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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': 1, 'A3': 2, 'A4': 1, 'A5': -2, 'A6': 2, 'A7': 1, 'A8': 1, 'A9': 1, 'Lhash': '544069300091567453', 'a10': [-0.6324555320336759, 0], 'a2': [0.7071067811865475, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.5, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.8164965809277261, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 207.81865630058442, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [7, [1, -1]], [11, [1, 1]], [13, [1]]], 'bad_primes': [2, 7, 11, 13], 'central_character': '26026.1', 'coefficient_field': '1.1.1.1', 'conductor': 26026, 'conductor_radical': 2002, 'degree': 2, 'euler_factors': [[1, -1], [1, -2, 3], [1, 2, 5], [1, -1], [1, 1], [1], [1, 0, 17], [1, 4, 19], [1, -4, 23], [1, -2, 29], [1, -10, 31], [1, -6, 37], [1, 0, 41], [1, 4, 43], [1, 10, 47], [1, 14, 53], [1, 10, 59], [1, 8, 61], [1, 8, 67], [1, -4, 71], [1, 4, 73], [1, -16, 79], [1, 4, 83], [1, 10, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 17, 'label': '2-26026-1.1-c1-0-17', 'leading_term': '10.4320527464', '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/26026/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.500340929643933, 4.314837658758735, 4.719135100261145, 3.367067635014592, 0.8261871746086711, -1.484263061430566, -2.196462380585841, -1.104614120920604, 0.5942557645479815, 1.367506414400846, 0.817681201897647, 0.008956785363289192, 0.1650518766829234, 1.146484196800228, 1.598002758167065, 0.7543483101657306, -0.366268702618364, -0.205621903026428, 0.9842325997369487, 0.9609254902431761, -1.663071373893955, -4.993916581853965, -5.541348972884276, -2.560041417519252, 0.5539164452377746, 0.2290125769059133, -2.752798737570275, -4.303909275278545, -2.462859326651221, 0.241089430655264, 0.75726848569699, -0.1427818161547135, 0.2957791760874082, 1.796057026911196, 1.172523308401208, -2.045972703169726, -3.601686325743466, -0.4804172037040969, 3.708106930411392, 3.062693510286479, -2.026616188391881, -5.050709515801651, -2.643269033224878, 0.9048163995157338, 0.643145137534691, -1.680804246381553, -1.28581836272143, 1.530131736407022, 2.226383858077673, -0.1287232603762429, -1.472678386587864, 0.207438272146835, 1.80535213862996, 0.8998661495652217, -0.2645406020313316, 0.6252101016299058, 1.729528459066265, 0.8666710929858432, -0.3363323934973455, 0.0660351638899888, 0.4344958083343237, -0.5918642807525558, -0.3057491500024549, 2.769071526623307, 3.975232581940905, -0.3216257592147602, -4.58992074465473, -1.768302803967267, 3.885023328993875, 2.07080808161331, -6.463326752935642, -9.841848678789855, -3.472931876794753, 3.349561423740331, 2.837685471324309, -0.6797200937708733, -0.8366847657700929, 0.5455623187370268, -0.1403803587575149, -0.7410688361719588, 0.9965140412407772, 2.046145880038599, 0.423465351480317, -0.6465740737215057, 0.08601960702117124, -1.228227084566359, -4.891291732659189, -5.038861269976508, -0.3262916103042192, 2.479877225135008, 0.1721291126068309, -1.838414739596769, -0.397115508113661, 0.3178668511128885, -1.3622698272411, -0.9841873395307593, 2.128568990226999, 2.772905705609161, 0.3412963428598861, -0.2012116303700556, 1.041948337791383, -0.5230263308402278, -3.227470998556025, -1.843800053793013, 1.085874402285957, -0.02405172983975697, -1.963533101069861, 0.4524745542319782, 2.309152626778551, -1.844493079330924, -5.123424071851113, -0.6843324045587579, 3.684076501767159, -0.3090213343019788, -4.940688914361621, -0.8194810279226298, 5.323026914992482, 3.60493423544628, -1.482512224902005, -1.502186198723678], 'positive_zeros': ['1.328389165260069', '2.156998309949883', '3.005109338609371', '3.180191675544484', '4.149425613316880', '4.549026026361099', '5.119086465010038', '6.186464321683340', '6.524351832372770', '7.470068503961033', '7.950301467872566', '8.188535661901408', '8.852198166340833', '9.524940196366388', '10.15764678029673', '10.91625210794567', '11.31711301023970', '11.86723820675337', '12.48787542839644', '12.97810606873416', '13.65031015434629', '13.88687963307091', '14.64818030892283', '14.98104979992921', '15.37542282468328', '15.78472273537834', '16.48627524580386', '17.06956460545326', '17.56777916295229', '18.35371887763578', '18.93862134881680', '19.37603793117737', '19.72416804895259'], 'prelabel': '2-26026-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.415916769341603, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 544069300091567453, 'z1': {'__RealLiteral__': 0, 'data': '1.328389165260069', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.156998309949883', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '3.005109338609371', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 207.81865630058442, 'bad_primes': [2, 7, 11, 13], 'central_character': '1.1', 'conductor': 26026, 'conductor_radical': 2002, 'degree': 2, 'dirichlet_coefficients': [1, 1, 2, 1, -2, 2, 1, 1, 1, -2, -1, 2, 0, 1, -4, 1, 0, 1, -4, -2, 2, -1, 4, 2, -1, 0, -4, 1, 2, -4, 10, 1, -2, 0, -2, 1, 6, -4, 0, -2, 0, 2, -4, -1, -2, 4, -10, 2, 1, -1, 0, 0, -14, -4, 2, 1, -8, 2, -10, -4, -8, 10, 1, 1, 0, -2, -8, 0, 8, -2, 4, 1, -4, 6, -2, -4, -1, 0, 16, -2, -11, 0, -4, 2, 0, -4, 4, -1, -10, -2, 0, 4, 20, -10, 8, 2, -6, 1, -1, -1], 'euler11': [1, 1, 0], 'euler13': [1, 0, 0], 'euler17': [1, 0, 17], 'euler19': [1, 4, 19], 'euler2': [1, -1, 0], 'euler23': [1, -4, 23], 'euler29': [1, -2, 29], 'euler3': [1, -2, 3], 'euler31': [1, -10, 31], 'euler37': [1, -6, 37], 'euler41': [1, 0, 41], 'euler43': [1, 4, 43], 'euler47': [1, 10, 47], 'euler5': [1, 2, 5], 'euler53': [1, 14, 53], 'euler59': [1, 10, 59], 'euler61': [1, 8, 61], 'euler67': [1, 8, 67], 'euler7': [1, -1, 0], 'euler71': [1, -4, 71], 'euler73': [1, 4, 73], 'euler79': [1, -16, 79], 'euler83': [1, 4, 83], 'euler89': [1, 10, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, -1, 0], [1, -2, 3], [1, 2, 5], [1, -1, 0], [1, 1, 0], [1, 0, 0], [1, 0, 17], [1, 4, 19], [1, -4, 23], [1, -2, 29], [1, -10, 31], [1, -6, 37], [1, 0, 41], [1, 4, 43], [1, 10, 47], [1, 14, 53], [1, 10, 59], [1, 8, 61], [1, 8, 67], [1, -4, 71], [1, 4, 73], [1, -16, 79], [1, 4, 83], [1, 10, 89], [1, 6, 97]], 'index': 17, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/26026/r'], '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': '2-26026-1.1-c1-0-17', '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': '2-26026-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.415916769341603, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 544069300091567453, 'z1': {'__RealLiteral__': 0, 'data': '1.328389165260069', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '544069300091567453', 'Lhash_array': ['544069300091567453'], 'label': '2-26026-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/26026/r'}