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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -4, 'Lhash': '1425559434695546253551043585675', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.611670552024722, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [7, [1, 0, -1]], [17, [1, 2, 17]]], 'bad_primes': [2, 7, 17], 'central_character': '56644.1', 'coefficient_field': '1.1.1.1', 'conductor': 56644, 'conductor_radical': 238, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, 0, 4, 0, 9], [1, 0, -4, 0, 25], [1, 0, -1], [1, 0, -4, 0, 121], [1, -6, 34, -78, 169], [1, 2, 17], [1, -6, 46, -114, 361], [1, 0, -30, 0, 529], [1, 0, 16, 0, 841], [1, 0, 10, 0, 961], [1, 0, -16, 0, 1369], [1, 0, 66, 0, 1681], [1, -4, 54, -172, 1849], [1, 4, 62, 188, 2209], [1, -4, 46, -212, 2809], [1, 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3.9084337444517327, 3.8979925213883484, 3.481736599657995, 2.733414766608217, 1.7818500465657463], 'positive_zeros': ['1.12456810610028248142942155042087', '2.33544513817312020241594604877419', '3.15975507943514566352418698190542', '3.56197239650088456581969530402147', '4.50012905256360902366657811456199', '5.36365823075046758414969005609549', '5.69733939940589390360289879976886', '6.33636412935708458449486201354398', '6.74533334945065280154032721832791', '7.44346269170023091679455439481441', '8.069518567281400568465291177137682', '8.452125071981328787779137017900777', '8.964498816962928487035486683895553', '9.377784940033828757275953165273422', '10.01369863191046656342482592275808'], 'prelabel': '4-238e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.37856431409872, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 523998570114934980, 'z1': {'__RealLiteral__': 0, 'data': '1.12456810610028248142942155042087', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.33544513817312020241594604877419', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.15975507943514566352418698190542', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.611670552024722, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 56644, 'conductor_radical': 238, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 0, 0, -4, 0, 0, 0, 6, 0, 0, 1, -2, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 1, 0, 0, 6, 4, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 1, 0, 0, 8, -2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 7, 0, 22, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], 'euler11': [1, 0, -4, 0, 121], 'euler13': [1, -6, 34, -78, 169], 'euler17': [1, 2, 17, 0, 0], 'euler19': [1, -6, 46, -114, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 0, -30, 0, 529], 'euler29': [1, 0, 16, 0, 841], 'euler3': [1, 0, 4, 0, 9], 'euler31': [1, 0, 10, 0, 961], 'euler37': [1, 0, -16, 0, 1369], 'euler41': [1, 0, 66, 0, 1681], 'euler43': [1, -4, 54, -172, 1849], 'euler47': [1, 4, 62, 188, 2209], 'euler5': [1, 0, -4, 0, 25], 'euler53': [1, -4, 46, -212, 2809], 'euler59': [1, 6, 78, 354, 3481], 'euler61': [1, 0, 28, 0, 3721], 'euler67': [1, -8, 134, -536, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 0, 86, 0, 5041], 'euler73': [1, 0, 126, 0, 5329], 'euler79': [1, 0, 38, 0, 6241], 'euler83': [1, -22, 286, -1826, 6889], 'euler89': [1, 12, 198, 1068, 7921], 'euler97': [1, 0, -94, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 0, 4, 0, 9], [1, 0, -4, 0, 25], [1, 0, -1, 0, 0], [1, 0, -4, 0, 121], [1, -6, 34, -78, 169], [1, 2, 17, 0, 0], [1, -6, 46, -114, 361], [1, 0, -30, 0, 529], [1, 0, 16, 0, 841], [1, 0, 10, 0, 961], [1, 0, -16, 0, 1369], [1, 0, 66, 0, 1681], [1, -4, 54, -172, 1849], [1, 4, 62, 188, 2209], [1, -4, 46, -212, 2809], [1, 6, 78, 354, 3481], [1, 0, 28, 0, 3721], [1, -8, 134, -536, 4489], [1, 0, 86, 0, 5041], [1, 0, 126, 0, 5329], [1, 0, 38, 0, 6241], [1, -22, 286, -1826, 6889], [1, 12, 198, 1068, 7921], [1, 0, -94, 0, 9409]], 'index': 1, 'instance_types': ['ECNF', 'ECNF', 'HMF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.17.1/196.1/c', 'EllipticCurve/2.2.17.1/196.1/e', 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-196.1-e', 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-196.1-c'], 'is_instance_Artin': False, 'is_instance_BMF': False, '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': '4-238e2-1.1-c1e2-0-1', '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': '4-238e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.37856431409872, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 523998570114934980, 'z1': {'__RealLiteral__': 0, 'data': '1.12456810610028248142942155042087', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9489932
{'Lhash': '1425559434695546253551043585675', 'Lhash_array': ['1425559434695546253551043585675'], 'factors': ['4-238e2-1.1-c1e2-0-1'], 'label': '4-238e2-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-196.1-c'}
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id: 9489833
{'Lhash': '1425559434695546253551043585675', 'Lhash_array': ['1425559434695546253551043585675'], 'factors': ['4-238e2-1.1-c1e2-0-1'], 'label': '4-238e2-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-196.1-e'}
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id: 9489831
{'Lhash': '1425559434695546253551043585675', 'Lhash_array': ['1425559434695546253551043585675'], 'factors': ['4-238e2-1.1-c1e2-0-1'], 'label': '4-238e2-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.17.1/196.1/e'}
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id: 9489827
{'Lhash': '1425559434695546253551043585675', 'Lhash_array': ['1425559434695546253551043585675'], 'factors': ['4-238e2-1.1-c1e2-0-1'], 'label': '4-238e2-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.17.1/196.1/c'}