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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': -2, 'A3': 0, 'A4': 2, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '1792534695453311465', 'a10': [-0.6324555320336759, 0], 'a2': [-1.414213562373095, 0], 'a3': [0.0, 0], 'a4': [1.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 565.380771511676, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -1]], [7, [1]], [17, [1]]], 'bad_primes': [5, 7, 17], 'central_character': '70805.1', 'coefficient_field': '1.1.1.1', 'conductor': 70805, 'conductor_radical': 595, 'degree': 2, 'euler_factors': [[1, 2, 2], [1, 0, 3], [1, -1], [1], [1, -2, 11], [1, -3, 13], [1], [1, 0, 19], [1, -1, 23], [1, 8, 29], [1, -9, 31], [1, 3, 37], [1, -3, 41], [1, -6, 43], [1, 3, 47], [1, 4, 53], [1, -6, 59], [1, 15, 61], [1, -4, 67], [1, -2, 71], [1, -6, 73], [1, -10, 79], [1, 15, 83], [1, 0, 89], [1, 12, 97]], 'gamma_factors': [[], [0]], 'index': 33, 'label': '2-70805-1.1-c1-0-33', 'leading_term': '3.39787087099', '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/70805/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.7538836244360717, 0.9817778691419548, 0.4604229066045044, -0.3879229597411686, -0.6423515309682101, 0.190105657063284, 1.313984491600273, 1.191623195194727, -0.5476811864192683, -2.017986903702613, -0.8616833539426345, 2.459042456330424, 4.170908264451183, 1.371851788309533, -3.569952922043716, -4.763478568128231, 0.04129010221301442, 5.744840715733751, 5.578492646605254, -0.2701019858680285, -4.709669572747557, -2.989611916030599, 1.422411666941342, 2.471095136928007, 0.1429668004793939, -0.6035306264927225, 1.79511797261027, 3.311983828185241, 1.296677604913863, -1.270165306333615, -0.9692905362621801, 0.7056361709049875, 0.6496839755292676, -0.5025732551356724, -0.3807089699778623, 0.4197936697547144, 0.04361770383081499, -0.454478313668586, 0.6983779338983924, 1.760970472258281, 0.4422539763935842, -1.17168671441604, -0.18671519370262, 1.291851539355547, 0.3573660418755887, -0.02584223207738012, 3.387871257672512, 5.572449362517963, 0.5837010775606833, -5.848525612456648, -3.616455193804017, 4.235274371124882, 5.633032256519575, -0.2131393889835493, -2.686296668541205, 0.2099286999882387, -0.6257472404899393, -6.301741135801441, -6.793946443495734, -0.1210328780798789, 3.348508590151228, -0.3091838630922722, -2.644636030622568, 0.5549135251780491, 2.98703184699488, 1.279084637073573, -0.172589701624492, 0.4116439276090569, 0.0895465271770908, -0.8687380200590458, -0.1613512235747861, 0.4026709281036456, -0.8842822592028816, -1.091037553712381, 0.7464464814185258, 0.9839889245734468, -0.3983017534569826, 0.3260818308425855, 1.569966564728796, -0.318172612218652, -1.801970232573896, 0.5744297747358286, 1.590323395607887, -0.6916829304049938, 1.985163004878398, 10.09289411941078, 10.66706493405481, 1.465710974619217, -3.079468120980655, 0.9514803841963191, 1.854502412826359, -0.7833781340812801, 4.240636133026515, 12.37060054849174, 8.782974650907056, -2.185531734495694, -4.780664946175419, -0.4379769368296907, -0.3786898012396361, -2.951971911125753, -1.666834130717916, 0.3344944059476185, -0.2094056475675446, -0.008931797424527177, 0.9657761825591629, -0.0826928679484884, -0.366051091186432, 2.085403177456559, 2.686970925345348, 0.4155389763319445, -0.1527490416725017, 0.5265566212976475, -0.4841846175998945, -0.6831102629208056, 0.5236657178037503, -0.7972193904946301, -2.121714813299674, 0.9091772450418117, 2.316081509832475, -1.215574716614407], 'positive_zeros': ['0.8815928450515981', '1.459930965185880', '2.183603562691694', '2.822228341186323', '3.568296597284640', '4.248428675241142', '4.989650443100574', '5.661560785353069', '6.265649735564542', '6.586144405533126', '7.355540862255739', '7.883339323489255', '8.380990096508142', '8.851530376513337', '9.262500311613480', '9.637747513791596', '10.30108379372721', '10.77342259931111', '11.31089535876312', '11.50400924422962', '12.26882536740560', '12.86321468713443', '13.49100707771924', '13.98057464647486', '14.21034316827504', '15.00436791107368', '15.48373739328934', '15.96698726154079', '16.67066155472745', '16.86347238561341', '17.26928181204116', '17.78309643449262', '18.10341231308768', '18.65275104092732', '19.16272026429645', '19.45281015133463', '19.97168366799963'], 'prelabel': '2-70805-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.77773688793103, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1792534695453311465, 'z1': {'__RealLiteral__': 0, 'data': '0.8815928450515981', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.459930965185880', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.183603562691694', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 565.380771511676, 'bad_primes': [5, 7, 17], 'central_character': '1.1', 'conductor': 70805, 'conductor_radical': 595, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 2, 1, 0, 0, 0, -3, -2, 2, 0, 3, 0, 0, -4, 0, 6, 0, 2, 0, -4, 1, 0, 1, -6, 0, 0, -8, 0, 9, 8, 0, 0, 0, -6, -3, 0, 0, 0, 3, 0, 6, 4, -3, -2, -3, 0, 0, -2, 0, 6, -4, 0, 2, 0, 0, 16, 6, 0, -15, -18, 0, -8, 3, 0, 4, 0, 0, 0, 2, 0, 6, 6, 0, 0, 0, 0, 10, -4, 9, -6, -15, 0, 0, -12, 0, 0, 0, 6, 0, 2, 0, 6, 0, 0, -12, 0, -6, 2], 'euler11': [1, -2, 11], 'euler13': [1, -3, 13], 'euler17': [1, 0, 0], 'euler19': [1, 0, 19], 'euler2': [1, 2, 2], 'euler23': [1, -1, 23], 'euler29': [1, 8, 29], 'euler3': [1, 0, 3], 'euler31': [1, -9, 31], 'euler37': [1, 3, 37], 'euler41': [1, -3, 41], 'euler43': [1, -6, 43], 'euler47': [1, 3, 47], 'euler5': [1, -1, 0], 'euler53': [1, 4, 53], 'euler59': [1, -6, 59], 'euler61': [1, 15, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -2, 71], 'euler73': [1, -6, 73], 'euler79': [1, -10, 79], 'euler83': [1, 15, 83], 'euler89': [1, 0, 89], 'euler97': [1, 12, 97], 'euler_factors': [[1, 2, 2], [1, 0, 3], [1, -1, 0], [1, 0, 0], [1, -2, 11], [1, -3, 13], [1, 0, 0], [1, 0, 19], [1, -1, 23], [1, 8, 29], [1, -9, 31], [1, 3, 37], [1, -3, 41], [1, -6, 43], [1, 3, 47], [1, 4, 53], [1, -6, 59], [1, 15, 61], [1, -4, 67], [1, -2, 71], [1, -6, 73], [1, -10, 79], [1, 15, 83], [1, 0, 89], [1, 12, 97]], 'index': 33, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/70805/f'], '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': '2-70805-1.1-c1-0-33', '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': '2-70805-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.77773688793103, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1792534695453311465, 'z1': {'__RealLiteral__': 0, 'data': '0.8815928450515981', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1792534695453311465', 'Lhash_array': ['1792534695453311465'], 'label': '2-70805-1.1-c1-0-33', 'type': 'ECQ', 'url': 'EllipticCurve/Q/70805/f'}