Properties

Label 289.10.a.h.1.35
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(148.845356651\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.35
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q+40.9577 q^{2} -105.034 q^{3} +1165.53 q^{4} +2072.52 q^{5} -4301.96 q^{6} +5180.84 q^{7} +26767.1 q^{8} -8650.78 q^{9} +O(q^{10})\) \(q+40.9577 q^{2} -105.034 q^{3} +1165.53 q^{4} +2072.52 q^{5} -4301.96 q^{6} +5180.84 q^{7} +26767.1 q^{8} -8650.78 q^{9} +84885.6 q^{10} -83913.5 q^{11} -122421. q^{12} -38456.2 q^{13} +212195. q^{14} -217686. q^{15} +499564. q^{16} -354316. q^{18} +727879. q^{19} +2.41558e6 q^{20} -544167. q^{21} -3.43690e6 q^{22} +2.28425e6 q^{23} -2.81146e6 q^{24} +2.34222e6 q^{25} -1.57508e6 q^{26} +2.97602e6 q^{27} +6.03843e6 q^{28} +2.05994e6 q^{29} -8.91591e6 q^{30} +2.10705e6 q^{31} +6.75626e6 q^{32} +8.81380e6 q^{33} +1.07374e7 q^{35} -1.00827e7 q^{36} +1.39359e7 q^{37} +2.98122e7 q^{38} +4.03923e6 q^{39} +5.54753e7 q^{40} +2.53391e7 q^{41} -2.22878e7 q^{42} -2.22102e7 q^{43} -9.78037e7 q^{44} -1.79289e7 q^{45} +9.35575e7 q^{46} +1.95036e7 q^{47} -5.24714e7 q^{48} -1.35125e7 q^{49} +9.59317e7 q^{50} -4.48219e7 q^{52} -3.74339e6 q^{53} +1.21891e8 q^{54} -1.73912e8 q^{55} +1.38676e8 q^{56} -7.64523e7 q^{57} +8.43705e7 q^{58} -7.17696e7 q^{59} -2.53719e8 q^{60} -1.17343e7 q^{61} +8.63000e7 q^{62} -4.48183e7 q^{63} +2.09436e7 q^{64} -7.97013e7 q^{65} +3.60993e8 q^{66} +3.00544e8 q^{67} -2.39925e8 q^{69} +4.39779e8 q^{70} +1.31667e8 q^{71} -2.31556e8 q^{72} +3.21930e8 q^{73} +5.70782e8 q^{74} -2.46013e8 q^{75} +8.48364e8 q^{76} -4.34743e8 q^{77} +1.65437e8 q^{78} +3.05655e8 q^{79} +1.03536e9 q^{80} -1.42311e8 q^{81} +1.03783e9 q^{82} -4.83143e8 q^{83} -6.34243e8 q^{84} -9.09678e8 q^{86} -2.16365e8 q^{87} -2.24612e9 q^{88} +1.76273e8 q^{89} -7.34326e8 q^{90} -1.99236e8 q^{91} +2.66236e9 q^{92} -2.21313e8 q^{93} +7.98822e8 q^{94} +1.50854e9 q^{95} -7.09640e8 q^{96} -8.15034e8 q^{97} -5.53439e8 q^{98} +7.25917e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + 60000q^{10} + 76902q^{11} + 373248q^{12} + 54216q^{13} + 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} + 6439479q^{20} - 138102q^{21} + 267324q^{22} + 4041462q^{23} + 7653888q^{24} + 16582356q^{25} + 15822744q^{26} + 13281612q^{27} + 18614784q^{28} + 4005936q^{29} + 22471686q^{30} + 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} + 22076682q^{37} - 27401376q^{38} + 62736162q^{39} - 12231630q^{40} + 59641782q^{41} + 150001536q^{42} - 47951586q^{43} - 49578936q^{44} + 129308238q^{45} + 140524827q^{46} - 118557912q^{47} + 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} + 209848575q^{54} - 365439924q^{55} + 203095059q^{56} - 4614108q^{57} - 179071413q^{58} + 343015128q^{59} + 427179186q^{60} + 175597116q^{61} + 720602571q^{62} + 587415936q^{63} + 853082511q^{64} + 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} + 1308709542q^{71} - 275337849q^{72} + 494841342q^{73} + 1545361890q^{74} + 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} + 2270624538q^{78} + 1980107868q^{79} + 2897000199q^{80} + 1598298840q^{81} + 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} - 2705904618q^{88} + 148394658q^{89} + 117916215q^{90} + 636340896q^{91} - 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} + 4878626298q^{95} - 8390096634q^{96} - 891786822q^{97} + 4285627647q^{98} - 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 40.9577 1.81009 0.905045 0.425316i \(-0.139837\pi\)
0.905045 + 0.425316i \(0.139837\pi\)
\(3\) −105.034 −0.748662 −0.374331 0.927295i \(-0.622128\pi\)
−0.374331 + 0.927295i \(0.622128\pi\)
\(4\) 1165.53 2.27643
\(5\) 2072.52 1.48297 0.741487 0.670967i \(-0.234121\pi\)
0.741487 + 0.670967i \(0.234121\pi\)
\(6\) −4301.96 −1.35515
\(7\) 5180.84 0.815566 0.407783 0.913079i \(-0.366302\pi\)
0.407783 + 0.913079i \(0.366302\pi\)
\(8\) 26767.1 2.31044
\(9\) −8650.78 −0.439505
\(10\) 84885.6 2.68432
\(11\) −83913.5 −1.72808 −0.864042 0.503420i \(-0.832075\pi\)
−0.864042 + 0.503420i \(0.832075\pi\)
\(12\) −122421. −1.70427
\(13\) −38456.2 −0.373441 −0.186720 0.982413i \(-0.559786\pi\)
−0.186720 + 0.982413i \(0.559786\pi\)
\(14\) 212195. 1.47625
\(15\) −217686. −1.11025
\(16\) 499564. 1.90569
\(17\) 0 0
\(18\) −354316. −0.795544
\(19\) 727879. 1.28135 0.640675 0.767812i \(-0.278655\pi\)
0.640675 + 0.767812i \(0.278655\pi\)
\(20\) 2.41558e6 3.37588
\(21\) −544167. −0.610584
\(22\) −3.43690e6 −3.12799
\(23\) 2.28425e6 1.70203 0.851017 0.525139i \(-0.175987\pi\)
0.851017 + 0.525139i \(0.175987\pi\)
\(24\) −2.81146e6 −1.72974
\(25\) 2.34222e6 1.19921
\(26\) −1.57508e6 −0.675961
\(27\) 2.97602e6 1.07770
\(28\) 6.03843e6 1.85658
\(29\) 2.05994e6 0.540834 0.270417 0.962743i \(-0.412838\pi\)
0.270417 + 0.962743i \(0.412838\pi\)
\(30\) −8.91591e6 −2.00965
\(31\) 2.10705e6 0.409778 0.204889 0.978785i \(-0.434317\pi\)
0.204889 + 0.978785i \(0.434317\pi\)
\(32\) 6.75626e6 1.13902
\(33\) 8.81380e6 1.29375
\(34\) 0 0
\(35\) 1.07374e7 1.20946
\(36\) −1.00827e7 −1.00050
\(37\) 1.39359e7 1.22244 0.611220 0.791461i \(-0.290679\pi\)
0.611220 + 0.791461i \(0.290679\pi\)
\(38\) 2.98122e7 2.31936
\(39\) 4.03923e6 0.279581
\(40\) 5.54753e7 3.42633
\(41\) 2.53391e7 1.40044 0.700220 0.713927i \(-0.253085\pi\)
0.700220 + 0.713927i \(0.253085\pi\)
\(42\) −2.22878e7 −1.10521
\(43\) −2.22102e7 −0.990706 −0.495353 0.868692i \(-0.664961\pi\)
−0.495353 + 0.868692i \(0.664961\pi\)
\(44\) −9.78037e7 −3.93385
\(45\) −1.79289e7 −0.651775
\(46\) 9.35575e7 3.08083
\(47\) 1.95036e7 0.583008 0.291504 0.956570i \(-0.405844\pi\)
0.291504 + 0.956570i \(0.405844\pi\)
\(48\) −5.24714e7 −1.42672
\(49\) −1.35125e7 −0.334851
\(50\) 9.59317e7 2.17069
\(51\) 0 0
\(52\) −4.48219e7 −0.850110
\(53\) −3.74339e6 −0.0651663 −0.0325832 0.999469i \(-0.510373\pi\)
−0.0325832 + 0.999469i \(0.510373\pi\)
\(54\) 1.21891e8 1.95074
\(55\) −1.73912e8 −2.56271
\(56\) 1.38676e8 1.88432
\(57\) −7.64523e7 −0.959298
\(58\) 8.43705e7 0.978959
\(59\) −7.17696e7 −0.771092 −0.385546 0.922689i \(-0.625987\pi\)
−0.385546 + 0.922689i \(0.625987\pi\)
\(60\) −2.53719e8 −2.52739
\(61\) −1.17343e7 −0.108511 −0.0542554 0.998527i \(-0.517279\pi\)
−0.0542554 + 0.998527i \(0.517279\pi\)
\(62\) 8.63000e7 0.741734
\(63\) −4.48183e7 −0.358446
\(64\) 2.09436e7 0.156042
\(65\) −7.97013e7 −0.553803
\(66\) 3.60993e8 2.34181
\(67\) 3.00544e8 1.82209 0.911047 0.412302i \(-0.135275\pi\)
0.911047 + 0.412302i \(0.135275\pi\)
\(68\) 0 0
\(69\) −2.39925e8 −1.27425
\(70\) 4.39779e8 2.18924
\(71\) 1.31667e8 0.614913 0.307457 0.951562i \(-0.400522\pi\)
0.307457 + 0.951562i \(0.400522\pi\)
\(72\) −2.31556e8 −1.01545
\(73\) 3.21930e8 1.32681 0.663406 0.748260i \(-0.269110\pi\)
0.663406 + 0.748260i \(0.269110\pi\)
\(74\) 5.70782e8 2.21273
\(75\) −2.46013e8 −0.897807
\(76\) 8.48364e8 2.91690
\(77\) −4.34743e8 −1.40937
\(78\) 1.65437e8 0.506066
\(79\) 3.05655e8 0.882895 0.441448 0.897287i \(-0.354465\pi\)
0.441448 + 0.897287i \(0.354465\pi\)
\(80\) 1.03536e9 2.82609
\(81\) −1.42311e8 −0.367330
\(82\) 1.03783e9 2.53492
\(83\) −4.83143e8 −1.11744 −0.558720 0.829356i \(-0.688707\pi\)
−0.558720 + 0.829356i \(0.688707\pi\)
\(84\) −6.34243e8 −1.38995
\(85\) 0 0
\(86\) −9.09678e8 −1.79327
\(87\) −2.16365e8 −0.404902
\(88\) −2.24612e9 −3.99264
\(89\) 1.76273e8 0.297803 0.148902 0.988852i \(-0.452426\pi\)
0.148902 + 0.988852i \(0.452426\pi\)
\(90\) −7.34326e8 −1.17977
\(91\) −1.99236e8 −0.304566
\(92\) 2.66236e9 3.87455
\(93\) −2.21313e8 −0.306785
\(94\) 7.98822e8 1.05530
\(95\) 1.50854e9 1.90021
\(96\) −7.09640e8 −0.852741
\(97\) −8.15034e8 −0.934766 −0.467383 0.884055i \(-0.654803\pi\)
−0.467383 + 0.884055i \(0.654803\pi\)
\(98\) −5.53439e8 −0.606111
\(99\) 7.25917e8 0.759502
\(100\) 2.72992e9 2.72992
\(101\) 2.53858e8 0.242742 0.121371 0.992607i \(-0.461271\pi\)
0.121371 + 0.992607i \(0.461271\pi\)
\(102\) 0 0
\(103\) −1.52399e9 −1.33418 −0.667090 0.744977i \(-0.732460\pi\)
−0.667090 + 0.744977i \(0.732460\pi\)
\(104\) −1.02936e9 −0.862814
\(105\) −1.12780e9 −0.905480
\(106\) −1.53320e8 −0.117957
\(107\) −1.73003e9 −1.27593 −0.637966 0.770064i \(-0.720224\pi\)
−0.637966 + 0.770064i \(0.720224\pi\)
\(108\) 3.46864e9 2.45331
\(109\) −3.58188e8 −0.243048 −0.121524 0.992589i \(-0.538778\pi\)
−0.121524 + 0.992589i \(0.538778\pi\)
\(110\) −7.12305e9 −4.63873
\(111\) −1.46375e9 −0.915195
\(112\) 2.58817e9 1.55421
\(113\) −7.59574e8 −0.438245 −0.219123 0.975697i \(-0.570319\pi\)
−0.219123 + 0.975697i \(0.570319\pi\)
\(114\) −3.13131e9 −1.73642
\(115\) 4.73415e9 2.52407
\(116\) 2.40093e9 1.23117
\(117\) 3.32676e8 0.164129
\(118\) −2.93951e9 −1.39575
\(119\) 0 0
\(120\) −5.82681e9 −2.56516
\(121\) 4.68353e9 1.98627
\(122\) −4.80610e8 −0.196414
\(123\) −2.66148e9 −1.04846
\(124\) 2.45583e9 0.932828
\(125\) 8.06399e8 0.295430
\(126\) −1.83565e9 −0.648819
\(127\) 3.23828e9 1.10458 0.552291 0.833651i \(-0.313754\pi\)
0.552291 + 0.833651i \(0.313754\pi\)
\(128\) −2.60140e9 −0.856570
\(129\) 2.33284e9 0.741704
\(130\) −3.26438e9 −1.00243
\(131\) −2.74138e9 −0.813294 −0.406647 0.913585i \(-0.633302\pi\)
−0.406647 + 0.913585i \(0.633302\pi\)
\(132\) 1.02728e10 2.94513
\(133\) 3.77103e9 1.04503
\(134\) 1.23096e10 3.29815
\(135\) 6.16786e9 1.59821
\(136\) 0 0
\(137\) 6.82540e9 1.65533 0.827667 0.561220i \(-0.189668\pi\)
0.827667 + 0.561220i \(0.189668\pi\)
\(138\) −9.82675e9 −2.30650
\(139\) −2.21726e9 −0.503789 −0.251895 0.967755i \(-0.581054\pi\)
−0.251895 + 0.967755i \(0.581054\pi\)
\(140\) 1.25148e10 2.75326
\(141\) −2.04855e9 −0.436476
\(142\) 5.39277e9 1.11305
\(143\) 3.22700e9 0.645337
\(144\) −4.32162e9 −0.837559
\(145\) 4.26928e9 0.802044
\(146\) 1.31855e10 2.40165
\(147\) 1.41927e9 0.250690
\(148\) 1.62427e10 2.78279
\(149\) −4.15025e9 −0.689821 −0.344910 0.938636i \(-0.612091\pi\)
−0.344910 + 0.938636i \(0.612091\pi\)
\(150\) −1.00761e10 −1.62511
\(151\) 4.22098e8 0.0660719 0.0330359 0.999454i \(-0.489482\pi\)
0.0330359 + 0.999454i \(0.489482\pi\)
\(152\) 1.94832e10 2.96049
\(153\) 0 0
\(154\) −1.78061e10 −2.55108
\(155\) 4.36691e9 0.607690
\(156\) 4.70784e9 0.636445
\(157\) 1.77965e9 0.233769 0.116885 0.993146i \(-0.462709\pi\)
0.116885 + 0.993146i \(0.462709\pi\)
\(158\) 1.25189e10 1.59812
\(159\) 3.93184e8 0.0487876
\(160\) 1.40025e10 1.68914
\(161\) 1.18343e10 1.38812
\(162\) −5.82874e9 −0.664901
\(163\) −6.54651e9 −0.726383 −0.363192 0.931714i \(-0.618313\pi\)
−0.363192 + 0.931714i \(0.618313\pi\)
\(164\) 2.95335e10 3.18800
\(165\) 1.82668e10 1.91860
\(166\) −1.97884e10 −2.02267
\(167\) 1.94448e9 0.193454 0.0967271 0.995311i \(-0.469163\pi\)
0.0967271 + 0.995311i \(0.469163\pi\)
\(168\) −1.45657e10 −1.41072
\(169\) −9.12562e9 −0.860542
\(170\) 0 0
\(171\) −6.29672e9 −0.563160
\(172\) −2.58867e10 −2.25527
\(173\) 1.57301e10 1.33513 0.667567 0.744550i \(-0.267336\pi\)
0.667567 + 0.744550i \(0.267336\pi\)
\(174\) −8.86180e9 −0.732909
\(175\) 1.21347e10 0.978039
\(176\) −4.19202e10 −3.29319
\(177\) 7.53828e9 0.577288
\(178\) 7.21971e9 0.539051
\(179\) 4.51445e9 0.328674 0.164337 0.986404i \(-0.447451\pi\)
0.164337 + 0.986404i \(0.447451\pi\)
\(180\) −2.08967e10 −1.48372
\(181\) −2.26434e10 −1.56815 −0.784076 0.620665i \(-0.786863\pi\)
−0.784076 + 0.620665i \(0.786863\pi\)
\(182\) −8.16023e9 −0.551291
\(183\) 1.23251e9 0.0812380
\(184\) 6.11426e10 3.93245
\(185\) 2.88825e10 1.81285
\(186\) −9.06447e9 −0.555308
\(187\) 0 0
\(188\) 2.27320e10 1.32717
\(189\) 1.54183e10 0.878938
\(190\) 6.17864e10 3.43955
\(191\) −7.88641e9 −0.428775 −0.214387 0.976749i \(-0.568776\pi\)
−0.214387 + 0.976749i \(0.568776\pi\)
\(192\) −2.19980e9 −0.116823
\(193\) −1.42449e10 −0.739012 −0.369506 0.929228i \(-0.620473\pi\)
−0.369506 + 0.929228i \(0.620473\pi\)
\(194\) −3.33819e10 −1.69201
\(195\) 8.37138e9 0.414611
\(196\) −1.57492e10 −0.762264
\(197\) 3.25891e9 0.154161 0.0770805 0.997025i \(-0.475440\pi\)
0.0770805 + 0.997025i \(0.475440\pi\)
\(198\) 2.97319e10 1.37477
\(199\) −7.31449e9 −0.330632 −0.165316 0.986241i \(-0.552864\pi\)
−0.165316 + 0.986241i \(0.552864\pi\)
\(200\) 6.26942e10 2.77072
\(201\) −3.15674e10 −1.36413
\(202\) 1.03974e10 0.439385
\(203\) 1.06722e10 0.441086
\(204\) 0 0
\(205\) 5.25159e10 2.07682
\(206\) −6.24190e10 −2.41499
\(207\) −1.97605e10 −0.748052
\(208\) −1.92114e10 −0.711661
\(209\) −6.10789e10 −2.21428
\(210\) −4.61919e10 −1.63900
\(211\) 8.04733e8 0.0279499 0.0139750 0.999902i \(-0.495551\pi\)
0.0139750 + 0.999902i \(0.495551\pi\)
\(212\) −4.36303e9 −0.148346
\(213\) −1.38295e10 −0.460362
\(214\) −7.08581e10 −2.30955
\(215\) −4.60311e10 −1.46919
\(216\) 7.96593e10 2.48997
\(217\) 1.09163e10 0.334201
\(218\) −1.46705e10 −0.439938
\(219\) −3.38138e10 −0.993333
\(220\) −2.02700e11 −5.83381
\(221\) 0 0
\(222\) −5.99518e10 −1.65658
\(223\) 2.06904e10 0.560268 0.280134 0.959961i \(-0.409621\pi\)
0.280134 + 0.959961i \(0.409621\pi\)
\(224\) 3.50031e10 0.928947
\(225\) −2.02620e10 −0.527061
\(226\) −3.11104e10 −0.793264
\(227\) −3.22296e10 −0.805636 −0.402818 0.915280i \(-0.631969\pi\)
−0.402818 + 0.915280i \(0.631969\pi\)
\(228\) −8.91074e10 −2.18377
\(229\) −1.46098e10 −0.351064 −0.175532 0.984474i \(-0.556165\pi\)
−0.175532 + 0.984474i \(0.556165\pi\)
\(230\) 1.93900e11 4.56880
\(231\) 4.56630e10 1.05514
\(232\) 5.51386e10 1.24957
\(233\) 1.40255e10 0.311758 0.155879 0.987776i \(-0.450179\pi\)
0.155879 + 0.987776i \(0.450179\pi\)
\(234\) 1.36256e10 0.297088
\(235\) 4.04216e10 0.864587
\(236\) −8.36496e10 −1.75533
\(237\) −3.21043e10 −0.660990
\(238\) 0 0
\(239\) −4.43516e9 −0.0879264 −0.0439632 0.999033i \(-0.513998\pi\)
−0.0439632 + 0.999033i \(0.513998\pi\)
\(240\) −1.08748e11 −2.11578
\(241\) 1.91454e10 0.365584 0.182792 0.983152i \(-0.441487\pi\)
0.182792 + 0.983152i \(0.441487\pi\)
\(242\) 1.91826e11 3.59533
\(243\) −4.36294e10 −0.802697
\(244\) −1.36767e10 −0.247017
\(245\) −2.80048e10 −0.496576
\(246\) −1.09008e11 −1.89780
\(247\) −2.79915e10 −0.478508
\(248\) 5.63996e10 0.946768
\(249\) 5.07467e10 0.836585
\(250\) 3.30282e10 0.534755
\(251\) −8.63881e9 −0.137380 −0.0686898 0.997638i \(-0.521882\pi\)
−0.0686898 + 0.997638i \(0.521882\pi\)
\(252\) −5.22371e10 −0.815975
\(253\) −1.91679e11 −2.94126
\(254\) 1.32633e11 1.99939
\(255\) 0 0
\(256\) −1.17271e11 −1.70651
\(257\) −1.14783e11 −1.64127 −0.820634 0.571455i \(-0.806379\pi\)
−0.820634 + 0.571455i \(0.806379\pi\)
\(258\) 9.55475e10 1.34255
\(259\) 7.21998e10 0.996981
\(260\) −9.28942e10 −1.26069
\(261\) −1.78201e10 −0.237699
\(262\) −1.12280e11 −1.47214
\(263\) 3.42476e10 0.441397 0.220699 0.975342i \(-0.429166\pi\)
0.220699 + 0.975342i \(0.429166\pi\)
\(264\) 2.35920e11 2.98914
\(265\) −7.75825e9 −0.0966400
\(266\) 1.54452e11 1.89159
\(267\) −1.85147e10 −0.222954
\(268\) 3.50293e11 4.14786
\(269\) 6.94696e10 0.808927 0.404464 0.914554i \(-0.367458\pi\)
0.404464 + 0.914554i \(0.367458\pi\)
\(270\) 2.52621e11 2.89290
\(271\) −1.06575e9 −0.0120031 −0.00600154 0.999982i \(-0.501910\pi\)
−0.00600154 + 0.999982i \(0.501910\pi\)
\(272\) 0 0
\(273\) 2.09266e10 0.228017
\(274\) 2.79552e11 2.99630
\(275\) −1.96544e11 −2.07234
\(276\) −2.79639e11 −2.90073
\(277\) 9.88531e10 1.00886 0.504431 0.863452i \(-0.331702\pi\)
0.504431 + 0.863452i \(0.331702\pi\)
\(278\) −9.08136e10 −0.911904
\(279\) −1.82277e10 −0.180099
\(280\) 2.87409e11 2.79440
\(281\) −1.79379e11 −1.71630 −0.858151 0.513398i \(-0.828386\pi\)
−0.858151 + 0.513398i \(0.828386\pi\)
\(282\) −8.39038e10 −0.790061
\(283\) 3.09384e10 0.286720 0.143360 0.989671i \(-0.454209\pi\)
0.143360 + 0.989671i \(0.454209\pi\)
\(284\) 1.53462e11 1.39980
\(285\) −1.58449e11 −1.42262
\(286\) 1.32170e11 1.16812
\(287\) 1.31278e11 1.14215
\(288\) −5.84469e10 −0.500605
\(289\) 0 0
\(290\) 1.74860e11 1.45177
\(291\) 8.56066e10 0.699824
\(292\) 3.75219e11 3.02039
\(293\) 1.72026e10 0.136361 0.0681803 0.997673i \(-0.478281\pi\)
0.0681803 + 0.997673i \(0.478281\pi\)
\(294\) 5.81301e10 0.453772
\(295\) −1.48744e11 −1.14351
\(296\) 3.73023e11 2.82438
\(297\) −2.49728e11 −1.86236
\(298\) −1.69985e11 −1.24864
\(299\) −8.78436e10 −0.635608
\(300\) −2.86736e11 −2.04379
\(301\) −1.15068e11 −0.807986
\(302\) 1.72881e10 0.119596
\(303\) −2.66638e10 −0.181732
\(304\) 3.63622e11 2.44185
\(305\) −2.43196e10 −0.160919
\(306\) 0 0
\(307\) −1.84456e11 −1.18514 −0.592570 0.805519i \(-0.701887\pi\)
−0.592570 + 0.805519i \(0.701887\pi\)
\(308\) −5.06706e11 −3.20832
\(309\) 1.60071e11 0.998850
\(310\) 1.78859e11 1.09997
\(311\) 1.97872e11 1.19939 0.599697 0.800227i \(-0.295288\pi\)
0.599697 + 0.800227i \(0.295288\pi\)
\(312\) 1.08118e11 0.645956
\(313\) −8.05381e10 −0.474299 −0.237149 0.971473i \(-0.576213\pi\)
−0.237149 + 0.971473i \(0.576213\pi\)
\(314\) 7.28905e10 0.423143
\(315\) −9.28869e10 −0.531566
\(316\) 3.56250e11 2.00985
\(317\) −1.37985e11 −0.767475 −0.383738 0.923442i \(-0.625363\pi\)
−0.383738 + 0.923442i \(0.625363\pi\)
\(318\) 1.61039e10 0.0883099
\(319\) −1.72857e11 −0.934607
\(320\) 4.34061e10 0.231407
\(321\) 1.81713e11 0.955242
\(322\) 4.84707e11 2.51262
\(323\) 0 0
\(324\) −1.65868e11 −0.836200
\(325\) −9.00728e10 −0.447835
\(326\) −2.68130e11 −1.31482
\(327\) 3.76220e10 0.181961
\(328\) 6.78254e11 3.23564
\(329\) 1.01045e11 0.475482
\(330\) 7.48165e11 3.47284
\(331\) −1.12292e11 −0.514189 −0.257095 0.966386i \(-0.582765\pi\)
−0.257095 + 0.966386i \(0.582765\pi\)
\(332\) −5.63118e11 −2.54377
\(333\) −1.20556e11 −0.537269
\(334\) 7.96412e10 0.350170
\(335\) 6.22883e11 2.70212
\(336\) −2.71846e11 −1.16358
\(337\) 2.22819e11 0.941063 0.470531 0.882383i \(-0.344062\pi\)
0.470531 + 0.882383i \(0.344062\pi\)
\(338\) −3.73764e11 −1.55766
\(339\) 7.97814e10 0.328098
\(340\) 0 0
\(341\) −1.76810e11 −0.708130
\(342\) −2.57899e11 −1.01937
\(343\) −2.79072e11 −1.08866
\(344\) −5.94502e11 −2.28897
\(345\) −4.97249e11 −1.88968
\(346\) 6.44269e11 2.41671
\(347\) 8.77169e10 0.324788 0.162394 0.986726i \(-0.448078\pi\)
0.162394 + 0.986726i \(0.448078\pi\)
\(348\) −2.52180e11 −0.921730
\(349\) −3.18539e11 −1.14934 −0.574669 0.818386i \(-0.694869\pi\)
−0.574669 + 0.818386i \(0.694869\pi\)
\(350\) 4.97007e11 1.77034
\(351\) −1.14447e11 −0.402458
\(352\) −5.66942e11 −1.96832
\(353\) −5.28579e11 −1.81186 −0.905928 0.423432i \(-0.860825\pi\)
−0.905928 + 0.423432i \(0.860825\pi\)
\(354\) 3.08750e11 1.04494
\(355\) 2.72882e11 0.911901
\(356\) 2.05451e11 0.677927
\(357\) 0 0
\(358\) 1.84901e11 0.594930
\(359\) 4.14566e11 1.31725 0.658625 0.752471i \(-0.271138\pi\)
0.658625 + 0.752471i \(0.271138\pi\)
\(360\) −4.79904e11 −1.50589
\(361\) 2.07120e11 0.641858
\(362\) −9.27421e11 −2.83850
\(363\) −4.91932e11 −1.48705
\(364\) −2.32215e11 −0.693321
\(365\) 6.67207e11 1.96763
\(366\) 5.04805e10 0.147048
\(367\) 2.91075e11 0.837543 0.418771 0.908092i \(-0.362461\pi\)
0.418771 + 0.908092i \(0.362461\pi\)
\(368\) 1.14113e12 3.24354
\(369\) −2.19203e11 −0.615500
\(370\) 1.18296e12 3.28142
\(371\) −1.93939e10 −0.0531475
\(372\) −2.57947e11 −0.698373
\(373\) −8.23127e10 −0.220180 −0.110090 0.993922i \(-0.535114\pi\)
−0.110090 + 0.993922i \(0.535114\pi\)
\(374\) 0 0
\(375\) −8.46997e10 −0.221177
\(376\) 5.22054e11 1.34701
\(377\) −7.92176e10 −0.201970
\(378\) 6.31498e11 1.59096
\(379\) 5.54877e11 1.38140 0.690701 0.723140i \(-0.257302\pi\)
0.690701 + 0.723140i \(0.257302\pi\)
\(380\) 1.75825e12 4.32569
\(381\) −3.40131e11 −0.826959
\(382\) −3.23009e11 −0.776121
\(383\) 5.79022e11 1.37499 0.687496 0.726188i \(-0.258710\pi\)
0.687496 + 0.726188i \(0.258710\pi\)
\(384\) 2.73237e11 0.641282
\(385\) −9.01014e11 −2.09006
\(386\) −5.83438e11 −1.33768
\(387\) 1.92136e11 0.435420
\(388\) −9.49946e11 −2.12792
\(389\) 5.29321e11 1.17205 0.586025 0.810293i \(-0.300692\pi\)
0.586025 + 0.810293i \(0.300692\pi\)
\(390\) 3.42872e11 0.750484
\(391\) 0 0
\(392\) −3.61689e11 −0.773655
\(393\) 2.87939e11 0.608883
\(394\) 1.33477e11 0.279045
\(395\) 6.33476e11 1.30931
\(396\) 8.46078e11 1.72895
\(397\) −4.75199e10 −0.0960105 −0.0480052 0.998847i \(-0.515286\pi\)
−0.0480052 + 0.998847i \(0.515286\pi\)
\(398\) −2.99584e11 −0.598474
\(399\) −3.96087e11 −0.782372
\(400\) 1.17009e12 2.28533
\(401\) 5.62820e11 1.08697 0.543487 0.839417i \(-0.317104\pi\)
0.543487 + 0.839417i \(0.317104\pi\)
\(402\) −1.29293e12 −2.46920
\(403\) −8.10293e10 −0.153028
\(404\) 2.95879e11 0.552584
\(405\) −2.94943e11 −0.544742
\(406\) 4.37110e11 0.798406
\(407\) −1.16941e12 −2.11248
\(408\) 0 0
\(409\) −1.86774e11 −0.330037 −0.165018 0.986290i \(-0.552768\pi\)
−0.165018 + 0.986290i \(0.552768\pi\)
\(410\) 2.15093e12 3.75923
\(411\) −7.16902e11 −1.23929
\(412\) −1.77626e12 −3.03716
\(413\) −3.71827e11 −0.628877
\(414\) −8.09345e11 −1.35404
\(415\) −1.00132e12 −1.65714
\(416\) −2.59820e11 −0.425356
\(417\) 2.32888e11 0.377168
\(418\) −2.50165e12 −4.00805
\(419\) 5.54170e11 0.878375 0.439187 0.898395i \(-0.355266\pi\)
0.439187 + 0.898395i \(0.355266\pi\)
\(420\) −1.31448e12 −2.06126
\(421\) −4.58096e11 −0.710701 −0.355351 0.934733i \(-0.615639\pi\)
−0.355351 + 0.934733i \(0.615639\pi\)
\(422\) 3.29600e10 0.0505919
\(423\) −1.68721e11 −0.256235
\(424\) −1.00199e11 −0.150563
\(425\) 0 0
\(426\) −5.66426e11 −0.833297
\(427\) −6.07936e10 −0.0884978
\(428\) −2.01641e12 −2.90456
\(429\) −3.38946e11 −0.483139
\(430\) −1.88533e12 −2.65937
\(431\) −3.33640e11 −0.465726 −0.232863 0.972510i \(-0.574809\pi\)
−0.232863 + 0.972510i \(0.574809\pi\)
\(432\) 1.48671e12 2.05376
\(433\) −7.14343e11 −0.976588 −0.488294 0.872679i \(-0.662381\pi\)
−0.488294 + 0.872679i \(0.662381\pi\)
\(434\) 4.47107e11 0.604934
\(435\) −4.48421e11 −0.600460
\(436\) −4.17478e11 −0.553280
\(437\) 1.66266e12 2.18090
\(438\) −1.38493e12 −1.79802
\(439\) −5.11066e11 −0.656729 −0.328365 0.944551i \(-0.606497\pi\)
−0.328365 + 0.944551i \(0.606497\pi\)
\(440\) −4.65512e12 −5.92099
\(441\) 1.16893e11 0.147169
\(442\) 0 0
\(443\) 5.01063e11 0.618124 0.309062 0.951042i \(-0.399985\pi\)
0.309062 + 0.951042i \(0.399985\pi\)
\(444\) −1.70604e12 −2.08337
\(445\) 3.65328e11 0.441635
\(446\) 8.47428e11 1.01414
\(447\) 4.35919e11 0.516443
\(448\) 1.08506e11 0.127263
\(449\) −1.40379e12 −1.63002 −0.815011 0.579445i \(-0.803269\pi\)
−0.815011 + 0.579445i \(0.803269\pi\)
\(450\) −8.29884e11 −0.954028
\(451\) −2.12630e12 −2.42008
\(452\) −8.85307e11 −0.997633
\(453\) −4.43348e10 −0.0494655
\(454\) −1.32005e12 −1.45827
\(455\) −4.12920e11 −0.451663
\(456\) −2.04640e12 −2.21641
\(457\) 1.21248e12 1.30032 0.650161 0.759797i \(-0.274702\pi\)
0.650161 + 0.759797i \(0.274702\pi\)
\(458\) −5.98385e11 −0.635457
\(459\) 0 0
\(460\) 5.51779e12 5.74586
\(461\) 9.45438e10 0.0974942 0.0487471 0.998811i \(-0.484477\pi\)
0.0487471 + 0.998811i \(0.484477\pi\)
\(462\) 1.87025e12 1.90990
\(463\) 6.27192e11 0.634287 0.317144 0.948378i \(-0.397276\pi\)
0.317144 + 0.948378i \(0.397276\pi\)
\(464\) 1.02907e12 1.03066
\(465\) −4.58676e11 −0.454954
\(466\) 5.74453e11 0.564310
\(467\) 1.46476e12 1.42508 0.712542 0.701630i \(-0.247544\pi\)
0.712542 + 0.701630i \(0.247544\pi\)
\(468\) 3.87744e11 0.373627
\(469\) 1.55707e12 1.48604
\(470\) 1.65558e12 1.56498
\(471\) −1.86925e11 −0.175014
\(472\) −1.92106e12 −1.78157
\(473\) 1.86374e12 1.71202
\(474\) −1.31492e12 −1.19645
\(475\) 1.70485e12 1.53661
\(476\) 0 0
\(477\) 3.23832e10 0.0286409
\(478\) −1.81654e11 −0.159155
\(479\) 1.19999e12 1.04152 0.520761 0.853703i \(-0.325648\pi\)
0.520761 + 0.853703i \(0.325648\pi\)
\(480\) −1.47074e12 −1.26459
\(481\) −5.35922e11 −0.456509
\(482\) 7.84149e11 0.661740
\(483\) −1.24301e12 −1.03923
\(484\) 5.45879e12 4.52160
\(485\) −1.68917e12 −1.38623
\(486\) −1.78696e12 −1.45295
\(487\) 2.37860e11 0.191620 0.0958100 0.995400i \(-0.469456\pi\)
0.0958100 + 0.995400i \(0.469456\pi\)
\(488\) −3.14093e11 −0.250708
\(489\) 6.87609e11 0.543816
\(490\) −1.14701e12 −0.898847
\(491\) −2.34046e12 −1.81734 −0.908668 0.417520i \(-0.862899\pi\)
−0.908668 + 0.417520i \(0.862899\pi\)
\(492\) −3.10204e12 −2.38673
\(493\) 0 0
\(494\) −1.14646e12 −0.866143
\(495\) 1.50448e12 1.12632
\(496\) 1.05261e12 0.780908
\(497\) 6.82146e11 0.501503
\(498\) 2.07846e12 1.51429
\(499\) −1.92746e12 −1.39166 −0.695829 0.718207i \(-0.744963\pi\)
−0.695829 + 0.718207i \(0.744963\pi\)
\(500\) 9.39882e11 0.672525
\(501\) −2.04237e11 −0.144832
\(502\) −3.53825e11 −0.248669
\(503\) −5.96651e11 −0.415589 −0.207795 0.978172i \(-0.566629\pi\)
−0.207795 + 0.978172i \(0.566629\pi\)
\(504\) −1.19965e12 −0.828169
\(505\) 5.26126e11 0.359980
\(506\) −7.85074e12 −5.32394
\(507\) 9.58504e11 0.644255
\(508\) 3.77432e12 2.51450
\(509\) 1.05883e12 0.699190 0.349595 0.936901i \(-0.386319\pi\)
0.349595 + 0.936901i \(0.386319\pi\)
\(510\) 0 0
\(511\) 1.66787e12 1.08210
\(512\) −3.47121e12 −2.23237
\(513\) 2.16618e12 1.38091
\(514\) −4.70125e12 −2.97084
\(515\) −3.15850e12 −1.97856
\(516\) 2.71899e12 1.68843
\(517\) −1.63662e12 −1.00749
\(518\) 2.95713e12 1.80463
\(519\) −1.65220e12 −0.999564
\(520\) −2.13337e12 −1.27953
\(521\) −3.10824e12 −1.84818 −0.924091 0.382172i \(-0.875176\pi\)
−0.924091 + 0.382172i \(0.875176\pi\)
\(522\) −7.29870e11 −0.430257
\(523\) 1.18130e12 0.690400 0.345200 0.938529i \(-0.387811\pi\)
0.345200 + 0.938529i \(0.387811\pi\)
\(524\) −3.19516e12 −1.85140
\(525\) −1.27456e12 −0.732221
\(526\) 1.40270e12 0.798968
\(527\) 0 0
\(528\) 4.40306e12 2.46548
\(529\) 3.41664e12 1.89692
\(530\) −3.17760e11 −0.174927
\(531\) 6.20863e11 0.338899
\(532\) 4.39524e12 2.37892
\(533\) −9.74447e11 −0.522981
\(534\) −7.58318e11 −0.403567
\(535\) −3.58553e12 −1.89218
\(536\) 8.04467e12 4.20985
\(537\) −4.74172e11 −0.246066
\(538\) 2.84531e12 1.46423
\(539\) 1.13388e12 0.578651
\(540\) 7.18883e12 3.63820
\(541\) −3.43819e12 −1.72561 −0.862803 0.505540i \(-0.831293\pi\)
−0.862803 + 0.505540i \(0.831293\pi\)
\(542\) −4.36506e10 −0.0217267
\(543\) 2.37834e12 1.17402
\(544\) 0 0
\(545\) −7.42351e11 −0.360433
\(546\) 8.57104e11 0.412731
\(547\) −1.60640e12 −0.767201 −0.383601 0.923499i \(-0.625316\pi\)
−0.383601 + 0.923499i \(0.625316\pi\)
\(548\) 7.95521e12 3.76824
\(549\) 1.01511e11 0.0476911
\(550\) −8.04997e12 −3.75113
\(551\) 1.49939e12 0.692998
\(552\) −6.42207e12 −2.94408
\(553\) 1.58355e12 0.720060
\(554\) 4.04879e12 1.82613
\(555\) −3.03365e12 −1.35721
\(556\) −2.58428e12 −1.14684
\(557\) −1.82680e12 −0.804160 −0.402080 0.915604i \(-0.631713\pi\)
−0.402080 + 0.915604i \(0.631713\pi\)
\(558\) −7.46562e11 −0.325996
\(559\) 8.54121e11 0.369970
\(560\) 5.36403e12 2.30486
\(561\) 0 0
\(562\) −7.34695e12 −3.10666
\(563\) −2.07582e12 −0.870768 −0.435384 0.900245i \(-0.643387\pi\)
−0.435384 + 0.900245i \(0.643387\pi\)
\(564\) −2.38765e12 −0.993606
\(565\) −1.57423e12 −0.649907
\(566\) 1.26716e12 0.518989
\(567\) −7.37293e11 −0.299582
\(568\) 3.52433e12 1.42072
\(569\) −2.00630e12 −0.802398 −0.401199 0.915991i \(-0.631406\pi\)
−0.401199 + 0.915991i \(0.631406\pi\)
\(570\) −6.48970e12 −2.57506
\(571\) −4.13921e12 −1.62950 −0.814750 0.579812i \(-0.803126\pi\)
−0.814750 + 0.579812i \(0.803126\pi\)
\(572\) 3.76116e12 1.46906
\(573\) 8.28345e11 0.321008
\(574\) 5.37684e12 2.06740
\(575\) 5.35020e12 2.04110
\(576\) −1.81179e11 −0.0685814
\(577\) −1.32648e12 −0.498207 −0.249103 0.968477i \(-0.580136\pi\)
−0.249103 + 0.968477i \(0.580136\pi\)
\(578\) 0 0
\(579\) 1.49620e12 0.553270
\(580\) 4.97597e12 1.82579
\(581\) −2.50309e12 −0.911347
\(582\) 3.50624e12 1.26674
\(583\) 3.14121e11 0.112613
\(584\) 8.61713e12 3.06552
\(585\) 6.89478e11 0.243399
\(586\) 7.04576e11 0.246825
\(587\) 1.74995e12 0.608350 0.304175 0.952616i \(-0.401619\pi\)
0.304175 + 0.952616i \(0.401619\pi\)
\(588\) 1.65420e12 0.570678
\(589\) 1.53368e12 0.525068
\(590\) −6.09220e12 −2.06986
\(591\) −3.42298e11 −0.115415
\(592\) 6.96189e12 2.32959
\(593\) 1.45962e12 0.484723 0.242361 0.970186i \(-0.422078\pi\)
0.242361 + 0.970186i \(0.422078\pi\)
\(594\) −1.02283e13 −3.37104
\(595\) 0 0
\(596\) −4.83724e12 −1.57033
\(597\) 7.68272e11 0.247532
\(598\) −3.59787e12 −1.15051
\(599\) 5.09467e12 1.61695 0.808473 0.588534i \(-0.200295\pi\)
0.808473 + 0.588534i \(0.200295\pi\)
\(600\) −6.58505e12 −2.07433
\(601\) 3.21832e12 1.00622 0.503111 0.864222i \(-0.332189\pi\)
0.503111 + 0.864222i \(0.332189\pi\)
\(602\) −4.71290e12 −1.46253
\(603\) −2.59994e12 −0.800820
\(604\) 4.91968e11 0.150408
\(605\) 9.70671e12 2.94559
\(606\) −1.09209e12 −0.328951
\(607\) 6.15206e12 1.83938 0.919690 0.392645i \(-0.128440\pi\)
0.919690 + 0.392645i \(0.128440\pi\)
\(608\) 4.91774e12 1.45948
\(609\) −1.12095e12 −0.330225
\(610\) −9.96073e11 −0.291278
\(611\) −7.50035e11 −0.217719
\(612\) 0 0
\(613\) −4.67903e12 −1.33839 −0.669196 0.743086i \(-0.733361\pi\)
−0.669196 + 0.743086i \(0.733361\pi\)
\(614\) −7.55488e12 −2.14521
\(615\) −5.51597e12 −1.55483
\(616\) −1.16368e13 −3.25627
\(617\) −1.42170e12 −0.394933 −0.197467 0.980310i \(-0.563271\pi\)
−0.197467 + 0.980310i \(0.563271\pi\)
\(618\) 6.55615e12 1.80801
\(619\) −2.99905e12 −0.821061 −0.410531 0.911847i \(-0.634656\pi\)
−0.410531 + 0.911847i \(0.634656\pi\)
\(620\) 5.08977e12 1.38336
\(621\) 6.79797e12 1.83429
\(622\) 8.10436e12 2.17101
\(623\) 9.13240e11 0.242878
\(624\) 2.01785e12 0.532794
\(625\) −2.90336e12 −0.761099
\(626\) −3.29865e12 −0.858523
\(627\) 6.41538e12 1.65775
\(628\) 2.07424e12 0.532158
\(629\) 0 0
\(630\) −3.80443e12 −0.962182
\(631\) −3.26952e12 −0.821017 −0.410508 0.911857i \(-0.634649\pi\)
−0.410508 + 0.911857i \(0.634649\pi\)
\(632\) 8.18148e12 2.03988
\(633\) −8.45246e10 −0.0209251
\(634\) −5.65153e12 −1.38920
\(635\) 6.71141e12 1.63807
\(636\) 4.58268e11 0.111061
\(637\) 5.19638e11 0.125047
\(638\) −7.07982e12 −1.69172
\(639\) −1.13902e12 −0.270258
\(640\) −5.39146e12 −1.27027
\(641\) −2.29784e12 −0.537598 −0.268799 0.963196i \(-0.586627\pi\)
−0.268799 + 0.963196i \(0.586627\pi\)
\(642\) 7.44254e12 1.72907
\(643\) −1.34089e12 −0.309345 −0.154673 0.987966i \(-0.549432\pi\)
−0.154673 + 0.987966i \(0.549432\pi\)
\(644\) 1.37933e13 3.15995
\(645\) 4.83485e12 1.09993
\(646\) 0 0
\(647\) 6.20336e12 1.39174 0.695869 0.718168i \(-0.255019\pi\)
0.695869 + 0.718168i \(0.255019\pi\)
\(648\) −3.80925e12 −0.848696
\(649\) 6.02244e12 1.33251
\(650\) −3.68917e12 −0.810622
\(651\) −1.14659e12 −0.250203
\(652\) −7.63016e12 −1.65356
\(653\) 5.36324e11 0.115430 0.0577149 0.998333i \(-0.481619\pi\)
0.0577149 + 0.998333i \(0.481619\pi\)
\(654\) 1.54091e12 0.329365
\(655\) −5.68156e12 −1.20610
\(656\) 1.26585e13 2.66880
\(657\) −2.78495e12 −0.583140
\(658\) 4.13857e12 0.860665
\(659\) 3.60641e11 0.0744887 0.0372443 0.999306i \(-0.488142\pi\)
0.0372443 + 0.999306i \(0.488142\pi\)
\(660\) 2.12905e13 4.36755
\(661\) −6.10771e12 −1.24443 −0.622216 0.782845i \(-0.713768\pi\)
−0.622216 + 0.782845i \(0.713768\pi\)
\(662\) −4.59922e12 −0.930729
\(663\) 0 0
\(664\) −1.29323e13 −2.58178
\(665\) 7.81553e12 1.54975
\(666\) −4.93771e12 −0.972504
\(667\) 4.70542e12 0.920518
\(668\) 2.26634e12 0.440384
\(669\) −2.17320e12 −0.419452
\(670\) 2.55118e13 4.89108
\(671\) 9.84667e11 0.187516
\(672\) −3.67653e12 −0.695467
\(673\) −5.35107e12 −1.00548 −0.502739 0.864438i \(-0.667674\pi\)
−0.502739 + 0.864438i \(0.667674\pi\)
\(674\) 9.12616e12 1.70341
\(675\) 6.97048e12 1.29240
\(676\) −1.06362e13 −1.95896
\(677\) 2.46559e12 0.451099 0.225550 0.974232i \(-0.427582\pi\)
0.225550 + 0.974232i \(0.427582\pi\)
\(678\) 3.26766e12 0.593886
\(679\) −4.22256e12 −0.762364
\(680\) 0 0
\(681\) 3.38522e12 0.603149
\(682\) −7.24174e12 −1.28178
\(683\) −8.41114e12 −1.47898 −0.739489 0.673169i \(-0.764933\pi\)
−0.739489 + 0.673169i \(0.764933\pi\)
\(684\) −7.33901e12 −1.28199
\(685\) 1.41458e13 2.45482
\(686\) −1.14301e13 −1.97057
\(687\) 1.53454e12 0.262828
\(688\) −1.10954e13 −1.88797
\(689\) 1.43957e11 0.0243358
\(690\) −2.03661e13 −3.42049
\(691\) −3.08875e12 −0.515384 −0.257692 0.966227i \(-0.582962\pi\)
−0.257692 + 0.966227i \(0.582962\pi\)
\(692\) 1.83339e13 3.03933
\(693\) 3.76086e12 0.619424
\(694\) 3.59268e12 0.587896
\(695\) −4.59531e12 −0.747107
\(696\) −5.79145e12 −0.935504
\(697\) 0 0
\(698\) −1.30466e13 −2.08040
\(699\) −1.47316e12 −0.233401
\(700\) 1.41433e13 2.22643
\(701\) −9.89703e12 −1.54801 −0.774005 0.633180i \(-0.781749\pi\)
−0.774005 + 0.633180i \(0.781749\pi\)
\(702\) −4.68746e12 −0.728485
\(703\) 1.01437e13 1.56637
\(704\) −1.75745e12 −0.269654
\(705\) −4.24566e12 −0.647283
\(706\) −2.16494e13 −3.27962
\(707\) 1.31520e12 0.197972
\(708\) 8.78608e12 1.31415
\(709\) 6.74854e12 1.00300 0.501501 0.865157i \(-0.332781\pi\)
0.501501 + 0.865157i \(0.332781\pi\)
\(710\) 1.11766e13 1.65062
\(711\) −2.64415e12 −0.388037
\(712\) 4.71830e12 0.688058
\(713\) 4.81304e12 0.697455
\(714\) 0 0
\(715\) 6.68802e12 0.957018
\(716\) 5.26172e12 0.748203
\(717\) 4.65845e11 0.0658272
\(718\) 1.69796e13 2.38434
\(719\) 8.19160e12 1.14311 0.571556 0.820563i \(-0.306340\pi\)
0.571556 + 0.820563i \(0.306340\pi\)
\(720\) −8.95665e12 −1.24208
\(721\) −7.89555e12 −1.08811
\(722\) 8.48314e12 1.16182
\(723\) −2.01092e12 −0.273699
\(724\) −2.63916e13 −3.56978
\(725\) 4.82483e12 0.648577
\(726\) −2.01484e13 −2.69169
\(727\) 5.33262e12 0.708004 0.354002 0.935245i \(-0.384821\pi\)
0.354002 + 0.935245i \(0.384821\pi\)
\(728\) −5.33295e12 −0.703682
\(729\) 7.38370e12 0.968279
\(730\) 2.73272e13 3.56158
\(731\) 0 0
\(732\) 1.43652e12 0.184932
\(733\) −7.95146e12 −1.01737 −0.508685 0.860953i \(-0.669868\pi\)
−0.508685 + 0.860953i \(0.669868\pi\)
\(734\) 1.19217e13 1.51603
\(735\) 2.94147e12 0.371768
\(736\) 1.54330e13 1.93865
\(737\) −2.52197e13 −3.14873
\(738\) −8.97805e12 −1.11411
\(739\) −2.28266e11 −0.0281541 −0.0140770 0.999901i \(-0.504481\pi\)
−0.0140770 + 0.999901i \(0.504481\pi\)
\(740\) 3.36634e13 4.12681
\(741\) 2.94007e12 0.358241
\(742\) −7.94329e11 −0.0962017
\(743\) −8.49426e12 −1.02253 −0.511265 0.859423i \(-0.670823\pi\)
−0.511265 + 0.859423i \(0.670823\pi\)
\(744\) −5.92390e12 −0.708810
\(745\) −8.60148e12 −1.02299
\(746\) −3.37134e12 −0.398545
\(747\) 4.17956e12 0.491121
\(748\) 0 0
\(749\) −8.96304e12 −1.04061
\(750\) −3.46910e12 −0.400351
\(751\) 7.62165e12 0.874318 0.437159 0.899384i \(-0.355985\pi\)
0.437159 + 0.899384i \(0.355985\pi\)
\(752\) 9.74331e12 1.11103
\(753\) 9.07372e11 0.102851
\(754\) −3.24457e12 −0.365583
\(755\) 8.74806e11 0.0979830
\(756\) 1.79705e13 2.00084
\(757\) 1.21708e13 1.34706 0.673532 0.739158i \(-0.264776\pi\)
0.673532 + 0.739158i \(0.264776\pi\)
\(758\) 2.27265e13 2.50046
\(759\) 2.01329e13 2.20201
\(760\) 4.03793e13 4.39033
\(761\) −1.72056e13 −1.85968 −0.929840 0.367964i \(-0.880055\pi\)
−0.929840 + 0.367964i \(0.880055\pi\)
\(762\) −1.39310e13 −1.49687
\(763\) −1.85571e12 −0.198221
\(764\) −9.19185e12 −0.976074
\(765\) 0 0
\(766\) 2.37154e13 2.48886
\(767\) 2.75999e12 0.287957
\(768\) 1.23174e13 1.27760
\(769\) −1.42533e13 −1.46976 −0.734879 0.678198i \(-0.762761\pi\)
−0.734879 + 0.678198i \(0.762761\pi\)
\(770\) −3.69034e13 −3.78319
\(771\) 1.20562e13 1.22875
\(772\) −1.66029e13 −1.68231
\(773\) −3.75655e12 −0.378426 −0.189213 0.981936i \(-0.560594\pi\)
−0.189213 + 0.981936i \(0.560594\pi\)
\(774\) 7.86942e12 0.788150
\(775\) 4.93518e12 0.491411
\(776\) −2.18160e13 −2.15972
\(777\) −7.58346e12 −0.746402
\(778\) 2.16798e13 2.12152
\(779\) 1.84438e13 1.79445
\(780\) 9.75709e12 0.943832
\(781\) −1.10486e13 −1.06262
\(782\) 0 0
\(783\) 6.13044e12 0.582859
\(784\) −6.75034e12 −0.638122
\(785\) 3.68837e12 0.346674
\(786\) 1.17933e13 1.10213
\(787\) 1.53858e13 1.42967 0.714833 0.699296i \(-0.246503\pi\)
0.714833 + 0.699296i \(0.246503\pi\)
\(788\) 3.79836e12 0.350936
\(789\) −3.59718e12 −0.330457
\(790\) 2.59457e13 2.36997
\(791\) −3.93524e12 −0.357418
\(792\) 1.94307e13 1.75479
\(793\) 4.51257e11 0.0405224
\(794\) −1.94631e12 −0.173788
\(795\) 8.14883e11 0.0723507
\(796\) −8.52525e12 −0.752659
\(797\) −1.86441e13 −1.63674 −0.818370 0.574692i \(-0.805122\pi\)
−0.818370 + 0.574692i \(0.805122\pi\)
\(798\) −1.62228e13 −1.41616
\(799\) 0 0
\(800\) 1.58246e13 1.36593
\(801\) −1.52489e12 −0.130886
\(802\) 2.30518e13 1.96752
\(803\) −2.70143e13 −2.29284
\(804\) −3.67928e13 −3.10535
\(805\) 2.45269e13 2.05855
\(806\) −3.31877e12 −0.276994
\(807\) −7.29670e12 −0.605613
\(808\) 6.79503e12 0.560842
\(809\) −1.03571e13 −0.850099 −0.425050 0.905170i \(-0.639743\pi\)
−0.425050 + 0.905170i \(0.639743\pi\)
\(810\) −1.20802e13 −0.986031
\(811\) −1.65829e13 −1.34607 −0.673035 0.739611i \(-0.735010\pi\)
−0.673035 + 0.739611i \(0.735010\pi\)
\(812\) 1.24388e13 1.00410
\(813\) 1.11940e11 0.00898626
\(814\) −4.78963e13 −3.82378
\(815\) −1.35678e13 −1.07721
\(816\) 0 0
\(817\) −1.61663e13 −1.26944
\(818\) −7.64984e12 −0.597396
\(819\) 1.72354e12 0.133858
\(820\) 6.12088e13 4.72772
\(821\) −4.69704e11 −0.0360811 −0.0180406 0.999837i \(-0.505743\pi\)
−0.0180406 + 0.999837i \(0.505743\pi\)
\(822\) −2.93626e13 −2.24322
\(823\) −9.83346e12 −0.747149 −0.373574 0.927600i \(-0.621868\pi\)
−0.373574 + 0.927600i \(0.621868\pi\)
\(824\) −4.07927e13 −3.08255
\(825\) 2.06438e13 1.55149
\(826\) −1.52292e13 −1.13832
\(827\) 1.86474e13 1.38625 0.693126 0.720816i \(-0.256233\pi\)
0.693126 + 0.720816i \(0.256233\pi\)
\(828\) −2.30315e13 −1.70289
\(829\) −1.30982e13 −0.963202 −0.481601 0.876391i \(-0.659945\pi\)
−0.481601 + 0.876391i \(0.659945\pi\)
\(830\) −4.10119e13 −2.99957
\(831\) −1.03830e13 −0.755296
\(832\) −8.05413e11 −0.0582725
\(833\) 0 0
\(834\) 9.53855e12 0.682708
\(835\) 4.02997e12 0.286888
\(836\) −7.11892e13 −5.04064
\(837\) 6.27064e12 0.441618
\(838\) 2.26975e13 1.58994
\(839\) −1.02237e13 −0.712325 −0.356163 0.934424i \(-0.615915\pi\)
−0.356163 + 0.934424i \(0.615915\pi\)
\(840\) −3.01878e13 −2.09206
\(841\) −1.02638e13 −0.707498
\(842\) −1.87625e13 −1.28643
\(843\) 1.88410e13 1.28493
\(844\) 9.37940e11 0.0636259
\(845\) −1.89130e13 −1.27616
\(846\) −6.91044e12 −0.463809
\(847\) 2.42646e13 1.61994
\(848\) −1.87006e12 −0.124187
\(849\) −3.24959e12 −0.214657
\(850\) 0 0
\(851\) 3.18331e13 2.08063
\(852\) −1.61188e13 −1.04798
\(853\) 2.01132e13 1.30080 0.650399 0.759593i \(-0.274602\pi\)
0.650399 + 0.759593i \(0.274602\pi\)
\(854\) −2.48996e12 −0.160189
\(855\) −1.30501e13 −0.835152
\(856\) −4.63079e13 −2.94797
\(857\) −1.09459e13 −0.693168 −0.346584 0.938019i \(-0.612658\pi\)
−0.346584 + 0.938019i \(0.612658\pi\)
\(858\) −1.38824e13 −0.874525
\(859\) 2.56259e13 1.60587 0.802935 0.596066i \(-0.203270\pi\)
0.802935 + 0.596066i \(0.203270\pi\)
\(860\) −5.36506e13 −3.34450
\(861\) −1.37887e13 −0.855086
\(862\) −1.36651e13 −0.843006
\(863\) 2.79069e13 1.71263 0.856313 0.516456i \(-0.172749\pi\)
0.856313 + 0.516456i \(0.172749\pi\)
\(864\) 2.01068e13 1.22753
\(865\) 3.26010e13 1.97997
\(866\) −2.92578e13 −1.76771
\(867\) 0 0
\(868\) 1.27233e13 0.760783
\(869\) −2.56486e13 −1.52572
\(870\) −1.83663e13 −1.08689
\(871\) −1.15578e13 −0.680444
\(872\) −9.58763e12 −0.561548
\(873\) 7.05068e12 0.410834
\(874\) 6.80985e13 3.94763
\(875\) 4.17783e12 0.240943
\(876\) −3.94109e13 −2.26125
\(877\) 3.22173e12 0.183904 0.0919520 0.995763i \(-0.470689\pi\)
0.0919520 + 0.995763i \(0.470689\pi\)
\(878\) −2.09321e13 −1.18874
\(879\) −1.80686e12 −0.102088
\(880\) −8.68805e13 −4.88371
\(881\) 2.98527e13 1.66952 0.834762 0.550611i \(-0.185605\pi\)
0.834762 + 0.550611i \(0.185605\pi\)
\(882\) 4.78767e12 0.266389
\(883\) 2.33030e13 1.29000 0.644998 0.764184i \(-0.276858\pi\)
0.644998 + 0.764184i \(0.276858\pi\)
\(884\) 0 0
\(885\) 1.56232e13 0.856103
\(886\) 2.05224e13 1.11886
\(887\) −1.81953e13 −0.986966 −0.493483 0.869755i \(-0.664276\pi\)
−0.493483 + 0.869755i \(0.664276\pi\)
\(888\) −3.91803e13 −2.11451
\(889\) 1.67770e13 0.900860
\(890\) 1.49630e13 0.799399
\(891\) 1.19418e13 0.634777
\(892\) 2.41152e13 1.27541
\(893\) 1.41963e13 0.747038
\(894\) 1.78542e13 0.934807
\(895\) 9.35628e12 0.487416
\(896\) −1.34775e13 −0.698590
\(897\) 9.22659e12 0.475856
\(898\) −5.74959e13 −2.95049
\(899\) 4.34041e12 0.221622
\(900\) −2.36160e13 −1.19981
\(901\) 0 0
\(902\) −8.70881e13 −4.38056
\(903\) 1.20861e13 0.604909
\(904\) −2.03316e13 −1.01254
\(905\) −4.69289e13 −2.32553
\(906\) −1.81585e12 −0.0895371
\(907\) −8.29665e12 −0.407071 −0.203535 0.979068i \(-0.565243\pi\)
−0.203535 + 0.979068i \(0.565243\pi\)
\(908\) −3.75646e13 −1.83397
\(909\) −2.19607e12 −0.106686
\(910\) −1.69122e13 −0.817551
\(911\) −1.97513e13 −0.950089 −0.475044 0.879962i \(-0.657568\pi\)
−0.475044 + 0.879962i \(0.657568\pi\)
\(912\) −3.81929e13 −1.82812
\(913\) 4.05422e13 1.93103
\(914\) 4.96602e13 2.35370
\(915\) 2.55439e12 0.120474
\(916\) −1.70282e13 −0.799170
\(917\) −1.42026e13 −0.663296
\(918\) 0 0
\(919\) 2.17107e13 1.00405 0.502023 0.864854i \(-0.332589\pi\)
0.502023 + 0.864854i \(0.332589\pi\)
\(920\) 1.26719e14 5.83173
\(921\) 1.93742e13 0.887270
\(922\) 3.87229e12 0.176473
\(923\) −5.06341e12 −0.229634
\(924\) 5.32215e13 2.40195
\(925\) 3.26409e13 1.46597
\(926\) 2.56883e13 1.14812
\(927\) 1.31837e13 0.586379
\(928\) 1.39175e13 0.616022
\(929\) −2.57045e13 −1.13224 −0.566119 0.824324i \(-0.691556\pi\)
−0.566119 + 0.824324i \(0.691556\pi\)
\(930\) −1.87863e13 −0.823508
\(931\) −9.83543e12 −0.429062
\(932\) 1.63472e13 0.709694
\(933\) −2.07833e13 −0.897941
\(934\) 5.99931e13 2.57953
\(935\) 0 0
\(936\) 8.90476e12 0.379211
\(937\) 6.39027e12 0.270827 0.135413 0.990789i \(-0.456764\pi\)
0.135413 + 0.990789i \(0.456764\pi\)
\(938\) 6.37739e13 2.68986
\(939\) 8.45927e12 0.355089
\(940\) 4.71126e13 1.96817
\(941\) 4.18227e13 1.73884 0.869419 0.494076i \(-0.164493\pi\)
0.869419 + 0.494076i \(0.164493\pi\)
\(942\) −7.65600e12 −0.316791
\(943\) 5.78809e13 2.38360
\(944\) −3.58535e13 −1.46946
\(945\) 3.19547e13 1.30344
\(946\) 7.63343e13 3.09891
\(947\) 2.86239e13 1.15652 0.578260 0.815852i \(-0.303732\pi\)
0.578260 + 0.815852i \(0.303732\pi\)
\(948\) −3.74185e13 −1.50470
\(949\) −1.23802e13 −0.495485
\(950\) 6.98266e13 2.78141
\(951\) 1.44931e13 0.574580
\(952\) 0 0
\(953\) 4.18770e13 1.64459 0.822295 0.569062i \(-0.192693\pi\)
0.822295 + 0.569062i \(0.192693\pi\)
\(954\) 1.32634e12 0.0518427
\(955\) −1.63448e13 −0.635862
\(956\) −5.16932e12 −0.200158
\(957\) 1.81559e13 0.699705
\(958\) 4.91488e13 1.88525
\(959\) 3.53613e13 1.35003
\(960\) −4.55913e12 −0.173245
\(961\) −2.19999e13 −0.832082
\(962\) −2.19501e13 −0.826322
\(963\) 1.49661e13 0.560779
\(964\) 2.23145e13 0.832224
\(965\) −2.95228e13 −1.09594
\(966\) −5.09109e13 −1.88111
\(967\) 1.10971e13 0.408124 0.204062 0.978958i \(-0.434586\pi\)
0.204062 + 0.978958i \(0.434586\pi\)
\(968\) 1.25364e14 4.58918
\(969\) 0 0
\(970\) −6.91846e13 −2.50921
\(971\) −1.62887e12 −0.0588029 −0.0294015 0.999568i \(-0.509360\pi\)
−0.0294015 + 0.999568i \(0.509360\pi\)
\(972\) −5.08514e13 −1.82728
\(973\) −1.14873e13 −0.410874
\(974\) 9.74219e12 0.346850
\(975\) 9.46074e12 0.335277
\(976\) −5.86204e12 −0.206788
\(977\) −4.55973e12 −0.160108 −0.0800541 0.996791i \(-0.525509\pi\)
−0.0800541 + 0.996791i \(0.525509\pi\)
\(978\) 2.81629e13 0.984355
\(979\) −1.47916e13 −0.514629
\(980\) −3.26405e13 −1.13042
\(981\) 3.09860e12 0.106821
\(982\) −9.58599e13 −3.28954
\(983\) 1.34574e13 0.459694 0.229847 0.973227i \(-0.426177\pi\)
0.229847 + 0.973227i \(0.426177\pi\)
\(984\) −7.12400e13 −2.42240
\(985\) 6.75416e12 0.228617
\(986\) 0 0
\(987\) −1.06132e13 −0.355975
\(988\) −3.26249e13 −1.08929
\(989\) −5.07336e13 −1.68621
\(990\) 6.16199e13 2.03874
\(991\) 1.26466e13 0.416525 0.208262 0.978073i \(-0.433219\pi\)
0.208262 + 0.978073i \(0.433219\pi\)
\(992\) 1.42358e13 0.466745
\(993\) 1.17945e13 0.384954
\(994\) 2.79391e13 0.907765
\(995\) −1.51594e13 −0.490319
\(996\) 5.91467e13 1.90442
\(997\) 4.22854e13 1.35538 0.677692 0.735346i \(-0.262980\pi\)
0.677692 + 0.735346i \(0.262980\pi\)
\(998\) −7.89442e13 −2.51903
\(999\) 4.14736e13 1.31743
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.1.35 yes 36
17.16 even 2 289.10.a.g.1.35 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.35 36 17.16 even 2
289.10.a.h.1.35 yes 36 1.1 even 1 trivial