Properties

Label 289.10.a.i.1.1
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

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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: \(52\)
Twist minimal: no (minimal twist has level 17)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-41.2664 q^{2} -175.384 q^{3} +1190.92 q^{4} +699.952 q^{5} +7237.48 q^{6} +8848.92 q^{7} -28016.5 q^{8} +11076.6 q^{9} +O(q^{10})\) \(q-41.2664 q^{2} -175.384 q^{3} +1190.92 q^{4} +699.952 q^{5} +7237.48 q^{6} +8848.92 q^{7} -28016.5 q^{8} +11076.6 q^{9} -28884.5 q^{10} +90585.7 q^{11} -208868. q^{12} -26249.8 q^{13} -365163. q^{14} -122760. q^{15} +546392. q^{16} -457091. q^{18} +379311. q^{19} +833585. q^{20} -1.55196e6 q^{21} -3.73815e6 q^{22} -199283. q^{23} +4.91365e6 q^{24} -1.46319e6 q^{25} +1.08324e6 q^{26} +1.50943e6 q^{27} +1.05383e7 q^{28} +1.64726e6 q^{29} +5.06588e6 q^{30} +6.16598e6 q^{31} -8.20319e6 q^{32} -1.58873e7 q^{33} +6.19382e6 q^{35} +1.31913e7 q^{36} +2.00498e7 q^{37} -1.56528e7 q^{38} +4.60380e6 q^{39} -1.96102e7 q^{40} +2.54059e7 q^{41} +6.40439e7 q^{42} -445870. q^{43} +1.07880e8 q^{44} +7.75308e6 q^{45} +8.22371e6 q^{46} +1.95869e7 q^{47} -9.58285e7 q^{48} +3.79498e7 q^{49} +6.03807e7 q^{50} -3.12614e7 q^{52} +5.99655e7 q^{53} -6.22887e7 q^{54} +6.34056e7 q^{55} -2.47916e8 q^{56} -6.65251e7 q^{57} -6.79767e7 q^{58} -1.04158e7 q^{59} -1.46198e8 q^{60} +1.47082e8 q^{61} -2.54448e8 q^{62} +9.80159e7 q^{63} +5.87635e7 q^{64} -1.83736e7 q^{65} +6.55612e8 q^{66} -1.11288e8 q^{67} +3.49511e7 q^{69} -2.55597e8 q^{70} +9.69765e7 q^{71} -3.10328e8 q^{72} +6.26027e6 q^{73} -8.27383e8 q^{74} +2.56621e8 q^{75} +4.51728e8 q^{76} +8.01586e8 q^{77} -1.89982e8 q^{78} +3.35598e8 q^{79} +3.82448e8 q^{80} -4.82750e8 q^{81} -1.04841e9 q^{82} -4.77542e8 q^{83} -1.84826e9 q^{84} +1.83995e7 q^{86} -2.88904e8 q^{87} -2.53790e9 q^{88} -1.92204e8 q^{89} -3.19942e8 q^{90} -2.32283e8 q^{91} -2.37330e8 q^{92} -1.08142e9 q^{93} -8.08282e8 q^{94} +2.65499e8 q^{95} +1.43871e9 q^{96} -2.12176e8 q^{97} -1.56605e9 q^{98} +1.00338e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + O(q^{10}) \) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + 156200q^{13} + 1207872q^{15} + 3407880q^{16} + 2193336q^{18} + 1185568q^{19} + 5198336q^{21} + 13827692q^{25} + 3618944q^{26} - 9167544q^{30} + 61884888q^{32} + 1635208q^{33} + 46992776q^{35} + 156027320q^{36} + 84813952q^{38} - 4635776q^{42} + 125448912q^{43} + 164193176q^{47} + 270850284q^{49} - 226223888q^{50} + 103553016q^{52} + 426167208q^{53} + 677761520q^{55} + 375214512q^{59} + 336918024q^{60} + 190014416q^{64} + 1377178928q^{66} + 311910088q^{67} + 533688136q^{69} + 1477690280q^{70} + 2757942680q^{72} + 4047975520q^{76} + 3440336432q^{77} + 3266558756q^{81} + 2072890608q^{83} + 2630025952q^{84} + 1538547296q^{86} - 1010436256q^{87} + 1873849184q^{89} - 1998451624q^{93} - 6880776704q^{94} - 4667454128q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −41.2664 −1.82374 −0.911868 0.410484i \(-0.865360\pi\)
−0.911868 + 0.410484i \(0.865360\pi\)
\(3\) −175.384 −1.25010 −0.625050 0.780585i \(-0.714921\pi\)
−0.625050 + 0.780585i \(0.714921\pi\)
\(4\) 1190.92 2.32601
\(5\) 699.952 0.500845 0.250422 0.968137i \(-0.419431\pi\)
0.250422 + 0.968137i \(0.419431\pi\)
\(6\) 7237.48 2.27985
\(7\) 8848.92 1.39299 0.696497 0.717560i \(-0.254741\pi\)
0.696497 + 0.717560i \(0.254741\pi\)
\(8\) −28016.5 −2.41830
\(9\) 11076.6 0.562749
\(10\) −28884.5 −0.913408
\(11\) 90585.7 1.86549 0.932744 0.360539i \(-0.117407\pi\)
0.932744 + 0.360539i \(0.117407\pi\)
\(12\) −208868. −2.90775
\(13\) −26249.8 −0.254907 −0.127453 0.991845i \(-0.540680\pi\)
−0.127453 + 0.991845i \(0.540680\pi\)
\(14\) −365163. −2.54045
\(15\) −122760. −0.626106
\(16\) 546392. 2.08432
\(17\) 0 0
\(18\) −457091. −1.02631
\(19\) 379311. 0.667735 0.333867 0.942620i \(-0.391646\pi\)
0.333867 + 0.942620i \(0.391646\pi\)
\(20\) 833585. 1.16497
\(21\) −1.55196e6 −1.74138
\(22\) −3.73815e6 −3.40216
\(23\) −199283. −0.148489 −0.0742447 0.997240i \(-0.523655\pi\)
−0.0742447 + 0.997240i \(0.523655\pi\)
\(24\) 4.91365e6 3.02311
\(25\) −1.46319e6 −0.749155
\(26\) 1.08324e6 0.464882
\(27\) 1.50943e6 0.546607
\(28\) 1.05383e7 3.24012
\(29\) 1.64726e6 0.432486 0.216243 0.976340i \(-0.430620\pi\)
0.216243 + 0.976340i \(0.430620\pi\)
\(30\) 5.06588e6 1.14185
\(31\) 6.16598e6 1.19915 0.599577 0.800317i \(-0.295336\pi\)
0.599577 + 0.800317i \(0.295336\pi\)
\(32\) −8.20319e6 −1.38295
\(33\) −1.58873e7 −2.33205
\(34\) 0 0
\(35\) 6.19382e6 0.697673
\(36\) 1.31913e7 1.30896
\(37\) 2.00498e7 1.75874 0.879371 0.476138i \(-0.157964\pi\)
0.879371 + 0.476138i \(0.157964\pi\)
\(38\) −1.56528e7 −1.21777
\(39\) 4.60380e6 0.318659
\(40\) −1.96102e7 −1.21119
\(41\) 2.54059e7 1.40413 0.702064 0.712114i \(-0.252262\pi\)
0.702064 + 0.712114i \(0.252262\pi\)
\(42\) 6.40439e7 3.17582
\(43\) −445870. −0.0198884 −0.00994420 0.999951i \(-0.503165\pi\)
−0.00994420 + 0.999951i \(0.503165\pi\)
\(44\) 1.07880e8 4.33915
\(45\) 7.75308e6 0.281850
\(46\) 8.22371e6 0.270805
\(47\) 1.95869e7 0.585498 0.292749 0.956189i \(-0.405430\pi\)
0.292749 + 0.956189i \(0.405430\pi\)
\(48\) −9.58285e7 −2.60561
\(49\) 3.79498e7 0.940432
\(50\) 6.03807e7 1.36626
\(51\) 0 0
\(52\) −3.12614e7 −0.592916
\(53\) 5.99655e7 1.04390 0.521951 0.852975i \(-0.325204\pi\)
0.521951 + 0.852975i \(0.325204\pi\)
\(54\) −6.22887e7 −0.996867
\(55\) 6.34056e7 0.934320
\(56\) −2.47916e8 −3.36867
\(57\) −6.65251e7 −0.834735
\(58\) −6.79767e7 −0.788740
\(59\) −1.04158e7 −0.111907 −0.0559535 0.998433i \(-0.517820\pi\)
−0.0559535 + 0.998433i \(0.517820\pi\)
\(60\) −1.46198e8 −1.45633
\(61\) 1.47082e8 1.36011 0.680056 0.733160i \(-0.261955\pi\)
0.680056 + 0.733160i \(0.261955\pi\)
\(62\) −2.54448e8 −2.18694
\(63\) 9.80159e7 0.783906
\(64\) 5.87635e7 0.437822
\(65\) −1.83736e7 −0.127669
\(66\) 6.55612e8 4.25304
\(67\) −1.11288e8 −0.674703 −0.337352 0.941379i \(-0.609531\pi\)
−0.337352 + 0.941379i \(0.609531\pi\)
\(68\) 0 0
\(69\) 3.49511e7 0.185627
\(70\) −2.55597e8 −1.27237
\(71\) 9.69765e7 0.452902 0.226451 0.974023i \(-0.427288\pi\)
0.226451 + 0.974023i \(0.427288\pi\)
\(72\) −3.10328e8 −1.36089
\(73\) 6.26027e6 0.0258012 0.0129006 0.999917i \(-0.495893\pi\)
0.0129006 + 0.999917i \(0.495893\pi\)
\(74\) −8.27383e8 −3.20748
\(75\) 2.56621e8 0.936518
\(76\) 4.51728e8 1.55316
\(77\) 8.01586e8 2.59861
\(78\) −1.89982e8 −0.581149
\(79\) 3.35598e8 0.969388 0.484694 0.874684i \(-0.338931\pi\)
0.484694 + 0.874684i \(0.338931\pi\)
\(80\) 3.82448e8 1.04392
\(81\) −4.82750e8 −1.24606
\(82\) −1.04841e9 −2.56076
\(83\) −4.77542e8 −1.10449 −0.552243 0.833683i \(-0.686228\pi\)
−0.552243 + 0.833683i \(0.686228\pi\)
\(84\) −1.84826e9 −4.05047
\(85\) 0 0
\(86\) 1.83995e7 0.0362712
\(87\) −2.88904e8 −0.540651
\(88\) −2.53790e9 −4.51130
\(89\) −1.92204e8 −0.324719 −0.162359 0.986732i \(-0.551910\pi\)
−0.162359 + 0.986732i \(0.551910\pi\)
\(90\) −3.19942e8 −0.514020
\(91\) −2.32283e8 −0.355083
\(92\) −2.37330e8 −0.345388
\(93\) −1.08142e9 −1.49906
\(94\) −8.08282e8 −1.06779
\(95\) 2.65499e8 0.334431
\(96\) 1.43871e9 1.72883
\(97\) −2.12176e8 −0.243345 −0.121673 0.992570i \(-0.538826\pi\)
−0.121673 + 0.992570i \(0.538826\pi\)
\(98\) −1.56605e9 −1.71510
\(99\) 1.00338e9 1.04980
\(100\) −1.74254e9 −1.74254
\(101\) 1.38707e9 1.32633 0.663164 0.748474i \(-0.269213\pi\)
0.663164 + 0.748474i \(0.269213\pi\)
\(102\) 0 0
\(103\) 7.73415e6 0.00677088 0.00338544 0.999994i \(-0.498922\pi\)
0.00338544 + 0.999994i \(0.498922\pi\)
\(104\) 7.35429e8 0.616440
\(105\) −1.08630e9 −0.872161
\(106\) −2.47456e9 −1.90380
\(107\) −5.67291e8 −0.418388 −0.209194 0.977874i \(-0.567084\pi\)
−0.209194 + 0.977874i \(0.567084\pi\)
\(108\) 1.79761e9 1.27142
\(109\) −6.09841e8 −0.413807 −0.206903 0.978361i \(-0.566339\pi\)
−0.206903 + 0.978361i \(0.566339\pi\)
\(110\) −2.61652e9 −1.70395
\(111\) −3.51641e9 −2.19860
\(112\) 4.83498e9 2.90345
\(113\) 3.03208e9 1.74940 0.874698 0.484667i \(-0.161059\pi\)
0.874698 + 0.484667i \(0.161059\pi\)
\(114\) 2.74525e9 1.52234
\(115\) −1.39489e8 −0.0743701
\(116\) 1.96176e9 1.00597
\(117\) −2.90758e8 −0.143448
\(118\) 4.29822e8 0.204089
\(119\) 0 0
\(120\) 3.43932e9 1.51411
\(121\) 5.84782e9 2.48005
\(122\) −6.06954e9 −2.48049
\(123\) −4.45578e9 −1.75530
\(124\) 7.34318e9 2.78925
\(125\) −2.39126e9 −0.876055
\(126\) −4.04476e9 −1.42964
\(127\) −2.97440e9 −1.01457 −0.507286 0.861778i \(-0.669351\pi\)
−0.507286 + 0.861778i \(0.669351\pi\)
\(128\) 1.77507e9 0.584482
\(129\) 7.81985e7 0.0248625
\(130\) 7.58213e8 0.232834
\(131\) −1.96884e9 −0.584103 −0.292051 0.956403i \(-0.594338\pi\)
−0.292051 + 0.956403i \(0.594338\pi\)
\(132\) −1.89205e10 −5.42437
\(133\) 3.35649e9 0.930151
\(134\) 4.59247e9 1.23048
\(135\) 1.05653e9 0.273765
\(136\) 0 0
\(137\) 3.63646e9 0.881935 0.440968 0.897523i \(-0.354635\pi\)
0.440968 + 0.897523i \(0.354635\pi\)
\(138\) −1.44231e9 −0.338534
\(139\) 2.98093e9 0.677307 0.338653 0.940911i \(-0.390029\pi\)
0.338653 + 0.940911i \(0.390029\pi\)
\(140\) 7.37633e9 1.62280
\(141\) −3.43523e9 −0.731931
\(142\) −4.00187e9 −0.825973
\(143\) −2.37786e9 −0.475526
\(144\) 6.05216e9 1.17295
\(145\) 1.15300e9 0.216608
\(146\) −2.58339e8 −0.0470546
\(147\) −6.65579e9 −1.17563
\(148\) 2.38777e10 4.09085
\(149\) 3.23876e9 0.538319 0.269160 0.963096i \(-0.413254\pi\)
0.269160 + 0.963096i \(0.413254\pi\)
\(150\) −1.05898e10 −1.70796
\(151\) −1.17467e9 −0.183874 −0.0919368 0.995765i \(-0.529306\pi\)
−0.0919368 + 0.995765i \(0.529306\pi\)
\(152\) −1.06270e10 −1.61478
\(153\) 0 0
\(154\) −3.30786e10 −4.73919
\(155\) 4.31589e9 0.600590
\(156\) 5.48275e9 0.741204
\(157\) −3.41677e9 −0.448815 −0.224407 0.974495i \(-0.572045\pi\)
−0.224407 + 0.974495i \(0.572045\pi\)
\(158\) −1.38489e10 −1.76791
\(159\) −1.05170e10 −1.30498
\(160\) −5.74183e9 −0.692645
\(161\) −1.76344e9 −0.206845
\(162\) 1.99214e10 2.27249
\(163\) −1.00303e10 −1.11293 −0.556465 0.830871i \(-0.687843\pi\)
−0.556465 + 0.830871i \(0.687843\pi\)
\(164\) 3.02563e10 3.26602
\(165\) −1.11203e10 −1.16799
\(166\) 1.97065e10 2.01429
\(167\) −6.74539e9 −0.671094 −0.335547 0.942024i \(-0.608921\pi\)
−0.335547 + 0.942024i \(0.608921\pi\)
\(168\) 4.34805e10 4.21117
\(169\) −9.91545e9 −0.935023
\(170\) 0 0
\(171\) 4.20147e9 0.375767
\(172\) −5.30995e8 −0.0462607
\(173\) 6.83966e9 0.580533 0.290267 0.956946i \(-0.406256\pi\)
0.290267 + 0.956946i \(0.406256\pi\)
\(174\) 1.19220e10 0.986004
\(175\) −1.29477e10 −1.04357
\(176\) 4.94953e10 3.88828
\(177\) 1.82676e9 0.139895
\(178\) 7.93157e9 0.592201
\(179\) 8.27428e9 0.602409 0.301205 0.953559i \(-0.402611\pi\)
0.301205 + 0.953559i \(0.402611\pi\)
\(180\) 9.23328e9 0.655586
\(181\) −6.86242e9 −0.475252 −0.237626 0.971357i \(-0.576369\pi\)
−0.237626 + 0.971357i \(0.576369\pi\)
\(182\) 9.58547e9 0.647578
\(183\) −2.57958e10 −1.70028
\(184\) 5.58322e9 0.359091
\(185\) 1.40339e10 0.880856
\(186\) 4.46262e10 2.73389
\(187\) 0 0
\(188\) 2.33264e10 1.36188
\(189\) 1.33568e10 0.761421
\(190\) −1.09562e10 −0.609915
\(191\) 3.87326e9 0.210585 0.105292 0.994441i \(-0.466422\pi\)
0.105292 + 0.994441i \(0.466422\pi\)
\(192\) −1.03062e10 −0.547321
\(193\) −2.20422e10 −1.14353 −0.571765 0.820417i \(-0.693741\pi\)
−0.571765 + 0.820417i \(0.693741\pi\)
\(194\) 8.75573e9 0.443797
\(195\) 3.22244e9 0.159599
\(196\) 4.51951e10 2.18746
\(197\) 1.88786e10 0.893043 0.446521 0.894773i \(-0.352663\pi\)
0.446521 + 0.894773i \(0.352663\pi\)
\(198\) −4.14059e10 −1.91456
\(199\) 1.72935e10 0.781709 0.390854 0.920453i \(-0.372180\pi\)
0.390854 + 0.920453i \(0.372180\pi\)
\(200\) 4.09936e10 1.81168
\(201\) 1.95182e10 0.843446
\(202\) −5.72392e10 −2.41887
\(203\) 1.45765e10 0.602450
\(204\) 0 0
\(205\) 1.77829e10 0.703250
\(206\) −3.19161e8 −0.0123483
\(207\) −2.20738e9 −0.0835622
\(208\) −1.43427e10 −0.531307
\(209\) 3.43601e10 1.24565
\(210\) 4.48276e10 1.59059
\(211\) −4.22364e9 −0.146695 −0.0733476 0.997306i \(-0.523368\pi\)
−0.0733476 + 0.997306i \(0.523368\pi\)
\(212\) 7.14140e10 2.42813
\(213\) −1.70081e10 −0.566172
\(214\) 2.34101e10 0.763029
\(215\) −3.12087e8 −0.00996100
\(216\) −4.22889e10 −1.32186
\(217\) 5.45623e10 1.67041
\(218\) 2.51660e10 0.754674
\(219\) −1.09795e9 −0.0322541
\(220\) 7.55109e10 2.17324
\(221\) 0 0
\(222\) 1.45110e11 4.00967
\(223\) −3.32949e10 −0.901584 −0.450792 0.892629i \(-0.648858\pi\)
−0.450792 + 0.892629i \(0.648858\pi\)
\(224\) −7.25894e10 −1.92645
\(225\) −1.62072e10 −0.421586
\(226\) −1.25123e11 −3.19044
\(227\) 5.61856e10 1.40446 0.702229 0.711951i \(-0.252188\pi\)
0.702229 + 0.711951i \(0.252188\pi\)
\(228\) −7.92259e10 −1.94160
\(229\) −5.10412e10 −1.22648 −0.613241 0.789896i \(-0.710135\pi\)
−0.613241 + 0.789896i \(0.710135\pi\)
\(230\) 5.75620e9 0.135631
\(231\) −1.40585e11 −3.24853
\(232\) −4.61506e10 −1.04588
\(233\) −5.13207e10 −1.14075 −0.570376 0.821384i \(-0.693203\pi\)
−0.570376 + 0.821384i \(0.693203\pi\)
\(234\) 1.19986e10 0.261612
\(235\) 1.37099e10 0.293244
\(236\) −1.24043e10 −0.260297
\(237\) −5.88586e10 −1.21183
\(238\) 0 0
\(239\) −7.40848e9 −0.146872 −0.0734360 0.997300i \(-0.523396\pi\)
−0.0734360 + 0.997300i \(0.523396\pi\)
\(240\) −6.70753e10 −1.30500
\(241\) −9.23211e9 −0.176289 −0.0881443 0.996108i \(-0.528094\pi\)
−0.0881443 + 0.996108i \(0.528094\pi\)
\(242\) −2.41319e11 −4.52295
\(243\) 5.49566e10 1.01109
\(244\) 1.75163e11 3.16364
\(245\) 2.65630e10 0.471010
\(246\) 1.83874e11 3.20120
\(247\) −9.95684e9 −0.170210
\(248\) −1.72749e11 −2.89991
\(249\) 8.37534e10 1.38072
\(250\) 9.86786e10 1.59769
\(251\) 6.79026e10 1.07983 0.539914 0.841720i \(-0.318457\pi\)
0.539914 + 0.841720i \(0.318457\pi\)
\(252\) 1.16729e11 1.82337
\(253\) −1.80522e10 −0.277005
\(254\) 1.22743e11 1.85031
\(255\) 0 0
\(256\) −1.03338e11 −1.50376
\(257\) −4.71754e10 −0.674553 −0.337276 0.941406i \(-0.609506\pi\)
−0.337276 + 0.941406i \(0.609506\pi\)
\(258\) −3.22697e9 −0.0453426
\(259\) 1.77419e11 2.44992
\(260\) −2.18815e10 −0.296959
\(261\) 1.82461e10 0.243381
\(262\) 8.12469e10 1.06525
\(263\) −1.02251e11 −1.31786 −0.658929 0.752206i \(-0.728990\pi\)
−0.658929 + 0.752206i \(0.728990\pi\)
\(264\) 4.45107e11 5.63958
\(265\) 4.19729e10 0.522833
\(266\) −1.38510e11 −1.69635
\(267\) 3.37095e10 0.405931
\(268\) −1.32535e11 −1.56937
\(269\) −1.29503e11 −1.50798 −0.753990 0.656886i \(-0.771873\pi\)
−0.753990 + 0.656886i \(0.771873\pi\)
\(270\) −4.35991e10 −0.499276
\(271\) −1.37457e9 −0.0154813 −0.00774064 0.999970i \(-0.502464\pi\)
−0.00774064 + 0.999970i \(0.502464\pi\)
\(272\) 0 0
\(273\) 4.07387e10 0.443890
\(274\) −1.50064e11 −1.60842
\(275\) −1.32544e11 −1.39754
\(276\) 4.16239e10 0.431770
\(277\) −1.09412e11 −1.11662 −0.558310 0.829633i \(-0.688550\pi\)
−0.558310 + 0.829633i \(0.688550\pi\)
\(278\) −1.23012e11 −1.23523
\(279\) 6.82981e10 0.674822
\(280\) −1.73529e11 −1.68718
\(281\) −5.78233e10 −0.553254 −0.276627 0.960977i \(-0.589217\pi\)
−0.276627 + 0.960977i \(0.589217\pi\)
\(282\) 1.41760e11 1.33485
\(283\) −7.68143e10 −0.711874 −0.355937 0.934510i \(-0.615838\pi\)
−0.355937 + 0.934510i \(0.615838\pi\)
\(284\) 1.15491e11 1.05345
\(285\) −4.65644e10 −0.418073
\(286\) 9.81257e10 0.867233
\(287\) 2.24814e11 1.95594
\(288\) −9.08633e10 −0.778256
\(289\) 0 0
\(290\) −4.75804e10 −0.395036
\(291\) 3.72122e10 0.304206
\(292\) 7.45546e9 0.0600139
\(293\) 1.53859e11 1.21960 0.609802 0.792554i \(-0.291249\pi\)
0.609802 + 0.792554i \(0.291249\pi\)
\(294\) 2.74661e11 2.14404
\(295\) −7.29054e9 −0.0560480
\(296\) −5.61725e11 −4.25316
\(297\) 1.36733e11 1.01969
\(298\) −1.33652e11 −0.981752
\(299\) 5.23115e9 0.0378509
\(300\) 3.05614e11 2.17835
\(301\) −3.94547e9 −0.0277044
\(302\) 4.84744e10 0.335337
\(303\) −2.43269e11 −1.65804
\(304\) 2.07252e11 1.39177
\(305\) 1.02950e11 0.681205
\(306\) 0 0
\(307\) 7.97146e10 0.512171 0.256086 0.966654i \(-0.417567\pi\)
0.256086 + 0.966654i \(0.417567\pi\)
\(308\) 9.54623e11 6.04441
\(309\) −1.35645e9 −0.00846428
\(310\) −1.78101e11 −1.09532
\(311\) −2.53546e10 −0.153687 −0.0768433 0.997043i \(-0.524484\pi\)
−0.0768433 + 0.997043i \(0.524484\pi\)
\(312\) −1.28983e11 −0.770611
\(313\) 1.21031e10 0.0712763 0.0356382 0.999365i \(-0.488654\pi\)
0.0356382 + 0.999365i \(0.488654\pi\)
\(314\) 1.40998e11 0.818520
\(315\) 6.86064e10 0.392615
\(316\) 3.99670e11 2.25481
\(317\) 2.26225e11 1.25827 0.629135 0.777296i \(-0.283409\pi\)
0.629135 + 0.777296i \(0.283409\pi\)
\(318\) 4.33999e11 2.37994
\(319\) 1.49219e11 0.806798
\(320\) 4.11316e10 0.219281
\(321\) 9.94939e10 0.523026
\(322\) 7.27709e10 0.377230
\(323\) 0 0
\(324\) −5.74916e11 −2.89836
\(325\) 3.84085e10 0.190965
\(326\) 4.13913e11 2.02969
\(327\) 1.06956e11 0.517300
\(328\) −7.11784e11 −3.39560
\(329\) 1.73323e11 0.815595
\(330\) 4.58897e11 2.13011
\(331\) −7.16543e10 −0.328107 −0.164054 0.986451i \(-0.552457\pi\)
−0.164054 + 0.986451i \(0.552457\pi\)
\(332\) −5.68714e11 −2.56905
\(333\) 2.22083e11 0.989730
\(334\) 2.78358e11 1.22390
\(335\) −7.78964e10 −0.337922
\(336\) −8.47979e11 −3.62960
\(337\) −1.03196e11 −0.435843 −0.217922 0.975966i \(-0.569928\pi\)
−0.217922 + 0.975966i \(0.569928\pi\)
\(338\) 4.09175e11 1.70523
\(339\) −5.31780e11 −2.18692
\(340\) 0 0
\(341\) 5.58550e11 2.23701
\(342\) −1.73380e11 −0.685300
\(343\) −2.12710e10 −0.0829782
\(344\) 1.24917e10 0.0480961
\(345\) 2.44641e10 0.0929700
\(346\) −2.82248e11 −1.05874
\(347\) 1.44300e10 0.0534297 0.0267149 0.999643i \(-0.491495\pi\)
0.0267149 + 0.999643i \(0.491495\pi\)
\(348\) −3.44061e11 −1.25756
\(349\) −5.24580e11 −1.89277 −0.946384 0.323045i \(-0.895293\pi\)
−0.946384 + 0.323045i \(0.895293\pi\)
\(350\) 5.34304e11 1.90319
\(351\) −3.96222e10 −0.139334
\(352\) −7.43091e11 −2.57988
\(353\) −3.33276e11 −1.14240 −0.571200 0.820811i \(-0.693522\pi\)
−0.571200 + 0.820811i \(0.693522\pi\)
\(354\) −7.53839e10 −0.255131
\(355\) 6.78788e10 0.226833
\(356\) −2.28899e11 −0.755300
\(357\) 0 0
\(358\) −3.41450e11 −1.09864
\(359\) −1.56163e11 −0.496195 −0.248098 0.968735i \(-0.579805\pi\)
−0.248098 + 0.968735i \(0.579805\pi\)
\(360\) −2.17214e11 −0.681596
\(361\) −1.78811e11 −0.554130
\(362\) 2.83188e11 0.866734
\(363\) −1.02562e12 −3.10031
\(364\) −2.76630e11 −0.825928
\(365\) 4.38188e9 0.0129224
\(366\) 1.06450e12 3.10086
\(367\) −5.01847e11 −1.44402 −0.722012 0.691881i \(-0.756782\pi\)
−0.722012 + 0.691881i \(0.756782\pi\)
\(368\) −1.08887e11 −0.309499
\(369\) 2.81410e11 0.790171
\(370\) −5.79128e11 −1.60645
\(371\) 5.30630e11 1.45415
\(372\) −1.28788e12 −3.48683
\(373\) −4.29931e11 −1.15003 −0.575015 0.818143i \(-0.695004\pi\)
−0.575015 + 0.818143i \(0.695004\pi\)
\(374\) 0 0
\(375\) 4.19389e11 1.09516
\(376\) −5.48757e11 −1.41591
\(377\) −4.32404e10 −0.110244
\(378\) −5.51188e11 −1.38863
\(379\) 5.20247e11 1.29519 0.647595 0.761985i \(-0.275775\pi\)
0.647595 + 0.761985i \(0.275775\pi\)
\(380\) 3.16188e11 0.777892
\(381\) 5.21663e11 1.26832
\(382\) −1.59836e11 −0.384051
\(383\) 5.98804e10 0.142197 0.0710985 0.997469i \(-0.477350\pi\)
0.0710985 + 0.997469i \(0.477350\pi\)
\(384\) −3.11320e11 −0.730661
\(385\) 5.61071e11 1.30150
\(386\) 9.09604e11 2.08550
\(387\) −4.93872e9 −0.0111922
\(388\) −2.52684e11 −0.566024
\(389\) 5.55917e10 0.123094 0.0615470 0.998104i \(-0.480397\pi\)
0.0615470 + 0.998104i \(0.480397\pi\)
\(390\) −1.32979e11 −0.291066
\(391\) 0 0
\(392\) −1.06322e12 −2.27424
\(393\) 3.45303e11 0.730186
\(394\) −7.79053e11 −1.62867
\(395\) 2.34902e11 0.485513
\(396\) 1.19494e12 2.44185
\(397\) 2.15249e11 0.434894 0.217447 0.976072i \(-0.430227\pi\)
0.217447 + 0.976072i \(0.430227\pi\)
\(398\) −7.13643e11 −1.42563
\(399\) −5.88675e11 −1.16278
\(400\) −7.99477e11 −1.56148
\(401\) −2.85995e11 −0.552344 −0.276172 0.961108i \(-0.589066\pi\)
−0.276172 + 0.961108i \(0.589066\pi\)
\(402\) −8.05446e11 −1.53822
\(403\) −1.61856e11 −0.305672
\(404\) 1.65188e12 3.08505
\(405\) −3.37902e11 −0.624084
\(406\) −6.01520e11 −1.09871
\(407\) 1.81622e12 3.28091
\(408\) 0 0
\(409\) 2.43866e11 0.430919 0.215460 0.976513i \(-0.430875\pi\)
0.215460 + 0.976513i \(0.430875\pi\)
\(410\) −7.33836e11 −1.28254
\(411\) −6.37778e11 −1.10251
\(412\) 9.21074e9 0.0157492
\(413\) −9.21683e10 −0.155886
\(414\) 9.10906e10 0.152395
\(415\) −3.34257e11 −0.553176
\(416\) 2.15332e11 0.352524
\(417\) −5.22808e11 −0.846701
\(418\) −1.41792e12 −2.27174
\(419\) −1.03402e12 −1.63894 −0.819472 0.573119i \(-0.805733\pi\)
−0.819472 + 0.573119i \(0.805733\pi\)
\(420\) −1.29369e12 −2.02866
\(421\) 1.12377e12 1.74344 0.871720 0.490004i \(-0.163005\pi\)
0.871720 + 0.490004i \(0.163005\pi\)
\(422\) 1.74294e11 0.267533
\(423\) 2.16956e11 0.329488
\(424\) −1.68002e12 −2.52446
\(425\) 0 0
\(426\) 7.01865e11 1.03255
\(427\) 1.30152e12 1.89463
\(428\) −6.75597e11 −0.973175
\(429\) 4.17039e11 0.594454
\(430\) 1.28787e10 0.0181662
\(431\) −2.79192e11 −0.389722 −0.194861 0.980831i \(-0.562426\pi\)
−0.194861 + 0.980831i \(0.562426\pi\)
\(432\) 8.24740e11 1.13930
\(433\) −5.92406e11 −0.809886 −0.404943 0.914342i \(-0.632709\pi\)
−0.404943 + 0.914342i \(0.632709\pi\)
\(434\) −2.25159e12 −3.04639
\(435\) −2.02219e11 −0.270782
\(436\) −7.26271e11 −0.962520
\(437\) −7.55903e10 −0.0991515
\(438\) 4.53085e10 0.0588229
\(439\) −1.19622e12 −1.53716 −0.768580 0.639754i \(-0.779036\pi\)
−0.768580 + 0.639754i \(0.779036\pi\)
\(440\) −1.77641e12 −2.25946
\(441\) 4.20354e11 0.529227
\(442\) 0 0
\(443\) 6.14827e11 0.758466 0.379233 0.925301i \(-0.376188\pi\)
0.379233 + 0.925301i \(0.376188\pi\)
\(444\) −4.18776e12 −5.11397
\(445\) −1.34534e11 −0.162634
\(446\) 1.37396e12 1.64425
\(447\) −5.68026e11 −0.672953
\(448\) 5.19993e11 0.609883
\(449\) 1.57287e12 1.82636 0.913178 0.407562i \(-0.133621\pi\)
0.913178 + 0.407562i \(0.133621\pi\)
\(450\) 6.68812e11 0.768861
\(451\) 2.30141e12 2.61938
\(452\) 3.61097e12 4.06912
\(453\) 2.06018e11 0.229860
\(454\) −2.31858e12 −2.56136
\(455\) −1.62587e11 −0.177842
\(456\) 1.86380e12 2.01864
\(457\) −1.08480e12 −1.16340 −0.581699 0.813404i \(-0.697612\pi\)
−0.581699 + 0.813404i \(0.697612\pi\)
\(458\) 2.10629e12 2.23678
\(459\) 0 0
\(460\) −1.66120e11 −0.172986
\(461\) 1.24066e12 1.27938 0.639691 0.768633i \(-0.279062\pi\)
0.639691 + 0.768633i \(0.279062\pi\)
\(462\) 5.80146e12 5.92445
\(463\) −1.73183e12 −1.75142 −0.875710 0.482837i \(-0.839607\pi\)
−0.875710 + 0.482837i \(0.839607\pi\)
\(464\) 9.00052e11 0.901439
\(465\) −7.56939e11 −0.750797
\(466\) 2.11782e12 2.08043
\(467\) −1.47573e12 −1.43575 −0.717877 0.696170i \(-0.754886\pi\)
−0.717877 + 0.696170i \(0.754886\pi\)
\(468\) −3.46269e11 −0.333663
\(469\) −9.84781e11 −0.939857
\(470\) −5.65758e11 −0.534799
\(471\) 5.99247e11 0.561063
\(472\) 2.91814e11 0.270624
\(473\) −4.03894e10 −0.0371016
\(474\) 2.42888e12 2.21006
\(475\) −5.55005e11 −0.500237
\(476\) 0 0
\(477\) 6.64213e11 0.587455
\(478\) 3.05722e11 0.267856
\(479\) 1.07230e12 0.930691 0.465345 0.885129i \(-0.345930\pi\)
0.465345 + 0.885129i \(0.345930\pi\)
\(480\) 1.00703e12 0.865875
\(481\) −5.26303e11 −0.448315
\(482\) 3.80976e11 0.321504
\(483\) 3.09280e11 0.258577
\(484\) 6.96428e12 5.76862
\(485\) −1.48513e11 −0.121878
\(486\) −2.26786e12 −1.84397
\(487\) 2.21909e12 1.78770 0.893848 0.448370i \(-0.147995\pi\)
0.893848 + 0.448370i \(0.147995\pi\)
\(488\) −4.12072e12 −3.28916
\(489\) 1.75915e12 1.39127
\(490\) −1.09616e12 −0.858998
\(491\) 1.84461e12 1.43231 0.716155 0.697941i \(-0.245900\pi\)
0.716155 + 0.697941i \(0.245900\pi\)
\(492\) −5.30647e12 −4.08285
\(493\) 0 0
\(494\) 4.10883e11 0.310418
\(495\) 7.02318e11 0.525788
\(496\) 3.36904e12 2.49942
\(497\) 8.58137e11 0.630889
\(498\) −3.45620e12 −2.51807
\(499\) −8.68109e11 −0.626790 −0.313395 0.949623i \(-0.601466\pi\)
−0.313395 + 0.949623i \(0.601466\pi\)
\(500\) −2.84779e12 −2.03771
\(501\) 1.18303e12 0.838934
\(502\) −2.80210e12 −1.96932
\(503\) −9.49807e11 −0.661575 −0.330788 0.943705i \(-0.607314\pi\)
−0.330788 + 0.943705i \(0.607314\pi\)
\(504\) −2.74606e12 −1.89572
\(505\) 9.70879e11 0.664284
\(506\) 7.44950e11 0.505184
\(507\) 1.73901e12 1.16887
\(508\) −3.54227e12 −2.35991
\(509\) 1.21433e12 0.801872 0.400936 0.916106i \(-0.368685\pi\)
0.400936 + 0.916106i \(0.368685\pi\)
\(510\) 0 0
\(511\) 5.53966e10 0.0359409
\(512\) 3.35555e12 2.15798
\(513\) 5.72542e11 0.364989
\(514\) 1.94676e12 1.23021
\(515\) 5.41353e9 0.00339116
\(516\) 9.31280e10 0.0578305
\(517\) 1.77429e12 1.09224
\(518\) −7.32145e12 −4.46800
\(519\) −1.19957e12 −0.725724
\(520\) 5.14765e11 0.308741
\(521\) −3.04153e12 −1.80852 −0.904258 0.426985i \(-0.859576\pi\)
−0.904258 + 0.426985i \(0.859576\pi\)
\(522\) −7.52950e11 −0.443863
\(523\) 2.35988e12 1.37922 0.689608 0.724183i \(-0.257783\pi\)
0.689608 + 0.724183i \(0.257783\pi\)
\(524\) −2.34472e12 −1.35863
\(525\) 2.27082e12 1.30456
\(526\) 4.21955e12 2.40342
\(527\) 0 0
\(528\) −8.68069e12 −4.86073
\(529\) −1.76144e12 −0.977951
\(530\) −1.73207e12 −0.953509
\(531\) −1.15371e11 −0.0629756
\(532\) 3.99731e12 2.16354
\(533\) −6.66899e11 −0.357921
\(534\) −1.39107e12 −0.740311
\(535\) −3.97076e11 −0.209547
\(536\) 3.11791e12 1.63163
\(537\) −1.45118e12 −0.753072
\(538\) 5.34414e12 2.75016
\(539\) 3.43771e12 1.75436
\(540\) 1.25824e12 0.636782
\(541\) −8.17432e10 −0.0410264 −0.0205132 0.999790i \(-0.506530\pi\)
−0.0205132 + 0.999790i \(0.506530\pi\)
\(542\) 5.67238e10 0.0282337
\(543\) 1.20356e12 0.594112
\(544\) 0 0
\(545\) −4.26860e11 −0.207253
\(546\) −1.68114e12 −0.809537
\(547\) 2.18248e12 1.04233 0.521167 0.853454i \(-0.325497\pi\)
0.521167 + 0.853454i \(0.325497\pi\)
\(548\) 4.33073e12 2.05139
\(549\) 1.62917e12 0.765402
\(550\) 5.46963e12 2.54874
\(551\) 6.24825e11 0.288786
\(552\) −9.79209e11 −0.448900
\(553\) 2.96968e12 1.35035
\(554\) 4.51503e12 2.03642
\(555\) −2.46132e12 −1.10116
\(556\) 3.55005e12 1.57542
\(557\) −3.53439e11 −0.155584 −0.0777921 0.996970i \(-0.524787\pi\)
−0.0777921 + 0.996970i \(0.524787\pi\)
\(558\) −2.81842e12 −1.23070
\(559\) 1.17040e10 0.00506969
\(560\) 3.38425e12 1.45418
\(561\) 0 0
\(562\) 2.38616e12 1.00899
\(563\) 1.08142e10 0.00453634 0.00226817 0.999997i \(-0.499278\pi\)
0.00226817 + 0.999997i \(0.499278\pi\)
\(564\) −4.09108e12 −1.70248
\(565\) 2.12231e12 0.876176
\(566\) 3.16985e12 1.29827
\(567\) −4.27182e12 −1.73576
\(568\) −2.71694e12 −1.09525
\(569\) 3.31804e12 1.32702 0.663508 0.748169i \(-0.269067\pi\)
0.663508 + 0.748169i \(0.269067\pi\)
\(570\) 1.92154e12 0.762454
\(571\) −1.02415e12 −0.403184 −0.201592 0.979470i \(-0.564611\pi\)
−0.201592 + 0.979470i \(0.564611\pi\)
\(572\) −2.83183e12 −1.10608
\(573\) −6.79309e11 −0.263252
\(574\) −9.27729e12 −3.56712
\(575\) 2.91590e11 0.111242
\(576\) 6.50898e11 0.246384
\(577\) −2.29132e12 −0.860585 −0.430293 0.902689i \(-0.641590\pi\)
−0.430293 + 0.902689i \(0.641590\pi\)
\(578\) 0 0
\(579\) 3.86586e12 1.42953
\(580\) 1.37313e12 0.503833
\(581\) −4.22574e12 −1.53854
\(582\) −1.53562e12 −0.554791
\(583\) 5.43201e12 1.94739
\(584\) −1.75391e11 −0.0623949
\(585\) −2.03517e11 −0.0718454
\(586\) −6.34921e12 −2.22423
\(587\) −2.59032e12 −0.900495 −0.450247 0.892904i \(-0.648664\pi\)
−0.450247 + 0.892904i \(0.648664\pi\)
\(588\) −7.92651e12 −2.73454
\(589\) 2.33882e12 0.800717
\(590\) 3.00854e11 0.102217
\(591\) −3.31101e12 −1.11639
\(592\) 1.09550e13 3.66578
\(593\) 1.13589e12 0.377216 0.188608 0.982052i \(-0.439602\pi\)
0.188608 + 0.982052i \(0.439602\pi\)
\(594\) −5.64247e12 −1.85964
\(595\) 0 0
\(596\) 3.85709e12 1.25214
\(597\) −3.03301e12 −0.977214
\(598\) −2.15871e11 −0.0690301
\(599\) −1.61658e12 −0.513071 −0.256535 0.966535i \(-0.582581\pi\)
−0.256535 + 0.966535i \(0.582581\pi\)
\(600\) −7.18962e12 −2.26478
\(601\) 3.21649e12 1.00565 0.502825 0.864388i \(-0.332294\pi\)
0.502825 + 0.864388i \(0.332294\pi\)
\(602\) 1.62815e11 0.0505256
\(603\) −1.23269e12 −0.379689
\(604\) −1.39894e12 −0.427692
\(605\) 4.09319e12 1.24212
\(606\) 1.00389e13 3.02383
\(607\) 3.09505e11 0.0925377 0.0462688 0.998929i \(-0.485267\pi\)
0.0462688 + 0.998929i \(0.485267\pi\)
\(608\) −3.11156e12 −0.923446
\(609\) −2.55649e12 −0.753123
\(610\) −4.24839e12 −1.24234
\(611\) −5.14153e11 −0.149247
\(612\) 0 0
\(613\) −9.05807e11 −0.259098 −0.129549 0.991573i \(-0.541353\pi\)
−0.129549 + 0.991573i \(0.541353\pi\)
\(614\) −3.28954e12 −0.934065
\(615\) −3.11883e12 −0.879132
\(616\) −2.24577e13 −6.28422
\(617\) 3.56373e12 0.989968 0.494984 0.868902i \(-0.335174\pi\)
0.494984 + 0.868902i \(0.335174\pi\)
\(618\) 5.59758e10 0.0154366
\(619\) 5.84557e12 1.60036 0.800182 0.599757i \(-0.204736\pi\)
0.800182 + 0.599757i \(0.204736\pi\)
\(620\) 5.13987e12 1.39698
\(621\) −3.00804e11 −0.0811654
\(622\) 1.04630e12 0.280284
\(623\) −1.70080e12 −0.452331
\(624\) 2.51548e12 0.664187
\(625\) 1.18403e12 0.310387
\(626\) −4.99450e11 −0.129989
\(627\) −6.02622e12 −1.55719
\(628\) −4.06909e12 −1.04395
\(629\) 0 0
\(630\) −2.83114e12 −0.716026
\(631\) 6.52192e12 1.63773 0.818866 0.573984i \(-0.194603\pi\)
0.818866 + 0.573984i \(0.194603\pi\)
\(632\) −9.40229e12 −2.34427
\(633\) 7.40759e11 0.183384
\(634\) −9.33550e12 −2.29475
\(635\) −2.08194e12 −0.508143
\(636\) −1.25249e13 −3.03540
\(637\) −9.96176e11 −0.239722
\(638\) −6.15771e12 −1.47139
\(639\) 1.07417e12 0.254870
\(640\) 1.24247e12 0.292735
\(641\) 4.50098e12 1.05304 0.526521 0.850162i \(-0.323496\pi\)
0.526521 + 0.850162i \(0.323496\pi\)
\(642\) −4.10576e12 −0.953862
\(643\) 6.50124e12 1.49985 0.749923 0.661525i \(-0.230091\pi\)
0.749923 + 0.661525i \(0.230091\pi\)
\(644\) −2.10011e12 −0.481123
\(645\) 5.47352e10 0.0124522
\(646\) 0 0
\(647\) −4.54317e11 −0.101927 −0.0509635 0.998701i \(-0.516229\pi\)
−0.0509635 + 0.998701i \(0.516229\pi\)
\(648\) 1.35250e13 3.01335
\(649\) −9.43520e11 −0.208761
\(650\) −1.58498e12 −0.348269
\(651\) −9.56936e12 −2.08818
\(652\) −1.19452e13 −2.58869
\(653\) −6.21441e12 −1.33749 −0.668745 0.743492i \(-0.733168\pi\)
−0.668745 + 0.743492i \(0.733168\pi\)
\(654\) −4.41371e12 −0.943418
\(655\) −1.37809e12 −0.292545
\(656\) 1.38816e13 2.92665
\(657\) 6.93424e10 0.0145196
\(658\) −7.15242e12 −1.48743
\(659\) 3.63356e12 0.750494 0.375247 0.926925i \(-0.377558\pi\)
0.375247 + 0.926925i \(0.377558\pi\)
\(660\) −1.32434e13 −2.71677
\(661\) 3.58304e12 0.730038 0.365019 0.931000i \(-0.381063\pi\)
0.365019 + 0.931000i \(0.381063\pi\)
\(662\) 2.95692e12 0.598381
\(663\) 0 0
\(664\) 1.33791e13 2.67098
\(665\) 2.34938e12 0.465861
\(666\) −9.16458e12 −1.80501
\(667\) −3.28272e11 −0.0642196
\(668\) −8.03321e12 −1.56097
\(669\) 5.83940e12 1.12707
\(670\) 3.21451e12 0.616280
\(671\) 1.33235e13 2.53728
\(672\) 1.27310e13 2.40825
\(673\) 2.38054e12 0.447308 0.223654 0.974669i \(-0.428201\pi\)
0.223654 + 0.974669i \(0.428201\pi\)
\(674\) 4.25855e12 0.794863
\(675\) −2.20858e12 −0.409493
\(676\) −1.18085e13 −2.17487
\(677\) −7.75240e12 −1.41836 −0.709181 0.705027i \(-0.750935\pi\)
−0.709181 + 0.705027i \(0.750935\pi\)
\(678\) 2.19446e13 3.98836
\(679\) −1.87753e12 −0.338978
\(680\) 0 0
\(681\) −9.85407e12 −1.75571
\(682\) −2.30494e13 −4.07971
\(683\) 5.35319e12 0.941282 0.470641 0.882325i \(-0.344023\pi\)
0.470641 + 0.882325i \(0.344023\pi\)
\(684\) 5.00361e12 0.874039
\(685\) 2.54535e12 0.441713
\(686\) 8.77777e11 0.151330
\(687\) 8.95181e12 1.53322
\(688\) −2.43620e11 −0.0414538
\(689\) −1.57408e12 −0.266098
\(690\) −1.00955e12 −0.169553
\(691\) 1.40491e12 0.234422 0.117211 0.993107i \(-0.462605\pi\)
0.117211 + 0.993107i \(0.462605\pi\)
\(692\) 8.14547e12 1.35033
\(693\) 8.87884e12 1.46237
\(694\) −5.95474e11 −0.0974417
\(695\) 2.08651e12 0.339226
\(696\) 8.09408e12 1.30745
\(697\) 0 0
\(698\) 2.16475e13 3.45191
\(699\) 9.00084e12 1.42605
\(700\) −1.54196e13 −2.42735
\(701\) 6.06553e12 0.948720 0.474360 0.880331i \(-0.342680\pi\)
0.474360 + 0.880331i \(0.342680\pi\)
\(702\) 1.63507e12 0.254108
\(703\) 7.60510e12 1.17437
\(704\) 5.32313e12 0.816752
\(705\) −2.40450e12 −0.366584
\(706\) 1.37531e13 2.08344
\(707\) 1.22740e13 1.84757
\(708\) 2.17552e12 0.325397
\(709\) 4.47055e12 0.664436 0.332218 0.943203i \(-0.392203\pi\)
0.332218 + 0.943203i \(0.392203\pi\)
\(710\) −2.80112e12 −0.413684
\(711\) 3.71728e12 0.545522
\(712\) 5.38489e12 0.785266
\(713\) −1.22878e12 −0.178062
\(714\) 0 0
\(715\) −1.66439e12 −0.238164
\(716\) 9.85400e12 1.40121
\(717\) 1.29933e12 0.183604
\(718\) 6.44428e12 0.904929
\(719\) 1.09463e13 1.52752 0.763760 0.645500i \(-0.223351\pi\)
0.763760 + 0.645500i \(0.223351\pi\)
\(720\) 4.23622e12 0.587465
\(721\) 6.84389e10 0.00943180
\(722\) 7.37889e12 1.01059
\(723\) 1.61916e12 0.220378
\(724\) −8.17258e12 −1.10544
\(725\) −2.41026e12 −0.323999
\(726\) 4.23235e13 5.65414
\(727\) 4.35490e12 0.578194 0.289097 0.957300i \(-0.406645\pi\)
0.289097 + 0.957300i \(0.406645\pi\)
\(728\) 6.50775e12 0.858697
\(729\) −1.36549e11 −0.0179067
\(730\) −1.80825e11 −0.0235670
\(731\) 0 0
\(732\) −3.07207e13 −3.95486
\(733\) −2.30603e12 −0.295051 −0.147525 0.989058i \(-0.547131\pi\)
−0.147525 + 0.989058i \(0.547131\pi\)
\(734\) 2.07094e13 2.63352
\(735\) −4.65873e12 −0.588810
\(736\) 1.63476e12 0.205354
\(737\) −1.00811e13 −1.25865
\(738\) −1.16128e13 −1.44106
\(739\) −1.13265e13 −1.39700 −0.698498 0.715612i \(-0.746148\pi\)
−0.698498 + 0.715612i \(0.746148\pi\)
\(740\) 1.67132e13 2.04888
\(741\) 1.74627e12 0.212780
\(742\) −2.18972e13 −2.65198
\(743\) −1.47703e13 −1.77803 −0.889016 0.457877i \(-0.848610\pi\)
−0.889016 + 0.457877i \(0.848610\pi\)
\(744\) 3.02975e13 3.62517
\(745\) 2.26697e12 0.269614
\(746\) 1.77417e13 2.09735
\(747\) −5.28954e12 −0.621549
\(748\) 0 0
\(749\) −5.01992e12 −0.582812
\(750\) −1.73067e13 −1.99727
\(751\) −4.97306e12 −0.570485 −0.285243 0.958455i \(-0.592074\pi\)
−0.285243 + 0.958455i \(0.592074\pi\)
\(752\) 1.07021e13 1.22037
\(753\) −1.19090e13 −1.34989
\(754\) 1.78438e12 0.201055
\(755\) −8.22212e11 −0.0920921
\(756\) 1.59069e13 1.77107
\(757\) −4.59977e12 −0.509102 −0.254551 0.967059i \(-0.581928\pi\)
−0.254551 + 0.967059i \(0.581928\pi\)
\(758\) −2.14687e13 −2.36208
\(759\) 3.16607e12 0.346284
\(760\) −7.43837e12 −0.808754
\(761\) −1.36003e13 −1.47000 −0.734999 0.678068i \(-0.762817\pi\)
−0.734999 + 0.678068i \(0.762817\pi\)
\(762\) −2.15272e13 −2.31307
\(763\) −5.39644e12 −0.576430
\(764\) 4.61274e12 0.489823
\(765\) 0 0
\(766\) −2.47105e12 −0.259330
\(767\) 2.73412e11 0.0285258
\(768\) 1.81238e13 1.87985
\(769\) −3.92919e12 −0.405168 −0.202584 0.979265i \(-0.564934\pi\)
−0.202584 + 0.979265i \(0.564934\pi\)
\(770\) −2.31534e13 −2.37360
\(771\) 8.27381e12 0.843258
\(772\) −2.62505e13 −2.65986
\(773\) 1.26776e11 0.0127711 0.00638557 0.999980i \(-0.497967\pi\)
0.00638557 + 0.999980i \(0.497967\pi\)
\(774\) 2.03803e11 0.0204116
\(775\) −9.02202e12 −0.898351
\(776\) 5.94443e12 0.588481
\(777\) −3.11165e13 −3.06264
\(778\) −2.29407e12 −0.224491
\(779\) 9.63672e12 0.937585
\(780\) 3.83766e12 0.371228
\(781\) 8.78468e12 0.844883
\(782\) 0 0
\(783\) 2.48643e12 0.236400
\(784\) 2.07355e13 1.96016
\(785\) −2.39157e12 −0.224787
\(786\) −1.42494e13 −1.33167
\(787\) −5.21193e12 −0.484298 −0.242149 0.970239i \(-0.577852\pi\)
−0.242149 + 0.970239i \(0.577852\pi\)
\(788\) 2.24829e13 2.07723
\(789\) 1.79333e13 1.64745
\(790\) −9.69359e12 −0.885447
\(791\) 2.68307e13 2.43690
\(792\) −2.81112e13 −2.53873
\(793\) −3.86087e12 −0.346702
\(794\) −8.88255e12 −0.793132
\(795\) −7.36138e12 −0.653593
\(796\) 2.05952e13 1.81826
\(797\) −2.04646e13 −1.79656 −0.898280 0.439424i \(-0.855183\pi\)
−0.898280 + 0.439424i \(0.855183\pi\)
\(798\) 2.42925e13 2.12060
\(799\) 0 0
\(800\) 1.20028e13 1.03605
\(801\) −2.12896e12 −0.182735
\(802\) 1.18020e13 1.00733
\(803\) 5.67091e11 0.0481318
\(804\) 2.32446e13 1.96187
\(805\) −1.23432e12 −0.103597
\(806\) 6.67922e12 0.557465
\(807\) 2.27128e13 1.88512
\(808\) −3.88608e13 −3.20745
\(809\) −2.47572e12 −0.203204 −0.101602 0.994825i \(-0.532397\pi\)
−0.101602 + 0.994825i \(0.532397\pi\)
\(810\) 1.39440e13 1.13816
\(811\) 3.77855e12 0.306713 0.153356 0.988171i \(-0.450992\pi\)
0.153356 + 0.988171i \(0.450992\pi\)
\(812\) 1.73594e13 1.40131
\(813\) 2.41079e11 0.0193531
\(814\) −7.49491e13 −5.98352
\(815\) −7.02070e12 −0.557405
\(816\) 0 0
\(817\) −1.69123e11 −0.0132802
\(818\) −1.00635e13 −0.785883
\(819\) −2.57290e12 −0.199823
\(820\) 2.11779e13 1.63577
\(821\) 8.59353e12 0.660127 0.330063 0.943959i \(-0.392930\pi\)
0.330063 + 0.943959i \(0.392930\pi\)
\(822\) 2.63188e13 2.01068
\(823\) −8.64495e12 −0.656846 −0.328423 0.944531i \(-0.606517\pi\)
−0.328423 + 0.944531i \(0.606517\pi\)
\(824\) −2.16684e11 −0.0163740
\(825\) 2.32462e13 1.74706
\(826\) 3.80346e12 0.284294
\(827\) −1.08552e13 −0.806979 −0.403490 0.914984i \(-0.632203\pi\)
−0.403490 + 0.914984i \(0.632203\pi\)
\(828\) −2.62881e12 −0.194367
\(829\) −1.09679e13 −0.806547 −0.403274 0.915079i \(-0.632128\pi\)
−0.403274 + 0.915079i \(0.632128\pi\)
\(830\) 1.37936e13 1.00885
\(831\) 1.91891e13 1.39589
\(832\) −1.54253e12 −0.111604
\(833\) 0 0
\(834\) 2.15744e13 1.54416
\(835\) −4.72145e12 −0.336114
\(836\) 4.09201e13 2.89740
\(837\) 9.30711e12 0.655466
\(838\) 4.26702e13 2.98900
\(839\) −7.29579e12 −0.508327 −0.254164 0.967161i \(-0.581800\pi\)
−0.254164 + 0.967161i \(0.581800\pi\)
\(840\) 3.04343e13 2.10914
\(841\) −1.17937e13 −0.812956
\(842\) −4.63739e13 −3.17957
\(843\) 1.01413e13 0.691622
\(844\) −5.03001e12 −0.341215
\(845\) −6.94033e12 −0.468301
\(846\) −8.95300e12 −0.600900
\(847\) 5.17469e13 3.45469
\(848\) 3.27646e13 2.17583
\(849\) 1.34720e13 0.889913
\(850\) 0 0
\(851\) −3.99558e12 −0.261154
\(852\) −2.02553e13 −1.31692
\(853\) −2.42665e13 −1.56941 −0.784704 0.619871i \(-0.787185\pi\)
−0.784704 + 0.619871i \(0.787185\pi\)
\(854\) −5.37089e13 −3.45530
\(855\) 2.94083e12 0.188201
\(856\) 1.58935e13 1.01179
\(857\) −6.43774e12 −0.407680 −0.203840 0.979004i \(-0.565342\pi\)
−0.203840 + 0.979004i \(0.565342\pi\)
\(858\) −1.72097e13 −1.08413
\(859\) −1.05863e13 −0.663399 −0.331699 0.943385i \(-0.607622\pi\)
−0.331699 + 0.943385i \(0.607622\pi\)
\(860\) −3.71671e11 −0.0231694
\(861\) −3.94289e13 −2.44512
\(862\) 1.15212e13 0.710750
\(863\) −5.29030e11 −0.0324662 −0.0162331 0.999868i \(-0.505167\pi\)
−0.0162331 + 0.999868i \(0.505167\pi\)
\(864\) −1.23821e13 −0.755933
\(865\) 4.78743e12 0.290757
\(866\) 2.44465e13 1.47702
\(867\) 0 0
\(868\) 6.49793e13 3.88540
\(869\) 3.04004e13 1.80838
\(870\) 8.34484e12 0.493835
\(871\) 2.92130e12 0.171986
\(872\) 1.70856e13 1.00071
\(873\) −2.35018e12 −0.136942
\(874\) 3.11934e12 0.180826
\(875\) −2.11600e13 −1.22034
\(876\) −1.30757e12 −0.0750233
\(877\) 8.95643e12 0.511254 0.255627 0.966775i \(-0.417718\pi\)
0.255627 + 0.966775i \(0.417718\pi\)
\(878\) 4.93635e13 2.80337
\(879\) −2.69844e13 −1.52463
\(880\) 3.46443e13 1.94742
\(881\) 9.86603e12 0.551761 0.275880 0.961192i \(-0.411031\pi\)
0.275880 + 0.961192i \(0.411031\pi\)
\(882\) −1.73465e13 −0.965170
\(883\) −2.95451e13 −1.63555 −0.817773 0.575541i \(-0.804791\pi\)
−0.817773 + 0.575541i \(0.804791\pi\)
\(884\) 0 0
\(885\) 1.27864e12 0.0700656
\(886\) −2.53717e13 −1.38324
\(887\) 1.21200e13 0.657425 0.328712 0.944430i \(-0.393385\pi\)
0.328712 + 0.944430i \(0.393385\pi\)
\(888\) 9.85177e13 5.31687
\(889\) −2.63202e13 −1.41329
\(890\) 5.55172e12 0.296601
\(891\) −4.37303e13 −2.32452
\(892\) −3.96515e13 −2.09710
\(893\) 7.42953e12 0.390958
\(894\) 2.34404e13 1.22729
\(895\) 5.79160e12 0.301714
\(896\) 1.57075e13 0.814180
\(897\) −9.17460e11 −0.0473174
\(898\) −6.49069e13 −3.33079
\(899\) 1.01570e13 0.518617
\(900\) −1.93014e13 −0.980614
\(901\) 0 0
\(902\) −9.49709e13 −4.77706
\(903\) 6.91972e11 0.0346333
\(904\) −8.49485e13 −4.23056
\(905\) −4.80336e12 −0.238027
\(906\) −8.50164e12 −0.419205
\(907\) 3.13056e13 1.53599 0.767997 0.640453i \(-0.221254\pi\)
0.767997 + 0.640453i \(0.221254\pi\)
\(908\) 6.69125e13 3.26679
\(909\) 1.53639e13 0.746389
\(910\) 6.70937e12 0.324336
\(911\) −2.59379e13 −1.24768 −0.623838 0.781554i \(-0.714427\pi\)
−0.623838 + 0.781554i \(0.714427\pi\)
\(912\) −3.63488e13 −1.73986
\(913\) −4.32585e13 −2.06041
\(914\) 4.47659e13 2.12173
\(915\) −1.80558e13 −0.851574
\(916\) −6.07859e13 −2.85281
\(917\) −1.74221e13 −0.813651
\(918\) 0 0
\(919\) −2.19375e13 −1.01454 −0.507268 0.861788i \(-0.669345\pi\)
−0.507268 + 0.861788i \(0.669345\pi\)
\(920\) 3.90799e12 0.179849
\(921\) −1.39807e13 −0.640265
\(922\) −5.11978e13 −2.33325
\(923\) −2.54561e12 −0.115448
\(924\) −1.67426e14 −7.55611
\(925\) −2.93367e13 −1.31757
\(926\) 7.14664e13 3.19413
\(927\) 8.56680e10 0.00381031
\(928\) −1.35128e13 −0.598108
\(929\) 1.67080e12 0.0735960 0.0367980 0.999323i \(-0.488284\pi\)
0.0367980 + 0.999323i \(0.488284\pi\)
\(930\) 3.12362e13 1.36926
\(931\) 1.43948e13 0.627959
\(932\) −6.11188e13 −2.65340
\(933\) 4.44680e12 0.192123
\(934\) 6.08980e13 2.61844
\(935\) 0 0
\(936\) 8.14604e12 0.346901
\(937\) 4.07852e13 1.72852 0.864260 0.503046i \(-0.167787\pi\)
0.864260 + 0.503046i \(0.167787\pi\)
\(938\) 4.06384e13 1.71405
\(939\) −2.12268e12 −0.0891025
\(940\) 1.63274e13 0.682088
\(941\) 1.37791e13 0.572884 0.286442 0.958098i \(-0.407527\pi\)
0.286442 + 0.958098i \(0.407527\pi\)
\(942\) −2.47288e13 −1.02323
\(943\) −5.06296e12 −0.208498
\(944\) −5.69109e12 −0.233250
\(945\) 9.34912e12 0.381353
\(946\) 1.66673e12 0.0676635
\(947\) 1.07895e13 0.435939 0.217969 0.975956i \(-0.430057\pi\)
0.217969 + 0.975956i \(0.430057\pi\)
\(948\) −7.00958e13 −2.81873
\(949\) −1.64331e11 −0.00657690
\(950\) 2.29031e13 0.912300
\(951\) −3.96763e13 −1.57296
\(952\) 0 0
\(953\) −3.87488e13 −1.52174 −0.760870 0.648905i \(-0.775227\pi\)
−0.760870 + 0.648905i \(0.775227\pi\)
\(954\) −2.74097e13 −1.07136
\(955\) 2.71110e12 0.105470
\(956\) −8.82290e12 −0.341626
\(957\) −2.61706e13 −1.00858
\(958\) −4.42499e13 −1.69733
\(959\) 3.21788e13 1.22853
\(960\) −7.21383e12 −0.274123
\(961\) 1.15797e13 0.437969
\(962\) 2.17187e13 0.817608
\(963\) −6.28365e12 −0.235447
\(964\) −1.09947e13 −0.410049
\(965\) −1.54285e13 −0.572731
\(966\) −1.27629e13 −0.471575
\(967\) 3.06413e13 1.12691 0.563454 0.826148i \(-0.309472\pi\)
0.563454 + 0.826148i \(0.309472\pi\)
\(968\) −1.63836e14 −5.99749
\(969\) 0 0
\(970\) 6.12859e12 0.222274
\(971\) −4.68780e13 −1.69232 −0.846160 0.532929i \(-0.821091\pi\)
−0.846160 + 0.532929i \(0.821091\pi\)
\(972\) 6.54489e13 2.35182
\(973\) 2.63780e13 0.943484
\(974\) −9.15737e13 −3.26029
\(975\) −6.73625e12 −0.238725
\(976\) 8.03644e13 2.83491
\(977\) 1.42867e13 0.501656 0.250828 0.968032i \(-0.419297\pi\)
0.250828 + 0.968032i \(0.419297\pi\)
\(978\) −7.25937e13 −2.53731
\(979\) −1.74109e13 −0.605759
\(980\) 3.16344e13 1.09558
\(981\) −6.75496e12 −0.232869
\(982\) −7.61203e13 −2.61215
\(983\) −7.35838e12 −0.251357 −0.125679 0.992071i \(-0.540111\pi\)
−0.125679 + 0.992071i \(0.540111\pi\)
\(984\) 1.24836e14 4.24483
\(985\) 1.32141e13 0.447276
\(986\) 0 0
\(987\) −3.03981e13 −1.01958
\(988\) −1.18578e13 −0.395911
\(989\) 8.88544e10 0.00295322
\(990\) −2.89821e13 −0.958898
\(991\) 3.30115e13 1.08726 0.543630 0.839325i \(-0.317049\pi\)
0.543630 + 0.839325i \(0.317049\pi\)
\(992\) −5.05807e13 −1.65837
\(993\) 1.25670e13 0.410167
\(994\) −3.54123e13 −1.15057
\(995\) 1.21046e13 0.391515
\(996\) 9.97434e13 3.21157
\(997\) 2.85504e13 0.915132 0.457566 0.889176i \(-0.348721\pi\)
0.457566 + 0.889176i \(0.348721\pi\)
\(998\) 3.58238e13 1.14310
\(999\) 3.02637e13 0.961341
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.i.1.1 52
17.3 odd 16 17.10.d.a.9.1 yes 52
17.6 odd 16 17.10.d.a.2.1 52
17.16 even 2 inner 289.10.a.i.1.2 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.d.a.2.1 52 17.6 odd 16
17.10.d.a.9.1 yes 52 17.3 odd 16
289.10.a.i.1.1 52 1.1 even 1 trivial
289.10.a.i.1.2 52 17.16 even 2 inner