Properties

Label 289.10.a.g.1.16
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 1.16
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-8.02687 q^{2} +214.990 q^{3} -447.569 q^{4} +357.217 q^{5} -1725.70 q^{6} +11795.1 q^{7} +7702.34 q^{8} +26537.7 q^{9} +O(q^{10})\) \(q-8.02687 q^{2} +214.990 q^{3} -447.569 q^{4} +357.217 q^{5} -1725.70 q^{6} +11795.1 q^{7} +7702.34 q^{8} +26537.7 q^{9} -2867.34 q^{10} -78102.7 q^{11} -96223.0 q^{12} +30340.9 q^{13} -94677.6 q^{14} +76798.2 q^{15} +167330. q^{16} -213015. q^{18} -211548. q^{19} -159880. q^{20} +2.53582e6 q^{21} +626920. q^{22} -2.01657e6 q^{23} +1.65593e6 q^{24} -1.82552e6 q^{25} -243542. q^{26} +1.47370e6 q^{27} -5.27911e6 q^{28} -4.53168e6 q^{29} -616449. q^{30} +1.97954e6 q^{31} -5.28673e6 q^{32} -1.67913e7 q^{33} +4.21341e6 q^{35} -1.18775e7 q^{36} +1.66543e6 q^{37} +1.69807e6 q^{38} +6.52299e6 q^{39} +2.75141e6 q^{40} -1.02406e7 q^{41} -2.03547e7 q^{42} -3.61815e7 q^{43} +3.49564e7 q^{44} +9.47974e6 q^{45} +1.61868e7 q^{46} -3.61082e7 q^{47} +3.59742e7 q^{48} +9.87702e7 q^{49} +1.46532e7 q^{50} -1.35796e7 q^{52} -3.15213e7 q^{53} -1.18292e7 q^{54} -2.78996e7 q^{55} +9.08497e7 q^{56} -4.54808e7 q^{57} +3.63752e7 q^{58} +1.04359e8 q^{59} -3.43725e7 q^{60} -1.28240e8 q^{61} -1.58896e7 q^{62} +3.13015e8 q^{63} -4.32369e7 q^{64} +1.08383e7 q^{65} +1.34782e8 q^{66} +2.11054e8 q^{67} -4.33543e8 q^{69} -3.38205e7 q^{70} -1.32982e8 q^{71} +2.04403e8 q^{72} +4.13767e8 q^{73} -1.33682e7 q^{74} -3.92469e8 q^{75} +9.46826e7 q^{76} -9.21227e8 q^{77} -5.23592e7 q^{78} -1.92667e8 q^{79} +5.97731e7 q^{80} -2.05511e8 q^{81} +8.21998e7 q^{82} -6.55561e7 q^{83} -1.13496e9 q^{84} +2.90424e8 q^{86} -9.74266e8 q^{87} -6.01574e8 q^{88} -3.70418e8 q^{89} -7.60927e7 q^{90} +3.57873e8 q^{91} +9.02556e8 q^{92} +4.25582e8 q^{93} +2.89836e8 q^{94} -7.55688e7 q^{95} -1.13660e9 q^{96} -2.80144e8 q^{97} -7.92816e8 q^{98} -2.07267e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.02687 −0.354741 −0.177371 0.984144i \(-0.556759\pi\)
−0.177371 + 0.984144i \(0.556759\pi\)
\(3\) 214.990 1.53240 0.766201 0.642601i \(-0.222145\pi\)
0.766201 + 0.642601i \(0.222145\pi\)
\(4\) −447.569 −0.874159
\(5\) 357.217 0.255604 0.127802 0.991800i \(-0.459208\pi\)
0.127802 + 0.991800i \(0.459208\pi\)
\(6\) −1725.70 −0.543606
\(7\) 11795.1 1.85678 0.928388 0.371612i \(-0.121195\pi\)
0.928388 + 0.371612i \(0.121195\pi\)
\(8\) 7702.34 0.664841
\(9\) 26537.7 1.34826
\(10\) −2867.34 −0.0906732
\(11\) −78102.7 −1.60842 −0.804209 0.594347i \(-0.797411\pi\)
−0.804209 + 0.594347i \(0.797411\pi\)
\(12\) −96223.0 −1.33956
\(13\) 30340.9 0.294634 0.147317 0.989089i \(-0.452936\pi\)
0.147317 + 0.989089i \(0.452936\pi\)
\(14\) −94677.6 −0.658675
\(15\) 76798.2 0.391688
\(16\) 167330. 0.638312
\(17\) 0 0
\(18\) −213015. −0.478282
\(19\) −211548. −0.372408 −0.186204 0.982511i \(-0.559618\pi\)
−0.186204 + 0.982511i \(0.559618\pi\)
\(20\) −159880. −0.223438
\(21\) 2.53582e6 2.84533
\(22\) 626920. 0.570572
\(23\) −2.01657e6 −1.50258 −0.751292 0.659970i \(-0.770569\pi\)
−0.751292 + 0.659970i \(0.770569\pi\)
\(24\) 1.65593e6 1.01880
\(25\) −1.82552e6 −0.934667
\(26\) −243542. −0.104519
\(27\) 1.47370e6 0.533670
\(28\) −5.27911e6 −1.62312
\(29\) −4.53168e6 −1.18978 −0.594892 0.803805i \(-0.702805\pi\)
−0.594892 + 0.803805i \(0.702805\pi\)
\(30\) −616449. −0.138948
\(31\) 1.97954e6 0.384980 0.192490 0.981299i \(-0.438344\pi\)
0.192490 + 0.981299i \(0.438344\pi\)
\(32\) −5.28673e6 −0.891277
\(33\) −1.67913e7 −2.46474
\(34\) 0 0
\(35\) 4.21341e6 0.474599
\(36\) −1.18775e7 −1.17859
\(37\) 1.66543e6 0.146090 0.0730448 0.997329i \(-0.476728\pi\)
0.0730448 + 0.997329i \(0.476728\pi\)
\(38\) 1.69807e6 0.132108
\(39\) 6.52299e6 0.451498
\(40\) 2.75141e6 0.169936
\(41\) −1.02406e7 −0.565974 −0.282987 0.959124i \(-0.591325\pi\)
−0.282987 + 0.959124i \(0.591325\pi\)
\(42\) −2.03547e7 −1.00935
\(43\) −3.61815e7 −1.61391 −0.806954 0.590615i \(-0.798885\pi\)
−0.806954 + 0.590615i \(0.798885\pi\)
\(44\) 3.49564e7 1.40601
\(45\) 9.47974e6 0.344620
\(46\) 1.61868e7 0.533028
\(47\) −3.61082e7 −1.07936 −0.539679 0.841871i \(-0.681454\pi\)
−0.539679 + 0.841871i \(0.681454\pi\)
\(48\) 3.59742e7 0.978151
\(49\) 9.87702e7 2.44762
\(50\) 1.46532e7 0.331565
\(51\) 0 0
\(52\) −1.35796e7 −0.257557
\(53\) −3.15213e7 −0.548736 −0.274368 0.961625i \(-0.588469\pi\)
−0.274368 + 0.961625i \(0.588469\pi\)
\(54\) −1.18292e7 −0.189315
\(55\) −2.78996e7 −0.411118
\(56\) 9.08497e7 1.23446
\(57\) −4.54808e7 −0.570678
\(58\) 3.63752e7 0.422065
\(59\) 1.04359e8 1.12123 0.560616 0.828076i \(-0.310564\pi\)
0.560616 + 0.828076i \(0.310564\pi\)
\(60\) −3.43725e7 −0.342398
\(61\) −1.28240e8 −1.18587 −0.592937 0.805249i \(-0.702032\pi\)
−0.592937 + 0.805249i \(0.702032\pi\)
\(62\) −1.58896e7 −0.136568
\(63\) 3.13015e8 2.50341
\(64\) −4.32369e7 −0.322140
\(65\) 1.08383e7 0.0753097
\(66\) 1.34782e8 0.874346
\(67\) 2.11054e8 1.27955 0.639775 0.768563i \(-0.279028\pi\)
0.639775 + 0.768563i \(0.279028\pi\)
\(68\) 0 0
\(69\) −4.33543e8 −2.30256
\(70\) −3.38205e7 −0.168360
\(71\) −1.32982e8 −0.621055 −0.310528 0.950564i \(-0.600506\pi\)
−0.310528 + 0.950564i \(0.600506\pi\)
\(72\) 2.04403e8 0.896377
\(73\) 4.13767e8 1.70531 0.852654 0.522476i \(-0.174991\pi\)
0.852654 + 0.522476i \(0.174991\pi\)
\(74\) −1.33682e7 −0.0518240
\(75\) −3.92469e8 −1.43229
\(76\) 9.46826e7 0.325543
\(77\) −9.21227e8 −2.98647
\(78\) −5.23592e7 −0.160165
\(79\) −1.92667e8 −0.556525 −0.278262 0.960505i \(-0.589759\pi\)
−0.278262 + 0.960505i \(0.589759\pi\)
\(80\) 5.97731e7 0.163155
\(81\) −2.05511e8 −0.530460
\(82\) 8.21998e7 0.200774
\(83\) −6.55561e7 −0.151622 −0.0758109 0.997122i \(-0.524155\pi\)
−0.0758109 + 0.997122i \(0.524155\pi\)
\(84\) −1.13496e9 −2.48727
\(85\) 0 0
\(86\) 2.90424e8 0.572519
\(87\) −9.74266e8 −1.82323
\(88\) −6.01574e8 −1.06934
\(89\) −3.70418e8 −0.625802 −0.312901 0.949786i \(-0.601301\pi\)
−0.312901 + 0.949786i \(0.601301\pi\)
\(90\) −7.60927e7 −0.122251
\(91\) 3.57873e8 0.547070
\(92\) 9.02556e8 1.31350
\(93\) 4.25582e8 0.589944
\(94\) 2.89836e8 0.382893
\(95\) −7.55688e7 −0.0951889
\(96\) −1.13660e9 −1.36579
\(97\) −2.80144e8 −0.321299 −0.160649 0.987012i \(-0.551359\pi\)
−0.160649 + 0.987012i \(0.551359\pi\)
\(98\) −7.92816e8 −0.868270
\(99\) −2.07267e9 −2.16856
\(100\) 8.17047e8 0.817047
\(101\) −4.77793e8 −0.456871 −0.228435 0.973559i \(-0.573361\pi\)
−0.228435 + 0.973559i \(0.573361\pi\)
\(102\) 0 0
\(103\) −2.78188e8 −0.243541 −0.121770 0.992558i \(-0.538857\pi\)
−0.121770 + 0.992558i \(0.538857\pi\)
\(104\) 2.33696e8 0.195885
\(105\) 9.05840e8 0.727277
\(106\) 2.53018e8 0.194659
\(107\) 5.07198e8 0.374068 0.187034 0.982353i \(-0.440113\pi\)
0.187034 + 0.982353i \(0.440113\pi\)
\(108\) −6.59583e8 −0.466512
\(109\) 2.49113e9 1.69035 0.845177 0.534486i \(-0.179495\pi\)
0.845177 + 0.534486i \(0.179495\pi\)
\(110\) 2.23947e8 0.145840
\(111\) 3.58051e8 0.223868
\(112\) 1.97367e9 1.18520
\(113\) 9.97822e8 0.575705 0.287853 0.957675i \(-0.407059\pi\)
0.287853 + 0.957675i \(0.407059\pi\)
\(114\) 3.65069e8 0.202443
\(115\) −7.20355e8 −0.384066
\(116\) 2.02824e9 1.04006
\(117\) 8.05178e8 0.397243
\(118\) −8.37676e8 −0.397747
\(119\) 0 0
\(120\) 5.91526e8 0.260410
\(121\) 3.74208e9 1.58701
\(122\) 1.02936e9 0.420678
\(123\) −2.20162e9 −0.867300
\(124\) −8.85983e8 −0.336533
\(125\) −1.34980e9 −0.494508
\(126\) −2.51253e9 −0.888063
\(127\) 2.26270e9 0.771810 0.385905 0.922539i \(-0.373889\pi\)
0.385905 + 0.922539i \(0.373889\pi\)
\(128\) 3.05386e9 1.00555
\(129\) −7.77866e9 −2.47316
\(130\) −8.69976e7 −0.0267154
\(131\) −4.73592e9 −1.40502 −0.702512 0.711672i \(-0.747938\pi\)
−0.702512 + 0.711672i \(0.747938\pi\)
\(132\) 7.51527e9 2.15458
\(133\) −2.49523e9 −0.691478
\(134\) −1.69410e9 −0.453909
\(135\) 5.26432e8 0.136408
\(136\) 0 0
\(137\) −3.93985e9 −0.955513 −0.477757 0.878492i \(-0.658550\pi\)
−0.477757 + 0.878492i \(0.658550\pi\)
\(138\) 3.48000e9 0.816814
\(139\) −2.03489e8 −0.0462353 −0.0231177 0.999733i \(-0.507359\pi\)
−0.0231177 + 0.999733i \(0.507359\pi\)
\(140\) −1.88579e9 −0.414875
\(141\) −7.76290e9 −1.65401
\(142\) 1.06743e9 0.220314
\(143\) −2.36970e9 −0.473895
\(144\) 4.44055e9 0.860609
\(145\) −1.61879e9 −0.304114
\(146\) −3.32126e9 −0.604943
\(147\) 2.12346e10 3.75073
\(148\) −7.45396e8 −0.127705
\(149\) 2.97490e9 0.494463 0.247231 0.968956i \(-0.420479\pi\)
0.247231 + 0.968956i \(0.420479\pi\)
\(150\) 3.15030e9 0.508090
\(151\) −4.66116e9 −0.729622 −0.364811 0.931082i \(-0.618866\pi\)
−0.364811 + 0.931082i \(0.618866\pi\)
\(152\) −1.62942e9 −0.247592
\(153\) 0 0
\(154\) 7.39457e9 1.05942
\(155\) 7.07128e8 0.0984023
\(156\) −2.91949e9 −0.394681
\(157\) 1.25323e10 1.64620 0.823099 0.567898i \(-0.192243\pi\)
0.823099 + 0.567898i \(0.192243\pi\)
\(158\) 1.54651e9 0.197422
\(159\) −6.77677e9 −0.840884
\(160\) −1.88851e9 −0.227814
\(161\) −2.37856e10 −2.78996
\(162\) 1.64961e9 0.188176
\(163\) 1.01809e10 1.12964 0.564822 0.825213i \(-0.308945\pi\)
0.564822 + 0.825213i \(0.308945\pi\)
\(164\) 4.58336e9 0.494751
\(165\) −5.99814e9 −0.629998
\(166\) 5.26210e8 0.0537864
\(167\) −9.25639e9 −0.920911 −0.460455 0.887683i \(-0.652314\pi\)
−0.460455 + 0.887683i \(0.652314\pi\)
\(168\) 1.95318e10 1.89169
\(169\) −9.68393e9 −0.913191
\(170\) 0 0
\(171\) −5.61402e9 −0.502101
\(172\) 1.61937e10 1.41081
\(173\) 1.14334e10 0.970437 0.485218 0.874393i \(-0.338740\pi\)
0.485218 + 0.874393i \(0.338740\pi\)
\(174\) 7.82031e9 0.646774
\(175\) −2.15322e10 −1.73547
\(176\) −1.30689e10 −1.02667
\(177\) 2.24361e10 1.71818
\(178\) 2.97330e9 0.221998
\(179\) 1.76347e8 0.0128389 0.00641947 0.999979i \(-0.497957\pi\)
0.00641947 + 0.999979i \(0.497957\pi\)
\(180\) −4.24284e9 −0.301252
\(181\) −7.92156e9 −0.548602 −0.274301 0.961644i \(-0.588446\pi\)
−0.274301 + 0.961644i \(0.588446\pi\)
\(182\) −2.87260e9 −0.194068
\(183\) −2.75703e10 −1.81724
\(184\) −1.55323e10 −0.998979
\(185\) 5.94921e8 0.0373411
\(186\) −3.41610e9 −0.209277
\(187\) 0 0
\(188\) 1.61609e10 0.943530
\(189\) 1.73824e10 0.990905
\(190\) 6.06581e8 0.0337674
\(191\) −2.22255e9 −0.120838 −0.0604188 0.998173i \(-0.519244\pi\)
−0.0604188 + 0.998173i \(0.519244\pi\)
\(192\) −9.29550e9 −0.493648
\(193\) −7.32845e9 −0.380193 −0.190097 0.981765i \(-0.560880\pi\)
−0.190097 + 0.981765i \(0.560880\pi\)
\(194\) 2.24868e9 0.113978
\(195\) 2.33012e9 0.115405
\(196\) −4.42065e10 −2.13961
\(197\) −2.02827e10 −0.959462 −0.479731 0.877416i \(-0.659266\pi\)
−0.479731 + 0.877416i \(0.659266\pi\)
\(198\) 1.66371e10 0.769277
\(199\) −2.54331e7 −0.00114964 −0.000574819 1.00000i \(-0.500183\pi\)
−0.000574819 1.00000i \(0.500183\pi\)
\(200\) −1.40608e10 −0.621405
\(201\) 4.53745e10 1.96078
\(202\) 3.83518e9 0.162071
\(203\) −5.34515e10 −2.20916
\(204\) 0 0
\(205\) −3.65811e9 −0.144665
\(206\) 2.23298e9 0.0863939
\(207\) −5.35153e10 −2.02587
\(208\) 5.07693e9 0.188069
\(209\) 1.65225e10 0.598987
\(210\) −7.27107e9 −0.257995
\(211\) −1.74152e10 −0.604864 −0.302432 0.953171i \(-0.597799\pi\)
−0.302432 + 0.953171i \(0.597799\pi\)
\(212\) 1.41080e10 0.479682
\(213\) −2.85898e10 −0.951707
\(214\) −4.07121e9 −0.132697
\(215\) −1.29247e10 −0.412521
\(216\) 1.13510e10 0.354806
\(217\) 2.33489e10 0.714821
\(218\) −1.99960e10 −0.599638
\(219\) 8.89558e10 2.61322
\(220\) 1.24870e10 0.359382
\(221\) 0 0
\(222\) −2.87403e9 −0.0794152
\(223\) −9.16498e9 −0.248176 −0.124088 0.992271i \(-0.539601\pi\)
−0.124088 + 0.992271i \(0.539601\pi\)
\(224\) −6.23574e10 −1.65490
\(225\) −4.84452e10 −1.26017
\(226\) −8.00940e9 −0.204226
\(227\) −7.63415e10 −1.90829 −0.954145 0.299345i \(-0.903232\pi\)
−0.954145 + 0.299345i \(0.903232\pi\)
\(228\) 2.03558e10 0.498863
\(229\) 3.54702e10 0.852324 0.426162 0.904647i \(-0.359865\pi\)
0.426162 + 0.904647i \(0.359865\pi\)
\(230\) 5.78220e9 0.136244
\(231\) −1.98055e11 −4.57648
\(232\) −3.49046e10 −0.791018
\(233\) 7.22694e10 1.60640 0.803199 0.595711i \(-0.203130\pi\)
0.803199 + 0.595711i \(0.203130\pi\)
\(234\) −6.46307e9 −0.140918
\(235\) −1.28985e10 −0.275888
\(236\) −4.67078e10 −0.980135
\(237\) −4.14214e10 −0.852820
\(238\) 0 0
\(239\) −4.92709e10 −0.976787 −0.488394 0.872623i \(-0.662417\pi\)
−0.488394 + 0.872623i \(0.662417\pi\)
\(240\) 1.28506e10 0.250019
\(241\) −5.50366e10 −1.05093 −0.525467 0.850814i \(-0.676109\pi\)
−0.525467 + 0.850814i \(0.676109\pi\)
\(242\) −3.00372e10 −0.562977
\(243\) −7.31897e10 −1.34655
\(244\) 5.73962e10 1.03664
\(245\) 3.52824e10 0.625621
\(246\) 1.76721e10 0.307667
\(247\) −6.41857e9 −0.109724
\(248\) 1.52471e10 0.255950
\(249\) −1.40939e10 −0.232345
\(250\) 1.08347e10 0.175422
\(251\) −7.69545e10 −1.22378 −0.611889 0.790944i \(-0.709590\pi\)
−0.611889 + 0.790944i \(0.709590\pi\)
\(252\) −1.40096e11 −2.18838
\(253\) 1.57500e11 2.41678
\(254\) −1.81624e10 −0.273793
\(255\) 0 0
\(256\) −2.37571e9 −0.0345711
\(257\) 5.68659e10 0.813117 0.406559 0.913625i \(-0.366729\pi\)
0.406559 + 0.913625i \(0.366729\pi\)
\(258\) 6.24384e10 0.877330
\(259\) 1.96439e10 0.271256
\(260\) −4.85089e9 −0.0658326
\(261\) −1.20261e11 −1.60413
\(262\) 3.80146e10 0.498420
\(263\) −6.91993e10 −0.891869 −0.445934 0.895066i \(-0.647129\pi\)
−0.445934 + 0.895066i \(0.647129\pi\)
\(264\) −1.29332e11 −1.63866
\(265\) −1.12600e10 −0.140259
\(266\) 2.00289e10 0.245296
\(267\) −7.96361e10 −0.958980
\(268\) −9.44613e10 −1.11853
\(269\) 1.06868e11 1.24441 0.622204 0.782855i \(-0.286237\pi\)
0.622204 + 0.782855i \(0.286237\pi\)
\(270\) −4.22560e9 −0.0483895
\(271\) −8.13710e10 −0.916448 −0.458224 0.888837i \(-0.651514\pi\)
−0.458224 + 0.888837i \(0.651514\pi\)
\(272\) 0 0
\(273\) 7.69391e10 0.838331
\(274\) 3.16246e10 0.338960
\(275\) 1.42578e11 1.50333
\(276\) 1.94041e11 2.01281
\(277\) −9.42500e10 −0.961884 −0.480942 0.876753i \(-0.659705\pi\)
−0.480942 + 0.876753i \(0.659705\pi\)
\(278\) 1.63338e9 0.0164016
\(279\) 5.25326e10 0.519051
\(280\) 3.24531e10 0.315533
\(281\) 6.07310e10 0.581074 0.290537 0.956864i \(-0.406166\pi\)
0.290537 + 0.956864i \(0.406166\pi\)
\(282\) 6.23119e10 0.586745
\(283\) 7.56640e10 0.701214 0.350607 0.936523i \(-0.385975\pi\)
0.350607 + 0.936523i \(0.385975\pi\)
\(284\) 5.95187e10 0.542901
\(285\) −1.62465e10 −0.145868
\(286\) 1.90213e10 0.168110
\(287\) −1.20788e11 −1.05089
\(288\) −1.40298e11 −1.20167
\(289\) 0 0
\(290\) 1.29939e10 0.107882
\(291\) −6.02283e10 −0.492359
\(292\) −1.85189e11 −1.49071
\(293\) −1.94342e11 −1.54050 −0.770252 0.637740i \(-0.779870\pi\)
−0.770252 + 0.637740i \(0.779870\pi\)
\(294\) −1.70448e11 −1.33054
\(295\) 3.72788e10 0.286591
\(296\) 1.28277e10 0.0971264
\(297\) −1.15100e11 −0.858364
\(298\) −2.38791e10 −0.175406
\(299\) −6.11846e10 −0.442712
\(300\) 1.75657e11 1.25204
\(301\) −4.26764e11 −2.99666
\(302\) 3.74146e10 0.258827
\(303\) −1.02721e11 −0.700110
\(304\) −3.53983e10 −0.237712
\(305\) −4.58095e10 −0.303114
\(306\) 0 0
\(307\) 5.59360e7 0.000359392 0 0.000179696 1.00000i \(-0.499943\pi\)
0.000179696 1.00000i \(0.499943\pi\)
\(308\) 4.12313e11 2.61065
\(309\) −5.98077e10 −0.373202
\(310\) −5.67603e9 −0.0349073
\(311\) 2.85539e11 1.73079 0.865394 0.501093i \(-0.167068\pi\)
0.865394 + 0.501093i \(0.167068\pi\)
\(312\) 5.02423e10 0.300174
\(313\) −1.14880e11 −0.676543 −0.338271 0.941049i \(-0.609842\pi\)
−0.338271 + 0.941049i \(0.609842\pi\)
\(314\) −1.00595e11 −0.583974
\(315\) 1.11814e11 0.639882
\(316\) 8.62317e10 0.486491
\(317\) 3.13755e11 1.74512 0.872558 0.488511i \(-0.162460\pi\)
0.872558 + 0.488511i \(0.162460\pi\)
\(318\) 5.43963e10 0.298296
\(319\) 3.53936e11 1.91367
\(320\) −1.54450e10 −0.0823402
\(321\) 1.09042e11 0.573222
\(322\) 1.90924e11 0.989714
\(323\) 0 0
\(324\) 9.19805e10 0.463707
\(325\) −5.53879e10 −0.275385
\(326\) −8.17207e10 −0.400731
\(327\) 5.35569e11 2.59030
\(328\) −7.88764e10 −0.376283
\(329\) −4.25899e11 −2.00413
\(330\) 4.81464e10 0.223486
\(331\) −3.69358e10 −0.169131 −0.0845653 0.996418i \(-0.526950\pi\)
−0.0845653 + 0.996418i \(0.526950\pi\)
\(332\) 2.93409e10 0.132541
\(333\) 4.41968e10 0.196966
\(334\) 7.42999e10 0.326685
\(335\) 7.53922e10 0.327058
\(336\) 4.24319e11 1.81621
\(337\) 3.75633e11 1.58646 0.793230 0.608922i \(-0.208398\pi\)
0.793230 + 0.608922i \(0.208398\pi\)
\(338\) 7.77317e10 0.323946
\(339\) 2.14522e11 0.882212
\(340\) 0 0
\(341\) −1.54608e11 −0.619208
\(342\) 4.50630e10 0.178116
\(343\) 6.89028e11 2.68790
\(344\) −2.78682e11 −1.07299
\(345\) −1.54869e11 −0.588544
\(346\) −9.17743e10 −0.344254
\(347\) −2.70508e11 −1.00161 −0.500803 0.865561i \(-0.666962\pi\)
−0.500803 + 0.865561i \(0.666962\pi\)
\(348\) 4.36052e11 1.59379
\(349\) 1.21042e11 0.436740 0.218370 0.975866i \(-0.429926\pi\)
0.218370 + 0.975866i \(0.429926\pi\)
\(350\) 1.72836e11 0.615641
\(351\) 4.47134e10 0.157237
\(352\) 4.12908e11 1.43355
\(353\) −1.57474e11 −0.539786 −0.269893 0.962890i \(-0.586988\pi\)
−0.269893 + 0.962890i \(0.586988\pi\)
\(354\) −1.80092e11 −0.609508
\(355\) −4.75035e10 −0.158744
\(356\) 1.65788e11 0.547050
\(357\) 0 0
\(358\) −1.41551e9 −0.00455450
\(359\) 7.77740e10 0.247121 0.123560 0.992337i \(-0.460569\pi\)
0.123560 + 0.992337i \(0.460569\pi\)
\(360\) 7.30162e10 0.229117
\(361\) −2.77935e11 −0.861313
\(362\) 6.35854e10 0.194612
\(363\) 8.04510e11 2.43193
\(364\) −1.60173e11 −0.478226
\(365\) 1.47805e11 0.435884
\(366\) 2.21303e11 0.644648
\(367\) −5.08018e11 −1.46178 −0.730889 0.682496i \(-0.760894\pi\)
−0.730889 + 0.682496i \(0.760894\pi\)
\(368\) −3.37433e11 −0.959118
\(369\) −2.71762e11 −0.763079
\(370\) −4.77536e9 −0.0132464
\(371\) −3.71796e11 −1.01888
\(372\) −1.90478e11 −0.515704
\(373\) −2.86982e11 −0.767653 −0.383827 0.923405i \(-0.625394\pi\)
−0.383827 + 0.923405i \(0.625394\pi\)
\(374\) 0 0
\(375\) −2.90193e11 −0.757786
\(376\) −2.78118e11 −0.717601
\(377\) −1.37495e11 −0.350551
\(378\) −1.39526e11 −0.351515
\(379\) −3.16204e11 −0.787210 −0.393605 0.919280i \(-0.628772\pi\)
−0.393605 + 0.919280i \(0.628772\pi\)
\(380\) 3.38223e10 0.0832102
\(381\) 4.86458e11 1.18272
\(382\) 1.78402e10 0.0428661
\(383\) 9.49479e9 0.0225471 0.0112736 0.999936i \(-0.496411\pi\)
0.0112736 + 0.999936i \(0.496411\pi\)
\(384\) 6.56551e11 1.54091
\(385\) −3.29078e11 −0.763354
\(386\) 5.88246e10 0.134870
\(387\) −9.60175e11 −2.17596
\(388\) 1.25384e11 0.280866
\(389\) −4.09089e11 −0.905825 −0.452912 0.891555i \(-0.649615\pi\)
−0.452912 + 0.891555i \(0.649615\pi\)
\(390\) −1.87036e10 −0.0409388
\(391\) 0 0
\(392\) 7.60762e11 1.62728
\(393\) −1.01818e12 −2.15306
\(394\) 1.62807e11 0.340361
\(395\) −6.88239e10 −0.142250
\(396\) 9.27663e11 1.89567
\(397\) 8.91592e10 0.180139 0.0900697 0.995935i \(-0.471291\pi\)
0.0900697 + 0.995935i \(0.471291\pi\)
\(398\) 2.04149e8 0.000407824 0
\(399\) −5.36450e11 −1.05962
\(400\) −3.05464e11 −0.596609
\(401\) 5.58430e11 1.07850 0.539248 0.842147i \(-0.318708\pi\)
0.539248 + 0.842147i \(0.318708\pi\)
\(402\) −3.64216e11 −0.695571
\(403\) 6.00611e10 0.113428
\(404\) 2.13845e11 0.399378
\(405\) −7.34122e10 −0.135588
\(406\) 4.29049e11 0.783681
\(407\) −1.30075e11 −0.234973
\(408\) 0 0
\(409\) −1.04657e12 −1.84932 −0.924661 0.380791i \(-0.875652\pi\)
−0.924661 + 0.380791i \(0.875652\pi\)
\(410\) 2.93632e10 0.0513187
\(411\) −8.47028e11 −1.46423
\(412\) 1.24509e11 0.212893
\(413\) 1.23092e12 2.08188
\(414\) 4.29560e11 0.718659
\(415\) −2.34178e10 −0.0387551
\(416\) −1.60404e11 −0.262601
\(417\) −4.37481e10 −0.0708511
\(418\) −1.32624e11 −0.212485
\(419\) −8.33570e11 −1.32123 −0.660616 0.750724i \(-0.729705\pi\)
−0.660616 + 0.750724i \(0.729705\pi\)
\(420\) −4.05426e11 −0.635756
\(421\) 6.24599e10 0.0969018 0.0484509 0.998826i \(-0.484572\pi\)
0.0484509 + 0.998826i \(0.484572\pi\)
\(422\) 1.39790e11 0.214570
\(423\) −9.58230e11 −1.45525
\(424\) −2.42788e11 −0.364822
\(425\) 0 0
\(426\) 2.29487e11 0.337609
\(427\) −1.51260e12 −2.20190
\(428\) −2.27006e11 −0.326994
\(429\) −5.09463e11 −0.726197
\(430\) 1.03745e11 0.146338
\(431\) 8.32234e11 1.16171 0.580855 0.814007i \(-0.302718\pi\)
0.580855 + 0.814007i \(0.302718\pi\)
\(432\) 2.46594e11 0.340648
\(433\) 6.04620e11 0.826584 0.413292 0.910598i \(-0.364379\pi\)
0.413292 + 0.910598i \(0.364379\pi\)
\(434\) −1.87419e11 −0.253576
\(435\) −3.48025e11 −0.466024
\(436\) −1.11496e12 −1.47764
\(437\) 4.26603e11 0.559574
\(438\) −7.14037e11 −0.927016
\(439\) 3.64873e11 0.468869 0.234434 0.972132i \(-0.424676\pi\)
0.234434 + 0.972132i \(0.424676\pi\)
\(440\) −2.14893e11 −0.273328
\(441\) 2.62114e12 3.30002
\(442\) 0 0
\(443\) −9.22214e10 −0.113767 −0.0568833 0.998381i \(-0.518116\pi\)
−0.0568833 + 0.998381i \(0.518116\pi\)
\(444\) −1.60253e11 −0.195696
\(445\) −1.32320e11 −0.159957
\(446\) 7.35662e10 0.0880382
\(447\) 6.39573e11 0.757716
\(448\) −5.09982e11 −0.598142
\(449\) 3.94256e11 0.457794 0.228897 0.973451i \(-0.426488\pi\)
0.228897 + 0.973451i \(0.426488\pi\)
\(450\) 3.88864e11 0.447034
\(451\) 7.99816e11 0.910323
\(452\) −4.46595e11 −0.503258
\(453\) −1.00210e12 −1.11807
\(454\) 6.12784e11 0.676949
\(455\) 1.27838e11 0.139833
\(456\) −3.50309e11 −0.379410
\(457\) −3.01453e11 −0.323294 −0.161647 0.986849i \(-0.551681\pi\)
−0.161647 + 0.986849i \(0.551681\pi\)
\(458\) −2.84715e11 −0.302354
\(459\) 0 0
\(460\) 3.22409e11 0.335735
\(461\) 5.11194e11 0.527147 0.263574 0.964639i \(-0.415099\pi\)
0.263574 + 0.964639i \(0.415099\pi\)
\(462\) 1.58976e12 1.62346
\(463\) 1.06656e12 1.07863 0.539313 0.842105i \(-0.318684\pi\)
0.539313 + 0.842105i \(0.318684\pi\)
\(464\) −7.58285e11 −0.759454
\(465\) 1.52025e11 0.150792
\(466\) −5.80098e11 −0.569855
\(467\) 1.33553e12 1.29936 0.649678 0.760210i \(-0.274904\pi\)
0.649678 + 0.760210i \(0.274904\pi\)
\(468\) −3.60373e11 −0.347253
\(469\) 2.48940e12 2.37584
\(470\) 1.03534e11 0.0978688
\(471\) 2.69432e12 2.52264
\(472\) 8.03808e11 0.745441
\(473\) 2.82587e12 2.59584
\(474\) 3.32485e11 0.302530
\(475\) 3.86186e11 0.348077
\(476\) 0 0
\(477\) −8.36505e11 −0.739836
\(478\) 3.95491e11 0.346507
\(479\) 1.45285e11 0.126099 0.0630493 0.998010i \(-0.479917\pi\)
0.0630493 + 0.998010i \(0.479917\pi\)
\(480\) −4.06012e11 −0.349102
\(481\) 5.05307e10 0.0430430
\(482\) 4.41772e11 0.372809
\(483\) −5.11367e12 −4.27534
\(484\) −1.67484e12 −1.38730
\(485\) −1.00072e11 −0.0821252
\(486\) 5.87485e11 0.477676
\(487\) 9.83443e11 0.792262 0.396131 0.918194i \(-0.370353\pi\)
0.396131 + 0.918194i \(0.370353\pi\)
\(488\) −9.87747e11 −0.788418
\(489\) 2.18879e12 1.73107
\(490\) −2.83208e11 −0.221933
\(491\) 1.59951e12 1.24200 0.620999 0.783812i \(-0.286727\pi\)
0.620999 + 0.783812i \(0.286727\pi\)
\(492\) 9.85378e11 0.758158
\(493\) 0 0
\(494\) 5.15210e10 0.0389236
\(495\) −7.40393e11 −0.554293
\(496\) 3.31237e11 0.245737
\(497\) −1.56853e12 −1.15316
\(498\) 1.13130e11 0.0824225
\(499\) −1.17686e12 −0.849713 −0.424857 0.905261i \(-0.639675\pi\)
−0.424857 + 0.905261i \(0.639675\pi\)
\(500\) 6.04128e11 0.432279
\(501\) −1.99003e12 −1.41121
\(502\) 6.17704e11 0.434124
\(503\) 6.65667e11 0.463661 0.231831 0.972756i \(-0.425528\pi\)
0.231831 + 0.972756i \(0.425528\pi\)
\(504\) 2.41095e12 1.66437
\(505\) −1.70676e11 −0.116778
\(506\) −1.26423e12 −0.857332
\(507\) −2.08195e12 −1.39938
\(508\) −1.01271e12 −0.674684
\(509\) 1.56094e12 1.03076 0.515380 0.856962i \(-0.327651\pi\)
0.515380 + 0.856962i \(0.327651\pi\)
\(510\) 0 0
\(511\) 4.88041e12 3.16638
\(512\) −1.54451e12 −0.993289
\(513\) −3.11759e11 −0.198743
\(514\) −4.56456e11 −0.288446
\(515\) −9.93737e10 −0.0622500
\(516\) 3.48149e12 2.16193
\(517\) 2.82015e12 1.73606
\(518\) −1.57679e11 −0.0962255
\(519\) 2.45806e12 1.48710
\(520\) 8.34802e10 0.0500690
\(521\) 1.37048e11 0.0814897 0.0407449 0.999170i \(-0.487027\pi\)
0.0407449 + 0.999170i \(0.487027\pi\)
\(522\) 9.65316e11 0.569053
\(523\) 7.68959e11 0.449413 0.224707 0.974426i \(-0.427858\pi\)
0.224707 + 0.974426i \(0.427858\pi\)
\(524\) 2.11965e12 1.22821
\(525\) −4.62920e12 −2.65943
\(526\) 5.55454e11 0.316383
\(527\) 0 0
\(528\) −2.80968e12 −1.57328
\(529\) 2.26541e12 1.25776
\(530\) 9.03823e10 0.0497556
\(531\) 2.76945e12 1.51171
\(532\) 1.11679e12 0.604461
\(533\) −3.10708e11 −0.166755
\(534\) 6.39229e11 0.340190
\(535\) 1.81180e11 0.0956132
\(536\) 1.62561e12 0.850697
\(537\) 3.79128e10 0.0196744
\(538\) −8.57817e11 −0.441443
\(539\) −7.71422e12 −3.93679
\(540\) −2.35615e11 −0.119242
\(541\) −1.61587e12 −0.810994 −0.405497 0.914096i \(-0.632902\pi\)
−0.405497 + 0.914096i \(0.632902\pi\)
\(542\) 6.53155e11 0.325102
\(543\) −1.70306e12 −0.840678
\(544\) 0 0
\(545\) 8.89876e11 0.432061
\(546\) −6.17581e11 −0.297390
\(547\) −6.21965e11 −0.297046 −0.148523 0.988909i \(-0.547452\pi\)
−0.148523 + 0.988909i \(0.547452\pi\)
\(548\) 1.76335e12 0.835270
\(549\) −3.40319e12 −1.59886
\(550\) −1.14446e12 −0.533294
\(551\) 9.58670e11 0.443085
\(552\) −3.33930e12 −1.53084
\(553\) −2.27252e12 −1.03334
\(554\) 7.56533e11 0.341220
\(555\) 1.27902e11 0.0572215
\(556\) 9.10754e10 0.0404170
\(557\) 3.24481e11 0.142837 0.0714186 0.997446i \(-0.477247\pi\)
0.0714186 + 0.997446i \(0.477247\pi\)
\(558\) −4.21673e11 −0.184129
\(559\) −1.09778e12 −0.475512
\(560\) 7.05028e11 0.302943
\(561\) 0 0
\(562\) −4.87480e11 −0.206131
\(563\) 2.81084e12 1.17910 0.589548 0.807733i \(-0.299306\pi\)
0.589548 + 0.807733i \(0.299306\pi\)
\(564\) 3.47444e12 1.44587
\(565\) 3.56440e11 0.147153
\(566\) −6.07345e11 −0.248749
\(567\) −2.42402e12 −0.984946
\(568\) −1.02427e12 −0.412903
\(569\) 1.34010e12 0.535960 0.267980 0.963424i \(-0.413644\pi\)
0.267980 + 0.963424i \(0.413644\pi\)
\(570\) 1.30409e11 0.0517452
\(571\) 3.36420e12 1.32440 0.662200 0.749327i \(-0.269623\pi\)
0.662200 + 0.749327i \(0.269623\pi\)
\(572\) 1.06061e12 0.414259
\(573\) −4.77827e11 −0.185172
\(574\) 9.69552e11 0.372793
\(575\) 3.68130e12 1.40441
\(576\) −1.14741e12 −0.434327
\(577\) −2.59598e12 −0.975014 −0.487507 0.873119i \(-0.662094\pi\)
−0.487507 + 0.873119i \(0.662094\pi\)
\(578\) 0 0
\(579\) −1.57554e12 −0.582609
\(580\) 7.24523e11 0.265844
\(581\) −7.73239e11 −0.281528
\(582\) 4.83445e11 0.174660
\(583\) 2.46190e12 0.882596
\(584\) 3.18697e12 1.13376
\(585\) 2.87624e11 0.101537
\(586\) 1.55996e12 0.546480
\(587\) 1.24760e12 0.433714 0.216857 0.976203i \(-0.430420\pi\)
0.216857 + 0.976203i \(0.430420\pi\)
\(588\) −9.50396e12 −3.27874
\(589\) −4.18770e11 −0.143369
\(590\) −2.99232e11 −0.101666
\(591\) −4.36058e12 −1.47028
\(592\) 2.78676e11 0.0932508
\(593\) 2.13010e12 0.707382 0.353691 0.935362i \(-0.384926\pi\)
0.353691 + 0.935362i \(0.384926\pi\)
\(594\) 9.23893e11 0.304497
\(595\) 0 0
\(596\) −1.33147e12 −0.432239
\(597\) −5.46787e9 −0.00176171
\(598\) 4.91121e11 0.157048
\(599\) −2.02782e12 −0.643588 −0.321794 0.946810i \(-0.604286\pi\)
−0.321794 + 0.946810i \(0.604286\pi\)
\(600\) −3.02293e12 −0.952242
\(601\) −3.00967e12 −0.940988 −0.470494 0.882403i \(-0.655924\pi\)
−0.470494 + 0.882403i \(0.655924\pi\)
\(602\) 3.42558e12 1.06304
\(603\) 5.60090e12 1.72516
\(604\) 2.08619e12 0.637805
\(605\) 1.33674e12 0.405645
\(606\) 8.24526e11 0.248358
\(607\) 4.01134e12 1.19934 0.599668 0.800249i \(-0.295299\pi\)
0.599668 + 0.800249i \(0.295299\pi\)
\(608\) 1.11840e12 0.331918
\(609\) −1.14915e13 −3.38533
\(610\) 3.67707e11 0.107527
\(611\) −1.09555e12 −0.318016
\(612\) 0 0
\(613\) −4.20582e11 −0.120303 −0.0601517 0.998189i \(-0.519158\pi\)
−0.0601517 + 0.998189i \(0.519158\pi\)
\(614\) −4.48991e8 −0.000127491 0
\(615\) −7.86457e11 −0.221685
\(616\) −7.09561e12 −1.98553
\(617\) −3.55275e11 −0.0986920 −0.0493460 0.998782i \(-0.515714\pi\)
−0.0493460 + 0.998782i \(0.515714\pi\)
\(618\) 4.80069e11 0.132390
\(619\) −4.53480e12 −1.24151 −0.620755 0.784005i \(-0.713174\pi\)
−0.620755 + 0.784005i \(0.713174\pi\)
\(620\) −3.16489e11 −0.0860192
\(621\) −2.97183e12 −0.801883
\(622\) −2.29199e12 −0.613981
\(623\) −4.36910e12 −1.16197
\(624\) 1.09149e12 0.288197
\(625\) 3.08330e12 0.808268
\(626\) 9.22128e11 0.239997
\(627\) 3.55217e12 0.917889
\(628\) −5.60907e12 −1.43904
\(629\) 0 0
\(630\) −8.97519e11 −0.226992
\(631\) −1.28442e12 −0.322533 −0.161267 0.986911i \(-0.551558\pi\)
−0.161267 + 0.986911i \(0.551558\pi\)
\(632\) −1.48398e12 −0.370001
\(633\) −3.74410e12 −0.926895
\(634\) −2.51847e12 −0.619064
\(635\) 8.08276e11 0.197278
\(636\) 3.03308e12 0.735066
\(637\) 2.99677e12 0.721152
\(638\) −2.84100e12 −0.678857
\(639\) −3.52904e12 −0.837342
\(640\) 1.09089e12 0.257023
\(641\) 6.39328e12 1.49576 0.747882 0.663832i \(-0.231071\pi\)
0.747882 + 0.663832i \(0.231071\pi\)
\(642\) −8.75270e11 −0.203345
\(643\) 1.81216e12 0.418069 0.209035 0.977908i \(-0.432968\pi\)
0.209035 + 0.977908i \(0.432968\pi\)
\(644\) 1.06457e13 2.43887
\(645\) −2.77867e12 −0.632148
\(646\) 0 0
\(647\) 8.15032e12 1.82854 0.914272 0.405102i \(-0.132764\pi\)
0.914272 + 0.405102i \(0.132764\pi\)
\(648\) −1.58292e12 −0.352672
\(649\) −8.15071e12 −1.80341
\(650\) 4.44592e11 0.0976903
\(651\) 5.01978e12 1.09539
\(652\) −4.55665e12 −0.987488
\(653\) −3.61715e11 −0.0778498 −0.0389249 0.999242i \(-0.512393\pi\)
−0.0389249 + 0.999242i \(0.512393\pi\)
\(654\) −4.29895e12 −0.918887
\(655\) −1.69175e12 −0.359130
\(656\) −1.71355e12 −0.361268
\(657\) 1.09804e13 2.29919
\(658\) 3.41864e12 0.710946
\(659\) 1.47257e12 0.304152 0.152076 0.988369i \(-0.451404\pi\)
0.152076 + 0.988369i \(0.451404\pi\)
\(660\) 2.68459e12 0.550718
\(661\) 7.77332e12 1.58380 0.791900 0.610651i \(-0.209092\pi\)
0.791900 + 0.610651i \(0.209092\pi\)
\(662\) 2.96479e11 0.0599976
\(663\) 0 0
\(664\) −5.04935e11 −0.100804
\(665\) −8.91339e11 −0.176744
\(666\) −3.54762e11 −0.0698720
\(667\) 9.13846e12 1.78775
\(668\) 4.14288e12 0.805022
\(669\) −1.97038e12 −0.380306
\(670\) −6.05163e11 −0.116021
\(671\) 1.00159e13 1.90738
\(672\) −1.34062e13 −2.53597
\(673\) −1.26810e12 −0.238278 −0.119139 0.992878i \(-0.538013\pi\)
−0.119139 + 0.992878i \(0.538013\pi\)
\(674\) −3.01516e12 −0.562782
\(675\) −2.69027e12 −0.498803
\(676\) 4.33423e12 0.798274
\(677\) −1.17739e12 −0.215412 −0.107706 0.994183i \(-0.534351\pi\)
−0.107706 + 0.994183i \(0.534351\pi\)
\(678\) −1.72194e12 −0.312957
\(679\) −3.30432e12 −0.596580
\(680\) 0 0
\(681\) −1.64127e13 −2.92427
\(682\) 1.24102e12 0.219659
\(683\) −4.40941e12 −0.775332 −0.387666 0.921800i \(-0.626719\pi\)
−0.387666 + 0.921800i \(0.626719\pi\)
\(684\) 2.51266e12 0.438916
\(685\) −1.40738e12 −0.244233
\(686\) −5.53074e12 −0.953509
\(687\) 7.62575e12 1.30610
\(688\) −6.05424e12 −1.03018
\(689\) −9.56385e11 −0.161676
\(690\) 1.24312e12 0.208781
\(691\) −5.05184e12 −0.842943 −0.421472 0.906842i \(-0.638486\pi\)
−0.421472 + 0.906842i \(0.638486\pi\)
\(692\) −5.11723e12 −0.848316
\(693\) −2.44473e13 −4.02653
\(694\) 2.17133e12 0.355311
\(695\) −7.26897e10 −0.0118179
\(696\) −7.50413e12 −1.21216
\(697\) 0 0
\(698\) −9.71592e11 −0.154930
\(699\) 1.55372e13 2.46165
\(700\) 9.63713e12 1.51707
\(701\) 4.88708e12 0.764396 0.382198 0.924080i \(-0.375167\pi\)
0.382198 + 0.924080i \(0.375167\pi\)
\(702\) −3.58909e11 −0.0557785
\(703\) −3.52320e11 −0.0544049
\(704\) 3.37692e12 0.518135
\(705\) −2.77304e12 −0.422772
\(706\) 1.26402e12 0.191484
\(707\) −5.63560e12 −0.848307
\(708\) −1.00417e13 −1.50196
\(709\) −4.41652e12 −0.656405 −0.328203 0.944607i \(-0.606443\pi\)
−0.328203 + 0.944607i \(0.606443\pi\)
\(710\) 3.81304e11 0.0563131
\(711\) −5.11294e12 −0.750339
\(712\) −2.85308e12 −0.416059
\(713\) −3.99190e12 −0.578464
\(714\) 0 0
\(715\) −8.46499e11 −0.121129
\(716\) −7.89274e10 −0.0112233
\(717\) −1.05928e13 −1.49683
\(718\) −6.24282e11 −0.0876639
\(719\) −1.05956e13 −1.47859 −0.739294 0.673382i \(-0.764841\pi\)
−0.739294 + 0.673382i \(0.764841\pi\)
\(720\) 1.58624e12 0.219975
\(721\) −3.28125e12 −0.452200
\(722\) 2.23095e12 0.305543
\(723\) −1.18323e13 −1.61045
\(724\) 3.54545e12 0.479565
\(725\) 8.27268e12 1.11205
\(726\) −6.45770e12 −0.862707
\(727\) −2.24449e11 −0.0297998 −0.0148999 0.999889i \(-0.504743\pi\)
−0.0148999 + 0.999889i \(0.504743\pi\)
\(728\) 2.75646e12 0.363714
\(729\) −1.16900e13 −1.53299
\(730\) −1.18641e12 −0.154626
\(731\) 0 0
\(732\) 1.23396e13 1.58855
\(733\) −8.03928e12 −1.02861 −0.514304 0.857608i \(-0.671950\pi\)
−0.514304 + 0.857608i \(0.671950\pi\)
\(734\) 4.07779e12 0.518553
\(735\) 7.58537e12 0.958703
\(736\) 1.06611e13 1.33922
\(737\) −1.64839e13 −2.05805
\(738\) 2.18140e12 0.270695
\(739\) −7.09200e12 −0.874719 −0.437360 0.899287i \(-0.644086\pi\)
−0.437360 + 0.899287i \(0.644086\pi\)
\(740\) −2.66269e11 −0.0326420
\(741\) −1.37993e12 −0.168141
\(742\) 2.98436e12 0.361438
\(743\) 5.81906e12 0.700492 0.350246 0.936658i \(-0.386098\pi\)
0.350246 + 0.936658i \(0.386098\pi\)
\(744\) 3.27798e12 0.392219
\(745\) 1.06268e12 0.126387
\(746\) 2.30357e12 0.272318
\(747\) −1.73971e12 −0.204425
\(748\) 0 0
\(749\) 5.98243e12 0.694560
\(750\) 2.32934e12 0.268818
\(751\) 6.10894e11 0.0700787 0.0350393 0.999386i \(-0.488844\pi\)
0.0350393 + 0.999386i \(0.488844\pi\)
\(752\) −6.04197e12 −0.688967
\(753\) −1.65445e13 −1.87532
\(754\) 1.10366e12 0.124355
\(755\) −1.66505e12 −0.186494
\(756\) −7.77984e12 −0.866208
\(757\) 9.06353e12 1.00315 0.501575 0.865114i \(-0.332754\pi\)
0.501575 + 0.865114i \(0.332754\pi\)
\(758\) 2.53813e12 0.279256
\(759\) 3.38609e13 3.70348
\(760\) −5.82057e11 −0.0632855
\(761\) 6.47208e12 0.699540 0.349770 0.936836i \(-0.386260\pi\)
0.349770 + 0.936836i \(0.386260\pi\)
\(762\) −3.90474e12 −0.419560
\(763\) 2.93831e13 3.13861
\(764\) 9.94747e11 0.105631
\(765\) 0 0
\(766\) −7.62135e10 −0.00799838
\(767\) 3.16634e12 0.330353
\(768\) −5.10754e11 −0.0529769
\(769\) −1.46020e12 −0.150572 −0.0752860 0.997162i \(-0.523987\pi\)
−0.0752860 + 0.997162i \(0.523987\pi\)
\(770\) 2.64147e12 0.270793
\(771\) 1.22256e13 1.24602
\(772\) 3.27999e12 0.332349
\(773\) −1.12146e13 −1.12973 −0.564867 0.825182i \(-0.691073\pi\)
−0.564867 + 0.825182i \(0.691073\pi\)
\(774\) 7.70721e12 0.771903
\(775\) −3.61370e12 −0.359828
\(776\) −2.15777e12 −0.213613
\(777\) 4.22324e12 0.415673
\(778\) 3.28370e12 0.321333
\(779\) 2.16638e12 0.210773
\(780\) −1.04289e12 −0.100882
\(781\) 1.03862e13 0.998916
\(782\) 0 0
\(783\) −6.67834e12 −0.634952
\(784\) 1.65272e13 1.56234
\(785\) 4.47675e12 0.420775
\(786\) 8.17277e12 0.763779
\(787\) −1.52729e13 −1.41917 −0.709584 0.704620i \(-0.751117\pi\)
−0.709584 + 0.704620i \(0.751117\pi\)
\(788\) 9.07792e12 0.838722
\(789\) −1.48772e13 −1.36670
\(790\) 5.52441e11 0.0504619
\(791\) 1.17694e13 1.06896
\(792\) −1.59644e13 −1.44175
\(793\) −3.89091e12 −0.349399
\(794\) −7.15669e11 −0.0639028
\(795\) −2.42078e12 −0.214933
\(796\) 1.13831e10 0.00100497
\(797\) −1.90733e13 −1.67442 −0.837209 0.546883i \(-0.815814\pi\)
−0.837209 + 0.546883i \(0.815814\pi\)
\(798\) 4.30601e12 0.375891
\(799\) 0 0
\(800\) 9.65104e12 0.833047
\(801\) −9.83005e12 −0.843741
\(802\) −4.48244e12 −0.382587
\(803\) −3.23163e13 −2.74285
\(804\) −2.03082e13 −1.71404
\(805\) −8.49664e12 −0.713125
\(806\) −4.82103e11 −0.0402376
\(807\) 2.29756e13 1.90693
\(808\) −3.68012e12 −0.303747
\(809\) 2.83376e12 0.232592 0.116296 0.993215i \(-0.462898\pi\)
0.116296 + 0.993215i \(0.462898\pi\)
\(810\) 5.89270e11 0.0480985
\(811\) −2.17990e13 −1.76947 −0.884735 0.466095i \(-0.845660\pi\)
−0.884735 + 0.466095i \(0.845660\pi\)
\(812\) 2.39233e13 1.93116
\(813\) −1.74940e13 −1.40437
\(814\) 1.04409e12 0.0833546
\(815\) 3.63679e12 0.288741
\(816\) 0 0
\(817\) 7.65414e12 0.601031
\(818\) 8.40067e12 0.656031
\(819\) 9.49714e12 0.737590
\(820\) 1.63726e12 0.126460
\(821\) 3.03817e12 0.233382 0.116691 0.993168i \(-0.462771\pi\)
0.116691 + 0.993168i \(0.462771\pi\)
\(822\) 6.79899e12 0.519423
\(823\) 4.30524e12 0.327113 0.163557 0.986534i \(-0.447703\pi\)
0.163557 + 0.986534i \(0.447703\pi\)
\(824\) −2.14270e12 −0.161916
\(825\) 3.06529e13 2.30371
\(826\) −9.88045e12 −0.738527
\(827\) −1.92853e13 −1.43368 −0.716839 0.697238i \(-0.754412\pi\)
−0.716839 + 0.697238i \(0.754412\pi\)
\(828\) 2.39518e13 1.77093
\(829\) 7.67396e12 0.564319 0.282159 0.959368i \(-0.408949\pi\)
0.282159 + 0.959368i \(0.408949\pi\)
\(830\) 1.87971e11 0.0137480
\(831\) −2.02628e13 −1.47399
\(832\) −1.31184e12 −0.0949134
\(833\) 0 0
\(834\) 3.51160e11 0.0251338
\(835\) −3.30654e12 −0.235388
\(836\) −7.39496e12 −0.523610
\(837\) 2.91726e12 0.205452
\(838\) 6.69096e12 0.468695
\(839\) −1.54174e13 −1.07419 −0.537096 0.843521i \(-0.680479\pi\)
−0.537096 + 0.843521i \(0.680479\pi\)
\(840\) 6.97709e12 0.483524
\(841\) 6.02898e12 0.415587
\(842\) −5.01358e11 −0.0343751
\(843\) 1.30566e13 0.890440
\(844\) 7.79452e12 0.528747
\(845\) −3.45927e12 −0.233415
\(846\) 7.69159e12 0.516237
\(847\) 4.41381e13 2.94672
\(848\) −5.27446e12 −0.350265
\(849\) 1.62670e13 1.07454
\(850\) 0 0
\(851\) −3.35847e12 −0.219512
\(852\) 1.27959e13 0.831943
\(853\) 1.45905e13 0.943627 0.471814 0.881698i \(-0.343600\pi\)
0.471814 + 0.881698i \(0.343600\pi\)
\(854\) 1.21414e13 0.781105
\(855\) −2.00542e12 −0.128339
\(856\) 3.90661e12 0.248696
\(857\) −1.78943e13 −1.13319 −0.566593 0.823998i \(-0.691739\pi\)
−0.566593 + 0.823998i \(0.691739\pi\)
\(858\) 4.08939e12 0.257612
\(859\) 9.39436e12 0.588705 0.294353 0.955697i \(-0.404896\pi\)
0.294353 + 0.955697i \(0.404896\pi\)
\(860\) 5.78468e12 0.360609
\(861\) −2.59683e13 −1.61038
\(862\) −6.68024e12 −0.412106
\(863\) −2.64114e13 −1.62085 −0.810425 0.585843i \(-0.800764\pi\)
−0.810425 + 0.585843i \(0.800764\pi\)
\(864\) −7.79107e12 −0.475647
\(865\) 4.08420e12 0.248047
\(866\) −4.85321e12 −0.293223
\(867\) 0 0
\(868\) −1.04502e13 −0.624867
\(869\) 1.50478e13 0.895125
\(870\) 2.79355e12 0.165318
\(871\) 6.40356e12 0.376999
\(872\) 1.91876e13 1.12382
\(873\) −7.43440e12 −0.433193
\(874\) −3.42429e12 −0.198504
\(875\) −1.59210e13 −0.918191
\(876\) −3.98139e13 −2.28437
\(877\) 1.52236e13 0.868998 0.434499 0.900672i \(-0.356925\pi\)
0.434499 + 0.900672i \(0.356925\pi\)
\(878\) −2.92879e12 −0.166327
\(879\) −4.17816e13 −2.36067
\(880\) −4.66844e12 −0.262422
\(881\) −3.66329e12 −0.204871 −0.102435 0.994740i \(-0.532663\pi\)
−0.102435 + 0.994740i \(0.532663\pi\)
\(882\) −2.10395e13 −1.17065
\(883\) 6.26349e12 0.346732 0.173366 0.984857i \(-0.444536\pi\)
0.173366 + 0.984857i \(0.444536\pi\)
\(884\) 0 0
\(885\) 8.01458e12 0.439173
\(886\) 7.40250e11 0.0403577
\(887\) −2.21639e13 −1.20224 −0.601119 0.799160i \(-0.705278\pi\)
−0.601119 + 0.799160i \(0.705278\pi\)
\(888\) 2.75783e12 0.148837
\(889\) 2.66887e13 1.43308
\(890\) 1.06211e12 0.0567434
\(891\) 1.60510e13 0.853202
\(892\) 4.10197e12 0.216945
\(893\) 7.63863e12 0.401961
\(894\) −5.13377e12 −0.268793
\(895\) 6.29942e10 0.00328168
\(896\) 3.60206e13 1.86709
\(897\) −1.31541e13 −0.678414
\(898\) −3.16464e12 −0.162398
\(899\) −8.97066e12 −0.458043
\(900\) 2.16826e13 1.10159
\(901\) 0 0
\(902\) −6.42002e12 −0.322929
\(903\) −9.17499e13 −4.59210
\(904\) 7.68557e12 0.382753
\(905\) −2.82972e12 −0.140225
\(906\) 8.04376e12 0.396627
\(907\) 2.10781e13 1.03419 0.517093 0.855929i \(-0.327014\pi\)
0.517093 + 0.855929i \(0.327014\pi\)
\(908\) 3.41681e13 1.66815
\(909\) −1.26795e13 −0.615979
\(910\) −1.02614e12 −0.0496046
\(911\) 2.85612e13 1.37387 0.686933 0.726721i \(-0.258956\pi\)
0.686933 + 0.726721i \(0.258956\pi\)
\(912\) −7.61029e12 −0.364271
\(913\) 5.12010e12 0.243871
\(914\) 2.41973e12 0.114686
\(915\) −9.84858e12 −0.464493
\(916\) −1.58754e13 −0.745066
\(917\) −5.58605e13 −2.60881
\(918\) 0 0
\(919\) 1.36453e13 0.631050 0.315525 0.948917i \(-0.397819\pi\)
0.315525 + 0.948917i \(0.397819\pi\)
\(920\) −5.54842e12 −0.255343
\(921\) 1.20257e10 0.000550733 0
\(922\) −4.10329e12 −0.187001
\(923\) −4.03479e12 −0.182984
\(924\) 8.86432e13 4.00057
\(925\) −3.04028e12 −0.136545
\(926\) −8.56114e12 −0.382633
\(927\) −7.38249e12 −0.328355
\(928\) 2.39578e13 1.06043
\(929\) −1.59082e13 −0.700728 −0.350364 0.936614i \(-0.613942\pi\)
−0.350364 + 0.936614i \(0.613942\pi\)
\(930\) −1.22029e12 −0.0534921
\(931\) −2.08947e13 −0.911511
\(932\) −3.23456e13 −1.40425
\(933\) 6.13881e13 2.65226
\(934\) −1.07201e13 −0.460935
\(935\) 0 0
\(936\) 6.20176e12 0.264103
\(937\) −1.91186e13 −0.810266 −0.405133 0.914258i \(-0.632775\pi\)
−0.405133 + 0.914258i \(0.632775\pi\)
\(938\) −1.99821e13 −0.842807
\(939\) −2.46981e13 −1.03674
\(940\) 5.77296e12 0.241170
\(941\) −3.13271e13 −1.30247 −0.651233 0.758878i \(-0.725748\pi\)
−0.651233 + 0.758878i \(0.725748\pi\)
\(942\) −2.16270e13 −0.894883
\(943\) 2.06509e13 0.850424
\(944\) 1.74623e13 0.715696
\(945\) 6.20930e12 0.253279
\(946\) −2.26829e13 −0.920850
\(947\) 2.14307e13 0.865888 0.432944 0.901421i \(-0.357475\pi\)
0.432944 + 0.901421i \(0.357475\pi\)
\(948\) 1.85390e13 0.745500
\(949\) 1.25541e13 0.502442
\(950\) −3.09987e12 −0.123477
\(951\) 6.74542e13 2.67422
\(952\) 0 0
\(953\) −2.15688e13 −0.847047 −0.423523 0.905885i \(-0.639207\pi\)
−0.423523 + 0.905885i \(0.639207\pi\)
\(954\) 6.71452e12 0.262450
\(955\) −7.93935e11 −0.0308866
\(956\) 2.20521e13 0.853867
\(957\) 7.60928e13 2.93251
\(958\) −1.16618e12 −0.0447324
\(959\) −4.64708e13 −1.77417
\(960\) −3.32051e12 −0.126178
\(961\) −2.25210e13 −0.851791
\(962\) −4.05603e11 −0.0152691
\(963\) 1.34599e13 0.504339
\(964\) 2.46327e13 0.918682
\(965\) −2.61785e12 −0.0971789
\(966\) 4.10468e13 1.51664
\(967\) 1.53274e13 0.563702 0.281851 0.959458i \(-0.409052\pi\)
0.281851 + 0.959458i \(0.409052\pi\)
\(968\) 2.88228e13 1.05511
\(969\) 0 0
\(970\) 8.03269e11 0.0291332
\(971\) −3.76272e13 −1.35836 −0.679180 0.733971i \(-0.737665\pi\)
−0.679180 + 0.733971i \(0.737665\pi\)
\(972\) 3.27575e13 1.17710
\(973\) −2.40017e12 −0.0858487
\(974\) −7.89398e12 −0.281048
\(975\) −1.19079e13 −0.422000
\(976\) −2.14583e13 −0.756958
\(977\) −1.14340e13 −0.401489 −0.200745 0.979644i \(-0.564336\pi\)
−0.200745 + 0.979644i \(0.564336\pi\)
\(978\) −1.75692e13 −0.614081
\(979\) 2.89306e13 1.00655
\(980\) −1.57913e13 −0.546892
\(981\) 6.61091e13 2.27903
\(982\) −1.28391e13 −0.440588
\(983\) 2.31190e13 0.789728 0.394864 0.918740i \(-0.370792\pi\)
0.394864 + 0.918740i \(0.370792\pi\)
\(984\) −1.69576e13 −0.576617
\(985\) −7.24534e12 −0.245242
\(986\) 0 0
\(987\) −9.15640e13 −3.07113
\(988\) 2.87275e12 0.0959162
\(989\) 7.29626e13 2.42503
\(990\) 5.94304e12 0.196630
\(991\) −2.31346e13 −0.761959 −0.380979 0.924584i \(-0.624413\pi\)
−0.380979 + 0.924584i \(0.624413\pi\)
\(992\) −1.04653e13 −0.343123
\(993\) −7.94084e12 −0.259176
\(994\) 1.25904e13 0.409073
\(995\) −9.08515e9 −0.000293852 0
\(996\) 6.30800e12 0.203107
\(997\) 2.87388e13 0.921171 0.460586 0.887615i \(-0.347639\pi\)
0.460586 + 0.887615i \(0.347639\pi\)
\(998\) 9.44651e12 0.301428
\(999\) 2.45435e12 0.0779636
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.1.16 36
17.16 even 2 289.10.a.h.1.16 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.16 36 1.1 even 1 trivial
289.10.a.h.1.16 yes 36 17.16 even 2