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lfunc_lfunctions • Show schema
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{'Lhash': '4437967660179076015246627298977', 'a10': [0.6592942907319955, 1.141931208687903], 'a2': [-0.18544450731843132, -0.3211993086601015], 'a3': [-0.8948757769144338, -1.4829690974163245], 'a4': [0.9312206694108486, -1.6129215124778908], 'a5': [-3.555210667954188, 0.0], 'a6': [-0.3103788512933226, 0.5624419545204165], 'a7': [-0.12487558165809358, 0.21629085205653428], 'a8': [-1.4325370622482636, 0.0], 'a9': [-1.398394687783577, 2.6541462463810603], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8948757769144338, 1.4829690974163245]]], [19, [[1.0, 0], [4.076603748054556, 1.543146746536943]]]], 'bad_primes': [3, 19], 'central_character': '171.106', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '721435246939772204204173155972', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.18544450731843132, 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'8.903939025951671251649943896989722', '10.61836573188522546898992865797596', '11.17992413211721713612210388279531', '12.13202022809577139371576750970076', '12.73332521688780339062390574199698'], 'prelabel': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.924007851680735, 'root_number': '-0.9716375662884033 + 0.2364750299231374*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.46200392584', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.50093918575044161238629048013', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.02357147971554509162260395969', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.77345663818748392520885061981', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.106', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/g/c/106/8'], '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': '2-171-171.106-c1-0-17', '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': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.4620039258403675, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.50093918575044161238629048013', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4437967660179076015246627298977', 'Lhash_array': ['4437967660179076015246627298977'], 'label': '2-171-171.106-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/g/c/106/8'}