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lfunc_lfunctions • Show schema
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{'Lhash': '2420063080954629368053959006819', 'a10': 0, 'a2': -1, 'a3': 1, 'a4': 1, 'a5': 0, 'a6': -1, 'a7': -3, 'a8': -1, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.58578819202164, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [5, [1]], [19, [1, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '950.1', 'coefficient_field': '1.1.1.1', 'conductor': 950, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[1, 1], [1, -1, 3], [1], [1, 3, 7], [1, -2, 11], [1, -1, 13], [1, 3, 17], [1, 1], [1, -1, 23], [1, 5, 29], [1, 8, 31], [1, -2, 37], [1, 8, 41], [1, 4, 43], [1, 8, 47], [1, -1, 53], [1, -15, 59], [1, -2, 61], [1, 3, 67], [1, -2, 71], [1, 9, 73], [1, 10, 79], [1, -6, 83], [1, 0, 89], [1, -2, 97], [1, -2, 101], [1, -6, 103], [1, -7, 107], [1, 15, 109], [1, 14, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, -1, 3], 1]], [1], [[[1, 3, 7], 1]], [[[1, -2, 11], 1]], [[[1, -1, 13], 1]], [[[1, 3, 17], 1]], [[[1, 1], 1]], [[[1, -1, 23], 1]], [[[1, 5, 29], 1]], [[[1, 8, 31], 1]], [[[1, -2, 37], 1]], [[[1, 8, 41], 1]], [[[1, 4, 43], 1]], [[[1, 8, 47], 1]], [[[1, -1, 53], 1]], [[[1, -15, 59], 1]], [[[1, -2, 61], 1]], [[[1, 3, 67], 1]], [[[1, -2, 71], 1]], [[[1, 9, 73], 1]], [[[1, 10, 79], 1]], [[[1, -6, 83], 1]], [[[1, 0, 89], 1]], [[[1, -2, 97], 1]], [[[1, -2, 101], 1]], [[[1, -6, 103], 1]], [[[1, -7, 107], 1]], [[[1, 15, 109], 1]], [[[1, 14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-950-1.1-c1-0-25', '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/950/2/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.786457628385223e-121, 0.25059787516055815, 0.5030763692733471, 0.7572208733319267, 1.0091350959728345, 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-0.343307240790062, 1.2792009894628924, 2.4195268655926943, 2.6913496266380683, 2.029851543897603, 0.7136196812237301, -0.7407858332816707, -1.7730412376820863, -1.989748108228649], 'positive_zeros': ['1.90909315273381969795467705090704', '3.08844310830142045553246780848914', '3.84969924867073870114275032750534', '5.47809446086921756820160858624720', '6.43803628048625394061789390103344', '7.08084872197682116999638941334321', '8.187366436155753750941904167188171', '8.925019181414506634794762446017378', '9.400115216603937442308106741391248'], 'prelabel': '2-950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.7542309619967678, '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': 1061223908540289351, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90909315273381969795467705091', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08844310830142045553246780849', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84969924867073870114275032751', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.58578819202164, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 950, 'conductor_radical': 190, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, -3, -1, -2, 0, 2, 1, 1, 3, 0, 1, -3, 2, -1, 0, -3, -2, 1, -1, 0, -1, -5, -3, -5, 0, -8, -1, 2, 3, 0, -2, 2, 1, 1, 0, -8, 3, -4, 2, 0, -1, -8, 1, 2, 0, -3, 1, 1, 5, 0, 3, -1, 5, 15, 0, 2, 8, 6, 1, 0, -2, -3, -3, 1, 0, 2, 2, -9, -2, 0, -1, -6, -1, -10, 0, 1, 8, 6, -3, 0, 4, -5, -2, 0, 0, -3, 1, -8, 8, 0, -1, 2, -2, -4, 0], 'euler11': [1, -2, 11], 'euler13': [1, -1, 13], 'euler17': [1, 3, 17], 'euler19': [1, 1, 0], 'euler2': [1, 1, 0], 'euler23': [1, -1, 23], 'euler29': [1, 5, 29], 'euler3': [1, -1, 3], 'euler31': [1, 8, 31], 'euler37': [1, -2, 37], 'euler41': [1, 8, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -1, 53], 'euler59': [1, -15, 59], 'euler61': [1, -2, 61], 'euler67': [1, 3, 67], 'euler7': [1, 3, 7], 'euler71': [1, -2, 71], 'euler73': [1, 9, 73], 'euler79': [1, 10, 79], 'euler83': [1, -6, 83], 'euler89': [1, 0, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 0], [1, -1, 3], [1, 0, 0], [1, 3, 7], [1, -2, 11], [1, -1, 13], [1, 3, 17], [1, 1, 0], [1, -1, 23], [1, 5, 29], [1, 8, 31], [1, -2, 37], [1, 8, 41], [1, 4, 43], [1, 8, 47], [1, -1, 53], [1, -15, 59], [1, -2, 61], [1, 3, 67], [1, -2, 71], [1, 9, 73], [1, 10, 79], [1, -6, 83], [1, 0, 89], [1, -2, 97]], 'index': 25, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/950/b', 'ModularForm/GL2/Q/holomorphic/950/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/950/2/a/b'], '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': '2-950-1.1-c1-0-25', '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': '2-950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.7542309619967678, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1061223908540289351, 'z1': {'__RealLiteral__': 0, 'data': '1.90909315273381969795467705091', 'prec': 103}}
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lfunc_instances • Show schema
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id: 18389230
{'Lhash': '2420063080954629368053959006819', 'Lhash_array': ['2420063080954629368053959006819'], 'label': '2-950-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/950/2/a/b'}
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id: 24551167
{'Lhash': '2420063080954629368053959006819', 'Lhash_array': ['2420063080954629368053959006819'], 'label': '2-950-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/950/2/a/b/1/1'}
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id: 90026
{'Lhash': '1061223908540289351', 'Lhash_array': ['1061223908540289351'], 'label': '2-950-1.1-c1-0-25', 'type': 'ECQ', 'url': 'EllipticCurve/Q/950/b'}