Properties

Label 177.12.a.d.1.4
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-67.4662 q^{2} +243.000 q^{3} +2503.69 q^{4} -169.543 q^{5} -16394.3 q^{6} +65772.9 q^{7} -30743.5 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-67.4662 q^{2} +243.000 q^{3} +2503.69 q^{4} -169.543 q^{5} -16394.3 q^{6} +65772.9 q^{7} -30743.5 q^{8} +59049.0 q^{9} +11438.4 q^{10} -851602. q^{11} +608396. q^{12} -64569.7 q^{13} -4.43745e6 q^{14} -41198.8 q^{15} -3.05340e6 q^{16} +4.48109e6 q^{17} -3.98381e6 q^{18} -8.64046e6 q^{19} -424482. q^{20} +1.59828e7 q^{21} +5.74544e7 q^{22} -8.74923e6 q^{23} -7.47068e6 q^{24} -4.87994e7 q^{25} +4.35627e6 q^{26} +1.43489e7 q^{27} +1.64675e8 q^{28} +1.62922e8 q^{29} +2.77953e6 q^{30} -2.58081e8 q^{31} +2.68964e8 q^{32} -2.06939e8 q^{33} -3.02322e8 q^{34} -1.11513e7 q^{35} +1.47840e8 q^{36} +6.12752e7 q^{37} +5.82939e8 q^{38} -1.56904e7 q^{39} +5.21234e6 q^{40} +1.09619e9 q^{41} -1.07830e9 q^{42} +2.73022e8 q^{43} -2.13215e9 q^{44} -1.00113e7 q^{45} +5.90277e8 q^{46} +2.85354e8 q^{47} -7.41977e8 q^{48} +2.34875e9 q^{49} +3.29231e9 q^{50} +1.08890e9 q^{51} -1.61662e8 q^{52} +3.57388e9 q^{53} -9.68066e8 q^{54} +1.44383e8 q^{55} -2.02209e9 q^{56} -2.09963e9 q^{57} -1.09917e10 q^{58} +7.14924e8 q^{59} -1.03149e8 q^{60} -5.00064e9 q^{61} +1.74117e10 q^{62} +3.88382e9 q^{63} -1.18926e10 q^{64} +1.09473e7 q^{65} +1.39614e10 q^{66} +1.14088e10 q^{67} +1.12192e10 q^{68} -2.12606e9 q^{69} +7.52336e8 q^{70} +1.70442e10 q^{71} -1.81538e9 q^{72} -1.15800e9 q^{73} -4.13400e9 q^{74} -1.18582e10 q^{75} -2.16330e10 q^{76} -5.60123e10 q^{77} +1.05857e9 q^{78} +5.14025e8 q^{79} +5.17682e8 q^{80} +3.48678e9 q^{81} -7.39556e10 q^{82} -4.94656e9 q^{83} +4.00160e10 q^{84} -7.59735e8 q^{85} -1.84197e10 q^{86} +3.95901e10 q^{87} +2.61813e10 q^{88} -6.81005e10 q^{89} +6.75425e8 q^{90} -4.24693e9 q^{91} -2.19053e10 q^{92} -6.27136e10 q^{93} -1.92517e10 q^{94} +1.46493e9 q^{95} +6.53583e10 q^{96} -7.84607e10 q^{97} -1.58461e11 q^{98} -5.02863e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + O(q^{10}) \) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + 616281q^{10} + 1082362q^{11} + 7099002q^{12} + 503712q^{13} + 1321669q^{14} + 6454566q^{15} + 34870338q^{16} + 13513579q^{17} + 5668704q^{18} + 35971687q^{19} + 96105997q^{20} + 34586919q^{21} - 47598882q^{22} + 61380539q^{23} + 80756433q^{24} + 294744746q^{25} + 62820734q^{26} + 401769396q^{27} + 148068294q^{28} + 322339307q^{29} + 149756283q^{30} + 151247077q^{31} + 466383494q^{32} + 263013966q^{33} + 684479860q^{34} + 960297361q^{35} + 1725057486q^{36} + 863508437q^{37} + 992640509q^{38} + 122402016q^{39} + 3067680252q^{40} + 3081170377q^{41} + 321165567q^{42} + 2554238300q^{43} + 4350123570q^{44} + 1568459538q^{45} - 1987059155q^{46} + 6203398333q^{47} + 8473492134q^{48} + 10327857997q^{49} + 17577682253q^{50} + 3283799697q^{51} + 32137181618q^{52} + 14571770754q^{53} + 1377495072q^{54} + 18251419334q^{55} + 33498842836q^{56} + 8741119941q^{57} + 11860778276q^{58} + 20017880372q^{59} + 23353757271q^{60} + 2761613771q^{61} + 13785829526q^{62} + 8404621317q^{63} + 86547545293q^{64} + 32034985256q^{65} - 11566528326q^{66} + 39381333296q^{67} + 38995496621q^{68} + 14915470977q^{69} + 8551800364q^{70} + 26130020296q^{71} + 19623813219q^{72} + 41382402799q^{73} + 23815315058q^{74} + 71622973278q^{75} + 10611720128q^{76} - 8426124313q^{77} + 15265438362q^{78} + 59825111206q^{79} + 4009687655q^{80} + 97629963228q^{81} - 39592715115q^{82} + 35433122727q^{83} + 35980595442q^{84} - 8950496085q^{85} - 182032360688q^{86} + 78328451601q^{87} - 220003602335q^{88} + 102303043039q^{89} + 36390776769q^{90} - 111146323655q^{91} - 163000203526q^{92} + 36753039711q^{93} - 81314346008q^{94} + 208102168887q^{95} + 113331189042q^{96} - 171891031490q^{97} + 72304707792q^{98} + 63912393738q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −67.4662 −1.49081 −0.745403 0.666614i \(-0.767743\pi\)
−0.745403 + 0.666614i \(0.767743\pi\)
\(3\) 243.000 0.577350
\(4\) 2503.69 1.22250
\(5\) −169.543 −0.0242630 −0.0121315 0.999926i \(-0.503862\pi\)
−0.0121315 + 0.999926i \(0.503862\pi\)
\(6\) −16394.3 −0.860718
\(7\) 65772.9 1.47913 0.739567 0.673083i \(-0.235030\pi\)
0.739567 + 0.673083i \(0.235030\pi\)
\(8\) −30743.5 −0.331710
\(9\) 59049.0 0.333333
\(10\) 11438.4 0.0361714
\(11\) −851602. −1.59433 −0.797163 0.603764i \(-0.793667\pi\)
−0.797163 + 0.603764i \(0.793667\pi\)
\(12\) 608396. 0.705813
\(13\) −64569.7 −0.0482325 −0.0241163 0.999709i \(-0.507677\pi\)
−0.0241163 + 0.999709i \(0.507677\pi\)
\(14\) −4.43745e6 −2.20510
\(15\) −41198.8 −0.0140082
\(16\) −3.05340e6 −0.727988
\(17\) 4.48109e6 0.765446 0.382723 0.923863i \(-0.374986\pi\)
0.382723 + 0.923863i \(0.374986\pi\)
\(18\) −3.98381e6 −0.496935
\(19\) −8.64046e6 −0.800557 −0.400278 0.916394i \(-0.631087\pi\)
−0.400278 + 0.916394i \(0.631087\pi\)
\(20\) −424482. −0.0296616
\(21\) 1.59828e7 0.853979
\(22\) 5.74544e7 2.37683
\(23\) −8.74923e6 −0.283444 −0.141722 0.989907i \(-0.545264\pi\)
−0.141722 + 0.989907i \(0.545264\pi\)
\(24\) −7.47068e6 −0.191513
\(25\) −4.87994e7 −0.999411
\(26\) 4.35627e6 0.0719054
\(27\) 1.43489e7 0.192450
\(28\) 1.64675e8 1.80825
\(29\) 1.62922e8 1.47500 0.737499 0.675348i \(-0.236007\pi\)
0.737499 + 0.675348i \(0.236007\pi\)
\(30\) 2.77953e6 0.0208835
\(31\) −2.58081e8 −1.61907 −0.809536 0.587071i \(-0.800281\pi\)
−0.809536 + 0.587071i \(0.800281\pi\)
\(32\) 2.68964e8 1.41700
\(33\) −2.06939e8 −0.920484
\(34\) −3.02322e8 −1.14113
\(35\) −1.11513e7 −0.0358882
\(36\) 1.47840e8 0.407501
\(37\) 6.12752e7 0.145270 0.0726348 0.997359i \(-0.476859\pi\)
0.0726348 + 0.997359i \(0.476859\pi\)
\(38\) 5.82939e8 1.19348
\(39\) −1.56904e7 −0.0278471
\(40\) 5.21234e6 0.00804827
\(41\) 1.09619e9 1.47766 0.738829 0.673893i \(-0.235379\pi\)
0.738829 + 0.673893i \(0.235379\pi\)
\(42\) −1.07830e9 −1.27312
\(43\) 2.73022e8 0.283218 0.141609 0.989923i \(-0.454772\pi\)
0.141609 + 0.989923i \(0.454772\pi\)
\(44\) −2.13215e9 −1.94907
\(45\) −1.00113e7 −0.00808765
\(46\) 5.90277e8 0.422560
\(47\) 2.85354e8 0.181487 0.0907434 0.995874i \(-0.471076\pi\)
0.0907434 + 0.995874i \(0.471076\pi\)
\(48\) −7.41977e8 −0.420304
\(49\) 2.34875e9 1.18784
\(50\) 3.29231e9 1.48993
\(51\) 1.08890e9 0.441930
\(52\) −1.61662e8 −0.0589645
\(53\) 3.57388e9 1.17388 0.586939 0.809631i \(-0.300333\pi\)
0.586939 + 0.809631i \(0.300333\pi\)
\(54\) −9.68066e8 −0.286906
\(55\) 1.44383e8 0.0386830
\(56\) −2.02209e9 −0.490644
\(57\) −2.09963e9 −0.462202
\(58\) −1.09917e10 −2.19894
\(59\) 7.14924e8 0.130189
\(60\) −1.03149e8 −0.0171251
\(61\) −5.00064e9 −0.758073 −0.379037 0.925382i \(-0.623745\pi\)
−0.379037 + 0.925382i \(0.623745\pi\)
\(62\) 1.74117e10 2.41372
\(63\) 3.88382e9 0.493045
\(64\) −1.18926e10 −1.38448
\(65\) 1.09473e7 0.00117026
\(66\) 1.39614e10 1.37226
\(67\) 1.14088e10 1.03236 0.516178 0.856482i \(-0.327354\pi\)
0.516178 + 0.856482i \(0.327354\pi\)
\(68\) 1.12192e10 0.935760
\(69\) −2.12606e9 −0.163646
\(70\) 7.52336e8 0.0535023
\(71\) 1.70442e10 1.12113 0.560566 0.828110i \(-0.310584\pi\)
0.560566 + 0.828110i \(0.310584\pi\)
\(72\) −1.81538e9 −0.110570
\(73\) −1.15800e9 −0.0653779 −0.0326889 0.999466i \(-0.510407\pi\)
−0.0326889 + 0.999466i \(0.510407\pi\)
\(74\) −4.13400e9 −0.216569
\(75\) −1.18582e10 −0.577010
\(76\) −2.16330e10 −0.978684
\(77\) −5.60123e10 −2.35822
\(78\) 1.05857e9 0.0415146
\(79\) 5.14025e8 0.0187947 0.00939735 0.999956i \(-0.497009\pi\)
0.00939735 + 0.999956i \(0.497009\pi\)
\(80\) 5.17682e8 0.0176631
\(81\) 3.48678e9 0.111111
\(82\) −7.39556e10 −2.20290
\(83\) −4.94656e9 −0.137839 −0.0689197 0.997622i \(-0.521955\pi\)
−0.0689197 + 0.997622i \(0.521955\pi\)
\(84\) 4.00160e10 1.04399
\(85\) −7.59735e8 −0.0185720
\(86\) −1.84197e10 −0.422223
\(87\) 3.95901e10 0.851591
\(88\) 2.61813e10 0.528854
\(89\) −6.81005e10 −1.29272 −0.646361 0.763032i \(-0.723710\pi\)
−0.646361 + 0.763032i \(0.723710\pi\)
\(90\) 6.75425e8 0.0120571
\(91\) −4.24693e9 −0.0713424
\(92\) −2.19053e10 −0.346511
\(93\) −6.27136e10 −0.934771
\(94\) −1.92517e10 −0.270562
\(95\) 1.46493e9 0.0194239
\(96\) 6.53583e10 0.818105
\(97\) −7.84607e10 −0.927700 −0.463850 0.885914i \(-0.653532\pi\)
−0.463850 + 0.885914i \(0.653532\pi\)
\(98\) −1.58461e11 −1.77084
\(99\) −5.02863e10 −0.531442
\(100\) −1.22178e11 −1.22178
\(101\) 3.26246e9 0.0308871 0.0154435 0.999881i \(-0.495084\pi\)
0.0154435 + 0.999881i \(0.495084\pi\)
\(102\) −7.34642e10 −0.658832
\(103\) −1.84747e10 −0.157026 −0.0785132 0.996913i \(-0.525017\pi\)
−0.0785132 + 0.996913i \(0.525017\pi\)
\(104\) 1.98510e9 0.0159992
\(105\) −2.70977e9 −0.0207200
\(106\) −2.41116e11 −1.75002
\(107\) −2.22331e11 −1.53246 −0.766229 0.642568i \(-0.777869\pi\)
−0.766229 + 0.642568i \(0.777869\pi\)
\(108\) 3.59252e10 0.235271
\(109\) −1.79474e10 −0.111726 −0.0558631 0.998438i \(-0.517791\pi\)
−0.0558631 + 0.998438i \(0.517791\pi\)
\(110\) −9.74096e9 −0.0576689
\(111\) 1.48899e10 0.0838715
\(112\) −2.00831e11 −1.07679
\(113\) 9.25443e10 0.472518 0.236259 0.971690i \(-0.424079\pi\)
0.236259 + 0.971690i \(0.424079\pi\)
\(114\) 1.41654e11 0.689053
\(115\) 1.48337e9 0.00687718
\(116\) 4.07907e11 1.80319
\(117\) −3.81277e9 −0.0160775
\(118\) −4.82332e10 −0.194086
\(119\) 2.94734e11 1.13220
\(120\) 1.26660e9 0.00464667
\(121\) 4.39915e11 1.54187
\(122\) 3.37374e11 1.13014
\(123\) 2.66374e11 0.853126
\(124\) −6.46153e11 −1.97932
\(125\) 1.65520e10 0.0485116
\(126\) −2.62027e11 −0.735034
\(127\) 5.63726e11 1.51408 0.757038 0.653370i \(-0.226646\pi\)
0.757038 + 0.653370i \(0.226646\pi\)
\(128\) 2.51512e11 0.646998
\(129\) 6.63443e10 0.163516
\(130\) −7.38573e8 −0.00174464
\(131\) 2.25503e11 0.510693 0.255346 0.966850i \(-0.417811\pi\)
0.255346 + 0.966850i \(0.417811\pi\)
\(132\) −5.18112e11 −1.12530
\(133\) −5.68308e11 −1.18413
\(134\) −7.69710e11 −1.53904
\(135\) −2.43275e9 −0.00466941
\(136\) −1.37765e11 −0.253906
\(137\) 8.78053e11 1.55438 0.777191 0.629265i \(-0.216644\pi\)
0.777191 + 0.629265i \(0.216644\pi\)
\(138\) 1.43437e11 0.243965
\(139\) 4.95579e11 0.810086 0.405043 0.914298i \(-0.367257\pi\)
0.405043 + 0.914298i \(0.367257\pi\)
\(140\) −2.79194e10 −0.0438734
\(141\) 6.93409e10 0.104781
\(142\) −1.14991e12 −1.67139
\(143\) 5.49877e10 0.0768984
\(144\) −1.80300e11 −0.242663
\(145\) −2.76223e10 −0.0357878
\(146\) 7.81255e10 0.0974658
\(147\) 5.70745e11 0.685799
\(148\) 1.53414e11 0.177593
\(149\) 4.30474e11 0.480200 0.240100 0.970748i \(-0.422820\pi\)
0.240100 + 0.970748i \(0.422820\pi\)
\(150\) 8.00031e11 0.860211
\(151\) 7.89752e11 0.818686 0.409343 0.912381i \(-0.365758\pi\)
0.409343 + 0.912381i \(0.365758\pi\)
\(152\) 2.65638e11 0.265553
\(153\) 2.64604e11 0.255149
\(154\) 3.77894e12 3.51565
\(155\) 4.37556e10 0.0392834
\(156\) −3.92839e10 −0.0340432
\(157\) 3.35317e11 0.280548 0.140274 0.990113i \(-0.455202\pi\)
0.140274 + 0.990113i \(0.455202\pi\)
\(158\) −3.46793e10 −0.0280193
\(159\) 8.68453e11 0.677738
\(160\) −4.56009e10 −0.0343806
\(161\) −5.75462e11 −0.419251
\(162\) −2.35240e11 −0.165645
\(163\) 5.24082e11 0.356753 0.178376 0.983962i \(-0.442916\pi\)
0.178376 + 0.983962i \(0.442916\pi\)
\(164\) 2.74451e12 1.80644
\(165\) 3.50850e10 0.0223337
\(166\) 3.33725e11 0.205492
\(167\) 6.04526e11 0.360143 0.180071 0.983654i \(-0.442367\pi\)
0.180071 + 0.983654i \(0.442367\pi\)
\(168\) −4.91368e11 −0.283274
\(169\) −1.78799e12 −0.997674
\(170\) 5.12564e10 0.0276872
\(171\) −5.10211e11 −0.266852
\(172\) 6.83562e11 0.346235
\(173\) −2.60831e12 −1.27969 −0.639846 0.768503i \(-0.721002\pi\)
−0.639846 + 0.768503i \(0.721002\pi\)
\(174\) −2.67099e12 −1.26956
\(175\) −3.20968e12 −1.47826
\(176\) 2.60029e12 1.16065
\(177\) 1.73727e11 0.0751646
\(178\) 4.59448e12 1.92720
\(179\) 2.59282e12 1.05458 0.527292 0.849684i \(-0.323208\pi\)
0.527292 + 0.849684i \(0.323208\pi\)
\(180\) −2.50652e10 −0.00988718
\(181\) 1.19060e12 0.455547 0.227774 0.973714i \(-0.426855\pi\)
0.227774 + 0.973714i \(0.426855\pi\)
\(182\) 2.86524e11 0.106358
\(183\) −1.21515e12 −0.437674
\(184\) 2.68982e11 0.0940212
\(185\) −1.03887e10 −0.00352467
\(186\) 4.23105e12 1.39356
\(187\) −3.81610e12 −1.22037
\(188\) 7.14436e11 0.221868
\(189\) 9.43769e11 0.284660
\(190\) −9.88330e10 −0.0289572
\(191\) 6.53664e12 1.86068 0.930338 0.366703i \(-0.119513\pi\)
0.930338 + 0.366703i \(0.119513\pi\)
\(192\) −2.88991e12 −0.799332
\(193\) −1.16867e12 −0.314141 −0.157071 0.987587i \(-0.550205\pi\)
−0.157071 + 0.987587i \(0.550205\pi\)
\(194\) 5.29344e12 1.38302
\(195\) 2.66019e9 0.000675652 0
\(196\) 5.88053e12 1.45214
\(197\) −3.62189e12 −0.869704 −0.434852 0.900502i \(-0.643199\pi\)
−0.434852 + 0.900502i \(0.643199\pi\)
\(198\) 3.39262e12 0.792277
\(199\) 3.21209e12 0.729618 0.364809 0.931082i \(-0.381134\pi\)
0.364809 + 0.931082i \(0.381134\pi\)
\(200\) 1.50027e12 0.331515
\(201\) 2.77234e12 0.596031
\(202\) −2.20105e11 −0.0460467
\(203\) 1.07159e13 2.18172
\(204\) 2.72628e12 0.540261
\(205\) −1.85850e11 −0.0358523
\(206\) 1.24642e12 0.234096
\(207\) −5.16633e11 −0.0944812
\(208\) 1.97157e11 0.0351127
\(209\) 7.35824e12 1.27635
\(210\) 1.82818e11 0.0308896
\(211\) −7.23792e12 −1.19141 −0.595703 0.803204i \(-0.703127\pi\)
−0.595703 + 0.803204i \(0.703127\pi\)
\(212\) 8.94788e12 1.43507
\(213\) 4.14175e12 0.647286
\(214\) 1.49998e13 2.28460
\(215\) −4.62888e10 −0.00687171
\(216\) −4.41136e11 −0.0638377
\(217\) −1.69747e13 −2.39482
\(218\) 1.21084e12 0.166562
\(219\) −2.81393e11 −0.0377459
\(220\) 3.61489e11 0.0472902
\(221\) −2.89342e11 −0.0369194
\(222\) −1.00456e12 −0.125036
\(223\) 1.22787e13 1.49099 0.745497 0.666509i \(-0.232212\pi\)
0.745497 + 0.666509i \(0.232212\pi\)
\(224\) 1.76906e13 2.09593
\(225\) −2.88155e12 −0.333137
\(226\) −6.24361e12 −0.704433
\(227\) 3.31881e12 0.365460 0.182730 0.983163i \(-0.441507\pi\)
0.182730 + 0.983163i \(0.441507\pi\)
\(228\) −5.25682e12 −0.565043
\(229\) 8.44412e12 0.886052 0.443026 0.896509i \(-0.353905\pi\)
0.443026 + 0.896509i \(0.353905\pi\)
\(230\) −1.00077e11 −0.0102525
\(231\) −1.36110e13 −1.36152
\(232\) −5.00881e12 −0.489272
\(233\) −3.56568e12 −0.340162 −0.170081 0.985430i \(-0.554403\pi\)
−0.170081 + 0.985430i \(0.554403\pi\)
\(234\) 2.57233e11 0.0239685
\(235\) −4.83796e10 −0.00440340
\(236\) 1.78995e12 0.159156
\(237\) 1.24908e11 0.0108511
\(238\) −1.98846e13 −1.68789
\(239\) 4.22044e12 0.350082 0.175041 0.984561i \(-0.443994\pi\)
0.175041 + 0.984561i \(0.443994\pi\)
\(240\) 1.25797e11 0.0101978
\(241\) 8.04748e12 0.637626 0.318813 0.947818i \(-0.396716\pi\)
0.318813 + 0.947818i \(0.396716\pi\)
\(242\) −2.96794e13 −2.29864
\(243\) 8.47289e11 0.0641500
\(244\) −1.25200e13 −0.926747
\(245\) −3.98212e11 −0.0288205
\(246\) −1.79712e13 −1.27185
\(247\) 5.57912e11 0.0386129
\(248\) 7.93431e12 0.537063
\(249\) −1.20201e12 −0.0795816
\(250\) −1.11670e12 −0.0723214
\(251\) −7.29754e12 −0.462350 −0.231175 0.972912i \(-0.574257\pi\)
−0.231175 + 0.972912i \(0.574257\pi\)
\(252\) 9.72388e12 0.602749
\(253\) 7.45086e12 0.451902
\(254\) −3.80325e13 −2.25720
\(255\) −1.84616e11 −0.0107225
\(256\) 7.38757e12 0.419935
\(257\) −2.27868e13 −1.26780 −0.633900 0.773415i \(-0.718547\pi\)
−0.633900 + 0.773415i \(0.718547\pi\)
\(258\) −4.47600e12 −0.243771
\(259\) 4.03024e12 0.214873
\(260\) 2.74086e10 0.00143065
\(261\) 9.62040e12 0.491666
\(262\) −1.52138e13 −0.761344
\(263\) 3.57299e12 0.175096 0.0875478 0.996160i \(-0.472097\pi\)
0.0875478 + 0.996160i \(0.472097\pi\)
\(264\) 6.36205e12 0.305334
\(265\) −6.05925e11 −0.0284817
\(266\) 3.83416e13 1.76531
\(267\) −1.65484e13 −0.746353
\(268\) 2.85641e13 1.26206
\(269\) 3.87184e13 1.67602 0.838011 0.545653i \(-0.183718\pi\)
0.838011 + 0.545653i \(0.183718\pi\)
\(270\) 1.64128e11 0.00696118
\(271\) −3.02431e12 −0.125688 −0.0628442 0.998023i \(-0.520017\pi\)
−0.0628442 + 0.998023i \(0.520017\pi\)
\(272\) −1.36826e13 −0.557235
\(273\) −1.03200e12 −0.0411896
\(274\) −5.92389e13 −2.31728
\(275\) 4.15577e13 1.59339
\(276\) −5.32300e12 −0.200058
\(277\) −5.00826e13 −1.84522 −0.922610 0.385734i \(-0.873948\pi\)
−0.922610 + 0.385734i \(0.873948\pi\)
\(278\) −3.34348e13 −1.20768
\(279\) −1.52394e13 −0.539690
\(280\) 3.42831e11 0.0119045
\(281\) 3.16837e13 1.07883 0.539413 0.842042i \(-0.318646\pi\)
0.539413 + 0.842042i \(0.318646\pi\)
\(282\) −4.67817e12 −0.156209
\(283\) 3.40171e13 1.11397 0.556983 0.830524i \(-0.311959\pi\)
0.556983 + 0.830524i \(0.311959\pi\)
\(284\) 4.26735e13 1.37059
\(285\) 3.55977e11 0.0112144
\(286\) −3.70981e12 −0.114641
\(287\) 7.20994e13 2.18565
\(288\) 1.58821e13 0.472333
\(289\) −1.41917e13 −0.414093
\(290\) 1.86357e12 0.0533527
\(291\) −1.90659e13 −0.535608
\(292\) −2.89926e12 −0.0799247
\(293\) 8.97620e11 0.0242840 0.0121420 0.999926i \(-0.496135\pi\)
0.0121420 + 0.999926i \(0.496135\pi\)
\(294\) −3.85060e13 −1.02239
\(295\) −1.21210e11 −0.00315877
\(296\) −1.88382e12 −0.0481875
\(297\) −1.22196e13 −0.306828
\(298\) −2.90424e13 −0.715886
\(299\) 5.64935e11 0.0136712
\(300\) −2.96894e13 −0.705397
\(301\) 1.79574e13 0.418918
\(302\) −5.32815e13 −1.22050
\(303\) 7.92777e11 0.0178327
\(304\) 2.63828e13 0.582796
\(305\) 8.47820e11 0.0183931
\(306\) −1.78518e13 −0.380377
\(307\) 2.31111e13 0.483682 0.241841 0.970316i \(-0.422249\pi\)
0.241841 + 0.970316i \(0.422249\pi\)
\(308\) −1.40237e14 −2.88294
\(309\) −4.48935e12 −0.0906593
\(310\) −2.95203e12 −0.0585640
\(311\) 6.81672e13 1.32860 0.664298 0.747468i \(-0.268730\pi\)
0.664298 + 0.747468i \(0.268730\pi\)
\(312\) 4.82379e11 0.00923716
\(313\) 6.75405e13 1.27078 0.635390 0.772191i \(-0.280839\pi\)
0.635390 + 0.772191i \(0.280839\pi\)
\(314\) −2.26226e13 −0.418243
\(315\) −6.58473e11 −0.0119627
\(316\) 1.28696e12 0.0229766
\(317\) −3.94816e13 −0.692737 −0.346368 0.938099i \(-0.612585\pi\)
−0.346368 + 0.938099i \(0.612585\pi\)
\(318\) −5.85912e13 −1.01038
\(319\) −1.38745e14 −2.35163
\(320\) 2.01631e12 0.0335917
\(321\) −5.40263e13 −0.884765
\(322\) 3.88242e13 0.625023
\(323\) −3.87187e13 −0.612783
\(324\) 8.72982e12 0.135834
\(325\) 3.15096e12 0.0482041
\(326\) −3.53578e13 −0.531849
\(327\) −4.36121e12 −0.0645052
\(328\) −3.37007e13 −0.490154
\(329\) 1.87685e13 0.268443
\(330\) −2.36705e12 −0.0332952
\(331\) 4.14501e13 0.573418 0.286709 0.958018i \(-0.407439\pi\)
0.286709 + 0.958018i \(0.407439\pi\)
\(332\) −1.23846e13 −0.168509
\(333\) 3.61824e12 0.0484232
\(334\) −4.07851e13 −0.536903
\(335\) −1.93428e12 −0.0250480
\(336\) −4.88020e13 −0.621686
\(337\) −3.96138e13 −0.496457 −0.248228 0.968702i \(-0.579848\pi\)
−0.248228 + 0.968702i \(0.579848\pi\)
\(338\) 1.20629e14 1.48734
\(339\) 2.24883e13 0.272808
\(340\) −1.90214e12 −0.0227043
\(341\) 2.19782e14 2.58133
\(342\) 3.44220e13 0.397825
\(343\) 2.44293e13 0.277839
\(344\) −8.39366e12 −0.0939464
\(345\) 3.60458e11 0.00397054
\(346\) 1.75973e14 1.90777
\(347\) 2.47444e12 0.0264037 0.0132019 0.999913i \(-0.495798\pi\)
0.0132019 + 0.999913i \(0.495798\pi\)
\(348\) 9.91213e13 1.04107
\(349\) 1.14708e14 1.18591 0.592956 0.805235i \(-0.297961\pi\)
0.592956 + 0.805235i \(0.297961\pi\)
\(350\) 2.16545e14 2.20381
\(351\) −9.26504e11 −0.00928236
\(352\) −2.29051e14 −2.25916
\(353\) 1.25470e14 1.21837 0.609183 0.793030i \(-0.291498\pi\)
0.609183 + 0.793030i \(0.291498\pi\)
\(354\) −1.17207e13 −0.112056
\(355\) −2.88972e12 −0.0272020
\(356\) −1.70502e14 −1.58036
\(357\) 7.16204e13 0.653674
\(358\) −1.74928e14 −1.57218
\(359\) −1.44977e14 −1.28316 −0.641580 0.767056i \(-0.721721\pi\)
−0.641580 + 0.767056i \(0.721721\pi\)
\(360\) 3.07783e11 0.00268276
\(361\) −4.18327e13 −0.359109
\(362\) −8.03252e13 −0.679133
\(363\) 1.06899e14 0.890202
\(364\) −1.06330e13 −0.0872164
\(365\) 1.96329e11 0.00158626
\(366\) 8.19819e13 0.652487
\(367\) −2.36110e14 −1.85119 −0.925594 0.378518i \(-0.876434\pi\)
−0.925594 + 0.378518i \(0.876434\pi\)
\(368\) 2.67149e13 0.206344
\(369\) 6.47288e13 0.492552
\(370\) 7.00889e11 0.00525460
\(371\) 2.35064e14 1.73632
\(372\) −1.57015e14 −1.14276
\(373\) −1.59228e14 −1.14188 −0.570940 0.820992i \(-0.693421\pi\)
−0.570940 + 0.820992i \(0.693421\pi\)
\(374\) 2.57458e14 1.81934
\(375\) 4.02214e12 0.0280082
\(376\) −8.77278e12 −0.0602010
\(377\) −1.05198e13 −0.0711429
\(378\) −6.36725e13 −0.424372
\(379\) 2.40271e14 1.57829 0.789144 0.614208i \(-0.210525\pi\)
0.789144 + 0.614208i \(0.210525\pi\)
\(380\) 3.66772e12 0.0237458
\(381\) 1.36986e14 0.874153
\(382\) −4.41002e14 −2.77391
\(383\) 2.44363e14 1.51510 0.757550 0.652777i \(-0.226396\pi\)
0.757550 + 0.652777i \(0.226396\pi\)
\(384\) 6.11173e13 0.373545
\(385\) 9.49647e12 0.0572174
\(386\) 7.88454e13 0.468324
\(387\) 1.61217e13 0.0944060
\(388\) −1.96441e14 −1.13412
\(389\) 1.43407e14 0.816295 0.408148 0.912916i \(-0.366175\pi\)
0.408148 + 0.912916i \(0.366175\pi\)
\(390\) −1.79473e11 −0.00100727
\(391\) −3.92061e13 −0.216961
\(392\) −7.22088e13 −0.394018
\(393\) 5.47972e13 0.294849
\(394\) 2.44355e14 1.29656
\(395\) −8.71491e10 −0.000456015 0
\(396\) −1.25901e14 −0.649690
\(397\) 1.64826e13 0.0838839 0.0419420 0.999120i \(-0.486646\pi\)
0.0419420 + 0.999120i \(0.486646\pi\)
\(398\) −2.16708e14 −1.08772
\(399\) −1.38099e14 −0.683658
\(400\) 1.49004e14 0.727559
\(401\) −9.03944e13 −0.435359 −0.217679 0.976020i \(-0.569849\pi\)
−0.217679 + 0.976020i \(0.569849\pi\)
\(402\) −1.87039e14 −0.888566
\(403\) 1.66642e13 0.0780919
\(404\) 8.16817e12 0.0377596
\(405\) −5.91158e11 −0.00269588
\(406\) −7.22959e14 −3.25252
\(407\) −5.21821e13 −0.231607
\(408\) −3.34768e13 −0.146593
\(409\) 3.76497e14 1.62661 0.813305 0.581838i \(-0.197666\pi\)
0.813305 + 0.581838i \(0.197666\pi\)
\(410\) 1.25386e13 0.0534489
\(411\) 2.13367e14 0.897423
\(412\) −4.62549e13 −0.191965
\(413\) 4.70226e13 0.192567
\(414\) 3.48553e13 0.140853
\(415\) 8.38652e11 0.00334439
\(416\) −1.73669e13 −0.0683455
\(417\) 1.20426e14 0.467703
\(418\) −4.96432e14 −1.90279
\(419\) −3.16379e14 −1.19683 −0.598413 0.801188i \(-0.704202\pi\)
−0.598413 + 0.801188i \(0.704202\pi\)
\(420\) −6.78441e12 −0.0253303
\(421\) −1.16430e14 −0.429056 −0.214528 0.976718i \(-0.568821\pi\)
−0.214528 + 0.976718i \(0.568821\pi\)
\(422\) 4.88315e14 1.77616
\(423\) 1.68498e13 0.0604956
\(424\) −1.09874e14 −0.389387
\(425\) −2.18674e14 −0.764995
\(426\) −2.79428e14 −0.964978
\(427\) −3.28906e14 −1.12129
\(428\) −5.56647e14 −1.87344
\(429\) 1.33620e13 0.0443973
\(430\) 3.12293e12 0.0102444
\(431\) −1.17999e14 −0.382167 −0.191083 0.981574i \(-0.561200\pi\)
−0.191083 + 0.981574i \(0.561200\pi\)
\(432\) −4.38130e13 −0.140101
\(433\) −3.75432e14 −1.18535 −0.592676 0.805441i \(-0.701929\pi\)
−0.592676 + 0.805441i \(0.701929\pi\)
\(434\) 1.14522e15 3.57022
\(435\) −6.71221e12 −0.0206621
\(436\) −4.49346e13 −0.136586
\(437\) 7.55974e13 0.226913
\(438\) 1.89845e13 0.0562719
\(439\) −3.21075e13 −0.0939835 −0.0469917 0.998895i \(-0.514963\pi\)
−0.0469917 + 0.998895i \(0.514963\pi\)
\(440\) −4.43884e12 −0.0128316
\(441\) 1.38691e14 0.395946
\(442\) 1.95208e13 0.0550397
\(443\) 4.03275e14 1.12300 0.561502 0.827476i \(-0.310224\pi\)
0.561502 + 0.827476i \(0.310224\pi\)
\(444\) 3.72796e13 0.102533
\(445\) 1.15459e13 0.0313652
\(446\) −8.28398e14 −2.22278
\(447\) 1.04605e14 0.277244
\(448\) −7.82212e14 −2.04784
\(449\) −5.84948e14 −1.51273 −0.756366 0.654148i \(-0.773027\pi\)
−0.756366 + 0.654148i \(0.773027\pi\)
\(450\) 1.94408e14 0.496643
\(451\) −9.33516e14 −2.35587
\(452\) 2.31702e14 0.577655
\(453\) 1.91910e14 0.472668
\(454\) −2.23908e14 −0.544831
\(455\) 7.20036e11 0.00173098
\(456\) 6.45501e13 0.153317
\(457\) 4.51440e14 1.05940 0.529701 0.848185i \(-0.322304\pi\)
0.529701 + 0.848185i \(0.322304\pi\)
\(458\) −5.69692e14 −1.32093
\(459\) 6.42987e13 0.147310
\(460\) 3.71389e12 0.00840738
\(461\) −6.82451e14 −1.52657 −0.763284 0.646063i \(-0.776414\pi\)
−0.763284 + 0.646063i \(0.776414\pi\)
\(462\) 9.18282e14 2.02976
\(463\) −3.08000e14 −0.672751 −0.336376 0.941728i \(-0.609201\pi\)
−0.336376 + 0.941728i \(0.609201\pi\)
\(464\) −4.97467e14 −1.07378
\(465\) 1.06326e13 0.0226803
\(466\) 2.40563e14 0.507115
\(467\) −2.27817e13 −0.0474617 −0.0237308 0.999718i \(-0.507554\pi\)
−0.0237308 + 0.999718i \(0.507554\pi\)
\(468\) −9.54600e12 −0.0196548
\(469\) 7.50391e14 1.52699
\(470\) 3.26398e12 0.00656462
\(471\) 8.14821e13 0.161975
\(472\) −2.19793e13 −0.0431850
\(473\) −2.32506e14 −0.451542
\(474\) −8.42708e12 −0.0161769
\(475\) 4.21649e14 0.800085
\(476\) 7.37922e14 1.38412
\(477\) 2.11034e14 0.391292
\(478\) −2.84737e14 −0.521904
\(479\) 3.10826e14 0.563212 0.281606 0.959530i \(-0.409133\pi\)
0.281606 + 0.959530i \(0.409133\pi\)
\(480\) −1.10810e13 −0.0198496
\(481\) −3.95652e12 −0.00700673
\(482\) −5.42933e14 −0.950577
\(483\) −1.39837e14 −0.242055
\(484\) 1.10141e15 1.88495
\(485\) 1.33024e13 0.0225087
\(486\) −5.71633e13 −0.0956353
\(487\) −2.12017e14 −0.350721 −0.175360 0.984504i \(-0.556109\pi\)
−0.175360 + 0.984504i \(0.556109\pi\)
\(488\) 1.53737e14 0.251461
\(489\) 1.27352e14 0.205971
\(490\) 2.68659e13 0.0429658
\(491\) 4.60829e14 0.728771 0.364386 0.931248i \(-0.381279\pi\)
0.364386 + 0.931248i \(0.381279\pi\)
\(492\) 6.66916e14 1.04295
\(493\) 7.30069e14 1.12903
\(494\) −3.76402e13 −0.0575643
\(495\) 8.52566e12 0.0128943
\(496\) 7.88024e14 1.17866
\(497\) 1.12105e15 1.65831
\(498\) 8.10953e13 0.118641
\(499\) 1.37256e15 1.98600 0.993001 0.118109i \(-0.0376832\pi\)
0.993001 + 0.118109i \(0.0376832\pi\)
\(500\) 4.14411e13 0.0593056
\(501\) 1.46900e14 0.207928
\(502\) 4.92337e14 0.689275
\(503\) −2.53209e14 −0.350635 −0.175317 0.984512i \(-0.556095\pi\)
−0.175317 + 0.984512i \(0.556095\pi\)
\(504\) −1.19402e14 −0.163548
\(505\) −5.53125e11 −0.000749412 0
\(506\) −5.02682e14 −0.673698
\(507\) −4.34482e14 −0.576007
\(508\) 1.41140e15 1.85097
\(509\) −6.32882e14 −0.821060 −0.410530 0.911847i \(-0.634656\pi\)
−0.410530 + 0.911847i \(0.634656\pi\)
\(510\) 1.24553e13 0.0159852
\(511\) −7.61647e13 −0.0967027
\(512\) −1.01351e15 −1.27304
\(513\) −1.23981e14 −0.154067
\(514\) 1.53734e15 1.89004
\(515\) 3.13225e12 0.00380993
\(516\) 1.66105e14 0.199899
\(517\) −2.43008e14 −0.289349
\(518\) −2.71905e14 −0.320335
\(519\) −6.33819e14 −0.738830
\(520\) −3.36559e11 −0.000388189 0
\(521\) 1.46198e15 1.66853 0.834263 0.551366i \(-0.185893\pi\)
0.834263 + 0.551366i \(0.185893\pi\)
\(522\) −6.49052e14 −0.732979
\(523\) 6.47747e14 0.723846 0.361923 0.932208i \(-0.382120\pi\)
0.361923 + 0.932208i \(0.382120\pi\)
\(524\) 5.64588e14 0.624324
\(525\) −7.79951e14 −0.853476
\(526\) −2.41056e14 −0.261034
\(527\) −1.15648e15 −1.23931
\(528\) 6.31869e14 0.670102
\(529\) −8.76261e14 −0.919660
\(530\) 4.08794e13 0.0424607
\(531\) 4.22156e13 0.0433963
\(532\) −1.42287e15 −1.44760
\(533\) −7.07805e13 −0.0712712
\(534\) 1.11646e15 1.11267
\(535\) 3.76945e13 0.0371819
\(536\) −3.50747e14 −0.342443
\(537\) 6.30056e14 0.608864
\(538\) −2.61218e15 −2.49862
\(539\) −2.00020e15 −1.89380
\(540\) −6.09085e12 −0.00570837
\(541\) 1.79622e15 1.66638 0.833191 0.552985i \(-0.186511\pi\)
0.833191 + 0.552985i \(0.186511\pi\)
\(542\) 2.04039e14 0.187377
\(543\) 2.89316e14 0.263010
\(544\) 1.20525e15 1.08464
\(545\) 3.04284e12 0.00271081
\(546\) 6.96254e13 0.0614057
\(547\) 3.15025e14 0.275052 0.137526 0.990498i \(-0.456085\pi\)
0.137526 + 0.990498i \(0.456085\pi\)
\(548\) 2.19837e15 1.90024
\(549\) −2.95283e14 −0.252691
\(550\) −2.80374e15 −2.37543
\(551\) −1.40772e15 −1.18082
\(552\) 6.53627e13 0.0542832
\(553\) 3.38089e13 0.0277999
\(554\) 3.37888e15 2.75087
\(555\) −2.52447e12 −0.00203497
\(556\) 1.24077e15 0.990333
\(557\) 1.05585e15 0.834444 0.417222 0.908805i \(-0.363004\pi\)
0.417222 + 0.908805i \(0.363004\pi\)
\(558\) 1.02814e15 0.804574
\(559\) −1.76289e13 −0.0136603
\(560\) 3.40494e13 0.0261262
\(561\) −9.27313e14 −0.704581
\(562\) −2.13758e15 −1.60832
\(563\) 2.02103e15 1.50583 0.752916 0.658117i \(-0.228647\pi\)
0.752916 + 0.658117i \(0.228647\pi\)
\(564\) 1.73608e14 0.128096
\(565\) −1.56902e13 −0.0114647
\(566\) −2.29500e15 −1.66071
\(567\) 2.29336e14 0.164348
\(568\) −5.24000e14 −0.371891
\(569\) −3.45715e14 −0.242997 −0.121498 0.992592i \(-0.538770\pi\)
−0.121498 + 0.992592i \(0.538770\pi\)
\(570\) −2.40164e13 −0.0167185
\(571\) 1.56621e15 1.07982 0.539911 0.841722i \(-0.318458\pi\)
0.539911 + 0.841722i \(0.318458\pi\)
\(572\) 1.37672e14 0.0940086
\(573\) 1.58840e15 1.07426
\(574\) −4.86427e15 −3.25839
\(575\) 4.26957e14 0.283277
\(576\) −7.02248e14 −0.461495
\(577\) 2.47269e15 1.60954 0.804771 0.593585i \(-0.202288\pi\)
0.804771 + 0.593585i \(0.202288\pi\)
\(578\) 9.57463e14 0.617332
\(579\) −2.83986e14 −0.181370
\(580\) −6.91575e13 −0.0437507
\(581\) −3.25349e14 −0.203883
\(582\) 1.28631e15 0.798488
\(583\) −3.04352e15 −1.87154
\(584\) 3.56009e13 0.0216865
\(585\) 6.46427e11 0.000390088 0
\(586\) −6.05590e13 −0.0362028
\(587\) 4.42798e14 0.262238 0.131119 0.991367i \(-0.458143\pi\)
0.131119 + 0.991367i \(0.458143\pi\)
\(588\) 1.42897e15 0.838392
\(589\) 2.22993e15 1.29616
\(590\) 8.17758e12 0.00470911
\(591\) −8.80120e14 −0.502124
\(592\) −1.87098e14 −0.105755
\(593\) 2.62869e15 1.47210 0.736052 0.676925i \(-0.236688\pi\)
0.736052 + 0.676925i \(0.236688\pi\)
\(594\) 8.24407e14 0.457421
\(595\) −4.99700e13 −0.0274704
\(596\) 1.07777e15 0.587047
\(597\) 7.80538e14 0.421245
\(598\) −3.81140e13 −0.0203811
\(599\) 1.68909e15 0.894966 0.447483 0.894293i \(-0.352321\pi\)
0.447483 + 0.894293i \(0.352321\pi\)
\(600\) 3.64565e14 0.191400
\(601\) 2.39749e15 1.24723 0.623615 0.781731i \(-0.285663\pi\)
0.623615 + 0.781731i \(0.285663\pi\)
\(602\) −1.21152e15 −0.624525
\(603\) 6.73679e14 0.344118
\(604\) 1.97729e15 1.00085
\(605\) −7.45843e13 −0.0374104
\(606\) −5.34856e13 −0.0265851
\(607\) −1.71531e15 −0.844899 −0.422450 0.906386i \(-0.638830\pi\)
−0.422450 + 0.906386i \(0.638830\pi\)
\(608\) −2.32398e15 −1.13439
\(609\) 2.60396e15 1.25962
\(610\) −5.71992e13 −0.0274205
\(611\) −1.84252e13 −0.00875357
\(612\) 6.62485e14 0.311920
\(613\) −1.32113e15 −0.616473 −0.308237 0.951310i \(-0.599739\pi\)
−0.308237 + 0.951310i \(0.599739\pi\)
\(614\) −1.55922e15 −0.721076
\(615\) −4.51616e13 −0.0206993
\(616\) 1.72202e15 0.782247
\(617\) 1.03999e15 0.468233 0.234116 0.972209i \(-0.424780\pi\)
0.234116 + 0.972209i \(0.424780\pi\)
\(618\) 3.02880e14 0.135155
\(619\) 2.90474e15 1.28472 0.642361 0.766402i \(-0.277955\pi\)
0.642361 + 0.766402i \(0.277955\pi\)
\(620\) 1.09550e14 0.0480242
\(621\) −1.25542e14 −0.0545488
\(622\) −4.59898e15 −1.98068
\(623\) −4.47916e15 −1.91211
\(624\) 4.79092e13 0.0202723
\(625\) 2.37998e15 0.998234
\(626\) −4.55670e15 −1.89449
\(627\) 1.78805e15 0.736900
\(628\) 8.39530e14 0.342971
\(629\) 2.74579e14 0.111196
\(630\) 4.44247e13 0.0178341
\(631\) −5.42978e14 −0.216083 −0.108042 0.994146i \(-0.534458\pi\)
−0.108042 + 0.994146i \(0.534458\pi\)
\(632\) −1.58030e13 −0.00623440
\(633\) −1.75881e15 −0.687859
\(634\) 2.66367e15 1.03274
\(635\) −9.55756e13 −0.0367360
\(636\) 2.17434e15 0.828538
\(637\) −1.51658e14 −0.0572925
\(638\) 9.36060e15 3.50582
\(639\) 1.00645e15 0.373711
\(640\) −4.26419e13 −0.0156981
\(641\) −4.49603e15 −1.64101 −0.820503 0.571642i \(-0.806307\pi\)
−0.820503 + 0.571642i \(0.806307\pi\)
\(642\) 3.64495e15 1.31901
\(643\) −1.07318e15 −0.385044 −0.192522 0.981293i \(-0.561667\pi\)
−0.192522 + 0.981293i \(0.561667\pi\)
\(644\) −1.44078e15 −0.512536
\(645\) −1.12482e13 −0.00396738
\(646\) 2.61220e15 0.913540
\(647\) 3.03792e15 1.05342 0.526712 0.850044i \(-0.323425\pi\)
0.526712 + 0.850044i \(0.323425\pi\)
\(648\) −1.07196e14 −0.0368567
\(649\) −6.08831e14 −0.207564
\(650\) −2.12583e14 −0.0718631
\(651\) −4.12485e15 −1.38265
\(652\) 1.31214e15 0.436132
\(653\) 5.16352e15 1.70186 0.850930 0.525279i \(-0.176039\pi\)
0.850930 + 0.525279i \(0.176039\pi\)
\(654\) 2.94235e14 0.0961648
\(655\) −3.82323e13 −0.0123909
\(656\) −3.34710e15 −1.07572
\(657\) −6.83784e13 −0.0217926
\(658\) −1.26624e15 −0.400197
\(659\) −3.90470e15 −1.22382 −0.611910 0.790927i \(-0.709599\pi\)
−0.611910 + 0.790927i \(0.709599\pi\)
\(660\) 8.78419e13 0.0273030
\(661\) −5.81767e15 −1.79325 −0.896626 0.442789i \(-0.853989\pi\)
−0.896626 + 0.442789i \(0.853989\pi\)
\(662\) −2.79648e15 −0.854856
\(663\) −7.03102e13 −0.0213154
\(664\) 1.52075e14 0.0457228
\(665\) 9.63524e13 0.0287305
\(666\) −2.44109e14 −0.0721897
\(667\) −1.42544e15 −0.418079
\(668\) 1.51354e15 0.440276
\(669\) 2.98373e15 0.860826
\(670\) 1.30498e14 0.0373417
\(671\) 4.25855e15 1.20862
\(672\) 4.29881e15 1.21009
\(673\) 4.90313e14 0.136896 0.0684480 0.997655i \(-0.478195\pi\)
0.0684480 + 0.997655i \(0.478195\pi\)
\(674\) 2.67259e15 0.740121
\(675\) −7.00218e14 −0.192337
\(676\) −4.47657e15 −1.21966
\(677\) −5.37352e15 −1.45218 −0.726091 0.687599i \(-0.758665\pi\)
−0.726091 + 0.687599i \(0.758665\pi\)
\(678\) −1.51720e15 −0.406705
\(679\) −5.16058e15 −1.37219
\(680\) 2.33569e13 0.00616051
\(681\) 8.06471e14 0.210999
\(682\) −1.48279e16 −3.84826
\(683\) 3.66009e15 0.942276 0.471138 0.882059i \(-0.343843\pi\)
0.471138 + 0.882059i \(0.343843\pi\)
\(684\) −1.27741e15 −0.326228
\(685\) −1.48867e14 −0.0377139
\(686\) −1.64815e15 −0.414204
\(687\) 2.05192e15 0.511562
\(688\) −8.33646e14 −0.206179
\(689\) −2.30764e14 −0.0566191
\(690\) −2.43187e13 −0.00591931
\(691\) −6.87405e15 −1.65991 −0.829953 0.557833i \(-0.811633\pi\)
−0.829953 + 0.557833i \(0.811633\pi\)
\(692\) −6.53039e15 −1.56443
\(693\) −3.30747e15 −0.786074
\(694\) −1.66941e14 −0.0393629
\(695\) −8.40216e13 −0.0196551
\(696\) −1.21714e15 −0.282481
\(697\) 4.91211e15 1.13107
\(698\) −7.73889e15 −1.76796
\(699\) −8.66461e14 −0.196392
\(700\) −8.03603e15 −1.80718
\(701\) 3.87733e15 0.865134 0.432567 0.901602i \(-0.357608\pi\)
0.432567 + 0.901602i \(0.357608\pi\)
\(702\) 6.25077e13 0.0138382
\(703\) −5.29446e14 −0.116297
\(704\) 1.01278e16 2.20732
\(705\) −1.17562e13 −0.00254231
\(706\) −8.46496e15 −1.81635
\(707\) 2.14581e14 0.0456862
\(708\) 4.34957e14 0.0918890
\(709\) −7.08025e15 −1.48421 −0.742103 0.670286i \(-0.766172\pi\)
−0.742103 + 0.670286i \(0.766172\pi\)
\(710\) 1.94959e14 0.0405529
\(711\) 3.03527e13 0.00626490
\(712\) 2.09365e15 0.428809
\(713\) 2.25801e15 0.458915
\(714\) −4.83195e15 −0.974502
\(715\) −9.32275e12 −0.00186578
\(716\) 6.49162e15 1.28923
\(717\) 1.02557e15 0.202120
\(718\) 9.78107e15 1.91294
\(719\) 2.44004e15 0.473573 0.236787 0.971562i \(-0.423906\pi\)
0.236787 + 0.971562i \(0.423906\pi\)
\(720\) 3.05686e13 0.00588771
\(721\) −1.21514e15 −0.232263
\(722\) 2.82229e15 0.535362
\(723\) 1.95554e15 0.368134
\(724\) 2.98089e15 0.556908
\(725\) −7.95051e15 −1.47413
\(726\) −7.21209e15 −1.32712
\(727\) 1.00123e15 0.182849 0.0914247 0.995812i \(-0.470858\pi\)
0.0914247 + 0.995812i \(0.470858\pi\)
\(728\) 1.30566e14 0.0236650
\(729\) 2.05891e14 0.0370370
\(730\) −1.32456e13 −0.00236481
\(731\) 1.22344e15 0.216788
\(732\) −3.04237e15 −0.535058
\(733\) 3.47124e15 0.605917 0.302958 0.953004i \(-0.402026\pi\)
0.302958 + 0.953004i \(0.402026\pi\)
\(734\) 1.59294e16 2.75976
\(735\) −9.67656e13 −0.0166395
\(736\) −2.35323e15 −0.401640
\(737\) −9.71578e15 −1.64591
\(738\) −4.36701e15 −0.734300
\(739\) −6.59520e15 −1.10074 −0.550369 0.834922i \(-0.685513\pi\)
−0.550369 + 0.834922i \(0.685513\pi\)
\(740\) −2.60102e13 −0.00430892
\(741\) 1.35573e14 0.0222932
\(742\) −1.58589e16 −2.58852
\(743\) 7.66685e15 1.24216 0.621081 0.783746i \(-0.286694\pi\)
0.621081 + 0.783746i \(0.286694\pi\)
\(744\) 1.92804e15 0.310073
\(745\) −7.29836e13 −0.0116511
\(746\) 1.07425e16 1.70232
\(747\) −2.92089e14 −0.0459465
\(748\) −9.55434e15 −1.49191
\(749\) −1.46233e16 −2.26671
\(750\) −2.71358e14 −0.0417548
\(751\) 8.14775e15 1.24457 0.622283 0.782792i \(-0.286205\pi\)
0.622283 + 0.782792i \(0.286205\pi\)
\(752\) −8.71299e14 −0.132120
\(753\) −1.77330e15 −0.266938
\(754\) 7.09733e14 0.106060
\(755\) −1.33896e14 −0.0198637
\(756\) 2.36290e15 0.347997
\(757\) −5.62091e15 −0.821825 −0.410913 0.911675i \(-0.634790\pi\)
−0.410913 + 0.911675i \(0.634790\pi\)
\(758\) −1.62102e16 −2.35292
\(759\) 1.81056e15 0.260905
\(760\) −4.50370e13 −0.00644310
\(761\) −8.24946e15 −1.17168 −0.585842 0.810426i \(-0.699236\pi\)
−0.585842 + 0.810426i \(0.699236\pi\)
\(762\) −9.24189e15 −1.30319
\(763\) −1.18045e15 −0.165258
\(764\) 1.63657e16 2.27468
\(765\) −4.48616e13 −0.00619066
\(766\) −1.64862e16 −2.25872
\(767\) −4.61624e13 −0.00627934
\(768\) 1.79518e15 0.242449
\(769\) 5.54028e15 0.742911 0.371455 0.928451i \(-0.378859\pi\)
0.371455 + 0.928451i \(0.378859\pi\)
\(770\) −6.40691e14 −0.0853001
\(771\) −5.53719e15 −0.731965
\(772\) −2.92597e15 −0.384039
\(773\) 9.42666e14 0.122849 0.0614244 0.998112i \(-0.480436\pi\)
0.0614244 + 0.998112i \(0.480436\pi\)
\(774\) −1.08767e15 −0.140741
\(775\) 1.25942e16 1.61812
\(776\) 2.41216e15 0.307728
\(777\) 9.79349e14 0.124057
\(778\) −9.67512e15 −1.21694
\(779\) −9.47157e15 −1.18295
\(780\) 6.66030e12 0.000825987 0
\(781\) −1.45149e16 −1.78745
\(782\) 2.64508e15 0.323446
\(783\) 2.33776e15 0.283864
\(784\) −7.17167e15 −0.864733
\(785\) −5.68505e13 −0.00680693
\(786\) −3.69696e15 −0.439562
\(787\) 4.74422e15 0.560149 0.280074 0.959978i \(-0.409641\pi\)
0.280074 + 0.959978i \(0.409641\pi\)
\(788\) −9.06809e15 −1.06322
\(789\) 8.68236e14 0.101091
\(790\) 5.87962e12 0.000679830 0
\(791\) 6.08691e15 0.698918
\(792\) 1.54598e15 0.176285
\(793\) 3.22889e14 0.0365638
\(794\) −1.11202e15 −0.125055
\(795\) −1.47240e14 −0.0164439
\(796\) 8.04207e15 0.891961
\(797\) 1.86196e15 0.205093 0.102546 0.994728i \(-0.467301\pi\)
0.102546 + 0.994728i \(0.467301\pi\)
\(798\) 9.31701e15 1.01920
\(799\) 1.27869e15 0.138918
\(800\) −1.31253e16 −1.41617
\(801\) −4.02126e15 −0.430907
\(802\) 6.09856e15 0.649036
\(803\) 9.86151e14 0.104234
\(804\) 6.94108e15 0.728650
\(805\) 9.75653e13 0.0101723
\(806\) −1.12427e15 −0.116420
\(807\) 9.40857e15 0.967652
\(808\) −1.00299e14 −0.0102456
\(809\) 1.77383e16 1.79968 0.899838 0.436225i \(-0.143685\pi\)
0.899838 + 0.436225i \(0.143685\pi\)
\(810\) 3.98832e13 0.00401904
\(811\) 1.29473e16 1.29587 0.647937 0.761694i \(-0.275632\pi\)
0.647937 + 0.761694i \(0.275632\pi\)
\(812\) 2.68292e16 2.66716
\(813\) −7.34907e14 −0.0725662
\(814\) 3.52053e15 0.345282
\(815\) −8.88542e13 −0.00865587
\(816\) −3.32486e15 −0.321720
\(817\) −2.35904e15 −0.226732
\(818\) −2.54008e16 −2.42496
\(819\) −2.50777e14 −0.0237808
\(820\) −4.65311e14 −0.0438296
\(821\) −1.79237e16 −1.67702 −0.838512 0.544883i \(-0.816574\pi\)
−0.838512 + 0.544883i \(0.816574\pi\)
\(822\) −1.43951e16 −1.33788
\(823\) 8.64977e15 0.798556 0.399278 0.916830i \(-0.369261\pi\)
0.399278 + 0.916830i \(0.369261\pi\)
\(824\) 5.67978e14 0.0520873
\(825\) 1.00985e16 0.919942
\(826\) −3.17244e15 −0.287080
\(827\) 1.66067e16 1.49281 0.746403 0.665494i \(-0.231779\pi\)
0.746403 + 0.665494i \(0.231779\pi\)
\(828\) −1.29349e15 −0.115504
\(829\) 1.98415e14 0.0176005 0.00880025 0.999961i \(-0.497199\pi\)
0.00880025 + 0.999961i \(0.497199\pi\)
\(830\) −5.65806e13 −0.00498584
\(831\) −1.21701e16 −1.06534
\(832\) 7.67903e14 0.0667772
\(833\) 1.05249e16 0.909226
\(834\) −8.12466e15 −0.697255
\(835\) −1.02493e14 −0.00873812
\(836\) 1.84227e16 1.56034
\(837\) −3.70317e15 −0.311590
\(838\) 2.13449e16 1.78423
\(839\) 2.10750e16 1.75015 0.875077 0.483984i \(-0.160811\pi\)
0.875077 + 0.483984i \(0.160811\pi\)
\(840\) 8.33078e13 0.00687305
\(841\) 1.43432e16 1.17562
\(842\) 7.85510e15 0.639640
\(843\) 7.69914e15 0.622860
\(844\) −1.81215e16 −1.45650
\(845\) 3.03141e14 0.0242065
\(846\) −1.13679e15 −0.0901872
\(847\) 2.89345e16 2.28064
\(848\) −1.09125e16 −0.854569
\(849\) 8.26615e15 0.643148
\(850\) 1.47531e16 1.14046
\(851\) −5.36111e14 −0.0411758
\(852\) 1.03697e16 0.791309
\(853\) 3.17382e15 0.240637 0.120319 0.992735i \(-0.461608\pi\)
0.120319 + 0.992735i \(0.461608\pi\)
\(854\) 2.21901e16 1.67163
\(855\) 8.65024e13 0.00647462
\(856\) 6.83523e15 0.508332
\(857\) −1.00250e16 −0.740784 −0.370392 0.928876i \(-0.620777\pi\)
−0.370392 + 0.928876i \(0.620777\pi\)
\(858\) −9.01484e14 −0.0661878
\(859\) −3.59308e15 −0.262123 −0.131061 0.991374i \(-0.541839\pi\)
−0.131061 + 0.991374i \(0.541839\pi\)
\(860\) −1.15893e14 −0.00840069
\(861\) 1.75202e16 1.26189
\(862\) 7.96093e15 0.569737
\(863\) 2.13704e16 1.51968 0.759841 0.650109i \(-0.225277\pi\)
0.759841 + 0.650109i \(0.225277\pi\)
\(864\) 3.85934e15 0.272702
\(865\) 4.42219e14 0.0310491
\(866\) 2.53289e16 1.76713
\(867\) −3.44860e15 −0.239077
\(868\) −4.24994e16 −2.92768
\(869\) −4.37745e14 −0.0299649
\(870\) 4.52847e14 0.0308032
\(871\) −7.36664e14 −0.0497931
\(872\) 5.51766e14 0.0370608
\(873\) −4.63302e15 −0.309233
\(874\) −5.10027e15 −0.338283
\(875\) 1.08867e15 0.0717552
\(876\) −7.04520e14 −0.0461446
\(877\) −1.44168e16 −0.938362 −0.469181 0.883102i \(-0.655451\pi\)
−0.469181 + 0.883102i \(0.655451\pi\)
\(878\) 2.16617e15 0.140111
\(879\) 2.18122e14 0.0140204
\(880\) −4.40859e14 −0.0281608
\(881\) −2.28978e15 −0.145354 −0.0726769 0.997356i \(-0.523154\pi\)
−0.0726769 + 0.997356i \(0.523154\pi\)
\(882\) −9.35696e15 −0.590279
\(883\) −1.36279e16 −0.854366 −0.427183 0.904165i \(-0.640494\pi\)
−0.427183 + 0.904165i \(0.640494\pi\)
\(884\) −7.24423e14 −0.0451341
\(885\) −2.94540e13 −0.00182372
\(886\) −2.72075e16 −1.67418
\(887\) −2.29093e16 −1.40098 −0.700488 0.713664i \(-0.747034\pi\)
−0.700488 + 0.713664i \(0.747034\pi\)
\(888\) −4.57767e14 −0.0278210
\(889\) 3.70779e16 2.23952
\(890\) −7.78960e14 −0.0467595
\(891\) −2.96935e15 −0.177147
\(892\) 3.07421e16 1.82275
\(893\) −2.46559e15 −0.145290
\(894\) −7.05731e15 −0.413317
\(895\) −4.39593e14 −0.0255873
\(896\) 1.65426e16 0.956998
\(897\) 1.37279e14 0.00789308
\(898\) 3.94642e16 2.25519
\(899\) −4.20471e16 −2.38813
\(900\) −7.21451e15 −0.407261
\(901\) 1.60149e16 0.898539
\(902\) 6.29808e16 3.51214
\(903\) 4.36366e15 0.241862
\(904\) −2.84514e15 −0.156739
\(905\) −2.01857e14 −0.0110529
\(906\) −1.29474e16 −0.704657
\(907\) −3.19683e16 −1.72934 −0.864668 0.502344i \(-0.832471\pi\)
−0.864668 + 0.502344i \(0.832471\pi\)
\(908\) 8.30927e15 0.446777
\(909\) 1.92645e14 0.0102957
\(910\) −4.85781e13 −0.00258055
\(911\) 4.71409e15 0.248912 0.124456 0.992225i \(-0.460281\pi\)
0.124456 + 0.992225i \(0.460281\pi\)
\(912\) 6.41102e15 0.336477
\(913\) 4.21250e15 0.219761
\(914\) −3.04569e16 −1.57936
\(915\) 2.06020e14 0.0106193
\(916\) 2.11414e16 1.08320
\(917\) 1.48320e16 0.755383
\(918\) −4.33799e15 −0.219611
\(919\) −2.18519e16 −1.09965 −0.549825 0.835280i \(-0.685306\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(920\) −4.56039e13 −0.00228123
\(921\) 5.61600e15 0.279254
\(922\) 4.60423e16 2.27582
\(923\) −1.10054e15 −0.0540750
\(924\) −3.40777e16 −1.66446
\(925\) −2.99019e15 −0.145184
\(926\) 2.07796e16 1.00294
\(927\) −1.09091e15 −0.0523422
\(928\) 4.38203e16 2.09007
\(929\) 2.01713e16 0.956418 0.478209 0.878246i \(-0.341286\pi\)
0.478209 + 0.878246i \(0.341286\pi\)
\(930\) −7.17342e14 −0.0338119
\(931\) −2.02942e16 −0.950932
\(932\) −8.92736e15 −0.415849
\(933\) 1.65646e16 0.767066
\(934\) 1.53699e15 0.0707561
\(935\) 6.46992e14 0.0296098
\(936\) 1.17218e14 0.00533308
\(937\) −1.57861e16 −0.714015 −0.357007 0.934102i \(-0.616203\pi\)
−0.357007 + 0.934102i \(0.616203\pi\)
\(938\) −5.06260e16 −2.27645
\(939\) 1.64123e16 0.733685
\(940\) −1.21127e14 −0.00538318
\(941\) −9.22140e15 −0.407431 −0.203715 0.979030i \(-0.565302\pi\)
−0.203715 + 0.979030i \(0.565302\pi\)
\(942\) −5.49729e15 −0.241473
\(943\) −9.59080e15 −0.418833
\(944\) −2.18295e15 −0.0947760
\(945\) −1.60009e14 −0.00690668
\(946\) 1.56863e16 0.673162
\(947\) 4.52101e16 1.92890 0.964451 0.264260i \(-0.0851278\pi\)
0.964451 + 0.264260i \(0.0851278\pi\)
\(948\) 3.12731e14 0.0132655
\(949\) 7.47714e13 0.00315334
\(950\) −2.84471e16 −1.19277
\(951\) −9.59402e15 −0.399952
\(952\) −9.06117e15 −0.375561
\(953\) −1.36142e16 −0.561025 −0.280512 0.959850i \(-0.590504\pi\)
−0.280512 + 0.959850i \(0.590504\pi\)
\(954\) −1.42377e16 −0.583341
\(955\) −1.10824e15 −0.0451455
\(956\) 1.05667e16 0.427976
\(957\) −3.37150e16 −1.35771
\(958\) −2.09703e16 −0.839641
\(959\) 5.77521e16 2.29914
\(960\) 4.89962e14 0.0193942
\(961\) 4.11971e16 1.62139
\(962\) 2.66931e14 0.0104457
\(963\) −1.31284e16 −0.510819
\(964\) 2.01484e16 0.779501
\(965\) 1.98138e14 0.00762199
\(966\) 9.43429e15 0.360857
\(967\) −2.03858e16 −0.775322 −0.387661 0.921802i \(-0.626717\pi\)
−0.387661 + 0.921802i \(0.626717\pi\)
\(968\) −1.35245e16 −0.511456
\(969\) −9.40864e15 −0.353790
\(970\) −8.97464e14 −0.0335562
\(971\) −6.86008e15 −0.255049 −0.127524 0.991835i \(-0.540703\pi\)
−0.127524 + 0.991835i \(0.540703\pi\)
\(972\) 2.12135e15 0.0784237
\(973\) 3.25956e16 1.19823
\(974\) 1.43040e16 0.522857
\(975\) 7.65683e14 0.0278307
\(976\) 1.52690e16 0.551868
\(977\) −8.98868e15 −0.323054 −0.161527 0.986868i \(-0.551642\pi\)
−0.161527 + 0.986868i \(0.551642\pi\)
\(978\) −8.59195e15 −0.307063
\(979\) 5.79945e16 2.06102
\(980\) −9.96999e14 −0.0352331
\(981\) −1.05977e15 −0.0372421
\(982\) −3.10904e16 −1.08646
\(983\) −3.43270e16 −1.19286 −0.596432 0.802664i \(-0.703415\pi\)
−0.596432 + 0.802664i \(0.703415\pi\)
\(984\) −8.18927e15 −0.282991
\(985\) 6.14065e14 0.0211016
\(986\) −4.92550e16 −1.68317
\(987\) 4.56075e15 0.154986
\(988\) 1.39684e15 0.0472044
\(989\) −2.38873e15 −0.0802764
\(990\) −5.75194e14 −0.0192230
\(991\) −4.41564e16 −1.46754 −0.733768 0.679400i \(-0.762240\pi\)
−0.733768 + 0.679400i \(0.762240\pi\)
\(992\) −6.94144e16 −2.29422
\(993\) 1.00724e16 0.331063
\(994\) −7.56329e16 −2.47221
\(995\) −5.44586e14 −0.0177027
\(996\) −3.00947e15 −0.0972889
\(997\) 8.85676e15 0.284742 0.142371 0.989813i \(-0.454527\pi\)
0.142371 + 0.989813i \(0.454527\pi\)
\(998\) −9.26017e16 −2.96074
\(999\) 8.79232e14 0.0279572
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 177.12.a.d.1.4 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.d.1.4 28 1.1 even 1 trivial