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lfunc_lfunctions • Show schema
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{'Lhash': '1728282969007799063348283914624', 'a10': [-1.0897902135516373, -0.21677275132473922], 'a2': [0.7856949583871021, 0.7856949583871021], 'a3': [0.0, 0.0], 'a4': [0.0, 0.23463313526982046], 'a5': [-0.8314696123025452, 0.5555702330196022], 'a6': [0.0, 0.0], 'a7': [0.541196100146197, -0.541196100146197], 'a8': [0.6013448869350453, -0.6013448869350453], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8309432460339491, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.8314696123025452, -0.5555702330196022]]], [37, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [3, 5, 37], 'central_character': '1665.73', 'coefficient_field': 'CDF', 'conductor': 1665, 'conductor_radical': 555, 'conjugate': '1764316044229322437986345216186', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7856949583871021, -0.7856949583871021], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 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'2.68714448969150889852724049192083', '3.44580391231882145781215977081277', '4.51306741342798443651633843935222', '4.96702387584230812479305420985171', '5.85978998243760471572498979873585', '7.28757009420429972206599181677495', '7.921875902588193360036365931851627', '8.556267122489901198917283168257806', '9.492217386175447014694625663863423'], 'prelabel': '2-1665-185.73-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9115608844361133, 'root_angle': -0.13064590441260832, 'root_number': '0.68158307634114592341131769048314 - 0.73174073963757112120419324839706*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.13064590441260832', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36337486740955026041383577639', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68714448969150889852724049192', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44580391231882145781215977081', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8309432460339491, 'bad_primes': [3, 5, 37], 'central_character': '185.73', 'conductor': 1665, 'conductor_radical': 555, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1665/1/t/a/73/6'], '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': '2-1665-185.73-c0-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1665-185.73-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9115608844361133, 'root_angle': -0.13064590441260832, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36337486740955026041383577639', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1728282969007799063348283914624', 'Lhash_array': ['1728282969007799063348283914624'], 'factors': ['2-1665-185.73-c0-0-4'], 'label': '2-1665-185.73-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1665/1/t/a/73/6'}