Properties

Label 289.10.a.g.1.9
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 1.9
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-22.6693 q^{2} -265.602 q^{3} +1.89626 q^{4} -368.101 q^{5} +6021.01 q^{6} +2877.49 q^{7} +11563.7 q^{8} +50861.5 q^{9} +O(q^{10})\) \(q-22.6693 q^{2} -265.602 q^{3} +1.89626 q^{4} -368.101 q^{5} +6021.01 q^{6} +2877.49 q^{7} +11563.7 q^{8} +50861.5 q^{9} +8344.59 q^{10} +63835.2 q^{11} -503.651 q^{12} -149124. q^{13} -65230.7 q^{14} +97768.4 q^{15} -263111. q^{16} -1.15299e6 q^{18} +444434. q^{19} -698.016 q^{20} -764268. q^{21} -1.44710e6 q^{22} +1.56940e6 q^{23} -3.07134e6 q^{24} -1.81763e6 q^{25} +3.38054e6 q^{26} -8.28107e6 q^{27} +5456.48 q^{28} -5.40558e6 q^{29} -2.21634e6 q^{30} -759714. q^{31} +43937.0 q^{32} -1.69548e7 q^{33} -1.05921e6 q^{35} +96446.6 q^{36} -3.93163e6 q^{37} -1.00750e7 q^{38} +3.96077e7 q^{39} -4.25661e6 q^{40} +9.97180e6 q^{41} +1.73254e7 q^{42} +2.04493e7 q^{43} +121048. q^{44} -1.87222e7 q^{45} -3.55771e7 q^{46} +4.76880e7 q^{47} +6.98829e7 q^{48} -3.20736e7 q^{49} +4.12043e7 q^{50} -282778. q^{52} -5.80242e6 q^{53} +1.87726e8 q^{54} -2.34978e7 q^{55} +3.32744e7 q^{56} -1.18043e8 q^{57} +1.22540e8 q^{58} +9.50173e7 q^{59} +185394. q^{60} -1.59704e8 q^{61} +1.72222e7 q^{62} +1.46353e8 q^{63} +1.33717e8 q^{64} +5.48928e7 q^{65} +3.84352e8 q^{66} +8.38127e7 q^{67} -4.16835e8 q^{69} +2.40115e7 q^{70} -3.10856e8 q^{71} +5.88146e8 q^{72} -3.37571e8 q^{73} +8.91273e7 q^{74} +4.82765e8 q^{75} +842764. q^{76} +1.83685e8 q^{77} -8.97878e8 q^{78} +5.51861e7 q^{79} +9.68516e7 q^{80} +1.19836e9 q^{81} -2.26053e8 q^{82} +3.47302e8 q^{83} -1.44925e6 q^{84} -4.63570e8 q^{86} +1.43573e9 q^{87} +7.38171e8 q^{88} -3.74829e8 q^{89} +4.24418e8 q^{90} -4.29104e8 q^{91} +2.97598e6 q^{92} +2.01782e8 q^{93} -1.08105e9 q^{94} -1.63597e8 q^{95} -1.16698e7 q^{96} -1.18045e9 q^{97} +7.27087e8 q^{98} +3.24675e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −22.6693 −1.00185 −0.500925 0.865491i \(-0.667007\pi\)
−0.500925 + 0.865491i \(0.667007\pi\)
\(3\) −265.602 −1.89315 −0.946577 0.322479i \(-0.895484\pi\)
−0.946577 + 0.322479i \(0.895484\pi\)
\(4\) 1.89626 0.00370363
\(5\) −368.101 −0.263392 −0.131696 0.991290i \(-0.542042\pi\)
−0.131696 + 0.991290i \(0.542042\pi\)
\(6\) 6021.01 1.89666
\(7\) 2877.49 0.452974 0.226487 0.974014i \(-0.427276\pi\)
0.226487 + 0.974014i \(0.427276\pi\)
\(8\) 11563.7 0.998140
\(9\) 50861.5 2.58403
\(10\) 8344.59 0.263879
\(11\) 63835.2 1.31460 0.657300 0.753629i \(-0.271699\pi\)
0.657300 + 0.753629i \(0.271699\pi\)
\(12\) −503.651 −0.00701155
\(13\) −149124. −1.44812 −0.724058 0.689740i \(-0.757725\pi\)
−0.724058 + 0.689740i \(0.757725\pi\)
\(14\) −65230.7 −0.453812
\(15\) 97768.4 0.498641
\(16\) −263111. −1.00369
\(17\) 0 0
\(18\) −1.15299e6 −2.58881
\(19\) 444434. 0.782378 0.391189 0.920310i \(-0.372064\pi\)
0.391189 + 0.920310i \(0.372064\pi\)
\(20\) −698.016 −0.000975507 0
\(21\) −764268. −0.857549
\(22\) −1.44710e6 −1.31703
\(23\) 1.56940e6 1.16938 0.584692 0.811255i \(-0.301215\pi\)
0.584692 + 0.811255i \(0.301215\pi\)
\(24\) −3.07134e6 −1.88963
\(25\) −1.81763e6 −0.930625
\(26\) 3.38054e6 1.45079
\(27\) −8.28107e6 −2.99881
\(28\) 5456.48 0.00167765
\(29\) −5.40558e6 −1.41922 −0.709612 0.704593i \(-0.751130\pi\)
−0.709612 + 0.704593i \(0.751130\pi\)
\(30\) −2.21634e6 −0.499564
\(31\) −759714. −0.147748 −0.0738742 0.997268i \(-0.523536\pi\)
−0.0738742 + 0.997268i \(0.523536\pi\)
\(32\) 43937.0 0.00740723
\(33\) −1.69548e7 −2.48874
\(34\) 0 0
\(35\) −1.05921e6 −0.119310
\(36\) 96446.6 0.00957031
\(37\) −3.93163e6 −0.344878 −0.172439 0.985020i \(-0.555165\pi\)
−0.172439 + 0.985020i \(0.555165\pi\)
\(38\) −1.00750e7 −0.783825
\(39\) 3.96077e7 2.74150
\(40\) −4.25661e6 −0.262902
\(41\) 9.97180e6 0.551120 0.275560 0.961284i \(-0.411137\pi\)
0.275560 + 0.961284i \(0.411137\pi\)
\(42\) 1.73254e7 0.859135
\(43\) 2.04493e7 0.912157 0.456079 0.889939i \(-0.349254\pi\)
0.456079 + 0.889939i \(0.349254\pi\)
\(44\) 121048. 0.00486880
\(45\) −1.87222e7 −0.680612
\(46\) −3.55771e7 −1.17155
\(47\) 4.76880e7 1.42551 0.712753 0.701416i \(-0.247448\pi\)
0.712753 + 0.701416i \(0.247448\pi\)
\(48\) 6.98829e7 1.90014
\(49\) −3.20736e7 −0.794815
\(50\) 4.12043e7 0.932347
\(51\) 0 0
\(52\) −282778. −0.00536329
\(53\) −5.80242e6 −0.101011 −0.0505054 0.998724i \(-0.516083\pi\)
−0.0505054 + 0.998724i \(0.516083\pi\)
\(54\) 1.87726e8 3.00436
\(55\) −2.34978e7 −0.346255
\(56\) 3.32744e7 0.452131
\(57\) −1.18043e8 −1.48116
\(58\) 1.22540e8 1.42185
\(59\) 9.50173e7 1.02087 0.510433 0.859918i \(-0.329485\pi\)
0.510433 + 0.859918i \(0.329485\pi\)
\(60\) 185394. 0.00184678
\(61\) −1.59704e8 −1.47683 −0.738417 0.674344i \(-0.764426\pi\)
−0.738417 + 0.674344i \(0.764426\pi\)
\(62\) 1.72222e7 0.148022
\(63\) 1.46353e8 1.17050
\(64\) 1.33717e8 0.996269
\(65\) 5.48928e7 0.381422
\(66\) 3.84352e8 2.49334
\(67\) 8.38127e7 0.508128 0.254064 0.967187i \(-0.418233\pi\)
0.254064 + 0.967187i \(0.418233\pi\)
\(68\) 0 0
\(69\) −4.16835e8 −2.21382
\(70\) 2.40115e7 0.119530
\(71\) −3.10856e8 −1.45177 −0.725883 0.687818i \(-0.758569\pi\)
−0.725883 + 0.687818i \(0.758569\pi\)
\(72\) 5.88146e8 2.57922
\(73\) −3.37571e8 −1.39127 −0.695636 0.718394i \(-0.744877\pi\)
−0.695636 + 0.718394i \(0.744877\pi\)
\(74\) 8.91273e7 0.345516
\(75\) 4.82765e8 1.76182
\(76\) 842764. 0.00289764
\(77\) 1.83685e8 0.595479
\(78\) −8.97878e8 −2.74658
\(79\) 5.51861e7 0.159407 0.0797035 0.996819i \(-0.474603\pi\)
0.0797035 + 0.996819i \(0.474603\pi\)
\(80\) 9.68516e7 0.264364
\(81\) 1.19836e9 3.09318
\(82\) −2.26053e8 −0.552139
\(83\) 3.47302e8 0.803259 0.401630 0.915802i \(-0.368444\pi\)
0.401630 + 0.915802i \(0.368444\pi\)
\(84\) −1.44925e6 −0.00317605
\(85\) 0 0
\(86\) −4.63570e8 −0.913845
\(87\) 1.43573e9 2.68681
\(88\) 7.38171e8 1.31215
\(89\) −3.74829e8 −0.633254 −0.316627 0.948550i \(-0.602550\pi\)
−0.316627 + 0.948550i \(0.602550\pi\)
\(90\) 4.24418e8 0.681872
\(91\) −4.29104e8 −0.655958
\(92\) 2.97598e6 0.00433097
\(93\) 2.01782e8 0.279710
\(94\) −1.08105e9 −1.42814
\(95\) −1.63597e8 −0.206072
\(96\) −1.16698e7 −0.0140230
\(97\) −1.18045e9 −1.35386 −0.676930 0.736048i \(-0.736690\pi\)
−0.676930 + 0.736048i \(0.736690\pi\)
\(98\) 7.27087e8 0.796285
\(99\) 3.24675e9 3.39696
\(100\) −3.44669e6 −0.00344669
\(101\) 8.07593e8 0.772229 0.386115 0.922451i \(-0.373817\pi\)
0.386115 + 0.922451i \(0.373817\pi\)
\(102\) 0 0
\(103\) −6.25799e8 −0.547857 −0.273929 0.961750i \(-0.588323\pi\)
−0.273929 + 0.961750i \(0.588323\pi\)
\(104\) −1.72443e9 −1.44542
\(105\) 2.81328e8 0.225871
\(106\) 1.31537e8 0.101198
\(107\) 2.57640e9 1.90015 0.950073 0.312027i \(-0.101008\pi\)
0.950073 + 0.312027i \(0.101008\pi\)
\(108\) −1.57031e7 −0.0111065
\(109\) 4.19046e8 0.284343 0.142171 0.989842i \(-0.454592\pi\)
0.142171 + 0.989842i \(0.454592\pi\)
\(110\) 5.32679e8 0.346895
\(111\) 1.04425e9 0.652907
\(112\) −7.57101e8 −0.454645
\(113\) 1.22248e9 0.705326 0.352663 0.935750i \(-0.385276\pi\)
0.352663 + 0.935750i \(0.385276\pi\)
\(114\) 2.67594e9 1.48390
\(115\) −5.77696e8 −0.308006
\(116\) −1.02504e7 −0.00525629
\(117\) −7.58468e9 −3.74197
\(118\) −2.15397e9 −1.02275
\(119\) 0 0
\(120\) 1.13056e9 0.497713
\(121\) 1.71699e9 0.728171
\(122\) 3.62038e9 1.47957
\(123\) −2.64853e9 −1.04335
\(124\) −1.44062e6 −0.000547206 0
\(125\) 1.38802e9 0.508511
\(126\) −3.31773e9 −1.17266
\(127\) −3.50661e9 −1.19611 −0.598055 0.801455i \(-0.704059\pi\)
−0.598055 + 0.801455i \(0.704059\pi\)
\(128\) −3.05376e9 −1.00552
\(129\) −5.43137e9 −1.72685
\(130\) −1.24438e9 −0.382127
\(131\) 1.25792e9 0.373193 0.186597 0.982437i \(-0.440254\pi\)
0.186597 + 0.982437i \(0.440254\pi\)
\(132\) −3.21507e7 −0.00921738
\(133\) 1.27886e9 0.354396
\(134\) −1.89997e9 −0.509068
\(135\) 3.04827e9 0.789863
\(136\) 0 0
\(137\) 6.74406e9 1.63561 0.817804 0.575497i \(-0.195191\pi\)
0.817804 + 0.575497i \(0.195191\pi\)
\(138\) 9.44934e9 2.21792
\(139\) −8.02375e9 −1.82310 −0.911551 0.411188i \(-0.865114\pi\)
−0.911551 + 0.411188i \(0.865114\pi\)
\(140\) −2.00854e6 −0.000441879 0
\(141\) −1.26660e10 −2.69870
\(142\) 7.04689e9 1.45445
\(143\) −9.51938e9 −1.90369
\(144\) −1.33822e10 −2.59357
\(145\) 1.98980e9 0.373812
\(146\) 7.65249e9 1.39385
\(147\) 8.51883e9 1.50471
\(148\) −7.45540e6 −0.00127730
\(149\) 9.84116e8 0.163572 0.0817859 0.996650i \(-0.473938\pi\)
0.0817859 + 0.996650i \(0.473938\pi\)
\(150\) −1.09439e10 −1.76508
\(151\) 5.81240e8 0.0909827 0.0454914 0.998965i \(-0.485515\pi\)
0.0454914 + 0.998965i \(0.485515\pi\)
\(152\) 5.13930e9 0.780922
\(153\) 0 0
\(154\) −4.16401e9 −0.596580
\(155\) 2.79652e8 0.0389157
\(156\) 7.51065e7 0.0101535
\(157\) 7.86711e9 1.03340 0.516698 0.856168i \(-0.327161\pi\)
0.516698 + 0.856168i \(0.327161\pi\)
\(158\) −1.25103e9 −0.159702
\(159\) 1.54114e9 0.191229
\(160\) −1.61733e7 −0.00195100
\(161\) 4.51592e9 0.529700
\(162\) −2.71660e10 −3.09891
\(163\) 1.00543e10 1.11560 0.557798 0.829976i \(-0.311646\pi\)
0.557798 + 0.829976i \(0.311646\pi\)
\(164\) 1.89091e7 0.00204115
\(165\) 6.24107e9 0.655513
\(166\) −7.87308e9 −0.804745
\(167\) 3.17548e9 0.315926 0.157963 0.987445i \(-0.449507\pi\)
0.157963 + 0.987445i \(0.449507\pi\)
\(168\) −8.83775e9 −0.855953
\(169\) 1.16335e10 1.09704
\(170\) 0 0
\(171\) 2.26046e10 2.02169
\(172\) 3.87772e7 0.00337830
\(173\) 5.55102e9 0.471157 0.235579 0.971855i \(-0.424302\pi\)
0.235579 + 0.971855i \(0.424302\pi\)
\(174\) −3.25470e10 −2.69178
\(175\) −5.23020e9 −0.421548
\(176\) −1.67958e10 −1.31945
\(177\) −2.52368e10 −1.93266
\(178\) 8.49710e9 0.634426
\(179\) −6.84671e9 −0.498475 −0.249237 0.968442i \(-0.580180\pi\)
−0.249237 + 0.968442i \(0.580180\pi\)
\(180\) −3.55021e7 −0.00252074
\(181\) −1.81450e10 −1.25662 −0.628310 0.777963i \(-0.716253\pi\)
−0.628310 + 0.777963i \(0.716253\pi\)
\(182\) 9.72747e9 0.657171
\(183\) 4.24177e10 2.79587
\(184\) 1.81480e10 1.16721
\(185\) 1.44724e9 0.0908380
\(186\) −4.57425e9 −0.280228
\(187\) 0 0
\(188\) 9.04289e7 0.00527955
\(189\) −2.38287e10 −1.35838
\(190\) 3.70862e9 0.206453
\(191\) −2.55856e10 −1.39106 −0.695530 0.718497i \(-0.744830\pi\)
−0.695530 + 0.718497i \(0.744830\pi\)
\(192\) −3.55155e10 −1.88609
\(193\) 6.73140e9 0.349219 0.174609 0.984638i \(-0.444134\pi\)
0.174609 + 0.984638i \(0.444134\pi\)
\(194\) 2.67599e10 1.35636
\(195\) −1.45796e10 −0.722090
\(196\) −6.08200e7 −0.00294370
\(197\) −8.13977e9 −0.385047 −0.192524 0.981292i \(-0.561667\pi\)
−0.192524 + 0.981292i \(0.561667\pi\)
\(198\) −7.36016e10 −3.40325
\(199\) −2.96922e10 −1.34216 −0.671079 0.741386i \(-0.734169\pi\)
−0.671079 + 0.741386i \(0.734169\pi\)
\(200\) −2.10185e10 −0.928893
\(201\) −2.22608e10 −0.961965
\(202\) −1.83075e10 −0.773658
\(203\) −1.55545e10 −0.642871
\(204\) 0 0
\(205\) −3.67063e9 −0.145160
\(206\) 1.41864e10 0.548871
\(207\) 7.98218e10 3.02172
\(208\) 3.92363e10 1.45346
\(209\) 2.83706e10 1.02851
\(210\) −6.37750e9 −0.226289
\(211\) −1.10644e10 −0.384288 −0.192144 0.981367i \(-0.561544\pi\)
−0.192144 + 0.981367i \(0.561544\pi\)
\(212\) −1.10029e7 −0.000374107 0
\(213\) 8.25640e10 2.74842
\(214\) −5.84052e10 −1.90366
\(215\) −7.52740e9 −0.240255
\(216\) −9.57596e10 −2.99323
\(217\) −2.18607e9 −0.0669261
\(218\) −9.49947e9 −0.284869
\(219\) 8.96595e10 2.63389
\(220\) −4.45580e7 −0.00128240
\(221\) 0 0
\(222\) −2.36724e10 −0.654115
\(223\) 1.25174e10 0.338956 0.169478 0.985534i \(-0.445792\pi\)
0.169478 + 0.985534i \(0.445792\pi\)
\(224\) 1.26428e8 0.00335528
\(225\) −9.24472e10 −2.40476
\(226\) −2.77128e10 −0.706631
\(227\) 2.61220e10 0.652966 0.326483 0.945203i \(-0.394136\pi\)
0.326483 + 0.945203i \(0.394136\pi\)
\(228\) −2.23840e8 −0.00548568
\(229\) −7.37974e9 −0.177330 −0.0886649 0.996062i \(-0.528260\pi\)
−0.0886649 + 0.996062i \(0.528260\pi\)
\(230\) 1.30960e10 0.308576
\(231\) −4.87872e10 −1.12733
\(232\) −6.25084e10 −1.41658
\(233\) 1.54320e10 0.343021 0.171510 0.985182i \(-0.445135\pi\)
0.171510 + 0.985182i \(0.445135\pi\)
\(234\) 1.71939e11 3.74890
\(235\) −1.75540e10 −0.375466
\(236\) 1.80178e8 0.00378091
\(237\) −1.46575e10 −0.301782
\(238\) 0 0
\(239\) 2.77534e10 0.550205 0.275103 0.961415i \(-0.411288\pi\)
0.275103 + 0.961415i \(0.411288\pi\)
\(240\) −2.57240e10 −0.500481
\(241\) 2.70806e10 0.517109 0.258554 0.965997i \(-0.416754\pi\)
0.258554 + 0.965997i \(0.416754\pi\)
\(242\) −3.89229e10 −0.729518
\(243\) −1.55291e11 −2.85706
\(244\) −3.02841e8 −0.00546966
\(245\) 1.18063e10 0.209348
\(246\) 6.00403e10 1.04528
\(247\) −6.62759e10 −1.13297
\(248\) −8.78510e9 −0.147474
\(249\) −9.22441e10 −1.52069
\(250\) −3.14654e10 −0.509451
\(251\) 2.29993e10 0.365748 0.182874 0.983136i \(-0.441460\pi\)
0.182874 + 0.983136i \(0.441460\pi\)
\(252\) 2.77524e8 0.00433510
\(253\) 1.00183e11 1.53727
\(254\) 7.94924e10 1.19832
\(255\) 0 0
\(256\) 7.63525e8 0.0111108
\(257\) 1.95178e10 0.279082 0.139541 0.990216i \(-0.455437\pi\)
0.139541 + 0.990216i \(0.455437\pi\)
\(258\) 1.23125e11 1.73005
\(259\) −1.13132e10 −0.156221
\(260\) 1.04091e8 0.00141265
\(261\) −2.74935e11 −3.66732
\(262\) −2.85162e10 −0.373884
\(263\) 1.09688e11 1.41370 0.706849 0.707365i \(-0.250116\pi\)
0.706849 + 0.707365i \(0.250116\pi\)
\(264\) −1.96060e11 −2.48411
\(265\) 2.13588e9 0.0266054
\(266\) −2.89907e10 −0.355052
\(267\) 9.95553e10 1.19885
\(268\) 1.58931e8 0.00188192
\(269\) −5.43556e10 −0.632935 −0.316468 0.948603i \(-0.602497\pi\)
−0.316468 + 0.948603i \(0.602497\pi\)
\(270\) −6.91021e10 −0.791324
\(271\) 8.19304e10 0.922748 0.461374 0.887206i \(-0.347357\pi\)
0.461374 + 0.887206i \(0.347357\pi\)
\(272\) 0 0
\(273\) 1.13971e11 1.24183
\(274\) −1.52883e11 −1.63863
\(275\) −1.16029e11 −1.22340
\(276\) −7.90428e8 −0.00819919
\(277\) 7.10833e10 0.725452 0.362726 0.931896i \(-0.381846\pi\)
0.362726 + 0.931896i \(0.381846\pi\)
\(278\) 1.81893e11 1.82647
\(279\) −3.86402e10 −0.381786
\(280\) −1.22483e10 −0.119088
\(281\) 6.64689e10 0.635975 0.317988 0.948095i \(-0.396993\pi\)
0.317988 + 0.948095i \(0.396993\pi\)
\(282\) 2.87130e11 2.70369
\(283\) 6.72043e10 0.622813 0.311407 0.950277i \(-0.399200\pi\)
0.311407 + 0.950277i \(0.399200\pi\)
\(284\) −5.89464e8 −0.00537681
\(285\) 4.34517e10 0.390126
\(286\) 2.15797e11 1.90721
\(287\) 2.86938e10 0.249643
\(288\) 2.23470e9 0.0191405
\(289\) 0 0
\(290\) −4.51073e10 −0.374503
\(291\) 3.13529e11 2.56306
\(292\) −6.40123e8 −0.00515276
\(293\) −9.43640e10 −0.748001 −0.374000 0.927429i \(-0.622014\pi\)
−0.374000 + 0.927429i \(0.622014\pi\)
\(294\) −1.93116e11 −1.50749
\(295\) −3.49760e10 −0.268888
\(296\) −4.54642e10 −0.344236
\(297\) −5.28624e11 −3.94224
\(298\) −2.23092e10 −0.163874
\(299\) −2.34035e11 −1.69340
\(300\) 9.15449e8 0.00652512
\(301\) 5.88426e10 0.413183
\(302\) −1.31763e10 −0.0911511
\(303\) −2.14498e11 −1.46195
\(304\) −1.16936e11 −0.785265
\(305\) 5.87873e10 0.388986
\(306\) 0 0
\(307\) 1.72103e11 1.10577 0.552886 0.833257i \(-0.313526\pi\)
0.552886 + 0.833257i \(0.313526\pi\)
\(308\) 3.48315e8 0.00220544
\(309\) 1.66214e11 1.03718
\(310\) −6.33951e9 −0.0389877
\(311\) −9.33037e10 −0.565558 −0.282779 0.959185i \(-0.591256\pi\)
−0.282779 + 0.959185i \(0.591256\pi\)
\(312\) 4.58011e11 2.73640
\(313\) −2.05133e11 −1.20805 −0.604027 0.796964i \(-0.706438\pi\)
−0.604027 + 0.796964i \(0.706438\pi\)
\(314\) −1.78342e11 −1.03531
\(315\) −5.38729e10 −0.308299
\(316\) 1.04647e8 0.000590386 0
\(317\) −7.07072e10 −0.393276 −0.196638 0.980476i \(-0.563002\pi\)
−0.196638 + 0.980476i \(0.563002\pi\)
\(318\) −3.49364e10 −0.191583
\(319\) −3.45066e11 −1.86571
\(320\) −4.92214e10 −0.262409
\(321\) −6.84298e11 −3.59727
\(322\) −1.02373e11 −0.530680
\(323\) 0 0
\(324\) 2.27241e9 0.0114560
\(325\) 2.71052e11 1.34765
\(326\) −2.27924e11 −1.11766
\(327\) −1.11300e11 −0.538305
\(328\) 1.15311e11 0.550095
\(329\) 1.37222e11 0.645716
\(330\) −1.41481e11 −0.656726
\(331\) 2.55639e11 1.17058 0.585289 0.810825i \(-0.300981\pi\)
0.585289 + 0.810825i \(0.300981\pi\)
\(332\) 6.58575e8 0.00297498
\(333\) −1.99969e11 −0.891175
\(334\) −7.19858e10 −0.316510
\(335\) −3.08516e10 −0.133837
\(336\) 2.01087e11 0.860713
\(337\) 6.33659e10 0.267622 0.133811 0.991007i \(-0.457279\pi\)
0.133811 + 0.991007i \(0.457279\pi\)
\(338\) −2.63724e11 −1.09907
\(339\) −3.24694e11 −1.33529
\(340\) 0 0
\(341\) −4.84966e10 −0.194230
\(342\) −5.12430e11 −2.02543
\(343\) −2.08409e11 −0.813004
\(344\) 2.36469e11 0.910460
\(345\) 1.53437e11 0.583103
\(346\) −1.25838e11 −0.472029
\(347\) −3.16301e11 −1.17116 −0.585582 0.810613i \(-0.699134\pi\)
−0.585582 + 0.810613i \(0.699134\pi\)
\(348\) 2.72252e9 0.00995096
\(349\) 3.49570e11 1.26131 0.630653 0.776065i \(-0.282787\pi\)
0.630653 + 0.776065i \(0.282787\pi\)
\(350\) 1.18565e11 0.422328
\(351\) 1.23491e12 4.34263
\(352\) 2.80473e9 0.00973754
\(353\) −4.06731e11 −1.39419 −0.697093 0.716980i \(-0.745524\pi\)
−0.697093 + 0.716980i \(0.745524\pi\)
\(354\) 5.72100e11 1.93623
\(355\) 1.14427e11 0.382383
\(356\) −7.10773e8 −0.00234534
\(357\) 0 0
\(358\) 1.55210e11 0.499397
\(359\) 1.97113e11 0.626311 0.313156 0.949702i \(-0.398614\pi\)
0.313156 + 0.949702i \(0.398614\pi\)
\(360\) −2.16497e11 −0.679346
\(361\) −1.25166e11 −0.387885
\(362\) 4.11335e11 1.25894
\(363\) −4.56036e11 −1.37854
\(364\) −8.13693e8 −0.00242943
\(365\) 1.24260e11 0.366450
\(366\) −9.61580e11 −2.80105
\(367\) −5.26961e10 −0.151629 −0.0758143 0.997122i \(-0.524156\pi\)
−0.0758143 + 0.997122i \(0.524156\pi\)
\(368\) −4.12926e11 −1.17370
\(369\) 5.07180e11 1.42411
\(370\) −3.28079e10 −0.0910060
\(371\) −1.66964e10 −0.0457553
\(372\) 3.82631e8 0.00103595
\(373\) 5.23122e11 1.39931 0.699655 0.714481i \(-0.253337\pi\)
0.699655 + 0.714481i \(0.253337\pi\)
\(374\) 0 0
\(375\) −3.68661e11 −0.962689
\(376\) 5.51449e11 1.42285
\(377\) 8.06102e11 2.05520
\(378\) 5.40179e11 1.36090
\(379\) 1.64935e11 0.410616 0.205308 0.978697i \(-0.434180\pi\)
0.205308 + 0.978697i \(0.434180\pi\)
\(380\) −3.10222e8 −0.000763215 0
\(381\) 9.31363e11 2.26442
\(382\) 5.80008e11 1.39363
\(383\) −2.35006e11 −0.558064 −0.279032 0.960282i \(-0.590013\pi\)
−0.279032 + 0.960282i \(0.590013\pi\)
\(384\) 8.11086e11 1.90360
\(385\) −6.76148e10 −0.156844
\(386\) −1.52596e11 −0.349865
\(387\) 1.04008e12 2.35704
\(388\) −2.23843e9 −0.00501420
\(389\) 6.18805e11 1.37019 0.685095 0.728454i \(-0.259761\pi\)
0.685095 + 0.728454i \(0.259761\pi\)
\(390\) 3.30510e11 0.723426
\(391\) 0 0
\(392\) −3.70890e11 −0.793336
\(393\) −3.34107e11 −0.706512
\(394\) 1.84523e11 0.385760
\(395\) −2.03141e10 −0.0419865
\(396\) 6.15669e9 0.0125811
\(397\) 6.88154e11 1.39036 0.695182 0.718834i \(-0.255324\pi\)
0.695182 + 0.718834i \(0.255324\pi\)
\(398\) 6.73101e11 1.34464
\(399\) −3.39667e11 −0.670927
\(400\) 4.78238e11 0.934059
\(401\) −5.46201e11 −1.05488 −0.527439 0.849593i \(-0.676848\pi\)
−0.527439 + 0.849593i \(0.676848\pi\)
\(402\) 5.04637e11 0.963744
\(403\) 1.13292e11 0.213957
\(404\) 1.53141e9 0.00286006
\(405\) −4.41119e11 −0.814719
\(406\) 3.52609e11 0.644060
\(407\) −2.50977e11 −0.453376
\(408\) 0 0
\(409\) 3.45616e11 0.610715 0.305358 0.952238i \(-0.401224\pi\)
0.305358 + 0.952238i \(0.401224\pi\)
\(410\) 8.32105e10 0.145429
\(411\) −1.79124e12 −3.09646
\(412\) −1.18668e9 −0.00202906
\(413\) 2.73411e11 0.462425
\(414\) −1.80950e12 −3.02731
\(415\) −1.27842e11 −0.211572
\(416\) −6.55208e9 −0.0107265
\(417\) 2.13112e12 3.45141
\(418\) −6.43140e11 −1.03042
\(419\) −2.32307e11 −0.368212 −0.184106 0.982906i \(-0.558939\pi\)
−0.184106 + 0.982906i \(0.558939\pi\)
\(420\) 5.33471e8 0.000836545 0
\(421\) 2.50534e10 0.0388684 0.0194342 0.999811i \(-0.493814\pi\)
0.0194342 + 0.999811i \(0.493814\pi\)
\(422\) 2.50822e11 0.384999
\(423\) 2.42548e12 3.68355
\(424\) −6.70974e10 −0.100823
\(425\) 0 0
\(426\) −1.87167e12 −2.75350
\(427\) −4.59547e11 −0.668967
\(428\) 4.88554e9 0.00703745
\(429\) 2.52837e12 3.60398
\(430\) 1.70641e11 0.240699
\(431\) 6.39146e11 0.892180 0.446090 0.894988i \(-0.352816\pi\)
0.446090 + 0.894988i \(0.352816\pi\)
\(432\) 2.17884e12 3.00988
\(433\) −5.80057e11 −0.793003 −0.396502 0.918034i \(-0.629776\pi\)
−0.396502 + 0.918034i \(0.629776\pi\)
\(434\) 4.95567e10 0.0670499
\(435\) −5.28495e11 −0.707683
\(436\) 7.94621e8 0.00105310
\(437\) 6.97493e11 0.914900
\(438\) −2.03252e12 −2.63877
\(439\) 3.04632e11 0.391458 0.195729 0.980658i \(-0.437293\pi\)
0.195729 + 0.980658i \(0.437293\pi\)
\(440\) −2.71721e11 −0.345610
\(441\) −1.63131e12 −2.05383
\(442\) 0 0
\(443\) 3.18193e10 0.0392530 0.0196265 0.999807i \(-0.493752\pi\)
0.0196265 + 0.999807i \(0.493752\pi\)
\(444\) 1.98017e9 0.00241813
\(445\) 1.37975e11 0.166794
\(446\) −2.83761e11 −0.339583
\(447\) −2.61383e11 −0.309666
\(448\) 3.84769e11 0.451284
\(449\) −5.35918e11 −0.622286 −0.311143 0.950363i \(-0.600712\pi\)
−0.311143 + 0.950363i \(0.600712\pi\)
\(450\) 2.09571e12 2.40921
\(451\) 6.36552e11 0.724502
\(452\) 2.31815e9 0.00261227
\(453\) −1.54378e11 −0.172244
\(454\) −5.92168e11 −0.654174
\(455\) 1.57954e11 0.172774
\(456\) −1.36501e12 −1.47841
\(457\) −9.04468e11 −0.969997 −0.484998 0.874515i \(-0.661180\pi\)
−0.484998 + 0.874515i \(0.661180\pi\)
\(458\) 1.67293e11 0.177658
\(459\) 0 0
\(460\) −1.09546e9 −0.00114074
\(461\) −1.82659e12 −1.88359 −0.941795 0.336187i \(-0.890863\pi\)
−0.941795 + 0.336187i \(0.890863\pi\)
\(462\) 1.10597e12 1.12942
\(463\) −1.31941e12 −1.33434 −0.667170 0.744906i \(-0.732494\pi\)
−0.667170 + 0.744906i \(0.732494\pi\)
\(464\) 1.42227e12 1.42446
\(465\) −7.42761e10 −0.0736734
\(466\) −3.49832e11 −0.343656
\(467\) 1.68454e12 1.63891 0.819456 0.573142i \(-0.194276\pi\)
0.819456 + 0.573142i \(0.194276\pi\)
\(468\) −1.43825e10 −0.0138589
\(469\) 2.41170e11 0.230169
\(470\) 3.97937e11 0.376161
\(471\) −2.08952e12 −1.95638
\(472\) 1.09875e12 1.01897
\(473\) 1.30538e12 1.19912
\(474\) 3.32276e11 0.302340
\(475\) −8.07816e11 −0.728100
\(476\) 0 0
\(477\) −2.95120e11 −0.261015
\(478\) −6.29148e11 −0.551223
\(479\) −2.54147e11 −0.220585 −0.110292 0.993899i \(-0.535179\pi\)
−0.110292 + 0.993899i \(0.535179\pi\)
\(480\) 4.29566e9 0.00369355
\(481\) 5.86302e11 0.499423
\(482\) −6.13898e11 −0.518065
\(483\) −1.19944e12 −1.00280
\(484\) 3.25586e9 0.00269688
\(485\) 4.34524e11 0.356595
\(486\) 3.52034e12 2.86234
\(487\) −7.07971e11 −0.570342 −0.285171 0.958477i \(-0.592050\pi\)
−0.285171 + 0.958477i \(0.592050\pi\)
\(488\) −1.84677e12 −1.47409
\(489\) −2.67044e12 −2.11200
\(490\) −2.67641e11 −0.209735
\(491\) −8.71726e11 −0.676882 −0.338441 0.940988i \(-0.609900\pi\)
−0.338441 + 0.940988i \(0.609900\pi\)
\(492\) −5.02230e9 −0.00386420
\(493\) 0 0
\(494\) 1.50243e12 1.13507
\(495\) −1.19513e12 −0.894732
\(496\) 1.99889e11 0.148294
\(497\) −8.94486e11 −0.657612
\(498\) 2.09111e12 1.52351
\(499\) 9.44233e11 0.681752 0.340876 0.940108i \(-0.389276\pi\)
0.340876 + 0.940108i \(0.389276\pi\)
\(500\) 2.63204e9 0.00188334
\(501\) −8.43414e11 −0.598096
\(502\) −5.21377e11 −0.366425
\(503\) 1.32525e12 0.923082 0.461541 0.887119i \(-0.347297\pi\)
0.461541 + 0.887119i \(0.347297\pi\)
\(504\) 1.69239e12 1.16832
\(505\) −2.97276e11 −0.203399
\(506\) −2.27107e12 −1.54012
\(507\) −3.08989e12 −2.07686
\(508\) −6.64945e9 −0.00442995
\(509\) 1.27464e11 0.0841703 0.0420851 0.999114i \(-0.486600\pi\)
0.0420851 + 0.999114i \(0.486600\pi\)
\(510\) 0 0
\(511\) −9.71357e11 −0.630210
\(512\) 1.54622e12 0.994388
\(513\) −3.68039e12 −2.34620
\(514\) −4.42455e11 −0.279599
\(515\) 2.30357e11 0.144301
\(516\) −1.02993e10 −0.00639564
\(517\) 3.04417e12 1.87397
\(518\) 2.56463e11 0.156510
\(519\) −1.47436e12 −0.891973
\(520\) 6.34763e11 0.380712
\(521\) −3.80565e11 −0.226287 −0.113143 0.993579i \(-0.536092\pi\)
−0.113143 + 0.993579i \(0.536092\pi\)
\(522\) 6.23259e12 3.67410
\(523\) −2.07388e12 −1.21207 −0.606033 0.795439i \(-0.707240\pi\)
−0.606033 + 0.795439i \(0.707240\pi\)
\(524\) 2.38535e9 0.00138217
\(525\) 1.38915e12 0.798056
\(526\) −2.48654e12 −1.41631
\(527\) 0 0
\(528\) 4.46099e12 2.49792
\(529\) 6.61850e11 0.367459
\(530\) −4.84189e10 −0.0266547
\(531\) 4.83272e12 2.63795
\(532\) 2.42505e9 0.00131256
\(533\) −1.48704e12 −0.798085
\(534\) −2.25685e12 −1.20107
\(535\) −9.48378e11 −0.500483
\(536\) 9.69184e11 0.507183
\(537\) 1.81850e12 0.943689
\(538\) 1.23220e12 0.634106
\(539\) −2.04743e12 −1.04486
\(540\) 5.78032e9 0.00292536
\(541\) −1.51143e11 −0.0758580 −0.0379290 0.999280i \(-0.512076\pi\)
−0.0379290 + 0.999280i \(0.512076\pi\)
\(542\) −1.85730e12 −0.924455
\(543\) 4.81935e12 2.37897
\(544\) 0 0
\(545\) −1.54251e11 −0.0748936
\(546\) −2.58364e12 −1.24413
\(547\) −3.07902e12 −1.47051 −0.735257 0.677788i \(-0.762939\pi\)
−0.735257 + 0.677788i \(0.762939\pi\)
\(548\) 1.27885e10 0.00605769
\(549\) −8.12279e12 −3.81619
\(550\) 2.63029e12 1.22566
\(551\) −2.40242e12 −1.11037
\(552\) −4.82015e12 −2.20970
\(553\) 1.58797e11 0.0722072
\(554\) −1.61141e12 −0.726795
\(555\) −3.84390e11 −0.171970
\(556\) −1.52151e10 −0.00675210
\(557\) 1.33787e12 0.588933 0.294467 0.955662i \(-0.404858\pi\)
0.294467 + 0.955662i \(0.404858\pi\)
\(558\) 8.75945e11 0.382493
\(559\) −3.04948e12 −1.32091
\(560\) 2.78690e11 0.119750
\(561\) 0 0
\(562\) −1.50680e12 −0.637152
\(563\) 1.95942e12 0.821940 0.410970 0.911649i \(-0.365190\pi\)
0.410970 + 0.911649i \(0.365190\pi\)
\(564\) −2.40181e10 −0.00999500
\(565\) −4.49997e11 −0.185777
\(566\) −1.52347e12 −0.623966
\(567\) 3.44828e12 1.40113
\(568\) −3.59464e12 −1.44907
\(569\) −3.13617e12 −1.25428 −0.627139 0.778907i \(-0.715774\pi\)
−0.627139 + 0.778907i \(0.715774\pi\)
\(570\) −9.85018e11 −0.390847
\(571\) −8.05728e11 −0.317195 −0.158597 0.987343i \(-0.550697\pi\)
−0.158597 + 0.987343i \(0.550697\pi\)
\(572\) −1.80512e10 −0.00705058
\(573\) 6.79560e12 2.63349
\(574\) −6.50467e11 −0.250105
\(575\) −2.85257e12 −1.08826
\(576\) 6.80104e12 2.57439
\(577\) −5.19088e12 −1.94962 −0.974810 0.223039i \(-0.928402\pi\)
−0.974810 + 0.223039i \(0.928402\pi\)
\(578\) 0 0
\(579\) −1.78787e12 −0.661124
\(580\) 3.77318e9 0.00138446
\(581\) 9.99358e11 0.363855
\(582\) −7.10748e12 −2.56781
\(583\) −3.70399e11 −0.132789
\(584\) −3.90356e12 −1.38868
\(585\) 2.79193e12 0.985605
\(586\) 2.13916e12 0.749384
\(587\) 9.87567e11 0.343317 0.171659 0.985157i \(-0.445087\pi\)
0.171659 + 0.985157i \(0.445087\pi\)
\(588\) 1.61539e10 0.00557288
\(589\) −3.37643e11 −0.115595
\(590\) 7.92880e11 0.269385
\(591\) 2.16194e12 0.728954
\(592\) 1.03446e12 0.346150
\(593\) −3.64711e12 −1.21116 −0.605582 0.795783i \(-0.707060\pi\)
−0.605582 + 0.795783i \(0.707060\pi\)
\(594\) 1.19835e13 3.94953
\(595\) 0 0
\(596\) 1.86614e9 0.000605810 0
\(597\) 7.88632e12 2.54091
\(598\) 5.30540e12 1.69654
\(599\) 1.88140e12 0.597117 0.298559 0.954391i \(-0.403494\pi\)
0.298559 + 0.954391i \(0.403494\pi\)
\(600\) 5.58255e12 1.75854
\(601\) 1.11397e12 0.348287 0.174144 0.984720i \(-0.444284\pi\)
0.174144 + 0.984720i \(0.444284\pi\)
\(602\) −1.33392e12 −0.413948
\(603\) 4.26284e12 1.31302
\(604\) 1.10218e9 0.000336967 0
\(605\) −6.32026e11 −0.191794
\(606\) 4.86252e12 1.46465
\(607\) −2.22636e12 −0.665652 −0.332826 0.942988i \(-0.608002\pi\)
−0.332826 + 0.942988i \(0.608002\pi\)
\(608\) 1.95271e10 0.00579525
\(609\) 4.13131e12 1.21705
\(610\) −1.33267e12 −0.389706
\(611\) −7.11144e12 −2.06430
\(612\) 0 0
\(613\) 1.60812e12 0.459989 0.229995 0.973192i \(-0.426129\pi\)
0.229995 + 0.973192i \(0.426129\pi\)
\(614\) −3.90145e12 −1.10782
\(615\) 9.74927e11 0.274811
\(616\) 2.12408e12 0.594371
\(617\) 3.71835e12 1.03292 0.516461 0.856311i \(-0.327249\pi\)
0.516461 + 0.856311i \(0.327249\pi\)
\(618\) −3.76794e12 −1.03910
\(619\) 5.70656e12 1.56231 0.781154 0.624338i \(-0.214631\pi\)
0.781154 + 0.624338i \(0.214631\pi\)
\(620\) 5.30293e8 0.000144130 0
\(621\) −1.29963e13 −3.50676
\(622\) 2.11513e12 0.566604
\(623\) −1.07857e12 −0.286847
\(624\) −1.04212e13 −2.75162
\(625\) 3.03912e12 0.796687
\(626\) 4.65022e12 1.21029
\(627\) −7.53528e12 −1.94713
\(628\) 1.49181e10 0.00382732
\(629\) 0 0
\(630\) 1.22126e12 0.308870
\(631\) −6.04936e12 −1.51907 −0.759534 0.650467i \(-0.774573\pi\)
−0.759534 + 0.650467i \(0.774573\pi\)
\(632\) 6.38154e11 0.159110
\(633\) 2.93873e12 0.727516
\(634\) 1.60288e12 0.394003
\(635\) 1.29079e12 0.315045
\(636\) 2.92240e9 0.000708243 0
\(637\) 4.78296e12 1.15098
\(638\) 7.82240e12 1.86916
\(639\) −1.58106e13 −3.75141
\(640\) 1.12409e12 0.264846
\(641\) −4.07126e12 −0.952506 −0.476253 0.879308i \(-0.658005\pi\)
−0.476253 + 0.879308i \(0.658005\pi\)
\(642\) 1.55126e13 3.60392
\(643\) 6.67925e12 1.54091 0.770457 0.637492i \(-0.220028\pi\)
0.770457 + 0.637492i \(0.220028\pi\)
\(644\) 8.56337e9 0.00196182
\(645\) 1.99929e12 0.454839
\(646\) 0 0
\(647\) −3.54638e12 −0.795640 −0.397820 0.917463i \(-0.630233\pi\)
−0.397820 + 0.917463i \(0.630233\pi\)
\(648\) 1.38575e13 3.08743
\(649\) 6.06545e12 1.34203
\(650\) −6.14456e12 −1.35015
\(651\) 5.80625e11 0.126701
\(652\) 1.90656e10 0.00413176
\(653\) −6.92871e12 −1.49123 −0.745613 0.666379i \(-0.767843\pi\)
−0.745613 + 0.666379i \(0.767843\pi\)
\(654\) 2.52308e12 0.539301
\(655\) −4.63043e11 −0.0982960
\(656\) −2.62369e12 −0.553153
\(657\) −1.71694e13 −3.59509
\(658\) −3.11072e12 −0.646911
\(659\) 2.61478e12 0.540071 0.270035 0.962850i \(-0.412965\pi\)
0.270035 + 0.962850i \(0.412965\pi\)
\(660\) 1.18347e10 0.00242778
\(661\) −1.25747e12 −0.256207 −0.128104 0.991761i \(-0.540889\pi\)
−0.128104 + 0.991761i \(0.540889\pi\)
\(662\) −5.79514e12 −1.17274
\(663\) 0 0
\(664\) 4.01609e12 0.801765
\(665\) −4.70748e11 −0.0933451
\(666\) 4.53315e12 0.892824
\(667\) −8.48349e12 −1.65962
\(668\) 6.02153e9 0.00117007
\(669\) −3.32465e12 −0.641695
\(670\) 6.99383e11 0.134084
\(671\) −1.01947e13 −1.94145
\(672\) −3.35797e10 −0.00635206
\(673\) −8.91607e12 −1.67535 −0.837676 0.546168i \(-0.816086\pi\)
−0.837676 + 0.546168i \(0.816086\pi\)
\(674\) −1.43646e12 −0.268117
\(675\) 1.50519e13 2.79077
\(676\) 2.20602e10 0.00406303
\(677\) −7.73461e12 −1.41511 −0.707554 0.706660i \(-0.750201\pi\)
−0.707554 + 0.706660i \(0.750201\pi\)
\(678\) 7.36058e12 1.33776
\(679\) −3.39672e12 −0.613262
\(680\) 0 0
\(681\) −6.93807e12 −1.23617
\(682\) 1.09938e12 0.194589
\(683\) 6.47827e12 1.13911 0.569555 0.821953i \(-0.307115\pi\)
0.569555 + 0.821953i \(0.307115\pi\)
\(684\) 4.28642e10 0.00748759
\(685\) −2.48250e12 −0.430806
\(686\) 4.72448e12 0.814508
\(687\) 1.96008e12 0.335712
\(688\) −5.38043e12 −0.915523
\(689\) 8.65282e11 0.146275
\(690\) −3.47831e12 −0.584182
\(691\) −9.23897e11 −0.154160 −0.0770801 0.997025i \(-0.524560\pi\)
−0.0770801 + 0.997025i \(0.524560\pi\)
\(692\) 1.05262e10 0.00174499
\(693\) 9.34251e12 1.53874
\(694\) 7.17031e12 1.17333
\(695\) 2.95355e12 0.480190
\(696\) 1.66024e13 2.68181
\(697\) 0 0
\(698\) −7.92451e12 −1.26364
\(699\) −4.09877e12 −0.649391
\(700\) −9.91783e9 −0.00156126
\(701\) 1.13633e13 1.77735 0.888673 0.458542i \(-0.151628\pi\)
0.888673 + 0.458542i \(0.151628\pi\)
\(702\) −2.79945e13 −4.35066
\(703\) −1.74735e12 −0.269825
\(704\) 8.53585e12 1.30969
\(705\) 4.66238e12 0.710815
\(706\) 9.22029e12 1.39677
\(707\) 2.32384e12 0.349799
\(708\) −4.78556e10 −0.00715785
\(709\) −9.41131e12 −1.39876 −0.699378 0.714752i \(-0.746540\pi\)
−0.699378 + 0.714752i \(0.746540\pi\)
\(710\) −2.59397e12 −0.383091
\(711\) 2.80684e12 0.411913
\(712\) −4.33440e12 −0.632076
\(713\) −1.19229e12 −0.172775
\(714\) 0 0
\(715\) 3.50409e12 0.501417
\(716\) −1.29831e10 −0.00184617
\(717\) −7.37135e12 −1.04162
\(718\) −4.46841e12 −0.627470
\(719\) 4.24063e12 0.591767 0.295883 0.955224i \(-0.404386\pi\)
0.295883 + 0.955224i \(0.404386\pi\)
\(720\) 4.92601e12 0.683124
\(721\) −1.80073e12 −0.248165
\(722\) 2.83742e12 0.388603
\(723\) −7.19267e12 −0.978966
\(724\) −3.44077e10 −0.00465406
\(725\) 9.82532e12 1.32076
\(726\) 1.03380e13 1.38109
\(727\) −4.23459e12 −0.562221 −0.281110 0.959675i \(-0.590703\pi\)
−0.281110 + 0.959675i \(0.590703\pi\)
\(728\) −4.96202e12 −0.654738
\(729\) 1.76583e13 2.31566
\(730\) −2.81689e12 −0.367128
\(731\) 0 0
\(732\) 8.04351e10 0.0103549
\(733\) 3.24959e12 0.415778 0.207889 0.978152i \(-0.433341\pi\)
0.207889 + 0.978152i \(0.433341\pi\)
\(734\) 1.19458e12 0.151909
\(735\) −3.13579e12 −0.396327
\(736\) 6.89546e10 0.00866190
\(737\) 5.35020e12 0.667985
\(738\) −1.14974e13 −1.42675
\(739\) −1.56819e13 −1.93419 −0.967094 0.254421i \(-0.918115\pi\)
−0.967094 + 0.254421i \(0.918115\pi\)
\(740\) 2.74434e9 0.000336431 0
\(741\) 1.76030e13 2.14489
\(742\) 3.78496e11 0.0458399
\(743\) −8.43750e11 −0.101570 −0.0507848 0.998710i \(-0.516172\pi\)
−0.0507848 + 0.998710i \(0.516172\pi\)
\(744\) 2.33334e12 0.279190
\(745\) −3.62254e11 −0.0430835
\(746\) −1.18588e13 −1.40190
\(747\) 1.76643e13 2.07565
\(748\) 0 0
\(749\) 7.41358e12 0.860716
\(750\) 8.35727e12 0.964470
\(751\) −3.24193e11 −0.0371898 −0.0185949 0.999827i \(-0.505919\pi\)
−0.0185949 + 0.999827i \(0.505919\pi\)
\(752\) −1.25473e13 −1.43077
\(753\) −6.10866e12 −0.692418
\(754\) −1.82738e13 −2.05900
\(755\) −2.13955e11 −0.0239641
\(756\) −4.51854e10 −0.00503095
\(757\) −1.54452e13 −1.70947 −0.854734 0.519066i \(-0.826280\pi\)
−0.854734 + 0.519066i \(0.826280\pi\)
\(758\) −3.73896e12 −0.411376
\(759\) −2.66087e13 −2.91029
\(760\) −1.89178e12 −0.205688
\(761\) 5.33814e12 0.576978 0.288489 0.957483i \(-0.406847\pi\)
0.288489 + 0.957483i \(0.406847\pi\)
\(762\) −2.11133e13 −2.26861
\(763\) 1.20580e12 0.128800
\(764\) −4.85170e10 −0.00515198
\(765\) 0 0
\(766\) 5.32741e12 0.559096
\(767\) −1.41694e13 −1.47833
\(768\) −2.02794e11 −0.0210344
\(769\) −2.39607e12 −0.247076 −0.123538 0.992340i \(-0.539424\pi\)
−0.123538 + 0.992340i \(0.539424\pi\)
\(770\) 1.53278e12 0.157134
\(771\) −5.18398e12 −0.528346
\(772\) 1.27645e10 0.00129338
\(773\) 9.42867e12 0.949823 0.474911 0.880034i \(-0.342480\pi\)
0.474911 + 0.880034i \(0.342480\pi\)
\(774\) −2.35779e13 −2.36140
\(775\) 1.38088e12 0.137498
\(776\) −1.36503e13 −1.35134
\(777\) 3.00482e12 0.295749
\(778\) −1.40279e13 −1.37272
\(779\) 4.43181e12 0.431184
\(780\) −2.76468e10 −0.00267436
\(781\) −1.98436e13 −1.90849
\(782\) 0 0
\(783\) 4.47639e13 4.25599
\(784\) 8.43894e12 0.797748
\(785\) −2.89589e12 −0.272188
\(786\) 7.57397e12 0.707819
\(787\) 2.88613e12 0.268182 0.134091 0.990969i \(-0.457189\pi\)
0.134091 + 0.990969i \(0.457189\pi\)
\(788\) −1.54351e10 −0.00142607
\(789\) −2.91333e13 −2.67635
\(790\) 4.60505e11 0.0420642
\(791\) 3.51768e12 0.319494
\(792\) 3.75444e13 3.39064
\(793\) 2.38157e13 2.13863
\(794\) −1.56000e13 −1.39294
\(795\) −5.67294e11 −0.0503682
\(796\) −5.63042e10 −0.00497087
\(797\) −1.80483e13 −1.58443 −0.792215 0.610242i \(-0.791072\pi\)
−0.792215 + 0.610242i \(0.791072\pi\)
\(798\) 7.70000e12 0.672168
\(799\) 0 0
\(800\) −7.98611e10 −0.00689335
\(801\) −1.90643e13 −1.63635
\(802\) 1.23820e13 1.05683
\(803\) −2.15489e13 −1.82897
\(804\) −4.22123e10 −0.00356277
\(805\) −1.66232e12 −0.139519
\(806\) −2.56824e12 −0.214353
\(807\) 1.44370e13 1.19824
\(808\) 9.33875e12 0.770793
\(809\) 6.07623e12 0.498731 0.249365 0.968410i \(-0.419778\pi\)
0.249365 + 0.968410i \(0.419778\pi\)
\(810\) 9.99984e12 0.816226
\(811\) −1.74997e12 −0.142048 −0.0710242 0.997475i \(-0.522627\pi\)
−0.0710242 + 0.997475i \(0.522627\pi\)
\(812\) −2.94954e10 −0.00238096
\(813\) −2.17609e13 −1.74690
\(814\) 5.68946e12 0.454215
\(815\) −3.70100e12 −0.293839
\(816\) 0 0
\(817\) 9.08836e12 0.713652
\(818\) −7.83486e12 −0.611845
\(819\) −2.18248e13 −1.69502
\(820\) −6.96047e9 −0.000537621 0
\(821\) 1.32681e12 0.101921 0.0509605 0.998701i \(-0.483772\pi\)
0.0509605 + 0.998701i \(0.483772\pi\)
\(822\) 4.06061e13 3.10218
\(823\) 1.26504e13 0.961179 0.480589 0.876946i \(-0.340423\pi\)
0.480589 + 0.876946i \(0.340423\pi\)
\(824\) −7.23654e12 −0.546838
\(825\) 3.08174e13 2.31608
\(826\) −6.19804e12 −0.463281
\(827\) −4.79691e12 −0.356604 −0.178302 0.983976i \(-0.557060\pi\)
−0.178302 + 0.983976i \(0.557060\pi\)
\(828\) 1.51363e11 0.0111914
\(829\) −1.79243e13 −1.31810 −0.659048 0.752101i \(-0.729041\pi\)
−0.659048 + 0.752101i \(0.729041\pi\)
\(830\) 2.89809e12 0.211963
\(831\) −1.88799e13 −1.37339
\(832\) −1.99404e13 −1.44271
\(833\) 0 0
\(834\) −4.83111e13 −3.45780
\(835\) −1.16890e12 −0.0832122
\(836\) 5.37980e10 0.00380924
\(837\) 6.29125e12 0.443070
\(838\) 5.26622e12 0.368894
\(839\) −2.74032e12 −0.190929 −0.0954645 0.995433i \(-0.530434\pi\)
−0.0954645 + 0.995433i \(0.530434\pi\)
\(840\) 3.25319e12 0.225451
\(841\) 1.47131e13 1.01420
\(842\) −5.67942e11 −0.0389403
\(843\) −1.76543e13 −1.20400
\(844\) −2.09810e10 −0.00142326
\(845\) −4.28232e12 −0.288951
\(846\) −5.49839e13 −3.69036
\(847\) 4.94062e12 0.329842
\(848\) 1.52668e12 0.101384
\(849\) −1.78496e13 −1.17908
\(850\) 0 0
\(851\) −6.17029e12 −0.403295
\(852\) 1.56563e11 0.0101791
\(853\) −4.45814e12 −0.288325 −0.144163 0.989554i \(-0.546049\pi\)
−0.144163 + 0.989554i \(0.546049\pi\)
\(854\) 1.04176e13 0.670205
\(855\) −8.32078e12 −0.532496
\(856\) 2.97927e13 1.89661
\(857\) −2.22703e13 −1.41030 −0.705151 0.709057i \(-0.749121\pi\)
−0.705151 + 0.709057i \(0.749121\pi\)
\(858\) −5.73163e13 −3.61065
\(859\) 1.75068e13 1.09708 0.548539 0.836125i \(-0.315184\pi\)
0.548539 + 0.836125i \(0.315184\pi\)
\(860\) −1.42739e10 −0.000889816 0
\(861\) −7.62112e12 −0.472612
\(862\) −1.44890e13 −0.893831
\(863\) −1.01521e13 −0.623028 −0.311514 0.950242i \(-0.600836\pi\)
−0.311514 + 0.950242i \(0.600836\pi\)
\(864\) −3.63846e11 −0.0222129
\(865\) −2.04334e12 −0.124099
\(866\) 1.31495e13 0.794471
\(867\) 0 0
\(868\) −4.14536e9 −0.000247870 0
\(869\) 3.52282e12 0.209556
\(870\) 1.19806e13 0.708993
\(871\) −1.24985e13 −0.735828
\(872\) 4.84572e12 0.283814
\(873\) −6.00392e13 −3.49841
\(874\) −1.58117e13 −0.916593
\(875\) 3.99401e12 0.230342
\(876\) 1.70018e11 0.00975498
\(877\) −9.33904e12 −0.533094 −0.266547 0.963822i \(-0.585883\pi\)
−0.266547 + 0.963822i \(0.585883\pi\)
\(878\) −6.90579e12 −0.392182
\(879\) 2.50633e13 1.41608
\(880\) 6.18254e12 0.347532
\(881\) 4.63896e12 0.259435 0.129718 0.991551i \(-0.458593\pi\)
0.129718 + 0.991551i \(0.458593\pi\)
\(882\) 3.69807e13 2.05763
\(883\) 1.70186e13 0.942108 0.471054 0.882104i \(-0.343874\pi\)
0.471054 + 0.882104i \(0.343874\pi\)
\(884\) 0 0
\(885\) 9.28969e12 0.509046
\(886\) −7.21320e11 −0.0393257
\(887\) −9.95483e12 −0.539980 −0.269990 0.962863i \(-0.587020\pi\)
−0.269990 + 0.962863i \(0.587020\pi\)
\(888\) 1.20754e13 0.651692
\(889\) −1.00902e13 −0.541806
\(890\) −3.12779e12 −0.167103
\(891\) 7.64977e13 4.06630
\(892\) 2.37363e10 0.00125537
\(893\) 2.11942e13 1.11528
\(894\) 5.92537e12 0.310239
\(895\) 2.52028e12 0.131294
\(896\) −8.78718e12 −0.455474
\(897\) 6.21602e13 3.20587
\(898\) 1.21489e13 0.623437
\(899\) 4.10669e12 0.209688
\(900\) −1.75304e11 −0.00890636
\(901\) 0 0
\(902\) −1.44302e13 −0.725842
\(903\) −1.56287e13 −0.782219
\(904\) 1.41364e13 0.704014
\(905\) 6.67920e12 0.330983
\(906\) 3.49965e12 0.172563
\(907\) 2.53299e13 1.24280 0.621400 0.783494i \(-0.286564\pi\)
0.621400 + 0.783494i \(0.286564\pi\)
\(908\) 4.95342e10 0.00241835
\(909\) 4.10754e13 1.99546
\(910\) −3.58069e12 −0.173094
\(911\) 8.70542e12 0.418752 0.209376 0.977835i \(-0.432857\pi\)
0.209376 + 0.977835i \(0.432857\pi\)
\(912\) 3.10584e13 1.48663
\(913\) 2.21701e13 1.05596
\(914\) 2.05036e13 0.971792
\(915\) −1.56140e13 −0.736410
\(916\) −1.39939e10 −0.000656765 0
\(917\) 3.61967e12 0.169047
\(918\) 0 0
\(919\) 4.10103e13 1.89659 0.948295 0.317391i \(-0.102807\pi\)
0.948295 + 0.317391i \(0.102807\pi\)
\(920\) −6.68030e12 −0.307433
\(921\) −4.57109e13 −2.09340
\(922\) 4.14074e13 1.88708
\(923\) 4.63562e13 2.10233
\(924\) −9.25133e10 −0.00417523
\(925\) 7.14624e12 0.320952
\(926\) 2.99102e13 1.33681
\(927\) −3.18291e13 −1.41568
\(928\) −2.37505e11 −0.0105125
\(929\) −9.53729e12 −0.420102 −0.210051 0.977690i \(-0.567363\pi\)
−0.210051 + 0.977690i \(0.567363\pi\)
\(930\) 1.68379e12 0.0738097
\(931\) −1.42546e13 −0.621845
\(932\) 2.92631e10 0.00127042
\(933\) 2.47816e13 1.07069
\(934\) −3.81873e13 −1.64194
\(935\) 0 0
\(936\) −8.77068e13 −3.73501
\(937\) 4.18393e13 1.77320 0.886598 0.462542i \(-0.153062\pi\)
0.886598 + 0.462542i \(0.153062\pi\)
\(938\) −5.46716e12 −0.230594
\(939\) 5.44838e13 2.28703
\(940\) −3.32870e10 −0.00139059
\(941\) −3.73218e13 −1.55171 −0.775854 0.630913i \(-0.782680\pi\)
−0.775854 + 0.630913i \(0.782680\pi\)
\(942\) 4.73679e13 1.96000
\(943\) 1.56497e13 0.644471
\(944\) −2.50001e13 −1.02463
\(945\) 8.77137e12 0.357787
\(946\) −2.95921e13 −1.20134
\(947\) 1.29470e13 0.523111 0.261555 0.965188i \(-0.415765\pi\)
0.261555 + 0.965188i \(0.415765\pi\)
\(948\) −2.77945e10 −0.00111769
\(949\) 5.03400e13 2.01472
\(950\) 1.83126e13 0.729447
\(951\) 1.87800e13 0.744531
\(952\) 0 0
\(953\) 2.82478e12 0.110935 0.0554673 0.998461i \(-0.482335\pi\)
0.0554673 + 0.998461i \(0.482335\pi\)
\(954\) 6.69015e12 0.261498
\(955\) 9.41810e12 0.366394
\(956\) 5.26276e10 0.00203776
\(957\) 9.16503e13 3.53208
\(958\) 5.76133e12 0.220993
\(959\) 1.94060e13 0.740887
\(960\) 1.30733e13 0.496781
\(961\) −2.58625e13 −0.978170
\(962\) −1.32910e13 −0.500347
\(963\) 1.31040e14 4.91004
\(964\) 5.13519e10 0.00191518
\(965\) −2.47784e12 −0.0919813
\(966\) 2.71904e13 1.00466
\(967\) 4.09001e13 1.50420 0.752100 0.659049i \(-0.229041\pi\)
0.752100 + 0.659049i \(0.229041\pi\)
\(968\) 1.98547e13 0.726817
\(969\) 0 0
\(970\) −9.85034e12 −0.357255
\(971\) −2.01184e13 −0.726286 −0.363143 0.931733i \(-0.618296\pi\)
−0.363143 + 0.931733i \(0.618296\pi\)
\(972\) −2.94473e11 −0.0105815
\(973\) −2.30883e13 −0.825817
\(974\) 1.60492e13 0.571397
\(975\) −7.19920e13 −2.55131
\(976\) 4.20200e13 1.48228
\(977\) −6.28033e11 −0.0220524 −0.0110262 0.999939i \(-0.503510\pi\)
−0.0110262 + 0.999939i \(0.503510\pi\)
\(978\) 6.05370e13 2.11590
\(979\) −2.39273e13 −0.832475
\(980\) 2.23879e10 0.000775348 0
\(981\) 2.13133e13 0.734751
\(982\) 1.97614e13 0.678135
\(983\) −3.88302e13 −1.32641 −0.663206 0.748437i \(-0.730805\pi\)
−0.663206 + 0.748437i \(0.730805\pi\)
\(984\) −3.06268e13 −1.04141
\(985\) 2.99626e12 0.101418
\(986\) 0 0
\(987\) −3.64464e13 −1.22244
\(988\) −1.25676e11 −0.00419612
\(989\) 3.20930e13 1.06666
\(990\) 2.70928e13 0.896388
\(991\) −3.63709e13 −1.19791 −0.598953 0.800784i \(-0.704416\pi\)
−0.598953 + 0.800784i \(0.704416\pi\)
\(992\) −3.33796e10 −0.00109441
\(993\) −6.78981e13 −2.21608
\(994\) 2.02774e13 0.658829
\(995\) 1.09297e13 0.353514
\(996\) −1.74919e11 −0.00563209
\(997\) −1.69767e13 −0.544158 −0.272079 0.962275i \(-0.587711\pi\)
−0.272079 + 0.962275i \(0.587711\pi\)
\(998\) −2.14051e13 −0.683014
\(999\) 3.25581e13 1.03422
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.1.9 36
17.16 even 2 289.10.a.h.1.9 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.9 36 1.1 even 1 trivial
289.10.a.h.1.9 yes 36 17.16 even 2