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{'algebraic': True, 'analytic_conductor': 1.4088313763458886, 'bad_primes': [19], 'central_character': '1.1', 'conductor': 6859, 'conductor_radical': 19, 'degree': 6, 'dirichlet_coefficients': [1, 3, 1, 3, 14, 3, -35, 1, -16, 42, 16, 3, 65, -105, 14, -33, 29, -48, -57, 42, -35, 48, -101, 1, -108, 195, -151, -105, 377, 42, -140, -27, 16, 87, -490, -48, -290, -171, 65, 14, 956, -105, -570, 48, -224, -303, 66, -33, 49, -324, 29, 195, 817, -453, 224, -35, -57, 1131, 265, 42, 988, -420, 560, 47, 910, 48, -207, 87, -101, -1470, 846, -16, 627, -870, -108, -171, -560, 195, 382, -462, -456, 2868, -766, -105, 406, -1710, 377, 16, -172, -672, -2275, -303, -140, 198, -798, -27, -2450, 147, -256, -324], 'euler11': [1, -16, 3942, -41410, 5246802, -28344976, 2357947691], 'euler13': [1, -65, 7335, -280762, 16114995, -313742585, 10604499373], 'euler17': [1, -29, 5514, -503573, 27090282, -699989501, 118587876497], 'euler19': [1, 57, 1083, 6859, 0, 0, 0], 'euler2': [1, -3, 6, -10, 48, -192, 512], 'euler23': [1, 101, 31877, 2079558, 387847459, 14951624789, 1801152661463], 'euler29': [1, -377, 81935, -13844910, 1998312715, -224248392017, 14507145975869], 'euler3': [1, -1, 17, 118, 459, -729, 19683], 'euler31': [1, 140, 51757, 5897128, 1541892787, 124250515340, 26439622160671], 'euler37': [1, 290, 105187, 19377292, 5328037111, 744060658610, 129961739795077], 'euler41': [1, -956, 508879, -163355096, 35072449559, -4541099654396, 327381934393961], 'euler43': [1, 570, 145938, 24674476, 11603092566, 3603176937930, 502592611936843], 'euler47': [1, -66, 280158, -10764012, 29086844034, -711428211714, 1119130473102767], 'euler5': [1, -14, 304, -3572, 38000, -218750, 1953125], 'euler53': [1, -817, 657711, -260089834, 97918040547, -18108283042393, 3299763591802133], 'euler59': [1, -265, 458145, -77293258, 94093361955, -11177841414865, 8662995818654939], 'euler61': [1, -988, 726644, -371638582, 164934381764, -50902129868668, 11694146092834141], 'euler67': [1, 207, 842361, 117000634, 253351021443, 18724885108983, 27206534396294947], 'euler7': [1, 35, 1176, 21691, 403368, 4117715, 40353607], 'euler71': [1, -846, 1246593, -603857484, 446169347223, -108372840197166, 45848500718449031], 'euler73': [1, -627, 811566, -342245479, 315712970622, -94886559883203, 58871586708267913], 'euler79': [1, -382, 809229, -432705284, 398981456931, -92859408009022, 119851595982618319], 'euler83': [1, 766, 1679713, 797249332, 960438057131, 250436326000654, 186940255267540403], 'euler89': [1, 172, 1270123, 165585880, 895397341187, 85480782045292, 350356403707485209], 'euler97': [1, 2450, 4122563, 4668536612, 3762551940899, 2040781412076050, 760231058654565217], 'euler_factors': [[1, -3, 6, -10, 48, -192, 512], [1, -1, 17, 118, 459, -729, 19683], [1, -14, 304, -3572, 38000, -218750, 1953125], [1, 35, 1176, 21691, 403368, 4117715, 40353607], [1, -16, 3942, -41410, 5246802, -28344976, 2357947691], [1, -65, 7335, -280762, 16114995, -313742585, 10604499373], [1, -29, 5514, -503573, 27090282, -699989501, 118587876497], [1, 57, 1083, 6859, 0, 0, 0], [1, 101, 31877, 2079558, 387847459, 14951624789, 1801152661463], [1, -377, 81935, -13844910, 1998312715, -224248392017, 14507145975869], [1, 140, 51757, 5897128, 1541892787, 124250515340, 26439622160671], [1, 290, 105187, 19377292, 5328037111, 744060658610, 129961739795077], [1, -956, 508879, -163355096, 35072449559, -4541099654396, 327381934393961], [1, 570, 145938, 24674476, 11603092566, 3603176937930, 502592611936843], [1, -66, 280158, -10764012, 29086844034, -711428211714, 1119130473102767], [1, -817, 657711, -260089834, 97918040547, -18108283042393, 3299763591802133], [1, -265, 458145, -77293258, 94093361955, -11177841414865, 8662995818654939], [1, -988, 726644, -371638582, 164934381764, -50902129868668, 11694146092834141], [1, 207, 842361, 117000634, 253351021443, 18724885108983, 27206534396294947], [1, -846, 1246593, -603857484, 446169347223, -108372840197166, 45848500718449031], [1, -627, 811566, -342245479, 315712970622, -94886559883203, 58871586708267913], [1, -382, 809229, -432705284, 398981456931, -92859408009022, 119851595982618319], [1, 766, 1679713, 797249332, 960438057131, 250436326000654, 186940255267540403], [1, 172, 1270123, 165585880, 895397341187, 85480782045292, 350356403707485209], [1, 2450, 4122563, 4668536612, 3762551940899, 2040781412076050, 760231058654565217]], 'id': 9593305, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/19/4/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '6-19e3-1.1-c3e3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 0, 'prelabel': '6-19e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.0587900122824507, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e3-0', 'trace_hash': 2040319790454064452, 'z1': {'__RealLiteral__': 0, 'data': '2.42435818975861193846168331153', 'prec': 103}}