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lfunc_lfunctions • Show schema
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{'A10': -4, 'A2': 2, 'A3': 1, 'A4': 2, 'A5': -2, 'A6': 2, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '521379156466710456', 'a10': [-1.2649110640673518, 0], 'a2': [1.414213562373095, 0], 'a3': [0.5773502691896258, 0], 'a4': [1.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.8164965809277261, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 259.4100010465337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [7, [1]], [13, [1, 1]], [17, [1, 1]]], 'bad_primes': [3, 7, 13, 17], 'central_character': '32487.1', 'coefficient_field': '1.1.1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'euler_factors': [[1, -2, 2], [1, -1], [1, 2, 5], [1], [1, 5, 11], [1, 1], [1, 1], [1, 8, 19], [1, -6, 23], [1, 8, 29], [1, 9, 31], [1, -9, 37], [1, 7, 41], [1, 1, 43], [1, -12, 47], [1, -3, 53], [1, 12, 59], [1, -10, 61], [1, -4, 67], [1, 9, 71], [1, -6, 73], [1, -14, 79], [1, -12, 83], [1, 8, 89], [1, -9, 97]], 'gamma_factors': [[], [0]], 'index': 0, 'label': '2-32487-1.1-c1-0-0', 'leading_term': '1.91303149787', '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': 0, 'origin': 'EllipticCurve/Q/32487/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.913031497867899, 0.9995092359459186, -1.556187386167625, -4.988189996481609, -7.818303513701751, -8.480726603687382, -6.473833540443619, -2.99579780650123, -0.2131739425293962, 0.4609161617196729, -0.4728936297575195, -1.258492091277804, -0.7879266022500846, 0.3124182518353655, 0.6753490818979565, 0.03808108553249909, -0.4578252622062458, 0.0414235417053436, 0.7691288866499727, 0.4288029343910563, -0.6862477678011305, -0.8200867230840486, 0.5790102048274695, 1.481756947562959, -0.1510361335823312, -3.019967534771992, -3.598976995563015, -0.9667839810667987, 1.497490705983157, 0.7256358554875294, -1.443703494791992, -0.9529747243708897, 1.93759464590149, 2.490833524545229, -1.082624235241557, -3.901509312431735, -1.363477610563882, 2.95642620453979, 1.398234083539704, -6.398308199648098, -11.86231768113345, -9.003837015445054, -2.365291042849536, 0.2285540223441446, -1.370311186750964, -1.37877219328311, 1.746473596344844, 3.489783564654126, 1.465524779461585, -0.9474534752834034, -0.7712978521384343, 0.2617312868932593, 0.03463594281024377, -0.1593204720275642, 0.8249317938650972, 0.9598614443662004, -1.019413007576501, -2.549291794768691, -1.563899235620499, -0.06699381143609637, -0.001632620600381061, 0.1364834156143898, 0.9782730855605916, -0.1921422661589888, -3.275155750796762, -3.057661542134334, 1.20737913639518, 1.362905185429882, -6.411881883983758, -11.70034637287274, -4.288183546750041, 8.18303930269444, 10.47207857919645, 2.694318188007238, -2.048083514097606, 0.1621059714294844, 0.680713269635507, -3.559064986858827, -5.116900427977629, -1.116399197647642, 1.807485905188004, 0.4327676808582615, -0.4747709873857901, 1.088636919029539, 1.202192619696189, -0.7671655399009621, -1.013348712945632, 0.1690624890998693, -0.8537080758897236, -2.732561608213468, -1.502287247912233, 1.125792772279369, 1.084992270760638, -0.3117868249069023, -0.161795846851222, 0.1865028519304072, 0.006190004048029682, 2.104157805077392, 5.354566005169172, 4.36650067898825, 0.4184046405561552, 0.2837890793245469, 2.387637235991293, -0.6516668889382397, -5.842148687269869, -4.066242220988433, 1.448108392712353, 0.743400655426413, -2.972886539580897, -0.5081666007618778, 3.050162408150273, -1.671221154687853, -7.083688379087617, -1.475835049018872, 7.48794421281295, 5.930143463048183, -1.53236343933508, -2.574163238439228, 0.5471993606194508, -0.5123213909654482, -3.13696747106443], 'positive_zeros': ['0.3649211691153178', '2.031930675516063', '2.397367540103456', '3.173973762920422', '3.761875540347305', '4.237890654173443', '4.847357327141144', '5.412454303858755', '5.986256131596635', '6.825330454696880', '7.326778965580426', '7.838280146300428', '8.438107465073191', '9.069082418259557', '9.555180448692692', '10.66197858305168', '10.81627726658330', '11.37427455322271', '12.12660638226240', '12.66186099059889', '13.01412488303200', '13.30948339087926', '13.89154316901981', '14.77389165650935', '14.99864717883754', '15.19439957448272', '15.73175274948233', '16.43027771927773', '16.81156699490995', '17.58039447638099', '18.34210959265051', '18.73664193372011', '19.05398810870026', '19.81185601279418'], 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 521379156466710456, 'z1': {'__RealLiteral__': 0, 'data': '0.3649211691153178', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '2.031930675516063', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.397367540103456', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 259.4100010465337, 'bad_primes': [3, 7, 13, 17], 'central_character': '1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'dirichlet_coefficients': [1, 2, 1, 2, -2, 2, 0, 0, 1, -4, -5, 2, -1, 0, -2, -4, -1, 2, -8, -4, 0, -10, 6, 0, -1, -2, 1, 0, -8, -4, -9, -8, -5, -2, 0, 2, 9, -16, -1, 0, -7, 0, -1, -10, -2, 12, 12, -4, 0, -2, -1, -2, 3, 2, 10, 0, -8, -16, -12, -4, 10, -18, 0, -8, 2, -10, 4, -2, 6, 0, -9, 0, 6, 18, -1, -16, 0, -2, 14, 8, 1, -14, 12, 0, 2, -2, -8, 0, -8, -4, 0, 12, -9, 24, 16, -8, 9, 0, -5, -2], 'euler11': [1, 5, 11], 'euler13': [1, 1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 8, 19], 'euler2': [1, -2, 2], 'euler23': [1, -6, 23], 'euler29': [1, 8, 29], 'euler3': [1, -1, 0], 'euler31': [1, 9, 31], 'euler37': [1, -9, 37], 'euler41': [1, 7, 41], 'euler43': [1, 1, 43], 'euler47': [1, -12, 47], 'euler5': [1, 2, 5], 'euler53': [1, -3, 53], 'euler59': [1, 12, 59], 'euler61': [1, -10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 9, 71], 'euler73': [1, -6, 73], 'euler79': [1, -14, 79], 'euler83': [1, -12, 83], 'euler89': [1, 8, 89], 'euler97': [1, -9, 97], 'euler_factors': [[1, -2, 2], [1, -1, 0], [1, 2, 5], [1, 0, 0], [1, 5, 11], [1, 1, 0], [1, 1, 0], [1, 8, 19], [1, -6, 23], [1, 8, 29], [1, 9, 31], [1, -9, 37], [1, 7, 41], [1, 1, 43], [1, -12, 47], [1, -3, 53], [1, 12, 59], [1, -10, 61], [1, -4, 67], [1, 9, 71], [1, -6, 73], [1, -14, 79], [1, -12, 83], [1, 8, 89], [1, -9, 97]], 'index': 0, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/o'], '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': '2-32487-1.1-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 521379156466710456, 'z1': {'__RealLiteral__': 0, 'data': '0.3649211691153178', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '521379156466710456', 'Lhash_array': ['521379156466710456'], 'label': '2-32487-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/o'}