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lfunc_lfunctions • Show schema
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{'Lhash': '680953506138277438824968636097', 'a10': [-35.75329784367044, -61.92652840337998], 'a2': [-1.6463673188697767, 2.851591844203404], 'a3': [0.0, 0.0], 'a4': [-1.421050697284914, -2.4613320078286516], 'a5': [-10.85823844833573, 18.807020673215334], 'a6': [0.0, 0.0], 'a7': [1.0876902086458338, 18.48829170069577], 'a8': [-16.983591396048464, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.151360991084982, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0876902086458338, -18.48829170069577]]]], 'bad_primes': [3, 7], 'central_character': '189.163', 'coefficient_field': 'CDF', 'conductor': 189, 'conductor_radical': 21, 'conjugate': '3328418870503682949747840657676', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.6463673188697767, -2.851591844203404], [-4.0, -6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [10.85823844833573, -18.807020673215334], [-62.5, 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'9.208407024993750800777556320341738', '10.77825016796798550169995450952749', '11.25898807366775336867792372209344'], 'prelabel': '2-189-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.339365357532024, 'root_angle': 0.6277886899079488, 'root_number': '-0.3907626845173295 + 0.9204914580748754*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.313894344954', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53717759926566335932561418132', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.22421567805574216186788462594', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51180788564657472370923776728', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.151360991084982, 'bad_primes': [3, 7], 'central_character': '7.2', 'conductor': 189, 'conductor_radical': 21, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/189/4/e/h/163/3'], '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': '2-189-7.2-c3-0-6', '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': '2-189-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.339365357532024, 'root_angle': 0.3138943449539744, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53717759926566335932561418132', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '680953506138277438824968636097', 'Lhash_array': ['680953506138277438824968636097'], 'label': '2-189-7.2-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/189/4/e/h/163/3'}