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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': -2, 'A5': -1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '2202413237921863315', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [-1.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1022.0452206713787, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [5, [1, 1]], [7, [1, -1]], [23, [1, 1]], [53, [1, -1]]], 'bad_primes': [3, 5, 7, 23, 53], 'central_character': '127995.1', 'coefficient_field': '1.1.1.1', 'conductor': 127995, 'conductor_radical': 127995, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, 1], [1, 1], [1, -1], [1, -5, 11], [1, -1, 13], [1, -3, 17], [1, 4, 19], [1, 1], [1, 4, 29], [1, 5, 31], [1, 3, 37], [1, 8, 41], [1, 8, 43], [1, -6, 47], [1, -1], [1, -11, 59], [1, -4, 61], [1, -12, 67], [1, 9, 71], [1, 8, 73], [1, -16, 79], [1, 16, 83], [1, 6, 89], [1, 16, 97]], 'gamma_factors': [[], [0]], 'index': 11, 'label': '2-127995-1.1-c1-0-11', 'leading_term': '4.51694881962', '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/127995/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.9664479447055314, 1.063951074176981, 0.03724740699394883, -1.236775685677297, -1.27292795897302, 0.2512614145334138, 1.355480745066436, -0.6016057636958458, -5.488238601903416, -9.39200133039274, -8.390651594342147, -3.258025788626494, 1.127584369876783, 1.575335828878808, 0.024324879821456, -0.113423518263422, 0.8742104482499108, 0.2538512104687665, -1.834242090960301, -2.251142494434354, -0.4497670001793543, 0.1482568070603646, -1.798426031792418, -2.554385561710883, 0.3628414998442389, 3.154193881463269, 1.840365821123954, -0.4582471128185201, 1.360716607581001, 5.073962450018502, 4.582650465647191, 0.5925360969747124, -0.7891002844072948, 1.010714196126525, 0.9352489322584622, -1.260122553385604, -0.6830247030724674, 2.307880039768688, 2.189315558552122, -0.6366721294629769, -0.1804602061463964, 3.145552129289544, 2.888149001645341, -0.7927501665187098, -1.427580414676053, 1.099163347580951, 1.195982855851579, -0.526872175658638, 0.6776593983150506, 2.682150268593791, 0.9837510918446927, -0.7714744441149228, 1.953177541851753, 4.228408655002455, 1.335919878085409, -1.266464981516613, 0.6911036180605062, 1.80126425991888, -0.4099988645709283, -0.1123398347960272, 2.418000494294594, -0.5749828948550737, -7.094967259818593, -6.916518348557091, -0.9554554814943682, 1.296920379230872, -0.09537613774338692, 0.640912379500924, 1.430614126934843, -0.5498701326681457, -0.7434416521055472, 1.774653080965541, 1.20953721215382, -1.560421004705392, -0.9836310700347489, -0.01468714845068937, -2.348384310935689, -1.913659149297996, 2.840665443279949, 2.462624845131719, -3.099430976977399, -2.375621823433251, 3.312583392820554, 2.113681160887098, -3.524057069350191, -3.149322387329093, 0.2923050240643733, 0.03294156716047055, -0.3126134162601796, 1.261731434342504, 0.2029586886861648, -1.731424220959619, -0.2769882886631788, 0.7634140572837208, -0.07920806967773811, 2.013000053904843, 3.495256731644728, -1.607420161535258, -5.112022279886473, -0.6144811642515053, 1.407847203334913, -3.011643093223209, -2.064482339761593, 4.30868219265097, 3.565388506998073, -1.919914554748797, -1.717014200131821, 0.664994901238413, -0.2891043290266364, -0.5077099725959555, 0.3648191740265257, -0.5395182523832313, 0.204193970614345, 1.155686176442548, -4.338462174655184, -9.348148262512757, -4.28041617121855, 1.606933538403532, -0.4335250761532508, -1.894932831967127], 'positive_zeros': ['0.7566730339660375', '1.465497999328419', '1.957200228591649', '3.163639880134601', '3.755136391417493', '4.030529408979894', '4.533685423469794', '5.320573548462062', '5.532370087539548', '6.226494851706805', '6.917924642883081', '7.141489908214885', '8.045932458684218', '8.372883244292230', '8.854612764868703', '9.308847110229467', '9.935197957294385', '10.26530012165719', '10.94246555901745', '11.39175149447325', '11.90128800715693', '12.17916112008303', '12.83701132897691', '13.11360677781629', '13.83497871155745', '14.18929728824410', '14.70385772286944', '15.01068635703815', '15.47672242686776', '16.30019719512032', '16.72519424511898', '16.89375078706667', '17.43923796133382', '17.82813880676246', '18.34819351187498', '18.89978821743103', '18.99600986727348', '19.60421385121508'], 'prelabel': '2-127995-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.969441982483502, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2202413237921863315, 'z1': {'__RealLiteral__': 0, 'data': '0.7566730339660375', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.465497999328419', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.957200228591649', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1022.0452206713787, 'bad_primes': [3, 5, 7, 23, 53], 'central_character': '1.1', 'conductor': 127995, 'conductor_radical': 127995, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, -2, -1, 0, 1, 0, 1, 0, 5, 2, 1, 0, 1, 4, 3, 0, -4, 2, -1, 0, -1, 0, 1, 0, -1, -2, -4, 0, -5, 0, -5, 0, -1, -2, -3, 0, -1, 0, -8, 0, -8, -10, -1, 0, 6, -4, 1, 0, -3, -2, 1, 0, -5, 0, 4, 0, 11, -2, 4, 0, 1, -8, -1, 0, 12, -6, 1, 0, -9, 0, -8, 0, -1, 8, 5, 0, 16, -4, 1, 0, -16, 2, -3, 0, 4, 0, -6, 0, 1, 2, 5, 0, 4, 0, -16, 0, 5, -2], 'euler11': [1, -5, 11], 'euler13': [1, -1, 13], 'euler17': [1, -3, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 2], 'euler23': [1, 1, 0], 'euler29': [1, 4, 29], 'euler3': [1, 1, 0], 'euler31': [1, 5, 31], 'euler37': [1, 3, 37], 'euler41': [1, 8, 41], 'euler43': [1, 8, 43], 'euler47': [1, -6, 47], 'euler5': [1, 1, 0], 'euler53': [1, -1, 0], 'euler59': [1, -11, 59], 'euler61': [1, -4, 61], 'euler67': [1, -12, 67], 'euler7': [1, -1, 0], 'euler71': [1, 9, 71], 'euler73': [1, 8, 73], 'euler79': [1, -16, 79], 'euler83': [1, 16, 83], 'euler89': [1, 6, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, 0, 2], [1, 1, 0], [1, 1, 0], [1, -1, 0], [1, -5, 11], [1, -1, 13], [1, -3, 17], [1, 4, 19], [1, 1, 0], [1, 4, 29], [1, 5, 31], [1, 3, 37], [1, 8, 41], [1, 8, 43], [1, -6, 47], [1, -1, 0], [1, -11, 59], [1, -4, 61], [1, -12, 67], [1, 9, 71], [1, 8, 73], [1, -16, 79], [1, 16, 83], [1, 6, 89], [1, 16, 97]], 'index': 11, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/127995/j'], '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': '2-127995-1.1-c1-0-11', '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': '2-127995-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.969441982483502, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2202413237921863315, 'z1': {'__RealLiteral__': 0, 'data': '0.7566730339660375', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2202413237921863315', 'Lhash_array': ['2202413237921863315'], 'label': '2-127995-1.1-c1-0-11', 'type': 'ECQ', 'url': 'EllipticCurve/Q/127995/j'}