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lfunc_lfunctions • Show schema
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{'Lhash': '893148268221577045957358581004', 'a10': 0, 'a2': -2, 'a3': 0, 'a4': 4, 'a5': 0, 'a6': 0, 'a7': -14, 'a8': -8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.55085950258329, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '450.1', 'coefficient_field': '1.1.1.1', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1, 2], [1], [1], [1, 14, 343], [1, 6, 1331], [1, 68, 2197], [1, -78, 4913], [1, -44, 6859], [1, -120, 12167], [1, 126, 24389], [1, 244, 29791], [1, -304, 50653], [1, -480, 68921], [1, 104, 79507], [1, -600, 103823], [1, 258, 148877], [1, 534, 205379], [1, -362, 226981], [1, -268, 300763], [1, -972, 357911], [1, 470, 389017], [1, -1244, 493039], [1, -396, 571787], [1, -972, 704969], [1, -46, 912673], [1, -1506, 1030301], [1, -1474, 1092727], [1, -924, 1225043], [1, -698, 1295029], [1, 222, 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'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/450/4/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.0434714668190135, 1.034446011651172, 1.007443346187993, 0.9626856633888121, 0.9005468475612171, 0.8215575411672458, 0.7264116946413204, 0.6159740801779974, 0.49128813606741406, 0.35358341705173474, 0.2042818613953529, 0.04500204901266898, -0.12243938170026294, -0.2960299673031251, -0.4735680587854869, -0.6526745406442206, -0.8308101932529763, -1.0052991264195592, -1.173358552508748, -1.3321349869023498, -1.4787467650035881, -1.6103325521419263, -1.7241052998649413, -1.817410874114724, -1.887790353216506, -1.933044772610277, -1.9513008855329579, -1.9410763215466496, -1.9013423653260353, -1.8315824539668861, -1.7318444096073464, -1.6027843922944776, -1.4457005820011388, -1.2625546837101955, -1.0559794994223641, 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True, 'rational': True, 'root_analytic_conductor': 5.1527526141455, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1014952344313838376, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70456975136585232026115801955', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39179668370222691032868037628', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.47009662258862233352870022221', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.55085950258329, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 4, 0, 0, -14, -8, 0, 0, -6, 0, -68, 28, 0, 16, 78, 0, 44, 0, 0, 12, 120, 0, 0, 136, 0, -56, -126, 0, -244, -32, 0, -156, 0, 0, 304, -88, 0, 0, 480, 0, -104, -24, 0, -240, 600, 0, -147, 0, 0, -272, -258, 0, 0, 112, 0, 252, -534, 0, 362, 488, 0, 64, 0, 0, 268, 312, 0, 0, 972, 0, -470, -608, 0, 176, 84, 0, 1244, 0, 0, -960, 396, 0, 0, 208, 0, 48, 972, 0, 952, 480, 0, -1200, 0, 0, 46, 294, 0, 0], 'euler11': [1, 6, 1331], 'euler13': [1, 68, 2197], 'euler17': [1, -78, 4913], 'euler19': [1, -44, 6859], 'euler2': [1, 2, 0], 'euler23': [1, -120, 12167], 'euler29': [1, 126, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 244, 29791], 'euler37': [1, -304, 50653], 'euler41': [1, -480, 68921], 'euler43': [1, 104, 79507], 'euler47': [1, -600, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 258, 148877], 'euler59': [1, 534, 205379], 'euler61': [1, -362, 226981], 'euler67': [1, -268, 300763], 'euler7': [1, 14, 343], 'euler71': [1, -972, 357911], 'euler73': [1, 470, 389017], 'euler79': [1, -1244, 493039], 'euler83': [1, -396, 571787], 'euler89': [1, -972, 704969], 'euler97': [1, -46, 912673], 'euler_factors': [[1, 2, 0], [1, 0, 0], [1, 0, 0], [1, 14, 343], [1, 6, 1331], [1, 68, 2197], [1, -78, 4913], [1, -44, 6859], [1, -120, 12167], [1, 126, 24389], [1, 244, 29791], [1, -304, 50653], [1, -480, 68921], [1, 104, 79507], [1, -600, 103823], [1, 258, 148877], [1, 534, 205379], [1, -362, 226981], [1, -268, 300763], [1, -972, 357911], [1, 470, 389017], [1, -1244, 493039], [1, -396, 571787], [1, -972, 704969], [1, -46, 912673]], 'index': 1, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/4/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/450/4/a/c'], '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': '2-450-1.1-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': '2-450-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.1527526141455, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1014952344313838376, 'z1': {'__RealLiteral__': 0, 'data': '0.70456975136585232026115801955', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20708606
{'Lhash': '893148268221577045957358581004', 'Lhash_array': ['893148268221577045957358581004'], 'label': '2-450-1.1-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/4/a/c'}
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id: 24561081
{'Lhash': '893148268221577045957358581004', 'Lhash_array': ['893148268221577045957358581004'], 'label': '2-450-1.1-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/4/a/c/1/1'}