Properties

Label 177.14.a.c.1.16
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 1.16
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+15.7636 q^{2} +729.000 q^{3} -7943.51 q^{4} -18232.0 q^{5} +11491.7 q^{6} -139545. q^{7} -254354. q^{8} +531441. q^{9} +O(q^{10})\) \(q+15.7636 q^{2} +729.000 q^{3} -7943.51 q^{4} -18232.0 q^{5} +11491.7 q^{6} -139545. q^{7} -254354. q^{8} +531441. q^{9} -287402. q^{10} +3.23072e6 q^{11} -5.79082e6 q^{12} -2.38685e7 q^{13} -2.19974e6 q^{14} -1.32911e7 q^{15} +6.10637e7 q^{16} -1.01242e8 q^{17} +8.37742e6 q^{18} -2.58492e8 q^{19} +1.44826e8 q^{20} -1.01729e8 q^{21} +5.09278e7 q^{22} +4.75562e8 q^{23} -1.85424e8 q^{24} -8.88297e8 q^{25} -3.76253e8 q^{26} +3.87420e8 q^{27} +1.10848e9 q^{28} -4.16682e9 q^{29} -2.09516e8 q^{30} +3.82269e9 q^{31} +3.04625e9 q^{32} +2.35519e9 q^{33} -1.59594e9 q^{34} +2.54420e9 q^{35} -4.22151e9 q^{36} -2.63978e9 q^{37} -4.07477e9 q^{38} -1.74001e10 q^{39} +4.63738e9 q^{40} -1.28469e10 q^{41} -1.60361e9 q^{42} -9.65991e9 q^{43} -2.56633e10 q^{44} -9.68924e9 q^{45} +7.49657e9 q^{46} -8.50024e9 q^{47} +4.45154e10 q^{48} -7.74161e10 q^{49} -1.40027e10 q^{50} -7.38057e10 q^{51} +1.89599e11 q^{52} -2.27914e11 q^{53} +6.10714e9 q^{54} -5.89025e10 q^{55} +3.54939e10 q^{56} -1.88441e11 q^{57} -6.56840e10 q^{58} -4.21805e10 q^{59} +1.05578e11 q^{60} -2.60650e11 q^{61} +6.02594e10 q^{62} -7.41602e10 q^{63} -4.52214e11 q^{64} +4.35170e11 q^{65} +3.71263e10 q^{66} +5.68861e11 q^{67} +8.04220e11 q^{68} +3.46685e11 q^{69} +4.01057e10 q^{70} -7.25827e11 q^{71} -1.35174e11 q^{72} +8.77552e11 q^{73} -4.16124e10 q^{74} -6.47568e11 q^{75} +2.05334e12 q^{76} -4.50832e11 q^{77} -2.74288e11 q^{78} -1.57064e12 q^{79} -1.11331e12 q^{80} +2.82430e11 q^{81} -2.02513e11 q^{82} -2.61026e12 q^{83} +8.08083e11 q^{84} +1.84585e12 q^{85} -1.52275e11 q^{86} -3.03761e12 q^{87} -8.21745e11 q^{88} -8.27525e11 q^{89} -1.52737e11 q^{90} +3.33074e12 q^{91} -3.77763e12 q^{92} +2.78674e12 q^{93} -1.33994e11 q^{94} +4.71284e12 q^{95} +2.22071e12 q^{96} +1.71471e12 q^{97} -1.22036e12 q^{98} +1.71694e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 15.7636 0.174165 0.0870824 0.996201i \(-0.472246\pi\)
0.0870824 + 0.996201i \(0.472246\pi\)
\(3\) 729.000 0.577350
\(4\) −7943.51 −0.969667
\(5\) −18232.0 −0.521831 −0.260915 0.965362i \(-0.584024\pi\)
−0.260915 + 0.965362i \(0.584024\pi\)
\(6\) 11491.7 0.100554
\(7\) −139545. −0.448310 −0.224155 0.974553i \(-0.571962\pi\)
−0.224155 + 0.974553i \(0.571962\pi\)
\(8\) −254354. −0.343046
\(9\) 531441. 0.333333
\(10\) −287402. −0.0908845
\(11\) 3.23072e6 0.549853 0.274927 0.961465i \(-0.411346\pi\)
0.274927 + 0.961465i \(0.411346\pi\)
\(12\) −5.79082e6 −0.559837
\(13\) −2.38685e7 −1.37149 −0.685745 0.727842i \(-0.740524\pi\)
−0.685745 + 0.727842i \(0.740524\pi\)
\(14\) −2.19974e6 −0.0780798
\(15\) −1.32911e7 −0.301279
\(16\) 6.10637e7 0.909920
\(17\) −1.01242e8 −1.01729 −0.508644 0.860977i \(-0.669853\pi\)
−0.508644 + 0.860977i \(0.669853\pi\)
\(18\) 8.37742e6 0.0580549
\(19\) −2.58492e8 −1.26052 −0.630260 0.776384i \(-0.717052\pi\)
−0.630260 + 0.776384i \(0.717052\pi\)
\(20\) 1.44826e8 0.506002
\(21\) −1.01729e8 −0.258832
\(22\) 5.09278e7 0.0957651
\(23\) 4.75562e8 0.669848 0.334924 0.942245i \(-0.391289\pi\)
0.334924 + 0.942245i \(0.391289\pi\)
\(24\) −1.85424e8 −0.198058
\(25\) −8.88297e8 −0.727693
\(26\) −3.76253e8 −0.238865
\(27\) 3.87420e8 0.192450
\(28\) 1.10848e9 0.434711
\(29\) −4.16682e9 −1.30082 −0.650411 0.759583i \(-0.725403\pi\)
−0.650411 + 0.759583i \(0.725403\pi\)
\(30\) −2.09516e8 −0.0524722
\(31\) 3.82269e9 0.773603 0.386802 0.922163i \(-0.373580\pi\)
0.386802 + 0.922163i \(0.373580\pi\)
\(32\) 3.04625e9 0.501522
\(33\) 2.35519e9 0.317458
\(34\) −1.59594e9 −0.177176
\(35\) 2.54420e9 0.233942
\(36\) −4.22151e9 −0.323222
\(37\) −2.63978e9 −0.169144 −0.0845720 0.996417i \(-0.526952\pi\)
−0.0845720 + 0.996417i \(0.526952\pi\)
\(38\) −4.07477e9 −0.219538
\(39\) −1.74001e10 −0.791830
\(40\) 4.63738e9 0.179012
\(41\) −1.28469e10 −0.422380 −0.211190 0.977445i \(-0.567734\pi\)
−0.211190 + 0.977445i \(0.567734\pi\)
\(42\) −1.60361e9 −0.0450794
\(43\) −9.65991e9 −0.233039 −0.116519 0.993188i \(-0.537174\pi\)
−0.116519 + 0.993188i \(0.537174\pi\)
\(44\) −2.56633e10 −0.533174
\(45\) −9.68924e9 −0.173944
\(46\) 7.49657e9 0.116664
\(47\) −8.50024e9 −0.115026 −0.0575129 0.998345i \(-0.518317\pi\)
−0.0575129 + 0.998345i \(0.518317\pi\)
\(48\) 4.45154e10 0.525343
\(49\) −7.74161e10 −0.799018
\(50\) −1.40027e10 −0.126738
\(51\) −7.38057e10 −0.587332
\(52\) 1.89599e11 1.32989
\(53\) −2.27914e11 −1.41246 −0.706232 0.707980i \(-0.749606\pi\)
−0.706232 + 0.707980i \(0.749606\pi\)
\(54\) 6.10714e9 0.0335180
\(55\) −5.89025e10 −0.286930
\(56\) 3.54939e10 0.153791
\(57\) −1.88441e11 −0.727761
\(58\) −6.56840e10 −0.226557
\(59\) −4.21805e10 −0.130189
\(60\) 1.05578e11 0.292140
\(61\) −2.60650e11 −0.647759 −0.323879 0.946098i \(-0.604987\pi\)
−0.323879 + 0.946098i \(0.604987\pi\)
\(62\) 6.02594e10 0.134734
\(63\) −7.41602e10 −0.149437
\(64\) −4.52214e11 −0.822573
\(65\) 4.35170e11 0.715686
\(66\) 3.71263e10 0.0552900
\(67\) 5.68861e11 0.768281 0.384141 0.923275i \(-0.374498\pi\)
0.384141 + 0.923275i \(0.374498\pi\)
\(68\) 8.04220e11 0.986431
\(69\) 3.46685e11 0.386737
\(70\) 4.01057e10 0.0407445
\(71\) −7.25827e11 −0.672440 −0.336220 0.941783i \(-0.609149\pi\)
−0.336220 + 0.941783i \(0.609149\pi\)
\(72\) −1.35174e11 −0.114349
\(73\) 8.77552e11 0.678694 0.339347 0.940661i \(-0.389794\pi\)
0.339347 + 0.940661i \(0.389794\pi\)
\(74\) −4.16124e10 −0.0294589
\(75\) −6.47568e11 −0.420134
\(76\) 2.05334e12 1.22228
\(77\) −4.50832e11 −0.246505
\(78\) −2.74288e11 −0.137909
\(79\) −1.57064e12 −0.726944 −0.363472 0.931605i \(-0.618409\pi\)
−0.363472 + 0.931605i \(0.618409\pi\)
\(80\) −1.11331e12 −0.474824
\(81\) 2.82430e11 0.111111
\(82\) −2.02513e11 −0.0735636
\(83\) −2.61026e12 −0.876346 −0.438173 0.898891i \(-0.644374\pi\)
−0.438173 + 0.898891i \(0.644374\pi\)
\(84\) 8.08083e11 0.250981
\(85\) 1.84585e12 0.530853
\(86\) −1.52275e11 −0.0405871
\(87\) −3.03761e12 −0.751030
\(88\) −8.21745e11 −0.188625
\(89\) −8.27525e11 −0.176501 −0.0882503 0.996098i \(-0.528128\pi\)
−0.0882503 + 0.996098i \(0.528128\pi\)
\(90\) −1.52737e11 −0.0302948
\(91\) 3.33074e12 0.614853
\(92\) −3.77763e12 −0.649529
\(93\) 2.78674e12 0.446640
\(94\) −1.33994e11 −0.0200334
\(95\) 4.71284e12 0.657778
\(96\) 2.22071e12 0.289554
\(97\) 1.71471e12 0.209014 0.104507 0.994524i \(-0.466674\pi\)
0.104507 + 0.994524i \(0.466674\pi\)
\(98\) −1.22036e12 −0.139161
\(99\) 1.71694e12 0.183284
\(100\) 7.05619e12 0.705619
\(101\) 1.17495e13 1.10136 0.550681 0.834716i \(-0.314368\pi\)
0.550681 + 0.834716i \(0.314368\pi\)
\(102\) −1.16344e12 −0.102293
\(103\) 6.37459e12 0.526030 0.263015 0.964792i \(-0.415283\pi\)
0.263015 + 0.964792i \(0.415283\pi\)
\(104\) 6.07103e12 0.470485
\(105\) 1.85472e12 0.135066
\(106\) −3.59274e12 −0.246001
\(107\) 1.04542e13 0.673434 0.336717 0.941606i \(-0.390683\pi\)
0.336717 + 0.941606i \(0.390683\pi\)
\(108\) −3.07748e12 −0.186612
\(109\) 2.75248e13 1.57200 0.785999 0.618228i \(-0.212149\pi\)
0.785999 + 0.618228i \(0.212149\pi\)
\(110\) −9.28516e11 −0.0499732
\(111\) −1.92440e12 −0.0976553
\(112\) −8.52116e12 −0.407926
\(113\) 2.37831e13 1.07463 0.537316 0.843381i \(-0.319438\pi\)
0.537316 + 0.843381i \(0.319438\pi\)
\(114\) −2.97051e12 −0.126750
\(115\) −8.67046e12 −0.349547
\(116\) 3.30992e13 1.26136
\(117\) −1.26847e13 −0.457163
\(118\) −6.64917e11 −0.0226743
\(119\) 1.41279e13 0.456061
\(120\) 3.38065e12 0.103353
\(121\) −2.40852e13 −0.697661
\(122\) −4.10878e12 −0.112817
\(123\) −9.36538e12 −0.243861
\(124\) −3.03656e13 −0.750137
\(125\) 3.84513e13 0.901563
\(126\) −1.16903e12 −0.0260266
\(127\) −4.11078e13 −0.869360 −0.434680 0.900585i \(-0.643139\pi\)
−0.434680 + 0.900585i \(0.643139\pi\)
\(128\) −3.20834e13 −0.644786
\(129\) −7.04207e12 −0.134545
\(130\) 6.85985e12 0.124647
\(131\) 1.23740e13 0.213918 0.106959 0.994263i \(-0.465889\pi\)
0.106959 + 0.994263i \(0.465889\pi\)
\(132\) −1.87085e13 −0.307828
\(133\) 3.60715e13 0.565104
\(134\) 8.96730e12 0.133808
\(135\) −7.06346e12 −0.100426
\(136\) 2.57514e13 0.348977
\(137\) −3.40714e13 −0.440257 −0.220129 0.975471i \(-0.570648\pi\)
−0.220129 + 0.975471i \(0.570648\pi\)
\(138\) 5.46500e12 0.0673560
\(139\) 1.13870e14 1.33910 0.669548 0.742768i \(-0.266488\pi\)
0.669548 + 0.742768i \(0.266488\pi\)
\(140\) −2.02098e13 −0.226846
\(141\) −6.19668e12 −0.0664102
\(142\) −1.14416e13 −0.117115
\(143\) −7.71123e13 −0.754119
\(144\) 3.24518e13 0.303307
\(145\) 7.59695e13 0.678809
\(146\) 1.38334e13 0.118205
\(147\) −5.64363e13 −0.461313
\(148\) 2.09691e13 0.164013
\(149\) −1.47280e14 −1.10264 −0.551319 0.834295i \(-0.685875\pi\)
−0.551319 + 0.834295i \(0.685875\pi\)
\(150\) −1.02080e13 −0.0731724
\(151\) 4.88280e13 0.335211 0.167606 0.985854i \(-0.446396\pi\)
0.167606 + 0.985854i \(0.446396\pi\)
\(152\) 6.57485e13 0.432417
\(153\) −5.38043e13 −0.339096
\(154\) −7.10674e12 −0.0429324
\(155\) −6.96954e13 −0.403690
\(156\) 1.38218e14 0.767812
\(157\) −3.25508e12 −0.0173466 −0.00867329 0.999962i \(-0.502761\pi\)
−0.00867329 + 0.999962i \(0.502761\pi\)
\(158\) −2.47589e13 −0.126608
\(159\) −1.66149e14 −0.815487
\(160\) −5.55393e13 −0.261710
\(161\) −6.63626e13 −0.300300
\(162\) 4.45210e12 0.0193516
\(163\) −6.74761e13 −0.281793 −0.140897 0.990024i \(-0.544999\pi\)
−0.140897 + 0.990024i \(0.544999\pi\)
\(164\) 1.02049e14 0.409567
\(165\) −4.29400e13 −0.165659
\(166\) −4.11470e13 −0.152629
\(167\) −3.07390e14 −1.09656 −0.548280 0.836295i \(-0.684717\pi\)
−0.548280 + 0.836295i \(0.684717\pi\)
\(168\) 2.58751e13 0.0887914
\(169\) 2.66829e14 0.880986
\(170\) 2.90973e13 0.0924558
\(171\) −1.37373e14 −0.420173
\(172\) 7.67335e13 0.225970
\(173\) 3.08654e14 0.875331 0.437666 0.899138i \(-0.355805\pi\)
0.437666 + 0.899138i \(0.355805\pi\)
\(174\) −4.78837e13 −0.130803
\(175\) 1.23958e14 0.326232
\(176\) 1.97280e14 0.500323
\(177\) −3.07496e13 −0.0751646
\(178\) −1.30448e13 −0.0307402
\(179\) −3.28530e14 −0.746501 −0.373251 0.927731i \(-0.621757\pi\)
−0.373251 + 0.927731i \(0.621757\pi\)
\(180\) 7.69666e13 0.168667
\(181\) 5.32127e14 1.12488 0.562438 0.826840i \(-0.309864\pi\)
0.562438 + 0.826840i \(0.309864\pi\)
\(182\) 5.25044e13 0.107086
\(183\) −1.90014e14 −0.373984
\(184\) −1.20961e14 −0.229789
\(185\) 4.81285e13 0.0882645
\(186\) 4.39291e13 0.0777890
\(187\) −3.27086e14 −0.559360
\(188\) 6.75218e13 0.111537
\(189\) −5.40628e13 −0.0862773
\(190\) 7.42913e13 0.114562
\(191\) 2.94971e14 0.439605 0.219802 0.975544i \(-0.429459\pi\)
0.219802 + 0.975544i \(0.429459\pi\)
\(192\) −3.29664e14 −0.474912
\(193\) 1.06851e15 1.48818 0.744089 0.668081i \(-0.232884\pi\)
0.744089 + 0.668081i \(0.232884\pi\)
\(194\) 2.70300e13 0.0364028
\(195\) 3.17239e14 0.413202
\(196\) 6.14955e14 0.774781
\(197\) 7.01474e14 0.855030 0.427515 0.904008i \(-0.359389\pi\)
0.427515 + 0.904008i \(0.359389\pi\)
\(198\) 2.70651e13 0.0319217
\(199\) −2.11109e14 −0.240969 −0.120485 0.992715i \(-0.538445\pi\)
−0.120485 + 0.992715i \(0.538445\pi\)
\(200\) 2.25941e14 0.249632
\(201\) 4.14700e14 0.443567
\(202\) 1.85214e14 0.191818
\(203\) 5.81461e14 0.583171
\(204\) 5.86276e14 0.569516
\(205\) 2.34225e14 0.220411
\(206\) 1.00487e14 0.0916159
\(207\) 2.52733e14 0.223283
\(208\) −1.45750e15 −1.24795
\(209\) −8.35117e14 −0.693101
\(210\) 2.92370e13 0.0235238
\(211\) 1.62145e15 1.26493 0.632466 0.774588i \(-0.282043\pi\)
0.632466 + 0.774588i \(0.282043\pi\)
\(212\) 1.81044e15 1.36962
\(213\) −5.29128e14 −0.388234
\(214\) 1.64795e14 0.117288
\(215\) 1.76120e14 0.121607
\(216\) −9.85418e13 −0.0660193
\(217\) −5.33439e14 −0.346814
\(218\) 4.33890e14 0.273787
\(219\) 6.39735e14 0.391844
\(220\) 4.67893e14 0.278227
\(221\) 2.41650e15 1.39520
\(222\) −3.03354e13 −0.0170081
\(223\) −1.10451e15 −0.601434 −0.300717 0.953713i \(-0.597226\pi\)
−0.300717 + 0.953713i \(0.597226\pi\)
\(224\) −4.25090e14 −0.224838
\(225\) −4.72077e14 −0.242564
\(226\) 3.74908e14 0.187163
\(227\) −2.06780e15 −1.00309 −0.501546 0.865131i \(-0.667235\pi\)
−0.501546 + 0.865131i \(0.667235\pi\)
\(228\) 1.49688e15 0.705686
\(229\) −4.51272e14 −0.206779 −0.103390 0.994641i \(-0.532969\pi\)
−0.103390 + 0.994641i \(0.532969\pi\)
\(230\) −1.36678e14 −0.0608788
\(231\) −3.28657e14 −0.142320
\(232\) 1.05985e15 0.446242
\(233\) −1.49728e15 −0.613043 −0.306521 0.951864i \(-0.599165\pi\)
−0.306521 + 0.951864i \(0.599165\pi\)
\(234\) −1.99956e14 −0.0796218
\(235\) 1.54977e14 0.0600240
\(236\) 3.35061e14 0.126240
\(237\) −1.14500e15 −0.419701
\(238\) 2.22707e14 0.0794297
\(239\) 3.83611e15 1.33139 0.665694 0.746224i \(-0.268135\pi\)
0.665694 + 0.746224i \(0.268135\pi\)
\(240\) −8.11606e14 −0.274140
\(241\) 4.70369e15 1.54642 0.773211 0.634149i \(-0.218649\pi\)
0.773211 + 0.634149i \(0.218649\pi\)
\(242\) −3.79669e14 −0.121508
\(243\) 2.05891e14 0.0641500
\(244\) 2.07047e15 0.628110
\(245\) 1.41145e15 0.416952
\(246\) −1.47632e14 −0.0424720
\(247\) 6.16982e15 1.72879
\(248\) −9.72316e14 −0.265382
\(249\) −1.90288e15 −0.505959
\(250\) 6.06131e14 0.157021
\(251\) 4.10602e14 0.103643 0.0518217 0.998656i \(-0.483497\pi\)
0.0518217 + 0.998656i \(0.483497\pi\)
\(252\) 5.89092e14 0.144904
\(253\) 1.53641e15 0.368318
\(254\) −6.48006e14 −0.151412
\(255\) 1.34563e15 0.306488
\(256\) 3.19879e15 0.710274
\(257\) −4.75664e14 −0.102976 −0.0514879 0.998674i \(-0.516396\pi\)
−0.0514879 + 0.998674i \(0.516396\pi\)
\(258\) −1.11008e14 −0.0234330
\(259\) 3.68369e14 0.0758289
\(260\) −3.45678e15 −0.693977
\(261\) −2.21442e15 −0.433607
\(262\) 1.95059e14 0.0372570
\(263\) 1.53185e15 0.285434 0.142717 0.989764i \(-0.454416\pi\)
0.142717 + 0.989764i \(0.454416\pi\)
\(264\) −5.99052e14 −0.108903
\(265\) 4.15533e15 0.737067
\(266\) 5.68616e14 0.0984211
\(267\) −6.03266e14 −0.101903
\(268\) −4.51876e15 −0.744977
\(269\) 1.68579e15 0.271278 0.135639 0.990758i \(-0.456691\pi\)
0.135639 + 0.990758i \(0.456691\pi\)
\(270\) −1.11345e14 −0.0174907
\(271\) 6.76700e15 1.03776 0.518879 0.854848i \(-0.326350\pi\)
0.518879 + 0.854848i \(0.326350\pi\)
\(272\) −6.18223e15 −0.925652
\(273\) 2.42811e15 0.354986
\(274\) −5.37088e14 −0.0766773
\(275\) −2.86984e15 −0.400124
\(276\) −2.75389e15 −0.375006
\(277\) 3.37402e15 0.448776 0.224388 0.974500i \(-0.427962\pi\)
0.224388 + 0.974500i \(0.427962\pi\)
\(278\) 1.79500e15 0.233223
\(279\) 2.03154e15 0.257868
\(280\) −6.47125e14 −0.0802530
\(281\) 3.77808e15 0.457804 0.228902 0.973449i \(-0.426486\pi\)
0.228902 + 0.973449i \(0.426486\pi\)
\(282\) −9.76819e13 −0.0115663
\(283\) 5.13345e15 0.594015 0.297008 0.954875i \(-0.404011\pi\)
0.297008 + 0.954875i \(0.404011\pi\)
\(284\) 5.76561e15 0.652043
\(285\) 3.43566e15 0.379768
\(286\) −1.21557e15 −0.131341
\(287\) 1.79273e15 0.189357
\(288\) 1.61890e15 0.167174
\(289\) 3.45440e14 0.0348768
\(290\) 1.19755e15 0.118225
\(291\) 1.25003e15 0.120674
\(292\) −6.97084e15 −0.658107
\(293\) 2.49166e15 0.230065 0.115032 0.993362i \(-0.463303\pi\)
0.115032 + 0.993362i \(0.463303\pi\)
\(294\) −8.89639e14 −0.0803445
\(295\) 7.69036e14 0.0679366
\(296\) 6.71437e14 0.0580242
\(297\) 1.25165e15 0.105819
\(298\) −2.32166e15 −0.192041
\(299\) −1.13509e16 −0.918690
\(300\) 5.14396e15 0.407389
\(301\) 1.34800e15 0.104474
\(302\) 7.69704e14 0.0583820
\(303\) 8.56537e15 0.635871
\(304\) −1.57845e16 −1.14697
\(305\) 4.75217e15 0.338021
\(306\) −8.48150e14 −0.0590586
\(307\) −1.26502e16 −0.862377 −0.431188 0.902262i \(-0.641906\pi\)
−0.431188 + 0.902262i \(0.641906\pi\)
\(308\) 3.58119e15 0.239027
\(309\) 4.64708e15 0.303704
\(310\) −1.09865e15 −0.0703086
\(311\) −9.93149e15 −0.622403 −0.311202 0.950344i \(-0.600731\pi\)
−0.311202 + 0.950344i \(0.600731\pi\)
\(312\) 4.42578e15 0.271635
\(313\) −2.22102e16 −1.33510 −0.667550 0.744565i \(-0.732657\pi\)
−0.667550 + 0.744565i \(0.732657\pi\)
\(314\) −5.13118e13 −0.00302116
\(315\) 1.35209e15 0.0779807
\(316\) 1.24764e16 0.704893
\(317\) 1.61054e16 0.891429 0.445715 0.895175i \(-0.352950\pi\)
0.445715 + 0.895175i \(0.352950\pi\)
\(318\) −2.61911e15 −0.142029
\(319\) −1.34618e16 −0.715261
\(320\) 8.24477e15 0.429244
\(321\) 7.62109e15 0.388807
\(322\) −1.04611e15 −0.0523016
\(323\) 2.61704e16 1.28231
\(324\) −2.24348e15 −0.107741
\(325\) 2.12023e16 0.998023
\(326\) −1.06367e15 −0.0490784
\(327\) 2.00656e16 0.907593
\(328\) 3.26765e15 0.144896
\(329\) 1.18617e15 0.0515672
\(330\) −6.76888e14 −0.0288520
\(331\) 1.38595e16 0.579251 0.289625 0.957140i \(-0.406469\pi\)
0.289625 + 0.957140i \(0.406469\pi\)
\(332\) 2.07346e16 0.849764
\(333\) −1.40289e15 −0.0563813
\(334\) −4.84557e15 −0.190982
\(335\) −1.03715e16 −0.400913
\(336\) −6.21193e15 −0.235516
\(337\) 3.12002e16 1.16028 0.580141 0.814516i \(-0.302997\pi\)
0.580141 + 0.814516i \(0.302997\pi\)
\(338\) 4.20618e15 0.153437
\(339\) 1.73379e16 0.620439
\(340\) −1.46625e16 −0.514750
\(341\) 1.23500e16 0.425368
\(342\) −2.16550e15 −0.0731793
\(343\) 2.43235e16 0.806518
\(344\) 2.45703e15 0.0799431
\(345\) −6.32076e15 −0.201811
\(346\) 4.86550e15 0.152452
\(347\) −6.10608e16 −1.87768 −0.938838 0.344359i \(-0.888096\pi\)
−0.938838 + 0.344359i \(0.888096\pi\)
\(348\) 2.41293e16 0.728248
\(349\) 1.98135e16 0.586943 0.293471 0.955968i \(-0.405189\pi\)
0.293471 + 0.955968i \(0.405189\pi\)
\(350\) 1.95402e15 0.0568181
\(351\) −9.24713e15 −0.263943
\(352\) 9.84157e15 0.275764
\(353\) 8.83504e15 0.243037 0.121519 0.992589i \(-0.461224\pi\)
0.121519 + 0.992589i \(0.461224\pi\)
\(354\) −4.84724e14 −0.0130910
\(355\) 1.32333e16 0.350900
\(356\) 6.57345e15 0.171147
\(357\) 1.02993e16 0.263307
\(358\) −5.17882e15 −0.130014
\(359\) −1.66153e16 −0.409632 −0.204816 0.978801i \(-0.565660\pi\)
−0.204816 + 0.978801i \(0.565660\pi\)
\(360\) 2.46449e15 0.0596707
\(361\) 2.47654e16 0.588909
\(362\) 8.38823e15 0.195914
\(363\) −1.75581e16 −0.402795
\(364\) −2.64577e16 −0.596202
\(365\) −1.59995e16 −0.354164
\(366\) −2.99530e15 −0.0651348
\(367\) −5.49392e16 −1.17369 −0.586844 0.809700i \(-0.699630\pi\)
−0.586844 + 0.809700i \(0.699630\pi\)
\(368\) 2.90396e16 0.609508
\(369\) −6.82736e15 −0.140793
\(370\) 7.58678e14 0.0153726
\(371\) 3.18043e16 0.633222
\(372\) −2.21365e16 −0.433092
\(373\) −8.97584e15 −0.172571 −0.0862855 0.996270i \(-0.527500\pi\)
−0.0862855 + 0.996270i \(0.527500\pi\)
\(374\) −5.15605e15 −0.0974207
\(375\) 2.80310e16 0.520518
\(376\) 2.16207e15 0.0394592
\(377\) 9.94556e16 1.78406
\(378\) −8.52224e14 −0.0150265
\(379\) −1.06818e16 −0.185135 −0.0925677 0.995706i \(-0.529507\pi\)
−0.0925677 + 0.995706i \(0.529507\pi\)
\(380\) −3.74365e16 −0.637825
\(381\) −2.99676e16 −0.501925
\(382\) 4.64980e15 0.0765637
\(383\) −1.62056e16 −0.262345 −0.131172 0.991360i \(-0.541874\pi\)
−0.131172 + 0.991360i \(0.541874\pi\)
\(384\) −2.33888e16 −0.372267
\(385\) 8.21958e15 0.128634
\(386\) 1.68435e16 0.259188
\(387\) −5.13367e15 −0.0776795
\(388\) −1.36208e16 −0.202674
\(389\) 2.24733e16 0.328848 0.164424 0.986390i \(-0.447423\pi\)
0.164424 + 0.986390i \(0.447423\pi\)
\(390\) 5.00083e15 0.0719651
\(391\) −4.81470e16 −0.681429
\(392\) 1.96911e16 0.274100
\(393\) 9.02066e15 0.123506
\(394\) 1.10578e16 0.148916
\(395\) 2.86359e16 0.379342
\(396\) −1.36385e16 −0.177725
\(397\) −7.11388e15 −0.0911944 −0.0455972 0.998960i \(-0.514519\pi\)
−0.0455972 + 0.998960i \(0.514519\pi\)
\(398\) −3.32784e15 −0.0419684
\(399\) 2.62961e16 0.326263
\(400\) −5.42427e16 −0.662142
\(401\) 4.23862e16 0.509080 0.254540 0.967062i \(-0.418076\pi\)
0.254540 + 0.967062i \(0.418076\pi\)
\(402\) 6.53716e15 0.0772538
\(403\) −9.12418e16 −1.06099
\(404\) −9.33321e16 −1.06795
\(405\) −5.14926e15 −0.0579812
\(406\) 9.16591e15 0.101568
\(407\) −8.52839e15 −0.0930044
\(408\) 1.87727e16 0.201482
\(409\) −1.56061e17 −1.64851 −0.824256 0.566218i \(-0.808406\pi\)
−0.824256 + 0.566218i \(0.808406\pi\)
\(410\) 3.69222e15 0.0383878
\(411\) −2.48381e16 −0.254183
\(412\) −5.06366e16 −0.510074
\(413\) 5.88610e15 0.0583650
\(414\) 3.98398e15 0.0388880
\(415\) 4.75903e16 0.457304
\(416\) −7.27093e16 −0.687833
\(417\) 8.30110e16 0.773128
\(418\) −1.31644e16 −0.120714
\(419\) −1.09388e17 −0.987590 −0.493795 0.869578i \(-0.664391\pi\)
−0.493795 + 0.869578i \(0.664391\pi\)
\(420\) −1.47330e16 −0.130969
\(421\) −9.24208e16 −0.808977 −0.404488 0.914543i \(-0.632550\pi\)
−0.404488 + 0.914543i \(0.632550\pi\)
\(422\) 2.55598e16 0.220306
\(423\) −4.51738e15 −0.0383419
\(424\) 5.79707e16 0.484541
\(425\) 8.99333e16 0.740274
\(426\) −8.34096e15 −0.0676166
\(427\) 3.63725e16 0.290397
\(428\) −8.30428e16 −0.653006
\(429\) −5.62149e16 −0.435391
\(430\) 2.77628e15 0.0211796
\(431\) 2.57918e16 0.193811 0.0969055 0.995294i \(-0.469106\pi\)
0.0969055 + 0.995294i \(0.469106\pi\)
\(432\) 2.36573e16 0.175114
\(433\) 2.50867e16 0.182924 0.0914622 0.995809i \(-0.470846\pi\)
0.0914622 + 0.995809i \(0.470846\pi\)
\(434\) −8.40892e15 −0.0604028
\(435\) 5.53818e16 0.391910
\(436\) −2.18644e17 −1.52431
\(437\) −1.22929e17 −0.844357
\(438\) 1.00845e16 0.0682455
\(439\) −2.02033e17 −1.34711 −0.673554 0.739138i \(-0.735233\pi\)
−0.673554 + 0.739138i \(0.735233\pi\)
\(440\) 1.49821e16 0.0984305
\(441\) −4.11421e16 −0.266339
\(442\) 3.80927e16 0.242995
\(443\) −3.97660e16 −0.249970 −0.124985 0.992159i \(-0.539888\pi\)
−0.124985 + 0.992159i \(0.539888\pi\)
\(444\) 1.52865e16 0.0946931
\(445\) 1.50875e16 0.0921034
\(446\) −1.74110e16 −0.104749
\(447\) −1.07367e17 −0.636608
\(448\) 6.31044e16 0.368768
\(449\) −1.30832e17 −0.753553 −0.376776 0.926304i \(-0.622967\pi\)
−0.376776 + 0.926304i \(0.622967\pi\)
\(450\) −7.44163e15 −0.0422461
\(451\) −4.15047e16 −0.232247
\(452\) −1.88922e17 −1.04203
\(453\) 3.55956e16 0.193534
\(454\) −3.25960e16 −0.174703
\(455\) −6.07261e16 −0.320849
\(456\) 4.79306e16 0.249656
\(457\) −2.28383e17 −1.17276 −0.586380 0.810036i \(-0.699448\pi\)
−0.586380 + 0.810036i \(0.699448\pi\)
\(458\) −7.11366e15 −0.0360137
\(459\) −3.92234e16 −0.195777
\(460\) 6.88739e16 0.338944
\(461\) −2.20757e17 −1.07117 −0.535585 0.844482i \(-0.679909\pi\)
−0.535585 + 0.844482i \(0.679909\pi\)
\(462\) −5.18081e15 −0.0247871
\(463\) 7.89781e16 0.372589 0.186295 0.982494i \(-0.440352\pi\)
0.186295 + 0.982494i \(0.440352\pi\)
\(464\) −2.54441e17 −1.18364
\(465\) −5.08079e16 −0.233071
\(466\) −2.36026e16 −0.106770
\(467\) 2.06630e17 0.921792 0.460896 0.887454i \(-0.347528\pi\)
0.460896 + 0.887454i \(0.347528\pi\)
\(468\) 1.00761e17 0.443296
\(469\) −7.93820e16 −0.344428
\(470\) 2.44299e15 0.0104541
\(471\) −2.37295e15 −0.0100151
\(472\) 1.07288e16 0.0446608
\(473\) −3.12084e16 −0.128137
\(474\) −1.80493e16 −0.0730971
\(475\) 2.29618e17 0.917271
\(476\) −1.12225e17 −0.442227
\(477\) −1.21123e17 −0.470821
\(478\) 6.04709e16 0.231881
\(479\) −2.57008e17 −0.972224 −0.486112 0.873897i \(-0.661585\pi\)
−0.486112 + 0.873897i \(0.661585\pi\)
\(480\) −4.04881e16 −0.151098
\(481\) 6.30075e16 0.231979
\(482\) 7.41471e16 0.269332
\(483\) −4.83783e16 −0.173378
\(484\) 1.91321e17 0.676499
\(485\) −3.12627e16 −0.109070
\(486\) 3.24558e15 0.0111727
\(487\) 1.92173e17 0.652761 0.326380 0.945239i \(-0.394171\pi\)
0.326380 + 0.945239i \(0.394171\pi\)
\(488\) 6.62972e16 0.222211
\(489\) −4.91901e16 −0.162693
\(490\) 2.22495e16 0.0726184
\(491\) −2.06038e17 −0.663618 −0.331809 0.943347i \(-0.607659\pi\)
−0.331809 + 0.943347i \(0.607659\pi\)
\(492\) 7.43940e16 0.236464
\(493\) 4.21859e17 1.32331
\(494\) 9.72585e16 0.301094
\(495\) −3.13032e16 −0.0956435
\(496\) 2.33428e17 0.703917
\(497\) 1.01286e17 0.301462
\(498\) −2.99962e16 −0.0881202
\(499\) −4.93431e17 −1.43078 −0.715390 0.698725i \(-0.753751\pi\)
−0.715390 + 0.698725i \(0.753751\pi\)
\(500\) −3.05438e17 −0.874216
\(501\) −2.24087e17 −0.633099
\(502\) 6.47256e15 0.0180510
\(503\) 6.15141e17 1.69349 0.846745 0.531998i \(-0.178559\pi\)
0.846745 + 0.531998i \(0.178559\pi\)
\(504\) 1.88629e16 0.0512637
\(505\) −2.14217e17 −0.574724
\(506\) 2.42193e16 0.0641481
\(507\) 1.94518e17 0.508638
\(508\) 3.26540e17 0.842990
\(509\) 1.78379e17 0.454651 0.227325 0.973819i \(-0.427002\pi\)
0.227325 + 0.973819i \(0.427002\pi\)
\(510\) 2.12119e16 0.0533794
\(511\) −1.22458e17 −0.304266
\(512\) 3.13251e17 0.768490
\(513\) −1.00145e17 −0.242587
\(514\) −7.49817e15 −0.0179347
\(515\) −1.16222e17 −0.274499
\(516\) 5.59388e16 0.130464
\(517\) −2.74619e16 −0.0632473
\(518\) 5.80682e15 0.0132067
\(519\) 2.25009e17 0.505373
\(520\) −1.10687e17 −0.245514
\(521\) −2.18660e17 −0.478987 −0.239493 0.970898i \(-0.576981\pi\)
−0.239493 + 0.970898i \(0.576981\pi\)
\(522\) −3.49072e16 −0.0755191
\(523\) 1.56982e17 0.335420 0.167710 0.985836i \(-0.446363\pi\)
0.167710 + 0.985836i \(0.446363\pi\)
\(524\) −9.82932e16 −0.207429
\(525\) 9.03652e16 0.188350
\(526\) 2.41475e16 0.0497125
\(527\) −3.87018e17 −0.786978
\(528\) 1.43817e17 0.288861
\(529\) −2.77877e17 −0.551303
\(530\) 6.55029e16 0.128371
\(531\) −2.24165e16 −0.0433963
\(532\) −2.86534e17 −0.547962
\(533\) 3.06636e17 0.579290
\(534\) −9.50964e15 −0.0177478
\(535\) −1.90601e17 −0.351418
\(536\) −1.44692e17 −0.263556
\(537\) −2.39498e17 −0.430993
\(538\) 2.65741e16 0.0472470
\(539\) −2.50110e17 −0.439343
\(540\) 5.61086e16 0.0973801
\(541\) −6.46967e17 −1.10943 −0.554715 0.832040i \(-0.687173\pi\)
−0.554715 + 0.832040i \(0.687173\pi\)
\(542\) 1.06672e17 0.180741
\(543\) 3.87920e17 0.649447
\(544\) −3.08409e17 −0.510193
\(545\) −5.01833e17 −0.820317
\(546\) 3.82757e16 0.0618260
\(547\) 8.98334e17 1.43390 0.716952 0.697122i \(-0.245537\pi\)
0.716952 + 0.697122i \(0.245537\pi\)
\(548\) 2.70646e17 0.426903
\(549\) −1.38520e17 −0.215920
\(550\) −4.52390e16 −0.0696875
\(551\) 1.07709e18 1.63971
\(552\) −8.81805e16 −0.132669
\(553\) 2.19176e17 0.325896
\(554\) 5.31867e16 0.0781609
\(555\) 3.50857e16 0.0509595
\(556\) −9.04525e17 −1.29848
\(557\) −7.42893e17 −1.05406 −0.527032 0.849845i \(-0.676695\pi\)
−0.527032 + 0.849845i \(0.676695\pi\)
\(558\) 3.20243e16 0.0449115
\(559\) 2.30567e17 0.319610
\(560\) 1.55358e17 0.212869
\(561\) −2.38446e17 −0.322946
\(562\) 5.95561e16 0.0797334
\(563\) −8.33322e17 −1.10283 −0.551415 0.834231i \(-0.685912\pi\)
−0.551415 + 0.834231i \(0.685912\pi\)
\(564\) 4.92234e16 0.0643957
\(565\) −4.33615e17 −0.560776
\(566\) 8.09217e16 0.103457
\(567\) −3.94118e16 −0.0498122
\(568\) 1.84617e17 0.230678
\(569\) 6.40960e17 0.791774 0.395887 0.918299i \(-0.370437\pi\)
0.395887 + 0.918299i \(0.370437\pi\)
\(570\) 5.41583e16 0.0661422
\(571\) 5.18121e17 0.625600 0.312800 0.949819i \(-0.398733\pi\)
0.312800 + 0.949819i \(0.398733\pi\)
\(572\) 6.12543e17 0.731244
\(573\) 2.15034e17 0.253806
\(574\) 2.82598e16 0.0329793
\(575\) −4.22440e17 −0.487444
\(576\) −2.40325e17 −0.274191
\(577\) 5.83813e17 0.658614 0.329307 0.944223i \(-0.393185\pi\)
0.329307 + 0.944223i \(0.393185\pi\)
\(578\) 5.44538e15 0.00607431
\(579\) 7.78941e17 0.859200
\(580\) −6.03465e17 −0.658218
\(581\) 3.64250e17 0.392875
\(582\) 1.97049e16 0.0210172
\(583\) −7.36326e17 −0.776648
\(584\) −2.23209e17 −0.232824
\(585\) 2.31267e17 0.238562
\(586\) 3.92775e16 0.0400691
\(587\) −4.95142e17 −0.499554 −0.249777 0.968303i \(-0.580357\pi\)
−0.249777 + 0.968303i \(0.580357\pi\)
\(588\) 4.48302e17 0.447320
\(589\) −9.88137e17 −0.975142
\(590\) 1.21228e16 0.0118322
\(591\) 5.11375e17 0.493652
\(592\) −1.61195e17 −0.153907
\(593\) 1.75043e18 1.65307 0.826533 0.562889i \(-0.190310\pi\)
0.826533 + 0.562889i \(0.190310\pi\)
\(594\) 1.97305e16 0.0184300
\(595\) −2.57580e17 −0.237987
\(596\) 1.16992e18 1.06919
\(597\) −1.53899e17 −0.139124
\(598\) −1.78932e17 −0.160003
\(599\) 6.76756e17 0.598629 0.299315 0.954154i \(-0.403242\pi\)
0.299315 + 0.954154i \(0.403242\pi\)
\(600\) 1.64711e17 0.144125
\(601\) −1.42278e18 −1.23155 −0.615777 0.787921i \(-0.711158\pi\)
−0.615777 + 0.787921i \(0.711158\pi\)
\(602\) 2.12493e16 0.0181956
\(603\) 3.02316e17 0.256094
\(604\) −3.87865e17 −0.325043
\(605\) 4.39121e17 0.364061
\(606\) 1.35021e17 0.110746
\(607\) 4.69979e17 0.381375 0.190688 0.981651i \(-0.438928\pi\)
0.190688 + 0.981651i \(0.438928\pi\)
\(608\) −7.87432e17 −0.632179
\(609\) 4.23885e17 0.336694
\(610\) 7.49113e16 0.0588713
\(611\) 2.02888e17 0.157757
\(612\) 4.27395e17 0.328810
\(613\) −1.20625e18 −0.918215 −0.459108 0.888381i \(-0.651831\pi\)
−0.459108 + 0.888381i \(0.651831\pi\)
\(614\) −1.99412e17 −0.150196
\(615\) 1.70750e17 0.127254
\(616\) 1.14671e17 0.0845626
\(617\) −1.16341e18 −0.848944 −0.424472 0.905441i \(-0.639540\pi\)
−0.424472 + 0.905441i \(0.639540\pi\)
\(618\) 7.32547e16 0.0528945
\(619\) −3.75951e17 −0.268622 −0.134311 0.990939i \(-0.542882\pi\)
−0.134311 + 0.990939i \(0.542882\pi\)
\(620\) 5.53626e17 0.391445
\(621\) 1.84243e17 0.128912
\(622\) −1.56556e17 −0.108401
\(623\) 1.15477e17 0.0791270
\(624\) −1.06252e18 −0.720502
\(625\) 3.83301e17 0.257229
\(626\) −3.50112e17 −0.232527
\(627\) −6.08800e17 −0.400162
\(628\) 2.58568e16 0.0168204
\(629\) 2.67258e17 0.172068
\(630\) 2.13138e16 0.0135815
\(631\) 2.70281e16 0.0170461 0.00852305 0.999964i \(-0.497287\pi\)
0.00852305 + 0.999964i \(0.497287\pi\)
\(632\) 3.99498e17 0.249375
\(633\) 1.18204e18 0.730309
\(634\) 2.53879e17 0.155256
\(635\) 7.49478e17 0.453659
\(636\) 1.31981e18 0.790750
\(637\) 1.84780e18 1.09585
\(638\) −2.12207e17 −0.124573
\(639\) −3.85734e17 −0.224147
\(640\) 5.84945e17 0.336469
\(641\) 2.48481e18 1.41487 0.707434 0.706779i \(-0.249852\pi\)
0.707434 + 0.706779i \(0.249852\pi\)
\(642\) 1.20136e17 0.0677165
\(643\) −1.45568e17 −0.0812259 −0.0406129 0.999175i \(-0.512931\pi\)
−0.0406129 + 0.999175i \(0.512931\pi\)
\(644\) 5.27152e17 0.291191
\(645\) 1.28391e17 0.0702097
\(646\) 4.12539e17 0.223334
\(647\) 2.92156e18 1.56580 0.782901 0.622147i \(-0.213739\pi\)
0.782901 + 0.622147i \(0.213739\pi\)
\(648\) −7.18370e16 −0.0381163
\(649\) −1.36273e17 −0.0715848
\(650\) 3.34224e17 0.173821
\(651\) −3.88877e17 −0.200233
\(652\) 5.35997e17 0.273246
\(653\) 2.21261e18 1.11678 0.558392 0.829578i \(-0.311419\pi\)
0.558392 + 0.829578i \(0.311419\pi\)
\(654\) 3.16306e17 0.158071
\(655\) −2.25603e17 −0.111629
\(656\) −7.84479e17 −0.384332
\(657\) 4.66367e17 0.226231
\(658\) 1.86983e16 0.00898120
\(659\) 3.78224e18 1.79884 0.899422 0.437081i \(-0.143988\pi\)
0.899422 + 0.437081i \(0.143988\pi\)
\(660\) 3.41094e17 0.160634
\(661\) −3.18733e18 −1.48634 −0.743170 0.669103i \(-0.766679\pi\)
−0.743170 + 0.669103i \(0.766679\pi\)
\(662\) 2.18476e17 0.100885
\(663\) 1.76163e18 0.805520
\(664\) 6.63928e17 0.300628
\(665\) −6.57655e17 −0.294888
\(666\) −2.21145e16 −0.00981964
\(667\) −1.98158e18 −0.871353
\(668\) 2.44175e18 1.06330
\(669\) −8.05187e17 −0.347238
\(670\) −1.63492e17 −0.0698249
\(671\) −8.42086e17 −0.356172
\(672\) −3.09891e17 −0.129810
\(673\) −2.91932e18 −1.21111 −0.605555 0.795803i \(-0.707049\pi\)
−0.605555 + 0.795803i \(0.707049\pi\)
\(674\) 4.91828e17 0.202080
\(675\) −3.44144e17 −0.140045
\(676\) −2.11956e18 −0.854263
\(677\) 3.61300e18 1.44225 0.721126 0.692804i \(-0.243625\pi\)
0.721126 + 0.692804i \(0.243625\pi\)
\(678\) 2.73308e17 0.108059
\(679\) −2.39280e17 −0.0937030
\(680\) −4.69499e17 −0.182107
\(681\) −1.50743e18 −0.579136
\(682\) 1.94681e17 0.0740842
\(683\) −2.60194e18 −0.980759 −0.490379 0.871509i \(-0.663142\pi\)
−0.490379 + 0.871509i \(0.663142\pi\)
\(684\) 1.09123e18 0.407428
\(685\) 6.21190e17 0.229740
\(686\) 3.83426e17 0.140467
\(687\) −3.28977e17 −0.119384
\(688\) −5.89870e17 −0.212047
\(689\) 5.43995e18 1.93718
\(690\) −9.96380e16 −0.0351484
\(691\) 3.85234e17 0.134622 0.0673112 0.997732i \(-0.478558\pi\)
0.0673112 + 0.997732i \(0.478558\pi\)
\(692\) −2.45180e18 −0.848780
\(693\) −2.39591e17 −0.0821683
\(694\) −9.62537e17 −0.327025
\(695\) −2.07607e18 −0.698782
\(696\) 7.72627e17 0.257638
\(697\) 1.30065e18 0.429682
\(698\) 3.12332e17 0.102225
\(699\) −1.09152e18 −0.353941
\(700\) −9.84660e17 −0.316336
\(701\) −6.06621e18 −1.93086 −0.965429 0.260667i \(-0.916057\pi\)
−0.965429 + 0.260667i \(0.916057\pi\)
\(702\) −1.45768e17 −0.0459696
\(703\) 6.82363e17 0.213209
\(704\) −1.46098e18 −0.452294
\(705\) 1.12978e17 0.0346549
\(706\) 1.39272e17 0.0423285
\(707\) −1.63959e18 −0.493751
\(708\) 2.44260e17 0.0728846
\(709\) −2.16340e18 −0.639642 −0.319821 0.947478i \(-0.603623\pi\)
−0.319821 + 0.947478i \(0.603623\pi\)
\(710\) 2.08604e17 0.0611144
\(711\) −8.34703e17 −0.242315
\(712\) 2.10484e17 0.0605479
\(713\) 1.81793e18 0.518197
\(714\) 1.62353e17 0.0458588
\(715\) 1.40591e18 0.393522
\(716\) 2.60968e18 0.723857
\(717\) 2.79653e18 0.768678
\(718\) −2.61916e17 −0.0713434
\(719\) 5.11957e18 1.38196 0.690980 0.722874i \(-0.257179\pi\)
0.690980 + 0.722874i \(0.257179\pi\)
\(720\) −5.91661e17 −0.158275
\(721\) −8.89546e17 −0.235825
\(722\) 3.90391e17 0.102567
\(723\) 3.42899e18 0.892827
\(724\) −4.22695e18 −1.09075
\(725\) 3.70137e18 0.946598
\(726\) −2.76778e17 −0.0701527
\(727\) 4.51835e18 1.13503 0.567513 0.823364i \(-0.307906\pi\)
0.567513 + 0.823364i \(0.307906\pi\)
\(728\) −8.47185e17 −0.210923
\(729\) 1.50095e17 0.0370370
\(730\) −2.52210e17 −0.0616828
\(731\) 9.77992e17 0.237068
\(732\) 1.50938e18 0.362640
\(733\) 4.95103e17 0.117902 0.0589508 0.998261i \(-0.481224\pi\)
0.0589508 + 0.998261i \(0.481224\pi\)
\(734\) −8.66039e17 −0.204415
\(735\) 1.02895e18 0.240727
\(736\) 1.44868e18 0.335944
\(737\) 1.83783e18 0.422442
\(738\) −1.07624e17 −0.0245212
\(739\) 2.42268e18 0.547150 0.273575 0.961851i \(-0.411794\pi\)
0.273575 + 0.961851i \(0.411794\pi\)
\(740\) −3.82309e17 −0.0855872
\(741\) 4.49780e18 0.998117
\(742\) 5.01351e17 0.110285
\(743\) −3.28077e18 −0.715398 −0.357699 0.933837i \(-0.616439\pi\)
−0.357699 + 0.933837i \(0.616439\pi\)
\(744\) −7.08818e17 −0.153218
\(745\) 2.68521e18 0.575390
\(746\) −1.41492e17 −0.0300558
\(747\) −1.38720e18 −0.292115
\(748\) 2.59821e18 0.542392
\(749\) −1.45883e18 −0.301907
\(750\) 4.41870e17 0.0906558
\(751\) −7.28331e18 −1.48139 −0.740695 0.671841i \(-0.765504\pi\)
−0.740695 + 0.671841i \(0.765504\pi\)
\(752\) −5.19056e17 −0.104664
\(753\) 2.99329e17 0.0598386
\(754\) 1.56778e18 0.310721
\(755\) −8.90232e17 −0.174924
\(756\) 4.29448e17 0.0836602
\(757\) −5.35060e18 −1.03343 −0.516713 0.856159i \(-0.672844\pi\)
−0.516713 + 0.856159i \(0.672844\pi\)
\(758\) −1.68384e17 −0.0322441
\(759\) 1.12004e18 0.212649
\(760\) −1.19873e18 −0.225648
\(761\) 6.63517e18 1.23837 0.619187 0.785244i \(-0.287462\pi\)
0.619187 + 0.785244i \(0.287462\pi\)
\(762\) −4.72397e17 −0.0874177
\(763\) −3.84096e18 −0.704743
\(764\) −2.34310e18 −0.426270
\(765\) 9.80962e17 0.176951
\(766\) −2.55458e17 −0.0456912
\(767\) 1.00678e18 0.178553
\(768\) 2.33192e18 0.410077
\(769\) −1.29357e18 −0.225564 −0.112782 0.993620i \(-0.535976\pi\)
−0.112782 + 0.993620i \(0.535976\pi\)
\(770\) 1.29570e17 0.0224035
\(771\) −3.46759e17 −0.0594531
\(772\) −8.48769e18 −1.44304
\(773\) −4.23657e18 −0.714245 −0.357123 0.934058i \(-0.616242\pi\)
−0.357123 + 0.934058i \(0.616242\pi\)
\(774\) −8.09251e16 −0.0135290
\(775\) −3.39568e18 −0.562945
\(776\) −4.36143e17 −0.0717015
\(777\) 2.68541e17 0.0437799
\(778\) 3.54261e17 0.0572737
\(779\) 3.32082e18 0.532418
\(780\) −2.51999e18 −0.400668
\(781\) −2.34494e18 −0.369744
\(782\) −7.58970e17 −0.118681
\(783\) −1.61431e18 −0.250343
\(784\) −4.72731e18 −0.727043
\(785\) 5.93467e16 0.00905198
\(786\) 1.42198e17 0.0215103
\(787\) −1.20264e19 −1.80426 −0.902129 0.431467i \(-0.857996\pi\)
−0.902129 + 0.431467i \(0.857996\pi\)
\(788\) −5.57217e18 −0.829094
\(789\) 1.11672e18 0.164795
\(790\) 4.51405e17 0.0660679
\(791\) −3.31883e18 −0.481768
\(792\) −4.36709e17 −0.0628751
\(793\) 6.22131e18 0.888395
\(794\) −1.12140e17 −0.0158829
\(795\) 3.02923e18 0.425546
\(796\) 1.67695e18 0.233660
\(797\) 8.20407e18 1.13384 0.566918 0.823774i \(-0.308136\pi\)
0.566918 + 0.823774i \(0.308136\pi\)
\(798\) 4.14521e17 0.0568235
\(799\) 8.60585e17 0.117015
\(800\) −2.70597e18 −0.364954
\(801\) −4.39781e17 −0.0588335
\(802\) 6.68158e17 0.0886637
\(803\) 2.83512e18 0.373182
\(804\) −3.29417e18 −0.430113
\(805\) 1.20992e18 0.156706
\(806\) −1.43830e18 −0.184787
\(807\) 1.22894e18 0.156622
\(808\) −2.98852e18 −0.377818
\(809\) 7.02387e18 0.880868 0.440434 0.897785i \(-0.354825\pi\)
0.440434 + 0.897785i \(0.354825\pi\)
\(810\) −8.11708e16 −0.0100983
\(811\) 6.61867e18 0.816836 0.408418 0.912795i \(-0.366081\pi\)
0.408418 + 0.912795i \(0.366081\pi\)
\(812\) −4.61884e18 −0.565482
\(813\) 4.93314e18 0.599150
\(814\) −1.34438e17 −0.0161981
\(815\) 1.23023e18 0.147048
\(816\) −4.50685e18 −0.534425
\(817\) 2.49701e18 0.293750
\(818\) −2.46008e18 −0.287113
\(819\) 1.77009e18 0.204951
\(820\) −1.86057e18 −0.213725
\(821\) −5.90029e18 −0.672424 −0.336212 0.941786i \(-0.609146\pi\)
−0.336212 + 0.941786i \(0.609146\pi\)
\(822\) −3.91537e17 −0.0442696
\(823\) −1.71526e19 −1.92412 −0.962059 0.272842i \(-0.912037\pi\)
−0.962059 + 0.272842i \(0.912037\pi\)
\(824\) −1.62140e18 −0.180453
\(825\) −2.09211e18 −0.231012
\(826\) 9.27861e16 0.0101651
\(827\) 1.00880e19 1.09653 0.548263 0.836306i \(-0.315289\pi\)
0.548263 + 0.836306i \(0.315289\pi\)
\(828\) −2.00759e18 −0.216510
\(829\) 4.06157e18 0.434599 0.217300 0.976105i \(-0.430275\pi\)
0.217300 + 0.976105i \(0.430275\pi\)
\(830\) 7.50194e17 0.0796463
\(831\) 2.45966e18 0.259101
\(832\) 1.07937e19 1.12815
\(833\) 7.83779e18 0.812832
\(834\) 1.30855e18 0.134652
\(835\) 5.60433e18 0.572219
\(836\) 6.63376e18 0.672077
\(837\) 1.48099e18 0.148880
\(838\) −1.72434e18 −0.172003
\(839\) 1.07822e19 1.06722 0.533609 0.845731i \(-0.320835\pi\)
0.533609 + 0.845731i \(0.320835\pi\)
\(840\) −4.71754e17 −0.0463341
\(841\) 7.10175e18 0.692136
\(842\) −1.45688e18 −0.140895
\(843\) 2.75422e18 0.264314
\(844\) −1.28800e19 −1.22656
\(845\) −4.86483e18 −0.459726
\(846\) −7.12101e16 −0.00667781
\(847\) 3.36098e18 0.312769
\(848\) −1.39173e19 −1.28523
\(849\) 3.74229e18 0.342955
\(850\) 1.41767e18 0.128930
\(851\) −1.25538e18 −0.113301
\(852\) 4.20313e18 0.376457
\(853\) −1.01275e19 −0.900185 −0.450093 0.892982i \(-0.648609\pi\)
−0.450093 + 0.892982i \(0.648609\pi\)
\(854\) 5.73361e17 0.0505769
\(855\) 2.50460e18 0.219259
\(856\) −2.65906e18 −0.231019
\(857\) 7.67025e17 0.0661354 0.0330677 0.999453i \(-0.489472\pi\)
0.0330677 + 0.999453i \(0.489472\pi\)
\(858\) −8.86149e17 −0.0758297
\(859\) −6.06115e18 −0.514754 −0.257377 0.966311i \(-0.582858\pi\)
−0.257377 + 0.966311i \(0.582858\pi\)
\(860\) −1.39901e18 −0.117918
\(861\) 1.30690e18 0.109325
\(862\) 4.06571e17 0.0337551
\(863\) −1.02067e19 −0.841041 −0.420520 0.907283i \(-0.638152\pi\)
−0.420520 + 0.907283i \(0.638152\pi\)
\(864\) 1.18018e18 0.0965180
\(865\) −5.62739e18 −0.456775
\(866\) 3.95456e17 0.0318590
\(867\) 2.51826e17 0.0201361
\(868\) 4.23738e18 0.336294
\(869\) −5.07430e18 −0.399712
\(870\) 8.73016e17 0.0682570
\(871\) −1.35779e19 −1.05369
\(872\) −7.00103e18 −0.539268
\(873\) 9.11268e17 0.0696713
\(874\) −1.93781e18 −0.147057
\(875\) −5.36571e18 −0.404180
\(876\) −5.08174e18 −0.379958
\(877\) −1.88380e19 −1.39809 −0.699047 0.715075i \(-0.746392\pi\)
−0.699047 + 0.715075i \(0.746392\pi\)
\(878\) −3.18476e18 −0.234619
\(879\) 1.81642e18 0.132828
\(880\) −3.59681e18 −0.261084
\(881\) 1.43776e19 1.03596 0.517982 0.855392i \(-0.326684\pi\)
0.517982 + 0.855392i \(0.326684\pi\)
\(882\) −6.48547e17 −0.0463869
\(883\) −8.90008e18 −0.631902 −0.315951 0.948776i \(-0.602323\pi\)
−0.315951 + 0.948776i \(0.602323\pi\)
\(884\) −1.91955e19 −1.35288
\(885\) 5.60627e17 0.0392232
\(886\) −6.26854e17 −0.0435359
\(887\) −1.38680e19 −0.956115 −0.478057 0.878329i \(-0.658659\pi\)
−0.478057 + 0.878329i \(0.658659\pi\)
\(888\) 4.89478e17 0.0335003
\(889\) 5.73640e18 0.389743
\(890\) 2.37832e17 0.0160412
\(891\) 9.12451e17 0.0610948
\(892\) 8.77368e18 0.583190
\(893\) 2.19725e18 0.144992
\(894\) −1.69249e18 −0.110875
\(895\) 5.98977e18 0.389547
\(896\) 4.47709e18 0.289064
\(897\) −8.27484e18 −0.530406
\(898\) −2.06239e18 −0.131242
\(899\) −1.59285e19 −1.00632
\(900\) 3.74995e18 0.235206
\(901\) 2.30745e19 1.43688
\(902\) −6.54263e17 −0.0404492
\(903\) 9.82689e17 0.0603178
\(904\) −6.04933e18 −0.368648
\(905\) −9.70174e18 −0.586995
\(906\) 5.61114e17 0.0337068
\(907\) −2.39637e19 −1.42924 −0.714621 0.699512i \(-0.753401\pi\)
−0.714621 + 0.699512i \(0.753401\pi\)
\(908\) 1.64256e19 0.972666
\(909\) 6.24416e18 0.367120
\(910\) −9.57261e17 −0.0558806
\(911\) −1.36444e19 −0.790834 −0.395417 0.918502i \(-0.629400\pi\)
−0.395417 + 0.918502i \(0.629400\pi\)
\(912\) −1.15069e19 −0.662204
\(913\) −8.43301e18 −0.481862
\(914\) −3.60014e18 −0.204253
\(915\) 3.46433e18 0.195156
\(916\) 3.58468e18 0.200507
\(917\) −1.72674e18 −0.0959016
\(918\) −6.18301e17 −0.0340975
\(919\) −2.82254e19 −1.54557 −0.772785 0.634667i \(-0.781137\pi\)
−0.772785 + 0.634667i \(0.781137\pi\)
\(920\) 2.20536e18 0.119911
\(921\) −9.22197e18 −0.497893
\(922\) −3.47992e18 −0.186560
\(923\) 1.73244e19 0.922246
\(924\) 2.61069e18 0.138003
\(925\) 2.34491e18 0.123085
\(926\) 1.24498e18 0.0648919
\(927\) 3.38772e18 0.175343
\(928\) −1.26932e19 −0.652391
\(929\) −4.94985e18 −0.252633 −0.126316 0.991990i \(-0.540315\pi\)
−0.126316 + 0.991990i \(0.540315\pi\)
\(930\) −8.00916e17 −0.0405927
\(931\) 2.00115e19 1.00718
\(932\) 1.18937e19 0.594447
\(933\) −7.24006e18 −0.359345
\(934\) 3.25723e18 0.160544
\(935\) 5.96343e18 0.291891
\(936\) 3.22640e18 0.156828
\(937\) −7.56255e18 −0.365057 −0.182529 0.983201i \(-0.558428\pi\)
−0.182529 + 0.983201i \(0.558428\pi\)
\(938\) −1.25135e18 −0.0599873
\(939\) −1.61912e19 −0.770821
\(940\) −1.23106e18 −0.0582033
\(941\) 3.25933e19 1.53037 0.765184 0.643812i \(-0.222648\pi\)
0.765184 + 0.643812i \(0.222648\pi\)
\(942\) −3.74063e16 −0.00174427
\(943\) −6.10949e18 −0.282930
\(944\) −2.57570e18 −0.118461
\(945\) 9.85674e17 0.0450222
\(946\) −4.91957e17 −0.0223170
\(947\) 1.86275e19 0.839227 0.419614 0.907703i \(-0.362166\pi\)
0.419614 + 0.907703i \(0.362166\pi\)
\(948\) 9.09529e18 0.406970
\(949\) −2.09458e19 −0.930823
\(950\) 3.61960e18 0.159756
\(951\) 1.17409e19 0.514667
\(952\) −3.59349e18 −0.156450
\(953\) 2.69966e19 1.16736 0.583681 0.811983i \(-0.301612\pi\)
0.583681 + 0.811983i \(0.301612\pi\)
\(954\) −1.90933e18 −0.0820005
\(955\) −5.37792e18 −0.229399
\(956\) −3.04722e19 −1.29100
\(957\) −9.81367e18 −0.412956
\(958\) −4.05137e18 −0.169327
\(959\) 4.75451e18 0.197372
\(960\) 6.01044e18 0.247824
\(961\) −9.80457e18 −0.401538
\(962\) 9.93225e17 0.0404026
\(963\) 5.55577e18 0.224478
\(964\) −3.73638e19 −1.49951
\(965\) −1.94810e19 −0.776577
\(966\) −7.62616e17 −0.0301964
\(967\) −5.49531e18 −0.216132 −0.108066 0.994144i \(-0.534466\pi\)
−0.108066 + 0.994144i \(0.534466\pi\)
\(968\) 6.12615e18 0.239330
\(969\) 1.90782e19 0.740343
\(970\) −4.92812e17 −0.0189961
\(971\) −4.70150e19 −1.80016 −0.900082 0.435721i \(-0.856493\pi\)
−0.900082 + 0.435721i \(0.856493\pi\)
\(972\) −1.63550e18 −0.0622041
\(973\) −1.58900e19 −0.600331
\(974\) 3.02934e18 0.113688
\(975\) 1.54565e19 0.576209
\(976\) −1.59162e19 −0.589409
\(977\) 1.66428e19 0.612227 0.306114 0.951995i \(-0.400971\pi\)
0.306114 + 0.951995i \(0.400971\pi\)
\(978\) −7.75412e17 −0.0283355
\(979\) −2.67350e18 −0.0970494
\(980\) −1.12119e19 −0.404305
\(981\) 1.46278e19 0.523999
\(982\) −3.24790e18 −0.115579
\(983\) −1.54727e19 −0.546975 −0.273488 0.961875i \(-0.588177\pi\)
−0.273488 + 0.961875i \(0.588177\pi\)
\(984\) 2.38212e18 0.0836556
\(985\) −1.27893e19 −0.446181
\(986\) 6.65001e18 0.230474
\(987\) 8.64719e17 0.0297724
\(988\) −4.90100e19 −1.67635
\(989\) −4.59389e18 −0.156100
\(990\) −4.93451e17 −0.0166577
\(991\) 4.34221e19 1.45624 0.728118 0.685452i \(-0.240395\pi\)
0.728118 + 0.685452i \(0.240395\pi\)
\(992\) 1.16449e19 0.387979
\(993\) 1.01036e19 0.334430
\(994\) 1.59663e18 0.0525040
\(995\) 3.84894e18 0.125745
\(996\) 1.51155e19 0.490611
\(997\) 4.09575e19 1.32073 0.660367 0.750943i \(-0.270401\pi\)
0.660367 + 0.750943i \(0.270401\pi\)
\(998\) −7.77825e18 −0.249192
\(999\) −1.02270e18 −0.0325518
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.1.16 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.16 31 1.1 even 1 trivial