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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 0, 'Lhash': '1639953783394329241', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 119.58396206706956, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 13], 'central_character': '14976.1', 'coefficient_field': '1.1.1.1', 'conductor': 14976, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1], [1], [1, 0, 5], [1, 4, 7], [1, -4, 11], [1, -1], [1, 4, 17], [1, -6, 19], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, -6, 37], [1, -6, 41], [1, 4, 43], [1, 8, 47], [1, 6, 53], [1, -12, 59], [1, -10, 61], [1, 2, 67], [1, 12, 71], [1, 10, 73], [1, 10, 79], [1, -4, 83], [1, 10, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 6, 'label': '2-14976-1.1-c1-0-6', 'leading_term': '1.72218873748', '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/14976/p', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.722188737484907, 1.386027789221113, 0.4485745364360538, -0.7790855786854393, -1.665751659845608, -1.510652581709057, -0.08493336189418996, 1.968607386450554, 3.367880992110988, 3.09882201759267, 1.345776533455998, -0.4790668925682984, -0.8851494866735022, 0.2759602554692786, 1.569575729283099, 1.409753968045366, -0.1340428589329679, -1.172044306454545, 0.03122659678042168, 2.909301295775348, 4.823721417043113, 3.778361453993097, 0.704509007610524, -1.471626231767522, -1.11208933959982, 0.3864993650175596, 0.6212952406599359, -0.5301710526471919, -0.7397329772675355, 1.376808654673675, 3.818553489664533, 3.383727827718776, -0.02981088311199716, -2.849520203893067, -2.176179996582164, 0.5721899931965737, 1.727487998629208, 0.3366084943653395, -0.9671131413826195, -0.3346319889735487, 0.3126027379714939, -1.612104004129082, -4.756927575528158, -5.077713542367851, -1.639502423671119, 1.681053466929422, 1.562213407972589, -0.1484067401520485, 0.4052014148194268, 2.981274046055637, 3.706257751240845, 1.349951271024847, -0.671738266661804, 0.1473229521812949, 1.378246713775357, -0.06600349483253157, -2.371897086669834, -1.558054565209105, 1.609160522901177, 2.167817418128141, -1.291682300033044, -4.183315432745984, -2.982298557742788, -0.3107494400473573, 0.09633499265915116, -0.3801346909183423, 1.491901278203294, 4.13372715679417, 3.35069931690094, -0.0980560999461853, -1.198990416444929, 0.8541611235235848, 1.134273882012188, -2.437887066663682, -5.127317218643721, -3.149099323957423, 0.1859126347430919, 0.4201050004318038, -0.8927477768643926, -0.3184364022702005, 0.4809692948042408, -1.606844515900888, -3.825247582975806, -1.322732228676037, 3.700542634205323, 4.471953110850818, 0.517403206634428, -1.924700562868761, -0.4708058280392015, 0.6857248524894082, -0.3465172949580497, -0.1264437884925504, 2.10167785906328, 1.9531367761652, -1.304413246929492, -1.918206171290352, 2.29919771454313, 5.285980167667802, 2.871418354473322, -0.456478295200961, -0.2864413478035456, 0.2840866466904185, -1.938782505464755, -3.33640649470551, -0.803672283158514, 1.564279596095863, 0.1863524363688821, -1.07967932025095, 1.039352969067934, 2.064175977178071, -1.618095763809131, -4.819002072761736, -2.466511395407686, 1.261458262040483, 1.018032998290563, -0.3700134306484413, 1.050293767862902, 2.176381228536736, 0.107953801500667, -0.8955994810665394, 2.001210426033624], 'positive_zeros': ['0.5926616672340666', '1.510967449248098', '2.670863323228263', '3.204715626059907', '3.980295847531562', '4.496687545612345', '5.559313456727462', '6.178218270648005', '6.644618457157043', '7.116365132968853', '7.998062576743343', '8.696073084409415', '9.295012728910753', '9.821511026325105', '10.08212348458565', '11.10135507984234', '11.71866946241061', '11.94302451980890', '12.87906427258556', '13.22853615181774', '13.74363573370334', '14.37313127258940', '14.92251578792338', '15.80143887752674', '16.03208765022513', '16.34452875465970', '17.24203386410628', '17.65822321198790', '18.10082433676963', '18.97938408069497', '19.32212871037292', '19.80666858248236'], 'prelabel': '2-14976-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.93544521576829, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1639953783394329241, 'z1': {'__RealLiteral__': 0, 'data': '0.5926616672340666', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.510967449248098', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.670863323228263', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 119.58396206706956, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 14976, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 1, 0, 0, 0, -4, 0, 6, 0, 0, 0, 0, 0, -5, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, -4, 0, 0, 0, -8, 0, 9, 0, 0, 0, -6, 0, 0, 0, 0, 0, 12, 0, 10, 0, 0, 0, 0, 0, -2, 0, 0, 0, -12, 0, -10, 0, 0, 0, -16, 0, -10, 0, 0, 0, 4, 0, 0, 0, 0, 0, -10, 0, -4, 0, 0, 0, 0, 0, 14, 0, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, -1, 0], 'euler17': [1, 4, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -6, 37], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 5], 'euler53': [1, 6, 53], 'euler59': [1, -12, 59], 'euler61': [1, -10, 61], 'euler67': [1, 2, 67], 'euler7': [1, 4, 7], 'euler71': [1, 12, 71], 'euler73': [1, 10, 73], 'euler79': [1, 10, 79], 'euler83': [1, -4, 83], 'euler89': [1, 10, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 5], [1, 4, 7], [1, -4, 11], [1, -1, 0], [1, 4, 17], [1, -6, 19], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, -6, 37], [1, -6, 41], [1, 4, 43], [1, 8, 47], [1, 6, 53], [1, -12, 59], [1, -10, 61], [1, 2, 67], [1, 12, 71], [1, 10, 73], [1, 10, 79], [1, -4, 83], [1, 10, 89], [1, -14, 97]], 'index': 6, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/14976/p'], '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': '2-14976-1.1-c1-0-6', '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': '2-14976-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.93544521576829, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1639953783394329241, 'z1': {'__RealLiteral__': 0, 'data': '0.5926616672340666', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1639953783394329241', 'Lhash_array': ['1639953783394329241'], 'factors': ['2-14976-1.1-c1-0-6'], 'label': '2-14976-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/14976/p'}