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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 0, 'Lhash': '183886055866994628', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 764.6474497557813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]], [7, [1, -1]], [19, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '95760.1', 'coefficient_field': '1.1.1.1', 'conductor': 95760, 'conductor_radical': 3990, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1, -1], [1, 1, 11], [1, -1, 13], [1, -4, 17], [1, -1], [1, -7, 23], [1, -8, 29], [1, 9, 31], [1, -12, 37], [1, 6, 41], [1, 5, 43], [1, -12, 47], [1, 11, 53], [1, 9, 59], [1, -5, 61], [1, 0, 67], [1, -1, 71], [1, -1, 73], [1, -8, 79], [1, 15, 83], [1, 16, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 131, 'label': '2-95760-1.1-c1-0-131', 'leading_term': '7.23363889145', '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/95760/bv', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.640789611167471, 2.344663122485114, 1.64867562047859, 0.180744069459043, -0.462051854282847, 0.8466540688280095, 3.225271364540799, 4.242723946091597, 2.539185445367606, -0.2667160885878692, -1.2048237498581, 0.3456129258151932, 1.718120066664234, 0.5779076202370536, -1.603715715058679, -1.486988419512472, 1.124373738678531, 2.725607226757033, 1.370222856923313, -0.2184796742421952, 0.9765903783275574, 3.073540779196504, 2.129935023615998, -1.026468626495633, -1.50409014460389, 1.760918330664053, 3.938004115298491, 2.048899849030896, -0.3468552992013388, 0.4019459942543793, 1.830950122601794, 0.4420114130005266, -1.451774519630849, -0.1508951121581784, 1.897539739581925, 0.2883943920106249, -2.629611534083354, -1.490649796312147, 1.955778452657568, 1.58332579700835, -1.887153991622024, -2.264802185886254, 0.6204225022452612, 1.270849431452422, -0.4453101129801232, 0.3485865248695072, 2.868893167302998, 1.880776130021586, -1.36229161224624, -1.274503220694628, 0.637146097130751, -1.075268493204176, -3.919709867409761, -1.837459946748485, 2.262597087769626, 1.803606577215455, -0.6314816897511552, 0.786853773825417, 3.062632837636931, 1.336839731376451, -0.5784390498333296, 1.127937639860903, 1.602089031902922, -1.917795813377566, -3.393893576266096, -0.6402311381896454, 0.1723651532168287, -1.58788388823545, 0.4732539194351486, 4.813953118588388, 3.790577943002138, -0.5360260873766747, -0.8062057918232244, 0.7038182839388561, -1.006885726549704, -1.687573369192781, 1.755070829978115, 2.838209996315492, -0.5674341099569291, -1.272040041974093, 1.403904956463818, 0.7329098042537792, -1.639386072201903, 0.1750291873262065, 2.051188456337918, -0.7537422781127325, -2.218877889304925, 0.4168321658414208, -0.4848759812343241, -5.384982048742927, -5.233713889315678, -0.5591136815144045, 0.6267908815239506, -0.3372715724802233, 0.4306440874238129, -1.471226553079921, -5.994645037412566, -4.785216441774408, 0.8318027802387735, 1.702565922701594, -0.2421213902031691, 0.6952962924581946, -0.7338353107250382, -6.680591269473712, -7.608559486921985, -2.020991811339486, 0.5669525641808337, -0.16762913114635, 1.304173628746047, 1.271160046723593, -2.174860323124184, -1.659022753234447, 2.168165970447546, 1.211052255241374, -1.242131380207712, 0.6399819345209999, 0.2398159901489075, -4.83806037075992, -4.980053584441398, -0.2888654874733855], 'positive_zeros': ['1.035280872921251', '1.384381912977826', '2.472164287398032', '2.957804464461230', '3.561657739657646', '4.152657817003058', '4.931427316687540', '5.121028155433013', '5.914486358574740', '6.382943642811987', '7.188513904453350', '7.443737443534635', '8.043974696893221', '8.514322152500299', '9.021486621990550', '9.600682554982883', '10.11415046366560', '10.69504485212974', '11.17556803826575', '11.46268383583622', '12.13478050468138', '12.63977435524053', '12.91230915701697', '13.59842078682476', '14.15796449452401', '14.42980624256769', '15.12161496582805', '15.37838267336794', '15.88002473472149', '16.56568147598363', '16.77763557172851', '17.22272062970871', '17.96016645501857', '18.34841672091482', '18.64705632314874', '19.13841848331922', '19.70964647216871'], 'prelabel': '2-95760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.652259396942256, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 183886055866994628, 'z1': {'__RealLiteral__': 0, 'data': '1.035280872921251', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.384381912977826', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.472164287398032', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 764.6474497557813, 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '1.1', 'conductor': 95760, 'conductor_radical': 3990, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 4, 0, 1, 0, 0, 0, 7, 0, 1, 0, 0, 0, 8, 0, -9, 0, 0, 0, -1, 0, 12, 0, 0, 0, -6, 0, -5, 0, 0, 0, 12, 0, 1, 0, 0, 0, -11, 0, 1, 0, 0, 0, -9, 0, 5, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 8, 0, 0, 0, -15, 0, -4, 0, 0, 0, -16, 0, 1, 0, 0, 0, -1, 0, -10, 0, 0, 0], 'euler11': [1, 1, 11], 'euler13': [1, -1, 13], 'euler17': [1, -4, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, -7, 23], 'euler29': [1, -8, 29], 'euler3': [1, 0, 0], 'euler31': [1, 9, 31], 'euler37': [1, -12, 37], 'euler41': [1, 6, 41], 'euler43': [1, 5, 43], 'euler47': [1, -12, 47], 'euler5': [1, 1, 0], 'euler53': [1, 11, 53], 'euler59': [1, 9, 59], 'euler61': [1, -5, 61], 'euler67': [1, 0, 67], 'euler7': [1, -1, 0], 'euler71': [1, -1, 71], 'euler73': [1, -1, 73], 'euler79': [1, -8, 79], 'euler83': [1, 15, 83], 'euler89': [1, 16, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 1, 11], [1, -1, 13], [1, -4, 17], [1, -1, 0], [1, -7, 23], [1, -8, 29], [1, 9, 31], [1, -12, 37], [1, 6, 41], [1, 5, 43], [1, -12, 47], [1, 11, 53], [1, 9, 59], [1, -5, 61], [1, 0, 67], [1, -1, 71], [1, -1, 73], [1, -8, 79], [1, 15, 83], [1, 16, 89], [1, 10, 97]], 'index': 131, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/95760/bv'], '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': '2-95760-1.1-c1-0-131', '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': '2-95760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.652259396942256, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 183886055866994628, 'z1': {'__RealLiteral__': 0, 'data': '1.035280872921251', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '183886055866994628', 'Lhash_array': ['183886055866994628'], 'factors': ['2-95760-1.1-c1-0-131'], 'label': '2-95760-1.1-c1-0-131', 'type': 'ECQ', 'url': 'EllipticCurve/Q/95760/bv'}