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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 1, 'A9': 2, 'Lhash': '1342000322552882875331031939735', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.097221779792148, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [7, [1, 0, 7]], [11, [1, 0, -1]]], 'bad_primes': [2, 7, 11], 'central_character': '189728.1', 'coefficient_field': '1.1.1.1', 'conductor': 189728, 'conductor_radical': 154, 'degree': 4, 'euler_factors': [[1, -1], [1, 0, -2, 0, 9], [1, 0, -10, 0, 25], [1, 0, 7], [1, 0, -1], [1, 0, -18, 0, 169], [1, 0, -26, 0, 289], [1, 0, 6, 0, 361], [1, 0, -18, 0, 529], [1, 4, 62, 116, 841], [1, 0, -10, 0, 961], [1, 4, 78, 148, 1369], [1, 0, -74, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, 86, 0, 2209], [1, -28, 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-0.6518938931234997, 0.11627519423112997, 0.8134866859658924, 1.3294620632703507], 'positive_zeros': ['1.05865158925595700954317475020749', '2.01705469370341431396968543751068', '2.75386392283221271014365340677569', '3.43901875101765770181944718210923', '4.01880193632796957500043528001332', '4.55978687407873991200208708116152', '5.13419306901755155276020089857699', '5.55424893264437314769560336816017', '6.15586689609603382481791658368099', '6.84693669503363575874611229047612', '7.07845764333392661979449060344873', '7.44090205001602193090431329743704', '8.282024530209696904037410734491168', '8.550966502145525084864492626185337', '9.138355316340654241373080875062970'], 'prelabel': '4-189728-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8649681129131175, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1389012372760077, 'z1': {'__RealLiteral__': 0, 'data': '1.05865158925595700954317475020749', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.01705469370341431396968543751068', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.75386392283221271014365340677569', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.097221779792148, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 189728, 'conductor_radical': 154, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -4, 0, 0, 1, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 10, 0, 0, 28, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 10], 'euler11': [1, 0, -1, 0, 0], 'euler13': [1, 0, -18, 0, 169], 'euler17': [1, 0, -26, 0, 289], 'euler19': [1, 0, 6, 0, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, -18, 0, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 0, -10, 0, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 0, -74, 0, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, 86, 0, 2209], 'euler5': [1, 0, -10, 0, 25], 'euler53': [1, -28, 302, -1484, 2809], 'euler59': [1, 0, 46, 0, 3481], 'euler61': [1, 0, -50, 0, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, 7, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 54, 0, 5329], 'euler79': [1, 0, -98, 0, 6241], 'euler83': [1, 0, -122, 0, 6889], 'euler89': [1, 0, -50, 0, 7921], 'euler97': [1, 0, 94, 0, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 0, -2, 0, 9], [1, 0, -10, 0, 25], [1, 0, 7, 0, 0], [1, 0, -1, 0, 0], [1, 0, -18, 0, 169], [1, 0, -26, 0, 289], [1, 0, 6, 0, 361], [1, 0, -18, 0, 529], [1, 4, 62, 116, 841], [1, 0, -10, 0, 961], [1, 4, 78, 148, 1369], [1, 0, -74, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, 86, 0, 2209], [1, -28, 302, -1484, 2809], [1, 0, 46, 0, 3481], [1, 0, -50, 0, 3721], [1, 0, 118, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, 54, 0, 5329], [1, 0, -98, 0, 6241], [1, 0, -122, 0, 6889], [1, 0, -50, 0, 7921], [1, 0, 94, 0, 9409]], 'index': 8, 'instance_types': ['ECNF', 'BMF', 'BMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.0.7.1/3872.5/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/3872.14/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/3872.5/d', 'EllipticCurve/2.0.7.1/3872.14/d'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-189728-1.1-c1e2-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-189728-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8649681129131175, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1389012372760077, 'z1': {'__RealLiteral__': 0, 'data': '1.05865158925595700954317475020749', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9638076
{'Lhash': '1342000322552882875331031939735', 'Lhash_array': ['1342000322552882875331031939735'], 'label': '4-189728-1.1-c1e2-0-8', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/3872.14/d'}
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id: 9637815
{'Lhash': '1342000322552882875331031939735', 'Lhash_array': ['1342000322552882875331031939735'], 'label': '4-189728-1.1-c1e2-0-8', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/3872.5/d'}
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id: 9637755
{'Lhash': '1342000322552882875331031939735', 'Lhash_array': ['1342000322552882875331031939735'], 'label': '4-189728-1.1-c1e2-0-8', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/3872.14/d'}
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id: 9637562
{'Lhash': '1342000322552882875331031939735', 'Lhash_array': ['1342000322552882875331031939735'], 'label': '4-189728-1.1-c1e2-0-8', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/3872.5/d'}