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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': 1, 'A9': 0, 'Lhash': '1352398987983013360', 'a10': [0.31622776601683794, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 674.5282860345642, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [13, [1, -1]], [19, [1]]], 'bad_primes': [2, 3, 13, 19], 'central_character': '84474.1', 'coefficient_field': '1.1.1.1', 'conductor': 84474, 'conductor_radical': 1482, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, -1, 5], [1, -1, 7], [1, -2, 11], [1, -1], [1, -3, 17], [1], [1, -4, 23], [1, -2, 29], [1, 4, 31], [1, 3, 37], [1, 0, 41], [1, 5, 43], [1, 13, 47], [1, -12, 53], [1, 10, 59], [1, 8, 61], [1, -2, 67], [1, 5, 71], [1, 10, 73], [1, -4, 79], [1, 0, 83], [1, -6, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 52, 'label': '2-84474-1.1-c1-0-52', 'leading_term': '12.9423521249', '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/84474/by', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 3.028435556144235, 4.843007597105982, 4.587974674742211, 2.54255251029144, 0.3688227666346034, -0.1233362595768044, 1.157574767787748, 2.267687038608249, 1.334954231433932, -1.073109286952087, -2.423034927220878, -1.379282126893435, 0.3406716250181945, 0.2252522932522724, -1.477161242289541, -2.056659234392184, -0.3862917461419934, 1.240922906765474, 0.5534325382450132, -1.133853732397303, -1.054189004364586, 0.3980725569311393, 0.3144474589826768, -1.57223048337681, -2.124279774536306, -0.3550472206568066, 0.2937124680719522, -2.134315692666772, -3.895365438113251, 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-1.887670990106641, -1.875706376322618, 1.867624624065427, 2.124044167649524, -0.1369910028806404, 0.2055795159493106, 0.7859798268399208, -0.7432185788403424, -0.1259950574986587, 2.696056169106192, 2.022538324419112, -0.8641826312393667, -0.6127399668394794, 0.1347837851611518, -1.935461155279128, -1.887105272902718, 1.745435218443759, 2.309586079754772, -0.37940757628222, -0.309319236952202, 0.363386175885115, -2.362714997627251, -3.104039911391573, -0.0763981428017591, -0.9407483344663584, -3.855563300619893, 1.136458838875732, 8.45434820182278, 5.620613736110383, -1.083176030105973, -0.6350276669579968, 0.3640967087344248, -3.801399560099801, -3.541193120232504, 3.059090833110974, 4.400116192819038, 0.01656397636643348, -0.846684887113161, -0.00636334054665211, -2.144891844554295, -2.060334550427447], 'positive_zeros': ['1.323443490626808', '1.541588409149582', '2.391902063613329', '3.185690348587705', '3.540309772856769', '4.294222179987117', '4.825901175634098', '5.425615907609626', '5.800747584185348', '6.549904526241087', '6.801171845172943', '7.598072361857074', '8.004134359405401', '8.644564548306784', '9.243585803173620', '9.678790460367650', '10.33820977393198', '10.71394849373289', '11.37320757618557', '11.78333549570029', '12.14257661083263', '12.81711334086098', '13.28698266669658', '13.62729067962968', '14.23270170871939', '14.57987033034741', '15.01980507549701', '15.45010201980905', '16.17933101587594', '16.48378904302104', '17.00067862739113', '17.42117094178457', '18.01606240104277', '18.32447519517195', '19.03309223042858', '19.44262663696951', '19.87405465645651'], 'prelabel': '2-84474-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.971682387449686, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1352398987983013360, 'z1': {'__RealLiteral__': 0, 'data': '1.323443490626808', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.541588409149582', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.391902063613329', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 674.5282860345642, 'bad_primes': [2, 3, 13, 19], 'central_character': '1.1', 'conductor': 84474, 'conductor_radical': 1482, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 3, 0, 0, 1, 0, 2, 4, 0, -4, 1, 0, 1, 2, 0, -4, 1, 0, 3, 1, 0, -3, 0, 0, 1, 0, 0, -5, 2, 0, 4, -13, 0, -6, -4, 0, 1, 12, 0, 2, 1, 0, 2, -10, 0, -8, -4, 0, 1, 1, 0, 2, 3, 0, 1, -5, 0, -10, -3, 0, 0, 2, 0, 4, 1, 0, 0, 0, 0, 3, -5, 0, 2, 6, 0, 1, 4, 0, -13, 0, 0, -14, -6, 0, -4], 'euler11': [1, -2, 11], 'euler13': [1, -1, 0], 'euler17': [1, -3, 17], 'euler19': [1, 0, 0], 'euler2': [1, -1, 0], 'euler23': [1, -4, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, 3, 37], 'euler41': [1, 0, 41], 'euler43': [1, 5, 43], 'euler47': [1, 13, 47], 'euler5': [1, -1, 5], 'euler53': [1, -12, 53], 'euler59': [1, 10, 59], 'euler61': [1, 8, 61], 'euler67': [1, -2, 67], 'euler7': [1, -1, 7], 'euler71': [1, 5, 71], 'euler73': [1, 10, 73], 'euler79': [1, -4, 79], 'euler83': [1, 0, 83], 'euler89': [1, -6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, -1, 5], [1, -1, 7], [1, -2, 11], [1, -1, 0], [1, -3, 17], [1, 0, 0], [1, -4, 23], [1, -2, 29], [1, 4, 31], [1, 3, 37], [1, 0, 41], [1, 5, 43], [1, 13, 47], [1, -12, 53], [1, 10, 59], [1, 8, 61], [1, -2, 67], [1, 5, 71], [1, 10, 73], [1, -4, 79], [1, 0, 83], [1, -6, 89], [1, 14, 97]], 'index': 52, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/84474/by'], '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': '2-84474-1.1-c1-0-52', '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': '2-84474-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.971682387449686, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1352398987983013360, 'z1': {'__RealLiteral__': 0, 'data': '1.323443490626808', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1352398987983013360', 'Lhash_array': ['1352398987983013360'], 'label': '2-84474-1.1-c1-0-52', 'type': 'ECQ', 'url': 'EllipticCurve/Q/84474/by'}