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lfunc_lfunctions • Show schema
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{'Lhash': '2197896085895081181124433568093', 'a10': [0.0, 0.0], 'a2': [2.6457513110645907, 0.0], 'a3': [1.0, 0.0], 'a4': [5.0, 0.0], 'a5': [0.0, 0.0], 'a6': [2.6457513110645907, 0.0], 'a7': [-1.6457513110645905, 0.0], 'a8': [7.937253933193772, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.37868228803246, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 19], 'central_character': '1425.1', 'coefficient_field': 'CDF', 'conductor': 1425, 'conductor_radical': 285, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.6457513110645907, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.6457513110645905, 0], [7.0, 0]], [[1.0, 0], [-0.3542486889354094, 0], [11.0, 0]], [[1.0, 0], [-0.3542486889354094, 0], [13.0, 0]], [[1.0, 0], [-4.0, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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[0]], 'group': 'GL2', 'index': 48, 'label': '2-1425-1.1-c1-0-48', 'leading_term': '6.23474162888175435396662852871', '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/1425/2/a/p/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [6.234741628881754, 6.233417914957696, 6.229064447014198, 6.220557013754305, 6.206095649626894, 6.183308059721797, 6.149381548647423, 6.1012134788852075, 6.0355705550379755, 5.949248547317928, 5.839225889557541, 5.702806426187415, 5.537748113194795, 5.342375558983126, 5.115674929583293, 4.857370035258622, 4.567978492871402, 4.2488468472324294, 3.9021635378025867, 3.530948686671449, 3.13901990248211, 2.730933661134228, 2.3119023368468428, 1.8876876014543884, 1.4644716601956271, 1.0487086157299574, 0.646959110263528, 0.26571224640420527, 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'6.26988906281124121992944018435342', '6.64390645269505056568588734418765', '7.76167606018827966499497845131145', '8.460777693018554677663563743162368', '10.00230922795690139354083738255476'], 'prelabel': '2-1425-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3732302453334637, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.73383429590091245764133311669', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87575319184643748254046897491', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50505424964921679592495139236', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.37868228803246, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 1425, 'conductor_radical': 285, 'degree': 2, 'index': 48, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1425/2/a/p/1/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-1425-1.1-c1-0-48', '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': '2-1425-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3732302453334637, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73383429590091245764133311669', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2197896085895081181124433568093', 'Lhash_array': ['2197896085895081181124433568093'], 'factors': ['2-1425-1.1-c1-0-48'], 'label': '2-1425-1.1-c1-0-48', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1425/2/a/p/1/2'}