Properties

Label 177.12.a.a.1.20
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $26$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(1\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+40.1266 q^{2} -243.000 q^{3} -437.857 q^{4} +10858.4 q^{5} -9750.76 q^{6} -2158.10 q^{7} -99749.0 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+40.1266 q^{2} -243.000 q^{3} -437.857 q^{4} +10858.4 q^{5} -9750.76 q^{6} -2158.10 q^{7} -99749.0 q^{8} +59049.0 q^{9} +435712. q^{10} -558147. q^{11} +106399. q^{12} +1.91592e6 q^{13} -86597.0 q^{14} -2.63860e6 q^{15} -3.10585e6 q^{16} +3.75206e6 q^{17} +2.36943e6 q^{18} -1.12096e7 q^{19} -4.75444e6 q^{20} +524417. q^{21} -2.23966e7 q^{22} -2.13872e7 q^{23} +2.42390e7 q^{24} +6.90776e7 q^{25} +7.68793e7 q^{26} -1.43489e7 q^{27} +944937. q^{28} -6.39291e7 q^{29} -1.05878e8 q^{30} -1.05258e7 q^{31} +7.96585e7 q^{32} +1.35630e8 q^{33} +1.50557e8 q^{34} -2.34336e7 q^{35} -2.58550e7 q^{36} +1.08708e8 q^{37} -4.49804e8 q^{38} -4.65568e8 q^{39} -1.08312e9 q^{40} +4.74439e8 q^{41} +2.10431e7 q^{42} -2.55553e8 q^{43} +2.44389e8 q^{44} +6.41180e8 q^{45} -8.58193e8 q^{46} -1.53163e8 q^{47} +7.54723e8 q^{48} -1.97267e9 q^{49} +2.77185e9 q^{50} -9.11750e8 q^{51} -8.38898e8 q^{52} +1.48167e8 q^{53} -5.75773e8 q^{54} -6.06061e9 q^{55} +2.15268e8 q^{56} +2.72394e9 q^{57} -2.56526e9 q^{58} +7.14924e8 q^{59} +1.15533e9 q^{60} -5.86726e9 q^{61} -4.22364e8 q^{62} -1.27433e8 q^{63} +9.55721e9 q^{64} +2.08039e10 q^{65} +5.44236e9 q^{66} +2.74066e9 q^{67} -1.64286e9 q^{68} +5.19708e9 q^{69} -9.40309e8 q^{70} +1.81330e10 q^{71} -5.89008e9 q^{72} -1.43546e9 q^{73} +4.36210e9 q^{74} -1.67859e10 q^{75} +4.90821e9 q^{76} +1.20454e9 q^{77} -1.86817e10 q^{78} -1.94641e10 q^{79} -3.37247e10 q^{80} +3.48678e9 q^{81} +1.90376e10 q^{82} -2.81052e10 q^{83} -2.29620e8 q^{84} +4.07415e10 q^{85} -1.02545e10 q^{86} +1.55348e10 q^{87} +5.56746e10 q^{88} -1.07723e10 q^{89} +2.57284e10 q^{90} -4.13474e9 q^{91} +9.36451e9 q^{92} +2.55776e9 q^{93} -6.14589e9 q^{94} -1.21719e11 q^{95} -1.93570e10 q^{96} -2.86797e10 q^{97} -7.91565e10 q^{98} -3.29581e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 40.1266 0.886681 0.443340 0.896353i \(-0.353793\pi\)
0.443340 + 0.896353i \(0.353793\pi\)
\(3\) −243.000 −0.577350
\(4\) −437.857 −0.213797
\(5\) 10858.4 1.55393 0.776967 0.629542i \(-0.216757\pi\)
0.776967 + 0.629542i \(0.216757\pi\)
\(6\) −9750.76 −0.511925
\(7\) −2158.10 −0.0485324 −0.0242662 0.999706i \(-0.507725\pi\)
−0.0242662 + 0.999706i \(0.507725\pi\)
\(8\) −99749.0 −1.07625
\(9\) 59049.0 0.333333
\(10\) 435712. 1.37784
\(11\) −558147. −1.04493 −0.522467 0.852659i \(-0.674988\pi\)
−0.522467 + 0.852659i \(0.674988\pi\)
\(12\) 106399. 0.123436
\(13\) 1.91592e6 1.43116 0.715581 0.698530i \(-0.246162\pi\)
0.715581 + 0.698530i \(0.246162\pi\)
\(14\) −86597.0 −0.0430327
\(15\) −2.63860e6 −0.897164
\(16\) −3.10585e6 −0.740493
\(17\) 3.75206e6 0.640915 0.320457 0.947263i \(-0.396163\pi\)
0.320457 + 0.947263i \(0.396163\pi\)
\(18\) 2.36943e6 0.295560
\(19\) −1.12096e7 −1.03859 −0.519297 0.854594i \(-0.673806\pi\)
−0.519297 + 0.854594i \(0.673806\pi\)
\(20\) −4.75444e6 −0.332227
\(21\) 524417. 0.0280202
\(22\) −2.23966e7 −0.926524
\(23\) −2.13872e7 −0.692867 −0.346433 0.938075i \(-0.612607\pi\)
−0.346433 + 0.938075i \(0.612607\pi\)
\(24\) 2.42390e7 0.621374
\(25\) 6.90776e7 1.41471
\(26\) 7.68793e7 1.26898
\(27\) −1.43489e7 −0.192450
\(28\) 944937. 0.0103761
\(29\) −6.39291e7 −0.578775 −0.289388 0.957212i \(-0.593452\pi\)
−0.289388 + 0.957212i \(0.593452\pi\)
\(30\) −1.05878e8 −0.795498
\(31\) −1.05258e7 −0.0660336 −0.0330168 0.999455i \(-0.510511\pi\)
−0.0330168 + 0.999455i \(0.510511\pi\)
\(32\) 7.96585e7 0.419669
\(33\) 1.35630e8 0.603293
\(34\) 1.50557e8 0.568287
\(35\) −2.34336e7 −0.0754161
\(36\) −2.58550e7 −0.0712658
\(37\) 1.08708e8 0.257723 0.128862 0.991663i \(-0.458868\pi\)
0.128862 + 0.991663i \(0.458868\pi\)
\(38\) −4.49804e8 −0.920902
\(39\) −4.65568e8 −0.826281
\(40\) −1.08312e9 −1.67242
\(41\) 4.74439e8 0.639542 0.319771 0.947495i \(-0.396394\pi\)
0.319771 + 0.947495i \(0.396394\pi\)
\(42\) 2.10431e7 0.0248450
\(43\) −2.55553e8 −0.265097 −0.132548 0.991177i \(-0.542316\pi\)
−0.132548 + 0.991177i \(0.542316\pi\)
\(44\) 2.44389e8 0.223404
\(45\) 6.41180e8 0.517978
\(46\) −8.58193e8 −0.614352
\(47\) −1.53163e8 −0.0974125 −0.0487062 0.998813i \(-0.515510\pi\)
−0.0487062 + 0.998813i \(0.515510\pi\)
\(48\) 7.54723e8 0.427524
\(49\) −1.97267e9 −0.997645
\(50\) 2.77185e9 1.25440
\(51\) −9.11750e8 −0.370032
\(52\) −8.38898e8 −0.305978
\(53\) 1.48167e8 0.0486669 0.0243334 0.999704i \(-0.492254\pi\)
0.0243334 + 0.999704i \(0.492254\pi\)
\(54\) −5.75773e8 −0.170642
\(55\) −6.06061e9 −1.62376
\(56\) 2.15268e8 0.0522330
\(57\) 2.72394e9 0.599633
\(58\) −2.56526e9 −0.513189
\(59\) 7.14924e8 0.130189
\(60\) 1.15533e9 0.191811
\(61\) −5.86726e9 −0.889449 −0.444724 0.895667i \(-0.646698\pi\)
−0.444724 + 0.895667i \(0.646698\pi\)
\(62\) −4.22364e8 −0.0585507
\(63\) −1.27433e8 −0.0161775
\(64\) 9.55721e9 1.11261
\(65\) 2.08039e10 2.22393
\(66\) 5.44236e9 0.534929
\(67\) 2.74066e9 0.247996 0.123998 0.992282i \(-0.460428\pi\)
0.123998 + 0.992282i \(0.460428\pi\)
\(68\) −1.64286e9 −0.137026
\(69\) 5.19708e9 0.400027
\(70\) −9.40309e8 −0.0668700
\(71\) 1.81330e10 1.19275 0.596374 0.802707i \(-0.296608\pi\)
0.596374 + 0.802707i \(0.296608\pi\)
\(72\) −5.89008e9 −0.358750
\(73\) −1.43546e9 −0.0810432 −0.0405216 0.999179i \(-0.512902\pi\)
−0.0405216 + 0.999179i \(0.512902\pi\)
\(74\) 4.36210e9 0.228518
\(75\) −1.67859e10 −0.816783
\(76\) 4.90821e9 0.222049
\(77\) 1.20454e9 0.0507132
\(78\) −1.86817e10 −0.732648
\(79\) −1.94641e10 −0.711682 −0.355841 0.934547i \(-0.615805\pi\)
−0.355841 + 0.934547i \(0.615805\pi\)
\(80\) −3.37247e10 −1.15068
\(81\) 3.48678e9 0.111111
\(82\) 1.90376e10 0.567070
\(83\) −2.81052e10 −0.783172 −0.391586 0.920141i \(-0.628074\pi\)
−0.391586 + 0.920141i \(0.628074\pi\)
\(84\) −2.29620e8 −0.00599064
\(85\) 4.07415e10 0.995939
\(86\) −1.02545e10 −0.235056
\(87\) 1.55348e10 0.334156
\(88\) 5.56746e10 1.12461
\(89\) −1.07723e10 −0.204486 −0.102243 0.994759i \(-0.532602\pi\)
−0.102243 + 0.994759i \(0.532602\pi\)
\(90\) 2.57284e10 0.459281
\(91\) −4.13474e9 −0.0694576
\(92\) 9.36451e9 0.148133
\(93\) 2.55776e9 0.0381245
\(94\) −6.14589e9 −0.0863738
\(95\) −1.21719e11 −1.61391
\(96\) −1.93570e10 −0.242296
\(97\) −2.86797e10 −0.339101 −0.169551 0.985521i \(-0.554232\pi\)
−0.169551 + 0.985521i \(0.554232\pi\)
\(98\) −7.91565e10 −0.884592
\(99\) −3.29581e10 −0.348312
\(100\) −3.02461e10 −0.302461
\(101\) −1.71283e11 −1.62161 −0.810806 0.585315i \(-0.800971\pi\)
−0.810806 + 0.585315i \(0.800971\pi\)
\(102\) −3.65854e10 −0.328101
\(103\) −7.69354e10 −0.653915 −0.326957 0.945039i \(-0.606023\pi\)
−0.326957 + 0.945039i \(0.606023\pi\)
\(104\) −1.91111e11 −1.54029
\(105\) 5.69435e9 0.0435415
\(106\) 5.94543e9 0.0431520
\(107\) −1.36485e11 −0.940750 −0.470375 0.882467i \(-0.655881\pi\)
−0.470375 + 0.882467i \(0.655881\pi\)
\(108\) 6.28277e9 0.0411453
\(109\) −2.74257e10 −0.170731 −0.0853654 0.996350i \(-0.527206\pi\)
−0.0853654 + 0.996350i \(0.527206\pi\)
\(110\) −2.43192e11 −1.43976
\(111\) −2.64162e10 −0.148797
\(112\) 6.70273e9 0.0359379
\(113\) −7.83794e10 −0.400194 −0.200097 0.979776i \(-0.564126\pi\)
−0.200097 + 0.979776i \(0.564126\pi\)
\(114\) 1.09302e11 0.531683
\(115\) −2.32231e11 −1.07667
\(116\) 2.79918e10 0.123741
\(117\) 1.13133e11 0.477054
\(118\) 2.86875e10 0.115436
\(119\) −8.09730e9 −0.0311051
\(120\) 2.63198e11 0.965573
\(121\) 2.62169e10 0.0918887
\(122\) −2.35433e11 −0.788657
\(123\) −1.15289e11 −0.369240
\(124\) 4.60878e9 0.0141178
\(125\) 2.19878e11 0.644430
\(126\) −5.11347e9 −0.0143442
\(127\) −5.37437e11 −1.44347 −0.721734 0.692170i \(-0.756655\pi\)
−0.721734 + 0.692170i \(0.756655\pi\)
\(128\) 2.20358e11 0.566857
\(129\) 6.20994e10 0.153054
\(130\) 8.34789e11 1.97191
\(131\) −5.78286e11 −1.30964 −0.654818 0.755786i \(-0.727255\pi\)
−0.654818 + 0.755786i \(0.727255\pi\)
\(132\) −5.93865e10 −0.128983
\(133\) 2.41914e10 0.0504055
\(134\) 1.09973e11 0.219893
\(135\) −1.55807e11 −0.299055
\(136\) −3.74264e11 −0.689785
\(137\) 2.75240e10 0.0487246 0.0243623 0.999703i \(-0.492244\pi\)
0.0243623 + 0.999703i \(0.492244\pi\)
\(138\) 2.08541e11 0.354696
\(139\) 3.79830e11 0.620880 0.310440 0.950593i \(-0.399524\pi\)
0.310440 + 0.950593i \(0.399524\pi\)
\(140\) 1.02605e10 0.0161238
\(141\) 3.72185e10 0.0562411
\(142\) 7.27615e11 1.05759
\(143\) −1.06936e12 −1.49547
\(144\) −1.83398e11 −0.246831
\(145\) −6.94171e11 −0.899378
\(146\) −5.76003e10 −0.0718594
\(147\) 4.79359e11 0.575990
\(148\) −4.75988e10 −0.0551006
\(149\) −1.48988e12 −1.66198 −0.830991 0.556286i \(-0.812226\pi\)
−0.830991 + 0.556286i \(0.812226\pi\)
\(150\) −6.73559e11 −0.724225
\(151\) −7.02101e11 −0.727824 −0.363912 0.931433i \(-0.618559\pi\)
−0.363912 + 0.931433i \(0.618559\pi\)
\(152\) 1.11815e12 1.11779
\(153\) 2.21555e11 0.213638
\(154\) 4.83339e10 0.0449664
\(155\) −1.14294e11 −0.102612
\(156\) 2.03852e11 0.176657
\(157\) 5.96631e11 0.499181 0.249590 0.968351i \(-0.419704\pi\)
0.249590 + 0.968351i \(0.419704\pi\)
\(158\) −7.81029e11 −0.631034
\(159\) −3.60045e10 −0.0280978
\(160\) 8.64967e11 0.652138
\(161\) 4.61555e10 0.0336265
\(162\) 1.39913e11 0.0985201
\(163\) −1.53294e12 −1.04350 −0.521752 0.853097i \(-0.674721\pi\)
−0.521752 + 0.853097i \(0.674721\pi\)
\(164\) −2.07736e11 −0.136732
\(165\) 1.47273e12 0.937478
\(166\) −1.12777e12 −0.694424
\(167\) −2.13729e12 −1.27328 −0.636638 0.771163i \(-0.719675\pi\)
−0.636638 + 0.771163i \(0.719675\pi\)
\(168\) −5.23101e10 −0.0301567
\(169\) 1.87858e12 1.04822
\(170\) 1.63482e12 0.883080
\(171\) −6.61917e11 −0.346198
\(172\) 1.11896e11 0.0566770
\(173\) 9.85994e11 0.483750 0.241875 0.970307i \(-0.422238\pi\)
0.241875 + 0.970307i \(0.422238\pi\)
\(174\) 6.23358e11 0.296290
\(175\) −1.49076e11 −0.0686592
\(176\) 1.73352e12 0.773767
\(177\) −1.73727e11 −0.0751646
\(178\) −4.32255e11 −0.181313
\(179\) 1.30693e12 0.531572 0.265786 0.964032i \(-0.414369\pi\)
0.265786 + 0.964032i \(0.414369\pi\)
\(180\) −2.80745e11 −0.110742
\(181\) 3.58189e12 1.37050 0.685251 0.728307i \(-0.259692\pi\)
0.685251 + 0.728307i \(0.259692\pi\)
\(182\) −1.65913e11 −0.0615868
\(183\) 1.42574e12 0.513524
\(184\) 2.13335e12 0.745699
\(185\) 1.18040e12 0.400485
\(186\) 1.02634e11 0.0338043
\(187\) −2.09420e12 −0.669714
\(188\) 6.70633e10 0.0208265
\(189\) 3.09663e10 0.00934006
\(190\) −4.88417e12 −1.43102
\(191\) −3.87812e12 −1.10392 −0.551960 0.833870i \(-0.686120\pi\)
−0.551960 + 0.833870i \(0.686120\pi\)
\(192\) −2.32240e12 −0.642363
\(193\) −2.07161e12 −0.556856 −0.278428 0.960457i \(-0.589813\pi\)
−0.278428 + 0.960457i \(0.589813\pi\)
\(194\) −1.15082e12 −0.300675
\(195\) −5.05534e12 −1.28399
\(196\) 8.63747e11 0.213294
\(197\) −2.68438e12 −0.644585 −0.322292 0.946640i \(-0.604453\pi\)
−0.322292 + 0.946640i \(0.604453\pi\)
\(198\) −1.32249e12 −0.308841
\(199\) −2.89870e12 −0.658433 −0.329216 0.944254i \(-0.606785\pi\)
−0.329216 + 0.944254i \(0.606785\pi\)
\(200\) −6.89042e12 −1.52258
\(201\) −6.65981e11 −0.143180
\(202\) −6.87301e12 −1.43785
\(203\) 1.37965e11 0.0280893
\(204\) 3.99216e11 0.0791119
\(205\) 5.15167e12 0.993806
\(206\) −3.08715e12 −0.579814
\(207\) −1.26289e12 −0.230956
\(208\) −5.95056e12 −1.05977
\(209\) 6.25662e12 1.08526
\(210\) 2.28495e11 0.0386074
\(211\) −3.14739e12 −0.518081 −0.259041 0.965866i \(-0.583406\pi\)
−0.259041 + 0.965866i \(0.583406\pi\)
\(212\) −6.48758e10 −0.0104048
\(213\) −4.40632e12 −0.688633
\(214\) −5.47668e12 −0.834145
\(215\) −2.77491e12 −0.411943
\(216\) 1.43129e12 0.207125
\(217\) 2.27156e10 0.00320477
\(218\) −1.10050e12 −0.151384
\(219\) 3.48818e11 0.0467903
\(220\) 2.65368e12 0.347155
\(221\) 7.18863e12 0.917252
\(222\) −1.05999e12 −0.131935
\(223\) 9.66744e12 1.17391 0.586955 0.809620i \(-0.300327\pi\)
0.586955 + 0.809620i \(0.300327\pi\)
\(224\) −1.71911e11 −0.0203676
\(225\) 4.07896e12 0.471570
\(226\) −3.14510e12 −0.354844
\(227\) 1.62019e13 1.78412 0.892058 0.451920i \(-0.149261\pi\)
0.892058 + 0.451920i \(0.149261\pi\)
\(228\) −1.19270e12 −0.128200
\(229\) −4.47309e12 −0.469367 −0.234683 0.972072i \(-0.575405\pi\)
−0.234683 + 0.972072i \(0.575405\pi\)
\(230\) −9.31864e12 −0.954662
\(231\) −2.92702e11 −0.0292793
\(232\) 6.37687e12 0.622907
\(233\) 1.56446e13 1.49247 0.746236 0.665682i \(-0.231859\pi\)
0.746236 + 0.665682i \(0.231859\pi\)
\(234\) 4.53964e12 0.422994
\(235\) −1.66311e12 −0.151372
\(236\) −3.13035e11 −0.0278340
\(237\) 4.72978e12 0.410890
\(238\) −3.24917e11 −0.0275803
\(239\) −1.58472e13 −1.31451 −0.657253 0.753670i \(-0.728282\pi\)
−0.657253 + 0.753670i \(0.728282\pi\)
\(240\) 8.19511e12 0.664344
\(241\) −2.76301e11 −0.0218921 −0.0109461 0.999940i \(-0.503484\pi\)
−0.0109461 + 0.999940i \(0.503484\pi\)
\(242\) 1.05200e12 0.0814760
\(243\) −8.47289e11 −0.0641500
\(244\) 2.56902e12 0.190162
\(245\) −2.14201e13 −1.55027
\(246\) −4.62614e12 −0.327398
\(247\) −2.14767e13 −1.48640
\(248\) 1.04994e12 0.0710687
\(249\) 6.82957e12 0.452165
\(250\) 8.82294e12 0.571404
\(251\) −1.15243e13 −0.730143 −0.365071 0.930980i \(-0.618955\pi\)
−0.365071 + 0.930980i \(0.618955\pi\)
\(252\) 5.57976e10 0.00345870
\(253\) 1.19372e13 0.724001
\(254\) −2.15655e13 −1.27990
\(255\) −9.90018e12 −0.575006
\(256\) −1.07310e13 −0.609985
\(257\) 2.04756e13 1.13921 0.569606 0.821918i \(-0.307096\pi\)
0.569606 + 0.821918i \(0.307096\pi\)
\(258\) 2.49184e12 0.135710
\(259\) −2.34603e11 −0.0125079
\(260\) −9.10912e12 −0.475470
\(261\) −3.77495e12 −0.192925
\(262\) −2.32047e13 −1.16123
\(263\) −1.74761e13 −0.856422 −0.428211 0.903679i \(-0.640856\pi\)
−0.428211 + 0.903679i \(0.640856\pi\)
\(264\) −1.35289e13 −0.649295
\(265\) 1.60886e12 0.0756251
\(266\) 9.70720e11 0.0446936
\(267\) 2.61766e12 0.118060
\(268\) −1.20002e12 −0.0530208
\(269\) −4.83367e12 −0.209237 −0.104619 0.994512i \(-0.533362\pi\)
−0.104619 + 0.994512i \(0.533362\pi\)
\(270\) −6.25199e12 −0.265166
\(271\) −5.58792e12 −0.232231 −0.116115 0.993236i \(-0.537044\pi\)
−0.116115 + 0.993236i \(0.537044\pi\)
\(272\) −1.16533e13 −0.474593
\(273\) 1.00474e12 0.0401014
\(274\) 1.10444e12 0.0432032
\(275\) −3.85555e13 −1.47828
\(276\) −2.27558e12 −0.0855247
\(277\) −2.08713e13 −0.768971 −0.384486 0.923131i \(-0.625621\pi\)
−0.384486 + 0.923131i \(0.625621\pi\)
\(278\) 1.52413e13 0.550522
\(279\) −6.21537e11 −0.0220112
\(280\) 2.33747e12 0.0811666
\(281\) −1.47528e13 −0.502330 −0.251165 0.967944i \(-0.580814\pi\)
−0.251165 + 0.967944i \(0.580814\pi\)
\(282\) 1.49345e12 0.0498679
\(283\) 4.39824e13 1.44030 0.720150 0.693818i \(-0.244073\pi\)
0.720150 + 0.693818i \(0.244073\pi\)
\(284\) −7.93965e12 −0.255006
\(285\) 2.95777e13 0.931790
\(286\) −4.29100e13 −1.32600
\(287\) −1.02389e12 −0.0310385
\(288\) 4.70376e12 0.139890
\(289\) −2.01940e13 −0.589228
\(290\) −2.78547e13 −0.797461
\(291\) 6.96916e12 0.195780
\(292\) 6.28528e11 0.0173268
\(293\) −5.15348e12 −0.139421 −0.0697106 0.997567i \(-0.522208\pi\)
−0.0697106 + 0.997567i \(0.522208\pi\)
\(294\) 1.92350e13 0.510720
\(295\) 7.76296e12 0.202305
\(296\) −1.08436e13 −0.277375
\(297\) 8.00881e12 0.201098
\(298\) −5.97837e13 −1.47365
\(299\) −4.09760e13 −0.991604
\(300\) 7.34980e12 0.174626
\(301\) 5.51508e11 0.0128658
\(302\) −2.81729e13 −0.645347
\(303\) 4.16218e13 0.936238
\(304\) 3.48154e13 0.769072
\(305\) −6.37093e13 −1.38214
\(306\) 8.89025e12 0.189429
\(307\) 4.55568e13 0.953438 0.476719 0.879056i \(-0.341826\pi\)
0.476719 + 0.879056i \(0.341826\pi\)
\(308\) −5.27414e11 −0.0108423
\(309\) 1.86953e13 0.377538
\(310\) −4.58621e12 −0.0909839
\(311\) 5.09748e13 0.993512 0.496756 0.867890i \(-0.334524\pi\)
0.496756 + 0.867890i \(0.334524\pi\)
\(312\) 4.64399e13 0.889286
\(313\) 9.18436e13 1.72805 0.864023 0.503453i \(-0.167937\pi\)
0.864023 + 0.503453i \(0.167937\pi\)
\(314\) 2.39408e13 0.442614
\(315\) −1.38373e12 −0.0251387
\(316\) 8.52250e12 0.152156
\(317\) 4.83350e13 0.848077 0.424039 0.905644i \(-0.360612\pi\)
0.424039 + 0.905644i \(0.360612\pi\)
\(318\) −1.44474e12 −0.0249138
\(319\) 3.56819e13 0.604782
\(320\) 1.03776e14 1.72892
\(321\) 3.31659e13 0.543142
\(322\) 1.85206e12 0.0298159
\(323\) −4.20591e13 −0.665651
\(324\) −1.52671e12 −0.0237553
\(325\) 1.32347e14 2.02468
\(326\) −6.15117e13 −0.925254
\(327\) 6.66444e12 0.0985715
\(328\) −4.73248e13 −0.688308
\(329\) 3.30540e11 0.00472766
\(330\) 5.90956e13 0.831243
\(331\) 5.34555e13 0.739500 0.369750 0.929131i \(-0.379443\pi\)
0.369750 + 0.929131i \(0.379443\pi\)
\(332\) 1.23061e13 0.167440
\(333\) 6.41913e12 0.0859078
\(334\) −8.57621e13 −1.12899
\(335\) 2.97593e13 0.385369
\(336\) −1.62876e12 −0.0207488
\(337\) 1.11660e14 1.39937 0.699683 0.714453i \(-0.253324\pi\)
0.699683 + 0.714453i \(0.253324\pi\)
\(338\) 7.53811e13 0.929438
\(339\) 1.90462e13 0.231052
\(340\) −1.78389e13 −0.212929
\(341\) 5.87494e12 0.0690008
\(342\) −2.65605e13 −0.306967
\(343\) 8.52447e12 0.0969504
\(344\) 2.54912e13 0.285311
\(345\) 5.64322e13 0.621615
\(346\) 3.95646e13 0.428931
\(347\) −6.57924e12 −0.0702043 −0.0351021 0.999384i \(-0.511176\pi\)
−0.0351021 + 0.999384i \(0.511176\pi\)
\(348\) −6.80201e12 −0.0714417
\(349\) −1.00714e14 −1.04124 −0.520621 0.853788i \(-0.674299\pi\)
−0.520621 + 0.853788i \(0.674299\pi\)
\(350\) −5.98191e12 −0.0608788
\(351\) −2.74913e13 −0.275427
\(352\) −4.44612e13 −0.438527
\(353\) 1.51736e14 1.47343 0.736713 0.676206i \(-0.236377\pi\)
0.736713 + 0.676206i \(0.236377\pi\)
\(354\) −6.97106e12 −0.0666470
\(355\) 1.96896e14 1.85345
\(356\) 4.71672e12 0.0437185
\(357\) 1.96764e12 0.0179586
\(358\) 5.24428e13 0.471335
\(359\) −1.24269e14 −1.09988 −0.549940 0.835204i \(-0.685349\pi\)
−0.549940 + 0.835204i \(0.685349\pi\)
\(360\) −6.39570e13 −0.557474
\(361\) 9.16534e12 0.0786790
\(362\) 1.43729e14 1.21520
\(363\) −6.37071e12 −0.0530520
\(364\) 1.81042e12 0.0148499
\(365\) −1.55869e13 −0.125936
\(366\) 5.72102e13 0.455331
\(367\) 7.27399e13 0.570308 0.285154 0.958482i \(-0.407955\pi\)
0.285154 + 0.958482i \(0.407955\pi\)
\(368\) 6.64254e13 0.513063
\(369\) 2.80152e13 0.213181
\(370\) 4.73656e13 0.355102
\(371\) −3.19758e11 −0.00236192
\(372\) −1.11993e12 −0.00815092
\(373\) 1.81085e14 1.29862 0.649311 0.760523i \(-0.275057\pi\)
0.649311 + 0.760523i \(0.275057\pi\)
\(374\) −8.40331e13 −0.593823
\(375\) −5.34303e13 −0.372062
\(376\) 1.52778e13 0.104840
\(377\) −1.22483e14 −0.828321
\(378\) 1.24257e12 0.00828165
\(379\) 9.85582e13 0.647407 0.323703 0.946159i \(-0.395072\pi\)
0.323703 + 0.946159i \(0.395072\pi\)
\(380\) 5.32955e13 0.345049
\(381\) 1.30597e14 0.833387
\(382\) −1.55616e14 −0.978825
\(383\) 1.40097e14 0.868632 0.434316 0.900761i \(-0.356990\pi\)
0.434316 + 0.900761i \(0.356990\pi\)
\(384\) −5.35469e13 −0.327275
\(385\) 1.30794e13 0.0788049
\(386\) −8.31266e13 −0.493753
\(387\) −1.50902e13 −0.0883657
\(388\) 1.25576e13 0.0724990
\(389\) −1.72756e14 −0.983353 −0.491677 0.870778i \(-0.663616\pi\)
−0.491677 + 0.870778i \(0.663616\pi\)
\(390\) −2.02854e14 −1.13849
\(391\) −8.02458e13 −0.444069
\(392\) 1.96772e14 1.07372
\(393\) 1.40524e14 0.756119
\(394\) −1.07715e14 −0.571541
\(395\) −2.11350e14 −1.10591
\(396\) 1.44309e13 0.0744681
\(397\) 8.48196e13 0.431667 0.215833 0.976430i \(-0.430753\pi\)
0.215833 + 0.976430i \(0.430753\pi\)
\(398\) −1.16315e14 −0.583820
\(399\) −5.87852e12 −0.0291016
\(400\) −2.14545e14 −1.04758
\(401\) 3.89323e14 1.87506 0.937531 0.347902i \(-0.113106\pi\)
0.937531 + 0.347902i \(0.113106\pi\)
\(402\) −2.67235e13 −0.126955
\(403\) −2.01665e13 −0.0945047
\(404\) 7.49975e13 0.346696
\(405\) 3.78610e13 0.172659
\(406\) 5.53607e12 0.0249063
\(407\) −6.06754e13 −0.269304
\(408\) 9.09461e13 0.398248
\(409\) −3.33404e14 −1.44043 −0.720216 0.693750i \(-0.755957\pi\)
−0.720216 + 0.693750i \(0.755957\pi\)
\(410\) 2.06719e14 0.881189
\(411\) −6.68833e12 −0.0281312
\(412\) 3.36867e13 0.139805
\(413\) −1.54288e12 −0.00631838
\(414\) −5.06755e13 −0.204784
\(415\) −3.05179e14 −1.21700
\(416\) 1.52619e14 0.600615
\(417\) −9.22986e13 −0.358465
\(418\) 2.51057e14 0.962282
\(419\) −1.70717e14 −0.645803 −0.322902 0.946433i \(-0.604658\pi\)
−0.322902 + 0.946433i \(0.604658\pi\)
\(420\) −2.49331e12 −0.00930906
\(421\) −4.50291e14 −1.65937 −0.829683 0.558235i \(-0.811479\pi\)
−0.829683 + 0.558235i \(0.811479\pi\)
\(422\) −1.26294e14 −0.459372
\(423\) −9.04410e12 −0.0324708
\(424\) −1.47795e13 −0.0523778
\(425\) 2.59183e14 0.906708
\(426\) −1.76810e14 −0.610598
\(427\) 1.26621e13 0.0431671
\(428\) 5.97609e13 0.201130
\(429\) 2.59856e14 0.863410
\(430\) −1.11348e14 −0.365262
\(431\) 2.26249e12 0.00732761 0.00366380 0.999993i \(-0.498834\pi\)
0.00366380 + 0.999993i \(0.498834\pi\)
\(432\) 4.45656e13 0.142508
\(433\) −3.42076e14 −1.08004 −0.540020 0.841652i \(-0.681583\pi\)
−0.540020 + 0.841652i \(0.681583\pi\)
\(434\) 9.11501e11 0.00284160
\(435\) 1.68683e14 0.519256
\(436\) 1.20085e13 0.0365018
\(437\) 2.39742e14 0.719608
\(438\) 1.39969e13 0.0414881
\(439\) −3.48639e14 −1.02052 −0.510260 0.860020i \(-0.670451\pi\)
−0.510260 + 0.860020i \(0.670451\pi\)
\(440\) 6.04540e14 1.74757
\(441\) −1.16484e14 −0.332548
\(442\) 2.88455e14 0.813310
\(443\) 3.29245e14 0.916851 0.458425 0.888733i \(-0.348414\pi\)
0.458425 + 0.888733i \(0.348414\pi\)
\(444\) 1.15665e13 0.0318123
\(445\) −1.16970e14 −0.317757
\(446\) 3.87921e14 1.04088
\(447\) 3.62040e14 0.959545
\(448\) −2.06254e13 −0.0539974
\(449\) −6.86507e14 −1.77537 −0.887687 0.460448i \(-0.847689\pi\)
−0.887687 + 0.460448i \(0.847689\pi\)
\(450\) 1.63675e14 0.418132
\(451\) −2.64807e14 −0.668280
\(452\) 3.43190e13 0.0855604
\(453\) 1.70610e14 0.420209
\(454\) 6.50126e14 1.58194
\(455\) −4.48968e13 −0.107933
\(456\) −2.71710e14 −0.645355
\(457\) −5.36365e14 −1.25870 −0.629348 0.777123i \(-0.716678\pi\)
−0.629348 + 0.777123i \(0.716678\pi\)
\(458\) −1.79490e14 −0.416179
\(459\) −5.38379e13 −0.123344
\(460\) 1.01684e14 0.230189
\(461\) −4.90388e14 −1.09694 −0.548472 0.836169i \(-0.684790\pi\)
−0.548472 + 0.836169i \(0.684790\pi\)
\(462\) −1.17451e13 −0.0259614
\(463\) 2.19955e14 0.480438 0.240219 0.970719i \(-0.422781\pi\)
0.240219 + 0.970719i \(0.422781\pi\)
\(464\) 1.98555e14 0.428579
\(465\) 2.77733e13 0.0592429
\(466\) 6.27763e14 1.32335
\(467\) 4.97412e14 1.03627 0.518135 0.855299i \(-0.326626\pi\)
0.518135 + 0.855299i \(0.326626\pi\)
\(468\) −4.95361e13 −0.101993
\(469\) −5.91461e12 −0.0120358
\(470\) −6.67348e13 −0.134219
\(471\) −1.44981e14 −0.288202
\(472\) −7.13130e13 −0.140116
\(473\) 1.42636e14 0.277009
\(474\) 1.89790e14 0.364328
\(475\) −7.74334e14 −1.46931
\(476\) 3.54546e12 0.00665019
\(477\) 8.74910e12 0.0162223
\(478\) −6.35892e14 −1.16555
\(479\) −2.32774e14 −0.421783 −0.210892 0.977509i \(-0.567637\pi\)
−0.210892 + 0.977509i \(0.567637\pi\)
\(480\) −2.10187e14 −0.376512
\(481\) 2.08277e14 0.368844
\(482\) −1.10870e13 −0.0194113
\(483\) −1.12158e13 −0.0194143
\(484\) −1.14793e13 −0.0196456
\(485\) −3.11416e14 −0.526941
\(486\) −3.39988e13 −0.0568806
\(487\) −7.87944e14 −1.30342 −0.651712 0.758466i \(-0.725949\pi\)
−0.651712 + 0.758466i \(0.725949\pi\)
\(488\) 5.85253e14 0.957270
\(489\) 3.72505e14 0.602467
\(490\) −8.59516e14 −1.37460
\(491\) 6.20707e14 0.981609 0.490805 0.871270i \(-0.336703\pi\)
0.490805 + 0.871270i \(0.336703\pi\)
\(492\) 5.04800e13 0.0789425
\(493\) −2.39866e14 −0.370946
\(494\) −8.61787e14 −1.31796
\(495\) −3.57873e14 −0.541253
\(496\) 3.26915e13 0.0488974
\(497\) −3.91327e13 −0.0578869
\(498\) 2.74047e14 0.400926
\(499\) 1.10067e15 1.59259 0.796295 0.604909i \(-0.206791\pi\)
0.796295 + 0.604909i \(0.206791\pi\)
\(500\) −9.62749e13 −0.137777
\(501\) 5.19361e14 0.735126
\(502\) −4.62430e14 −0.647404
\(503\) −5.36081e14 −0.742346 −0.371173 0.928564i \(-0.621044\pi\)
−0.371173 + 0.928564i \(0.621044\pi\)
\(504\) 1.27114e13 0.0174110
\(505\) −1.85987e15 −2.51988
\(506\) 4.78998e14 0.641958
\(507\) −4.56495e14 −0.605191
\(508\) 2.35321e14 0.308610
\(509\) −4.38157e13 −0.0568436 −0.0284218 0.999596i \(-0.509048\pi\)
−0.0284218 + 0.999596i \(0.509048\pi\)
\(510\) −3.97260e14 −0.509846
\(511\) 3.09787e12 0.00393322
\(512\) −8.81890e14 −1.10772
\(513\) 1.60846e14 0.199878
\(514\) 8.21616e14 1.01012
\(515\) −8.35398e14 −1.01614
\(516\) −2.71907e13 −0.0327225
\(517\) 8.54873e13 0.101790
\(518\) −9.41383e12 −0.0110905
\(519\) −2.39596e14 −0.279293
\(520\) −2.07517e15 −2.39351
\(521\) 1.26388e15 1.44245 0.721223 0.692703i \(-0.243580\pi\)
0.721223 + 0.692703i \(0.243580\pi\)
\(522\) −1.51476e14 −0.171063
\(523\) 1.39636e14 0.156041 0.0780203 0.996952i \(-0.475140\pi\)
0.0780203 + 0.996952i \(0.475140\pi\)
\(524\) 2.53207e14 0.279997
\(525\) 3.62255e13 0.0396404
\(526\) −7.01256e14 −0.759373
\(527\) −3.94933e13 −0.0423219
\(528\) −4.21247e14 −0.446735
\(529\) −4.95400e14 −0.519935
\(530\) 6.45581e13 0.0670553
\(531\) 4.22156e13 0.0433963
\(532\) −1.05924e13 −0.0107766
\(533\) 9.08987e14 0.915288
\(534\) 1.05038e14 0.104681
\(535\) −1.48201e15 −1.46186
\(536\) −2.73378e14 −0.266905
\(537\) −3.17585e14 −0.306903
\(538\) −1.93959e14 −0.185527
\(539\) 1.10104e15 1.04247
\(540\) 6.82211e13 0.0639371
\(541\) 1.31181e15 1.21698 0.608492 0.793560i \(-0.291775\pi\)
0.608492 + 0.793560i \(0.291775\pi\)
\(542\) −2.24224e14 −0.205914
\(543\) −8.70399e14 −0.791260
\(544\) 2.98883e14 0.268972
\(545\) −2.97800e14 −0.265304
\(546\) 4.03168e13 0.0355571
\(547\) 1.39679e15 1.21955 0.609775 0.792575i \(-0.291260\pi\)
0.609775 + 0.792575i \(0.291260\pi\)
\(548\) −1.20516e13 −0.0104172
\(549\) −3.46456e14 −0.296483
\(550\) −1.54710e15 −1.31076
\(551\) 7.16621e14 0.601113
\(552\) −5.18403e14 −0.430529
\(553\) 4.20054e13 0.0345396
\(554\) −8.37493e14 −0.681832
\(555\) −2.86838e14 −0.231220
\(556\) −1.66311e14 −0.132742
\(557\) −4.83859e13 −0.0382398 −0.0191199 0.999817i \(-0.506086\pi\)
−0.0191199 + 0.999817i \(0.506086\pi\)
\(558\) −2.49401e13 −0.0195169
\(559\) −4.89619e14 −0.379396
\(560\) 7.27812e13 0.0558451
\(561\) 5.08891e14 0.386660
\(562\) −5.91979e14 −0.445406
\(563\) −6.29975e14 −0.469383 −0.234691 0.972070i \(-0.575408\pi\)
−0.234691 + 0.972070i \(0.575408\pi\)
\(564\) −1.62964e13 −0.0120242
\(565\) −8.51078e14 −0.621875
\(566\) 1.76486e15 1.27709
\(567\) −7.52482e12 −0.00539249
\(568\) −1.80875e15 −1.28370
\(569\) 1.74779e15 1.22849 0.614244 0.789116i \(-0.289461\pi\)
0.614244 + 0.789116i \(0.289461\pi\)
\(570\) 1.18685e15 0.826200
\(571\) −1.39780e15 −0.963709 −0.481855 0.876251i \(-0.660037\pi\)
−0.481855 + 0.876251i \(0.660037\pi\)
\(572\) 4.68229e14 0.319727
\(573\) 9.42383e14 0.637349
\(574\) −4.10850e13 −0.0275212
\(575\) −1.47737e15 −0.980205
\(576\) 5.64344e14 0.370869
\(577\) 8.30902e14 0.540858 0.270429 0.962740i \(-0.412835\pi\)
0.270429 + 0.962740i \(0.412835\pi\)
\(578\) −8.10315e14 −0.522457
\(579\) 5.03401e14 0.321501
\(580\) 3.03947e14 0.192285
\(581\) 6.06538e13 0.0380092
\(582\) 2.79649e14 0.173595
\(583\) −8.26989e13 −0.0508537
\(584\) 1.43186e14 0.0872228
\(585\) 1.22845e15 0.741310
\(586\) −2.06792e14 −0.123622
\(587\) 2.27138e15 1.34518 0.672590 0.740015i \(-0.265182\pi\)
0.672590 + 0.740015i \(0.265182\pi\)
\(588\) −2.09891e14 −0.123145
\(589\) 1.17990e14 0.0685821
\(590\) 3.11501e14 0.179380
\(591\) 6.52305e14 0.372151
\(592\) −3.37633e14 −0.190843
\(593\) −1.99332e15 −1.11629 −0.558143 0.829745i \(-0.688486\pi\)
−0.558143 + 0.829745i \(0.688486\pi\)
\(594\) 3.21366e14 0.178310
\(595\) −8.79240e13 −0.0483353
\(596\) 6.52353e14 0.355327
\(597\) 7.04384e14 0.380146
\(598\) −1.64423e15 −0.879236
\(599\) −2.10272e15 −1.11412 −0.557061 0.830471i \(-0.688071\pi\)
−0.557061 + 0.830471i \(0.688071\pi\)
\(600\) 1.67437e15 0.879063
\(601\) 2.78719e15 1.44996 0.724982 0.688768i \(-0.241848\pi\)
0.724982 + 0.688768i \(0.241848\pi\)
\(602\) 2.21301e13 0.0114078
\(603\) 1.61833e14 0.0826652
\(604\) 3.07420e14 0.155607
\(605\) 2.84675e14 0.142789
\(606\) 1.67014e15 0.830144
\(607\) −1.91153e15 −0.941549 −0.470774 0.882254i \(-0.656025\pi\)
−0.470774 + 0.882254i \(0.656025\pi\)
\(608\) −8.92942e14 −0.435867
\(609\) −3.35256e13 −0.0162174
\(610\) −2.55644e15 −1.22552
\(611\) −2.93447e14 −0.139413
\(612\) −9.70095e13 −0.0456753
\(613\) −1.74172e15 −0.812728 −0.406364 0.913711i \(-0.633203\pi\)
−0.406364 + 0.913711i \(0.633203\pi\)
\(614\) 1.82804e15 0.845395
\(615\) −1.25186e15 −0.573774
\(616\) −1.20151e14 −0.0545801
\(617\) 1.16947e15 0.526529 0.263264 0.964724i \(-0.415201\pi\)
0.263264 + 0.964724i \(0.415201\pi\)
\(618\) 7.50178e14 0.334756
\(619\) −2.65006e15 −1.17208 −0.586039 0.810283i \(-0.699313\pi\)
−0.586039 + 0.810283i \(0.699313\pi\)
\(620\) 5.00442e13 0.0219381
\(621\) 3.06882e14 0.133342
\(622\) 2.04544e15 0.880928
\(623\) 2.32476e13 0.00992417
\(624\) 1.44599e15 0.611856
\(625\) −9.85402e14 −0.413307
\(626\) 3.68537e15 1.53222
\(627\) −1.52036e15 −0.626577
\(628\) −2.61239e14 −0.106724
\(629\) 4.07880e14 0.165179
\(630\) −5.55243e13 −0.0222900
\(631\) −5.42479e14 −0.215885 −0.107942 0.994157i \(-0.534426\pi\)
−0.107942 + 0.994157i \(0.534426\pi\)
\(632\) 1.94153e15 0.765948
\(633\) 7.64817e14 0.299114
\(634\) 1.93952e15 0.751974
\(635\) −5.83573e15 −2.24305
\(636\) 1.57648e13 0.00600724
\(637\) −3.77947e15 −1.42779
\(638\) 1.43179e15 0.536249
\(639\) 1.07073e15 0.397582
\(640\) 2.39274e15 0.880858
\(641\) 3.75984e15 1.37231 0.686153 0.727458i \(-0.259298\pi\)
0.686153 + 0.727458i \(0.259298\pi\)
\(642\) 1.33083e15 0.481594
\(643\) 3.89589e15 1.39780 0.698901 0.715218i \(-0.253673\pi\)
0.698901 + 0.715218i \(0.253673\pi\)
\(644\) −2.02095e13 −0.00718925
\(645\) 6.74303e14 0.237835
\(646\) −1.68769e15 −0.590220
\(647\) 9.79556e14 0.339669 0.169834 0.985473i \(-0.445677\pi\)
0.169834 + 0.985473i \(0.445677\pi\)
\(648\) −3.47803e14 −0.119583
\(649\) −3.99033e14 −0.136039
\(650\) 5.31063e15 1.79524
\(651\) −5.51990e12 −0.00185027
\(652\) 6.71209e14 0.223098
\(653\) −3.23399e15 −1.06590 −0.532950 0.846147i \(-0.678917\pi\)
−0.532950 + 0.846147i \(0.678917\pi\)
\(654\) 2.67421e14 0.0874014
\(655\) −6.27929e15 −2.03509
\(656\) −1.47354e15 −0.473577
\(657\) −8.47627e13 −0.0270144
\(658\) 1.32634e13 0.00419192
\(659\) −3.35560e15 −1.05172 −0.525861 0.850571i \(-0.676257\pi\)
−0.525861 + 0.850571i \(0.676257\pi\)
\(660\) −6.44844e14 −0.200430
\(661\) 4.39193e15 1.35378 0.676890 0.736085i \(-0.263327\pi\)
0.676890 + 0.736085i \(0.263327\pi\)
\(662\) 2.14499e15 0.655701
\(663\) −1.74684e15 −0.529576
\(664\) 2.80347e15 0.842890
\(665\) 2.62681e14 0.0783267
\(666\) 2.57578e14 0.0761728
\(667\) 1.36726e15 0.401014
\(668\) 9.35827e14 0.272223
\(669\) −2.34919e15 −0.677757
\(670\) 1.19414e15 0.341699
\(671\) 3.27479e15 0.929416
\(672\) 4.17743e13 0.0117592
\(673\) −2.16401e14 −0.0604195 −0.0302097 0.999544i \(-0.509618\pi\)
−0.0302097 + 0.999544i \(0.509618\pi\)
\(674\) 4.48052e15 1.24079
\(675\) −9.91188e14 −0.272261
\(676\) −8.22550e14 −0.224107
\(677\) −4.65762e14 −0.125871 −0.0629356 0.998018i \(-0.520046\pi\)
−0.0629356 + 0.998018i \(0.520046\pi\)
\(678\) 7.64259e14 0.204869
\(679\) 6.18935e13 0.0164574
\(680\) −4.06392e15 −1.07188
\(681\) −3.93706e15 −1.03006
\(682\) 2.35741e14 0.0611817
\(683\) 1.65412e15 0.425845 0.212923 0.977069i \(-0.431702\pi\)
0.212923 + 0.977069i \(0.431702\pi\)
\(684\) 2.89825e14 0.0740163
\(685\) 2.98868e14 0.0757148
\(686\) 3.42058e14 0.0859641
\(687\) 1.08696e15 0.270989
\(688\) 7.93711e14 0.196303
\(689\) 2.83875e14 0.0696501
\(690\) 2.26443e15 0.551174
\(691\) −6.25409e15 −1.51020 −0.755101 0.655609i \(-0.772412\pi\)
−0.755101 + 0.655609i \(0.772412\pi\)
\(692\) −4.31724e14 −0.103424
\(693\) 7.11266e13 0.0169044
\(694\) −2.64002e14 −0.0622488
\(695\) 4.12436e15 0.964806
\(696\) −1.54958e15 −0.359636
\(697\) 1.78012e15 0.409892
\(698\) −4.04132e15 −0.923248
\(699\) −3.80163e15 −0.861679
\(700\) 6.52740e13 0.0146792
\(701\) −1.83887e15 −0.410300 −0.205150 0.978731i \(-0.565768\pi\)
−0.205150 + 0.978731i \(0.565768\pi\)
\(702\) −1.10313e15 −0.244216
\(703\) −1.21858e15 −0.267670
\(704\) −5.33434e15 −1.16260
\(705\) 4.04135e14 0.0873949
\(706\) 6.08866e15 1.30646
\(707\) 3.69645e14 0.0787007
\(708\) 7.60674e13 0.0160700
\(709\) 9.16067e15 1.92032 0.960158 0.279456i \(-0.0901541\pi\)
0.960158 + 0.279456i \(0.0901541\pi\)
\(710\) 7.90076e15 1.64342
\(711\) −1.14934e15 −0.237227
\(712\) 1.07452e15 0.220078
\(713\) 2.25116e14 0.0457525
\(714\) 7.89548e13 0.0159235
\(715\) −1.16116e16 −2.32386
\(716\) −5.72251e14 −0.113649
\(717\) 3.85086e15 0.758931
\(718\) −4.98651e15 −0.975241
\(719\) −5.97641e14 −0.115993 −0.0579965 0.998317i \(-0.518471\pi\)
−0.0579965 + 0.998317i \(0.518471\pi\)
\(720\) −1.99141e15 −0.383559
\(721\) 1.66034e14 0.0317360
\(722\) 3.67774e14 0.0697631
\(723\) 6.71410e13 0.0126394
\(724\) −1.56835e15 −0.293010
\(725\) −4.41607e15 −0.818798
\(726\) −2.55635e14 −0.0470402
\(727\) 3.53545e15 0.645662 0.322831 0.946457i \(-0.395365\pi\)
0.322831 + 0.946457i \(0.395365\pi\)
\(728\) 4.12436e14 0.0747538
\(729\) 2.05891e14 0.0370370
\(730\) −6.25449e14 −0.111665
\(731\) −9.58850e14 −0.169905
\(732\) −6.24272e14 −0.109790
\(733\) −2.96392e15 −0.517362 −0.258681 0.965963i \(-0.583288\pi\)
−0.258681 + 0.965963i \(0.583288\pi\)
\(734\) 2.91880e15 0.505681
\(735\) 5.20509e15 0.895051
\(736\) −1.70367e15 −0.290775
\(737\) −1.52969e15 −0.259139
\(738\) 1.12415e15 0.189023
\(739\) −3.78463e15 −0.631654 −0.315827 0.948817i \(-0.602282\pi\)
−0.315827 + 0.948817i \(0.602282\pi\)
\(740\) −5.16848e14 −0.0856226
\(741\) 5.21884e15 0.858171
\(742\) −1.28308e13 −0.00209427
\(743\) 1.09269e16 1.77036 0.885178 0.465253i \(-0.154037\pi\)
0.885178 + 0.465253i \(0.154037\pi\)
\(744\) −2.55134e14 −0.0410315
\(745\) −1.61777e16 −2.58261
\(746\) 7.26631e15 1.15146
\(747\) −1.65958e15 −0.261057
\(748\) 9.16961e14 0.143183
\(749\) 2.94548e14 0.0456568
\(750\) −2.14397e15 −0.329900
\(751\) −2.74996e14 −0.0420055 −0.0210028 0.999779i \(-0.506686\pi\)
−0.0210028 + 0.999779i \(0.506686\pi\)
\(752\) 4.75701e14 0.0721333
\(753\) 2.80040e15 0.421548
\(754\) −4.91483e15 −0.734456
\(755\) −7.62372e15 −1.13099
\(756\) −1.35588e13 −0.00199688
\(757\) 2.81151e15 0.411067 0.205534 0.978650i \(-0.434107\pi\)
0.205534 + 0.978650i \(0.434107\pi\)
\(758\) 3.95480e15 0.574043
\(759\) −2.90074e15 −0.418002
\(760\) 1.21413e16 1.73697
\(761\) 6.70712e15 0.952622 0.476311 0.879277i \(-0.341974\pi\)
0.476311 + 0.879277i \(0.341974\pi\)
\(762\) 5.24042e15 0.738948
\(763\) 5.91873e13 0.00828597
\(764\) 1.69806e15 0.236015
\(765\) 2.40574e15 0.331980
\(766\) 5.62162e15 0.770199
\(767\) 1.36974e15 0.186321
\(768\) 2.60763e15 0.352175
\(769\) 7.23241e15 0.969814 0.484907 0.874566i \(-0.338854\pi\)
0.484907 + 0.874566i \(0.338854\pi\)
\(770\) 5.24831e14 0.0698748
\(771\) −4.97557e15 −0.657724
\(772\) 9.07069e14 0.119054
\(773\) 1.30804e16 1.70464 0.852322 0.523018i \(-0.175194\pi\)
0.852322 + 0.523018i \(0.175194\pi\)
\(774\) −6.05517e14 −0.0783521
\(775\) −7.27095e14 −0.0934183
\(776\) 2.86077e15 0.364958
\(777\) 5.70086e13 0.00722146
\(778\) −6.93210e15 −0.871920
\(779\) −5.31828e15 −0.664225
\(780\) 2.21352e15 0.274513
\(781\) −1.01209e16 −1.24634
\(782\) −3.21999e15 −0.393747
\(783\) 9.17313e14 0.111385
\(784\) 6.12682e15 0.738749
\(785\) 6.47848e15 0.775694
\(786\) 5.63873e15 0.670436
\(787\) 4.25105e15 0.501921 0.250960 0.967997i \(-0.419254\pi\)
0.250960 + 0.967997i \(0.419254\pi\)
\(788\) 1.17538e15 0.137810
\(789\) 4.24669e15 0.494455
\(790\) −8.48075e15 −0.980586
\(791\) 1.69150e14 0.0194224
\(792\) 3.28753e15 0.374871
\(793\) −1.12412e16 −1.27294
\(794\) 3.40352e15 0.382750
\(795\) −3.90953e14 −0.0436622
\(796\) 1.26922e15 0.140771
\(797\) 1.64370e15 0.181052 0.0905259 0.995894i \(-0.471145\pi\)
0.0905259 + 0.995894i \(0.471145\pi\)
\(798\) −2.35885e14 −0.0258038
\(799\) −5.74675e14 −0.0624331
\(800\) 5.50262e15 0.593710
\(801\) −6.36092e14 −0.0681619
\(802\) 1.56222e16 1.66258
\(803\) 8.01201e14 0.0846848
\(804\) 2.91604e14 0.0306116
\(805\) 5.01177e14 0.0522533
\(806\) −8.09214e14 −0.0837955
\(807\) 1.17458e15 0.120803
\(808\) 1.70853e16 1.74526
\(809\) −1.93364e16 −1.96182 −0.980908 0.194471i \(-0.937701\pi\)
−0.980908 + 0.194471i \(0.937701\pi\)
\(810\) 1.51923e15 0.153094
\(811\) 5.64125e15 0.564626 0.282313 0.959322i \(-0.408898\pi\)
0.282313 + 0.959322i \(0.408898\pi\)
\(812\) −6.04090e13 −0.00600542
\(813\) 1.35787e15 0.134078
\(814\) −2.43470e15 −0.238787
\(815\) −1.66454e16 −1.62154
\(816\) 2.83176e15 0.274007
\(817\) 2.86465e15 0.275328
\(818\) −1.33784e16 −1.27720
\(819\) −2.44152e14 −0.0231525
\(820\) −2.25569e15 −0.212473
\(821\) −1.49473e16 −1.39854 −0.699271 0.714856i \(-0.746492\pi\)
−0.699271 + 0.714856i \(0.746492\pi\)
\(822\) −2.68380e14 −0.0249434
\(823\) −3.25771e15 −0.300756 −0.150378 0.988629i \(-0.548049\pi\)
−0.150378 + 0.988629i \(0.548049\pi\)
\(824\) 7.67422e15 0.703776
\(825\) 9.36898e15 0.853485
\(826\) −6.19103e13 −0.00560238
\(827\) −1.34022e16 −1.20475 −0.602373 0.798214i \(-0.705778\pi\)
−0.602373 + 0.798214i \(0.705778\pi\)
\(828\) 5.52965e14 0.0493777
\(829\) 1.18044e16 1.04712 0.523559 0.851989i \(-0.324604\pi\)
0.523559 + 0.851989i \(0.324604\pi\)
\(830\) −1.22458e16 −1.07909
\(831\) 5.07172e15 0.443966
\(832\) 1.83108e16 1.59232
\(833\) −7.40157e15 −0.639405
\(834\) −3.70363e15 −0.317844
\(835\) −2.32076e16 −1.97859
\(836\) −2.73951e15 −0.232027
\(837\) 1.51033e14 0.0127082
\(838\) −6.85030e15 −0.572621
\(839\) −1.85159e16 −1.53764 −0.768819 0.639466i \(-0.779155\pi\)
−0.768819 + 0.639466i \(0.779155\pi\)
\(840\) −5.68006e14 −0.0468616
\(841\) −8.11357e15 −0.665019
\(842\) −1.80687e16 −1.47133
\(843\) 3.58493e15 0.290020
\(844\) 1.37811e15 0.110764
\(845\) 2.03985e16 1.62887
\(846\) −3.62909e14 −0.0287913
\(847\) −5.65787e13 −0.00445958
\(848\) −4.60184e14 −0.0360375
\(849\) −1.06877e16 −0.831558
\(850\) 1.04001e16 0.803961
\(851\) −2.32496e15 −0.178568
\(852\) 1.92934e15 0.147228
\(853\) −1.44922e16 −1.09879 −0.549395 0.835563i \(-0.685142\pi\)
−0.549395 + 0.835563i \(0.685142\pi\)
\(854\) 5.08087e14 0.0382754
\(855\) −7.18738e15 −0.537969
\(856\) 1.36142e16 1.01248
\(857\) 1.32162e15 0.0976589 0.0488294 0.998807i \(-0.484451\pi\)
0.0488294 + 0.998807i \(0.484451\pi\)
\(858\) 1.04271e16 0.765569
\(859\) 1.00009e16 0.729586 0.364793 0.931089i \(-0.381140\pi\)
0.364793 + 0.931089i \(0.381140\pi\)
\(860\) 1.21501e15 0.0880723
\(861\) 2.48804e14 0.0179201
\(862\) 9.07861e13 0.00649725
\(863\) −5.30862e15 −0.377505 −0.188752 0.982025i \(-0.560444\pi\)
−0.188752 + 0.982025i \(0.560444\pi\)
\(864\) −1.14301e15 −0.0807654
\(865\) 1.07064e16 0.751715
\(866\) −1.37264e16 −0.957650
\(867\) 4.90713e15 0.340191
\(868\) −9.94620e12 −0.000685171 0
\(869\) 1.08639e16 0.743661
\(870\) 6.76869e15 0.460414
\(871\) 5.25088e15 0.354922
\(872\) 2.73568e15 0.183749
\(873\) −1.69351e15 −0.113034
\(874\) 9.62002e15 0.638062
\(875\) −4.74517e14 −0.0312757
\(876\) −1.52732e14 −0.0100036
\(877\) −8.01495e15 −0.521679 −0.260839 0.965382i \(-0.583999\pi\)
−0.260839 + 0.965382i \(0.583999\pi\)
\(878\) −1.39897e16 −0.904875
\(879\) 1.25230e15 0.0804948
\(880\) 1.88234e16 1.20238
\(881\) −2.14390e16 −1.36093 −0.680466 0.732779i \(-0.738223\pi\)
−0.680466 + 0.732779i \(0.738223\pi\)
\(882\) −4.67411e15 −0.294864
\(883\) −1.67860e16 −1.05235 −0.526177 0.850375i \(-0.676375\pi\)
−0.526177 + 0.850375i \(0.676375\pi\)
\(884\) −3.14759e15 −0.196106
\(885\) −1.88640e15 −0.116801
\(886\) 1.32115e16 0.812954
\(887\) 2.63626e16 1.61216 0.806079 0.591808i \(-0.201585\pi\)
0.806079 + 0.591808i \(0.201585\pi\)
\(888\) 2.63498e15 0.160143
\(889\) 1.15984e15 0.0700550
\(890\) −4.69361e15 −0.281749
\(891\) −1.94614e15 −0.116104
\(892\) −4.23296e15 −0.250979
\(893\) 1.71689e15 0.101172
\(894\) 1.45274e16 0.850810
\(895\) 1.41913e16 0.826028
\(896\) −4.75553e14 −0.0275109
\(897\) 9.95718e15 0.572503
\(898\) −2.75472e16 −1.57419
\(899\) 6.72904e14 0.0382186
\(900\) −1.78600e15 −0.100820
\(901\) 5.55930e14 0.0311913
\(902\) −1.06258e16 −0.592551
\(903\) −1.34017e14 −0.00742806
\(904\) 7.81826e15 0.430709
\(905\) 3.88937e16 2.12967
\(906\) 6.84602e15 0.372591
\(907\) 5.82362e15 0.315031 0.157515 0.987517i \(-0.449652\pi\)
0.157515 + 0.987517i \(0.449652\pi\)
\(908\) −7.09411e15 −0.381439
\(909\) −1.01141e16 −0.540537
\(910\) −1.80155e15 −0.0957017
\(911\) −8.45962e14 −0.0446684 −0.0223342 0.999751i \(-0.507110\pi\)
−0.0223342 + 0.999751i \(0.507110\pi\)
\(912\) −8.46015e15 −0.444024
\(913\) 1.56869e16 0.818364
\(914\) −2.15225e16 −1.11606
\(915\) 1.54813e16 0.797981
\(916\) 1.95857e15 0.100349
\(917\) 1.24800e15 0.0635598
\(918\) −2.16033e15 −0.109367
\(919\) 5.10553e15 0.256925 0.128462 0.991714i \(-0.458996\pi\)
0.128462 + 0.991714i \(0.458996\pi\)
\(920\) 2.31648e16 1.15877
\(921\) −1.10703e16 −0.550468
\(922\) −1.96776e16 −0.972639
\(923\) 3.47413e16 1.70701
\(924\) 1.28162e14 0.00625983
\(925\) 7.50932e15 0.364604
\(926\) 8.82603e15 0.425996
\(927\) −4.54296e15 −0.217972
\(928\) −5.09250e15 −0.242894
\(929\) 7.11854e15 0.337524 0.168762 0.985657i \(-0.446023\pi\)
0.168762 + 0.985657i \(0.446023\pi\)
\(930\) 1.11445e15 0.0525296
\(931\) 2.21129e16 1.03615
\(932\) −6.85008e15 −0.319086
\(933\) −1.23869e16 −0.573605
\(934\) 1.99594e16 0.918841
\(935\) −2.27398e16 −1.04069
\(936\) −1.12849e16 −0.513429
\(937\) 1.39346e16 0.630271 0.315135 0.949047i \(-0.397950\pi\)
0.315135 + 0.949047i \(0.397950\pi\)
\(938\) −2.37333e14 −0.0106719
\(939\) −2.23180e16 −0.997687
\(940\) 7.28203e14 0.0323630
\(941\) −2.95060e16 −1.30367 −0.651834 0.758362i \(-0.726000\pi\)
−0.651834 + 0.758362i \(0.726000\pi\)
\(942\) −5.81761e15 −0.255543
\(943\) −1.01469e16 −0.443118
\(944\) −2.22045e15 −0.0964040
\(945\) 3.36246e14 0.0145138
\(946\) 5.72351e15 0.245619
\(947\) −2.92627e16 −1.24850 −0.624251 0.781224i \(-0.714596\pi\)
−0.624251 + 0.781224i \(0.714596\pi\)
\(948\) −2.07097e15 −0.0878471
\(949\) −2.75023e15 −0.115986
\(950\) −3.10714e16 −1.30281
\(951\) −1.17454e16 −0.489638
\(952\) 8.07697e14 0.0334769
\(953\) −1.08778e16 −0.448259 −0.224130 0.974559i \(-0.571954\pi\)
−0.224130 + 0.974559i \(0.571954\pi\)
\(954\) 3.51072e14 0.0143840
\(955\) −4.21103e16 −1.71542
\(956\) 6.93879e15 0.281038
\(957\) −8.67070e15 −0.349171
\(958\) −9.34043e15 −0.373987
\(959\) −5.93994e13 −0.00236472
\(960\) −2.52177e16 −0.998190
\(961\) −2.52977e16 −0.995640
\(962\) 8.35743e15 0.327047
\(963\) −8.05930e15 −0.313583
\(964\) 1.20980e14 0.00468048
\(965\) −2.24944e16 −0.865317
\(966\) −4.50052e14 −0.0172142
\(967\) −3.45076e16 −1.31241 −0.656204 0.754584i \(-0.727839\pi\)
−0.656204 + 0.754584i \(0.727839\pi\)
\(968\) −2.61511e15 −0.0988953
\(969\) 1.02204e16 0.384314
\(970\) −1.24961e16 −0.467228
\(971\) 1.99218e16 0.740666 0.370333 0.928899i \(-0.379244\pi\)
0.370333 + 0.928899i \(0.379244\pi\)
\(972\) 3.70991e14 0.0137151
\(973\) −8.19709e14 −0.0301328
\(974\) −3.16175e16 −1.15572
\(975\) −3.21603e16 −1.16895
\(976\) 1.82228e16 0.658631
\(977\) −8.01737e15 −0.288145 −0.144073 0.989567i \(-0.546020\pi\)
−0.144073 + 0.989567i \(0.546020\pi\)
\(978\) 1.49474e16 0.534196
\(979\) 6.01252e15 0.213674
\(980\) 9.37894e15 0.331444
\(981\) −1.61946e15 −0.0569103
\(982\) 2.49069e16 0.870374
\(983\) 4.41167e16 1.53306 0.766530 0.642209i \(-0.221982\pi\)
0.766530 + 0.642209i \(0.221982\pi\)
\(984\) 1.14999e16 0.397395
\(985\) −2.91482e16 −1.00164
\(986\) −9.62500e15 −0.328910
\(987\) −8.03211e13 −0.00272951
\(988\) 9.40373e15 0.317788
\(989\) 5.46555e15 0.183677
\(990\) −1.43602e16 −0.479919
\(991\) −4.98490e16 −1.65673 −0.828364 0.560190i \(-0.810728\pi\)
−0.828364 + 0.560190i \(0.810728\pi\)
\(992\) −8.38468e14 −0.0277123
\(993\) −1.29897e16 −0.426951
\(994\) −1.57026e15 −0.0513272
\(995\) −3.14754e16 −1.02316
\(996\) −2.99037e15 −0.0966716
\(997\) −3.71813e16 −1.19537 −0.597684 0.801732i \(-0.703912\pi\)
−0.597684 + 0.801732i \(0.703912\pi\)
\(998\) 4.41661e16 1.41212
\(999\) −1.55985e15 −0.0495989
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 177.12.a.a.1.20 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.a.1.20 26 1.1 even 1 trivial