Properties

Label 177.10.a.b.1.19
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+34.8201 q^{2} -81.0000 q^{3} +700.437 q^{4} -913.273 q^{5} -2820.43 q^{6} -1305.26 q^{7} +6561.40 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+34.8201 q^{2} -81.0000 q^{3} +700.437 q^{4} -913.273 q^{5} -2820.43 q^{6} -1305.26 q^{7} +6561.40 q^{8} +6561.00 q^{9} -31800.2 q^{10} +67784.1 q^{11} -56735.4 q^{12} +35597.5 q^{13} -45449.3 q^{14} +73975.1 q^{15} -130155. q^{16} +122703. q^{17} +228454. q^{18} -426361. q^{19} -639690. q^{20} +105726. q^{21} +2.36025e6 q^{22} +62806.5 q^{23} -531474. q^{24} -1.11906e6 q^{25} +1.23951e6 q^{26} -531441. q^{27} -914253. q^{28} -602445. q^{29} +2.57582e6 q^{30} +5.48687e6 q^{31} -7.89146e6 q^{32} -5.49051e6 q^{33} +4.27254e6 q^{34} +1.19206e6 q^{35} +4.59557e6 q^{36} -6.71960e6 q^{37} -1.48459e7 q^{38} -2.88339e6 q^{39} -5.99235e6 q^{40} -3.26258e7 q^{41} +3.68139e6 q^{42} -520430. q^{43} +4.74785e7 q^{44} -5.99198e6 q^{45} +2.18693e6 q^{46} -4.65341e7 q^{47} +1.05426e7 q^{48} -3.86499e7 q^{49} -3.89657e7 q^{50} -9.93898e6 q^{51} +2.49338e7 q^{52} -9.11193e7 q^{53} -1.85048e7 q^{54} -6.19054e7 q^{55} -8.56434e6 q^{56} +3.45353e7 q^{57} -2.09772e7 q^{58} -1.21174e7 q^{59} +5.18149e7 q^{60} +6.62621e7 q^{61} +1.91053e8 q^{62} -8.56381e6 q^{63} -2.08142e8 q^{64} -3.25102e7 q^{65} -1.91180e8 q^{66} -1.85333e7 q^{67} +8.59461e7 q^{68} -5.08733e6 q^{69} +4.15076e7 q^{70} +3.02257e8 q^{71} +4.30494e7 q^{72} -2.05549e8 q^{73} -2.33977e8 q^{74} +9.06437e7 q^{75} -2.98639e8 q^{76} -8.84759e7 q^{77} -1.00400e8 q^{78} +4.56363e8 q^{79} +1.18867e8 q^{80} +4.30467e7 q^{81} -1.13603e9 q^{82} -3.38841e8 q^{83} +7.40545e7 q^{84} -1.12062e8 q^{85} -1.81214e7 q^{86} +4.87981e7 q^{87} +4.44759e8 q^{88} -3.61357e8 q^{89} -2.08641e8 q^{90} -4.64640e7 q^{91} +4.39920e7 q^{92} -4.44436e8 q^{93} -1.62032e9 q^{94} +3.89384e8 q^{95} +6.39208e8 q^{96} -5.78879e8 q^{97} -1.34579e9 q^{98} +4.44732e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 34.8201 1.53884 0.769422 0.638741i \(-0.220544\pi\)
0.769422 + 0.638741i \(0.220544\pi\)
\(3\) −81.0000 −0.577350
\(4\) 700.437 1.36804
\(5\) −913.273 −0.653485 −0.326742 0.945113i \(-0.605951\pi\)
−0.326742 + 0.945113i \(0.605951\pi\)
\(6\) −2820.43 −0.888452
\(7\) −1305.26 −0.205474 −0.102737 0.994709i \(-0.532760\pi\)
−0.102737 + 0.994709i \(0.532760\pi\)
\(8\) 6561.40 0.566359
\(9\) 6561.00 0.333333
\(10\) −31800.2 −1.00561
\(11\) 67784.1 1.39592 0.697961 0.716136i \(-0.254091\pi\)
0.697961 + 0.716136i \(0.254091\pi\)
\(12\) −56735.4 −0.789839
\(13\) 35597.5 0.345680 0.172840 0.984950i \(-0.444706\pi\)
0.172840 + 0.984950i \(0.444706\pi\)
\(14\) −45449.3 −0.316192
\(15\) 73975.1 0.377290
\(16\) −130155. −0.496503
\(17\) 122703. 0.356317 0.178159 0.984002i \(-0.442986\pi\)
0.178159 + 0.984002i \(0.442986\pi\)
\(18\) 228454. 0.512948
\(19\) −426361. −0.750562 −0.375281 0.926911i \(-0.622454\pi\)
−0.375281 + 0.926911i \(0.622454\pi\)
\(20\) −639690. −0.893994
\(21\) 105726. 0.118630
\(22\) 2.36025e6 2.14811
\(23\) 62806.5 0.0467982 0.0233991 0.999726i \(-0.492551\pi\)
0.0233991 + 0.999726i \(0.492551\pi\)
\(24\) −531474. −0.326988
\(25\) −1.11906e6 −0.572958
\(26\) 1.23951e6 0.531947
\(27\) −531441. −0.192450
\(28\) −914253. −0.281096
\(29\) −602445. −0.158171 −0.0790855 0.996868i \(-0.525200\pi\)
−0.0790855 + 0.996868i \(0.525200\pi\)
\(30\) 2.57582e6 0.580590
\(31\) 5.48687e6 1.06708 0.533540 0.845775i \(-0.320861\pi\)
0.533540 + 0.845775i \(0.320861\pi\)
\(32\) −7.89146e6 −1.33040
\(33\) −5.49051e6 −0.805936
\(34\) 4.27254e6 0.548316
\(35\) 1.19206e6 0.134274
\(36\) 4.59557e6 0.456014
\(37\) −6.71960e6 −0.589434 −0.294717 0.955585i \(-0.595225\pi\)
−0.294717 + 0.955585i \(0.595225\pi\)
\(38\) −1.48459e7 −1.15500
\(39\) −2.88339e6 −0.199578
\(40\) −5.99235e6 −0.370107
\(41\) −3.26258e7 −1.80316 −0.901579 0.432614i \(-0.857591\pi\)
−0.901579 + 0.432614i \(0.857591\pi\)
\(42\) 3.68139e6 0.182553
\(43\) −520430. −0.0232142 −0.0116071 0.999933i \(-0.503695\pi\)
−0.0116071 + 0.999933i \(0.503695\pi\)
\(44\) 4.74785e7 1.90968
\(45\) −5.99198e6 −0.217828
\(46\) 2.18693e6 0.0720152
\(47\) −4.65341e7 −1.39101 −0.695506 0.718520i \(-0.744820\pi\)
−0.695506 + 0.718520i \(0.744820\pi\)
\(48\) 1.05426e7 0.286656
\(49\) −3.86499e7 −0.957781
\(50\) −3.89657e7 −0.881693
\(51\) −9.93898e6 −0.205720
\(52\) 2.49338e7 0.472904
\(53\) −9.11193e7 −1.58624 −0.793120 0.609066i \(-0.791545\pi\)
−0.793120 + 0.609066i \(0.791545\pi\)
\(54\) −1.85048e7 −0.296151
\(55\) −6.19054e7 −0.912213
\(56\) −8.56434e6 −0.116372
\(57\) 3.45353e7 0.433337
\(58\) −2.09772e7 −0.243400
\(59\) −1.21174e7 −0.130189
\(60\) 5.18149e7 0.516148
\(61\) 6.62621e7 0.612746 0.306373 0.951911i \(-0.400884\pi\)
0.306373 + 0.951911i \(0.400884\pi\)
\(62\) 1.91053e8 1.64207
\(63\) −8.56381e6 −0.0684912
\(64\) −2.08142e8 −1.55078
\(65\) −3.25102e7 −0.225896
\(66\) −1.91180e8 −1.24021
\(67\) −1.85333e7 −0.112361 −0.0561807 0.998421i \(-0.517892\pi\)
−0.0561807 + 0.998421i \(0.517892\pi\)
\(68\) 8.59461e7 0.487457
\(69\) −5.08733e6 −0.0270190
\(70\) 4.15076e7 0.206627
\(71\) 3.02257e8 1.41160 0.705802 0.708409i \(-0.250587\pi\)
0.705802 + 0.708409i \(0.250587\pi\)
\(72\) 4.30494e7 0.188786
\(73\) −2.05549e8 −0.847154 −0.423577 0.905860i \(-0.639226\pi\)
−0.423577 + 0.905860i \(0.639226\pi\)
\(74\) −2.33977e8 −0.907048
\(75\) 9.06437e7 0.330797
\(76\) −2.98639e8 −1.02680
\(77\) −8.84759e7 −0.286825
\(78\) −1.00400e8 −0.307120
\(79\) 4.56363e8 1.31822 0.659111 0.752046i \(-0.270933\pi\)
0.659111 + 0.752046i \(0.270933\pi\)
\(80\) 1.18867e8 0.324457
\(81\) 4.30467e7 0.111111
\(82\) −1.13603e9 −2.77478
\(83\) −3.38841e8 −0.783691 −0.391846 0.920031i \(-0.628163\pi\)
−0.391846 + 0.920031i \(0.628163\pi\)
\(84\) 7.40545e7 0.162291
\(85\) −1.12062e8 −0.232848
\(86\) −1.81214e7 −0.0357231
\(87\) 4.87981e7 0.0913200
\(88\) 4.44759e8 0.790593
\(89\) −3.61357e8 −0.610495 −0.305247 0.952273i \(-0.598739\pi\)
−0.305247 + 0.952273i \(0.598739\pi\)
\(90\) −2.08641e8 −0.335204
\(91\) −4.64640e7 −0.0710281
\(92\) 4.39920e7 0.0640219
\(93\) −4.44436e8 −0.616079
\(94\) −1.62032e9 −2.14055
\(95\) 3.89384e8 0.490481
\(96\) 6.39208e8 0.768107
\(97\) −5.78879e8 −0.663918 −0.331959 0.943294i \(-0.607710\pi\)
−0.331959 + 0.943294i \(0.607710\pi\)
\(98\) −1.34579e9 −1.47388
\(99\) 4.44732e8 0.465307
\(100\) −7.83830e8 −0.783830
\(101\) 1.11912e9 1.07012 0.535058 0.844815i \(-0.320290\pi\)
0.535058 + 0.844815i \(0.320290\pi\)
\(102\) −3.46076e8 −0.316571
\(103\) −2.19095e9 −1.91807 −0.959037 0.283282i \(-0.908577\pi\)
−0.959037 + 0.283282i \(0.908577\pi\)
\(104\) 2.33569e8 0.195779
\(105\) −9.65568e7 −0.0775230
\(106\) −3.17278e9 −2.44098
\(107\) −1.99859e9 −1.47399 −0.736997 0.675895i \(-0.763757\pi\)
−0.736997 + 0.675895i \(0.763757\pi\)
\(108\) −3.72241e8 −0.263280
\(109\) 1.72291e8 0.116908 0.0584539 0.998290i \(-0.481383\pi\)
0.0584539 + 0.998290i \(0.481383\pi\)
\(110\) −2.15555e9 −1.40375
\(111\) 5.44287e8 0.340310
\(112\) 1.69887e8 0.102018
\(113\) 1.65253e9 0.953445 0.476723 0.879054i \(-0.341825\pi\)
0.476723 + 0.879054i \(0.341825\pi\)
\(114\) 1.20252e9 0.666839
\(115\) −5.73595e7 −0.0305819
\(116\) −4.21975e8 −0.216384
\(117\) 2.33555e8 0.115227
\(118\) −4.21927e8 −0.200340
\(119\) −1.60160e8 −0.0732137
\(120\) 4.85380e8 0.213681
\(121\) 2.23674e9 0.948596
\(122\) 2.30725e9 0.942921
\(123\) 2.64269e9 1.04105
\(124\) 3.84321e9 1.45981
\(125\) 2.80574e9 1.02790
\(126\) −2.98193e8 −0.105397
\(127\) −1.14606e8 −0.0390921 −0.0195460 0.999809i \(-0.506222\pi\)
−0.0195460 + 0.999809i \(0.506222\pi\)
\(128\) −3.20708e9 −1.05600
\(129\) 4.21548e7 0.0134027
\(130\) −1.13201e9 −0.347619
\(131\) −3.87344e9 −1.14915 −0.574574 0.818453i \(-0.694832\pi\)
−0.574574 + 0.818453i \(0.694832\pi\)
\(132\) −3.84576e9 −1.10255
\(133\) 5.56513e8 0.154221
\(134\) −6.45332e8 −0.172907
\(135\) 4.85351e8 0.125763
\(136\) 8.05107e8 0.201803
\(137\) −2.67007e8 −0.0647561 −0.0323780 0.999476i \(-0.510308\pi\)
−0.0323780 + 0.999476i \(0.510308\pi\)
\(138\) −1.77141e8 −0.0415780
\(139\) 7.18570e9 1.63269 0.816343 0.577568i \(-0.195998\pi\)
0.816343 + 0.577568i \(0.195998\pi\)
\(140\) 8.34963e8 0.183692
\(141\) 3.76926e9 0.803102
\(142\) 1.05246e10 2.17224
\(143\) 2.41294e9 0.482542
\(144\) −8.53949e8 −0.165501
\(145\) 5.50197e8 0.103362
\(146\) −7.15723e9 −1.30364
\(147\) 3.13064e9 0.552975
\(148\) −4.70666e9 −0.806371
\(149\) −2.77970e9 −0.462020 −0.231010 0.972951i \(-0.574203\pi\)
−0.231010 + 0.972951i \(0.574203\pi\)
\(150\) 3.15622e9 0.509046
\(151\) −1.97660e9 −0.309402 −0.154701 0.987961i \(-0.549441\pi\)
−0.154701 + 0.987961i \(0.549441\pi\)
\(152\) −2.79753e9 −0.425088
\(153\) 8.05057e8 0.118772
\(154\) −3.08074e9 −0.441379
\(155\) −5.01101e9 −0.697320
\(156\) −2.01964e9 −0.273032
\(157\) 1.85219e9 0.243297 0.121649 0.992573i \(-0.461182\pi\)
0.121649 + 0.992573i \(0.461182\pi\)
\(158\) 1.58906e10 2.02854
\(159\) 7.38066e9 0.915816
\(160\) 7.20705e9 0.869396
\(161\) −8.19789e7 −0.00961580
\(162\) 1.49889e9 0.170983
\(163\) −7.67652e9 −0.851766 −0.425883 0.904778i \(-0.640036\pi\)
−0.425883 + 0.904778i \(0.640036\pi\)
\(164\) −2.28523e10 −2.46680
\(165\) 5.01434e9 0.526667
\(166\) −1.17985e10 −1.20598
\(167\) 1.72701e10 1.71819 0.859093 0.511819i \(-0.171028\pi\)
0.859093 + 0.511819i \(0.171028\pi\)
\(168\) 6.93712e8 0.0671873
\(169\) −9.33732e9 −0.880505
\(170\) −3.90200e9 −0.358316
\(171\) −2.79736e9 −0.250187
\(172\) −3.64528e8 −0.0317580
\(173\) −1.40653e10 −1.19383 −0.596914 0.802305i \(-0.703607\pi\)
−0.596914 + 0.802305i \(0.703607\pi\)
\(174\) 1.69915e9 0.140527
\(175\) 1.46066e9 0.117728
\(176\) −8.82247e9 −0.693080
\(177\) 9.81506e8 0.0751646
\(178\) −1.25825e10 −0.939456
\(179\) 3.57355e9 0.260173 0.130086 0.991503i \(-0.458475\pi\)
0.130086 + 0.991503i \(0.458475\pi\)
\(180\) −4.19701e9 −0.297998
\(181\) −1.99450e9 −0.138128 −0.0690638 0.997612i \(-0.522001\pi\)
−0.0690638 + 0.997612i \(0.522001\pi\)
\(182\) −1.61788e9 −0.109301
\(183\) −5.36723e9 −0.353769
\(184\) 4.12099e8 0.0265046
\(185\) 6.13683e9 0.385186
\(186\) −1.54753e10 −0.948050
\(187\) 8.31735e9 0.497391
\(188\) −3.25942e10 −1.90296
\(189\) 6.93669e8 0.0395434
\(190\) 1.35584e10 0.754774
\(191\) −1.81344e10 −0.985947 −0.492973 0.870044i \(-0.664090\pi\)
−0.492973 + 0.870044i \(0.664090\pi\)
\(192\) 1.68595e10 0.895341
\(193\) 1.18946e10 0.617080 0.308540 0.951211i \(-0.400160\pi\)
0.308540 + 0.951211i \(0.400160\pi\)
\(194\) −2.01566e10 −1.02167
\(195\) 2.63333e9 0.130421
\(196\) −2.70718e10 −1.31028
\(197\) −2.80544e10 −1.32710 −0.663550 0.748132i \(-0.730951\pi\)
−0.663550 + 0.748132i \(0.730951\pi\)
\(198\) 1.54856e10 0.716035
\(199\) 9.08899e9 0.410844 0.205422 0.978674i \(-0.434143\pi\)
0.205422 + 0.978674i \(0.434143\pi\)
\(200\) −7.34259e9 −0.324500
\(201\) 1.50120e9 0.0648719
\(202\) 3.89679e10 1.64674
\(203\) 7.86348e8 0.0324999
\(204\) −6.96163e9 −0.281433
\(205\) 2.97963e10 1.17834
\(206\) −7.62891e10 −2.95162
\(207\) 4.12074e8 0.0155994
\(208\) −4.63320e9 −0.171631
\(209\) −2.89005e10 −1.04773
\(210\) −3.36211e9 −0.119296
\(211\) 1.39839e10 0.485689 0.242844 0.970065i \(-0.421920\pi\)
0.242844 + 0.970065i \(0.421920\pi\)
\(212\) −6.38233e10 −2.17004
\(213\) −2.44828e10 −0.814990
\(214\) −6.95909e10 −2.26825
\(215\) 4.75294e8 0.0151701
\(216\) −3.48700e9 −0.108996
\(217\) −7.16179e9 −0.219257
\(218\) 5.99919e9 0.179903
\(219\) 1.66495e10 0.489105
\(220\) −4.33609e10 −1.24795
\(221\) 4.36793e9 0.123172
\(222\) 1.89521e10 0.523684
\(223\) 2.21746e10 0.600459 0.300230 0.953867i \(-0.402937\pi\)
0.300230 + 0.953867i \(0.402937\pi\)
\(224\) 1.03004e10 0.273362
\(225\) −7.34214e9 −0.190986
\(226\) 5.75411e10 1.46720
\(227\) −3.93832e10 −0.984453 −0.492226 0.870467i \(-0.663817\pi\)
−0.492226 + 0.870467i \(0.663817\pi\)
\(228\) 2.41898e10 0.592824
\(229\) −2.26140e10 −0.543398 −0.271699 0.962382i \(-0.587586\pi\)
−0.271699 + 0.962382i \(0.587586\pi\)
\(230\) −1.99726e9 −0.0470608
\(231\) 7.16655e9 0.165598
\(232\) −3.95289e9 −0.0895815
\(233\) 6.74922e10 1.50021 0.750105 0.661319i \(-0.230003\pi\)
0.750105 + 0.661319i \(0.230003\pi\)
\(234\) 8.13240e9 0.177316
\(235\) 4.24983e10 0.909006
\(236\) −8.48745e9 −0.178104
\(237\) −3.69654e10 −0.761076
\(238\) −5.57678e9 −0.112665
\(239\) 9.04335e10 1.79283 0.896414 0.443217i \(-0.146163\pi\)
0.896414 + 0.443217i \(0.146163\pi\)
\(240\) −9.62825e9 −0.187326
\(241\) 7.42878e10 1.41854 0.709269 0.704938i \(-0.249025\pi\)
0.709269 + 0.704938i \(0.249025\pi\)
\(242\) 7.78835e10 1.45974
\(243\) −3.48678e9 −0.0641500
\(244\) 4.64124e10 0.838263
\(245\) 3.52979e10 0.625895
\(246\) 9.20187e10 1.60202
\(247\) −1.51774e10 −0.259454
\(248\) 3.60016e10 0.604350
\(249\) 2.74462e10 0.452464
\(250\) 9.76961e10 1.58178
\(251\) −1.00228e10 −0.159388 −0.0796939 0.996819i \(-0.525394\pi\)
−0.0796939 + 0.996819i \(0.525394\pi\)
\(252\) −5.99842e9 −0.0936988
\(253\) 4.25729e9 0.0653266
\(254\) −3.99057e9 −0.0601566
\(255\) 9.07700e9 0.134435
\(256\) −5.10222e9 −0.0742471
\(257\) −8.19063e10 −1.17117 −0.585583 0.810613i \(-0.699134\pi\)
−0.585583 + 0.810613i \(0.699134\pi\)
\(258\) 1.46783e9 0.0206247
\(259\) 8.77083e9 0.121113
\(260\) −2.27714e10 −0.309036
\(261\) −3.95264e9 −0.0527236
\(262\) −1.34873e11 −1.76836
\(263\) 1.14867e11 1.48045 0.740225 0.672359i \(-0.234719\pi\)
0.740225 + 0.672359i \(0.234719\pi\)
\(264\) −3.60255e10 −0.456449
\(265\) 8.32167e10 1.03658
\(266\) 1.93778e10 0.237322
\(267\) 2.92700e10 0.352469
\(268\) −1.29814e10 −0.153715
\(269\) −2.34014e10 −0.272494 −0.136247 0.990675i \(-0.543504\pi\)
−0.136247 + 0.990675i \(0.543504\pi\)
\(270\) 1.68999e10 0.193530
\(271\) −3.31269e10 −0.373095 −0.186547 0.982446i \(-0.559730\pi\)
−0.186547 + 0.982446i \(0.559730\pi\)
\(272\) −1.59705e10 −0.176913
\(273\) 3.76358e9 0.0410081
\(274\) −9.29721e9 −0.0996495
\(275\) −7.58544e10 −0.799804
\(276\) −3.56335e9 −0.0369631
\(277\) 8.16288e10 0.833076 0.416538 0.909118i \(-0.363243\pi\)
0.416538 + 0.909118i \(0.363243\pi\)
\(278\) 2.50207e11 2.51245
\(279\) 3.59993e10 0.355693
\(280\) 7.82158e9 0.0760472
\(281\) −2.57241e10 −0.246129 −0.123064 0.992399i \(-0.539272\pi\)
−0.123064 + 0.992399i \(0.539272\pi\)
\(282\) 1.31246e11 1.23585
\(283\) 2.86834e10 0.265822 0.132911 0.991128i \(-0.457568\pi\)
0.132911 + 0.991128i \(0.457568\pi\)
\(284\) 2.11712e11 1.93113
\(285\) −3.15401e10 −0.283179
\(286\) 8.40189e10 0.742557
\(287\) 4.25852e10 0.370502
\(288\) −5.17759e10 −0.443467
\(289\) −1.03532e11 −0.873038
\(290\) 1.91579e10 0.159058
\(291\) 4.68892e10 0.383313
\(292\) −1.43974e11 −1.15894
\(293\) 8.31371e10 0.659008 0.329504 0.944154i \(-0.393119\pi\)
0.329504 + 0.944154i \(0.393119\pi\)
\(294\) 1.09009e11 0.850942
\(295\) 1.10665e10 0.0850765
\(296\) −4.40900e10 −0.333832
\(297\) −3.60233e10 −0.268645
\(298\) −9.67895e10 −0.710976
\(299\) 2.23575e9 0.0161772
\(300\) 6.34902e10 0.452545
\(301\) 6.79296e8 0.00476991
\(302\) −6.88253e10 −0.476121
\(303\) −9.06488e10 −0.617831
\(304\) 5.54932e10 0.372657
\(305\) −6.05153e10 −0.400420
\(306\) 2.80321e10 0.182772
\(307\) −3.09958e10 −0.199150 −0.0995751 0.995030i \(-0.531748\pi\)
−0.0995751 + 0.995030i \(0.531748\pi\)
\(308\) −6.19719e10 −0.392389
\(309\) 1.77467e11 1.10740
\(310\) −1.74484e11 −1.07307
\(311\) −3.74590e10 −0.227057 −0.113528 0.993535i \(-0.536215\pi\)
−0.113528 + 0.993535i \(0.536215\pi\)
\(312\) −1.89191e10 −0.113033
\(313\) −2.70736e11 −1.59440 −0.797199 0.603717i \(-0.793686\pi\)
−0.797199 + 0.603717i \(0.793686\pi\)
\(314\) 6.44933e10 0.374396
\(315\) 7.82110e9 0.0447580
\(316\) 3.19654e11 1.80338
\(317\) 3.47299e11 1.93169 0.965843 0.259127i \(-0.0834349\pi\)
0.965843 + 0.259127i \(0.0834349\pi\)
\(318\) 2.56995e11 1.40930
\(319\) −4.08362e10 −0.220794
\(320\) 1.90090e11 1.01341
\(321\) 1.61886e11 0.851011
\(322\) −2.85451e9 −0.0147972
\(323\) −5.23160e10 −0.267438
\(324\) 3.01515e10 0.152005
\(325\) −3.98356e10 −0.198060
\(326\) −2.67297e11 −1.31073
\(327\) −1.39556e10 −0.0674967
\(328\) −2.14071e11 −1.02124
\(329\) 6.07391e10 0.285816
\(330\) 1.74600e11 0.810458
\(331\) −1.37406e11 −0.629185 −0.314593 0.949227i \(-0.601868\pi\)
−0.314593 + 0.949227i \(0.601868\pi\)
\(332\) −2.37337e11 −1.07212
\(333\) −4.40873e10 −0.196478
\(334\) 6.01346e11 2.64402
\(335\) 1.69260e10 0.0734265
\(336\) −1.37608e10 −0.0589003
\(337\) −2.32579e11 −0.982282 −0.491141 0.871080i \(-0.663420\pi\)
−0.491141 + 0.871080i \(0.663420\pi\)
\(338\) −3.25126e11 −1.35496
\(339\) −1.33855e11 −0.550472
\(340\) −7.84922e10 −0.318545
\(341\) 3.71923e11 1.48956
\(342\) −9.74042e10 −0.384999
\(343\) 1.03120e11 0.402272
\(344\) −3.41475e9 −0.0131476
\(345\) 4.64612e9 0.0176565
\(346\) −4.89755e11 −1.83711
\(347\) 1.41713e11 0.524719 0.262360 0.964970i \(-0.415499\pi\)
0.262360 + 0.964970i \(0.415499\pi\)
\(348\) 3.41800e10 0.124930
\(349\) −9.57812e10 −0.345594 −0.172797 0.984957i \(-0.555280\pi\)
−0.172797 + 0.984957i \(0.555280\pi\)
\(350\) 5.08604e10 0.181165
\(351\) −1.89180e10 −0.0665261
\(352\) −5.34916e11 −1.85713
\(353\) 9.36174e10 0.320901 0.160450 0.987044i \(-0.448705\pi\)
0.160450 + 0.987044i \(0.448705\pi\)
\(354\) 3.41761e10 0.115667
\(355\) −2.76043e11 −0.922462
\(356\) −2.53108e11 −0.835182
\(357\) 1.29730e10 0.0422700
\(358\) 1.24431e11 0.400365
\(359\) 5.09847e11 1.62000 0.809999 0.586431i \(-0.199467\pi\)
0.809999 + 0.586431i \(0.199467\pi\)
\(360\) −3.93158e10 −0.123369
\(361\) −1.40904e11 −0.436656
\(362\) −6.94486e10 −0.212557
\(363\) −1.81176e11 −0.547672
\(364\) −3.25451e10 −0.0971694
\(365\) 1.87722e11 0.553602
\(366\) −1.86887e11 −0.544396
\(367\) 4.06963e10 0.117100 0.0585501 0.998284i \(-0.481352\pi\)
0.0585501 + 0.998284i \(0.481352\pi\)
\(368\) −8.17461e9 −0.0232355
\(369\) −2.14058e11 −0.601053
\(370\) 2.13685e11 0.592742
\(371\) 1.18934e11 0.325930
\(372\) −3.11300e11 −0.842822
\(373\) 3.23363e11 0.864969 0.432484 0.901641i \(-0.357637\pi\)
0.432484 + 0.901641i \(0.357637\pi\)
\(374\) 2.89611e11 0.765407
\(375\) −2.27265e11 −0.593461
\(376\) −3.05329e11 −0.787813
\(377\) −2.14455e10 −0.0546765
\(378\) 2.41536e10 0.0608512
\(379\) 4.33723e11 1.07978 0.539891 0.841735i \(-0.318466\pi\)
0.539891 + 0.841735i \(0.318466\pi\)
\(380\) 2.72739e11 0.670998
\(381\) 9.28305e9 0.0225698
\(382\) −6.31442e11 −1.51722
\(383\) −3.26234e11 −0.774702 −0.387351 0.921932i \(-0.626610\pi\)
−0.387351 + 0.921932i \(0.626610\pi\)
\(384\) 2.59773e11 0.609683
\(385\) 8.08027e10 0.187436
\(386\) 4.14170e11 0.949590
\(387\) −3.41454e9 −0.00773807
\(388\) −4.05468e11 −0.908268
\(389\) −7.50132e11 −1.66098 −0.830490 0.557033i \(-0.811940\pi\)
−0.830490 + 0.557033i \(0.811940\pi\)
\(390\) 9.16926e10 0.200698
\(391\) 7.70657e9 0.0166750
\(392\) −2.53598e11 −0.542448
\(393\) 3.13749e11 0.663461
\(394\) −9.76857e11 −2.04220
\(395\) −4.16784e11 −0.861438
\(396\) 3.11507e11 0.636560
\(397\) −5.03118e10 −0.101651 −0.0508256 0.998708i \(-0.516185\pi\)
−0.0508256 + 0.998708i \(0.516185\pi\)
\(398\) 3.16479e11 0.632225
\(399\) −4.50775e10 −0.0890394
\(400\) 1.45651e11 0.284475
\(401\) 8.16322e11 1.57656 0.788282 0.615314i \(-0.210971\pi\)
0.788282 + 0.615314i \(0.210971\pi\)
\(402\) 5.22719e10 0.0998277
\(403\) 1.95319e11 0.368868
\(404\) 7.83874e11 1.46396
\(405\) −3.93134e10 −0.0726094
\(406\) 2.73807e10 0.0500124
\(407\) −4.55482e11 −0.822804
\(408\) −6.52137e10 −0.116511
\(409\) −9.72499e11 −1.71844 −0.859220 0.511607i \(-0.829050\pi\)
−0.859220 + 0.511607i \(0.829050\pi\)
\(410\) 1.03751e12 1.81328
\(411\) 2.16276e10 0.0373869
\(412\) −1.53462e12 −2.62400
\(413\) 1.58163e10 0.0267504
\(414\) 1.43484e10 0.0240051
\(415\) 3.09455e11 0.512130
\(416\) −2.80916e11 −0.459893
\(417\) −5.82042e11 −0.942631
\(418\) −1.00632e12 −1.61229
\(419\) 1.26868e11 0.201090 0.100545 0.994933i \(-0.467941\pi\)
0.100545 + 0.994933i \(0.467941\pi\)
\(420\) −6.76320e10 −0.106055
\(421\) 2.96147e10 0.0459450 0.0229725 0.999736i \(-0.492687\pi\)
0.0229725 + 0.999736i \(0.492687\pi\)
\(422\) 4.86921e11 0.747399
\(423\) −3.05310e11 −0.463671
\(424\) −5.97870e11 −0.898381
\(425\) −1.37312e11 −0.204155
\(426\) −8.52492e11 −1.25414
\(427\) −8.64893e10 −0.125903
\(428\) −1.39988e12 −2.01649
\(429\) −1.95448e11 −0.278596
\(430\) 1.65498e10 0.0233445
\(431\) −8.45775e11 −1.18061 −0.590306 0.807180i \(-0.700993\pi\)
−0.590306 + 0.807180i \(0.700993\pi\)
\(432\) 6.91699e10 0.0955521
\(433\) −7.36248e11 −1.00653 −0.503267 0.864131i \(-0.667869\pi\)
−0.503267 + 0.864131i \(0.667869\pi\)
\(434\) −2.49374e11 −0.337402
\(435\) −4.45659e10 −0.0596762
\(436\) 1.20679e11 0.159935
\(437\) −2.67783e10 −0.0351250
\(438\) 5.79735e11 0.752656
\(439\) −6.89894e11 −0.886528 −0.443264 0.896391i \(-0.646180\pi\)
−0.443264 + 0.896391i \(0.646180\pi\)
\(440\) −4.06186e11 −0.516640
\(441\) −2.53582e11 −0.319260
\(442\) 1.52092e11 0.189542
\(443\) 7.68420e11 0.947942 0.473971 0.880540i \(-0.342820\pi\)
0.473971 + 0.880540i \(0.342820\pi\)
\(444\) 3.81239e11 0.465559
\(445\) 3.30018e11 0.398949
\(446\) 7.72120e11 0.924013
\(447\) 2.25156e11 0.266747
\(448\) 2.71679e11 0.318643
\(449\) −1.22056e11 −0.141726 −0.0708629 0.997486i \(-0.522575\pi\)
−0.0708629 + 0.997486i \(0.522575\pi\)
\(450\) −2.55654e11 −0.293898
\(451\) −2.21151e12 −2.51707
\(452\) 1.15749e12 1.30435
\(453\) 1.60105e11 0.178633
\(454\) −1.37133e12 −1.51492
\(455\) 4.24343e10 0.0464158
\(456\) 2.26600e11 0.245425
\(457\) 1.71755e11 0.184198 0.0920992 0.995750i \(-0.470642\pi\)
0.0920992 + 0.995750i \(0.470642\pi\)
\(458\) −7.87422e11 −0.836205
\(459\) −6.52096e10 −0.0685732
\(460\) −4.01767e10 −0.0418374
\(461\) −2.81481e10 −0.0290265 −0.0145132 0.999895i \(-0.504620\pi\)
−0.0145132 + 0.999895i \(0.504620\pi\)
\(462\) 2.49540e11 0.254830
\(463\) 3.34262e10 0.0338043 0.0169022 0.999857i \(-0.494620\pi\)
0.0169022 + 0.999857i \(0.494620\pi\)
\(464\) 7.84115e10 0.0785324
\(465\) 4.05892e11 0.402598
\(466\) 2.35008e12 2.30859
\(467\) 2.55215e10 0.0248302 0.0124151 0.999923i \(-0.496048\pi\)
0.0124151 + 0.999923i \(0.496048\pi\)
\(468\) 1.63591e11 0.157635
\(469\) 2.41908e10 0.0230873
\(470\) 1.47980e12 1.39882
\(471\) −1.50027e11 −0.140468
\(472\) −7.95069e10 −0.0737337
\(473\) −3.52769e10 −0.0324052
\(474\) −1.28714e12 −1.17118
\(475\) 4.77123e11 0.430040
\(476\) −1.12182e11 −0.100159
\(477\) −5.97834e11 −0.528747
\(478\) 3.14890e12 2.75888
\(479\) −1.97153e12 −1.71117 −0.855586 0.517661i \(-0.826803\pi\)
−0.855586 + 0.517661i \(0.826803\pi\)
\(480\) −5.83771e11 −0.501946
\(481\) −2.39201e11 −0.203756
\(482\) 2.58671e12 2.18291
\(483\) 6.64029e9 0.00555169
\(484\) 1.56670e12 1.29772
\(485\) 5.28674e11 0.433860
\(486\) −1.21410e11 −0.0987169
\(487\) 2.05628e11 0.165654 0.0828269 0.996564i \(-0.473605\pi\)
0.0828269 + 0.996564i \(0.473605\pi\)
\(488\) 4.34772e11 0.347035
\(489\) 6.21798e11 0.491767
\(490\) 1.22908e12 0.963155
\(491\) 2.82095e11 0.219042 0.109521 0.993984i \(-0.465068\pi\)
0.109521 + 0.993984i \(0.465068\pi\)
\(492\) 1.85104e12 1.42421
\(493\) −7.39221e10 −0.0563590
\(494\) −5.28478e11 −0.399260
\(495\) −4.06161e11 −0.304071
\(496\) −7.14145e11 −0.529809
\(497\) −3.94524e11 −0.290048
\(498\) 9.55677e11 0.696272
\(499\) 1.70553e11 0.123142 0.0615709 0.998103i \(-0.480389\pi\)
0.0615709 + 0.998103i \(0.480389\pi\)
\(500\) 1.96525e12 1.40622
\(501\) −1.39888e12 −0.991995
\(502\) −3.48993e11 −0.245273
\(503\) 3.31028e11 0.230573 0.115286 0.993332i \(-0.463221\pi\)
0.115286 + 0.993332i \(0.463221\pi\)
\(504\) −5.61907e10 −0.0387906
\(505\) −1.02206e12 −0.699304
\(506\) 1.48239e11 0.100528
\(507\) 7.56323e11 0.508360
\(508\) −8.02740e10 −0.0534796
\(509\) −1.19140e12 −0.786732 −0.393366 0.919382i \(-0.628689\pi\)
−0.393366 + 0.919382i \(0.628689\pi\)
\(510\) 3.16062e11 0.206874
\(511\) 2.68295e11 0.174068
\(512\) 1.46436e12 0.941747
\(513\) 2.26586e11 0.144446
\(514\) −2.85198e12 −1.80224
\(515\) 2.00094e12 1.25343
\(516\) 2.95268e10 0.0183355
\(517\) −3.15427e12 −1.94174
\(518\) 3.05401e11 0.186374
\(519\) 1.13929e12 0.689257
\(520\) −2.13313e11 −0.127939
\(521\) 2.38998e12 1.42110 0.710550 0.703647i \(-0.248446\pi\)
0.710550 + 0.703647i \(0.248446\pi\)
\(522\) −1.37631e11 −0.0811335
\(523\) −8.44568e11 −0.493602 −0.246801 0.969066i \(-0.579379\pi\)
−0.246801 + 0.969066i \(0.579379\pi\)
\(524\) −2.71310e12 −1.57208
\(525\) −1.18314e11 −0.0679701
\(526\) 3.99967e12 2.27818
\(527\) 6.73258e11 0.380219
\(528\) 7.14620e11 0.400150
\(529\) −1.79721e12 −0.997810
\(530\) 2.89761e12 1.59514
\(531\) −7.95020e10 −0.0433963
\(532\) 3.89802e11 0.210980
\(533\) −1.16140e12 −0.623316
\(534\) 1.01918e12 0.542395
\(535\) 1.82525e12 0.963233
\(536\) −1.21605e11 −0.0636369
\(537\) −2.89458e11 −0.150211
\(538\) −8.14840e11 −0.419326
\(539\) −2.61985e12 −1.33699
\(540\) 3.39958e11 0.172049
\(541\) −7.01041e11 −0.351849 −0.175924 0.984404i \(-0.556291\pi\)
−0.175924 + 0.984404i \(0.556291\pi\)
\(542\) −1.15348e12 −0.574135
\(543\) 1.61554e11 0.0797480
\(544\) −9.68309e11 −0.474044
\(545\) −1.57349e11 −0.0763974
\(546\) 1.31048e11 0.0631050
\(547\) 9.24049e11 0.441318 0.220659 0.975351i \(-0.429179\pi\)
0.220659 + 0.975351i \(0.429179\pi\)
\(548\) −1.87022e11 −0.0885890
\(549\) 4.34746e11 0.204249
\(550\) −2.64125e12 −1.23077
\(551\) 2.56859e11 0.118717
\(552\) −3.33800e10 −0.0153024
\(553\) −5.95673e11 −0.270860
\(554\) 2.84232e12 1.28197
\(555\) −4.97083e11 −0.222387
\(556\) 5.03313e12 2.23358
\(557\) 2.45138e11 0.107910 0.0539551 0.998543i \(-0.482817\pi\)
0.0539551 + 0.998543i \(0.482817\pi\)
\(558\) 1.25350e12 0.547357
\(559\) −1.85260e10 −0.00802468
\(560\) −1.55153e11 −0.0666674
\(561\) −6.73705e11 −0.287169
\(562\) −8.95717e11 −0.378754
\(563\) 9.57177e11 0.401518 0.200759 0.979641i \(-0.435659\pi\)
0.200759 + 0.979641i \(0.435659\pi\)
\(564\) 2.64013e12 1.09868
\(565\) −1.50921e12 −0.623062
\(566\) 9.98758e11 0.409059
\(567\) −5.61872e10 −0.0228304
\(568\) 1.98323e12 0.799475
\(569\) 2.78904e12 1.11545 0.557724 0.830027i \(-0.311675\pi\)
0.557724 + 0.830027i \(0.311675\pi\)
\(570\) −1.09823e12 −0.435769
\(571\) 1.09475e12 0.430977 0.215489 0.976506i \(-0.430866\pi\)
0.215489 + 0.976506i \(0.430866\pi\)
\(572\) 1.69012e12 0.660137
\(573\) 1.46889e12 0.569237
\(574\) 1.48282e12 0.570144
\(575\) −7.02841e10 −0.0268134
\(576\) −1.36562e12 −0.516925
\(577\) −2.45219e11 −0.0921008 −0.0460504 0.998939i \(-0.514663\pi\)
−0.0460504 + 0.998939i \(0.514663\pi\)
\(578\) −3.60498e12 −1.34347
\(579\) −9.63462e11 −0.356271
\(580\) 3.85378e11 0.141404
\(581\) 4.42276e11 0.161028
\(582\) 1.63268e12 0.589860
\(583\) −6.17644e12 −2.21427
\(584\) −1.34869e12 −0.479793
\(585\) −2.13299e11 −0.0752988
\(586\) 2.89484e12 1.01411
\(587\) −4.06626e12 −1.41359 −0.706796 0.707417i \(-0.749860\pi\)
−0.706796 + 0.707417i \(0.749860\pi\)
\(588\) 2.19282e12 0.756493
\(589\) −2.33939e12 −0.800910
\(590\) 3.85335e11 0.130919
\(591\) 2.27241e12 0.766201
\(592\) 8.74592e11 0.292656
\(593\) 3.27334e11 0.108704 0.0543519 0.998522i \(-0.482691\pi\)
0.0543519 + 0.998522i \(0.482691\pi\)
\(594\) −1.25433e12 −0.413403
\(595\) 1.46270e11 0.0478441
\(596\) −1.94701e12 −0.632062
\(597\) −7.36208e11 −0.237201
\(598\) 7.78491e10 0.0248942
\(599\) −5.51362e12 −1.74991 −0.874956 0.484202i \(-0.839110\pi\)
−0.874956 + 0.484202i \(0.839110\pi\)
\(600\) 5.94750e11 0.187350
\(601\) 1.67559e12 0.523881 0.261941 0.965084i \(-0.415638\pi\)
0.261941 + 0.965084i \(0.415638\pi\)
\(602\) 2.36531e10 0.00734014
\(603\) −1.21597e11 −0.0374538
\(604\) −1.38448e12 −0.423274
\(605\) −2.04275e12 −0.619893
\(606\) −3.15640e12 −0.950746
\(607\) −4.84043e12 −1.44722 −0.723611 0.690208i \(-0.757519\pi\)
−0.723611 + 0.690208i \(0.757519\pi\)
\(608\) 3.36461e12 0.998548
\(609\) −6.36942e10 −0.0187639
\(610\) −2.10715e12 −0.616185
\(611\) −1.65650e12 −0.480845
\(612\) 5.63892e11 0.162486
\(613\) −3.98712e12 −1.14048 −0.570240 0.821478i \(-0.693150\pi\)
−0.570240 + 0.821478i \(0.693150\pi\)
\(614\) −1.07928e12 −0.306461
\(615\) −2.41350e12 −0.680313
\(616\) −5.80527e11 −0.162446
\(617\) 1.01386e12 0.281641 0.140820 0.990035i \(-0.455026\pi\)
0.140820 + 0.990035i \(0.455026\pi\)
\(618\) 6.17942e12 1.70412
\(619\) −1.11173e12 −0.304361 −0.152181 0.988353i \(-0.548630\pi\)
−0.152181 + 0.988353i \(0.548630\pi\)
\(620\) −3.50990e12 −0.953964
\(621\) −3.33780e10 −0.00900632
\(622\) −1.30432e12 −0.349405
\(623\) 4.71666e11 0.125441
\(624\) 3.75289e11 0.0990913
\(625\) −3.76746e11 −0.0987617
\(626\) −9.42705e12 −2.45353
\(627\) 2.34094e12 0.604905
\(628\) 1.29734e12 0.332841
\(629\) −8.24518e11 −0.210026
\(630\) 2.72331e11 0.0688755
\(631\) 5.31416e12 1.33445 0.667225 0.744856i \(-0.267482\pi\)
0.667225 + 0.744856i \(0.267482\pi\)
\(632\) 2.99438e12 0.746587
\(633\) −1.13270e12 −0.280413
\(634\) 1.20930e13 2.97256
\(635\) 1.04666e11 0.0255461
\(636\) 5.16969e12 1.25287
\(637\) −1.37584e12 −0.331085
\(638\) −1.42192e12 −0.339768
\(639\) 1.98311e12 0.470535
\(640\) 2.92894e12 0.690081
\(641\) −5.10915e12 −1.19533 −0.597664 0.801747i \(-0.703904\pi\)
−0.597664 + 0.801747i \(0.703904\pi\)
\(642\) 5.63687e12 1.30957
\(643\) 9.16548e11 0.211449 0.105725 0.994395i \(-0.466284\pi\)
0.105725 + 0.994395i \(0.466284\pi\)
\(644\) −5.74211e10 −0.0131548
\(645\) −3.84988e10 −0.00875848
\(646\) −1.82165e12 −0.411546
\(647\) −1.56251e12 −0.350554 −0.175277 0.984519i \(-0.556082\pi\)
−0.175277 + 0.984519i \(0.556082\pi\)
\(648\) 2.82447e11 0.0629288
\(649\) −8.21365e11 −0.181733
\(650\) −1.38708e12 −0.304783
\(651\) 5.80105e11 0.126588
\(652\) −5.37692e12 −1.16525
\(653\) 4.18928e12 0.901634 0.450817 0.892616i \(-0.351133\pi\)
0.450817 + 0.892616i \(0.351133\pi\)
\(654\) −4.85934e11 −0.103867
\(655\) 3.53751e12 0.750951
\(656\) 4.24643e12 0.895274
\(657\) −1.34861e12 −0.282385
\(658\) 2.11494e12 0.439827
\(659\) 2.80694e12 0.579761 0.289880 0.957063i \(-0.406384\pi\)
0.289880 + 0.957063i \(0.406384\pi\)
\(660\) 3.51223e12 0.720502
\(661\) 6.73837e12 1.37293 0.686465 0.727163i \(-0.259162\pi\)
0.686465 + 0.727163i \(0.259162\pi\)
\(662\) −4.78448e12 −0.968218
\(663\) −3.53802e11 −0.0711131
\(664\) −2.22328e12 −0.443851
\(665\) −5.08248e11 −0.100781
\(666\) −1.53512e12 −0.302349
\(667\) −3.78375e10 −0.00740212
\(668\) 1.20966e13 2.35055
\(669\) −1.79614e12 −0.346675
\(670\) 5.89364e11 0.112992
\(671\) 4.49152e12 0.855346
\(672\) −8.34333e11 −0.157826
\(673\) 6.34420e12 1.19209 0.596045 0.802951i \(-0.296738\pi\)
0.596045 + 0.802951i \(0.296738\pi\)
\(674\) −8.09843e12 −1.51158
\(675\) 5.94713e11 0.110266
\(676\) −6.54021e12 −1.20457
\(677\) 1.72678e12 0.315928 0.157964 0.987445i \(-0.449507\pi\)
0.157964 + 0.987445i \(0.449507\pi\)
\(678\) −4.66083e12 −0.847090
\(679\) 7.55587e11 0.136418
\(680\) −7.35282e11 −0.131875
\(681\) 3.19004e12 0.568374
\(682\) 1.29504e13 2.29220
\(683\) 1.07112e12 0.188342 0.0941708 0.995556i \(-0.469980\pi\)
0.0941708 + 0.995556i \(0.469980\pi\)
\(684\) −1.95937e12 −0.342267
\(685\) 2.43850e11 0.0423171
\(686\) 3.59065e12 0.619034
\(687\) 1.83174e12 0.313731
\(688\) 6.77367e10 0.0115259
\(689\) −3.24362e12 −0.548331
\(690\) 1.61778e11 0.0271706
\(691\) −2.31254e12 −0.385868 −0.192934 0.981212i \(-0.561800\pi\)
−0.192934 + 0.981212i \(0.561800\pi\)
\(692\) −9.85186e12 −1.63321
\(693\) −5.80491e11 −0.0956083
\(694\) 4.93446e12 0.807461
\(695\) −6.56250e12 −1.06694
\(696\) 3.20184e11 0.0517199
\(697\) −4.00330e12 −0.642496
\(698\) −3.33511e12 −0.531815
\(699\) −5.46687e12 −0.866146
\(700\) 1.02310e12 0.161056
\(701\) 1.00626e13 1.57390 0.786950 0.617017i \(-0.211659\pi\)
0.786950 + 0.617017i \(0.211659\pi\)
\(702\) −6.58724e11 −0.102373
\(703\) 2.86498e12 0.442407
\(704\) −1.41087e13 −2.16476
\(705\) −3.44237e12 −0.524815
\(706\) 3.25977e12 0.493816
\(707\) −1.46074e12 −0.219880
\(708\) 6.87484e11 0.102828
\(709\) 1.11083e12 0.165098 0.0825488 0.996587i \(-0.473694\pi\)
0.0825488 + 0.996587i \(0.473694\pi\)
\(710\) −9.61182e12 −1.41953
\(711\) 2.99420e12 0.439407
\(712\) −2.37101e12 −0.345759
\(713\) 3.44611e11 0.0499375
\(714\) 4.51719e11 0.0650469
\(715\) −2.20368e12 −0.315334
\(716\) 2.50305e12 0.355927
\(717\) −7.32511e12 −1.03509
\(718\) 1.77529e13 2.49293
\(719\) −8.25712e12 −1.15225 −0.576127 0.817360i \(-0.695437\pi\)
−0.576127 + 0.817360i \(0.695437\pi\)
\(720\) 7.79889e11 0.108152
\(721\) 2.85976e12 0.394113
\(722\) −4.90628e12 −0.671946
\(723\) −6.01731e12 −0.818993
\(724\) −1.39702e12 −0.188964
\(725\) 6.74171e11 0.0906252
\(726\) −6.30856e12 −0.842783
\(727\) 2.11241e12 0.280462 0.140231 0.990119i \(-0.455216\pi\)
0.140231 + 0.990119i \(0.455216\pi\)
\(728\) −3.04869e11 −0.0402274
\(729\) 2.82430e11 0.0370370
\(730\) 6.53650e12 0.851907
\(731\) −6.38585e10 −0.00827162
\(732\) −3.75941e12 −0.483971
\(733\) −6.44023e12 −0.824012 −0.412006 0.911181i \(-0.635172\pi\)
−0.412006 + 0.911181i \(0.635172\pi\)
\(734\) 1.41705e12 0.180199
\(735\) −2.85913e12 −0.361361
\(736\) −4.95635e11 −0.0622604
\(737\) −1.25627e12 −0.156848
\(738\) −7.45351e12 −0.924927
\(739\) −9.42197e12 −1.16210 −0.581048 0.813869i \(-0.697357\pi\)
−0.581048 + 0.813869i \(0.697357\pi\)
\(740\) 4.29846e12 0.526951
\(741\) 1.22937e12 0.149796
\(742\) 4.14130e12 0.501556
\(743\) −1.14547e12 −0.137890 −0.0689449 0.997620i \(-0.521963\pi\)
−0.0689449 + 0.997620i \(0.521963\pi\)
\(744\) −2.91613e12 −0.348922
\(745\) 2.53863e12 0.301923
\(746\) 1.12595e13 1.33105
\(747\) −2.22314e12 −0.261230
\(748\) 5.82578e12 0.680451
\(749\) 2.60868e12 0.302867
\(750\) −7.91338e12 −0.913243
\(751\) 4.56219e12 0.523352 0.261676 0.965156i \(-0.415725\pi\)
0.261676 + 0.965156i \(0.415725\pi\)
\(752\) 6.05667e12 0.690642
\(753\) 8.11843e11 0.0920226
\(754\) −7.46735e11 −0.0841386
\(755\) 1.80517e12 0.202189
\(756\) 4.85872e11 0.0540970
\(757\) −9.37649e12 −1.03779 −0.518894 0.854839i \(-0.673656\pi\)
−0.518894 + 0.854839i \(0.673656\pi\)
\(758\) 1.51023e13 1.66162
\(759\) −3.44840e11 −0.0377164
\(760\) 2.55491e12 0.277788
\(761\) 1.75158e13 1.89321 0.946605 0.322394i \(-0.104488\pi\)
0.946605 + 0.322394i \(0.104488\pi\)
\(762\) 3.23236e11 0.0347314
\(763\) −2.24885e11 −0.0240215
\(764\) −1.27020e13 −1.34882
\(765\) −7.35237e11 −0.0776159
\(766\) −1.13595e13 −1.19215
\(767\) −4.31347e11 −0.0450037
\(768\) 4.13280e11 0.0428666
\(769\) 1.85532e13 1.91316 0.956580 0.291470i \(-0.0941442\pi\)
0.956580 + 0.291470i \(0.0941442\pi\)
\(770\) 2.81355e12 0.288434
\(771\) 6.63441e12 0.676172
\(772\) 8.33141e12 0.844191
\(773\) −9.95968e12 −1.00332 −0.501658 0.865066i \(-0.667276\pi\)
−0.501658 + 0.865066i \(0.667276\pi\)
\(774\) −1.18894e11 −0.0119077
\(775\) −6.14012e12 −0.611392
\(776\) −3.79826e12 −0.376016
\(777\) −7.10437e11 −0.0699247
\(778\) −2.61197e13 −2.55599
\(779\) 1.39104e13 1.35338
\(780\) 1.84448e12 0.178422
\(781\) 2.04882e13 1.97049
\(782\) 2.68343e11 0.0256602
\(783\) 3.20164e11 0.0304400
\(784\) 5.03049e12 0.475541
\(785\) −1.69155e12 −0.158991
\(786\) 1.09248e13 1.02096
\(787\) −2.93761e12 −0.272965 −0.136483 0.990642i \(-0.543580\pi\)
−0.136483 + 0.990642i \(0.543580\pi\)
\(788\) −1.96504e13 −1.81553
\(789\) −9.30422e12 −0.854739
\(790\) −1.45124e13 −1.32562
\(791\) −2.15698e12 −0.195908
\(792\) 2.91806e12 0.263531
\(793\) 2.35876e12 0.211814
\(794\) −1.75186e12 −0.156425
\(795\) −6.74056e12 −0.598472
\(796\) 6.36627e12 0.562051
\(797\) −6.03187e11 −0.0529529 −0.0264764 0.999649i \(-0.508429\pi\)
−0.0264764 + 0.999649i \(0.508429\pi\)
\(798\) −1.56960e12 −0.137018
\(799\) −5.70990e12 −0.495641
\(800\) 8.83100e12 0.762263
\(801\) −2.37087e12 −0.203498
\(802\) 2.84244e13 2.42609
\(803\) −1.39330e13 −1.18256
\(804\) 1.05150e12 0.0887475
\(805\) 7.48691e10 0.00628378
\(806\) 6.80101e12 0.567630
\(807\) 1.89552e12 0.157325
\(808\) 7.34300e12 0.606070
\(809\) 1.12693e13 0.924975 0.462488 0.886626i \(-0.346957\pi\)
0.462488 + 0.886626i \(0.346957\pi\)
\(810\) −1.36890e12 −0.111735
\(811\) −6.55655e12 −0.532208 −0.266104 0.963944i \(-0.585736\pi\)
−0.266104 + 0.963944i \(0.585736\pi\)
\(812\) 5.50788e11 0.0444613
\(813\) 2.68328e12 0.215406
\(814\) −1.58599e13 −1.26617
\(815\) 7.01075e12 0.556616
\(816\) 1.29361e12 0.102141
\(817\) 2.21891e11 0.0174237
\(818\) −3.38625e13 −2.64441
\(819\) −3.04850e11 −0.0236760
\(820\) 2.08704e13 1.61201
\(821\) −9.21418e12 −0.707803 −0.353902 0.935283i \(-0.615145\pi\)
−0.353902 + 0.935283i \(0.615145\pi\)
\(822\) 7.53074e11 0.0575327
\(823\) −4.75017e12 −0.360919 −0.180460 0.983582i \(-0.557759\pi\)
−0.180460 + 0.983582i \(0.557759\pi\)
\(824\) −1.43757e13 −1.08632
\(825\) 6.14420e12 0.461767
\(826\) 5.50725e11 0.0411647
\(827\) 1.61227e13 1.19857 0.599285 0.800536i \(-0.295452\pi\)
0.599285 + 0.800536i \(0.295452\pi\)
\(828\) 2.88632e11 0.0213406
\(829\) −6.58919e12 −0.484548 −0.242274 0.970208i \(-0.577893\pi\)
−0.242274 + 0.970208i \(0.577893\pi\)
\(830\) 1.07752e13 0.788089
\(831\) −6.61194e12 −0.480977
\(832\) −7.40931e12 −0.536072
\(833\) −4.74248e12 −0.341274
\(834\) −2.02667e13 −1.45056
\(835\) −1.57723e13 −1.12281
\(836\) −2.02430e13 −1.43333
\(837\) −2.91595e12 −0.205360
\(838\) 4.41756e12 0.309446
\(839\) −1.34080e13 −0.934189 −0.467095 0.884207i \(-0.654699\pi\)
−0.467095 + 0.884207i \(0.654699\pi\)
\(840\) −6.33548e11 −0.0439059
\(841\) −1.41442e13 −0.974982
\(842\) 1.03119e12 0.0707021
\(843\) 2.08366e12 0.142103
\(844\) 9.79486e12 0.664442
\(845\) 8.52752e12 0.575397
\(846\) −1.06309e13 −0.713517
\(847\) −2.91953e12 −0.194912
\(848\) 1.18597e13 0.787573
\(849\) −2.32335e12 −0.153473
\(850\) −4.78122e12 −0.314162
\(851\) −4.22035e11 −0.0275845
\(852\) −1.71487e13 −1.11494
\(853\) −1.09860e13 −0.710508 −0.355254 0.934770i \(-0.615606\pi\)
−0.355254 + 0.934770i \(0.615606\pi\)
\(854\) −3.01156e12 −0.193745
\(855\) 2.55475e12 0.163494
\(856\) −1.31135e13 −0.834810
\(857\) 2.81411e13 1.78208 0.891042 0.453922i \(-0.149975\pi\)
0.891042 + 0.453922i \(0.149975\pi\)
\(858\) −6.80553e12 −0.428715
\(859\) −2.38495e12 −0.149455 −0.0747274 0.997204i \(-0.523809\pi\)
−0.0747274 + 0.997204i \(0.523809\pi\)
\(860\) 3.32914e11 0.0207534
\(861\) −3.44940e12 −0.213909
\(862\) −2.94500e13 −1.81678
\(863\) −1.95313e13 −1.19862 −0.599310 0.800517i \(-0.704558\pi\)
−0.599310 + 0.800517i \(0.704558\pi\)
\(864\) 4.19384e12 0.256036
\(865\) 1.28455e13 0.780148
\(866\) −2.56362e13 −1.54890
\(867\) 8.38607e12 0.504049
\(868\) −5.01639e12 −0.299952
\(869\) 3.09342e13 1.84013
\(870\) −1.55179e12 −0.0918324
\(871\) −6.59740e11 −0.0388411
\(872\) 1.13047e12 0.0662118
\(873\) −3.79802e12 −0.221306
\(874\) −9.32421e11 −0.0540519
\(875\) −3.66222e12 −0.211207
\(876\) 1.16619e13 0.669115
\(877\) −1.20441e13 −0.687507 −0.343753 0.939060i \(-0.611698\pi\)
−0.343753 + 0.939060i \(0.611698\pi\)
\(878\) −2.40222e13 −1.36423
\(879\) −6.73410e12 −0.380478
\(880\) 8.05732e12 0.452917
\(881\) 1.89332e13 1.05884 0.529422 0.848359i \(-0.322409\pi\)
0.529422 + 0.848359i \(0.322409\pi\)
\(882\) −8.82974e12 −0.491292
\(883\) 3.36047e13 1.86027 0.930136 0.367214i \(-0.119688\pi\)
0.930136 + 0.367214i \(0.119688\pi\)
\(884\) 3.05946e12 0.168504
\(885\) −8.96383e11 −0.0491189
\(886\) 2.67564e13 1.45874
\(887\) 1.38919e13 0.753540 0.376770 0.926307i \(-0.377035\pi\)
0.376770 + 0.926307i \(0.377035\pi\)
\(888\) 3.57129e12 0.192738
\(889\) 1.49590e11 0.00803239
\(890\) 1.14912e13 0.613920
\(891\) 2.91788e12 0.155102
\(892\) 1.55319e13 0.821453
\(893\) 1.98404e13 1.04404
\(894\) 7.83995e12 0.410482
\(895\) −3.26363e12 −0.170019
\(896\) 4.18607e12 0.216981
\(897\) −1.81096e11 −0.00933991
\(898\) −4.24998e12 −0.218094
\(899\) −3.30554e12 −0.168781
\(900\) −5.14271e12 −0.261277
\(901\) −1.11806e13 −0.565204
\(902\) −7.70050e13 −3.87338
\(903\) −5.50230e10 −0.00275391
\(904\) 1.08429e13 0.539992
\(905\) 1.82152e12 0.0902642
\(906\) 5.57485e12 0.274888
\(907\) −3.69220e13 −1.81156 −0.905781 0.423747i \(-0.860715\pi\)
−0.905781 + 0.423747i \(0.860715\pi\)
\(908\) −2.75855e13 −1.34677
\(909\) 7.34255e12 0.356705
\(910\) 1.47756e12 0.0714266
\(911\) 1.87155e13 0.900260 0.450130 0.892963i \(-0.351378\pi\)
0.450130 + 0.892963i \(0.351378\pi\)
\(912\) −4.49495e12 −0.215153
\(913\) −2.29681e13 −1.09397
\(914\) 5.98052e12 0.283453
\(915\) 4.90174e12 0.231183
\(916\) −1.58397e13 −0.743391
\(917\) 5.05585e12 0.236120
\(918\) −2.27060e12 −0.105524
\(919\) −4.00592e12 −0.185260 −0.0926301 0.995701i \(-0.529527\pi\)
−0.0926301 + 0.995701i \(0.529527\pi\)
\(920\) −3.76359e11 −0.0173204
\(921\) 2.51066e12 0.114979
\(922\) −9.80117e11 −0.0446672
\(923\) 1.07596e13 0.487963
\(924\) 5.01972e12 0.226546
\(925\) 7.51962e12 0.337721
\(926\) 1.16390e12 0.0520196
\(927\) −1.43748e13 −0.639358
\(928\) 4.75417e12 0.210431
\(929\) −1.03981e13 −0.458020 −0.229010 0.973424i \(-0.573549\pi\)
−0.229010 + 0.973424i \(0.573549\pi\)
\(930\) 1.41332e13 0.619536
\(931\) 1.64788e13 0.718874
\(932\) 4.72741e13 2.05235
\(933\) 3.03418e12 0.131091
\(934\) 8.88661e11 0.0382098
\(935\) −7.59600e12 −0.325037
\(936\) 1.53245e12 0.0652596
\(937\) 9.12371e11 0.0386673 0.0193336 0.999813i \(-0.493846\pi\)
0.0193336 + 0.999813i \(0.493846\pi\)
\(938\) 8.42327e11 0.0355278
\(939\) 2.19296e13 0.920526
\(940\) 2.97674e13 1.24356
\(941\) 2.95495e13 1.22856 0.614281 0.789088i \(-0.289446\pi\)
0.614281 + 0.789088i \(0.289446\pi\)
\(942\) −5.22396e12 −0.216158
\(943\) −2.04911e12 −0.0843846
\(944\) 1.57714e12 0.0646392
\(945\) −6.33509e11 −0.0258410
\(946\) −1.22834e12 −0.0498666
\(947\) −1.67431e13 −0.676490 −0.338245 0.941058i \(-0.609833\pi\)
−0.338245 + 0.941058i \(0.609833\pi\)
\(948\) −2.58920e13 −1.04118
\(949\) −7.31702e12 −0.292844
\(950\) 1.66135e13 0.661765
\(951\) −2.81312e13 −1.11526
\(952\) −1.05087e12 −0.0414653
\(953\) 1.69592e13 0.666021 0.333011 0.942923i \(-0.391936\pi\)
0.333011 + 0.942923i \(0.391936\pi\)
\(954\) −2.08166e13 −0.813659
\(955\) 1.65617e13 0.644301
\(956\) 6.33430e13 2.45266
\(957\) 3.30773e12 0.127476
\(958\) −6.86488e13 −2.63323
\(959\) 3.48514e11 0.0133057
\(960\) −1.53973e13 −0.585092
\(961\) 3.66611e12 0.138660
\(962\) −8.32898e12 −0.313548
\(963\) −1.31127e13 −0.491332
\(964\) 5.20339e13 1.94062
\(965\) −1.08630e13 −0.403252
\(966\) 2.31215e11 0.00854318
\(967\) 3.38548e13 1.24509 0.622546 0.782584i \(-0.286099\pi\)
0.622546 + 0.782584i \(0.286099\pi\)
\(968\) 1.46762e13 0.537246
\(969\) 4.23760e12 0.154405
\(970\) 1.84085e13 0.667644
\(971\) 5.39236e13 1.94667 0.973335 0.229387i \(-0.0736720\pi\)
0.973335 + 0.229387i \(0.0736720\pi\)
\(972\) −2.44227e12 −0.0877599
\(973\) −9.37921e12 −0.335474
\(974\) 7.15998e12 0.254916
\(975\) 3.22669e12 0.114350
\(976\) −8.62437e12 −0.304231
\(977\) 2.81619e13 0.988864 0.494432 0.869216i \(-0.335376\pi\)
0.494432 + 0.869216i \(0.335376\pi\)
\(978\) 2.16510e13 0.756753
\(979\) −2.44943e13 −0.852203
\(980\) 2.47240e13 0.856251
\(981\) 1.13040e12 0.0389693
\(982\) 9.82255e12 0.337072
\(983\) −3.04185e13 −1.03908 −0.519538 0.854447i \(-0.673896\pi\)
−0.519538 + 0.854447i \(0.673896\pi\)
\(984\) 1.73398e13 0.589611
\(985\) 2.56213e13 0.867239
\(986\) −2.57397e12 −0.0867277
\(987\) −4.91987e12 −0.165016
\(988\) −1.06308e13 −0.354944
\(989\) −3.26864e10 −0.00108638
\(990\) −1.41426e13 −0.467918
\(991\) −2.64875e12 −0.0872387 −0.0436194 0.999048i \(-0.513889\pi\)
−0.0436194 + 0.999048i \(0.513889\pi\)
\(992\) −4.32994e13 −1.41964
\(993\) 1.11299e13 0.363260
\(994\) −1.37373e13 −0.446338
\(995\) −8.30072e12 −0.268480
\(996\) 1.92243e13 0.618990
\(997\) 7.48989e12 0.240075 0.120038 0.992769i \(-0.461698\pi\)
0.120038 + 0.992769i \(0.461698\pi\)
\(998\) 5.93865e12 0.189496
\(999\) 3.57107e12 0.113437
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 177.10.a.b.1.19 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.b.1.19 21 1.1 even 1 trivial