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lfunc_lfunctions • Show schema
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{'Lhash': '386455045865512546776079532957', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -8, 'a5': 0, 'a6': 0, 'a7': -37, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.82628925387493, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '675.1', 'coefficient_field': '1.1.1.1', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, 0, 8], [1], [1], [1, 37, 343], [1, 0, 1331], [1, 70, 2197], [1, 0, 4913], [1, 163, 6859], [1, 0, 12167], [1, 0, 24389], [1, 19, 29791], [1, 433, 50653], [1, 0, 68921], [1, -449, 79507], [1, 0, 103823], [1, 0, 148877], [1, 0, 205379], [1, -719, 226981], [1, 880, 300763], [1, 0, 357911], [1, 271, 389017], [1, -503, 493039], [1, 0, 571787], [1, 0, 704969], [1, 523, 912673], [1, 0, 1030301], [1, 19, 1092727], [1, 0, 1225043], [1, -2213, 1295029], [1, 0, 1442897]], 'euler_factors_factorization': [[[[1, 0, 8], 1]], 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'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/675/4/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.31188555666880136, 0.2985123914788785, 0.25853150172798056, 0.19235977406924626, 0.10069545341570033, -0.015477155974899475, -0.1548819872639984, -0.31594533594309837, -0.4967908145002536, -0.6952362646593243, -0.9087938304188472, -1.1346744160355755, -1.3697977177938871, -1.6108089269828354, -1.8541030557406852, -2.0958576405830276, -2.332074335093678, -2.558629619220066, -2.771334534787468, -2.966003013203966, -3.138528000869901, -3.2849642205123946, -3.401616043428997, -3.485128600132969, -3.5325799374564846, -3.541571751475783, -3.5103160004248997, -3.437714542489259, -3.3234288616743335, -3.167936951220651, -2.9725745268909822, -2.739557948177914, -2.4719865375301997, -2.1738224062355203, -1.8498464170894529, -1.5055895308901062, -1.1472394844110332, -0.781523515894192, -0.41556867025812294, 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6.310807337724305, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1607348400355329097, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.30485927730869586333584222951', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44758715374932890799598401928', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56661797203057567929459651624', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.82628925387493, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, -8, 0, 0, -37, 0, 0, 0, 0, 0, -70, 0, 0, 64, 0, 0, -163, 0, 0, 0, 0, 0, 0, 0, 0, 296, 0, 0, -19, 0, 0, 0, 0, 0, -433, 0, 0, 0, 0, 0, 449, 0, 0, 0, 0, 0, 1026, 0, 0, 560, 0, 0, 0, 0, 0, 0, 0, 0, 719, 0, 0, -512, 0, 0, -880, 0, 0, 0, 0, 0, -271, 0, 0, 1304, 0, 0, 503, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2590, 0, 0, 0, 0, 0, -523, 0, 0, 0], 'euler11': [1, 0, 1331], 'euler13': [1, 70, 2197], 'euler17': [1, 0, 4913], 'euler19': [1, 163, 6859], 'euler2': [1, 0, 8], 'euler23': [1, 0, 12167], 'euler29': [1, 0, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 19, 29791], 'euler37': [1, 433, 50653], 'euler41': [1, 0, 68921], 'euler43': [1, -449, 79507], 'euler47': [1, 0, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 0, 148877], 'euler59': [1, 0, 205379], 'euler61': [1, -719, 226981], 'euler67': [1, 880, 300763], 'euler7': [1, 37, 343], 'euler71': [1, 0, 357911], 'euler73': [1, 271, 389017], 'euler79': [1, -503, 493039], 'euler83': [1, 0, 571787], 'euler89': [1, 0, 704969], 'euler97': [1, 523, 912673], 'euler_factors': [[1, 0, 8], [1, 0, 0], [1, 0, 0], [1, 37, 343], [1, 0, 1331], [1, 70, 2197], [1, 0, 4913], [1, 163, 6859], [1, 0, 12167], [1, 0, 24389], [1, 19, 29791], [1, 433, 50653], [1, 0, 68921], [1, -449, 79507], [1, 0, 103823], [1, 0, 148877], [1, 0, 205379], [1, -719, 226981], [1, 880, 300763], [1, 0, 357911], [1, 271, 389017], [1, -503, 493039], [1, 0, 571787], [1, 0, 704969], [1, 523, 912673]], 'index': 1, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/4/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/675/4/a/d'], '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': '2-675-1.1-c3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-675-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.310807337724305, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1607348400355329097, 'z1': {'__RealLiteral__': 0, 'data': '0.30485927730869586333584222951', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20147425
{'Lhash': '386455045865512546776079532957', 'Lhash_array': ['386455045865512546776079532957'], 'factors': ['2-675-1.1-c3-0-1'], 'label': '2-675-1.1-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/4/a/d'}
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id: 24568409
{'Lhash': '386455045865512546776079532957', 'Lhash_array': ['386455045865512546776079532957'], 'factors': ['2-675-1.1-c3-0-1'], 'label': '2-675-1.1-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/4/a/d/1/1'}