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lfunc_lfunctions • Show schema
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{'Lhash': '2517926358860396380521710174012', 'a10': [106.29994331067581, 184.11690265578193], 'a2': [-2.5413812651491097, 4.401801472641931], 'a3': [0.0, 0.0], 'a4': [3.08276253029822, 5.339501330146107], 'a5': [20.9138126514911, -36.22378609235936], 'a6': [0.0, 0.0], 'a7': [-127.15867542417507, -25.25215365804061], 'a8': [-193.98630072715727, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.104180648217781, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [127.15867542417507, 25.25215365804061]]]], 'bad_primes': [3, 7], 'central_character': '63.37', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '220406881098286352787655416529', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.5413812651491097, -4.401801472641931], [-16.0, -27.712812921102035]], [[1.0, 0], [0, 0]], [[1.0, 0], [-20.9138126514911, 36.22378609235936], [-1562.5, 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'6.86895219639836137764741346849235', '8.818165706125496889832270657626767', '10.00006840313375839032572918112881', '10.54776121950410922423217440206517', '11.92844222642365824583954889326702', '12.86646995168249289393100286301422', '14.36978427380195443985950356023616'], 'prelabel': '2-63-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.5422276407538825, 'root_number': '-0.13227326352094587 + 0.9912132887312994*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.271113820377', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98629366673045850786259681431', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34937414094138546247709352559', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.80111432001345467078370952337', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.104180648217781, 'bad_primes': [3, 7], 'central_character': '7.2', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/6/e/d/37/1'], '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': '2-63-7.2-c5-0-11', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-63-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.27111382037694126, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98629366673045850786259681431', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2517926358860396380521710174012', 'Lhash_array': ['2517926358860396380521710174012'], 'label': '2-63-7.2-c5-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/6/e/d/37/1'}