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lfunc_lfunctions • Show schema
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{'Lhash': '1873777259351834157150561844269', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.116186243894532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [7, [1, -1]], [19, [1, -1]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '2394.1', 'coefficient_field': '1.1.1.1', 'conductor': 2394, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 0, 5], [1, -1], [1, 6, 11], [1, -2, 13], [1, 0, 17], [1, -1], [1, -6, 23], [1, 6, 29], [1, -8, 31], [1, 10, 37], [1, -6, 41], [1, 4, 43], [1, 6, 47], [1, 6, 53], [1, 12, 59], [1, -2, 61], [1, 4, 67], [1, 0, 71], [1, -2, 73], [1, 4, 79], [1, 6, 83], [1, -6, 89], [1, -14, 97], [1, 12, 101], [1, 4, 103], [1, 0, 107], [1, -2, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, 0, 5], 1]], [[[1, -1], 1]], [[[1, 6, 11], 1]], [[[1, -2, 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4.018585674856016, 3.7475622219522813, 3.352618663974194, 2.8538262084239574, 2.2765332036420634, 1.6501490175531401, 1.0066975631142747, 0.37921164795440226, -0.1999509746379039, -0.7007833808509895], 'positive_zeros': ['1.47814962499483450164849405751345', '2.57033400147183809405890786244251', '3.42948835695246631266124027247231', '4.76918027065692334568092858821512', '5.44565375834713779887264721264436', '6.31820508463320297458061667389247', '7.33615990354905827830525466936520', '7.87462094921647883942664875297472', '8.490670546431863178338078429994546'], 'prelabel': '2-2394-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.372206107206582, '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': 84777102138716365, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47814962499483450164849405751', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57033400147183809405890786244', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42948835695246631266124027247', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.116186243894532, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 2394, 'conductor_radical': 798, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, 1, -1, 0, 0, -6, 0, 2, -1, 0, 1, 0, 0, 1, 0, 0, 6, 6, 0, -5, -2, 0, 1, -6, 0, 8, -1, 0, 0, 0, 0, -10, -1, 0, 0, 6, 0, -4, -6, 0, -6, -6, 0, 1, 5, 0, 2, -6, 0, 0, -1, 0, 6, -12, 0, 2, -8, 0, 1, 0, 0, -4, 0, 0, 0, 0, 0, 2, 10, 0, 1, -6, 0, -4, 0, 0, -6, -6, 0, 0, 4, 0, 6, 6, 0, 2, 6, 0, 6, 0, 0, 14, -1, 0, -5], 'euler11': [1, 6, 11], 'euler13': [1, -2, 13], 'euler17': [1, 0, 17], 'euler19': [1, -1, 0], 'euler2': [1, 1, 0], 'euler23': [1, -6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, 10, 37], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 5], 'euler53': [1, 6, 53], 'euler59': [1, 12, 59], 'euler61': [1, -2, 61], 'euler67': [1, 4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, -2, 73], 'euler79': [1, 4, 79], 'euler83': [1, 6, 83], 'euler89': [1, -6, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 0, 5], [1, -1, 0], [1, 6, 11], [1, -2, 13], [1, 0, 17], [1, -1, 0], [1, -6, 23], [1, 6, 29], [1, -8, 31], [1, 10, 37], [1, -6, 41], [1, 4, 43], [1, 6, 47], [1, 6, 53], [1, 12, 59], [1, -2, 61], [1, 4, 67], [1, 0, 71], [1, -2, 73], [1, 4, 79], [1, 6, 83], [1, -6, 89], [1, -14, 97]], 'index': 33, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2394/c', 'ModularForm/GL2/Q/holomorphic/2394/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/2394/2/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': '2-2394-1.1-c1-0-33', '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': '2-2394-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.372206107206582, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 84777102138716365, 'z1': {'__RealLiteral__': 0, 'data': '1.47814962499483450164849405751', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20620200
{'Lhash': '1873777259351834157150561844269', 'Lhash_array': ['1873777259351834157150561844269'], 'label': '2-2394-1.1-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/2/a/c'}
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id: 24557000
{'Lhash': '1873777259351834157150561844269', 'Lhash_array': ['1873777259351834157150561844269'], 'label': '2-2394-1.1-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/2/a/c/1/1'}
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id: 31230
{'Lhash': '84777102138716365', 'Lhash_array': ['84777102138716365'], 'label': '2-2394-1.1-c1-0-33', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2394/c'}