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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': -3, 'A5': 0, 'A6': 0, 'A7': -6, 'A8': 0, 'A9': 1, 'Lhash': '4237173508544063636651108775687', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [-1.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-2.2677868380553634, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2174883174379692, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 2, 3]], [379, [1, 12, 390, 379]]], 'bad_primes': [3, 379], 'central_character': '3411.1', 'coefficient_field': '1.1.1.1', 'conductor': 3411, 'conductor_radical': 1137, 'degree': 4, 'euler_factors': [[1, 0, 3, 0, 4], [1, 2, 3], [1, 0, -1, 0, 25], [1, 6, 19, 42, 49], [1, 0, -3, 0, 121], [1, -5, 30, -65, 169], [1, 0, -4, 0, 289], [1, 9, 52, 171, 361], [1, 0, -2, 0, 529], [1, 0, -16, 0, 841], [1, -2, 62, -62, 961], [1, 16, 138, 592, 1369], [1, 0, -19, 0, 1681], [1, 3, 82, 129, 1849], [1, 0, -55, 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1.4794379203632448, 2.06537658537851, 2.4679396659087494], 'positive_zeros': ['3.34254052952856063975225663394009', '4.03936375515308084295939588308768', '5.01094266926562858529869899608945', '5.89846952311957618693090452483102', '6.41170868431526283729680636959164', '6.84996672400503775780963825268373', '8.368184913151009783371565215147437', '8.761020043918534300736028943085218', '9.298818815832352824793294835629138', '10.09884140552019139191044688155567', '10.47881770793489996875163931921055', '11.02103899512350083464916962730841', '12.05468628216561216405853219287227', '12.52904316215616694165779948271568'], 'prelabel': '4-3411-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6829029414675669, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1089164867145581850, 'z1': {'__RealLiteral__': 0, 'data': '3.34254052952856063975225663394009', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '4.03936375515308084295939588308768', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.01094266926562858529869899608945', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2174883174379692, 'bad_primes': [3, 379], 'central_character': '1.1', 'conductor': 3411, 'conductor_radical': 1137, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, -3, 0, 0, -6, 0, 1, 0, 0, 6, 5, 0, 0, 5, 0, 0, -9, 0, 12, 0, 0, 0, 1, 0, 4, 18, 0, 0, 2, 0, 0, 0, 0, -3, -16, 0, -10, 0, 0, 0, -3, 0, 0, 0, 0, -10, 17, 0, 0, -15, 0, 0, 0, 0, 18, 0, 0, 0, -6, 0, -6, -3, 0, 0, -1, 0, 0, 0, 0, 0, 5, 0, -2, 27, 0, 0, 2, 0, -11, 0, 0, -36, 0, 0, 0, 0, 0, 0, -30, 0, -4, 0, 0, 0, 5, 0, 0, -3], 'euler11': [1, 0, -3, 0, 121], 'euler13': [1, -5, 30, -65, 169], 'euler17': [1, 0, -4, 0, 289], 'euler19': [1, 9, 52, 171, 361], 'euler2': [1, 0, 3, 0, 4], 'euler23': [1, 0, -2, 0, 529], 'euler29': [1, 0, -16, 0, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, -2, 62, -62, 961], 'euler37': [1, 16, 138, 592, 1369], 'euler41': [1, 0, -19, 0, 1681], 'euler43': [1, 3, 82, 129, 1849], 'euler47': [1, 0, -55, 0, 2209], 'euler5': [1, 0, -1, 0, 25], 'euler53': [1, 0, -40, 0, 2809], 'euler59': [1, 0, -109, 0, 3481], 'euler61': [1, 6, 115, 366, 3721], 'euler67': [1, 1, 104, 67, 4489], 'euler7': [1, 6, 19, 42, 49], 'euler71': [1, 0, -121, 0, 5041], 'euler73': [1, -5, 96, -365, 5329], 'euler79': [1, -2, 78, -158, 6241], 'euler83': [1, 0, 50, 0, 6889], 'euler89': [1, 0, 10, 0, 7921], 'euler97': [1, -5, 188, -485, 9409], 'euler_factors': [[1, 0, 3, 0, 4], [1, 2, 3, 0, 0], [1, 0, -1, 0, 25], [1, 6, 19, 42, 49], [1, 0, -3, 0, 121], [1, -5, 30, -65, 169], [1, 0, -4, 0, 289], [1, 9, 52, 171, 361], [1, 0, -2, 0, 529], [1, 0, -16, 0, 841], [1, -2, 62, -62, 961], [1, 16, 138, 592, 1369], [1, 0, -19, 0, 1681], [1, 3, 82, 129, 1849], [1, 0, -55, 0, 2209], [1, 0, -40, 0, 2809], [1, 0, -109, 0, 3481], [1, 6, 115, 366, 3721], [1, 1, 104, 67, 4489], [1, 0, -121, 0, 5041], [1, -5, 96, -365, 5329], [1, -2, 78, -158, 6241], [1, 0, 50, 0, 6889], [1, 0, 10, 0, 7921], [1, -5, 188, -485, 9409]], 'index': 1, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/379.2/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/379.2/a', 'EllipticCurve/2.0.3.1/379.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/379.1/a'], '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': '4-3411-1.1-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': 1, 'prelabel': '4-3411-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6829029414675669, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1089164867145581850, 'z1': {'__RealLiteral__': 0, 'data': '3.34254052952856063975225663394009', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9760188
{'Lhash': '4237173508544063636651108775687', 'Lhash_array': ['4237173508544063636651108775687'], 'label': '4-3411-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/379.1/a'}
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id: 9760034
{'Lhash': '4237173508544063636651108775687', 'Lhash_array': ['4237173508544063636651108775687'], 'label': '4-3411-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/379.1/a'}
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id: 9759687
{'Lhash': '4237173508544063636651108775687', 'Lhash_array': ['4237173508544063636651108775687'], 'label': '4-3411-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/379.2/a'}
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id: 9759372
{'Lhash': '4237173508544063636651108775687', 'Lhash_array': ['4237173508544063636651108775687'], 'label': '4-3411-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/379.2/a'}