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lfunc_lfunctions • Show schema
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{'Lhash': '263319734715451709599824581248', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-3.398979485566356, -1.9624017209617515], 'a6': [0, 0], 'a7': [-6.398979485566356, -11.083357585591886], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.084589681459306, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1728.449', 'coefficient_field': 'CDF', 'conductor': 1728, 'conductor_radical': 6, 'conjugate': '792244200491509730800614257654', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.398979485566356, 1.9624017209617515], [12.5, 21.650635094610966]], [[1.0, 0], [6.398979485566356, 11.083357585591886], [-24.5, 42.4352447854375]], [[1.0, 0], [14.297958971132712, -8.254930460845696], [60.5, -104.78907385791707]], [[1.0, 0], [1.3989794855663562, 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'2-12e3-9.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': -0.22222222222222227, 'root_number': '0.76604444311897803520239265055541667393583245708039524585 - 0.6427876096865393263226434099072634329075598842056817904*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1111111111111111', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.20772264429018792308871420732', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.31103504013228149963099954614', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92046249838482300599648958405', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.084589681459306, 'bad_primes': [2, 3], 'central_character': '9.5', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/3/q/e/449/1'], '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': '2-12e3-9.5-c2-0-6', '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': '2-12e3-9.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': -0.11111111111111113, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.20772264429018792308871420732', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '263319734715451709599824581248', 'Lhash_array': ['263319734715451709599824581248'], 'label': '2-12e3-9.5-c2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/3/q/e/449/1'}