Properties

Label 177.14.a.b.1.15
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $31$
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: \(31\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-32.6149 q^{2} -729.000 q^{3} -7128.27 q^{4} -49381.7 q^{5} +23776.2 q^{6} -593230. q^{7} +499669. q^{8} +531441. q^{9} +O(q^{10})\) \(q-32.6149 q^{2} -729.000 q^{3} -7128.27 q^{4} -49381.7 q^{5} +23776.2 q^{6} -593230. q^{7} +499669. q^{8} +531441. q^{9} +1.61058e6 q^{10} -7.46381e6 q^{11} +5.19651e6 q^{12} -3.21219e7 q^{13} +1.93481e7 q^{14} +3.59993e7 q^{15} +4.20982e7 q^{16} -1.18628e7 q^{17} -1.73329e7 q^{18} -3.23570e8 q^{19} +3.52006e8 q^{20} +4.32465e8 q^{21} +2.43431e8 q^{22} -7.23407e8 q^{23} -3.64258e8 q^{24} +1.21785e9 q^{25} +1.04765e9 q^{26} -3.87420e8 q^{27} +4.22871e9 q^{28} -1.75782e9 q^{29} -1.17411e9 q^{30} -3.99789e9 q^{31} -5.46631e9 q^{32} +5.44112e9 q^{33} +3.86903e8 q^{34} +2.92947e10 q^{35} -3.78825e9 q^{36} +1.32018e7 q^{37} +1.05532e10 q^{38} +2.34168e10 q^{39} -2.46745e10 q^{40} -2.57951e10 q^{41} -1.41048e10 q^{42} +5.80646e10 q^{43} +5.32041e10 q^{44} -2.62435e10 q^{45} +2.35938e10 q^{46} -6.92329e10 q^{47} -3.06896e10 q^{48} +2.55033e11 q^{49} -3.97201e10 q^{50} +8.64797e9 q^{51} +2.28973e11 q^{52} +3.07489e11 q^{53} +1.26357e10 q^{54} +3.68576e11 q^{55} -2.96419e11 q^{56} +2.35883e11 q^{57} +5.73310e10 q^{58} -4.21805e10 q^{59} -2.56613e11 q^{60} +1.31563e11 q^{61} +1.30391e11 q^{62} -3.15267e11 q^{63} -1.66585e11 q^{64} +1.58623e12 q^{65} -1.77461e11 q^{66} -2.68168e11 q^{67} +8.45612e10 q^{68} +5.27364e11 q^{69} -9.55444e11 q^{70} -1.88084e12 q^{71} +2.65544e11 q^{72} -7.87484e11 q^{73} -4.30574e8 q^{74} -8.87814e11 q^{75} +2.30650e12 q^{76} +4.42776e12 q^{77} -7.63738e11 q^{78} -1.97942e12 q^{79} -2.07888e12 q^{80} +2.82430e11 q^{81} +8.41303e11 q^{82} -2.48510e11 q^{83} -3.08273e12 q^{84} +5.85805e11 q^{85} -1.89377e12 q^{86} +1.28145e12 q^{87} -3.72943e12 q^{88} -5.76318e11 q^{89} +8.55928e11 q^{90} +1.90557e13 q^{91} +5.15664e12 q^{92} +2.91446e12 q^{93} +2.25802e12 q^{94} +1.59785e13 q^{95} +3.98494e12 q^{96} +6.37387e12 q^{97} -8.31788e12 q^{98} -3.96658e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −32.6149 −0.360347 −0.180173 0.983635i \(-0.557666\pi\)
−0.180173 + 0.983635i \(0.557666\pi\)
\(3\) −729.000 −0.577350
\(4\) −7128.27 −0.870150
\(5\) −49381.7 −1.41339 −0.706694 0.707520i \(-0.749814\pi\)
−0.706694 + 0.707520i \(0.749814\pi\)
\(6\) 23776.2 0.208046
\(7\) −593230. −1.90584 −0.952919 0.303224i \(-0.901937\pi\)
−0.952919 + 0.303224i \(0.901937\pi\)
\(8\) 499669. 0.673903
\(9\) 531441. 0.333333
\(10\) 1.61058e6 0.509310
\(11\) −7.46381e6 −1.27031 −0.635153 0.772386i \(-0.719063\pi\)
−0.635153 + 0.772386i \(0.719063\pi\)
\(12\) 5.19651e6 0.502381
\(13\) −3.21219e7 −1.84573 −0.922867 0.385119i \(-0.874160\pi\)
−0.922867 + 0.385119i \(0.874160\pi\)
\(14\) 1.93481e7 0.686763
\(15\) 3.59993e7 0.816020
\(16\) 4.20982e7 0.627311
\(17\) −1.18628e7 −0.119198 −0.0595990 0.998222i \(-0.518982\pi\)
−0.0595990 + 0.998222i \(0.518982\pi\)
\(18\) −1.73329e7 −0.120116
\(19\) −3.23570e8 −1.57787 −0.788933 0.614479i \(-0.789366\pi\)
−0.788933 + 0.614479i \(0.789366\pi\)
\(20\) 3.52006e8 1.22986
\(21\) 4.32465e8 1.10034
\(22\) 2.43431e8 0.457751
\(23\) −7.23407e8 −1.01895 −0.509474 0.860486i \(-0.670160\pi\)
−0.509474 + 0.860486i \(0.670160\pi\)
\(24\) −3.64258e8 −0.389078
\(25\) 1.21785e9 0.997664
\(26\) 1.04765e9 0.665104
\(27\) −3.87420e8 −0.192450
\(28\) 4.22871e9 1.65837
\(29\) −1.75782e9 −0.548766 −0.274383 0.961620i \(-0.588474\pi\)
−0.274383 + 0.961620i \(0.588474\pi\)
\(30\) −1.17411e9 −0.294050
\(31\) −3.99789e9 −0.809058 −0.404529 0.914525i \(-0.632565\pi\)
−0.404529 + 0.914525i \(0.632565\pi\)
\(32\) −5.46631e9 −0.899952
\(33\) 5.44112e9 0.733411
\(34\) 3.86903e8 0.0429526
\(35\) 2.92947e10 2.69369
\(36\) −3.78825e9 −0.290050
\(37\) 1.32018e7 0.000845903 0 0.000422951 1.00000i \(-0.499865\pi\)
0.000422951 1.00000i \(0.499865\pi\)
\(38\) 1.05532e10 0.568579
\(39\) 2.34168e10 1.06563
\(40\) −2.46745e10 −0.952486
\(41\) −2.57951e10 −0.848089 −0.424044 0.905641i \(-0.639390\pi\)
−0.424044 + 0.905641i \(0.639390\pi\)
\(42\) −1.41048e10 −0.396503
\(43\) 5.80646e10 1.40077 0.700385 0.713765i \(-0.253012\pi\)
0.700385 + 0.713765i \(0.253012\pi\)
\(44\) 5.32041e10 1.10536
\(45\) −2.62435e10 −0.471129
\(46\) 2.35938e10 0.367174
\(47\) −6.92329e10 −0.936864 −0.468432 0.883500i \(-0.655181\pi\)
−0.468432 + 0.883500i \(0.655181\pi\)
\(48\) −3.06896e10 −0.362178
\(49\) 2.55033e11 2.63222
\(50\) −3.97201e10 −0.359505
\(51\) 8.64797e9 0.0688190
\(52\) 2.28973e11 1.60607
\(53\) 3.07489e11 1.90562 0.952812 0.303562i \(-0.0981759\pi\)
0.952812 + 0.303562i \(0.0981759\pi\)
\(54\) 1.26357e10 0.0693488
\(55\) 3.68576e11 1.79543
\(56\) −2.96419e11 −1.28435
\(57\) 2.35883e11 0.910982
\(58\) 5.73310e10 0.197746
\(59\) −4.21805e10 −0.130189
\(60\) −2.56613e11 −0.710060
\(61\) 1.31563e11 0.326957 0.163479 0.986547i \(-0.447729\pi\)
0.163479 + 0.986547i \(0.447729\pi\)
\(62\) 1.30391e11 0.291541
\(63\) −3.15267e11 −0.635280
\(64\) −1.66585e11 −0.303016
\(65\) 1.58623e12 2.60874
\(66\) −1.77461e11 −0.264282
\(67\) −2.68168e11 −0.362178 −0.181089 0.983467i \(-0.557962\pi\)
−0.181089 + 0.983467i \(0.557962\pi\)
\(68\) 8.45612e10 0.103720
\(69\) 5.27364e11 0.588289
\(70\) −9.55444e11 −0.970662
\(71\) −1.88084e12 −1.74250 −0.871252 0.490837i \(-0.836691\pi\)
−0.871252 + 0.490837i \(0.836691\pi\)
\(72\) 2.65544e11 0.224634
\(73\) −7.87484e11 −0.609036 −0.304518 0.952507i \(-0.598495\pi\)
−0.304518 + 0.952507i \(0.598495\pi\)
\(74\) −4.30574e8 −0.000304818 0
\(75\) −8.87814e11 −0.576002
\(76\) 2.30650e12 1.37298
\(77\) 4.42776e12 2.42100
\(78\) −7.63738e11 −0.383998
\(79\) −1.97942e12 −0.916140 −0.458070 0.888916i \(-0.651459\pi\)
−0.458070 + 0.888916i \(0.651459\pi\)
\(80\) −2.07888e12 −0.886634
\(81\) 2.82430e11 0.111111
\(82\) 8.41303e11 0.305606
\(83\) −2.48510e11 −0.0834327 −0.0417164 0.999129i \(-0.513283\pi\)
−0.0417164 + 0.999129i \(0.513283\pi\)
\(84\) −3.08273e12 −0.957458
\(85\) 5.85805e11 0.168473
\(86\) −1.89377e12 −0.504763
\(87\) 1.28145e12 0.316830
\(88\) −3.72943e12 −0.856062
\(89\) −5.76318e11 −0.122921 −0.0614607 0.998110i \(-0.519576\pi\)
−0.0614607 + 0.998110i \(0.519576\pi\)
\(90\) 8.55928e11 0.169770
\(91\) 1.90557e13 3.51767
\(92\) 5.15664e12 0.886637
\(93\) 2.91446e12 0.467110
\(94\) 2.25802e12 0.337596
\(95\) 1.59785e13 2.23014
\(96\) 3.98494e12 0.519588
\(97\) 6.37387e12 0.776939 0.388469 0.921462i \(-0.373004\pi\)
0.388469 + 0.921462i \(0.373004\pi\)
\(98\) −8.31788e12 −0.948513
\(99\) −3.96658e12 −0.423435
\(100\) −8.68117e12 −0.868117
\(101\) −1.09909e13 −1.03025 −0.515126 0.857114i \(-0.672255\pi\)
−0.515126 + 0.857114i \(0.672255\pi\)
\(102\) −2.82053e11 −0.0247987
\(103\) 1.84278e13 1.52066 0.760330 0.649537i \(-0.225037\pi\)
0.760330 + 0.649537i \(0.225037\pi\)
\(104\) −1.60503e13 −1.24385
\(105\) −2.13559e13 −1.55520
\(106\) −1.00287e13 −0.686685
\(107\) −3.02082e12 −0.194594 −0.0972972 0.995255i \(-0.531020\pi\)
−0.0972972 + 0.995255i \(0.531020\pi\)
\(108\) 2.76164e12 0.167460
\(109\) −1.23735e13 −0.706674 −0.353337 0.935496i \(-0.614953\pi\)
−0.353337 + 0.935496i \(0.614953\pi\)
\(110\) −1.20211e13 −0.646979
\(111\) −9.62408e9 −0.000488382 0
\(112\) −2.49739e13 −1.19555
\(113\) −1.12544e12 −0.0508527 −0.0254264 0.999677i \(-0.508094\pi\)
−0.0254264 + 0.999677i \(0.508094\pi\)
\(114\) −7.69329e12 −0.328269
\(115\) 3.57231e13 1.44017
\(116\) 1.25302e13 0.477509
\(117\) −1.70709e13 −0.615245
\(118\) 1.37571e12 0.0469132
\(119\) 7.03737e12 0.227172
\(120\) 1.79877e13 0.549918
\(121\) 2.11858e13 0.613677
\(122\) −4.29092e12 −0.117818
\(123\) 1.88046e13 0.489644
\(124\) 2.84980e13 0.704002
\(125\) 1.40820e11 0.00330179
\(126\) 1.02824e13 0.228921
\(127\) −5.23070e13 −1.10621 −0.553103 0.833113i \(-0.686556\pi\)
−0.553103 + 0.833113i \(0.686556\pi\)
\(128\) 5.02132e13 1.00914
\(129\) −4.23291e13 −0.808735
\(130\) −5.17348e13 −0.940050
\(131\) −2.08064e13 −0.359694 −0.179847 0.983695i \(-0.557560\pi\)
−0.179847 + 0.983695i \(0.557560\pi\)
\(132\) −3.87858e13 −0.638178
\(133\) 1.91952e14 3.00716
\(134\) 8.74628e12 0.130510
\(135\) 1.91315e13 0.272007
\(136\) −5.92746e12 −0.0803278
\(137\) −1.29775e14 −1.67690 −0.838448 0.544982i \(-0.816537\pi\)
−0.838448 + 0.544982i \(0.816537\pi\)
\(138\) −1.71999e13 −0.211988
\(139\) −1.29110e14 −1.51832 −0.759160 0.650904i \(-0.774390\pi\)
−0.759160 + 0.650904i \(0.774390\pi\)
\(140\) −2.08821e14 −2.34391
\(141\) 5.04708e13 0.540898
\(142\) 6.13435e13 0.627906
\(143\) 2.39752e14 2.34465
\(144\) 2.23727e13 0.209104
\(145\) 8.68041e13 0.775619
\(146\) 2.56837e13 0.219464
\(147\) −1.85919e14 −1.51971
\(148\) −9.41057e10 −0.000736062 0
\(149\) 7.93459e13 0.594037 0.297019 0.954872i \(-0.404008\pi\)
0.297019 + 0.954872i \(0.404008\pi\)
\(150\) 2.89559e13 0.207560
\(151\) 1.38875e14 0.953401 0.476700 0.879066i \(-0.341833\pi\)
0.476700 + 0.879066i \(0.341833\pi\)
\(152\) −1.61678e14 −1.06333
\(153\) −6.30437e12 −0.0397326
\(154\) −1.44411e14 −0.872399
\(155\) 1.97423e14 1.14351
\(156\) −1.66922e14 −0.927262
\(157\) 2.73625e14 1.45817 0.729086 0.684422i \(-0.239945\pi\)
0.729086 + 0.684422i \(0.239945\pi\)
\(158\) 6.45585e13 0.330128
\(159\) −2.24160e14 −1.10021
\(160\) 2.69936e14 1.27198
\(161\) 4.29147e14 1.94195
\(162\) −9.21140e12 −0.0400385
\(163\) −3.32716e14 −1.38949 −0.694743 0.719258i \(-0.744482\pi\)
−0.694743 + 0.719258i \(0.744482\pi\)
\(164\) 1.83874e14 0.737965
\(165\) −2.68692e14 −1.03659
\(166\) 8.10513e12 0.0300647
\(167\) 7.36631e13 0.262781 0.131390 0.991331i \(-0.458056\pi\)
0.131390 + 0.991331i \(0.458056\pi\)
\(168\) 2.16089e14 0.741520
\(169\) 7.28940e14 2.40673
\(170\) −1.91060e13 −0.0607087
\(171\) −1.71959e14 −0.525956
\(172\) −4.13900e14 −1.21888
\(173\) −1.87114e14 −0.530648 −0.265324 0.964159i \(-0.585479\pi\)
−0.265324 + 0.964159i \(0.585479\pi\)
\(174\) −4.17943e13 −0.114169
\(175\) −7.22467e14 −1.90139
\(176\) −3.14213e14 −0.796877
\(177\) 3.07496e13 0.0751646
\(178\) 1.87965e13 0.0442943
\(179\) −1.42845e14 −0.324579 −0.162289 0.986743i \(-0.551888\pi\)
−0.162289 + 0.986743i \(0.551888\pi\)
\(180\) 1.87071e14 0.409953
\(181\) −7.50258e14 −1.58599 −0.792994 0.609229i \(-0.791479\pi\)
−0.792994 + 0.609229i \(0.791479\pi\)
\(182\) −6.21498e14 −1.26758
\(183\) −9.59097e13 −0.188769
\(184\) −3.61464e14 −0.686671
\(185\) −6.51925e11 −0.00119559
\(186\) −9.50548e13 −0.168322
\(187\) 8.85416e13 0.151418
\(188\) 4.93511e14 0.815212
\(189\) 2.29830e14 0.366779
\(190\) −5.21136e14 −0.803623
\(191\) 9.67976e14 1.44261 0.721303 0.692619i \(-0.243543\pi\)
0.721303 + 0.692619i \(0.243543\pi\)
\(192\) 1.21440e14 0.174947
\(193\) −8.10463e14 −1.12878 −0.564392 0.825507i \(-0.690889\pi\)
−0.564392 + 0.825507i \(0.690889\pi\)
\(194\) −2.07883e14 −0.279967
\(195\) −1.15636e15 −1.50616
\(196\) −1.81795e15 −2.29043
\(197\) −2.58693e14 −0.315323 −0.157661 0.987493i \(-0.550395\pi\)
−0.157661 + 0.987493i \(0.550395\pi\)
\(198\) 1.29369e14 0.152584
\(199\) −1.10138e15 −1.25716 −0.628582 0.777743i \(-0.716364\pi\)
−0.628582 + 0.777743i \(0.716364\pi\)
\(200\) 6.08522e14 0.672328
\(201\) 1.95495e14 0.209103
\(202\) 3.58466e14 0.371248
\(203\) 1.04279e15 1.04586
\(204\) −6.16451e13 −0.0598828
\(205\) 1.27380e15 1.19868
\(206\) −6.01021e14 −0.547965
\(207\) −3.84448e14 −0.339649
\(208\) −1.35227e15 −1.15785
\(209\) 2.41507e15 2.00437
\(210\) 6.96519e14 0.560412
\(211\) −9.00591e14 −0.702574 −0.351287 0.936268i \(-0.614256\pi\)
−0.351287 + 0.936268i \(0.614256\pi\)
\(212\) −2.19187e15 −1.65818
\(213\) 1.37114e15 1.00603
\(214\) 9.85236e13 0.0701215
\(215\) −2.86733e15 −1.97983
\(216\) −1.93582e14 −0.129693
\(217\) 2.37167e15 1.54193
\(218\) 4.03559e14 0.254648
\(219\) 5.74076e14 0.351627
\(220\) −2.62731e15 −1.56230
\(221\) 3.81055e14 0.220008
\(222\) 3.13888e11 0.000175987 0
\(223\) 6.59002e14 0.358844 0.179422 0.983772i \(-0.442577\pi\)
0.179422 + 0.983772i \(0.442577\pi\)
\(224\) 3.24278e15 1.71516
\(225\) 6.47216e14 0.332555
\(226\) 3.67062e13 0.0183246
\(227\) 1.47614e14 0.0716077 0.0358039 0.999359i \(-0.488601\pi\)
0.0358039 + 0.999359i \(0.488601\pi\)
\(228\) −1.68144e15 −0.792691
\(229\) −1.52534e15 −0.698935 −0.349468 0.936948i \(-0.613638\pi\)
−0.349468 + 0.936948i \(0.613638\pi\)
\(230\) −1.16510e15 −0.518960
\(231\) −3.22784e15 −1.39776
\(232\) −8.78327e14 −0.369815
\(233\) 4.99824e14 0.204646 0.102323 0.994751i \(-0.467372\pi\)
0.102323 + 0.994751i \(0.467372\pi\)
\(234\) 5.56765e14 0.221701
\(235\) 3.41884e15 1.32415
\(236\) 3.00674e14 0.113284
\(237\) 1.44300e15 0.528933
\(238\) −2.29523e14 −0.0818607
\(239\) −3.20105e15 −1.11098 −0.555489 0.831524i \(-0.687469\pi\)
−0.555489 + 0.831524i \(0.687469\pi\)
\(240\) 1.51550e15 0.511898
\(241\) 3.80901e15 1.25228 0.626139 0.779711i \(-0.284634\pi\)
0.626139 + 0.779711i \(0.284634\pi\)
\(242\) −6.90971e14 −0.221136
\(243\) −2.05891e14 −0.0641500
\(244\) −9.37819e14 −0.284502
\(245\) −1.25940e16 −3.72035
\(246\) −6.13310e14 −0.176442
\(247\) 1.03937e16 2.91232
\(248\) −1.99762e15 −0.545226
\(249\) 1.81164e14 0.0481699
\(250\) −4.59283e12 −0.00118979
\(251\) −1.73870e15 −0.438879 −0.219440 0.975626i \(-0.570423\pi\)
−0.219440 + 0.975626i \(0.570423\pi\)
\(252\) 2.24731e15 0.552789
\(253\) 5.39937e15 1.29437
\(254\) 1.70599e15 0.398618
\(255\) −4.27052e14 −0.0972679
\(256\) −2.73032e14 −0.0606253
\(257\) −8.48539e15 −1.83699 −0.918495 0.395433i \(-0.870594\pi\)
−0.918495 + 0.395433i \(0.870594\pi\)
\(258\) 1.38056e15 0.291425
\(259\) −7.83168e12 −0.00161215
\(260\) −1.13071e16 −2.26999
\(261\) −9.34177e14 −0.182922
\(262\) 6.78597e14 0.129614
\(263\) −8.76144e15 −1.63254 −0.816269 0.577672i \(-0.803961\pi\)
−0.816269 + 0.577672i \(0.803961\pi\)
\(264\) 2.71876e15 0.494248
\(265\) −1.51844e16 −2.69338
\(266\) −6.26048e15 −1.08362
\(267\) 4.20136e14 0.0709686
\(268\) 1.91158e15 0.315149
\(269\) −3.68286e15 −0.592646 −0.296323 0.955088i \(-0.595761\pi\)
−0.296323 + 0.955088i \(0.595761\pi\)
\(270\) −6.23971e14 −0.0980167
\(271\) −4.77488e15 −0.732254 −0.366127 0.930565i \(-0.619316\pi\)
−0.366127 + 0.930565i \(0.619316\pi\)
\(272\) −4.99401e14 −0.0747742
\(273\) −1.38916e16 −2.03093
\(274\) 4.23258e15 0.604264
\(275\) −9.08981e15 −1.26734
\(276\) −3.75919e15 −0.511900
\(277\) 2.27248e15 0.302260 0.151130 0.988514i \(-0.451709\pi\)
0.151130 + 0.988514i \(0.451709\pi\)
\(278\) 4.21090e15 0.547122
\(279\) −2.12464e15 −0.269686
\(280\) 1.46377e16 1.81528
\(281\) 5.04454e15 0.611266 0.305633 0.952149i \(-0.401132\pi\)
0.305633 + 0.952149i \(0.401132\pi\)
\(282\) −1.64610e15 −0.194911
\(283\) −6.57935e15 −0.761327 −0.380663 0.924714i \(-0.624304\pi\)
−0.380663 + 0.924714i \(0.624304\pi\)
\(284\) 1.34072e16 1.51624
\(285\) −1.16483e16 −1.28757
\(286\) −7.81947e15 −0.844886
\(287\) 1.53024e16 1.61632
\(288\) −2.90502e15 −0.299984
\(289\) −9.76385e15 −0.985792
\(290\) −2.83111e15 −0.279492
\(291\) −4.64655e15 −0.448566
\(292\) 5.61340e15 0.529953
\(293\) 6.70612e15 0.619201 0.309601 0.950867i \(-0.399805\pi\)
0.309601 + 0.950867i \(0.399805\pi\)
\(294\) 6.06374e15 0.547624
\(295\) 2.08295e15 0.184007
\(296\) 6.59650e12 0.000570056 0
\(297\) 2.89163e15 0.244470
\(298\) −2.58786e15 −0.214059
\(299\) 2.32372e16 1.88071
\(300\) 6.32858e15 0.501208
\(301\) −3.44457e16 −2.66964
\(302\) −4.52941e15 −0.343555
\(303\) 8.01235e15 0.594817
\(304\) −1.36217e16 −0.989814
\(305\) −6.49682e15 −0.462117
\(306\) 2.05616e14 0.0143175
\(307\) −4.66913e15 −0.318300 −0.159150 0.987254i \(-0.550875\pi\)
−0.159150 + 0.987254i \(0.550875\pi\)
\(308\) −3.15623e16 −2.10663
\(309\) −1.34339e16 −0.877953
\(310\) −6.43891e15 −0.412061
\(311\) −1.33184e16 −0.834663 −0.417331 0.908754i \(-0.637035\pi\)
−0.417331 + 0.908754i \(0.637035\pi\)
\(312\) 1.17007e16 0.718134
\(313\) −2.68156e15 −0.161194 −0.0805971 0.996747i \(-0.525683\pi\)
−0.0805971 + 0.996747i \(0.525683\pi\)
\(314\) −8.92426e15 −0.525448
\(315\) 1.55684e16 0.897896
\(316\) 1.41098e16 0.797179
\(317\) 1.64263e16 0.909188 0.454594 0.890699i \(-0.349784\pi\)
0.454594 + 0.890699i \(0.349784\pi\)
\(318\) 7.31094e15 0.396458
\(319\) 1.31200e16 0.697100
\(320\) 8.22625e15 0.428279
\(321\) 2.20218e15 0.112349
\(322\) −1.39966e16 −0.699775
\(323\) 3.83845e15 0.188078
\(324\) −2.01323e15 −0.0966833
\(325\) −3.91197e16 −1.84142
\(326\) 1.08515e16 0.500697
\(327\) 9.02026e15 0.407999
\(328\) −1.28890e16 −0.571529
\(329\) 4.10711e16 1.78551
\(330\) 8.76335e15 0.373534
\(331\) 3.69112e16 1.54268 0.771340 0.636423i \(-0.219587\pi\)
0.771340 + 0.636423i \(0.219587\pi\)
\(332\) 1.77145e15 0.0725990
\(333\) 7.01595e12 0.000281968 0
\(334\) −2.40251e15 −0.0946921
\(335\) 1.32426e16 0.511897
\(336\) 1.82060e16 0.690254
\(337\) 2.34882e16 0.873486 0.436743 0.899586i \(-0.356132\pi\)
0.436743 + 0.899586i \(0.356132\pi\)
\(338\) −2.37743e16 −0.867259
\(339\) 8.20449e14 0.0293598
\(340\) −4.17578e15 −0.146597
\(341\) 2.98395e16 1.02775
\(342\) 5.60841e15 0.189526
\(343\) −9.38160e16 −3.11075
\(344\) 2.90131e16 0.943983
\(345\) −2.60421e16 −0.831481
\(346\) 6.10270e15 0.191217
\(347\) −5.54474e16 −1.70506 −0.852530 0.522679i \(-0.824933\pi\)
−0.852530 + 0.522679i \(0.824933\pi\)
\(348\) −9.13452e15 −0.275690
\(349\) 1.44672e16 0.428568 0.214284 0.976771i \(-0.431258\pi\)
0.214284 + 0.976771i \(0.431258\pi\)
\(350\) 2.35632e16 0.685159
\(351\) 1.24447e16 0.355212
\(352\) 4.07995e16 1.14321
\(353\) 1.03356e16 0.284314 0.142157 0.989844i \(-0.454596\pi\)
0.142157 + 0.989844i \(0.454596\pi\)
\(354\) −1.00289e15 −0.0270853
\(355\) 9.28793e16 2.46283
\(356\) 4.10815e15 0.106960
\(357\) −5.13024e15 −0.131158
\(358\) 4.65887e15 0.116961
\(359\) 4.31346e16 1.06344 0.531719 0.846921i \(-0.321546\pi\)
0.531719 + 0.846921i \(0.321546\pi\)
\(360\) −1.31130e16 −0.317495
\(361\) 6.26448e16 1.48966
\(362\) 2.44696e16 0.571506
\(363\) −1.54444e16 −0.354306
\(364\) −1.35834e17 −3.06090
\(365\) 3.88873e16 0.860804
\(366\) 3.12808e15 0.0680223
\(367\) −6.09304e16 −1.30168 −0.650840 0.759215i \(-0.725583\pi\)
−0.650840 + 0.759215i \(0.725583\pi\)
\(368\) −3.04541e16 −0.639197
\(369\) −1.37085e16 −0.282696
\(370\) 2.12625e13 0.000430826 0
\(371\) −1.82412e17 −3.63181
\(372\) −2.07751e16 −0.406456
\(373\) −2.48061e16 −0.476926 −0.238463 0.971152i \(-0.576644\pi\)
−0.238463 + 0.971152i \(0.576644\pi\)
\(374\) −2.88777e15 −0.0545629
\(375\) −1.02658e14 −0.00190629
\(376\) −3.45935e16 −0.631355
\(377\) 5.64644e16 1.01288
\(378\) −7.49586e15 −0.132168
\(379\) 6.71368e16 1.16361 0.581803 0.813330i \(-0.302347\pi\)
0.581803 + 0.813330i \(0.302347\pi\)
\(380\) −1.13899e17 −1.94055
\(381\) 3.81318e16 0.638668
\(382\) −3.15704e16 −0.519839
\(383\) −4.37732e15 −0.0708624 −0.0354312 0.999372i \(-0.511280\pi\)
−0.0354312 + 0.999372i \(0.511280\pi\)
\(384\) −3.66054e16 −0.582629
\(385\) −2.18650e17 −3.42181
\(386\) 2.64331e16 0.406754
\(387\) 3.08579e16 0.466923
\(388\) −4.54346e16 −0.676053
\(389\) 1.30948e15 0.0191614 0.00958069 0.999954i \(-0.496950\pi\)
0.00958069 + 0.999954i \(0.496950\pi\)
\(390\) 3.77147e16 0.542738
\(391\) 8.58162e15 0.121456
\(392\) 1.27432e17 1.77386
\(393\) 1.51678e16 0.207669
\(394\) 8.43726e15 0.113625
\(395\) 9.77471e16 1.29486
\(396\) 2.82748e16 0.368452
\(397\) −6.82367e16 −0.874742 −0.437371 0.899281i \(-0.644090\pi\)
−0.437371 + 0.899281i \(0.644090\pi\)
\(398\) 3.59214e16 0.453015
\(399\) −1.39933e17 −1.73618
\(400\) 5.12693e16 0.625846
\(401\) 1.20322e17 1.44513 0.722563 0.691305i \(-0.242964\pi\)
0.722563 + 0.691305i \(0.242964\pi\)
\(402\) −6.37604e15 −0.0753497
\(403\) 1.28420e17 1.49331
\(404\) 7.83460e16 0.896474
\(405\) −1.39469e16 −0.157043
\(406\) −3.40105e16 −0.376872
\(407\) −9.85354e13 −0.00107455
\(408\) 4.32112e15 0.0463773
\(409\) 1.41649e17 1.49628 0.748140 0.663541i \(-0.230947\pi\)
0.748140 + 0.663541i \(0.230947\pi\)
\(410\) −4.15450e16 −0.431940
\(411\) 9.46057e16 0.968156
\(412\) −1.31358e17 −1.32320
\(413\) 2.50228e16 0.248119
\(414\) 1.25387e16 0.122391
\(415\) 1.22719e16 0.117923
\(416\) 1.75588e17 1.66107
\(417\) 9.41211e16 0.876603
\(418\) −7.87672e16 −0.722270
\(419\) 9.73646e16 0.879043 0.439522 0.898232i \(-0.355148\pi\)
0.439522 + 0.898232i \(0.355148\pi\)
\(420\) 1.52230e17 1.35326
\(421\) −3.87678e16 −0.339342 −0.169671 0.985501i \(-0.554271\pi\)
−0.169671 + 0.985501i \(0.554271\pi\)
\(422\) 2.93727e16 0.253170
\(423\) −3.67932e16 −0.312288
\(424\) 1.53643e17 1.28420
\(425\) −1.44471e16 −0.118919
\(426\) −4.47194e16 −0.362521
\(427\) −7.80474e16 −0.623128
\(428\) 2.15332e16 0.169326
\(429\) −1.74779e17 −1.35368
\(430\) 9.35177e16 0.713426
\(431\) 1.81275e17 1.36219 0.681093 0.732197i \(-0.261505\pi\)
0.681093 + 0.732197i \(0.261505\pi\)
\(432\) −1.63097e16 −0.120726
\(433\) 1.53686e17 1.12063 0.560314 0.828280i \(-0.310680\pi\)
0.560314 + 0.828280i \(0.310680\pi\)
\(434\) −7.73517e16 −0.555631
\(435\) −6.32802e16 −0.447804
\(436\) 8.82014e16 0.614913
\(437\) 2.34073e17 1.60776
\(438\) −1.87234e16 −0.126708
\(439\) 9.58773e16 0.639288 0.319644 0.947538i \(-0.396437\pi\)
0.319644 + 0.947538i \(0.396437\pi\)
\(440\) 1.84166e17 1.20995
\(441\) 1.35535e17 0.877407
\(442\) −1.24281e16 −0.0792791
\(443\) 8.53921e16 0.536776 0.268388 0.963311i \(-0.413509\pi\)
0.268388 + 0.963311i \(0.413509\pi\)
\(444\) 6.86030e13 0.000424966 0
\(445\) 2.84596e16 0.173735
\(446\) −2.14933e16 −0.129308
\(447\) −5.78431e16 −0.342967
\(448\) 9.88233e16 0.577500
\(449\) 4.57049e16 0.263246 0.131623 0.991300i \(-0.457981\pi\)
0.131623 + 0.991300i \(0.457981\pi\)
\(450\) −2.11089e16 −0.119835
\(451\) 1.92529e17 1.07733
\(452\) 8.02247e15 0.0442495
\(453\) −1.01240e17 −0.550446
\(454\) −4.81442e15 −0.0258036
\(455\) −9.41002e17 −4.97183
\(456\) 1.17863e17 0.613913
\(457\) 8.21711e16 0.421952 0.210976 0.977491i \(-0.432336\pi\)
0.210976 + 0.977491i \(0.432336\pi\)
\(458\) 4.97489e16 0.251859
\(459\) 4.59589e15 0.0229397
\(460\) −2.54644e17 −1.25316
\(461\) −4.06761e16 −0.197371 −0.0986855 0.995119i \(-0.531464\pi\)
−0.0986855 + 0.995119i \(0.531464\pi\)
\(462\) 1.05276e17 0.503680
\(463\) −1.51468e17 −0.714569 −0.357284 0.933996i \(-0.616297\pi\)
−0.357284 + 0.933996i \(0.616297\pi\)
\(464\) −7.40009e16 −0.344247
\(465\) −1.43921e17 −0.660207
\(466\) −1.63017e16 −0.0737436
\(467\) 1.42903e17 0.637503 0.318751 0.947838i \(-0.396737\pi\)
0.318751 + 0.947838i \(0.396737\pi\)
\(468\) 1.21686e17 0.535355
\(469\) 1.59086e17 0.690252
\(470\) −1.11505e17 −0.477154
\(471\) −1.99473e17 −0.841876
\(472\) −2.10763e16 −0.0877347
\(473\) −4.33384e17 −1.77941
\(474\) −4.70631e16 −0.190600
\(475\) −3.94061e17 −1.57418
\(476\) −5.01643e16 −0.197674
\(477\) 1.63413e17 0.635208
\(478\) 1.04402e17 0.400338
\(479\) 3.12586e17 1.18247 0.591233 0.806501i \(-0.298641\pi\)
0.591233 + 0.806501i \(0.298641\pi\)
\(480\) −1.96783e17 −0.734379
\(481\) −4.24065e14 −0.00156131
\(482\) −1.24230e17 −0.451255
\(483\) −3.12848e17 −1.12118
\(484\) −1.51018e17 −0.533991
\(485\) −3.14753e17 −1.09812
\(486\) 6.71511e15 0.0231163
\(487\) 1.02307e17 0.347511 0.173755 0.984789i \(-0.444410\pi\)
0.173755 + 0.984789i \(0.444410\pi\)
\(488\) 6.57381e16 0.220337
\(489\) 2.42550e17 0.802220
\(490\) 4.10751e17 1.34062
\(491\) 3.46345e17 1.11552 0.557762 0.830001i \(-0.311660\pi\)
0.557762 + 0.830001i \(0.311660\pi\)
\(492\) −1.34044e17 −0.426064
\(493\) 2.08526e16 0.0654118
\(494\) −3.38989e17 −1.04945
\(495\) 1.95876e17 0.598478
\(496\) −1.68304e17 −0.507531
\(497\) 1.11577e18 3.32093
\(498\) −5.90864e15 −0.0173579
\(499\) −4.97714e17 −1.44320 −0.721599 0.692311i \(-0.756593\pi\)
−0.721599 + 0.692311i \(0.756593\pi\)
\(500\) −1.00380e15 −0.00287305
\(501\) −5.37004e16 −0.151716
\(502\) 5.67074e16 0.158149
\(503\) 4.86081e17 1.33819 0.669093 0.743178i \(-0.266683\pi\)
0.669093 + 0.743178i \(0.266683\pi\)
\(504\) −1.57529e17 −0.428117
\(505\) 5.42749e17 1.45615
\(506\) −1.76100e17 −0.466424
\(507\) −5.31397e17 −1.38953
\(508\) 3.72858e17 0.962565
\(509\) −1.14739e17 −0.292446 −0.146223 0.989252i \(-0.546712\pi\)
−0.146223 + 0.989252i \(0.546712\pi\)
\(510\) 1.39282e16 0.0350502
\(511\) 4.67159e17 1.16072
\(512\) −4.02441e17 −0.987297
\(513\) 1.25358e17 0.303661
\(514\) 2.76750e17 0.661953
\(515\) −9.09997e17 −2.14928
\(516\) 3.01733e17 0.703721
\(517\) 5.16741e17 1.19010
\(518\) 2.55429e14 0.000580935 0
\(519\) 1.36406e17 0.306370
\(520\) 7.92591e17 1.75804
\(521\) −7.05193e16 −0.154477 −0.0772383 0.997013i \(-0.524610\pi\)
−0.0772383 + 0.997013i \(0.524610\pi\)
\(522\) 3.04681e16 0.0659154
\(523\) −3.02176e17 −0.645653 −0.322826 0.946458i \(-0.604633\pi\)
−0.322826 + 0.946458i \(0.604633\pi\)
\(524\) 1.48313e17 0.312987
\(525\) 5.26678e17 1.09777
\(526\) 2.85753e17 0.588280
\(527\) 4.74261e16 0.0964380
\(528\) 2.29061e17 0.460077
\(529\) 1.92811e16 0.0382534
\(530\) 4.95236e17 0.970553
\(531\) −2.24165e16 −0.0433963
\(532\) −1.36828e18 −2.61668
\(533\) 8.28586e17 1.56535
\(534\) −1.37027e16 −0.0255733
\(535\) 1.49173e17 0.275037
\(536\) −1.33995e17 −0.244072
\(537\) 1.04134e17 0.187396
\(538\) 1.20116e17 0.213558
\(539\) −1.90352e18 −3.34373
\(540\) −1.36374e17 −0.236687
\(541\) −9.37497e17 −1.60764 −0.803818 0.594876i \(-0.797201\pi\)
−0.803818 + 0.594876i \(0.797201\pi\)
\(542\) 1.55732e17 0.263865
\(543\) 5.46938e17 0.915671
\(544\) 6.48457e16 0.107272
\(545\) 6.11023e17 0.998804
\(546\) 4.53072e17 0.731839
\(547\) 2.15393e17 0.343806 0.171903 0.985114i \(-0.445008\pi\)
0.171903 + 0.985114i \(0.445008\pi\)
\(548\) 9.25069e17 1.45915
\(549\) 6.99181e16 0.108986
\(550\) 2.96463e17 0.456681
\(551\) 5.68778e17 0.865880
\(552\) 2.63507e17 0.396450
\(553\) 1.17425e18 1.74601
\(554\) −7.41165e16 −0.108918
\(555\) 4.75254e14 0.000690273 0
\(556\) 9.20330e17 1.32117
\(557\) −5.89344e17 −0.836200 −0.418100 0.908401i \(-0.637304\pi\)
−0.418100 + 0.908401i \(0.637304\pi\)
\(558\) 6.92949e16 0.0971805
\(559\) −1.86515e18 −2.58545
\(560\) 1.23325e18 1.68978
\(561\) −6.45468e16 −0.0874211
\(562\) −1.64527e17 −0.220268
\(563\) −9.24963e17 −1.22411 −0.612054 0.790816i \(-0.709656\pi\)
−0.612054 + 0.790816i \(0.709656\pi\)
\(564\) −3.59769e17 −0.470663
\(565\) 5.55764e16 0.0718746
\(566\) 2.14585e17 0.274342
\(567\) −1.67546e17 −0.211760
\(568\) −9.39799e17 −1.17428
\(569\) 1.17097e18 1.44650 0.723248 0.690588i \(-0.242648\pi\)
0.723248 + 0.690588i \(0.242648\pi\)
\(570\) 3.79908e17 0.463972
\(571\) 1.34858e18 1.62832 0.814162 0.580638i \(-0.197197\pi\)
0.814162 + 0.580638i \(0.197197\pi\)
\(572\) −1.70901e18 −2.04019
\(573\) −7.05655e17 −0.832889
\(574\) −4.99086e17 −0.582436
\(575\) −8.81002e17 −1.01657
\(576\) −8.85301e16 −0.101005
\(577\) −5.35816e17 −0.604467 −0.302234 0.953234i \(-0.597732\pi\)
−0.302234 + 0.953234i \(0.597732\pi\)
\(578\) 3.18447e17 0.355227
\(579\) 5.90827e17 0.651703
\(580\) −6.18763e17 −0.674905
\(581\) 1.47424e17 0.159009
\(582\) 1.51547e17 0.161639
\(583\) −2.29504e18 −2.42072
\(584\) −3.93481e17 −0.410431
\(585\) 8.42990e17 0.869579
\(586\) −2.18719e17 −0.223127
\(587\) 3.42527e17 0.345579 0.172790 0.984959i \(-0.444722\pi\)
0.172790 + 0.984959i \(0.444722\pi\)
\(588\) 1.32528e18 1.32238
\(589\) 1.29360e18 1.27659
\(590\) −6.79351e16 −0.0663065
\(591\) 1.88588e17 0.182052
\(592\) 5.55769e14 0.000530644 0
\(593\) 7.46915e17 0.705368 0.352684 0.935743i \(-0.385269\pi\)
0.352684 + 0.935743i \(0.385269\pi\)
\(594\) −9.43103e16 −0.0880942
\(595\) −3.47517e17 −0.321082
\(596\) −5.65599e17 −0.516901
\(597\) 8.02906e17 0.725824
\(598\) −7.57878e17 −0.677706
\(599\) 1.27547e18 1.12823 0.564114 0.825697i \(-0.309218\pi\)
0.564114 + 0.825697i \(0.309218\pi\)
\(600\) −4.43613e17 −0.388169
\(601\) −1.90753e17 −0.165115 −0.0825577 0.996586i \(-0.526309\pi\)
−0.0825577 + 0.996586i \(0.526309\pi\)
\(602\) 1.12344e18 0.961997
\(603\) −1.42516e17 −0.120726
\(604\) −9.89942e17 −0.829602
\(605\) −1.04619e18 −0.867363
\(606\) −2.61322e17 −0.214340
\(607\) −1.14134e18 −0.926163 −0.463081 0.886316i \(-0.653256\pi\)
−0.463081 + 0.886316i \(0.653256\pi\)
\(608\) 1.76874e18 1.42001
\(609\) −7.60195e17 −0.603827
\(610\) 2.11893e17 0.166522
\(611\) 2.22389e18 1.72920
\(612\) 4.49393e16 0.0345734
\(613\) −2.01905e18 −1.53693 −0.768466 0.639891i \(-0.778980\pi\)
−0.768466 + 0.639891i \(0.778980\pi\)
\(614\) 1.52283e17 0.114698
\(615\) −9.28603e17 −0.692057
\(616\) 2.21241e18 1.63152
\(617\) 1.09685e17 0.0800372 0.0400186 0.999199i \(-0.487258\pi\)
0.0400186 + 0.999199i \(0.487258\pi\)
\(618\) 4.38144e17 0.316368
\(619\) 1.27610e18 0.911793 0.455896 0.890033i \(-0.349319\pi\)
0.455896 + 0.890033i \(0.349319\pi\)
\(620\) −1.40728e18 −0.995027
\(621\) 2.80263e17 0.196096
\(622\) 4.34380e17 0.300768
\(623\) 3.41889e17 0.234268
\(624\) 9.85806e17 0.668485
\(625\) −1.49359e18 −1.00233
\(626\) 8.74588e16 0.0580858
\(627\) −1.76058e18 −1.15723
\(628\) −1.95048e18 −1.26883
\(629\) −1.56610e14 −0.000100830 0
\(630\) −5.07762e17 −0.323554
\(631\) −1.14820e18 −0.724144 −0.362072 0.932150i \(-0.617931\pi\)
−0.362072 + 0.932150i \(0.617931\pi\)
\(632\) −9.89054e17 −0.617389
\(633\) 6.56531e17 0.405631
\(634\) −5.35741e17 −0.327623
\(635\) 2.58301e18 1.56350
\(636\) 1.59787e18 0.957350
\(637\) −8.19215e18 −4.85838
\(638\) −4.27908e17 −0.251198
\(639\) −9.99558e17 −0.580834
\(640\) −2.47961e18 −1.42631
\(641\) 8.40358e17 0.478506 0.239253 0.970957i \(-0.423098\pi\)
0.239253 + 0.970957i \(0.423098\pi\)
\(642\) −7.18237e16 −0.0404846
\(643\) −4.24702e17 −0.236981 −0.118490 0.992955i \(-0.537805\pi\)
−0.118490 + 0.992955i \(0.537805\pi\)
\(644\) −3.05908e18 −1.68979
\(645\) 2.09029e18 1.14306
\(646\) −1.25190e17 −0.0677735
\(647\) −2.33545e18 −1.25168 −0.625839 0.779953i \(-0.715243\pi\)
−0.625839 + 0.779953i \(0.715243\pi\)
\(648\) 1.41121e17 0.0748781
\(649\) 3.14828e17 0.165380
\(650\) 1.27588e18 0.663551
\(651\) −1.72895e18 −0.890236
\(652\) 2.37169e18 1.20906
\(653\) −1.42232e18 −0.717898 −0.358949 0.933357i \(-0.616865\pi\)
−0.358949 + 0.933357i \(0.616865\pi\)
\(654\) −2.94195e17 −0.147021
\(655\) 1.02745e18 0.508386
\(656\) −1.08592e18 −0.532016
\(657\) −4.18501e17 −0.203012
\(658\) −1.33953e18 −0.643403
\(659\) 3.43005e18 1.63134 0.815672 0.578515i \(-0.196368\pi\)
0.815672 + 0.578515i \(0.196368\pi\)
\(660\) 1.91531e18 0.901993
\(661\) −3.05212e18 −1.42328 −0.711642 0.702542i \(-0.752048\pi\)
−0.711642 + 0.702542i \(0.752048\pi\)
\(662\) −1.20385e18 −0.555900
\(663\) −2.77789e17 −0.127021
\(664\) −1.24173e17 −0.0562255
\(665\) −9.47891e18 −4.25028
\(666\) −2.28824e14 −0.000101606 0
\(667\) 1.27162e18 0.559164
\(668\) −5.25091e17 −0.228659
\(669\) −4.80413e17 −0.207178
\(670\) −4.31906e17 −0.184461
\(671\) −9.81964e17 −0.415336
\(672\) −2.36399e18 −0.990251
\(673\) 5.47273e17 0.227042 0.113521 0.993536i \(-0.463787\pi\)
0.113521 + 0.993536i \(0.463787\pi\)
\(674\) −7.66066e17 −0.314758
\(675\) −4.71821e17 −0.192001
\(676\) −5.19608e18 −2.09422
\(677\) 1.76536e18 0.704702 0.352351 0.935868i \(-0.385382\pi\)
0.352351 + 0.935868i \(0.385382\pi\)
\(678\) −2.67588e16 −0.0105797
\(679\) −3.78117e18 −1.48072
\(680\) 2.92708e17 0.113534
\(681\) −1.07611e17 −0.0413427
\(682\) −9.73211e17 −0.370347
\(683\) 5.51479e17 0.207871 0.103936 0.994584i \(-0.466856\pi\)
0.103936 + 0.994584i \(0.466856\pi\)
\(684\) 1.22577e18 0.457660
\(685\) 6.40849e18 2.37010
\(686\) 3.05980e18 1.12095
\(687\) 1.11198e18 0.403530
\(688\) 2.44441e18 0.878719
\(689\) −9.87714e18 −3.51727
\(690\) 8.49361e17 0.299622
\(691\) 3.12190e17 0.109097 0.0545484 0.998511i \(-0.482628\pi\)
0.0545484 + 0.998511i \(0.482628\pi\)
\(692\) 1.33380e18 0.461744
\(693\) 2.35309e18 0.806999
\(694\) 1.80841e18 0.614413
\(695\) 6.37567e18 2.14597
\(696\) 6.40300e17 0.213513
\(697\) 3.06001e17 0.101090
\(698\) −4.71846e17 −0.154433
\(699\) −3.64372e17 −0.118152
\(700\) 5.14994e18 1.65449
\(701\) 3.33857e18 1.06266 0.531329 0.847166i \(-0.321693\pi\)
0.531329 + 0.847166i \(0.321693\pi\)
\(702\) −4.05881e17 −0.127999
\(703\) −4.27170e15 −0.00133472
\(704\) 1.24336e18 0.384923
\(705\) −2.49233e18 −0.764499
\(706\) −3.37093e17 −0.102452
\(707\) 6.52013e18 1.96350
\(708\) −2.19192e17 −0.0654045
\(709\) 4.09782e18 1.21158 0.605790 0.795625i \(-0.292857\pi\)
0.605790 + 0.795625i \(0.292857\pi\)
\(710\) −3.02925e18 −0.887474
\(711\) −1.05194e18 −0.305380
\(712\) −2.87968e17 −0.0828370
\(713\) 2.89210e18 0.824387
\(714\) 1.67322e17 0.0472623
\(715\) −1.18393e19 −3.31389
\(716\) 1.01824e18 0.282432
\(717\) 2.33356e18 0.641424
\(718\) −1.40683e18 −0.383207
\(719\) −6.78179e18 −1.83065 −0.915327 0.402711i \(-0.868068\pi\)
−0.915327 + 0.402711i \(0.868068\pi\)
\(720\) −1.10480e18 −0.295545
\(721\) −1.09319e19 −2.89813
\(722\) −2.04315e18 −0.536796
\(723\) −2.77677e18 −0.723003
\(724\) 5.34804e18 1.38005
\(725\) −2.14076e18 −0.547484
\(726\) 5.03718e17 0.127673
\(727\) −1.21628e18 −0.305535 −0.152767 0.988262i \(-0.548819\pi\)
−0.152767 + 0.988262i \(0.548819\pi\)
\(728\) 9.52152e18 2.37057
\(729\) 1.50095e17 0.0370370
\(730\) −1.26830e18 −0.310188
\(731\) −6.88809e17 −0.166969
\(732\) 6.83670e17 0.164257
\(733\) −6.38425e18 −1.52032 −0.760158 0.649738i \(-0.774878\pi\)
−0.760158 + 0.649738i \(0.774878\pi\)
\(734\) 1.98724e18 0.469056
\(735\) 9.18102e18 2.14794
\(736\) 3.95437e18 0.917004
\(737\) 2.00156e18 0.460076
\(738\) 4.47103e17 0.101869
\(739\) −4.65232e18 −1.05070 −0.525352 0.850885i \(-0.676066\pi\)
−0.525352 + 0.850885i \(0.676066\pi\)
\(740\) 4.64710e15 0.00104034
\(741\) −7.57700e18 −1.68143
\(742\) 5.94935e18 1.30871
\(743\) −1.39759e18 −0.304756 −0.152378 0.988322i \(-0.548693\pi\)
−0.152378 + 0.988322i \(0.548693\pi\)
\(744\) 1.45626e18 0.314787
\(745\) −3.91824e18 −0.839605
\(746\) 8.09048e17 0.171859
\(747\) −1.32068e17 −0.0278109
\(748\) −6.31149e17 −0.131756
\(749\) 1.79204e18 0.370865
\(750\) 3.34817e15 0.000686926 0
\(751\) 2.75161e18 0.559664 0.279832 0.960049i \(-0.409721\pi\)
0.279832 + 0.960049i \(0.409721\pi\)
\(752\) −2.91458e18 −0.587705
\(753\) 1.26751e18 0.253387
\(754\) −1.84158e18 −0.364987
\(755\) −6.85791e18 −1.34752
\(756\) −1.63829e18 −0.319153
\(757\) 1.44803e18 0.279676 0.139838 0.990174i \(-0.455342\pi\)
0.139838 + 0.990174i \(0.455342\pi\)
\(758\) −2.18966e18 −0.419302
\(759\) −3.93614e18 −0.747307
\(760\) 7.98394e18 1.50290
\(761\) 7.31139e17 0.136458 0.0682292 0.997670i \(-0.478265\pi\)
0.0682292 + 0.997670i \(0.478265\pi\)
\(762\) −1.24366e18 −0.230142
\(763\) 7.34032e18 1.34681
\(764\) −6.90000e18 −1.25528
\(765\) 3.11321e17 0.0561576
\(766\) 1.42766e17 0.0255351
\(767\) 1.35492e18 0.240294
\(768\) 1.99040e17 0.0350021
\(769\) −1.33513e18 −0.232811 −0.116405 0.993202i \(-0.537137\pi\)
−0.116405 + 0.993202i \(0.537137\pi\)
\(770\) 7.13126e18 1.23304
\(771\) 6.18585e18 1.06059
\(772\) 5.77720e18 0.982211
\(773\) 7.68371e18 1.29540 0.647700 0.761895i \(-0.275731\pi\)
0.647700 + 0.761895i \(0.275731\pi\)
\(774\) −1.00643e18 −0.168254
\(775\) −4.86883e18 −0.807168
\(776\) 3.18482e18 0.523581
\(777\) 5.70930e15 0.000930778 0
\(778\) −4.27086e16 −0.00690474
\(779\) 8.34652e18 1.33817
\(780\) 8.24288e18 1.31058
\(781\) 1.40383e19 2.21351
\(782\) −2.79889e17 −0.0437664
\(783\) 6.81015e17 0.105610
\(784\) 1.07364e19 1.65122
\(785\) −1.35121e19 −2.06096
\(786\) −4.94697e17 −0.0748329
\(787\) −1.22732e19 −1.84129 −0.920646 0.390399i \(-0.872337\pi\)
−0.920646 + 0.390399i \(0.872337\pi\)
\(788\) 1.84404e18 0.274378
\(789\) 6.38709e18 0.942546
\(790\) −3.18801e18 −0.466599
\(791\) 6.67648e17 0.0969171
\(792\) −1.98197e18 −0.285354
\(793\) −4.22606e18 −0.603476
\(794\) 2.22553e18 0.315211
\(795\) 1.10694e19 1.55503
\(796\) 7.85093e18 1.09392
\(797\) 1.13007e19 1.56181 0.780904 0.624651i \(-0.214759\pi\)
0.780904 + 0.624651i \(0.214759\pi\)
\(798\) 4.56389e18 0.625629
\(799\) 8.21295e17 0.111672
\(800\) −6.65716e18 −0.897850
\(801\) −3.06279e17 −0.0409738
\(802\) −3.92428e18 −0.520747
\(803\) 5.87763e18 0.773662
\(804\) −1.39354e18 −0.181951
\(805\) −2.11920e19 −2.74473
\(806\) −4.18839e18 −0.538108
\(807\) 2.68481e18 0.342165
\(808\) −5.49180e18 −0.694290
\(809\) 1.47159e19 1.84553 0.922765 0.385364i \(-0.125924\pi\)
0.922765 + 0.385364i \(0.125924\pi\)
\(810\) 4.54875e17 0.0565900
\(811\) 9.51436e17 0.117421 0.0587103 0.998275i \(-0.481301\pi\)
0.0587103 + 0.998275i \(0.481301\pi\)
\(812\) −7.43330e18 −0.910055
\(813\) 3.48088e18 0.422767
\(814\) 3.21372e15 0.000387212 0
\(815\) 1.64301e19 1.96388
\(816\) 3.64064e17 0.0431709
\(817\) −1.87880e19 −2.21023
\(818\) −4.61987e18 −0.539180
\(819\) 1.01270e19 1.17256
\(820\) −9.08002e18 −1.04303
\(821\) 7.29378e17 0.0831231 0.0415616 0.999136i \(-0.486767\pi\)
0.0415616 + 0.999136i \(0.486767\pi\)
\(822\) −3.08555e18 −0.348872
\(823\) 1.50596e19 1.68933 0.844663 0.535299i \(-0.179801\pi\)
0.844663 + 0.535299i \(0.179801\pi\)
\(824\) 9.20780e18 1.02478
\(825\) 6.62647e18 0.731698
\(826\) −8.16115e17 −0.0894089
\(827\) 1.03556e19 1.12562 0.562808 0.826588i \(-0.309721\pi\)
0.562808 + 0.826588i \(0.309721\pi\)
\(828\) 2.74045e18 0.295546
\(829\) 4.59391e18 0.491562 0.245781 0.969325i \(-0.420956\pi\)
0.245781 + 0.969325i \(0.420956\pi\)
\(830\) −4.00245e17 −0.0424931
\(831\) −1.65663e18 −0.174510
\(832\) 5.35102e18 0.559288
\(833\) −3.02541e18 −0.313755
\(834\) −3.06975e18 −0.315881
\(835\) −3.63761e18 −0.371411
\(836\) −1.72153e19 −1.74411
\(837\) 1.54886e18 0.155703
\(838\) −3.17554e18 −0.316760
\(839\) −1.09522e19 −1.08405 −0.542025 0.840362i \(-0.682342\pi\)
−0.542025 + 0.840362i \(0.682342\pi\)
\(840\) −1.06709e19 −1.04805
\(841\) −7.17070e18 −0.698856
\(842\) 1.26441e18 0.122281
\(843\) −3.67747e18 −0.352915
\(844\) 6.41966e18 0.611345
\(845\) −3.59963e19 −3.40165
\(846\) 1.20001e18 0.112532
\(847\) −1.25680e19 −1.16957
\(848\) 1.29447e19 1.19542
\(849\) 4.79635e18 0.439552
\(850\) 4.71191e17 0.0428523
\(851\) −9.55024e15 −0.000861930 0
\(852\) −9.77382e18 −0.875401
\(853\) 6.06853e18 0.539405 0.269703 0.962944i \(-0.413075\pi\)
0.269703 + 0.962944i \(0.413075\pi\)
\(854\) 2.54551e18 0.224542
\(855\) 8.49161e18 0.743379
\(856\) −1.50941e18 −0.131138
\(857\) −1.77836e19 −1.53336 −0.766679 0.642030i \(-0.778092\pi\)
−0.766679 + 0.642030i \(0.778092\pi\)
\(858\) 5.70039e18 0.487795
\(859\) −3.69923e18 −0.314163 −0.157082 0.987586i \(-0.550209\pi\)
−0.157082 + 0.987586i \(0.550209\pi\)
\(860\) 2.04391e19 1.72275
\(861\) −1.11555e19 −0.933183
\(862\) −5.91227e18 −0.490859
\(863\) −2.31117e18 −0.190441 −0.0952206 0.995456i \(-0.530356\pi\)
−0.0952206 + 0.995456i \(0.530356\pi\)
\(864\) 2.11776e18 0.173196
\(865\) 9.24001e18 0.750012
\(866\) −5.01243e18 −0.403815
\(867\) 7.11785e18 0.569147
\(868\) −1.69059e19 −1.34171
\(869\) 1.47740e19 1.16378
\(870\) 2.06388e18 0.161365
\(871\) 8.61407e18 0.668483
\(872\) −6.18264e18 −0.476230
\(873\) 3.38733e18 0.258980
\(874\) −7.63426e18 −0.579352
\(875\) −8.35388e16 −0.00629268
\(876\) −4.09217e18 −0.305968
\(877\) −2.10598e19 −1.56299 −0.781495 0.623912i \(-0.785542\pi\)
−0.781495 + 0.623912i \(0.785542\pi\)
\(878\) −3.12703e18 −0.230365
\(879\) −4.88876e18 −0.357496
\(880\) 1.55164e19 1.12630
\(881\) −2.90922e18 −0.209620 −0.104810 0.994492i \(-0.533424\pi\)
−0.104810 + 0.994492i \(0.533424\pi\)
\(882\) −4.42046e18 −0.316171
\(883\) 8.09516e18 0.574753 0.287376 0.957818i \(-0.407217\pi\)
0.287376 + 0.957818i \(0.407217\pi\)
\(884\) −2.71626e18 −0.191440
\(885\) −1.51847e18 −0.106237
\(886\) −2.78505e18 −0.193426
\(887\) −2.60308e18 −0.179467 −0.0897334 0.995966i \(-0.528602\pi\)
−0.0897334 + 0.995966i \(0.528602\pi\)
\(888\) −4.80885e15 −0.000329122 0
\(889\) 3.10301e19 2.10825
\(890\) −9.28206e17 −0.0626050
\(891\) −2.10800e18 −0.141145
\(892\) −4.69755e18 −0.312248
\(893\) 2.24017e19 1.47825
\(894\) 1.88655e18 0.123587
\(895\) 7.05393e18 0.458756
\(896\) −2.97880e19 −1.92326
\(897\) −1.69399e19 −1.08583
\(898\) −1.49066e18 −0.0948598
\(899\) 7.02756e18 0.443983
\(900\) −4.61353e18 −0.289372
\(901\) −3.64768e18 −0.227146
\(902\) −6.27932e18 −0.388213
\(903\) 2.51109e19 1.54132
\(904\) −5.62349e17 −0.0342698
\(905\) 3.70490e19 2.24162
\(906\) 3.30194e18 0.198352
\(907\) 1.56993e19 0.936338 0.468169 0.883639i \(-0.344914\pi\)
0.468169 + 0.883639i \(0.344914\pi\)
\(908\) −1.05223e18 −0.0623095
\(909\) −5.84101e18 −0.343417
\(910\) 3.06907e19 1.79158
\(911\) −2.52252e19 −1.46206 −0.731031 0.682344i \(-0.760961\pi\)
−0.731031 + 0.682344i \(0.760961\pi\)
\(912\) 9.93023e18 0.571469
\(913\) 1.85483e18 0.105985
\(914\) −2.68000e18 −0.152049
\(915\) 4.73618e18 0.266803
\(916\) 1.08731e19 0.608179
\(917\) 1.23430e19 0.685518
\(918\) −1.49894e17 −0.00826623
\(919\) 5.88065e18 0.322014 0.161007 0.986953i \(-0.448526\pi\)
0.161007 + 0.986953i \(0.448526\pi\)
\(920\) 1.78497e19 0.970533
\(921\) 3.40379e18 0.183770
\(922\) 1.32665e18 0.0711220
\(923\) 6.04162e19 3.21620
\(924\) 2.30089e19 1.21626
\(925\) 1.60778e16 0.000843927 0
\(926\) 4.94010e18 0.257493
\(927\) 9.79330e18 0.506886
\(928\) 9.60879e18 0.493863
\(929\) 2.49712e19 1.27449 0.637247 0.770660i \(-0.280073\pi\)
0.637247 + 0.770660i \(0.280073\pi\)
\(930\) 4.69397e18 0.237904
\(931\) −8.25212e19 −4.15330
\(932\) −3.56288e18 −0.178073
\(933\) 9.70915e18 0.481893
\(934\) −4.66077e18 −0.229722
\(935\) −4.37234e18 −0.214012
\(936\) −8.52978e18 −0.414615
\(937\) −3.36764e18 −0.162562 −0.0812809 0.996691i \(-0.525901\pi\)
−0.0812809 + 0.996691i \(0.525901\pi\)
\(938\) −5.18856e18 −0.248730
\(939\) 1.95486e18 0.0930655
\(940\) −2.43704e19 −1.15221
\(941\) 2.58779e19 1.21506 0.607528 0.794298i \(-0.292161\pi\)
0.607528 + 0.794298i \(0.292161\pi\)
\(942\) 6.50578e18 0.303367
\(943\) 1.86603e19 0.864158
\(944\) −1.77572e18 −0.0816690
\(945\) −1.13494e19 −0.518401
\(946\) 1.41348e19 0.641203
\(947\) −2.93965e19 −1.32440 −0.662202 0.749326i \(-0.730378\pi\)
−0.662202 + 0.749326i \(0.730378\pi\)
\(948\) −1.02861e19 −0.460251
\(949\) 2.52955e19 1.12412
\(950\) 1.28522e19 0.567251
\(951\) −1.19748e19 −0.524920
\(952\) 3.51635e18 0.153092
\(953\) −2.37641e19 −1.02758 −0.513792 0.857915i \(-0.671760\pi\)
−0.513792 + 0.857915i \(0.671760\pi\)
\(954\) −5.32968e18 −0.228895
\(955\) −4.78003e19 −2.03896
\(956\) 2.28179e19 0.966718
\(957\) −9.56450e18 −0.402471
\(958\) −1.01950e19 −0.426098
\(959\) 7.69863e19 3.19589
\(960\) −5.99694e18 −0.247267
\(961\) −8.43444e18 −0.345425
\(962\) 1.38308e16 0.000562614 0
\(963\) −1.60539e18 −0.0648648
\(964\) −2.71516e19 −1.08967
\(965\) 4.00220e19 1.59541
\(966\) 1.02035e19 0.404015
\(967\) 4.21463e17 0.0165763 0.00828815 0.999966i \(-0.497362\pi\)
0.00828815 + 0.999966i \(0.497362\pi\)
\(968\) 1.05859e19 0.413558
\(969\) −2.79823e18 −0.108587
\(970\) 1.02656e19 0.395702
\(971\) 3.40026e19 1.30193 0.650964 0.759109i \(-0.274365\pi\)
0.650964 + 0.759109i \(0.274365\pi\)
\(972\) 1.46765e18 0.0558202
\(973\) 7.65919e19 2.89367
\(974\) −3.33674e18 −0.125224
\(975\) 2.85182e19 1.06315
\(976\) 5.53857e18 0.205104
\(977\) −2.63305e19 −0.968600 −0.484300 0.874902i \(-0.660926\pi\)
−0.484300 + 0.874902i \(0.660926\pi\)
\(978\) −7.91073e18 −0.289077
\(979\) 4.30153e18 0.156148
\(980\) 8.97733e19 3.23726
\(981\) −6.57577e18 −0.235558
\(982\) −1.12960e19 −0.401976
\(983\) −2.63878e19 −0.932836 −0.466418 0.884564i \(-0.654456\pi\)
−0.466418 + 0.884564i \(0.654456\pi\)
\(984\) 9.39607e18 0.329973
\(985\) 1.27747e19 0.445673
\(986\) −6.80106e17 −0.0235709
\(987\) −2.99408e19 −1.03087
\(988\) −7.40890e19 −2.53416
\(989\) −4.20044e19 −1.42731
\(990\) −6.38848e18 −0.215660
\(991\) 6.22964e18 0.208922 0.104461 0.994529i \(-0.466688\pi\)
0.104461 + 0.994529i \(0.466688\pi\)
\(992\) 2.18537e19 0.728114
\(993\) −2.69083e19 −0.890667
\(994\) −3.63908e19 −1.19669
\(995\) 5.43880e19 1.77686
\(996\) −1.29138e18 −0.0419150
\(997\) −2.53077e19 −0.816083 −0.408042 0.912963i \(-0.633788\pi\)
−0.408042 + 0.912963i \(0.633788\pi\)
\(998\) 1.62329e19 0.520052
\(999\) −5.11463e15 −0.000162794 0
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.b.1.15 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.15 31 1.1 even 1 trivial