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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 1, 'A9': 0, 'Lhash': '800046091335540734', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 578.5161626441767, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1]], [7, [1, -1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '72450.1', 'coefficient_field': '1.1.1.1', 'conductor': 72450, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1, -1], [1], [1], [1, -1], [1, -4, 11], [1, 4, 13], [1, -4, 17], [1, 2, 19], [1, 1], [1, -6, 29], [1, 4, 31], [1, 2, 37], [1, -10, 41], [1, 12, 43], [1, 0, 47], [1, 4, 53], [1, -2, 59], [1, -10, 61], [1, 12, 67], [1, 6, 71], [1, 12, 73], [1, -2, 79], [1, 4, 83], [1, -10, 89], [1, 18, 97]], 'gamma_factors': [[], [0]], 'index': 121, 'label': '2-72450-1.1-c1-0-121', 'leading_term': '11.3123533745', '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/72450/ex', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.638568704272128, 4.163987693977768, 3.780533307263395, 1.733374362715212, -0.406853239645554, -0.8259529319663056, 0.7396741894144857, 2.482645966665632, 2.330129701049559, 0.3777340238113533, -1.04866912642223, -0.1925958046898283, 1.815110666201687, 2.356769890396506, 0.8594191302517967, -0.4260946960899318, 0.2666031897278308, 1.567653901927587, 1.141761701386795, -0.4707402258322953, -0.5558990129488147, 1.250862239713502, 1.979527856417889, 0.0713419763614357, -1.717505658173314, -0.6370757545979241, 1.262270586247128, 0.4018146025261265, -1.90652043450887, -1.294651653031604, 1.761628141148913, 1.858138874935098, -2.06800434685503, -3.835457878982641, 0.07568100278202879, 3.978144650651071, 1.913158894251367, -2.395582924758091, -1.918356170237874, 1.730287702076561, 1.654380925624379, -1.835495643199895, -2.047724467090938, 1.857323560287803, 3.654574157666602, 1.346981406525437, -0.3072362284818124, 0.4959982555798686, 0.2111912948652122, -1.523244387285524, -0.7941761546252311, 1.869726548695775, 1.493051768891589, -1.674451577353149, -2.288112936894208, 0.05183332631704823, 0.8268506081618743, -0.1882317206475737, 0.05561567988379186, -0.06182428810700163, -3.1104554382022, -4.839688259879776, -1.178774014765155, 2.669552213270938, 1.324012557621618, -0.5048718867629145, 1.897083584857017, 3.354700624186489, 0.3120115839039022, -0.7690334307713091, 2.44443057728016, 1.187143646243766, -6.690101881191227, -9.831201827056555, -3.789815722580687, 0.9706568782527764, -0.861526950655546, -1.877710370529501, 0.4763102419143191, -0.1565934981480826, -3.321764624717467, -2.349358721283565, 0.7802195739555728, -0.2397099118063072, -2.574967444452446, -1.179271525972646, 0.5906280247979622, -0.1539790607439707, 0.4877110973861177, 2.681486720119387, 1.519925786129928, -1.249768517275637, -0.5052301942366261, 0.7489936038224053, -1.326737945550203, -2.109892297401467, 0.6677517078461022, 1.341447547112805, -0.574167594916092, 0.1430274488238718, 1.043067151869853, -1.774555454290118, -1.624166248089884, 4.558001185621862, 5.948213201289604, -0.9131117490373214, -3.914710596757587, -0.1527783024837686, -0.170438470182971, -3.493844035436654, -1.22015880914983, 2.021049200483674, -1.246057749488041, -3.039889931382289, 2.499631585369545, 5.427689000736543, 1.196713757536453, -1.274831474686628, 0.1778851770291946, -0.03870869177923228], 'positive_zeros': ['1.190646361006802', '1.656147103184717', '2.545408789743150', '3.025081492597777', '3.878281200732706', '4.201277337644628', '4.920759846676297', '5.341072389062664', '6.007009670683534', '6.569597994648543', '7.041246399696004', '7.606789525861226', '8.131209677295109', '8.746481668302728', '9.348776181364855', '9.876216775220684', '10.37009794157873', '10.89061842742700', '11.64790120775689', '11.88250543910161', '12.28188888481851', '12.82297868138700', '13.36957535022359', '13.99417501021348', '14.44435914318853', '14.73240532297295', '14.99021867023336', '15.80712123530357', '16.37052980976178', '16.59418577563047', '17.27329813797799', '17.57337585873107', '18.04625557192054', '18.90410859317626', '19.17781327641899', '19.69591483692508', '19.98659524384117'], 'prelabel': '2-72450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.052362932655424, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 800046091335540734, 'z1': {'__RealLiteral__': 0, 'data': '1.190646361006802', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.656147103184717', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.545408789743150', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 578.5161626441767, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 72450, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 4, 0, -4, 1, 0, 1, 4, 0, -2, 0, 0, 4, -1, 0, 0, -4, 0, 1, 6, 0, -4, 1, 0, 4, 0, 0, -2, -2, 0, 0, 10, 0, -12, 4, 0, -1, 0, 0, 1, 0, 0, -4, -4, 0, 0, 1, 0, 6, 2, 0, 10, -4, 0, 1, 0, 0, -12, 4, 0, 0, -6, 0, -12, -2, 0, -2, 4, 0, 2, 0, 0, 10, -4, 0, 0, -12, 0, 4, 10, 0, -4, -1, 0, 0, 0, 0, -18, 1, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, 4, 13], 'euler17': [1, -4, 17], 'euler19': [1, 2, 19], 'euler2': [1, -1, 0], 'euler23': [1, 1, 0], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, -10, 41], 'euler43': [1, 12, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 4, 53], 'euler59': [1, -2, 59], 'euler61': [1, -10, 61], 'euler67': [1, 12, 67], 'euler7': [1, -1, 0], 'euler71': [1, 6, 71], 'euler73': [1, 12, 73], 'euler79': [1, -2, 79], 'euler83': [1, 4, 83], 'euler89': [1, -10, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 0, 0], [1, -1, 0], [1, -4, 11], [1, 4, 13], [1, -4, 17], [1, 2, 19], [1, 1, 0], [1, -6, 29], [1, 4, 31], [1, 2, 37], [1, -10, 41], [1, 12, 43], [1, 0, 47], [1, 4, 53], [1, -2, 59], [1, -10, 61], [1, 12, 67], [1, 6, 71], [1, 12, 73], [1, -2, 79], [1, 4, 83], [1, -10, 89], [1, 18, 97]], 'index': 121, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/72450/ex'], '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': '2-72450-1.1-c1-0-121', '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': '2-72450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.052362932655424, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 800046091335540734, 'z1': {'__RealLiteral__': 0, 'data': '1.190646361006802', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '800046091335540734', 'Lhash_array': ['800046091335540734'], 'label': '2-72450-1.1-c1-0-121', 'type': 'ECQ', 'url': 'EllipticCurve/Q/72450/ex'}