Properties

Label 177.14.a.c.1.3
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 1.3
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-138.949 q^{2} +729.000 q^{3} +11114.9 q^{4} -41433.2 q^{5} -101294. q^{6} -70948.7 q^{7} -406128. q^{8} +531441. q^{9} +O(q^{10})\) \(q-138.949 q^{2} +729.000 q^{3} +11114.9 q^{4} -41433.2 q^{5} -101294. q^{6} -70948.7 q^{7} -406128. q^{8} +531441. q^{9} +5.75710e6 q^{10} -5.18939e6 q^{11} +8.10273e6 q^{12} +2.69393e7 q^{13} +9.85826e6 q^{14} -3.02048e7 q^{15} -3.46218e7 q^{16} +1.85474e8 q^{17} -7.38433e7 q^{18} +3.25790e8 q^{19} -4.60523e8 q^{20} -5.17216e7 q^{21} +7.21062e8 q^{22} +1.17438e9 q^{23} -2.96067e8 q^{24} +4.96003e8 q^{25} -3.74319e9 q^{26} +3.87420e8 q^{27} -7.88584e8 q^{28} +2.93323e9 q^{29} +4.19693e9 q^{30} -1.23680e9 q^{31} +8.13766e9 q^{32} -3.78307e9 q^{33} -2.57715e10 q^{34} +2.93963e9 q^{35} +5.90689e9 q^{36} -1.79980e10 q^{37} -4.52682e10 q^{38} +1.96388e10 q^{39} +1.68272e10 q^{40} +5.41462e10 q^{41} +7.18667e9 q^{42} -4.68366e10 q^{43} -5.76794e10 q^{44} -2.20193e10 q^{45} -1.63179e11 q^{46} +2.60361e10 q^{47} -2.52393e10 q^{48} -9.18553e10 q^{49} -6.89192e10 q^{50} +1.35211e11 q^{51} +2.99426e11 q^{52} +1.43333e11 q^{53} -5.38317e10 q^{54} +2.15013e11 q^{55} +2.88142e10 q^{56} +2.37501e11 q^{57} -4.07569e11 q^{58} -4.21805e10 q^{59} -3.35722e11 q^{60} +5.85159e11 q^{61} +1.71852e11 q^{62} -3.77050e10 q^{63} -8.47100e11 q^{64} -1.11618e12 q^{65} +5.25654e11 q^{66} -1.43954e11 q^{67} +2.06152e12 q^{68} +8.56122e11 q^{69} -4.08459e11 q^{70} +9.28219e11 q^{71} -2.15833e11 q^{72} +1.49894e12 q^{73} +2.50081e12 q^{74} +3.61586e11 q^{75} +3.62111e12 q^{76} +3.68181e11 q^{77} -2.72879e12 q^{78} -2.13123e12 q^{79} +1.43449e12 q^{80} +2.82430e11 q^{81} -7.52357e12 q^{82} +5.02222e11 q^{83} -5.74878e11 q^{84} -7.68478e12 q^{85} +6.50790e12 q^{86} +2.13832e12 q^{87} +2.10756e12 q^{88} +2.89567e12 q^{89} +3.05956e12 q^{90} -1.91131e12 q^{91} +1.30530e13 q^{92} -9.01626e11 q^{93} -3.61770e12 q^{94} -1.34985e13 q^{95} +5.93236e12 q^{96} +1.54484e12 q^{97} +1.27632e13 q^{98} -2.75786e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −138.949 −1.53519 −0.767593 0.640938i \(-0.778546\pi\)
−0.767593 + 0.640938i \(0.778546\pi\)
\(3\) 729.000 0.577350
\(4\) 11114.9 1.35679
\(5\) −41433.2 −1.18589 −0.592943 0.805244i \(-0.702034\pi\)
−0.592943 + 0.805244i \(0.702034\pi\)
\(6\) −101294. −0.886340
\(7\) −70948.7 −0.227933 −0.113966 0.993485i \(-0.536356\pi\)
−0.113966 + 0.993485i \(0.536356\pi\)
\(8\) −406128. −0.547745
\(9\) 531441. 0.333333
\(10\) 5.75710e6 1.82055
\(11\) −5.18939e6 −0.883211 −0.441605 0.897209i \(-0.645591\pi\)
−0.441605 + 0.897209i \(0.645591\pi\)
\(12\) 8.10273e6 0.783345
\(13\) 2.69393e7 1.54794 0.773971 0.633221i \(-0.218268\pi\)
0.773971 + 0.633221i \(0.218268\pi\)
\(14\) 9.85826e6 0.349919
\(15\) −3.02048e7 −0.684672
\(16\) −3.46218e7 −0.515904
\(17\) 1.85474e8 1.86366 0.931828 0.362901i \(-0.118214\pi\)
0.931828 + 0.362901i \(0.118214\pi\)
\(18\) −7.38433e7 −0.511728
\(19\) 3.25790e8 1.58869 0.794345 0.607466i \(-0.207814\pi\)
0.794345 + 0.607466i \(0.207814\pi\)
\(20\) −4.60523e8 −1.60900
\(21\) −5.17216e7 −0.131597
\(22\) 7.21062e8 1.35589
\(23\) 1.17438e9 1.65416 0.827079 0.562086i \(-0.190001\pi\)
0.827079 + 0.562086i \(0.190001\pi\)
\(24\) −2.96067e8 −0.316240
\(25\) 4.96003e8 0.406326
\(26\) −3.74319e9 −2.37638
\(27\) 3.87420e8 0.192450
\(28\) −7.88584e8 −0.309258
\(29\) 2.93323e9 0.915711 0.457856 0.889027i \(-0.348618\pi\)
0.457856 + 0.889027i \(0.348618\pi\)
\(30\) 4.19693e9 1.05110
\(31\) −1.23680e9 −0.250292 −0.125146 0.992138i \(-0.539940\pi\)
−0.125146 + 0.992138i \(0.539940\pi\)
\(32\) 8.13766e9 1.33975
\(33\) −3.78307e9 −0.509922
\(34\) −2.57715e10 −2.86106
\(35\) 2.93963e9 0.270302
\(36\) 5.90689e9 0.452265
\(37\) −1.79980e10 −1.15322 −0.576611 0.817019i \(-0.695625\pi\)
−0.576611 + 0.817019i \(0.695625\pi\)
\(38\) −4.52682e10 −2.43893
\(39\) 1.96388e10 0.893705
\(40\) 1.68272e10 0.649563
\(41\) 5.41462e10 1.78022 0.890109 0.455748i \(-0.150628\pi\)
0.890109 + 0.455748i \(0.150628\pi\)
\(42\) 7.18667e9 0.202026
\(43\) −4.68366e10 −1.12990 −0.564950 0.825125i \(-0.691105\pi\)
−0.564950 + 0.825125i \(0.691105\pi\)
\(44\) −5.76794e10 −1.19833
\(45\) −2.20193e10 −0.395295
\(46\) −1.63179e11 −2.53944
\(47\) 2.60361e10 0.352322 0.176161 0.984361i \(-0.443632\pi\)
0.176161 + 0.984361i \(0.443632\pi\)
\(48\) −2.52393e10 −0.297858
\(49\) −9.18553e10 −0.948047
\(50\) −6.89192e10 −0.623785
\(51\) 1.35211e11 1.07598
\(52\) 2.99426e11 2.10024
\(53\) 1.43333e11 0.888288 0.444144 0.895955i \(-0.353508\pi\)
0.444144 + 0.895955i \(0.353508\pi\)
\(54\) −5.38317e10 −0.295447
\(55\) 2.15013e11 1.04739
\(56\) 2.88142e10 0.124849
\(57\) 2.37501e11 0.917231
\(58\) −4.07569e11 −1.40579
\(59\) −4.21805e10 −0.130189
\(60\) −3.35722e11 −0.928958
\(61\) 5.85159e11 1.45422 0.727110 0.686521i \(-0.240863\pi\)
0.727110 + 0.686521i \(0.240863\pi\)
\(62\) 1.71852e11 0.384245
\(63\) −3.77050e10 −0.0759776
\(64\) −8.47100e11 −1.54087
\(65\) −1.11618e12 −1.83568
\(66\) 5.25654e11 0.782824
\(67\) −1.43954e11 −0.194419 −0.0972096 0.995264i \(-0.530992\pi\)
−0.0972096 + 0.995264i \(0.530992\pi\)
\(68\) 2.06152e12 2.52860
\(69\) 8.56122e11 0.955029
\(70\) −4.08459e11 −0.414964
\(71\) 9.28219e11 0.859946 0.429973 0.902842i \(-0.358523\pi\)
0.429973 + 0.902842i \(0.358523\pi\)
\(72\) −2.15833e11 −0.182582
\(73\) 1.49894e12 1.15927 0.579635 0.814876i \(-0.303195\pi\)
0.579635 + 0.814876i \(0.303195\pi\)
\(74\) 2.50081e12 1.77041
\(75\) 3.61586e11 0.234592
\(76\) 3.62111e12 2.15553
\(77\) 3.68181e11 0.201313
\(78\) −2.72879e12 −1.37200
\(79\) −2.13123e12 −0.986401 −0.493200 0.869916i \(-0.664173\pi\)
−0.493200 + 0.869916i \(0.664173\pi\)
\(80\) 1.43449e12 0.611804
\(81\) 2.82430e11 0.111111
\(82\) −7.52357e12 −2.73296
\(83\) 5.02222e11 0.168612 0.0843060 0.996440i \(-0.473133\pi\)
0.0843060 + 0.996440i \(0.473133\pi\)
\(84\) −5.74878e11 −0.178550
\(85\) −7.68478e12 −2.21008
\(86\) 6.50790e12 1.73461
\(87\) 2.13832e12 0.528686
\(88\) 2.10756e12 0.483774
\(89\) 2.89567e12 0.617609 0.308804 0.951126i \(-0.400071\pi\)
0.308804 + 0.951126i \(0.400071\pi\)
\(90\) 3.05956e12 0.606852
\(91\) −1.91131e12 −0.352827
\(92\) 1.30530e13 2.24435
\(93\) −9.01626e11 −0.144506
\(94\) −3.61770e12 −0.540880
\(95\) −1.34985e13 −1.88401
\(96\) 5.93236e12 0.773507
\(97\) 1.54484e12 0.188308 0.0941539 0.995558i \(-0.469985\pi\)
0.0941539 + 0.995558i \(0.469985\pi\)
\(98\) 1.27632e13 1.45543
\(99\) −2.75786e12 −0.294404
\(100\) 5.51300e12 0.551300
\(101\) −1.77667e13 −1.66540 −0.832701 0.553723i \(-0.813206\pi\)
−0.832701 + 0.553723i \(0.813206\pi\)
\(102\) −1.87874e13 −1.65183
\(103\) 1.44864e13 1.19541 0.597706 0.801716i \(-0.296079\pi\)
0.597706 + 0.801716i \(0.296079\pi\)
\(104\) −1.09408e13 −0.847877
\(105\) 2.14299e12 0.156059
\(106\) −1.99160e13 −1.36369
\(107\) −1.12737e13 −0.726227 −0.363113 0.931745i \(-0.618286\pi\)
−0.363113 + 0.931745i \(0.618286\pi\)
\(108\) 4.30612e12 0.261115
\(109\) −3.38427e12 −0.193283 −0.0966414 0.995319i \(-0.530810\pi\)
−0.0966414 + 0.995319i \(0.530810\pi\)
\(110\) −2.98759e13 −1.60793
\(111\) −1.31205e13 −0.665813
\(112\) 2.45637e12 0.117592
\(113\) −8.65959e12 −0.391280 −0.195640 0.980676i \(-0.562678\pi\)
−0.195640 + 0.980676i \(0.562678\pi\)
\(114\) −3.30005e13 −1.40812
\(115\) −4.86582e13 −1.96164
\(116\) 3.26024e13 1.24243
\(117\) 1.43167e13 0.515981
\(118\) 5.86095e12 0.199864
\(119\) −1.31592e13 −0.424788
\(120\) 1.22670e13 0.375025
\(121\) −7.59290e12 −0.219939
\(122\) −8.13073e13 −2.23250
\(123\) 3.94726e13 1.02781
\(124\) −1.37468e13 −0.339595
\(125\) 3.00266e13 0.704030
\(126\) 5.23908e12 0.116640
\(127\) −7.84144e13 −1.65833 −0.829166 0.559003i \(-0.811184\pi\)
−0.829166 + 0.559003i \(0.811184\pi\)
\(128\) 5.10400e13 1.02576
\(129\) −3.41439e13 −0.652348
\(130\) 1.55092e14 2.81811
\(131\) 7.97712e12 0.137906 0.0689529 0.997620i \(-0.478034\pi\)
0.0689529 + 0.997620i \(0.478034\pi\)
\(132\) −4.20483e13 −0.691859
\(133\) −2.31144e13 −0.362115
\(134\) 2.00023e13 0.298469
\(135\) −1.60521e13 −0.228224
\(136\) −7.53263e13 −1.02081
\(137\) −1.43376e14 −1.85264 −0.926321 0.376735i \(-0.877047\pi\)
−0.926321 + 0.376735i \(0.877047\pi\)
\(138\) −1.18957e14 −1.46615
\(139\) 2.41401e13 0.283885 0.141943 0.989875i \(-0.454665\pi\)
0.141943 + 0.989875i \(0.454665\pi\)
\(140\) 3.26735e13 0.366745
\(141\) 1.89803e13 0.203413
\(142\) −1.28975e14 −1.32018
\(143\) −1.39799e14 −1.36716
\(144\) −1.83994e13 −0.171968
\(145\) −1.21533e14 −1.08593
\(146\) −2.08276e14 −1.77969
\(147\) −6.69625e13 −0.547355
\(148\) −2.00045e14 −1.56468
\(149\) 1.01737e14 0.761671 0.380836 0.924643i \(-0.375636\pi\)
0.380836 + 0.924643i \(0.375636\pi\)
\(150\) −5.02421e13 −0.360142
\(151\) 1.83739e14 1.26139 0.630696 0.776030i \(-0.282769\pi\)
0.630696 + 0.776030i \(0.282769\pi\)
\(152\) −1.32312e14 −0.870197
\(153\) 9.85686e13 0.621218
\(154\) −5.11584e13 −0.309052
\(155\) 5.12444e13 0.296818
\(156\) 2.18282e14 1.21257
\(157\) 1.16751e13 0.0622173 0.0311087 0.999516i \(-0.490096\pi\)
0.0311087 + 0.999516i \(0.490096\pi\)
\(158\) 2.96132e14 1.51431
\(159\) 1.04490e14 0.512853
\(160\) −3.37169e14 −1.58879
\(161\) −8.33206e13 −0.377037
\(162\) −3.92433e13 −0.170576
\(163\) 1.62999e14 0.680714 0.340357 0.940296i \(-0.389452\pi\)
0.340357 + 0.940296i \(0.389452\pi\)
\(164\) 6.01827e14 2.41539
\(165\) 1.56744e14 0.604709
\(166\) −6.97834e13 −0.258851
\(167\) 1.69086e14 0.603185 0.301593 0.953437i \(-0.402482\pi\)
0.301593 + 0.953437i \(0.402482\pi\)
\(168\) 2.10056e13 0.0720816
\(169\) 4.22851e14 1.39612
\(170\) 1.06779e15 3.39289
\(171\) 1.73138e14 0.529564
\(172\) −5.20582e14 −1.53304
\(173\) 3.60649e14 1.02279 0.511394 0.859346i \(-0.329129\pi\)
0.511394 + 0.859346i \(0.329129\pi\)
\(174\) −2.97118e14 −0.811631
\(175\) −3.51908e13 −0.0926150
\(176\) 1.79666e14 0.455652
\(177\) −3.07496e13 −0.0751646
\(178\) −4.02350e14 −0.948144
\(179\) 1.24489e14 0.282869 0.141434 0.989948i \(-0.454829\pi\)
0.141434 + 0.989948i \(0.454829\pi\)
\(180\) −2.44741e14 −0.536334
\(181\) −8.33659e14 −1.76229 −0.881146 0.472844i \(-0.843227\pi\)
−0.881146 + 0.472844i \(0.843227\pi\)
\(182\) 2.65575e14 0.541655
\(183\) 4.26581e14 0.839594
\(184\) −4.76948e14 −0.906056
\(185\) 7.45714e14 1.36759
\(186\) 1.25280e14 0.221844
\(187\) −9.62499e14 −1.64600
\(188\) 2.89388e14 0.478029
\(189\) −2.74870e13 −0.0438657
\(190\) 1.87561e15 2.89230
\(191\) −1.36584e14 −0.203555 −0.101778 0.994807i \(-0.532453\pi\)
−0.101778 + 0.994807i \(0.532453\pi\)
\(192\) −6.17536e14 −0.889619
\(193\) 9.83407e14 1.36965 0.684827 0.728706i \(-0.259878\pi\)
0.684827 + 0.728706i \(0.259878\pi\)
\(194\) −2.14655e14 −0.289087
\(195\) −8.13695e14 −1.05983
\(196\) −1.02096e15 −1.28630
\(197\) −4.96889e14 −0.605660 −0.302830 0.953045i \(-0.597931\pi\)
−0.302830 + 0.953045i \(0.597931\pi\)
\(198\) 3.83202e14 0.451964
\(199\) −5.60855e12 −0.00640185 −0.00320093 0.999995i \(-0.501019\pi\)
−0.00320093 + 0.999995i \(0.501019\pi\)
\(200\) −2.01441e14 −0.222563
\(201\) −1.04943e14 −0.112248
\(202\) 2.46867e15 2.55670
\(203\) −2.08109e14 −0.208721
\(204\) 1.50285e15 1.45989
\(205\) −2.24345e15 −2.11113
\(206\) −2.01287e15 −1.83518
\(207\) 6.24113e14 0.551386
\(208\) −9.32686e14 −0.798590
\(209\) −1.69065e15 −1.40315
\(210\) −2.97766e14 −0.239580
\(211\) 3.99701e14 0.311816 0.155908 0.987772i \(-0.450170\pi\)
0.155908 + 0.987772i \(0.450170\pi\)
\(212\) 1.59313e15 1.20522
\(213\) 6.76671e14 0.496490
\(214\) 1.56647e15 1.11489
\(215\) 1.94059e15 1.33993
\(216\) −1.57342e14 −0.105413
\(217\) 8.77492e13 0.0570499
\(218\) 4.70242e14 0.296725
\(219\) 1.09272e15 0.669305
\(220\) 2.38984e15 1.42109
\(221\) 4.99655e15 2.88483
\(222\) 1.82309e15 1.02215
\(223\) −2.93097e15 −1.59599 −0.797994 0.602665i \(-0.794105\pi\)
−0.797994 + 0.602665i \(0.794105\pi\)
\(224\) −5.77356e14 −0.305374
\(225\) 2.63596e14 0.135442
\(226\) 1.20324e15 0.600687
\(227\) −1.07733e15 −0.522612 −0.261306 0.965256i \(-0.584153\pi\)
−0.261306 + 0.965256i \(0.584153\pi\)
\(228\) 2.63979e15 1.24449
\(229\) −2.49956e15 −1.14534 −0.572669 0.819787i \(-0.694092\pi\)
−0.572669 + 0.819787i \(0.694092\pi\)
\(230\) 6.76101e15 3.01149
\(231\) 2.68404e14 0.116228
\(232\) −1.19127e15 −0.501576
\(233\) −2.90153e15 −1.18799 −0.593996 0.804468i \(-0.702451\pi\)
−0.593996 + 0.804468i \(0.702451\pi\)
\(234\) −1.98929e15 −0.792126
\(235\) −1.07876e15 −0.417814
\(236\) −4.68831e14 −0.176640
\(237\) −1.55366e15 −0.569499
\(238\) 1.82845e15 0.652129
\(239\) 4.58142e15 1.59006 0.795031 0.606569i \(-0.207455\pi\)
0.795031 + 0.606569i \(0.207455\pi\)
\(240\) 1.04574e15 0.353225
\(241\) 4.26214e15 1.40125 0.700627 0.713528i \(-0.252904\pi\)
0.700627 + 0.713528i \(0.252904\pi\)
\(242\) 1.05503e15 0.337647
\(243\) 2.05891e14 0.0641500
\(244\) 6.50396e15 1.97308
\(245\) 3.80585e15 1.12428
\(246\) −5.48468e15 −1.57788
\(247\) 8.77656e15 2.45920
\(248\) 5.02298e14 0.137096
\(249\) 3.66120e14 0.0973482
\(250\) −4.17217e15 −1.08082
\(251\) 6.52652e15 1.64741 0.823707 0.567016i \(-0.191902\pi\)
0.823707 + 0.567016i \(0.191902\pi\)
\(252\) −4.19086e14 −0.103086
\(253\) −6.09431e15 −1.46097
\(254\) 1.08956e16 2.54585
\(255\) −5.60221e15 −1.27599
\(256\) −1.52522e14 −0.0338667
\(257\) 3.00150e15 0.649789 0.324895 0.945750i \(-0.394671\pi\)
0.324895 + 0.945750i \(0.394671\pi\)
\(258\) 4.74426e15 1.00148
\(259\) 1.27693e15 0.262857
\(260\) −1.24062e16 −2.49064
\(261\) 1.55884e15 0.305237
\(262\) −1.10841e15 −0.211711
\(263\) 3.71597e15 0.692404 0.346202 0.938160i \(-0.387471\pi\)
0.346202 + 0.938160i \(0.387471\pi\)
\(264\) 1.53641e15 0.279307
\(265\) −5.93875e15 −1.05341
\(266\) 3.21172e15 0.555914
\(267\) 2.11094e15 0.356577
\(268\) −1.60003e15 −0.263787
\(269\) 4.47192e15 0.719621 0.359811 0.933025i \(-0.382841\pi\)
0.359811 + 0.933025i \(0.382841\pi\)
\(270\) 2.23042e15 0.350366
\(271\) −4.48733e15 −0.688158 −0.344079 0.938941i \(-0.611809\pi\)
−0.344079 + 0.938941i \(0.611809\pi\)
\(272\) −6.42144e15 −0.961468
\(273\) −1.39334e15 −0.203705
\(274\) 1.99219e16 2.84415
\(275\) −2.57395e15 −0.358871
\(276\) 9.51567e15 1.29578
\(277\) −1.04846e16 −1.39454 −0.697271 0.716807i \(-0.745603\pi\)
−0.697271 + 0.716807i \(0.745603\pi\)
\(278\) −3.35424e15 −0.435816
\(279\) −6.57285e14 −0.0834308
\(280\) −1.19387e15 −0.148057
\(281\) −1.08002e16 −1.30870 −0.654352 0.756190i \(-0.727058\pi\)
−0.654352 + 0.756190i \(0.727058\pi\)
\(282\) −2.63730e15 −0.312277
\(283\) 5.90391e15 0.683169 0.341584 0.939851i \(-0.389037\pi\)
0.341584 + 0.939851i \(0.389037\pi\)
\(284\) 1.03170e16 1.16677
\(285\) −9.84041e15 −1.08773
\(286\) 1.94249e16 2.09884
\(287\) −3.84160e15 −0.405770
\(288\) 4.32469e15 0.446584
\(289\) 2.44961e16 2.47321
\(290\) 1.68869e16 1.66710
\(291\) 1.12619e15 0.108720
\(292\) 1.66605e16 1.57289
\(293\) −1.88698e16 −1.74232 −0.871158 0.491003i \(-0.836630\pi\)
−0.871158 + 0.491003i \(0.836630\pi\)
\(294\) 9.30438e15 0.840291
\(295\) 1.74767e15 0.154389
\(296\) 7.30949e15 0.631671
\(297\) −2.01048e15 −0.169974
\(298\) −1.41362e16 −1.16931
\(299\) 3.16369e16 2.56054
\(300\) 4.01898e15 0.318293
\(301\) 3.32299e15 0.257542
\(302\) −2.55303e16 −1.93647
\(303\) −1.29520e16 −0.961520
\(304\) −1.12794e16 −0.819613
\(305\) −2.42450e16 −1.72454
\(306\) −1.36960e16 −0.953685
\(307\) 1.00079e16 0.682247 0.341123 0.940019i \(-0.389193\pi\)
0.341123 + 0.940019i \(0.389193\pi\)
\(308\) 4.09228e15 0.273140
\(309\) 1.05606e16 0.690171
\(310\) −7.12037e15 −0.455671
\(311\) −1.68400e16 −1.05536 −0.527679 0.849444i \(-0.676938\pi\)
−0.527679 + 0.849444i \(0.676938\pi\)
\(312\) −7.97585e15 −0.489522
\(313\) −6.43117e15 −0.386591 −0.193296 0.981141i \(-0.561918\pi\)
−0.193296 + 0.981141i \(0.561918\pi\)
\(314\) −1.62224e15 −0.0955151
\(315\) 1.56224e15 0.0901008
\(316\) −2.36883e16 −1.33834
\(317\) −1.76534e16 −0.977111 −0.488556 0.872533i \(-0.662476\pi\)
−0.488556 + 0.872533i \(0.662476\pi\)
\(318\) −1.45188e16 −0.787325
\(319\) −1.52217e16 −0.808766
\(320\) 3.50980e16 1.82729
\(321\) −8.21853e15 −0.419287
\(322\) 1.15773e16 0.578822
\(323\) 6.04256e16 2.96077
\(324\) 3.13916e15 0.150755
\(325\) 1.33620e16 0.628968
\(326\) −2.26485e16 −1.04502
\(327\) −2.46714e15 −0.111592
\(328\) −2.19903e16 −0.975104
\(329\) −1.84723e15 −0.0803059
\(330\) −2.17795e16 −0.928341
\(331\) 3.65153e16 1.52613 0.763067 0.646319i \(-0.223693\pi\)
0.763067 + 0.646319i \(0.223693\pi\)
\(332\) 5.58213e15 0.228772
\(333\) −9.56487e15 −0.384407
\(334\) −2.34944e16 −0.926001
\(335\) 5.96449e15 0.230559
\(336\) 1.79069e15 0.0678915
\(337\) −1.46271e16 −0.543956 −0.271978 0.962303i \(-0.587678\pi\)
−0.271978 + 0.962303i \(0.587678\pi\)
\(338\) −5.87548e16 −2.14331
\(339\) −6.31284e15 −0.225906
\(340\) −8.54152e16 −2.99863
\(341\) 6.41823e15 0.221061
\(342\) −2.40574e16 −0.812978
\(343\) 1.33912e16 0.444024
\(344\) 1.90216e16 0.618897
\(345\) −3.54718e16 −1.13256
\(346\) −5.01119e16 −1.57017
\(347\) 4.07037e15 0.125168 0.0625839 0.998040i \(-0.480066\pi\)
0.0625839 + 0.998040i \(0.480066\pi\)
\(348\) 2.37671e16 0.717318
\(349\) 3.81341e16 1.12966 0.564831 0.825207i \(-0.308941\pi\)
0.564831 + 0.825207i \(0.308941\pi\)
\(350\) 4.88972e15 0.142181
\(351\) 1.04368e16 0.297902
\(352\) −4.22295e16 −1.18328
\(353\) 7.20818e15 0.198285 0.0991426 0.995073i \(-0.468390\pi\)
0.0991426 + 0.995073i \(0.468390\pi\)
\(354\) 4.27263e15 0.115392
\(355\) −3.84590e16 −1.01980
\(356\) 3.21849e16 0.837968
\(357\) −9.59302e15 −0.245252
\(358\) −1.72976e16 −0.434256
\(359\) 6.56684e16 1.61898 0.809492 0.587131i \(-0.199743\pi\)
0.809492 + 0.587131i \(0.199743\pi\)
\(360\) 8.94265e15 0.216521
\(361\) 6.40862e16 1.52394
\(362\) 1.15836e17 2.70544
\(363\) −5.53522e15 −0.126982
\(364\) −2.12439e16 −0.478713
\(365\) −6.21057e16 −1.37476
\(366\) −5.92730e16 −1.28893
\(367\) 3.21659e16 0.687174 0.343587 0.939121i \(-0.388358\pi\)
0.343587 + 0.939121i \(0.388358\pi\)
\(368\) −4.06590e16 −0.853387
\(369\) 2.87755e16 0.593406
\(370\) −1.03616e17 −2.09950
\(371\) −1.01693e16 −0.202470
\(372\) −1.00214e16 −0.196065
\(373\) 1.36046e16 0.261565 0.130782 0.991411i \(-0.458251\pi\)
0.130782 + 0.991411i \(0.458251\pi\)
\(374\) 1.33738e17 2.52691
\(375\) 2.18894e16 0.406472
\(376\) −1.05740e16 −0.192983
\(377\) 7.90191e16 1.41747
\(378\) 3.81929e15 0.0673420
\(379\) 2.41382e16 0.418360 0.209180 0.977877i \(-0.432921\pi\)
0.209180 + 0.977877i \(0.432921\pi\)
\(380\) −1.50034e17 −2.55621
\(381\) −5.71641e16 −0.957438
\(382\) 1.89782e16 0.312495
\(383\) 9.00843e16 1.45833 0.729167 0.684335i \(-0.239908\pi\)
0.729167 + 0.684335i \(0.239908\pi\)
\(384\) 3.72082e16 0.592223
\(385\) −1.52549e16 −0.238734
\(386\) −1.36644e17 −2.10267
\(387\) −2.48909e16 −0.376633
\(388\) 1.71707e16 0.255495
\(389\) −2.97279e16 −0.435002 −0.217501 0.976060i \(-0.569791\pi\)
−0.217501 + 0.976060i \(0.569791\pi\)
\(390\) 1.13062e17 1.62704
\(391\) 2.17817e17 3.08278
\(392\) 3.73050e16 0.519287
\(393\) 5.81532e15 0.0796199
\(394\) 6.90423e16 0.929800
\(395\) 8.83034e16 1.16976
\(396\) −3.06532e16 −0.399445
\(397\) −1.34288e17 −1.72147 −0.860736 0.509051i \(-0.829996\pi\)
−0.860736 + 0.509051i \(0.829996\pi\)
\(398\) 7.79303e14 0.00982803
\(399\) −1.68504e16 −0.209067
\(400\) −1.71725e16 −0.209625
\(401\) −2.15972e16 −0.259393 −0.129697 0.991554i \(-0.541400\pi\)
−0.129697 + 0.991554i \(0.541400\pi\)
\(402\) 1.45817e16 0.172321
\(403\) −3.33185e16 −0.387438
\(404\) −1.97475e17 −2.25961
\(405\) −1.17019e16 −0.131765
\(406\) 2.89165e16 0.320425
\(407\) 9.33987e16 1.01854
\(408\) −5.49129e16 −0.589363
\(409\) 3.86915e16 0.408708 0.204354 0.978897i \(-0.434491\pi\)
0.204354 + 0.978897i \(0.434491\pi\)
\(410\) 3.11725e17 3.24098
\(411\) −1.04521e17 −1.06962
\(412\) 1.61014e17 1.62193
\(413\) 2.99265e15 0.0296743
\(414\) −8.67199e16 −0.846480
\(415\) −2.08087e16 −0.199955
\(416\) 2.19223e17 2.07386
\(417\) 1.75981e16 0.163901
\(418\) 2.34915e17 2.15409
\(419\) 9.01511e16 0.813917 0.406958 0.913447i \(-0.366589\pi\)
0.406958 + 0.913447i \(0.366589\pi\)
\(420\) 2.38190e16 0.211740
\(421\) −1.54430e16 −0.135176 −0.0675878 0.997713i \(-0.521530\pi\)
−0.0675878 + 0.997713i \(0.521530\pi\)
\(422\) −5.55381e16 −0.478696
\(423\) 1.38367e16 0.117441
\(424\) −5.82117e16 −0.486555
\(425\) 9.19957e16 0.757251
\(426\) −9.40229e16 −0.762204
\(427\) −4.15163e16 −0.331465
\(428\) −1.25306e17 −0.985340
\(429\) −1.01913e17 −0.789329
\(430\) −2.69643e17 −2.05705
\(431\) −1.21401e17 −0.912266 −0.456133 0.889912i \(-0.650766\pi\)
−0.456133 + 0.889912i \(0.650766\pi\)
\(432\) −1.34132e16 −0.0992858
\(433\) −5.65871e16 −0.412616 −0.206308 0.978487i \(-0.566145\pi\)
−0.206308 + 0.978487i \(0.566145\pi\)
\(434\) −1.21927e16 −0.0875822
\(435\) −8.85974e16 −0.626962
\(436\) −3.76157e16 −0.262245
\(437\) 3.82601e17 2.62795
\(438\) −1.51833e17 −1.02751
\(439\) 2.21807e16 0.147895 0.0739477 0.997262i \(-0.476440\pi\)
0.0739477 + 0.997262i \(0.476440\pi\)
\(440\) −8.73228e16 −0.573701
\(441\) −4.88157e16 −0.316016
\(442\) −6.94266e17 −4.42875
\(443\) 7.82941e15 0.0492158 0.0246079 0.999697i \(-0.492166\pi\)
0.0246079 + 0.999697i \(0.492166\pi\)
\(444\) −1.45833e17 −0.903371
\(445\) −1.19977e17 −0.732414
\(446\) 4.07256e17 2.45014
\(447\) 7.41662e16 0.439751
\(448\) 6.01006e16 0.351214
\(449\) 2.55848e17 1.47361 0.736803 0.676107i \(-0.236334\pi\)
0.736803 + 0.676107i \(0.236334\pi\)
\(450\) −3.66265e16 −0.207928
\(451\) −2.80986e17 −1.57231
\(452\) −9.62501e16 −0.530886
\(453\) 1.33945e17 0.728265
\(454\) 1.49693e17 0.802306
\(455\) 7.91915e16 0.418412
\(456\) −9.64558e16 −0.502408
\(457\) −9.76623e16 −0.501501 −0.250751 0.968052i \(-0.580677\pi\)
−0.250751 + 0.968052i \(0.580677\pi\)
\(458\) 3.47312e17 1.75831
\(459\) 7.18565e16 0.358661
\(460\) −5.40829e17 −2.66155
\(461\) 9.01704e16 0.437530 0.218765 0.975778i \(-0.429797\pi\)
0.218765 + 0.975778i \(0.429797\pi\)
\(462\) −3.72945e16 −0.178431
\(463\) 4.03703e17 1.90452 0.952260 0.305288i \(-0.0987528\pi\)
0.952260 + 0.305288i \(0.0987528\pi\)
\(464\) −1.01553e17 −0.472420
\(465\) 3.73572e16 0.171368
\(466\) 4.03165e17 1.82379
\(467\) −4.66211e16 −0.207980 −0.103990 0.994578i \(-0.533161\pi\)
−0.103990 + 0.994578i \(0.533161\pi\)
\(468\) 1.59127e17 0.700079
\(469\) 1.02134e16 0.0443145
\(470\) 1.49893e17 0.641422
\(471\) 8.51112e15 0.0359212
\(472\) 1.71307e16 0.0713103
\(473\) 2.43053e17 0.997940
\(474\) 2.15880e17 0.874286
\(475\) 1.61593e17 0.645526
\(476\) −1.46262e17 −0.576350
\(477\) 7.61732e16 0.296096
\(478\) −6.36585e17 −2.44104
\(479\) −3.28090e17 −1.24111 −0.620557 0.784161i \(-0.713093\pi\)
−0.620557 + 0.784161i \(0.713093\pi\)
\(480\) −2.45796e17 −0.917291
\(481\) −4.84853e17 −1.78512
\(482\) −5.92221e17 −2.15118
\(483\) −6.07407e16 −0.217682
\(484\) −8.43939e16 −0.298412
\(485\) −6.40078e16 −0.223312
\(486\) −2.86084e16 −0.0984822
\(487\) −1.00806e17 −0.342410 −0.171205 0.985235i \(-0.554766\pi\)
−0.171205 + 0.985235i \(0.554766\pi\)
\(488\) −2.37650e17 −0.796541
\(489\) 1.18826e17 0.393010
\(490\) −5.28820e17 −1.72597
\(491\) −4.60172e17 −1.48214 −0.741072 0.671426i \(-0.765682\pi\)
−0.741072 + 0.671426i \(0.765682\pi\)
\(492\) 4.38732e17 1.39452
\(493\) 5.44038e17 1.70657
\(494\) −1.21949e18 −3.77533
\(495\) 1.14267e17 0.349129
\(496\) 4.28201e16 0.129127
\(497\) −6.58559e16 −0.196010
\(498\) −5.08721e16 −0.149448
\(499\) −2.88208e17 −0.835704 −0.417852 0.908515i \(-0.637217\pi\)
−0.417852 + 0.908515i \(0.637217\pi\)
\(500\) 3.33741e17 0.955224
\(501\) 1.23264e17 0.348249
\(502\) −9.06854e17 −2.52908
\(503\) 9.44084e16 0.259907 0.129954 0.991520i \(-0.458517\pi\)
0.129954 + 0.991520i \(0.458517\pi\)
\(504\) 1.53131e16 0.0416163
\(505\) 7.36132e17 1.97498
\(506\) 8.46799e17 2.24286
\(507\) 3.08258e17 0.806052
\(508\) −8.71564e17 −2.25001
\(509\) −3.43197e16 −0.0874737 −0.0437369 0.999043i \(-0.513926\pi\)
−0.0437369 + 0.999043i \(0.513926\pi\)
\(510\) 7.78421e17 1.95888
\(511\) −1.06348e17 −0.264236
\(512\) −3.96927e17 −0.973769
\(513\) 1.26218e17 0.305744
\(514\) −4.17055e17 −0.997547
\(515\) −6.00216e17 −1.41762
\(516\) −3.79504e17 −0.885102
\(517\) −1.35112e17 −0.311175
\(518\) −1.77429e17 −0.403535
\(519\) 2.62913e17 0.590507
\(520\) 4.53312e17 1.00549
\(521\) −3.51007e17 −0.768900 −0.384450 0.923146i \(-0.625609\pi\)
−0.384450 + 0.923146i \(0.625609\pi\)
\(522\) −2.16599e17 −0.468596
\(523\) −8.27856e17 −1.76886 −0.884431 0.466671i \(-0.845453\pi\)
−0.884431 + 0.466671i \(0.845453\pi\)
\(524\) 8.86645e16 0.187110
\(525\) −2.56541e16 −0.0534713
\(526\) −5.16330e17 −1.06297
\(527\) −2.29394e17 −0.466459
\(528\) 1.30976e17 0.263071
\(529\) 8.75128e17 1.73624
\(530\) 8.25184e17 1.61718
\(531\) −2.24165e16 −0.0433963
\(532\) −2.56913e17 −0.491315
\(533\) 1.45866e18 2.75567
\(534\) −2.93313e17 −0.547411
\(535\) 4.67105e17 0.861222
\(536\) 5.84640e16 0.106492
\(537\) 9.07523e16 0.163314
\(538\) −6.21369e17 −1.10475
\(539\) 4.76673e17 0.837325
\(540\) −1.78416e17 −0.309653
\(541\) −3.57711e17 −0.613409 −0.306704 0.951805i \(-0.599226\pi\)
−0.306704 + 0.951805i \(0.599226\pi\)
\(542\) 6.23511e17 1.05645
\(543\) −6.07738e17 −1.01746
\(544\) 1.50933e18 2.49684
\(545\) 1.40221e17 0.229211
\(546\) 1.93604e17 0.312724
\(547\) −1.74264e17 −0.278157 −0.139079 0.990281i \(-0.544414\pi\)
−0.139079 + 0.990281i \(0.544414\pi\)
\(548\) −1.59360e18 −2.51365
\(549\) 3.10978e17 0.484740
\(550\) 3.57649e17 0.550934
\(551\) 9.55616e17 1.45478
\(552\) −3.47695e17 −0.523112
\(553\) 1.51208e17 0.224833
\(554\) 1.45682e18 2.14088
\(555\) 5.43625e17 0.789578
\(556\) 2.68314e17 0.385173
\(557\) 6.12253e16 0.0868704 0.0434352 0.999056i \(-0.486170\pi\)
0.0434352 + 0.999056i \(0.486170\pi\)
\(558\) 9.13292e16 0.128082
\(559\) −1.26174e18 −1.74902
\(560\) −1.01775e17 −0.139450
\(561\) −7.01662e17 −0.950318
\(562\) 1.50068e18 2.00910
\(563\) −4.31503e16 −0.0571057 −0.0285528 0.999592i \(-0.509090\pi\)
−0.0285528 + 0.999592i \(0.509090\pi\)
\(564\) 2.10964e17 0.275990
\(565\) 3.58794e17 0.464013
\(566\) −8.20343e17 −1.04879
\(567\) −2.00380e16 −0.0253259
\(568\) −3.76976e17 −0.471031
\(569\) 1.29788e17 0.160326 0.0801632 0.996782i \(-0.474456\pi\)
0.0801632 + 0.996782i \(0.474456\pi\)
\(570\) 1.36732e18 1.66987
\(571\) −9.58576e17 −1.15742 −0.578711 0.815533i \(-0.696444\pi\)
−0.578711 + 0.815533i \(0.696444\pi\)
\(572\) −1.55384e18 −1.85495
\(573\) −9.95695e16 −0.117523
\(574\) 5.33787e17 0.622932
\(575\) 5.82495e17 0.672127
\(576\) −4.50183e17 −0.513622
\(577\) 1.44548e18 1.63068 0.815339 0.578984i \(-0.196551\pi\)
0.815339 + 0.578984i \(0.196551\pi\)
\(578\) −3.40371e18 −3.79684
\(579\) 7.16904e17 0.790770
\(580\) −1.35082e18 −1.47338
\(581\) −3.56320e16 −0.0384322
\(582\) −1.56483e17 −0.166905
\(583\) −7.43813e17 −0.784545
\(584\) −6.08760e17 −0.634984
\(585\) −5.93184e17 −0.611894
\(586\) 2.62194e18 2.67478
\(587\) −4.85405e17 −0.489730 −0.244865 0.969557i \(-0.578744\pi\)
−0.244865 + 0.969557i \(0.578744\pi\)
\(588\) −7.44279e17 −0.742648
\(589\) −4.02937e17 −0.397637
\(590\) −2.42838e17 −0.237016
\(591\) −3.62232e17 −0.349678
\(592\) 6.23122e17 0.594952
\(593\) −1.12161e17 −0.105922 −0.0529612 0.998597i \(-0.516866\pi\)
−0.0529612 + 0.998597i \(0.516866\pi\)
\(594\) 2.79354e17 0.260941
\(595\) 5.45225e17 0.503751
\(596\) 1.13079e18 1.03343
\(597\) −4.08863e15 −0.00369611
\(598\) −4.39592e18 −3.93090
\(599\) 9.43281e17 0.834386 0.417193 0.908818i \(-0.363014\pi\)
0.417193 + 0.908818i \(0.363014\pi\)
\(600\) −1.46850e17 −0.128497
\(601\) −2.15525e18 −1.86558 −0.932789 0.360422i \(-0.882633\pi\)
−0.932789 + 0.360422i \(0.882633\pi\)
\(602\) −4.61727e17 −0.395374
\(603\) −7.65033e16 −0.0648064
\(604\) 2.04223e18 1.71145
\(605\) 3.14598e17 0.260823
\(606\) 1.79966e18 1.47611
\(607\) −1.05989e18 −0.860068 −0.430034 0.902813i \(-0.641498\pi\)
−0.430034 + 0.902813i \(0.641498\pi\)
\(608\) 2.65117e18 2.12845
\(609\) −1.51711e17 −0.120505
\(610\) 3.36882e18 2.64749
\(611\) 7.01395e17 0.545374
\(612\) 1.09558e18 0.842865
\(613\) −1.04123e18 −0.792601 −0.396300 0.918121i \(-0.629706\pi\)
−0.396300 + 0.918121i \(0.629706\pi\)
\(614\) −1.39058e18 −1.04738
\(615\) −1.63547e18 −1.21886
\(616\) −1.49529e17 −0.110268
\(617\) −1.32142e18 −0.964245 −0.482123 0.876104i \(-0.660134\pi\)
−0.482123 + 0.876104i \(0.660134\pi\)
\(618\) −1.46738e18 −1.05954
\(619\) 1.24518e18 0.889701 0.444850 0.895605i \(-0.353257\pi\)
0.444850 + 0.895605i \(0.353257\pi\)
\(620\) 5.69575e17 0.402721
\(621\) 4.54978e17 0.318343
\(622\) 2.33990e18 1.62017
\(623\) −2.05444e17 −0.140773
\(624\) −6.79928e17 −0.461066
\(625\) −1.84957e18 −1.24123
\(626\) 8.93606e17 0.593489
\(627\) −1.23249e18 −0.810108
\(628\) 1.29767e17 0.0844161
\(629\) −3.33816e18 −2.14921
\(630\) −2.17072e17 −0.138321
\(631\) 2.50990e18 1.58295 0.791473 0.611204i \(-0.209314\pi\)
0.791473 + 0.611204i \(0.209314\pi\)
\(632\) 8.65551e17 0.540296
\(633\) 2.91382e17 0.180027
\(634\) 2.45293e18 1.50005
\(635\) 3.24895e18 1.96659
\(636\) 1.16139e18 0.695836
\(637\) −2.47452e18 −1.46752
\(638\) 2.11504e18 1.24161
\(639\) 4.93293e17 0.286649
\(640\) −2.11475e18 −1.21643
\(641\) 7.47974e17 0.425902 0.212951 0.977063i \(-0.431693\pi\)
0.212951 + 0.977063i \(0.431693\pi\)
\(642\) 1.14196e18 0.643683
\(643\) 4.39565e17 0.245274 0.122637 0.992452i \(-0.460865\pi\)
0.122637 + 0.992452i \(0.460865\pi\)
\(644\) −9.26096e17 −0.511562
\(645\) 1.41469e18 0.773611
\(646\) −8.39609e18 −4.54533
\(647\) 1.42137e18 0.761780 0.380890 0.924620i \(-0.375618\pi\)
0.380890 + 0.924620i \(0.375618\pi\)
\(648\) −1.14703e17 −0.0608605
\(649\) 2.18891e17 0.114984
\(650\) −1.85663e18 −0.965583
\(651\) 6.39692e16 0.0329378
\(652\) 1.81171e18 0.923588
\(653\) −8.42454e17 −0.425217 −0.212609 0.977137i \(-0.568196\pi\)
−0.212609 + 0.977137i \(0.568196\pi\)
\(654\) 3.42806e17 0.171314
\(655\) −3.30517e17 −0.163541
\(656\) −1.87464e18 −0.918422
\(657\) 7.96596e17 0.386423
\(658\) 2.56671e17 0.123284
\(659\) 2.67379e18 1.27166 0.635831 0.771829i \(-0.280658\pi\)
0.635831 + 0.771829i \(0.280658\pi\)
\(660\) 1.74219e18 0.820466
\(661\) 2.15043e18 1.00280 0.501401 0.865215i \(-0.332818\pi\)
0.501401 + 0.865215i \(0.332818\pi\)
\(662\) −5.07377e18 −2.34290
\(663\) 3.64248e18 1.66556
\(664\) −2.03967e17 −0.0923563
\(665\) 9.57701e17 0.429427
\(666\) 1.32903e18 0.590136
\(667\) 3.44472e18 1.51473
\(668\) 1.87937e18 0.818398
\(669\) −2.13668e18 −0.921444
\(670\) −8.28760e17 −0.353951
\(671\) −3.03662e18 −1.28438
\(672\) −4.20893e17 −0.176308
\(673\) 3.45008e18 1.43130 0.715652 0.698457i \(-0.246130\pi\)
0.715652 + 0.698457i \(0.246130\pi\)
\(674\) 2.03242e18 0.835074
\(675\) 1.92162e17 0.0781974
\(676\) 4.69993e18 1.89425
\(677\) 2.80155e18 1.11834 0.559168 0.829054i \(-0.311121\pi\)
0.559168 + 0.829054i \(0.311121\pi\)
\(678\) 8.77164e17 0.346807
\(679\) −1.09605e17 −0.0429216
\(680\) 3.12101e18 1.21056
\(681\) −7.85371e17 −0.301730
\(682\) −8.91808e17 −0.339370
\(683\) 3.34878e18 1.26227 0.631135 0.775673i \(-0.282589\pi\)
0.631135 + 0.775673i \(0.282589\pi\)
\(684\) 1.92441e18 0.718509
\(685\) 5.94050e18 2.19702
\(686\) −1.86069e18 −0.681659
\(687\) −1.82218e18 −0.661261
\(688\) 1.62156e18 0.582921
\(689\) 3.86130e18 1.37502
\(690\) 4.92878e18 1.73868
\(691\) −4.63969e18 −1.62137 −0.810684 0.585484i \(-0.800905\pi\)
−0.810684 + 0.585484i \(0.800905\pi\)
\(692\) 4.00857e18 1.38771
\(693\) 1.95666e17 0.0671043
\(694\) −5.65575e17 −0.192156
\(695\) −1.00020e18 −0.336655
\(696\) −8.68433e17 −0.289585
\(697\) 1.00427e19 3.31771
\(698\) −5.29870e18 −1.73424
\(699\) −2.11522e18 −0.685888
\(700\) −3.91140e17 −0.125659
\(701\) 1.36370e18 0.434062 0.217031 0.976165i \(-0.430363\pi\)
0.217031 + 0.976165i \(0.430363\pi\)
\(702\) −1.45019e18 −0.457334
\(703\) −5.86357e18 −1.83211
\(704\) 4.39593e18 1.36091
\(705\) −7.86415e17 −0.241225
\(706\) −1.00157e18 −0.304404
\(707\) 1.26053e18 0.379600
\(708\) −3.41777e17 −0.101983
\(709\) −2.65012e18 −0.783548 −0.391774 0.920061i \(-0.628138\pi\)
−0.391774 + 0.920061i \(0.628138\pi\)
\(710\) 5.34385e18 1.56558
\(711\) −1.13262e18 −0.328800
\(712\) −1.17601e18 −0.338292
\(713\) −1.45247e18 −0.414023
\(714\) 1.33294e18 0.376507
\(715\) 5.79230e18 1.62129
\(716\) 1.38367e18 0.383795
\(717\) 3.33986e18 0.918023
\(718\) −9.12456e18 −2.48544
\(719\) −5.97402e18 −1.61261 −0.806305 0.591500i \(-0.798536\pi\)
−0.806305 + 0.591500i \(0.798536\pi\)
\(720\) 7.62346e17 0.203935
\(721\) −1.02779e18 −0.272474
\(722\) −8.90472e18 −2.33953
\(723\) 3.10710e18 0.809014
\(724\) −9.26600e18 −2.39107
\(725\) 1.45489e18 0.372077
\(726\) 7.69114e17 0.194941
\(727\) −1.37966e17 −0.0346576 −0.0173288 0.999850i \(-0.505516\pi\)
−0.0173288 + 0.999850i \(0.505516\pi\)
\(728\) 7.76236e17 0.193259
\(729\) 1.50095e17 0.0370370
\(730\) 8.62953e18 2.11051
\(731\) −8.68698e18 −2.10574
\(732\) 4.74139e18 1.13916
\(733\) 6.64805e18 1.58314 0.791568 0.611081i \(-0.209265\pi\)
0.791568 + 0.611081i \(0.209265\pi\)
\(734\) −4.46943e18 −1.05494
\(735\) 2.77447e18 0.649101
\(736\) 9.55669e18 2.21616
\(737\) 7.47037e17 0.171713
\(738\) −3.99833e18 −0.910988
\(739\) −1.06037e18 −0.239480 −0.119740 0.992805i \(-0.538206\pi\)
−0.119740 + 0.992805i \(0.538206\pi\)
\(740\) 8.28850e18 1.85554
\(741\) 6.39811e18 1.41982
\(742\) 1.41302e18 0.310829
\(743\) 7.25562e18 1.58215 0.791074 0.611721i \(-0.209522\pi\)
0.791074 + 0.611721i \(0.209522\pi\)
\(744\) 3.66176e17 0.0791526
\(745\) −4.21528e18 −0.903255
\(746\) −1.89035e18 −0.401550
\(747\) 2.66902e17 0.0562040
\(748\) −1.06980e19 −2.23328
\(749\) 7.99855e17 0.165531
\(750\) −3.04151e18 −0.624010
\(751\) 8.39096e18 1.70668 0.853340 0.521356i \(-0.174573\pi\)
0.853340 + 0.521356i \(0.174573\pi\)
\(752\) −9.01416e17 −0.181765
\(753\) 4.75783e18 0.951134
\(754\) −1.09796e19 −2.17608
\(755\) −7.61287e18 −1.49587
\(756\) −3.05514e17 −0.0595167
\(757\) −7.30335e17 −0.141058 −0.0705292 0.997510i \(-0.522469\pi\)
−0.0705292 + 0.997510i \(0.522469\pi\)
\(758\) −3.35398e18 −0.642259
\(759\) −4.44275e18 −0.843491
\(760\) 5.48212e18 1.03195
\(761\) −1.96604e18 −0.366937 −0.183469 0.983026i \(-0.558733\pi\)
−0.183469 + 0.983026i \(0.558733\pi\)
\(762\) 7.94290e18 1.46985
\(763\) 2.40110e17 0.0440555
\(764\) −1.51811e18 −0.276182
\(765\) −4.08401e18 −0.736694
\(766\) −1.25171e19 −2.23881
\(767\) −1.13631e18 −0.201525
\(768\) −1.11189e17 −0.0195530
\(769\) −3.49818e18 −0.609988 −0.304994 0.952354i \(-0.598654\pi\)
−0.304994 + 0.952354i \(0.598654\pi\)
\(770\) 2.11965e18 0.366501
\(771\) 2.18809e18 0.375156
\(772\) 1.09304e19 1.85834
\(773\) 1.14812e19 1.93562 0.967809 0.251687i \(-0.0809854\pi\)
0.967809 + 0.251687i \(0.0809854\pi\)
\(774\) 3.45857e18 0.578202
\(775\) −6.13455e17 −0.101700
\(776\) −6.27405e17 −0.103145
\(777\) 9.30885e17 0.151761
\(778\) 4.13066e18 0.667809
\(779\) 1.76403e19 2.82821
\(780\) −9.04411e18 −1.43797
\(781\) −4.81689e18 −0.759513
\(782\) −3.02655e19 −4.73264
\(783\) 1.13639e18 0.176229
\(784\) 3.18019e18 0.489101
\(785\) −4.83734e17 −0.0737826
\(786\) −8.08033e17 −0.122231
\(787\) −9.59380e18 −1.43931 −0.719656 0.694331i \(-0.755700\pi\)
−0.719656 + 0.694331i \(0.755700\pi\)
\(788\) −5.52285e18 −0.821756
\(789\) 2.70894e18 0.399759
\(790\) −1.22697e19 −1.79580
\(791\) 6.14387e17 0.0891856
\(792\) 1.12004e18 0.161258
\(793\) 1.57638e19 2.25105
\(794\) 1.86592e19 2.64278
\(795\) −4.32935e18 −0.608186
\(796\) −6.23382e16 −0.00868599
\(797\) −6.90283e18 −0.953999 −0.476999 0.878904i \(-0.658276\pi\)
−0.476999 + 0.878904i \(0.658276\pi\)
\(798\) 2.34135e18 0.320957
\(799\) 4.82903e18 0.656607
\(800\) 4.03630e18 0.544376
\(801\) 1.53888e18 0.205870
\(802\) 3.00091e18 0.398217
\(803\) −7.77857e18 −1.02388
\(804\) −1.16642e18 −0.152297
\(805\) 3.45223e18 0.447123
\(806\) 4.62957e18 0.594789
\(807\) 3.26003e18 0.415474
\(808\) 7.21557e18 0.912215
\(809\) −1.20433e19 −1.51035 −0.755176 0.655522i \(-0.772449\pi\)
−0.755176 + 0.655522i \(0.772449\pi\)
\(810\) 1.62597e18 0.202284
\(811\) −4.40733e18 −0.543927 −0.271963 0.962308i \(-0.587673\pi\)
−0.271963 + 0.962308i \(0.587673\pi\)
\(812\) −2.31310e18 −0.283191
\(813\) −3.27127e18 −0.397308
\(814\) −1.29777e19 −1.56364
\(815\) −6.75355e18 −0.807249
\(816\) −4.68123e18 −0.555104
\(817\) −1.52589e19 −1.79506
\(818\) −5.37614e18 −0.627443
\(819\) −1.01575e18 −0.117609
\(820\) −2.49356e19 −2.86437
\(821\) 1.01852e19 1.16075 0.580373 0.814351i \(-0.302907\pi\)
0.580373 + 0.814351i \(0.302907\pi\)
\(822\) 1.45231e19 1.64207
\(823\) −1.33841e19 −1.50137 −0.750687 0.660658i \(-0.770277\pi\)
−0.750687 + 0.660658i \(0.770277\pi\)
\(824\) −5.88332e18 −0.654780
\(825\) −1.87641e18 −0.207194
\(826\) −4.15826e17 −0.0455556
\(827\) −4.64686e18 −0.505096 −0.252548 0.967584i \(-0.581269\pi\)
−0.252548 + 0.967584i \(0.581269\pi\)
\(828\) 6.93692e18 0.748117
\(829\) −1.17913e19 −1.26170 −0.630850 0.775905i \(-0.717294\pi\)
−0.630850 + 0.775905i \(0.717294\pi\)
\(830\) 2.89134e18 0.306967
\(831\) −7.64325e18 −0.805140
\(832\) −2.28203e19 −2.38517
\(833\) −1.70368e19 −1.76683
\(834\) −2.44524e18 −0.251619
\(835\) −7.00577e18 −0.715309
\(836\) −1.87914e19 −1.90378
\(837\) −4.79161e17 −0.0481688
\(838\) −1.25264e19 −1.24951
\(839\) 1.84904e19 1.83018 0.915090 0.403250i \(-0.132120\pi\)
0.915090 + 0.403250i \(0.132120\pi\)
\(840\) −8.70328e17 −0.0854806
\(841\) −1.65681e18 −0.161473
\(842\) 2.14579e18 0.207519
\(843\) −7.87335e18 −0.755580
\(844\) 4.44262e18 0.423071
\(845\) −1.75201e19 −1.65564
\(846\) −1.92259e18 −0.180293
\(847\) 5.38706e17 0.0501314
\(848\) −4.96245e18 −0.458272
\(849\) 4.30395e18 0.394428
\(850\) −1.27827e19 −1.16252
\(851\) −2.11365e19 −1.90761
\(852\) 7.52110e18 0.673634
\(853\) 1.44059e19 1.28047 0.640237 0.768177i \(-0.278836\pi\)
0.640237 + 0.768177i \(0.278836\pi\)
\(854\) 5.76865e18 0.508859
\(855\) −7.17366e18 −0.628002
\(856\) 4.57857e18 0.397787
\(857\) −2.08680e19 −1.79931 −0.899656 0.436600i \(-0.856182\pi\)
−0.899656 + 0.436600i \(0.856182\pi\)
\(858\) 1.41608e19 1.21177
\(859\) 1.98253e18 0.168370 0.0841849 0.996450i \(-0.473171\pi\)
0.0841849 + 0.996450i \(0.473171\pi\)
\(860\) 2.15693e19 1.81801
\(861\) −2.80053e18 −0.234271
\(862\) 1.68686e19 1.40050
\(863\) 1.29868e19 1.07012 0.535060 0.844814i \(-0.320289\pi\)
0.535060 + 0.844814i \(0.320289\pi\)
\(864\) 3.15270e18 0.257836
\(865\) −1.49428e19 −1.21291
\(866\) 7.86273e18 0.633442
\(867\) 1.78577e19 1.42791
\(868\) 9.75320e17 0.0774050
\(869\) 1.10598e19 0.871199
\(870\) 1.23105e19 0.962502
\(871\) −3.87803e18 −0.300949
\(872\) 1.37445e18 0.105870
\(873\) 8.20994e17 0.0627693
\(874\) −5.31620e19 −4.03438
\(875\) −2.13035e18 −0.160472
\(876\) 1.21455e19 0.908109
\(877\) 1.98747e18 0.147504 0.0737519 0.997277i \(-0.476503\pi\)
0.0737519 + 0.997277i \(0.476503\pi\)
\(878\) −3.08198e18 −0.227047
\(879\) −1.37561e19 −1.00593
\(880\) −7.44413e18 −0.540352
\(881\) 1.97321e19 1.42177 0.710887 0.703306i \(-0.248294\pi\)
0.710887 + 0.703306i \(0.248294\pi\)
\(882\) 6.78289e18 0.485142
\(883\) 8.30718e18 0.589806 0.294903 0.955527i \(-0.404713\pi\)
0.294903 + 0.955527i \(0.404713\pi\)
\(884\) 5.55359e19 3.91412
\(885\) 1.27405e18 0.0891366
\(886\) −1.08789e18 −0.0755554
\(887\) −1.77383e19 −1.22295 −0.611475 0.791264i \(-0.709424\pi\)
−0.611475 + 0.791264i \(0.709424\pi\)
\(888\) 5.32862e18 0.364695
\(889\) 5.56340e18 0.377988
\(890\) 1.66706e19 1.12439
\(891\) −1.46564e18 −0.0981345
\(892\) −3.25773e19 −2.16543
\(893\) 8.48231e18 0.559731
\(894\) −1.03053e19 −0.675099
\(895\) −5.15796e18 −0.335450
\(896\) −3.62122e18 −0.233805
\(897\) 2.30633e19 1.47833
\(898\) −3.55499e19 −2.26226
\(899\) −3.62781e18 −0.229196
\(900\) 2.92983e18 0.183767
\(901\) 2.65846e19 1.65546
\(902\) 3.90428e19 2.41378
\(903\) 2.42246e18 0.148692
\(904\) 3.51690e18 0.214321
\(905\) 3.45411e19 2.08988
\(906\) −1.86116e19 −1.11802
\(907\) −1.26981e19 −0.757344 −0.378672 0.925531i \(-0.623619\pi\)
−0.378672 + 0.925531i \(0.623619\pi\)
\(908\) −1.19743e19 −0.709076
\(909\) −9.44198e18 −0.555134
\(910\) −1.10036e19 −0.642341
\(911\) −7.29103e18 −0.422590 −0.211295 0.977422i \(-0.567768\pi\)
−0.211295 + 0.977422i \(0.567768\pi\)
\(912\) −8.22270e18 −0.473204
\(913\) −2.60623e18 −0.148920
\(914\) 1.35701e19 0.769897
\(915\) −1.76746e19 −0.995663
\(916\) −2.77823e19 −1.55399
\(917\) −5.65966e17 −0.0314333
\(918\) −9.98440e18 −0.550610
\(919\) −2.66229e19 −1.45782 −0.728911 0.684608i \(-0.759973\pi\)
−0.728911 + 0.684608i \(0.759973\pi\)
\(920\) 1.97615e19 1.07448
\(921\) 7.29573e18 0.393895
\(922\) −1.25291e19 −0.671689
\(923\) 2.50056e19 1.33115
\(924\) 2.98327e18 0.157697
\(925\) −8.92706e18 −0.468584
\(926\) −5.60942e19 −2.92379
\(927\) 7.69865e18 0.398471
\(928\) 2.38696e19 1.22683
\(929\) −3.20490e19 −1.63573 −0.817866 0.575409i \(-0.804843\pi\)
−0.817866 + 0.575409i \(0.804843\pi\)
\(930\) −5.19075e18 −0.263082
\(931\) −2.99255e19 −1.50615
\(932\) −3.22501e19 −1.61186
\(933\) −1.22764e19 −0.609311
\(934\) 6.47796e18 0.319288
\(935\) 3.98794e19 1.95197
\(936\) −5.81439e18 −0.282626
\(937\) 2.05096e19 0.990032 0.495016 0.868884i \(-0.335162\pi\)
0.495016 + 0.868884i \(0.335162\pi\)
\(938\) −1.41914e18 −0.0680310
\(939\) −4.68833e18 −0.223199
\(940\) −1.19902e19 −0.566888
\(941\) 2.23551e19 1.04965 0.524824 0.851211i \(-0.324131\pi\)
0.524824 + 0.851211i \(0.324131\pi\)
\(942\) −1.18261e18 −0.0551457
\(943\) 6.35881e19 2.94476
\(944\) 1.46036e18 0.0671650
\(945\) 1.13887e18 0.0520197
\(946\) −3.37721e19 −1.53202
\(947\) −7.36937e18 −0.332013 −0.166007 0.986125i \(-0.553087\pi\)
−0.166007 + 0.986125i \(0.553087\pi\)
\(948\) −1.72687e19 −0.772692
\(949\) 4.03803e19 1.79448
\(950\) −2.24532e19 −0.991002
\(951\) −1.28694e19 −0.564136
\(952\) 5.34430e18 0.232676
\(953\) −2.53079e19 −1.09434 −0.547170 0.837022i \(-0.684295\pi\)
−0.547170 + 0.837022i \(0.684295\pi\)
\(954\) −1.05842e19 −0.454562
\(955\) 5.65909e18 0.241393
\(956\) 5.09218e19 2.15739
\(957\) −1.10966e19 −0.466941
\(958\) 4.55878e19 1.90534
\(959\) 1.01723e19 0.422278
\(960\) 2.55864e19 1.05499
\(961\) −2.28879e19 −0.937354
\(962\) 6.73700e19 2.74049
\(963\) −5.99131e18 −0.242076
\(964\) 4.73731e19 1.90121
\(965\) −4.07457e19 −1.62425
\(966\) 8.43987e18 0.334183
\(967\) −1.05027e19 −0.413075 −0.206538 0.978439i \(-0.566220\pi\)
−0.206538 + 0.978439i \(0.566220\pi\)
\(968\) 3.08369e18 0.120470
\(969\) 4.40503e19 1.70940
\(970\) 8.89382e18 0.342825
\(971\) −2.74594e19 −1.05140 −0.525698 0.850671i \(-0.676196\pi\)
−0.525698 + 0.850671i \(0.676196\pi\)
\(972\) 2.28845e18 0.0870384
\(973\) −1.71271e18 −0.0647068
\(974\) 1.40068e19 0.525663
\(975\) 9.74088e18 0.363135
\(976\) −2.02592e19 −0.750238
\(977\) 1.41607e19 0.520918 0.260459 0.965485i \(-0.416126\pi\)
0.260459 + 0.965485i \(0.416126\pi\)
\(978\) −1.65108e19 −0.603343
\(979\) −1.50268e19 −0.545479
\(980\) 4.23015e19 1.52541
\(981\) −1.79854e18 −0.0644276
\(982\) 6.39405e19 2.27537
\(983\) 2.85506e19 1.00929 0.504647 0.863326i \(-0.331623\pi\)
0.504647 + 0.863326i \(0.331623\pi\)
\(984\) −1.60309e19 −0.562977
\(985\) 2.05877e19 0.718244
\(986\) −7.55936e19 −2.61990
\(987\) −1.34663e18 −0.0463646
\(988\) 9.75502e19 3.33663
\(989\) −5.50039e19 −1.86903
\(990\) −1.58773e19 −0.535978
\(991\) −9.64838e18 −0.323576 −0.161788 0.986826i \(-0.551726\pi\)
−0.161788 + 0.986826i \(0.551726\pi\)
\(992\) −1.00646e19 −0.335330
\(993\) 2.66196e19 0.881114
\(994\) 9.15062e18 0.300912
\(995\) 2.32380e17 0.00759187
\(996\) 4.06937e18 0.132081
\(997\) −1.29828e19 −0.418650 −0.209325 0.977846i \(-0.567127\pi\)
−0.209325 + 0.977846i \(0.567127\pi\)
\(998\) 4.00462e19 1.28296
\(999\) −6.97279e18 −0.221938
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.1.3 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.3 31 1.1 even 1 trivial