Properties

Label 177.14.a.a.1.12
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $30$
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: \(30\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-44.2174 q^{2} +729.000 q^{3} -6236.82 q^{4} +14897.9 q^{5} -32234.5 q^{6} +473501. q^{7} +638005. q^{8} +531441. q^{9} +O(q^{10})\) \(q-44.2174 q^{2} +729.000 q^{3} -6236.82 q^{4} +14897.9 q^{5} -32234.5 q^{6} +473501. q^{7} +638005. q^{8} +531441. q^{9} -658745. q^{10} -5.62449e6 q^{11} -4.54664e6 q^{12} -1.37488e7 q^{13} -2.09370e7 q^{14} +1.08605e7 q^{15} +2.28811e7 q^{16} +1.90754e8 q^{17} -2.34989e7 q^{18} -2.39269e8 q^{19} -9.29153e7 q^{20} +3.45182e8 q^{21} +2.48700e8 q^{22} +8.48230e8 q^{23} +4.65106e8 q^{24} -9.98757e8 q^{25} +6.07938e8 q^{26} +3.87420e8 q^{27} -2.95314e9 q^{28} -2.26512e9 q^{29} -4.80225e8 q^{30} +6.87064e8 q^{31} -6.23828e9 q^{32} -4.10025e9 q^{33} -8.43464e9 q^{34} +7.05415e9 q^{35} -3.31450e9 q^{36} -1.85095e10 q^{37} +1.05798e10 q^{38} -1.00229e10 q^{39} +9.50491e9 q^{40} -2.65666e10 q^{41} -1.52630e10 q^{42} -8.00165e10 q^{43} +3.50790e10 q^{44} +7.91734e9 q^{45} -3.75065e10 q^{46} -1.28932e11 q^{47} +1.66804e10 q^{48} +1.27314e11 q^{49} +4.41624e10 q^{50} +1.39060e11 q^{51} +8.57491e10 q^{52} +2.46479e11 q^{53} -1.71307e10 q^{54} -8.37929e10 q^{55} +3.02096e11 q^{56} -1.74427e11 q^{57} +1.00157e11 q^{58} +4.21805e10 q^{59} -6.77353e10 q^{60} +6.06790e11 q^{61} -3.03802e10 q^{62} +2.51638e11 q^{63} +8.83981e10 q^{64} -2.04828e11 q^{65} +1.81303e11 q^{66} +1.30921e11 q^{67} -1.18970e12 q^{68} +6.18360e11 q^{69} -3.11916e11 q^{70} -1.05368e12 q^{71} +3.39062e11 q^{72} -1.45214e12 q^{73} +8.18440e11 q^{74} -7.28094e11 q^{75} +1.49228e12 q^{76} -2.66320e12 q^{77} +4.43187e11 q^{78} +9.47431e10 q^{79} +3.40880e11 q^{80} +2.82430e11 q^{81} +1.17471e12 q^{82} +4.49947e12 q^{83} -2.15284e12 q^{84} +2.84182e12 q^{85} +3.53812e12 q^{86} -1.65127e12 q^{87} -3.58845e12 q^{88} +4.97158e11 q^{89} -3.50084e11 q^{90} -6.51009e12 q^{91} -5.29026e12 q^{92} +5.00869e11 q^{93} +5.70103e12 q^{94} -3.56459e12 q^{95} -4.54771e12 q^{96} -1.63570e12 q^{97} -5.62949e12 q^{98} -2.98909e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −44.2174 −0.488538 −0.244269 0.969708i \(-0.578548\pi\)
−0.244269 + 0.969708i \(0.578548\pi\)
\(3\) 729.000 0.577350
\(4\) −6236.82 −0.761331
\(5\) 14897.9 0.426402 0.213201 0.977008i \(-0.431611\pi\)
0.213201 + 0.977008i \(0.431611\pi\)
\(6\) −32234.5 −0.282057
\(7\) 473501. 1.52119 0.760595 0.649227i \(-0.224907\pi\)
0.760595 + 0.649227i \(0.224907\pi\)
\(8\) 638005. 0.860477
\(9\) 531441. 0.333333
\(10\) −658745. −0.208313
\(11\) −5.62449e6 −0.957262 −0.478631 0.878016i \(-0.658867\pi\)
−0.478631 + 0.878016i \(0.658867\pi\)
\(12\) −4.54664e6 −0.439555
\(13\) −1.37488e7 −0.790014 −0.395007 0.918678i \(-0.629258\pi\)
−0.395007 + 0.918678i \(0.629258\pi\)
\(14\) −2.09370e7 −0.743159
\(15\) 1.08605e7 0.246183
\(16\) 2.28811e7 0.340956
\(17\) 1.90754e8 1.91670 0.958352 0.285588i \(-0.0921890\pi\)
0.958352 + 0.285588i \(0.0921890\pi\)
\(18\) −2.34989e7 −0.162846
\(19\) −2.39269e8 −1.16678 −0.583388 0.812194i \(-0.698273\pi\)
−0.583388 + 0.812194i \(0.698273\pi\)
\(20\) −9.29153e7 −0.324633
\(21\) 3.45182e8 0.878259
\(22\) 2.48700e8 0.467659
\(23\) 8.48230e8 1.19477 0.597383 0.801956i \(-0.296207\pi\)
0.597383 + 0.801956i \(0.296207\pi\)
\(24\) 4.65106e8 0.496796
\(25\) −9.98757e8 −0.818182
\(26\) 6.07938e8 0.385951
\(27\) 3.87420e8 0.192450
\(28\) −2.95314e9 −1.15813
\(29\) −2.26512e9 −0.707137 −0.353568 0.935409i \(-0.615032\pi\)
−0.353568 + 0.935409i \(0.615032\pi\)
\(30\) −4.80225e8 −0.120270
\(31\) 6.87064e8 0.139042 0.0695210 0.997580i \(-0.477853\pi\)
0.0695210 + 0.997580i \(0.477853\pi\)
\(32\) −6.23828e9 −1.02705
\(33\) −4.10025e9 −0.552676
\(34\) −8.43464e9 −0.936383
\(35\) 7.05415e9 0.648638
\(36\) −3.31450e9 −0.253777
\(37\) −1.85095e10 −1.18599 −0.592997 0.805205i \(-0.702055\pi\)
−0.592997 + 0.805205i \(0.702055\pi\)
\(38\) 1.05798e10 0.570014
\(39\) −1.00229e10 −0.456115
\(40\) 9.50491e9 0.366909
\(41\) −2.65666e10 −0.873456 −0.436728 0.899593i \(-0.643863\pi\)
−0.436728 + 0.899593i \(0.643863\pi\)
\(42\) −1.52630e10 −0.429063
\(43\) −8.00165e10 −1.93034 −0.965172 0.261617i \(-0.915744\pi\)
−0.965172 + 0.261617i \(0.915744\pi\)
\(44\) 3.50790e10 0.728793
\(45\) 7.91734e9 0.142134
\(46\) −3.75065e10 −0.583688
\(47\) −1.28932e11 −1.74471 −0.872357 0.488869i \(-0.837410\pi\)
−0.872357 + 0.488869i \(0.837410\pi\)
\(48\) 1.66804e10 0.196851
\(49\) 1.27314e11 1.31402
\(50\) 4.41624e10 0.399713
\(51\) 1.39060e11 1.10661
\(52\) 8.57491e10 0.601462
\(53\) 2.46479e11 1.52752 0.763760 0.645500i \(-0.223351\pi\)
0.763760 + 0.645500i \(0.223351\pi\)
\(54\) −1.71307e10 −0.0940191
\(55\) −8.37929e10 −0.408178
\(56\) 3.02096e11 1.30895
\(57\) −1.74427e11 −0.673638
\(58\) 1.00157e11 0.345463
\(59\) 4.21805e10 0.130189
\(60\) −6.77353e10 −0.187427
\(61\) 6.06790e11 1.50798 0.753989 0.656888i \(-0.228127\pi\)
0.753989 + 0.656888i \(0.228127\pi\)
\(62\) −3.03802e10 −0.0679272
\(63\) 2.51638e11 0.507063
\(64\) 8.83981e10 0.160795
\(65\) −2.04828e11 −0.336863
\(66\) 1.81303e11 0.270003
\(67\) 1.30921e11 0.176817 0.0884086 0.996084i \(-0.471822\pi\)
0.0884086 + 0.996084i \(0.471822\pi\)
\(68\) −1.18970e12 −1.45925
\(69\) 6.18360e11 0.689798
\(70\) −3.11916e11 −0.316884
\(71\) −1.05368e12 −0.976175 −0.488088 0.872795i \(-0.662305\pi\)
−0.488088 + 0.872795i \(0.662305\pi\)
\(72\) 3.39062e11 0.286826
\(73\) −1.45214e12 −1.12308 −0.561538 0.827451i \(-0.689790\pi\)
−0.561538 + 0.827451i \(0.689790\pi\)
\(74\) 8.18440e11 0.579403
\(75\) −7.28094e11 −0.472377
\(76\) 1.49228e12 0.888303
\(77\) −2.66320e12 −1.45618
\(78\) 4.43187e11 0.222829
\(79\) 9.47431e10 0.0438502 0.0219251 0.999760i \(-0.493020\pi\)
0.0219251 + 0.999760i \(0.493020\pi\)
\(80\) 3.40880e11 0.145384
\(81\) 2.82430e11 0.111111
\(82\) 1.17471e12 0.426716
\(83\) 4.49947e12 1.51062 0.755308 0.655370i \(-0.227487\pi\)
0.755308 + 0.655370i \(0.227487\pi\)
\(84\) −2.15284e12 −0.668646
\(85\) 2.84182e12 0.817286
\(86\) 3.53812e12 0.943046
\(87\) −1.65127e12 −0.408265
\(88\) −3.58845e12 −0.823702
\(89\) 4.97158e11 0.106038 0.0530188 0.998594i \(-0.483116\pi\)
0.0530188 + 0.998594i \(0.483116\pi\)
\(90\) −3.50084e11 −0.0694378
\(91\) −6.51009e12 −1.20176
\(92\) −5.29026e12 −0.909612
\(93\) 5.00869e11 0.0802759
\(94\) 5.70103e12 0.852359
\(95\) −3.56459e12 −0.497515
\(96\) −4.54771e12 −0.592965
\(97\) −1.63570e12 −0.199382 −0.0996911 0.995018i \(-0.531785\pi\)
−0.0996911 + 0.995018i \(0.531785\pi\)
\(98\) −5.62949e12 −0.641947
\(99\) −2.98909e12 −0.319087
\(100\) 6.22907e12 0.622907
\(101\) 7.02588e12 0.658585 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(102\) −6.14885e12 −0.540621
\(103\) −6.28234e12 −0.518417 −0.259209 0.965821i \(-0.583462\pi\)
−0.259209 + 0.965821i \(0.583462\pi\)
\(104\) −8.77183e12 −0.679788
\(105\) 5.14247e12 0.374491
\(106\) −1.08987e13 −0.746251
\(107\) −2.66456e12 −0.171645 −0.0858223 0.996310i \(-0.527352\pi\)
−0.0858223 + 0.996310i \(0.527352\pi\)
\(108\) −2.41627e12 −0.146518
\(109\) 2.75266e13 1.57210 0.786050 0.618163i \(-0.212123\pi\)
0.786050 + 0.618163i \(0.212123\pi\)
\(110\) 3.70510e12 0.199410
\(111\) −1.34934e13 −0.684734
\(112\) 1.08342e13 0.518658
\(113\) 5.68272e12 0.256771 0.128386 0.991724i \(-0.459021\pi\)
0.128386 + 0.991724i \(0.459021\pi\)
\(114\) 7.71270e12 0.329098
\(115\) 1.26368e13 0.509450
\(116\) 1.41271e13 0.538365
\(117\) −7.30670e12 −0.263338
\(118\) −1.86511e12 −0.0636022
\(119\) 9.03221e13 2.91567
\(120\) 6.92908e12 0.211835
\(121\) −2.88780e12 −0.0836492
\(122\) −2.68307e13 −0.736704
\(123\) −1.93671e13 −0.504290
\(124\) −4.28509e12 −0.105857
\(125\) −3.30652e13 −0.775276
\(126\) −1.11268e13 −0.247720
\(127\) −3.37035e13 −0.712773 −0.356386 0.934339i \(-0.615991\pi\)
−0.356386 + 0.934339i \(0.615991\pi\)
\(128\) 4.71953e13 0.948492
\(129\) −5.83320e13 −1.11448
\(130\) 9.05698e12 0.164570
\(131\) 4.65155e13 0.804144 0.402072 0.915608i \(-0.368290\pi\)
0.402072 + 0.915608i \(0.368290\pi\)
\(132\) 2.55726e13 0.420769
\(133\) −1.13294e14 −1.77489
\(134\) −5.78900e12 −0.0863818
\(135\) 5.77174e12 0.0820611
\(136\) 1.21702e14 1.64928
\(137\) −1.23746e14 −1.59900 −0.799498 0.600669i \(-0.794901\pi\)
−0.799498 + 0.600669i \(0.794901\pi\)
\(138\) −2.73423e13 −0.336993
\(139\) 1.38699e13 0.163108 0.0815541 0.996669i \(-0.474012\pi\)
0.0815541 + 0.996669i \(0.474012\pi\)
\(140\) −4.39955e13 −0.493828
\(141\) −9.39914e13 −1.00731
\(142\) 4.65908e13 0.476899
\(143\) 7.73303e13 0.756250
\(144\) 1.21600e13 0.113652
\(145\) −3.37454e13 −0.301524
\(146\) 6.42098e13 0.548665
\(147\) 9.28118e13 0.758649
\(148\) 1.15440e14 0.902934
\(149\) −8.35651e13 −0.625625 −0.312813 0.949815i \(-0.601271\pi\)
−0.312813 + 0.949815i \(0.601271\pi\)
\(150\) 3.21944e13 0.230774
\(151\) −5.63763e13 −0.387032 −0.193516 0.981097i \(-0.561989\pi\)
−0.193516 + 0.981097i \(0.561989\pi\)
\(152\) −1.52655e14 −1.00398
\(153\) 1.01374e14 0.638902
\(154\) 1.17760e14 0.711398
\(155\) 1.02358e13 0.0592877
\(156\) 6.25111e13 0.347254
\(157\) 7.91560e12 0.0421829 0.0210914 0.999778i \(-0.493286\pi\)
0.0210914 + 0.999778i \(0.493286\pi\)
\(158\) −4.18929e12 −0.0214225
\(159\) 1.79683e14 0.881914
\(160\) −9.29370e13 −0.437934
\(161\) 4.01638e14 1.81747
\(162\) −1.24883e13 −0.0542820
\(163\) −1.46318e13 −0.0611053 −0.0305526 0.999533i \(-0.509727\pi\)
−0.0305526 + 0.999533i \(0.509727\pi\)
\(164\) 1.65691e14 0.664989
\(165\) −6.10850e13 −0.235662
\(166\) −1.98955e14 −0.737993
\(167\) −2.35885e14 −0.841479 −0.420739 0.907182i \(-0.638229\pi\)
−0.420739 + 0.907182i \(0.638229\pi\)
\(168\) 2.20228e14 0.755722
\(169\) −1.13844e14 −0.375879
\(170\) −1.25658e14 −0.399275
\(171\) −1.27157e14 −0.388925
\(172\) 4.99049e14 1.46963
\(173\) −9.02605e13 −0.255975 −0.127988 0.991776i \(-0.540852\pi\)
−0.127988 + 0.991776i \(0.540852\pi\)
\(174\) 7.30148e13 0.199453
\(175\) −4.72912e14 −1.24461
\(176\) −1.28695e14 −0.326384
\(177\) 3.07496e13 0.0751646
\(178\) −2.19830e13 −0.0518033
\(179\) −4.73759e14 −1.07650 −0.538248 0.842787i \(-0.680914\pi\)
−0.538248 + 0.842787i \(0.680914\pi\)
\(180\) −4.93790e13 −0.108211
\(181\) −3.94362e14 −0.833652 −0.416826 0.908986i \(-0.636858\pi\)
−0.416826 + 0.908986i \(0.636858\pi\)
\(182\) 2.87859e14 0.587105
\(183\) 4.42350e14 0.870631
\(184\) 5.41175e14 1.02807
\(185\) −2.75751e14 −0.505710
\(186\) −2.21471e13 −0.0392178
\(187\) −1.07289e15 −1.83479
\(188\) 8.04126e14 1.32831
\(189\) 1.83444e14 0.292753
\(190\) 1.57617e14 0.243055
\(191\) 1.12171e15 1.67172 0.835860 0.548943i \(-0.184969\pi\)
0.835860 + 0.548943i \(0.184969\pi\)
\(192\) 6.44422e13 0.0928352
\(193\) −9.55941e14 −1.33140 −0.665700 0.746219i \(-0.731867\pi\)
−0.665700 + 0.746219i \(0.731867\pi\)
\(194\) 7.23262e13 0.0974058
\(195\) −1.49320e14 −0.194488
\(196\) −7.94034e14 −1.00040
\(197\) 1.29129e15 1.57395 0.786976 0.616983i \(-0.211645\pi\)
0.786976 + 0.616983i \(0.211645\pi\)
\(198\) 1.32170e14 0.155886
\(199\) −2.34104e14 −0.267217 −0.133609 0.991034i \(-0.542657\pi\)
−0.133609 + 0.991034i \(0.542657\pi\)
\(200\) −6.37212e14 −0.704026
\(201\) 9.54417e13 0.102085
\(202\) −3.10666e14 −0.321744
\(203\) −1.07253e15 −1.07569
\(204\) −8.67290e14 −0.842496
\(205\) −3.95786e14 −0.372443
\(206\) 2.77789e14 0.253266
\(207\) 4.50784e14 0.398255
\(208\) −3.14589e14 −0.269360
\(209\) 1.34576e15 1.11691
\(210\) −2.27387e14 −0.182953
\(211\) −2.23736e15 −1.74542 −0.872709 0.488241i \(-0.837639\pi\)
−0.872709 + 0.488241i \(0.837639\pi\)
\(212\) −1.53725e15 −1.16295
\(213\) −7.68130e14 −0.563595
\(214\) 1.17820e14 0.0838549
\(215\) −1.19208e15 −0.823102
\(216\) 2.47176e14 0.165599
\(217\) 3.25325e14 0.211509
\(218\) −1.21715e15 −0.768030
\(219\) −1.05861e15 −0.648409
\(220\) 5.22602e14 0.310759
\(221\) −2.62265e15 −1.51422
\(222\) 5.96643e14 0.334518
\(223\) −3.19039e15 −1.73725 −0.868626 0.495468i \(-0.834996\pi\)
−0.868626 + 0.495468i \(0.834996\pi\)
\(224\) −2.95383e15 −1.56233
\(225\) −5.30780e14 −0.272727
\(226\) −2.51275e14 −0.125442
\(227\) −6.78365e14 −0.329075 −0.164538 0.986371i \(-0.552613\pi\)
−0.164538 + 0.986371i \(0.552613\pi\)
\(228\) 1.08787e15 0.512862
\(229\) 2.07816e15 0.952245 0.476123 0.879379i \(-0.342042\pi\)
0.476123 + 0.879379i \(0.342042\pi\)
\(230\) −5.58767e14 −0.248886
\(231\) −1.94147e15 −0.840724
\(232\) −1.44515e15 −0.608474
\(233\) 8.65199e13 0.0354244 0.0177122 0.999843i \(-0.494362\pi\)
0.0177122 + 0.999843i \(0.494362\pi\)
\(234\) 3.23083e14 0.128650
\(235\) −1.92081e15 −0.743949
\(236\) −2.63073e14 −0.0991168
\(237\) 6.90677e13 0.0253169
\(238\) −3.99381e15 −1.42442
\(239\) −2.97537e15 −1.03265 −0.516326 0.856392i \(-0.672701\pi\)
−0.516326 + 0.856392i \(0.672701\pi\)
\(240\) 2.48502e14 0.0839375
\(241\) 1.38612e15 0.455710 0.227855 0.973695i \(-0.426829\pi\)
0.227855 + 0.973695i \(0.426829\pi\)
\(242\) 1.27691e14 0.0408658
\(243\) 2.05891e14 0.0641500
\(244\) −3.78444e15 −1.14807
\(245\) 1.89671e15 0.560300
\(246\) 8.56361e14 0.246365
\(247\) 3.28967e15 0.921769
\(248\) 4.38350e14 0.119642
\(249\) 3.28012e15 0.872154
\(250\) 1.46206e15 0.378751
\(251\) −4.33970e15 −1.09542 −0.547710 0.836668i \(-0.684500\pi\)
−0.547710 + 0.836668i \(0.684500\pi\)
\(252\) −1.56942e15 −0.386043
\(253\) −4.77087e15 −1.14370
\(254\) 1.49028e15 0.348216
\(255\) 2.07169e15 0.471860
\(256\) −2.81101e15 −0.624169
\(257\) 6.59104e14 0.142688 0.0713442 0.997452i \(-0.477271\pi\)
0.0713442 + 0.997452i \(0.477271\pi\)
\(258\) 2.57929e15 0.544468
\(259\) −8.76424e15 −1.80412
\(260\) 1.27748e15 0.256464
\(261\) −1.20378e15 −0.235712
\(262\) −2.05679e15 −0.392855
\(263\) −3.76994e15 −0.702461 −0.351231 0.936289i \(-0.614237\pi\)
−0.351231 + 0.936289i \(0.614237\pi\)
\(264\) −2.61598e15 −0.475564
\(265\) 3.67201e15 0.651337
\(266\) 5.00956e15 0.867099
\(267\) 3.62428e14 0.0612208
\(268\) −8.16533e14 −0.134616
\(269\) −9.46874e14 −0.152371 −0.0761855 0.997094i \(-0.524274\pi\)
−0.0761855 + 0.997094i \(0.524274\pi\)
\(270\) −2.55211e14 −0.0400899
\(271\) 1.35782e15 0.208230 0.104115 0.994565i \(-0.466799\pi\)
0.104115 + 0.994565i \(0.466799\pi\)
\(272\) 4.36467e15 0.653511
\(273\) −4.74586e15 −0.693837
\(274\) 5.47172e15 0.781169
\(275\) 5.61750e15 0.783214
\(276\) −3.85660e15 −0.525165
\(277\) 1.45446e16 1.93456 0.967280 0.253712i \(-0.0816517\pi\)
0.967280 + 0.253712i \(0.0816517\pi\)
\(278\) −6.13289e14 −0.0796845
\(279\) 3.65134e14 0.0463473
\(280\) 4.50058e15 0.558138
\(281\) −1.08921e16 −1.31984 −0.659918 0.751337i \(-0.729409\pi\)
−0.659918 + 0.751337i \(0.729409\pi\)
\(282\) 4.15605e15 0.492110
\(283\) 1.28425e15 0.148607 0.0743034 0.997236i \(-0.476327\pi\)
0.0743034 + 0.997236i \(0.476327\pi\)
\(284\) 6.57159e15 0.743193
\(285\) −2.59859e15 −0.287241
\(286\) −3.41934e15 −0.369457
\(287\) −1.25793e16 −1.32869
\(288\) −3.31528e15 −0.342349
\(289\) 2.64824e16 2.67376
\(290\) 1.49213e15 0.147306
\(291\) −1.19242e15 −0.115113
\(292\) 9.05673e15 0.855033
\(293\) −1.63989e16 −1.51417 −0.757085 0.653316i \(-0.773377\pi\)
−0.757085 + 0.653316i \(0.773377\pi\)
\(294\) −4.10390e15 −0.370628
\(295\) 6.28400e14 0.0555128
\(296\) −1.18091e16 −1.02052
\(297\) −2.17904e15 −0.184225
\(298\) 3.69503e15 0.305642
\(299\) −1.16622e16 −0.943881
\(300\) 4.54099e15 0.359635
\(301\) −3.78879e16 −2.93642
\(302\) 2.49281e15 0.189080
\(303\) 5.12187e15 0.380234
\(304\) −5.47474e15 −0.397819
\(305\) 9.03988e15 0.643004
\(306\) −4.48251e15 −0.312128
\(307\) 1.15451e16 0.787043 0.393522 0.919315i \(-0.371257\pi\)
0.393522 + 0.919315i \(0.371257\pi\)
\(308\) 1.66099e16 1.10863
\(309\) −4.57983e15 −0.299308
\(310\) −4.52599e14 −0.0289643
\(311\) −2.58262e15 −0.161852 −0.0809260 0.996720i \(-0.525788\pi\)
−0.0809260 + 0.996720i \(0.525788\pi\)
\(312\) −6.39467e15 −0.392476
\(313\) 1.58178e16 0.950839 0.475420 0.879759i \(-0.342296\pi\)
0.475420 + 0.879759i \(0.342296\pi\)
\(314\) −3.50007e14 −0.0206079
\(315\) 3.74886e15 0.216213
\(316\) −5.90896e14 −0.0333845
\(317\) 1.23606e15 0.0684157 0.0342079 0.999415i \(-0.489109\pi\)
0.0342079 + 0.999415i \(0.489109\pi\)
\(318\) −7.94513e15 −0.430848
\(319\) 1.27401e16 0.676915
\(320\) 1.31694e15 0.0685634
\(321\) −1.94246e15 −0.0990991
\(322\) −1.77594e16 −0.887901
\(323\) −4.56414e16 −2.23636
\(324\) −1.76146e15 −0.0845923
\(325\) 1.37318e16 0.646375
\(326\) 6.46980e14 0.0298522
\(327\) 2.00669e16 0.907653
\(328\) −1.69496e16 −0.751589
\(329\) −6.10494e16 −2.65404
\(330\) 2.70102e15 0.115130
\(331\) 2.43886e15 0.101931 0.0509654 0.998700i \(-0.483770\pi\)
0.0509654 + 0.998700i \(0.483770\pi\)
\(332\) −2.80624e16 −1.15008
\(333\) −9.83668e15 −0.395331
\(334\) 1.04302e16 0.411094
\(335\) 1.95045e15 0.0753951
\(336\) 7.89816e15 0.299447
\(337\) −3.73870e16 −1.39036 −0.695179 0.718837i \(-0.744675\pi\)
−0.695179 + 0.718837i \(0.744675\pi\)
\(338\) 5.03390e15 0.183631
\(339\) 4.14270e15 0.148247
\(340\) −1.77240e16 −0.622225
\(341\) −3.86438e15 −0.133100
\(342\) 5.62256e15 0.190005
\(343\) 1.44062e16 0.477681
\(344\) −5.10509e16 −1.66102
\(345\) 9.21224e15 0.294131
\(346\) 3.99108e15 0.125054
\(347\) 6.97870e15 0.214602 0.107301 0.994227i \(-0.465779\pi\)
0.107301 + 0.994227i \(0.465779\pi\)
\(348\) 1.02987e16 0.310825
\(349\) 3.93172e16 1.16471 0.582354 0.812935i \(-0.302132\pi\)
0.582354 + 0.812935i \(0.302132\pi\)
\(350\) 2.09109e16 0.608039
\(351\) −5.32659e15 −0.152038
\(352\) 3.50872e16 0.983152
\(353\) 2.99842e15 0.0824817 0.0412408 0.999149i \(-0.486869\pi\)
0.0412408 + 0.999149i \(0.486869\pi\)
\(354\) −1.35967e15 −0.0367207
\(355\) −1.56975e16 −0.416243
\(356\) −3.10069e15 −0.0807296
\(357\) 6.58448e16 1.68336
\(358\) 2.09484e16 0.525909
\(359\) −2.98048e16 −0.734806 −0.367403 0.930062i \(-0.619753\pi\)
−0.367403 + 0.930062i \(0.619753\pi\)
\(360\) 5.05130e15 0.122303
\(361\) 1.51965e16 0.361366
\(362\) 1.74377e16 0.407270
\(363\) −2.10520e15 −0.0482949
\(364\) 4.06023e16 0.914937
\(365\) −2.16338e16 −0.478882
\(366\) −1.95596e16 −0.425336
\(367\) −2.33299e16 −0.498406 −0.249203 0.968451i \(-0.580169\pi\)
−0.249203 + 0.968451i \(0.580169\pi\)
\(368\) 1.94085e16 0.407362
\(369\) −1.41186e16 −0.291152
\(370\) 1.21930e16 0.247058
\(371\) 1.16708e17 2.32365
\(372\) −3.12383e15 −0.0611165
\(373\) −8.12135e16 −1.56142 −0.780712 0.624892i \(-0.785143\pi\)
−0.780712 + 0.624892i \(0.785143\pi\)
\(374\) 4.74405e16 0.896364
\(375\) −2.41045e16 −0.447606
\(376\) −8.22592e16 −1.50129
\(377\) 3.11427e16 0.558648
\(378\) −8.11141e15 −0.143021
\(379\) −1.05622e17 −1.83062 −0.915309 0.402752i \(-0.868054\pi\)
−0.915309 + 0.402752i \(0.868054\pi\)
\(380\) 2.22317e16 0.378774
\(381\) −2.45699e16 −0.411520
\(382\) −4.95991e16 −0.816698
\(383\) 7.65692e14 0.0123955 0.00619773 0.999981i \(-0.498027\pi\)
0.00619773 + 0.999981i \(0.498027\pi\)
\(384\) 3.44053e16 0.547612
\(385\) −3.96760e16 −0.620917
\(386\) 4.22692e16 0.650439
\(387\) −4.25241e16 −0.643448
\(388\) 1.02016e16 0.151796
\(389\) −6.70250e16 −0.980764 −0.490382 0.871507i \(-0.663143\pi\)
−0.490382 + 0.871507i \(0.663143\pi\)
\(390\) 6.60254e15 0.0950147
\(391\) 1.61803e17 2.29001
\(392\) 8.12269e16 1.13068
\(393\) 3.39098e16 0.464273
\(394\) −5.70973e16 −0.768935
\(395\) 1.41147e15 0.0186978
\(396\) 1.86424e16 0.242931
\(397\) 1.20104e17 1.53964 0.769820 0.638262i \(-0.220346\pi\)
0.769820 + 0.638262i \(0.220346\pi\)
\(398\) 1.03515e16 0.130546
\(399\) −8.25912e16 −1.02473
\(400\) −2.28527e16 −0.278964
\(401\) −6.36394e16 −0.764342 −0.382171 0.924092i \(-0.624823\pi\)
−0.382171 + 0.924092i \(0.624823\pi\)
\(402\) −4.22018e15 −0.0498726
\(403\) −9.44633e15 −0.109845
\(404\) −4.38192e16 −0.501401
\(405\) 4.20760e15 0.0473780
\(406\) 4.74246e16 0.525515
\(407\) 1.04106e17 1.13531
\(408\) 8.87207e16 0.952212
\(409\) 6.97030e16 0.736292 0.368146 0.929768i \(-0.379993\pi\)
0.368146 + 0.929768i \(0.379993\pi\)
\(410\) 1.75006e16 0.181953
\(411\) −9.02108e16 −0.923180
\(412\) 3.91819e16 0.394687
\(413\) 1.99725e16 0.198042
\(414\) −1.99325e16 −0.194563
\(415\) 6.70325e16 0.644129
\(416\) 8.57692e16 0.811381
\(417\) 1.01111e16 0.0941706
\(418\) −5.95062e16 −0.545653
\(419\) 4.45589e16 0.402294 0.201147 0.979561i \(-0.435533\pi\)
0.201147 + 0.979561i \(0.435533\pi\)
\(420\) −3.20727e16 −0.285112
\(421\) −9.19806e16 −0.805123 −0.402562 0.915393i \(-0.631880\pi\)
−0.402562 + 0.915393i \(0.631880\pi\)
\(422\) 9.89301e16 0.852702
\(423\) −6.85197e16 −0.581572
\(424\) 1.57255e17 1.31440
\(425\) −1.90517e17 −1.56821
\(426\) 3.39647e16 0.275337
\(427\) 2.87316e17 2.29392
\(428\) 1.66184e16 0.130678
\(429\) 5.63738e16 0.436621
\(430\) 5.27104e16 0.402116
\(431\) −3.66494e16 −0.275400 −0.137700 0.990474i \(-0.543971\pi\)
−0.137700 + 0.990474i \(0.543971\pi\)
\(432\) 8.86462e15 0.0656169
\(433\) −4.93879e16 −0.360122 −0.180061 0.983655i \(-0.557630\pi\)
−0.180061 + 0.983655i \(0.557630\pi\)
\(434\) −1.43850e16 −0.103330
\(435\) −2.46004e16 −0.174085
\(436\) −1.71678e17 −1.19689
\(437\) −2.02955e17 −1.39402
\(438\) 4.68089e16 0.316772
\(439\) −5.19055e16 −0.346094 −0.173047 0.984914i \(-0.555361\pi\)
−0.173047 + 0.984914i \(0.555361\pi\)
\(440\) −5.34603e16 −0.351228
\(441\) 6.76598e16 0.438006
\(442\) 1.15967e17 0.739755
\(443\) −1.57657e17 −0.991033 −0.495517 0.868598i \(-0.665021\pi\)
−0.495517 + 0.868598i \(0.665021\pi\)
\(444\) 8.41559e16 0.521309
\(445\) 7.40660e15 0.0452146
\(446\) 1.41071e17 0.848713
\(447\) −6.09190e16 −0.361205
\(448\) 4.18566e16 0.244600
\(449\) −1.00305e17 −0.577724 −0.288862 0.957371i \(-0.593277\pi\)
−0.288862 + 0.957371i \(0.593277\pi\)
\(450\) 2.34697e16 0.133238
\(451\) 1.49424e17 0.836127
\(452\) −3.54421e16 −0.195488
\(453\) −4.10983e16 −0.223453
\(454\) 2.99955e16 0.160766
\(455\) −9.69864e16 −0.512433
\(456\) −1.11285e17 −0.579650
\(457\) −5.63806e16 −0.289517 −0.144759 0.989467i \(-0.546241\pi\)
−0.144759 + 0.989467i \(0.546241\pi\)
\(458\) −9.18909e16 −0.465208
\(459\) 7.39019e16 0.368870
\(460\) −7.88136e16 −0.387860
\(461\) −1.20880e17 −0.586541 −0.293270 0.956030i \(-0.594744\pi\)
−0.293270 + 0.956030i \(0.594744\pi\)
\(462\) 8.58469e16 0.410726
\(463\) 1.67790e17 0.791572 0.395786 0.918343i \(-0.370472\pi\)
0.395786 + 0.918343i \(0.370472\pi\)
\(464\) −5.18284e16 −0.241102
\(465\) 7.46188e15 0.0342298
\(466\) −3.82569e15 −0.0173062
\(467\) 3.70336e17 1.65210 0.826049 0.563598i \(-0.190583\pi\)
0.826049 + 0.563598i \(0.190583\pi\)
\(468\) 4.55706e16 0.200487
\(469\) 6.19914e16 0.268972
\(470\) 8.49332e16 0.363447
\(471\) 5.77048e15 0.0243543
\(472\) 2.69114e16 0.112025
\(473\) 4.50052e17 1.84784
\(474\) −3.05399e15 −0.0123683
\(475\) 2.38971e17 0.954634
\(476\) −5.63323e17 −2.21979
\(477\) 1.30989e17 0.509173
\(478\) 1.31563e17 0.504489
\(479\) 6.66464e16 0.252114 0.126057 0.992023i \(-0.459768\pi\)
0.126057 + 0.992023i \(0.459768\pi\)
\(480\) −6.77511e16 −0.252842
\(481\) 2.54484e17 0.936951
\(482\) −6.12904e16 −0.222632
\(483\) 2.92794e17 1.04931
\(484\) 1.80107e16 0.0636847
\(485\) −2.43684e16 −0.0850169
\(486\) −9.10397e15 −0.0313397
\(487\) 3.56614e16 0.121132 0.0605662 0.998164i \(-0.480709\pi\)
0.0605662 + 0.998164i \(0.480709\pi\)
\(488\) 3.87135e17 1.29758
\(489\) −1.06666e16 −0.0352791
\(490\) −8.38674e16 −0.273727
\(491\) 2.91939e16 0.0940293 0.0470146 0.998894i \(-0.485029\pi\)
0.0470146 + 0.998894i \(0.485029\pi\)
\(492\) 1.20789e17 0.383932
\(493\) −4.32079e17 −1.35537
\(494\) −1.45461e17 −0.450319
\(495\) −4.45310e16 −0.136059
\(496\) 1.57208e16 0.0474071
\(497\) −4.98916e17 −1.48495
\(498\) −1.45038e17 −0.426080
\(499\) 6.02093e17 1.74586 0.872932 0.487842i \(-0.162216\pi\)
0.872932 + 0.487842i \(0.162216\pi\)
\(500\) 2.06222e17 0.590241
\(501\) −1.71960e17 −0.485828
\(502\) 1.91890e17 0.535154
\(503\) −2.10322e17 −0.579020 −0.289510 0.957175i \(-0.593492\pi\)
−0.289510 + 0.957175i \(0.593492\pi\)
\(504\) 1.60546e17 0.436316
\(505\) 1.04671e17 0.280822
\(506\) 2.10955e17 0.558743
\(507\) −8.29925e16 −0.217014
\(508\) 2.10203e17 0.542656
\(509\) 4.81081e17 1.22618 0.613088 0.790015i \(-0.289927\pi\)
0.613088 + 0.790015i \(0.289927\pi\)
\(510\) −9.16047e16 −0.230522
\(511\) −6.87589e17 −1.70841
\(512\) −2.62328e17 −0.643562
\(513\) −9.26976e16 −0.224546
\(514\) −2.91438e16 −0.0697086
\(515\) −9.35935e16 −0.221054
\(516\) 3.63807e17 0.848491
\(517\) 7.25177e17 1.67015
\(518\) 3.87532e17 0.881381
\(519\) −6.57999e16 −0.147787
\(520\) −1.30682e17 −0.289863
\(521\) 5.80316e16 0.127122 0.0635608 0.997978i \(-0.479754\pi\)
0.0635608 + 0.997978i \(0.479754\pi\)
\(522\) 5.32278e16 0.115154
\(523\) −2.89417e17 −0.618391 −0.309195 0.950999i \(-0.600060\pi\)
−0.309195 + 0.950999i \(0.600060\pi\)
\(524\) −2.90109e17 −0.612220
\(525\) −3.44753e17 −0.718576
\(526\) 1.66697e17 0.343179
\(527\) 1.31060e17 0.266502
\(528\) −9.38185e16 −0.188438
\(529\) 2.15458e17 0.427466
\(530\) −1.62367e17 −0.318203
\(531\) 2.24165e16 0.0433963
\(532\) 7.06594e17 1.35128
\(533\) 3.65260e17 0.690042
\(534\) −1.60256e16 −0.0299087
\(535\) −3.96962e16 −0.0731896
\(536\) 8.35285e16 0.152147
\(537\) −3.45370e17 −0.621515
\(538\) 4.18683e16 0.0744390
\(539\) −7.16076e17 −1.25786
\(540\) −3.59973e16 −0.0624756
\(541\) −2.95677e17 −0.507032 −0.253516 0.967331i \(-0.581587\pi\)
−0.253516 + 0.967331i \(0.581587\pi\)
\(542\) −6.00395e16 −0.101728
\(543\) −2.87490e17 −0.481309
\(544\) −1.18998e18 −1.96854
\(545\) 4.10087e17 0.670346
\(546\) 2.09849e17 0.338965
\(547\) −9.39910e17 −1.50027 −0.750134 0.661286i \(-0.770011\pi\)
−0.750134 + 0.661286i \(0.770011\pi\)
\(548\) 7.71781e17 1.21736
\(549\) 3.22473e17 0.502659
\(550\) −2.48391e17 −0.382630
\(551\) 5.41971e17 0.825070
\(552\) 3.94517e17 0.593555
\(553\) 4.48609e16 0.0667044
\(554\) −6.43122e17 −0.945105
\(555\) −2.01023e17 −0.291972
\(556\) −8.65039e16 −0.124179
\(557\) 6.16218e17 0.874330 0.437165 0.899381i \(-0.355983\pi\)
0.437165 + 0.899381i \(0.355983\pi\)
\(558\) −1.61453e16 −0.0226424
\(559\) 1.10013e18 1.52500
\(560\) 1.61407e17 0.221157
\(561\) −7.82139e17 −1.05932
\(562\) 4.81620e17 0.644790
\(563\) −6.77170e17 −0.896175 −0.448088 0.893990i \(-0.647895\pi\)
−0.448088 + 0.893990i \(0.647895\pi\)
\(564\) 5.86208e17 0.766897
\(565\) 8.46603e16 0.109488
\(566\) −5.67863e16 −0.0726001
\(567\) 1.33731e17 0.169021
\(568\) −6.72250e17 −0.839976
\(569\) −4.29749e17 −0.530866 −0.265433 0.964129i \(-0.585515\pi\)
−0.265433 + 0.964129i \(0.585515\pi\)
\(570\) 1.14903e17 0.140328
\(571\) 1.18834e18 1.43485 0.717423 0.696637i \(-0.245321\pi\)
0.717423 + 0.696637i \(0.245321\pi\)
\(572\) −4.82295e17 −0.575757
\(573\) 8.17726e17 0.965168
\(574\) 5.56224e17 0.649117
\(575\) −8.47176e17 −0.977536
\(576\) 4.69784e16 0.0535984
\(577\) −2.62221e17 −0.295818 −0.147909 0.989001i \(-0.547254\pi\)
−0.147909 + 0.989001i \(0.547254\pi\)
\(578\) −1.17098e18 −1.30623
\(579\) −6.96881e17 −0.768685
\(580\) 2.10464e17 0.229560
\(581\) 2.13050e18 2.29793
\(582\) 5.27258e16 0.0562372
\(583\) −1.38632e18 −1.46224
\(584\) −9.26471e17 −0.966381
\(585\) −1.08854e17 −0.112288
\(586\) 7.25116e17 0.739729
\(587\) −1.57347e18 −1.58749 −0.793745 0.608250i \(-0.791872\pi\)
−0.793745 + 0.608250i \(0.791872\pi\)
\(588\) −5.78851e17 −0.577583
\(589\) −1.64393e17 −0.162231
\(590\) −2.77862e16 −0.0271201
\(591\) 9.41347e17 0.908722
\(592\) −4.23518e17 −0.404371
\(593\) −8.97746e17 −0.847809 −0.423904 0.905707i \(-0.639341\pi\)
−0.423904 + 0.905707i \(0.639341\pi\)
\(594\) 9.63516e16 0.0900010
\(595\) 1.34561e18 1.24325
\(596\) 5.21181e17 0.476308
\(597\) −1.70662e17 −0.154278
\(598\) 5.15672e17 0.461122
\(599\) 9.76390e17 0.863673 0.431836 0.901952i \(-0.357866\pi\)
0.431836 + 0.901952i \(0.357866\pi\)
\(600\) −4.64527e17 −0.406470
\(601\) 1.28535e18 1.11260 0.556299 0.830982i \(-0.312221\pi\)
0.556299 + 0.830982i \(0.312221\pi\)
\(602\) 1.67530e18 1.43455
\(603\) 6.95770e16 0.0589390
\(604\) 3.51609e17 0.294659
\(605\) −4.30220e16 −0.0356682
\(606\) −2.26476e17 −0.185759
\(607\) −2.35015e18 −1.90708 −0.953539 0.301269i \(-0.902590\pi\)
−0.953539 + 0.301269i \(0.902590\pi\)
\(608\) 1.49262e18 1.19833
\(609\) −7.81877e17 −0.621049
\(610\) −3.99720e17 −0.314132
\(611\) 1.77267e18 1.37835
\(612\) −6.32254e17 −0.486416
\(613\) 1.19210e18 0.907444 0.453722 0.891143i \(-0.350096\pi\)
0.453722 + 0.891143i \(0.350096\pi\)
\(614\) −5.10495e17 −0.384500
\(615\) −2.88528e17 −0.215030
\(616\) −1.69914e18 −1.25301
\(617\) −1.32168e18 −0.964435 −0.482218 0.876051i \(-0.660169\pi\)
−0.482218 + 0.876051i \(0.660169\pi\)
\(618\) 2.02508e17 0.146223
\(619\) −1.31387e18 −0.938780 −0.469390 0.882991i \(-0.655526\pi\)
−0.469390 + 0.882991i \(0.655526\pi\)
\(620\) −6.38387e16 −0.0451376
\(621\) 3.28622e17 0.229933
\(622\) 1.14197e17 0.0790708
\(623\) 2.35405e17 0.161303
\(624\) −2.29336e17 −0.155515
\(625\) 7.26584e17 0.487603
\(626\) −6.99421e17 −0.464521
\(627\) 9.81063e17 0.644848
\(628\) −4.93682e16 −0.0321151
\(629\) −3.53075e18 −2.27320
\(630\) −1.65765e17 −0.105628
\(631\) 2.19393e17 0.138367 0.0691834 0.997604i \(-0.477961\pi\)
0.0691834 + 0.997604i \(0.477961\pi\)
\(632\) 6.04465e16 0.0377320
\(633\) −1.63103e18 −1.00772
\(634\) −5.46555e16 −0.0334237
\(635\) −5.02110e17 −0.303928
\(636\) −1.12065e18 −0.671429
\(637\) −1.75042e18 −1.03809
\(638\) −5.63335e17 −0.330699
\(639\) −5.59967e17 −0.325392
\(640\) 7.03109e17 0.404439
\(641\) 9.07607e17 0.516798 0.258399 0.966038i \(-0.416805\pi\)
0.258399 + 0.966038i \(0.416805\pi\)
\(642\) 8.58906e16 0.0484136
\(643\) 1.88340e18 1.05092 0.525462 0.850817i \(-0.323893\pi\)
0.525462 + 0.850817i \(0.323893\pi\)
\(644\) −2.50494e18 −1.38369
\(645\) −8.69023e17 −0.475218
\(646\) 2.01814e18 1.09255
\(647\) 1.34923e18 0.723118 0.361559 0.932349i \(-0.382245\pi\)
0.361559 + 0.932349i \(0.382245\pi\)
\(648\) 1.80191e17 0.0956085
\(649\) −2.37244e17 −0.124625
\(650\) −6.07182e17 −0.315778
\(651\) 2.37162e17 0.122115
\(652\) 9.12560e16 0.0465213
\(653\) 1.71614e18 0.866199 0.433100 0.901346i \(-0.357420\pi\)
0.433100 + 0.901346i \(0.357420\pi\)
\(654\) −8.87305e17 −0.443422
\(655\) 6.92981e17 0.342889
\(656\) −6.07875e17 −0.297810
\(657\) −7.71726e17 −0.374359
\(658\) 2.69944e18 1.29660
\(659\) −1.28135e18 −0.609415 −0.304708 0.952446i \(-0.598559\pi\)
−0.304708 + 0.952446i \(0.598559\pi\)
\(660\) 3.80977e17 0.179417
\(661\) −1.79244e18 −0.835864 −0.417932 0.908478i \(-0.637245\pi\)
−0.417932 + 0.908478i \(0.637245\pi\)
\(662\) −1.07840e17 −0.0497971
\(663\) −1.91191e18 −0.874237
\(664\) 2.87069e18 1.29985
\(665\) −1.68784e18 −0.756815
\(666\) 4.34952e17 0.193134
\(667\) −1.92134e18 −0.844863
\(668\) 1.47117e18 0.640644
\(669\) −2.32580e18 −1.00300
\(670\) −8.62438e16 −0.0368334
\(671\) −3.41289e18 −1.44353
\(672\) −2.15334e18 −0.902013
\(673\) 6.34042e16 0.0263039 0.0131519 0.999914i \(-0.495813\pi\)
0.0131519 + 0.999914i \(0.495813\pi\)
\(674\) 1.65316e18 0.679242
\(675\) −3.86939e17 −0.157459
\(676\) 7.10026e17 0.286168
\(677\) −9.29177e17 −0.370913 −0.185457 0.982652i \(-0.559376\pi\)
−0.185457 + 0.982652i \(0.559376\pi\)
\(678\) −1.83179e17 −0.0724242
\(679\) −7.74504e17 −0.303298
\(680\) 1.81310e18 0.703256
\(681\) −4.94528e17 −0.189992
\(682\) 1.70873e17 0.0650242
\(683\) −3.07516e18 −1.15913 −0.579566 0.814925i \(-0.696778\pi\)
−0.579566 + 0.814925i \(0.696778\pi\)
\(684\) 7.93057e17 0.296101
\(685\) −1.84355e18 −0.681814
\(686\) −6.37005e17 −0.233365
\(687\) 1.51498e18 0.549779
\(688\) −1.83087e18 −0.658162
\(689\) −3.38880e18 −1.20676
\(690\) −4.07341e17 −0.143694
\(691\) −2.73730e18 −0.956565 −0.478283 0.878206i \(-0.658741\pi\)
−0.478283 + 0.878206i \(0.658741\pi\)
\(692\) 5.62939e17 0.194882
\(693\) −1.41533e18 −0.485392
\(694\) −3.08580e17 −0.104841
\(695\) 2.06631e17 0.0695497
\(696\) −1.05352e18 −0.351303
\(697\) −5.06768e18 −1.67416
\(698\) −1.73850e18 −0.569004
\(699\) 6.30730e16 0.0204523
\(700\) 2.94947e18 0.947560
\(701\) −4.73652e17 −0.150762 −0.0753811 0.997155i \(-0.524017\pi\)
−0.0753811 + 0.997155i \(0.524017\pi\)
\(702\) 2.35528e17 0.0742764
\(703\) 4.42873e18 1.38379
\(704\) −4.97194e17 −0.153923
\(705\) −1.40027e18 −0.429519
\(706\) −1.32582e17 −0.0402954
\(707\) 3.32676e18 1.00183
\(708\) −1.91780e17 −0.0572251
\(709\) 2.44513e18 0.722938 0.361469 0.932384i \(-0.382275\pi\)
0.361469 + 0.932384i \(0.382275\pi\)
\(710\) 6.94103e17 0.203350
\(711\) 5.03503e16 0.0146167
\(712\) 3.17189e17 0.0912428
\(713\) 5.82788e17 0.166123
\(714\) −2.91148e18 −0.822387
\(715\) 1.15206e18 0.322466
\(716\) 2.95475e18 0.819570
\(717\) −2.16904e18 −0.596202
\(718\) 1.31789e18 0.358981
\(719\) 4.08649e18 1.10309 0.551547 0.834144i \(-0.314038\pi\)
0.551547 + 0.834144i \(0.314038\pi\)
\(720\) 1.81158e17 0.0484614
\(721\) −2.97469e18 −0.788611
\(722\) −6.71950e17 −0.176541
\(723\) 1.01048e18 0.263104
\(724\) 2.45957e18 0.634685
\(725\) 2.26230e18 0.578566
\(726\) 9.30866e16 0.0235939
\(727\) 7.13650e18 1.79272 0.896358 0.443331i \(-0.146203\pi\)
0.896358 + 0.443331i \(0.146203\pi\)
\(728\) −4.15347e18 −1.03409
\(729\) 1.50095e17 0.0370370
\(730\) 9.56589e17 0.233952
\(731\) −1.52635e19 −3.69990
\(732\) −2.75886e18 −0.662838
\(733\) 2.80764e18 0.668598 0.334299 0.942467i \(-0.391501\pi\)
0.334299 + 0.942467i \(0.391501\pi\)
\(734\) 1.03159e18 0.243490
\(735\) 1.38270e18 0.323489
\(736\) −5.29150e18 −1.22708
\(737\) −7.36366e17 −0.169260
\(738\) 6.24287e17 0.142239
\(739\) 4.67894e18 1.05672 0.528359 0.849021i \(-0.322808\pi\)
0.528359 + 0.849021i \(0.322808\pi\)
\(740\) 1.71981e18 0.385013
\(741\) 2.39817e18 0.532183
\(742\) −5.16053e18 −1.13519
\(743\) 7.01746e18 1.53022 0.765108 0.643902i \(-0.222686\pi\)
0.765108 + 0.643902i \(0.222686\pi\)
\(744\) 3.19557e17 0.0690755
\(745\) −1.24494e18 −0.266768
\(746\) 3.59105e18 0.762814
\(747\) 2.39120e18 0.503539
\(748\) 6.69145e18 1.39688
\(749\) −1.26167e18 −0.261104
\(750\) 1.06584e18 0.218672
\(751\) 6.91693e18 1.40687 0.703434 0.710760i \(-0.251649\pi\)
0.703434 + 0.710760i \(0.251649\pi\)
\(752\) −2.95011e18 −0.594870
\(753\) −3.16364e18 −0.632441
\(754\) −1.37705e18 −0.272920
\(755\) −8.39887e17 −0.165031
\(756\) −1.14411e18 −0.222882
\(757\) −4.84887e18 −0.936520 −0.468260 0.883591i \(-0.655119\pi\)
−0.468260 + 0.883591i \(0.655119\pi\)
\(758\) 4.67031e18 0.894326
\(759\) −3.47796e18 −0.660318
\(760\) −2.27423e18 −0.428100
\(761\) −9.04988e18 −1.68905 −0.844525 0.535517i \(-0.820117\pi\)
−0.844525 + 0.535517i \(0.820117\pi\)
\(762\) 1.08642e18 0.201043
\(763\) 1.30339e19 2.39146
\(764\) −6.99590e18 −1.27273
\(765\) 1.51026e18 0.272429
\(766\) −3.38569e16 −0.00605565
\(767\) −5.79934e17 −0.102851
\(768\) −2.04922e18 −0.360364
\(769\) −2.90761e18 −0.507007 −0.253504 0.967334i \(-0.581583\pi\)
−0.253504 + 0.967334i \(0.581583\pi\)
\(770\) 1.75437e18 0.303341
\(771\) 4.80487e17 0.0823811
\(772\) 5.96204e18 1.01364
\(773\) 1.55467e18 0.262103 0.131052 0.991376i \(-0.458165\pi\)
0.131052 + 0.991376i \(0.458165\pi\)
\(774\) 1.88030e18 0.314349
\(775\) −6.86209e17 −0.113762
\(776\) −1.04358e18 −0.171564
\(777\) −6.38913e18 −1.04161
\(778\) 2.96367e18 0.479140
\(779\) 6.35656e18 1.01913
\(780\) 9.31282e17 0.148070
\(781\) 5.92639e18 0.934456
\(782\) −7.15451e18 −1.11876
\(783\) −8.77552e17 −0.136088
\(784\) 2.91309e18 0.448022
\(785\) 1.17926e17 0.0179869
\(786\) −1.49940e18 −0.226815
\(787\) 5.65108e18 0.847805 0.423902 0.905708i \(-0.360660\pi\)
0.423902 + 0.905708i \(0.360660\pi\)
\(788\) −8.05352e18 −1.19830
\(789\) −2.74829e18 −0.405566
\(790\) −6.24115e16 −0.00913458
\(791\) 2.69077e18 0.390597
\(792\) −1.90705e18 −0.274567
\(793\) −8.34267e18 −1.19132
\(794\) −5.31068e18 −0.752172
\(795\) 2.67690e18 0.376050
\(796\) 1.46007e18 0.203441
\(797\) −2.10870e18 −0.291430 −0.145715 0.989327i \(-0.546548\pi\)
−0.145715 + 0.989327i \(0.546548\pi\)
\(798\) 3.65197e18 0.500620
\(799\) −2.45943e19 −3.34410
\(800\) 6.23052e18 0.840310
\(801\) 2.64210e17 0.0353458
\(802\) 2.81397e18 0.373410
\(803\) 8.16754e18 1.07508
\(804\) −5.95253e17 −0.0777208
\(805\) 5.98354e18 0.774971
\(806\) 4.17692e17 0.0536634
\(807\) −6.90271e17 −0.0879714
\(808\) 4.48255e18 0.566697
\(809\) 4.06041e18 0.509219 0.254609 0.967044i \(-0.418053\pi\)
0.254609 + 0.967044i \(0.418053\pi\)
\(810\) −1.86049e17 −0.0231459
\(811\) 7.82447e17 0.0965650 0.0482825 0.998834i \(-0.484625\pi\)
0.0482825 + 0.998834i \(0.484625\pi\)
\(812\) 6.68920e18 0.818955
\(813\) 9.89854e17 0.120222
\(814\) −4.60331e18 −0.554640
\(815\) −2.17983e17 −0.0260554
\(816\) 3.18184e18 0.377305
\(817\) 1.91454e19 2.25228
\(818\) −3.08208e18 −0.359706
\(819\) −3.45973e18 −0.400587
\(820\) 2.46845e18 0.283553
\(821\) 8.67478e18 0.988617 0.494308 0.869287i \(-0.335421\pi\)
0.494308 + 0.869287i \(0.335421\pi\)
\(822\) 3.98888e18 0.451008
\(823\) −2.87394e18 −0.322388 −0.161194 0.986923i \(-0.551534\pi\)
−0.161194 + 0.986923i \(0.551534\pi\)
\(824\) −4.00816e18 −0.446086
\(825\) 4.09516e18 0.452189
\(826\) −8.83132e17 −0.0967510
\(827\) −8.01024e18 −0.870682 −0.435341 0.900266i \(-0.643372\pi\)
−0.435341 + 0.900266i \(0.643372\pi\)
\(828\) −2.81146e18 −0.303204
\(829\) −9.97891e18 −1.06777 −0.533886 0.845556i \(-0.679269\pi\)
−0.533886 + 0.845556i \(0.679269\pi\)
\(830\) −2.96400e18 −0.314681
\(831\) 1.06030e19 1.11692
\(832\) −1.21537e18 −0.127030
\(833\) 2.42856e19 2.51858
\(834\) −4.47088e17 −0.0460059
\(835\) −3.51418e18 −0.358808
\(836\) −8.39330e18 −0.850338
\(837\) 2.66183e17 0.0267586
\(838\) −1.97028e18 −0.196536
\(839\) 1.57978e19 1.56366 0.781831 0.623491i \(-0.214286\pi\)
0.781831 + 0.623491i \(0.214286\pi\)
\(840\) 3.28092e18 0.322241
\(841\) −5.12988e18 −0.499958
\(842\) 4.06714e18 0.393333
\(843\) −7.94033e18 −0.762008
\(844\) 1.39540e19 1.32884
\(845\) −1.69604e18 −0.160275
\(846\) 3.02976e18 0.284120
\(847\) −1.36737e18 −0.127246
\(848\) 5.63973e18 0.520817
\(849\) 9.36221e17 0.0857982
\(850\) 8.42415e18 0.766131
\(851\) −1.57003e19 −1.41699
\(852\) 4.79069e18 0.429082
\(853\) 7.10936e17 0.0631919 0.0315960 0.999501i \(-0.489941\pi\)
0.0315960 + 0.999501i \(0.489941\pi\)
\(854\) −1.27043e19 −1.12067
\(855\) −1.89437e18 −0.165838
\(856\) −1.70000e18 −0.147696
\(857\) 1.28817e19 1.11070 0.555350 0.831617i \(-0.312584\pi\)
0.555350 + 0.831617i \(0.312584\pi\)
\(858\) −2.49270e18 −0.213306
\(859\) 2.25964e19 1.91904 0.959519 0.281645i \(-0.0908800\pi\)
0.959519 + 0.281645i \(0.0908800\pi\)
\(860\) 7.43476e18 0.626653
\(861\) −9.17032e18 −0.767121
\(862\) 1.62054e18 0.134543
\(863\) −1.69103e19 −1.39341 −0.696707 0.717356i \(-0.745352\pi\)
−0.696707 + 0.717356i \(0.745352\pi\)
\(864\) −2.41684e18 −0.197655
\(865\) −1.34469e18 −0.109148
\(866\) 2.18381e18 0.175933
\(867\) 1.93057e19 1.54369
\(868\) −2.02899e18 −0.161029
\(869\) −5.32882e17 −0.0419761
\(870\) 1.08776e18 0.0850471
\(871\) −1.80002e18 −0.139688
\(872\) 1.75621e19 1.35276
\(873\) −8.69276e17 −0.0664608
\(874\) 8.97414e18 0.681033
\(875\) −1.56564e19 −1.17934
\(876\) 6.60236e18 0.493654
\(877\) −2.01142e19 −1.49281 −0.746405 0.665491i \(-0.768222\pi\)
−0.746405 + 0.665491i \(0.768222\pi\)
\(878\) 2.29513e18 0.169080
\(879\) −1.19548e19 −0.874207
\(880\) −1.91728e18 −0.139171
\(881\) −1.66197e19 −1.19751 −0.598754 0.800933i \(-0.704337\pi\)
−0.598754 + 0.800933i \(0.704337\pi\)
\(882\) −2.99174e18 −0.213982
\(883\) 1.56643e19 1.11216 0.556079 0.831129i \(-0.312305\pi\)
0.556079 + 0.831129i \(0.312305\pi\)
\(884\) 1.63570e19 1.15282
\(885\) 4.58104e17 0.0320503
\(886\) 6.97117e18 0.484157
\(887\) 1.06391e19 0.733504 0.366752 0.930319i \(-0.380470\pi\)
0.366752 + 0.930319i \(0.380470\pi\)
\(888\) −8.60885e18 −0.589197
\(889\) −1.59586e19 −1.08426
\(890\) −3.27500e17 −0.0220890
\(891\) −1.58852e18 −0.106362
\(892\) 1.98979e19 1.32262
\(893\) 3.08494e19 2.03569
\(894\) 2.69368e18 0.176462
\(895\) −7.05799e18 −0.459020
\(896\) 2.23470e19 1.44284
\(897\) −8.50174e18 −0.544950
\(898\) 4.43521e18 0.282240
\(899\) −1.55628e18 −0.0983217
\(900\) 3.31038e18 0.207636
\(901\) 4.70168e19 2.92781
\(902\) −6.60713e18 −0.408479
\(903\) −2.76203e19 −1.69534
\(904\) 3.62560e18 0.220945
\(905\) −5.87516e18 −0.355471
\(906\) 1.81726e18 0.109165
\(907\) 8.52215e18 0.508278 0.254139 0.967168i \(-0.418208\pi\)
0.254139 + 0.967168i \(0.418208\pi\)
\(908\) 4.23084e18 0.250535
\(909\) 3.73384e18 0.219528
\(910\) 4.28849e18 0.250343
\(911\) −1.45978e19 −0.846092 −0.423046 0.906108i \(-0.639039\pi\)
−0.423046 + 0.906108i \(0.639039\pi\)
\(912\) −3.99109e18 −0.229681
\(913\) −2.53073e19 −1.44606
\(914\) 2.49300e18 0.141440
\(915\) 6.59007e18 0.371239
\(916\) −1.29611e19 −0.724974
\(917\) 2.20251e19 1.22326
\(918\) −3.26775e18 −0.180207
\(919\) 3.06603e19 1.67890 0.839450 0.543437i \(-0.182877\pi\)
0.839450 + 0.543437i \(0.182877\pi\)
\(920\) 8.06235e18 0.438370
\(921\) 8.41639e18 0.454400
\(922\) 5.34499e18 0.286547
\(923\) 1.44868e19 0.771192
\(924\) 1.21086e19 0.640069
\(925\) 1.84864e19 0.970358
\(926\) −7.41925e18 −0.386713
\(927\) −3.33869e18 −0.172806
\(928\) 1.41304e19 0.726262
\(929\) −3.57344e19 −1.82383 −0.911916 0.410378i \(-0.865397\pi\)
−0.911916 + 0.410378i \(0.865397\pi\)
\(930\) −3.29945e17 −0.0167225
\(931\) −3.04622e19 −1.53316
\(932\) −5.39609e17 −0.0269697
\(933\) −1.88273e18 −0.0934453
\(934\) −1.63753e19 −0.807112
\(935\) −1.59838e19 −0.782357
\(936\) −4.66171e18 −0.226596
\(937\) 3.54595e19 1.71169 0.855844 0.517233i \(-0.173038\pi\)
0.855844 + 0.517233i \(0.173038\pi\)
\(938\) −2.74110e18 −0.131403
\(939\) 1.15312e19 0.548967
\(940\) 1.19798e19 0.566392
\(941\) −3.26670e19 −1.53383 −0.766915 0.641749i \(-0.778209\pi\)
−0.766915 + 0.641749i \(0.778209\pi\)
\(942\) −2.55155e17 −0.0118980
\(943\) −2.25346e19 −1.04358
\(944\) 9.65139e17 0.0443886
\(945\) 2.73292e18 0.124830
\(946\) −1.99001e19 −0.902742
\(947\) −1.43139e19 −0.644886 −0.322443 0.946589i \(-0.604504\pi\)
−0.322443 + 0.946589i \(0.604504\pi\)
\(948\) −4.30763e17 −0.0192745
\(949\) 1.99652e19 0.887246
\(950\) −1.05667e19 −0.466375
\(951\) 9.01091e17 0.0394998
\(952\) 5.76259e19 2.50887
\(953\) 5.17993e18 0.223986 0.111993 0.993709i \(-0.464277\pi\)
0.111993 + 0.993709i \(0.464277\pi\)
\(954\) −5.79200e18 −0.248750
\(955\) 1.67111e19 0.712824
\(956\) 1.85568e19 0.786190
\(957\) 9.28755e18 0.390817
\(958\) −2.94693e18 −0.123167
\(959\) −5.85938e19 −2.43238
\(960\) 9.60051e17 0.0395851
\(961\) −2.39455e19 −0.980667
\(962\) −1.12526e19 −0.457736
\(963\) −1.41605e18 −0.0572149
\(964\) −8.64496e18 −0.346946
\(965\) −1.42415e19 −0.567712
\(966\) −1.29466e19 −0.512630
\(967\) 7.35443e18 0.289252 0.144626 0.989486i \(-0.453802\pi\)
0.144626 + 0.989486i \(0.453802\pi\)
\(968\) −1.84243e18 −0.0719782
\(969\) −3.32726e19 −1.29117
\(970\) 1.07751e18 0.0415340
\(971\) 4.34657e18 0.166426 0.0832131 0.996532i \(-0.473482\pi\)
0.0832131 + 0.996532i \(0.473482\pi\)
\(972\) −1.28411e18 −0.0488394
\(973\) 6.56739e18 0.248119
\(974\) −1.57685e18 −0.0591777
\(975\) 1.00105e19 0.373185
\(976\) 1.38841e19 0.514153
\(977\) 1.39032e19 0.511445 0.255722 0.966750i \(-0.417687\pi\)
0.255722 + 0.966750i \(0.417687\pi\)
\(978\) 4.71649e17 0.0172352
\(979\) −2.79626e18 −0.101506
\(980\) −1.18294e19 −0.426573
\(981\) 1.46288e19 0.524033
\(982\) −1.29088e18 −0.0459369
\(983\) −5.29076e19 −1.87034 −0.935170 0.354199i \(-0.884753\pi\)
−0.935170 + 0.354199i \(0.884753\pi\)
\(984\) −1.23563e19 −0.433930
\(985\) 1.92374e19 0.671136
\(986\) 1.91054e19 0.662150
\(987\) −4.45050e19 −1.53231
\(988\) −2.05171e19 −0.701771
\(989\) −6.78724e19 −2.30631
\(990\) 1.96904e18 0.0664702
\(991\) −7.55353e18 −0.253321 −0.126660 0.991946i \(-0.540426\pi\)
−0.126660 + 0.991946i \(0.540426\pi\)
\(992\) −4.28610e18 −0.142803
\(993\) 1.77793e18 0.0588498
\(994\) 2.20608e19 0.725453
\(995\) −3.48765e18 −0.113942
\(996\) −2.04575e19 −0.663998
\(997\) 3.67023e19 1.18352 0.591759 0.806115i \(-0.298434\pi\)
0.591759 + 0.806115i \(0.298434\pi\)
\(998\) −2.66230e19 −0.852920
\(999\) −7.17094e18 −0.228245
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.1.12 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.12 30 1.1 even 1 trivial