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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 1, 'A5': 1, 'A6': 0, 'A7': 8, 'A8': 0, 'A9': 3, 'Lhash': '1247736579813721573,2285608403964147289', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.5, 0], 'a5': [0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [3.0237157840738176, 0], 'a8': [0.0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 82.92100757199617, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [3, [1, 2, 1]], [5, [1, -1]], [17, [1, 6, 17]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '1300500.1', 'coefficient_field': '1.1.1.1', 'conductor': 1300500, 'conductor_radical': 510, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, 2, 1], [1, -1], [1, -8, 30, -56, 49], [1, 0, 22, 0, 121], [1, 0, 22, 0, 169], [1, 6, 17], [1, 8, 54, 152, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 0, -2, 0, 961], [1, 4, 78, 148, 1369], [1, 0, 46, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, 94, 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'trace_hash': 1227501974564174911, 'z1': {'__RealLiteral__': 0, 'data': '0.74314124481069084021545695804574', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.67422833535095353270525529505899', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.07452981833800877942993394416205', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 82.92100757199617, 'bad_primes': [2, 3, 5, 17], 'central_character': '1.1', 'conductor': 1300500, 'conductor_radical': 510, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 1, 1, 0, 8, 0, 3, 0, 0, -2, 0, 0, -2, 1, -6, 0, -8, 1, -16, 0, 0, 0, 1, 0, -4, 8, 0, 0, 0, 0, 0, 0, 8, 3, -4, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 34, 0, 12, 0, 0, 0, 0, 0, 16, 0, 0, -2, 0, 0, 24, 1, 0, 0, 0, -6, 0, 0, 0, 0, -4, 0, -2, -8, 0, 0, 0, 1, 5, 0, 0, -16, -6, 0, 0, 0, 36, 0, 0, 0, 0, 0, -8, 0, -4, 0, 0, 1], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 6, 17, 0, 0], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, -1, 0, 0, 0], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 0, 22, 0, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, -8, 30, -56, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 4, 150, 292, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, -36, 502, -3204, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 2, 1, 0, 0], [1, -1, 0, 0, 0], [1, -8, 30, -56, 49], [1, 0, 22, 0, 121], [1, 0, 22, 0, 169], [1, 6, 17, 0, 0], [1, 8, 54, 152, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 0, -2, 0, 961], [1, 4, 78, 148, 1369], [1, 0, 46, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, 118, 0, 3481], [1, 0, 22, 0, 3721], [1, 0, 118, 0, 4489], [1, 0, 142, 0, 5041], [1, 4, 150, 292, 5329], [1, 0, 94, 0, 6241], [1, 0, 22, 0, 6889], [1, -36, 502, -3204, 7921], [1, 4, 198, 388, 9409]], 'index': 6, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.85.1/holomorphic/2.2.85.1-180.1-r', 'EllipticCurve/2.2.85.1/180.1/r'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-1300500-1.1-c1e2-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-1300500-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.0176310699725626, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1227501974564174911, 'z1': {'__RealLiteral__': 0, 'data': '0.74314124481069084021545695804574', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9469584
{'Lhash': '1247736579813721573,2285608403964147289', 'Lhash_array': ['1247736579813721573', '2285608403964147289'], 'label': '4-1300500-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.85.1/180.1/r'}
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id: 9469235
{'Lhash': '1247736579813721573,2285608403964147289', 'Lhash_array': ['1247736579813721573', '2285608403964147289'], 'label': '4-1300500-1.1-c1e2-0-6', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.85.1/holomorphic/2.2.85.1-180.1-r'}