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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '916559162821447720795585024729', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.826951360517942, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 3]], [13, [1, -2, 1]]], 'bad_primes': [2, 3, 13], 'central_character': '389376.1', 'coefficient_field': '1.1.1.1', 'conductor': 389376, 'conductor_radical': 78, 'degree': 4, 'euler_factors': [[1], [1, 0, 3], [1, 0, -6, 0, 25], [1, 0, 10, 0, 49], [1, 0, 6, 0, 121], [1, -2, 1], [1, 0, -34, 0, 289], [1, 0, 2, 0, 361], [1, 0, 30, 0, 529], [1, 0, 6, 0, 841], [1, 0, 58, 0, 961], [1, -12, 110, -444, 1369], [1, 0, -46, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, 30, 0, 2209], [1, 0, 38, 0, 2809], [1, 0, 102, 0, 3481], [1, -20, 222, -1220, 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1.334033775103065, 1.4593461743418608, 1.2481384316175783, 0.6777239130501835], 'positive_zeros': ['0.72303769087193999777882316520360', '1.69700716249594300102508312051612', '2.69497732809296656017134883825688', '2.93644284879871507582036754109854', '3.71881926097417044047389251732682', '4.26544794148396911059189832207121', '4.88933286777764064689943008792999', '5.34431561740731235987198154637665', '5.93643016225762466699723255429159', '6.26064685202341561068211875645527', '6.77724896569408764166163605636256', '7.27713404731043592296087914733590', '7.905993200326771452323105466003984', '8.196622274861918133837480639755938', '8.683688373796292193134200727855990'], 'prelabel': '4-624e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.232188407399317, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2139862981908790450, 'z1': {'__RealLiteral__': 0, 'data': '0.72303769087193999777882316520360', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.69700716249594300102508312051612', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.69497732809296656017134883825688', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.826951360517942, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 389376, 'conductor_radical': 78, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, 0, -34, 0, 289], 'euler19': [1, 0, 2, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, 0, 6, 0, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 0, 58, 0, 961], 'euler37': [1, -12, 110, -444, 1369], 'euler41': [1, 0, -46, 0, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, 0, 38, 0, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, -20, 222, -1220, 3721], 'euler67': [1, 0, 130, 0, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 0, -114, 0, 5041], 'euler73': [1, 28, 342, 2044, 5329], 'euler79': [1, 0, 142, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, -142, 0, 7921], 'euler97': [1, -20, 294, -1940, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 3, 0, 0], [1, 0, -6, 0, 25], [1, 0, 10, 0, 49], [1, 0, 6, 0, 121], [1, -2, 1, 0, 0], [1, 0, -34, 0, 289], [1, 0, 2, 0, 361], [1, 0, 30, 0, 529], [1, 0, 6, 0, 841], [1, 0, 58, 0, 961], [1, -12, 110, -444, 1369], [1, 0, -46, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, 30, 0, 2209], [1, 0, 38, 0, 2809], [1, 0, 102, 0, 3481], [1, -20, 222, -1220, 3721], [1, 0, 130, 0, 4489], [1, 0, -114, 0, 5041], [1, 28, 342, 2044, 5329], [1, 0, 142, 0, 6241], [1, 0, 22, 0, 6889], [1, 0, -142, 0, 7921], [1, -20, 294, -1940, 9409]], 'index': 20, 'instance_types': ['HMF', 'HMF', 'ECNF', 'ECNF', 'ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-2704.1-v', 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-2704.1-c', 'EllipticCurve/2.2.12.1/2704.1/v', 'EllipticCurve/2.2.12.1/2704.1/c', 'EllipticCurve/2.0.3.1/43264.2/i', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/43264.2/m', 'EllipticCurve/2.0.3.1/43264.2/m', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/43264.2/i'], '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': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-624e2-1.1-c1e2-0-20', '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': '4-624e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.232188407399317, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2139862981908790450, 'z1': {'__RealLiteral__': 0, 'data': '0.72303769087193999777882316520360', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9768493
{'Lhash': '916559162821447720795585024729', 'Lhash_array': ['916559162821447720795585024729'], 'label': '4-624e2-1.1-c1e2-0-20', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/43264.2/i'}
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id: 9768253
{'Lhash': '916559162821447720795585024729', 'Lhash_array': ['916559162821447720795585024729'], 'label': '4-624e2-1.1-c1e2-0-20', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/43264.2/m'}
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id: 9767220
{'Lhash': '916559162821447720795585024729', 'Lhash_array': ['916559162821447720795585024729'], 'label': '4-624e2-1.1-c1e2-0-20', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/43264.2/m'}
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id: 9767218
{'Lhash': '916559162821447720795585024729', 'Lhash_array': ['916559162821447720795585024729'], 'label': '4-624e2-1.1-c1e2-0-20', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/43264.2/i'}
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id: 9576027
{'Lhash': '916559162821447720795585024729', 'Lhash_array': ['916559162821447720795585024729'], 'label': '4-624e2-1.1-c1e2-0-20', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/2704.1/c'}
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id: 9575510
{'Lhash': '916559162821447720795585024729', 'Lhash_array': ['916559162821447720795585024729'], 'label': '4-624e2-1.1-c1e2-0-20', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/2704.1/v'}
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id: 9575340
{'Lhash': '916559162821447720795585024729', 'Lhash_array': ['916559162821447720795585024729'], 'label': '4-624e2-1.1-c1e2-0-20', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-2704.1-c'}
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id: 9575245
{'Lhash': '916559162821447720795585024729', 'Lhash_array': ['916559162821447720795585024729'], 'label': '4-624e2-1.1-c1e2-0-20', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-2704.1-v'}