Properties

Label 289.10.a.h.1.20
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 1.20
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.64758 q^{2} +62.7112 q^{3} -504.990 q^{4} +1957.56 q^{5} +166.033 q^{6} +4153.19 q^{7} -2692.56 q^{8} -15750.3 q^{9} +O(q^{10})\) \(q+2.64758 q^{2} +62.7112 q^{3} -504.990 q^{4} +1957.56 q^{5} +166.033 q^{6} +4153.19 q^{7} -2692.56 q^{8} -15750.3 q^{9} +5182.80 q^{10} +73075.6 q^{11} -31668.5 q^{12} -54341.7 q^{13} +10995.9 q^{14} +122761. q^{15} +251426. q^{16} -41700.2 q^{18} +811429. q^{19} -988551. q^{20} +260451. q^{21} +193473. q^{22} +163008. q^{23} -168854. q^{24} +1.87893e6 q^{25} -143874. q^{26} -2.22206e6 q^{27} -2.09732e6 q^{28} -5.42890e6 q^{29} +325020. q^{30} +946104. q^{31} +2.04426e6 q^{32} +4.58266e6 q^{33} +8.13013e6 q^{35} +7.95375e6 q^{36} +1.91041e7 q^{37} +2.14832e6 q^{38} -3.40783e6 q^{39} -5.27086e6 q^{40} +2.07663e7 q^{41} +689566. q^{42} -3.17001e7 q^{43} -3.69025e7 q^{44} -3.08322e7 q^{45} +431577. q^{46} +4.92240e7 q^{47} +1.57672e7 q^{48} -2.31046e7 q^{49} +4.97462e6 q^{50} +2.74420e7 q^{52} +6.39542e7 q^{53} -5.88309e6 q^{54} +1.43050e8 q^{55} -1.11827e7 q^{56} +5.08857e7 q^{57} -1.43734e7 q^{58} -1.75333e7 q^{59} -6.19932e7 q^{60} -1.01852e8 q^{61} +2.50489e6 q^{62} -6.54140e7 q^{63} -1.23318e8 q^{64} -1.06377e8 q^{65} +1.21329e7 q^{66} +5.10956e7 q^{67} +1.02224e7 q^{69} +2.15252e7 q^{70} -1.39323e8 q^{71} +4.24087e7 q^{72} +1.70150e8 q^{73} +5.05796e7 q^{74} +1.17830e8 q^{75} -4.09764e8 q^{76} +3.03497e8 q^{77} -9.02250e6 q^{78} -4.92862e8 q^{79} +4.92183e8 q^{80} +1.70665e8 q^{81} +5.49803e7 q^{82} +3.76175e8 q^{83} -1.31525e8 q^{84} -8.39284e7 q^{86} -3.40453e8 q^{87} -1.96761e8 q^{88} -8.85727e8 q^{89} -8.16308e7 q^{90} -2.25691e8 q^{91} -8.23176e7 q^{92} +5.93313e7 q^{93} +1.30325e8 q^{94} +1.58842e9 q^{95} +1.28198e8 q^{96} -1.16492e8 q^{97} -6.11713e7 q^{98} -1.15096e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + 60000q^{10} + 76902q^{11} + 373248q^{12} + 54216q^{13} + 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} + 6439479q^{20} - 138102q^{21} + 267324q^{22} + 4041462q^{23} + 7653888q^{24} + 16582356q^{25} + 15822744q^{26} + 13281612q^{27} + 18614784q^{28} + 4005936q^{29} + 22471686q^{30} + 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} + 22076682q^{37} - 27401376q^{38} + 62736162q^{39} - 12231630q^{40} + 59641782q^{41} + 150001536q^{42} - 47951586q^{43} - 49578936q^{44} + 129308238q^{45} + 140524827q^{46} - 118557912q^{47} + 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} + 209848575q^{54} - 365439924q^{55} + 203095059q^{56} - 4614108q^{57} - 179071413q^{58} + 343015128q^{59} + 427179186q^{60} + 175597116q^{61} + 720602571q^{62} + 587415936q^{63} + 853082511q^{64} + 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} + 1308709542q^{71} - 275337849q^{72} + 494841342q^{73} + 1545361890q^{74} + 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} + 2270624538q^{78} + 1980107868q^{79} + 2897000199q^{80} + 1598298840q^{81} + 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} - 2705904618q^{88} + 148394658q^{89} + 117916215q^{90} + 636340896q^{91} - 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} + 4878626298q^{95} - 8390096634q^{96} - 891786822q^{97} + 4285627647q^{98} - 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.64758 0.117008 0.0585038 0.998287i \(-0.481367\pi\)
0.0585038 + 0.998287i \(0.481367\pi\)
\(3\) 62.7112 0.446992 0.223496 0.974705i \(-0.428253\pi\)
0.223496 + 0.974705i \(0.428253\pi\)
\(4\) −504.990 −0.986309
\(5\) 1957.56 1.40072 0.700359 0.713791i \(-0.253023\pi\)
0.700359 + 0.713791i \(0.253023\pi\)
\(6\) 166.033 0.0523014
\(7\) 4153.19 0.653793 0.326897 0.945060i \(-0.393997\pi\)
0.326897 + 0.945060i \(0.393997\pi\)
\(8\) −2692.56 −0.232413
\(9\) −15750.3 −0.800199
\(10\) 5182.80 0.163895
\(11\) 73075.6 1.50489 0.752446 0.658654i \(-0.228874\pi\)
0.752446 + 0.658654i \(0.228874\pi\)
\(12\) −31668.5 −0.440872
\(13\) −54341.7 −0.527701 −0.263850 0.964564i \(-0.584993\pi\)
−0.263850 + 0.964564i \(0.584993\pi\)
\(14\) 10995.9 0.0764988
\(15\) 122761. 0.626109
\(16\) 251426. 0.959115
\(17\) 0 0
\(18\) −41700.2 −0.0936293
\(19\) 811429. 1.42843 0.714216 0.699925i \(-0.246783\pi\)
0.714216 + 0.699925i \(0.246783\pi\)
\(20\) −988551. −1.38154
\(21\) 260451. 0.292240
\(22\) 193473. 0.176084
\(23\) 163008. 0.121460 0.0607301 0.998154i \(-0.480657\pi\)
0.0607301 + 0.998154i \(0.480657\pi\)
\(24\) −168854. −0.103887
\(25\) 1.87893e6 0.962012
\(26\) −143874. −0.0617450
\(27\) −2.22206e6 −0.804674
\(28\) −2.09732e6 −0.644843
\(29\) −5.42890e6 −1.42535 −0.712674 0.701496i \(-0.752516\pi\)
−0.712674 + 0.701496i \(0.752516\pi\)
\(30\) 325020. 0.0732595
\(31\) 946104. 0.183997 0.0919986 0.995759i \(-0.470674\pi\)
0.0919986 + 0.995759i \(0.470674\pi\)
\(32\) 2.04426e6 0.344637
\(33\) 4.58266e6 0.672674
\(34\) 0 0
\(35\) 8.13013e6 0.915781
\(36\) 7.95375e6 0.789243
\(37\) 1.91041e7 1.67579 0.837893 0.545834i \(-0.183787\pi\)
0.837893 + 0.545834i \(0.183787\pi\)
\(38\) 2.14832e6 0.167137
\(39\) −3.40783e6 −0.235878
\(40\) −5.27086e6 −0.325545
\(41\) 2.07663e7 1.14771 0.573853 0.818958i \(-0.305448\pi\)
0.573853 + 0.818958i \(0.305448\pi\)
\(42\) 689566. 0.0341943
\(43\) −3.17001e7 −1.41401 −0.707004 0.707209i \(-0.749954\pi\)
−0.707004 + 0.707209i \(0.749954\pi\)
\(44\) −3.69025e7 −1.48429
\(45\) −3.08322e7 −1.12085
\(46\) 431577. 0.0142118
\(47\) 4.92240e7 1.47142 0.735710 0.677296i \(-0.236849\pi\)
0.735710 + 0.677296i \(0.236849\pi\)
\(48\) 1.57672e7 0.428716
\(49\) −2.31046e7 −0.572554
\(50\) 4.97462e6 0.112563
\(51\) 0 0
\(52\) 2.74420e7 0.520476
\(53\) 6.39542e7 1.11334 0.556670 0.830734i \(-0.312079\pi\)
0.556670 + 0.830734i \(0.312079\pi\)
\(54\) −5.88309e6 −0.0941529
\(55\) 1.43050e8 2.10793
\(56\) −1.11827e7 −0.151950
\(57\) 5.08857e7 0.638497
\(58\) −1.43734e7 −0.166776
\(59\) −1.75333e7 −0.188378 −0.0941889 0.995554i \(-0.530026\pi\)
−0.0941889 + 0.995554i \(0.530026\pi\)
\(60\) −6.19932e7 −0.617537
\(61\) −1.01852e8 −0.941860 −0.470930 0.882171i \(-0.656082\pi\)
−0.470930 + 0.882171i \(0.656082\pi\)
\(62\) 2.50489e6 0.0215291
\(63\) −6.54140e7 −0.523165
\(64\) −1.23318e8 −0.918790
\(65\) −1.06377e8 −0.739160
\(66\) 1.21329e7 0.0787080
\(67\) 5.10956e7 0.309775 0.154888 0.987932i \(-0.450498\pi\)
0.154888 + 0.987932i \(0.450498\pi\)
\(68\) 0 0
\(69\) 1.02224e7 0.0542917
\(70\) 2.15252e7 0.107153
\(71\) −1.39323e8 −0.650671 −0.325336 0.945599i \(-0.605477\pi\)
−0.325336 + 0.945599i \(0.605477\pi\)
\(72\) 4.24087e7 0.185977
\(73\) 1.70150e8 0.701260 0.350630 0.936514i \(-0.385967\pi\)
0.350630 + 0.936514i \(0.385967\pi\)
\(74\) 5.05796e7 0.196080
\(75\) 1.17830e8 0.430011
\(76\) −4.09764e8 −1.40888
\(77\) 3.03497e8 0.983889
\(78\) −9.02250e6 −0.0275995
\(79\) −4.92862e8 −1.42365 −0.711825 0.702356i \(-0.752131\pi\)
−0.711825 + 0.702356i \(0.752131\pi\)
\(80\) 4.92183e8 1.34345
\(81\) 1.70665e8 0.440516
\(82\) 5.49803e7 0.134290
\(83\) 3.76175e8 0.870039 0.435020 0.900421i \(-0.356741\pi\)
0.435020 + 0.900421i \(0.356741\pi\)
\(84\) −1.31525e8 −0.288239
\(85\) 0 0
\(86\) −8.39284e7 −0.165450
\(87\) −3.40453e8 −0.637118
\(88\) −1.96761e8 −0.349757
\(89\) −8.85727e8 −1.49639 −0.748195 0.663479i \(-0.769079\pi\)
−0.748195 + 0.663479i \(0.769079\pi\)
\(90\) −8.16308e7 −0.131148
\(91\) −2.25691e8 −0.345007
\(92\) −8.23176e7 −0.119797
\(93\) 5.93313e7 0.0822452
\(94\) 1.30325e8 0.172167
\(95\) 1.58842e9 2.00083
\(96\) 1.28198e8 0.154050
\(97\) −1.16492e8 −0.133605 −0.0668026 0.997766i \(-0.521280\pi\)
−0.0668026 + 0.997766i \(0.521280\pi\)
\(98\) −6.11713e7 −0.0669932
\(99\) −1.15096e9 −1.20421
\(100\) −9.48842e8 −0.948842
\(101\) −5.35257e7 −0.0511819 −0.0255910 0.999672i \(-0.508147\pi\)
−0.0255910 + 0.999672i \(0.508147\pi\)
\(102\) 0 0
\(103\) −3.19474e8 −0.279684 −0.139842 0.990174i \(-0.544660\pi\)
−0.139842 + 0.990174i \(0.544660\pi\)
\(104\) 1.46318e8 0.122645
\(105\) 5.09850e8 0.409346
\(106\) 1.69324e8 0.130269
\(107\) 1.63184e9 1.20351 0.601755 0.798681i \(-0.294468\pi\)
0.601755 + 0.798681i \(0.294468\pi\)
\(108\) 1.12212e9 0.793657
\(109\) −8.10335e8 −0.549852 −0.274926 0.961465i \(-0.588653\pi\)
−0.274926 + 0.961465i \(0.588653\pi\)
\(110\) 3.78737e8 0.246644
\(111\) 1.19804e9 0.749063
\(112\) 1.04422e9 0.627063
\(113\) 1.89909e9 1.09570 0.547850 0.836576i \(-0.315446\pi\)
0.547850 + 0.836576i \(0.315446\pi\)
\(114\) 1.34724e8 0.0747090
\(115\) 3.19099e8 0.170132
\(116\) 2.74154e9 1.40583
\(117\) 8.55898e8 0.422265
\(118\) −4.64208e7 −0.0220416
\(119\) 0 0
\(120\) −3.30542e8 −0.145516
\(121\) 2.98210e9 1.26470
\(122\) −2.69662e8 −0.110205
\(123\) 1.30228e9 0.513015
\(124\) −4.77773e8 −0.181478
\(125\) −1.45241e8 −0.0532100
\(126\) −1.73189e8 −0.0612142
\(127\) 3.55227e9 1.21168 0.605842 0.795585i \(-0.292836\pi\)
0.605842 + 0.795585i \(0.292836\pi\)
\(128\) −1.37316e9 −0.452142
\(129\) −1.98795e9 −0.632050
\(130\) −2.81642e8 −0.0864874
\(131\) 1.16394e9 0.345312 0.172656 0.984982i \(-0.444765\pi\)
0.172656 + 0.984982i \(0.444765\pi\)
\(132\) −2.31420e9 −0.663465
\(133\) 3.37002e9 0.933899
\(134\) 1.35280e8 0.0362460
\(135\) −4.34983e9 −1.12712
\(136\) 0 0
\(137\) 6.06374e9 1.47061 0.735306 0.677735i \(-0.237038\pi\)
0.735306 + 0.677735i \(0.237038\pi\)
\(138\) 2.70647e7 0.00635254
\(139\) 7.71758e9 1.75353 0.876767 0.480915i \(-0.159695\pi\)
0.876767 + 0.480915i \(0.159695\pi\)
\(140\) −4.10564e9 −0.903243
\(141\) 3.08690e9 0.657713
\(142\) −3.68870e8 −0.0761335
\(143\) −3.97105e9 −0.794133
\(144\) −3.96004e9 −0.767483
\(145\) −1.06274e10 −1.99651
\(146\) 4.50486e8 0.0820528
\(147\) −1.44892e9 −0.255927
\(148\) −9.64738e9 −1.65284
\(149\) −2.01142e9 −0.334322 −0.167161 0.985930i \(-0.553460\pi\)
−0.167161 + 0.985930i \(0.553460\pi\)
\(150\) 3.11964e8 0.0503146
\(151\) 6.98565e9 1.09348 0.546740 0.837303i \(-0.315869\pi\)
0.546740 + 0.837303i \(0.315869\pi\)
\(152\) −2.18482e9 −0.331986
\(153\) 0 0
\(154\) 8.03532e8 0.115122
\(155\) 1.85206e9 0.257728
\(156\) 1.72092e9 0.232648
\(157\) 9.93532e9 1.30507 0.652535 0.757759i \(-0.273706\pi\)
0.652535 + 0.757759i \(0.273706\pi\)
\(158\) −1.30489e9 −0.166578
\(159\) 4.01064e9 0.497653
\(160\) 4.00177e9 0.482739
\(161\) 6.77004e8 0.0794099
\(162\) 4.51849e8 0.0515437
\(163\) 4.23700e9 0.470126 0.235063 0.971980i \(-0.424470\pi\)
0.235063 + 0.971980i \(0.424470\pi\)
\(164\) −1.04868e10 −1.13199
\(165\) 8.97084e9 0.942227
\(166\) 9.95954e8 0.101801
\(167\) −9.26222e9 −0.921491 −0.460745 0.887532i \(-0.652418\pi\)
−0.460745 + 0.887532i \(0.652418\pi\)
\(168\) −7.01282e8 −0.0679205
\(169\) −7.65148e9 −0.721532
\(170\) 0 0
\(171\) −1.27803e10 −1.14303
\(172\) 1.60082e10 1.39465
\(173\) −6.09534e9 −0.517357 −0.258679 0.965963i \(-0.583287\pi\)
−0.258679 + 0.965963i \(0.583287\pi\)
\(174\) −9.01375e8 −0.0745477
\(175\) 7.80355e9 0.628957
\(176\) 1.83731e10 1.44336
\(177\) −1.09953e9 −0.0842033
\(178\) −2.34503e9 −0.175089
\(179\) −1.48711e10 −1.08269 −0.541346 0.840800i \(-0.682085\pi\)
−0.541346 + 0.840800i \(0.682085\pi\)
\(180\) 1.55700e10 1.10551
\(181\) −7.88421e9 −0.546015 −0.273008 0.962012i \(-0.588018\pi\)
−0.273008 + 0.962012i \(0.588018\pi\)
\(182\) −5.97535e8 −0.0403685
\(183\) −6.38727e9 −0.421003
\(184\) −4.38910e8 −0.0282290
\(185\) 3.73975e10 2.34731
\(186\) 1.57084e8 0.00962331
\(187\) 0 0
\(188\) −2.48577e10 −1.45128
\(189\) −9.22866e9 −0.526090
\(190\) 4.20548e9 0.234112
\(191\) 1.18806e10 0.645933 0.322967 0.946410i \(-0.395320\pi\)
0.322967 + 0.946410i \(0.395320\pi\)
\(192\) −7.73341e9 −0.410691
\(193\) 2.37247e10 1.23082 0.615408 0.788209i \(-0.288991\pi\)
0.615408 + 0.788209i \(0.288991\pi\)
\(194\) −3.08422e8 −0.0156328
\(195\) −6.67104e9 −0.330398
\(196\) 1.16676e10 0.564715
\(197\) 4.00628e10 1.89515 0.947575 0.319534i \(-0.103526\pi\)
0.947575 + 0.319534i \(0.103526\pi\)
\(198\) −3.04727e9 −0.140902
\(199\) 1.01005e10 0.456569 0.228284 0.973595i \(-0.426688\pi\)
0.228284 + 0.973595i \(0.426688\pi\)
\(200\) −5.05914e9 −0.223584
\(201\) 3.20426e9 0.138467
\(202\) −1.41714e8 −0.00598867
\(203\) −2.25472e10 −0.931883
\(204\) 0 0
\(205\) 4.06513e10 1.60761
\(206\) −8.45833e8 −0.0327252
\(207\) −2.56743e9 −0.0971923
\(208\) −1.36629e10 −0.506126
\(209\) 5.92957e10 2.14964
\(210\) 1.34987e9 0.0478966
\(211\) −2.18033e10 −0.757272 −0.378636 0.925546i \(-0.623607\pi\)
−0.378636 + 0.925546i \(0.623607\pi\)
\(212\) −3.22963e10 −1.09810
\(213\) −8.73714e9 −0.290845
\(214\) 4.32042e9 0.140820
\(215\) −6.20549e10 −1.98063
\(216\) 5.98305e9 0.187017
\(217\) 3.92935e9 0.120296
\(218\) −2.14543e9 −0.0643368
\(219\) 1.06703e10 0.313457
\(220\) −7.22389e10 −2.07907
\(221\) 0 0
\(222\) 3.17191e9 0.0876460
\(223\) 6.76777e10 1.83262 0.916312 0.400464i \(-0.131151\pi\)
0.916312 + 0.400464i \(0.131151\pi\)
\(224\) 8.49021e9 0.225321
\(225\) −2.95937e10 −0.769801
\(226\) 5.02798e9 0.128205
\(227\) −1.78509e10 −0.446215 −0.223107 0.974794i \(-0.571620\pi\)
−0.223107 + 0.974794i \(0.571620\pi\)
\(228\) −2.56968e10 −0.629756
\(229\) 6.47885e10 1.55682 0.778410 0.627757i \(-0.216027\pi\)
0.778410 + 0.627757i \(0.216027\pi\)
\(230\) 8.44840e8 0.0199067
\(231\) 1.90326e10 0.439790
\(232\) 1.46177e10 0.331270
\(233\) 4.23546e10 0.941454 0.470727 0.882279i \(-0.343992\pi\)
0.470727 + 0.882279i \(0.343992\pi\)
\(234\) 2.26606e9 0.0494083
\(235\) 9.63592e10 2.06105
\(236\) 8.85415e9 0.185799
\(237\) −3.09080e10 −0.636360
\(238\) 0 0
\(239\) −1.90315e10 −0.377297 −0.188649 0.982045i \(-0.560411\pi\)
−0.188649 + 0.982045i \(0.560411\pi\)
\(240\) 3.08654e10 0.600511
\(241\) 5.40492e10 1.03208 0.516039 0.856565i \(-0.327406\pi\)
0.516039 + 0.856565i \(0.327406\pi\)
\(242\) 7.89534e9 0.147980
\(243\) 5.44395e10 1.00158
\(244\) 5.14344e10 0.928965
\(245\) −4.52288e10 −0.801987
\(246\) 3.44788e9 0.0600267
\(247\) −4.40944e10 −0.753785
\(248\) −2.54744e9 −0.0427634
\(249\) 2.35904e10 0.388900
\(250\) −3.84536e8 −0.00622597
\(251\) −1.87837e10 −0.298709 −0.149355 0.988784i \(-0.547720\pi\)
−0.149355 + 0.988784i \(0.547720\pi\)
\(252\) 3.30334e10 0.516002
\(253\) 1.19119e10 0.182785
\(254\) 9.40492e9 0.141776
\(255\) 0 0
\(256\) 5.95032e10 0.865886
\(257\) 1.37193e11 1.96170 0.980849 0.194769i \(-0.0623956\pi\)
0.980849 + 0.194769i \(0.0623956\pi\)
\(258\) −5.26325e9 −0.0739546
\(259\) 7.93429e10 1.09562
\(260\) 5.37195e10 0.729041
\(261\) 8.55068e10 1.14056
\(262\) 3.08164e9 0.0404041
\(263\) 9.80468e10 1.26367 0.631833 0.775104i \(-0.282303\pi\)
0.631833 + 0.775104i \(0.282303\pi\)
\(264\) −1.23391e10 −0.156338
\(265\) 1.25194e11 1.55948
\(266\) 8.92239e9 0.109273
\(267\) −5.55450e10 −0.668874
\(268\) −2.58028e10 −0.305534
\(269\) −5.66085e9 −0.0659168 −0.0329584 0.999457i \(-0.510493\pi\)
−0.0329584 + 0.999457i \(0.510493\pi\)
\(270\) −1.15165e10 −0.131882
\(271\) −1.95830e10 −0.220555 −0.110277 0.993901i \(-0.535174\pi\)
−0.110277 + 0.993901i \(0.535174\pi\)
\(272\) 0 0
\(273\) −1.41534e10 −0.154215
\(274\) 1.60542e10 0.172073
\(275\) 1.37304e11 1.44772
\(276\) −5.16223e9 −0.0535484
\(277\) −1.58344e10 −0.161601 −0.0808004 0.996730i \(-0.525748\pi\)
−0.0808004 + 0.996730i \(0.525748\pi\)
\(278\) 2.04329e10 0.205177
\(279\) −1.49014e10 −0.147234
\(280\) −2.18909e10 −0.212840
\(281\) −5.48078e10 −0.524401 −0.262201 0.965013i \(-0.584448\pi\)
−0.262201 + 0.965013i \(0.584448\pi\)
\(282\) 8.17280e9 0.0769573
\(283\) −1.85037e11 −1.71482 −0.857410 0.514633i \(-0.827928\pi\)
−0.857410 + 0.514633i \(0.827928\pi\)
\(284\) 7.03570e10 0.641763
\(285\) 9.96120e10 0.894355
\(286\) −1.05137e10 −0.0929196
\(287\) 8.62462e10 0.750363
\(288\) −3.21978e10 −0.275778
\(289\) 0 0
\(290\) −2.81369e10 −0.233607
\(291\) −7.30536e9 −0.0597204
\(292\) −8.59241e10 −0.691659
\(293\) −4.24953e10 −0.336850 −0.168425 0.985714i \(-0.553868\pi\)
−0.168425 + 0.985714i \(0.553868\pi\)
\(294\) −3.83613e9 −0.0299454
\(295\) −3.43226e10 −0.263864
\(296\) −5.14390e10 −0.389475
\(297\) −1.62379e11 −1.21095
\(298\) −5.32540e9 −0.0391182
\(299\) −8.85814e9 −0.0640947
\(300\) −5.95030e10 −0.424124
\(301\) −1.31656e11 −0.924469
\(302\) 1.84951e10 0.127945
\(303\) −3.35666e9 −0.0228779
\(304\) 2.04015e11 1.37003
\(305\) −1.99382e11 −1.31928
\(306\) 0 0
\(307\) −6.29686e10 −0.404577 −0.202289 0.979326i \(-0.564838\pi\)
−0.202289 + 0.979326i \(0.564838\pi\)
\(308\) −1.53263e11 −0.970418
\(309\) −2.00346e10 −0.125017
\(310\) 4.90347e9 0.0301562
\(311\) 3.29544e10 0.199752 0.0998761 0.995000i \(-0.468155\pi\)
0.0998761 + 0.995000i \(0.468155\pi\)
\(312\) 9.17579e9 0.0548211
\(313\) 2.52444e11 1.48667 0.743336 0.668918i \(-0.233242\pi\)
0.743336 + 0.668918i \(0.233242\pi\)
\(314\) 2.63046e10 0.152703
\(315\) −1.28052e11 −0.732806
\(316\) 2.48891e11 1.40416
\(317\) 9.07757e10 0.504897 0.252449 0.967610i \(-0.418764\pi\)
0.252449 + 0.967610i \(0.418764\pi\)
\(318\) 1.06185e10 0.0582292
\(319\) −3.96720e11 −2.14499
\(320\) −2.41403e11 −1.28697
\(321\) 1.02334e11 0.537959
\(322\) 1.79242e9 0.00929156
\(323\) 0 0
\(324\) −8.61842e10 −0.434485
\(325\) −1.02104e11 −0.507655
\(326\) 1.12178e10 0.0550083
\(327\) −5.08171e10 −0.245779
\(328\) −5.59145e10 −0.266742
\(329\) 2.04437e11 0.962005
\(330\) 2.37510e10 0.110248
\(331\) −3.94437e11 −1.80614 −0.903070 0.429493i \(-0.858692\pi\)
−0.903070 + 0.429493i \(0.858692\pi\)
\(332\) −1.89965e11 −0.858128
\(333\) −3.00895e11 −1.34096
\(334\) −2.45225e10 −0.107821
\(335\) 1.00023e11 0.433908
\(336\) 6.54843e10 0.280292
\(337\) −8.92786e10 −0.377062 −0.188531 0.982067i \(-0.560373\pi\)
−0.188531 + 0.982067i \(0.560373\pi\)
\(338\) −2.02579e10 −0.0844247
\(339\) 1.19094e11 0.489769
\(340\) 0 0
\(341\) 6.91371e10 0.276896
\(342\) −3.38368e10 −0.133743
\(343\) −2.63554e11 −1.02813
\(344\) 8.53544e10 0.328634
\(345\) 2.00111e10 0.0760474
\(346\) −1.61379e10 −0.0605347
\(347\) −4.33744e11 −1.60602 −0.803010 0.595965i \(-0.796770\pi\)
−0.803010 + 0.595965i \(0.796770\pi\)
\(348\) 1.71925e11 0.628396
\(349\) 4.64877e11 1.67735 0.838676 0.544631i \(-0.183330\pi\)
0.838676 + 0.544631i \(0.183330\pi\)
\(350\) 2.06605e10 0.0735928
\(351\) 1.20751e11 0.424627
\(352\) 1.49386e11 0.518641
\(353\) −1.39662e10 −0.0478731 −0.0239366 0.999713i \(-0.507620\pi\)
−0.0239366 + 0.999713i \(0.507620\pi\)
\(354\) −2.91110e9 −0.00985242
\(355\) −2.72735e11 −0.911407
\(356\) 4.47284e11 1.47590
\(357\) 0 0
\(358\) −3.93725e10 −0.126683
\(359\) 1.24630e11 0.396003 0.198002 0.980202i \(-0.436555\pi\)
0.198002 + 0.980202i \(0.436555\pi\)
\(360\) 8.30177e10 0.260501
\(361\) 3.35730e11 1.04042
\(362\) −2.08741e10 −0.0638879
\(363\) 1.87011e11 0.565310
\(364\) 1.13972e11 0.340284
\(365\) 3.33080e11 0.982268
\(366\) −1.69108e10 −0.0492606
\(367\) 1.08338e9 0.00311734 0.00155867 0.999999i \(-0.499504\pi\)
0.00155867 + 0.999999i \(0.499504\pi\)
\(368\) 4.09846e10 0.116494
\(369\) −3.27075e11 −0.918393
\(370\) 9.90128e10 0.274652
\(371\) 2.65614e11 0.727894
\(372\) −2.99617e10 −0.0811192
\(373\) −4.07410e11 −1.08979 −0.544895 0.838505i \(-0.683430\pi\)
−0.544895 + 0.838505i \(0.683430\pi\)
\(374\) 0 0
\(375\) −9.10822e9 −0.0237844
\(376\) −1.32539e11 −0.341978
\(377\) 2.95015e11 0.752157
\(378\) −2.44336e10 −0.0615566
\(379\) −6.55713e11 −1.63244 −0.816220 0.577742i \(-0.803934\pi\)
−0.816220 + 0.577742i \(0.803934\pi\)
\(380\) −8.02139e11 −1.97344
\(381\) 2.22767e11 0.541613
\(382\) 3.14548e10 0.0755791
\(383\) −2.37402e11 −0.563755 −0.281877 0.959450i \(-0.590957\pi\)
−0.281877 + 0.959450i \(0.590957\pi\)
\(384\) −8.61123e10 −0.202104
\(385\) 5.94114e11 1.37815
\(386\) 6.28131e10 0.144015
\(387\) 4.99286e11 1.13149
\(388\) 5.88274e10 0.131776
\(389\) −6.60328e11 −1.46213 −0.731066 0.682307i \(-0.760977\pi\)
−0.731066 + 0.682307i \(0.760977\pi\)
\(390\) −1.76621e10 −0.0386591
\(391\) 0 0
\(392\) 6.22106e10 0.133069
\(393\) 7.29923e10 0.154351
\(394\) 1.06069e11 0.221747
\(395\) −9.64809e11 −1.99413
\(396\) 5.81225e11 1.18773
\(397\) −5.84346e11 −1.18063 −0.590314 0.807174i \(-0.700996\pi\)
−0.590314 + 0.807174i \(0.700996\pi\)
\(398\) 2.67420e10 0.0534220
\(399\) 2.11338e11 0.417445
\(400\) 4.72412e11 0.922681
\(401\) −7.67959e11 −1.48316 −0.741581 0.670863i \(-0.765924\pi\)
−0.741581 + 0.670863i \(0.765924\pi\)
\(402\) 8.48354e9 0.0162017
\(403\) −5.14129e10 −0.0970955
\(404\) 2.70300e10 0.0504812
\(405\) 3.34088e11 0.617039
\(406\) −5.96956e10 −0.109037
\(407\) 1.39604e12 2.52188
\(408\) 0 0
\(409\) 1.00813e12 1.78140 0.890699 0.454594i \(-0.150216\pi\)
0.890699 + 0.454594i \(0.150216\pi\)
\(410\) 1.07627e11 0.188103
\(411\) 3.80265e11 0.657352
\(412\) 1.61331e11 0.275855
\(413\) −7.28191e10 −0.123160
\(414\) −6.79747e9 −0.0113722
\(415\) 7.36387e11 1.21868
\(416\) −1.11089e11 −0.181865
\(417\) 4.83978e11 0.783815
\(418\) 1.56990e11 0.251524
\(419\) −2.58434e11 −0.409626 −0.204813 0.978801i \(-0.565659\pi\)
−0.204813 + 0.978801i \(0.565659\pi\)
\(420\) −2.57469e11 −0.403742
\(421\) 3.46983e11 0.538318 0.269159 0.963096i \(-0.413254\pi\)
0.269159 + 0.963096i \(0.413254\pi\)
\(422\) −5.77261e10 −0.0886066
\(423\) −7.75294e11 −1.17743
\(424\) −1.72201e11 −0.258755
\(425\) 0 0
\(426\) −2.31323e10 −0.0340310
\(427\) −4.23012e11 −0.615782
\(428\) −8.24062e11 −1.18703
\(429\) −2.49029e11 −0.354971
\(430\) −1.64295e11 −0.231748
\(431\) −8.62289e10 −0.120366 −0.0601832 0.998187i \(-0.519168\pi\)
−0.0601832 + 0.998187i \(0.519168\pi\)
\(432\) −5.58685e11 −0.771775
\(433\) 7.77469e11 1.06289 0.531444 0.847093i \(-0.321650\pi\)
0.531444 + 0.847093i \(0.321650\pi\)
\(434\) 1.04033e10 0.0140756
\(435\) −6.66458e11 −0.892424
\(436\) 4.09211e11 0.542324
\(437\) 1.32270e11 0.173498
\(438\) 2.82505e10 0.0366769
\(439\) −1.06090e10 −0.0136328 −0.00681638 0.999977i \(-0.502170\pi\)
−0.00681638 + 0.999977i \(0.502170\pi\)
\(440\) −3.85171e11 −0.489911
\(441\) 3.63905e11 0.458157
\(442\) 0 0
\(443\) −9.16044e11 −1.13006 −0.565028 0.825072i \(-0.691135\pi\)
−0.565028 + 0.825072i \(0.691135\pi\)
\(444\) −6.04999e11 −0.738807
\(445\) −1.73387e12 −2.09602
\(446\) 1.79182e11 0.214431
\(447\) −1.26139e11 −0.149439
\(448\) −5.12163e11 −0.600699
\(449\) 1.22897e11 0.142703 0.0713515 0.997451i \(-0.477269\pi\)
0.0713515 + 0.997451i \(0.477269\pi\)
\(450\) −7.83517e10 −0.0900725
\(451\) 1.51751e12 1.72718
\(452\) −9.59021e11 −1.08070
\(453\) 4.38078e11 0.488776
\(454\) −4.72617e10 −0.0522105
\(455\) −4.41805e11 −0.483258
\(456\) −1.37013e11 −0.148395
\(457\) 2.98540e11 0.320169 0.160085 0.987103i \(-0.448823\pi\)
0.160085 + 0.987103i \(0.448823\pi\)
\(458\) 1.71533e11 0.182160
\(459\) 0 0
\(460\) −1.61142e11 −0.167802
\(461\) −8.70582e11 −0.897751 −0.448875 0.893594i \(-0.648175\pi\)
−0.448875 + 0.893594i \(0.648175\pi\)
\(462\) 5.03904e10 0.0514588
\(463\) 6.99496e11 0.707409 0.353705 0.935357i \(-0.384922\pi\)
0.353705 + 0.935357i \(0.384922\pi\)
\(464\) −1.36497e12 −1.36707
\(465\) 1.16145e11 0.115202
\(466\) 1.12137e11 0.110157
\(467\) −1.26028e12 −1.22614 −0.613071 0.790028i \(-0.710066\pi\)
−0.613071 + 0.790028i \(0.710066\pi\)
\(468\) −4.32220e11 −0.416484
\(469\) 2.12210e11 0.202529
\(470\) 2.55119e11 0.241158
\(471\) 6.23056e11 0.583355
\(472\) 4.72095e10 0.0437815
\(473\) −2.31650e12 −2.12793
\(474\) −8.18313e10 −0.0744589
\(475\) 1.52462e12 1.37417
\(476\) 0 0
\(477\) −1.00730e12 −0.890893
\(478\) −5.03875e10 −0.0441466
\(479\) 3.89735e11 0.338267 0.169134 0.985593i \(-0.445903\pi\)
0.169134 + 0.985593i \(0.445903\pi\)
\(480\) 2.50956e11 0.215780
\(481\) −1.03815e12 −0.884314
\(482\) 1.43100e11 0.120761
\(483\) 4.24557e10 0.0354956
\(484\) −1.50593e12 −1.24739
\(485\) −2.28041e11 −0.187143
\(486\) 1.44133e11 0.117193
\(487\) 1.53901e11 0.123983 0.0619915 0.998077i \(-0.480255\pi\)
0.0619915 + 0.998077i \(0.480255\pi\)
\(488\) 2.74243e11 0.218901
\(489\) 2.65707e11 0.210142
\(490\) −1.19747e11 −0.0938386
\(491\) 5.36570e11 0.416639 0.208320 0.978061i \(-0.433201\pi\)
0.208320 + 0.978061i \(0.433201\pi\)
\(492\) −6.57637e11 −0.505992
\(493\) 0 0
\(494\) −1.16743e11 −0.0881985
\(495\) −2.25308e12 −1.68676
\(496\) 2.37875e11 0.176475
\(497\) −5.78637e11 −0.425405
\(498\) 6.24574e10 0.0455043
\(499\) −1.60206e12 −1.15671 −0.578357 0.815784i \(-0.696306\pi\)
−0.578357 + 0.815784i \(0.696306\pi\)
\(500\) 7.33452e10 0.0524815
\(501\) −5.80845e11 −0.411899
\(502\) −4.97312e10 −0.0349512
\(503\) −1.37869e12 −0.960305 −0.480153 0.877185i \(-0.659419\pi\)
−0.480153 + 0.877185i \(0.659419\pi\)
\(504\) 1.76131e11 0.121590
\(505\) −1.04780e11 −0.0716915
\(506\) 3.15378e10 0.0213872
\(507\) −4.79834e11 −0.322519
\(508\) −1.79386e12 −1.19510
\(509\) 2.44499e10 0.0161454 0.00807268 0.999967i \(-0.497430\pi\)
0.00807268 + 0.999967i \(0.497430\pi\)
\(510\) 0 0
\(511\) 7.06665e11 0.458479
\(512\) 8.60596e11 0.553458
\(513\) −1.80305e12 −1.14942
\(514\) 3.63229e11 0.229534
\(515\) −6.25391e11 −0.391759
\(516\) 1.00389e12 0.623397
\(517\) 3.59708e12 2.21433
\(518\) 2.10067e11 0.128196
\(519\) −3.82246e11 −0.231254
\(520\) 2.86427e11 0.171791
\(521\) −1.86370e12 −1.10817 −0.554085 0.832460i \(-0.686932\pi\)
−0.554085 + 0.832460i \(0.686932\pi\)
\(522\) 2.26386e11 0.133454
\(523\) −2.38491e11 −0.139384 −0.0696922 0.997569i \(-0.522202\pi\)
−0.0696922 + 0.997569i \(0.522202\pi\)
\(524\) −5.87781e11 −0.340584
\(525\) 4.89370e11 0.281139
\(526\) 2.59587e11 0.147859
\(527\) 0 0
\(528\) 1.15220e12 0.645172
\(529\) −1.77458e12 −0.985247
\(530\) 3.31462e11 0.182470
\(531\) 2.76155e11 0.150740
\(532\) −1.70183e12 −0.921114
\(533\) −1.12847e12 −0.605646
\(534\) −1.47060e11 −0.0782633
\(535\) 3.19443e12 1.68578
\(536\) −1.37578e11 −0.0719958
\(537\) −9.32586e11 −0.483954
\(538\) −1.49875e10 −0.00771277
\(539\) −1.68838e12 −0.861632
\(540\) 2.19662e12 1.11169
\(541\) 2.77186e12 1.39118 0.695589 0.718440i \(-0.255143\pi\)
0.695589 + 0.718440i \(0.255143\pi\)
\(542\) −5.18475e10 −0.0258066
\(543\) −4.94428e11 −0.244064
\(544\) 0 0
\(545\) −1.58628e12 −0.770187
\(546\) −3.74721e10 −0.0180444
\(547\) 3.03753e12 1.45070 0.725350 0.688381i \(-0.241678\pi\)
0.725350 + 0.688381i \(0.241678\pi\)
\(548\) −3.06213e12 −1.45048
\(549\) 1.60420e12 0.753675
\(550\) 3.63523e11 0.169395
\(551\) −4.40517e12 −2.03601
\(552\) −2.75246e10 −0.0126181
\(553\) −2.04695e12 −0.930774
\(554\) −4.19229e10 −0.0189085
\(555\) 2.34524e12 1.04923
\(556\) −3.89730e12 −1.72953
\(557\) −3.89518e12 −1.71467 −0.857333 0.514762i \(-0.827880\pi\)
−0.857333 + 0.514762i \(0.827880\pi\)
\(558\) −3.94527e10 −0.0172275
\(559\) 1.72263e12 0.746173
\(560\) 2.04413e12 0.878339
\(561\) 0 0
\(562\) −1.45108e11 −0.0613589
\(563\) 1.96578e12 0.824609 0.412305 0.911046i \(-0.364724\pi\)
0.412305 + 0.911046i \(0.364724\pi\)
\(564\) −1.55885e12 −0.648708
\(565\) 3.71758e12 1.53477
\(566\) −4.89899e11 −0.200647
\(567\) 7.08804e11 0.288007
\(568\) 3.75137e11 0.151225
\(569\) 2.20719e12 0.882744 0.441372 0.897324i \(-0.354492\pi\)
0.441372 + 0.897324i \(0.354492\pi\)
\(570\) 2.63731e11 0.104646
\(571\) −1.23698e12 −0.486970 −0.243485 0.969905i \(-0.578291\pi\)
−0.243485 + 0.969905i \(0.578291\pi\)
\(572\) 2.00534e12 0.783261
\(573\) 7.45045e11 0.288727
\(574\) 2.28344e11 0.0877982
\(575\) 3.06281e11 0.116846
\(576\) 1.94229e12 0.735214
\(577\) −9.00191e10 −0.0338099 −0.0169049 0.999857i \(-0.505381\pi\)
−0.0169049 + 0.999857i \(0.505381\pi\)
\(578\) 0 0
\(579\) 1.48781e12 0.550164
\(580\) 5.36674e12 1.96918
\(581\) 1.56233e12 0.568826
\(582\) −1.93415e10 −0.00698774
\(583\) 4.67349e12 1.67546
\(584\) −4.58140e11 −0.162982
\(585\) 1.67547e12 0.591475
\(586\) −1.12510e11 −0.0394141
\(587\) 4.18602e12 1.45522 0.727612 0.685989i \(-0.240630\pi\)
0.727612 + 0.685989i \(0.240630\pi\)
\(588\) 7.31690e11 0.252423
\(589\) 7.67697e11 0.262828
\(590\) −9.08717e10 −0.0308741
\(591\) 2.51239e12 0.847116
\(592\) 4.80327e12 1.60727
\(593\) −5.01785e12 −1.66637 −0.833185 0.552994i \(-0.813485\pi\)
−0.833185 + 0.552994i \(0.813485\pi\)
\(594\) −4.29911e11 −0.141690
\(595\) 0 0
\(596\) 1.01575e12 0.329745
\(597\) 6.33417e11 0.204082
\(598\) −2.34526e10 −0.00749956
\(599\) −1.55548e12 −0.493679 −0.246840 0.969056i \(-0.579392\pi\)
−0.246840 + 0.969056i \(0.579392\pi\)
\(600\) −3.17264e11 −0.0999403
\(601\) −5.68739e11 −0.177819 −0.0889094 0.996040i \(-0.528338\pi\)
−0.0889094 + 0.996040i \(0.528338\pi\)
\(602\) −3.48571e11 −0.108170
\(603\) −8.04771e11 −0.247882
\(604\) −3.52769e12 −1.07851
\(605\) 5.83765e12 1.77149
\(606\) −8.88703e9 −0.00267689
\(607\) 5.26859e12 1.57524 0.787618 0.616164i \(-0.211314\pi\)
0.787618 + 0.616164i \(0.211314\pi\)
\(608\) 1.65878e12 0.492290
\(609\) −1.41396e12 −0.416544
\(610\) −5.27880e11 −0.154366
\(611\) −2.67492e12 −0.776470
\(612\) 0 0
\(613\) 1.52329e12 0.435724 0.217862 0.975980i \(-0.430092\pi\)
0.217862 + 0.975980i \(0.430092\pi\)
\(614\) −1.66714e11 −0.0473386
\(615\) 2.54929e12 0.718590
\(616\) −8.17184e11 −0.228669
\(617\) 2.76333e11 0.0767625 0.0383813 0.999263i \(-0.487780\pi\)
0.0383813 + 0.999263i \(0.487780\pi\)
\(618\) −5.30432e10 −0.0146279
\(619\) −5.66715e12 −1.55152 −0.775759 0.631029i \(-0.782633\pi\)
−0.775759 + 0.631029i \(0.782633\pi\)
\(620\) −9.35272e11 −0.254200
\(621\) −3.62215e11 −0.0977359
\(622\) 8.72494e10 0.0233725
\(623\) −3.67859e12 −0.978330
\(624\) −8.56818e11 −0.226234
\(625\) −3.95410e12 −1.03654
\(626\) 6.68365e11 0.173952
\(627\) 3.71850e12 0.960869
\(628\) −5.01724e12 −1.28720
\(629\) 0 0
\(630\) −3.39028e11 −0.0857439
\(631\) −3.55453e12 −0.892586 −0.446293 0.894887i \(-0.647256\pi\)
−0.446293 + 0.894887i \(0.647256\pi\)
\(632\) 1.32706e12 0.330875
\(633\) −1.36731e12 −0.338494
\(634\) 2.40336e11 0.0590768
\(635\) 6.95380e12 1.69723
\(636\) −2.02534e12 −0.490840
\(637\) 1.25554e12 0.302137
\(638\) −1.05035e12 −0.250981
\(639\) 2.19439e12 0.520666
\(640\) −2.68804e12 −0.633324
\(641\) 6.59526e12 1.54302 0.771508 0.636219i \(-0.219503\pi\)
0.771508 + 0.636219i \(0.219503\pi\)
\(642\) 2.70939e11 0.0629453
\(643\) −1.25758e12 −0.290125 −0.145063 0.989422i \(-0.546338\pi\)
−0.145063 + 0.989422i \(0.546338\pi\)
\(644\) −3.41881e11 −0.0783228
\(645\) −3.89153e12 −0.885324
\(646\) 0 0
\(647\) −1.68475e12 −0.377978 −0.188989 0.981979i \(-0.560521\pi\)
−0.188989 + 0.981979i \(0.560521\pi\)
\(648\) −4.59526e11 −0.102382
\(649\) −1.28126e12 −0.283488
\(650\) −2.70329e11 −0.0593994
\(651\) 2.46414e11 0.0537714
\(652\) −2.13964e12 −0.463690
\(653\) 4.63150e12 0.996810 0.498405 0.866944i \(-0.333919\pi\)
0.498405 + 0.866944i \(0.333919\pi\)
\(654\) −1.34542e11 −0.0287580
\(655\) 2.27850e12 0.483685
\(656\) 5.22118e12 1.10078
\(657\) −2.67992e12 −0.561147
\(658\) 5.41262e11 0.112562
\(659\) −3.98192e12 −0.822447 −0.411223 0.911535i \(-0.634898\pi\)
−0.411223 + 0.911535i \(0.634898\pi\)
\(660\) −4.53019e12 −0.929327
\(661\) 2.53278e12 0.516050 0.258025 0.966138i \(-0.416928\pi\)
0.258025 + 0.966138i \(0.416928\pi\)
\(662\) −1.04430e12 −0.211332
\(663\) 0 0
\(664\) −1.01288e12 −0.202209
\(665\) 6.59703e12 1.30813
\(666\) −7.96644e11 −0.156903
\(667\) −8.84955e11 −0.173123
\(668\) 4.67733e12 0.908875
\(669\) 4.24415e12 0.819168
\(670\) 2.64818e11 0.0507705
\(671\) −7.44291e12 −1.41740
\(672\) 5.32431e11 0.100717
\(673\) 3.73705e12 0.702200 0.351100 0.936338i \(-0.385808\pi\)
0.351100 + 0.936338i \(0.385808\pi\)
\(674\) −2.36372e11 −0.0441191
\(675\) −4.17510e12 −0.774106
\(676\) 3.86393e12 0.711653
\(677\) −1.41128e12 −0.258204 −0.129102 0.991631i \(-0.541209\pi\)
−0.129102 + 0.991631i \(0.541209\pi\)
\(678\) 3.15311e11 0.0573067
\(679\) −4.83814e11 −0.0873502
\(680\) 0 0
\(681\) −1.11945e12 −0.199454
\(682\) 1.83046e11 0.0323989
\(683\) −5.44425e11 −0.0957293 −0.0478646 0.998854i \(-0.515242\pi\)
−0.0478646 + 0.998854i \(0.515242\pi\)
\(684\) 6.45391e12 1.12738
\(685\) 1.18702e13 2.05991
\(686\) −6.97780e11 −0.120298
\(687\) 4.06296e12 0.695885
\(688\) −7.97023e12 −1.35620
\(689\) −3.47538e12 −0.587510
\(690\) 5.29809e10 0.00889812
\(691\) −6.71997e12 −1.12128 −0.560642 0.828058i \(-0.689446\pi\)
−0.560642 + 0.828058i \(0.689446\pi\)
\(692\) 3.07809e12 0.510274
\(693\) −4.78017e12 −0.787306
\(694\) −1.14837e12 −0.187917
\(695\) 1.51076e13 2.45621
\(696\) 9.16690e11 0.148075
\(697\) 0 0
\(698\) 1.23080e12 0.196263
\(699\) 2.65611e12 0.420822
\(700\) −3.94072e12 −0.620346
\(701\) 1.89005e12 0.295625 0.147813 0.989015i \(-0.452777\pi\)
0.147813 + 0.989015i \(0.452777\pi\)
\(702\) 3.19697e11 0.0496846
\(703\) 1.55016e13 2.39375
\(704\) −9.01153e12 −1.38268
\(705\) 6.04280e12 0.921270
\(706\) −3.69766e10 −0.00560152
\(707\) −2.22303e11 −0.0334624
\(708\) 5.55254e11 0.0830505
\(709\) −4.56043e12 −0.677794 −0.338897 0.940823i \(-0.610054\pi\)
−0.338897 + 0.940823i \(0.610054\pi\)
\(710\) −7.22086e11 −0.106642
\(711\) 7.76273e12 1.13920
\(712\) 2.38488e12 0.347781
\(713\) 1.54223e11 0.0223484
\(714\) 0 0
\(715\) −7.77358e12 −1.11236
\(716\) 7.50977e12 1.06787
\(717\) −1.19349e12 −0.168649
\(718\) 3.29969e11 0.0463354
\(719\) −7.71771e12 −1.07698 −0.538491 0.842631i \(-0.681005\pi\)
−0.538491 + 0.842631i \(0.681005\pi\)
\(720\) −7.75203e12 −1.07503
\(721\) −1.32684e12 −0.182856
\(722\) 8.88872e11 0.121737
\(723\) 3.38949e12 0.461330
\(724\) 3.98145e12 0.538540
\(725\) −1.02005e13 −1.37120
\(726\) 4.95126e11 0.0661456
\(727\) 8.85989e12 1.17631 0.588157 0.808747i \(-0.299854\pi\)
0.588157 + 0.808747i \(0.299854\pi\)
\(728\) 6.07688e11 0.0801843
\(729\) 5.47663e10 0.00718190
\(730\) 8.81854e11 0.114933
\(731\) 0 0
\(732\) 3.22551e12 0.415240
\(733\) 2.76655e12 0.353974 0.176987 0.984213i \(-0.443365\pi\)
0.176987 + 0.984213i \(0.443365\pi\)
\(734\) 2.86834e9 0.000364752 0
\(735\) −2.83635e12 −0.358482
\(736\) 3.33232e11 0.0418597
\(737\) 3.73384e12 0.466178
\(738\) −8.65957e11 −0.107459
\(739\) 3.07557e12 0.379338 0.189669 0.981848i \(-0.439259\pi\)
0.189669 + 0.981848i \(0.439259\pi\)
\(740\) −1.88854e13 −2.31517
\(741\) −2.76521e12 −0.336935
\(742\) 7.03234e11 0.0851691
\(743\) −3.96916e12 −0.477803 −0.238901 0.971044i \(-0.576787\pi\)
−0.238901 + 0.971044i \(0.576787\pi\)
\(744\) −1.59753e11 −0.0191149
\(745\) −3.93749e12 −0.468291
\(746\) −1.07865e12 −0.127514
\(747\) −5.92488e12 −0.696204
\(748\) 0 0
\(749\) 6.77733e12 0.786847
\(750\) −2.41147e10 −0.00278296
\(751\) 1.22028e13 1.39984 0.699919 0.714222i \(-0.253219\pi\)
0.699919 + 0.714222i \(0.253219\pi\)
\(752\) 1.23762e13 1.41126
\(753\) −1.17795e12 −0.133520
\(754\) 7.81077e11 0.0880081
\(755\) 1.36749e13 1.53166
\(756\) 4.66038e12 0.518888
\(757\) −1.03259e13 −1.14287 −0.571435 0.820647i \(-0.693613\pi\)
−0.571435 + 0.820647i \(0.693613\pi\)
\(758\) −1.73605e12 −0.191008
\(759\) 7.47011e11 0.0817032
\(760\) −4.27693e12 −0.465020
\(761\) −1.04160e13 −1.12583 −0.562914 0.826516i \(-0.690320\pi\)
−0.562914 + 0.826516i \(0.690320\pi\)
\(762\) 5.89794e11 0.0633728
\(763\) −3.36548e12 −0.359489
\(764\) −5.99958e12 −0.637090
\(765\) 0 0
\(766\) −6.28541e11 −0.0659636
\(767\) 9.52789e11 0.0994071
\(768\) 3.73152e12 0.387044
\(769\) −1.00395e13 −1.03524 −0.517622 0.855610i \(-0.673183\pi\)
−0.517622 + 0.855610i \(0.673183\pi\)
\(770\) 1.57296e12 0.161254
\(771\) 8.60352e12 0.876863
\(772\) −1.19808e13 −1.21397
\(773\) 5.92570e12 0.596942 0.298471 0.954419i \(-0.403523\pi\)
0.298471 + 0.954419i \(0.403523\pi\)
\(774\) 1.32190e12 0.132393
\(775\) 1.77766e12 0.177008
\(776\) 3.13662e11 0.0310516
\(777\) 4.97569e12 0.489732
\(778\) −1.74827e12 −0.171080
\(779\) 1.68504e13 1.63942
\(780\) 3.36881e12 0.325875
\(781\) −1.01811e13 −0.979190
\(782\) 0 0
\(783\) 1.20634e13 1.14694
\(784\) −5.80911e12 −0.549145
\(785\) 1.94490e13 1.82803
\(786\) 1.93253e11 0.0180603
\(787\) 2.24816e12 0.208901 0.104451 0.994530i \(-0.466692\pi\)
0.104451 + 0.994530i \(0.466692\pi\)
\(788\) −2.02313e13 −1.86920
\(789\) 6.14863e12 0.564848
\(790\) −2.55441e12 −0.233329
\(791\) 7.88727e12 0.716362
\(792\) 3.09904e12 0.279875
\(793\) 5.53482e12 0.497020
\(794\) −1.54710e12 −0.138142
\(795\) 7.85109e12 0.697072
\(796\) −5.10068e12 −0.450318
\(797\) −1.51847e13 −1.33305 −0.666523 0.745485i \(-0.732218\pi\)
−0.666523 + 0.745485i \(0.732218\pi\)
\(798\) 5.59534e11 0.0488442
\(799\) 0 0
\(800\) 3.84103e12 0.331545
\(801\) 1.39505e13 1.19741
\(802\) −2.03323e12 −0.173541
\(803\) 1.24338e13 1.05532
\(804\) −1.61812e12 −0.136571
\(805\) 1.32528e12 0.111231
\(806\) −1.36120e11 −0.0113609
\(807\) −3.54999e11 −0.0294643
\(808\) 1.44121e11 0.0118954
\(809\) −9.96291e12 −0.817745 −0.408873 0.912592i \(-0.634078\pi\)
−0.408873 + 0.912592i \(0.634078\pi\)
\(810\) 8.84523e11 0.0721983
\(811\) 1.30630e13 1.06035 0.530176 0.847887i \(-0.322126\pi\)
0.530176 + 0.847887i \(0.322126\pi\)
\(812\) 1.13861e13 0.919125
\(813\) −1.22807e12 −0.0985862
\(814\) 3.69614e12 0.295079
\(815\) 8.29420e12 0.658514
\(816\) 0 0
\(817\) −2.57224e13 −2.01981
\(818\) 2.66910e12 0.208437
\(819\) 3.55471e12 0.276074
\(820\) −2.05285e13 −1.58560
\(821\) 3.57592e12 0.274690 0.137345 0.990523i \(-0.456143\pi\)
0.137345 + 0.990523i \(0.456143\pi\)
\(822\) 1.00678e12 0.0769151
\(823\) −2.09663e13 −1.59302 −0.796512 0.604623i \(-0.793324\pi\)
−0.796512 + 0.604623i \(0.793324\pi\)
\(824\) 8.60204e11 0.0650024
\(825\) 8.61050e12 0.647121
\(826\) −1.92794e11 −0.0144107
\(827\) 1.74701e13 1.29873 0.649366 0.760476i \(-0.275034\pi\)
0.649366 + 0.760476i \(0.275034\pi\)
\(828\) 1.29653e12 0.0958617
\(829\) −2.25587e13 −1.65890 −0.829448 0.558584i \(-0.811345\pi\)
−0.829448 + 0.558584i \(0.811345\pi\)
\(830\) 1.94964e12 0.142595
\(831\) −9.92996e11 −0.0722342
\(832\) 6.70130e12 0.484846
\(833\) 0 0
\(834\) 1.28137e12 0.0917123
\(835\) −1.81314e13 −1.29075
\(836\) −2.99438e13 −2.12021
\(837\) −2.10230e12 −0.148058
\(838\) −6.84225e11 −0.0479293
\(839\) 2.00947e12 0.140008 0.0700039 0.997547i \(-0.477699\pi\)
0.0700039 + 0.997547i \(0.477699\pi\)
\(840\) −1.37280e12 −0.0951375
\(841\) 1.49658e13 1.03162
\(842\) 9.18665e11 0.0629873
\(843\) −3.43706e12 −0.234403
\(844\) 1.10105e13 0.746905
\(845\) −1.49783e13 −1.01066
\(846\) −2.05265e12 −0.137768
\(847\) 1.23852e13 0.826853
\(848\) 1.60798e13 1.06782
\(849\) −1.16039e13 −0.766510
\(850\) 0 0
\(851\) 3.11412e12 0.203542
\(852\) 4.41217e12 0.286863
\(853\) −1.92491e13 −1.24491 −0.622457 0.782654i \(-0.713865\pi\)
−0.622457 + 0.782654i \(0.713865\pi\)
\(854\) −1.11996e12 −0.0720511
\(855\) −2.50182e13 −1.60106
\(856\) −4.39382e12 −0.279712
\(857\) 1.66278e12 0.105298 0.0526492 0.998613i \(-0.483233\pi\)
0.0526492 + 0.998613i \(0.483233\pi\)
\(858\) −6.59325e11 −0.0415343
\(859\) 9.33148e12 0.584765 0.292382 0.956301i \(-0.405552\pi\)
0.292382 + 0.956301i \(0.405552\pi\)
\(860\) 3.13371e13 1.95351
\(861\) 5.40860e12 0.335406
\(862\) −2.28298e11 −0.0140838
\(863\) −1.24232e13 −0.762401 −0.381200 0.924492i \(-0.624489\pi\)
−0.381200 + 0.924492i \(0.624489\pi\)
\(864\) −4.54248e12 −0.277320
\(865\) −1.19320e13 −0.724672
\(866\) 2.05841e12 0.124366
\(867\) 0 0
\(868\) −1.98428e12 −0.118649
\(869\) −3.60162e13 −2.14244
\(870\) −1.76450e12 −0.104420
\(871\) −2.77662e12 −0.163469
\(872\) 2.18188e12 0.127793
\(873\) 1.83479e12 0.106911
\(874\) 3.50194e11 0.0203006
\(875\) −6.03212e11 −0.0347884
\(876\) −5.38840e12 −0.309166
\(877\) −1.23664e13 −0.705903 −0.352952 0.935642i \(-0.614822\pi\)
−0.352952 + 0.935642i \(0.614822\pi\)
\(878\) −2.80881e10 −0.00159514
\(879\) −2.66493e12 −0.150569
\(880\) 3.59666e13 2.02175
\(881\) −2.42210e13 −1.35457 −0.677283 0.735723i \(-0.736843\pi\)
−0.677283 + 0.735723i \(0.736843\pi\)
\(882\) 9.63467e11 0.0536078
\(883\) 2.87422e13 1.59110 0.795548 0.605891i \(-0.207183\pi\)
0.795548 + 0.605891i \(0.207183\pi\)
\(884\) 0 0
\(885\) −2.15241e12 −0.117945
\(886\) −2.42530e12 −0.132225
\(887\) 5.52286e12 0.299577 0.149788 0.988718i \(-0.452141\pi\)
0.149788 + 0.988718i \(0.452141\pi\)
\(888\) −3.22580e12 −0.174092
\(889\) 1.47533e13 0.792191
\(890\) −4.59055e12 −0.245250
\(891\) 1.24714e13 0.662929
\(892\) −3.41766e13 −1.80753
\(893\) 3.99418e13 2.10182
\(894\) −3.33962e11 −0.0174855
\(895\) −2.91112e13 −1.51655
\(896\) −5.70298e12 −0.295608
\(897\) −5.55504e11 −0.0286498
\(898\) 3.25380e11 0.0166973
\(899\) −5.13630e12 −0.262260
\(900\) 1.49445e13 0.759262
\(901\) 0 0
\(902\) 4.01772e12 0.202093
\(903\) −8.25632e12 −0.413230
\(904\) −5.11341e12 −0.254655
\(905\) −1.54338e13 −0.764813
\(906\) 1.15985e12 0.0571905
\(907\) −1.32164e13 −0.648458 −0.324229 0.945979i \(-0.605105\pi\)
−0.324229 + 0.945979i \(0.605105\pi\)
\(908\) 9.01454e12 0.440106
\(909\) 8.43047e11 0.0409557
\(910\) −1.16971e12 −0.0565449
\(911\) −1.79264e13 −0.862305 −0.431152 0.902279i \(-0.641893\pi\)
−0.431152 + 0.902279i \(0.641893\pi\)
\(912\) 1.27940e13 0.612392
\(913\) 2.74892e13 1.30932
\(914\) 7.90408e11 0.0374622
\(915\) −1.25035e13 −0.589707
\(916\) −3.27176e13 −1.53550
\(917\) 4.83408e12 0.225763
\(918\) 0 0
\(919\) −1.17404e13 −0.542955 −0.271478 0.962445i \(-0.587512\pi\)
−0.271478 + 0.962445i \(0.587512\pi\)
\(920\) −8.59194e11 −0.0395408
\(921\) −3.94884e12 −0.180843
\(922\) −2.30494e12 −0.105044
\(923\) 7.57107e12 0.343360
\(924\) −9.61130e12 −0.433769
\(925\) 3.58953e13 1.61213
\(926\) 1.85197e12 0.0827722
\(927\) 5.03182e12 0.223803
\(928\) −1.10981e13 −0.491227
\(929\) 6.80294e12 0.299658 0.149829 0.988712i \(-0.452128\pi\)
0.149829 + 0.988712i \(0.452128\pi\)
\(930\) 3.07503e11 0.0134796
\(931\) −1.87478e13 −0.817855
\(932\) −2.13887e13 −0.928565
\(933\) 2.06661e12 0.0892875
\(934\) −3.33669e12 −0.143468
\(935\) 0 0
\(936\) −2.30456e12 −0.0981401
\(937\) 1.18659e12 0.0502889 0.0251444 0.999684i \(-0.491995\pi\)
0.0251444 + 0.999684i \(0.491995\pi\)
\(938\) 5.61842e11 0.0236974
\(939\) 1.58311e13 0.664530
\(940\) −4.86604e13 −2.03283
\(941\) −2.04736e13 −0.851219 −0.425610 0.904907i \(-0.639940\pi\)
−0.425610 + 0.904907i \(0.639940\pi\)
\(942\) 1.64959e12 0.0682569
\(943\) 3.38507e12 0.139401
\(944\) −4.40833e12 −0.180676
\(945\) −1.80657e13 −0.736904
\(946\) −6.13312e12 −0.248984
\(947\) 1.56711e11 0.00633178 0.00316589 0.999995i \(-0.498992\pi\)
0.00316589 + 0.999995i \(0.498992\pi\)
\(948\) 1.56082e13 0.627648
\(949\) −9.24624e12 −0.370056
\(950\) 4.03655e12 0.160788
\(951\) 5.69265e12 0.225685
\(952\) 0 0
\(953\) 1.16177e13 0.456249 0.228124 0.973632i \(-0.426741\pi\)
0.228124 + 0.973632i \(0.426741\pi\)
\(954\) −2.66690e12 −0.104241
\(955\) 2.32570e13 0.904771
\(956\) 9.61074e12 0.372132
\(957\) −2.48788e13 −0.958795
\(958\) 1.03186e12 0.0395798
\(959\) 2.51839e13 0.961477
\(960\) −1.51386e13 −0.575263
\(961\) −2.55445e13 −0.966145
\(962\) −2.74858e12 −0.103471
\(963\) −2.57019e13 −0.963047
\(964\) −2.72943e13 −1.01795
\(965\) 4.64426e13 1.72403
\(966\) 1.12405e11 0.00415325
\(967\) −2.83183e13 −1.04147 −0.520736 0.853718i \(-0.674342\pi\)
−0.520736 + 0.853718i \(0.674342\pi\)
\(968\) −8.02948e12 −0.293933
\(969\) 0 0
\(970\) −6.03756e11 −0.0218972
\(971\) −2.45044e13 −0.884623 −0.442311 0.896862i \(-0.645841\pi\)
−0.442311 + 0.896862i \(0.645841\pi\)
\(972\) −2.74914e13 −0.987868
\(973\) 3.20526e13 1.14645
\(974\) 4.07466e11 0.0145070
\(975\) −6.40307e12 −0.226917
\(976\) −2.56083e13 −0.903352
\(977\) 1.92163e13 0.674753 0.337376 0.941370i \(-0.390461\pi\)
0.337376 + 0.941370i \(0.390461\pi\)
\(978\) 7.03481e11 0.0245883
\(979\) −6.47251e13 −2.25191
\(980\) 2.28401e13 0.791007
\(981\) 1.27630e13 0.439990
\(982\) 1.42061e12 0.0487499
\(983\) 4.13553e13 1.41267 0.706334 0.707878i \(-0.250347\pi\)
0.706334 + 0.707878i \(0.250347\pi\)
\(984\) −3.50646e12 −0.119232
\(985\) 7.84255e13 2.65457
\(986\) 0 0
\(987\) 1.28205e13 0.430008
\(988\) 2.22673e13 0.743465
\(989\) −5.16737e12 −0.171746
\(990\) −5.96522e12 −0.197364
\(991\) 1.07977e12 0.0355631 0.0177816 0.999842i \(-0.494340\pi\)
0.0177816 + 0.999842i \(0.494340\pi\)
\(992\) 1.93409e12 0.0634122
\(993\) −2.47356e13 −0.807329
\(994\) −1.53199e12 −0.0497756
\(995\) 1.97725e13 0.639524
\(996\) −1.19129e13 −0.383576
\(997\) 3.60906e13 1.15682 0.578411 0.815746i \(-0.303673\pi\)
0.578411 + 0.815746i \(0.303673\pi\)
\(998\) −4.24158e12 −0.135344
\(999\) −4.24505e13 −1.34846
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.1.20 yes 36
17.16 even 2 289.10.a.g.1.20 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.20 36 17.16 even 2
289.10.a.h.1.20 yes 36 1.1 even 1 trivial