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lfunc_lfunctions • Show schema
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{'Lhash': '1020594597732312078785863520216', 'a10': 0, 'a2': -1, 'a3': 1, 'a4': 1, 'a5': 0, 'a6': -1, 'a7': -4, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [5, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.1', 'coefficient_field': '1.1.1.1', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1], [1, 4, 7], [1, 0, 11], [1, -1], [1, 0, 17], [1, -5, 19], [1, 0, 23], [1, -3, 29], [1, 4, 31], [1, 7, 37], [1, -3, 41], [1, -2, 43], [1, -9, 47], [1, -9, 53], [1, -6, 59], [1, -8, 61], [1, -5, 67], [1, 3, 71], [1, 4, 73], [1, -11, 79], [1, 6, 83], [1, -6, 89], [1, -8, 97], [1, -18, 101], [1, 16, 103], [1, -9, 107], [1, -11, 109], [1, -18, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, -1], 1]], [1], [[[1, 4, 7], 1]], [[[1, 0, 11], 1]], [[[1, -1], 1]], [[[1, 0, 17], 1]], [[[1, -5, 19], 1]], [[[1, 0, 23], 1]], [[[1, -3, 29], 1]], [[[1, 4, 31], 1]], [[[1, 7, 37], 1]], [[[1, -3, 41], 1]], [[[1, -2, 43], 1]], [[[1, -9, 47], 1]], [[[1, -9, 53], 1]], [[[1, -6, 59], 1]], [[[1, -8, 61], 1]], [[[1, -5, 67], 1]], [[[1, 3, 71], 1]], [[[1, 4, 73], 1]], [[[1, -11, 79], 1]], [[[1, 6, 83], 1]], [[[1, -6, 89], 1]], [[[1, -8, 97], 1]], [[[1, -18, 101], 1]], [[[1, 16, 103], 1]], [[[1, -9, 107], 1]], [[[1, -11, 109], 1]], [[[1, -18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-1950-1.1-c1-0-4', 'leading_term': '1.261653142702910388368401053652200000000000000000000000000000000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1950/2/a/f', 'plot_delta': {'__RealLiteral__': 0, 'data': 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-1.8316856371267352, -2.5871049734480387, -3.256313206972739, -3.7967863639516315, -4.174028976013476, -4.363856116654388, -4.353969136932698, -4.1447147047061925, -3.7489741898526123, -3.191192003692765, -2.5056127863770477, -1.7338539050111417, -0.9219874372308966, -0.11734113241365648], 'positive_zeros': ['0.805107178230786108851722746579533', '2.28203067662838759760760090270340', '3.21110717019141316546603900404989', '3.86541777052856340745686880082943', '5.34655100340507626856083927354310', '6.21942354210226036235913961669847', '7.04556559344328990168385895474132', '7.55763254790499154685263093337183', '8.696657713782855691873839819406335', '9.078339016738156498544771857710652'], 'prelabel': '2-1950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1483904674628522328, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.805107178230786108851722746580', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.28203067662838759760760090270', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.21110717019141316546603900405', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.570828394149682, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, -4, -1, 1, 0, 0, 1, 1, 4, 0, 1, 0, -1, 5, 0, -4, 0, 0, -1, 0, -1, 1, -4, 3, 0, -4, -1, 0, 0, 0, 1, -7, -5, 1, 0, 3, 4, 2, 0, 0, 0, 9, 1, 9, 0, 0, 1, 9, -1, 0, 4, 5, -3, 6, 0, 8, 4, -4, 1, 0, 0, 5, 0, 0, 0, -3, -1, -4, 7, 0, 5, 0, -1, 11, 0, 1, -3, -6, -4, 0, -2, 3, 0, 6, 0, -4, 0, -4, -9, 0, -1, 8, -9, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -1, 0], 'euler17': [1, 0, 17], 'euler19': [1, -5, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -3, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 7, 37], 'euler41': [1, -3, 41], 'euler43': [1, -2, 43], 'euler47': [1, -9, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, -6, 59], 'euler61': [1, -8, 61], 'euler67': [1, -5, 67], 'euler7': [1, 4, 7], 'euler71': [1, 3, 71], 'euler73': [1, 4, 73], 'euler79': [1, -11, 79], 'euler83': [1, 6, 83], 'euler89': [1, -6, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 0, 0], [1, 4, 7], [1, 0, 11], [1, -1, 0], [1, 0, 17], [1, -5, 19], [1, 0, 23], [1, -3, 29], [1, 4, 31], [1, 7, 37], [1, -3, 41], [1, -2, 43], [1, -9, 47], [1, -9, 53], [1, -6, 59], [1, -8, 61], [1, -5, 67], [1, 3, 71], [1, 4, 73], [1, -11, 79], [1, 6, 83], [1, -6, 89], [1, -8, 97]], 'index': 4, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1950/f', 'ModularForm/GL2/Q/holomorphic/1950/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/1950/2/a/f'], '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': '2-1950-1.1-c1-0-4', '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': '2-1950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1483904674628522328, 'z1': {'__RealLiteral__': 0, 'data': '0.805107178230786108851722746580', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20701975
{'Lhash': '1020594597732312078785863520216', 'Lhash_array': ['1020594597732312078785863520216'], 'label': '2-1950-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/a/f'}
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id: 24555206
{'Lhash': '1020594597732312078785863520216', 'Lhash_array': ['1020594597732312078785863520216'], 'label': '2-1950-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/a/f/1/1'}
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id: 103873
{'Lhash': '1483904674628522328', 'Lhash_array': ['1483904674628522328'], 'label': '2-1950-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1950/f'}