Properties

Label 177.12.a.a.1.5
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 1.5
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-66.9000 q^{2} -243.000 q^{3} +2427.61 q^{4} -5686.53 q^{5} +16256.7 q^{6} +26687.5 q^{7} -25395.7 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-66.9000 q^{2} -243.000 q^{3} +2427.61 q^{4} -5686.53 q^{5} +16256.7 q^{6} +26687.5 q^{7} -25395.7 q^{8} +59049.0 q^{9} +380429. q^{10} +282948. q^{11} -589908. q^{12} +1.28590e6 q^{13} -1.78539e6 q^{14} +1.38183e6 q^{15} -3.27277e6 q^{16} -4.91113e6 q^{17} -3.95038e6 q^{18} -4.23666e6 q^{19} -1.38047e7 q^{20} -6.48505e6 q^{21} -1.89292e7 q^{22} +3.04935e7 q^{23} +6.17115e6 q^{24} -1.64915e7 q^{25} -8.60268e7 q^{26} -1.43489e7 q^{27} +6.47867e7 q^{28} +1.00209e8 q^{29} -9.24442e7 q^{30} -1.83681e8 q^{31} +2.70958e8 q^{32} -6.87563e7 q^{33} +3.28555e8 q^{34} -1.51759e8 q^{35} +1.43348e8 q^{36} -4.83150e8 q^{37} +2.83432e8 q^{38} -3.12474e8 q^{39} +1.44413e8 q^{40} -4.31814e8 q^{41} +4.33850e8 q^{42} -3.19027e8 q^{43} +6.86886e8 q^{44} -3.35784e8 q^{45} -2.04002e9 q^{46} +1.15008e9 q^{47} +7.95283e8 q^{48} -1.26511e9 q^{49} +1.10328e9 q^{50} +1.19341e9 q^{51} +3.12167e9 q^{52} -1.32282e9 q^{53} +9.59942e8 q^{54} -1.60899e9 q^{55} -6.77747e8 q^{56} +1.02951e9 q^{57} -6.70395e9 q^{58} +7.14924e8 q^{59} +3.35453e9 q^{60} +4.52154e9 q^{61} +1.22882e10 q^{62} +1.57587e9 q^{63} -1.14245e10 q^{64} -7.31233e9 q^{65} +4.59980e9 q^{66} +1.21583e10 q^{67} -1.19223e10 q^{68} -7.40993e9 q^{69} +1.01527e10 q^{70} +2.63791e10 q^{71} -1.49959e9 q^{72} -1.30795e9 q^{73} +3.23227e10 q^{74} +4.00743e9 q^{75} -1.02849e10 q^{76} +7.55116e9 q^{77} +2.09045e10 q^{78} -1.29817e10 q^{79} +1.86107e10 q^{80} +3.48678e9 q^{81} +2.88883e10 q^{82} -6.28207e10 q^{83} -1.57432e10 q^{84} +2.79273e10 q^{85} +2.13429e10 q^{86} -2.43507e10 q^{87} -7.18566e9 q^{88} +4.23991e10 q^{89} +2.24639e10 q^{90} +3.43175e10 q^{91} +7.40263e10 q^{92} +4.46344e10 q^{93} -7.69402e10 q^{94} +2.40919e10 q^{95} -6.58429e10 q^{96} +5.43637e10 q^{97} +8.46356e10 q^{98} +1.67078e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −66.9000 −1.47829 −0.739147 0.673544i \(-0.764771\pi\)
−0.739147 + 0.673544i \(0.764771\pi\)
\(3\) −243.000 −0.577350
\(4\) 2427.61 1.18535
\(5\) −5686.53 −0.813790 −0.406895 0.913475i \(-0.633389\pi\)
−0.406895 + 0.913475i \(0.633389\pi\)
\(6\) 16256.7 0.853494
\(7\) 26687.5 0.600162 0.300081 0.953914i \(-0.402986\pi\)
0.300081 + 0.953914i \(0.402986\pi\)
\(8\) −25395.7 −0.274009
\(9\) 59049.0 0.333333
\(10\) 380429. 1.20302
\(11\) 282948. 0.529720 0.264860 0.964287i \(-0.414674\pi\)
0.264860 + 0.964287i \(0.414674\pi\)
\(12\) −589908. −0.684365
\(13\) 1.28590e6 0.960549 0.480275 0.877118i \(-0.340537\pi\)
0.480275 + 0.877118i \(0.340537\pi\)
\(14\) −1.78539e6 −0.887216
\(15\) 1.38183e6 0.469842
\(16\) −3.27277e6 −0.780289
\(17\) −4.91113e6 −0.838905 −0.419452 0.907777i \(-0.637778\pi\)
−0.419452 + 0.907777i \(0.637778\pi\)
\(18\) −3.95038e6 −0.492765
\(19\) −4.23666e6 −0.392535 −0.196268 0.980550i \(-0.562882\pi\)
−0.196268 + 0.980550i \(0.562882\pi\)
\(20\) −1.38047e7 −0.964630
\(21\) −6.48505e6 −0.346503
\(22\) −1.89292e7 −0.783083
\(23\) 3.04935e7 0.987881 0.493941 0.869496i \(-0.335556\pi\)
0.493941 + 0.869496i \(0.335556\pi\)
\(24\) 6.17115e6 0.158199
\(25\) −1.64915e7 −0.337745
\(26\) −8.60268e7 −1.41997
\(27\) −1.43489e7 −0.192450
\(28\) 6.47867e7 0.711404
\(29\) 1.00209e8 0.907227 0.453614 0.891198i \(-0.350135\pi\)
0.453614 + 0.891198i \(0.350135\pi\)
\(30\) −9.24442e7 −0.694565
\(31\) −1.83681e8 −1.15232 −0.576161 0.817336i \(-0.695450\pi\)
−0.576161 + 0.817336i \(0.695450\pi\)
\(32\) 2.70958e8 1.42751
\(33\) −6.87563e7 −0.305834
\(34\) 3.28555e8 1.24015
\(35\) −1.51759e8 −0.488406
\(36\) 1.43348e8 0.395118
\(37\) −4.83150e8 −1.14544 −0.572720 0.819751i \(-0.694112\pi\)
−0.572720 + 0.819751i \(0.694112\pi\)
\(38\) 2.83432e8 0.580283
\(39\) −3.12474e8 −0.554573
\(40\) 1.44413e8 0.222986
\(41\) −4.31814e8 −0.582084 −0.291042 0.956710i \(-0.594002\pi\)
−0.291042 + 0.956710i \(0.594002\pi\)
\(42\) 4.33850e8 0.512234
\(43\) −3.19027e8 −0.330941 −0.165470 0.986215i \(-0.552914\pi\)
−0.165470 + 0.986215i \(0.552914\pi\)
\(44\) 6.86886e8 0.627907
\(45\) −3.35784e8 −0.271263
\(46\) −2.04002e9 −1.46038
\(47\) 1.15008e9 0.731457 0.365729 0.930721i \(-0.380820\pi\)
0.365729 + 0.930721i \(0.380820\pi\)
\(48\) 7.95283e8 0.450500
\(49\) −1.26511e9 −0.639806
\(50\) 1.10328e9 0.499287
\(51\) 1.19341e9 0.484342
\(52\) 3.12167e9 1.13859
\(53\) −1.32282e9 −0.434495 −0.217247 0.976117i \(-0.569708\pi\)
−0.217247 + 0.976117i \(0.569708\pi\)
\(54\) 9.59942e8 0.284498
\(55\) −1.60899e9 −0.431081
\(56\) −6.77747e8 −0.164450
\(57\) 1.02951e9 0.226630
\(58\) −6.70395e9 −1.34115
\(59\) 7.14924e8 0.130189
\(60\) 3.35453e9 0.556930
\(61\) 4.52154e9 0.685444 0.342722 0.939437i \(-0.388651\pi\)
0.342722 + 0.939437i \(0.388651\pi\)
\(62\) 1.22882e10 1.70347
\(63\) 1.57587e9 0.200054
\(64\) −1.14245e10 −1.32999
\(65\) −7.31233e9 −0.781686
\(66\) 4.59980e9 0.452113
\(67\) 1.21583e10 1.10017 0.550087 0.835107i \(-0.314594\pi\)
0.550087 + 0.835107i \(0.314594\pi\)
\(68\) −1.19223e10 −0.994400
\(69\) −7.40993e9 −0.570353
\(70\) 1.01527e10 0.722007
\(71\) 2.63791e10 1.73516 0.867580 0.497298i \(-0.165675\pi\)
0.867580 + 0.497298i \(0.165675\pi\)
\(72\) −1.49959e9 −0.0913364
\(73\) −1.30795e9 −0.0738438 −0.0369219 0.999318i \(-0.511755\pi\)
−0.0369219 + 0.999318i \(0.511755\pi\)
\(74\) 3.23227e10 1.69330
\(75\) 4.00743e9 0.194997
\(76\) −1.02849e10 −0.465294
\(77\) 7.55116e9 0.317918
\(78\) 2.09045e10 0.819823
\(79\) −1.29817e10 −0.474662 −0.237331 0.971429i \(-0.576273\pi\)
−0.237331 + 0.971429i \(0.576273\pi\)
\(80\) 1.86107e10 0.634991
\(81\) 3.48678e9 0.111111
\(82\) 2.88883e10 0.860491
\(83\) −6.28207e10 −1.75055 −0.875273 0.483630i \(-0.839318\pi\)
−0.875273 + 0.483630i \(0.839318\pi\)
\(84\) −1.57432e10 −0.410730
\(85\) 2.79273e10 0.682693
\(86\) 2.13429e10 0.489228
\(87\) −2.43507e10 −0.523788
\(88\) −7.18566e9 −0.145148
\(89\) 4.23991e10 0.804845 0.402422 0.915454i \(-0.368168\pi\)
0.402422 + 0.915454i \(0.368168\pi\)
\(90\) 2.24639e10 0.401007
\(91\) 3.43175e10 0.576485
\(92\) 7.40263e10 1.17099
\(93\) 4.46344e10 0.665294
\(94\) −7.69402e10 −1.08131
\(95\) 2.40919e10 0.319441
\(96\) −6.58429e10 −0.824171
\(97\) 5.43637e10 0.642783 0.321391 0.946946i \(-0.395850\pi\)
0.321391 + 0.946946i \(0.395850\pi\)
\(98\) 8.46356e10 0.945822
\(99\) 1.67078e10 0.176573
\(100\) −4.00348e10 −0.400348
\(101\) 2.15225e10 0.203763 0.101881 0.994797i \(-0.467514\pi\)
0.101881 + 0.994797i \(0.467514\pi\)
\(102\) −7.98388e10 −0.716000
\(103\) 1.12937e11 0.959911 0.479956 0.877293i \(-0.340653\pi\)
0.479956 + 0.877293i \(0.340653\pi\)
\(104\) −3.26564e10 −0.263199
\(105\) 3.68775e10 0.281981
\(106\) 8.84968e10 0.642311
\(107\) 2.55906e11 1.76388 0.881942 0.471357i \(-0.156236\pi\)
0.881942 + 0.471357i \(0.156236\pi\)
\(108\) −3.48335e10 −0.228122
\(109\) 2.26916e10 0.141260 0.0706300 0.997503i \(-0.477499\pi\)
0.0706300 + 0.997503i \(0.477499\pi\)
\(110\) 1.07642e11 0.637265
\(111\) 1.17405e11 0.661320
\(112\) −8.73419e10 −0.468299
\(113\) 2.38933e11 1.21996 0.609979 0.792417i \(-0.291178\pi\)
0.609979 + 0.792417i \(0.291178\pi\)
\(114\) −6.88741e10 −0.335026
\(115\) −1.73402e11 −0.803928
\(116\) 2.43267e11 1.07539
\(117\) 7.59313e10 0.320183
\(118\) −4.78284e10 −0.192458
\(119\) −1.31066e11 −0.503478
\(120\) −3.50925e10 −0.128741
\(121\) −2.05252e11 −0.719396
\(122\) −3.02491e11 −1.01329
\(123\) 1.04931e11 0.336066
\(124\) −4.45904e11 −1.36591
\(125\) 3.71442e11 1.08864
\(126\) −1.05426e11 −0.295739
\(127\) 2.39317e11 0.642767 0.321384 0.946949i \(-0.395852\pi\)
0.321384 + 0.946949i \(0.395852\pi\)
\(128\) 2.09375e11 0.538604
\(129\) 7.75235e10 0.191069
\(130\) 4.89194e11 1.15556
\(131\) −3.16017e11 −0.715679 −0.357840 0.933783i \(-0.616487\pi\)
−0.357840 + 0.933783i \(0.616487\pi\)
\(132\) −1.66913e11 −0.362522
\(133\) −1.13066e11 −0.235585
\(134\) −8.13391e11 −1.62638
\(135\) 8.15955e10 0.156614
\(136\) 1.24722e11 0.229868
\(137\) −9.07763e11 −1.60698 −0.803488 0.595322i \(-0.797025\pi\)
−0.803488 + 0.595322i \(0.797025\pi\)
\(138\) 4.95724e11 0.843150
\(139\) −6.26986e11 −1.02489 −0.512444 0.858721i \(-0.671260\pi\)
−0.512444 + 0.858721i \(0.671260\pi\)
\(140\) −3.68412e11 −0.578934
\(141\) −2.79469e11 −0.422307
\(142\) −1.76476e12 −2.56508
\(143\) 3.63843e11 0.508823
\(144\) −1.93254e11 −0.260096
\(145\) −5.69840e11 −0.738293
\(146\) 8.75015e10 0.109163
\(147\) 3.07421e11 0.369392
\(148\) −1.17290e12 −1.35775
\(149\) −6.38390e11 −0.712134 −0.356067 0.934460i \(-0.615882\pi\)
−0.356067 + 0.934460i \(0.615882\pi\)
\(150\) −2.68097e11 −0.288263
\(151\) −1.10415e12 −1.14460 −0.572302 0.820043i \(-0.693950\pi\)
−0.572302 + 0.820043i \(0.693950\pi\)
\(152\) 1.07593e11 0.107558
\(153\) −2.89998e11 −0.279635
\(154\) −5.05173e11 −0.469976
\(155\) 1.04451e12 0.937749
\(156\) −7.58565e11 −0.657366
\(157\) −1.69080e12 −1.41463 −0.707316 0.706898i \(-0.750094\pi\)
−0.707316 + 0.706898i \(0.750094\pi\)
\(158\) 8.68479e11 0.701690
\(159\) 3.21446e11 0.250856
\(160\) −1.54081e12 −1.16169
\(161\) 8.13795e11 0.592888
\(162\) −2.33266e11 −0.164255
\(163\) 1.43370e12 0.975948 0.487974 0.872858i \(-0.337736\pi\)
0.487974 + 0.872858i \(0.337736\pi\)
\(164\) −1.04827e12 −0.689976
\(165\) 3.90985e11 0.248885
\(166\) 4.20270e12 2.58782
\(167\) −5.68321e11 −0.338574 −0.169287 0.985567i \(-0.554146\pi\)
−0.169287 + 0.985567i \(0.554146\pi\)
\(168\) 1.64692e11 0.0949451
\(169\) −1.38615e11 −0.0773454
\(170\) −1.86834e12 −1.00922
\(171\) −2.50170e11 −0.130845
\(172\) −7.74471e11 −0.392282
\(173\) 3.65112e12 1.79132 0.895659 0.444741i \(-0.146704\pi\)
0.895659 + 0.444741i \(0.146704\pi\)
\(174\) 1.62906e12 0.774313
\(175\) −4.40115e11 −0.202702
\(176\) −9.26023e11 −0.413335
\(177\) −1.73727e11 −0.0751646
\(178\) −2.83650e12 −1.18980
\(179\) −2.92612e12 −1.19015 −0.595074 0.803671i \(-0.702877\pi\)
−0.595074 + 0.803671i \(0.702877\pi\)
\(180\) −8.15152e11 −0.321543
\(181\) −8.42623e11 −0.322404 −0.161202 0.986921i \(-0.551537\pi\)
−0.161202 + 0.986921i \(0.551537\pi\)
\(182\) −2.29584e12 −0.852214
\(183\) −1.09873e12 −0.395742
\(184\) −7.74405e11 −0.270689
\(185\) 2.74745e12 0.932149
\(186\) −2.98604e12 −0.983500
\(187\) −1.38960e12 −0.444385
\(188\) 2.79194e12 0.867037
\(189\) −3.82936e11 −0.115501
\(190\) −1.61175e12 −0.472229
\(191\) 3.36937e12 0.959102 0.479551 0.877514i \(-0.340800\pi\)
0.479551 + 0.877514i \(0.340800\pi\)
\(192\) 2.77615e12 0.767867
\(193\) −2.62087e12 −0.704498 −0.352249 0.935906i \(-0.614583\pi\)
−0.352249 + 0.935906i \(0.614583\pi\)
\(194\) −3.63693e12 −0.950222
\(195\) 1.77690e12 0.451306
\(196\) −3.07118e12 −0.758397
\(197\) −3.85437e12 −0.925528 −0.462764 0.886481i \(-0.653142\pi\)
−0.462764 + 0.886481i \(0.653142\pi\)
\(198\) −1.11775e12 −0.261028
\(199\) 6.03566e12 1.37099 0.685493 0.728080i \(-0.259587\pi\)
0.685493 + 0.728080i \(0.259587\pi\)
\(200\) 4.18812e11 0.0925453
\(201\) −2.95447e12 −0.635186
\(202\) −1.43985e12 −0.301222
\(203\) 2.67431e12 0.544483
\(204\) 2.89712e12 0.574117
\(205\) 2.45552e12 0.473694
\(206\) −7.55548e12 −1.41903
\(207\) 1.80061e12 0.329294
\(208\) −4.20846e12 −0.749506
\(209\) −1.19875e12 −0.207934
\(210\) −2.46710e12 −0.416851
\(211\) 2.87168e12 0.472696 0.236348 0.971668i \(-0.424049\pi\)
0.236348 + 0.971668i \(0.424049\pi\)
\(212\) −3.21129e12 −0.515030
\(213\) −6.41013e12 −1.00179
\(214\) −1.71201e13 −2.60754
\(215\) 1.81416e12 0.269317
\(216\) 3.64400e11 0.0527331
\(217\) −4.90197e12 −0.691580
\(218\) −1.51807e12 −0.208824
\(219\) 3.17831e11 0.0426337
\(220\) −3.90600e12 −0.510985
\(221\) −6.31524e12 −0.805809
\(222\) −7.85442e12 −0.977626
\(223\) −2.02890e11 −0.0246368 −0.0123184 0.999924i \(-0.503921\pi\)
−0.0123184 + 0.999924i \(0.503921\pi\)
\(224\) 7.23120e12 0.856734
\(225\) −9.73805e11 −0.112582
\(226\) −1.59846e13 −1.80346
\(227\) 6.43975e10 0.00709132 0.00354566 0.999994i \(-0.498871\pi\)
0.00354566 + 0.999994i \(0.498871\pi\)
\(228\) 2.49924e12 0.268637
\(229\) −5.01326e12 −0.526047 −0.263024 0.964789i \(-0.584720\pi\)
−0.263024 + 0.964789i \(0.584720\pi\)
\(230\) 1.16006e13 1.18844
\(231\) −1.83493e12 −0.183550
\(232\) −2.54487e12 −0.248589
\(233\) −1.08417e12 −0.103428 −0.0517142 0.998662i \(-0.516468\pi\)
−0.0517142 + 0.998662i \(0.516468\pi\)
\(234\) −5.07980e12 −0.473325
\(235\) −6.53996e12 −0.595253
\(236\) 1.73556e12 0.154320
\(237\) 3.15457e12 0.274046
\(238\) 8.76829e12 0.744289
\(239\) −1.15366e13 −0.956950 −0.478475 0.878101i \(-0.658810\pi\)
−0.478475 + 0.878101i \(0.658810\pi\)
\(240\) −4.52240e12 −0.366612
\(241\) 1.51057e13 1.19687 0.598434 0.801172i \(-0.295790\pi\)
0.598434 + 0.801172i \(0.295790\pi\)
\(242\) 1.37314e13 1.06348
\(243\) −8.47289e11 −0.0641500
\(244\) 1.09765e13 0.812495
\(245\) 7.19407e12 0.520668
\(246\) −7.01987e12 −0.496805
\(247\) −5.44793e12 −0.377049
\(248\) 4.66470e12 0.315747
\(249\) 1.52654e13 1.01068
\(250\) −2.48495e13 −1.60934
\(251\) −1.46102e13 −0.925658 −0.462829 0.886448i \(-0.653166\pi\)
−0.462829 + 0.886448i \(0.653166\pi\)
\(252\) 3.82559e12 0.237135
\(253\) 8.62808e12 0.523301
\(254\) −1.60103e13 −0.950199
\(255\) −6.78634e12 −0.394153
\(256\) 9.39017e12 0.533769
\(257\) −2.37008e13 −1.31865 −0.659327 0.751856i \(-0.729159\pi\)
−0.659327 + 0.751856i \(0.729159\pi\)
\(258\) −5.18632e12 −0.282456
\(259\) −1.28941e13 −0.687449
\(260\) −1.77515e13 −0.926575
\(261\) 5.91722e12 0.302409
\(262\) 2.11415e13 1.05798
\(263\) 1.05117e13 0.515129 0.257564 0.966261i \(-0.417080\pi\)
0.257564 + 0.966261i \(0.417080\pi\)
\(264\) 1.74612e12 0.0838014
\(265\) 7.52227e12 0.353587
\(266\) 7.56409e12 0.348263
\(267\) −1.03030e13 −0.464677
\(268\) 2.95156e13 1.30410
\(269\) −1.72454e12 −0.0746510 −0.0373255 0.999303i \(-0.511884\pi\)
−0.0373255 + 0.999303i \(0.511884\pi\)
\(270\) −5.45874e12 −0.231522
\(271\) −4.51661e12 −0.187707 −0.0938537 0.995586i \(-0.529919\pi\)
−0.0938537 + 0.995586i \(0.529919\pi\)
\(272\) 1.60730e13 0.654588
\(273\) −8.33915e12 −0.332834
\(274\) 6.07293e13 2.37558
\(275\) −4.66623e12 −0.178911
\(276\) −1.79884e13 −0.676071
\(277\) 7.49024e12 0.275967 0.137983 0.990435i \(-0.455938\pi\)
0.137983 + 0.990435i \(0.455938\pi\)
\(278\) 4.19453e13 1.51509
\(279\) −1.08462e13 −0.384108
\(280\) 3.85403e12 0.133828
\(281\) 5.21166e13 1.77456 0.887281 0.461230i \(-0.152592\pi\)
0.887281 + 0.461230i \(0.152592\pi\)
\(282\) 1.86965e13 0.624294
\(283\) −1.20033e13 −0.393073 −0.196537 0.980496i \(-0.562969\pi\)
−0.196537 + 0.980496i \(0.562969\pi\)
\(284\) 6.40381e13 2.05678
\(285\) −5.85433e12 −0.184430
\(286\) −2.43411e13 −0.752190
\(287\) −1.15240e13 −0.349344
\(288\) 1.59998e13 0.475835
\(289\) −1.01527e13 −0.296239
\(290\) 3.81223e13 1.09141
\(291\) −1.32104e13 −0.371111
\(292\) −3.17518e12 −0.0875311
\(293\) 3.11650e13 0.843131 0.421565 0.906798i \(-0.361481\pi\)
0.421565 + 0.906798i \(0.361481\pi\)
\(294\) −2.05664e13 −0.546071
\(295\) −4.06544e12 −0.105946
\(296\) 1.22699e13 0.313861
\(297\) −4.05999e12 −0.101945
\(298\) 4.27083e13 1.05274
\(299\) 3.92117e13 0.948908
\(300\) 9.72846e12 0.231141
\(301\) −8.51401e12 −0.198618
\(302\) 7.38677e13 1.69206
\(303\) −5.22997e12 −0.117643
\(304\) 1.38656e13 0.306291
\(305\) −2.57119e13 −0.557808
\(306\) 1.94008e13 0.413383
\(307\) −2.42596e13 −0.507718 −0.253859 0.967241i \(-0.581700\pi\)
−0.253859 + 0.967241i \(0.581700\pi\)
\(308\) 1.83313e13 0.376845
\(309\) −2.74437e13 −0.554205
\(310\) −6.98774e13 −1.38627
\(311\) 7.39191e13 1.44070 0.720351 0.693609i \(-0.243981\pi\)
0.720351 + 0.693609i \(0.243981\pi\)
\(312\) 7.93550e12 0.151958
\(313\) −3.42215e13 −0.643881 −0.321940 0.946760i \(-0.604335\pi\)
−0.321940 + 0.946760i \(0.604335\pi\)
\(314\) 1.13114e14 2.09124
\(315\) −8.96123e12 −0.162802
\(316\) −3.15146e13 −0.562643
\(317\) 1.74596e13 0.306344 0.153172 0.988200i \(-0.451051\pi\)
0.153172 + 0.988200i \(0.451051\pi\)
\(318\) −2.15047e13 −0.370838
\(319\) 2.83538e13 0.480577
\(320\) 6.49657e13 1.08233
\(321\) −6.21852e13 −1.01838
\(322\) −5.44429e13 −0.876463
\(323\) 2.08068e13 0.329300
\(324\) 8.46454e12 0.131706
\(325\) −2.12064e13 −0.324421
\(326\) −9.59145e13 −1.44274
\(327\) −5.51406e12 −0.0815566
\(328\) 1.09662e13 0.159496
\(329\) 3.06927e13 0.438993
\(330\) −2.61569e13 −0.367925
\(331\) 1.41060e14 1.95141 0.975706 0.219084i \(-0.0703068\pi\)
0.975706 + 0.219084i \(0.0703068\pi\)
\(332\) −1.52504e14 −2.07502
\(333\) −2.85295e13 −0.381814
\(334\) 3.80207e13 0.500512
\(335\) −6.91386e13 −0.895312
\(336\) 2.12241e13 0.270373
\(337\) −3.86749e12 −0.0484690 −0.0242345 0.999706i \(-0.507715\pi\)
−0.0242345 + 0.999706i \(0.507715\pi\)
\(338\) 9.27336e12 0.114339
\(339\) −5.80608e13 −0.704343
\(340\) 6.77966e13 0.809233
\(341\) −5.19721e13 −0.610409
\(342\) 1.67364e13 0.193428
\(343\) −8.65323e13 −0.984149
\(344\) 8.10190e12 0.0906809
\(345\) 4.21368e13 0.464148
\(346\) −2.44260e14 −2.64810
\(347\) −4.70102e12 −0.0501626 −0.0250813 0.999685i \(-0.507984\pi\)
−0.0250813 + 0.999685i \(0.507984\pi\)
\(348\) −5.91139e13 −0.620875
\(349\) −1.29440e14 −1.33822 −0.669112 0.743162i \(-0.733325\pi\)
−0.669112 + 0.743162i \(0.733325\pi\)
\(350\) 2.94437e13 0.299653
\(351\) −1.84513e13 −0.184858
\(352\) 7.66671e13 0.756179
\(353\) −5.55019e13 −0.538948 −0.269474 0.963008i \(-0.586850\pi\)
−0.269474 + 0.963008i \(0.586850\pi\)
\(354\) 1.16223e13 0.111115
\(355\) −1.50006e14 −1.41206
\(356\) 1.02928e14 0.954027
\(357\) 3.18490e13 0.290683
\(358\) 1.95758e14 1.75939
\(359\) 1.26971e14 1.12379 0.561893 0.827210i \(-0.310073\pi\)
0.561893 + 0.827210i \(0.310073\pi\)
\(360\) 8.52747e12 0.0743287
\(361\) −9.85410e13 −0.845916
\(362\) 5.63714e13 0.476609
\(363\) 4.98763e13 0.415344
\(364\) 8.33094e13 0.683339
\(365\) 7.43768e12 0.0600934
\(366\) 7.35053e13 0.585023
\(367\) −5.95911e13 −0.467216 −0.233608 0.972331i \(-0.575053\pi\)
−0.233608 + 0.972331i \(0.575053\pi\)
\(368\) −9.97982e13 −0.770832
\(369\) −2.54982e13 −0.194028
\(370\) −1.83804e14 −1.37799
\(371\) −3.53028e13 −0.260767
\(372\) 1.08355e14 0.788609
\(373\) −4.28866e13 −0.307555 −0.153778 0.988105i \(-0.549144\pi\)
−0.153778 + 0.988105i \(0.549144\pi\)
\(374\) 9.29639e13 0.656932
\(375\) −9.02604e13 −0.628529
\(376\) −2.92070e13 −0.200426
\(377\) 1.28859e14 0.871436
\(378\) 2.56184e13 0.170745
\(379\) 2.27560e13 0.149479 0.0747395 0.997203i \(-0.476187\pi\)
0.0747395 + 0.997203i \(0.476187\pi\)
\(380\) 5.84857e13 0.378652
\(381\) −5.81541e13 −0.371102
\(382\) −2.25410e14 −1.41783
\(383\) 9.29424e13 0.576263 0.288131 0.957591i \(-0.406966\pi\)
0.288131 + 0.957591i \(0.406966\pi\)
\(384\) −5.08781e13 −0.310963
\(385\) −4.29399e13 −0.258718
\(386\) 1.75336e14 1.04146
\(387\) −1.88382e13 −0.110314
\(388\) 1.31974e14 0.761926
\(389\) 1.07869e14 0.614006 0.307003 0.951709i \(-0.400674\pi\)
0.307003 + 0.951709i \(0.400674\pi\)
\(390\) −1.18874e14 −0.667164
\(391\) −1.49758e14 −0.828738
\(392\) 3.21282e13 0.175313
\(393\) 7.67922e13 0.413198
\(394\) 2.57858e14 1.36820
\(395\) 7.38212e13 0.386275
\(396\) 4.05600e13 0.209302
\(397\) −2.79738e13 −0.142365 −0.0711826 0.997463i \(-0.522677\pi\)
−0.0711826 + 0.997463i \(0.522677\pi\)
\(398\) −4.03785e14 −2.02672
\(399\) 2.74750e13 0.136015
\(400\) 5.39727e13 0.263539
\(401\) 2.90854e13 0.140082 0.0700409 0.997544i \(-0.477687\pi\)
0.0700409 + 0.997544i \(0.477687\pi\)
\(402\) 1.97654e14 0.938993
\(403\) −2.36195e14 −1.10686
\(404\) 5.22482e13 0.241531
\(405\) −1.98277e13 −0.0904212
\(406\) −1.78912e14 −0.804906
\(407\) −1.36706e14 −0.606763
\(408\) −3.03074e13 −0.132714
\(409\) −2.71616e14 −1.17348 −0.586742 0.809774i \(-0.699590\pi\)
−0.586742 + 0.809774i \(0.699590\pi\)
\(410\) −1.64274e14 −0.700259
\(411\) 2.20586e14 0.927787
\(412\) 2.74166e14 1.13784
\(413\) 1.90795e13 0.0781344
\(414\) −1.20461e14 −0.486793
\(415\) 3.57232e14 1.42458
\(416\) 3.48426e14 1.37119
\(417\) 1.52358e14 0.591719
\(418\) 8.01966e13 0.307388
\(419\) 1.26526e14 0.478635 0.239317 0.970941i \(-0.423076\pi\)
0.239317 + 0.970941i \(0.423076\pi\)
\(420\) 8.95240e13 0.334248
\(421\) −1.78571e14 −0.658051 −0.329025 0.944321i \(-0.606720\pi\)
−0.329025 + 0.944321i \(0.606720\pi\)
\(422\) −1.92115e14 −0.698784
\(423\) 6.79110e13 0.243819
\(424\) 3.35940e13 0.119056
\(425\) 8.09918e13 0.283336
\(426\) 4.28837e14 1.48095
\(427\) 1.20668e14 0.411377
\(428\) 6.21240e14 2.09083
\(429\) −8.84140e13 −0.293769
\(430\) −1.21367e14 −0.398129
\(431\) 2.71648e14 0.879795 0.439898 0.898048i \(-0.355015\pi\)
0.439898 + 0.898048i \(0.355015\pi\)
\(432\) 4.69606e13 0.150167
\(433\) −3.49275e14 −1.10277 −0.551384 0.834252i \(-0.685900\pi\)
−0.551384 + 0.834252i \(0.685900\pi\)
\(434\) 3.27942e14 1.02236
\(435\) 1.38471e14 0.426254
\(436\) 5.50863e13 0.167443
\(437\) −1.29191e14 −0.387778
\(438\) −2.12629e13 −0.0630252
\(439\) 6.49482e13 0.190113 0.0950566 0.995472i \(-0.469697\pi\)
0.0950566 + 0.995472i \(0.469697\pi\)
\(440\) 4.08615e13 0.118120
\(441\) −7.47032e13 −0.213269
\(442\) 4.22489e14 1.19122
\(443\) −2.80298e14 −0.780547 −0.390273 0.920699i \(-0.627620\pi\)
−0.390273 + 0.920699i \(0.627620\pi\)
\(444\) 2.85014e14 0.783899
\(445\) −2.41104e14 −0.654975
\(446\) 1.35733e13 0.0364204
\(447\) 1.55129e14 0.411151
\(448\) −3.04891e14 −0.798206
\(449\) −4.83240e14 −1.24971 −0.624853 0.780743i \(-0.714841\pi\)
−0.624853 + 0.780743i \(0.714841\pi\)
\(450\) 6.51475e13 0.166429
\(451\) −1.22181e14 −0.308342
\(452\) 5.80036e14 1.44608
\(453\) 2.68309e14 0.660838
\(454\) −4.30819e12 −0.0104831
\(455\) −1.95147e14 −0.469138
\(456\) −2.61451e13 −0.0620988
\(457\) −4.72542e14 −1.10892 −0.554461 0.832210i \(-0.687076\pi\)
−0.554461 + 0.832210i \(0.687076\pi\)
\(458\) 3.35387e14 0.777653
\(459\) 7.04694e13 0.161447
\(460\) −4.20953e14 −0.952940
\(461\) 7.26202e14 1.62444 0.812218 0.583354i \(-0.198260\pi\)
0.812218 + 0.583354i \(0.198260\pi\)
\(462\) 1.22757e14 0.271341
\(463\) 2.66401e14 0.581890 0.290945 0.956740i \(-0.406030\pi\)
0.290945 + 0.956740i \(0.406030\pi\)
\(464\) −3.27960e14 −0.707899
\(465\) −2.53815e14 −0.541410
\(466\) 7.25309e13 0.152898
\(467\) −8.75398e14 −1.82374 −0.911870 0.410479i \(-0.865361\pi\)
−0.911870 + 0.410479i \(0.865361\pi\)
\(468\) 1.84331e14 0.379531
\(469\) 3.24474e14 0.660283
\(470\) 4.37523e14 0.879959
\(471\) 4.10864e14 0.816738
\(472\) −1.81560e13 −0.0356730
\(473\) −9.02679e13 −0.175306
\(474\) −2.11040e14 −0.405121
\(475\) 6.98687e13 0.132577
\(476\) −3.18176e14 −0.596801
\(477\) −7.81113e13 −0.144832
\(478\) 7.71798e14 1.41465
\(479\) −3.50732e14 −0.635521 −0.317761 0.948171i \(-0.602931\pi\)
−0.317761 + 0.948171i \(0.602931\pi\)
\(480\) 3.74418e14 0.670702
\(481\) −6.21284e14 −1.10025
\(482\) −1.01057e15 −1.76932
\(483\) −1.97752e14 −0.342304
\(484\) −4.98272e14 −0.852740
\(485\) −3.09141e14 −0.523090
\(486\) 5.66836e13 0.0948326
\(487\) −3.92805e14 −0.649782 −0.324891 0.945752i \(-0.605328\pi\)
−0.324891 + 0.945752i \(0.605328\pi\)
\(488\) −1.14828e14 −0.187818
\(489\) −3.48389e14 −0.563464
\(490\) −4.81283e14 −0.769701
\(491\) −1.10794e15 −1.75213 −0.876066 0.482192i \(-0.839841\pi\)
−0.876066 + 0.482192i \(0.839841\pi\)
\(492\) 2.54731e14 0.398358
\(493\) −4.92138e14 −0.761077
\(494\) 3.64466e14 0.557390
\(495\) −9.50094e13 −0.143694
\(496\) 6.01144e14 0.899144
\(497\) 7.03992e14 1.04138
\(498\) −1.02126e15 −1.49408
\(499\) 7.31455e14 1.05836 0.529182 0.848509i \(-0.322499\pi\)
0.529182 + 0.848509i \(0.322499\pi\)
\(500\) 9.01715e14 1.29043
\(501\) 1.38102e14 0.195476
\(502\) 9.77422e14 1.36840
\(503\) 9.77802e14 1.35403 0.677013 0.735971i \(-0.263274\pi\)
0.677013 + 0.735971i \(0.263274\pi\)
\(504\) −4.00203e13 −0.0548166
\(505\) −1.22388e14 −0.165820
\(506\) −5.77219e14 −0.773593
\(507\) 3.36835e13 0.0446554
\(508\) 5.80969e14 0.761907
\(509\) −7.70280e14 −0.999311 −0.499655 0.866224i \(-0.666540\pi\)
−0.499655 + 0.866224i \(0.666540\pi\)
\(510\) 4.54006e14 0.582674
\(511\) −3.49058e13 −0.0443182
\(512\) −1.05700e15 −1.32767
\(513\) 6.07914e13 0.0755435
\(514\) 1.58558e15 1.94936
\(515\) −6.42219e14 −0.781167
\(516\) 1.88197e14 0.226484
\(517\) 3.25412e14 0.387468
\(518\) 8.62612e14 1.01625
\(519\) −8.87223e14 −1.03422
\(520\) 1.85702e14 0.214189
\(521\) −5.29303e14 −0.604083 −0.302041 0.953295i \(-0.597668\pi\)
−0.302041 + 0.953295i \(0.597668\pi\)
\(522\) −3.95862e14 −0.447050
\(523\) 2.66049e14 0.297305 0.148653 0.988889i \(-0.452506\pi\)
0.148653 + 0.988889i \(0.452506\pi\)
\(524\) −7.67165e14 −0.848334
\(525\) 1.06948e14 0.117030
\(526\) −7.03231e14 −0.761512
\(527\) 9.02080e14 0.966689
\(528\) 2.25024e14 0.238639
\(529\) −2.29541e13 −0.0240910
\(530\) −5.03240e14 −0.522706
\(531\) 4.22156e13 0.0433963
\(532\) −2.74479e14 −0.279251
\(533\) −5.55271e14 −0.559120
\(534\) 6.89270e14 0.686930
\(535\) −1.45522e15 −1.43543
\(536\) −3.08769e14 −0.301458
\(537\) 7.11048e14 0.687132
\(538\) 1.15372e14 0.110356
\(539\) −3.57959e14 −0.338918
\(540\) 1.98082e14 0.185643
\(541\) 5.18467e14 0.480991 0.240495 0.970650i \(-0.422690\pi\)
0.240495 + 0.970650i \(0.422690\pi\)
\(542\) 3.02161e14 0.277487
\(543\) 2.04757e14 0.186140
\(544\) −1.33071e15 −1.19754
\(545\) −1.29037e14 −0.114956
\(546\) 5.57889e14 0.492026
\(547\) −3.81590e14 −0.333171 −0.166585 0.986027i \(-0.553274\pi\)
−0.166585 + 0.986027i \(0.553274\pi\)
\(548\) −2.20369e15 −1.90484
\(549\) 2.66992e14 0.228481
\(550\) 3.12170e14 0.264483
\(551\) −4.24550e14 −0.356119
\(552\) 1.88180e14 0.156282
\(553\) −3.46450e14 −0.284874
\(554\) −5.01097e14 −0.407960
\(555\) −6.67630e14 −0.538176
\(556\) −1.52207e15 −1.21486
\(557\) −5.81758e14 −0.459768 −0.229884 0.973218i \(-0.573835\pi\)
−0.229884 + 0.973218i \(0.573835\pi\)
\(558\) 7.25608e14 0.567824
\(559\) −4.10237e14 −0.317885
\(560\) 4.96672e14 0.381097
\(561\) 3.37672e14 0.256566
\(562\) −3.48660e15 −2.62333
\(563\) −1.95441e15 −1.45619 −0.728097 0.685474i \(-0.759595\pi\)
−0.728097 + 0.685474i \(0.759595\pi\)
\(564\) −6.78441e14 −0.500584
\(565\) −1.35870e15 −0.992790
\(566\) 8.03017e14 0.581078
\(567\) 9.30534e13 0.0666846
\(568\) −6.69916e14 −0.475450
\(569\) 4.68451e14 0.329266 0.164633 0.986355i \(-0.447356\pi\)
0.164633 + 0.986355i \(0.447356\pi\)
\(570\) 3.91655e14 0.272641
\(571\) 1.80483e15 1.24434 0.622169 0.782883i \(-0.286252\pi\)
0.622169 + 0.782883i \(0.286252\pi\)
\(572\) 8.83269e14 0.603135
\(573\) −8.18756e14 −0.553738
\(574\) 7.70957e14 0.516434
\(575\) −5.02883e14 −0.333652
\(576\) −6.74605e14 −0.443328
\(577\) 1.86255e14 0.121239 0.0606195 0.998161i \(-0.480692\pi\)
0.0606195 + 0.998161i \(0.480692\pi\)
\(578\) 6.79213e14 0.437928
\(579\) 6.36870e14 0.406742
\(580\) −1.38335e15 −0.875139
\(581\) −1.67653e15 −1.05061
\(582\) 8.83773e14 0.548611
\(583\) −3.74290e14 −0.230161
\(584\) 3.32162e13 0.0202339
\(585\) −4.31786e14 −0.260562
\(586\) −2.08494e15 −1.24640
\(587\) −1.85232e15 −1.09700 −0.548501 0.836150i \(-0.684801\pi\)
−0.548501 + 0.836150i \(0.684801\pi\)
\(588\) 7.46297e14 0.437861
\(589\) 7.78192e14 0.452327
\(590\) 2.71978e14 0.156620
\(591\) 9.36613e14 0.534354
\(592\) 1.58124e15 0.893774
\(593\) −2.53968e15 −1.42226 −0.711129 0.703062i \(-0.751816\pi\)
−0.711129 + 0.703062i \(0.751816\pi\)
\(594\) 2.71613e14 0.150704
\(595\) 7.45310e14 0.409726
\(596\) −1.54976e15 −0.844131
\(597\) −1.46667e15 −0.791539
\(598\) −2.62326e15 −1.40277
\(599\) 2.39471e15 1.26884 0.634418 0.772990i \(-0.281240\pi\)
0.634418 + 0.772990i \(0.281240\pi\)
\(600\) −1.01771e14 −0.0534311
\(601\) −5.26533e14 −0.273915 −0.136958 0.990577i \(-0.543732\pi\)
−0.136958 + 0.990577i \(0.543732\pi\)
\(602\) 5.69587e14 0.293616
\(603\) 7.17936e14 0.366725
\(604\) −2.68045e15 −1.35676
\(605\) 1.16717e15 0.585438
\(606\) 3.49885e14 0.173910
\(607\) 5.86876e14 0.289074 0.144537 0.989499i \(-0.453831\pi\)
0.144537 + 0.989499i \(0.453831\pi\)
\(608\) −1.14796e15 −0.560346
\(609\) −6.49858e14 −0.314357
\(610\) 1.72012e15 0.824605
\(611\) 1.47889e15 0.702601
\(612\) −7.04000e14 −0.331467
\(613\) −2.13130e15 −0.994515 −0.497258 0.867603i \(-0.665660\pi\)
−0.497258 + 0.867603i \(0.665660\pi\)
\(614\) 1.62297e15 0.750556
\(615\) −5.96692e14 −0.273487
\(616\) −1.91767e14 −0.0871124
\(617\) −4.23326e14 −0.190593 −0.0952964 0.995449i \(-0.530380\pi\)
−0.0952964 + 0.995449i \(0.530380\pi\)
\(618\) 1.83598e15 0.819278
\(619\) 6.04776e14 0.267483 0.133741 0.991016i \(-0.457301\pi\)
0.133741 + 0.991016i \(0.457301\pi\)
\(620\) 2.53565e15 1.11157
\(621\) −4.37549e14 −0.190118
\(622\) −4.94518e15 −2.12978
\(623\) 1.13153e15 0.483037
\(624\) 1.02266e15 0.432727
\(625\) −1.30697e15 −0.548183
\(626\) 2.28942e15 0.951846
\(627\) 2.91297e14 0.120051
\(628\) −4.10459e15 −1.67684
\(629\) 2.37281e15 0.960916
\(630\) 5.99506e14 0.240669
\(631\) 7.18347e14 0.285873 0.142936 0.989732i \(-0.454346\pi\)
0.142936 + 0.989732i \(0.454346\pi\)
\(632\) 3.29681e14 0.130062
\(633\) −6.97817e14 −0.272911
\(634\) −1.16805e15 −0.452866
\(635\) −1.36089e15 −0.523078
\(636\) 7.80344e14 0.297353
\(637\) −1.62680e15 −0.614565
\(638\) −1.89687e15 −0.710434
\(639\) 1.55766e15 0.578386
\(640\) −1.19062e15 −0.438311
\(641\) 1.07268e15 0.391519 0.195759 0.980652i \(-0.437283\pi\)
0.195759 + 0.980652i \(0.437283\pi\)
\(642\) 4.16019e15 1.50546
\(643\) 2.66156e15 0.954939 0.477470 0.878648i \(-0.341554\pi\)
0.477470 + 0.878648i \(0.341554\pi\)
\(644\) 1.97557e15 0.702783
\(645\) −4.40840e14 −0.155490
\(646\) −1.39197e15 −0.486802
\(647\) −3.31850e15 −1.15071 −0.575357 0.817902i \(-0.695137\pi\)
−0.575357 + 0.817902i \(0.695137\pi\)
\(648\) −8.85493e13 −0.0304455
\(649\) 2.02286e14 0.0689637
\(650\) 1.41871e15 0.479590
\(651\) 1.19118e15 0.399284
\(652\) 3.48046e15 1.15684
\(653\) 3.50654e15 1.15573 0.577865 0.816132i \(-0.303886\pi\)
0.577865 + 0.816132i \(0.303886\pi\)
\(654\) 3.68891e14 0.120565
\(655\) 1.79704e15 0.582413
\(656\) 1.41323e15 0.454193
\(657\) −7.72329e13 −0.0246146
\(658\) −2.05334e15 −0.648960
\(659\) −3.21725e15 −1.00836 −0.504180 0.863599i \(-0.668205\pi\)
−0.504180 + 0.863599i \(0.668205\pi\)
\(660\) 9.49159e14 0.295017
\(661\) −1.56999e14 −0.0483938 −0.0241969 0.999707i \(-0.507703\pi\)
−0.0241969 + 0.999707i \(0.507703\pi\)
\(662\) −9.43689e15 −2.88476
\(663\) 1.53460e15 0.465234
\(664\) 1.59538e15 0.479666
\(665\) 6.42952e14 0.191716
\(666\) 1.90862e15 0.564433
\(667\) 3.05571e15 0.896233
\(668\) −1.37966e15 −0.401330
\(669\) 4.93023e13 0.0142241
\(670\) 4.62537e15 1.32353
\(671\) 1.27936e15 0.363094
\(672\) −1.75718e15 −0.494636
\(673\) −4.28054e15 −1.19513 −0.597566 0.801820i \(-0.703865\pi\)
−0.597566 + 0.801820i \(0.703865\pi\)
\(674\) 2.58735e14 0.0716515
\(675\) 2.36635e14 0.0649991
\(676\) −3.36504e14 −0.0916817
\(677\) 2.31899e15 0.626701 0.313351 0.949637i \(-0.398548\pi\)
0.313351 + 0.949637i \(0.398548\pi\)
\(678\) 3.88426e15 1.04123
\(679\) 1.45083e15 0.385773
\(680\) −7.09234e14 −0.187064
\(681\) −1.56486e13 −0.00409417
\(682\) 3.47693e15 0.902364
\(683\) −6.35794e15 −1.63683 −0.818413 0.574630i \(-0.805146\pi\)
−0.818413 + 0.574630i \(0.805146\pi\)
\(684\) −6.07316e14 −0.155098
\(685\) 5.16202e15 1.30774
\(686\) 5.78901e15 1.45486
\(687\) 1.21822e15 0.303714
\(688\) 1.04410e15 0.258229
\(689\) −1.70102e15 −0.417353
\(690\) −2.81895e15 −0.686148
\(691\) 6.58604e14 0.159036 0.0795179 0.996833i \(-0.474662\pi\)
0.0795179 + 0.996833i \(0.474662\pi\)
\(692\) 8.86349e15 2.12335
\(693\) 4.45889e14 0.105973
\(694\) 3.14498e14 0.0741551
\(695\) 3.56537e15 0.834044
\(696\) 6.18403e14 0.143523
\(697\) 2.12070e15 0.488313
\(698\) 8.65953e15 1.97829
\(699\) 2.63453e14 0.0597144
\(700\) −1.06843e15 −0.240273
\(701\) 6.66341e15 1.48678 0.743391 0.668857i \(-0.233216\pi\)
0.743391 + 0.668857i \(0.233216\pi\)
\(702\) 1.23439e15 0.273274
\(703\) 2.04694e15 0.449626
\(704\) −3.23253e15 −0.704520
\(705\) 1.58921e15 0.343670
\(706\) 3.71308e15 0.796724
\(707\) 5.74381e14 0.122291
\(708\) −4.21740e14 −0.0890967
\(709\) 4.88271e15 1.02354 0.511772 0.859121i \(-0.328989\pi\)
0.511772 + 0.859121i \(0.328989\pi\)
\(710\) 1.00354e16 2.08743
\(711\) −7.66559e14 −0.158221
\(712\) −1.07676e15 −0.220535
\(713\) −5.60107e15 −1.13836
\(714\) −2.13070e15 −0.429716
\(715\) −2.06901e15 −0.414075
\(716\) −7.10348e15 −1.41075
\(717\) 2.80339e15 0.552495
\(718\) −8.49433e15 −1.66129
\(719\) 6.15063e15 1.19374 0.596872 0.802337i \(-0.296410\pi\)
0.596872 + 0.802337i \(0.296410\pi\)
\(720\) 1.09894e15 0.211664
\(721\) 3.01400e15 0.576102
\(722\) 6.59239e15 1.25051
\(723\) −3.67068e15 −0.691012
\(724\) −2.04556e15 −0.382164
\(725\) −1.65259e15 −0.306412
\(726\) −3.33672e15 −0.614000
\(727\) −6.39610e15 −1.16809 −0.584045 0.811721i \(-0.698531\pi\)
−0.584045 + 0.811721i \(0.698531\pi\)
\(728\) −8.71516e14 −0.157962
\(729\) 2.05891e14 0.0370370
\(730\) −4.97580e14 −0.0888357
\(731\) 1.56678e15 0.277628
\(732\) −2.66729e15 −0.469094
\(733\) −5.15349e15 −0.899558 −0.449779 0.893140i \(-0.648497\pi\)
−0.449779 + 0.893140i \(0.648497\pi\)
\(734\) 3.98664e15 0.690684
\(735\) −1.74816e15 −0.300608
\(736\) 8.26248e15 1.41021
\(737\) 3.44017e15 0.582785
\(738\) 1.70583e15 0.286830
\(739\) −8.68311e15 −1.44921 −0.724604 0.689165i \(-0.757977\pi\)
−0.724604 + 0.689165i \(0.757977\pi\)
\(740\) 6.66973e15 1.10493
\(741\) 1.32385e15 0.217690
\(742\) 2.36176e15 0.385490
\(743\) −5.07891e14 −0.0822872 −0.0411436 0.999153i \(-0.513100\pi\)
−0.0411436 + 0.999153i \(0.513100\pi\)
\(744\) −1.13352e15 −0.182297
\(745\) 3.63023e15 0.579528
\(746\) 2.86912e15 0.454658
\(747\) −3.70950e15 −0.583515
\(748\) −3.37339e15 −0.526754
\(749\) 6.82949e15 1.05862
\(750\) 6.03842e15 0.929151
\(751\) −2.30518e15 −0.352116 −0.176058 0.984380i \(-0.556335\pi\)
−0.176058 + 0.984380i \(0.556335\pi\)
\(752\) −3.76394e15 −0.570748
\(753\) 3.55028e15 0.534429
\(754\) −8.62063e15 −1.28824
\(755\) 6.27879e15 0.931468
\(756\) −9.29618e14 −0.136910
\(757\) 1.28362e15 0.187676 0.0938382 0.995587i \(-0.470086\pi\)
0.0938382 + 0.995587i \(0.470086\pi\)
\(758\) −1.52238e15 −0.220974
\(759\) −2.09662e15 −0.302128
\(760\) −6.11831e14 −0.0875299
\(761\) −4.41140e15 −0.626557 −0.313278 0.949661i \(-0.601427\pi\)
−0.313278 + 0.949661i \(0.601427\pi\)
\(762\) 3.89051e15 0.548598
\(763\) 6.05582e14 0.0847789
\(764\) 8.17950e15 1.13688
\(765\) 1.64908e15 0.227564
\(766\) −6.21784e15 −0.851886
\(767\) 9.19323e14 0.125053
\(768\) −2.28181e15 −0.308172
\(769\) −1.01419e16 −1.35995 −0.679977 0.733233i \(-0.738010\pi\)
−0.679977 + 0.733233i \(0.738010\pi\)
\(770\) 2.87268e15 0.382462
\(771\) 5.75929e15 0.761325
\(772\) −6.36243e15 −0.835080
\(773\) −4.95978e15 −0.646361 −0.323181 0.946337i \(-0.604752\pi\)
−0.323181 + 0.946337i \(0.604752\pi\)
\(774\) 1.26028e15 0.163076
\(775\) 3.02916e15 0.389192
\(776\) −1.38060e15 −0.176128
\(777\) 3.13325e15 0.396899
\(778\) −7.21641e15 −0.907681
\(779\) 1.82945e15 0.228488
\(780\) 4.31360e15 0.534958
\(781\) 7.46392e15 0.919149
\(782\) 1.00188e16 1.22512
\(783\) −1.43788e15 −0.174596
\(784\) 4.14040e15 0.499233
\(785\) 9.61478e15 1.15121
\(786\) −5.13739e15 −0.610828
\(787\) 9.30653e15 1.09882 0.549410 0.835553i \(-0.314852\pi\)
0.549410 + 0.835553i \(0.314852\pi\)
\(788\) −9.35691e15 −1.09708
\(789\) −2.55434e15 −0.297410
\(790\) −4.93863e15 −0.571028
\(791\) 6.37652e15 0.732172
\(792\) −4.24306e14 −0.0483828
\(793\) 5.81426e15 0.658403
\(794\) 1.87145e15 0.210458
\(795\) −1.82791e15 −0.204144
\(796\) 1.46522e16 1.62510
\(797\) 1.45081e16 1.59804 0.799021 0.601303i \(-0.205351\pi\)
0.799021 + 0.601303i \(0.205351\pi\)
\(798\) −1.83807e15 −0.201070
\(799\) −5.64819e15 −0.613623
\(800\) −4.46850e15 −0.482133
\(801\) 2.50363e15 0.268282
\(802\) −1.94581e15 −0.207082
\(803\) −3.70081e14 −0.0391166
\(804\) −7.17229e15 −0.752921
\(805\) −4.62767e15 −0.482487
\(806\) 1.58015e16 1.63627
\(807\) 4.19063e14 0.0430998
\(808\) −5.46579e14 −0.0558329
\(809\) −1.65147e16 −1.67554 −0.837768 0.546027i \(-0.816140\pi\)
−0.837768 + 0.546027i \(0.816140\pi\)
\(810\) 1.32647e15 0.133669
\(811\) −8.53438e15 −0.854196 −0.427098 0.904205i \(-0.640464\pi\)
−0.427098 + 0.904205i \(0.640464\pi\)
\(812\) 6.49218e15 0.645405
\(813\) 1.09754e15 0.108373
\(814\) 9.14565e15 0.896975
\(815\) −8.15279e15 −0.794217
\(816\) −3.90574e15 −0.377926
\(817\) 1.35161e15 0.129906
\(818\) 1.81711e16 1.73475
\(819\) 2.02641e15 0.192162
\(820\) 5.96105e15 0.561496
\(821\) −1.65806e16 −1.55137 −0.775683 0.631123i \(-0.782594\pi\)
−0.775683 + 0.631123i \(0.782594\pi\)
\(822\) −1.47572e16 −1.37154
\(823\) −1.86136e15 −0.171843 −0.0859216 0.996302i \(-0.527383\pi\)
−0.0859216 + 0.996302i \(0.527383\pi\)
\(824\) −2.86811e15 −0.263025
\(825\) 1.13389e15 0.103294
\(826\) −1.27642e15 −0.115506
\(827\) 3.16390e15 0.284408 0.142204 0.989837i \(-0.454581\pi\)
0.142204 + 0.989837i \(0.454581\pi\)
\(828\) 4.37118e15 0.390330
\(829\) −1.59763e16 −1.41718 −0.708591 0.705620i \(-0.750669\pi\)
−0.708591 + 0.705620i \(0.750669\pi\)
\(830\) −2.38988e16 −2.10594
\(831\) −1.82013e15 −0.159330
\(832\) −1.46908e16 −1.27752
\(833\) 6.21310e15 0.536736
\(834\) −1.01927e16 −0.874735
\(835\) 3.23178e15 0.275528
\(836\) −2.91010e15 −0.246476
\(837\) 2.63562e15 0.221765
\(838\) −8.46462e15 −0.707563
\(839\) −1.01739e16 −0.844885 −0.422442 0.906390i \(-0.638827\pi\)
−0.422442 + 0.906390i \(0.638827\pi\)
\(840\) −9.36529e14 −0.0772654
\(841\) −2.15874e15 −0.176939
\(842\) 1.19464e16 0.972793
\(843\) −1.26643e16 −1.02454
\(844\) 6.97130e15 0.560313
\(845\) 7.88241e14 0.0629429
\(846\) −4.54324e15 −0.360437
\(847\) −5.47766e15 −0.431754
\(848\) 4.32929e15 0.339031
\(849\) 2.91679e15 0.226941
\(850\) −5.41835e15 −0.418854
\(851\) −1.47330e16 −1.13156
\(852\) −1.55613e16 −1.18748
\(853\) −8.79916e15 −0.667147 −0.333573 0.942724i \(-0.608255\pi\)
−0.333573 + 0.942724i \(0.608255\pi\)
\(854\) −8.07272e15 −0.608137
\(855\) 1.42260e15 0.106480
\(856\) −6.49892e15 −0.483321
\(857\) −1.52913e16 −1.12993 −0.564963 0.825116i \(-0.691110\pi\)
−0.564963 + 0.825116i \(0.691110\pi\)
\(858\) 5.91489e15 0.434277
\(859\) −1.76287e16 −1.28605 −0.643025 0.765845i \(-0.722321\pi\)
−0.643025 + 0.765845i \(0.722321\pi\)
\(860\) 4.40406e15 0.319236
\(861\) 2.80034e15 0.201694
\(862\) −1.81732e16 −1.30060
\(863\) −1.29163e16 −0.918496 −0.459248 0.888308i \(-0.651881\pi\)
−0.459248 + 0.888308i \(0.651881\pi\)
\(864\) −3.88796e15 −0.274724
\(865\) −2.07622e16 −1.45776
\(866\) 2.33665e16 1.63022
\(867\) 2.46710e15 0.171033
\(868\) −1.19001e16 −0.819768
\(869\) −3.67316e15 −0.251438
\(870\) −9.26371e15 −0.630128
\(871\) 1.56344e16 1.05677
\(872\) −5.76269e14 −0.0387066
\(873\) 3.21012e15 0.214261
\(874\) 8.64286e15 0.573250
\(875\) 9.91285e15 0.653362
\(876\) 7.71568e14 0.0505361
\(877\) 9.20752e15 0.599301 0.299650 0.954049i \(-0.403130\pi\)
0.299650 + 0.954049i \(0.403130\pi\)
\(878\) −4.34503e15 −0.281043
\(879\) −7.57309e15 −0.486782
\(880\) 5.26586e15 0.336368
\(881\) −1.38703e16 −0.880480 −0.440240 0.897880i \(-0.645107\pi\)
−0.440240 + 0.897880i \(0.645107\pi\)
\(882\) 4.99764e15 0.315274
\(883\) 2.21230e15 0.138695 0.0693473 0.997593i \(-0.477908\pi\)
0.0693473 + 0.997593i \(0.477908\pi\)
\(884\) −1.53309e16 −0.955170
\(885\) 9.87902e14 0.0611682
\(886\) 1.87519e16 1.15388
\(887\) −3.40669e15 −0.208331 −0.104165 0.994560i \(-0.533217\pi\)
−0.104165 + 0.994560i \(0.533217\pi\)
\(888\) −2.98159e15 −0.181208
\(889\) 6.38678e15 0.385764
\(890\) 1.61299e16 0.968246
\(891\) 9.86578e14 0.0588578
\(892\) −4.92537e14 −0.0292033
\(893\) −4.87249e15 −0.287123
\(894\) −1.03781e16 −0.607802
\(895\) 1.66395e16 0.968531
\(896\) 5.58769e15 0.323250
\(897\) −9.52845e15 −0.547852
\(898\) 3.23287e16 1.84743
\(899\) −1.84064e16 −1.04542
\(900\) −2.36401e15 −0.133449
\(901\) 6.49656e15 0.364500
\(902\) 8.17390e15 0.455820
\(903\) 2.06891e15 0.114672
\(904\) −6.06787e15 −0.334280
\(905\) 4.79160e15 0.262370
\(906\) −1.79499e16 −0.976913
\(907\) −2.12226e16 −1.14805 −0.574023 0.818839i \(-0.694618\pi\)
−0.574023 + 0.818839i \(0.694618\pi\)
\(908\) 1.56332e14 0.00840573
\(909\) 1.27088e15 0.0679210
\(910\) 1.30554e16 0.693524
\(911\) −3.16343e16 −1.67035 −0.835176 0.549983i \(-0.814634\pi\)
−0.835176 + 0.549983i \(0.814634\pi\)
\(912\) −3.36934e15 −0.176837
\(913\) −1.77750e16 −0.927300
\(914\) 3.16130e16 1.63931
\(915\) 6.24799e15 0.322051
\(916\) −1.21702e16 −0.623553
\(917\) −8.43370e15 −0.429523
\(918\) −4.71440e15 −0.238667
\(919\) 3.53008e16 1.77643 0.888216 0.459425i \(-0.151945\pi\)
0.888216 + 0.459425i \(0.151945\pi\)
\(920\) 4.40368e15 0.220284
\(921\) 5.89508e15 0.293131
\(922\) −4.85829e16 −2.40140
\(923\) 3.39210e16 1.66671
\(924\) −4.45450e15 −0.217572
\(925\) 7.96785e15 0.386867
\(926\) −1.78222e16 −0.860205
\(927\) 6.66881e15 0.319970
\(928\) 2.71524e16 1.29507
\(929\) 2.83247e16 1.34301 0.671505 0.741000i \(-0.265648\pi\)
0.671505 + 0.741000i \(0.265648\pi\)
\(930\) 1.69802e16 0.800363
\(931\) 5.35982e15 0.251147
\(932\) −2.63194e15 −0.122599
\(933\) −1.79623e16 −0.831790
\(934\) 5.85641e16 2.69603
\(935\) 7.90198e15 0.361636
\(936\) −1.92833e15 −0.0877331
\(937\) −6.67418e15 −0.301877 −0.150939 0.988543i \(-0.548230\pi\)
−0.150939 + 0.988543i \(0.548230\pi\)
\(938\) −2.17073e16 −0.976092
\(939\) 8.31583e15 0.371745
\(940\) −1.58764e16 −0.705586
\(941\) −2.20696e16 −0.975106 −0.487553 0.873093i \(-0.662110\pi\)
−0.487553 + 0.873093i \(0.662110\pi\)
\(942\) −2.74868e16 −1.20738
\(943\) −1.31675e16 −0.575029
\(944\) −2.33978e15 −0.101585
\(945\) 2.17758e15 0.0939937
\(946\) 6.03892e15 0.259154
\(947\) −2.03690e16 −0.869049 −0.434525 0.900660i \(-0.643084\pi\)
−0.434525 + 0.900660i \(0.643084\pi\)
\(948\) 7.65804e15 0.324842
\(949\) −1.68189e15 −0.0709306
\(950\) −4.67422e15 −0.195988
\(951\) −4.24269e15 −0.176868
\(952\) 3.32851e15 0.137958
\(953\) −2.99023e16 −1.23224 −0.616118 0.787654i \(-0.711296\pi\)
−0.616118 + 0.787654i \(0.711296\pi\)
\(954\) 5.22565e15 0.214104
\(955\) −1.91600e16 −0.780508
\(956\) −2.80063e16 −1.13433
\(957\) −6.88998e15 −0.277461
\(958\) 2.34640e16 0.939487
\(959\) −2.42259e16 −0.964445
\(960\) −1.57867e16 −0.624883
\(961\) 8.33011e15 0.327848
\(962\) 4.15639e16 1.62650
\(963\) 1.51110e16 0.587961
\(964\) 3.66706e16 1.41871
\(965\) 1.49036e16 0.573314
\(966\) 1.32296e16 0.506026
\(967\) −1.85775e16 −0.706550 −0.353275 0.935520i \(-0.614932\pi\)
−0.353275 + 0.935520i \(0.614932\pi\)
\(968\) 5.21252e15 0.197121
\(969\) −5.05605e15 −0.190121
\(970\) 2.06815e16 0.773282
\(971\) −1.34524e16 −0.500143 −0.250071 0.968227i \(-0.580454\pi\)
−0.250071 + 0.968227i \(0.580454\pi\)
\(972\) −2.05688e15 −0.0760406
\(973\) −1.67327e16 −0.615098
\(974\) 2.62786e16 0.960569
\(975\) 5.15316e15 0.187304
\(976\) −1.47979e16 −0.534844
\(977\) 1.65741e16 0.595674 0.297837 0.954617i \(-0.403735\pi\)
0.297837 + 0.954617i \(0.403735\pi\)
\(978\) 2.33072e16 0.832966
\(979\) 1.19968e16 0.426343
\(980\) 1.74644e16 0.617177
\(981\) 1.33992e15 0.0470867
\(982\) 7.41209e16 2.59017
\(983\) −6.50952e15 −0.226206 −0.113103 0.993583i \(-0.536079\pi\)
−0.113103 + 0.993583i \(0.536079\pi\)
\(984\) −2.66479e15 −0.0920852
\(985\) 2.19180e16 0.753186
\(986\) 3.29240e16 1.12510
\(987\) −7.45832e15 −0.253453
\(988\) −1.32254e16 −0.446937
\(989\) −9.72825e15 −0.326930
\(990\) 6.35613e15 0.212422
\(991\) 4.78987e14 0.0159191 0.00795955 0.999968i \(-0.497466\pi\)
0.00795955 + 0.999968i \(0.497466\pi\)
\(992\) −4.97698e16 −1.64495
\(993\) −3.42775e16 −1.12665
\(994\) −4.70970e16 −1.53946
\(995\) −3.43220e16 −1.11569
\(996\) 3.70585e16 1.19801
\(997\) −5.55846e15 −0.178703 −0.0893513 0.996000i \(-0.528479\pi\)
−0.0893513 + 0.996000i \(0.528479\pi\)
\(998\) −4.89343e16 −1.56457
\(999\) 6.93268e15 0.220440
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.1.5 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.a.1.5 26 1.1 even 1 trivial