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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': '916000263801864050', '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': 719.3722718097154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1, -1]], [7, [1, -1]], [11, [1, 1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11, 13], 'central_character': '90090.1', 'coefficient_field': '1.1.1.1', 'conductor': 90090, 'conductor_radical': 30030, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -6, 17], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, -8, 31], [1, 10, 37], [1, -6, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, 10, 61], [1, -8, 67], [1, 12, 71], [1, -14, 73], [1, -8, 79], [1, 0, 83], [1, 6, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 40, 'label': '2-90090-1.1-c1-0-40', 'leading_term': '5.38881186485', '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/90090/dr', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.388811864850906, 4.422535346767072, 1.903018337074934, -0.9400301994078664, -2.396909043509333, -1.600060584840205, 0.3755237619894054, 1.274268239354933, 0.01360381257204413, -1.948055101726691, -2.244252513590938, -0.6111729647265624, 0.6456620048211728, -0.2480375105994, -1.903017257769386, -1.575340928242327, 0.804068803255648, 2.331592745348251, 1.36308897317514, -0.05195645909520869, 0.4773405289860391, 1.765959869810255, 1.127974344478096, -0.8349274524338606, -1.100023841008906, 0.3020716451373478, -0.03424829249951567, -2.616164285864918, -3.181888102179364, 0.2053387534956599, 2.944759125540184, 1.113204320337427, -1.571051073543506, -0.06380731893434123, 2.570071333441708, 0.023820609503489, -5.437627094522449, -5.576698746175216, 0.004356544302125593, 2.951107733525833, 0.1291923824751595, -2.193694164444624, -0.6168266099437864, -0.03426361974566735, -2.884956509750853, -3.858330683531379, -0.3026867654218589, 2.405122109074136, 0.9950476054368749, -0.2701023719197431, 1.01647020476334, 0.9042409474084127, -1.816586599973708, -2.521477615309423, -0.1521952724405568, 0.8517483826061578, -0.1158584012720379, 0.5355327582105218, 1.713351705478861, -0.1730157716923891, -2.352196461466546, -0.7262725890561573, 0.9923613111485553, -1.05811306610679, -1.866141578416923, 2.094119386339763, 4.29178639186092, 1.093868948832357, -0.5034430624137302, 2.153557257982738, 1.628350376314249, -2.632622198683995, -1.485692883997758, 4.503221899927249, 4.879780246773239, 0.3983226686757612, 0.9322209785370547, 4.510407073865174, 2.304073940878315, -1.751265544166586, 0.7749304464737343, 5.02701391082533, 3.334551912530131, -0.07382131005789078, -0.0220600589733702, 0.2976937861577578, -0.02223869809449968, 2.383607177447973, 4.434709992965492, 1.667963022882126, -1.100359225737897, 0.4338411115775124, 1.384563353434497, -0.2776303095637264, 0.1801834194637642, 1.507668943429772, -0.9167780537112672, -2.867272665187145, -0.2091789057278463, 1.258783328408139, -0.647844535995473, 0.3095398104444995, 2.853576398022876, 0.859419193869362, -0.7040318306262852, 2.774168108310986, 2.213883384484441, -4.766114757951646, -4.938887701907994, 3.020423331516053, 4.670968156692556, -0.3465765518661453, -0.5290252975633865, 1.088024437516624, -3.034796875360449, -5.394223265814882, -0.8554084707720103, 1.602380553263277, -0.563053558436259, -0.2582881871503869, 1.050977683226289], 'positive_zeros': ['0.6610190136397434', '1.450641330031811', '2.001669868456192', '2.835310957037980', '3.213090255871888', '3.922509726470623', '4.730982194051607', '4.893645419427958', '5.638686020107332', '6.191559018173428', '6.495419938276744', '7.237689896240559', '7.830871941761953', '8.254818010563151', '8.751119490275260', '9.499809457886080', '10.00836800630883', '10.58540616986603', '10.74419993024673', '11.51774788356765', '12.12727881028180', '12.33451621580937', '12.84330547287609', '13.51618896154174', '13.96150037545326', '14.15305086215230', '14.73576358350533', '15.31577558122042', '15.65512226445135', '16.13858899120760', '16.83144488252721', '17.06557988168190', '17.59439462956126', '18.06433498035695', '18.78810645097304', '18.92125284326168', '19.61334278927975', '19.96153484337678'], 'prelabel': '2-90090-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.821116155181077, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 916000263801864050, 'z1': {'__RealLiteral__': 0, 'data': '0.6610190136397434', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.450641330031811', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.001669868456192', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 719.3722718097154, 'bad_primes': [2, 3, 5, 7, 11, 13], 'central_character': '1.1', 'conductor': 90090, 'conductor_radical': 30030, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, -1, 0, 1, 1, 0, 1, 6, 0, -4, 1, 0, -1, 0, 0, 1, 1, 0, 1, 6, 0, 8, 1, 0, 6, 1, 0, -10, -4, 0, 1, 6, 0, -4, -1, 0, 0, 0, 0, 1, 1, 0, 1, -6, 0, -1, 1, 0, 6, -12, 0, -10, 8, 0, 1, 1, 0, 8, 6, 0, 1, -12, 0, 14, -10, 0, -4, -1, 0, 8, 1, 0, 6, 0, 0, 6, -4, 0, -1, -6, 0, 1, 0, 0, 0, -4, 0, 14, 1, 0, 1], 'euler11': [1, 1, 0], 'euler13': [1, -1, 0], 'euler17': [1, -6, 17], 'euler19': [1, 4, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, 10, 37], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 12, 59], 'euler61': [1, 10, 61], 'euler67': [1, -8, 67], 'euler7': [1, -1, 0], 'euler71': [1, 12, 71], 'euler73': [1, -14, 73], 'euler79': [1, -8, 79], 'euler83': [1, 0, 83], 'euler89': [1, 6, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 1, 0], [1, -1, 0], [1, -6, 17], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, -8, 31], [1, 10, 37], [1, -6, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, 10, 61], [1, -8, 67], [1, 12, 71], [1, -14, 73], [1, -8, 79], [1, 0, 83], [1, 6, 89], [1, -14, 97]], 'index': 40, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/90090/dr'], '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': '2-90090-1.1-c1-0-40', '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': '2-90090-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.821116155181077, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 916000263801864050, 'z1': {'__RealLiteral__': 0, 'data': '0.6610190136397434', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '916000263801864050', 'Lhash_array': ['916000263801864050'], 'label': '2-90090-1.1-c1-0-40', 'type': 'ECQ', 'url': 'EllipticCurve/Q/90090/dr'}