Properties

Label 289.10.a.h.1.17
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 1.17
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-7.00956 q^{2} +248.596 q^{3} -462.866 q^{4} -1624.49 q^{5} -1742.55 q^{6} -8782.15 q^{7} +6833.38 q^{8} +42117.0 q^{9} +O(q^{10})\) \(q-7.00956 q^{2} +248.596 q^{3} -462.866 q^{4} -1624.49 q^{5} -1742.55 q^{6} -8782.15 q^{7} +6833.38 q^{8} +42117.0 q^{9} +11386.9 q^{10} -52453.2 q^{11} -115067. q^{12} +14453.2 q^{13} +61559.0 q^{14} -403841. q^{15} +189088. q^{16} -295222. q^{18} -931720. q^{19} +751920. q^{20} -2.18321e6 q^{21} +367674. q^{22} +1.37040e6 q^{23} +1.69875e6 q^{24} +685836. q^{25} -101311. q^{26} +5.57701e6 q^{27} +4.06496e6 q^{28} -4.42440e6 q^{29} +2.83075e6 q^{30} -2.02178e6 q^{31} -4.82412e6 q^{32} -1.30397e7 q^{33} +1.42665e7 q^{35} -1.94945e7 q^{36} -1.55332e7 q^{37} +6.53095e6 q^{38} +3.59301e6 q^{39} -1.11007e7 q^{40} -8.35453e6 q^{41} +1.53033e7 q^{42} -2.42190e7 q^{43} +2.42788e7 q^{44} -6.84186e7 q^{45} -9.60592e6 q^{46} -2.77645e7 q^{47} +4.70066e7 q^{48} +3.67726e7 q^{49} -4.80741e6 q^{50} -6.68990e6 q^{52} +1.77712e6 q^{53} -3.90924e7 q^{54} +8.52096e7 q^{55} -6.00118e7 q^{56} -2.31622e8 q^{57} +3.10131e7 q^{58} -1.56378e8 q^{59} +1.86924e8 q^{60} +2.14150e8 q^{61} +1.41718e7 q^{62} -3.69878e8 q^{63} -6.29983e7 q^{64} -2.34791e7 q^{65} +9.14023e7 q^{66} +5.42382e7 q^{67} +3.40677e8 q^{69} -1.00002e8 q^{70} +2.38979e8 q^{71} +2.87802e8 q^{72} +3.24831e8 q^{73} +1.08881e8 q^{74} +1.70496e8 q^{75} +4.31262e8 q^{76} +4.60652e8 q^{77} -2.51854e7 q^{78} +3.05262e8 q^{79} -3.07172e8 q^{80} +5.57434e8 q^{81} +5.85616e7 q^{82} +1.35790e8 q^{83} +1.01053e9 q^{84} +1.69764e8 q^{86} -1.09989e9 q^{87} -3.58433e8 q^{88} +1.08876e9 q^{89} +4.79584e8 q^{90} -1.26930e8 q^{91} -6.34313e8 q^{92} -5.02607e8 q^{93} +1.94617e8 q^{94} +1.51357e9 q^{95} -1.19926e9 q^{96} +7.22732e8 q^{97} -2.57760e8 q^{98} -2.20917e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + 60000q^{10} + 76902q^{11} + 373248q^{12} + 54216q^{13} + 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} + 6439479q^{20} - 138102q^{21} + 267324q^{22} + 4041462q^{23} + 7653888q^{24} + 16582356q^{25} + 15822744q^{26} + 13281612q^{27} + 18614784q^{28} + 4005936q^{29} + 22471686q^{30} + 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} + 22076682q^{37} - 27401376q^{38} + 62736162q^{39} - 12231630q^{40} + 59641782q^{41} + 150001536q^{42} - 47951586q^{43} - 49578936q^{44} + 129308238q^{45} + 140524827q^{46} - 118557912q^{47} + 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} + 209848575q^{54} - 365439924q^{55} + 203095059q^{56} - 4614108q^{57} - 179071413q^{58} + 343015128q^{59} + 427179186q^{60} + 175597116q^{61} + 720602571q^{62} + 587415936q^{63} + 853082511q^{64} + 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} + 1308709542q^{71} - 275337849q^{72} + 494841342q^{73} + 1545361890q^{74} + 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} + 2270624538q^{78} + 1980107868q^{79} + 2897000199q^{80} + 1598298840q^{81} + 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} - 2705904618q^{88} + 148394658q^{89} + 117916215q^{90} + 636340896q^{91} - 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} + 4878626298q^{95} - 8390096634q^{96} - 891786822q^{97} + 4285627647q^{98} - 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.00956 −0.309782 −0.154891 0.987932i \(-0.549503\pi\)
−0.154891 + 0.987932i \(0.549503\pi\)
\(3\) 248.596 1.77194 0.885969 0.463744i \(-0.153494\pi\)
0.885969 + 0.463744i \(0.153494\pi\)
\(4\) −462.866 −0.904035
\(5\) −1624.49 −1.16239 −0.581194 0.813765i \(-0.697414\pi\)
−0.581194 + 0.813765i \(0.697414\pi\)
\(6\) −1742.55 −0.548914
\(7\) −8782.15 −1.38248 −0.691242 0.722624i \(-0.742936\pi\)
−0.691242 + 0.722624i \(0.742936\pi\)
\(8\) 6833.38 0.589835
\(9\) 42117.0 2.13977
\(10\) 11386.9 0.360087
\(11\) −52453.2 −1.08020 −0.540101 0.841600i \(-0.681614\pi\)
−0.540101 + 0.841600i \(0.681614\pi\)
\(12\) −115067. −1.60190
\(13\) 14453.2 0.140352 0.0701761 0.997535i \(-0.477644\pi\)
0.0701761 + 0.997535i \(0.477644\pi\)
\(14\) 61559.0 0.428268
\(15\) −403841. −2.05968
\(16\) 189088. 0.721315
\(17\) 0 0
\(18\) −295222. −0.662861
\(19\) −931720. −1.64019 −0.820095 0.572227i \(-0.806080\pi\)
−0.820095 + 0.572227i \(0.806080\pi\)
\(20\) 751920. 1.05084
\(21\) −2.18321e6 −2.44968
\(22\) 367674. 0.334627
\(23\) 1.37040e6 1.02111 0.510556 0.859845i \(-0.329440\pi\)
0.510556 + 0.859845i \(0.329440\pi\)
\(24\) 1.69875e6 1.04515
\(25\) 685836. 0.351148
\(26\) −101311. −0.0434786
\(27\) 5.57701e6 2.01960
\(28\) 4.06496e6 1.24981
\(29\) −4.42440e6 −1.16162 −0.580810 0.814039i \(-0.697264\pi\)
−0.580810 + 0.814039i \(0.697264\pi\)
\(30\) 2.83075e6 0.638052
\(31\) −2.02178e6 −0.393194 −0.196597 0.980484i \(-0.562989\pi\)
−0.196597 + 0.980484i \(0.562989\pi\)
\(32\) −4.82412e6 −0.813286
\(33\) −1.30397e7 −1.91405
\(34\) 0 0
\(35\) 1.42665e7 1.60698
\(36\) −1.94945e7 −1.93442
\(37\) −1.55332e7 −1.36255 −0.681277 0.732026i \(-0.738575\pi\)
−0.681277 + 0.732026i \(0.738575\pi\)
\(38\) 6.53095e6 0.508101
\(39\) 3.59301e6 0.248696
\(40\) −1.11007e7 −0.685618
\(41\) −8.35453e6 −0.461737 −0.230869 0.972985i \(-0.574157\pi\)
−0.230869 + 0.972985i \(0.574157\pi\)
\(42\) 1.53033e7 0.758865
\(43\) −2.42190e7 −1.08031 −0.540154 0.841566i \(-0.681634\pi\)
−0.540154 + 0.841566i \(0.681634\pi\)
\(44\) 2.42788e7 0.976541
\(45\) −6.84186e7 −2.48724
\(46\) −9.60592e6 −0.316322
\(47\) −2.77645e7 −0.829945 −0.414973 0.909834i \(-0.636209\pi\)
−0.414973 + 0.909834i \(0.636209\pi\)
\(48\) 4.70066e7 1.27813
\(49\) 3.67726e7 0.911260
\(50\) −4.80741e6 −0.108779
\(51\) 0 0
\(52\) −6.68990e6 −0.126883
\(53\) 1.77712e6 0.0309369 0.0154684 0.999880i \(-0.495076\pi\)
0.0154684 + 0.999880i \(0.495076\pi\)
\(54\) −3.90924e7 −0.625634
\(55\) 8.52096e7 1.25561
\(56\) −6.00118e7 −0.815437
\(57\) −2.31622e8 −2.90632
\(58\) 3.10131e7 0.359848
\(59\) −1.56378e8 −1.68012 −0.840062 0.542491i \(-0.817481\pi\)
−0.840062 + 0.542491i \(0.817481\pi\)
\(60\) 1.86924e8 1.86203
\(61\) 2.14150e8 1.98031 0.990157 0.139959i \(-0.0446971\pi\)
0.990157 + 0.139959i \(0.0446971\pi\)
\(62\) 1.41718e7 0.121804
\(63\) −3.69878e8 −2.95819
\(64\) −6.29983e7 −0.469374
\(65\) −2.34791e7 −0.163144
\(66\) 9.14023e7 0.592938
\(67\) 5.42382e7 0.328828 0.164414 0.986391i \(-0.447427\pi\)
0.164414 + 0.986391i \(0.447427\pi\)
\(68\) 0 0
\(69\) 3.40677e8 1.80935
\(70\) −1.00002e8 −0.497814
\(71\) 2.38979e8 1.11608 0.558042 0.829812i \(-0.311553\pi\)
0.558042 + 0.829812i \(0.311553\pi\)
\(72\) 2.87802e8 1.26211
\(73\) 3.24831e8 1.33876 0.669382 0.742918i \(-0.266559\pi\)
0.669382 + 0.742918i \(0.266559\pi\)
\(74\) 1.08881e8 0.422094
\(75\) 1.70496e8 0.622212
\(76\) 4.31262e8 1.48279
\(77\) 4.60652e8 1.49336
\(78\) −2.51854e7 −0.0770414
\(79\) 3.05262e8 0.881760 0.440880 0.897566i \(-0.354666\pi\)
0.440880 + 0.897566i \(0.354666\pi\)
\(80\) −3.07172e8 −0.838449
\(81\) 5.57434e8 1.43884
\(82\) 5.85616e7 0.143038
\(83\) 1.35790e8 0.314062 0.157031 0.987594i \(-0.449808\pi\)
0.157031 + 0.987594i \(0.449808\pi\)
\(84\) 1.01053e9 2.21459
\(85\) 0 0
\(86\) 1.69764e8 0.334660
\(87\) −1.09989e9 −2.05832
\(88\) −3.58433e8 −0.637141
\(89\) 1.08876e9 1.83941 0.919703 0.392616i \(-0.128430\pi\)
0.919703 + 0.392616i \(0.128430\pi\)
\(90\) 4.79584e8 0.770502
\(91\) −1.26930e8 −0.194035
\(92\) −6.34313e8 −0.923121
\(93\) −5.02607e8 −0.696716
\(94\) 1.94617e8 0.257102
\(95\) 1.51357e9 1.90654
\(96\) −1.19926e9 −1.44109
\(97\) 7.22732e8 0.828904 0.414452 0.910071i \(-0.363973\pi\)
0.414452 + 0.910071i \(0.363973\pi\)
\(98\) −2.57760e8 −0.282292
\(99\) −2.20917e9 −2.31138
\(100\) −3.17450e8 −0.317450
\(101\) −2.47246e8 −0.236420 −0.118210 0.992989i \(-0.537716\pi\)
−0.118210 + 0.992989i \(0.537716\pi\)
\(102\) 0 0
\(103\) 1.21679e9 1.06524 0.532621 0.846354i \(-0.321207\pi\)
0.532621 + 0.846354i \(0.321207\pi\)
\(104\) 9.87644e7 0.0827847
\(105\) 3.54660e9 2.84748
\(106\) −1.24569e7 −0.00958368
\(107\) −4.94831e8 −0.364947 −0.182474 0.983211i \(-0.558410\pi\)
−0.182474 + 0.983211i \(0.558410\pi\)
\(108\) −2.58141e9 −1.82579
\(109\) −8.73972e8 −0.593032 −0.296516 0.955028i \(-0.595825\pi\)
−0.296516 + 0.955028i \(0.595825\pi\)
\(110\) −5.97282e8 −0.388966
\(111\) −3.86150e9 −2.41436
\(112\) −1.66060e9 −0.997206
\(113\) 1.44323e9 0.832691 0.416345 0.909207i \(-0.363311\pi\)
0.416345 + 0.909207i \(0.363311\pi\)
\(114\) 1.62357e9 0.900324
\(115\) −2.22620e9 −1.18693
\(116\) 2.04791e9 1.05014
\(117\) 6.08727e8 0.300321
\(118\) 1.09614e9 0.520471
\(119\) 0 0
\(120\) −2.75960e9 −1.21487
\(121\) 3.93390e8 0.166836
\(122\) −1.50110e9 −0.613465
\(123\) −2.07690e9 −0.818170
\(124\) 9.35815e8 0.355461
\(125\) 2.05870e9 0.754219
\(126\) 2.59268e9 0.916394
\(127\) 1.54660e9 0.527547 0.263774 0.964585i \(-0.415033\pi\)
0.263774 + 0.964585i \(0.415033\pi\)
\(128\) 2.91154e9 0.958689
\(129\) −6.02074e9 −1.91424
\(130\) 1.64578e8 0.0505390
\(131\) 3.97813e8 0.118021 0.0590104 0.998257i \(-0.481205\pi\)
0.0590104 + 0.998257i \(0.481205\pi\)
\(132\) 6.03562e9 1.73037
\(133\) 8.18251e9 2.26754
\(134\) −3.80186e8 −0.101865
\(135\) −9.05979e9 −2.34756
\(136\) 0 0
\(137\) 1.76046e8 0.0426956 0.0213478 0.999772i \(-0.493204\pi\)
0.0213478 + 0.999772i \(0.493204\pi\)
\(138\) −2.38800e9 −0.560503
\(139\) 1.08750e9 0.247094 0.123547 0.992339i \(-0.460573\pi\)
0.123547 + 0.992339i \(0.460573\pi\)
\(140\) −6.60348e9 −1.45277
\(141\) −6.90215e9 −1.47061
\(142\) −1.67514e9 −0.345743
\(143\) −7.58117e8 −0.151609
\(144\) 7.96384e9 1.54345
\(145\) 7.18739e9 1.35025
\(146\) −2.27692e9 −0.414725
\(147\) 9.14153e9 1.61470
\(148\) 7.18980e9 1.23180
\(149\) −1.37802e9 −0.229044 −0.114522 0.993421i \(-0.536534\pi\)
−0.114522 + 0.993421i \(0.536534\pi\)
\(150\) −1.19510e9 −0.192750
\(151\) 1.19046e9 0.186345 0.0931726 0.995650i \(-0.470299\pi\)
0.0931726 + 0.995650i \(0.470299\pi\)
\(152\) −6.36680e9 −0.967442
\(153\) 0 0
\(154\) −3.22897e9 −0.462616
\(155\) 3.28436e9 0.457044
\(156\) −1.66308e9 −0.224830
\(157\) −5.46787e9 −0.718240 −0.359120 0.933291i \(-0.616923\pi\)
−0.359120 + 0.933291i \(0.616923\pi\)
\(158\) −2.13975e9 −0.273153
\(159\) 4.41786e8 0.0548183
\(160\) 7.83672e9 0.945354
\(161\) −1.20351e10 −1.41167
\(162\) −3.90737e9 −0.445725
\(163\) −8.81919e8 −0.0978553 −0.0489276 0.998802i \(-0.515580\pi\)
−0.0489276 + 0.998802i \(0.515580\pi\)
\(164\) 3.86703e9 0.417427
\(165\) 2.11828e10 2.22487
\(166\) −9.51827e8 −0.0972908
\(167\) −6.76444e8 −0.0672988 −0.0336494 0.999434i \(-0.510713\pi\)
−0.0336494 + 0.999434i \(0.510713\pi\)
\(168\) −1.49187e10 −1.44491
\(169\) −1.03956e10 −0.980301
\(170\) 0 0
\(171\) −3.92413e10 −3.50963
\(172\) 1.12101e10 0.976636
\(173\) 7.28714e9 0.618514 0.309257 0.950978i \(-0.399920\pi\)
0.309257 + 0.950978i \(0.399920\pi\)
\(174\) 7.70974e9 0.637629
\(175\) −6.02311e9 −0.485456
\(176\) −9.91829e9 −0.779166
\(177\) −3.88749e10 −2.97708
\(178\) −7.63173e9 −0.569814
\(179\) −7.99107e8 −0.0581790 −0.0290895 0.999577i \(-0.509261\pi\)
−0.0290895 + 0.999577i \(0.509261\pi\)
\(180\) 3.16687e10 2.24855
\(181\) −1.62217e10 −1.12342 −0.561711 0.827333i \(-0.689857\pi\)
−0.561711 + 0.827333i \(0.689857\pi\)
\(182\) 8.89726e8 0.0601084
\(183\) 5.32369e10 3.50900
\(184\) 9.36449e9 0.602288
\(185\) 2.52335e10 1.58382
\(186\) 3.52306e9 0.215830
\(187\) 0 0
\(188\) 1.28512e10 0.750300
\(189\) −4.89782e10 −2.79206
\(190\) −1.06094e10 −0.590611
\(191\) 2.65734e10 1.44476 0.722382 0.691494i \(-0.243047\pi\)
0.722382 + 0.691494i \(0.243047\pi\)
\(192\) −1.56611e10 −0.831702
\(193\) 8.35519e8 0.0433460 0.0216730 0.999765i \(-0.493101\pi\)
0.0216730 + 0.999765i \(0.493101\pi\)
\(194\) −5.06603e9 −0.256779
\(195\) −5.83681e9 −0.289081
\(196\) −1.70208e10 −0.823811
\(197\) −2.26220e10 −1.07012 −0.535061 0.844813i \(-0.679712\pi\)
−0.535061 + 0.844813i \(0.679712\pi\)
\(198\) 1.54853e10 0.716023
\(199\) −7.37113e9 −0.333192 −0.166596 0.986025i \(-0.553278\pi\)
−0.166596 + 0.986025i \(0.553278\pi\)
\(200\) 4.68658e9 0.207119
\(201\) 1.34834e10 0.582663
\(202\) 1.73309e9 0.0732386
\(203\) 3.88558e10 1.60592
\(204\) 0 0
\(205\) 1.35718e10 0.536718
\(206\) −8.52916e9 −0.329992
\(207\) 5.77173e10 2.18494
\(208\) 2.73294e9 0.101238
\(209\) 4.88717e10 1.77174
\(210\) −2.48601e10 −0.882096
\(211\) 4.36911e10 1.51748 0.758739 0.651395i \(-0.225816\pi\)
0.758739 + 0.651395i \(0.225816\pi\)
\(212\) −8.22571e8 −0.0279680
\(213\) 5.94093e10 1.97763
\(214\) 3.46855e9 0.113054
\(215\) 3.93434e10 1.25574
\(216\) 3.81099e10 1.19123
\(217\) 1.77556e10 0.543584
\(218\) 6.12616e9 0.183711
\(219\) 8.07516e10 2.37221
\(220\) −3.94406e10 −1.13512
\(221\) 0 0
\(222\) 2.70674e10 0.747925
\(223\) −4.77247e10 −1.29232 −0.646162 0.763201i \(-0.723627\pi\)
−0.646162 + 0.763201i \(0.723627\pi\)
\(224\) 4.23661e10 1.12435
\(225\) 2.88854e10 0.751375
\(226\) −1.01164e10 −0.257952
\(227\) 1.11533e10 0.278795 0.139398 0.990236i \(-0.455483\pi\)
0.139398 + 0.990236i \(0.455483\pi\)
\(228\) 1.07210e11 2.62741
\(229\) −3.24445e9 −0.0779617 −0.0389809 0.999240i \(-0.512411\pi\)
−0.0389809 + 0.999240i \(0.512411\pi\)
\(230\) 1.56047e10 0.367689
\(231\) 1.14516e11 2.64614
\(232\) −3.02336e10 −0.685164
\(233\) −3.64924e10 −0.811149 −0.405575 0.914062i \(-0.632929\pi\)
−0.405575 + 0.914062i \(0.632929\pi\)
\(234\) −4.26691e9 −0.0930340
\(235\) 4.51031e10 0.964719
\(236\) 7.23820e10 1.51889
\(237\) 7.58869e10 1.56242
\(238\) 0 0
\(239\) −8.38967e10 −1.66324 −0.831619 0.555347i \(-0.812586\pi\)
−0.831619 + 0.555347i \(0.812586\pi\)
\(240\) −7.63617e10 −1.48568
\(241\) 3.00413e10 0.573644 0.286822 0.957984i \(-0.407401\pi\)
0.286822 + 0.957984i \(0.407401\pi\)
\(242\) −2.75749e9 −0.0516827
\(243\) 2.88037e10 0.529931
\(244\) −9.91229e10 −1.79027
\(245\) −5.97367e10 −1.05924
\(246\) 1.45582e10 0.253454
\(247\) −1.34664e10 −0.230204
\(248\) −1.38156e10 −0.231920
\(249\) 3.37568e10 0.556499
\(250\) −1.44306e10 −0.233643
\(251\) −4.24314e10 −0.674770 −0.337385 0.941367i \(-0.609542\pi\)
−0.337385 + 0.941367i \(0.609542\pi\)
\(252\) 1.71204e11 2.67431
\(253\) −7.18820e10 −1.10301
\(254\) −1.08410e10 −0.163425
\(255\) 0 0
\(256\) 1.18465e10 0.172390
\(257\) −6.81051e10 −0.973824 −0.486912 0.873451i \(-0.661877\pi\)
−0.486912 + 0.873451i \(0.661877\pi\)
\(258\) 4.22027e10 0.592996
\(259\) 1.36415e11 1.88371
\(260\) 1.08677e10 0.147488
\(261\) −1.86343e11 −2.48559
\(262\) −2.78850e9 −0.0365607
\(263\) 5.16210e10 0.665313 0.332656 0.943048i \(-0.392055\pi\)
0.332656 + 0.943048i \(0.392055\pi\)
\(264\) −8.91050e10 −1.12898
\(265\) −2.88692e9 −0.0359607
\(266\) −5.73558e10 −0.702441
\(267\) 2.70662e11 3.25931
\(268\) −2.51050e10 −0.297272
\(269\) −9.39280e10 −1.09373 −0.546865 0.837221i \(-0.684179\pi\)
−0.546865 + 0.837221i \(0.684179\pi\)
\(270\) 6.35051e10 0.727230
\(271\) 5.18776e10 0.584276 0.292138 0.956376i \(-0.405633\pi\)
0.292138 + 0.956376i \(0.405633\pi\)
\(272\) 0 0
\(273\) −3.15544e10 −0.343818
\(274\) −1.23400e9 −0.0132263
\(275\) −3.59743e10 −0.379311
\(276\) −1.57688e11 −1.63571
\(277\) −3.86848e9 −0.0394804 −0.0197402 0.999805i \(-0.506284\pi\)
−0.0197402 + 0.999805i \(0.506284\pi\)
\(278\) −7.62288e9 −0.0765451
\(279\) −8.51515e10 −0.841343
\(280\) 9.74885e10 0.947855
\(281\) −8.99774e10 −0.860904 −0.430452 0.902613i \(-0.641646\pi\)
−0.430452 + 0.902613i \(0.641646\pi\)
\(282\) 4.83810e10 0.455569
\(283\) 1.82003e11 1.68671 0.843353 0.537360i \(-0.180578\pi\)
0.843353 + 0.537360i \(0.180578\pi\)
\(284\) −1.10615e11 −1.00898
\(285\) 3.76267e11 3.37827
\(286\) 5.31407e9 0.0469656
\(287\) 7.33708e10 0.638344
\(288\) −2.03178e11 −1.74024
\(289\) 0 0
\(290\) −5.03804e10 −0.418284
\(291\) 1.79668e11 1.46877
\(292\) −1.50353e11 −1.21029
\(293\) −2.62335e10 −0.207947 −0.103973 0.994580i \(-0.533156\pi\)
−0.103973 + 0.994580i \(0.533156\pi\)
\(294\) −6.40781e10 −0.500203
\(295\) 2.54034e11 1.95296
\(296\) −1.06144e11 −0.803682
\(297\) −2.92532e11 −2.18157
\(298\) 9.65934e9 0.0709536
\(299\) 1.98067e10 0.143315
\(300\) −7.89169e10 −0.562502
\(301\) 2.12695e11 1.49351
\(302\) −8.34459e9 −0.0577263
\(303\) −6.14645e10 −0.418922
\(304\) −1.76177e11 −1.18309
\(305\) −3.47884e11 −2.30190
\(306\) 0 0
\(307\) −1.12502e11 −0.722830 −0.361415 0.932405i \(-0.617706\pi\)
−0.361415 + 0.932405i \(0.617706\pi\)
\(308\) −2.13220e11 −1.35005
\(309\) 3.02489e11 1.88754
\(310\) −2.30219e10 −0.141584
\(311\) −1.05036e11 −0.636674 −0.318337 0.947978i \(-0.603124\pi\)
−0.318337 + 0.947978i \(0.603124\pi\)
\(312\) 2.45524e10 0.146689
\(313\) 2.38828e11 1.40648 0.703242 0.710950i \(-0.251735\pi\)
0.703242 + 0.710950i \(0.251735\pi\)
\(314\) 3.83274e10 0.222498
\(315\) 6.00863e11 3.43857
\(316\) −1.41295e11 −0.797142
\(317\) 8.68678e10 0.483161 0.241581 0.970381i \(-0.422334\pi\)
0.241581 + 0.970381i \(0.422334\pi\)
\(318\) −3.09673e9 −0.0169817
\(319\) 2.32074e11 1.25478
\(320\) 1.02340e11 0.545595
\(321\) −1.23013e11 −0.646664
\(322\) 8.43607e10 0.437309
\(323\) 0 0
\(324\) −2.58017e11 −1.30076
\(325\) 9.91253e9 0.0492844
\(326\) 6.18186e9 0.0303138
\(327\) −2.17266e11 −1.05082
\(328\) −5.70897e10 −0.272349
\(329\) 2.43832e11 1.14739
\(330\) −1.48482e11 −0.689225
\(331\) −2.31728e11 −1.06109 −0.530546 0.847656i \(-0.678013\pi\)
−0.530546 + 0.847656i \(0.678013\pi\)
\(332\) −6.28525e10 −0.283923
\(333\) −6.54213e11 −2.91555
\(334\) 4.74157e9 0.0208479
\(335\) −8.81093e10 −0.382226
\(336\) −4.12820e11 −1.76699
\(337\) −1.29186e11 −0.545610 −0.272805 0.962069i \(-0.587951\pi\)
−0.272805 + 0.962069i \(0.587951\pi\)
\(338\) 7.28686e10 0.303679
\(339\) 3.58782e11 1.47548
\(340\) 0 0
\(341\) 1.06049e11 0.424729
\(342\) 2.75064e11 1.08722
\(343\) 3.14488e10 0.122682
\(344\) −1.65497e11 −0.637204
\(345\) −5.53426e11 −2.10316
\(346\) −5.10796e10 −0.191604
\(347\) −3.89281e11 −1.44139 −0.720693 0.693254i \(-0.756176\pi\)
−0.720693 + 0.693254i \(0.756176\pi\)
\(348\) 5.09102e11 1.86079
\(349\) −1.79089e11 −0.646181 −0.323090 0.946368i \(-0.604722\pi\)
−0.323090 + 0.946368i \(0.604722\pi\)
\(350\) 4.22194e10 0.150385
\(351\) 8.06058e10 0.283455
\(352\) 2.53040e11 0.878513
\(353\) 1.53076e11 0.524711 0.262355 0.964971i \(-0.415501\pi\)
0.262355 + 0.964971i \(0.415501\pi\)
\(354\) 2.72496e11 0.922244
\(355\) −3.88219e11 −1.29732
\(356\) −5.03950e11 −1.66289
\(357\) 0 0
\(358\) 5.60139e9 0.0180228
\(359\) 4.54830e11 1.44519 0.722593 0.691274i \(-0.242950\pi\)
0.722593 + 0.691274i \(0.242950\pi\)
\(360\) −4.67530e11 −1.46706
\(361\) 5.45415e11 1.69022
\(362\) 1.13707e11 0.348016
\(363\) 9.77953e10 0.295623
\(364\) 5.87518e10 0.175414
\(365\) −5.27683e11 −1.55616
\(366\) −3.73167e11 −1.08702
\(367\) 2.38622e11 0.686616 0.343308 0.939223i \(-0.388453\pi\)
0.343308 + 0.939223i \(0.388453\pi\)
\(368\) 2.59127e11 0.736543
\(369\) −3.51868e11 −0.988010
\(370\) −1.76876e11 −0.490638
\(371\) −1.56070e10 −0.0427697
\(372\) 2.32640e11 0.629856
\(373\) 2.17508e11 0.581816 0.290908 0.956751i \(-0.406043\pi\)
0.290908 + 0.956751i \(0.406043\pi\)
\(374\) 0 0
\(375\) 5.11784e11 1.33643
\(376\) −1.89725e11 −0.489531
\(377\) −6.39469e10 −0.163036
\(378\) 3.43316e11 0.864929
\(379\) 1.13663e11 0.282972 0.141486 0.989940i \(-0.454812\pi\)
0.141486 + 0.989940i \(0.454812\pi\)
\(380\) −7.00579e11 −1.72358
\(381\) 3.84479e11 0.934782
\(382\) −1.86268e11 −0.447562
\(383\) −3.84471e11 −0.912996 −0.456498 0.889724i \(-0.650896\pi\)
−0.456498 + 0.889724i \(0.650896\pi\)
\(384\) 7.23797e11 1.69874
\(385\) −7.48324e11 −1.73587
\(386\) −5.85662e9 −0.0134278
\(387\) −1.02003e12 −2.31161
\(388\) −3.34528e11 −0.749359
\(389\) 4.29907e11 0.951921 0.475961 0.879467i \(-0.342100\pi\)
0.475961 + 0.879467i \(0.342100\pi\)
\(390\) 4.09135e10 0.0895520
\(391\) 0 0
\(392\) 2.51281e11 0.537493
\(393\) 9.88948e10 0.209126
\(394\) 1.58571e11 0.331504
\(395\) −4.95894e11 −1.02495
\(396\) 1.02255e12 2.08957
\(397\) 7.51343e10 0.151803 0.0759017 0.997115i \(-0.475816\pi\)
0.0759017 + 0.997115i \(0.475816\pi\)
\(398\) 5.16683e10 0.103217
\(399\) 2.03414e12 4.01793
\(400\) 1.29684e11 0.253288
\(401\) −4.04002e11 −0.780251 −0.390125 0.920762i \(-0.627568\pi\)
−0.390125 + 0.920762i \(0.627568\pi\)
\(402\) −9.45128e10 −0.180498
\(403\) −2.92213e10 −0.0551857
\(404\) 1.14442e11 0.213732
\(405\) −9.05545e11 −1.67249
\(406\) −2.72362e11 −0.497484
\(407\) 8.14767e11 1.47183
\(408\) 0 0
\(409\) 9.13773e11 1.61467 0.807334 0.590094i \(-0.200909\pi\)
0.807334 + 0.590094i \(0.200909\pi\)
\(410\) −9.51326e10 −0.166265
\(411\) 4.37643e10 0.0756541
\(412\) −5.63211e11 −0.963016
\(413\) 1.37333e12 2.32274
\(414\) −4.04573e11 −0.676855
\(415\) −2.20589e11 −0.365063
\(416\) −6.97240e10 −0.114146
\(417\) 2.70348e11 0.437835
\(418\) −3.42569e11 −0.548852
\(419\) −1.00256e12 −1.58909 −0.794546 0.607204i \(-0.792291\pi\)
−0.794546 + 0.607204i \(0.792291\pi\)
\(420\) −1.64160e12 −2.57422
\(421\) −2.42505e11 −0.376229 −0.188114 0.982147i \(-0.560238\pi\)
−0.188114 + 0.982147i \(0.560238\pi\)
\(422\) −3.06256e11 −0.470087
\(423\) −1.16936e12 −1.77589
\(424\) 1.21438e10 0.0182477
\(425\) 0 0
\(426\) −4.16433e11 −0.612635
\(427\) −1.88070e12 −2.73775
\(428\) 2.29040e11 0.329925
\(429\) −1.88465e11 −0.268641
\(430\) −2.75780e11 −0.389004
\(431\) 9.69783e11 1.35371 0.676857 0.736114i \(-0.263341\pi\)
0.676857 + 0.736114i \(0.263341\pi\)
\(432\) 1.05455e12 1.45677
\(433\) −1.45177e12 −1.98473 −0.992366 0.123330i \(-0.960642\pi\)
−0.992366 + 0.123330i \(0.960642\pi\)
\(434\) −1.24459e11 −0.168392
\(435\) 1.78676e12 2.39257
\(436\) 4.04532e11 0.536122
\(437\) −1.27683e12 −1.67482
\(438\) −5.66033e11 −0.734867
\(439\) 4.81662e11 0.618945 0.309473 0.950908i \(-0.399847\pi\)
0.309473 + 0.950908i \(0.399847\pi\)
\(440\) 5.82270e11 0.740606
\(441\) 1.54875e12 1.94988
\(442\) 0 0
\(443\) 7.63906e11 0.942374 0.471187 0.882033i \(-0.343826\pi\)
0.471187 + 0.882033i \(0.343826\pi\)
\(444\) 1.78736e12 2.18267
\(445\) −1.76868e12 −2.13810
\(446\) 3.34529e11 0.400338
\(447\) −3.42571e11 −0.405852
\(448\) 5.53261e11 0.648902
\(449\) 6.18932e11 0.718678 0.359339 0.933207i \(-0.383002\pi\)
0.359339 + 0.933207i \(0.383002\pi\)
\(450\) −2.02474e11 −0.232762
\(451\) 4.38222e11 0.498769
\(452\) −6.68024e11 −0.752782
\(453\) 2.95943e11 0.330192
\(454\) −7.81795e10 −0.0863657
\(455\) 2.06197e11 0.225544
\(456\) −1.58276e12 −1.71425
\(457\) 7.94938e11 0.852532 0.426266 0.904598i \(-0.359829\pi\)
0.426266 + 0.904598i \(0.359829\pi\)
\(458\) 2.27422e10 0.0241511
\(459\) 0 0
\(460\) 1.03043e12 1.07303
\(461\) 1.01020e12 1.04173 0.520863 0.853640i \(-0.325610\pi\)
0.520863 + 0.853640i \(0.325610\pi\)
\(462\) −8.02709e11 −0.819727
\(463\) 1.72927e12 1.74883 0.874414 0.485180i \(-0.161246\pi\)
0.874414 + 0.485180i \(0.161246\pi\)
\(464\) −8.36604e11 −0.837893
\(465\) 8.16479e11 0.809854
\(466\) 2.55796e11 0.251279
\(467\) −6.73051e10 −0.0654820 −0.0327410 0.999464i \(-0.510424\pi\)
−0.0327410 + 0.999464i \(0.510424\pi\)
\(468\) −2.81759e11 −0.271501
\(469\) −4.76328e11 −0.454599
\(470\) −3.16153e11 −0.298852
\(471\) −1.35929e12 −1.27268
\(472\) −1.06859e12 −0.990996
\(473\) 1.27036e12 1.16695
\(474\) −5.31934e11 −0.484011
\(475\) −6.39007e11 −0.575949
\(476\) 0 0
\(477\) 7.48472e10 0.0661977
\(478\) 5.88079e11 0.515241
\(479\) 2.10574e12 1.82766 0.913830 0.406097i \(-0.133111\pi\)
0.913830 + 0.406097i \(0.133111\pi\)
\(480\) 1.94818e12 1.67511
\(481\) −2.24505e11 −0.191238
\(482\) −2.10577e11 −0.177704
\(483\) −2.99188e12 −2.50139
\(484\) −1.82087e11 −0.150826
\(485\) −1.17407e12 −0.963509
\(486\) −2.01901e11 −0.164163
\(487\) 1.06942e12 0.861522 0.430761 0.902466i \(-0.358245\pi\)
0.430761 + 0.902466i \(0.358245\pi\)
\(488\) 1.46337e12 1.16806
\(489\) −2.19242e11 −0.173394
\(490\) 4.18728e11 0.328133
\(491\) 3.63691e10 0.0282400 0.0141200 0.999900i \(-0.495505\pi\)
0.0141200 + 0.999900i \(0.495505\pi\)
\(492\) 9.61329e11 0.739654
\(493\) 0 0
\(494\) 9.43932e10 0.0713131
\(495\) 3.58877e12 2.68672
\(496\) −3.82296e11 −0.283617
\(497\) −2.09875e12 −1.54297
\(498\) −2.36621e11 −0.172393
\(499\) 1.51766e12 1.09578 0.547888 0.836552i \(-0.315432\pi\)
0.547888 + 0.836552i \(0.315432\pi\)
\(500\) −9.52901e11 −0.681840
\(501\) −1.68161e11 −0.119249
\(502\) 2.97426e11 0.209031
\(503\) −1.28396e12 −0.894328 −0.447164 0.894452i \(-0.647566\pi\)
−0.447164 + 0.894452i \(0.647566\pi\)
\(504\) −2.52752e12 −1.74485
\(505\) 4.01649e11 0.274812
\(506\) 5.03861e11 0.341691
\(507\) −2.58431e12 −1.73703
\(508\) −7.15869e11 −0.476921
\(509\) −1.62951e12 −1.07604 −0.538018 0.842934i \(-0.680827\pi\)
−0.538018 + 0.842934i \(0.680827\pi\)
\(510\) 0 0
\(511\) −2.85271e12 −1.85082
\(512\) −1.57375e12 −1.01209
\(513\) −5.19622e12 −3.31252
\(514\) 4.77387e11 0.301673
\(515\) −1.97666e12 −1.23822
\(516\) 2.78680e12 1.73054
\(517\) 1.45634e12 0.896509
\(518\) −9.56210e11 −0.583538
\(519\) 1.81155e12 1.09597
\(520\) −1.60442e11 −0.0962280
\(521\) −2.49853e12 −1.48565 −0.742823 0.669488i \(-0.766513\pi\)
−0.742823 + 0.669488i \(0.766513\pi\)
\(522\) 1.30618e12 0.769992
\(523\) −2.86852e12 −1.67649 −0.838244 0.545295i \(-0.816417\pi\)
−0.838244 + 0.545295i \(0.816417\pi\)
\(524\) −1.84134e11 −0.106695
\(525\) −1.49732e12 −0.860198
\(526\) −3.61841e11 −0.206102
\(527\) 0 0
\(528\) −2.46565e12 −1.38063
\(529\) 7.68525e10 0.0426685
\(530\) 2.02360e10 0.0111400
\(531\) −6.58617e12 −3.59507
\(532\) −3.78741e12 −2.04993
\(533\) −1.20750e11 −0.0648059
\(534\) −1.89722e12 −1.00968
\(535\) 8.03847e11 0.424210
\(536\) 3.70630e11 0.193954
\(537\) −1.98655e11 −0.103090
\(538\) 6.58394e11 0.338817
\(539\) −1.92884e12 −0.984344
\(540\) 4.19347e12 2.12227
\(541\) 5.94020e11 0.298135 0.149068 0.988827i \(-0.452373\pi\)
0.149068 + 0.988827i \(0.452373\pi\)
\(542\) −3.63639e11 −0.180998
\(543\) −4.03266e12 −1.99064
\(544\) 0 0
\(545\) 1.41976e12 0.689334
\(546\) 2.21182e11 0.106508
\(547\) 6.01511e11 0.287277 0.143639 0.989630i \(-0.454120\pi\)
0.143639 + 0.989630i \(0.454120\pi\)
\(548\) −8.14857e10 −0.0385984
\(549\) 9.01937e12 4.23741
\(550\) 2.52164e11 0.117503
\(551\) 4.12231e12 1.90528
\(552\) 2.32798e12 1.06722
\(553\) −2.68085e12 −1.21902
\(554\) 2.71163e10 0.0122303
\(555\) 6.27296e12 2.80643
\(556\) −5.03366e11 −0.223382
\(557\) 2.06033e12 0.906959 0.453480 0.891267i \(-0.350182\pi\)
0.453480 + 0.891267i \(0.350182\pi\)
\(558\) 5.96874e11 0.260633
\(559\) −3.50042e11 −0.151624
\(560\) 2.69763e12 1.15914
\(561\) 0 0
\(562\) 6.30702e11 0.266692
\(563\) 2.45629e12 1.03037 0.515183 0.857080i \(-0.327724\pi\)
0.515183 + 0.857080i \(0.327724\pi\)
\(564\) 3.19477e12 1.32949
\(565\) −2.34452e12 −0.967910
\(566\) −1.27576e12 −0.522511
\(567\) −4.89547e12 −1.98917
\(568\) 1.63304e12 0.658306
\(569\) −3.63389e11 −0.145334 −0.0726669 0.997356i \(-0.523151\pi\)
−0.0726669 + 0.997356i \(0.523151\pi\)
\(570\) −2.63747e12 −1.04653
\(571\) 2.95458e11 0.116314 0.0581572 0.998307i \(-0.481478\pi\)
0.0581572 + 0.998307i \(0.481478\pi\)
\(572\) 3.50907e11 0.137060
\(573\) 6.60605e12 2.56003
\(574\) −5.14297e11 −0.197747
\(575\) 9.39871e11 0.358561
\(576\) −2.65330e12 −1.00435
\(577\) −3.92296e12 −1.47341 −0.736703 0.676217i \(-0.763618\pi\)
−0.736703 + 0.676217i \(0.763618\pi\)
\(578\) 0 0
\(579\) 2.07707e11 0.0768064
\(580\) −3.32680e12 −1.22068
\(581\) −1.19253e12 −0.434186
\(582\) −1.25940e12 −0.454997
\(583\) −9.32159e10 −0.0334181
\(584\) 2.21969e12 0.789650
\(585\) −9.88869e11 −0.349090
\(586\) 1.83885e11 0.0644181
\(587\) −9.38917e11 −0.326404 −0.163202 0.986593i \(-0.552182\pi\)
−0.163202 + 0.986593i \(0.552182\pi\)
\(588\) −4.23130e12 −1.45974
\(589\) 1.88374e12 0.644913
\(590\) −1.78067e12 −0.604990
\(591\) −5.62375e12 −1.89619
\(592\) −2.93715e12 −0.982831
\(593\) −1.11640e12 −0.370743 −0.185372 0.982668i \(-0.559349\pi\)
−0.185372 + 0.982668i \(0.559349\pi\)
\(594\) 2.05052e12 0.675811
\(595\) 0 0
\(596\) 6.37841e11 0.207064
\(597\) −1.83243e12 −0.590396
\(598\) −1.38837e11 −0.0443965
\(599\) 3.47623e12 1.10329 0.551643 0.834080i \(-0.314001\pi\)
0.551643 + 0.834080i \(0.314001\pi\)
\(600\) 1.16506e12 0.367003
\(601\) −2.69936e12 −0.843969 −0.421984 0.906603i \(-0.638666\pi\)
−0.421984 + 0.906603i \(0.638666\pi\)
\(602\) −1.49090e12 −0.462661
\(603\) 2.28435e12 0.703615
\(604\) −5.51023e11 −0.168463
\(605\) −6.39058e11 −0.193928
\(606\) 4.30839e11 0.129774
\(607\) 2.93363e10 0.00877114 0.00438557 0.999990i \(-0.498604\pi\)
0.00438557 + 0.999990i \(0.498604\pi\)
\(608\) 4.49473e12 1.33394
\(609\) 9.65940e12 2.84559
\(610\) 2.43852e12 0.713085
\(611\) −4.01286e11 −0.116485
\(612\) 0 0
\(613\) 8.08148e11 0.231163 0.115582 0.993298i \(-0.463127\pi\)
0.115582 + 0.993298i \(0.463127\pi\)
\(614\) 7.88587e11 0.223919
\(615\) 3.37391e12 0.951032
\(616\) 3.14781e12 0.880837
\(617\) −6.66373e12 −1.85112 −0.925559 0.378603i \(-0.876405\pi\)
−0.925559 + 0.378603i \(0.876405\pi\)
\(618\) −2.12032e12 −0.584726
\(619\) −3.87308e12 −1.06035 −0.530175 0.847888i \(-0.677874\pi\)
−0.530175 + 0.847888i \(0.677874\pi\)
\(620\) −1.52022e12 −0.413184
\(621\) 7.64276e12 2.06223
\(622\) 7.36257e11 0.197230
\(623\) −9.56166e12 −2.54295
\(624\) 6.79397e11 0.179388
\(625\) −4.68385e12 −1.22784
\(626\) −1.67408e12 −0.435703
\(627\) 1.21493e13 3.13941
\(628\) 2.53089e12 0.649315
\(629\) 0 0
\(630\) −4.21178e12 −1.06521
\(631\) −5.76051e12 −1.44653 −0.723267 0.690568i \(-0.757360\pi\)
−0.723267 + 0.690568i \(0.757360\pi\)
\(632\) 2.08597e12 0.520093
\(633\) 1.08614e13 2.68888
\(634\) −6.08905e11 −0.149674
\(635\) −2.51243e12 −0.613215
\(636\) −2.04488e11 −0.0495576
\(637\) 5.31483e11 0.127897
\(638\) −1.62674e12 −0.388709
\(639\) 1.00651e13 2.38816
\(640\) −4.72976e12 −1.11437
\(641\) 2.94103e12 0.688079 0.344039 0.938955i \(-0.388205\pi\)
0.344039 + 0.938955i \(0.388205\pi\)
\(642\) 8.62267e11 0.200325
\(643\) 4.08339e12 0.942044 0.471022 0.882122i \(-0.343885\pi\)
0.471022 + 0.882122i \(0.343885\pi\)
\(644\) 5.57064e12 1.27620
\(645\) 9.78062e12 2.22509
\(646\) 0 0
\(647\) 4.11077e12 0.922262 0.461131 0.887332i \(-0.347444\pi\)
0.461131 + 0.887332i \(0.347444\pi\)
\(648\) 3.80916e12 0.848676
\(649\) 8.20252e12 1.81487
\(650\) −6.94825e10 −0.0152674
\(651\) 4.41397e12 0.963198
\(652\) 4.08210e11 0.0884646
\(653\) 4.38279e12 0.943282 0.471641 0.881791i \(-0.343662\pi\)
0.471641 + 0.881791i \(0.343662\pi\)
\(654\) 1.52294e12 0.325524
\(655\) −6.46243e11 −0.137186
\(656\) −1.57975e12 −0.333058
\(657\) 1.36809e13 2.86464
\(658\) −1.70916e12 −0.355439
\(659\) 1.21956e12 0.251894 0.125947 0.992037i \(-0.459803\pi\)
0.125947 + 0.992037i \(0.459803\pi\)
\(660\) −9.80479e12 −2.01136
\(661\) −6.37742e12 −1.29939 −0.649694 0.760196i \(-0.725103\pi\)
−0.649694 + 0.760196i \(0.725103\pi\)
\(662\) 1.62431e12 0.328707
\(663\) 0 0
\(664\) 9.27904e11 0.185245
\(665\) −1.32924e13 −2.63576
\(666\) 4.58574e12 0.903183
\(667\) −6.06322e12 −1.18614
\(668\) 3.13103e11 0.0608405
\(669\) −1.18642e13 −2.28992
\(670\) 6.17608e11 0.118407
\(671\) −1.12329e13 −2.13914
\(672\) 1.05321e13 1.99229
\(673\) 1.25663e12 0.236124 0.118062 0.993006i \(-0.462332\pi\)
0.118062 + 0.993006i \(0.462332\pi\)
\(674\) 9.05539e11 0.169020
\(675\) 3.82491e12 0.709177
\(676\) 4.81177e12 0.886227
\(677\) −9.83587e11 −0.179955 −0.0899775 0.995944i \(-0.528679\pi\)
−0.0899775 + 0.995944i \(0.528679\pi\)
\(678\) −2.51491e12 −0.457076
\(679\) −6.34714e12 −1.14595
\(680\) 0 0
\(681\) 2.77266e12 0.494008
\(682\) −7.43357e11 −0.131573
\(683\) 5.43786e12 0.956169 0.478084 0.878314i \(-0.341331\pi\)
0.478084 + 0.878314i \(0.341331\pi\)
\(684\) 1.81635e13 3.17283
\(685\) −2.85985e11 −0.0496289
\(686\) −2.20443e11 −0.0380047
\(687\) −8.06558e11 −0.138143
\(688\) −4.57952e12 −0.779242
\(689\) 2.56852e10 0.00434206
\(690\) 3.87927e12 0.651522
\(691\) −7.35157e12 −1.22667 −0.613337 0.789821i \(-0.710173\pi\)
−0.613337 + 0.789821i \(0.710173\pi\)
\(692\) −3.37297e12 −0.559159
\(693\) 1.94013e13 3.19544
\(694\) 2.72869e12 0.446515
\(695\) −1.76663e12 −0.287219
\(696\) −7.51597e12 −1.21407
\(697\) 0 0
\(698\) 1.25533e12 0.200175
\(699\) −9.07187e12 −1.43731
\(700\) 2.78790e12 0.438869
\(701\) −2.91902e12 −0.456568 −0.228284 0.973595i \(-0.573311\pi\)
−0.228284 + 0.973595i \(0.573311\pi\)
\(702\) −5.65011e11 −0.0878092
\(703\) 1.44726e13 2.23485
\(704\) 3.30446e12 0.507019
\(705\) 1.12125e13 1.70942
\(706\) −1.07299e12 −0.162546
\(707\) 2.17136e12 0.326846
\(708\) 1.79939e13 2.69138
\(709\) −1.06024e13 −1.57577 −0.787887 0.615819i \(-0.788825\pi\)
−0.787887 + 0.615819i \(0.788825\pi\)
\(710\) 2.72124e12 0.401887
\(711\) 1.28567e13 1.88676
\(712\) 7.43992e12 1.08495
\(713\) −2.77066e12 −0.401495
\(714\) 0 0
\(715\) 1.23155e12 0.176228
\(716\) 3.69880e11 0.0525959
\(717\) −2.08564e13 −2.94716
\(718\) −3.18816e12 −0.447692
\(719\) 1.29087e13 1.80137 0.900683 0.434477i \(-0.143067\pi\)
0.900683 + 0.434477i \(0.143067\pi\)
\(720\) −1.29372e13 −1.79408
\(721\) −1.06860e13 −1.47268
\(722\) −3.82312e12 −0.523601
\(723\) 7.46816e12 1.01646
\(724\) 7.50848e12 1.01561
\(725\) −3.03441e12 −0.407900
\(726\) −6.85502e11 −0.0915786
\(727\) 9.77625e12 1.29798 0.648989 0.760797i \(-0.275192\pi\)
0.648989 + 0.760797i \(0.275192\pi\)
\(728\) −8.67364e11 −0.114448
\(729\) −3.81150e12 −0.499830
\(730\) 3.69883e12 0.482071
\(731\) 0 0
\(732\) −2.46416e13 −3.17226
\(733\) 4.87882e11 0.0624233 0.0312116 0.999513i \(-0.490063\pi\)
0.0312116 + 0.999513i \(0.490063\pi\)
\(734\) −1.67264e12 −0.212701
\(735\) −1.48503e13 −1.87690
\(736\) −6.61099e12 −0.830455
\(737\) −2.84497e12 −0.355201
\(738\) 2.46644e12 0.306067
\(739\) −1.08646e13 −1.34003 −0.670017 0.742346i \(-0.733713\pi\)
−0.670017 + 0.742346i \(0.733713\pi\)
\(740\) −1.16797e13 −1.43183
\(741\) −3.34768e12 −0.407908
\(742\) 1.09398e11 0.0132493
\(743\) 1.10195e13 1.32651 0.663257 0.748392i \(-0.269174\pi\)
0.663257 + 0.748392i \(0.269174\pi\)
\(744\) −3.43451e12 −0.410947
\(745\) 2.23858e12 0.266238
\(746\) −1.52464e12 −0.180236
\(747\) 5.71907e12 0.672020
\(748\) 0 0
\(749\) 4.34568e12 0.504533
\(750\) −3.58738e12 −0.414001
\(751\) 3.58977e12 0.411801 0.205900 0.978573i \(-0.433988\pi\)
0.205900 + 0.978573i \(0.433988\pi\)
\(752\) −5.24995e12 −0.598652
\(753\) −1.05483e13 −1.19565
\(754\) 4.48239e11 0.0505055
\(755\) −1.93389e12 −0.216606
\(756\) 2.26703e13 2.52412
\(757\) −2.28696e12 −0.253120 −0.126560 0.991959i \(-0.540394\pi\)
−0.126560 + 0.991959i \(0.540394\pi\)
\(758\) −7.96729e11 −0.0876596
\(759\) −1.78696e13 −1.95446
\(760\) 1.03428e13 1.12454
\(761\) −1.64862e13 −1.78193 −0.890963 0.454075i \(-0.849970\pi\)
−0.890963 + 0.454075i \(0.849970\pi\)
\(762\) −2.69503e12 −0.289578
\(763\) 7.67536e12 0.819857
\(764\) −1.22999e13 −1.30612
\(765\) 0 0
\(766\) 2.69497e12 0.282829
\(767\) −2.26016e12 −0.235809
\(768\) 2.94500e12 0.305464
\(769\) 1.24332e13 1.28208 0.641041 0.767507i \(-0.278503\pi\)
0.641041 + 0.767507i \(0.278503\pi\)
\(770\) 5.24542e12 0.537740
\(771\) −1.69307e13 −1.72556
\(772\) −3.86734e11 −0.0391863
\(773\) 1.06939e12 0.107728 0.0538642 0.998548i \(-0.482846\pi\)
0.0538642 + 0.998548i \(0.482846\pi\)
\(774\) 7.14997e12 0.716093
\(775\) −1.38661e12 −0.138069
\(776\) 4.93870e12 0.488917
\(777\) 3.39123e13 3.33781
\(778\) −3.01346e12 −0.294888
\(779\) 7.78409e12 0.757337
\(780\) 2.70166e12 0.261339
\(781\) −1.25352e13 −1.20560
\(782\) 0 0
\(783\) −2.46750e13 −2.34600
\(784\) 6.95328e12 0.657305
\(785\) 8.88249e12 0.834875
\(786\) −6.93209e11 −0.0647833
\(787\) −1.51542e13 −1.40815 −0.704073 0.710128i \(-0.748637\pi\)
−0.704073 + 0.710128i \(0.748637\pi\)
\(788\) 1.04710e13 0.967429
\(789\) 1.28328e13 1.17889
\(790\) 3.47600e12 0.317510
\(791\) −1.26747e13 −1.15118
\(792\) −1.50961e13 −1.36333
\(793\) 3.09516e12 0.277942
\(794\) −5.26659e11 −0.0470259
\(795\) −7.17677e11 −0.0637201
\(796\) 3.41184e12 0.301218
\(797\) 1.45731e12 0.127935 0.0639675 0.997952i \(-0.479625\pi\)
0.0639675 + 0.997952i \(0.479625\pi\)
\(798\) −1.42584e13 −1.24468
\(799\) 0 0
\(800\) −3.30855e12 −0.285583
\(801\) 4.58554e13 3.93590
\(802\) 2.83188e12 0.241707
\(803\) −1.70384e13 −1.44614
\(804\) −6.24101e12 −0.526748
\(805\) 1.95509e13 1.64091
\(806\) 2.04828e11 0.0170955
\(807\) −2.33501e13 −1.93802
\(808\) −1.68953e12 −0.139449
\(809\) 3.25669e12 0.267306 0.133653 0.991028i \(-0.457329\pi\)
0.133653 + 0.991028i \(0.457329\pi\)
\(810\) 6.34747e12 0.518106
\(811\) −3.09214e12 −0.250995 −0.125498 0.992094i \(-0.540053\pi\)
−0.125498 + 0.992094i \(0.540053\pi\)
\(812\) −1.79850e13 −1.45181
\(813\) 1.28966e13 1.03530
\(814\) −5.71116e12 −0.455947
\(815\) 1.43267e12 0.113746
\(816\) 0 0
\(817\) 2.25653e13 1.77191
\(818\) −6.40515e12 −0.500195
\(819\) −5.34593e12 −0.415189
\(820\) −6.28194e12 −0.485212
\(821\) −2.16404e13 −1.66235 −0.831173 0.556014i \(-0.812330\pi\)
−0.831173 + 0.556014i \(0.812330\pi\)
\(822\) −3.06769e11 −0.0234362
\(823\) −1.30860e13 −0.994274 −0.497137 0.867672i \(-0.665615\pi\)
−0.497137 + 0.867672i \(0.665615\pi\)
\(824\) 8.31479e12 0.628317
\(825\) −8.94306e12 −0.672115
\(826\) −9.62647e12 −0.719543
\(827\) 2.09145e13 1.55479 0.777395 0.629012i \(-0.216541\pi\)
0.777395 + 0.629012i \(0.216541\pi\)
\(828\) −2.67154e13 −1.97526
\(829\) 1.62798e13 1.19716 0.598582 0.801062i \(-0.295731\pi\)
0.598582 + 0.801062i \(0.295731\pi\)
\(830\) 1.54623e12 0.113090
\(831\) −9.61688e11 −0.0699568
\(832\) −9.10529e11 −0.0658777
\(833\) 0 0
\(834\) −1.89502e12 −0.135633
\(835\) 1.09887e12 0.0782274
\(836\) −2.26211e13 −1.60171
\(837\) −1.12755e13 −0.794093
\(838\) 7.02753e12 0.492271
\(839\) 1.90100e13 1.32450 0.662250 0.749283i \(-0.269601\pi\)
0.662250 + 0.749283i \(0.269601\pi\)
\(840\) 2.42353e13 1.67954
\(841\) 5.06820e12 0.349359
\(842\) 1.69986e12 0.116549
\(843\) −2.23680e13 −1.52547
\(844\) −2.02231e13 −1.37185
\(845\) 1.68875e13 1.13949
\(846\) 8.19669e12 0.550138
\(847\) −3.45481e12 −0.230648
\(848\) 3.36034e11 0.0223152
\(849\) 4.52452e13 2.98874
\(850\) 0 0
\(851\) −2.12868e13 −1.39132
\(852\) −2.74985e13 −1.78785
\(853\) 2.05191e13 1.32705 0.663526 0.748153i \(-0.269059\pi\)
0.663526 + 0.748153i \(0.269059\pi\)
\(854\) 1.31829e13 0.848105
\(855\) 6.37470e13 4.07955
\(856\) −3.38137e12 −0.215259
\(857\) −2.96637e12 −0.187850 −0.0939250 0.995579i \(-0.529941\pi\)
−0.0939250 + 0.995579i \(0.529941\pi\)
\(858\) 1.32106e12 0.0832202
\(859\) 1.06159e13 0.665257 0.332628 0.943058i \(-0.392065\pi\)
0.332628 + 0.943058i \(0.392065\pi\)
\(860\) −1.82107e13 −1.13523
\(861\) 1.82397e13 1.13111
\(862\) −6.79775e12 −0.419356
\(863\) −1.32698e13 −0.814356 −0.407178 0.913349i \(-0.633487\pi\)
−0.407178 + 0.913349i \(0.633487\pi\)
\(864\) −2.69042e13 −1.64251
\(865\) −1.18379e13 −0.718954
\(866\) 1.01763e13 0.614833
\(867\) 0 0
\(868\) −8.21847e12 −0.491419
\(869\) −1.60120e13 −0.952479
\(870\) −1.25244e13 −0.741173
\(871\) 7.83917e11 0.0461518
\(872\) −5.97218e12 −0.349791
\(873\) 3.04393e13 1.77366
\(874\) 8.95003e12 0.518828
\(875\) −1.80798e13 −1.04269
\(876\) −3.73772e13 −2.14456
\(877\) 1.84228e13 1.05162 0.525808 0.850603i \(-0.323763\pi\)
0.525808 + 0.850603i \(0.323763\pi\)
\(878\) −3.37624e12 −0.191738
\(879\) −6.52155e12 −0.368469
\(880\) 1.61121e13 0.905694
\(881\) −1.68763e12 −0.0943813 −0.0471907 0.998886i \(-0.515027\pi\)
−0.0471907 + 0.998886i \(0.515027\pi\)
\(882\) −1.08561e13 −0.604038
\(883\) 4.77050e12 0.264083 0.132042 0.991244i \(-0.457847\pi\)
0.132042 + 0.991244i \(0.457847\pi\)
\(884\) 0 0
\(885\) 6.31518e13 3.46052
\(886\) −5.35464e12 −0.291930
\(887\) 1.25350e13 0.679936 0.339968 0.940437i \(-0.389584\pi\)
0.339968 + 0.940437i \(0.389584\pi\)
\(888\) −2.63871e13 −1.42408
\(889\) −1.35825e13 −0.729325
\(890\) 1.23977e13 0.662346
\(891\) −2.92392e13 −1.55423
\(892\) 2.20901e13 1.16831
\(893\) 2.58687e13 1.36127
\(894\) 2.40128e12 0.125725
\(895\) 1.29814e12 0.0676266
\(896\) −2.55696e13 −1.32537
\(897\) 4.92388e12 0.253946
\(898\) −4.33844e12 −0.222633
\(899\) 8.94518e12 0.456742
\(900\) −1.33701e13 −0.679269
\(901\) 0 0
\(902\) −3.07174e12 −0.154510
\(903\) 5.28751e13 2.64640
\(904\) 9.86217e12 0.491150
\(905\) 2.63520e13 1.30585
\(906\) −2.07443e12 −0.102288
\(907\) −1.39545e13 −0.684668 −0.342334 0.939578i \(-0.611217\pi\)
−0.342334 + 0.939578i \(0.611217\pi\)
\(908\) −5.16247e12 −0.252041
\(909\) −1.04133e13 −0.505883
\(910\) −1.44535e12 −0.0698693
\(911\) 1.75468e13 0.844045 0.422022 0.906585i \(-0.361320\pi\)
0.422022 + 0.906585i \(0.361320\pi\)
\(912\) −4.37970e13 −2.09637
\(913\) −7.12261e12 −0.339251
\(914\) −5.57217e12 −0.264099
\(915\) −8.64827e13 −4.07882
\(916\) 1.50175e12 0.0704801
\(917\) −3.49366e12 −0.163162
\(918\) 0 0
\(919\) 5.57783e12 0.257956 0.128978 0.991647i \(-0.458830\pi\)
0.128978 + 0.991647i \(0.458830\pi\)
\(920\) −1.52125e13 −0.700092
\(921\) −2.79675e13 −1.28081
\(922\) −7.08106e12 −0.322708
\(923\) 3.45402e12 0.156645
\(924\) −5.30057e13 −2.39221
\(925\) −1.06532e13 −0.478458
\(926\) −1.21214e13 −0.541755
\(927\) 5.12476e13 2.27937
\(928\) 2.13438e13 0.944728
\(929\) −2.46767e13 −1.08697 −0.543483 0.839420i \(-0.682895\pi\)
−0.543483 + 0.839420i \(0.682895\pi\)
\(930\) −5.72316e12 −0.250878
\(931\) −3.42618e13 −1.49464
\(932\) 1.68911e13 0.733308
\(933\) −2.61116e13 −1.12815
\(934\) 4.71779e11 0.0202851
\(935\) 0 0
\(936\) 4.15966e12 0.177140
\(937\) 3.72310e13 1.57789 0.788944 0.614465i \(-0.210628\pi\)
0.788944 + 0.614465i \(0.210628\pi\)
\(938\) 3.33885e12 0.140827
\(939\) 5.93716e13 2.49220
\(940\) −2.08767e13 −0.872140
\(941\) 2.09390e13 0.870569 0.435284 0.900293i \(-0.356648\pi\)
0.435284 + 0.900293i \(0.356648\pi\)
\(942\) 9.52803e12 0.394252
\(943\) −1.14491e13 −0.471485
\(944\) −2.95692e13 −1.21190
\(945\) 7.95645e13 3.24546
\(946\) −8.90468e12 −0.361500
\(947\) −3.50065e13 −1.41440 −0.707202 0.707011i \(-0.750043\pi\)
−0.707202 + 0.707011i \(0.750043\pi\)
\(948\) −3.51255e13 −1.41249
\(949\) 4.69485e12 0.187899
\(950\) 4.47916e12 0.178419
\(951\) 2.15950e13 0.856132
\(952\) 0 0
\(953\) 4.83362e12 0.189825 0.0949127 0.995486i \(-0.469743\pi\)
0.0949127 + 0.995486i \(0.469743\pi\)
\(954\) −5.24646e11 −0.0205068
\(955\) −4.31682e13 −1.67938
\(956\) 3.88329e13 1.50363
\(957\) 5.76927e13 2.22340
\(958\) −1.47603e13 −0.566176
\(959\) −1.54606e12 −0.0590260
\(960\) 2.54413e13 0.966761
\(961\) −2.23520e13 −0.845399
\(962\) 1.57368e12 0.0592419
\(963\) −2.08408e13 −0.780902
\(964\) −1.39051e13 −0.518595
\(965\) −1.35729e12 −0.0503849
\(966\) 2.09717e13 0.774885
\(967\) 2.43474e13 0.895436 0.447718 0.894175i \(-0.352237\pi\)
0.447718 + 0.894175i \(0.352237\pi\)
\(968\) 2.68819e12 0.0984057
\(969\) 0 0
\(970\) 8.22971e12 0.298478
\(971\) −1.35465e13 −0.489034 −0.244517 0.969645i \(-0.578629\pi\)
−0.244517 + 0.969645i \(0.578629\pi\)
\(972\) −1.33322e13 −0.479076
\(973\) −9.55057e12 −0.341603
\(974\) −7.49614e12 −0.266884
\(975\) 2.46422e12 0.0873289
\(976\) 4.04933e13 1.42843
\(977\) 3.05916e13 1.07418 0.537090 0.843525i \(-0.319524\pi\)
0.537090 + 0.843525i \(0.319524\pi\)
\(978\) 1.53679e12 0.0537142
\(979\) −5.71090e13 −1.98693
\(980\) 2.76501e13 0.957589
\(981\) −3.68091e13 −1.26895
\(982\) −2.54931e11 −0.00874825
\(983\) −8.75389e12 −0.299027 −0.149514 0.988760i \(-0.547771\pi\)
−0.149514 + 0.988760i \(0.547771\pi\)
\(984\) −1.41923e13 −0.482585
\(985\) 3.67492e13 1.24390
\(986\) 0 0
\(987\) 6.06157e13 2.03310
\(988\) 6.23312e12 0.208113
\(989\) −3.31897e13 −1.10311
\(990\) −2.51557e13 −0.832297
\(991\) 9.06157e12 0.298450 0.149225 0.988803i \(-0.452322\pi\)
0.149225 + 0.988803i \(0.452322\pi\)
\(992\) 9.75332e12 0.319779
\(993\) −5.76068e13 −1.88019
\(994\) 1.47113e13 0.477983
\(995\) 1.19743e13 0.387299
\(996\) −1.56249e13 −0.503095
\(997\) −1.22306e13 −0.392030 −0.196015 0.980601i \(-0.562800\pi\)
−0.196015 + 0.980601i \(0.562800\pi\)
\(998\) −1.06381e13 −0.339451
\(999\) −8.66290e13 −2.75181
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.1.17 yes 36
17.16 even 2 289.10.a.g.1.17 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.17 36 17.16 even 2
289.10.a.h.1.17 yes 36 1.1 even 1 trivial