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lfunc_lfunctions • Show schema
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{'Lhash': '859786001907998541169464830260', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0950163090857463, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 59.40869910383263, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '7440.1', 'coefficient_field': 'CDF', 'conductor': 7440, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0950163090857463, 0], [7.0, 0]], [[1.0, 0], [5.257106813636097, 0], [11.0, 0]], [[1.0, 0], [-1.249755442950615, 0], [13.0, 0]], [[1.0, 0], [2.6462001489713605, 0], [17.0, 0]], [[1.0, 0], [3.2571068136360974, 0], [19.0, 0]], [[1.0, 0], 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 24, 'label': '2-7440-1.1-c1-0-24', 'leading_term': '2.01619896099961855474013833958', '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/7440/2/a/bx/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [2.0161989609996187, 2.006310469115613, 1.976623585659972, 1.9270807039988394, 1.8576074293479783, 1.7681435057418642, 1.6586832605884232, 1.5293230199036683, 1.3803126012082618, 1.2121078485718622, 1.0254212141292054, 0.8212675768572041, 0.601002781538741, 0.36635274014320696, 0.1194313332358226, -0.13725424118731128, -0.400811612520345, -0.6679854094331671, -0.9351935894572666, -1.1985776580664351, -1.4540661131900294, -1.6974500587365635, -1.9244695446294005, -2.1309088164215075, -2.312698302587203, 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'5.73654220455693233574349618621850', '6.69255355774799945198599148354675', '7.32026123466063937142825815829164', '7.944123999161817654312071101028981'], 'prelabel': '2-7440-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.7077038801339945, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67825156376149831247504244290', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.96681361718451913361454680802', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.73148620575302581181106812991', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 59.40869910383263, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 7440, 'conductor_radical': 930, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7440/2/a/bx/1/3'], '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': '2-7440-1.1-c1-0-24', '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': '2-7440-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.7077038801339945, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67825156376149831247504244290', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '859786001907998541169464830260', 'Lhash_array': ['859786001907998541169464830260'], 'factors': ['2-7440-1.1-c1-0-24'], 'label': '2-7440-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7440/2/a/bx/1/3'}