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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '1337354088301278292', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1542.7097670511378, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [7, [1, 1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '193200.1', 'coefficient_field': '1.1.1.1', 'conductor': 193200, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, 1], [1, -1, 11], [1, 4, 13], [1, 0, 17], [1, -4, 19], [1, 1], [1, 6, 29], [1, 2, 31], [1, -6, 37], [1, 9, 41], [1, 2, 43], [1, 8, 47], [1, -1, 53], [1, -1, 59], [1, 1, 61], [1, -8, 67], [1, 6, 71], [1, -12, 73], [1, 14, 79], [1, 0, 83], [1, 0, 89], [1, -17, 97]], 'gamma_factors': [[], [0]], 'index': 111, 'label': '2-193200-1.1-c1-0-111', 'leading_term': '8.24932473066', '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/193200/et', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.795371629398433, 2.141099668864276, 0.4808459599037676, -2.021917907008453, -3.094059753327728, -1.689980116970153, 0.4817972766875665, 0.7746529235961794, -0.9377742068916379, -1.93299058903386, -0.5083917686035287, 1.368959307460183, 1.08134897790351, -0.2498674653567094, 0.5889856064005506, 3.21164269220502, 3.578588731404797, 0.7330585909302948, -0.9093919841831349, 1.242809341158979, 3.073353273628818, 0.5953839018005026, -2.613090401516186, -1.121047085504225, 2.701888483135649, 2.516317638444289, -1.032260610794408, -2.032057956859842, -0.2349491084528461, -0.5227126587862932, -2.592996001640402, -1.683351390900188, 1.1723101114826, 0.6029161957277676, -2.302378366844807, -1.961260698729157, 0.6756927923582182, 0.6850465786500354, -0.4935174203619819, 0.6737305302076724, 0.5425622465897251, -4.091040408559848, -6.714326757763805, -2.368534297447796, 1.819686167792821, -0.08598375651755344, -1.799733472634725, 1.327071756828064, 2.85628351481929, -0.3169073379502032, -1.46552665008437, 1.002305058928315, 0.7192065763027412, -1.755100130549582, -0.4105931395309005, 2.167730309146096, 0.5808528559279159, -1.385839752367261, -0.2306784528641892, -0.7941290777844489, -3.631531209617605, -2.49886344635203, 0.5354096616977388, -1.369602107331084, -3.900166734500379, -0.8958871482327762, 1.582860735839387, -0.2883521237569045, 1.186287244961097, 6.3066301355073, 5.168767560758373, -0.5431193031949206, -0.992466304998467, 0.8817105783694186, -1.543693149962987, -2.810414648379116, 0.5096820730235239, 1.571192565905278, -0.2852431743845252, 0.3170720538075274, 0.5704997335848913, -1.682804872074367, -0.06117073426233022, 4.094978995625103, 2.181051697303327, -1.895927638768222, -0.4300542161467888, 0.9784147688342926, -1.060612053460219, 0.4634094909677564, 3.078392882778703, -0.8922411925262762, -3.749403680038651, 1.435119893404404, 4.209656094092575, 0.1574078275117809, -1.082355498680114, 0.4221269811121065, -1.704258625183052, -2.62185107163604, -0.0129469055910955, -0.9308257531649528, -3.257594444516395, -0.9847031543892726, 0.200567406113741, -2.034535209255358, -0.8765930840548922, 1.039482031303592, -0.9529275649172553, 0.2757780128355535, 4.275589785082634, 0.94333108072464, -3.983031074807296, -0.8767365254099851, 1.31209490756053, -2.271114615403442, -1.896377745411873, 0.7422032662388063, -1.863376426433539, -2.785369051832962], 'positive_zeros': ['0.7980030356845892', '1.683638890805328', '2.129417676082443', '2.806538003592021', '3.433978774515922', '3.671112202992686', '4.562782175201971', '4.893163282068347', '5.536757615808755', '6.068858002809635', '6.675654057326518', '7.303132491137431', '7.406278574687697', '8.134961425324152', '8.551403102538024', '9.175232860164530', '9.609514739627184', '9.900159174019069', '10.29313547688341', '11.10412096337783', '11.49376993580503', '11.91569266145479', '12.47762284461594', '12.90150328179575', '13.31561883419425', '13.78100658097566', '14.29872781939659', '14.80946758196536', '14.88059409264483', '15.67854991450977', '15.89979232943444', '16.55296835585564', '16.96238004859269', '17.17228333758642', '17.96938115172459', '18.34459798836736', '18.63437367182918', '19.21453634439470', '19.69866376904281', '19.94767737291317'], 'prelabel': '2-193200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 39.27734419549186, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1337354088301278292, 'z1': {'__RealLiteral__': 0, 'data': '0.7980030356845892', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.683638890805328', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.129417676082443', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1542.7097670511378, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 193200, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 1, 0, -4, 0, 0, 0, 0, 0, 4, 0, -1, 0, -1, 0, 0, 0, 1, 0, -6, 0, -2, 0, 1, 0, 0, 0, 6, 0, -4, 0, -9, 0, -2, 0, 0, 0, -8, 0, 1, 0, 0, 0, 1, 0, 0, 0, 4, 0, 1, 0, -1, 0, -1, 0, 0, 0, 8, 0, -1, 0, -6, 0, 12, 0, 0, 0, -1, 0, -14, 0, 1, 0, 0, 0, 0, 0, -6, 0, 0, 0, 4, 0, -2, 0, 0, 0, 17, 0, 1, 0], 'euler11': [1, -1, 11], 'euler13': [1, 4, 13], 'euler17': [1, 0, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 2, 31], 'euler37': [1, -6, 37], 'euler41': [1, 9, 41], 'euler43': [1, 2, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -1, 53], 'euler59': [1, -1, 59], 'euler61': [1, 1, 61], 'euler67': [1, -8, 67], 'euler7': [1, 1, 0], 'euler71': [1, 6, 71], 'euler73': [1, -12, 73], 'euler79': [1, 14, 79], 'euler83': [1, 0, 83], 'euler89': [1, 0, 89], 'euler97': [1, -17, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 1, 0], [1, -1, 11], [1, 4, 13], [1, 0, 17], [1, -4, 19], [1, 1, 0], [1, 6, 29], [1, 2, 31], [1, -6, 37], [1, 9, 41], [1, 2, 43], [1, 8, 47], [1, -1, 53], [1, -1, 59], [1, 1, 61], [1, -8, 67], [1, 6, 71], [1, -12, 73], [1, 14, 79], [1, 0, 83], [1, 0, 89], [1, -17, 97]], 'index': 111, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/193200/et'], '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': '2-193200-1.1-c1-0-111', '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': '2-193200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 39.27734419549186, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1337354088301278292, 'z1': {'__RealLiteral__': 0, 'data': '0.7980030356845892', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1337354088301278292', 'Lhash_array': ['1337354088301278292'], 'label': '2-193200-1.1-c1-0-111', 'type': 'ECQ', 'url': 'EllipticCurve/Q/193200/et'}