Properties

Label 289.10.a.h.1.8
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
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: \(0\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-26.9492 q^{2} +20.4039 q^{3} +214.258 q^{4} +1220.88 q^{5} -549.868 q^{6} -4892.40 q^{7} +8023.91 q^{8} -19266.7 q^{9} +O(q^{10})\) \(q-26.9492 q^{2} +20.4039 q^{3} +214.258 q^{4} +1220.88 q^{5} -549.868 q^{6} -4892.40 q^{7} +8023.91 q^{8} -19266.7 q^{9} -32901.7 q^{10} +90391.9 q^{11} +4371.69 q^{12} +114220. q^{13} +131846. q^{14} +24910.7 q^{15} -325938. q^{16} +519221. q^{18} +864034. q^{19} +261583. q^{20} -99824.0 q^{21} -2.43599e6 q^{22} +1.60148e6 q^{23} +163719. q^{24} -462573. q^{25} -3.07812e6 q^{26} -794725. q^{27} -1.04823e6 q^{28} +1.73683e6 q^{29} -671323. q^{30} -1.24125e6 q^{31} +4.67550e6 q^{32} +1.84435e6 q^{33} -5.97305e6 q^{35} -4.12803e6 q^{36} -762881. q^{37} -2.32850e7 q^{38} +2.33052e6 q^{39} +9.79625e6 q^{40} +2.60499e7 q^{41} +2.69017e6 q^{42} +4.19945e7 q^{43} +1.93672e7 q^{44} -2.35223e7 q^{45} -4.31586e7 q^{46} +1.74865e7 q^{47} -6.65039e6 q^{48} -1.64180e7 q^{49} +1.24659e7 q^{50} +2.44724e7 q^{52} +3.19270e7 q^{53} +2.14172e7 q^{54} +1.10358e8 q^{55} -3.92562e7 q^{56} +1.76296e7 q^{57} -4.68062e7 q^{58} -8.87378e7 q^{59} +5.33731e6 q^{60} +8.13726e7 q^{61} +3.34507e7 q^{62} +9.42604e7 q^{63} +4.08791e7 q^{64} +1.39449e8 q^{65} -4.97036e7 q^{66} +1.53073e8 q^{67} +3.26764e7 q^{69} +1.60969e8 q^{70} -3.08494e8 q^{71} -1.54594e8 q^{72} -2.12590e8 q^{73} +2.05590e7 q^{74} -9.43827e6 q^{75} +1.85126e8 q^{76} -4.42234e8 q^{77} -6.28057e7 q^{78} -3.93764e8 q^{79} -3.97931e8 q^{80} +3.63011e8 q^{81} -7.02024e8 q^{82} -6.17768e8 q^{83} -2.13881e7 q^{84} -1.13172e9 q^{86} +3.54381e7 q^{87} +7.25296e8 q^{88} +7.46742e8 q^{89} +6.33908e8 q^{90} -5.58808e8 q^{91} +3.43129e8 q^{92} -2.53264e7 q^{93} -4.71248e8 q^{94} +1.05488e9 q^{95} +9.53984e7 q^{96} +1.98363e7 q^{97} +4.42452e8 q^{98} -1.74155e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + 60000q^{10} + 76902q^{11} + 373248q^{12} + 54216q^{13} + 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} + 6439479q^{20} - 138102q^{21} + 267324q^{22} + 4041462q^{23} + 7653888q^{24} + 16582356q^{25} + 15822744q^{26} + 13281612q^{27} + 18614784q^{28} + 4005936q^{29} + 22471686q^{30} + 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} + 22076682q^{37} - 27401376q^{38} + 62736162q^{39} - 12231630q^{40} + 59641782q^{41} + 150001536q^{42} - 47951586q^{43} - 49578936q^{44} + 129308238q^{45} + 140524827q^{46} - 118557912q^{47} + 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} + 209848575q^{54} - 365439924q^{55} + 203095059q^{56} - 4614108q^{57} - 179071413q^{58} + 343015128q^{59} + 427179186q^{60} + 175597116q^{61} + 720602571q^{62} + 587415936q^{63} + 853082511q^{64} + 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} + 1308709542q^{71} - 275337849q^{72} + 494841342q^{73} + 1545361890q^{74} + 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} + 2270624538q^{78} + 1980107868q^{79} + 2897000199q^{80} + 1598298840q^{81} + 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} - 2705904618q^{88} + 148394658q^{89} + 117916215q^{90} + 636340896q^{91} - 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} + 4878626298q^{95} - 8390096634q^{96} - 891786822q^{97} + 4285627647q^{98} - 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −26.9492 −1.19100 −0.595498 0.803357i \(-0.703045\pi\)
−0.595498 + 0.803357i \(0.703045\pi\)
\(3\) 20.4039 0.145434 0.0727172 0.997353i \(-0.476833\pi\)
0.0727172 + 0.997353i \(0.476833\pi\)
\(4\) 214.258 0.418472
\(5\) 1220.88 0.873592 0.436796 0.899561i \(-0.356113\pi\)
0.436796 + 0.899561i \(0.356113\pi\)
\(6\) −549.868 −0.173212
\(7\) −4892.40 −0.770160 −0.385080 0.922883i \(-0.625826\pi\)
−0.385080 + 0.922883i \(0.625826\pi\)
\(8\) 8023.91 0.692598
\(9\) −19266.7 −0.978849
\(10\) −32901.7 −1.04044
\(11\) 90391.9 1.86150 0.930749 0.365659i \(-0.119156\pi\)
0.930749 + 0.365659i \(0.119156\pi\)
\(12\) 4371.69 0.0608602
\(13\) 114220. 1.10916 0.554582 0.832129i \(-0.312878\pi\)
0.554582 + 0.832129i \(0.312878\pi\)
\(14\) 131846. 0.917258
\(15\) 24910.7 0.127050
\(16\) −325938. −1.24335
\(17\) 0 0
\(18\) 519221. 1.16581
\(19\) 864034. 1.52104 0.760518 0.649317i \(-0.224945\pi\)
0.760518 + 0.649317i \(0.224945\pi\)
\(20\) 261583. 0.365574
\(21\) −99824.0 −0.112008
\(22\) −2.43599e6 −2.21704
\(23\) 1.60148e6 1.19329 0.596646 0.802505i \(-0.296500\pi\)
0.596646 + 0.802505i \(0.296500\pi\)
\(24\) 163719. 0.100728
\(25\) −462573. −0.236837
\(26\) −3.07812e6 −1.32101
\(27\) −794725. −0.287793
\(28\) −1.04823e6 −0.322290
\(29\) 1.73683e6 0.456002 0.228001 0.973661i \(-0.426781\pi\)
0.228001 + 0.973661i \(0.426781\pi\)
\(30\) −671323. −0.151316
\(31\) −1.24125e6 −0.241397 −0.120699 0.992689i \(-0.538513\pi\)
−0.120699 + 0.992689i \(0.538513\pi\)
\(32\) 4.67550e6 0.788231
\(33\) 1.84435e6 0.270726
\(34\) 0 0
\(35\) −5.97305e6 −0.672806
\(36\) −4.12803e6 −0.409621
\(37\) −762881. −0.0669189 −0.0334595 0.999440i \(-0.510652\pi\)
−0.0334595 + 0.999440i \(0.510652\pi\)
\(38\) −2.32850e7 −1.81155
\(39\) 2.33052e6 0.161311
\(40\) 9.79625e6 0.605048
\(41\) 2.60499e7 1.43972 0.719862 0.694117i \(-0.244205\pi\)
0.719862 + 0.694117i \(0.244205\pi\)
\(42\) 2.69017e6 0.133401
\(43\) 4.19945e7 1.87320 0.936599 0.350402i \(-0.113955\pi\)
0.936599 + 0.350402i \(0.113955\pi\)
\(44\) 1.93672e7 0.778984
\(45\) −2.35223e7 −0.855114
\(46\) −4.31586e7 −1.42121
\(47\) 1.74865e7 0.522713 0.261357 0.965242i \(-0.415830\pi\)
0.261357 + 0.965242i \(0.415830\pi\)
\(48\) −6.65039e6 −0.180826
\(49\) −1.64180e7 −0.406853
\(50\) 1.24659e7 0.282072
\(51\) 0 0
\(52\) 2.44724e7 0.464154
\(53\) 3.19270e7 0.555797 0.277898 0.960610i \(-0.410362\pi\)
0.277898 + 0.960610i \(0.410362\pi\)
\(54\) 2.14172e7 0.342760
\(55\) 1.10358e8 1.62619
\(56\) −3.92562e7 −0.533411
\(57\) 1.76296e7 0.221211
\(58\) −4.68062e7 −0.543097
\(59\) −8.87378e7 −0.953398 −0.476699 0.879066i \(-0.658167\pi\)
−0.476699 + 0.879066i \(0.658167\pi\)
\(60\) 5.33731e6 0.0531670
\(61\) 8.13726e7 0.752478 0.376239 0.926523i \(-0.377217\pi\)
0.376239 + 0.926523i \(0.377217\pi\)
\(62\) 3.34507e7 0.287503
\(63\) 9.42604e7 0.753870
\(64\) 4.08791e7 0.304573
\(65\) 1.39449e8 0.968956
\(66\) −4.97036e7 −0.322433
\(67\) 1.53073e8 0.928027 0.464014 0.885828i \(-0.346409\pi\)
0.464014 + 0.885828i \(0.346409\pi\)
\(68\) 0 0
\(69\) 3.26764e7 0.173546
\(70\) 1.60969e8 0.801309
\(71\) −3.08494e8 −1.44074 −0.720368 0.693593i \(-0.756027\pi\)
−0.720368 + 0.693593i \(0.756027\pi\)
\(72\) −1.54594e8 −0.677948
\(73\) −2.12590e8 −0.876173 −0.438086 0.898933i \(-0.644344\pi\)
−0.438086 + 0.898933i \(0.644344\pi\)
\(74\) 2.05590e7 0.0797002
\(75\) −9.43827e6 −0.0344443
\(76\) 1.85126e8 0.636511
\(77\) −4.42234e8 −1.43365
\(78\) −6.28057e7 −0.192120
\(79\) −3.93764e8 −1.13740 −0.568702 0.822544i \(-0.692554\pi\)
−0.568702 + 0.822544i \(0.692554\pi\)
\(80\) −3.97931e8 −1.08618
\(81\) 3.63011e8 0.936994
\(82\) −7.02024e8 −1.71471
\(83\) −6.17768e8 −1.42881 −0.714404 0.699734i \(-0.753302\pi\)
−0.714404 + 0.699734i \(0.753302\pi\)
\(84\) −2.13881e7 −0.0468721
\(85\) 0 0
\(86\) −1.13172e9 −2.23097
\(87\) 3.54381e7 0.0663184
\(88\) 7.25296e8 1.28927
\(89\) 7.46742e8 1.26158 0.630791 0.775953i \(-0.282730\pi\)
0.630791 + 0.775953i \(0.282730\pi\)
\(90\) 6.33908e8 1.01844
\(91\) −5.58808e8 −0.854233
\(92\) 3.43129e8 0.499359
\(93\) −2.53264e7 −0.0351075
\(94\) −4.71248e8 −0.622549
\(95\) 1.05488e9 1.32876
\(96\) 9.53984e7 0.114636
\(97\) 1.98363e7 0.0227503 0.0113751 0.999935i \(-0.496379\pi\)
0.0113751 + 0.999935i \(0.496379\pi\)
\(98\) 4.42452e8 0.484561
\(99\) −1.74155e9 −1.82212
\(100\) −9.91097e7 −0.0991097
\(101\) −5.44823e8 −0.520966 −0.260483 0.965478i \(-0.583882\pi\)
−0.260483 + 0.965478i \(0.583882\pi\)
\(102\) 0 0
\(103\) 1.08729e9 0.951871 0.475935 0.879480i \(-0.342110\pi\)
0.475935 + 0.879480i \(0.342110\pi\)
\(104\) 9.16488e8 0.768204
\(105\) −1.21873e8 −0.0978491
\(106\) −8.60405e8 −0.661952
\(107\) −9.36864e8 −0.690955 −0.345477 0.938427i \(-0.612283\pi\)
−0.345477 + 0.938427i \(0.612283\pi\)
\(108\) −1.70276e8 −0.120433
\(109\) −2.94426e8 −0.199782 −0.0998910 0.994998i \(-0.531849\pi\)
−0.0998910 + 0.994998i \(0.531849\pi\)
\(110\) −2.97405e9 −1.93679
\(111\) −1.55657e7 −0.00973231
\(112\) 1.59462e9 0.957581
\(113\) −1.06461e9 −0.614237 −0.307119 0.951671i \(-0.599365\pi\)
−0.307119 + 0.951671i \(0.599365\pi\)
\(114\) −4.75104e8 −0.263461
\(115\) 1.95522e9 1.04245
\(116\) 3.72129e8 0.190824
\(117\) −2.20063e9 −1.08570
\(118\) 2.39141e9 1.13549
\(119\) 0 0
\(120\) 1.99881e8 0.0879948
\(121\) 5.81275e9 2.46517
\(122\) −2.19292e9 −0.896199
\(123\) 5.31520e8 0.209385
\(124\) −2.65948e8 −0.101018
\(125\) −2.94928e9 −1.08049
\(126\) −2.54024e9 −0.897857
\(127\) −6.56388e8 −0.223895 −0.111947 0.993714i \(-0.535709\pi\)
−0.111947 + 0.993714i \(0.535709\pi\)
\(128\) −3.49552e9 −1.15098
\(129\) 8.56850e8 0.272428
\(130\) −3.75802e9 −1.15402
\(131\) −4.18207e9 −1.24071 −0.620355 0.784321i \(-0.713011\pi\)
−0.620355 + 0.784321i \(0.713011\pi\)
\(132\) 3.95165e8 0.113291
\(133\) −4.22720e9 −1.17144
\(134\) −4.12518e9 −1.10528
\(135\) −9.70265e8 −0.251413
\(136\) 0 0
\(137\) −4.88438e8 −0.118459 −0.0592293 0.998244i \(-0.518864\pi\)
−0.0592293 + 0.998244i \(0.518864\pi\)
\(138\) −8.80602e8 −0.206692
\(139\) −4.99993e9 −1.13605 −0.568025 0.823011i \(-0.692292\pi\)
−0.568025 + 0.823011i \(0.692292\pi\)
\(140\) −1.27977e9 −0.281550
\(141\) 3.56793e8 0.0760205
\(142\) 8.31366e9 1.71591
\(143\) 1.03245e10 2.06471
\(144\) 6.27974e9 1.21705
\(145\) 2.12047e9 0.398360
\(146\) 5.72912e9 1.04352
\(147\) −3.34991e8 −0.0591705
\(148\) −1.63453e8 −0.0280037
\(149\) 3.59475e9 0.597489 0.298745 0.954333i \(-0.403432\pi\)
0.298745 + 0.954333i \(0.403432\pi\)
\(150\) 2.54354e8 0.0410230
\(151\) −1.10303e9 −0.172660 −0.0863298 0.996267i \(-0.527514\pi\)
−0.0863298 + 0.996267i \(0.527514\pi\)
\(152\) 6.93293e9 1.05347
\(153\) 0 0
\(154\) 1.19178e10 1.70747
\(155\) −1.51542e9 −0.210883
\(156\) 4.99332e8 0.0675039
\(157\) −8.13616e9 −1.06874 −0.534368 0.845252i \(-0.679451\pi\)
−0.534368 + 0.845252i \(0.679451\pi\)
\(158\) 1.06116e10 1.35464
\(159\) 6.51434e8 0.0808320
\(160\) 5.70824e9 0.688592
\(161\) −7.83509e9 −0.919025
\(162\) −9.78283e9 −1.11596
\(163\) 3.43437e9 0.381068 0.190534 0.981681i \(-0.438978\pi\)
0.190534 + 0.981681i \(0.438978\pi\)
\(164\) 5.58139e9 0.602484
\(165\) 2.25173e9 0.236504
\(166\) 1.66483e10 1.70170
\(167\) 4.41406e8 0.0439151 0.0219575 0.999759i \(-0.493010\pi\)
0.0219575 + 0.999759i \(0.493010\pi\)
\(168\) −8.00979e8 −0.0775763
\(169\) 2.44162e9 0.230244
\(170\) 0 0
\(171\) −1.66471e10 −1.48886
\(172\) 8.99763e9 0.783881
\(173\) 1.16031e10 0.984838 0.492419 0.870358i \(-0.336113\pi\)
0.492419 + 0.870358i \(0.336113\pi\)
\(174\) −9.55028e8 −0.0789849
\(175\) 2.26309e9 0.182403
\(176\) −2.94621e10 −2.31450
\(177\) −1.81059e9 −0.138657
\(178\) −2.01241e10 −1.50254
\(179\) −1.11368e9 −0.0810816 −0.0405408 0.999178i \(-0.512908\pi\)
−0.0405408 + 0.999178i \(0.512908\pi\)
\(180\) −5.03984e9 −0.357841
\(181\) 2.27345e10 1.57446 0.787229 0.616661i \(-0.211515\pi\)
0.787229 + 0.616661i \(0.211515\pi\)
\(182\) 1.50594e10 1.01739
\(183\) 1.66032e9 0.109436
\(184\) 1.28501e10 0.826471
\(185\) −9.31387e8 −0.0584598
\(186\) 6.82525e8 0.0418129
\(187\) 0 0
\(188\) 3.74662e9 0.218741
\(189\) 3.88811e9 0.221646
\(190\) −2.84282e10 −1.58255
\(191\) −1.39886e10 −0.760544 −0.380272 0.924875i \(-0.624170\pi\)
−0.380272 + 0.924875i \(0.624170\pi\)
\(192\) 8.34092e8 0.0442954
\(193\) 3.49366e10 1.81248 0.906238 0.422767i \(-0.138941\pi\)
0.906238 + 0.422767i \(0.138941\pi\)
\(194\) −5.34571e8 −0.0270955
\(195\) 2.84529e9 0.140920
\(196\) −3.51768e9 −0.170257
\(197\) −1.47793e10 −0.699126 −0.349563 0.936913i \(-0.613670\pi\)
−0.349563 + 0.936913i \(0.613670\pi\)
\(198\) 4.69334e10 2.17014
\(199\) 1.24263e10 0.561700 0.280850 0.959752i \(-0.409384\pi\)
0.280850 + 0.959752i \(0.409384\pi\)
\(200\) −3.71164e9 −0.164033
\(201\) 3.12327e9 0.134967
\(202\) 1.46825e10 0.620469
\(203\) −8.49728e9 −0.351195
\(204\) 0 0
\(205\) 3.18039e10 1.25773
\(206\) −2.93016e10 −1.13367
\(207\) −3.08552e10 −1.16805
\(208\) −3.72285e10 −1.37908
\(209\) 7.81017e10 2.83140
\(210\) 3.28438e9 0.116538
\(211\) 3.46615e10 1.20386 0.601931 0.798548i \(-0.294398\pi\)
0.601931 + 0.798548i \(0.294398\pi\)
\(212\) 6.84059e9 0.232585
\(213\) −6.29447e9 −0.209532
\(214\) 2.52477e10 0.822925
\(215\) 5.12703e10 1.63641
\(216\) −6.37680e9 −0.199325
\(217\) 6.07271e9 0.185915
\(218\) 7.93453e9 0.237940
\(219\) −4.33766e9 −0.127426
\(220\) 2.36450e10 0.680515
\(221\) 0 0
\(222\) 4.19483e8 0.0115911
\(223\) −3.38261e10 −0.915966 −0.457983 0.888961i \(-0.651428\pi\)
−0.457983 + 0.888961i \(0.651428\pi\)
\(224\) −2.28745e10 −0.607064
\(225\) 8.91224e9 0.231828
\(226\) 2.86903e10 0.731554
\(227\) −1.62331e10 −0.405775 −0.202887 0.979202i \(-0.565033\pi\)
−0.202887 + 0.979202i \(0.565033\pi\)
\(228\) 3.77729e9 0.0925706
\(229\) 5.53406e10 1.32979 0.664896 0.746936i \(-0.268476\pi\)
0.664896 + 0.746936i \(0.268476\pi\)
\(230\) −5.26915e10 −1.24155
\(231\) −9.02328e9 −0.208502
\(232\) 1.39362e10 0.315826
\(233\) 3.33712e10 0.741772 0.370886 0.928678i \(-0.379054\pi\)
0.370886 + 0.928678i \(0.379054\pi\)
\(234\) 5.93052e10 1.29307
\(235\) 2.13490e10 0.456638
\(236\) −1.90127e10 −0.398970
\(237\) −8.03432e9 −0.165418
\(238\) 0 0
\(239\) 7.77200e10 1.54079 0.770393 0.637569i \(-0.220060\pi\)
0.770393 + 0.637569i \(0.220060\pi\)
\(240\) −8.11934e9 −0.157968
\(241\) −2.18341e10 −0.416925 −0.208463 0.978030i \(-0.566846\pi\)
−0.208463 + 0.978030i \(0.566846\pi\)
\(242\) −1.56649e11 −2.93601
\(243\) 2.30494e10 0.424064
\(244\) 1.74347e10 0.314891
\(245\) −2.00444e10 −0.355424
\(246\) −1.43240e10 −0.249377
\(247\) 9.86896e10 1.68708
\(248\) −9.95970e9 −0.167191
\(249\) −1.26049e10 −0.207798
\(250\) 7.94807e10 1.28686
\(251\) 1.67155e10 0.265819 0.132910 0.991128i \(-0.457568\pi\)
0.132910 + 0.991128i \(0.457568\pi\)
\(252\) 2.01960e10 0.315474
\(253\) 1.44761e11 2.22131
\(254\) 1.76891e10 0.266658
\(255\) 0 0
\(256\) 7.32711e10 1.06624
\(257\) 1.17094e11 1.67431 0.837156 0.546964i \(-0.184217\pi\)
0.837156 + 0.546964i \(0.184217\pi\)
\(258\) −2.30914e10 −0.324460
\(259\) 3.73232e9 0.0515383
\(260\) 2.98779e10 0.405481
\(261\) −3.34630e10 −0.446357
\(262\) 1.12703e11 1.47768
\(263\) −1.02193e11 −1.31710 −0.658551 0.752536i \(-0.728830\pi\)
−0.658551 + 0.752536i \(0.728830\pi\)
\(264\) 1.47989e10 0.187504
\(265\) 3.89790e10 0.485540
\(266\) 1.13920e11 1.39518
\(267\) 1.52364e10 0.183477
\(268\) 3.27970e10 0.388353
\(269\) 1.53946e11 1.79260 0.896299 0.443450i \(-0.146246\pi\)
0.896299 + 0.443450i \(0.146246\pi\)
\(270\) 2.61478e10 0.299432
\(271\) 4.06059e10 0.457328 0.228664 0.973505i \(-0.426564\pi\)
0.228664 + 0.973505i \(0.426564\pi\)
\(272\) 0 0
\(273\) −1.14019e10 −0.124235
\(274\) 1.31630e10 0.141084
\(275\) −4.18128e10 −0.440872
\(276\) 7.00117e9 0.0726239
\(277\) 1.48740e11 1.51799 0.758993 0.651099i \(-0.225692\pi\)
0.758993 + 0.651099i \(0.225692\pi\)
\(278\) 1.34744e11 1.35303
\(279\) 2.39148e10 0.236292
\(280\) −4.79272e10 −0.465984
\(281\) −1.82559e11 −1.74673 −0.873365 0.487067i \(-0.838067\pi\)
−0.873365 + 0.487067i \(0.838067\pi\)
\(282\) −9.61528e9 −0.0905401
\(283\) 1.13202e11 1.04909 0.524546 0.851382i \(-0.324235\pi\)
0.524546 + 0.851382i \(0.324235\pi\)
\(284\) −6.60972e10 −0.602907
\(285\) 2.15237e10 0.193248
\(286\) −2.78237e11 −2.45906
\(287\) −1.27447e11 −1.10882
\(288\) −9.00815e10 −0.771559
\(289\) 0 0
\(290\) −5.71448e10 −0.474445
\(291\) 4.04737e8 0.00330868
\(292\) −4.55490e10 −0.366654
\(293\) −9.88878e10 −0.783860 −0.391930 0.919995i \(-0.628192\pi\)
−0.391930 + 0.919995i \(0.628192\pi\)
\(294\) 9.02773e9 0.0704718
\(295\) −1.08338e11 −0.832881
\(296\) −6.12129e9 −0.0463479
\(297\) −7.18367e10 −0.535725
\(298\) −9.68755e10 −0.711608
\(299\) 1.82920e11 1.32356
\(300\) −2.02222e9 −0.0144140
\(301\) −2.05454e11 −1.44266
\(302\) 2.97257e10 0.205637
\(303\) −1.11165e10 −0.0757664
\(304\) −2.81621e11 −1.89119
\(305\) 9.93463e10 0.657359
\(306\) 0 0
\(307\) −1.32346e11 −0.850334 −0.425167 0.905115i \(-0.639785\pi\)
−0.425167 + 0.905115i \(0.639785\pi\)
\(308\) −9.47519e10 −0.599943
\(309\) 2.21849e10 0.138435
\(310\) 4.08394e10 0.251161
\(311\) −2.91738e11 −1.76836 −0.884181 0.467144i \(-0.845283\pi\)
−0.884181 + 0.467144i \(0.845283\pi\)
\(312\) 1.86999e10 0.111723
\(313\) 2.79377e10 0.164528 0.0822642 0.996611i \(-0.473785\pi\)
0.0822642 + 0.996611i \(0.473785\pi\)
\(314\) 2.19263e11 1.27286
\(315\) 1.15081e11 0.658575
\(316\) −8.43670e10 −0.475971
\(317\) −2.06834e11 −1.15041 −0.575207 0.818008i \(-0.695079\pi\)
−0.575207 + 0.818008i \(0.695079\pi\)
\(318\) −1.75556e10 −0.0962706
\(319\) 1.56996e11 0.848847
\(320\) 4.99085e10 0.266072
\(321\) −1.91157e10 −0.100489
\(322\) 2.11149e11 1.09456
\(323\) 0 0
\(324\) 7.77778e10 0.392106
\(325\) −5.28349e10 −0.262691
\(326\) −9.25534e10 −0.453851
\(327\) −6.00743e9 −0.0290552
\(328\) 2.09022e11 0.997149
\(329\) −8.55512e10 −0.402573
\(330\) −6.06822e10 −0.281675
\(331\) −2.13845e11 −0.979203 −0.489601 0.871946i \(-0.662858\pi\)
−0.489601 + 0.871946i \(0.662858\pi\)
\(332\) −1.32361e11 −0.597916
\(333\) 1.46982e10 0.0655035
\(334\) −1.18955e10 −0.0523027
\(335\) 1.86884e11 0.810717
\(336\) 3.25364e10 0.139265
\(337\) −2.72147e11 −1.14939 −0.574697 0.818366i \(-0.694880\pi\)
−0.574697 + 0.818366i \(0.694880\pi\)
\(338\) −6.57996e10 −0.274219
\(339\) −2.17221e10 −0.0893312
\(340\) 0 0
\(341\) −1.12199e11 −0.449361
\(342\) 4.48625e11 1.77323
\(343\) 2.77750e11 1.08350
\(344\) 3.36960e11 1.29737
\(345\) 3.98940e10 0.151608
\(346\) −3.12693e11 −1.17294
\(347\) 1.46260e11 0.541555 0.270777 0.962642i \(-0.412719\pi\)
0.270777 + 0.962642i \(0.412719\pi\)
\(348\) 7.59288e9 0.0277524
\(349\) −1.97033e11 −0.710927 −0.355464 0.934690i \(-0.615677\pi\)
−0.355464 + 0.934690i \(0.615677\pi\)
\(350\) −6.09884e10 −0.217241
\(351\) −9.07731e10 −0.319209
\(352\) 4.22628e11 1.46729
\(353\) 1.79594e11 0.615610 0.307805 0.951449i \(-0.400406\pi\)
0.307805 + 0.951449i \(0.400406\pi\)
\(354\) 4.87940e10 0.165140
\(355\) −3.76635e11 −1.25861
\(356\) 1.59995e11 0.527937
\(357\) 0 0
\(358\) 3.00128e10 0.0965679
\(359\) 2.48013e11 0.788043 0.394021 0.919101i \(-0.371084\pi\)
0.394021 + 0.919101i \(0.371084\pi\)
\(360\) −1.88741e11 −0.592250
\(361\) 4.23867e11 1.31355
\(362\) −6.12675e11 −1.87517
\(363\) 1.18603e11 0.358521
\(364\) −1.19729e11 −0.357473
\(365\) −2.59547e11 −0.765417
\(366\) −4.47442e10 −0.130338
\(367\) 5.21437e11 1.50039 0.750195 0.661216i \(-0.229959\pi\)
0.750195 + 0.661216i \(0.229959\pi\)
\(368\) −5.21983e11 −1.48368
\(369\) −5.01896e11 −1.40927
\(370\) 2.51001e10 0.0696254
\(371\) −1.56200e11 −0.428053
\(372\) −5.42637e9 −0.0146915
\(373\) −5.99693e11 −1.60413 −0.802065 0.597237i \(-0.796265\pi\)
−0.802065 + 0.597237i \(0.796265\pi\)
\(374\) 0 0
\(375\) −6.01768e10 −0.157141
\(376\) 1.40310e11 0.362030
\(377\) 1.98380e11 0.505781
\(378\) −1.04781e11 −0.263980
\(379\) 9.27561e10 0.230922 0.115461 0.993312i \(-0.463165\pi\)
0.115461 + 0.993312i \(0.463165\pi\)
\(380\) 2.26017e11 0.556051
\(381\) −1.33929e10 −0.0325620
\(382\) 3.76981e11 0.905805
\(383\) 6.05110e11 1.43694 0.718472 0.695555i \(-0.244842\pi\)
0.718472 + 0.695555i \(0.244842\pi\)
\(384\) −7.13221e10 −0.167392
\(385\) −5.39915e11 −1.25243
\(386\) −9.41511e11 −2.15865
\(387\) −8.09094e11 −1.83358
\(388\) 4.25007e9 0.00952036
\(389\) 7.62830e11 1.68910 0.844548 0.535480i \(-0.179869\pi\)
0.844548 + 0.535480i \(0.179869\pi\)
\(390\) −7.66783e10 −0.167835
\(391\) 0 0
\(392\) −1.31737e11 −0.281786
\(393\) −8.53304e10 −0.180442
\(394\) 3.98290e11 0.832657
\(395\) −4.80740e11 −0.993627
\(396\) −3.73141e11 −0.762508
\(397\) −8.86527e10 −0.179116 −0.0895580 0.995982i \(-0.528545\pi\)
−0.0895580 + 0.995982i \(0.528545\pi\)
\(398\) −3.34880e11 −0.668983
\(399\) −8.62513e10 −0.170368
\(400\) 1.50770e11 0.294472
\(401\) 6.95370e11 1.34297 0.671485 0.741019i \(-0.265657\pi\)
0.671485 + 0.741019i \(0.265657\pi\)
\(402\) −8.41696e10 −0.160745
\(403\) −1.41775e11 −0.267749
\(404\) −1.16733e11 −0.218010
\(405\) 4.43193e11 0.818550
\(406\) 2.28995e11 0.418271
\(407\) −6.89583e10 −0.124569
\(408\) 0 0
\(409\) −3.29107e11 −0.581543 −0.290771 0.956793i \(-0.593912\pi\)
−0.290771 + 0.956793i \(0.593912\pi\)
\(410\) −8.57088e11 −1.49795
\(411\) −9.96602e9 −0.0172280
\(412\) 2.32960e11 0.398331
\(413\) 4.34141e11 0.734269
\(414\) 8.31522e11 1.39115
\(415\) −7.54221e11 −1.24819
\(416\) 5.34034e11 0.874277
\(417\) −1.02018e11 −0.165221
\(418\) −2.10477e12 −3.37219
\(419\) 7.10268e10 0.112579 0.0562897 0.998414i \(-0.482073\pi\)
0.0562897 + 0.998414i \(0.482073\pi\)
\(420\) −2.61123e10 −0.0409471
\(421\) −6.19951e11 −0.961807 −0.480904 0.876773i \(-0.659691\pi\)
−0.480904 + 0.876773i \(0.659691\pi\)
\(422\) −9.34099e11 −1.43379
\(423\) −3.36908e11 −0.511657
\(424\) 2.56179e11 0.384944
\(425\) 0 0
\(426\) 1.69631e11 0.249552
\(427\) −3.98108e11 −0.579529
\(428\) −2.00730e11 −0.289145
\(429\) 2.10660e11 0.300279
\(430\) −1.38169e12 −1.94896
\(431\) −5.72129e11 −0.798631 −0.399316 0.916814i \(-0.630752\pi\)
−0.399316 + 0.916814i \(0.630752\pi\)
\(432\) 2.59031e11 0.357828
\(433\) 1.85587e10 0.0253718 0.0126859 0.999920i \(-0.495962\pi\)
0.0126859 + 0.999920i \(0.495962\pi\)
\(434\) −1.63654e11 −0.221424
\(435\) 4.32657e10 0.0579352
\(436\) −6.30829e10 −0.0836032
\(437\) 1.38373e12 1.81504
\(438\) 1.16896e11 0.151763
\(439\) −1.96136e11 −0.252038 −0.126019 0.992028i \(-0.540220\pi\)
−0.126019 + 0.992028i \(0.540220\pi\)
\(440\) 8.85501e11 1.12629
\(441\) 3.16320e11 0.398248
\(442\) 0 0
\(443\) 1.73153e11 0.213606 0.106803 0.994280i \(-0.465939\pi\)
0.106803 + 0.994280i \(0.465939\pi\)
\(444\) −3.33508e9 −0.00407270
\(445\) 9.11684e11 1.10211
\(446\) 9.11584e11 1.09091
\(447\) 7.33468e10 0.0868955
\(448\) −1.99997e11 −0.234570
\(449\) −2.19116e11 −0.254428 −0.127214 0.991875i \(-0.540604\pi\)
−0.127214 + 0.991875i \(0.540604\pi\)
\(450\) −2.40177e11 −0.276106
\(451\) 2.35470e12 2.68004
\(452\) −2.28100e11 −0.257041
\(453\) −2.25061e10 −0.0251106
\(454\) 4.37468e11 0.483276
\(455\) −6.82239e11 −0.746251
\(456\) 1.41459e11 0.153210
\(457\) 4.00079e11 0.429065 0.214532 0.976717i \(-0.431177\pi\)
0.214532 + 0.976717i \(0.431177\pi\)
\(458\) −1.49138e12 −1.58378
\(459\) 0 0
\(460\) 4.18920e11 0.436236
\(461\) 6.96330e11 0.718061 0.359030 0.933326i \(-0.383107\pi\)
0.359030 + 0.933326i \(0.383107\pi\)
\(462\) 2.43170e11 0.248325
\(463\) 1.04638e12 1.05821 0.529106 0.848556i \(-0.322527\pi\)
0.529106 + 0.848556i \(0.322527\pi\)
\(464\) −5.66099e11 −0.566972
\(465\) −3.09205e10 −0.0306696
\(466\) −8.99327e11 −0.883448
\(467\) 1.17010e12 1.13840 0.569202 0.822198i \(-0.307252\pi\)
0.569202 + 0.822198i \(0.307252\pi\)
\(468\) −4.71502e11 −0.454336
\(469\) −7.48893e11 −0.714730
\(470\) −5.75338e11 −0.543854
\(471\) −1.66009e11 −0.155431
\(472\) −7.12024e11 −0.660322
\(473\) 3.79596e12 3.48695
\(474\) 2.16518e11 0.197012
\(475\) −3.99678e11 −0.360238
\(476\) 0 0
\(477\) −6.15127e11 −0.544041
\(478\) −2.09449e12 −1.83507
\(479\) 1.23985e12 1.07611 0.538057 0.842908i \(-0.319158\pi\)
0.538057 + 0.842908i \(0.319158\pi\)
\(480\) 1.16470e11 0.100145
\(481\) −8.71359e10 −0.0742240
\(482\) 5.88410e11 0.496556
\(483\) −1.59866e11 −0.133658
\(484\) 1.24543e12 1.03161
\(485\) 2.42177e10 0.0198745
\(486\) −6.21162e11 −0.505058
\(487\) 1.21764e12 0.980934 0.490467 0.871460i \(-0.336826\pi\)
0.490467 + 0.871460i \(0.336826\pi\)
\(488\) 6.52926e11 0.521165
\(489\) 7.00744e10 0.0554204
\(490\) 5.40181e11 0.423309
\(491\) 6.56579e11 0.509824 0.254912 0.966964i \(-0.417954\pi\)
0.254912 + 0.966964i \(0.417954\pi\)
\(492\) 1.13882e11 0.0876219
\(493\) 0 0
\(494\) −2.65960e12 −2.00930
\(495\) −2.12623e12 −1.59179
\(496\) 4.04571e11 0.300142
\(497\) 1.50928e12 1.10960
\(498\) 3.39690e11 0.247486
\(499\) −1.66940e12 −1.20534 −0.602669 0.797991i \(-0.705896\pi\)
−0.602669 + 0.797991i \(0.705896\pi\)
\(500\) −6.31906e11 −0.452155
\(501\) 9.00639e9 0.00638676
\(502\) −4.50468e11 −0.316590
\(503\) −4.93759e11 −0.343922 −0.171961 0.985104i \(-0.555010\pi\)
−0.171961 + 0.985104i \(0.555010\pi\)
\(504\) 7.56337e11 0.522129
\(505\) −6.65165e11 −0.455112
\(506\) −3.90119e12 −2.64557
\(507\) 4.98185e10 0.0334854
\(508\) −1.40636e11 −0.0936937
\(509\) −2.29659e12 −1.51654 −0.758268 0.651943i \(-0.773954\pi\)
−0.758268 + 0.651943i \(0.773954\pi\)
\(510\) 0 0
\(511\) 1.04008e12 0.674793
\(512\) −1.84892e11 −0.118906
\(513\) −6.86669e11 −0.437743
\(514\) −3.15559e12 −1.99410
\(515\) 1.32745e12 0.831546
\(516\) 1.83587e11 0.114003
\(517\) 1.58064e12 0.973029
\(518\) −1.00583e11 −0.0613819
\(519\) 2.36747e11 0.143229
\(520\) 1.11892e12 0.671097
\(521\) 1.03325e12 0.614377 0.307188 0.951649i \(-0.400612\pi\)
0.307188 + 0.951649i \(0.400612\pi\)
\(522\) 9.01800e11 0.531610
\(523\) 8.50931e11 0.497321 0.248660 0.968591i \(-0.420010\pi\)
0.248660 + 0.968591i \(0.420010\pi\)
\(524\) −8.96040e11 −0.519202
\(525\) 4.61758e10 0.0265276
\(526\) 2.75401e12 1.56866
\(527\) 0 0
\(528\) −6.01142e11 −0.336608
\(529\) 7.63587e11 0.423944
\(530\) −1.05045e12 −0.578276
\(531\) 1.70968e12 0.933233
\(532\) −9.05710e11 −0.490215
\(533\) 2.97541e12 1.59689
\(534\) −4.10609e11 −0.218521
\(535\) −1.14380e12 −0.603613
\(536\) 1.22824e12 0.642750
\(537\) −2.27234e10 −0.0117921
\(538\) −4.14872e12 −2.13498
\(539\) −1.48405e12 −0.757357
\(540\) −2.07887e11 −0.105209
\(541\) −1.53052e12 −0.768161 −0.384080 0.923300i \(-0.625481\pi\)
−0.384080 + 0.923300i \(0.625481\pi\)
\(542\) −1.09430e12 −0.544676
\(543\) 4.63871e11 0.228980
\(544\) 0 0
\(545\) −3.59459e11 −0.174528
\(546\) 3.07271e11 0.147963
\(547\) 1.12770e12 0.538579 0.269289 0.963059i \(-0.413211\pi\)
0.269289 + 0.963059i \(0.413211\pi\)
\(548\) −1.04651e11 −0.0495716
\(549\) −1.56778e12 −0.736562
\(550\) 1.12682e12 0.525077
\(551\) 1.50068e12 0.693596
\(552\) 2.62193e11 0.120197
\(553\) 1.92645e12 0.875983
\(554\) −4.00841e12 −1.80792
\(555\) −1.90039e10 −0.00850207
\(556\) −1.07127e12 −0.475405
\(557\) 1.25702e12 0.553340 0.276670 0.960965i \(-0.410769\pi\)
0.276670 + 0.960965i \(0.410769\pi\)
\(558\) −6.44485e11 −0.281422
\(559\) 4.79659e12 2.07768
\(560\) 1.94684e12 0.836535
\(561\) 0 0
\(562\) 4.91982e12 2.08035
\(563\) 1.88611e12 0.791185 0.395593 0.918426i \(-0.370539\pi\)
0.395593 + 0.918426i \(0.370539\pi\)
\(564\) 7.64457e10 0.0318124
\(565\) −1.29976e12 −0.536593
\(566\) −3.05069e12 −1.24947
\(567\) −1.77599e12 −0.721635
\(568\) −2.47533e12 −0.997850
\(569\) −2.29668e12 −0.918535 −0.459267 0.888298i \(-0.651888\pi\)
−0.459267 + 0.888298i \(0.651888\pi\)
\(570\) −5.80046e11 −0.230158
\(571\) 5.17537e11 0.203741 0.101871 0.994798i \(-0.467517\pi\)
0.101871 + 0.994798i \(0.467517\pi\)
\(572\) 2.21211e12 0.864021
\(573\) −2.85422e11 −0.110609
\(574\) 3.43458e12 1.32060
\(575\) −7.40801e11 −0.282616
\(576\) −7.87604e11 −0.298131
\(577\) −4.42858e12 −1.66331 −0.831656 0.555291i \(-0.812607\pi\)
−0.831656 + 0.555291i \(0.812607\pi\)
\(578\) 0 0
\(579\) 7.12842e11 0.263596
\(580\) 4.54326e11 0.166702
\(581\) 3.02237e12 1.10041
\(582\) −1.09073e10 −0.00394062
\(583\) 2.88594e12 1.03461
\(584\) −1.70580e12 −0.606835
\(585\) −2.68671e12 −0.948462
\(586\) 2.66494e12 0.933574
\(587\) −3.58678e12 −1.24690 −0.623452 0.781861i \(-0.714270\pi\)
−0.623452 + 0.781861i \(0.714270\pi\)
\(588\) −7.17744e10 −0.0247612
\(589\) −1.07248e12 −0.367174
\(590\) 2.91963e12 0.991958
\(591\) −3.01555e11 −0.101677
\(592\) 2.48652e11 0.0832039
\(593\) −5.90244e12 −1.96013 −0.980067 0.198667i \(-0.936339\pi\)
−0.980067 + 0.198667i \(0.936339\pi\)
\(594\) 1.93594e12 0.638047
\(595\) 0 0
\(596\) 7.70202e11 0.250033
\(597\) 2.53546e11 0.0816906
\(598\) −4.92955e12 −1.57635
\(599\) 8.98381e10 0.0285128 0.0142564 0.999898i \(-0.495462\pi\)
0.0142564 + 0.999898i \(0.495462\pi\)
\(600\) −7.57319e10 −0.0238560
\(601\) 3.87756e10 0.0121234 0.00606168 0.999982i \(-0.498070\pi\)
0.00606168 + 0.999982i \(0.498070\pi\)
\(602\) 5.53681e12 1.71821
\(603\) −2.94920e12 −0.908398
\(604\) −2.36332e11 −0.0722532
\(605\) 7.09668e12 2.15356
\(606\) 2.99581e11 0.0902375
\(607\) −4.02539e12 −1.20353 −0.601767 0.798672i \(-0.705536\pi\)
−0.601767 + 0.798672i \(0.705536\pi\)
\(608\) 4.03979e12 1.19893
\(609\) −1.73377e11 −0.0510758
\(610\) −2.67730e12 −0.782912
\(611\) 1.99731e12 0.579774
\(612\) 0 0
\(613\) −1.68203e12 −0.481128 −0.240564 0.970633i \(-0.577332\pi\)
−0.240564 + 0.970633i \(0.577332\pi\)
\(614\) 3.56663e12 1.01274
\(615\) 6.48923e11 0.182917
\(616\) −3.54844e12 −0.992943
\(617\) 3.08394e12 0.856689 0.428344 0.903616i \(-0.359097\pi\)
0.428344 + 0.903616i \(0.359097\pi\)
\(618\) −5.97866e11 −0.164875
\(619\) 5.43988e11 0.148930 0.0744649 0.997224i \(-0.476275\pi\)
0.0744649 + 0.997224i \(0.476275\pi\)
\(620\) −3.24691e11 −0.0882485
\(621\) −1.27274e12 −0.343420
\(622\) 7.86210e12 2.10611
\(623\) −3.65336e12 −0.971620
\(624\) −7.59605e11 −0.200566
\(625\) −2.69726e12 −0.707071
\(626\) −7.52898e11 −0.195953
\(627\) 1.59358e12 0.411784
\(628\) −1.74323e12 −0.447236
\(629\) 0 0
\(630\) −3.10133e12 −0.784360
\(631\) 4.83979e12 1.21533 0.607665 0.794193i \(-0.292106\pi\)
0.607665 + 0.794193i \(0.292106\pi\)
\(632\) −3.15953e12 −0.787763
\(633\) 7.07229e11 0.175083
\(634\) 5.57399e12 1.37014
\(635\) −8.01373e11 −0.195593
\(636\) 1.39575e11 0.0338259
\(637\) −1.87526e12 −0.451267
\(638\) −4.23090e12 −1.01097
\(639\) 5.94366e12 1.41026
\(640\) −4.26761e12 −1.00548
\(641\) −4.45073e11 −0.104129 −0.0520643 0.998644i \(-0.516580\pi\)
−0.0520643 + 0.998644i \(0.516580\pi\)
\(642\) 5.15151e11 0.119682
\(643\) −6.18246e12 −1.42630 −0.713152 0.701010i \(-0.752733\pi\)
−0.713152 + 0.701010i \(0.752733\pi\)
\(644\) −1.67873e12 −0.384586
\(645\) 1.04611e12 0.237990
\(646\) 0 0
\(647\) 4.44313e11 0.0996828 0.0498414 0.998757i \(-0.484128\pi\)
0.0498414 + 0.998757i \(0.484128\pi\)
\(648\) 2.91276e12 0.648960
\(649\) −8.02118e12 −1.77475
\(650\) 1.42386e12 0.312864
\(651\) 1.23907e11 0.0270384
\(652\) 7.35839e11 0.159466
\(653\) 6.17383e12 1.32876 0.664378 0.747397i \(-0.268697\pi\)
0.664378 + 0.747397i \(0.268697\pi\)
\(654\) 1.61895e11 0.0346046
\(655\) −5.10581e12 −1.08387
\(656\) −8.49065e12 −1.79008
\(657\) 4.09590e12 0.857640
\(658\) 2.30553e12 0.479463
\(659\) 7.68232e12 1.58675 0.793374 0.608735i \(-0.208323\pi\)
0.793374 + 0.608735i \(0.208323\pi\)
\(660\) 4.82450e11 0.0989702
\(661\) −7.12469e12 −1.45164 −0.725821 0.687884i \(-0.758540\pi\)
−0.725821 + 0.687884i \(0.758540\pi\)
\(662\) 5.76294e12 1.16623
\(663\) 0 0
\(664\) −4.95691e12 −0.989589
\(665\) −5.16091e12 −1.02336
\(666\) −3.96104e11 −0.0780144
\(667\) 2.78150e12 0.544143
\(668\) 9.45745e10 0.0183772
\(669\) −6.90183e11 −0.133213
\(670\) −5.03635e12 −0.965561
\(671\) 7.35542e12 1.40074
\(672\) −4.66728e11 −0.0882880
\(673\) −1.48990e12 −0.279956 −0.139978 0.990155i \(-0.544703\pi\)
−0.139978 + 0.990155i \(0.544703\pi\)
\(674\) 7.33414e12 1.36892
\(675\) 3.67618e11 0.0681600
\(676\) 5.23136e11 0.0963505
\(677\) −2.00832e12 −0.367438 −0.183719 0.982979i \(-0.558814\pi\)
−0.183719 + 0.982979i \(0.558814\pi\)
\(678\) 5.85393e11 0.106393
\(679\) −9.70470e10 −0.0175214
\(680\) 0 0
\(681\) −3.31218e11 −0.0590136
\(682\) 3.02368e12 0.535187
\(683\) 4.93569e12 0.867870 0.433935 0.900944i \(-0.357125\pi\)
0.433935 + 0.900944i \(0.357125\pi\)
\(684\) −3.56676e12 −0.623048
\(685\) −5.96325e11 −0.103484
\(686\) −7.48512e12 −1.29045
\(687\) 1.12916e12 0.193398
\(688\) −1.36876e13 −2.32905
\(689\) 3.64668e12 0.616470
\(690\) −1.07511e12 −0.180565
\(691\) 1.12902e13 1.88387 0.941934 0.335798i \(-0.109006\pi\)
0.941934 + 0.335798i \(0.109006\pi\)
\(692\) 2.48604e12 0.412127
\(693\) 8.52037e12 1.40333
\(694\) −3.94158e12 −0.644990
\(695\) −6.10433e12 −0.992444
\(696\) 2.84352e11 0.0459320
\(697\) 0 0
\(698\) 5.30988e12 0.846711
\(699\) 6.80903e11 0.107879
\(700\) 4.84884e11 0.0763303
\(701\) −6.20736e12 −0.970904 −0.485452 0.874263i \(-0.661345\pi\)
−0.485452 + 0.874263i \(0.661345\pi\)
\(702\) 2.44626e12 0.380177
\(703\) −6.59155e11 −0.101786
\(704\) 3.69514e12 0.566962
\(705\) 4.35602e11 0.0664109
\(706\) −4.83991e12 −0.733189
\(707\) 2.66550e12 0.401227
\(708\) −3.87934e11 −0.0580240
\(709\) 1.90163e12 0.282629 0.141315 0.989965i \(-0.454867\pi\)
0.141315 + 0.989965i \(0.454867\pi\)
\(710\) 1.01500e13 1.49901
\(711\) 7.58653e12 1.11335
\(712\) 5.99179e12 0.873769
\(713\) −1.98784e12 −0.288057
\(714\) 0 0
\(715\) 1.26050e13 1.80371
\(716\) −2.38615e11 −0.0339304
\(717\) 1.58579e12 0.224083
\(718\) −6.68375e12 −0.938556
\(719\) −4.62958e12 −0.646043 −0.323022 0.946392i \(-0.604699\pi\)
−0.323022 + 0.946392i \(0.604699\pi\)
\(720\) 7.66682e12 1.06321
\(721\) −5.31946e12 −0.733093
\(722\) −1.14229e13 −1.56443
\(723\) −4.45500e11 −0.0606353
\(724\) 4.87103e12 0.658866
\(725\) −8.03411e11 −0.107998
\(726\) −3.19624e12 −0.426997
\(727\) −4.11644e11 −0.0546533 −0.0273267 0.999627i \(-0.508699\pi\)
−0.0273267 + 0.999627i \(0.508699\pi\)
\(728\) −4.48383e12 −0.591640
\(729\) −6.67484e12 −0.875320
\(730\) 6.99458e12 0.911609
\(731\) 0 0
\(732\) 3.55736e11 0.0457960
\(733\) −4.17503e11 −0.0534185 −0.0267093 0.999643i \(-0.508503\pi\)
−0.0267093 + 0.999643i \(0.508503\pi\)
\(734\) −1.40523e13 −1.78696
\(735\) −4.08984e11 −0.0516909
\(736\) 7.48773e12 0.940589
\(737\) 1.38365e13 1.72752
\(738\) 1.35257e13 1.67844
\(739\) 9.55303e12 1.17826 0.589130 0.808038i \(-0.299471\pi\)
0.589130 + 0.808038i \(0.299471\pi\)
\(740\) −1.99557e11 −0.0244638
\(741\) 2.01365e12 0.245359
\(742\) 4.20945e12 0.509809
\(743\) −5.13979e12 −0.618722 −0.309361 0.950945i \(-0.600115\pi\)
−0.309361 + 0.950945i \(0.600115\pi\)
\(744\) −2.03217e11 −0.0243154
\(745\) 4.38876e12 0.521962
\(746\) 1.61612e13 1.91051
\(747\) 1.19023e13 1.39859
\(748\) 0 0
\(749\) 4.58352e12 0.532146
\(750\) 1.62171e12 0.187154
\(751\) 7.08291e12 0.812516 0.406258 0.913758i \(-0.366833\pi\)
0.406258 + 0.913758i \(0.366833\pi\)
\(752\) −5.69952e12 −0.649917
\(753\) 3.41060e11 0.0386593
\(754\) −5.34618e12 −0.602383
\(755\) −1.34667e12 −0.150834
\(756\) 8.33058e11 0.0927528
\(757\) −9.55210e12 −1.05722 −0.528612 0.848863i \(-0.677287\pi\)
−0.528612 + 0.848863i \(0.677287\pi\)
\(758\) −2.49970e12 −0.275028
\(759\) 2.95368e12 0.323055
\(760\) 8.46429e12 0.920300
\(761\) −8.35916e12 −0.903508 −0.451754 0.892143i \(-0.649201\pi\)
−0.451754 + 0.892143i \(0.649201\pi\)
\(762\) 3.60927e11 0.0387812
\(763\) 1.44045e12 0.153864
\(764\) −2.99716e12 −0.318266
\(765\) 0 0
\(766\) −1.63072e13 −1.71140
\(767\) −1.01356e13 −1.05747
\(768\) 1.49502e12 0.155067
\(769\) −4.20920e10 −0.00434041 −0.00217021 0.999998i \(-0.500691\pi\)
−0.00217021 + 0.999998i \(0.500691\pi\)
\(770\) 1.45503e13 1.49163
\(771\) 2.38918e12 0.243503
\(772\) 7.48543e12 0.758470
\(773\) −1.22458e12 −0.123362 −0.0616808 0.998096i \(-0.519646\pi\)
−0.0616808 + 0.998096i \(0.519646\pi\)
\(774\) 2.18044e13 2.18378
\(775\) 5.74169e11 0.0571719
\(776\) 1.59164e11 0.0157568
\(777\) 7.61538e10 0.00749544
\(778\) −2.05576e13 −2.01171
\(779\) 2.25080e13 2.18987
\(780\) 6.09626e11 0.0589709
\(781\) −2.78854e13 −2.68192
\(782\) 0 0
\(783\) −1.38030e12 −0.131234
\(784\) 5.35124e12 0.505863
\(785\) −9.93329e12 −0.933640
\(786\) 2.29958e12 0.214906
\(787\) 1.03160e13 0.958570 0.479285 0.877659i \(-0.340896\pi\)
0.479285 + 0.877659i \(0.340896\pi\)
\(788\) −3.16658e12 −0.292565
\(789\) −2.08513e12 −0.191552
\(790\) 1.29555e13 1.18341
\(791\) 5.20848e12 0.473061
\(792\) −1.39741e13 −1.26200
\(793\) 9.29435e12 0.834621
\(794\) 2.38912e12 0.213327
\(795\) 7.95324e11 0.0706142
\(796\) 2.66244e12 0.235056
\(797\) 1.05845e13 0.929196 0.464598 0.885522i \(-0.346199\pi\)
0.464598 + 0.885522i \(0.346199\pi\)
\(798\) 2.32440e12 0.202907
\(799\) 0 0
\(800\) −2.16276e12 −0.186682
\(801\) −1.43872e13 −1.23490
\(802\) −1.87396e13 −1.59947
\(803\) −1.92164e13 −1.63099
\(804\) 6.69185e11 0.0564799
\(805\) −9.56572e12 −0.802853
\(806\) 3.82073e12 0.318888
\(807\) 3.14110e12 0.260705
\(808\) −4.37161e12 −0.360820
\(809\) 5.95200e12 0.488534 0.244267 0.969708i \(-0.421453\pi\)
0.244267 + 0.969708i \(0.421453\pi\)
\(810\) −1.19437e13 −0.974890
\(811\) 1.22320e13 0.992896 0.496448 0.868066i \(-0.334637\pi\)
0.496448 + 0.868066i \(0.334637\pi\)
\(812\) −1.82061e12 −0.146965
\(813\) 8.28519e11 0.0665112
\(814\) 1.85837e12 0.148362
\(815\) 4.19296e12 0.332898
\(816\) 0 0
\(817\) 3.62846e13 2.84920
\(818\) 8.86915e12 0.692615
\(819\) 1.07664e13 0.836165
\(820\) 6.81422e12 0.526325
\(821\) −6.29236e12 −0.483359 −0.241679 0.970356i \(-0.577698\pi\)
−0.241679 + 0.970356i \(0.577698\pi\)
\(822\) 2.68576e11 0.0205184
\(823\) −3.82855e12 −0.290894 −0.145447 0.989366i \(-0.546462\pi\)
−0.145447 + 0.989366i \(0.546462\pi\)
\(824\) 8.72432e12 0.659263
\(825\) −8.53144e11 −0.0641179
\(826\) −1.16997e13 −0.874512
\(827\) 6.54281e12 0.486395 0.243198 0.969977i \(-0.421804\pi\)
0.243198 + 0.969977i \(0.421804\pi\)
\(828\) −6.61097e12 −0.488797
\(829\) 1.48419e13 1.09142 0.545711 0.837973i \(-0.316260\pi\)
0.545711 + 0.837973i \(0.316260\pi\)
\(830\) 2.03256e13 1.48660
\(831\) 3.03487e12 0.220767
\(832\) 4.66919e12 0.337821
\(833\) 0 0
\(834\) 2.74930e12 0.196777
\(835\) 5.38904e11 0.0383639
\(836\) 1.67339e13 1.18486
\(837\) 9.86454e11 0.0694724
\(838\) −1.91411e12 −0.134082
\(839\) 1.53149e13 1.06705 0.533526 0.845784i \(-0.320867\pi\)
0.533526 + 0.845784i \(0.320867\pi\)
\(840\) −9.77900e11 −0.0677701
\(841\) −1.14906e13 −0.792062
\(842\) 1.67072e13 1.14551
\(843\) −3.72492e12 −0.254035
\(844\) 7.42649e12 0.503782
\(845\) 2.98093e12 0.201139
\(846\) 9.07938e12 0.609382
\(847\) −2.84383e13 −1.89858
\(848\) −1.04062e13 −0.691052
\(849\) 2.30975e12 0.152574
\(850\) 0 0
\(851\) −1.22174e12 −0.0798538
\(852\) −1.34864e12 −0.0876834
\(853\) 1.38576e13 0.896224 0.448112 0.893977i \(-0.352097\pi\)
0.448112 + 0.893977i \(0.352097\pi\)
\(854\) 1.07287e13 0.690216
\(855\) −2.03241e13 −1.30066
\(856\) −7.51731e12 −0.478554
\(857\) −2.49616e13 −1.58073 −0.790367 0.612634i \(-0.790110\pi\)
−0.790367 + 0.612634i \(0.790110\pi\)
\(858\) −5.67712e12 −0.357631
\(859\) −2.53111e13 −1.58614 −0.793071 0.609130i \(-0.791519\pi\)
−0.793071 + 0.609130i \(0.791519\pi\)
\(860\) 1.09850e13 0.684792
\(861\) −2.60041e12 −0.161260
\(862\) 1.54184e13 0.951167
\(863\) −1.28027e13 −0.785692 −0.392846 0.919604i \(-0.628509\pi\)
−0.392846 + 0.919604i \(0.628509\pi\)
\(864\) −3.71574e12 −0.226847
\(865\) 1.41660e13 0.860347
\(866\) −5.00140e11 −0.0302177
\(867\) 0 0
\(868\) 1.30112e12 0.0778001
\(869\) −3.55931e13 −2.11727
\(870\) −1.16598e12 −0.0690006
\(871\) 1.74839e13 1.02933
\(872\) −2.36244e12 −0.138369
\(873\) −3.82179e11 −0.0222691
\(874\) −3.72905e13 −2.16170
\(875\) 1.44291e13 0.832151
\(876\) −9.29376e11 −0.0533240
\(877\) −3.41529e13 −1.94953 −0.974763 0.223240i \(-0.928336\pi\)
−0.974763 + 0.223240i \(0.928336\pi\)
\(878\) 5.28570e12 0.300177
\(879\) −2.01769e12 −0.114000
\(880\) −3.59698e13 −2.02193
\(881\) −1.43259e13 −0.801181 −0.400591 0.916257i \(-0.631195\pi\)
−0.400591 + 0.916257i \(0.631195\pi\)
\(882\) −8.52457e12 −0.474312
\(883\) −2.75197e13 −1.52342 −0.761711 0.647916i \(-0.775641\pi\)
−0.761711 + 0.647916i \(0.775641\pi\)
\(884\) 0 0
\(885\) −2.21052e12 −0.121130
\(886\) −4.66634e12 −0.254404
\(887\) 1.55573e13 0.843877 0.421938 0.906624i \(-0.361350\pi\)
0.421938 + 0.906624i \(0.361350\pi\)
\(888\) −1.24898e11 −0.00674058
\(889\) 3.21132e12 0.172435
\(890\) −2.45691e13 −1.31261
\(891\) 3.28132e13 1.74421
\(892\) −7.24749e12 −0.383306
\(893\) 1.51090e13 0.795066
\(894\) −1.97664e12 −0.103492
\(895\) −1.35967e12 −0.0708322
\(896\) 1.71015e13 0.886436
\(897\) 3.73229e12 0.192490
\(898\) 5.90499e12 0.303023
\(899\) −2.15585e12 −0.110078
\(900\) 1.90951e12 0.0970134
\(901\) 0 0
\(902\) −6.34573e13 −3.19192
\(903\) −4.19205e12 −0.209813
\(904\) −8.54231e12 −0.425419
\(905\) 2.77561e13 1.37543
\(906\) 6.06520e11 0.0299067
\(907\) 1.46031e13 0.716494 0.358247 0.933627i \(-0.383375\pi\)
0.358247 + 0.933627i \(0.383375\pi\)
\(908\) −3.47807e12 −0.169805
\(909\) 1.04969e13 0.509947
\(910\) 1.83858e13 0.888783
\(911\) 1.79784e12 0.0864807 0.0432404 0.999065i \(-0.486232\pi\)
0.0432404 + 0.999065i \(0.486232\pi\)
\(912\) −5.74616e12 −0.275043
\(913\) −5.58412e13 −2.65972
\(914\) −1.07818e13 −0.511014
\(915\) 2.02705e12 0.0956026
\(916\) 1.18571e13 0.556481
\(917\) 2.04604e13 0.955545
\(918\) 0 0
\(919\) −6.20132e12 −0.286790 −0.143395 0.989666i \(-0.545802\pi\)
−0.143395 + 0.989666i \(0.545802\pi\)
\(920\) 1.56885e13 0.721998
\(921\) −2.70038e12 −0.123668
\(922\) −1.87655e13 −0.855207
\(923\) −3.52361e13 −1.59801
\(924\) −1.93331e12 −0.0872523
\(925\) 3.52888e11 0.0158489
\(926\) −2.81989e13 −1.26033
\(927\) −2.09485e13 −0.931737
\(928\) 8.12057e12 0.359435
\(929\) −4.48551e12 −0.197579 −0.0987896 0.995108i \(-0.531497\pi\)
−0.0987896 + 0.995108i \(0.531497\pi\)
\(930\) 8.33282e11 0.0365274
\(931\) −1.41857e13 −0.618839
\(932\) 7.15004e12 0.310411
\(933\) −5.95259e12 −0.257181
\(934\) −3.15332e13 −1.35583
\(935\) 0 0
\(936\) −1.76577e13 −0.751956
\(937\) 3.19604e13 1.35451 0.677257 0.735746i \(-0.263168\pi\)
0.677257 + 0.735746i \(0.263168\pi\)
\(938\) 2.01820e13 0.851240
\(939\) 5.70037e11 0.0239281
\(940\) 4.57419e12 0.191090
\(941\) 3.68931e13 1.53388 0.766941 0.641718i \(-0.221778\pi\)
0.766941 + 0.641718i \(0.221778\pi\)
\(942\) 4.47381e12 0.185118
\(943\) 4.17184e13 1.71801
\(944\) 2.89230e13 1.18541
\(945\) 4.74693e12 0.193629
\(946\) −1.02298e14 −4.15295
\(947\) −3.52895e13 −1.42584 −0.712920 0.701246i \(-0.752628\pi\)
−0.712920 + 0.701246i \(0.752628\pi\)
\(948\) −1.72141e12 −0.0692226
\(949\) −2.42819e13 −0.971819
\(950\) 1.07710e13 0.429042
\(951\) −4.22021e12 −0.167310
\(952\) 0 0
\(953\) 1.19331e11 0.00468634 0.00234317 0.999997i \(-0.499254\pi\)
0.00234317 + 0.999997i \(0.499254\pi\)
\(954\) 1.65771e13 0.647951
\(955\) −1.70784e13 −0.664405
\(956\) 1.66521e13 0.644776
\(957\) 3.20332e12 0.123452
\(958\) −3.34129e13 −1.28165
\(959\) 2.38963e12 0.0912321
\(960\) 1.01833e12 0.0386961
\(961\) −2.48989e13 −0.941727
\(962\) 2.34824e12 0.0884005
\(963\) 1.80503e13 0.676340
\(964\) −4.67812e12 −0.174471
\(965\) 4.26534e13 1.58336
\(966\) 4.30826e12 0.159186
\(967\) −3.07077e13 −1.12935 −0.564674 0.825314i \(-0.690998\pi\)
−0.564674 + 0.825314i \(0.690998\pi\)
\(968\) 4.66410e13 1.70737
\(969\) 0 0
\(970\) −6.52648e11 −0.0236704
\(971\) −2.09057e13 −0.754706 −0.377353 0.926069i \(-0.623166\pi\)
−0.377353 + 0.926069i \(0.623166\pi\)
\(972\) 4.93851e12 0.177459
\(973\) 2.44617e13 0.874940
\(974\) −3.28145e13 −1.16829
\(975\) −1.07804e12 −0.0382043
\(976\) −2.65224e13 −0.935596
\(977\) −1.72144e12 −0.0604459 −0.0302230 0.999543i \(-0.509622\pi\)
−0.0302230 + 0.999543i \(0.509622\pi\)
\(978\) −1.88845e12 −0.0660055
\(979\) 6.74994e13 2.34843
\(980\) −4.29467e12 −0.148735
\(981\) 5.67261e12 0.195556
\(982\) −1.76942e13 −0.607198
\(983\) 2.07042e13 0.707241 0.353621 0.935389i \(-0.384950\pi\)
0.353621 + 0.935389i \(0.384950\pi\)
\(984\) 4.26486e12 0.145020
\(985\) −1.80438e13 −0.610751
\(986\) 0 0
\(987\) −1.74558e12 −0.0585479
\(988\) 2.11450e13 0.705995
\(989\) 6.72533e13 2.23527
\(990\) 5.73001e13 1.89582
\(991\) −4.22967e13 −1.39308 −0.696539 0.717519i \(-0.745278\pi\)
−0.696539 + 0.717519i \(0.745278\pi\)
\(992\) −5.80348e12 −0.190277
\(993\) −4.36326e12 −0.142410
\(994\) −4.06738e13 −1.32153
\(995\) 1.51711e13 0.490697
\(996\) −2.70069e12 −0.0869575
\(997\) −5.58372e13 −1.78976 −0.894882 0.446303i \(-0.852740\pi\)
−0.894882 + 0.446303i \(0.852740\pi\)
\(998\) 4.49891e13 1.43555
\(999\) 6.06280e11 0.0192588
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.h.1.8 yes 36
17.16 even 2 289.10.a.g.1.8 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.8 36 17.16 even 2
289.10.a.h.1.8 yes 36 1.1 even 1 trivial