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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -4, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '906478665263567321,1588924079463638771', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-1.788854381999832, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.07345251881810042, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]]], 'bad_primes': [2, 3], 'central_character': '1152.1', 'coefficient_field': '1.1.1.1', 'conductor': 1152, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1, 4, 14, 20, 25], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, 4, 30, 52, 169], [1, -4, 38, -68, 289], [1, 0, 22, 0, 361], [1, 0, -18, 0, 529], [1, -12, 94, -348, 841], [1, 0, -2, 0, 961], [1, -12, 110, -444, 1369], [1, 12, 118, 492, 1681], [1, 0, 70, 0, 1849], [1, 0, 94, 0, 2209], [1, 4, 110, 212, 2809], [1, 0, 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0.844180116048717, 1.3019268906372985, 1.7584235867408553, 2.1560622091278567, 2.4430542717322816], 'positive_zeros': ['3.14826068230388029805668446658192', '4.25303028692796488061253338186834', '5.01357758335939619070346679817703', '6.42897107072744719896577758454500', '7.26958585488936859387169650645128', '8.098990694093691505068092710868270', '8.173282349834764667604075089133192', '9.656797755147918818405236990829344', '9.964671915727173343349228861429439', '11.02059068705223596291987853205165', '11.58204746144152243175303945055362', '12.31725686074733747032880351584204', '12.32215863397544621963398389319428', '13.40929752839485230085938675600611', '14.18198826155077042068868714860043'], 'prelabel': '4-1152-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5205970145886866, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 189559735513512141, 'z1': {'__RealLiteral__': 0, 'data': '3.14826068230388029805668446658192', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '4.25303028692796488061253338186834', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.01357758335939619070346679817703', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.07345251881810042, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 1152, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -4, 0, 0, 0, 1, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, -12, 0, 0, 0, -4, 0, 0, 0, -14, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -16, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 4, 30, 52, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -18, 0, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, -12, 110, -444, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 4, 14, 20, 25], 'euler53': [1, 4, 110, 212, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 0, 78, 0, 5041], 'euler73': [1, -20, 246, -1460, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, 150, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, 4, 14, 20, 25], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, 4, 30, 52, 169], [1, -4, 38, -68, 289], [1, 0, 22, 0, 361], [1, 0, -18, 0, 529], [1, -12, 94, -348, 841], [1, 0, -2, 0, 961], [1, -12, 110, -444, 1369], [1, 12, 118, 492, 1681], [1, 0, 70, 0, 1849], [1, 0, 94, 0, 2209], [1, 4, 110, 212, 2809], [1, 0, 102, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, 118, 0, 4489], [1, 0, 78, 0, 5041], [1, -20, 246, -1460, 5329], [1, 0, 94, 0, 6241], [1, 0, 150, 0, 6889], [1, 12, 214, 1068, 7921], [1, -4, 198, -388, 9409]], 'index': 0, 'instance_types': ['G2Q', 'BMF', 'ECNF'], 'instance_urls': ['Genus2Curve/Q/1152/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/72.1/a', 'EllipticCurve/2.0.4.1/72.1/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': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-1152-1.1-c1e2-0-0', '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': '4-1152-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5205970145886866, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 189559735513512141, 'z1': {'__RealLiteral__': 0, 'data': '3.14826068230388029805668446658192', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9736672
{'Lhash': '906478665263567321,1588924079463638771', 'Lhash_array': ['906478665263567321', '1588924079463638771'], 'label': '4-1152-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/72.1/a'}
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id: 9737128
{'Lhash': '906478665263567321,1588924079463638771', 'Lhash_array': ['906478665263567321', '1588924079463638771'], 'label': '4-1152-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/72.1/a'}
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id: 9952792
{'Lhash': '189559735513512141', 'Lhash_array': ['189559735513512141'], 'label': '4-1152-1.1-c1e2-0-0', 'type': 'ECQP', 'url': 'EllipticCurve/Q/24/a|EllipticCurve/Q/48/a'}
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id: 1223764
{'Lhash': '189559735513512141', 'Lhash_array': ['189559735513512141'], 'label': '4-1152-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/1152/a'}