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lfunc_lfunctions • Show schema
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{'Lhash': '1337871174848408345318630902702', 'a10': [4.042572100532158, 7.0019402713821375], 'a2': [-3.131362884240757, 1.807893204146804], 'a3': [-2.1244323435207266, -2.1182037715486755], 'a4': [4.536955675200395, -7.858237741135045], 'a5': [0.0, -2.23606797749979], 'a6': [10.481854794162393, 2.7921178749655198], 'a7': [6.873141581141799, -1.3266215758759574], 'a8': [0.0, 18.346179697665843], 'a9': [0.026425564393933457, 8.99996120489119], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.583128327349353, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.1244323435207266, 2.1182037715486755]]], [5, [[1.0, 0], [0, 2.23606797749979]]], [7, [[1.0, 0], [-6.873141581141799, 1.3266215758759574]]]], 'bad_primes': [3, 5, 7], 'central_character': '315.191', 'coefficient_field': 'CDF', 'conductor': 315, 'conductor_radical': 105, 'conjugate': '969269102607339654113350907947', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'positive_zeros': ['1.05539426606001396885916479639593', '2.64937604324051162151145298678670', '4.06219009821867044326330291311798', '5.54910246559034174374513996831395', '7.00127672655255176816131663327814', '8.058464218893830219819118071940813', '8.833878255933600149007481084137809', '10.14790690936647641754061405001701', '10.27665084515402277007514915096905', '11.26306098792476878608259489770309'], 'prelabel': '2-315-63.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.92969765118337, 'root_angle': 0.1404223230412277, 'root_number': '0.9042613463456547 + 0.42697941110215604*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0702111615206', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05539426606001396885916479640', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64937604324051162151145298679', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.06219009821867044326330291312', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.583128327349353, 'bad_primes': [3, 5, 7], 'central_character': '63.2', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/315/3/bd/a/191/4'], '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': '2-315-63.2-c2-0-30', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-315-63.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.92969765118337, 'root_angle': 0.07021116152061385, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05539426606001396885916479640', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1337871174848408345318630902702', 'Lhash_array': ['1337871174848408345318630902702'], 'label': '2-315-63.2-c2-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/3/bd/a/191/4'}