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lfunc_lfunctions • Show schema
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{'Lhash': '2322700907167167255914439333774', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [2.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.5, 0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [1.0, 1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8304441810213163, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 3.4641016151377544]]]], 'bad_primes': [2, 13], 'central_character': '104.9', 'coefficient_field': 'CDF', 'conductor': 104, 'conductor_radical': 26, 'conjugate': '3091774026348189342726273702770', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386], [-1.5, -2.598076211353316]], [[1.0, 0], [-2.0, 0], [5.0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386], [-3.5, 6.06217782649107]], [[1.0, 0], [0.5, -0.8660254037844386], [-5.5, -9.526279441628825]], [[1.0, 0], [1.0, 3.4641016151377544]], 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2.206208521153588, 2.2939387779629175, 1.8077274281002447, 0.8663246103832013], 'positive_zeros': ['1.83228794018555686871150659946407', '4.14345910193158530011875188027498', '5.92135947979335187446502644487897', '6.71491554184052603124923928704232', '8.167516996140399180117337750496891', '9.525959149125548442170278174527351', '10.44024030447475025031996535876255', '11.76004934409619127987703453910860', '12.68662080982883412099499869639481', '13.67338800469130127364851304742943'], 'prelabel': '2-104-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.911287101314024, 'root_angle': -0.17074856945180006, 'root_number': '0.8595425350987749 - 0.5110642135348272*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0853742847259', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.83228794018555686871150659946', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.14345910193158530011875188027', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.92135947979335187446502644488', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8304441810213163, 'bad_primes': [2, 13], 'central_character': '13.9', 'conductor': 104, 'conductor_radical': 26, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/104/2/i/a/9/1'], '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': '2-104-13.9-c1-0-1', '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': '2-104-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.911287101314024, 'root_angle': -0.08537428472590003, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83228794018555686871150659946', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2322700907167167255914439333774', 'Lhash_array': ['2322700907167167255914439333774'], 'label': '2-104-13.9-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/104/2/i/a/9/1'}