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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 1, 'A4': 1, 'A5': -1, 'A6': -1, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '1901733098284869388', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 434.3063365937442, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [5, [1, 1]], [7, [1]], [37, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 37], 'central_character': '54390.1', 'coefficient_field': '1.1.1.1', 'conductor': 54390, 'conductor_radical': 7770, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1, 1], [1], [1, -3, 11], [1, 6, 13], [1, -3, 17], [1, -6, 19], [1, 1, 23], [1, -3, 29], [1, 0, 31], [1, 1], [1, -9, 41], [1, -2, 43], [1, 13, 47], [1, -1, 53], [1, 3, 59], [1, -3, 61], [1, -3, 67], [1, -16, 71], [1, 6, 73], [1, 5, 79], [1, 17, 83], [1, -12, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 58, 'label': '2-54390-1.1-c1-0-58', 'leading_term': '5.36457534594', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/54390/u', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.227855872592227, 1.804052978190302, 1.324517453586666, 0.07583718862347144, -0.8655348239559233, -0.4256475327621404, 1.2765486037772, 2.708973768667673, 2.373519091002785, 0.6285399993010323, -0.4187494186248751, 0.6294536963902205, 2.419516589650372, 2.232019431500864, -0.3137777819693294, -2.082925567685553, -0.1749397306490853, 3.75627670029303, 4.907431540009494, 1.618802992246288, -1.761279592181962, -0.2049959806650906, 5.057421120190517, 7.77831617662563, 4.903910945807594, 0.3701086017564186, 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0.963840914376887, 0.644375653590966, -0.3932854463262787, 0.02983888645425948, -0.9254845194450411, -3.76270197890435, -2.897417237089709, 1.68505933183734, 2.143535550670306, -1.633156591817465, -0.8022313093029476, 3.944208599551738, 2.666265051104217, -3.107222907147556, -2.641156040175072, 1.486792631474326, -2.34153154805781, -10.80957087539092, -10.86614392609452, -3.665865931529194, 0.01386424699782147, -0.05454920445091245, 1.498146000351795, 2.034134119589658, -0.9716051616584668, -2.059649412538614, 0.5221165977862338, 0.8985909877230098, -1.418290304373007, -1.230557983504082, 0.434135628377467, -0.1262369257570748, -0.3930647074139673, 1.046481502677724, 0.2190611011252471, -1.473288704357189, 1.422452484913672, 4.832859801812204, 1.924400429650673, -1.963211508614092, -0.3057703374190878, 1.157994478000745, -1.440894792789556, -1.356890324381542], 'positive_zeros': ['1.014516831200962', '1.574754205342636', '2.599753168710671', '2.903631517043632', '3.722784680442806', '4.261871022603437', '5.094749646297035', '5.511775418886331', '6.530128946563272', '6.874409773064345', '7.559585511455676', '7.833351393345454', '8.345665036434130', '9.129772213615202', '9.552896824088995', '9.805411591289028', '10.37984096135527', '11.17278511019923', '11.60539552725396', '12.18611347420812', '12.38725639148488', '13.07221781288403', '13.94855391671909', '14.21893158501398', '14.77517094484527', '15.00000917936089', '15.86045343982895', '16.14899526269956', '16.57239332547391', '17.32015045554675', '17.49598311598343', '18.11872082306040', '18.73681636159567', '19.09054143444106', '19.61989862037022', '19.98394397189989'], 'prelabel': '2-54390-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.840017672587138, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1901733098284869388, 'z1': {'__RealLiteral__': 0, 'data': '1.014516831200962', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.574754205342636', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.599753168710671', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 434.3063365937442, 'bad_primes': [2, 3, 5, 7, 37], 'central_character': '1.1', 'conductor': 54390, 'conductor_radical': 7770, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, -1, -1, 0, -1, 1, 1, 3, 1, -6, 0, -1, 1, 3, -1, 6, -1, 0, -3, -1, -1, 1, 6, 1, 0, 3, 1, 0, -1, 3, -3, 0, 1, -1, -6, -6, 1, 9, 0, 2, 3, -1, 1, -13, 1, 0, -1, 3, -6, 1, -1, -3, 0, 6, -3, -3, -1, 3, 0, 0, 1, 6, -3, 3, 3, -1, 0, 16, -1, -6, 1, 1, 6, 0, 6, -5, -1, 1, -9, -17, 0, -3, -2, 3, -3, 12, 1, 0, -1, 0, 13, -6, -1, -8, 0, 3, 1], 'euler11': [1, -3, 11], 'euler13': [1, 6, 13], 'euler17': [1, -3, 17], 'euler19': [1, -6, 19], 'euler2': [1, 1, 0], 'euler23': [1, 1, 23], 'euler29': [1, -3, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 1, 0], 'euler41': [1, -9, 41], 'euler43': [1, -2, 43], 'euler47': [1, 13, 47], 'euler5': [1, 1, 0], 'euler53': [1, -1, 53], 'euler59': [1, 3, 59], 'euler61': [1, -3, 61], 'euler67': [1, -3, 67], 'euler7': [1, 0, 0], 'euler71': [1, -16, 71], 'euler73': [1, 6, 73], 'euler79': [1, 5, 79], 'euler83': [1, 17, 83], 'euler89': [1, -12, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 1, 0], [1, 0, 0], [1, -3, 11], [1, 6, 13], [1, -3, 17], [1, -6, 19], [1, 1, 23], [1, -3, 29], [1, 0, 31], [1, 1, 0], [1, -9, 41], [1, -2, 43], [1, 13, 47], [1, -1, 53], [1, 3, 59], [1, -3, 61], [1, -3, 67], [1, -16, 71], [1, 6, 73], [1, 5, 79], [1, 17, 83], [1, -12, 89], [1, 8, 97]], 'index': 58, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/54390/u'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-54390-1.1-c1-0-58', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-54390-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.840017672587138, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1901733098284869388, 'z1': {'__RealLiteral__': 0, 'data': '1.014516831200962', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1901733098284869388', 'Lhash_array': ['1901733098284869388'], 'label': '2-54390-1.1-c1-0-58', 'type': 'ECQ', 'url': 'EllipticCurve/Q/54390/u'}