Properties

Label 177.14.a.a.1.1
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 1.1
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-169.531 q^{2} +729.000 q^{3} +20548.9 q^{4} -21413.6 q^{5} -123588. q^{6} +361154. q^{7} -2.09488e6 q^{8} +531441. q^{9} +O(q^{10})\) \(q-169.531 q^{2} +729.000 q^{3} +20548.9 q^{4} -21413.6 q^{5} -123588. q^{6} +361154. q^{7} -2.09488e6 q^{8} +531441. q^{9} +3.63027e6 q^{10} -6.55650e6 q^{11} +1.49801e7 q^{12} +3.19555e6 q^{13} -6.12269e7 q^{14} -1.56105e7 q^{15} +1.86812e8 q^{16} +2.70339e7 q^{17} -9.00959e7 q^{18} -6.84109e7 q^{19} -4.40025e8 q^{20} +2.63281e8 q^{21} +1.11153e9 q^{22} -5.78204e8 q^{23} -1.52717e9 q^{24} -7.62162e8 q^{25} -5.41746e8 q^{26} +3.87420e8 q^{27} +7.42131e9 q^{28} +3.44992e9 q^{29} +2.64647e9 q^{30} +9.42535e9 q^{31} -1.45092e10 q^{32} -4.77969e9 q^{33} -4.58309e9 q^{34} -7.73360e9 q^{35} +1.09205e10 q^{36} +1.03645e10 q^{37} +1.15978e10 q^{38} +2.32956e9 q^{39} +4.48589e10 q^{40} -2.19371e9 q^{41} -4.46344e10 q^{42} -2.12752e10 q^{43} -1.34729e11 q^{44} -1.13801e10 q^{45} +9.80237e10 q^{46} +3.14969e10 q^{47} +1.36186e11 q^{48} +3.35431e10 q^{49} +1.29210e11 q^{50} +1.97077e10 q^{51} +6.56650e10 q^{52} -2.87264e11 q^{53} -6.56799e10 q^{54} +1.40398e11 q^{55} -7.56575e11 q^{56} -4.98715e10 q^{57} -5.84870e11 q^{58} +4.21805e10 q^{59} -3.20779e11 q^{60} -5.01289e10 q^{61} -1.59789e12 q^{62} +1.91932e11 q^{63} +9.29400e11 q^{64} -6.84282e10 q^{65} +8.10307e11 q^{66} -5.06275e11 q^{67} +5.55516e11 q^{68} -4.21511e11 q^{69} +1.31109e12 q^{70} -1.47759e12 q^{71} -1.11331e12 q^{72} -5.72451e11 q^{73} -1.75710e12 q^{74} -5.55616e11 q^{75} -1.40577e12 q^{76} -2.36790e12 q^{77} -3.94933e11 q^{78} +1.61549e12 q^{79} -4.00031e12 q^{80} +2.82430e11 q^{81} +3.71903e11 q^{82} +2.15856e12 q^{83} +5.41014e12 q^{84} -5.78892e11 q^{85} +3.60682e12 q^{86} +2.51499e12 q^{87} +1.37351e13 q^{88} +1.78420e12 q^{89} +1.92928e12 q^{90} +1.15409e12 q^{91} -1.18815e13 q^{92} +6.87108e12 q^{93} -5.33972e12 q^{94} +1.46492e12 q^{95} -1.05772e13 q^{96} -3.76742e11 q^{97} -5.68661e12 q^{98} -3.48439e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −169.531 −1.87308 −0.936538 0.350567i \(-0.885989\pi\)
−0.936538 + 0.350567i \(0.885989\pi\)
\(3\) 729.000 0.577350
\(4\) 20548.9 2.50841
\(5\) −21413.6 −0.612892 −0.306446 0.951888i \(-0.599140\pi\)
−0.306446 + 0.951888i \(0.599140\pi\)
\(6\) −123588. −1.08142
\(7\) 361154. 1.16026 0.580130 0.814524i \(-0.303002\pi\)
0.580130 + 0.814524i \(0.303002\pi\)
\(8\) −2.09488e6 −2.82537
\(9\) 531441. 0.333333
\(10\) 3.63027e6 1.14799
\(11\) −6.55650e6 −1.11589 −0.557943 0.829880i \(-0.688409\pi\)
−0.557943 + 0.829880i \(0.688409\pi\)
\(12\) 1.49801e7 1.44823
\(13\) 3.19555e6 0.183617 0.0918087 0.995777i \(-0.470735\pi\)
0.0918087 + 0.995777i \(0.470735\pi\)
\(14\) −6.12269e7 −2.17325
\(15\) −1.56105e7 −0.353854
\(16\) 1.86812e8 2.78371
\(17\) 2.70339e7 0.271638 0.135819 0.990734i \(-0.456633\pi\)
0.135819 + 0.990734i \(0.456633\pi\)
\(18\) −9.00959e7 −0.624358
\(19\) −6.84109e7 −0.333601 −0.166800 0.985991i \(-0.553344\pi\)
−0.166800 + 0.985991i \(0.553344\pi\)
\(20\) −4.40025e8 −1.53739
\(21\) 2.63281e8 0.669876
\(22\) 1.11153e9 2.09014
\(23\) −5.78204e8 −0.814423 −0.407212 0.913334i \(-0.633499\pi\)
−0.407212 + 0.913334i \(0.633499\pi\)
\(24\) −1.52717e9 −1.63123
\(25\) −7.62162e8 −0.624363
\(26\) −5.41746e8 −0.343929
\(27\) 3.87420e8 0.192450
\(28\) 7.42131e9 2.91041
\(29\) 3.44992e9 1.07702 0.538508 0.842620i \(-0.318988\pi\)
0.538508 + 0.842620i \(0.318988\pi\)
\(30\) 2.64647e9 0.662794
\(31\) 9.42535e9 1.90742 0.953710 0.300727i \(-0.0972293\pi\)
0.953710 + 0.300727i \(0.0972293\pi\)
\(32\) −1.45092e10 −2.38874
\(33\) −4.77969e9 −0.644257
\(34\) −4.58309e9 −0.508798
\(35\) −7.73360e9 −0.711114
\(36\) 1.09205e10 0.836137
\(37\) 1.03645e10 0.664103 0.332052 0.943261i \(-0.392259\pi\)
0.332052 + 0.943261i \(0.392259\pi\)
\(38\) 1.15978e10 0.624859
\(39\) 2.32956e9 0.106012
\(40\) 4.48589e10 1.73164
\(41\) −2.19371e9 −0.0721248 −0.0360624 0.999350i \(-0.511482\pi\)
−0.0360624 + 0.999350i \(0.511482\pi\)
\(42\) −4.46344e10 −1.25473
\(43\) −2.12752e10 −0.513250 −0.256625 0.966511i \(-0.582611\pi\)
−0.256625 + 0.966511i \(0.582611\pi\)
\(44\) −1.34729e11 −2.79910
\(45\) −1.13801e10 −0.204297
\(46\) 9.80237e10 1.52548
\(47\) 3.14969e10 0.426219 0.213109 0.977028i \(-0.431641\pi\)
0.213109 + 0.977028i \(0.431641\pi\)
\(48\) 1.36186e11 1.60718
\(49\) 3.35431e10 0.346201
\(50\) 1.29210e11 1.16948
\(51\) 1.97077e10 0.156830
\(52\) 6.56650e10 0.460588
\(53\) −2.87264e11 −1.78028 −0.890138 0.455691i \(-0.849392\pi\)
−0.890138 + 0.455691i \(0.849392\pi\)
\(54\) −6.56799e10 −0.360473
\(55\) 1.40398e11 0.683917
\(56\) −7.56575e11 −3.27816
\(57\) −4.98715e10 −0.192604
\(58\) −5.84870e11 −2.01733
\(59\) 4.21805e10 0.130189
\(60\) −3.20779e11 −0.887610
\(61\) −5.01289e10 −0.124579 −0.0622894 0.998058i \(-0.519840\pi\)
−0.0622894 + 0.998058i \(0.519840\pi\)
\(62\) −1.59789e12 −3.57274
\(63\) 1.91932e11 0.386753
\(64\) 9.29400e11 1.69057
\(65\) −6.84282e10 −0.112538
\(66\) 8.10307e11 1.20674
\(67\) −5.06275e11 −0.683755 −0.341878 0.939744i \(-0.611063\pi\)
−0.341878 + 0.939744i \(0.611063\pi\)
\(68\) 5.55516e11 0.681379
\(69\) −4.21511e11 −0.470207
\(70\) 1.31109e12 1.33197
\(71\) −1.47759e12 −1.36891 −0.684454 0.729056i \(-0.739959\pi\)
−0.684454 + 0.729056i \(0.739959\pi\)
\(72\) −1.11331e12 −0.941789
\(73\) −5.72451e11 −0.442731 −0.221365 0.975191i \(-0.571051\pi\)
−0.221365 + 0.975191i \(0.571051\pi\)
\(74\) −1.75710e12 −1.24392
\(75\) −5.55616e11 −0.360476
\(76\) −1.40577e12 −0.836807
\(77\) −2.36790e12 −1.29472
\(78\) −3.94933e11 −0.198568
\(79\) 1.61549e12 0.747702 0.373851 0.927489i \(-0.378037\pi\)
0.373851 + 0.927489i \(0.378037\pi\)
\(80\) −4.00031e12 −1.70612
\(81\) 2.82430e11 0.111111
\(82\) 3.71903e11 0.135095
\(83\) 2.15856e12 0.724697 0.362348 0.932043i \(-0.381975\pi\)
0.362348 + 0.932043i \(0.381975\pi\)
\(84\) 5.41014e12 1.68032
\(85\) −5.78892e11 −0.166485
\(86\) 3.60682e12 0.961355
\(87\) 2.51499e12 0.621816
\(88\) 1.37351e13 3.15278
\(89\) 1.78420e12 0.380547 0.190274 0.981731i \(-0.439062\pi\)
0.190274 + 0.981731i \(0.439062\pi\)
\(90\) 1.92928e12 0.382664
\(91\) 1.15409e12 0.213044
\(92\) −1.18815e13 −2.04291
\(93\) 6.87108e12 1.10125
\(94\) −5.33972e12 −0.798339
\(95\) 1.46492e12 0.204461
\(96\) −1.05772e13 −1.37914
\(97\) −3.76742e11 −0.0459227 −0.0229613 0.999736i \(-0.507309\pi\)
−0.0229613 + 0.999736i \(0.507309\pi\)
\(98\) −5.68661e12 −0.648461
\(99\) −3.48439e12 −0.371962
\(100\) −1.56616e13 −1.56616
\(101\) −1.25220e13 −1.17377 −0.586887 0.809669i \(-0.699647\pi\)
−0.586887 + 0.809669i \(0.699647\pi\)
\(102\) −3.34107e12 −0.293755
\(103\) −3.17368e12 −0.261892 −0.130946 0.991390i \(-0.541801\pi\)
−0.130946 + 0.991390i \(0.541801\pi\)
\(104\) −6.69430e12 −0.518786
\(105\) −5.63779e12 −0.410562
\(106\) 4.87002e13 3.33459
\(107\) −8.62759e12 −0.555770 −0.277885 0.960614i \(-0.589633\pi\)
−0.277885 + 0.960614i \(0.589633\pi\)
\(108\) 7.96106e12 0.482744
\(109\) 1.98524e13 1.13381 0.566906 0.823783i \(-0.308140\pi\)
0.566906 + 0.823783i \(0.308140\pi\)
\(110\) −2.38019e13 −1.28103
\(111\) 7.55569e12 0.383420
\(112\) 6.74678e13 3.22983
\(113\) 3.65518e13 1.65158 0.825789 0.563979i \(-0.190730\pi\)
0.825789 + 0.563979i \(0.190730\pi\)
\(114\) 8.45479e12 0.360762
\(115\) 1.23814e13 0.499154
\(116\) 7.08921e13 2.70160
\(117\) 1.69825e12 0.0612058
\(118\) −7.15093e12 −0.243854
\(119\) 9.76338e12 0.315170
\(120\) 3.27022e13 0.999766
\(121\) 8.46495e12 0.245199
\(122\) 8.49842e12 0.233345
\(123\) −1.59922e12 −0.0416412
\(124\) 1.93681e14 4.78459
\(125\) 4.24602e13 0.995560
\(126\) −3.25385e13 −0.724418
\(127\) 6.84567e13 1.44774 0.723872 0.689934i \(-0.242360\pi\)
0.723872 + 0.689934i \(0.242360\pi\)
\(128\) −3.87033e13 −0.777827
\(129\) −1.55096e13 −0.296325
\(130\) 1.16007e13 0.210792
\(131\) 5.40307e13 0.934065 0.467032 0.884240i \(-0.345323\pi\)
0.467032 + 0.884240i \(0.345323\pi\)
\(132\) −9.82173e13 −1.61606
\(133\) −2.47069e13 −0.387063
\(134\) 8.58296e13 1.28072
\(135\) −8.29606e12 −0.117951
\(136\) −5.66327e13 −0.767476
\(137\) −3.82436e13 −0.494168 −0.247084 0.968994i \(-0.579472\pi\)
−0.247084 + 0.968994i \(0.579472\pi\)
\(138\) 7.14593e13 0.880734
\(139\) −1.12280e14 −1.32040 −0.660201 0.751089i \(-0.729529\pi\)
−0.660201 + 0.751089i \(0.729529\pi\)
\(140\) −1.58917e14 −1.78377
\(141\) 2.29613e13 0.246077
\(142\) 2.50498e14 2.56407
\(143\) −2.09516e13 −0.204896
\(144\) 9.92794e13 0.927904
\(145\) −7.38752e13 −0.660095
\(146\) 9.70484e13 0.829268
\(147\) 2.44529e13 0.199879
\(148\) 2.12978e14 1.66584
\(149\) −3.45852e13 −0.258928 −0.129464 0.991584i \(-0.541326\pi\)
−0.129464 + 0.991584i \(0.541326\pi\)
\(150\) 9.41944e13 0.675199
\(151\) −1.39958e14 −0.960831 −0.480416 0.877041i \(-0.659514\pi\)
−0.480416 + 0.877041i \(0.659514\pi\)
\(152\) 1.43313e14 0.942543
\(153\) 1.43669e13 0.0905459
\(154\) 4.01434e14 2.42510
\(155\) −2.01830e14 −1.16904
\(156\) 4.78698e13 0.265920
\(157\) 9.14522e13 0.487356 0.243678 0.969856i \(-0.421646\pi\)
0.243678 + 0.969856i \(0.421646\pi\)
\(158\) −2.73876e14 −1.40050
\(159\) −2.09415e14 −1.02784
\(160\) 3.10693e14 1.46404
\(161\) −2.08821e14 −0.944942
\(162\) −4.78807e13 −0.208119
\(163\) −2.06673e14 −0.863108 −0.431554 0.902087i \(-0.642035\pi\)
−0.431554 + 0.902087i \(0.642035\pi\)
\(164\) −4.50783e13 −0.180918
\(165\) 1.02350e14 0.394860
\(166\) −3.65943e14 −1.35741
\(167\) −1.94548e13 −0.0694016 −0.0347008 0.999398i \(-0.511048\pi\)
−0.0347008 + 0.999398i \(0.511048\pi\)
\(168\) −5.51543e14 −1.89264
\(169\) −2.92664e14 −0.966285
\(170\) 9.81403e13 0.311838
\(171\) −3.63563e13 −0.111200
\(172\) −4.37182e14 −1.28744
\(173\) 4.09717e14 1.16194 0.580971 0.813925i \(-0.302673\pi\)
0.580971 + 0.813925i \(0.302673\pi\)
\(174\) −4.26370e14 −1.16471
\(175\) −2.75258e14 −0.724423
\(176\) −1.22483e15 −3.10630
\(177\) 3.07496e13 0.0751646
\(178\) −3.02478e14 −0.712794
\(179\) 7.18549e14 1.63272 0.816360 0.577543i \(-0.195988\pi\)
0.816360 + 0.577543i \(0.195988\pi\)
\(180\) −2.33848e14 −0.512462
\(181\) −4.94149e14 −1.04459 −0.522297 0.852764i \(-0.674925\pi\)
−0.522297 + 0.852764i \(0.674925\pi\)
\(182\) −1.95654e14 −0.399047
\(183\) −3.65440e13 −0.0719256
\(184\) 1.21127e15 2.30104
\(185\) −2.21940e14 −0.407024
\(186\) −1.16486e15 −2.06272
\(187\) −1.77247e14 −0.303116
\(188\) 6.47227e14 1.06913
\(189\) 1.39918e14 0.223292
\(190\) −2.48350e14 −0.382971
\(191\) −7.56869e14 −1.12799 −0.563993 0.825780i \(-0.690735\pi\)
−0.563993 + 0.825780i \(0.690735\pi\)
\(192\) 6.77533e14 0.976050
\(193\) 5.42119e13 0.0755044 0.0377522 0.999287i \(-0.487980\pi\)
0.0377522 + 0.999287i \(0.487980\pi\)
\(194\) 6.38695e13 0.0860166
\(195\) −4.98841e13 −0.0649737
\(196\) 6.89274e14 0.868415
\(197\) −3.73102e14 −0.454775 −0.227388 0.973804i \(-0.573018\pi\)
−0.227388 + 0.973804i \(0.573018\pi\)
\(198\) 5.90714e14 0.696712
\(199\) −3.01874e14 −0.344573 −0.172286 0.985047i \(-0.555115\pi\)
−0.172286 + 0.985047i \(0.555115\pi\)
\(200\) 1.59664e15 1.76405
\(201\) −3.69075e14 −0.394766
\(202\) 2.12287e15 2.19857
\(203\) 1.24595e15 1.24962
\(204\) 4.04971e14 0.393394
\(205\) 4.69752e13 0.0442047
\(206\) 5.38039e14 0.490543
\(207\) −3.07281e14 −0.271474
\(208\) 5.96966e14 0.511138
\(209\) 4.48536e14 0.372260
\(210\) 9.55783e14 0.769013
\(211\) 1.87437e15 1.46225 0.731123 0.682246i \(-0.238997\pi\)
0.731123 + 0.682246i \(0.238997\pi\)
\(212\) −5.90295e15 −4.46566
\(213\) −1.07716e15 −0.790339
\(214\) 1.46265e15 1.04100
\(215\) 4.55578e14 0.314567
\(216\) −8.11600e14 −0.543742
\(217\) 3.40400e15 2.21310
\(218\) −3.36561e15 −2.12371
\(219\) −4.17317e14 −0.255611
\(220\) 2.88503e15 1.71555
\(221\) 8.63880e13 0.0498774
\(222\) −1.28093e15 −0.718175
\(223\) 1.88601e14 0.102698 0.0513490 0.998681i \(-0.483648\pi\)
0.0513490 + 0.998681i \(0.483648\pi\)
\(224\) −5.24005e15 −2.77155
\(225\) −4.05044e14 −0.208121
\(226\) −6.19668e15 −3.09353
\(227\) −3.16490e15 −1.53529 −0.767647 0.640873i \(-0.778573\pi\)
−0.767647 + 0.640873i \(0.778573\pi\)
\(228\) −1.02480e15 −0.483131
\(229\) 2.86580e15 1.31315 0.656577 0.754259i \(-0.272004\pi\)
0.656577 + 0.754259i \(0.272004\pi\)
\(230\) −2.09904e15 −0.934952
\(231\) −1.72620e15 −0.747505
\(232\) −7.22718e15 −3.04297
\(233\) −1.63684e14 −0.0670183 −0.0335092 0.999438i \(-0.510668\pi\)
−0.0335092 + 0.999438i \(0.510668\pi\)
\(234\) −2.87906e14 −0.114643
\(235\) −6.74462e14 −0.261226
\(236\) 8.66763e14 0.326567
\(237\) 1.17769e15 0.431686
\(238\) −1.65520e15 −0.590337
\(239\) −1.56852e15 −0.544381 −0.272191 0.962243i \(-0.587748\pi\)
−0.272191 + 0.962243i \(0.587748\pi\)
\(240\) −2.91622e15 −0.985026
\(241\) −1.53250e15 −0.503835 −0.251918 0.967749i \(-0.581061\pi\)
−0.251918 + 0.967749i \(0.581061\pi\)
\(242\) −1.43507e15 −0.459277
\(243\) 2.05891e14 0.0641500
\(244\) −1.03009e15 −0.312495
\(245\) −7.18278e14 −0.212184
\(246\) 2.71117e14 0.0779972
\(247\) −2.18610e14 −0.0612549
\(248\) −1.97450e16 −5.38916
\(249\) 1.57359e15 0.418404
\(250\) −7.19834e15 −1.86476
\(251\) −5.07634e15 −1.28136 −0.640680 0.767808i \(-0.721348\pi\)
−0.640680 + 0.767808i \(0.721348\pi\)
\(252\) 3.94399e15 0.970135
\(253\) 3.79099e15 0.908803
\(254\) −1.16056e16 −2.71173
\(255\) −4.22012e14 −0.0961200
\(256\) −1.05222e15 −0.233640
\(257\) 5.57883e15 1.20775 0.603876 0.797078i \(-0.293622\pi\)
0.603876 + 0.797078i \(0.293622\pi\)
\(258\) 2.62937e15 0.555039
\(259\) 3.74317e15 0.770532
\(260\) −1.40612e15 −0.282291
\(261\) 1.83343e15 0.359006
\(262\) −9.15990e15 −1.74957
\(263\) 1.41314e15 0.263313 0.131656 0.991295i \(-0.457970\pi\)
0.131656 + 0.991295i \(0.457970\pi\)
\(264\) 1.00129e16 1.82026
\(265\) 6.15134e15 1.09112
\(266\) 4.18859e15 0.724998
\(267\) 1.30068e15 0.219709
\(268\) −1.04034e16 −1.71514
\(269\) 4.22038e15 0.679144 0.339572 0.940580i \(-0.389718\pi\)
0.339572 + 0.940580i \(0.389718\pi\)
\(270\) 1.40644e15 0.220931
\(271\) −2.83121e15 −0.434181 −0.217091 0.976151i \(-0.569657\pi\)
−0.217091 + 0.976151i \(0.569657\pi\)
\(272\) 5.05024e15 0.756161
\(273\) 8.41328e14 0.123001
\(274\) 6.48348e15 0.925614
\(275\) 4.99711e15 0.696717
\(276\) −8.66158e15 −1.17947
\(277\) 5.67990e15 0.755479 0.377740 0.925912i \(-0.376701\pi\)
0.377740 + 0.925912i \(0.376701\pi\)
\(278\) 1.90350e16 2.47321
\(279\) 5.00902e15 0.635807
\(280\) 1.62010e16 2.00916
\(281\) −6.84857e15 −0.829868 −0.414934 0.909852i \(-0.636195\pi\)
−0.414934 + 0.909852i \(0.636195\pi\)
\(282\) −3.89266e15 −0.460921
\(283\) −1.19895e16 −1.38736 −0.693678 0.720285i \(-0.744011\pi\)
−0.693678 + 0.720285i \(0.744011\pi\)
\(284\) −3.03628e16 −3.43378
\(285\) 1.06793e15 0.118046
\(286\) 3.55196e15 0.383785
\(287\) −7.92267e14 −0.0836834
\(288\) −7.71077e15 −0.796245
\(289\) −9.17375e15 −0.926213
\(290\) 1.25242e16 1.23641
\(291\) −2.74645e14 −0.0265135
\(292\) −1.17632e16 −1.11055
\(293\) 1.17508e16 1.08499 0.542496 0.840058i \(-0.317479\pi\)
0.542496 + 0.840058i \(0.317479\pi\)
\(294\) −4.14554e15 −0.374389
\(295\) −9.03236e14 −0.0797918
\(296\) −2.17123e16 −1.87633
\(297\) −2.54012e15 −0.214752
\(298\) 5.86328e15 0.484992
\(299\) −1.84768e15 −0.149542
\(300\) −1.14173e16 −0.904222
\(301\) −7.68362e15 −0.595503
\(302\) 2.37273e16 1.79971
\(303\) −9.12853e15 −0.677679
\(304\) −1.27800e16 −0.928648
\(305\) 1.07344e15 0.0763534
\(306\) −2.43564e15 −0.169599
\(307\) 1.55258e16 1.05841 0.529206 0.848493i \(-0.322490\pi\)
0.529206 + 0.848493i \(0.322490\pi\)
\(308\) −4.86578e16 −3.24768
\(309\) −2.31361e15 −0.151203
\(310\) 3.42166e16 2.18971
\(311\) −2.18300e15 −0.136808 −0.0684041 0.997658i \(-0.521791\pi\)
−0.0684041 + 0.997658i \(0.521791\pi\)
\(312\) −4.88014e15 −0.299521
\(313\) −2.13942e16 −1.28605 −0.643024 0.765846i \(-0.722320\pi\)
−0.643024 + 0.765846i \(0.722320\pi\)
\(314\) −1.55040e16 −0.912854
\(315\) −4.10995e15 −0.237038
\(316\) 3.31966e16 1.87554
\(317\) 5.87276e15 0.325055 0.162528 0.986704i \(-0.448035\pi\)
0.162528 + 0.986704i \(0.448035\pi\)
\(318\) 3.55024e16 1.92523
\(319\) −2.26194e16 −1.20183
\(320\) −1.99018e16 −1.03614
\(321\) −6.28951e15 −0.320874
\(322\) 3.54016e16 1.76995
\(323\) −1.84941e15 −0.0906185
\(324\) 5.80362e15 0.278712
\(325\) −2.43553e15 −0.114644
\(326\) 3.50376e16 1.61667
\(327\) 1.44724e16 0.654606
\(328\) 4.59557e15 0.203779
\(329\) 1.13752e16 0.494524
\(330\) −1.73516e16 −0.739602
\(331\) −5.76612e15 −0.240991 −0.120496 0.992714i \(-0.538448\pi\)
−0.120496 + 0.992714i \(0.538448\pi\)
\(332\) 4.43560e16 1.81784
\(333\) 5.50810e15 0.221368
\(334\) 3.29820e15 0.129994
\(335\) 1.08412e16 0.419068
\(336\) 4.91840e16 1.86474
\(337\) −1.33634e16 −0.496961 −0.248481 0.968637i \(-0.579931\pi\)
−0.248481 + 0.968637i \(0.579931\pi\)
\(338\) 4.96157e16 1.80992
\(339\) 2.66463e16 0.953539
\(340\) −1.18956e16 −0.417612
\(341\) −6.17973e16 −2.12846
\(342\) 6.16354e15 0.208286
\(343\) −2.28776e16 −0.758576
\(344\) 4.45690e16 1.45012
\(345\) 9.02605e15 0.288187
\(346\) −6.94599e16 −2.17640
\(347\) −4.82874e15 −0.148488 −0.0742441 0.997240i \(-0.523654\pi\)
−0.0742441 + 0.997240i \(0.523654\pi\)
\(348\) 5.16804e16 1.55977
\(349\) 3.20684e16 0.949974 0.474987 0.879993i \(-0.342453\pi\)
0.474987 + 0.879993i \(0.342453\pi\)
\(350\) 4.66648e16 1.35690
\(351\) 1.23802e15 0.0353372
\(352\) 9.51294e16 2.66555
\(353\) −5.60978e16 −1.54316 −0.771579 0.636134i \(-0.780533\pi\)
−0.771579 + 0.636134i \(0.780533\pi\)
\(354\) −5.21302e15 −0.140789
\(355\) 3.16404e16 0.838993
\(356\) 3.66634e16 0.954569
\(357\) 7.11750e15 0.181964
\(358\) −1.21817e17 −3.05821
\(359\) −3.53481e16 −0.871470 −0.435735 0.900075i \(-0.643512\pi\)
−0.435735 + 0.900075i \(0.643512\pi\)
\(360\) 2.38399e16 0.577215
\(361\) −3.73729e16 −0.888711
\(362\) 8.37738e16 1.95660
\(363\) 6.17095e15 0.141566
\(364\) 2.37152e16 0.534401
\(365\) 1.22582e16 0.271346
\(366\) 6.19535e15 0.134722
\(367\) 4.60564e16 0.983922 0.491961 0.870617i \(-0.336280\pi\)
0.491961 + 0.870617i \(0.336280\pi\)
\(368\) −1.08015e17 −2.26712
\(369\) −1.16583e15 −0.0240416
\(370\) 3.76258e16 0.762386
\(371\) −1.03746e17 −2.06558
\(372\) 1.41193e17 2.76239
\(373\) −9.12768e16 −1.75490 −0.877451 0.479666i \(-0.840758\pi\)
−0.877451 + 0.479666i \(0.840758\pi\)
\(374\) 3.00490e16 0.567760
\(375\) 3.09535e16 0.574787
\(376\) −6.59824e16 −1.20422
\(377\) 1.10244e16 0.197759
\(378\) −2.37206e16 −0.418243
\(379\) −2.08075e16 −0.360633 −0.180317 0.983609i \(-0.557712\pi\)
−0.180317 + 0.983609i \(0.557712\pi\)
\(380\) 3.01025e16 0.512873
\(381\) 4.99049e16 0.835856
\(382\) 1.28313e17 2.11280
\(383\) −4.14608e16 −0.671191 −0.335595 0.942006i \(-0.608937\pi\)
−0.335595 + 0.942006i \(0.608937\pi\)
\(384\) −2.82147e16 −0.449079
\(385\) 5.07053e16 0.793521
\(386\) −9.19062e15 −0.141425
\(387\) −1.13065e16 −0.171083
\(388\) −7.74162e15 −0.115193
\(389\) 1.25116e17 1.83080 0.915398 0.402551i \(-0.131876\pi\)
0.915398 + 0.402551i \(0.131876\pi\)
\(390\) 8.45693e15 0.121701
\(391\) −1.56311e16 −0.221228
\(392\) −7.02689e16 −0.978146
\(393\) 3.93884e16 0.539283
\(394\) 6.32525e16 0.851829
\(395\) −3.45934e16 −0.458261
\(396\) −7.16004e16 −0.933032
\(397\) −1.83934e16 −0.235789 −0.117894 0.993026i \(-0.537614\pi\)
−0.117894 + 0.993026i \(0.537614\pi\)
\(398\) 5.11771e16 0.645411
\(399\) −1.80113e16 −0.223471
\(400\) −1.42381e17 −1.73805
\(401\) −1.57173e17 −1.88773 −0.943864 0.330333i \(-0.892839\pi\)
−0.943864 + 0.330333i \(0.892839\pi\)
\(402\) 6.25698e16 0.739427
\(403\) 3.01192e16 0.350236
\(404\) −2.57313e17 −2.94431
\(405\) −6.04783e15 −0.0680992
\(406\) −2.11228e17 −2.34063
\(407\) −6.79546e16 −0.741063
\(408\) −4.12853e16 −0.443102
\(409\) 3.84365e16 0.406015 0.203008 0.979177i \(-0.434928\pi\)
0.203008 + 0.979177i \(0.434928\pi\)
\(410\) −7.96377e15 −0.0827987
\(411\) −2.78796e16 −0.285308
\(412\) −6.52157e16 −0.656931
\(413\) 1.52337e16 0.151053
\(414\) 5.20938e16 0.508492
\(415\) −4.62225e16 −0.444161
\(416\) −4.63648e16 −0.438613
\(417\) −8.18522e16 −0.762335
\(418\) −7.60409e16 −0.697271
\(419\) −1.88832e17 −1.70484 −0.852419 0.522859i \(-0.824866\pi\)
−0.852419 + 0.522859i \(0.824866\pi\)
\(420\) −1.15850e17 −1.02986
\(421\) −4.66069e16 −0.407959 −0.203979 0.978975i \(-0.565388\pi\)
−0.203979 + 0.978975i \(0.565388\pi\)
\(422\) −3.17765e17 −2.73890
\(423\) 1.67388e16 0.142073
\(424\) 6.01783e17 5.02993
\(425\) −2.06042e16 −0.169600
\(426\) 1.82613e17 1.48036
\(427\) −1.81042e16 −0.144544
\(428\) −1.77287e17 −1.39410
\(429\) −1.52737e16 −0.118297
\(430\) −7.72348e16 −0.589207
\(431\) −4.58448e16 −0.344499 −0.172250 0.985053i \(-0.555104\pi\)
−0.172250 + 0.985053i \(0.555104\pi\)
\(432\) 7.23747e16 0.535726
\(433\) −1.55194e17 −1.13163 −0.565814 0.824533i \(-0.691438\pi\)
−0.565814 + 0.824533i \(0.691438\pi\)
\(434\) −5.77085e17 −4.14531
\(435\) −5.38550e16 −0.381106
\(436\) 4.07945e17 2.84406
\(437\) 3.95554e16 0.271692
\(438\) 7.07483e16 0.478778
\(439\) 2.33386e17 1.55617 0.778083 0.628162i \(-0.216192\pi\)
0.778083 + 0.628162i \(0.216192\pi\)
\(440\) −2.94117e17 −1.93232
\(441\) 1.78262e16 0.115400
\(442\) −1.46455e16 −0.0934241
\(443\) −1.78080e17 −1.11942 −0.559708 0.828690i \(-0.689087\pi\)
−0.559708 + 0.828690i \(0.689087\pi\)
\(444\) 1.55261e17 0.961775
\(445\) −3.82061e16 −0.233235
\(446\) −3.19738e16 −0.192361
\(447\) −2.52126e16 −0.149492
\(448\) 3.35656e17 1.96150
\(449\) 7.79242e15 0.0448819 0.0224409 0.999748i \(-0.492856\pi\)
0.0224409 + 0.999748i \(0.492856\pi\)
\(450\) 6.86677e16 0.389826
\(451\) 1.43831e16 0.0804829
\(452\) 7.51099e17 4.14283
\(453\) −1.02029e17 −0.554736
\(454\) 5.36550e17 2.87572
\(455\) −2.47131e16 −0.130573
\(456\) 1.04475e17 0.544178
\(457\) −2.40369e17 −1.23431 −0.617155 0.786842i \(-0.711715\pi\)
−0.617155 + 0.786842i \(0.711715\pi\)
\(458\) −4.85844e17 −2.45964
\(459\) 1.04735e16 0.0522767
\(460\) 2.54424e17 1.25208
\(461\) 2.59508e17 1.25920 0.629599 0.776920i \(-0.283219\pi\)
0.629599 + 0.776920i \(0.283219\pi\)
\(462\) 2.92646e17 1.40013
\(463\) 5.00655e16 0.236190 0.118095 0.993002i \(-0.462321\pi\)
0.118095 + 0.993002i \(0.462321\pi\)
\(464\) 6.44486e17 2.99810
\(465\) −1.47134e17 −0.674948
\(466\) 2.77496e16 0.125530
\(467\) −2.14821e17 −0.958332 −0.479166 0.877724i \(-0.659061\pi\)
−0.479166 + 0.877724i \(0.659061\pi\)
\(468\) 3.48971e16 0.153529
\(469\) −1.82843e17 −0.793333
\(470\) 1.14343e17 0.489296
\(471\) 6.66686e16 0.281375
\(472\) −8.83632e16 −0.367831
\(473\) 1.39491e17 0.572728
\(474\) −1.99656e17 −0.808580
\(475\) 5.21402e16 0.208288
\(476\) 2.00627e17 0.790576
\(477\) −1.52664e17 −0.593425
\(478\) 2.65913e17 1.01967
\(479\) −3.43840e17 −1.30069 −0.650347 0.759637i \(-0.725377\pi\)
−0.650347 + 0.759637i \(0.725377\pi\)
\(480\) 2.26496e17 0.845262
\(481\) 3.31202e16 0.121941
\(482\) 2.59806e17 0.943721
\(483\) −1.52230e17 −0.545563
\(484\) 1.73945e17 0.615061
\(485\) 8.06739e15 0.0281457
\(486\) −3.49050e16 −0.120158
\(487\) 2.26271e17 0.768583 0.384291 0.923212i \(-0.374446\pi\)
0.384291 + 0.923212i \(0.374446\pi\)
\(488\) 1.05014e17 0.351981
\(489\) −1.50665e17 −0.498315
\(490\) 1.21771e17 0.397437
\(491\) −2.91151e17 −0.937754 −0.468877 0.883264i \(-0.655341\pi\)
−0.468877 + 0.883264i \(0.655341\pi\)
\(492\) −3.28621e16 −0.104453
\(493\) 9.32647e16 0.292558
\(494\) 3.70613e16 0.114735
\(495\) 7.46133e16 0.227972
\(496\) 1.76077e18 5.30971
\(497\) −5.33637e17 −1.58829
\(498\) −2.66773e17 −0.783702
\(499\) 1.03775e17 0.300911 0.150455 0.988617i \(-0.451926\pi\)
0.150455 + 0.988617i \(0.451926\pi\)
\(500\) 8.72511e17 2.49727
\(501\) −1.41825e16 −0.0400690
\(502\) 8.60599e17 2.40008
\(503\) 2.61519e17 0.719965 0.359983 0.932959i \(-0.382783\pi\)
0.359983 + 0.932959i \(0.382783\pi\)
\(504\) −4.02075e17 −1.09272
\(505\) 2.68141e17 0.719397
\(506\) −6.42692e17 −1.70226
\(507\) −2.13352e17 −0.557885
\(508\) 1.40671e18 3.63154
\(509\) 4.60629e17 1.17405 0.587024 0.809569i \(-0.300299\pi\)
0.587024 + 0.809569i \(0.300299\pi\)
\(510\) 7.15443e16 0.180040
\(511\) −2.06743e17 −0.513682
\(512\) 4.95442e17 1.21545
\(513\) −2.65038e16 −0.0642015
\(514\) −9.45787e17 −2.26221
\(515\) 6.79599e16 0.160511
\(516\) −3.18706e17 −0.743304
\(517\) −2.06510e17 −0.475611
\(518\) −6.34584e17 −1.44326
\(519\) 2.98684e17 0.670847
\(520\) 1.43349e17 0.317960
\(521\) −3.91504e17 −0.857611 −0.428806 0.903397i \(-0.641066\pi\)
−0.428806 + 0.903397i \(0.641066\pi\)
\(522\) −3.10824e17 −0.672444
\(523\) −2.55045e17 −0.544949 −0.272475 0.962163i \(-0.587842\pi\)
−0.272475 + 0.962163i \(0.587842\pi\)
\(524\) 1.11027e18 2.34302
\(525\) −2.00663e17 −0.418246
\(526\) −2.39571e17 −0.493205
\(527\) 2.54804e17 0.518127
\(528\) −8.92901e17 −1.79342
\(529\) −1.69717e17 −0.336715
\(530\) −1.04285e18 −2.04375
\(531\) 2.24165e16 0.0433963
\(532\) −5.07699e17 −0.970913
\(533\) −7.01011e15 −0.0132434
\(534\) −2.20506e17 −0.411532
\(535\) 1.84747e17 0.340627
\(536\) 1.06059e18 1.93186
\(537\) 5.23823e17 0.942652
\(538\) −7.15487e17 −1.27209
\(539\) −2.19925e17 −0.386321
\(540\) −1.70475e17 −0.295870
\(541\) 2.32630e17 0.398918 0.199459 0.979906i \(-0.436081\pi\)
0.199459 + 0.979906i \(0.436081\pi\)
\(542\) 4.79978e17 0.813254
\(543\) −3.60235e17 −0.603097
\(544\) −3.92239e17 −0.648870
\(545\) −4.25111e17 −0.694904
\(546\) −1.42632e17 −0.230390
\(547\) −6.70986e16 −0.107102 −0.0535508 0.998565i \(-0.517054\pi\)
−0.0535508 + 0.998565i \(0.517054\pi\)
\(548\) −7.85863e17 −1.23958
\(549\) −2.66405e16 −0.0415263
\(550\) −8.47167e17 −1.30500
\(551\) −2.36012e17 −0.359293
\(552\) 8.83015e17 1.32851
\(553\) 5.83441e17 0.867528
\(554\) −9.62922e17 −1.41507
\(555\) −1.61794e17 −0.234995
\(556\) −2.30723e18 −3.31211
\(557\) −3.30516e17 −0.468958 −0.234479 0.972121i \(-0.575338\pi\)
−0.234479 + 0.972121i \(0.575338\pi\)
\(558\) −8.49186e17 −1.19091
\(559\) −6.79860e16 −0.0942416
\(560\) −1.44473e18 −1.97954
\(561\) −1.29213e17 −0.175004
\(562\) 1.16105e18 1.55440
\(563\) 5.93581e17 0.785553 0.392777 0.919634i \(-0.371515\pi\)
0.392777 + 0.919634i \(0.371515\pi\)
\(564\) 4.71829e17 0.617263
\(565\) −7.82705e17 −1.01224
\(566\) 2.03259e18 2.59862
\(567\) 1.02001e17 0.128918
\(568\) 3.09537e18 3.86766
\(569\) 4.04856e17 0.500116 0.250058 0.968231i \(-0.419550\pi\)
0.250058 + 0.968231i \(0.419550\pi\)
\(570\) −1.81047e17 −0.221109
\(571\) 3.47447e17 0.419521 0.209760 0.977753i \(-0.432732\pi\)
0.209760 + 0.977753i \(0.432732\pi\)
\(572\) −4.30533e17 −0.513963
\(573\) −5.51757e17 −0.651243
\(574\) 1.34314e17 0.156745
\(575\) 4.40685e17 0.508496
\(576\) 4.93921e17 0.563523
\(577\) −6.95052e17 −0.784106 −0.392053 0.919943i \(-0.628235\pi\)
−0.392053 + 0.919943i \(0.628235\pi\)
\(578\) 1.55524e18 1.73487
\(579\) 3.95205e16 0.0435925
\(580\) −1.51805e18 −1.65579
\(581\) 7.79572e17 0.840836
\(582\) 4.65609e16 0.0496617
\(583\) 1.88344e18 1.98658
\(584\) 1.19922e18 1.25088
\(585\) −3.63655e16 −0.0375126
\(586\) −1.99212e18 −2.03227
\(587\) −9.96401e17 −1.00528 −0.502639 0.864496i \(-0.667638\pi\)
−0.502639 + 0.864496i \(0.667638\pi\)
\(588\) 5.02481e17 0.501380
\(589\) −6.44796e17 −0.636316
\(590\) 1.53127e17 0.149456
\(591\) −2.71991e17 −0.262565
\(592\) 1.93620e18 1.84867
\(593\) −1.57234e18 −1.48488 −0.742440 0.669912i \(-0.766332\pi\)
−0.742440 + 0.669912i \(0.766332\pi\)
\(594\) 4.30630e17 0.402247
\(595\) −2.09069e17 −0.193165
\(596\) −7.10688e17 −0.649499
\(597\) −2.20066e17 −0.198939
\(598\) 3.13240e17 0.280104
\(599\) 2.19233e18 1.93924 0.969622 0.244609i \(-0.0786595\pi\)
0.969622 + 0.244609i \(0.0786595\pi\)
\(600\) 1.16395e18 1.01848
\(601\) −2.21514e18 −1.91742 −0.958710 0.284385i \(-0.908211\pi\)
−0.958710 + 0.284385i \(0.908211\pi\)
\(602\) 1.30262e18 1.11542
\(603\) −2.69056e17 −0.227918
\(604\) −2.87598e18 −2.41016
\(605\) −1.81265e17 −0.150281
\(606\) 1.54757e18 1.26934
\(607\) 1.51399e18 1.22856 0.614280 0.789088i \(-0.289447\pi\)
0.614280 + 0.789088i \(0.289447\pi\)
\(608\) 9.92586e17 0.796883
\(609\) 9.08300e17 0.721468
\(610\) −1.81982e17 −0.143016
\(611\) 1.00650e17 0.0782611
\(612\) 2.95224e17 0.227126
\(613\) −3.48013e17 −0.264912 −0.132456 0.991189i \(-0.542286\pi\)
−0.132456 + 0.991189i \(0.542286\pi\)
\(614\) −2.63211e18 −1.98249
\(615\) 3.42449e16 0.0255216
\(616\) 4.96048e18 3.65805
\(617\) −3.95948e17 −0.288925 −0.144462 0.989510i \(-0.546145\pi\)
−0.144462 + 0.989510i \(0.546145\pi\)
\(618\) 3.92230e17 0.283215
\(619\) 5.67935e17 0.405797 0.202899 0.979200i \(-0.434964\pi\)
0.202899 + 0.979200i \(0.434964\pi\)
\(620\) −4.14739e18 −2.93244
\(621\) −2.24008e17 −0.156736
\(622\) 3.70088e17 0.256252
\(623\) 6.44371e17 0.441534
\(624\) 4.35188e17 0.295106
\(625\) 2.11478e16 0.0141920
\(626\) 3.62698e18 2.40886
\(627\) 3.26983e17 0.214924
\(628\) 1.87924e18 1.22249
\(629\) 2.80191e17 0.180395
\(630\) 6.96766e17 0.443990
\(631\) −1.34988e18 −0.851344 −0.425672 0.904878i \(-0.639962\pi\)
−0.425672 + 0.904878i \(0.639962\pi\)
\(632\) −3.38426e18 −2.11253
\(633\) 1.36642e18 0.844228
\(634\) −9.95617e17 −0.608853
\(635\) −1.46590e18 −0.887312
\(636\) −4.30325e18 −2.57825
\(637\) 1.07189e17 0.0635686
\(638\) 3.83470e18 2.25111
\(639\) −7.85251e17 −0.456302
\(640\) 8.28776e17 0.476724
\(641\) −2.93146e18 −1.66920 −0.834598 0.550859i \(-0.814300\pi\)
−0.834598 + 0.550859i \(0.814300\pi\)
\(642\) 1.06627e18 0.601021
\(643\) −2.95486e18 −1.64879 −0.824397 0.566013i \(-0.808485\pi\)
−0.824397 + 0.566013i \(0.808485\pi\)
\(644\) −4.29103e18 −2.37030
\(645\) 3.32117e17 0.181615
\(646\) 3.13533e17 0.169735
\(647\) 1.50205e18 0.805021 0.402510 0.915415i \(-0.368138\pi\)
0.402510 + 0.915415i \(0.368138\pi\)
\(648\) −5.91657e17 −0.313930
\(649\) −2.76557e17 −0.145276
\(650\) 4.12898e17 0.214737
\(651\) 2.48152e18 1.27774
\(652\) −4.24691e18 −2.16503
\(653\) −2.58043e18 −1.30243 −0.651217 0.758892i \(-0.725741\pi\)
−0.651217 + 0.758892i \(0.725741\pi\)
\(654\) −2.45353e18 −1.22613
\(655\) −1.15699e18 −0.572481
\(656\) −4.09811e17 −0.200775
\(657\) −3.04224e17 −0.147577
\(658\) −1.92846e18 −0.926280
\(659\) −1.84356e18 −0.876804 −0.438402 0.898779i \(-0.644455\pi\)
−0.438402 + 0.898779i \(0.644455\pi\)
\(660\) 2.10318e18 0.990471
\(661\) −1.41603e18 −0.660334 −0.330167 0.943922i \(-0.607105\pi\)
−0.330167 + 0.943922i \(0.607105\pi\)
\(662\) 9.77538e17 0.451395
\(663\) 6.29769e16 0.0287967
\(664\) −4.52193e18 −2.04753
\(665\) 5.29062e17 0.237228
\(666\) −9.33796e17 −0.414638
\(667\) −1.99476e18 −0.877147
\(668\) −3.99774e17 −0.174088
\(669\) 1.37490e17 0.0592927
\(670\) −1.83792e18 −0.784946
\(671\) 3.28670e17 0.139016
\(672\) −3.81999e18 −1.60016
\(673\) 1.59678e18 0.662439 0.331220 0.943554i \(-0.392540\pi\)
0.331220 + 0.943554i \(0.392540\pi\)
\(674\) 2.26552e18 0.930846
\(675\) −2.95277e17 −0.120159
\(676\) −6.01391e18 −2.42384
\(677\) 1.26442e18 0.504737 0.252368 0.967631i \(-0.418791\pi\)
0.252368 + 0.967631i \(0.418791\pi\)
\(678\) −4.51738e18 −1.78605
\(679\) −1.36062e17 −0.0532822
\(680\) 1.21271e18 0.470380
\(681\) −2.30721e18 −0.886403
\(682\) 1.04766e19 3.98677
\(683\) 2.94317e18 1.10938 0.554691 0.832056i \(-0.312836\pi\)
0.554691 + 0.832056i \(0.312836\pi\)
\(684\) −7.47083e17 −0.278936
\(685\) 8.18932e17 0.302872
\(686\) 3.87847e18 1.42087
\(687\) 2.08917e18 0.758150
\(688\) −3.97446e18 −1.42874
\(689\) −9.17965e17 −0.326890
\(690\) −1.53020e18 −0.539795
\(691\) 4.80100e18 1.67774 0.838870 0.544333i \(-0.183217\pi\)
0.838870 + 0.544333i \(0.183217\pi\)
\(692\) 8.41923e18 2.91462
\(693\) −1.25840e18 −0.431572
\(694\) 8.18622e17 0.278129
\(695\) 2.40432e18 0.809265
\(696\) −5.26862e18 −1.75686
\(697\) −5.93045e16 −0.0195918
\(698\) −5.43660e18 −1.77937
\(699\) −1.19326e17 −0.0386931
\(700\) −5.65624e18 −1.81715
\(701\) 2.27265e18 0.723378 0.361689 0.932299i \(-0.382200\pi\)
0.361689 + 0.932299i \(0.382200\pi\)
\(702\) −2.09884e17 −0.0661892
\(703\) −7.09042e17 −0.221545
\(704\) −6.09361e18 −1.88648
\(705\) −4.91683e17 −0.150819
\(706\) 9.51034e18 2.89045
\(707\) −4.52236e18 −1.36188
\(708\) 6.31871e17 0.188544
\(709\) −4.95978e18 −1.46643 −0.733216 0.679996i \(-0.761982\pi\)
−0.733216 + 0.679996i \(0.761982\pi\)
\(710\) −5.36405e18 −1.57150
\(711\) 8.58538e17 0.249234
\(712\) −3.73769e18 −1.07519
\(713\) −5.44977e18 −1.55345
\(714\) −1.20664e18 −0.340831
\(715\) 4.48649e17 0.125579
\(716\) 1.47654e19 4.09553
\(717\) −1.14345e18 −0.314299
\(718\) 5.99262e18 1.63233
\(719\) 8.04577e17 0.217185 0.108592 0.994086i \(-0.465366\pi\)
0.108592 + 0.994086i \(0.465366\pi\)
\(720\) −2.12593e18 −0.568705
\(721\) −1.14619e18 −0.303862
\(722\) 6.33589e18 1.66462
\(723\) −1.11719e18 −0.290889
\(724\) −1.01542e19 −2.62027
\(725\) −2.62940e18 −0.672449
\(726\) −1.04617e18 −0.265164
\(727\) −2.49801e18 −0.627509 −0.313755 0.949504i \(-0.601587\pi\)
−0.313755 + 0.949504i \(0.601587\pi\)
\(728\) −2.41767e18 −0.601926
\(729\) 1.50095e17 0.0370370
\(730\) −2.07815e18 −0.508252
\(731\) −5.75151e17 −0.139418
\(732\) −7.50938e17 −0.180419
\(733\) −4.59618e18 −1.09451 −0.547256 0.836965i \(-0.684328\pi\)
−0.547256 + 0.836965i \(0.684328\pi\)
\(734\) −7.80801e18 −1.84296
\(735\) −5.23625e17 −0.122505
\(736\) 8.38927e18 1.94544
\(737\) 3.31939e18 0.762992
\(738\) 1.97644e17 0.0450317
\(739\) −4.80740e18 −1.08573 −0.542864 0.839820i \(-0.682660\pi\)
−0.542864 + 0.839820i \(0.682660\pi\)
\(740\) −4.56063e18 −1.02098
\(741\) −1.59367e17 −0.0353655
\(742\) 1.75883e19 3.86899
\(743\) −9.31952e17 −0.203220 −0.101610 0.994824i \(-0.532399\pi\)
−0.101610 + 0.994824i \(0.532399\pi\)
\(744\) −1.43941e19 −3.11143
\(745\) 7.40593e17 0.158695
\(746\) 1.54743e19 3.28706
\(747\) 1.14715e18 0.241566
\(748\) −3.64224e18 −0.760340
\(749\) −3.11589e18 −0.644837
\(750\) −5.24759e18 −1.07662
\(751\) −4.00906e18 −0.815422 −0.407711 0.913111i \(-0.633673\pi\)
−0.407711 + 0.913111i \(0.633673\pi\)
\(752\) 5.88400e18 1.18647
\(753\) −3.70065e18 −0.739794
\(754\) −1.86898e18 −0.370417
\(755\) 2.99700e18 0.588886
\(756\) 2.87517e18 0.560108
\(757\) −3.00730e18 −0.580835 −0.290418 0.956900i \(-0.593794\pi\)
−0.290418 + 0.956900i \(0.593794\pi\)
\(758\) 3.52753e18 0.675493
\(759\) 2.76363e18 0.524697
\(760\) −3.06884e18 −0.577678
\(761\) 7.28236e18 1.35916 0.679582 0.733600i \(-0.262161\pi\)
0.679582 + 0.733600i \(0.262161\pi\)
\(762\) −8.46046e18 −1.56562
\(763\) 7.16977e18 1.31551
\(764\) −1.55528e19 −2.82945
\(765\) −3.07647e17 −0.0554949
\(766\) 7.02891e18 1.25719
\(767\) 1.34790e17 0.0239049
\(768\) −7.67071e17 −0.134892
\(769\) −2.34981e18 −0.409744 −0.204872 0.978789i \(-0.565678\pi\)
−0.204872 + 0.978789i \(0.565678\pi\)
\(770\) −8.59614e18 −1.48633
\(771\) 4.06697e18 0.697296
\(772\) 1.11399e18 0.189396
\(773\) −5.57007e18 −0.939061 −0.469530 0.882916i \(-0.655577\pi\)
−0.469530 + 0.882916i \(0.655577\pi\)
\(774\) 1.91681e18 0.320452
\(775\) −7.18364e18 −1.19092
\(776\) 7.89229e17 0.129748
\(777\) 2.72877e18 0.444867
\(778\) −2.12111e19 −3.42922
\(779\) 1.50074e17 0.0240609
\(780\) −1.02506e18 −0.162981
\(781\) 9.68780e18 1.52754
\(782\) 2.64996e18 0.414377
\(783\) 1.33657e18 0.207272
\(784\) 6.26625e18 0.963725
\(785\) −1.95832e18 −0.298697
\(786\) −6.67757e18 −1.01012
\(787\) −9.32424e18 −1.39887 −0.699435 0.714696i \(-0.746565\pi\)
−0.699435 + 0.714696i \(0.746565\pi\)
\(788\) −7.66683e18 −1.14076
\(789\) 1.03018e18 0.152024
\(790\) 5.86467e18 0.858357
\(791\) 1.32008e19 1.91626
\(792\) 7.29939e18 1.05093
\(793\) −1.60189e17 −0.0228748
\(794\) 3.11825e18 0.441650
\(795\) 4.48433e18 0.629957
\(796\) −6.20318e18 −0.864330
\(797\) −8.06553e18 −1.11469 −0.557345 0.830281i \(-0.688180\pi\)
−0.557345 + 0.830281i \(0.688180\pi\)
\(798\) 3.05348e18 0.418578
\(799\) 8.51484e17 0.115777
\(800\) 1.10583e19 1.49144
\(801\) 9.48197e17 0.126849
\(802\) 2.66458e19 3.53586
\(803\) 3.75327e18 0.494037
\(804\) −7.58408e18 −0.990236
\(805\) 4.47160e18 0.579148
\(806\) −5.10615e18 −0.656017
\(807\) 3.07666e18 0.392104
\(808\) 2.62321e19 3.31634
\(809\) −4.86012e18 −0.609511 −0.304756 0.952431i \(-0.598575\pi\)
−0.304756 + 0.952431i \(0.598575\pi\)
\(810\) 1.02530e18 0.127555
\(811\) 9.37387e18 1.15687 0.578433 0.815730i \(-0.303664\pi\)
0.578433 + 0.815730i \(0.303664\pi\)
\(812\) 2.56030e19 3.13456
\(813\) −2.06395e18 −0.250675
\(814\) 1.15204e19 1.38807
\(815\) 4.42562e18 0.528992
\(816\) 3.68163e18 0.436570
\(817\) 1.45546e18 0.171220
\(818\) −6.51619e18 −0.760497
\(819\) 6.13328e17 0.0710146
\(820\) 9.65289e17 0.110884
\(821\) 7.55050e18 0.860489 0.430245 0.902712i \(-0.358427\pi\)
0.430245 + 0.902712i \(0.358427\pi\)
\(822\) 4.72646e18 0.534403
\(823\) 2.08667e18 0.234075 0.117038 0.993127i \(-0.462660\pi\)
0.117038 + 0.993127i \(0.462660\pi\)
\(824\) 6.64849e18 0.739939
\(825\) 3.64289e18 0.402250
\(826\) −2.58258e18 −0.282933
\(827\) −1.53200e19 −1.66523 −0.832613 0.553856i \(-0.813156\pi\)
−0.832613 + 0.553856i \(0.813156\pi\)
\(828\) −6.31429e18 −0.680969
\(829\) 1.39829e19 1.49621 0.748107 0.663578i \(-0.230963\pi\)
0.748107 + 0.663578i \(0.230963\pi\)
\(830\) 7.83616e18 0.831947
\(831\) 4.14065e18 0.436176
\(832\) 2.96994e18 0.310418
\(833\) 9.06800e17 0.0940413
\(834\) 1.38765e19 1.42791
\(835\) 4.16597e17 0.0425357
\(836\) 9.21691e18 0.933780
\(837\) 3.65157e18 0.367083
\(838\) 3.20129e19 3.19329
\(839\) −1.92209e18 −0.190249 −0.0951244 0.995465i \(-0.530325\pi\)
−0.0951244 + 0.995465i \(0.530325\pi\)
\(840\) 1.18105e19 1.15999
\(841\) 1.64134e18 0.159965
\(842\) 7.90133e18 0.764137
\(843\) −4.99261e18 −0.479124
\(844\) 3.85163e19 3.66791
\(845\) 6.26697e18 0.592228
\(846\) −2.83775e18 −0.266113
\(847\) 3.05715e18 0.284495
\(848\) −5.36642e19 −4.95577
\(849\) −8.74032e18 −0.800990
\(850\) 3.49305e18 0.317674
\(851\) −5.99277e18 −0.540861
\(852\) −2.21345e19 −1.98249
\(853\) −1.89443e19 −1.68387 −0.841937 0.539575i \(-0.818585\pi\)
−0.841937 + 0.539575i \(0.818585\pi\)
\(854\) 3.06924e18 0.270741
\(855\) 7.78519e17 0.0681537
\(856\) 1.80738e19 1.57025
\(857\) 7.63925e18 0.658681 0.329341 0.944211i \(-0.393174\pi\)
0.329341 + 0.944211i \(0.393174\pi\)
\(858\) 2.58938e18 0.221579
\(859\) 2.24819e19 1.90931 0.954656 0.297712i \(-0.0962235\pi\)
0.954656 + 0.297712i \(0.0962235\pi\)
\(860\) 9.36163e18 0.789063
\(861\) −5.77563e17 −0.0483146
\(862\) 7.77214e18 0.645273
\(863\) −8.51970e18 −0.702028 −0.351014 0.936370i \(-0.614163\pi\)
−0.351014 + 0.936370i \(0.614163\pi\)
\(864\) −5.62115e18 −0.459712
\(865\) −8.77350e18 −0.712145
\(866\) 2.63102e19 2.11962
\(867\) −6.68766e18 −0.534749
\(868\) 6.99485e19 5.55137
\(869\) −1.05920e19 −0.834349
\(870\) 9.13012e18 0.713841
\(871\) −1.61783e18 −0.125549
\(872\) −4.15884e19 −3.20343
\(873\) −2.00216e17 −0.0153076
\(874\) −6.70589e18 −0.508900
\(875\) 1.53347e19 1.15511
\(876\) −8.57540e18 −0.641177
\(877\) −2.01059e19 −1.49220 −0.746099 0.665835i \(-0.768076\pi\)
−0.746099 + 0.665835i \(0.768076\pi\)
\(878\) −3.95663e19 −2.91482
\(879\) 8.56630e18 0.626420
\(880\) 2.62280e19 1.90383
\(881\) −1.11063e18 −0.0800249 −0.0400125 0.999199i \(-0.512740\pi\)
−0.0400125 + 0.999199i \(0.512740\pi\)
\(882\) −3.02210e18 −0.216154
\(883\) 4.92034e18 0.349342 0.174671 0.984627i \(-0.444114\pi\)
0.174671 + 0.984627i \(0.444114\pi\)
\(884\) 1.77518e18 0.125113
\(885\) −6.58459e17 −0.0460678
\(886\) 3.01902e19 2.09675
\(887\) −2.53874e19 −1.75031 −0.875155 0.483842i \(-0.839241\pi\)
−0.875155 + 0.483842i \(0.839241\pi\)
\(888\) −1.58283e19 −1.08330
\(889\) 2.47234e19 1.67976
\(890\) 6.47714e18 0.436866
\(891\) −1.85175e18 −0.123987
\(892\) 3.87554e18 0.257609
\(893\) −2.15473e18 −0.142187
\(894\) 4.27433e18 0.280010
\(895\) −1.53867e19 −1.00068
\(896\) −1.39778e19 −0.902481
\(897\) −1.34696e18 −0.0863383
\(898\) −1.32106e18 −0.0840671
\(899\) 3.25167e19 2.05432
\(900\) −8.32321e18 −0.522053
\(901\) −7.76584e18 −0.483590
\(902\) −2.43838e18 −0.150751
\(903\) −5.60136e18 −0.343814
\(904\) −7.65717e19 −4.66631
\(905\) 1.05815e19 0.640224
\(906\) 1.72972e19 1.03906
\(907\) −8.19639e18 −0.488850 −0.244425 0.969668i \(-0.578599\pi\)
−0.244425 + 0.969668i \(0.578599\pi\)
\(908\) −6.50352e19 −3.85115
\(909\) −6.65470e18 −0.391258
\(910\) 4.18965e18 0.244573
\(911\) 4.68189e18 0.271364 0.135682 0.990752i \(-0.456677\pi\)
0.135682 + 0.990752i \(0.456677\pi\)
\(912\) −9.31659e18 −0.536155
\(913\) −1.41526e19 −0.808678
\(914\) 4.07502e19 2.31195
\(915\) 7.82537e17 0.0440827
\(916\) 5.88891e19 3.29393
\(917\) 1.95134e19 1.08376
\(918\) −1.77558e18 −0.0979182
\(919\) −8.45116e18 −0.462770 −0.231385 0.972862i \(-0.574326\pi\)
−0.231385 + 0.972862i \(0.574326\pi\)
\(920\) −2.59376e19 −1.41029
\(921\) 1.13183e19 0.611075
\(922\) −4.39947e19 −2.35857
\(923\) −4.72170e18 −0.251355
\(924\) −3.54716e19 −1.87505
\(925\) −7.89940e18 −0.414642
\(926\) −8.48767e18 −0.442402
\(927\) −1.68662e18 −0.0872972
\(928\) −5.00556e19 −2.57271
\(929\) 1.21984e19 0.622587 0.311293 0.950314i \(-0.399238\pi\)
0.311293 + 0.950314i \(0.399238\pi\)
\(930\) 2.49439e19 1.26423
\(931\) −2.29471e18 −0.115493
\(932\) −3.36353e18 −0.168109
\(933\) −1.59141e18 −0.0789862
\(934\) 3.64188e19 1.79503
\(935\) 3.79550e18 0.185778
\(936\) −3.55763e18 −0.172929
\(937\) −3.13677e19 −1.51417 −0.757086 0.653315i \(-0.773378\pi\)
−0.757086 + 0.653315i \(0.773378\pi\)
\(938\) 3.09977e19 1.48597
\(939\) −1.55963e19 −0.742500
\(940\) −1.38595e19 −0.655262
\(941\) 2.61583e19 1.22822 0.614111 0.789220i \(-0.289515\pi\)
0.614111 + 0.789220i \(0.289515\pi\)
\(942\) −1.13024e19 −0.527037
\(943\) 1.26841e18 0.0587401
\(944\) 7.87982e18 0.362408
\(945\) −2.99615e18 −0.136854
\(946\) −2.36481e19 −1.07276
\(947\) 8.37461e18 0.377303 0.188651 0.982044i \(-0.439588\pi\)
0.188651 + 0.982044i \(0.439588\pi\)
\(948\) 2.42003e19 1.08285
\(949\) −1.82930e18 −0.0812931
\(950\) −8.83939e18 −0.390139
\(951\) 4.28124e18 0.187671
\(952\) −2.04531e19 −0.890471
\(953\) −2.89783e19 −1.25305 −0.626525 0.779401i \(-0.715524\pi\)
−0.626525 + 0.779401i \(0.715524\pi\)
\(954\) 2.58813e19 1.11153
\(955\) 1.62073e19 0.691334
\(956\) −3.22313e19 −1.36553
\(957\) −1.64896e19 −0.693875
\(958\) 5.82916e19 2.43630
\(959\) −1.38118e19 −0.573363
\(960\) −1.45084e19 −0.598214
\(961\) 6.44197e19 2.63825
\(962\) −5.61491e18 −0.228404
\(963\) −4.58505e18 −0.185257
\(964\) −3.14911e19 −1.26383
\(965\) −1.16087e18 −0.0462761
\(966\) 2.58078e19 1.02188
\(967\) −4.09484e19 −1.61052 −0.805258 0.592924i \(-0.797973\pi\)
−0.805258 + 0.592924i \(0.797973\pi\)
\(968\) −1.77331e19 −0.692778
\(969\) −1.34822e18 −0.0523186
\(970\) −1.36768e18 −0.0527189
\(971\) −6.74802e18 −0.258376 −0.129188 0.991620i \(-0.541237\pi\)
−0.129188 + 0.991620i \(0.541237\pi\)
\(972\) 4.23084e18 0.160915
\(973\) −4.05504e19 −1.53201
\(974\) −3.83600e19 −1.43961
\(975\) −1.77550e18 −0.0661897
\(976\) −9.36466e18 −0.346791
\(977\) 4.29813e19 1.58112 0.790560 0.612384i \(-0.209789\pi\)
0.790560 + 0.612384i \(0.209789\pi\)
\(978\) 2.55424e19 0.933382
\(979\) −1.16981e19 −0.424647
\(980\) −1.47598e19 −0.532245
\(981\) 1.05504e19 0.377937
\(982\) 4.93593e19 1.75648
\(983\) 3.22411e19 1.13976 0.569878 0.821729i \(-0.306990\pi\)
0.569878 + 0.821729i \(0.306990\pi\)
\(984\) 3.35017e18 0.117652
\(985\) 7.98945e18 0.278728
\(986\) −1.58113e19 −0.547984
\(987\) 8.29255e18 0.285514
\(988\) −4.49220e18 −0.153652
\(989\) 1.23014e19 0.418003
\(990\) −1.26493e19 −0.427010
\(991\) −3.08700e18 −0.103528 −0.0517639 0.998659i \(-0.516484\pi\)
−0.0517639 + 0.998659i \(0.516484\pi\)
\(992\) −1.36754e20 −4.55632
\(993\) −4.20350e18 −0.139136
\(994\) 9.04681e19 2.97498
\(995\) 6.46421e18 0.211186
\(996\) 3.23355e19 1.04953
\(997\) 4.33114e19 1.39664 0.698318 0.715787i \(-0.253932\pi\)
0.698318 + 0.715787i \(0.253932\pi\)
\(998\) −1.75931e19 −0.563628
\(999\) 4.01541e18 0.127807
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.1.1 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.1 30 1.1 even 1 trivial