Properties

Label 289.10.a.g.1.11
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 1.11
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-21.2323 q^{2} -64.4551 q^{3} -61.1895 q^{4} -398.305 q^{5} +1368.53 q^{6} +3851.88 q^{7} +12170.1 q^{8} -15528.5 q^{9} +O(q^{10})\) \(q-21.2323 q^{2} -64.4551 q^{3} -61.1895 q^{4} -398.305 q^{5} +1368.53 q^{6} +3851.88 q^{7} +12170.1 q^{8} -15528.5 q^{9} +8456.93 q^{10} +57855.9 q^{11} +3943.98 q^{12} +18882.5 q^{13} -81784.2 q^{14} +25672.8 q^{15} -227071. q^{16} +329707. q^{18} -786629. q^{19} +24372.1 q^{20} -248273. q^{21} -1.22841e6 q^{22} +821658. q^{23} -784427. q^{24} -1.79448e6 q^{25} -400918. q^{26} +2.26956e6 q^{27} -235694. q^{28} +1.71388e6 q^{29} -545093. q^{30} -7.63150e6 q^{31} -1.40987e6 q^{32} -3.72911e6 q^{33} -1.53422e6 q^{35} +950183. q^{36} +8.29440e6 q^{37} +1.67020e7 q^{38} -1.21707e6 q^{39} -4.84742e6 q^{40} +9.40014e6 q^{41} +5.27141e6 q^{42} -1.23821e6 q^{43} -3.54017e6 q^{44} +6.18509e6 q^{45} -1.74457e7 q^{46} -5.62823e6 q^{47} +1.46359e7 q^{48} -2.55167e7 q^{49} +3.81009e7 q^{50} -1.15541e6 q^{52} +5.02821e7 q^{53} -4.81881e7 q^{54} -2.30443e7 q^{55} +4.68778e7 q^{56} +5.07023e7 q^{57} -3.63896e7 q^{58} +3.74512e7 q^{59} -1.57091e6 q^{60} +5.48296e7 q^{61} +1.62034e8 q^{62} -5.98140e7 q^{63} +1.46195e8 q^{64} -7.52098e6 q^{65} +7.91775e7 q^{66} -1.56686e8 q^{67} -5.29601e7 q^{69} +3.25751e7 q^{70} +2.37280e8 q^{71} -1.88984e8 q^{72} -4.12331e7 q^{73} -1.76109e8 q^{74} +1.15663e8 q^{75} +4.81335e7 q^{76} +2.22854e8 q^{77} +2.58412e7 q^{78} +1.46264e8 q^{79} +9.04435e7 q^{80} +1.59363e8 q^{81} -1.99586e8 q^{82} +8.36517e7 q^{83} +1.51917e7 q^{84} +2.62900e7 q^{86} -1.10468e8 q^{87} +7.04114e8 q^{88} +9.53686e8 q^{89} -1.31324e8 q^{90} +7.27329e7 q^{91} -5.02768e7 q^{92} +4.91889e8 q^{93} +1.19500e8 q^{94} +3.13318e8 q^{95} +9.08734e7 q^{96} -1.21808e9 q^{97} +5.41777e8 q^{98} -8.98417e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −21.2323 −0.938344 −0.469172 0.883107i \(-0.655448\pi\)
−0.469172 + 0.883107i \(0.655448\pi\)
\(3\) −64.4551 −0.459422 −0.229711 0.973259i \(-0.573778\pi\)
−0.229711 + 0.973259i \(0.573778\pi\)
\(4\) −61.1895 −0.119511
\(5\) −398.305 −0.285004 −0.142502 0.989795i \(-0.545515\pi\)
−0.142502 + 0.989795i \(0.545515\pi\)
\(6\) 1368.53 0.431096
\(7\) 3851.88 0.606361 0.303180 0.952933i \(-0.401952\pi\)
0.303180 + 0.952933i \(0.401952\pi\)
\(8\) 12170.1 1.05049
\(9\) −15528.5 −0.788931
\(10\) 8456.93 0.267432
\(11\) 57855.9 1.19146 0.595731 0.803184i \(-0.296862\pi\)
0.595731 + 0.803184i \(0.296862\pi\)
\(12\) 3943.98 0.0549059
\(13\) 18882.5 0.183364 0.0916819 0.995788i \(-0.470776\pi\)
0.0916819 + 0.995788i \(0.470776\pi\)
\(14\) −81784.2 −0.568975
\(15\) 25672.8 0.130937
\(16\) −227071. −0.866206
\(17\) 0 0
\(18\) 329707. 0.740289
\(19\) −786629. −1.38477 −0.692387 0.721526i \(-0.743441\pi\)
−0.692387 + 0.721526i \(0.743441\pi\)
\(20\) 24372.1 0.0340610
\(21\) −248273. −0.278576
\(22\) −1.22841e6 −1.11800
\(23\) 821658. 0.612232 0.306116 0.951994i \(-0.400971\pi\)
0.306116 + 0.951994i \(0.400971\pi\)
\(24\) −784427. −0.482617
\(25\) −1.79448e6 −0.918773
\(26\) −400918. −0.172058
\(27\) 2.26956e6 0.821875
\(28\) −235694. −0.0724666
\(29\) 1.71388e6 0.449975 0.224988 0.974362i \(-0.427766\pi\)
0.224988 + 0.974362i \(0.427766\pi\)
\(30\) −545093. −0.122864
\(31\) −7.63150e6 −1.48416 −0.742082 0.670309i \(-0.766162\pi\)
−0.742082 + 0.670309i \(0.766162\pi\)
\(32\) −1.40987e6 −0.237687
\(33\) −3.72911e6 −0.547384
\(34\) 0 0
\(35\) −1.53422e6 −0.172815
\(36\) 950183. 0.0942858
\(37\) 8.29440e6 0.727574 0.363787 0.931482i \(-0.381484\pi\)
0.363787 + 0.931482i \(0.381484\pi\)
\(38\) 1.67020e7 1.29939
\(39\) −1.21707e6 −0.0842414
\(40\) −4.84742e6 −0.299393
\(41\) 9.40014e6 0.519525 0.259763 0.965672i \(-0.416356\pi\)
0.259763 + 0.965672i \(0.416356\pi\)
\(42\) 5.27141e6 0.261400
\(43\) −1.23821e6 −0.0552314 −0.0276157 0.999619i \(-0.508791\pi\)
−0.0276157 + 0.999619i \(0.508791\pi\)
\(44\) −3.54017e6 −0.142393
\(45\) 6.18509e6 0.224848
\(46\) −1.74457e7 −0.574484
\(47\) −5.62823e6 −0.168241 −0.0841204 0.996456i \(-0.526808\pi\)
−0.0841204 + 0.996456i \(0.526808\pi\)
\(48\) 1.46359e7 0.397954
\(49\) −2.55167e7 −0.632326
\(50\) 3.81009e7 0.862125
\(51\) 0 0
\(52\) −1.15541e6 −0.0219139
\(53\) 5.02821e7 0.875330 0.437665 0.899138i \(-0.355806\pi\)
0.437665 + 0.899138i \(0.355806\pi\)
\(54\) −4.81881e7 −0.771201
\(55\) −2.30443e7 −0.339571
\(56\) 4.68778e7 0.636974
\(57\) 5.07023e7 0.636196
\(58\) −3.63896e7 −0.422232
\(59\) 3.74512e7 0.402376 0.201188 0.979553i \(-0.435520\pi\)
0.201188 + 0.979553i \(0.435520\pi\)
\(60\) −1.57091e6 −0.0156484
\(61\) 5.48296e7 0.507026 0.253513 0.967332i \(-0.418414\pi\)
0.253513 + 0.967332i \(0.418414\pi\)
\(62\) 1.62034e8 1.39266
\(63\) −5.98140e7 −0.478377
\(64\) 1.46195e8 1.08924
\(65\) −7.52098e6 −0.0522594
\(66\) 7.91775e7 0.513635
\(67\) −1.56686e8 −0.949934 −0.474967 0.880004i \(-0.657540\pi\)
−0.474967 + 0.880004i \(0.657540\pi\)
\(68\) 0 0
\(69\) −5.29601e7 −0.281273
\(70\) 3.25751e7 0.162160
\(71\) 2.37280e8 1.10815 0.554074 0.832467i \(-0.313072\pi\)
0.554074 + 0.832467i \(0.313072\pi\)
\(72\) −1.88984e8 −0.828761
\(73\) −4.12331e7 −0.169939 −0.0849696 0.996384i \(-0.527079\pi\)
−0.0849696 + 0.996384i \(0.527079\pi\)
\(74\) −1.76109e8 −0.682715
\(75\) 1.15663e8 0.422105
\(76\) 4.81335e7 0.165495
\(77\) 2.22854e8 0.722456
\(78\) 2.58412e7 0.0790474
\(79\) 1.46264e8 0.422489 0.211244 0.977433i \(-0.432248\pi\)
0.211244 + 0.977433i \(0.432248\pi\)
\(80\) 9.04435e7 0.246872
\(81\) 1.59363e8 0.411344
\(82\) −1.99586e8 −0.487493
\(83\) 8.36517e7 0.193474 0.0967371 0.995310i \(-0.469159\pi\)
0.0967371 + 0.995310i \(0.469159\pi\)
\(84\) 1.51917e7 0.0332928
\(85\) 0 0
\(86\) 2.62900e7 0.0518260
\(87\) −1.10468e8 −0.206729
\(88\) 7.04114e8 1.25161
\(89\) 9.53686e8 1.61120 0.805602 0.592458i \(-0.201842\pi\)
0.805602 + 0.592458i \(0.201842\pi\)
\(90\) −1.31324e8 −0.210985
\(91\) 7.27329e7 0.111185
\(92\) −5.02768e7 −0.0731682
\(93\) 4.91889e8 0.681858
\(94\) 1.19500e8 0.157868
\(95\) 3.13318e8 0.394666
\(96\) 9.08734e7 0.109198
\(97\) −1.21808e9 −1.39702 −0.698509 0.715601i \(-0.746153\pi\)
−0.698509 + 0.715601i \(0.746153\pi\)
\(98\) 5.41777e8 0.593340
\(99\) −8.98417e8 −0.939982
\(100\) 1.09803e8 0.109803
\(101\) −1.85970e9 −1.77826 −0.889132 0.457652i \(-0.848691\pi\)
−0.889132 + 0.457652i \(0.848691\pi\)
\(102\) 0 0
\(103\) −1.82228e9 −1.59532 −0.797660 0.603107i \(-0.793929\pi\)
−0.797660 + 0.603107i \(0.793929\pi\)
\(104\) 2.29802e8 0.192621
\(105\) 9.88885e7 0.0793951
\(106\) −1.06760e9 −0.821360
\(107\) 1.89558e9 1.39802 0.699012 0.715109i \(-0.253623\pi\)
0.699012 + 0.715109i \(0.253623\pi\)
\(108\) −1.38873e8 −0.0982228
\(109\) 1.15703e9 0.785104 0.392552 0.919730i \(-0.371592\pi\)
0.392552 + 0.919730i \(0.371592\pi\)
\(110\) 4.89283e8 0.318635
\(111\) −5.34617e8 −0.334264
\(112\) −8.74649e8 −0.525234
\(113\) 3.34864e9 1.93204 0.966018 0.258473i \(-0.0832194\pi\)
0.966018 + 0.258473i \(0.0832194\pi\)
\(114\) −1.07653e9 −0.596971
\(115\) −3.27270e8 −0.174488
\(116\) −1.04871e8 −0.0537769
\(117\) −2.93217e8 −0.144661
\(118\) −7.95176e8 −0.377567
\(119\) 0 0
\(120\) 3.12441e8 0.137548
\(121\) 9.89355e8 0.419583
\(122\) −1.16416e9 −0.475765
\(123\) −6.05887e8 −0.238681
\(124\) 4.66967e8 0.177374
\(125\) 1.49269e9 0.546858
\(126\) 1.26999e9 0.448882
\(127\) 3.51461e9 1.19884 0.599418 0.800436i \(-0.295399\pi\)
0.599418 + 0.800436i \(0.295399\pi\)
\(128\) −2.38220e9 −0.784393
\(129\) 7.98089e7 0.0253745
\(130\) 1.59688e8 0.0490373
\(131\) 2.53404e9 0.751783 0.375892 0.926664i \(-0.377337\pi\)
0.375892 + 0.926664i \(0.377337\pi\)
\(132\) 2.28182e8 0.0654183
\(133\) −3.03000e9 −0.839673
\(134\) 3.32680e9 0.891364
\(135\) −9.03979e8 −0.234237
\(136\) 0 0
\(137\) −3.06420e9 −0.743146 −0.371573 0.928404i \(-0.621181\pi\)
−0.371573 + 0.928404i \(0.621181\pi\)
\(138\) 1.12446e9 0.263931
\(139\) 3.98153e9 0.904655 0.452327 0.891852i \(-0.350594\pi\)
0.452327 + 0.891852i \(0.350594\pi\)
\(140\) 9.38782e7 0.0206533
\(141\) 3.62768e8 0.0772935
\(142\) −5.03799e9 −1.03982
\(143\) 1.09246e9 0.218471
\(144\) 3.52608e9 0.683377
\(145\) −6.82646e8 −0.128245
\(146\) 8.75474e8 0.159461
\(147\) 1.64468e9 0.290505
\(148\) −5.07530e8 −0.0869529
\(149\) 1.25034e9 0.207822 0.103911 0.994587i \(-0.466864\pi\)
0.103911 + 0.994587i \(0.466864\pi\)
\(150\) −2.45580e9 −0.396079
\(151\) 1.16543e10 1.82427 0.912137 0.409885i \(-0.134431\pi\)
0.912137 + 0.409885i \(0.134431\pi\)
\(152\) −9.57338e9 −1.45469
\(153\) 0 0
\(154\) −4.73170e9 −0.677912
\(155\) 3.03966e9 0.422993
\(156\) 7.44720e7 0.0100677
\(157\) 4.36782e9 0.573742 0.286871 0.957969i \(-0.407385\pi\)
0.286871 + 0.957969i \(0.407385\pi\)
\(158\) −3.10552e9 −0.396440
\(159\) −3.24094e9 −0.402146
\(160\) 5.61559e8 0.0677416
\(161\) 3.16492e9 0.371233
\(162\) −3.38364e9 −0.385982
\(163\) −1.39760e10 −1.55073 −0.775367 0.631511i \(-0.782435\pi\)
−0.775367 + 0.631511i \(0.782435\pi\)
\(164\) −5.75189e8 −0.0620889
\(165\) 1.48532e9 0.156007
\(166\) −1.77612e9 −0.181545
\(167\) −4.41364e9 −0.439109 −0.219555 0.975600i \(-0.570460\pi\)
−0.219555 + 0.975600i \(0.570460\pi\)
\(168\) −3.02152e9 −0.292640
\(169\) −1.02480e10 −0.966378
\(170\) 0 0
\(171\) 1.22152e10 1.09249
\(172\) 7.57653e7 0.00660074
\(173\) −1.72782e10 −1.46653 −0.733267 0.679941i \(-0.762006\pi\)
−0.733267 + 0.679941i \(0.762006\pi\)
\(174\) 2.34549e9 0.193983
\(175\) −6.91211e9 −0.557108
\(176\) −1.31374e10 −1.03205
\(177\) −2.41392e9 −0.184860
\(178\) −2.02489e10 −1.51186
\(179\) −1.48464e10 −1.08089 −0.540445 0.841379i \(-0.681744\pi\)
−0.540445 + 0.841379i \(0.681744\pi\)
\(180\) −3.78463e8 −0.0268718
\(181\) 4.63118e9 0.320729 0.160364 0.987058i \(-0.448733\pi\)
0.160364 + 0.987058i \(0.448733\pi\)
\(182\) −1.54429e9 −0.104329
\(183\) −3.53405e9 −0.232939
\(184\) 9.99968e9 0.643141
\(185\) −3.30370e9 −0.207361
\(186\) −1.04439e10 −0.639817
\(187\) 0 0
\(188\) 3.44388e8 0.0201066
\(189\) 8.74208e9 0.498353
\(190\) −6.65247e9 −0.370332
\(191\) −5.36986e9 −0.291953 −0.145977 0.989288i \(-0.546632\pi\)
−0.145977 + 0.989288i \(0.546632\pi\)
\(192\) −9.42302e9 −0.500420
\(193\) −6.19209e9 −0.321240 −0.160620 0.987016i \(-0.551349\pi\)
−0.160620 + 0.987016i \(0.551349\pi\)
\(194\) 2.58626e10 1.31088
\(195\) 4.84766e8 0.0240091
\(196\) 1.56135e9 0.0755698
\(197\) −2.78857e10 −1.31912 −0.659558 0.751653i \(-0.729257\pi\)
−0.659558 + 0.751653i \(0.729257\pi\)
\(198\) 1.90755e10 0.882026
\(199\) −3.10537e10 −1.40370 −0.701851 0.712324i \(-0.747643\pi\)
−0.701851 + 0.712324i \(0.747643\pi\)
\(200\) −2.18390e10 −0.965158
\(201\) 1.00992e10 0.436420
\(202\) 3.94856e10 1.66862
\(203\) 6.60164e9 0.272847
\(204\) 0 0
\(205\) −3.74412e9 −0.148067
\(206\) 3.86912e10 1.49696
\(207\) −1.27591e10 −0.483009
\(208\) −4.28766e9 −0.158831
\(209\) −4.55111e10 −1.64991
\(210\) −2.09963e9 −0.0744999
\(211\) −5.99281e9 −0.208142 −0.104071 0.994570i \(-0.533187\pi\)
−0.104071 + 0.994570i \(0.533187\pi\)
\(212\) −3.07673e9 −0.104611
\(213\) −1.52939e10 −0.509108
\(214\) −4.02475e10 −1.31183
\(215\) 4.93185e8 0.0157412
\(216\) 2.76209e10 0.863368
\(217\) −2.93956e10 −0.899940
\(218\) −2.45665e10 −0.736698
\(219\) 2.65769e9 0.0780738
\(220\) 1.41007e9 0.0405824
\(221\) 0 0
\(222\) 1.13511e10 0.313654
\(223\) 5.94964e10 1.61109 0.805544 0.592536i \(-0.201873\pi\)
0.805544 + 0.592536i \(0.201873\pi\)
\(224\) −5.43065e9 −0.144124
\(225\) 2.78656e10 0.724849
\(226\) −7.10993e10 −1.81291
\(227\) −7.39599e10 −1.84876 −0.924379 0.381475i \(-0.875416\pi\)
−0.924379 + 0.381475i \(0.875416\pi\)
\(228\) −3.10245e9 −0.0760322
\(229\) −4.92124e10 −1.18254 −0.591269 0.806474i \(-0.701373\pi\)
−0.591269 + 0.806474i \(0.701373\pi\)
\(230\) 6.94870e9 0.163730
\(231\) −1.43641e10 −0.331912
\(232\) 2.08581e10 0.472693
\(233\) 4.09686e10 0.910646 0.455323 0.890326i \(-0.349524\pi\)
0.455323 + 0.890326i \(0.349524\pi\)
\(234\) 6.22567e9 0.135742
\(235\) 2.24175e9 0.0479493
\(236\) −2.29162e9 −0.0480883
\(237\) −9.42746e9 −0.194101
\(238\) 0 0
\(239\) 8.62890e10 1.71066 0.855332 0.518080i \(-0.173353\pi\)
0.855332 + 0.518080i \(0.173353\pi\)
\(240\) −5.82955e9 −0.113419
\(241\) −6.30098e10 −1.20318 −0.601591 0.798804i \(-0.705466\pi\)
−0.601591 + 0.798804i \(0.705466\pi\)
\(242\) −2.10063e10 −0.393713
\(243\) −5.49436e10 −1.01086
\(244\) −3.35499e9 −0.0605951
\(245\) 1.01634e10 0.180216
\(246\) 1.28644e10 0.223965
\(247\) −1.48535e10 −0.253918
\(248\) −9.28763e10 −1.55909
\(249\) −5.39178e9 −0.0888864
\(250\) −3.16932e10 −0.513141
\(251\) 3.24383e10 0.515854 0.257927 0.966164i \(-0.416961\pi\)
0.257927 + 0.966164i \(0.416961\pi\)
\(252\) 3.65999e9 0.0571712
\(253\) 4.75377e10 0.729451
\(254\) −7.46232e10 −1.12492
\(255\) 0 0
\(256\) −2.42722e10 −0.353207
\(257\) 2.45445e10 0.350958 0.175479 0.984483i \(-0.443853\pi\)
0.175479 + 0.984483i \(0.443853\pi\)
\(258\) −1.69453e9 −0.0238100
\(259\) 3.19490e10 0.441172
\(260\) 4.60205e8 0.00624556
\(261\) −2.66140e10 −0.355000
\(262\) −5.38035e10 −0.705431
\(263\) −1.95967e10 −0.252570 −0.126285 0.991994i \(-0.540305\pi\)
−0.126285 + 0.991994i \(0.540305\pi\)
\(264\) −4.53837e10 −0.575019
\(265\) −2.00276e10 −0.249472
\(266\) 6.43339e10 0.787902
\(267\) −6.14700e10 −0.740222
\(268\) 9.58753e9 0.113527
\(269\) −3.80419e10 −0.442973 −0.221486 0.975163i \(-0.571091\pi\)
−0.221486 + 0.975163i \(0.571091\pi\)
\(270\) 1.91935e10 0.219795
\(271\) −1.13318e11 −1.27625 −0.638125 0.769933i \(-0.720290\pi\)
−0.638125 + 0.769933i \(0.720290\pi\)
\(272\) 0 0
\(273\) −4.68801e9 −0.0510807
\(274\) 6.50599e10 0.697326
\(275\) −1.03821e11 −1.09468
\(276\) 3.24060e9 0.0336151
\(277\) −6.42382e10 −0.655594 −0.327797 0.944748i \(-0.606306\pi\)
−0.327797 + 0.944748i \(0.606306\pi\)
\(278\) −8.45369e10 −0.848877
\(279\) 1.18506e11 1.17090
\(280\) −1.86717e10 −0.181540
\(281\) −6.78724e10 −0.649404 −0.324702 0.945816i \(-0.605264\pi\)
−0.324702 + 0.945816i \(0.605264\pi\)
\(282\) −7.70240e9 −0.0725279
\(283\) −4.27495e10 −0.396180 −0.198090 0.980184i \(-0.563474\pi\)
−0.198090 + 0.980184i \(0.563474\pi\)
\(284\) −1.45190e10 −0.132436
\(285\) −2.01950e10 −0.181318
\(286\) −2.31955e10 −0.205001
\(287\) 3.62082e10 0.315020
\(288\) 2.18932e10 0.187518
\(289\) 0 0
\(290\) 1.44941e10 0.120338
\(291\) 7.85114e10 0.641821
\(292\) 2.52303e9 0.0203096
\(293\) 3.38660e10 0.268448 0.134224 0.990951i \(-0.457146\pi\)
0.134224 + 0.990951i \(0.457146\pi\)
\(294\) −3.49203e10 −0.272593
\(295\) −1.49170e10 −0.114679
\(296\) 1.00944e11 0.764306
\(297\) 1.31308e11 0.979233
\(298\) −2.65476e10 −0.195008
\(299\) 1.55149e10 0.112261
\(300\) −7.07738e9 −0.0504460
\(301\) −4.76943e9 −0.0334901
\(302\) −2.47448e11 −1.71180
\(303\) 1.19867e11 0.816973
\(304\) 1.78621e11 1.19950
\(305\) −2.18389e10 −0.144504
\(306\) 0 0
\(307\) −1.43665e11 −0.923056 −0.461528 0.887126i \(-0.652699\pi\)
−0.461528 + 0.887126i \(0.652699\pi\)
\(308\) −1.36363e10 −0.0863413
\(309\) 1.17455e11 0.732926
\(310\) −6.45391e10 −0.396913
\(311\) 2.41669e11 1.46487 0.732436 0.680836i \(-0.238383\pi\)
0.732436 + 0.680836i \(0.238383\pi\)
\(312\) −1.48119e10 −0.0884944
\(313\) 3.00713e10 0.177093 0.0885467 0.996072i \(-0.471778\pi\)
0.0885467 + 0.996072i \(0.471778\pi\)
\(314\) −9.27390e10 −0.538367
\(315\) 2.38242e10 0.136339
\(316\) −8.94981e9 −0.0504919
\(317\) 2.08347e11 1.15883 0.579417 0.815031i \(-0.303280\pi\)
0.579417 + 0.815031i \(0.303280\pi\)
\(318\) 6.88125e10 0.377351
\(319\) 9.91579e10 0.536129
\(320\) −5.82302e10 −0.310437
\(321\) −1.22180e11 −0.642284
\(322\) −6.71986e10 −0.348345
\(323\) 0 0
\(324\) −9.75135e9 −0.0491600
\(325\) −3.38842e10 −0.168470
\(326\) 2.96742e11 1.45512
\(327\) −7.45768e10 −0.360694
\(328\) 1.14401e11 0.545754
\(329\) −2.16792e10 −0.102015
\(330\) −3.15368e10 −0.146388
\(331\) 3.16856e11 1.45090 0.725448 0.688277i \(-0.241633\pi\)
0.725448 + 0.688277i \(0.241633\pi\)
\(332\) −5.11860e9 −0.0231223
\(333\) −1.28800e11 −0.574006
\(334\) 9.37116e10 0.412035
\(335\) 6.24088e10 0.270735
\(336\) 5.63756e10 0.241304
\(337\) −4.30379e11 −1.81768 −0.908838 0.417149i \(-0.863029\pi\)
−0.908838 + 0.417149i \(0.863029\pi\)
\(338\) 2.17588e11 0.906795
\(339\) −2.15837e11 −0.887620
\(340\) 0 0
\(341\) −4.41527e11 −1.76833
\(342\) −2.59357e11 −1.02513
\(343\) −2.53724e11 −0.989779
\(344\) −1.50692e10 −0.0580198
\(345\) 2.10943e10 0.0801638
\(346\) 3.66857e11 1.37611
\(347\) −1.95226e11 −0.722863 −0.361431 0.932399i \(-0.617712\pi\)
−0.361431 + 0.932399i \(0.617712\pi\)
\(348\) 6.75949e9 0.0247063
\(349\) −1.86031e11 −0.671230 −0.335615 0.941999i \(-0.608944\pi\)
−0.335615 + 0.941999i \(0.608944\pi\)
\(350\) 1.46760e11 0.522759
\(351\) 4.28550e10 0.150702
\(352\) −8.15693e10 −0.283195
\(353\) 4.03261e11 1.38229 0.691146 0.722715i \(-0.257106\pi\)
0.691146 + 0.722715i \(0.257106\pi\)
\(354\) 5.12532e10 0.173463
\(355\) −9.45097e10 −0.315827
\(356\) −5.83556e10 −0.192556
\(357\) 0 0
\(358\) 3.15222e11 1.01425
\(359\) −8.31340e10 −0.264152 −0.132076 0.991240i \(-0.542164\pi\)
−0.132076 + 0.991240i \(0.542164\pi\)
\(360\) 7.52734e10 0.236200
\(361\) 2.96098e11 0.917600
\(362\) −9.83305e10 −0.300954
\(363\) −6.37690e10 −0.192766
\(364\) −4.45049e9 −0.0132878
\(365\) 1.64234e10 0.0484333
\(366\) 7.50359e10 0.218577
\(367\) 1.69270e11 0.487059 0.243530 0.969893i \(-0.421695\pi\)
0.243530 + 0.969893i \(0.421695\pi\)
\(368\) −1.86575e11 −0.530319
\(369\) −1.45970e11 −0.409870
\(370\) 7.01452e10 0.194576
\(371\) 1.93680e11 0.530766
\(372\) −3.00985e10 −0.0814894
\(373\) 3.17477e11 0.849223 0.424612 0.905376i \(-0.360411\pi\)
0.424612 + 0.905376i \(0.360411\pi\)
\(374\) 0 0
\(375\) −9.62115e10 −0.251239
\(376\) −6.84963e10 −0.176735
\(377\) 3.23622e10 0.0825092
\(378\) −1.85614e11 −0.467626
\(379\) 6.44843e11 1.60538 0.802690 0.596397i \(-0.203401\pi\)
0.802690 + 0.596397i \(0.203401\pi\)
\(380\) −1.91718e10 −0.0471668
\(381\) −2.26534e11 −0.550772
\(382\) 1.14015e11 0.273952
\(383\) 4.18939e11 0.994846 0.497423 0.867508i \(-0.334280\pi\)
0.497423 + 0.867508i \(0.334280\pi\)
\(384\) 1.53545e11 0.360368
\(385\) −8.87637e10 −0.205903
\(386\) 1.31472e11 0.301433
\(387\) 1.92276e10 0.0435737
\(388\) 7.45336e10 0.166959
\(389\) −7.48004e11 −1.65627 −0.828134 0.560530i \(-0.810598\pi\)
−0.828134 + 0.560530i \(0.810598\pi\)
\(390\) −1.02927e10 −0.0225288
\(391\) 0 0
\(392\) −3.10541e11 −0.664250
\(393\) −1.63332e11 −0.345386
\(394\) 5.92077e11 1.23779
\(395\) −5.82576e10 −0.120411
\(396\) 5.49737e10 0.112338
\(397\) 6.24540e9 0.0126184 0.00630918 0.999980i \(-0.497992\pi\)
0.00630918 + 0.999980i \(0.497992\pi\)
\(398\) 6.59342e11 1.31715
\(399\) 1.95299e11 0.385764
\(400\) 4.07474e11 0.795847
\(401\) 5.27612e11 1.01898 0.509489 0.860477i \(-0.329834\pi\)
0.509489 + 0.860477i \(0.329834\pi\)
\(402\) −2.14429e11 −0.409513
\(403\) −1.44102e11 −0.272142
\(404\) 1.13794e11 0.212522
\(405\) −6.34751e10 −0.117235
\(406\) −1.40168e11 −0.256025
\(407\) 4.79880e11 0.866877
\(408\) 0 0
\(409\) 3.85068e11 0.680429 0.340214 0.940348i \(-0.389500\pi\)
0.340214 + 0.940348i \(0.389500\pi\)
\(410\) 7.94963e10 0.138938
\(411\) 1.97503e11 0.341418
\(412\) 1.11504e11 0.190658
\(413\) 1.44258e11 0.243985
\(414\) 2.70906e11 0.453228
\(415\) −3.33189e10 −0.0551409
\(416\) −2.66218e10 −0.0435831
\(417\) −2.56630e11 −0.415618
\(418\) 9.66306e11 1.54818
\(419\) −2.72620e11 −0.432110 −0.216055 0.976381i \(-0.569319\pi\)
−0.216055 + 0.976381i \(0.569319\pi\)
\(420\) −6.05094e9 −0.00948857
\(421\) −3.26170e11 −0.506028 −0.253014 0.967463i \(-0.581422\pi\)
−0.253014 + 0.967463i \(0.581422\pi\)
\(422\) 1.27241e11 0.195309
\(423\) 8.73981e10 0.132730
\(424\) 6.11939e11 0.919522
\(425\) 0 0
\(426\) 3.24725e11 0.477718
\(427\) 2.11197e11 0.307441
\(428\) −1.15990e11 −0.167079
\(429\) −7.04148e10 −0.100370
\(430\) −1.04714e10 −0.0147706
\(431\) 8.94389e11 1.24847 0.624236 0.781236i \(-0.285410\pi\)
0.624236 + 0.781236i \(0.285410\pi\)
\(432\) −5.15352e11 −0.711913
\(433\) −6.57153e11 −0.898403 −0.449202 0.893430i \(-0.648291\pi\)
−0.449202 + 0.893430i \(0.648291\pi\)
\(434\) 6.24136e11 0.844453
\(435\) 4.40000e10 0.0589185
\(436\) −7.07984e10 −0.0938284
\(437\) −6.46340e11 −0.847803
\(438\) −5.64288e10 −0.0732601
\(439\) 7.30710e11 0.938976 0.469488 0.882939i \(-0.344439\pi\)
0.469488 + 0.882939i \(0.344439\pi\)
\(440\) −2.80452e11 −0.356715
\(441\) 3.96236e11 0.498862
\(442\) 0 0
\(443\) 8.53914e11 1.05341 0.526705 0.850048i \(-0.323427\pi\)
0.526705 + 0.850048i \(0.323427\pi\)
\(444\) 3.27129e10 0.0399481
\(445\) −3.79858e11 −0.459199
\(446\) −1.26325e12 −1.51175
\(447\) −8.05910e10 −0.0954778
\(448\) 5.63125e11 0.660471
\(449\) −7.82728e11 −0.908871 −0.454435 0.890780i \(-0.650159\pi\)
−0.454435 + 0.890780i \(0.650159\pi\)
\(450\) −5.91651e11 −0.680157
\(451\) 5.43853e11 0.618995
\(452\) −2.04902e11 −0.230899
\(453\) −7.51180e11 −0.838112
\(454\) 1.57034e12 1.73477
\(455\) −2.89699e10 −0.0316881
\(456\) 6.17054e11 0.668315
\(457\) −1.29347e12 −1.38718 −0.693590 0.720370i \(-0.743972\pi\)
−0.693590 + 0.720370i \(0.743972\pi\)
\(458\) 1.04489e12 1.10963
\(459\) 0 0
\(460\) 2.00255e10 0.0208532
\(461\) −1.76880e12 −1.82400 −0.912000 0.410191i \(-0.865462\pi\)
−0.912000 + 0.410191i \(0.865462\pi\)
\(462\) 3.04982e11 0.311448
\(463\) 1.10120e12 1.11366 0.556829 0.830627i \(-0.312018\pi\)
0.556829 + 0.830627i \(0.312018\pi\)
\(464\) −3.89172e11 −0.389772
\(465\) −1.95922e11 −0.194332
\(466\) −8.69858e11 −0.854499
\(467\) −5.83654e11 −0.567845 −0.283922 0.958847i \(-0.591636\pi\)
−0.283922 + 0.958847i \(0.591636\pi\)
\(468\) 1.79418e10 0.0172886
\(469\) −6.03535e11 −0.576003
\(470\) −4.75975e10 −0.0449929
\(471\) −2.81529e11 −0.263590
\(472\) 4.55786e11 0.422690
\(473\) −7.16376e10 −0.0658061
\(474\) 2.00167e11 0.182133
\(475\) 1.41159e12 1.27229
\(476\) 0 0
\(477\) −7.80807e11 −0.690575
\(478\) −1.83211e12 −1.60519
\(479\) −9.68349e11 −0.840470 −0.420235 0.907415i \(-0.638052\pi\)
−0.420235 + 0.907415i \(0.638052\pi\)
\(480\) −3.61953e10 −0.0311220
\(481\) 1.56619e11 0.133411
\(482\) 1.33784e12 1.12900
\(483\) −2.03996e11 −0.170553
\(484\) −6.05381e10 −0.0501447
\(485\) 4.85166e11 0.398156
\(486\) 1.16658e12 0.948530
\(487\) −7.26481e11 −0.585254 −0.292627 0.956227i \(-0.594529\pi\)
−0.292627 + 0.956227i \(0.594529\pi\)
\(488\) 6.67283e11 0.532624
\(489\) 9.00822e11 0.712441
\(490\) −2.15793e11 −0.169104
\(491\) −1.63273e12 −1.26779 −0.633897 0.773418i \(-0.718545\pi\)
−0.633897 + 0.773418i \(0.718545\pi\)
\(492\) 3.70739e10 0.0285250
\(493\) 0 0
\(494\) 3.15374e11 0.238262
\(495\) 3.57844e11 0.267899
\(496\) 1.73289e12 1.28559
\(497\) 9.13972e11 0.671938
\(498\) 1.14480e11 0.0834060
\(499\) −1.74280e12 −1.25833 −0.629165 0.777272i \(-0.716603\pi\)
−0.629165 + 0.777272i \(0.716603\pi\)
\(500\) −9.13369e10 −0.0653554
\(501\) 2.84481e11 0.201736
\(502\) −6.88741e11 −0.484049
\(503\) −4.24077e11 −0.295385 −0.147692 0.989033i \(-0.547185\pi\)
−0.147692 + 0.989033i \(0.547185\pi\)
\(504\) −7.27944e11 −0.502528
\(505\) 7.40727e11 0.506812
\(506\) −1.00934e12 −0.684476
\(507\) 6.60533e11 0.443975
\(508\) −2.15057e11 −0.143274
\(509\) 1.03436e12 0.683030 0.341515 0.939876i \(-0.389060\pi\)
0.341515 + 0.939876i \(0.389060\pi\)
\(510\) 0 0
\(511\) −1.58825e11 −0.103044
\(512\) 1.73504e12 1.11582
\(513\) −1.78531e12 −1.13811
\(514\) −5.21136e11 −0.329319
\(515\) 7.25824e11 0.454673
\(516\) −4.88347e9 −0.00303253
\(517\) −3.25626e11 −0.200453
\(518\) −6.78351e11 −0.413971
\(519\) 1.11367e12 0.673758
\(520\) −9.15313e10 −0.0548978
\(521\) −2.77034e12 −1.64726 −0.823631 0.567126i \(-0.808055\pi\)
−0.823631 + 0.567126i \(0.808055\pi\)
\(522\) 5.65076e11 0.333112
\(523\) −1.80710e12 −1.05615 −0.528073 0.849199i \(-0.677085\pi\)
−0.528073 + 0.849199i \(0.677085\pi\)
\(524\) −1.55057e11 −0.0898462
\(525\) 4.45521e11 0.255948
\(526\) 4.16083e11 0.236998
\(527\) 0 0
\(528\) 8.46772e11 0.474148
\(529\) −1.12603e12 −0.625172
\(530\) 4.25232e11 0.234091
\(531\) −5.81563e11 −0.317447
\(532\) 1.85404e11 0.100350
\(533\) 1.77498e11 0.0952622
\(534\) 1.30515e12 0.694583
\(535\) −7.55019e11 −0.398443
\(536\) −1.90689e12 −0.997892
\(537\) 9.56924e11 0.496585
\(538\) 8.07717e11 0.415661
\(539\) −1.47629e12 −0.753393
\(540\) 5.53140e10 0.0279939
\(541\) 3.71654e12 1.86531 0.932654 0.360772i \(-0.117487\pi\)
0.932654 + 0.360772i \(0.117487\pi\)
\(542\) 2.40599e12 1.19756
\(543\) −2.98503e11 −0.147350
\(544\) 0 0
\(545\) −4.60853e11 −0.223758
\(546\) 9.95373e10 0.0479312
\(547\) −3.59458e11 −0.171674 −0.0858372 0.996309i \(-0.527357\pi\)
−0.0858372 + 0.996309i \(0.527357\pi\)
\(548\) 1.87497e11 0.0888139
\(549\) −8.51423e11 −0.400009
\(550\) 2.20436e12 1.02719
\(551\) −1.34819e12 −0.623114
\(552\) −6.44531e11 −0.295473
\(553\) 5.63390e11 0.256181
\(554\) 1.36393e12 0.615172
\(555\) 2.12940e11 0.0952664
\(556\) −2.43628e11 −0.108116
\(557\) 7.21729e10 0.0317706 0.0158853 0.999874i \(-0.494943\pi\)
0.0158853 + 0.999874i \(0.494943\pi\)
\(558\) −2.51615e12 −1.09871
\(559\) −2.33804e10 −0.0101274
\(560\) 3.48377e11 0.149694
\(561\) 0 0
\(562\) 1.44109e12 0.609364
\(563\) −9.06094e11 −0.380089 −0.190045 0.981775i \(-0.560863\pi\)
−0.190045 + 0.981775i \(0.560863\pi\)
\(564\) −2.21976e10 −0.00923740
\(565\) −1.33378e12 −0.550638
\(566\) 9.07670e11 0.371753
\(567\) 6.13847e11 0.249423
\(568\) 2.88773e12 1.16409
\(569\) 4.41941e12 1.76750 0.883749 0.467962i \(-0.155012\pi\)
0.883749 + 0.467962i \(0.155012\pi\)
\(570\) 4.28786e11 0.170139
\(571\) −6.14608e10 −0.0241956 −0.0120978 0.999927i \(-0.503851\pi\)
−0.0120978 + 0.999927i \(0.503851\pi\)
\(572\) −6.68472e10 −0.0261096
\(573\) 3.46115e11 0.134130
\(574\) −7.68782e11 −0.295597
\(575\) −1.47445e12 −0.562502
\(576\) −2.27020e12 −0.859334
\(577\) −4.50208e12 −1.69092 −0.845459 0.534041i \(-0.820673\pi\)
−0.845459 + 0.534041i \(0.820673\pi\)
\(578\) 0 0
\(579\) 3.99112e11 0.147585
\(580\) 4.17708e10 0.0153266
\(581\) 3.22216e11 0.117315
\(582\) −1.66698e12 −0.602249
\(583\) 2.90911e12 1.04292
\(584\) −5.01813e11 −0.178519
\(585\) 1.16790e11 0.0412291
\(586\) −7.19054e11 −0.251896
\(587\) −1.77497e12 −0.617048 −0.308524 0.951216i \(-0.599835\pi\)
−0.308524 + 0.951216i \(0.599835\pi\)
\(588\) −1.00637e11 −0.0347184
\(589\) 6.00316e12 2.05523
\(590\) 3.16723e11 0.107608
\(591\) 1.79738e12 0.606031
\(592\) −1.88342e12 −0.630229
\(593\) 2.40742e12 0.799476 0.399738 0.916629i \(-0.369101\pi\)
0.399738 + 0.916629i \(0.369101\pi\)
\(594\) −2.78796e12 −0.918857
\(595\) 0 0
\(596\) −7.65078e10 −0.0248369
\(597\) 2.00157e12 0.644891
\(598\) −3.29418e11 −0.105340
\(599\) 1.95233e12 0.619629 0.309814 0.950797i \(-0.399733\pi\)
0.309814 + 0.950797i \(0.399733\pi\)
\(600\) 1.40764e12 0.443415
\(601\) −3.26884e12 −1.02202 −0.511010 0.859575i \(-0.670728\pi\)
−0.511010 + 0.859575i \(0.670728\pi\)
\(602\) 1.01266e11 0.0314253
\(603\) 2.43310e12 0.749432
\(604\) −7.13121e11 −0.218020
\(605\) −3.94065e11 −0.119583
\(606\) −2.54505e12 −0.766602
\(607\) −1.38191e12 −0.413171 −0.206586 0.978429i \(-0.566235\pi\)
−0.206586 + 0.978429i \(0.566235\pi\)
\(608\) 1.10905e12 0.329142
\(609\) −4.25510e11 −0.125352
\(610\) 4.63690e11 0.135595
\(611\) −1.06275e11 −0.0308493
\(612\) 0 0
\(613\) −5.58587e12 −1.59779 −0.798893 0.601473i \(-0.794581\pi\)
−0.798893 + 0.601473i \(0.794581\pi\)
\(614\) 3.05034e12 0.866144
\(615\) 2.41328e11 0.0680251
\(616\) 2.71216e12 0.758930
\(617\) −5.10855e12 −1.41911 −0.709553 0.704652i \(-0.751103\pi\)
−0.709553 + 0.704652i \(0.751103\pi\)
\(618\) −2.49385e12 −0.687736
\(619\) −1.71845e12 −0.470466 −0.235233 0.971939i \(-0.575585\pi\)
−0.235233 + 0.971939i \(0.575585\pi\)
\(620\) −1.85995e11 −0.0505522
\(621\) 1.86481e12 0.503178
\(622\) −5.13119e12 −1.37455
\(623\) 3.67348e12 0.976971
\(624\) 2.76362e11 0.0729704
\(625\) 2.91029e12 0.762916
\(626\) −6.38482e11 −0.166175
\(627\) 2.93343e12 0.758004
\(628\) −2.67265e11 −0.0685683
\(629\) 0 0
\(630\) −5.05843e11 −0.127933
\(631\) −1.38543e12 −0.347899 −0.173950 0.984755i \(-0.555653\pi\)
−0.173950 + 0.984755i \(0.555653\pi\)
\(632\) 1.78005e12 0.443818
\(633\) 3.86267e11 0.0956250
\(634\) −4.42369e12 −1.08738
\(635\) −1.39989e12 −0.341673
\(636\) 1.98311e11 0.0480607
\(637\) −4.81817e11 −0.115946
\(638\) −2.10535e12 −0.503073
\(639\) −3.68461e12 −0.874253
\(640\) 9.48844e11 0.223555
\(641\) −2.91632e12 −0.682299 −0.341149 0.940009i \(-0.610816\pi\)
−0.341149 + 0.940009i \(0.610816\pi\)
\(642\) 2.59416e12 0.602683
\(643\) −6.28300e12 −1.44950 −0.724749 0.689013i \(-0.758044\pi\)
−0.724749 + 0.689013i \(0.758044\pi\)
\(644\) −1.93660e11 −0.0443664
\(645\) −3.17883e10 −0.00723183
\(646\) 0 0
\(647\) −6.41096e12 −1.43832 −0.719158 0.694847i \(-0.755472\pi\)
−0.719158 + 0.694847i \(0.755472\pi\)
\(648\) 1.93947e12 0.432111
\(649\) 2.16677e12 0.479416
\(650\) 7.19439e11 0.158083
\(651\) 1.89470e12 0.413452
\(652\) 8.55182e11 0.185329
\(653\) 4.86499e12 1.04706 0.523531 0.852007i \(-0.324614\pi\)
0.523531 + 0.852007i \(0.324614\pi\)
\(654\) 1.58344e12 0.338455
\(655\) −1.00932e12 −0.214261
\(656\) −2.13450e12 −0.450016
\(657\) 6.40290e11 0.134070
\(658\) 4.60300e11 0.0957248
\(659\) −3.83458e12 −0.792016 −0.396008 0.918247i \(-0.629605\pi\)
−0.396008 + 0.918247i \(0.629605\pi\)
\(660\) −9.08861e10 −0.0186445
\(661\) 8.14305e11 0.165913 0.0829565 0.996553i \(-0.473564\pi\)
0.0829565 + 0.996553i \(0.473564\pi\)
\(662\) −6.72758e12 −1.36144
\(663\) 0 0
\(664\) 1.01805e12 0.203242
\(665\) 1.20686e12 0.239310
\(666\) 2.73472e12 0.538615
\(667\) 1.40822e12 0.275489
\(668\) 2.70068e11 0.0524782
\(669\) −3.83485e12 −0.740169
\(670\) −1.32508e12 −0.254042
\(671\) 3.17221e12 0.604103
\(672\) 3.50033e11 0.0662137
\(673\) 4.30358e12 0.808652 0.404326 0.914615i \(-0.367506\pi\)
0.404326 + 0.914615i \(0.367506\pi\)
\(674\) 9.13794e12 1.70561
\(675\) −4.07268e12 −0.755116
\(676\) 6.27067e11 0.115492
\(677\) 1.91909e11 0.0351113 0.0175556 0.999846i \(-0.494412\pi\)
0.0175556 + 0.999846i \(0.494412\pi\)
\(678\) 4.58272e12 0.832893
\(679\) −4.69188e12 −0.847097
\(680\) 0 0
\(681\) 4.76710e12 0.849361
\(682\) 9.37463e12 1.65930
\(683\) −4.03721e12 −0.709886 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(684\) −7.47442e11 −0.130564
\(685\) 1.22048e12 0.211799
\(686\) 5.38715e12 0.928753
\(687\) 3.17199e12 0.543284
\(688\) 2.81161e11 0.0478418
\(689\) 9.49449e11 0.160504
\(690\) −4.47880e11 −0.0752212
\(691\) 8.05343e12 1.34379 0.671893 0.740649i \(-0.265482\pi\)
0.671893 + 0.740649i \(0.265482\pi\)
\(692\) 1.05725e12 0.175267
\(693\) −3.46059e12 −0.569968
\(694\) 4.14510e12 0.678294
\(695\) −1.58586e12 −0.257830
\(696\) −1.34441e12 −0.217166
\(697\) 0 0
\(698\) 3.94987e12 0.629845
\(699\) −2.64064e12 −0.418371
\(700\) 4.22948e11 0.0665804
\(701\) −7.33234e12 −1.14686 −0.573432 0.819254i \(-0.694388\pi\)
−0.573432 + 0.819254i \(0.694388\pi\)
\(702\) −9.09910e11 −0.141410
\(703\) −6.52462e12 −1.00753
\(704\) 8.45824e12 1.29779
\(705\) −1.44492e11 −0.0220290
\(706\) −8.56215e12 −1.29706
\(707\) −7.16332e12 −1.07827
\(708\) 1.47707e11 0.0220928
\(709\) −7.00566e12 −1.04122 −0.520608 0.853796i \(-0.674295\pi\)
−0.520608 + 0.853796i \(0.674295\pi\)
\(710\) 2.00666e12 0.296354
\(711\) −2.27126e12 −0.333315
\(712\) 1.16065e13 1.69255
\(713\) −6.27048e12 −0.908653
\(714\) 0 0
\(715\) −4.35133e11 −0.0622651
\(716\) 9.08441e11 0.129178
\(717\) −5.56177e12 −0.785917
\(718\) 1.76513e12 0.247865
\(719\) −9.87945e12 −1.37865 −0.689323 0.724454i \(-0.742092\pi\)
−0.689323 + 0.724454i \(0.742092\pi\)
\(720\) −1.40445e12 −0.194765
\(721\) −7.01920e12 −0.967340
\(722\) −6.28685e12 −0.861024
\(723\) 4.06131e12 0.552769
\(724\) −2.83379e11 −0.0383305
\(725\) −3.07552e12 −0.413425
\(726\) 1.35396e12 0.180880
\(727\) −1.06391e13 −1.41253 −0.706266 0.707947i \(-0.749622\pi\)
−0.706266 + 0.707947i \(0.749622\pi\)
\(728\) 8.85169e11 0.116798
\(729\) 4.04654e11 0.0530652
\(730\) −3.48706e11 −0.0454471
\(731\) 0 0
\(732\) 2.16247e11 0.0278387
\(733\) 6.87663e12 0.879849 0.439924 0.898035i \(-0.355005\pi\)
0.439924 + 0.898035i \(0.355005\pi\)
\(734\) −3.59398e12 −0.457029
\(735\) −6.55084e11 −0.0827950
\(736\) −1.15843e12 −0.145519
\(737\) −9.06520e12 −1.13181
\(738\) 3.09929e12 0.384599
\(739\) −9.11004e12 −1.12362 −0.561811 0.827265i \(-0.689895\pi\)
−0.561811 + 0.827265i \(0.689895\pi\)
\(740\) 2.02152e11 0.0247819
\(741\) 9.57385e11 0.116655
\(742\) −4.11228e12 −0.498041
\(743\) 5.65338e12 0.680548 0.340274 0.940326i \(-0.389480\pi\)
0.340274 + 0.940326i \(0.389480\pi\)
\(744\) 5.98636e12 0.716282
\(745\) −4.98018e11 −0.0592300
\(746\) −6.74076e12 −0.796863
\(747\) −1.29899e12 −0.152638
\(748\) 0 0
\(749\) 7.30154e12 0.847708
\(750\) 2.04279e12 0.235748
\(751\) −5.02019e12 −0.575891 −0.287945 0.957647i \(-0.592972\pi\)
−0.287945 + 0.957647i \(0.592972\pi\)
\(752\) 1.27801e12 0.145731
\(753\) −2.09082e12 −0.236995
\(754\) −6.87125e11 −0.0774220
\(755\) −4.64197e12 −0.519925
\(756\) −5.34923e11 −0.0595585
\(757\) −1.11047e13 −1.22907 −0.614536 0.788889i \(-0.710657\pi\)
−0.614536 + 0.788889i \(0.710657\pi\)
\(758\) −1.36915e13 −1.50640
\(759\) −3.06405e12 −0.335126
\(760\) 3.81313e12 0.414591
\(761\) −1.20295e13 −1.30022 −0.650108 0.759841i \(-0.725277\pi\)
−0.650108 + 0.759841i \(0.725277\pi\)
\(762\) 4.80985e12 0.516814
\(763\) 4.45676e12 0.476056
\(764\) 3.28579e11 0.0348915
\(765\) 0 0
\(766\) −8.89503e12 −0.933508
\(767\) 7.07172e11 0.0737812
\(768\) 1.56447e12 0.162271
\(769\) 1.19597e13 1.23325 0.616624 0.787258i \(-0.288500\pi\)
0.616624 + 0.787258i \(0.288500\pi\)
\(770\) 1.88466e12 0.193208
\(771\) −1.58202e12 −0.161238
\(772\) 3.78891e11 0.0383916
\(773\) 1.28955e13 1.29907 0.649533 0.760333i \(-0.274964\pi\)
0.649533 + 0.760333i \(0.274964\pi\)
\(774\) −4.08245e11 −0.0408872
\(775\) 1.36946e13 1.36361
\(776\) −1.48242e13 −1.46755
\(777\) −2.05928e12 −0.202684
\(778\) 1.58818e13 1.55415
\(779\) −7.39442e12 −0.719425
\(780\) −2.96626e10 −0.00286935
\(781\) 1.37280e13 1.32032
\(782\) 0 0
\(783\) 3.88975e12 0.369823
\(784\) 5.79409e12 0.547725
\(785\) −1.73973e12 −0.163519
\(786\) 3.46791e12 0.324091
\(787\) −1.19313e13 −1.10867 −0.554335 0.832293i \(-0.687027\pi\)
−0.554335 + 0.832293i \(0.687027\pi\)
\(788\) 1.70631e12 0.157649
\(789\) 1.26311e12 0.116036
\(790\) 1.23694e12 0.112987
\(791\) 1.28985e13 1.17151
\(792\) −1.09339e13 −0.987438
\(793\) 1.03532e12 0.0929703
\(794\) −1.32604e11 −0.0118404
\(795\) 1.29088e12 0.114613
\(796\) 1.90016e12 0.167757
\(797\) 3.92641e12 0.344693 0.172347 0.985036i \(-0.444865\pi\)
0.172347 + 0.985036i \(0.444865\pi\)
\(798\) −4.14665e12 −0.361980
\(799\) 0 0
\(800\) 2.52998e12 0.218380
\(801\) −1.48093e13 −1.27113
\(802\) −1.12024e13 −0.956153
\(803\) −2.38558e12 −0.202476
\(804\) −6.17965e11 −0.0521569
\(805\) −1.26061e12 −0.105803
\(806\) 3.05961e12 0.255363
\(807\) 2.45200e12 0.203511
\(808\) −2.26328e13 −1.86804
\(809\) −1.18171e13 −0.969937 −0.484969 0.874532i \(-0.661169\pi\)
−0.484969 + 0.874532i \(0.661169\pi\)
\(810\) 1.34772e12 0.110006
\(811\) 2.28011e13 1.85081 0.925406 0.378976i \(-0.123724\pi\)
0.925406 + 0.378976i \(0.123724\pi\)
\(812\) −4.03951e11 −0.0326082
\(813\) 7.30390e12 0.586337
\(814\) −1.01889e13 −0.813429
\(815\) 5.56669e12 0.441965
\(816\) 0 0
\(817\) 9.74011e11 0.0764830
\(818\) −8.17588e12 −0.638476
\(819\) −1.12944e12 −0.0877171
\(820\) 2.29101e11 0.0176956
\(821\) −6.28999e12 −0.483176 −0.241588 0.970379i \(-0.577668\pi\)
−0.241588 + 0.970379i \(0.577668\pi\)
\(822\) −4.19345e12 −0.320367
\(823\) −1.47598e13 −1.12146 −0.560728 0.828000i \(-0.689479\pi\)
−0.560728 + 0.828000i \(0.689479\pi\)
\(824\) −2.21774e13 −1.67586
\(825\) 6.69180e12 0.502922
\(826\) −3.06292e12 −0.228942
\(827\) −1.16508e12 −0.0866122 −0.0433061 0.999062i \(-0.513789\pi\)
−0.0433061 + 0.999062i \(0.513789\pi\)
\(828\) 7.80726e11 0.0577247
\(829\) −2.10717e13 −1.54955 −0.774774 0.632238i \(-0.782137\pi\)
−0.774774 + 0.632238i \(0.782137\pi\)
\(830\) 7.07437e11 0.0517411
\(831\) 4.14048e12 0.301194
\(832\) 2.76052e12 0.199727
\(833\) 0 0
\(834\) 5.44884e12 0.389993
\(835\) 1.75797e12 0.125148
\(836\) 2.78480e12 0.197182
\(837\) −1.73202e13 −1.21980
\(838\) 5.78835e12 0.405468
\(839\) −1.60286e11 −0.0111678 −0.00558388 0.999984i \(-0.501777\pi\)
−0.00558388 + 0.999984i \(0.501777\pi\)
\(840\) 1.20349e12 0.0834035
\(841\) −1.15698e13 −0.797522
\(842\) 6.92534e12 0.474828
\(843\) 4.37473e12 0.298351
\(844\) 3.66697e11 0.0248752
\(845\) 4.08181e12 0.275421
\(846\) −1.85566e12 −0.124547
\(847\) 3.81087e12 0.254419
\(848\) −1.14176e13 −0.758216
\(849\) 2.75542e12 0.182014
\(850\) 0 0
\(851\) 6.81516e12 0.445444
\(852\) 9.35826e11 0.0608439
\(853\) −8.02673e12 −0.519120 −0.259560 0.965727i \(-0.583578\pi\)
−0.259560 + 0.965727i \(0.583578\pi\)
\(854\) −4.48419e12 −0.288485
\(855\) −4.86538e12 −0.311364
\(856\) 2.30694e13 1.46861
\(857\) −1.46074e13 −0.925040 −0.462520 0.886609i \(-0.653055\pi\)
−0.462520 + 0.886609i \(0.653055\pi\)
\(858\) 1.49507e12 0.0941820
\(859\) 9.67406e12 0.606233 0.303117 0.952953i \(-0.401973\pi\)
0.303117 + 0.952953i \(0.401973\pi\)
\(860\) −3.01777e10 −0.00188124
\(861\) −2.33380e12 −0.144727
\(862\) −1.89899e13 −1.17150
\(863\) −1.28618e13 −0.789318 −0.394659 0.918828i \(-0.629137\pi\)
−0.394659 + 0.918828i \(0.629137\pi\)
\(864\) −3.19979e12 −0.195348
\(865\) 6.88201e12 0.417968
\(866\) 1.39529e13 0.843011
\(867\) 0 0
\(868\) 1.79870e12 0.107552
\(869\) 8.46222e12 0.503379
\(870\) −9.34222e11 −0.0552858
\(871\) −2.95862e12 −0.174183
\(872\) 1.40813e13 0.824741
\(873\) 1.89150e13 1.10215
\(874\) 1.37233e13 0.795530
\(875\) 5.74965e12 0.331593
\(876\) −1.62623e11 −0.00933066
\(877\) 3.18137e13 1.81600 0.908000 0.418970i \(-0.137609\pi\)
0.908000 + 0.418970i \(0.137609\pi\)
\(878\) −1.55146e13 −0.881082
\(879\) −2.18284e12 −0.123331
\(880\) 5.23269e12 0.294139
\(881\) 3.55268e12 0.198685 0.0993425 0.995053i \(-0.468326\pi\)
0.0993425 + 0.995053i \(0.468326\pi\)
\(882\) −8.41301e12 −0.468104
\(883\) 6.90201e12 0.382079 0.191039 0.981582i \(-0.438814\pi\)
0.191039 + 0.981582i \(0.438814\pi\)
\(884\) 0 0
\(885\) 9.61478e11 0.0526859
\(886\) −1.81306e13 −0.988461
\(887\) −2.48053e11 −0.0134551 −0.00672756 0.999977i \(-0.502141\pi\)
−0.00672756 + 0.999977i \(0.502141\pi\)
\(888\) −6.50635e12 −0.351139
\(889\) 1.35378e13 0.726928
\(890\) 8.06526e12 0.430887
\(891\) 9.22009e12 0.490101
\(892\) −3.64056e12 −0.192542
\(893\) 4.42733e12 0.232975
\(894\) 1.71113e12 0.0895911
\(895\) 5.91338e12 0.308058
\(896\) −9.17595e12 −0.475626
\(897\) −1.00002e12 −0.0515752
\(898\) 1.66191e13 0.852833
\(899\) −1.30795e13 −0.667838
\(900\) −1.70508e12 −0.0866272
\(901\) 0 0
\(902\) −1.15473e13 −0.580830
\(903\) 3.07414e11 0.0153861
\(904\) 4.07534e13 2.02958
\(905\) −1.84462e12 −0.0914089
\(906\) 1.59493e13 0.786437
\(907\) −2.41672e13 −1.18575 −0.592876 0.805294i \(-0.702008\pi\)
−0.592876 + 0.805294i \(0.702008\pi\)
\(908\) 4.52557e12 0.220946
\(909\) 2.88784e13 1.40293
\(910\) 6.15097e11 0.0297343
\(911\) 3.01501e13 1.45029 0.725146 0.688595i \(-0.241772\pi\)
0.725146 + 0.688595i \(0.241772\pi\)
\(912\) −1.15130e13 −0.551077
\(913\) 4.83974e12 0.230517
\(914\) 2.74633e13 1.30165
\(915\) 1.40763e12 0.0663885
\(916\) 3.01128e12 0.141326
\(917\) 9.76081e12 0.455852
\(918\) 0 0
\(919\) −1.09318e13 −0.505558 −0.252779 0.967524i \(-0.581345\pi\)
−0.252779 + 0.967524i \(0.581345\pi\)
\(920\) −3.98292e12 −0.183298
\(921\) 9.25994e12 0.424072
\(922\) 3.75557e13 1.71154
\(923\) 4.48043e12 0.203194
\(924\) 8.78930e11 0.0396671
\(925\) −1.48841e13 −0.668475
\(926\) −2.33810e13 −1.04499
\(927\) 2.82974e13 1.25860
\(928\) −2.41635e12 −0.106953
\(929\) 9.34286e12 0.411537 0.205769 0.978601i \(-0.434031\pi\)
0.205769 + 0.978601i \(0.434031\pi\)
\(930\) 4.15987e12 0.182350
\(931\) 2.00722e13 0.875629
\(932\) −2.50685e12 −0.108832
\(933\) −1.55768e13 −0.672994
\(934\) 1.23923e13 0.532834
\(935\) 0 0
\(936\) −3.56849e12 −0.151965
\(937\) −3.26873e13 −1.38532 −0.692660 0.721264i \(-0.743561\pi\)
−0.692660 + 0.721264i \(0.743561\pi\)
\(938\) 1.28144e13 0.540489
\(939\) −1.93825e12 −0.0813606
\(940\) −1.37172e11 −0.00573045
\(941\) 6.47375e12 0.269155 0.134578 0.990903i \(-0.457032\pi\)
0.134578 + 0.990903i \(0.457032\pi\)
\(942\) 5.97750e12 0.247338
\(943\) 7.72370e12 0.318070
\(944\) −8.50408e12 −0.348541
\(945\) −3.48202e12 −0.142032
\(946\) 1.52103e12 0.0617487
\(947\) −1.29609e13 −0.523674 −0.261837 0.965112i \(-0.584328\pi\)
−0.261837 + 0.965112i \(0.584328\pi\)
\(948\) 5.76861e11 0.0231971
\(949\) −7.78583e11 −0.0311607
\(950\) −2.99713e13 −1.19385
\(951\) −1.34290e13 −0.532394
\(952\) 0 0
\(953\) 7.79031e12 0.305940 0.152970 0.988231i \(-0.451116\pi\)
0.152970 + 0.988231i \(0.451116\pi\)
\(954\) 1.65783e13 0.647997
\(955\) 2.13884e12 0.0832077
\(956\) −5.27998e12 −0.204443
\(957\) −6.39123e12 −0.246309
\(958\) 2.05603e13 0.788650
\(959\) −1.18029e13 −0.450615
\(960\) 3.75324e12 0.142622
\(961\) 3.18001e13 1.20275
\(962\) −3.32538e12 −0.125185
\(963\) −2.94356e13 −1.10295
\(964\) 3.85554e12 0.143793
\(965\) 2.46634e12 0.0915545
\(966\) 4.33130e12 0.160037
\(967\) 1.11152e13 0.408789 0.204395 0.978889i \(-0.434477\pi\)
0.204395 + 0.978889i \(0.434477\pi\)
\(968\) 1.20406e13 0.440766
\(969\) 0 0
\(970\) −1.03012e13 −0.373607
\(971\) −2.99153e13 −1.07996 −0.539979 0.841678i \(-0.681568\pi\)
−0.539979 + 0.841678i \(0.681568\pi\)
\(972\) 3.36197e12 0.120808
\(973\) 1.53363e13 0.548547
\(974\) 1.54249e13 0.549169
\(975\) 2.18401e12 0.0773987
\(976\) −1.24502e13 −0.439189
\(977\) 3.43150e13 1.20492 0.602460 0.798149i \(-0.294187\pi\)
0.602460 + 0.798149i \(0.294187\pi\)
\(978\) −1.91265e13 −0.668515
\(979\) 5.51763e13 1.91969
\(980\) −6.21894e11 −0.0215377
\(981\) −1.79671e13 −0.619393
\(982\) 3.46667e13 1.18963
\(983\) −3.36007e13 −1.14778 −0.573888 0.818934i \(-0.694566\pi\)
−0.573888 + 0.818934i \(0.694566\pi\)
\(984\) −7.37372e12 −0.250732
\(985\) 1.11070e13 0.375953
\(986\) 0 0
\(987\) 1.39734e12 0.0468678
\(988\) 9.08878e11 0.0303459
\(989\) −1.01738e12 −0.0338144
\(990\) −7.59785e12 −0.251381
\(991\) 5.72727e13 1.88633 0.943163 0.332332i \(-0.107835\pi\)
0.943163 + 0.332332i \(0.107835\pi\)
\(992\) 1.07594e13 0.352766
\(993\) −2.04230e13 −0.666573
\(994\) −1.94057e13 −0.630509
\(995\) 1.23689e13 0.400060
\(996\) 3.29920e11 0.0106229
\(997\) 6.10726e13 1.95757 0.978786 0.204883i \(-0.0656814\pi\)
0.978786 + 0.204883i \(0.0656814\pi\)
\(998\) 3.70036e13 1.18075
\(999\) 1.88247e13 0.597975
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.1.11 36
17.16 even 2 289.10.a.h.1.11 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.11 36 1.1 even 1 trivial
289.10.a.h.1.11 yes 36 17.16 even 2