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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': -3, 'Lhash': '1712471600892761704', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 1892.390647582729, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]], [23, [1]]], 'bad_primes': [2, 7, 23], 'central_character': '236992.1', 'coefficient_field': '1.1.1.1', 'conductor': 236992, 'conductor_radical': 322, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, -2, 5], [1, -1], [1, 4, 11], [1, 2, 13], [1, -6, 17], [1, -8, 19], [1], [1, 6, 29], [1, -8, 31], [1, 2, 37], [1, -2, 41], [1, 4, 43], [1, 8, 47], [1, -6, 53], [1, 0, 59], [1, 6, 61], [1, 4, 67], [1, 8, 71], [1, -10, 73], [1, 16, 79], [1, -8, 83], [1, -6, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 52, 'label': '2-236992-1.1-c1-0-52', 'leading_term': '8.60458121874', '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/236992/br', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.877542795765808, 2.291771488698216, 0.7767023504808545, -1.352825399113866, -1.870415891119854, -0.1480458056569412, 1.680554979088708, 1.18898874326068, -0.9568695000118044, -1.764859586366765, -0.419041408899299, 0.306717188836812, -1.238944379914095, -1.942471310038221, 1.615228900313128, 6.68206436429815, 7.103522531718486, 2.38932970847433, -1.430458505541912, -1.017413931228598, 0.2793649423450368, -0.2266754573621762, -0.1106342794759644, 1.594112255956772, 0.7599031207575796, -3.715308099911185, -5.671526525444442, -1.757877027508836, 2.099704534903579, 1.023391321146598, -0.7815783909155019, 0.4177972812321617, 0.3095549140516499, -3.516238100526128, -5.033880450877046, -1.282600666748861, 1.396987784772831, -0.2837030545272197, -1.040683525032941, 0.8399583970529212, 0.5401518085625505, -1.086468804786024, 1.511578606410615, 5.323464321251895, 3.460238489191204, -0.6025740791017196, -0.4630578128917788, -0.1607482526941536, -3.79513962416023, -4.733185255673141, 0.3129551119752203, 3.146435839022089, 0.6345651556963184, -0.1831461946402647, 1.66680731956134, 0.862804605174956, -0.3777375640763959, 1.496864477735866, 1.269503076376902, -2.26734552770377, -1.083869988030167, 3.860248080671605, 2.834031320623626, -1.60085461629877, -0.2186760812284219, 2.860017926090694, 0.8400586600477424, -0.7533842331358795, 1.292049689642448, 0.7873126084499961, -1.627145100451988, -0.5599853124708404, 0.001207980607723038, -2.411250283281867, -0.854567566940933, 3.001595192810619, 0.006600900474521291, -4.60938016125543, -1.522104418622405, 2.03708560838336, -0.6190079161563578, -1.807717877176004, 0.656664593483346, 0.4329665831248056, 0.1185984837294458, 2.634310572155553, 1.289154568233293, -2.616881040995226, -0.531294636415203, 2.80230494881942, 0.74738972714878, 0.1675975171243368, 2.124575017983867, -1.508766617553179, -5.576794619402202, -2.086440959487079, 0.6569567986219751, -1.749755264973322, -1.038310443794668, 1.098211605562856, -1.645396610725039, -2.79115881994688, 0.2507289048059075, 0.2817568885197138, -0.2582038878436166, 2.206120393920205, 0.4387430144747722, -2.969751827904481, 1.774273451526939, 6.30118116324205, 1.711044837634029, -1.4301090578962, 0.871285907342577, -0.1189923783113322, -1.809165320175576, 0.2175788302958788, -0.07253976162487949, -0.8462240189067227, 2.540018783288598, 2.148152659934366], 'positive_zeros': ['0.8358381532153690', '1.516126965049083', '2.140458950627619', '2.821309813078050', '3.080030861428350', '3.667990817685198', '4.623881321896032', '5.159942430340384', '5.433355947152378', '5.770182656624031', '6.302087140812472', '7.086195296872239', '7.600676637737405', '7.939653090094008', '8.278977500233881', '9.076138301942471', '9.469850056596899', '9.892299295387861', '10.31366019974057', '10.65798034092053', '11.44669165392966', '11.82842196092660', '11.97656036324432', '12.73616185767574', '13.31436863430137', '13.52904360440972', '14.10716390313306', '14.33113356525898', '14.84083638899190', '15.30343732525322', '15.89056746854066', '16.26338961043782', '16.81801639759401', '17.10948731567831', '17.56923712569682', '18.07508308972296', '18.25018556462785', '18.79622599468558', '19.25027140276149', '19.82028894691823'], 'prelabel': '2-236992-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.50161660884258, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1712471600892761704, 'z1': {'__RealLiteral__': 0, 'data': '0.8358381532153690', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.516126965049083', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.140458950627619', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1892.390647582729, 'bad_primes': [2, 7, 23], 'central_character': '1.1', 'conductor': 236992, 'conductor_radical': 322, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 1, 0, -3, 0, -4, 0, -2, 0, 0, 0, 6, 0, 8, 0, 0, 0, 0, 0, -1, 0, 0, 0, -6, 0, 8, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, -4, 0, -6, 0, -8, 0, 1, 0, 0, 0, 6, 0, -8, 0, 0, 0, 0, 0, -6, 0, -3, 0, -4, 0, -4, 0, 0, 0, -8, 0, 10, 0, 0, 0, -4, 0, -16, 0, 9, 0, 8, 0, 12, 0, 0, 0, 6, 0, -2, 0, 0, 0, 16, 0, 6, 0, 12, 0], 'euler11': [1, 4, 11], 'euler13': [1, 2, 13], 'euler17': [1, -6, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 0], 'euler29': [1, 6, 29], 'euler3': [1, 0, 3], 'euler31': [1, -8, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 6, 61], 'euler67': [1, 4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -10, 73], 'euler79': [1, 16, 79], 'euler83': [1, -8, 83], 'euler89': [1, -6, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, -2, 5], [1, -1, 0], [1, 4, 11], [1, 2, 13], [1, -6, 17], [1, -8, 19], [1, 0, 0], [1, 6, 29], [1, -8, 31], [1, 2, 37], [1, -2, 41], [1, 4, 43], [1, 8, 47], [1, -6, 53], [1, 0, 59], [1, 6, 61], [1, 4, 67], [1, 8, 71], [1, -10, 73], [1, 16, 79], [1, -8, 83], [1, -6, 89], [1, -6, 97]], 'index': 52, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/236992/br'], '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': '2-236992-1.1-c1-0-52', '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': '2-236992-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.50161660884258, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1712471600892761704, 'z1': {'__RealLiteral__': 0, 'data': '0.8358381532153690', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1712471600892761704', 'Lhash_array': ['1712471600892761704'], 'label': '2-236992-1.1-c1-0-52', 'type': 'ECQ', 'url': 'EllipticCurve/Q/236992/br'}