Properties

Label 289.10.a.g.1.21
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $1$
Dimension $36$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.21
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.41399 q^{2} +128.596 q^{3} -482.689 q^{4} +1448.98 q^{5} +696.216 q^{6} -9443.95 q^{7} -5385.24 q^{8} -3146.14 q^{9} +O(q^{10})\) \(q+5.41399 q^{2} +128.596 q^{3} -482.689 q^{4} +1448.98 q^{5} +696.216 q^{6} -9443.95 q^{7} -5385.24 q^{8} -3146.14 q^{9} +7844.76 q^{10} +53314.9 q^{11} -62071.7 q^{12} +50477.7 q^{13} -51129.5 q^{14} +186332. q^{15} +217981. q^{16} -17033.2 q^{18} -361216. q^{19} -699405. q^{20} -1.21445e6 q^{21} +288646. q^{22} +378125. q^{23} -692518. q^{24} +146411. q^{25} +273286. q^{26} -2.93573e6 q^{27} +4.55849e6 q^{28} +4.53701e6 q^{29} +1.00880e6 q^{30} +7.59551e6 q^{31} +3.93739e6 q^{32} +6.85606e6 q^{33} -1.36841e7 q^{35} +1.51861e6 q^{36} +1.33174e7 q^{37} -1.95562e6 q^{38} +6.49122e6 q^{39} -7.80309e6 q^{40} -1.88813e7 q^{41} -6.57503e6 q^{42} -1.12895e7 q^{43} -2.57345e7 q^{44} -4.55869e6 q^{45} +2.04717e6 q^{46} -2.82338e7 q^{47} +2.80314e7 q^{48} +4.88347e7 q^{49} +792671. q^{50} -2.43650e7 q^{52} -1.10817e8 q^{53} -1.58940e7 q^{54} +7.72520e7 q^{55} +5.08579e7 q^{56} -4.64508e7 q^{57} +2.45633e7 q^{58} -1.66374e8 q^{59} -8.99405e7 q^{60} +1.24581e8 q^{61} +4.11221e7 q^{62} +2.97120e7 q^{63} -9.02893e7 q^{64} +7.31411e7 q^{65} +3.71187e7 q^{66} -2.73657e8 q^{67} +4.86253e7 q^{69} -7.40855e7 q^{70} -1.28257e8 q^{71} +1.69427e7 q^{72} +1.38744e8 q^{73} +7.21004e7 q^{74} +1.88279e7 q^{75} +1.74355e8 q^{76} -5.03503e8 q^{77} +3.51434e7 q^{78} -6.51178e8 q^{79} +3.15850e8 q^{80} -3.15597e8 q^{81} -1.02223e8 q^{82} +2.90303e8 q^{83} +5.86202e8 q^{84} -6.11212e7 q^{86} +5.83440e8 q^{87} -2.87113e8 q^{88} -8.64347e7 q^{89} -2.46807e7 q^{90} -4.76709e8 q^{91} -1.82517e8 q^{92} +9.76750e8 q^{93} -1.52857e8 q^{94} -5.23394e8 q^{95} +5.06331e8 q^{96} +9.69081e8 q^{97} +2.64391e8 q^{98} -1.67736e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.41399 0.239267 0.119633 0.992818i \(-0.461828\pi\)
0.119633 + 0.992818i \(0.461828\pi\)
\(3\) 128.596 0.916602 0.458301 0.888797i \(-0.348458\pi\)
0.458301 + 0.888797i \(0.348458\pi\)
\(4\) −482.689 −0.942751
\(5\) 1448.98 1.03680 0.518402 0.855137i \(-0.326527\pi\)
0.518402 + 0.855137i \(0.326527\pi\)
\(6\) 696.216 0.219313
\(7\) −9443.95 −1.48666 −0.743332 0.668923i \(-0.766756\pi\)
−0.743332 + 0.668923i \(0.766756\pi\)
\(8\) −5385.24 −0.464836
\(9\) −3146.14 −0.159841
\(10\) 7844.76 0.248073
\(11\) 53314.9 1.09795 0.548973 0.835840i \(-0.315019\pi\)
0.548973 + 0.835840i \(0.315019\pi\)
\(12\) −62071.7 −0.864128
\(13\) 50477.7 0.490179 0.245090 0.969500i \(-0.421183\pi\)
0.245090 + 0.969500i \(0.421183\pi\)
\(14\) −51129.5 −0.355709
\(15\) 186332. 0.950337
\(16\) 217981. 0.831531
\(17\) 0 0
\(18\) −17033.2 −0.0382446
\(19\) −361216. −0.635881 −0.317940 0.948111i \(-0.602991\pi\)
−0.317940 + 0.948111i \(0.602991\pi\)
\(20\) −699405. −0.977448
\(21\) −1.21445e6 −1.36268
\(22\) 288646. 0.262702
\(23\) 378125. 0.281748 0.140874 0.990028i \(-0.455009\pi\)
0.140874 + 0.990028i \(0.455009\pi\)
\(24\) −692518. −0.426070
\(25\) 146411. 0.0749627
\(26\) 273286. 0.117284
\(27\) −2.93573e6 −1.06311
\(28\) 4.55849e6 1.40155
\(29\) 4.53701e6 1.19118 0.595592 0.803287i \(-0.296918\pi\)
0.595592 + 0.803287i \(0.296918\pi\)
\(30\) 1.00880e6 0.227384
\(31\) 7.59551e6 1.47717 0.738583 0.674162i \(-0.235495\pi\)
0.738583 + 0.674162i \(0.235495\pi\)
\(32\) 3.93739e6 0.663794
\(33\) 6.85606e6 1.00638
\(34\) 0 0
\(35\) −1.36841e7 −1.54138
\(36\) 1.51861e6 0.150690
\(37\) 1.33174e7 1.16819 0.584093 0.811687i \(-0.301450\pi\)
0.584093 + 0.811687i \(0.301450\pi\)
\(38\) −1.95562e6 −0.152145
\(39\) 6.49122e6 0.449299
\(40\) −7.80309e6 −0.481944
\(41\) −1.88813e7 −1.04353 −0.521765 0.853089i \(-0.674726\pi\)
−0.521765 + 0.853089i \(0.674726\pi\)
\(42\) −6.57503e6 −0.326044
\(43\) −1.12895e7 −0.503578 −0.251789 0.967782i \(-0.581019\pi\)
−0.251789 + 0.967782i \(0.581019\pi\)
\(44\) −2.57345e7 −1.03509
\(45\) −4.55869e6 −0.165724
\(46\) 2.04717e6 0.0674129
\(47\) −2.82338e7 −0.843973 −0.421986 0.906602i \(-0.638667\pi\)
−0.421986 + 0.906602i \(0.638667\pi\)
\(48\) 2.80314e7 0.762183
\(49\) 4.88347e7 1.21017
\(50\) 792671. 0.0179361
\(51\) 0 0
\(52\) −2.43650e7 −0.462117
\(53\) −1.10817e8 −1.92914 −0.964570 0.263828i \(-0.915015\pi\)
−0.964570 + 0.263828i \(0.915015\pi\)
\(54\) −1.58940e7 −0.254368
\(55\) 7.72520e7 1.13836
\(56\) 5.08579e7 0.691055
\(57\) −4.64508e7 −0.582850
\(58\) 2.45633e7 0.285011
\(59\) −1.66374e8 −1.78752 −0.893761 0.448543i \(-0.851943\pi\)
−0.893761 + 0.448543i \(0.851943\pi\)
\(60\) −8.99405e7 −0.895931
\(61\) 1.24581e8 1.15204 0.576019 0.817436i \(-0.304605\pi\)
0.576019 + 0.817436i \(0.304605\pi\)
\(62\) 4.11221e7 0.353437
\(63\) 2.97120e7 0.237629
\(64\) −9.02893e7 −0.672707
\(65\) 7.31411e7 0.508220
\(66\) 3.71187e7 0.240793
\(67\) −2.73657e8 −1.65909 −0.829543 0.558442i \(-0.811399\pi\)
−0.829543 + 0.558442i \(0.811399\pi\)
\(68\) 0 0
\(69\) 4.86253e7 0.258250
\(70\) −7.40855e7 −0.368801
\(71\) −1.28257e8 −0.598990 −0.299495 0.954098i \(-0.596818\pi\)
−0.299495 + 0.954098i \(0.596818\pi\)
\(72\) 1.69427e7 0.0742998
\(73\) 1.38744e8 0.571825 0.285912 0.958256i \(-0.407703\pi\)
0.285912 + 0.958256i \(0.407703\pi\)
\(74\) 7.21004e7 0.279508
\(75\) 1.88279e7 0.0687109
\(76\) 1.74355e8 0.599477
\(77\) −5.03503e8 −1.63228
\(78\) 3.51434e7 0.107502
\(79\) −6.51178e8 −1.88095 −0.940476 0.339861i \(-0.889620\pi\)
−0.940476 + 0.339861i \(0.889620\pi\)
\(80\) 3.15850e8 0.862135
\(81\) −3.15597e8 −0.814610
\(82\) −1.02223e8 −0.249682
\(83\) 2.90303e8 0.671430 0.335715 0.941964i \(-0.391022\pi\)
0.335715 + 0.941964i \(0.391022\pi\)
\(84\) 5.86202e8 1.28467
\(85\) 0 0
\(86\) −6.11212e7 −0.120489
\(87\) 5.83440e8 1.09184
\(88\) −2.87113e8 −0.510365
\(89\) −8.64347e7 −0.146027 −0.0730135 0.997331i \(-0.523262\pi\)
−0.0730135 + 0.997331i \(0.523262\pi\)
\(90\) −2.46807e7 −0.0396522
\(91\) −4.76709e8 −0.728731
\(92\) −1.82517e8 −0.265618
\(93\) 9.76750e8 1.35397
\(94\) −1.52857e8 −0.201935
\(95\) −5.23394e8 −0.659284
\(96\) 5.06331e8 0.608435
\(97\) 9.69081e8 1.11144 0.555722 0.831368i \(-0.312442\pi\)
0.555722 + 0.831368i \(0.312442\pi\)
\(98\) 2.64391e8 0.289553
\(99\) −1.67736e8 −0.175497
\(100\) −7.06712e7 −0.0706712
\(101\) −1.61123e8 −0.154068 −0.0770340 0.997028i \(-0.524545\pi\)
−0.0770340 + 0.997028i \(0.524545\pi\)
\(102\) 0 0
\(103\) 6.13713e8 0.537276 0.268638 0.963241i \(-0.413426\pi\)
0.268638 + 0.963241i \(0.413426\pi\)
\(104\) −2.71835e8 −0.227853
\(105\) −1.75971e9 −1.41283
\(106\) −5.99961e8 −0.461579
\(107\) −3.82243e8 −0.281911 −0.140956 0.990016i \(-0.545017\pi\)
−0.140956 + 0.990016i \(0.545017\pi\)
\(108\) 1.41704e9 1.00225
\(109\) 7.12993e8 0.483800 0.241900 0.970301i \(-0.422229\pi\)
0.241900 + 0.970301i \(0.422229\pi\)
\(110\) 4.18242e8 0.272371
\(111\) 1.71256e9 1.07076
\(112\) −2.05860e9 −1.23621
\(113\) −1.25446e9 −0.723775 −0.361888 0.932222i \(-0.617868\pi\)
−0.361888 + 0.932222i \(0.617868\pi\)
\(114\) −2.51484e8 −0.139457
\(115\) 5.47895e8 0.292117
\(116\) −2.18996e9 −1.12299
\(117\) −1.58810e8 −0.0783506
\(118\) −9.00748e8 −0.427695
\(119\) 0 0
\(120\) −1.00344e9 −0.441751
\(121\) 4.84527e8 0.205487
\(122\) 6.74480e8 0.275645
\(123\) −2.42805e9 −0.956501
\(124\) −3.66627e9 −1.39260
\(125\) −2.61789e9 −0.959082
\(126\) 1.60861e8 0.0568569
\(127\) −4.71287e9 −1.60757 −0.803783 0.594923i \(-0.797183\pi\)
−0.803783 + 0.594923i \(0.797183\pi\)
\(128\) −2.50477e9 −0.824751
\(129\) −1.45178e9 −0.461580
\(130\) 3.95986e8 0.121600
\(131\) −5.24689e9 −1.55661 −0.778307 0.627884i \(-0.783921\pi\)
−0.778307 + 0.627884i \(0.783921\pi\)
\(132\) −3.30934e9 −0.948766
\(133\) 3.41131e9 0.945341
\(134\) −1.48157e9 −0.396965
\(135\) −4.25381e9 −1.10224
\(136\) 0 0
\(137\) 3.50319e9 0.849613 0.424806 0.905284i \(-0.360342\pi\)
0.424806 + 0.905284i \(0.360342\pi\)
\(138\) 2.63257e8 0.0617908
\(139\) 5.88400e9 1.33692 0.668461 0.743747i \(-0.266953\pi\)
0.668461 + 0.743747i \(0.266953\pi\)
\(140\) 6.60515e9 1.45314
\(141\) −3.63074e9 −0.773587
\(142\) −6.94384e8 −0.143319
\(143\) 2.69121e9 0.538190
\(144\) −6.85800e8 −0.132913
\(145\) 6.57402e9 1.23502
\(146\) 7.51162e8 0.136819
\(147\) 6.27993e9 1.10924
\(148\) −6.42816e9 −1.10131
\(149\) 5.04607e8 0.0838716 0.0419358 0.999120i \(-0.486648\pi\)
0.0419358 + 0.999120i \(0.486648\pi\)
\(150\) 1.01934e8 0.0164403
\(151\) 4.88828e9 0.765174 0.382587 0.923920i \(-0.375033\pi\)
0.382587 + 0.923920i \(0.375033\pi\)
\(152\) 1.94523e9 0.295580
\(153\) 0 0
\(154\) −2.72596e9 −0.390550
\(155\) 1.10057e10 1.53153
\(156\) −3.13324e9 −0.423577
\(157\) −8.97747e8 −0.117925 −0.0589624 0.998260i \(-0.518779\pi\)
−0.0589624 + 0.998260i \(0.518779\pi\)
\(158\) −3.52547e9 −0.450050
\(159\) −1.42505e10 −1.76825
\(160\) 5.70519e9 0.688225
\(161\) −3.57100e9 −0.418864
\(162\) −1.70864e9 −0.194909
\(163\) −8.17404e9 −0.906970 −0.453485 0.891264i \(-0.649819\pi\)
−0.453485 + 0.891264i \(0.649819\pi\)
\(164\) 9.11379e9 0.983789
\(165\) 9.93428e9 1.04342
\(166\) 1.57170e9 0.160651
\(167\) 2.12188e9 0.211104 0.105552 0.994414i \(-0.466339\pi\)
0.105552 + 0.994414i \(0.466339\pi\)
\(168\) 6.54011e9 0.633422
\(169\) −8.05650e9 −0.759724
\(170\) 0 0
\(171\) 1.13644e9 0.101640
\(172\) 5.44931e9 0.474748
\(173\) −1.36572e10 −1.15919 −0.579594 0.814905i \(-0.696789\pi\)
−0.579594 + 0.814905i \(0.696789\pi\)
\(174\) 3.15874e9 0.261241
\(175\) −1.38270e9 −0.111444
\(176\) 1.16216e10 0.912977
\(177\) −2.13950e10 −1.63845
\(178\) −4.67957e8 −0.0349394
\(179\) −2.02667e10 −1.47552 −0.737759 0.675064i \(-0.764116\pi\)
−0.737759 + 0.675064i \(0.764116\pi\)
\(180\) 2.20043e9 0.156236
\(181\) 2.65298e10 1.83730 0.918651 0.395070i \(-0.129280\pi\)
0.918651 + 0.395070i \(0.129280\pi\)
\(182\) −2.58090e9 −0.174361
\(183\) 1.60206e10 1.05596
\(184\) −2.03629e9 −0.130966
\(185\) 1.92966e10 1.21118
\(186\) 5.28812e9 0.323961
\(187\) 0 0
\(188\) 1.36281e10 0.795656
\(189\) 2.77249e10 1.58049
\(190\) −2.83365e9 −0.157745
\(191\) 2.39093e9 0.129992 0.0649960 0.997886i \(-0.479297\pi\)
0.0649960 + 0.997886i \(0.479297\pi\)
\(192\) −1.16108e10 −0.616605
\(193\) −3.20320e10 −1.66179 −0.830896 0.556427i \(-0.812172\pi\)
−0.830896 + 0.556427i \(0.812172\pi\)
\(194\) 5.24660e9 0.265932
\(195\) 9.40563e9 0.465835
\(196\) −2.35719e10 −1.14089
\(197\) −2.47491e10 −1.17074 −0.585370 0.810766i \(-0.699051\pi\)
−0.585370 + 0.810766i \(0.699051\pi\)
\(198\) −9.08123e8 −0.0419905
\(199\) 1.05656e10 0.477591 0.238796 0.971070i \(-0.423247\pi\)
0.238796 + 0.971070i \(0.423247\pi\)
\(200\) −7.88461e8 −0.0348454
\(201\) −3.51911e10 −1.52072
\(202\) −8.72321e8 −0.0368634
\(203\) −4.28473e10 −1.77089
\(204\) 0 0
\(205\) −2.73586e10 −1.08194
\(206\) 3.32264e9 0.128552
\(207\) −1.18964e9 −0.0450347
\(208\) 1.10032e10 0.407599
\(209\) −1.92582e10 −0.698163
\(210\) −9.52708e9 −0.338044
\(211\) 4.57152e10 1.58778 0.793889 0.608062i \(-0.208053\pi\)
0.793889 + 0.608062i \(0.208053\pi\)
\(212\) 5.34899e10 1.81870
\(213\) −1.64933e10 −0.549035
\(214\) −2.06946e9 −0.0674520
\(215\) −1.63582e10 −0.522111
\(216\) 1.58096e10 0.494173
\(217\) −7.17317e10 −2.19605
\(218\) 3.86014e9 0.115757
\(219\) 1.78419e10 0.524136
\(220\) −3.72887e10 −1.07319
\(221\) 0 0
\(222\) 9.27180e9 0.256198
\(223\) −1.06039e10 −0.287141 −0.143571 0.989640i \(-0.545858\pi\)
−0.143571 + 0.989640i \(0.545858\pi\)
\(224\) −3.71845e10 −0.986839
\(225\) −4.60632e8 −0.0119821
\(226\) −6.79164e9 −0.173175
\(227\) −3.17793e9 −0.0794379 −0.0397190 0.999211i \(-0.512646\pi\)
−0.0397190 + 0.999211i \(0.512646\pi\)
\(228\) 2.24213e10 0.549482
\(229\) −5.66623e10 −1.36155 −0.680777 0.732491i \(-0.738358\pi\)
−0.680777 + 0.732491i \(0.738358\pi\)
\(230\) 2.96630e9 0.0698940
\(231\) −6.47483e10 −1.49615
\(232\) −2.44329e10 −0.553705
\(233\) −6.44249e10 −1.43203 −0.716015 0.698085i \(-0.754036\pi\)
−0.716015 + 0.698085i \(0.754036\pi\)
\(234\) −8.59798e8 −0.0187467
\(235\) −4.09101e10 −0.875034
\(236\) 8.03069e10 1.68519
\(237\) −8.37387e10 −1.72408
\(238\) 0 0
\(239\) −3.83304e10 −0.759894 −0.379947 0.925008i \(-0.624058\pi\)
−0.379947 + 0.925008i \(0.624058\pi\)
\(240\) 4.06169e10 0.790235
\(241\) −7.17784e9 −0.137062 −0.0685310 0.997649i \(-0.521831\pi\)
−0.0685310 + 0.997649i \(0.521831\pi\)
\(242\) 2.62322e9 0.0491661
\(243\) 1.71996e10 0.316439
\(244\) −6.01338e10 −1.08609
\(245\) 7.07603e10 1.25471
\(246\) −1.31455e10 −0.228859
\(247\) −1.82334e10 −0.311695
\(248\) −4.09036e10 −0.686640
\(249\) 3.73318e10 0.615434
\(250\) −1.41732e10 −0.229477
\(251\) −6.44186e10 −1.02442 −0.512212 0.858859i \(-0.671174\pi\)
−0.512212 + 0.858859i \(0.671174\pi\)
\(252\) −1.43417e10 −0.224025
\(253\) 2.01597e10 0.309344
\(254\) −2.55155e10 −0.384637
\(255\) 0 0
\(256\) 3.26673e10 0.475372
\(257\) −1.76291e10 −0.252076 −0.126038 0.992025i \(-0.540226\pi\)
−0.126038 + 0.992025i \(0.540226\pi\)
\(258\) −7.85993e9 −0.110441
\(259\) −1.25769e11 −1.73670
\(260\) −3.53044e10 −0.479125
\(261\) −1.42741e10 −0.190400
\(262\) −2.84066e10 −0.372446
\(263\) 7.05351e10 0.909084 0.454542 0.890725i \(-0.349803\pi\)
0.454542 + 0.890725i \(0.349803\pi\)
\(264\) −3.69215e10 −0.467802
\(265\) −1.60571e11 −2.00014
\(266\) 1.84688e10 0.226189
\(267\) −1.11151e10 −0.133849
\(268\) 1.32091e11 1.56411
\(269\) 5.82993e10 0.678857 0.339428 0.940632i \(-0.389766\pi\)
0.339428 + 0.940632i \(0.389766\pi\)
\(270\) −2.30301e10 −0.263729
\(271\) −5.65565e10 −0.636973 −0.318486 0.947927i \(-0.603175\pi\)
−0.318486 + 0.947927i \(0.603175\pi\)
\(272\) 0 0
\(273\) −6.13028e10 −0.667957
\(274\) 1.89662e10 0.203284
\(275\) 7.80591e9 0.0823050
\(276\) −2.34709e10 −0.243466
\(277\) −1.21584e11 −1.24085 −0.620423 0.784268i \(-0.713039\pi\)
−0.620423 + 0.784268i \(0.713039\pi\)
\(278\) 3.18559e10 0.319881
\(279\) −2.38966e10 −0.236111
\(280\) 7.36920e10 0.716489
\(281\) −1.34239e10 −0.128440 −0.0642202 0.997936i \(-0.520456\pi\)
−0.0642202 + 0.997936i \(0.520456\pi\)
\(282\) −1.96568e10 −0.185094
\(283\) 1.50629e11 1.39595 0.697975 0.716122i \(-0.254084\pi\)
0.697975 + 0.716122i \(0.254084\pi\)
\(284\) 6.19084e10 0.564699
\(285\) −6.73062e10 −0.604301
\(286\) 1.45702e10 0.128771
\(287\) 1.78314e11 1.55138
\(288\) −1.23876e10 −0.106101
\(289\) 0 0
\(290\) 3.55917e10 0.295500
\(291\) 1.24620e11 1.01875
\(292\) −6.69704e10 −0.539088
\(293\) 2.31251e11 1.83307 0.916535 0.399954i \(-0.130974\pi\)
0.916535 + 0.399954i \(0.130974\pi\)
\(294\) 3.39995e10 0.265405
\(295\) −2.41072e11 −1.85331
\(296\) −7.17174e10 −0.543015
\(297\) −1.56518e11 −1.16724
\(298\) 2.73194e9 0.0200677
\(299\) 1.90869e10 0.138107
\(300\) −9.08801e9 −0.0647773
\(301\) 1.06617e11 0.748650
\(302\) 2.64651e10 0.183081
\(303\) −2.07198e10 −0.141219
\(304\) −7.87382e10 −0.528755
\(305\) 1.80515e11 1.19444
\(306\) 0 0
\(307\) −3.24870e10 −0.208731 −0.104365 0.994539i \(-0.533281\pi\)
−0.104365 + 0.994539i \(0.533281\pi\)
\(308\) 2.43035e11 1.53883
\(309\) 7.89208e10 0.492469
\(310\) 5.95849e10 0.366445
\(311\) −2.43533e11 −1.47617 −0.738086 0.674707i \(-0.764270\pi\)
−0.738086 + 0.674707i \(0.764270\pi\)
\(312\) −3.49568e10 −0.208851
\(313\) 1.00730e9 0.00593212 0.00296606 0.999996i \(-0.499056\pi\)
0.00296606 + 0.999996i \(0.499056\pi\)
\(314\) −4.86039e9 −0.0282155
\(315\) 4.30521e10 0.246375
\(316\) 3.14316e11 1.77327
\(317\) 2.11430e11 1.17598 0.587991 0.808868i \(-0.299919\pi\)
0.587991 + 0.808868i \(0.299919\pi\)
\(318\) −7.71523e10 −0.423084
\(319\) 2.41890e11 1.30786
\(320\) −1.30827e11 −0.697466
\(321\) −4.91548e10 −0.258400
\(322\) −1.93333e10 −0.100220
\(323\) 0 0
\(324\) 1.52335e11 0.767975
\(325\) 7.39052e9 0.0367451
\(326\) −4.42542e10 −0.217008
\(327\) 9.16878e10 0.443452
\(328\) 1.01680e11 0.485070
\(329\) 2.66638e11 1.25470
\(330\) 5.37841e10 0.249656
\(331\) −1.05381e11 −0.482543 −0.241271 0.970458i \(-0.577564\pi\)
−0.241271 + 0.970458i \(0.577564\pi\)
\(332\) −1.40126e11 −0.632992
\(333\) −4.18985e10 −0.186724
\(334\) 1.14878e10 0.0505102
\(335\) −3.96522e11 −1.72015
\(336\) −2.64727e11 −1.13311
\(337\) −2.53745e10 −0.107167 −0.0535836 0.998563i \(-0.517064\pi\)
−0.0535836 + 0.998563i \(0.517064\pi\)
\(338\) −4.36178e10 −0.181777
\(339\) −1.61318e11 −0.663414
\(340\) 0 0
\(341\) 4.04954e11 1.62185
\(342\) 6.15267e9 0.0243190
\(343\) −8.00947e10 −0.312450
\(344\) 6.07966e10 0.234081
\(345\) 7.04569e10 0.267755
\(346\) −7.39400e10 −0.277356
\(347\) 1.47329e9 0.00545515 0.00272757 0.999996i \(-0.499132\pi\)
0.00272757 + 0.999996i \(0.499132\pi\)
\(348\) −2.81620e11 −1.02933
\(349\) −4.79754e10 −0.173103 −0.0865513 0.996247i \(-0.527585\pi\)
−0.0865513 + 0.996247i \(0.527585\pi\)
\(350\) −7.48595e9 −0.0266649
\(351\) −1.48189e11 −0.521115
\(352\) 2.09921e11 0.728811
\(353\) −1.19962e11 −0.411203 −0.205601 0.978636i \(-0.565915\pi\)
−0.205601 + 0.978636i \(0.565915\pi\)
\(354\) −1.15832e11 −0.392026
\(355\) −1.85842e11 −0.621035
\(356\) 4.17210e10 0.137667
\(357\) 0 0
\(358\) −1.09724e11 −0.353043
\(359\) −3.49206e11 −1.10958 −0.554788 0.831992i \(-0.687201\pi\)
−0.554788 + 0.831992i \(0.687201\pi\)
\(360\) 2.45497e10 0.0770343
\(361\) −1.92211e11 −0.595656
\(362\) 1.43632e11 0.439606
\(363\) 6.23080e10 0.188349
\(364\) 2.30102e11 0.687012
\(365\) 2.01038e11 0.592870
\(366\) 8.67352e10 0.252657
\(367\) 3.99938e11 1.15079 0.575395 0.817876i \(-0.304848\pi\)
0.575395 + 0.817876i \(0.304848\pi\)
\(368\) 8.24241e10 0.234282
\(369\) 5.94033e10 0.166798
\(370\) 1.04472e11 0.289795
\(371\) 1.04655e12 2.86798
\(372\) −4.71466e11 −1.27646
\(373\) 2.53082e11 0.676973 0.338487 0.940971i \(-0.390085\pi\)
0.338487 + 0.940971i \(0.390085\pi\)
\(374\) 0 0
\(375\) −3.36649e11 −0.879097
\(376\) 1.52046e11 0.392309
\(377\) 2.29018e11 0.583893
\(378\) 1.50102e11 0.378159
\(379\) −3.64607e11 −0.907714 −0.453857 0.891075i \(-0.649952\pi\)
−0.453857 + 0.891075i \(0.649952\pi\)
\(380\) 2.52636e11 0.621541
\(381\) −6.06055e11 −1.47350
\(382\) 1.29445e10 0.0311028
\(383\) 5.96099e11 1.41555 0.707773 0.706440i \(-0.249700\pi\)
0.707773 + 0.706440i \(0.249700\pi\)
\(384\) −3.22102e11 −0.755968
\(385\) −7.29565e11 −1.69235
\(386\) −1.73421e11 −0.397612
\(387\) 3.55184e10 0.0804922
\(388\) −4.67765e11 −1.04781
\(389\) 5.78216e11 1.28032 0.640158 0.768243i \(-0.278869\pi\)
0.640158 + 0.768243i \(0.278869\pi\)
\(390\) 5.09220e10 0.111459
\(391\) 0 0
\(392\) −2.62986e11 −0.562530
\(393\) −6.74727e11 −1.42680
\(394\) −1.33991e11 −0.280120
\(395\) −9.43542e11 −1.95018
\(396\) 8.09644e10 0.165450
\(397\) 9.41819e10 0.190288 0.0951438 0.995464i \(-0.469669\pi\)
0.0951438 + 0.995464i \(0.469669\pi\)
\(398\) 5.72022e10 0.114272
\(399\) 4.38679e11 0.866501
\(400\) 3.19149e10 0.0623338
\(401\) −5.33397e11 −1.03015 −0.515075 0.857145i \(-0.672236\pi\)
−0.515075 + 0.857145i \(0.672236\pi\)
\(402\) −1.90524e11 −0.363859
\(403\) 3.83404e11 0.724076
\(404\) 7.77724e10 0.145248
\(405\) −4.57293e11 −0.844591
\(406\) −2.31975e11 −0.423715
\(407\) 7.10016e11 1.28261
\(408\) 0 0
\(409\) −3.13190e11 −0.553418 −0.276709 0.960954i \(-0.589244\pi\)
−0.276709 + 0.960954i \(0.589244\pi\)
\(410\) −1.48119e11 −0.258871
\(411\) 4.50495e11 0.778757
\(412\) −2.96232e11 −0.506518
\(413\) 1.57123e12 2.65745
\(414\) −6.44068e9 −0.0107753
\(415\) 4.20643e11 0.696142
\(416\) 1.98750e11 0.325378
\(417\) 7.56657e11 1.22542
\(418\) −1.04264e11 −0.167047
\(419\) −9.82119e11 −1.55669 −0.778343 0.627839i \(-0.783940\pi\)
−0.778343 + 0.627839i \(0.783940\pi\)
\(420\) 8.49394e11 1.33195
\(421\) 1.73588e11 0.269308 0.134654 0.990893i \(-0.457008\pi\)
0.134654 + 0.990893i \(0.457008\pi\)
\(422\) 2.47502e11 0.379903
\(423\) 8.88275e10 0.134901
\(424\) 5.96774e11 0.896734
\(425\) 0 0
\(426\) −8.92948e10 −0.131366
\(427\) −1.17654e12 −1.71269
\(428\) 1.84504e11 0.265772
\(429\) 3.46078e11 0.493306
\(430\) −8.85633e10 −0.124924
\(431\) 3.54330e11 0.494606 0.247303 0.968938i \(-0.420456\pi\)
0.247303 + 0.968938i \(0.420456\pi\)
\(432\) −6.39933e11 −0.884011
\(433\) 6.69890e7 9.15815e−5 0 4.57907e−5 1.00000i \(-0.499985\pi\)
4.57907e−5 1.00000i \(0.499985\pi\)
\(434\) −3.88355e11 −0.525442
\(435\) 8.45391e11 1.13203
\(436\) −3.44154e11 −0.456103
\(437\) −1.36585e11 −0.179158
\(438\) 9.65962e10 0.125408
\(439\) 4.51683e11 0.580422 0.290211 0.956963i \(-0.406275\pi\)
0.290211 + 0.956963i \(0.406275\pi\)
\(440\) −4.16021e11 −0.529149
\(441\) −1.53641e11 −0.193434
\(442\) 0 0
\(443\) 7.61003e11 0.938792 0.469396 0.882988i \(-0.344472\pi\)
0.469396 + 0.882988i \(0.344472\pi\)
\(444\) −8.26634e11 −1.00946
\(445\) −1.25242e11 −0.151401
\(446\) −5.74097e10 −0.0687034
\(447\) 6.48903e10 0.0768769
\(448\) 8.52688e11 1.00009
\(449\) 5.03740e9 0.00584921 0.00292461 0.999996i \(-0.499069\pi\)
0.00292461 + 0.999996i \(0.499069\pi\)
\(450\) −2.49386e9 −0.00286692
\(451\) −1.00665e12 −1.14574
\(452\) 6.05513e11 0.682340
\(453\) 6.28612e11 0.701360
\(454\) −1.72053e10 −0.0190069
\(455\) −6.90741e11 −0.755552
\(456\) 2.50149e11 0.270930
\(457\) −7.31493e11 −0.784490 −0.392245 0.919861i \(-0.628301\pi\)
−0.392245 + 0.919861i \(0.628301\pi\)
\(458\) −3.06769e11 −0.325775
\(459\) 0 0
\(460\) −2.64463e11 −0.275394
\(461\) 7.48760e11 0.772126 0.386063 0.922472i \(-0.373835\pi\)
0.386063 + 0.922472i \(0.373835\pi\)
\(462\) −3.50547e11 −0.357979
\(463\) 1.32071e11 0.133565 0.0667827 0.997768i \(-0.478727\pi\)
0.0667827 + 0.997768i \(0.478727\pi\)
\(464\) 9.88981e11 0.990506
\(465\) 1.41529e12 1.40381
\(466\) −3.48796e11 −0.342637
\(467\) −1.16300e11 −0.113150 −0.0565750 0.998398i \(-0.518018\pi\)
−0.0565750 + 0.998398i \(0.518018\pi\)
\(468\) 7.66559e10 0.0738651
\(469\) 2.58440e12 2.46650
\(470\) −2.21487e11 −0.209367
\(471\) −1.15446e11 −0.108090
\(472\) 8.95964e11 0.830905
\(473\) −6.01898e11 −0.552901
\(474\) −4.53361e11 −0.412516
\(475\) −5.28862e10 −0.0476673
\(476\) 0 0
\(477\) 3.48645e11 0.308355
\(478\) −2.07521e11 −0.181818
\(479\) −2.63575e11 −0.228768 −0.114384 0.993437i \(-0.536489\pi\)
−0.114384 + 0.993437i \(0.536489\pi\)
\(480\) 7.33663e11 0.630828
\(481\) 6.72233e11 0.572620
\(482\) −3.88608e10 −0.0327944
\(483\) −4.59215e11 −0.383931
\(484\) −2.33876e11 −0.193723
\(485\) 1.40418e12 1.15235
\(486\) 9.31185e10 0.0757134
\(487\) −5.21302e11 −0.419961 −0.209981 0.977706i \(-0.567340\pi\)
−0.209981 + 0.977706i \(0.567340\pi\)
\(488\) −6.70898e11 −0.535509
\(489\) −1.05115e12 −0.831330
\(490\) 3.83096e11 0.300210
\(491\) −2.46427e12 −1.91347 −0.956737 0.290955i \(-0.906027\pi\)
−0.956737 + 0.290955i \(0.906027\pi\)
\(492\) 1.17199e12 0.901743
\(493\) 0 0
\(494\) −9.87153e10 −0.0745784
\(495\) −2.43046e11 −0.181956
\(496\) 1.65568e12 1.22831
\(497\) 1.21126e12 0.890497
\(498\) 2.02114e11 0.147253
\(499\) −1.19804e12 −0.865009 −0.432505 0.901632i \(-0.642370\pi\)
−0.432505 + 0.901632i \(0.642370\pi\)
\(500\) 1.26362e12 0.904176
\(501\) 2.72865e11 0.193498
\(502\) −3.48762e11 −0.245111
\(503\) 2.80910e12 1.95664 0.978322 0.207090i \(-0.0663992\pi\)
0.978322 + 0.207090i \(0.0663992\pi\)
\(504\) −1.60006e11 −0.110459
\(505\) −2.33464e11 −0.159738
\(506\) 1.09144e11 0.0740158
\(507\) −1.03603e12 −0.696365
\(508\) 2.27485e12 1.51553
\(509\) 1.29541e12 0.855416 0.427708 0.903917i \(-0.359321\pi\)
0.427708 + 0.903917i \(0.359321\pi\)
\(510\) 0 0
\(511\) −1.31030e12 −0.850111
\(512\) 1.45930e12 0.938492
\(513\) 1.06043e12 0.676013
\(514\) −9.54439e10 −0.0603134
\(515\) 8.89256e11 0.557050
\(516\) 7.00758e11 0.435155
\(517\) −1.50528e12 −0.926637
\(518\) −6.80913e11 −0.415535
\(519\) −1.75626e12 −1.06251
\(520\) −3.93882e11 −0.236239
\(521\) 2.01682e12 1.19922 0.599609 0.800293i \(-0.295323\pi\)
0.599609 + 0.800293i \(0.295323\pi\)
\(522\) −7.72798e10 −0.0455563
\(523\) 2.41603e12 1.41203 0.706017 0.708195i \(-0.250490\pi\)
0.706017 + 0.708195i \(0.250490\pi\)
\(524\) 2.53261e12 1.46750
\(525\) −1.77810e11 −0.102150
\(526\) 3.81876e11 0.217514
\(527\) 0 0
\(528\) 1.49449e12 0.836837
\(529\) −1.65817e12 −0.920618
\(530\) −8.69329e11 −0.478567
\(531\) 5.23437e11 0.285719
\(532\) −1.64660e12 −0.891221
\(533\) −9.53086e11 −0.511516
\(534\) −6.01772e10 −0.0320255
\(535\) −5.53861e11 −0.292287
\(536\) 1.47371e12 0.771204
\(537\) −2.60621e12 −1.35246
\(538\) 3.15632e11 0.162428
\(539\) 2.60361e12 1.32870
\(540\) 2.05326e12 1.03914
\(541\) −5.24241e11 −0.263114 −0.131557 0.991309i \(-0.541998\pi\)
−0.131557 + 0.991309i \(0.541998\pi\)
\(542\) −3.06197e11 −0.152407
\(543\) 3.41162e12 1.68407
\(544\) 0 0
\(545\) 1.03311e12 0.501606
\(546\) −3.31893e11 −0.159820
\(547\) 1.39403e12 0.665777 0.332888 0.942966i \(-0.391977\pi\)
0.332888 + 0.942966i \(0.391977\pi\)
\(548\) −1.69095e12 −0.800973
\(549\) −3.91950e11 −0.184143
\(550\) 4.22611e10 0.0196929
\(551\) −1.63884e12 −0.757451
\(552\) −2.61859e11 −0.120044
\(553\) 6.14969e12 2.79634
\(554\) −6.58255e11 −0.296893
\(555\) 2.48146e12 1.11017
\(556\) −2.84014e12 −1.26038
\(557\) −3.95429e11 −0.174069 −0.0870343 0.996205i \(-0.527739\pi\)
−0.0870343 + 0.996205i \(0.527739\pi\)
\(558\) −1.29376e11 −0.0564936
\(559\) −5.69868e11 −0.246843
\(560\) −2.98287e12 −1.28170
\(561\) 0 0
\(562\) −7.26772e10 −0.0307316
\(563\) 2.92242e12 1.22590 0.612951 0.790121i \(-0.289982\pi\)
0.612951 + 0.790121i \(0.289982\pi\)
\(564\) 1.75252e12 0.729300
\(565\) −1.81768e12 −0.750413
\(566\) 8.15505e11 0.334005
\(567\) 2.98048e12 1.21105
\(568\) 6.90696e11 0.278432
\(569\) 6.55993e11 0.262358 0.131179 0.991359i \(-0.458124\pi\)
0.131179 + 0.991359i \(0.458124\pi\)
\(570\) −3.64395e11 −0.144589
\(571\) −1.68512e12 −0.663391 −0.331695 0.943387i \(-0.607621\pi\)
−0.331695 + 0.943387i \(0.607621\pi\)
\(572\) −1.29902e12 −0.507380
\(573\) 3.07463e11 0.119151
\(574\) 9.65392e11 0.371193
\(575\) 5.53619e10 0.0211206
\(576\) 2.84063e11 0.107526
\(577\) −3.07782e12 −1.15599 −0.577993 0.816042i \(-0.696164\pi\)
−0.577993 + 0.816042i \(0.696164\pi\)
\(578\) 0 0
\(579\) −4.11918e12 −1.52320
\(580\) −3.17321e12 −1.16432
\(581\) −2.74161e12 −0.998191
\(582\) 6.74690e11 0.243754
\(583\) −5.90817e12 −2.11809
\(584\) −7.47172e11 −0.265805
\(585\) −2.30113e11 −0.0812342
\(586\) 1.25199e12 0.438593
\(587\) −1.96540e12 −0.683250 −0.341625 0.939836i \(-0.610977\pi\)
−0.341625 + 0.939836i \(0.610977\pi\)
\(588\) −3.03125e12 −1.04574
\(589\) −2.74362e12 −0.939302
\(590\) −1.30516e12 −0.443436
\(591\) −3.18262e12 −1.07310
\(592\) 2.90294e12 0.971383
\(593\) 1.10021e12 0.365367 0.182683 0.983172i \(-0.441522\pi\)
0.182683 + 0.983172i \(0.441522\pi\)
\(594\) −8.47388e11 −0.279282
\(595\) 0 0
\(596\) −2.43568e11 −0.0790700
\(597\) 1.35869e12 0.437761
\(598\) 1.03336e11 0.0330444
\(599\) −5.63562e12 −1.78863 −0.894315 0.447437i \(-0.852337\pi\)
−0.894315 + 0.447437i \(0.852337\pi\)
\(600\) −1.01393e11 −0.0319393
\(601\) −3.46470e12 −1.08325 −0.541627 0.840619i \(-0.682191\pi\)
−0.541627 + 0.840619i \(0.682191\pi\)
\(602\) 5.77226e11 0.179127
\(603\) 8.60963e11 0.265190
\(604\) −2.35952e12 −0.721368
\(605\) 7.02068e11 0.213049
\(606\) −1.12177e11 −0.0337890
\(607\) −2.58507e12 −0.772900 −0.386450 0.922310i \(-0.626299\pi\)
−0.386450 + 0.922310i \(0.626299\pi\)
\(608\) −1.42225e12 −0.422094
\(609\) −5.50998e12 −1.62320
\(610\) 9.77307e11 0.285790
\(611\) −1.42518e12 −0.413698
\(612\) 0 0
\(613\) 5.46982e12 1.56459 0.782296 0.622906i \(-0.214048\pi\)
0.782296 + 0.622906i \(0.214048\pi\)
\(614\) −1.75884e11 −0.0499424
\(615\) −3.51820e12 −0.991704
\(616\) 2.71148e12 0.758741
\(617\) 4.06569e12 1.12941 0.564704 0.825294i \(-0.308990\pi\)
0.564704 + 0.825294i \(0.308990\pi\)
\(618\) 4.27277e11 0.117831
\(619\) 2.50487e12 0.685767 0.342883 0.939378i \(-0.388596\pi\)
0.342883 + 0.939378i \(0.388596\pi\)
\(620\) −5.31234e12 −1.44385
\(621\) −1.11007e12 −0.299529
\(622\) −1.31849e12 −0.353199
\(623\) 8.16285e11 0.217093
\(624\) 1.41496e12 0.373606
\(625\) −4.07922e12 −1.06934
\(626\) 5.45352e9 0.00141936
\(627\) −2.47652e12 −0.639938
\(628\) 4.33332e11 0.111174
\(629\) 0 0
\(630\) 2.33084e11 0.0589494
\(631\) 3.07145e12 0.771279 0.385640 0.922650i \(-0.373981\pi\)
0.385640 + 0.922650i \(0.373981\pi\)
\(632\) 3.50675e12 0.874334
\(633\) 5.87878e12 1.45536
\(634\) 1.14468e12 0.281374
\(635\) −6.82885e12 −1.66673
\(636\) 6.87858e12 1.66702
\(637\) 2.46506e12 0.593199
\(638\) 1.30959e12 0.312927
\(639\) 4.03516e11 0.0957430
\(640\) −3.62935e12 −0.855105
\(641\) 1.02073e12 0.238809 0.119404 0.992846i \(-0.461902\pi\)
0.119404 + 0.992846i \(0.461902\pi\)
\(642\) −2.66124e11 −0.0618266
\(643\) −1.45556e12 −0.335801 −0.167900 0.985804i \(-0.553699\pi\)
−0.167900 + 0.985804i \(0.553699\pi\)
\(644\) 1.72368e12 0.394884
\(645\) −2.10360e12 −0.478568
\(646\) 0 0
\(647\) −3.55404e11 −0.0797357 −0.0398679 0.999205i \(-0.512694\pi\)
−0.0398679 + 0.999205i \(0.512694\pi\)
\(648\) 1.69956e12 0.378660
\(649\) −8.87021e12 −1.96260
\(650\) 4.00122e10 0.00879190
\(651\) −9.22438e12 −2.01290
\(652\) 3.94552e12 0.855047
\(653\) 4.75410e12 1.02320 0.511598 0.859225i \(-0.329054\pi\)
0.511598 + 0.859225i \(0.329054\pi\)
\(654\) 4.96397e11 0.106103
\(655\) −7.60262e12 −1.61390
\(656\) −4.11577e12 −0.867727
\(657\) −4.36510e11 −0.0914009
\(658\) 1.44358e12 0.300209
\(659\) −5.01255e12 −1.03532 −0.517660 0.855586i \(-0.673197\pi\)
−0.517660 + 0.855586i \(0.673197\pi\)
\(660\) −4.79517e12 −0.983685
\(661\) 7.92167e12 1.61402 0.807012 0.590534i \(-0.201083\pi\)
0.807012 + 0.590534i \(0.201083\pi\)
\(662\) −5.70531e11 −0.115457
\(663\) 0 0
\(664\) −1.56335e12 −0.312105
\(665\) 4.94291e12 0.980133
\(666\) −2.26838e11 −0.0446768
\(667\) 1.71556e12 0.335613
\(668\) −1.02421e12 −0.199019
\(669\) −1.36362e12 −0.263194
\(670\) −2.14677e12 −0.411575
\(671\) 6.64201e12 1.26488
\(672\) −4.78177e12 −0.904538
\(673\) −9.72451e11 −0.182726 −0.0913629 0.995818i \(-0.529122\pi\)
−0.0913629 + 0.995818i \(0.529122\pi\)
\(674\) −1.37377e11 −0.0256416
\(675\) −4.29825e11 −0.0796938
\(676\) 3.88878e12 0.716231
\(677\) 2.68897e12 0.491968 0.245984 0.969274i \(-0.420889\pi\)
0.245984 + 0.969274i \(0.420889\pi\)
\(678\) −8.73375e11 −0.158733
\(679\) −9.15196e12 −1.65234
\(680\) 0 0
\(681\) −4.08668e11 −0.0728129
\(682\) 2.19242e12 0.388055
\(683\) −5.44998e12 −0.958300 −0.479150 0.877733i \(-0.659055\pi\)
−0.479150 + 0.877733i \(0.659055\pi\)
\(684\) −5.48546e11 −0.0958209
\(685\) 5.07604e12 0.880882
\(686\) −4.33632e11 −0.0747589
\(687\) −7.28653e12 −1.24800
\(688\) −2.46089e12 −0.418741
\(689\) −5.59377e12 −0.945624
\(690\) 3.81453e11 0.0640649
\(691\) 6.45907e12 1.07775 0.538876 0.842385i \(-0.318849\pi\)
0.538876 + 0.842385i \(0.318849\pi\)
\(692\) 6.59218e12 1.09283
\(693\) 1.58409e12 0.260904
\(694\) 7.97640e9 0.00130524
\(695\) 8.52578e12 1.38613
\(696\) −3.14196e12 −0.507527
\(697\) 0 0
\(698\) −2.59738e11 −0.0414178
\(699\) −8.28476e12 −1.31260
\(700\) 6.67415e11 0.105064
\(701\) −1.69528e12 −0.265161 −0.132580 0.991172i \(-0.542326\pi\)
−0.132580 + 0.991172i \(0.542326\pi\)
\(702\) −8.02294e11 −0.124686
\(703\) −4.81046e12 −0.742827
\(704\) −4.81376e12 −0.738597
\(705\) −5.26086e12 −0.802058
\(706\) −6.49472e11 −0.0983873
\(707\) 1.52164e12 0.229047
\(708\) 1.03271e13 1.54465
\(709\) 8.47386e12 1.25943 0.629714 0.776827i \(-0.283172\pi\)
0.629714 + 0.776827i \(0.283172\pi\)
\(710\) −1.00615e12 −0.148593
\(711\) 2.04870e12 0.300653
\(712\) 4.65471e11 0.0678786
\(713\) 2.87205e12 0.416188
\(714\) 0 0
\(715\) 3.89951e12 0.557998
\(716\) 9.78252e12 1.39105
\(717\) −4.92913e12 −0.696521
\(718\) −1.89060e12 −0.265485
\(719\) −4.90262e12 −0.684145 −0.342072 0.939674i \(-0.611129\pi\)
−0.342072 + 0.939674i \(0.611129\pi\)
\(720\) −9.93709e11 −0.137804
\(721\) −5.79588e12 −0.798749
\(722\) −1.04063e12 −0.142521
\(723\) −9.23040e11 −0.125631
\(724\) −1.28056e13 −1.73212
\(725\) 6.64270e11 0.0892943
\(726\) 3.37335e11 0.0450658
\(727\) 1.95230e12 0.259204 0.129602 0.991566i \(-0.458630\pi\)
0.129602 + 0.991566i \(0.458630\pi\)
\(728\) 2.56719e12 0.338741
\(729\) 8.42368e12 1.10466
\(730\) 1.08842e12 0.141854
\(731\) 0 0
\(732\) −7.73295e12 −0.995509
\(733\) 7.11010e12 0.909720 0.454860 0.890563i \(-0.349689\pi\)
0.454860 + 0.890563i \(0.349689\pi\)
\(734\) 2.16526e12 0.275346
\(735\) 9.09947e12 1.15007
\(736\) 1.48883e12 0.187022
\(737\) −1.45900e13 −1.82159
\(738\) 3.21609e11 0.0399094
\(739\) 1.39531e13 1.72096 0.860479 0.509486i \(-0.170164\pi\)
0.860479 + 0.509486i \(0.170164\pi\)
\(740\) −9.31427e12 −1.14184
\(741\) −2.34473e12 −0.285701
\(742\) 5.66600e12 0.686213
\(743\) −1.59226e13 −1.91674 −0.958371 0.285525i \(-0.907832\pi\)
−0.958371 + 0.285525i \(0.907832\pi\)
\(744\) −5.26003e12 −0.629376
\(745\) 7.31164e11 0.0869584
\(746\) 1.37018e12 0.161977
\(747\) −9.13337e11 −0.107322
\(748\) 0 0
\(749\) 3.60988e12 0.419107
\(750\) −1.82262e12 −0.210339
\(751\) 1.25896e13 1.44421 0.722107 0.691781i \(-0.243174\pi\)
0.722107 + 0.691781i \(0.243174\pi\)
\(752\) −6.15442e12 −0.701790
\(753\) −8.28395e12 −0.938988
\(754\) 1.23990e12 0.139706
\(755\) 7.08301e12 0.793335
\(756\) −1.33825e13 −1.49001
\(757\) 1.73721e13 1.92275 0.961373 0.275249i \(-0.0887602\pi\)
0.961373 + 0.275249i \(0.0887602\pi\)
\(758\) −1.97398e12 −0.217186
\(759\) 2.59245e12 0.283545
\(760\) 2.81860e12 0.306459
\(761\) 1.03599e13 1.11976 0.559882 0.828572i \(-0.310846\pi\)
0.559882 + 0.828572i \(0.310846\pi\)
\(762\) −3.28118e12 −0.352559
\(763\) −6.73347e12 −0.719248
\(764\) −1.15408e12 −0.122550
\(765\) 0 0
\(766\) 3.22728e12 0.338694
\(767\) −8.39819e12 −0.876206
\(768\) 4.20087e12 0.435727
\(769\) 4.12658e11 0.0425522 0.0212761 0.999774i \(-0.493227\pi\)
0.0212761 + 0.999774i \(0.493227\pi\)
\(770\) −3.94986e12 −0.404924
\(771\) −2.26703e12 −0.231053
\(772\) 1.54615e13 1.56666
\(773\) −6.07702e12 −0.612185 −0.306093 0.952002i \(-0.599022\pi\)
−0.306093 + 0.952002i \(0.599022\pi\)
\(774\) 1.92296e11 0.0192591
\(775\) 1.11207e12 0.110732
\(776\) −5.21873e12 −0.516639
\(777\) −1.61734e13 −1.59186
\(778\) 3.13046e12 0.306337
\(779\) 6.82023e12 0.663560
\(780\) −4.53999e12 −0.439167
\(781\) −6.83802e12 −0.657659
\(782\) 0 0
\(783\) −1.33194e13 −1.26636
\(784\) 1.06450e13 1.00629
\(785\) −1.30081e12 −0.122265
\(786\) −3.65297e12 −0.341385
\(787\) 1.63722e12 0.152132 0.0760660 0.997103i \(-0.475764\pi\)
0.0760660 + 0.997103i \(0.475764\pi\)
\(788\) 1.19461e13 1.10372
\(789\) 9.07051e12 0.833269
\(790\) −5.10833e12 −0.466613
\(791\) 1.18471e13 1.07601
\(792\) 9.03300e11 0.0815772
\(793\) 6.28856e12 0.564705
\(794\) 5.09900e11 0.0455295
\(795\) −2.06487e13 −1.83333
\(796\) −5.09991e12 −0.450250
\(797\) 6.48377e12 0.569200 0.284600 0.958646i \(-0.408139\pi\)
0.284600 + 0.958646i \(0.408139\pi\)
\(798\) 2.37501e12 0.207325
\(799\) 0 0
\(800\) 5.76479e11 0.0497598
\(801\) 2.71936e11 0.0233411
\(802\) −2.88781e12 −0.246481
\(803\) 7.39714e12 0.627833
\(804\) 1.69863e13 1.43366
\(805\) −5.17429e12 −0.434280
\(806\) 2.07575e12 0.173247
\(807\) 7.49704e12 0.622241
\(808\) 8.67688e11 0.0716164
\(809\) 1.49241e12 0.122496 0.0612478 0.998123i \(-0.480492\pi\)
0.0612478 + 0.998123i \(0.480492\pi\)
\(810\) −2.47578e12 −0.202083
\(811\) −1.02148e13 −0.829153 −0.414576 0.910015i \(-0.636070\pi\)
−0.414576 + 0.910015i \(0.636070\pi\)
\(812\) 2.06819e13 1.66951
\(813\) −7.27293e12 −0.583851
\(814\) 3.84402e12 0.306885
\(815\) −1.18440e13 −0.940350
\(816\) 0 0
\(817\) 4.07794e12 0.320215
\(818\) −1.69561e12 −0.132415
\(819\) 1.49980e12 0.116481
\(820\) 1.32057e13 1.02000
\(821\) −2.08043e13 −1.59812 −0.799060 0.601251i \(-0.794669\pi\)
−0.799060 + 0.601251i \(0.794669\pi\)
\(822\) 2.43898e12 0.186331
\(823\) −1.92775e13 −1.46471 −0.732354 0.680924i \(-0.761578\pi\)
−0.732354 + 0.680924i \(0.761578\pi\)
\(824\) −3.30499e12 −0.249746
\(825\) 1.00381e12 0.0754409
\(826\) 8.50662e12 0.635839
\(827\) 1.99779e11 0.0148517 0.00742583 0.999972i \(-0.497636\pi\)
0.00742583 + 0.999972i \(0.497636\pi\)
\(828\) 5.74224e11 0.0424566
\(829\) −1.49162e13 −1.09689 −0.548446 0.836186i \(-0.684780\pi\)
−0.548446 + 0.836186i \(0.684780\pi\)
\(830\) 2.27736e12 0.166564
\(831\) −1.56352e13 −1.13736
\(832\) −4.55760e12 −0.329747
\(833\) 0 0
\(834\) 4.09653e12 0.293204
\(835\) 3.07456e12 0.218874
\(836\) 9.29570e12 0.658194
\(837\) −2.22984e13 −1.57039
\(838\) −5.31719e12 −0.372464
\(839\) 1.89640e13 1.32130 0.660649 0.750695i \(-0.270281\pi\)
0.660649 + 0.750695i \(0.270281\pi\)
\(840\) 9.47648e12 0.656735
\(841\) 6.07730e12 0.418918
\(842\) 9.39803e11 0.0644366
\(843\) −1.72626e12 −0.117729
\(844\) −2.20662e13 −1.49688
\(845\) −1.16737e13 −0.787685
\(846\) 4.80912e11 0.0322774
\(847\) −4.57585e12 −0.305489
\(848\) −2.41559e13 −1.60414
\(849\) 1.93703e13 1.27953
\(850\) 0 0
\(851\) 5.03565e12 0.329134
\(852\) 7.96115e12 0.517604
\(853\) −4.00742e12 −0.259176 −0.129588 0.991568i \(-0.541365\pi\)
−0.129588 + 0.991568i \(0.541365\pi\)
\(854\) −6.36976e12 −0.409791
\(855\) 1.64667e12 0.105380
\(856\) 2.05847e12 0.131042
\(857\) −1.02490e13 −0.649033 −0.324517 0.945880i \(-0.605202\pi\)
−0.324517 + 0.945880i \(0.605202\pi\)
\(858\) 1.87367e12 0.118032
\(859\) 9.08859e12 0.569544 0.284772 0.958595i \(-0.408082\pi\)
0.284772 + 0.958595i \(0.408082\pi\)
\(860\) 7.89593e12 0.492221
\(861\) 2.29304e13 1.42200
\(862\) 1.91834e12 0.118343
\(863\) 1.47122e13 0.902878 0.451439 0.892302i \(-0.350911\pi\)
0.451439 + 0.892302i \(0.350911\pi\)
\(864\) −1.15591e13 −0.705688
\(865\) −1.97890e13 −1.20185
\(866\) 3.62678e8 2.19124e−5 0
\(867\) 0 0
\(868\) 3.46241e13 2.07033
\(869\) −3.47175e13 −2.06518
\(870\) 4.57694e12 0.270856
\(871\) −1.38136e13 −0.813250
\(872\) −3.83964e12 −0.224888
\(873\) −3.04887e12 −0.177654
\(874\) −7.39469e11 −0.0428666
\(875\) 2.47232e13 1.42583
\(876\) −8.61211e12 −0.494130
\(877\) 2.05098e12 0.117075 0.0585373 0.998285i \(-0.481356\pi\)
0.0585373 + 0.998285i \(0.481356\pi\)
\(878\) 2.44541e12 0.138876
\(879\) 2.97379e13 1.68020
\(880\) 1.68395e13 0.946578
\(881\) −1.10960e13 −0.620550 −0.310275 0.950647i \(-0.600421\pi\)
−0.310275 + 0.950647i \(0.600421\pi\)
\(882\) −8.31811e11 −0.0462824
\(883\) 1.24270e13 0.687931 0.343965 0.938982i \(-0.388230\pi\)
0.343965 + 0.938982i \(0.388230\pi\)
\(884\) 0 0
\(885\) −3.10009e13 −1.69875
\(886\) 4.12006e12 0.224622
\(887\) −1.86959e13 −1.01412 −0.507061 0.861910i \(-0.669268\pi\)
−0.507061 + 0.861910i \(0.669268\pi\)
\(888\) −9.22255e12 −0.497729
\(889\) 4.45081e13 2.38991
\(890\) −6.78059e11 −0.0362253
\(891\) −1.68260e13 −0.894398
\(892\) 5.11840e12 0.270703
\(893\) 1.01985e13 0.536666
\(894\) 3.51315e11 0.0183941
\(895\) −2.93660e13 −1.52982
\(896\) 2.36549e13 1.22613
\(897\) 2.45449e12 0.126589
\(898\) 2.72724e10 0.00139952
\(899\) 3.44609e13 1.75958
\(900\) 2.22342e11 0.0112961
\(901\) 0 0
\(902\) −5.45002e12 −0.274138
\(903\) 1.37105e13 0.686214
\(904\) 6.75556e12 0.336437
\(905\) 3.84411e13 1.90492
\(906\) 3.40330e12 0.167812
\(907\) 1.01605e13 0.498519 0.249259 0.968437i \(-0.419813\pi\)
0.249259 + 0.968437i \(0.419813\pi\)
\(908\) 1.53395e12 0.0748902
\(909\) 5.06917e11 0.0246263
\(910\) −3.73967e12 −0.180779
\(911\) 4.35827e12 0.209644 0.104822 0.994491i \(-0.466573\pi\)
0.104822 + 0.994491i \(0.466573\pi\)
\(912\) −1.01254e13 −0.484658
\(913\) 1.54775e13 0.737194
\(914\) −3.96030e12 −0.187702
\(915\) 2.32134e13 1.09482
\(916\) 2.73503e13 1.28361
\(917\) 4.95514e13 2.31416
\(918\) 0 0
\(919\) −9.96170e12 −0.460695 −0.230348 0.973108i \(-0.573986\pi\)
−0.230348 + 0.973108i \(0.573986\pi\)
\(920\) −2.95054e12 −0.135787
\(921\) −4.17768e12 −0.191323
\(922\) 4.05378e12 0.184744
\(923\) −6.47414e12 −0.293612
\(924\) 3.12533e13 1.41050
\(925\) 1.94982e12 0.0875704
\(926\) 7.15033e11 0.0319578
\(927\) −1.93083e12 −0.0858786
\(928\) 1.78640e13 0.790701
\(929\) −1.47335e13 −0.648985 −0.324492 0.945888i \(-0.605193\pi\)
−0.324492 + 0.945888i \(0.605193\pi\)
\(930\) 7.66237e12 0.335884
\(931\) −1.76399e13 −0.769523
\(932\) 3.10972e13 1.35005
\(933\) −3.13173e13 −1.35306
\(934\) −6.29649e11 −0.0270731
\(935\) 0 0
\(936\) 8.55231e11 0.0364202
\(937\) −3.24887e13 −1.37691 −0.688453 0.725280i \(-0.741710\pi\)
−0.688453 + 0.725280i \(0.741710\pi\)
\(938\) 1.39919e13 0.590153
\(939\) 1.29535e11 0.00543739
\(940\) 1.97468e13 0.824940
\(941\) −1.89258e13 −0.786868 −0.393434 0.919353i \(-0.628713\pi\)
−0.393434 + 0.919353i \(0.628713\pi\)
\(942\) −6.25026e11 −0.0258624
\(943\) −7.13950e12 −0.294012
\(944\) −3.62664e13 −1.48638
\(945\) 4.01728e13 1.63866
\(946\) −3.25867e12 −0.132291
\(947\) −1.03479e13 −0.418097 −0.209049 0.977905i \(-0.567037\pi\)
−0.209049 + 0.977905i \(0.567037\pi\)
\(948\) 4.04197e13 1.62538
\(949\) 7.00351e12 0.280297
\(950\) −2.86325e11 −0.0114052
\(951\) 2.71890e13 1.07791
\(952\) 0 0
\(953\) −2.52060e13 −0.989888 −0.494944 0.868925i \(-0.664811\pi\)
−0.494944 + 0.868925i \(0.664811\pi\)
\(954\) 1.88756e12 0.0737792
\(955\) 3.46441e12 0.134776
\(956\) 1.85017e13 0.716391
\(957\) 3.11060e13 1.19878
\(958\) −1.42700e12 −0.0547366
\(959\) −3.30839e13 −1.26309
\(960\) −1.68238e13 −0.639299
\(961\) 3.12522e13 1.18202
\(962\) 3.63946e12 0.137009
\(963\) 1.20259e12 0.0450609
\(964\) 3.46466e12 0.129215
\(965\) −4.64137e13 −1.72295
\(966\) −2.48619e12 −0.0918621
\(967\) −2.89363e13 −1.06420 −0.532101 0.846681i \(-0.678597\pi\)
−0.532101 + 0.846681i \(0.678597\pi\)
\(968\) −2.60929e12 −0.0955176
\(969\) 0 0
\(970\) 7.60221e12 0.275719
\(971\) −5.37388e13 −1.94000 −0.969999 0.243110i \(-0.921833\pi\)
−0.969999 + 0.243110i \(0.921833\pi\)
\(972\) −8.30205e12 −0.298323
\(973\) −5.55682e13 −1.98755
\(974\) −2.82233e12 −0.100483
\(975\) 9.50389e11 0.0336807
\(976\) 2.71563e13 0.957956
\(977\) −4.64572e13 −1.63128 −0.815638 0.578562i \(-0.803614\pi\)
−0.815638 + 0.578562i \(0.803614\pi\)
\(978\) −5.69090e12 −0.198910
\(979\) −4.60825e12 −0.160330
\(980\) −3.41552e13 −1.18288
\(981\) −2.24318e12 −0.0773310
\(982\) −1.33416e13 −0.457831
\(983\) 2.41824e13 0.826055 0.413027 0.910719i \(-0.364471\pi\)
0.413027 + 0.910719i \(0.364471\pi\)
\(984\) 1.30757e13 0.444616
\(985\) −3.58608e13 −1.21383
\(986\) 0 0
\(987\) 3.42885e13 1.15006
\(988\) 8.80104e12 0.293851
\(989\) −4.26884e12 −0.141882
\(990\) −1.31585e12 −0.0435360
\(991\) 2.08758e13 0.687563 0.343781 0.939050i \(-0.388292\pi\)
0.343781 + 0.939050i \(0.388292\pi\)
\(992\) 2.99065e13 0.980534
\(993\) −1.35515e13 −0.442300
\(994\) 6.55773e12 0.213066
\(995\) 1.53094e13 0.495169
\(996\) −1.80196e13 −0.580201
\(997\) 1.59134e13 0.510075 0.255038 0.966931i \(-0.417912\pi\)
0.255038 + 0.966931i \(0.417912\pi\)
\(998\) −6.48621e12 −0.206968
\(999\) −3.90963e13 −1.24191
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 289.10.a.g.1.21 36
17.16 even 2 289.10.a.h.1.21 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.21 36 1.1 even 1 trivial
289.10.a.h.1.21 yes 36 17.16 even 2