Properties

Label 289.10.a.h.1.22
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 1.22
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q+10.7250 q^{2} +53.3726 q^{3} -396.975 q^{4} -85.7107 q^{5} +572.419 q^{6} +4510.26 q^{7} -9748.72 q^{8} -16834.4 q^{9} +O(q^{10})\) \(q+10.7250 q^{2} +53.3726 q^{3} -396.975 q^{4} -85.7107 q^{5} +572.419 q^{6} +4510.26 q^{7} -9748.72 q^{8} -16834.4 q^{9} -919.244 q^{10} -31525.7 q^{11} -21187.6 q^{12} -6484.90 q^{13} +48372.4 q^{14} -4574.61 q^{15} +98696.8 q^{16} -180548. q^{18} +508379. q^{19} +34025.1 q^{20} +240725. q^{21} -338112. q^{22} -1.78877e6 q^{23} -520315. q^{24} -1.94578e6 q^{25} -69550.3 q^{26} -1.94903e6 q^{27} -1.79046e6 q^{28} -1.55740e6 q^{29} -49062.5 q^{30} +2.05480e6 q^{31} +6.04986e6 q^{32} -1.68261e6 q^{33} -386578. q^{35} +6.68283e6 q^{36} -7.61805e6 q^{37} +5.45235e6 q^{38} -346116. q^{39} +835570. q^{40} +5.31174e6 q^{41} +2.58176e6 q^{42} +2.91537e7 q^{43} +1.25149e7 q^{44} +1.44289e6 q^{45} -1.91844e7 q^{46} +1.71037e7 q^{47} +5.26771e6 q^{48} -2.00111e7 q^{49} -2.08684e7 q^{50} +2.57435e6 q^{52} -4.87721e7 q^{53} -2.09032e7 q^{54} +2.70209e6 q^{55} -4.39693e7 q^{56} +2.71336e7 q^{57} -1.67030e7 q^{58} -1.48825e7 q^{59} +1.81601e6 q^{60} +1.92173e8 q^{61} +2.20376e7 q^{62} -7.59274e7 q^{63} +1.43517e7 q^{64} +555826. q^{65} -1.80459e7 q^{66} +3.41459e7 q^{67} -9.54712e7 q^{69} -4.14603e6 q^{70} -1.63417e8 q^{71} +1.64113e8 q^{72} +8.46020e7 q^{73} -8.17032e7 q^{74} -1.03851e8 q^{75} -2.01814e8 q^{76} -1.42189e8 q^{77} -3.71208e6 q^{78} -3.66702e8 q^{79} -8.45938e6 q^{80} +2.27326e8 q^{81} +5.69682e7 q^{82} +5.02953e8 q^{83} -9.55618e7 q^{84} +3.12672e8 q^{86} -8.31223e7 q^{87} +3.07335e8 q^{88} +8.00609e7 q^{89} +1.54749e7 q^{90} -2.92486e7 q^{91} +7.10096e8 q^{92} +1.09670e8 q^{93} +1.83437e8 q^{94} -4.35736e7 q^{95} +3.22897e8 q^{96} +1.90554e8 q^{97} -2.14618e8 q^{98} +5.30715e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + 60000q^{10} + 76902q^{11} + 373248q^{12} + 54216q^{13} + 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} + 6439479q^{20} - 138102q^{21} + 267324q^{22} + 4041462q^{23} + 7653888q^{24} + 16582356q^{25} + 15822744q^{26} + 13281612q^{27} + 18614784q^{28} + 4005936q^{29} + 22471686q^{30} + 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} + 22076682q^{37} - 27401376q^{38} + 62736162q^{39} - 12231630q^{40} + 59641782q^{41} + 150001536q^{42} - 47951586q^{43} - 49578936q^{44} + 129308238q^{45} + 140524827q^{46} - 118557912q^{47} + 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} + 209848575q^{54} - 365439924q^{55} + 203095059q^{56} - 4614108q^{57} - 179071413q^{58} + 343015128q^{59} + 427179186q^{60} + 175597116q^{61} + 720602571q^{62} + 587415936q^{63} + 853082511q^{64} + 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} + 1308709542q^{71} - 275337849q^{72} + 494841342q^{73} + 1545361890q^{74} + 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} + 2270624538q^{78} + 1980107868q^{79} + 2897000199q^{80} + 1598298840q^{81} + 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} - 2705904618q^{88} + 148394658q^{89} + 117916215q^{90} + 636340896q^{91} - 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} + 4878626298q^{95} - 8390096634q^{96} - 891786822q^{97} + 4285627647q^{98} - 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.7250 0.473980 0.236990 0.971512i \(-0.423839\pi\)
0.236990 + 0.971512i \(0.423839\pi\)
\(3\) 53.3726 0.380428 0.190214 0.981743i \(-0.439082\pi\)
0.190214 + 0.981743i \(0.439082\pi\)
\(4\) −396.975 −0.775343
\(5\) −85.7107 −0.0613296 −0.0306648 0.999530i \(-0.509762\pi\)
−0.0306648 + 0.999530i \(0.509762\pi\)
\(6\) 572.419 0.180316
\(7\) 4510.26 0.710004 0.355002 0.934866i \(-0.384480\pi\)
0.355002 + 0.934866i \(0.384480\pi\)
\(8\) −9748.72 −0.841478
\(9\) −16834.4 −0.855274
\(10\) −919.244 −0.0290690
\(11\) −31525.7 −0.649229 −0.324614 0.945846i \(-0.605234\pi\)
−0.324614 + 0.945846i \(0.605234\pi\)
\(12\) −21187.6 −0.294962
\(13\) −6484.90 −0.0629736 −0.0314868 0.999504i \(-0.510024\pi\)
−0.0314868 + 0.999504i \(0.510024\pi\)
\(14\) 48372.4 0.336528
\(15\) −4574.61 −0.0233315
\(16\) 98696.8 0.376499
\(17\) 0 0
\(18\) −180548. −0.405383
\(19\) 508379. 0.894946 0.447473 0.894297i \(-0.352324\pi\)
0.447473 + 0.894297i \(0.352324\pi\)
\(20\) 34025.1 0.0475515
\(21\) 240725. 0.270106
\(22\) −338112. −0.307722
\(23\) −1.78877e6 −1.33284 −0.666420 0.745576i \(-0.732174\pi\)
−0.666420 + 0.745576i \(0.732174\pi\)
\(24\) −520315. −0.320122
\(25\) −1.94578e6 −0.996239
\(26\) −69550.3 −0.0298483
\(27\) −1.94903e6 −0.705799
\(28\) −1.79046e6 −0.550496
\(29\) −1.55740e6 −0.408891 −0.204446 0.978878i \(-0.565539\pi\)
−0.204446 + 0.978878i \(0.565539\pi\)
\(30\) −49062.5 −0.0110587
\(31\) 2.05480e6 0.399615 0.199807 0.979835i \(-0.435968\pi\)
0.199807 + 0.979835i \(0.435968\pi\)
\(32\) 6.04986e6 1.01993
\(33\) −1.68261e6 −0.246985
\(34\) 0 0
\(35\) −386578. −0.0435443
\(36\) 6.68283e6 0.663130
\(37\) −7.61805e6 −0.668245 −0.334123 0.942530i \(-0.608440\pi\)
−0.334123 + 0.942530i \(0.608440\pi\)
\(38\) 5.45235e6 0.424187
\(39\) −346116. −0.0239569
\(40\) 835570. 0.0516075
\(41\) 5.31174e6 0.293569 0.146784 0.989169i \(-0.453108\pi\)
0.146784 + 0.989169i \(0.453108\pi\)
\(42\) 2.58176e6 0.128025
\(43\) 2.91537e7 1.30042 0.650212 0.759753i \(-0.274680\pi\)
0.650212 + 0.759753i \(0.274680\pi\)
\(44\) 1.25149e7 0.503375
\(45\) 1.44289e6 0.0524536
\(46\) −1.91844e7 −0.631740
\(47\) 1.71037e7 0.511271 0.255635 0.966773i \(-0.417715\pi\)
0.255635 + 0.966773i \(0.417715\pi\)
\(48\) 5.26771e6 0.143231
\(49\) −2.00111e7 −0.495895
\(50\) −2.08684e7 −0.472198
\(51\) 0 0
\(52\) 2.57435e6 0.0488261
\(53\) −4.87721e7 −0.849043 −0.424522 0.905418i \(-0.639558\pi\)
−0.424522 + 0.905418i \(0.639558\pi\)
\(54\) −2.09032e7 −0.334535
\(55\) 2.70209e6 0.0398169
\(56\) −4.39693e7 −0.597452
\(57\) 2.71336e7 0.340463
\(58\) −1.67030e7 −0.193806
\(59\) −1.48825e7 −0.159898 −0.0799488 0.996799i \(-0.525476\pi\)
−0.0799488 + 0.996799i \(0.525476\pi\)
\(60\) 1.81601e6 0.0180899
\(61\) 1.92173e8 1.77708 0.888541 0.458797i \(-0.151719\pi\)
0.888541 + 0.458797i \(0.151719\pi\)
\(62\) 2.20376e7 0.189410
\(63\) −7.59274e7 −0.607248
\(64\) 1.43517e7 0.106929
\(65\) 555826. 0.00386215
\(66\) −1.80459e7 −0.117066
\(67\) 3.41459e7 0.207015 0.103508 0.994629i \(-0.466993\pi\)
0.103508 + 0.994629i \(0.466993\pi\)
\(68\) 0 0
\(69\) −9.54712e7 −0.507051
\(70\) −4.14603e6 −0.0206391
\(71\) −1.63417e8 −0.763196 −0.381598 0.924328i \(-0.624626\pi\)
−0.381598 + 0.924328i \(0.624626\pi\)
\(72\) 1.64113e8 0.719694
\(73\) 8.46020e7 0.348681 0.174340 0.984685i \(-0.444221\pi\)
0.174340 + 0.984685i \(0.444221\pi\)
\(74\) −8.17032e7 −0.316735
\(75\) −1.03851e8 −0.378998
\(76\) −2.01814e8 −0.693890
\(77\) −1.42189e8 −0.460955
\(78\) −3.71208e6 −0.0113551
\(79\) −3.66702e8 −1.05923 −0.529617 0.848237i \(-0.677664\pi\)
−0.529617 + 0.848237i \(0.677664\pi\)
\(80\) −8.45938e6 −0.0230905
\(81\) 2.27326e8 0.586768
\(82\) 5.69682e7 0.139146
\(83\) 5.02953e8 1.16326 0.581629 0.813454i \(-0.302415\pi\)
0.581629 + 0.813454i \(0.302415\pi\)
\(84\) −9.55618e7 −0.209424
\(85\) 0 0
\(86\) 3.12672e8 0.616375
\(87\) −8.31223e7 −0.155554
\(88\) 3.07335e8 0.546311
\(89\) 8.00609e7 0.135259 0.0676293 0.997711i \(-0.478456\pi\)
0.0676293 + 0.997711i \(0.478456\pi\)
\(90\) 1.54749e7 0.0248620
\(91\) −2.92486e7 −0.0447115
\(92\) 7.10096e8 1.03341
\(93\) 1.09670e8 0.152025
\(94\) 1.83437e8 0.242332
\(95\) −4.35736e7 −0.0548867
\(96\) 3.22897e8 0.388011
\(97\) 1.90554e8 0.218547 0.109274 0.994012i \(-0.465148\pi\)
0.109274 + 0.994012i \(0.465148\pi\)
\(98\) −2.14618e8 −0.235044
\(99\) 5.30715e8 0.555268
\(100\) 7.72426e8 0.772426
\(101\) 1.48512e9 1.42009 0.710043 0.704158i \(-0.248675\pi\)
0.710043 + 0.704158i \(0.248675\pi\)
\(102\) 0 0
\(103\) −1.36804e9 −1.19766 −0.598829 0.800877i \(-0.704367\pi\)
−0.598829 + 0.800877i \(0.704367\pi\)
\(104\) 6.32195e7 0.0529909
\(105\) −2.06327e7 −0.0165655
\(106\) −5.23078e8 −0.402430
\(107\) 1.07471e9 0.792619 0.396309 0.918117i \(-0.370291\pi\)
0.396309 + 0.918117i \(0.370291\pi\)
\(108\) 7.73716e8 0.547236
\(109\) 1.15724e9 0.785245 0.392623 0.919700i \(-0.371568\pi\)
0.392623 + 0.919700i \(0.371568\pi\)
\(110\) 2.89798e7 0.0188725
\(111\) −4.06595e8 −0.254220
\(112\) 4.45149e8 0.267315
\(113\) 1.48036e9 0.854109 0.427055 0.904226i \(-0.359551\pi\)
0.427055 + 0.904226i \(0.359551\pi\)
\(114\) 2.91006e8 0.161373
\(115\) 1.53316e8 0.0817426
\(116\) 6.18248e8 0.317031
\(117\) 1.09169e8 0.0538597
\(118\) −1.59614e8 −0.0757883
\(119\) 0 0
\(120\) 4.45966e7 0.0196330
\(121\) −1.36408e9 −0.578502
\(122\) 2.06104e9 0.842302
\(123\) 2.83502e8 0.111682
\(124\) −8.15704e8 −0.309838
\(125\) 3.34178e8 0.122429
\(126\) −8.14318e8 −0.287824
\(127\) 1.39247e9 0.474975 0.237487 0.971391i \(-0.423676\pi\)
0.237487 + 0.971391i \(0.423676\pi\)
\(128\) −2.94361e9 −0.969249
\(129\) 1.55601e9 0.494718
\(130\) 5.96121e6 0.00183058
\(131\) 5.23614e9 1.55342 0.776712 0.629856i \(-0.216886\pi\)
0.776712 + 0.629856i \(0.216886\pi\)
\(132\) 6.67955e8 0.191498
\(133\) 2.29293e9 0.635415
\(134\) 3.66214e8 0.0981212
\(135\) 1.67053e8 0.0432864
\(136\) 0 0
\(137\) −4.92226e9 −1.19377 −0.596887 0.802325i \(-0.703596\pi\)
−0.596887 + 0.802325i \(0.703596\pi\)
\(138\) −1.02392e9 −0.240332
\(139\) −2.60255e9 −0.591333 −0.295667 0.955291i \(-0.595542\pi\)
−0.295667 + 0.955291i \(0.595542\pi\)
\(140\) 1.53462e8 0.0337617
\(141\) 9.12872e8 0.194502
\(142\) −1.75264e9 −0.361740
\(143\) 2.04441e8 0.0408843
\(144\) −1.66150e9 −0.322009
\(145\) 1.33486e8 0.0250771
\(146\) 9.07352e8 0.165268
\(147\) −1.06805e9 −0.188652
\(148\) 3.02418e9 0.518119
\(149\) 9.01492e9 1.49839 0.749193 0.662352i \(-0.230442\pi\)
0.749193 + 0.662352i \(0.230442\pi\)
\(150\) −1.11380e9 −0.179637
\(151\) 7.98640e9 1.25013 0.625064 0.780573i \(-0.285073\pi\)
0.625064 + 0.780573i \(0.285073\pi\)
\(152\) −4.95605e9 −0.753077
\(153\) 0 0
\(154\) −1.52497e9 −0.218484
\(155\) −1.76118e8 −0.0245082
\(156\) 1.37400e8 0.0185748
\(157\) −1.80627e9 −0.237266 −0.118633 0.992938i \(-0.537851\pi\)
−0.118633 + 0.992938i \(0.537851\pi\)
\(158\) −3.93286e9 −0.502056
\(159\) −2.60309e9 −0.323000
\(160\) −5.18538e8 −0.0625520
\(161\) −8.06781e9 −0.946322
\(162\) 2.43806e9 0.278117
\(163\) −6.70881e8 −0.0744392 −0.0372196 0.999307i \(-0.511850\pi\)
−0.0372196 + 0.999307i \(0.511850\pi\)
\(164\) −2.10863e9 −0.227616
\(165\) 1.44218e8 0.0151475
\(166\) 5.39415e9 0.551362
\(167\) 1.10815e10 1.10248 0.551242 0.834345i \(-0.314154\pi\)
0.551242 + 0.834345i \(0.314154\pi\)
\(168\) −2.34676e9 −0.227288
\(169\) −1.05624e10 −0.996034
\(170\) 0 0
\(171\) −8.55824e9 −0.765424
\(172\) −1.15733e10 −1.00827
\(173\) 1.48057e10 1.25667 0.628337 0.777941i \(-0.283736\pi\)
0.628337 + 0.777941i \(0.283736\pi\)
\(174\) −8.91483e8 −0.0737295
\(175\) −8.77597e9 −0.707333
\(176\) −3.11149e9 −0.244434
\(177\) −7.94318e8 −0.0608296
\(178\) 8.58649e8 0.0641100
\(179\) 1.92425e10 1.40095 0.700476 0.713676i \(-0.252971\pi\)
0.700476 + 0.713676i \(0.252971\pi\)
\(180\) −5.72790e8 −0.0406695
\(181\) 2.28736e10 1.58410 0.792048 0.610459i \(-0.209015\pi\)
0.792048 + 0.610459i \(0.209015\pi\)
\(182\) −3.13690e8 −0.0211924
\(183\) 1.02568e10 0.676053
\(184\) 1.74382e10 1.12156
\(185\) 6.52949e8 0.0409832
\(186\) 1.17621e9 0.0720568
\(187\) 0 0
\(188\) −6.78977e9 −0.396410
\(189\) −8.79063e9 −0.501120
\(190\) −4.67325e8 −0.0260152
\(191\) 1.88324e10 1.02390 0.511948 0.859017i \(-0.328924\pi\)
0.511948 + 0.859017i \(0.328924\pi\)
\(192\) 7.65989e8 0.0406787
\(193\) −2.59035e10 −1.34385 −0.671924 0.740620i \(-0.734532\pi\)
−0.671924 + 0.740620i \(0.734532\pi\)
\(194\) 2.04368e9 0.103587
\(195\) 2.96659e7 0.00146927
\(196\) 7.94393e9 0.384488
\(197\) 1.18331e10 0.559757 0.279879 0.960035i \(-0.409706\pi\)
0.279879 + 0.960035i \(0.409706\pi\)
\(198\) 5.69189e9 0.263186
\(199\) 3.42416e10 1.54780 0.773901 0.633307i \(-0.218303\pi\)
0.773901 + 0.633307i \(0.218303\pi\)
\(200\) 1.89688e10 0.838313
\(201\) 1.82246e9 0.0787545
\(202\) 1.59278e10 0.673093
\(203\) −7.02426e9 −0.290314
\(204\) 0 0
\(205\) −4.55273e8 −0.0180045
\(206\) −1.46722e10 −0.567666
\(207\) 3.01127e10 1.13994
\(208\) −6.40039e8 −0.0237095
\(209\) −1.60270e10 −0.581025
\(210\) −2.21285e8 −0.00785171
\(211\) −1.80185e10 −0.625819 −0.312910 0.949783i \(-0.601304\pi\)
−0.312910 + 0.949783i \(0.601304\pi\)
\(212\) 1.93613e10 0.658299
\(213\) −8.72202e9 −0.290341
\(214\) 1.15262e10 0.375686
\(215\) −2.49878e9 −0.0797545
\(216\) 1.90005e10 0.593914
\(217\) 9.26768e9 0.283728
\(218\) 1.24114e10 0.372191
\(219\) 4.51543e9 0.132648
\(220\) −1.07266e9 −0.0308718
\(221\) 0 0
\(222\) −4.36072e9 −0.120495
\(223\) −6.99529e10 −1.89424 −0.947118 0.320886i \(-0.896019\pi\)
−0.947118 + 0.320886i \(0.896019\pi\)
\(224\) 2.72865e10 0.724155
\(225\) 3.27559e10 0.852057
\(226\) 1.58768e10 0.404831
\(227\) −7.03288e10 −1.75799 −0.878996 0.476830i \(-0.841786\pi\)
−0.878996 + 0.476830i \(0.841786\pi\)
\(228\) −1.07714e10 −0.263975
\(229\) −5.34700e9 −0.128485 −0.0642423 0.997934i \(-0.520463\pi\)
−0.0642423 + 0.997934i \(0.520463\pi\)
\(230\) 1.64431e9 0.0387444
\(231\) −7.58901e9 −0.175360
\(232\) 1.51826e10 0.344073
\(233\) 6.84853e10 1.52228 0.761142 0.648585i \(-0.224639\pi\)
0.761142 + 0.648585i \(0.224639\pi\)
\(234\) 1.17083e9 0.0255284
\(235\) −1.46597e9 −0.0313560
\(236\) 5.90799e9 0.123975
\(237\) −1.95719e10 −0.402963
\(238\) 0 0
\(239\) −2.52056e9 −0.0499696 −0.0249848 0.999688i \(-0.507954\pi\)
−0.0249848 + 0.999688i \(0.507954\pi\)
\(240\) −4.51499e8 −0.00878429
\(241\) 9.69476e10 1.85123 0.925615 0.378468i \(-0.123549\pi\)
0.925615 + 0.378468i \(0.123549\pi\)
\(242\) −1.46297e10 −0.274199
\(243\) 5.04957e10 0.929022
\(244\) −7.62879e10 −1.37785
\(245\) 1.71517e9 0.0304130
\(246\) 3.04054e9 0.0529350
\(247\) −3.29679e9 −0.0563580
\(248\) −2.00316e10 −0.336267
\(249\) 2.68439e10 0.442537
\(250\) 3.58404e9 0.0580287
\(251\) 1.22305e11 1.94496 0.972481 0.232984i \(-0.0748489\pi\)
0.972481 + 0.232984i \(0.0748489\pi\)
\(252\) 3.01413e10 0.470825
\(253\) 5.63921e10 0.865318
\(254\) 1.49342e10 0.225129
\(255\) 0 0
\(256\) −3.89181e10 −0.566334
\(257\) −7.99606e10 −1.14334 −0.571672 0.820482i \(-0.693705\pi\)
−0.571672 + 0.820482i \(0.693705\pi\)
\(258\) 1.66881e10 0.234487
\(259\) −3.43594e10 −0.474457
\(260\) −2.20649e8 −0.00299449
\(261\) 2.62178e10 0.349714
\(262\) 5.61573e10 0.736293
\(263\) −3.97042e10 −0.511723 −0.255862 0.966713i \(-0.582359\pi\)
−0.255862 + 0.966713i \(0.582359\pi\)
\(264\) 1.64033e10 0.207832
\(265\) 4.18029e9 0.0520715
\(266\) 2.45915e10 0.301174
\(267\) 4.27306e9 0.0514563
\(268\) −1.35551e10 −0.160508
\(269\) 1.12054e11 1.30479 0.652395 0.757879i \(-0.273765\pi\)
0.652395 + 0.757879i \(0.273765\pi\)
\(270\) 1.79163e9 0.0205169
\(271\) 8.52215e9 0.0959815 0.0479907 0.998848i \(-0.484718\pi\)
0.0479907 + 0.998848i \(0.484718\pi\)
\(272\) 0 0
\(273\) −1.56108e9 −0.0170095
\(274\) −5.27911e10 −0.565826
\(275\) 6.13420e10 0.646787
\(276\) 3.78997e10 0.393138
\(277\) −1.24828e11 −1.27395 −0.636977 0.770883i \(-0.719815\pi\)
−0.636977 + 0.770883i \(0.719815\pi\)
\(278\) −2.79122e10 −0.280280
\(279\) −3.45912e10 −0.341780
\(280\) 3.76864e9 0.0366415
\(281\) 3.96570e10 0.379438 0.189719 0.981838i \(-0.439242\pi\)
0.189719 + 0.981838i \(0.439242\pi\)
\(282\) 9.79051e9 0.0921901
\(283\) 7.61061e10 0.705311 0.352655 0.935753i \(-0.385279\pi\)
0.352655 + 0.935753i \(0.385279\pi\)
\(284\) 6.48727e10 0.591738
\(285\) −2.32564e9 −0.0208805
\(286\) 2.19262e9 0.0193783
\(287\) 2.39574e10 0.208435
\(288\) −1.01846e11 −0.872320
\(289\) 0 0
\(290\) 1.43163e9 0.0118861
\(291\) 1.01704e10 0.0831416
\(292\) −3.35849e10 −0.270347
\(293\) 7.22311e10 0.572558 0.286279 0.958146i \(-0.407582\pi\)
0.286279 + 0.958146i \(0.407582\pi\)
\(294\) −1.14548e10 −0.0894176
\(295\) 1.27559e9 0.00980646
\(296\) 7.42662e10 0.562314
\(297\) 6.14445e10 0.458225
\(298\) 9.66846e10 0.710206
\(299\) 1.16000e10 0.0839338
\(300\) 4.12264e10 0.293853
\(301\) 1.31491e11 0.923306
\(302\) 8.56538e10 0.592537
\(303\) 7.92647e10 0.540241
\(304\) 5.01754e10 0.336946
\(305\) −1.64713e10 −0.108988
\(306\) 0 0
\(307\) −2.11970e11 −1.36192 −0.680962 0.732319i \(-0.738438\pi\)
−0.680962 + 0.732319i \(0.738438\pi\)
\(308\) 5.64456e10 0.357398
\(309\) −7.30161e10 −0.455623
\(310\) −1.88886e9 −0.0116164
\(311\) −2.52341e10 −0.152956 −0.0764778 0.997071i \(-0.524367\pi\)
−0.0764778 + 0.997071i \(0.524367\pi\)
\(312\) 3.37419e9 0.0201592
\(313\) −1.99311e11 −1.17377 −0.586885 0.809671i \(-0.699646\pi\)
−0.586885 + 0.809671i \(0.699646\pi\)
\(314\) −1.93722e10 −0.112459
\(315\) 6.50779e9 0.0372423
\(316\) 1.45572e11 0.821269
\(317\) −2.14588e11 −1.19355 −0.596774 0.802410i \(-0.703551\pi\)
−0.596774 + 0.802410i \(0.703551\pi\)
\(318\) −2.79181e10 −0.153096
\(319\) 4.90980e10 0.265464
\(320\) −1.23010e9 −0.00655789
\(321\) 5.73601e10 0.301535
\(322\) −8.65268e10 −0.448538
\(323\) 0 0
\(324\) −9.02428e10 −0.454946
\(325\) 1.26182e10 0.0627367
\(326\) −7.19517e9 −0.0352827
\(327\) 6.17651e10 0.298730
\(328\) −5.17827e10 −0.247031
\(329\) 7.71424e10 0.363004
\(330\) 1.54673e9 0.00717962
\(331\) −2.28406e11 −1.04588 −0.522940 0.852370i \(-0.675165\pi\)
−0.522940 + 0.852370i \(0.675165\pi\)
\(332\) −1.99660e11 −0.901924
\(333\) 1.28245e11 0.571533
\(334\) 1.18848e11 0.522556
\(335\) −2.92667e9 −0.0126962
\(336\) 2.37588e10 0.101694
\(337\) −3.98649e10 −0.168367 −0.0841834 0.996450i \(-0.526828\pi\)
−0.0841834 + 0.996450i \(0.526828\pi\)
\(338\) −1.13282e11 −0.472101
\(339\) 7.90105e10 0.324927
\(340\) 0 0
\(341\) −6.47789e10 −0.259441
\(342\) −9.17868e10 −0.362796
\(343\) −2.72261e11 −1.06209
\(344\) −2.84211e11 −1.09428
\(345\) 8.18290e9 0.0310972
\(346\) 1.58791e11 0.595639
\(347\) 2.09902e11 0.777202 0.388601 0.921406i \(-0.372959\pi\)
0.388601 + 0.921406i \(0.372959\pi\)
\(348\) 3.29975e10 0.120608
\(349\) −1.18382e11 −0.427143 −0.213571 0.976927i \(-0.568510\pi\)
−0.213571 + 0.976927i \(0.568510\pi\)
\(350\) −9.41219e10 −0.335262
\(351\) 1.26393e10 0.0444467
\(352\) −1.90726e11 −0.662168
\(353\) 1.27894e11 0.438395 0.219197 0.975681i \(-0.429656\pi\)
0.219197 + 0.975681i \(0.429656\pi\)
\(354\) −8.51903e9 −0.0288320
\(355\) 1.40066e10 0.0468065
\(356\) −3.17822e10 −0.104872
\(357\) 0 0
\(358\) 2.06375e11 0.664024
\(359\) 3.73004e11 1.18519 0.592596 0.805500i \(-0.298103\pi\)
0.592596 + 0.805500i \(0.298103\pi\)
\(360\) −1.40663e10 −0.0441386
\(361\) −6.42380e10 −0.199072
\(362\) 2.45319e11 0.750830
\(363\) −7.28044e10 −0.220079
\(364\) 1.16110e10 0.0346667
\(365\) −7.25130e9 −0.0213844
\(366\) 1.10003e11 0.320436
\(367\) −1.77243e11 −0.510003 −0.255002 0.966941i \(-0.582076\pi\)
−0.255002 + 0.966941i \(0.582076\pi\)
\(368\) −1.76546e11 −0.501813
\(369\) −8.94198e10 −0.251082
\(370\) 7.00284e9 0.0194253
\(371\) −2.19975e11 −0.602824
\(372\) −4.35363e10 −0.117871
\(373\) 3.59334e11 0.961189 0.480595 0.876943i \(-0.340421\pi\)
0.480595 + 0.876943i \(0.340421\pi\)
\(374\) 0 0
\(375\) 1.78360e10 0.0465753
\(376\) −1.66740e11 −0.430223
\(377\) 1.00996e10 0.0257494
\(378\) −9.42791e10 −0.237521
\(379\) 3.22981e11 0.804081 0.402041 0.915622i \(-0.368301\pi\)
0.402041 + 0.915622i \(0.368301\pi\)
\(380\) 1.72976e10 0.0425560
\(381\) 7.43200e10 0.180694
\(382\) 2.01977e11 0.485306
\(383\) −1.00894e11 −0.239591 −0.119796 0.992799i \(-0.538224\pi\)
−0.119796 + 0.992799i \(0.538224\pi\)
\(384\) −1.57108e11 −0.368730
\(385\) 1.21871e10 0.0282702
\(386\) −2.77814e11 −0.636958
\(387\) −4.90783e11 −1.11222
\(388\) −7.56453e10 −0.169449
\(389\) 1.56379e11 0.346263 0.173131 0.984899i \(-0.444611\pi\)
0.173131 + 0.984899i \(0.444611\pi\)
\(390\) 3.18165e8 0.000696405 0
\(391\) 0 0
\(392\) 1.95083e11 0.417284
\(393\) 2.79466e11 0.590967
\(394\) 1.26909e11 0.265314
\(395\) 3.14303e10 0.0649624
\(396\) −2.10681e11 −0.430523
\(397\) 7.86417e11 1.58890 0.794448 0.607332i \(-0.207760\pi\)
0.794448 + 0.607332i \(0.207760\pi\)
\(398\) 3.67240e11 0.733628
\(399\) 1.22379e11 0.241730
\(400\) −1.92042e11 −0.375082
\(401\) 1.63679e11 0.316114 0.158057 0.987430i \(-0.449477\pi\)
0.158057 + 0.987430i \(0.449477\pi\)
\(402\) 1.95458e10 0.0373281
\(403\) −1.33252e10 −0.0251652
\(404\) −5.89555e11 −1.10105
\(405\) −1.94843e10 −0.0359863
\(406\) −7.53349e10 −0.137603
\(407\) 2.40164e11 0.433844
\(408\) 0 0
\(409\) 5.24910e11 0.927534 0.463767 0.885957i \(-0.346497\pi\)
0.463767 + 0.885957i \(0.346497\pi\)
\(410\) −4.88279e9 −0.00853376
\(411\) −2.62714e11 −0.454146
\(412\) 5.43080e11 0.928595
\(413\) −6.71240e10 −0.113528
\(414\) 3.22958e11 0.540311
\(415\) −4.31085e10 −0.0713422
\(416\) −3.92328e10 −0.0642287
\(417\) −1.38905e11 −0.224960
\(418\) −1.71889e11 −0.275394
\(419\) −4.60592e11 −0.730052 −0.365026 0.930997i \(-0.618940\pi\)
−0.365026 + 0.930997i \(0.618940\pi\)
\(420\) 8.19067e9 0.0128439
\(421\) −1.28301e12 −1.99050 −0.995249 0.0973671i \(-0.968958\pi\)
−0.995249 + 0.0973671i \(0.968958\pi\)
\(422\) −1.93248e11 −0.296626
\(423\) −2.87931e11 −0.437277
\(424\) 4.75465e11 0.714451
\(425\) 0 0
\(426\) −9.35433e10 −0.137616
\(427\) 8.66750e11 1.26174
\(428\) −4.26633e11 −0.614551
\(429\) 1.09116e10 0.0155535
\(430\) −2.67993e10 −0.0378021
\(431\) −6.90653e11 −0.964079 −0.482039 0.876150i \(-0.660104\pi\)
−0.482039 + 0.876150i \(0.660104\pi\)
\(432\) −1.92363e11 −0.265732
\(433\) 4.81087e11 0.657701 0.328850 0.944382i \(-0.393339\pi\)
0.328850 + 0.944382i \(0.393339\pi\)
\(434\) 9.93954e10 0.134482
\(435\) 7.12447e9 0.00954006
\(436\) −4.59397e11 −0.608834
\(437\) −9.09372e11 −1.19282
\(438\) 4.84278e10 0.0628726
\(439\) −9.71396e11 −1.24826 −0.624131 0.781320i \(-0.714547\pi\)
−0.624131 + 0.781320i \(0.714547\pi\)
\(440\) −2.63419e10 −0.0335051
\(441\) 3.36875e11 0.424126
\(442\) 0 0
\(443\) 1.18504e12 1.46189 0.730946 0.682435i \(-0.239079\pi\)
0.730946 + 0.682435i \(0.239079\pi\)
\(444\) 1.61408e11 0.197107
\(445\) −6.86208e9 −0.00829536
\(446\) −7.50242e11 −0.897831
\(447\) 4.81150e11 0.570029
\(448\) 6.47300e10 0.0759198
\(449\) −1.07515e12 −1.24842 −0.624208 0.781258i \(-0.714578\pi\)
−0.624208 + 0.781258i \(0.714578\pi\)
\(450\) 3.51306e11 0.403858
\(451\) −1.67456e11 −0.190593
\(452\) −5.87665e11 −0.662227
\(453\) 4.26255e11 0.475585
\(454\) −7.54273e11 −0.833253
\(455\) 2.50692e9 0.00274214
\(456\) −2.64517e11 −0.286492
\(457\) −1.74356e12 −1.86988 −0.934941 0.354803i \(-0.884548\pi\)
−0.934941 + 0.354803i \(0.884548\pi\)
\(458\) −5.73464e10 −0.0608992
\(459\) 0 0
\(460\) −6.08629e10 −0.0633785
\(461\) 5.00512e11 0.516131 0.258066 0.966127i \(-0.416915\pi\)
0.258066 + 0.966127i \(0.416915\pi\)
\(462\) −8.13918e10 −0.0831174
\(463\) 2.96663e11 0.300019 0.150009 0.988685i \(-0.452070\pi\)
0.150009 + 0.988685i \(0.452070\pi\)
\(464\) −1.53710e11 −0.153947
\(465\) −9.39990e9 −0.00932362
\(466\) 7.34502e11 0.721533
\(467\) −1.49213e12 −1.45171 −0.725854 0.687848i \(-0.758555\pi\)
−0.725854 + 0.687848i \(0.758555\pi\)
\(468\) −4.33375e10 −0.0417597
\(469\) 1.54007e11 0.146982
\(470\) −1.57225e10 −0.0148621
\(471\) −9.64055e10 −0.0902626
\(472\) 1.45085e11 0.134550
\(473\) −9.19089e11 −0.844272
\(474\) −2.09907e11 −0.190996
\(475\) −9.89194e11 −0.891580
\(476\) 0 0
\(477\) 8.21047e11 0.726165
\(478\) −2.70328e10 −0.0236846
\(479\) −1.59309e12 −1.38271 −0.691355 0.722515i \(-0.742986\pi\)
−0.691355 + 0.722515i \(0.742986\pi\)
\(480\) −2.76758e10 −0.0237965
\(481\) 4.94023e10 0.0420818
\(482\) 1.03976e12 0.877446
\(483\) −4.30600e11 −0.360008
\(484\) 5.41505e11 0.448537
\(485\) −1.63325e10 −0.0134034
\(486\) 5.41564e11 0.440338
\(487\) −1.59961e12 −1.28865 −0.644324 0.764752i \(-0.722861\pi\)
−0.644324 + 0.764752i \(0.722861\pi\)
\(488\) −1.87344e12 −1.49538
\(489\) −3.58067e10 −0.0283188
\(490\) 1.83951e10 0.0144152
\(491\) −5.94395e10 −0.0461539 −0.0230769 0.999734i \(-0.507346\pi\)
−0.0230769 + 0.999734i \(0.507346\pi\)
\(492\) −1.12543e11 −0.0865917
\(493\) 0 0
\(494\) −3.53579e10 −0.0267126
\(495\) −4.54880e10 −0.0340544
\(496\) 2.02802e11 0.150454
\(497\) −7.37056e11 −0.541872
\(498\) 2.87900e11 0.209754
\(499\) 6.12547e11 0.442269 0.221135 0.975243i \(-0.429024\pi\)
0.221135 + 0.975243i \(0.429024\pi\)
\(500\) −1.32660e11 −0.0949241
\(501\) 5.91446e11 0.419417
\(502\) 1.31171e12 0.921874
\(503\) −1.79381e12 −1.24945 −0.624726 0.780844i \(-0.714789\pi\)
−0.624726 + 0.780844i \(0.714789\pi\)
\(504\) 7.40195e11 0.510986
\(505\) −1.27291e11 −0.0870934
\(506\) 6.04803e11 0.410144
\(507\) −5.63746e11 −0.378920
\(508\) −5.52778e11 −0.368268
\(509\) −7.83948e11 −0.517675 −0.258837 0.965921i \(-0.583339\pi\)
−0.258837 + 0.965921i \(0.583339\pi\)
\(510\) 0 0
\(511\) 3.81577e11 0.247565
\(512\) 1.08973e12 0.700817
\(513\) −9.90846e11 −0.631652
\(514\) −8.57573e11 −0.541923
\(515\) 1.17256e11 0.0734519
\(516\) −6.17697e11 −0.383576
\(517\) −5.39208e11 −0.331932
\(518\) −3.68503e11 −0.224883
\(519\) 7.90222e11 0.478075
\(520\) −5.41859e9 −0.00324991
\(521\) −9.27420e11 −0.551451 −0.275725 0.961236i \(-0.588918\pi\)
−0.275725 + 0.961236i \(0.588918\pi\)
\(522\) 2.81184e11 0.165758
\(523\) −2.22342e12 −1.29946 −0.649731 0.760164i \(-0.725118\pi\)
−0.649731 + 0.760164i \(0.725118\pi\)
\(524\) −2.07862e12 −1.20444
\(525\) −4.68397e11 −0.269090
\(526\) −4.25825e11 −0.242547
\(527\) 0 0
\(528\) −1.66068e11 −0.0929895
\(529\) 1.39853e12 0.776465
\(530\) 4.48334e10 0.0246809
\(531\) 2.50537e11 0.136756
\(532\) −9.10235e11 −0.492664
\(533\) −3.44461e10 −0.0184871
\(534\) 4.58284e10 0.0243893
\(535\) −9.21142e10 −0.0486110
\(536\) −3.32879e11 −0.174199
\(537\) 1.02702e12 0.532962
\(538\) 1.20177e12 0.618445
\(539\) 6.30865e11 0.321949
\(540\) −6.63158e10 −0.0335618
\(541\) 2.88963e12 1.45029 0.725145 0.688597i \(-0.241773\pi\)
0.725145 + 0.688597i \(0.241773\pi\)
\(542\) 9.13997e10 0.0454934
\(543\) 1.22083e12 0.602635
\(544\) 0 0
\(545\) −9.91881e10 −0.0481588
\(546\) −1.67425e10 −0.00806218
\(547\) 7.62225e11 0.364032 0.182016 0.983296i \(-0.441738\pi\)
0.182016 + 0.983296i \(0.441738\pi\)
\(548\) 1.95402e12 0.925584
\(549\) −3.23511e12 −1.51989
\(550\) 6.57890e11 0.306564
\(551\) −7.91748e11 −0.365936
\(552\) 9.30722e11 0.426672
\(553\) −1.65392e12 −0.752060
\(554\) −1.33878e12 −0.603829
\(555\) 3.48496e10 0.0155912
\(556\) 1.03315e12 0.458486
\(557\) −1.15854e12 −0.509991 −0.254996 0.966942i \(-0.582074\pi\)
−0.254996 + 0.966942i \(0.582074\pi\)
\(558\) −3.70989e11 −0.161997
\(559\) −1.89059e11 −0.0818924
\(560\) −3.81540e10 −0.0163943
\(561\) 0 0
\(562\) 4.25319e11 0.179846
\(563\) −1.68046e12 −0.704919 −0.352460 0.935827i \(-0.614655\pi\)
−0.352460 + 0.935827i \(0.614655\pi\)
\(564\) −3.62388e11 −0.150806
\(565\) −1.26882e11 −0.0523822
\(566\) 8.16235e11 0.334304
\(567\) 1.02530e12 0.416608
\(568\) 1.59311e12 0.642212
\(569\) −9.26592e11 −0.370581 −0.185291 0.982684i \(-0.559323\pi\)
−0.185291 + 0.982684i \(0.559323\pi\)
\(570\) −2.49424e10 −0.00989693
\(571\) 2.85270e11 0.112304 0.0561518 0.998422i \(-0.482117\pi\)
0.0561518 + 0.998422i \(0.482117\pi\)
\(572\) −8.11581e10 −0.0316993
\(573\) 1.00514e12 0.389519
\(574\) 2.56942e11 0.0987941
\(575\) 3.48054e12 1.32783
\(576\) −2.41602e11 −0.0914533
\(577\) 8.48052e11 0.318516 0.159258 0.987237i \(-0.449090\pi\)
0.159258 + 0.987237i \(0.449090\pi\)
\(578\) 0 0
\(579\) −1.38254e12 −0.511238
\(580\) −5.29905e10 −0.0194434
\(581\) 2.26845e12 0.825918
\(582\) 1.09077e11 0.0394075
\(583\) 1.53757e12 0.551223
\(584\) −8.24761e11 −0.293407
\(585\) −9.35697e9 −0.00330319
\(586\) 7.74675e11 0.271381
\(587\) −1.26388e12 −0.439373 −0.219686 0.975571i \(-0.570503\pi\)
−0.219686 + 0.975571i \(0.570503\pi\)
\(588\) 4.23988e11 0.146270
\(589\) 1.04462e12 0.357634
\(590\) 1.36806e10 0.00464807
\(591\) 6.31563e11 0.212948
\(592\) −7.51877e11 −0.251593
\(593\) 5.10144e12 1.69413 0.847065 0.531489i \(-0.178367\pi\)
0.847065 + 0.531489i \(0.178367\pi\)
\(594\) 6.58989e11 0.217190
\(595\) 0 0
\(596\) −3.57870e12 −1.16176
\(597\) 1.82756e12 0.588828
\(598\) 1.24409e11 0.0397830
\(599\) −3.14052e12 −0.996738 −0.498369 0.866965i \(-0.666067\pi\)
−0.498369 + 0.866965i \(0.666067\pi\)
\(600\) 1.01242e12 0.318918
\(601\) −1.47610e12 −0.461509 −0.230754 0.973012i \(-0.574119\pi\)
−0.230754 + 0.973012i \(0.574119\pi\)
\(602\) 1.41023e12 0.437629
\(603\) −5.74825e11 −0.177055
\(604\) −3.17040e12 −0.969278
\(605\) 1.16916e11 0.0354793
\(606\) 8.50110e11 0.256064
\(607\) 1.75134e12 0.523627 0.261814 0.965118i \(-0.415679\pi\)
0.261814 + 0.965118i \(0.415679\pi\)
\(608\) 3.07563e12 0.912783
\(609\) −3.74903e11 −0.110444
\(610\) −1.76654e11 −0.0516581
\(611\) −1.10916e11 −0.0321965
\(612\) 0 0
\(613\) 1.53717e12 0.439694 0.219847 0.975534i \(-0.429444\pi\)
0.219847 + 0.975534i \(0.429444\pi\)
\(614\) −2.27337e12 −0.645525
\(615\) −2.42991e10 −0.00684941
\(616\) 1.38616e12 0.387883
\(617\) 6.14608e12 1.70732 0.853659 0.520832i \(-0.174378\pi\)
0.853659 + 0.520832i \(0.174378\pi\)
\(618\) −7.83094e11 −0.215956
\(619\) 1.18984e12 0.325748 0.162874 0.986647i \(-0.447924\pi\)
0.162874 + 0.986647i \(0.447924\pi\)
\(620\) 6.99146e10 0.0190023
\(621\) 3.48635e12 0.940718
\(622\) −2.70634e11 −0.0724979
\(623\) 3.61096e11 0.0960342
\(624\) −3.41606e10 −0.00901976
\(625\) 3.77171e12 0.988730
\(626\) −2.13761e12 −0.556344
\(627\) −8.55404e11 −0.221038
\(628\) 7.17045e11 0.183962
\(629\) 0 0
\(630\) 6.97958e10 0.0176521
\(631\) −7.35552e12 −1.84706 −0.923531 0.383524i \(-0.874710\pi\)
−0.923531 + 0.383524i \(0.874710\pi\)
\(632\) 3.57488e12 0.891321
\(633\) −9.61698e11 −0.238079
\(634\) −2.30145e12 −0.565718
\(635\) −1.19350e11 −0.0291300
\(636\) 1.03336e12 0.250436
\(637\) 1.29770e11 0.0312283
\(638\) 5.26574e11 0.125825
\(639\) 2.75103e12 0.652741
\(640\) 2.52299e11 0.0594436
\(641\) 4.43828e12 1.03837 0.519186 0.854661i \(-0.326235\pi\)
0.519186 + 0.854661i \(0.326235\pi\)
\(642\) 6.15185e11 0.142922
\(643\) 4.13998e12 0.955099 0.477550 0.878605i \(-0.341525\pi\)
0.477550 + 0.878605i \(0.341525\pi\)
\(644\) 3.20272e12 0.733724
\(645\) −1.33367e11 −0.0303409
\(646\) 0 0
\(647\) −8.23149e11 −0.184675 −0.0923377 0.995728i \(-0.529434\pi\)
−0.0923377 + 0.995728i \(0.529434\pi\)
\(648\) −2.21614e12 −0.493752
\(649\) 4.69181e11 0.103810
\(650\) 1.35329e11 0.0297360
\(651\) 4.94640e11 0.107938
\(652\) 2.66323e11 0.0577159
\(653\) 7.00981e10 0.0150868 0.00754339 0.999972i \(-0.497599\pi\)
0.00754339 + 0.999972i \(0.497599\pi\)
\(654\) 6.62428e11 0.141592
\(655\) −4.48793e11 −0.0952709
\(656\) 5.24252e11 0.110528
\(657\) −1.42422e12 −0.298217
\(658\) 8.27349e11 0.172057
\(659\) 2.88785e12 0.596472 0.298236 0.954492i \(-0.403602\pi\)
0.298236 + 0.954492i \(0.403602\pi\)
\(660\) −5.72509e10 −0.0117445
\(661\) 5.63361e12 1.14784 0.573919 0.818912i \(-0.305422\pi\)
0.573919 + 0.818912i \(0.305422\pi\)
\(662\) −2.44964e12 −0.495726
\(663\) 0 0
\(664\) −4.90315e12 −0.978856
\(665\) −1.96528e11 −0.0389698
\(666\) 1.37542e12 0.270895
\(667\) 2.78582e12 0.544987
\(668\) −4.39906e12 −0.854803
\(669\) −3.73357e12 −0.720621
\(670\) −3.13885e10 −0.00601774
\(671\) −6.05838e12 −1.15373
\(672\) 1.45635e12 0.275489
\(673\) 7.23222e12 1.35895 0.679475 0.733699i \(-0.262208\pi\)
0.679475 + 0.733699i \(0.262208\pi\)
\(674\) −4.27549e11 −0.0798025
\(675\) 3.79238e12 0.703144
\(676\) 4.19303e12 0.772268
\(677\) 7.50966e12 1.37395 0.686975 0.726681i \(-0.258938\pi\)
0.686975 + 0.726681i \(0.258938\pi\)
\(678\) 8.47384e11 0.154009
\(679\) 8.59449e11 0.155169
\(680\) 0 0
\(681\) −3.75363e12 −0.668790
\(682\) −6.94751e11 −0.122970
\(683\) −1.37129e12 −0.241121 −0.120560 0.992706i \(-0.538469\pi\)
−0.120560 + 0.992706i \(0.538469\pi\)
\(684\) 3.39741e12 0.593466
\(685\) 4.21891e11 0.0732138
\(686\) −2.91999e12 −0.503410
\(687\) −2.85384e11 −0.0488792
\(688\) 2.87737e12 0.489608
\(689\) 3.16282e11 0.0534673
\(690\) 8.77613e10 0.0147395
\(691\) 6.89373e12 1.15028 0.575140 0.818055i \(-0.304948\pi\)
0.575140 + 0.818055i \(0.304948\pi\)
\(692\) −5.87752e12 −0.974353
\(693\) 2.39366e12 0.394243
\(694\) 2.25119e12 0.368378
\(695\) 2.23066e11 0.0362662
\(696\) 8.10336e11 0.130895
\(697\) 0 0
\(698\) −1.26965e12 −0.202457
\(699\) 3.65524e12 0.579120
\(700\) 3.48385e12 0.548426
\(701\) 4.32595e12 0.676629 0.338315 0.941033i \(-0.390143\pi\)
0.338315 + 0.941033i \(0.390143\pi\)
\(702\) 1.35555e11 0.0210669
\(703\) −3.87286e12 −0.598043
\(704\) −4.52448e11 −0.0694212
\(705\) −7.82429e10 −0.0119287
\(706\) 1.37166e12 0.207791
\(707\) 6.69827e12 1.00827
\(708\) 3.15325e11 0.0471638
\(709\) 8.57015e12 1.27374 0.636870 0.770971i \(-0.280229\pi\)
0.636870 + 0.770971i \(0.280229\pi\)
\(710\) 1.50220e11 0.0221854
\(711\) 6.17320e12 0.905935
\(712\) −7.80491e11 −0.113817
\(713\) −3.67555e12 −0.532623
\(714\) 0 0
\(715\) −1.75228e10 −0.00250742
\(716\) −7.63880e12 −1.08622
\(717\) −1.34529e11 −0.0190099
\(718\) 4.00045e12 0.561758
\(719\) −6.91965e12 −0.965615 −0.482807 0.875727i \(-0.660383\pi\)
−0.482807 + 0.875727i \(0.660383\pi\)
\(720\) 1.42408e11 0.0197487
\(721\) −6.17024e12 −0.850341
\(722\) −6.88949e11 −0.0943561
\(723\) 5.17435e12 0.704260
\(724\) −9.08027e12 −1.22822
\(725\) 3.03035e12 0.407353
\(726\) −7.80824e11 −0.104313
\(727\) −2.79887e12 −0.371602 −0.185801 0.982587i \(-0.559488\pi\)
−0.185801 + 0.982587i \(0.559488\pi\)
\(728\) 2.85137e11 0.0376237
\(729\) −1.77937e12 −0.233341
\(730\) −7.77699e10 −0.0101358
\(731\) 0 0
\(732\) −4.07168e12 −0.524172
\(733\) −6.24246e12 −0.798707 −0.399354 0.916797i \(-0.630765\pi\)
−0.399354 + 0.916797i \(0.630765\pi\)
\(734\) −1.90093e12 −0.241732
\(735\) 9.15431e10 0.0115700
\(736\) −1.08218e13 −1.35941
\(737\) −1.07647e12 −0.134400
\(738\) −9.59023e11 −0.119008
\(739\) −4.03767e12 −0.498002 −0.249001 0.968503i \(-0.580102\pi\)
−0.249001 + 0.968503i \(0.580102\pi\)
\(740\) −2.59204e11 −0.0317760
\(741\) −1.75958e11 −0.0214402
\(742\) −2.35922e12 −0.285727
\(743\) 2.86891e12 0.345356 0.172678 0.984978i \(-0.444758\pi\)
0.172678 + 0.984978i \(0.444758\pi\)
\(744\) −1.06914e12 −0.127925
\(745\) −7.72675e11 −0.0918954
\(746\) 3.85384e12 0.455585
\(747\) −8.46690e12 −0.994905
\(748\) 0 0
\(749\) 4.84723e12 0.562762
\(750\) 1.91290e11 0.0220758
\(751\) 1.28197e13 1.47061 0.735307 0.677734i \(-0.237038\pi\)
0.735307 + 0.677734i \(0.237038\pi\)
\(752\) 1.68809e12 0.192493
\(753\) 6.52772e12 0.739919
\(754\) 1.08317e11 0.0122047
\(755\) −6.84520e11 −0.0766699
\(756\) 3.48966e12 0.388540
\(757\) 7.97188e12 0.882327 0.441163 0.897427i \(-0.354566\pi\)
0.441163 + 0.897427i \(0.354566\pi\)
\(758\) 3.46395e12 0.381119
\(759\) 3.00980e12 0.329192
\(760\) 4.24787e11 0.0461859
\(761\) 1.58619e13 1.71444 0.857222 0.514948i \(-0.172189\pi\)
0.857222 + 0.514948i \(0.172189\pi\)
\(762\) 7.97079e11 0.0856454
\(763\) 5.21947e12 0.557527
\(764\) −7.47600e12 −0.793870
\(765\) 0 0
\(766\) −1.08208e12 −0.113561
\(767\) 9.65116e10 0.0100693
\(768\) −2.07716e12 −0.215449
\(769\) −1.90312e13 −1.96244 −0.981221 0.192885i \(-0.938216\pi\)
−0.981221 + 0.192885i \(0.938216\pi\)
\(770\) 1.30707e11 0.0133995
\(771\) −4.26771e12 −0.434961
\(772\) 1.02830e13 1.04194
\(773\) −3.15285e12 −0.317611 −0.158805 0.987310i \(-0.550764\pi\)
−0.158805 + 0.987310i \(0.550764\pi\)
\(774\) −5.26363e12 −0.527170
\(775\) −3.99818e12 −0.398112
\(776\) −1.85766e12 −0.183903
\(777\) −1.83385e12 −0.180497
\(778\) 1.67716e12 0.164122
\(779\) 2.70038e12 0.262728
\(780\) −1.17766e10 −0.00113919
\(781\) 5.15185e12 0.495488
\(782\) 0 0
\(783\) 3.03541e12 0.288595
\(784\) −1.97504e12 −0.186704
\(785\) 1.54817e11 0.0145514
\(786\) 2.99726e12 0.280107
\(787\) 1.38558e13 1.28749 0.643745 0.765240i \(-0.277380\pi\)
0.643745 + 0.765240i \(0.277380\pi\)
\(788\) −4.69744e12 −0.434004
\(789\) −2.11912e12 −0.194674
\(790\) 3.37089e11 0.0307909
\(791\) 6.67680e12 0.606421
\(792\) −5.17379e12 −0.467246
\(793\) −1.24622e12 −0.111909
\(794\) 8.43428e12 0.753106
\(795\) 2.23113e11 0.0198095
\(796\) −1.35931e13 −1.20008
\(797\) −1.66687e13 −1.46332 −0.731662 0.681668i \(-0.761255\pi\)
−0.731662 + 0.681668i \(0.761255\pi\)
\(798\) 1.31251e12 0.114575
\(799\) 0 0
\(800\) −1.17717e13 −1.01609
\(801\) −1.34777e12 −0.115683
\(802\) 1.75545e12 0.149832
\(803\) −2.66714e12 −0.226373
\(804\) −7.23472e11 −0.0610617
\(805\) 6.91498e11 0.0580376
\(806\) −1.42912e11 −0.0119278
\(807\) 5.98059e12 0.496379
\(808\) −1.44780e13 −1.19497
\(809\) −1.04805e13 −0.860231 −0.430115 0.902774i \(-0.641527\pi\)
−0.430115 + 0.902774i \(0.641527\pi\)
\(810\) −2.08968e11 −0.0170568
\(811\) 1.18989e13 0.965860 0.482930 0.875659i \(-0.339573\pi\)
0.482930 + 0.875659i \(0.339573\pi\)
\(812\) 2.78846e12 0.225093
\(813\) 4.54850e11 0.0365141
\(814\) 2.57575e12 0.205634
\(815\) 5.75017e10 0.00456533
\(816\) 0 0
\(817\) 1.48211e13 1.16381
\(818\) 5.62964e12 0.439633
\(819\) 4.92382e11 0.0382406
\(820\) 1.80732e11 0.0139596
\(821\) 2.38314e12 0.183065 0.0915324 0.995802i \(-0.470823\pi\)
0.0915324 + 0.995802i \(0.470823\pi\)
\(822\) −2.81760e12 −0.215256
\(823\) −1.35076e13 −1.02631 −0.513155 0.858296i \(-0.671523\pi\)
−0.513155 + 0.858296i \(0.671523\pi\)
\(824\) 1.33367e13 1.00780
\(825\) 3.27399e12 0.246056
\(826\) −7.19902e11 −0.0538100
\(827\) 1.30268e12 0.0968417 0.0484208 0.998827i \(-0.484581\pi\)
0.0484208 + 0.998827i \(0.484581\pi\)
\(828\) −1.19540e13 −0.883847
\(829\) −1.65695e13 −1.21847 −0.609234 0.792991i \(-0.708523\pi\)
−0.609234 + 0.792991i \(0.708523\pi\)
\(830\) −4.62337e11 −0.0338148
\(831\) −6.66241e12 −0.484649
\(832\) −9.30695e10 −0.00673368
\(833\) 0 0
\(834\) −1.48975e12 −0.106627
\(835\) −9.49800e11 −0.0676150
\(836\) 6.36233e12 0.450493
\(837\) −4.00486e12 −0.282048
\(838\) −4.93983e12 −0.346030
\(839\) 1.58393e13 1.10359 0.551794 0.833981i \(-0.313944\pi\)
0.551794 + 0.833981i \(0.313944\pi\)
\(840\) 2.01142e11 0.0139395
\(841\) −1.20817e13 −0.832808
\(842\) −1.37603e13 −0.943457
\(843\) 2.11660e12 0.144349
\(844\) 7.15292e12 0.485224
\(845\) 9.05315e11 0.0610864
\(846\) −3.08804e12 −0.207261
\(847\) −6.15235e12 −0.410739
\(848\) −4.81365e12 −0.319664
\(849\) 4.06198e12 0.268320
\(850\) 0 0
\(851\) 1.36269e13 0.890665
\(852\) 3.46243e12 0.225114
\(853\) 1.78273e12 0.115296 0.0576481 0.998337i \(-0.481640\pi\)
0.0576481 + 0.998337i \(0.481640\pi\)
\(854\) 9.29585e12 0.598038
\(855\) 7.33533e11 0.0469432
\(856\) −1.04770e13 −0.666971
\(857\) 4.16362e12 0.263668 0.131834 0.991272i \(-0.457913\pi\)
0.131834 + 0.991272i \(0.457913\pi\)
\(858\) 1.17026e11 0.00737207
\(859\) −3.08310e11 −0.0193205 −0.00966026 0.999953i \(-0.503075\pi\)
−0.00966026 + 0.999953i \(0.503075\pi\)
\(860\) 9.91955e11 0.0618370
\(861\) 1.27867e12 0.0792946
\(862\) −7.40723e12 −0.456954
\(863\) −2.48841e13 −1.52712 −0.763562 0.645735i \(-0.776551\pi\)
−0.763562 + 0.645735i \(0.776551\pi\)
\(864\) −1.17914e13 −0.719866
\(865\) −1.26901e12 −0.0770714
\(866\) 5.15964e12 0.311737
\(867\) 0 0
\(868\) −3.67904e12 −0.219986
\(869\) 1.15605e13 0.687685
\(870\) 7.64097e10 0.00452180
\(871\) −2.21433e11 −0.0130365
\(872\) −1.12816e13 −0.660766
\(873\) −3.20786e12 −0.186918
\(874\) −9.75297e12 −0.565374
\(875\) 1.50723e12 0.0869247
\(876\) −1.79252e12 −0.102848
\(877\) −1.78295e13 −1.01775 −0.508874 0.860841i \(-0.669938\pi\)
−0.508874 + 0.860841i \(0.669938\pi\)
\(878\) −1.04182e13 −0.591652
\(879\) 3.85516e12 0.217818
\(880\) 2.66688e11 0.0149910
\(881\) 1.94178e13 1.08595 0.542974 0.839749i \(-0.317298\pi\)
0.542974 + 0.839749i \(0.317298\pi\)
\(882\) 3.61297e12 0.201027
\(883\) 1.76231e13 0.975574 0.487787 0.872963i \(-0.337804\pi\)
0.487787 + 0.872963i \(0.337804\pi\)
\(884\) 0 0
\(885\) 6.80816e10 0.00373066
\(886\) 1.27095e13 0.692908
\(887\) −2.04207e13 −1.10768 −0.553841 0.832622i \(-0.686839\pi\)
−0.553841 + 0.832622i \(0.686839\pi\)
\(888\) 3.96378e12 0.213920
\(889\) 6.28043e12 0.337234
\(890\) −7.35954e10 −0.00393184
\(891\) −7.16661e12 −0.380947
\(892\) 2.77696e13 1.46868
\(893\) 8.69519e12 0.457560
\(894\) 5.16031e12 0.270182
\(895\) −1.64929e12 −0.0859198
\(896\) −1.32764e13 −0.688170
\(897\) 6.19121e11 0.0319308
\(898\) −1.15309e13 −0.591725
\(899\) −3.20013e12 −0.163399
\(900\) −1.30033e13 −0.660636
\(901\) 0 0
\(902\) −1.79596e12 −0.0903374
\(903\) 7.01800e12 0.351252
\(904\) −1.44316e13 −0.718714
\(905\) −1.96052e12 −0.0971520
\(906\) 4.57157e12 0.225418
\(907\) 3.48284e13 1.70884 0.854418 0.519587i \(-0.173914\pi\)
0.854418 + 0.519587i \(0.173914\pi\)
\(908\) 2.79188e13 1.36305
\(909\) −2.50010e13 −1.21456
\(910\) 2.68866e10 0.00129972
\(911\) 2.39979e13 1.15436 0.577179 0.816618i \(-0.304154\pi\)
0.577179 + 0.816618i \(0.304154\pi\)
\(912\) 2.67800e12 0.128184
\(913\) −1.58560e13 −0.755221
\(914\) −1.86996e13 −0.886288
\(915\) −8.79115e11 −0.0414621
\(916\) 2.12263e12 0.0996195
\(917\) 2.36164e13 1.10294
\(918\) 0 0
\(919\) 1.68855e13 0.780896 0.390448 0.920625i \(-0.372320\pi\)
0.390448 + 0.920625i \(0.372320\pi\)
\(920\) −1.49464e12 −0.0687846
\(921\) −1.13134e13 −0.518114
\(922\) 5.36796e12 0.244636
\(923\) 1.05975e12 0.0480612
\(924\) 3.01265e12 0.135964
\(925\) 1.48230e13 0.665732
\(926\) 3.18169e12 0.142203
\(927\) 2.30301e13 1.02433
\(928\) −9.42203e12 −0.417041
\(929\) −2.44294e13 −1.07607 −0.538037 0.842921i \(-0.680834\pi\)
−0.538037 + 0.842921i \(0.680834\pi\)
\(930\) −1.00813e11 −0.00441922
\(931\) −1.01733e13 −0.443799
\(932\) −2.71870e13 −1.18029
\(933\) −1.34681e12 −0.0581886
\(934\) −1.60030e13 −0.688082
\(935\) 0 0
\(936\) −1.06426e12 −0.0453217
\(937\) 7.06840e12 0.299566 0.149783 0.988719i \(-0.452142\pi\)
0.149783 + 0.988719i \(0.452142\pi\)
\(938\) 1.65172e12 0.0696665
\(939\) −1.06378e13 −0.446535
\(940\) 5.81956e11 0.0243117
\(941\) 3.45639e13 1.43704 0.718521 0.695506i \(-0.244820\pi\)
0.718521 + 0.695506i \(0.244820\pi\)
\(942\) −1.03394e12 −0.0427827
\(943\) −9.50146e12 −0.391280
\(944\) −1.46886e12 −0.0602012
\(945\) 7.53451e11 0.0307335
\(946\) −9.85719e12 −0.400169
\(947\) −3.93920e13 −1.59160 −0.795799 0.605560i \(-0.792949\pi\)
−0.795799 + 0.605560i \(0.792949\pi\)
\(948\) 7.76955e12 0.312434
\(949\) −5.48636e11 −0.0219577
\(950\) −1.06091e13 −0.422591
\(951\) −1.14531e13 −0.454059
\(952\) 0 0
\(953\) 3.51103e13 1.37885 0.689425 0.724357i \(-0.257863\pi\)
0.689425 + 0.724357i \(0.257863\pi\)
\(954\) 8.80569e12 0.344188
\(955\) −1.61414e12 −0.0627951
\(956\) 1.00060e12 0.0387435
\(957\) 2.62049e12 0.100990
\(958\) −1.70858e13 −0.655377
\(959\) −2.22007e13 −0.847585
\(960\) −6.56535e10 −0.00249481
\(961\) −2.22174e13 −0.840308
\(962\) 5.29837e11 0.0199460
\(963\) −1.80921e13 −0.677906
\(964\) −3.84858e13 −1.43534
\(965\) 2.22021e12 0.0824177
\(966\) −4.61817e12 −0.170637
\(967\) −1.93513e12 −0.0711690 −0.0355845 0.999367i \(-0.511329\pi\)
−0.0355845 + 0.999367i \(0.511329\pi\)
\(968\) 1.32980e13 0.486797
\(969\) 0 0
\(970\) −1.75166e11 −0.00635296
\(971\) 1.69806e13 0.613010 0.306505 0.951869i \(-0.400840\pi\)
0.306505 + 0.951869i \(0.400840\pi\)
\(972\) −2.00456e13 −0.720311
\(973\) −1.17382e13 −0.419849
\(974\) −1.71558e13 −0.610794
\(975\) 6.73466e11 0.0238668
\(976\) 1.89668e13 0.669069
\(977\) −1.76777e13 −0.620726 −0.310363 0.950618i \(-0.600451\pi\)
−0.310363 + 0.950618i \(0.600451\pi\)
\(978\) −3.84025e11 −0.0134226
\(979\) −2.52397e12 −0.0878138
\(980\) −6.80880e11 −0.0235805
\(981\) −1.94814e13 −0.671600
\(982\) −6.37486e11 −0.0218760
\(983\) −5.81116e12 −0.198505 −0.0992527 0.995062i \(-0.531645\pi\)
−0.0992527 + 0.995062i \(0.531645\pi\)
\(984\) −2.76378e12 −0.0939778
\(985\) −1.01422e12 −0.0343297
\(986\) 0 0
\(987\) 4.11729e12 0.138097
\(988\) 1.30875e12 0.0436967
\(989\) −5.21491e13 −1.73326
\(990\) −4.87856e11 −0.0161411
\(991\) 5.41563e13 1.78368 0.891841 0.452348i \(-0.149414\pi\)
0.891841 + 0.452348i \(0.149414\pi\)
\(992\) 1.24312e13 0.407579
\(993\) −1.21906e13 −0.397882
\(994\) −7.90489e12 −0.256837
\(995\) −2.93487e12 −0.0949261
\(996\) −1.06564e13 −0.343117
\(997\) 9.07988e11 0.0291040 0.0145520 0.999894i \(-0.495368\pi\)
0.0145520 + 0.999894i \(0.495368\pi\)
\(998\) 6.56954e12 0.209627
\(999\) 1.48478e13 0.471647
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.1.22 yes 36
17.16 even 2 289.10.a.g.1.22 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.22 36 17.16 even 2
289.10.a.h.1.22 yes 36 1.1 even 1 trivial