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lfunc_lfunctions • Show schema
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{'Lhash': '3207410550803947465330027942379', 'a10': -2, 'a2': 2, 'a3': 1, 'a4': 2, 'a5': -1, 'a6': 2, 'a7': -1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5570828394149683, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [5, [1, 1]], [13, [1, 1]]], 'bad_primes': [3, 5, 13], 'central_character': '195.1', 'coefficient_field': '1.1.1.1', 'conductor': 195, 'conductor_radical': 195, 'degree': 2, 'euler_factors': [[1, -2, 2], [1, -1], [1, 1], [1, 1, 7], [1, -5, 11], [1, 1], [1, 7, 17], [1, 6, 19], [1, -3, 23], [1, -2, 29], [1, -2, 31], [1, -7, 37], [1, -9, 41], [1, 8, 43], [1, -10, 47], [1, -5, 53], [1, 0, 59], [1, -5, 61], [1, 4, 67], [1, -9, 71], [1, 6, 73], [1, 3, 79], [1, 4, 83], [1, -11, 89], [1, 11, 97], [1, 0, 101], [1, 4, 103], [1, 17, 107], [1, -4, 109], [1, -10, 113]], 'euler_factors_factorization': [[[[1, -2, 2], 1]], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, 1, 7], 1]], [[[1, -5, 11], 1]], [[[1, 1], 1]], [[[1, 7, 17], 1]], [[[1, 6, 19], 1]], [[[1, -3, 23], 1]], [[[1, -2, 29], 1]], [[[1, -2, 31], 1]], [[[1, -7, 37], 1]], [[[1, -9, 41], 1]], [[[1, 8, 43], 1]], [[[1, -10, 47], 1]], [[[1, -5, 53], 1]], [[[1, 0, 59], 1]], [[[1, -5, 61], 1]], [[[1, 4, 67], 1]], [[[1, -9, 71], 1]], [[[1, 6, 73], 1]], [[[1, 3, 79], 1]], [[[1, 4, 83], 1]], [[[1, -11, 89], 1]], [[[1, 11, 97], 1]], [[[1, 0, 101], 1]], [[[1, 4, 103], 1]], [[[1, 17, 107], 1]], [[[1, -4, 109], 1]], [[[1, -10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-195-1.1-c1-0-4', '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/195/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.4225847175064406, 2.4358034763181955, 2.473904483275741, 2.532441394595305, 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0.8067687643107652, 0.9131108493055221, 0.7717527076416588, 0.4396684391465527, 0.036254544788187786, -0.2986251297386195, -0.45224062568877293, -0.3768970643242545, -0.10592453941458711, 0.2575392288644429], 'positive_zeros': ['2.53020079052262607160250914109353', '3.93328920262448493706980455054148', '4.52648172003467775210616179347502', '6.28215256608024799923334344772716', '6.92169485416648038433791572414532', '8.599163171775301233119270744200006', '9.348864711978766678634703610950063', '10.94991870593933196961773601343959', '11.83093169319155993109511626781292', '12.76813114320736202184696722236355'], 'prelabel': '2-195-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2478312543829668, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1913758209604816592, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.53020079052262607160250914109', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.93328920262448493706980455054', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.52648172003467775210616179348', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5570828394149683, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 195, 'conductor_radical': 195, 'degree': 2, 'dirichlet_coefficients': [1, 2, 1, 2, -1, 2, -1, 0, 1, -2, 5, 2, -1, -2, -1, -4, -7, 2, -6, -2, -1, 10, 3, 0, 1, -2, 1, -2, 2, -2, 2, -8, 5, -14, 1, 2, 7, -12, -1, 0, 9, -2, -8, 10, -1, 6, 10, -4, -6, 2, -7, -2, 5, 2, -5, 0, -6, 4, 0, -2, 5, 4, -1, -8, 1, 10, -4, -14, 3, 2, 9, 0, -6, 14, 1, -12, -5, -2, -3, 4, 1, 18, -4, -2, 7, -16, 2, 0, 11, -2, 1, 6, 2, 20, 6, -8, -11, -12, 5, 2], 'euler11': [1, -5, 11], 'euler13': [1, 1, 0], 'euler17': [1, 7, 17], 'euler19': [1, 6, 19], 'euler2': [1, -2, 2], 'euler23': [1, -3, 23], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -2, 31], 'euler37': [1, -7, 37], 'euler41': [1, -9, 41], 'euler43': [1, 8, 43], 'euler47': [1, -10, 47], 'euler5': [1, 1, 0], 'euler53': [1, -5, 53], 'euler59': [1, 0, 59], 'euler61': [1, -5, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 7], 'euler71': [1, -9, 71], 'euler73': [1, 6, 73], 'euler79': [1, 3, 79], 'euler83': [1, 4, 83], 'euler89': [1, -11, 89], 'euler97': [1, 11, 97], 'euler_factors': [[1, -2, 2], [1, -1, 0], [1, 1, 0], [1, 1, 7], [1, -5, 11], [1, 1, 0], [1, 7, 17], [1, 6, 19], [1, -3, 23], [1, -2, 29], [1, -2, 31], [1, -7, 37], [1, -9, 41], [1, 8, 43], [1, -10, 47], [1, -5, 53], [1, 0, 59], [1, -5, 61], [1, 4, 67], [1, -9, 71], [1, 6, 73], [1, 3, 79], [1, 4, 83], [1, -11, 89], [1, 11, 97]], 'index': 4, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/195/c', 'ModularForm/GL2/Q/holomorphic/195/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/195/2/a/c'], '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': '2-195-1.1-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': '2-195-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2478312543829668, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1913758209604816592, 'z1': {'__RealLiteral__': 0, 'data': '2.53020079052262607160250914109', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10024957
{'Lhash': '3207410550803947465330027942379', 'Lhash_array': ['3207410550803947465330027942379'], 'label': '2-195-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/195/2/a/c'}
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id: 24547982
{'Lhash': '3207410550803947465330027942379', 'Lhash_array': ['3207410550803947465330027942379'], 'label': '2-195-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/195/2/a/c/1/1'}
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id: 22095
{'Lhash': '1913758209604816592', 'Lhash_array': ['1913758209604816592'], 'label': '2-195-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/195/c'}