Properties

Label 177.14.a.a.1.17
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 1.17
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+20.2681 q^{2} +729.000 q^{3} -7781.20 q^{4} +37235.2 q^{5} +14775.5 q^{6} -260203. q^{7} -323747. q^{8} +531441. q^{9} +O(q^{10})\) \(q+20.2681 q^{2} +729.000 q^{3} -7781.20 q^{4} +37235.2 q^{5} +14775.5 q^{6} -260203. q^{7} -323747. q^{8} +531441. q^{9} +754688. q^{10} -3.65189e6 q^{11} -5.67250e6 q^{12} -1.12723e7 q^{13} -5.27384e6 q^{14} +2.71444e7 q^{15} +5.71819e7 q^{16} +1.19917e6 q^{17} +1.07713e7 q^{18} +2.27610e8 q^{19} -2.89734e8 q^{20} -1.89688e8 q^{21} -7.40171e7 q^{22} +8.27084e8 q^{23} -2.36012e8 q^{24} +1.65755e8 q^{25} -2.28469e8 q^{26} +3.87420e8 q^{27} +2.02469e9 q^{28} +1.28935e9 q^{29} +5.50167e8 q^{30} +3.95570e9 q^{31} +3.81111e9 q^{32} -2.66223e9 q^{33} +2.43049e7 q^{34} -9.68871e9 q^{35} -4.13525e9 q^{36} -9.79767e9 q^{37} +4.61323e9 q^{38} -8.21754e9 q^{39} -1.20548e10 q^{40} -3.95888e10 q^{41} -3.84463e9 q^{42} +6.25386e10 q^{43} +2.84161e10 q^{44} +1.97883e10 q^{45} +1.67634e10 q^{46} -8.64293e10 q^{47} +4.16856e10 q^{48} -2.91833e10 q^{49} +3.35954e9 q^{50} +8.74193e8 q^{51} +8.77124e10 q^{52} -6.34614e10 q^{53} +7.85229e9 q^{54} -1.35979e11 q^{55} +8.42401e10 q^{56} +1.65928e11 q^{57} +2.61327e10 q^{58} +4.21805e10 q^{59} -2.11216e11 q^{60} +2.34994e11 q^{61} +8.01746e10 q^{62} -1.38283e11 q^{63} -3.91190e11 q^{64} -4.19728e11 q^{65} -5.39585e10 q^{66} -1.03321e12 q^{67} -9.33097e9 q^{68} +6.02944e11 q^{69} -1.96372e11 q^{70} -1.82046e12 q^{71} -1.72052e11 q^{72} +2.32022e12 q^{73} -1.98581e11 q^{74} +1.20835e11 q^{75} -1.77108e12 q^{76} +9.50235e11 q^{77} -1.66554e11 q^{78} -8.66988e11 q^{79} +2.12918e12 q^{80} +2.82430e11 q^{81} -8.02391e11 q^{82} +4.79621e12 q^{83} +1.47600e12 q^{84} +4.46512e10 q^{85} +1.26754e12 q^{86} +9.39937e11 q^{87} +1.18229e12 q^{88} -1.11732e12 q^{89} +4.01072e11 q^{90} +2.93310e12 q^{91} -6.43571e12 q^{92} +2.88370e12 q^{93} -1.75176e12 q^{94} +8.47509e12 q^{95} +2.77830e12 q^{96} -5.79568e12 q^{97} -5.91490e11 q^{98} -1.94077e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 20.2681 0.223933 0.111967 0.993712i \(-0.464285\pi\)
0.111967 + 0.993712i \(0.464285\pi\)
\(3\) 729.000 0.577350
\(4\) −7781.20 −0.949854
\(5\) 37235.2 1.06573 0.532866 0.846199i \(-0.321115\pi\)
0.532866 + 0.846199i \(0.321115\pi\)
\(6\) 14775.5 0.129288
\(7\) −260203. −0.835941 −0.417970 0.908461i \(-0.637258\pi\)
−0.417970 + 0.908461i \(0.637258\pi\)
\(8\) −323747. −0.436637
\(9\) 531441. 0.333333
\(10\) 754688. 0.238653
\(11\) −3.65189e6 −0.621535 −0.310768 0.950486i \(-0.600586\pi\)
−0.310768 + 0.950486i \(0.600586\pi\)
\(12\) −5.67250e6 −0.548398
\(13\) −1.12723e7 −0.647713 −0.323856 0.946106i \(-0.604979\pi\)
−0.323856 + 0.946106i \(0.604979\pi\)
\(14\) −5.27384e6 −0.187195
\(15\) 2.71444e7 0.615301
\(16\) 5.71819e7 0.852076
\(17\) 1.19917e6 0.0120493 0.00602465 0.999982i \(-0.498082\pi\)
0.00602465 + 0.999982i \(0.498082\pi\)
\(18\) 1.07713e7 0.0746445
\(19\) 2.27610e8 1.10992 0.554961 0.831876i \(-0.312733\pi\)
0.554961 + 0.831876i \(0.312733\pi\)
\(20\) −2.89734e8 −1.01229
\(21\) −1.89688e8 −0.482631
\(22\) −7.40171e7 −0.139182
\(23\) 8.27084e8 1.16498 0.582490 0.812838i \(-0.302078\pi\)
0.582490 + 0.812838i \(0.302078\pi\)
\(24\) −2.36012e8 −0.252093
\(25\) 1.65755e8 0.135786
\(26\) −2.28469e8 −0.145045
\(27\) 3.87420e8 0.192450
\(28\) 2.02469e9 0.794022
\(29\) 1.28935e9 0.402517 0.201258 0.979538i \(-0.435497\pi\)
0.201258 + 0.979538i \(0.435497\pi\)
\(30\) 5.50167e8 0.137786
\(31\) 3.95570e9 0.800520 0.400260 0.916402i \(-0.368920\pi\)
0.400260 + 0.916402i \(0.368920\pi\)
\(32\) 3.81111e9 0.627446
\(33\) −2.66223e9 −0.358843
\(34\) 2.43049e7 0.00269824
\(35\) −9.68871e9 −0.890889
\(36\) −4.13525e9 −0.316618
\(37\) −9.79767e9 −0.627786 −0.313893 0.949458i \(-0.601633\pi\)
−0.313893 + 0.949458i \(0.601633\pi\)
\(38\) 4.61323e9 0.248549
\(39\) −8.21754e9 −0.373957
\(40\) −1.20548e10 −0.465339
\(41\) −3.95888e10 −1.30160 −0.650799 0.759250i \(-0.725566\pi\)
−0.650799 + 0.759250i \(0.725566\pi\)
\(42\) −3.84463e9 −0.108077
\(43\) 6.25386e10 1.50870 0.754351 0.656471i \(-0.227952\pi\)
0.754351 + 0.656471i \(0.227952\pi\)
\(44\) 2.84161e10 0.590367
\(45\) 1.97883e10 0.355244
\(46\) 1.67634e10 0.260878
\(47\) −8.64293e10 −1.16957 −0.584783 0.811190i \(-0.698820\pi\)
−0.584783 + 0.811190i \(0.698820\pi\)
\(48\) 4.16856e10 0.491946
\(49\) −2.91833e10 −0.301203
\(50\) 3.35954e9 0.0304071
\(51\) 8.74193e8 0.00695667
\(52\) 8.77124e10 0.615232
\(53\) −6.34614e10 −0.393293 −0.196647 0.980474i \(-0.563005\pi\)
−0.196647 + 0.980474i \(0.563005\pi\)
\(54\) 7.85229e9 0.0430960
\(55\) −1.35979e11 −0.662390
\(56\) 8.42401e10 0.365003
\(57\) 1.65928e11 0.640814
\(58\) 2.61327e10 0.0901370
\(59\) 4.21805e10 0.130189
\(60\) −2.11216e11 −0.584446
\(61\) 2.34994e11 0.584001 0.292001 0.956418i \(-0.405679\pi\)
0.292001 + 0.956418i \(0.405679\pi\)
\(62\) 8.01746e10 0.179263
\(63\) −1.38283e11 −0.278647
\(64\) −3.91190e11 −0.711570
\(65\) −4.19728e11 −0.690289
\(66\) −5.39585e10 −0.0803570
\(67\) −1.03321e12 −1.39541 −0.697705 0.716385i \(-0.745795\pi\)
−0.697705 + 0.716385i \(0.745795\pi\)
\(68\) −9.33097e9 −0.0114451
\(69\) 6.02944e11 0.672602
\(70\) −1.96372e11 −0.199500
\(71\) −1.82046e12 −1.68656 −0.843279 0.537477i \(-0.819378\pi\)
−0.843279 + 0.537477i \(0.819378\pi\)
\(72\) −1.72052e11 −0.145546
\(73\) 2.32022e12 1.79445 0.897223 0.441578i \(-0.145581\pi\)
0.897223 + 0.441578i \(0.145581\pi\)
\(74\) −1.98581e11 −0.140582
\(75\) 1.20835e11 0.0783962
\(76\) −1.77108e12 −1.05426
\(77\) 9.50235e11 0.519567
\(78\) −1.66554e11 −0.0837415
\(79\) −8.66988e11 −0.401270 −0.200635 0.979666i \(-0.564301\pi\)
−0.200635 + 0.979666i \(0.564301\pi\)
\(80\) 2.12918e12 0.908085
\(81\) 2.82430e11 0.111111
\(82\) −8.02391e11 −0.291471
\(83\) 4.79621e12 1.61024 0.805120 0.593112i \(-0.202101\pi\)
0.805120 + 0.593112i \(0.202101\pi\)
\(84\) 1.47600e12 0.458429
\(85\) 4.46512e10 0.0128413
\(86\) 1.26754e12 0.337849
\(87\) 9.39937e11 0.232393
\(88\) 1.18229e12 0.271385
\(89\) −1.11732e12 −0.238309 −0.119155 0.992876i \(-0.538018\pi\)
−0.119155 + 0.992876i \(0.538018\pi\)
\(90\) 4.01072e11 0.0795511
\(91\) 2.93310e12 0.541449
\(92\) −6.43571e12 −1.10656
\(93\) 2.88370e12 0.462180
\(94\) −1.75176e12 −0.261905
\(95\) 8.47509e12 1.18288
\(96\) 2.77830e12 0.362256
\(97\) −5.79568e12 −0.706461 −0.353230 0.935536i \(-0.614917\pi\)
−0.353230 + 0.935536i \(0.614917\pi\)
\(98\) −5.91490e11 −0.0674494
\(99\) −1.94077e12 −0.207178
\(100\) −1.28977e12 −0.128977
\(101\) −1.86748e13 −1.75052 −0.875261 0.483651i \(-0.839310\pi\)
−0.875261 + 0.483651i \(0.839310\pi\)
\(102\) 1.77183e10 0.00155783
\(103\) 1.02575e13 0.846446 0.423223 0.906025i \(-0.360899\pi\)
0.423223 + 0.906025i \(0.360899\pi\)
\(104\) 3.64939e12 0.282816
\(105\) −7.06307e12 −0.514355
\(106\) −1.28624e12 −0.0880715
\(107\) 6.25992e12 0.403250 0.201625 0.979463i \(-0.435378\pi\)
0.201625 + 0.979463i \(0.435378\pi\)
\(108\) −3.01460e12 −0.182799
\(109\) −2.95409e13 −1.68714 −0.843572 0.537016i \(-0.819551\pi\)
−0.843572 + 0.537016i \(0.819551\pi\)
\(110\) −2.75604e12 −0.148331
\(111\) −7.14250e12 −0.362452
\(112\) −1.48789e13 −0.712285
\(113\) −1.42639e13 −0.644510 −0.322255 0.946653i \(-0.604441\pi\)
−0.322255 + 0.946653i \(0.604441\pi\)
\(114\) 3.36304e12 0.143500
\(115\) 3.07966e13 1.24156
\(116\) −1.00327e13 −0.382332
\(117\) −5.99059e12 −0.215904
\(118\) 8.54921e11 0.0291536
\(119\) −3.12027e11 −0.0100725
\(120\) −8.78793e12 −0.268663
\(121\) −2.11864e13 −0.613694
\(122\) 4.76290e12 0.130777
\(123\) −2.88602e13 −0.751478
\(124\) −3.07801e13 −0.760377
\(125\) −3.92812e13 −0.921021
\(126\) −2.80273e12 −0.0623984
\(127\) −9.44805e13 −1.99810 −0.999052 0.0435283i \(-0.986140\pi\)
−0.999052 + 0.0435283i \(0.986140\pi\)
\(128\) −3.91493e13 −0.786790
\(129\) 4.55907e13 0.871049
\(130\) −8.50710e12 −0.154579
\(131\) 8.46582e13 1.46354 0.731772 0.681550i \(-0.238694\pi\)
0.731772 + 0.681550i \(0.238694\pi\)
\(132\) 2.07154e13 0.340849
\(133\) −5.92248e13 −0.927829
\(134\) −2.09412e13 −0.312479
\(135\) 1.44257e13 0.205100
\(136\) −3.88227e11 −0.00526118
\(137\) 1.50791e14 1.94846 0.974231 0.225553i \(-0.0724189\pi\)
0.974231 + 0.225553i \(0.0724189\pi\)
\(138\) 1.22206e13 0.150618
\(139\) −9.82765e13 −1.15572 −0.577861 0.816135i \(-0.696112\pi\)
−0.577861 + 0.816135i \(0.696112\pi\)
\(140\) 7.53898e13 0.846215
\(141\) −6.30069e13 −0.675249
\(142\) −3.68973e13 −0.377677
\(143\) 4.11654e13 0.402576
\(144\) 3.03888e13 0.284025
\(145\) 4.80092e13 0.428975
\(146\) 4.70265e13 0.401836
\(147\) −2.12746e13 −0.173900
\(148\) 7.62377e13 0.596305
\(149\) 8.89272e13 0.665770 0.332885 0.942967i \(-0.391978\pi\)
0.332885 + 0.942967i \(0.391978\pi\)
\(150\) 2.44910e12 0.0175555
\(151\) −1.94784e14 −1.33722 −0.668611 0.743613i \(-0.733111\pi\)
−0.668611 + 0.743613i \(0.733111\pi\)
\(152\) −7.36880e13 −0.484634
\(153\) 6.37287e11 0.00401643
\(154\) 1.92595e13 0.116348
\(155\) 1.47291e14 0.853140
\(156\) 6.39423e13 0.355205
\(157\) −1.47791e14 −0.787590 −0.393795 0.919198i \(-0.628838\pi\)
−0.393795 + 0.919198i \(0.628838\pi\)
\(158\) −1.75722e13 −0.0898578
\(159\) −4.62634e13 −0.227068
\(160\) 1.41907e14 0.668689
\(161\) −2.15210e14 −0.973854
\(162\) 5.72432e12 0.0248815
\(163\) 3.01588e14 1.25949 0.629745 0.776802i \(-0.283159\pi\)
0.629745 + 0.776802i \(0.283159\pi\)
\(164\) 3.08048e14 1.23633
\(165\) −9.91286e13 −0.382431
\(166\) 9.72102e13 0.360586
\(167\) 3.24979e14 1.15930 0.579652 0.814864i \(-0.303188\pi\)
0.579652 + 0.814864i \(0.303188\pi\)
\(168\) 6.14110e13 0.210735
\(169\) −1.75809e14 −0.580468
\(170\) 9.04997e11 0.00287560
\(171\) 1.20961e14 0.369974
\(172\) −4.86626e14 −1.43305
\(173\) 1.23678e14 0.350747 0.175373 0.984502i \(-0.443887\pi\)
0.175373 + 0.984502i \(0.443887\pi\)
\(174\) 1.90508e13 0.0520406
\(175\) −4.31299e13 −0.113509
\(176\) −2.08822e14 −0.529595
\(177\) 3.07496e13 0.0751646
\(178\) −2.26459e13 −0.0533654
\(179\) 1.05827e13 0.0240466 0.0120233 0.999928i \(-0.496173\pi\)
0.0120233 + 0.999928i \(0.496173\pi\)
\(180\) −1.53977e14 −0.337430
\(181\) 3.55447e14 0.751389 0.375694 0.926744i \(-0.377404\pi\)
0.375694 + 0.926744i \(0.377404\pi\)
\(182\) 5.94485e13 0.121249
\(183\) 1.71311e14 0.337173
\(184\) −2.67766e14 −0.508674
\(185\) −3.64818e14 −0.669052
\(186\) 5.84473e13 0.103498
\(187\) −4.37923e12 −0.00748906
\(188\) 6.72524e14 1.11092
\(189\) −1.00808e14 −0.160877
\(190\) 1.71774e14 0.264887
\(191\) −5.65892e14 −0.843367 −0.421683 0.906743i \(-0.638561\pi\)
−0.421683 + 0.906743i \(0.638561\pi\)
\(192\) −2.85177e14 −0.410825
\(193\) 3.11831e14 0.434307 0.217153 0.976138i \(-0.430323\pi\)
0.217153 + 0.976138i \(0.430323\pi\)
\(194\) −1.17468e14 −0.158200
\(195\) −3.05981e14 −0.398538
\(196\) 2.27081e14 0.286099
\(197\) −9.42136e14 −1.14837 −0.574187 0.818724i \(-0.694682\pi\)
−0.574187 + 0.818724i \(0.694682\pi\)
\(198\) −3.93357e13 −0.0463942
\(199\) −9.81126e14 −1.11990 −0.559951 0.828526i \(-0.689180\pi\)
−0.559951 + 0.828526i \(0.689180\pi\)
\(200\) −5.36626e13 −0.0592893
\(201\) −7.53209e14 −0.805640
\(202\) −3.78504e14 −0.392000
\(203\) −3.35493e14 −0.336480
\(204\) −6.80227e12 −0.00660782
\(205\) −1.47409e15 −1.38716
\(206\) 2.07900e14 0.189548
\(207\) 4.39546e14 0.388327
\(208\) −6.44574e14 −0.551900
\(209\) −8.31207e14 −0.689856
\(210\) −1.43155e14 −0.115181
\(211\) −2.20890e15 −1.72322 −0.861609 0.507572i \(-0.830543\pi\)
−0.861609 + 0.507572i \(0.830543\pi\)
\(212\) 4.93806e14 0.373571
\(213\) −1.32711e15 −0.973734
\(214\) 1.26877e14 0.0903012
\(215\) 2.32864e15 1.60787
\(216\) −1.25426e14 −0.0840309
\(217\) −1.02929e15 −0.669187
\(218\) −5.98740e14 −0.377808
\(219\) 1.69144e15 1.03602
\(220\) 1.05808e15 0.629174
\(221\) −1.35174e13 −0.00780449
\(222\) −1.44765e14 −0.0811652
\(223\) 2.75705e15 1.50128 0.750641 0.660710i \(-0.229745\pi\)
0.750641 + 0.660710i \(0.229745\pi\)
\(224\) −9.91662e14 −0.524507
\(225\) 8.80888e13 0.0452620
\(226\) −2.89103e14 −0.144327
\(227\) −2.42183e15 −1.17483 −0.587417 0.809285i \(-0.699855\pi\)
−0.587417 + 0.809285i \(0.699855\pi\)
\(228\) −1.29112e15 −0.608680
\(229\) −2.45311e15 −1.12405 −0.562025 0.827120i \(-0.689978\pi\)
−0.562025 + 0.827120i \(0.689978\pi\)
\(230\) 6.24190e14 0.278026
\(231\) 6.92721e14 0.299972
\(232\) −4.17424e14 −0.175754
\(233\) −1.11480e15 −0.456440 −0.228220 0.973610i \(-0.573291\pi\)
−0.228220 + 0.973610i \(0.573291\pi\)
\(234\) −1.21418e14 −0.0483482
\(235\) −3.21821e15 −1.24644
\(236\) −3.28215e14 −0.123660
\(237\) −6.32034e14 −0.231674
\(238\) −6.32421e12 −0.00225557
\(239\) −4.69514e15 −1.62953 −0.814765 0.579792i \(-0.803134\pi\)
−0.814765 + 0.579792i \(0.803134\pi\)
\(240\) 1.55217e15 0.524283
\(241\) −2.64069e15 −0.868172 −0.434086 0.900871i \(-0.642929\pi\)
−0.434086 + 0.900871i \(0.642929\pi\)
\(242\) −4.29409e14 −0.137427
\(243\) 2.05891e14 0.0641500
\(244\) −1.82854e15 −0.554716
\(245\) −1.08664e15 −0.321002
\(246\) −5.84943e14 −0.168281
\(247\) −2.56570e15 −0.718911
\(248\) −1.28065e15 −0.349537
\(249\) 3.49644e15 0.929672
\(250\) −7.96157e14 −0.206247
\(251\) 6.73243e14 0.169939 0.0849694 0.996384i \(-0.472921\pi\)
0.0849694 + 0.996384i \(0.472921\pi\)
\(252\) 1.07601e15 0.264674
\(253\) −3.02042e15 −0.724076
\(254\) −1.91494e15 −0.447442
\(255\) 3.25507e13 0.00741395
\(256\) 2.41114e15 0.535381
\(257\) 3.51019e15 0.759915 0.379957 0.925004i \(-0.375939\pi\)
0.379957 + 0.925004i \(0.375939\pi\)
\(258\) 9.24038e14 0.195057
\(259\) 2.54939e15 0.524792
\(260\) 3.26599e15 0.655673
\(261\) 6.85214e14 0.134172
\(262\) 1.71586e15 0.327736
\(263\) −1.98866e15 −0.370551 −0.185276 0.982687i \(-0.559318\pi\)
−0.185276 + 0.982687i \(0.559318\pi\)
\(264\) 8.61889e14 0.156684
\(265\) −2.36300e15 −0.419145
\(266\) −1.20038e15 −0.207772
\(267\) −8.14523e14 −0.137588
\(268\) 8.03961e15 1.32544
\(269\) −9.30036e15 −1.49661 −0.748307 0.663352i \(-0.769133\pi\)
−0.748307 + 0.663352i \(0.769133\pi\)
\(270\) 2.92381e14 0.0459288
\(271\) 5.46784e15 0.838524 0.419262 0.907865i \(-0.362289\pi\)
0.419262 + 0.907865i \(0.362289\pi\)
\(272\) 6.85706e13 0.0102669
\(273\) 2.13823e15 0.312606
\(274\) 3.05625e15 0.436326
\(275\) −6.05318e14 −0.0843958
\(276\) −4.69163e15 −0.638873
\(277\) −2.91138e15 −0.387240 −0.193620 0.981077i \(-0.562023\pi\)
−0.193620 + 0.981077i \(0.562023\pi\)
\(278\) −1.99188e15 −0.258805
\(279\) 2.10222e15 0.266840
\(280\) 3.13669e15 0.388996
\(281\) 1.06664e15 0.129248 0.0646242 0.997910i \(-0.479415\pi\)
0.0646242 + 0.997910i \(0.479415\pi\)
\(282\) −1.27703e15 −0.151211
\(283\) −9.16327e15 −1.06032 −0.530162 0.847896i \(-0.677869\pi\)
−0.530162 + 0.847896i \(0.677869\pi\)
\(284\) 1.41653e16 1.60198
\(285\) 6.17834e15 0.682936
\(286\) 8.34346e14 0.0901503
\(287\) 1.03011e16 1.08806
\(288\) 2.02538e15 0.209149
\(289\) −9.90314e15 −0.999855
\(290\) 9.73057e14 0.0960619
\(291\) −4.22505e15 −0.407875
\(292\) −1.80541e16 −1.70446
\(293\) −1.50319e16 −1.38795 −0.693976 0.719998i \(-0.744143\pi\)
−0.693976 + 0.719998i \(0.744143\pi\)
\(294\) −4.31197e14 −0.0389419
\(295\) 1.57060e15 0.138747
\(296\) 3.17197e15 0.274115
\(297\) −1.41482e15 −0.119614
\(298\) 1.80239e15 0.149088
\(299\) −9.32317e15 −0.754572
\(300\) −9.40242e14 −0.0744649
\(301\) −1.62728e16 −1.26119
\(302\) −3.94791e15 −0.299449
\(303\) −1.36139e16 −1.01066
\(304\) 1.30152e16 0.945738
\(305\) 8.75006e15 0.622389
\(306\) 1.29166e13 0.000899414 0
\(307\) 1.70494e16 1.16228 0.581138 0.813805i \(-0.302608\pi\)
0.581138 + 0.813805i \(0.302608\pi\)
\(308\) −7.39397e15 −0.493512
\(309\) 7.47772e15 0.488696
\(310\) 2.98532e15 0.191047
\(311\) −2.43218e16 −1.52424 −0.762119 0.647437i \(-0.775841\pi\)
−0.762119 + 0.647437i \(0.775841\pi\)
\(312\) 2.66040e15 0.163284
\(313\) −1.02142e16 −0.613997 −0.306999 0.951710i \(-0.599325\pi\)
−0.306999 + 0.951710i \(0.599325\pi\)
\(314\) −2.99545e15 −0.176368
\(315\) −5.14898e15 −0.296963
\(316\) 6.74621e15 0.381148
\(317\) 2.78390e15 0.154088 0.0770439 0.997028i \(-0.475452\pi\)
0.0770439 + 0.997028i \(0.475452\pi\)
\(318\) −9.37672e14 −0.0508481
\(319\) −4.70857e15 −0.250178
\(320\) −1.45660e16 −0.758343
\(321\) 4.56348e15 0.232816
\(322\) −4.36190e15 −0.218079
\(323\) 2.72942e14 0.0133738
\(324\) −2.19764e15 −0.105539
\(325\) −1.86844e15 −0.0879504
\(326\) 6.11263e15 0.282042
\(327\) −2.15354e16 −0.974073
\(328\) 1.28168e16 0.568327
\(329\) 2.24892e16 0.977688
\(330\) −2.00915e15 −0.0856391
\(331\) 2.00007e16 0.835919 0.417959 0.908466i \(-0.362745\pi\)
0.417959 + 0.908466i \(0.362745\pi\)
\(332\) −3.73203e16 −1.52949
\(333\) −5.20688e15 −0.209262
\(334\) 6.58671e15 0.259607
\(335\) −3.84717e16 −1.48713
\(336\) −1.08467e16 −0.411238
\(337\) −1.16943e16 −0.434892 −0.217446 0.976072i \(-0.569773\pi\)
−0.217446 + 0.976072i \(0.569773\pi\)
\(338\) −3.56333e15 −0.129986
\(339\) −1.03984e16 −0.372108
\(340\) −3.47440e14 −0.0121974
\(341\) −1.44458e16 −0.497551
\(342\) 2.45166e15 0.0828496
\(343\) 3.28044e16 1.08773
\(344\) −2.02467e16 −0.658756
\(345\) 2.24507e16 0.716813
\(346\) 2.50673e15 0.0785439
\(347\) −1.94488e16 −0.598069 −0.299035 0.954242i \(-0.596665\pi\)
−0.299035 + 0.954242i \(0.596665\pi\)
\(348\) −7.31384e15 −0.220740
\(349\) −3.76420e16 −1.11508 −0.557542 0.830149i \(-0.688255\pi\)
−0.557542 + 0.830149i \(0.688255\pi\)
\(350\) −8.74162e14 −0.0254185
\(351\) −4.36714e15 −0.124652
\(352\) −1.39178e16 −0.389980
\(353\) −8.38237e15 −0.230585 −0.115292 0.993332i \(-0.536781\pi\)
−0.115292 + 0.993332i \(0.536781\pi\)
\(354\) 6.23237e14 0.0168319
\(355\) −6.77850e16 −1.79742
\(356\) 8.69405e15 0.226359
\(357\) −2.27468e14 −0.00581536
\(358\) 2.14493e14 0.00538484
\(359\) −2.36587e15 −0.0583279 −0.0291640 0.999575i \(-0.509284\pi\)
−0.0291640 + 0.999575i \(0.509284\pi\)
\(360\) −6.40640e15 −0.155113
\(361\) 9.75326e15 0.231928
\(362\) 7.20426e15 0.168261
\(363\) −1.54449e16 −0.354316
\(364\) −2.28230e16 −0.514298
\(365\) 8.63937e16 1.91240
\(366\) 3.47215e15 0.0755044
\(367\) −5.14627e15 −0.109942 −0.0549709 0.998488i \(-0.517507\pi\)
−0.0549709 + 0.998488i \(0.517507\pi\)
\(368\) 4.72942e16 0.992652
\(369\) −2.10391e16 −0.433866
\(370\) −7.39418e15 −0.149823
\(371\) 1.65129e16 0.328770
\(372\) −2.24387e16 −0.439004
\(373\) 1.00352e17 1.92938 0.964689 0.263390i \(-0.0848407\pi\)
0.964689 + 0.263390i \(0.0848407\pi\)
\(374\) −8.87589e13 −0.00167705
\(375\) −2.86360e16 −0.531752
\(376\) 2.79812e16 0.510676
\(377\) −1.45340e16 −0.260715
\(378\) −2.04319e15 −0.0360257
\(379\) −2.42425e16 −0.420168 −0.210084 0.977683i \(-0.567374\pi\)
−0.210084 + 0.977683i \(0.567374\pi\)
\(380\) −6.59464e16 −1.12356
\(381\) −6.88763e16 −1.15361
\(382\) −1.14696e16 −0.188858
\(383\) 9.54203e16 1.54472 0.772358 0.635187i \(-0.219077\pi\)
0.772358 + 0.635187i \(0.219077\pi\)
\(384\) −2.85398e16 −0.454253
\(385\) 3.53821e16 0.553719
\(386\) 6.32023e15 0.0972557
\(387\) 3.32356e16 0.502901
\(388\) 4.50973e16 0.671034
\(389\) 3.05347e16 0.446808 0.223404 0.974726i \(-0.428283\pi\)
0.223404 + 0.974726i \(0.428283\pi\)
\(390\) −6.20167e15 −0.0892460
\(391\) 9.91812e14 0.0140372
\(392\) 9.44800e15 0.131517
\(393\) 6.17158e16 0.844977
\(394\) −1.90953e16 −0.257159
\(395\) −3.22824e16 −0.427647
\(396\) 1.51015e16 0.196789
\(397\) 6.06540e16 0.777537 0.388768 0.921336i \(-0.372901\pi\)
0.388768 + 0.921336i \(0.372901\pi\)
\(398\) −1.98856e16 −0.250783
\(399\) −4.31749e16 −0.535683
\(400\) 9.47815e15 0.115700
\(401\) 1.51722e17 1.82225 0.911127 0.412127i \(-0.135214\pi\)
0.911127 + 0.412127i \(0.135214\pi\)
\(402\) −1.52661e16 −0.180410
\(403\) −4.45900e16 −0.518507
\(404\) 1.45313e17 1.66274
\(405\) 1.05163e16 0.118415
\(406\) −6.79983e15 −0.0753492
\(407\) 3.57801e16 0.390191
\(408\) −2.83018e14 −0.00303754
\(409\) 7.11676e16 0.751763 0.375882 0.926668i \(-0.377340\pi\)
0.375882 + 0.926668i \(0.377340\pi\)
\(410\) −2.98772e16 −0.310631
\(411\) 1.09927e17 1.12494
\(412\) −7.98157e16 −0.804000
\(413\) −1.09755e16 −0.108830
\(414\) 8.90878e15 0.0869593
\(415\) 1.78588e17 1.71608
\(416\) −4.29601e16 −0.406405
\(417\) −7.16435e16 −0.667256
\(418\) −1.68470e16 −0.154482
\(419\) 6.69555e16 0.604498 0.302249 0.953229i \(-0.402263\pi\)
0.302249 + 0.953229i \(0.402263\pi\)
\(420\) 5.49592e16 0.488562
\(421\) −1.33902e17 −1.17207 −0.586034 0.810287i \(-0.699311\pi\)
−0.586034 + 0.810287i \(0.699311\pi\)
\(422\) −4.47703e16 −0.385886
\(423\) −4.59321e16 −0.389855
\(424\) 2.05454e16 0.171727
\(425\) 1.98768e14 0.00163613
\(426\) −2.68981e16 −0.218052
\(427\) −6.11463e16 −0.488190
\(428\) −4.87097e16 −0.383029
\(429\) 3.00096e16 0.232427
\(430\) 4.71971e16 0.360056
\(431\) 9.04890e16 0.679976 0.339988 0.940430i \(-0.389577\pi\)
0.339988 + 0.940430i \(0.389577\pi\)
\(432\) 2.21534e16 0.163982
\(433\) 1.25862e17 0.917744 0.458872 0.888502i \(-0.348254\pi\)
0.458872 + 0.888502i \(0.348254\pi\)
\(434\) −2.08617e16 −0.149853
\(435\) 3.49987e16 0.247669
\(436\) 2.29864e17 1.60254
\(437\) 1.88252e17 1.29304
\(438\) 3.42823e16 0.232000
\(439\) 2.23521e17 1.49039 0.745193 0.666849i \(-0.232357\pi\)
0.745193 + 0.666849i \(0.232357\pi\)
\(440\) 4.40228e16 0.289224
\(441\) −1.55092e16 −0.100401
\(442\) −2.73973e14 −0.00174769
\(443\) −2.71670e17 −1.70772 −0.853862 0.520499i \(-0.825746\pi\)
−0.853862 + 0.520499i \(0.825746\pi\)
\(444\) 5.55773e16 0.344277
\(445\) −4.16034e16 −0.253974
\(446\) 5.58802e16 0.336187
\(447\) 6.48279e16 0.384382
\(448\) 1.01789e17 0.594830
\(449\) −1.17553e17 −0.677067 −0.338533 0.940954i \(-0.609931\pi\)
−0.338533 + 0.940954i \(0.609931\pi\)
\(450\) 1.78540e15 0.0101357
\(451\) 1.44574e17 0.808989
\(452\) 1.10991e17 0.612190
\(453\) −1.41998e17 −0.772045
\(454\) −4.90861e16 −0.263084
\(455\) 1.09214e17 0.577040
\(456\) −5.37186e16 −0.279803
\(457\) −1.17149e17 −0.601568 −0.300784 0.953692i \(-0.597248\pi\)
−0.300784 + 0.953692i \(0.597248\pi\)
\(458\) −4.97199e16 −0.251713
\(459\) 4.64582e14 0.00231889
\(460\) −2.39635e17 −1.17930
\(461\) 3.10327e17 1.50579 0.752895 0.658141i \(-0.228657\pi\)
0.752895 + 0.658141i \(0.228657\pi\)
\(462\) 1.40402e16 0.0671737
\(463\) −3.33096e17 −1.57142 −0.785711 0.618594i \(-0.787703\pi\)
−0.785711 + 0.618594i \(0.787703\pi\)
\(464\) 7.37275e16 0.342975
\(465\) 1.07375e17 0.492561
\(466\) −2.25949e16 −0.102212
\(467\) 3.01037e16 0.134295 0.0671475 0.997743i \(-0.478610\pi\)
0.0671475 + 0.997743i \(0.478610\pi\)
\(468\) 4.66140e16 0.205077
\(469\) 2.68844e17 1.16648
\(470\) −6.52271e16 −0.279121
\(471\) −1.07740e17 −0.454715
\(472\) −1.36558e16 −0.0568454
\(473\) −2.28384e17 −0.937711
\(474\) −1.28102e16 −0.0518794
\(475\) 3.77274e16 0.150712
\(476\) 2.42795e15 0.00956741
\(477\) −3.37260e16 −0.131098
\(478\) −9.51618e16 −0.364906
\(479\) 4.35672e16 0.164808 0.0824041 0.996599i \(-0.473740\pi\)
0.0824041 + 0.996599i \(0.473740\pi\)
\(480\) 1.03450e17 0.386068
\(481\) 1.10443e17 0.406625
\(482\) −5.35218e16 −0.194413
\(483\) −1.56888e17 −0.562255
\(484\) 1.64856e17 0.582920
\(485\) −2.15803e17 −0.752898
\(486\) 4.17303e15 0.0143653
\(487\) −1.29507e17 −0.439900 −0.219950 0.975511i \(-0.570589\pi\)
−0.219950 + 0.975511i \(0.570589\pi\)
\(488\) −7.60788e16 −0.254997
\(489\) 2.19858e17 0.727167
\(490\) −2.20242e16 −0.0718831
\(491\) −5.77715e16 −0.186073 −0.0930366 0.995663i \(-0.529657\pi\)
−0.0930366 + 0.995663i \(0.529657\pi\)
\(492\) 2.24567e17 0.713795
\(493\) 1.54615e15 0.00485005
\(494\) −5.20019e16 −0.160988
\(495\) −7.22647e16 −0.220797
\(496\) 2.26194e17 0.682104
\(497\) 4.73689e17 1.40986
\(498\) 7.08663e16 0.208185
\(499\) −1.68169e17 −0.487631 −0.243815 0.969822i \(-0.578399\pi\)
−0.243815 + 0.969822i \(0.578399\pi\)
\(500\) 3.05655e17 0.874835
\(501\) 2.36909e17 0.669325
\(502\) 1.36454e16 0.0380550
\(503\) −2.65765e17 −0.731653 −0.365827 0.930683i \(-0.619214\pi\)
−0.365827 + 0.930683i \(0.619214\pi\)
\(504\) 4.47686e16 0.121668
\(505\) −6.95360e17 −1.86559
\(506\) −6.12183e16 −0.162145
\(507\) −1.28165e17 −0.335134
\(508\) 7.35172e17 1.89791
\(509\) 2.76321e17 0.704285 0.352142 0.935946i \(-0.385453\pi\)
0.352142 + 0.935946i \(0.385453\pi\)
\(510\) 6.59743e14 0.00166023
\(511\) −6.03729e17 −1.50005
\(512\) 3.69580e17 0.906680
\(513\) 8.81807e16 0.213605
\(514\) 7.11450e16 0.170170
\(515\) 3.81940e17 0.902086
\(516\) −3.54750e17 −0.827370
\(517\) 3.15630e17 0.726926
\(518\) 5.16713e16 0.117518
\(519\) 9.01614e16 0.202504
\(520\) 1.35886e17 0.301406
\(521\) 4.26329e17 0.933898 0.466949 0.884284i \(-0.345353\pi\)
0.466949 + 0.884284i \(0.345353\pi\)
\(522\) 1.38880e16 0.0300457
\(523\) −7.71691e17 −1.64886 −0.824428 0.565967i \(-0.808503\pi\)
−0.824428 + 0.565967i \(0.808503\pi\)
\(524\) −6.58743e17 −1.39015
\(525\) −3.14417e16 −0.0655345
\(526\) −4.03064e16 −0.0829788
\(527\) 4.74355e15 0.00964571
\(528\) −1.52231e17 −0.305762
\(529\) 1.80031e17 0.357179
\(530\) −4.78935e16 −0.0938607
\(531\) 2.24165e16 0.0433963
\(532\) 4.60840e17 0.881302
\(533\) 4.46258e17 0.843062
\(534\) −1.65089e16 −0.0308105
\(535\) 2.33089e17 0.429757
\(536\) 3.34498e17 0.609288
\(537\) 7.71482e15 0.0138833
\(538\) −1.88501e17 −0.335142
\(539\) 1.06574e17 0.187208
\(540\) −1.12249e17 −0.194815
\(541\) 4.22179e17 0.723960 0.361980 0.932186i \(-0.382101\pi\)
0.361980 + 0.932186i \(0.382101\pi\)
\(542\) 1.10823e17 0.187774
\(543\) 2.59121e17 0.433814
\(544\) 4.57016e15 0.00756028
\(545\) −1.09996e18 −1.79804
\(546\) 4.33380e16 0.0700029
\(547\) 7.05080e17 1.12544 0.562718 0.826649i \(-0.309756\pi\)
0.562718 + 0.826649i \(0.309756\pi\)
\(548\) −1.17334e18 −1.85075
\(549\) 1.24886e17 0.194667
\(550\) −1.22687e16 −0.0188991
\(551\) 2.93469e17 0.446763
\(552\) −1.95201e17 −0.293683
\(553\) 2.25593e17 0.335438
\(554\) −5.90082e16 −0.0867160
\(555\) −2.65952e17 −0.386277
\(556\) 7.64709e17 1.09777
\(557\) −1.30350e17 −0.184949 −0.0924747 0.995715i \(-0.529478\pi\)
−0.0924747 + 0.995715i \(0.529478\pi\)
\(558\) 4.26081e16 0.0597544
\(559\) −7.04957e17 −0.977205
\(560\) −5.54019e17 −0.759106
\(561\) −3.19246e15 −0.00432381
\(562\) 2.16187e16 0.0289430
\(563\) −7.29767e16 −0.0965784 −0.0482892 0.998833i \(-0.515377\pi\)
−0.0482892 + 0.998833i \(0.515377\pi\)
\(564\) 4.90270e17 0.641388
\(565\) −5.31120e17 −0.686875
\(566\) −1.85722e17 −0.237442
\(567\) −7.34891e16 −0.0928823
\(568\) 5.89368e17 0.736414
\(569\) 4.09171e16 0.0505446 0.0252723 0.999681i \(-0.491955\pi\)
0.0252723 + 0.999681i \(0.491955\pi\)
\(570\) 1.25223e17 0.152932
\(571\) 9.73995e17 1.17604 0.588020 0.808847i \(-0.299908\pi\)
0.588020 + 0.808847i \(0.299908\pi\)
\(572\) −3.20316e17 −0.382388
\(573\) −4.12535e17 −0.486918
\(574\) 2.08785e17 0.243653
\(575\) 1.37093e17 0.158188
\(576\) −2.07894e17 −0.237190
\(577\) 5.17313e17 0.583594 0.291797 0.956480i \(-0.405747\pi\)
0.291797 + 0.956480i \(0.405747\pi\)
\(578\) −2.00718e17 −0.223901
\(579\) 2.27325e17 0.250747
\(580\) −3.73569e17 −0.407464
\(581\) −1.24799e18 −1.34606
\(582\) −8.56339e16 −0.0913369
\(583\) 2.31754e17 0.244446
\(584\) −7.51164e17 −0.783522
\(585\) −2.23060e17 −0.230096
\(586\) −3.04669e17 −0.310809
\(587\) −1.81895e18 −1.83516 −0.917581 0.397550i \(-0.869861\pi\)
−0.917581 + 0.397550i \(0.869861\pi\)
\(588\) 1.65542e17 0.165179
\(589\) 9.00356e17 0.888515
\(590\) 3.18331e16 0.0310700
\(591\) −6.86817e17 −0.663014
\(592\) −5.60249e17 −0.534922
\(593\) 1.78051e18 1.68147 0.840737 0.541444i \(-0.182122\pi\)
0.840737 + 0.541444i \(0.182122\pi\)
\(594\) −2.86757e16 −0.0267857
\(595\) −1.16184e16 −0.0107346
\(596\) −6.91961e17 −0.632384
\(597\) −7.15241e17 −0.646576
\(598\) −1.88963e17 −0.168974
\(599\) −6.99330e16 −0.0618597 −0.0309299 0.999522i \(-0.509847\pi\)
−0.0309299 + 0.999522i \(0.509847\pi\)
\(600\) −3.91200e16 −0.0342307
\(601\) 9.16608e17 0.793413 0.396707 0.917945i \(-0.370153\pi\)
0.396707 + 0.917945i \(0.370153\pi\)
\(602\) −3.29819e17 −0.282422
\(603\) −5.49089e17 −0.465137
\(604\) 1.51565e18 1.27016
\(605\) −7.88879e17 −0.654034
\(606\) −2.75929e17 −0.226321
\(607\) −1.82240e18 −1.47883 −0.739413 0.673252i \(-0.764897\pi\)
−0.739413 + 0.673252i \(0.764897\pi\)
\(608\) 8.67445e17 0.696416
\(609\) −2.44575e17 −0.194267
\(610\) 1.77347e17 0.139374
\(611\) 9.74260e17 0.757543
\(612\) −4.95886e15 −0.00381503
\(613\) 6.07209e17 0.462216 0.231108 0.972928i \(-0.425765\pi\)
0.231108 + 0.972928i \(0.425765\pi\)
\(614\) 3.45559e17 0.260272
\(615\) −1.07462e18 −0.800875
\(616\) −3.07636e17 −0.226862
\(617\) −9.03448e17 −0.659249 −0.329624 0.944112i \(-0.606922\pi\)
−0.329624 + 0.944112i \(0.606922\pi\)
\(618\) 1.51559e17 0.109435
\(619\) 5.61392e17 0.401122 0.200561 0.979681i \(-0.435723\pi\)
0.200561 + 0.979681i \(0.435723\pi\)
\(620\) −1.14610e18 −0.810359
\(621\) 3.20429e17 0.224201
\(622\) −4.92957e17 −0.341328
\(623\) 2.90729e17 0.199212
\(624\) −4.69894e17 −0.318640
\(625\) −1.66498e18 −1.11735
\(626\) −2.07023e17 −0.137495
\(627\) −6.05950e17 −0.398288
\(628\) 1.14999e18 0.748095
\(629\) −1.17491e16 −0.00756438
\(630\) −1.04360e17 −0.0665000
\(631\) 2.38611e17 0.150487 0.0752437 0.997165i \(-0.476027\pi\)
0.0752437 + 0.997165i \(0.476027\pi\)
\(632\) 2.80685e17 0.175210
\(633\) −1.61029e18 −0.994900
\(634\) 5.64245e16 0.0345054
\(635\) −3.51800e18 −2.12945
\(636\) 3.59985e17 0.215681
\(637\) 3.28964e17 0.195093
\(638\) −9.54340e16 −0.0560233
\(639\) −9.67465e17 −0.562186
\(640\) −1.45773e18 −0.838508
\(641\) −1.29112e18 −0.735173 −0.367587 0.929989i \(-0.619816\pi\)
−0.367587 + 0.929989i \(0.619816\pi\)
\(642\) 9.24933e16 0.0521354
\(643\) 2.63461e17 0.147010 0.0735048 0.997295i \(-0.476582\pi\)
0.0735048 + 0.997295i \(0.476582\pi\)
\(644\) 1.67459e18 0.925019
\(645\) 1.69758e18 0.928306
\(646\) 5.53203e15 0.00299484
\(647\) 2.41189e18 1.29264 0.646322 0.763065i \(-0.276306\pi\)
0.646322 + 0.763065i \(0.276306\pi\)
\(648\) −9.14357e16 −0.0485153
\(649\) −1.54039e17 −0.0809170
\(650\) −3.78698e16 −0.0196950
\(651\) −7.50349e17 −0.386355
\(652\) −2.34672e18 −1.19633
\(653\) 2.48036e18 1.25192 0.625962 0.779853i \(-0.284706\pi\)
0.625962 + 0.779853i \(0.284706\pi\)
\(654\) −4.36482e17 −0.218128
\(655\) 3.15226e18 1.55975
\(656\) −2.26376e18 −1.10906
\(657\) 1.23306e18 0.598149
\(658\) 4.55814e17 0.218937
\(659\) −3.34886e18 −1.59273 −0.796363 0.604818i \(-0.793246\pi\)
−0.796363 + 0.604818i \(0.793246\pi\)
\(660\) 7.71340e17 0.363254
\(661\) 3.07225e18 1.43267 0.716335 0.697756i \(-0.245818\pi\)
0.716335 + 0.697756i \(0.245818\pi\)
\(662\) 4.05378e17 0.187190
\(663\) −9.85421e15 −0.00450592
\(664\) −1.55276e18 −0.703091
\(665\) −2.20525e18 −0.988818
\(666\) −1.05534e17 −0.0468608
\(667\) 1.06640e18 0.468924
\(668\) −2.52872e18 −1.10117
\(669\) 2.00989e18 0.866766
\(670\) −7.79750e17 −0.333019
\(671\) −8.58175e17 −0.362977
\(672\) −7.22922e17 −0.302825
\(673\) −2.55408e18 −1.05959 −0.529793 0.848127i \(-0.677730\pi\)
−0.529793 + 0.848127i \(0.677730\pi\)
\(674\) −2.37023e17 −0.0973869
\(675\) 6.42167e16 0.0261321
\(676\) 1.36801e18 0.551360
\(677\) 2.53140e18 1.01050 0.505248 0.862974i \(-0.331401\pi\)
0.505248 + 0.862974i \(0.331401\pi\)
\(678\) −2.10756e17 −0.0833274
\(679\) 1.50805e18 0.590559
\(680\) −1.44557e16 −0.00560701
\(681\) −1.76552e18 −0.678290
\(682\) −2.92789e17 −0.111418
\(683\) 4.04309e18 1.52398 0.761989 0.647590i \(-0.224223\pi\)
0.761989 + 0.647590i \(0.224223\pi\)
\(684\) −9.41224e17 −0.351421
\(685\) 5.61473e18 2.07654
\(686\) 6.64885e17 0.243579
\(687\) −1.78832e18 −0.648971
\(688\) 3.57608e18 1.28553
\(689\) 7.15359e17 0.254741
\(690\) 4.55034e17 0.160519
\(691\) −8.98529e17 −0.313996 −0.156998 0.987599i \(-0.550182\pi\)
−0.156998 + 0.987599i \(0.550182\pi\)
\(692\) −9.62365e17 −0.333158
\(693\) 5.04994e17 0.173189
\(694\) −3.94191e17 −0.133928
\(695\) −3.65934e18 −1.23169
\(696\) −3.04302e17 −0.101472
\(697\) −4.74736e16 −0.0156834
\(698\) −7.62933e17 −0.249704
\(699\) −8.12689e17 −0.263526
\(700\) 3.35602e17 0.107817
\(701\) −6.58631e17 −0.209640 −0.104820 0.994491i \(-0.533427\pi\)
−0.104820 + 0.994491i \(0.533427\pi\)
\(702\) −8.85137e16 −0.0279138
\(703\) −2.23005e18 −0.696794
\(704\) 1.42858e18 0.442266
\(705\) −2.34607e18 −0.719635
\(706\) −1.69895e17 −0.0516357
\(707\) 4.85925e18 1.46333
\(708\) −2.39269e17 −0.0713954
\(709\) −3.43007e18 −1.01415 −0.507075 0.861902i \(-0.669273\pi\)
−0.507075 + 0.861902i \(0.669273\pi\)
\(710\) −1.37388e18 −0.402502
\(711\) −4.60753e17 −0.133757
\(712\) 3.61728e17 0.104055
\(713\) 3.27169e18 0.932590
\(714\) −4.61035e15 −0.00130225
\(715\) 1.53280e18 0.429039
\(716\) −8.23465e16 −0.0228408
\(717\) −3.42276e18 −0.940809
\(718\) −4.79517e16 −0.0130616
\(719\) −6.67822e18 −1.80270 −0.901348 0.433095i \(-0.857421\pi\)
−0.901348 + 0.433095i \(0.857421\pi\)
\(720\) 1.13153e18 0.302695
\(721\) −2.66903e18 −0.707579
\(722\) 1.97680e17 0.0519364
\(723\) −1.92506e18 −0.501239
\(724\) −2.76581e18 −0.713709
\(725\) 2.13716e17 0.0546562
\(726\) −3.13039e17 −0.0793433
\(727\) −3.20133e18 −0.804185 −0.402093 0.915599i \(-0.631717\pi\)
−0.402093 + 0.915599i \(0.631717\pi\)
\(728\) −9.49583e17 −0.236417
\(729\) 1.50095e17 0.0370370
\(730\) 1.75104e18 0.428250
\(731\) 7.49943e16 0.0181788
\(732\) −1.33301e18 −0.320265
\(733\) 4.37078e18 1.04084 0.520419 0.853911i \(-0.325776\pi\)
0.520419 + 0.853911i \(0.325776\pi\)
\(734\) −1.04305e17 −0.0246196
\(735\) −7.92163e17 −0.185331
\(736\) 3.15210e18 0.730962
\(737\) 3.77317e18 0.867296
\(738\) −4.26423e17 −0.0971571
\(739\) 1.92305e18 0.434311 0.217156 0.976137i \(-0.430322\pi\)
0.217156 + 0.976137i \(0.430322\pi\)
\(740\) 2.83872e18 0.635502
\(741\) −1.87039e18 −0.415063
\(742\) 3.34685e17 0.0736226
\(743\) −4.32359e18 −0.942795 −0.471398 0.881921i \(-0.656250\pi\)
−0.471398 + 0.881921i \(0.656250\pi\)
\(744\) −9.33591e17 −0.201805
\(745\) 3.31122e18 0.709532
\(746\) 2.03394e18 0.432052
\(747\) 2.54890e18 0.536746
\(748\) 3.40757e16 0.00711352
\(749\) −1.62885e18 −0.337093
\(750\) −5.80398e17 −0.119077
\(751\) 5.07232e18 1.03168 0.515842 0.856684i \(-0.327479\pi\)
0.515842 + 0.856684i \(0.327479\pi\)
\(752\) −4.94219e18 −0.996559
\(753\) 4.90794e17 0.0981142
\(754\) −2.94577e17 −0.0583829
\(755\) −7.25282e18 −1.42512
\(756\) 7.84408e17 0.152810
\(757\) −5.58408e18 −1.07852 −0.539260 0.842139i \(-0.681296\pi\)
−0.539260 + 0.842139i \(0.681296\pi\)
\(758\) −4.91351e17 −0.0940897
\(759\) −2.20189e18 −0.418045
\(760\) −2.74379e18 −0.516490
\(761\) −8.29736e18 −1.54860 −0.774300 0.632818i \(-0.781898\pi\)
−0.774300 + 0.632818i \(0.781898\pi\)
\(762\) −1.39599e18 −0.258331
\(763\) 7.68665e18 1.41035
\(764\) 4.40332e18 0.801075
\(765\) 2.37295e16 0.00428045
\(766\) 1.93399e18 0.345914
\(767\) −4.75473e17 −0.0843250
\(768\) 1.75772e18 0.309103
\(769\) −2.23920e18 −0.390456 −0.195228 0.980758i \(-0.562545\pi\)
−0.195228 + 0.980758i \(0.562545\pi\)
\(770\) 7.17130e17 0.123996
\(771\) 2.55893e18 0.438737
\(772\) −2.42642e18 −0.412528
\(773\) −4.08081e18 −0.687987 −0.343993 0.938972i \(-0.611780\pi\)
−0.343993 + 0.938972i \(0.611780\pi\)
\(774\) 6.73624e17 0.112616
\(775\) 6.55675e17 0.108700
\(776\) 1.87633e18 0.308467
\(777\) 1.85850e18 0.302989
\(778\) 6.18882e17 0.100055
\(779\) −9.01080e18 −1.44467
\(780\) 2.38090e18 0.378553
\(781\) 6.64811e18 1.04825
\(782\) 2.01022e16 0.00314340
\(783\) 4.99521e17 0.0774644
\(784\) −1.66875e18 −0.256648
\(785\) −5.50302e18 −0.839360
\(786\) 1.25087e18 0.189219
\(787\) −6.06501e18 −0.909904 −0.454952 0.890516i \(-0.650344\pi\)
−0.454952 + 0.890516i \(0.650344\pi\)
\(788\) 7.33095e18 1.09079
\(789\) −1.44973e18 −0.213938
\(790\) −6.54305e17 −0.0957644
\(791\) 3.71152e18 0.538772
\(792\) 6.28317e17 0.0904618
\(793\) −2.64894e18 −0.378265
\(794\) 1.22934e18 0.174116
\(795\) −1.72262e18 −0.241994
\(796\) 7.63434e18 1.06374
\(797\) −7.96070e18 −1.10020 −0.550101 0.835098i \(-0.685411\pi\)
−0.550101 + 0.835098i \(0.685411\pi\)
\(798\) −8.75075e17 −0.119957
\(799\) −1.03643e17 −0.0140925
\(800\) 6.31708e17 0.0851984
\(801\) −5.93787e17 −0.0794364
\(802\) 3.07511e18 0.408063
\(803\) −8.47319e18 −1.11531
\(804\) 5.86087e18 0.765241
\(805\) −8.01338e18 −1.03787
\(806\) −9.03756e17 −0.116111
\(807\) −6.77996e18 −0.864071
\(808\) 6.04592e18 0.764343
\(809\) 1.32286e19 1.65901 0.829506 0.558498i \(-0.188622\pi\)
0.829506 + 0.558498i \(0.188622\pi\)
\(810\) 2.13146e17 0.0265170
\(811\) 3.65880e18 0.451547 0.225774 0.974180i \(-0.427509\pi\)
0.225774 + 0.974180i \(0.427509\pi\)
\(812\) 2.61054e18 0.319607
\(813\) 3.98606e18 0.484122
\(814\) 7.25195e17 0.0873768
\(815\) 1.12297e19 1.34228
\(816\) 4.99880e16 0.00592761
\(817\) 1.42344e19 1.67454
\(818\) 1.44244e18 0.168345
\(819\) 1.55877e18 0.180483
\(820\) 1.14702e19 1.31760
\(821\) 7.77387e17 0.0885945 0.0442972 0.999018i \(-0.485895\pi\)
0.0442972 + 0.999018i \(0.485895\pi\)
\(822\) 2.22801e18 0.251913
\(823\) −1.08514e19 −1.21726 −0.608632 0.793452i \(-0.708282\pi\)
−0.608632 + 0.793452i \(0.708282\pi\)
\(824\) −3.32084e18 −0.369590
\(825\) −4.41277e17 −0.0487260
\(826\) −2.22453e17 −0.0243707
\(827\) −1.03453e18 −0.112449 −0.0562245 0.998418i \(-0.517906\pi\)
−0.0562245 + 0.998418i \(0.517906\pi\)
\(828\) −3.42020e18 −0.368854
\(829\) 1.51881e19 1.62517 0.812586 0.582841i \(-0.198059\pi\)
0.812586 + 0.582841i \(0.198059\pi\)
\(830\) 3.61964e18 0.384289
\(831\) −2.12240e18 −0.223573
\(832\) 4.40962e18 0.460893
\(833\) −3.49956e16 −0.00362929
\(834\) −1.45208e18 −0.149421
\(835\) 1.21006e19 1.23551
\(836\) 6.46779e18 0.655262
\(837\) 1.53252e18 0.154060
\(838\) 1.35706e18 0.135367
\(839\) −1.21356e19 −1.20118 −0.600590 0.799557i \(-0.705067\pi\)
−0.600590 + 0.799557i \(0.705067\pi\)
\(840\) 2.28665e18 0.224587
\(841\) −8.59820e18 −0.837980
\(842\) −2.71394e18 −0.262465
\(843\) 7.77578e17 0.0746216
\(844\) 1.71879e19 1.63681
\(845\) −6.54629e18 −0.618624
\(846\) −9.30957e17 −0.0873016
\(847\) 5.51277e18 0.513012
\(848\) −3.62884e18 −0.335116
\(849\) −6.68002e18 −0.612178
\(850\) 4.02865e15 0.000366384 0
\(851\) −8.10349e18 −0.731358
\(852\) 1.03265e19 0.924905
\(853\) −4.98941e18 −0.443487 −0.221743 0.975105i \(-0.571175\pi\)
−0.221743 + 0.975105i \(0.571175\pi\)
\(854\) −1.23932e18 −0.109322
\(855\) 4.50401e18 0.394294
\(856\) −2.02663e18 −0.176074
\(857\) −1.34349e19 −1.15841 −0.579203 0.815184i \(-0.696636\pi\)
−0.579203 + 0.815184i \(0.696636\pi\)
\(858\) 6.08238e17 0.0520483
\(859\) 1.54647e19 1.31336 0.656682 0.754167i \(-0.271959\pi\)
0.656682 + 0.754167i \(0.271959\pi\)
\(860\) −1.81196e19 −1.52724
\(861\) 7.50952e18 0.628191
\(862\) 1.83404e18 0.152269
\(863\) 1.22655e19 1.01069 0.505343 0.862918i \(-0.331366\pi\)
0.505343 + 0.862918i \(0.331366\pi\)
\(864\) 1.47650e18 0.120752
\(865\) 4.60518e18 0.373802
\(866\) 2.55098e18 0.205514
\(867\) −7.21939e18 −0.577266
\(868\) 8.00908e18 0.635630
\(869\) 3.16615e18 0.249404
\(870\) 7.09359e17 0.0554614
\(871\) 1.16467e19 0.903825
\(872\) 9.56380e18 0.736670
\(873\) −3.08006e18 −0.235487
\(874\) 3.81553e18 0.289554
\(875\) 1.02211e19 0.769919
\(876\) −1.31614e19 −0.984071
\(877\) −1.59480e19 −1.18361 −0.591806 0.806080i \(-0.701585\pi\)
−0.591806 + 0.806080i \(0.701585\pi\)
\(878\) 4.53035e18 0.333747
\(879\) −1.09583e19 −0.801335
\(880\) −7.77552e18 −0.564407
\(881\) 1.59840e19 1.15171 0.575855 0.817552i \(-0.304669\pi\)
0.575855 + 0.817552i \(0.304669\pi\)
\(882\) −3.14342e17 −0.0224831
\(883\) −1.31205e19 −0.931552 −0.465776 0.884903i \(-0.654225\pi\)
−0.465776 + 0.884903i \(0.654225\pi\)
\(884\) 1.05182e17 0.00741312
\(885\) 1.14497e18 0.0801054
\(886\) −5.50625e18 −0.382417
\(887\) −1.38459e19 −0.954589 −0.477295 0.878743i \(-0.658383\pi\)
−0.477295 + 0.878743i \(0.658383\pi\)
\(888\) 2.31236e18 0.158260
\(889\) 2.45841e19 1.67030
\(890\) −8.43224e17 −0.0568732
\(891\) −1.03140e18 −0.0690595
\(892\) −2.14531e19 −1.42600
\(893\) −1.96722e19 −1.29813
\(894\) 1.31394e18 0.0860760
\(895\) 3.94050e17 0.0256272
\(896\) 1.01868e19 0.657710
\(897\) −6.79659e18 −0.435653
\(898\) −2.38258e18 −0.151618
\(899\) 5.10028e18 0.322223
\(900\) −6.85437e17 −0.0429923
\(901\) −7.61008e16 −0.00473891
\(902\) 2.93025e18 0.181160
\(903\) −1.18628e19 −0.728146
\(904\) 4.61791e18 0.281417
\(905\) 1.32351e19 0.800779
\(906\) −2.87803e18 −0.172887
\(907\) 1.97436e19 1.17755 0.588774 0.808298i \(-0.299611\pi\)
0.588774 + 0.808298i \(0.299611\pi\)
\(908\) 1.88448e19 1.11592
\(909\) −9.92456e18 −0.583507
\(910\) 2.21357e18 0.129219
\(911\) 1.52223e19 0.882289 0.441144 0.897436i \(-0.354573\pi\)
0.441144 + 0.897436i \(0.354573\pi\)
\(912\) 9.48805e18 0.546022
\(913\) −1.75152e19 −1.00082
\(914\) −2.37440e18 −0.134711
\(915\) 6.37879e18 0.359337
\(916\) 1.90881e19 1.06768
\(917\) −2.20283e19 −1.22344
\(918\) 9.41622e15 0.000519277 0
\(919\) 2.52342e19 1.38178 0.690891 0.722959i \(-0.257219\pi\)
0.690891 + 0.722959i \(0.257219\pi\)
\(920\) −9.97031e18 −0.542110
\(921\) 1.24290e19 0.671040
\(922\) 6.28976e18 0.337197
\(923\) 2.05208e19 1.09240
\(924\) −5.39020e18 −0.284929
\(925\) −1.62401e18 −0.0852446
\(926\) −6.75123e18 −0.351894
\(927\) 5.45125e18 0.282149
\(928\) 4.91385e18 0.252558
\(929\) 2.40117e19 1.22552 0.612761 0.790268i \(-0.290059\pi\)
0.612761 + 0.790268i \(0.290059\pi\)
\(930\) 2.17630e18 0.110301
\(931\) −6.64240e18 −0.334312
\(932\) 8.67449e18 0.433551
\(933\) −1.77306e19 −0.880019
\(934\) 6.10146e17 0.0300732
\(935\) −1.63061e17 −0.00798134
\(936\) 1.93943e18 0.0942719
\(937\) 2.86440e19 1.38270 0.691348 0.722522i \(-0.257017\pi\)
0.691348 + 0.722522i \(0.257017\pi\)
\(938\) 5.44897e18 0.261214
\(939\) −7.44616e18 −0.354492
\(940\) 2.50415e19 1.18394
\(941\) −8.65885e18 −0.406563 −0.203282 0.979120i \(-0.565161\pi\)
−0.203282 + 0.979120i \(0.565161\pi\)
\(942\) −2.18368e18 −0.101826
\(943\) −3.27432e19 −1.51634
\(944\) 2.41196e18 0.110931
\(945\) −3.75361e18 −0.171452
\(946\) −4.62893e18 −0.209985
\(947\) −1.63214e19 −0.735333 −0.367666 0.929958i \(-0.619843\pi\)
−0.367666 + 0.929958i \(0.619843\pi\)
\(948\) 4.91799e18 0.220056
\(949\) −2.61543e19 −1.16229
\(950\) 7.64664e17 0.0337495
\(951\) 2.02946e18 0.0889626
\(952\) 1.01018e17 0.00439803
\(953\) 3.63811e19 1.57316 0.786579 0.617490i \(-0.211850\pi\)
0.786579 + 0.617490i \(0.211850\pi\)
\(954\) −6.83563e17 −0.0293572
\(955\) −2.10711e19 −0.898804
\(956\) 3.65338e19 1.54781
\(957\) −3.43255e18 −0.144441
\(958\) 8.83026e17 0.0369061
\(959\) −3.92363e19 −1.62880
\(960\) −1.06186e19 −0.437830
\(961\) −8.77000e18 −0.359168
\(962\) 2.23847e18 0.0910569
\(963\) 3.32678e18 0.134417
\(964\) 2.05477e19 0.824637
\(965\) 1.16111e19 0.462855
\(966\) −3.17983e18 −0.125908
\(967\) 1.62928e18 0.0640801 0.0320400 0.999487i \(-0.489800\pi\)
0.0320400 + 0.999487i \(0.489800\pi\)
\(968\) 6.85903e18 0.267962
\(969\) 1.98975e17 0.00772136
\(970\) −4.37393e18 −0.168599
\(971\) −3.44638e19 −1.31959 −0.659794 0.751446i \(-0.729357\pi\)
−0.659794 + 0.751446i \(0.729357\pi\)
\(972\) −1.60208e18 −0.0609332
\(973\) 2.55719e19 0.966115
\(974\) −2.62486e18 −0.0985083
\(975\) −1.36209e18 −0.0507782
\(976\) 1.34374e19 0.497613
\(977\) 3.91424e18 0.143990 0.0719950 0.997405i \(-0.477063\pi\)
0.0719950 + 0.997405i \(0.477063\pi\)
\(978\) 4.45611e18 0.162837
\(979\) 4.08032e18 0.148117
\(980\) 8.45539e18 0.304905
\(981\) −1.56993e19 −0.562381
\(982\) −1.17092e18 −0.0416680
\(983\) −7.57855e18 −0.267910 −0.133955 0.990987i \(-0.542768\pi\)
−0.133955 + 0.990987i \(0.542768\pi\)
\(984\) 9.34341e18 0.328124
\(985\) −3.50806e19 −1.22386
\(986\) 3.13375e16 0.00108609
\(987\) 1.63946e19 0.564468
\(988\) 1.99642e19 0.682860
\(989\) 5.17247e19 1.75761
\(990\) −1.46467e18 −0.0494438
\(991\) −6.07749e18 −0.203819 −0.101910 0.994794i \(-0.532495\pi\)
−0.101910 + 0.994794i \(0.532495\pi\)
\(992\) 1.50756e19 0.502283
\(993\) 1.45805e19 0.482618
\(994\) 9.60079e18 0.315715
\(995\) −3.65324e19 −1.19352
\(996\) −2.72065e19 −0.883053
\(997\) −1.62386e19 −0.523637 −0.261819 0.965117i \(-0.584322\pi\)
−0.261819 + 0.965117i \(0.584322\pi\)
\(998\) −3.40846e18 −0.109197
\(999\) −3.79582e18 −0.120817
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.1.17 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.17 30 1.1 even 1 trivial