Properties

Label 289.10.a.g.1.17
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 1.17
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 \(-0.846506\pi\)
−0.885969 + 0.463744i \(0.846506\pi\)
\(4\) −462.866 −0.904035
\(5\) 1624.49 1.16239 0.581194 0.813765i \(-0.302586\pi\)
0.581194 + 0.813765i \(0.302586\pi\)
\(6\) 1742.55 0.548914
\(7\) 8782.15 1.38248 0.691242 0.722624i \(-0.257064\pi\)
0.691242 + 0.722624i \(0.257064\pi\)
\(8\) 6833.38 0.589835
\(9\) 42117.0 2.13977
\(10\) −11386.9 −0.360087
\(11\) 52453.2 1.08020 0.540101 0.841600i \(-0.318386\pi\)
0.540101 + 0.841600i \(0.318386\pi\)
\(12\) 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 \(-0.670560\pi\)
−0.510556 + 0.859845i \(0.670560\pi\)
\(24\) −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 \(-0.302736\pi\)
0.580810 + 0.814039i \(0.302736\pi\)
\(30\) 2.83075e6 0.638052
\(31\) 2.02178e6 0.393194 0.196597 0.980484i \(-0.437011\pi\)
0.196597 + 0.980484i \(0.437011\pi\)
\(32\) −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 \(-0.261425\pi\)
0.681277 + 0.732026i \(0.261425\pi\)
\(38\) 6.53095e6 0.508101
\(39\) −3.59301e6 −0.248696
\(40\) 1.11007e7 0.685618
\(41\) 8.35453e6 0.461737 0.230869 0.972985i \(-0.425843\pi\)
0.230869 + 0.972985i \(0.425843\pi\)
\(42\) 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 \(-0.955303\pi\)
−0.990157 + 0.139959i \(0.955303\pi\)
\(62\) −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 \(-0.688447\pi\)
−0.558042 + 0.829812i \(0.688447\pi\)
\(72\) 2.87802e8 1.26211
\(73\) −3.24831e8 −1.33876 −0.669382 0.742918i \(-0.733441\pi\)
−0.669382 + 0.742918i \(0.733441\pi\)
\(74\) −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 \(-0.645334\pi\)
−0.440880 + 0.897566i \(0.645334\pi\)
\(80\) 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 \(-0.636027\pi\)
−0.414452 + 0.910071i \(0.636027\pi\)
\(98\) −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 \(-0.441590\pi\)
0.182474 + 0.983211i \(0.441590\pi\)
\(108\) 2.58141e9 1.82579
\(109\) 8.73972e8 0.593032 0.296516 0.955028i \(-0.404175\pi\)
0.296516 + 0.955028i \(0.404175\pi\)
\(110\) −5.97282e8 −0.388966
\(111\) −3.86150e9 −2.41436
\(112\) 1.66060e9 0.997206
\(113\) −1.44323e9 −0.832691 −0.416345 0.909207i \(-0.636689\pi\)
−0.416345 + 0.909207i \(0.636689\pi\)
\(114\) −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 \(-0.518795\pi\)
−0.0590104 + 0.998257i \(0.518795\pi\)
\(132\) 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 \(-0.539427\pi\)
−0.123547 + 0.992339i \(0.539427\pi\)
\(140\) −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 \(-0.484420\pi\)
0.0489276 + 0.998802i \(0.484420\pi\)
\(164\) −3.86703e9 −0.417427
\(165\) −2.11828e10 −2.22487
\(166\) −9.51827e8 −0.0972908
\(167\) 6.76444e8 0.0672988 0.0336494 0.999434i \(-0.489287\pi\)
0.0336494 + 0.999434i \(0.489287\pi\)
\(168\) −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 \(-0.600080\pi\)
−0.309257 + 0.950978i \(0.600080\pi\)
\(174\) 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 \(-0.310143\pi\)
0.561711 + 0.827333i \(0.310143\pi\)
\(182\) −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 \(-0.506899\pi\)
−0.0216730 + 0.999765i \(0.506899\pi\)
\(194\) 5.06603e9 0.256779
\(195\) −5.83681e9 −0.289081
\(196\) −1.70208e10 −0.823811
\(197\) 2.26220e10 1.07012 0.535061 0.844813i \(-0.320288\pi\)
0.535061 + 0.844813i \(0.320288\pi\)
\(198\) −1.54853e10 −0.716023
\(199\) 7.37113e9 0.333192 0.166596 0.986025i \(-0.446722\pi\)
0.166596 + 0.986025i \(0.446722\pi\)
\(200\) 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 \(-0.774184\pi\)
−0.758739 + 0.651395i \(0.774184\pi\)
\(212\) −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 \(-0.544517\pi\)
−0.139398 + 0.990236i \(0.544517\pi\)
\(228\) −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 \(-0.367071\pi\)
0.405575 + 0.914062i \(0.367071\pi\)
\(234\) −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 \(-0.592599\pi\)
−0.286822 + 0.957984i \(0.592599\pi\)
\(242\) −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 \(-0.315821\pi\)
0.546865 + 0.837221i \(0.315821\pi\)
\(270\) 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 \(-0.493716\pi\)
0.0197402 + 0.999805i \(0.493716\pi\)
\(278\) 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 \(-0.819422\pi\)
−0.843353 + 0.537360i \(0.819422\pi\)
\(284\) 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 \(-0.396876\pi\)
0.318337 + 0.947978i \(0.396876\pi\)
\(312\) −2.45524e10 −0.146689
\(313\) −2.38828e11 −1.40648 −0.703242 0.710950i \(-0.748265\pi\)
−0.703242 + 0.710950i \(0.748265\pi\)
\(314\) 3.83274e10 0.222498
\(315\) 6.00863e11 3.43857
\(316\) 1.41295e11 0.797142
\(317\) −8.68678e10 −0.483161 −0.241581 0.970381i \(-0.577666\pi\)
−0.241581 + 0.970381i \(0.577666\pi\)
\(318\) 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 \(-0.412049\pi\)
0.272805 + 0.962069i \(0.412049\pi\)
\(338\) 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 \(-0.243824\pi\)
0.720693 + 0.693254i \(0.243824\pi\)
\(348\) 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 \(-0.611547\pi\)
−0.343308 + 0.939223i \(0.611547\pi\)
\(368\) −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 \(-0.545188\pi\)
−0.141486 + 0.989940i \(0.545188\pi\)
\(380\) 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 \(-0.524184\pi\)
−0.0759017 + 0.997115i \(0.524184\pi\)
\(398\) −5.16683e10 −0.103217
\(399\) 2.03414e12 4.01793
\(400\) 1.29684e11 0.253288
\(401\) 4.04002e11 0.780251 0.390125 0.920762i \(-0.372432\pi\)
0.390125 + 0.920762i \(0.372432\pi\)
\(402\) 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 \(-0.207709\pi\)
0.794546 + 0.607204i \(0.207709\pi\)
\(420\) 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 \(-0.736659\pi\)
−0.676857 + 0.736114i \(0.736659\pi\)
\(432\) −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 \(-0.600153\pi\)
−0.309473 + 0.950908i \(0.600153\pi\)
\(440\) 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 \(-0.616998\pi\)
−0.359339 + 0.933207i \(0.616998\pi\)
\(450\) −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 \(-0.866889\pi\)
−0.913830 + 0.406097i \(0.866889\pi\)
\(480\) 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 \(-0.641755\pi\)
−0.430761 + 0.902466i \(0.641755\pi\)
\(488\) −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 \(-0.684568\pi\)
−0.547888 + 0.836552i \(0.684568\pi\)
\(500\) 9.52901e11 0.681840
\(501\) −1.68161e11 −0.119249
\(502\) 2.97426e11 0.209031
\(503\) 1.28396e12 0.894328 0.447164 0.894452i \(-0.352434\pi\)
0.447164 + 0.894452i \(0.352434\pi\)
\(504\) 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 \(-0.233487\pi\)
0.742823 + 0.669488i \(0.233487\pi\)
\(522\) −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 \(-0.547627\pi\)
−0.149068 + 0.988827i \(0.547627\pi\)
\(542\) −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 \(-0.545880\pi\)
−0.143639 + 0.989630i \(0.545880\pi\)
\(548\) −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 \(-0.518522\pi\)
−0.0581572 + 0.998307i \(0.518522\pi\)
\(572\) −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 \(-0.361334\pi\)
0.421984 + 0.906603i \(0.361334\pi\)
\(602\) 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 \(-0.501396\pi\)
−0.00438557 + 0.999990i \(0.501396\pi\)
\(608\) 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 \(-0.123595\pi\)
0.925559 + 0.378603i \(0.123595\pi\)
\(618\) 2.12032e12 0.584726
\(619\) 3.87308e12 1.06035 0.530175 0.847888i \(-0.322126\pi\)
0.530175 + 0.847888i \(0.322126\pi\)
\(620\) −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 \(-0.611795\pi\)
−0.344039 + 0.938955i \(0.611795\pi\)
\(642\) 8.62267e11 0.200325
\(643\) −4.08339e12 −0.942044 −0.471022 0.882122i \(-0.656115\pi\)
−0.471022 + 0.882122i \(0.656115\pi\)
\(644\) 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 \(-0.656338\pi\)
−0.471641 + 0.881791i \(0.656338\pi\)
\(654\) 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 \(-0.537668\pi\)
−0.118062 + 0.993006i \(0.537668\pi\)
\(674\) −9.05539e11 −0.169020
\(675\) −3.82491e12 −0.709177
\(676\) 4.81177e12 0.886227
\(677\) 9.83587e11 0.179955 0.0899775 0.995944i \(-0.471321\pi\)
0.0899775 + 0.995944i \(0.471321\pi\)
\(678\) −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 \(-0.658669\pi\)
−0.478084 + 0.878314i \(0.658669\pi\)
\(684\) 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 \(-0.289827\pi\)
0.613337 + 0.789821i \(0.289827\pi\)
\(692\) 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 \(-0.211175\pi\)
0.787887 + 0.615819i \(0.211175\pi\)
\(710\) 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 \(-0.856933\pi\)
−0.900683 + 0.434477i \(0.856933\pi\)
\(720\) 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 \(-0.730826\pi\)
−0.663257 + 0.748392i \(0.730826\pi\)
\(744\) −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 \(-0.566012\pi\)
−0.205900 + 0.978573i \(0.566012\pi\)
\(752\) −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 \(-0.251363\pi\)
0.704073 + 0.710128i \(0.251363\pi\)
\(788\) −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 \(-0.542671\pi\)
−0.133653 + 0.991028i \(0.542671\pi\)
\(810\) −6.34747e12 −0.518106
\(811\) 3.09214e12 0.250995 0.125498 0.992094i \(-0.459947\pi\)
0.125498 + 0.992094i \(0.459947\pi\)
\(812\) −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 \(-0.187670\pi\)
0.831173 + 0.556014i \(0.187670\pi\)
\(822\) 3.06769e11 0.0234362
\(823\) 1.30860e13 0.994274 0.497137 0.867672i \(-0.334385\pi\)
0.497137 + 0.867672i \(0.334385\pi\)
\(824\) 8.31479e12 0.628317
\(825\) −8.94306e12 −0.672115
\(826\) 9.62647e12 0.719543
\(827\) −2.09145e13 −1.55479 −0.777395 0.629012i \(-0.783459\pi\)
−0.777395 + 0.629012i \(0.783459\pi\)
\(828\) 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 \(-0.730399\pi\)
−0.662250 + 0.749283i \(0.730399\pi\)
\(840\) −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 \(-0.730941\pi\)
−0.663526 + 0.748153i \(0.730941\pi\)
\(854\) 1.31829e13 0.848105
\(855\) −6.37470e13 −4.07955
\(856\) 3.38137e12 0.215259
\(857\) 2.96637e12 0.187850 0.0939250 0.995579i \(-0.470059\pi\)
0.0939250 + 0.995579i \(0.470059\pi\)
\(858\) 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 \(-0.676237\pi\)
−0.525808 + 0.850603i \(0.676237\pi\)
\(878\) 3.37624e12 0.191738
\(879\) 6.52155e12 0.368469
\(880\) 1.61121e13 0.905694
\(881\) 1.68763e12 0.0943813 0.0471907 0.998886i \(-0.484973\pi\)
0.0471907 + 0.998886i \(0.484973\pi\)
\(882\) −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 \(-0.610416\pi\)
−0.339968 + 0.940437i \(0.610416\pi\)
\(888\) −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 \(-0.388783\pi\)
0.342334 + 0.939578i \(0.388783\pi\)
\(908\) 5.16247e12 0.252041
\(909\) −1.04133e13 −0.505883
\(910\) −1.44535e12 −0.0698693
\(911\) −1.75468e13 −0.844045 −0.422022 0.906585i \(-0.638680\pi\)
−0.422022 + 0.906585i \(0.638680\pi\)
\(912\) 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 \(-0.317105\pi\)
0.543483 + 0.839420i \(0.317105\pi\)
\(930\) 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 \(-0.643352\pi\)
−0.435284 + 0.900293i \(0.643352\pi\)
\(942\) −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 \(-0.249957\pi\)
0.707202 + 0.707011i \(0.249957\pi\)
\(948\) −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 \(-0.452229\pi\)
0.149514 + 0.988760i \(0.452229\pi\)
\(984\) −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 \(-0.547678\pi\)
−0.149225 + 0.988803i \(0.547678\pi\)
\(992\) −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 \(-0.437200\pi\)
0.196015 + 0.980601i \(0.437200\pi\)
\(998\) 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.g.1.17 36
17.16 even 2 289.10.a.h.1.17 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.17 36 1.1 even 1 trivial
289.10.a.h.1.17 yes 36 17.16 even 2