Properties

Label 177.14.a.a.1.18
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 1.18
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+23.4632 q^{2} +729.000 q^{3} -7641.48 q^{4} -42940.2 q^{5} +17104.7 q^{6} +465285. q^{7} -371505. q^{8} +531441. q^{9} +O(q^{10})\) \(q+23.4632 q^{2} +729.000 q^{3} -7641.48 q^{4} -42940.2 q^{5} +17104.7 q^{6} +465285. q^{7} -371505. q^{8} +531441. q^{9} -1.00752e6 q^{10} -5.09098e6 q^{11} -5.57064e6 q^{12} -1.16169e7 q^{13} +1.09171e7 q^{14} -3.13034e7 q^{15} +5.38823e7 q^{16} -1.31984e8 q^{17} +1.24693e7 q^{18} +3.44436e8 q^{19} +3.28127e8 q^{20} +3.39193e8 q^{21} -1.19451e8 q^{22} +8.75950e8 q^{23} -2.70827e8 q^{24} +6.23161e8 q^{25} -2.72571e8 q^{26} +3.87420e8 q^{27} -3.55546e9 q^{28} +1.80413e9 q^{29} -7.34480e8 q^{30} -4.43512e9 q^{31} +4.30762e9 q^{32} -3.71133e9 q^{33} -3.09678e9 q^{34} -1.99794e10 q^{35} -4.06099e9 q^{36} +2.28026e10 q^{37} +8.08159e9 q^{38} -8.46874e9 q^{39} +1.59525e10 q^{40} -2.03965e10 q^{41} +7.95856e9 q^{42} -2.91031e10 q^{43} +3.89026e10 q^{44} -2.28202e10 q^{45} +2.05526e10 q^{46} -1.00354e10 q^{47} +3.92802e10 q^{48} +1.19601e11 q^{49} +1.46214e10 q^{50} -9.62164e10 q^{51} +8.87705e10 q^{52} -9.81816e10 q^{53} +9.09014e9 q^{54} +2.18608e11 q^{55} -1.72855e11 q^{56} +2.51094e11 q^{57} +4.23307e10 q^{58} +4.21805e10 q^{59} +2.39204e11 q^{60} +6.23812e11 q^{61} -1.04062e11 q^{62} +2.47271e11 q^{63} -3.40333e11 q^{64} +4.98834e11 q^{65} -8.70797e10 q^{66} +9.29357e10 q^{67} +1.00855e12 q^{68} +6.38568e11 q^{69} -4.68782e11 q^{70} +8.86501e11 q^{71} -1.97433e11 q^{72} +5.94002e11 q^{73} +5.35022e11 q^{74} +4.54284e11 q^{75} -2.63200e12 q^{76} -2.36876e12 q^{77} -1.98704e11 q^{78} -1.79250e12 q^{79} -2.31372e12 q^{80} +2.82430e11 q^{81} -4.78569e11 q^{82} +6.61354e10 q^{83} -2.59193e12 q^{84} +5.66743e12 q^{85} -6.82854e11 q^{86} +1.31521e12 q^{87} +1.89132e12 q^{88} -2.43839e12 q^{89} -5.35436e11 q^{90} -5.40518e12 q^{91} -6.69355e12 q^{92} -3.23320e12 q^{93} -2.35464e11 q^{94} -1.47902e13 q^{95} +3.14025e12 q^{96} +8.12616e12 q^{97} +2.80623e12 q^{98} -2.70556e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 23.4632 0.259235 0.129617 0.991564i \(-0.458625\pi\)
0.129617 + 0.991564i \(0.458625\pi\)
\(3\) 729.000 0.577350
\(4\) −7641.48 −0.932797
\(5\) −42940.2 −1.22902 −0.614511 0.788908i \(-0.710647\pi\)
−0.614511 + 0.788908i \(0.710647\pi\)
\(6\) 17104.7 0.149669
\(7\) 465285. 1.49480 0.747398 0.664377i \(-0.231303\pi\)
0.747398 + 0.664377i \(0.231303\pi\)
\(8\) −371505. −0.501048
\(9\) 531441. 0.333333
\(10\) −1.00752e6 −0.318605
\(11\) −5.09098e6 −0.866461 −0.433231 0.901283i \(-0.642626\pi\)
−0.433231 + 0.901283i \(0.642626\pi\)
\(12\) −5.57064e6 −0.538551
\(13\) −1.16169e7 −0.667513 −0.333756 0.942659i \(-0.608316\pi\)
−0.333756 + 0.942659i \(0.608316\pi\)
\(14\) 1.09171e7 0.387503
\(15\) −3.13034e7 −0.709576
\(16\) 5.38823e7 0.802908
\(17\) −1.31984e8 −1.32618 −0.663092 0.748538i \(-0.730756\pi\)
−0.663092 + 0.748538i \(0.730756\pi\)
\(18\) 1.24693e7 0.0864115
\(19\) 3.44436e8 1.67962 0.839809 0.542881i \(-0.182667\pi\)
0.839809 + 0.542881i \(0.182667\pi\)
\(20\) 3.28127e8 1.14643
\(21\) 3.39193e8 0.863020
\(22\) −1.19451e8 −0.224617
\(23\) 8.75950e8 1.23381 0.616905 0.787038i \(-0.288386\pi\)
0.616905 + 0.787038i \(0.288386\pi\)
\(24\) −2.70827e8 −0.289280
\(25\) 6.23161e8 0.510494
\(26\) −2.72571e8 −0.173042
\(27\) 3.87420e8 0.192450
\(28\) −3.55546e9 −1.39434
\(29\) 1.80413e9 0.563223 0.281612 0.959528i \(-0.409131\pi\)
0.281612 + 0.959528i \(0.409131\pi\)
\(30\) −7.34480e8 −0.183947
\(31\) −4.43512e9 −0.897542 −0.448771 0.893647i \(-0.648138\pi\)
−0.448771 + 0.893647i \(0.648138\pi\)
\(32\) 4.30762e9 0.709190
\(33\) −3.71133e9 −0.500252
\(34\) −3.09678e9 −0.343793
\(35\) −1.99794e10 −1.83714
\(36\) −4.06099e9 −0.310932
\(37\) 2.28026e10 1.46107 0.730537 0.682873i \(-0.239270\pi\)
0.730537 + 0.682873i \(0.239270\pi\)
\(38\) 8.08159e9 0.435415
\(39\) −8.46874e9 −0.385389
\(40\) 1.59525e10 0.615799
\(41\) −2.03965e10 −0.670596 −0.335298 0.942112i \(-0.608837\pi\)
−0.335298 + 0.942112i \(0.608837\pi\)
\(42\) 7.95856e9 0.223725
\(43\) −2.91031e10 −0.702093 −0.351047 0.936358i \(-0.614174\pi\)
−0.351047 + 0.936358i \(0.614174\pi\)
\(44\) 3.89026e10 0.808233
\(45\) −2.28202e10 −0.409674
\(46\) 2.05526e10 0.319846
\(47\) −1.00354e10 −0.135800 −0.0679001 0.997692i \(-0.521630\pi\)
−0.0679001 + 0.997692i \(0.521630\pi\)
\(48\) 3.92802e10 0.463559
\(49\) 1.19601e11 1.23441
\(50\) 1.46214e10 0.132338
\(51\) −9.62164e10 −0.765673
\(52\) 8.87705e10 0.622654
\(53\) −9.81816e10 −0.608467 −0.304233 0.952597i \(-0.598400\pi\)
−0.304233 + 0.952597i \(0.598400\pi\)
\(54\) 9.09014e9 0.0498897
\(55\) 2.18608e11 1.06490
\(56\) −1.72855e11 −0.748964
\(57\) 2.51094e11 0.969728
\(58\) 4.23307e10 0.146007
\(59\) 4.21805e10 0.130189
\(60\) 2.39204e11 0.661890
\(61\) 6.23812e11 1.55028 0.775140 0.631790i \(-0.217679\pi\)
0.775140 + 0.631790i \(0.217679\pi\)
\(62\) −1.04062e11 −0.232674
\(63\) 2.47271e11 0.498265
\(64\) −3.40333e11 −0.619062
\(65\) 4.98834e11 0.820387
\(66\) −8.70797e10 −0.129683
\(67\) 9.29357e10 0.125515 0.0627576 0.998029i \(-0.480010\pi\)
0.0627576 + 0.998029i \(0.480010\pi\)
\(68\) 1.00855e12 1.23706
\(69\) 6.38568e11 0.712341
\(70\) −4.68782e11 −0.476249
\(71\) 8.86501e11 0.821296 0.410648 0.911794i \(-0.365302\pi\)
0.410648 + 0.911794i \(0.365302\pi\)
\(72\) −1.97433e11 −0.167016
\(73\) 5.94002e11 0.459398 0.229699 0.973262i \(-0.426226\pi\)
0.229699 + 0.973262i \(0.426226\pi\)
\(74\) 5.35022e11 0.378761
\(75\) 4.54284e11 0.294734
\(76\) −2.63200e12 −1.56674
\(77\) −2.36876e12 −1.29518
\(78\) −1.98704e11 −0.0999061
\(79\) −1.79250e12 −0.829627 −0.414813 0.909906i \(-0.636153\pi\)
−0.414813 + 0.909906i \(0.636153\pi\)
\(80\) −2.31372e12 −0.986792
\(81\) 2.82430e11 0.111111
\(82\) −4.78569e11 −0.173842
\(83\) 6.61354e10 0.0222038 0.0111019 0.999938i \(-0.496466\pi\)
0.0111019 + 0.999938i \(0.496466\pi\)
\(84\) −2.59193e12 −0.805023
\(85\) 5.66743e12 1.62991
\(86\) −6.82854e11 −0.182007
\(87\) 1.31521e12 0.325177
\(88\) 1.89132e12 0.434139
\(89\) −2.43839e12 −0.520077 −0.260039 0.965598i \(-0.583735\pi\)
−0.260039 + 0.965598i \(0.583735\pi\)
\(90\) −5.35436e11 −0.106202
\(91\) −5.40518e12 −0.997795
\(92\) −6.69355e12 −1.15090
\(93\) −3.23320e12 −0.518196
\(94\) −2.35464e11 −0.0352041
\(95\) −1.47902e13 −2.06429
\(96\) 3.14025e12 0.409451
\(97\) 8.12616e12 0.990534 0.495267 0.868741i \(-0.335070\pi\)
0.495267 + 0.868741i \(0.335070\pi\)
\(98\) 2.80623e12 0.320002
\(99\) −2.70556e12 −0.288820
\(100\) −4.76187e12 −0.476187
\(101\) 2.42241e12 0.227069 0.113535 0.993534i \(-0.463783\pi\)
0.113535 + 0.993534i \(0.463783\pi\)
\(102\) −2.25755e12 −0.198489
\(103\) 1.82199e12 0.150350 0.0751752 0.997170i \(-0.476048\pi\)
0.0751752 + 0.997170i \(0.476048\pi\)
\(104\) 4.31574e12 0.334456
\(105\) −1.45650e13 −1.06067
\(106\) −2.30366e12 −0.157736
\(107\) −2.86070e13 −1.84280 −0.921399 0.388619i \(-0.872952\pi\)
−0.921399 + 0.388619i \(0.872952\pi\)
\(108\) −2.96046e12 −0.179517
\(109\) 1.40572e11 0.00802836 0.00401418 0.999992i \(-0.498722\pi\)
0.00401418 + 0.999992i \(0.498722\pi\)
\(110\) 5.12925e12 0.276059
\(111\) 1.66231e13 0.843552
\(112\) 2.50706e13 1.20018
\(113\) −2.32425e13 −1.05020 −0.525101 0.851040i \(-0.675972\pi\)
−0.525101 + 0.851040i \(0.675972\pi\)
\(114\) 5.89148e12 0.251387
\(115\) −3.76135e13 −1.51638
\(116\) −1.37862e13 −0.525373
\(117\) −6.17371e12 −0.222504
\(118\) 9.89692e11 0.0337495
\(119\) −6.14102e13 −1.98237
\(120\) 1.16294e13 0.355532
\(121\) −8.60461e12 −0.249245
\(122\) 1.46367e13 0.401886
\(123\) −1.48691e13 −0.387169
\(124\) 3.38909e13 0.837224
\(125\) 2.56586e13 0.601614
\(126\) 5.80179e12 0.129168
\(127\) 7.39372e13 1.56365 0.781824 0.623499i \(-0.214290\pi\)
0.781824 + 0.623499i \(0.214290\pi\)
\(128\) −4.32733e13 −0.869672
\(129\) −2.12162e13 −0.405354
\(130\) 1.17043e13 0.212673
\(131\) 3.01459e13 0.521152 0.260576 0.965453i \(-0.416087\pi\)
0.260576 + 0.965453i \(0.416087\pi\)
\(132\) 2.83600e13 0.466633
\(133\) 1.60261e14 2.51069
\(134\) 2.18057e12 0.0325379
\(135\) −1.66359e13 −0.236525
\(136\) 4.90327e13 0.664482
\(137\) −5.45041e13 −0.704281 −0.352140 0.935947i \(-0.614546\pi\)
−0.352140 + 0.935947i \(0.614546\pi\)
\(138\) 1.49829e13 0.184663
\(139\) −1.14807e14 −1.35012 −0.675059 0.737764i \(-0.735882\pi\)
−0.675059 + 0.737764i \(0.735882\pi\)
\(140\) 1.52672e14 1.71367
\(141\) −7.31583e12 −0.0784042
\(142\) 2.08002e13 0.212908
\(143\) 5.91416e13 0.578374
\(144\) 2.86352e13 0.267636
\(145\) −7.74697e13 −0.692214
\(146\) 1.39372e13 0.119092
\(147\) 8.71891e13 0.712688
\(148\) −1.74245e14 −1.36289
\(149\) −2.41162e14 −1.80550 −0.902752 0.430161i \(-0.858457\pi\)
−0.902752 + 0.430161i \(0.858457\pi\)
\(150\) 1.06590e13 0.0764052
\(151\) 1.25659e12 0.00862671 0.00431335 0.999991i \(-0.498627\pi\)
0.00431335 + 0.999991i \(0.498627\pi\)
\(152\) −1.27960e14 −0.841570
\(153\) −7.01418e13 −0.442061
\(154\) −5.55787e13 −0.335756
\(155\) 1.90445e14 1.10310
\(156\) 6.47137e13 0.359490
\(157\) 5.17780e13 0.275929 0.137965 0.990437i \(-0.455944\pi\)
0.137965 + 0.990437i \(0.455944\pi\)
\(158\) −4.20578e13 −0.215068
\(159\) −7.15744e13 −0.351299
\(160\) −1.84970e14 −0.871609
\(161\) 4.07566e14 1.84429
\(162\) 6.62671e12 0.0288038
\(163\) −4.74498e14 −1.98160 −0.990799 0.135344i \(-0.956786\pi\)
−0.990799 + 0.135344i \(0.956786\pi\)
\(164\) 1.55860e14 0.625531
\(165\) 1.59365e14 0.614820
\(166\) 1.55175e12 0.00575599
\(167\) −1.54677e14 −0.551783 −0.275892 0.961189i \(-0.588973\pi\)
−0.275892 + 0.961189i \(0.588973\pi\)
\(168\) −1.26012e14 −0.432415
\(169\) −1.67922e14 −0.554427
\(170\) 1.32976e14 0.422529
\(171\) 1.83048e14 0.559873
\(172\) 2.22391e14 0.654911
\(173\) −4.43602e14 −1.25804 −0.629019 0.777390i \(-0.716543\pi\)
−0.629019 + 0.777390i \(0.716543\pi\)
\(174\) 3.08591e13 0.0842972
\(175\) 2.89947e14 0.763083
\(176\) −2.74314e14 −0.695689
\(177\) 3.07496e13 0.0751646
\(178\) −5.72125e13 −0.134822
\(179\) −5.31994e14 −1.20882 −0.604411 0.796673i \(-0.706591\pi\)
−0.604411 + 0.796673i \(0.706591\pi\)
\(180\) 1.74380e14 0.382143
\(181\) −3.03074e14 −0.640675 −0.320337 0.947304i \(-0.603796\pi\)
−0.320337 + 0.947304i \(0.603796\pi\)
\(182\) −1.26823e14 −0.258663
\(183\) 4.54759e14 0.895054
\(184\) −3.25419e14 −0.618198
\(185\) −9.79148e14 −1.79569
\(186\) −7.58614e13 −0.134334
\(187\) 6.71929e14 1.14909
\(188\) 7.66855e13 0.126674
\(189\) 1.80261e14 0.287673
\(190\) −3.47026e14 −0.535135
\(191\) 3.82667e14 0.570302 0.285151 0.958483i \(-0.407956\pi\)
0.285151 + 0.958483i \(0.407956\pi\)
\(192\) −2.48103e14 −0.357416
\(193\) 6.33672e14 0.882555 0.441278 0.897371i \(-0.354525\pi\)
0.441278 + 0.897371i \(0.354525\pi\)
\(194\) 1.90666e14 0.256781
\(195\) 3.63650e14 0.473651
\(196\) −9.13928e14 −1.15146
\(197\) −8.41826e14 −1.02610 −0.513052 0.858357i \(-0.671485\pi\)
−0.513052 + 0.858357i \(0.671485\pi\)
\(198\) −6.34811e13 −0.0748723
\(199\) −9.92384e14 −1.13275 −0.566376 0.824147i \(-0.691655\pi\)
−0.566376 + 0.824147i \(0.691655\pi\)
\(200\) −2.31507e14 −0.255782
\(201\) 6.77502e13 0.0724663
\(202\) 5.68375e13 0.0588642
\(203\) 8.39434e14 0.841904
\(204\) 7.35236e14 0.714217
\(205\) 8.75832e14 0.824177
\(206\) 4.27498e13 0.0389760
\(207\) 4.65516e14 0.411270
\(208\) −6.25947e14 −0.535952
\(209\) −1.75352e15 −1.45532
\(210\) −3.41742e14 −0.274963
\(211\) −1.11914e15 −0.873070 −0.436535 0.899687i \(-0.643794\pi\)
−0.436535 + 0.899687i \(0.643794\pi\)
\(212\) 7.50252e14 0.567576
\(213\) 6.46259e14 0.474176
\(214\) −6.71213e14 −0.477717
\(215\) 1.24970e15 0.862888
\(216\) −1.43929e14 −0.0964267
\(217\) −2.06360e15 −1.34164
\(218\) 3.29828e12 0.00208123
\(219\) 4.33027e14 0.265234
\(220\) −1.67049e15 −0.993335
\(221\) 1.53325e15 0.885245
\(222\) 3.90031e14 0.218678
\(223\) 3.38362e14 0.184247 0.0921234 0.995748i \(-0.470635\pi\)
0.0921234 + 0.995748i \(0.470635\pi\)
\(224\) 2.00427e15 1.06009
\(225\) 3.31173e14 0.170165
\(226\) −5.45344e14 −0.272249
\(227\) 1.14511e15 0.555494 0.277747 0.960654i \(-0.410412\pi\)
0.277747 + 0.960654i \(0.410412\pi\)
\(228\) −1.91873e15 −0.904560
\(229\) −2.70744e15 −1.24059 −0.620296 0.784368i \(-0.712987\pi\)
−0.620296 + 0.784368i \(0.712987\pi\)
\(230\) −8.82535e14 −0.393098
\(231\) −1.72682e15 −0.747774
\(232\) −6.70242e14 −0.282202
\(233\) −3.33942e15 −1.36728 −0.683641 0.729819i \(-0.739605\pi\)
−0.683641 + 0.729819i \(0.739605\pi\)
\(234\) −1.44855e14 −0.0576808
\(235\) 4.30924e14 0.166901
\(236\) −3.22322e14 −0.121440
\(237\) −1.30673e15 −0.478985
\(238\) −1.44088e15 −0.513900
\(239\) 5.44214e14 0.188879 0.0944394 0.995531i \(-0.469894\pi\)
0.0944394 + 0.995531i \(0.469894\pi\)
\(240\) −1.68670e15 −0.569724
\(241\) −1.37933e15 −0.453478 −0.226739 0.973956i \(-0.572806\pi\)
−0.226739 + 0.973956i \(0.572806\pi\)
\(242\) −2.01892e14 −0.0646129
\(243\) 2.05891e14 0.0641500
\(244\) −4.76685e15 −1.44610
\(245\) −5.13570e15 −1.51712
\(246\) −3.48877e14 −0.100368
\(247\) −4.00129e15 −1.12117
\(248\) 1.64767e15 0.449711
\(249\) 4.82127e13 0.0128194
\(250\) 6.02034e14 0.155959
\(251\) 2.74009e15 0.691650 0.345825 0.938299i \(-0.387599\pi\)
0.345825 + 0.938299i \(0.387599\pi\)
\(252\) −1.88952e15 −0.464780
\(253\) −4.45945e15 −1.06905
\(254\) 1.73481e15 0.405352
\(255\) 4.13156e15 0.941028
\(256\) 1.77267e15 0.393613
\(257\) −8.07009e14 −0.174708 −0.0873540 0.996177i \(-0.527841\pi\)
−0.0873540 + 0.996177i \(0.527841\pi\)
\(258\) −4.97800e14 −0.105082
\(259\) 1.06097e16 2.18401
\(260\) −3.81183e15 −0.765255
\(261\) 9.58788e14 0.187741
\(262\) 7.07320e14 0.135101
\(263\) −2.47483e15 −0.461140 −0.230570 0.973056i \(-0.574059\pi\)
−0.230570 + 0.973056i \(0.574059\pi\)
\(264\) 1.37877e15 0.250650
\(265\) 4.21594e15 0.747819
\(266\) 3.76024e15 0.650857
\(267\) −1.77759e15 −0.300267
\(268\) −7.10166e14 −0.117080
\(269\) 4.86911e15 0.783537 0.391769 0.920064i \(-0.371863\pi\)
0.391769 + 0.920064i \(0.371863\pi\)
\(270\) −3.90333e14 −0.0613155
\(271\) −1.03565e16 −1.58823 −0.794115 0.607767i \(-0.792065\pi\)
−0.794115 + 0.607767i \(0.792065\pi\)
\(272\) −7.11161e15 −1.06480
\(273\) −3.94038e15 −0.576077
\(274\) −1.27884e15 −0.182574
\(275\) −3.17250e15 −0.442323
\(276\) −4.87960e15 −0.664470
\(277\) 8.85578e15 1.17790 0.588950 0.808169i \(-0.299541\pi\)
0.588950 + 0.808169i \(0.299541\pi\)
\(278\) −2.69374e15 −0.349997
\(279\) −2.35701e15 −0.299181
\(280\) 7.42246e15 0.920493
\(281\) 1.22751e16 1.48743 0.743713 0.668499i \(-0.233063\pi\)
0.743713 + 0.668499i \(0.233063\pi\)
\(282\) −1.71653e14 −0.0203251
\(283\) 4.79624e15 0.554995 0.277498 0.960726i \(-0.410495\pi\)
0.277498 + 0.960726i \(0.410495\pi\)
\(284\) −6.77418e15 −0.766103
\(285\) −1.07820e16 −1.19182
\(286\) 1.38765e15 0.149935
\(287\) −9.49020e15 −1.00240
\(288\) 2.28925e15 0.236397
\(289\) 7.51523e15 0.758764
\(290\) −1.81769e15 −0.179446
\(291\) 5.92397e15 0.571885
\(292\) −4.53905e15 −0.428525
\(293\) 1.85085e16 1.70896 0.854478 0.519487i \(-0.173877\pi\)
0.854478 + 0.519487i \(0.173877\pi\)
\(294\) 2.04574e15 0.184753
\(295\) −1.81124e15 −0.160005
\(296\) −8.47126e15 −0.732069
\(297\) −1.97235e15 −0.166751
\(298\) −5.65845e15 −0.468049
\(299\) −1.01758e16 −0.823584
\(300\) −3.47140e15 −0.274927
\(301\) −1.35412e16 −1.04949
\(302\) 2.94838e13 0.00223634
\(303\) 1.76593e15 0.131098
\(304\) 1.85590e16 1.34858
\(305\) −2.67867e16 −1.90533
\(306\) −1.64575e15 −0.114598
\(307\) −2.61476e16 −1.78251 −0.891257 0.453498i \(-0.850176\pi\)
−0.891257 + 0.453498i \(0.850176\pi\)
\(308\) 1.81008e16 1.20814
\(309\) 1.32823e15 0.0868048
\(310\) 4.46846e15 0.285961
\(311\) 1.96600e16 1.23209 0.616044 0.787712i \(-0.288734\pi\)
0.616044 + 0.787712i \(0.288734\pi\)
\(312\) 3.14618e15 0.193098
\(313\) −8.52107e15 −0.512219 −0.256110 0.966648i \(-0.582441\pi\)
−0.256110 + 0.966648i \(0.582441\pi\)
\(314\) 1.21488e15 0.0715304
\(315\) −1.06179e16 −0.612378
\(316\) 1.36973e16 0.773874
\(317\) −2.70021e15 −0.149456 −0.0747278 0.997204i \(-0.523809\pi\)
−0.0747278 + 0.997204i \(0.523809\pi\)
\(318\) −1.67937e15 −0.0910688
\(319\) −9.18479e15 −0.488011
\(320\) 1.46140e16 0.760840
\(321\) −2.08545e16 −1.06394
\(322\) 9.56283e15 0.478105
\(323\) −4.54601e16 −2.22748
\(324\) −2.15818e15 −0.103644
\(325\) −7.23922e15 −0.340761
\(326\) −1.11333e16 −0.513699
\(327\) 1.02477e14 0.00463518
\(328\) 7.57741e15 0.336001
\(329\) −4.66934e15 −0.202993
\(330\) 3.73922e15 0.159383
\(331\) 2.30716e16 0.964265 0.482132 0.876098i \(-0.339862\pi\)
0.482132 + 0.876098i \(0.339862\pi\)
\(332\) −5.05372e14 −0.0207116
\(333\) 1.21182e16 0.487025
\(334\) −3.62922e15 −0.143041
\(335\) −3.99068e15 −0.154261
\(336\) 1.82765e16 0.692926
\(337\) −4.79250e16 −1.78224 −0.891122 0.453763i \(-0.850081\pi\)
−0.891122 + 0.453763i \(0.850081\pi\)
\(338\) −3.93999e15 −0.143727
\(339\) −1.69438e16 −0.606334
\(340\) −4.33075e16 −1.52037
\(341\) 2.25791e16 0.777685
\(342\) 4.29489e15 0.145138
\(343\) 1.05675e16 0.350399
\(344\) 1.08120e16 0.351782
\(345\) −2.74202e16 −0.875482
\(346\) −1.04083e16 −0.326127
\(347\) −9.99222e15 −0.307270 −0.153635 0.988128i \(-0.549098\pi\)
−0.153635 + 0.988128i \(0.549098\pi\)
\(348\) −1.00501e16 −0.303324
\(349\) 3.73842e16 1.10745 0.553723 0.832701i \(-0.313207\pi\)
0.553723 + 0.832701i \(0.313207\pi\)
\(350\) 6.80311e15 0.197818
\(351\) −4.50064e15 −0.128463
\(352\) −2.19300e16 −0.614485
\(353\) −4.95769e16 −1.36378 −0.681889 0.731456i \(-0.738841\pi\)
−0.681889 + 0.731456i \(0.738841\pi\)
\(354\) 7.21485e14 0.0194853
\(355\) −3.80666e16 −1.00939
\(356\) 1.86329e16 0.485127
\(357\) −4.47681e16 −1.14452
\(358\) −1.24823e16 −0.313368
\(359\) 4.35057e16 1.07259 0.536294 0.844032i \(-0.319824\pi\)
0.536294 + 0.844032i \(0.319824\pi\)
\(360\) 8.47781e15 0.205266
\(361\) 7.65835e16 1.82112
\(362\) −7.11109e15 −0.166085
\(363\) −6.27276e15 −0.143902
\(364\) 4.13036e16 0.930740
\(365\) −2.55066e16 −0.564610
\(366\) 1.06701e16 0.232029
\(367\) −9.09253e16 −1.94247 −0.971237 0.238114i \(-0.923471\pi\)
−0.971237 + 0.238114i \(0.923471\pi\)
\(368\) 4.71982e16 0.990637
\(369\) −1.08396e16 −0.223532
\(370\) −2.29740e16 −0.465506
\(371\) −4.56824e16 −0.909533
\(372\) 2.47065e16 0.483372
\(373\) 9.59177e16 1.84413 0.922065 0.387035i \(-0.126501\pi\)
0.922065 + 0.387035i \(0.126501\pi\)
\(374\) 1.57656e16 0.297883
\(375\) 1.87051e16 0.347342
\(376\) 3.72821e15 0.0680424
\(377\) −2.09584e16 −0.375959
\(378\) 4.22950e15 0.0745749
\(379\) 4.49958e16 0.779861 0.389931 0.920844i \(-0.372499\pi\)
0.389931 + 0.920844i \(0.372499\pi\)
\(380\) 1.13019e17 1.92556
\(381\) 5.39002e16 0.902772
\(382\) 8.97862e15 0.147842
\(383\) −1.34081e16 −0.217058 −0.108529 0.994093i \(-0.534614\pi\)
−0.108529 + 0.994093i \(0.534614\pi\)
\(384\) −3.15463e16 −0.502105
\(385\) 1.01715e17 1.59181
\(386\) 1.48680e16 0.228789
\(387\) −1.54666e16 −0.234031
\(388\) −6.20959e16 −0.923967
\(389\) −3.56783e16 −0.522073 −0.261037 0.965329i \(-0.584064\pi\)
−0.261037 + 0.965329i \(0.584064\pi\)
\(390\) 8.53240e15 0.122787
\(391\) −1.15612e17 −1.63626
\(392\) −4.44323e16 −0.618500
\(393\) 2.19764e16 0.300887
\(394\) −1.97520e16 −0.266002
\(395\) 7.69703e16 1.01963
\(396\) 2.06744e16 0.269411
\(397\) −1.47697e17 −1.89336 −0.946682 0.322170i \(-0.895588\pi\)
−0.946682 + 0.322170i \(0.895588\pi\)
\(398\) −2.32846e16 −0.293649
\(399\) 1.16830e17 1.44955
\(400\) 3.35773e16 0.409880
\(401\) −1.26099e17 −1.51452 −0.757258 0.653116i \(-0.773461\pi\)
−0.757258 + 0.653116i \(0.773461\pi\)
\(402\) 1.58964e15 0.0187858
\(403\) 5.15225e16 0.599120
\(404\) −1.85108e16 −0.211810
\(405\) −1.21276e16 −0.136558
\(406\) 1.96958e16 0.218251
\(407\) −1.16087e17 −1.26596
\(408\) 3.57449e16 0.383639
\(409\) 7.26487e16 0.767408 0.383704 0.923456i \(-0.374648\pi\)
0.383704 + 0.923456i \(0.374648\pi\)
\(410\) 2.05499e16 0.213655
\(411\) −3.97335e16 −0.406617
\(412\) −1.39227e16 −0.140246
\(413\) 1.96260e16 0.194606
\(414\) 1.09225e16 0.106615
\(415\) −2.83987e15 −0.0272889
\(416\) −5.00413e16 −0.473393
\(417\) −8.36942e16 −0.779491
\(418\) −4.11433e16 −0.377271
\(419\) −8.31638e16 −0.750832 −0.375416 0.926856i \(-0.622500\pi\)
−0.375416 + 0.926856i \(0.622500\pi\)
\(420\) 1.11298e17 0.989391
\(421\) 1.15142e17 1.00786 0.503929 0.863745i \(-0.331887\pi\)
0.503929 + 0.863745i \(0.331887\pi\)
\(422\) −2.62587e16 −0.226330
\(423\) −5.33324e15 −0.0452667
\(424\) 3.64749e16 0.304871
\(425\) −8.22474e16 −0.677008
\(426\) 1.51633e16 0.122923
\(427\) 2.90250e17 2.31735
\(428\) 2.18600e17 1.71896
\(429\) 4.31142e16 0.333924
\(430\) 2.93219e16 0.223690
\(431\) 2.10924e17 1.58498 0.792491 0.609883i \(-0.208784\pi\)
0.792491 + 0.609883i \(0.208784\pi\)
\(432\) 2.08751e16 0.154520
\(433\) −2.21040e16 −0.161176 −0.0805878 0.996748i \(-0.525680\pi\)
−0.0805878 + 0.996748i \(0.525680\pi\)
\(434\) −4.84186e16 −0.347800
\(435\) −5.64754e16 −0.399650
\(436\) −1.07418e15 −0.00748884
\(437\) 3.01709e17 2.07233
\(438\) 1.01602e16 0.0687577
\(439\) 2.48152e17 1.65462 0.827309 0.561746i \(-0.189870\pi\)
0.827309 + 0.561746i \(0.189870\pi\)
\(440\) −8.12139e16 −0.533566
\(441\) 6.35609e16 0.411471
\(442\) 3.59750e16 0.229486
\(443\) −2.05903e17 −1.29431 −0.647157 0.762357i \(-0.724042\pi\)
−0.647157 + 0.762357i \(0.724042\pi\)
\(444\) −1.27025e17 −0.786863
\(445\) 1.04705e17 0.639186
\(446\) 7.93907e15 0.0477632
\(447\) −1.75807e17 −1.04241
\(448\) −1.58352e17 −0.925371
\(449\) 1.07785e17 0.620809 0.310404 0.950605i \(-0.399536\pi\)
0.310404 + 0.950605i \(0.399536\pi\)
\(450\) 7.77040e15 0.0441125
\(451\) 1.03838e17 0.581046
\(452\) 1.77607e17 0.979626
\(453\) 9.16058e14 0.00498063
\(454\) 2.68680e16 0.144003
\(455\) 2.32100e17 1.22631
\(456\) −9.32827e16 −0.485880
\(457\) 2.70654e17 1.38982 0.694911 0.719095i \(-0.255444\pi\)
0.694911 + 0.719095i \(0.255444\pi\)
\(458\) −6.35254e16 −0.321604
\(459\) −5.11334e16 −0.255224
\(460\) 2.87423e17 1.41447
\(461\) 5.29700e16 0.257024 0.128512 0.991708i \(-0.458980\pi\)
0.128512 + 0.991708i \(0.458980\pi\)
\(462\) −4.05169e16 −0.193849
\(463\) 9.27693e16 0.437651 0.218825 0.975764i \(-0.429778\pi\)
0.218825 + 0.975764i \(0.429778\pi\)
\(464\) 9.72106e16 0.452217
\(465\) 1.38835e17 0.636874
\(466\) −7.83537e16 −0.354447
\(467\) −1.53203e17 −0.683452 −0.341726 0.939800i \(-0.611011\pi\)
−0.341726 + 0.939800i \(0.611011\pi\)
\(468\) 4.71763e16 0.207551
\(469\) 4.32416e16 0.187620
\(470\) 1.01109e16 0.0432666
\(471\) 3.77462e16 0.159308
\(472\) −1.56703e16 −0.0652309
\(473\) 1.48164e17 0.608337
\(474\) −3.06602e16 −0.124170
\(475\) 2.14639e17 0.857435
\(476\) 4.69265e17 1.84915
\(477\) −5.21777e16 −0.202822
\(478\) 1.27690e16 0.0489639
\(479\) 2.26038e17 0.855068 0.427534 0.903999i \(-0.359382\pi\)
0.427534 + 0.903999i \(0.359382\pi\)
\(480\) −1.34843e17 −0.503224
\(481\) −2.64896e17 −0.975286
\(482\) −3.23635e16 −0.117557
\(483\) 2.97116e17 1.06480
\(484\) 6.57519e16 0.232495
\(485\) −3.48939e17 −1.21739
\(486\) 4.83087e15 0.0166299
\(487\) 1.50663e17 0.511763 0.255882 0.966708i \(-0.417634\pi\)
0.255882 + 0.966708i \(0.417634\pi\)
\(488\) −2.31749e17 −0.776765
\(489\) −3.45909e17 −1.14408
\(490\) −1.20500e17 −0.393290
\(491\) 2.43748e17 0.785075 0.392538 0.919736i \(-0.371597\pi\)
0.392538 + 0.919736i \(0.371597\pi\)
\(492\) 1.13622e17 0.361150
\(493\) −2.38116e17 −0.746938
\(494\) −9.38833e16 −0.290645
\(495\) 1.16177e17 0.354966
\(496\) −2.38974e17 −0.720644
\(497\) 4.12475e17 1.22767
\(498\) 1.13123e15 0.00332322
\(499\) −2.86718e17 −0.831383 −0.415691 0.909506i \(-0.636460\pi\)
−0.415691 + 0.909506i \(0.636460\pi\)
\(500\) −1.96070e17 −0.561184
\(501\) −1.12759e17 −0.318572
\(502\) 6.42915e16 0.179300
\(503\) −1.86373e17 −0.513086 −0.256543 0.966533i \(-0.582584\pi\)
−0.256543 + 0.966533i \(0.582584\pi\)
\(504\) −9.18625e16 −0.249655
\(505\) −1.04019e17 −0.279073
\(506\) −1.04633e17 −0.277134
\(507\) −1.22415e17 −0.320098
\(508\) −5.64990e17 −1.45857
\(509\) −3.46437e17 −0.882995 −0.441497 0.897263i \(-0.645553\pi\)
−0.441497 + 0.897263i \(0.645553\pi\)
\(510\) 9.69397e16 0.243947
\(511\) 2.76380e17 0.686706
\(512\) 3.96088e17 0.971710
\(513\) 1.33442e17 0.323243
\(514\) −1.89350e16 −0.0452904
\(515\) −7.82368e16 −0.184784
\(516\) 1.62123e17 0.378113
\(517\) 5.10902e16 0.117666
\(518\) 2.48938e17 0.566170
\(519\) −3.23386e17 −0.726329
\(520\) −1.85319e17 −0.411054
\(521\) 5.66116e17 1.24011 0.620055 0.784558i \(-0.287110\pi\)
0.620055 + 0.784558i \(0.287110\pi\)
\(522\) 2.24963e16 0.0486690
\(523\) −2.93993e17 −0.628168 −0.314084 0.949395i \(-0.601697\pi\)
−0.314084 + 0.949395i \(0.601697\pi\)
\(524\) −2.30359e17 −0.486130
\(525\) 2.11372e17 0.440566
\(526\) −5.80675e16 −0.119544
\(527\) 5.85366e17 1.19031
\(528\) −1.99975e17 −0.401656
\(529\) 2.63252e17 0.522288
\(530\) 9.89197e16 0.193861
\(531\) 2.24165e16 0.0433963
\(532\) −1.22463e18 −2.34196
\(533\) 2.36945e17 0.447632
\(534\) −4.17079e16 −0.0778395
\(535\) 1.22839e18 2.26484
\(536\) −3.45261e16 −0.0628892
\(537\) −3.87824e17 −0.697914
\(538\) 1.14245e17 0.203120
\(539\) −6.08887e17 −1.06957
\(540\) 1.27123e17 0.220630
\(541\) −2.99202e17 −0.513078 −0.256539 0.966534i \(-0.582582\pi\)
−0.256539 + 0.966534i \(0.582582\pi\)
\(542\) −2.42998e17 −0.411724
\(543\) −2.20941e17 −0.369894
\(544\) −5.68537e17 −0.940516
\(545\) −6.03620e15 −0.00986703
\(546\) −9.24540e16 −0.149339
\(547\) −5.73154e17 −0.914858 −0.457429 0.889246i \(-0.651230\pi\)
−0.457429 + 0.889246i \(0.651230\pi\)
\(548\) 4.16492e17 0.656951
\(549\) 3.31519e17 0.516760
\(550\) −7.44372e16 −0.114665
\(551\) 6.21408e17 0.946001
\(552\) −2.37231e17 −0.356917
\(553\) −8.34023e17 −1.24012
\(554\) 2.07785e17 0.305352
\(555\) −7.13799e17 −1.03674
\(556\) 8.77294e17 1.25939
\(557\) −1.37623e18 −1.95268 −0.976340 0.216242i \(-0.930620\pi\)
−0.976340 + 0.216242i \(0.930620\pi\)
\(558\) −5.53030e16 −0.0775580
\(559\) 3.38089e17 0.468656
\(560\) −1.07654e18 −1.47505
\(561\) 4.89836e17 0.663426
\(562\) 2.88014e17 0.385592
\(563\) 3.06279e17 0.405333 0.202667 0.979248i \(-0.435039\pi\)
0.202667 + 0.979248i \(0.435039\pi\)
\(564\) 5.59038e16 0.0731353
\(565\) 9.98038e17 1.29072
\(566\) 1.12535e17 0.143874
\(567\) 1.31410e17 0.166088
\(568\) −3.29339e17 −0.411509
\(569\) −1.13571e18 −1.40294 −0.701470 0.712699i \(-0.747473\pi\)
−0.701470 + 0.712699i \(0.747473\pi\)
\(570\) −2.52982e17 −0.308960
\(571\) −7.93156e16 −0.0957687 −0.0478844 0.998853i \(-0.515248\pi\)
−0.0478844 + 0.998853i \(0.515248\pi\)
\(572\) −4.51929e17 −0.539506
\(573\) 2.78965e17 0.329264
\(574\) −2.22671e17 −0.259858
\(575\) 5.45858e17 0.629852
\(576\) −1.80867e17 −0.206354
\(577\) 1.50666e18 1.69970 0.849852 0.527021i \(-0.176691\pi\)
0.849852 + 0.527021i \(0.176691\pi\)
\(578\) 1.76332e17 0.196698
\(579\) 4.61947e17 0.509544
\(580\) 5.91983e17 0.645695
\(581\) 3.07718e16 0.0331901
\(582\) 1.38996e17 0.148252
\(583\) 4.99841e17 0.527213
\(584\) −2.20674e17 −0.230180
\(585\) 2.65101e17 0.273462
\(586\) 4.34269e17 0.443021
\(587\) 1.02890e18 1.03807 0.519034 0.854753i \(-0.326292\pi\)
0.519034 + 0.854753i \(0.326292\pi\)
\(588\) −6.66254e17 −0.664794
\(589\) −1.52762e18 −1.50753
\(590\) −4.24976e16 −0.0414788
\(591\) −6.13691e17 −0.592422
\(592\) 1.22865e18 1.17311
\(593\) −1.55951e18 −1.47276 −0.736380 0.676568i \(-0.763467\pi\)
−0.736380 + 0.676568i \(0.763467\pi\)
\(594\) −4.62777e16 −0.0432275
\(595\) 2.63697e18 2.43638
\(596\) 1.84284e18 1.68417
\(597\) −7.23448e17 −0.653995
\(598\) −2.38758e17 −0.213502
\(599\) 1.89090e18 1.67261 0.836304 0.548265i \(-0.184712\pi\)
0.836304 + 0.548265i \(0.184712\pi\)
\(600\) −1.68769e17 −0.147676
\(601\) −1.44307e18 −1.24912 −0.624560 0.780977i \(-0.714722\pi\)
−0.624560 + 0.780977i \(0.714722\pi\)
\(602\) −3.17722e17 −0.272063
\(603\) 4.93899e16 0.0418384
\(604\) −9.60224e15 −0.00804697
\(605\) 3.69484e17 0.306327
\(606\) 4.14346e16 0.0339853
\(607\) 6.01678e17 0.488245 0.244122 0.969744i \(-0.421500\pi\)
0.244122 + 0.969744i \(0.421500\pi\)
\(608\) 1.48370e18 1.19117
\(609\) 6.11947e17 0.486073
\(610\) −6.28502e17 −0.493927
\(611\) 1.16581e17 0.0906483
\(612\) 5.35987e17 0.412354
\(613\) 2.93236e17 0.223215 0.111608 0.993752i \(-0.464400\pi\)
0.111608 + 0.993752i \(0.464400\pi\)
\(614\) −6.13508e17 −0.462090
\(615\) 6.38481e17 0.475839
\(616\) 8.80004e17 0.648948
\(617\) 6.96174e16 0.0508001 0.0254000 0.999677i \(-0.491914\pi\)
0.0254000 + 0.999677i \(0.491914\pi\)
\(618\) 3.11646e16 0.0225028
\(619\) −1.04982e17 −0.0750109 −0.0375054 0.999296i \(-0.511941\pi\)
−0.0375054 + 0.999296i \(0.511941\pi\)
\(620\) −1.45528e18 −1.02897
\(621\) 3.39361e17 0.237447
\(622\) 4.61288e17 0.319400
\(623\) −1.13455e18 −0.777409
\(624\) −4.56315e17 −0.309432
\(625\) −1.86248e18 −1.24989
\(626\) −1.99932e17 −0.132785
\(627\) −1.27832e18 −0.840232
\(628\) −3.95661e17 −0.257386
\(629\) −3.00958e18 −1.93765
\(630\) −2.49130e17 −0.158750
\(631\) 8.19997e17 0.517156 0.258578 0.965990i \(-0.416746\pi\)
0.258578 + 0.965990i \(0.416746\pi\)
\(632\) 6.65922e17 0.415683
\(633\) −8.15854e17 −0.504067
\(634\) −6.33557e16 −0.0387441
\(635\) −3.17488e18 −1.92176
\(636\) 5.46934e17 0.327690
\(637\) −1.38940e18 −0.823986
\(638\) −2.15505e17 −0.126509
\(639\) 4.71123e17 0.273765
\(640\) 1.85817e18 1.06885
\(641\) −2.40634e18 −1.37019 −0.685094 0.728454i \(-0.740239\pi\)
−0.685094 + 0.728454i \(0.740239\pi\)
\(642\) −4.89314e17 −0.275810
\(643\) −1.72725e16 −0.00963796 −0.00481898 0.999988i \(-0.501534\pi\)
−0.00481898 + 0.999988i \(0.501534\pi\)
\(644\) −3.11441e18 −1.72035
\(645\) 9.11028e17 0.498188
\(646\) −1.06664e18 −0.577441
\(647\) −3.10906e18 −1.66629 −0.833146 0.553053i \(-0.813463\pi\)
−0.833146 + 0.553053i \(0.813463\pi\)
\(648\) −1.04924e17 −0.0556720
\(649\) −2.14740e17 −0.112804
\(650\) −1.69856e17 −0.0883370
\(651\) −1.50436e18 −0.774597
\(652\) 3.62587e18 1.84843
\(653\) −2.17531e18 −1.09796 −0.548979 0.835836i \(-0.684983\pi\)
−0.548979 + 0.835836i \(0.684983\pi\)
\(654\) 2.40444e15 0.00120160
\(655\) −1.29447e18 −0.640507
\(656\) −1.09901e18 −0.538428
\(657\) 3.15677e17 0.153133
\(658\) −1.09558e17 −0.0526229
\(659\) 1.71325e18 0.814828 0.407414 0.913244i \(-0.366431\pi\)
0.407414 + 0.913244i \(0.366431\pi\)
\(660\) −1.21779e18 −0.573502
\(661\) −2.17739e18 −1.01537 −0.507687 0.861542i \(-0.669499\pi\)
−0.507687 + 0.861542i \(0.669499\pi\)
\(662\) 5.41335e17 0.249971
\(663\) 1.11774e18 0.511096
\(664\) −2.45696e16 −0.0111252
\(665\) −6.88165e18 −3.08569
\(666\) 2.84333e17 0.126254
\(667\) 1.58033e18 0.694911
\(668\) 1.18196e18 0.514702
\(669\) 2.46666e17 0.106375
\(670\) −9.36344e16 −0.0399898
\(671\) −3.17582e18 −1.34326
\(672\) 1.46111e18 0.612045
\(673\) 4.59601e17 0.190670 0.0953350 0.995445i \(-0.469608\pi\)
0.0953350 + 0.995445i \(0.469608\pi\)
\(674\) −1.12447e18 −0.462020
\(675\) 2.41425e17 0.0982445
\(676\) 1.28317e18 0.517168
\(677\) −3.23745e17 −0.129234 −0.0646169 0.997910i \(-0.520583\pi\)
−0.0646169 + 0.997910i \(0.520583\pi\)
\(678\) −3.97556e17 −0.157183
\(679\) 3.78098e18 1.48064
\(680\) −2.10548e18 −0.816662
\(681\) 8.34785e17 0.320714
\(682\) 5.29780e17 0.201603
\(683\) 8.71450e17 0.328479 0.164240 0.986420i \(-0.447483\pi\)
0.164240 + 0.986420i \(0.447483\pi\)
\(684\) −1.39875e18 −0.522248
\(685\) 2.34042e18 0.865576
\(686\) 2.47949e17 0.0908355
\(687\) −1.97373e18 −0.716256
\(688\) −1.56814e18 −0.563717
\(689\) 1.14057e18 0.406159
\(690\) −6.43368e17 −0.226955
\(691\) 4.46357e17 0.155982 0.0779911 0.996954i \(-0.475149\pi\)
0.0779911 + 0.996954i \(0.475149\pi\)
\(692\) 3.38978e18 1.17350
\(693\) −1.25885e18 −0.431727
\(694\) −2.34450e17 −0.0796551
\(695\) 4.92984e18 1.65932
\(696\) −4.88607e17 −0.162929
\(697\) 2.69202e18 0.889334
\(698\) 8.77154e17 0.287088
\(699\) −2.43444e18 −0.789401
\(700\) −2.21563e18 −0.711802
\(701\) −5.10790e18 −1.62583 −0.812915 0.582383i \(-0.802121\pi\)
−0.812915 + 0.582383i \(0.802121\pi\)
\(702\) −1.05600e17 −0.0333020
\(703\) 7.85403e18 2.45405
\(704\) 1.73263e18 0.536393
\(705\) 3.14144e17 0.0963605
\(706\) −1.16323e18 −0.353538
\(707\) 1.12711e18 0.339422
\(708\) −2.34972e17 −0.0701133
\(709\) −8.24200e17 −0.243687 −0.121843 0.992549i \(-0.538881\pi\)
−0.121843 + 0.992549i \(0.538881\pi\)
\(710\) −8.93165e17 −0.261669
\(711\) −9.52607e17 −0.276542
\(712\) 9.05873e17 0.260584
\(713\) −3.88495e18 −1.10740
\(714\) −1.05040e18 −0.296700
\(715\) −2.53955e18 −0.710834
\(716\) 4.06522e18 1.12759
\(717\) 3.96732e17 0.109049
\(718\) 1.02079e18 0.278052
\(719\) −2.69969e18 −0.728745 −0.364372 0.931253i \(-0.618716\pi\)
−0.364372 + 0.931253i \(0.618716\pi\)
\(720\) −1.22960e18 −0.328931
\(721\) 8.47745e17 0.224743
\(722\) 1.79690e18 0.472097
\(723\) −1.00553e18 −0.261816
\(724\) 2.31593e18 0.597620
\(725\) 1.12426e18 0.287522
\(726\) −1.47179e17 −0.0373043
\(727\) 2.32467e18 0.583967 0.291983 0.956423i \(-0.405685\pi\)
0.291983 + 0.956423i \(0.405685\pi\)
\(728\) 2.00805e18 0.499943
\(729\) 1.50095e17 0.0370370
\(730\) −5.98467e17 −0.146366
\(731\) 3.84115e18 0.931105
\(732\) −3.47503e18 −0.834904
\(733\) −8.06668e17 −0.192096 −0.0960481 0.995377i \(-0.530620\pi\)
−0.0960481 + 0.995377i \(0.530620\pi\)
\(734\) −2.13340e18 −0.503557
\(735\) −3.74392e18 −0.875909
\(736\) 3.77326e18 0.875005
\(737\) −4.73134e17 −0.108754
\(738\) −2.54331e17 −0.0579473
\(739\) 1.31742e18 0.297533 0.148767 0.988872i \(-0.452470\pi\)
0.148767 + 0.988872i \(0.452470\pi\)
\(740\) 7.48213e18 1.67502
\(741\) −2.91694e18 −0.647306
\(742\) −1.07186e18 −0.235783
\(743\) −3.72040e18 −0.811264 −0.405632 0.914036i \(-0.632949\pi\)
−0.405632 + 0.914036i \(0.632949\pi\)
\(744\) 1.20115e18 0.259641
\(745\) 1.03556e19 2.21900
\(746\) 2.25054e18 0.478062
\(747\) 3.51471e16 0.00740126
\(748\) −5.13453e18 −1.07187
\(749\) −1.33104e19 −2.75460
\(750\) 4.38883e17 0.0900431
\(751\) −4.70727e17 −0.0957436 −0.0478718 0.998853i \(-0.515244\pi\)
−0.0478718 + 0.998853i \(0.515244\pi\)
\(752\) −5.40732e17 −0.109035
\(753\) 1.99753e18 0.399324
\(754\) −4.91753e17 −0.0974615
\(755\) −5.39585e16 −0.0106024
\(756\) −1.37746e18 −0.268341
\(757\) 6.20384e18 1.19822 0.599111 0.800666i \(-0.295521\pi\)
0.599111 + 0.800666i \(0.295521\pi\)
\(758\) 1.05575e18 0.202167
\(759\) −3.25094e18 −0.617216
\(760\) 5.49462e18 1.03431
\(761\) −3.00044e18 −0.559996 −0.279998 0.960001i \(-0.590334\pi\)
−0.279998 + 0.960001i \(0.590334\pi\)
\(762\) 1.26467e18 0.234030
\(763\) 6.54061e16 0.0120008
\(764\) −2.92414e18 −0.531976
\(765\) 3.01190e18 0.543303
\(766\) −3.14599e17 −0.0562691
\(767\) −4.90008e17 −0.0869028
\(768\) 1.29228e18 0.227252
\(769\) −1.39383e18 −0.243047 −0.121523 0.992589i \(-0.538778\pi\)
−0.121523 + 0.992589i \(0.538778\pi\)
\(770\) 2.38656e18 0.412651
\(771\) −5.88309e17 −0.100868
\(772\) −4.84219e18 −0.823245
\(773\) 1.14584e19 1.93177 0.965886 0.258966i \(-0.0833817\pi\)
0.965886 + 0.258966i \(0.0833817\pi\)
\(774\) −3.62897e17 −0.0606690
\(775\) −2.76380e18 −0.458189
\(776\) −3.01891e18 −0.496305
\(777\) 7.73446e18 1.26094
\(778\) −8.37128e17 −0.135339
\(779\) −7.02531e18 −1.12635
\(780\) −2.77882e18 −0.441820
\(781\) −4.51316e18 −0.711621
\(782\) −2.71262e18 −0.424175
\(783\) 6.98957e17 0.108392
\(784\) 6.44437e18 0.991120
\(785\) −2.22336e18 −0.339123
\(786\) 5.15636e17 0.0780004
\(787\) 1.20819e19 1.81260 0.906298 0.422639i \(-0.138896\pi\)
0.906298 + 0.422639i \(0.138896\pi\)
\(788\) 6.43279e18 0.957148
\(789\) −1.80415e18 −0.266239
\(790\) 1.80597e18 0.264323
\(791\) −1.08144e19 −1.56984
\(792\) 1.00513e18 0.144713
\(793\) −7.24679e18 −1.03483
\(794\) −3.46545e18 −0.490825
\(795\) 3.07342e18 0.431753
\(796\) 7.58328e18 1.05663
\(797\) 1.27604e19 1.76353 0.881767 0.471685i \(-0.156354\pi\)
0.881767 + 0.471685i \(0.156354\pi\)
\(798\) 2.74122e18 0.375772
\(799\) 1.32452e18 0.180096
\(800\) 2.68434e18 0.362037
\(801\) −1.29586e18 −0.173359
\(802\) −2.95869e18 −0.392615
\(803\) −3.02405e18 −0.398051
\(804\) −5.17711e17 −0.0675964
\(805\) −1.75010e19 −2.26668
\(806\) 1.20888e18 0.155313
\(807\) 3.54958e18 0.452375
\(808\) −8.99936e17 −0.113773
\(809\) −3.17267e18 −0.397886 −0.198943 0.980011i \(-0.563751\pi\)
−0.198943 + 0.980011i \(0.563751\pi\)
\(810\) −2.84553e17 −0.0354005
\(811\) 1.77978e18 0.219650 0.109825 0.993951i \(-0.464971\pi\)
0.109825 + 0.993951i \(0.464971\pi\)
\(812\) −6.41452e18 −0.785326
\(813\) −7.54991e18 −0.916966
\(814\) −2.72379e18 −0.328182
\(815\) 2.03751e19 2.43543
\(816\) −5.18436e18 −0.614765
\(817\) −1.00242e19 −1.17925
\(818\) 1.70457e18 0.198939
\(819\) −2.87254e18 −0.332598
\(820\) −6.69265e18 −0.768791
\(821\) 5.66433e16 0.00645533 0.00322766 0.999995i \(-0.498973\pi\)
0.00322766 + 0.999995i \(0.498973\pi\)
\(822\) −9.32277e17 −0.105409
\(823\) 9.77457e18 1.09647 0.548237 0.836323i \(-0.315299\pi\)
0.548237 + 0.836323i \(0.315299\pi\)
\(824\) −6.76878e17 −0.0753327
\(825\) −2.31275e18 −0.255375
\(826\) 4.60489e17 0.0504485
\(827\) −9.59993e18 −1.04348 −0.521738 0.853106i \(-0.674716\pi\)
−0.521738 + 0.853106i \(0.674716\pi\)
\(828\) −3.55723e18 −0.383632
\(829\) −4.71408e18 −0.504420 −0.252210 0.967672i \(-0.581157\pi\)
−0.252210 + 0.967672i \(0.581157\pi\)
\(830\) −6.66326e16 −0.00707423
\(831\) 6.45587e18 0.680061
\(832\) 3.95362e18 0.413232
\(833\) −1.57854e19 −1.63706
\(834\) −1.96374e18 −0.202071
\(835\) 6.64187e18 0.678153
\(836\) 1.33995e19 1.35752
\(837\) −1.71826e18 −0.172732
\(838\) −1.95129e18 −0.194642
\(839\) −9.51094e18 −0.941393 −0.470696 0.882295i \(-0.655997\pi\)
−0.470696 + 0.882295i \(0.655997\pi\)
\(840\) 5.41097e18 0.531447
\(841\) −7.00575e18 −0.682779
\(842\) 2.70160e18 0.261272
\(843\) 8.94858e18 0.858766
\(844\) 8.55189e18 0.814397
\(845\) 7.21061e18 0.681402
\(846\) −1.25135e17 −0.0117347
\(847\) −4.00359e18 −0.372570
\(848\) −5.29025e18 −0.488543
\(849\) 3.49646e18 0.320427
\(850\) −1.92979e18 −0.175504
\(851\) 1.99739e19 1.80269
\(852\) −4.93837e18 −0.442310
\(853\) −2.04112e19 −1.81426 −0.907130 0.420851i \(-0.861732\pi\)
−0.907130 + 0.420851i \(0.861732\pi\)
\(854\) 6.81022e18 0.600737
\(855\) −7.86011e18 −0.688096
\(856\) 1.06276e19 0.923330
\(857\) 6.28073e18 0.541545 0.270772 0.962643i \(-0.412721\pi\)
0.270772 + 0.962643i \(0.412721\pi\)
\(858\) 1.01160e18 0.0865648
\(859\) −2.98862e18 −0.253814 −0.126907 0.991915i \(-0.540505\pi\)
−0.126907 + 0.991915i \(0.540505\pi\)
\(860\) −9.54952e18 −0.804899
\(861\) −6.91835e18 −0.578738
\(862\) 4.94897e18 0.410882
\(863\) 1.79148e19 1.47619 0.738096 0.674696i \(-0.235725\pi\)
0.738096 + 0.674696i \(0.235725\pi\)
\(864\) 1.66886e18 0.136484
\(865\) 1.90484e19 1.54616
\(866\) −5.18631e17 −0.0417823
\(867\) 5.47861e18 0.438072
\(868\) 1.57689e19 1.25148
\(869\) 9.12558e18 0.718840
\(870\) −1.32510e18 −0.103603
\(871\) −1.07963e18 −0.0837830
\(872\) −5.22232e16 −0.00402260
\(873\) 4.31858e18 0.330178
\(874\) 7.07907e18 0.537220
\(875\) 1.19386e19 0.899290
\(876\) −3.30897e18 −0.247409
\(877\) −1.82573e19 −1.35500 −0.677498 0.735524i \(-0.736936\pi\)
−0.677498 + 0.735524i \(0.736936\pi\)
\(878\) 5.82244e18 0.428935
\(879\) 1.34927e19 0.986667
\(880\) 1.17791e19 0.855017
\(881\) 3.27063e18 0.235661 0.117830 0.993034i \(-0.462406\pi\)
0.117830 + 0.993034i \(0.462406\pi\)
\(882\) 1.49134e18 0.106667
\(883\) −1.57266e19 −1.11658 −0.558291 0.829645i \(-0.688543\pi\)
−0.558291 + 0.829645i \(0.688543\pi\)
\(884\) −1.17163e19 −0.825754
\(885\) −1.32040e18 −0.0923789
\(886\) −4.83116e18 −0.335531
\(887\) −1.30055e19 −0.896650 −0.448325 0.893871i \(-0.647979\pi\)
−0.448325 + 0.893871i \(0.647979\pi\)
\(888\) −6.17555e18 −0.422660
\(889\) 3.44019e19 2.33733
\(890\) 2.45672e18 0.165699
\(891\) −1.43784e18 −0.0962735
\(892\) −2.58559e18 −0.171865
\(893\) −3.45657e18 −0.228092
\(894\) −4.12501e18 −0.270228
\(895\) 2.28440e19 1.48567
\(896\) −2.01344e19 −1.29998
\(897\) −7.41819e18 −0.475497
\(898\) 2.52899e18 0.160935
\(899\) −8.00153e18 −0.505516
\(900\) −2.53065e18 −0.158729
\(901\) 1.29584e19 0.806939
\(902\) 2.43638e18 0.150627
\(903\) −9.87157e18 −0.605921
\(904\) 8.63470e18 0.526202
\(905\) 1.30141e19 0.787403
\(906\) 2.14937e16 0.00129115
\(907\) 2.57482e19 1.53567 0.767837 0.640645i \(-0.221333\pi\)
0.767837 + 0.640645i \(0.221333\pi\)
\(908\) −8.75033e18 −0.518163
\(909\) 1.28737e18 0.0756897
\(910\) 5.44581e18 0.317902
\(911\) 2.02515e19 1.17378 0.586892 0.809666i \(-0.300351\pi\)
0.586892 + 0.809666i \(0.300351\pi\)
\(912\) 1.35295e19 0.778603
\(913\) −3.36694e17 −0.0192387
\(914\) 6.35042e18 0.360290
\(915\) −1.95275e19 −1.10004
\(916\) 2.06889e19 1.15722
\(917\) 1.40264e19 0.779016
\(918\) −1.19975e18 −0.0661629
\(919\) −2.07716e19 −1.13742 −0.568709 0.822539i \(-0.692557\pi\)
−0.568709 + 0.822539i \(0.692557\pi\)
\(920\) 1.39736e19 0.759779
\(921\) −1.90616e19 −1.02914
\(922\) 1.24285e18 0.0666296
\(923\) −1.02984e19 −0.548226
\(924\) 1.31955e19 0.697521
\(925\) 1.42097e19 0.745869
\(926\) 2.17667e18 0.113454
\(927\) 9.68281e17 0.0501168
\(928\) 7.77150e18 0.399432
\(929\) 1.29993e19 0.663464 0.331732 0.943374i \(-0.392367\pi\)
0.331732 + 0.943374i \(0.392367\pi\)
\(930\) 3.25751e18 0.165100
\(931\) 4.11949e19 2.07334
\(932\) 2.55181e19 1.27540
\(933\) 1.43322e19 0.711347
\(934\) −3.59464e18 −0.177174
\(935\) −2.88528e19 −1.41225
\(936\) 2.29356e18 0.111485
\(937\) −1.57863e19 −0.762032 −0.381016 0.924568i \(-0.624426\pi\)
−0.381016 + 0.924568i \(0.624426\pi\)
\(938\) 1.01459e18 0.0486375
\(939\) −6.21186e18 −0.295730
\(940\) −3.29290e18 −0.155685
\(941\) −8.05060e18 −0.378004 −0.189002 0.981977i \(-0.560525\pi\)
−0.189002 + 0.981977i \(0.560525\pi\)
\(942\) 8.85648e17 0.0412981
\(943\) −1.78663e19 −0.827389
\(944\) 2.27278e18 0.104530
\(945\) −7.74045e18 −0.353557
\(946\) 3.47640e18 0.157702
\(947\) 1.64694e19 0.741996 0.370998 0.928634i \(-0.379016\pi\)
0.370998 + 0.928634i \(0.379016\pi\)
\(948\) 9.98536e18 0.446796
\(949\) −6.90048e18 −0.306654
\(950\) 5.03614e18 0.222277
\(951\) −1.96845e18 −0.0862883
\(952\) 2.28142e19 0.993264
\(953\) −3.40652e19 −1.47302 −0.736508 0.676429i \(-0.763527\pi\)
−0.736508 + 0.676429i \(0.763527\pi\)
\(954\) −1.22426e18 −0.0525786
\(955\) −1.64318e19 −0.700913
\(956\) −4.15860e18 −0.176186
\(957\) −6.69571e18 −0.281753
\(958\) 5.30359e18 0.221663
\(959\) −2.53599e19 −1.05276
\(960\) 1.06536e19 0.439271
\(961\) −4.74724e18 −0.194419
\(962\) −6.21531e18 −0.252828
\(963\) −1.52029e19 −0.614266
\(964\) 1.05401e19 0.423003
\(965\) −2.72100e19 −1.08468
\(966\) 6.97130e18 0.276034
\(967\) 2.03093e19 0.798771 0.399385 0.916783i \(-0.369224\pi\)
0.399385 + 0.916783i \(0.369224\pi\)
\(968\) 3.19665e18 0.124884
\(969\) −3.31404e19 −1.28604
\(970\) −8.18725e18 −0.315589
\(971\) −3.98158e19 −1.52451 −0.762256 0.647276i \(-0.775908\pi\)
−0.762256 + 0.647276i \(0.775908\pi\)
\(972\) −1.57331e18 −0.0598390
\(973\) −5.34179e19 −2.01815
\(974\) 3.53505e18 0.132667
\(975\) −5.27739e18 −0.196738
\(976\) 3.36124e19 1.24473
\(977\) 9.05664e18 0.333160 0.166580 0.986028i \(-0.446728\pi\)
0.166580 + 0.986028i \(0.446728\pi\)
\(978\) −8.11616e18 −0.296584
\(979\) 1.24138e19 0.450627
\(980\) 3.92443e19 1.41516
\(981\) 7.47058e16 0.00267612
\(982\) 5.71912e18 0.203519
\(983\) −3.09961e19 −1.09574 −0.547872 0.836562i \(-0.684562\pi\)
−0.547872 + 0.836562i \(0.684562\pi\)
\(984\) 5.52393e18 0.193990
\(985\) 3.61482e19 1.26110
\(986\) −5.58698e18 −0.193632
\(987\) −3.40395e18 −0.117198
\(988\) 3.05758e19 1.04582
\(989\) −2.54929e19 −0.866250
\(990\) 2.72589e18 0.0920196
\(991\) 4.27504e19 1.43371 0.716855 0.697222i \(-0.245581\pi\)
0.716855 + 0.697222i \(0.245581\pi\)
\(992\) −1.91048e19 −0.636527
\(993\) 1.68192e19 0.556719
\(994\) 9.67801e18 0.318254
\(995\) 4.26132e19 1.39218
\(996\) −3.68417e17 −0.0119579
\(997\) −7.52229e18 −0.242567 −0.121283 0.992618i \(-0.538701\pi\)
−0.121283 + 0.992618i \(0.538701\pi\)
\(998\) −6.72732e18 −0.215523
\(999\) 8.83418e18 0.281184
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.1.18 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.18 30 1.1 even 1 trivial