Properties

Label 177.14.a.a.1.10
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $30$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(1\)
Dimension: \(30\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-73.9227 q^{2} +729.000 q^{3} -2727.43 q^{4} -22721.6 q^{5} -53889.7 q^{6} +405591. q^{7} +807194. q^{8} +531441. q^{9} +O(q^{10})\) \(q-73.9227 q^{2} +729.000 q^{3} -2727.43 q^{4} -22721.6 q^{5} -53889.7 q^{6} +405591. q^{7} +807194. q^{8} +531441. q^{9} +1.67964e6 q^{10} -6.65185e6 q^{11} -1.98830e6 q^{12} +2.06527e7 q^{13} -2.99824e7 q^{14} -1.65640e7 q^{15} -3.73269e7 q^{16} +2.16354e7 q^{17} -3.92856e7 q^{18} +1.30507e8 q^{19} +6.19715e7 q^{20} +2.95676e8 q^{21} +4.91723e8 q^{22} -7.96941e8 q^{23} +5.88444e8 q^{24} -7.04433e8 q^{25} -1.52670e9 q^{26} +3.87420e8 q^{27} -1.10622e9 q^{28} -3.04026e9 q^{29} +1.22446e9 q^{30} -2.02696e9 q^{31} -3.85323e9 q^{32} -4.84920e9 q^{33} -1.59935e9 q^{34} -9.21566e9 q^{35} -1.44947e9 q^{36} +5.59860e9 q^{37} -9.64743e9 q^{38} +1.50558e10 q^{39} -1.83407e10 q^{40} +3.73394e9 q^{41} -2.18572e10 q^{42} +6.33576e10 q^{43} +1.81425e10 q^{44} -1.20752e10 q^{45} +5.89121e10 q^{46} -2.15292e10 q^{47} -2.72113e10 q^{48} +6.76148e10 q^{49} +5.20736e10 q^{50} +1.57722e10 q^{51} -5.63287e10 q^{52} -2.07104e11 q^{53} -2.86392e10 q^{54} +1.51141e11 q^{55} +3.27390e11 q^{56} +9.51395e10 q^{57} +2.24744e11 q^{58} +4.21805e10 q^{59} +4.51772e10 q^{60} -1.72658e11 q^{61} +1.49838e11 q^{62} +2.15548e11 q^{63} +5.90623e11 q^{64} -4.69261e11 q^{65} +3.58466e11 q^{66} +6.74693e11 q^{67} -5.90090e10 q^{68} -5.80970e11 q^{69} +6.81247e11 q^{70} +3.55112e10 q^{71} +4.28976e11 q^{72} +2.22111e11 q^{73} -4.13864e11 q^{74} -5.13532e11 q^{75} -3.55948e11 q^{76} -2.69793e12 q^{77} -1.11297e12 q^{78} -5.78321e11 q^{79} +8.48126e11 q^{80} +2.82430e11 q^{81} -2.76023e11 q^{82} -3.89792e12 q^{83} -8.06434e11 q^{84} -4.91590e11 q^{85} -4.68357e12 q^{86} -2.21635e12 q^{87} -5.36934e12 q^{88} +5.37443e12 q^{89} +8.92630e11 q^{90} +8.37654e12 q^{91} +2.17360e12 q^{92} -1.47765e12 q^{93} +1.59150e12 q^{94} -2.96532e12 q^{95} -2.80900e12 q^{96} -7.20961e12 q^{97} -4.99827e12 q^{98} -3.53507e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −73.9227 −0.816739 −0.408369 0.912817i \(-0.633902\pi\)
−0.408369 + 0.912817i \(0.633902\pi\)
\(3\) 729.000 0.577350
\(4\) −2727.43 −0.332938
\(5\) −22721.6 −0.650329 −0.325165 0.945657i \(-0.605420\pi\)
−0.325165 + 0.945657i \(0.605420\pi\)
\(6\) −53889.7 −0.471544
\(7\) 405591. 1.30302 0.651509 0.758640i \(-0.274136\pi\)
0.651509 + 0.758640i \(0.274136\pi\)
\(8\) 807194. 1.08866
\(9\) 531441. 0.333333
\(10\) 1.67964e6 0.531149
\(11\) −6.65185e6 −1.13211 −0.566057 0.824366i \(-0.691532\pi\)
−0.566057 + 0.824366i \(0.691532\pi\)
\(12\) −1.98830e6 −0.192222
\(13\) 2.06527e7 1.18671 0.593355 0.804941i \(-0.297803\pi\)
0.593355 + 0.804941i \(0.297803\pi\)
\(14\) −2.99824e7 −1.06423
\(15\) −1.65640e7 −0.375468
\(16\) −3.73269e7 −0.556214
\(17\) 2.16354e7 0.217394 0.108697 0.994075i \(-0.465332\pi\)
0.108697 + 0.994075i \(0.465332\pi\)
\(18\) −3.92856e7 −0.272246
\(19\) 1.30507e8 0.636407 0.318204 0.948022i \(-0.396920\pi\)
0.318204 + 0.948022i \(0.396920\pi\)
\(20\) 6.19715e7 0.216519
\(21\) 2.95676e8 0.752298
\(22\) 4.91723e8 0.924641
\(23\) −7.96941e8 −1.12252 −0.561262 0.827638i \(-0.689684\pi\)
−0.561262 + 0.827638i \(0.689684\pi\)
\(24\) 5.88444e8 0.628539
\(25\) −7.04433e8 −0.577072
\(26\) −1.52670e9 −0.969232
\(27\) 3.87420e8 0.192450
\(28\) −1.10622e9 −0.433825
\(29\) −3.04026e9 −0.949125 −0.474563 0.880222i \(-0.657394\pi\)
−0.474563 + 0.880222i \(0.657394\pi\)
\(30\) 1.22446e9 0.306659
\(31\) −2.02696e9 −0.410198 −0.205099 0.978741i \(-0.565752\pi\)
−0.205099 + 0.978741i \(0.565752\pi\)
\(32\) −3.85323e9 −0.634380
\(33\) −4.84920e9 −0.653626
\(34\) −1.59935e9 −0.177554
\(35\) −9.21566e9 −0.847392
\(36\) −1.44947e9 −0.110979
\(37\) 5.59860e9 0.358730 0.179365 0.983783i \(-0.442596\pi\)
0.179365 + 0.983783i \(0.442596\pi\)
\(38\) −9.64743e9 −0.519778
\(39\) 1.50558e10 0.685148
\(40\) −1.83407e10 −0.707989
\(41\) 3.73394e9 0.122764 0.0613822 0.998114i \(-0.480449\pi\)
0.0613822 + 0.998114i \(0.480449\pi\)
\(42\) −2.18572e10 −0.614431
\(43\) 6.33576e10 1.52846 0.764229 0.644945i \(-0.223120\pi\)
0.764229 + 0.644945i \(0.223120\pi\)
\(44\) 1.81425e10 0.376924
\(45\) −1.20752e10 −0.216776
\(46\) 5.89121e10 0.916808
\(47\) −2.15292e10 −0.291334 −0.145667 0.989334i \(-0.546533\pi\)
−0.145667 + 0.989334i \(0.546533\pi\)
\(48\) −2.72113e10 −0.321130
\(49\) 6.76148e10 0.697858
\(50\) 5.20736e10 0.471317
\(51\) 1.57722e10 0.125512
\(52\) −5.63287e10 −0.395101
\(53\) −2.07104e11 −1.28350 −0.641748 0.766916i \(-0.721790\pi\)
−0.641748 + 0.766916i \(0.721790\pi\)
\(54\) −2.86392e10 −0.157181
\(55\) 1.51141e11 0.736247
\(56\) 3.27390e11 1.41855
\(57\) 9.51395e10 0.367430
\(58\) 2.24744e11 0.775187
\(59\) 4.21805e10 0.130189
\(60\) 4.51772e10 0.125008
\(61\) −1.72658e11 −0.429084 −0.214542 0.976715i \(-0.568826\pi\)
−0.214542 + 0.976715i \(0.568826\pi\)
\(62\) 1.49838e11 0.335025
\(63\) 2.15548e11 0.434340
\(64\) 5.90623e11 1.07434
\(65\) −4.69261e11 −0.771753
\(66\) 3.58466e11 0.533842
\(67\) 6.74693e11 0.911214 0.455607 0.890181i \(-0.349422\pi\)
0.455607 + 0.890181i \(0.349422\pi\)
\(68\) −5.90090e10 −0.0723787
\(69\) −5.80970e11 −0.648089
\(70\) 6.81247e11 0.692097
\(71\) 3.55112e10 0.0328993 0.0164496 0.999865i \(-0.494764\pi\)
0.0164496 + 0.999865i \(0.494764\pi\)
\(72\) 4.28976e11 0.362887
\(73\) 2.22111e11 0.171779 0.0858896 0.996305i \(-0.472627\pi\)
0.0858896 + 0.996305i \(0.472627\pi\)
\(74\) −4.13864e11 −0.292989
\(75\) −5.13532e11 −0.333173
\(76\) −3.55948e11 −0.211884
\(77\) −2.69793e12 −1.47517
\(78\) −1.11297e12 −0.559586
\(79\) −5.78321e11 −0.267666 −0.133833 0.991004i \(-0.542729\pi\)
−0.133833 + 0.991004i \(0.542729\pi\)
\(80\) 8.48126e11 0.361722
\(81\) 2.82430e11 0.111111
\(82\) −2.76023e11 −0.100266
\(83\) −3.89792e12 −1.30865 −0.654327 0.756211i \(-0.727048\pi\)
−0.654327 + 0.756211i \(0.727048\pi\)
\(84\) −8.06434e11 −0.250469
\(85\) −4.91590e11 −0.141378
\(86\) −4.68357e12 −1.24835
\(87\) −2.21635e12 −0.547978
\(88\) −5.36934e12 −1.23249
\(89\) 5.37443e12 1.14630 0.573149 0.819451i \(-0.305722\pi\)
0.573149 + 0.819451i \(0.305722\pi\)
\(90\) 8.92630e11 0.177050
\(91\) 8.37654e12 1.54631
\(92\) 2.17360e12 0.373731
\(93\) −1.47765e12 −0.236828
\(94\) 1.59150e12 0.237944
\(95\) −2.96532e12 −0.413874
\(96\) −2.80900e12 −0.366260
\(97\) −7.20961e12 −0.878811 −0.439405 0.898289i \(-0.644811\pi\)
−0.439405 + 0.898289i \(0.644811\pi\)
\(98\) −4.99827e12 −0.569968
\(99\) −3.53507e12 −0.377371
\(100\) 1.92129e12 0.192129
\(101\) −1.99582e12 −0.187082 −0.0935412 0.995615i \(-0.529819\pi\)
−0.0935412 + 0.995615i \(0.529819\pi\)
\(102\) −1.16592e12 −0.102511
\(103\) 9.85943e12 0.813598 0.406799 0.913518i \(-0.366645\pi\)
0.406799 + 0.913518i \(0.366645\pi\)
\(104\) 1.66707e13 1.29193
\(105\) −6.71822e12 −0.489242
\(106\) 1.53097e13 1.04828
\(107\) 2.52989e13 1.62970 0.814848 0.579675i \(-0.196820\pi\)
0.814848 + 0.579675i \(0.196820\pi\)
\(108\) −1.05666e12 −0.0640740
\(109\) −1.25521e13 −0.716877 −0.358438 0.933553i \(-0.616691\pi\)
−0.358438 + 0.933553i \(0.616691\pi\)
\(110\) −1.11727e13 −0.601321
\(111\) 4.08138e12 0.207113
\(112\) −1.51394e13 −0.724757
\(113\) 2.02967e13 0.917097 0.458549 0.888669i \(-0.348369\pi\)
0.458549 + 0.888669i \(0.348369\pi\)
\(114\) −7.03298e12 −0.300094
\(115\) 1.81078e13 0.730010
\(116\) 8.29209e12 0.316000
\(117\) 1.09757e13 0.395570
\(118\) −3.11810e12 −0.106330
\(119\) 8.77512e12 0.283268
\(120\) −1.33704e13 −0.408758
\(121\) 9.72444e12 0.281682
\(122\) 1.27633e13 0.350449
\(123\) 2.72204e12 0.0708780
\(124\) 5.52839e12 0.136571
\(125\) 4.37421e13 1.02562
\(126\) −1.59339e13 −0.354742
\(127\) −7.48199e13 −1.58232 −0.791158 0.611612i \(-0.790521\pi\)
−0.791158 + 0.611612i \(0.790521\pi\)
\(128\) −1.20948e13 −0.243072
\(129\) 4.61877e13 0.882456
\(130\) 3.46891e13 0.630320
\(131\) −5.97698e13 −1.03328 −0.516641 0.856202i \(-0.672818\pi\)
−0.516641 + 0.856202i \(0.672818\pi\)
\(132\) 1.32259e13 0.217617
\(133\) 5.29324e13 0.829251
\(134\) −4.98752e13 −0.744223
\(135\) −8.80280e12 −0.125156
\(136\) 1.74640e13 0.236668
\(137\) 6.52191e13 0.842735 0.421367 0.906890i \(-0.361550\pi\)
0.421367 + 0.906890i \(0.361550\pi\)
\(138\) 4.29469e13 0.529319
\(139\) 7.83997e13 0.921973 0.460987 0.887407i \(-0.347496\pi\)
0.460987 + 0.887407i \(0.347496\pi\)
\(140\) 2.51351e13 0.282129
\(141\) −1.56948e13 −0.168202
\(142\) −2.62509e12 −0.0268701
\(143\) −1.37379e14 −1.34349
\(144\) −1.98370e13 −0.185405
\(145\) 6.90795e13 0.617244
\(146\) −1.64190e13 −0.140299
\(147\) 4.92912e13 0.402909
\(148\) −1.52698e13 −0.119435
\(149\) −5.43424e13 −0.406844 −0.203422 0.979091i \(-0.565206\pi\)
−0.203422 + 0.979091i \(0.565206\pi\)
\(150\) 3.79617e13 0.272115
\(151\) 2.63424e14 1.80844 0.904222 0.427064i \(-0.140452\pi\)
0.904222 + 0.427064i \(0.140452\pi\)
\(152\) 1.05344e14 0.692832
\(153\) 1.14979e13 0.0724646
\(154\) 1.99438e14 1.20483
\(155\) 4.60557e13 0.266764
\(156\) −4.10636e13 −0.228112
\(157\) −3.57640e14 −1.90589 −0.952947 0.303136i \(-0.901966\pi\)
−0.952947 + 0.303136i \(0.901966\pi\)
\(158\) 4.27511e13 0.218613
\(159\) −1.50978e14 −0.741027
\(160\) 8.75514e13 0.412556
\(161\) −3.23232e14 −1.46267
\(162\) −2.08780e13 −0.0907487
\(163\) −6.38714e12 −0.0266739 −0.0133370 0.999911i \(-0.504245\pi\)
−0.0133370 + 0.999911i \(0.504245\pi\)
\(164\) −1.01841e13 −0.0408729
\(165\) 1.10181e14 0.425072
\(166\) 2.88145e14 1.06883
\(167\) −9.22707e13 −0.329160 −0.164580 0.986364i \(-0.552627\pi\)
−0.164580 + 0.986364i \(0.552627\pi\)
\(168\) 2.38668e14 0.818999
\(169\) 1.23658e14 0.408281
\(170\) 3.63397e13 0.115468
\(171\) 6.93567e13 0.212136
\(172\) −1.72803e14 −0.508882
\(173\) −6.02265e14 −1.70800 −0.854000 0.520272i \(-0.825830\pi\)
−0.854000 + 0.520272i \(0.825830\pi\)
\(174\) 1.63839e14 0.447555
\(175\) −2.85712e14 −0.751935
\(176\) 2.48293e14 0.629698
\(177\) 3.07496e13 0.0751646
\(178\) −3.97293e14 −0.936226
\(179\) 1.25780e13 0.0285803 0.0142902 0.999898i \(-0.495451\pi\)
0.0142902 + 0.999898i \(0.495451\pi\)
\(180\) 3.29342e13 0.0721731
\(181\) −5.90066e13 −0.124735 −0.0623677 0.998053i \(-0.519865\pi\)
−0.0623677 + 0.998053i \(0.519865\pi\)
\(182\) −6.19217e14 −1.26293
\(183\) −1.25867e14 −0.247732
\(184\) −6.43286e14 −1.22205
\(185\) −1.27209e14 −0.233293
\(186\) 1.09232e14 0.193427
\(187\) −1.43916e14 −0.246114
\(188\) 5.87194e13 0.0969963
\(189\) 1.57134e14 0.250766
\(190\) 2.19205e14 0.338027
\(191\) 4.09226e14 0.609882 0.304941 0.952371i \(-0.401363\pi\)
0.304941 + 0.952371i \(0.401363\pi\)
\(192\) 4.30564e14 0.620269
\(193\) 6.63173e14 0.923644 0.461822 0.886973i \(-0.347196\pi\)
0.461822 + 0.886973i \(0.347196\pi\)
\(194\) 5.32954e14 0.717759
\(195\) −3.42092e14 −0.445572
\(196\) −1.84415e14 −0.232344
\(197\) 1.17801e15 1.43588 0.717942 0.696103i \(-0.245084\pi\)
0.717942 + 0.696103i \(0.245084\pi\)
\(198\) 2.61322e14 0.308214
\(199\) −9.99388e14 −1.14075 −0.570373 0.821386i \(-0.693201\pi\)
−0.570373 + 0.821386i \(0.693201\pi\)
\(200\) −5.68614e14 −0.628236
\(201\) 4.91851e14 0.526089
\(202\) 1.47537e14 0.152797
\(203\) −1.23310e15 −1.23673
\(204\) −4.30176e13 −0.0417878
\(205\) −8.48410e13 −0.0798373
\(206\) −7.28836e14 −0.664497
\(207\) −4.23527e14 −0.374175
\(208\) −7.70901e14 −0.660065
\(209\) −8.68113e14 −0.720486
\(210\) 4.96629e14 0.399583
\(211\) −6.25962e14 −0.488329 −0.244164 0.969734i \(-0.578514\pi\)
−0.244164 + 0.969734i \(0.578514\pi\)
\(212\) 5.64860e14 0.427325
\(213\) 2.58877e13 0.0189944
\(214\) −1.87016e15 −1.33104
\(215\) −1.43958e15 −0.994001
\(216\) 3.12724e14 0.209513
\(217\) −8.22116e14 −0.534496
\(218\) 9.27886e14 0.585501
\(219\) 1.61919e14 0.0991768
\(220\) −4.12225e14 −0.245125
\(221\) 4.46829e14 0.257983
\(222\) −3.01707e14 −0.169157
\(223\) −1.95755e15 −1.06594 −0.532968 0.846136i \(-0.678923\pi\)
−0.532968 + 0.846136i \(0.678923\pi\)
\(224\) −1.56283e15 −0.826610
\(225\) −3.74365e14 −0.192357
\(226\) −1.50039e15 −0.749029
\(227\) −6.83556e14 −0.331594 −0.165797 0.986160i \(-0.553020\pi\)
−0.165797 + 0.986160i \(0.553020\pi\)
\(228\) −2.59486e14 −0.122331
\(229\) −1.85010e15 −0.847744 −0.423872 0.905722i \(-0.639329\pi\)
−0.423872 + 0.905722i \(0.639329\pi\)
\(230\) −1.33858e15 −0.596227
\(231\) −1.96679e15 −0.851688
\(232\) −2.45408e15 −1.03328
\(233\) −1.56061e15 −0.638971 −0.319486 0.947591i \(-0.603510\pi\)
−0.319486 + 0.947591i \(0.603510\pi\)
\(234\) −8.11353e14 −0.323077
\(235\) 4.89177e14 0.189463
\(236\) −1.15044e14 −0.0433449
\(237\) −4.21596e14 −0.154537
\(238\) −6.48681e14 −0.231356
\(239\) −3.48409e15 −1.20921 −0.604606 0.796524i \(-0.706670\pi\)
−0.604606 + 0.796524i \(0.706670\pi\)
\(240\) 6.18284e14 0.208840
\(241\) −1.87385e15 −0.616061 −0.308031 0.951376i \(-0.599670\pi\)
−0.308031 + 0.951376i \(0.599670\pi\)
\(242\) −7.18857e14 −0.230061
\(243\) 2.05891e14 0.0641500
\(244\) 4.70912e14 0.142858
\(245\) −1.53631e15 −0.453838
\(246\) −2.01221e14 −0.0578888
\(247\) 2.69532e15 0.755231
\(248\) −1.63615e15 −0.446567
\(249\) −2.84158e15 −0.755552
\(250\) −3.23354e15 −0.837660
\(251\) 3.05131e15 0.770207 0.385104 0.922873i \(-0.374166\pi\)
0.385104 + 0.922873i \(0.374166\pi\)
\(252\) −5.87891e14 −0.144608
\(253\) 5.30114e15 1.27082
\(254\) 5.53090e15 1.29234
\(255\) −3.58369e14 −0.0816243
\(256\) −3.94430e15 −0.875811
\(257\) 2.01896e15 0.437082 0.218541 0.975828i \(-0.429870\pi\)
0.218541 + 0.975828i \(0.429870\pi\)
\(258\) −3.41432e15 −0.720736
\(259\) 2.27074e15 0.467432
\(260\) 1.27988e15 0.256946
\(261\) −1.61572e15 −0.316375
\(262\) 4.41835e15 0.843921
\(263\) −5.63699e15 −1.05035 −0.525176 0.850994i \(-0.676000\pi\)
−0.525176 + 0.850994i \(0.676000\pi\)
\(264\) −3.91425e15 −0.711578
\(265\) 4.70572e15 0.834695
\(266\) −3.91291e15 −0.677281
\(267\) 3.91796e15 0.661816
\(268\) −1.84018e15 −0.303378
\(269\) −3.56599e15 −0.573839 −0.286920 0.957955i \(-0.592631\pi\)
−0.286920 + 0.957955i \(0.592631\pi\)
\(270\) 6.50727e14 0.102220
\(271\) −7.85140e15 −1.20406 −0.602028 0.798475i \(-0.705640\pi\)
−0.602028 + 0.798475i \(0.705640\pi\)
\(272\) −8.07582e14 −0.120917
\(273\) 6.10650e15 0.892760
\(274\) −4.82117e15 −0.688294
\(275\) 4.68579e15 0.653311
\(276\) 1.58456e15 0.215774
\(277\) 8.54872e15 1.13706 0.568529 0.822663i \(-0.307513\pi\)
0.568529 + 0.822663i \(0.307513\pi\)
\(278\) −5.79552e15 −0.753011
\(279\) −1.07721e15 −0.136733
\(280\) −7.43883e15 −0.922523
\(281\) 1.27072e16 1.53978 0.769892 0.638174i \(-0.220310\pi\)
0.769892 + 0.638174i \(0.220310\pi\)
\(282\) 1.16020e15 0.137377
\(283\) −5.88727e15 −0.681244 −0.340622 0.940200i \(-0.610638\pi\)
−0.340622 + 0.940200i \(0.610638\pi\)
\(284\) −9.68543e13 −0.0109534
\(285\) −2.16172e15 −0.238950
\(286\) 1.01554e16 1.09728
\(287\) 1.51445e15 0.159964
\(288\) −2.04776e15 −0.211460
\(289\) −9.43649e15 −0.952740
\(290\) −5.10654e15 −0.504127
\(291\) −5.25580e15 −0.507382
\(292\) −6.05791e14 −0.0571918
\(293\) −1.39837e16 −1.29117 −0.645585 0.763688i \(-0.723386\pi\)
−0.645585 + 0.763688i \(0.723386\pi\)
\(294\) −3.64374e15 −0.329071
\(295\) −9.58408e14 −0.0846657
\(296\) 4.51916e15 0.390536
\(297\) −2.57706e15 −0.217875
\(298\) 4.01714e15 0.332285
\(299\) −1.64590e16 −1.33211
\(300\) 1.40062e15 0.110926
\(301\) 2.56972e16 1.99161
\(302\) −1.94730e16 −1.47703
\(303\) −1.45495e15 −0.108012
\(304\) −4.87142e15 −0.353979
\(305\) 3.92306e15 0.279046
\(306\) −8.49959e14 −0.0591846
\(307\) 1.64488e14 0.0112133 0.00560667 0.999984i \(-0.498215\pi\)
0.00560667 + 0.999984i \(0.498215\pi\)
\(308\) 7.35841e15 0.491139
\(309\) 7.18753e15 0.469731
\(310\) −3.40456e15 −0.217877
\(311\) −2.72673e16 −1.70884 −0.854418 0.519586i \(-0.826086\pi\)
−0.854418 + 0.519586i \(0.826086\pi\)
\(312\) 1.21530e16 0.745894
\(313\) −1.85330e16 −1.11406 −0.557028 0.830494i \(-0.688058\pi\)
−0.557028 + 0.830494i \(0.688058\pi\)
\(314\) 2.64378e16 1.55662
\(315\) −4.89758e15 −0.282464
\(316\) 1.57733e15 0.0891161
\(317\) −1.76561e16 −0.977260 −0.488630 0.872491i \(-0.662503\pi\)
−0.488630 + 0.872491i \(0.662503\pi\)
\(318\) 1.11607e16 0.605225
\(319\) 2.02234e16 1.07452
\(320\) −1.34199e16 −0.698673
\(321\) 1.84429e16 0.940905
\(322\) 2.38942e16 1.19462
\(323\) 2.82357e15 0.138351
\(324\) −7.70307e14 −0.0369931
\(325\) −1.45484e16 −0.684817
\(326\) 4.72155e14 0.0217856
\(327\) −9.15049e15 −0.413889
\(328\) 3.01402e15 0.133649
\(329\) −8.73204e15 −0.379614
\(330\) −8.14492e15 −0.347173
\(331\) 5.12050e15 0.214008 0.107004 0.994259i \(-0.465874\pi\)
0.107004 + 0.994259i \(0.465874\pi\)
\(332\) 1.06313e16 0.435701
\(333\) 2.97532e15 0.119577
\(334\) 6.82091e15 0.268838
\(335\) −1.53301e16 −0.592589
\(336\) −1.10367e16 −0.418439
\(337\) 8.62510e15 0.320752 0.160376 0.987056i \(-0.448729\pi\)
0.160376 + 0.987056i \(0.448729\pi\)
\(338\) −9.14116e15 −0.333459
\(339\) 1.47963e16 0.529486
\(340\) 1.34078e15 0.0470700
\(341\) 1.34830e16 0.464391
\(342\) −5.12704e15 −0.173259
\(343\) −1.18733e16 −0.393696
\(344\) 5.11419e16 1.66397
\(345\) 1.32006e16 0.421471
\(346\) 4.45211e16 1.39499
\(347\) −5.69006e16 −1.74975 −0.874874 0.484351i \(-0.839056\pi\)
−0.874874 + 0.484351i \(0.839056\pi\)
\(348\) 6.04493e15 0.182443
\(349\) −4.99645e16 −1.48012 −0.740058 0.672543i \(-0.765202\pi\)
−0.740058 + 0.672543i \(0.765202\pi\)
\(350\) 2.11206e16 0.614135
\(351\) 8.00127e15 0.228383
\(352\) 2.56311e16 0.718191
\(353\) −1.03749e16 −0.285395 −0.142698 0.989766i \(-0.545578\pi\)
−0.142698 + 0.989766i \(0.545578\pi\)
\(354\) −2.27310e15 −0.0613898
\(355\) −8.06871e14 −0.0213954
\(356\) −1.46584e16 −0.381646
\(357\) 6.39706e15 0.163545
\(358\) −9.29800e14 −0.0233426
\(359\) −6.87515e16 −1.69500 −0.847498 0.530799i \(-0.821892\pi\)
−0.847498 + 0.530799i \(0.821892\pi\)
\(360\) −9.74701e15 −0.235996
\(361\) −2.50209e16 −0.594986
\(362\) 4.36193e15 0.101876
\(363\) 7.08912e15 0.162629
\(364\) −2.28464e16 −0.514824
\(365\) −5.04670e15 −0.111713
\(366\) 9.30447e15 0.202332
\(367\) 1.71367e16 0.366099 0.183050 0.983104i \(-0.441403\pi\)
0.183050 + 0.983104i \(0.441403\pi\)
\(368\) 2.97473e16 0.624363
\(369\) 1.98437e15 0.0409215
\(370\) 9.40363e15 0.190539
\(371\) −8.39993e16 −1.67242
\(372\) 4.03020e15 0.0788491
\(373\) 5.47060e16 1.05179 0.525893 0.850550i \(-0.323731\pi\)
0.525893 + 0.850550i \(0.323731\pi\)
\(374\) 1.06386e16 0.201011
\(375\) 3.18880e16 0.592140
\(376\) −1.73782e16 −0.317165
\(377\) −6.27895e16 −1.12634
\(378\) −1.16158e16 −0.204810
\(379\) 2.25107e16 0.390152 0.195076 0.980788i \(-0.437505\pi\)
0.195076 + 0.980788i \(0.437505\pi\)
\(380\) 8.08771e15 0.137795
\(381\) −5.45437e16 −0.913551
\(382\) −3.02511e16 −0.498114
\(383\) 1.35313e16 0.219052 0.109526 0.993984i \(-0.465067\pi\)
0.109526 + 0.993984i \(0.465067\pi\)
\(384\) −8.81713e15 −0.140338
\(385\) 6.13012e16 0.959344
\(386\) −4.90236e16 −0.754376
\(387\) 3.36708e16 0.509486
\(388\) 1.96637e16 0.292590
\(389\) 3.04140e16 0.445043 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(390\) 2.52883e16 0.363915
\(391\) −1.72421e16 −0.244030
\(392\) 5.45783e16 0.759732
\(393\) −4.35722e16 −0.596565
\(394\) −8.70818e16 −1.17274
\(395\) 1.31404e16 0.174071
\(396\) 9.64165e15 0.125641
\(397\) 4.37303e16 0.560588 0.280294 0.959914i \(-0.409568\pi\)
0.280294 + 0.959914i \(0.409568\pi\)
\(398\) 7.38775e16 0.931691
\(399\) 3.85877e16 0.478768
\(400\) 2.62943e16 0.320975
\(401\) 2.43011e16 0.291869 0.145934 0.989294i \(-0.453381\pi\)
0.145934 + 0.989294i \(0.453381\pi\)
\(402\) −3.63590e16 −0.429677
\(403\) −4.18622e16 −0.486787
\(404\) 5.44346e15 0.0622868
\(405\) −6.41724e15 −0.0722588
\(406\) 9.11542e16 1.01008
\(407\) −3.72411e16 −0.406124
\(408\) 1.27312e16 0.136640
\(409\) 2.90956e16 0.307345 0.153673 0.988122i \(-0.450890\pi\)
0.153673 + 0.988122i \(0.450890\pi\)
\(410\) 6.27168e15 0.0652062
\(411\) 4.75447e16 0.486553
\(412\) −2.68909e16 −0.270878
\(413\) 1.71080e16 0.169639
\(414\) 3.13083e16 0.305603
\(415\) 8.85668e16 0.851057
\(416\) −7.95795e16 −0.752826
\(417\) 5.71534e16 0.532301
\(418\) 6.41733e16 0.588448
\(419\) 2.68455e16 0.242371 0.121185 0.992630i \(-0.461330\pi\)
0.121185 + 0.992630i \(0.461330\pi\)
\(420\) 1.83235e16 0.162887
\(421\) −1.46995e17 −1.28668 −0.643338 0.765582i \(-0.722451\pi\)
−0.643338 + 0.765582i \(0.722451\pi\)
\(422\) 4.62728e16 0.398837
\(423\) −1.14415e16 −0.0971115
\(424\) −1.67173e17 −1.39729
\(425\) −1.52407e16 −0.125452
\(426\) −1.91369e15 −0.0155135
\(427\) −7.00284e16 −0.559104
\(428\) −6.90009e16 −0.542588
\(429\) −1.00149e17 −0.775665
\(430\) 1.06418e17 0.811839
\(431\) −4.04267e16 −0.303785 −0.151892 0.988397i \(-0.548537\pi\)
−0.151892 + 0.988397i \(0.548537\pi\)
\(432\) −1.44612e16 −0.107043
\(433\) 1.95272e17 1.42386 0.711931 0.702250i \(-0.247821\pi\)
0.711931 + 0.702250i \(0.247821\pi\)
\(434\) 6.07731e16 0.436544
\(435\) 5.03589e16 0.356366
\(436\) 3.42350e16 0.238676
\(437\) −1.04006e17 −0.714382
\(438\) −1.19695e16 −0.0810015
\(439\) −1.80564e17 −1.20396 −0.601981 0.798510i \(-0.705622\pi\)
−0.601981 + 0.798510i \(0.705622\pi\)
\(440\) 1.22000e17 0.801524
\(441\) 3.59333e16 0.232619
\(442\) −3.30308e16 −0.210705
\(443\) 2.79182e16 0.175494 0.0877472 0.996143i \(-0.472033\pi\)
0.0877472 + 0.996143i \(0.472033\pi\)
\(444\) −1.11317e16 −0.0689558
\(445\) −1.22116e17 −0.745471
\(446\) 1.44707e17 0.870591
\(447\) −3.96156e16 −0.234892
\(448\) 2.39551e17 1.39988
\(449\) −1.61837e17 −0.932131 −0.466066 0.884750i \(-0.654329\pi\)
−0.466066 + 0.884750i \(0.654329\pi\)
\(450\) 2.76741e16 0.157106
\(451\) −2.48376e16 −0.138983
\(452\) −5.53578e16 −0.305337
\(453\) 1.92036e17 1.04411
\(454\) 5.05303e16 0.270825
\(455\) −1.90328e17 −1.00561
\(456\) 7.67961e16 0.400007
\(457\) 2.19082e17 1.12500 0.562500 0.826797i \(-0.309840\pi\)
0.562500 + 0.826797i \(0.309840\pi\)
\(458\) 1.36765e17 0.692385
\(459\) 8.38200e15 0.0418374
\(460\) −4.93876e16 −0.243048
\(461\) −2.60837e16 −0.126565 −0.0632823 0.997996i \(-0.520157\pi\)
−0.0632823 + 0.997996i \(0.520157\pi\)
\(462\) 1.45391e17 0.695606
\(463\) 3.11269e17 1.46845 0.734225 0.678906i \(-0.237546\pi\)
0.734225 + 0.678906i \(0.237546\pi\)
\(464\) 1.13483e17 0.527917
\(465\) 3.35746e16 0.154016
\(466\) 1.15365e17 0.521872
\(467\) −6.18115e16 −0.275746 −0.137873 0.990450i \(-0.544027\pi\)
−0.137873 + 0.990450i \(0.544027\pi\)
\(468\) −2.99354e16 −0.131700
\(469\) 2.73649e17 1.18733
\(470\) −3.61613e16 −0.154742
\(471\) −2.60720e17 −1.10037
\(472\) 3.40479e16 0.141732
\(473\) −4.21445e17 −1.73039
\(474\) 3.11655e16 0.126216
\(475\) −9.19334e16 −0.367253
\(476\) −2.39335e16 −0.0943108
\(477\) −1.10063e17 −0.427832
\(478\) 2.57553e17 0.987610
\(479\) 8.98587e16 0.339922 0.169961 0.985451i \(-0.445636\pi\)
0.169961 + 0.985451i \(0.445636\pi\)
\(480\) 6.38250e16 0.238189
\(481\) 1.15626e17 0.425709
\(482\) 1.38520e17 0.503161
\(483\) −2.35636e17 −0.844473
\(484\) −2.65227e16 −0.0937828
\(485\) 1.63814e17 0.571516
\(486\) −1.52200e16 −0.0523938
\(487\) 4.61636e17 1.56806 0.784028 0.620725i \(-0.213162\pi\)
0.784028 + 0.620725i \(0.213162\pi\)
\(488\) −1.39368e17 −0.467127
\(489\) −4.65623e15 −0.0154002
\(490\) 1.13569e17 0.370667
\(491\) −2.59579e17 −0.836066 −0.418033 0.908432i \(-0.637280\pi\)
−0.418033 + 0.908432i \(0.637280\pi\)
\(492\) −7.42418e15 −0.0235980
\(493\) −6.57772e16 −0.206334
\(494\) −1.99245e17 −0.616826
\(495\) 8.03223e16 0.245416
\(496\) 7.56601e16 0.228158
\(497\) 1.44030e16 0.0428684
\(498\) 2.10058e17 0.617089
\(499\) 4.39408e17 1.27413 0.637066 0.770809i \(-0.280148\pi\)
0.637066 + 0.770809i \(0.280148\pi\)
\(500\) −1.19304e17 −0.341467
\(501\) −6.72654e16 −0.190041
\(502\) −2.25561e17 −0.629058
\(503\) 6.89573e17 1.89840 0.949202 0.314668i \(-0.101893\pi\)
0.949202 + 0.314668i \(0.101893\pi\)
\(504\) 1.73989e17 0.472849
\(505\) 4.53482e16 0.121665
\(506\) −3.91875e17 −1.03793
\(507\) 9.01469e16 0.235721
\(508\) 2.04066e17 0.526813
\(509\) 1.60134e17 0.408147 0.204074 0.978956i \(-0.434582\pi\)
0.204074 + 0.978956i \(0.434582\pi\)
\(510\) 2.64916e16 0.0666658
\(511\) 9.00860e16 0.223832
\(512\) 3.90654e17 0.958380
\(513\) 5.05611e16 0.122477
\(514\) −1.49247e17 −0.356982
\(515\) −2.24022e17 −0.529107
\(516\) −1.25974e17 −0.293803
\(517\) 1.43209e17 0.329824
\(518\) −1.67859e17 −0.381770
\(519\) −4.39051e17 −0.986115
\(520\) −3.78785e17 −0.840178
\(521\) −1.08470e17 −0.237611 −0.118805 0.992918i \(-0.537906\pi\)
−0.118805 + 0.992918i \(0.537906\pi\)
\(522\) 1.19438e17 0.258396
\(523\) 6.19612e17 1.32391 0.661955 0.749543i \(-0.269727\pi\)
0.661955 + 0.749543i \(0.269727\pi\)
\(524\) 1.63018e17 0.344019
\(525\) −2.08284e17 −0.434130
\(526\) 4.16702e17 0.857863
\(527\) −4.38541e16 −0.0891746
\(528\) 1.81006e17 0.363556
\(529\) 1.31079e17 0.260059
\(530\) −3.47860e17 −0.681727
\(531\) 2.24165e16 0.0433963
\(532\) −1.44369e17 −0.276089
\(533\) 7.71159e16 0.145686
\(534\) −2.89626e17 −0.540530
\(535\) −5.74830e17 −1.05984
\(536\) 5.44608e17 0.992004
\(537\) 9.16936e15 0.0165009
\(538\) 2.63608e17 0.468677
\(539\) −4.49764e17 −0.790055
\(540\) 2.40090e16 0.0416692
\(541\) −8.20789e17 −1.40750 −0.703752 0.710446i \(-0.748493\pi\)
−0.703752 + 0.710446i \(0.748493\pi\)
\(542\) 5.80397e17 0.983399
\(543\) −4.30158e16 −0.0720160
\(544\) −8.33661e16 −0.137910
\(545\) 2.85204e17 0.466206
\(546\) −4.51409e17 −0.729152
\(547\) −2.43277e16 −0.0388314 −0.0194157 0.999811i \(-0.506181\pi\)
−0.0194157 + 0.999811i \(0.506181\pi\)
\(548\) −1.77880e17 −0.280579
\(549\) −9.17574e16 −0.143028
\(550\) −3.46386e17 −0.533584
\(551\) −3.96775e17 −0.604030
\(552\) −4.68956e17 −0.705550
\(553\) −2.34562e17 −0.348773
\(554\) −6.31945e17 −0.928679
\(555\) −9.27353e16 −0.134692
\(556\) −2.13830e17 −0.306960
\(557\) 4.44633e17 0.630875 0.315437 0.948946i \(-0.397849\pi\)
0.315437 + 0.948946i \(0.397849\pi\)
\(558\) 7.96303e16 0.111675
\(559\) 1.30850e18 1.81384
\(560\) 3.43992e17 0.471331
\(561\) −1.04914e17 −0.142094
\(562\) −9.39353e17 −1.25760
\(563\) 1.40313e18 1.85693 0.928463 0.371424i \(-0.121130\pi\)
0.928463 + 0.371424i \(0.121130\pi\)
\(564\) 4.28064e16 0.0560009
\(565\) −4.61173e17 −0.596415
\(566\) 4.35203e17 0.556398
\(567\) 1.14551e17 0.144780
\(568\) 2.86644e16 0.0358162
\(569\) 3.41246e16 0.0421539 0.0210770 0.999778i \(-0.493290\pi\)
0.0210770 + 0.999778i \(0.493290\pi\)
\(570\) 1.59800e17 0.195160
\(571\) −7.95222e17 −0.960182 −0.480091 0.877219i \(-0.659396\pi\)
−0.480091 + 0.877219i \(0.659396\pi\)
\(572\) 3.74690e17 0.447300
\(573\) 2.98326e17 0.352116
\(574\) −1.11952e17 −0.130649
\(575\) 5.61392e17 0.647777
\(576\) 3.13881e17 0.358112
\(577\) −5.90770e17 −0.666462 −0.333231 0.942845i \(-0.608139\pi\)
−0.333231 + 0.942845i \(0.608139\pi\)
\(578\) 6.97571e17 0.778139
\(579\) 4.83453e17 0.533266
\(580\) −1.88409e17 −0.205504
\(581\) −1.58096e18 −1.70520
\(582\) 3.88523e17 0.414398
\(583\) 1.37762e18 1.45306
\(584\) 1.79286e17 0.187009
\(585\) −2.49385e17 −0.257251
\(586\) 1.03372e18 1.05455
\(587\) 9.85934e17 0.994718 0.497359 0.867545i \(-0.334303\pi\)
0.497359 + 0.867545i \(0.334303\pi\)
\(588\) −1.34438e17 −0.134144
\(589\) −2.64532e17 −0.261053
\(590\) 7.08481e16 0.0691497
\(591\) 8.58770e17 0.829008
\(592\) −2.08978e17 −0.199531
\(593\) 6.26668e17 0.591809 0.295905 0.955218i \(-0.404379\pi\)
0.295905 + 0.955218i \(0.404379\pi\)
\(594\) 1.90504e17 0.177947
\(595\) −1.99384e17 −0.184218
\(596\) 1.48215e17 0.135454
\(597\) −7.28554e17 −0.658610
\(598\) 1.21669e18 1.08799
\(599\) −1.83224e18 −1.62072 −0.810359 0.585934i \(-0.800728\pi\)
−0.810359 + 0.585934i \(0.800728\pi\)
\(600\) −4.14520e17 −0.362712
\(601\) −7.92129e17 −0.685665 −0.342832 0.939397i \(-0.611386\pi\)
−0.342832 + 0.939397i \(0.611386\pi\)
\(602\) −1.89961e18 −1.62663
\(603\) 3.58560e17 0.303738
\(604\) −7.18470e17 −0.602100
\(605\) −2.20955e17 −0.183186
\(606\) 1.07554e17 0.0882176
\(607\) 1.53324e18 1.24418 0.622092 0.782944i \(-0.286283\pi\)
0.622092 + 0.782944i \(0.286283\pi\)
\(608\) −5.02873e17 −0.403724
\(609\) −8.98930e17 −0.714025
\(610\) −2.90003e17 −0.227907
\(611\) −4.44636e17 −0.345730
\(612\) −3.13598e16 −0.0241262
\(613\) −3.11862e17 −0.237394 −0.118697 0.992931i \(-0.537872\pi\)
−0.118697 + 0.992931i \(0.537872\pi\)
\(614\) −1.21594e16 −0.00915836
\(615\) −6.18491e16 −0.0460941
\(616\) −2.17775e18 −1.60596
\(617\) −9.04006e17 −0.659656 −0.329828 0.944041i \(-0.606991\pi\)
−0.329828 + 0.944041i \(0.606991\pi\)
\(618\) −5.31322e17 −0.383648
\(619\) −1.66469e18 −1.18945 −0.594724 0.803930i \(-0.702739\pi\)
−0.594724 + 0.803930i \(0.702739\pi\)
\(620\) −1.25614e17 −0.0888159
\(621\) −3.08751e17 −0.216030
\(622\) 2.01568e18 1.39567
\(623\) 2.17982e18 1.49365
\(624\) −5.61987e17 −0.381089
\(625\) −1.33986e17 −0.0899165
\(626\) 1.37001e18 0.909892
\(627\) −6.32854e17 −0.415973
\(628\) 9.75439e17 0.634545
\(629\) 1.21128e17 0.0779857
\(630\) 3.62042e17 0.230699
\(631\) 2.29635e18 1.44826 0.724132 0.689661i \(-0.242241\pi\)
0.724132 + 0.689661i \(0.242241\pi\)
\(632\) −4.66817e17 −0.291397
\(633\) −4.56326e17 −0.281937
\(634\) 1.30519e18 0.798166
\(635\) 1.70003e18 1.02903
\(636\) 4.11783e17 0.246716
\(637\) 1.39643e18 0.828156
\(638\) −1.49497e18 −0.877600
\(639\) 1.88721e16 0.0109664
\(640\) 2.74814e17 0.158077
\(641\) −2.04247e18 −1.16300 −0.581498 0.813548i \(-0.697533\pi\)
−0.581498 + 0.813548i \(0.697533\pi\)
\(642\) −1.36335e18 −0.768474
\(643\) 1.39038e18 0.775825 0.387912 0.921696i \(-0.373196\pi\)
0.387912 + 0.921696i \(0.373196\pi\)
\(644\) 8.81592e17 0.486978
\(645\) −1.04946e18 −0.573887
\(646\) −2.08726e17 −0.112997
\(647\) −2.12148e18 −1.13700 −0.568501 0.822683i \(-0.692476\pi\)
−0.568501 + 0.822683i \(0.692476\pi\)
\(648\) 2.27975e17 0.120962
\(649\) −2.80579e17 −0.147389
\(650\) 1.07546e18 0.559316
\(651\) −5.99322e17 −0.308592
\(652\) 1.74205e16 0.00888077
\(653\) −3.44621e18 −1.73943 −0.869713 0.493558i \(-0.835696\pi\)
−0.869713 + 0.493558i \(0.835696\pi\)
\(654\) 6.76429e17 0.338039
\(655\) 1.35806e18 0.671973
\(656\) −1.39376e17 −0.0682833
\(657\) 1.18039e17 0.0572597
\(658\) 6.45497e17 0.310046
\(659\) −3.67266e18 −1.74673 −0.873364 0.487067i \(-0.838067\pi\)
−0.873364 + 0.487067i \(0.838067\pi\)
\(660\) −3.00512e17 −0.141523
\(661\) −3.05397e18 −1.42415 −0.712075 0.702103i \(-0.752245\pi\)
−0.712075 + 0.702103i \(0.752245\pi\)
\(662\) −3.78521e17 −0.174789
\(663\) 3.25738e17 0.148947
\(664\) −3.14638e18 −1.42468
\(665\) −1.20271e18 −0.539286
\(666\) −2.19944e17 −0.0976630
\(667\) 2.42291e18 1.06542
\(668\) 2.51662e17 0.109590
\(669\) −1.42705e18 −0.615418
\(670\) 1.13324e18 0.483990
\(671\) 1.14849e18 0.485772
\(672\) −1.13931e18 −0.477243
\(673\) −2.24216e18 −0.930182 −0.465091 0.885263i \(-0.653978\pi\)
−0.465091 + 0.885263i \(0.653978\pi\)
\(674\) −6.37591e17 −0.261971
\(675\) −2.72912e17 −0.111058
\(676\) −3.37269e17 −0.135932
\(677\) −3.35268e18 −1.33834 −0.669169 0.743110i \(-0.733350\pi\)
−0.669169 + 0.743110i \(0.733350\pi\)
\(678\) −1.09378e18 −0.432452
\(679\) −2.92415e18 −1.14511
\(680\) −3.96809e17 −0.153912
\(681\) −4.98312e17 −0.191446
\(682\) −9.96703e17 −0.379286
\(683\) −5.18072e17 −0.195279 −0.0976395 0.995222i \(-0.531129\pi\)
−0.0976395 + 0.995222i \(0.531129\pi\)
\(684\) −1.89166e17 −0.0706281
\(685\) −1.48188e18 −0.548055
\(686\) 8.77710e17 0.321547
\(687\) −1.34872e18 −0.489445
\(688\) −2.36494e18 −0.850150
\(689\) −4.27724e18 −1.52314
\(690\) −9.75821e17 −0.344232
\(691\) −3.30114e18 −1.15360 −0.576801 0.816884i \(-0.695699\pi\)
−0.576801 + 0.816884i \(0.695699\pi\)
\(692\) 1.64264e18 0.568659
\(693\) −1.43379e18 −0.491722
\(694\) 4.20625e18 1.42909
\(695\) −1.78136e18 −0.599586
\(696\) −1.78902e18 −0.596563
\(697\) 8.07853e16 0.0266882
\(698\) 3.69351e18 1.20887
\(699\) −1.13769e18 −0.368910
\(700\) 7.79258e17 0.250348
\(701\) −1.46369e17 −0.0465889 −0.0232944 0.999729i \(-0.507416\pi\)
−0.0232944 + 0.999729i \(0.507416\pi\)
\(702\) −5.91476e17 −0.186529
\(703\) 7.30656e17 0.228299
\(704\) −3.92874e18 −1.21627
\(705\) 3.56610e17 0.109387
\(706\) 7.66939e17 0.233093
\(707\) −8.09487e17 −0.243772
\(708\) −8.38674e16 −0.0250252
\(709\) −1.86794e18 −0.552284 −0.276142 0.961117i \(-0.589056\pi\)
−0.276142 + 0.961117i \(0.589056\pi\)
\(710\) 5.96461e16 0.0174744
\(711\) −3.07343e17 −0.0892219
\(712\) 4.33821e18 1.24793
\(713\) 1.61537e18 0.460457
\(714\) −4.72888e17 −0.133573
\(715\) 3.12146e18 0.873712
\(716\) −3.43056e16 −0.00951548
\(717\) −2.53990e18 −0.698139
\(718\) 5.08230e18 1.38437
\(719\) −4.52864e18 −1.22245 −0.611224 0.791458i \(-0.709323\pi\)
−0.611224 + 0.791458i \(0.709323\pi\)
\(720\) 4.50729e17 0.120574
\(721\) 3.99889e18 1.06013
\(722\) 1.84962e18 0.485948
\(723\) −1.36604e18 −0.355683
\(724\) 1.60936e17 0.0415292
\(725\) 2.14166e18 0.547713
\(726\) −5.24047e17 −0.132826
\(727\) −3.33011e18 −0.836537 −0.418269 0.908323i \(-0.637363\pi\)
−0.418269 + 0.908323i \(0.637363\pi\)
\(728\) 6.76149e18 1.68340
\(729\) 1.50095e17 0.0370370
\(730\) 3.73066e17 0.0912404
\(731\) 1.37077e18 0.332277
\(732\) 3.43295e17 0.0824793
\(733\) −4.12137e18 −0.981446 −0.490723 0.871316i \(-0.663267\pi\)
−0.490723 + 0.871316i \(0.663267\pi\)
\(734\) −1.26680e18 −0.299007
\(735\) −1.11997e18 −0.262023
\(736\) 3.07080e18 0.712107
\(737\) −4.48796e18 −1.03160
\(738\) −1.46690e17 −0.0334221
\(739\) 3.01257e18 0.680374 0.340187 0.940358i \(-0.389510\pi\)
0.340187 + 0.940358i \(0.389510\pi\)
\(740\) 3.46953e17 0.0776721
\(741\) 1.96489e18 0.436033
\(742\) 6.20946e18 1.36593
\(743\) 2.14100e18 0.466864 0.233432 0.972373i \(-0.425004\pi\)
0.233432 + 0.972373i \(0.425004\pi\)
\(744\) −1.19275e18 −0.257826
\(745\) 1.23475e18 0.264583
\(746\) −4.04402e18 −0.859035
\(747\) −2.07151e18 −0.436218
\(748\) 3.92519e17 0.0819409
\(749\) 1.02610e19 2.12352
\(750\) −2.35725e18 −0.483623
\(751\) 6.79051e18 1.38116 0.690578 0.723258i \(-0.257356\pi\)
0.690578 + 0.723258i \(0.257356\pi\)
\(752\) 8.03618e17 0.162044
\(753\) 2.22441e18 0.444679
\(754\) 4.64157e18 0.919923
\(755\) −5.98540e18 −1.17608
\(756\) −4.28572e17 −0.0834896
\(757\) 7.85706e17 0.151753 0.0758765 0.997117i \(-0.475825\pi\)
0.0758765 + 0.997117i \(0.475825\pi\)
\(758\) −1.66405e18 −0.318652
\(759\) 3.86453e18 0.733711
\(760\) −2.39359e18 −0.450569
\(761\) 4.22023e18 0.787655 0.393828 0.919184i \(-0.371151\pi\)
0.393828 + 0.919184i \(0.371151\pi\)
\(762\) 4.03202e18 0.746132
\(763\) −5.09102e18 −0.934104
\(764\) −1.11613e18 −0.203053
\(765\) −2.61251e17 −0.0471258
\(766\) −1.00027e18 −0.178908
\(767\) 8.71141e17 0.154497
\(768\) −2.87540e18 −0.505650
\(769\) −4.73172e17 −0.0825084 −0.0412542 0.999149i \(-0.513135\pi\)
−0.0412542 + 0.999149i \(0.513135\pi\)
\(770\) −4.53155e18 −0.783533
\(771\) 1.47182e18 0.252349
\(772\) −1.80876e18 −0.307516
\(773\) −5.60410e18 −0.944799 −0.472400 0.881384i \(-0.656612\pi\)
−0.472400 + 0.881384i \(0.656612\pi\)
\(774\) −2.48904e18 −0.416117
\(775\) 1.42786e18 0.236714
\(776\) −5.81955e18 −0.956728
\(777\) 1.65537e18 0.269872
\(778\) −2.24829e18 −0.363484
\(779\) 4.87305e17 0.0781281
\(780\) 9.33031e17 0.148348
\(781\) −2.36215e17 −0.0372457
\(782\) 1.27459e18 0.199308
\(783\) −1.17786e18 −0.182659
\(784\) −2.52385e18 −0.388159
\(785\) 8.12615e18 1.23946
\(786\) 3.22098e18 0.487238
\(787\) 8.83339e17 0.132523 0.0662616 0.997802i \(-0.478893\pi\)
0.0662616 + 0.997802i \(0.478893\pi\)
\(788\) −3.21294e18 −0.478060
\(789\) −4.10936e18 −0.606421
\(790\) −9.71371e17 −0.142170
\(791\) 8.23215e18 1.19500
\(792\) −2.85349e18 −0.410830
\(793\) −3.56585e18 −0.509198
\(794\) −3.23266e18 −0.457854
\(795\) 3.43047e18 0.481911
\(796\) 2.72576e18 0.379798
\(797\) 5.83844e18 0.806897 0.403448 0.915002i \(-0.367812\pi\)
0.403448 + 0.915002i \(0.367812\pi\)
\(798\) −2.85251e18 −0.391028
\(799\) −4.65793e17 −0.0633343
\(800\) 2.71434e18 0.366083
\(801\) 2.85619e18 0.382099
\(802\) −1.79640e18 −0.238381
\(803\) −1.47745e18 −0.194474
\(804\) −1.34149e18 −0.175155
\(805\) 7.34434e18 0.951217
\(806\) 3.09456e18 0.397578
\(807\) −2.59961e18 −0.331306
\(808\) −1.61102e18 −0.203669
\(809\) 3.17753e18 0.398496 0.199248 0.979949i \(-0.436150\pi\)
0.199248 + 0.979949i \(0.436150\pi\)
\(810\) 4.74380e17 0.0590166
\(811\) 1.45204e18 0.179202 0.0896008 0.995978i \(-0.471441\pi\)
0.0896008 + 0.995978i \(0.471441\pi\)
\(812\) 3.36320e18 0.411754
\(813\) −5.72367e18 −0.695162
\(814\) 2.75296e18 0.331697
\(815\) 1.45126e17 0.0173468
\(816\) −5.88728e17 −0.0698117
\(817\) 8.26860e18 0.972722
\(818\) −2.15083e18 −0.251021
\(819\) 4.45164e18 0.515435
\(820\) 2.31398e17 0.0265809
\(821\) −4.77895e18 −0.544630 −0.272315 0.962208i \(-0.587789\pi\)
−0.272315 + 0.962208i \(0.587789\pi\)
\(822\) −3.51463e18 −0.397387
\(823\) −6.12708e18 −0.687314 −0.343657 0.939095i \(-0.611666\pi\)
−0.343657 + 0.939095i \(0.611666\pi\)
\(824\) 7.95848e18 0.885733
\(825\) 3.41594e18 0.377189
\(826\) −1.26467e18 −0.138550
\(827\) 8.31290e18 0.903581 0.451790 0.892124i \(-0.350785\pi\)
0.451790 + 0.892124i \(0.350785\pi\)
\(828\) 1.15514e18 0.124577
\(829\) −1.14288e19 −1.22292 −0.611459 0.791276i \(-0.709417\pi\)
−0.611459 + 0.791276i \(0.709417\pi\)
\(830\) −6.54710e18 −0.695091
\(831\) 6.23202e18 0.656481
\(832\) 1.21980e19 1.27493
\(833\) 1.46287e18 0.151710
\(834\) −4.22493e18 −0.434751
\(835\) 2.09654e18 0.214062
\(836\) 2.36772e18 0.239877
\(837\) −7.85286e17 −0.0789427
\(838\) −1.98449e18 −0.197954
\(839\) −6.25053e18 −0.618677 −0.309338 0.950952i \(-0.600108\pi\)
−0.309338 + 0.950952i \(0.600108\pi\)
\(840\) −5.42290e18 −0.532619
\(841\) −1.01745e18 −0.0991610
\(842\) 1.08663e19 1.05088
\(843\) 9.26357e18 0.888995
\(844\) 1.70727e18 0.162583
\(845\) −2.80971e18 −0.265517
\(846\) 8.45787e17 0.0793147
\(847\) 3.94414e18 0.367037
\(848\) 7.73053e18 0.713898
\(849\) −4.29182e18 −0.393316
\(850\) 1.12663e18 0.102461
\(851\) −4.46175e18 −0.402683
\(852\) −7.06068e16 −0.00632396
\(853\) 1.41877e19 1.26108 0.630541 0.776156i \(-0.282833\pi\)
0.630541 + 0.776156i \(0.282833\pi\)
\(854\) 5.17669e18 0.456642
\(855\) −1.57589e18 −0.137958
\(856\) 2.04211e19 1.77419
\(857\) 3.03510e18 0.261696 0.130848 0.991402i \(-0.458230\pi\)
0.130848 + 0.991402i \(0.458230\pi\)
\(858\) 7.40329e18 0.633516
\(859\) 3.39531e18 0.288353 0.144176 0.989552i \(-0.453947\pi\)
0.144176 + 0.989552i \(0.453947\pi\)
\(860\) 3.92636e18 0.330941
\(861\) 1.10404e18 0.0923554
\(862\) 2.98845e18 0.248113
\(863\) −1.00010e19 −0.824087 −0.412043 0.911164i \(-0.635185\pi\)
−0.412043 + 0.911164i \(0.635185\pi\)
\(864\) −1.49282e18 −0.122087
\(865\) 1.36844e19 1.11076
\(866\) −1.44350e19 −1.16292
\(867\) −6.87920e18 −0.550065
\(868\) 2.24226e18 0.177954
\(869\) 3.84690e18 0.303028
\(870\) −3.72267e18 −0.291058
\(871\) 1.39342e19 1.08135
\(872\) −1.01320e19 −0.780437
\(873\) −3.83148e18 −0.292937
\(874\) 7.68843e18 0.583463
\(875\) 1.77414e19 1.33640
\(876\) −4.41621e17 −0.0330197
\(877\) −7.20095e18 −0.534432 −0.267216 0.963637i \(-0.586104\pi\)
−0.267216 + 0.963637i \(0.586104\pi\)
\(878\) 1.33478e19 0.983322
\(879\) −1.01941e19 −0.745457
\(880\) −5.64161e18 −0.409511
\(881\) 1.65348e19 1.19140 0.595698 0.803208i \(-0.296875\pi\)
0.595698 + 0.803208i \(0.296875\pi\)
\(882\) −2.65629e18 −0.189989
\(883\) −6.17888e18 −0.438697 −0.219349 0.975647i \(-0.570393\pi\)
−0.219349 + 0.975647i \(0.570393\pi\)
\(884\) −1.21869e18 −0.0858925
\(885\) −6.98679e17 −0.0488817
\(886\) −2.06379e18 −0.143333
\(887\) 4.08100e18 0.281361 0.140680 0.990055i \(-0.455071\pi\)
0.140680 + 0.990055i \(0.455071\pi\)
\(888\) 3.29446e18 0.225476
\(889\) −3.03463e19 −2.06179
\(890\) 9.02712e18 0.608855
\(891\) −1.87868e18 −0.125790
\(892\) 5.33907e18 0.354891
\(893\) −2.80971e18 −0.185407
\(894\) 2.92850e18 0.191845
\(895\) −2.85792e17 −0.0185866
\(896\) −4.90555e18 −0.316727
\(897\) −1.19986e19 −0.769094
\(898\) 1.19634e19 0.761307
\(899\) 6.16248e18 0.389330
\(900\) 1.02105e18 0.0640431
\(901\) −4.48077e18 −0.279024
\(902\) 1.83607e18 0.113513
\(903\) 1.87333e19 1.14986
\(904\) 1.63834e19 0.998409
\(905\) 1.34072e18 0.0811191
\(906\) −1.41958e19 −0.852761
\(907\) 1.35829e19 0.810112 0.405056 0.914292i \(-0.367252\pi\)
0.405056 + 0.914292i \(0.367252\pi\)
\(908\) 1.86435e18 0.110400
\(909\) −1.06066e18 −0.0623608
\(910\) 1.40696e19 0.821319
\(911\) −1.54250e19 −0.894038 −0.447019 0.894525i \(-0.647514\pi\)
−0.447019 + 0.894525i \(0.647514\pi\)
\(912\) −3.55126e18 −0.204370
\(913\) 2.59284e19 1.48155
\(914\) −1.61952e19 −0.918830
\(915\) 2.85991e18 0.161107
\(916\) 5.04602e18 0.282246
\(917\) −2.42421e19 −1.34639
\(918\) −6.19620e17 −0.0341703
\(919\) 2.04618e19 1.12045 0.560226 0.828340i \(-0.310714\pi\)
0.560226 + 0.828340i \(0.310714\pi\)
\(920\) 1.46165e19 0.794734
\(921\) 1.19912e17 0.00647402
\(922\) 1.92818e18 0.103370
\(923\) 7.33402e17 0.0390419
\(924\) 5.36428e18 0.283559
\(925\) −3.94384e18 −0.207013
\(926\) −2.30099e19 −1.19934
\(927\) 5.23971e18 0.271199
\(928\) 1.17148e19 0.602107
\(929\) −3.95502e18 −0.201858 −0.100929 0.994894i \(-0.532182\pi\)
−0.100929 + 0.994894i \(0.532182\pi\)
\(930\) −2.48193e18 −0.125791
\(931\) 8.82420e18 0.444122
\(932\) 4.25646e18 0.212738
\(933\) −1.98779e19 −0.986597
\(934\) 4.56927e18 0.225212
\(935\) 3.26999e18 0.160055
\(936\) 8.85951e18 0.430642
\(937\) 2.30300e19 1.11170 0.555848 0.831284i \(-0.312394\pi\)
0.555848 + 0.831284i \(0.312394\pi\)
\(938\) −2.02289e19 −0.969737
\(939\) −1.35105e19 −0.643200
\(940\) −1.33420e18 −0.0630796
\(941\) 3.96413e18 0.186130 0.0930648 0.995660i \(-0.470334\pi\)
0.0930648 + 0.995660i \(0.470334\pi\)
\(942\) 1.92731e19 0.898714
\(943\) −2.97573e18 −0.137806
\(944\) −1.57447e18 −0.0724129
\(945\) −3.57034e18 −0.163081
\(946\) 3.11544e19 1.41328
\(947\) −2.82175e19 −1.27129 −0.635644 0.771982i \(-0.719265\pi\)
−0.635644 + 0.771982i \(0.719265\pi\)
\(948\) 1.14987e18 0.0514512
\(949\) 4.58718e18 0.203852
\(950\) 6.79597e18 0.299949
\(951\) −1.28713e19 −0.564221
\(952\) 7.08322e18 0.308383
\(953\) −1.14223e19 −0.493914 −0.246957 0.969026i \(-0.579431\pi\)
−0.246957 + 0.969026i \(0.579431\pi\)
\(954\) 8.13618e18 0.349427
\(955\) −9.29825e18 −0.396624
\(956\) 9.50260e18 0.402593
\(957\) 1.47428e19 0.620373
\(958\) −6.64260e18 −0.277627
\(959\) 2.64522e19 1.09810
\(960\) −9.78310e18 −0.403379
\(961\) −2.03090e19 −0.831737
\(962\) −8.54740e18 −0.347693
\(963\) 1.34449e19 0.543232
\(964\) 5.11079e18 0.205110
\(965\) −1.50683e19 −0.600673
\(966\) 1.74189e19 0.689713
\(967\) −2.70774e19 −1.06496 −0.532482 0.846441i \(-0.678741\pi\)
−0.532482 + 0.846441i \(0.678741\pi\)
\(968\) 7.84951e18 0.306657
\(969\) 2.05838e18 0.0798769
\(970\) −1.21096e19 −0.466779
\(971\) −4.38871e19 −1.68040 −0.840198 0.542280i \(-0.817561\pi\)
−0.840198 + 0.542280i \(0.817561\pi\)
\(972\) −5.61553e17 −0.0213580
\(973\) 3.17982e19 1.20135
\(974\) −3.41254e19 −1.28069
\(975\) −1.06058e19 −0.395379
\(976\) 6.44478e18 0.238662
\(977\) −3.09328e18 −0.113790 −0.0568950 0.998380i \(-0.518120\pi\)
−0.0568950 + 0.998380i \(0.518120\pi\)
\(978\) 3.44201e17 0.0125779
\(979\) −3.57499e19 −1.29774
\(980\) 4.19019e18 0.151100
\(981\) −6.67071e18 −0.238959
\(982\) 1.91888e19 0.682847
\(983\) 1.53172e19 0.541480 0.270740 0.962653i \(-0.412732\pi\)
0.270740 + 0.962653i \(0.412732\pi\)
\(984\) 2.19722e18 0.0771622
\(985\) −2.67663e19 −0.933797
\(986\) 4.86243e18 0.168521
\(987\) −6.36566e18 −0.219170
\(988\) −7.35129e18 −0.251445
\(989\) −5.04923e19 −1.71573
\(990\) −5.93764e18 −0.200440
\(991\) −4.12391e19 −1.38303 −0.691514 0.722363i \(-0.743056\pi\)
−0.691514 + 0.722363i \(0.743056\pi\)
\(992\) 7.81034e18 0.260222
\(993\) 3.73284e18 0.123558
\(994\) −1.06471e18 −0.0350123
\(995\) 2.27077e19 0.741861
\(996\) 7.75021e18 0.251552
\(997\) 5.20025e18 0.167689 0.0838447 0.996479i \(-0.473280\pi\)
0.0838447 + 0.996479i \(0.473280\pi\)
\(998\) −3.24823e19 −1.04063
\(999\) 2.16901e18 0.0690377
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.14.a.a.1.10 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.10 30 1.1 even 1 trivial