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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 5, 'Lhash': '1413725931879682693897004010128', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [1.6666666666666667, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 51.02909710113032, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1, 3, 5]], [41, [1, 1, 41, 41]], [61, [1, -2, 58, 61]]], 'bad_primes': [2, 5, 41, 61], 'central_character': '800320.1', 'coefficient_field': '1.1.1.1', 'conductor': 800320, 'conductor_radical': 25010, 'degree': 4, 'euler_factors': [[1], [1, 0, -5, 0, 9], [1, -1, 3, 5], [1, 0, -10, 0, 49], [1, 0, 5, 0, 121], [1, -12, 62, -156, 169], [1, -5, 40, -85, 289], [1, 0, -32, 0, 361], [1, 0, 18, 0, 529], [1, -4, 58, -116, 841], [1, 0, 30, 0, 961], [1, 21, 184, 777, 1369], [1, 1, 41, 41], [1, 0, 41, 0, 1849], [1, 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0.08615304697055166, -0.48459805022099195, -1.210654189615027, -1.9631254538289804, -2.6109887869135666, -3.041247261009561, -3.1760331604371146], 'positive_zeros': ['1.11523311835702496158253562485953', '1.40628897199210914480781914949947', '1.99302602612246717545843835321984', '3.20707633685834028559904709708851', '3.45863745802712588196399639345825', '4.07172866143636139222097398660097', '4.28108882289940864842916454477621', '5.23349678651743309954780579446846', '5.59710797076793673100512138178044', '5.91441632932643969745087073459640', '6.58018193046949069737628023531035', '6.88427827452403242273004071673322', '7.17887758609772624441644062621924', '7.942313961823255569318744323019529', '8.288559563281819420350494292332020'], 'prelabel': '4-800320-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.672726200457916, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1827730688307557184, 'z1': {'__RealLiteral__': 0, 'data': '1.11523311835702496158253562485953', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.40628897199210914480781914949947', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '1.99302602612246717545843835321984', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 51.02909710113032, 'bad_primes': [2, 5, 41, 61], 'central_character': '1.1', 'conductor': 800320, 'conductor_radical': 25010, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 12, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -21, 0, 0, 0, -1, 0, 0, 0, 5, 0, 0, 0, 10, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 5, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0], 'euler11': [1, 0, 5, 0, 121], 'euler13': [1, -12, 62, -156, 169], 'euler17': [1, -5, 40, -85, 289], 'euler19': [1, 0, -32, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 18, 0, 529], 'euler29': [1, -4, 58, -116, 841], 'euler3': [1, 0, -5, 0, 9], 'euler31': [1, 0, 30, 0, 961], 'euler37': [1, 21, 184, 777, 1369], 'euler41': [1, 1, 41, 41, 0], 'euler43': [1, 0, 41, 0, 1849], 'euler47': [1, 0, -83, 0, 2209], 'euler5': [1, -1, 3, 5, 0], 'euler53': [1, -1, 86, -53, 2809], 'euler59': [1, 0, -56, 0, 3481], 'euler61': [1, -2, 58, 61, 0], 'euler67': [1, 0, 64, 0, 4489], 'euler7': [1, 0, -10, 0, 49], 'euler71': [1, 0, -6, 0, 5041], 'euler73': [1, 4, 134, 292, 5329], 'euler79': [1, 0, -3, 0, 6241], 'euler83': [1, 0, -112, 0, 6889], 'euler89': [1, 16, 193, 1424, 7921], 'euler97': [1, 7, -4, 679, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -5, 0, 9], [1, -1, 3, 5, 0], [1, 0, -10, 0, 49], [1, 0, 5, 0, 121], [1, -12, 62, -156, 169], [1, -5, 40, -85, 289], [1, 0, -32, 0, 361], [1, 0, 18, 0, 529], [1, -4, 58, -116, 841], [1, 0, 30, 0, 961], [1, 21, 184, 777, 1369], [1, 1, 41, 41, 0], [1, 0, 41, 0, 1849], [1, 0, -83, 0, 2209], [1, -1, 86, -53, 2809], [1, 0, -56, 0, 3481], [1, -2, 58, 61, 0], [1, 0, 64, 0, 4489], [1, 0, -6, 0, 5041], [1, 4, 134, 292, 5329], [1, 0, -3, 0, 6241], [1, 0, -112, 0, 6889], [1, 16, 193, 1424, 7921], [1, 7, -4, 679, 9409]], 'index': 1, 'instance_types': ['BMF', 'BMF', 'ECNF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/50020.7/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/50020.2/a', 'EllipticCurve/2.0.4.1/50020.7/b', 'EllipticCurve/2.0.4.1/50020.2/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': '4-800320-1.1-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': '4-800320-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.672726200457916, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1827730688307557184, 'z1': {'__RealLiteral__': 0, 'data': '1.11523311835702496158253562485953', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9696657
{'Lhash': '1413725931879682693897004010128', 'Lhash_array': ['1413725931879682693897004010128'], 'label': '4-800320-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/50020.2/a'}
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id: 9696581
{'Lhash': '1413725931879682693897004010128', 'Lhash_array': ['1413725931879682693897004010128'], 'label': '4-800320-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/50020.7/b'}
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id: 9696128
{'Lhash': '1413725931879682693897004010128', 'Lhash_array': ['1413725931879682693897004010128'], 'label': '4-800320-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/50020.2/a'}
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id: 9695416
{'Lhash': '1413725931879682693897004010128', 'Lhash_array': ['1413725931879682693897004010128'], 'label': '4-800320-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/50020.7/b'}