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lfunc_lfunctions • Show schema
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{'Lhash': '1225387721615410819776344663093', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.6625077511098136, 0], 'a6': [0, 0], 'a7': [0, 3.572664554992563], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.89599051676739, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.87826090972485, -3.0776835371752536]]]], 'bad_primes': [2, 3, 13], 'central_character': '3744.1585', 'coefficient_field': 'CDF', 'conductor': 3744, 'conductor_radical': 78, 'conjugate': '125533877135664454452231615365', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.6625077511098136, 0], [5.0, 0]], [[1.0, 0], [0, -3.572664554992563], [-7.0, 0]], [[1.0, 0], [-1.0274862967460157, 0], [11.0, 0]], [[1.0, 0], [1.87826090972485, -3.0776835371752536]], [[1.0, 0], [5.052510667480122, 0], [17.0, 0]], [[1.0, 0], 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'2.32970290292608137012075445937147', '3.43909376981696124980487830632045', '4.20052813319229153477112545509554', '4.62046308521651940029600119285317', '5.85704497643038250882720067792586', '6.58625311510430993697973253722105', '7.47983850797115059783418118714447', '7.79098812869012517568830846865208', '8.537896114307573217728566255914130'], 'prelabel': '2-3744-104.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.467722607884145, 'root_angle': 0.574416929226997, 'root_number': '-0.2316638143202216822635272092864486250371971540401958152 + 0.9727959072357396855107014456689538622844754021084681303*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2872084646134985', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.966660467320246193919145738151', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.32970290292608137012075445937', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43909376981696124980487830632', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.89599051676739, 'bad_primes': [2, 3, 13], 'central_character': '104.77', 'conductor': 3744, 'conductor_radical': 78, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3744/2/m/h/1585/7'], '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': '2-3744-104.77-c1-0-38', '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': '2-3744-104.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.467722607884145, 'root_angle': 0.2872084646134985, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.966660467320246193919145738151', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1225387721615410819776344663093', 'Lhash_array': ['1225387721615410819776344663093'], 'label': '2-3744-104.77-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3744/2/m/h/1585/7'}