Properties

Label 29.12.a.a.1.8
Level $29$
Weight $12$
Character 29.1
Self dual yes
Analytic conductor $22.282$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.2819522362\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} - 388180519304 x^{4} + 193065378004825 x^{3} + 1279291654973975 x^{2} - 65244901875230266 x - 758324542468966858\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{13}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(33.9131\) of defining polynomial
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q+30.9131 q^{2} +543.939 q^{3} -1092.38 q^{4} -6165.86 q^{5} +16814.8 q^{6} +8452.88 q^{7} -97078.9 q^{8} +118722. q^{9} +O(q^{10})\) \(q+30.9131 q^{2} +543.939 q^{3} -1092.38 q^{4} -6165.86 q^{5} +16814.8 q^{6} +8452.88 q^{7} -97078.9 q^{8} +118722. q^{9} -190606. q^{10} -456924. q^{11} -594188. q^{12} -1.58605e6 q^{13} +261305. q^{14} -3.35385e6 q^{15} -763810. q^{16} -2.76267e6 q^{17} +3.67007e6 q^{18} +1.02298e7 q^{19} +6.73547e6 q^{20} +4.59785e6 q^{21} -1.41249e7 q^{22} -4.57080e6 q^{23} -5.28049e7 q^{24} -1.08103e7 q^{25} -4.90296e7 q^{26} -3.17795e7 q^{27} -9.23377e6 q^{28} +2.05111e7 q^{29} -1.03678e8 q^{30} -1.86010e7 q^{31} +1.75206e8 q^{32} -2.48538e8 q^{33} -8.54025e7 q^{34} -5.21193e7 q^{35} -1.29690e8 q^{36} -3.49895e8 q^{37} +3.16236e8 q^{38} -8.62712e8 q^{39} +5.98575e8 q^{40} +4.05592e8 q^{41} +1.42134e8 q^{42} -5.45192e8 q^{43} +4.99135e8 q^{44} -7.32025e8 q^{45} -1.41298e8 q^{46} +2.57186e8 q^{47} -4.15466e8 q^{48} -1.90588e9 q^{49} -3.34178e8 q^{50} -1.50272e9 q^{51} +1.73257e9 q^{52} +2.86140e9 q^{53} -9.82402e8 q^{54} +2.81733e9 q^{55} -8.20596e8 q^{56} +5.56441e9 q^{57} +6.34063e8 q^{58} +9.78675e8 q^{59} +3.66368e9 q^{60} +6.10378e9 q^{61} -5.75015e8 q^{62} +1.00354e9 q^{63} +6.98043e9 q^{64} +9.77935e9 q^{65} -7.68309e9 q^{66} +2.11078e10 q^{67} +3.01788e9 q^{68} -2.48623e9 q^{69} -1.61117e9 q^{70} -5.71117e9 q^{71} -1.15254e10 q^{72} -3.20418e10 q^{73} -1.08163e10 q^{74} -5.88012e9 q^{75} -1.11749e10 q^{76} -3.86232e9 q^{77} -2.66691e10 q^{78} +2.00645e9 q^{79} +4.70955e9 q^{80} -3.83174e10 q^{81} +1.25381e10 q^{82} +1.74717e10 q^{83} -5.02260e9 q^{84} +1.70342e10 q^{85} -1.68536e10 q^{86} +1.11568e10 q^{87} +4.43576e10 q^{88} +2.66978e9 q^{89} -2.26292e10 q^{90} -1.34067e10 q^{91} +4.99306e9 q^{92} -1.01178e10 q^{93} +7.95043e9 q^{94} -6.30758e10 q^{95} +9.53012e10 q^{96} -4.71279e10 q^{97} -5.89165e10 q^{98} -5.42470e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 32q^{2} - 982q^{3} + 9146q^{4} - 2740q^{5} - 28202q^{6} - 49432q^{7} - 150054q^{8} + 330749q^{9} + O(q^{10}) \) \( 11q - 32q^{2} - 982q^{3} + 9146q^{4} - 2740q^{5} - 28202q^{6} - 49432q^{7} - 150054q^{8} + 330749q^{9} - 685834q^{10} - 612246q^{11} + 2578538q^{12} + 1510364q^{13} + 3955400q^{14} - 2462818q^{15} + 3024818q^{16} - 3291098q^{17} - 27885614q^{18} - 44121388q^{19} - 49472662q^{20} - 46916800q^{21} - 43435618q^{22} - 88684076q^{23} - 224700678q^{24} - 44195521q^{25} - 324999762q^{26} - 236304286q^{27} - 391274848q^{28} + 225622639q^{29} - 494910382q^{30} - 292235934q^{31} - 632542514q^{32} - 1079766410q^{33} - 1113307936q^{34} - 1312820120q^{35} - 2236726492q^{36} - 1380429338q^{37} - 1222857284q^{38} - 1186931090q^{39} - 2713154106q^{40} - 1062067494q^{41} + 205598960q^{42} + 74588594q^{43} + 52891466q^{44} + 4527996830q^{45} - 87670324q^{46} - 1821239394q^{47} + 2666035542q^{48} + 4692522003q^{49} + 9494259926q^{50} + 8768158380q^{51} + 3266669866q^{52} + 7818635688q^{53} + 17402728558q^{54} - 191002682q^{55} + 11263587512q^{56} + 15495358340q^{57} - 656356768q^{58} + 1230002712q^{59} + 31834046430q^{60} - 18602654230q^{61} + 22075953162q^{62} - 9964531456q^{63} + 11813658086q^{64} + 32245789334q^{65} + 42677188354q^{66} + 27481284652q^{67} + 29588811820q^{68} - 20565315068q^{69} + 42862666712q^{70} - 20347168516q^{71} + 47061083616q^{72} - 57740010478q^{73} - 2640709564q^{74} - 23544691000q^{75} - 33350650772q^{76} + 871959792q^{77} - 15384525342q^{78} - 120245016462q^{79} - 84319695274q^{80} - 48880047865q^{81} - 111495532412q^{82} - 142463983824q^{83} - 134146226376q^{84} - 181628566552q^{85} + 47870165542q^{86} - 20141948318q^{87} - 180608014462q^{88} - 96700717270q^{89} - 25522461244q^{90} - 355162031176q^{91} - 22429477796q^{92} - 172582115142q^{93} + 172608565078q^{94} - 195922150708q^{95} + 226391047758q^{96} - 303190852014q^{97} - 123776497136q^{98} - 139125462440q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 30.9131 0.683089 0.341545 0.939866i \(-0.389050\pi\)
0.341545 + 0.939866i \(0.389050\pi\)
\(3\) 543.939 1.29236 0.646179 0.763186i \(-0.276366\pi\)
0.646179 + 0.763186i \(0.276366\pi\)
\(4\) −1092.38 −0.533389
\(5\) −6165.86 −0.882386 −0.441193 0.897412i \(-0.645445\pi\)
−0.441193 + 0.897412i \(0.645445\pi\)
\(6\) 16814.8 0.882796
\(7\) 8452.88 0.190093 0.0950464 0.995473i \(-0.469700\pi\)
0.0950464 + 0.995473i \(0.469700\pi\)
\(8\) −97078.9 −1.04744
\(9\) 118722. 0.670191
\(10\) −190606. −0.602749
\(11\) −456924. −0.855429 −0.427714 0.903914i \(-0.640681\pi\)
−0.427714 + 0.903914i \(0.640681\pi\)
\(12\) −594188. −0.689330
\(13\) −1.58605e6 −1.18475 −0.592376 0.805662i \(-0.701810\pi\)
−0.592376 + 0.805662i \(0.701810\pi\)
\(14\) 261305. 0.129850
\(15\) −3.35385e6 −1.14036
\(16\) −763810. −0.182107
\(17\) −2.76267e6 −0.471910 −0.235955 0.971764i \(-0.575822\pi\)
−0.235955 + 0.971764i \(0.575822\pi\)
\(18\) 3.67007e6 0.457800
\(19\) 1.02298e7 0.947817 0.473908 0.880574i \(-0.342843\pi\)
0.473908 + 0.880574i \(0.342843\pi\)
\(20\) 6.73547e6 0.470656
\(21\) 4.59785e6 0.245668
\(22\) −1.41249e7 −0.584334
\(23\) −4.57080e6 −0.148078 −0.0740388 0.997255i \(-0.523589\pi\)
−0.0740388 + 0.997255i \(0.523589\pi\)
\(24\) −5.28049e7 −1.35367
\(25\) −1.08103e7 −0.221394
\(26\) −4.90296e7 −0.809291
\(27\) −3.17795e7 −0.426232
\(28\) −9.23377e6 −0.101393
\(29\) 2.05111e7 0.185695
\(30\) −1.03678e8 −0.778967
\(31\) −1.86010e7 −0.116694 −0.0583469 0.998296i \(-0.518583\pi\)
−0.0583469 + 0.998296i \(0.518583\pi\)
\(32\) 1.75206e8 0.923047
\(33\) −2.48538e8 −1.10552
\(34\) −8.54025e7 −0.322357
\(35\) −5.21193e7 −0.167735
\(36\) −1.29690e8 −0.357472
\(37\) −3.49895e8 −0.829524 −0.414762 0.909930i \(-0.636135\pi\)
−0.414762 + 0.909930i \(0.636135\pi\)
\(38\) 3.16236e8 0.647443
\(39\) −8.62712e8 −1.53112
\(40\) 5.98575e8 0.924248
\(41\) 4.05592e8 0.546737 0.273369 0.961909i \(-0.411862\pi\)
0.273369 + 0.961909i \(0.411862\pi\)
\(42\) 1.42134e8 0.167813
\(43\) −5.45192e8 −0.565553 −0.282777 0.959186i \(-0.591255\pi\)
−0.282777 + 0.959186i \(0.591255\pi\)
\(44\) 4.99135e8 0.456277
\(45\) −7.32025e8 −0.591367
\(46\) −1.41298e8 −0.101150
\(47\) 2.57186e8 0.163572 0.0817862 0.996650i \(-0.473938\pi\)
0.0817862 + 0.996650i \(0.473938\pi\)
\(48\) −4.15466e8 −0.235347
\(49\) −1.90588e9 −0.963865
\(50\) −3.34178e8 −0.151232
\(51\) −1.50272e9 −0.609877
\(52\) 1.73257e9 0.631934
\(53\) 2.86140e9 0.939857 0.469929 0.882704i \(-0.344280\pi\)
0.469929 + 0.882704i \(0.344280\pi\)
\(54\) −9.82402e8 −0.291154
\(55\) 2.81733e9 0.754819
\(56\) −8.20596e8 −0.199111
\(57\) 5.56441e9 1.22492
\(58\) 6.34063e8 0.126846
\(59\) 9.78675e8 0.178218 0.0891092 0.996022i \(-0.471598\pi\)
0.0891092 + 0.996022i \(0.471598\pi\)
\(60\) 3.66368e9 0.608256
\(61\) 6.10378e9 0.925305 0.462653 0.886540i \(-0.346898\pi\)
0.462653 + 0.886540i \(0.346898\pi\)
\(62\) −5.75015e8 −0.0797123
\(63\) 1.00354e9 0.127398
\(64\) 6.98043e9 0.812630
\(65\) 9.77935e9 1.04541
\(66\) −7.68309e9 −0.755169
\(67\) 2.11078e10 1.90999 0.954995 0.296622i \(-0.0958602\pi\)
0.954995 + 0.296622i \(0.0958602\pi\)
\(68\) 3.01788e9 0.251712
\(69\) −2.48623e9 −0.191369
\(70\) −1.61117e9 −0.114578
\(71\) −5.71117e9 −0.375668 −0.187834 0.982201i \(-0.560147\pi\)
−0.187834 + 0.982201i \(0.560147\pi\)
\(72\) −1.15254e10 −0.701985
\(73\) −3.20418e10 −1.80901 −0.904504 0.426464i \(-0.859759\pi\)
−0.904504 + 0.426464i \(0.859759\pi\)
\(74\) −1.08163e10 −0.566639
\(75\) −5.88012e9 −0.286121
\(76\) −1.11749e10 −0.505555
\(77\) −3.86232e9 −0.162611
\(78\) −2.66691e10 −1.04589
\(79\) 2.00645e9 0.0733634 0.0366817 0.999327i \(-0.488321\pi\)
0.0366817 + 0.999327i \(0.488321\pi\)
\(80\) 4.70955e9 0.160688
\(81\) −3.83174e10 −1.22104
\(82\) 1.25381e10 0.373470
\(83\) 1.74717e10 0.486863 0.243431 0.969918i \(-0.421727\pi\)
0.243431 + 0.969918i \(0.421727\pi\)
\(84\) −5.02260e9 −0.131037
\(85\) 1.70342e10 0.416407
\(86\) −1.68536e10 −0.386323
\(87\) 1.11568e10 0.239985
\(88\) 4.43576e10 0.896012
\(89\) 2.66978e9 0.0506793 0.0253397 0.999679i \(-0.491933\pi\)
0.0253397 + 0.999679i \(0.491933\pi\)
\(90\) −2.26292e10 −0.403956
\(91\) −1.34067e10 −0.225213
\(92\) 4.99306e9 0.0789830
\(93\) −1.01178e10 −0.150810
\(94\) 7.95043e9 0.111734
\(95\) −6.30758e10 −0.836341
\(96\) 9.53012e10 1.19291
\(97\) −4.71279e10 −0.557228 −0.278614 0.960403i \(-0.589875\pi\)
−0.278614 + 0.960403i \(0.589875\pi\)
\(98\) −5.89165e10 −0.658405
\(99\) −5.42470e10 −0.573300
\(100\) 1.18089e10 0.118089
\(101\) −1.14953e11 −1.08831 −0.544157 0.838984i \(-0.683150\pi\)
−0.544157 + 0.838984i \(0.683150\pi\)
\(102\) −4.64537e10 −0.416600
\(103\) 2.20861e11 1.87722 0.938608 0.344985i \(-0.112116\pi\)
0.938608 + 0.344985i \(0.112116\pi\)
\(104\) 1.53972e11 1.24096
\(105\) −2.83497e10 −0.216774
\(106\) 8.84548e10 0.642006
\(107\) 1.25674e11 0.866233 0.433117 0.901338i \(-0.357414\pi\)
0.433117 + 0.901338i \(0.357414\pi\)
\(108\) 3.47153e10 0.227348
\(109\) −1.83444e11 −1.14198 −0.570988 0.820958i \(-0.693440\pi\)
−0.570988 + 0.820958i \(0.693440\pi\)
\(110\) 8.70923e10 0.515609
\(111\) −1.90322e11 −1.07204
\(112\) −6.45640e9 −0.0346171
\(113\) −2.20021e11 −1.12340 −0.561698 0.827342i \(-0.689852\pi\)
−0.561698 + 0.827342i \(0.689852\pi\)
\(114\) 1.72013e11 0.836729
\(115\) 2.81829e10 0.130662
\(116\) −2.24060e10 −0.0990479
\(117\) −1.88299e11 −0.794010
\(118\) 3.02539e10 0.121739
\(119\) −2.33525e10 −0.0897067
\(120\) 3.25588e11 1.19446
\(121\) −7.65324e10 −0.268241
\(122\) 1.88687e11 0.632066
\(123\) 2.20617e11 0.706580
\(124\) 2.03194e10 0.0622432
\(125\) 3.67722e11 1.07774
\(126\) 3.10227e10 0.0870244
\(127\) 2.27277e11 0.610430 0.305215 0.952284i \(-0.401272\pi\)
0.305215 + 0.952284i \(0.401272\pi\)
\(128\) −1.43035e11 −0.367948
\(129\) −2.96551e11 −0.730897
\(130\) 3.02310e11 0.714108
\(131\) −4.64818e11 −1.05267 −0.526333 0.850278i \(-0.676434\pi\)
−0.526333 + 0.850278i \(0.676434\pi\)
\(132\) 2.71499e11 0.589673
\(133\) 8.64717e10 0.180173
\(134\) 6.52506e11 1.30469
\(135\) 1.95948e11 0.376101
\(136\) 2.68197e11 0.494298
\(137\) −8.70791e11 −1.54153 −0.770763 0.637123i \(-0.780125\pi\)
−0.770763 + 0.637123i \(0.780125\pi\)
\(138\) −7.68572e10 −0.130722
\(139\) −4.84555e11 −0.792066 −0.396033 0.918236i \(-0.629613\pi\)
−0.396033 + 0.918236i \(0.629613\pi\)
\(140\) 5.69341e10 0.0894682
\(141\) 1.39894e11 0.211394
\(142\) −1.76550e11 −0.256615
\(143\) 7.24702e11 1.01347
\(144\) −9.06813e10 −0.122046
\(145\) −1.26469e11 −0.163855
\(146\) −9.90510e11 −1.23571
\(147\) −1.03668e12 −1.24566
\(148\) 3.82219e11 0.442459
\(149\) −2.65277e11 −0.295920 −0.147960 0.988993i \(-0.547271\pi\)
−0.147960 + 0.988993i \(0.547271\pi\)
\(150\) −1.81773e11 −0.195446
\(151\) −4.88755e11 −0.506661 −0.253331 0.967380i \(-0.581526\pi\)
−0.253331 + 0.967380i \(0.581526\pi\)
\(152\) −9.93102e11 −0.992783
\(153\) −3.27990e11 −0.316270
\(154\) −1.19396e11 −0.111078
\(155\) 1.14691e11 0.102969
\(156\) 9.42411e11 0.816686
\(157\) −1.40009e12 −1.17141 −0.585705 0.810524i \(-0.699182\pi\)
−0.585705 + 0.810524i \(0.699182\pi\)
\(158\) 6.20256e10 0.0501138
\(159\) 1.55643e12 1.21463
\(160\) −1.08029e12 −0.814484
\(161\) −3.86364e10 −0.0281485
\(162\) −1.18451e12 −0.834076
\(163\) −5.97037e11 −0.406414 −0.203207 0.979136i \(-0.565137\pi\)
−0.203207 + 0.979136i \(0.565137\pi\)
\(164\) −4.43062e11 −0.291624
\(165\) 1.53245e12 0.975497
\(166\) 5.40105e11 0.332571
\(167\) −8.57218e11 −0.510682 −0.255341 0.966851i \(-0.582188\pi\)
−0.255341 + 0.966851i \(0.582188\pi\)
\(168\) −4.46354e11 −0.257323
\(169\) 7.23384e11 0.403638
\(170\) 5.26580e11 0.284443
\(171\) 1.21451e12 0.635218
\(172\) 5.95558e11 0.301660
\(173\) 1.77551e12 0.871104 0.435552 0.900164i \(-0.356553\pi\)
0.435552 + 0.900164i \(0.356553\pi\)
\(174\) 3.44891e11 0.163931
\(175\) −9.13778e10 −0.0420854
\(176\) 3.49003e11 0.155779
\(177\) 5.32339e11 0.230322
\(178\) 8.25312e10 0.0346185
\(179\) −1.48356e12 −0.603411 −0.301706 0.953401i \(-0.597556\pi\)
−0.301706 + 0.953401i \(0.597556\pi\)
\(180\) 7.99651e11 0.315429
\(181\) −4.81102e12 −1.84079 −0.920396 0.390987i \(-0.872134\pi\)
−0.920396 + 0.390987i \(0.872134\pi\)
\(182\) −4.14441e11 −0.153840
\(183\) 3.32008e12 1.19583
\(184\) 4.43728e11 0.155103
\(185\) 2.15741e12 0.731960
\(186\) −3.12773e11 −0.103017
\(187\) 1.26233e12 0.403686
\(188\) −2.80946e11 −0.0872478
\(189\) −2.68628e11 −0.0810236
\(190\) −1.94987e12 −0.571295
\(191\) 2.14249e12 0.609867 0.304933 0.952374i \(-0.401366\pi\)
0.304933 + 0.952374i \(0.401366\pi\)
\(192\) 3.79693e12 1.05021
\(193\) −3.06980e12 −0.825172 −0.412586 0.910919i \(-0.635374\pi\)
−0.412586 + 0.910919i \(0.635374\pi\)
\(194\) −1.45687e12 −0.380637
\(195\) 5.31937e12 1.35104
\(196\) 2.08194e12 0.514115
\(197\) −6.87761e12 −1.65148 −0.825740 0.564052i \(-0.809242\pi\)
−0.825740 + 0.564052i \(0.809242\pi\)
\(198\) −1.67694e12 −0.391615
\(199\) 2.80182e12 0.636427 0.318214 0.948019i \(-0.396917\pi\)
0.318214 + 0.948019i \(0.396917\pi\)
\(200\) 1.04945e12 0.231897
\(201\) 1.14813e13 2.46839
\(202\) −3.55356e12 −0.743415
\(203\) 1.73378e11 0.0352993
\(204\) 1.64154e12 0.325302
\(205\) −2.50083e12 −0.482433
\(206\) 6.82750e12 1.28231
\(207\) −5.42656e11 −0.0992401
\(208\) 1.21144e12 0.215751
\(209\) −4.67426e12 −0.810790
\(210\) −8.76377e11 −0.148076
\(211\) 7.26139e12 1.19527 0.597635 0.801768i \(-0.296107\pi\)
0.597635 + 0.801768i \(0.296107\pi\)
\(212\) −3.12574e12 −0.501310
\(213\) −3.10652e12 −0.485497
\(214\) 3.88497e12 0.591714
\(215\) 3.36158e12 0.499036
\(216\) 3.08512e12 0.446453
\(217\) −1.57232e11 −0.0221826
\(218\) −5.67081e12 −0.780071
\(219\) −1.74288e13 −2.33789
\(220\) −3.07760e12 −0.402612
\(221\) 4.38172e12 0.559097
\(222\) −5.88343e12 −0.732300
\(223\) −1.04017e12 −0.126307 −0.0631535 0.998004i \(-0.520116\pi\)
−0.0631535 + 0.998004i \(0.520116\pi\)
\(224\) 1.48099e12 0.175464
\(225\) −1.28342e12 −0.148376
\(226\) −6.80153e12 −0.767380
\(227\) −1.37568e13 −1.51487 −0.757435 0.652910i \(-0.773548\pi\)
−0.757435 + 0.652910i \(0.773548\pi\)
\(228\) −6.07846e12 −0.653359
\(229\) −3.48055e12 −0.365219 −0.182609 0.983186i \(-0.558454\pi\)
−0.182609 + 0.983186i \(0.558454\pi\)
\(230\) 8.71221e11 0.0892535
\(231\) −2.10087e12 −0.210151
\(232\) −1.99120e12 −0.194505
\(233\) −2.14416e12 −0.204550 −0.102275 0.994756i \(-0.532612\pi\)
−0.102275 + 0.994756i \(0.532612\pi\)
\(234\) −5.82090e12 −0.542379
\(235\) −1.58578e12 −0.144334
\(236\) −1.06909e12 −0.0950598
\(237\) 1.09139e12 0.0948119
\(238\) −7.21897e11 −0.0612777
\(239\) 2.07449e13 1.72077 0.860387 0.509641i \(-0.170222\pi\)
0.860387 + 0.509641i \(0.170222\pi\)
\(240\) 2.56171e12 0.207667
\(241\) 3.85887e12 0.305750 0.152875 0.988246i \(-0.451147\pi\)
0.152875 + 0.988246i \(0.451147\pi\)
\(242\) −2.36585e12 −0.183233
\(243\) −1.52127e13 −1.15178
\(244\) −6.66766e12 −0.493548
\(245\) 1.17514e13 0.850501
\(246\) 6.81996e12 0.482657
\(247\) −1.62250e13 −1.12293
\(248\) 1.80577e12 0.122230
\(249\) 9.50356e12 0.629201
\(250\) 1.13674e13 0.736194
\(251\) 1.83565e13 1.16301 0.581506 0.813542i \(-0.302464\pi\)
0.581506 + 0.813542i \(0.302464\pi\)
\(252\) −1.09625e12 −0.0679529
\(253\) 2.08851e12 0.126670
\(254\) 7.02584e12 0.416978
\(255\) 9.26557e12 0.538147
\(256\) −1.87176e13 −1.06397
\(257\) 3.54585e13 1.97282 0.986412 0.164290i \(-0.0525334\pi\)
0.986412 + 0.164290i \(0.0525334\pi\)
\(258\) −9.16731e12 −0.499268
\(259\) −2.95762e12 −0.157686
\(260\) −1.06828e13 −0.557610
\(261\) 2.43513e12 0.124451
\(262\) −1.43690e13 −0.719065
\(263\) 2.92866e13 1.43520 0.717601 0.696455i \(-0.245240\pi\)
0.717601 + 0.696455i \(0.245240\pi\)
\(264\) 2.41278e13 1.15797
\(265\) −1.76430e13 −0.829317
\(266\) 2.67311e12 0.123074
\(267\) 1.45220e12 0.0654959
\(268\) −2.30577e13 −1.01877
\(269\) 3.25011e13 1.40689 0.703445 0.710749i \(-0.251644\pi\)
0.703445 + 0.710749i \(0.251644\pi\)
\(270\) 6.05735e12 0.256911
\(271\) −2.42500e13 −1.00781 −0.503907 0.863758i \(-0.668104\pi\)
−0.503907 + 0.863758i \(0.668104\pi\)
\(272\) 2.11015e12 0.0859379
\(273\) −7.29240e12 −0.291056
\(274\) −2.69188e13 −1.05300
\(275\) 4.93946e12 0.189387
\(276\) 2.71592e12 0.102074
\(277\) −3.35541e13 −1.23625 −0.618125 0.786079i \(-0.712108\pi\)
−0.618125 + 0.786079i \(0.712108\pi\)
\(278\) −1.49791e13 −0.541052
\(279\) −2.20836e12 −0.0782071
\(280\) 5.05968e12 0.175693
\(281\) 2.99054e13 1.01827 0.509137 0.860686i \(-0.329965\pi\)
0.509137 + 0.860686i \(0.329965\pi\)
\(282\) 4.32454e12 0.144401
\(283\) 5.38626e13 1.76385 0.881926 0.471389i \(-0.156247\pi\)
0.881926 + 0.471389i \(0.156247\pi\)
\(284\) 6.23877e12 0.200377
\(285\) −3.43094e13 −1.08085
\(286\) 2.24028e13 0.692291
\(287\) 3.42842e12 0.103931
\(288\) 2.08008e13 0.618617
\(289\) −2.66396e13 −0.777301
\(290\) −3.90954e12 −0.111928
\(291\) −2.56347e13 −0.720139
\(292\) 3.50018e13 0.964906
\(293\) 2.24694e13 0.607884 0.303942 0.952691i \(-0.401697\pi\)
0.303942 + 0.952691i \(0.401697\pi\)
\(294\) −3.20470e13 −0.850896
\(295\) −6.03438e12 −0.157258
\(296\) 3.39675e13 0.868878
\(297\) 1.45208e13 0.364611
\(298\) −8.20052e12 −0.202140
\(299\) 7.24950e12 0.175435
\(300\) 6.42333e12 0.152614
\(301\) −4.60845e12 −0.107508
\(302\) −1.51089e13 −0.346095
\(303\) −6.25275e13 −1.40649
\(304\) −7.81366e12 −0.172604
\(305\) −3.76351e13 −0.816477
\(306\) −1.01392e13 −0.216040
\(307\) −1.53567e13 −0.321394 −0.160697 0.987004i \(-0.551374\pi\)
−0.160697 + 0.987004i \(0.551374\pi\)
\(308\) 4.21913e12 0.0867349
\(309\) 1.20135e14 2.42604
\(310\) 3.54547e12 0.0703370
\(311\) 3.86505e13 0.753308 0.376654 0.926354i \(-0.377075\pi\)
0.376654 + 0.926354i \(0.377075\pi\)
\(312\) 8.37511e13 1.60376
\(313\) −4.54140e13 −0.854468 −0.427234 0.904141i \(-0.640512\pi\)
−0.427234 + 0.904141i \(0.640512\pi\)
\(314\) −4.32812e13 −0.800178
\(315\) −6.18772e12 −0.112415
\(316\) −2.19181e12 −0.0391313
\(317\) −7.27574e12 −0.127659 −0.0638295 0.997961i \(-0.520331\pi\)
−0.0638295 + 0.997961i \(0.520331\pi\)
\(318\) 4.81140e13 0.829702
\(319\) −9.37203e12 −0.158849
\(320\) −4.30404e13 −0.717053
\(321\) 6.83590e13 1.11948
\(322\) −1.19437e12 −0.0192279
\(323\) −2.82617e13 −0.447284
\(324\) 4.18572e13 0.651287
\(325\) 1.71456e13 0.262297
\(326\) −1.84562e13 −0.277617
\(327\) −9.97821e13 −1.47584
\(328\) −3.93745e13 −0.572675
\(329\) 2.17397e12 0.0310939
\(330\) 4.73729e13 0.666351
\(331\) −9.00769e13 −1.24612 −0.623059 0.782175i \(-0.714110\pi\)
−0.623059 + 0.782175i \(0.714110\pi\)
\(332\) −1.90858e13 −0.259687
\(333\) −4.15404e13 −0.555939
\(334\) −2.64993e13 −0.348842
\(335\) −1.30148e14 −1.68535
\(336\) −3.51188e12 −0.0447377
\(337\) −1.09026e14 −1.36637 −0.683183 0.730247i \(-0.739405\pi\)
−0.683183 + 0.730247i \(0.739405\pi\)
\(338\) 2.23620e13 0.275721
\(339\) −1.19678e14 −1.45183
\(340\) −1.86079e13 −0.222107
\(341\) 8.49925e12 0.0998233
\(342\) 3.75443e13 0.433910
\(343\) −3.28242e13 −0.373316
\(344\) 5.29267e13 0.592384
\(345\) 1.53298e13 0.168862
\(346\) 5.48865e13 0.595042
\(347\) −9.88635e13 −1.05493 −0.527465 0.849576i \(-0.676858\pi\)
−0.527465 + 0.849576i \(0.676858\pi\)
\(348\) −1.21875e13 −0.128005
\(349\) 4.39363e13 0.454238 0.227119 0.973867i \(-0.427069\pi\)
0.227119 + 0.973867i \(0.427069\pi\)
\(350\) −2.82477e12 −0.0287481
\(351\) 5.04037e13 0.504979
\(352\) −8.00557e13 −0.789601
\(353\) 1.89566e14 1.84077 0.920385 0.391013i \(-0.127875\pi\)
0.920385 + 0.391013i \(0.127875\pi\)
\(354\) 1.64562e13 0.157330
\(355\) 3.52143e13 0.331484
\(356\) −2.91642e12 −0.0270318
\(357\) −1.27023e13 −0.115933
\(358\) −4.58614e13 −0.412184
\(359\) 9.61153e13 0.850694 0.425347 0.905030i \(-0.360152\pi\)
0.425347 + 0.905030i \(0.360152\pi\)
\(360\) 7.10642e13 0.619422
\(361\) −1.18405e13 −0.101644
\(362\) −1.48723e14 −1.25743
\(363\) −4.16289e13 −0.346664
\(364\) 1.46452e13 0.120126
\(365\) 1.97565e14 1.59624
\(366\) 1.02634e14 0.816856
\(367\) 6.15690e13 0.482724 0.241362 0.970435i \(-0.422406\pi\)
0.241362 + 0.970435i \(0.422406\pi\)
\(368\) 3.49122e12 0.0269659
\(369\) 4.81528e13 0.366418
\(370\) 6.66921e13 0.499994
\(371\) 2.41871e13 0.178660
\(372\) 1.10525e13 0.0804406
\(373\) 1.67703e14 1.20266 0.601330 0.799001i \(-0.294638\pi\)
0.601330 + 0.799001i \(0.294638\pi\)
\(374\) 3.90224e13 0.275753
\(375\) 2.00018e14 1.39283
\(376\) −2.49674e13 −0.171332
\(377\) −3.25316e13 −0.220003
\(378\) −8.30412e12 −0.0553463
\(379\) −3.55256e13 −0.233360 −0.116680 0.993170i \(-0.537225\pi\)
−0.116680 + 0.993170i \(0.537225\pi\)
\(380\) 6.89029e13 0.446095
\(381\) 1.23625e14 0.788894
\(382\) 6.62309e13 0.416593
\(383\) −2.93299e14 −1.81851 −0.909257 0.416235i \(-0.863349\pi\)
−0.909257 + 0.416235i \(0.863349\pi\)
\(384\) −7.78021e13 −0.475521
\(385\) 2.38145e13 0.143486
\(386\) −9.48968e13 −0.563666
\(387\) −6.47265e13 −0.379028
\(388\) 5.14816e13 0.297220
\(389\) −2.33407e14 −1.32859 −0.664294 0.747471i \(-0.731268\pi\)
−0.664294 + 0.747471i \(0.731268\pi\)
\(390\) 1.64438e14 0.922883
\(391\) 1.26276e13 0.0698793
\(392\) 1.85020e14 1.00959
\(393\) −2.52832e14 −1.36042
\(394\) −2.12608e14 −1.12811
\(395\) −1.23715e13 −0.0647349
\(396\) 5.92584e13 0.305792
\(397\) 3.29462e12 0.0167671 0.00838354 0.999965i \(-0.497331\pi\)
0.00838354 + 0.999965i \(0.497331\pi\)
\(398\) 8.66130e13 0.434736
\(399\) 4.70353e13 0.232848
\(400\) 8.25699e12 0.0403173
\(401\) −1.82842e14 −0.880606 −0.440303 0.897849i \(-0.645129\pi\)
−0.440303 + 0.897849i \(0.645129\pi\)
\(402\) 3.54923e14 1.68613
\(403\) 2.95021e13 0.138253
\(404\) 1.25573e14 0.580495
\(405\) 2.36260e14 1.07742
\(406\) 5.35966e12 0.0241126
\(407\) 1.59876e14 0.709599
\(408\) 1.45882e14 0.638811
\(409\) 2.44493e14 1.05630 0.528152 0.849150i \(-0.322885\pi\)
0.528152 + 0.849150i \(0.322885\pi\)
\(410\) −7.73083e13 −0.329545
\(411\) −4.73657e14 −1.99220
\(412\) −2.41264e14 −1.00129
\(413\) 8.27262e12 0.0338780
\(414\) −1.67752e13 −0.0677899
\(415\) −1.07728e14 −0.429601
\(416\) −2.77885e14 −1.09358
\(417\) −2.63568e14 −1.02363
\(418\) −1.44496e14 −0.553842
\(419\) −1.80116e13 −0.0681358 −0.0340679 0.999420i \(-0.510846\pi\)
−0.0340679 + 0.999420i \(0.510846\pi\)
\(420\) 3.09687e13 0.115625
\(421\) −3.46365e14 −1.27639 −0.638193 0.769877i \(-0.720318\pi\)
−0.638193 + 0.769877i \(0.720318\pi\)
\(422\) 2.24472e14 0.816476
\(423\) 3.05338e13 0.109625
\(424\) −2.77782e14 −0.984445
\(425\) 2.98651e13 0.104478
\(426\) −9.60322e13 −0.331638
\(427\) 5.15946e13 0.175894
\(428\) −1.37284e14 −0.462039
\(429\) 3.94194e14 1.30977
\(430\) 1.03917e14 0.340886
\(431\) −2.61420e14 −0.846670 −0.423335 0.905973i \(-0.639141\pi\)
−0.423335 + 0.905973i \(0.639141\pi\)
\(432\) 2.42735e13 0.0776196
\(433\) 1.18456e14 0.374001 0.187001 0.982360i \(-0.440123\pi\)
0.187001 + 0.982360i \(0.440123\pi\)
\(434\) −4.86053e12 −0.0151527
\(435\) −6.87913e13 −0.211759
\(436\) 2.00390e14 0.609118
\(437\) −4.67586e13 −0.140350
\(438\) −5.38776e14 −1.59699
\(439\) 2.73272e14 0.799910 0.399955 0.916535i \(-0.369026\pi\)
0.399955 + 0.916535i \(0.369026\pi\)
\(440\) −2.73503e14 −0.790629
\(441\) −2.26270e14 −0.645973
\(442\) 1.35452e14 0.381913
\(443\) −2.68138e13 −0.0746686 −0.0373343 0.999303i \(-0.511887\pi\)
−0.0373343 + 0.999303i \(0.511887\pi\)
\(444\) 2.07904e14 0.571816
\(445\) −1.64615e13 −0.0447187
\(446\) −3.21548e13 −0.0862789
\(447\) −1.44294e14 −0.382435
\(448\) 5.90048e13 0.154475
\(449\) 4.98402e14 1.28892 0.644458 0.764639i \(-0.277083\pi\)
0.644458 + 0.764639i \(0.277083\pi\)
\(450\) −3.96744e13 −0.101354
\(451\) −1.85325e14 −0.467695
\(452\) 2.40347e14 0.599208
\(453\) −2.65853e14 −0.654788
\(454\) −4.25265e14 −1.03479
\(455\) 8.26636e13 0.198725
\(456\) −5.40187e14 −1.28303
\(457\) 4.40553e13 0.103385 0.0516927 0.998663i \(-0.483538\pi\)
0.0516927 + 0.998663i \(0.483538\pi\)
\(458\) −1.07595e14 −0.249477
\(459\) 8.77961e13 0.201143
\(460\) −3.07865e13 −0.0696935
\(461\) 4.19399e14 0.938150 0.469075 0.883158i \(-0.344587\pi\)
0.469075 + 0.883158i \(0.344587\pi\)
\(462\) −6.49442e13 −0.143552
\(463\) 7.77752e14 1.69881 0.849407 0.527738i \(-0.176960\pi\)
0.849407 + 0.527738i \(0.176960\pi\)
\(464\) −1.56666e13 −0.0338163
\(465\) 6.23851e13 0.133073
\(466\) −6.62824e13 −0.139726
\(467\) 2.21898e14 0.462285 0.231143 0.972920i \(-0.425754\pi\)
0.231143 + 0.972920i \(0.425754\pi\)
\(468\) 2.05694e14 0.423516
\(469\) 1.78421e14 0.363075
\(470\) −4.90212e13 −0.0985930
\(471\) −7.61566e14 −1.51388
\(472\) −9.50087e13 −0.186673
\(473\) 2.49111e14 0.483790
\(474\) 3.37381e13 0.0647649
\(475\) −1.10587e14 −0.209841
\(476\) 2.55098e13 0.0478486
\(477\) 3.39712e14 0.629883
\(478\) 6.41290e14 1.17544
\(479\) −8.63306e13 −0.156430 −0.0782149 0.996937i \(-0.524922\pi\)
−0.0782149 + 0.996937i \(0.524922\pi\)
\(480\) −5.87614e14 −1.05261
\(481\) 5.54951e14 0.982780
\(482\) 1.19289e14 0.208854
\(483\) −2.10158e13 −0.0363779
\(484\) 8.36025e13 0.143077
\(485\) 2.90584e14 0.491691
\(486\) −4.70270e14 −0.786771
\(487\) 8.20942e14 1.35801 0.679005 0.734133i \(-0.262411\pi\)
0.679005 + 0.734133i \(0.262411\pi\)
\(488\) −5.92549e14 −0.969203
\(489\) −3.24751e14 −0.525233
\(490\) 3.63271e14 0.580968
\(491\) 1.43945e14 0.227640 0.113820 0.993501i \(-0.463691\pi\)
0.113820 + 0.993501i \(0.463691\pi\)
\(492\) −2.40998e14 −0.376882
\(493\) −5.66655e13 −0.0876315
\(494\) −5.01565e14 −0.767060
\(495\) 3.34480e14 0.505873
\(496\) 1.42077e13 0.0212507
\(497\) −4.82758e13 −0.0714117
\(498\) 2.93784e14 0.429801
\(499\) 4.42279e14 0.639945 0.319973 0.947427i \(-0.396326\pi\)
0.319973 + 0.947427i \(0.396326\pi\)
\(500\) −4.01693e14 −0.574856
\(501\) −4.66274e14 −0.659985
\(502\) 5.67456e14 0.794441
\(503\) 7.02029e14 0.972146 0.486073 0.873918i \(-0.338429\pi\)
0.486073 + 0.873918i \(0.338429\pi\)
\(504\) −9.74230e13 −0.133442
\(505\) 7.08786e14 0.960313
\(506\) 6.45622e13 0.0865268
\(507\) 3.93477e14 0.521645
\(508\) −2.48274e14 −0.325597
\(509\) 1.26187e15 1.63706 0.818532 0.574461i \(-0.194788\pi\)
0.818532 + 0.574461i \(0.194788\pi\)
\(510\) 2.86427e14 0.367603
\(511\) −2.70845e14 −0.343879
\(512\) −2.85683e14 −0.358839
\(513\) −3.25099e14 −0.403990
\(514\) 1.09613e15 1.34761
\(515\) −1.36180e15 −1.65643
\(516\) 3.23947e14 0.389853
\(517\) −1.17515e14 −0.139925
\(518\) −9.14293e13 −0.107714
\(519\) 9.65769e14 1.12578
\(520\) −9.49368e14 −1.09501
\(521\) −1.05945e15 −1.20913 −0.604565 0.796555i \(-0.706653\pi\)
−0.604565 + 0.796555i \(0.706653\pi\)
\(522\) 7.52774e13 0.0850113
\(523\) −1.79848e14 −0.200977 −0.100488 0.994938i \(-0.532041\pi\)
−0.100488 + 0.994938i \(0.532041\pi\)
\(524\) 5.07758e14 0.561481
\(525\) −4.97039e13 −0.0543894
\(526\) 9.05340e14 0.980371
\(527\) 5.13884e13 0.0550690
\(528\) 1.89836e14 0.201323
\(529\) −9.31918e14 −0.978073
\(530\) −5.45400e14 −0.566497
\(531\) 1.16191e14 0.119440
\(532\) −9.44600e13 −0.0961024
\(533\) −6.43289e14 −0.647748
\(534\) 4.48919e13 0.0447395
\(535\) −7.74889e14 −0.764352
\(536\) −2.04912e15 −2.00060
\(537\) −8.06966e14 −0.779824
\(538\) 1.00471e15 0.961032
\(539\) 8.70840e14 0.824518
\(540\) −2.14050e14 −0.200608
\(541\) −2.63503e14 −0.244456 −0.122228 0.992502i \(-0.539004\pi\)
−0.122228 + 0.992502i \(0.539004\pi\)
\(542\) −7.49641e14 −0.688426
\(543\) −2.61690e15 −2.37896
\(544\) −4.84035e14 −0.435595
\(545\) 1.13109e15 1.00766
\(546\) −2.25431e14 −0.198817
\(547\) −1.78221e15 −1.55607 −0.778036 0.628219i \(-0.783784\pi\)
−0.778036 + 0.628219i \(0.783784\pi\)
\(548\) 9.51235e14 0.822233
\(549\) 7.24655e14 0.620131
\(550\) 1.52694e14 0.129368
\(551\) 2.09826e14 0.176005
\(552\) 2.41361e14 0.200448
\(553\) 1.69603e13 0.0139459
\(554\) −1.03726e15 −0.844469
\(555\) 1.17350e15 0.945955
\(556\) 5.29318e14 0.422480
\(557\) 4.27839e14 0.338125 0.169062 0.985605i \(-0.445926\pi\)
0.169062 + 0.985605i \(0.445926\pi\)
\(558\) −6.82671e13 −0.0534224
\(559\) 8.64701e14 0.670040
\(560\) 3.98092e13 0.0305457
\(561\) 6.86629e14 0.521707
\(562\) 9.24467e14 0.695571
\(563\) 9.47616e14 0.706051 0.353026 0.935614i \(-0.385153\pi\)
0.353026 + 0.935614i \(0.385153\pi\)
\(564\) −1.52817e14 −0.112755
\(565\) 1.35662e15 0.991270
\(566\) 1.66506e15 1.20487
\(567\) −3.23892e14 −0.232110
\(568\) 5.54434e14 0.393490
\(569\) −1.54228e15 −1.08404 −0.542021 0.840365i \(-0.682341\pi\)
−0.542021 + 0.840365i \(0.682341\pi\)
\(570\) −1.06061e15 −0.738318
\(571\) −2.54264e15 −1.75302 −0.876509 0.481386i \(-0.840134\pi\)
−0.876509 + 0.481386i \(0.840134\pi\)
\(572\) −7.91651e14 −0.540575
\(573\) 1.16538e15 0.788166
\(574\) 1.05983e14 0.0709940
\(575\) 4.94115e13 0.0327835
\(576\) 8.28733e14 0.544617
\(577\) 5.19529e14 0.338176 0.169088 0.985601i \(-0.445918\pi\)
0.169088 + 0.985601i \(0.445918\pi\)
\(578\) −8.23511e14 −0.530966
\(579\) −1.66978e15 −1.06642
\(580\) 1.38152e14 0.0873985
\(581\) 1.47687e14 0.0925491
\(582\) −7.92447e14 −0.491919
\(583\) −1.30744e15 −0.803981
\(584\) 3.11058e15 1.89483
\(585\) 1.16103e15 0.700624
\(586\) 6.94600e14 0.415239
\(587\) −3.14123e15 −1.86033 −0.930165 0.367142i \(-0.880336\pi\)
−0.930165 + 0.367142i \(0.880336\pi\)
\(588\) 1.13245e15 0.664421
\(589\) −1.90286e14 −0.110604
\(590\) −1.86541e14 −0.107421
\(591\) −3.74100e15 −2.13430
\(592\) 2.67254e14 0.151062
\(593\) −1.55824e15 −0.872634 −0.436317 0.899793i \(-0.643717\pi\)
−0.436317 + 0.899793i \(0.643717\pi\)
\(594\) 4.48883e14 0.249062
\(595\) 1.43988e14 0.0791560
\(596\) 2.89783e14 0.157841
\(597\) 1.52402e15 0.822492
\(598\) 2.24104e14 0.119838
\(599\) −1.68384e15 −0.892181 −0.446090 0.894988i \(-0.647184\pi\)
−0.446090 + 0.894988i \(0.647184\pi\)
\(600\) 5.70835e14 0.299695
\(601\) −5.99073e14 −0.311652 −0.155826 0.987785i \(-0.549804\pi\)
−0.155826 + 0.987785i \(0.549804\pi\)
\(602\) −1.42461e14 −0.0734372
\(603\) 2.50596e15 1.28006
\(604\) 5.33907e14 0.270248
\(605\) 4.71888e14 0.236692
\(606\) −1.93292e15 −0.960758
\(607\) −2.54207e15 −1.25213 −0.626064 0.779771i \(-0.715335\pi\)
−0.626064 + 0.779771i \(0.715335\pi\)
\(608\) 1.79233e15 0.874879
\(609\) 9.43071e13 0.0456194
\(610\) −1.16342e15 −0.557727
\(611\) −4.07910e14 −0.193793
\(612\) 3.58290e14 0.168695
\(613\) 1.94855e15 0.909240 0.454620 0.890686i \(-0.349775\pi\)
0.454620 + 0.890686i \(0.349775\pi\)
\(614\) −4.74723e14 −0.219540
\(615\) −1.36030e15 −0.623477
\(616\) 3.74950e14 0.170325
\(617\) 2.66659e15 1.20057 0.600286 0.799785i \(-0.295053\pi\)
0.600286 + 0.799785i \(0.295053\pi\)
\(618\) 3.71374e15 1.65720
\(619\) −1.45237e15 −0.642362 −0.321181 0.947018i \(-0.604080\pi\)
−0.321181 + 0.947018i \(0.604080\pi\)
\(620\) −1.25287e14 −0.0549226
\(621\) 1.45258e14 0.0631154
\(622\) 1.19481e15 0.514576
\(623\) 2.25673e13 0.00963377
\(624\) 6.58948e14 0.278828
\(625\) −1.73948e15 −0.729591
\(626\) −1.40389e15 −0.583678
\(627\) −2.54251e15 −1.04783
\(628\) 1.52944e15 0.624818
\(629\) 9.66644e14 0.391461
\(630\) −1.91281e14 −0.0767892
\(631\) 1.59115e15 0.633214 0.316607 0.948557i \(-0.397456\pi\)
0.316607 + 0.948557i \(0.397456\pi\)
\(632\) −1.94784e14 −0.0768439
\(633\) 3.94975e15 1.54472
\(634\) −2.24916e14 −0.0872025
\(635\) −1.40136e15 −0.538635
\(636\) −1.70021e15 −0.647872
\(637\) 3.02281e15 1.14194
\(638\) −2.89718e14 −0.108508
\(639\) −6.78043e14 −0.251769
\(640\) 8.81932e14 0.324672
\(641\) 4.39261e15 1.60326 0.801630 0.597820i \(-0.203966\pi\)
0.801630 + 0.597820i \(0.203966\pi\)
\(642\) 2.11319e15 0.764707
\(643\) 9.85800e14 0.353694 0.176847 0.984238i \(-0.443410\pi\)
0.176847 + 0.984238i \(0.443410\pi\)
\(644\) 4.22057e13 0.0150141
\(645\) 1.82849e15 0.644934
\(646\) −8.73655e14 −0.305535
\(647\) 7.75343e13 0.0268856 0.0134428 0.999910i \(-0.495721\pi\)
0.0134428 + 0.999910i \(0.495721\pi\)
\(648\) 3.71981e15 1.27896
\(649\) −4.47180e14 −0.152453
\(650\) 5.30023e14 0.179172
\(651\) −8.55247e13 −0.0286679
\(652\) 6.52192e14 0.216777
\(653\) 5.07913e15 1.67405 0.837023 0.547168i \(-0.184294\pi\)
0.837023 + 0.547168i \(0.184294\pi\)
\(654\) −3.08457e15 −1.00813
\(655\) 2.86600e15 0.928859
\(656\) −3.09796e14 −0.0995644
\(657\) −3.80407e15 −1.21238
\(658\) 6.72040e13 0.0212399
\(659\) 1.35108e15 0.423458 0.211729 0.977328i \(-0.432091\pi\)
0.211729 + 0.977328i \(0.432091\pi\)
\(660\) −1.67402e15 −0.520320
\(661\) 4.07858e15 1.25719 0.628596 0.777732i \(-0.283630\pi\)
0.628596 + 0.777732i \(0.283630\pi\)
\(662\) −2.78455e15 −0.851210
\(663\) 2.38339e15 0.722553
\(664\) −1.69614e15 −0.509960
\(665\) −5.33172e14 −0.158982
\(666\) −1.28414e15 −0.379756
\(667\) −9.37524e13 −0.0274973
\(668\) 9.36409e14 0.272393
\(669\) −5.65788e14 −0.163234
\(670\) −4.02326e15 −1.15124
\(671\) −2.78896e15 −0.791533
\(672\) 8.05570e14 0.226763
\(673\) −5.20381e15 −1.45291 −0.726454 0.687215i \(-0.758833\pi\)
−0.726454 + 0.687215i \(0.758833\pi\)
\(674\) −3.37034e15 −0.933350
\(675\) 3.43544e14 0.0943653
\(676\) −7.90211e14 −0.215296
\(677\) −3.91496e15 −1.05801 −0.529005 0.848619i \(-0.677435\pi\)
−0.529005 + 0.848619i \(0.677435\pi\)
\(678\) −3.69962e15 −0.991730
\(679\) −3.98366e14 −0.105925
\(680\) −1.65366e15 −0.436162
\(681\) −7.48286e15 −1.95776
\(682\) 2.62738e14 0.0681882
\(683\) 1.55743e15 0.400954 0.200477 0.979698i \(-0.435751\pi\)
0.200477 + 0.979698i \(0.435751\pi\)
\(684\) −1.32671e15 −0.338818
\(685\) 5.36918e15 1.36022
\(686\) −1.01470e15 −0.255008
\(687\) −1.89321e15 −0.471993
\(688\) 4.16424e14 0.102991
\(689\) −4.53832e15 −1.11350
\(690\) 4.73891e14 0.115348
\(691\) 3.79974e15 0.917538 0.458769 0.888555i \(-0.348290\pi\)
0.458769 + 0.888555i \(0.348290\pi\)
\(692\) −1.93954e15 −0.464637
\(693\) −4.58543e14 −0.108980
\(694\) −3.05618e15 −0.720612
\(695\) 2.98770e15 0.698908
\(696\) −1.08309e15 −0.251370
\(697\) −1.12052e15 −0.258011
\(698\) 1.35821e15 0.310285
\(699\) −1.16629e15 −0.264351
\(700\) 9.98194e13 0.0224479
\(701\) −2.38592e15 −0.532361 −0.266181 0.963923i \(-0.585762\pi\)
−0.266181 + 0.963923i \(0.585762\pi\)
\(702\) 1.55814e15 0.344946
\(703\) −3.57938e15 −0.786236
\(704\) −3.18953e15 −0.695147
\(705\) −8.62565e14 −0.186531
\(706\) 5.86007e15 1.25741
\(707\) −9.71686e14 −0.206880
\(708\) −5.81518e14 −0.122851
\(709\) −4.94373e15 −1.03634 −0.518168 0.855279i \(-0.673386\pi\)
−0.518168 + 0.855279i \(0.673386\pi\)
\(710\) 1.08858e15 0.226433
\(711\) 2.38210e14 0.0491675
\(712\) −2.59179e14 −0.0530836
\(713\) 8.50216e13 0.0172797
\(714\) −3.92668e14 −0.0791927
\(715\) −4.46842e15 −0.894274
\(716\) 1.62061e15 0.321853
\(717\) 1.12840e16 2.22386
\(718\) 2.97122e15 0.581100
\(719\) 3.97715e15 0.771904 0.385952 0.922519i \(-0.373873\pi\)
0.385952 + 0.922519i \(0.373873\pi\)
\(720\) 5.59128e14 0.107692
\(721\) 1.86691e15 0.356845
\(722\) −3.66026e14 −0.0694316
\(723\) 2.09899e15 0.395138
\(724\) 5.25547e15 0.981859
\(725\) −2.21731e14 −0.0411119
\(726\) −1.28688e15 −0.236802
\(727\) −1.01916e16 −1.86125 −0.930625 0.365974i \(-0.880736\pi\)
−0.930625 + 0.365974i \(0.880736\pi\)
\(728\) 1.30150e15 0.235897
\(729\) −1.48695e15 −0.267482
\(730\) 6.10735e15 1.09038
\(731\) 1.50618e15 0.266890
\(732\) −3.62680e15 −0.637841
\(733\) 6.33891e15 1.10648 0.553239 0.833022i \(-0.313392\pi\)
0.553239 + 0.833022i \(0.313392\pi\)
\(734\) 1.90329e15 0.329743
\(735\) 6.39202e15 1.09915
\(736\) −8.00831e14 −0.136682
\(737\) −9.64464e15 −1.63386
\(738\) 1.48855e15 0.250296
\(739\) −6.78577e15 −1.13254 −0.566271 0.824219i \(-0.691615\pi\)
−0.566271 + 0.824219i \(0.691615\pi\)
\(740\) −2.35671e15 −0.390420
\(741\) −8.82541e15 −1.45123
\(742\) 7.47698e14 0.122041
\(743\) 9.85625e15 1.59688 0.798441 0.602073i \(-0.205658\pi\)
0.798441 + 0.602073i \(0.205658\pi\)
\(744\) 9.82227e14 0.157965
\(745\) 1.63566e15 0.261116
\(746\) 5.18423e15 0.821524
\(747\) 2.07428e15 0.326291
\(748\) −1.37894e15 −0.215322
\(749\) 1.06231e15 0.164665
\(750\) 6.18318e15 0.951426
\(751\) 3.01620e14 0.0460723 0.0230362 0.999735i \(-0.492667\pi\)
0.0230362 + 0.999735i \(0.492667\pi\)
\(752\) −1.96442e14 −0.0297876
\(753\) 9.98481e15 1.50303
\(754\) −1.00565e15 −0.150282
\(755\) 3.01360e15 0.447071
\(756\) 2.93444e14 0.0432171
\(757\) −6.11741e14 −0.0894417 −0.0447209 0.999000i \(-0.514240\pi\)
−0.0447209 + 0.999000i \(0.514240\pi\)
\(758\) −1.09821e15 −0.159405
\(759\) 1.13602e15 0.163703
\(760\) 6.12333e15 0.876018
\(761\) 1.15259e15 0.163704 0.0818520 0.996644i \(-0.473917\pi\)
0.0818520 + 0.996644i \(0.473917\pi\)
\(762\) 3.82163e15 0.538885
\(763\) −1.55063e15 −0.217081
\(764\) −2.34041e15 −0.325296
\(765\) 2.02234e15 0.279072
\(766\) −9.06676e15 −1.24221
\(767\) −1.55222e15 −0.211145
\(768\) −1.01812e16 −1.37503
\(769\) −1.20278e16 −1.61284 −0.806418 0.591346i \(-0.798597\pi\)
−0.806418 + 0.591346i \(0.798597\pi\)
\(770\) 7.36181e14 0.0980134
\(771\) 1.92873e16 2.54960
\(772\) 3.35339e15 0.440138
\(773\) −1.67790e15 −0.218665 −0.109333 0.994005i \(-0.534871\pi\)
−0.109333 + 0.994005i \(0.534871\pi\)
\(774\) −2.00089e15 −0.258910
\(775\) 2.01082e14 0.0258353
\(776\) 4.57512e15 0.583664
\(777\) −1.60877e15 −0.203787
\(778\) −7.21532e15 −0.907544
\(779\) 4.14915e15 0.518207
\(780\) −5.81077e15 −0.720632
\(781\) 2.60957e15 0.321357
\(782\) 3.90358e14 0.0477338
\(783\) −6.51834e14 −0.0791493
\(784\) 1.45573e15 0.175526
\(785\) 8.63279e15 1.03364
\(786\) −7.81583e15 −0.929290
\(787\) −9.90983e15 −1.17005 −0.585026 0.811014i \(-0.698916\pi\)
−0.585026 + 0.811014i \(0.698916\pi\)
\(788\) 7.51297e15 0.880881
\(789\) 1.59301e16 1.85480
\(790\) −3.82441e14 −0.0442197
\(791\) −1.85981e15 −0.213549
\(792\) 5.26624e15 0.600499
\(793\) −9.68089e15 −1.09626
\(794\) 1.01847e14 0.0114534
\(795\) −9.59672e15 −1.07178
\(796\) −3.06066e15 −0.339463
\(797\) −4.31203e15 −0.474964 −0.237482 0.971392i \(-0.576322\pi\)
−0.237482 + 0.971392i \(0.576322\pi\)
\(798\) 1.45401e15 0.159056
\(799\) −7.10520e14 −0.0771915
\(800\) −1.89402e15 −0.204357
\(801\) 3.16963e14 0.0339648
\(802\) −5.65220e15 −0.601532
\(803\) 1.46406e16 1.54748
\(804\) −1.25420e16 −1.31661
\(805\) 2.38227e14 0.0248378
\(806\) 9.12001e14 0.0944393
\(807\) 1.76786e16 1.81821
\(808\) 1.11595e16 1.13994
\(809\) −6.10637e15 −0.619535 −0.309768 0.950812i \(-0.600251\pi\)
−0.309768 + 0.950812i \(0.600251\pi\)
\(810\) 7.30352e15 0.735977
\(811\) −9.72944e15 −0.973808 −0.486904 0.873456i \(-0.661874\pi\)
−0.486904 + 0.873456i \(0.661874\pi\)
\(812\) −1.89395e14 −0.0188283
\(813\) −1.31905e16 −1.30246
\(814\) 4.94225e15 0.484719
\(815\) 3.68125e15 0.358615
\(816\) 1.14779e15 0.111063
\(817\) −5.57724e15 −0.536041
\(818\) 7.55804e15 0.721549
\(819\) −1.59167e15 −0.150935
\(820\) 2.73186e15 0.257325
\(821\) 1.94055e15 0.181567 0.0907834 0.995871i \(-0.471063\pi\)
0.0907834 + 0.995871i \(0.471063\pi\)
\(822\) −1.46422e16 −1.36085
\(823\) 1.23186e16 1.13727 0.568634 0.822590i \(-0.307472\pi\)
0.568634 + 0.822590i \(0.307472\pi\)
\(824\) −2.14409e16 −1.96627
\(825\) 2.68677e15 0.244756
\(826\) 2.55732e14 0.0231417
\(827\) 2.11773e16 1.90366 0.951831 0.306625i \(-0.0991996\pi\)
0.951831 + 0.306625i \(0.0991996\pi\)
\(828\) 5.92787e14 0.0529336
\(829\) −1.02746e16 −0.911414 −0.455707 0.890130i \(-0.650614\pi\)
−0.455707 + 0.890130i \(0.650614\pi\)
\(830\) −3.33022e15 −0.293456
\(831\) −1.82514e16 −1.59768
\(832\) −1.10713e16 −0.962765
\(833\) 5.26530e15 0.454858
\(834\) −8.14770e15 −0.699233
\(835\) 5.28549e15 0.450619
\(836\) 5.10607e15 0.432467
\(837\) 5.91131e14 0.0497386
\(838\) −5.56794e14 −0.0465428
\(839\) 6.73136e15 0.559000 0.279500 0.960146i \(-0.409831\pi\)
0.279500 + 0.960146i \(0.409831\pi\)
\(840\) 2.75216e15 0.227058
\(841\) 4.20707e14 0.0344828
\(842\) −1.07072e16 −0.871885
\(843\) 1.62667e16 1.31597
\(844\) −7.93220e15 −0.637544
\(845\) −4.46029e15 −0.356165
\(846\) 9.43893e14 0.0748834
\(847\) −6.46919e14 −0.0509907
\(848\) −2.18557e15 −0.171154
\(849\) 2.92980e16 2.27953
\(850\) 9.23224e14 0.0713679
\(851\) 1.59930e15 0.122834
\(852\) 3.39351e15 0.258959
\(853\) −2.02766e16 −1.53736 −0.768681 0.639633i \(-0.779086\pi\)
−0.768681 + 0.639633i \(0.779086\pi\)
\(854\) 1.59495e15 0.120151
\(855\) −7.48851e15 −0.560508
\(856\) −1.22003e16 −0.907329
\(857\) −2.50853e16 −1.85364 −0.926818 0.375512i \(-0.877467\pi\)
−0.926818 + 0.375512i \(0.877467\pi\)
\(858\) 1.21857e16 0.894689
\(859\) 6.88156e15 0.502024 0.251012 0.967984i \(-0.419237\pi\)
0.251012 + 0.967984i \(0.419237\pi\)
\(860\) −3.67213e15 −0.266181
\(861\) 1.86485e15 0.134316
\(862\) −8.08130e15 −0.578351
\(863\) 5.69018e13 0.00404638 0.00202319 0.999998i \(-0.499356\pi\)
0.00202319 + 0.999998i \(0.499356\pi\)
\(864\) −5.56795e15 −0.393432
\(865\) −1.09476e16 −0.768650
\(866\) 3.66184e15 0.255476
\(867\) −1.44903e16 −1.00455
\(868\) 1.71758e14 0.0118320
\(869\) −9.16795e14 −0.0627572
\(870\) −2.12655e15 −0.144651
\(871\) −3.34779e16 −2.26286
\(872\) 1.78085e16 1.19615
\(873\) −5.59513e15 −0.373449
\(874\) −1.44545e15 −0.0958718
\(875\) 3.10831e15 0.204871
\(876\) 1.90388e16 1.24700
\(877\) 2.00469e15 0.130482 0.0652408 0.997870i \(-0.479218\pi\)
0.0652408 + 0.997870i \(0.479218\pi\)
\(878\) 8.44769e15 0.546410
\(879\) 1.22220e16 0.785603
\(880\) −2.15190e15 −0.137457
\(881\) −2.62684e16 −1.66750 −0.833751 0.552140i \(-0.813811\pi\)
−0.833751 + 0.552140i \(0.813811\pi\)
\(882\) −6.99470e15 −0.441257
\(883\) 1.53593e16 0.962916 0.481458 0.876469i \(-0.340107\pi\)
0.481458 + 0.876469i \(0.340107\pi\)
\(884\) −4.78651e15 −0.298216
\(885\) −3.28233e15 −0.203233
\(886\) −8.28897e14 −0.0510053
\(887\) 2.06637e15 0.126365 0.0631826 0.998002i \(-0.479875\pi\)
0.0631826 + 0.998002i \(0.479875\pi\)
\(888\) 1.84762e16 1.12290
\(889\) 1.92115e15 0.116038
\(890\) −5.08876e14 −0.0305469
\(891\) 1.75081e16 1.04451
\(892\) 1.13626e15 0.0673708
\(893\) 2.63098e15 0.155037
\(894\) −4.46058e15 −0.261237
\(895\) 9.14743e15 0.532442
\(896\) −1.20906e15 −0.0699443
\(897\) 3.94328e15 0.226725
\(898\) 1.54071e16 0.880445
\(899\) −3.81529e14 −0.0216695
\(900\) 1.40198e15 0.0791423
\(901\) −7.90510e15 −0.443528
\(902\) −5.72896e15 −0.319477
\(903\) −2.50671e15 −0.138938
\(904\) 2.13594e16 1.17669
\(905\) 2.96641e16 1.62429
\(906\) −8.21832e15 −0.447279
\(907\) 3.60909e16 1.95235 0.976175 0.216986i \(-0.0696227\pi\)
0.976175 + 0.216986i \(0.0696227\pi\)
\(908\) 1.50277e16 0.808016
\(909\) −1.36475e16 −0.729377
\(910\) 2.55539e15 0.135747
\(911\) −2.96381e16 −1.56495 −0.782473 0.622685i \(-0.786042\pi\)
−0.782473 + 0.622685i \(0.786042\pi\)
\(912\) −4.25015e15 −0.223066
\(913\) −7.98325e15 −0.416477
\(914\) 1.36189e15 0.0706215
\(915\) −2.04712e16 −1.05518
\(916\) 3.80209e15 0.194804
\(917\) −3.92905e15 −0.200104
\(918\) 2.71405e15 0.137399
\(919\) −9.30854e15 −0.468431 −0.234216 0.972185i \(-0.575252\pi\)
−0.234216 + 0.972185i \(0.575252\pi\)
\(920\) −2.73597e15 −0.136860
\(921\) −8.35311e15 −0.415356
\(922\) 1.29649e16 0.640840
\(923\) 9.05818e15 0.445073
\(924\) 2.29495e15 0.112093
\(925\) 3.78246e15 0.183652
\(926\) 2.40427e16 1.16044
\(927\) 2.62211e16 1.25809
\(928\) 3.59367e15 0.171405
\(929\) −1.29838e16 −0.615624 −0.307812 0.951447i \(-0.599597\pi\)
−0.307812 + 0.951447i \(0.599597\pi\)
\(930\) 1.92852e15 0.0909006
\(931\) −1.94968e16 −0.913567
\(932\) 2.34224e15 0.109105
\(933\) 2.10235e16 0.973544
\(934\) 6.85954e15 0.315782
\(935\) −7.78334e15 −0.356207
\(936\) 1.82799e16 0.831679
\(937\) −2.39113e16 −1.08152 −0.540761 0.841176i \(-0.681864\pi\)
−0.540761 + 0.841176i \(0.681864\pi\)
\(938\) 5.51556e15 0.248013
\(939\) −2.47024e16 −1.10428
\(940\) 1.73227e15 0.0769862
\(941\) 2.73040e15 0.120638 0.0603189 0.998179i \(-0.480788\pi\)
0.0603189 + 0.998179i \(0.480788\pi\)
\(942\) −2.35423e16 −1.03412
\(943\) −1.85388e15 −0.0809595
\(944\) −7.47522e14 −0.0324547
\(945\) 1.65632e15 0.0714941
\(946\) 7.70080e15 0.330472
\(947\) −2.61239e16 −1.11458 −0.557292 0.830317i \(-0.688159\pi\)
−0.557292 + 0.830317i \(0.688159\pi\)
\(948\) −1.19221e15 −0.0505716
\(949\) 5.08197e16 2.14323
\(950\) −3.41859e15 −0.143340
\(951\) −3.95756e15 −0.164981
\(952\) 2.26703e15 0.0939625
\(953\) 1.02664e16 0.423066 0.211533 0.977371i \(-0.432154\pi\)
0.211533 + 0.977371i \(0.432154\pi\)
\(954\) 1.05016e16 0.430266
\(955\) −1.32103e16 −0.538138
\(956\) −2.26614e16 −0.917842
\(957\) −5.09781e15 −0.205290
\(958\) −2.66874e15 −0.106855
\(959\) −7.36069e15 −0.293033
\(960\) −2.34113e16 −0.926690
\(961\) −2.50625e16 −0.986383
\(962\) 1.71552e16 0.671326
\(963\) 1.49203e16 0.580541
\(964\) −4.21535e15 −0.163084
\(965\) 1.89279e16 0.728120
\(966\) −6.49664e14 −0.0248493
\(967\) 3.75814e16 1.42931 0.714656 0.699476i \(-0.246583\pi\)
0.714656 + 0.699476i \(0.246583\pi\)
\(968\) 7.42968e15 0.280967
\(969\) −1.53726e16 −0.578052
\(970\) 8.98285e15 0.335869
\(971\) 2.34840e15 0.0873107 0.0436553 0.999047i \(-0.486100\pi\)
0.0436553 + 0.999047i \(0.486100\pi\)
\(972\) 1.66180e16 0.614349
\(973\) −4.09588e15 −0.150566
\(974\) 2.53779e16 0.927642
\(975\) 9.32614e15 0.338982
\(976\) −4.66213e15 −0.168504
\(977\) 6.37431e15 0.229094 0.114547 0.993418i \(-0.463458\pi\)
0.114547 + 0.993418i \(0.463458\pi\)
\(978\) −1.00391e16 −0.358781
\(979\) −1.21989e15 −0.0433526
\(980\) −1.28370e16 −0.453648
\(981\) −2.17788e16 −0.765342
\(982\) 4.44978e15 0.155498
\(983\) 3.13081e16 1.08796 0.543980 0.839098i \(-0.316917\pi\)
0.543980 + 0.839098i \(0.316917\pi\)
\(984\) −2.14173e16 −0.740102
\(985\) 4.24064e16 1.45724
\(986\) −1.75170e15 −0.0598601
\(987\) 1.18250e15 0.0401845
\(988\) 1.77239e16 0.598958
\(989\) 2.49197e15 0.0837457
\(990\) 1.03398e16 0.345556
\(991\) −1.05224e16 −0.349713 −0.174856 0.984594i \(-0.555946\pi\)
−0.174856 + 0.984594i \(0.555946\pi\)
\(992\) −3.25901e15 −0.107714
\(993\) −4.89963e16 −1.61043
\(994\) −1.49235e15 −0.0487806
\(995\) −1.72757e16 −0.561575
\(996\) −1.03815e16 −0.335609
\(997\) −3.58375e16 −1.15216 −0.576082 0.817392i \(-0.695419\pi\)
−0.576082 + 0.817392i \(0.695419\pi\)
\(998\) 1.36722e16 0.437140
\(999\) 1.11195e16 0.353570
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 29.12.a.a.1.8 11
3.2 odd 2 261.12.a.a.1.4 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.12.a.a.1.8 11 1.1 even 1 trivial
261.12.a.a.1.4 11 3.2 odd 2