Properties

Label 289.10.a.i.1.3
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

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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: \(0\)
Dimension: \(52\)
Twist minimal: no (minimal twist has level 17)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-40.6100 q^{2} -102.962 q^{3} +1137.17 q^{4} -769.524 q^{5} +4181.30 q^{6} +1567.27 q^{7} -25388.3 q^{8} -9081.79 q^{9} +O(q^{10})\) \(q-40.6100 q^{2} -102.962 q^{3} +1137.17 q^{4} -769.524 q^{5} +4181.30 q^{6} +1567.27 q^{7} -25388.3 q^{8} -9081.79 q^{9} +31250.4 q^{10} -17032.6 q^{11} -117086. q^{12} +141996. q^{13} -63646.7 q^{14} +79231.9 q^{15} +448786. q^{16} +368812. q^{18} -743799. q^{19} -875082. q^{20} -161369. q^{21} +691694. q^{22} -1.55554e6 q^{23} +2.61403e6 q^{24} -1.36096e6 q^{25} -5.76647e6 q^{26} +2.96169e6 q^{27} +1.78225e6 q^{28} +5.73876e6 q^{29} -3.21761e6 q^{30} -4.58990e6 q^{31} -5.22641e6 q^{32} +1.75371e6 q^{33} -1.20605e6 q^{35} -1.03276e7 q^{36} -5.48318e6 q^{37} +3.02057e7 q^{38} -1.46203e7 q^{39} +1.95369e7 q^{40} +1.81160e7 q^{41} +6.55320e6 q^{42} +2.79841e7 q^{43} -1.93690e7 q^{44} +6.98865e6 q^{45} +6.31705e7 q^{46} +2.65154e7 q^{47} -4.62080e7 q^{48} -3.78973e7 q^{49} +5.52685e7 q^{50} +1.61474e8 q^{52} +7.58163e7 q^{53} -1.20274e8 q^{54} +1.31070e7 q^{55} -3.97902e7 q^{56} +7.65832e7 q^{57} -2.33051e8 q^{58} -4.75661e7 q^{59} +9.01004e7 q^{60} -1.40302e8 q^{61} +1.86396e8 q^{62} -1.42336e7 q^{63} -1.75339e7 q^{64} -1.09270e8 q^{65} -7.12184e7 q^{66} -7.10319e7 q^{67} +1.60162e8 q^{69} +4.89776e7 q^{70} -7.14261e7 q^{71} +2.30571e8 q^{72} -3.40249e8 q^{73} +2.22672e8 q^{74} +1.40127e8 q^{75} -8.45829e8 q^{76} -2.66946e7 q^{77} +5.93729e8 q^{78} +3.20837e8 q^{79} -3.45352e8 q^{80} -1.26185e8 q^{81} -7.35691e8 q^{82} +3.26635e8 q^{83} -1.83505e8 q^{84} -1.13644e9 q^{86} -5.90875e8 q^{87} +4.32429e8 q^{88} -2.75879e8 q^{89} -2.83809e8 q^{90} +2.22546e8 q^{91} -1.76892e9 q^{92} +4.72586e8 q^{93} -1.07679e9 q^{94} +5.72371e8 q^{95} +5.38123e8 q^{96} -6.65935e8 q^{97} +1.53901e9 q^{98} +1.54687e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + O(q^{10}) \) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + 156200q^{13} + 1207872q^{15} + 3407880q^{16} + 2193336q^{18} + 1185568q^{19} + 5198336q^{21} + 13827692q^{25} + 3618944q^{26} - 9167544q^{30} + 61884888q^{32} + 1635208q^{33} + 46992776q^{35} + 156027320q^{36} + 84813952q^{38} - 4635776q^{42} + 125448912q^{43} + 164193176q^{47} + 270850284q^{49} - 226223888q^{50} + 103553016q^{52} + 426167208q^{53} + 677761520q^{55} + 375214512q^{59} + 336918024q^{60} + 190014416q^{64} + 1377178928q^{66} + 311910088q^{67} + 533688136q^{69} + 1477690280q^{70} + 2757942680q^{72} + 4047975520q^{76} + 3440336432q^{77} + 3266558756q^{81} + 2072890608q^{83} + 2630025952q^{84} + 1538547296q^{86} - 1010436256q^{87} + 1873849184q^{89} - 1998451624q^{93} - 6880776704q^{94} - 4667454128q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −40.6100 −1.79473 −0.897363 0.441293i \(-0.854520\pi\)
−0.897363 + 0.441293i \(0.854520\pi\)
\(3\) −102.962 −0.733892 −0.366946 0.930242i \(-0.619597\pi\)
−0.366946 + 0.930242i \(0.619597\pi\)
\(4\) 1137.17 2.22104
\(5\) −769.524 −0.550627 −0.275313 0.961355i \(-0.588782\pi\)
−0.275313 + 0.961355i \(0.588782\pi\)
\(6\) 4181.30 1.31713
\(7\) 1567.27 0.246718 0.123359 0.992362i \(-0.460633\pi\)
0.123359 + 0.992362i \(0.460633\pi\)
\(8\) −25388.3 −2.19144
\(9\) −9081.79 −0.461403
\(10\) 31250.4 0.988224
\(11\) −17032.6 −0.350763 −0.175382 0.984501i \(-0.556116\pi\)
−0.175382 + 0.984501i \(0.556116\pi\)
\(12\) −117086. −1.63000
\(13\) 141996. 1.37890 0.689449 0.724334i \(-0.257853\pi\)
0.689449 + 0.724334i \(0.257853\pi\)
\(14\) −63646.7 −0.442792
\(15\) 79231.9 0.404100
\(16\) 448786. 1.71198
\(17\) 0 0
\(18\) 368812. 0.828091
\(19\) −743799. −1.30938 −0.654688 0.755899i \(-0.727200\pi\)
−0.654688 + 0.755899i \(0.727200\pi\)
\(20\) −875082. −1.22296
\(21\) −161369. −0.181065
\(22\) 691694. 0.629524
\(23\) −1.55554e6 −1.15906 −0.579530 0.814951i \(-0.696764\pi\)
−0.579530 + 0.814951i \(0.696764\pi\)
\(24\) 2.61403e6 1.60828
\(25\) −1.36096e6 −0.696810
\(26\) −5.76647e6 −2.47474
\(27\) 2.96169e6 1.07251
\(28\) 1.78225e6 0.547972
\(29\) 5.73876e6 1.50670 0.753350 0.657619i \(-0.228436\pi\)
0.753350 + 0.657619i \(0.228436\pi\)
\(30\) −3.21761e6 −0.725249
\(31\) −4.58990e6 −0.892639 −0.446320 0.894874i \(-0.647266\pi\)
−0.446320 + 0.894874i \(0.647266\pi\)
\(32\) −5.22641e6 −0.881107
\(33\) 1.75371e6 0.257422
\(34\) 0 0
\(35\) −1.20605e6 −0.135850
\(36\) −1.03276e7 −1.02479
\(37\) −5.48318e6 −0.480977 −0.240489 0.970652i \(-0.577308\pi\)
−0.240489 + 0.970652i \(0.577308\pi\)
\(38\) 3.02057e7 2.34997
\(39\) −1.46203e7 −1.01196
\(40\) 1.95369e7 1.20666
\(41\) 1.81160e7 1.00123 0.500616 0.865669i \(-0.333107\pi\)
0.500616 + 0.865669i \(0.333107\pi\)
\(42\) 6.55320e6 0.324961
\(43\) 2.79841e7 1.24826 0.624128 0.781322i \(-0.285454\pi\)
0.624128 + 0.781322i \(0.285454\pi\)
\(44\) −1.93690e7 −0.779060
\(45\) 6.98865e6 0.254061
\(46\) 6.31705e7 2.08020
\(47\) 2.65154e7 0.792607 0.396304 0.918119i \(-0.370293\pi\)
0.396304 + 0.918119i \(0.370293\pi\)
\(48\) −4.62080e7 −1.25641
\(49\) −3.78973e7 −0.939130
\(50\) 5.52685e7 1.25058
\(51\) 0 0
\(52\) 1.61474e8 3.06259
\(53\) 7.58163e7 1.31984 0.659920 0.751336i \(-0.270590\pi\)
0.659920 + 0.751336i \(0.270590\pi\)
\(54\) −1.20274e8 −1.92486
\(55\) 1.31070e7 0.193140
\(56\) −3.97902e7 −0.540667
\(57\) 7.65832e7 0.960941
\(58\) −2.33051e8 −2.70411
\(59\) −4.75661e7 −0.511051 −0.255525 0.966802i \(-0.582248\pi\)
−0.255525 + 0.966802i \(0.582248\pi\)
\(60\) 9.01004e7 0.897524
\(61\) −1.40302e8 −1.29742 −0.648709 0.761036i \(-0.724691\pi\)
−0.648709 + 0.761036i \(0.724691\pi\)
\(62\) 1.86396e8 1.60204
\(63\) −1.42336e7 −0.113836
\(64\) −1.75339e7 −0.130638
\(65\) −1.09270e8 −0.759258
\(66\) −7.12184e7 −0.462002
\(67\) −7.10319e7 −0.430643 −0.215321 0.976543i \(-0.569080\pi\)
−0.215321 + 0.976543i \(0.569080\pi\)
\(68\) 0 0
\(69\) 1.60162e8 0.850625
\(70\) 4.89776e7 0.243813
\(71\) −7.14261e7 −0.333576 −0.166788 0.985993i \(-0.553339\pi\)
−0.166788 + 0.985993i \(0.553339\pi\)
\(72\) 2.30571e8 1.01113
\(73\) −3.40249e8 −1.40231 −0.701154 0.713010i \(-0.747332\pi\)
−0.701154 + 0.713010i \(0.747332\pi\)
\(74\) 2.22672e8 0.863222
\(75\) 1.40127e8 0.511384
\(76\) −8.45829e8 −2.90818
\(77\) −2.66946e7 −0.0865397
\(78\) 5.93729e8 1.81619
\(79\) 3.20837e8 0.926750 0.463375 0.886162i \(-0.346638\pi\)
0.463375 + 0.886162i \(0.346638\pi\)
\(80\) −3.45352e8 −0.942664
\(81\) −1.26185e8 −0.325705
\(82\) −7.35691e8 −1.79694
\(83\) 3.26635e8 0.755459 0.377729 0.925916i \(-0.376705\pi\)
0.377729 + 0.925916i \(0.376705\pi\)
\(84\) −1.83505e8 −0.402152
\(85\) 0 0
\(86\) −1.13644e9 −2.24028
\(87\) −5.90875e8 −1.10576
\(88\) 4.32429e8 0.768675
\(89\) −2.75879e8 −0.466084 −0.233042 0.972467i \(-0.574868\pi\)
−0.233042 + 0.972467i \(0.574868\pi\)
\(90\) −2.83809e8 −0.455969
\(91\) 2.22546e8 0.340199
\(92\) −1.76892e9 −2.57432
\(93\) 4.72586e8 0.655101
\(94\) −1.07679e9 −1.42251
\(95\) 5.72371e8 0.720977
\(96\) 5.38123e8 0.646637
\(97\) −6.65935e8 −0.763764 −0.381882 0.924211i \(-0.624724\pi\)
−0.381882 + 0.924211i \(0.624724\pi\)
\(98\) 1.53901e9 1.68548
\(99\) 1.54687e8 0.161843
\(100\) −1.54764e9 −1.54764
\(101\) 6.92506e8 0.662182 0.331091 0.943599i \(-0.392583\pi\)
0.331091 + 0.943599i \(0.392583\pi\)
\(102\) 0 0
\(103\) −1.77196e9 −1.55127 −0.775633 0.631184i \(-0.782569\pi\)
−0.775633 + 0.631184i \(0.782569\pi\)
\(104\) −3.60505e9 −3.02177
\(105\) 1.24177e8 0.0996989
\(106\) −3.07890e9 −2.36875
\(107\) −7.73032e8 −0.570126 −0.285063 0.958509i \(-0.592014\pi\)
−0.285063 + 0.958509i \(0.592014\pi\)
\(108\) 3.36795e9 2.38209
\(109\) −2.12026e9 −1.43870 −0.719350 0.694648i \(-0.755560\pi\)
−0.719350 + 0.694648i \(0.755560\pi\)
\(110\) −5.32275e8 −0.346633
\(111\) 5.64560e8 0.352985
\(112\) 7.03367e8 0.422378
\(113\) −2.21312e9 −1.27688 −0.638442 0.769670i \(-0.720421\pi\)
−0.638442 + 0.769670i \(0.720421\pi\)
\(114\) −3.11004e9 −1.72463
\(115\) 1.19703e9 0.638210
\(116\) 6.52596e9 3.34644
\(117\) −1.28958e9 −0.636227
\(118\) 1.93166e9 0.917196
\(119\) 0 0
\(120\) −2.01156e9 −0.885560
\(121\) −2.06784e9 −0.876965
\(122\) 5.69767e9 2.32851
\(123\) −1.86526e9 −0.734797
\(124\) −5.21952e9 −1.98259
\(125\) 2.55027e9 0.934309
\(126\) 5.78026e8 0.204305
\(127\) 3.54124e8 0.120792 0.0603960 0.998174i \(-0.480764\pi\)
0.0603960 + 0.998174i \(0.480764\pi\)
\(128\) 3.38798e9 1.11557
\(129\) −2.88131e9 −0.916085
\(130\) 4.43744e9 1.36266
\(131\) 2.62702e9 0.779368 0.389684 0.920949i \(-0.372584\pi\)
0.389684 + 0.920949i \(0.372584\pi\)
\(132\) 1.99428e9 0.571746
\(133\) −1.16573e9 −0.323047
\(134\) 2.88461e9 0.772885
\(135\) −2.27909e9 −0.590553
\(136\) 0 0
\(137\) −3.91153e9 −0.948646 −0.474323 0.880351i \(-0.657307\pi\)
−0.474323 + 0.880351i \(0.657307\pi\)
\(138\) −6.50418e9 −1.52664
\(139\) −3.69492e9 −0.839534 −0.419767 0.907632i \(-0.637888\pi\)
−0.419767 + 0.907632i \(0.637888\pi\)
\(140\) −1.37149e9 −0.301728
\(141\) −2.73009e9 −0.581688
\(142\) 2.90061e9 0.598677
\(143\) −2.41857e9 −0.483667
\(144\) −4.07578e9 −0.789914
\(145\) −4.41611e9 −0.829629
\(146\) 1.38175e10 2.51676
\(147\) 3.90199e9 0.689220
\(148\) −6.23532e9 −1.06827
\(149\) −6.36801e9 −1.05844 −0.529219 0.848485i \(-0.677515\pi\)
−0.529219 + 0.848485i \(0.677515\pi\)
\(150\) −5.69057e9 −0.917793
\(151\) −8.92054e9 −1.39635 −0.698176 0.715926i \(-0.746005\pi\)
−0.698176 + 0.715926i \(0.746005\pi\)
\(152\) 1.88838e10 2.86941
\(153\) 0 0
\(154\) 1.08407e9 0.155315
\(155\) 3.53204e9 0.491511
\(156\) −1.66258e10 −2.24761
\(157\) 4.57442e9 0.600879 0.300440 0.953801i \(-0.402867\pi\)
0.300440 + 0.953801i \(0.402867\pi\)
\(158\) −1.30292e10 −1.66326
\(159\) −7.80622e9 −0.968620
\(160\) 4.02185e9 0.485161
\(161\) −2.43795e9 −0.285961
\(162\) 5.12436e9 0.584551
\(163\) 6.61139e9 0.733582 0.366791 0.930303i \(-0.380456\pi\)
0.366791 + 0.930303i \(0.380456\pi\)
\(164\) 2.06010e10 2.22378
\(165\) −1.34953e9 −0.141744
\(166\) −1.32646e10 −1.35584
\(167\) −1.30049e10 −1.29384 −0.646922 0.762556i \(-0.723944\pi\)
−0.646922 + 0.762556i \(0.723944\pi\)
\(168\) 4.09689e9 0.396791
\(169\) 9.55847e9 0.901359
\(170\) 0 0
\(171\) 6.75503e9 0.604150
\(172\) 3.18228e10 2.77243
\(173\) 4.07288e9 0.345696 0.172848 0.984949i \(-0.444703\pi\)
0.172848 + 0.984949i \(0.444703\pi\)
\(174\) 2.39954e10 1.98453
\(175\) −2.13298e9 −0.171916
\(176\) −7.64400e9 −0.600501
\(177\) 4.89751e9 0.375056
\(178\) 1.12035e10 0.836492
\(179\) 2.47219e10 1.79988 0.899938 0.436017i \(-0.143611\pi\)
0.899938 + 0.436017i \(0.143611\pi\)
\(180\) 7.94731e9 0.564279
\(181\) −3.57700e9 −0.247722 −0.123861 0.992300i \(-0.539528\pi\)
−0.123861 + 0.992300i \(0.539528\pi\)
\(182\) −9.03759e9 −0.610565
\(183\) 1.44458e10 0.952165
\(184\) 3.94925e10 2.54001
\(185\) 4.21943e9 0.264839
\(186\) −1.91917e10 −1.17573
\(187\) 0 0
\(188\) 3.01526e10 1.76041
\(189\) 4.64175e9 0.264608
\(190\) −2.32440e10 −1.29396
\(191\) 1.56335e10 0.849975 0.424988 0.905199i \(-0.360278\pi\)
0.424988 + 0.905199i \(0.360278\pi\)
\(192\) 1.80533e9 0.0958742
\(193\) 7.93673e9 0.411750 0.205875 0.978578i \(-0.433996\pi\)
0.205875 + 0.978578i \(0.433996\pi\)
\(194\) 2.70436e10 1.37075
\(195\) 1.12506e10 0.557213
\(196\) −4.30958e10 −2.08585
\(197\) −2.65269e10 −1.25484 −0.627421 0.778680i \(-0.715889\pi\)
−0.627421 + 0.778680i \(0.715889\pi\)
\(198\) −6.28182e9 −0.290464
\(199\) 4.18654e10 1.89241 0.946206 0.323563i \(-0.104881\pi\)
0.946206 + 0.323563i \(0.104881\pi\)
\(200\) 3.45524e10 1.52701
\(201\) 7.31360e9 0.316045
\(202\) −2.81227e10 −1.18844
\(203\) 8.99416e9 0.371731
\(204\) 0 0
\(205\) −1.39407e10 −0.551305
\(206\) 7.19593e10 2.78410
\(207\) 1.41271e10 0.534794
\(208\) 6.37260e10 2.36065
\(209\) 1.26688e10 0.459281
\(210\) −5.04284e9 −0.178932
\(211\) −2.51533e10 −0.873623 −0.436812 0.899553i \(-0.643892\pi\)
−0.436812 + 0.899553i \(0.643892\pi\)
\(212\) 8.62163e10 2.93142
\(213\) 7.35419e9 0.244808
\(214\) 3.13928e10 1.02322
\(215\) −2.15344e10 −0.687323
\(216\) −7.51921e10 −2.35034
\(217\) −7.19360e9 −0.220230
\(218\) 8.61038e10 2.58207
\(219\) 3.50327e10 1.02914
\(220\) 1.49049e10 0.428971
\(221\) 0 0
\(222\) −2.29268e10 −0.633512
\(223\) −3.42839e10 −0.928365 −0.464182 0.885740i \(-0.653652\pi\)
−0.464182 + 0.885740i \(0.653652\pi\)
\(224\) −8.19117e9 −0.217385
\(225\) 1.23599e10 0.321510
\(226\) 8.98748e10 2.29166
\(227\) −3.92494e10 −0.981107 −0.490553 0.871411i \(-0.663205\pi\)
−0.490553 + 0.871411i \(0.663205\pi\)
\(228\) 8.70884e10 2.13429
\(229\) 3.19695e10 0.768203 0.384102 0.923291i \(-0.374511\pi\)
0.384102 + 0.923291i \(0.374511\pi\)
\(230\) −4.86112e10 −1.14541
\(231\) 2.74854e9 0.0635108
\(232\) −1.45697e11 −3.30184
\(233\) −8.59764e10 −1.91107 −0.955537 0.294872i \(-0.904723\pi\)
−0.955537 + 0.294872i \(0.904723\pi\)
\(234\) 5.23699e10 1.14185
\(235\) −2.04042e10 −0.436431
\(236\) −5.40909e10 −1.13506
\(237\) −3.30341e10 −0.680135
\(238\) 0 0
\(239\) 3.27519e10 0.649300 0.324650 0.945834i \(-0.394753\pi\)
0.324650 + 0.945834i \(0.394753\pi\)
\(240\) 3.55582e10 0.691813
\(241\) 2.29656e9 0.0438533 0.0219266 0.999760i \(-0.493020\pi\)
0.0219266 + 0.999760i \(0.493020\pi\)
\(242\) 8.39749e10 1.57391
\(243\) −4.53026e10 −0.833479
\(244\) −1.59548e11 −2.88162
\(245\) 2.91629e10 0.517110
\(246\) 7.57484e10 1.31876
\(247\) −1.05617e11 −1.80550
\(248\) 1.16530e11 1.95616
\(249\) −3.36310e10 −0.554425
\(250\) −1.03566e11 −1.67683
\(251\) −4.29930e10 −0.683700 −0.341850 0.939755i \(-0.611053\pi\)
−0.341850 + 0.939755i \(0.611053\pi\)
\(252\) −1.61860e10 −0.252836
\(253\) 2.64949e10 0.406556
\(254\) −1.43810e10 −0.216789
\(255\) 0 0
\(256\) −1.28608e11 −1.87150
\(257\) −1.68780e10 −0.241336 −0.120668 0.992693i \(-0.538504\pi\)
−0.120668 + 0.992693i \(0.538504\pi\)
\(258\) 1.17010e11 1.64412
\(259\) −8.59359e9 −0.118666
\(260\) −1.24258e11 −1.68634
\(261\) −5.21182e10 −0.695196
\(262\) −1.06683e11 −1.39875
\(263\) −1.88404e10 −0.242823 −0.121412 0.992602i \(-0.538742\pi\)
−0.121412 + 0.992602i \(0.538742\pi\)
\(264\) −4.45238e10 −0.564124
\(265\) −5.83425e10 −0.726739
\(266\) 4.73403e10 0.579781
\(267\) 2.84051e10 0.342055
\(268\) −8.07756e10 −0.956475
\(269\) 9.27652e10 1.08019 0.540094 0.841604i \(-0.318388\pi\)
0.540094 + 0.841604i \(0.318388\pi\)
\(270\) 9.25538e10 1.05988
\(271\) 1.11257e11 1.25304 0.626519 0.779406i \(-0.284479\pi\)
0.626519 + 0.779406i \(0.284479\pi\)
\(272\) 0 0
\(273\) −2.29138e10 −0.249670
\(274\) 1.58847e11 1.70256
\(275\) 2.31807e10 0.244415
\(276\) 1.82132e11 1.88927
\(277\) 1.24749e11 1.27314 0.636572 0.771217i \(-0.280352\pi\)
0.636572 + 0.771217i \(0.280352\pi\)
\(278\) 1.50051e11 1.50673
\(279\) 4.16845e10 0.411866
\(280\) 3.06195e10 0.297706
\(281\) 8.65210e10 0.827834 0.413917 0.910315i \(-0.364160\pi\)
0.413917 + 0.910315i \(0.364160\pi\)
\(282\) 1.10869e11 1.04397
\(283\) 1.35344e11 1.25429 0.627146 0.778901i \(-0.284223\pi\)
0.627146 + 0.778901i \(0.284223\pi\)
\(284\) −8.12238e10 −0.740885
\(285\) −5.89326e10 −0.529119
\(286\) 9.82181e10 0.868049
\(287\) 2.83926e10 0.247022
\(288\) 4.74652e10 0.406545
\(289\) 0 0
\(290\) 1.79338e11 1.48896
\(291\) 6.85661e10 0.560520
\(292\) −3.86922e11 −3.11458
\(293\) −8.66175e10 −0.686596 −0.343298 0.939227i \(-0.611544\pi\)
−0.343298 + 0.939227i \(0.611544\pi\)
\(294\) −1.58460e11 −1.23696
\(295\) 3.66033e10 0.281398
\(296\) 1.39208e11 1.05403
\(297\) −5.04452e10 −0.376198
\(298\) 2.58605e11 1.89961
\(299\) −2.20881e11 −1.59823
\(300\) 1.59349e11 1.13580
\(301\) 4.38585e10 0.307968
\(302\) 3.62263e11 2.50607
\(303\) −7.13019e10 −0.485970
\(304\) −3.33807e11 −2.24163
\(305\) 1.07966e11 0.714393
\(306\) 0 0
\(307\) 1.77951e11 1.14335 0.571674 0.820481i \(-0.306294\pi\)
0.571674 + 0.820481i \(0.306294\pi\)
\(308\) −3.03564e10 −0.192208
\(309\) 1.82445e11 1.13846
\(310\) −1.43436e11 −0.882127
\(311\) −7.17574e10 −0.434956 −0.217478 0.976065i \(-0.569783\pi\)
−0.217478 + 0.976065i \(0.569783\pi\)
\(312\) 3.71183e11 2.21765
\(313\) −2.65394e11 −1.56294 −0.781469 0.623944i \(-0.785529\pi\)
−0.781469 + 0.623944i \(0.785529\pi\)
\(314\) −1.85767e11 −1.07841
\(315\) 1.09531e10 0.0626814
\(316\) 3.64847e11 2.05835
\(317\) 7.54472e9 0.0419640 0.0209820 0.999780i \(-0.493321\pi\)
0.0209820 + 0.999780i \(0.493321\pi\)
\(318\) 3.17011e11 1.73841
\(319\) −9.77460e10 −0.528495
\(320\) 1.34928e10 0.0719328
\(321\) 7.95931e10 0.418411
\(322\) 9.90050e10 0.513222
\(323\) 0 0
\(324\) −1.43494e11 −0.723404
\(325\) −1.93251e11 −0.960830
\(326\) −2.68489e11 −1.31658
\(327\) 2.18307e11 1.05585
\(328\) −4.59934e11 −2.19414
\(329\) 4.15567e10 0.195551
\(330\) 5.48042e10 0.254391
\(331\) 2.63533e11 1.20673 0.603365 0.797466i \(-0.293826\pi\)
0.603365 + 0.797466i \(0.293826\pi\)
\(332\) 3.71440e11 1.67790
\(333\) 4.97970e10 0.221924
\(334\) 5.28128e11 2.32210
\(335\) 5.46608e10 0.237123
\(336\) −7.24202e10 −0.309980
\(337\) −9.26802e10 −0.391429 −0.195714 0.980661i \(-0.562703\pi\)
−0.195714 + 0.980661i \(0.562703\pi\)
\(338\) −3.88169e11 −1.61769
\(339\) 2.27867e11 0.937095
\(340\) 0 0
\(341\) 7.81780e10 0.313105
\(342\) −2.74322e11 −1.08428
\(343\) −1.22640e11 −0.478419
\(344\) −7.10469e11 −2.73547
\(345\) −1.23248e11 −0.468377
\(346\) −1.65400e11 −0.620429
\(347\) −1.66519e11 −0.616568 −0.308284 0.951294i \(-0.599755\pi\)
−0.308284 + 0.951294i \(0.599755\pi\)
\(348\) −6.71927e11 −2.45593
\(349\) −2.48718e11 −0.897413 −0.448707 0.893679i \(-0.648115\pi\)
−0.448707 + 0.893679i \(0.648115\pi\)
\(350\) 8.66204e10 0.308542
\(351\) 4.20549e11 1.47888
\(352\) 8.90194e10 0.309060
\(353\) −2.22039e10 −0.0761102 −0.0380551 0.999276i \(-0.512116\pi\)
−0.0380551 + 0.999276i \(0.512116\pi\)
\(354\) −1.98888e11 −0.673123
\(355\) 5.49641e10 0.183676
\(356\) −3.13722e11 −1.03519
\(357\) 0 0
\(358\) −1.00396e12 −3.23029
\(359\) −3.21561e11 −1.02174 −0.510868 0.859659i \(-0.670676\pi\)
−0.510868 + 0.859659i \(0.670676\pi\)
\(360\) −1.77430e11 −0.556757
\(361\) 2.30550e11 0.714467
\(362\) 1.45262e11 0.444594
\(363\) 2.12909e11 0.643598
\(364\) 2.53073e11 0.755597
\(365\) 2.61829e11 0.772148
\(366\) −5.86645e11 −1.70888
\(367\) 3.84324e10 0.110586 0.0552931 0.998470i \(-0.482391\pi\)
0.0552931 + 0.998470i \(0.482391\pi\)
\(368\) −6.98105e11 −1.98429
\(369\) −1.64526e11 −0.461972
\(370\) −1.71351e11 −0.475313
\(371\) 1.18824e11 0.325629
\(372\) 5.37413e11 1.45501
\(373\) 2.79837e11 0.748540 0.374270 0.927320i \(-0.377893\pi\)
0.374270 + 0.927320i \(0.377893\pi\)
\(374\) 0 0
\(375\) −2.62581e11 −0.685682
\(376\) −6.73181e11 −1.73695
\(377\) 8.14883e11 2.07759
\(378\) −1.88501e11 −0.474899
\(379\) 2.19767e11 0.547125 0.273563 0.961854i \(-0.411798\pi\)
0.273563 + 0.961854i \(0.411798\pi\)
\(380\) 6.50885e11 1.60132
\(381\) −3.64613e10 −0.0886483
\(382\) −6.34877e11 −1.52547
\(383\) 5.65339e11 1.34250 0.671250 0.741231i \(-0.265758\pi\)
0.671250 + 0.741231i \(0.265758\pi\)
\(384\) −3.48833e11 −0.818705
\(385\) 2.05421e10 0.0476511
\(386\) −3.22311e11 −0.738978
\(387\) −2.54146e11 −0.575949
\(388\) −7.57283e11 −1.69635
\(389\) 5.16400e11 1.14344 0.571719 0.820449i \(-0.306277\pi\)
0.571719 + 0.820449i \(0.306277\pi\)
\(390\) −4.56888e11 −1.00004
\(391\) 0 0
\(392\) 9.62148e11 2.05804
\(393\) −2.70484e11 −0.571972
\(394\) 1.07726e12 2.25210
\(395\) −2.46892e11 −0.510293
\(396\) 1.75905e11 0.359460
\(397\) −2.44886e11 −0.494774 −0.247387 0.968917i \(-0.579572\pi\)
−0.247387 + 0.968917i \(0.579572\pi\)
\(398\) −1.70015e12 −3.39636
\(399\) 1.20026e11 0.237082
\(400\) −6.10779e11 −1.19293
\(401\) −5.01628e11 −0.968796 −0.484398 0.874848i \(-0.660961\pi\)
−0.484398 + 0.874848i \(0.660961\pi\)
\(402\) −2.97005e11 −0.567214
\(403\) −6.51750e11 −1.23086
\(404\) 7.87499e11 1.47073
\(405\) 9.71022e10 0.179342
\(406\) −3.65253e11 −0.667155
\(407\) 9.33928e10 0.168709
\(408\) 0 0
\(409\) 1.25612e11 0.221960 0.110980 0.993823i \(-0.464601\pi\)
0.110980 + 0.993823i \(0.464601\pi\)
\(410\) 5.66132e11 0.989442
\(411\) 4.02740e11 0.696203
\(412\) −2.01503e12 −3.44543
\(413\) −7.45488e10 −0.126086
\(414\) −5.73702e11 −0.959808
\(415\) −2.51353e11 −0.415976
\(416\) −7.42131e11 −1.21496
\(417\) 3.80437e11 0.616127
\(418\) −5.14482e11 −0.824284
\(419\) −6.58138e11 −1.04317 −0.521584 0.853200i \(-0.674659\pi\)
−0.521584 + 0.853200i \(0.674659\pi\)
\(420\) 1.41211e11 0.221435
\(421\) 2.88370e11 0.447384 0.223692 0.974660i \(-0.428189\pi\)
0.223692 + 0.974660i \(0.428189\pi\)
\(422\) 1.02148e12 1.56791
\(423\) −2.40807e11 −0.365711
\(424\) −1.92485e12 −2.89234
\(425\) 0 0
\(426\) −2.98654e11 −0.439364
\(427\) −2.19891e11 −0.320097
\(428\) −8.79072e11 −1.26627
\(429\) 2.49021e11 0.354959
\(430\) 8.74514e11 1.23356
\(431\) −3.20484e11 −0.447362 −0.223681 0.974662i \(-0.571807\pi\)
−0.223681 + 0.974662i \(0.571807\pi\)
\(432\) 1.32916e12 1.83612
\(433\) 1.13300e12 1.54894 0.774470 0.632610i \(-0.218016\pi\)
0.774470 + 0.632610i \(0.218016\pi\)
\(434\) 2.92132e11 0.395253
\(435\) 4.54693e11 0.608858
\(436\) −2.41110e12 −3.19541
\(437\) 1.15701e12 1.51765
\(438\) −1.42268e12 −1.84703
\(439\) −2.56493e11 −0.329599 −0.164799 0.986327i \(-0.552698\pi\)
−0.164799 + 0.986327i \(0.552698\pi\)
\(440\) −3.32764e11 −0.423253
\(441\) 3.44175e11 0.433317
\(442\) 0 0
\(443\) −3.11296e11 −0.384023 −0.192011 0.981393i \(-0.561501\pi\)
−0.192011 + 0.981393i \(0.561501\pi\)
\(444\) 6.42002e11 0.783995
\(445\) 2.12296e11 0.256638
\(446\) 1.39227e12 1.66616
\(447\) 6.55665e11 0.776780
\(448\) −2.74803e10 −0.0322308
\(449\) −1.40238e12 −1.62838 −0.814190 0.580598i \(-0.802819\pi\)
−0.814190 + 0.580598i \(0.802819\pi\)
\(450\) −5.01937e11 −0.577023
\(451\) −3.08563e11 −0.351196
\(452\) −2.51670e12 −2.83601
\(453\) 9.18479e11 1.02477
\(454\) 1.59392e12 1.76082
\(455\) −1.71254e11 −0.187323
\(456\) −1.94432e12 −2.10584
\(457\) 8.60205e11 0.922527 0.461263 0.887263i \(-0.347396\pi\)
0.461263 + 0.887263i \(0.347396\pi\)
\(458\) −1.29828e12 −1.37871
\(459\) 0 0
\(460\) 1.36123e12 1.41749
\(461\) 1.43574e12 1.48054 0.740272 0.672307i \(-0.234697\pi\)
0.740272 + 0.672307i \(0.234697\pi\)
\(462\) −1.11618e11 −0.113984
\(463\) 1.35035e12 1.36563 0.682814 0.730592i \(-0.260756\pi\)
0.682814 + 0.730592i \(0.260756\pi\)
\(464\) 2.57548e12 2.57945
\(465\) −3.63667e11 −0.360716
\(466\) 3.49150e12 3.42985
\(467\) 1.64014e12 1.59571 0.797857 0.602847i \(-0.205967\pi\)
0.797857 + 0.602847i \(0.205967\pi\)
\(468\) −1.46648e12 −1.41309
\(469\) −1.11326e11 −0.106247
\(470\) 8.28617e11 0.783273
\(471\) −4.70992e11 −0.440981
\(472\) 1.20762e12 1.11993
\(473\) −4.76643e11 −0.437842
\(474\) 1.34151e12 1.22066
\(475\) 1.01228e12 0.912387
\(476\) 0 0
\(477\) −6.88548e11 −0.608978
\(478\) −1.33005e12 −1.16532
\(479\) −2.75788e11 −0.239368 −0.119684 0.992812i \(-0.538188\pi\)
−0.119684 + 0.992812i \(0.538188\pi\)
\(480\) −4.14098e11 −0.356056
\(481\) −7.78591e11 −0.663218
\(482\) −9.32635e10 −0.0787046
\(483\) 2.51016e11 0.209865
\(484\) −2.35149e12 −1.94778
\(485\) 5.12453e11 0.420548
\(486\) 1.83974e12 1.49587
\(487\) 6.65187e11 0.535875 0.267937 0.963436i \(-0.413658\pi\)
0.267937 + 0.963436i \(0.413658\pi\)
\(488\) 3.56203e12 2.84321
\(489\) −6.80723e11 −0.538370
\(490\) −1.18430e12 −0.928071
\(491\) 1.08124e11 0.0839570 0.0419785 0.999119i \(-0.486634\pi\)
0.0419785 + 0.999119i \(0.486634\pi\)
\(492\) −2.12113e12 −1.63201
\(493\) 0 0
\(494\) 4.28910e12 3.24037
\(495\) −1.19035e11 −0.0891151
\(496\) −2.05989e12 −1.52818
\(497\) −1.11944e11 −0.0822992
\(498\) 1.36576e12 0.995041
\(499\) −1.19150e12 −0.860280 −0.430140 0.902762i \(-0.641536\pi\)
−0.430140 + 0.902762i \(0.641536\pi\)
\(500\) 2.90009e12 2.07514
\(501\) 1.33901e12 0.949542
\(502\) 1.74594e12 1.22705
\(503\) −2.63721e12 −1.83692 −0.918458 0.395518i \(-0.870565\pi\)
−0.918458 + 0.395518i \(0.870565\pi\)
\(504\) 3.61366e11 0.249465
\(505\) −5.32900e11 −0.364615
\(506\) −1.07596e12 −0.729656
\(507\) −9.84160e11 −0.661500
\(508\) 4.02700e11 0.268284
\(509\) 1.59065e12 1.05038 0.525189 0.850986i \(-0.323995\pi\)
0.525189 + 0.850986i \(0.323995\pi\)
\(510\) 0 0
\(511\) −5.33260e11 −0.345975
\(512\) 3.48814e12 2.24326
\(513\) −2.20290e12 −1.40432
\(514\) 6.85416e11 0.433132
\(515\) 1.36357e12 0.854169
\(516\) −3.27654e12 −2.03466
\(517\) −4.51627e11 −0.278018
\(518\) 3.48986e11 0.212973
\(519\) −4.19352e11 −0.253703
\(520\) 2.77417e12 1.66386
\(521\) 2.27882e12 1.35500 0.677501 0.735522i \(-0.263063\pi\)
0.677501 + 0.735522i \(0.263063\pi\)
\(522\) 2.11652e12 1.24769
\(523\) −4.41293e11 −0.257910 −0.128955 0.991650i \(-0.541162\pi\)
−0.128955 + 0.991650i \(0.541162\pi\)
\(524\) 2.98738e12 1.73101
\(525\) 2.19616e11 0.126168
\(526\) 7.65110e11 0.435801
\(527\) 0 0
\(528\) 7.87043e11 0.440703
\(529\) 6.18555e11 0.343422
\(530\) 2.36929e12 1.30430
\(531\) 4.31986e11 0.235800
\(532\) −1.32564e12 −0.717501
\(533\) 2.57241e12 1.38060
\(534\) −1.15353e12 −0.613895
\(535\) 5.94867e11 0.313926
\(536\) 1.80338e12 0.943725
\(537\) −2.54542e12 −1.32091
\(538\) −3.76720e12 −1.93864
\(539\) 6.45490e11 0.329412
\(540\) −2.59172e12 −1.31164
\(541\) 1.02615e12 0.515018 0.257509 0.966276i \(-0.417098\pi\)
0.257509 + 0.966276i \(0.417098\pi\)
\(542\) −4.51813e12 −2.24886
\(543\) 3.68296e11 0.181801
\(544\) 0 0
\(545\) 1.63159e12 0.792186
\(546\) 9.30530e11 0.448088
\(547\) 3.05683e12 1.45992 0.729960 0.683490i \(-0.239539\pi\)
0.729960 + 0.683490i \(0.239539\pi\)
\(548\) −4.44809e12 −2.10698
\(549\) 1.27419e12 0.598633
\(550\) −9.41367e11 −0.438659
\(551\) −4.26848e12 −1.97284
\(552\) −4.06624e12 −1.86409
\(553\) 5.02837e11 0.228646
\(554\) −5.06606e12 −2.28495
\(555\) −4.34442e11 −0.194363
\(556\) −4.20176e12 −1.86464
\(557\) 1.36756e12 0.602002 0.301001 0.953624i \(-0.402679\pi\)
0.301001 + 0.953624i \(0.402679\pi\)
\(558\) −1.69281e12 −0.739187
\(559\) 3.97364e12 1.72122
\(560\) −5.41258e11 −0.232572
\(561\) 0 0
\(562\) −3.51362e12 −1.48573
\(563\) 9.34193e11 0.391876 0.195938 0.980616i \(-0.437225\pi\)
0.195938 + 0.980616i \(0.437225\pi\)
\(564\) −3.10458e12 −1.29195
\(565\) 1.70305e12 0.703087
\(566\) −5.49631e12 −2.25111
\(567\) −1.97765e11 −0.0803573
\(568\) 1.81339e12 0.731009
\(569\) −3.19843e11 −0.127918 −0.0639589 0.997953i \(-0.520373\pi\)
−0.0639589 + 0.997953i \(0.520373\pi\)
\(570\) 2.39325e12 0.949624
\(571\) 4.20176e12 1.65413 0.827064 0.562108i \(-0.190009\pi\)
0.827064 + 0.562108i \(0.190009\pi\)
\(572\) −2.75033e12 −1.07424
\(573\) −1.60966e12 −0.623790
\(574\) −1.15302e12 −0.443338
\(575\) 2.11703e12 0.807646
\(576\) 1.59240e11 0.0602767
\(577\) −2.55609e12 −0.960029 −0.480014 0.877261i \(-0.659369\pi\)
−0.480014 + 0.877261i \(0.659369\pi\)
\(578\) 0 0
\(579\) −8.17183e11 −0.302180
\(580\) −5.02188e12 −1.84264
\(581\) 5.11923e11 0.186385
\(582\) −2.78447e12 −1.00598
\(583\) −1.29135e12 −0.462952
\(584\) 8.63833e12 3.07307
\(585\) 9.92363e11 0.350324
\(586\) 3.51754e12 1.23225
\(587\) 1.14636e12 0.398519 0.199259 0.979947i \(-0.436146\pi\)
0.199259 + 0.979947i \(0.436146\pi\)
\(588\) 4.43724e12 1.53079
\(589\) 3.41397e12 1.16880
\(590\) −1.48646e12 −0.505032
\(591\) 2.73127e12 0.920918
\(592\) −2.46077e12 −0.823425
\(593\) 3.04937e12 1.01266 0.506331 0.862339i \(-0.331002\pi\)
0.506331 + 0.862339i \(0.331002\pi\)
\(594\) 2.04858e12 0.675172
\(595\) 0 0
\(596\) −7.24154e12 −2.35084
\(597\) −4.31055e12 −1.38883
\(598\) 8.96999e12 2.86838
\(599\) −3.29572e12 −1.04599 −0.522997 0.852334i \(-0.675186\pi\)
−0.522997 + 0.852334i \(0.675186\pi\)
\(600\) −3.55759e12 −1.12066
\(601\) 7.69804e11 0.240683 0.120341 0.992733i \(-0.461601\pi\)
0.120341 + 0.992733i \(0.461601\pi\)
\(602\) −1.78110e12 −0.552717
\(603\) 6.45097e11 0.198700
\(604\) −1.01442e13 −3.10136
\(605\) 1.59125e12 0.482880
\(606\) 2.89557e12 0.872183
\(607\) −1.60628e12 −0.480255 −0.240127 0.970741i \(-0.577189\pi\)
−0.240127 + 0.970741i \(0.577189\pi\)
\(608\) 3.88740e12 1.15370
\(609\) −9.26058e11 −0.272810
\(610\) −4.38450e12 −1.28214
\(611\) 3.76509e12 1.09292
\(612\) 0 0
\(613\) −4.16207e12 −1.19052 −0.595261 0.803533i \(-0.702951\pi\)
−0.595261 + 0.803533i \(0.702951\pi\)
\(614\) −7.22661e12 −2.05200
\(615\) 1.43536e12 0.404599
\(616\) 6.77731e11 0.189646
\(617\) 3.92295e12 1.08976 0.544879 0.838515i \(-0.316576\pi\)
0.544879 + 0.838515i \(0.316576\pi\)
\(618\) −7.40909e12 −2.04323
\(619\) −1.03693e12 −0.283885 −0.141943 0.989875i \(-0.545335\pi\)
−0.141943 + 0.989875i \(0.545335\pi\)
\(620\) 4.01654e12 1.09167
\(621\) −4.60702e12 −1.24311
\(622\) 2.91407e12 0.780626
\(623\) −4.32376e11 −0.114991
\(624\) −6.56137e12 −1.73246
\(625\) 6.95630e11 0.182355
\(626\) 1.07777e13 2.80505
\(627\) −1.30441e12 −0.337063
\(628\) 5.20190e12 1.33458
\(629\) 0 0
\(630\) −4.44805e11 −0.112496
\(631\) −4.47475e12 −1.12366 −0.561832 0.827251i \(-0.689903\pi\)
−0.561832 + 0.827251i \(0.689903\pi\)
\(632\) −8.14551e12 −2.03091
\(633\) 2.58984e12 0.641145
\(634\) −3.06391e11 −0.0753138
\(635\) −2.72507e11 −0.0665113
\(636\) −8.87702e12 −2.15135
\(637\) −5.38128e12 −1.29496
\(638\) 3.96947e12 0.948504
\(639\) 6.48677e11 0.153913
\(640\) −2.60713e12 −0.614261
\(641\) −7.27990e10 −0.0170319 −0.00851597 0.999964i \(-0.502711\pi\)
−0.00851597 + 0.999964i \(0.502711\pi\)
\(642\) −3.23228e12 −0.750932
\(643\) 1.86086e11 0.0429303 0.0214652 0.999770i \(-0.493167\pi\)
0.0214652 + 0.999770i \(0.493167\pi\)
\(644\) −2.77237e12 −0.635132
\(645\) 2.21723e12 0.504421
\(646\) 0 0
\(647\) 2.89537e12 0.649583 0.324791 0.945786i \(-0.394706\pi\)
0.324791 + 0.945786i \(0.394706\pi\)
\(648\) 3.20361e12 0.713761
\(649\) 8.10176e11 0.179258
\(650\) 7.84793e12 1.72443
\(651\) 7.40668e11 0.161625
\(652\) 7.51830e12 1.62932
\(653\) 4.46865e12 0.961761 0.480880 0.876786i \(-0.340317\pi\)
0.480880 + 0.876786i \(0.340317\pi\)
\(654\) −8.86544e12 −1.89496
\(655\) −2.02156e12 −0.429141
\(656\) 8.13022e12 1.71409
\(657\) 3.09007e12 0.647029
\(658\) −1.68762e12 −0.350960
\(659\) 4.32558e12 0.893429 0.446714 0.894677i \(-0.352594\pi\)
0.446714 + 0.894677i \(0.352594\pi\)
\(660\) −1.53464e12 −0.314818
\(661\) −3.49165e12 −0.711417 −0.355709 0.934597i \(-0.615760\pi\)
−0.355709 + 0.934597i \(0.615760\pi\)
\(662\) −1.07021e13 −2.16575
\(663\) 0 0
\(664\) −8.29269e12 −1.65554
\(665\) 8.97058e11 0.177878
\(666\) −2.02226e12 −0.398293
\(667\) −8.92687e12 −1.74636
\(668\) −1.47888e13 −2.87368
\(669\) 3.52995e12 0.681319
\(670\) −2.21977e12 −0.425571
\(671\) 2.38971e12 0.455087
\(672\) 8.43381e11 0.159537
\(673\) −7.03831e12 −1.32251 −0.661257 0.750159i \(-0.729977\pi\)
−0.661257 + 0.750159i \(0.729977\pi\)
\(674\) 3.76374e12 0.702507
\(675\) −4.03073e12 −0.747337
\(676\) 1.08696e13 2.00196
\(677\) −5.38586e12 −0.985385 −0.492692 0.870203i \(-0.663987\pi\)
−0.492692 + 0.870203i \(0.663987\pi\)
\(678\) −9.25370e12 −1.68183
\(679\) −1.04370e12 −0.188434
\(680\) 0 0
\(681\) 4.04120e12 0.720026
\(682\) −3.17481e12 −0.561938
\(683\) −3.57812e12 −0.629162 −0.314581 0.949231i \(-0.601864\pi\)
−0.314581 + 0.949231i \(0.601864\pi\)
\(684\) 7.68164e12 1.34184
\(685\) 3.01001e12 0.522349
\(686\) 4.98041e12 0.858631
\(687\) −3.29165e12 −0.563778
\(688\) 1.25589e13 2.13699
\(689\) 1.07656e13 1.81993
\(690\) 5.00512e12 0.840608
\(691\) 9.36146e12 1.56204 0.781020 0.624505i \(-0.214699\pi\)
0.781020 + 0.624505i \(0.214699\pi\)
\(692\) 4.63157e12 0.767804
\(693\) 2.42435e11 0.0399297
\(694\) 6.76234e12 1.10657
\(695\) 2.84333e12 0.462270
\(696\) 1.50013e13 2.42319
\(697\) 0 0
\(698\) 1.01004e13 1.61061
\(699\) 8.85231e12 1.40252
\(700\) −2.42557e12 −0.381832
\(701\) 7.85905e12 1.22925 0.614624 0.788821i \(-0.289308\pi\)
0.614624 + 0.788821i \(0.289308\pi\)
\(702\) −1.70785e13 −2.65419
\(703\) 4.07838e12 0.629780
\(704\) 2.98649e11 0.0458230
\(705\) 2.10087e12 0.320293
\(706\) 9.01701e11 0.136597
\(707\) 1.08534e12 0.163372
\(708\) 5.56932e12 0.833015
\(709\) 7.23260e12 1.07495 0.537473 0.843281i \(-0.319379\pi\)
0.537473 + 0.843281i \(0.319379\pi\)
\(710\) −2.23209e12 −0.329647
\(711\) −2.91378e12 −0.427605
\(712\) 7.00410e12 1.02139
\(713\) 7.13978e12 1.03462
\(714\) 0 0
\(715\) 1.86115e12 0.266320
\(716\) 2.81131e13 3.99760
\(717\) −3.37221e12 −0.476516
\(718\) 1.30586e13 1.83374
\(719\) 3.43266e12 0.479016 0.239508 0.970894i \(-0.423014\pi\)
0.239508 + 0.970894i \(0.423014\pi\)
\(720\) 3.13641e12 0.434948
\(721\) −2.77713e12 −0.382726
\(722\) −9.36262e12 −1.28227
\(723\) −2.36459e11 −0.0321836
\(724\) −4.06767e12 −0.550202
\(725\) −7.81021e12 −1.04988
\(726\) −8.64624e12 −1.15508
\(727\) −4.17490e12 −0.554295 −0.277148 0.960827i \(-0.589389\pi\)
−0.277148 + 0.960827i \(0.589389\pi\)
\(728\) −5.65006e12 −0.745525
\(729\) 7.14815e12 0.937389
\(730\) −1.06329e13 −1.38579
\(731\) 0 0
\(732\) 1.64274e13 2.11480
\(733\) 5.29693e11 0.0677729 0.0338865 0.999426i \(-0.489212\pi\)
0.0338865 + 0.999426i \(0.489212\pi\)
\(734\) −1.56074e12 −0.198472
\(735\) −3.00267e12 −0.379503
\(736\) 8.12990e12 1.02126
\(737\) 1.20986e12 0.151054
\(738\) 6.68139e12 0.829112
\(739\) 4.99613e12 0.616217 0.308109 0.951351i \(-0.400304\pi\)
0.308109 + 0.951351i \(0.400304\pi\)
\(740\) 4.79823e12 0.588218
\(741\) 1.08745e13 1.32504
\(742\) −4.82546e12 −0.584414
\(743\) 4.24607e12 0.511138 0.255569 0.966791i \(-0.417737\pi\)
0.255569 + 0.966791i \(0.417737\pi\)
\(744\) −1.19982e13 −1.43561
\(745\) 4.90034e12 0.582805
\(746\) −1.13642e13 −1.34342
\(747\) −2.96643e12 −0.348571
\(748\) 0 0
\(749\) −1.21155e12 −0.140660
\(750\) 1.06634e13 1.23061
\(751\) −1.61654e13 −1.85441 −0.927204 0.374556i \(-0.877795\pi\)
−0.927204 + 0.374556i \(0.877795\pi\)
\(752\) 1.18998e13 1.35693
\(753\) 4.42665e12 0.501762
\(754\) −3.30924e13 −3.72870
\(755\) 6.86457e12 0.768869
\(756\) 5.27847e12 0.587706
\(757\) −1.65437e13 −1.83106 −0.915528 0.402254i \(-0.868227\pi\)
−0.915528 + 0.402254i \(0.868227\pi\)
\(758\) −8.92476e12 −0.981940
\(759\) −2.72797e12 −0.298368
\(760\) −1.45315e13 −1.57998
\(761\) 4.75009e12 0.513418 0.256709 0.966489i \(-0.417362\pi\)
0.256709 + 0.966489i \(0.417362\pi\)
\(762\) 1.48070e12 0.159099
\(763\) −3.32301e12 −0.354954
\(764\) 1.77780e13 1.88783
\(765\) 0 0
\(766\) −2.29584e13 −2.40942
\(767\) −6.75422e12 −0.704687
\(768\) 1.32418e13 1.37348
\(769\) −9.86330e12 −1.01708 −0.508538 0.861039i \(-0.669814\pi\)
−0.508538 + 0.861039i \(0.669814\pi\)
\(770\) −8.34217e11 −0.0855206
\(771\) 1.73780e12 0.177114
\(772\) 9.02543e12 0.914514
\(773\) −3.02810e12 −0.305044 −0.152522 0.988300i \(-0.548740\pi\)
−0.152522 + 0.988300i \(0.548740\pi\)
\(774\) 1.03209e13 1.03367
\(775\) 6.24667e12 0.622000
\(776\) 1.69069e13 1.67374
\(777\) 8.84815e11 0.0870879
\(778\) −2.09710e13 −2.05216
\(779\) −1.34747e13 −1.31099
\(780\) 1.27939e13 1.23759
\(781\) 1.21657e12 0.117006
\(782\) 0 0
\(783\) 1.69964e13 1.61595
\(784\) −1.70078e13 −1.60778
\(785\) −3.52012e12 −0.330860
\(786\) 1.09844e13 1.02653
\(787\) 1.11143e13 1.03275 0.516374 0.856363i \(-0.327281\pi\)
0.516374 + 0.856363i \(0.327281\pi\)
\(788\) −3.01657e13 −2.78706
\(789\) 1.93985e12 0.178206
\(790\) 1.00263e13 0.915837
\(791\) −3.46854e12 −0.315031
\(792\) −3.92723e12 −0.354669
\(793\) −1.99224e13 −1.78901
\(794\) 9.94483e12 0.887984
\(795\) 6.00707e12 0.533348
\(796\) 4.76082e13 4.20313
\(797\) 8.24068e12 0.723437 0.361718 0.932287i \(-0.382190\pi\)
0.361718 + 0.932287i \(0.382190\pi\)
\(798\) −4.87426e12 −0.425497
\(799\) 0 0
\(800\) 7.11293e12 0.613965
\(801\) 2.50548e12 0.215052
\(802\) 2.03711e13 1.73872
\(803\) 5.79532e12 0.491878
\(804\) 8.31683e12 0.701949
\(805\) 1.87606e12 0.157458
\(806\) 2.64676e13 2.20905
\(807\) −9.55131e12 −0.792742
\(808\) −1.75815e13 −1.45113
\(809\) 6.01180e12 0.493442 0.246721 0.969087i \(-0.420647\pi\)
0.246721 + 0.969087i \(0.420647\pi\)
\(810\) −3.94332e12 −0.321869
\(811\) −1.46588e13 −1.18989 −0.594943 0.803768i \(-0.702825\pi\)
−0.594943 + 0.803768i \(0.702825\pi\)
\(812\) 1.02279e13 0.825629
\(813\) −1.14552e13 −0.919594
\(814\) −3.79268e12 −0.302787
\(815\) −5.08762e12 −0.403930
\(816\) 0 0
\(817\) −2.08146e13 −1.63444
\(818\) −5.10109e12 −0.398357
\(819\) −2.02112e12 −0.156969
\(820\) −1.58530e13 −1.22447
\(821\) −1.36762e13 −1.05056 −0.525280 0.850929i \(-0.676040\pi\)
−0.525280 + 0.850929i \(0.676040\pi\)
\(822\) −1.63553e13 −1.24949
\(823\) 1.23214e13 0.936180 0.468090 0.883681i \(-0.344942\pi\)
0.468090 + 0.883681i \(0.344942\pi\)
\(824\) 4.49871e13 3.39950
\(825\) −2.38673e12 −0.179375
\(826\) 3.02743e12 0.226289
\(827\) −1.87511e13 −1.39397 −0.696983 0.717088i \(-0.745475\pi\)
−0.696983 + 0.717088i \(0.745475\pi\)
\(828\) 1.60650e13 1.18780
\(829\) 6.45929e12 0.474995 0.237498 0.971388i \(-0.423673\pi\)
0.237498 + 0.971388i \(0.423673\pi\)
\(830\) 1.02075e13 0.746562
\(831\) −1.28444e13 −0.934351
\(832\) −2.48976e12 −0.180136
\(833\) 0 0
\(834\) −1.54495e13 −1.10578
\(835\) 1.00076e13 0.712425
\(836\) 1.44067e13 1.02008
\(837\) −1.35939e13 −0.957366
\(838\) 2.67270e13 1.87220
\(839\) 2.06836e13 1.44111 0.720557 0.693396i \(-0.243886\pi\)
0.720557 + 0.693396i \(0.243886\pi\)
\(840\) −3.15265e12 −0.218484
\(841\) 1.84262e13 1.27015
\(842\) −1.17107e13 −0.802931
\(843\) −8.90839e12 −0.607541
\(844\) −2.86037e13 −1.94035
\(845\) −7.35547e12 −0.496312
\(846\) 9.77919e12 0.656351
\(847\) −3.24085e12 −0.216363
\(848\) 3.40253e13 2.25955
\(849\) −1.39353e13 −0.920515
\(850\) 0 0
\(851\) 8.52930e12 0.557482
\(852\) 8.36298e12 0.543730
\(853\) −2.64082e12 −0.170793 −0.0853963 0.996347i \(-0.527216\pi\)
−0.0853963 + 0.996347i \(0.527216\pi\)
\(854\) 8.92977e12 0.574486
\(855\) −5.19816e12 −0.332661
\(856\) 1.96260e13 1.24939
\(857\) 1.71578e13 1.08654 0.543272 0.839557i \(-0.317185\pi\)
0.543272 + 0.839557i \(0.317185\pi\)
\(858\) −1.01127e13 −0.637054
\(859\) 8.08574e12 0.506700 0.253350 0.967375i \(-0.418468\pi\)
0.253350 + 0.967375i \(0.418468\pi\)
\(860\) −2.44884e13 −1.52657
\(861\) −2.92336e12 −0.181288
\(862\) 1.30149e13 0.802893
\(863\) −1.72986e13 −1.06161 −0.530803 0.847495i \(-0.678109\pi\)
−0.530803 + 0.847495i \(0.678109\pi\)
\(864\) −1.54790e13 −0.944998
\(865\) −3.13418e12 −0.190349
\(866\) −4.60112e13 −2.77992
\(867\) 0 0
\(868\) −8.18037e12 −0.489141
\(869\) −5.46469e12 −0.325070
\(870\) −1.84651e13 −1.09273
\(871\) −1.00863e13 −0.593812
\(872\) 5.38298e13 3.15282
\(873\) 6.04788e12 0.352403
\(874\) −4.69862e13 −2.72376
\(875\) 3.99694e12 0.230511
\(876\) 3.98383e13 2.28577
\(877\) 1.81609e12 0.103666 0.0518332 0.998656i \(-0.483494\pi\)
0.0518332 + 0.998656i \(0.483494\pi\)
\(878\) 1.04162e13 0.591540
\(879\) 8.91833e12 0.503887
\(880\) 5.88224e12 0.330652
\(881\) −3.76167e12 −0.210372 −0.105186 0.994453i \(-0.533544\pi\)
−0.105186 + 0.994453i \(0.533544\pi\)
\(882\) −1.39770e13 −0.777686
\(883\) 3.03716e13 1.68130 0.840649 0.541581i \(-0.182174\pi\)
0.840649 + 0.541581i \(0.182174\pi\)
\(884\) 0 0
\(885\) −3.76875e12 −0.206516
\(886\) 1.26417e13 0.689215
\(887\) −8.30135e12 −0.450290 −0.225145 0.974325i \(-0.572286\pi\)
−0.225145 + 0.974325i \(0.572286\pi\)
\(888\) −1.43332e13 −0.773544
\(889\) 5.55006e11 0.0298016
\(890\) −8.62133e12 −0.460595
\(891\) 2.14925e12 0.114245
\(892\) −3.89868e13 −2.06194
\(893\) −1.97221e13 −1.03782
\(894\) −2.66266e13 −1.39411
\(895\) −1.90241e13 −0.991060
\(896\) 5.30986e12 0.275231
\(897\) 2.27424e13 1.17293
\(898\) 5.69505e13 2.92250
\(899\) −2.63403e13 −1.34494
\(900\) 1.40554e13 0.714088
\(901\) 0 0
\(902\) 1.25307e13 0.630300
\(903\) −4.51577e12 −0.226015
\(904\) 5.61873e13 2.79821
\(905\) 2.75259e12 0.136402
\(906\) −3.72994e13 −1.83918
\(907\) 1.31615e13 0.645763 0.322882 0.946439i \(-0.395348\pi\)
0.322882 + 0.946439i \(0.395348\pi\)
\(908\) −4.46333e13 −2.17908
\(909\) −6.28919e12 −0.305533
\(910\) 6.95465e12 0.336193
\(911\) 2.85075e13 1.37128 0.685641 0.727940i \(-0.259522\pi\)
0.685641 + 0.727940i \(0.259522\pi\)
\(912\) 3.43695e13 1.64512
\(913\) −5.56344e12 −0.264987
\(914\) −3.49329e13 −1.65568
\(915\) −1.11164e13 −0.524287
\(916\) 3.63549e13 1.70621
\(917\) 4.11724e12 0.192284
\(918\) 0 0
\(919\) 2.80490e13 1.29717 0.648585 0.761142i \(-0.275361\pi\)
0.648585 + 0.761142i \(0.275361\pi\)
\(920\) −3.03904e13 −1.39859
\(921\) −1.83223e13 −0.839094
\(922\) −5.83054e13 −2.65717
\(923\) −1.01422e13 −0.459967
\(924\) 3.12556e12 0.141060
\(925\) 7.46237e12 0.335150
\(926\) −5.48378e13 −2.45093
\(927\) 1.60926e13 0.715759
\(928\) −2.99931e13 −1.32756
\(929\) 3.51380e13 1.54777 0.773886 0.633325i \(-0.218310\pi\)
0.773886 + 0.633325i \(0.218310\pi\)
\(930\) 1.47685e13 0.647386
\(931\) 2.81880e13 1.22967
\(932\) −9.77700e13 −4.24457
\(933\) 7.38830e12 0.319210
\(934\) −6.66061e13 −2.86387
\(935\) 0 0
\(936\) 3.27403e13 1.39425
\(937\) −4.23191e12 −0.179353 −0.0896765 0.995971i \(-0.528583\pi\)
−0.0896765 + 0.995971i \(0.528583\pi\)
\(938\) 4.52094e12 0.190685
\(939\) 2.73256e13 1.14703
\(940\) −2.32032e13 −0.969331
\(941\) −2.94937e13 −1.22624 −0.613121 0.789989i \(-0.710086\pi\)
−0.613121 + 0.789989i \(0.710086\pi\)
\(942\) 1.91270e13 0.791439
\(943\) −2.81802e13 −1.16049
\(944\) −2.13470e13 −0.874910
\(945\) −3.57194e12 −0.145700
\(946\) 1.93565e13 0.785807
\(947\) −4.70153e12 −0.189961 −0.0949805 0.995479i \(-0.530279\pi\)
−0.0949805 + 0.995479i \(0.530279\pi\)
\(948\) −3.75655e13 −1.51061
\(949\) −4.83141e13 −1.93364
\(950\) −4.11087e13 −1.63749
\(951\) −7.76821e11 −0.0307970
\(952\) 0 0
\(953\) 8.96893e12 0.352227 0.176114 0.984370i \(-0.443647\pi\)
0.176114 + 0.984370i \(0.443647\pi\)
\(954\) 2.79619e13 1.09295
\(955\) −1.20304e13 −0.468019
\(956\) 3.72446e13 1.44212
\(957\) 1.00641e13 0.387858
\(958\) 1.11998e13 0.429600
\(959\) −6.13040e12 −0.234048
\(960\) −1.38925e12 −0.0527909
\(961\) −5.37241e12 −0.203195
\(962\) 3.16186e13 1.19030
\(963\) 7.02052e12 0.263058
\(964\) 2.61159e12 0.0973999
\(965\) −6.10750e12 −0.226720
\(966\) −1.01938e13 −0.376650
\(967\) 2.26056e13 0.831375 0.415688 0.909507i \(-0.363541\pi\)
0.415688 + 0.909507i \(0.363541\pi\)
\(968\) 5.24989e13 1.92181
\(969\) 0 0
\(970\) −2.08107e13 −0.754769
\(971\) −2.62758e12 −0.0948569 −0.0474284 0.998875i \(-0.515103\pi\)
−0.0474284 + 0.998875i \(0.515103\pi\)
\(972\) −5.15169e13 −1.85119
\(973\) −5.79092e12 −0.207128
\(974\) −2.70132e13 −0.961748
\(975\) 1.98976e13 0.705146
\(976\) −6.29657e13 −2.22116
\(977\) −4.61018e13 −1.61880 −0.809399 0.587260i \(-0.800207\pi\)
−0.809399 + 0.587260i \(0.800207\pi\)
\(978\) 2.76442e13 0.966226
\(979\) 4.69894e12 0.163485
\(980\) 3.31632e13 1.14852
\(981\) 1.92558e13 0.663820
\(982\) −4.39093e12 −0.150680
\(983\) −3.21788e13 −1.09921 −0.549603 0.835426i \(-0.685221\pi\)
−0.549603 + 0.835426i \(0.685221\pi\)
\(984\) 4.73559e13 1.61026
\(985\) 2.04131e13 0.690949
\(986\) 0 0
\(987\) −4.27877e12 −0.143513
\(988\) −1.20105e14 −4.01008
\(989\) −4.35304e13 −1.44680
\(990\) 4.83401e12 0.159937
\(991\) 4.93442e13 1.62519 0.812595 0.582828i \(-0.198054\pi\)
0.812595 + 0.582828i \(0.198054\pi\)
\(992\) 2.39887e13 0.786511
\(993\) −2.71340e13 −0.885609
\(994\) 4.54603e12 0.147705
\(995\) −3.22164e13 −1.04201
\(996\) −3.82443e13 −1.23140
\(997\) −3.09242e13 −0.991222 −0.495611 0.868545i \(-0.665056\pi\)
−0.495611 + 0.868545i \(0.665056\pi\)
\(998\) 4.83866e13 1.54397
\(999\) −1.62394e13 −0.515853
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.i.1.3 52
17.5 odd 16 17.10.d.a.8.13 52
17.7 odd 16 17.10.d.a.15.13 yes 52
17.16 even 2 inner 289.10.a.i.1.4 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.d.a.8.13 52 17.5 odd 16
17.10.d.a.15.13 yes 52 17.7 odd 16
289.10.a.i.1.3 52 1.1 even 1 trivial
289.10.a.i.1.4 52 17.16 even 2 inner