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lfunc_lfunctions • Show schema
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{'Lhash': '977445581402146803466020827416', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.28331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '7800.1', 'coefficient_field': '1.1.1.1', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, -2, 7], [1, 0, 11], [1, 1], [1, -4, 17], [1, -6, 19], [1, 6, 23], [1, -4, 29], [1, -8, 31], [1, -6, 37], [1, -6, 41], [1, 4, 43], [1, 8, 47], [1, 2, 53], [1, 0, 59], [1, 2, 61], [1, -4, 67], [1, 8, 71], [1, 0, 73], [1, -16, 79], [1, -4, 83], [1, 6, 89], [1, 16, 97], [1, 0, 101], [1, -8, 103], [1, -12, 107], [1, -8, 109], [1, -16, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [1], [[[1, -2, 7], 1]], [[[1, 0, 11], 1]], [[[1, 1], 1]], [[[1, -4, 17], 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-0.6121468662072805, -0.6798278042686572, -0.6652883192560332, -0.5764091273768452, -0.4257269594747873, -0.2296187133409037, -0.007245253211116295, 0.22068371362290254, 0.43325086672281843, 0.6106985548538274, 0.7357394748808315, 0.794730348576189, 0.7786352565601846, 0.683716805396033], 'positive_zeros': ['0.77106860614917570896246748944594', '1.58864990401304168322356395337667', '2.68727288426056290994599474574617', '3.54791455598267040520875396042491', '4.55018293538489446400556372224881', '4.97946564076675613100018722732924', '5.79600071764111841459942651371755', '6.33949481008680480500487088605029', '7.22795569086376819706411624695675', '7.986622336300113308442054608512249'], 'prelabel': '2-7800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 411061251454312509, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77106860614917570896246748945', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.58864990401304168322356395338', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.68727288426056290994599474575', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.28331357659873, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 4, 0, 6, 0, -2, 0, -6, 0, 0, 0, -1, 0, 4, 0, 8, 0, 0, 0, 0, 0, 6, 0, 1, 0, 6, 0, -4, 0, 0, 0, -8, 0, -3, 0, -4, 0, -2, 0, 0, 0, -6, 0, 0, 0, -2, 0, 2, 0, 0, 0, 4, 0, 6, 0, -8, 0, 0, 0, 0, 0, 0, 0, 16, 0, 1, 0, 4, 0, 0, 0, -4, 0, -6, 0, -2, 0, -8, 0, 0, 0, -16, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 1, 0], 'euler17': [1, -4, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -4, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -6, 37], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, 0, 59], 'euler61': [1, 2, 61], 'euler67': [1, -4, 67], 'euler7': [1, -2, 7], 'euler71': [1, 8, 71], 'euler73': [1, 0, 73], 'euler79': [1, -16, 79], 'euler83': [1, -4, 83], 'euler89': [1, 6, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, -2, 7], [1, 0, 11], [1, 1, 0], [1, -4, 17], [1, -6, 19], [1, 6, 23], [1, -4, 29], [1, -8, 31], [1, -6, 37], [1, -6, 41], [1, 4, 43], [1, 8, 47], [1, 2, 53], [1, 0, 59], [1, 2, 61], [1, -4, 67], [1, 8, 71], [1, 0, 73], [1, -16, 79], [1, -4, 83], [1, 6, 89], [1, 16, 97]], 'index': 34, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/7800/h', 'ModularForm/GL2/Q/holomorphic/7800/2/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/7800/2/a/h'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-7800-1.1-c1-0-34', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-7800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 411061251454312509, 'z1': {'__RealLiteral__': 0, 'data': '0.77106860614917570896246748945', 'prec': 103}}
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lfunc_instances • Show schema
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id: 22066165
{'Lhash': '977445581402146803466020827416', 'Lhash_array': ['977445581402146803466020827416'], 'label': '2-7800-1.1-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/h'}
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id: 24581204
{'Lhash': '977445581402146803466020827416', 'Lhash_array': ['977445581402146803466020827416'], 'label': '2-7800-1.1-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/h/1/1'}
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id: 28023
{'Lhash': '411061251454312509', 'Lhash_array': ['411061251454312509'], 'label': '2-7800-1.1-c1-0-34', 'type': 'ECQ', 'url': 'EllipticCurve/Q/7800/h'}