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lfunc_lfunctions • Show schema
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{'Lhash': '818088671458942855848987716542,1076272439481461441253417964031', 'a10': -25, 'a2': -5, 'a3': 0, 'a4': 8, 'a5': 5, 'a6': 0, 'a7': -9, 'a8': 5, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 571.007993663993, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -5, 25]]], 'bad_primes': [3, 5], 'central_character': '405.1', 'coefficient_field': '1.1.1.1', 'conductor': 164025, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, 5, 17, 40, 64], [1], [1, -5, 25], [1, 9, -262, 3087, 117649], [1, 8, -1267, 10648, 1771561], [1, 43, -348, 94471, 4826809], [1, -244, 24710, -1198772, 24137569], [1, 118, 17199, 809362, 47045881], [1, 213, 33202, 2591571, 148035889], [1, -224, 25787, -5463136, 594823321], [1, -36, -28495, -1072476, 887503681], [1, -412, 143742, -20869036, 2565726409], [1, -413, 101648, -28464373, 4750104241], [1, -392, 74157, -31166744, 6321363049], [1, 311, -7102, 32288953, 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'trace_hash': 644436434078407068, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64535816991815658587434041234', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.849029250873772318234458793979', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.94667960305857927765196463026', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 571.007993663993, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 164025, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, -5, 0, 8, 5, 0, -9, 5, 0, -25, -8, 0, -43, 45, 0, -25, 244, 0, -118, 40, 0, 40, -213, 0, 0, 215, 0, -72, 224, 0, 36, 40, 0, -1220, -45, 0, 412, 590, 0, 25, 413, 0, 392, -64, 0, 1065, -311, 0, 343, 0, 0, -344, 754, 0, -40, -45, 0, -1120, 337, 0, -40, -180, 0, -487, -215, 0, -348, 1952, 0, 225, -124, 0, -2428, -2060, 0, -944, 72, 0, 294, -125, 0, -2065, 534, 0, 1220, -1960, 0, -40, 1620, 0, 387, -1704, 0, 1555, -590, 0, 928, -1715, 0, 0], 'euler11': [1, 8, -1267, 10648, 1771561], 'euler13': [1, 43, -348, 94471, 4826809], 'euler17': [1, -244, 24710, -1198772, 24137569], 'euler19': [1, 118, 17199, 809362, 47045881], 'euler2': [1, 5, 17, 40, 64], 'euler23': [1, 213, 33202, 2591571, 148035889], 'euler29': [1, -224, 25787, -5463136, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -36, -28495, -1072476, 887503681], 'euler37': [1, -412, 143742, -20869036, 2565726409], 'euler41': [1, -413, 101648, -28464373, 4750104241], 'euler43': [1, -392, 74157, -31166744, 6321363049], 'euler47': [1, 311, -7102, 32288953, 10779215329], 'euler5': [1, -5, 25, 0, 0], 'euler53': [1, -754, 439883, -112253258, 22164361129], 'euler59': [1, -337, -91810, -69212723, 42180533641], 'euler61': [1, 40, -225381, 9079240, 51520374361], 'euler67': [1, 348, -179659, 104665524, 90458382169], 'euler7': [1, 9, -262, 3087, 117649], 'euler71': [1, 124, 719666, 44380964, 128100283921], 'euler73': [1, 2428, 2251830, 944533276, 151334226289], 'euler79': [1, -294, -406603, -144953466, 243087455521], 'euler83': [1, -534, -286631, -305334258, 326940373369], 'euler89': [1, -1620, 2066038, -1142049780, 496981290961], 'euler97': [1, -928, -51489, -846960544, 832972004929], 'euler_factors': [[1, 5, 17, 40, 64], [1, 0, 0, 0, 0], [1, -5, 25, 0, 0], [1, 9, -262, 3087, 117649], [1, 8, -1267, 10648, 1771561], [1, 43, -348, 94471, 4826809], [1, -244, 24710, -1198772, 24137569], [1, 118, 17199, 809362, 47045881], [1, 213, 33202, 2591571, 148035889], [1, -224, 25787, -5463136, 594823321], [1, -36, -28495, -1072476, 887503681], [1, -412, 143742, -20869036, 2565726409], [1, -413, 101648, -28464373, 4750104241], [1, -392, 74157, -31166744, 6321363049], [1, 311, -7102, 32288953, 10779215329], [1, -754, 439883, -112253258, 22164361129], [1, -337, -91810, -69212723, 42180533641], [1, 40, -225381, 9079240, 51520374361], [1, 348, -179659, 104665524, 90458382169], [1, 124, 719666, 44380964, 128100283921], [1, 2428, 2251830, 944533276, 151334226289], [1, -294, -406603, -144953466, 243087455521], [1, -534, -286631, -305334258, 326940373369], [1, -1620, 2066038, -1142049780, 496981290961], [1, -928, -51489, -846960544, 832972004929]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/a'], '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': '4-405e2-1.1-c3e2-0-8', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-405e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.88833034402596, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 644436434078407068, 'z1': {'__RealLiteral__': 0, 'data': '0.64535816991815658587434041234', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '818088671458942855848987716542,1076272439481461441253417964031', 'Lhash_array': ['818088671458942855848987716542', '1076272439481461441253417964031'], 'label': '4-405e2-1.1-c3e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/a'}