Properties

Label 177.14.a.a.1.7
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 1.7
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-112.878 q^{2} +729.000 q^{3} +4549.48 q^{4} +37606.3 q^{5} -82288.2 q^{6} -60488.5 q^{7} +411161. q^{8} +531441. q^{9} +O(q^{10})\) \(q-112.878 q^{2} +729.000 q^{3} +4549.48 q^{4} +37606.3 q^{5} -82288.2 q^{6} -60488.5 q^{7} +411161. q^{8} +531441. q^{9} -4.24493e6 q^{10} -5.38497e6 q^{11} +3.31657e6 q^{12} +1.78547e7 q^{13} +6.82784e6 q^{14} +2.74150e7 q^{15} -8.36804e7 q^{16} -7.26826e7 q^{17} -5.99881e7 q^{18} +2.05937e8 q^{19} +1.71089e8 q^{20} -4.40961e7 q^{21} +6.07846e8 q^{22} -2.11582e8 q^{23} +2.99736e8 q^{24} +1.93529e8 q^{25} -2.01541e9 q^{26} +3.87420e8 q^{27} -2.75192e8 q^{28} +4.90852e9 q^{29} -3.09455e9 q^{30} -5.76225e9 q^{31} +6.07747e9 q^{32} -3.92564e9 q^{33} +8.20427e9 q^{34} -2.27475e9 q^{35} +2.41778e9 q^{36} +5.09808e8 q^{37} -2.32458e10 q^{38} +1.30161e10 q^{39} +1.54622e10 q^{40} -4.36319e9 q^{41} +4.97749e9 q^{42} -1.35776e9 q^{43} -2.44988e10 q^{44} +1.99855e10 q^{45} +2.38830e10 q^{46} -1.26930e11 q^{47} -6.10030e10 q^{48} -9.32301e10 q^{49} -2.18452e10 q^{50} -5.29856e10 q^{51} +8.12297e10 q^{52} -2.89318e10 q^{53} -4.37313e10 q^{54} -2.02509e11 q^{55} -2.48705e10 q^{56} +1.50128e11 q^{57} -5.54065e11 q^{58} +4.21805e10 q^{59} +1.24724e11 q^{60} +2.30201e11 q^{61} +6.50432e11 q^{62} -3.21461e10 q^{63} -5.03064e8 q^{64} +6.71449e11 q^{65} +4.43119e11 q^{66} -1.70285e11 q^{67} -3.30668e11 q^{68} -1.54243e11 q^{69} +2.56769e11 q^{70} -1.48653e12 q^{71} +2.18508e11 q^{72} -1.87627e12 q^{73} -5.75462e10 q^{74} +1.41083e11 q^{75} +9.36907e11 q^{76} +3.25729e11 q^{77} -1.46923e12 q^{78} -2.52869e12 q^{79} -3.14691e12 q^{80} +2.82430e11 q^{81} +4.92509e11 q^{82} -1.34332e12 q^{83} -2.00615e11 q^{84} -2.73332e12 q^{85} +1.53261e11 q^{86} +3.57831e12 q^{87} -2.21409e12 q^{88} -1.41898e12 q^{89} -2.25593e12 q^{90} -1.08001e12 q^{91} -9.62587e11 q^{92} -4.20068e12 q^{93} +1.43276e13 q^{94} +7.74453e12 q^{95} +4.43047e12 q^{96} +1.48907e13 q^{97} +1.05236e13 q^{98} -2.86179e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −112.878 −1.24714 −0.623570 0.781768i \(-0.714318\pi\)
−0.623570 + 0.781768i \(0.714318\pi\)
\(3\) 729.000 0.577350
\(4\) 4549.48 0.555357
\(5\) 37606.3 1.07635 0.538177 0.842832i \(-0.319113\pi\)
0.538177 + 0.842832i \(0.319113\pi\)
\(6\) −82288.2 −0.720036
\(7\) −60488.5 −0.194328 −0.0971641 0.995268i \(-0.530977\pi\)
−0.0971641 + 0.995268i \(0.530977\pi\)
\(8\) 411161. 0.554532
\(9\) 531441. 0.333333
\(10\) −4.24493e6 −1.34236
\(11\) −5.38497e6 −0.916497 −0.458248 0.888824i \(-0.651523\pi\)
−0.458248 + 0.888824i \(0.651523\pi\)
\(12\) 3.31657e6 0.320635
\(13\) 1.78547e7 1.02594 0.512969 0.858407i \(-0.328546\pi\)
0.512969 + 0.858407i \(0.328546\pi\)
\(14\) 6.82784e6 0.242354
\(15\) 2.74150e7 0.621434
\(16\) −8.36804e7 −1.24694
\(17\) −7.26826e7 −0.730318 −0.365159 0.930945i \(-0.618985\pi\)
−0.365159 + 0.930945i \(0.618985\pi\)
\(18\) −5.99881e7 −0.415713
\(19\) 2.05937e8 1.00424 0.502119 0.864799i \(-0.332554\pi\)
0.502119 + 0.864799i \(0.332554\pi\)
\(20\) 1.71089e8 0.597761
\(21\) −4.40961e7 −0.112195
\(22\) 6.07846e8 1.14300
\(23\) −2.11582e8 −0.298021 −0.149011 0.988836i \(-0.547609\pi\)
−0.149011 + 0.988836i \(0.547609\pi\)
\(24\) 2.99736e8 0.320159
\(25\) 1.93529e8 0.158539
\(26\) −2.01541e9 −1.27949
\(27\) 3.87420e8 0.192450
\(28\) −2.75192e8 −0.107921
\(29\) 4.90852e9 1.53237 0.766185 0.642620i \(-0.222152\pi\)
0.766185 + 0.642620i \(0.222152\pi\)
\(30\) −3.09455e9 −0.775014
\(31\) −5.76225e9 −1.16611 −0.583057 0.812431i \(-0.698144\pi\)
−0.583057 + 0.812431i \(0.698144\pi\)
\(32\) 6.07747e9 1.00057
\(33\) −3.92564e9 −0.529140
\(34\) 8.20427e9 0.910809
\(35\) −2.27475e9 −0.209166
\(36\) 2.41778e9 0.185119
\(37\) 5.09808e8 0.0326659 0.0163330 0.999867i \(-0.494801\pi\)
0.0163330 + 0.999867i \(0.494801\pi\)
\(38\) −2.32458e10 −1.25242
\(39\) 1.30161e10 0.592326
\(40\) 1.54622e10 0.596873
\(41\) −4.36319e9 −0.143453 −0.0717264 0.997424i \(-0.522851\pi\)
−0.0717264 + 0.997424i \(0.522851\pi\)
\(42\) 4.97749e9 0.139923
\(43\) −1.35776e9 −0.0327550 −0.0163775 0.999866i \(-0.505213\pi\)
−0.0163775 + 0.999866i \(0.505213\pi\)
\(44\) −2.44988e10 −0.508982
\(45\) 1.99855e10 0.358785
\(46\) 2.38830e10 0.371674
\(47\) −1.26930e11 −1.71762 −0.858812 0.512291i \(-0.828797\pi\)
−0.858812 + 0.512291i \(0.828797\pi\)
\(48\) −6.10030e10 −0.719919
\(49\) −9.32301e10 −0.962237
\(50\) −2.18452e10 −0.197720
\(51\) −5.29856e10 −0.421649
\(52\) 8.12297e10 0.569761
\(53\) −2.89318e10 −0.179301 −0.0896504 0.995973i \(-0.528575\pi\)
−0.0896504 + 0.995973i \(0.528575\pi\)
\(54\) −4.37313e10 −0.240012
\(55\) −2.02509e11 −0.986475
\(56\) −2.48705e10 −0.107761
\(57\) 1.50128e11 0.579797
\(58\) −5.54065e11 −1.91108
\(59\) 4.21805e10 0.130189
\(60\) 1.24724e11 0.345117
\(61\) 2.30201e11 0.572088 0.286044 0.958216i \(-0.407660\pi\)
0.286044 + 0.958216i \(0.407660\pi\)
\(62\) 6.50432e11 1.45431
\(63\) −3.21461e10 −0.0647761
\(64\) −5.03064e8 −0.000915069 0
\(65\) 6.71449e11 1.10427
\(66\) 4.43119e11 0.659911
\(67\) −1.70285e11 −0.229980 −0.114990 0.993367i \(-0.536684\pi\)
−0.114990 + 0.993367i \(0.536684\pi\)
\(68\) −3.30668e11 −0.405587
\(69\) −1.54243e11 −0.172063
\(70\) 2.56769e11 0.260859
\(71\) −1.48653e12 −1.37719 −0.688594 0.725147i \(-0.741772\pi\)
−0.688594 + 0.725147i \(0.741772\pi\)
\(72\) 2.18508e11 0.184844
\(73\) −1.87627e12 −1.45110 −0.725550 0.688170i \(-0.758414\pi\)
−0.725550 + 0.688170i \(0.758414\pi\)
\(74\) −5.75462e10 −0.0407390
\(75\) 1.41083e11 0.0915325
\(76\) 9.36907e11 0.557710
\(77\) 3.25729e11 0.178101
\(78\) −1.46923e12 −0.738713
\(79\) −2.52869e12 −1.17036 −0.585180 0.810904i \(-0.698976\pi\)
−0.585180 + 0.810904i \(0.698976\pi\)
\(80\) −3.14691e12 −1.34214
\(81\) 2.82430e11 0.111111
\(82\) 4.92509e11 0.178906
\(83\) −1.34332e12 −0.450995 −0.225498 0.974244i \(-0.572401\pi\)
−0.225498 + 0.974244i \(0.572401\pi\)
\(84\) −2.00615e11 −0.0623085
\(85\) −2.73332e12 −0.786081
\(86\) 1.53261e11 0.0408500
\(87\) 3.57831e12 0.884715
\(88\) −2.21409e12 −0.508227
\(89\) −1.41898e12 −0.302650 −0.151325 0.988484i \(-0.548354\pi\)
−0.151325 + 0.988484i \(0.548354\pi\)
\(90\) −2.25593e12 −0.447455
\(91\) −1.08001e12 −0.199369
\(92\) −9.62587e11 −0.165508
\(93\) −4.20068e12 −0.673256
\(94\) 1.43276e13 2.14212
\(95\) 7.74453e12 1.08092
\(96\) 4.43047e12 0.577680
\(97\) 1.48907e13 1.81509 0.907543 0.419958i \(-0.137955\pi\)
0.907543 + 0.419958i \(0.137955\pi\)
\(98\) 1.05236e13 1.20004
\(99\) −2.86179e12 −0.305499
\(100\) 8.80457e11 0.0880457
\(101\) 2.00384e13 1.87834 0.939169 0.343456i \(-0.111597\pi\)
0.939169 + 0.343456i \(0.111597\pi\)
\(102\) 5.98092e12 0.525856
\(103\) −1.87483e13 −1.54710 −0.773551 0.633734i \(-0.781521\pi\)
−0.773551 + 0.633734i \(0.781521\pi\)
\(104\) 7.34116e12 0.568916
\(105\) −1.65829e12 −0.120762
\(106\) 3.26577e12 0.223613
\(107\) 7.48333e11 0.0482059 0.0241030 0.999709i \(-0.492327\pi\)
0.0241030 + 0.999709i \(0.492327\pi\)
\(108\) 1.76256e12 0.106878
\(109\) −5.69983e12 −0.325529 −0.162765 0.986665i \(-0.552041\pi\)
−0.162765 + 0.986665i \(0.552041\pi\)
\(110\) 2.28588e13 1.23027
\(111\) 3.71650e11 0.0188597
\(112\) 5.06171e12 0.242315
\(113\) 3.56191e13 1.60944 0.804718 0.593658i \(-0.202317\pi\)
0.804718 + 0.593658i \(0.202317\pi\)
\(114\) −1.69462e13 −0.723087
\(115\) −7.95680e12 −0.320777
\(116\) 2.23312e13 0.851012
\(117\) 9.48873e12 0.341979
\(118\) −4.76126e12 −0.162364
\(119\) 4.39646e12 0.141921
\(120\) 1.12720e13 0.344605
\(121\) −5.52481e12 −0.160034
\(122\) −2.59847e13 −0.713474
\(123\) −3.18077e12 −0.0828226
\(124\) −2.62152e13 −0.647609
\(125\) −3.86282e13 −0.905710
\(126\) 3.62859e12 0.0807848
\(127\) 7.89356e13 1.66936 0.834678 0.550738i \(-0.185654\pi\)
0.834678 + 0.550738i \(0.185654\pi\)
\(128\) −4.97298e13 −0.999429
\(129\) −9.89806e11 −0.0189111
\(130\) −7.57920e13 −1.37718
\(131\) 1.09063e14 1.88545 0.942724 0.333575i \(-0.108255\pi\)
0.942724 + 0.333575i \(0.108255\pi\)
\(132\) −1.78596e13 −0.293861
\(133\) −1.24568e13 −0.195152
\(134\) 1.92214e13 0.286817
\(135\) 1.45694e13 0.207145
\(136\) −2.98842e13 −0.404985
\(137\) −1.02328e14 −1.32224 −0.661118 0.750282i \(-0.729918\pi\)
−0.661118 + 0.750282i \(0.729918\pi\)
\(138\) 1.74107e13 0.214586
\(139\) 9.41040e13 1.10665 0.553327 0.832964i \(-0.313358\pi\)
0.553327 + 0.832964i \(0.313358\pi\)
\(140\) −1.03489e13 −0.116162
\(141\) −9.25319e13 −0.991670
\(142\) 1.67796e14 1.71754
\(143\) −9.61471e13 −0.940269
\(144\) −4.44712e13 −0.415645
\(145\) 1.84591e14 1.64937
\(146\) 2.11790e14 1.80972
\(147\) −6.79648e13 −0.555548
\(148\) 2.31936e12 0.0181412
\(149\) 1.84740e14 1.38309 0.691544 0.722334i \(-0.256931\pi\)
0.691544 + 0.722334i \(0.256931\pi\)
\(150\) −1.59252e13 −0.114154
\(151\) −1.90572e14 −1.30831 −0.654153 0.756363i \(-0.726975\pi\)
−0.654153 + 0.756363i \(0.726975\pi\)
\(152\) 8.46733e13 0.556882
\(153\) −3.86265e13 −0.243439
\(154\) −3.67677e13 −0.222117
\(155\) −2.16697e14 −1.25515
\(156\) 5.92164e13 0.328952
\(157\) 1.24248e13 0.0662125 0.0331063 0.999452i \(-0.489460\pi\)
0.0331063 + 0.999452i \(0.489460\pi\)
\(158\) 2.85434e14 1.45960
\(159\) −2.10913e13 −0.103519
\(160\) 2.28551e14 1.07697
\(161\) 1.27983e13 0.0579139
\(162\) −3.18801e13 −0.138571
\(163\) 5.65179e13 0.236030 0.118015 0.993012i \(-0.462347\pi\)
0.118015 + 0.993012i \(0.462347\pi\)
\(164\) −1.98503e13 −0.0796675
\(165\) −1.47629e14 −0.569542
\(166\) 1.51632e14 0.562454
\(167\) −2.93952e14 −1.04862 −0.524311 0.851527i \(-0.675677\pi\)
−0.524311 + 0.851527i \(0.675677\pi\)
\(168\) −1.81306e13 −0.0622160
\(169\) 1.59157e13 0.0525487
\(170\) 3.08532e14 0.980353
\(171\) 1.09443e14 0.334746
\(172\) −6.17710e12 −0.0181907
\(173\) 1.71073e14 0.485158 0.242579 0.970132i \(-0.422007\pi\)
0.242579 + 0.970132i \(0.422007\pi\)
\(174\) −4.03914e14 −1.10336
\(175\) −1.17063e13 −0.0308086
\(176\) 4.50617e14 1.14281
\(177\) 3.07496e13 0.0751646
\(178\) 1.60171e14 0.377446
\(179\) −5.94981e14 −1.35194 −0.675971 0.736928i \(-0.736276\pi\)
−0.675971 + 0.736928i \(0.736276\pi\)
\(180\) 9.09238e13 0.199254
\(181\) 5.40767e14 1.14314 0.571570 0.820553i \(-0.306334\pi\)
0.571570 + 0.820553i \(0.306334\pi\)
\(182\) 1.21909e14 0.248641
\(183\) 1.67816e14 0.330295
\(184\) −8.69941e13 −0.165262
\(185\) 1.91720e13 0.0351601
\(186\) 4.74165e14 0.839644
\(187\) 3.91393e14 0.669334
\(188\) −5.77465e14 −0.953894
\(189\) −2.34345e13 −0.0373985
\(190\) −8.74188e14 −1.34805
\(191\) −4.12874e14 −0.615319 −0.307660 0.951496i \(-0.599546\pi\)
−0.307660 + 0.951496i \(0.599546\pi\)
\(192\) −3.66734e11 −0.000528315 0
\(193\) −1.00065e15 −1.39366 −0.696831 0.717235i \(-0.745407\pi\)
−0.696831 + 0.717235i \(0.745407\pi\)
\(194\) −1.68083e15 −2.26367
\(195\) 4.89487e14 0.637552
\(196\) −4.24149e14 −0.534384
\(197\) −1.03802e15 −1.26524 −0.632622 0.774460i \(-0.718021\pi\)
−0.632622 + 0.774460i \(0.718021\pi\)
\(198\) 3.23034e14 0.381000
\(199\) 3.01937e14 0.344645 0.172322 0.985041i \(-0.444873\pi\)
0.172322 + 0.985041i \(0.444873\pi\)
\(200\) 7.95715e13 0.0879150
\(201\) −1.24137e14 −0.132779
\(202\) −2.26190e15 −2.34255
\(203\) −2.96909e14 −0.297783
\(204\) −2.41057e14 −0.234166
\(205\) −1.64083e14 −0.154406
\(206\) 2.11627e15 1.92945
\(207\) −1.12443e14 −0.0993404
\(208\) −1.49409e15 −1.27928
\(209\) −1.10897e15 −0.920380
\(210\) 1.87185e14 0.150607
\(211\) 1.70594e15 1.33085 0.665424 0.746466i \(-0.268251\pi\)
0.665424 + 0.746466i \(0.268251\pi\)
\(212\) −1.31625e14 −0.0995759
\(213\) −1.08368e15 −0.795120
\(214\) −8.44705e13 −0.0601195
\(215\) −5.10602e13 −0.0352560
\(216\) 1.59292e14 0.106720
\(217\) 3.48550e14 0.226609
\(218\) 6.43387e14 0.405980
\(219\) −1.36780e15 −0.837792
\(220\) −9.21310e14 −0.547846
\(221\) −1.29773e15 −0.749261
\(222\) −4.19511e13 −0.0235207
\(223\) 1.57255e14 0.0856294 0.0428147 0.999083i \(-0.486367\pi\)
0.0428147 + 0.999083i \(0.486367\pi\)
\(224\) −3.67617e14 −0.194439
\(225\) 1.02849e14 0.0528463
\(226\) −4.02062e15 −2.00719
\(227\) −1.32918e15 −0.644784 −0.322392 0.946606i \(-0.604487\pi\)
−0.322392 + 0.946606i \(0.604487\pi\)
\(228\) 6.83005e14 0.321994
\(229\) −3.49747e15 −1.60259 −0.801296 0.598268i \(-0.795856\pi\)
−0.801296 + 0.598268i \(0.795856\pi\)
\(230\) 8.98149e14 0.400053
\(231\) 2.37456e14 0.102827
\(232\) 2.01819e15 0.849749
\(233\) −7.41920e14 −0.303769 −0.151884 0.988398i \(-0.548534\pi\)
−0.151884 + 0.988398i \(0.548534\pi\)
\(234\) −1.07107e15 −0.426496
\(235\) −4.77336e15 −1.84877
\(236\) 1.91900e14 0.0723013
\(237\) −1.84341e15 −0.675707
\(238\) −4.96265e14 −0.176996
\(239\) −5.56819e15 −1.93254 −0.966268 0.257539i \(-0.917089\pi\)
−0.966268 + 0.257539i \(0.917089\pi\)
\(240\) −2.29410e15 −0.774888
\(241\) 1.25296e15 0.411933 0.205967 0.978559i \(-0.433966\pi\)
0.205967 + 0.978559i \(0.433966\pi\)
\(242\) 6.23631e14 0.199585
\(243\) 2.05891e14 0.0641500
\(244\) 1.04729e15 0.317713
\(245\) −3.50604e15 −1.03571
\(246\) 3.59039e14 0.103291
\(247\) 3.67695e15 1.03029
\(248\) −2.36921e15 −0.646648
\(249\) −9.79281e14 −0.260382
\(250\) 4.36028e15 1.12955
\(251\) −5.16714e15 −1.30428 −0.652140 0.758099i \(-0.726128\pi\)
−0.652140 + 0.758099i \(0.726128\pi\)
\(252\) −1.46248e14 −0.0359738
\(253\) 1.13936e15 0.273135
\(254\) −8.91011e15 −2.08192
\(255\) −1.99259e15 −0.453844
\(256\) 5.61753e15 1.24734
\(257\) −2.18653e15 −0.473359 −0.236679 0.971588i \(-0.576059\pi\)
−0.236679 + 0.971588i \(0.576059\pi\)
\(258\) 1.11727e14 0.0235848
\(259\) −3.08375e13 −0.00634791
\(260\) 3.05475e15 0.613265
\(261\) 2.60859e15 0.510790
\(262\) −1.23108e16 −2.35142
\(263\) 4.80148e15 0.894670 0.447335 0.894366i \(-0.352373\pi\)
0.447335 + 0.894366i \(0.352373\pi\)
\(264\) −1.61407e15 −0.293425
\(265\) −1.08802e15 −0.192991
\(266\) 1.40610e15 0.243381
\(267\) −1.03443e15 −0.174735
\(268\) −7.74707e14 −0.127721
\(269\) −1.07930e16 −1.73681 −0.868404 0.495858i \(-0.834854\pi\)
−0.868404 + 0.495858i \(0.834854\pi\)
\(270\) −1.64457e15 −0.258338
\(271\) 7.90679e15 1.21255 0.606275 0.795255i \(-0.292663\pi\)
0.606275 + 0.795255i \(0.292663\pi\)
\(272\) 6.08211e15 0.910660
\(273\) −7.87324e14 −0.115106
\(274\) 1.15506e16 1.64901
\(275\) −1.04215e15 −0.145300
\(276\) −7.01726e14 −0.0955561
\(277\) −4.13424e15 −0.549892 −0.274946 0.961460i \(-0.588660\pi\)
−0.274946 + 0.961460i \(0.588660\pi\)
\(278\) −1.06223e16 −1.38015
\(279\) −3.06229e15 −0.388705
\(280\) −9.35288e14 −0.115989
\(281\) 2.12797e15 0.257854 0.128927 0.991654i \(-0.458847\pi\)
0.128927 + 0.991654i \(0.458847\pi\)
\(282\) 1.04448e16 1.23675
\(283\) 8.05949e15 0.932601 0.466300 0.884626i \(-0.345587\pi\)
0.466300 + 0.884626i \(0.345587\pi\)
\(284\) −6.76292e15 −0.764830
\(285\) 5.64576e15 0.624067
\(286\) 1.08529e16 1.17265
\(287\) 2.63923e14 0.0278769
\(288\) 3.22981e15 0.333523
\(289\) −4.62182e15 −0.466635
\(290\) −2.08363e16 −2.05700
\(291\) 1.08553e16 1.04794
\(292\) −8.53606e15 −0.805878
\(293\) −5.20186e15 −0.480307 −0.240153 0.970735i \(-0.577198\pi\)
−0.240153 + 0.970735i \(0.577198\pi\)
\(294\) 7.67174e15 0.692845
\(295\) 1.58625e15 0.140129
\(296\) 2.09613e14 0.0181143
\(297\) −2.08625e15 −0.176380
\(298\) −2.08531e16 −1.72490
\(299\) −3.77773e15 −0.305751
\(300\) 6.41853e14 0.0508332
\(301\) 8.21288e13 0.00636522
\(302\) 2.15114e16 1.63164
\(303\) 1.46080e16 1.08446
\(304\) −1.72329e16 −1.25222
\(305\) 8.65700e15 0.615770
\(306\) 4.36009e15 0.303603
\(307\) −9.62580e15 −0.656202 −0.328101 0.944643i \(-0.606409\pi\)
−0.328101 + 0.944643i \(0.606409\pi\)
\(308\) 1.48190e15 0.0989096
\(309\) −1.36675e16 −0.893220
\(310\) 2.44603e16 1.56535
\(311\) −2.75576e16 −1.72703 −0.863514 0.504325i \(-0.831741\pi\)
−0.863514 + 0.504325i \(0.831741\pi\)
\(312\) 5.35170e15 0.328464
\(313\) 2.39181e16 1.43777 0.718883 0.695131i \(-0.244654\pi\)
0.718883 + 0.695131i \(0.244654\pi\)
\(314\) −1.40248e15 −0.0825763
\(315\) −1.20889e15 −0.0697220
\(316\) −1.15042e16 −0.649967
\(317\) −4.59540e15 −0.254354 −0.127177 0.991880i \(-0.540592\pi\)
−0.127177 + 0.991880i \(0.540592\pi\)
\(318\) 2.38075e15 0.129103
\(319\) −2.64323e16 −1.40441
\(320\) −1.89184e13 −0.000984938 0
\(321\) 5.45535e14 0.0278317
\(322\) −1.44465e15 −0.0722267
\(323\) −1.49680e16 −0.733413
\(324\) 1.28491e15 0.0617063
\(325\) 3.45541e15 0.162651
\(326\) −6.37964e15 −0.294362
\(327\) −4.15518e15 −0.187944
\(328\) −1.79397e15 −0.0795492
\(329\) 7.67781e15 0.333783
\(330\) 1.66641e16 0.710298
\(331\) −2.20324e16 −0.920831 −0.460415 0.887704i \(-0.652300\pi\)
−0.460415 + 0.887704i \(0.652300\pi\)
\(332\) −6.11141e15 −0.250463
\(333\) 2.70933e14 0.0108886
\(334\) 3.31807e16 1.30778
\(335\) −6.40377e15 −0.247539
\(336\) 3.68998e15 0.139900
\(337\) 3.26438e16 1.21397 0.606983 0.794715i \(-0.292380\pi\)
0.606983 + 0.794715i \(0.292380\pi\)
\(338\) −1.79653e15 −0.0655356
\(339\) 2.59664e16 0.929208
\(340\) −1.24352e16 −0.436556
\(341\) 3.10295e16 1.06874
\(342\) −1.23538e16 −0.417475
\(343\) 1.15000e16 0.381318
\(344\) −5.58257e14 −0.0181637
\(345\) −5.80051e15 −0.185200
\(346\) −1.93105e16 −0.605059
\(347\) −2.58464e16 −0.794801 −0.397400 0.917645i \(-0.630088\pi\)
−0.397400 + 0.917645i \(0.630088\pi\)
\(348\) 1.62795e16 0.491332
\(349\) 1.49249e16 0.442127 0.221063 0.975259i \(-0.429047\pi\)
0.221063 + 0.975259i \(0.429047\pi\)
\(350\) 1.32138e15 0.0384226
\(351\) 6.91728e15 0.197442
\(352\) −3.27270e16 −0.917019
\(353\) 3.75129e16 1.03192 0.515958 0.856614i \(-0.327436\pi\)
0.515958 + 0.856614i \(0.327436\pi\)
\(354\) −3.47096e15 −0.0937407
\(355\) −5.59027e16 −1.48234
\(356\) −6.45561e15 −0.168079
\(357\) 3.20502e15 0.0819384
\(358\) 6.71603e16 1.68606
\(359\) 3.72336e16 0.917953 0.458977 0.888448i \(-0.348216\pi\)
0.458977 + 0.888448i \(0.348216\pi\)
\(360\) 8.21726e15 0.198958
\(361\) 3.57124e14 0.00849224
\(362\) −6.10408e16 −1.42566
\(363\) −4.02759e15 −0.0923958
\(364\) −4.91347e15 −0.110721
\(365\) −7.05596e16 −1.56190
\(366\) −1.89428e16 −0.411924
\(367\) 3.69154e16 0.788639 0.394319 0.918973i \(-0.370980\pi\)
0.394319 + 0.918973i \(0.370980\pi\)
\(368\) 1.77053e16 0.371613
\(369\) −2.31878e15 −0.0478176
\(370\) −2.16410e15 −0.0438496
\(371\) 1.75004e15 0.0348432
\(372\) −1.91109e16 −0.373897
\(373\) 5.13533e16 0.987328 0.493664 0.869653i \(-0.335657\pi\)
0.493664 + 0.869653i \(0.335657\pi\)
\(374\) −4.41798e16 −0.834753
\(375\) −2.81600e16 −0.522912
\(376\) −5.21886e16 −0.952478
\(377\) 8.76403e16 1.57212
\(378\) 2.64524e15 0.0466411
\(379\) 3.45756e16 0.599260 0.299630 0.954056i \(-0.403137\pi\)
0.299630 + 0.954056i \(0.403137\pi\)
\(380\) 3.52336e16 0.600293
\(381\) 5.75441e16 0.963803
\(382\) 4.66045e16 0.767389
\(383\) −7.39616e16 −1.19733 −0.598666 0.800999i \(-0.704302\pi\)
−0.598666 + 0.800999i \(0.704302\pi\)
\(384\) −3.62530e16 −0.577021
\(385\) 1.22495e16 0.191700
\(386\) 1.12951e17 1.73809
\(387\) −7.21568e14 −0.0109183
\(388\) 6.77448e16 1.00802
\(389\) 3.29116e16 0.481589 0.240795 0.970576i \(-0.422592\pi\)
0.240795 + 0.970576i \(0.422592\pi\)
\(390\) −5.52523e16 −0.795117
\(391\) 1.53783e16 0.217650
\(392\) −3.83326e16 −0.533591
\(393\) 7.95070e16 1.08856
\(394\) 1.17170e17 1.57794
\(395\) −9.50945e16 −1.25972
\(396\) −1.30197e16 −0.169661
\(397\) −4.79591e15 −0.0614798 −0.0307399 0.999527i \(-0.509786\pi\)
−0.0307399 + 0.999527i \(0.509786\pi\)
\(398\) −3.40821e16 −0.429820
\(399\) −9.08103e15 −0.112671
\(400\) −1.61946e16 −0.197688
\(401\) −1.13071e17 −1.35804 −0.679020 0.734119i \(-0.737595\pi\)
−0.679020 + 0.734119i \(0.737595\pi\)
\(402\) 1.40124e16 0.165594
\(403\) −1.02883e17 −1.19636
\(404\) 9.11643e16 1.04315
\(405\) 1.06211e16 0.119595
\(406\) 3.35146e16 0.371377
\(407\) −2.74530e15 −0.0299382
\(408\) −2.17856e16 −0.233818
\(409\) −1.02879e17 −1.08674 −0.543369 0.839494i \(-0.682852\pi\)
−0.543369 + 0.839494i \(0.682852\pi\)
\(410\) 1.85214e16 0.192566
\(411\) −7.45968e16 −0.763394
\(412\) −8.52949e16 −0.859193
\(413\) −2.55144e15 −0.0252994
\(414\) 1.26924e16 0.123891
\(415\) −5.05173e16 −0.485431
\(416\) 1.08511e17 1.02652
\(417\) 6.86018e16 0.638927
\(418\) 1.25178e17 1.14784
\(419\) −1.30846e17 −1.18132 −0.590661 0.806920i \(-0.701133\pi\)
−0.590661 + 0.806920i \(0.701133\pi\)
\(420\) −7.54437e15 −0.0670660
\(421\) 1.95222e17 1.70881 0.854407 0.519605i \(-0.173921\pi\)
0.854407 + 0.519605i \(0.173921\pi\)
\(422\) −1.92564e17 −1.65975
\(423\) −6.74558e16 −0.572541
\(424\) −1.18956e16 −0.0994281
\(425\) −1.40662e16 −0.115784
\(426\) 1.22323e17 0.991625
\(427\) −1.39245e16 −0.111173
\(428\) 3.40453e15 0.0267715
\(429\) −7.00912e16 −0.542864
\(430\) 5.76358e15 0.0439691
\(431\) −6.29681e16 −0.473171 −0.236586 0.971611i \(-0.576028\pi\)
−0.236586 + 0.971611i \(0.576028\pi\)
\(432\) −3.24195e16 −0.239973
\(433\) −7.19886e16 −0.524919 −0.262460 0.964943i \(-0.584534\pi\)
−0.262460 + 0.964943i \(0.584534\pi\)
\(434\) −3.93437e16 −0.282613
\(435\) 1.34567e17 0.952267
\(436\) −2.59313e16 −0.180785
\(437\) −4.35725e16 −0.299284
\(438\) 1.54395e17 1.04484
\(439\) 2.01569e16 0.134402 0.0672008 0.997739i \(-0.478593\pi\)
0.0672008 + 0.997739i \(0.478593\pi\)
\(440\) −8.32636e16 −0.547032
\(441\) −4.95463e16 −0.320746
\(442\) 1.46485e17 0.934433
\(443\) −1.48799e17 −0.935351 −0.467676 0.883900i \(-0.654908\pi\)
−0.467676 + 0.883900i \(0.654908\pi\)
\(444\) 1.69081e15 0.0104739
\(445\) −5.33624e16 −0.325758
\(446\) −1.77507e16 −0.106792
\(447\) 1.34675e17 0.798526
\(448\) 3.04296e13 0.000177824 0
\(449\) 1.70580e17 0.982485 0.491242 0.871023i \(-0.336543\pi\)
0.491242 + 0.871023i \(0.336543\pi\)
\(450\) −1.16094e16 −0.0659067
\(451\) 2.34957e16 0.131474
\(452\) 1.62049e17 0.893811
\(453\) −1.38927e17 −0.755350
\(454\) 1.50035e17 0.804135
\(455\) −4.06150e16 −0.214591
\(456\) 6.17268e16 0.321516
\(457\) −1.64203e17 −0.843190 −0.421595 0.906784i \(-0.638530\pi\)
−0.421595 + 0.906784i \(0.638530\pi\)
\(458\) 3.94788e17 1.99866
\(459\) −2.81587e16 −0.140550
\(460\) −3.61993e16 −0.178145
\(461\) −2.46285e17 −1.19504 −0.597519 0.801855i \(-0.703847\pi\)
−0.597519 + 0.801855i \(0.703847\pi\)
\(462\) −2.68036e16 −0.128239
\(463\) −1.89854e17 −0.895659 −0.447829 0.894119i \(-0.647803\pi\)
−0.447829 + 0.894119i \(0.647803\pi\)
\(464\) −4.10747e17 −1.91077
\(465\) −1.57972e17 −0.724662
\(466\) 8.37465e16 0.378842
\(467\) −3.77881e17 −1.68576 −0.842880 0.538102i \(-0.819141\pi\)
−0.842880 + 0.538102i \(0.819141\pi\)
\(468\) 4.31688e16 0.189920
\(469\) 1.03003e16 0.0446915
\(470\) 5.38808e17 2.30568
\(471\) 9.05765e15 0.0382278
\(472\) 1.73430e16 0.0721939
\(473\) 7.31149e15 0.0300198
\(474\) 2.08081e17 0.842701
\(475\) 3.98548e16 0.159211
\(476\) 2.00016e16 0.0788170
\(477\) −1.53755e16 −0.0597669
\(478\) 6.28527e17 2.41014
\(479\) −2.06918e17 −0.782738 −0.391369 0.920234i \(-0.627998\pi\)
−0.391369 + 0.920234i \(0.627998\pi\)
\(480\) 1.66614e17 0.621788
\(481\) 9.10247e15 0.0335132
\(482\) −1.41432e17 −0.513738
\(483\) 9.32994e15 0.0334366
\(484\) −2.51350e16 −0.0888760
\(485\) 5.59982e17 1.95368
\(486\) −2.32406e16 −0.0800040
\(487\) 2.82990e17 0.961241 0.480620 0.876929i \(-0.340412\pi\)
0.480620 + 0.876929i \(0.340412\pi\)
\(488\) 9.46496e16 0.317241
\(489\) 4.12015e16 0.136272
\(490\) 3.95755e17 1.29167
\(491\) 5.16102e17 1.66229 0.831144 0.556057i \(-0.187687\pi\)
0.831144 + 0.556057i \(0.187687\pi\)
\(492\) −1.44708e16 −0.0459961
\(493\) −3.56764e17 −1.11912
\(494\) −4.15047e17 −1.28491
\(495\) −1.07621e17 −0.328825
\(496\) 4.82187e17 1.45407
\(497\) 8.99177e16 0.267626
\(498\) 1.10539e17 0.324733
\(499\) −4.45068e17 −1.29054 −0.645272 0.763953i \(-0.723256\pi\)
−0.645272 + 0.763953i \(0.723256\pi\)
\(500\) −1.75738e17 −0.502992
\(501\) −2.14291e17 −0.605422
\(502\) 5.83257e17 1.62662
\(503\) −5.08695e16 −0.140044 −0.0700221 0.997545i \(-0.522307\pi\)
−0.0700221 + 0.997545i \(0.522307\pi\)
\(504\) −1.32172e16 −0.0359204
\(505\) 7.53569e17 2.02176
\(506\) −1.28609e17 −0.340638
\(507\) 1.16025e16 0.0303390
\(508\) 3.59116e17 0.927088
\(509\) −5.39326e17 −1.37463 −0.687315 0.726359i \(-0.741211\pi\)
−0.687315 + 0.726359i \(0.741211\pi\)
\(510\) 2.24920e17 0.566007
\(511\) 1.13493e17 0.281989
\(512\) −2.26710e17 −0.556181
\(513\) 7.97843e16 0.193266
\(514\) 2.46812e17 0.590345
\(515\) −7.05052e17 −1.66523
\(516\) −4.50310e15 −0.0105024
\(517\) 6.83514e17 1.57420
\(518\) 3.48088e15 0.00791673
\(519\) 1.24713e17 0.280106
\(520\) 2.76074e17 0.612355
\(521\) −1.85031e17 −0.405321 −0.202660 0.979249i \(-0.564959\pi\)
−0.202660 + 0.979249i \(0.564959\pi\)
\(522\) −2.94453e17 −0.637027
\(523\) 5.78358e16 0.123577 0.0617883 0.998089i \(-0.480320\pi\)
0.0617883 + 0.998089i \(0.480320\pi\)
\(524\) 4.96181e17 1.04710
\(525\) −8.53388e15 −0.0177873
\(526\) −5.41983e17 −1.11578
\(527\) 4.18815e17 0.851634
\(528\) 3.28500e17 0.659803
\(529\) −4.59270e17 −0.911183
\(530\) 1.22813e17 0.240687
\(531\) 2.24165e16 0.0433963
\(532\) −5.66722e16 −0.108379
\(533\) −7.79036e16 −0.147174
\(534\) 1.16765e17 0.217919
\(535\) 2.81420e16 0.0518867
\(536\) −7.00144e16 −0.127531
\(537\) −4.33741e17 −0.780544
\(538\) 1.21829e18 2.16604
\(539\) 5.02042e17 0.881886
\(540\) 6.62834e16 0.115039
\(541\) −9.84842e17 −1.68882 −0.844412 0.535695i \(-0.820050\pi\)
−0.844412 + 0.535695i \(0.820050\pi\)
\(542\) −8.92504e17 −1.51222
\(543\) 3.94219e17 0.659992
\(544\) −4.41726e17 −0.730735
\(545\) −2.14349e17 −0.350385
\(546\) 8.88717e16 0.143553
\(547\) −5.30697e17 −0.847089 −0.423545 0.905875i \(-0.639214\pi\)
−0.423545 + 0.905875i \(0.639214\pi\)
\(548\) −4.65538e17 −0.734313
\(549\) 1.22338e17 0.190696
\(550\) 1.17636e17 0.181210
\(551\) 1.01085e18 1.53886
\(552\) −6.34187e16 −0.0954143
\(553\) 1.52957e17 0.227434
\(554\) 4.66666e17 0.685792
\(555\) 1.39764e16 0.0202997
\(556\) 4.28124e17 0.614587
\(557\) 2.55005e17 0.361818 0.180909 0.983500i \(-0.442096\pi\)
0.180909 + 0.983500i \(0.442096\pi\)
\(558\) 3.45666e17 0.484769
\(559\) −2.42424e16 −0.0336046
\(560\) 1.90352e17 0.260817
\(561\) 2.85326e17 0.386440
\(562\) −2.40201e17 −0.321580
\(563\) 2.29203e17 0.303331 0.151665 0.988432i \(-0.451536\pi\)
0.151665 + 0.988432i \(0.451536\pi\)
\(564\) −4.20972e17 −0.550731
\(565\) 1.33950e18 1.73232
\(566\) −9.09740e17 −1.16308
\(567\) −1.70837e16 −0.0215920
\(568\) −6.11201e17 −0.763695
\(569\) 3.00295e17 0.370953 0.185477 0.982649i \(-0.440617\pi\)
0.185477 + 0.982649i \(0.440617\pi\)
\(570\) −6.37283e17 −0.778298
\(571\) −2.35916e17 −0.284854 −0.142427 0.989805i \(-0.545491\pi\)
−0.142427 + 0.989805i \(0.545491\pi\)
\(572\) −4.37419e17 −0.522184
\(573\) −3.00985e17 −0.355255
\(574\) −2.97912e16 −0.0347664
\(575\) −4.09472e16 −0.0472480
\(576\) −2.67349e14 −0.000305023 0
\(577\) 4.01859e17 0.453348 0.226674 0.973971i \(-0.427215\pi\)
0.226674 + 0.973971i \(0.427215\pi\)
\(578\) 5.21703e17 0.581959
\(579\) −7.29470e17 −0.804631
\(580\) 8.39795e17 0.915991
\(581\) 8.12555e16 0.0876411
\(582\) −1.22532e18 −1.30693
\(583\) 1.55797e17 0.164329
\(584\) −7.71449e17 −0.804681
\(585\) 3.56836e17 0.368091
\(586\) 5.87176e17 0.599010
\(587\) −3.28742e17 −0.331671 −0.165836 0.986153i \(-0.553032\pi\)
−0.165836 + 0.986153i \(0.553032\pi\)
\(588\) −3.09205e17 −0.308527
\(589\) −1.18666e18 −1.17105
\(590\) −1.79053e17 −0.174761
\(591\) −7.56715e17 −0.730489
\(592\) −4.26609e16 −0.0407323
\(593\) −3.60972e17 −0.340893 −0.170447 0.985367i \(-0.554521\pi\)
−0.170447 + 0.985367i \(0.554521\pi\)
\(594\) 2.35492e17 0.219970
\(595\) 1.65335e17 0.152758
\(596\) 8.40471e17 0.768107
\(597\) 2.20112e17 0.198981
\(598\) 4.26423e17 0.381315
\(599\) −5.53752e17 −0.489825 −0.244912 0.969545i \(-0.578759\pi\)
−0.244912 + 0.969545i \(0.578759\pi\)
\(600\) 5.80077e16 0.0507577
\(601\) 3.16392e17 0.273868 0.136934 0.990580i \(-0.456275\pi\)
0.136934 + 0.990580i \(0.456275\pi\)
\(602\) −9.27055e15 −0.00793831
\(603\) −9.04962e16 −0.0766598
\(604\) −8.67004e17 −0.726576
\(605\) −2.07768e17 −0.172253
\(606\) −1.64892e18 −1.35247
\(607\) −1.18964e18 −0.965360 −0.482680 0.875797i \(-0.660337\pi\)
−0.482680 + 0.875797i \(0.660337\pi\)
\(608\) 1.25158e18 1.00481
\(609\) −2.16447e17 −0.171925
\(610\) −9.77186e17 −0.767951
\(611\) −2.26630e18 −1.76218
\(612\) −1.75731e17 −0.135196
\(613\) 5.22634e17 0.397836 0.198918 0.980016i \(-0.436257\pi\)
0.198918 + 0.980016i \(0.436257\pi\)
\(614\) 1.08654e18 0.818375
\(615\) −1.19617e17 −0.0891464
\(616\) 1.33927e17 0.0987628
\(617\) 4.74752e16 0.0346428 0.0173214 0.999850i \(-0.494486\pi\)
0.0173214 + 0.999850i \(0.494486\pi\)
\(618\) 1.54276e18 1.11397
\(619\) −2.02115e18 −1.44414 −0.722070 0.691820i \(-0.756809\pi\)
−0.722070 + 0.691820i \(0.756809\pi\)
\(620\) −9.85858e17 −0.697057
\(621\) −8.19711e16 −0.0573542
\(622\) 3.11065e18 2.15384
\(623\) 8.58318e16 0.0588134
\(624\) −1.08919e18 −0.738592
\(625\) −1.68890e18 −1.13340
\(626\) −2.69983e18 −1.79309
\(627\) −8.08436e17 −0.531382
\(628\) 5.65262e16 0.0367716
\(629\) −3.70541e16 −0.0238565
\(630\) 1.36458e17 0.0869531
\(631\) 3.30428e17 0.208394 0.104197 0.994557i \(-0.466773\pi\)
0.104197 + 0.994557i \(0.466773\pi\)
\(632\) −1.03970e18 −0.649002
\(633\) 1.24363e18 0.768365
\(634\) 5.18721e17 0.317215
\(635\) 2.96848e18 1.79682
\(636\) −9.59544e16 −0.0574902
\(637\) −1.66460e18 −0.987195
\(638\) 2.98362e18 1.75150
\(639\) −7.90001e17 −0.459062
\(640\) −1.87015e18 −1.07574
\(641\) 1.91323e18 1.08941 0.544704 0.838629i \(-0.316642\pi\)
0.544704 + 0.838629i \(0.316642\pi\)
\(642\) −6.15790e16 −0.0347100
\(643\) 2.29819e18 1.28237 0.641186 0.767386i \(-0.278443\pi\)
0.641186 + 0.767386i \(0.278443\pi\)
\(644\) 5.82255e16 0.0321629
\(645\) −3.72229e16 −0.0203550
\(646\) 1.68956e18 0.914668
\(647\) 1.04365e18 0.559344 0.279672 0.960096i \(-0.409774\pi\)
0.279672 + 0.960096i \(0.409774\pi\)
\(648\) 1.16124e17 0.0616147
\(649\) −2.27141e17 −0.119318
\(650\) −3.90040e17 −0.202849
\(651\) 2.54093e17 0.130833
\(652\) 2.57127e17 0.131081
\(653\) −2.93783e18 −1.48283 −0.741413 0.671049i \(-0.765844\pi\)
−0.741413 + 0.671049i \(0.765844\pi\)
\(654\) 4.69029e17 0.234393
\(655\) 4.10146e18 2.02941
\(656\) 3.65114e17 0.178877
\(657\) −9.97128e17 −0.483700
\(658\) −8.66657e17 −0.416274
\(659\) 3.86883e18 1.84003 0.920014 0.391886i \(-0.128177\pi\)
0.920014 + 0.391886i \(0.128177\pi\)
\(660\) −6.71635e17 −0.316299
\(661\) −3.25119e18 −1.51612 −0.758059 0.652186i \(-0.773852\pi\)
−0.758059 + 0.652186i \(0.773852\pi\)
\(662\) 2.48698e18 1.14840
\(663\) −9.46042e17 −0.432586
\(664\) −5.52321e17 −0.250091
\(665\) −4.68455e17 −0.210052
\(666\) −3.05824e16 −0.0135797
\(667\) −1.03855e18 −0.456679
\(668\) −1.33733e18 −0.582359
\(669\) 1.14639e17 0.0494382
\(670\) 7.22846e17 0.308716
\(671\) −1.23962e18 −0.524317
\(672\) −2.67993e17 −0.112259
\(673\) −1.43947e18 −0.597179 −0.298590 0.954382i \(-0.596516\pi\)
−0.298590 + 0.954382i \(0.596516\pi\)
\(674\) −3.68477e18 −1.51398
\(675\) 7.49771e16 0.0305108
\(676\) 7.24082e16 0.0291833
\(677\) 4.50455e18 1.79815 0.899073 0.437799i \(-0.144242\pi\)
0.899073 + 0.437799i \(0.144242\pi\)
\(678\) −2.93103e18 −1.15885
\(679\) −9.00714e17 −0.352723
\(680\) −1.12383e18 −0.435907
\(681\) −9.68969e17 −0.372266
\(682\) −3.50256e18 −1.33287
\(683\) −3.11602e18 −1.17453 −0.587267 0.809393i \(-0.699796\pi\)
−0.587267 + 0.809393i \(0.699796\pi\)
\(684\) 4.97911e17 0.185903
\(685\) −3.84816e18 −1.42320
\(686\) −1.29810e18 −0.475557
\(687\) −2.54965e18 −0.925257
\(688\) 1.13618e17 0.0408434
\(689\) −5.16569e17 −0.183952
\(690\) 6.54751e17 0.230971
\(691\) −2.28134e18 −0.797227 −0.398613 0.917119i \(-0.630508\pi\)
−0.398613 + 0.917119i \(0.630508\pi\)
\(692\) 7.78295e17 0.269436
\(693\) 1.73106e17 0.0593670
\(694\) 2.91749e18 0.991228
\(695\) 3.53890e18 1.19115
\(696\) 1.47126e18 0.490603
\(697\) 3.17128e17 0.104766
\(698\) −1.68470e18 −0.551394
\(699\) −5.40859e17 −0.175381
\(700\) −5.32575e16 −0.0171098
\(701\) 2.07987e18 0.662016 0.331008 0.943628i \(-0.392611\pi\)
0.331008 + 0.943628i \(0.392611\pi\)
\(702\) −7.80810e17 −0.246238
\(703\) 1.04988e17 0.0328043
\(704\) 2.70899e15 0.000838657 0
\(705\) −3.47978e18 −1.06739
\(706\) −4.23438e18 −1.28694
\(707\) −1.21209e18 −0.365014
\(708\) 1.39895e17 0.0417432
\(709\) −4.44743e18 −1.31495 −0.657474 0.753477i \(-0.728375\pi\)
−0.657474 + 0.753477i \(0.728375\pi\)
\(710\) 6.31019e18 1.84869
\(711\) −1.34385e18 −0.390120
\(712\) −5.83428e17 −0.167829
\(713\) 1.21919e18 0.347527
\(714\) −3.61777e17 −0.102189
\(715\) −3.61573e18 −1.01206
\(716\) −2.70685e18 −0.750810
\(717\) −4.05921e18 −1.11575
\(718\) −4.20286e18 −1.14482
\(719\) −4.13508e18 −1.11621 −0.558105 0.829770i \(-0.688471\pi\)
−0.558105 + 0.829770i \(0.688471\pi\)
\(720\) −1.67240e18 −0.447382
\(721\) 1.13405e18 0.300646
\(722\) −4.03115e16 −0.0105910
\(723\) 9.13409e17 0.237830
\(724\) 2.46021e18 0.634851
\(725\) 9.49942e17 0.242940
\(726\) 4.54627e17 0.115230
\(727\) 2.82326e18 0.709214 0.354607 0.935016i \(-0.384615\pi\)
0.354607 + 0.935016i \(0.384615\pi\)
\(728\) −4.44056e17 −0.110556
\(729\) 1.50095e17 0.0370370
\(730\) 7.96464e18 1.94790
\(731\) 9.86853e16 0.0239216
\(732\) 7.63478e17 0.183432
\(733\) −1.09963e18 −0.261862 −0.130931 0.991391i \(-0.541797\pi\)
−0.130931 + 0.991391i \(0.541797\pi\)
\(734\) −4.16694e18 −0.983543
\(735\) −2.55590e18 −0.597966
\(736\) −1.28588e18 −0.298191
\(737\) 9.16977e17 0.210775
\(738\) 2.61740e17 0.0596352
\(739\) −3.16812e18 −0.715506 −0.357753 0.933816i \(-0.616457\pi\)
−0.357753 + 0.933816i \(0.616457\pi\)
\(740\) 8.72225e16 0.0195264
\(741\) 2.68050e18 0.594835
\(742\) −1.97542e17 −0.0434543
\(743\) −6.30790e18 −1.37549 −0.687745 0.725952i \(-0.741399\pi\)
−0.687745 + 0.725952i \(0.741399\pi\)
\(744\) −1.72715e18 −0.373342
\(745\) 6.94738e18 1.48869
\(746\) −5.79667e18 −1.23134
\(747\) −7.13896e17 −0.150332
\(748\) 1.78064e18 0.371719
\(749\) −4.52656e16 −0.00936777
\(750\) 3.17864e18 0.652144
\(751\) 1.38416e18 0.281531 0.140765 0.990043i \(-0.455044\pi\)
0.140765 + 0.990043i \(0.455044\pi\)
\(752\) 1.06216e19 2.14177
\(753\) −3.76684e18 −0.753026
\(754\) −9.89267e18 −1.96065
\(755\) −7.16671e18 −1.40820
\(756\) −1.06615e17 −0.0207695
\(757\) 1.50601e18 0.290873 0.145436 0.989368i \(-0.453541\pi\)
0.145436 + 0.989368i \(0.453541\pi\)
\(758\) −3.90283e18 −0.747360
\(759\) 8.30594e17 0.157695
\(760\) 3.18425e18 0.599402
\(761\) −5.30144e17 −0.0989450 −0.0494725 0.998775i \(-0.515754\pi\)
−0.0494725 + 0.998775i \(0.515754\pi\)
\(762\) −6.49547e18 −1.20200
\(763\) 3.44775e17 0.0632595
\(764\) −1.87836e18 −0.341722
\(765\) −1.45260e18 −0.262027
\(766\) 8.34866e18 1.49324
\(767\) 7.53121e17 0.133566
\(768\) 4.09518e18 0.720154
\(769\) 8.41617e18 1.46755 0.733776 0.679391i \(-0.237756\pi\)
0.733776 + 0.679391i \(0.237756\pi\)
\(770\) −1.38270e18 −0.239077
\(771\) −1.59398e18 −0.273294
\(772\) −4.55242e18 −0.773980
\(773\) −5.35077e18 −0.902090 −0.451045 0.892501i \(-0.648949\pi\)
−0.451045 + 0.892501i \(0.648949\pi\)
\(774\) 8.14493e16 0.0136167
\(775\) −1.11516e18 −0.184874
\(776\) 6.12245e18 1.00652
\(777\) −2.24806e16 −0.00366497
\(778\) −3.71500e18 −0.600609
\(779\) −8.98543e17 −0.144061
\(780\) 2.22691e18 0.354069
\(781\) 8.00489e18 1.26219
\(782\) −1.73587e18 −0.271440
\(783\) 1.90166e18 0.294905
\(784\) 7.80154e18 1.19985
\(785\) 4.67249e17 0.0712682
\(786\) −8.97460e18 −1.35759
\(787\) 1.03442e19 1.55189 0.775947 0.630798i \(-0.217272\pi\)
0.775947 + 0.630798i \(0.217272\pi\)
\(788\) −4.72245e18 −0.702662
\(789\) 3.50028e18 0.516538
\(790\) 1.07341e19 1.57105
\(791\) −2.15455e18 −0.312759
\(792\) −1.17666e18 −0.169409
\(793\) 4.11017e18 0.586927
\(794\) 5.41353e17 0.0766739
\(795\) −7.93164e17 −0.111424
\(796\) 1.37366e18 0.191401
\(797\) 2.65964e18 0.367573 0.183786 0.982966i \(-0.441165\pi\)
0.183786 + 0.982966i \(0.441165\pi\)
\(798\) 1.02505e18 0.140516
\(799\) 9.22559e18 1.25441
\(800\) 1.17617e18 0.158629
\(801\) −7.54102e17 −0.100883
\(802\) 1.27632e19 1.69367
\(803\) 1.01037e19 1.32993
\(804\) −5.64761e17 −0.0737396
\(805\) 4.81295e17 0.0623359
\(806\) 1.16133e19 1.49203
\(807\) −7.86808e18 −1.00275
\(808\) 8.23900e18 1.04160
\(809\) −6.86795e18 −0.861314 −0.430657 0.902516i \(-0.641718\pi\)
−0.430657 + 0.902516i \(0.641718\pi\)
\(810\) −1.19889e18 −0.149152
\(811\) 3.89506e18 0.480705 0.240352 0.970686i \(-0.422737\pi\)
0.240352 + 0.970686i \(0.422737\pi\)
\(812\) −1.35078e18 −0.165376
\(813\) 5.76405e18 0.700067
\(814\) 3.09884e17 0.0373371
\(815\) 2.12543e18 0.254052
\(816\) 4.43386e18 0.525770
\(817\) −2.79613e17 −0.0328938
\(818\) 1.16128e19 1.35531
\(819\) −5.73959e17 −0.0664562
\(820\) −7.46495e17 −0.0857505
\(821\) 3.11330e18 0.354806 0.177403 0.984138i \(-0.443230\pi\)
0.177403 + 0.984138i \(0.443230\pi\)
\(822\) 8.42035e18 0.952058
\(823\) −1.17761e19 −1.32100 −0.660501 0.750825i \(-0.729656\pi\)
−0.660501 + 0.750825i \(0.729656\pi\)
\(824\) −7.70855e18 −0.857918
\(825\) −7.59726e17 −0.0838892
\(826\) 2.88002e17 0.0315518
\(827\) −6.06239e18 −0.658958 −0.329479 0.944163i \(-0.606873\pi\)
−0.329479 + 0.944163i \(0.606873\pi\)
\(828\) −5.11558e17 −0.0551694
\(829\) 9.26464e18 0.991343 0.495672 0.868510i \(-0.334922\pi\)
0.495672 + 0.868510i \(0.334922\pi\)
\(830\) 5.70230e18 0.605400
\(831\) −3.01386e18 −0.317480
\(832\) −8.98207e15 −0.000938804 0
\(833\) 6.77621e18 0.702739
\(834\) −7.74364e18 −0.796831
\(835\) −1.10544e19 −1.12869
\(836\) −5.04522e18 −0.511139
\(837\) −2.23241e18 −0.224419
\(838\) 1.47696e19 1.47327
\(839\) 1.26271e19 1.24983 0.624917 0.780691i \(-0.285133\pi\)
0.624917 + 0.780691i \(0.285133\pi\)
\(840\) −6.81825e17 −0.0669665
\(841\) 1.38330e19 1.34816
\(842\) −2.20363e19 −2.13113
\(843\) 1.55129e18 0.148872
\(844\) 7.76115e18 0.739095
\(845\) 5.98530e17 0.0565610
\(846\) 7.61428e18 0.714039
\(847\) 3.34188e17 0.0310991
\(848\) 2.42103e18 0.223577
\(849\) 5.87537e18 0.538437
\(850\) 1.58777e18 0.144399
\(851\) −1.07866e17 −0.00973514
\(852\) −4.93017e18 −0.441575
\(853\) 1.35794e18 0.120702 0.0603508 0.998177i \(-0.480778\pi\)
0.0603508 + 0.998177i \(0.480778\pi\)
\(854\) 1.57177e18 0.138648
\(855\) 4.11576e18 0.360305
\(856\) 3.07685e17 0.0267317
\(857\) 1.32280e18 0.114056 0.0570280 0.998373i \(-0.481838\pi\)
0.0570280 + 0.998373i \(0.481838\pi\)
\(858\) 7.91177e18 0.677027
\(859\) 4.68816e18 0.398150 0.199075 0.979984i \(-0.436206\pi\)
0.199075 + 0.979984i \(0.436206\pi\)
\(860\) −2.32298e17 −0.0195796
\(861\) 1.92400e17 0.0160948
\(862\) 7.10772e18 0.590111
\(863\) 1.90241e19 1.56759 0.783797 0.621017i \(-0.213280\pi\)
0.783797 + 0.621017i \(0.213280\pi\)
\(864\) 2.35453e18 0.192560
\(865\) 6.43343e18 0.522202
\(866\) 8.12595e18 0.654648
\(867\) −3.36931e18 −0.269412
\(868\) 1.58572e18 0.125849
\(869\) 1.36169e19 1.07263
\(870\) −1.51897e19 −1.18761
\(871\) −3.04038e18 −0.235945
\(872\) −2.34355e18 −0.180516
\(873\) 7.91350e18 0.605029
\(874\) 4.91839e18 0.373249
\(875\) 2.33656e18 0.176005
\(876\) −6.22279e18 −0.465274
\(877\) 1.15848e19 0.859785 0.429893 0.902880i \(-0.358551\pi\)
0.429893 + 0.902880i \(0.358551\pi\)
\(878\) −2.27527e18 −0.167617
\(879\) −3.79215e18 −0.277305
\(880\) 1.69460e19 1.23007
\(881\) −2.59103e19 −1.86693 −0.933465 0.358667i \(-0.883231\pi\)
−0.933465 + 0.358667i \(0.883231\pi\)
\(882\) 5.59270e18 0.400014
\(883\) −3.41825e18 −0.242694 −0.121347 0.992610i \(-0.538721\pi\)
−0.121347 + 0.992610i \(0.538721\pi\)
\(884\) −5.90398e18 −0.416107
\(885\) 1.15638e18 0.0809038
\(886\) 1.67961e19 1.16651
\(887\) −5.83477e18 −0.402272 −0.201136 0.979563i \(-0.564463\pi\)
−0.201136 + 0.979563i \(0.564463\pi\)
\(888\) 1.52808e17 0.0104583
\(889\) −4.77470e18 −0.324403
\(890\) 6.02345e18 0.406266
\(891\) −1.52087e18 −0.101833
\(892\) 7.15429e17 0.0475549
\(893\) −2.61396e19 −1.72490
\(894\) −1.52019e19 −0.995874
\(895\) −2.23750e19 −1.45517
\(896\) 3.00808e18 0.194217
\(897\) −2.75397e18 −0.176526
\(898\) −1.92547e19 −1.22530
\(899\) −2.82841e19 −1.78692
\(900\) 4.67911e17 0.0293486
\(901\) 2.10284e18 0.130947
\(902\) −2.65215e18 −0.163966
\(903\) 5.98719e16 0.00367496
\(904\) 1.46452e19 0.892484
\(905\) 2.03362e19 1.23042
\(906\) 1.56818e19 0.942027
\(907\) 8.30355e18 0.495241 0.247620 0.968857i \(-0.420351\pi\)
0.247620 + 0.968857i \(0.420351\pi\)
\(908\) −6.04706e18 −0.358085
\(909\) 1.06492e19 0.626113
\(910\) 4.58455e18 0.267625
\(911\) 4.71643e18 0.273366 0.136683 0.990615i \(-0.456356\pi\)
0.136683 + 0.990615i \(0.456356\pi\)
\(912\) −1.25628e19 −0.722969
\(913\) 7.23374e18 0.413336
\(914\) 1.85349e19 1.05158
\(915\) 6.31095e18 0.355515
\(916\) −1.59117e19 −0.890010
\(917\) −6.59707e18 −0.366396
\(918\) 3.17850e18 0.175285
\(919\) −1.67823e19 −0.918968 −0.459484 0.888186i \(-0.651966\pi\)
−0.459484 + 0.888186i \(0.651966\pi\)
\(920\) −3.27152e18 −0.177881
\(921\) −7.01721e18 −0.378858
\(922\) 2.78002e19 1.49038
\(923\) −2.65415e19 −1.41291
\(924\) 1.08030e18 0.0571055
\(925\) 9.86626e16 0.00517882
\(926\) 2.14303e19 1.11701
\(927\) −9.96359e18 −0.515701
\(928\) 2.98314e19 1.53324
\(929\) −4.47502e18 −0.228398 −0.114199 0.993458i \(-0.536430\pi\)
−0.114199 + 0.993458i \(0.536430\pi\)
\(930\) 1.78316e19 0.903755
\(931\) −1.91996e19 −0.966314
\(932\) −3.37535e18 −0.168700
\(933\) −2.00895e19 −0.997100
\(934\) 4.26545e19 2.10238
\(935\) 1.47188e19 0.720441
\(936\) 3.90139e18 0.189639
\(937\) 2.18745e19 1.05592 0.527959 0.849270i \(-0.322957\pi\)
0.527959 + 0.849270i \(0.322957\pi\)
\(938\) −1.16268e18 −0.0557365
\(939\) 1.74363e19 0.830095
\(940\) −2.17163e19 −1.02673
\(941\) 3.27197e19 1.53630 0.768151 0.640269i \(-0.221177\pi\)
0.768151 + 0.640269i \(0.221177\pi\)
\(942\) −1.02241e18 −0.0476754
\(943\) 9.23172e17 0.0427520
\(944\) −3.52969e18 −0.162337
\(945\) −8.81284e17 −0.0402540
\(946\) −8.25307e17 −0.0374389
\(947\) −3.33673e19 −1.50330 −0.751652 0.659560i \(-0.770743\pi\)
−0.751652 + 0.659560i \(0.770743\pi\)
\(948\) −8.38658e18 −0.375259
\(949\) −3.35003e19 −1.48874
\(950\) −4.49874e18 −0.198558
\(951\) −3.35005e18 −0.146851
\(952\) 1.80765e18 0.0787000
\(953\) 1.58341e18 0.0684682 0.0342341 0.999414i \(-0.489101\pi\)
0.0342341 + 0.999414i \(0.489101\pi\)
\(954\) 1.73556e18 0.0745377
\(955\) −1.55267e19 −0.662302
\(956\) −2.53324e19 −1.07325
\(957\) −1.92691e19 −0.810838
\(958\) 2.33565e19 0.976183
\(959\) 6.18965e18 0.256948
\(960\) −1.37915e16 −0.000568654 0
\(961\) 8.78595e18 0.359821
\(962\) −1.02747e18 −0.0417957
\(963\) 3.97695e17 0.0160686
\(964\) 5.70033e18 0.228770
\(965\) −3.76305e19 −1.50008
\(966\) −1.05315e18 −0.0417001
\(967\) 1.74059e19 0.684579 0.342290 0.939595i \(-0.388798\pi\)
0.342290 + 0.939595i \(0.388798\pi\)
\(968\) −2.27159e18 −0.0887441
\(969\) −1.09117e19 −0.423436
\(970\) −6.32097e19 −2.43651
\(971\) 4.41500e18 0.169046 0.0845231 0.996422i \(-0.473063\pi\)
0.0845231 + 0.996422i \(0.473063\pi\)
\(972\) 9.36698e17 0.0356261
\(973\) −5.69221e18 −0.215054
\(974\) −3.19433e19 −1.19880
\(975\) 2.51899e18 0.0939067
\(976\) −1.92633e19 −0.713357
\(977\) −3.40810e19 −1.25371 −0.626856 0.779135i \(-0.715658\pi\)
−0.626856 + 0.779135i \(0.715658\pi\)
\(978\) −4.65075e18 −0.169950
\(979\) 7.64115e18 0.277377
\(980\) −1.59507e19 −0.575187
\(981\) −3.02912e18 −0.108510
\(982\) −5.82567e19 −2.07310
\(983\) −1.48223e19 −0.523983 −0.261992 0.965070i \(-0.584379\pi\)
−0.261992 + 0.965070i \(0.584379\pi\)
\(984\) −1.30781e18 −0.0459278
\(985\) −3.90360e19 −1.36185
\(986\) 4.02709e19 1.39570
\(987\) 5.59712e18 0.192710
\(988\) 1.67282e19 0.572176
\(989\) 2.87277e17 0.00976168
\(990\) 1.21481e19 0.410091
\(991\) 3.49904e18 0.117347 0.0586733 0.998277i \(-0.481313\pi\)
0.0586733 + 0.998277i \(0.481313\pi\)
\(992\) −3.50199e19 −1.16678
\(993\) −1.60616e19 −0.531642
\(994\) −1.01498e19 −0.333767
\(995\) 1.13547e19 0.370960
\(996\) −4.45522e18 −0.144605
\(997\) 8.94587e18 0.288472 0.144236 0.989543i \(-0.453928\pi\)
0.144236 + 0.989543i \(0.453928\pi\)
\(998\) 5.02385e19 1.60949
\(999\) 1.97510e17 0.00628656
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.1.7 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.7 30 1.1 even 1 trivial