Properties

Label 289.10.a.g.1.8
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 1.8
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 \(-0.523167\pi\)
−0.0727172 + 0.997353i \(0.523167\pi\)
\(4\) 214.258 0.418472
\(5\) −1220.88 −0.873592 −0.436796 0.899561i \(-0.643887\pi\)
−0.436796 + 0.899561i \(0.643887\pi\)
\(6\) 549.868 0.173212
\(7\) 4892.40 0.770160 0.385080 0.922883i \(-0.374174\pi\)
0.385080 + 0.922883i \(0.374174\pi\)
\(8\) 8023.91 0.692598
\(9\) −19266.7 −0.978849
\(10\) 32901.7 1.04044
\(11\) −90391.9 −1.86150 −0.930749 0.365659i \(-0.880844\pi\)
−0.930749 + 0.365659i \(0.880844\pi\)
\(12\) −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 \(-0.703500\pi\)
−0.596646 + 0.802505i \(0.703500\pi\)
\(24\) −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 \(-0.573219\pi\)
−0.228001 + 0.973661i \(0.573219\pi\)
\(30\) −671323. −0.151316
\(31\) 1.24125e6 0.241397 0.120699 0.992689i \(-0.461487\pi\)
0.120699 + 0.992689i \(0.461487\pi\)
\(32\) 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 \(-0.489348\pi\)
0.0334595 + 0.999440i \(0.489348\pi\)
\(38\) −2.32850e7 −1.81155
\(39\) −2.33052e6 −0.161311
\(40\) −9.79625e6 −0.605048
\(41\) −2.60499e7 −1.43972 −0.719862 0.694117i \(-0.755795\pi\)
−0.719862 + 0.694117i \(0.755795\pi\)
\(42\) 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 \(-0.622783\pi\)
−0.376239 + 0.926523i \(0.622783\pi\)
\(62\) −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 \(-0.243973\pi\)
0.720368 + 0.693593i \(0.243973\pi\)
\(72\) −1.54594e8 −0.677948
\(73\) 2.12590e8 0.876173 0.438086 0.898933i \(-0.355656\pi\)
0.438086 + 0.898933i \(0.355656\pi\)
\(74\) −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 \(-0.307446\pi\)
0.568702 + 0.822544i \(0.307446\pi\)
\(80\) 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 \(-0.503621\pi\)
−0.0113751 + 0.999935i \(0.503621\pi\)
\(98\) 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 \(-0.387717\pi\)
0.345477 + 0.938427i \(0.387717\pi\)
\(108\) 1.70276e8 0.120433
\(109\) 2.94426e8 0.199782 0.0998910 0.994998i \(-0.468151\pi\)
0.0998910 + 0.994998i \(0.468151\pi\)
\(110\) −2.97405e9 −1.93679
\(111\) −1.55657e7 −0.00973231
\(112\) −1.59462e9 −0.957581
\(113\) 1.06461e9 0.614237 0.307119 0.951671i \(-0.400635\pi\)
0.307119 + 0.951671i \(0.400635\pi\)
\(114\) 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 \(-0.286989\pi\)
0.620355 + 0.784321i \(0.286989\pi\)
\(132\) 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 \(-0.307708\pi\)
0.568025 + 0.823011i \(0.307708\pi\)
\(140\) −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 \(-0.561022\pi\)
−0.190534 + 0.981681i \(0.561022\pi\)
\(164\) −5.58139e9 −0.602484
\(165\) −2.25173e9 −0.236504
\(166\) 1.66483e10 1.70170
\(167\) −4.41406e8 −0.0439151 −0.0219575 0.999759i \(-0.506990\pi\)
−0.0219575 + 0.999759i \(0.506990\pi\)
\(168\) −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 \(-0.663887\pi\)
−0.492419 + 0.870358i \(0.663887\pi\)
\(174\) −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 \(-0.788485\pi\)
−0.787229 + 0.616661i \(0.788485\pi\)
\(182\) −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 \(-0.861059\pi\)
−0.906238 + 0.422767i \(0.861059\pi\)
\(194\) 5.34571e8 0.0270955
\(195\) 2.84529e9 0.140920
\(196\) −3.51768e9 −0.170257
\(197\) 1.47793e10 0.699126 0.349563 0.936913i \(-0.386330\pi\)
0.349563 + 0.936913i \(0.386330\pi\)
\(198\) −4.69334e10 −2.17014
\(199\) −1.24263e10 −0.561700 −0.280850 0.959752i \(-0.590616\pi\)
−0.280850 + 0.959752i \(0.590616\pi\)
\(200\) −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 \(-0.705602\pi\)
−0.601931 + 0.798548i \(0.705602\pi\)
\(212\) 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 \(-0.434967\pi\)
0.202887 + 0.979202i \(0.434967\pi\)
\(228\) −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 \(-0.620946\pi\)
−0.370886 + 0.928678i \(0.620946\pi\)
\(234\) 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 \(-0.433154\pi\)
0.208463 + 0.978030i \(0.433154\pi\)
\(242\) −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 \(-0.853754\pi\)
−0.896299 + 0.443450i \(0.853754\pi\)
\(270\) 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 \(-0.774308\pi\)
−0.758993 + 0.651099i \(0.774308\pi\)
\(278\) −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 \(-0.675765\pi\)
−0.524546 + 0.851382i \(0.675765\pi\)
\(284\) 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 \(-0.154717\pi\)
0.884181 + 0.467144i \(0.154717\pi\)
\(312\) −1.86999e10 −0.111723
\(313\) −2.79377e10 −0.164528 −0.0822642 0.996611i \(-0.526215\pi\)
−0.0822642 + 0.996611i \(0.526215\pi\)
\(314\) 2.19263e11 1.27286
\(315\) 1.15081e11 0.658575
\(316\) 8.43670e10 0.475971
\(317\) 2.06834e11 1.15041 0.575207 0.818008i \(-0.304921\pi\)
0.575207 + 0.818008i \(0.304921\pi\)
\(318\) 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 \(-0.305120\pi\)
0.574697 + 0.818366i \(0.305120\pi\)
\(338\) −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 \(-0.587281\pi\)
−0.270777 + 0.962642i \(0.587281\pi\)
\(348\) 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 \(-0.770041\pi\)
−0.750195 + 0.661216i \(0.770041\pi\)
\(368\) 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 \(-0.536835\pi\)
−0.115461 + 0.993312i \(0.536835\pi\)
\(380\) −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 \(-0.471455\pi\)
0.0895580 + 0.995982i \(0.471455\pi\)
\(398\) 3.34880e11 0.668983
\(399\) −8.62513e10 −0.170368
\(400\) 1.50770e11 0.294472
\(401\) −6.95370e11 −1.34297 −0.671485 0.741019i \(-0.734343\pi\)
−0.671485 + 0.741019i \(0.734343\pi\)
\(402\) 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 \(-0.517927\pi\)
−0.0562897 + 0.998414i \(0.517927\pi\)
\(420\) 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 \(-0.369248\pi\)
0.399316 + 0.916814i \(0.369248\pi\)
\(432\) −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 \(-0.459780\pi\)
0.126019 + 0.992028i \(0.459780\pi\)
\(440\) 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 \(-0.459396\pi\)
0.127214 + 0.991875i \(0.459396\pi\)
\(450\) −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 \(-0.680842\pi\)
−0.538057 + 0.842908i \(0.680842\pi\)
\(480\) 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 \(-0.663174\pi\)
−0.490467 + 0.871460i \(0.663174\pi\)
\(488\) −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 \(-0.294104\pi\)
0.602669 + 0.797991i \(0.294104\pi\)
\(500\) 6.31906e11 0.452155
\(501\) 9.00639e9 0.00638676
\(502\) −4.50468e11 −0.316590
\(503\) 4.93759e11 0.343922 0.171961 0.985104i \(-0.444990\pi\)
0.171961 + 0.985104i \(0.444990\pi\)
\(504\) −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 \(-0.599388\pi\)
−0.307188 + 0.951649i \(0.599388\pi\)
\(522\) −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 \(-0.374519\pi\)
0.384080 + 0.923300i \(0.374519\pi\)
\(542\) −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 \(-0.586789\pi\)
−0.269289 + 0.963059i \(0.586789\pi\)
\(548\) −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 \(-0.532483\pi\)
−0.101871 + 0.994798i \(0.532483\pi\)
\(572\) −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 \(-0.501930\pi\)
−0.00606168 + 0.999982i \(0.501930\pi\)
\(602\) −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 \(-0.294464\pi\)
0.601767 + 0.798672i \(0.294464\pi\)
\(608\) 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 \(-0.640903\pi\)
−0.428344 + 0.903616i \(0.640903\pi\)
\(618\) 5.97866e11 0.164875
\(619\) −5.43988e11 −0.148930 −0.0744649 0.997224i \(-0.523725\pi\)
−0.0744649 + 0.997224i \(0.523725\pi\)
\(620\) −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 \(-0.483420\pi\)
0.0520643 + 0.998644i \(0.483420\pi\)
\(642\) 5.15151e11 0.119682
\(643\) 6.18246e12 1.42630 0.713152 0.701010i \(-0.247267\pi\)
0.713152 + 0.701010i \(0.247267\pi\)
\(644\) −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 \(-0.731303\pi\)
−0.664378 + 0.747397i \(0.731303\pi\)
\(654\) 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 \(-0.455297\pi\)
0.139978 + 0.990155i \(0.455297\pi\)
\(674\) −7.33414e12 −1.36892
\(675\) −3.67618e11 −0.0681600
\(676\) 5.23136e11 0.0963505
\(677\) 2.00832e12 0.367438 0.183719 0.982979i \(-0.441186\pi\)
0.183719 + 0.982979i \(0.441186\pi\)
\(678\) 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 \(-0.642875\pi\)
−0.433935 + 0.900944i \(0.642875\pi\)
\(684\) −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 \(-0.890994\pi\)
−0.941934 + 0.335798i \(0.890994\pi\)
\(692\) −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 \(-0.545133\pi\)
−0.141315 + 0.989965i \(0.545133\pi\)
\(710\) 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 \(-0.395301\pi\)
0.323022 + 0.946392i \(0.395301\pi\)
\(720\) −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 \(-0.399885\pi\)
0.309361 + 0.950945i \(0.399885\pi\)
\(744\) −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 \(-0.633167\pi\)
−0.406258 + 0.913758i \(0.633167\pi\)
\(752\) −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 \(-0.659104\pi\)
−0.479285 + 0.877659i \(0.659104\pi\)
\(788\) 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 \(-0.578547\pi\)
−0.244267 + 0.969708i \(0.578547\pi\)
\(810\) 1.19437e13 0.974890
\(811\) −1.22320e13 −0.992896 −0.496448 0.868066i \(-0.665363\pi\)
−0.496448 + 0.868066i \(0.665363\pi\)
\(812\) −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 \(-0.422302\pi\)
0.241679 + 0.970356i \(0.422302\pi\)
\(822\) −2.68576e11 −0.0205184
\(823\) 3.82855e12 0.290894 0.145447 0.989366i \(-0.453538\pi\)
0.145447 + 0.989366i \(0.453538\pi\)
\(824\) 8.72432e12 0.659263
\(825\) −8.53144e11 −0.0641179
\(826\) 1.16997e13 0.874512
\(827\) −6.54281e12 −0.486395 −0.243198 0.969977i \(-0.578196\pi\)
−0.243198 + 0.969977i \(0.578196\pi\)
\(828\) 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 \(-0.679133\pi\)
−0.533526 + 0.845784i \(0.679133\pi\)
\(840\) 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 \(-0.647903\pi\)
−0.448112 + 0.893977i \(0.647903\pi\)
\(854\) 1.07287e13 0.690216
\(855\) 2.03241e13 1.30066
\(856\) 7.51731e12 0.478554
\(857\) 2.49616e13 1.58073 0.790367 0.612634i \(-0.209890\pi\)
0.790367 + 0.612634i \(0.209890\pi\)
\(858\) −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 \(-0.0716635\pi\)
0.974763 + 0.223240i \(0.0716635\pi\)
\(878\) −5.28570e12 −0.300177
\(879\) 2.01769e12 0.114000
\(880\) −3.59698e13 −2.02193
\(881\) 1.43259e13 0.801181 0.400591 0.916257i \(-0.368805\pi\)
0.400591 + 0.916257i \(0.368805\pi\)
\(882\) −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 \(-0.638650\pi\)
−0.421938 + 0.906624i \(0.638650\pi\)
\(888\) −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 \(-0.616625\pi\)
−0.358247 + 0.933627i \(0.616625\pi\)
\(908\) 3.47807e12 0.169805
\(909\) 1.04969e13 0.509947
\(910\) 1.83858e13 0.888783
\(911\) −1.79784e12 −0.0864807 −0.0432404 0.999065i \(-0.513768\pi\)
−0.0432404 + 0.999065i \(0.513768\pi\)
\(912\) 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 \(-0.468503\pi\)
0.0987896 + 0.995108i \(0.468503\pi\)
\(930\) −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 \(-0.778222\pi\)
−0.766941 + 0.641718i \(0.778222\pi\)
\(942\) −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 \(-0.247372\pi\)
0.712920 + 0.701246i \(0.247372\pi\)
\(948\) −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 \(-0.615050\pi\)
−0.353621 + 0.935389i \(0.615050\pi\)
\(984\) 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 \(-0.254722\pi\)
0.696539 + 0.717519i \(0.254722\pi\)
\(992\) 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 \(-0.147260\pi\)
0.894882 + 0.446303i \(0.147260\pi\)
\(998\) −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.g.1.8 36
17.16 even 2 289.10.a.h.1.8 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.8 36 1.1 even 1 trivial
289.10.a.h.1.8 yes 36 17.16 even 2