Properties

Label 177.12.a.a.1.4
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 1.4
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-68.1728 q^{2} -243.000 q^{3} +2599.53 q^{4} -12352.0 q^{5} +16566.0 q^{6} +47034.4 q^{7} -37599.4 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-68.1728 q^{2} -243.000 q^{3} +2599.53 q^{4} -12352.0 q^{5} +16566.0 q^{6} +47034.4 q^{7} -37599.4 q^{8} +59049.0 q^{9} +842068. q^{10} +995461. q^{11} -631686. q^{12} -2.04259e6 q^{13} -3.20647e6 q^{14} +3.00153e6 q^{15} -2.76058e6 q^{16} +4.93058e6 q^{17} -4.02554e6 q^{18} -7.46358e6 q^{19} -3.21093e7 q^{20} -1.14294e7 q^{21} -6.78634e7 q^{22} -6.09728e7 q^{23} +9.13666e6 q^{24} +1.03743e8 q^{25} +1.39249e8 q^{26} -1.43489e7 q^{27} +1.22267e8 q^{28} -1.21948e7 q^{29} -2.04623e8 q^{30} -9.81146e7 q^{31} +2.65200e8 q^{32} -2.41897e8 q^{33} -3.36132e8 q^{34} -5.80968e8 q^{35} +1.53500e8 q^{36} +5.10983e8 q^{37} +5.08813e8 q^{38} +4.96349e8 q^{39} +4.64427e8 q^{40} +9.11904e8 q^{41} +7.79172e8 q^{42} -5.23146e8 q^{43} +2.58773e9 q^{44} -7.29371e8 q^{45} +4.15669e9 q^{46} -2.51018e9 q^{47} +6.70821e8 q^{48} +2.34909e8 q^{49} -7.07245e9 q^{50} -1.19813e9 q^{51} -5.30977e9 q^{52} +2.99867e9 q^{53} +9.78205e8 q^{54} -1.22959e10 q^{55} -1.76847e9 q^{56} +1.81365e9 q^{57} +8.31353e8 q^{58} +7.14924e8 q^{59} +7.80257e9 q^{60} -5.25954e9 q^{61} +6.68875e9 q^{62} +2.77733e9 q^{63} -1.24258e10 q^{64} +2.52300e10 q^{65} +1.64908e10 q^{66} +4.16427e9 q^{67} +1.28172e10 q^{68} +1.48164e10 q^{69} +3.96062e10 q^{70} -2.59373e9 q^{71} -2.22021e9 q^{72} -5.20691e9 q^{73} -3.48351e10 q^{74} -2.52095e10 q^{75} -1.94018e10 q^{76} +4.68209e10 q^{77} -3.38375e10 q^{78} +1.63649e10 q^{79} +3.40986e10 q^{80} +3.48678e9 q^{81} -6.21671e10 q^{82} +5.97866e10 q^{83} -2.97110e10 q^{84} -6.09024e10 q^{85} +3.56644e10 q^{86} +2.96333e9 q^{87} -3.74288e10 q^{88} +8.53534e10 q^{89} +4.97233e10 q^{90} -9.60719e10 q^{91} -1.58501e11 q^{92} +2.38419e10 q^{93} +1.71126e11 q^{94} +9.21900e10 q^{95} -6.44437e10 q^{96} +9.77581e10 q^{97} -1.60144e10 q^{98} +5.87810e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −68.1728 −1.50642 −0.753210 0.657780i \(-0.771496\pi\)
−0.753210 + 0.657780i \(0.771496\pi\)
\(3\) −243.000 −0.577350
\(4\) 2599.53 1.26930
\(5\) −12352.0 −1.76767 −0.883835 0.467799i \(-0.845047\pi\)
−0.883835 + 0.467799i \(0.845047\pi\)
\(6\) 16566.0 0.869732
\(7\) 47034.4 1.05773 0.528867 0.848705i \(-0.322617\pi\)
0.528867 + 0.848705i \(0.322617\pi\)
\(8\) −37599.4 −0.405682
\(9\) 59049.0 0.333333
\(10\) 842068. 2.66285
\(11\) 995461. 1.86365 0.931825 0.362907i \(-0.118216\pi\)
0.931825 + 0.362907i \(0.118216\pi\)
\(12\) −631686. −0.732832
\(13\) −2.04259e6 −1.52578 −0.762891 0.646527i \(-0.776221\pi\)
−0.762891 + 0.646527i \(0.776221\pi\)
\(14\) −3.20647e6 −1.59339
\(15\) 3.00153e6 1.02056
\(16\) −2.76058e6 −0.658174
\(17\) 4.93058e6 0.842227 0.421113 0.907008i \(-0.361639\pi\)
0.421113 + 0.907008i \(0.361639\pi\)
\(18\) −4.02554e6 −0.502140
\(19\) −7.46358e6 −0.691517 −0.345758 0.938324i \(-0.612378\pi\)
−0.345758 + 0.938324i \(0.612378\pi\)
\(20\) −3.21093e7 −2.24371
\(21\) −1.14294e7 −0.610683
\(22\) −6.78634e7 −2.80744
\(23\) −6.09728e7 −1.97530 −0.987650 0.156675i \(-0.949923\pi\)
−0.987650 + 0.156675i \(0.949923\pi\)
\(24\) 9.13666e6 0.234221
\(25\) 1.03743e8 2.12466
\(26\) 1.39249e8 2.29847
\(27\) −1.43489e7 −0.192450
\(28\) 1.22267e8 1.34258
\(29\) −1.21948e7 −0.110404 −0.0552021 0.998475i \(-0.517580\pi\)
−0.0552021 + 0.998475i \(0.517580\pi\)
\(30\) −2.04623e8 −1.53740
\(31\) −9.81146e7 −0.615523 −0.307762 0.951463i \(-0.599580\pi\)
−0.307762 + 0.951463i \(0.599580\pi\)
\(32\) 2.65200e8 1.39717
\(33\) −2.41897e8 −1.07598
\(34\) −3.36132e8 −1.26875
\(35\) −5.80968e8 −1.86972
\(36\) 1.53500e8 0.423101
\(37\) 5.10983e8 1.21143 0.605713 0.795683i \(-0.292888\pi\)
0.605713 + 0.795683i \(0.292888\pi\)
\(38\) 5.08813e8 1.04171
\(39\) 4.96349e8 0.880910
\(40\) 4.64427e8 0.717113
\(41\) 9.11904e8 1.22924 0.614622 0.788822i \(-0.289309\pi\)
0.614622 + 0.788822i \(0.289309\pi\)
\(42\) 7.79172e8 0.919945
\(43\) −5.23146e8 −0.542684 −0.271342 0.962483i \(-0.587467\pi\)
−0.271342 + 0.962483i \(0.587467\pi\)
\(44\) 2.58773e9 2.36554
\(45\) −7.29371e8 −0.589223
\(46\) 4.15669e9 2.97563
\(47\) −2.51018e9 −1.59649 −0.798246 0.602331i \(-0.794239\pi\)
−0.798246 + 0.602331i \(0.794239\pi\)
\(48\) 6.70821e8 0.379997
\(49\) 2.34909e8 0.118801
\(50\) −7.07245e9 −3.20063
\(51\) −1.19813e9 −0.486260
\(52\) −5.30977e9 −1.93668
\(53\) 2.99867e9 0.984945 0.492472 0.870328i \(-0.336093\pi\)
0.492472 + 0.870328i \(0.336093\pi\)
\(54\) 9.78205e8 0.289911
\(55\) −1.22959e10 −3.29432
\(56\) −1.76847e9 −0.429104
\(57\) 1.81365e9 0.399247
\(58\) 8.31353e8 0.166315
\(59\) 7.14924e8 0.130189
\(60\) 7.80257e9 1.29541
\(61\) −5.25954e9 −0.797322 −0.398661 0.917098i \(-0.630525\pi\)
−0.398661 + 0.917098i \(0.630525\pi\)
\(62\) 6.68875e9 0.927237
\(63\) 2.77733e9 0.352578
\(64\) −1.24258e10 −1.44655
\(65\) 2.52300e10 2.69708
\(66\) 1.64908e10 1.62088
\(67\) 4.16427e9 0.376814 0.188407 0.982091i \(-0.439668\pi\)
0.188407 + 0.982091i \(0.439668\pi\)
\(68\) 1.28172e10 1.06904
\(69\) 1.48164e10 1.14044
\(70\) 3.96062e10 2.81659
\(71\) −2.59373e9 −0.170610 −0.0853050 0.996355i \(-0.527186\pi\)
−0.0853050 + 0.996355i \(0.527186\pi\)
\(72\) −2.22021e9 −0.135227
\(73\) −5.20691e9 −0.293971 −0.146985 0.989139i \(-0.546957\pi\)
−0.146985 + 0.989139i \(0.546957\pi\)
\(74\) −3.48351e10 −1.82492
\(75\) −2.52095e10 −1.22667
\(76\) −1.94018e10 −0.877744
\(77\) 4.68209e10 1.97125
\(78\) −3.38375e10 −1.32702
\(79\) 1.63649e10 0.598364 0.299182 0.954196i \(-0.403286\pi\)
0.299182 + 0.954196i \(0.403286\pi\)
\(80\) 3.40986e10 1.16343
\(81\) 3.48678e9 0.111111
\(82\) −6.21671e10 −1.85176
\(83\) 5.97866e10 1.66600 0.832999 0.553274i \(-0.186622\pi\)
0.832999 + 0.553274i \(0.186622\pi\)
\(84\) −2.97110e10 −0.775141
\(85\) −6.09024e10 −1.48878
\(86\) 3.56644e10 0.817510
\(87\) 2.96333e9 0.0637419
\(88\) −3.74288e10 −0.756050
\(89\) 8.53534e10 1.62023 0.810113 0.586273i \(-0.199405\pi\)
0.810113 + 0.586273i \(0.199405\pi\)
\(90\) 4.97233e10 0.887618
\(91\) −9.60719e10 −1.61387
\(92\) −1.58501e11 −2.50725
\(93\) 2.38419e10 0.355373
\(94\) 1.71126e11 2.40499
\(95\) 9.21900e10 1.22237
\(96\) −6.44437e10 −0.806656
\(97\) 9.77581e10 1.15587 0.577934 0.816083i \(-0.303859\pi\)
0.577934 + 0.816083i \(0.303859\pi\)
\(98\) −1.60144e10 −0.178965
\(99\) 5.87810e10 0.621217
\(100\) 2.69683e11 2.69683
\(101\) 7.15210e10 0.677121 0.338560 0.940945i \(-0.390060\pi\)
0.338560 + 0.940945i \(0.390060\pi\)
\(102\) 8.16800e10 0.732512
\(103\) −2.26703e11 −1.92687 −0.963436 0.267940i \(-0.913657\pi\)
−0.963436 + 0.267940i \(0.913657\pi\)
\(104\) 7.68001e10 0.618983
\(105\) 1.41175e11 1.07949
\(106\) −2.04428e11 −1.48374
\(107\) 6.09715e10 0.420258 0.210129 0.977674i \(-0.432612\pi\)
0.210129 + 0.977674i \(0.432612\pi\)
\(108\) −3.73004e10 −0.244277
\(109\) 1.22518e10 0.0762698 0.0381349 0.999273i \(-0.487858\pi\)
0.0381349 + 0.999273i \(0.487858\pi\)
\(110\) 8.38246e11 4.96263
\(111\) −1.24169e11 −0.699417
\(112\) −1.29842e11 −0.696173
\(113\) 5.27228e10 0.269195 0.134598 0.990900i \(-0.457026\pi\)
0.134598 + 0.990900i \(0.457026\pi\)
\(114\) −1.23642e11 −0.601434
\(115\) 7.53134e11 3.49168
\(116\) −3.17007e10 −0.140136
\(117\) −1.20613e11 −0.508594
\(118\) −4.87384e10 −0.196119
\(119\) 2.31907e11 0.890852
\(120\) −1.12856e11 −0.414025
\(121\) 7.05631e11 2.47319
\(122\) 3.58557e11 1.20110
\(123\) −2.21593e11 −0.709704
\(124\) −2.55052e11 −0.781285
\(125\) −6.78307e11 −1.98802
\(126\) −1.89339e11 −0.531131
\(127\) −6.29747e11 −1.69140 −0.845699 0.533660i \(-0.820816\pi\)
−0.845699 + 0.533660i \(0.820816\pi\)
\(128\) 3.03970e11 0.781943
\(129\) 1.27125e11 0.313319
\(130\) −1.72000e12 −4.06293
\(131\) 2.40547e11 0.544763 0.272381 0.962189i \(-0.412189\pi\)
0.272381 + 0.962189i \(0.412189\pi\)
\(132\) −6.28819e11 −1.36574
\(133\) −3.51045e11 −0.731441
\(134\) −2.83890e11 −0.567641
\(135\) 1.77237e11 0.340188
\(136\) −1.85387e11 −0.341677
\(137\) −5.62152e11 −0.995154 −0.497577 0.867420i \(-0.665777\pi\)
−0.497577 + 0.867420i \(0.665777\pi\)
\(138\) −1.01008e12 −1.71798
\(139\) −7.08735e11 −1.15852 −0.579259 0.815144i \(-0.696658\pi\)
−0.579259 + 0.815144i \(0.696658\pi\)
\(140\) −1.51024e12 −2.37325
\(141\) 6.09974e11 0.921735
\(142\) 1.76822e11 0.257010
\(143\) −2.03332e12 −2.84352
\(144\) −1.63010e11 −0.219391
\(145\) 1.50630e11 0.195158
\(146\) 3.54970e11 0.442844
\(147\) −5.70829e10 −0.0685900
\(148\) 1.32832e12 1.53767
\(149\) 1.07853e12 1.20312 0.601558 0.798829i \(-0.294547\pi\)
0.601558 + 0.798829i \(0.294547\pi\)
\(150\) 1.71861e12 1.84788
\(151\) −1.63944e11 −0.169950 −0.0849751 0.996383i \(-0.527081\pi\)
−0.0849751 + 0.996383i \(0.527081\pi\)
\(152\) 2.80626e11 0.280536
\(153\) 2.91146e11 0.280742
\(154\) −3.19191e12 −2.96953
\(155\) 1.21191e12 1.08804
\(156\) 1.29027e12 1.11814
\(157\) −3.34239e11 −0.279646 −0.139823 0.990177i \(-0.544653\pi\)
−0.139823 + 0.990177i \(0.544653\pi\)
\(158\) −1.11564e12 −0.901388
\(159\) −7.28677e11 −0.568658
\(160\) −3.27574e12 −2.46973
\(161\) −2.86782e12 −2.08934
\(162\) −2.37704e11 −0.167380
\(163\) −1.10253e12 −0.750511 −0.375256 0.926921i \(-0.622445\pi\)
−0.375256 + 0.926921i \(0.622445\pi\)
\(164\) 2.37052e12 1.56028
\(165\) 2.98791e12 1.90198
\(166\) −4.07582e12 −2.50969
\(167\) −4.93688e11 −0.294112 −0.147056 0.989128i \(-0.546980\pi\)
−0.147056 + 0.989128i \(0.546980\pi\)
\(168\) 4.29737e11 0.247743
\(169\) 2.38001e12 1.32801
\(170\) 4.15189e12 2.24273
\(171\) −4.40717e11 −0.230506
\(172\) −1.35994e12 −0.688830
\(173\) −1.44961e11 −0.0711210 −0.0355605 0.999368i \(-0.511322\pi\)
−0.0355605 + 0.999368i \(0.511322\pi\)
\(174\) −2.02019e11 −0.0960221
\(175\) 4.87949e12 2.24732
\(176\) −2.74805e12 −1.22661
\(177\) −1.73727e11 −0.0751646
\(178\) −5.81878e12 −2.44074
\(179\) 4.44571e12 1.80821 0.904106 0.427309i \(-0.140538\pi\)
0.904106 + 0.427309i \(0.140538\pi\)
\(180\) −1.89602e12 −0.747902
\(181\) −1.76207e12 −0.674205 −0.337102 0.941468i \(-0.609447\pi\)
−0.337102 + 0.941468i \(0.609447\pi\)
\(182\) 6.54949e12 2.43117
\(183\) 1.27807e12 0.460334
\(184\) 2.29254e12 0.801345
\(185\) −6.31165e12 −2.14140
\(186\) −1.62537e12 −0.535340
\(187\) 4.90820e12 1.56962
\(188\) −6.52529e12 −2.02643
\(189\) −6.74892e11 −0.203561
\(190\) −6.28485e12 −1.84141
\(191\) 2.15378e12 0.613080 0.306540 0.951858i \(-0.400829\pi\)
0.306540 + 0.951858i \(0.400829\pi\)
\(192\) 3.01946e12 0.835166
\(193\) 6.89616e12 1.85371 0.926855 0.375418i \(-0.122501\pi\)
0.926855 + 0.375418i \(0.122501\pi\)
\(194\) −6.66445e12 −1.74122
\(195\) −6.13089e12 −1.55716
\(196\) 6.10653e11 0.150795
\(197\) 3.06746e12 0.736571 0.368285 0.929713i \(-0.379945\pi\)
0.368285 + 0.929713i \(0.379945\pi\)
\(198\) −4.00726e12 −0.935814
\(199\) 3.48181e12 0.790885 0.395442 0.918491i \(-0.370591\pi\)
0.395442 + 0.918491i \(0.370591\pi\)
\(200\) −3.90068e12 −0.861936
\(201\) −1.01192e12 −0.217554
\(202\) −4.87579e12 −1.02003
\(203\) −5.73575e11 −0.116778
\(204\) −3.11458e12 −0.617211
\(205\) −1.12638e13 −2.17290
\(206\) 1.54550e13 2.90268
\(207\) −3.60038e12 −0.658433
\(208\) 5.63873e12 1.00423
\(209\) −7.42971e12 −1.28875
\(210\) −9.62430e12 −1.62616
\(211\) −4.77189e12 −0.785483 −0.392741 0.919649i \(-0.628473\pi\)
−0.392741 + 0.919649i \(0.628473\pi\)
\(212\) 7.79514e12 1.25019
\(213\) 6.30278e11 0.0985018
\(214\) −4.15660e12 −0.633086
\(215\) 6.46189e12 0.959285
\(216\) 5.39510e11 0.0780736
\(217\) −4.61476e12 −0.651060
\(218\) −8.35236e11 −0.114894
\(219\) 1.26528e12 0.169724
\(220\) −3.19636e13 −4.18149
\(221\) −1.00711e13 −1.28505
\(222\) 8.46494e12 1.05362
\(223\) 1.33120e13 1.61647 0.808234 0.588862i \(-0.200424\pi\)
0.808234 + 0.588862i \(0.200424\pi\)
\(224\) 1.24735e13 1.47783
\(225\) 6.12592e12 0.708219
\(226\) −3.59426e12 −0.405521
\(227\) −6.30597e12 −0.694400 −0.347200 0.937791i \(-0.612868\pi\)
−0.347200 + 0.937791i \(0.612868\pi\)
\(228\) 4.71464e12 0.506765
\(229\) 1.17737e12 0.123543 0.0617714 0.998090i \(-0.480325\pi\)
0.0617714 + 0.998090i \(0.480325\pi\)
\(230\) −5.13433e13 −5.25994
\(231\) −1.13775e13 −1.13810
\(232\) 4.58517e11 0.0447890
\(233\) 5.71269e11 0.0544983 0.0272492 0.999629i \(-0.491325\pi\)
0.0272492 + 0.999629i \(0.491325\pi\)
\(234\) 8.22251e12 0.766156
\(235\) 3.10057e13 2.82207
\(236\) 1.85847e12 0.165249
\(237\) −3.97668e12 −0.345466
\(238\) −1.58098e13 −1.34200
\(239\) 1.35214e12 0.112159 0.0560793 0.998426i \(-0.482140\pi\)
0.0560793 + 0.998426i \(0.482140\pi\)
\(240\) −8.28597e12 −0.671709
\(241\) 1.11511e13 0.883533 0.441766 0.897130i \(-0.354352\pi\)
0.441766 + 0.897130i \(0.354352\pi\)
\(242\) −4.81049e13 −3.72567
\(243\) −8.47289e11 −0.0641500
\(244\) −1.36723e13 −1.01204
\(245\) −2.90159e12 −0.210002
\(246\) 1.51066e13 1.06911
\(247\) 1.52450e13 1.05510
\(248\) 3.68905e12 0.249707
\(249\) −1.45281e13 −0.961864
\(250\) 4.62421e13 2.99480
\(251\) −2.00365e13 −1.26945 −0.634727 0.772737i \(-0.718887\pi\)
−0.634727 + 0.772737i \(0.718887\pi\)
\(252\) 7.21977e12 0.447528
\(253\) −6.06961e13 −3.68127
\(254\) 4.29316e13 2.54796
\(255\) 1.47993e13 0.859547
\(256\) 4.72552e12 0.268615
\(257\) −2.97578e13 −1.65565 −0.827824 0.560987i \(-0.810422\pi\)
−0.827824 + 0.560987i \(0.810422\pi\)
\(258\) −8.66644e12 −0.471989
\(259\) 2.40338e13 1.28137
\(260\) 6.55861e13 3.42341
\(261\) −7.20090e11 −0.0368014
\(262\) −1.63987e13 −0.820641
\(263\) −1.52340e12 −0.0746549 −0.0373274 0.999303i \(-0.511884\pi\)
−0.0373274 + 0.999303i \(0.511884\pi\)
\(264\) 9.09519e12 0.436506
\(265\) −3.70395e13 −1.74106
\(266\) 2.39317e13 1.10186
\(267\) −2.07409e13 −0.935438
\(268\) 1.08251e13 0.478291
\(269\) −6.67744e12 −0.289050 −0.144525 0.989501i \(-0.546165\pi\)
−0.144525 + 0.989501i \(0.546165\pi\)
\(270\) −1.20828e13 −0.512466
\(271\) −4.15385e13 −1.72631 −0.863157 0.504935i \(-0.831516\pi\)
−0.863157 + 0.504935i \(0.831516\pi\)
\(272\) −1.36113e13 −0.554332
\(273\) 2.33455e13 0.931769
\(274\) 3.83235e13 1.49912
\(275\) 1.03272e14 3.95962
\(276\) 3.85157e13 1.44756
\(277\) 7.23607e12 0.266602 0.133301 0.991076i \(-0.457442\pi\)
0.133301 + 0.991076i \(0.457442\pi\)
\(278\) 4.83165e13 1.74521
\(279\) −5.79357e12 −0.205174
\(280\) 2.18440e13 0.758514
\(281\) 1.29866e13 0.442192 0.221096 0.975252i \(-0.429037\pi\)
0.221096 + 0.975252i \(0.429037\pi\)
\(282\) −4.15836e13 −1.38852
\(283\) −2.31296e13 −0.757431 −0.378716 0.925513i \(-0.623634\pi\)
−0.378716 + 0.925513i \(0.623634\pi\)
\(284\) −6.74249e12 −0.216556
\(285\) −2.24022e13 −0.705737
\(286\) 1.38617e14 4.28354
\(287\) 4.28909e13 1.30021
\(288\) 1.56598e13 0.465723
\(289\) −9.96126e12 −0.290654
\(290\) −1.02688e13 −0.293990
\(291\) −2.37552e13 −0.667341
\(292\) −1.35355e13 −0.373138
\(293\) −2.67762e13 −0.724398 −0.362199 0.932101i \(-0.617974\pi\)
−0.362199 + 0.932101i \(0.617974\pi\)
\(294\) 3.89150e12 0.103325
\(295\) −8.83072e12 −0.230131
\(296\) −1.92127e13 −0.491454
\(297\) −1.42838e13 −0.358660
\(298\) −7.35263e13 −1.81240
\(299\) 1.24542e14 3.01388
\(300\) −6.55330e13 −1.55702
\(301\) −2.46059e13 −0.574015
\(302\) 1.11765e13 0.256016
\(303\) −1.73796e13 −0.390936
\(304\) 2.06038e13 0.455138
\(305\) 6.49657e13 1.40940
\(306\) −1.98482e13 −0.422916
\(307\) 4.45166e13 0.931667 0.465834 0.884872i \(-0.345755\pi\)
0.465834 + 0.884872i \(0.345755\pi\)
\(308\) 1.21712e14 2.50211
\(309\) 5.50889e13 1.11248
\(310\) −8.26192e13 −1.63905
\(311\) −2.12268e13 −0.413717 −0.206858 0.978371i \(-0.566324\pi\)
−0.206858 + 0.978371i \(0.566324\pi\)
\(312\) −1.86624e13 −0.357370
\(313\) −5.80501e12 −0.109222 −0.0546109 0.998508i \(-0.517392\pi\)
−0.0546109 + 0.998508i \(0.517392\pi\)
\(314\) 2.27860e13 0.421264
\(315\) −3.43056e13 −0.623242
\(316\) 4.25412e13 0.759505
\(317\) 6.96405e13 1.22190 0.610951 0.791669i \(-0.290787\pi\)
0.610951 + 0.791669i \(0.290787\pi\)
\(318\) 4.96760e13 0.856638
\(319\) −1.21394e13 −0.205755
\(320\) 1.53483e14 2.55702
\(321\) −1.48161e13 −0.242636
\(322\) 1.95507e14 3.14743
\(323\) −3.67998e13 −0.582414
\(324\) 9.06400e12 0.141034
\(325\) −2.11904e14 −3.24176
\(326\) 7.51623e13 1.13059
\(327\) −2.97718e12 −0.0440344
\(328\) −3.42871e13 −0.498683
\(329\) −1.18065e14 −1.68866
\(330\) −2.03694e14 −2.86518
\(331\) −9.83540e13 −1.36062 −0.680312 0.732923i \(-0.738156\pi\)
−0.680312 + 0.732923i \(0.738156\pi\)
\(332\) 1.55417e14 2.11466
\(333\) 3.01730e13 0.403809
\(334\) 3.36561e13 0.443056
\(335\) −5.14369e13 −0.666083
\(336\) 3.15517e13 0.401936
\(337\) 6.68819e13 0.838194 0.419097 0.907942i \(-0.362347\pi\)
0.419097 + 0.907942i \(0.362347\pi\)
\(338\) −1.62252e14 −2.00054
\(339\) −1.28116e13 −0.155420
\(340\) −1.58318e14 −1.88971
\(341\) −9.76693e13 −1.14712
\(342\) 3.00449e13 0.347238
\(343\) −8.19536e13 −0.932074
\(344\) 1.96700e13 0.220157
\(345\) −1.83012e14 −2.01592
\(346\) 9.88240e12 0.107138
\(347\) −3.55484e13 −0.379322 −0.189661 0.981850i \(-0.560739\pi\)
−0.189661 + 0.981850i \(0.560739\pi\)
\(348\) 7.70328e12 0.0809077
\(349\) 2.76566e13 0.285929 0.142965 0.989728i \(-0.454336\pi\)
0.142965 + 0.989728i \(0.454336\pi\)
\(350\) −3.32649e14 −3.38541
\(351\) 2.93089e13 0.293637
\(352\) 2.63997e14 2.60384
\(353\) −4.16636e13 −0.404572 −0.202286 0.979327i \(-0.564837\pi\)
−0.202286 + 0.979327i \(0.564837\pi\)
\(354\) 1.18434e13 0.113229
\(355\) 3.20377e13 0.301582
\(356\) 2.21879e14 2.05656
\(357\) −5.63534e13 −0.514334
\(358\) −3.03076e14 −2.72393
\(359\) 4.61181e13 0.408180 0.204090 0.978952i \(-0.434577\pi\)
0.204090 + 0.978952i \(0.434577\pi\)
\(360\) 2.74239e13 0.239038
\(361\) −6.07852e13 −0.521805
\(362\) 1.20125e14 1.01564
\(363\) −1.71468e14 −1.42790
\(364\) −2.49742e14 −2.04849
\(365\) 6.43156e13 0.519644
\(366\) −8.71295e13 −0.693456
\(367\) 3.82762e13 0.300099 0.150050 0.988678i \(-0.452057\pi\)
0.150050 + 0.988678i \(0.452057\pi\)
\(368\) 1.68320e14 1.30009
\(369\) 5.38470e13 0.409748
\(370\) 4.30283e14 3.22585
\(371\) 1.41041e14 1.04181
\(372\) 6.19776e13 0.451075
\(373\) 7.22448e13 0.518093 0.259047 0.965865i \(-0.416592\pi\)
0.259047 + 0.965865i \(0.416592\pi\)
\(374\) −3.34606e14 −2.36450
\(375\) 1.64829e14 1.14778
\(376\) 9.43813e13 0.647669
\(377\) 2.49089e13 0.168453
\(378\) 4.60093e13 0.306648
\(379\) 2.32060e13 0.152435 0.0762176 0.997091i \(-0.475716\pi\)
0.0762176 + 0.997091i \(0.475716\pi\)
\(380\) 2.39651e14 1.55156
\(381\) 1.53029e14 0.976529
\(382\) −1.46829e14 −0.923556
\(383\) 2.17383e14 1.34782 0.673911 0.738812i \(-0.264613\pi\)
0.673911 + 0.738812i \(0.264613\pi\)
\(384\) −7.38646e13 −0.451455
\(385\) −5.78331e14 −3.48451
\(386\) −4.70130e14 −2.79247
\(387\) −3.08913e13 −0.180895
\(388\) 2.54125e14 1.46715
\(389\) 1.17108e13 0.0666598 0.0333299 0.999444i \(-0.489389\pi\)
0.0333299 + 0.999444i \(0.489389\pi\)
\(390\) 4.17960e14 2.34574
\(391\) −3.00631e14 −1.66365
\(392\) −8.83244e12 −0.0481956
\(393\) −5.84528e13 −0.314519
\(394\) −2.09117e14 −1.10958
\(395\) −2.02139e14 −1.05771
\(396\) 1.52803e14 0.788512
\(397\) 2.63187e14 1.33942 0.669709 0.742624i \(-0.266419\pi\)
0.669709 + 0.742624i \(0.266419\pi\)
\(398\) −2.37365e14 −1.19141
\(399\) 8.53040e13 0.422297
\(400\) −2.86391e14 −1.39839
\(401\) 1.45838e14 0.702389 0.351194 0.936303i \(-0.385776\pi\)
0.351194 + 0.936303i \(0.385776\pi\)
\(402\) 6.89852e13 0.327727
\(403\) 2.00408e14 0.939154
\(404\) 1.85921e14 0.859471
\(405\) −4.30687e13 −0.196408
\(406\) 3.91022e13 0.175917
\(407\) 5.08664e14 2.25768
\(408\) 4.50490e13 0.197267
\(409\) 1.92954e14 0.833634 0.416817 0.908991i \(-0.363146\pi\)
0.416817 + 0.908991i \(0.363146\pi\)
\(410\) 7.67886e14 3.27330
\(411\) 1.36603e14 0.574553
\(412\) −5.89322e14 −2.44578
\(413\) 3.36260e13 0.137705
\(414\) 2.45448e14 0.991878
\(415\) −7.38482e14 −2.94493
\(416\) −5.41695e14 −2.13178
\(417\) 1.72223e14 0.668871
\(418\) 5.06504e14 1.94139
\(419\) −8.40554e13 −0.317972 −0.158986 0.987281i \(-0.550822\pi\)
−0.158986 + 0.987281i \(0.550822\pi\)
\(420\) 3.66989e14 1.37019
\(421\) 2.11462e14 0.779256 0.389628 0.920972i \(-0.372604\pi\)
0.389628 + 0.920972i \(0.372604\pi\)
\(422\) 3.25313e14 1.18327
\(423\) −1.48224e14 −0.532164
\(424\) −1.12748e14 −0.399575
\(425\) 5.11513e14 1.78944
\(426\) −4.29678e13 −0.148385
\(427\) −2.47379e14 −0.843354
\(428\) 1.58497e14 0.533435
\(429\) 4.94096e14 1.64171
\(430\) −4.40525e14 −1.44509
\(431\) −4.79806e14 −1.55396 −0.776982 0.629523i \(-0.783250\pi\)
−0.776982 + 0.629523i \(0.783250\pi\)
\(432\) 3.96113e13 0.126666
\(433\) −3.62226e14 −1.14366 −0.571829 0.820373i \(-0.693766\pi\)
−0.571829 + 0.820373i \(0.693766\pi\)
\(434\) 3.14601e14 0.980770
\(435\) −3.66030e13 −0.112675
\(436\) 3.18488e13 0.0968094
\(437\) 4.55076e14 1.36595
\(438\) −8.62576e13 −0.255676
\(439\) 4.61354e14 1.35045 0.675226 0.737611i \(-0.264046\pi\)
0.675226 + 0.737611i \(0.264046\pi\)
\(440\) 4.62319e14 1.33645
\(441\) 1.38711e13 0.0396005
\(442\) 6.86578e14 1.93583
\(443\) 9.15313e13 0.254888 0.127444 0.991846i \(-0.459323\pi\)
0.127444 + 0.991846i \(0.459323\pi\)
\(444\) −3.22781e14 −0.887772
\(445\) −1.05428e15 −2.86403
\(446\) −9.07517e14 −2.43508
\(447\) −2.62083e14 −0.694619
\(448\) −5.84439e14 −1.53007
\(449\) −2.98662e14 −0.772370 −0.386185 0.922421i \(-0.626207\pi\)
−0.386185 + 0.922421i \(0.626207\pi\)
\(450\) −4.17621e14 −1.06688
\(451\) 9.07765e14 2.29088
\(452\) 1.37055e14 0.341690
\(453\) 3.98383e13 0.0981207
\(454\) 4.29896e14 1.04606
\(455\) 1.18668e15 2.85279
\(456\) −6.81922e13 −0.161968
\(457\) −2.09616e14 −0.491911 −0.245955 0.969281i \(-0.579102\pi\)
−0.245955 + 0.969281i \(0.579102\pi\)
\(458\) −8.02645e13 −0.186107
\(459\) −7.07485e13 −0.162087
\(460\) 1.95780e15 4.43200
\(461\) 2.81206e14 0.629028 0.314514 0.949253i \(-0.398158\pi\)
0.314514 + 0.949253i \(0.398158\pi\)
\(462\) 7.75635e14 1.71446
\(463\) −4.32113e14 −0.943848 −0.471924 0.881639i \(-0.656440\pi\)
−0.471924 + 0.881639i \(0.656440\pi\)
\(464\) 3.36647e13 0.0726652
\(465\) −2.94494e14 −0.628181
\(466\) −3.89450e13 −0.0820974
\(467\) −5.36221e14 −1.11712 −0.558562 0.829463i \(-0.688647\pi\)
−0.558562 + 0.829463i \(0.688647\pi\)
\(468\) −3.13537e14 −0.645559
\(469\) 1.95864e14 0.398569
\(470\) −2.11374e15 −4.25123
\(471\) 8.12200e13 0.161454
\(472\) −2.68807e13 −0.0528153
\(473\) −5.20772e14 −1.01137
\(474\) 2.71102e14 0.520417
\(475\) −7.74295e14 −1.46924
\(476\) 6.02849e14 1.13076
\(477\) 1.77069e14 0.328315
\(478\) −9.21790e13 −0.168958
\(479\) −8.10801e14 −1.46916 −0.734579 0.678523i \(-0.762621\pi\)
−0.734579 + 0.678523i \(0.762621\pi\)
\(480\) 7.96006e14 1.42590
\(481\) −1.04373e15 −1.84837
\(482\) −7.60200e14 −1.33097
\(483\) 6.96880e14 1.20628
\(484\) 1.83431e15 3.13923
\(485\) −1.20751e15 −2.04319
\(486\) 5.77620e13 0.0966369
\(487\) −2.25678e14 −0.373319 −0.186659 0.982425i \(-0.559766\pi\)
−0.186659 + 0.982425i \(0.559766\pi\)
\(488\) 1.97756e14 0.323459
\(489\) 2.67914e14 0.433308
\(490\) 1.97810e14 0.316351
\(491\) −3.53313e14 −0.558743 −0.279371 0.960183i \(-0.590126\pi\)
−0.279371 + 0.960183i \(0.590126\pi\)
\(492\) −5.76037e14 −0.900829
\(493\) −6.01274e13 −0.0929854
\(494\) −1.03930e15 −1.58943
\(495\) −7.26061e14 −1.09811
\(496\) 2.70853e14 0.405121
\(497\) −1.21995e14 −0.180460
\(498\) 9.90425e14 1.44897
\(499\) 1.05969e15 1.53330 0.766649 0.642067i \(-0.221923\pi\)
0.766649 + 0.642067i \(0.221923\pi\)
\(500\) −1.76328e15 −2.52340
\(501\) 1.19966e14 0.169805
\(502\) 1.36595e15 1.91233
\(503\) −8.41626e14 −1.16545 −0.582727 0.812668i \(-0.698014\pi\)
−0.582727 + 0.812668i \(0.698014\pi\)
\(504\) −1.04426e14 −0.143035
\(505\) −8.83425e14 −1.19693
\(506\) 4.13782e15 5.54554
\(507\) −5.78342e14 −0.766727
\(508\) −1.63705e15 −2.14690
\(509\) −1.34537e14 −0.174540 −0.0872698 0.996185i \(-0.527814\pi\)
−0.0872698 + 0.996185i \(0.527814\pi\)
\(510\) −1.00891e15 −1.29484
\(511\) −2.44904e14 −0.310943
\(512\) −9.44682e14 −1.18659
\(513\) 1.07094e14 0.133082
\(514\) 2.02867e15 2.49410
\(515\) 2.80023e15 3.40607
\(516\) 3.30464e14 0.397696
\(517\) −2.49879e15 −2.97530
\(518\) −1.63845e15 −1.93028
\(519\) 3.52255e13 0.0410617
\(520\) −9.48633e14 −1.09416
\(521\) −1.89622e14 −0.216411 −0.108206 0.994129i \(-0.534511\pi\)
−0.108206 + 0.994129i \(0.534511\pi\)
\(522\) 4.90906e13 0.0554384
\(523\) 1.54008e12 0.00172101 0.000860506 1.00000i \(-0.499726\pi\)
0.000860506 1.00000i \(0.499726\pi\)
\(524\) 6.25309e14 0.691468
\(525\) −1.18572e15 −1.29749
\(526\) 1.03855e14 0.112462
\(527\) −4.83762e14 −0.518410
\(528\) 6.67777e14 0.708182
\(529\) 2.76487e15 2.90181
\(530\) 2.52509e15 2.62276
\(531\) 4.22156e13 0.0433963
\(532\) −9.12553e14 −0.928419
\(533\) −1.86264e15 −1.87556
\(534\) 1.41396e15 1.40916
\(535\) −7.53118e14 −0.742878
\(536\) −1.56574e14 −0.152867
\(537\) −1.08031e15 −1.04397
\(538\) 4.55220e14 0.435430
\(539\) 2.33843e14 0.221404
\(540\) 4.60734e14 0.431802
\(541\) 2.38586e14 0.221340 0.110670 0.993857i \(-0.464700\pi\)
0.110670 + 0.993857i \(0.464700\pi\)
\(542\) 2.83180e15 2.60056
\(543\) 4.28184e14 0.389252
\(544\) 1.30759e15 1.17673
\(545\) −1.51333e14 −0.134820
\(546\) −1.59153e15 −1.40364
\(547\) 4.04060e14 0.352789 0.176395 0.984320i \(-0.443557\pi\)
0.176395 + 0.984320i \(0.443557\pi\)
\(548\) −1.46133e15 −1.26315
\(549\) −3.10570e14 −0.265774
\(550\) −7.04035e15 −5.96485
\(551\) 9.10169e13 0.0763463
\(552\) −5.57088e14 −0.462657
\(553\) 7.69716e14 0.632910
\(554\) −4.93303e14 −0.401615
\(555\) 1.53373e15 1.23634
\(556\) −1.84238e15 −1.47051
\(557\) −5.90750e14 −0.466875 −0.233437 0.972372i \(-0.574997\pi\)
−0.233437 + 0.972372i \(0.574997\pi\)
\(558\) 3.94964e14 0.309079
\(559\) 1.06857e15 0.828017
\(560\) 1.60381e15 1.23060
\(561\) −1.19269e15 −0.906219
\(562\) −8.85334e14 −0.666127
\(563\) −1.48992e15 −1.11011 −0.555056 0.831813i \(-0.687303\pi\)
−0.555056 + 0.831813i \(0.687303\pi\)
\(564\) 1.58565e15 1.16996
\(565\) −6.51231e14 −0.475848
\(566\) 1.57681e15 1.14101
\(567\) 1.63999e14 0.117526
\(568\) 9.75229e13 0.0692135
\(569\) −1.08556e15 −0.763018 −0.381509 0.924365i \(-0.624596\pi\)
−0.381509 + 0.924365i \(0.624596\pi\)
\(570\) 1.52722e15 1.06314
\(571\) −7.39126e14 −0.509589 −0.254794 0.966995i \(-0.582008\pi\)
−0.254794 + 0.966995i \(0.582008\pi\)
\(572\) −5.28567e15 −3.60929
\(573\) −5.23368e14 −0.353962
\(574\) −2.92399e15 −1.95867
\(575\) −6.32550e15 −4.19684
\(576\) −7.33729e14 −0.482183
\(577\) 3.01763e15 1.96426 0.982130 0.188205i \(-0.0602671\pi\)
0.982130 + 0.188205i \(0.0602671\pi\)
\(578\) 6.79087e14 0.437847
\(579\) −1.67577e15 −1.07024
\(580\) 3.91567e14 0.247715
\(581\) 2.81203e15 1.76218
\(582\) 1.61946e15 1.00530
\(583\) 2.98506e15 1.83559
\(584\) 1.95777e14 0.119259
\(585\) 1.48981e15 0.899026
\(586\) 1.82541e15 1.09125
\(587\) −1.18221e15 −0.700140 −0.350070 0.936723i \(-0.613842\pi\)
−0.350070 + 0.936723i \(0.613842\pi\)
\(588\) −1.48389e14 −0.0870614
\(589\) 7.32287e14 0.425645
\(590\) 6.02015e14 0.346674
\(591\) −7.45392e14 −0.425259
\(592\) −1.41061e15 −0.797329
\(593\) −1.94166e13 −0.0108736 −0.00543678 0.999985i \(-0.501731\pi\)
−0.00543678 + 0.999985i \(0.501731\pi\)
\(594\) 9.73765e14 0.540292
\(595\) −2.86451e15 −1.57473
\(596\) 2.80367e15 1.52712
\(597\) −8.46080e14 −0.456618
\(598\) −8.49040e15 −4.54017
\(599\) −1.33131e15 −0.705392 −0.352696 0.935738i \(-0.614735\pi\)
−0.352696 + 0.935738i \(0.614735\pi\)
\(600\) 9.47864e14 0.497639
\(601\) −9.07370e14 −0.472036 −0.236018 0.971749i \(-0.575842\pi\)
−0.236018 + 0.971749i \(0.575842\pi\)
\(602\) 1.67745e15 0.864708
\(603\) 2.45896e14 0.125605
\(604\) −4.26177e14 −0.215718
\(605\) −8.71594e15 −4.37179
\(606\) 1.18482e15 0.588914
\(607\) −2.22958e15 −1.09821 −0.549106 0.835753i \(-0.685032\pi\)
−0.549106 + 0.835753i \(0.685032\pi\)
\(608\) −1.97934e15 −0.966166
\(609\) 1.39379e14 0.0674220
\(610\) −4.42889e15 −2.12315
\(611\) 5.12727e15 2.43590
\(612\) 7.56843e14 0.356347
\(613\) 1.27510e15 0.594992 0.297496 0.954723i \(-0.403848\pi\)
0.297496 + 0.954723i \(0.403848\pi\)
\(614\) −3.03482e15 −1.40348
\(615\) 2.73711e15 1.25452
\(616\) −1.76044e15 −0.799700
\(617\) 6.25132e14 0.281452 0.140726 0.990049i \(-0.455056\pi\)
0.140726 + 0.990049i \(0.455056\pi\)
\(618\) −3.75556e15 −1.67586
\(619\) 4.18398e15 1.85051 0.925255 0.379345i \(-0.123851\pi\)
0.925255 + 0.379345i \(0.123851\pi\)
\(620\) 3.15039e15 1.38105
\(621\) 8.74893e14 0.380147
\(622\) 1.44709e15 0.623231
\(623\) 4.01455e15 1.71377
\(624\) −1.37021e15 −0.579792
\(625\) 3.31285e15 1.38951
\(626\) 3.95744e14 0.164534
\(627\) 1.80542e15 0.744058
\(628\) −8.68864e14 −0.354955
\(629\) 2.51944e15 1.02030
\(630\) 2.33871e15 0.938864
\(631\) −3.91655e15 −1.55863 −0.779314 0.626633i \(-0.784432\pi\)
−0.779314 + 0.626633i \(0.784432\pi\)
\(632\) −6.15312e14 −0.242746
\(633\) 1.15957e15 0.453499
\(634\) −4.74759e15 −1.84070
\(635\) 7.77862e15 2.98983
\(636\) −1.89422e15 −0.721799
\(637\) −4.79823e14 −0.181265
\(638\) 8.27580e14 0.309953
\(639\) −1.53157e14 −0.0568700
\(640\) −3.75462e15 −1.38222
\(641\) −2.88221e15 −1.05198 −0.525988 0.850492i \(-0.676304\pi\)
−0.525988 + 0.850492i \(0.676304\pi\)
\(642\) 1.01005e15 0.365512
\(643\) −1.52329e15 −0.546541 −0.273271 0.961937i \(-0.588105\pi\)
−0.273271 + 0.961937i \(0.588105\pi\)
\(644\) −7.45499e15 −2.65201
\(645\) −1.57024e15 −0.553844
\(646\) 2.50875e15 0.877360
\(647\) −1.29862e15 −0.450307 −0.225154 0.974323i \(-0.572288\pi\)
−0.225154 + 0.974323i \(0.572288\pi\)
\(648\) −1.31101e14 −0.0450758
\(649\) 7.11679e14 0.242627
\(650\) 1.44461e16 4.88346
\(651\) 1.12139e15 0.375890
\(652\) −2.86605e15 −0.952626
\(653\) −3.31342e15 −1.09208 −0.546040 0.837759i \(-0.683865\pi\)
−0.546040 + 0.837759i \(0.683865\pi\)
\(654\) 2.02962e14 0.0663343
\(655\) −2.97123e15 −0.962960
\(656\) −2.51739e15 −0.809056
\(657\) −3.07463e14 −0.0979903
\(658\) 8.04881e15 2.54384
\(659\) 1.50578e15 0.471945 0.235972 0.971760i \(-0.424173\pi\)
0.235972 + 0.971760i \(0.424173\pi\)
\(660\) 7.76715e15 2.41418
\(661\) −1.62543e15 −0.501025 −0.250513 0.968113i \(-0.580599\pi\)
−0.250513 + 0.968113i \(0.580599\pi\)
\(662\) 6.70507e15 2.04967
\(663\) 2.44729e15 0.741926
\(664\) −2.24794e15 −0.675866
\(665\) 4.33610e15 1.29295
\(666\) −2.05698e15 −0.608306
\(667\) 7.43551e14 0.218081
\(668\) −1.28336e15 −0.373316
\(669\) −3.23482e15 −0.933268
\(670\) 3.50660e15 1.00340
\(671\) −5.23567e15 −1.48593
\(672\) −3.03107e15 −0.853228
\(673\) −5.30873e15 −1.48220 −0.741101 0.671393i \(-0.765696\pi\)
−0.741101 + 0.671393i \(0.765696\pi\)
\(674\) −4.55953e15 −1.26267
\(675\) −1.48860e15 −0.408890
\(676\) 6.18690e15 1.68565
\(677\) −4.75556e15 −1.28518 −0.642590 0.766210i \(-0.722140\pi\)
−0.642590 + 0.766210i \(0.722140\pi\)
\(678\) 8.73406e14 0.234128
\(679\) 4.59800e15 1.22260
\(680\) 2.28989e15 0.603971
\(681\) 1.53235e15 0.400912
\(682\) 6.65839e15 1.72805
\(683\) 5.31997e15 1.36961 0.684803 0.728728i \(-0.259888\pi\)
0.684803 + 0.728728i \(0.259888\pi\)
\(684\) −1.14566e15 −0.292581
\(685\) 6.94368e15 1.75910
\(686\) 5.58701e15 1.40409
\(687\) −2.86101e14 −0.0713274
\(688\) 1.44419e15 0.357180
\(689\) −6.12505e15 −1.50281
\(690\) 1.24764e16 3.03683
\(691\) −4.37423e15 −1.05626 −0.528132 0.849162i \(-0.677107\pi\)
−0.528132 + 0.849162i \(0.677107\pi\)
\(692\) −3.76831e14 −0.0902740
\(693\) 2.76473e15 0.657082
\(694\) 2.42343e15 0.571418
\(695\) 8.75428e15 2.04788
\(696\) −1.11420e14 −0.0258590
\(697\) 4.49622e15 1.03530
\(698\) −1.88543e15 −0.430730
\(699\) −1.38818e14 −0.0314646
\(700\) 1.26844e16 2.85253
\(701\) 3.30107e15 0.736555 0.368278 0.929716i \(-0.379948\pi\)
0.368278 + 0.929716i \(0.379948\pi\)
\(702\) −1.99807e15 −0.442340
\(703\) −3.81377e15 −0.837722
\(704\) −1.23694e16 −2.69586
\(705\) −7.53438e15 −1.62932
\(706\) 2.84032e15 0.609455
\(707\) 3.36395e15 0.716214
\(708\) −4.51608e14 −0.0954066
\(709\) −1.78661e15 −0.374520 −0.187260 0.982310i \(-0.559961\pi\)
−0.187260 + 0.982310i \(0.559961\pi\)
\(710\) −2.18410e15 −0.454310
\(711\) 9.66334e14 0.199455
\(712\) −3.20924e15 −0.657298
\(713\) 5.98233e15 1.21584
\(714\) 3.84177e15 0.774803
\(715\) 2.51155e16 5.02641
\(716\) 1.15568e16 2.29517
\(717\) −3.28569e14 −0.0647548
\(718\) −3.14400e15 −0.614890
\(719\) −3.21462e15 −0.623908 −0.311954 0.950097i \(-0.600983\pi\)
−0.311954 + 0.950097i \(0.600983\pi\)
\(720\) 2.01349e15 0.387811
\(721\) −1.06628e16 −2.03812
\(722\) 4.14390e15 0.786057
\(723\) −2.70971e15 −0.510108
\(724\) −4.58056e15 −0.855770
\(725\) −1.26512e15 −0.234571
\(726\) 1.16895e16 2.15102
\(727\) −5.04622e15 −0.921567 −0.460784 0.887513i \(-0.652432\pi\)
−0.460784 + 0.887513i \(0.652432\pi\)
\(728\) 3.61225e15 0.654719
\(729\) 2.05891e14 0.0370370
\(730\) −4.38457e15 −0.782802
\(731\) −2.57942e15 −0.457063
\(732\) 3.32238e15 0.584303
\(733\) −4.67581e15 −0.816178 −0.408089 0.912942i \(-0.633805\pi\)
−0.408089 + 0.912942i \(0.633805\pi\)
\(734\) −2.60939e15 −0.452076
\(735\) 7.05086e14 0.121244
\(736\) −1.61700e16 −2.75983
\(737\) 4.14537e15 0.702250
\(738\) −3.67090e15 −0.617253
\(739\) 8.34283e15 1.39242 0.696208 0.717840i \(-0.254869\pi\)
0.696208 + 0.717840i \(0.254869\pi\)
\(740\) −1.64073e16 −2.71809
\(741\) −3.70454e15 −0.609164
\(742\) −9.61515e15 −1.56940
\(743\) −5.43413e15 −0.880423 −0.440212 0.897894i \(-0.645097\pi\)
−0.440212 + 0.897894i \(0.645097\pi\)
\(744\) −8.96440e14 −0.144168
\(745\) −1.33220e16 −2.12671
\(746\) −4.92513e15 −0.780467
\(747\) 3.53034e15 0.555333
\(748\) 1.27590e16 1.99232
\(749\) 2.86776e15 0.444521
\(750\) −1.12368e16 −1.72905
\(751\) 5.91094e15 0.902895 0.451447 0.892298i \(-0.350908\pi\)
0.451447 + 0.892298i \(0.350908\pi\)
\(752\) 6.92956e15 1.05077
\(753\) 4.86888e15 0.732919
\(754\) −1.69811e15 −0.253761
\(755\) 2.02503e15 0.300416
\(756\) −1.75440e15 −0.258380
\(757\) −7.83452e15 −1.14547 −0.572737 0.819739i \(-0.694118\pi\)
−0.572737 + 0.819739i \(0.694118\pi\)
\(758\) −1.58202e15 −0.229631
\(759\) 1.47491e16 2.12538
\(760\) −3.46629e15 −0.495895
\(761\) 1.16409e16 1.65337 0.826687 0.562662i \(-0.190223\pi\)
0.826687 + 0.562662i \(0.190223\pi\)
\(762\) −1.04324e16 −1.47106
\(763\) 5.76254e14 0.0806731
\(764\) 5.59881e15 0.778184
\(765\) −3.59623e15 −0.496260
\(766\) −1.48196e16 −2.03039
\(767\) −1.46030e15 −0.198640
\(768\) −1.14830e15 −0.155085
\(769\) 3.72079e15 0.498930 0.249465 0.968384i \(-0.419745\pi\)
0.249465 + 0.968384i \(0.419745\pi\)
\(770\) 3.94264e16 5.24914
\(771\) 7.23114e15 0.955889
\(772\) 1.79268e16 2.35292
\(773\) 7.08772e13 0.00923676 0.00461838 0.999989i \(-0.498530\pi\)
0.00461838 + 0.999989i \(0.498530\pi\)
\(774\) 2.10594e15 0.272503
\(775\) −1.01787e16 −1.30778
\(776\) −3.67565e15 −0.468915
\(777\) −5.84021e15 −0.739798
\(778\) −7.98358e14 −0.100418
\(779\) −6.80607e15 −0.850042
\(780\) −1.59374e16 −1.97651
\(781\) −2.58196e15 −0.317958
\(782\) 2.04949e16 2.50616
\(783\) 1.74982e14 0.0212473
\(784\) −6.48486e14 −0.0781920
\(785\) 4.12851e15 0.494322
\(786\) 3.98489e15 0.473798
\(787\) −7.47370e15 −0.882419 −0.441209 0.897404i \(-0.645450\pi\)
−0.441209 + 0.897404i \(0.645450\pi\)
\(788\) 7.97395e15 0.934931
\(789\) 3.70187e14 0.0431020
\(790\) 1.37804e16 1.59336
\(791\) 2.47979e15 0.284737
\(792\) −2.21013e15 −0.252017
\(793\) 1.07431e16 1.21654
\(794\) −1.79422e16 −2.01773
\(795\) 9.00060e15 1.00520
\(796\) 9.05108e15 1.00387
\(797\) 9.45897e15 1.04189 0.520946 0.853589i \(-0.325579\pi\)
0.520946 + 0.853589i \(0.325579\pi\)
\(798\) −5.81541e15 −0.636158
\(799\) −1.23767e16 −1.34461
\(800\) 2.75127e16 2.96850
\(801\) 5.04003e15 0.540076
\(802\) −9.94221e15 −1.05809
\(803\) −5.18328e15 −0.547859
\(804\) −2.63051e15 −0.276142
\(805\) 3.54232e16 3.69327
\(806\) −1.36624e16 −1.41476
\(807\) 1.62262e15 0.166883
\(808\) −2.68915e15 −0.274696
\(809\) −8.07445e15 −0.819212 −0.409606 0.912263i \(-0.634334\pi\)
−0.409606 + 0.912263i \(0.634334\pi\)
\(810\) 2.93611e15 0.295873
\(811\) −9.74910e15 −0.975776 −0.487888 0.872906i \(-0.662232\pi\)
−0.487888 + 0.872906i \(0.662232\pi\)
\(812\) −1.49103e15 −0.148227
\(813\) 1.00939e16 0.996688
\(814\) −3.46770e16 −3.40101
\(815\) 1.36184e16 1.32666
\(816\) 3.30754e15 0.320044
\(817\) 3.90455e15 0.375275
\(818\) −1.31542e16 −1.25580
\(819\) −5.67295e15 −0.537957
\(820\) −2.92806e16 −2.75806
\(821\) 8.93636e15 0.836129 0.418064 0.908417i \(-0.362709\pi\)
0.418064 + 0.908417i \(0.362709\pi\)
\(822\) −9.31260e15 −0.865518
\(823\) −1.99105e16 −1.83815 −0.919077 0.394077i \(-0.871064\pi\)
−0.919077 + 0.394077i \(0.871064\pi\)
\(824\) 8.52390e15 0.781698
\(825\) −2.50951e16 −2.28609
\(826\) −2.29238e15 −0.207442
\(827\) −6.19967e15 −0.557299 −0.278649 0.960393i \(-0.589887\pi\)
−0.278649 + 0.960393i \(0.589887\pi\)
\(828\) −9.35931e15 −0.835751
\(829\) −1.71179e16 −1.51845 −0.759227 0.650826i \(-0.774423\pi\)
−0.759227 + 0.650826i \(0.774423\pi\)
\(830\) 5.03444e16 4.43631
\(831\) −1.75836e15 −0.153923
\(832\) 2.53807e16 2.20712
\(833\) 1.15824e15 0.100058
\(834\) −1.17409e16 −1.00760
\(835\) 6.09802e15 0.519892
\(836\) −1.93138e16 −1.63581
\(837\) 1.40784e15 0.118458
\(838\) 5.73029e15 0.478999
\(839\) −6.25974e15 −0.519835 −0.259918 0.965631i \(-0.583695\pi\)
−0.259918 + 0.965631i \(0.583695\pi\)
\(840\) −5.30810e15 −0.437928
\(841\) −1.20518e16 −0.987811
\(842\) −1.44159e16 −1.17389
\(843\) −3.15575e15 −0.255300
\(844\) −1.24047e16 −0.997015
\(845\) −2.93978e16 −2.34748
\(846\) 1.01048e16 0.801663
\(847\) 3.31890e16 2.61598
\(848\) −8.27808e15 −0.648265
\(849\) 5.62050e15 0.437303
\(850\) −3.48713e16 −2.69565
\(851\) −3.11561e16 −2.39293
\(852\) 1.63843e15 0.125029
\(853\) 6.28237e14 0.0476326 0.0238163 0.999716i \(-0.492418\pi\)
0.0238163 + 0.999716i \(0.492418\pi\)
\(854\) 1.68645e16 1.27045
\(855\) 5.44372e15 0.407458
\(856\) −2.29249e15 −0.170491
\(857\) −1.48020e16 −1.09377 −0.546885 0.837208i \(-0.684186\pi\)
−0.546885 + 0.837208i \(0.684186\pi\)
\(858\) −3.36839e16 −2.47310
\(859\) 2.02138e16 1.47464 0.737319 0.675545i \(-0.236092\pi\)
0.737319 + 0.675545i \(0.236092\pi\)
\(860\) 1.67979e16 1.21762
\(861\) −1.04225e16 −0.750678
\(862\) 3.27097e16 2.34092
\(863\) −1.72387e16 −1.22587 −0.612935 0.790133i \(-0.710011\pi\)
−0.612935 + 0.790133i \(0.710011\pi\)
\(864\) −3.80533e15 −0.268885
\(865\) 1.79055e15 0.125718
\(866\) 2.46939e16 1.72283
\(867\) 2.42059e15 0.167809
\(868\) −1.19962e16 −0.826392
\(869\) 1.62907e16 1.11514
\(870\) 2.49533e15 0.169735
\(871\) −8.50589e15 −0.574936
\(872\) −4.60659e14 −0.0309413
\(873\) 5.77252e15 0.385289
\(874\) −3.10238e16 −2.05770
\(875\) −3.19038e16 −2.10280
\(876\) 3.28913e15 0.215431
\(877\) −8.38600e15 −0.545830 −0.272915 0.962038i \(-0.587988\pi\)
−0.272915 + 0.962038i \(0.587988\pi\)
\(878\) −3.14518e16 −2.03435
\(879\) 6.50662e15 0.418232
\(880\) 3.39439e16 2.16824
\(881\) −3.07062e15 −0.194921 −0.0974603 0.995239i \(-0.531072\pi\)
−0.0974603 + 0.995239i \(0.531072\pi\)
\(882\) −9.45635e14 −0.0596549
\(883\) 1.96212e14 0.0123010 0.00615051 0.999981i \(-0.498042\pi\)
0.00615051 + 0.999981i \(0.498042\pi\)
\(884\) −2.61803e16 −1.63112
\(885\) 2.14587e15 0.132866
\(886\) −6.23995e15 −0.383968
\(887\) 4.87530e15 0.298141 0.149070 0.988827i \(-0.452372\pi\)
0.149070 + 0.988827i \(0.452372\pi\)
\(888\) 4.66868e15 0.283741
\(889\) −2.96198e16 −1.78905
\(890\) 7.18734e16 4.31443
\(891\) 3.47096e15 0.207072
\(892\) 3.46050e16 2.05179
\(893\) 1.87349e16 1.10400
\(894\) 1.78669e16 1.04639
\(895\) −5.49132e16 −3.19632
\(896\) 1.42970e16 0.827088
\(897\) −3.02638e16 −1.74006
\(898\) 2.03606e16 1.16351
\(899\) 1.19649e15 0.0679563
\(900\) 1.59245e16 0.898944
\(901\) 1.47852e16 0.829547
\(902\) −6.18849e16 −3.45103
\(903\) 5.97923e15 0.331408
\(904\) −1.98235e15 −0.109208
\(905\) 2.17651e16 1.19177
\(906\) −2.71589e15 −0.147811
\(907\) −2.14404e16 −1.15983 −0.579914 0.814678i \(-0.696914\pi\)
−0.579914 + 0.814678i \(0.696914\pi\)
\(908\) −1.63926e16 −0.881404
\(909\) 4.22325e15 0.225707
\(910\) −8.08991e16 −4.29750
\(911\) 1.14567e16 0.604932 0.302466 0.953160i \(-0.402190\pi\)
0.302466 + 0.953160i \(0.402190\pi\)
\(912\) −5.00673e15 −0.262774
\(913\) 5.95153e16 3.10484
\(914\) 1.42901e16 0.741024
\(915\) −1.57867e16 −0.813718
\(916\) 3.06061e15 0.156813
\(917\) 1.13140e16 0.576214
\(918\) 4.82312e15 0.244171
\(919\) −1.48996e16 −0.749792 −0.374896 0.927067i \(-0.622322\pi\)
−0.374896 + 0.927067i \(0.622322\pi\)
\(920\) −2.83174e16 −1.41651
\(921\) −1.08175e16 −0.537898
\(922\) −1.91706e16 −0.947581
\(923\) 5.29793e15 0.260314
\(924\) −2.95761e16 −1.44459
\(925\) 5.30109e16 2.57387
\(926\) 2.94584e16 1.42183
\(927\) −1.33866e16 −0.642290
\(928\) −3.23406e15 −0.154253
\(929\) −9.94200e15 −0.471398 −0.235699 0.971826i \(-0.575738\pi\)
−0.235699 + 0.971826i \(0.575738\pi\)
\(930\) 2.00765e16 0.946305
\(931\) −1.75326e15 −0.0821531
\(932\) 1.48503e15 0.0691749
\(933\) 5.15812e15 0.238859
\(934\) 3.65557e16 1.68286
\(935\) −6.06260e16 −2.77456
\(936\) 4.53497e15 0.206328
\(937\) −1.00880e16 −0.456287 −0.228144 0.973627i \(-0.573266\pi\)
−0.228144 + 0.973627i \(0.573266\pi\)
\(938\) −1.33526e16 −0.600413
\(939\) 1.41062e15 0.0630592
\(940\) 8.06002e16 3.58206
\(941\) 2.92727e16 1.29336 0.646681 0.762761i \(-0.276157\pi\)
0.646681 + 0.762761i \(0.276157\pi\)
\(942\) −5.53699e15 −0.243217
\(943\) −5.56014e16 −2.42813
\(944\) −1.97361e15 −0.0856870
\(945\) 8.33625e15 0.359829
\(946\) 3.55025e16 1.52355
\(947\) −2.79988e16 −1.19458 −0.597289 0.802026i \(-0.703755\pi\)
−0.597289 + 0.802026i \(0.703755\pi\)
\(948\) −1.03375e16 −0.438500
\(949\) 1.06356e16 0.448535
\(950\) 5.27858e16 2.21329
\(951\) −1.69227e16 −0.705465
\(952\) −8.71957e15 −0.361403
\(953\) 2.95213e16 1.21653 0.608267 0.793732i \(-0.291865\pi\)
0.608267 + 0.793732i \(0.291865\pi\)
\(954\) −1.20713e16 −0.494580
\(955\) −2.66034e16 −1.08372
\(956\) 3.51492e15 0.142363
\(957\) 2.94989e15 0.118793
\(958\) 5.52746e16 2.21317
\(959\) −2.64405e16 −1.05261
\(960\) −3.72963e16 −1.47630
\(961\) −1.57820e16 −0.621131
\(962\) 7.11539e16 2.78443
\(963\) 3.60031e15 0.140086
\(964\) 2.89875e16 1.12147
\(965\) −8.51811e16 −3.27675
\(966\) −4.75083e16 −1.81717
\(967\) 4.26808e15 0.162326 0.0811629 0.996701i \(-0.474137\pi\)
0.0811629 + 0.996701i \(0.474137\pi\)
\(968\) −2.65313e16 −1.00333
\(969\) 8.94235e15 0.336257
\(970\) 8.23190e16 3.07791
\(971\) −4.89156e16 −1.81862 −0.909310 0.416120i \(-0.863390\pi\)
−0.909310 + 0.416120i \(0.863390\pi\)
\(972\) −2.20255e15 −0.0814258
\(973\) −3.33349e16 −1.22540
\(974\) 1.53851e16 0.562375
\(975\) 5.14927e16 1.87163
\(976\) 1.45194e16 0.524776
\(977\) −4.27989e16 −1.53820 −0.769100 0.639129i \(-0.779295\pi\)
−0.769100 + 0.639129i \(0.779295\pi\)
\(978\) −1.82644e16 −0.652744
\(979\) 8.49660e16 3.01954
\(980\) −7.54277e15 −0.266555
\(981\) 7.23454e14 0.0254233
\(982\) 2.40864e16 0.841701
\(983\) −4.05053e16 −1.40756 −0.703780 0.710418i \(-0.748506\pi\)
−0.703780 + 0.710418i \(0.748506\pi\)
\(984\) 8.33176e15 0.287914
\(985\) −3.78891e16 −1.30201
\(986\) 4.09906e15 0.140075
\(987\) 2.86898e16 0.974951
\(988\) 3.96299e16 1.33925
\(989\) 3.18977e16 1.07196
\(990\) 4.94976e16 1.65421
\(991\) 4.18063e16 1.38943 0.694715 0.719285i \(-0.255530\pi\)
0.694715 + 0.719285i \(0.255530\pi\)
\(992\) −2.60200e16 −0.859990
\(993\) 2.39000e16 0.785556
\(994\) 8.31673e15 0.271849
\(995\) −4.30072e16 −1.39802
\(996\) −3.77664e16 −1.22090
\(997\) 4.00612e16 1.28795 0.643977 0.765045i \(-0.277283\pi\)
0.643977 + 0.765045i \(0.277283\pi\)
\(998\) −7.22421e16 −2.30979
\(999\) −7.33205e15 −0.233139
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.1.4 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.a.1.4 26 1.1 even 1 trivial