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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '2036346291145878239', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 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': 256.03232904103356, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [167, [1, 1]]], 'bad_primes': [2, 3, 167], 'central_character': '32064.1', 'coefficient_field': '1.1.1.1', 'conductor': 32064, 'conductor_radical': 1002, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1, 5], [1, -1, 7], [1, -2, 11], [1, -6, 13], [1, 4, 17], [1, 4, 19], [1, 8, 23], [1, -2, 29], [1, -5, 31], [1, 3, 37], [1, 6, 41], [1, 8, 43], [1, 3, 47], [1, -7, 53], [1, -11, 59], [1, 4, 61], [1, 7, 67], [1, -4, 71], [1, -6, 73], [1, 4, 79], [1, 15, 83], [1, -9, 89], [1, 13, 97]], 'gamma_factors': [[], [0]], 'index': 20, 'label': '2-32064-1.1-c1-0-20', 'leading_term': '8.1459223579', '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/32064/u', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.936254188894027, 3.255618535404916, 3.396822479621921, 2.254245387732405, 0.5398431385744089, -0.5310419987524072, -0.2424553826061785, 0.8073475151159156, 1.10205541218944, -0.252205625579956, -2.343768390862439, -3.161678857508253, -1.779130811913826, 0.3984961248866551, 1.102335236134097, -0.0215647303571622, -0.7892332819834084, 0.7648337452533432, 3.473174983917851, 4.023775275781967, 1.145666131209208, -2.366345173481397, -2.906909787086794, -0.6310968306662713, 0.9394533460409621, -0.008306711817900814, -0.9522381367597175, 1.124974547202523, 4.853577221205824, 5.947016290445552, 3.188731724866218, 0.07819396059173073, -0.3782450605566994, 0.2927902627098013, -0.6581722950440723, -2.190842636727369, -1.244803738559343, 1.579246441774535, 2.340802946296277, 0.1941103446746483, -0.8722710473910398, 1.380800596664331, 3.313548984699687, 1.266189407777429, -2.015199738447189, -1.671155560361394, 0.9570360240841207, 0.3190565119736536, -3.831071017064622, -5.523051487943703, -2.168387453247801, 1.455065344439436, 1.283653892668723, -0.1606915908464482, 0.3428157403015379, 0.7927691811125985, -1.170272337122247, -2.673231298587598, -0.7227412394773823, 1.57089336649631, 0.292260488961575, -1.872769706259916, -0.6362934099403891, 1.394241291040765, -0.6169967008434587, -3.940274120633466, -2.366731631258437, 2.395216209122237, 3.276099819085199, 0.1034331602560749, -1.005393216500219, 0.6311940140449205, -0.01757416588834817, -2.750324052905963, -2.125181384869307, 1.467898580818609, 1.914704823474658, -1.109374833960569, -1.847689777917177, 0.2237156121802103, 0.05684300893907948, -2.257476945055289, -1.859488190901297, 0.5970345017054606, 0.4878296075475241, -0.7539476069202831, 1.138292289630339, 3.091465367589888, 0.05680280605403156, -3.704283850988075, -1.635242523463831, 2.144963016890539, 0.2917245561201295, -3.726069992804233, -2.71524716686115, 0.424349170149742, -0.4786938846512448, -2.381818948579262, -0.2095499253736127, 2.471250623989495, 1.362460504743707, -0.027229278575791, 0.9628124667305904, 0.4933998629112203, -1.889595091589395, -0.9128165242567975, 2.524110079724391, 1.723534430801955, -1.992558529808018, -1.590373495118332, 1.085453392930631, -0.4345195747304328, -3.09386768258038, -1.198368464441614, 0.3519947263001532, -3.905358204528501, -7.360999174776914, -3.780905343583218, 0.6344532123435181, 0.1640942546174142], 'positive_zeros': ['1.344049507102246', '1.812131194500516', '2.467953534590007', '3.447553215155438', '3.996216668553897', '4.418412081352115', '5.322504994214969', '6.065920800705894', '6.498718639434491', '6.909799025177097', '8.010530316585747', '8.363699747011581', '8.640240909120010', '9.361079758092519', '10.02062916077611', '10.37956420399979', '11.08435068837604', '11.64932275809658', '12.02422157833544', '12.87453990579153', '13.45177613278753', '13.67028798150986', '14.13061830744288', '14.80900727521215', '15.27674768071546', '15.80845270180539', '16.20784444909235', '16.87069880870515', '17.50861632896198', '17.90389888342146', '18.24822741439876', '18.89531410799904', '19.41131062682742', '19.96957703023099'], 'prelabel': '2-32064-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.001010250638352, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2036346291145878239, 'z1': {'__RealLiteral__': 0, 'data': '1.344049507102246', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.812131194500516', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.467953534590007', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 256.03232904103356, 'bad_primes': [2, 3, 167], 'central_character': '1.1', 'conductor': 32064, 'conductor_radical': 1002, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 6, 0, 1, 0, -4, 0, -4, 0, 1, 0, -8, 0, -4, 0, 1, 0, 2, 0, 5, 0, 2, 0, 1, 0, -3, 0, 6, 0, -6, 0, -8, 0, 1, 0, -3, 0, -6, 0, -4, 0, 7, 0, 2, 0, -4, 0, 11, 0, -4, 0, 1, 0, 6, 0, -7, 0, -8, 0, 4, 0, 6, 0, -4, 0, 2, 0, -4, 0, 1, 0, -15, 0, -4, 0, 2, 0, 9, 0, 6, 0, 5, 0, -4, 0, -13, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, -6, 13], 'euler17': [1, 4, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -5, 31], 'euler37': [1, 3, 37], 'euler41': [1, 6, 41], 'euler43': [1, 8, 43], 'euler47': [1, 3, 47], 'euler5': [1, -1, 5], 'euler53': [1, -7, 53], 'euler59': [1, -11, 59], 'euler61': [1, 4, 61], 'euler67': [1, 7, 67], 'euler7': [1, -1, 7], 'euler71': [1, -4, 71], 'euler73': [1, -6, 73], 'euler79': [1, 4, 79], 'euler83': [1, 15, 83], 'euler89': [1, -9, 89], 'euler97': [1, 13, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 5], [1, -1, 7], [1, -2, 11], [1, -6, 13], [1, 4, 17], [1, 4, 19], [1, 8, 23], [1, -2, 29], [1, -5, 31], [1, 3, 37], [1, 6, 41], [1, 8, 43], [1, 3, 47], [1, -7, 53], [1, -11, 59], [1, 4, 61], [1, 7, 67], [1, -4, 71], [1, -6, 73], [1, 4, 79], [1, 15, 83], [1, -9, 89], [1, 13, 97]], 'index': 20, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32064/u'], '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': '2-32064-1.1-c1-0-20', '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': '2-32064-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.001010250638352, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2036346291145878239, 'z1': {'__RealLiteral__': 0, 'data': '1.344049507102246', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '2036346291145878239', 'Lhash_array': ['2036346291145878239'], 'label': '2-32064-1.1-c1-0-20', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32064/u'}