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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 2, 'A4': 1, 'A5': 0, 'A6': -2, 'A7': -2, 'A8': -1, 'A9': 1, 'Lhash': '650418157230141865', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [-0.8164965809277261, 0], 'a7': [-0.7559289460184544, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 821.2613847888691, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [5, [1]], [11, [1]], [17, [1, -1]]], 'bad_primes': [2, 5, 11, 17], 'central_character': '102850.1', 'coefficient_field': '1.1.1.1', 'conductor': 102850, 'conductor_radical': 1870, 'degree': 2, 'euler_factors': [[1, 1], [1, -2, 3], [1], [1, 2, 7], [1], [1, 6, 13], [1, -1], [1, -8, 19], [1, -2, 23], [1, 6, 29], [1, 2, 31], [1, 6, 37], [1, 2, 41], [1, 4, 43], [1, 4, 47], [1, -10, 53], [1, 0, 59], [1, -10, 61], [1, 8, 67], [1, -14, 71], [1, -10, 73], [1, -14, 79], [1, 4, 83], [1, -6, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 62, 'label': '2-102850-1.1-c1-0-62', 'leading_term': '5.84478456567', '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/102850/bo', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.285230343432969, 1.588214646563535, 0.4175078318903345, -1.613460283523029, -2.908687341612574, -2.275233105101545, -0.3551002409727773, 0.834244136082996, 0.2144750289366764, -0.9439608306605375, -0.7226116597748996, 0.620113628537767, 0.968048066155149, -0.002064669403051928, 0.6762705405549848, 5.094711376675276, 9.935263036473017, 9.4023478832097, 3.257352130458774, -1.671684850464529, -0.3710170775598766, 3.145064706347641, 1.595605341149338, -4.654508997838844, -8.0312715361389, -4.962995829151858, -0.4807028402580117, 0.2652424196389617, -0.9301286848605892, -0.3702004490532743, 0.8104671962009153, -0.02716334737602607, -1.258467864342813, -0.1499323968881472, 1.639992269228289, 1.235164967213485, -0.08203887814794406, -0.05284908365623255, -0.1191679866729992, -1.33877185248685, -0.5600390778359935, 3.003294236930254, 3.47082619752158, -1.947567552677602, -6.013613723799067, -3.01755154514113, 0.9037815098055454, -0.9001015414507493, -3.221185457959575, 0.3521998479211159, 4.345936187166801, 1.917593249223581, -1.75268338487596, 0.1247554657961681, 2.879263068378081, 0.6096220529782627, -2.085335990479871, -0.445308044795609, 0.9904044380789417, -0.7212348348706615, -0.5193014289904359, 2.562369355974937, 2.26055514791424, -1.244487846439949, -1.059255057365123, 1.790896979310296, 0.8103940797636835, -1.511600199599039, 0.6816406118752515, 2.995194645929866, -0.2885053395587344, -3.629680293624763, -1.474837804191204, 0.9367586237593231, -0.49819432951068, -1.267216915763019, 0.3731294464051122, 0.5638908139124327, -0.3090954350427784, 0.1550079132530301, -0.4742379534659997, -2.227919602212386, -0.5866045328358377, 1.653131057960915, -1.687967702834971, -4.480416820087269, 1.019961163763516, 6.03835658713109, 2.152891627955068, -1.023896100009688, 1.697528267239764, -2.509091874701841, -15.45465886237544, -18.66423458645317, -7.704064448503844, 0.3177451941563515, -0.5597241510560598, -0.4622698887934567, 1.857669338387311, 0.9309892419382533, -0.264529921473193, 1.133579740279112, 0.915895512480867, -0.8284845448040338, -0.2966556375301797, 0.346800914697516, -0.2987434942206741, 1.021441823059863, 1.740963627339115, -1.704863817934859, -2.459472467224061, 2.762356224427968, 4.288486614686823, 0.007622270689518769, -0.4721140547738643, 2.034706146624025, 0.2407207530872185, -1.156883910879933, 1.332458704444619, -0.4919134218458491], 'positive_zeros': ['0.8047622861649161', '1.799157822399621', '2.291216318165431', '2.886437298833928', '3.499341280017172', '3.655432892656869', '4.882316398342087', '5.273980224404798', '5.821938217079988', '6.798480208158294', '7.055133423691255', '7.561237132851788', '7.995888144044222', '8.517774526873698', '9.225130785342782', '9.530177320909158', '9.708754195534198', '10.29649653809974', '10.92499985950922', '11.65860180195686', '11.93608989597843', '12.48396415577272', '13.10154805749295', '13.49190150328114', '14.03928967427852', '14.54197526356929', '14.91144724840933', '15.29740396613670', '15.90459458885503', '16.33570135995118', '16.81547866073314', '17.20391683192758', '17.73536438317378', '18.35791299402375', '18.69213636109585', '19.19377103789271', '19.63022343238653', '19.93987665582553'], 'prelabel': '2-102850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.65765839682072, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 650418157230141865, 'z1': {'__RealLiteral__': 0, 'data': '0.8047622861649161', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.799157822399621', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.291216318165431', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 821.2613847888691, 'bad_primes': [2, 5, 11, 17], 'central_character': '1.1', 'conductor': 102850, 'conductor_radical': 1870, 'degree': 2, 'dirichlet_coefficients': [1, -1, 2, 1, 0, -2, -2, -1, 1, 0, 0, 2, -6, 2, 0, 1, 1, -1, 8, 0, -4, 0, 2, -2, 0, 6, -4, -2, -6, 0, -2, -1, 0, -1, 0, 1, -6, -8, -12, 0, -2, 4, -4, 0, 0, -2, -4, 2, -3, 0, 2, -6, 10, 4, 0, 2, 16, 6, 0, 0, 10, 2, -2, 1, 0, 0, -8, 1, 4, 0, 14, -1, 10, 6, 0, 8, 0, 12, 14, 0, -11, 2, -4, -4, 0, 4, -12, 0, 6, 0, 12, 2, -4, 4, 0, -2, 14, 3, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 6, 13], 'euler17': [1, -1, 0], 'euler19': [1, -8, 19], 'euler2': [1, 1, 0], 'euler23': [1, -2, 23], 'euler29': [1, 6, 29], 'euler3': [1, -2, 3], 'euler31': [1, 2, 31], 'euler37': [1, 6, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, 0, 59], 'euler61': [1, -10, 61], 'euler67': [1, 8, 67], 'euler7': [1, 2, 7], 'euler71': [1, -14, 71], 'euler73': [1, -10, 73], 'euler79': [1, -14, 79], 'euler83': [1, 4, 83], 'euler89': [1, -6, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 1, 0], [1, -2, 3], [1, 0, 0], [1, 2, 7], [1, 0, 0], [1, 6, 13], [1, -1, 0], [1, -8, 19], [1, -2, 23], [1, 6, 29], [1, 2, 31], [1, 6, 37], [1, 2, 41], [1, 4, 43], [1, 4, 47], [1, -10, 53], [1, 0, 59], [1, -10, 61], [1, 8, 67], [1, -14, 71], [1, -10, 73], [1, -14, 79], [1, 4, 83], [1, -6, 89], [1, -14, 97]], 'index': 62, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/102850/bo'], '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': '2-102850-1.1-c1-0-62', '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': '2-102850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.65765839682072, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 650418157230141865, 'z1': {'__RealLiteral__': 0, 'data': '0.8047622861649161', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '650418157230141865', 'Lhash_array': ['650418157230141865'], 'factors': ['2-102850-1.1-c1-0-62'], 'label': '2-102850-1.1-c1-0-62', 'type': 'ECQ', 'url': 'EllipticCurve/Q/102850/bo'}