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lfunc_lfunctions • Show schema
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{'Lhash': '344621260986464139053411922813', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.6971809200621023, 1.585540527612385], 'a4': [0, 0], 'a5': [2.0076726741232305, 3.4773910765491083], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-2.027877529402721, -2.2108172076731076], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.390407277702577, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.6971809200621023, -1.585540527612385]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1176.521', 'coefficient_field': 'CDF', 'conductor': 1176, 'conductor_radical': 42, 'conjugate': '2836928002726590908377616904690', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.6971809200621023, -1.585540527612385]], [[1.0, 0], [-2.0076726741232305, -3.4773910765491083], [-2.5, 4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.266338284132579, 1.885821287608325], [5.5, 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'9.132138118083791819720052068863471'], 'prelabel': '2-1176-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0643771435158853, 'root_angle': 0.42944956160134173, 'root_number': '-0.90334908353811004252746015102150785148476821245007692922 + 0.4289060891044293436913503865162515599997614414620122625*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4294495616013418', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27185823990018866055760531006', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77550124155596717862855185287', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.36592465785926988082257129811', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.390407277702577, 'bad_primes': [2, 3, 7], 'central_character': '21.17', 'conductor': 1176, 'conductor_radical': 42, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1176/2/u/c/521/10'], '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': '2-1176-21.17-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1176-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0643771435158853, 'root_angle': 0.42944956160134173, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.27185823990018866055760531006', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '344621260986464139053411922813', 'Lhash_array': ['344621260986464139053411922813'], 'factors': ['2-1176-21.17-c1-0-1'], 'label': '2-1176-21.17-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1176/2/u/c/521/10'}