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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': '612664834272095198', '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, -6, 19], [1, 4, 23], [1, -8, 29], [1, 1, 31], [1, -1, 37], [1, -3, 41], [1, -11, 43], [1, 2, 47], [1, 3, 53], [1, -4, 59], [1, 0, 61], [1, -2, 67], [1, 11, 71], [1, -14, 73], [1, 4, 79], [1, 14, 83], [1, 2, 89], [1, -13, 97]], 'gamma_factors': [[], [0]], 'index': 9, 'label': '2-32487-1.1-c1-0-9', 'leading_term': '9.92091254788', '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/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [9.92091254788071, 9.065537543236163, 6.590940207038408, 3.046919526744674, -0.296157140962578, -1.962718989333979, -1.370577659039047, 0.520566282192348, 1.860379452720086, 1.505140468091678, 0.06212117158198946, -0.8125627194419187, -0.2536327653300467, 0.8740962113919234, 1.113750941767024, 0.3034029321312271, -0.2285165890023728, 0.4560097865077166, 1.445064511037191, 1.133398270167973, -0.4015907716664691, -1.255870298178644, -0.3294262001544586, 0.9741506971358631, 0.7939779921299147, -0.1728374384898867, 0.4336844403161823, 2.565856375907107, 2.898683885507251, -0.341738797258099, -3.512499704541071, -1.541690186515959, 4.61023177081789, 8.074171073769731, 4.973790024733607, -0.1920961061664355, -0.9810210113261176, 1.903547369544385, 2.574046954589363, -0.1115991082918269, -0.5087328915855235, 4.320988726857215, 8.73632786194297, 6.325442101689306, -0.3916940475358952, -3.607519105668348, -1.399003215939785, 0.8938874292724547, -0.04791140628801675, -1.305213044009804, -0.14571959556929, 1.270662292838343, 0.4458538154866128, -1.002969089867248, -0.7878318053364808, 0.0800922735573627, 0.01889192244157901, -0.1052766426976371, 0.2009682281243905, -0.8245261236366668, -3.057296655827208, -3.019359088849233, -0.1471929653039413, 0.9160210038762562, -1.274942592178958, -0.8461458809455684, 4.966546959361488, 8.55201169437461, 3.580178544914418, -3.17381243264217, -2.365039574932955, 2.064109937141864, 0.5045206658954857, -4.213564532583587, -1.552501967559468, 6.984149517046232, 9.162062186617177, 2.522922897705883, -2.43405863373411, -0.6540409595034209, 1.220287409029155, -0.8545165949917602, -2.142362277136074, -0.1059656269053835, 1.171246805806699, 0.06518426164952841, -0.135102251987695, 0.9904900135897129, 0.6287000602645381, -0.4888898789877698, 0.007898449675861957, 0.116670350899261, -2.141362237783069, -3.062647899522009, -0.101052094018753, 2.238162786747903, 0.7781152453116262, -0.4351859904203989, 1.032845841317018, 1.450298373656201, 0.01183124696943252, 0.5493891863222525, 1.574928428169556, -1.379903241281805, -3.640097072073825, 1.825800380381115, 8.364857130296437, 5.526250688397179, -0.5618456275043955, 1.710320270197593, 6.106175810694997, 0.3846941008672103, -8.296565273307762, -5.433358920981944, 3.73924711668358, 4.385508117855921, -1.681999473170232, -3.044912814832299, -0.2349829393599097, -0.2120727084006762, -1.453396552309689], 'positive_zeros': ['0.9735986889105930', '1.684273134306449', '2.510964423705192', '3.054633385005685', '3.839540426583355', '4.133347639968469', '4.938099016010476', '5.553549344207786', '6.188673163540017', '6.423339855366376', '7.229613559895115', '7.819919394303478', '8.737241929719872', '9.095945623613841', '9.739685777661591', '10.04248896189747', '10.98423888267335', '11.61462319591902', '11.99359320739600', '12.51879598968837', '13.06455515888382', '13.71358286727999', '14.01287570369509', '14.32677685512026', '14.61277083187154', '15.51321006423894', '15.87138720378236', '16.30000754777856', '17.11298368571502', '17.61873305207305', '18.02470359137054', '18.54879167686407', '19.33898830864435', '19.80113591487604'], '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': 612664834272095198, 'z1': {'__RealLiteral__': 0, 'data': '0.9735986889105930', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.684273134306449', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.510964423705192', '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, 6, 4, 0, 10, -4, 0, -1, 2, 1, 0, 8, 4, -1, -8, 5, 2, 0, 2, 1, 12, 1, 0, 3, 0, 11, 10, 2, -8, -2, -4, 0, -2, 1, 2, -3, 2, 10, 0, 6, 16, 4, 4, 0, -2, 0, -8, 2, 10, 2, 2, -4, 0, -11, 0, 14, 2, -1, 12, 0, 2, -4, -8, 1, 6, -14, 0, 2, 22, 8, 0, -2, 4, 0, -8, -1, -4, 12, -8, 13, 0, 5, -2], 'euler11': [1, -5, 11], 'euler13': [1, -1, 0], 'euler17': [1, -1, 0], 'euler19': [1, -6, 19], 'euler2': [1, -2, 2], 'euler23': [1, 4, 23], 'euler29': [1, -8, 29], 'euler3': [1, -1, 0], 'euler31': [1, 1, 31], 'euler37': [1, -1, 37], 'euler41': [1, -3, 41], 'euler43': [1, -11, 43], 'euler47': [1, 2, 47], 'euler5': [1, -2, 5], 'euler53': [1, 3, 53], 'euler59': [1, -4, 59], 'euler61': [1, 0, 61], 'euler67': [1, -2, 67], 'euler7': [1, 0, 0], 'euler71': [1, 11, 71], 'euler73': [1, -14, 73], 'euler79': [1, 4, 79], 'euler83': [1, 14, 83], 'euler89': [1, 2, 89], 'euler97': [1, -13, 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, -6, 19], [1, 4, 23], [1, -8, 29], [1, 1, 31], [1, -1, 37], [1, -3, 41], [1, -11, 43], [1, 2, 47], [1, 3, 53], [1, -4, 59], [1, 0, 61], [1, -2, 67], [1, 11, 71], [1, -14, 73], [1, 4, 79], [1, 14, 83], [1, 2, 89], [1, -13, 97]], 'index': 9, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/r'], '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-c1-0-9', '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': 612664834272095198, 'z1': {'__RealLiteral__': 0, 'data': '0.9735986889105930', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '612664834272095198', 'Lhash_array': ['612664834272095198'], 'label': '2-32487-1.1-c1-0-9', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/r'}