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lfunc_lfunctions • Show schema
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{'Lhash': '1704681984239074625014086498155', 'a10': -2, 'a2': -2, 'a3': 0, 'a4': 2, 'a5': 1, 'a6': 0, 'a7': 5, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 60.72623073718376, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -1]], [13, [1]]], 'bad_primes': [3, 5, 13], 'central_character': '7605.1', 'coefficient_field': '1.1.1.1', 'conductor': 7605, 'conductor_radical': 195, 'degree': 2, 'euler_factors': [[1, 2, 2], [1], [1, -1], [1, -5, 7], [1, 2, 11], [1], [1, 2, 17], [1, 0, 19], [1, 6, 23], [1, -4, 29], [1, 7, 31], [1, 2, 37], [1, 6, 41], [1, -1, 43], [1, -8, 47], [1, -4, 53], [1, 12, 59], [1, 13, 61], [1, 7, 67], [1, 12, 71], [1, -15, 73], [1, -3, 79], [1, 8, 83], [1, 14, 89], [1, 5, 97], [1, -18, 101], [1, 7, 103], [1, 4, 107], [1, 11, 109], [1, -2, 113]], 'euler_factors_factorization': [[[[1, 2, 2], 1]], [1], [[[1, -1], 1]], [[[1, -5, 7], 1]], [[[1, 2, 11], 1]], [1], [[[1, 2, 17], 1]], [[[1, 0, 19], 1]], [[[1, 6, 23], 1]], [[[1, -4, 29], 1]], [[[1, 7, 31], 1]], [[[1, 2, 37], 1]], [[[1, 6, 41], 1]], [[[1, -1, 43], 1]], [[[1, -8, 47], 1]], [[[1, -4, 53], 1]], [[[1, 12, 59], 1]], [[[1, 13, 61], 1]], [[[1, 7, 67], 1]], [[[1, 12, 71], 1]], [[[1, -15, 73], 1]], [[[1, -3, 79], 1]], [[[1, 8, 83], 1]], [[[1, 14, 89], 1]], [[[1, 5, 97], 1]], [[[1, -18, 101], 1]], [[[1, 7, 103], 1]], [[[1, 4, 107], 1]], [[[1, 11, 109], 1]], [[[1, -2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 218, 'label': '2-7605-1.1-c1-0-218', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/7605/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.7711864909225397e-61, 0.1253039994813335, 0.24961856238459046, 0.37193298991513574, 0.49119636141173517, 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-2.716505192195583, -2.4601394855344565, -2.0891783092802285, -1.616992072598425, -1.0638867162279417, -0.4564188707934455, 0.17367403532719325, 0.7908862508455833, 1.3576354872173, 1.8361527626832679], 'positive_zeros': ['1.34475697320078698804067361472106', '1.86315542563040252055657950845933', '2.61280199081632125119869153918208', '4.09272495499005085504981921439673', '4.76304990812899016071365029911310', '5.43210262742652919238429528027042', '6.27120901501207590227932710168629', '7.32424451922789077347092107222228', '7.63191830349450506511065357206776'], 'prelabel': '2-7605-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.79270368596059, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 2280365678027830245, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34475697320078698804067361472', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86315542563040252055657950846', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.61280199081632125119869153918', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 60.72623073718376, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 7605, 'conductor_radical': 195, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 2, 1, 0, 5, 0, 0, -2, -2, 0, 0, -10, 0, -4, -2, 0, 0, 2, 0, 4, -6, 0, 1, 0, 0, 10, 4, 0, -7, 8, 0, 4, 5, 0, -2, 0, 0, 0, -6, 0, 1, -4, 0, 12, 8, 0, 18, -2, 0, 0, 4, 0, -2, 0, 0, -8, -12, 0, -13, 14, 0, -8, 0, 0, -7, -4, 0, -10, -12, 0, 15, 4, 0, 0, -10, 0, 3, -4, 0, 12, -8, 0, -2, -2, 0, 0, -14, 0, 0, -12, 0, -16, 0, 0, -5, -36, 0, 2], 'euler11': [1, 2, 11], 'euler13': [1, 0, 0], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 2, 2], 'euler23': [1, 6, 23], 'euler29': [1, -4, 29], 'euler3': [1, 0, 0], 'euler31': [1, 7, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -1, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, -4, 53], 'euler59': [1, 12, 59], 'euler61': [1, 13, 61], 'euler67': [1, 7, 67], 'euler7': [1, -5, 7], 'euler71': [1, 12, 71], 'euler73': [1, -15, 73], 'euler79': [1, -3, 79], 'euler83': [1, 8, 83], 'euler89': [1, 14, 89], 'euler97': [1, 5, 97], 'euler_factors': [[1, 2, 2], [1, 0, 0], [1, -1, 0], [1, -5, 7], [1, 2, 11], [1, 0, 0], [1, 2, 17], [1, 0, 19], [1, 6, 23], [1, -4, 29], [1, 7, 31], [1, 2, 37], [1, 6, 41], [1, -1, 43], [1, -8, 47], [1, -4, 53], [1, 12, 59], [1, 13, 61], [1, 7, 67], [1, 12, 71], [1, -15, 73], [1, -3, 79], [1, 8, 83], [1, 14, 89], [1, 5, 97]], 'index': 218, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/7605/a', 'ModularForm/GL2/Q/holomorphic/7605/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/7605/2/a/a'], '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': '2-7605-1.1-c1-0-218', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-7605-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.79270368596059, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2280365678027830245, 'z1': {'__RealLiteral__': 0, 'data': '1.34475697320078698804067361472', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21957004
{'Lhash': '1704681984239074625014086498155', 'Lhash_array': ['1704681984239074625014086498155'], 'label': '2-7605-1.1-c1-0-218', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7605/2/a/a'}
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id: 24580334
{'Lhash': '1704681984239074625014086498155', 'Lhash_array': ['1704681984239074625014086498155'], 'label': '2-7605-1.1-c1-0-218', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7605/2/a/a/1/1'}
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id: 24073
{'Lhash': '2280365678027830245', 'Lhash_array': ['2280365678027830245'], 'label': '2-7605-1.1-c1-0-218', 'type': 'ECQ', 'url': 'EllipticCurve/Q/7605/a'}