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lfunc_lfunctions • Show schema
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{'Lhash': '988728773259940560532789105002', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 1.4142135623730951], 'a4': [0.0, 0.0], 'a5': [-0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [-0.724744871391589, -1.255294939775204], 'a8': [0.0, 0.0], 'a9': [-1.0, 2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.599383156425752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, -1.4142135623730951]]]], 'bad_primes': [2, 3], 'central_character': '576.193', 'coefficient_field': 'CDF', 'conductor': 576, 'conductor_radical': 6, 'conjugate': '2640815139947833637651008332849', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, -1.4142135623730951]], [[1.0, 0], [0.5, -0.8660254037844386], [-2.5, -4.330127018922194]], [[1.0, 0], [0.724744871391589, 1.255294939775204], [-3.5, 6.06217782649107]], [[1.0, 0], [-1.724744871391589, -2.987345747344081], [-5.5, 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'root_angle': -0.6140487742528296, 'root_number': '-0.3506778225230657 - 0.9364961637884489*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.307024387126', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77996947509189724206880637229', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48120016549726666044315873454', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41686170466394717851233553985', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.599383156425752, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 576, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/576/2/i/m/193/2'], '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': '2-24e2-9.4-c1-0-4', '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': '2-24e2-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.144617251731822, 'root_angle': -0.3070243871264148, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77996947509189724206880637229', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '988728773259940560532789105002', 'Lhash_array': ['988728773259940560532789105002'], 'label': '2-24e2-9.4-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/576/2/i/m/193/2'}