Properties

Label 1.26.a.a.1.1
Level $1$
Weight $26$
Character 1.1
Self dual yes
Analytic conductor $3.960$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.95996779952\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q-48.0000 q^{2} -195804. q^{3} -3.35521e7 q^{4} -7.41990e8 q^{5} +9.39859e6 q^{6} +3.90806e10 q^{7} +3.22111e9 q^{8} -8.08949e11 q^{9} +O(q^{10})\) \(q-48.0000 q^{2} -195804. q^{3} -3.35521e7 q^{4} -7.41990e8 q^{5} +9.39859e6 q^{6} +3.90806e10 q^{7} +3.22111e9 q^{8} -8.08949e11 q^{9} +3.56155e10 q^{10} +8.41952e12 q^{11} +6.56964e12 q^{12} -8.16510e13 q^{13} -1.87587e12 q^{14} +1.45285e14 q^{15} +1.12567e15 q^{16} -2.51990e15 q^{17} +3.88296e13 q^{18} -6.08206e15 q^{19} +2.48953e16 q^{20} -7.65214e15 q^{21} -4.04137e14 q^{22} -9.49953e16 q^{23} -6.30707e14 q^{24} +2.52526e17 q^{25} +3.91925e15 q^{26} +3.24298e17 q^{27} -1.31124e18 q^{28} -2.71247e17 q^{29} -6.97366e15 q^{30} +4.29167e18 q^{31} -1.62115e17 q^{32} -1.64857e18 q^{33} +1.20955e17 q^{34} -2.89974e19 q^{35} +2.71420e19 q^{36} +2.03015e19 q^{37} +2.91939e17 q^{38} +1.59876e19 q^{39} -2.39003e18 q^{40} -1.83744e20 q^{41} +3.67303e17 q^{42} +3.00902e20 q^{43} -2.82493e20 q^{44} +6.00232e20 q^{45} +4.55977e18 q^{46} -9.24361e20 q^{47} -2.20410e20 q^{48} +1.86224e20 q^{49} -1.21212e19 q^{50} +4.93407e20 q^{51} +2.73957e21 q^{52} -9.90292e20 q^{53} -1.55663e19 q^{54} -6.24719e21 q^{55} +1.25883e20 q^{56} +1.19089e21 q^{57} +1.30199e19 q^{58} +1.30526e22 q^{59} -4.87461e21 q^{60} +9.01545e21 q^{61} -2.06000e20 q^{62} -3.16142e22 q^{63} -3.77634e22 q^{64} +6.05842e22 q^{65} +7.91316e19 q^{66} -2.66891e22 q^{67} +8.45480e22 q^{68} +1.86005e22 q^{69} +1.39188e21 q^{70} -1.92391e23 q^{71} -2.60572e21 q^{72} +4.24046e22 q^{73} -9.74471e20 q^{74} -4.94455e22 q^{75} +2.04066e23 q^{76} +3.29040e23 q^{77} -7.67405e20 q^{78} -2.71681e23 q^{79} -8.35234e23 q^{80} +6.21915e23 q^{81} +8.81972e21 q^{82} -9.31454e23 q^{83} +2.56745e23 q^{84} +1.86974e24 q^{85} -1.44433e22 q^{86} +5.31112e22 q^{87} +2.71202e22 q^{88} -1.76364e24 q^{89} -2.88111e22 q^{90} -3.19097e24 q^{91} +3.18729e24 q^{92} -8.40325e23 q^{93} +4.43693e22 q^{94} +4.51282e24 q^{95} +3.17427e22 q^{96} +2.82924e24 q^{97} -8.93877e21 q^{98} -6.81096e24 q^{99} +O(q^{100})\)

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 \(-0.533919\pi\)
−0.106359 + 0.994328i \(0.533919\pi\)
\(4\) −3.35521e7 −0.999931
\(5\) −7.41990e8 −1.35917 −0.679584 0.733598i \(-0.737840\pi\)
−0.679584 + 0.733598i \(0.737840\pi\)
\(6\) 9.39859e6 0.00176267
\(7\) 3.90806e10 1.06718 0.533588 0.845745i \(-0.320843\pi\)
0.533588 + 0.845745i \(0.320843\pi\)
\(8\) 3.22111e9 0.0165722
\(9\) −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 \(-0.661546\pi\)
−0.486004 + 0.873957i \(0.661546\pi\)
\(14\) −1.87587e12 −0.00884305
\(15\) 1.45285e14 0.289120
\(16\) 1.12567e15 0.999794
\(17\) −2.51990e15 −1.04899 −0.524496 0.851413i \(-0.675746\pi\)
−0.524496 + 0.851413i \(0.675746\pi\)
\(18\) 3.88296e13 0.00791145
\(19\) −6.08206e15 −0.630421 −0.315210 0.949022i \(-0.602075\pi\)
−0.315210 + 0.949022i \(0.602075\pi\)
\(20\) 2.48953e16 1.35907
\(21\) −7.65214e15 −0.227008
\(22\) −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
\(28\) −1.31124e18 −1.06710
\(29\) −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 \(-0.337253\pi\)
0.489299 + 0.872116i \(0.337253\pi\)
\(32\) −1.62115e17 −0.0248569
\(33\) −1.64857e18 −0.172062
\(34\) 1.20955e17 0.00869237
\(35\) −2.89974e19 −1.45047
\(36\) 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 \(-0.719369\pi\)
−0.635895 + 0.771775i \(0.719369\pi\)
\(42\) 3.67303e17 0.00188108
\(43\) 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 \(-0.697031\pi\)
−0.580214 + 0.814464i \(0.697031\pi\)
\(48\) −2.20410e20 −0.212675
\(49\) 1.86224e20 0.138863
\(50\) −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
\(56\) 1.25883e20 0.0176855
\(57\) 1.19089e21 0.134102
\(58\) 1.30199e19 0.00117966
\(59\) 1.30526e22 0.955093 0.477547 0.878606i \(-0.341526\pi\)
0.477547 + 0.878606i \(0.341526\pi\)
\(60\) −4.87461e21 −0.289101
\(61\) 9.01545e21 0.434875 0.217438 0.976074i \(-0.430230\pi\)
0.217438 + 0.976074i \(0.430230\pi\)
\(62\) −2.06000e20 −0.00810907
\(63\) −3.16142e22 −1.01889
\(64\) −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
\(70\) 1.39188e21 0.0120192
\(71\) −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 \(-0.465442\pi\)
0.108355 + 0.994112i \(0.465442\pi\)
\(74\) −9.74471e20 −0.00420119
\(75\) −4.94455e22 −0.180244
\(76\) 2.04066e23 0.630377
\(77\) 3.29040e23 0.863206
\(78\) −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 \(-0.658729\pi\)
−0.478251 + 0.878223i \(0.658729\pi\)
\(84\) 2.56745e23 0.226993
\(85\) 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 \(-0.623541\pi\)
−0.378446 + 0.925623i \(0.623541\pi\)
\(90\) −2.88111e22 −0.0107530
\(91\) −3.19097e24 −1.03730
\(92\) 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 \(-0.433626\pi\)
0.207011 + 0.978339i \(0.433626\pi\)
\(98\) −8.93877e21 −0.00115067
\(99\) −6.81096e24 −0.772269
\(100\) −8.47278e24 −0.847278
\(101\) 1.86342e24 0.164549 0.0822744 0.996610i \(-0.473782\pi\)
0.0822744 + 0.996610i \(0.473782\pi\)
\(102\) −2.36835e22 −0.00184903
\(103\) 4.85812e24 0.335740 0.167870 0.985809i \(-0.446311\pi\)
0.167870 + 0.985809i \(0.446311\pi\)
\(104\) −2.63007e23 −0.0161084
\(105\) 5.67781e24 0.308542
\(106\) 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
\(112\) 4.39918e25 1.06696
\(113\) −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
\(119\) −9.84792e25 −1.11946
\(120\) 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
\(126\) 1.51748e24 0.00844291
\(127\) 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 \(-0.596739\pi\)
−0.299257 + 0.954173i \(0.596739\pi\)
\(132\) 5.53132e25 0.172050
\(133\) −2.37690e26 −0.672769
\(134\) 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 \(-0.629239\pi\)
−0.394952 + 0.918702i \(0.629239\pi\)
\(140\) 9.72925e26 1.45037
\(141\) 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
\(147\) −3.64635e25 −0.0295387
\(148\) −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
\(154\) −1.57939e25 −0.00715287
\(155\) −3.18437e27 −1.33008
\(156\) −5.36418e26 −0.206750
\(157\) −3.41505e26 −0.121521 −0.0607605 0.998152i \(-0.519353\pi\)
−0.0607605 + 0.998152i \(0.519353\pi\)
\(158\) 1.30407e25 0.00428634
\(159\) 1.93903e26 0.0589008
\(160\) 1.20287e26 0.0337847
\(161\) −3.71247e27 −0.964583
\(162\) −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 \(-0.737838\pi\)
−0.679581 + 0.733600i \(0.737838\pi\)
\(168\) −2.46484e25 −0.00376204
\(169\) −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 \(-0.603257\pi\)
−0.318731 + 0.947845i \(0.603257\pi\)
\(174\) −2.54934e24 −0.000250935 0
\(175\) 9.86886e27 0.904256
\(176\) 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 \(-0.579198\pi\)
−0.246249 + 0.969207i \(0.579198\pi\)
\(182\) 1.53167e26 0.00859551
\(183\) −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
\(189\) 1.26738e28 0.443744
\(190\) −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
\(196\) −6.24823e27 −0.138853
\(197\) −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 \(-0.493446\pi\)
0.0205891 + 0.999788i \(0.493446\pi\)
\(200\) 8.13414e26 0.0140423
\(201\) 5.22583e27 0.0847626
\(202\) −8.94444e25 −0.00136352
\(203\) −1.06005e28 −0.151924
\(204\) −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
\(210\) −2.72535e26 −0.00255671
\(211\) −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
\(217\) 1.67721e29 1.04434
\(218\) 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 \(-0.747323\pi\)
−0.701135 + 0.713029i \(0.747323\pi\)
\(224\) −6.33554e27 −0.0265267
\(225\) −2.04281e29 −0.808994
\(226\) 3.58308e27 0.0134246
\(227\) 3.85094e29 1.36535 0.682674 0.730723i \(-0.260817\pi\)
0.682674 + 0.730723i \(0.260817\pi\)
\(228\) −3.99569e28 −0.134093
\(229\) −5.68261e29 −1.80553 −0.902765 0.430134i \(-0.858466\pi\)
−0.902765 + 0.430134i \(0.858466\pi\)
\(230\) −3.38331e27 −0.0101799
\(231\) −6.44273e28 −0.183620
\(232\) −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
\(238\) 4.72700e27 0.00927628
\(239\) −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 \(-0.586369\pi\)
−0.268020 + 0.963413i \(0.586369\pi\)
\(242\) 1.79802e27 0.00286486
\(243\) −3.96547e29 −0.600090
\(244\) −3.02488e29 −0.434845
\(245\) −1.38177e29 −0.188738
\(246\) −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 \(-0.398407\pi\)
0.313771 + 0.949499i \(0.398407\pi\)
\(252\) 1.06072e30 1.01882
\(253\) −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 \(-0.830763\pi\)
−0.861960 + 0.506977i \(0.830763\pi\)
\(258\) 2.82805e27 0.00202414
\(259\) 7.93394e29 0.541056
\(260\) −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
\(266\) 1.14091e28 0.00557484
\(267\) 3.45327e29 0.161005
\(268\) 8.95475e29 0.398445
\(269\) 3.62259e30 1.53856 0.769282 0.638910i \(-0.220614\pi\)
0.769282 + 0.638910i \(0.220614\pi\)
\(270\) 1.15500e28 0.00468313
\(271\) −3.62767e30 −1.40447 −0.702234 0.711946i \(-0.747814\pi\)
−0.702234 + 0.711946i \(0.747814\pi\)
\(272\) −2.83657e30 −1.04877
\(273\) 6.24805e29 0.220654
\(274\) −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
\(280\) −9.34040e28 −0.0240375
\(281\) 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 \(-0.358327\pi\)
0.430530 + 0.902576i \(0.358327\pi\)
\(284\) 6.45511e30 1.39131
\(285\) −8.83629e29 −0.182267
\(286\) 3.29982e28 0.00651500
\(287\) −7.18084e30 −1.35722
\(288\) 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 \(-0.496980\pi\)
0.00948615 + 0.999955i \(0.496980\pi\)
\(294\) 1.75025e27 0.000244770 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
\(301\) 1.17594e31 1.22548
\(302\) −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 \(-0.301229\pi\)
0.584657 + 0.811281i \(0.301229\pi\)
\(308\) −1.10400e31 −0.863146
\(309\) −9.51239e29 −0.0714182
\(310\) 1.52850e29 0.0110216
\(311\) −2.24630e31 −1.55584 −0.777918 0.628366i \(-0.783724\pi\)
−0.777918 + 0.628366i \(0.783724\pi\)
\(312\) 5.14979e28 0.00342655
\(313\) −1.37956e30 −0.0881934 −0.0440967 0.999027i \(-0.514041\pi\)
−0.0440967 + 0.999027i \(0.514041\pi\)
\(314\) 1.63922e28 0.00100697
\(315\) 2.34574e31 1.38484
\(316\) 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
\(322\) 1.78199e29 0.00799293
\(323\) 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
\(329\) −3.61246e31 −1.23838
\(330\) −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
\(336\) −8.61377e30 −0.226961
\(337\) 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
\(343\) −4.51320e31 −0.918984
\(344\) 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 \(-0.589653\pi\)
−0.277943 + 0.960598i \(0.589653\pi\)
\(350\) −4.73705e29 −0.00749303
\(351\) −2.64793e31 −0.404173
\(352\) −1.36493e30 −0.0201060
\(353\) 1.30313e31 0.185269 0.0926346 0.995700i \(-0.470471\pi\)
0.0926346 + 0.995700i \(0.470471\pi\)
\(354\) 1.22676e29 0.00168352
\(355\) 1.42752e32 1.89116
\(356\) 5.91737e31 0.756840
\(357\) 1.92826e31 0.238130
\(358\) −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
\(364\) 1.07064e32 1.03723
\(365\) −3.14638e31 −0.294544
\(366\) 8.47325e28 0.000766543 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
\(369\) 1.48640e32 1.21424
\(370\) 7.23048e29 0.00571012
\(371\) −3.87012e31 −0.295495
\(372\) 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
\(378\) −6.08341e29 −0.00367705
\(379\) 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 \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(384\) −1.42003e30 −0.00704949
\(385\) −2.44144e32 −1.17324
\(386\) −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
\(392\) 5.99850e29 0.00230127
\(393\) 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 \(-0.735740\pi\)
−0.674730 + 0.738065i \(0.735740\pi\)
\(398\) −1.07540e29 −0.000341219 0
\(399\) 4.65407e31 0.143111
\(400\) 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
\(406\) 5.08824e29 0.00125890
\(407\) 1.70929e32 0.410095
\(408\) 1.58932e30 0.00369793
\(409\) 1.34430e32 0.303358 0.151679 0.988430i \(-0.451532\pi\)
0.151679 + 0.988430i \(0.451532\pi\)
\(410\) −6.54415e30 −0.0143237
\(411\) −1.21068e32 −0.257044
\(412\) −1.63000e32 −0.335717
\(413\) 5.10102e32 1.01925
\(414\) −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 \(-0.545799\pi\)
−0.143387 + 0.989667i \(0.545799\pi\)
\(420\) −1.90503e32 −0.308521
\(421\) −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
\(427\) 3.52329e32 0.464088
\(428\) −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 \(-0.386074\pi\)
0.350318 + 0.936631i \(0.386074\pi\)
\(434\) −8.05060e30 −0.00865380
\(435\) −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 \(-0.742705\pi\)
−0.690718 + 0.723124i \(0.742705\pi\)
\(440\) −2.01229e31 −0.0182193
\(441\) −1.50646e32 −0.132579
\(442\) −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
\(448\) −1.47581e33 −1.06674
\(449\) −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
\(455\) 2.36767e33 1.40987
\(456\) 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 \(-0.503671\pi\)
−0.0115327 + 0.999933i \(0.503671\pi\)
\(462\) 3.09251e30 0.00152155
\(463\) 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 \(-0.694853\pi\)
−0.574628 + 0.818415i \(0.694853\pi\)
\(468\) −2.21617e33 −0.927962
\(469\) −1.04302e33 −0.425240
\(470\) −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
\(476\) 3.30419e33 1.11938
\(477\) 8.01096e32 0.264366
\(478\) 6.91313e30 0.00222242
\(479\) 1.97240e33 0.617733 0.308867 0.951105i \(-0.400050\pi\)
0.308867 + 0.951105i \(0.400050\pi\)
\(480\) −2.35528e31 −0.00718665
\(481\) −1.65764e33 −0.492806
\(482\) 1.53339e31 0.00444185
\(483\) 7.26917e32 0.205185
\(484\) 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
\(490\) 6.63248e30 0.00156396
\(491\) −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
\(497\) −7.51874e33 −1.48488
\(498\) −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 \(-0.368443\pi\)
0.401633 + 0.915801i \(0.368443\pi\)
\(504\) −1.01833e32 −0.0168852
\(505\) −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 \(-0.453897\pi\)
0.144332 + 0.989529i \(0.453897\pi\)
\(510\) 1.75729e31 0.00251314
\(511\) 1.65720e33 0.231267
\(512\) −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
\(518\) −3.80829e31 −0.00448341
\(519\) 1.17992e33 0.135600
\(520\) 1.95149e32 0.0218940
\(521\) 7.39782e33 0.810274 0.405137 0.914256i \(-0.367224\pi\)
0.405137 + 0.914256i \(0.367224\pi\)
\(522\) −1.05324e31 −0.00112628
\(523\) 1.70332e34 1.77838 0.889191 0.457535i \(-0.151268\pi\)
0.889191 + 0.457535i \(0.151268\pi\)
\(524\) 5.87063e33 0.598472
\(525\) −1.93236e33 −0.192352
\(526\) −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
\(532\) 7.97502e33 0.672723
\(533\) 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
\(539\) 1.56792e33 0.112322
\(540\) 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
\(546\) −2.99906e31 −0.00182843
\(547\) 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
\(553\) −1.06175e34 −0.552022
\(554\) 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
\(560\) −3.26415e34 −1.45017
\(561\) 4.15424e33 0.180491
\(562\) −1.72712e32 −0.00733870
\(563\) −1.80804e34 −0.751371 −0.375685 0.926747i \(-0.622593\pi\)
−0.375685 + 0.926747i \(0.622593\pi\)
\(564\) −6.07272e33 −0.246828
\(565\) 5.53878e34 2.20195
\(566\) −1.83487e32 −0.00713510
\(567\) 2.43048e34 0.924493
\(568\) −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
\(574\) 3.44680e32 0.0112465
\(575\) −2.39888e34 −0.765878
\(576\) 3.05487e34 0.954357
\(577\) −7.31490e31 −0.00223620 −0.00111810 0.999999i \(-0.500356\pi\)
−0.00111810 + 0.999999i \(0.500356\pi\)
\(578\) −2.78049e31 −0.000831808 0
\(579\) −4.08674e33 −0.119645
\(580\) −6.75278e33 −0.193479
\(581\) −3.64018e34 −1.02075
\(582\) 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 \(-0.280360\pi\)
0.636551 + 0.771234i \(0.280360\pi\)
\(588\) 1.22343e33 0.0295367
\(589\) −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 \(-0.415823\pi\)
0.261379 + 0.965236i \(0.415823\pi\)
\(594\) −1.31061e32 −0.00278703
\(595\) 7.30706e34 1.52153
\(596\) −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 \(-0.588975\pi\)
−0.275896 + 0.961187i \(0.588975\pi\)
\(602\) −5.64452e32 −0.0101548
\(603\) 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 \(-0.805459\pi\)
−0.818978 + 0.573825i \(0.805459\pi\)
\(608\) 9.85991e32 0.0156703
\(609\) 2.07562e33 0.0323170
\(610\) 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
\(616\) 1.05987e33 0.0143053
\(617\) 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 \(-0.208781\pi\)
0.792496 + 0.609878i \(0.208781\pi\)
\(620\) 1.06842e35 1.32999
\(621\) −3.08068e34 −0.375839
\(622\) 1.07823e33 0.0128923
\(623\) −6.89239e34 −0.807736
\(624\) 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
\(630\) −1.12596e33 −0.0114753
\(631\) 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
\(637\) −1.52054e34 −0.134976
\(638\) 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 \(-0.433456\pi\)
0.207535 + 0.978228i \(0.433456\pi\)
\(644\) 1.24561e35 0.964517
\(645\) 4.37164e34 0.332008
\(646\) −7.35656e32 −0.00547985
\(647\) −2.03021e35 −1.48333 −0.741665 0.670770i \(-0.765964\pi\)
−0.741665 + 0.670770i \(0.765964\pi\)
\(648\) 2.00326e33 0.0143565
\(649\) 1.09896e35 0.772546
\(650\) 9.89711e32 0.00682483
\(651\) −3.28404e34 −0.222150
\(652\) −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
\(658\) 1.73398e33 0.0102617
\(659\) −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 \(-0.425445\pi\)
0.232086 + 0.972695i \(0.425445\pi\)
\(662\) 2.76171e32 0.00151514
\(663\) −4.02872e34 −0.216894
\(664\) −3.00032e33 −0.0158514
\(665\) 1.76364e35 0.914406
\(666\) 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
\(672\) 1.24052e33 0.00564273
\(673\) −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 \(-0.448548\pi\)
0.160938 + 0.986964i \(0.448548\pi\)
\(678\) −7.01582e32 −0.00285567
\(679\) 1.10568e35 0.441834
\(680\) 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
\(686\) 2.16634e33 0.00761508
\(687\) 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 \(-0.543922\pi\)
−0.137549 + 0.990495i \(0.543922\pi\)
\(692\) 2.02186e35 0.637419
\(693\) −2.66176e35 −0.824146
\(694\) −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
\(700\) −3.31121e35 −0.904193
\(701\) 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
\(707\) 7.28238e34 0.175602
\(708\) 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
\(714\) −9.25566e32 −0.00197324
\(715\) 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 \(-0.433119\pi\)
0.208571 + 0.978007i \(0.433119\pi\)
\(720\) 6.75662e35 1.29740
\(721\) 1.89858e35 0.358293
\(722\) 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 \(-0.356489\pi\)
0.435734 + 0.900076i \(0.356489\pi\)
\(728\) −1.02785e34 −0.0171904
\(729\) −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 \(-0.456525\pi\)
0.136157 + 0.990687i \(0.456525\pi\)
\(734\) 9.90213e33 0.0149461
\(735\) 2.70555e34 0.0401481
\(736\) 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
\(742\) 1.85766e33 0.00244860
\(743\) 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
\(749\) 1.40027e36 1.64131
\(750\) 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
\(756\) −4.25232e35 −0.443714
\(757\) 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 \(-0.0759807\pi\)
0.971646 + 0.236440i \(0.0759807\pi\)
\(762\) 3.15703e33 0.00298429
\(763\) −1.86725e36 −1.73639
\(764\) −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 \(-0.394593\pi\)
0.325128 + 0.945670i \(0.394593\pi\)
\(770\) 1.17189e34 0.00972195
\(771\) 4.49265e35 0.366710
\(772\) −7.00286e35 −0.562418
\(773\) 1.96060e36 1.54934 0.774668 0.632368i \(-0.217917\pi\)
0.774668 + 0.632368i \(0.217917\pi\)
\(774\) 1.16839e34 0.00908501
\(775\) 1.08376e36 0.829202
\(776\) 9.11331e33 0.00686127
\(777\) −1.55350e35 −0.115093
\(778\) −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
\(784\) 2.09627e35 0.138834
\(785\) 2.53393e35 0.165167
\(786\) −1.64448e33 −0.00105498
\(787\) −8.92654e35 −0.563637 −0.281818 0.959468i \(-0.590938\pi\)
−0.281818 + 0.959468i \(0.590938\pi\)
\(788\) 2.01101e36 1.24979
\(789\) −1.51418e35 −0.0926224
\(790\) −9.67606e33 −0.00582586
\(791\) −2.91727e36 −1.72890
\(792\) −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 \(-0.718968\pi\)
−0.634921 + 0.772577i \(0.718968\pi\)
\(798\) −2.23396e33 −0.00118587
\(799\) 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
\(805\) 2.75462e36 1.31103
\(806\) 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 \(-0.306286\pi\)
0.571695 + 0.820467i \(0.306286\pi\)
\(812\) 3.55669e35 0.151913
\(813\) 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
\(819\) 2.58133e36 0.990366
\(820\) −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
\(826\) −2.44849e34 −0.00844594
\(827\) 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 \(-0.675635\pi\)
−0.524199 + 0.851596i \(0.675635\pi\)
\(830\) −3.31742e34 −0.0107727
\(831\) 4.98924e35 0.159596
\(832\) 3.08342e36 0.971608
\(833\) −4.69267e35 −0.145666
\(834\) −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 \(-0.669217\pi\)
−0.506922 + 0.861992i \(0.669217\pi\)
\(840\) 1.82889e34 0.00511324
\(841\) −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
\(847\) −1.46391e36 −0.368954
\(848\) −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 \(-0.564888\pi\)
−0.202442 + 0.979294i \(0.564888\pi\)
\(854\) −1.69118e34 −0.00384562
\(855\) −3.65065e36 −0.818075
\(856\) 1.15414e35 0.0254880
\(857\) 7.10324e36 1.54595 0.772976 0.634435i \(-0.218767\pi\)
0.772976 + 0.634435i \(0.218767\pi\)
\(858\) −6.46118e33 −0.00138586
\(859\) −7.56695e36 −1.59958 −0.799791 0.600279i \(-0.795056\pi\)
−0.799791 + 0.600279i \(0.795056\pi\)
\(860\) 7.49105e36 1.56067
\(861\) 1.40604e36 0.288707
\(862\) 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
\(868\) −5.62739e36 −1.04426
\(869\) −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
\(875\) 1.31931e36 0.221435
\(876\) 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 \(-0.798475\pi\)
−0.806191 + 0.591655i \(0.798475\pi\)
\(882\) 7.23102e33 0.00109861
\(883\) 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 \(-0.557290\pi\)
−0.179011 + 0.983847i \(0.557290\pi\)
\(888\) −1.28043e34 −0.00178728
\(889\) 1.31273e37 1.80678
\(890\) −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
\(896\) 2.83425e35 0.0353661
\(897\) −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
\(903\) −2.30254e36 −0.260682
\(904\) −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
\(910\) −1.13648e35 −0.0116827
\(911\) −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
\(917\) −6.83795e36 −0.638718
\(918\) 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
\(924\) 2.16167e36 0.183607
\(925\) 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 \(-0.436146\pi\)
0.199260 + 0.979947i \(0.436146\pi\)
\(930\) −2.99286e34 −0.00234450
\(931\) −1.13263e36 −0.0875419
\(932\) −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 \(-0.707610\pi\)
−0.606956 + 0.794735i \(0.707610\pi\)
\(938\) 5.00652e34 0.00352371
\(939\) 2.70123e35 0.0187604
\(940\) −2.30123e37 −1.57711
\(941\) −1.51254e37 −1.02291 −0.511455 0.859310i \(-0.670893\pi\)
−0.511455 + 0.859310i \(0.670893\pi\)
\(942\) −3.20967e33 −0.000214202 0
\(943\) 1.74548e37 1.14953
\(944\) 1.46929e37 0.954897
\(945\) −9.40380e36 −0.603123
\(946\) −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
\(952\) −3.17213e35 −0.0185519
\(953\) 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
\(959\) 2.41640e37 1.28955
\(960\) −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
\(966\) −3.48920e34 −0.00170025
\(967\) 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 \(-0.624646\pi\)
−0.381655 + 0.924305i \(0.624646\pi\)
\(972\) 1.33050e37 0.600049
\(973\) −1.89331e37 −0.842967
\(974\) 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
\(980\) 4.63612e36 0.188725
\(981\) 3.86512e37 1.55346
\(982\) 3.46860e35 0.0137645
\(983\) 2.26759e37 0.888476 0.444238 0.895909i \(-0.353475\pi\)
0.444238 + 0.895909i \(0.353475\pi\)
\(984\) 1.15889e35 0.00448335
\(985\) 4.44726e37 1.69879
\(986\) −3.28087e34 −0.00123745
\(987\) 7.07334e36 0.263427
\(988\) −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
\(994\) 3.60899e35 0.0123043
\(995\) −1.66237e36 −0.0559680
\(996\) −6.11932e36 −0.203452
\(997\) 2.34599e37 0.770260 0.385130 0.922862i \(-0.374157\pi\)
0.385130 + 0.922862i \(0.374157\pi\)
\(998\) −3.93518e35 −0.0127595
\(999\) 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 1.26.a.a.1.1 1
3.2 odd 2 9.26.a.a.1.1 1
4.3 odd 2 16.26.a.b.1.1 1
5.2 odd 4 25.26.b.a.24.1 2
5.3 odd 4 25.26.b.a.24.2 2
5.4 even 2 25.26.a.a.1.1 1
7.6 odd 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 1.1 even 1 trivial
9.26.a.a.1.1 1 3.2 odd 2
16.26.a.b.1.1 1 4.3 odd 2
25.26.a.a.1.1 1 5.4 even 2
25.26.b.a.24.1 2 5.2 odd 4
25.26.b.a.24.2 2 5.3 odd 4
49.26.a.a.1.1 1 7.6 odd 2