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lfunc_lfunctions • Show schema
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{'Lhash': '788779001733364173155222897599', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-3.3117376914898995, 5.73609794300137], 'a6': [0, 0], 'a7': [-8.468084720591406, 4.889050992954005], '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': '1728.1279', 'coefficient_field': 'CDF', 'conductor': 1728, 'conductor_radical': 6, 'conjugate': '951366490682341513317107488624', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.3117376914898995, -5.73609794300137], [-12.5, -21.650635094610966]], [[1.0, 0], [8.468084720591406, -4.889050992954005], [24.5, -42.4352447854375]], [[1.0, 0], [-10.062305898749054, 5.809475019311125], [60.5, -104.78907385791707]], [[1.0, 0], [-8.935213074469699, 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False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': -0.13945268301824937, 'root_number': '0.64006992882575510784644923867269589058156793147098858 - 0.76831665751367957079475617948748930532595003584519627*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.13945268301824937', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62223691732670770157375763182', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.61209278386186234806112718698', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29942540513124194009142602075', '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': '36.31', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/3/o/d/1279/1'], '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': '2-12e3-36.31-c2-0-21', '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': '2-12e3-36.31-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': -0.13945268301824937, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62223691732670770157375763182', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '788779001733364173155222897599', 'Lhash_array': ['788779001733364173155222897599'], 'factors': ['2-12e3-36.31-c2-0-21'], 'label': '2-12e3-36.31-c2-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/3/o/d/1279/1'}