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lfunc_lfunctions • Show schema
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{'Lhash': '1570187158632546179736914485427', 'a10': [-15.0, 0], 'a2': [-1.5, 2.598076211353316], 'a3': [0, 0], 'a4': [-0.5, -0.8660254037844386], 'a5': [2.5, 4.330127018922194], 'a6': [0, 0], 'a7': [-10.0, 17.320508075688775], 'a8': [-21.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.89577355232496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.5, -4.330127018922194]]]], 'bad_primes': [3, 5], 'central_character': '405.136', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '217542173632692287842729542269', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5, -2.598076211353316], [-4.0, -6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.5, -4.330127018922194]], [[1.0, 0], [10.0, -17.320508075688775], [-171.5, -297.04671349806245]], [[1.0, 0], [-12.0, 20.784609690826528], [-665.5, -1152.6798124370878]], [[1.0, 0], [37.0, 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1111111111111111', 'prec': 60}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23865926332527884056524629186', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34432299216424244253065808139', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78692971906753789824311146710', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.89577355232496, 'bad_primes': [3, 5], 'central_character': '9.7', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/d/136/1'], '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': '2-405-9.7-c3-0-30', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-405-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.11111111111111113, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23865926332527884056524629186', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1570187158632546179736914485427', 'Lhash_array': ['1570187158632546179736914485427'], 'label': '2-405-9.7-c3-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/d/136/1'}