Properties

Label 289.10.a.i.1.14
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 1.14
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-25.4513 q^{2} +80.7952 q^{3} +135.770 q^{4} -783.444 q^{5} -2056.34 q^{6} -5744.00 q^{7} +9575.55 q^{8} -13155.1 q^{9} +O(q^{10})\) \(q-25.4513 q^{2} +80.7952 q^{3} +135.770 q^{4} -783.444 q^{5} -2056.34 q^{6} -5744.00 q^{7} +9575.55 q^{8} -13155.1 q^{9} +19939.7 q^{10} +2593.14 q^{11} +10969.6 q^{12} -108940. q^{13} +146193. q^{14} -63298.5 q^{15} -313225. q^{16} +334816. q^{18} +95650.6 q^{19} -106369. q^{20} -464088. q^{21} -65999.0 q^{22} -92928.9 q^{23} +773658. q^{24} -1.33934e6 q^{25} +2.77268e6 q^{26} -2.65316e6 q^{27} -779865. q^{28} -2.91402e6 q^{29} +1.61103e6 q^{30} -2.18026e6 q^{31} +3.06931e6 q^{32} +209513. q^{33} +4.50010e6 q^{35} -1.78608e6 q^{36} -1.09912e7 q^{37} -2.43444e6 q^{38} -8.80185e6 q^{39} -7.50190e6 q^{40} -1.11239e7 q^{41} +1.18116e7 q^{42} +1.20690e7 q^{43} +352072. q^{44} +1.03063e7 q^{45} +2.36516e6 q^{46} -5.88161e7 q^{47} -2.53071e7 q^{48} -7.36005e6 q^{49} +3.40880e7 q^{50} -1.47909e7 q^{52} -1.85335e7 q^{53} +6.75265e7 q^{54} -2.03158e6 q^{55} -5.50020e7 q^{56} +7.72811e6 q^{57} +7.41657e7 q^{58} -9.51920e7 q^{59} -8.59406e6 q^{60} +4.53894e7 q^{61} +5.54905e7 q^{62} +7.55632e7 q^{63} +8.22531e7 q^{64} +8.53486e7 q^{65} -5.33240e6 q^{66} +2.09338e8 q^{67} -7.50820e6 q^{69} -1.14534e8 q^{70} -2.05372e8 q^{71} -1.25968e8 q^{72} -1.16456e8 q^{73} +2.79740e8 q^{74} -1.08212e8 q^{75} +1.29865e7 q^{76} -1.48950e7 q^{77} +2.24019e8 q^{78} +3.90576e8 q^{79} +2.45394e8 q^{80} +4.45700e7 q^{81} +2.83118e8 q^{82} -2.81235e8 q^{83} -6.30093e7 q^{84} -3.07172e8 q^{86} -2.35439e8 q^{87} +2.48308e7 q^{88} -9.72872e8 q^{89} -2.62310e8 q^{90} +6.25753e8 q^{91} -1.26170e7 q^{92} -1.76154e8 q^{93} +1.49695e9 q^{94} -7.49369e7 q^{95} +2.47985e8 q^{96} -1.27923e9 q^{97} +1.87323e8 q^{98} -3.41132e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + O(q^{10}) \) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + 156200q^{13} + 1207872q^{15} + 3407880q^{16} + 2193336q^{18} + 1185568q^{19} + 5198336q^{21} + 13827692q^{25} + 3618944q^{26} - 9167544q^{30} + 61884888q^{32} + 1635208q^{33} + 46992776q^{35} + 156027320q^{36} + 84813952q^{38} - 4635776q^{42} + 125448912q^{43} + 164193176q^{47} + 270850284q^{49} - 226223888q^{50} + 103553016q^{52} + 426167208q^{53} + 677761520q^{55} + 375214512q^{59} + 336918024q^{60} + 190014416q^{64} + 1377178928q^{66} + 311910088q^{67} + 533688136q^{69} + 1477690280q^{70} + 2757942680q^{72} + 4047975520q^{76} + 3440336432q^{77} + 3266558756q^{81} + 2072890608q^{83} + 2630025952q^{84} + 1538547296q^{86} - 1010436256q^{87} + 1873849184q^{89} - 1998451624q^{93} - 6880776704q^{94} - 4667454128q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −25.4513 −1.12480 −0.562400 0.826865i \(-0.690122\pi\)
−0.562400 + 0.826865i \(0.690122\pi\)
\(3\) 80.7952 0.575890 0.287945 0.957647i \(-0.407028\pi\)
0.287945 + 0.957647i \(0.407028\pi\)
\(4\) 135.770 0.265177
\(5\) −783.444 −0.560587 −0.280293 0.959914i \(-0.590432\pi\)
−0.280293 + 0.959914i \(0.590432\pi\)
\(6\) −2056.34 −0.647762
\(7\) −5744.00 −0.904219 −0.452109 0.891963i \(-0.649328\pi\)
−0.452109 + 0.891963i \(0.649328\pi\)
\(8\) 9575.55 0.826530
\(9\) −13155.1 −0.668350
\(10\) 19939.7 0.630549
\(11\) 2593.14 0.0534022 0.0267011 0.999643i \(-0.491500\pi\)
0.0267011 + 0.999643i \(0.491500\pi\)
\(12\) 10969.6 0.152713
\(13\) −108940. −1.05790 −0.528949 0.848654i \(-0.677414\pi\)
−0.528949 + 0.848654i \(0.677414\pi\)
\(14\) 146193. 1.01707
\(15\) −63298.5 −0.322837
\(16\) −313225. −1.19486
\(17\) 0 0
\(18\) 334816. 0.751761
\(19\) 95650.6 0.168382 0.0841912 0.996450i \(-0.473169\pi\)
0.0841912 + 0.996450i \(0.473169\pi\)
\(20\) −106369. −0.148655
\(21\) −464088. −0.520731
\(22\) −65999.0 −0.0600669
\(23\) −92928.9 −0.0692429 −0.0346215 0.999400i \(-0.511023\pi\)
−0.0346215 + 0.999400i \(0.511023\pi\)
\(24\) 773658. 0.475990
\(25\) −1.33934e6 −0.685742
\(26\) 2.77268e6 1.18992
\(27\) −2.65316e6 −0.960787
\(28\) −779865. −0.239778
\(29\) −2.91402e6 −0.765071 −0.382536 0.923941i \(-0.624949\pi\)
−0.382536 + 0.923941i \(0.624949\pi\)
\(30\) 1.61103e6 0.363127
\(31\) −2.18026e6 −0.424014 −0.212007 0.977268i \(-0.568000\pi\)
−0.212007 + 0.977268i \(0.568000\pi\)
\(32\) 3.06931e6 0.517447
\(33\) 209513. 0.0307538
\(34\) 0 0
\(35\) 4.50010e6 0.506893
\(36\) −1.78608e6 −0.177231
\(37\) −1.09912e7 −0.964131 −0.482066 0.876135i \(-0.660113\pi\)
−0.482066 + 0.876135i \(0.660113\pi\)
\(38\) −2.43444e6 −0.189397
\(39\) −8.80185e6 −0.609233
\(40\) −7.50190e6 −0.463342
\(41\) −1.11239e7 −0.614794 −0.307397 0.951581i \(-0.599458\pi\)
−0.307397 + 0.951581i \(0.599458\pi\)
\(42\) 1.18116e7 0.585718
\(43\) 1.20690e7 0.538348 0.269174 0.963092i \(-0.413249\pi\)
0.269174 + 0.963092i \(0.413249\pi\)
\(44\) 352072. 0.0141610
\(45\) 1.03063e7 0.374669
\(46\) 2.36516e6 0.0778845
\(47\) −5.88161e7 −1.75815 −0.879075 0.476684i \(-0.841839\pi\)
−0.879075 + 0.476684i \(0.841839\pi\)
\(48\) −2.53071e7 −0.688107
\(49\) −7.36005e6 −0.182389
\(50\) 3.40880e7 0.771323
\(51\) 0 0
\(52\) −1.47909e7 −0.280530
\(53\) −1.85335e7 −0.322638 −0.161319 0.986902i \(-0.551575\pi\)
−0.161319 + 0.986902i \(0.551575\pi\)
\(54\) 6.75265e7 1.08069
\(55\) −2.03158e6 −0.0299366
\(56\) −5.50020e7 −0.747364
\(57\) 7.72811e6 0.0969697
\(58\) 7.41657e7 0.860553
\(59\) −9.51920e7 −1.02274 −0.511372 0.859360i \(-0.670862\pi\)
−0.511372 + 0.859360i \(0.670862\pi\)
\(60\) −8.59406e6 −0.0856087
\(61\) 4.53894e7 0.419730 0.209865 0.977730i \(-0.432697\pi\)
0.209865 + 0.977730i \(0.432697\pi\)
\(62\) 5.54905e7 0.476932
\(63\) 7.55632e7 0.604335
\(64\) 8.22531e7 0.612833
\(65\) 8.53486e7 0.593043
\(66\) −5.33240e6 −0.0345919
\(67\) 2.09338e8 1.26915 0.634574 0.772862i \(-0.281176\pi\)
0.634574 + 0.772862i \(0.281176\pi\)
\(68\) 0 0
\(69\) −7.50820e6 −0.0398763
\(70\) −1.14534e8 −0.570154
\(71\) −2.05372e8 −0.959132 −0.479566 0.877506i \(-0.659206\pi\)
−0.479566 + 0.877506i \(0.659206\pi\)
\(72\) −1.25968e8 −0.552412
\(73\) −1.16456e8 −0.479966 −0.239983 0.970777i \(-0.577142\pi\)
−0.239983 + 0.970777i \(0.577142\pi\)
\(74\) 2.79740e8 1.08446
\(75\) −1.08212e8 −0.394912
\(76\) 1.29865e7 0.0446510
\(77\) −1.48950e7 −0.0482873
\(78\) 2.24019e8 0.685265
\(79\) 3.90576e8 1.12819 0.564096 0.825709i \(-0.309225\pi\)
0.564096 + 0.825709i \(0.309225\pi\)
\(80\) 2.45394e8 0.669822
\(81\) 4.45700e7 0.115043
\(82\) 2.83118e8 0.691521
\(83\) −2.81235e8 −0.650455 −0.325227 0.945636i \(-0.605441\pi\)
−0.325227 + 0.945636i \(0.605441\pi\)
\(84\) −6.30093e7 −0.138086
\(85\) 0 0
\(86\) −3.07172e8 −0.605534
\(87\) −2.35439e8 −0.440597
\(88\) 2.48308e7 0.0441385
\(89\) −9.72872e8 −1.64362 −0.821809 0.569763i \(-0.807035\pi\)
−0.821809 + 0.569763i \(0.807035\pi\)
\(90\) −2.62310e8 −0.421427
\(91\) 6.25753e8 0.956570
\(92\) −1.26170e7 −0.0183616
\(93\) −1.76154e8 −0.244186
\(94\) 1.49695e9 1.97757
\(95\) −7.49369e7 −0.0943929
\(96\) 2.47985e8 0.297993
\(97\) −1.27923e9 −1.46715 −0.733575 0.679609i \(-0.762149\pi\)
−0.733575 + 0.679609i \(0.762149\pi\)
\(98\) 1.87323e8 0.205151
\(99\) −3.41132e7 −0.0356914
\(100\) −1.81843e8 −0.181843
\(101\) −8.97078e7 −0.0857796 −0.0428898 0.999080i \(-0.513656\pi\)
−0.0428898 + 0.999080i \(0.513656\pi\)
\(102\) 0 0
\(103\) −1.43613e9 −1.25726 −0.628630 0.777705i \(-0.716384\pi\)
−0.628630 + 0.777705i \(0.716384\pi\)
\(104\) −1.04316e9 −0.874384
\(105\) 3.63587e8 0.291915
\(106\) 4.71701e8 0.362903
\(107\) −2.21353e9 −1.63252 −0.816259 0.577687i \(-0.803956\pi\)
−0.816259 + 0.577687i \(0.803956\pi\)
\(108\) −3.60221e8 −0.254778
\(109\) −1.92348e9 −1.30517 −0.652587 0.757714i \(-0.726316\pi\)
−0.652587 + 0.757714i \(0.726316\pi\)
\(110\) 5.17065e7 0.0336727
\(111\) −8.88033e8 −0.555234
\(112\) 1.79916e9 1.08041
\(113\) 2.87568e9 1.65916 0.829578 0.558391i \(-0.188581\pi\)
0.829578 + 0.558391i \(0.188581\pi\)
\(114\) −1.96691e8 −0.109072
\(115\) 7.28046e7 0.0388167
\(116\) −3.95638e8 −0.202879
\(117\) 1.43313e9 0.707046
\(118\) 2.42276e9 1.15038
\(119\) 0 0
\(120\) −6.06118e8 −0.266834
\(121\) −2.35122e9 −0.997148
\(122\) −1.15522e9 −0.472113
\(123\) −8.98757e8 −0.354054
\(124\) −2.96015e8 −0.112439
\(125\) 2.57946e9 0.945005
\(126\) −1.92318e9 −0.679756
\(127\) −4.75500e9 −1.62193 −0.810967 0.585091i \(-0.801059\pi\)
−0.810967 + 0.585091i \(0.801059\pi\)
\(128\) −3.66494e9 −1.20676
\(129\) 9.75116e8 0.310029
\(130\) −2.17224e9 −0.667056
\(131\) −3.33130e9 −0.988310 −0.494155 0.869374i \(-0.664523\pi\)
−0.494155 + 0.869374i \(0.664523\pi\)
\(132\) 2.84457e7 0.00815519
\(133\) −5.49417e8 −0.152254
\(134\) −5.32794e9 −1.42754
\(135\) 2.07860e9 0.538604
\(136\) 0 0
\(137\) 3.02387e8 0.0733366 0.0366683 0.999327i \(-0.488326\pi\)
0.0366683 + 0.999327i \(0.488326\pi\)
\(138\) 1.91094e8 0.0448529
\(139\) 4.37194e9 0.993362 0.496681 0.867933i \(-0.334552\pi\)
0.496681 + 0.867933i \(0.334552\pi\)
\(140\) 6.10981e8 0.134416
\(141\) −4.75206e9 −1.01250
\(142\) 5.22699e9 1.07883
\(143\) −2.82498e8 −0.0564941
\(144\) 4.12052e9 0.798584
\(145\) 2.28297e9 0.428889
\(146\) 2.96397e9 0.539866
\(147\) −5.94656e8 −0.105036
\(148\) −1.49228e9 −0.255665
\(149\) 4.14348e9 0.688696 0.344348 0.938842i \(-0.388100\pi\)
0.344348 + 0.938842i \(0.388100\pi\)
\(150\) 2.75415e9 0.444198
\(151\) −2.51094e9 −0.393043 −0.196521 0.980500i \(-0.562964\pi\)
−0.196521 + 0.980500i \(0.562964\pi\)
\(152\) 9.15907e8 0.139173
\(153\) 0 0
\(154\) 3.79098e8 0.0543136
\(155\) 1.70811e9 0.237697
\(156\) −1.19503e9 −0.161554
\(157\) 1.22353e10 1.60719 0.803594 0.595177i \(-0.202918\pi\)
0.803594 + 0.595177i \(0.202918\pi\)
\(158\) −9.94067e9 −1.26899
\(159\) −1.49741e9 −0.185804
\(160\) −2.40463e9 −0.290074
\(161\) 5.33784e8 0.0626107
\(162\) −1.13436e9 −0.129400
\(163\) 1.89763e9 0.210556 0.105278 0.994443i \(-0.466427\pi\)
0.105278 + 0.994443i \(0.466427\pi\)
\(164\) −1.51030e9 −0.163029
\(165\) −1.64142e8 −0.0172402
\(166\) 7.15779e9 0.731632
\(167\) 9.60173e9 0.955268 0.477634 0.878559i \(-0.341494\pi\)
0.477634 + 0.878559i \(0.341494\pi\)
\(168\) −4.44389e9 −0.430399
\(169\) 1.26349e9 0.119147
\(170\) 0 0
\(171\) −1.25830e9 −0.112538
\(172\) 1.63861e9 0.142757
\(173\) −1.86000e10 −1.57872 −0.789359 0.613932i \(-0.789587\pi\)
−0.789359 + 0.613932i \(0.789587\pi\)
\(174\) 5.99223e9 0.495584
\(175\) 7.69317e9 0.620061
\(176\) −8.12237e8 −0.0638081
\(177\) −7.69106e9 −0.588988
\(178\) 2.47609e10 1.84874
\(179\) −8.64877e8 −0.0629674 −0.0314837 0.999504i \(-0.510023\pi\)
−0.0314837 + 0.999504i \(0.510023\pi\)
\(180\) 1.39929e9 0.0993533
\(181\) 1.36211e10 0.943322 0.471661 0.881780i \(-0.343655\pi\)
0.471661 + 0.881780i \(0.343655\pi\)
\(182\) −1.59263e10 −1.07595
\(183\) 3.66725e9 0.241719
\(184\) −8.89845e8 −0.0572313
\(185\) 8.61097e9 0.540479
\(186\) 4.48337e9 0.274660
\(187\) 0 0
\(188\) −7.98548e9 −0.466220
\(189\) 1.52398e10 0.868761
\(190\) 1.90724e9 0.106173
\(191\) 1.73416e10 0.942844 0.471422 0.881908i \(-0.343741\pi\)
0.471422 + 0.881908i \(0.343741\pi\)
\(192\) 6.64565e9 0.352925
\(193\) −2.27653e10 −1.18104 −0.590522 0.807022i \(-0.701078\pi\)
−0.590522 + 0.807022i \(0.701078\pi\)
\(194\) 3.25580e10 1.65025
\(195\) 6.89576e9 0.341528
\(196\) −9.99276e8 −0.0483652
\(197\) 1.74962e10 0.827646 0.413823 0.910357i \(-0.364193\pi\)
0.413823 + 0.910357i \(0.364193\pi\)
\(198\) 8.68226e8 0.0401457
\(199\) −2.80077e10 −1.26602 −0.633008 0.774146i \(-0.718180\pi\)
−0.633008 + 0.774146i \(0.718180\pi\)
\(200\) −1.28249e10 −0.566787
\(201\) 1.69135e10 0.730890
\(202\) 2.28318e9 0.0964850
\(203\) 1.67381e10 0.691792
\(204\) 0 0
\(205\) 8.71495e9 0.344645
\(206\) 3.65513e10 1.41417
\(207\) 1.22249e9 0.0462785
\(208\) 3.41228e10 1.26404
\(209\) 2.48036e8 0.00899199
\(210\) −9.25377e9 −0.328346
\(211\) 3.44587e10 1.19682 0.598409 0.801191i \(-0.295800\pi\)
0.598409 + 0.801191i \(0.295800\pi\)
\(212\) −2.51629e9 −0.0855559
\(213\) −1.65931e10 −0.552355
\(214\) 5.63372e10 1.83626
\(215\) −9.45538e9 −0.301791
\(216\) −2.54055e10 −0.794119
\(217\) 1.25234e10 0.383402
\(218\) 4.89551e10 1.46806
\(219\) −9.40911e9 −0.276408
\(220\) −2.75829e8 −0.00793848
\(221\) 0 0
\(222\) 2.26016e10 0.624527
\(223\) 5.53067e10 1.49764 0.748818 0.662776i \(-0.230622\pi\)
0.748818 + 0.662776i \(0.230622\pi\)
\(224\) −1.76301e10 −0.467885
\(225\) 1.76192e10 0.458316
\(226\) −7.31898e10 −1.86622
\(227\) −5.01007e10 −1.25235 −0.626177 0.779681i \(-0.715381\pi\)
−0.626177 + 0.779681i \(0.715381\pi\)
\(228\) 1.04925e9 0.0257141
\(229\) 7.23759e10 1.73914 0.869569 0.493812i \(-0.164397\pi\)
0.869569 + 0.493812i \(0.164397\pi\)
\(230\) −1.85297e9 −0.0436610
\(231\) −1.20345e9 −0.0278082
\(232\) −2.79033e10 −0.632354
\(233\) 4.45995e10 0.991353 0.495676 0.868507i \(-0.334920\pi\)
0.495676 + 0.868507i \(0.334920\pi\)
\(234\) −3.64749e10 −0.795286
\(235\) 4.60791e10 0.985596
\(236\) −1.29243e10 −0.271207
\(237\) 3.15566e10 0.649715
\(238\) 0 0
\(239\) −6.46746e10 −1.28216 −0.641081 0.767473i \(-0.721514\pi\)
−0.641081 + 0.767473i \(0.721514\pi\)
\(240\) 1.98267e10 0.385744
\(241\) 6.97798e9 0.133246 0.0666228 0.997778i \(-0.478778\pi\)
0.0666228 + 0.997778i \(0.478778\pi\)
\(242\) 5.98418e10 1.12159
\(243\) 5.58232e10 1.02704
\(244\) 6.16254e9 0.111303
\(245\) 5.76618e9 0.102245
\(246\) 2.28746e10 0.398240
\(247\) −1.04202e10 −0.178131
\(248\) −2.08772e10 −0.350461
\(249\) −2.27224e10 −0.374591
\(250\) −6.56508e10 −1.06294
\(251\) 4.27892e10 0.680460 0.340230 0.940342i \(-0.389495\pi\)
0.340230 + 0.940342i \(0.389495\pi\)
\(252\) 1.02592e10 0.160255
\(253\) −2.40978e8 −0.00369773
\(254\) 1.21021e11 1.82435
\(255\) 0 0
\(256\) 5.11640e10 0.744534
\(257\) 2.86215e10 0.409255 0.204627 0.978840i \(-0.434402\pi\)
0.204627 + 0.978840i \(0.434402\pi\)
\(258\) −2.48180e10 −0.348721
\(259\) 6.31333e10 0.871786
\(260\) 1.15878e10 0.157261
\(261\) 3.83344e10 0.511336
\(262\) 8.47861e10 1.11165
\(263\) 1.14839e11 1.48009 0.740043 0.672560i \(-0.234805\pi\)
0.740043 + 0.672560i \(0.234805\pi\)
\(264\) 2.00621e9 0.0254190
\(265\) 1.45199e10 0.180866
\(266\) 1.39834e10 0.171256
\(267\) −7.86034e10 −0.946543
\(268\) 2.84219e10 0.336548
\(269\) 8.32291e10 0.969148 0.484574 0.874750i \(-0.338975\pi\)
0.484574 + 0.874750i \(0.338975\pi\)
\(270\) −5.29033e10 −0.605823
\(271\) −2.33646e10 −0.263146 −0.131573 0.991307i \(-0.542003\pi\)
−0.131573 + 0.991307i \(0.542003\pi\)
\(272\) 0 0
\(273\) 5.05578e10 0.550879
\(274\) −7.69615e9 −0.0824890
\(275\) −3.47310e9 −0.0366202
\(276\) −1.01939e9 −0.0105743
\(277\) −1.27545e11 −1.30168 −0.650839 0.759216i \(-0.725583\pi\)
−0.650839 + 0.759216i \(0.725583\pi\)
\(278\) −1.11272e11 −1.11733
\(279\) 2.86816e10 0.283390
\(280\) 4.30910e10 0.418962
\(281\) 4.64733e10 0.444657 0.222329 0.974972i \(-0.428634\pi\)
0.222329 + 0.974972i \(0.428634\pi\)
\(282\) 1.20946e11 1.13886
\(283\) 4.19339e10 0.388621 0.194311 0.980940i \(-0.437753\pi\)
0.194311 + 0.980940i \(0.437753\pi\)
\(284\) −2.78834e10 −0.254339
\(285\) −6.05454e9 −0.0543600
\(286\) 7.18995e9 0.0635446
\(287\) 6.38957e10 0.555908
\(288\) −4.03772e10 −0.345836
\(289\) 0 0
\(290\) −5.81047e10 −0.482415
\(291\) −1.03355e11 −0.844917
\(292\) −1.58113e10 −0.127276
\(293\) 1.45256e11 1.15141 0.575705 0.817658i \(-0.304728\pi\)
0.575705 + 0.817658i \(0.304728\pi\)
\(294\) 1.51348e10 0.118144
\(295\) 7.45776e10 0.573336
\(296\) −1.05246e11 −0.796883
\(297\) −6.88003e9 −0.0513082
\(298\) −1.05457e11 −0.774645
\(299\) 1.01237e10 0.0732519
\(300\) −1.46920e10 −0.104721
\(301\) −6.93243e10 −0.486784
\(302\) 6.39067e10 0.442095
\(303\) −7.24796e9 −0.0493996
\(304\) −2.99601e10 −0.201193
\(305\) −3.55601e10 −0.235295
\(306\) 0 0
\(307\) −1.59150e11 −1.02255 −0.511275 0.859417i \(-0.670827\pi\)
−0.511275 + 0.859417i \(0.670827\pi\)
\(308\) −2.02230e9 −0.0128047
\(309\) −1.16032e11 −0.724043
\(310\) −4.34737e10 −0.267362
\(311\) −6.44453e10 −0.390634 −0.195317 0.980740i \(-0.562574\pi\)
−0.195317 + 0.980740i \(0.562574\pi\)
\(312\) −8.42825e10 −0.503549
\(313\) −1.46687e11 −0.863859 −0.431929 0.901907i \(-0.642167\pi\)
−0.431929 + 0.901907i \(0.642167\pi\)
\(314\) −3.11405e11 −1.80777
\(315\) −5.91995e10 −0.338782
\(316\) 5.30286e10 0.299170
\(317\) 2.69726e11 1.50022 0.750111 0.661311i \(-0.230000\pi\)
0.750111 + 0.661311i \(0.230000\pi\)
\(318\) 3.81112e10 0.208992
\(319\) −7.55648e9 −0.0408565
\(320\) −6.44407e10 −0.343546
\(321\) −1.78842e11 −0.940151
\(322\) −1.35855e10 −0.0704246
\(323\) 0 0
\(324\) 6.05128e9 0.0305067
\(325\) 1.45908e11 0.725445
\(326\) −4.82972e10 −0.236833
\(327\) −1.55408e11 −0.751637
\(328\) −1.06517e11 −0.508146
\(329\) 3.37840e11 1.58975
\(330\) 4.17763e9 0.0193918
\(331\) −6.83090e10 −0.312789 −0.156395 0.987695i \(-0.549987\pi\)
−0.156395 + 0.987695i \(0.549987\pi\)
\(332\) −3.81833e10 −0.172485
\(333\) 1.44590e11 0.644378
\(334\) −2.44377e11 −1.07449
\(335\) −1.64005e11 −0.711468
\(336\) 1.45364e11 0.622199
\(337\) −3.32556e11 −1.40453 −0.702263 0.711917i \(-0.747827\pi\)
−0.702263 + 0.711917i \(0.747827\pi\)
\(338\) −3.21575e10 −0.134016
\(339\) 2.32341e11 0.955492
\(340\) 0 0
\(341\) −5.65373e9 −0.0226433
\(342\) 3.20253e10 0.126583
\(343\) 2.74067e11 1.06914
\(344\) 1.15567e11 0.444960
\(345\) 5.88226e9 0.0223541
\(346\) 4.73394e11 1.77574
\(347\) −4.91489e11 −1.81983 −0.909916 0.414792i \(-0.863855\pi\)
−0.909916 + 0.414792i \(0.863855\pi\)
\(348\) −3.19656e10 −0.116836
\(349\) 3.69150e11 1.33195 0.665976 0.745973i \(-0.268015\pi\)
0.665976 + 0.745973i \(0.268015\pi\)
\(350\) −1.95802e11 −0.697445
\(351\) 2.89036e11 1.01641
\(352\) 7.95916e9 0.0276328
\(353\) 6.87046e10 0.235505 0.117752 0.993043i \(-0.462431\pi\)
0.117752 + 0.993043i \(0.462431\pi\)
\(354\) 1.95748e11 0.662494
\(355\) 1.60897e11 0.537677
\(356\) −1.32087e11 −0.435849
\(357\) 0 0
\(358\) 2.20123e10 0.0708258
\(359\) −2.85442e11 −0.906971 −0.453486 0.891264i \(-0.649820\pi\)
−0.453486 + 0.891264i \(0.649820\pi\)
\(360\) 9.86886e10 0.309675
\(361\) −3.13539e11 −0.971647
\(362\) −3.46676e11 −1.06105
\(363\) −1.89967e11 −0.574248
\(364\) 8.49588e10 0.253660
\(365\) 9.12370e10 0.269063
\(366\) −9.33363e10 −0.271885
\(367\) 1.61232e11 0.463931 0.231966 0.972724i \(-0.425484\pi\)
0.231966 + 0.972724i \(0.425484\pi\)
\(368\) 2.91076e10 0.0827355
\(369\) 1.46336e11 0.410898
\(370\) −2.19161e11 −0.607932
\(371\) 1.06456e11 0.291735
\(372\) −2.39166e10 −0.0647523
\(373\) −1.20896e10 −0.0323388 −0.0161694 0.999869i \(-0.505147\pi\)
−0.0161694 + 0.999869i \(0.505147\pi\)
\(374\) 0 0
\(375\) 2.08408e11 0.544219
\(376\) −5.63196e11 −1.45316
\(377\) 3.17454e11 0.809367
\(378\) −3.87873e11 −0.977183
\(379\) 3.36624e11 0.838047 0.419023 0.907975i \(-0.362373\pi\)
0.419023 + 0.907975i \(0.362373\pi\)
\(380\) −1.01742e10 −0.0250308
\(381\) −3.84181e11 −0.934056
\(382\) −4.41368e11 −1.06051
\(383\) −2.76830e11 −0.657383 −0.328692 0.944437i \(-0.606608\pi\)
−0.328692 + 0.944437i \(0.606608\pi\)
\(384\) −2.96109e11 −0.694963
\(385\) 1.16694e10 0.0270692
\(386\) 5.79408e11 1.32844
\(387\) −1.58769e11 −0.359805
\(388\) −1.73681e11 −0.389054
\(389\) 1.58309e11 0.350536 0.175268 0.984521i \(-0.443921\pi\)
0.175268 + 0.984521i \(0.443921\pi\)
\(390\) −1.75506e11 −0.384151
\(391\) 0 0
\(392\) −7.04764e10 −0.150750
\(393\) −2.69153e11 −0.569158
\(394\) −4.45301e11 −0.930937
\(395\) −3.05994e11 −0.632450
\(396\) −4.63156e9 −0.00946452
\(397\) −2.73210e11 −0.552000 −0.276000 0.961158i \(-0.589009\pi\)
−0.276000 + 0.961158i \(0.589009\pi\)
\(398\) 7.12834e11 1.42401
\(399\) −4.43903e10 −0.0876818
\(400\) 4.19515e11 0.819365
\(401\) −9.21298e11 −1.77931 −0.889653 0.456637i \(-0.849054\pi\)
−0.889653 + 0.456637i \(0.849054\pi\)
\(402\) −4.30472e11 −0.822105
\(403\) 2.37518e11 0.448564
\(404\) −1.21797e10 −0.0227467
\(405\) −3.49181e10 −0.0644915
\(406\) −4.26008e11 −0.778128
\(407\) −2.85017e10 −0.0514868
\(408\) 0 0
\(409\) −8.51756e11 −1.50508 −0.752541 0.658545i \(-0.771172\pi\)
−0.752541 + 0.658545i \(0.771172\pi\)
\(410\) −2.21807e11 −0.387657
\(411\) 2.44314e10 0.0422338
\(412\) −1.94983e11 −0.333396
\(413\) 5.46783e11 0.924783
\(414\) −3.11141e10 −0.0520541
\(415\) 2.20332e11 0.364637
\(416\) −3.34372e11 −0.547406
\(417\) 3.53232e11 0.572068
\(418\) −6.31284e9 −0.0101142
\(419\) 1.81027e11 0.286932 0.143466 0.989655i \(-0.454175\pi\)
0.143466 + 0.989655i \(0.454175\pi\)
\(420\) 4.93643e10 0.0774090
\(421\) −4.26322e11 −0.661406 −0.330703 0.943735i \(-0.607286\pi\)
−0.330703 + 0.943735i \(0.607286\pi\)
\(422\) −8.77021e11 −1.34618
\(423\) 7.73734e11 1.17506
\(424\) −1.77468e11 −0.266670
\(425\) 0 0
\(426\) 4.22315e11 0.621289
\(427\) −2.60717e11 −0.379528
\(428\) −3.00531e11 −0.432905
\(429\) −2.28245e10 −0.0325344
\(430\) 2.40652e11 0.339454
\(431\) −3.32704e10 −0.0464419 −0.0232210 0.999730i \(-0.507392\pi\)
−0.0232210 + 0.999730i \(0.507392\pi\)
\(432\) 8.31037e11 1.14800
\(433\) 8.54358e11 1.16800 0.584002 0.811752i \(-0.301486\pi\)
0.584002 + 0.811752i \(0.301486\pi\)
\(434\) −3.18738e11 −0.431250
\(435\) 1.84453e11 0.246993
\(436\) −2.61152e11 −0.346101
\(437\) −8.88870e9 −0.0116593
\(438\) 2.39474e11 0.310903
\(439\) −3.21290e11 −0.412864 −0.206432 0.978461i \(-0.566185\pi\)
−0.206432 + 0.978461i \(0.566185\pi\)
\(440\) −1.94535e10 −0.0247435
\(441\) 9.68224e10 0.121900
\(442\) 0 0
\(443\) 1.17716e12 1.45218 0.726089 0.687601i \(-0.241336\pi\)
0.726089 + 0.687601i \(0.241336\pi\)
\(444\) −1.20569e11 −0.147235
\(445\) 7.62191e11 0.921391
\(446\) −1.40763e12 −1.68454
\(447\) 3.34773e11 0.396613
\(448\) −4.72462e11 −0.554135
\(449\) 4.16601e10 0.0483740 0.0241870 0.999707i \(-0.492300\pi\)
0.0241870 + 0.999707i \(0.492300\pi\)
\(450\) −4.48432e11 −0.515514
\(451\) −2.88459e10 −0.0328314
\(452\) 3.90432e11 0.439969
\(453\) −2.02872e11 −0.226349
\(454\) 1.27513e12 1.40865
\(455\) −4.90243e11 −0.536241
\(456\) 7.40008e10 0.0801484
\(457\) 9.56563e11 1.02587 0.512933 0.858429i \(-0.328559\pi\)
0.512933 + 0.858429i \(0.328559\pi\)
\(458\) −1.84206e12 −1.95618
\(459\) 0 0
\(460\) 9.88471e9 0.0102933
\(461\) 1.45395e12 1.49932 0.749661 0.661822i \(-0.230217\pi\)
0.749661 + 0.661822i \(0.230217\pi\)
\(462\) 3.06293e10 0.0312787
\(463\) 3.76717e11 0.380978 0.190489 0.981689i \(-0.438993\pi\)
0.190489 + 0.981689i \(0.438993\pi\)
\(464\) 9.12744e11 0.914151
\(465\) 1.38007e11 0.136887
\(466\) −1.13512e12 −1.11507
\(467\) −8.09866e11 −0.787929 −0.393964 0.919126i \(-0.628897\pi\)
−0.393964 + 0.919126i \(0.628897\pi\)
\(468\) 1.94576e11 0.187492
\(469\) −1.20244e12 −1.14759
\(470\) −1.17278e12 −1.10860
\(471\) 9.88555e11 0.925564
\(472\) −9.11516e11 −0.845328
\(473\) 3.12966e10 0.0287490
\(474\) −8.03158e11 −0.730800
\(475\) −1.28109e11 −0.115467
\(476\) 0 0
\(477\) 2.43810e11 0.215635
\(478\) 1.64605e12 1.44218
\(479\) 2.67750e11 0.232391 0.116196 0.993226i \(-0.462930\pi\)
0.116196 + 0.993226i \(0.462930\pi\)
\(480\) −1.94283e11 −0.167051
\(481\) 1.19738e12 1.01995
\(482\) −1.77599e11 −0.149875
\(483\) 4.31271e10 0.0360569
\(484\) −3.19226e11 −0.264420
\(485\) 1.00220e12 0.822465
\(486\) −1.42078e12 −1.15521
\(487\) 8.91220e11 0.717967 0.358984 0.933344i \(-0.383123\pi\)
0.358984 + 0.933344i \(0.383123\pi\)
\(488\) 4.34628e11 0.346920
\(489\) 1.53319e11 0.121257
\(490\) −1.46757e11 −0.115005
\(491\) 1.52071e12 1.18081 0.590405 0.807107i \(-0.298968\pi\)
0.590405 + 0.807107i \(0.298968\pi\)
\(492\) −1.22025e11 −0.0938868
\(493\) 0 0
\(494\) 2.65208e11 0.200362
\(495\) 2.67258e10 0.0200081
\(496\) 6.82912e11 0.506637
\(497\) 1.17966e12 0.867265
\(498\) 5.78315e11 0.421340
\(499\) −1.68185e12 −1.21432 −0.607162 0.794578i \(-0.707692\pi\)
−0.607162 + 0.794578i \(0.707692\pi\)
\(500\) 3.50215e11 0.250593
\(501\) 7.75773e11 0.550130
\(502\) −1.08904e12 −0.765382
\(503\) −1.69051e12 −1.17750 −0.588752 0.808314i \(-0.700381\pi\)
−0.588752 + 0.808314i \(0.700381\pi\)
\(504\) 7.23559e11 0.499501
\(505\) 7.02811e10 0.0480869
\(506\) 6.13321e9 0.00415921
\(507\) 1.02084e11 0.0686154
\(508\) −6.45588e11 −0.430099
\(509\) 5.84673e11 0.386085 0.193043 0.981190i \(-0.438164\pi\)
0.193043 + 0.981190i \(0.438164\pi\)
\(510\) 0 0
\(511\) 6.68926e11 0.433994
\(512\) 5.74257e11 0.369310
\(513\) −2.53777e11 −0.161779
\(514\) −7.28456e11 −0.460330
\(515\) 1.12512e12 0.704803
\(516\) 1.32392e11 0.0822124
\(517\) −1.52519e11 −0.0938891
\(518\) −1.60683e12 −0.980585
\(519\) −1.50279e12 −0.909168
\(520\) 8.17260e11 0.490168
\(521\) −1.46396e12 −0.870483 −0.435241 0.900314i \(-0.643337\pi\)
−0.435241 + 0.900314i \(0.643337\pi\)
\(522\) −9.75661e11 −0.575151
\(523\) 1.26928e12 0.741822 0.370911 0.928668i \(-0.379045\pi\)
0.370911 + 0.928668i \(0.379045\pi\)
\(524\) −4.52292e11 −0.262077
\(525\) 6.21571e11 0.357087
\(526\) −2.92279e12 −1.66480
\(527\) 0 0
\(528\) −6.56248e10 −0.0367465
\(529\) −1.79252e12 −0.995205
\(530\) −3.69551e11 −0.203439
\(531\) 1.25226e12 0.683551
\(532\) −7.45946e10 −0.0403743
\(533\) 1.21184e12 0.650389
\(534\) 2.00056e12 1.06467
\(535\) 1.73417e12 0.915168
\(536\) 2.00453e12 1.04899
\(537\) −6.98779e10 −0.0362623
\(538\) −2.11829e12 −1.09010
\(539\) −1.90857e10 −0.00973997
\(540\) 2.82213e11 0.142825
\(541\) −2.67177e12 −1.34095 −0.670473 0.741934i \(-0.733909\pi\)
−0.670473 + 0.741934i \(0.733909\pi\)
\(542\) 5.94660e11 0.295986
\(543\) 1.10052e12 0.543250
\(544\) 0 0
\(545\) 1.50694e12 0.731663
\(546\) −1.28676e12 −0.619630
\(547\) −1.35773e12 −0.648442 −0.324221 0.945981i \(-0.605102\pi\)
−0.324221 + 0.945981i \(0.605102\pi\)
\(548\) 4.10552e10 0.0194471
\(549\) −5.97104e11 −0.280527
\(550\) 8.83951e10 0.0411904
\(551\) −2.78728e11 −0.128824
\(552\) −7.18951e10 −0.0329590
\(553\) −2.24347e12 −1.02013
\(554\) 3.24618e12 1.46413
\(555\) 6.95725e11 0.311257
\(556\) 5.93580e11 0.263416
\(557\) −2.10630e11 −0.0927199 −0.0463599 0.998925i \(-0.514762\pi\)
−0.0463599 + 0.998925i \(0.514762\pi\)
\(558\) −7.29986e11 −0.318758
\(559\) −1.31480e12 −0.569516
\(560\) −1.40954e12 −0.605665
\(561\) 0 0
\(562\) −1.18281e12 −0.500151
\(563\) −1.83542e12 −0.769923 −0.384961 0.922933i \(-0.625785\pi\)
−0.384961 + 0.922933i \(0.625785\pi\)
\(564\) −6.45189e11 −0.268492
\(565\) −2.25293e12 −0.930101
\(566\) −1.06727e12 −0.437121
\(567\) −2.56010e11 −0.104024
\(568\) −1.96655e12 −0.792752
\(569\) 3.55367e12 1.42125 0.710627 0.703569i \(-0.248411\pi\)
0.710627 + 0.703569i \(0.248411\pi\)
\(570\) 1.54096e11 0.0611441
\(571\) −2.88312e12 −1.13501 −0.567505 0.823370i \(-0.692091\pi\)
−0.567505 + 0.823370i \(0.692091\pi\)
\(572\) −3.83548e10 −0.0149809
\(573\) 1.40112e12 0.542975
\(574\) −1.62623e12 −0.625286
\(575\) 1.24463e11 0.0474828
\(576\) −1.08205e12 −0.409587
\(577\) 1.69258e12 0.635710 0.317855 0.948139i \(-0.397037\pi\)
0.317855 + 0.948139i \(0.397037\pi\)
\(578\) 0 0
\(579\) −1.83933e12 −0.680151
\(580\) 3.09960e11 0.113731
\(581\) 1.61541e12 0.588153
\(582\) 2.63053e12 0.950363
\(583\) −4.80599e10 −0.0172296
\(584\) −1.11513e12 −0.396706
\(585\) −1.12277e12 −0.396361
\(586\) −3.69696e12 −1.29511
\(587\) 1.14137e12 0.396786 0.198393 0.980123i \(-0.436428\pi\)
0.198393 + 0.980123i \(0.436428\pi\)
\(588\) −8.07367e10 −0.0278531
\(589\) −2.08543e11 −0.0713965
\(590\) −1.89810e12 −0.644889
\(591\) 1.41360e12 0.476633
\(592\) 3.44271e12 1.15200
\(593\) −2.80279e12 −0.930775 −0.465387 0.885107i \(-0.654085\pi\)
−0.465387 + 0.885107i \(0.654085\pi\)
\(594\) 1.75106e11 0.0577115
\(595\) 0 0
\(596\) 5.62562e11 0.182626
\(597\) −2.26289e12 −0.729086
\(598\) −2.57662e11 −0.0823938
\(599\) −1.23194e12 −0.390993 −0.195497 0.980704i \(-0.562632\pi\)
−0.195497 + 0.980704i \(0.562632\pi\)
\(600\) −1.03619e12 −0.326407
\(601\) 1.57757e12 0.493233 0.246617 0.969113i \(-0.420681\pi\)
0.246617 + 0.969113i \(0.420681\pi\)
\(602\) 1.76440e12 0.547535
\(603\) −2.75388e12 −0.848235
\(604\) −3.40911e11 −0.104226
\(605\) 1.84205e12 0.558988
\(606\) 1.84470e11 0.0555648
\(607\) −6.19694e12 −1.85280 −0.926399 0.376544i \(-0.877112\pi\)
−0.926399 + 0.376544i \(0.877112\pi\)
\(608\) 2.93581e11 0.0871289
\(609\) 1.35236e12 0.398396
\(610\) 9.05051e11 0.264660
\(611\) 6.40744e12 1.85994
\(612\) 0 0
\(613\) −6.17001e12 −1.76487 −0.882436 0.470432i \(-0.844098\pi\)
−0.882436 + 0.470432i \(0.844098\pi\)
\(614\) 4.05059e12 1.15017
\(615\) 7.04126e11 0.198478
\(616\) −1.42628e11 −0.0399109
\(617\) −5.25289e12 −1.45920 −0.729600 0.683874i \(-0.760294\pi\)
−0.729600 + 0.683874i \(0.760294\pi\)
\(618\) 2.95317e12 0.814404
\(619\) −3.86095e12 −1.05703 −0.528514 0.848925i \(-0.677251\pi\)
−0.528514 + 0.848925i \(0.677251\pi\)
\(620\) 2.31911e11 0.0630317
\(621\) 2.46555e11 0.0665277
\(622\) 1.64022e12 0.439385
\(623\) 5.58818e12 1.48619
\(624\) 2.75696e12 0.727946
\(625\) 5.95035e11 0.155985
\(626\) 3.73339e12 0.971669
\(627\) 2.00401e10 0.00517840
\(628\) 1.66119e12 0.426189
\(629\) 0 0
\(630\) 1.50671e12 0.381063
\(631\) −1.39505e12 −0.350314 −0.175157 0.984541i \(-0.556043\pi\)
−0.175157 + 0.984541i \(0.556043\pi\)
\(632\) 3.73998e12 0.932485
\(633\) 2.78410e12 0.689236
\(634\) −6.86488e12 −1.68745
\(635\) 3.72527e12 0.909235
\(636\) −2.03304e11 −0.0492708
\(637\) 8.01806e11 0.192949
\(638\) 1.92322e11 0.0459554
\(639\) 2.70170e12 0.641037
\(640\) 2.87127e12 0.676495
\(641\) −4.45436e11 −0.104214 −0.0521068 0.998642i \(-0.516594\pi\)
−0.0521068 + 0.998642i \(0.516594\pi\)
\(642\) 4.55177e12 1.05748
\(643\) 2.04454e12 0.471678 0.235839 0.971792i \(-0.424216\pi\)
0.235839 + 0.971792i \(0.424216\pi\)
\(644\) 7.24720e10 0.0166029
\(645\) −7.63949e11 −0.173798
\(646\) 0 0
\(647\) 5.07293e12 1.13812 0.569062 0.822295i \(-0.307307\pi\)
0.569062 + 0.822295i \(0.307307\pi\)
\(648\) 4.26782e11 0.0950864
\(649\) −2.46847e11 −0.0546168
\(650\) −3.71356e12 −0.815981
\(651\) 1.01183e12 0.220797
\(652\) 2.57642e11 0.0558344
\(653\) −6.33100e12 −1.36258 −0.681292 0.732012i \(-0.738581\pi\)
−0.681292 + 0.732012i \(0.738581\pi\)
\(654\) 3.95534e12 0.845441
\(655\) 2.60989e12 0.554034
\(656\) 3.48428e12 0.734591
\(657\) 1.53200e12 0.320785
\(658\) −8.59847e12 −1.78815
\(659\) −3.82450e12 −0.789934 −0.394967 0.918695i \(-0.629244\pi\)
−0.394967 + 0.918695i \(0.629244\pi\)
\(660\) −2.22856e10 −0.00457169
\(661\) 5.35631e12 1.09134 0.545669 0.838001i \(-0.316276\pi\)
0.545669 + 0.838001i \(0.316276\pi\)
\(662\) 1.73855e12 0.351826
\(663\) 0 0
\(664\) −2.69297e12 −0.537620
\(665\) 4.30438e11 0.0853518
\(666\) −3.68002e12 −0.724796
\(667\) 2.70797e11 0.0529758
\(668\) 1.30363e12 0.253315
\(669\) 4.46851e12 0.862473
\(670\) 4.17414e12 0.800259
\(671\) 1.17701e11 0.0224145
\(672\) −1.42443e12 −0.269451
\(673\) 9.69427e12 1.82158 0.910788 0.412873i \(-0.135475\pi\)
0.910788 + 0.412873i \(0.135475\pi\)
\(674\) 8.46399e12 1.57981
\(675\) 3.55349e12 0.658852
\(676\) 1.71545e11 0.0315949
\(677\) −4.82449e12 −0.882678 −0.441339 0.897341i \(-0.645496\pi\)
−0.441339 + 0.897341i \(0.645496\pi\)
\(678\) −5.91338e12 −1.07474
\(679\) 7.34787e12 1.32662
\(680\) 0 0
\(681\) −4.04789e12 −0.721219
\(682\) 1.43895e11 0.0254692
\(683\) −7.33823e12 −1.29032 −0.645161 0.764046i \(-0.723210\pi\)
−0.645161 + 0.764046i \(0.723210\pi\)
\(684\) −1.70840e11 −0.0298425
\(685\) −2.36903e11 −0.0411115
\(686\) −6.97538e12 −1.20257
\(687\) 5.84762e12 1.00155
\(688\) −3.78031e12 −0.643249
\(689\) 2.01904e12 0.341317
\(690\) −1.49711e11 −0.0251440
\(691\) −7.59504e12 −1.26730 −0.633649 0.773621i \(-0.718444\pi\)
−0.633649 + 0.773621i \(0.718444\pi\)
\(692\) −2.52532e12 −0.418639
\(693\) 1.95946e11 0.0322728
\(694\) 1.25091e13 2.04695
\(695\) −3.42517e12 −0.556866
\(696\) −2.25446e12 −0.364167
\(697\) 0 0
\(698\) −9.39536e12 −1.49818
\(699\) 3.60342e12 0.570910
\(700\) 1.04451e12 0.164426
\(701\) 5.36973e12 0.839887 0.419944 0.907550i \(-0.362050\pi\)
0.419944 + 0.907550i \(0.362050\pi\)
\(702\) −7.35636e12 −1.14326
\(703\) −1.05131e12 −0.162343
\(704\) 2.13294e11 0.0327267
\(705\) 3.72297e12 0.567595
\(706\) −1.74862e12 −0.264896
\(707\) 5.15282e11 0.0775635
\(708\) −1.04422e12 −0.156186
\(709\) −7.02128e12 −1.04354 −0.521769 0.853087i \(-0.674728\pi\)
−0.521769 + 0.853087i \(0.674728\pi\)
\(710\) −4.09505e12 −0.604780
\(711\) −5.13808e12 −0.754028
\(712\) −9.31578e12 −1.35850
\(713\) 2.02609e11 0.0293600
\(714\) 0 0
\(715\) 2.21321e11 0.0316698
\(716\) −1.17425e11 −0.0166975
\(717\) −5.22539e12 −0.738385
\(718\) 7.26489e12 1.02016
\(719\) −2.98659e12 −0.416769 −0.208384 0.978047i \(-0.566821\pi\)
−0.208384 + 0.978047i \(0.566821\pi\)
\(720\) −3.22819e12 −0.447676
\(721\) 8.24911e12 1.13684
\(722\) 7.97998e12 1.09291
\(723\) 5.63787e11 0.0767349
\(724\) 1.84935e12 0.250147
\(725\) 3.90287e12 0.524642
\(726\) 4.83493e12 0.645914
\(727\) 1.37734e13 1.82868 0.914339 0.404950i \(-0.132711\pi\)
0.914339 + 0.404950i \(0.132711\pi\)
\(728\) 5.99193e12 0.790634
\(729\) 3.63298e12 0.476419
\(730\) −2.32210e12 −0.302642
\(731\) 0 0
\(732\) 4.97903e11 0.0640981
\(733\) −3.47927e10 −0.00445164 −0.00222582 0.999998i \(-0.500709\pi\)
−0.00222582 + 0.999998i \(0.500709\pi\)
\(734\) −4.10357e12 −0.521830
\(735\) 4.65880e11 0.0588818
\(736\) −2.85228e11 −0.0358295
\(737\) 5.42844e11 0.0677753
\(738\) −3.72446e12 −0.462178
\(739\) 3.58403e12 0.442051 0.221025 0.975268i \(-0.429060\pi\)
0.221025 + 0.975268i \(0.429060\pi\)
\(740\) 1.16911e12 0.143322
\(741\) −8.41902e11 −0.102584
\(742\) −2.70945e12 −0.328144
\(743\) −7.13249e12 −0.858601 −0.429301 0.903162i \(-0.641240\pi\)
−0.429301 + 0.903162i \(0.641240\pi\)
\(744\) −1.68677e12 −0.201827
\(745\) −3.24619e12 −0.386074
\(746\) 3.07697e11 0.0363747
\(747\) 3.69968e12 0.434732
\(748\) 0 0
\(749\) 1.27145e13 1.47615
\(750\) −5.30426e12 −0.612138
\(751\) 6.98174e12 0.800911 0.400455 0.916316i \(-0.368852\pi\)
0.400455 + 0.916316i \(0.368852\pi\)
\(752\) 1.84227e13 2.10074
\(753\) 3.45716e12 0.391870
\(754\) −8.07964e12 −0.910376
\(755\) 1.96718e12 0.220335
\(756\) 2.06911e12 0.230375
\(757\) −7.16189e12 −0.792677 −0.396338 0.918105i \(-0.629719\pi\)
−0.396338 + 0.918105i \(0.629719\pi\)
\(758\) −8.56752e12 −0.942636
\(759\) −1.94698e10 −0.00212948
\(760\) −7.17562e11 −0.0780186
\(761\) −1.69932e12 −0.183672 −0.0918360 0.995774i \(-0.529274\pi\)
−0.0918360 + 0.995774i \(0.529274\pi\)
\(762\) 9.77791e12 1.05063
\(763\) 1.10485e13 1.18016
\(764\) 2.35448e12 0.250020
\(765\) 0 0
\(766\) 7.04569e12 0.739425
\(767\) 1.03702e13 1.08196
\(768\) 4.13380e12 0.428770
\(769\) −5.97176e12 −0.615791 −0.307896 0.951420i \(-0.599625\pi\)
−0.307896 + 0.951420i \(0.599625\pi\)
\(770\) −2.97002e11 −0.0304475
\(771\) 2.31248e12 0.235686
\(772\) −3.09086e12 −0.313185
\(773\) 3.23402e12 0.325788 0.162894 0.986644i \(-0.447917\pi\)
0.162894 + 0.986644i \(0.447917\pi\)
\(774\) 4.04089e12 0.404709
\(775\) 2.92011e12 0.290765
\(776\) −1.22493e13 −1.21264
\(777\) 5.10087e12 0.502053
\(778\) −4.02917e12 −0.394283
\(779\) −1.06401e12 −0.103520
\(780\) 9.36240e11 0.0905652
\(781\) −5.32559e11 −0.0512198
\(782\) 0 0
\(783\) 7.73137e12 0.735070
\(784\) 2.30535e12 0.217929
\(785\) −9.58569e12 −0.900969
\(786\) 6.85031e12 0.640190
\(787\) 1.34733e13 1.25195 0.625974 0.779844i \(-0.284702\pi\)
0.625974 + 0.779844i \(0.284702\pi\)
\(788\) 2.37546e12 0.219472
\(789\) 9.27840e12 0.852367
\(790\) 7.78796e12 0.711380
\(791\) −1.65179e13 −1.50024
\(792\) −3.26652e11 −0.0295000
\(793\) −4.94474e12 −0.444032
\(794\) 6.95356e12 0.620890
\(795\) 1.17314e12 0.104159
\(796\) −3.80262e12 −0.335718
\(797\) −3.19049e12 −0.280089 −0.140044 0.990145i \(-0.544724\pi\)
−0.140044 + 0.990145i \(0.544724\pi\)
\(798\) 1.12979e12 0.0986246
\(799\) 0 0
\(800\) −4.11085e12 −0.354835
\(801\) 1.27983e13 1.09851
\(802\) 2.34483e13 2.00136
\(803\) −3.01988e11 −0.0256313
\(804\) 2.29636e12 0.193815
\(805\) −4.18190e11 −0.0350988
\(806\) −6.04515e12 −0.504545
\(807\) 6.72451e12 0.558123
\(808\) −8.59001e11 −0.0708994
\(809\) 5.90985e11 0.0485074 0.0242537 0.999706i \(-0.492279\pi\)
0.0242537 + 0.999706i \(0.492279\pi\)
\(810\) 8.88711e11 0.0725401
\(811\) −1.20312e13 −0.976595 −0.488297 0.872677i \(-0.662382\pi\)
−0.488297 + 0.872677i \(0.662382\pi\)
\(812\) 2.27254e12 0.183447
\(813\) −1.88775e12 −0.151543
\(814\) 7.25406e11 0.0579124
\(815\) −1.48669e12 −0.118035
\(816\) 0 0
\(817\) 1.15441e12 0.0906482
\(818\) 2.16783e13 1.69292
\(819\) −8.23187e12 −0.639324
\(820\) 1.18323e12 0.0913919
\(821\) 1.33649e13 1.02665 0.513325 0.858194i \(-0.328413\pi\)
0.513325 + 0.858194i \(0.328413\pi\)
\(822\) −6.21812e11 −0.0475046
\(823\) −1.17056e13 −0.889397 −0.444698 0.895680i \(-0.646689\pi\)
−0.444698 + 0.895680i \(0.646689\pi\)
\(824\) −1.37517e13 −1.03916
\(825\) −2.80610e11 −0.0210892
\(826\) −1.39164e13 −1.04020
\(827\) −2.08998e13 −1.55370 −0.776849 0.629687i \(-0.783183\pi\)
−0.776849 + 0.629687i \(0.783183\pi\)
\(828\) 1.65978e11 0.0122720
\(829\) −3.37506e12 −0.248191 −0.124096 0.992270i \(-0.539603\pi\)
−0.124096 + 0.992270i \(0.539603\pi\)
\(830\) −5.60773e12 −0.410143
\(831\) −1.03050e13 −0.749623
\(832\) −8.96067e12 −0.648314
\(833\) 0 0
\(834\) −8.99022e12 −0.643462
\(835\) −7.52242e12 −0.535511
\(836\) 3.36759e10 0.00238447
\(837\) 5.78458e12 0.407387
\(838\) −4.60737e12 −0.322742
\(839\) −1.34167e13 −0.934794 −0.467397 0.884047i \(-0.654808\pi\)
−0.467397 + 0.884047i \(0.654808\pi\)
\(840\) 3.48154e12 0.241276
\(841\) −6.01562e12 −0.414666
\(842\) 1.08505e13 0.743950
\(843\) 3.75482e12 0.256074
\(844\) 4.67848e12 0.317368
\(845\) −9.89874e11 −0.0667920
\(846\) −1.96926e13 −1.32171
\(847\) 1.35054e13 0.901640
\(848\) 5.80514e12 0.385506
\(849\) 3.38806e12 0.223803
\(850\) 0 0
\(851\) 1.02140e12 0.0667593
\(852\) −2.25285e12 −0.146472
\(853\) 7.18446e12 0.464647 0.232324 0.972639i \(-0.425367\pi\)
0.232324 + 0.972639i \(0.425367\pi\)
\(854\) 6.63559e12 0.426893
\(855\) 9.85806e11 0.0630876
\(856\) −2.11957e13 −1.34932
\(857\) 1.77742e13 1.12558 0.562790 0.826600i \(-0.309728\pi\)
0.562790 + 0.826600i \(0.309728\pi\)
\(858\) 5.80913e11 0.0365947
\(859\) −4.33599e12 −0.271718 −0.135859 0.990728i \(-0.543379\pi\)
−0.135859 + 0.990728i \(0.543379\pi\)
\(860\) −1.28376e12 −0.0800278
\(861\) 5.16246e12 0.320142
\(862\) 8.46775e11 0.0522379
\(863\) 2.34250e13 1.43758 0.718790 0.695228i \(-0.244696\pi\)
0.718790 + 0.695228i \(0.244696\pi\)
\(864\) −8.14338e12 −0.497156
\(865\) 1.45720e13 0.885008
\(866\) −2.17446e13 −1.31377
\(867\) 0 0
\(868\) 1.70031e12 0.101669
\(869\) 1.01282e12 0.0602480
\(870\) −4.69458e12 −0.277818
\(871\) −2.28054e13 −1.34263
\(872\) −1.84184e13 −1.07877
\(873\) 1.68284e13 0.980570
\(874\) 2.26229e11 0.0131144
\(875\) −1.48164e13 −0.854491
\(876\) −1.27748e12 −0.0732968
\(877\) 9.16908e12 0.523393 0.261696 0.965150i \(-0.415718\pi\)
0.261696 + 0.965150i \(0.415718\pi\)
\(878\) 8.17727e12 0.464390
\(879\) 1.17360e13 0.663085
\(880\) 6.36342e11 0.0357700
\(881\) −3.09781e13 −1.73246 −0.866230 0.499645i \(-0.833464\pi\)
−0.866230 + 0.499645i \(0.833464\pi\)
\(882\) −2.46426e12 −0.137113
\(883\) −3.55305e13 −1.96688 −0.983441 0.181231i \(-0.941992\pi\)
−0.983441 + 0.181231i \(0.941992\pi\)
\(884\) 0 0
\(885\) 6.02551e12 0.330179
\(886\) −2.99604e13 −1.63341
\(887\) −3.33279e13 −1.80780 −0.903902 0.427740i \(-0.859310\pi\)
−0.903902 + 0.427740i \(0.859310\pi\)
\(888\) −8.50340e12 −0.458917
\(889\) 2.73127e13 1.46658
\(890\) −1.93988e13 −1.03638
\(891\) 1.15576e11 0.00614355
\(892\) 7.50901e12 0.397138
\(893\) −5.62580e12 −0.296041
\(894\) −8.52043e12 −0.446111
\(895\) 6.77583e11 0.0352987
\(896\) 2.10514e13 1.09118
\(897\) 8.17946e11 0.0421851
\(898\) −1.06031e12 −0.0544111
\(899\) 6.35332e12 0.324401
\(900\) 2.39217e12 0.121535
\(901\) 0 0
\(902\) 7.34166e11 0.0369287
\(903\) −5.60107e12 −0.280334
\(904\) 2.75362e13 1.37134
\(905\) −1.06714e13 −0.528814
\(906\) 5.16335e12 0.254598
\(907\) 3.18916e13 1.56475 0.782373 0.622810i \(-0.214009\pi\)
0.782373 + 0.622810i \(0.214009\pi\)
\(908\) −6.80219e12 −0.332095
\(909\) 1.18012e12 0.0573309
\(910\) 1.24773e13 0.603164
\(911\) −7.61425e12 −0.366264 −0.183132 0.983088i \(-0.558624\pi\)
−0.183132 + 0.983088i \(0.558624\pi\)
\(912\) −2.42063e12 −0.115865
\(913\) −7.29281e11 −0.0347357
\(914\) −2.43458e13 −1.15389
\(915\) −2.87308e12 −0.135504
\(916\) 9.82650e12 0.461179
\(917\) 1.91350e13 0.893649
\(918\) 0 0
\(919\) −2.31210e13 −1.06927 −0.534635 0.845083i \(-0.679551\pi\)
−0.534635 + 0.845083i \(0.679551\pi\)
\(920\) 6.97143e11 0.0320831
\(921\) −1.28586e13 −0.588877
\(922\) −3.70049e13 −1.68644
\(923\) 2.23733e13 1.01466
\(924\) −1.63392e11 −0.00737408
\(925\) 1.47209e13 0.661146
\(926\) −9.58794e12 −0.428525
\(927\) 1.88924e13 0.840290
\(928\) −8.94404e12 −0.395884
\(929\) 1.71091e13 0.753627 0.376813 0.926289i \(-0.377020\pi\)
0.376813 + 0.926289i \(0.377020\pi\)
\(930\) −3.51247e12 −0.153971
\(931\) −7.03993e11 −0.0307110
\(932\) 6.05529e12 0.262883
\(933\) −5.20687e12 −0.224962
\(934\) 2.06122e13 0.886263
\(935\) 0 0
\(936\) 1.37230e13 0.584395
\(937\) −2.00547e13 −0.849939 −0.424969 0.905208i \(-0.639715\pi\)
−0.424969 + 0.905208i \(0.639715\pi\)
\(938\) 3.06037e13 1.29081
\(939\) −1.18516e13 −0.497488
\(940\) 6.25618e12 0.261357
\(941\) 3.17254e13 1.31903 0.659514 0.751692i \(-0.270762\pi\)
0.659514 + 0.751692i \(0.270762\pi\)
\(942\) −2.51600e13 −1.04108
\(943\) 1.03373e12 0.0425701
\(944\) 2.98165e13 1.22203
\(945\) −1.19395e13 −0.487016
\(946\) −7.96541e11 −0.0323369
\(947\) 3.38012e13 1.36571 0.682854 0.730555i \(-0.260739\pi\)
0.682854 + 0.730555i \(0.260739\pi\)
\(948\) 4.28445e12 0.172289
\(949\) 1.26868e13 0.507755
\(950\) 3.26054e12 0.129877
\(951\) 2.17925e13 0.863964
\(952\) 0 0
\(953\) 1.11972e13 0.439737 0.219868 0.975530i \(-0.429437\pi\)
0.219868 + 0.975530i \(0.429437\pi\)
\(954\) −6.20529e12 −0.242546
\(955\) −1.35862e13 −0.528546
\(956\) −8.78089e12 −0.339999
\(957\) −6.10527e11 −0.0235289
\(958\) −6.81459e12 −0.261394
\(959\) −1.73691e12 −0.0663123
\(960\) −5.20649e12 −0.197845
\(961\) −2.16861e13 −0.820212
\(962\) −3.04750e13 −1.14724
\(963\) 2.91193e13 1.09109
\(964\) 9.47403e11 0.0353336
\(965\) 1.78354e13 0.662077
\(966\) −1.09764e12 −0.0405568
\(967\) −8.04781e12 −0.295977 −0.147989 0.988989i \(-0.547280\pi\)
−0.147989 + 0.988989i \(0.547280\pi\)
\(968\) −2.25142e13 −0.824173
\(969\) 0 0
\(970\) −2.55074e13 −0.925109
\(971\) −3.30383e13 −1.19270 −0.596351 0.802724i \(-0.703383\pi\)
−0.596351 + 0.802724i \(0.703383\pi\)
\(972\) 7.57914e12 0.272347
\(973\) −2.51124e13 −0.898217
\(974\) −2.26827e13 −0.807570
\(975\) 1.17887e13 0.417777
\(976\) −1.42171e13 −0.501518
\(977\) −4.36000e13 −1.53095 −0.765475 0.643466i \(-0.777496\pi\)
−0.765475 + 0.643466i \(0.777496\pi\)
\(978\) −3.90218e12 −0.136390
\(979\) −2.52280e12 −0.0877729
\(980\) 7.82877e11 0.0271129
\(981\) 2.53036e13 0.872313
\(982\) −3.87041e13 −1.32818
\(983\) −5.21672e13 −1.78200 −0.890998 0.454008i \(-0.849994\pi\)
−0.890998 + 0.454008i \(0.849994\pi\)
\(984\) −8.60609e12 −0.292636
\(985\) −1.37073e13 −0.463968
\(986\) 0 0
\(987\) 2.72958e13 0.915522
\(988\) −1.41476e12 −0.0472362
\(989\) −1.12156e12 −0.0372768
\(990\) −6.80206e11 −0.0225052
\(991\) −5.63343e13 −1.85542 −0.927709 0.373305i \(-0.878225\pi\)
−0.927709 + 0.373305i \(0.878225\pi\)
\(992\) −6.69189e12 −0.219405
\(993\) −5.51904e12 −0.180132
\(994\) −3.00238e13 −0.975501
\(995\) 2.19425e13 0.709712
\(996\) −3.08503e12 −0.0993326
\(997\) −2.50390e13 −0.802581 −0.401291 0.915951i \(-0.631438\pi\)
−0.401291 + 0.915951i \(0.631438\pi\)
\(998\) 4.28053e13 1.36587
\(999\) 2.91614e13 0.926325
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.1.14 52
17.5 odd 16 17.10.d.a.8.11 52
17.7 odd 16 17.10.d.a.15.11 yes 52
17.16 even 2 inner 289.10.a.i.1.13 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.d.a.8.11 52 17.5 odd 16
17.10.d.a.15.11 yes 52 17.7 odd 16
289.10.a.i.1.13 52 17.16 even 2 inner
289.10.a.i.1.14 52 1.1 even 1 trivial