Properties

Label 177.14.a.c.1.14
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 1.14
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-7.03559 q^{2} +729.000 q^{3} -8142.50 q^{4} +12466.0 q^{5} -5128.95 q^{6} -179621. q^{7} +114923. q^{8} +531441. q^{9} +O(q^{10})\) \(q-7.03559 q^{2} +729.000 q^{3} -8142.50 q^{4} +12466.0 q^{5} -5128.95 q^{6} -179621. q^{7} +114923. q^{8} +531441. q^{9} -87705.8 q^{10} -8.91138e6 q^{11} -5.93588e6 q^{12} +2.94142e7 q^{13} +1.26374e6 q^{14} +9.08773e6 q^{15} +6.58948e7 q^{16} -1.63264e7 q^{17} -3.73900e6 q^{18} -1.07100e8 q^{19} -1.01505e8 q^{20} -1.30944e8 q^{21} +6.26968e7 q^{22} +5.82137e8 q^{23} +8.37788e7 q^{24} -1.06530e9 q^{25} -2.06946e8 q^{26} +3.87420e8 q^{27} +1.46257e9 q^{28} -1.37246e9 q^{29} -6.39375e7 q^{30} -5.70742e9 q^{31} -1.40506e9 q^{32} -6.49640e9 q^{33} +1.14866e8 q^{34} -2.23916e9 q^{35} -4.32726e9 q^{36} +6.03624e9 q^{37} +7.53511e8 q^{38} +2.14429e10 q^{39} +1.43263e9 q^{40} -1.15612e10 q^{41} +9.21268e8 q^{42} -1.85518e9 q^{43} +7.25609e10 q^{44} +6.62495e9 q^{45} -4.09568e9 q^{46} +4.15668e9 q^{47} +4.80373e10 q^{48} -6.46252e10 q^{49} +7.49503e9 q^{50} -1.19020e10 q^{51} -2.39505e11 q^{52} +1.45626e11 q^{53} -2.72573e9 q^{54} -1.11089e11 q^{55} -2.06426e10 q^{56} -7.80758e10 q^{57} +9.65605e9 q^{58} -4.21805e10 q^{59} -7.39968e10 q^{60} -4.25126e11 q^{61} +4.01551e10 q^{62} -9.54581e10 q^{63} -5.29925e11 q^{64} +3.66678e11 q^{65} +4.57060e10 q^{66} +2.63627e11 q^{67} +1.32938e11 q^{68} +4.24378e11 q^{69} +1.57538e10 q^{70} +3.12180e11 q^{71} +6.10747e10 q^{72} -7.30451e11 q^{73} -4.24686e10 q^{74} -7.76605e11 q^{75} +8.72060e11 q^{76} +1.60067e12 q^{77} -1.50864e11 q^{78} +2.67532e12 q^{79} +8.21446e11 q^{80} +2.82430e11 q^{81} +8.13402e10 q^{82} -1.18393e12 q^{83} +1.06621e12 q^{84} -2.03526e11 q^{85} +1.30523e10 q^{86} -1.00052e12 q^{87} -1.02412e12 q^{88} +3.66061e11 q^{89} -4.66105e10 q^{90} -5.28341e12 q^{91} -4.74005e12 q^{92} -4.16071e12 q^{93} -2.92447e10 q^{94} -1.33511e12 q^{95} -1.02429e12 q^{96} +1.46548e13 q^{97} +4.54676e11 q^{98} -4.73587e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.03559 −0.0777330 −0.0388665 0.999244i \(-0.512375\pi\)
−0.0388665 + 0.999244i \(0.512375\pi\)
\(3\) 729.000 0.577350
\(4\) −8142.50 −0.993958
\(5\) 12466.0 0.356798 0.178399 0.983958i \(-0.442908\pi\)
0.178399 + 0.983958i \(0.442908\pi\)
\(6\) −5128.95 −0.0448792
\(7\) −179621. −0.577060 −0.288530 0.957471i \(-0.593166\pi\)
−0.288530 + 0.957471i \(0.593166\pi\)
\(8\) 114923. 0.154996
\(9\) 531441. 0.333333
\(10\) −87705.8 −0.0277350
\(11\) −8.91138e6 −1.51668 −0.758338 0.651862i \(-0.773988\pi\)
−0.758338 + 0.651862i \(0.773988\pi\)
\(12\) −5.93588e6 −0.573862
\(13\) 2.94142e7 1.69015 0.845074 0.534649i \(-0.179556\pi\)
0.845074 + 0.534649i \(0.179556\pi\)
\(14\) 1.26374e6 0.0448566
\(15\) 9.08773e6 0.205998
\(16\) 6.58948e7 0.981909
\(17\) −1.63264e7 −0.164049 −0.0820245 0.996630i \(-0.526139\pi\)
−0.0820245 + 0.996630i \(0.526139\pi\)
\(18\) −3.73900e6 −0.0259110
\(19\) −1.07100e8 −0.522264 −0.261132 0.965303i \(-0.584096\pi\)
−0.261132 + 0.965303i \(0.584096\pi\)
\(20\) −1.01505e8 −0.354642
\(21\) −1.30944e8 −0.333166
\(22\) 6.26968e7 0.117896
\(23\) 5.82137e8 0.819964 0.409982 0.912094i \(-0.365535\pi\)
0.409982 + 0.912094i \(0.365535\pi\)
\(24\) 8.37788e7 0.0894872
\(25\) −1.06530e9 −0.872695
\(26\) −2.06946e8 −0.131380
\(27\) 3.87420e8 0.192450
\(28\) 1.46257e9 0.573573
\(29\) −1.37246e9 −0.428462 −0.214231 0.976783i \(-0.568724\pi\)
−0.214231 + 0.976783i \(0.568724\pi\)
\(30\) −6.39375e7 −0.0160128
\(31\) −5.70742e9 −1.15502 −0.577509 0.816384i \(-0.695975\pi\)
−0.577509 + 0.816384i \(0.695975\pi\)
\(32\) −1.40506e9 −0.231323
\(33\) −6.49640e9 −0.875653
\(34\) 1.14866e8 0.0127520
\(35\) −2.23916e9 −0.205894
\(36\) −4.32726e9 −0.331319
\(37\) 6.03624e9 0.386773 0.193386 0.981123i \(-0.438053\pi\)
0.193386 + 0.981123i \(0.438053\pi\)
\(38\) 7.53511e8 0.0405972
\(39\) 2.14429e10 0.975808
\(40\) 1.43263e9 0.0553024
\(41\) −1.15612e10 −0.380110 −0.190055 0.981773i \(-0.560867\pi\)
−0.190055 + 0.981773i \(0.560867\pi\)
\(42\) 9.21268e8 0.0258980
\(43\) −1.85518e9 −0.0447549 −0.0223775 0.999750i \(-0.507124\pi\)
−0.0223775 + 0.999750i \(0.507124\pi\)
\(44\) 7.25609e10 1.50751
\(45\) 6.62495e9 0.118933
\(46\) −4.09568e9 −0.0637383
\(47\) 4.15668e9 0.0562484 0.0281242 0.999604i \(-0.491047\pi\)
0.0281242 + 0.999604i \(0.491047\pi\)
\(48\) 4.80373e10 0.566906
\(49\) −6.46252e10 −0.667002
\(50\) 7.49503e9 0.0678372
\(51\) −1.19020e10 −0.0947137
\(52\) −2.39505e11 −1.67994
\(53\) 1.45626e11 0.902499 0.451249 0.892398i \(-0.350978\pi\)
0.451249 + 0.892398i \(0.350978\pi\)
\(54\) −2.72573e9 −0.0149597
\(55\) −1.11089e11 −0.541147
\(56\) −2.06426e10 −0.0894421
\(57\) −7.80758e10 −0.301529
\(58\) 9.65605e9 0.0333056
\(59\) −4.21805e10 −0.130189
\(60\) −7.39968e10 −0.204753
\(61\) −4.25126e11 −1.05651 −0.528255 0.849086i \(-0.677154\pi\)
−0.528255 + 0.849086i \(0.677154\pi\)
\(62\) 4.01551e10 0.0897831
\(63\) −9.54581e10 −0.192353
\(64\) −5.29925e11 −0.963928
\(65\) 3.66678e11 0.603042
\(66\) 4.57060e10 0.0680672
\(67\) 2.63627e11 0.356044 0.178022 0.984026i \(-0.443030\pi\)
0.178022 + 0.984026i \(0.443030\pi\)
\(68\) 1.32938e11 0.163058
\(69\) 4.24378e11 0.473406
\(70\) 1.57538e10 0.0160048
\(71\) 3.12180e11 0.289218 0.144609 0.989489i \(-0.453808\pi\)
0.144609 + 0.989489i \(0.453808\pi\)
\(72\) 6.10747e10 0.0516655
\(73\) −7.30451e11 −0.564927 −0.282464 0.959278i \(-0.591152\pi\)
−0.282464 + 0.959278i \(0.591152\pi\)
\(74\) −4.24686e10 −0.0300650
\(75\) −7.76605e11 −0.503851
\(76\) 8.72060e11 0.519109
\(77\) 1.60067e12 0.875212
\(78\) −1.50864e11 −0.0758525
\(79\) 2.67532e12 1.23823 0.619113 0.785302i \(-0.287492\pi\)
0.619113 + 0.785302i \(0.287492\pi\)
\(80\) 8.21446e11 0.350344
\(81\) 2.82430e11 0.111111
\(82\) 8.13402e10 0.0295471
\(83\) −1.18393e12 −0.397484 −0.198742 0.980052i \(-0.563686\pi\)
−0.198742 + 0.980052i \(0.563686\pi\)
\(84\) 1.06621e12 0.331152
\(85\) −2.03526e11 −0.0585324
\(86\) 1.30523e10 0.00347894
\(87\) −1.00052e12 −0.247372
\(88\) −1.02412e12 −0.235079
\(89\) 3.66061e11 0.0780762 0.0390381 0.999238i \(-0.487571\pi\)
0.0390381 + 0.999238i \(0.487571\pi\)
\(90\) −4.66105e10 −0.00924501
\(91\) −5.28341e12 −0.975317
\(92\) −4.74005e12 −0.815009
\(93\) −4.16071e12 −0.666850
\(94\) −2.92447e10 −0.00437236
\(95\) −1.33511e12 −0.186343
\(96\) −1.02429e12 −0.133554
\(97\) 1.46548e13 1.78634 0.893169 0.449722i \(-0.148477\pi\)
0.893169 + 0.449722i \(0.148477\pi\)
\(98\) 4.54676e11 0.0518481
\(99\) −4.73587e12 −0.505558
\(100\) 8.67422e12 0.867422
\(101\) −1.06442e13 −0.997754 −0.498877 0.866673i \(-0.666254\pi\)
−0.498877 + 0.866673i \(0.666254\pi\)
\(102\) 8.37374e10 0.00736239
\(103\) 1.23712e13 1.02087 0.510433 0.859918i \(-0.329485\pi\)
0.510433 + 0.859918i \(0.329485\pi\)
\(104\) 3.38036e12 0.261967
\(105\) −1.63235e12 −0.118873
\(106\) −1.02457e12 −0.0701540
\(107\) −6.47425e12 −0.417057 −0.208528 0.978016i \(-0.566867\pi\)
−0.208528 + 0.978016i \(0.566867\pi\)
\(108\) −3.15457e12 −0.191287
\(109\) 4.60180e12 0.262818 0.131409 0.991328i \(-0.458050\pi\)
0.131409 + 0.991328i \(0.458050\pi\)
\(110\) 7.81580e11 0.0420650
\(111\) 4.40042e12 0.223303
\(112\) −1.18361e13 −0.566620
\(113\) 4.25972e12 0.192474 0.0962368 0.995358i \(-0.469319\pi\)
0.0962368 + 0.995358i \(0.469319\pi\)
\(114\) 5.49309e11 0.0234388
\(115\) 7.25694e12 0.292562
\(116\) 1.11752e13 0.425873
\(117\) 1.56319e13 0.563383
\(118\) 2.96765e11 0.0101200
\(119\) 2.93258e12 0.0946660
\(120\) 1.04439e12 0.0319289
\(121\) 4.48900e13 1.30030
\(122\) 2.99101e12 0.0821258
\(123\) −8.42815e12 −0.219457
\(124\) 4.64727e13 1.14804
\(125\) −2.84974e13 −0.668174
\(126\) 6.71604e11 0.0149522
\(127\) 5.28410e13 1.11750 0.558749 0.829337i \(-0.311282\pi\)
0.558749 + 0.829337i \(0.311282\pi\)
\(128\) 1.52386e13 0.306252
\(129\) −1.35243e12 −0.0258393
\(130\) −2.57980e12 −0.0468763
\(131\) 2.73432e13 0.472700 0.236350 0.971668i \(-0.424049\pi\)
0.236350 + 0.971668i \(0.424049\pi\)
\(132\) 5.28969e13 0.870362
\(133\) 1.92374e13 0.301378
\(134\) −1.85477e12 −0.0276764
\(135\) 4.82959e12 0.0686659
\(136\) −1.87628e12 −0.0254270
\(137\) 1.79816e13 0.232351 0.116176 0.993229i \(-0.462936\pi\)
0.116176 + 0.993229i \(0.462936\pi\)
\(138\) −2.98575e12 −0.0367993
\(139\) −7.96675e13 −0.936883 −0.468441 0.883495i \(-0.655184\pi\)
−0.468441 + 0.883495i \(0.655184\pi\)
\(140\) 1.82324e13 0.204650
\(141\) 3.03022e12 0.0324750
\(142\) −2.19637e12 −0.0224818
\(143\) −2.62121e14 −2.56341
\(144\) 3.50192e13 0.327303
\(145\) −1.71091e13 −0.152874
\(146\) 5.13915e12 0.0439135
\(147\) −4.71118e13 −0.385094
\(148\) −4.91501e13 −0.384436
\(149\) −1.42990e14 −1.07052 −0.535260 0.844687i \(-0.679786\pi\)
−0.535260 + 0.844687i \(0.679786\pi\)
\(150\) 5.46387e12 0.0391658
\(151\) −6.78139e12 −0.0465552 −0.0232776 0.999729i \(-0.507410\pi\)
−0.0232776 + 0.999729i \(0.507410\pi\)
\(152\) −1.23082e13 −0.0809491
\(153\) −8.67654e12 −0.0546830
\(154\) −1.12617e13 −0.0680329
\(155\) −7.11488e13 −0.412109
\(156\) −1.74599e14 −0.969912
\(157\) −2.37938e13 −0.126799 −0.0633995 0.997988i \(-0.520194\pi\)
−0.0633995 + 0.997988i \(0.520194\pi\)
\(158\) −1.88225e13 −0.0962511
\(159\) 1.06162e14 0.521058
\(160\) −1.75155e13 −0.0825357
\(161\) −1.04564e14 −0.473168
\(162\) −1.98706e12 −0.00863700
\(163\) −3.02948e14 −1.26517 −0.632586 0.774491i \(-0.718006\pi\)
−0.632586 + 0.774491i \(0.718006\pi\)
\(164\) 9.41374e13 0.377813
\(165\) −8.09842e13 −0.312431
\(166\) 8.32967e12 0.0308976
\(167\) 3.90932e14 1.39458 0.697291 0.716788i \(-0.254388\pi\)
0.697291 + 0.716788i \(0.254388\pi\)
\(168\) −1.50485e13 −0.0516394
\(169\) 5.62319e14 1.85660
\(170\) 1.43192e12 0.00454990
\(171\) −5.69172e13 −0.174088
\(172\) 1.51058e13 0.0444845
\(173\) 3.21297e14 0.911185 0.455592 0.890188i \(-0.349427\pi\)
0.455592 + 0.890188i \(0.349427\pi\)
\(174\) 7.03926e12 0.0192290
\(175\) 1.91351e14 0.503597
\(176\) −5.87214e14 −1.48924
\(177\) −3.07496e13 −0.0751646
\(178\) −2.57546e12 −0.00606910
\(179\) 5.49082e14 1.24765 0.623825 0.781564i \(-0.285578\pi\)
0.623825 + 0.781564i \(0.285578\pi\)
\(180\) −5.39437e13 −0.118214
\(181\) −1.94033e14 −0.410172 −0.205086 0.978744i \(-0.565747\pi\)
−0.205086 + 0.978744i \(0.565747\pi\)
\(182\) 3.71719e13 0.0758143
\(183\) −3.09917e14 −0.609977
\(184\) 6.69009e13 0.127091
\(185\) 7.52480e13 0.138000
\(186\) 2.92731e13 0.0518363
\(187\) 1.45491e14 0.248809
\(188\) −3.38458e13 −0.0559085
\(189\) −6.95890e13 −0.111055
\(190\) 9.39328e12 0.0144850
\(191\) 4.48927e14 0.669051 0.334525 0.942387i \(-0.391424\pi\)
0.334525 + 0.942387i \(0.391424\pi\)
\(192\) −3.86315e14 −0.556524
\(193\) 5.66130e14 0.788485 0.394243 0.919006i \(-0.371007\pi\)
0.394243 + 0.919006i \(0.371007\pi\)
\(194\) −1.03105e14 −0.138857
\(195\) 2.67308e14 0.348167
\(196\) 5.26211e14 0.662972
\(197\) −1.04131e14 −0.126925 −0.0634626 0.997984i \(-0.520214\pi\)
−0.0634626 + 0.997984i \(0.520214\pi\)
\(198\) 3.33197e13 0.0392986
\(199\) 6.44197e13 0.0735315 0.0367658 0.999324i \(-0.488294\pi\)
0.0367658 + 0.999324i \(0.488294\pi\)
\(200\) −1.22428e14 −0.135265
\(201\) 1.92184e14 0.205562
\(202\) 7.48882e13 0.0775585
\(203\) 2.46523e14 0.247248
\(204\) 9.69118e13 0.0941414
\(205\) −1.44123e14 −0.135623
\(206\) −8.70384e13 −0.0793549
\(207\) 3.09372e14 0.273321
\(208\) 1.93824e15 1.65957
\(209\) 9.54408e14 0.792105
\(210\) 1.14845e13 0.00924035
\(211\) 9.34027e14 0.728657 0.364329 0.931270i \(-0.381298\pi\)
0.364329 + 0.931270i \(0.381298\pi\)
\(212\) −1.18576e15 −0.897046
\(213\) 2.27579e14 0.166980
\(214\) 4.55502e13 0.0324191
\(215\) −2.31267e13 −0.0159685
\(216\) 4.45235e13 0.0298291
\(217\) 1.02517e15 0.666514
\(218\) −3.23764e13 −0.0204297
\(219\) −5.32499e14 −0.326161
\(220\) 9.04546e14 0.537877
\(221\) −4.80229e14 −0.277267
\(222\) −3.09596e13 −0.0173580
\(223\) 1.24475e15 0.677799 0.338900 0.940823i \(-0.389945\pi\)
0.338900 + 0.940823i \(0.389945\pi\)
\(224\) 2.52378e14 0.133487
\(225\) −5.66145e14 −0.290898
\(226\) −2.99696e13 −0.0149616
\(227\) 3.20457e15 1.55454 0.777270 0.629167i \(-0.216604\pi\)
0.777270 + 0.629167i \(0.216604\pi\)
\(228\) 6.35732e14 0.299707
\(229\) 3.77559e15 1.73003 0.865016 0.501744i \(-0.167308\pi\)
0.865016 + 0.501744i \(0.167308\pi\)
\(230\) −5.10568e13 −0.0227417
\(231\) 1.16689e15 0.505304
\(232\) −1.57727e14 −0.0664100
\(233\) 2.48828e15 1.01879 0.509397 0.860532i \(-0.329869\pi\)
0.509397 + 0.860532i \(0.329869\pi\)
\(234\) −1.09980e14 −0.0437935
\(235\) 5.18172e13 0.0200693
\(236\) 3.43455e14 0.129402
\(237\) 1.95031e15 0.714890
\(238\) −2.06324e13 −0.00735868
\(239\) 3.56407e15 1.23697 0.618486 0.785796i \(-0.287746\pi\)
0.618486 + 0.785796i \(0.287746\pi\)
\(240\) 5.98834e14 0.202271
\(241\) 1.24378e14 0.0408914 0.0204457 0.999791i \(-0.493491\pi\)
0.0204457 + 0.999791i \(0.493491\pi\)
\(242\) −3.15828e14 −0.101077
\(243\) 2.05891e14 0.0641500
\(244\) 3.46159e15 1.05013
\(245\) −8.05619e14 −0.237985
\(246\) 5.92970e13 0.0170590
\(247\) −3.15025e15 −0.882705
\(248\) −6.55913e14 −0.179024
\(249\) −8.63087e14 −0.229487
\(250\) 2.00496e14 0.0519392
\(251\) 3.21526e15 0.811590 0.405795 0.913964i \(-0.366995\pi\)
0.405795 + 0.913964i \(0.366995\pi\)
\(252\) 7.77268e14 0.191191
\(253\) −5.18765e15 −1.24362
\(254\) −3.71767e14 −0.0868665
\(255\) −1.48370e14 −0.0337937
\(256\) 4.23393e15 0.940122
\(257\) −2.73468e15 −0.592026 −0.296013 0.955184i \(-0.595657\pi\)
−0.296013 + 0.955184i \(0.595657\pi\)
\(258\) 9.51511e12 0.00200856
\(259\) −1.08424e15 −0.223191
\(260\) −2.98567e15 −0.599398
\(261\) −7.29380e14 −0.142821
\(262\) −1.92376e14 −0.0367444
\(263\) −7.63743e15 −1.42310 −0.711549 0.702636i \(-0.752006\pi\)
−0.711549 + 0.702636i \(0.752006\pi\)
\(264\) −7.46585e14 −0.135723
\(265\) 1.81538e15 0.322010
\(266\) −1.35347e14 −0.0234270
\(267\) 2.66859e14 0.0450773
\(268\) −2.14658e15 −0.353893
\(269\) −1.61454e15 −0.259811 −0.129906 0.991526i \(-0.541467\pi\)
−0.129906 + 0.991526i \(0.541467\pi\)
\(270\) −3.39790e13 −0.00533761
\(271\) 1.26053e16 1.93310 0.966549 0.256483i \(-0.0825637\pi\)
0.966549 + 0.256483i \(0.0825637\pi\)
\(272\) −1.07583e15 −0.161081
\(273\) −3.85161e15 −0.563099
\(274\) −1.26511e14 −0.0180614
\(275\) 9.49331e15 1.32359
\(276\) −3.45550e15 −0.470546
\(277\) −3.71246e15 −0.493791 −0.246895 0.969042i \(-0.579410\pi\)
−0.246895 + 0.969042i \(0.579410\pi\)
\(278\) 5.60508e14 0.0728267
\(279\) −3.03316e15 −0.385006
\(280\) −2.57331e14 −0.0319128
\(281\) 1.22310e16 1.48208 0.741039 0.671462i \(-0.234333\pi\)
0.741039 + 0.671462i \(0.234333\pi\)
\(282\) −2.13194e13 −0.00252438
\(283\) 2.91187e15 0.336946 0.168473 0.985706i \(-0.446116\pi\)
0.168473 + 0.985706i \(0.446116\pi\)
\(284\) −2.54192e15 −0.287470
\(285\) −9.73294e14 −0.107585
\(286\) 1.84418e15 0.199261
\(287\) 2.07665e15 0.219346
\(288\) −7.46705e14 −0.0771077
\(289\) −9.63803e15 −0.973088
\(290\) 1.20373e14 0.0118834
\(291\) 1.06833e16 1.03134
\(292\) 5.94770e15 0.561514
\(293\) 1.09631e16 1.01227 0.506133 0.862455i \(-0.331074\pi\)
0.506133 + 0.862455i \(0.331074\pi\)
\(294\) 3.31459e14 0.0299345
\(295\) −5.25823e14 −0.0464512
\(296\) 6.93703e14 0.0599483
\(297\) −3.45245e15 −0.291884
\(298\) 1.00602e15 0.0832148
\(299\) 1.71231e16 1.38586
\(300\) 6.32350e15 0.500806
\(301\) 3.33230e14 0.0258263
\(302\) 4.77111e13 0.00361888
\(303\) −7.75961e15 −0.576054
\(304\) −7.05732e15 −0.512816
\(305\) −5.29963e15 −0.376961
\(306\) 6.10446e13 0.00425068
\(307\) 1.75297e16 1.19502 0.597510 0.801861i \(-0.296157\pi\)
0.597510 + 0.801861i \(0.296157\pi\)
\(308\) −1.30335e16 −0.869924
\(309\) 9.01857e15 0.589397
\(310\) 5.00574e14 0.0320344
\(311\) 2.05232e16 1.28618 0.643092 0.765789i \(-0.277651\pi\)
0.643092 + 0.765789i \(0.277651\pi\)
\(312\) 2.46428e15 0.151247
\(313\) −1.67629e16 −1.00765 −0.503826 0.863805i \(-0.668075\pi\)
−0.503826 + 0.863805i \(0.668075\pi\)
\(314\) 1.67403e14 0.00985647
\(315\) −1.18998e15 −0.0686313
\(316\) −2.17838e16 −1.23074
\(317\) 1.94562e15 0.107689 0.0538447 0.998549i \(-0.482852\pi\)
0.0538447 + 0.998549i \(0.482852\pi\)
\(318\) −7.46909e14 −0.0405034
\(319\) 1.22305e16 0.649837
\(320\) −6.60605e15 −0.343928
\(321\) −4.71973e15 −0.240788
\(322\) 7.35672e14 0.0367808
\(323\) 1.74856e15 0.0856769
\(324\) −2.29968e15 −0.110440
\(325\) −3.13350e16 −1.47498
\(326\) 2.13142e15 0.0983456
\(327\) 3.35471e15 0.151738
\(328\) −1.32865e15 −0.0589157
\(329\) −7.46628e14 −0.0324587
\(330\) 5.69772e14 0.0242863
\(331\) 3.46353e16 1.44756 0.723781 0.690030i \(-0.242403\pi\)
0.723781 + 0.690030i \(0.242403\pi\)
\(332\) 9.64018e15 0.395082
\(333\) 3.20791e15 0.128924
\(334\) −2.75044e15 −0.108405
\(335\) 3.28638e15 0.127036
\(336\) −8.62853e15 −0.327138
\(337\) 8.51087e15 0.316504 0.158252 0.987399i \(-0.449414\pi\)
0.158252 + 0.987399i \(0.449414\pi\)
\(338\) −3.95625e15 −0.144319
\(339\) 3.10533e15 0.111125
\(340\) 1.65721e15 0.0581787
\(341\) 5.08610e16 1.75179
\(342\) 4.00446e14 0.0135324
\(343\) 2.90114e16 0.961960
\(344\) −2.13202e14 −0.00693685
\(345\) 5.29031e15 0.168911
\(346\) −2.26051e15 −0.0708292
\(347\) 5.87073e16 1.80530 0.902652 0.430370i \(-0.141617\pi\)
0.902652 + 0.430370i \(0.141617\pi\)
\(348\) 8.14675e15 0.245878
\(349\) −3.61511e16 −1.07092 −0.535459 0.844561i \(-0.679861\pi\)
−0.535459 + 0.844561i \(0.679861\pi\)
\(350\) −1.34627e15 −0.0391461
\(351\) 1.13957e16 0.325269
\(352\) 1.25210e16 0.350842
\(353\) −1.87312e16 −0.515264 −0.257632 0.966243i \(-0.582942\pi\)
−0.257632 + 0.966243i \(0.582942\pi\)
\(354\) 2.16342e14 0.00584277
\(355\) 3.89164e15 0.103192
\(356\) −2.98066e15 −0.0776045
\(357\) 2.13785e15 0.0546555
\(358\) −3.86312e15 −0.0969836
\(359\) −4.30600e16 −1.06160 −0.530799 0.847497i \(-0.678108\pi\)
−0.530799 + 0.847497i \(0.678108\pi\)
\(360\) 7.61359e14 0.0184341
\(361\) −3.05826e16 −0.727240
\(362\) 1.36514e15 0.0318839
\(363\) 3.27248e16 0.750731
\(364\) 4.30202e16 0.969423
\(365\) −9.10582e15 −0.201565
\(366\) 2.18045e15 0.0474153
\(367\) 4.70659e16 1.00549 0.502744 0.864436i \(-0.332324\pi\)
0.502744 + 0.864436i \(0.332324\pi\)
\(368\) 3.83598e16 0.805130
\(369\) −6.14412e15 −0.126703
\(370\) −5.29414e14 −0.0107271
\(371\) −2.61576e16 −0.520796
\(372\) 3.38786e16 0.662821
\(373\) −2.01671e15 −0.0387736 −0.0193868 0.999812i \(-0.506171\pi\)
−0.0193868 + 0.999812i \(0.506171\pi\)
\(374\) −1.02362e15 −0.0193407
\(375\) −2.07746e16 −0.385771
\(376\) 4.77697e14 0.00871830
\(377\) −4.03697e16 −0.724164
\(378\) 4.89600e14 0.00863266
\(379\) −1.27882e16 −0.221643 −0.110822 0.993840i \(-0.535348\pi\)
−0.110822 + 0.993840i \(0.535348\pi\)
\(380\) 1.08711e16 0.185217
\(381\) 3.85211e16 0.645188
\(382\) −3.15847e15 −0.0520073
\(383\) 2.55954e16 0.414352 0.207176 0.978304i \(-0.433573\pi\)
0.207176 + 0.978304i \(0.433573\pi\)
\(384\) 1.11089e16 0.176815
\(385\) 1.99540e16 0.312274
\(386\) −3.98306e15 −0.0612914
\(387\) −9.85918e14 −0.0149183
\(388\) −1.19327e17 −1.77554
\(389\) −1.14620e17 −1.67722 −0.838608 0.544735i \(-0.816630\pi\)
−0.838608 + 0.544735i \(0.816630\pi\)
\(390\) −1.88067e15 −0.0270641
\(391\) −9.50423e15 −0.134514
\(392\) −7.42691e15 −0.103383
\(393\) 1.99332e16 0.272914
\(394\) 7.32620e14 0.00986628
\(395\) 3.33506e16 0.441797
\(396\) 3.85619e16 0.502504
\(397\) −7.43340e16 −0.952904 −0.476452 0.879200i \(-0.658077\pi\)
−0.476452 + 0.879200i \(0.658077\pi\)
\(398\) −4.53230e14 −0.00571583
\(399\) 1.40241e16 0.174000
\(400\) −7.01978e16 −0.856907
\(401\) −7.00311e16 −0.841109 −0.420555 0.907267i \(-0.638164\pi\)
−0.420555 + 0.907267i \(0.638164\pi\)
\(402\) −1.35213e15 −0.0159790
\(403\) −1.67879e17 −1.95215
\(404\) 8.66703e16 0.991725
\(405\) 3.52077e15 0.0396443
\(406\) −1.73443e15 −0.0192193
\(407\) −5.37913e16 −0.586608
\(408\) −1.36781e15 −0.0146803
\(409\) −4.06796e16 −0.429710 −0.214855 0.976646i \(-0.568928\pi\)
−0.214855 + 0.976646i \(0.568928\pi\)
\(410\) 1.01399e15 0.0105424
\(411\) 1.31086e16 0.134148
\(412\) −1.00732e17 −1.01470
\(413\) 7.57652e15 0.0751268
\(414\) −2.17661e15 −0.0212461
\(415\) −1.47589e16 −0.141822
\(416\) −4.13286e16 −0.390971
\(417\) −5.80776e16 −0.540909
\(418\) −6.71482e15 −0.0615728
\(419\) 9.40621e16 0.849227 0.424613 0.905375i \(-0.360410\pi\)
0.424613 + 0.905375i \(0.360410\pi\)
\(420\) 1.32914e16 0.118155
\(421\) −1.72503e16 −0.150996 −0.0754978 0.997146i \(-0.524055\pi\)
−0.0754978 + 0.997146i \(0.524055\pi\)
\(422\) −6.57143e15 −0.0566408
\(423\) 2.20903e15 0.0187495
\(424\) 1.67358e16 0.139884
\(425\) 1.73926e16 0.143165
\(426\) −1.60115e15 −0.0129799
\(427\) 7.63617e16 0.609669
\(428\) 5.27166e16 0.414537
\(429\) −1.91086e17 −1.47998
\(430\) 1.62710e14 0.00124128
\(431\) −1.23734e17 −0.929795 −0.464898 0.885364i \(-0.653909\pi\)
−0.464898 + 0.885364i \(0.653909\pi\)
\(432\) 2.55290e16 0.188969
\(433\) −3.00092e16 −0.218818 −0.109409 0.993997i \(-0.534896\pi\)
−0.109409 + 0.993997i \(0.534896\pi\)
\(434\) −7.21271e15 −0.0518102
\(435\) −1.24725e16 −0.0882621
\(436\) −3.74702e16 −0.261230
\(437\) −6.23468e16 −0.428238
\(438\) 3.74644e15 0.0253535
\(439\) 1.25024e17 0.833630 0.416815 0.908991i \(-0.363146\pi\)
0.416815 + 0.908991i \(0.363146\pi\)
\(440\) −1.27667e16 −0.0838759
\(441\) −3.43445e16 −0.222334
\(442\) 3.37869e15 0.0215528
\(443\) −2.66955e17 −1.67808 −0.839041 0.544068i \(-0.816883\pi\)
−0.839041 + 0.544068i \(0.816883\pi\)
\(444\) −3.58304e16 −0.221954
\(445\) 4.56333e15 0.0278575
\(446\) −8.75757e15 −0.0526874
\(447\) −1.04240e17 −0.618065
\(448\) 9.51858e16 0.556244
\(449\) 2.78758e17 1.60556 0.802778 0.596278i \(-0.203354\pi\)
0.802778 + 0.596278i \(0.203354\pi\)
\(450\) 3.98316e15 0.0226124
\(451\) 1.03027e17 0.576504
\(452\) −3.46848e16 −0.191311
\(453\) −4.94363e15 −0.0268787
\(454\) −2.25461e16 −0.120839
\(455\) −6.58632e16 −0.347991
\(456\) −8.97269e15 −0.0467360
\(457\) 8.18878e16 0.420498 0.210249 0.977648i \(-0.432573\pi\)
0.210249 + 0.977648i \(0.432573\pi\)
\(458\) −2.65635e16 −0.134481
\(459\) −6.32520e15 −0.0315712
\(460\) −5.90896e16 −0.290794
\(461\) −2.00345e17 −0.972128 −0.486064 0.873923i \(-0.661568\pi\)
−0.486064 + 0.873923i \(0.661568\pi\)
\(462\) −8.20977e15 −0.0392788
\(463\) −8.54155e16 −0.402958 −0.201479 0.979493i \(-0.564575\pi\)
−0.201479 + 0.979493i \(0.564575\pi\)
\(464\) −9.04378e16 −0.420710
\(465\) −5.18675e16 −0.237931
\(466\) −1.75065e16 −0.0791939
\(467\) 9.72001e16 0.433618 0.216809 0.976214i \(-0.430435\pi\)
0.216809 + 0.976214i \(0.430435\pi\)
\(468\) −1.27283e17 −0.559979
\(469\) −4.73530e16 −0.205459
\(470\) −3.64565e14 −0.00156005
\(471\) −1.73457e16 −0.0732074
\(472\) −4.84751e15 −0.0201788
\(473\) 1.65322e16 0.0678787
\(474\) −1.37216e16 −0.0555706
\(475\) 1.14094e17 0.455777
\(476\) −2.38785e16 −0.0940940
\(477\) 7.73918e16 0.300833
\(478\) −2.50753e16 −0.0961536
\(479\) −2.68070e17 −1.01407 −0.507035 0.861925i \(-0.669258\pi\)
−0.507035 + 0.861925i \(0.669258\pi\)
\(480\) −1.27688e16 −0.0476520
\(481\) 1.77551e17 0.653703
\(482\) −8.75071e14 −0.00317861
\(483\) −7.62274e16 −0.273184
\(484\) −3.65517e17 −1.29245
\(485\) 1.82687e17 0.637362
\(486\) −1.44857e15 −0.00498658
\(487\) 2.93239e17 0.996054 0.498027 0.867161i \(-0.334058\pi\)
0.498027 + 0.867161i \(0.334058\pi\)
\(488\) −4.88567e16 −0.163755
\(489\) −2.20849e17 −0.730447
\(490\) 5.66801e15 0.0184993
\(491\) 2.35700e17 0.759154 0.379577 0.925160i \(-0.376070\pi\)
0.379577 + 0.925160i \(0.376070\pi\)
\(492\) 6.86262e16 0.218131
\(493\) 2.24073e16 0.0702887
\(494\) 2.21639e16 0.0686153
\(495\) −5.90375e16 −0.180382
\(496\) −3.76089e17 −1.13412
\(497\) −5.60741e16 −0.166896
\(498\) 6.07233e15 0.0178388
\(499\) 2.95486e17 0.856807 0.428404 0.903587i \(-0.359076\pi\)
0.428404 + 0.903587i \(0.359076\pi\)
\(500\) 2.32040e17 0.664137
\(501\) 2.84990e17 0.805163
\(502\) −2.26213e16 −0.0630874
\(503\) 6.45285e15 0.0177648 0.00888238 0.999961i \(-0.497173\pi\)
0.00888238 + 0.999961i \(0.497173\pi\)
\(504\) −1.09703e16 −0.0298140
\(505\) −1.32691e17 −0.355997
\(506\) 3.64982e16 0.0966703
\(507\) 4.09931e17 1.07191
\(508\) −4.30258e17 −1.11075
\(509\) −2.90108e17 −0.739425 −0.369713 0.929146i \(-0.620544\pi\)
−0.369713 + 0.929146i \(0.620544\pi\)
\(510\) 1.04387e15 0.00262689
\(511\) 1.31205e17 0.325997
\(512\) −1.54623e17 −0.379331
\(513\) −4.14927e16 −0.100510
\(514\) 1.92401e16 0.0460200
\(515\) 1.54219e17 0.364243
\(516\) 1.10121e16 0.0256831
\(517\) −3.70418e16 −0.0853106
\(518\) 7.62826e15 0.0173493
\(519\) 2.34225e17 0.526073
\(520\) 4.21397e16 0.0934694
\(521\) −4.12174e17 −0.902891 −0.451445 0.892299i \(-0.649091\pi\)
−0.451445 + 0.892299i \(0.649091\pi\)
\(522\) 5.13162e15 0.0111019
\(523\) −2.59656e17 −0.554802 −0.277401 0.960754i \(-0.589473\pi\)
−0.277401 + 0.960754i \(0.589473\pi\)
\(524\) −2.22642e17 −0.469844
\(525\) 1.39495e17 0.290752
\(526\) 5.37338e16 0.110622
\(527\) 9.31819e16 0.189480
\(528\) −4.28079e17 −0.859812
\(529\) −1.65152e17 −0.327660
\(530\) −1.27723e16 −0.0250308
\(531\) −2.24165e16 −0.0433963
\(532\) −1.56641e17 −0.299557
\(533\) −3.40065e17 −0.642443
\(534\) −1.87751e15 −0.00350400
\(535\) −8.07082e16 −0.148805
\(536\) 3.02968e16 0.0551855
\(537\) 4.00281e17 0.720331
\(538\) 1.13592e16 0.0201959
\(539\) 5.75900e17 1.01163
\(540\) −3.93250e16 −0.0682510
\(541\) −3.59080e17 −0.615757 −0.307878 0.951426i \(-0.599619\pi\)
−0.307878 + 0.951426i \(0.599619\pi\)
\(542\) −8.86859e16 −0.150266
\(543\) −1.41450e17 −0.236813
\(544\) 2.29396e16 0.0379483
\(545\) 5.73661e16 0.0937731
\(546\) 2.70983e16 0.0437714
\(547\) −6.59660e17 −1.05294 −0.526469 0.850194i \(-0.676484\pi\)
−0.526469 + 0.850194i \(0.676484\pi\)
\(548\) −1.46415e17 −0.230947
\(549\) −2.25929e17 −0.352170
\(550\) −6.67910e16 −0.102887
\(551\) 1.46990e17 0.223770
\(552\) 4.87708e16 0.0733763
\(553\) −4.80545e17 −0.714530
\(554\) 2.61193e16 0.0383839
\(555\) 5.48558e16 0.0796742
\(556\) 6.48693e17 0.931222
\(557\) 2.33181e17 0.330853 0.165426 0.986222i \(-0.447100\pi\)
0.165426 + 0.986222i \(0.447100\pi\)
\(558\) 2.13401e16 0.0299277
\(559\) −5.45686e16 −0.0756425
\(560\) −1.47549e17 −0.202169
\(561\) 1.06063e17 0.143650
\(562\) −8.60523e16 −0.115206
\(563\) −9.44765e17 −1.25031 −0.625157 0.780499i \(-0.714965\pi\)
−0.625157 + 0.780499i \(0.714965\pi\)
\(564\) −2.46736e16 −0.0322788
\(565\) 5.31017e16 0.0686742
\(566\) −2.04867e16 −0.0261918
\(567\) −5.07304e16 −0.0641177
\(568\) 3.58766e16 0.0448277
\(569\) 9.68935e17 1.19692 0.598460 0.801153i \(-0.295780\pi\)
0.598460 + 0.801153i \(0.295780\pi\)
\(570\) 6.84770e15 0.00836292
\(571\) 5.42831e17 0.655436 0.327718 0.944776i \(-0.393720\pi\)
0.327718 + 0.944776i \(0.393720\pi\)
\(572\) 2.13432e18 2.54792
\(573\) 3.27268e17 0.386276
\(574\) −1.46104e16 −0.0170504
\(575\) −6.20152e17 −0.715578
\(576\) −2.81624e17 −0.321309
\(577\) −7.74916e17 −0.874203 −0.437101 0.899412i \(-0.643995\pi\)
−0.437101 + 0.899412i \(0.643995\pi\)
\(578\) 6.78092e16 0.0756411
\(579\) 4.12709e17 0.455232
\(580\) 1.39311e17 0.151951
\(581\) 2.12660e17 0.229372
\(582\) −7.51637e16 −0.0801694
\(583\) −1.29773e18 −1.36880
\(584\) −8.39455e16 −0.0875617
\(585\) 1.94868e17 0.201014
\(586\) −7.71321e16 −0.0786866
\(587\) −1.28751e17 −0.129898 −0.0649491 0.997889i \(-0.520688\pi\)
−0.0649491 + 0.997889i \(0.520688\pi\)
\(588\) 3.83608e17 0.382767
\(589\) 6.11264e17 0.603225
\(590\) 3.69948e15 0.00361079
\(591\) −7.59112e16 −0.0732803
\(592\) 3.97757e17 0.379776
\(593\) 2.83120e17 0.267372 0.133686 0.991024i \(-0.457319\pi\)
0.133686 + 0.991024i \(0.457319\pi\)
\(594\) 2.42900e16 0.0226891
\(595\) 3.65576e16 0.0337767
\(596\) 1.16430e18 1.06405
\(597\) 4.69619e16 0.0424534
\(598\) −1.20471e17 −0.107727
\(599\) −3.18328e17 −0.281579 −0.140789 0.990040i \(-0.544964\pi\)
−0.140789 + 0.990040i \(0.544964\pi\)
\(600\) −8.92497e16 −0.0780950
\(601\) 3.31331e17 0.286799 0.143399 0.989665i \(-0.454197\pi\)
0.143399 + 0.989665i \(0.454197\pi\)
\(602\) −2.34447e15 −0.00200755
\(603\) 1.40102e17 0.118681
\(604\) 5.52174e16 0.0462739
\(605\) 5.59600e17 0.463946
\(606\) 5.45935e16 0.0447784
\(607\) 5.29921e17 0.430016 0.215008 0.976612i \(-0.431022\pi\)
0.215008 + 0.976612i \(0.431022\pi\)
\(608\) 1.50481e17 0.120812
\(609\) 1.79715e17 0.142749
\(610\) 3.72860e16 0.0293023
\(611\) 1.22265e17 0.0950682
\(612\) 7.06487e16 0.0543526
\(613\) −2.12461e18 −1.61728 −0.808640 0.588303i \(-0.799796\pi\)
−0.808640 + 0.588303i \(0.799796\pi\)
\(614\) −1.23332e17 −0.0928925
\(615\) −1.05065e17 −0.0783018
\(616\) 1.83954e17 0.135655
\(617\) −1.71451e17 −0.125108 −0.0625542 0.998042i \(-0.519925\pi\)
−0.0625542 + 0.998042i \(0.519925\pi\)
\(618\) −6.34510e16 −0.0458156
\(619\) 1.45191e18 1.03741 0.518704 0.854954i \(-0.326415\pi\)
0.518704 + 0.854954i \(0.326415\pi\)
\(620\) 5.79329e17 0.409618
\(621\) 2.25532e17 0.157802
\(622\) −1.44393e17 −0.0999791
\(623\) −6.57524e16 −0.0450546
\(624\) 1.41298e18 0.958155
\(625\) 9.45168e17 0.634291
\(626\) 1.17937e17 0.0783278
\(627\) 6.95763e17 0.457322
\(628\) 1.93741e17 0.126033
\(629\) −9.85504e16 −0.0634496
\(630\) 8.37224e15 0.00533492
\(631\) −1.56293e18 −0.985708 −0.492854 0.870112i \(-0.664046\pi\)
−0.492854 + 0.870112i \(0.664046\pi\)
\(632\) 3.07456e17 0.191921
\(633\) 6.80905e17 0.420691
\(634\) −1.36886e16 −0.00837102
\(635\) 6.58717e17 0.398721
\(636\) −8.64421e17 −0.517909
\(637\) −1.90090e18 −1.12733
\(638\) −8.60487e16 −0.0505138
\(639\) 1.65905e17 0.0964060
\(640\) 1.89964e17 0.109270
\(641\) −1.11430e18 −0.634488 −0.317244 0.948344i \(-0.602757\pi\)
−0.317244 + 0.948344i \(0.602757\pi\)
\(642\) 3.32061e16 0.0187172
\(643\) −1.82846e18 −1.02027 −0.510133 0.860096i \(-0.670404\pi\)
−0.510133 + 0.860096i \(0.670404\pi\)
\(644\) 8.51415e17 0.470309
\(645\) −1.68594e16 −0.00921941
\(646\) −1.23021e16 −0.00665993
\(647\) 2.98220e18 1.59830 0.799152 0.601129i \(-0.205282\pi\)
0.799152 + 0.601129i \(0.205282\pi\)
\(648\) 3.24576e16 0.0172218
\(649\) 3.75887e17 0.197454
\(650\) 2.20460e17 0.114655
\(651\) 7.47352e17 0.384812
\(652\) 2.46676e18 1.25753
\(653\) 2.52221e18 1.27305 0.636525 0.771256i \(-0.280371\pi\)
0.636525 + 0.771256i \(0.280371\pi\)
\(654\) −2.36024e16 −0.0117951
\(655\) 3.40861e17 0.168659
\(656\) −7.61826e17 −0.373234
\(657\) −3.88192e17 −0.188309
\(658\) 5.25297e15 0.00252311
\(659\) 1.01758e18 0.483963 0.241982 0.970281i \(-0.422203\pi\)
0.241982 + 0.970281i \(0.422203\pi\)
\(660\) 6.59414e17 0.310544
\(661\) −6.78275e17 −0.316298 −0.158149 0.987415i \(-0.550553\pi\)
−0.158149 + 0.987415i \(0.550553\pi\)
\(662\) −2.43680e17 −0.112523
\(663\) −3.50087e17 −0.160080
\(664\) −1.36061e17 −0.0616086
\(665\) 2.39814e17 0.107531
\(666\) −2.25695e16 −0.0100217
\(667\) −7.98959e17 −0.351323
\(668\) −3.18317e18 −1.38616
\(669\) 9.07424e17 0.391328
\(670\) −2.31216e16 −0.00987489
\(671\) 3.78846e18 1.60238
\(672\) 1.83984e17 0.0770689
\(673\) 1.41680e18 0.587776 0.293888 0.955840i \(-0.405051\pi\)
0.293888 + 0.955840i \(0.405051\pi\)
\(674\) −5.98790e16 −0.0246028
\(675\) −4.12720e17 −0.167950
\(676\) −4.57868e18 −1.84539
\(677\) 4.12787e18 1.64778 0.823890 0.566749i \(-0.191799\pi\)
0.823890 + 0.566749i \(0.191799\pi\)
\(678\) −2.18479e16 −0.00863806
\(679\) −2.63231e18 −1.03082
\(680\) −2.33898e16 −0.00907231
\(681\) 2.33613e18 0.897514
\(682\) −3.57837e17 −0.136172
\(683\) −4.54626e18 −1.71364 −0.856820 0.515615i \(-0.827563\pi\)
−0.856820 + 0.515615i \(0.827563\pi\)
\(684\) 4.63449e17 0.173036
\(685\) 2.24159e17 0.0829025
\(686\) −2.04112e17 −0.0747760
\(687\) 2.75241e18 0.998835
\(688\) −1.22247e17 −0.0439453
\(689\) 4.28348e18 1.52536
\(690\) −3.72204e16 −0.0131299
\(691\) 1.09870e18 0.383946 0.191973 0.981400i \(-0.438511\pi\)
0.191973 + 0.981400i \(0.438511\pi\)
\(692\) −2.61616e18 −0.905679
\(693\) 8.50664e17 0.291737
\(694\) −4.13041e17 −0.140332
\(695\) −9.93137e17 −0.334278
\(696\) −1.14983e17 −0.0383418
\(697\) 1.88754e17 0.0623567
\(698\) 2.54344e17 0.0832457
\(699\) 1.81396e18 0.588201
\(700\) −1.55807e18 −0.500554
\(701\) 7.97555e17 0.253859 0.126930 0.991912i \(-0.459488\pi\)
0.126930 + 0.991912i \(0.459488\pi\)
\(702\) −8.01752e16 −0.0252842
\(703\) −6.46481e17 −0.201998
\(704\) 4.72236e18 1.46197
\(705\) 3.77748e16 0.0115870
\(706\) 1.31785e17 0.0400531
\(707\) 1.91192e18 0.575764
\(708\) 2.50379e17 0.0747104
\(709\) 1.42619e18 0.421675 0.210838 0.977521i \(-0.432381\pi\)
0.210838 + 0.977521i \(0.432381\pi\)
\(710\) −2.73800e16 −0.00802146
\(711\) 1.42178e18 0.412742
\(712\) 4.20688e16 0.0121015
\(713\) −3.32250e18 −0.947073
\(714\) −1.50410e16 −0.00424853
\(715\) −3.26761e18 −0.914619
\(716\) −4.47090e18 −1.24011
\(717\) 2.59821e18 0.714166
\(718\) 3.02953e17 0.0825213
\(719\) 2.76714e18 0.746954 0.373477 0.927639i \(-0.378165\pi\)
0.373477 + 0.927639i \(0.378165\pi\)
\(720\) 4.36550e17 0.116781
\(721\) −2.22212e18 −0.589100
\(722\) 2.15167e17 0.0565306
\(723\) 9.06714e16 0.0236087
\(724\) 1.57992e18 0.407693
\(725\) 1.46208e18 0.373916
\(726\) −2.30239e17 −0.0583566
\(727\) −1.88892e18 −0.474505 −0.237252 0.971448i \(-0.576247\pi\)
−0.237252 + 0.971448i \(0.576247\pi\)
\(728\) −6.07185e17 −0.151171
\(729\) 1.50095e17 0.0370370
\(730\) 6.40648e16 0.0156683
\(731\) 3.02885e16 0.00734200
\(732\) 2.52350e18 0.606291
\(733\) 2.87686e18 0.685082 0.342541 0.939503i \(-0.388712\pi\)
0.342541 + 0.939503i \(0.388712\pi\)
\(734\) −3.31136e17 −0.0781596
\(735\) −5.87296e17 −0.137401
\(736\) −8.17936e17 −0.189677
\(737\) −2.34928e18 −0.540003
\(738\) 4.32275e16 0.00984904
\(739\) −4.90104e16 −0.0110688 −0.00553438 0.999985i \(-0.501762\pi\)
−0.00553438 + 0.999985i \(0.501762\pi\)
\(740\) −6.12706e17 −0.137166
\(741\) −2.29654e18 −0.509630
\(742\) 1.84034e17 0.0404830
\(743\) 2.87146e18 0.626146 0.313073 0.949729i \(-0.398641\pi\)
0.313073 + 0.949729i \(0.398641\pi\)
\(744\) −4.78161e17 −0.103359
\(745\) −1.78252e18 −0.381960
\(746\) 1.41887e16 0.00301399
\(747\) −6.29191e17 −0.132495
\(748\) −1.18466e18 −0.247306
\(749\) 1.16291e18 0.240667
\(750\) 1.46162e17 0.0299871
\(751\) 4.30483e18 0.875581 0.437791 0.899077i \(-0.355761\pi\)
0.437791 + 0.899077i \(0.355761\pi\)
\(752\) 2.73904e17 0.0552308
\(753\) 2.34392e18 0.468572
\(754\) 2.84025e17 0.0562915
\(755\) −8.45369e16 −0.0166108
\(756\) 5.66628e17 0.110384
\(757\) −1.57319e18 −0.303849 −0.151925 0.988392i \(-0.548547\pi\)
−0.151925 + 0.988392i \(0.548547\pi\)
\(758\) 8.99725e16 0.0172290
\(759\) −3.78180e18 −0.718004
\(760\) −1.53435e17 −0.0288825
\(761\) 4.55145e18 0.849472 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(762\) −2.71018e17 −0.0501524
\(763\) −8.26582e17 −0.151662
\(764\) −3.65539e18 −0.665008
\(765\) −1.08162e17 −0.0195108
\(766\) −1.80079e17 −0.0322089
\(767\) −1.24071e18 −0.220039
\(768\) 3.08654e18 0.542780
\(769\) 5.31422e18 0.926655 0.463327 0.886187i \(-0.346655\pi\)
0.463327 + 0.886187i \(0.346655\pi\)
\(770\) −1.40388e17 −0.0242740
\(771\) −1.99358e18 −0.341806
\(772\) −4.60971e18 −0.783721
\(773\) −5.62082e18 −0.947617 −0.473809 0.880628i \(-0.657121\pi\)
−0.473809 + 0.880628i \(0.657121\pi\)
\(774\) 6.93652e15 0.00115965
\(775\) 6.08012e18 1.00798
\(776\) 1.68417e18 0.276876
\(777\) −7.90410e17 −0.128859
\(778\) 8.06422e17 0.130375
\(779\) 1.23821e18 0.198518
\(780\) −2.17656e18 −0.346063
\(781\) −2.78195e18 −0.438650
\(782\) 6.68679e16 0.0104562
\(783\) −5.31718e17 −0.0824575
\(784\) −4.25846e18 −0.654936
\(785\) −2.96614e17 −0.0452417
\(786\) −1.40242e17 −0.0212144
\(787\) 4.85685e18 0.728651 0.364325 0.931272i \(-0.381300\pi\)
0.364325 + 0.931272i \(0.381300\pi\)
\(788\) 8.47883e17 0.126158
\(789\) −5.56769e18 −0.821626
\(790\) −2.34641e17 −0.0343422
\(791\) −7.65136e17 −0.111069
\(792\) −5.44260e17 −0.0783597
\(793\) −1.25047e19 −1.78566
\(794\) 5.22984e17 0.0740722
\(795\) 1.32341e18 0.185913
\(796\) −5.24537e17 −0.0730872
\(797\) 9.06607e18 1.25297 0.626484 0.779434i \(-0.284493\pi\)
0.626484 + 0.779434i \(0.284493\pi\)
\(798\) −9.86677e16 −0.0135256
\(799\) −6.78638e16 −0.00922750
\(800\) 1.49681e18 0.201875
\(801\) 1.94540e17 0.0260254
\(802\) 4.92710e17 0.0653820
\(803\) 6.50933e18 0.856811
\(804\) −1.56486e18 −0.204320
\(805\) −1.30350e18 −0.168826
\(806\) 1.18113e18 0.151747
\(807\) −1.17700e18 −0.150002
\(808\) −1.22326e18 −0.154648
\(809\) 1.42718e18 0.178984 0.0894918 0.995988i \(-0.471476\pi\)
0.0894918 + 0.995988i \(0.471476\pi\)
\(810\) −2.47707e16 −0.00308167
\(811\) −6.88423e18 −0.849610 −0.424805 0.905285i \(-0.639657\pi\)
−0.424805 + 0.905285i \(0.639657\pi\)
\(812\) −2.00731e18 −0.245754
\(813\) 9.18928e18 1.11607
\(814\) 3.78454e17 0.0455989
\(815\) −3.77656e18 −0.451411
\(816\) −7.84278e17 −0.0930003
\(817\) 1.98689e17 0.0233739
\(818\) 2.86205e17 0.0334027
\(819\) −2.80782e18 −0.325106
\(820\) 1.17352e18 0.134803
\(821\) −3.82786e18 −0.436240 −0.218120 0.975922i \(-0.569992\pi\)
−0.218120 + 0.975922i \(0.569992\pi\)
\(822\) −9.22267e16 −0.0104277
\(823\) −4.05729e18 −0.455132 −0.227566 0.973763i \(-0.573077\pi\)
−0.227566 + 0.973763i \(0.573077\pi\)
\(824\) 1.42173e18 0.158230
\(825\) 6.92062e18 0.764178
\(826\) −5.33053e16 −0.00583983
\(827\) 3.43912e18 0.373819 0.186909 0.982377i \(-0.440153\pi\)
0.186909 + 0.982377i \(0.440153\pi\)
\(828\) −2.51906e18 −0.271670
\(829\) −1.20942e19 −1.29411 −0.647055 0.762443i \(-0.724000\pi\)
−0.647055 + 0.762443i \(0.724000\pi\)
\(830\) 1.03838e17 0.0110242
\(831\) −2.70638e18 −0.285090
\(832\) −1.55873e19 −1.62918
\(833\) 1.05510e18 0.109421
\(834\) 4.08611e17 0.0420465
\(835\) 4.87337e18 0.497585
\(836\) −7.77126e18 −0.787319
\(837\) −2.21117e18 −0.222283
\(838\) −6.61783e17 −0.0660130
\(839\) −7.44376e18 −0.736783 −0.368391 0.929671i \(-0.620091\pi\)
−0.368391 + 0.929671i \(0.620091\pi\)
\(840\) −1.87594e17 −0.0184249
\(841\) −8.37699e18 −0.816421
\(842\) 1.21366e17 0.0117373
\(843\) 8.91640e18 0.855678
\(844\) −7.60531e18 −0.724254
\(845\) 7.00988e18 0.662433
\(846\) −1.55418e16 −0.00145745
\(847\) −8.06321e18 −0.750353
\(848\) 9.59602e18 0.886172
\(849\) 2.12275e18 0.194536
\(850\) −1.22367e17 −0.0111286
\(851\) 3.51392e18 0.317139
\(852\) −1.85306e18 −0.165971
\(853\) −2.12204e19 −1.88619 −0.943093 0.332529i \(-0.892098\pi\)
−0.943093 + 0.332529i \(0.892098\pi\)
\(854\) −5.37250e17 −0.0473915
\(855\) −7.09531e17 −0.0621143
\(856\) −7.44040e17 −0.0646423
\(857\) 1.88453e18 0.162490 0.0812452 0.996694i \(-0.474110\pi\)
0.0812452 + 0.996694i \(0.474110\pi\)
\(858\) 1.34440e18 0.115044
\(859\) 7.91055e18 0.671817 0.335909 0.941895i \(-0.390957\pi\)
0.335909 + 0.941895i \(0.390957\pi\)
\(860\) 1.88309e17 0.0158720
\(861\) 1.51388e18 0.126640
\(862\) 8.70543e17 0.0722758
\(863\) 3.54292e18 0.291938 0.145969 0.989289i \(-0.453370\pi\)
0.145969 + 0.989289i \(0.453370\pi\)
\(864\) −5.44348e17 −0.0445182
\(865\) 4.00529e18 0.325109
\(866\) 2.11133e17 0.0170094
\(867\) −7.02612e18 −0.561813
\(868\) −8.34748e18 −0.662487
\(869\) −2.38408e19 −1.87799
\(870\) 8.77516e16 0.00686088
\(871\) 7.75437e18 0.601768
\(872\) 5.28852e17 0.0407359
\(873\) 7.78816e18 0.595446
\(874\) 4.38647e17 0.0332882
\(875\) 5.11874e18 0.385576
\(876\) 4.33587e18 0.324190
\(877\) −1.44911e19 −1.07548 −0.537741 0.843110i \(-0.680722\pi\)
−0.537741 + 0.843110i \(0.680722\pi\)
\(878\) −8.79616e17 −0.0648006
\(879\) 7.99212e18 0.584432
\(880\) −7.32022e18 −0.531357
\(881\) −4.15928e18 −0.299692 −0.149846 0.988709i \(-0.547878\pi\)
−0.149846 + 0.988709i \(0.547878\pi\)
\(882\) 2.41634e17 0.0172827
\(883\) 7.17085e18 0.509127 0.254564 0.967056i \(-0.418068\pi\)
0.254564 + 0.967056i \(0.418068\pi\)
\(884\) 3.91026e18 0.275592
\(885\) −3.83325e17 −0.0268186
\(886\) 1.87818e18 0.130442
\(887\) −6.89321e18 −0.475246 −0.237623 0.971357i \(-0.576368\pi\)
−0.237623 + 0.971357i \(0.576368\pi\)
\(888\) 5.05709e17 0.0346112
\(889\) −9.49137e18 −0.644863
\(890\) −3.21057e16 −0.00216545
\(891\) −2.51684e18 −0.168519
\(892\) −1.01354e19 −0.673704
\(893\) −4.45180e17 −0.0293765
\(894\) 7.33388e17 0.0480441
\(895\) 6.84487e18 0.445159
\(896\) −2.73717e18 −0.176726
\(897\) 1.24827e19 0.800127
\(898\) −1.96122e18 −0.124805
\(899\) 7.83319e18 0.494881
\(900\) 4.60983e18 0.289141
\(901\) −2.37756e18 −0.148054
\(902\) −7.24854e17 −0.0448134
\(903\) 2.42924e17 0.0149108
\(904\) 4.89539e17 0.0298327
\(905\) −2.41882e18 −0.146349
\(906\) 3.47814e16 0.00208936
\(907\) 2.30526e19 1.37490 0.687452 0.726230i \(-0.258729\pi\)
0.687452 + 0.726230i \(0.258729\pi\)
\(908\) −2.60932e19 −1.54515
\(909\) −5.65676e18 −0.332585
\(910\) 4.63386e17 0.0270504
\(911\) 1.67243e18 0.0969344 0.0484672 0.998825i \(-0.484566\pi\)
0.0484672 + 0.998825i \(0.484566\pi\)
\(912\) −5.14479e18 −0.296075
\(913\) 1.05505e19 0.602854
\(914\) −5.76129e17 −0.0326866
\(915\) −3.86343e18 −0.217639
\(916\) −3.07427e19 −1.71958
\(917\) −4.91142e18 −0.272776
\(918\) 4.45015e16 0.00245413
\(919\) −1.51946e18 −0.0832027 −0.0416013 0.999134i \(-0.513246\pi\)
−0.0416013 + 0.999134i \(0.513246\pi\)
\(920\) 8.33988e17 0.0453460
\(921\) 1.27792e19 0.689945
\(922\) 1.40955e18 0.0755664
\(923\) 9.18251e18 0.488821
\(924\) −9.50142e18 −0.502251
\(925\) −6.43042e18 −0.337534
\(926\) 6.00948e17 0.0313232
\(927\) 6.57454e18 0.340288
\(928\) 1.92838e18 0.0991131
\(929\) 2.11638e19 1.08017 0.540084 0.841611i \(-0.318392\pi\)
0.540084 + 0.841611i \(0.318392\pi\)
\(930\) 3.64918e17 0.0184951
\(931\) 6.92135e18 0.348351
\(932\) −2.02608e19 −1.01264
\(933\) 1.49614e19 0.742579
\(934\) −6.83860e17 −0.0337064
\(935\) 1.81370e18 0.0887746
\(936\) 1.79646e18 0.0873223
\(937\) −1.20261e19 −0.580519 −0.290259 0.956948i \(-0.593742\pi\)
−0.290259 + 0.956948i \(0.593742\pi\)
\(938\) 3.33157e17 0.0159709
\(939\) −1.22201e19 −0.581768
\(940\) −4.21922e17 −0.0199481
\(941\) −3.92961e19 −1.84509 −0.922544 0.385893i \(-0.873894\pi\)
−0.922544 + 0.385893i \(0.873894\pi\)
\(942\) 1.22037e17 0.00569064
\(943\) −6.73023e18 −0.311677
\(944\) −2.77948e18 −0.127834
\(945\) −8.67498e17 −0.0396243
\(946\) −1.16314e17 −0.00527642
\(947\) −1.46194e19 −0.658648 −0.329324 0.944217i \(-0.606821\pi\)
−0.329324 + 0.944217i \(0.606821\pi\)
\(948\) −1.58804e19 −0.710570
\(949\) −2.14856e19 −0.954811
\(950\) −8.02716e17 −0.0354290
\(951\) 1.41836e18 0.0621745
\(952\) 3.37020e17 0.0146729
\(953\) 1.43682e19 0.621298 0.310649 0.950525i \(-0.399454\pi\)
0.310649 + 0.950525i \(0.399454\pi\)
\(954\) −5.44497e17 −0.0233847
\(955\) 5.59633e18 0.238716
\(956\) −2.90204e19 −1.22950
\(957\) 8.91603e18 0.375184
\(958\) 1.88603e18 0.0788267
\(959\) −3.22988e18 −0.134080
\(960\) −4.81581e18 −0.198567
\(961\) 8.15710e18 0.334067
\(962\) −1.24918e18 −0.0508143
\(963\) −3.44068e18 −0.139019
\(964\) −1.01275e18 −0.0406443
\(965\) 7.05739e18 0.281330
\(966\) 5.36305e17 0.0212354
\(967\) −4.32204e19 −1.69987 −0.849936 0.526886i \(-0.823360\pi\)
−0.849936 + 0.526886i \(0.823360\pi\)
\(968\) 5.15889e18 0.201542
\(969\) 1.27470e18 0.0494656
\(970\) −1.28531e18 −0.0495441
\(971\) 3.91080e19 1.49741 0.748705 0.662903i \(-0.230676\pi\)
0.748705 + 0.662903i \(0.230676\pi\)
\(972\) −1.67647e18 −0.0637624
\(973\) 1.43100e19 0.540637
\(974\) −2.06311e18 −0.0774263
\(975\) −2.28432e19 −0.851583
\(976\) −2.80136e19 −1.03740
\(977\) −5.18308e18 −0.190666 −0.0953329 0.995445i \(-0.530392\pi\)
−0.0953329 + 0.995445i \(0.530392\pi\)
\(978\) 1.55381e18 0.0567799
\(979\) −3.26211e18 −0.118416
\(980\) 6.55975e18 0.236547
\(981\) 2.44559e18 0.0876061
\(982\) −1.65829e18 −0.0590113
\(983\) 4.57127e19 1.61599 0.807996 0.589188i \(-0.200552\pi\)
0.807996 + 0.589188i \(0.200552\pi\)
\(984\) −9.68587e17 −0.0340150
\(985\) −1.29809e18 −0.0452867
\(986\) −1.57649e17 −0.00546375
\(987\) −5.44292e17 −0.0187400
\(988\) 2.56509e19 0.877371
\(989\) −1.07997e18 −0.0366974
\(990\) 4.15364e17 0.0140217
\(991\) −2.18298e19 −0.732100 −0.366050 0.930595i \(-0.619290\pi\)
−0.366050 + 0.930595i \(0.619290\pi\)
\(992\) 8.01925e18 0.267182
\(993\) 2.52491e19 0.835750
\(994\) 3.94514e17 0.0129733
\(995\) 8.03057e17 0.0262359
\(996\) 7.02769e18 0.228101
\(997\) 5.24614e19 1.69169 0.845846 0.533427i \(-0.179096\pi\)
0.845846 + 0.533427i \(0.179096\pi\)
\(998\) −2.07892e18 −0.0666022
\(999\) 2.33856e18 0.0744344
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.1.14 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.14 31 1.1 even 1 trivial