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lfunc_lfunctions • Show schema
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{'Lhash': '2291060985583639690342752681037', 'a10': [1.0, 0.0], 'a2': [0.9238795325112867, -0.3826834323650898], 'a3': [-0.7071067811865476, -0.7071067811865476], 'a4': [0.7071067811865476, -0.7071067811865476], 'a5': [0.9238795325112867, 0.3826834323650898], 'a6': [-0.9238795325112867, -0.3826834323650898], 'a7': [0.0, 0.0], 'a8': [0.3826834323650898, -0.9238795325112867], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9238795325112867, 0.3826834323650898]]], [3, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [-0.9238795325112867, -0.3826834323650898]]], [13, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.1403', 'coefficient_field': 'CDF', 'conductor': 1560, 'conductor_radical': 390, 'conjugate': '1680565324786999019991258785019', 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0.8868487229574958], 'positive_zeros': ['1.80732844300405348404991807915604', '3.13590189295346853960459546997102', '4.14203036302488975250800946887011', '5.02932300600768411978431185198046', '5.51663551428012382424857220620880', '6.36533320991465972118048379281108', '6.95113432790355447440706308222184', '8.292284072281854212493352227974781', '8.950260243622399241841978300250027', '10.01311893890531292421213068726044'], 'prelabel': '2-1560-1560.1403-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': 0.42620819117478337, 'root_number': '0.22975292054736118352393736938184 + 0.97324898946773016378805774830813*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21310409558739168', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80732844300405348404991807916', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.13590189295346853960459546997', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14203036302488975250800946887', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.1403', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/1/cs/e/1403/4'], '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': '2-1560-1560.1403-c0-0-17', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1560-1560.1403-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': 0.21310409558739168, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.80732844300405348404991807916', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2291060985583639690342752681037', 'Lhash_array': ['2291060985583639690342752681037'], 'label': '2-1560-1560.1403-c0-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/1/cs/e/1403/4'}