Properties

Label 49.26.a.a.1.1
Level $49$
Weight $26$
Character 49.1
Self dual yes
Analytic conductor $194.038$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 49.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(194.038422177\)
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 \(\chi\) \(=\) 49.1

$q$-expansion

\(f(q)\) \(=\) \(q-48.0000 q^{2} +195804. q^{3} -3.35521e7 q^{4} +7.41990e8 q^{5} -9.39859e6 q^{6} +3.22111e9 q^{8} -8.08949e11 q^{9} +O(q^{10})\) \(q-48.0000 q^{2} +195804. q^{3} -3.35521e7 q^{4} +7.41990e8 q^{5} -9.39859e6 q^{6} +3.22111e9 q^{8} -8.08949e11 q^{9} -3.56155e10 q^{10} +8.41952e12 q^{11} -6.56964e12 q^{12} +8.16510e13 q^{13} +1.45285e14 q^{15} +1.12567e15 q^{16} +2.51990e15 q^{17} +3.88296e13 q^{18} +6.08206e15 q^{19} -2.48953e16 q^{20} -4.04137e14 q^{22} -9.49953e16 q^{23} +6.30707e14 q^{24} +2.52526e17 q^{25} -3.91925e15 q^{26} -3.24298e17 q^{27} -2.71247e17 q^{29} -6.97366e15 q^{30} -4.29167e18 q^{31} -1.62115e17 q^{32} +1.64857e18 q^{33} -1.20955e17 q^{34} +2.71420e19 q^{36} +2.03015e19 q^{37} -2.91939e17 q^{38} +1.59876e19 q^{39} +2.39003e18 q^{40} +1.83744e20 q^{41} +3.00902e20 q^{43} -2.82493e20 q^{44} -6.00232e20 q^{45} +4.55977e18 q^{46} +9.24361e20 q^{47} +2.20410e20 q^{48} -1.21212e19 q^{50} +4.93407e20 q^{51} -2.73957e21 q^{52} -9.90292e20 q^{53} +1.55663e19 q^{54} +6.24719e21 q^{55} +1.19089e21 q^{57} +1.30199e19 q^{58} -1.30526e22 q^{59} -4.87461e21 q^{60} -9.01545e21 q^{61} +2.06000e20 q^{62} -3.77634e22 q^{64} +6.05842e22 q^{65} -7.91316e19 q^{66} -2.66891e22 q^{67} -8.45480e22 q^{68} -1.86005e22 q^{69} -1.92391e23 q^{71} -2.60572e21 q^{72} -4.24046e22 q^{73} -9.74471e20 q^{74} +4.94455e22 q^{75} -2.04066e23 q^{76} -7.67405e20 q^{78} -2.71681e23 q^{79} +8.35234e23 q^{80} +6.21915e23 q^{81} -8.81972e21 q^{82} +9.31454e23 q^{83} +1.86974e24 q^{85} -1.44433e22 q^{86} -5.31112e22 q^{87} +2.71202e22 q^{88} +1.76364e24 q^{89} +2.88111e22 q^{90} +3.18729e24 q^{92} -8.40325e23 q^{93} -4.43693e22 q^{94} +4.51282e24 q^{95} -3.17427e22 q^{96} -2.82924e24 q^{97} -6.81096e24 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −48.0000 −0.00828641 −0.00414320 0.999991i \(-0.501319\pi\)
−0.00414320 + 0.999991i \(0.501319\pi\)
\(3\) 195804. 0.212719 0.106359 0.994328i \(-0.466081\pi\)
0.106359 + 0.994328i \(0.466081\pi\)
\(4\) −3.35521e7 −0.999931
\(5\) 7.41990e8 1.35917 0.679584 0.733598i \(-0.262160\pi\)
0.679584 + 0.733598i \(0.262160\pi\)
\(6\) −9.39859e6 −0.00176267
\(7\) 0 0
\(8\) 3.22111e9 0.0165722
\(9\) −8.08949e11 −0.954751
\(10\) −3.56155e10 −0.0112626
\(11\) 8.41952e12 0.808870 0.404435 0.914567i \(-0.367468\pi\)
0.404435 + 0.914567i \(0.367468\pi\)
\(12\) −6.56964e12 −0.212704
\(13\) 8.16510e13 0.972008 0.486004 0.873957i \(-0.338454\pi\)
0.486004 + 0.873957i \(0.338454\pi\)
\(14\) 0 0
\(15\) 1.45285e14 0.289120
\(16\) 1.12567e15 0.999794
\(17\) 2.51990e15 1.04899 0.524496 0.851413i \(-0.324254\pi\)
0.524496 + 0.851413i \(0.324254\pi\)
\(18\) 3.88296e13 0.00791145
\(19\) 6.08206e15 0.630421 0.315210 0.949022i \(-0.397925\pi\)
0.315210 + 0.949022i \(0.397925\pi\)
\(20\) −2.48953e16 −1.35907
\(21\) 0 0
\(22\) −4.04137e14 −0.00670262
\(23\) −9.49953e16 −0.903866 −0.451933 0.892052i \(-0.649265\pi\)
−0.451933 + 0.892052i \(0.649265\pi\)
\(24\) 6.30707e14 0.00352523
\(25\) 2.52526e17 0.847336
\(26\) −3.91925e15 −0.00805445
\(27\) −3.24298e17 −0.415812
\(28\) 0 0
\(29\) −2.71247e17 −0.142361 −0.0711803 0.997463i \(-0.522677\pi\)
−0.0711803 + 0.997463i \(0.522677\pi\)
\(30\) −6.97366e15 −0.00239577
\(31\) −4.29167e18 −0.978599 −0.489299 0.872116i \(-0.662747\pi\)
−0.489299 + 0.872116i \(0.662747\pi\)
\(32\) −1.62115e17 −0.0248569
\(33\) 1.64857e18 0.172062
\(34\) −1.20955e17 −0.00869237
\(35\) 0 0
\(36\) 2.71420e19 0.954685
\(37\) 2.03015e19 0.506998 0.253499 0.967336i \(-0.418419\pi\)
0.253499 + 0.967336i \(0.418419\pi\)
\(38\) −2.91939e17 −0.00522392
\(39\) 1.59876e19 0.206764
\(40\) 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
\(45\) −6.00232e20 −1.29767
\(46\) 4.55977e18 0.00748980
\(47\) 9.24361e20 1.16043 0.580214 0.814464i \(-0.302969\pi\)
0.580214 + 0.814464i \(0.302969\pi\)
\(48\) 2.20410e20 0.212675
\(49\) 0 0
\(50\) −1.21212e19 −0.00702137
\(51\) 4.93407e20 0.223140
\(52\) −2.73957e21 −0.971941
\(53\) −9.90292e20 −0.276895 −0.138447 0.990370i \(-0.544211\pi\)
−0.138447 + 0.990370i \(0.544211\pi\)
\(54\) 1.55663e19 0.00344559
\(55\) 6.24719e21 1.09939
\(56\) 0 0
\(57\) 1.19089e21 0.134102
\(58\) 1.30199e19 0.00117966
\(59\) −1.30526e22 −0.955093 −0.477547 0.878606i \(-0.658474\pi\)
−0.477547 + 0.878606i \(0.658474\pi\)
\(60\) −4.87461e21 −0.289101
\(61\) −9.01545e21 −0.434875 −0.217438 0.976074i \(-0.569770\pi\)
−0.217438 + 0.976074i \(0.569770\pi\)
\(62\) 2.06000e20 0.00810907
\(63\) 0 0
\(64\) −3.77634e22 −0.999588
\(65\) 6.05842e22 1.32112
\(66\) −7.91316e19 −0.00142577
\(67\) −2.66891e22 −0.398473 −0.199236 0.979951i \(-0.563846\pi\)
−0.199236 + 0.979951i \(0.563846\pi\)
\(68\) −8.45480e22 −1.04892
\(69\) −1.86005e22 −0.192269
\(70\) 0 0
\(71\) −1.92391e23 −1.39141 −0.695704 0.718329i \(-0.744907\pi\)
−0.695704 + 0.718329i \(0.744907\pi\)
\(72\) −2.60572e21 −0.0158224
\(73\) −4.24046e22 −0.216709 −0.108355 0.994112i \(-0.534558\pi\)
−0.108355 + 0.994112i \(0.534558\pi\)
\(74\) −9.74471e20 −0.00420119
\(75\) 4.94455e22 0.180244
\(76\) −2.04066e23 −0.630377
\(77\) 0 0
\(78\) −7.67405e20 −0.00171333
\(79\) −2.71681e23 −0.517274 −0.258637 0.965975i \(-0.583273\pi\)
−0.258637 + 0.965975i \(0.583273\pi\)
\(80\) 8.35234e23 1.35889
\(81\) 6.21915e23 0.866300
\(82\) −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
\(87\) −5.31112e22 −0.0302828
\(88\) 2.71202e22 0.0134048
\(89\) 1.76364e24 0.756892 0.378446 0.925623i \(-0.376459\pi\)
0.378446 + 0.925623i \(0.376459\pi\)
\(90\) 2.88111e22 0.0107530
\(91\) 0 0
\(92\) 3.18729e24 0.903804
\(93\) −8.40325e23 −0.208166
\(94\) −4.43693e22 −0.00961578
\(95\) 4.51282e24 0.856847
\(96\) −3.17427e22 −0.00528754
\(97\) −2.82924e24 −0.414022 −0.207011 0.978339i \(-0.566374\pi\)
−0.207011 + 0.978339i \(0.566374\pi\)
\(98\) 0 0
\(99\) −6.81096e24 −0.772269
\(100\) −8.47278e24 −0.847278
\(101\) −1.86342e24 −0.164549 −0.0822744 0.996610i \(-0.526218\pi\)
−0.0822744 + 0.996610i \(0.526218\pi\)
\(102\) −2.36835e22 −0.00184903
\(103\) −4.85812e24 −0.335740 −0.167870 0.985809i \(-0.553689\pi\)
−0.167870 + 0.985809i \(0.553689\pi\)
\(104\) 2.63007e23 0.0161084
\(105\) 0 0
\(106\) 4.75340e22 0.00229446
\(107\) 3.58304e25 1.53799 0.768997 0.639252i \(-0.220756\pi\)
0.768997 + 0.639252i \(0.220756\pi\)
\(108\) 1.08809e25 0.415784
\(109\) −4.77795e25 −1.62709 −0.813543 0.581505i \(-0.802464\pi\)
−0.813543 + 0.581505i \(0.802464\pi\)
\(110\) −2.99865e23 −0.00910999
\(111\) 3.97511e24 0.107848
\(112\) 0 0
\(113\) −7.46476e25 −1.62008 −0.810038 0.586378i \(-0.800553\pi\)
−0.810038 + 0.586378i \(0.800553\pi\)
\(114\) −5.71628e22 −0.00111123
\(115\) −7.04855e25 −1.22851
\(116\) 9.10091e24 0.142351
\(117\) −6.60516e25 −0.928025
\(118\) 6.26523e23 0.00791429
\(119\) 0 0
\(120\) 4.67978e23 0.00479137
\(121\) −3.74588e25 −0.345730
\(122\) 4.32742e23 0.00360355
\(123\) 3.59779e25 0.270534
\(124\) 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
\(129\) 5.89178e25 0.244273
\(130\) −2.90804e24 −0.0109474
\(131\) 1.74971e26 0.598513 0.299257 0.954173i \(-0.403261\pi\)
0.299257 + 0.954173i \(0.403261\pi\)
\(132\) −5.53132e25 −0.172050
\(133\) 0 0
\(134\) 1.28108e24 0.00330191
\(135\) −2.40626e26 −0.565158
\(136\) 8.11689e24 0.0173841
\(137\) 6.18313e26 1.20837 0.604187 0.796843i \(-0.293498\pi\)
0.604187 + 0.796843i \(0.293498\pi\)
\(138\) 8.92822e23 0.00159322
\(139\) 4.84462e26 0.789905 0.394952 0.918702i \(-0.370761\pi\)
0.394952 + 0.918702i \(0.370761\pi\)
\(140\) 0 0
\(141\) 1.80994e26 0.246845
\(142\) 9.23474e24 0.0115298
\(143\) 6.87462e26 0.786228
\(144\) −9.10608e26 −0.954554
\(145\) −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 \(-0.399742\pi\)
0.309787 + 0.950806i \(0.399742\pi\)
\(150\) −2.37339e24 −0.00149358
\(151\) 1.16190e27 0.672907 0.336454 0.941700i \(-0.390772\pi\)
0.336454 + 0.941700i \(0.390772\pi\)
\(152\) 1.95910e25 0.0104475
\(153\) −2.03847e27 −1.00152
\(154\) 0 0
\(155\) −3.18437e27 −1.33008
\(156\) −5.36418e26 −0.206750
\(157\) 3.41505e26 0.121521 0.0607605 0.998152i \(-0.480647\pi\)
0.0607605 + 0.998152i \(0.480647\pi\)
\(158\) 1.30407e25 0.00428634
\(159\) −1.93903e26 −0.0589008
\(160\) −1.20287e26 −0.0337847
\(161\) 0 0
\(162\) −2.98519e25 −0.00717851
\(163\) 4.63202e27 1.03140 0.515698 0.856771i \(-0.327533\pi\)
0.515698 + 0.856771i \(0.327533\pi\)
\(164\) −6.16501e27 −1.27170
\(165\) 1.22323e27 0.233861
\(166\) −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
\(171\) −4.92008e27 −0.601895
\(172\) −1.00959e28 −1.14826
\(173\) 6.02602e27 0.637462 0.318731 0.947845i \(-0.396743\pi\)
0.318731 + 0.947845i \(0.396743\pi\)
\(174\) 2.54934e24 0.000250935 0
\(175\) 0 0
\(176\) 9.47758e27 0.808703
\(177\) −2.55575e27 −0.203166
\(178\) −8.46545e25 −0.00627191
\(179\) 2.41023e28 1.66493 0.832463 0.554081i \(-0.186930\pi\)
0.832463 + 0.554081i \(0.186930\pi\)
\(180\) 2.01391e28 1.29758
\(181\) 8.19193e27 0.492498 0.246249 0.969207i \(-0.420802\pi\)
0.246249 + 0.969207i \(0.420802\pi\)
\(182\) 0 0
\(183\) −1.76526e27 −0.0925061
\(184\) −3.05991e26 −0.0149791
\(185\) 1.50635e28 0.689095
\(186\) 4.03356e25 0.00172495
\(187\) 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 \(-0.473069\pi\)
0.0845066 + 0.996423i \(0.473069\pi\)
\(192\) −7.39422e27 −0.212631
\(193\) 2.08716e28 0.562457 0.281228 0.959641i \(-0.409258\pi\)
0.281228 + 0.959641i \(0.409258\pi\)
\(194\) 1.35804e26 0.00343075
\(195\) 1.18626e28 0.281027
\(196\) 0 0
\(197\) −5.99370e28 −1.24988 −0.624938 0.780674i \(-0.714876\pi\)
−0.624938 + 0.780674i \(0.714876\pi\)
\(198\) 3.26926e26 0.00639933
\(199\) −2.24042e27 −0.0411782 −0.0205891 0.999788i \(-0.506554\pi\)
−0.0205891 + 0.999788i \(0.506554\pi\)
\(200\) 8.13414e26 0.0140423
\(201\) −5.22583e27 −0.0847626
\(202\) 8.94444e25 0.00136352
\(203\) 0 0
\(204\) −1.65548e28 −0.223125
\(205\) 1.36336e29 1.72858
\(206\) 2.33190e26 0.00278208
\(207\) 7.68464e28 0.862967
\(208\) 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
\(213\) −3.76708e28 −0.295979
\(214\) −1.71986e27 −0.0127444
\(215\) 2.23266e29 1.56078
\(216\) −1.04460e27 −0.00689094
\(217\) 0 0
\(218\) 2.29342e27 0.0134827
\(219\) −8.30299e27 −0.0460981
\(220\) −2.09607e29 −1.09931
\(221\) 2.05752e29 1.01963
\(222\) −1.90805e26 −0.000893673 0
\(223\) 3.16696e29 1.40227 0.701135 0.713029i \(-0.252677\pi\)
0.701135 + 0.713029i \(0.252677\pi\)
\(224\) 0 0
\(225\) −2.04281e29 −0.808994
\(226\) 3.58308e27 0.0134246
\(227\) −3.85094e29 −1.36535 −0.682674 0.730723i \(-0.739183\pi\)
−0.682674 + 0.730723i \(0.739183\pi\)
\(228\) −3.99569e28 −0.134093
\(229\) 5.68261e29 1.80553 0.902765 0.430134i \(-0.141534\pi\)
0.902765 + 0.430134i \(0.141534\pi\)
\(230\) 3.38331e27 0.0101799
\(231\) 0 0
\(232\) −8.73718e26 −0.00235924
\(233\) 4.95586e29 1.26815 0.634075 0.773272i \(-0.281381\pi\)
0.634075 + 0.773272i \(0.281381\pi\)
\(234\) 3.17048e27 0.00769000
\(235\) 6.85867e29 1.57722
\(236\) 4.37941e29 0.955028
\(237\) −5.31962e28 −0.110034
\(238\) 0 0
\(239\) −1.44023e29 −0.268200 −0.134100 0.990968i \(-0.542814\pi\)
−0.134100 + 0.990968i \(0.542814\pi\)
\(240\) 1.63542e29 0.289061
\(241\) 3.19456e29 0.536041 0.268020 0.963413i \(-0.413631\pi\)
0.268020 + 0.963413i \(0.413631\pi\)
\(242\) 1.79802e27 0.00286486
\(243\) 3.96547e29 0.600090
\(244\) 3.02488e29 0.434845
\(245\) 0 0
\(246\) −1.72694e27 −0.00224175
\(247\) 4.96606e29 0.612774
\(248\) −1.38239e28 −0.0162176
\(249\) 1.82383e29 0.203466
\(250\) 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
\(255\) 3.66103e29 0.303285
\(256\) 1.26678e30 0.999313
\(257\) 2.29446e30 1.72392 0.861960 0.506977i \(-0.169237\pi\)
0.861960 + 0.506977i \(0.169237\pi\)
\(258\) −2.82805e27 −0.00202414
\(259\) 0 0
\(260\) −2.03273e30 −1.32103
\(261\) 2.19425e29 0.135919
\(262\) −8.39859e27 −0.00495952
\(263\) 7.73316e29 0.435422 0.217711 0.976013i \(-0.430141\pi\)
0.217711 + 0.976013i \(0.430141\pi\)
\(264\) 5.31025e27 0.00285145
\(265\) −7.34787e29 −0.376347
\(266\) 0 0
\(267\) 3.45327e29 0.161005
\(268\) 8.95475e29 0.398445
\(269\) −3.62259e30 −1.53856 −0.769282 0.638910i \(-0.779386\pi\)
−0.769282 + 0.638910i \(0.779386\pi\)
\(270\) 1.15500e28 0.00468313
\(271\) 3.62767e30 1.40447 0.702234 0.711946i \(-0.252186\pi\)
0.702234 + 0.711946i \(0.252186\pi\)
\(272\) 2.83657e30 1.04877
\(273\) 0 0
\(274\) −2.96790e28 −0.0100131
\(275\) 2.12614e30 0.685384
\(276\) 6.24085e29 0.192256
\(277\) −2.54808e30 −0.750266 −0.375133 0.926971i \(-0.622403\pi\)
−0.375133 + 0.926971i \(0.622403\pi\)
\(278\) −2.32542e28 −0.00654547
\(279\) 3.47174e30 0.934318
\(280\) 0 0
\(281\) 3.59817e30 0.885631 0.442816 0.896613i \(-0.353980\pi\)
0.442816 + 0.896613i \(0.353980\pi\)
\(282\) −8.68769e27 −0.00204546
\(283\) −3.82265e30 −0.861061 −0.430530 0.902576i \(-0.641673\pi\)
−0.430530 + 0.902576i \(0.641673\pi\)
\(284\) 6.45511e30 1.39131
\(285\) 8.83629e29 0.182267
\(286\) −3.29982e28 −0.00651500
\(287\) 0 0
\(288\) 1.31143e29 0.0237322
\(289\) 5.79269e29 0.100382
\(290\) 9.66060e27 0.00160335
\(291\) −5.53977e29 −0.0880702
\(292\) 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
\(297\) −2.73043e30 −0.336338
\(298\) −4.34673e28 −0.00513404
\(299\) −7.75646e30 −0.878565
\(300\) −1.65900e30 −0.180232
\(301\) 0 0
\(302\) −5.57710e28 −0.00557599
\(303\) −3.64866e29 −0.0350026
\(304\) 6.84638e30 0.630291
\(305\) −6.68937e30 −0.591068
\(306\) 9.78466e28 0.00829904
\(307\) −1.43602e31 −1.16931 −0.584657 0.811281i \(-0.698771\pi\)
−0.584657 + 0.811281i \(0.698771\pi\)
\(308\) 0 0
\(309\) −9.51239e29 −0.0714182
\(310\) 1.52850e29 0.0110216
\(311\) 2.24630e31 1.55584 0.777918 0.628366i \(-0.216276\pi\)
0.777918 + 0.628366i \(0.216276\pi\)
\(312\) 5.14979e28 0.00342655
\(313\) 1.37956e30 0.0881934 0.0440967 0.999027i \(-0.485959\pi\)
0.0440967 + 0.999027i \(0.485959\pi\)
\(314\) −1.63922e28 −0.00100697
\(315\) 0 0
\(316\) 9.11548e30 0.517239
\(317\) −1.02787e31 −0.560655 −0.280327 0.959904i \(-0.590443\pi\)
−0.280327 + 0.959904i \(0.590443\pi\)
\(318\) 9.30735e27 0.000488076 0
\(319\) −2.28377e30 −0.115151
\(320\) −2.80200e31 −1.35861
\(321\) 7.01574e30 0.327160
\(322\) 0 0
\(323\) 1.53262e31 0.661306
\(324\) −2.08666e31 −0.866240
\(325\) 2.06190e31 0.823617
\(326\) −2.22337e29 −0.00854656
\(327\) −9.35542e30 −0.346112
\(328\) 5.91861e29 0.0210764
\(329\) 0 0
\(330\) −5.87148e28 −0.00193787
\(331\) −5.75356e30 −0.182847 −0.0914233 0.995812i \(-0.529142\pi\)
−0.0914233 + 0.995812i \(0.529142\pi\)
\(332\) −3.12523e31 −0.956435
\(333\) −1.64229e31 −0.484057
\(334\) −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
\(339\) −1.46163e31 −0.344621
\(340\) −6.27338e31 −1.42566
\(341\) −3.61337e31 −0.791559
\(342\) 2.36164e29 0.00498754
\(343\) 0 0
\(344\) 9.69239e29 0.0190305
\(345\) −1.38013e31 −0.261326
\(346\) −2.89249e29 −0.00528227
\(347\) 9.41781e29 0.0165894 0.00829472 0.999966i \(-0.497360\pi\)
0.00829472 + 0.999966i \(0.497360\pi\)
\(348\) 1.78200e30 0.0302807
\(349\) 3.39081e31 0.555886 0.277943 0.960598i \(-0.410347\pi\)
0.277943 + 0.960598i \(0.410347\pi\)
\(350\) 0 0
\(351\) −2.64793e31 −0.404173
\(352\) −1.36493e30 −0.0201060
\(353\) −1.30313e31 −0.185269 −0.0926346 0.995700i \(-0.529529\pi\)
−0.0926346 + 0.995700i \(0.529529\pi\)
\(354\) 1.22676e29 0.00168352
\(355\) −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 \(-0.770190\pi\)
−0.750506 + 0.660864i \(0.770190\pi\)
\(360\) −1.93342e30 −0.0215052
\(361\) −5.60851e31 −0.602570
\(362\) −3.93213e29 −0.00408104
\(363\) −7.33459e30 −0.0735433
\(364\) 0 0
\(365\) −3.14638e31 −0.294544
\(366\) 8.47325e28 0.000766543 0
\(367\) 2.06294e32 1.80369 0.901844 0.432061i \(-0.142214\pi\)
0.901844 + 0.432061i \(0.142214\pi\)
\(368\) −1.06933e32 −0.903680
\(369\) −1.48640e32 −1.21424
\(370\) −7.23048e29 −0.00571012
\(371\) 0 0
\(372\) 2.81947e31 0.208152
\(373\) 2.46051e32 1.75657 0.878283 0.478142i \(-0.158689\pi\)
0.878283 + 0.478142i \(0.158689\pi\)
\(374\) −1.01838e30 −0.00703099
\(375\) −6.61009e30 −0.0441384
\(376\) 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
\(381\) 6.57715e31 0.360143
\(382\) −2.64289e29 −0.00140051
\(383\) −1.33051e32 −0.682393 −0.341196 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(384\) 1.42003e30 0.00704949
\(385\) 0 0
\(386\) −1.00184e30 −0.00466075
\(387\) −2.43414e32 −1.09637
\(388\) 9.49271e31 0.413993
\(389\) 2.40509e32 1.01569 0.507844 0.861449i \(-0.330443\pi\)
0.507844 + 0.861449i \(0.330443\pi\)
\(390\) −5.69407e29 −0.00232871
\(391\) −2.39379e32 −0.948147
\(392\) 0 0
\(393\) 3.42599e31 0.127315
\(394\) 2.87698e30 0.0103570
\(395\) −2.01585e32 −0.703062
\(396\) 2.28522e32 0.772216
\(397\) 4.12137e32 1.34946 0.674730 0.738065i \(-0.264260\pi\)
0.674730 + 0.738065i \(0.264260\pi\)
\(398\) 1.07540e29 0.000341219 0
\(399\) 0 0
\(400\) 2.84260e32 0.847161
\(401\) −7.16647e31 −0.207014 −0.103507 0.994629i \(-0.533006\pi\)
−0.103507 + 0.994629i \(0.533006\pi\)
\(402\) 2.50840e29 0.000702377 0
\(403\) −3.50419e32 −0.951206
\(404\) 6.25219e31 0.164537
\(405\) 4.61454e32 1.17745
\(406\) 0 0
\(407\) 1.70929e32 0.410095
\(408\) 1.58932e30 0.00369793
\(409\) −1.34430e32 −0.303358 −0.151679 0.988430i \(-0.548468\pi\)
−0.151679 + 0.988430i \(0.548468\pi\)
\(410\) −6.54415e30 −0.0143237
\(411\) 1.21068e32 0.257044
\(412\) 1.63000e32 0.335717
\(413\) 0 0
\(414\) −3.68863e30 −0.00715089
\(415\) 6.91130e32 1.30004
\(416\) −1.32368e31 −0.0241612
\(417\) 9.48596e31 0.168028
\(418\) −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
\(423\) −7.47761e32 −1.10792
\(424\) −3.18984e30 −0.00458877
\(425\) 6.36340e32 0.888848
\(426\) 1.80820e30 0.00245260
\(427\) 0 0
\(428\) −1.20219e33 −1.53789
\(429\) 1.34608e32 0.167245
\(430\) −1.07168e31 −0.0129333
\(431\) −7.83836e31 −0.0918881 −0.0459441 0.998944i \(-0.514630\pi\)
−0.0459441 + 0.998944i \(0.514630\pi\)
\(432\) −3.65052e32 −0.415727
\(433\) −6.33273e32 −0.700635 −0.350318 0.936631i \(-0.613926\pi\)
−0.350318 + 0.936631i \(0.613926\pi\)
\(434\) 0 0
\(435\) −3.94080e31 −0.0411594
\(436\) 1.60310e33 1.62697
\(437\) −5.77767e32 −0.569816
\(438\) 3.98543e29 0.000381988 0
\(439\) 1.48299e33 1.38144 0.690718 0.723124i \(-0.257295\pi\)
0.690718 + 0.723124i \(0.257295\pi\)
\(440\) 2.01229e31 0.0182193
\(441\) 0 0
\(442\) −9.87612e30 −0.00844905
\(443\) −1.20901e33 −1.00551 −0.502753 0.864430i \(-0.667679\pi\)
−0.502753 + 0.864430i \(0.667679\pi\)
\(444\) −1.33373e32 −0.107841
\(445\) 1.30860e33 1.02874
\(446\) −1.52014e31 −0.0116198
\(447\) 1.77314e32 0.131795
\(448\) 0 0
\(449\) −9.48861e32 −0.666996 −0.333498 0.942751i \(-0.608229\pi\)
−0.333498 + 0.942751i \(0.608229\pi\)
\(450\) 9.80547e30 0.00670366
\(451\) 1.54704e33 1.02871
\(452\) 2.50459e33 1.61996
\(453\) 2.27504e32 0.143140
\(454\) 1.84845e31 0.0113138
\(455\) 0 0
\(456\) 3.83600e30 0.00222238
\(457\) 1.90644e33 1.07466 0.537329 0.843373i \(-0.319433\pi\)
0.537329 + 0.843373i \(0.319433\pi\)
\(458\) −2.72765e31 −0.0149614
\(459\) −8.17199e32 −0.436183
\(460\) 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
\(465\) −6.23513e32 −0.282933
\(466\) −2.37882e31 −0.0105084
\(467\) 2.67225e33 1.14926 0.574628 0.818415i \(-0.305147\pi\)
0.574628 + 0.818415i \(0.305147\pi\)
\(468\) 2.21617e33 0.927962
\(469\) 0 0
\(470\) −3.29216e31 −0.0130695
\(471\) 6.68680e31 0.0258498
\(472\) −4.20438e31 −0.0158280
\(473\) 2.53345e33 0.928854
\(474\) 2.55342e30 0.000911786 0
\(475\) 1.53588e33 0.534178
\(476\) 0 0
\(477\) 8.01096e32 0.264366
\(478\) 6.91313e30 0.00222242
\(479\) −1.97240e33 −0.617733 −0.308867 0.951105i \(-0.599950\pi\)
−0.308867 + 0.951105i \(0.599950\pi\)
\(480\) −2.35528e31 −0.00718665
\(481\) 1.65764e33 0.492806
\(482\) −1.53339e31 −0.00444185
\(483\) 0 0
\(484\) 1.25682e33 0.345706
\(485\) −2.09927e33 −0.562725
\(486\) −1.90343e31 −0.00497259
\(487\) −3.96366e32 −0.100922 −0.0504608 0.998726i \(-0.516069\pi\)
−0.0504608 + 0.998726i \(0.516069\pi\)
\(488\) −2.90398e31 −0.00720686
\(489\) 9.06968e32 0.219397
\(490\) 0 0
\(491\) −7.22626e33 −1.66110 −0.830548 0.556947i \(-0.811973\pi\)
−0.830548 + 0.556947i \(0.811973\pi\)
\(492\) −1.20713e33 −0.270515
\(493\) −6.83515e32 −0.149335
\(494\) −2.38371e31 −0.00507769
\(495\) −5.05366e33 −1.04964
\(496\) −4.83099e33 −0.978397
\(497\) 0 0
\(498\) −8.75436e30 −0.00168600
\(499\) 8.19830e33 1.53981 0.769905 0.638159i \(-0.220304\pi\)
0.769905 + 0.638159i \(0.220304\pi\)
\(500\) 1.13268e33 0.207482
\(501\) 1.61826e33 0.289119
\(502\) 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
\(507\) −7.62689e31 −0.0117422
\(508\) −1.12703e34 −1.69293
\(509\) −1.96955e33 −0.288665 −0.144332 0.989529i \(-0.546103\pi\)
−0.144332 + 0.989529i \(0.546103\pi\)
\(510\) −1.75729e31 −0.00251314
\(511\) 0 0
\(512\) −3.04153e32 −0.0414207
\(513\) −1.97240e33 −0.262137
\(514\) −1.10134e32 −0.0142851
\(515\) −3.60468e33 −0.456327
\(516\) −1.97682e33 −0.244256
\(517\) 7.78267e33 0.938635
\(518\) 0 0
\(519\) 1.17992e33 0.135600
\(520\) 1.95149e32 0.0218940
\(521\) −7.39782e33 −0.810274 −0.405137 0.914256i \(-0.632776\pi\)
−0.405137 + 0.914256i \(0.632776\pi\)
\(522\) −1.05324e31 −0.00112628
\(523\) −1.70332e34 −1.77838 −0.889191 0.457535i \(-0.848732\pi\)
−0.889191 + 0.457535i \(0.848732\pi\)
\(524\) −5.87063e33 −0.598472
\(525\) 0 0
\(526\) −3.71192e31 −0.00360808
\(527\) −1.08146e34 −1.02654
\(528\) 1.85575e33 0.172026
\(529\) −2.02166e33 −0.183026
\(530\) 3.52698e31 0.00311856
\(531\) 1.05589e34 0.911876
\(532\) 0 0
\(533\) 1.50029e34 1.23619
\(534\) −1.65757e31 −0.00133415
\(535\) 2.65858e34 2.09039
\(536\) −8.59686e31 −0.00660358
\(537\) 4.71932e33 0.354161
\(538\) 1.73884e32 0.0127492
\(539\) 0 0
\(540\) 8.07351e33 0.565120
\(541\) −1.28681e34 −0.880134 −0.440067 0.897965i \(-0.645045\pi\)
−0.440067 + 0.897965i \(0.645045\pi\)
\(542\) −1.74128e32 −0.0116380
\(543\) 1.60401e33 0.104764
\(544\) −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
\(549\) 7.29304e33 0.415197
\(550\) −1.02055e32 −0.00567937
\(551\) −1.64974e33 −0.0897471
\(552\) −5.99142e31 −0.00318633
\(553\) 0 0
\(554\) 1.22308e32 0.00621701
\(555\) 2.94949e33 0.146583
\(556\) −1.62547e34 −0.789851
\(557\) −3.28751e33 −0.156198 −0.0780992 0.996946i \(-0.524885\pi\)
−0.0780992 + 0.996946i \(0.524885\pi\)
\(558\) −1.66644e32 −0.00774214
\(559\) 2.45689e34 1.11619
\(560\) 0 0
\(561\) 4.15424e33 0.180491
\(562\) −1.72712e32 −0.00733870
\(563\) 1.80804e34 0.751371 0.375685 0.926747i \(-0.377407\pi\)
0.375685 + 0.926747i \(0.377407\pi\)
\(564\) −6.07272e33 −0.246828
\(565\) −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 \(-0.517734\pi\)
−0.0556854 + 0.998448i \(0.517734\pi\)
\(570\) −4.24142e31 −0.00151034
\(571\) −1.29884e34 −0.452486 −0.226243 0.974071i \(-0.572644\pi\)
−0.226243 + 0.974071i \(0.572644\pi\)
\(572\) −2.30658e34 −0.786174
\(573\) 1.07810e33 0.0359523
\(574\) 0 0
\(575\) −2.39888e34 −0.765878
\(576\) 3.05487e34 0.954357
\(577\) 7.31490e31 0.00223620 0.00111810 0.999999i \(-0.499644\pi\)
0.00111810 + 0.999999i \(0.499644\pi\)
\(578\) −2.78049e31 −0.000831808 0
\(579\) 4.08674e33 0.119645
\(580\) 6.75278e33 0.193479
\(581\) 0 0
\(582\) 2.65909e31 0.000729786 0
\(583\) −8.33778e33 −0.223972
\(584\) −1.36590e32 −0.00359136
\(585\) −4.90096e34 −1.26134
\(586\) 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
\(591\) −1.17359e34 −0.265872
\(592\) 2.28527e34 0.506894
\(593\) −2.40705e34 −0.522758 −0.261379 0.965236i \(-0.584177\pi\)
−0.261379 + 0.965236i \(0.584177\pi\)
\(594\) 1.31061e32 0.00278703
\(595\) 0 0
\(596\) −3.03838e34 −0.619531
\(597\) −4.38684e32 −0.00875937
\(598\) 3.72310e32 0.00728015
\(599\) −8.30672e33 −0.159072 −0.0795361 0.996832i \(-0.525344\pi\)
−0.0795361 + 0.996832i \(0.525344\pi\)
\(600\) 1.59270e32 0.00298705
\(601\) 3.00405e34 0.551792 0.275896 0.961187i \(-0.411025\pi\)
0.275896 + 0.961187i \(0.411025\pi\)
\(602\) 0 0
\(603\) 2.15901e34 0.380442
\(604\) −3.89841e34 −0.672861
\(605\) −2.77941e34 −0.469905
\(606\) 1.75136e31 0.000290046 0
\(607\) 1.00963e35 1.63796 0.818978 0.573825i \(-0.194541\pi\)
0.818978 + 0.573825i \(0.194541\pi\)
\(608\) −9.85991e32 −0.0156703
\(609\) 0 0
\(610\) 3.21090e32 0.00489783
\(611\) 7.54750e34 1.12795
\(612\) 6.83951e34 1.00146
\(613\) −1.02453e33 −0.0146983 −0.00734915 0.999973i \(-0.502339\pi\)
−0.00734915 + 0.999973i \(0.502339\pi\)
\(614\) 6.89290e32 0.00968941
\(615\) 2.66952e34 0.367701
\(616\) 0 0
\(617\) 4.53271e34 0.599505 0.299753 0.954017i \(-0.403096\pi\)
0.299753 + 0.954017i \(0.403096\pi\)
\(618\) 4.56595e31 0.000591800 0
\(619\) −1.24784e35 −1.58499 −0.792496 0.609878i \(-0.791219\pi\)
−0.792496 + 0.609878i \(0.791219\pi\)
\(620\) 1.06842e35 1.32999
\(621\) 3.08068e34 0.375839
\(622\) −1.07823e33 −0.0128923
\(623\) 0 0
\(624\) 1.79967e34 0.206722
\(625\) −1.00307e35 −1.12936
\(626\) −6.62189e31 −0.000730807 0
\(627\) 1.00267e34 0.108471
\(628\) −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
\(633\) −1.47338e34 −0.141503
\(634\) 4.93375e32 0.00464581
\(635\) 2.49238e35 2.30114
\(636\) 6.50586e33 0.0588967
\(637\) 0 0
\(638\) 1.09621e32 0.000954190 0
\(639\) 1.55634e35 1.32845
\(640\) 5.38114e33 0.0450427
\(641\) 8.30494e34 0.681728 0.340864 0.940113i \(-0.389280\pi\)
0.340864 + 0.940113i \(0.389280\pi\)
\(642\) −3.36756e32 −0.00271098
\(643\) −5.25724e34 −0.415069 −0.207535 0.978228i \(-0.566544\pi\)
−0.207535 + 0.978228i \(0.566544\pi\)
\(644\) 0 0
\(645\) 4.37164e34 0.332008
\(646\) −7.35656e32 −0.00547985
\(647\) 2.03021e35 1.48333 0.741665 0.670770i \(-0.234036\pi\)
0.741665 + 0.670770i \(0.234036\pi\)
\(648\) 2.00326e33 0.0143565
\(649\) −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 \(-0.316253\pi\)
0.545728 + 0.837962i \(0.316253\pi\)
\(654\) 4.49060e32 0.00286802
\(655\) 1.29826e35 0.813479
\(656\) 2.06835e35 1.27153
\(657\) 3.43032e34 0.206903
\(658\) 0 0
\(659\) −2.92521e35 −1.69859 −0.849296 0.527917i \(-0.822973\pi\)
−0.849296 + 0.527917i \(0.822973\pi\)
\(660\) −4.10418e34 −0.233845
\(661\) −8.30227e34 −0.464172 −0.232086 0.972695i \(-0.574555\pi\)
−0.232086 + 0.972695i \(0.574555\pi\)
\(662\) 2.76171e32 0.00151514
\(663\) 4.02872e34 0.216894
\(664\) 3.00032e33 0.0158514
\(665\) 0 0
\(666\) 7.88298e32 0.00401109
\(667\) 2.57672e34 0.128675
\(668\) −2.77298e35 −1.35907
\(669\) 6.20103e34 0.298289
\(670\) 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
\(675\) −8.18936e34 −0.352333
\(676\) 1.30691e34 0.0551966
\(677\) −7.76333e34 −0.321877 −0.160938 0.986964i \(-0.551452\pi\)
−0.160938 + 0.986964i \(0.551452\pi\)
\(678\) 7.01582e32 0.00285567
\(679\) 0 0
\(680\) 6.02265e33 0.0236280
\(681\) −7.54029e34 −0.290435
\(682\) 1.73442e33 0.00655918
\(683\) −2.49909e35 −0.927945 −0.463973 0.885850i \(-0.653576\pi\)
−0.463973 + 0.885850i \(0.653576\pi\)
\(684\) 1.65079e35 0.601853
\(685\) 4.58782e35 1.64238
\(686\) 0 0
\(687\) 1.11268e35 0.384070
\(688\) 3.38716e35 1.14810
\(689\) −8.08584e34 −0.269144
\(690\) 6.62465e32 0.00216545
\(691\) 8.56964e34 0.275098 0.137549 0.990495i \(-0.456078\pi\)
0.137549 + 0.990495i \(0.456078\pi\)
\(692\) −2.02186e35 −0.637419
\(693\) 0 0
\(694\) −4.52055e31 −0.000137467 0
\(695\) 3.59466e35 1.07361
\(696\) −1.71077e32 −0.000501854 0
\(697\) 4.63017e35 1.33410
\(698\) −1.62759e33 −0.00460630
\(699\) 9.70378e34 0.269759
\(700\) 0 0
\(701\) 4.53464e35 1.21637 0.608187 0.793793i \(-0.291897\pi\)
0.608187 + 0.793793i \(0.291897\pi\)
\(702\) 1.27101e33 0.00334914
\(703\) 1.23475e35 0.319622
\(704\) −3.17949e35 −0.808536
\(705\) 1.34295e35 0.335504
\(706\) 6.25502e32 0.00153522
\(707\) 0 0
\(708\) 8.57507e34 0.203152
\(709\) −4.93254e35 −1.14813 −0.574067 0.818808i \(-0.694635\pi\)
−0.574067 + 0.818808i \(0.694635\pi\)
\(710\) 6.85209e33 0.0156709
\(711\) 2.19776e35 0.493868
\(712\) 5.68087e33 0.0125434
\(713\) 4.07688e35 0.884522
\(714\) 0 0
\(715\) 5.10090e35 1.06862
\(716\) −8.08682e35 −1.66481
\(717\) −2.82004e34 −0.0570513
\(718\) 6.25613e33 0.0124380
\(719\) −2.13499e35 −0.417142 −0.208571 0.978007i \(-0.566881\pi\)
−0.208571 + 0.978007i \(0.566881\pi\)
\(720\) −6.75662e35 −1.29740
\(721\) 0 0
\(722\) 2.69208e33 0.00499314
\(723\) 6.25508e34 0.114026
\(724\) −2.74857e35 −0.492464
\(725\) −6.84968e34 −0.120627
\(726\) 3.52060e32 0.000609409 0
\(727\) −5.12190e35 −0.871467 −0.435734 0.900076i \(-0.643511\pi\)
−0.435734 + 0.900076i \(0.643511\pi\)
\(728\) 0 0
\(729\) −4.49296e35 −0.738649
\(730\) 1.51026e33 0.00244071
\(731\) 7.58243e35 1.20459
\(732\) 5.92283e34 0.0924998
\(733\) −1.77366e35 −0.272315 −0.136157 0.990687i \(-0.543475\pi\)
−0.136157 + 0.990687i \(0.543475\pi\)
\(734\) −9.90213e33 −0.0149461
\(735\) 0 0
\(736\) 1.54001e34 0.0224674
\(737\) −2.24709e35 −0.322312
\(738\) 7.13471e33 0.0100617
\(739\) −1.13535e36 −1.57425 −0.787124 0.616794i \(-0.788431\pi\)
−0.787124 + 0.616794i \(0.788431\pi\)
\(740\) −5.05412e35 −0.689048
\(741\) 9.72375e34 0.130349
\(742\) 0 0
\(743\) 4.03749e34 0.0523301 0.0261651 0.999658i \(-0.491670\pi\)
0.0261651 + 0.999658i \(0.491670\pi\)
\(744\) −2.70678e33 −0.00344978
\(745\) 6.71923e35 0.842104
\(746\) −1.18104e34 −0.0145556
\(747\) −7.53500e35 −0.913220
\(748\) −7.11853e35 −0.848439
\(749\) 0 0
\(750\) 3.17284e32 0.000365749 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
\(753\) −1.21727e35 −0.133490
\(754\) 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
\(759\) −1.56607e35 −0.155521
\(760\) 1.45363e34 0.0141999
\(761\) −2.02230e36 −1.94329 −0.971646 0.236440i \(-0.924019\pi\)
−0.971646 + 0.236440i \(0.924019\pi\)
\(762\) −3.15703e33 −0.00298429
\(763\) 0 0
\(764\) −1.84739e35 −0.169002
\(765\) −1.51253e36 −1.36124
\(766\) 6.38646e33 0.00565458
\(767\) −1.06576e36 −0.928358
\(768\) 2.48041e35 0.212573
\(769\) −7.71193e35 −0.650255 −0.325128 0.945670i \(-0.605407\pi\)
−0.325128 + 0.945670i \(0.605407\pi\)
\(770\) 0 0
\(771\) 4.49265e35 0.366710
\(772\) −7.00286e35 −0.562418
\(773\) −1.96060e36 −1.54934 −0.774668 0.632368i \(-0.782083\pi\)
−0.774668 + 0.632368i \(0.782083\pi\)
\(774\) 1.16839e34 0.00908501
\(775\) −1.08376e36 −0.829202
\(776\) −9.11331e33 −0.00686127
\(777\) 0 0
\(778\) −1.15444e34 −0.00841641
\(779\) 1.11754e36 0.801763
\(780\) −3.98017e35 −0.281008
\(781\) −1.61983e36 −1.12547
\(782\) 1.14902e34 0.00785674
\(783\) 8.79649e34 0.0591953
\(784\) 0 0
\(785\) 2.53393e35 0.165167
\(786\) −1.64448e33 −0.00105498
\(787\) 8.92654e35 0.563637 0.281818 0.959468i \(-0.409062\pi\)
0.281818 + 0.959468i \(0.409062\pi\)
\(788\) 2.01101e36 1.24979
\(789\) 1.51418e35 0.0926224
\(790\) 9.67606e33 0.00582586
\(791\) 0 0
\(792\) −2.19389e34 −0.0127982
\(793\) −7.36121e35 −0.422702
\(794\) −1.97826e34 −0.0111822
\(795\) −1.43874e35 −0.0800560
\(796\) 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
\(801\) −1.42669e36 −0.722643
\(802\) 3.43990e33 0.00171541
\(803\) −3.57026e35 −0.175289
\(804\) 1.75338e35 0.0847568
\(805\) 0 0
\(806\) 1.68201e34 0.00788208
\(807\) −7.09317e35 −0.327281
\(808\) −6.00231e33 −0.00272694
\(809\) −1.29617e36 −0.579834 −0.289917 0.957052i \(-0.593628\pi\)
−0.289917 + 0.957052i \(0.593628\pi\)
\(810\) −2.21498e34 −0.00975680
\(811\) −2.63606e36 −1.14339 −0.571695 0.820467i \(-0.693714\pi\)
−0.571695 + 0.820467i \(0.693714\pi\)
\(812\) 0 0
\(813\) 7.10313e35 0.298757
\(814\) −8.20458e33 −0.00339822
\(815\) 3.43691e36 1.40184
\(816\) 5.55412e35 0.223094
\(817\) 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 \(-0.535151\pi\)
−0.110205 + 0.993909i \(0.535151\pi\)
\(822\) −5.81127e33 −0.00212997
\(823\) 4.76928e35 0.172169 0.0860845 0.996288i \(-0.472564\pi\)
0.0860845 + 0.996288i \(0.472564\pi\)
\(824\) −1.56486e34 −0.00556396
\(825\) 4.16308e35 0.145794
\(826\) 0 0
\(827\) 4.17794e36 1.41953 0.709763 0.704440i \(-0.248802\pi\)
0.709763 + 0.704440i \(0.248802\pi\)
\(828\) −2.57836e36 −0.862908
\(829\) 3.18023e36 1.04840 0.524199 0.851596i \(-0.324365\pi\)
0.524199 + 0.851596i \(0.324365\pi\)
\(830\) −3.31742e34 −0.0107727
\(831\) −4.98924e35 −0.159596
\(832\) −3.08342e36 −0.971608
\(833\) 0 0
\(834\) −4.55326e33 −0.00139235
\(835\) 6.13232e36 1.84733
\(836\) −1.71814e36 −0.509893
\(837\) 1.39178e36 0.406913
\(838\) −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
\(843\) 7.04537e35 0.188390
\(844\) 2.52471e36 0.665168
\(845\) −2.89018e35 −0.0750266
\(846\) 3.58925e34 0.00918068
\(847\) 0 0
\(848\) −1.11474e36 −0.276838
\(849\) −7.48489e35 −0.183164
\(850\) −3.05443e34 −0.00736535
\(851\) −1.92855e36 −0.458258
\(852\) 1.26394e36 0.295958
\(853\) 1.75466e36 0.404884 0.202442 0.979294i \(-0.435112\pi\)
0.202442 + 0.979294i \(0.435112\pi\)
\(854\) 0 0
\(855\) −3.65065e36 −0.818075
\(856\) 1.15414e35 0.0254880
\(857\) −7.10324e36 −1.54595 −0.772976 0.634435i \(-0.781233\pi\)
−0.772976 + 0.634435i \(0.781233\pi\)
\(858\) −6.46118e33 −0.00138586
\(859\) 7.56695e36 1.59958 0.799791 0.600279i \(-0.204944\pi\)
0.799791 + 0.600279i \(0.204944\pi\)
\(860\) −7.49105e36 −1.56067
\(861\) 0 0
\(862\) 3.76241e33 0.000761423 0
\(863\) 5.72195e36 1.14132 0.570662 0.821185i \(-0.306687\pi\)
0.570662 + 0.821185i \(0.306687\pi\)
\(864\) 5.25735e34 0.0103358
\(865\) 4.47125e36 0.866418
\(866\) 3.03971e34 0.00580575
\(867\) 1.13423e35 0.0213532
\(868\) 0 0
\(869\) −2.28742e36 −0.418407
\(870\) 1.89158e33 0.000341063 0
\(871\) −2.17919e36 −0.387318
\(872\) −1.53903e35 −0.0269645
\(873\) 2.28871e36 0.395288
\(874\) 2.77328e34 0.00472173
\(875\) 0 0
\(876\) 2.78583e35 0.0460949
\(877\) 3.21926e36 0.525123 0.262561 0.964915i \(-0.415433\pi\)
0.262561 + 0.964915i \(0.415433\pi\)
\(878\) −7.11834e34 −0.0114471
\(879\) −2.54558e34 −0.00403576
\(880\) 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
\(885\) −1.89634e36 −0.276137
\(886\) 5.80326e34 0.00833202
\(887\) 2.52904e36 0.358022 0.179011 0.983847i \(-0.442710\pi\)
0.179011 + 0.983847i \(0.442710\pi\)
\(888\) 1.28043e34 0.00178728
\(889\) 0 0
\(890\) −6.28128e34 −0.00852458
\(891\) 5.23622e36 0.700723
\(892\) −1.06258e37 −1.40217
\(893\) 5.62202e36 0.731558
\(894\) −8.51107e33 −0.00109211
\(895\) 1.78836e37 2.26291
\(896\) 0 0
\(897\) −1.51875e36 −0.186887
\(898\) 4.55453e34 0.00552700
\(899\) 1.16410e36 0.139314
\(900\) 6.85405e36 0.808939
\(901\) −2.49544e36 −0.290460
\(902\) −7.42578e34 −0.00852433
\(903\) 0 0
\(904\) −2.40448e35 −0.0268483
\(905\) 6.07833e36 0.669387
\(906\) −1.09202e34 −0.00118612
\(907\) −4.93129e36 −0.528286 −0.264143 0.964484i \(-0.585089\pi\)
−0.264143 + 0.964484i \(0.585089\pi\)
\(908\) 1.29207e37 1.36525
\(909\) 1.50742e36 0.157103
\(910\) 0 0
\(911\) −7.10548e36 −0.720466 −0.360233 0.932862i \(-0.617303\pi\)
−0.360233 + 0.932862i \(0.617303\pi\)
\(912\) 1.34055e36 0.134075
\(913\) 7.84240e36 0.773685
\(914\) −9.15090e34 −0.00890505
\(915\) −1.30981e36 −0.125731
\(916\) −1.90664e37 −1.80541
\(917\) 0 0
\(918\) 3.92255e34 0.00361439
\(919\) 2.64155e36 0.240112 0.120056 0.992767i \(-0.461693\pi\)
0.120056 + 0.992767i \(0.461693\pi\)
\(920\) −2.27042e35 −0.0203591
\(921\) −2.81179e36 −0.248735
\(922\) −2.19009e33 −0.000191129 0
\(923\) −1.57089e37 −1.35246
\(924\) 0 0
\(925\) 5.12665e36 0.429597
\(926\) −1.02490e35 −0.00847316
\(927\) 3.92997e36 0.320548
\(928\) 4.39731e34 0.00353865
\(929\) −5.01934e36 −0.398520 −0.199260 0.979947i \(-0.563854\pi\)
−0.199260 + 0.979947i \(0.563854\pi\)
\(930\) 2.99286e34 0.00234450
\(931\) 0 0
\(932\) −1.66280e37 −1.26806
\(933\) 4.39835e36 0.330955
\(934\) −1.28268e35 −0.00952320
\(935\) 1.57423e37 1.15325
\(936\) −2.12760e35 −0.0153795
\(937\) 1.70189e37 1.21391 0.606956 0.794735i \(-0.292390\pi\)
0.606956 + 0.794735i \(0.292390\pi\)
\(938\) 0 0
\(939\) 2.70123e35 0.0187604
\(940\) −2.30123e37 −1.57711
\(941\) 1.51254e37 1.02291 0.511455 0.859310i \(-0.329107\pi\)
0.511455 + 0.859310i \(0.329107\pi\)
\(942\) −3.20967e33 −0.000214202 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 \(-0.483557\pi\)
0.0516351 + 0.998666i \(0.483557\pi\)
\(948\) 1.78485e36 0.110026
\(949\) −3.46238e36 −0.210643
\(950\) −7.37220e34 −0.00442642
\(951\) −2.01260e36 −0.119262
\(952\) 0 0
\(953\) 2.77784e37 1.60341 0.801706 0.597718i \(-0.203926\pi\)
0.801706 + 0.597718i \(0.203926\pi\)
\(954\) −3.84526e34 −0.00219064
\(955\) 4.08541e36 0.229717
\(956\) 4.83229e36 0.268182
\(957\) −4.47171e35 −0.0244948
\(958\) 9.46752e34 0.00511879
\(959\) 0 0
\(960\) −5.48644e36 −0.289001
\(961\) −8.14395e35 −0.0423441
\(962\) −7.95666e34 −0.00408359
\(963\) −2.89850e37 −1.46840
\(964\) −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
\(969\) 3.00093e36 0.140672
\(970\) 1.00765e35 0.00466297
\(971\) 1.67087e37 0.763311 0.381655 0.924305i \(-0.375354\pi\)
0.381655 + 0.924305i \(0.375354\pi\)
\(972\) −1.33050e37 −0.600049
\(973\) 0 0
\(974\) 1.90256e34 0.000836277 0
\(975\) 4.03728e36 0.175199
\(976\) −1.01484e37 −0.434786
\(977\) −3.54376e37 −1.49893 −0.749466 0.662043i \(-0.769690\pi\)
−0.749466 + 0.662043i \(0.769690\pi\)
\(978\) −4.35345e34 −0.00181802
\(979\) 1.48490e37 0.612227
\(980\) 0 0
\(981\) 3.86512e37 1.55346
\(982\) 3.46860e35 0.0137645
\(983\) −2.26759e37 −0.888476 −0.444238 0.895909i \(-0.646525\pi\)
−0.444238 + 0.895909i \(0.646525\pi\)
\(984\) 1.15889e35 0.00448335
\(985\) −4.44726e37 −1.69879
\(986\) 3.28087e34 0.00123745
\(987\) 0 0
\(988\) −1.66622e37 −0.612732
\(989\) −2.85843e37 −1.03794
\(990\) 2.42576e35 0.00869777
\(991\) −1.82706e36 −0.0646891 −0.0323445 0.999477i \(-0.510297\pi\)
−0.0323445 + 0.999477i \(0.510297\pi\)
\(992\) 6.95742e35 0.0243250
\(993\) −1.12657e36 −0.0388949
\(994\) 0 0
\(995\) −1.66237e36 −0.0559680
\(996\) −6.11932e36 −0.203452
\(997\) −2.34599e37 −0.770260 −0.385130 0.922862i \(-0.625843\pi\)
−0.385130 + 0.922862i \(0.625843\pi\)
\(998\) −3.93518e35 −0.0127595
\(999\) −6.58373e36 −0.210816
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 49.26.a.a.1.1 1
7.6 odd 2 1.26.a.a.1.1 1
21.20 even 2 9.26.a.a.1.1 1
28.27 even 2 16.26.a.b.1.1 1
35.13 even 4 25.26.b.a.24.2 2
35.27 even 4 25.26.b.a.24.1 2
35.34 odd 2 25.26.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.26.a.a.1.1 1 7.6 odd 2
9.26.a.a.1.1 1 21.20 even 2
16.26.a.b.1.1 1 28.27 even 2
25.26.a.a.1.1 1 35.34 odd 2
25.26.b.a.24.1 2 35.27 even 4
25.26.b.a.24.2 2 35.13 even 4
49.26.a.a.1.1 1 1.1 even 1 trivial