Properties

Label 177.14.a.b.1.14
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 1.14
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-42.0742 q^{2} -729.000 q^{3} -6421.76 q^{4} -29646.8 q^{5} +30672.1 q^{6} +519485. q^{7} +614862. q^{8} +531441. q^{9} +O(q^{10})\) \(q-42.0742 q^{2} -729.000 q^{3} -6421.76 q^{4} -29646.8 q^{5} +30672.1 q^{6} +519485. q^{7} +614862. q^{8} +531441. q^{9} +1.24737e6 q^{10} +5.17537e6 q^{11} +4.68146e6 q^{12} -1.50807e7 q^{13} -2.18569e7 q^{14} +2.16125e7 q^{15} +2.67372e7 q^{16} -4.83523e7 q^{17} -2.23600e7 q^{18} -1.21451e8 q^{19} +1.90385e8 q^{20} -3.78705e8 q^{21} -2.17750e8 q^{22} +1.03178e6 q^{23} -4.48235e8 q^{24} -3.41770e8 q^{25} +6.34508e8 q^{26} -3.87420e8 q^{27} -3.33601e9 q^{28} -2.75011e9 q^{29} -9.09329e8 q^{30} -7.52220e8 q^{31} -6.16190e9 q^{32} -3.77285e9 q^{33} +2.03438e9 q^{34} -1.54011e10 q^{35} -3.41279e9 q^{36} +2.97989e10 q^{37} +5.10997e9 q^{38} +1.09938e10 q^{39} -1.82287e10 q^{40} -2.00571e10 q^{41} +1.59337e10 q^{42} -4.09695e10 q^{43} -3.32350e10 q^{44} -1.57555e10 q^{45} -4.34111e7 q^{46} +1.04296e11 q^{47} -1.94915e10 q^{48} +1.72976e11 q^{49} +1.43797e10 q^{50} +3.52488e10 q^{51} +9.68446e10 q^{52} +2.07363e11 q^{53} +1.63004e10 q^{54} -1.53433e11 q^{55} +3.19412e11 q^{56} +8.85381e10 q^{57} +1.15709e11 q^{58} -4.21805e10 q^{59} -1.38790e11 q^{60} -1.41464e11 q^{61} +3.16490e10 q^{62} +2.76076e11 q^{63} +4.02254e10 q^{64} +4.47094e11 q^{65} +1.58739e11 q^{66} +7.07112e11 q^{67} +3.10507e11 q^{68} -7.52164e8 q^{69} +6.47988e11 q^{70} +1.32663e9 q^{71} +3.26763e11 q^{72} +6.69188e11 q^{73} -1.25376e12 q^{74} +2.49151e11 q^{75} +7.79932e11 q^{76} +2.68853e12 q^{77} -4.62556e11 q^{78} -3.83781e11 q^{79} -7.92674e11 q^{80} +2.82430e11 q^{81} +8.43888e11 q^{82} -3.96671e12 q^{83} +2.43195e12 q^{84} +1.43349e12 q^{85} +1.72376e12 q^{86} +2.00483e12 q^{87} +3.18214e12 q^{88} -2.74811e12 q^{89} +6.62901e11 q^{90} -7.83420e12 q^{91} -6.62582e9 q^{92} +5.48368e11 q^{93} -4.38816e12 q^{94} +3.60065e12 q^{95} +4.49202e12 q^{96} -1.54618e13 q^{97} -7.27783e12 q^{98} +2.75040e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −42.0742 −0.464859 −0.232429 0.972613i \(-0.574667\pi\)
−0.232429 + 0.972613i \(0.574667\pi\)
\(3\) −729.000 −0.577350
\(4\) −6421.76 −0.783907
\(5\) −29646.8 −0.848541 −0.424270 0.905536i \(-0.639469\pi\)
−0.424270 + 0.905536i \(0.639469\pi\)
\(6\) 30672.1 0.268386
\(7\) 519485. 1.66892 0.834461 0.551067i \(-0.185779\pi\)
0.834461 + 0.551067i \(0.185779\pi\)
\(8\) 614862. 0.829264
\(9\) 531441. 0.333333
\(10\) 1.24737e6 0.394452
\(11\) 5.17537e6 0.880824 0.440412 0.897796i \(-0.354832\pi\)
0.440412 + 0.897796i \(0.354832\pi\)
\(12\) 4.68146e6 0.452589
\(13\) −1.50807e7 −0.866542 −0.433271 0.901264i \(-0.642641\pi\)
−0.433271 + 0.901264i \(0.642641\pi\)
\(14\) −2.18569e7 −0.775813
\(15\) 2.16125e7 0.489905
\(16\) 2.67372e7 0.398416
\(17\) −4.83523e7 −0.485847 −0.242923 0.970045i \(-0.578106\pi\)
−0.242923 + 0.970045i \(0.578106\pi\)
\(18\) −2.23600e7 −0.154953
\(19\) −1.21451e8 −0.592249 −0.296124 0.955149i \(-0.595694\pi\)
−0.296124 + 0.955149i \(0.595694\pi\)
\(20\) 1.90385e8 0.665177
\(21\) −3.78705e8 −0.963553
\(22\) −2.17750e8 −0.409458
\(23\) 1.03178e6 0.00145330 0.000726648 1.00000i \(-0.499769\pi\)
0.000726648 1.00000i \(0.499769\pi\)
\(24\) −4.48235e8 −0.478776
\(25\) −3.41770e8 −0.279978
\(26\) 6.34508e8 0.402819
\(27\) −3.87420e8 −0.192450
\(28\) −3.33601e9 −1.30828
\(29\) −2.75011e9 −0.858545 −0.429272 0.903175i \(-0.641230\pi\)
−0.429272 + 0.903175i \(0.641230\pi\)
\(30\) −9.09329e8 −0.227737
\(31\) −7.52220e8 −0.152228 −0.0761139 0.997099i \(-0.524251\pi\)
−0.0761139 + 0.997099i \(0.524251\pi\)
\(32\) −6.16190e9 −1.01447
\(33\) −3.77285e9 −0.508544
\(34\) 2.03438e9 0.225850
\(35\) −1.54011e10 −1.41615
\(36\) −3.41279e9 −0.261302
\(37\) 2.97989e10 1.90936 0.954681 0.297631i \(-0.0961964\pi\)
0.954681 + 0.297631i \(0.0961964\pi\)
\(38\) 5.10997e9 0.275312
\(39\) 1.09938e10 0.500298
\(40\) −1.82287e10 −0.703665
\(41\) −2.00571e10 −0.659438 −0.329719 0.944079i \(-0.606954\pi\)
−0.329719 + 0.944079i \(0.606954\pi\)
\(42\) 1.59337e10 0.447916
\(43\) −4.09695e10 −0.988362 −0.494181 0.869359i \(-0.664532\pi\)
−0.494181 + 0.869359i \(0.664532\pi\)
\(44\) −3.32350e10 −0.690483
\(45\) −1.57555e10 −0.282847
\(46\) −4.34111e7 −0.000675577 0
\(47\) 1.04296e11 1.41134 0.705668 0.708543i \(-0.250647\pi\)
0.705668 + 0.708543i \(0.250647\pi\)
\(48\) −1.94915e10 −0.230026
\(49\) 1.72976e11 1.78530
\(50\) 1.43797e10 0.130150
\(51\) 3.52488e10 0.280504
\(52\) 9.68446e10 0.679288
\(53\) 2.07363e11 1.28510 0.642551 0.766243i \(-0.277876\pi\)
0.642551 + 0.766243i \(0.277876\pi\)
\(54\) 1.63004e10 0.0894621
\(55\) −1.53433e11 −0.747415
\(56\) 3.19412e11 1.38398
\(57\) 8.85381e10 0.341935
\(58\) 1.15709e11 0.399102
\(59\) −4.21805e10 −0.130189
\(60\) −1.38790e11 −0.384040
\(61\) −1.41464e11 −0.351561 −0.175781 0.984429i \(-0.556245\pi\)
−0.175781 + 0.984429i \(0.556245\pi\)
\(62\) 3.16490e10 0.0707644
\(63\) 2.76076e11 0.556307
\(64\) 4.02254e10 0.0731696
\(65\) 4.47094e11 0.735296
\(66\) 1.58739e11 0.236401
\(67\) 7.07112e11 0.954997 0.477499 0.878633i \(-0.341544\pi\)
0.477499 + 0.878633i \(0.341544\pi\)
\(68\) 3.10507e11 0.380858
\(69\) −7.52164e8 −0.000839061 0
\(70\) 6.47988e11 0.658309
\(71\) 1.32663e9 0.00122905 0.000614525 1.00000i \(-0.499804\pi\)
0.000614525 1.00000i \(0.499804\pi\)
\(72\) 3.26763e11 0.276421
\(73\) 6.69188e11 0.517547 0.258774 0.965938i \(-0.416682\pi\)
0.258774 + 0.965938i \(0.416682\pi\)
\(74\) −1.25376e12 −0.887583
\(75\) 2.49151e11 0.161646
\(76\) 7.79932e11 0.464268
\(77\) 2.68853e12 1.47003
\(78\) −4.62556e11 −0.232568
\(79\) −3.83781e11 −0.177626 −0.0888132 0.996048i \(-0.528307\pi\)
−0.0888132 + 0.996048i \(0.528307\pi\)
\(80\) −7.92674e11 −0.338072
\(81\) 2.82430e11 0.111111
\(82\) 8.43888e11 0.306545
\(83\) −3.96671e12 −1.33175 −0.665875 0.746063i \(-0.731942\pi\)
−0.665875 + 0.746063i \(0.731942\pi\)
\(84\) 2.43195e12 0.755335
\(85\) 1.43349e12 0.412261
\(86\) 1.72376e12 0.459449
\(87\) 2.00483e12 0.495681
\(88\) 3.18214e12 0.730436
\(89\) −2.74811e12 −0.586138 −0.293069 0.956091i \(-0.594676\pi\)
−0.293069 + 0.956091i \(0.594676\pi\)
\(90\) 6.62901e11 0.131484
\(91\) −7.83420e12 −1.44619
\(92\) −6.62582e9 −0.00113925
\(93\) 5.48368e11 0.0878887
\(94\) −4.38816e12 −0.656071
\(95\) 3.60065e12 0.502547
\(96\) 4.49202e12 0.585705
\(97\) −1.54618e13 −1.88471 −0.942353 0.334621i \(-0.891392\pi\)
−0.942353 + 0.334621i \(0.891392\pi\)
\(98\) −7.27783e12 −0.829913
\(99\) 2.75040e12 0.293608
\(100\) 2.19477e12 0.219477
\(101\) −2.70633e12 −0.253683 −0.126841 0.991923i \(-0.540484\pi\)
−0.126841 + 0.991923i \(0.540484\pi\)
\(102\) −1.48307e12 −0.130395
\(103\) −1.35987e13 −1.12216 −0.561079 0.827762i \(-0.689614\pi\)
−0.561079 + 0.827762i \(0.689614\pi\)
\(104\) −9.27255e12 −0.718592
\(105\) 1.12274e13 0.817614
\(106\) −8.72462e12 −0.597391
\(107\) 2.39297e13 1.54149 0.770747 0.637141i \(-0.219883\pi\)
0.770747 + 0.637141i \(0.219883\pi\)
\(108\) 2.48792e12 0.150863
\(109\) 1.35576e13 0.774305 0.387152 0.922016i \(-0.373459\pi\)
0.387152 + 0.922016i \(0.373459\pi\)
\(110\) 6.45558e12 0.347442
\(111\) −2.17234e13 −1.10237
\(112\) 1.38896e13 0.664925
\(113\) 8.03222e12 0.362933 0.181466 0.983397i \(-0.441916\pi\)
0.181466 + 0.983397i \(0.441916\pi\)
\(114\) −3.72517e12 −0.158951
\(115\) −3.05888e10 −0.00123318
\(116\) 1.76605e13 0.673019
\(117\) −8.01450e12 −0.288847
\(118\) 1.77471e12 0.0605194
\(119\) −2.51183e13 −0.810840
\(120\) 1.32887e13 0.406261
\(121\) −7.73825e12 −0.224150
\(122\) 5.95197e12 0.163426
\(123\) 1.46217e13 0.380727
\(124\) 4.83058e12 0.119332
\(125\) 4.63223e13 1.08611
\(126\) −1.16157e13 −0.258604
\(127\) 4.69736e13 0.993413 0.496707 0.867919i \(-0.334543\pi\)
0.496707 + 0.867919i \(0.334543\pi\)
\(128\) 4.87858e13 0.980458
\(129\) 2.98668e13 0.570631
\(130\) −1.88111e13 −0.341809
\(131\) 8.75068e13 1.51279 0.756394 0.654116i \(-0.226959\pi\)
0.756394 + 0.654116i \(0.226959\pi\)
\(132\) 2.42283e13 0.398651
\(133\) −6.30923e13 −0.988417
\(134\) −2.97512e13 −0.443939
\(135\) 1.14858e13 0.163302
\(136\) −2.97300e13 −0.402895
\(137\) 3.36875e13 0.435297 0.217648 0.976027i \(-0.430161\pi\)
0.217648 + 0.976027i \(0.430161\pi\)
\(138\) 3.16467e10 0.000390045 0
\(139\) −1.32566e14 −1.55896 −0.779482 0.626424i \(-0.784518\pi\)
−0.779482 + 0.626424i \(0.784518\pi\)
\(140\) 9.89021e13 1.11013
\(141\) −7.60316e13 −0.814835
\(142\) −5.58167e10 −0.000571334 0
\(143\) −7.80482e13 −0.763271
\(144\) 1.42093e13 0.132805
\(145\) 8.15319e13 0.728510
\(146\) −2.81556e13 −0.240586
\(147\) −1.26100e14 −1.03074
\(148\) −1.91361e14 −1.49676
\(149\) −9.98894e13 −0.747840 −0.373920 0.927461i \(-0.621986\pi\)
−0.373920 + 0.927461i \(0.621986\pi\)
\(150\) −1.04828e13 −0.0751423
\(151\) 2.35342e14 1.61566 0.807828 0.589418i \(-0.200643\pi\)
0.807828 + 0.589418i \(0.200643\pi\)
\(152\) −7.46759e13 −0.491131
\(153\) −2.56964e13 −0.161949
\(154\) −1.13118e14 −0.683354
\(155\) 2.23009e13 0.129171
\(156\) −7.05997e13 −0.392187
\(157\) −1.47239e14 −0.784649 −0.392325 0.919827i \(-0.628329\pi\)
−0.392325 + 0.919827i \(0.628329\pi\)
\(158\) 1.61473e13 0.0825712
\(159\) −1.51168e14 −0.741954
\(160\) 1.82681e14 0.860820
\(161\) 5.35992e11 0.00242544
\(162\) −1.18830e13 −0.0516509
\(163\) 4.04430e14 1.68898 0.844489 0.535573i \(-0.179904\pi\)
0.844489 + 0.535573i \(0.179904\pi\)
\(164\) 1.28802e14 0.516938
\(165\) 1.11853e14 0.431520
\(166\) 1.66896e14 0.619076
\(167\) 1.05281e14 0.375572 0.187786 0.982210i \(-0.439869\pi\)
0.187786 + 0.982210i \(0.439869\pi\)
\(168\) −2.32851e14 −0.799040
\(169\) −7.54478e13 −0.249105
\(170\) −6.03130e13 −0.191643
\(171\) −6.45443e13 −0.197416
\(172\) 2.63097e14 0.774783
\(173\) −4.71850e14 −1.33815 −0.669075 0.743195i \(-0.733309\pi\)
−0.669075 + 0.743195i \(0.733309\pi\)
\(174\) −8.43516e13 −0.230422
\(175\) −1.77545e14 −0.467262
\(176\) 1.38375e14 0.350934
\(177\) 3.07496e13 0.0751646
\(178\) 1.15625e14 0.272471
\(179\) −2.39788e14 −0.544858 −0.272429 0.962176i \(-0.587827\pi\)
−0.272429 + 0.962176i \(0.587827\pi\)
\(180\) 1.01178e14 0.221726
\(181\) −9.22930e13 −0.195100 −0.0975502 0.995231i \(-0.531101\pi\)
−0.0975502 + 0.995231i \(0.531101\pi\)
\(182\) 3.29618e14 0.672274
\(183\) 1.03127e14 0.202974
\(184\) 6.34400e11 0.00120517
\(185\) −8.83441e14 −1.62017
\(186\) −2.30722e13 −0.0408558
\(187\) −2.50241e14 −0.427945
\(188\) −6.69762e14 −1.10636
\(189\) −2.01259e14 −0.321184
\(190\) −1.51494e14 −0.233613
\(191\) 7.45616e14 1.11122 0.555608 0.831444i \(-0.312485\pi\)
0.555608 + 0.831444i \(0.312485\pi\)
\(192\) −2.93243e13 −0.0422445
\(193\) −1.17016e14 −0.162975 −0.0814877 0.996674i \(-0.525967\pi\)
−0.0814877 + 0.996674i \(0.525967\pi\)
\(194\) 6.50542e14 0.876122
\(195\) −3.25932e14 −0.424524
\(196\) −1.11081e15 −1.39951
\(197\) 4.65777e14 0.567737 0.283869 0.958863i \(-0.408382\pi\)
0.283869 + 0.958863i \(0.408382\pi\)
\(198\) −1.15721e14 −0.136486
\(199\) 1.14963e15 1.31224 0.656118 0.754659i \(-0.272197\pi\)
0.656118 + 0.754659i \(0.272197\pi\)
\(200\) −2.10142e14 −0.232176
\(201\) −5.15485e14 −0.551368
\(202\) 1.13866e14 0.117927
\(203\) −1.42864e15 −1.43284
\(204\) −2.26360e14 −0.219889
\(205\) 5.94630e14 0.559560
\(206\) 5.72153e14 0.521645
\(207\) 5.48328e11 0.000484432 0
\(208\) −4.03216e14 −0.345244
\(209\) −6.28556e14 −0.521667
\(210\) −4.72383e14 −0.380075
\(211\) 2.89074e14 0.225514 0.112757 0.993623i \(-0.464032\pi\)
0.112757 + 0.993623i \(0.464032\pi\)
\(212\) −1.33163e15 −1.00740
\(213\) −9.67110e11 −0.000709592 0
\(214\) −1.00682e15 −0.716577
\(215\) 1.21462e15 0.838666
\(216\) −2.38210e14 −0.159592
\(217\) −3.90767e14 −0.254056
\(218\) −5.70427e14 −0.359942
\(219\) −4.87838e14 −0.298806
\(220\) 9.85311e14 0.585904
\(221\) 7.29186e14 0.421006
\(222\) 9.13993e14 0.512446
\(223\) 1.08863e15 0.592785 0.296393 0.955066i \(-0.404216\pi\)
0.296393 + 0.955066i \(0.404216\pi\)
\(224\) −3.20102e15 −1.69307
\(225\) −1.81631e14 −0.0933261
\(226\) −3.37949e14 −0.168712
\(227\) 2.58105e15 1.25207 0.626034 0.779796i \(-0.284677\pi\)
0.626034 + 0.779796i \(0.284677\pi\)
\(228\) −5.68571e14 −0.268045
\(229\) 7.44687e14 0.341227 0.170613 0.985338i \(-0.445425\pi\)
0.170613 + 0.985338i \(0.445425\pi\)
\(230\) 1.28700e12 0.000573255 0
\(231\) −1.95994e15 −0.848720
\(232\) −1.69094e15 −0.711960
\(233\) −8.04669e14 −0.329461 −0.164730 0.986339i \(-0.552675\pi\)
−0.164730 + 0.986339i \(0.552675\pi\)
\(234\) 3.37204e14 0.134273
\(235\) −3.09203e15 −1.19758
\(236\) 2.70873e14 0.102056
\(237\) 2.79777e14 0.102553
\(238\) 1.05683e15 0.376926
\(239\) −3.27505e15 −1.13666 −0.568332 0.822799i \(-0.692411\pi\)
−0.568332 + 0.822799i \(0.692411\pi\)
\(240\) 5.77859e14 0.195186
\(241\) −4.16019e15 −1.36774 −0.683868 0.729606i \(-0.739703\pi\)
−0.683868 + 0.729606i \(0.739703\pi\)
\(242\) 3.25581e14 0.104198
\(243\) −2.05891e14 −0.0641500
\(244\) 9.08447e14 0.275591
\(245\) −5.12819e15 −1.51490
\(246\) −6.15194e14 −0.176984
\(247\) 1.83157e15 0.513209
\(248\) −4.62512e14 −0.126237
\(249\) 2.89173e15 0.768887
\(250\) −1.94898e15 −0.504889
\(251\) −4.91997e15 −1.24189 −0.620945 0.783854i \(-0.713251\pi\)
−0.620945 + 0.783854i \(0.713251\pi\)
\(252\) −1.77289e15 −0.436093
\(253\) 5.33982e12 0.00128010
\(254\) −1.97638e15 −0.461797
\(255\) −1.04502e15 −0.238019
\(256\) −2.38215e15 −0.528944
\(257\) −5.09014e15 −1.10196 −0.550979 0.834519i \(-0.685745\pi\)
−0.550979 + 0.834519i \(0.685745\pi\)
\(258\) −1.25662e15 −0.265263
\(259\) 1.54801e16 3.18658
\(260\) −2.87113e15 −0.576404
\(261\) −1.46152e15 −0.286182
\(262\) −3.68178e15 −0.703233
\(263\) 1.12234e15 0.209129 0.104564 0.994518i \(-0.466655\pi\)
0.104564 + 0.994518i \(0.466655\pi\)
\(264\) −2.31978e15 −0.421717
\(265\) −6.14765e15 −1.09046
\(266\) 2.65456e15 0.459474
\(267\) 2.00337e15 0.338407
\(268\) −4.54091e15 −0.748628
\(269\) 7.55630e15 1.21596 0.607980 0.793953i \(-0.291980\pi\)
0.607980 + 0.793953i \(0.291980\pi\)
\(270\) −4.83255e14 −0.0759122
\(271\) 1.30920e15 0.200773 0.100387 0.994948i \(-0.467992\pi\)
0.100387 + 0.994948i \(0.467992\pi\)
\(272\) −1.29281e15 −0.193569
\(273\) 5.71113e15 0.834959
\(274\) −1.41738e15 −0.202351
\(275\) −1.76879e15 −0.246611
\(276\) 4.83022e12 0.000657746 0
\(277\) −4.81062e15 −0.639856 −0.319928 0.947442i \(-0.603659\pi\)
−0.319928 + 0.947442i \(0.603659\pi\)
\(278\) 5.57761e15 0.724698
\(279\) −3.99761e14 −0.0507426
\(280\) −9.46954e15 −1.17436
\(281\) −7.61790e15 −0.923090 −0.461545 0.887117i \(-0.652705\pi\)
−0.461545 + 0.887117i \(0.652705\pi\)
\(282\) 3.19897e15 0.378783
\(283\) −3.79838e15 −0.439528 −0.219764 0.975553i \(-0.570529\pi\)
−0.219764 + 0.975553i \(0.570529\pi\)
\(284\) −8.51928e12 −0.000963460 0
\(285\) −2.62487e15 −0.290146
\(286\) 3.28381e15 0.354813
\(287\) −1.04194e16 −1.10055
\(288\) −3.27469e15 −0.338157
\(289\) −7.56663e15 −0.763953
\(290\) −3.43039e15 −0.338654
\(291\) 1.12716e16 1.08814
\(292\) −4.29737e15 −0.405709
\(293\) −8.76568e14 −0.0809368 −0.0404684 0.999181i \(-0.512885\pi\)
−0.0404684 + 0.999181i \(0.512885\pi\)
\(294\) 5.30554e15 0.479150
\(295\) 1.25052e15 0.110471
\(296\) 1.83222e16 1.58337
\(297\) −2.00504e15 −0.169515
\(298\) 4.20276e15 0.347640
\(299\) −1.55599e13 −0.00125934
\(300\) −1.59999e15 −0.126715
\(301\) −2.12831e16 −1.64950
\(302\) −9.90182e15 −0.751052
\(303\) 1.97291e15 0.146464
\(304\) −3.24728e15 −0.235961
\(305\) 4.19395e15 0.298314
\(306\) 1.08116e15 0.0752833
\(307\) −6.06330e15 −0.413342 −0.206671 0.978410i \(-0.566263\pi\)
−0.206671 + 0.978410i \(0.566263\pi\)
\(308\) −1.72651e16 −1.15236
\(309\) 9.91342e15 0.647878
\(310\) −9.38293e14 −0.0600465
\(311\) −1.63509e16 −1.02471 −0.512354 0.858774i \(-0.671227\pi\)
−0.512354 + 0.858774i \(0.671227\pi\)
\(312\) 6.75969e15 0.414879
\(313\) −1.57463e16 −0.946541 −0.473271 0.880917i \(-0.656927\pi\)
−0.473271 + 0.880917i \(0.656927\pi\)
\(314\) 6.19497e15 0.364751
\(315\) −8.18477e15 −0.472050
\(316\) 2.46455e15 0.139243
\(317\) 2.70870e16 1.49926 0.749628 0.661860i \(-0.230233\pi\)
0.749628 + 0.661860i \(0.230233\pi\)
\(318\) 6.36025e15 0.344904
\(319\) −1.42328e16 −0.756226
\(320\) −1.19256e15 −0.0620874
\(321\) −1.74447e16 −0.889982
\(322\) −2.25514e13 −0.00112749
\(323\) 5.87246e15 0.287742
\(324\) −1.81370e15 −0.0871007
\(325\) 5.15413e15 0.242613
\(326\) −1.70161e16 −0.785136
\(327\) −9.88352e15 −0.447045
\(328\) −1.23324e16 −0.546848
\(329\) 5.41801e16 2.35541
\(330\) −4.70612e15 −0.200596
\(331\) 3.49968e15 0.146267 0.0731335 0.997322i \(-0.476700\pi\)
0.0731335 + 0.997322i \(0.476700\pi\)
\(332\) 2.54733e16 1.04397
\(333\) 1.58363e16 0.636454
\(334\) −4.42962e15 −0.174588
\(335\) −2.09636e16 −0.810354
\(336\) −1.01255e16 −0.383895
\(337\) −7.30781e15 −0.271764 −0.135882 0.990725i \(-0.543387\pi\)
−0.135882 + 0.990725i \(0.543387\pi\)
\(338\) 3.17440e15 0.115799
\(339\) −5.85549e15 −0.209539
\(340\) −9.20554e15 −0.323174
\(341\) −3.89302e15 −0.134086
\(342\) 2.71565e15 0.0917707
\(343\) 3.95261e16 1.31061
\(344\) −2.51906e16 −0.819613
\(345\) 2.22993e13 0.000711978 0
\(346\) 1.98527e16 0.622050
\(347\) 1.04858e16 0.322449 0.161224 0.986918i \(-0.448456\pi\)
0.161224 + 0.986918i \(0.448456\pi\)
\(348\) −1.28745e16 −0.388568
\(349\) −5.48359e16 −1.62442 −0.812212 0.583362i \(-0.801737\pi\)
−0.812212 + 0.583362i \(0.801737\pi\)
\(350\) 7.47005e15 0.217211
\(351\) 5.84257e15 0.166766
\(352\) −3.18901e16 −0.893570
\(353\) −4.50440e16 −1.23909 −0.619543 0.784963i \(-0.712682\pi\)
−0.619543 + 0.784963i \(0.712682\pi\)
\(354\) −1.29376e15 −0.0349409
\(355\) −3.93302e13 −0.00104290
\(356\) 1.76477e16 0.459477
\(357\) 1.83113e16 0.468139
\(358\) 1.00889e16 0.253282
\(359\) 4.67877e16 1.15350 0.576750 0.816921i \(-0.304321\pi\)
0.576750 + 0.816921i \(0.304321\pi\)
\(360\) −9.68748e15 −0.234555
\(361\) −2.73025e16 −0.649241
\(362\) 3.88316e15 0.0906941
\(363\) 5.64118e15 0.129413
\(364\) 5.03094e16 1.13368
\(365\) −1.98393e16 −0.439160
\(366\) −4.33899e15 −0.0943542
\(367\) 8.30206e16 1.77360 0.886802 0.462150i \(-0.152922\pi\)
0.886802 + 0.462150i \(0.152922\pi\)
\(368\) 2.75868e13 0.000579017 0
\(369\) −1.06592e16 −0.219813
\(370\) 3.71700e16 0.753151
\(371\) 1.07722e17 2.14474
\(372\) −3.52149e15 −0.0688966
\(373\) −1.23123e16 −0.236719 −0.118359 0.992971i \(-0.537763\pi\)
−0.118359 + 0.992971i \(0.537763\pi\)
\(374\) 1.05287e16 0.198934
\(375\) −3.37690e16 −0.627068
\(376\) 6.41275e16 1.17037
\(377\) 4.14735e16 0.743965
\(378\) 8.46782e15 0.149305
\(379\) −8.67394e16 −1.50336 −0.751678 0.659530i \(-0.770755\pi\)
−0.751678 + 0.659530i \(0.770755\pi\)
\(380\) −2.31225e16 −0.393950
\(381\) −3.42438e16 −0.573547
\(382\) −3.13712e16 −0.516558
\(383\) −9.33161e15 −0.151065 −0.0755326 0.997143i \(-0.524066\pi\)
−0.0755326 + 0.997143i \(0.524066\pi\)
\(384\) −3.55649e16 −0.566068
\(385\) −7.97063e16 −1.24738
\(386\) 4.92335e15 0.0757605
\(387\) −2.17729e16 −0.329454
\(388\) 9.92920e16 1.47743
\(389\) 3.33207e16 0.487575 0.243787 0.969829i \(-0.421610\pi\)
0.243787 + 0.969829i \(0.421610\pi\)
\(390\) 1.37133e16 0.197343
\(391\) −4.98887e13 −0.000706079 0
\(392\) 1.06356e17 1.48049
\(393\) −6.37924e16 −0.873409
\(394\) −1.95972e16 −0.263918
\(395\) 1.13779e16 0.150723
\(396\) −1.76624e16 −0.230161
\(397\) −8.45703e16 −1.08413 −0.542063 0.840338i \(-0.682356\pi\)
−0.542063 + 0.840338i \(0.682356\pi\)
\(398\) −4.83696e16 −0.610004
\(399\) 4.59943e16 0.570663
\(400\) −9.13800e15 −0.111548
\(401\) −1.34825e17 −1.61931 −0.809657 0.586903i \(-0.800347\pi\)
−0.809657 + 0.586903i \(0.800347\pi\)
\(402\) 2.16886e16 0.256308
\(403\) 1.13440e16 0.131912
\(404\) 1.73794e16 0.198864
\(405\) −8.37313e15 −0.0942823
\(406\) 6.01089e16 0.666070
\(407\) 1.54220e17 1.68181
\(408\) 2.16732e16 0.232612
\(409\) −9.46427e16 −0.999736 −0.499868 0.866102i \(-0.666618\pi\)
−0.499868 + 0.866102i \(0.666618\pi\)
\(410\) −2.50186e16 −0.260116
\(411\) −2.45582e16 −0.251319
\(412\) 8.73274e16 0.879667
\(413\) −2.19122e16 −0.217275
\(414\) −2.30705e13 −0.000225192 0
\(415\) 1.17600e17 1.13005
\(416\) 9.29257e16 0.879082
\(417\) 9.66407e16 0.900069
\(418\) 2.64460e16 0.242501
\(419\) 8.90865e16 0.804305 0.402153 0.915573i \(-0.368262\pi\)
0.402153 + 0.915573i \(0.368262\pi\)
\(420\) −7.20996e16 −0.640933
\(421\) 2.41521e16 0.211408 0.105704 0.994398i \(-0.466290\pi\)
0.105704 + 0.994398i \(0.466290\pi\)
\(422\) −1.21626e16 −0.104832
\(423\) 5.54270e16 0.470445
\(424\) 1.27500e17 1.06569
\(425\) 1.65254e16 0.136026
\(426\) 4.06904e13 0.000329860 0
\(427\) −7.34884e16 −0.586729
\(428\) −1.53671e17 −1.20839
\(429\) 5.68971e16 0.440675
\(430\) −5.11040e16 −0.389861
\(431\) −1.59848e17 −1.20117 −0.600584 0.799561i \(-0.705065\pi\)
−0.600584 + 0.799561i \(0.705065\pi\)
\(432\) −1.03586e16 −0.0766752
\(433\) 1.98866e17 1.45007 0.725035 0.688712i \(-0.241824\pi\)
0.725035 + 0.688712i \(0.241824\pi\)
\(434\) 1.64412e16 0.118100
\(435\) −5.94368e16 −0.420606
\(436\) −8.70639e16 −0.606982
\(437\) −1.25311e14 −0.000860714 0
\(438\) 2.05254e16 0.138902
\(439\) −2.64129e17 −1.76115 −0.880576 0.473904i \(-0.842844\pi\)
−0.880576 + 0.473904i \(0.842844\pi\)
\(440\) −9.43403e16 −0.619805
\(441\) 9.19266e16 0.595101
\(442\) −3.06799e16 −0.195708
\(443\) 1.74987e17 1.09997 0.549987 0.835173i \(-0.314633\pi\)
0.549987 + 0.835173i \(0.314633\pi\)
\(444\) 1.39502e17 0.864156
\(445\) 8.14728e16 0.497362
\(446\) −4.58031e16 −0.275561
\(447\) 7.28194e16 0.431765
\(448\) 2.08965e16 0.122114
\(449\) 4.30946e16 0.248211 0.124106 0.992269i \(-0.460394\pi\)
0.124106 + 0.992269i \(0.460394\pi\)
\(450\) 7.64197e15 0.0433834
\(451\) −1.03803e17 −0.580849
\(452\) −5.15810e16 −0.284505
\(453\) −1.71564e17 −0.932800
\(454\) −1.08595e17 −0.582034
\(455\) 2.32259e17 1.22715
\(456\) 5.44387e16 0.283555
\(457\) −3.34947e17 −1.71997 −0.859984 0.510322i \(-0.829526\pi\)
−0.859984 + 0.510322i \(0.829526\pi\)
\(458\) −3.13321e16 −0.158622
\(459\) 1.87327e16 0.0935012
\(460\) 1.96434e14 0.000966699 0
\(461\) 2.87280e17 1.39395 0.696977 0.717093i \(-0.254528\pi\)
0.696977 + 0.717093i \(0.254528\pi\)
\(462\) 8.24628e16 0.394535
\(463\) 4.24478e16 0.200253 0.100126 0.994975i \(-0.468075\pi\)
0.100126 + 0.994975i \(0.468075\pi\)
\(464\) −7.35303e16 −0.342058
\(465\) −1.62574e16 −0.0745772
\(466\) 3.38558e16 0.153153
\(467\) 3.42928e16 0.152983 0.0764915 0.997070i \(-0.475628\pi\)
0.0764915 + 0.997070i \(0.475628\pi\)
\(468\) 5.14672e16 0.226429
\(469\) 3.67334e17 1.59382
\(470\) 1.30095e17 0.556703
\(471\) 1.07337e17 0.453018
\(472\) −2.59352e16 −0.107961
\(473\) −2.12033e17 −0.870573
\(474\) −1.17714e16 −0.0476725
\(475\) 4.15085e16 0.165817
\(476\) 1.61304e17 0.635623
\(477\) 1.10201e17 0.428368
\(478\) 1.37795e17 0.528388
\(479\) 4.39963e17 1.66431 0.832157 0.554540i \(-0.187106\pi\)
0.832157 + 0.554540i \(0.187106\pi\)
\(480\) −1.33174e17 −0.496995
\(481\) −4.49387e17 −1.65454
\(482\) 1.75037e17 0.635804
\(483\) −3.90738e14 −0.00140033
\(484\) 4.96932e16 0.175712
\(485\) 4.58393e17 1.59925
\(486\) 8.66270e15 0.0298207
\(487\) −1.14430e17 −0.388687 −0.194343 0.980934i \(-0.562258\pi\)
−0.194343 + 0.980934i \(0.562258\pi\)
\(488\) −8.69807e16 −0.291537
\(489\) −2.94830e17 −0.975132
\(490\) 2.15764e17 0.704215
\(491\) −3.51378e17 −1.13173 −0.565867 0.824496i \(-0.691458\pi\)
−0.565867 + 0.824496i \(0.691458\pi\)
\(492\) −9.38968e16 −0.298454
\(493\) 1.32974e17 0.417121
\(494\) −7.70619e16 −0.238569
\(495\) −8.15407e16 −0.249138
\(496\) −2.01123e16 −0.0606500
\(497\) 6.89163e14 0.00205119
\(498\) −1.21667e17 −0.357424
\(499\) −3.75672e17 −1.08932 −0.544659 0.838658i \(-0.683341\pi\)
−0.544659 + 0.838658i \(0.683341\pi\)
\(500\) −2.97471e17 −0.851412
\(501\) −7.67499e16 −0.216837
\(502\) 2.07004e17 0.577304
\(503\) 6.23517e16 0.171655 0.0858275 0.996310i \(-0.472647\pi\)
0.0858275 + 0.996310i \(0.472647\pi\)
\(504\) 1.69749e17 0.461326
\(505\) 8.02339e16 0.215260
\(506\) −2.24669e14 −0.000595065 0
\(507\) 5.50014e16 0.143821
\(508\) −3.01653e17 −0.778743
\(509\) 4.79539e17 1.22224 0.611122 0.791536i \(-0.290718\pi\)
0.611122 + 0.791536i \(0.290718\pi\)
\(510\) 4.39682e16 0.110645
\(511\) 3.47634e17 0.863746
\(512\) −2.99426e17 −0.734574
\(513\) 4.70528e16 0.113978
\(514\) 2.14164e17 0.512254
\(515\) 4.03157e17 0.952197
\(516\) −1.91797e17 −0.447321
\(517\) 5.39769e17 1.24314
\(518\) −6.51311e17 −1.48131
\(519\) 3.43979e17 0.772581
\(520\) 2.74901e17 0.609755
\(521\) 2.02174e17 0.442875 0.221437 0.975175i \(-0.428925\pi\)
0.221437 + 0.975175i \(0.428925\pi\)
\(522\) 6.14923e16 0.133034
\(523\) −6.54643e17 −1.39876 −0.699380 0.714750i \(-0.746541\pi\)
−0.699380 + 0.714750i \(0.746541\pi\)
\(524\) −5.61948e17 −1.18588
\(525\) 1.29430e17 0.269774
\(526\) −4.72217e16 −0.0972153
\(527\) 3.63716e16 0.0739594
\(528\) −1.00875e17 −0.202612
\(529\) −5.04035e17 −0.999998
\(530\) 2.58657e17 0.506911
\(531\) −2.24165e16 −0.0433963
\(532\) 4.05163e17 0.774827
\(533\) 3.02476e17 0.571431
\(534\) −8.42904e16 −0.157311
\(535\) −7.09438e17 −1.30802
\(536\) 4.34777e17 0.791945
\(537\) 1.74806e17 0.314574
\(538\) −3.17925e17 −0.565249
\(539\) 8.95215e17 1.57254
\(540\) −7.37589e16 −0.128013
\(541\) −1.59102e17 −0.272830 −0.136415 0.990652i \(-0.543558\pi\)
−0.136415 + 0.990652i \(0.543558\pi\)
\(542\) −5.50836e16 −0.0933312
\(543\) 6.72816e16 0.112641
\(544\) 2.97942e17 0.492878
\(545\) −4.01941e17 −0.657029
\(546\) −2.40291e17 −0.388138
\(547\) 1.62299e17 0.259059 0.129529 0.991576i \(-0.458653\pi\)
0.129529 + 0.991576i \(0.458653\pi\)
\(548\) −2.16333e17 −0.341232
\(549\) −7.51796e16 −0.117187
\(550\) 7.44203e16 0.114639
\(551\) 3.34005e17 0.508472
\(552\) −4.62478e14 −0.000695804 0
\(553\) −1.99369e17 −0.296445
\(554\) 2.02403e17 0.297443
\(555\) 6.44028e17 0.935407
\(556\) 8.51308e17 1.22208
\(557\) 2.97528e17 0.422152 0.211076 0.977470i \(-0.432303\pi\)
0.211076 + 0.977470i \(0.432303\pi\)
\(558\) 1.68196e16 0.0235881
\(559\) 6.17849e17 0.856457
\(560\) −4.11782e17 −0.564216
\(561\) 1.82426e17 0.247074
\(562\) 3.20517e17 0.429106
\(563\) −6.10404e17 −0.807817 −0.403909 0.914799i \(-0.632349\pi\)
−0.403909 + 0.914799i \(0.632349\pi\)
\(564\) 4.88257e17 0.638754
\(565\) −2.38130e17 −0.307963
\(566\) 1.59814e17 0.204318
\(567\) 1.46718e17 0.185436
\(568\) 8.15692e14 0.00101921
\(569\) −2.91779e17 −0.360433 −0.180217 0.983627i \(-0.557680\pi\)
−0.180217 + 0.983627i \(0.557680\pi\)
\(570\) 1.10439e17 0.134877
\(571\) 6.49232e17 0.783908 0.391954 0.919985i \(-0.371799\pi\)
0.391954 + 0.919985i \(0.371799\pi\)
\(572\) 5.01207e17 0.598333
\(573\) −5.43554e17 −0.641561
\(574\) 4.38388e17 0.511601
\(575\) −3.52630e14 −0.000406891 0
\(576\) 2.13774e16 0.0243899
\(577\) −3.50407e17 −0.395303 −0.197652 0.980272i \(-0.563331\pi\)
−0.197652 + 0.980272i \(0.563331\pi\)
\(578\) 3.18360e17 0.355130
\(579\) 8.53046e16 0.0940939
\(580\) −5.23579e17 −0.571084
\(581\) −2.06065e18 −2.22259
\(582\) −4.74245e17 −0.505829
\(583\) 1.07318e18 1.13195
\(584\) 4.11459e17 0.429183
\(585\) 2.37604e17 0.245099
\(586\) 3.68809e16 0.0376242
\(587\) −7.37728e17 −0.744301 −0.372150 0.928172i \(-0.621379\pi\)
−0.372150 + 0.928172i \(0.621379\pi\)
\(588\) 8.09782e17 0.808007
\(589\) 9.13582e16 0.0901567
\(590\) −5.26145e16 −0.0513532
\(591\) −3.39551e17 −0.327783
\(592\) 7.96739e17 0.760720
\(593\) −7.46191e17 −0.704684 −0.352342 0.935871i \(-0.614615\pi\)
−0.352342 + 0.935871i \(0.614615\pi\)
\(594\) 8.43606e16 0.0788003
\(595\) 7.44678e17 0.688031
\(596\) 6.41466e17 0.586236
\(597\) −8.38078e17 −0.757619
\(598\) 6.54670e14 0.000585416 0
\(599\) 2.57448e17 0.227727 0.113863 0.993496i \(-0.463677\pi\)
0.113863 + 0.993496i \(0.463677\pi\)
\(600\) 1.53193e17 0.134047
\(601\) −4.42336e17 −0.382885 −0.191442 0.981504i \(-0.561317\pi\)
−0.191442 + 0.981504i \(0.561317\pi\)
\(602\) 8.95468e17 0.766784
\(603\) 3.75788e17 0.318332
\(604\) −1.51131e18 −1.26652
\(605\) 2.29414e17 0.190200
\(606\) −8.30087e16 −0.0680850
\(607\) −1.20369e18 −0.976762 −0.488381 0.872630i \(-0.662412\pi\)
−0.488381 + 0.872630i \(0.662412\pi\)
\(608\) 7.48372e17 0.600820
\(609\) 1.04148e18 0.827253
\(610\) −1.76457e17 −0.138674
\(611\) −1.57285e18 −1.22298
\(612\) 1.65016e17 0.126953
\(613\) −2.42900e18 −1.84899 −0.924495 0.381194i \(-0.875513\pi\)
−0.924495 + 0.381194i \(0.875513\pi\)
\(614\) 2.55109e17 0.192146
\(615\) −4.33485e17 −0.323062
\(616\) 1.65308e18 1.21904
\(617\) 1.65295e18 1.20616 0.603082 0.797679i \(-0.293939\pi\)
0.603082 + 0.797679i \(0.293939\pi\)
\(618\) −4.17099e17 −0.301172
\(619\) −1.73811e17 −0.124190 −0.0620951 0.998070i \(-0.519778\pi\)
−0.0620951 + 0.998070i \(0.519778\pi\)
\(620\) −1.43211e17 −0.101258
\(621\) −3.99731e14 −0.000279687 0
\(622\) 6.87953e17 0.476345
\(623\) −1.42760e18 −0.978218
\(624\) 2.93945e17 0.199327
\(625\) −9.56109e17 −0.641634
\(626\) 6.62512e17 0.440008
\(627\) 4.58218e17 0.301185
\(628\) 9.45535e17 0.615092
\(629\) −1.44084e18 −0.927657
\(630\) 3.44367e17 0.219436
\(631\) −6.50398e17 −0.410193 −0.205097 0.978742i \(-0.565751\pi\)
−0.205097 + 0.978742i \(0.565751\pi\)
\(632\) −2.35973e17 −0.147299
\(633\) −2.10735e17 −0.130200
\(634\) −1.13966e18 −0.696942
\(635\) −1.39262e18 −0.842952
\(636\) 9.70762e17 0.581623
\(637\) −2.60860e18 −1.54704
\(638\) 5.98835e17 0.351538
\(639\) 7.05023e14 0.000409683 0
\(640\) −1.44634e18 −0.831959
\(641\) −1.96015e18 −1.11612 −0.558062 0.829799i \(-0.688455\pi\)
−0.558062 + 0.829799i \(0.688455\pi\)
\(642\) 7.33972e17 0.413716
\(643\) −1.03447e18 −0.577226 −0.288613 0.957446i \(-0.593194\pi\)
−0.288613 + 0.957446i \(0.593194\pi\)
\(644\) −3.44202e15 −0.00190132
\(645\) −8.85455e17 −0.484204
\(646\) −2.47079e17 −0.133759
\(647\) 1.32889e18 0.712214 0.356107 0.934445i \(-0.384104\pi\)
0.356107 + 0.934445i \(0.384104\pi\)
\(648\) 1.73655e17 0.0921405
\(649\) −2.18300e17 −0.114673
\(650\) −2.16856e17 −0.112781
\(651\) 2.84869e17 0.146679
\(652\) −2.59715e18 −1.32400
\(653\) −2.51128e18 −1.26753 −0.633767 0.773524i \(-0.718492\pi\)
−0.633767 + 0.773524i \(0.718492\pi\)
\(654\) 4.15841e17 0.207813
\(655\) −2.59430e18 −1.28366
\(656\) −5.36273e17 −0.262731
\(657\) 3.55634e17 0.172516
\(658\) −2.27958e18 −1.09493
\(659\) 5.35629e16 0.0254747 0.0127373 0.999919i \(-0.495945\pi\)
0.0127373 + 0.999919i \(0.495945\pi\)
\(660\) −7.18292e17 −0.338272
\(661\) −4.15725e18 −1.93864 −0.969318 0.245811i \(-0.920946\pi\)
−0.969318 + 0.245811i \(0.920946\pi\)
\(662\) −1.47246e17 −0.0679935
\(663\) −5.31577e17 −0.243068
\(664\) −2.43898e18 −1.10437
\(665\) 1.87048e18 0.838713
\(666\) −6.66301e17 −0.295861
\(667\) −2.83750e15 −0.00124772
\(668\) −6.76090e17 −0.294414
\(669\) −7.93609e17 −0.342245
\(670\) 8.82027e17 0.376700
\(671\) −7.32127e17 −0.309664
\(672\) 2.33354e18 0.977497
\(673\) −3.25282e17 −0.134947 −0.0674733 0.997721i \(-0.521494\pi\)
−0.0674733 + 0.997721i \(0.521494\pi\)
\(674\) 3.07470e17 0.126332
\(675\) 1.32409e17 0.0538818
\(676\) 4.84508e17 0.195275
\(677\) −6.07475e17 −0.242495 −0.121247 0.992622i \(-0.538689\pi\)
−0.121247 + 0.992622i \(0.538689\pi\)
\(678\) 2.46365e17 0.0974061
\(679\) −8.03218e18 −3.14543
\(680\) 8.81400e17 0.341873
\(681\) −1.88158e18 −0.722882
\(682\) 1.63796e17 0.0623309
\(683\) −2.15000e17 −0.0810408 −0.0405204 0.999179i \(-0.512902\pi\)
−0.0405204 + 0.999179i \(0.512902\pi\)
\(684\) 4.14488e17 0.154756
\(685\) −9.98727e17 −0.369367
\(686\) −1.66303e18 −0.609247
\(687\) −5.42877e17 −0.197007
\(688\) −1.09541e18 −0.393779
\(689\) −3.12718e18 −1.11360
\(690\) −9.38224e14 −0.000330969 0
\(691\) 1.89309e18 0.661552 0.330776 0.943709i \(-0.392689\pi\)
0.330776 + 0.943709i \(0.392689\pi\)
\(692\) 3.03011e18 1.04898
\(693\) 1.42879e18 0.490009
\(694\) −4.41182e17 −0.149893
\(695\) 3.93016e18 1.32285
\(696\) 1.23269e18 0.411050
\(697\) 9.69809e17 0.320386
\(698\) 2.30717e18 0.755127
\(699\) 5.86604e17 0.190214
\(700\) 1.14015e18 0.366290
\(701\) 2.71417e18 0.863913 0.431956 0.901895i \(-0.357823\pi\)
0.431956 + 0.901895i \(0.357823\pi\)
\(702\) −2.45821e17 −0.0775226
\(703\) −3.61911e18 −1.13082
\(704\) 2.08182e17 0.0644496
\(705\) 2.25409e18 0.691421
\(706\) 1.89519e18 0.576000
\(707\) −1.40590e18 −0.423377
\(708\) −1.97467e17 −0.0589220
\(709\) −2.89163e18 −0.854953 −0.427476 0.904027i \(-0.640597\pi\)
−0.427476 + 0.904027i \(0.640597\pi\)
\(710\) 1.65479e15 0.000484800 0
\(711\) −2.03957e17 −0.0592088
\(712\) −1.68971e18 −0.486063
\(713\) −7.76122e14 −0.000221232 0
\(714\) −7.70431e17 −0.217618
\(715\) 2.31388e18 0.647666
\(716\) 1.53986e18 0.427117
\(717\) 2.38751e18 0.656253
\(718\) −1.96855e18 −0.536215
\(719\) −1.40046e18 −0.378037 −0.189019 0.981974i \(-0.560531\pi\)
−0.189019 + 0.981974i \(0.560531\pi\)
\(720\) −4.21259e17 −0.112691
\(721\) −7.06431e18 −1.87280
\(722\) 1.14873e18 0.301805
\(723\) 3.03278e18 0.789662
\(724\) 5.92684e17 0.152941
\(725\) 9.39905e17 0.240374
\(726\) −2.37348e17 −0.0601586
\(727\) 2.30094e18 0.578006 0.289003 0.957328i \(-0.406676\pi\)
0.289003 + 0.957328i \(0.406676\pi\)
\(728\) −4.81695e18 −1.19927
\(729\) 1.50095e17 0.0370370
\(730\) 8.34722e17 0.204147
\(731\) 1.98097e18 0.480192
\(732\) −6.62258e17 −0.159113
\(733\) 5.18870e17 0.123561 0.0617807 0.998090i \(-0.480322\pi\)
0.0617807 + 0.998090i \(0.480322\pi\)
\(734\) −3.49302e18 −0.824475
\(735\) 3.73845e18 0.874629
\(736\) −6.35770e15 −0.00147433
\(737\) 3.65957e18 0.841184
\(738\) 4.48477e17 0.102182
\(739\) 4.45497e18 1.00613 0.503067 0.864247i \(-0.332205\pi\)
0.503067 + 0.864247i \(0.332205\pi\)
\(740\) 5.67325e18 1.27006
\(741\) −1.33522e18 −0.296301
\(742\) −4.53232e18 −0.996999
\(743\) 4.91263e18 1.07124 0.535620 0.844459i \(-0.320078\pi\)
0.535620 + 0.844459i \(0.320078\pi\)
\(744\) 3.37171e17 0.0728830
\(745\) 2.96140e18 0.634573
\(746\) 5.18031e17 0.110041
\(747\) −2.10807e18 −0.443917
\(748\) 1.60699e18 0.335469
\(749\) 1.24311e19 2.57263
\(750\) 1.42080e18 0.291498
\(751\) 8.42095e16 0.0171278 0.00856390 0.999963i \(-0.497274\pi\)
0.00856390 + 0.999963i \(0.497274\pi\)
\(752\) 2.78858e18 0.562299
\(753\) 3.58666e18 0.717006
\(754\) −1.74497e18 −0.345838
\(755\) −6.97713e18 −1.37095
\(756\) 1.29244e18 0.251778
\(757\) −3.82632e18 −0.739022 −0.369511 0.929226i \(-0.620475\pi\)
−0.369511 + 0.929226i \(0.620475\pi\)
\(758\) 3.64949e18 0.698848
\(759\) −3.89273e15 −0.000739065 0
\(760\) 2.21390e18 0.416745
\(761\) −7.67763e18 −1.43294 −0.716468 0.697620i \(-0.754242\pi\)
−0.716468 + 0.697620i \(0.754242\pi\)
\(762\) 1.44078e18 0.266618
\(763\) 7.04300e18 1.29225
\(764\) −4.78817e18 −0.871090
\(765\) 7.61816e17 0.137420
\(766\) 3.92620e17 0.0702240
\(767\) 6.36112e17 0.112814
\(768\) 1.73659e18 0.305386
\(769\) −3.01793e18 −0.526246 −0.263123 0.964762i \(-0.584752\pi\)
−0.263123 + 0.964762i \(0.584752\pi\)
\(770\) 3.35358e18 0.579854
\(771\) 3.71071e18 0.636215
\(772\) 7.51448e17 0.127758
\(773\) 3.04317e18 0.513050 0.256525 0.966538i \(-0.417422\pi\)
0.256525 + 0.966538i \(0.417422\pi\)
\(774\) 9.16077e17 0.153150
\(775\) 2.57086e17 0.0426205
\(776\) −9.50687e18 −1.56292
\(777\) −1.12850e19 −1.83977
\(778\) −1.40194e18 −0.226653
\(779\) 2.43597e18 0.390552
\(780\) 2.09306e18 0.332787
\(781\) 6.86578e15 0.00108258
\(782\) 2.09903e15 0.000328227 0
\(783\) 1.06545e18 0.165227
\(784\) 4.62490e18 0.711293
\(785\) 4.36517e18 0.665807
\(786\) 2.68401e18 0.406012
\(787\) 4.82693e18 0.724161 0.362081 0.932147i \(-0.382067\pi\)
0.362081 + 0.932147i \(0.382067\pi\)
\(788\) −2.99111e18 −0.445053
\(789\) −8.18189e17 −0.120741
\(790\) −4.78715e17 −0.0700650
\(791\) 4.17262e18 0.605706
\(792\) 1.69112e18 0.243479
\(793\) 2.13337e18 0.304643
\(794\) 3.55823e18 0.503965
\(795\) 4.48163e18 0.629579
\(796\) −7.38263e18 −1.02867
\(797\) −5.54998e18 −0.767029 −0.383515 0.923535i \(-0.625286\pi\)
−0.383515 + 0.923535i \(0.625286\pi\)
\(798\) −1.93517e18 −0.265278
\(799\) −5.04294e18 −0.685693
\(800\) 2.10595e18 0.284030
\(801\) −1.46046e18 −0.195379
\(802\) 5.67264e18 0.752752
\(803\) 3.46330e18 0.455868
\(804\) 3.31032e18 0.432221
\(805\) −1.58905e16 −0.00205808
\(806\) −4.77290e17 −0.0613203
\(807\) −5.50854e18 −0.702035
\(808\) −1.66402e18 −0.210370
\(809\) −8.09954e18 −1.01577 −0.507885 0.861425i \(-0.669572\pi\)
−0.507885 + 0.861425i \(0.669572\pi\)
\(810\) 3.52293e17 0.0438279
\(811\) 1.04477e19 1.28939 0.644697 0.764438i \(-0.276983\pi\)
0.644697 + 0.764438i \(0.276983\pi\)
\(812\) 9.17440e18 1.12322
\(813\) −9.54408e17 −0.115917
\(814\) −6.48869e18 −0.781804
\(815\) −1.19901e19 −1.43317
\(816\) 9.42457e17 0.111757
\(817\) 4.97581e18 0.585356
\(818\) 3.98201e18 0.464736
\(819\) −4.16342e18 −0.482064
\(820\) −3.81857e18 −0.438643
\(821\) −5.88504e18 −0.670686 −0.335343 0.942096i \(-0.608852\pi\)
−0.335343 + 0.942096i \(0.608852\pi\)
\(822\) 1.03327e18 0.116828
\(823\) 1.26926e19 1.42381 0.711904 0.702276i \(-0.247833\pi\)
0.711904 + 0.702276i \(0.247833\pi\)
\(824\) −8.36130e18 −0.930566
\(825\) 1.28945e18 0.142381
\(826\) 9.21937e17 0.101002
\(827\) 5.76038e17 0.0626131 0.0313065 0.999510i \(-0.490033\pi\)
0.0313065 + 0.999510i \(0.490033\pi\)
\(828\) −3.52123e15 −0.000379750 0
\(829\) −1.73735e19 −1.85901 −0.929506 0.368808i \(-0.879766\pi\)
−0.929506 + 0.368808i \(0.879766\pi\)
\(830\) −4.94794e18 −0.525311
\(831\) 3.50694e18 0.369421
\(832\) −6.06628e17 −0.0634046
\(833\) −8.36379e18 −0.867383
\(834\) −4.06608e18 −0.418405
\(835\) −3.12125e18 −0.318688
\(836\) 4.03644e18 0.408938
\(837\) 2.91425e17 0.0292962
\(838\) −3.74824e18 −0.373888
\(839\) −6.92308e18 −0.685246 −0.342623 0.939473i \(-0.611315\pi\)
−0.342623 + 0.939473i \(0.611315\pi\)
\(840\) 6.90330e18 0.678018
\(841\) −2.69753e18 −0.262901
\(842\) −1.01618e18 −0.0982748
\(843\) 5.55345e18 0.532946
\(844\) −1.85636e18 −0.176782
\(845\) 2.23678e18 0.211376
\(846\) −2.33205e18 −0.218690
\(847\) −4.01991e18 −0.374088
\(848\) 5.54431e18 0.512005
\(849\) 2.76902e18 0.253761
\(850\) −6.95292e17 −0.0632331
\(851\) 3.07457e16 0.00277487
\(852\) 6.21055e15 0.000556254 0
\(853\) 1.47745e19 1.31324 0.656619 0.754222i \(-0.271986\pi\)
0.656619 + 0.754222i \(0.271986\pi\)
\(854\) 3.09196e18 0.272746
\(855\) 1.91353e18 0.167516
\(856\) 1.47134e19 1.27831
\(857\) −1.53348e19 −1.32222 −0.661108 0.750291i \(-0.729914\pi\)
−0.661108 + 0.750291i \(0.729914\pi\)
\(858\) −2.39390e18 −0.204851
\(859\) −1.65089e18 −0.140205 −0.0701023 0.997540i \(-0.522333\pi\)
−0.0701023 + 0.997540i \(0.522333\pi\)
\(860\) −7.79997e18 −0.657435
\(861\) 7.59574e18 0.635403
\(862\) 6.72546e18 0.558373
\(863\) 1.77571e19 1.46319 0.731596 0.681738i \(-0.238776\pi\)
0.731596 + 0.681738i \(0.238776\pi\)
\(864\) 2.38725e18 0.195235
\(865\) 1.39889e19 1.13547
\(866\) −8.36712e18 −0.674077
\(867\) 5.51607e18 0.441068
\(868\) 2.50941e18 0.199156
\(869\) −1.98621e18 −0.156458
\(870\) 2.50075e18 0.195522
\(871\) −1.06637e19 −0.827545
\(872\) 8.33608e18 0.642103
\(873\) −8.21703e18 −0.628235
\(874\) 5.27234e15 0.000400110 0
\(875\) 2.40638e19 1.81264
\(876\) 3.13278e18 0.234236
\(877\) 1.31264e19 0.974204 0.487102 0.873345i \(-0.338054\pi\)
0.487102 + 0.873345i \(0.338054\pi\)
\(878\) 1.11130e19 0.818687
\(879\) 6.39018e17 0.0467289
\(880\) −4.10238e18 −0.297782
\(881\) 1.27348e19 0.917594 0.458797 0.888541i \(-0.348281\pi\)
0.458797 + 0.888541i \(0.348281\pi\)
\(882\) −3.86774e18 −0.276638
\(883\) 4.63386e17 0.0329002 0.0164501 0.999865i \(-0.494764\pi\)
0.0164501 + 0.999865i \(0.494764\pi\)
\(884\) −4.68266e18 −0.330030
\(885\) −9.11628e17 −0.0637802
\(886\) −7.36245e18 −0.511332
\(887\) 6.90504e18 0.476061 0.238030 0.971258i \(-0.423498\pi\)
0.238030 + 0.971258i \(0.423498\pi\)
\(888\) −1.33569e19 −0.914157
\(889\) 2.44021e19 1.65793
\(890\) −3.42790e18 −0.231203
\(891\) 1.46168e18 0.0978693
\(892\) −6.99090e18 −0.464688
\(893\) −1.26669e19 −0.835862
\(894\) −3.06382e18 −0.200710
\(895\) 7.10895e18 0.462334
\(896\) 2.53435e19 1.63631
\(897\) 1.13432e16 0.000727082 0
\(898\) −1.81317e18 −0.115383
\(899\) 2.06869e18 0.130694
\(900\) 1.16639e18 0.0731589
\(901\) −1.00265e19 −0.624363
\(902\) 4.36743e18 0.270012
\(903\) 1.55154e19 0.952339
\(904\) 4.93871e18 0.300967
\(905\) 2.73619e18 0.165551
\(906\) 7.21843e18 0.433620
\(907\) −1.26250e19 −0.752979 −0.376490 0.926421i \(-0.622869\pi\)
−0.376490 + 0.926421i \(0.622869\pi\)
\(908\) −1.65749e19 −0.981504
\(909\) −1.43825e18 −0.0845610
\(910\) −9.77211e18 −0.570452
\(911\) 1.04074e19 0.603217 0.301608 0.953432i \(-0.402477\pi\)
0.301608 + 0.953432i \(0.402477\pi\)
\(912\) 2.36726e18 0.136232
\(913\) −2.05292e19 −1.17304
\(914\) 1.40926e19 0.799542
\(915\) −3.05739e18 −0.172232
\(916\) −4.78220e18 −0.267490
\(917\) 4.54585e19 2.52473
\(918\) −7.88162e17 −0.0434648
\(919\) −3.88121e18 −0.212528 −0.106264 0.994338i \(-0.533889\pi\)
−0.106264 + 0.994338i \(0.533889\pi\)
\(920\) −1.88079e16 −0.00102263
\(921\) 4.42015e18 0.238643
\(922\) −1.20871e19 −0.647992
\(923\) −2.00064e16 −0.00106502
\(924\) 1.25863e19 0.665317
\(925\) −1.01844e19 −0.534580
\(926\) −1.78596e18 −0.0930893
\(927\) −7.22689e18 −0.374053
\(928\) 1.69459e19 0.870969
\(929\) −1.37647e19 −0.702528 −0.351264 0.936277i \(-0.614248\pi\)
−0.351264 + 0.936277i \(0.614248\pi\)
\(930\) 6.84016e17 0.0346678
\(931\) −2.10082e19 −1.05734
\(932\) 5.16740e18 0.258267
\(933\) 1.19198e19 0.591616
\(934\) −1.44284e18 −0.0711154
\(935\) 7.41885e18 0.363129
\(936\) −4.92781e18 −0.239531
\(937\) 2.77960e18 0.134176 0.0670881 0.997747i \(-0.478629\pi\)
0.0670881 + 0.997747i \(0.478629\pi\)
\(938\) −1.54553e19 −0.740899
\(939\) 1.14790e19 0.546486
\(940\) 1.98563e19 0.938788
\(941\) −1.79211e19 −0.841457 −0.420729 0.907187i \(-0.638225\pi\)
−0.420729 + 0.907187i \(0.638225\pi\)
\(942\) −4.51613e18 −0.210589
\(943\) −2.06945e16 −0.000958359 0
\(944\) −1.12779e18 −0.0518693
\(945\) 5.96669e18 0.272538
\(946\) 8.92110e18 0.404693
\(947\) 2.78571e19 1.25505 0.627526 0.778596i \(-0.284068\pi\)
0.627526 + 0.778596i \(0.284068\pi\)
\(948\) −1.79666e18 −0.0803917
\(949\) −1.00918e19 −0.448476
\(950\) −1.74644e18 −0.0770814
\(951\) −1.97464e19 −0.865595
\(952\) −1.54443e19 −0.672401
\(953\) 4.26175e19 1.84282 0.921412 0.388586i \(-0.127036\pi\)
0.921412 + 0.388586i \(0.127036\pi\)
\(954\) −4.63662e18 −0.199130
\(955\) −2.21051e19 −0.942913
\(956\) 2.10316e19 0.891038
\(957\) 1.03757e19 0.436608
\(958\) −1.85111e19 −0.773671
\(959\) 1.75002e19 0.726476
\(960\) 8.69373e17 0.0358462
\(961\) −2.38517e19 −0.976827
\(962\) 1.89076e19 0.769128
\(963\) 1.27172e19 0.513831
\(964\) 2.67157e19 1.07218
\(965\) 3.46915e18 0.138291
\(966\) 1.64400e16 0.000650954 0
\(967\) −4.36536e19 −1.71691 −0.858455 0.512889i \(-0.828575\pi\)
−0.858455 + 0.512889i \(0.828575\pi\)
\(968\) −4.75796e18 −0.185879
\(969\) −4.28102e18 −0.166128
\(970\) −1.92865e19 −0.743425
\(971\) 2.50166e19 0.957864 0.478932 0.877852i \(-0.341024\pi\)
0.478932 + 0.877852i \(0.341024\pi\)
\(972\) 1.32218e18 0.0502876
\(973\) −6.88662e19 −2.60179
\(974\) 4.81453e18 0.180684
\(975\) −3.75736e18 −0.140073
\(976\) −3.78235e18 −0.140068
\(977\) 2.16619e19 0.796858 0.398429 0.917199i \(-0.369555\pi\)
0.398429 + 0.917199i \(0.369555\pi\)
\(978\) 1.24047e19 0.453298
\(979\) −1.42225e19 −0.516284
\(980\) 3.29320e19 1.18754
\(981\) 7.20508e18 0.258102
\(982\) 1.47839e19 0.526096
\(983\) −4.85622e19 −1.71672 −0.858362 0.513045i \(-0.828517\pi\)
−0.858362 + 0.513045i \(0.828517\pi\)
\(984\) 8.99031e18 0.315723
\(985\) −1.38088e19 −0.481748
\(986\) −5.59478e18 −0.193902
\(987\) −3.94973e19 −1.35990
\(988\) −1.17619e19 −0.402308
\(989\) −4.22714e16 −0.00143638
\(990\) 3.43076e18 0.115814
\(991\) −4.20059e19 −1.40874 −0.704370 0.709833i \(-0.748771\pi\)
−0.704370 + 0.709833i \(0.748771\pi\)
\(992\) 4.63510e18 0.154431
\(993\) −2.55127e18 −0.0844473
\(994\) −2.89960e16 −0.000953512 0
\(995\) −3.40827e19 −1.11349
\(996\) −1.85700e19 −0.602735
\(997\) 3.88938e19 1.25419 0.627094 0.778944i \(-0.284244\pi\)
0.627094 + 0.778944i \(0.284244\pi\)
\(998\) 1.58061e19 0.506379
\(999\) −1.15447e19 −0.367457
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.1.14 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.14 31 1.1 even 1 trivial