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{'Lhash': '1054329743804858165518210762919,1253917806818431516631728799897,1651040143261537410618062249126', 'a10': 6, 'a2': 3, 'a3': 0, 'a4': 6, 'a5': 2, 'a6': 0, 'a7': 4, 'a8': 10, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27107.38941169118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -3, 3, -1]], [3, [1]], [11, [1, -3, 3, -1]], [19, [1, 3, 3, 1]]], 'bad_primes': [2, 3, 11, 19], 'central_character': '3762.1', 'coefficient_field': '1.1.1.1', 'conductor': 53242246728, 'conductor_radical': 1254, 'degree': 6, 'euler_factors': [[1, -3, 3, -1], [1], [1, -2, 7, -12, 35, -50, 125], [1, -4, 17, -48, 119, -196, 343], [1, -3, 3, -1], [1, 6, 23, 52, 299, 1014, 2197], [1, -2, 15, -60, 255, -578, 4913], [1, 3, 3, 1], [1, 0, 41, 56, 943, 0, 12167], [1, -10, 83, -476, 2407, -8410, 24389], [1, 0, 9, -56, 279, 0, 29791], [1, -14, 167, -1092, 6179, -19166, 50653], [1, -14, 151, -1092, 6191, -23534, 68921], [1, -20, 225, 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37229614023337807, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.831719516099337876024932480099', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '0.989166736159533695213484769145', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.30244102196952541630099255480', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 27107.38941169118, 'bad_primes': [2, 3, 11, 19], 'central_character': '1.1', 'conductor': 53242246728, 'conductor_radical': 1254, 'degree': 6, 'dirichlet_coefficients': [1, 3, 0, 6, 2, 0, 4, 10, 0, 6, 3, 0, -6, 12, 0, 15, 2, 0, -3, 12, 0, 9, 0, 0, -3, -18, 0, 24, 10, 0, 0, 21, 0, 6, 8, 0, 14, -9, 0, 20, 14, 0, 20, 18, 0, 0, 8, 0, -1, -9, 0, -36, 18, 0, 6, 40, 0, 30, 8, 0, -14, 0, 0, 28, -12, 0, -8, 12, 0, 24, 20, 0, -6, 42, 0, -18, 12, 0, -8, 30, 0, 42, -8, 0, 4, 60, 0, 30, 22, 0, -24, 0, 0, 24, -6, 0, -22, -3, 0, -18], 'euler11': [1, -3, 3, -1, 0, 0, 0], 'euler13': [1, 6, 23, 52, 299, 1014, 2197], 'euler17': [1, -2, 15, -60, 255, -578, 4913], 'euler19': [1, 3, 3, 1, 0, 0, 0], 'euler2': [1, -3, 3, -1, 0, 0, 0], 'euler23': [1, 0, 41, 56, 943, 0, 12167], 'euler29': [1, -10, 83, -476, 2407, -8410, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, 9, -56, 279, 0, 29791], 'euler37': [1, -14, 167, -1092, 6179, -19166, 50653], 'euler41': [1, -14, 151, -1092, 6191, -23534, 68921], 'euler43': [1, -20, 225, -1784, 9675, -36980, 79507], 'euler47': [1, -8, -15, 600, -705, -17672, 103823], 'euler5': [1, -2, 7, -12, 35, -50, 125], 'euler53': [1, -18, 239, -1900, 12667, -50562, 148877], 'euler59': [1, -8, 161, -880, 9499, -27848, 205379], 'euler61': [1, 14, 183, 1652, 11163, 52094, 226981], 'euler67': [1, 8, 73, 560, 4891, 35912, 300763], 'euler7': [1, -4, 17, -48, 119, -196, 343], 'euler71': [1, -20, 281, -2512, 19951, -100820, 357911], 'euler73': [1, 6, 119, 1108, 8687, 31974, 389017], 'euler79': [1, 8, 249, 1256, 19671, 49928, 493039], 'euler83': [1, 8, 121, 816, 10043, 55112, 571787], 'euler89': [1, -22, 391, -4020, 34799, -174262, 704969], 'euler97': [1, 22, 415, 4372, 40255, 206998, 912673], 'euler_factors': [[1, -3, 3, -1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -2, 7, -12, 35, -50, 125], [1, -4, 17, -48, 119, -196, 343], [1, -3, 3, -1, 0, 0, 0], [1, 6, 23, 52, 299, 1014, 2197], [1, -2, 15, -60, 255, -578, 4913], [1, 3, 3, 1, 0, 0, 0], [1, 0, 41, 56, 943, 0, 12167], [1, -10, 83, -476, 2407, -8410, 24389], [1, 0, 9, -56, 279, 0, 29791], [1, -14, 167, -1092, 6179, -19166, 50653], [1, -14, 151, -1092, 6191, -23534, 68921], [1, -20, 225, -1784, 9675, -36980, 79507], [1, -8, -15, 600, -705, -17672, 103823], [1, -18, 239, -1900, 12667, -50562, 148877], [1, -8, 161, -880, 9499, -27848, 205379], [1, 14, 183, 1652, 11163, 52094, 226981], [1, 8, 73, 560, 4891, 35912, 300763], [1, -20, 281, -2512, 19951, -100820, 357911], [1, 6, 119, 1108, 8687, 31974, 389017], [1, 8, 249, 1256, 19671, 49928, 493039], [1, 8, 121, 816, 10043, 55112, 571787], [1, -22, 391, -4020, 34799, -174262, 704969], [1, 22, 415, 4372, 40255, 206998, 912673]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3762/2/a/bf'], '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': '6-3762e3-1.1-c1e3-0-1', 'motivic_weight': 1, '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': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-3762e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.480850412153728, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 37229614023337807, 'z1': {'__RealLiteral__': 0, 'data': '0.831719516099337876024932480099', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1054329743804858165518210762919,1253917806818431516631728799897,1651040143261537410618062249126', 'Lhash_array': ['1054329743804858165518210762919', '1253917806818431516631728799897', '1651040143261537410618062249126'], 'factors': ['2-3762-1.1-c1-0-17', '2-3762-1.1-c1-0-28', '2-3762-1.1-c1-0-47'], 'label': '6-3762e3-1.1-c1e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3762/2/a/bf'}