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lfunc_lfunctions • Show schema
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{'Lhash': '2559885578888619915911367577510', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, -1.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.8660254037844386, -0.5], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.408734245346429, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.8660254037844386, 0.5]]], [13, [[1.0, 0], [0.8660254037844386, 0.5]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.46', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '1502636161600859661177692957103', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5, 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'positive_zeros': ['2.01939365502429053450448712524062', '3.07170183736791462023445336777086', '4.33702109191745518472809897414827', '5.06868123916336621326220287198530', '6.32081880523776641423373293889895', '7.44263098902453268022039894308742', '7.895346977098269944492767465347068', '8.920243341890646112675628599458760', '9.474683452929971466347792091887218', '10.81221757945136576433777930049262'], 'prelabel': '2-819-91.46-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6393232713943933, 'root_angle': 0.3452970502076801, 'root_number': '0.46710487103774756852190277525830 + 0.88420192233041950831646346306552*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17264852510384004', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.01939365502429053450448712524', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07170183736791462023445336777', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.33702109191745518472809897415', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.408734245346429, 'bad_primes': [3, 7, 13], 'central_character': '91.46', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/1/eu/a/46/1'], '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': '2-819-91.46-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-819-91.46-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6393232713943933, 'root_angle': 0.17264852510384004, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.01939365502429053450448712524', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2559885578888619915911367577510', 'Lhash_array': ['2559885578888619915911367577510'], 'label': '2-819-91.46-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/1/eu/a/46/1'}