Properties

Label 289.10.a.g.1.5
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $1$
Dimension $36$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(148.845356651\)
Analytic rank: \(1\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-35.4923 q^{2} +64.4314 q^{3} +747.701 q^{4} +1779.33 q^{5} -2286.82 q^{6} -1603.15 q^{7} -8365.56 q^{8} -15531.6 q^{9} +O(q^{10})\) \(q-35.4923 q^{2} +64.4314 q^{3} +747.701 q^{4} +1779.33 q^{5} -2286.82 q^{6} -1603.15 q^{7} -8365.56 q^{8} -15531.6 q^{9} -63152.6 q^{10} -38189.5 q^{11} +48175.4 q^{12} -116430. q^{13} +56899.3 q^{14} +114645. q^{15} -85910.2 q^{16} +551251. q^{18} +850642. q^{19} +1.33041e6 q^{20} -103293. q^{21} +1.35543e6 q^{22} +1.05393e6 q^{23} -539005. q^{24} +1.21290e6 q^{25} +4.13238e6 q^{26} -2.26893e6 q^{27} -1.19867e6 q^{28} -1.44727e6 q^{29} -4.06901e6 q^{30} +5.24487e6 q^{31} +7.33231e6 q^{32} -2.46061e6 q^{33} -2.85253e6 q^{35} -1.16130e7 q^{36} -5.51006e6 q^{37} -3.01912e7 q^{38} -7.50177e6 q^{39} -1.48851e7 q^{40} +2.30276e7 q^{41} +3.66611e6 q^{42} +1.73443e7 q^{43} -2.85543e7 q^{44} -2.76359e7 q^{45} -3.74062e7 q^{46} +5.62789e7 q^{47} -5.53532e6 q^{48} -3.77835e7 q^{49} -4.30487e7 q^{50} -8.70551e7 q^{52} -7.72272e7 q^{53} +8.05293e7 q^{54} -6.79519e7 q^{55} +1.34112e7 q^{56} +5.48081e7 q^{57} +5.13670e7 q^{58} +9.35882e7 q^{59} +8.57202e7 q^{60} -1.85319e8 q^{61} -1.86152e8 q^{62} +2.48994e7 q^{63} -2.16254e8 q^{64} -2.07168e8 q^{65} +8.73325e7 q^{66} -2.00683e8 q^{67} +6.79060e7 q^{69} +1.01243e8 q^{70} -7.05304e7 q^{71} +1.29930e8 q^{72} +2.21792e8 q^{73} +1.95564e8 q^{74} +7.81491e7 q^{75} +6.36026e8 q^{76} +6.12234e7 q^{77} +2.66255e8 q^{78} +6.34329e8 q^{79} -1.52863e8 q^{80} +1.59518e8 q^{81} -8.17300e8 q^{82} -5.88521e7 q^{83} -7.72323e7 q^{84} -6.15590e8 q^{86} -9.32498e7 q^{87} +3.19477e8 q^{88} -7.76608e8 q^{89} +9.80860e8 q^{90} +1.86655e8 q^{91} +7.88022e8 q^{92} +3.37935e8 q^{93} -1.99747e9 q^{94} +1.51358e9 q^{95} +4.72431e8 q^{96} +6.87791e8 q^{97} +1.34102e9 q^{98} +5.93144e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −35.4923 −1.56855 −0.784276 0.620413i \(-0.786965\pi\)
−0.784276 + 0.620413i \(0.786965\pi\)
\(3\) 64.4314 0.459253 0.229627 0.973279i \(-0.426250\pi\)
0.229627 + 0.973279i \(0.426250\pi\)
\(4\) 747.701 1.46035
\(5\) 1779.33 1.27319 0.636594 0.771199i \(-0.280343\pi\)
0.636594 + 0.771199i \(0.280343\pi\)
\(6\) −2286.82 −0.720362
\(7\) −1603.15 −0.252367 −0.126183 0.992007i \(-0.540273\pi\)
−0.126183 + 0.992007i \(0.540273\pi\)
\(8\) −8365.56 −0.722088
\(9\) −15531.6 −0.789087
\(10\) −63152.6 −1.99706
\(11\) −38189.5 −0.786461 −0.393230 0.919440i \(-0.628643\pi\)
−0.393230 + 0.919440i \(0.628643\pi\)
\(12\) 48175.4 0.670672
\(13\) −116430. −1.13063 −0.565316 0.824875i \(-0.691246\pi\)
−0.565316 + 0.824875i \(0.691246\pi\)
\(14\) 56899.3 0.395850
\(15\) 114645. 0.584715
\(16\) −85910.2 −0.327722
\(17\) 0 0
\(18\) 551251. 1.23772
\(19\) 850642. 1.49746 0.748731 0.662874i \(-0.230664\pi\)
0.748731 + 0.662874i \(0.230664\pi\)
\(20\) 1.33041e6 1.85930
\(21\) −103293. −0.115900
\(22\) 1.35543e6 1.23360
\(23\) 1.05393e6 0.785299 0.392649 0.919688i \(-0.371559\pi\)
0.392649 + 0.919688i \(0.371559\pi\)
\(24\) −539005. −0.331621
\(25\) 1.21290e6 0.621006
\(26\) 4.13238e6 1.77345
\(27\) −2.26893e6 −0.821644
\(28\) −1.19867e6 −0.368545
\(29\) −1.44727e6 −0.379979 −0.189989 0.981786i \(-0.560845\pi\)
−0.189989 + 0.981786i \(0.560845\pi\)
\(30\) −4.06901e6 −0.917156
\(31\) 5.24487e6 1.02002 0.510008 0.860170i \(-0.329642\pi\)
0.510008 + 0.860170i \(0.329642\pi\)
\(32\) 7.33231e6 1.23614
\(33\) −2.46061e6 −0.361185
\(34\) 0 0
\(35\) −2.85253e6 −0.321310
\(36\) −1.16130e7 −1.15235
\(37\) −5.51006e6 −0.483335 −0.241667 0.970359i \(-0.577694\pi\)
−0.241667 + 0.970359i \(0.577694\pi\)
\(38\) −3.01912e7 −2.34885
\(39\) −7.50177e6 −0.519246
\(40\) −1.48851e7 −0.919353
\(41\) 2.30276e7 1.27268 0.636342 0.771407i \(-0.280447\pi\)
0.636342 + 0.771407i \(0.280447\pi\)
\(42\) 3.66611e6 0.181796
\(43\) 1.73443e7 0.773659 0.386830 0.922151i \(-0.373570\pi\)
0.386830 + 0.922151i \(0.373570\pi\)
\(44\) −2.85543e7 −1.14851
\(45\) −2.76359e7 −1.00466
\(46\) −3.74062e7 −1.23178
\(47\) 5.62789e7 1.68231 0.841154 0.540796i \(-0.181877\pi\)
0.841154 + 0.540796i \(0.181877\pi\)
\(48\) −5.53532e6 −0.150507
\(49\) −3.77835e7 −0.936311
\(50\) −4.30487e7 −0.974080
\(51\) 0 0
\(52\) −8.70551e7 −1.65112
\(53\) −7.72272e7 −1.34440 −0.672201 0.740369i \(-0.734651\pi\)
−0.672201 + 0.740369i \(0.734651\pi\)
\(54\) 8.05293e7 1.28879
\(55\) −6.79519e7 −1.00131
\(56\) 1.34112e7 0.182231
\(57\) 5.48081e7 0.687714
\(58\) 5.13670e7 0.596016
\(59\) 9.35882e7 1.00551 0.502756 0.864428i \(-0.332319\pi\)
0.502756 + 0.864428i \(0.332319\pi\)
\(60\) 8.57202e7 0.853891
\(61\) −1.85319e8 −1.71371 −0.856853 0.515560i \(-0.827584\pi\)
−0.856853 + 0.515560i \(0.827584\pi\)
\(62\) −1.86152e8 −1.59995
\(63\) 2.48994e7 0.199139
\(64\) −2.16254e8 −1.61122
\(65\) −2.07168e8 −1.43951
\(66\) 8.73325e7 0.566537
\(67\) −2.00683e8 −1.21667 −0.608337 0.793679i \(-0.708163\pi\)
−0.608337 + 0.793679i \(0.708163\pi\)
\(68\) 0 0
\(69\) 6.79060e7 0.360651
\(70\) 1.01243e8 0.503992
\(71\) −7.05304e7 −0.329392 −0.164696 0.986344i \(-0.552664\pi\)
−0.164696 + 0.986344i \(0.552664\pi\)
\(72\) 1.29930e8 0.569790
\(73\) 2.21792e8 0.914099 0.457049 0.889441i \(-0.348906\pi\)
0.457049 + 0.889441i \(0.348906\pi\)
\(74\) 1.95564e8 0.758136
\(75\) 7.81491e7 0.285199
\(76\) 6.36026e8 2.18682
\(77\) 6.12234e7 0.198477
\(78\) 2.66255e8 0.814464
\(79\) 6.34329e8 1.83228 0.916141 0.400856i \(-0.131287\pi\)
0.916141 + 0.400856i \(0.131287\pi\)
\(80\) −1.52863e8 −0.417251
\(81\) 1.59518e8 0.411744
\(82\) −8.17300e8 −1.99627
\(83\) −5.88521e7 −0.136116 −0.0680582 0.997681i \(-0.521680\pi\)
−0.0680582 + 0.997681i \(0.521680\pi\)
\(84\) −7.72323e7 −0.169255
\(85\) 0 0
\(86\) −6.15590e8 −1.21352
\(87\) −9.32498e7 −0.174506
\(88\) 3.19477e8 0.567894
\(89\) −7.76608e8 −1.31204 −0.656020 0.754743i \(-0.727761\pi\)
−0.656020 + 0.754743i \(0.727761\pi\)
\(90\) 9.80860e8 1.57585
\(91\) 1.86655e8 0.285334
\(92\) 7.88022e8 1.14681
\(93\) 3.37935e8 0.468446
\(94\) −1.99747e9 −2.63879
\(95\) 1.51358e9 1.90655
\(96\) 4.72431e8 0.567699
\(97\) 6.87791e8 0.788831 0.394415 0.918932i \(-0.370947\pi\)
0.394415 + 0.918932i \(0.370947\pi\)
\(98\) 1.34102e9 1.46865
\(99\) 5.93144e8 0.620586
\(100\) 9.06889e8 0.906889
\(101\) −1.32312e9 −1.26518 −0.632590 0.774487i \(-0.718008\pi\)
−0.632590 + 0.774487i \(0.718008\pi\)
\(102\) 0 0
\(103\) −1.63204e9 −1.42877 −0.714387 0.699751i \(-0.753294\pi\)
−0.714387 + 0.699751i \(0.753294\pi\)
\(104\) 9.74005e8 0.816415
\(105\) −1.83793e8 −0.147563
\(106\) 2.74097e9 2.10876
\(107\) 9.81220e8 0.723668 0.361834 0.932243i \(-0.382151\pi\)
0.361834 + 0.932243i \(0.382151\pi\)
\(108\) −1.69648e9 −1.19989
\(109\) −9.30599e8 −0.631456 −0.315728 0.948850i \(-0.602249\pi\)
−0.315728 + 0.948850i \(0.602249\pi\)
\(110\) 2.41177e9 1.57061
\(111\) −3.55021e8 −0.221973
\(112\) 1.37727e8 0.0827061
\(113\) 2.85541e9 1.64746 0.823732 0.566979i \(-0.191888\pi\)
0.823732 + 0.566979i \(0.191888\pi\)
\(114\) −1.94526e9 −1.07871
\(115\) 1.87529e9 0.999833
\(116\) −1.08213e9 −0.554903
\(117\) 1.80835e9 0.892166
\(118\) −3.32166e9 −1.57720
\(119\) 0 0
\(120\) −9.59069e8 −0.422216
\(121\) −8.99508e8 −0.381479
\(122\) 6.57740e9 2.68804
\(123\) 1.48370e9 0.584484
\(124\) 3.92159e9 1.48958
\(125\) −1.31710e9 −0.482530
\(126\) −8.83737e8 −0.312360
\(127\) −6.04257e8 −0.206113 −0.103056 0.994676i \(-0.532862\pi\)
−0.103056 + 0.994676i \(0.532862\pi\)
\(128\) 3.92121e9 1.29115
\(129\) 1.11752e9 0.355305
\(130\) 7.35288e9 2.25794
\(131\) −2.35573e9 −0.698885 −0.349442 0.936958i \(-0.613629\pi\)
−0.349442 + 0.936958i \(0.613629\pi\)
\(132\) −1.83980e9 −0.527457
\(133\) −1.36371e9 −0.377910
\(134\) 7.12270e9 1.90841
\(135\) −4.03718e9 −1.04611
\(136\) 0 0
\(137\) −3.70241e9 −0.897928 −0.448964 0.893550i \(-0.648207\pi\)
−0.448964 + 0.893550i \(0.648207\pi\)
\(138\) −2.41014e9 −0.565699
\(139\) 2.24358e9 0.509772 0.254886 0.966971i \(-0.417962\pi\)
0.254886 + 0.966971i \(0.417962\pi\)
\(140\) −2.13284e9 −0.469227
\(141\) 3.62613e9 0.772605
\(142\) 2.50328e9 0.516669
\(143\) 4.44642e9 0.889197
\(144\) 1.33432e9 0.258601
\(145\) −2.57518e9 −0.483784
\(146\) −7.87190e9 −1.43381
\(147\) −2.43445e9 −0.430004
\(148\) −4.11987e9 −0.705840
\(149\) 2.50473e9 0.416316 0.208158 0.978095i \(-0.433253\pi\)
0.208158 + 0.978095i \(0.433253\pi\)
\(150\) −2.77369e9 −0.447349
\(151\) −6.86721e9 −1.07494 −0.537470 0.843283i \(-0.680620\pi\)
−0.537470 + 0.843283i \(0.680620\pi\)
\(152\) −7.11610e9 −1.08130
\(153\) 0 0
\(154\) −2.17296e9 −0.311321
\(155\) 9.33237e9 1.29867
\(156\) −5.60908e9 −0.758283
\(157\) −1.19135e10 −1.56492 −0.782461 0.622700i \(-0.786036\pi\)
−0.782461 + 0.622700i \(0.786036\pi\)
\(158\) −2.25138e10 −2.87403
\(159\) −4.97586e9 −0.617420
\(160\) 1.30466e10 1.57383
\(161\) −1.68960e9 −0.198183
\(162\) −5.66166e9 −0.645842
\(163\) −3.24459e9 −0.360011 −0.180005 0.983666i \(-0.557612\pi\)
−0.180005 + 0.983666i \(0.557612\pi\)
\(164\) 1.72177e10 1.85857
\(165\) −4.37824e9 −0.459856
\(166\) 2.08879e9 0.213506
\(167\) −8.72685e9 −0.868227 −0.434114 0.900858i \(-0.642938\pi\)
−0.434114 + 0.900858i \(0.642938\pi\)
\(168\) 8.64104e8 0.0836902
\(169\) 2.95152e9 0.278327
\(170\) 0 0
\(171\) −1.32118e10 −1.18163
\(172\) 1.29684e10 1.12982
\(173\) 5.55058e9 0.471119 0.235559 0.971860i \(-0.424308\pi\)
0.235559 + 0.971860i \(0.424308\pi\)
\(174\) 3.30965e9 0.273722
\(175\) −1.94446e9 −0.156721
\(176\) 3.28087e9 0.257740
\(177\) 6.03002e9 0.461784
\(178\) 2.75636e10 2.05800
\(179\) 1.54065e10 1.12167 0.560834 0.827928i \(-0.310480\pi\)
0.560834 + 0.827928i \(0.310480\pi\)
\(180\) −2.06634e10 −1.46715
\(181\) −2.46062e10 −1.70409 −0.852043 0.523472i \(-0.824637\pi\)
−0.852043 + 0.523472i \(0.824637\pi\)
\(182\) −6.62481e9 −0.447561
\(183\) −1.19404e10 −0.787025
\(184\) −8.81668e9 −0.567055
\(185\) −9.80423e9 −0.615376
\(186\) −1.19941e10 −0.734781
\(187\) 0 0
\(188\) 4.20798e10 2.45676
\(189\) 3.63742e9 0.207356
\(190\) −5.37202e10 −2.99052
\(191\) 1.53953e10 0.837025 0.418513 0.908211i \(-0.362552\pi\)
0.418513 + 0.908211i \(0.362552\pi\)
\(192\) −1.39336e10 −0.739958
\(193\) −3.75476e10 −1.94793 −0.973967 0.226689i \(-0.927210\pi\)
−0.973967 + 0.226689i \(0.927210\pi\)
\(194\) −2.44113e10 −1.23732
\(195\) −1.33482e10 −0.661097
\(196\) −2.82508e10 −1.36734
\(197\) −1.69699e10 −0.802752 −0.401376 0.915913i \(-0.631468\pi\)
−0.401376 + 0.915913i \(0.631468\pi\)
\(198\) −2.10520e10 −0.973421
\(199\) 3.68433e10 1.66541 0.832703 0.553720i \(-0.186792\pi\)
0.832703 + 0.553720i \(0.186792\pi\)
\(200\) −1.01466e10 −0.448421
\(201\) −1.29303e10 −0.558761
\(202\) 4.69605e10 1.98450
\(203\) 2.32019e9 0.0958941
\(204\) 0 0
\(205\) 4.09737e10 1.62037
\(206\) 5.79248e10 2.24111
\(207\) −1.63692e10 −0.619669
\(208\) 1.00026e10 0.370532
\(209\) −3.24856e10 −1.17770
\(210\) 6.52322e9 0.231460
\(211\) 2.86188e9 0.0993988 0.0496994 0.998764i \(-0.484174\pi\)
0.0496994 + 0.998764i \(0.484174\pi\)
\(212\) −5.77428e10 −1.96330
\(213\) −4.54437e9 −0.151274
\(214\) −3.48257e10 −1.13511
\(215\) 3.08614e10 0.985013
\(216\) 1.89808e10 0.593299
\(217\) −8.40830e9 −0.257418
\(218\) 3.30290e10 0.990471
\(219\) 1.42904e10 0.419803
\(220\) −5.08077e10 −1.46227
\(221\) 0 0
\(222\) 1.26005e10 0.348176
\(223\) −8.66212e9 −0.234559 −0.117279 0.993099i \(-0.537417\pi\)
−0.117279 + 0.993099i \(0.537417\pi\)
\(224\) −1.17548e10 −0.311960
\(225\) −1.88383e10 −0.490028
\(226\) −1.01345e11 −2.58413
\(227\) −3.39293e10 −0.848122 −0.424061 0.905634i \(-0.639396\pi\)
−0.424061 + 0.905634i \(0.639396\pi\)
\(228\) 4.09801e10 1.00431
\(229\) −4.32441e10 −1.03912 −0.519561 0.854433i \(-0.673905\pi\)
−0.519561 + 0.854433i \(0.673905\pi\)
\(230\) −6.65582e10 −1.56829
\(231\) 3.94471e9 0.0911510
\(232\) 1.21072e10 0.274378
\(233\) −2.83037e10 −0.629131 −0.314566 0.949236i \(-0.601859\pi\)
−0.314566 + 0.949236i \(0.601859\pi\)
\(234\) −6.41824e10 −1.39941
\(235\) 1.00139e11 2.14189
\(236\) 6.99760e10 1.46840
\(237\) 4.08707e10 0.841481
\(238\) 0 0
\(239\) −4.13610e10 −0.819976 −0.409988 0.912091i \(-0.634467\pi\)
−0.409988 + 0.912091i \(0.634467\pi\)
\(240\) −9.84918e9 −0.191624
\(241\) −4.75351e10 −0.907691 −0.453846 0.891080i \(-0.649948\pi\)
−0.453846 + 0.891080i \(0.649948\pi\)
\(242\) 3.19256e10 0.598370
\(243\) 5.49373e10 1.01074
\(244\) −1.38563e11 −2.50262
\(245\) −6.72295e10 −1.19210
\(246\) −5.26598e10 −0.916793
\(247\) −9.90406e10 −1.69308
\(248\) −4.38763e10 −0.736541
\(249\) −3.79192e9 −0.0625119
\(250\) 4.67469e10 0.756873
\(251\) −1.97131e10 −0.313490 −0.156745 0.987639i \(-0.550100\pi\)
−0.156745 + 0.987639i \(0.550100\pi\)
\(252\) 1.86173e10 0.290814
\(253\) −4.02489e10 −0.617607
\(254\) 2.14465e10 0.323299
\(255\) 0 0
\(256\) −2.84505e10 −0.414009
\(257\) 1.37584e9 0.0196729 0.00983643 0.999952i \(-0.496869\pi\)
0.00983643 + 0.999952i \(0.496869\pi\)
\(258\) −3.96633e10 −0.557315
\(259\) 8.83343e9 0.121978
\(260\) −1.54900e11 −2.10219
\(261\) 2.24784e10 0.299836
\(262\) 8.36104e10 1.09624
\(263\) −6.61395e10 −0.852432 −0.426216 0.904621i \(-0.640154\pi\)
−0.426216 + 0.904621i \(0.640154\pi\)
\(264\) 2.05843e10 0.260807
\(265\) −1.37413e11 −1.71167
\(266\) 4.84010e10 0.592771
\(267\) −5.00380e10 −0.602558
\(268\) −1.50051e11 −1.77677
\(269\) −1.71759e10 −0.200002 −0.100001 0.994987i \(-0.531885\pi\)
−0.100001 + 0.994987i \(0.531885\pi\)
\(270\) 1.43289e11 1.64087
\(271\) −3.72624e10 −0.419671 −0.209835 0.977737i \(-0.567293\pi\)
−0.209835 + 0.977737i \(0.567293\pi\)
\(272\) 0 0
\(273\) 1.20264e10 0.131040
\(274\) 1.31407e11 1.40845
\(275\) −4.63202e10 −0.488397
\(276\) 5.07734e10 0.526678
\(277\) 3.67272e10 0.374825 0.187413 0.982281i \(-0.439990\pi\)
0.187413 + 0.982281i \(0.439990\pi\)
\(278\) −7.96299e10 −0.799603
\(279\) −8.14612e10 −0.804881
\(280\) 2.38630e10 0.232014
\(281\) 1.47776e11 1.41392 0.706962 0.707252i \(-0.250065\pi\)
0.706962 + 0.707252i \(0.250065\pi\)
\(282\) −1.28700e11 −1.21187
\(283\) 1.11330e11 1.03175 0.515873 0.856665i \(-0.327468\pi\)
0.515873 + 0.856665i \(0.327468\pi\)
\(284\) −5.27356e10 −0.481029
\(285\) 9.75219e10 0.875589
\(286\) −1.57813e11 −1.39475
\(287\) −3.69166e10 −0.321183
\(288\) −1.13883e11 −0.975418
\(289\) 0 0
\(290\) 9.13990e10 0.758840
\(291\) 4.43154e10 0.362273
\(292\) 1.65834e11 1.33491
\(293\) 1.00582e11 0.797290 0.398645 0.917105i \(-0.369480\pi\)
0.398645 + 0.917105i \(0.369480\pi\)
\(294\) 8.64040e10 0.674483
\(295\) 1.66525e11 1.28021
\(296\) 4.60947e10 0.349010
\(297\) 8.66492e10 0.646191
\(298\) −8.88987e10 −0.653013
\(299\) −1.22709e11 −0.887884
\(300\) 5.84321e10 0.416491
\(301\) −2.78055e10 −0.195246
\(302\) 2.43733e11 1.68610
\(303\) −8.52504e10 −0.581038
\(304\) −7.30789e10 −0.490751
\(305\) −3.29745e11 −2.18187
\(306\) 0 0
\(307\) −1.00813e11 −0.647733 −0.323866 0.946103i \(-0.604983\pi\)
−0.323866 + 0.946103i \(0.604983\pi\)
\(308\) 4.57768e10 0.289846
\(309\) −1.05155e11 −0.656169
\(310\) −3.31227e11 −2.03703
\(311\) −6.42046e10 −0.389175 −0.194587 0.980885i \(-0.562337\pi\)
−0.194587 + 0.980885i \(0.562337\pi\)
\(312\) 6.27565e10 0.374941
\(313\) 1.95618e11 1.15202 0.576008 0.817444i \(-0.304610\pi\)
0.576008 + 0.817444i \(0.304610\pi\)
\(314\) 4.22839e11 2.45466
\(315\) 4.43044e10 0.253542
\(316\) 4.74288e11 2.67578
\(317\) −2.98622e11 −1.66095 −0.830473 0.557059i \(-0.811930\pi\)
−0.830473 + 0.557059i \(0.811930\pi\)
\(318\) 1.76605e11 0.968456
\(319\) 5.52707e10 0.298838
\(320\) −3.84789e11 −2.05139
\(321\) 6.32214e10 0.332347
\(322\) 5.99677e10 0.310861
\(323\) 0 0
\(324\) 1.19272e11 0.601292
\(325\) −1.41219e11 −0.702129
\(326\) 1.15158e11 0.564695
\(327\) −5.99598e10 −0.289998
\(328\) −1.92638e11 −0.918990
\(329\) −9.02234e10 −0.424559
\(330\) 1.55394e11 0.721307
\(331\) 2.80470e11 1.28428 0.642140 0.766587i \(-0.278047\pi\)
0.642140 + 0.766587i \(0.278047\pi\)
\(332\) −4.40037e10 −0.198778
\(333\) 8.55799e10 0.381393
\(334\) 3.09736e11 1.36186
\(335\) −3.57082e11 −1.54905
\(336\) 8.87393e9 0.0379830
\(337\) 1.33080e11 0.562053 0.281027 0.959700i \(-0.409325\pi\)
0.281027 + 0.959700i \(0.409325\pi\)
\(338\) −1.04756e11 −0.436571
\(339\) 1.83978e11 0.756603
\(340\) 0 0
\(341\) −2.00299e11 −0.802203
\(342\) 4.68918e11 1.85344
\(343\) 1.25265e11 0.488661
\(344\) −1.45095e11 −0.558650
\(345\) 1.20827e11 0.459176
\(346\) −1.97002e11 −0.738974
\(347\) 1.27576e10 0.0472373 0.0236187 0.999721i \(-0.492481\pi\)
0.0236187 + 0.999721i \(0.492481\pi\)
\(348\) −6.97230e10 −0.254841
\(349\) 9.97908e10 0.360061 0.180030 0.983661i \(-0.442380\pi\)
0.180030 + 0.983661i \(0.442380\pi\)
\(350\) 6.90134e10 0.245826
\(351\) 2.64172e11 0.928976
\(352\) −2.80018e11 −0.972173
\(353\) 2.18588e11 0.749272 0.374636 0.927172i \(-0.377768\pi\)
0.374636 + 0.927172i \(0.377768\pi\)
\(354\) −2.14019e11 −0.724333
\(355\) −1.25497e11 −0.419378
\(356\) −5.80671e11 −1.91604
\(357\) 0 0
\(358\) −5.46811e11 −1.75940
\(359\) −2.37311e11 −0.754038 −0.377019 0.926205i \(-0.623051\pi\)
−0.377019 + 0.926205i \(0.623051\pi\)
\(360\) 2.31190e11 0.725449
\(361\) 4.00904e11 1.24239
\(362\) 8.73331e11 2.67295
\(363\) −5.79566e10 −0.175196
\(364\) 1.39562e11 0.416688
\(365\) 3.94642e11 1.16382
\(366\) 4.23792e11 1.23449
\(367\) 7.38520e10 0.212503 0.106251 0.994339i \(-0.466115\pi\)
0.106251 + 0.994339i \(0.466115\pi\)
\(368\) −9.05431e10 −0.257359
\(369\) −3.57655e11 −1.00426
\(370\) 3.47974e11 0.965249
\(371\) 1.23807e11 0.339282
\(372\) 2.52674e11 0.684096
\(373\) 1.63830e11 0.438232 0.219116 0.975699i \(-0.429683\pi\)
0.219116 + 0.975699i \(0.429683\pi\)
\(374\) 0 0
\(375\) −8.48628e10 −0.221603
\(376\) −4.70805e11 −1.21477
\(377\) 1.68506e11 0.429616
\(378\) −1.29100e11 −0.325248
\(379\) 5.52844e11 1.37634 0.688171 0.725548i \(-0.258414\pi\)
0.688171 + 0.725548i \(0.258414\pi\)
\(380\) 1.13170e12 2.78424
\(381\) −3.89332e10 −0.0946580
\(382\) −5.46415e11 −1.31292
\(383\) −4.45678e11 −1.05834 −0.529172 0.848515i \(-0.677497\pi\)
−0.529172 + 0.848515i \(0.677497\pi\)
\(384\) 2.52649e11 0.592963
\(385\) 1.08937e11 0.252698
\(386\) 1.33265e12 3.05543
\(387\) −2.69385e11 −0.610484
\(388\) 5.14262e11 1.15197
\(389\) 1.27952e11 0.283317 0.141659 0.989916i \(-0.454756\pi\)
0.141659 + 0.989916i \(0.454756\pi\)
\(390\) 4.73756e11 1.03697
\(391\) 0 0
\(392\) 3.16080e11 0.676099
\(393\) −1.51783e11 −0.320965
\(394\) 6.02300e11 1.25916
\(395\) 1.12868e12 2.33284
\(396\) 4.43494e11 0.906274
\(397\) −3.31658e11 −0.670091 −0.335045 0.942202i \(-0.608752\pi\)
−0.335045 + 0.942202i \(0.608752\pi\)
\(398\) −1.30765e12 −2.61227
\(399\) −8.78655e10 −0.173556
\(400\) −1.04201e11 −0.203517
\(401\) −6.03112e11 −1.16479 −0.582396 0.812905i \(-0.697885\pi\)
−0.582396 + 0.812905i \(0.697885\pi\)
\(402\) 4.58925e11 0.876445
\(403\) −6.10662e11 −1.15326
\(404\) −9.89297e11 −1.84761
\(405\) 2.83836e11 0.524228
\(406\) −8.23489e10 −0.150415
\(407\) 2.10426e11 0.380124
\(408\) 0 0
\(409\) −4.86595e11 −0.859830 −0.429915 0.902869i \(-0.641456\pi\)
−0.429915 + 0.902869i \(0.641456\pi\)
\(410\) −1.45425e12 −2.54163
\(411\) −2.38551e11 −0.412376
\(412\) −1.22028e12 −2.08651
\(413\) −1.50036e11 −0.253758
\(414\) 5.80978e11 0.971982
\(415\) −1.04717e11 −0.173302
\(416\) −8.53704e11 −1.39761
\(417\) 1.44557e11 0.234114
\(418\) 1.15299e12 1.84728
\(419\) −5.39425e11 −0.855003 −0.427502 0.904015i \(-0.640606\pi\)
−0.427502 + 0.904015i \(0.640606\pi\)
\(420\) −1.37422e11 −0.215494
\(421\) 9.96515e11 1.54602 0.773008 0.634396i \(-0.218751\pi\)
0.773008 + 0.634396i \(0.218751\pi\)
\(422\) −1.01575e11 −0.155912
\(423\) −8.74101e11 −1.32749
\(424\) 6.46049e11 0.970776
\(425\) 0 0
\(426\) 1.61290e11 0.237282
\(427\) 2.97094e11 0.432483
\(428\) 7.33659e11 1.05681
\(429\) 2.86489e11 0.408367
\(430\) −1.09534e12 −1.54504
\(431\) −1.04616e12 −1.46033 −0.730167 0.683268i \(-0.760558\pi\)
−0.730167 + 0.683268i \(0.760558\pi\)
\(432\) 1.94924e11 0.269270
\(433\) −4.38391e11 −0.599330 −0.299665 0.954044i \(-0.596875\pi\)
−0.299665 + 0.954044i \(0.596875\pi\)
\(434\) 2.98430e11 0.403774
\(435\) −1.65923e11 −0.222179
\(436\) −6.95809e11 −0.922149
\(437\) 8.96514e11 1.17595
\(438\) −5.07198e11 −0.658482
\(439\) 1.24765e12 1.60325 0.801626 0.597825i \(-0.203968\pi\)
0.801626 + 0.597825i \(0.203968\pi\)
\(440\) 5.68456e11 0.723035
\(441\) 5.86838e11 0.738830
\(442\) 0 0
\(443\) −4.55140e11 −0.561472 −0.280736 0.959785i \(-0.590578\pi\)
−0.280736 + 0.959785i \(0.590578\pi\)
\(444\) −2.65449e11 −0.324159
\(445\) −1.38185e12 −1.67047
\(446\) 3.07438e11 0.367918
\(447\) 1.61384e11 0.191195
\(448\) 3.46688e11 0.406619
\(449\) −4.52274e11 −0.525161 −0.262581 0.964910i \(-0.584574\pi\)
−0.262581 + 0.964910i \(0.584574\pi\)
\(450\) 6.68614e11 0.768634
\(451\) −8.79412e11 −1.00092
\(452\) 2.13500e12 2.40588
\(453\) −4.42464e11 −0.493669
\(454\) 1.20423e12 1.33032
\(455\) 3.32122e11 0.363284
\(456\) −4.58500e11 −0.496590
\(457\) −7.54079e11 −0.808712 −0.404356 0.914602i \(-0.632504\pi\)
−0.404356 + 0.914602i \(0.632504\pi\)
\(458\) 1.53483e12 1.62992
\(459\) 0 0
\(460\) 1.40215e12 1.46011
\(461\) −8.30299e11 −0.856210 −0.428105 0.903729i \(-0.640819\pi\)
−0.428105 + 0.903729i \(0.640819\pi\)
\(462\) −1.40007e11 −0.142975
\(463\) −1.63965e12 −1.65820 −0.829098 0.559104i \(-0.811145\pi\)
−0.829098 + 0.559104i \(0.811145\pi\)
\(464\) 1.24336e11 0.124527
\(465\) 6.01298e11 0.596419
\(466\) 1.00456e12 0.986824
\(467\) 5.39940e10 0.0525314 0.0262657 0.999655i \(-0.491638\pi\)
0.0262657 + 0.999655i \(0.491638\pi\)
\(468\) 1.35210e12 1.30288
\(469\) 3.21725e11 0.307048
\(470\) −3.55416e12 −3.35967
\(471\) −7.67607e11 −0.718695
\(472\) −7.82918e11 −0.726068
\(473\) −6.62372e11 −0.608453
\(474\) −1.45059e12 −1.31991
\(475\) 1.03175e12 0.929933
\(476\) 0 0
\(477\) 1.19946e12 1.06085
\(478\) 1.46800e12 1.28617
\(479\) −1.51563e12 −1.31548 −0.657740 0.753245i \(-0.728487\pi\)
−0.657740 + 0.753245i \(0.728487\pi\)
\(480\) 8.40613e11 0.722788
\(481\) 6.41538e11 0.546474
\(482\) 1.68713e12 1.42376
\(483\) −1.08863e11 −0.0910163
\(484\) −6.72563e11 −0.557094
\(485\) 1.22381e12 1.00433
\(486\) −1.94985e12 −1.58540
\(487\) −1.37608e12 −1.10857 −0.554287 0.832326i \(-0.687009\pi\)
−0.554287 + 0.832326i \(0.687009\pi\)
\(488\) 1.55030e12 1.23745
\(489\) −2.09053e11 −0.165336
\(490\) 2.38613e12 1.86987
\(491\) −1.98919e12 −1.54457 −0.772287 0.635273i \(-0.780887\pi\)
−0.772287 + 0.635273i \(0.780887\pi\)
\(492\) 1.10936e12 0.853553
\(493\) 0 0
\(494\) 3.51517e12 2.65568
\(495\) 1.05540e12 0.790122
\(496\) −4.50588e11 −0.334281
\(497\) 1.13071e11 0.0831277
\(498\) 1.34584e11 0.0980531
\(499\) 6.52474e11 0.471098 0.235549 0.971863i \(-0.424311\pi\)
0.235549 + 0.971863i \(0.424311\pi\)
\(500\) −9.84798e11 −0.704664
\(501\) −5.62283e11 −0.398736
\(502\) 6.99663e11 0.491725
\(503\) −1.99625e12 −1.39046 −0.695229 0.718788i \(-0.744697\pi\)
−0.695229 + 0.718788i \(0.744697\pi\)
\(504\) −2.08298e11 −0.143796
\(505\) −2.35427e12 −1.61081
\(506\) 1.42853e12 0.968748
\(507\) 1.90171e11 0.127823
\(508\) −4.51804e11 −0.300998
\(509\) −1.28730e12 −0.850063 −0.425032 0.905179i \(-0.639737\pi\)
−0.425032 + 0.905179i \(0.639737\pi\)
\(510\) 0 0
\(511\) −3.55565e11 −0.230688
\(512\) −9.97889e11 −0.641752
\(513\) −1.93004e12 −1.23038
\(514\) −4.88315e10 −0.0308579
\(515\) −2.90395e12 −1.81910
\(516\) 8.35571e11 0.518871
\(517\) −2.14927e12 −1.32307
\(518\) −3.13519e11 −0.191328
\(519\) 3.57631e11 0.216363
\(520\) 1.73308e12 1.03945
\(521\) 8.54672e11 0.508194 0.254097 0.967179i \(-0.418222\pi\)
0.254097 + 0.967179i \(0.418222\pi\)
\(522\) −7.97811e11 −0.470308
\(523\) −4.36274e11 −0.254978 −0.127489 0.991840i \(-0.540692\pi\)
−0.127489 + 0.991840i \(0.540692\pi\)
\(524\) −1.76138e12 −1.02062
\(525\) −1.25284e11 −0.0719748
\(526\) 2.34744e12 1.33708
\(527\) 0 0
\(528\) 2.11391e11 0.118368
\(529\) −6.90392e11 −0.383306
\(530\) 4.87710e12 2.68485
\(531\) −1.45357e12 −0.793436
\(532\) −1.01964e12 −0.551882
\(533\) −2.68111e12 −1.43894
\(534\) 1.77596e12 0.945144
\(535\) 1.74592e12 0.921365
\(536\) 1.67883e12 0.878545
\(537\) 9.92661e11 0.515130
\(538\) 6.09612e11 0.313714
\(539\) 1.44293e12 0.736372
\(540\) −3.01860e12 −1.52768
\(541\) −2.18108e12 −1.09467 −0.547337 0.836913i \(-0.684358\pi\)
−0.547337 + 0.836913i \(0.684358\pi\)
\(542\) 1.32253e12 0.658275
\(543\) −1.58541e12 −0.782607
\(544\) 0 0
\(545\) −1.65585e12 −0.803962
\(546\) −4.26846e11 −0.205544
\(547\) −2.19466e12 −1.04815 −0.524077 0.851671i \(-0.675589\pi\)
−0.524077 + 0.851671i \(0.675589\pi\)
\(548\) −2.76829e12 −1.31129
\(549\) 2.87830e12 1.35226
\(550\) 1.64401e12 0.766076
\(551\) −1.23111e12 −0.569004
\(552\) −5.68071e11 −0.260422
\(553\) −1.01692e12 −0.462407
\(554\) −1.30353e12 −0.587932
\(555\) −6.31700e11 −0.282613
\(556\) 1.67753e12 0.744447
\(557\) 2.19414e12 0.965864 0.482932 0.875658i \(-0.339572\pi\)
0.482932 + 0.875658i \(0.339572\pi\)
\(558\) 2.89124e12 1.26250
\(559\) −2.01941e12 −0.874723
\(560\) 2.45062e11 0.105300
\(561\) 0 0
\(562\) −5.24491e12 −2.21781
\(563\) −2.03940e12 −0.855489 −0.427745 0.903900i \(-0.640692\pi\)
−0.427745 + 0.903900i \(0.640692\pi\)
\(564\) 2.71126e12 1.12828
\(565\) 5.08073e12 2.09753
\(566\) −3.95135e12 −1.61835
\(567\) −2.55731e11 −0.103911
\(568\) 5.90026e11 0.237850
\(569\) −3.56626e12 −1.42629 −0.713144 0.701017i \(-0.752730\pi\)
−0.713144 + 0.701017i \(0.752730\pi\)
\(570\) −3.46127e12 −1.37341
\(571\) 2.49685e12 0.982945 0.491473 0.870893i \(-0.336459\pi\)
0.491473 + 0.870893i \(0.336459\pi\)
\(572\) 3.32459e12 1.29854
\(573\) 9.91942e11 0.384406
\(574\) 1.31025e12 0.503792
\(575\) 1.27831e12 0.487675
\(576\) 3.35878e12 1.27139
\(577\) 3.19650e12 1.20056 0.600279 0.799791i \(-0.295056\pi\)
0.600279 + 0.799791i \(0.295056\pi\)
\(578\) 0 0
\(579\) −2.41925e12 −0.894595
\(580\) −1.92547e12 −0.706496
\(581\) 9.43486e10 0.0343513
\(582\) −1.57285e12 −0.568244
\(583\) 2.94927e12 1.05732
\(584\) −1.85541e12 −0.660059
\(585\) 3.21765e12 1.13589
\(586\) −3.56989e12 −1.25059
\(587\) 4.21874e12 1.46660 0.733299 0.679906i \(-0.237979\pi\)
0.733299 + 0.679906i \(0.237979\pi\)
\(588\) −1.82024e12 −0.627957
\(589\) 4.46151e12 1.52744
\(590\) −5.91034e12 −2.00807
\(591\) −1.09340e12 −0.368666
\(592\) 4.73370e11 0.158399
\(593\) −1.41657e12 −0.470427 −0.235214 0.971944i \(-0.575579\pi\)
−0.235214 + 0.971944i \(0.575579\pi\)
\(594\) −3.07538e12 −1.01358
\(595\) 0 0
\(596\) 1.87279e12 0.607969
\(597\) 2.37387e12 0.764843
\(598\) 4.35522e12 1.39269
\(599\) 4.20552e12 1.33475 0.667374 0.744722i \(-0.267418\pi\)
0.667374 + 0.744722i \(0.267418\pi\)
\(600\) −6.53760e11 −0.205939
\(601\) −4.21313e12 −1.31725 −0.658627 0.752469i \(-0.728863\pi\)
−0.658627 + 0.752469i \(0.728863\pi\)
\(602\) 9.86882e11 0.306253
\(603\) 3.11693e12 0.960061
\(604\) −5.13462e12 −1.56979
\(605\) −1.60052e12 −0.485695
\(606\) 3.02573e12 0.911388
\(607\) −5.49794e11 −0.164381 −0.0821904 0.996617i \(-0.526192\pi\)
−0.0821904 + 0.996617i \(0.526192\pi\)
\(608\) 6.23718e12 1.85107
\(609\) 1.49493e11 0.0440396
\(610\) 1.17034e13 3.42238
\(611\) −6.55257e12 −1.90207
\(612\) 0 0
\(613\) 4.73227e11 0.135362 0.0676810 0.997707i \(-0.478440\pi\)
0.0676810 + 0.997707i \(0.478440\pi\)
\(614\) 3.57810e12 1.01600
\(615\) 2.63999e12 0.744158
\(616\) −5.12168e11 −0.143318
\(617\) 6.13226e12 1.70348 0.851740 0.523964i \(-0.175547\pi\)
0.851740 + 0.523964i \(0.175547\pi\)
\(618\) 3.73218e12 1.02923
\(619\) −2.20706e12 −0.604237 −0.302118 0.953270i \(-0.597694\pi\)
−0.302118 + 0.953270i \(0.597694\pi\)
\(620\) 6.97782e12 1.89652
\(621\) −2.39128e12 −0.645236
\(622\) 2.27877e12 0.610440
\(623\) 1.24502e12 0.331115
\(624\) 6.44479e11 0.170168
\(625\) −4.71251e12 −1.23536
\(626\) −6.94292e12 −1.80700
\(627\) −2.09309e12 −0.540860
\(628\) −8.90777e12 −2.28534
\(629\) 0 0
\(630\) −1.57246e12 −0.397693
\(631\) 5.73681e12 1.44058 0.720291 0.693672i \(-0.244008\pi\)
0.720291 + 0.693672i \(0.244008\pi\)
\(632\) −5.30651e12 −1.32307
\(633\) 1.84395e11 0.0456492
\(634\) 1.05988e13 2.60528
\(635\) −1.07518e12 −0.262420
\(636\) −3.72045e12 −0.901652
\(637\) 4.39915e12 1.05862
\(638\) −1.96168e12 −0.468744
\(639\) 1.09545e12 0.259919
\(640\) 6.97715e12 1.64387
\(641\) −3.02882e12 −0.708618 −0.354309 0.935128i \(-0.615284\pi\)
−0.354309 + 0.935128i \(0.615284\pi\)
\(642\) −2.24387e12 −0.521303
\(643\) 3.56039e12 0.821389 0.410694 0.911773i \(-0.365286\pi\)
0.410694 + 0.911773i \(0.365286\pi\)
\(644\) −1.26331e12 −0.289418
\(645\) 1.98844e12 0.452370
\(646\) 0 0
\(647\) −1.12696e12 −0.252835 −0.126418 0.991977i \(-0.540348\pi\)
−0.126418 + 0.991977i \(0.540348\pi\)
\(648\) −1.33446e12 −0.297315
\(649\) −3.57409e12 −0.790796
\(650\) 5.01217e12 1.10133
\(651\) −5.41759e11 −0.118220
\(652\) −2.42598e12 −0.525743
\(653\) 5.96043e11 0.128283 0.0641413 0.997941i \(-0.479569\pi\)
0.0641413 + 0.997941i \(0.479569\pi\)
\(654\) 2.12811e12 0.454877
\(655\) −4.19164e12 −0.889811
\(656\) −1.97830e12 −0.417086
\(657\) −3.44478e12 −0.721303
\(658\) 3.20223e12 0.665942
\(659\) 3.31591e12 0.684887 0.342443 0.939538i \(-0.388745\pi\)
0.342443 + 0.939538i \(0.388745\pi\)
\(660\) −3.27361e12 −0.671552
\(661\) 7.15298e12 1.45740 0.728702 0.684831i \(-0.240124\pi\)
0.728702 + 0.684831i \(0.240124\pi\)
\(662\) −9.95450e12 −2.01446
\(663\) 0 0
\(664\) 4.92330e11 0.0982880
\(665\) −2.42649e12 −0.481150
\(666\) −3.03743e12 −0.598235
\(667\) −1.52532e12 −0.298397
\(668\) −6.52507e12 −1.26792
\(669\) −5.58112e11 −0.107722
\(670\) 1.26737e13 2.42977
\(671\) 7.07726e12 1.34776
\(672\) −7.57377e11 −0.143268
\(673\) 1.72634e12 0.324384 0.162192 0.986759i \(-0.448144\pi\)
0.162192 + 0.986759i \(0.448144\pi\)
\(674\) −4.72330e12 −0.881609
\(675\) −2.75199e12 −0.510246
\(676\) 2.20686e12 0.406456
\(677\) −9.74400e12 −1.78274 −0.891370 0.453276i \(-0.850255\pi\)
−0.891370 + 0.453276i \(0.850255\pi\)
\(678\) −6.52981e12 −1.18677
\(679\) −1.10263e12 −0.199075
\(680\) 0 0
\(681\) −2.18611e12 −0.389503
\(682\) 7.10907e12 1.25830
\(683\) 5.73218e12 1.00792 0.503961 0.863726i \(-0.331876\pi\)
0.503961 + 0.863726i \(0.331876\pi\)
\(684\) −9.87850e12 −1.72559
\(685\) −6.58781e12 −1.14323
\(686\) −4.44595e12 −0.766489
\(687\) −2.78628e12 −0.477220
\(688\) −1.49006e12 −0.253545
\(689\) 8.99159e12 1.52002
\(690\) −4.28844e12 −0.720241
\(691\) 1.94747e12 0.324952 0.162476 0.986712i \(-0.448052\pi\)
0.162476 + 0.986712i \(0.448052\pi\)
\(692\) 4.15017e12 0.688000
\(693\) −9.50898e11 −0.156615
\(694\) −4.52795e11 −0.0740942
\(695\) 3.99208e12 0.649035
\(696\) 7.80087e11 0.126009
\(697\) 0 0
\(698\) −3.54180e12 −0.564774
\(699\) −1.82365e12 −0.288930
\(700\) −1.45388e12 −0.228869
\(701\) −4.61502e12 −0.721842 −0.360921 0.932596i \(-0.617538\pi\)
−0.360921 + 0.932596i \(0.617538\pi\)
\(702\) −9.37606e12 −1.45715
\(703\) −4.68709e12 −0.723776
\(704\) 8.25865e12 1.26716
\(705\) 6.45210e12 0.983671
\(706\) −7.75817e12 −1.17527
\(707\) 2.12115e12 0.319290
\(708\) 4.50865e12 0.674368
\(709\) 2.50294e12 0.372000 0.186000 0.982550i \(-0.440448\pi\)
0.186000 + 0.982550i \(0.440448\pi\)
\(710\) 4.45417e12 0.657816
\(711\) −9.85213e12 −1.44583
\(712\) 6.49676e12 0.947408
\(713\) 5.52771e12 0.801018
\(714\) 0 0
\(715\) 7.91166e12 1.13211
\(716\) 1.15194e13 1.63803
\(717\) −2.66495e12 −0.376576
\(718\) 8.42272e12 1.18275
\(719\) −1.15159e13 −1.60701 −0.803504 0.595300i \(-0.797033\pi\)
−0.803504 + 0.595300i \(0.797033\pi\)
\(720\) 2.37421e12 0.329247
\(721\) 2.61640e12 0.360575
\(722\) −1.42290e13 −1.94875
\(723\) −3.06276e12 −0.416860
\(724\) −1.83981e13 −2.48857
\(725\) −1.75540e12 −0.235969
\(726\) 2.05701e12 0.274803
\(727\) −4.59761e12 −0.610418 −0.305209 0.952285i \(-0.598726\pi\)
−0.305209 + 0.952285i \(0.598726\pi\)
\(728\) −1.56147e12 −0.206036
\(729\) 3.99890e11 0.0524405
\(730\) −1.40067e13 −1.82551
\(731\) 0 0
\(732\) −8.92784e12 −1.14933
\(733\) −5.97894e12 −0.764991 −0.382495 0.923957i \(-0.624935\pi\)
−0.382495 + 0.923957i \(0.624935\pi\)
\(734\) −2.62118e12 −0.333322
\(735\) −4.33169e12 −0.547475
\(736\) 7.72772e12 0.970736
\(737\) 7.66399e12 0.956866
\(738\) 1.26940e13 1.57523
\(739\) 6.24601e12 0.770376 0.385188 0.922838i \(-0.374137\pi\)
0.385188 + 0.922838i \(0.374137\pi\)
\(740\) −7.33063e12 −0.898666
\(741\) −6.38132e12 −0.777551
\(742\) −4.39418e12 −0.532182
\(743\) −7.10024e12 −0.854719 −0.427360 0.904082i \(-0.640556\pi\)
−0.427360 + 0.904082i \(0.640556\pi\)
\(744\) −2.82701e12 −0.338259
\(745\) 4.45676e12 0.530049
\(746\) −5.81470e12 −0.687390
\(747\) 9.14066e11 0.107408
\(748\) 0 0
\(749\) −1.57304e12 −0.182630
\(750\) 3.01197e12 0.347596
\(751\) −1.86664e12 −0.214132 −0.107066 0.994252i \(-0.534146\pi\)
−0.107066 + 0.994252i \(0.534146\pi\)
\(752\) −4.83494e12 −0.551329
\(753\) −1.27014e12 −0.143971
\(754\) −5.98068e12 −0.673875
\(755\) −1.22191e13 −1.36860
\(756\) 2.71971e12 0.302812
\(757\) 1.50795e13 1.66900 0.834498 0.551012i \(-0.185758\pi\)
0.834498 + 0.551012i \(0.185758\pi\)
\(758\) −1.96217e13 −2.15886
\(759\) −2.59330e12 −0.283638
\(760\) −1.26619e13 −1.37670
\(761\) −1.49680e13 −1.61782 −0.808912 0.587929i \(-0.799943\pi\)
−0.808912 + 0.587929i \(0.799943\pi\)
\(762\) 1.38183e12 0.148476
\(763\) 1.49189e12 0.159359
\(764\) 1.15111e13 1.22235
\(765\) 0 0
\(766\) 1.58181e13 1.66007
\(767\) −1.08965e13 −1.13686
\(768\) −1.83311e12 −0.190135
\(769\) 4.90137e12 0.505416 0.252708 0.967543i \(-0.418679\pi\)
0.252708 + 0.967543i \(0.418679\pi\)
\(770\) −3.86642e12 −0.396370
\(771\) 8.86470e10 0.00903482
\(772\) −2.80744e13 −2.84467
\(773\) −1.28051e13 −1.28996 −0.644978 0.764201i \(-0.723133\pi\)
−0.644978 + 0.764201i \(0.723133\pi\)
\(774\) 9.56109e12 0.957576
\(775\) 6.36152e12 0.633437
\(776\) −5.75376e12 −0.569605
\(777\) 5.69151e11 0.0560186
\(778\) −4.54130e12 −0.444398
\(779\) 1.95882e13 1.90580
\(780\) −9.98043e12 −0.965436
\(781\) 2.69352e12 0.259054
\(782\) 0 0
\(783\) 3.28376e12 0.312207
\(784\) 3.24599e12 0.306849
\(785\) −2.11982e13 −1.99244
\(786\) 5.38713e12 0.503450
\(787\) −7.79210e12 −0.724050 −0.362025 0.932168i \(-0.617914\pi\)
−0.362025 + 0.932168i \(0.617914\pi\)
\(788\) −1.26884e13 −1.17230
\(789\) −4.26146e12 −0.391482
\(790\) −4.00595e13 −3.65918
\(791\) −4.57765e12 −0.415766
\(792\) −4.96198e12 −0.448117
\(793\) 2.15768e13 1.93757
\(794\) 1.17713e13 1.05107
\(795\) −8.85371e12 −0.786092
\(796\) 2.75478e13 2.43208
\(797\) 1.20701e13 1.05961 0.529807 0.848118i \(-0.322264\pi\)
0.529807 + 0.848118i \(0.322264\pi\)
\(798\) 3.11854e12 0.272232
\(799\) 0 0
\(800\) 8.89339e12 0.767648
\(801\) 1.20620e13 1.03531
\(802\) 2.14058e13 1.82704
\(803\) −8.47013e12 −0.718903
\(804\) −9.66799e12 −0.815989
\(805\) −3.00636e12 −0.252325
\(806\) 2.16738e13 1.80895
\(807\) −1.10667e12 −0.0918516
\(808\) 1.10686e13 0.913572
\(809\) 1.04899e13 0.860999 0.430500 0.902591i \(-0.358337\pi\)
0.430500 + 0.902591i \(0.358337\pi\)
\(810\) −1.00740e13 −0.822278
\(811\) 4.24679e12 0.344721 0.172360 0.985034i \(-0.444861\pi\)
0.172360 + 0.985034i \(0.444861\pi\)
\(812\) 1.73481e12 0.140039
\(813\) −2.40087e12 −0.192735
\(814\) −7.46851e12 −0.596244
\(815\) −5.77321e12 −0.458361
\(816\) 0 0
\(817\) 1.47538e13 1.15853
\(818\) 1.72703e13 1.34869
\(819\) −2.89905e12 −0.225153
\(820\) 3.06361e13 2.36631
\(821\) −8.29736e12 −0.637376 −0.318688 0.947860i \(-0.603242\pi\)
−0.318688 + 0.947860i \(0.603242\pi\)
\(822\) 8.46673e12 0.646833
\(823\) −1.69218e13 −1.28572 −0.642860 0.765984i \(-0.722252\pi\)
−0.642860 + 0.765984i \(0.722252\pi\)
\(824\) 1.36529e13 1.03170
\(825\) −2.98448e12 −0.224298
\(826\) 5.32511e12 0.398032
\(827\) −5.01967e12 −0.373165 −0.186582 0.982439i \(-0.559741\pi\)
−0.186582 + 0.982439i \(0.559741\pi\)
\(828\) −1.22392e13 −0.904935
\(829\) 8.26746e12 0.607963 0.303981 0.952678i \(-0.401684\pi\)
0.303981 + 0.952678i \(0.401684\pi\)
\(830\) 3.71666e12 0.271833
\(831\) 2.36638e12 0.172140
\(832\) 2.51786e13 1.82170
\(833\) 0 0
\(834\) −5.13067e12 −0.367220
\(835\) −1.55280e13 −1.10542
\(836\) −2.42895e13 −1.71985
\(837\) −1.19002e13 −0.838090
\(838\) 1.91454e13 1.34112
\(839\) −1.09618e13 −0.763751 −0.381875 0.924214i \(-0.624722\pi\)
−0.381875 + 0.924214i \(0.624722\pi\)
\(840\) 1.53753e12 0.106553
\(841\) −1.24125e13 −0.855616
\(842\) −3.53686e13 −2.42501
\(843\) 9.52143e12 0.649349
\(844\) 2.13983e12 0.145157
\(845\) 5.25174e12 0.354363
\(846\) 3.10238e13 2.08223
\(847\) 1.44204e12 0.0962727
\(848\) 6.63461e12 0.440589
\(849\) 7.17315e12 0.473833
\(850\) 0 0
\(851\) −5.80719e12 −0.379562
\(852\) −3.39783e12 −0.220914
\(853\) 5.66078e12 0.366105 0.183052 0.983103i \(-0.441402\pi\)
0.183052 + 0.983103i \(0.441402\pi\)
\(854\) −1.05446e13 −0.678372
\(855\) −2.35082e13 −1.50443
\(856\) −8.20845e12 −0.522552
\(857\) 2.86169e13 1.81221 0.906106 0.423050i \(-0.139041\pi\)
0.906106 + 0.423050i \(0.139041\pi\)
\(858\) −1.01681e13 −0.640544
\(859\) −2.17190e13 −1.36104 −0.680521 0.732729i \(-0.738246\pi\)
−0.680521 + 0.732729i \(0.738246\pi\)
\(860\) 2.30751e13 1.43847
\(861\) −2.37859e12 −0.147504
\(862\) 3.71308e13 2.29061
\(863\) −2.05248e13 −1.25959 −0.629796 0.776761i \(-0.716861\pi\)
−0.629796 + 0.776761i \(0.716861\pi\)
\(864\) −1.66365e13 −1.01566
\(865\) 9.87632e12 0.599823
\(866\) 1.55595e13 0.940080
\(867\) 0 0
\(868\) −6.28690e12 −0.375922
\(869\) −2.42247e13 −1.44102
\(870\) 5.88897e12 0.348500
\(871\) 2.33656e13 1.37561
\(872\) 7.78498e12 0.455967
\(873\) −1.06825e13 −0.622456
\(874\) −3.18193e13 −1.84455
\(875\) 2.11151e12 0.121775
\(876\) 1.06849e13 0.613060
\(877\) 3.10724e13 1.77369 0.886843 0.462072i \(-0.152894\pi\)
0.886843 + 0.462072i \(0.152894\pi\)
\(878\) −4.42819e13 −2.51478
\(879\) 6.48065e12 0.366158
\(880\) 5.83776e12 0.328152
\(881\) 4.35667e12 0.243648 0.121824 0.992552i \(-0.461126\pi\)
0.121824 + 0.992552i \(0.461126\pi\)
\(882\) −2.08282e13 −1.15889
\(883\) 1.30562e13 0.722758 0.361379 0.932419i \(-0.382306\pi\)
0.361379 + 0.932419i \(0.382306\pi\)
\(884\) 0 0
\(885\) 1.07294e13 0.587938
\(886\) 1.61539e13 0.880697
\(887\) 3.11601e13 1.69022 0.845108 0.534596i \(-0.179536\pi\)
0.845108 + 0.534596i \(0.179536\pi\)
\(888\) 2.96995e12 0.160284
\(889\) 9.68714e11 0.0520161
\(890\) 4.90448e13 2.62022
\(891\) −6.09192e12 −0.323821
\(892\) −6.47667e12 −0.342539
\(893\) 4.78732e13 2.51919
\(894\) −5.72787e12 −0.299898
\(895\) 2.74133e13 1.42809
\(896\) −6.28628e12 −0.325843
\(897\) −7.90631e12 −0.407763
\(898\) 1.60522e13 0.823742
\(899\) −7.59076e12 −0.387585
\(900\) −1.40854e13 −0.715614
\(901\) 0 0
\(902\) 3.12123e13 1.56999
\(903\) −1.79155e12 −0.0896673
\(904\) −2.38871e13 −1.18961
\(905\) −4.37827e13 −2.16962
\(906\) 1.57041e13 0.774346
\(907\) 1.75730e13 0.862208 0.431104 0.902302i \(-0.358124\pi\)
0.431104 + 0.902302i \(0.358124\pi\)
\(908\) −2.53689e13 −1.23856
\(909\) 2.05501e13 0.998337
\(910\) −1.17877e13 −0.569829
\(911\) −3.26951e12 −0.157272 −0.0786358 0.996903i \(-0.525056\pi\)
−0.0786358 + 0.996903i \(0.525056\pi\)
\(912\) −4.70858e12 −0.225379
\(913\) 2.24753e12 0.107050
\(914\) 2.67640e13 1.26851
\(915\) −2.12459e13 −1.00203
\(916\) −3.23336e13 −1.51749
\(917\) 3.77659e12 0.176375
\(918\) 0 0
\(919\) −1.28770e13 −0.595517 −0.297759 0.954641i \(-0.596239\pi\)
−0.297759 + 0.954641i \(0.596239\pi\)
\(920\) −1.56878e13 −0.721967
\(921\) −6.49556e12 −0.297473
\(922\) 2.94692e13 1.34301
\(923\) 8.21187e12 0.372421
\(924\) 2.94947e12 0.133113
\(925\) −6.68316e12 −0.300154
\(926\) 5.81947e13 2.60096
\(927\) 2.53482e13 1.12743
\(928\) −1.06119e13 −0.469705
\(929\) −8.08221e12 −0.356008 −0.178004 0.984030i \(-0.556964\pi\)
−0.178004 + 0.984030i \(0.556964\pi\)
\(930\) −2.13414e13 −0.935514
\(931\) −3.21403e13 −1.40209
\(932\) −2.11627e13 −0.918754
\(933\) −4.13679e12 −0.178730
\(934\) −1.91637e12 −0.0823983
\(935\) 0 0
\(936\) −1.51278e13 −0.644222
\(937\) 6.49112e12 0.275101 0.137550 0.990495i \(-0.456077\pi\)
0.137550 + 0.990495i \(0.456077\pi\)
\(938\) −1.14187e13 −0.481621
\(939\) 1.26039e13 0.529067
\(940\) 7.48740e13 3.12792
\(941\) −1.21565e11 −0.00505423 −0.00252711 0.999997i \(-0.500804\pi\)
−0.00252711 + 0.999997i \(0.500804\pi\)
\(942\) 2.72441e13 1.12731
\(943\) 2.42694e13 0.999437
\(944\) −8.04019e12 −0.329528
\(945\) 6.47219e12 0.264003
\(946\) 2.35091e13 0.954389
\(947\) 4.00324e12 0.161747 0.0808735 0.996724i \(-0.474229\pi\)
0.0808735 + 0.996724i \(0.474229\pi\)
\(948\) 3.05591e13 1.22886
\(949\) −2.58233e13 −1.03351
\(950\) −3.66190e13 −1.45865
\(951\) −1.92407e13 −0.762795
\(952\) 0 0
\(953\) −3.60121e13 −1.41426 −0.707131 0.707082i \(-0.750011\pi\)
−0.707131 + 0.707082i \(0.750011\pi\)
\(954\) −4.25716e13 −1.66400
\(955\) 2.73934e13 1.06569
\(956\) −3.09257e13 −1.19745
\(957\) 3.56117e12 0.137242
\(958\) 5.37932e13 2.06340
\(959\) 5.93550e12 0.226607
\(960\) −2.47925e13 −0.942105
\(961\) 1.06905e12 0.0404336
\(962\) −2.27696e13 −0.857172
\(963\) −1.52399e13 −0.571037
\(964\) −3.55421e13 −1.32555
\(965\) −6.68097e13 −2.48009
\(966\) 3.86380e12 0.142764
\(967\) 4.03493e13 1.48394 0.741972 0.670431i \(-0.233891\pi\)
0.741972 + 0.670431i \(0.233891\pi\)
\(968\) 7.52489e12 0.275461
\(969\) 0 0
\(970\) −4.34358e13 −1.57534
\(971\) 1.94578e13 0.702435 0.351218 0.936294i \(-0.385768\pi\)
0.351218 + 0.936294i \(0.385768\pi\)
\(972\) 4.10766e13 1.47604
\(973\) −3.59680e12 −0.128649
\(974\) 4.88404e13 1.73886
\(975\) −9.09892e12 −0.322455
\(976\) 1.59208e13 0.561619
\(977\) 4.00163e13 1.40511 0.702557 0.711627i \(-0.252042\pi\)
0.702557 + 0.711627i \(0.252042\pi\)
\(978\) 7.41978e12 0.259338
\(979\) 2.96583e13 1.03187
\(980\) −5.02676e13 −1.74089
\(981\) 1.44537e13 0.498273
\(982\) 7.06007e13 2.42274
\(983\) 1.03796e13 0.354559 0.177280 0.984161i \(-0.443270\pi\)
0.177280 + 0.984161i \(0.443270\pi\)
\(984\) −1.24120e13 −0.422049
\(985\) −3.01951e13 −1.02205
\(986\) 0 0
\(987\) −5.81322e12 −0.194980
\(988\) −7.40527e13 −2.47249
\(989\) 1.82797e13 0.607554
\(990\) −3.74586e13 −1.23935
\(991\) −1.11004e13 −0.365601 −0.182800 0.983150i \(-0.558516\pi\)
−0.182800 + 0.983150i \(0.558516\pi\)
\(992\) 3.84570e13 1.26088
\(993\) 1.80711e13 0.589810
\(994\) −4.01313e12 −0.130390
\(995\) 6.55566e13 2.12037
\(996\) −2.83522e12 −0.0912894
\(997\) 5.51871e12 0.176892 0.0884462 0.996081i \(-0.471810\pi\)
0.0884462 + 0.996081i \(0.471810\pi\)
\(998\) −2.31578e13 −0.738941
\(999\) 1.25019e13 0.397129
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 289.10.a.g.1.5 36
17.16 even 2 289.10.a.h.1.5 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.5 36 1.1 even 1 trivial
289.10.a.h.1.5 yes 36 17.16 even 2