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lfunc_lfunctions • Show schema
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{'Lhash': '689804940669540524897591691470', 'a10': [0.0, 0.0], 'a2': [0.45066642319171424, -0.7805771422333861], 'a3': [-1.6088595251733315, -0.6415380177815203], 'a4': [0.5937995500151734, 1.028490990137817], 'a5': [0.0, 0.0], 'a6': [-1.2258288801817554, 0.9667193265996614], 'a7': [-2.6436471233425354, -0.10549828075726309], 'a8': [2.8730877699596076, 0.0], 'a9': [2.1768579434819153, 2.064289101337234], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.192146106117222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.6088595251733315, 0.6415380177815203]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.6436471233425354, 0.10549828075726309]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.299', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'conjugate': '2234099872636750101981773937803', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.45066642319171424, 0.7805771422333861], [-1.0, 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[-0.21434383617916988, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-525-105.89-c1-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/525/2/q/g/299/13', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9390654179327034, 0.7692955004531372, 0.5781212828361013, 0.3578507280281954, 0.10080798914534946, -0.19902571985318152, -0.5445864141782573, -0.9346038472881133, -1.362803104403503, -1.8174528896315392, -2.2813073373588932, -2.732007092841721, -3.1430021837497324, -3.485030771398936, -3.7281375388284603, -3.844149478249888, -3.809453214535386, -3.6078462771590987, -3.2331755645412503, -2.6914405997594804, -2.002037078572537, -1.1978551726665516, -0.3240304333394186, 0.5647292805593138, 1.4081583754050961, 2.145529935978739, 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'7.74634623855530554884309639419791', '9.061835459584913961698504542441181', '10.08949735920607783407465859570880', '10.74767951667867477803441817984240'], 'prelabel': '2-525-105.89-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0474731026602577, 'root_angle': -0.34526460781730606, 'root_number': '0.46719498715689906 - 0.8841543100474402*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.172632303909', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.54416014992250007972419467253', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.79538109128827371094282708047', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27852549947121728234308838349', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.192146106117222, 'bad_primes': [3, 5, 7], 'central_character': '105.89', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/2/q/g/299/13'], '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': '2-525-105.89-c1-0-8', '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': '2-525-105.89-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0474731026602577, 'root_angle': -0.17263230390865303, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.54416014992250007972419467253', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '689804940669540524897591691470', 'Lhash_array': ['689804940669540524897591691470'], 'label': '2-525-105.89-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/2/q/g/299/13'}