878e19 0.636419
\(922\) −1.09084e18 −0.0584801
\(923\) 3.37984e18 0.179923
\(924\) −3.30080e18 −0.174482
\(925\) −4.93065e19 −2.58811
\(926\) −2.04030e18 −0.106346
\(927\) 3.41784e18 0.176902
\(928\) 3.25763e18 0.167433
\(929\) −1.07094e17 −0.00546590 −0.00273295 0.999996i \(-0.500870\pi\)
−0.00273295 + 0.999996i \(0.500870\pi\)
\(930\) −2.15540e18 −0.109242
\(931\) 4.88325e18 0.245774
\(932\) 7.15856e18 0.357785
\(933\) 8.48414e18 0.421092
\(934\) −2.77104e17 −0.0136581
\(935\) 6.15862e19 3.01445
\(936\) 3.52366e17 0.0171278
\(937\) 5.74239e18 0.277195 0.138597 0.990349i \(-0.455741\pi\)
0.138597 + 0.990349i \(0.455741\pi\)
\(938\) −9.51737e17 −0.0456245
\(939\) 1.44902e19 0.689840
\(940\) 6.68236e19 3.15936
\(941\) 4.99015e18 0.234305 0.117152 0.993114i \(-0.462623\pi\)
0.117152 + 0.993114i \(0.462623\pi\)
\(942\) 1.25899e18 0.0587071
\(943\) 1.54181e18 0.0714010
\(944\) 2.73469e18 0.125774
\(945\) 1.54986e18 0.0707921
\(946\) −3.95417e18 −0.179375
\(947\) −2.93709e19 −1.32325 −0.661626 0.749834i \(-0.730133\pi\)
−0.661626 + 0.749834i \(0.730133\pi\)
\(948\) −2.17705e19 −0.974124
\(949\) 4.87330e18 0.216567
\(950\) −1.13275e18 −0.0499954
\(951\) −1.09861e18 −0.0481582
\(952\) 1.37258e18 0.0597581
\(953\) 1.23577e19 0.534360 0.267180 0.963647i \(-0.413908\pi\)
0.267180 + 0.963647i \(0.413908\pi\)
\(954\) 1.41009e17 0.00605595
\(955\) 1.77388e19 0.756664
\(956\) −3.04800e19 −1.29133
\(957\) −1.01812e19 −0.428422
\(958\) 8.02836e17 0.0335545
\(959\) −2.55036e18 −0.105872
\(960\) 2.19200e19 0.903810
\(961\) 2.92066e18 0.119613
\(962\) 9.04303e17 0.0367854
\(963\) 7.83373e18 0.316518
\(964\) 6.10236e18 0.244904
\(965\) 3.73577e19 1.48920
\(966\) 3.87112e16 0.00153280
\(967\) −4.45933e19 −1.75387 −0.876936 0.480608i \(-0.840416\pi\)
−0.876936 + 0.480608i \(0.840416\pi\)
\(968\) −5.12935e18 −0.200388
\(969\) −4.94461e18 −0.191879
\(970\) 6.68581e18 0.257714
\(971\) −2.67149e19 −1.02289 −0.511444 0.859317i \(-0.670889\pi\)
−0.511444 + 0.859317i \(0.670889\pi\)
\(972\) −1.66752e18 −0.0634221
\(973\) −6.36715e17 −0.0240553
\(974\) −1.67567e18 −0.0628862
\(975\) −6.82888e18 −0.254577
\(976\) 5.38839e18 0.199543
\(977\) −1.10744e19 −0.407387 −0.203693 0.979035i \(-0.565295\pi\)
−0.203693 + 0.979035i \(0.565295\pi\)
\(978\) 2.32111e18 0.0848188
\(979\) 6.48511e19 2.35413
\(980\) −4.38132e19 −1.57992
\(981\) −7.09836e18 −0.254278
\(982\) 2.39308e18 0.0851595
\(983\) 1.41399e18 0.0499860 0.0249930 0.999688i \(-0.492044\pi\)
0.0249930 + 0.999688i \(0.492044\pi\)
\(984\) 2.18642e18 0.0767832
\(985\) −2.58637e18 −0.0902308
\(986\) 2.10476e18 0.0729462
\(987\) −6.99515e18 −0.240844
\(988\) −1.81001e18 −0.0619100
\(989\) −4.04028e18 −0.137289
\(990\) 2.46313e18 0.0831493
\(991\) −1.40952e19 −0.472706 −0.236353 0.971667i \(-0.575952\pi\)
−0.236353 + 0.971667i \(0.575952\pi\)
\(992\) 9.99613e18 0.333047
\(993\) −7.99918e18 −0.264774
\(994\) 5.26555e17 0.0173154
\(995\) −7.87239e19 −2.57192
\(996\) 1.57884e19 0.512452
\(997\) −3.49134e19 −1.12583 −0.562917 0.826514i \(-0.690321\pi\)
−0.562917 + 0.826514i \(0.690321\pi\)
\(998\) −3.01146e18 −0.0964781
\(999\) −8.60809e18 −0.273988
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.1.16 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.16 30 1.1 even 1 trivial