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lfunc_lfunctions • Show schema
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{'Lhash': '2342749057706344448071510830648', 'a10': [0.0, 0.0], 'a2': [-0.9090389553440874, 1.0833504408394037], 'a3': [0.0, 0.0], 'a4': [-0.3472963553338607, -1.969615506024416], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [2.449489742783178, 1.4142135623730951], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.174306050978972, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9090389553440874, -1.0833504408394037]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '648.35', 'coefficient_field': 'CDF', 'conductor': 648, 'conductor_radical': 6, 'conjugate': '305337032132545052983443955694', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9090389553440874, -1.0833504408394037]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [3.83022221559489, 3.2139380484326967]], [[1.0, 0], [0, 0], [6.5778483455013586, 2.3941410032796813]], [[1.0, 0], [2.1889281422492397, 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False, 'root_analytic_conductor': 2.2747101026238425, 'root_angle': 0.5770117372157925, 'root_number': '-0.23958609581803014 + 0.9708751220886617*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.288505868608', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84810314236789930441772259335', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76845288684522660434529357865', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27324542921197969843080313821', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.174306050978972, 'bad_primes': [2, 3], 'central_character': '216.11', 'conductor': 648, 'conductor_radical': 6, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/648/2/v/a/35/1'], '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': '2-648-216.11-c1-0-27', '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': '2-648-216.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2747101026238425, 'root_angle': 0.28850586860789623, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84810314236789930441772259335', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2342749057706344448071510830648', 'Lhash_array': ['2342749057706344448071510830648'], 'label': '2-648-216.11-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/648/2/v/a/35/1'}