Properties

Label 177.14.a.a.1.9
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 1.9
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-102.341 q^{2} +729.000 q^{3} +2281.63 q^{4} +1529.46 q^{5} -74606.4 q^{6} -106408. q^{7} +604872. q^{8} +531441. q^{9} +O(q^{10})\) \(q-102.341 q^{2} +729.000 q^{3} +2281.63 q^{4} +1529.46 q^{5} -74606.4 q^{6} -106408. q^{7} +604872. q^{8} +531441. q^{9} -156526. q^{10} +6.31074e6 q^{11} +1.66331e6 q^{12} +2.25991e7 q^{13} +1.08898e7 q^{14} +1.11498e6 q^{15} -8.05941e7 q^{16} -5.20100e7 q^{17} -5.43881e7 q^{18} -1.84618e8 q^{19} +3.48966e6 q^{20} -7.75713e7 q^{21} -6.45845e8 q^{22} +9.02060e8 q^{23} +4.40952e8 q^{24} -1.21836e9 q^{25} -2.31281e9 q^{26} +3.87420e8 q^{27} -2.42783e8 q^{28} -6.01315e9 q^{29} -1.14107e8 q^{30} +4.64702e8 q^{31} +3.29295e9 q^{32} +4.60053e9 q^{33} +5.32274e9 q^{34} -1.62746e8 q^{35} +1.21255e9 q^{36} -3.80685e9 q^{37} +1.88940e10 q^{38} +1.64747e10 q^{39} +9.25127e8 q^{40} +4.44026e10 q^{41} +7.93870e9 q^{42} -2.92077e10 q^{43} +1.43987e10 q^{44} +8.12817e8 q^{45} -9.23175e10 q^{46} +6.84933e10 q^{47} -5.87531e10 q^{48} -8.55664e10 q^{49} +1.24688e11 q^{50} -3.79153e10 q^{51} +5.15627e10 q^{52} -2.50028e11 q^{53} -3.96489e10 q^{54} +9.65202e9 q^{55} -6.43631e10 q^{56} -1.34587e11 q^{57} +6.15390e11 q^{58} +4.21805e10 q^{59} +2.54396e9 q^{60} +1.92463e9 q^{61} -4.75580e10 q^{62} -5.65495e10 q^{63} +3.23224e11 q^{64} +3.45644e10 q^{65} -4.70821e11 q^{66} -4.84490e11 q^{67} -1.18667e11 q^{68} +6.57602e11 q^{69} +1.66556e10 q^{70} -7.15002e11 q^{71} +3.21454e11 q^{72} -1.30970e12 q^{73} +3.89595e11 q^{74} -8.88187e11 q^{75} -4.21230e11 q^{76} -6.71511e11 q^{77} -1.68604e12 q^{78} +1.45826e12 q^{79} -1.23265e11 q^{80} +2.82430e11 q^{81} -4.54419e12 q^{82} +5.72285e12 q^{83} -1.76989e11 q^{84} -7.95471e10 q^{85} +2.98914e12 q^{86} -4.38358e12 q^{87} +3.81719e12 q^{88} -6.89076e12 q^{89} -8.31843e10 q^{90} -2.40472e12 q^{91} +2.05817e12 q^{92} +3.38768e11 q^{93} -7.00966e12 q^{94} -2.82366e11 q^{95} +2.40056e12 q^{96} -2.72516e12 q^{97} +8.75693e12 q^{98} +3.35378e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −102.341 −1.13072 −0.565358 0.824846i \(-0.691262\pi\)
−0.565358 + 0.824846i \(0.691262\pi\)
\(3\) 729.000 0.577350
\(4\) 2281.63 0.278519
\(5\) 1529.46 0.0437757 0.0218878 0.999760i \(-0.493032\pi\)
0.0218878 + 0.999760i \(0.493032\pi\)
\(6\) −74606.4 −0.652819
\(7\) −106408. −0.341850 −0.170925 0.985284i \(-0.554676\pi\)
−0.170925 + 0.985284i \(0.554676\pi\)
\(8\) 604872. 0.815790
\(9\) 531441. 0.333333
\(10\) −156526. −0.0494979
\(11\) 6.31074e6 1.07406 0.537029 0.843564i \(-0.319547\pi\)
0.537029 + 0.843564i \(0.319547\pi\)
\(12\) 1.66331e6 0.160803
\(13\) 2.25991e7 1.29855 0.649275 0.760553i \(-0.275072\pi\)
0.649275 + 0.760553i \(0.275072\pi\)
\(14\) 1.08898e7 0.386536
\(15\) 1.11498e6 0.0252739
\(16\) −8.05941e7 −1.20095
\(17\) −5.20100e7 −0.522599 −0.261299 0.965258i \(-0.584151\pi\)
−0.261299 + 0.965258i \(0.584151\pi\)
\(18\) −5.43881e7 −0.376905
\(19\) −1.84618e8 −0.900278 −0.450139 0.892959i \(-0.648625\pi\)
−0.450139 + 0.892959i \(0.648625\pi\)
\(20\) 3.48966e6 0.0121924
\(21\) −7.75713e7 −0.197367
\(22\) −6.45845e8 −1.21445
\(23\) 9.02060e8 1.27059 0.635294 0.772271i \(-0.280879\pi\)
0.635294 + 0.772271i \(0.280879\pi\)
\(24\) 4.40952e8 0.470997
\(25\) −1.21836e9 −0.998084
\(26\) −2.31281e9 −1.46829
\(27\) 3.87420e8 0.192450
\(28\) −2.42783e8 −0.0952118
\(29\) −6.01315e9 −1.87722 −0.938609 0.344982i \(-0.887885\pi\)
−0.938609 + 0.344982i \(0.887885\pi\)
\(30\) −1.14107e8 −0.0285776
\(31\) 4.64702e8 0.0940424 0.0470212 0.998894i \(-0.485027\pi\)
0.0470212 + 0.998894i \(0.485027\pi\)
\(32\) 3.29295e9 0.542139
\(33\) 4.60053e9 0.620107
\(34\) 5.32274e9 0.590911
\(35\) −1.62746e8 −0.0149647
\(36\) 1.21255e9 0.0928397
\(37\) −3.80685e9 −0.243924 −0.121962 0.992535i \(-0.538919\pi\)
−0.121962 + 0.992535i \(0.538919\pi\)
\(38\) 1.88940e10 1.01796
\(39\) 1.64747e10 0.749719
\(40\) 9.25127e8 0.0357118
\(41\) 4.44026e10 1.45987 0.729933 0.683519i \(-0.239551\pi\)
0.729933 + 0.683519i \(0.239551\pi\)
\(42\) 7.93870e9 0.223167
\(43\) −2.92077e10 −0.704616 −0.352308 0.935884i \(-0.614603\pi\)
−0.352308 + 0.935884i \(0.614603\pi\)
\(44\) 1.43987e10 0.299145
\(45\) 8.12817e8 0.0145919
\(46\) −9.23175e10 −1.43667
\(47\) 6.84933e10 0.926856 0.463428 0.886135i \(-0.346619\pi\)
0.463428 + 0.886135i \(0.346619\pi\)
\(48\) −5.87531e10 −0.693367
\(49\) −8.55664e10 −0.883138
\(50\) 1.24688e11 1.12855
\(51\) −3.79153e10 −0.301723
\(52\) 5.15627e10 0.361671
\(53\) −2.50028e11 −1.54951 −0.774756 0.632261i \(-0.782127\pi\)
−0.774756 + 0.632261i \(0.782127\pi\)
\(54\) −3.96489e10 −0.217606
\(55\) 9.65202e9 0.0470176
\(56\) −6.43631e10 −0.278878
\(57\) −1.34587e11 −0.519775
\(58\) 6.15390e11 2.12260
\(59\) 4.21805e10 0.130189
\(60\) 2.54396e9 0.00703926
\(61\) 1.92463e9 0.00478302 0.00239151 0.999997i \(-0.499239\pi\)
0.00239151 + 0.999997i \(0.499239\pi\)
\(62\) −4.75580e10 −0.106335
\(63\) −5.65495e10 −0.113950
\(64\) 3.23224e11 0.587941
\(65\) 3.45644e10 0.0568450
\(66\) −4.70821e11 −0.701166
\(67\) −4.84490e11 −0.654332 −0.327166 0.944967i \(-0.606094\pi\)
−0.327166 + 0.944967i \(0.606094\pi\)
\(68\) −1.18667e11 −0.145554
\(69\) 6.57602e11 0.733574
\(70\) 1.66556e10 0.0169209
\(71\) −7.15002e11 −0.662411 −0.331206 0.943559i \(-0.607455\pi\)
−0.331206 + 0.943559i \(0.607455\pi\)
\(72\) 3.21454e11 0.271930
\(73\) −1.30970e12 −1.01291 −0.506457 0.862265i \(-0.669045\pi\)
−0.506457 + 0.862265i \(0.669045\pi\)
\(74\) 3.89595e11 0.275809
\(75\) −8.88187e11 −0.576244
\(76\) −4.21230e11 −0.250744
\(77\) −6.71511e11 −0.367167
\(78\) −1.68604e12 −0.847719
\(79\) 1.45826e12 0.674932 0.337466 0.941338i \(-0.390430\pi\)
0.337466 + 0.941338i \(0.390430\pi\)
\(80\) −1.23265e11 −0.0525722
\(81\) 2.82430e11 0.111111
\(82\) −4.54419e12 −1.65069
\(83\) 5.72285e12 1.92134 0.960671 0.277689i \(-0.0895683\pi\)
0.960671 + 0.277689i \(0.0895683\pi\)
\(84\) −1.76989e11 −0.0549706
\(85\) −7.95471e10 −0.0228771
\(86\) 2.98914e12 0.796721
\(87\) −4.38358e12 −1.08381
\(88\) 3.81719e12 0.876206
\(89\) −6.89076e12 −1.46971 −0.734855 0.678224i \(-0.762750\pi\)
−0.734855 + 0.678224i \(0.762750\pi\)
\(90\) −8.31843e10 −0.0164993
\(91\) −2.40472e12 −0.443910
\(92\) 2.05817e12 0.353883
\(93\) 3.38768e11 0.0542954
\(94\) −7.00966e12 −1.04801
\(95\) −2.82366e11 −0.0394103
\(96\) 2.40056e12 0.313004
\(97\) −2.72516e12 −0.332182 −0.166091 0.986110i \(-0.553115\pi\)
−0.166091 + 0.986110i \(0.553115\pi\)
\(98\) 8.75693e12 0.998579
\(99\) 3.35378e12 0.358019
\(100\) −2.77985e12 −0.277985
\(101\) 1.25517e13 1.17656 0.588279 0.808658i \(-0.299806\pi\)
0.588279 + 0.808658i \(0.299806\pi\)
\(102\) 3.88028e12 0.341163
\(103\) 5.14295e12 0.424395 0.212198 0.977227i \(-0.431938\pi\)
0.212198 + 0.977227i \(0.431938\pi\)
\(104\) 1.36695e13 1.05935
\(105\) −1.18642e11 −0.00863989
\(106\) 2.55880e13 1.75206
\(107\) 7.13818e12 0.459826 0.229913 0.973211i \(-0.426156\pi\)
0.229913 + 0.973211i \(0.426156\pi\)
\(108\) 8.83949e11 0.0536010
\(109\) −1.53597e13 −0.877225 −0.438612 0.898676i \(-0.644530\pi\)
−0.438612 + 0.898676i \(0.644530\pi\)
\(110\) −9.87794e11 −0.0531636
\(111\) −2.77519e12 −0.140829
\(112\) 8.57584e12 0.410544
\(113\) −1.02932e13 −0.465094 −0.232547 0.972585i \(-0.574706\pi\)
−0.232547 + 0.972585i \(0.574706\pi\)
\(114\) 1.37737e13 0.587719
\(115\) 1.37966e12 0.0556208
\(116\) −1.37198e13 −0.522841
\(117\) 1.20101e13 0.432850
\(118\) −4.31679e12 −0.147207
\(119\) 5.53426e12 0.178651
\(120\) 6.74418e11 0.0206182
\(121\) 5.30268e12 0.153600
\(122\) −1.96968e11 −0.00540824
\(123\) 3.23695e13 0.842854
\(124\) 1.06028e12 0.0261926
\(125\) −3.73045e12 −0.0874675
\(126\) 5.78731e12 0.128845
\(127\) 6.31473e13 1.33546 0.667729 0.744404i \(-0.267266\pi\)
0.667729 + 0.744404i \(0.267266\pi\)
\(128\) −6.00548e13 −1.20693
\(129\) −2.12924e13 −0.406810
\(130\) −3.53734e12 −0.0642755
\(131\) 4.73681e12 0.0818885 0.0409442 0.999161i \(-0.486963\pi\)
0.0409442 + 0.999161i \(0.486963\pi\)
\(132\) 1.04967e13 0.172712
\(133\) 1.96448e13 0.307760
\(134\) 4.95830e13 0.739864
\(135\) 5.92544e11 0.00842463
\(136\) −3.14594e13 −0.426331
\(137\) 6.91099e13 0.893010 0.446505 0.894781i \(-0.352668\pi\)
0.446505 + 0.894781i \(0.352668\pi\)
\(138\) −6.72995e13 −0.829464
\(139\) −1.08617e14 −1.27733 −0.638663 0.769487i \(-0.720512\pi\)
−0.638663 + 0.769487i \(0.720512\pi\)
\(140\) −3.71327e11 −0.00416796
\(141\) 4.99316e13 0.535121
\(142\) 7.31738e13 0.748999
\(143\) 1.42617e14 1.39472
\(144\) −4.28310e13 −0.400315
\(145\) −9.19687e12 −0.0821765
\(146\) 1.34035e14 1.14532
\(147\) −6.23779e13 −0.509880
\(148\) −8.68580e12 −0.0679374
\(149\) −9.85943e13 −0.738144 −0.369072 0.929401i \(-0.620324\pi\)
−0.369072 + 0.929401i \(0.620324\pi\)
\(150\) 9.08977e13 0.651568
\(151\) 2.16339e14 1.48520 0.742598 0.669738i \(-0.233593\pi\)
0.742598 + 0.669738i \(0.233593\pi\)
\(152\) −1.11670e14 −0.734438
\(153\) −2.76402e13 −0.174200
\(154\) 6.87230e13 0.415162
\(155\) 7.10743e11 0.00411677
\(156\) 3.75892e13 0.208811
\(157\) 1.12977e14 0.602063 0.301032 0.953614i \(-0.402669\pi\)
0.301032 + 0.953614i \(0.402669\pi\)
\(158\) −1.49240e14 −0.763156
\(159\) −1.82270e14 −0.894611
\(160\) 5.03644e12 0.0237325
\(161\) −9.59862e13 −0.434351
\(162\) −2.89040e13 −0.125635
\(163\) 3.88172e14 1.62108 0.810541 0.585681i \(-0.199173\pi\)
0.810541 + 0.585681i \(0.199173\pi\)
\(164\) 1.01310e14 0.406600
\(165\) 7.03632e12 0.0271456
\(166\) −5.85681e14 −2.17249
\(167\) 3.68501e14 1.31456 0.657282 0.753645i \(-0.271706\pi\)
0.657282 + 0.753645i \(0.271706\pi\)
\(168\) −4.69207e13 −0.161010
\(169\) 2.07843e14 0.686235
\(170\) 8.14091e12 0.0258675
\(171\) −9.81138e13 −0.300093
\(172\) −6.66411e13 −0.196249
\(173\) −3.12651e14 −0.886666 −0.443333 0.896357i \(-0.646204\pi\)
−0.443333 + 0.896357i \(0.646204\pi\)
\(174\) 4.48619e14 1.22548
\(175\) 1.29643e14 0.341195
\(176\) −5.08608e14 −1.28989
\(177\) 3.07496e13 0.0751646
\(178\) 7.05205e14 1.66183
\(179\) −2.02854e14 −0.460935 −0.230467 0.973080i \(-0.574026\pi\)
−0.230467 + 0.973080i \(0.574026\pi\)
\(180\) 1.85455e12 0.00406412
\(181\) −4.19098e14 −0.885940 −0.442970 0.896536i \(-0.646075\pi\)
−0.442970 + 0.896536i \(0.646075\pi\)
\(182\) 2.46101e14 0.501936
\(183\) 1.40305e12 0.00276148
\(184\) 5.45631e14 1.03653
\(185\) −5.82242e12 −0.0106779
\(186\) −3.46698e13 −0.0613927
\(187\) −3.28221e14 −0.561301
\(188\) 1.56276e14 0.258147
\(189\) −4.12245e13 −0.0657891
\(190\) 2.88976e13 0.0445618
\(191\) −1.97529e14 −0.294384 −0.147192 0.989108i \(-0.547024\pi\)
−0.147192 + 0.989108i \(0.547024\pi\)
\(192\) 2.35630e14 0.339448
\(193\) −6.05085e14 −0.842740 −0.421370 0.906889i \(-0.638451\pi\)
−0.421370 + 0.906889i \(0.638451\pi\)
\(194\) 2.78895e14 0.375604
\(195\) 2.51974e13 0.0328195
\(196\) −1.95231e14 −0.245971
\(197\) −1.50473e15 −1.83412 −0.917061 0.398746i \(-0.869446\pi\)
−0.917061 + 0.398746i \(0.869446\pi\)
\(198\) −3.43229e14 −0.404818
\(199\) −6.00792e14 −0.685771 −0.342885 0.939377i \(-0.611404\pi\)
−0.342885 + 0.939377i \(0.611404\pi\)
\(200\) −7.36954e14 −0.814227
\(201\) −3.53193e14 −0.377779
\(202\) −1.28455e15 −1.33035
\(203\) 6.39846e14 0.641728
\(204\) −8.65085e13 −0.0840355
\(205\) 6.79119e13 0.0639066
\(206\) −5.26333e14 −0.479870
\(207\) 4.79392e14 0.423529
\(208\) −1.82135e15 −1.55949
\(209\) −1.16508e15 −0.966950
\(210\) 1.21419e13 0.00976927
\(211\) −5.03758e14 −0.392994 −0.196497 0.980504i \(-0.562957\pi\)
−0.196497 + 0.980504i \(0.562957\pi\)
\(212\) −5.70470e14 −0.431568
\(213\) −5.21236e14 −0.382443
\(214\) −7.30527e14 −0.519932
\(215\) −4.46720e13 −0.0308451
\(216\) 2.34340e14 0.156999
\(217\) −4.94479e13 −0.0321484
\(218\) 1.57192e15 0.991892
\(219\) −9.54770e14 −0.584806
\(220\) 2.20223e13 0.0130953
\(221\) −1.17538e15 −0.678621
\(222\) 2.84015e14 0.159238
\(223\) 1.84546e15 1.00490 0.502452 0.864605i \(-0.332432\pi\)
0.502452 + 0.864605i \(0.332432\pi\)
\(224\) −3.50396e14 −0.185330
\(225\) −6.47489e14 −0.332695
\(226\) 1.05341e15 0.525889
\(227\) −2.00281e15 −0.971563 −0.485782 0.874080i \(-0.661465\pi\)
−0.485782 + 0.874080i \(0.661465\pi\)
\(228\) −3.07077e14 −0.144767
\(229\) −3.33246e15 −1.52698 −0.763492 0.645817i \(-0.776517\pi\)
−0.763492 + 0.645817i \(0.776517\pi\)
\(230\) −1.41196e14 −0.0628914
\(231\) −4.89532e14 −0.211984
\(232\) −3.63718e15 −1.53142
\(233\) −6.34104e14 −0.259625 −0.129813 0.991539i \(-0.541438\pi\)
−0.129813 + 0.991539i \(0.541438\pi\)
\(234\) −1.22912e15 −0.489431
\(235\) 1.04758e14 0.0405738
\(236\) 9.62403e13 0.0362601
\(237\) 1.06307e15 0.389672
\(238\) −5.66381e14 −0.202003
\(239\) −4.18435e15 −1.45225 −0.726125 0.687563i \(-0.758681\pi\)
−0.726125 + 0.687563i \(0.758681\pi\)
\(240\) −8.98605e13 −0.0303526
\(241\) 2.57972e15 0.848127 0.424064 0.905632i \(-0.360603\pi\)
0.424064 + 0.905632i \(0.360603\pi\)
\(242\) −5.42681e14 −0.173678
\(243\) 2.05891e14 0.0641500
\(244\) 4.39128e12 0.00133216
\(245\) −1.30870e14 −0.0386600
\(246\) −3.31272e15 −0.953029
\(247\) −4.17220e15 −1.16906
\(248\) 2.81085e14 0.0767189
\(249\) 4.17196e15 1.10929
\(250\) 3.81777e14 0.0989009
\(251\) −5.22753e15 −1.31952 −0.659762 0.751475i \(-0.729343\pi\)
−0.659762 + 0.751475i \(0.729343\pi\)
\(252\) −1.29025e14 −0.0317373
\(253\) 5.69266e15 1.36468
\(254\) −6.46254e15 −1.51002
\(255\) −5.79899e13 −0.0132081
\(256\) 3.49821e15 0.776758
\(257\) −2.00233e15 −0.433482 −0.216741 0.976229i \(-0.569543\pi\)
−0.216741 + 0.976229i \(0.569543\pi\)
\(258\) 2.17908e15 0.459987
\(259\) 4.05078e14 0.0833854
\(260\) 7.88630e13 0.0158324
\(261\) −3.19563e15 −0.625740
\(262\) −4.84769e14 −0.0925926
\(263\) −5.60907e15 −1.04515 −0.522575 0.852593i \(-0.675028\pi\)
−0.522575 + 0.852593i \(0.675028\pi\)
\(264\) 2.78273e15 0.505878
\(265\) −3.82407e14 −0.0678309
\(266\) −2.01047e15 −0.347989
\(267\) −5.02336e15 −0.848538
\(268\) −1.10542e15 −0.182244
\(269\) 3.75970e15 0.605012 0.302506 0.953148i \(-0.402177\pi\)
0.302506 + 0.953148i \(0.402177\pi\)
\(270\) −6.06414e13 −0.00952587
\(271\) −5.50924e15 −0.844872 −0.422436 0.906393i \(-0.638825\pi\)
−0.422436 + 0.906393i \(0.638825\pi\)
\(272\) 4.19170e15 0.627613
\(273\) −1.75304e15 −0.256292
\(274\) −7.07276e15 −1.00974
\(275\) −7.68877e15 −1.07200
\(276\) 1.50040e15 0.204314
\(277\) 1.01600e16 1.35137 0.675683 0.737192i \(-0.263849\pi\)
0.675683 + 0.737192i \(0.263849\pi\)
\(278\) 1.11159e16 1.44429
\(279\) 2.46962e14 0.0313475
\(280\) −9.84407e13 −0.0122081
\(281\) −1.32081e16 −1.60048 −0.800241 0.599679i \(-0.795295\pi\)
−0.800241 + 0.599679i \(0.795295\pi\)
\(282\) −5.11004e15 −0.605069
\(283\) −1.14497e16 −1.32490 −0.662449 0.749107i \(-0.730483\pi\)
−0.662449 + 0.749107i \(0.730483\pi\)
\(284\) −1.63137e15 −0.184494
\(285\) −2.05845e14 −0.0227535
\(286\) −1.45955e16 −1.57703
\(287\) −4.72478e15 −0.499056
\(288\) 1.75001e15 0.180713
\(289\) −7.19954e15 −0.726890
\(290\) 9.41214e14 0.0929183
\(291\) −1.98664e15 −0.191785
\(292\) −2.98824e15 −0.282116
\(293\) 1.75776e16 1.62301 0.811505 0.584345i \(-0.198649\pi\)
0.811505 + 0.584345i \(0.198649\pi\)
\(294\) 6.38380e15 0.576530
\(295\) 6.45134e13 0.00569911
\(296\) −2.30265e15 −0.198991
\(297\) 2.44491e15 0.206702
\(298\) 1.00902e16 0.834632
\(299\) 2.03857e16 1.64992
\(300\) −2.02651e15 −0.160495
\(301\) 3.10793e15 0.240873
\(302\) −2.21402e16 −1.67933
\(303\) 9.15019e15 0.679286
\(304\) 1.48792e16 1.08118
\(305\) 2.94364e12 0.000209380 0
\(306\) 2.82872e15 0.196970
\(307\) 1.90489e16 1.29858 0.649292 0.760539i \(-0.275065\pi\)
0.649292 + 0.760539i \(0.275065\pi\)
\(308\) −1.53214e15 −0.102263
\(309\) 3.74921e15 0.245025
\(310\) −7.27380e13 −0.00465490
\(311\) 3.05342e14 0.0191357 0.00956784 0.999954i \(-0.496954\pi\)
0.00956784 + 0.999954i \(0.496954\pi\)
\(312\) 9.96510e15 0.611613
\(313\) −8.27645e14 −0.0497515 −0.0248757 0.999691i \(-0.507919\pi\)
−0.0248757 + 0.999691i \(0.507919\pi\)
\(314\) −1.15621e16 −0.680762
\(315\) −8.64901e13 −0.00498824
\(316\) 3.32721e15 0.187981
\(317\) 4.47773e15 0.247840 0.123920 0.992292i \(-0.460453\pi\)
0.123920 + 0.992292i \(0.460453\pi\)
\(318\) 1.86537e16 1.01155
\(319\) −3.79474e16 −2.01624
\(320\) 4.94358e14 0.0257375
\(321\) 5.20374e15 0.265480
\(322\) 9.82330e15 0.491128
\(323\) 9.60199e15 0.470484
\(324\) 6.44399e14 0.0309466
\(325\) −2.75339e16 −1.29606
\(326\) −3.97258e16 −1.83298
\(327\) −1.11972e16 −0.506466
\(328\) 2.68579e16 1.19094
\(329\) −7.28822e15 −0.316846
\(330\) −7.20102e14 −0.0306940
\(331\) 3.61947e16 1.51273 0.756367 0.654147i \(-0.226972\pi\)
0.756367 + 0.654147i \(0.226972\pi\)
\(332\) 1.30574e16 0.535130
\(333\) −2.02311e15 −0.0813079
\(334\) −3.77127e16 −1.48640
\(335\) −7.41007e14 −0.0286438
\(336\) 6.25179e15 0.237028
\(337\) −2.27536e16 −0.846166 −0.423083 0.906091i \(-0.639052\pi\)
−0.423083 + 0.906091i \(0.639052\pi\)
\(338\) −2.12708e16 −0.775937
\(339\) −7.50374e15 −0.268522
\(340\) −1.81497e14 −0.00637171
\(341\) 2.93261e15 0.101007
\(342\) 1.00410e16 0.339319
\(343\) 1.94147e16 0.643752
\(344\) −1.76669e16 −0.574819
\(345\) 1.00578e15 0.0321127
\(346\) 3.19969e16 1.00257
\(347\) −1.47556e16 −0.453748 −0.226874 0.973924i \(-0.572851\pi\)
−0.226874 + 0.973924i \(0.572851\pi\)
\(348\) −1.00017e16 −0.301862
\(349\) 5.27288e16 1.56200 0.781002 0.624528i \(-0.214709\pi\)
0.781002 + 0.624528i \(0.214709\pi\)
\(350\) −1.32678e16 −0.385795
\(351\) 8.75535e15 0.249906
\(352\) 2.07810e16 0.582288
\(353\) −1.22538e16 −0.337081 −0.168541 0.985695i \(-0.553905\pi\)
−0.168541 + 0.985695i \(0.553905\pi\)
\(354\) −3.14694e15 −0.0849898
\(355\) −1.09357e15 −0.0289975
\(356\) −1.57221e16 −0.409342
\(357\) 4.03448e15 0.103144
\(358\) 2.07603e16 0.521186
\(359\) 4.36531e16 1.07622 0.538110 0.842875i \(-0.319139\pi\)
0.538110 + 0.842875i \(0.319139\pi\)
\(360\) 4.91650e14 0.0119039
\(361\) −7.96906e15 −0.189500
\(362\) 4.28908e16 1.00175
\(363\) 3.86566e15 0.0886809
\(364\) −5.48667e15 −0.123637
\(365\) −2.00313e15 −0.0443410
\(366\) −1.43589e14 −0.00312245
\(367\) −3.93339e16 −0.840306 −0.420153 0.907453i \(-0.638024\pi\)
−0.420153 + 0.907453i \(0.638024\pi\)
\(368\) −7.27008e16 −1.52591
\(369\) 2.35973e16 0.486622
\(370\) 5.95870e14 0.0120737
\(371\) 2.66049e16 0.529701
\(372\) 7.72942e14 0.0151223
\(373\) 1.21380e16 0.233368 0.116684 0.993169i \(-0.462774\pi\)
0.116684 + 0.993169i \(0.462774\pi\)
\(374\) 3.35904e16 0.634673
\(375\) −2.71950e15 −0.0504994
\(376\) 4.14297e16 0.756120
\(377\) −1.35892e17 −2.43766
\(378\) 4.21895e15 0.0743888
\(379\) −7.55338e15 −0.130914 −0.0654570 0.997855i \(-0.520851\pi\)
−0.0654570 + 0.997855i \(0.520851\pi\)
\(380\) −6.44255e14 −0.0109765
\(381\) 4.60344e16 0.771027
\(382\) 2.02153e16 0.332865
\(383\) −9.47897e16 −1.53451 −0.767254 0.641343i \(-0.778378\pi\)
−0.767254 + 0.641343i \(0.778378\pi\)
\(384\) −4.37800e16 −0.696823
\(385\) −1.02705e15 −0.0160730
\(386\) 6.19248e16 0.952900
\(387\) −1.55222e16 −0.234872
\(388\) −6.21781e15 −0.0925190
\(389\) −1.09943e17 −1.60877 −0.804384 0.594109i \(-0.797505\pi\)
−0.804384 + 0.594109i \(0.797505\pi\)
\(390\) −2.57872e15 −0.0371095
\(391\) −4.69161e16 −0.664008
\(392\) −5.17567e16 −0.720456
\(393\) 3.45314e15 0.0472783
\(394\) 1.53995e17 2.07387
\(395\) 2.23035e15 0.0295456
\(396\) 7.65209e15 0.0997151
\(397\) 1.55360e16 0.199159 0.0995795 0.995030i \(-0.468250\pi\)
0.0995795 + 0.995030i \(0.468250\pi\)
\(398\) 6.14855e16 0.775412
\(399\) 1.43211e16 0.177685
\(400\) 9.81930e16 1.19864
\(401\) 1.37551e16 0.165206 0.0826031 0.996583i \(-0.473677\pi\)
0.0826031 + 0.996583i \(0.473677\pi\)
\(402\) 3.61460e16 0.427161
\(403\) 1.05018e16 0.122119
\(404\) 2.86383e16 0.327694
\(405\) 4.31965e14 0.00486396
\(406\) −6.54823e16 −0.725612
\(407\) −2.40240e16 −0.261988
\(408\) −2.29339e16 −0.246142
\(409\) 4.84606e16 0.511903 0.255951 0.966690i \(-0.417611\pi\)
0.255951 + 0.966690i \(0.417611\pi\)
\(410\) −6.95016e15 −0.0722603
\(411\) 5.03811e16 0.515580
\(412\) 1.17343e16 0.118202
\(413\) −4.48834e15 −0.0445051
\(414\) −4.90613e16 −0.478891
\(415\) 8.75287e15 0.0841081
\(416\) 7.44177e16 0.703995
\(417\) −7.91818e16 −0.737464
\(418\) 1.19235e17 1.09335
\(419\) −7.28361e15 −0.0657591 −0.0328795 0.999459i \(-0.510468\pi\)
−0.0328795 + 0.999459i \(0.510468\pi\)
\(420\) −2.70697e14 −0.00240637
\(421\) −1.01720e17 −0.890377 −0.445189 0.895437i \(-0.646863\pi\)
−0.445189 + 0.895437i \(0.646863\pi\)
\(422\) 5.15549e16 0.444364
\(423\) 3.64002e16 0.308952
\(424\) −1.51235e17 −1.26408
\(425\) 6.33671e16 0.521598
\(426\) 5.33437e16 0.432435
\(427\) −2.04795e14 −0.00163508
\(428\) 1.62867e16 0.128070
\(429\) 1.03968e17 0.805241
\(430\) 4.57177e15 0.0348770
\(431\) −1.41942e17 −1.06662 −0.533308 0.845921i \(-0.679051\pi\)
−0.533308 + 0.845921i \(0.679051\pi\)
\(432\) −3.12238e16 −0.231122
\(433\) −9.22989e16 −0.673016 −0.336508 0.941681i \(-0.609246\pi\)
−0.336508 + 0.941681i \(0.609246\pi\)
\(434\) 5.06054e15 0.0363508
\(435\) −6.70452e15 −0.0474446
\(436\) −3.50451e16 −0.244324
\(437\) −1.66537e17 −1.14388
\(438\) 9.77118e16 0.661250
\(439\) −2.62205e17 −1.74832 −0.874161 0.485637i \(-0.838588\pi\)
−0.874161 + 0.485637i \(0.838588\pi\)
\(440\) 5.83823e15 0.0383565
\(441\) −4.54735e16 −0.294379
\(442\) 1.20289e17 0.767328
\(443\) −5.28987e16 −0.332522 −0.166261 0.986082i \(-0.553169\pi\)
−0.166261 + 0.986082i \(0.553169\pi\)
\(444\) −6.33195e15 −0.0392237
\(445\) −1.05391e16 −0.0643376
\(446\) −1.88866e17 −1.13626
\(447\) −7.18753e16 −0.426168
\(448\) −3.43935e16 −0.200988
\(449\) −6.99570e16 −0.402930 −0.201465 0.979496i \(-0.564570\pi\)
−0.201465 + 0.979496i \(0.564570\pi\)
\(450\) 6.62645e16 0.376183
\(451\) 2.80213e17 1.56798
\(452\) −2.34852e16 −0.129537
\(453\) 1.57711e17 0.857478
\(454\) 2.04969e17 1.09856
\(455\) −3.67792e15 −0.0194325
\(456\) −8.14078e16 −0.424028
\(457\) −9.30047e16 −0.477584 −0.238792 0.971071i \(-0.576751\pi\)
−0.238792 + 0.971071i \(0.576751\pi\)
\(458\) 3.41047e17 1.72659
\(459\) −2.01497e16 −0.100574
\(460\) 3.14788e15 0.0154915
\(461\) −1.68488e16 −0.0817548 −0.0408774 0.999164i \(-0.513015\pi\)
−0.0408774 + 0.999164i \(0.513015\pi\)
\(462\) 5.00990e16 0.239694
\(463\) 1.80072e17 0.849513 0.424757 0.905308i \(-0.360360\pi\)
0.424757 + 0.905308i \(0.360360\pi\)
\(464\) 4.84624e17 2.25444
\(465\) 5.18132e14 0.00237682
\(466\) 6.48946e16 0.293562
\(467\) 8.00154e16 0.356955 0.178478 0.983944i \(-0.442883\pi\)
0.178478 + 0.983944i \(0.442883\pi\)
\(468\) 2.74025e16 0.120557
\(469\) 5.15535e16 0.223684
\(470\) −1.07210e16 −0.0458774
\(471\) 8.23602e16 0.347601
\(472\) 2.55138e16 0.106207
\(473\) −1.84322e17 −0.756798
\(474\) −1.08796e17 −0.440608
\(475\) 2.24932e17 0.898552
\(476\) 1.26271e16 0.0497576
\(477\) −1.32875e17 −0.516504
\(478\) 4.28229e17 1.64208
\(479\) 2.38875e17 0.903627 0.451813 0.892113i \(-0.350777\pi\)
0.451813 + 0.892113i \(0.350777\pi\)
\(480\) 3.67156e15 0.0137020
\(481\) −8.60312e16 −0.316747
\(482\) −2.64010e17 −0.958991
\(483\) −6.99740e16 −0.250773
\(484\) 1.20987e16 0.0427805
\(485\) −4.16803e15 −0.0145415
\(486\) −2.10711e16 −0.0725355
\(487\) −4.75150e17 −1.61396 −0.806980 0.590579i \(-0.798900\pi\)
−0.806980 + 0.590579i \(0.798900\pi\)
\(488\) 1.16415e15 0.00390194
\(489\) 2.82978e17 0.935933
\(490\) 1.33934e16 0.0437135
\(491\) −4.14099e17 −1.33375 −0.666875 0.745169i \(-0.732369\pi\)
−0.666875 + 0.745169i \(0.732369\pi\)
\(492\) 7.38551e16 0.234751
\(493\) 3.12744e17 0.981033
\(494\) 4.26987e17 1.32187
\(495\) 5.12948e15 0.0156725
\(496\) −3.74523e16 −0.112940
\(497\) 7.60817e16 0.226446
\(498\) −4.26961e17 −1.25429
\(499\) 2.83779e17 0.822861 0.411430 0.911441i \(-0.365029\pi\)
0.411430 + 0.911441i \(0.365029\pi\)
\(500\) −8.51151e15 −0.0243614
\(501\) 2.68637e17 0.758964
\(502\) 5.34989e17 1.49201
\(503\) 1.06001e17 0.291821 0.145910 0.989298i \(-0.453389\pi\)
0.145910 + 0.989298i \(0.453389\pi\)
\(504\) −3.42052e16 −0.0929594
\(505\) 1.91973e16 0.0515047
\(506\) −5.82592e17 −1.54307
\(507\) 1.51518e17 0.396198
\(508\) 1.44079e17 0.371951
\(509\) −7.25268e17 −1.84856 −0.924278 0.381719i \(-0.875332\pi\)
−0.924278 + 0.381719i \(0.875332\pi\)
\(510\) 5.93473e15 0.0149346
\(511\) 1.39362e17 0.346265
\(512\) 1.33960e17 0.328641
\(513\) −7.15249e16 −0.173258
\(514\) 2.04920e17 0.490145
\(515\) 7.86593e15 0.0185782
\(516\) −4.85814e16 −0.113304
\(517\) 4.32243e17 0.995497
\(518\) −4.14560e16 −0.0942852
\(519\) −2.27923e17 −0.511917
\(520\) 2.09070e16 0.0463736
\(521\) −5.54722e17 −1.21515 −0.607576 0.794262i \(-0.707858\pi\)
−0.607576 + 0.794262i \(0.707858\pi\)
\(522\) 3.27043e17 0.707534
\(523\) −2.91816e17 −0.623518 −0.311759 0.950161i \(-0.600918\pi\)
−0.311759 + 0.950161i \(0.600918\pi\)
\(524\) 1.08076e16 0.0228075
\(525\) 9.45100e16 0.196989
\(526\) 5.74036e17 1.18177
\(527\) −2.41691e16 −0.0491465
\(528\) −3.70775e17 −0.744716
\(529\) 3.09676e17 0.614393
\(530\) 3.91358e16 0.0766975
\(531\) 2.24165e16 0.0433963
\(532\) 4.48222e16 0.0857171
\(533\) 1.00346e18 1.89571
\(534\) 5.14095e17 0.959456
\(535\) 1.09176e16 0.0201292
\(536\) −2.93054e17 −0.533798
\(537\) −1.47881e17 −0.266121
\(538\) −3.84771e17 −0.684096
\(539\) −5.39987e17 −0.948541
\(540\) 1.35196e15 0.00234642
\(541\) 6.17352e17 1.05865 0.529323 0.848420i \(-0.322446\pi\)
0.529323 + 0.848420i \(0.322446\pi\)
\(542\) 5.63819e17 0.955311
\(543\) −3.05522e17 −0.511498
\(544\) −1.71266e17 −0.283321
\(545\) −2.34921e16 −0.0384011
\(546\) 1.79407e17 0.289793
\(547\) −1.41119e17 −0.225252 −0.112626 0.993637i \(-0.535926\pi\)
−0.112626 + 0.993637i \(0.535926\pi\)
\(548\) 1.57683e17 0.248720
\(549\) 1.02283e15 0.00159434
\(550\) 7.86875e17 1.21213
\(551\) 1.11014e18 1.69002
\(552\) 3.97765e17 0.598443
\(553\) −1.55171e17 −0.230726
\(554\) −1.03978e18 −1.52801
\(555\) −4.24454e15 −0.00616490
\(556\) −2.47824e17 −0.355759
\(557\) −1.27646e18 −1.81113 −0.905564 0.424211i \(-0.860552\pi\)
−0.905564 + 0.424211i \(0.860552\pi\)
\(558\) −2.52743e16 −0.0354451
\(559\) −6.60067e17 −0.914980
\(560\) 1.31164e16 0.0179718
\(561\) −2.39273e17 −0.324068
\(562\) 1.35173e18 1.80969
\(563\) 1.52130e17 0.201331 0.100666 0.994920i \(-0.467903\pi\)
0.100666 + 0.994920i \(0.467903\pi\)
\(564\) 1.13925e17 0.149041
\(565\) −1.57430e16 −0.0203598
\(566\) 1.17177e18 1.49808
\(567\) −3.00527e16 −0.0379834
\(568\) −4.32484e17 −0.540389
\(569\) −1.00692e18 −1.24385 −0.621923 0.783079i \(-0.713648\pi\)
−0.621923 + 0.783079i \(0.713648\pi\)
\(570\) 2.10663e16 0.0257278
\(571\) 6.00964e17 0.725628 0.362814 0.931862i \(-0.381816\pi\)
0.362814 + 0.931862i \(0.381816\pi\)
\(572\) 3.25398e17 0.388456
\(573\) −1.43999e17 −0.169963
\(574\) 4.83537e17 0.564290
\(575\) −1.09904e18 −1.26815
\(576\) 1.71774e17 0.195980
\(577\) 1.02307e18 1.15416 0.577078 0.816689i \(-0.304193\pi\)
0.577078 + 0.816689i \(0.304193\pi\)
\(578\) 7.36806e17 0.821907
\(579\) −4.41107e17 −0.486556
\(580\) −2.09838e16 −0.0228877
\(581\) −6.08956e17 −0.656812
\(582\) 2.03315e17 0.216855
\(583\) −1.57786e18 −1.66426
\(584\) −7.92199e17 −0.826325
\(585\) 1.83689e16 0.0189483
\(586\) −1.79891e18 −1.83516
\(587\) 9.39897e17 0.948271 0.474135 0.880452i \(-0.342761\pi\)
0.474135 + 0.880452i \(0.342761\pi\)
\(588\) −1.42323e17 −0.142011
\(589\) −8.57926e16 −0.0846643
\(590\) −6.60235e15 −0.00644407
\(591\) −1.09695e18 −1.05893
\(592\) 3.06809e17 0.292939
\(593\) 1.79832e18 1.69829 0.849144 0.528162i \(-0.177119\pi\)
0.849144 + 0.528162i \(0.177119\pi\)
\(594\) −2.50214e17 −0.233722
\(595\) 8.46443e15 0.00782056
\(596\) −2.24956e17 −0.205587
\(597\) −4.37977e17 −0.395930
\(598\) −2.08629e18 −1.86559
\(599\) 1.52088e18 1.34531 0.672654 0.739958i \(-0.265154\pi\)
0.672654 + 0.739958i \(0.265154\pi\)
\(600\) −5.37240e17 −0.470094
\(601\) −5.27603e17 −0.456692 −0.228346 0.973580i \(-0.573332\pi\)
−0.228346 + 0.973580i \(0.573332\pi\)
\(602\) −3.18068e17 −0.272359
\(603\) −2.57478e17 −0.218111
\(604\) 4.93604e17 0.413655
\(605\) 8.11024e15 0.00672394
\(606\) −9.36437e17 −0.768080
\(607\) −1.67289e18 −1.35750 −0.678750 0.734370i \(-0.737478\pi\)
−0.678750 + 0.734370i \(0.737478\pi\)
\(608\) −6.07939e17 −0.488075
\(609\) 4.66447e17 0.370502
\(610\) −3.01254e14 −0.000236749 0
\(611\) 1.54789e18 1.20357
\(612\) −6.30647e16 −0.0485179
\(613\) 7.87641e17 0.599564 0.299782 0.954008i \(-0.403086\pi\)
0.299782 + 0.954008i \(0.403086\pi\)
\(614\) −1.94948e18 −1.46833
\(615\) 4.95078e16 0.0368965
\(616\) −4.06178e17 −0.299531
\(617\) 3.24559e17 0.236831 0.118416 0.992964i \(-0.462218\pi\)
0.118416 + 0.992964i \(0.462218\pi\)
\(618\) −3.83697e17 −0.277053
\(619\) 1.69953e18 1.21434 0.607171 0.794571i \(-0.292304\pi\)
0.607171 + 0.794571i \(0.292304\pi\)
\(620\) 1.62165e15 0.00114660
\(621\) 3.49477e17 0.244525
\(622\) −3.12489e16 −0.0216370
\(623\) 7.33230e17 0.502421
\(624\) −1.32777e18 −0.900372
\(625\) 1.48156e18 0.994255
\(626\) 8.47018e16 0.0562548
\(627\) −8.49342e17 −0.558269
\(628\) 2.57771e17 0.167686
\(629\) 1.97994e17 0.127474
\(630\) 8.85146e15 0.00564029
\(631\) 1.32431e18 0.835218 0.417609 0.908627i \(-0.362868\pi\)
0.417609 + 0.908627i \(0.362868\pi\)
\(632\) 8.82062e17 0.550603
\(633\) −3.67239e17 −0.226895
\(634\) −4.58254e17 −0.280237
\(635\) 9.65812e16 0.0584606
\(636\) −4.15872e17 −0.249166
\(637\) −1.93372e18 −1.14680
\(638\) 3.88356e18 2.27980
\(639\) −3.79981e17 −0.220804
\(640\) −9.18514e16 −0.0528343
\(641\) −3.07525e18 −1.75107 −0.875536 0.483154i \(-0.839491\pi\)
−0.875536 + 0.483154i \(0.839491\pi\)
\(642\) −5.32554e17 −0.300183
\(643\) −1.63493e18 −0.912278 −0.456139 0.889908i \(-0.650768\pi\)
−0.456139 + 0.889908i \(0.650768\pi\)
\(644\) −2.19005e17 −0.120975
\(645\) −3.25659e16 −0.0178084
\(646\) −9.82675e17 −0.531984
\(647\) 1.20541e18 0.646039 0.323019 0.946392i \(-0.395302\pi\)
0.323019 + 0.946392i \(0.395302\pi\)
\(648\) 1.70834e17 0.0906434
\(649\) 2.66190e17 0.139830
\(650\) 2.81784e18 1.46548
\(651\) −3.60475e16 −0.0185609
\(652\) 8.85665e17 0.451502
\(653\) 1.53790e18 0.776233 0.388116 0.921610i \(-0.373126\pi\)
0.388116 + 0.921610i \(0.373126\pi\)
\(654\) 1.14593e18 0.572669
\(655\) 7.24476e15 0.00358472
\(656\) −3.57859e18 −1.75322
\(657\) −6.96027e17 −0.337638
\(658\) 7.45882e17 0.358263
\(659\) −3.71920e18 −1.76886 −0.884431 0.466671i \(-0.845453\pi\)
−0.884431 + 0.466671i \(0.845453\pi\)
\(660\) 1.60543e16 0.00756057
\(661\) 2.21280e18 1.03189 0.515944 0.856622i \(-0.327441\pi\)
0.515944 + 0.856622i \(0.327441\pi\)
\(662\) −3.70419e18 −1.71047
\(663\) −8.56850e17 −0.391802
\(664\) 3.46159e18 1.56741
\(665\) 3.00460e16 0.0134724
\(666\) 2.07047e17 0.0919362
\(667\) −5.42422e18 −2.38517
\(668\) 8.40782e17 0.366131
\(669\) 1.34534e18 0.580181
\(670\) 7.58352e16 0.0323880
\(671\) 1.21458e16 0.00513724
\(672\) −2.55438e17 −0.107001
\(673\) −4.99922e17 −0.207398 −0.103699 0.994609i \(-0.533068\pi\)
−0.103699 + 0.994609i \(0.533068\pi\)
\(674\) 2.32862e18 0.956773
\(675\) −4.72019e17 −0.192081
\(676\) 4.74221e17 0.191129
\(677\) −1.30863e18 −0.522384 −0.261192 0.965287i \(-0.584116\pi\)
−0.261192 + 0.965287i \(0.584116\pi\)
\(678\) 7.67938e17 0.303622
\(679\) 2.89979e17 0.113557
\(680\) −4.81158e16 −0.0186629
\(681\) −1.46005e18 −0.560932
\(682\) −3.00126e17 −0.114210
\(683\) −8.18357e17 −0.308467 −0.154233 0.988034i \(-0.549291\pi\)
−0.154233 + 0.988034i \(0.549291\pi\)
\(684\) −2.23859e17 −0.0835815
\(685\) 1.05701e17 0.0390921
\(686\) −1.98691e18 −0.727900
\(687\) −2.42937e18 −0.881605
\(688\) 2.35397e18 0.846206
\(689\) −5.65039e18 −2.01212
\(690\) −1.02932e17 −0.0363104
\(691\) 7.83108e17 0.273662 0.136831 0.990594i \(-0.456308\pi\)
0.136831 + 0.990594i \(0.456308\pi\)
\(692\) −7.13353e17 −0.246953
\(693\) −3.56869e17 −0.122389
\(694\) 1.51010e18 0.513060
\(695\) −1.66125e17 −0.0559158
\(696\) −2.65151e18 −0.884164
\(697\) −2.30938e18 −0.762925
\(698\) −5.39630e18 −1.76618
\(699\) −4.62262e17 −0.149895
\(700\) 2.95798e17 0.0950294
\(701\) −4.90218e18 −1.56035 −0.780175 0.625561i \(-0.784870\pi\)
−0.780175 + 0.625561i \(0.784870\pi\)
\(702\) −8.96029e17 −0.282573
\(703\) 7.02814e17 0.219599
\(704\) 2.03978e18 0.631482
\(705\) 7.63684e16 0.0234253
\(706\) 1.25406e18 0.381143
\(707\) −1.33560e18 −0.402207
\(708\) 7.01591e16 0.0209348
\(709\) −4.31843e18 −1.27681 −0.638404 0.769701i \(-0.720405\pi\)
−0.638404 + 0.769701i \(0.720405\pi\)
\(710\) 1.11916e17 0.0327879
\(711\) 7.74981e17 0.224977
\(712\) −4.16803e18 −1.19898
\(713\) 4.19189e17 0.119489
\(714\) −4.12892e17 −0.116627
\(715\) 2.18127e17 0.0610548
\(716\) −4.62838e17 −0.128379
\(717\) −3.05039e18 −0.838457
\(718\) −4.46749e18 −1.21690
\(719\) 2.27574e18 0.614307 0.307154 0.951660i \(-0.400623\pi\)
0.307154 + 0.951660i \(0.400623\pi\)
\(720\) −6.55083e16 −0.0175241
\(721\) −5.47250e17 −0.145080
\(722\) 8.15559e17 0.214271
\(723\) 1.88061e18 0.489667
\(724\) −9.56225e17 −0.246751
\(725\) 7.32620e18 1.87362
\(726\) −3.95614e17 −0.100273
\(727\) −2.45034e18 −0.615535 −0.307768 0.951462i \(-0.599582\pi\)
−0.307768 + 0.951462i \(0.599582\pi\)
\(728\) −1.45455e18 −0.362138
\(729\) 1.50095e17 0.0370370
\(730\) 2.05002e17 0.0501371
\(731\) 1.51909e18 0.368232
\(732\) 3.20124e15 0.000769124 0
\(733\) −1.01405e17 −0.0241481 −0.0120741 0.999927i \(-0.503843\pi\)
−0.0120741 + 0.999927i \(0.503843\pi\)
\(734\) 4.02546e18 0.950148
\(735\) −9.54045e16 −0.0223204
\(736\) 2.97044e18 0.688835
\(737\) −3.05749e18 −0.702790
\(738\) −2.41497e18 −0.550231
\(739\) −4.58611e18 −1.03575 −0.517875 0.855456i \(-0.673277\pi\)
−0.517875 + 0.855456i \(0.673277\pi\)
\(740\) −1.32846e16 −0.00297401
\(741\) −3.04154e18 −0.674955
\(742\) −2.72276e18 −0.598942
\(743\) −9.55597e17 −0.208376 −0.104188 0.994558i \(-0.533224\pi\)
−0.104188 + 0.994558i \(0.533224\pi\)
\(744\) 2.04911e17 0.0442937
\(745\) −1.50796e17 −0.0323128
\(746\) −1.24221e18 −0.263873
\(747\) 3.04136e18 0.640447
\(748\) −7.48878e17 −0.156333
\(749\) −7.59558e17 −0.157192
\(750\) 2.78316e17 0.0571005
\(751\) −2.08850e18 −0.424792 −0.212396 0.977184i \(-0.568127\pi\)
−0.212396 + 0.977184i \(0.568127\pi\)
\(752\) −5.52016e18 −1.11310
\(753\) −3.81087e18 −0.761827
\(754\) 1.39072e19 2.75631
\(755\) 3.30881e17 0.0650155
\(756\) −9.40591e16 −0.0183235
\(757\) 1.91674e18 0.370203 0.185101 0.982719i \(-0.440739\pi\)
0.185101 + 0.982719i \(0.440739\pi\)
\(758\) 7.73018e17 0.148027
\(759\) 4.14995e18 0.787901
\(760\) −1.70795e17 −0.0321505
\(761\) 8.83939e18 1.64976 0.824882 0.565304i \(-0.191241\pi\)
0.824882 + 0.565304i \(0.191241\pi\)
\(762\) −4.71119e18 −0.871813
\(763\) 1.63439e18 0.299880
\(764\) −4.50689e17 −0.0819917
\(765\) −4.22746e16 −0.00762571
\(766\) 9.70085e18 1.73509
\(767\) 9.53241e17 0.169057
\(768\) 2.55019e18 0.448461
\(769\) 7.22170e18 1.25927 0.629634 0.776892i \(-0.283205\pi\)
0.629634 + 0.776892i \(0.283205\pi\)
\(770\) 1.05109e17 0.0181740
\(771\) −1.45970e18 −0.250271
\(772\) −1.38058e18 −0.234719
\(773\) 1.06736e19 1.79946 0.899732 0.436444i \(-0.143762\pi\)
0.899732 + 0.436444i \(0.143762\pi\)
\(774\) 1.58855e18 0.265574
\(775\) −5.66176e17 −0.0938622
\(776\) −1.64838e18 −0.270991
\(777\) 2.95302e17 0.0481426
\(778\) 1.12516e19 1.81906
\(779\) −8.19753e18 −1.31428
\(780\) 5.74911e16 0.00914084
\(781\) −4.51219e18 −0.711468
\(782\) 4.80143e18 0.750804
\(783\) −2.32962e18 −0.361271
\(784\) 6.89615e18 1.06060
\(785\) 1.72794e17 0.0263557
\(786\) −3.53397e17 −0.0534584
\(787\) 2.08479e18 0.312771 0.156385 0.987696i \(-0.450016\pi\)
0.156385 + 0.987696i \(0.450016\pi\)
\(788\) −3.43324e18 −0.510838
\(789\) −4.08901e18 −0.603417
\(790\) −2.28256e17 −0.0334077
\(791\) 1.09528e18 0.158992
\(792\) 2.02861e18 0.292069
\(793\) 4.34948e16 0.00621100
\(794\) −1.58996e18 −0.225192
\(795\) −2.78775e17 −0.0391622
\(796\) −1.37078e18 −0.191000
\(797\) 1.23684e19 1.70936 0.854681 0.519153i \(-0.173753\pi\)
0.854681 + 0.519153i \(0.173753\pi\)
\(798\) −1.46563e18 −0.200912
\(799\) −3.56234e18 −0.484374
\(800\) −4.01201e18 −0.541100
\(801\) −3.66203e18 −0.489904
\(802\) −1.40771e18 −0.186801
\(803\) −8.26516e18 −1.08793
\(804\) −8.05855e17 −0.105219
\(805\) −1.46807e17 −0.0190140
\(806\) −1.07477e18 −0.138082
\(807\) 2.74082e18 0.349304
\(808\) 7.59217e18 0.959825
\(809\) −6.22916e18 −0.781204 −0.390602 0.920560i \(-0.627733\pi\)
−0.390602 + 0.920560i \(0.627733\pi\)
\(810\) −4.42076e16 −0.00549976
\(811\) 8.72181e17 0.107639 0.0538197 0.998551i \(-0.482860\pi\)
0.0538197 + 0.998551i \(0.482860\pi\)
\(812\) 1.45989e18 0.178733
\(813\) −4.01623e18 −0.487787
\(814\) 2.45863e18 0.296234
\(815\) 5.93694e17 0.0709640
\(816\) 3.05575e18 0.362353
\(817\) 5.39228e18 0.634350
\(818\) −4.95949e18 −0.578817
\(819\) −1.27797e18 −0.147970
\(820\) 1.54950e17 0.0177992
\(821\) 3.23751e18 0.368961 0.184481 0.982836i \(-0.440940\pi\)
0.184481 + 0.982836i \(0.440940\pi\)
\(822\) −5.15604e18 −0.582974
\(823\) 1.42567e19 1.59926 0.799631 0.600491i \(-0.205028\pi\)
0.799631 + 0.600491i \(0.205028\pi\)
\(824\) 3.11083e18 0.346217
\(825\) −5.60512e18 −0.618919
\(826\) 4.59340e17 0.0503227
\(827\) 1.74865e19 1.90072 0.950359 0.311157i \(-0.100717\pi\)
0.950359 + 0.311157i \(0.100717\pi\)
\(828\) 1.09379e18 0.117961
\(829\) 4.55030e18 0.486895 0.243447 0.969914i \(-0.421722\pi\)
0.243447 + 0.969914i \(0.421722\pi\)
\(830\) −8.95775e17 −0.0951024
\(831\) 7.40661e18 0.780212
\(832\) 7.30456e18 0.763471
\(833\) 4.45031e18 0.461527
\(834\) 8.10352e18 0.833863
\(835\) 5.63607e17 0.0575459
\(836\) −2.65827e18 −0.269314
\(837\) 1.80035e17 0.0180985
\(838\) 7.45410e17 0.0743548
\(839\) 5.01380e18 0.496266 0.248133 0.968726i \(-0.420183\pi\)
0.248133 + 0.968726i \(0.420183\pi\)
\(840\) −7.17633e16 −0.00704834
\(841\) 2.58973e19 2.52395
\(842\) 1.04101e19 1.00676
\(843\) −9.62874e18 −0.924038
\(844\) −1.14939e18 −0.109456
\(845\) 3.17888e17 0.0300404
\(846\) −3.72522e18 −0.349337
\(847\) −5.64247e17 −0.0525082
\(848\) 2.01508e19 1.86088
\(849\) −8.34684e18 −0.764931
\(850\) −6.48503e18 −0.589779
\(851\) −3.43400e18 −0.309926
\(852\) −1.18927e18 −0.106518
\(853\) 1.22198e19 1.08617 0.543083 0.839679i \(-0.317257\pi\)
0.543083 + 0.839679i \(0.317257\pi\)
\(854\) 2.09589e16 0.00184881
\(855\) −1.50061e17 −0.0131368
\(856\) 4.31769e18 0.375121
\(857\) −2.08802e19 −1.80036 −0.900180 0.435517i \(-0.856565\pi\)
−0.900180 + 0.435517i \(0.856565\pi\)
\(858\) −1.06401e19 −0.910499
\(859\) −9.24720e18 −0.785334 −0.392667 0.919681i \(-0.628448\pi\)
−0.392667 + 0.919681i \(0.628448\pi\)
\(860\) −1.01925e17 −0.00859093
\(861\) −3.44436e18 −0.288130
\(862\) 1.45264e19 1.20604
\(863\) −1.93714e19 −1.59621 −0.798107 0.602515i \(-0.794165\pi\)
−0.798107 + 0.602515i \(0.794165\pi\)
\(864\) 1.27576e18 0.104335
\(865\) −4.78187e17 −0.0388144
\(866\) 9.44594e18 0.760990
\(867\) −5.24847e18 −0.419670
\(868\) −1.12822e17 −0.00895395
\(869\) 9.20271e18 0.724915
\(870\) 6.86145e17 0.0536464
\(871\) −1.09490e19 −0.849684
\(872\) −9.29066e18 −0.715631
\(873\) −1.44826e18 −0.110727
\(874\) 1.70435e19 1.29341
\(875\) 3.96949e17 0.0299008
\(876\) −2.17843e18 −0.162880
\(877\) 6.89977e18 0.512079 0.256040 0.966666i \(-0.417582\pi\)
0.256040 + 0.966666i \(0.417582\pi\)
\(878\) 2.68342e19 1.97685
\(879\) 1.28141e19 0.937045
\(880\) −7.77896e17 −0.0564656
\(881\) −1.47931e19 −1.06590 −0.532950 0.846147i \(-0.678917\pi\)
−0.532950 + 0.846147i \(0.678917\pi\)
\(882\) 4.65379e18 0.332860
\(883\) 4.88085e18 0.346538 0.173269 0.984875i \(-0.444567\pi\)
0.173269 + 0.984875i \(0.444567\pi\)
\(884\) −2.68177e18 −0.189009
\(885\) 4.70303e16 0.00329038
\(886\) 5.41369e18 0.375988
\(887\) 2.31901e19 1.59882 0.799409 0.600787i \(-0.205146\pi\)
0.799409 + 0.600787i \(0.205146\pi\)
\(888\) −1.67863e18 −0.114887
\(889\) −6.71936e18 −0.456527
\(890\) 1.07858e18 0.0727476
\(891\) 1.78234e18 0.119340
\(892\) 4.21066e18 0.279885
\(893\) −1.26451e19 −0.834428
\(894\) 7.35577e18 0.481875
\(895\) −3.10257e17 −0.0201777
\(896\) 6.39030e18 0.412591
\(897\) 1.48612e19 0.952583
\(898\) 7.15945e18 0.455600
\(899\) −2.79432e18 −0.176538
\(900\) −1.47733e18 −0.0926617
\(901\) 1.30039e19 0.809773
\(902\) −2.86772e19 −1.77294
\(903\) 2.26568e18 0.139068
\(904\) −6.22606e18 −0.379419
\(905\) −6.40993e17 −0.0387826
\(906\) −1.61402e19 −0.969564
\(907\) −1.09262e19 −0.651659 −0.325829 0.945429i \(-0.605643\pi\)
−0.325829 + 0.945429i \(0.605643\pi\)
\(908\) −4.56966e18 −0.270599
\(909\) 6.67049e18 0.392186
\(910\) 3.76401e17 0.0219726
\(911\) −2.77598e18 −0.160897 −0.0804484 0.996759i \(-0.525635\pi\)
−0.0804484 + 0.996759i \(0.525635\pi\)
\(912\) 1.08469e19 0.624222
\(913\) 3.61154e19 2.06363
\(914\) 9.51817e18 0.540012
\(915\) 2.14591e15 0.000120886 0
\(916\) −7.60344e18 −0.425294
\(917\) −5.04034e17 −0.0279936
\(918\) 2.06214e18 0.113721
\(919\) 8.95952e18 0.490607 0.245304 0.969446i \(-0.421112\pi\)
0.245304 + 0.969446i \(0.421112\pi\)
\(920\) 8.34520e17 0.0453749
\(921\) 1.38866e19 0.749737
\(922\) 1.72432e18 0.0924415
\(923\) −1.61584e19 −0.860175
\(924\) −1.11693e18 −0.0590416
\(925\) 4.63812e18 0.243456
\(926\) −1.84287e19 −0.960558
\(927\) 2.73317e18 0.141465
\(928\) −1.98010e19 −1.01771
\(929\) −3.24021e19 −1.65375 −0.826877 0.562383i \(-0.809885\pi\)
−0.826877 + 0.562383i \(0.809885\pi\)
\(930\) −5.30260e16 −0.00268751
\(931\) 1.57971e19 0.795070
\(932\) −1.44679e18 −0.0723105
\(933\) 2.22594e17 0.0110480
\(934\) −8.18883e18 −0.403615
\(935\) −5.02001e17 −0.0245714
\(936\) 7.26456e18 0.353115
\(937\) 2.09195e19 1.00982 0.504909 0.863172i \(-0.331526\pi\)
0.504909 + 0.863172i \(0.331526\pi\)
\(938\) −5.27602e18 −0.252923
\(939\) −6.03353e17 −0.0287240
\(940\) 2.39018e17 0.0113006
\(941\) −8.55635e18 −0.401750 −0.200875 0.979617i \(-0.564379\pi\)
−0.200875 + 0.979617i \(0.564379\pi\)
\(942\) −8.42880e18 −0.393038
\(943\) 4.00538e19 1.85489
\(944\) −3.39950e18 −0.156350
\(945\) −6.30513e16 −0.00287996
\(946\) 1.88637e19 0.855724
\(947\) 6.95835e18 0.313495 0.156748 0.987639i \(-0.449899\pi\)
0.156748 + 0.987639i \(0.449899\pi\)
\(948\) 2.42554e18 0.108531
\(949\) −2.95980e19 −1.31532
\(950\) −2.30197e19 −1.01601
\(951\) 3.26426e18 0.143091
\(952\) 3.34752e18 0.145741
\(953\) −4.30005e19 −1.85939 −0.929693 0.368336i \(-0.879928\pi\)
−0.929693 + 0.368336i \(0.879928\pi\)
\(954\) 1.35985e19 0.584019
\(955\) −3.02113e17 −0.0128869
\(956\) −9.54712e18 −0.404479
\(957\) −2.76636e19 −1.16408
\(958\) −2.44466e19 −1.02175
\(959\) −7.35383e18 −0.305276
\(960\) 3.60387e17 0.0148596
\(961\) −2.42016e19 −0.991156
\(962\) 8.80450e18 0.358151
\(963\) 3.79352e18 0.153275
\(964\) 5.88595e18 0.236220
\(965\) −9.25452e17 −0.0368915
\(966\) 7.16119e18 0.283553
\(967\) 7.62426e18 0.299865 0.149932 0.988696i \(-0.452094\pi\)
0.149932 + 0.988696i \(0.452094\pi\)
\(968\) 3.20744e18 0.125305
\(969\) 6.99985e18 0.271634
\(970\) 4.26559e17 0.0164423
\(971\) 2.09545e19 0.802327 0.401164 0.916006i \(-0.368606\pi\)
0.401164 + 0.916006i \(0.368606\pi\)
\(972\) 4.69767e17 0.0178670
\(973\) 1.15577e19 0.436654
\(974\) 4.86272e19 1.82493
\(975\) −2.00722e19 −0.748282
\(976\) −1.55114e17 −0.00574415
\(977\) −5.08060e19 −1.86896 −0.934480 0.356015i \(-0.884135\pi\)
−0.934480 + 0.356015i \(0.884135\pi\)
\(978\) −2.89601e19 −1.05827
\(979\) −4.34858e19 −1.57855
\(980\) −2.98597e17 −0.0107675
\(981\) −8.16278e18 −0.292408
\(982\) 4.23792e19 1.50809
\(983\) 1.01969e19 0.360469 0.180235 0.983624i \(-0.442314\pi\)
0.180235 + 0.983624i \(0.442314\pi\)
\(984\) 1.95794e19 0.687592
\(985\) −2.30143e18 −0.0802900
\(986\) −3.20064e19 −1.10927
\(987\) −5.31311e18 −0.182931
\(988\) −9.51942e18 −0.325604
\(989\) −2.63471e19 −0.895277
\(990\) −5.24954e17 −0.0177212
\(991\) −5.55649e18 −0.186347 −0.0931734 0.995650i \(-0.529701\pi\)
−0.0931734 + 0.995650i \(0.529701\pi\)
\(992\) 1.53024e18 0.0509841
\(993\) 2.63859e19 0.873378
\(994\) −7.78626e18 −0.256046
\(995\) −9.18887e17 −0.0300201
\(996\) 9.51885e18 0.308958
\(997\) −5.87125e19 −1.89327 −0.946634 0.322310i \(-0.895541\pi\)
−0.946634 + 0.322310i \(0.895541\pi\)
\(998\) −2.90421e19 −0.930422
\(999\) −1.47485e18 −0.0469431
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.1.9 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.9 30 1.1 even 1 trivial