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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -3, 'A8': 0, 'A9': 1, 'Lhash': '272172096537665979', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 881.5484383149359, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [23, [1, -1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '110400.1', 'coefficient_field': '1.1.1.1', 'conductor': 110400, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, 3, 7], [1, -6, 11], [1, 2, 13], [1, 3, 17], [1, -6, 19], [1, -1], [1, -9, 29], [1, 3, 31], [1, -3, 37], [1, 3, 41], [1, 0, 43], [1, 4, 47], [1, 9, 53], [1, -3, 59], [1, -8, 61], [1, -3, 67], [1, 9, 71], [1, 6, 73], [1, 4, 79], [1, -3, 83], [1, 8, 89], [1, 18, 97]], 'gamma_factors': [[], [0]], 'index': 195, 'label': '2-110400-1.1-c1-0-195', 'leading_term': '8.60908772966', '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/110400/fv', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.953272138391811, 2.789107226490535, 1.925804448379653, 0.02850861715042429, -1.109674199216566, -0.161107167809917, 2.057194383461718, 3.091801590875516, 1.590234442682612, -0.8849473170548267, -1.674774867516705, -0.5110233713951796, 0.1717285175543861, -1.063370073433479, -2.289897961810892, -1.239109278797011, 0.5805715602567655, -0.3039260501873172, -3.459193956156552, -4.095619193477856, -0.1103829210468639, 3.914001917129754, 2.962310131178065, -0.9841207816093387, -2.254287975053888, -0.2637235636783864, 0.7204887542447107, -0.1538222273143423, 0.9221853425779902, 4.391856034694581, 5.242561636747425, 1.667936640579783, -1.119751866283827, 0.4318448507566617, 2.485113282985884, 1.305673892860025, -0.4207306885460302, 0.03692470494438402, 0.04581650866027507, -1.595074030275465, -0.3729292025101318, 4.821530103679589, 6.900411843856624, 2.289919063781421, -1.804061113818147, 0.2607709002791338, 3.065310926915452, 1.318157203976514, -0.5138556062410627, 1.487391545005358, 2.422226108790446, -0.824379589847735, -2.804671082505762, -0.772661943030561, 0.03072563694204996, -2.072073301244517, -2.071385159232357, 0.06981029222927551, -0.7194535042989731, -2.637742322416884, -0.207536343319015, 3.266491265870343, 1.83227295457371, -0.8300925326208038, 0.03176362347062917, -0.2509947394556261, -4.323841487956479, -5.11983742532591, -0.7414168979024525, 0.5873582767431906, -1.953827508946745, 0.1408806725746641, 5.685894196083048, 5.159916522713975, 0.04655989860119223, -0.9777747705840518, 0.8811667840744474, 0.388464978196205, -0.02586161829788396, 1.239125396042487, 0.4439104153393742, -0.1403519389575347, 4.461093564145435, 8.009819910426929, 3.290570945684895, -2.451870906118532, -1.661594512615589, 0.02883695152433152, -1.056801267220183, -0.01925346887367282, 1.212530177500813, -2.881209657874208, -5.596048144522382, -0.622007810769374, 2.627446647923571, -2.00626734892541, -4.85202127695075, -1.516328182901676, 0.1974538601308236, -0.7032874089113611, 0.4976758910557453, 0.499169253313602, -2.451070997668092, -1.800579791095507, 1.736712759416643, 0.9948859575963477, -1.028725138045954, 0.4338217292643394, 0.02689800506020895, -2.31767057757136, 1.450221816266672, 6.695592768255375, 3.307964438499405, -1.951704083689838, -0.4126967125005723, 0.8588751058059585, -1.49836745826, 0.08344710940920647, 3.350321653112531, 1.137290629307888], 'positive_zeros': ['1.003865674779443', '1.520346698558282', '2.403109345657348', '3.108182069893816', '3.318271964844962', '4.148670512727529', '4.468665867741233', '5.255357943890424', '5.933841993427247', '6.531745800432245', '6.948839961511736', '7.138045289394032', '8.107381776815156', '8.460922145811587', '9.156179811770339', '9.489977052213282', '9.759170700056558', '10.27283144050532', '11.10222530744034', '11.48331620717214', '12.12041323054252', '12.35623121706458', '12.94741444655662', '13.59823953144286', '13.75611434487720', '14.48707397268415', '14.66134928251943', '15.26195786606419', '15.88936202787426', '16.24489594363498', '16.47485689301202', '17.29869270263509', '17.56326668266991', '17.99336274946965', '18.75293266615878', '19.11957063375562', '19.58431540881314', '19.75717917316927'], 'prelabel': '2-110400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 29.690881400102217, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 272172096537665979, 'z1': {'__RealLiteral__': 0, 'data': '1.003865674779443', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.520346698558282', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.403109345657348', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 881.5484383149359, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 110400, 'conductor_radical': 690, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -3, 0, 1, 0, 6, 0, -2, 0, 0, 0, -3, 0, 6, 0, -3, 0, 1, 0, 0, 0, 1, 0, 9, 0, -3, 0, 6, 0, 0, 0, 3, 0, -2, 0, -3, 0, 0, 0, 0, 0, -4, 0, 2, 0, -3, 0, -9, 0, 0, 0, 6, 0, 3, 0, 8, 0, -3, 0, 0, 0, 3, 0, 1, 0, -9, 0, -6, 0, 0, 0, -18, 0, -4, 0, 1, 0, 3, 0, 0, 0, 9, 0, -8, 0, 6, 0, -3, 0, 0, 0, -18, 0, 6, 0], 'euler11': [1, -6, 11], 'euler13': [1, 2, 13], 'euler17': [1, 3, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, -9, 29], 'euler3': [1, -1, 0], 'euler31': [1, 3, 31], 'euler37': [1, -3, 37], 'euler41': [1, 3, 41], 'euler43': [1, 0, 43], 'euler47': [1, 4, 47], 'euler5': [1, 0, 0], 'euler53': [1, 9, 53], 'euler59': [1, -3, 59], 'euler61': [1, -8, 61], 'euler67': [1, -3, 67], 'euler7': [1, 3, 7], 'euler71': [1, 9, 71], 'euler73': [1, 6, 73], 'euler79': [1, 4, 79], 'euler83': [1, -3, 83], 'euler89': [1, 8, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 3, 7], [1, -6, 11], [1, 2, 13], [1, 3, 17], [1, -6, 19], [1, -1, 0], [1, -9, 29], [1, 3, 31], [1, -3, 37], [1, 3, 41], [1, 0, 43], [1, 4, 47], [1, 9, 53], [1, -3, 59], [1, -8, 61], [1, -3, 67], [1, 9, 71], [1, 6, 73], [1, 4, 79], [1, -3, 83], [1, 8, 89], [1, 18, 97]], 'index': 195, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/110400/fv'], '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': '2-110400-1.1-c1-0-195', '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': '2-110400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 29.690881400102217, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 272172096537665979, 'z1': {'__RealLiteral__': 0, 'data': '1.003865674779443', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '272172096537665979', 'Lhash_array': ['272172096537665979'], 'label': '2-110400-1.1-c1-0-195', 'type': 'ECQ', 'url': 'EllipticCurve/Q/110400/fv'}