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lfunc_lfunctions • Show schema
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{'Lhash': '2572039584246357374807028860338', 'a10': [-2.655045316662881, -6.553680978386612], 'a2': [0.36602540378443865, -1.3660254037844386], 'a3': [0.4482877360840268, 1.6730326074756159], 'a4': [-1.7320508075688772, -1.0], 'a5': [3.9903403353387263, -3.012836538574375], 'a6': [2.449489742783178, -5.755272054005115e-61], 'a7': [-5.534947526859684, -4.285365314055485], 'a8': [-2.0, 2.0], 'a9': [-2.598076211353316, 1.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.722085551566235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.36602540378443865, 1.3660254037844386]]], [3, [[1.0, 0], [-0.4482877360840268, -1.6730326074756159]]], [5, [[1.0, 0], [-3.9903403353387263, 3.012836538574375]]], [7, [[1.0, 0], [5.534947526859684, 4.285365314055485]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '210.67', 'coefficient_field': 'CDF', 'conductor': 210, 'conductor_radical': 210, 'conjugate': 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'positive_zeros': ['2.02898147469285633374841616308080', '3.57527433828007208905172680486929', '5.35548988323097417794575230690492', '6.45474567685517835841174390116857', '6.94618233376321694133092711042117', '8.282318397836358266628303250671035', '9.519708965119014342030231065233411', '10.02133655800746838515868771877503', '11.80103990826772877347003357480507', '12.49752079793126378030850539687790'], 'prelabel': '2-210-35.32-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': 0.514489201586451, 'root_number': '-0.04550345164203038 + 0.998964181484332*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.257244600793', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.02898147469285633374841616308', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.57527433828007208905172680487', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.35548988323097417794575230690', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.722085551566235, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.32', 'conductor': 210, 'conductor_radical': 210, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/210/3/v/a/67/7'], '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': '2-210-35.32-c2-0-13', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-210-35.32-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': 0.2572446007932255, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.02898147469285633374841616308', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2572039584246357374807028860338', 'Lhash_array': ['2572039584246357374807028860338'], 'label': '2-210-35.32-c2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/210/3/v/a/67/7'}