Properties

Label 177.12.a.d.1.11
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $1$

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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 1.11
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-33.1334 q^{2} +243.000 q^{3} -950.178 q^{4} -7615.06 q^{5} -8051.42 q^{6} +31854.1 q^{7} +99339.8 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-33.1334 q^{2} +243.000 q^{3} -950.178 q^{4} -7615.06 q^{5} -8051.42 q^{6} +31854.1 q^{7} +99339.8 q^{8} +59049.0 q^{9} +252313. q^{10} -99167.3 q^{11} -230893. q^{12} -2.33849e6 q^{13} -1.05543e6 q^{14} -1.85046e6 q^{15} -1.34550e6 q^{16} +6.72361e6 q^{17} -1.95649e6 q^{18} +1.10609e7 q^{19} +7.23566e6 q^{20} +7.74054e6 q^{21} +3.28575e6 q^{22} -5.57179e7 q^{23} +2.41396e7 q^{24} +9.16098e6 q^{25} +7.74820e7 q^{26} +1.43489e7 q^{27} -3.02670e7 q^{28} +1.29094e8 q^{29} +6.13120e7 q^{30} +2.79883e8 q^{31} -1.58867e8 q^{32} -2.40977e7 q^{33} -2.22776e8 q^{34} -2.42570e8 q^{35} -5.61070e7 q^{36} -4.52016e8 q^{37} -3.66487e8 q^{38} -5.68252e8 q^{39} -7.56479e8 q^{40} -1.17503e9 q^{41} -2.56470e8 q^{42} -2.54829e8 q^{43} +9.42266e7 q^{44} -4.49662e8 q^{45} +1.84613e9 q^{46} -5.43969e8 q^{47} -3.26957e8 q^{48} -9.62646e8 q^{49} -3.03535e8 q^{50} +1.63384e9 q^{51} +2.22198e9 q^{52} -1.96026e8 q^{53} -4.75428e8 q^{54} +7.55165e8 q^{55} +3.16438e9 q^{56} +2.68781e9 q^{57} -4.27732e9 q^{58} +7.14924e8 q^{59} +1.75826e9 q^{60} +2.08702e8 q^{61} -9.27347e9 q^{62} +1.88095e9 q^{63} +8.01939e9 q^{64} +1.78077e10 q^{65} +7.98438e8 q^{66} -1.67659e10 q^{67} -6.38863e9 q^{68} -1.35395e10 q^{69} +8.03719e9 q^{70} +1.37657e10 q^{71} +5.86592e9 q^{72} +1.74137e10 q^{73} +1.49768e10 q^{74} +2.22612e9 q^{75} -1.05099e10 q^{76} -3.15888e9 q^{77} +1.88281e10 q^{78} -4.30634e10 q^{79} +1.02461e10 q^{80} +3.48678e9 q^{81} +3.89326e10 q^{82} +1.24248e10 q^{83} -7.35488e9 q^{84} -5.12007e10 q^{85} +8.44337e9 q^{86} +3.13698e10 q^{87} -9.85127e9 q^{88} -7.87224e10 q^{89} +1.48988e10 q^{90} -7.44903e10 q^{91} +5.29419e10 q^{92} +6.80115e10 q^{93} +1.80236e10 q^{94} -8.42298e10 q^{95} -3.86046e10 q^{96} +4.05929e9 q^{97} +3.18957e10 q^{98} -5.85573e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + O(q^{10}) \) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + 616281q^{10} + 1082362q^{11} + 7099002q^{12} + 503712q^{13} + 1321669q^{14} + 6454566q^{15} + 34870338q^{16} + 13513579q^{17} + 5668704q^{18} + 35971687q^{19} + 96105997q^{20} + 34586919q^{21} - 47598882q^{22} + 61380539q^{23} + 80756433q^{24} + 294744746q^{25} + 62820734q^{26} + 401769396q^{27} + 148068294q^{28} + 322339307q^{29} + 149756283q^{30} + 151247077q^{31} + 466383494q^{32} + 263013966q^{33} + 684479860q^{34} + 960297361q^{35} + 1725057486q^{36} + 863508437q^{37} + 992640509q^{38} + 122402016q^{39} + 3067680252q^{40} + 3081170377q^{41} + 321165567q^{42} + 2554238300q^{43} + 4350123570q^{44} + 1568459538q^{45} - 1987059155q^{46} + 6203398333q^{47} + 8473492134q^{48} + 10327857997q^{49} + 17577682253q^{50} + 3283799697q^{51} + 32137181618q^{52} + 14571770754q^{53} + 1377495072q^{54} + 18251419334q^{55} + 33498842836q^{56} + 8741119941q^{57} + 11860778276q^{58} + 20017880372q^{59} + 23353757271q^{60} + 2761613771q^{61} + 13785829526q^{62} + 8404621317q^{63} + 86547545293q^{64} + 32034985256q^{65} - 11566528326q^{66} + 39381333296q^{67} + 38995496621q^{68} + 14915470977q^{69} + 8551800364q^{70} + 26130020296q^{71} + 19623813219q^{72} + 41382402799q^{73} + 23815315058q^{74} + 71622973278q^{75} + 10611720128q^{76} - 8426124313q^{77} + 15265438362q^{78} + 59825111206q^{79} + 4009687655q^{80} + 97629963228q^{81} - 39592715115q^{82} + 35433122727q^{83} + 35980595442q^{84} - 8950496085q^{85} - 182032360688q^{86} + 78328451601q^{87} - 220003602335q^{88} + 102303043039q^{89} + 36390776769q^{90} - 111146323655q^{91} - 163000203526q^{92} + 36753039711q^{93} - 81314346008q^{94} + 208102168887q^{95} + 113331189042q^{96} - 171891031490q^{97} + 72304707792q^{98} + 63912393738q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −33.1334 −0.732152 −0.366076 0.930585i \(-0.619299\pi\)
−0.366076 + 0.930585i \(0.619299\pi\)
\(3\) 243.000 0.577350
\(4\) −950.178 −0.463954
\(5\) −7615.06 −1.08978 −0.544889 0.838508i \(-0.683428\pi\)
−0.544889 + 0.838508i \(0.683428\pi\)
\(6\) −8051.42 −0.422708
\(7\) 31854.1 0.716350 0.358175 0.933654i \(-0.383399\pi\)
0.358175 + 0.933654i \(0.383399\pi\)
\(8\) 99339.8 1.07184
\(9\) 59049.0 0.333333
\(10\) 252313. 0.797883
\(11\) −99167.3 −0.185656 −0.0928280 0.995682i \(-0.529591\pi\)
−0.0928280 + 0.995682i \(0.529591\pi\)
\(12\) −230893. −0.267864
\(13\) −2.33849e6 −1.74681 −0.873406 0.486992i \(-0.838094\pi\)
−0.873406 + 0.486992i \(0.838094\pi\)
\(14\) −1.05543e6 −0.524477
\(15\) −1.85046e6 −0.629184
\(16\) −1.34550e6 −0.320793
\(17\) 6.72361e6 1.14851 0.574253 0.818678i \(-0.305292\pi\)
0.574253 + 0.818678i \(0.305292\pi\)
\(18\) −1.95649e6 −0.244051
\(19\) 1.10609e7 1.02482 0.512410 0.858741i \(-0.328753\pi\)
0.512410 + 0.858741i \(0.328753\pi\)
\(20\) 7.23566e6 0.505607
\(21\) 7.74054e6 0.413585
\(22\) 3.28575e6 0.135928
\(23\) −5.57179e7 −1.80506 −0.902531 0.430625i \(-0.858293\pi\)
−0.902531 + 0.430625i \(0.858293\pi\)
\(24\) 2.41396e7 0.618825
\(25\) 9.16098e6 0.187617
\(26\) 7.74820e7 1.27893
\(27\) 1.43489e7 0.192450
\(28\) −3.02670e7 −0.332354
\(29\) 1.29094e8 1.16874 0.584369 0.811488i \(-0.301342\pi\)
0.584369 + 0.811488i \(0.301342\pi\)
\(30\) 6.13120e7 0.460658
\(31\) 2.79883e8 1.75585 0.877924 0.478800i \(-0.158928\pi\)
0.877924 + 0.478800i \(0.158928\pi\)
\(32\) −1.58867e8 −0.836967
\(33\) −2.40977e7 −0.107189
\(34\) −2.22776e8 −0.840881
\(35\) −2.42570e8 −0.780663
\(36\) −5.61070e7 −0.154651
\(37\) −4.52016e8 −1.07163 −0.535814 0.844336i \(-0.679995\pi\)
−0.535814 + 0.844336i \(0.679995\pi\)
\(38\) −3.66487e8 −0.750324
\(39\) −5.68252e8 −1.00852
\(40\) −7.56479e8 −1.16806
\(41\) −1.17503e9 −1.58393 −0.791965 0.610566i \(-0.790942\pi\)
−0.791965 + 0.610566i \(0.790942\pi\)
\(42\) −2.56470e8 −0.302807
\(43\) −2.54829e8 −0.264346 −0.132173 0.991227i \(-0.542195\pi\)
−0.132173 + 0.991227i \(0.542195\pi\)
\(44\) 9.42266e7 0.0861358
\(45\) −4.49662e8 −0.363259
\(46\) 1.84613e9 1.32158
\(47\) −5.43969e8 −0.345968 −0.172984 0.984925i \(-0.555341\pi\)
−0.172984 + 0.984925i \(0.555341\pi\)
\(48\) −3.26957e8 −0.185210
\(49\) −9.62646e8 −0.486842
\(50\) −3.03535e8 −0.137364
\(51\) 1.63384e9 0.663091
\(52\) 2.22198e9 0.810441
\(53\) −1.96026e8 −0.0643868 −0.0321934 0.999482i \(-0.510249\pi\)
−0.0321934 + 0.999482i \(0.510249\pi\)
\(54\) −4.75428e8 −0.140903
\(55\) 7.55165e8 0.202324
\(56\) 3.16438e9 0.767810
\(57\) 2.68781e9 0.591680
\(58\) −4.27732e9 −0.855693
\(59\) 7.14924e8 0.130189
\(60\) 1.75826e9 0.291912
\(61\) 2.08702e8 0.0316383 0.0158191 0.999875i \(-0.494964\pi\)
0.0158191 + 0.999875i \(0.494964\pi\)
\(62\) −9.27347e9 −1.28555
\(63\) 1.88095e9 0.238783
\(64\) 8.01939e9 0.933580
\(65\) 1.78077e10 1.90364
\(66\) 7.98438e8 0.0784783
\(67\) −1.67659e10 −1.51711 −0.758553 0.651612i \(-0.774093\pi\)
−0.758553 + 0.651612i \(0.774093\pi\)
\(68\) −6.38863e9 −0.532854
\(69\) −1.35395e10 −1.04215
\(70\) 8.03719e9 0.571564
\(71\) 1.37657e10 0.905476 0.452738 0.891644i \(-0.350447\pi\)
0.452738 + 0.891644i \(0.350447\pi\)
\(72\) 5.86592e9 0.357279
\(73\) 1.74137e10 0.983140 0.491570 0.870838i \(-0.336423\pi\)
0.491570 + 0.870838i \(0.336423\pi\)
\(74\) 1.49768e10 0.784595
\(75\) 2.22612e9 0.108321
\(76\) −1.05099e10 −0.475469
\(77\) −3.15888e9 −0.132995
\(78\) 1.88281e10 0.738392
\(79\) −4.30634e10 −1.57456 −0.787280 0.616596i \(-0.788511\pi\)
−0.787280 + 0.616596i \(0.788511\pi\)
\(80\) 1.02461e10 0.349593
\(81\) 3.48678e9 0.111111
\(82\) 3.89326e10 1.15968
\(83\) 1.24248e10 0.346227 0.173113 0.984902i \(-0.444617\pi\)
0.173113 + 0.984902i \(0.444617\pi\)
\(84\) −7.35488e9 −0.191884
\(85\) −5.12007e10 −1.25162
\(86\) 8.44337e9 0.193542
\(87\) 3.13698e10 0.674771
\(88\) −9.85127e9 −0.198993
\(89\) −7.87224e10 −1.49435 −0.747177 0.664626i \(-0.768591\pi\)
−0.747177 + 0.664626i \(0.768591\pi\)
\(90\) 1.48988e10 0.265961
\(91\) −7.44903e10 −1.25133
\(92\) 5.29419e10 0.837465
\(93\) 6.80115e10 1.01374
\(94\) 1.80236e10 0.253301
\(95\) −8.42298e10 −1.11683
\(96\) −3.86046e10 −0.483223
\(97\) 4.05929e9 0.0479960 0.0239980 0.999712i \(-0.492360\pi\)
0.0239980 + 0.999712i \(0.492360\pi\)
\(98\) 3.18957e10 0.356442
\(99\) −5.85573e9 −0.0618853
\(100\) −8.70456e9 −0.0870456
\(101\) −1.60174e9 −0.0151644 −0.00758218 0.999971i \(-0.502414\pi\)
−0.00758218 + 0.999971i \(0.502414\pi\)
\(102\) −5.41346e10 −0.485483
\(103\) 5.39345e10 0.458418 0.229209 0.973377i \(-0.426386\pi\)
0.229209 + 0.973377i \(0.426386\pi\)
\(104\) −2.32305e11 −1.87230
\(105\) −5.89446e10 −0.450716
\(106\) 6.49501e9 0.0471409
\(107\) −1.13176e10 −0.0780091 −0.0390046 0.999239i \(-0.512419\pi\)
−0.0390046 + 0.999239i \(0.512419\pi\)
\(108\) −1.36340e10 −0.0892880
\(109\) −1.07676e11 −0.670308 −0.335154 0.942163i \(-0.608788\pi\)
−0.335154 + 0.942163i \(0.608788\pi\)
\(110\) −2.50212e10 −0.148132
\(111\) −1.09840e11 −0.618705
\(112\) −4.28597e10 −0.229800
\(113\) 2.25571e11 1.15173 0.575865 0.817545i \(-0.304665\pi\)
0.575865 + 0.817545i \(0.304665\pi\)
\(114\) −8.90563e10 −0.433200
\(115\) 4.24295e11 1.96712
\(116\) −1.22662e11 −0.542240
\(117\) −1.38085e11 −0.582271
\(118\) −2.36879e10 −0.0953180
\(119\) 2.14174e11 0.822733
\(120\) −1.83824e11 −0.674382
\(121\) −2.75478e11 −0.965532
\(122\) −6.91501e9 −0.0231640
\(123\) −2.85531e11 −0.914483
\(124\) −2.65938e11 −0.814632
\(125\) 3.02068e11 0.885317
\(126\) −6.23223e10 −0.174826
\(127\) 3.37316e11 0.905976 0.452988 0.891517i \(-0.350358\pi\)
0.452988 + 0.891517i \(0.350358\pi\)
\(128\) 5.96496e10 0.153445
\(129\) −6.19236e10 −0.152620
\(130\) −5.90030e11 −1.39375
\(131\) 8.15888e11 1.84773 0.923864 0.382720i \(-0.125013\pi\)
0.923864 + 0.382720i \(0.125013\pi\)
\(132\) 2.28971e10 0.0497305
\(133\) 3.52336e11 0.734130
\(134\) 5.55512e11 1.11075
\(135\) −1.09268e11 −0.209728
\(136\) 6.67923e11 1.23101
\(137\) −2.76493e8 −0.000489465 0 −0.000244732 1.00000i \(-0.500078\pi\)
−0.000244732 1.00000i \(0.500078\pi\)
\(138\) 4.48608e11 0.763014
\(139\) 1.88096e11 0.307467 0.153734 0.988112i \(-0.450870\pi\)
0.153734 + 0.988112i \(0.450870\pi\)
\(140\) 2.30485e11 0.362192
\(141\) −1.32185e11 −0.199745
\(142\) −4.56104e11 −0.662946
\(143\) 2.31901e11 0.324306
\(144\) −7.94506e10 −0.106931
\(145\) −9.83058e11 −1.27366
\(146\) −5.76975e11 −0.719808
\(147\) −2.33923e11 −0.281078
\(148\) 4.29495e11 0.497186
\(149\) −2.65066e11 −0.295685 −0.147843 0.989011i \(-0.547233\pi\)
−0.147843 + 0.989011i \(0.547233\pi\)
\(150\) −7.37589e10 −0.0793072
\(151\) 1.28494e12 1.33202 0.666009 0.745944i \(-0.268001\pi\)
0.666009 + 0.745944i \(0.268001\pi\)
\(152\) 1.09879e12 1.09844
\(153\) 3.97023e11 0.382836
\(154\) 1.04665e11 0.0973723
\(155\) −2.13132e12 −1.91348
\(156\) 5.39940e11 0.467908
\(157\) −4.16613e11 −0.348566 −0.174283 0.984696i \(-0.555761\pi\)
−0.174283 + 0.984696i \(0.555761\pi\)
\(158\) 1.42684e12 1.15282
\(159\) −4.76343e10 −0.0371737
\(160\) 1.20978e12 0.912109
\(161\) −1.77484e12 −1.29306
\(162\) −1.15529e11 −0.0813502
\(163\) 3.78137e11 0.257405 0.128703 0.991683i \(-0.458919\pi\)
0.128703 + 0.991683i \(0.458919\pi\)
\(164\) 1.11648e12 0.734871
\(165\) 1.83505e11 0.116812
\(166\) −4.11677e11 −0.253490
\(167\) 3.30555e12 1.96926 0.984630 0.174655i \(-0.0558809\pi\)
0.984630 + 0.174655i \(0.0558809\pi\)
\(168\) 7.68943e11 0.443296
\(169\) 3.67636e12 2.05136
\(170\) 1.69645e12 0.916374
\(171\) 6.53138e11 0.341607
\(172\) 2.42133e11 0.122644
\(173\) 4.89191e11 0.240008 0.120004 0.992773i \(-0.461709\pi\)
0.120004 + 0.992773i \(0.461709\pi\)
\(174\) −1.03939e12 −0.494035
\(175\) 2.91814e11 0.134399
\(176\) 1.33430e11 0.0595571
\(177\) 1.73727e11 0.0751646
\(178\) 2.60834e12 1.09409
\(179\) −3.03678e12 −1.23516 −0.617578 0.786510i \(-0.711886\pi\)
−0.617578 + 0.786510i \(0.711886\pi\)
\(180\) 4.27258e11 0.168536
\(181\) −3.34218e11 −0.127879 −0.0639393 0.997954i \(-0.520366\pi\)
−0.0639393 + 0.997954i \(0.520366\pi\)
\(182\) 2.46812e12 0.916163
\(183\) 5.07146e10 0.0182664
\(184\) −5.53501e12 −1.93473
\(185\) 3.44213e12 1.16784
\(186\) −2.25345e12 −0.742211
\(187\) −6.66763e11 −0.213227
\(188\) 5.16867e11 0.160513
\(189\) 4.57071e11 0.137862
\(190\) 2.79082e12 0.817686
\(191\) 3.03727e12 0.864571 0.432285 0.901737i \(-0.357707\pi\)
0.432285 + 0.901737i \(0.357707\pi\)
\(192\) 1.94871e12 0.539003
\(193\) 5.70463e12 1.53342 0.766712 0.641991i \(-0.221891\pi\)
0.766712 + 0.641991i \(0.221891\pi\)
\(194\) −1.34498e11 −0.0351404
\(195\) 4.32727e12 1.09907
\(196\) 9.14685e11 0.225872
\(197\) 4.35600e11 0.104598 0.0522991 0.998631i \(-0.483345\pi\)
0.0522991 + 0.998631i \(0.483345\pi\)
\(198\) 1.94020e11 0.0453094
\(199\) 3.56600e12 0.810009 0.405004 0.914315i \(-0.367270\pi\)
0.405004 + 0.914315i \(0.367270\pi\)
\(200\) 9.10051e11 0.201095
\(201\) −4.07412e12 −0.875901
\(202\) 5.30710e10 0.0111026
\(203\) 4.11217e12 0.837226
\(204\) −1.55244e12 −0.307644
\(205\) 8.94789e12 1.72613
\(206\) −1.78703e12 −0.335632
\(207\) −3.29009e12 −0.601687
\(208\) 3.14644e12 0.560365
\(209\) −1.09688e12 −0.190264
\(210\) 1.95304e12 0.329993
\(211\) −7.12598e12 −1.17298 −0.586491 0.809956i \(-0.699491\pi\)
−0.586491 + 0.809956i \(0.699491\pi\)
\(212\) 1.86260e11 0.0298725
\(213\) 3.34506e12 0.522777
\(214\) 3.74992e11 0.0571145
\(215\) 1.94054e12 0.288079
\(216\) 1.42542e12 0.206275
\(217\) 8.91540e12 1.25780
\(218\) 3.56768e12 0.490767
\(219\) 4.23153e12 0.567616
\(220\) −7.17541e11 −0.0938689
\(221\) −1.57231e13 −2.00623
\(222\) 3.63937e12 0.452986
\(223\) 2.54932e11 0.0309562 0.0154781 0.999880i \(-0.495073\pi\)
0.0154781 + 0.999880i \(0.495073\pi\)
\(224\) −5.06055e12 −0.599562
\(225\) 5.40947e11 0.0625390
\(226\) −7.47392e12 −0.843242
\(227\) −6.88194e12 −0.757824 −0.378912 0.925433i \(-0.623702\pi\)
−0.378912 + 0.925433i \(0.623702\pi\)
\(228\) −2.55390e12 −0.274512
\(229\) 1.08908e11 0.0114279 0.00571394 0.999984i \(-0.498181\pi\)
0.00571394 + 0.999984i \(0.498181\pi\)
\(230\) −1.40584e13 −1.44023
\(231\) −7.67608e11 −0.0767845
\(232\) 1.28242e13 1.25270
\(233\) 1.00418e13 0.957971 0.478985 0.877823i \(-0.341005\pi\)
0.478985 + 0.877823i \(0.341005\pi\)
\(234\) 4.57524e12 0.426311
\(235\) 4.14236e12 0.377029
\(236\) −6.79305e11 −0.0604016
\(237\) −1.04644e13 −0.909072
\(238\) −7.09632e12 −0.602366
\(239\) 1.63667e13 1.35760 0.678802 0.734322i \(-0.262500\pi\)
0.678802 + 0.734322i \(0.262500\pi\)
\(240\) 2.48980e12 0.201838
\(241\) 2.87914e12 0.228123 0.114062 0.993474i \(-0.463614\pi\)
0.114062 + 0.993474i \(0.463614\pi\)
\(242\) 9.12751e12 0.706916
\(243\) 8.47289e11 0.0641500
\(244\) −1.98304e11 −0.0146787
\(245\) 7.33060e12 0.530550
\(246\) 9.46062e12 0.669540
\(247\) −2.58659e13 −1.79017
\(248\) 2.78035e13 1.88198
\(249\) 3.01923e12 0.199894
\(250\) −1.00085e13 −0.648187
\(251\) 9.79800e12 0.620772 0.310386 0.950611i \(-0.399542\pi\)
0.310386 + 0.950611i \(0.399542\pi\)
\(252\) −1.78724e12 −0.110785
\(253\) 5.52540e12 0.335120
\(254\) −1.11764e13 −0.663312
\(255\) −1.24418e13 −0.722622
\(256\) −1.84001e13 −1.04593
\(257\) −6.46536e12 −0.359717 −0.179858 0.983693i \(-0.557564\pi\)
−0.179858 + 0.983693i \(0.557564\pi\)
\(258\) 2.05174e12 0.111741
\(259\) −1.43985e13 −0.767662
\(260\) −1.69205e13 −0.883201
\(261\) 7.62287e12 0.389579
\(262\) −2.70331e13 −1.35282
\(263\) 3.52320e13 1.72656 0.863278 0.504729i \(-0.168408\pi\)
0.863278 + 0.504729i \(0.168408\pi\)
\(264\) −2.39386e12 −0.114889
\(265\) 1.49275e12 0.0701673
\(266\) −1.16741e13 −0.537495
\(267\) −1.91295e13 −0.862765
\(268\) 1.59306e13 0.703867
\(269\) 3.95151e13 1.71051 0.855255 0.518207i \(-0.173400\pi\)
0.855255 + 0.518207i \(0.173400\pi\)
\(270\) 3.62041e12 0.153553
\(271\) −3.21606e13 −1.33657 −0.668286 0.743904i \(-0.732972\pi\)
−0.668286 + 0.743904i \(0.732972\pi\)
\(272\) −9.04664e12 −0.368433
\(273\) −1.81011e13 −0.722456
\(274\) 9.16116e9 0.000358362 0
\(275\) −9.08470e11 −0.0348322
\(276\) 1.28649e13 0.483511
\(277\) 3.18499e13 1.17346 0.586731 0.809782i \(-0.300415\pi\)
0.586731 + 0.809782i \(0.300415\pi\)
\(278\) −6.23227e12 −0.225113
\(279\) 1.65268e13 0.585282
\(280\) −2.40969e13 −0.836743
\(281\) 2.48402e13 0.845806 0.422903 0.906175i \(-0.361011\pi\)
0.422903 + 0.906175i \(0.361011\pi\)
\(282\) 4.37972e12 0.146244
\(283\) −2.30183e13 −0.753787 −0.376893 0.926257i \(-0.623008\pi\)
−0.376893 + 0.926257i \(0.623008\pi\)
\(284\) −1.30799e13 −0.420099
\(285\) −2.04678e13 −0.644800
\(286\) −7.68369e12 −0.237441
\(287\) −3.74293e13 −1.13465
\(288\) −9.38093e12 −0.278989
\(289\) 1.09351e13 0.319068
\(290\) 3.25721e13 0.932516
\(291\) 9.86406e11 0.0277105
\(292\) −1.65461e13 −0.456132
\(293\) 4.00130e13 1.08250 0.541252 0.840861i \(-0.317951\pi\)
0.541252 + 0.840861i \(0.317951\pi\)
\(294\) 7.75066e12 0.205792
\(295\) −5.44419e12 −0.141877
\(296\) −4.49032e13 −1.14861
\(297\) −1.42294e12 −0.0357295
\(298\) 8.78254e12 0.216486
\(299\) 1.30296e14 3.15310
\(300\) −2.11521e12 −0.0502558
\(301\) −8.11735e12 −0.189365
\(302\) −4.25745e13 −0.975239
\(303\) −3.89222e11 −0.00875515
\(304\) −1.48825e13 −0.328755
\(305\) −1.58928e12 −0.0344787
\(306\) −1.31547e13 −0.280294
\(307\) −7.35835e13 −1.54000 −0.769998 0.638046i \(-0.779743\pi\)
−0.769998 + 0.638046i \(0.779743\pi\)
\(308\) 3.00150e12 0.0617034
\(309\) 1.31061e13 0.264668
\(310\) 7.06180e13 1.40096
\(311\) −3.87432e13 −0.755115 −0.377557 0.925986i \(-0.623236\pi\)
−0.377557 + 0.925986i \(0.623236\pi\)
\(312\) −5.64501e13 −1.08097
\(313\) −6.86342e13 −1.29136 −0.645679 0.763609i \(-0.723426\pi\)
−0.645679 + 0.763609i \(0.723426\pi\)
\(314\) 1.38038e13 0.255203
\(315\) −1.43235e13 −0.260221
\(316\) 4.09178e13 0.730523
\(317\) 7.94681e13 1.39433 0.697167 0.716909i \(-0.254444\pi\)
0.697167 + 0.716909i \(0.254444\pi\)
\(318\) 1.57829e12 0.0272168
\(319\) −1.28019e13 −0.216983
\(320\) −6.10681e13 −1.01740
\(321\) −2.75019e12 −0.0450386
\(322\) 5.88066e13 0.946714
\(323\) 7.43695e13 1.17701
\(324\) −3.31306e12 −0.0515504
\(325\) −2.14228e13 −0.327732
\(326\) −1.25290e13 −0.188460
\(327\) −2.61653e13 −0.387002
\(328\) −1.16727e14 −1.69771
\(329\) −1.73276e13 −0.247834
\(330\) −6.08015e12 −0.0855239
\(331\) 1.06800e14 1.47747 0.738734 0.673997i \(-0.235424\pi\)
0.738734 + 0.673997i \(0.235424\pi\)
\(332\) −1.18058e13 −0.160633
\(333\) −2.66911e13 −0.357210
\(334\) −1.09524e14 −1.44180
\(335\) 1.27673e14 1.65331
\(336\) −1.04149e13 −0.132675
\(337\) 1.17087e14 1.46738 0.733691 0.679483i \(-0.237796\pi\)
0.733691 + 0.679483i \(0.237796\pi\)
\(338\) −1.21810e14 −1.50190
\(339\) 5.48136e13 0.664952
\(340\) 4.86498e13 0.580693
\(341\) −2.77552e13 −0.325984
\(342\) −2.16407e13 −0.250108
\(343\) −9.36501e13 −1.06510
\(344\) −2.53147e13 −0.283336
\(345\) 1.03104e14 1.13572
\(346\) −1.62086e13 −0.175722
\(347\) 3.75321e13 0.400489 0.200244 0.979746i \(-0.435826\pi\)
0.200244 + 0.979746i \(0.435826\pi\)
\(348\) −2.98069e13 −0.313063
\(349\) −5.49071e13 −0.567660 −0.283830 0.958875i \(-0.591605\pi\)
−0.283830 + 0.958875i \(0.591605\pi\)
\(350\) −9.66881e12 −0.0984008
\(351\) −3.35547e13 −0.336174
\(352\) 1.57544e13 0.155388
\(353\) 2.81865e13 0.273704 0.136852 0.990592i \(-0.456302\pi\)
0.136852 + 0.990592i \(0.456302\pi\)
\(354\) −5.75615e12 −0.0550319
\(355\) −1.04827e14 −0.986769
\(356\) 7.48002e13 0.693311
\(357\) 5.20444e13 0.475005
\(358\) 1.00619e14 0.904321
\(359\) −2.43931e13 −0.215898 −0.107949 0.994156i \(-0.534428\pi\)
−0.107949 + 0.994156i \(0.534428\pi\)
\(360\) −4.46693e13 −0.389355
\(361\) 5.85431e12 0.0502558
\(362\) 1.10738e13 0.0936265
\(363\) −6.69410e13 −0.557450
\(364\) 7.07790e13 0.580559
\(365\) −1.32606e14 −1.07141
\(366\) −1.68035e12 −0.0133737
\(367\) 4.60549e13 0.361088 0.180544 0.983567i \(-0.442214\pi\)
0.180544 + 0.983567i \(0.442214\pi\)
\(368\) 7.49687e13 0.579051
\(369\) −6.93841e13 −0.527977
\(370\) −1.14049e14 −0.855034
\(371\) −6.24423e12 −0.0461235
\(372\) −6.46230e13 −0.470328
\(373\) 1.15238e14 0.826416 0.413208 0.910637i \(-0.364408\pi\)
0.413208 + 0.910637i \(0.364408\pi\)
\(374\) 2.20921e13 0.156115
\(375\) 7.34024e13 0.511138
\(376\) −5.40378e13 −0.370821
\(377\) −3.01885e14 −2.04157
\(378\) −1.51443e13 −0.100936
\(379\) 1.20190e14 0.789503 0.394752 0.918788i \(-0.370831\pi\)
0.394752 + 0.918788i \(0.370831\pi\)
\(380\) 8.00332e13 0.518156
\(381\) 8.19678e13 0.523065
\(382\) −1.00635e14 −0.632997
\(383\) −7.39307e13 −0.458386 −0.229193 0.973381i \(-0.573609\pi\)
−0.229193 + 0.973381i \(0.573609\pi\)
\(384\) 1.44949e13 0.0885916
\(385\) 2.40551e13 0.144935
\(386\) −1.89014e14 −1.12270
\(387\) −1.50474e13 −0.0881154
\(388\) −3.85704e12 −0.0222679
\(389\) −3.62478e13 −0.206329 −0.103164 0.994664i \(-0.532897\pi\)
−0.103164 + 0.994664i \(0.532897\pi\)
\(390\) −1.43377e14 −0.804683
\(391\) −3.74626e14 −2.07313
\(392\) −9.56291e13 −0.521815
\(393\) 1.98261e14 1.06679
\(394\) −1.44329e13 −0.0765817
\(395\) 3.27930e14 1.71592
\(396\) 5.56399e12 0.0287119
\(397\) −1.65352e14 −0.841515 −0.420758 0.907173i \(-0.638236\pi\)
−0.420758 + 0.907173i \(0.638236\pi\)
\(398\) −1.18154e14 −0.593049
\(399\) 8.56177e13 0.423850
\(400\) −1.23261e13 −0.0601862
\(401\) 7.97032e13 0.383868 0.191934 0.981408i \(-0.438524\pi\)
0.191934 + 0.981408i \(0.438524\pi\)
\(402\) 1.34989e14 0.641293
\(403\) −6.54502e14 −3.06714
\(404\) 1.52194e12 0.00703556
\(405\) −2.65521e13 −0.121086
\(406\) −1.36250e14 −0.612976
\(407\) 4.48252e13 0.198954
\(408\) 1.62305e14 0.710725
\(409\) −2.79151e14 −1.20604 −0.603019 0.797727i \(-0.706036\pi\)
−0.603019 + 0.797727i \(0.706036\pi\)
\(410\) −2.96474e14 −1.26379
\(411\) −6.71878e10 −0.000282593 0
\(412\) −5.12474e13 −0.212685
\(413\) 2.27732e13 0.0932609
\(414\) 1.09012e14 0.440526
\(415\) −9.46157e13 −0.377310
\(416\) 3.71508e14 1.46203
\(417\) 4.57074e13 0.177516
\(418\) 3.63435e13 0.139302
\(419\) 3.51450e14 1.32950 0.664748 0.747068i \(-0.268539\pi\)
0.664748 + 0.747068i \(0.268539\pi\)
\(420\) 5.60079e13 0.209111
\(421\) 1.33484e14 0.491900 0.245950 0.969282i \(-0.420900\pi\)
0.245950 + 0.969282i \(0.420900\pi\)
\(422\) 2.36108e14 0.858800
\(423\) −3.21208e13 −0.115323
\(424\) −1.94732e13 −0.0690121
\(425\) 6.15949e13 0.215479
\(426\) −1.10833e14 −0.382752
\(427\) 6.64801e12 0.0226641
\(428\) 1.07538e13 0.0361926
\(429\) 5.63521e13 0.187238
\(430\) −6.42967e13 −0.210917
\(431\) 1.79025e14 0.579815 0.289907 0.957055i \(-0.406376\pi\)
0.289907 + 0.957055i \(0.406376\pi\)
\(432\) −1.93065e13 −0.0617366
\(433\) 1.72864e14 0.545786 0.272893 0.962044i \(-0.412020\pi\)
0.272893 + 0.962044i \(0.412020\pi\)
\(434\) −2.95398e14 −0.920902
\(435\) −2.38883e14 −0.735351
\(436\) 1.02312e14 0.310992
\(437\) −6.16293e14 −1.84986
\(438\) −1.40205e14 −0.415581
\(439\) −5.80238e14 −1.69844 −0.849222 0.528037i \(-0.822928\pi\)
−0.849222 + 0.528037i \(0.822928\pi\)
\(440\) 7.50180e13 0.216858
\(441\) −5.68433e13 −0.162281
\(442\) 5.20959e14 1.46886
\(443\) 3.25451e14 0.906286 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(444\) 1.04367e14 0.287051
\(445\) 5.99476e14 1.62851
\(446\) −8.44675e12 −0.0226646
\(447\) −6.44111e13 −0.170714
\(448\) 2.55450e14 0.668770
\(449\) −1.18005e14 −0.305172 −0.152586 0.988290i \(-0.548760\pi\)
−0.152586 + 0.988290i \(0.548760\pi\)
\(450\) −1.79234e13 −0.0457880
\(451\) 1.16524e14 0.294066
\(452\) −2.14332e14 −0.534350
\(453\) 3.12241e14 0.769041
\(454\) 2.28022e14 0.554842
\(455\) 5.67248e14 1.36367
\(456\) 2.67007e14 0.634184
\(457\) −1.55221e14 −0.364261 −0.182130 0.983274i \(-0.558299\pi\)
−0.182130 + 0.983274i \(0.558299\pi\)
\(458\) −3.60850e12 −0.00836694
\(459\) 9.64765e13 0.221030
\(460\) −4.03156e14 −0.912652
\(461\) 4.11776e14 0.921097 0.460549 0.887634i \(-0.347653\pi\)
0.460549 + 0.887634i \(0.347653\pi\)
\(462\) 2.54335e13 0.0562179
\(463\) −1.06071e14 −0.231687 −0.115844 0.993267i \(-0.536957\pi\)
−0.115844 + 0.993267i \(0.536957\pi\)
\(464\) −1.73696e14 −0.374923
\(465\) −5.17912e14 −1.10475
\(466\) −3.32718e14 −0.701380
\(467\) −6.90002e14 −1.43750 −0.718749 0.695270i \(-0.755285\pi\)
−0.718749 + 0.695270i \(0.755285\pi\)
\(468\) 1.31206e14 0.270147
\(469\) −5.34062e14 −1.08678
\(470\) −1.37250e14 −0.276042
\(471\) −1.01237e14 −0.201245
\(472\) 7.10205e13 0.139541
\(473\) 2.52708e13 0.0490775
\(474\) 3.46721e14 0.665579
\(475\) 1.01329e14 0.192274
\(476\) −2.03504e14 −0.381710
\(477\) −1.15751e13 −0.0214623
\(478\) −5.42285e14 −0.993971
\(479\) −9.23453e14 −1.67328 −0.836641 0.547751i \(-0.815484\pi\)
−0.836641 + 0.547751i \(0.815484\pi\)
\(480\) 2.93977e14 0.526606
\(481\) 1.05703e15 1.87193
\(482\) −9.53957e13 −0.167021
\(483\) −4.31287e14 −0.746547
\(484\) 2.61753e14 0.447962
\(485\) −3.09117e13 −0.0523050
\(486\) −2.80736e13 −0.0469676
\(487\) 1.07267e15 1.77443 0.887214 0.461357i \(-0.152637\pi\)
0.887214 + 0.461357i \(0.152637\pi\)
\(488\) 2.07324e13 0.0339110
\(489\) 9.18873e13 0.148613
\(490\) −2.42888e14 −0.388443
\(491\) −7.62052e13 −0.120514 −0.0602568 0.998183i \(-0.519192\pi\)
−0.0602568 + 0.998183i \(0.519192\pi\)
\(492\) 2.71305e14 0.424278
\(493\) 8.67978e14 1.34230
\(494\) 8.57025e14 1.31068
\(495\) 4.45917e13 0.0674413
\(496\) −3.76583e14 −0.563263
\(497\) 4.38493e14 0.648638
\(498\) −1.00037e14 −0.146353
\(499\) −8.39544e14 −1.21476 −0.607380 0.794411i \(-0.707779\pi\)
−0.607380 + 0.794411i \(0.707779\pi\)
\(500\) −2.87018e14 −0.410746
\(501\) 8.03248e14 1.13695
\(502\) −3.24641e14 −0.454499
\(503\) 3.99968e14 0.553862 0.276931 0.960890i \(-0.410683\pi\)
0.276931 + 0.960890i \(0.410683\pi\)
\(504\) 1.86853e14 0.255937
\(505\) 1.21973e13 0.0165258
\(506\) −1.83075e14 −0.245359
\(507\) 8.93355e14 1.18435
\(508\) −3.20510e14 −0.420331
\(509\) −4.77020e14 −0.618855 −0.309428 0.950923i \(-0.600137\pi\)
−0.309428 + 0.950923i \(0.600137\pi\)
\(510\) 4.12238e14 0.529069
\(511\) 5.54697e14 0.704273
\(512\) 4.87496e14 0.612331
\(513\) 1.58713e14 0.197227
\(514\) 2.14219e14 0.263367
\(515\) −4.10714e14 −0.499574
\(516\) 5.88384e13 0.0708088
\(517\) 5.39440e13 0.0642311
\(518\) 4.77073e14 0.562045
\(519\) 1.18873e14 0.138568
\(520\) 1.76901e15 2.04039
\(521\) −9.56053e14 −1.09113 −0.545563 0.838070i \(-0.683684\pi\)
−0.545563 + 0.838070i \(0.683684\pi\)
\(522\) −2.52572e14 −0.285231
\(523\) −1.61755e15 −1.80758 −0.903792 0.427972i \(-0.859228\pi\)
−0.903792 + 0.427972i \(0.859228\pi\)
\(524\) −7.75238e14 −0.857261
\(525\) 7.09109e13 0.0775956
\(526\) −1.16736e15 −1.26410
\(527\) 1.88182e15 2.01660
\(528\) 3.24235e13 0.0343853
\(529\) 2.15168e15 2.25825
\(530\) −4.94599e13 −0.0513731
\(531\) 4.22156e13 0.0433963
\(532\) −3.34782e14 −0.340603
\(533\) 2.74778e15 2.76683
\(534\) 6.33827e14 0.631675
\(535\) 8.61845e13 0.0850126
\(536\) −1.66552e15 −1.62609
\(537\) −7.37937e14 −0.713117
\(538\) −1.30927e15 −1.25235
\(539\) 9.54630e13 0.0903851
\(540\) 1.03824e14 0.0973041
\(541\) −1.86689e15 −1.73194 −0.865972 0.500092i \(-0.833300\pi\)
−0.865972 + 0.500092i \(0.833300\pi\)
\(542\) 1.06559e15 0.978574
\(543\) −8.12150e13 −0.0738307
\(544\) −1.06816e15 −0.961263
\(545\) 8.19961e14 0.730487
\(546\) 5.99752e14 0.528947
\(547\) −1.39540e15 −1.21834 −0.609169 0.793041i \(-0.708497\pi\)
−0.609169 + 0.793041i \(0.708497\pi\)
\(548\) 2.62718e11 0.000227089 0
\(549\) 1.23236e13 0.0105461
\(550\) 3.01007e13 0.0255025
\(551\) 1.42790e15 1.19775
\(552\) −1.34501e15 −1.11702
\(553\) −1.37174e15 −1.12794
\(554\) −1.05529e15 −0.859152
\(555\) 8.36437e14 0.674251
\(556\) −1.78725e14 −0.142651
\(557\) 1.41602e15 1.11909 0.559546 0.828800i \(-0.310976\pi\)
0.559546 + 0.828800i \(0.310976\pi\)
\(558\) −5.47589e14 −0.428516
\(559\) 5.95915e14 0.461763
\(560\) 3.26379e14 0.250431
\(561\) −1.62023e14 −0.123107
\(562\) −8.23041e14 −0.619258
\(563\) −1.01719e15 −0.757887 −0.378944 0.925420i \(-0.623713\pi\)
−0.378944 + 0.925420i \(0.623713\pi\)
\(564\) 1.25599e14 0.0926724
\(565\) −1.71773e15 −1.25513
\(566\) 7.62676e14 0.551886
\(567\) 1.11068e14 0.0795945
\(568\) 1.36748e15 0.970522
\(569\) −1.92682e14 −0.135433 −0.0677163 0.997705i \(-0.521571\pi\)
−0.0677163 + 0.997705i \(0.521571\pi\)
\(570\) 6.78169e14 0.472092
\(571\) 4.49619e14 0.309989 0.154994 0.987915i \(-0.450464\pi\)
0.154994 + 0.987915i \(0.450464\pi\)
\(572\) −2.20348e14 −0.150463
\(573\) 7.38058e14 0.499160
\(574\) 1.24016e15 0.830736
\(575\) −5.10431e14 −0.338660
\(576\) 4.73537e14 0.311193
\(577\) −5.79595e13 −0.0377275 −0.0188637 0.999822i \(-0.506005\pi\)
−0.0188637 + 0.999822i \(0.506005\pi\)
\(578\) −3.62316e14 −0.233606
\(579\) 1.38623e15 0.885323
\(580\) 9.34080e14 0.590922
\(581\) 3.95781e14 0.248020
\(582\) −3.26830e13 −0.0202883
\(583\) 1.94394e13 0.0119538
\(584\) 1.72987e15 1.05377
\(585\) 1.05153e15 0.634546
\(586\) −1.32577e15 −0.792557
\(587\) 1.51047e15 0.894545 0.447272 0.894398i \(-0.352395\pi\)
0.447272 + 0.894398i \(0.352395\pi\)
\(588\) 2.22268e14 0.130407
\(589\) 3.09577e15 1.79943
\(590\) 1.80385e14 0.103876
\(591\) 1.05851e14 0.0603898
\(592\) 6.08189e14 0.343771
\(593\) 1.43311e15 0.802561 0.401280 0.915955i \(-0.368565\pi\)
0.401280 + 0.915955i \(0.368565\pi\)
\(594\) 4.71469e13 0.0261594
\(595\) −1.63095e15 −0.896597
\(596\) 2.51860e14 0.137184
\(597\) 8.66539e14 0.467659
\(598\) −4.31714e15 −2.30855
\(599\) −1.05399e15 −0.558457 −0.279228 0.960225i \(-0.590079\pi\)
−0.279228 + 0.960225i \(0.590079\pi\)
\(600\) 2.21142e14 0.116102
\(601\) 2.55566e15 1.32952 0.664758 0.747059i \(-0.268535\pi\)
0.664758 + 0.747059i \(0.268535\pi\)
\(602\) 2.68956e14 0.138644
\(603\) −9.90010e14 −0.505702
\(604\) −1.22092e15 −0.617995
\(605\) 2.09778e15 1.05222
\(606\) 1.28963e13 0.00641010
\(607\) −4.23249e14 −0.208477 −0.104238 0.994552i \(-0.533241\pi\)
−0.104238 + 0.994552i \(0.533241\pi\)
\(608\) −1.75722e15 −0.857741
\(609\) 9.99257e14 0.483372
\(610\) 5.26582e13 0.0252436
\(611\) 1.27206e15 0.604342
\(612\) −3.77242e14 −0.177618
\(613\) 3.17218e15 1.48021 0.740107 0.672489i \(-0.234775\pi\)
0.740107 + 0.672489i \(0.234775\pi\)
\(614\) 2.43807e15 1.12751
\(615\) 2.17434e15 0.996584
\(616\) −3.13803e14 −0.142549
\(617\) 5.88656e13 0.0265029 0.0132514 0.999912i \(-0.495782\pi\)
0.0132514 + 0.999912i \(0.495782\pi\)
\(618\) −4.34249e14 −0.193777
\(619\) 6.94566e14 0.307195 0.153598 0.988133i \(-0.450914\pi\)
0.153598 + 0.988133i \(0.450914\pi\)
\(620\) 2.02514e15 0.887769
\(621\) −7.99492e14 −0.347384
\(622\) 1.28369e15 0.552859
\(623\) −2.50763e15 −1.07048
\(624\) 7.64585e14 0.323527
\(625\) −2.74758e15 −1.15242
\(626\) 2.27409e15 0.945470
\(627\) −2.66543e14 −0.109849
\(628\) 3.95856e14 0.161718
\(629\) −3.03918e15 −1.23077
\(630\) 4.74588e14 0.190521
\(631\) 2.97858e14 0.118535 0.0592677 0.998242i \(-0.481123\pi\)
0.0592677 + 0.998242i \(0.481123\pi\)
\(632\) −4.27791e15 −1.68767
\(633\) −1.73161e15 −0.677221
\(634\) −2.63305e15 −1.02086
\(635\) −2.56868e15 −0.987313
\(636\) 4.52611e13 0.0172469
\(637\) 2.25113e15 0.850422
\(638\) 4.24171e14 0.158865
\(639\) 8.12850e14 0.301825
\(640\) −4.54235e14 −0.167221
\(641\) −1.37938e15 −0.503458 −0.251729 0.967798i \(-0.580999\pi\)
−0.251729 + 0.967798i \(0.580999\pi\)
\(642\) 9.11231e13 0.0329751
\(643\) 3.94278e15 1.41463 0.707313 0.706900i \(-0.249907\pi\)
0.707313 + 0.706900i \(0.249907\pi\)
\(644\) 1.68642e15 0.599919
\(645\) 4.71552e14 0.166322
\(646\) −2.46412e15 −0.861752
\(647\) 2.88189e15 0.999317 0.499658 0.866222i \(-0.333459\pi\)
0.499658 + 0.866222i \(0.333459\pi\)
\(648\) 3.46377e14 0.119093
\(649\) −7.08971e13 −0.0241703
\(650\) 7.09811e14 0.239949
\(651\) 2.16644e15 0.726192
\(652\) −3.59297e14 −0.119424
\(653\) 2.74822e15 0.905794 0.452897 0.891563i \(-0.350390\pi\)
0.452897 + 0.891563i \(0.350390\pi\)
\(654\) 8.66946e14 0.283344
\(655\) −6.21303e15 −2.01362
\(656\) 1.58100e15 0.508114
\(657\) 1.02826e15 0.327713
\(658\) 5.74123e14 0.181452
\(659\) 3.87276e15 1.21381 0.606905 0.794774i \(-0.292411\pi\)
0.606905 + 0.794774i \(0.292411\pi\)
\(660\) −1.74362e14 −0.0541953
\(661\) 2.71094e15 0.835625 0.417812 0.908533i \(-0.362797\pi\)
0.417812 + 0.908533i \(0.362797\pi\)
\(662\) −3.53866e15 −1.08173
\(663\) −3.82071e15 −1.15830
\(664\) 1.23428e15 0.371098
\(665\) −2.68306e15 −0.800039
\(666\) 8.84367e14 0.261532
\(667\) −7.19285e15 −2.10964
\(668\) −3.14086e15 −0.913646
\(669\) 6.19484e13 0.0178725
\(670\) −4.23025e15 −1.21047
\(671\) −2.06964e13 −0.00587383
\(672\) −1.22971e15 −0.346157
\(673\) −4.09696e14 −0.114388 −0.0571938 0.998363i \(-0.518215\pi\)
−0.0571938 + 0.998363i \(0.518215\pi\)
\(674\) −3.87948e15 −1.07435
\(675\) 1.31450e14 0.0361069
\(676\) −3.49319e15 −0.951734
\(677\) 5.60783e15 1.51551 0.757753 0.652542i \(-0.226297\pi\)
0.757753 + 0.652542i \(0.226297\pi\)
\(678\) −1.81616e15 −0.486846
\(679\) 1.29305e14 0.0343820
\(680\) −5.08627e15 −1.34153
\(681\) −1.67231e15 −0.437530
\(682\) 9.19625e14 0.238669
\(683\) −5.41015e15 −1.39282 −0.696411 0.717643i \(-0.745221\pi\)
−0.696411 + 0.717643i \(0.745221\pi\)
\(684\) −6.20597e14 −0.158490
\(685\) 2.10551e12 0.000533408 0
\(686\) 3.10294e15 0.779815
\(687\) 2.64647e13 0.00659789
\(688\) 3.42874e14 0.0848004
\(689\) 4.58404e14 0.112472
\(690\) −3.41618e15 −0.831516
\(691\) −4.09841e15 −0.989660 −0.494830 0.868990i \(-0.664770\pi\)
−0.494830 + 0.868990i \(0.664770\pi\)
\(692\) −4.64818e14 −0.111352
\(693\) −1.86529e14 −0.0443316
\(694\) −1.24357e15 −0.293219
\(695\) −1.43236e15 −0.335071
\(696\) 3.11627e15 0.723244
\(697\) −7.90042e15 −1.81916
\(698\) 1.81926e15 0.415614
\(699\) 2.44015e15 0.553085
\(700\) −2.77276e14 −0.0623552
\(701\) 4.69655e15 1.04793 0.523963 0.851741i \(-0.324453\pi\)
0.523963 + 0.851741i \(0.324453\pi\)
\(702\) 1.11178e15 0.246131
\(703\) −4.99973e15 −1.09823
\(704\) −7.95262e14 −0.173325
\(705\) 1.00659e15 0.217678
\(706\) −9.33916e14 −0.200393
\(707\) −5.10219e13 −0.0108630
\(708\) −1.65071e14 −0.0348729
\(709\) −7.16964e13 −0.0150294 −0.00751472 0.999972i \(-0.502392\pi\)
−0.00751472 + 0.999972i \(0.502392\pi\)
\(710\) 3.47326e15 0.722464
\(711\) −2.54285e15 −0.524853
\(712\) −7.82027e15 −1.60170
\(713\) −1.55945e16 −3.16941
\(714\) −1.72441e15 −0.347776
\(715\) −1.76594e15 −0.353422
\(716\) 2.88548e15 0.573055
\(717\) 3.97711e15 0.783813
\(718\) 8.08227e14 0.158070
\(719\) 2.70106e14 0.0524234 0.0262117 0.999656i \(-0.491656\pi\)
0.0262117 + 0.999656i \(0.491656\pi\)
\(720\) 6.05021e14 0.116531
\(721\) 1.71803e15 0.328388
\(722\) −1.93973e14 −0.0367949
\(723\) 6.99631e14 0.131707
\(724\) 3.17567e14 0.0593298
\(725\) 1.18263e15 0.219275
\(726\) 2.21798e15 0.408138
\(727\) 4.20851e15 0.768579 0.384290 0.923213i \(-0.374446\pi\)
0.384290 + 0.923213i \(0.374446\pi\)
\(728\) −7.39985e15 −1.34122
\(729\) 2.05891e14 0.0370370
\(730\) 4.39370e15 0.784431
\(731\) −1.71337e15 −0.303604
\(732\) −4.81879e13 −0.00847475
\(733\) 5.46692e15 0.954269 0.477134 0.878830i \(-0.341675\pi\)
0.477134 + 0.878830i \(0.341675\pi\)
\(734\) −1.52596e15 −0.264371
\(735\) 1.78134e15 0.306313
\(736\) 8.85174e15 1.51078
\(737\) 1.66263e15 0.281660
\(738\) 2.29893e15 0.386559
\(739\) −9.20087e15 −1.53562 −0.767811 0.640676i \(-0.778654\pi\)
−0.767811 + 0.640676i \(0.778654\pi\)
\(740\) −3.27063e15 −0.541823
\(741\) −6.28541e15 −1.03355
\(742\) 2.06892e14 0.0337694
\(743\) 3.25954e15 0.528102 0.264051 0.964509i \(-0.414941\pi\)
0.264051 + 0.964509i \(0.414941\pi\)
\(744\) 6.75625e15 1.08656
\(745\) 2.01849e15 0.322231
\(746\) −3.81824e15 −0.605062
\(747\) 7.33673e14 0.115409
\(748\) 6.33543e14 0.0989276
\(749\) −3.60513e14 −0.0558818
\(750\) −2.43207e15 −0.374231
\(751\) −2.18002e15 −0.332998 −0.166499 0.986042i \(-0.553246\pi\)
−0.166499 + 0.986042i \(0.553246\pi\)
\(752\) 7.31912e14 0.110984
\(753\) 2.38091e15 0.358403
\(754\) 1.00025e16 1.49474
\(755\) −9.78490e15 −1.45160
\(756\) −4.34298e14 −0.0639615
\(757\) 1.25029e16 1.82804 0.914018 0.405675i \(-0.132963\pi\)
0.914018 + 0.405675i \(0.132963\pi\)
\(758\) −3.98232e15 −0.578036
\(759\) 1.34267e15 0.193482
\(760\) −8.36737e15 −1.19706
\(761\) 6.18184e15 0.878015 0.439008 0.898483i \(-0.355330\pi\)
0.439008 + 0.898483i \(0.355330\pi\)
\(762\) −2.71587e15 −0.382963
\(763\) −3.42993e15 −0.480175
\(764\) −2.88595e15 −0.401121
\(765\) −3.02335e15 −0.417206
\(766\) 2.44958e15 0.335608
\(767\) −1.67184e15 −0.227416
\(768\) −4.47123e15 −0.603865
\(769\) −1.63012e15 −0.218587 −0.109293 0.994010i \(-0.534859\pi\)
−0.109293 + 0.994010i \(0.534859\pi\)
\(770\) −7.97026e14 −0.106114
\(771\) −1.57108e15 −0.207683
\(772\) −5.42041e15 −0.711438
\(773\) 1.65012e15 0.215045 0.107522 0.994203i \(-0.465708\pi\)
0.107522 + 0.994203i \(0.465708\pi\)
\(774\) 4.98572e14 0.0645139
\(775\) 2.56400e15 0.329427
\(776\) 4.03249e14 0.0514439
\(777\) −3.49885e15 −0.443210
\(778\) 1.20101e15 0.151064
\(779\) −1.29969e16 −1.62324
\(780\) −4.11168e15 −0.509916
\(781\) −1.36511e15 −0.168107
\(782\) 1.24126e16 1.51784
\(783\) 1.85236e15 0.224924
\(784\) 1.29524e15 0.156176
\(785\) 3.17253e15 0.379859
\(786\) −6.56905e15 −0.781050
\(787\) −6.17546e15 −0.729136 −0.364568 0.931177i \(-0.618783\pi\)
−0.364568 + 0.931177i \(0.618783\pi\)
\(788\) −4.13898e14 −0.0485287
\(789\) 8.56138e15 0.996828
\(790\) −1.08654e16 −1.25631
\(791\) 7.18534e15 0.825043
\(792\) −5.81707e14 −0.0663309
\(793\) −4.88047e14 −0.0552661
\(794\) 5.47868e15 0.616117
\(795\) 3.62738e14 0.0405111
\(796\) −3.38834e15 −0.375807
\(797\) 5.51112e15 0.607043 0.303521 0.952825i \(-0.401838\pi\)
0.303521 + 0.952825i \(0.401838\pi\)
\(798\) −2.83680e15 −0.310323
\(799\) −3.65744e15 −0.397347
\(800\) −1.45538e15 −0.157029
\(801\) −4.64848e15 −0.498118
\(802\) −2.64084e15 −0.281049
\(803\) −1.72687e15 −0.182526
\(804\) 3.87113e15 0.406378
\(805\) 1.35155e16 1.40915
\(806\) 2.16859e16 2.24561
\(807\) 9.60218e15 0.987564
\(808\) −1.59116e14 −0.0162537
\(809\) 1.51244e16 1.53448 0.767238 0.641363i \(-0.221631\pi\)
0.767238 + 0.641363i \(0.221631\pi\)
\(810\) 8.79760e14 0.0886537
\(811\) −1.71215e15 −0.171367 −0.0856835 0.996322i \(-0.527307\pi\)
−0.0856835 + 0.996322i \(0.527307\pi\)
\(812\) −3.90729e15 −0.388434
\(813\) −7.81501e15 −0.771670
\(814\) −1.48521e15 −0.145665
\(815\) −2.87953e15 −0.280515
\(816\) −2.19833e15 −0.212715
\(817\) −2.81866e15 −0.270907
\(818\) 9.24922e15 0.883003
\(819\) −4.39858e15 −0.417110
\(820\) −8.50208e15 −0.800846
\(821\) 6.05932e14 0.0566939 0.0283469 0.999598i \(-0.490976\pi\)
0.0283469 + 0.999598i \(0.490976\pi\)
\(822\) 2.22616e12 0.000206901 0
\(823\) 8.30271e14 0.0766515 0.0383257 0.999265i \(-0.487798\pi\)
0.0383257 + 0.999265i \(0.487798\pi\)
\(824\) 5.35785e15 0.491349
\(825\) −2.20758e14 −0.0201104
\(826\) −7.54555e14 −0.0682811
\(827\) 1.05517e16 0.948507 0.474254 0.880388i \(-0.342718\pi\)
0.474254 + 0.880388i \(0.342718\pi\)
\(828\) 3.12617e15 0.279155
\(829\) −1.06911e15 −0.0948357 −0.0474179 0.998875i \(-0.515099\pi\)
−0.0474179 + 0.998875i \(0.515099\pi\)
\(830\) 3.13494e15 0.276248
\(831\) 7.73952e15 0.677498
\(832\) −1.87532e16 −1.63079
\(833\) −6.47246e15 −0.559142
\(834\) −1.51444e15 −0.129969
\(835\) −2.51719e16 −2.14606
\(836\) 1.04224e15 0.0882737
\(837\) 4.01601e15 0.337913
\(838\) −1.16448e16 −0.973393
\(839\) 1.83086e16 1.52042 0.760211 0.649676i \(-0.225096\pi\)
0.760211 + 0.649676i \(0.225096\pi\)
\(840\) −5.85555e15 −0.483094
\(841\) 4.46475e15 0.365948
\(842\) −4.42277e15 −0.360146
\(843\) 6.03618e15 0.488326
\(844\) 6.77095e15 0.544209
\(845\) −2.79957e16 −2.23552
\(846\) 1.06427e15 0.0844337
\(847\) −8.77508e15 −0.691659
\(848\) 2.63754e14 0.0206548
\(849\) −5.59346e15 −0.435199
\(850\) −2.04085e15 −0.157764
\(851\) 2.51854e16 1.93436
\(852\) −3.17840e15 −0.242544
\(853\) 1.27200e16 0.964420 0.482210 0.876056i \(-0.339834\pi\)
0.482210 + 0.876056i \(0.339834\pi\)
\(854\) −2.20271e14 −0.0165935
\(855\) −4.97368e15 −0.372276
\(856\) −1.12429e15 −0.0836130
\(857\) −3.18318e15 −0.235216 −0.117608 0.993060i \(-0.537523\pi\)
−0.117608 + 0.993060i \(0.537523\pi\)
\(858\) −1.86714e15 −0.137087
\(859\) −1.56173e16 −1.13931 −0.569656 0.821883i \(-0.692924\pi\)
−0.569656 + 0.821883i \(0.692924\pi\)
\(860\) −1.84386e15 −0.133655
\(861\) −9.09533e15 −0.655090
\(862\) −5.93171e15 −0.424512
\(863\) 1.20362e16 0.855911 0.427955 0.903800i \(-0.359234\pi\)
0.427955 + 0.903800i \(0.359234\pi\)
\(864\) −2.27957e15 −0.161074
\(865\) −3.72522e15 −0.261555
\(866\) −5.72759e15 −0.399598
\(867\) 2.65722e15 0.184214
\(868\) −8.47121e15 −0.583562
\(869\) 4.27048e15 0.292326
\(870\) 7.91501e15 0.538388
\(871\) 3.92069e16 2.65010
\(872\) −1.06965e16 −0.718460
\(873\) 2.39697e14 0.0159987
\(874\) 2.04199e16 1.35438
\(875\) 9.62208e15 0.634198
\(876\) −4.02071e15 −0.263348
\(877\) −4.22997e14 −0.0275321 −0.0137660 0.999905i \(-0.504382\pi\)
−0.0137660 + 0.999905i \(0.504382\pi\)
\(878\) 1.92252e16 1.24352
\(879\) 9.72316e15 0.624984
\(880\) −1.01608e15 −0.0649041
\(881\) −1.62941e16 −1.03434 −0.517171 0.855882i \(-0.673015\pi\)
−0.517171 + 0.855882i \(0.673015\pi\)
\(882\) 1.88341e15 0.118814
\(883\) 2.22431e16 1.39448 0.697240 0.716838i \(-0.254411\pi\)
0.697240 + 0.716838i \(0.254411\pi\)
\(884\) 1.49397e16 0.930797
\(885\) −1.32294e15 −0.0819128
\(886\) −1.07833e16 −0.663539
\(887\) −2.87196e15 −0.175630 −0.0878148 0.996137i \(-0.527988\pi\)
−0.0878148 + 0.996137i \(0.527988\pi\)
\(888\) −1.09115e16 −0.663151
\(889\) 1.07449e16 0.648996
\(890\) −1.98627e16 −1.19232
\(891\) −3.45775e14 −0.0206284
\(892\) −2.42230e14 −0.0143622
\(893\) −6.01682e15 −0.354555
\(894\) 2.13416e15 0.124989
\(895\) 2.31252e16 1.34605
\(896\) 1.90008e15 0.109920
\(897\) 3.16618e16 1.82045
\(898\) 3.90990e15 0.223432
\(899\) 3.61312e16 2.05212
\(900\) −5.13996e14 −0.0290152
\(901\) −1.31800e15 −0.0739486
\(902\) −3.86084e15 −0.215301
\(903\) −1.97252e15 −0.109330
\(904\) 2.24081e16 1.23447
\(905\) 2.54509e15 0.139359
\(906\) −1.03456e16 −0.563055
\(907\) 4.89137e15 0.264600 0.132300 0.991210i \(-0.457764\pi\)
0.132300 + 0.991210i \(0.457764\pi\)
\(908\) 6.53906e15 0.351595
\(909\) −9.45811e13 −0.00505479
\(910\) −1.87948e16 −0.998415
\(911\) 1.87122e16 0.988039 0.494020 0.869451i \(-0.335527\pi\)
0.494020 + 0.869451i \(0.335527\pi\)
\(912\) −3.61646e15 −0.189807
\(913\) −1.23214e15 −0.0642790
\(914\) 5.14302e15 0.266694
\(915\) −3.86195e14 −0.0199063
\(916\) −1.03482e14 −0.00530201
\(917\) 2.59893e16 1.32362
\(918\) −3.19659e15 −0.161828
\(919\) 9.46234e15 0.476171 0.238086 0.971244i \(-0.423480\pi\)
0.238086 + 0.971244i \(0.423480\pi\)
\(920\) 4.21494e16 2.10843
\(921\) −1.78808e16 −0.889117
\(922\) −1.36435e16 −0.674383
\(923\) −3.21909e16 −1.58170
\(924\) 7.29364e14 0.0356245
\(925\) −4.14091e15 −0.201056
\(926\) 3.51450e15 0.169630
\(927\) 3.18478e15 0.152806
\(928\) −2.05088e16 −0.978195
\(929\) 1.29084e16 0.612047 0.306023 0.952024i \(-0.401001\pi\)
0.306023 + 0.952024i \(0.401001\pi\)
\(930\) 1.71602e16 0.808845
\(931\) −1.06478e16 −0.498926
\(932\) −9.54145e15 −0.444454
\(933\) −9.41459e15 −0.435966
\(934\) 2.28621e16 1.05247
\(935\) 5.07744e15 0.232370
\(936\) −1.37174e16 −0.624099
\(937\) 2.51683e16 1.13838 0.569190 0.822206i \(-0.307257\pi\)
0.569190 + 0.822206i \(0.307257\pi\)
\(938\) 1.76953e16 0.795687
\(939\) −1.66781e16 −0.745566
\(940\) −3.93598e15 −0.174924
\(941\) 3.46430e16 1.53064 0.765319 0.643651i \(-0.222581\pi\)
0.765319 + 0.643651i \(0.222581\pi\)
\(942\) 3.35432e15 0.147342
\(943\) 6.54700e16 2.85909
\(944\) −9.61933e14 −0.0417637
\(945\) −3.48062e15 −0.150239
\(946\) −8.37306e14 −0.0359321
\(947\) −4.03973e16 −1.72356 −0.861781 0.507280i \(-0.830651\pi\)
−0.861781 + 0.507280i \(0.830651\pi\)
\(948\) 9.94304e15 0.421768
\(949\) −4.07217e16 −1.71736
\(950\) −3.35738e15 −0.140773
\(951\) 1.93107e16 0.805019
\(952\) 2.12760e16 0.881836
\(953\) 2.98955e16 1.23196 0.615978 0.787763i \(-0.288761\pi\)
0.615978 + 0.787763i \(0.288761\pi\)
\(954\) 3.83524e14 0.0157136
\(955\) −2.31290e16 −0.942190
\(956\) −1.55513e16 −0.629865
\(957\) −3.11086e15 −0.125275
\(958\) 3.05971e16 1.22510
\(959\) −8.80743e12 −0.000350628 0
\(960\) −1.48396e16 −0.587393
\(961\) 5.29259e16 2.08300
\(962\) −3.50231e16 −1.37054
\(963\) −6.68296e14 −0.0260030
\(964\) −2.73569e15 −0.105839
\(965\) −4.34411e16 −1.67109
\(966\) 1.42900e16 0.546585
\(967\) 3.83561e16 1.45878 0.729388 0.684100i \(-0.239805\pi\)
0.729388 + 0.684100i \(0.239805\pi\)
\(968\) −2.73659e16 −1.03489
\(969\) 1.80718e16 0.679549
\(970\) 1.02421e15 0.0382952
\(971\) 4.08201e16 1.51764 0.758819 0.651301i \(-0.225777\pi\)
0.758819 + 0.651301i \(0.225777\pi\)
\(972\) −8.05075e14 −0.0297627
\(973\) 5.99163e15 0.220254
\(974\) −3.55414e16 −1.29915
\(975\) −5.20575e15 −0.189216
\(976\) −2.80809e14 −0.0101493
\(977\) −5.42928e16 −1.95129 −0.975646 0.219351i \(-0.929606\pi\)
−0.975646 + 0.219351i \(0.929606\pi\)
\(978\) −3.04454e15 −0.108807
\(979\) 7.80669e15 0.277436
\(980\) −6.96538e15 −0.246151
\(981\) −6.35817e15 −0.223436
\(982\) 2.52494e15 0.0882343
\(983\) −4.45529e16 −1.54822 −0.774108 0.633053i \(-0.781801\pi\)
−0.774108 + 0.633053i \(0.781801\pi\)
\(984\) −2.83646e16 −0.980176
\(985\) −3.31712e15 −0.113989
\(986\) −2.87591e16 −0.982770
\(987\) −4.21061e15 −0.143087
\(988\) 2.45772e16 0.830556
\(989\) 1.41986e16 0.477161
\(990\) −1.47748e15 −0.0493773
\(991\) 2.11566e16 0.703140 0.351570 0.936162i \(-0.385648\pi\)
0.351570 + 0.936162i \(0.385648\pi\)
\(992\) −4.44641e16 −1.46959
\(993\) 2.59525e16 0.853017
\(994\) −1.45288e16 −0.474902
\(995\) −2.71553e16 −0.882730
\(996\) −2.86881e15 −0.0927416
\(997\) −4.98712e16 −1.60334 −0.801671 0.597766i \(-0.796055\pi\)
−0.801671 + 0.597766i \(0.796055\pi\)
\(998\) 2.78170e16 0.889389
\(999\) −6.48594e15 −0.206235
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.1.11 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.d.1.11 28 1.1 even 1 trivial