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lfunc_lfunctions • Show schema
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{'Lhash': '1052834011170463725016711879893', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 77.2552639555888, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [43, [1, 1]]], 'bad_primes': [3, 5, 43], 'central_character': '9675.1', 'coefficient_field': '1.1.1.1', 'conductor': 9675, 'conductor_radical': 645, 'degree': 2, 'euler_factors': [[1, 1, 2], [1], [1], [1, 4, 7], [1, 3, 11], [1, 1, 13], [1, 2, 17], [1, 0, 19], [1, -3, 23], [1, 0, 29], [1, -1, 31], [1, -10, 37], [1, 9, 41], [1, 1], [1, -5, 47], [1, -1, 53], [1, 1, 59], [1, 0, 61], [1, 12, 67], [1, 6, 71], [1, -14, 73], [1, -13, 79], [1, -9, 83], [1, -8, 89], [1, 9, 97], [1, -13, 101], [1, -16, 103], [1, -9, 107], [1, 1, 109], [1, 12, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [1], [1], [[[1, 4, 7], 1]], [[[1, 3, 11], 1]], [[[1, 1, 13], 1]], [[[1, 2, 17], 1]], [[[1, 0, 19], 1]], [[[1, -3, 23], 1]], [[[1, 0, 29], 1]], [[[1, -1, 31], 1]], [[[1, -10, 37], 1]], [[[1, 9, 41], 1]], [[[1, 1], 1]], [[[1, -5, 47], 1]], [[[1, -1, 53], 1]], [[[1, 1, 59], 1]], [[[1, 0, 61], 1]], [[[1, 12, 67], 1]], [[[1, 6, 71], 1]], [[[1, -14, 73], 1]], [[[1, -13, 79], 1]], [[[1, -9, 83], 1]], [[[1, -8, 89], 1]], [[[1, 9, 97], 1]], [[[1, -13, 101], 1]], [[[1, -16, 103], 1]], [[[1, -9, 107], 1]], [[[1, 1, 109], 1]], [[[1, 12, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 135, 'label': '2-9675-1.1-c1-0-135', '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/9675/2/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-4.588258334751135e-61, 0.0918364870024692, 0.1819526513465918, 0.26861002757234126, 0.35003670343515614, 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-0.8073056314840935, 0.2106616824622072, 1.2192825912556056, 2.1774926043807654, 3.046504648082656, 3.791780933861375, 4.3847925070442315, 4.8044665416688055], 'positive_zeros': ['0.830539591099400868994010661149746', '2.17296875465962166006828400425059', '2.99144331688627586872022512267750', '3.73209181949160162591589512479035', '4.62242978189937898508501818568472', '5.22687049962670872617582221608981', '6.13052836459108541751253637736092', '6.72974300617864097529050895282402', '7.50692021599299708555965947056575'], 'prelabel': '2-9675-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.78949736649308, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 553316222817431715, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.830539591099400868994010661150', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.17296875465962166006828400425', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99144331688627586872022512268', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 77.2552639555888, 'bad_primes': [3, 5, 43], 'central_character': '1.1', 'conductor': 9675, 'conductor_radical': 645, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, -1, 0, 0, -4, 3, 0, 0, -3, 0, -1, 4, 0, -1, -2, 0, 0, 0, 0, 3, 3, 0, 0, 1, 0, 4, 0, 0, 1, -5, 0, 2, 0, 0, 10, 0, 0, 0, -9, 0, -1, 3, 0, -3, 5, 0, 9, 0, 0, 1, 1, 0, 0, -12, 0, 0, -1, 0, 0, -1, 0, 7, 0, 0, -12, 2, 0, 0, -6, 0, 14, -10, 0, 0, 12, 0, 13, 0, 0, 9, 9, 0, 0, 1, 0, -9, 8, 0, 4, -3, 0, -5, 0, 0, -9, -9, 0, 0], 'euler11': [1, 3, 11], 'euler13': [1, 1, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 2], 'euler23': [1, -3, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -1, 31], 'euler37': [1, -10, 37], 'euler41': [1, 9, 41], 'euler43': [1, 1, 0], 'euler47': [1, -5, 47], 'euler5': [1, 0, 0], 'euler53': [1, -1, 53], 'euler59': [1, 1, 59], 'euler61': [1, 0, 61], 'euler67': [1, 12, 67], 'euler7': [1, 4, 7], 'euler71': [1, 6, 71], 'euler73': [1, -14, 73], 'euler79': [1, -13, 79], 'euler83': [1, -9, 83], 'euler89': [1, -8, 89], 'euler97': [1, 9, 97], 'euler_factors': [[1, 1, 2], [1, 0, 0], [1, 0, 0], [1, 4, 7], [1, 3, 11], [1, 1, 13], [1, 2, 17], [1, 0, 19], [1, -3, 23], [1, 0, 29], [1, -1, 31], [1, -10, 37], [1, 9, 41], [1, 1, 0], [1, -5, 47], [1, -1, 53], [1, 1, 59], [1, 0, 61], [1, 12, 67], [1, 6, 71], [1, -14, 73], [1, -13, 79], [1, -9, 83], [1, -8, 89], [1, 9, 97]], 'index': 135, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/9675/e', 'ModularForm/GL2/Q/holomorphic/9675/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/9675/2/a/e'], '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': '2-9675-1.1-c1-0-135', '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': '2-9675-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.78949736649308, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 553316222817431715, 'z1': {'__RealLiteral__': 0, 'data': '0.830539591099400868994010661150', 'prec': 107}}
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lfunc_instances • Show schema
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id: 22684153
{'Lhash': '1052834011170463725016711879893', 'Lhash_array': ['1052834011170463725016711879893'], 'factors': ['2-9675-1.1-c1-0-135'], 'label': '2-9675-1.1-c1-0-135', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9675/2/a/e'}
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id: 24589618
{'Lhash': '1052834011170463725016711879893', 'Lhash_array': ['1052834011170463725016711879893'], 'factors': ['2-9675-1.1-c1-0-135'], 'label': '2-9675-1.1-c1-0-135', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9675/2/a/e/1/1'}
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id: 101454
{'Lhash': '553316222817431715', 'Lhash_array': ['553316222817431715'], 'factors': ['2-9675-1.1-c1-0-135'], 'label': '2-9675-1.1-c1-0-135', 'type': 'ECQ', 'url': 'EllipticCurve/Q/9675/e'}