Properties

Label 177.14.a.b.1.4
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 1.4
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-151.259 q^{2} -729.000 q^{3} +14687.4 q^{4} +64912.3 q^{5} +110268. q^{6} -35238.1 q^{7} -982489. q^{8} +531441. q^{9} +O(q^{10})\) \(q-151.259 q^{2} -729.000 q^{3} +14687.4 q^{4} +64912.3 q^{5} +110268. q^{6} -35238.1 q^{7} -982489. q^{8} +531441. q^{9} -9.81859e6 q^{10} -846653. q^{11} -1.07071e7 q^{12} -6.32197e6 q^{13} +5.33010e6 q^{14} -4.73210e7 q^{15} +2.82916e7 q^{16} +8.25934e7 q^{17} -8.03854e7 q^{18} +3.86792e8 q^{19} +9.53392e8 q^{20} +2.56886e7 q^{21} +1.28064e8 q^{22} -5.52943e8 q^{23} +7.16235e8 q^{24} +2.99290e9 q^{25} +9.56257e8 q^{26} -3.87420e8 q^{27} -5.17556e8 q^{28} -3.29886e9 q^{29} +7.15775e9 q^{30} -1.19195e9 q^{31} +3.76919e9 q^{32} +6.17210e8 q^{33} -1.24930e10 q^{34} -2.28739e9 q^{35} +7.80548e9 q^{36} -2.10134e10 q^{37} -5.85059e10 q^{38} +4.60872e9 q^{39} -6.37756e10 q^{40} +5.49178e10 q^{41} -3.88564e9 q^{42} -1.86354e9 q^{43} -1.24351e10 q^{44} +3.44970e10 q^{45} +8.36378e10 q^{46} -1.24763e11 q^{47} -2.06246e10 q^{48} -9.56473e10 q^{49} -4.52704e11 q^{50} -6.02106e10 q^{51} -9.28533e10 q^{52} -2.31878e11 q^{53} +5.86010e10 q^{54} -5.49582e10 q^{55} +3.46211e10 q^{56} -2.81971e11 q^{57} +4.98984e11 q^{58} -4.21805e10 q^{59} -6.95023e11 q^{60} +2.65237e11 q^{61} +1.80294e11 q^{62} -1.87270e10 q^{63} -8.01889e11 q^{64} -4.10374e11 q^{65} -9.33588e10 q^{66} -6.42635e11 q^{67} +1.21308e12 q^{68} +4.03095e11 q^{69} +3.45989e11 q^{70} -1.49296e12 q^{71} -5.22135e11 q^{72} +8.05814e11 q^{73} +3.17848e12 q^{74} -2.18182e12 q^{75} +5.68096e12 q^{76} +2.98345e10 q^{77} -6.97112e11 q^{78} +2.72274e12 q^{79} +1.83647e12 q^{80} +2.82430e11 q^{81} -8.30683e12 q^{82} -5.25906e12 q^{83} +3.77299e11 q^{84} +5.36133e12 q^{85} +2.81877e11 q^{86} +2.40487e12 q^{87} +8.31828e11 q^{88} +2.96797e12 q^{89} -5.21800e12 q^{90} +2.22774e11 q^{91} -8.12129e12 q^{92} +8.68933e11 q^{93} +1.88715e13 q^{94} +2.51075e13 q^{95} -2.74774e12 q^{96} -1.05219e13 q^{97} +1.44675e13 q^{98} -4.49946e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −151.259 −1.67120 −0.835598 0.549342i \(-0.814879\pi\)
−0.835598 + 0.549342i \(0.814879\pi\)
\(3\) −729.000 −0.577350
\(4\) 14687.4 1.79289
\(5\) 64912.3 1.85790 0.928949 0.370208i \(-0.120714\pi\)
0.928949 + 0.370208i \(0.120714\pi\)
\(6\) 110268. 0.964865
\(7\) −35238.1 −0.113208 −0.0566038 0.998397i \(-0.518027\pi\)
−0.0566038 + 0.998397i \(0.518027\pi\)
\(8\) −982489. −1.32508
\(9\) 531441. 0.333333
\(10\) −9.81859e6 −3.10491
\(11\) −846653. −0.144096 −0.0720482 0.997401i \(-0.522954\pi\)
−0.0720482 + 0.997401i \(0.522954\pi\)
\(12\) −1.07071e7 −1.03513
\(13\) −6.32197e6 −0.363263 −0.181631 0.983367i \(-0.558138\pi\)
−0.181631 + 0.983367i \(0.558138\pi\)
\(14\) 5.33010e6 0.189192
\(15\) −4.73210e7 −1.07266
\(16\) 2.82916e7 0.421577
\(17\) 8.25934e7 0.829903 0.414952 0.909844i \(-0.363799\pi\)
0.414952 + 0.909844i \(0.363799\pi\)
\(18\) −8.03854e7 −0.557065
\(19\) 3.86792e8 1.88616 0.943080 0.332565i \(-0.107914\pi\)
0.943080 + 0.332565i \(0.107914\pi\)
\(20\) 9.53392e8 3.33102
\(21\) 2.56886e7 0.0653604
\(22\) 1.28064e8 0.240813
\(23\) −5.52943e8 −0.778842 −0.389421 0.921060i \(-0.627325\pi\)
−0.389421 + 0.921060i \(0.627325\pi\)
\(24\) 7.16235e8 0.765037
\(25\) 2.99290e9 2.45178
\(26\) 9.56257e8 0.607083
\(27\) −3.87420e8 −0.192450
\(28\) −5.17556e8 −0.202969
\(29\) −3.29886e9 −1.02986 −0.514929 0.857233i \(-0.672182\pi\)
−0.514929 + 0.857233i \(0.672182\pi\)
\(30\) 7.15775e9 1.79262
\(31\) −1.19195e9 −0.241217 −0.120608 0.992700i \(-0.538485\pi\)
−0.120608 + 0.992700i \(0.538485\pi\)
\(32\) 3.76919e9 0.620544
\(33\) 6.17210e8 0.0831941
\(34\) −1.24930e10 −1.38693
\(35\) −2.28739e9 −0.210328
\(36\) 7.80548e9 0.597632
\(37\) −2.10134e10 −1.34644 −0.673218 0.739444i \(-0.735088\pi\)
−0.673218 + 0.739444i \(0.735088\pi\)
\(38\) −5.85059e10 −3.15214
\(39\) 4.60872e9 0.209730
\(40\) −6.37756e10 −2.46187
\(41\) 5.49178e10 1.80559 0.902793 0.430076i \(-0.141513\pi\)
0.902793 + 0.430076i \(0.141513\pi\)
\(42\) −3.88564e9 −0.109230
\(43\) −1.86354e9 −0.0449565 −0.0224783 0.999747i \(-0.507156\pi\)
−0.0224783 + 0.999747i \(0.507156\pi\)
\(44\) −1.24351e10 −0.258350
\(45\) 3.44970e10 0.619299
\(46\) 8.36378e10 1.30160
\(47\) −1.24763e11 −1.68830 −0.844148 0.536110i \(-0.819893\pi\)
−0.844148 + 0.536110i \(0.819893\pi\)
\(48\) −2.06246e10 −0.243398
\(49\) −9.56473e10 −0.987184
\(50\) −4.52704e11 −4.09741
\(51\) −6.02106e10 −0.479145
\(52\) −9.28533e10 −0.651292
\(53\) −2.31878e11 −1.43703 −0.718516 0.695511i \(-0.755178\pi\)
−0.718516 + 0.695511i \(0.755178\pi\)
\(54\) 5.86010e10 0.321622
\(55\) −5.49582e10 −0.267716
\(56\) 3.46211e10 0.150009
\(57\) −2.81971e11 −1.08898
\(58\) 4.98984e11 1.72109
\(59\) −4.21805e10 −0.130189
\(60\) −6.95023e11 −1.92316
\(61\) 2.65237e11 0.659159 0.329580 0.944128i \(-0.393093\pi\)
0.329580 + 0.944128i \(0.393093\pi\)
\(62\) 1.80294e11 0.403121
\(63\) −1.87270e10 −0.0377359
\(64\) −8.01889e11 −1.45863
\(65\) −4.10374e11 −0.674905
\(66\) −9.33588e10 −0.139034
\(67\) −6.42635e11 −0.867917 −0.433958 0.900933i \(-0.642884\pi\)
−0.433958 + 0.900933i \(0.642884\pi\)
\(68\) 1.21308e12 1.48793
\(69\) 4.03095e11 0.449665
\(70\) 3.45989e11 0.351499
\(71\) −1.49296e12 −1.38315 −0.691575 0.722305i \(-0.743083\pi\)
−0.691575 + 0.722305i \(0.743083\pi\)
\(72\) −5.22135e11 −0.441694
\(73\) 8.05814e11 0.623212 0.311606 0.950211i \(-0.399133\pi\)
0.311606 + 0.950211i \(0.399133\pi\)
\(74\) 3.17848e12 2.25016
\(75\) −2.18182e12 −1.41554
\(76\) 5.68096e12 3.38169
\(77\) 2.98345e10 0.0163128
\(78\) −6.97112e11 −0.350500
\(79\) 2.72274e12 1.26017 0.630087 0.776525i \(-0.283019\pi\)
0.630087 + 0.776525i \(0.283019\pi\)
\(80\) 1.83647e12 0.783248
\(81\) 2.82430e11 0.111111
\(82\) −8.30683e12 −3.01749
\(83\) −5.25906e12 −1.76563 −0.882817 0.469718i \(-0.844356\pi\)
−0.882817 + 0.469718i \(0.844356\pi\)
\(84\) 3.77299e11 0.117184
\(85\) 5.36133e12 1.54187
\(86\) 2.81877e11 0.0751311
\(87\) 2.40487e12 0.594589
\(88\) 8.31828e11 0.190940
\(89\) 2.96797e12 0.633030 0.316515 0.948587i \(-0.397487\pi\)
0.316515 + 0.948587i \(0.397487\pi\)
\(90\) −5.21800e12 −1.03497
\(91\) 2.22774e11 0.0411241
\(92\) −8.12129e12 −1.39638
\(93\) 8.68933e11 0.139267
\(94\) 1.88715e13 2.82147
\(95\) 2.51075e13 3.50429
\(96\) −2.74774e12 −0.358271
\(97\) −1.05219e13 −1.28256 −0.641279 0.767308i \(-0.721596\pi\)
−0.641279 + 0.767308i \(0.721596\pi\)
\(98\) 1.44675e13 1.64978
\(99\) −4.49946e11 −0.0480321
\(100\) 4.39579e13 4.39579
\(101\) −1.71707e13 −1.60953 −0.804764 0.593595i \(-0.797708\pi\)
−0.804764 + 0.593595i \(0.797708\pi\)
\(102\) 9.10742e12 0.800745
\(103\) −2.24871e13 −1.85563 −0.927813 0.373045i \(-0.878314\pi\)
−0.927813 + 0.373045i \(0.878314\pi\)
\(104\) 6.21127e12 0.481353
\(105\) 1.66751e12 0.121433
\(106\) 3.50737e13 2.40156
\(107\) 1.48950e13 0.959504 0.479752 0.877404i \(-0.340727\pi\)
0.479752 + 0.877404i \(0.340727\pi\)
\(108\) −5.69020e12 −0.345043
\(109\) −6.24650e12 −0.356751 −0.178375 0.983963i \(-0.557084\pi\)
−0.178375 + 0.983963i \(0.557084\pi\)
\(110\) 8.31294e12 0.447406
\(111\) 1.53188e13 0.777365
\(112\) −9.96943e11 −0.0477258
\(113\) 1.07703e13 0.486653 0.243327 0.969944i \(-0.421761\pi\)
0.243327 + 0.969944i \(0.421761\pi\)
\(114\) 4.26508e13 1.81989
\(115\) −3.58928e13 −1.44701
\(116\) −4.84517e13 −1.84643
\(117\) −3.35976e12 −0.121088
\(118\) 6.38020e12 0.217571
\(119\) −2.91044e12 −0.0939513
\(120\) 4.64924e13 1.42136
\(121\) −3.38059e13 −0.979236
\(122\) −4.01196e13 −1.10158
\(123\) −4.00351e13 −1.04246
\(124\) −1.75067e13 −0.432476
\(125\) 1.15037e14 2.69726
\(126\) 2.83263e12 0.0630640
\(127\) 2.38612e13 0.504624 0.252312 0.967646i \(-0.418809\pi\)
0.252312 + 0.967646i \(0.418809\pi\)
\(128\) 9.04161e13 1.81711
\(129\) 1.35852e12 0.0259557
\(130\) 6.20728e13 1.12790
\(131\) −5.10666e13 −0.882822 −0.441411 0.897305i \(-0.645522\pi\)
−0.441411 + 0.897305i \(0.645522\pi\)
\(132\) 9.06521e12 0.149158
\(133\) −1.36298e13 −0.213528
\(134\) 9.72046e13 1.45046
\(135\) −2.51483e13 −0.357553
\(136\) −8.11472e13 −1.09969
\(137\) 1.00612e14 1.30007 0.650035 0.759904i \(-0.274754\pi\)
0.650035 + 0.759904i \(0.274754\pi\)
\(138\) −6.09720e13 −0.751478
\(139\) −6.63965e13 −0.780817 −0.390408 0.920642i \(-0.627666\pi\)
−0.390408 + 0.920642i \(0.627666\pi\)
\(140\) −3.35958e13 −0.377096
\(141\) 9.09520e13 0.974738
\(142\) 2.25824e14 2.31151
\(143\) 5.35252e12 0.0523449
\(144\) 1.50353e13 0.140526
\(145\) −2.14137e14 −1.91337
\(146\) −1.21887e14 −1.04151
\(147\) 6.97269e13 0.569951
\(148\) −3.08632e14 −2.41402
\(149\) 1.10223e14 0.825202 0.412601 0.910912i \(-0.364620\pi\)
0.412601 + 0.910912i \(0.364620\pi\)
\(150\) 3.30021e14 2.36564
\(151\) −9.61814e13 −0.660299 −0.330150 0.943929i \(-0.607099\pi\)
−0.330150 + 0.943929i \(0.607099\pi\)
\(152\) −3.80019e14 −2.49932
\(153\) 4.38935e13 0.276634
\(154\) −4.51274e12 −0.0272619
\(155\) −7.73723e13 −0.448156
\(156\) 6.76901e13 0.376024
\(157\) 1.65060e14 0.879618 0.439809 0.898091i \(-0.355046\pi\)
0.439809 + 0.898091i \(0.355046\pi\)
\(158\) −4.11840e14 −2.10600
\(159\) 1.69039e14 0.829670
\(160\) 2.44666e14 1.15291
\(161\) 1.94847e13 0.0881708
\(162\) −4.27201e13 −0.185688
\(163\) 1.55380e14 0.648897 0.324448 0.945903i \(-0.394821\pi\)
0.324448 + 0.945903i \(0.394821\pi\)
\(164\) 8.06599e14 3.23723
\(165\) 4.00645e13 0.154566
\(166\) 7.95482e14 2.95072
\(167\) −3.80240e14 −1.35644 −0.678220 0.734859i \(-0.737248\pi\)
−0.678220 + 0.734859i \(0.737248\pi\)
\(168\) −2.52388e13 −0.0866080
\(169\) −2.62908e14 −0.868040
\(170\) −8.10951e14 −2.57677
\(171\) 2.05557e14 0.628720
\(172\) −2.73705e13 −0.0806023
\(173\) 1.73919e14 0.493228 0.246614 0.969114i \(-0.420682\pi\)
0.246614 + 0.969114i \(0.420682\pi\)
\(174\) −3.63759e14 −0.993674
\(175\) −1.05464e14 −0.277561
\(176\) −2.39532e13 −0.0607478
\(177\) 3.07496e13 0.0751646
\(178\) −4.48933e14 −1.05792
\(179\) 3.26210e14 0.741230 0.370615 0.928787i \(-0.379147\pi\)
0.370615 + 0.928787i \(0.379147\pi\)
\(180\) 5.06672e14 1.11034
\(181\) −3.06032e14 −0.646927 −0.323464 0.946241i \(-0.604847\pi\)
−0.323464 + 0.946241i \(0.604847\pi\)
\(182\) −3.36967e13 −0.0687264
\(183\) −1.93358e14 −0.380566
\(184\) 5.43261e14 1.03203
\(185\) −1.36403e15 −2.50154
\(186\) −1.31434e14 −0.232742
\(187\) −6.99280e13 −0.119586
\(188\) −1.83244e15 −3.02694
\(189\) 1.36520e13 0.0217868
\(190\) −3.79775e15 −5.85636
\(191\) 9.30763e14 1.38715 0.693573 0.720386i \(-0.256035\pi\)
0.693573 + 0.720386i \(0.256035\pi\)
\(192\) 5.84577e14 0.842139
\(193\) −2.42712e14 −0.338040 −0.169020 0.985613i \(-0.554060\pi\)
−0.169020 + 0.985613i \(0.554060\pi\)
\(194\) 1.59153e15 2.14341
\(195\) 2.99162e14 0.389656
\(196\) −1.40481e15 −1.76992
\(197\) 8.35797e14 1.01876 0.509378 0.860543i \(-0.329875\pi\)
0.509378 + 0.860543i \(0.329875\pi\)
\(198\) 6.80586e13 0.0802711
\(199\) 6.29358e14 0.718377 0.359189 0.933265i \(-0.383053\pi\)
0.359189 + 0.933265i \(0.383053\pi\)
\(200\) −2.94049e15 −3.24882
\(201\) 4.68481e14 0.501092
\(202\) 2.59723e15 2.68984
\(203\) 1.16246e14 0.116588
\(204\) −8.84337e14 −0.859056
\(205\) 3.56484e15 3.35459
\(206\) 3.40138e15 3.10111
\(207\) −2.93857e14 −0.259614
\(208\) −1.78859e14 −0.153143
\(209\) −3.27478e14 −0.271789
\(210\) −2.52226e14 −0.202938
\(211\) −1.03086e15 −0.804198 −0.402099 0.915596i \(-0.631719\pi\)
−0.402099 + 0.915596i \(0.631719\pi\)
\(212\) −3.40568e15 −2.57645
\(213\) 1.08837e15 0.798562
\(214\) −2.25301e15 −1.60352
\(215\) −1.20966e14 −0.0835246
\(216\) 3.80637e14 0.255012
\(217\) 4.20022e13 0.0273076
\(218\) 9.44842e14 0.596200
\(219\) −5.87438e14 −0.359812
\(220\) −8.07193e14 −0.479987
\(221\) −5.22153e14 −0.301473
\(222\) −2.31711e15 −1.29913
\(223\) −2.31105e15 −1.25843 −0.629214 0.777232i \(-0.716623\pi\)
−0.629214 + 0.777232i \(0.716623\pi\)
\(224\) −1.32819e14 −0.0702503
\(225\) 1.59055e15 0.817261
\(226\) −1.62912e15 −0.813293
\(227\) 3.55441e12 0.00172425 0.000862123 1.00000i \(-0.499726\pi\)
0.000862123 1.00000i \(0.499726\pi\)
\(228\) −4.14142e15 −1.95242
\(229\) −2.69927e15 −1.23685 −0.618423 0.785845i \(-0.712228\pi\)
−0.618423 + 0.785845i \(0.712228\pi\)
\(230\) 5.42912e15 2.41823
\(231\) −2.17493e13 −0.00941821
\(232\) 3.24110e15 1.36465
\(233\) 1.99363e15 0.816265 0.408133 0.912923i \(-0.366180\pi\)
0.408133 + 0.912923i \(0.366180\pi\)
\(234\) 5.08194e14 0.202361
\(235\) −8.09863e15 −3.13668
\(236\) −6.19522e14 −0.233415
\(237\) −1.98488e15 −0.727562
\(238\) 4.40231e14 0.157011
\(239\) −8.90069e14 −0.308914 −0.154457 0.988000i \(-0.549363\pi\)
−0.154457 + 0.988000i \(0.549363\pi\)
\(240\) −1.33879e15 −0.452208
\(241\) −2.45265e15 −0.806351 −0.403176 0.915123i \(-0.632094\pi\)
−0.403176 + 0.915123i \(0.632094\pi\)
\(242\) 5.11346e15 1.63650
\(243\) −2.05891e14 −0.0641500
\(244\) 3.89564e15 1.18180
\(245\) −6.20868e15 −1.83409
\(246\) 6.05568e15 1.74215
\(247\) −2.44529e15 −0.685172
\(248\) 1.17108e15 0.319632
\(249\) 3.83385e15 1.01939
\(250\) −1.74005e16 −4.50766
\(251\) −1.12049e15 −0.282832 −0.141416 0.989950i \(-0.545166\pi\)
−0.141416 + 0.989950i \(0.545166\pi\)
\(252\) −2.75051e14 −0.0676564
\(253\) 4.68151e14 0.112228
\(254\) −3.60923e15 −0.843326
\(255\) −3.90841e15 −0.890202
\(256\) −7.10721e15 −1.57812
\(257\) −2.10640e15 −0.456010 −0.228005 0.973660i \(-0.573220\pi\)
−0.228005 + 0.973660i \(0.573220\pi\)
\(258\) −2.05488e14 −0.0433770
\(259\) 7.40474e14 0.152427
\(260\) −6.02732e15 −1.21003
\(261\) −1.75315e15 −0.343286
\(262\) 7.72430e15 1.47537
\(263\) 7.69691e15 1.43418 0.717090 0.696980i \(-0.245474\pi\)
0.717090 + 0.696980i \(0.245474\pi\)
\(264\) −6.06403e14 −0.110239
\(265\) −1.50517e16 −2.66986
\(266\) 2.06164e15 0.356847
\(267\) −2.16365e15 −0.365480
\(268\) −9.43863e15 −1.55608
\(269\) 2.48086e15 0.399220 0.199610 0.979875i \(-0.436032\pi\)
0.199610 + 0.979875i \(0.436032\pi\)
\(270\) 3.80392e15 0.597540
\(271\) −5.84551e15 −0.896442 −0.448221 0.893923i \(-0.647942\pi\)
−0.448221 + 0.893923i \(0.647942\pi\)
\(272\) 2.33670e15 0.349868
\(273\) −1.62403e14 −0.0237430
\(274\) −1.52185e16 −2.17267
\(275\) −2.53395e15 −0.353293
\(276\) 5.92042e15 0.806201
\(277\) 1.80975e15 0.240714 0.120357 0.992731i \(-0.461596\pi\)
0.120357 + 0.992731i \(0.461596\pi\)
\(278\) 1.00431e16 1.30490
\(279\) −6.33452e14 −0.0804056
\(280\) 2.24733e15 0.278702
\(281\) 1.03992e15 0.126011 0.0630053 0.998013i \(-0.479931\pi\)
0.0630053 + 0.998013i \(0.479931\pi\)
\(282\) −1.37573e16 −1.62898
\(283\) −3.26525e15 −0.377837 −0.188918 0.981993i \(-0.560498\pi\)
−0.188918 + 0.981993i \(0.560498\pi\)
\(284\) −2.19277e16 −2.47984
\(285\) −1.83034e16 −2.02320
\(286\) −8.09619e14 −0.0874785
\(287\) −1.93520e15 −0.204406
\(288\) 2.00310e15 0.206848
\(289\) −3.08291e15 −0.311261
\(290\) 3.23902e16 3.19762
\(291\) 7.67045e15 0.740485
\(292\) 1.18353e16 1.11735
\(293\) 7.12460e15 0.657841 0.328920 0.944358i \(-0.393315\pi\)
0.328920 + 0.944358i \(0.393315\pi\)
\(294\) −1.05468e16 −0.952500
\(295\) −2.73803e15 −0.241878
\(296\) 2.06455e16 1.78414
\(297\) 3.28011e14 0.0277314
\(298\) −1.66722e16 −1.37907
\(299\) 3.49569e15 0.282924
\(300\) −3.20453e16 −2.53791
\(301\) 6.56675e13 0.00508942
\(302\) 1.45483e16 1.10349
\(303\) 1.25174e16 0.929262
\(304\) 1.09429e16 0.795163
\(305\) 1.72171e16 1.22465
\(306\) −6.63931e15 −0.462310
\(307\) 1.28740e16 0.877637 0.438819 0.898576i \(-0.355397\pi\)
0.438819 + 0.898576i \(0.355397\pi\)
\(308\) 4.38191e14 0.0292472
\(309\) 1.63931e16 1.07135
\(310\) 1.17033e16 0.748957
\(311\) 1.89374e16 1.18680 0.593400 0.804908i \(-0.297785\pi\)
0.593400 + 0.804908i \(0.297785\pi\)
\(312\) −4.52802e15 −0.277909
\(313\) 2.12357e16 1.27652 0.638261 0.769820i \(-0.279654\pi\)
0.638261 + 0.769820i \(0.279654\pi\)
\(314\) −2.49669e16 −1.47001
\(315\) −1.21561e15 −0.0701094
\(316\) 3.99900e16 2.25936
\(317\) −1.07565e16 −0.595371 −0.297685 0.954664i \(-0.596215\pi\)
−0.297685 + 0.954664i \(0.596215\pi\)
\(318\) −2.55687e16 −1.38654
\(319\) 2.79299e15 0.148399
\(320\) −5.20525e16 −2.70998
\(321\) −1.08585e16 −0.553970
\(322\) −2.94724e15 −0.147351
\(323\) 3.19464e16 1.56533
\(324\) 4.14815e15 0.199211
\(325\) −1.89210e16 −0.890641
\(326\) −2.35027e16 −1.08443
\(327\) 4.55370e15 0.205970
\(328\) −5.39562e16 −2.39255
\(329\) 4.39640e15 0.191128
\(330\) −6.06013e15 −0.258310
\(331\) 4.13197e16 1.72693 0.863466 0.504408i \(-0.168289\pi\)
0.863466 + 0.504408i \(0.168289\pi\)
\(332\) −7.72419e16 −3.16559
\(333\) −1.11674e16 −0.448812
\(334\) 5.75148e16 2.26688
\(335\) −4.17149e16 −1.61250
\(336\) 7.26771e14 0.0275545
\(337\) −1.33796e16 −0.497563 −0.248781 0.968560i \(-0.580030\pi\)
−0.248781 + 0.968560i \(0.580030\pi\)
\(338\) 3.97673e16 1.45067
\(339\) −7.85158e15 −0.280969
\(340\) 7.87439e16 2.76442
\(341\) 1.00917e15 0.0347585
\(342\) −3.10924e16 −1.05071
\(343\) 6.78462e15 0.224964
\(344\) 1.83090e15 0.0595711
\(345\) 2.61658e16 0.835431
\(346\) −2.63069e16 −0.824281
\(347\) −9.16237e15 −0.281751 −0.140876 0.990027i \(-0.544992\pi\)
−0.140876 + 0.990027i \(0.544992\pi\)
\(348\) 3.53213e16 1.06603
\(349\) 3.46463e16 1.02634 0.513170 0.858287i \(-0.328471\pi\)
0.513170 + 0.858287i \(0.328471\pi\)
\(350\) 1.59524e16 0.463858
\(351\) 2.44926e15 0.0699099
\(352\) −3.19119e15 −0.0894182
\(353\) −4.07177e16 −1.12008 −0.560038 0.828467i \(-0.689213\pi\)
−0.560038 + 0.828467i \(0.689213\pi\)
\(354\) −4.65117e15 −0.125615
\(355\) −9.69115e16 −2.56975
\(356\) 4.35917e16 1.13496
\(357\) 2.12171e15 0.0542428
\(358\) −4.93424e16 −1.23874
\(359\) 7.17437e16 1.76876 0.884382 0.466764i \(-0.154580\pi\)
0.884382 + 0.466764i \(0.154580\pi\)
\(360\) −3.38930e16 −0.820623
\(361\) 1.07555e17 2.55760
\(362\) 4.62901e16 1.08114
\(363\) 2.46445e16 0.565362
\(364\) 3.27198e15 0.0737312
\(365\) 5.23072e16 1.15786
\(366\) 2.92472e16 0.636000
\(367\) 2.14448e16 0.458134 0.229067 0.973411i \(-0.426432\pi\)
0.229067 + 0.973411i \(0.426432\pi\)
\(368\) −1.56436e16 −0.328342
\(369\) 2.91856e16 0.601862
\(370\) 2.06322e17 4.18056
\(371\) 8.17094e15 0.162683
\(372\) 1.27624e16 0.249690
\(373\) −7.93176e16 −1.52497 −0.762486 0.647004i \(-0.776022\pi\)
−0.762486 + 0.647004i \(0.776022\pi\)
\(374\) 1.05773e16 0.199852
\(375\) −8.38622e16 −1.55727
\(376\) 1.22578e17 2.23713
\(377\) 2.08553e16 0.374109
\(378\) −2.06499e15 −0.0364100
\(379\) 1.83872e15 0.0318685 0.0159342 0.999873i \(-0.494928\pi\)
0.0159342 + 0.999873i \(0.494928\pi\)
\(380\) 3.68764e17 6.28283
\(381\) −1.73948e16 −0.291345
\(382\) −1.40787e17 −2.31819
\(383\) −9.66850e16 −1.56519 −0.782595 0.622531i \(-0.786105\pi\)
−0.782595 + 0.622531i \(0.786105\pi\)
\(384\) −6.59133e16 −1.04911
\(385\) 1.93662e15 0.0303075
\(386\) 3.67125e16 0.564932
\(387\) −9.90359e14 −0.0149855
\(388\) −1.54539e17 −2.29949
\(389\) −4.31007e16 −0.630685 −0.315342 0.948978i \(-0.602119\pi\)
−0.315342 + 0.948978i \(0.602119\pi\)
\(390\) −4.52511e16 −0.651192
\(391\) −4.56694e16 −0.646363
\(392\) 9.39724e16 1.30810
\(393\) 3.72275e16 0.509698
\(394\) −1.26422e17 −1.70254
\(395\) 1.76739e17 2.34127
\(396\) −6.60854e15 −0.0861166
\(397\) 1.16157e17 1.48904 0.744521 0.667599i \(-0.232678\pi\)
0.744521 + 0.667599i \(0.232678\pi\)
\(398\) −9.51962e16 −1.20055
\(399\) 9.93613e15 0.123280
\(400\) 8.46739e16 1.03362
\(401\) 5.34610e16 0.642094 0.321047 0.947063i \(-0.395965\pi\)
0.321047 + 0.947063i \(0.395965\pi\)
\(402\) −7.08621e16 −0.837423
\(403\) 7.53549e15 0.0876251
\(404\) −2.52193e17 −2.88572
\(405\) 1.83331e16 0.206433
\(406\) −1.75833e16 −0.194841
\(407\) 1.77911e16 0.194017
\(408\) 5.91563e16 0.634906
\(409\) 5.79161e16 0.611783 0.305892 0.952066i \(-0.401045\pi\)
0.305892 + 0.952066i \(0.401045\pi\)
\(410\) −5.39215e17 −5.60618
\(411\) −7.33462e16 −0.750596
\(412\) −3.30276e17 −3.32694
\(413\) 1.48636e15 0.0147384
\(414\) 4.44486e16 0.433866
\(415\) −3.41377e17 −3.28037
\(416\) −2.38287e16 −0.225421
\(417\) 4.84031e16 0.450805
\(418\) 4.95342e16 0.454213
\(419\) −5.56422e16 −0.502358 −0.251179 0.967941i \(-0.580818\pi\)
−0.251179 + 0.967941i \(0.580818\pi\)
\(420\) 2.44913e16 0.217717
\(421\) −1.16772e17 −1.02213 −0.511066 0.859542i \(-0.670749\pi\)
−0.511066 + 0.859542i \(0.670749\pi\)
\(422\) 1.55927e17 1.34397
\(423\) −6.63040e16 −0.562765
\(424\) 2.27818e17 1.90419
\(425\) 2.47194e17 2.03474
\(426\) −1.64626e17 −1.33455
\(427\) −9.34646e15 −0.0746218
\(428\) 2.18769e17 1.72029
\(429\) −3.90199e15 −0.0302213
\(430\) 1.82973e16 0.139586
\(431\) −5.27394e16 −0.396308 −0.198154 0.980171i \(-0.563495\pi\)
−0.198154 + 0.980171i \(0.563495\pi\)
\(432\) −1.09607e16 −0.0811326
\(433\) −2.11584e17 −1.54281 −0.771403 0.636347i \(-0.780445\pi\)
−0.771403 + 0.636347i \(0.780445\pi\)
\(434\) −6.35322e15 −0.0456363
\(435\) 1.56106e17 1.10468
\(436\) −9.17449e16 −0.639616
\(437\) −2.13874e17 −1.46902
\(438\) 8.88555e16 0.601316
\(439\) −2.14705e17 −1.43160 −0.715802 0.698303i \(-0.753939\pi\)
−0.715802 + 0.698303i \(0.753939\pi\)
\(440\) 5.39958e16 0.354746
\(441\) −5.08309e16 −0.329061
\(442\) 7.89806e16 0.503820
\(443\) −1.23709e17 −0.777637 −0.388818 0.921314i \(-0.627117\pi\)
−0.388818 + 0.921314i \(0.627117\pi\)
\(444\) 2.24993e17 1.39373
\(445\) 1.92658e17 1.17611
\(446\) 3.49569e17 2.10308
\(447\) −8.03523e16 −0.476431
\(448\) 2.82571e16 0.165128
\(449\) 1.66258e16 0.0957592 0.0478796 0.998853i \(-0.484754\pi\)
0.0478796 + 0.998853i \(0.484754\pi\)
\(450\) −2.40586e17 −1.36580
\(451\) −4.64963e16 −0.260178
\(452\) 1.58188e17 0.872518
\(453\) 7.01162e16 0.381224
\(454\) −5.37637e14 −0.00288155
\(455\) 1.44608e16 0.0764044
\(456\) 2.77034e17 1.44298
\(457\) −3.35081e17 −1.72066 −0.860329 0.509739i \(-0.829742\pi\)
−0.860329 + 0.509739i \(0.829742\pi\)
\(458\) 4.08290e17 2.06701
\(459\) −3.19984e16 −0.159715
\(460\) −5.27171e17 −2.59433
\(461\) 1.88360e16 0.0913972 0.0456986 0.998955i \(-0.485449\pi\)
0.0456986 + 0.998955i \(0.485449\pi\)
\(462\) 3.28979e15 0.0157397
\(463\) −3.49491e17 −1.64877 −0.824383 0.566032i \(-0.808478\pi\)
−0.824383 + 0.566032i \(0.808478\pi\)
\(464\) −9.33300e16 −0.434165
\(465\) 5.64044e16 0.258743
\(466\) −3.01555e17 −1.36414
\(467\) −1.43399e17 −0.639714 −0.319857 0.947466i \(-0.603635\pi\)
−0.319857 + 0.947466i \(0.603635\pi\)
\(468\) −4.93461e16 −0.217097
\(469\) 2.26453e16 0.0982548
\(470\) 1.22499e18 5.24201
\(471\) −1.20329e17 −0.507848
\(472\) 4.14419e16 0.172511
\(473\) 1.57777e15 0.00647807
\(474\) 3.00232e17 1.21590
\(475\) 1.15763e18 4.62446
\(476\) −4.27467e16 −0.168445
\(477\) −1.23229e17 −0.479010
\(478\) 1.34631e17 0.516256
\(479\) −3.49364e17 −1.32159 −0.660795 0.750566i \(-0.729781\pi\)
−0.660795 + 0.750566i \(0.729781\pi\)
\(480\) −1.78362e17 −0.665632
\(481\) 1.32846e17 0.489110
\(482\) 3.70986e17 1.34757
\(483\) −1.42043e16 −0.0509055
\(484\) −4.96520e17 −1.75567
\(485\) −6.82999e17 −2.38286
\(486\) 3.11430e16 0.107207
\(487\) 2.67667e17 0.909193 0.454597 0.890697i \(-0.349783\pi\)
0.454597 + 0.890697i \(0.349783\pi\)
\(488\) −2.60593e17 −0.873440
\(489\) −1.13272e17 −0.374641
\(490\) 9.39121e17 3.06512
\(491\) 2.79936e17 0.901630 0.450815 0.892617i \(-0.351133\pi\)
0.450815 + 0.892617i \(0.351133\pi\)
\(492\) −5.88011e17 −1.86901
\(493\) −2.72464e17 −0.854682
\(494\) 3.69872e17 1.14506
\(495\) −2.92070e16 −0.0892388
\(496\) −3.37222e16 −0.101692
\(497\) 5.26092e16 0.156583
\(498\) −5.79906e17 −1.70360
\(499\) 1.78178e17 0.516655 0.258328 0.966057i \(-0.416829\pi\)
0.258328 + 0.966057i \(0.416829\pi\)
\(500\) 1.68960e18 4.83591
\(501\) 2.77195e17 0.783141
\(502\) 1.69485e17 0.472668
\(503\) −1.20853e17 −0.332711 −0.166355 0.986066i \(-0.553200\pi\)
−0.166355 + 0.986066i \(0.553200\pi\)
\(504\) 1.83991e16 0.0500031
\(505\) −1.11459e18 −2.99034
\(506\) −7.08122e16 −0.187556
\(507\) 1.91660e17 0.501163
\(508\) 3.50459e17 0.904739
\(509\) 4.48694e17 1.14363 0.571814 0.820383i \(-0.306240\pi\)
0.571814 + 0.820383i \(0.306240\pi\)
\(510\) 5.91183e17 1.48770
\(511\) −2.83954e16 −0.0705524
\(512\) 3.34343e17 0.820232
\(513\) −1.49851e17 −0.362992
\(514\) 3.18612e17 0.762083
\(515\) −1.45969e18 −3.44756
\(516\) 1.99531e16 0.0465358
\(517\) 1.05631e17 0.243277
\(518\) −1.12004e17 −0.254735
\(519\) −1.26787e17 −0.284766
\(520\) 4.03188e17 0.894305
\(521\) 2.63047e17 0.576219 0.288109 0.957597i \(-0.406973\pi\)
0.288109 + 0.957597i \(0.406973\pi\)
\(522\) 2.65180e17 0.573698
\(523\) −1.31320e17 −0.280588 −0.140294 0.990110i \(-0.544805\pi\)
−0.140294 + 0.990110i \(0.544805\pi\)
\(524\) −7.50035e17 −1.58281
\(525\) 7.68834e16 0.160250
\(526\) −1.16423e18 −2.39680
\(527\) −9.84474e16 −0.200187
\(528\) 1.74619e16 0.0350728
\(529\) −1.98290e17 −0.393405
\(530\) 2.27671e18 4.46185
\(531\) −2.24165e16 −0.0433963
\(532\) −2.00186e17 −0.382833
\(533\) −3.47189e17 −0.655902
\(534\) 3.27272e17 0.610789
\(535\) 9.66871e17 1.78266
\(536\) 6.31382e17 1.15006
\(537\) −2.37807e17 −0.427949
\(538\) −3.75253e17 −0.667175
\(539\) 8.09801e16 0.142250
\(540\) −3.69364e17 −0.641054
\(541\) 2.10937e17 0.361718 0.180859 0.983509i \(-0.442112\pi\)
0.180859 + 0.983509i \(0.442112\pi\)
\(542\) 8.84188e17 1.49813
\(543\) 2.23097e17 0.373504
\(544\) 3.11310e17 0.514992
\(545\) −4.05475e17 −0.662806
\(546\) 2.45649e16 0.0396792
\(547\) −6.27933e17 −1.00230 −0.501148 0.865362i \(-0.667089\pi\)
−0.501148 + 0.865362i \(0.667089\pi\)
\(548\) 1.47773e18 2.33089
\(549\) 1.40958e17 0.219720
\(550\) 3.83283e17 0.590422
\(551\) −1.27597e18 −1.94248
\(552\) −3.96037e17 −0.595843
\(553\) −9.59444e16 −0.142661
\(554\) −2.73742e17 −0.402280
\(555\) 9.94377e17 1.44426
\(556\) −9.75192e17 −1.39992
\(557\) 5.59177e17 0.793396 0.396698 0.917949i \(-0.370156\pi\)
0.396698 + 0.917949i \(0.370156\pi\)
\(558\) 9.58156e16 0.134374
\(559\) 1.17812e16 0.0163310
\(560\) −6.47138e16 −0.0886696
\(561\) 5.09775e16 0.0690431
\(562\) −1.57297e17 −0.210588
\(563\) 4.12831e17 0.546346 0.273173 0.961965i \(-0.411927\pi\)
0.273173 + 0.961965i \(0.411927\pi\)
\(564\) 1.33585e18 1.74760
\(565\) 6.99127e17 0.904152
\(566\) 4.93899e17 0.631439
\(567\) −9.95229e15 −0.0125786
\(568\) 1.46682e18 1.83279
\(569\) 4.35537e17 0.538016 0.269008 0.963138i \(-0.413304\pi\)
0.269008 + 0.963138i \(0.413304\pi\)
\(570\) 2.76856e18 3.38117
\(571\) 1.13189e17 0.136668 0.0683342 0.997662i \(-0.478232\pi\)
0.0683342 + 0.997662i \(0.478232\pi\)
\(572\) 7.86146e16 0.0938488
\(573\) −6.78526e17 −0.800870
\(574\) 2.92717e17 0.341602
\(575\) −1.65490e18 −1.90955
\(576\) −4.26157e17 −0.486209
\(577\) −3.48334e17 −0.392965 −0.196482 0.980507i \(-0.562952\pi\)
−0.196482 + 0.980507i \(0.562952\pi\)
\(578\) 4.66319e17 0.520178
\(579\) 1.76937e17 0.195168
\(580\) −3.14511e18 −3.43047
\(581\) 1.85319e17 0.199883
\(582\) −1.16023e18 −1.23750
\(583\) 1.96320e17 0.207071
\(584\) −7.91704e17 −0.825808
\(585\) −2.18089e17 −0.224968
\(586\) −1.07766e18 −1.09938
\(587\) 3.23634e17 0.326518 0.163259 0.986583i \(-0.447799\pi\)
0.163259 + 0.986583i \(0.447799\pi\)
\(588\) 1.02411e18 1.02186
\(589\) −4.61037e17 −0.454974
\(590\) 4.14153e17 0.404225
\(591\) −6.09296e17 −0.588179
\(592\) −5.94503e17 −0.567627
\(593\) −4.53247e17 −0.428035 −0.214017 0.976830i \(-0.568655\pi\)
−0.214017 + 0.976830i \(0.568655\pi\)
\(594\) −4.96147e16 −0.0463445
\(595\) −1.88923e17 −0.174552
\(596\) 1.61888e18 1.47950
\(597\) −4.58802e17 −0.414755
\(598\) −5.28756e17 −0.472822
\(599\) −8.02630e17 −0.709972 −0.354986 0.934872i \(-0.615514\pi\)
−0.354986 + 0.934872i \(0.615514\pi\)
\(600\) 2.14362e18 1.87570
\(601\) 1.19626e18 1.03548 0.517741 0.855537i \(-0.326773\pi\)
0.517741 + 0.855537i \(0.326773\pi\)
\(602\) −9.93282e15 −0.00850542
\(603\) −3.41523e17 −0.289306
\(604\) −1.41265e18 −1.18385
\(605\) −2.19442e18 −1.81932
\(606\) −1.89338e18 −1.55298
\(607\) −2.42333e18 −1.96646 −0.983232 0.182361i \(-0.941626\pi\)
−0.983232 + 0.182361i \(0.941626\pi\)
\(608\) 1.45789e18 1.17045
\(609\) −8.47431e16 −0.0673119
\(610\) −2.60425e18 −2.04663
\(611\) 7.88746e17 0.613295
\(612\) 6.44682e17 0.495976
\(613\) −2.15648e18 −1.64154 −0.820771 0.571257i \(-0.806456\pi\)
−0.820771 + 0.571257i \(0.806456\pi\)
\(614\) −1.94732e18 −1.46670
\(615\) −2.59877e18 −1.93678
\(616\) −2.93121e16 −0.0216158
\(617\) 1.89909e17 0.138577 0.0692887 0.997597i \(-0.477927\pi\)
0.0692887 + 0.997597i \(0.477927\pi\)
\(618\) −2.47960e18 −1.79043
\(619\) 1.00865e18 0.720697 0.360348 0.932818i \(-0.382658\pi\)
0.360348 + 0.932818i \(0.382658\pi\)
\(620\) −1.13640e18 −0.803497
\(621\) 2.14221e17 0.149888
\(622\) −2.86446e18 −1.98337
\(623\) −1.04586e17 −0.0716638
\(624\) 1.30388e17 0.0884174
\(625\) 3.81389e18 2.55946
\(626\) −3.21210e18 −2.13332
\(627\) 2.38732e17 0.156917
\(628\) 2.42430e18 1.57706
\(629\) −1.73557e18 −1.11741
\(630\) 1.83873e17 0.117166
\(631\) −8.15155e17 −0.514102 −0.257051 0.966398i \(-0.582751\pi\)
−0.257051 + 0.966398i \(0.582751\pi\)
\(632\) −2.67507e18 −1.66983
\(633\) 7.51496e17 0.464304
\(634\) 1.62703e18 0.994981
\(635\) 1.54889e18 0.937540
\(636\) 2.48274e18 1.48751
\(637\) 6.04679e17 0.358607
\(638\) −4.22466e17 −0.248003
\(639\) −7.93421e17 −0.461050
\(640\) 5.86911e18 3.37600
\(641\) −2.00287e18 −1.14045 −0.570225 0.821489i \(-0.693144\pi\)
−0.570225 + 0.821489i \(0.693144\pi\)
\(642\) 1.64245e18 0.925793
\(643\) −6.60505e17 −0.368557 −0.184279 0.982874i \(-0.558995\pi\)
−0.184279 + 0.982874i \(0.558995\pi\)
\(644\) 2.86179e17 0.158081
\(645\) 8.81844e16 0.0482229
\(646\) −4.83220e18 −2.61597
\(647\) 1.50934e18 0.808925 0.404462 0.914555i \(-0.367459\pi\)
0.404462 + 0.914555i \(0.367459\pi\)
\(648\) −2.77484e17 −0.147231
\(649\) 3.57123e16 0.0187598
\(650\) 2.86198e18 1.48844
\(651\) −3.06196e16 −0.0157660
\(652\) 2.28213e18 1.16340
\(653\) −3.08451e18 −1.55686 −0.778432 0.627729i \(-0.783984\pi\)
−0.778432 + 0.627729i \(0.783984\pi\)
\(654\) −6.88790e17 −0.344216
\(655\) −3.31485e18 −1.64019
\(656\) 1.55371e18 0.761194
\(657\) 4.28243e17 0.207737
\(658\) −6.64997e17 −0.319412
\(659\) −2.30137e18 −1.09454 −0.547268 0.836957i \(-0.684332\pi\)
−0.547268 + 0.836957i \(0.684332\pi\)
\(660\) 5.88444e17 0.277121
\(661\) 3.33324e18 1.55438 0.777191 0.629265i \(-0.216644\pi\)
0.777191 + 0.629265i \(0.216644\pi\)
\(662\) −6.24999e18 −2.88604
\(663\) 3.80650e17 0.174055
\(664\) 5.16697e18 2.33961
\(665\) −8.84742e17 −0.396713
\(666\) 1.68917e18 0.750052
\(667\) 1.82408e18 0.802096
\(668\) −5.58473e18 −2.43195
\(669\) 1.68476e18 0.726554
\(670\) 6.30977e18 2.69480
\(671\) −2.24564e17 −0.0949825
\(672\) 9.68251e16 0.0405590
\(673\) 1.34611e18 0.558448 0.279224 0.960226i \(-0.409923\pi\)
0.279224 + 0.960226i \(0.409923\pi\)
\(674\) 2.02379e18 0.831525
\(675\) −1.15951e18 −0.471846
\(676\) −3.86143e18 −1.55630
\(677\) −4.97872e18 −1.98743 −0.993715 0.111942i \(-0.964293\pi\)
−0.993715 + 0.111942i \(0.964293\pi\)
\(678\) 1.18762e18 0.469555
\(679\) 3.70771e17 0.145195
\(680\) −5.26745e18 −2.04311
\(681\) −2.59116e15 −0.000995494 0
\(682\) −1.52646e17 −0.0580882
\(683\) −3.99309e18 −1.50513 −0.752566 0.658517i \(-0.771184\pi\)
−0.752566 + 0.658517i \(0.771184\pi\)
\(684\) 3.01910e18 1.12723
\(685\) 6.53096e18 2.41540
\(686\) −1.02624e18 −0.375959
\(687\) 1.96777e18 0.714094
\(688\) −5.27224e16 −0.0189527
\(689\) 1.46593e18 0.522020
\(690\) −3.95783e18 −1.39617
\(691\) −2.83371e18 −0.990256 −0.495128 0.868820i \(-0.664879\pi\)
−0.495128 + 0.868820i \(0.664879\pi\)
\(692\) 2.55442e18 0.884307
\(693\) 1.58553e16 0.00543760
\(694\) 1.38589e18 0.470862
\(695\) −4.30995e18 −1.45068
\(696\) −2.36276e18 −0.787879
\(697\) 4.53585e18 1.49846
\(698\) −5.24057e18 −1.71521
\(699\) −1.45336e18 −0.471271
\(700\) −1.54899e18 −0.497637
\(701\) 2.78936e18 0.887845 0.443923 0.896065i \(-0.353586\pi\)
0.443923 + 0.896065i \(0.353586\pi\)
\(702\) −3.70474e17 −0.116833
\(703\) −8.12782e18 −2.53959
\(704\) 6.78922e17 0.210183
\(705\) 5.90390e18 1.81096
\(706\) 6.15893e18 1.87187
\(707\) 6.05063e17 0.182211
\(708\) 4.51632e17 0.134762
\(709\) 8.97213e16 0.0265274 0.0132637 0.999912i \(-0.495778\pi\)
0.0132637 + 0.999912i \(0.495778\pi\)
\(710\) 1.46588e19 4.29456
\(711\) 1.44698e18 0.420058
\(712\) −2.91600e18 −0.838817
\(713\) 6.59081e17 0.187870
\(714\) −3.20928e17 −0.0906504
\(715\) 3.47444e17 0.0972514
\(716\) 4.79118e18 1.32895
\(717\) 6.48860e17 0.178352
\(718\) −1.08519e19 −2.95595
\(719\) −2.39931e18 −0.647662 −0.323831 0.946115i \(-0.604971\pi\)
−0.323831 + 0.946115i \(0.604971\pi\)
\(720\) 9.75976e17 0.261083
\(721\) 7.92402e17 0.210071
\(722\) −1.62687e19 −4.27425
\(723\) 1.78798e18 0.465547
\(724\) −4.49481e18 −1.15987
\(725\) −9.87316e18 −2.52499
\(726\) −3.72771e18 −0.944831
\(727\) 9.93810e17 0.249649 0.124824 0.992179i \(-0.460163\pi\)
0.124824 + 0.992179i \(0.460163\pi\)
\(728\) −2.18874e17 −0.0544928
\(729\) 1.50095e17 0.0370370
\(730\) −7.91195e18 −1.93502
\(731\) −1.53916e17 −0.0373095
\(732\) −2.83992e18 −0.682314
\(733\) −3.93573e18 −0.937237 −0.468619 0.883401i \(-0.655248\pi\)
−0.468619 + 0.883401i \(0.655248\pi\)
\(734\) −3.24373e18 −0.765632
\(735\) 4.52613e18 1.05891
\(736\) −2.08415e18 −0.483306
\(737\) 5.44089e17 0.125064
\(738\) −4.41459e18 −1.00583
\(739\) −7.49608e18 −1.69295 −0.846477 0.532426i \(-0.821281\pi\)
−0.846477 + 0.532426i \(0.821281\pi\)
\(740\) −2.00340e19 −4.48500
\(741\) 1.78261e18 0.395584
\(742\) −1.23593e18 −0.271875
\(743\) −7.38140e17 −0.160958 −0.0804788 0.996756i \(-0.525645\pi\)
−0.0804788 + 0.996756i \(0.525645\pi\)
\(744\) −8.53717e17 −0.184540
\(745\) 7.15480e18 1.53314
\(746\) 1.19975e19 2.54853
\(747\) −2.79488e18 −0.588544
\(748\) −1.02706e18 −0.214405
\(749\) −5.24873e17 −0.108623
\(750\) 1.26849e19 2.60250
\(751\) 1.18812e18 0.241657 0.120829 0.992673i \(-0.461445\pi\)
0.120829 + 0.992673i \(0.461445\pi\)
\(752\) −3.52973e18 −0.711748
\(753\) 8.16838e17 0.163293
\(754\) −3.15456e18 −0.625209
\(755\) −6.24335e18 −1.22677
\(756\) 2.00512e17 0.0390615
\(757\) 1.06498e17 0.0205692 0.0102846 0.999947i \(-0.496726\pi\)
0.0102846 + 0.999947i \(0.496726\pi\)
\(758\) −2.78124e17 −0.0532585
\(759\) −3.41282e17 −0.0647951
\(760\) −2.46679e19 −4.64348
\(761\) 1.38713e18 0.258891 0.129445 0.991587i \(-0.458680\pi\)
0.129445 + 0.991587i \(0.458680\pi\)
\(762\) 2.63113e18 0.486895
\(763\) 2.20115e17 0.0403869
\(764\) 1.36705e19 2.48701
\(765\) 2.84923e18 0.513958
\(766\) 1.46245e19 2.61574
\(767\) 2.66664e17 0.0472928
\(768\) 5.18115e18 0.911126
\(769\) 7.71703e16 0.0134564 0.00672820 0.999977i \(-0.497858\pi\)
0.00672820 + 0.999977i \(0.497858\pi\)
\(770\) −2.92933e17 −0.0506498
\(771\) 1.53556e18 0.263278
\(772\) −3.56481e18 −0.606071
\(773\) 6.74644e18 1.13739 0.568693 0.822550i \(-0.307449\pi\)
0.568693 + 0.822550i \(0.307449\pi\)
\(774\) 1.49801e17 0.0250437
\(775\) −3.56739e18 −0.591411
\(776\) 1.03376e19 1.69950
\(777\) −5.39805e17 −0.0880036
\(778\) 6.51939e18 1.05400
\(779\) 2.12417e19 3.40562
\(780\) 4.39392e18 0.698613
\(781\) 1.26402e18 0.199307
\(782\) 6.90793e18 1.08020
\(783\) 1.27805e18 0.198196
\(784\) −2.70601e18 −0.416175
\(785\) 1.07144e19 1.63424
\(786\) −5.63101e18 −0.851805
\(787\) −6.61858e18 −0.992954 −0.496477 0.868050i \(-0.665373\pi\)
−0.496477 + 0.868050i \(0.665373\pi\)
\(788\) 1.22757e19 1.82652
\(789\) −5.61104e18 −0.828024
\(790\) −2.67335e19 −3.91273
\(791\) −3.79527e17 −0.0550928
\(792\) 4.42068e17 0.0636466
\(793\) −1.67682e18 −0.239448
\(794\) −1.75698e19 −2.48848
\(795\) 1.09727e19 1.54144
\(796\) 9.24363e18 1.28797
\(797\) 1.10316e19 1.52462 0.762308 0.647214i \(-0.224066\pi\)
0.762308 + 0.647214i \(0.224066\pi\)
\(798\) −1.50293e18 −0.206025
\(799\) −1.03046e19 −1.40112
\(800\) 1.12808e19 1.52144
\(801\) 1.57730e18 0.211010
\(802\) −8.08647e18 −1.07306
\(803\) −6.82245e17 −0.0898027
\(804\) 6.88076e18 0.898405
\(805\) 1.26479e18 0.163812
\(806\) −1.13981e18 −0.146439
\(807\) −1.80855e18 −0.230490
\(808\) 1.68700e19 2.13276
\(809\) 2.41246e18 0.302549 0.151274 0.988492i \(-0.451662\pi\)
0.151274 + 0.988492i \(0.451662\pi\)
\(810\) −2.77306e18 −0.344990
\(811\) −2.50278e18 −0.308878 −0.154439 0.988002i \(-0.549357\pi\)
−0.154439 + 0.988002i \(0.549357\pi\)
\(812\) 1.70735e18 0.209030
\(813\) 4.26138e18 0.517561
\(814\) −2.69107e18 −0.324240
\(815\) 1.00861e19 1.20558
\(816\) −1.70345e18 −0.201997
\(817\) −7.20800e17 −0.0847952
\(818\) −8.76035e18 −1.02241
\(819\) 1.18391e17 0.0137080
\(820\) 5.23582e19 6.01443
\(821\) −4.69298e17 −0.0534833 −0.0267416 0.999642i \(-0.508513\pi\)
−0.0267416 + 0.999642i \(0.508513\pi\)
\(822\) 1.10943e19 1.25439
\(823\) −5.97438e18 −0.670184 −0.335092 0.942185i \(-0.608767\pi\)
−0.335092 + 0.942185i \(0.608767\pi\)
\(824\) 2.20933e19 2.45886
\(825\) 1.84725e18 0.203974
\(826\) −2.24826e17 −0.0246307
\(827\) 6.24146e18 0.678423 0.339212 0.940710i \(-0.389840\pi\)
0.339212 + 0.940710i \(0.389840\pi\)
\(828\) −4.31599e18 −0.465461
\(829\) 1.19846e19 1.28239 0.641195 0.767378i \(-0.278439\pi\)
0.641195 + 0.767378i \(0.278439\pi\)
\(830\) 5.16365e19 5.48213
\(831\) −1.31931e18 −0.138976
\(832\) 5.06952e18 0.529865
\(833\) −7.89984e18 −0.819267
\(834\) −7.32142e18 −0.753383
\(835\) −2.46822e19 −2.52013
\(836\) −4.80981e18 −0.487289
\(837\) 4.61787e17 0.0464222
\(838\) 8.41641e18 0.839539
\(839\) −1.31942e19 −1.30596 −0.652979 0.757376i \(-0.726481\pi\)
−0.652979 + 0.757376i \(0.726481\pi\)
\(840\) −1.63831e18 −0.160909
\(841\) 6.21862e17 0.0606066
\(842\) 1.76629e19 1.70818
\(843\) −7.58099e17 −0.0727523
\(844\) −1.51406e19 −1.44184
\(845\) −1.70659e19 −1.61273
\(846\) 1.00291e19 0.940491
\(847\) 1.19126e18 0.110857
\(848\) −6.56019e18 −0.605820
\(849\) 2.38037e18 0.218144
\(850\) −3.73904e19 −3.40045
\(851\) 1.16192e19 1.04866
\(852\) 1.59853e19 1.43174
\(853\) 9.01253e18 0.801084 0.400542 0.916278i \(-0.368822\pi\)
0.400542 + 0.916278i \(0.368822\pi\)
\(854\) 1.41374e18 0.124708
\(855\) 1.33432e19 1.16810
\(856\) −1.46342e19 −1.27142
\(857\) 1.75382e19 1.51221 0.756103 0.654453i \(-0.227101\pi\)
0.756103 + 0.654453i \(0.227101\pi\)
\(858\) 5.90212e17 0.0505057
\(859\) −3.38176e18 −0.287202 −0.143601 0.989636i \(-0.545868\pi\)
−0.143601 + 0.989636i \(0.545868\pi\)
\(860\) −1.77668e18 −0.149751
\(861\) 1.41076e18 0.118014
\(862\) 7.97733e18 0.662309
\(863\) −1.64437e18 −0.135497 −0.0677486 0.997702i \(-0.521582\pi\)
−0.0677486 + 0.997702i \(0.521582\pi\)
\(864\) −1.46026e18 −0.119424
\(865\) 1.12895e19 0.916368
\(866\) 3.20040e19 2.57833
\(867\) 2.24744e18 0.179707
\(868\) 6.16902e17 0.0489596
\(869\) −2.30522e18 −0.181587
\(870\) −2.36124e19 −1.84614
\(871\) 4.06272e18 0.315282
\(872\) 6.13712e18 0.472724
\(873\) −5.59176e18 −0.427519
\(874\) 3.23504e19 2.45502
\(875\) −4.05370e18 −0.305351
\(876\) −8.62794e18 −0.645105
\(877\) 1.31534e18 0.0976203 0.0488102 0.998808i \(-0.484457\pi\)
0.0488102 + 0.998808i \(0.484457\pi\)
\(878\) 3.24762e19 2.39249
\(879\) −5.19383e18 −0.379805
\(880\) −1.55485e18 −0.112863
\(881\) 1.37999e19 0.994334 0.497167 0.867655i \(-0.334374\pi\)
0.497167 + 0.867655i \(0.334374\pi\)
\(882\) 7.68865e18 0.549926
\(883\) 1.45218e19 1.03104 0.515520 0.856877i \(-0.327599\pi\)
0.515520 + 0.856877i \(0.327599\pi\)
\(884\) −7.66907e18 −0.540509
\(885\) 1.99603e18 0.139648
\(886\) 1.87121e19 1.29958
\(887\) 3.56456e18 0.245755 0.122878 0.992422i \(-0.460788\pi\)
0.122878 + 0.992422i \(0.460788\pi\)
\(888\) −1.50505e19 −1.03007
\(889\) −8.40824e17 −0.0571273
\(890\) −2.91413e19 −1.96550
\(891\) −2.39120e17 −0.0160107
\(892\) −3.39434e19 −2.25623
\(893\) −4.82572e19 −3.18440
\(894\) 1.21540e19 0.796209
\(895\) 2.11750e19 1.37713
\(896\) −3.18609e18 −0.205711
\(897\) −2.54836e18 −0.163346
\(898\) −2.51480e18 −0.160032
\(899\) 3.93208e18 0.248419
\(900\) 2.33610e19 1.46526
\(901\) −1.91516e19 −1.19260
\(902\) 7.03301e18 0.434809
\(903\) −4.78716e16 −0.00293838
\(904\) −1.05817e19 −0.644856
\(905\) −1.98652e19 −1.20192
\(906\) −1.06057e19 −0.637100
\(907\) −1.61526e19 −0.963372 −0.481686 0.876344i \(-0.659975\pi\)
−0.481686 + 0.876344i \(0.659975\pi\)
\(908\) 5.22050e16 0.00309139
\(909\) −9.12521e18 −0.536509
\(910\) −2.18733e18 −0.127687
\(911\) −2.26254e19 −1.31138 −0.655688 0.755032i \(-0.727621\pi\)
−0.655688 + 0.755032i \(0.727621\pi\)
\(912\) −7.97741e18 −0.459087
\(913\) 4.45260e18 0.254421
\(914\) 5.06841e19 2.87556
\(915\) −1.25513e19 −0.707052
\(916\) −3.96453e19 −2.21754
\(917\) 1.79949e18 0.0999422
\(918\) 4.84005e18 0.266915
\(919\) 1.71301e19 0.938013 0.469007 0.883195i \(-0.344612\pi\)
0.469007 + 0.883195i \(0.344612\pi\)
\(920\) 3.52643e19 1.91741
\(921\) −9.38517e18 −0.506704
\(922\) −2.84912e18 −0.152743
\(923\) 9.43846e18 0.502447
\(924\) −3.19441e17 −0.0168859
\(925\) −6.28911e19 −3.30117
\(926\) 5.28637e19 2.75541
\(927\) −1.19505e19 −0.618542
\(928\) −1.24340e19 −0.639072
\(929\) −3.94107e17 −0.0201146 −0.0100573 0.999949i \(-0.503201\pi\)
−0.0100573 + 0.999949i \(0.503201\pi\)
\(930\) −8.53169e18 −0.432410
\(931\) −3.69956e19 −1.86199
\(932\) 2.92813e19 1.46348
\(933\) −1.38054e19 −0.685199
\(934\) 2.16904e19 1.06909
\(935\) −4.53918e18 −0.222179
\(936\) 3.30092e18 0.160451
\(937\) 3.20171e19 1.54552 0.772760 0.634698i \(-0.218876\pi\)
0.772760 + 0.634698i \(0.218876\pi\)
\(938\) −3.42531e18 −0.164203
\(939\) −1.54808e19 −0.737001
\(940\) −1.18948e20 −5.62374
\(941\) 3.00723e18 0.141200 0.0706000 0.997505i \(-0.477509\pi\)
0.0706000 + 0.997505i \(0.477509\pi\)
\(942\) 1.82008e19 0.848713
\(943\) −3.03664e19 −1.40627
\(944\) −1.19335e18 −0.0548847
\(945\) 8.86181e17 0.0404777
\(946\) −2.38652e17 −0.0108261
\(947\) 1.83503e18 0.0826738 0.0413369 0.999145i \(-0.486838\pi\)
0.0413369 + 0.999145i \(0.486838\pi\)
\(948\) −2.91527e19 −1.30444
\(949\) −5.09433e18 −0.226390
\(950\) −1.75102e20 −7.72837
\(951\) 7.84152e18 0.343737
\(952\) 2.85947e18 0.124493
\(953\) −2.15614e19 −0.932340 −0.466170 0.884695i \(-0.654366\pi\)
−0.466170 + 0.884695i \(0.654366\pi\)
\(954\) 1.86396e19 0.800520
\(955\) 6.04180e19 2.57718
\(956\) −1.30728e19 −0.553850
\(957\) −2.03609e18 −0.0856781
\(958\) 5.28445e19 2.20864
\(959\) −3.54538e18 −0.147178
\(960\) 3.79462e19 1.56461
\(961\) −2.29968e19 −0.941814
\(962\) −2.00942e19 −0.817398
\(963\) 7.91583e18 0.319835
\(964\) −3.60230e19 −1.44570
\(965\) −1.57550e19 −0.628044
\(966\) 2.14854e18 0.0850730
\(967\) −2.27525e19 −0.894865 −0.447432 0.894318i \(-0.647662\pi\)
−0.447432 + 0.894318i \(0.647662\pi\)
\(968\) 3.32139e19 1.29757
\(969\) −2.32890e19 −0.903744
\(970\) 1.03310e20 3.98223
\(971\) −8.61735e18 −0.329950 −0.164975 0.986298i \(-0.552754\pi\)
−0.164975 + 0.986298i \(0.552754\pi\)
\(972\) −3.02400e18 −0.115014
\(973\) 2.33969e18 0.0883944
\(974\) −4.04871e19 −1.51944
\(975\) 1.37934e19 0.514212
\(976\) 7.50398e18 0.277887
\(977\) 3.20669e19 1.17962 0.589810 0.807542i \(-0.299202\pi\)
0.589810 + 0.807542i \(0.299202\pi\)
\(978\) 1.71334e19 0.626098
\(979\) −2.51284e18 −0.0912174
\(980\) −9.11894e19 −3.28833
\(981\) −3.31965e18 −0.118917
\(982\) −4.23429e19 −1.50680
\(983\) 5.11263e18 0.180737 0.0903683 0.995908i \(-0.471196\pi\)
0.0903683 + 0.995908i \(0.471196\pi\)
\(984\) 3.93340e19 1.38134
\(985\) 5.42535e19 1.89274
\(986\) 4.12128e19 1.42834
\(987\) −3.20498e18 −0.110348
\(988\) −3.59149e19 −1.22844
\(989\) 1.03043e18 0.0350140
\(990\) 4.41784e18 0.149135
\(991\) 4.91293e19 1.64764 0.823819 0.566853i \(-0.191839\pi\)
0.823819 + 0.566853i \(0.191839\pi\)
\(992\) −4.49269e18 −0.149686
\(993\) −3.01220e19 −0.997044
\(994\) −7.95763e18 −0.261681
\(995\) 4.08530e19 1.33467
\(996\) 5.63093e19 1.82766
\(997\) 5.73498e19 1.84933 0.924663 0.380787i \(-0.124347\pi\)
0.924663 + 0.380787i \(0.124347\pi\)
\(998\) −2.69511e19 −0.863432
\(999\) 8.14103e18 0.259122
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.1.4 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.4 31 1.1 even 1 trivial