Properties

Label 177.12.a.a.1.7
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 1.7
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-49.4794 q^{2} -243.000 q^{3} +400.209 q^{4} +6608.87 q^{5} +12023.5 q^{6} -17933.1 q^{7} +81531.7 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-49.4794 q^{2} -243.000 q^{3} +400.209 q^{4} +6608.87 q^{5} +12023.5 q^{6} -17933.1 q^{7} +81531.7 q^{8} +59049.0 q^{9} -327003. q^{10} +978139. q^{11} -97250.8 q^{12} +494374. q^{13} +887320. q^{14} -1.60596e6 q^{15} -4.85376e6 q^{16} -9.53772e6 q^{17} -2.92171e6 q^{18} +6.89884e6 q^{19} +2.64493e6 q^{20} +4.35775e6 q^{21} -4.83977e7 q^{22} +2.50424e7 q^{23} -1.98122e7 q^{24} -5.15090e6 q^{25} -2.44613e7 q^{26} -1.43489e7 q^{27} -7.17700e6 q^{28} -2.14527e8 q^{29} +7.94617e7 q^{30} +2.69999e8 q^{31} +7.31844e7 q^{32} -2.37688e8 q^{33} +4.71921e8 q^{34} -1.18518e8 q^{35} +2.36319e7 q^{36} -2.91399e8 q^{37} -3.41350e8 q^{38} -1.20133e8 q^{39} +5.38833e8 q^{40} -6.14837e8 q^{41} -2.15619e8 q^{42} -9.63348e8 q^{43} +3.91460e8 q^{44} +3.90247e8 q^{45} -1.23908e9 q^{46} -2.17341e9 q^{47} +1.17946e9 q^{48} -1.65573e9 q^{49} +2.54863e8 q^{50} +2.31767e9 q^{51} +1.97853e8 q^{52} +2.60466e9 q^{53} +7.09975e8 q^{54} +6.46440e9 q^{55} -1.46212e9 q^{56} -1.67642e9 q^{57} +1.06147e10 q^{58} +7.14924e8 q^{59} -6.42718e8 q^{60} +3.67189e9 q^{61} -1.33594e10 q^{62} -1.05893e9 q^{63} +6.31939e9 q^{64} +3.26726e9 q^{65} +1.17606e10 q^{66} +1.09092e10 q^{67} -3.81708e9 q^{68} -6.08530e9 q^{69} +5.86419e9 q^{70} -1.23634e10 q^{71} +4.81436e9 q^{72} +1.39653e10 q^{73} +1.44182e10 q^{74} +1.25167e9 q^{75} +2.76098e9 q^{76} -1.75411e10 q^{77} +5.94410e9 q^{78} +7.86947e9 q^{79} -3.20779e10 q^{80} +3.48678e9 q^{81} +3.04218e10 q^{82} +3.44891e10 q^{83} +1.74401e9 q^{84} -6.30336e10 q^{85} +4.76659e10 q^{86} +5.21301e10 q^{87} +7.97493e10 q^{88} +6.24194e10 q^{89} -1.93092e10 q^{90} -8.86567e9 q^{91} +1.00222e10 q^{92} -6.56098e10 q^{93} +1.07539e11 q^{94} +4.55936e10 q^{95} -1.77838e10 q^{96} -1.46326e11 q^{97} +8.19245e10 q^{98} +5.77581e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −49.4794 −1.09335 −0.546675 0.837345i \(-0.684107\pi\)
−0.546675 + 0.837345i \(0.684107\pi\)
\(3\) −243.000 −0.577350
\(4\) 400.209 0.195414
\(5\) 6608.87 0.945785 0.472893 0.881120i \(-0.343210\pi\)
0.472893 + 0.881120i \(0.343210\pi\)
\(6\) 12023.5 0.631246
\(7\) −17933.1 −0.403289 −0.201645 0.979459i \(-0.564629\pi\)
−0.201645 + 0.979459i \(0.564629\pi\)
\(8\) 81531.7 0.879694
\(9\) 59049.0 0.333333
\(10\) −327003. −1.03407
\(11\) 978139. 1.83122 0.915610 0.402067i \(-0.131708\pi\)
0.915610 + 0.402067i \(0.131708\pi\)
\(12\) −97250.8 −0.112823
\(13\) 494374. 0.369290 0.184645 0.982805i \(-0.440887\pi\)
0.184645 + 0.982805i \(0.440887\pi\)
\(14\) 887320. 0.440937
\(15\) −1.60596e6 −0.546049
\(16\) −4.85376e6 −1.15723
\(17\) −9.53772e6 −1.62920 −0.814602 0.580020i \(-0.803045\pi\)
−0.814602 + 0.580020i \(0.803045\pi\)
\(18\) −2.92171e6 −0.364450
\(19\) 6.89884e6 0.639192 0.319596 0.947554i \(-0.396453\pi\)
0.319596 + 0.947554i \(0.396453\pi\)
\(20\) 2.64493e6 0.184820
\(21\) 4.35775e6 0.232839
\(22\) −4.83977e7 −2.00217
\(23\) 2.50424e7 0.811283 0.405641 0.914032i \(-0.367048\pi\)
0.405641 + 0.914032i \(0.367048\pi\)
\(24\) −1.98122e7 −0.507891
\(25\) −5.15090e6 −0.105490
\(26\) −2.44613e7 −0.403763
\(27\) −1.43489e7 −0.192450
\(28\) −7.17700e6 −0.0788086
\(29\) −2.14527e8 −1.94220 −0.971099 0.238679i \(-0.923286\pi\)
−0.971099 + 0.238679i \(0.923286\pi\)
\(30\) 7.94617e7 0.597023
\(31\) 2.69999e8 1.69384 0.846921 0.531718i \(-0.178454\pi\)
0.846921 + 0.531718i \(0.178454\pi\)
\(32\) 7.31844e7 0.385561
\(33\) −2.37688e8 −1.05726
\(34\) 4.71921e8 1.78129
\(35\) −1.18518e8 −0.381425
\(36\) 2.36319e7 0.0651382
\(37\) −2.91399e8 −0.690841 −0.345420 0.938448i \(-0.612264\pi\)
−0.345420 + 0.938448i \(0.612264\pi\)
\(38\) −3.41350e8 −0.698860
\(39\) −1.20133e8 −0.213210
\(40\) 5.38833e8 0.832001
\(41\) −6.14837e8 −0.828798 −0.414399 0.910095i \(-0.636008\pi\)
−0.414399 + 0.910095i \(0.636008\pi\)
\(42\) −2.15619e8 −0.254575
\(43\) −9.63348e8 −0.999325 −0.499662 0.866220i \(-0.666543\pi\)
−0.499662 + 0.866220i \(0.666543\pi\)
\(44\) 3.91460e8 0.357847
\(45\) 3.90247e8 0.315262
\(46\) −1.23908e9 −0.887016
\(47\) −2.17341e9 −1.38231 −0.691153 0.722708i \(-0.742897\pi\)
−0.691153 + 0.722708i \(0.742897\pi\)
\(48\) 1.17946e9 0.668126
\(49\) −1.65573e9 −0.837358
\(50\) 2.54863e8 0.115338
\(51\) 2.31767e9 0.940622
\(52\) 1.97853e8 0.0721646
\(53\) 2.60466e9 0.855526 0.427763 0.903891i \(-0.359302\pi\)
0.427763 + 0.903891i \(0.359302\pi\)
\(54\) 7.09975e8 0.210415
\(55\) 6.46440e9 1.73194
\(56\) −1.46212e9 −0.354771
\(57\) −1.67642e9 −0.369038
\(58\) 1.06147e10 2.12350
\(59\) 7.14924e8 0.130189
\(60\) −6.42718e8 −0.106706
\(61\) 3.67189e9 0.556641 0.278321 0.960488i \(-0.410222\pi\)
0.278321 + 0.960488i \(0.410222\pi\)
\(62\) −1.33594e10 −1.85196
\(63\) −1.05893e9 −0.134430
\(64\) 6.31939e9 0.735674
\(65\) 3.26726e9 0.349269
\(66\) 1.17606e10 1.15595
\(67\) 1.09092e10 0.987151 0.493575 0.869703i \(-0.335690\pi\)
0.493575 + 0.869703i \(0.335690\pi\)
\(68\) −3.81708e9 −0.318370
\(69\) −6.08530e9 −0.468394
\(70\) 5.86419e9 0.417031
\(71\) −1.23634e10 −0.813237 −0.406618 0.913598i \(-0.633292\pi\)
−0.406618 + 0.913598i \(0.633292\pi\)
\(72\) 4.81436e9 0.293231
\(73\) 1.39653e10 0.788450 0.394225 0.919014i \(-0.371013\pi\)
0.394225 + 0.919014i \(0.371013\pi\)
\(74\) 1.44182e10 0.755331
\(75\) 1.25167e9 0.0609049
\(76\) 2.76098e9 0.124907
\(77\) −1.75411e10 −0.738512
\(78\) 5.94410e9 0.233113
\(79\) 7.86947e9 0.287738 0.143869 0.989597i \(-0.454046\pi\)
0.143869 + 0.989597i \(0.454046\pi\)
\(80\) −3.20779e10 −1.09449
\(81\) 3.48678e9 0.111111
\(82\) 3.04218e10 0.906167
\(83\) 3.44891e10 0.961064 0.480532 0.876977i \(-0.340444\pi\)
0.480532 + 0.876977i \(0.340444\pi\)
\(84\) 1.74401e9 0.0455002
\(85\) −6.30336e10 −1.54088
\(86\) 4.76659e10 1.09261
\(87\) 5.21301e10 1.12133
\(88\) 7.97493e10 1.61091
\(89\) 6.24194e10 1.18488 0.592440 0.805614i \(-0.298165\pi\)
0.592440 + 0.805614i \(0.298165\pi\)
\(90\) −1.93092e10 −0.344691
\(91\) −8.86567e9 −0.148931
\(92\) 1.00222e10 0.158536
\(93\) −6.56098e10 −0.977940
\(94\) 1.07539e11 1.51134
\(95\) 4.55936e10 0.604538
\(96\) −1.77838e10 −0.222604
\(97\) −1.46326e11 −1.73012 −0.865059 0.501669i \(-0.832719\pi\)
−0.865059 + 0.501669i \(0.832719\pi\)
\(98\) 8.19245e10 0.915525
\(99\) 5.77581e10 0.610407
\(100\) −2.06144e9 −0.0206144
\(101\) −8.77236e10 −0.830517 −0.415259 0.909703i \(-0.636309\pi\)
−0.415259 + 0.909703i \(0.636309\pi\)
\(102\) −1.14677e11 −1.02843
\(103\) −7.67208e10 −0.652091 −0.326046 0.945354i \(-0.605716\pi\)
−0.326046 + 0.945354i \(0.605716\pi\)
\(104\) 4.03071e10 0.324862
\(105\) 2.87998e10 0.220216
\(106\) −1.28877e11 −0.935389
\(107\) 1.37621e11 0.948580 0.474290 0.880369i \(-0.342705\pi\)
0.474290 + 0.880369i \(0.342705\pi\)
\(108\) −5.74256e9 −0.0376075
\(109\) −1.27808e11 −0.795635 −0.397817 0.917465i \(-0.630232\pi\)
−0.397817 + 0.917465i \(0.630232\pi\)
\(110\) −3.19854e11 −1.89362
\(111\) 7.08099e10 0.398857
\(112\) 8.70432e10 0.466698
\(113\) −7.20783e10 −0.368022 −0.184011 0.982924i \(-0.558908\pi\)
−0.184011 + 0.982924i \(0.558908\pi\)
\(114\) 8.29481e10 0.403487
\(115\) 1.65502e11 0.767299
\(116\) −8.58557e10 −0.379533
\(117\) 2.91923e10 0.123097
\(118\) −3.53740e10 −0.142342
\(119\) 1.71041e11 0.657041
\(120\) −1.30936e11 −0.480356
\(121\) 6.71443e11 2.35337
\(122\) −1.81683e11 −0.608604
\(123\) 1.49405e11 0.478507
\(124\) 1.08056e11 0.331001
\(125\) −3.56741e11 −1.04556
\(126\) 5.23954e10 0.146979
\(127\) −5.25572e11 −1.41160 −0.705800 0.708411i \(-0.749412\pi\)
−0.705800 + 0.708411i \(0.749412\pi\)
\(128\) −4.62561e11 −1.18991
\(129\) 2.34094e11 0.576960
\(130\) −1.61662e11 −0.381873
\(131\) 8.43429e11 1.91010 0.955051 0.296443i \(-0.0958005\pi\)
0.955051 + 0.296443i \(0.0958005\pi\)
\(132\) −9.51247e10 −0.206603
\(133\) −1.23718e11 −0.257779
\(134\) −5.39783e11 −1.07930
\(135\) −9.48301e10 −0.182016
\(136\) −7.77626e11 −1.43320
\(137\) −3.77154e11 −0.667660 −0.333830 0.942633i \(-0.608341\pi\)
−0.333830 + 0.942633i \(0.608341\pi\)
\(138\) 3.01097e11 0.512119
\(139\) 2.28213e11 0.373043 0.186522 0.982451i \(-0.440279\pi\)
0.186522 + 0.982451i \(0.440279\pi\)
\(140\) −4.74319e10 −0.0745360
\(141\) 5.28140e11 0.798075
\(142\) 6.11733e11 0.889153
\(143\) 4.83566e11 0.676251
\(144\) −2.86610e11 −0.385743
\(145\) −1.41778e12 −1.83690
\(146\) −6.90994e11 −0.862052
\(147\) 4.02342e11 0.483449
\(148\) −1.16620e11 −0.135000
\(149\) 3.80245e10 0.0424170 0.0212085 0.999775i \(-0.493249\pi\)
0.0212085 + 0.999775i \(0.493249\pi\)
\(150\) −6.19318e10 −0.0665904
\(151\) 2.56888e11 0.266299 0.133150 0.991096i \(-0.457491\pi\)
0.133150 + 0.991096i \(0.457491\pi\)
\(152\) 5.62474e11 0.562293
\(153\) −5.63193e11 −0.543068
\(154\) 8.67922e11 0.807452
\(155\) 1.78439e12 1.60201
\(156\) −4.80782e10 −0.0416642
\(157\) 1.51998e11 0.127172 0.0635859 0.997976i \(-0.479746\pi\)
0.0635859 + 0.997976i \(0.479746\pi\)
\(158\) −3.89377e11 −0.314598
\(159\) −6.32931e11 −0.493938
\(160\) 4.83666e11 0.364658
\(161\) −4.49088e11 −0.327182
\(162\) −1.72524e11 −0.121483
\(163\) −1.83131e12 −1.24661 −0.623304 0.781980i \(-0.714210\pi\)
−0.623304 + 0.781980i \(0.714210\pi\)
\(164\) −2.46063e11 −0.161959
\(165\) −1.57085e12 −0.999937
\(166\) −1.70650e12 −1.05078
\(167\) −2.90687e12 −1.73175 −0.865874 0.500262i \(-0.833237\pi\)
−0.865874 + 0.500262i \(0.833237\pi\)
\(168\) 3.55295e11 0.204827
\(169\) −1.54775e12 −0.863625
\(170\) 3.11886e12 1.68472
\(171\) 4.07370e11 0.213064
\(172\) −3.85540e11 −0.195283
\(173\) −2.33226e12 −1.14426 −0.572129 0.820164i \(-0.693882\pi\)
−0.572129 + 0.820164i \(0.693882\pi\)
\(174\) −2.57936e12 −1.22600
\(175\) 9.23718e10 0.0425432
\(176\) −4.74765e12 −2.11914
\(177\) −1.73727e11 −0.0751646
\(178\) −3.08847e12 −1.29549
\(179\) −9.95026e11 −0.404709 −0.202355 0.979312i \(-0.564859\pi\)
−0.202355 + 0.979312i \(0.564859\pi\)
\(180\) 1.56180e11 0.0616067
\(181\) 2.52323e12 0.965440 0.482720 0.875775i \(-0.339649\pi\)
0.482720 + 0.875775i \(0.339649\pi\)
\(182\) 4.38668e11 0.162833
\(183\) −8.92269e11 −0.321377
\(184\) 2.04175e12 0.713680
\(185\) −1.92582e12 −0.653387
\(186\) 3.24633e12 1.06923
\(187\) −9.32921e12 −2.98343
\(188\) −8.69820e11 −0.270123
\(189\) 2.57321e11 0.0776131
\(190\) −2.25594e12 −0.660972
\(191\) −4.70874e12 −1.34036 −0.670179 0.742199i \(-0.733783\pi\)
−0.670179 + 0.742199i \(0.733783\pi\)
\(192\) −1.53561e12 −0.424742
\(193\) 3.14793e11 0.0846175 0.0423088 0.999105i \(-0.486529\pi\)
0.0423088 + 0.999105i \(0.486529\pi\)
\(194\) 7.24010e12 1.89163
\(195\) −7.93943e11 −0.201650
\(196\) −6.62638e11 −0.163632
\(197\) −7.57251e11 −0.181834 −0.0909171 0.995858i \(-0.528980\pi\)
−0.0909171 + 0.995858i \(0.528980\pi\)
\(198\) −2.85784e12 −0.667388
\(199\) 7.43156e12 1.68806 0.844030 0.536295i \(-0.180177\pi\)
0.844030 + 0.536295i \(0.180177\pi\)
\(200\) −4.19962e11 −0.0927993
\(201\) −2.65095e12 −0.569932
\(202\) 4.34051e12 0.908046
\(203\) 3.84714e12 0.783267
\(204\) 9.27551e11 0.183811
\(205\) −4.06338e12 −0.783865
\(206\) 3.79610e12 0.712964
\(207\) 1.47873e12 0.270428
\(208\) −2.39958e12 −0.427352
\(209\) 6.74802e12 1.17050
\(210\) −1.42500e12 −0.240773
\(211\) −9.96014e12 −1.63950 −0.819751 0.572720i \(-0.805888\pi\)
−0.819751 + 0.572720i \(0.805888\pi\)
\(212\) 1.04241e12 0.167182
\(213\) 3.00431e12 0.469523
\(214\) −6.80940e12 −1.03713
\(215\) −6.36665e12 −0.945146
\(216\) −1.16989e12 −0.169297
\(217\) −4.84193e12 −0.683109
\(218\) 6.32388e12 0.869908
\(219\) −3.39357e12 −0.455212
\(220\) 2.58711e12 0.338446
\(221\) −4.71520e12 −0.601648
\(222\) −3.50363e12 −0.436090
\(223\) 3.30929e12 0.401844 0.200922 0.979607i \(-0.435606\pi\)
0.200922 + 0.979607i \(0.435606\pi\)
\(224\) −1.31242e12 −0.155493
\(225\) −3.04156e11 −0.0351635
\(226\) 3.56639e12 0.402376
\(227\) 8.21619e12 0.904749 0.452374 0.891828i \(-0.350577\pi\)
0.452374 + 0.891828i \(0.350577\pi\)
\(228\) −6.70917e11 −0.0721153
\(229\) −8.95761e12 −0.939933 −0.469967 0.882684i \(-0.655734\pi\)
−0.469967 + 0.882684i \(0.655734\pi\)
\(230\) −8.18893e12 −0.838927
\(231\) 4.26248e12 0.426380
\(232\) −1.74908e13 −1.70854
\(233\) 1.42913e13 1.36337 0.681686 0.731645i \(-0.261247\pi\)
0.681686 + 0.731645i \(0.261247\pi\)
\(234\) −1.44442e12 −0.134588
\(235\) −1.43638e13 −1.30736
\(236\) 2.86119e11 0.0254408
\(237\) −1.91228e12 −0.166125
\(238\) −8.46301e12 −0.718376
\(239\) 4.12148e12 0.341873 0.170936 0.985282i \(-0.445321\pi\)
0.170936 + 0.985282i \(0.445321\pi\)
\(240\) 7.79494e12 0.631903
\(241\) −1.92304e13 −1.52369 −0.761843 0.647762i \(-0.775705\pi\)
−0.761843 + 0.647762i \(0.775705\pi\)
\(242\) −3.32226e13 −2.57306
\(243\) −8.47289e11 −0.0641500
\(244\) 1.46952e12 0.108776
\(245\) −1.09425e13 −0.791960
\(246\) −7.39249e12 −0.523176
\(247\) 3.41061e12 0.236047
\(248\) 2.20135e13 1.49006
\(249\) −8.38085e12 −0.554871
\(250\) 1.76513e13 1.14316
\(251\) −2.89097e12 −0.183163 −0.0915817 0.995798i \(-0.529192\pi\)
−0.0915817 + 0.995798i \(0.529192\pi\)
\(252\) −4.23794e11 −0.0262695
\(253\) 2.44949e13 1.48564
\(254\) 2.60050e13 1.54337
\(255\) 1.53172e13 0.889626
\(256\) 9.94513e12 0.565315
\(257\) −1.53114e13 −0.851887 −0.425944 0.904750i \(-0.640058\pi\)
−0.425944 + 0.904750i \(0.640058\pi\)
\(258\) −1.15828e13 −0.630820
\(259\) 5.22569e12 0.278609
\(260\) 1.30758e12 0.0682522
\(261\) −1.26676e13 −0.647399
\(262\) −4.17323e13 −2.08841
\(263\) 1.35532e13 0.664179 0.332089 0.943248i \(-0.392246\pi\)
0.332089 + 0.943248i \(0.392246\pi\)
\(264\) −1.93791e13 −0.930061
\(265\) 1.72138e13 0.809143
\(266\) 6.12148e12 0.281843
\(267\) −1.51679e13 −0.684091
\(268\) 4.36598e12 0.192904
\(269\) 1.50247e13 0.650380 0.325190 0.945649i \(-0.394572\pi\)
0.325190 + 0.945649i \(0.394572\pi\)
\(270\) 4.69214e12 0.199008
\(271\) 4.05690e13 1.68602 0.843010 0.537898i \(-0.180781\pi\)
0.843010 + 0.537898i \(0.180781\pi\)
\(272\) 4.62939e13 1.88536
\(273\) 2.15436e12 0.0859851
\(274\) 1.86613e13 0.729986
\(275\) −5.03829e12 −0.193176
\(276\) −2.43539e12 −0.0915310
\(277\) −1.64608e13 −0.606474 −0.303237 0.952915i \(-0.598067\pi\)
−0.303237 + 0.952915i \(0.598067\pi\)
\(278\) −1.12918e13 −0.407867
\(279\) 1.59432e13 0.564614
\(280\) −9.66295e12 −0.335537
\(281\) −2.07851e13 −0.707728 −0.353864 0.935297i \(-0.615132\pi\)
−0.353864 + 0.935297i \(0.615132\pi\)
\(282\) −2.61320e13 −0.872575
\(283\) 5.01441e13 1.64208 0.821040 0.570871i \(-0.193395\pi\)
0.821040 + 0.570871i \(0.193395\pi\)
\(284\) −4.94794e12 −0.158918
\(285\) −1.10792e13 −0.349030
\(286\) −2.39266e13 −0.739379
\(287\) 1.10260e13 0.334246
\(288\) 4.32146e12 0.128520
\(289\) 5.66962e13 1.65431
\(290\) 7.01510e13 2.00838
\(291\) 3.55571e13 0.998885
\(292\) 5.58903e12 0.154075
\(293\) 1.21982e13 0.330008 0.165004 0.986293i \(-0.447236\pi\)
0.165004 + 0.986293i \(0.447236\pi\)
\(294\) −1.99076e13 −0.528579
\(295\) 4.72485e12 0.123131
\(296\) −2.37582e13 −0.607728
\(297\) −1.40352e13 −0.352419
\(298\) −1.88143e12 −0.0463766
\(299\) 1.23803e13 0.299598
\(300\) 5.00929e11 0.0119017
\(301\) 1.72758e13 0.403017
\(302\) −1.27106e13 −0.291158
\(303\) 2.13168e13 0.479499
\(304\) −3.34853e13 −0.739690
\(305\) 2.42671e13 0.526463
\(306\) 2.78664e13 0.593764
\(307\) −1.59534e13 −0.333880 −0.166940 0.985967i \(-0.553389\pi\)
−0.166940 + 0.985967i \(0.553389\pi\)
\(308\) −7.02010e12 −0.144316
\(309\) 1.86431e13 0.376485
\(310\) −8.82905e13 −1.75156
\(311\) 1.15687e13 0.225478 0.112739 0.993625i \(-0.464038\pi\)
0.112739 + 0.993625i \(0.464038\pi\)
\(312\) −9.79464e12 −0.187559
\(313\) −5.37759e13 −1.01180 −0.505899 0.862593i \(-0.668839\pi\)
−0.505899 + 0.862593i \(0.668839\pi\)
\(314\) −7.52078e12 −0.139043
\(315\) −6.99836e12 −0.127142
\(316\) 3.14943e12 0.0562281
\(317\) 2.98799e13 0.524267 0.262134 0.965032i \(-0.415574\pi\)
0.262134 + 0.965032i \(0.415574\pi\)
\(318\) 3.13170e13 0.540047
\(319\) −2.09837e14 −3.55659
\(320\) 4.17641e13 0.695790
\(321\) −3.34419e13 −0.547663
\(322\) 2.22206e13 0.357724
\(323\) −6.57992e13 −1.04137
\(324\) 1.39544e12 0.0217127
\(325\) −2.54647e12 −0.0389565
\(326\) 9.06120e13 1.36298
\(327\) 3.10575e13 0.459360
\(328\) −5.01287e13 −0.729089
\(329\) 3.89761e13 0.557469
\(330\) 7.77246e13 1.09328
\(331\) 5.89326e13 0.815270 0.407635 0.913145i \(-0.366354\pi\)
0.407635 + 0.913145i \(0.366354\pi\)
\(332\) 1.38028e13 0.187806
\(333\) −1.72068e13 −0.230280
\(334\) 1.43830e14 1.89341
\(335\) 7.20979e13 0.933632
\(336\) −2.11515e13 −0.269448
\(337\) −4.44507e13 −0.557075 −0.278538 0.960425i \(-0.589850\pi\)
−0.278538 + 0.960425i \(0.589850\pi\)
\(338\) 7.65819e13 0.944245
\(339\) 1.75150e13 0.212477
\(340\) −2.52266e13 −0.301110
\(341\) 2.64097e14 3.10180
\(342\) −2.01564e13 −0.232953
\(343\) 6.51521e13 0.740987
\(344\) −7.85434e13 −0.879100
\(345\) −4.02170e13 −0.443000
\(346\) 1.15399e14 1.25107
\(347\) −1.71346e14 −1.82836 −0.914181 0.405305i \(-0.867165\pi\)
−0.914181 + 0.405305i \(0.867165\pi\)
\(348\) 2.08629e13 0.219124
\(349\) −5.75830e13 −0.595325 −0.297663 0.954671i \(-0.596207\pi\)
−0.297663 + 0.954671i \(0.596207\pi\)
\(350\) −4.57050e12 −0.0465146
\(351\) −7.09373e12 −0.0710698
\(352\) 7.15845e13 0.706048
\(353\) 3.95768e13 0.384309 0.192154 0.981365i \(-0.438453\pi\)
0.192154 + 0.981365i \(0.438453\pi\)
\(354\) 8.59588e12 0.0821812
\(355\) −8.17082e13 −0.769147
\(356\) 2.49808e13 0.231543
\(357\) −4.15630e13 −0.379343
\(358\) 4.92333e13 0.442489
\(359\) −1.03541e14 −0.916418 −0.458209 0.888845i \(-0.651509\pi\)
−0.458209 + 0.888845i \(0.651509\pi\)
\(360\) 3.18175e13 0.277334
\(361\) −6.88963e13 −0.591434
\(362\) −1.24848e14 −1.05556
\(363\) −1.63161e14 −1.35872
\(364\) −3.54812e12 −0.0291032
\(365\) 9.22949e13 0.745704
\(366\) 4.41489e13 0.351378
\(367\) −7.22655e13 −0.566588 −0.283294 0.959033i \(-0.591427\pi\)
−0.283294 + 0.959033i \(0.591427\pi\)
\(368\) −1.21550e14 −0.938839
\(369\) −3.63055e13 −0.276266
\(370\) 9.52882e13 0.714381
\(371\) −4.67096e13 −0.345024
\(372\) −2.62576e13 −0.191104
\(373\) −8.53528e12 −0.0612096 −0.0306048 0.999532i \(-0.509743\pi\)
−0.0306048 + 0.999532i \(0.509743\pi\)
\(374\) 4.61604e14 3.26194
\(375\) 8.66880e13 0.603652
\(376\) −1.77202e14 −1.21601
\(377\) −1.06057e14 −0.717233
\(378\) −1.27321e13 −0.0848583
\(379\) 8.02058e13 0.526854 0.263427 0.964679i \(-0.415147\pi\)
0.263427 + 0.964679i \(0.415147\pi\)
\(380\) 1.82469e13 0.118136
\(381\) 1.27714e14 0.814988
\(382\) 2.32985e14 1.46548
\(383\) −4.42970e13 −0.274651 −0.137325 0.990526i \(-0.543851\pi\)
−0.137325 + 0.990526i \(0.543851\pi\)
\(384\) 1.12402e14 0.686995
\(385\) −1.15927e14 −0.698473
\(386\) −1.55758e13 −0.0925166
\(387\) −5.68847e13 −0.333108
\(388\) −5.85608e13 −0.338090
\(389\) −1.10253e14 −0.627578 −0.313789 0.949493i \(-0.601598\pi\)
−0.313789 + 0.949493i \(0.601598\pi\)
\(390\) 3.92838e13 0.220474
\(391\) −2.38847e14 −1.32175
\(392\) −1.34994e14 −0.736618
\(393\) −2.04953e14 −1.10280
\(394\) 3.74683e13 0.198808
\(395\) 5.20084e13 0.272138
\(396\) 2.31153e13 0.119282
\(397\) −3.54712e12 −0.0180521 −0.00902606 0.999959i \(-0.502873\pi\)
−0.00902606 + 0.999959i \(0.502873\pi\)
\(398\) −3.67709e14 −1.84564
\(399\) 3.00634e13 0.148829
\(400\) 2.50013e13 0.122076
\(401\) 2.96303e14 1.42706 0.713529 0.700625i \(-0.247096\pi\)
0.713529 + 0.700625i \(0.247096\pi\)
\(402\) 1.31167e14 0.623135
\(403\) 1.33481e14 0.625519
\(404\) −3.51077e13 −0.162295
\(405\) 2.30437e13 0.105087
\(406\) −1.90354e14 −0.856386
\(407\) −2.85028e14 −1.26508
\(408\) 1.88963e14 0.827459
\(409\) −1.60718e14 −0.694364 −0.347182 0.937798i \(-0.612861\pi\)
−0.347182 + 0.937798i \(0.612861\pi\)
\(410\) 2.01054e14 0.857039
\(411\) 9.16484e13 0.385474
\(412\) −3.07043e13 −0.127428
\(413\) −1.28208e13 −0.0525038
\(414\) −7.31665e13 −0.295672
\(415\) 2.27934e14 0.908960
\(416\) 3.61805e13 0.142384
\(417\) −5.54558e13 −0.215377
\(418\) −3.33888e14 −1.27977
\(419\) 2.71067e14 1.02541 0.512707 0.858564i \(-0.328643\pi\)
0.512707 + 0.858564i \(0.328643\pi\)
\(420\) 1.15259e13 0.0430334
\(421\) −2.58859e14 −0.953921 −0.476960 0.878925i \(-0.658261\pi\)
−0.476960 + 0.878925i \(0.658261\pi\)
\(422\) 4.92822e14 1.79255
\(423\) −1.28338e14 −0.460769
\(424\) 2.12362e14 0.752600
\(425\) 4.91279e13 0.171865
\(426\) −1.48651e14 −0.513353
\(427\) −6.58485e13 −0.224488
\(428\) 5.50772e13 0.185366
\(429\) −1.17507e14 −0.390434
\(430\) 3.15018e14 1.03338
\(431\) −6.24636e13 −0.202303 −0.101151 0.994871i \(-0.532253\pi\)
−0.101151 + 0.994871i \(0.532253\pi\)
\(432\) 6.96462e13 0.222709
\(433\) 4.04003e14 1.27556 0.637780 0.770219i \(-0.279853\pi\)
0.637780 + 0.770219i \(0.279853\pi\)
\(434\) 2.39576e14 0.746877
\(435\) 3.44521e14 1.06054
\(436\) −5.11501e13 −0.155479
\(437\) 1.72763e14 0.518565
\(438\) 1.67912e14 0.497706
\(439\) −3.42771e14 −1.00334 −0.501671 0.865059i \(-0.667281\pi\)
−0.501671 + 0.865059i \(0.667281\pi\)
\(440\) 5.27053e14 1.52358
\(441\) −9.77692e13 −0.279119
\(442\) 2.33305e14 0.657812
\(443\) −3.25901e14 −0.907538 −0.453769 0.891119i \(-0.649921\pi\)
−0.453769 + 0.891119i \(0.649921\pi\)
\(444\) 2.83387e13 0.0779425
\(445\) 4.12522e14 1.12064
\(446\) −1.63742e14 −0.439357
\(447\) −9.23996e12 −0.0244894
\(448\) −1.13326e14 −0.296690
\(449\) 1.57380e14 0.407000 0.203500 0.979075i \(-0.434768\pi\)
0.203500 + 0.979075i \(0.434768\pi\)
\(450\) 1.50494e13 0.0384460
\(451\) −6.01396e14 −1.51771
\(452\) −2.88464e13 −0.0719167
\(453\) −6.24237e13 −0.153748
\(454\) −4.06532e14 −0.989207
\(455\) −5.85921e13 −0.140856
\(456\) −1.36681e14 −0.324640
\(457\) −1.55301e14 −0.364447 −0.182224 0.983257i \(-0.558329\pi\)
−0.182224 + 0.983257i \(0.558329\pi\)
\(458\) 4.43217e14 1.02768
\(459\) 1.36856e14 0.313541
\(460\) 6.62353e13 0.149941
\(461\) −5.55644e13 −0.124292 −0.0621458 0.998067i \(-0.519794\pi\)
−0.0621458 + 0.998067i \(0.519794\pi\)
\(462\) −2.10905e14 −0.466183
\(463\) −2.11155e14 −0.461217 −0.230609 0.973047i \(-0.574072\pi\)
−0.230609 + 0.973047i \(0.574072\pi\)
\(464\) 1.04126e15 2.24756
\(465\) −4.33607e14 −0.924921
\(466\) −7.07125e14 −1.49064
\(467\) 5.95058e14 1.23970 0.619850 0.784720i \(-0.287193\pi\)
0.619850 + 0.784720i \(0.287193\pi\)
\(468\) 1.16830e13 0.0240549
\(469\) −1.95637e14 −0.398107
\(470\) 7.10713e14 1.42941
\(471\) −3.69356e13 −0.0734226
\(472\) 5.82890e13 0.114526
\(473\) −9.42288e14 −1.82998
\(474\) 9.46185e13 0.181633
\(475\) −3.55352e13 −0.0674286
\(476\) 6.84522e13 0.128395
\(477\) 1.53802e14 0.285175
\(478\) −2.03928e14 −0.373787
\(479\) −7.93679e14 −1.43813 −0.719067 0.694941i \(-0.755431\pi\)
−0.719067 + 0.694941i \(0.755431\pi\)
\(480\) −1.17531e14 −0.210536
\(481\) −1.44060e14 −0.255120
\(482\) 9.51510e14 1.66592
\(483\) 1.09128e14 0.188898
\(484\) 2.68718e14 0.459882
\(485\) −9.67048e14 −1.63632
\(486\) 4.19233e13 0.0701384
\(487\) 4.48179e14 0.741383 0.370691 0.928756i \(-0.379121\pi\)
0.370691 + 0.928756i \(0.379121\pi\)
\(488\) 2.99375e14 0.489674
\(489\) 4.45008e14 0.719729
\(490\) 5.41429e14 0.865890
\(491\) 1.28873e14 0.203804 0.101902 0.994794i \(-0.467507\pi\)
0.101902 + 0.994794i \(0.467507\pi\)
\(492\) 5.97934e13 0.0935072
\(493\) 2.04610e15 3.16424
\(494\) −1.68755e14 −0.258082
\(495\) 3.81716e14 0.577314
\(496\) −1.31051e15 −1.96016
\(497\) 2.21714e14 0.327970
\(498\) 4.14679e14 0.606668
\(499\) 3.76743e14 0.545120 0.272560 0.962139i \(-0.412130\pi\)
0.272560 + 0.962139i \(0.412130\pi\)
\(500\) −1.42771e14 −0.204317
\(501\) 7.06369e14 0.999825
\(502\) 1.43044e14 0.200262
\(503\) −8.75394e14 −1.21222 −0.606108 0.795383i \(-0.707270\pi\)
−0.606108 + 0.795383i \(0.707270\pi\)
\(504\) −8.63366e13 −0.118257
\(505\) −5.79754e14 −0.785491
\(506\) −1.21199e15 −1.62432
\(507\) 3.76104e14 0.498614
\(508\) −2.10339e14 −0.275847
\(509\) 4.28083e14 0.555367 0.277683 0.960673i \(-0.410433\pi\)
0.277683 + 0.960673i \(0.410433\pi\)
\(510\) −7.57884e14 −0.972673
\(511\) −2.50441e14 −0.317974
\(512\) 4.55247e14 0.571824
\(513\) −9.89908e13 −0.123013
\(514\) 7.57597e14 0.931411
\(515\) −5.07038e14 −0.616738
\(516\) 9.36863e13 0.112746
\(517\) −2.12590e15 −2.53131
\(518\) −2.58564e14 −0.304617
\(519\) 5.66740e14 0.660638
\(520\) 2.66385e14 0.307249
\(521\) 1.67398e15 1.91049 0.955243 0.295822i \(-0.0955935\pi\)
0.955243 + 0.295822i \(0.0955935\pi\)
\(522\) 6.26786e14 0.707834
\(523\) −1.29093e15 −1.44259 −0.721294 0.692629i \(-0.756452\pi\)
−0.721294 + 0.692629i \(0.756452\pi\)
\(524\) 3.37548e14 0.373261
\(525\) −2.24463e13 −0.0245623
\(526\) −6.70603e14 −0.726180
\(527\) −2.57518e15 −2.75962
\(528\) 1.15368e15 1.22349
\(529\) −3.25690e14 −0.341820
\(530\) −8.51730e14 −0.884677
\(531\) 4.22156e13 0.0433963
\(532\) −4.95129e13 −0.0503738
\(533\) −3.03960e14 −0.306067
\(534\) 7.50499e14 0.747951
\(535\) 9.09520e14 0.897153
\(536\) 8.89449e14 0.868390
\(537\) 2.41791e14 0.233659
\(538\) −7.43411e14 −0.711094
\(539\) −1.61953e15 −1.53339
\(540\) −3.79519e13 −0.0355686
\(541\) −1.55979e15 −1.44704 −0.723519 0.690304i \(-0.757477\pi\)
−0.723519 + 0.690304i \(0.757477\pi\)
\(542\) −2.00733e15 −1.84341
\(543\) −6.13146e14 −0.557397
\(544\) −6.98012e14 −0.628158
\(545\) −8.44670e14 −0.752500
\(546\) −1.06596e14 −0.0940119
\(547\) −6.95998e14 −0.607683 −0.303842 0.952723i \(-0.598269\pi\)
−0.303842 + 0.952723i \(0.598269\pi\)
\(548\) −1.50940e14 −0.130470
\(549\) 2.16821e14 0.185547
\(550\) 2.49292e14 0.211209
\(551\) −1.47999e15 −1.24144
\(552\) −4.96144e14 −0.412044
\(553\) −1.41124e14 −0.116042
\(554\) 8.14471e14 0.663089
\(555\) 4.67973e14 0.377233
\(556\) 9.13329e13 0.0728980
\(557\) −1.13537e15 −0.897294 −0.448647 0.893709i \(-0.648094\pi\)
−0.448647 + 0.893709i \(0.648094\pi\)
\(558\) −7.88858e14 −0.617321
\(559\) −4.76254e14 −0.369040
\(560\) 5.75257e14 0.441396
\(561\) 2.26700e15 1.72249
\(562\) 1.02843e15 0.773794
\(563\) −2.40860e15 −1.79460 −0.897301 0.441418i \(-0.854475\pi\)
−0.897301 + 0.441418i \(0.854475\pi\)
\(564\) 2.11366e14 0.155955
\(565\) −4.76357e14 −0.348069
\(566\) −2.48110e15 −1.79537
\(567\) −6.25289e13 −0.0448099
\(568\) −1.00801e15 −0.715399
\(569\) −2.65432e15 −1.86567 −0.932837 0.360300i \(-0.882674\pi\)
−0.932837 + 0.360300i \(0.882674\pi\)
\(570\) 5.48194e14 0.381612
\(571\) −2.55697e15 −1.76290 −0.881448 0.472281i \(-0.843431\pi\)
−0.881448 + 0.472281i \(0.843431\pi\)
\(572\) 1.93528e14 0.132149
\(573\) 1.14422e15 0.773856
\(574\) −5.45557e14 −0.365447
\(575\) −1.28991e14 −0.0855826
\(576\) 3.73154e14 0.245225
\(577\) 1.06655e15 0.694248 0.347124 0.937819i \(-0.387158\pi\)
0.347124 + 0.937819i \(0.387158\pi\)
\(578\) −2.80529e15 −1.80874
\(579\) −7.64948e13 −0.0488539
\(580\) −5.67409e14 −0.358957
\(581\) −6.18498e14 −0.387587
\(582\) −1.75934e15 −1.09213
\(583\) 2.54771e15 1.56666
\(584\) 1.13861e15 0.693595
\(585\) 1.92928e14 0.116423
\(586\) −6.03560e14 −0.360814
\(587\) 9.19059e14 0.544294 0.272147 0.962256i \(-0.412266\pi\)
0.272147 + 0.962256i \(0.412266\pi\)
\(588\) 1.61021e14 0.0944729
\(589\) 1.86268e15 1.08269
\(590\) −2.33782e14 −0.134625
\(591\) 1.84012e14 0.104982
\(592\) 1.41438e15 0.799460
\(593\) 3.09077e15 1.73088 0.865438 0.501016i \(-0.167040\pi\)
0.865438 + 0.501016i \(0.167040\pi\)
\(594\) 6.94454e14 0.385317
\(595\) 1.13039e15 0.621419
\(596\) 1.52178e13 0.00828889
\(597\) −1.80587e15 −0.974602
\(598\) −6.12569e14 −0.327566
\(599\) 1.52727e15 0.809225 0.404613 0.914488i \(-0.367406\pi\)
0.404613 + 0.914488i \(0.367406\pi\)
\(600\) 1.02051e14 0.0535777
\(601\) −7.54230e14 −0.392368 −0.196184 0.980567i \(-0.562855\pi\)
−0.196184 + 0.980567i \(0.562855\pi\)
\(602\) −8.54798e14 −0.440639
\(603\) 6.44180e14 0.329050
\(604\) 1.02809e14 0.0520387
\(605\) 4.43749e15 2.22578
\(606\) −1.05474e15 −0.524261
\(607\) −5.78289e14 −0.284844 −0.142422 0.989806i \(-0.545489\pi\)
−0.142422 + 0.989806i \(0.545489\pi\)
\(608\) 5.04887e14 0.246448
\(609\) −9.34856e14 −0.452220
\(610\) −1.20072e15 −0.575609
\(611\) −1.07448e15 −0.510471
\(612\) −2.25395e14 −0.106123
\(613\) 1.84316e15 0.860062 0.430031 0.902814i \(-0.358503\pi\)
0.430031 + 0.902814i \(0.358503\pi\)
\(614\) 7.89362e14 0.365048
\(615\) 9.87402e14 0.452565
\(616\) −1.43015e15 −0.649664
\(617\) 1.67834e15 0.755635 0.377817 0.925880i \(-0.376675\pi\)
0.377817 + 0.925880i \(0.376675\pi\)
\(618\) −9.22451e14 −0.411630
\(619\) −3.54325e15 −1.56712 −0.783562 0.621314i \(-0.786599\pi\)
−0.783562 + 0.621314i \(0.786599\pi\)
\(620\) 7.14129e14 0.313056
\(621\) −3.59331e14 −0.156131
\(622\) −5.72414e14 −0.246526
\(623\) −1.11937e15 −0.477850
\(624\) 5.83097e14 0.246732
\(625\) −2.10615e15 −0.883381
\(626\) 2.66080e15 1.10625
\(627\) −1.63977e15 −0.675789
\(628\) 6.08311e13 0.0248512
\(629\) 2.77928e15 1.12552
\(630\) 3.46274e14 0.139010
\(631\) 1.61670e15 0.643380 0.321690 0.946845i \(-0.395749\pi\)
0.321690 + 0.946845i \(0.395749\pi\)
\(632\) 6.41611e14 0.253121
\(633\) 2.42031e15 0.946567
\(634\) −1.47844e15 −0.573207
\(635\) −3.47344e15 −1.33507
\(636\) −2.53305e14 −0.0965226
\(637\) −8.18550e14 −0.309228
\(638\) 1.03826e16 3.88860
\(639\) −7.30047e14 −0.271079
\(640\) −3.05701e15 −1.12540
\(641\) 2.08616e15 0.761429 0.380714 0.924693i \(-0.375678\pi\)
0.380714 + 0.924693i \(0.375678\pi\)
\(642\) 1.65468e15 0.598787
\(643\) −2.94568e15 −1.05688 −0.528439 0.848971i \(-0.677222\pi\)
−0.528439 + 0.848971i \(0.677222\pi\)
\(644\) −1.79729e14 −0.0639361
\(645\) 1.54709e15 0.545681
\(646\) 3.25570e15 1.13859
\(647\) −4.38575e15 −1.52079 −0.760396 0.649459i \(-0.774995\pi\)
−0.760396 + 0.649459i \(0.774995\pi\)
\(648\) 2.84283e14 0.0977437
\(649\) 6.99295e14 0.238405
\(650\) 1.25998e14 0.0425931
\(651\) 1.17659e15 0.394393
\(652\) −7.32906e14 −0.243605
\(653\) −3.53489e15 −1.16507 −0.582537 0.812804i \(-0.697940\pi\)
−0.582537 + 0.812804i \(0.697940\pi\)
\(654\) −1.53670e15 −0.502241
\(655\) 5.57412e15 1.80655
\(656\) 2.98427e15 0.959108
\(657\) 8.24636e14 0.262817
\(658\) −1.92851e15 −0.609509
\(659\) 4.08134e15 1.27918 0.639592 0.768714i \(-0.279103\pi\)
0.639592 + 0.768714i \(0.279103\pi\)
\(660\) −6.28667e14 −0.195402
\(661\) −1.34229e15 −0.413751 −0.206876 0.978367i \(-0.566330\pi\)
−0.206876 + 0.978367i \(0.566330\pi\)
\(662\) −2.91595e15 −0.891376
\(663\) 1.14579e15 0.347362
\(664\) 2.81195e15 0.845442
\(665\) −8.17635e14 −0.243804
\(666\) 8.51382e14 0.251777
\(667\) −5.37227e15 −1.57567
\(668\) −1.16335e15 −0.338409
\(669\) −8.04157e14 −0.232005
\(670\) −3.56736e15 −1.02079
\(671\) 3.59162e15 1.01933
\(672\) 3.18919e14 0.0897738
\(673\) −2.73009e14 −0.0762244 −0.0381122 0.999273i \(-0.512134\pi\)
−0.0381122 + 0.999273i \(0.512134\pi\)
\(674\) 2.19939e15 0.609078
\(675\) 7.39098e13 0.0203016
\(676\) −6.19425e14 −0.168765
\(677\) 3.93378e15 1.06310 0.531549 0.847028i \(-0.321610\pi\)
0.531549 + 0.847028i \(0.321610\pi\)
\(678\) −8.66633e14 −0.232312
\(679\) 2.62408e15 0.697739
\(680\) −5.13924e15 −1.35550
\(681\) −1.99653e15 −0.522357
\(682\) −1.30673e16 −3.39135
\(683\) −7.36548e15 −1.89621 −0.948107 0.317952i \(-0.897005\pi\)
−0.948107 + 0.317952i \(0.897005\pi\)
\(684\) 1.63033e14 0.0416358
\(685\) −2.49256e15 −0.631463
\(686\) −3.22368e15 −0.810158
\(687\) 2.17670e15 0.542671
\(688\) 4.67586e15 1.15645
\(689\) 1.28767e15 0.315937
\(690\) 1.98991e15 0.484355
\(691\) 1.57534e15 0.380403 0.190202 0.981745i \(-0.439086\pi\)
0.190202 + 0.981745i \(0.439086\pi\)
\(692\) −9.33392e14 −0.223605
\(693\) −1.03578e15 −0.246171
\(694\) 8.47810e15 1.99904
\(695\) 1.50823e15 0.352819
\(696\) 4.25025e15 0.986425
\(697\) 5.86415e15 1.35028
\(698\) 2.84917e15 0.650899
\(699\) −3.47279e15 −0.787143
\(700\) 3.69680e13 0.00831355
\(701\) 4.21744e15 0.941021 0.470511 0.882394i \(-0.344070\pi\)
0.470511 + 0.882394i \(0.344070\pi\)
\(702\) 3.50993e14 0.0777042
\(703\) −2.01031e15 −0.441580
\(704\) 6.18124e15 1.34718
\(705\) 3.49041e15 0.754807
\(706\) −1.95824e15 −0.420184
\(707\) 1.57316e15 0.334939
\(708\) −6.95269e13 −0.0146883
\(709\) −5.25660e14 −0.110192 −0.0550960 0.998481i \(-0.517546\pi\)
−0.0550960 + 0.998481i \(0.517546\pi\)
\(710\) 4.04287e15 0.840947
\(711\) 4.64684e14 0.0959125
\(712\) 5.08916e15 1.04233
\(713\) 6.76142e15 1.37419
\(714\) 2.05651e15 0.414754
\(715\) 3.19583e15 0.639588
\(716\) −3.98218e14 −0.0790860
\(717\) −1.00152e15 −0.197380
\(718\) 5.12315e15 1.00197
\(719\) 1.25727e15 0.244016 0.122008 0.992529i \(-0.461067\pi\)
0.122008 + 0.992529i \(0.461067\pi\)
\(720\) −1.89417e15 −0.364830
\(721\) 1.37584e15 0.262981
\(722\) 3.40895e15 0.646644
\(723\) 4.67300e15 0.879701
\(724\) 1.00982e15 0.188661
\(725\) 1.10501e15 0.204883
\(726\) 8.07309e15 1.48555
\(727\) −2.64385e15 −0.482834 −0.241417 0.970421i \(-0.577612\pi\)
−0.241417 + 0.970421i \(0.577612\pi\)
\(728\) −7.22833e14 −0.131013
\(729\) 2.05891e14 0.0370370
\(730\) −4.56669e15 −0.815316
\(731\) 9.18814e15 1.62810
\(732\) −3.57094e14 −0.0628017
\(733\) −6.39802e15 −1.11680 −0.558398 0.829573i \(-0.688584\pi\)
−0.558398 + 0.829573i \(0.688584\pi\)
\(734\) 3.57565e15 0.619479
\(735\) 2.65903e15 0.457239
\(736\) 1.83271e15 0.312799
\(737\) 1.06708e16 1.80769
\(738\) 1.79637e15 0.302056
\(739\) −5.73297e15 −0.956831 −0.478416 0.878134i \(-0.658789\pi\)
−0.478416 + 0.878134i \(0.658789\pi\)
\(740\) −7.70729e14 −0.127681
\(741\) −8.28777e14 −0.136282
\(742\) 2.31116e15 0.377232
\(743\) 1.44597e15 0.234271 0.117136 0.993116i \(-0.462629\pi\)
0.117136 + 0.993116i \(0.462629\pi\)
\(744\) −5.34928e15 −0.860288
\(745\) 2.51299e14 0.0401173
\(746\) 4.22320e14 0.0669235
\(747\) 2.03655e15 0.320355
\(748\) −3.73363e15 −0.583006
\(749\) −2.46798e15 −0.382552
\(750\) −4.28927e15 −0.660003
\(751\) −4.83205e15 −0.738094 −0.369047 0.929411i \(-0.620316\pi\)
−0.369047 + 0.929411i \(0.620316\pi\)
\(752\) 1.05492e16 1.59964
\(753\) 7.02507e14 0.105749
\(754\) 5.24762e15 0.784187
\(755\) 1.69774e15 0.251862
\(756\) 1.02982e14 0.0151667
\(757\) −2.48126e15 −0.362781 −0.181390 0.983411i \(-0.558060\pi\)
−0.181390 + 0.983411i \(0.558060\pi\)
\(758\) −3.96853e15 −0.576036
\(759\) −5.95226e15 −0.857733
\(760\) 3.71732e15 0.531808
\(761\) −3.20037e15 −0.454552 −0.227276 0.973830i \(-0.572982\pi\)
−0.227276 + 0.973830i \(0.572982\pi\)
\(762\) −6.31921e15 −0.891067
\(763\) 2.29201e15 0.320871
\(764\) −1.88448e15 −0.261925
\(765\) −3.72207e15 −0.513626
\(766\) 2.19179e15 0.300289
\(767\) 3.53440e14 0.0480774
\(768\) −2.41667e15 −0.326385
\(769\) −9.86048e15 −1.32222 −0.661109 0.750289i \(-0.729914\pi\)
−0.661109 + 0.750289i \(0.729914\pi\)
\(770\) 5.73599e15 0.763676
\(771\) 3.72066e15 0.491837
\(772\) 1.25983e14 0.0165355
\(773\) −1.27501e16 −1.66160 −0.830801 0.556570i \(-0.812117\pi\)
−0.830801 + 0.556570i \(0.812117\pi\)
\(774\) 2.81462e15 0.364204
\(775\) −1.39074e15 −0.178684
\(776\) −1.19302e16 −1.52197
\(777\) −1.26984e15 −0.160855
\(778\) 5.45525e15 0.686162
\(779\) −4.24166e15 −0.529761
\(780\) −3.17743e14 −0.0394054
\(781\) −1.20931e16 −1.48922
\(782\) 1.18180e16 1.44513
\(783\) 3.07823e15 0.373776
\(784\) 8.03652e15 0.969013
\(785\) 1.00454e15 0.120277
\(786\) 1.01410e16 1.20574
\(787\) 1.71079e15 0.201992 0.100996 0.994887i \(-0.467797\pi\)
0.100996 + 0.994887i \(0.467797\pi\)
\(788\) −3.03058e14 −0.0355330
\(789\) −3.29342e15 −0.383464
\(790\) −2.57334e15 −0.297542
\(791\) 1.29259e15 0.148419
\(792\) 4.70912e15 0.536971
\(793\) 1.81529e15 0.205562
\(794\) 1.75509e14 0.0197373
\(795\) −4.18296e15 −0.467159
\(796\) 2.97418e15 0.329872
\(797\) 4.08760e15 0.450244 0.225122 0.974331i \(-0.427722\pi\)
0.225122 + 0.974331i \(0.427722\pi\)
\(798\) −1.48752e15 −0.162722
\(799\) 2.07294e16 2.25206
\(800\) −3.76965e14 −0.0406730
\(801\) 3.68580e15 0.394960
\(802\) −1.46609e16 −1.56027
\(803\) 1.36600e16 1.44383
\(804\) −1.06093e15 −0.111373
\(805\) −2.96797e15 −0.309444
\(806\) −6.60453e15 −0.683911
\(807\) −3.65100e15 −0.375497
\(808\) −7.15225e15 −0.730601
\(809\) −3.69053e15 −0.374431 −0.187215 0.982319i \(-0.559946\pi\)
−0.187215 + 0.982319i \(0.559946\pi\)
\(810\) −1.14019e15 −0.114897
\(811\) −6.57565e15 −0.658148 −0.329074 0.944304i \(-0.606737\pi\)
−0.329074 + 0.944304i \(0.606737\pi\)
\(812\) 1.53966e15 0.153062
\(813\) −9.85826e15 −0.973424
\(814\) 1.41030e16 1.38318
\(815\) −1.21029e16 −1.17902
\(816\) −1.12494e16 −1.08851
\(817\) −6.64598e15 −0.638760
\(818\) 7.95225e15 0.759183
\(819\) −5.23509e14 −0.0496435
\(820\) −1.62620e15 −0.153179
\(821\) −1.74407e15 −0.163183 −0.0815917 0.996666i \(-0.526000\pi\)
−0.0815917 + 0.996666i \(0.526000\pi\)
\(822\) −4.53471e15 −0.421458
\(823\) 1.16565e16 1.07614 0.538068 0.842901i \(-0.319154\pi\)
0.538068 + 0.842901i \(0.319154\pi\)
\(824\) −6.25517e15 −0.573640
\(825\) 1.22431e15 0.111530
\(826\) 6.34367e14 0.0574050
\(827\) −1.26350e16 −1.13578 −0.567892 0.823103i \(-0.692241\pi\)
−0.567892 + 0.823103i \(0.692241\pi\)
\(828\) 5.91800e14 0.0528455
\(829\) −1.58439e16 −1.40544 −0.702721 0.711466i \(-0.748032\pi\)
−0.702721 + 0.711466i \(0.748032\pi\)
\(830\) −1.12780e16 −0.993812
\(831\) 3.99998e15 0.350148
\(832\) 3.12414e15 0.271677
\(833\) 1.57919e16 1.36423
\(834\) 2.74392e15 0.235482
\(835\) −1.92111e16 −1.63786
\(836\) 2.70062e15 0.228733
\(837\) −3.87419e15 −0.325980
\(838\) −1.34122e16 −1.12114
\(839\) 9.87033e15 0.819673 0.409837 0.912159i \(-0.365586\pi\)
0.409837 + 0.912159i \(0.365586\pi\)
\(840\) 2.34810e15 0.193723
\(841\) 3.38214e16 2.77213
\(842\) 1.28082e16 1.04297
\(843\) 5.05077e15 0.408607
\(844\) −3.98614e15 −0.320382
\(845\) −1.02289e16 −0.816804
\(846\) 6.35008e15 0.503782
\(847\) −1.20411e16 −0.949088
\(848\) −1.26424e16 −0.990038
\(849\) −1.21850e16 −0.948055
\(850\) −2.43082e15 −0.187909
\(851\) −7.29731e15 −0.560467
\(852\) 1.20235e15 0.0917515
\(853\) 2.03104e15 0.153992 0.0769962 0.997031i \(-0.475467\pi\)
0.0769962 + 0.997031i \(0.475467\pi\)
\(854\) 3.25814e15 0.245444
\(855\) 2.69225e15 0.201513
\(856\) 1.12205e16 0.834460
\(857\) 1.13646e16 0.839765 0.419883 0.907578i \(-0.362071\pi\)
0.419883 + 0.907578i \(0.362071\pi\)
\(858\) 5.81415e15 0.426881
\(859\) −1.95756e16 −1.42808 −0.714041 0.700104i \(-0.753137\pi\)
−0.714041 + 0.700104i \(0.753137\pi\)
\(860\) −2.54799e15 −0.184695
\(861\) −2.67931e15 −0.192977
\(862\) 3.09066e15 0.221188
\(863\) 2.61983e16 1.86300 0.931500 0.363741i \(-0.118501\pi\)
0.931500 + 0.363741i \(0.118501\pi\)
\(864\) −1.05012e15 −0.0742013
\(865\) −1.54136e16 −1.08222
\(866\) −1.99898e16 −1.39463
\(867\) −1.37772e16 −0.955114
\(868\) −1.93778e15 −0.133489
\(869\) 7.69743e15 0.526911
\(870\) −1.70467e16 −1.15954
\(871\) 5.39325e15 0.364545
\(872\) −1.04204e16 −0.699915
\(873\) −8.64038e15 −0.576706
\(874\) −8.54822e15 −0.566973
\(875\) 6.39747e15 0.421662
\(876\) −1.35814e15 −0.0889550
\(877\) 3.54322e15 0.230622 0.115311 0.993329i \(-0.463214\pi\)
0.115311 + 0.993329i \(0.463214\pi\)
\(878\) 1.69601e16 1.09700
\(879\) −2.96417e15 −0.190530
\(880\) −3.13767e16 −2.00425
\(881\) −2.91262e16 −1.84891 −0.924457 0.381285i \(-0.875482\pi\)
−0.924457 + 0.381285i \(0.875482\pi\)
\(882\) 4.83756e15 0.305175
\(883\) 2.14395e16 1.34410 0.672049 0.740507i \(-0.265414\pi\)
0.672049 + 0.740507i \(0.265414\pi\)
\(884\) −1.88707e15 −0.117571
\(885\) −1.14814e15 −0.0710896
\(886\) 1.61254e16 0.992257
\(887\) 9.83610e15 0.601510 0.300755 0.953701i \(-0.402761\pi\)
0.300755 + 0.953701i \(0.402761\pi\)
\(888\) 5.77325e15 0.350872
\(889\) 9.42515e15 0.569283
\(890\) −2.04113e16 −1.22525
\(891\) 3.41056e15 0.203469
\(892\) 1.32441e15 0.0785262
\(893\) −1.49940e16 −0.883559
\(894\) 4.57188e14 0.0267755
\(895\) −6.57600e15 −0.382768
\(896\) 8.29517e15 0.479878
\(897\) −3.00841e15 −0.172973
\(898\) −7.78706e15 −0.444994
\(899\) −5.79221e16 −3.28978
\(900\) −1.21726e14 −0.00687145
\(901\) −2.48425e16 −1.39383
\(902\) 2.97567e16 1.65939
\(903\) −4.19803e15 −0.232682
\(904\) −5.87667e15 −0.323746
\(905\) 1.66757e16 0.913099
\(906\) 3.08868e15 0.168100
\(907\) −1.91807e16 −1.03759 −0.518793 0.854900i \(-0.673618\pi\)
−0.518793 + 0.854900i \(0.673618\pi\)
\(908\) 3.28819e15 0.176801
\(909\) −5.17999e15 −0.276839
\(910\) 2.89910e15 0.154005
\(911\) −1.87431e16 −0.989672 −0.494836 0.868986i \(-0.664772\pi\)
−0.494836 + 0.868986i \(0.664772\pi\)
\(912\) 8.13694e15 0.427060
\(913\) 3.37351e16 1.75992
\(914\) 7.68419e15 0.398468
\(915\) −5.89690e15 −0.303954
\(916\) −3.58491e15 −0.183677
\(917\) −1.51253e16 −0.770324
\(918\) −6.77154e15 −0.342810
\(919\) 3.72180e16 1.87291 0.936456 0.350786i \(-0.114085\pi\)
0.936456 + 0.350786i \(0.114085\pi\)
\(920\) 1.34936e16 0.674988
\(921\) 3.87666e15 0.192766
\(922\) 2.74929e15 0.135894
\(923\) −6.11215e15 −0.300320
\(924\) 1.70588e15 0.0833208
\(925\) 1.50097e15 0.0728771
\(926\) 1.04478e16 0.504272
\(927\) −4.53028e15 −0.217364
\(928\) −1.57000e16 −0.748836
\(929\) −1.68328e16 −0.798125 −0.399062 0.916924i \(-0.630664\pi\)
−0.399062 + 0.916924i \(0.630664\pi\)
\(930\) 2.14546e16 1.01126
\(931\) −1.14226e16 −0.535232
\(932\) 5.71951e15 0.266423
\(933\) −2.81120e15 −0.130180
\(934\) −2.94431e16 −1.35543
\(935\) −6.16556e16 −2.82169
\(936\) 2.38010e15 0.108287
\(937\) −1.40828e16 −0.636974 −0.318487 0.947927i \(-0.603175\pi\)
−0.318487 + 0.947927i \(0.603175\pi\)
\(938\) 9.67999e15 0.435271
\(939\) 1.30675e16 0.584162
\(940\) −5.74853e15 −0.255478
\(941\) 3.64793e16 1.61177 0.805887 0.592070i \(-0.201689\pi\)
0.805887 + 0.592070i \(0.201689\pi\)
\(942\) 1.82755e15 0.0802767
\(943\) −1.53970e16 −0.672390
\(944\) −3.47007e15 −0.150658
\(945\) 1.70060e15 0.0734053
\(946\) 4.66238e16 2.00081
\(947\) −1.27686e16 −0.544777 −0.272389 0.962187i \(-0.587814\pi\)
−0.272389 + 0.962187i \(0.587814\pi\)
\(948\) −7.65312e14 −0.0324633
\(949\) 6.90408e15 0.291167
\(950\) 1.75826e15 0.0737231
\(951\) −7.26081e15 −0.302686
\(952\) 1.39453e16 0.577995
\(953\) 1.72977e16 0.712814 0.356407 0.934331i \(-0.384002\pi\)
0.356407 + 0.934331i \(0.384002\pi\)
\(954\) −7.61004e15 −0.311796
\(955\) −3.11195e16 −1.26769
\(956\) 1.64945e15 0.0668069
\(957\) 5.09905e16 2.05340
\(958\) 3.92707e16 1.57238
\(959\) 6.76355e15 0.269260
\(960\) −1.01487e16 −0.401714
\(961\) 4.74910e16 1.86910
\(962\) 7.12799e15 0.278936
\(963\) 8.12638e15 0.316193
\(964\) −7.69619e15 −0.297750
\(965\) 2.08043e15 0.0800300
\(966\) −5.39960e15 −0.206532
\(967\) 3.00509e16 1.14291 0.571455 0.820634i \(-0.306379\pi\)
0.571455 + 0.820634i \(0.306379\pi\)
\(968\) 5.47439e16 2.07024
\(969\) 1.59892e16 0.601238
\(970\) 4.78489e16 1.78907
\(971\) −1.80996e16 −0.672921 −0.336461 0.941698i \(-0.609230\pi\)
−0.336461 + 0.941698i \(0.609230\pi\)
\(972\) −3.39092e14 −0.0125358
\(973\) −4.09257e15 −0.150444
\(974\) −2.21756e16 −0.810591
\(975\) 6.18793e14 0.0224916
\(976\) −1.78225e16 −0.644161
\(977\) 1.47747e16 0.531004 0.265502 0.964110i \(-0.414462\pi\)
0.265502 + 0.964110i \(0.414462\pi\)
\(978\) −2.20187e16 −0.786916
\(979\) 6.10548e16 2.16978
\(980\) −4.37929e15 −0.154761
\(981\) −7.54696e15 −0.265212
\(982\) −6.37654e15 −0.222829
\(983\) −4.87943e16 −1.69561 −0.847803 0.530311i \(-0.822075\pi\)
−0.847803 + 0.530311i \(0.822075\pi\)
\(984\) 1.21813e16 0.420940
\(985\) −5.00457e15 −0.171976
\(986\) −1.01240e17 −3.45962
\(987\) −9.47120e15 −0.321855
\(988\) 1.36496e15 0.0461270
\(989\) −2.41245e16 −0.810735
\(990\) −1.88871e16 −0.631206
\(991\) 8.57060e15 0.284843 0.142422 0.989806i \(-0.454511\pi\)
0.142422 + 0.989806i \(0.454511\pi\)
\(992\) 1.97597e16 0.653080
\(993\) −1.43206e16 −0.470697
\(994\) −1.09703e16 −0.358586
\(995\) 4.91143e16 1.59654
\(996\) −3.35409e15 −0.108430
\(997\) −4.60960e16 −1.48197 −0.740987 0.671520i \(-0.765642\pi\)
−0.740987 + 0.671520i \(0.765642\pi\)
\(998\) −1.86410e16 −0.596007
\(999\) 4.18125e15 0.132952
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.1.7 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.a.1.7 26 1.1 even 1 trivial