Properties

Label 9.26.a.a.1.1
Level $9$
Weight $26$
Character 9.1
Self dual yes
Analytic conductor $35.640$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 9.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(35.6397101957\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9.1

$q$-expansion

\(f(q)\) \(=\) \(q+48.0000 q^{2} -3.35521e7 q^{4} +7.41990e8 q^{5} +3.90806e10 q^{7} -3.22111e9 q^{8} +O(q^{10})\) \(q+48.0000 q^{2} -3.35521e7 q^{4} +7.41990e8 q^{5} +3.90806e10 q^{7} -3.22111e9 q^{8} +3.56155e10 q^{10} -8.41952e12 q^{11} -8.16510e13 q^{13} +1.87587e12 q^{14} +1.12567e15 q^{16} +2.51990e15 q^{17} -6.08206e15 q^{19} -2.48953e16 q^{20} -4.04137e14 q^{22} +9.49953e16 q^{23} +2.52526e17 q^{25} -3.91925e15 q^{26} -1.31124e18 q^{28} +2.71247e17 q^{29} +4.29167e18 q^{31} +1.62115e17 q^{32} +1.20955e17 q^{34} +2.89974e19 q^{35} +2.03015e19 q^{37} -2.91939e17 q^{38} -2.39003e18 q^{40} +1.83744e20 q^{41} +3.00902e20 q^{43} +2.82493e20 q^{44} +4.55977e18 q^{46} +9.24361e20 q^{47} +1.86224e20 q^{49} +1.21212e19 q^{50} +2.73957e21 q^{52} +9.90292e20 q^{53} -6.24719e21 q^{55} -1.25883e20 q^{56} +1.30199e19 q^{58} -1.30526e22 q^{59} +9.01545e21 q^{61} +2.06000e20 q^{62} -3.77634e22 q^{64} -6.05842e22 q^{65} -2.66891e22 q^{67} -8.45480e22 q^{68} +1.39188e21 q^{70} +1.92391e23 q^{71} +4.24046e22 q^{73} +9.74471e20 q^{74} +2.04066e23 q^{76} -3.29040e23 q^{77} -2.71681e23 q^{79} +8.35234e23 q^{80} +8.81972e21 q^{82} +9.31454e23 q^{83} +1.86974e24 q^{85} +1.44433e22 q^{86} +2.71202e22 q^{88} +1.76364e24 q^{89} -3.19097e24 q^{91} -3.18729e24 q^{92} +4.43693e22 q^{94} -4.51282e24 q^{95} +2.82924e24 q^{97} +8.93877e21 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 48.0000 0.00828641 0.00414320 0.999991i \(-0.498681\pi\)
0.00414320 + 0.999991i \(0.498681\pi\)
\(3\) 0 0
\(4\) −3.35521e7 −0.999931
\(5\) 7.41990e8 1.35917 0.679584 0.733598i \(-0.262160\pi\)
0.679584 + 0.733598i \(0.262160\pi\)
\(6\) 0 0
\(7\) 3.90806e10 1.06718 0.533588 0.845745i \(-0.320843\pi\)
0.533588 + 0.845745i \(0.320843\pi\)
\(8\) −3.22111e9 −0.0165722
\(9\) 0 0
\(10\) 3.56155e10 0.0112626
\(11\) −8.41952e12 −0.808870 −0.404435 0.914567i \(-0.632532\pi\)
−0.404435 + 0.914567i \(0.632532\pi\)
\(12\) 0 0
\(13\) −8.16510e13 −0.972008 −0.486004 0.873957i \(-0.661546\pi\)
−0.486004 + 0.873957i \(0.661546\pi\)
\(14\) 1.87587e12 0.00884305
\(15\) 0 0
\(16\) 1.12567e15 0.999794
\(17\) 2.51990e15 1.04899 0.524496 0.851413i \(-0.324254\pi\)
0.524496 + 0.851413i \(0.324254\pi\)
\(18\) 0 0
\(19\) −6.08206e15 −0.630421 −0.315210 0.949022i \(-0.602075\pi\)
−0.315210 + 0.949022i \(0.602075\pi\)
\(20\) −2.48953e16 −1.35907
\(21\) 0 0
\(22\) −4.04137e14 −0.00670262
\(23\) 9.49953e16 0.903866 0.451933 0.892052i \(-0.350735\pi\)
0.451933 + 0.892052i \(0.350735\pi\)
\(24\) 0 0
\(25\) 2.52526e17 0.847336
\(26\) −3.91925e15 −0.00805445
\(27\) 0 0
\(28\) −1.31124e18 −1.06710
\(29\) 2.71247e17 0.142361 0.0711803 0.997463i \(-0.477323\pi\)
0.0711803 + 0.997463i \(0.477323\pi\)
\(30\) 0 0
\(31\) 4.29167e18 0.978599 0.489299 0.872116i \(-0.337253\pi\)
0.489299 + 0.872116i \(0.337253\pi\)
\(32\) 1.62115e17 0.0248569
\(33\) 0 0
\(34\) 1.20955e17 0.00869237
\(35\) 2.89974e19 1.45047
\(36\) 0 0
\(37\) 2.03015e19 0.506998 0.253499 0.967336i \(-0.418419\pi\)
0.253499 + 0.967336i \(0.418419\pi\)
\(38\) −2.91939e17 −0.00522392
\(39\) 0 0
\(40\) −2.39003e18 −0.0225245
\(41\) 1.83744e20 1.27179 0.635895 0.771775i \(-0.280631\pi\)
0.635895 + 0.771775i \(0.280631\pi\)
\(42\) 0 0
\(43\) 3.00902e20 1.14834 0.574168 0.818737i \(-0.305326\pi\)
0.574168 + 0.818737i \(0.305326\pi\)
\(44\) 2.82493e20 0.808814
\(45\) 0 0
\(46\) 4.55977e18 0.00748980
\(47\) 9.24361e20 1.16043 0.580214 0.814464i \(-0.302969\pi\)
0.580214 + 0.814464i \(0.302969\pi\)
\(48\) 0 0
\(49\) 1.86224e20 0.138863
\(50\) 1.21212e19 0.00702137
\(51\) 0 0
\(52\) 2.73957e21 0.971941
\(53\) 9.90292e20 0.276895 0.138447 0.990370i \(-0.455789\pi\)
0.138447 + 0.990370i \(0.455789\pi\)
\(54\) 0 0
\(55\) −6.24719e21 −1.09939
\(56\) −1.25883e20 −0.0176855
\(57\) 0 0
\(58\) 1.30199e19 0.00117966
\(59\) −1.30526e22 −0.955093 −0.477547 0.878606i \(-0.658474\pi\)
−0.477547 + 0.878606i \(0.658474\pi\)
\(60\) 0 0
\(61\) 9.01545e21 0.434875 0.217438 0.976074i \(-0.430230\pi\)
0.217438 + 0.976074i \(0.430230\pi\)
\(62\) 2.06000e20 0.00810907
\(63\) 0 0
\(64\) −3.77634e22 −0.999588
\(65\) −6.05842e22 −1.32112
\(66\) 0 0
\(67\) −2.66891e22 −0.398473 −0.199236 0.979951i \(-0.563846\pi\)
−0.199236 + 0.979951i \(0.563846\pi\)
\(68\) −8.45480e22 −1.04892
\(69\) 0 0
\(70\) 1.39188e21 0.0120192
\(71\) 1.92391e23 1.39141 0.695704 0.718329i \(-0.255093\pi\)
0.695704 + 0.718329i \(0.255093\pi\)
\(72\) 0 0
\(73\) 4.24046e22 0.216709 0.108355 0.994112i \(-0.465442\pi\)
0.108355 + 0.994112i \(0.465442\pi\)
\(74\) 9.74471e20 0.00420119
\(75\) 0 0
\(76\) 2.04066e23 0.630377
\(77\) −3.29040e23 −0.863206
\(78\) 0 0
\(79\) −2.71681e23 −0.517274 −0.258637 0.965975i \(-0.583273\pi\)
−0.258637 + 0.965975i \(0.583273\pi\)
\(80\) 8.35234e23 1.35889
\(81\) 0 0
\(82\) 8.81972e21 0.0105386
\(83\) 9.31454e23 0.956501 0.478251 0.878223i \(-0.341271\pi\)
0.478251 + 0.878223i \(0.341271\pi\)
\(84\) 0 0
\(85\) 1.86974e24 1.42575
\(86\) 1.44433e22 0.00951558
\(87\) 0 0
\(88\) 2.71202e22 0.0134048
\(89\) 1.76364e24 0.756892 0.378446 0.925623i \(-0.376459\pi\)
0.378446 + 0.925623i \(0.376459\pi\)
\(90\) 0 0
\(91\) −3.19097e24 −1.03730
\(92\) −3.18729e24 −0.903804
\(93\) 0 0
\(94\) 4.43693e22 0.00961578
\(95\) −4.51282e24 −0.856847
\(96\) 0 0
\(97\) 2.82924e24 0.414022 0.207011 0.978339i \(-0.433626\pi\)
0.207011 + 0.978339i \(0.433626\pi\)
\(98\) 8.93877e21 0.00115067
\(99\) 0 0
\(100\) −8.47278e24 −0.847278
\(101\) −1.86342e24 −0.164549 −0.0822744 0.996610i \(-0.526218\pi\)
−0.0822744 + 0.996610i \(0.526218\pi\)
\(102\) 0 0
\(103\) 4.85812e24 0.335740 0.167870 0.985809i \(-0.446311\pi\)
0.167870 + 0.985809i \(0.446311\pi\)
\(104\) 2.63007e23 0.0161084
\(105\) 0 0
\(106\) 4.75340e22 0.00229446
\(107\) −3.58304e25 −1.53799 −0.768997 0.639252i \(-0.779244\pi\)
−0.768997 + 0.639252i \(0.779244\pi\)
\(108\) 0 0
\(109\) −4.77795e25 −1.62709 −0.813543 0.581505i \(-0.802464\pi\)
−0.813543 + 0.581505i \(0.802464\pi\)
\(110\) −2.99865e23 −0.00910999
\(111\) 0 0
\(112\) 4.39918e25 1.06696
\(113\) 7.46476e25 1.62008 0.810038 0.586378i \(-0.199447\pi\)
0.810038 + 0.586378i \(0.199447\pi\)
\(114\) 0 0
\(115\) 7.04855e25 1.22851
\(116\) −9.10091e24 −0.142351
\(117\) 0 0
\(118\) −6.26523e23 −0.00791429
\(119\) 9.84792e25 1.11946
\(120\) 0 0
\(121\) −3.74588e25 −0.345730
\(122\) 4.32742e23 0.00360355
\(123\) 0 0
\(124\) −1.43995e26 −0.978532
\(125\) −3.37587e25 −0.207496
\(126\) 0 0
\(127\) 3.35905e26 1.69305 0.846524 0.532350i \(-0.178691\pi\)
0.846524 + 0.532350i \(0.178691\pi\)
\(128\) −7.25231e24 −0.0331399
\(129\) 0 0
\(130\) −2.90804e24 −0.0109474
\(131\) 1.74971e26 0.598513 0.299257 0.954173i \(-0.403261\pi\)
0.299257 + 0.954173i \(0.403261\pi\)
\(132\) 0 0
\(133\) −2.37690e26 −0.672769
\(134\) −1.28108e24 −0.00330191
\(135\) 0 0
\(136\) −8.11689e24 −0.0173841
\(137\) −6.18313e26 −1.20837 −0.604187 0.796843i \(-0.706502\pi\)
−0.604187 + 0.796843i \(0.706502\pi\)
\(138\) 0 0
\(139\) −4.84462e26 −0.789905 −0.394952 0.918702i \(-0.629239\pi\)
−0.394952 + 0.918702i \(0.629239\pi\)
\(140\) −9.72925e26 −1.45037
\(141\) 0 0
\(142\) 9.23474e24 0.0115298
\(143\) 6.87462e26 0.786228
\(144\) 0 0
\(145\) 2.01262e26 0.193492
\(146\) 2.03542e24 0.00179574
\(147\) 0 0
\(148\) −6.81158e26 −0.506963
\(149\) −9.05569e26 −0.619574 −0.309787 0.950806i \(-0.600258\pi\)
−0.309787 + 0.950806i \(0.600258\pi\)
\(150\) 0 0
\(151\) 1.16190e27 0.672907 0.336454 0.941700i \(-0.390772\pi\)
0.336454 + 0.941700i \(0.390772\pi\)
\(152\) 1.95910e25 0.0104475
\(153\) 0 0
\(154\) −1.57939e25 −0.00715287
\(155\) 3.18437e27 1.33008
\(156\) 0 0
\(157\) −3.41505e26 −0.121521 −0.0607605 0.998152i \(-0.519353\pi\)
−0.0607605 + 0.998152i \(0.519353\pi\)
\(158\) −1.30407e25 −0.00428634
\(159\) 0 0
\(160\) 1.20287e26 0.0337847
\(161\) 3.71247e27 0.964583
\(162\) 0 0
\(163\) 4.63202e27 1.03140 0.515698 0.856771i \(-0.327533\pi\)
0.515698 + 0.856771i \(0.327533\pi\)
\(164\) −6.16501e27 −1.27170
\(165\) 0 0
\(166\) 4.47098e25 0.00792596
\(167\) 8.26470e27 1.35916 0.679581 0.733600i \(-0.262162\pi\)
0.679581 + 0.733600i \(0.262162\pi\)
\(168\) 0 0
\(169\) −3.89517e26 −0.0552004
\(170\) 8.97475e25 0.0118144
\(171\) 0 0
\(172\) −1.00959e28 −1.14826
\(173\) 6.02602e27 0.637462 0.318731 0.947845i \(-0.396743\pi\)
0.318731 + 0.947845i \(0.396743\pi\)
\(174\) 0 0
\(175\) 9.86886e27 0.904256
\(176\) −9.47758e27 −0.808703
\(177\) 0 0
\(178\) 8.46545e25 0.00627191
\(179\) −2.41023e28 −1.66493 −0.832463 0.554081i \(-0.813070\pi\)
−0.832463 + 0.554081i \(0.813070\pi\)
\(180\) 0 0
\(181\) −8.19193e27 −0.492498 −0.246249 0.969207i \(-0.579198\pi\)
−0.246249 + 0.969207i \(0.579198\pi\)
\(182\) −1.53167e26 −0.00859551
\(183\) 0 0
\(184\) −3.05991e26 −0.0149791
\(185\) 1.50635e28 0.689095
\(186\) 0 0
\(187\) −2.12163e28 −0.848497
\(188\) −3.10143e28 −1.16035
\(189\) 0 0
\(190\) −2.16616e26 −0.00710018
\(191\) −5.50602e27 −0.169013 −0.0845066 0.996423i \(-0.526931\pi\)
−0.0845066 + 0.996423i \(0.526931\pi\)
\(192\) 0 0
\(193\) 2.08716e28 0.562457 0.281228 0.959641i \(-0.409258\pi\)
0.281228 + 0.959641i \(0.409258\pi\)
\(194\) 1.35804e26 0.00343075
\(195\) 0 0
\(196\) −6.24823e27 −0.138853
\(197\) 5.99370e28 1.24988 0.624938 0.780674i \(-0.285124\pi\)
0.624938 + 0.780674i \(0.285124\pi\)
\(198\) 0 0
\(199\) 2.24042e27 0.0411782 0.0205891 0.999788i \(-0.493446\pi\)
0.0205891 + 0.999788i \(0.493446\pi\)
\(200\) −8.13414e26 −0.0140423
\(201\) 0 0
\(202\) −8.94444e25 −0.00136352
\(203\) 1.06005e28 0.151924
\(204\) 0 0
\(205\) 1.36336e29 1.72858
\(206\) 2.33190e26 0.00278208
\(207\) 0 0
\(208\) −9.19120e28 −0.971808
\(209\) 5.12080e28 0.509928
\(210\) 0 0
\(211\) −7.52475e28 −0.665214 −0.332607 0.943066i \(-0.607928\pi\)
−0.332607 + 0.943066i \(0.607928\pi\)
\(212\) −3.32264e28 −0.276876
\(213\) 0 0
\(214\) −1.71986e27 −0.0127444
\(215\) 2.23266e29 1.56078
\(216\) 0 0
\(217\) 1.67721e29 1.04434
\(218\) −2.29342e27 −0.0134827
\(219\) 0 0
\(220\) 2.09607e29 1.09931
\(221\) −2.05752e29 −1.01963
\(222\) 0 0
\(223\) −3.16696e29 −1.40227 −0.701135 0.713029i \(-0.747323\pi\)
−0.701135 + 0.713029i \(0.747323\pi\)
\(224\) 6.33554e27 0.0265267
\(225\) 0 0
\(226\) 3.58308e27 0.0134246
\(227\) −3.85094e29 −1.36535 −0.682674 0.730723i \(-0.739183\pi\)
−0.682674 + 0.730723i \(0.739183\pi\)
\(228\) 0 0
\(229\) −5.68261e29 −1.80553 −0.902765 0.430134i \(-0.858466\pi\)
−0.902765 + 0.430134i \(0.858466\pi\)
\(230\) 3.38331e27 0.0101799
\(231\) 0 0
\(232\) −8.73718e26 −0.00235924
\(233\) −4.95586e29 −1.26815 −0.634075 0.773272i \(-0.718619\pi\)
−0.634075 + 0.773272i \(0.718619\pi\)
\(234\) 0 0
\(235\) 6.85867e29 1.57722
\(236\) 4.37941e29 0.955028
\(237\) 0 0
\(238\) 4.72700e27 0.00927628
\(239\) 1.44023e29 0.268200 0.134100 0.990968i \(-0.457186\pi\)
0.134100 + 0.990968i \(0.457186\pi\)
\(240\) 0 0
\(241\) −3.19456e29 −0.536041 −0.268020 0.963413i \(-0.586369\pi\)
−0.268020 + 0.963413i \(0.586369\pi\)
\(242\) −1.79802e27 −0.00286486
\(243\) 0 0
\(244\) −3.02488e29 −0.434845
\(245\) 1.38177e29 0.188738
\(246\) 0 0
\(247\) 4.96606e29 0.612774
\(248\) −1.38239e28 −0.0162176
\(249\) 0 0
\(250\) −1.62042e27 −0.00171940
\(251\) −6.21677e29 −0.627543 −0.313771 0.949499i \(-0.601593\pi\)
−0.313771 + 0.949499i \(0.601593\pi\)
\(252\) 0 0
\(253\) −7.99814e29 −0.731110
\(254\) 1.61234e28 0.0140293
\(255\) 0 0
\(256\) 1.26678e30 0.999313
\(257\) 2.29446e30 1.72392 0.861960 0.506977i \(-0.169237\pi\)
0.861960 + 0.506977i \(0.169237\pi\)
\(258\) 0 0
\(259\) 7.93394e29 0.541056
\(260\) 2.03273e30 1.32103
\(261\) 0 0
\(262\) 8.39859e27 0.00495952
\(263\) −7.73316e29 −0.435422 −0.217711 0.976013i \(-0.569859\pi\)
−0.217711 + 0.976013i \(0.569859\pi\)
\(264\) 0 0
\(265\) 7.34787e29 0.376347
\(266\) −1.14091e28 −0.00557484
\(267\) 0 0
\(268\) 8.95475e29 0.398445
\(269\) −3.62259e30 −1.53856 −0.769282 0.638910i \(-0.779386\pi\)
−0.769282 + 0.638910i \(0.779386\pi\)
\(270\) 0 0
\(271\) −3.62767e30 −1.40447 −0.702234 0.711946i \(-0.747814\pi\)
−0.702234 + 0.711946i \(0.747814\pi\)
\(272\) 2.83657e30 1.04877
\(273\) 0 0
\(274\) −2.96790e28 −0.0100131
\(275\) −2.12614e30 −0.685384
\(276\) 0 0
\(277\) −2.54808e30 −0.750266 −0.375133 0.926971i \(-0.622403\pi\)
−0.375133 + 0.926971i \(0.622403\pi\)
\(278\) −2.32542e28 −0.00654547
\(279\) 0 0
\(280\) −9.34040e28 −0.0240375
\(281\) −3.59817e30 −0.885631 −0.442816 0.896613i \(-0.646020\pi\)
−0.442816 + 0.896613i \(0.646020\pi\)
\(282\) 0 0
\(283\) 3.82265e30 0.861061 0.430530 0.902576i \(-0.358327\pi\)
0.430530 + 0.902576i \(0.358327\pi\)
\(284\) −6.45511e30 −1.39131
\(285\) 0 0
\(286\) 3.29982e28 0.00651500
\(287\) 7.18084e30 1.35722
\(288\) 0 0
\(289\) 5.79269e29 0.100382
\(290\) 9.66060e27 0.00160335
\(291\) 0 0
\(292\) −1.42276e30 −0.216694
\(293\) −1.30007e29 −0.0189723 −0.00948615 0.999955i \(-0.503020\pi\)
−0.00948615 + 0.999955i \(0.503020\pi\)
\(294\) 0 0
\(295\) −9.68487e30 −1.29813
\(296\) −6.53934e28 −0.00840210
\(297\) 0 0
\(298\) −4.34673e28 −0.00513404
\(299\) −7.75646e30 −0.878565
\(300\) 0 0
\(301\) 1.17594e31 1.22548
\(302\) 5.57710e28 0.00557599
\(303\) 0 0
\(304\) −6.84638e30 −0.630291
\(305\) 6.68937e30 0.591068
\(306\) 0 0
\(307\) 1.43602e31 1.16931 0.584657 0.811281i \(-0.301229\pi\)
0.584657 + 0.811281i \(0.301229\pi\)
\(308\) 1.10400e31 0.863146
\(309\) 0 0
\(310\) 1.52850e29 0.0110216
\(311\) 2.24630e31 1.55584 0.777918 0.628366i \(-0.216276\pi\)
0.777918 + 0.628366i \(0.216276\pi\)
\(312\) 0 0
\(313\) −1.37956e30 −0.0881934 −0.0440967 0.999027i \(-0.514041\pi\)
−0.0440967 + 0.999027i \(0.514041\pi\)
\(314\) −1.63922e28 −0.00100697
\(315\) 0 0
\(316\) 9.11548e30 0.517239
\(317\) 1.02787e31 0.560655 0.280327 0.959904i \(-0.409557\pi\)
0.280327 + 0.959904i \(0.409557\pi\)
\(318\) 0 0
\(319\) −2.28377e30 −0.115151
\(320\) −2.80200e31 −1.35861
\(321\) 0 0
\(322\) 1.78199e29 0.00799293
\(323\) −1.53262e31 −0.661306
\(324\) 0 0
\(325\) −2.06190e31 −0.823617
\(326\) 2.22337e29 0.00854656
\(327\) 0 0
\(328\) −5.91861e29 −0.0210764
\(329\) 3.61246e31 1.23838
\(330\) 0 0
\(331\) −5.75356e30 −0.182847 −0.0914233 0.995812i \(-0.529142\pi\)
−0.0914233 + 0.995812i \(0.529142\pi\)
\(332\) −3.12523e31 −0.956435
\(333\) 0 0
\(334\) 3.96706e29 0.0112626
\(335\) −1.98030e31 −0.541591
\(336\) 0 0
\(337\) 6.69268e31 1.69913 0.849564 0.527485i \(-0.176865\pi\)
0.849564 + 0.527485i \(0.176865\pi\)
\(338\) −1.86968e28 −0.000457413 0
\(339\) 0 0
\(340\) −6.27338e31 −1.42566
\(341\) −3.61337e31 −0.791559
\(342\) 0 0
\(343\) −4.51320e31 −0.918984
\(344\) −9.69239e29 −0.0190305
\(345\) 0 0
\(346\) 2.89249e29 0.00528227
\(347\) −9.41781e29 −0.0165894 −0.00829472 0.999966i \(-0.502640\pi\)
−0.00829472 + 0.999966i \(0.502640\pi\)
\(348\) 0 0
\(349\) −3.39081e31 −0.555886 −0.277943 0.960598i \(-0.589653\pi\)
−0.277943 + 0.960598i \(0.589653\pi\)
\(350\) 4.73705e29 0.00749303
\(351\) 0 0
\(352\) −1.36493e30 −0.0201060
\(353\) −1.30313e31 −0.185269 −0.0926346 0.995700i \(-0.529529\pi\)
−0.0926346 + 0.995700i \(0.529529\pi\)
\(354\) 0 0
\(355\) 1.42752e32 1.89116
\(356\) −5.91737e31 −0.756840
\(357\) 0 0
\(358\) −1.15691e30 −0.0137963
\(359\) 1.30336e32 1.50101 0.750506 0.660864i \(-0.229810\pi\)
0.750506 + 0.660864i \(0.229810\pi\)
\(360\) 0 0
\(361\) −5.60851e31 −0.602570
\(362\) −3.93213e29 −0.00408104
\(363\) 0 0
\(364\) 1.07064e32 1.03723
\(365\) 3.14638e31 0.294544
\(366\) 0 0
\(367\) −2.06294e32 −1.80369 −0.901844 0.432061i \(-0.857786\pi\)
−0.901844 + 0.432061i \(0.857786\pi\)
\(368\) 1.06933e32 0.903680
\(369\) 0 0
\(370\) 7.23048e29 0.00571012
\(371\) 3.87012e31 0.295495
\(372\) 0 0
\(373\) 2.46051e32 1.75657 0.878283 0.478142i \(-0.158689\pi\)
0.878283 + 0.478142i \(0.158689\pi\)
\(374\) −1.01838e30 −0.00703099
\(375\) 0 0
\(376\) −2.97747e30 −0.0192309
\(377\) −2.21476e31 −0.138376
\(378\) 0 0
\(379\) 7.12743e31 0.416815 0.208407 0.978042i \(-0.433172\pi\)
0.208407 + 0.978042i \(0.433172\pi\)
\(380\) 1.51415e32 0.856788
\(381\) 0 0
\(382\) −2.64289e29 −0.00140051
\(383\) −1.33051e32 −0.682393 −0.341196 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(384\) 0 0
\(385\) −2.44144e32 −1.17324
\(386\) 1.00184e30 0.00466075
\(387\) 0 0
\(388\) −9.49271e31 −0.413993
\(389\) −2.40509e32 −1.01569 −0.507844 0.861449i \(-0.669557\pi\)
−0.507844 + 0.861449i \(0.669557\pi\)
\(390\) 0 0
\(391\) 2.39379e32 0.948147
\(392\) −5.99850e29 −0.00230127
\(393\) 0 0
\(394\) 2.87698e30 0.0103570
\(395\) −2.01585e32 −0.703062
\(396\) 0 0
\(397\) −4.12137e32 −1.34946 −0.674730 0.738065i \(-0.735740\pi\)
−0.674730 + 0.738065i \(0.735740\pi\)
\(398\) 1.07540e29 0.000341219 0
\(399\) 0 0
\(400\) 2.84260e32 0.847161
\(401\) 7.16647e31 0.207014 0.103507 0.994629i \(-0.466994\pi\)
0.103507 + 0.994629i \(0.466994\pi\)
\(402\) 0 0
\(403\) −3.50419e32 −0.951206
\(404\) 6.25219e31 0.164537
\(405\) 0 0
\(406\) 5.08824e29 0.00125890
\(407\) −1.70929e32 −0.410095
\(408\) 0 0
\(409\) 1.34430e32 0.303358 0.151679 0.988430i \(-0.451532\pi\)
0.151679 + 0.988430i \(0.451532\pi\)
\(410\) 6.54415e30 0.0143237
\(411\) 0 0
\(412\) −1.63000e32 −0.335717
\(413\) −5.10102e32 −1.01925
\(414\) 0 0
\(415\) 6.91130e32 1.30004
\(416\) −1.32368e31 −0.0241612
\(417\) 0 0
\(418\) 2.45798e30 0.00422547
\(419\) 1.71876e32 0.286774 0.143387 0.989667i \(-0.454201\pi\)
0.143387 + 0.989667i \(0.454201\pi\)
\(420\) 0 0
\(421\) −8.27664e32 −1.30115 −0.650576 0.759441i \(-0.725472\pi\)
−0.650576 + 0.759441i \(0.725472\pi\)
\(422\) −3.61188e30 −0.00551223
\(423\) 0 0
\(424\) −3.18984e30 −0.00458877
\(425\) 6.36340e32 0.888848
\(426\) 0 0
\(427\) 3.52329e32 0.464088
\(428\) 1.20219e33 1.53789
\(429\) 0 0
\(430\) 1.07168e31 0.0129333
\(431\) 7.83836e31 0.0918881 0.0459441 0.998944i \(-0.485370\pi\)
0.0459441 + 0.998944i \(0.485370\pi\)
\(432\) 0 0
\(433\) 6.33273e32 0.700635 0.350318 0.936631i \(-0.386074\pi\)
0.350318 + 0.936631i \(0.386074\pi\)
\(434\) 8.05060e30 0.00865380
\(435\) 0 0
\(436\) 1.60310e33 1.62697
\(437\) −5.77767e32 −0.569816
\(438\) 0 0
\(439\) −1.48299e33 −1.38144 −0.690718 0.723124i \(-0.742705\pi\)
−0.690718 + 0.723124i \(0.742705\pi\)
\(440\) 2.01229e31 0.0182193
\(441\) 0 0
\(442\) −9.87612e30 −0.00844905
\(443\) 1.20901e33 1.00551 0.502753 0.864430i \(-0.332321\pi\)
0.502753 + 0.864430i \(0.332321\pi\)
\(444\) 0 0
\(445\) 1.30860e33 1.02874
\(446\) −1.52014e31 −0.0116198
\(447\) 0 0
\(448\) −1.47581e33 −1.06674
\(449\) 9.48861e32 0.666996 0.333498 0.942751i \(-0.391771\pi\)
0.333498 + 0.942751i \(0.391771\pi\)
\(450\) 0 0
\(451\) −1.54704e33 −1.02871
\(452\) −2.50459e33 −1.61996
\(453\) 0 0
\(454\) −1.84845e31 −0.0113138
\(455\) −2.36767e33 −1.40987
\(456\) 0 0
\(457\) 1.90644e33 1.07466 0.537329 0.843373i \(-0.319433\pi\)
0.537329 + 0.843373i \(0.319433\pi\)
\(458\) −2.72765e31 −0.0149614
\(459\) 0 0
\(460\) −2.36494e33 −1.22842
\(461\) 4.56270e31 0.0230653 0.0115327 0.999933i \(-0.496329\pi\)
0.0115327 + 0.999933i \(0.496329\pi\)
\(462\) 0 0
\(463\) 2.13521e33 1.02254 0.511269 0.859421i \(-0.329176\pi\)
0.511269 + 0.859421i \(0.329176\pi\)
\(464\) 3.05334e32 0.142331
\(465\) 0 0
\(466\) −2.37882e31 −0.0105084
\(467\) 2.67225e33 1.14926 0.574628 0.818415i \(-0.305147\pi\)
0.574628 + 0.818415i \(0.305147\pi\)
\(468\) 0 0
\(469\) −1.04302e33 −0.425240
\(470\) 3.29216e31 0.0130695
\(471\) 0 0
\(472\) 4.20438e31 0.0158280
\(473\) −2.53345e33 −0.928854
\(474\) 0 0
\(475\) −1.53588e33 −0.534178
\(476\) −3.30419e33 −1.11938
\(477\) 0 0
\(478\) 6.91313e30 0.00222242
\(479\) −1.97240e33 −0.617733 −0.308867 0.951105i \(-0.599950\pi\)
−0.308867 + 0.951105i \(0.599950\pi\)
\(480\) 0 0
\(481\) −1.65764e33 −0.492806
\(482\) −1.53339e31 −0.00444185
\(483\) 0 0
\(484\) 1.25682e33 0.345706
\(485\) 2.09927e33 0.562725
\(486\) 0 0
\(487\) −3.96366e32 −0.100922 −0.0504608 0.998726i \(-0.516069\pi\)
−0.0504608 + 0.998726i \(0.516069\pi\)
\(488\) −2.90398e31 −0.00720686
\(489\) 0 0
\(490\) 6.63248e30 0.00156396
\(491\) 7.22626e33 1.66110 0.830548 0.556947i \(-0.188027\pi\)
0.830548 + 0.556947i \(0.188027\pi\)
\(492\) 0 0
\(493\) 6.83515e32 0.149335
\(494\) 2.38371e31 0.00507769
\(495\) 0 0
\(496\) 4.83099e33 0.978397
\(497\) 7.51874e33 1.48488
\(498\) 0 0
\(499\) 8.19830e33 1.53981 0.769905 0.638159i \(-0.220304\pi\)
0.769905 + 0.638159i \(0.220304\pi\)
\(500\) 1.13268e33 0.207482
\(501\) 0 0
\(502\) −2.98405e31 −0.00520008
\(503\) −4.72562e33 −0.803265 −0.401633 0.915801i \(-0.631557\pi\)
−0.401633 + 0.915801i \(0.631557\pi\)
\(504\) 0 0
\(505\) −1.38264e33 −0.223649
\(506\) −3.83911e31 −0.00605827
\(507\) 0 0
\(508\) −1.12703e34 −1.69293
\(509\) −1.96955e33 −0.288665 −0.144332 0.989529i \(-0.546103\pi\)
−0.144332 + 0.989529i \(0.546103\pi\)
\(510\) 0 0
\(511\) 1.65720e33 0.231267
\(512\) 3.04153e32 0.0414207
\(513\) 0 0
\(514\) 1.10134e32 0.0142851
\(515\) 3.60468e33 0.456327
\(516\) 0 0
\(517\) −7.78267e33 −0.938635
\(518\) 3.80829e31 0.00448341
\(519\) 0 0
\(520\) 1.95149e32 0.0218940
\(521\) −7.39782e33 −0.810274 −0.405137 0.914256i \(-0.632776\pi\)
−0.405137 + 0.914256i \(0.632776\pi\)
\(522\) 0 0
\(523\) 1.70332e34 1.77838 0.889191 0.457535i \(-0.151268\pi\)
0.889191 + 0.457535i \(0.151268\pi\)
\(524\) −5.87063e33 −0.598472
\(525\) 0 0
\(526\) −3.71192e31 −0.00360808
\(527\) 1.08146e34 1.02654
\(528\) 0 0
\(529\) −2.02166e33 −0.183026
\(530\) 3.52698e31 0.00311856
\(531\) 0 0
\(532\) 7.97502e33 0.672723
\(533\) −1.50029e34 −1.23619
\(534\) 0 0
\(535\) −2.65858e34 −2.09039
\(536\) 8.59686e31 0.00660358
\(537\) 0 0
\(538\) −1.73884e32 −0.0127492
\(539\) −1.56792e33 −0.112322
\(540\) 0 0
\(541\) −1.28681e34 −0.880134 −0.440067 0.897965i \(-0.645045\pi\)
−0.440067 + 0.897965i \(0.645045\pi\)
\(542\) −1.74128e32 −0.0116380
\(543\) 0 0
\(544\) 4.08513e32 0.0260747
\(545\) −3.54519e34 −2.21148
\(546\) 0 0
\(547\) 2.06624e34 1.23123 0.615616 0.788046i \(-0.288907\pi\)
0.615616 + 0.788046i \(0.288907\pi\)
\(548\) 2.07457e34 1.20829
\(549\) 0 0
\(550\) −1.02055e32 −0.00567937
\(551\) −1.64974e33 −0.0897471
\(552\) 0 0
\(553\) −1.06175e34 −0.552022
\(554\) −1.22308e32 −0.00621701
\(555\) 0 0
\(556\) 1.62547e34 0.789851
\(557\) 3.28751e33 0.156198 0.0780992 0.996946i \(-0.475115\pi\)
0.0780992 + 0.996946i \(0.475115\pi\)
\(558\) 0 0
\(559\) −2.45689e34 −1.11619
\(560\) 3.26415e34 1.45017
\(561\) 0 0
\(562\) −1.72712e32 −0.00733870
\(563\) 1.80804e34 0.751371 0.375685 0.926747i \(-0.377407\pi\)
0.375685 + 0.926747i \(0.377407\pi\)
\(564\) 0 0
\(565\) 5.53878e34 2.20195
\(566\) 1.83487e32 0.00713510
\(567\) 0 0
\(568\) −6.19712e32 −0.0230587
\(569\) 3.05967e33 0.111371 0.0556854 0.998448i \(-0.482266\pi\)
0.0556854 + 0.998448i \(0.482266\pi\)
\(570\) 0 0
\(571\) −1.29884e34 −0.452486 −0.226243 0.974071i \(-0.572644\pi\)
−0.226243 + 0.974071i \(0.572644\pi\)
\(572\) −2.30658e34 −0.786174
\(573\) 0 0
\(574\) 3.44680e32 0.0112465
\(575\) 2.39888e34 0.765878
\(576\) 0 0
\(577\) −7.31490e31 −0.00223620 −0.00111810 0.999999i \(-0.500356\pi\)
−0.00111810 + 0.999999i \(0.500356\pi\)
\(578\) 2.78049e31 0.000831808 0
\(579\) 0 0
\(580\) −6.75278e33 −0.193479
\(581\) 3.64018e34 1.02075
\(582\) 0 0
\(583\) −8.33778e33 −0.223972
\(584\) −1.36590e32 −0.00359136
\(585\) 0 0
\(586\) −6.24031e30 −0.000157212 0
\(587\) −5.16226e34 −1.27310 −0.636551 0.771234i \(-0.719640\pi\)
−0.636551 + 0.771234i \(0.719640\pi\)
\(588\) 0 0
\(589\) −2.61022e34 −0.616929
\(590\) −4.64874e32 −0.0107568
\(591\) 0 0
\(592\) 2.28527e34 0.506894
\(593\) −2.40705e34 −0.522758 −0.261379 0.965236i \(-0.584177\pi\)
−0.261379 + 0.965236i \(0.584177\pi\)
\(594\) 0 0
\(595\) 7.30706e34 1.52153
\(596\) 3.03838e34 0.619531
\(597\) 0 0
\(598\) −3.72310e32 −0.00728015
\(599\) 8.30672e33 0.159072 0.0795361 0.996832i \(-0.474656\pi\)
0.0795361 + 0.996832i \(0.474656\pi\)
\(600\) 0 0
\(601\) −3.00405e34 −0.551792 −0.275896 0.961187i \(-0.588975\pi\)
−0.275896 + 0.961187i \(0.588975\pi\)
\(602\) 5.64452e32 0.0101548
\(603\) 0 0
\(604\) −3.89841e34 −0.672861
\(605\) −2.77941e34 −0.469905
\(606\) 0 0
\(607\) −1.00963e35 −1.63796 −0.818978 0.573825i \(-0.805459\pi\)
−0.818978 + 0.573825i \(0.805459\pi\)
\(608\) −9.85991e32 −0.0156703
\(609\) 0 0
\(610\) 3.21090e32 0.00489783
\(611\) −7.54750e34 −1.12795
\(612\) 0 0
\(613\) −1.02453e33 −0.0146983 −0.00734915 0.999973i \(-0.502339\pi\)
−0.00734915 + 0.999973i \(0.502339\pi\)
\(614\) 6.89290e32 0.00968941
\(615\) 0 0
\(616\) 1.05987e33 0.0143053
\(617\) −4.53271e34 −0.599505 −0.299753 0.954017i \(-0.596904\pi\)
−0.299753 + 0.954017i \(0.596904\pi\)
\(618\) 0 0
\(619\) 1.24784e35 1.58499 0.792496 0.609878i \(-0.208781\pi\)
0.792496 + 0.609878i \(0.208781\pi\)
\(620\) −1.06842e35 −1.32999
\(621\) 0 0
\(622\) 1.07823e33 0.0128923
\(623\) 6.89239e34 0.807736
\(624\) 0 0
\(625\) −1.00307e35 −1.12936
\(626\) −6.62189e31 −0.000730807 0
\(627\) 0 0
\(628\) 1.14582e34 0.121513
\(629\) 5.11577e34 0.531836
\(630\) 0 0
\(631\) 4.83338e34 0.482930 0.241465 0.970410i \(-0.422372\pi\)
0.241465 + 0.970410i \(0.422372\pi\)
\(632\) 8.75116e32 0.00857239
\(633\) 0 0
\(634\) 4.93375e32 0.00464581
\(635\) 2.49238e35 2.30114
\(636\) 0 0
\(637\) −1.52054e34 −0.134976
\(638\) −1.09621e32 −0.000954190 0
\(639\) 0 0
\(640\) −5.38114e33 −0.0450427
\(641\) −8.30494e34 −0.681728 −0.340864 0.940113i \(-0.610720\pi\)
−0.340864 + 0.940113i \(0.610720\pi\)
\(642\) 0 0
\(643\) 5.25724e34 0.415069 0.207535 0.978228i \(-0.433456\pi\)
0.207535 + 0.978228i \(0.433456\pi\)
\(644\) −1.24561e35 −0.964517
\(645\) 0 0
\(646\) −7.35656e32 −0.00547985
\(647\) 2.03021e35 1.48333 0.741665 0.670770i \(-0.234036\pi\)
0.741665 + 0.670770i \(0.234036\pi\)
\(648\) 0 0
\(649\) 1.09896e35 0.772546
\(650\) −9.89711e32 −0.00682483
\(651\) 0 0
\(652\) −1.55414e35 −1.03132
\(653\) −1.67657e35 −1.09146 −0.545728 0.837962i \(-0.683747\pi\)
−0.545728 + 0.837962i \(0.683747\pi\)
\(654\) 0 0
\(655\) 1.29826e35 0.813479
\(656\) 2.06835e35 1.27153
\(657\) 0 0
\(658\) 1.73398e33 0.0102617
\(659\) 2.92521e35 1.69859 0.849296 0.527917i \(-0.177027\pi\)
0.849296 + 0.527917i \(0.177027\pi\)
\(660\) 0 0
\(661\) 8.30227e34 0.464172 0.232086 0.972695i \(-0.425445\pi\)
0.232086 + 0.972695i \(0.425445\pi\)
\(662\) −2.76171e32 −0.00151514
\(663\) 0 0
\(664\) −3.00032e33 −0.0158514
\(665\) −1.76364e35 −0.914406
\(666\) 0 0
\(667\) 2.57672e34 0.128675
\(668\) −2.77298e35 −1.35907
\(669\) 0 0
\(670\) −9.50545e32 −0.00448784
\(671\) −7.59057e34 −0.351757
\(672\) 0 0
\(673\) −3.23598e35 −1.44483 −0.722417 0.691458i \(-0.756969\pi\)
−0.722417 + 0.691458i \(0.756969\pi\)
\(674\) 3.21249e33 0.0140797
\(675\) 0 0
\(676\) 1.30691e34 0.0551966
\(677\) −7.76333e34 −0.321877 −0.160938 0.986964i \(-0.551452\pi\)
−0.160938 + 0.986964i \(0.551452\pi\)
\(678\) 0 0
\(679\) 1.10568e35 0.441834
\(680\) −6.02265e33 −0.0236280
\(681\) 0 0
\(682\) −1.73442e33 −0.00655918
\(683\) 2.49909e35 0.927945 0.463973 0.885850i \(-0.346424\pi\)
0.463973 + 0.885850i \(0.346424\pi\)
\(684\) 0 0
\(685\) −4.58782e35 −1.64238
\(686\) −2.16634e33 −0.00761508
\(687\) 0 0
\(688\) 3.38716e35 1.14810
\(689\) −8.08584e34 −0.269144
\(690\) 0 0
\(691\) −8.56964e34 −0.275098 −0.137549 0.990495i \(-0.543922\pi\)
−0.137549 + 0.990495i \(0.543922\pi\)
\(692\) −2.02186e35 −0.637419
\(693\) 0 0
\(694\) −4.52055e31 −0.000137467 0
\(695\) −3.59466e35 −1.07361
\(696\) 0 0
\(697\) 4.63017e35 1.33410
\(698\) −1.62759e33 −0.00460630
\(699\) 0 0
\(700\) −3.31121e35 −0.904193
\(701\) −4.53464e35 −1.21637 −0.608187 0.793793i \(-0.708103\pi\)
−0.608187 + 0.793793i \(0.708103\pi\)
\(702\) 0 0
\(703\) −1.23475e35 −0.319622
\(704\) 3.17949e35 0.808536
\(705\) 0 0
\(706\) −6.25502e32 −0.00153522
\(707\) −7.28238e34 −0.175602
\(708\) 0 0
\(709\) −4.93254e35 −1.14813 −0.574067 0.818808i \(-0.694635\pi\)
−0.574067 + 0.818808i \(0.694635\pi\)
\(710\) 6.85209e33 0.0156709
\(711\) 0 0
\(712\) −5.68087e33 −0.0125434
\(713\) 4.07688e35 0.884522
\(714\) 0 0
\(715\) 5.10090e35 1.06862
\(716\) 8.08682e35 1.66481
\(717\) 0 0
\(718\) 6.25613e33 0.0124380
\(719\) −2.13499e35 −0.417142 −0.208571 0.978007i \(-0.566881\pi\)
−0.208571 + 0.978007i \(0.566881\pi\)
\(720\) 0 0
\(721\) 1.89858e35 0.358293
\(722\) −2.69208e33 −0.00499314
\(723\) 0 0
\(724\) 2.74857e35 0.492464
\(725\) 6.84968e34 0.120627
\(726\) 0 0
\(727\) 5.12190e35 0.871467 0.435734 0.900076i \(-0.356489\pi\)
0.435734 + 0.900076i \(0.356489\pi\)
\(728\) 1.02785e34 0.0171904
\(729\) 0 0
\(730\) 1.51026e33 0.00244071
\(731\) 7.58243e35 1.20459
\(732\) 0 0
\(733\) 1.77366e35 0.272315 0.136157 0.990687i \(-0.456525\pi\)
0.136157 + 0.990687i \(0.456525\pi\)
\(734\) −9.90213e33 −0.0149461
\(735\) 0 0
\(736\) 1.54001e34 0.0224674
\(737\) 2.24709e35 0.322312
\(738\) 0 0
\(739\) −1.13535e36 −1.57425 −0.787124 0.616794i \(-0.788431\pi\)
−0.787124 + 0.616794i \(0.788431\pi\)
\(740\) −5.05412e35 −0.689048
\(741\) 0 0
\(742\) 1.85766e33 0.00244860
\(743\) −4.03749e34 −0.0523301 −0.0261651 0.999658i \(-0.508330\pi\)
−0.0261651 + 0.999658i \(0.508330\pi\)
\(744\) 0 0
\(745\) −6.71923e35 −0.842104
\(746\) 1.18104e34 0.0145556
\(747\) 0 0
\(748\) 7.11853e35 0.848439
\(749\) −1.40027e36 −1.64131
\(750\) 0 0
\(751\) 7.72405e35 0.875681 0.437840 0.899053i \(-0.355744\pi\)
0.437840 + 0.899053i \(0.355744\pi\)
\(752\) 1.04052e36 1.16019
\(753\) 0 0
\(754\) −1.06308e33 −0.00114664
\(755\) 8.62115e35 0.914594
\(756\) 0 0
\(757\) 3.31585e35 0.340327 0.170163 0.985416i \(-0.445570\pi\)
0.170163 + 0.985416i \(0.445570\pi\)
\(758\) 3.42117e33 0.00345390
\(759\) 0 0
\(760\) 1.45363e34 0.0141999
\(761\) −2.02230e36 −1.94329 −0.971646 0.236440i \(-0.924019\pi\)
−0.971646 + 0.236440i \(0.924019\pi\)
\(762\) 0 0
\(763\) −1.86725e36 −1.73639
\(764\) 1.84739e35 0.169002
\(765\) 0 0
\(766\) −6.38646e33 −0.00565458
\(767\) 1.06576e36 0.928358
\(768\) 0 0
\(769\) 7.71193e35 0.650255 0.325128 0.945670i \(-0.394593\pi\)
0.325128 + 0.945670i \(0.394593\pi\)
\(770\) −1.17189e34 −0.00972195
\(771\) 0 0
\(772\) −7.00286e35 −0.562418
\(773\) −1.96060e36 −1.54934 −0.774668 0.632368i \(-0.782083\pi\)
−0.774668 + 0.632368i \(0.782083\pi\)
\(774\) 0 0
\(775\) 1.08376e36 0.829202
\(776\) −9.11331e33 −0.00686127
\(777\) 0 0
\(778\) −1.15444e34 −0.00841641
\(779\) −1.11754e36 −0.801763
\(780\) 0 0
\(781\) −1.61983e36 −1.12547
\(782\) 1.14902e34 0.00785674
\(783\) 0 0
\(784\) 2.09627e35 0.138834
\(785\) −2.53393e35 −0.165167
\(786\) 0 0
\(787\) −8.92654e35 −0.563637 −0.281818 0.959468i \(-0.590938\pi\)
−0.281818 + 0.959468i \(0.590938\pi\)
\(788\) −2.01101e36 −1.24979
\(789\) 0 0
\(790\) −9.67606e33 −0.00582586
\(791\) 2.91727e36 1.72890
\(792\) 0 0
\(793\) −7.36121e35 −0.422702
\(794\) −1.97826e34 −0.0111822
\(795\) 0 0
\(796\) −7.51710e34 −0.0411753
\(797\) 2.35494e36 1.26984 0.634921 0.772577i \(-0.281032\pi\)
0.634921 + 0.772577i \(0.281032\pi\)
\(798\) 0 0
\(799\) 2.32930e36 1.21728
\(800\) 4.09381e34 0.0210622
\(801\) 0 0
\(802\) 3.43990e33 0.00171541
\(803\) −3.57026e35 −0.175289
\(804\) 0 0
\(805\) 2.75462e36 1.31103
\(806\) −1.68201e34 −0.00788208
\(807\) 0 0
\(808\) 6.00231e33 0.00272694
\(809\) 1.29617e36 0.579834 0.289917 0.957052i \(-0.406372\pi\)
0.289917 + 0.957052i \(0.406372\pi\)
\(810\) 0 0
\(811\) 2.63606e36 1.14339 0.571695 0.820467i \(-0.306286\pi\)
0.571695 + 0.820467i \(0.306286\pi\)
\(812\) −3.55669e35 −0.151913
\(813\) 0 0
\(814\) −8.20458e33 −0.00339822
\(815\) 3.43691e36 1.40184
\(816\) 0 0
\(817\) −1.83010e36 −0.723935
\(818\) 6.45265e33 0.00251375
\(819\) 0 0
\(820\) −4.57438e36 −1.72846
\(821\) 5.92271e35 0.220410 0.110205 0.993909i \(-0.464849\pi\)
0.110205 + 0.993909i \(0.464849\pi\)
\(822\) 0 0
\(823\) 4.76928e35 0.172169 0.0860845 0.996288i \(-0.472564\pi\)
0.0860845 + 0.996288i \(0.472564\pi\)
\(824\) −1.56486e34 −0.00556396
\(825\) 0 0
\(826\) −2.44849e34 −0.00844594
\(827\) −4.17794e36 −1.41953 −0.709763 0.704440i \(-0.751198\pi\)
−0.709763 + 0.704440i \(0.751198\pi\)
\(828\) 0 0
\(829\) −3.18023e36 −1.04840 −0.524199 0.851596i \(-0.675635\pi\)
−0.524199 + 0.851596i \(0.675635\pi\)
\(830\) 3.31742e34 0.0107727
\(831\) 0 0
\(832\) 3.08342e36 0.971608
\(833\) 4.69267e35 0.145666
\(834\) 0 0
\(835\) 6.13232e36 1.84733
\(836\) −1.71814e36 −0.509893
\(837\) 0 0
\(838\) 8.25006e33 0.00237633
\(839\) 3.57270e36 1.01384 0.506922 0.861992i \(-0.330783\pi\)
0.506922 + 0.861992i \(0.330783\pi\)
\(840\) 0 0
\(841\) −3.55679e36 −0.979733
\(842\) −3.97279e34 −0.0107819
\(843\) 0 0
\(844\) 2.52471e36 0.665168
\(845\) −2.89018e35 −0.0750266
\(846\) 0 0
\(847\) −1.46391e36 −0.368954
\(848\) 1.11474e36 0.276838
\(849\) 0 0
\(850\) 3.05443e34 0.00736535
\(851\) 1.92855e36 0.458258
\(852\) 0 0
\(853\) −1.75466e36 −0.404884 −0.202442 0.979294i \(-0.564888\pi\)
−0.202442 + 0.979294i \(0.564888\pi\)
\(854\) 1.69118e34 0.00384562
\(855\) 0 0
\(856\) 1.15414e35 0.0254880
\(857\) −7.10324e36 −1.54595 −0.772976 0.634435i \(-0.781233\pi\)
−0.772976 + 0.634435i \(0.781233\pi\)
\(858\) 0 0
\(859\) −7.56695e36 −1.59958 −0.799791 0.600279i \(-0.795056\pi\)
−0.799791 + 0.600279i \(0.795056\pi\)
\(860\) −7.49105e36 −1.56067
\(861\) 0 0
\(862\) 3.76241e33 0.000761423 0
\(863\) −5.72195e36 −1.14132 −0.570662 0.821185i \(-0.693313\pi\)
−0.570662 + 0.821185i \(0.693313\pi\)
\(864\) 0 0
\(865\) 4.47125e36 0.866418
\(866\) 3.03971e34 0.00580575
\(867\) 0 0
\(868\) −5.62739e36 −1.04426
\(869\) 2.28742e36 0.418407
\(870\) 0 0
\(871\) 2.17919e36 0.387318
\(872\) 1.53903e35 0.0269645
\(873\) 0 0
\(874\) −2.77328e34 −0.00472173
\(875\) −1.31931e36 −0.221435
\(876\) 0 0
\(877\) 3.21926e36 0.525123 0.262561 0.964915i \(-0.415433\pi\)
0.262561 + 0.964915i \(0.415433\pi\)
\(878\) −7.11834e34 −0.0114471
\(879\) 0 0
\(880\) −7.03227e36 −1.09916
\(881\) 1.04633e37 1.61238 0.806191 0.591655i \(-0.201525\pi\)
0.806191 + 0.591655i \(0.201525\pi\)
\(882\) 0 0
\(883\) 4.11745e36 0.616765 0.308382 0.951263i \(-0.400212\pi\)
0.308382 + 0.951263i \(0.400212\pi\)
\(884\) 6.90343e36 1.01956
\(885\) 0 0
\(886\) 5.80326e34 0.00833202
\(887\) 2.52904e36 0.358022 0.179011 0.983847i \(-0.442710\pi\)
0.179011 + 0.983847i \(0.442710\pi\)
\(888\) 0 0
\(889\) 1.31273e37 1.80678
\(890\) 6.28128e34 0.00852458
\(891\) 0 0
\(892\) 1.06258e37 1.40217
\(893\) −5.62202e36 −0.731558
\(894\) 0 0
\(895\) −1.78836e37 −2.26291
\(896\) −2.83425e35 −0.0353661
\(897\) 0 0
\(898\) 4.55453e34 0.00552700
\(899\) 1.16410e36 0.139314
\(900\) 0 0
\(901\) 2.49544e36 0.290460
\(902\) −7.42578e34 −0.00852433
\(903\) 0 0
\(904\) −2.40448e35 −0.0268483
\(905\) −6.07833e36 −0.669387
\(906\) 0 0
\(907\) −4.93129e36 −0.528286 −0.264143 0.964484i \(-0.585089\pi\)
−0.264143 + 0.964484i \(0.585089\pi\)
\(908\) 1.29207e37 1.36525
\(909\) 0 0
\(910\) −1.13648e35 −0.0116827
\(911\) 7.10548e36 0.720466 0.360233 0.932862i \(-0.382697\pi\)
0.360233 + 0.932862i \(0.382697\pi\)
\(912\) 0 0
\(913\) −7.84240e36 −0.773685
\(914\) 9.15090e34 0.00890505
\(915\) 0 0
\(916\) 1.90664e37 1.80541
\(917\) 6.83795e36 0.638718
\(918\) 0 0
\(919\) 2.64155e36 0.240112 0.120056 0.992767i \(-0.461693\pi\)
0.120056 + 0.992767i \(0.461693\pi\)
\(920\) −2.27042e35 −0.0203591
\(921\) 0 0
\(922\) 2.19009e33 0.000191129 0
\(923\) −1.57089e37 −1.35246
\(924\) 0 0
\(925\) 5.12665e36 0.429597
\(926\) 1.02490e35 0.00847316
\(927\) 0 0
\(928\) 4.39731e34 0.00353865
\(929\) −5.01934e36 −0.398520 −0.199260 0.979947i \(-0.563854\pi\)
−0.199260 + 0.979947i \(0.563854\pi\)
\(930\) 0 0
\(931\) −1.13263e36 −0.0875419
\(932\) 1.66280e37 1.26806
\(933\) 0 0
\(934\) 1.28268e35 0.00952320
\(935\) −1.57423e37 −1.15325
\(936\) 0 0
\(937\) −1.70189e37 −1.21391 −0.606956 0.794735i \(-0.707610\pi\)
−0.606956 + 0.794735i \(0.707610\pi\)
\(938\) −5.00652e34 −0.00352371
\(939\) 0 0
\(940\) −2.30123e37 −1.57711
\(941\) 1.51254e37 1.02291 0.511455 0.859310i \(-0.329107\pi\)
0.511455 + 0.859310i \(0.329107\pi\)
\(942\) 0 0
\(943\) 1.74548e37 1.14953
\(944\) −1.46929e37 −0.954897
\(945\) 0 0
\(946\) −1.21605e35 −0.00769687
\(947\) −1.65329e36 −0.103270 −0.0516351 0.998666i \(-0.516443\pi\)
−0.0516351 + 0.998666i \(0.516443\pi\)
\(948\) 0 0
\(949\) −3.46238e36 −0.210643
\(950\) −7.37220e34 −0.00442642
\(951\) 0 0
\(952\) −3.17213e35 −0.0185519
\(953\) −2.77784e37 −1.60341 −0.801706 0.597718i \(-0.796074\pi\)
−0.801706 + 0.597718i \(0.796074\pi\)
\(954\) 0 0
\(955\) −4.08541e36 −0.229717
\(956\) −4.83229e36 −0.268182
\(957\) 0 0
\(958\) −9.46752e34 −0.00511879
\(959\) −2.41640e37 −1.28955
\(960\) 0 0
\(961\) −8.14395e35 −0.0423441
\(962\) −7.95666e34 −0.00408359
\(963\) 0 0
\(964\) 1.07184e37 0.536004
\(965\) 1.54865e37 0.764473
\(966\) 0 0
\(967\) 3.82441e36 0.183965 0.0919823 0.995761i \(-0.470680\pi\)
0.0919823 + 0.995761i \(0.470680\pi\)
\(968\) 1.20659e35 0.00572952
\(969\) 0 0
\(970\) 1.00765e35 0.00466297
\(971\) 1.67087e37 0.763311 0.381655 0.924305i \(-0.375354\pi\)
0.381655 + 0.924305i \(0.375354\pi\)
\(972\) 0 0
\(973\) −1.89331e37 −0.842967
\(974\) −1.90256e34 −0.000836277 0
\(975\) 0 0
\(976\) 1.01484e37 0.434786
\(977\) 3.54376e37 1.49893 0.749466 0.662043i \(-0.230310\pi\)
0.749466 + 0.662043i \(0.230310\pi\)
\(978\) 0 0
\(979\) −1.48490e37 −0.612227
\(980\) −4.63612e36 −0.188725
\(981\) 0 0
\(982\) 3.46860e35 0.0137645
\(983\) −2.26759e37 −0.888476 −0.444238 0.895909i \(-0.646525\pi\)
−0.444238 + 0.895909i \(0.646525\pi\)
\(984\) 0 0
\(985\) 4.44726e37 1.69879
\(986\) 3.28087e34 0.00123745
\(987\) 0 0
\(988\) −1.66622e37 −0.612732
\(989\) 2.85843e37 1.03794
\(990\) 0 0
\(991\) −1.82706e36 −0.0646891 −0.0323445 0.999477i \(-0.510297\pi\)
−0.0323445 + 0.999477i \(0.510297\pi\)
\(992\) 6.95742e35 0.0243250
\(993\) 0 0
\(994\) 3.60899e35 0.0123043
\(995\) 1.66237e36 0.0559680
\(996\) 0 0
\(997\) 2.34599e37 0.770260 0.385130 0.922862i \(-0.374157\pi\)
0.385130 + 0.922862i \(0.374157\pi\)
\(998\) 3.93518e35 0.0127595
\(999\) 0 0
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 9.26.a.a.1.1 1
3.2 odd 2 1.26.a.a.1.1 1
12.11 even 2 16.26.a.b.1.1 1
15.2 even 4 25.26.b.a.24.1 2
15.8 even 4 25.26.b.a.24.2 2
15.14 odd 2 25.26.a.a.1.1 1
21.20 even 2 49.26.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.26.a.a.1.1 1 3.2 odd 2
9.26.a.a.1.1 1 1.1 even 1 trivial
16.26.a.b.1.1 1 12.11 even 2
25.26.a.a.1.1 1 15.14 odd 2
25.26.b.a.24.1 2 15.2 even 4
25.26.b.a.24.2 2 15.8 even 4
49.26.a.a.1.1 1 21.20 even 2