Properties

Label 177.14.a.c.1.1
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $0$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(0\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-170.157 q^{2} +729.000 q^{3} +20761.4 q^{4} +7033.25 q^{5} -124044. q^{6} -166219. q^{7} -2.13877e6 q^{8} +531441. q^{9} +O(q^{10})\) \(q-170.157 q^{2} +729.000 q^{3} +20761.4 q^{4} +7033.25 q^{5} -124044. q^{6} -166219. q^{7} -2.13877e6 q^{8} +531441. q^{9} -1.19676e6 q^{10} -2.55370e6 q^{11} +1.51351e7 q^{12} -9.38582e6 q^{13} +2.82834e7 q^{14} +5.12724e6 q^{15} +1.93850e8 q^{16} -4.94668e7 q^{17} -9.04284e7 q^{18} +8.01706e6 q^{19} +1.46020e8 q^{20} -1.21174e8 q^{21} +4.34530e8 q^{22} -4.03810e8 q^{23} -1.55917e9 q^{24} -1.17124e9 q^{25} +1.59706e9 q^{26} +3.87420e8 q^{27} -3.45095e9 q^{28} -1.78851e9 q^{29} -8.72436e8 q^{30} -7.59511e9 q^{31} -1.54641e10 q^{32} -1.86165e9 q^{33} +8.41713e9 q^{34} -1.16906e9 q^{35} +1.10335e10 q^{36} -2.95954e10 q^{37} -1.36416e9 q^{38} -6.84226e9 q^{39} -1.50425e10 q^{40} -1.30835e9 q^{41} +2.06186e10 q^{42} +1.57511e9 q^{43} -5.30185e10 q^{44} +3.73776e9 q^{45} +6.87111e10 q^{46} +1.19393e11 q^{47} +1.41317e11 q^{48} -6.92602e10 q^{49} +1.99294e11 q^{50} -3.60613e10 q^{51} -1.94863e11 q^{52} +6.19930e10 q^{53} -6.59223e10 q^{54} -1.79608e10 q^{55} +3.55506e11 q^{56} +5.84444e9 q^{57} +3.04328e11 q^{58} -4.21805e10 q^{59} +1.06449e11 q^{60} +4.65074e11 q^{61} +1.29236e12 q^{62} -8.83358e10 q^{63} +1.04331e12 q^{64} -6.60128e10 q^{65} +3.16773e11 q^{66} +8.10106e11 q^{67} -1.02700e12 q^{68} -2.94378e11 q^{69} +1.98924e11 q^{70} -2.60417e11 q^{71} -1.13663e12 q^{72} +4.55646e11 q^{73} +5.03586e12 q^{74} -8.53831e11 q^{75} +1.66446e11 q^{76} +4.24475e11 q^{77} +1.16426e12 q^{78} -3.34216e11 q^{79} +1.36340e12 q^{80} +2.82430e11 q^{81} +2.22626e11 q^{82} -3.25618e12 q^{83} -2.51574e12 q^{84} -3.47913e11 q^{85} -2.68017e11 q^{86} -1.30382e12 q^{87} +5.46179e12 q^{88} -5.57760e11 q^{89} -6.36006e11 q^{90} +1.56010e12 q^{91} -8.38367e12 q^{92} -5.53683e12 q^{93} -2.03156e13 q^{94} +5.63860e10 q^{95} -1.12733e13 q^{96} +8.44687e12 q^{97} +1.17851e13 q^{98} -1.35714e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −170.157 −1.87999 −0.939994 0.341192i \(-0.889169\pi\)
−0.939994 + 0.341192i \(0.889169\pi\)
\(3\) 729.000 0.577350
\(4\) 20761.4 2.53435
\(5\) 7033.25 0.201303 0.100652 0.994922i \(-0.467907\pi\)
0.100652 + 0.994922i \(0.467907\pi\)
\(6\) −124044. −1.08541
\(7\) −166219. −0.534004 −0.267002 0.963696i \(-0.586033\pi\)
−0.267002 + 0.963696i \(0.586033\pi\)
\(8\) −2.13877e6 −2.88456
\(9\) 531441. 0.333333
\(10\) −1.19676e6 −0.378448
\(11\) −2.55370e6 −0.434628 −0.217314 0.976102i \(-0.569730\pi\)
−0.217314 + 0.976102i \(0.569730\pi\)
\(12\) 1.51351e7 1.46321
\(13\) −9.38582e6 −0.539312 −0.269656 0.962957i \(-0.586910\pi\)
−0.269656 + 0.962957i \(0.586910\pi\)
\(14\) 2.82834e7 1.00392
\(15\) 5.12724e6 0.116223
\(16\) 1.93850e8 2.88859
\(17\) −4.94668e7 −0.497045 −0.248523 0.968626i \(-0.579945\pi\)
−0.248523 + 0.968626i \(0.579945\pi\)
\(18\) −9.04284e7 −0.626662
\(19\) 8.01706e6 0.0390946 0.0195473 0.999809i \(-0.493778\pi\)
0.0195473 + 0.999809i \(0.493778\pi\)
\(20\) 1.46020e8 0.510174
\(21\) −1.21174e8 −0.308307
\(22\) 4.34530e8 0.817095
\(23\) −4.03810e8 −0.568783 −0.284391 0.958708i \(-0.591791\pi\)
−0.284391 + 0.958708i \(0.591791\pi\)
\(24\) −1.55917e9 −1.66540
\(25\) −1.17124e9 −0.959477
\(26\) 1.59706e9 1.01390
\(27\) 3.87420e8 0.192450
\(28\) −3.45095e9 −1.35335
\(29\) −1.78851e9 −0.558347 −0.279174 0.960241i \(-0.590060\pi\)
−0.279174 + 0.960241i \(0.590060\pi\)
\(30\) −8.72436e8 −0.218497
\(31\) −7.59511e9 −1.53703 −0.768516 0.639831i \(-0.779005\pi\)
−0.768516 + 0.639831i \(0.779005\pi\)
\(32\) −1.54641e10 −2.54595
\(33\) −1.86165e9 −0.250933
\(34\) 8.41713e9 0.934439
\(35\) −1.16906e9 −0.107497
\(36\) 1.10335e10 0.844784
\(37\) −2.95954e10 −1.89632 −0.948162 0.317789i \(-0.897060\pi\)
−0.948162 + 0.317789i \(0.897060\pi\)
\(38\) −1.36416e9 −0.0734974
\(39\) −6.84226e9 −0.311372
\(40\) −1.50425e10 −0.580672
\(41\) −1.30835e9 −0.0430160 −0.0215080 0.999769i \(-0.506847\pi\)
−0.0215080 + 0.999769i \(0.506847\pi\)
\(42\) 2.06186e10 0.579614
\(43\) 1.57511e9 0.0379986 0.0189993 0.999819i \(-0.493952\pi\)
0.0189993 + 0.999819i \(0.493952\pi\)
\(44\) −5.30185e10 −1.10150
\(45\) 3.73776e9 0.0671011
\(46\) 6.87111e10 1.06930
\(47\) 1.19393e11 1.61563 0.807817 0.589433i \(-0.200649\pi\)
0.807817 + 0.589433i \(0.200649\pi\)
\(48\) 1.41317e11 1.66773
\(49\) −6.92602e10 −0.714840
\(50\) 1.99294e11 1.80380
\(51\) −3.60613e10 −0.286969
\(52\) −1.94863e11 −1.36681
\(53\) 6.19930e10 0.384193 0.192097 0.981376i \(-0.438471\pi\)
0.192097 + 0.981376i \(0.438471\pi\)
\(54\) −6.59223e10 −0.361804
\(55\) −1.79608e10 −0.0874921
\(56\) 3.55506e11 1.54037
\(57\) 5.84444e9 0.0225713
\(58\) 3.04328e11 1.04969
\(59\) −4.21805e10 −0.130189
\(60\) 1.06449e11 0.294549
\(61\) 4.65074e11 1.15579 0.577894 0.816112i \(-0.303875\pi\)
0.577894 + 0.816112i \(0.303875\pi\)
\(62\) 1.29236e12 2.88960
\(63\) −8.83358e10 −0.178001
\(64\) 1.04331e12 1.89776
\(65\) −6.60128e10 −0.108565
\(66\) 3.16773e11 0.471750
\(67\) 8.10106e11 1.09410 0.547048 0.837101i \(-0.315751\pi\)
0.547048 + 0.837101i \(0.315751\pi\)
\(68\) −1.02700e12 −1.25969
\(69\) −2.94378e11 −0.328387
\(70\) 1.98924e11 0.202092
\(71\) −2.60417e11 −0.241263 −0.120631 0.992697i \(-0.538492\pi\)
−0.120631 + 0.992697i \(0.538492\pi\)
\(72\) −1.13663e12 −0.961521
\(73\) 4.55646e11 0.352395 0.176197 0.984355i \(-0.443620\pi\)
0.176197 + 0.984355i \(0.443620\pi\)
\(74\) 5.03586e12 3.56506
\(75\) −8.53831e11 −0.553954
\(76\) 1.66446e11 0.0990796
\(77\) 4.24475e11 0.232093
\(78\) 1.16426e12 0.585376
\(79\) −3.34216e11 −0.154686 −0.0773429 0.997005i \(-0.524644\pi\)
−0.0773429 + 0.997005i \(0.524644\pi\)
\(80\) 1.36340e12 0.581483
\(81\) 2.82430e11 0.111111
\(82\) 2.22626e11 0.0808696
\(83\) −3.25618e12 −1.09320 −0.546602 0.837392i \(-0.684079\pi\)
−0.546602 + 0.837392i \(0.684079\pi\)
\(84\) −2.51574e12 −0.781359
\(85\) −3.47913e11 −0.100057
\(86\) −2.68017e11 −0.0714368
\(87\) −1.30382e12 −0.322362
\(88\) 5.46179e12 1.25371
\(89\) −5.57760e11 −0.118963 −0.0594816 0.998229i \(-0.518945\pi\)
−0.0594816 + 0.998229i \(0.518945\pi\)
\(90\) −6.36006e11 −0.126149
\(91\) 1.56010e12 0.287995
\(92\) −8.38367e12 −1.44150
\(93\) −5.53683e12 −0.887406
\(94\) −2.03156e13 −3.03737
\(95\) 5.63860e10 0.00786988
\(96\) −1.12733e13 −1.46991
\(97\) 8.44687e12 1.02963 0.514813 0.857302i \(-0.327861\pi\)
0.514813 + 0.857302i \(0.327861\pi\)
\(98\) 1.17851e13 1.34389
\(99\) −1.35714e12 −0.144876
\(100\) −2.43165e13 −2.43165
\(101\) 1.23286e13 1.15564 0.577822 0.816163i \(-0.303903\pi\)
0.577822 + 0.816163i \(0.303903\pi\)
\(102\) 6.13609e12 0.539499
\(103\) −9.41263e12 −0.776728 −0.388364 0.921506i \(-0.626960\pi\)
−0.388364 + 0.921506i \(0.626960\pi\)
\(104\) 2.00741e13 1.55568
\(105\) −8.52246e11 −0.0620633
\(106\) −1.05486e13 −0.722279
\(107\) 1.46915e12 0.0946392 0.0473196 0.998880i \(-0.484932\pi\)
0.0473196 + 0.998880i \(0.484932\pi\)
\(108\) 8.04340e12 0.487736
\(109\) −4.79233e12 −0.273700 −0.136850 0.990592i \(-0.543698\pi\)
−0.136850 + 0.990592i \(0.543698\pi\)
\(110\) 3.05616e12 0.164484
\(111\) −2.15750e13 −1.09484
\(112\) −3.22216e13 −1.54252
\(113\) 3.69814e12 0.167099 0.0835495 0.996504i \(-0.473374\pi\)
0.0835495 + 0.996504i \(0.473374\pi\)
\(114\) −9.94473e11 −0.0424337
\(115\) −2.84010e12 −0.114498
\(116\) −3.71320e13 −1.41505
\(117\) −4.98801e12 −0.179771
\(118\) 7.17731e12 0.244754
\(119\) 8.22234e12 0.265424
\(120\) −1.09660e13 −0.335251
\(121\) −2.80013e13 −0.811098
\(122\) −7.91357e13 −2.17287
\(123\) −9.53791e11 −0.0248353
\(124\) −1.57685e14 −3.89538
\(125\) −1.68231e13 −0.394449
\(126\) 1.50310e13 0.334640
\(127\) −3.80266e13 −0.804198 −0.402099 0.915596i \(-0.631719\pi\)
−0.402099 + 0.915596i \(0.631719\pi\)
\(128\) −5.08441e13 −1.02182
\(129\) 1.14826e12 0.0219385
\(130\) 1.12325e13 0.204102
\(131\) 5.84443e13 1.01037 0.505183 0.863012i \(-0.331425\pi\)
0.505183 + 0.863012i \(0.331425\pi\)
\(132\) −3.86505e13 −0.635952
\(133\) −1.33259e12 −0.0208767
\(134\) −1.37845e14 −2.05689
\(135\) 2.72483e12 0.0387408
\(136\) 1.05798e14 1.43376
\(137\) 8.27578e13 1.06936 0.534682 0.845053i \(-0.320431\pi\)
0.534682 + 0.845053i \(0.320431\pi\)
\(138\) 5.00904e13 0.617363
\(139\) −5.38267e13 −0.632997 −0.316499 0.948593i \(-0.602507\pi\)
−0.316499 + 0.948593i \(0.602507\pi\)
\(140\) −2.42714e13 −0.272435
\(141\) 8.70375e13 0.932787
\(142\) 4.43118e13 0.453571
\(143\) 2.39686e13 0.234400
\(144\) 1.03020e14 0.962864
\(145\) −1.25790e13 −0.112397
\(146\) −7.75315e13 −0.662498
\(147\) −5.04907e13 −0.412713
\(148\) −6.14442e14 −4.80595
\(149\) −2.71828e13 −0.203509 −0.101755 0.994810i \(-0.532446\pi\)
−0.101755 + 0.994810i \(0.532446\pi\)
\(150\) 1.45285e14 1.04143
\(151\) 1.41607e14 0.972151 0.486075 0.873917i \(-0.338428\pi\)
0.486075 + 0.873917i \(0.338428\pi\)
\(152\) −1.71467e13 −0.112771
\(153\) −2.62887e13 −0.165682
\(154\) −7.22273e13 −0.436332
\(155\) −5.34183e13 −0.309410
\(156\) −1.42055e14 −0.789127
\(157\) 2.25519e14 1.20181 0.600904 0.799321i \(-0.294807\pi\)
0.600904 + 0.799321i \(0.294807\pi\)
\(158\) 5.68691e13 0.290807
\(159\) 4.51929e13 0.221814
\(160\) −1.08763e14 −0.512508
\(161\) 6.71211e13 0.303732
\(162\) −4.80574e13 −0.208887
\(163\) −1.83787e13 −0.0767532 −0.0383766 0.999263i \(-0.512219\pi\)
−0.0383766 + 0.999263i \(0.512219\pi\)
\(164\) −2.71633e13 −0.109018
\(165\) −1.30934e13 −0.0505136
\(166\) 5.54063e14 2.05521
\(167\) 2.25320e14 0.803790 0.401895 0.915686i \(-0.368352\pi\)
0.401895 + 0.915686i \(0.368352\pi\)
\(168\) 2.59164e14 0.889332
\(169\) −2.14782e14 −0.709142
\(170\) 5.91998e13 0.188106
\(171\) 4.26060e12 0.0130315
\(172\) 3.27016e13 0.0963018
\(173\) −1.50083e14 −0.425628 −0.212814 0.977093i \(-0.568263\pi\)
−0.212814 + 0.977093i \(0.568263\pi\)
\(174\) 2.21855e14 0.606036
\(175\) 1.94682e14 0.512364
\(176\) −4.95035e14 −1.25546
\(177\) −3.07496e13 −0.0751646
\(178\) 9.49068e13 0.223649
\(179\) −3.55234e13 −0.0807179 −0.0403589 0.999185i \(-0.512850\pi\)
−0.0403589 + 0.999185i \(0.512850\pi\)
\(180\) 7.76011e13 0.170058
\(181\) 2.64803e14 0.559773 0.279887 0.960033i \(-0.409703\pi\)
0.279887 + 0.960033i \(0.409703\pi\)
\(182\) −2.65463e14 −0.541426
\(183\) 3.39039e14 0.667295
\(184\) 8.63659e14 1.64069
\(185\) −2.08152e14 −0.381736
\(186\) 9.42131e14 1.66831
\(187\) 1.26324e14 0.216030
\(188\) 2.47877e15 4.09459
\(189\) −6.43968e13 −0.102769
\(190\) −9.59448e12 −0.0147953
\(191\) −2.81830e14 −0.420020 −0.210010 0.977699i \(-0.567350\pi\)
−0.210010 + 0.977699i \(0.567350\pi\)
\(192\) 7.60571e14 1.09568
\(193\) −9.99271e14 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(194\) −1.43729e15 −1.93568
\(195\) −4.81233e13 −0.0626802
\(196\) −1.43794e15 −1.81166
\(197\) 5.75327e14 0.701268 0.350634 0.936513i \(-0.385966\pi\)
0.350634 + 0.936513i \(0.385966\pi\)
\(198\) 2.30927e14 0.272365
\(199\) −1.71490e15 −1.95746 −0.978732 0.205144i \(-0.934234\pi\)
−0.978732 + 0.205144i \(0.934234\pi\)
\(200\) 2.50501e15 2.76767
\(201\) 5.90567e14 0.631677
\(202\) −2.09779e15 −2.17259
\(203\) 2.97285e14 0.298159
\(204\) −7.48684e14 −0.727282
\(205\) −9.20198e12 −0.00865927
\(206\) 1.60163e15 1.46024
\(207\) −2.14601e14 −0.189594
\(208\) −1.81944e15 −1.55785
\(209\) −2.04732e13 −0.0169916
\(210\) 1.45016e14 0.116678
\(211\) −1.77117e15 −1.38173 −0.690866 0.722982i \(-0.742771\pi\)
−0.690866 + 0.722982i \(0.742771\pi\)
\(212\) 1.28706e15 0.973681
\(213\) −1.89844e14 −0.139293
\(214\) −2.49986e14 −0.177920
\(215\) 1.10782e13 0.00764924
\(216\) −8.28605e14 −0.555135
\(217\) 1.26245e15 0.820781
\(218\) 8.15449e14 0.514552
\(219\) 3.32166e14 0.203455
\(220\) −3.72892e14 −0.221736
\(221\) 4.64287e14 0.268063
\(222\) 3.67114e15 2.05829
\(223\) 9.09946e14 0.495489 0.247745 0.968825i \(-0.420311\pi\)
0.247745 + 0.968825i \(0.420311\pi\)
\(224\) 2.57043e15 1.35955
\(225\) −6.22443e14 −0.319826
\(226\) −6.29265e14 −0.314144
\(227\) 1.49961e15 0.727460 0.363730 0.931504i \(-0.381503\pi\)
0.363730 + 0.931504i \(0.381503\pi\)
\(228\) 1.21339e14 0.0572036
\(229\) −1.44673e14 −0.0662914 −0.0331457 0.999451i \(-0.510553\pi\)
−0.0331457 + 0.999451i \(0.510553\pi\)
\(230\) 4.83263e14 0.215255
\(231\) 3.09442e14 0.133999
\(232\) 3.82522e15 1.61059
\(233\) 3.68294e15 1.50793 0.753964 0.656915i \(-0.228139\pi\)
0.753964 + 0.656915i \(0.228139\pi\)
\(234\) 8.48745e14 0.337967
\(235\) 8.39721e14 0.325233
\(236\) −8.75728e14 −0.329945
\(237\) −2.43643e14 −0.0893079
\(238\) −1.39909e15 −0.498994
\(239\) −6.02546e14 −0.209124 −0.104562 0.994518i \(-0.533344\pi\)
−0.104562 + 0.994518i \(0.533344\pi\)
\(240\) 9.93916e14 0.335719
\(241\) 5.03873e14 0.165657 0.0828286 0.996564i \(-0.473605\pi\)
0.0828286 + 0.996564i \(0.473605\pi\)
\(242\) 4.76462e15 1.52485
\(243\) 2.05891e14 0.0641500
\(244\) 9.65560e15 2.92918
\(245\) −4.87124e14 −0.143900
\(246\) 1.62294e14 0.0466901
\(247\) −7.52467e13 −0.0210842
\(248\) 1.62442e16 4.43367
\(249\) −2.37376e15 −0.631162
\(250\) 2.86257e15 0.741560
\(251\) −2.48115e15 −0.626287 −0.313143 0.949706i \(-0.601382\pi\)
−0.313143 + 0.949706i \(0.601382\pi\)
\(252\) −1.83398e15 −0.451118
\(253\) 1.03121e15 0.247209
\(254\) 6.47049e15 1.51188
\(255\) −2.53628e14 −0.0577679
\(256\) 1.04708e14 0.0232498
\(257\) 7.50380e15 1.62449 0.812243 0.583319i \(-0.198246\pi\)
0.812243 + 0.583319i \(0.198246\pi\)
\(258\) −1.95384e14 −0.0412441
\(259\) 4.91932e15 1.01264
\(260\) −1.37052e15 −0.275143
\(261\) −9.50488e14 −0.186116
\(262\) −9.94471e15 −1.89948
\(263\) 6.65940e14 0.124086 0.0620430 0.998073i \(-0.480238\pi\)
0.0620430 + 0.998073i \(0.480238\pi\)
\(264\) 3.98165e15 0.723831
\(265\) 4.36013e14 0.0773394
\(266\) 2.26750e14 0.0392479
\(267\) −4.06607e14 −0.0686834
\(268\) 1.68190e16 2.77283
\(269\) 3.46513e14 0.0557609 0.0278804 0.999611i \(-0.491124\pi\)
0.0278804 + 0.999611i \(0.491124\pi\)
\(270\) −4.63648e14 −0.0728323
\(271\) −4.10330e15 −0.629264 −0.314632 0.949214i \(-0.601881\pi\)
−0.314632 + 0.949214i \(0.601881\pi\)
\(272\) −9.58915e15 −1.43576
\(273\) 1.13732e15 0.166274
\(274\) −1.40818e16 −2.01039
\(275\) 2.99099e15 0.417016
\(276\) −6.11170e15 −0.832248
\(277\) 2.44658e15 0.325417 0.162709 0.986674i \(-0.447977\pi\)
0.162709 + 0.986674i \(0.447977\pi\)
\(278\) 9.15900e15 1.19003
\(279\) −4.03635e15 −0.512344
\(280\) 2.50036e15 0.310081
\(281\) 4.71511e15 0.571347 0.285674 0.958327i \(-0.407783\pi\)
0.285674 + 0.958327i \(0.407783\pi\)
\(282\) −1.48100e16 −1.75363
\(283\) −3.74240e15 −0.433050 −0.216525 0.976277i \(-0.569472\pi\)
−0.216525 + 0.976277i \(0.569472\pi\)
\(284\) −5.40662e15 −0.611444
\(285\) 4.11054e13 0.00454368
\(286\) −4.07842e15 −0.440669
\(287\) 2.17474e14 0.0229707
\(288\) −8.21826e15 −0.848650
\(289\) −7.45761e15 −0.752946
\(290\) 2.14041e15 0.211305
\(291\) 6.15777e15 0.594455
\(292\) 9.45987e15 0.893093
\(293\) −3.63287e15 −0.335437 −0.167718 0.985835i \(-0.553640\pi\)
−0.167718 + 0.985835i \(0.553640\pi\)
\(294\) 8.59134e15 0.775896
\(295\) −2.96666e14 −0.0262075
\(296\) 6.32978e16 5.47007
\(297\) −9.89356e14 −0.0836442
\(298\) 4.62535e15 0.382594
\(299\) 3.79009e15 0.306751
\(300\) −1.77268e16 −1.40392
\(301\) −2.61814e14 −0.0202914
\(302\) −2.40954e16 −1.82763
\(303\) 8.98753e15 0.667211
\(304\) 1.55411e15 0.112928
\(305\) 3.27098e15 0.232664
\(306\) 4.47321e15 0.311480
\(307\) −1.47965e16 −1.00869 −0.504346 0.863501i \(-0.668266\pi\)
−0.504346 + 0.863501i \(0.668266\pi\)
\(308\) 8.81269e15 0.588205
\(309\) −6.86181e15 −0.448444
\(310\) 9.08950e15 0.581686
\(311\) −2.91507e15 −0.182686 −0.0913432 0.995819i \(-0.529116\pi\)
−0.0913432 + 0.995819i \(0.529116\pi\)
\(312\) 1.46341e16 0.898173
\(313\) 1.73118e15 0.104065 0.0520323 0.998645i \(-0.483430\pi\)
0.0520323 + 0.998645i \(0.483430\pi\)
\(314\) −3.83736e16 −2.25939
\(315\) −6.21287e14 −0.0358322
\(316\) −6.93879e15 −0.392028
\(317\) −1.45553e16 −0.805629 −0.402815 0.915282i \(-0.631968\pi\)
−0.402815 + 0.915282i \(0.631968\pi\)
\(318\) −7.68989e15 −0.417008
\(319\) 4.56732e15 0.242673
\(320\) 7.33784e15 0.382026
\(321\) 1.07101e15 0.0546399
\(322\) −1.14211e16 −0.571012
\(323\) −3.96579e14 −0.0194318
\(324\) 5.86364e15 0.281595
\(325\) 1.09930e16 0.517458
\(326\) 3.12727e15 0.144295
\(327\) −3.49361e15 −0.158021
\(328\) 2.79828e15 0.124083
\(329\) −1.98454e16 −0.862754
\(330\) 2.22794e15 0.0949649
\(331\) 3.05897e16 1.27848 0.639239 0.769008i \(-0.279250\pi\)
0.639239 + 0.769008i \(0.279250\pi\)
\(332\) −6.76030e16 −2.77057
\(333\) −1.57282e16 −0.632108
\(334\) −3.83398e16 −1.51111
\(335\) 5.69768e15 0.220245
\(336\) −2.34896e16 −0.890573
\(337\) 1.53397e16 0.570455 0.285228 0.958460i \(-0.407931\pi\)
0.285228 + 0.958460i \(0.407931\pi\)
\(338\) 3.65466e16 1.33318
\(339\) 2.69595e15 0.0964746
\(340\) −7.22316e15 −0.253580
\(341\) 1.93956e16 0.668037
\(342\) −7.24971e14 −0.0244991
\(343\) 2.76172e16 0.915731
\(344\) −3.36882e15 −0.109609
\(345\) −2.07043e15 −0.0661054
\(346\) 2.55376e16 0.800176
\(347\) 5.54727e15 0.170584 0.0852919 0.996356i \(-0.472818\pi\)
0.0852919 + 0.996356i \(0.472818\pi\)
\(348\) −2.70692e16 −0.816979
\(349\) 9.99234e14 0.0296007 0.0148003 0.999890i \(-0.495289\pi\)
0.0148003 + 0.999890i \(0.495289\pi\)
\(350\) −3.31265e16 −0.963238
\(351\) −3.63626e15 −0.103791
\(352\) 3.94907e16 1.10654
\(353\) −4.57025e16 −1.25720 −0.628600 0.777728i \(-0.716372\pi\)
−0.628600 + 0.777728i \(0.716372\pi\)
\(354\) 5.23226e15 0.141309
\(355\) −1.83158e15 −0.0485670
\(356\) −1.15799e16 −0.301495
\(357\) 5.99409e15 0.153243
\(358\) 6.04456e15 0.151749
\(359\) −1.82839e16 −0.450771 −0.225386 0.974270i \(-0.572364\pi\)
−0.225386 + 0.974270i \(0.572364\pi\)
\(360\) −7.99422e15 −0.193557
\(361\) −4.19887e16 −0.998472
\(362\) −4.50581e16 −1.05237
\(363\) −2.04130e16 −0.468288
\(364\) 3.23900e16 0.729880
\(365\) 3.20468e15 0.0709382
\(366\) −5.76899e16 −1.25451
\(367\) −4.89157e16 −1.04501 −0.522503 0.852637i \(-0.675002\pi\)
−0.522503 + 0.852637i \(0.675002\pi\)
\(368\) −7.82786e16 −1.64298
\(369\) −6.95313e14 −0.0143387
\(370\) 3.54184e16 0.717659
\(371\) −1.03044e16 −0.205161
\(372\) −1.14953e17 −2.24900
\(373\) 1.99499e16 0.383560 0.191780 0.981438i \(-0.438574\pi\)
0.191780 + 0.981438i \(0.438574\pi\)
\(374\) −2.14948e16 −0.406134
\(375\) −1.22640e16 −0.227735
\(376\) −2.55355e17 −4.66040
\(377\) 1.67866e16 0.301123
\(378\) 1.09576e16 0.193205
\(379\) 3.65263e16 0.633068 0.316534 0.948581i \(-0.397481\pi\)
0.316534 + 0.948581i \(0.397481\pi\)
\(380\) 1.17065e15 0.0199450
\(381\) −2.77214e16 −0.464304
\(382\) 4.79553e16 0.789633
\(383\) 2.23028e16 0.361050 0.180525 0.983570i \(-0.442220\pi\)
0.180525 + 0.983570i \(0.442220\pi\)
\(384\) −3.70653e16 −0.589950
\(385\) 2.98544e15 0.0467211
\(386\) 1.70033e17 2.61647
\(387\) 8.37080e14 0.0126662
\(388\) 1.75369e17 2.60944
\(389\) 5.46805e16 0.800129 0.400065 0.916487i \(-0.368988\pi\)
0.400065 + 0.916487i \(0.368988\pi\)
\(390\) 8.18852e15 0.117838
\(391\) 1.99752e16 0.282711
\(392\) 1.48132e17 2.06200
\(393\) 4.26059e16 0.583335
\(394\) −9.78959e16 −1.31837
\(395\) −2.35062e15 −0.0311388
\(396\) −2.81762e16 −0.367167
\(397\) 1.28646e17 1.64914 0.824569 0.565761i \(-0.191418\pi\)
0.824569 + 0.565761i \(0.191418\pi\)
\(398\) 2.91802e17 3.68001
\(399\) −9.71459e14 −0.0120531
\(400\) −2.27044e17 −2.77154
\(401\) 3.90820e16 0.469394 0.234697 0.972069i \(-0.424590\pi\)
0.234697 + 0.972069i \(0.424590\pi\)
\(402\) −1.00489e17 −1.18754
\(403\) 7.12863e16 0.828940
\(404\) 2.55959e17 2.92881
\(405\) 1.98640e15 0.0223670
\(406\) −5.05851e16 −0.560536
\(407\) 7.55777e16 0.824195
\(408\) 7.71271e16 0.827781
\(409\) 1.58381e17 1.67302 0.836511 0.547949i \(-0.184591\pi\)
0.836511 + 0.547949i \(0.184591\pi\)
\(410\) 1.56578e15 0.0162793
\(411\) 6.03305e16 0.617397
\(412\) −1.95420e17 −1.96850
\(413\) 7.01122e15 0.0695213
\(414\) 3.65159e16 0.356435
\(415\) −2.29016e16 −0.220066
\(416\) 1.45143e17 1.37306
\(417\) −3.92397e16 −0.365461
\(418\) 3.48366e15 0.0319440
\(419\) −1.75996e16 −0.158895 −0.0794476 0.996839i \(-0.525316\pi\)
−0.0794476 + 0.996839i \(0.525316\pi\)
\(420\) −1.76938e16 −0.157290
\(421\) −6.49651e16 −0.568652 −0.284326 0.958728i \(-0.591770\pi\)
−0.284326 + 0.958728i \(0.591770\pi\)
\(422\) 3.01377e17 2.59764
\(423\) 6.34504e16 0.538545
\(424\) −1.32589e17 −1.10823
\(425\) 5.79374e16 0.476904
\(426\) 3.23033e16 0.261869
\(427\) −7.73043e16 −0.617195
\(428\) 3.05016e16 0.239849
\(429\) 1.74731e16 0.135331
\(430\) −1.88503e15 −0.0143805
\(431\) 2.25555e17 1.69493 0.847463 0.530854i \(-0.178129\pi\)
0.847463 + 0.530854i \(0.178129\pi\)
\(432\) 7.51015e16 0.555910
\(433\) −7.21930e16 −0.526410 −0.263205 0.964740i \(-0.584780\pi\)
−0.263205 + 0.964740i \(0.584780\pi\)
\(434\) −2.14815e17 −1.54306
\(435\) −9.17012e15 −0.0648925
\(436\) −9.94956e16 −0.693652
\(437\) −3.23737e15 −0.0222363
\(438\) −5.65204e16 −0.382493
\(439\) 2.09300e17 1.39557 0.697783 0.716309i \(-0.254170\pi\)
0.697783 + 0.716309i \(0.254170\pi\)
\(440\) 3.84142e16 0.252377
\(441\) −3.68077e16 −0.238280
\(442\) −7.90016e16 −0.503955
\(443\) 2.71262e17 1.70516 0.852578 0.522600i \(-0.175038\pi\)
0.852578 + 0.522600i \(0.175038\pi\)
\(444\) −4.47928e17 −2.77472
\(445\) −3.92287e15 −0.0239477
\(446\) −1.54834e17 −0.931514
\(447\) −1.98163e16 −0.117496
\(448\) −1.73418e17 −1.01341
\(449\) 1.68893e17 0.972773 0.486386 0.873744i \(-0.338315\pi\)
0.486386 + 0.873744i \(0.338315\pi\)
\(450\) 1.05913e17 0.601268
\(451\) 3.34115e15 0.0186960
\(452\) 7.67787e16 0.423488
\(453\) 1.03231e17 0.561272
\(454\) −2.55168e17 −1.36762
\(455\) 1.09726e16 0.0579743
\(456\) −1.24999e16 −0.0651083
\(457\) −7.01661e16 −0.360306 −0.180153 0.983639i \(-0.557659\pi\)
−0.180153 + 0.983639i \(0.557659\pi\)
\(458\) 2.46171e16 0.124627
\(459\) −1.91645e16 −0.0956564
\(460\) −5.89645e16 −0.290178
\(461\) −2.49241e17 −1.20938 −0.604691 0.796460i \(-0.706703\pi\)
−0.604691 + 0.796460i \(0.706703\pi\)
\(462\) −5.26537e16 −0.251916
\(463\) 9.84433e16 0.464419 0.232209 0.972666i \(-0.425405\pi\)
0.232209 + 0.972666i \(0.425405\pi\)
\(464\) −3.46703e17 −1.61284
\(465\) −3.89419e16 −0.178638
\(466\) −6.26678e17 −2.83489
\(467\) 8.80036e16 0.392591 0.196296 0.980545i \(-0.437109\pi\)
0.196296 + 0.980545i \(0.437109\pi\)
\(468\) −1.03558e17 −0.455602
\(469\) −1.34655e17 −0.584252
\(470\) −1.42884e17 −0.611433
\(471\) 1.64403e17 0.693865
\(472\) 9.02147e16 0.375538
\(473\) −4.02237e15 −0.0165152
\(474\) 4.14576e16 0.167898
\(475\) −9.38988e15 −0.0375104
\(476\) 1.70707e17 0.672678
\(477\) 3.29456e16 0.128064
\(478\) 1.02527e17 0.393151
\(479\) 9.72567e16 0.367907 0.183954 0.982935i \(-0.441110\pi\)
0.183954 + 0.982935i \(0.441110\pi\)
\(480\) −7.92882e16 −0.295897
\(481\) 2.77777e17 1.02271
\(482\) −8.57375e16 −0.311433
\(483\) 4.89312e16 0.175360
\(484\) −5.81347e17 −2.05561
\(485\) 5.94090e16 0.207267
\(486\) −3.50338e16 −0.120601
\(487\) 2.54834e17 0.865604 0.432802 0.901489i \(-0.357525\pi\)
0.432802 + 0.901489i \(0.357525\pi\)
\(488\) −9.94689e17 −3.33395
\(489\) −1.33981e16 −0.0443135
\(490\) 8.28876e16 0.270530
\(491\) −4.17339e17 −1.34419 −0.672093 0.740467i \(-0.734605\pi\)
−0.672093 + 0.740467i \(0.734605\pi\)
\(492\) −1.98020e16 −0.0629415
\(493\) 8.84719e16 0.277524
\(494\) 1.28038e16 0.0396380
\(495\) −9.54512e15 −0.0291640
\(496\) −1.47231e18 −4.43986
\(497\) 4.32863e16 0.128835
\(498\) 4.03912e17 1.18658
\(499\) −5.29556e16 −0.153553 −0.0767765 0.997048i \(-0.524463\pi\)
−0.0767765 + 0.997048i \(0.524463\pi\)
\(500\) −3.49272e17 −0.999674
\(501\) 1.64258e17 0.464068
\(502\) 4.22184e17 1.17741
\(503\) 3.57602e17 0.984483 0.492241 0.870459i \(-0.336178\pi\)
0.492241 + 0.870459i \(0.336178\pi\)
\(504\) 1.88930e17 0.513456
\(505\) 8.67099e16 0.232635
\(506\) −1.75468e17 −0.464750
\(507\) −1.56576e17 −0.409424
\(508\) −7.89485e17 −2.03812
\(509\) 5.77008e17 1.47067 0.735337 0.677702i \(-0.237024\pi\)
0.735337 + 0.677702i \(0.237024\pi\)
\(510\) 4.31566e16 0.108603
\(511\) −7.57372e16 −0.188180
\(512\) 3.98698e17 0.978114
\(513\) 3.10598e15 0.00752376
\(514\) −1.27682e18 −3.05401
\(515\) −6.62014e16 −0.156358
\(516\) 2.38395e16 0.0555998
\(517\) −3.04894e17 −0.702200
\(518\) −8.37057e17 −1.90376
\(519\) −1.09410e17 −0.245737
\(520\) 1.41186e17 0.313164
\(521\) −4.44092e17 −0.972810 −0.486405 0.873733i \(-0.661692\pi\)
−0.486405 + 0.873733i \(0.661692\pi\)
\(522\) 1.61732e17 0.349895
\(523\) 6.78619e17 1.44999 0.724995 0.688755i \(-0.241842\pi\)
0.724995 + 0.688755i \(0.241842\pi\)
\(524\) 1.21339e18 2.56062
\(525\) 1.41923e17 0.295814
\(526\) −1.13314e17 −0.233280
\(527\) 3.75706e17 0.763975
\(528\) −3.60881e17 −0.724842
\(529\) −3.40974e17 −0.676486
\(530\) −7.41906e16 −0.145397
\(531\) −2.24165e16 −0.0433963
\(532\) −2.76665e16 −0.0529088
\(533\) 1.22800e16 0.0231991
\(534\) 6.91871e16 0.129124
\(535\) 1.03329e16 0.0190512
\(536\) −1.73263e18 −3.15599
\(537\) −2.58966e16 −0.0466025
\(538\) −5.89616e16 −0.104830
\(539\) 1.76870e17 0.310690
\(540\) 5.65712e16 0.0981830
\(541\) 6.99335e17 1.19923 0.599616 0.800288i \(-0.295320\pi\)
0.599616 + 0.800288i \(0.295320\pi\)
\(542\) 6.98206e17 1.18301
\(543\) 1.93041e17 0.323185
\(544\) 7.64961e17 1.26545
\(545\) −3.37057e16 −0.0550967
\(546\) −1.93522e17 −0.312593
\(547\) 5.92322e16 0.0945454 0.0472727 0.998882i \(-0.484947\pi\)
0.0472727 + 0.998882i \(0.484947\pi\)
\(548\) 1.71817e18 2.71014
\(549\) 2.47160e17 0.385263
\(550\) −5.08938e17 −0.783984
\(551\) −1.43386e16 −0.0218284
\(552\) 6.29608e17 0.947253
\(553\) 5.55531e16 0.0826028
\(554\) −4.16303e17 −0.611780
\(555\) −1.51742e17 −0.220396
\(556\) −1.11752e18 −1.60424
\(557\) 7.37090e17 1.04583 0.522916 0.852384i \(-0.324844\pi\)
0.522916 + 0.852384i \(0.324844\pi\)
\(558\) 6.86814e17 0.963200
\(559\) −1.47837e16 −0.0204931
\(560\) −2.26623e17 −0.310514
\(561\) 9.20899e16 0.124725
\(562\) −8.02308e17 −1.07413
\(563\) −1.24785e17 −0.165142 −0.0825711 0.996585i \(-0.526313\pi\)
−0.0825711 + 0.996585i \(0.526313\pi\)
\(564\) 1.80702e18 2.36401
\(565\) 2.60100e16 0.0336376
\(566\) 6.36795e17 0.814128
\(567\) −4.69452e16 −0.0593337
\(568\) 5.56973e17 0.695937
\(569\) −1.59085e18 −1.96517 −0.982584 0.185817i \(-0.940507\pi\)
−0.982584 + 0.185817i \(0.940507\pi\)
\(570\) −6.99437e15 −0.00854205
\(571\) 1.47573e18 1.78185 0.890926 0.454148i \(-0.150056\pi\)
0.890926 + 0.454148i \(0.150056\pi\)
\(572\) 4.97622e17 0.594053
\(573\) −2.05454e17 −0.242499
\(574\) −3.70047e16 −0.0431847
\(575\) 4.72957e17 0.545734
\(576\) 5.54456e17 0.632588
\(577\) −2.17224e17 −0.245056 −0.122528 0.992465i \(-0.539100\pi\)
−0.122528 + 0.992465i \(0.539100\pi\)
\(578\) 1.26896e18 1.41553
\(579\) −7.28469e17 −0.803526
\(580\) −2.61159e17 −0.284854
\(581\) 5.41241e17 0.583775
\(582\) −1.04779e18 −1.11757
\(583\) −1.58312e17 −0.166981
\(584\) −9.74525e17 −1.01651
\(585\) −3.50819e16 −0.0361885
\(586\) 6.18159e17 0.630617
\(587\) −1.98633e17 −0.200403 −0.100201 0.994967i \(-0.531949\pi\)
−0.100201 + 0.994967i \(0.531949\pi\)
\(588\) −1.04826e18 −1.04596
\(589\) −6.08905e16 −0.0600897
\(590\) 5.04798e16 0.0492697
\(591\) 4.19413e17 0.404877
\(592\) −5.73706e18 −5.47770
\(593\) −6.95171e17 −0.656502 −0.328251 0.944591i \(-0.606459\pi\)
−0.328251 + 0.944591i \(0.606459\pi\)
\(594\) 1.68346e17 0.157250
\(595\) 5.78298e16 0.0534308
\(596\) −5.64354e17 −0.515764
\(597\) −1.25016e18 −1.13014
\(598\) −6.44910e17 −0.576689
\(599\) 1.54769e18 1.36902 0.684508 0.729005i \(-0.260017\pi\)
0.684508 + 0.729005i \(0.260017\pi\)
\(600\) 1.82615e18 1.59792
\(601\) −1.19539e17 −0.103473 −0.0517363 0.998661i \(-0.516476\pi\)
−0.0517363 + 0.998661i \(0.516476\pi\)
\(602\) 4.45496e16 0.0381475
\(603\) 4.30524e17 0.364699
\(604\) 2.93996e18 2.46377
\(605\) −1.96940e17 −0.163277
\(606\) −1.52929e18 −1.25435
\(607\) 9.17599e16 0.0744606 0.0372303 0.999307i \(-0.488146\pi\)
0.0372303 + 0.999307i \(0.488146\pi\)
\(608\) −1.23977e17 −0.0995330
\(609\) 2.16721e17 0.172142
\(610\) −5.56581e17 −0.437406
\(611\) −1.12060e18 −0.871331
\(612\) −5.45791e17 −0.419896
\(613\) −5.26140e17 −0.400505 −0.200253 0.979744i \(-0.564176\pi\)
−0.200253 + 0.979744i \(0.564176\pi\)
\(614\) 2.51772e18 1.89633
\(615\) −6.70825e15 −0.00499943
\(616\) −9.07856e17 −0.669487
\(617\) −6.58913e17 −0.480811 −0.240406 0.970673i \(-0.577280\pi\)
−0.240406 + 0.970673i \(0.577280\pi\)
\(618\) 1.16758e18 0.843070
\(619\) −5.92220e17 −0.423150 −0.211575 0.977362i \(-0.567859\pi\)
−0.211575 + 0.977362i \(0.567859\pi\)
\(620\) −1.10904e18 −0.784153
\(621\) −1.56444e17 −0.109462
\(622\) 4.96020e17 0.343448
\(623\) 9.27105e16 0.0635268
\(624\) −1.32637e18 −0.899427
\(625\) 1.31141e18 0.880073
\(626\) −2.94572e17 −0.195640
\(627\) −1.49250e16 −0.00981012
\(628\) 4.68209e18 3.04581
\(629\) 1.46399e18 0.942559
\(630\) 1.05716e17 0.0673642
\(631\) 5.22450e17 0.329499 0.164750 0.986335i \(-0.447318\pi\)
0.164750 + 0.986335i \(0.447318\pi\)
\(632\) 7.14812e17 0.446201
\(633\) −1.29118e18 −0.797744
\(634\) 2.47668e18 1.51457
\(635\) −2.67450e17 −0.161888
\(636\) 9.38269e17 0.562155
\(637\) 6.50063e17 0.385522
\(638\) −7.77162e17 −0.456223
\(639\) −1.38396e17 −0.0804209
\(640\) −3.57599e17 −0.205696
\(641\) −2.26268e18 −1.28838 −0.644192 0.764864i \(-0.722806\pi\)
−0.644192 + 0.764864i \(0.722806\pi\)
\(642\) −1.82240e17 −0.102722
\(643\) 2.53174e18 1.41269 0.706347 0.707866i \(-0.250342\pi\)
0.706347 + 0.707866i \(0.250342\pi\)
\(644\) 1.39353e18 0.769764
\(645\) 8.07599e15 0.00441629
\(646\) 6.74807e16 0.0365315
\(647\) −2.92304e18 −1.56660 −0.783299 0.621645i \(-0.786465\pi\)
−0.783299 + 0.621645i \(0.786465\pi\)
\(648\) −6.04053e17 −0.320507
\(649\) 1.07717e17 0.0565838
\(650\) −1.87054e18 −0.972814
\(651\) 9.20329e17 0.473878
\(652\) −3.81569e17 −0.194520
\(653\) 2.04456e18 1.03196 0.515981 0.856600i \(-0.327428\pi\)
0.515981 + 0.856600i \(0.327428\pi\)
\(654\) 5.94462e17 0.297077
\(655\) 4.11053e17 0.203390
\(656\) −2.53625e17 −0.124256
\(657\) 2.42149e17 0.117465
\(658\) 3.37684e18 1.62197
\(659\) 2.35125e18 1.11826 0.559130 0.829080i \(-0.311135\pi\)
0.559130 + 0.829080i \(0.311135\pi\)
\(660\) −2.71838e17 −0.128019
\(661\) 3.60614e18 1.68164 0.840820 0.541314i \(-0.182073\pi\)
0.840820 + 0.541314i \(0.182073\pi\)
\(662\) −5.20505e18 −2.40352
\(663\) 3.38465e17 0.154766
\(664\) 6.96424e18 3.15342
\(665\) −9.37244e15 −0.00420254
\(666\) 2.67626e18 1.18835
\(667\) 7.22219e17 0.317578
\(668\) 4.67796e18 2.03709
\(669\) 6.63351e17 0.286071
\(670\) −9.69500e17 −0.414058
\(671\) −1.18766e18 −0.502338
\(672\) 1.87385e18 0.784935
\(673\) −3.12553e17 −0.129666 −0.0648329 0.997896i \(-0.520651\pi\)
−0.0648329 + 0.997896i \(0.520651\pi\)
\(674\) −2.61015e18 −1.07245
\(675\) −4.53761e17 −0.184651
\(676\) −4.45917e18 −1.79722
\(677\) −3.40538e17 −0.135937 −0.0679687 0.997687i \(-0.521652\pi\)
−0.0679687 + 0.997687i \(0.521652\pi\)
\(678\) −4.58734e17 −0.181371
\(679\) −1.40403e18 −0.549824
\(680\) 7.44107e17 0.288621
\(681\) 1.09321e18 0.419999
\(682\) −3.30030e18 −1.25590
\(683\) −2.60485e17 −0.0981858 −0.0490929 0.998794i \(-0.515633\pi\)
−0.0490929 + 0.998794i \(0.515633\pi\)
\(684\) 8.84560e16 0.0330265
\(685\) 5.82057e17 0.215266
\(686\) −4.69926e18 −1.72156
\(687\) −1.05467e17 −0.0382734
\(688\) 3.05336e17 0.109762
\(689\) −5.81855e17 −0.207200
\(690\) 3.52298e17 0.124277
\(691\) −4.25754e18 −1.48782 −0.743912 0.668278i \(-0.767032\pi\)
−0.743912 + 0.668278i \(0.767032\pi\)
\(692\) −3.11593e18 −1.07869
\(693\) 2.25583e17 0.0773643
\(694\) −9.43907e17 −0.320695
\(695\) −3.78577e17 −0.127425
\(696\) 2.78859e18 0.929874
\(697\) 6.47202e16 0.0213809
\(698\) −1.70027e17 −0.0556489
\(699\) 2.68486e18 0.870603
\(700\) 4.04188e18 1.29851
\(701\) −2.38102e17 −0.0757871 −0.0378935 0.999282i \(-0.512065\pi\)
−0.0378935 + 0.999282i \(0.512065\pi\)
\(702\) 6.18735e17 0.195125
\(703\) −2.37268e17 −0.0741360
\(704\) −2.66430e18 −0.824822
\(705\) 6.12157e17 0.187773
\(706\) 7.77661e18 2.36352
\(707\) −2.04925e18 −0.617118
\(708\) −6.38405e17 −0.190494
\(709\) −2.06732e18 −0.611234 −0.305617 0.952154i \(-0.598863\pi\)
−0.305617 + 0.952154i \(0.598863\pi\)
\(710\) 3.11656e17 0.0913053
\(711\) −1.77616e17 −0.0515619
\(712\) 1.19292e18 0.343157
\(713\) 3.06698e18 0.874237
\(714\) −1.01994e18 −0.288094
\(715\) 1.68577e17 0.0471856
\(716\) −7.37516e17 −0.204568
\(717\) −4.39256e17 −0.120738
\(718\) 3.11114e18 0.847444
\(719\) 1.41798e18 0.382766 0.191383 0.981515i \(-0.438703\pi\)
0.191383 + 0.981515i \(0.438703\pi\)
\(720\) 7.24564e17 0.193828
\(721\) 1.56456e18 0.414776
\(722\) 7.14467e18 1.87711
\(723\) 3.67323e17 0.0956422
\(724\) 5.49768e18 1.41866
\(725\) 2.09477e18 0.535721
\(726\) 3.47341e18 0.880375
\(727\) −6.93970e18 −1.74328 −0.871640 0.490146i \(-0.836943\pi\)
−0.871640 + 0.490146i \(0.836943\pi\)
\(728\) −3.33671e18 −0.830739
\(729\) 1.50095e17 0.0370370
\(730\) −5.45298e17 −0.133363
\(731\) −7.79159e16 −0.0188870
\(732\) 7.03894e18 1.69116
\(733\) 7.33084e18 1.74573 0.872866 0.487960i \(-0.162259\pi\)
0.872866 + 0.487960i \(0.162259\pi\)
\(734\) 8.32335e18 1.96460
\(735\) −3.55113e17 −0.0830805
\(736\) 6.24457e18 1.44809
\(737\) −2.06877e18 −0.475525
\(738\) 1.18312e17 0.0269565
\(739\) 5.55464e18 1.25449 0.627245 0.778822i \(-0.284183\pi\)
0.627245 + 0.778822i \(0.284183\pi\)
\(740\) −4.32152e18 −0.967454
\(741\) −5.48548e16 −0.0121730
\(742\) 1.75337e18 0.385699
\(743\) 4.83846e18 1.05507 0.527533 0.849534i \(-0.323117\pi\)
0.527533 + 0.849534i \(0.323117\pi\)
\(744\) 1.18420e19 2.55978
\(745\) −1.91184e17 −0.0409671
\(746\) −3.39461e18 −0.721087
\(747\) −1.73047e18 −0.364401
\(748\) 2.62266e18 0.547496
\(749\) −2.44201e17 −0.0505377
\(750\) 2.08681e18 0.428140
\(751\) −3.87384e18 −0.787921 −0.393960 0.919127i \(-0.628895\pi\)
−0.393960 + 0.919127i \(0.628895\pi\)
\(752\) 2.31444e19 4.66691
\(753\) −1.80876e18 −0.361587
\(754\) −2.85636e18 −0.566108
\(755\) 9.95955e17 0.195697
\(756\) −1.33697e18 −0.260453
\(757\) 6.22964e18 1.20321 0.601603 0.798795i \(-0.294529\pi\)
0.601603 + 0.798795i \(0.294529\pi\)
\(758\) −6.21520e18 −1.19016
\(759\) 7.51753e17 0.142726
\(760\) −1.20597e17 −0.0227012
\(761\) 9.05244e17 0.168953 0.0844764 0.996425i \(-0.473078\pi\)
0.0844764 + 0.996425i \(0.473078\pi\)
\(762\) 4.71698e18 0.872885
\(763\) 7.96578e17 0.146157
\(764\) −5.85119e18 −1.06448
\(765\) −1.84895e17 −0.0333523
\(766\) −3.79498e18 −0.678769
\(767\) 3.95899e17 0.0702125
\(768\) 7.63321e16 0.0134233
\(769\) 1.33698e18 0.233134 0.116567 0.993183i \(-0.462811\pi\)
0.116567 + 0.993183i \(0.462811\pi\)
\(770\) −5.07993e17 −0.0878351
\(771\) 5.47027e18 0.937898
\(772\) −2.07463e19 −3.52718
\(773\) −4.30300e18 −0.725446 −0.362723 0.931897i \(-0.618153\pi\)
−0.362723 + 0.931897i \(0.618153\pi\)
\(774\) −1.42435e17 −0.0238123
\(775\) 8.89567e18 1.47475
\(776\) −1.80660e19 −2.97002
\(777\) 3.58618e18 0.584650
\(778\) −9.30427e18 −1.50423
\(779\) −1.04892e16 −0.00168170
\(780\) −9.99108e17 −0.158854
\(781\) 6.65027e17 0.104859
\(782\) −3.39892e18 −0.531493
\(783\) −6.92905e17 −0.107454
\(784\) −1.34261e19 −2.06488
\(785\) 1.58613e18 0.241928
\(786\) −7.24969e18 −1.09666
\(787\) 1.00855e19 1.51309 0.756543 0.653944i \(-0.226887\pi\)
0.756543 + 0.653944i \(0.226887\pi\)
\(788\) 1.19446e19 1.77726
\(789\) 4.85470e17 0.0716411
\(790\) 3.99975e17 0.0585405
\(791\) −6.14703e17 −0.0892315
\(792\) 2.90262e18 0.417904
\(793\) −4.36510e18 −0.623331
\(794\) −2.18900e19 −3.10036
\(795\) 3.17853e17 0.0446519
\(796\) −3.56037e19 −4.96090
\(797\) −4.37856e18 −0.605135 −0.302567 0.953128i \(-0.597844\pi\)
−0.302567 + 0.953128i \(0.597844\pi\)
\(798\) 1.65301e17 0.0226598
\(799\) −5.90600e18 −0.803044
\(800\) 1.81121e19 2.44278
\(801\) −2.96417e17 −0.0396544
\(802\) −6.65007e18 −0.882455
\(803\) −1.16359e18 −0.153161
\(804\) 1.22610e19 1.60089
\(805\) 4.72079e17 0.0611423
\(806\) −1.21299e19 −1.55840
\(807\) 2.52608e17 0.0321936
\(808\) −2.63680e19 −3.33353
\(809\) 2.23400e18 0.280168 0.140084 0.990140i \(-0.455263\pi\)
0.140084 + 0.990140i \(0.455263\pi\)
\(810\) −3.38000e17 −0.0420498
\(811\) −1.91129e18 −0.235880 −0.117940 0.993021i \(-0.537629\pi\)
−0.117940 + 0.993021i \(0.537629\pi\)
\(812\) 6.17206e18 0.755641
\(813\) −2.99131e18 −0.363306
\(814\) −1.28601e19 −1.54948
\(815\) −1.29262e17 −0.0154507
\(816\) −6.99049e18 −0.828937
\(817\) 1.26278e16 0.00148554
\(818\) −2.69497e19 −3.14526
\(819\) 8.29103e17 0.0959982
\(820\) −1.91046e17 −0.0219457
\(821\) −1.04203e19 −1.18754 −0.593772 0.804633i \(-0.702362\pi\)
−0.593772 + 0.804633i \(0.702362\pi\)
\(822\) −1.02657e19 −1.16070
\(823\) −1.25178e19 −1.40420 −0.702101 0.712077i \(-0.747755\pi\)
−0.702101 + 0.712077i \(0.747755\pi\)
\(824\) 2.01315e19 2.24052
\(825\) 2.18043e18 0.240764
\(826\) −1.19301e18 −0.130699
\(827\) −1.03108e19 −1.12074 −0.560371 0.828241i \(-0.689342\pi\)
−0.560371 + 0.828241i \(0.689342\pi\)
\(828\) −4.45543e18 −0.480499
\(829\) −6.34381e18 −0.678806 −0.339403 0.940641i \(-0.610225\pi\)
−0.339403 + 0.940641i \(0.610225\pi\)
\(830\) 3.89686e18 0.413721
\(831\) 1.78356e18 0.187880
\(832\) −9.79229e18 −1.02349
\(833\) 3.42608e18 0.355308
\(834\) 6.67691e18 0.687063
\(835\) 1.58473e18 0.161806
\(836\) −4.25053e17 −0.0430628
\(837\) −2.94250e18 −0.295802
\(838\) 2.99469e18 0.298721
\(839\) 3.49763e18 0.346196 0.173098 0.984905i \(-0.444622\pi\)
0.173098 + 0.984905i \(0.444622\pi\)
\(840\) 1.82276e18 0.179025
\(841\) −7.06186e18 −0.688248
\(842\) 1.10543e19 1.06906
\(843\) 3.43731e18 0.329868
\(844\) −3.67720e19 −3.50180
\(845\) −1.51061e18 −0.142753
\(846\) −1.07965e19 −1.01246
\(847\) 4.65436e18 0.433130
\(848\) 1.20174e19 1.10978
\(849\) −2.72821e18 −0.250022
\(850\) −9.85845e18 −0.896573
\(851\) 1.19509e19 1.07860
\(852\) −3.94143e18 −0.353018
\(853\) −1.01560e19 −0.902725 −0.451362 0.892341i \(-0.649062\pi\)
−0.451362 + 0.892341i \(0.649062\pi\)
\(854\) 1.31539e19 1.16032
\(855\) 2.99658e16 0.00262329
\(856\) −3.14218e18 −0.272993
\(857\) 1.73329e19 1.49450 0.747248 0.664545i \(-0.231375\pi\)
0.747248 + 0.664545i \(0.231375\pi\)
\(858\) −2.97317e18 −0.254421
\(859\) −1.00287e19 −0.851702 −0.425851 0.904793i \(-0.640025\pi\)
−0.425851 + 0.904793i \(0.640025\pi\)
\(860\) 2.29999e17 0.0193859
\(861\) 1.58538e17 0.0132622
\(862\) −3.83798e19 −3.18644
\(863\) 1.67230e17 0.0137798 0.00688991 0.999976i \(-0.497807\pi\)
0.00688991 + 0.999976i \(0.497807\pi\)
\(864\) −5.99111e18 −0.489969
\(865\) −1.05557e18 −0.0856804
\(866\) 1.22842e19 0.989644
\(867\) −5.43660e18 −0.434713
\(868\) 2.62103e19 2.08015
\(869\) 8.53487e17 0.0672308
\(870\) 1.56036e18 0.121997
\(871\) −7.60351e18 −0.590060
\(872\) 1.02497e19 0.789505
\(873\) 4.48901e18 0.343209
\(874\) 5.50862e17 0.0418040
\(875\) 2.79633e18 0.210637
\(876\) 6.89624e18 0.515627
\(877\) −1.91325e19 −1.41996 −0.709978 0.704224i \(-0.751295\pi\)
−0.709978 + 0.704224i \(0.751295\pi\)
\(878\) −3.56139e19 −2.62365
\(879\) −2.64836e18 −0.193664
\(880\) −3.48171e18 −0.252729
\(881\) −1.48458e19 −1.06970 −0.534849 0.844948i \(-0.679632\pi\)
−0.534849 + 0.844948i \(0.679632\pi\)
\(882\) 6.26309e18 0.447963
\(883\) 1.02434e19 0.727276 0.363638 0.931540i \(-0.381535\pi\)
0.363638 + 0.931540i \(0.381535\pi\)
\(884\) 9.63925e18 0.679365
\(885\) −2.16270e17 −0.0151309
\(886\) −4.61571e19 −3.20567
\(887\) −9.36638e18 −0.645756 −0.322878 0.946441i \(-0.604650\pi\)
−0.322878 + 0.946441i \(0.604650\pi\)
\(888\) 4.61441e19 3.15814
\(889\) 6.32075e18 0.429444
\(890\) 6.67503e17 0.0450213
\(891\) −7.21241e17 −0.0482920
\(892\) 1.88918e19 1.25574
\(893\) 9.57182e17 0.0631626
\(894\) 3.37188e18 0.220891
\(895\) −2.49845e17 −0.0162488
\(896\) 8.45127e18 0.545657
\(897\) 2.76297e18 0.177103
\(898\) −2.87384e19 −1.82880
\(899\) 1.35839e19 0.858198
\(900\) −1.29228e19 −0.810551
\(901\) −3.06660e18 −0.190962
\(902\) −5.68520e17 −0.0351482
\(903\) −1.90863e17 −0.0117152
\(904\) −7.90950e18 −0.482008
\(905\) 1.86242e18 0.112684
\(906\) −1.75655e19 −1.05518
\(907\) −2.02775e18 −0.120939 −0.0604696 0.998170i \(-0.519260\pi\)
−0.0604696 + 0.998170i \(0.519260\pi\)
\(908\) 3.11339e19 1.84364
\(909\) 6.55191e18 0.385214
\(910\) −1.86707e18 −0.108991
\(911\) 1.57823e19 0.914747 0.457374 0.889275i \(-0.348790\pi\)
0.457374 + 0.889275i \(0.348790\pi\)
\(912\) 1.13295e18 0.0651992
\(913\) 8.31532e18 0.475137
\(914\) 1.19392e19 0.677371
\(915\) 2.38455e18 0.134329
\(916\) −3.00362e18 −0.168006
\(917\) −9.71457e18 −0.539539
\(918\) 3.26097e18 0.179833
\(919\) 1.43504e19 0.785804 0.392902 0.919580i \(-0.371471\pi\)
0.392902 + 0.919580i \(0.371471\pi\)
\(920\) 6.07433e18 0.330276
\(921\) −1.07866e19 −0.582369
\(922\) 4.24101e19 2.27362
\(923\) 2.44423e18 0.130116
\(924\) 6.42445e18 0.339601
\(925\) 3.46632e19 1.81948
\(926\) −1.67508e19 −0.873101
\(927\) −5.00226e18 −0.258909
\(928\) 2.76577e19 1.42152
\(929\) 1.02277e19 0.522006 0.261003 0.965338i \(-0.415947\pi\)
0.261003 + 0.965338i \(0.415947\pi\)
\(930\) 6.62624e18 0.335837
\(931\) −5.55263e17 −0.0279464
\(932\) 7.64630e19 3.82162
\(933\) −2.12509e18 −0.105474
\(934\) −1.49744e19 −0.738067
\(935\) 8.88465e17 0.0434875
\(936\) 1.06682e19 0.518560
\(937\) −1.82906e18 −0.0882920 −0.0441460 0.999025i \(-0.514057\pi\)
−0.0441460 + 0.999025i \(0.514057\pi\)
\(938\) 2.29125e19 1.09839
\(939\) 1.26203e18 0.0600817
\(940\) 1.74338e19 0.824254
\(941\) −1.95860e19 −0.919632 −0.459816 0.888014i \(-0.652085\pi\)
−0.459816 + 0.888014i \(0.652085\pi\)
\(942\) −2.79744e19 −1.30446
\(943\) 5.28327e17 0.0244668
\(944\) −8.17670e18 −0.376063
\(945\) −4.52919e17 −0.0206878
\(946\) 6.84435e17 0.0310484
\(947\) −3.22268e19 −1.45192 −0.725959 0.687738i \(-0.758604\pi\)
−0.725959 + 0.687738i \(0.758604\pi\)
\(948\) −5.05838e18 −0.226338
\(949\) −4.27661e18 −0.190051
\(950\) 1.59775e18 0.0705191
\(951\) −1.06108e19 −0.465130
\(952\) −1.75857e19 −0.765633
\(953\) 3.50779e19 1.51680 0.758402 0.651787i \(-0.225980\pi\)
0.758402 + 0.651787i \(0.225980\pi\)
\(954\) −5.60593e18 −0.240760
\(955\) −1.98218e18 −0.0845515
\(956\) −1.25097e19 −0.529994
\(957\) 3.32958e18 0.140108
\(958\) −1.65489e19 −0.691661
\(959\) −1.37559e19 −0.571044
\(960\) 5.34929e18 0.220563
\(961\) 3.32681e19 1.36247
\(962\) −4.72656e19 −1.92268
\(963\) 7.80765e17 0.0315464
\(964\) 1.04611e19 0.419834
\(965\) −7.02812e18 −0.280164
\(966\) −8.32600e18 −0.329674
\(967\) 8.43990e18 0.331944 0.165972 0.986130i \(-0.446924\pi\)
0.165972 + 0.986130i \(0.446924\pi\)
\(968\) 5.98885e19 2.33967
\(969\) −2.89106e17 −0.0112190
\(970\) −1.01089e19 −0.389660
\(971\) 1.46332e18 0.0560292 0.0280146 0.999608i \(-0.491082\pi\)
0.0280146 + 0.999608i \(0.491082\pi\)
\(972\) 4.27459e18 0.162579
\(973\) 8.94704e18 0.338023
\(974\) −4.33618e19 −1.62732
\(975\) 8.01391e18 0.298754
\(976\) 9.01547e19 3.33860
\(977\) −2.00744e19 −0.738460 −0.369230 0.929338i \(-0.620379\pi\)
−0.369230 + 0.929338i \(0.620379\pi\)
\(978\) 2.27978e18 0.0833087
\(979\) 1.42435e18 0.0517047
\(980\) −1.01134e19 −0.364693
\(981\) −2.54684e18 −0.0912333
\(982\) 7.10132e19 2.52705
\(983\) −3.24364e19 −1.14666 −0.573330 0.819324i \(-0.694349\pi\)
−0.573330 + 0.819324i \(0.694349\pi\)
\(984\) 2.03994e18 0.0716391
\(985\) 4.04642e18 0.141168
\(986\) −1.50541e19 −0.521742
\(987\) −1.44673e19 −0.498111
\(988\) −1.56223e18 −0.0534348
\(989\) −6.36047e17 −0.0216129
\(990\) 1.62417e18 0.0548280
\(991\) −2.00348e19 −0.671903 −0.335951 0.941879i \(-0.609058\pi\)
−0.335951 + 0.941879i \(0.609058\pi\)
\(992\) 1.17452e20 3.91321
\(993\) 2.22999e19 0.738129
\(994\) −7.36547e18 −0.242208
\(995\) −1.20613e19 −0.394044
\(996\) −4.92826e19 −1.59959
\(997\) 5.61755e19 1.81146 0.905729 0.423858i \(-0.139325\pi\)
0.905729 + 0.423858i \(0.139325\pi\)
\(998\) 9.01077e18 0.288678
\(999\) −1.14658e19 −0.364948
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.c.1.1 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.1 31 1.1 even 1 trivial