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lfunc_lfunctions • Show schema
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{'Lhash': '1734104998940939592588115237499', 'a10': [1.4384471871911697, 0.0], 'a2': [2.5615528128088303, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.4384471871911697, 0.0], 'a5': [0.5615528128088303, 0.0], 'a6': [0.0, 0.0], 'a7': [-18.177080940897135, 0.0], 'a8': [-24.177080940897135, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.5615528128088303, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5615528128088303, 0], [125.0, 0]], [[1.0, 0], [18.177080940897135, 0], [343.0, 0]], [[1.0, 0], [-64.73863375370597, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-25.546397817750115, 0], [4913.0, 0]], [[1.0, 0], 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'3.72241947582491897860110102450869', '4.23475697782100907485617697516566', '5.49901558430668191371463091425324', '6.06558753781027741166273109450136', '6.80309779537962226015820848108727', '7.78841939270955392669352595838404', '9.010070294823792919159932014861215'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36796763921283132514883258952', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91147160643551037658633816821', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72241947582491897860110102451', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 149, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/r/1/2'], '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': '2-39e2-1.1-c3-0-149', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36796763921283132514883258952', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1734104998940939592588115237499', 'Lhash_array': ['1734104998940939592588115237499'], 'label': '2-39e2-1.1-c3-0-149', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/r/1/2'}