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lfunc_lfunctions • Show schema
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{'Lhash': '3148031125513573942404559604944', 'a10': [3.0, 6.223015277861142e-61], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, -0.8660254037844386], 'a5': [-1.5, -2.598076211353316], 'a6': [0.0, 0.0], 'a7': [-0.5, 0.8660254037844386], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.127', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '2781717273802398972337870016212', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5, 2.598076211353316], [-2.5, 4.330127018922194]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [3.0, -5.196152422706632], [-5.5, 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1.208626381348464, 0.45147820477011474, -0.8429314114506097, -2.331001372246801], 'positive_zeros': ['2.48335868333655857253174963386762', '3.41515839077614286366190499299631', '4.57197135055793564194285155867987', '6.31597036463547930931719513458865', '7.08339702267189722087157721418581', '8.250330189856184009945970807373344', '8.905452988034738469766559974725993', '10.37963010064293986895324906345425', '10.90450564140489019519298308146176'], 'prelabel': '2-378-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.8888888888888888, 'root_number': '-0.9396926207859083 + 0.3420201433256689*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.444444444444', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.48335868333655857253174963387', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.41515839077614286366190499300', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.57197135055793564194285155868', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '9.7', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/f/a/127/1'], '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': '2-378-9.7-c1-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-378-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.4444444444444444, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.48335868333655857253174963387', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3148031125513573942404559604944', 'Lhash_array': ['3148031125513573942404559604944'], 'label': '2-378-9.7-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/f/a/127/1'}