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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': 1, 'A8': -1, 'A9': -2, 'Lhash': '229359424569045103', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 818.8658727282308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [5, [1]], [7, [1, -1]], [293, [1, 1]]], 'bad_primes': [2, 5, 7, 293], 'central_character': '102550.1', 'coefficient_field': '1.1.1.1', 'conductor': 102550, 'conductor_radical': 20510, 'degree': 2, 'euler_factors': [[1, 1], [1, 1, 3], [1], [1, -1], [1, 0, 11], [1, -2, 13], [1, -3, 17], [1, 0, 19], [1, 4, 23], [1, -6, 29], [1, 1, 31], [1, 2, 37], [1, 5, 41], [1, -5, 43], [1, -9, 47], [1, 2, 53], [1, 7, 59], [1, -12, 61], [1, -7, 67], [1, 8, 71], [1, -6, 73], [1, -7, 79], [1, -4, 83], [1, 5, 89], [1, 19, 97]], 'gamma_factors': [[], [0]], 'index': 14, 'label': '2-102550-1.1-c1-0-14', 'leading_term': '4.11227508353', '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/102550/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.8991729630453126, 1.103262128315203, 0.3800654465985056, -0.6006169547201444, -0.5936876818867505, 0.8758165405667891, 2.505373551041259, 2.271676283296078, -0.001305724660570916, -1.745769237325183, -0.4504609836631473, 2.708893784519956, 3.617136306446996, 0.5283956450492034, -2.867344647773294, -1.784500899388626, 2.930865449190529, 5.362512127865247, 2.472117900684548, -1.735376458740913, -2.190030189660955, 0.03375186381930772, 0.3005653326974362, -1.74161407466995, -2.100794655844625, 0.03732588211165587, 0.5757687425033312, -2.116686059347103, -3.843093055952624, -1.672350475577493, 0.9580867801825935, 0.4015091494829235, -0.9810526848174381, 0.09045974325315095, 1.310763574466997, -0.4692781551352911, -2.417169940576714, -0.6036682311496133, 2.320370339354568, 1.777710713744863, -0.3677633283670979, 0.1071955078178967, 1.584492969070574, 0.639316920621005, -0.5048972906523997, 1.063123792562091, 2.233916730342108, 0.5583741427195652, 0.2528807625854195, 2.763734949074983, 0.9850940490734088, -7.26692768914538, -11.6416528441162, -6.0737788862687, 0.004492373377097761, -1.226415963273517, -2.701405129459538, 1.669913780701535, 4.414404318353565, 0.1166187496533549, -3.323172200288704, -0.3521566181045702, 2.318545715047159, 0.3500089862194937, -0.8134644604153364, 0.9982381468300588, 1.013310690578908, -0.8942605819852978, -0.5602690476480514, 0.5938384619517058, -0.375018387890832, -0.6193371006348283, 1.047174873360162, 0.3025748047719637, -2.272934051465066, -1.367555561314877, 0.6332880507908176, -1.841057566018494, -4.468405912815221, -1.861736773343965, 0.4524931944813299, -1.335483643418733, -0.7485027272393193, 2.933361064472378, 1.482577079870451, -3.172827323901179, -1.708413514976048, 1.98078101971916, -0.6810752387213613, -3.406665583361755, 0.9552576949145664, 4.269057648526717, 1.1199609330812, -0.6973424205294008, 0.3185292163297042, -2.806450182817093, -6.241942907985485, -2.435804812472137, 1.891805518986802, -0.2548910905053382, -1.943654371125927, 0.4600882864524808, 0.3321418052848336, -1.62390493298384, 0.5612451243503025, 2.491281620065088, -0.5040945303982756, -2.027521275420201, 0.5111480299271549, 0.909420473585717, -0.5744278185507576, 0.3874685143353938, 0.8603580360897528, -0.5526466029808222, 0.3419846119252359, 1.296825806947873, -1.287875261153609, -1.647695707366539, 1.475324842112804, 0.1883934761091848], 'positive_zeros': ['0.8385138943966334', '1.375331924987141', '2.249873414772963', '2.788169335324449', '3.531310624282259', '4.102368940559752', '4.882046021071793', '5.495533227748519', '5.796104949711565', '6.495616047574935', '6.824687841427193', '7.631451296793365', '8.054808236915799', '8.488284608030876', '8.957062982605482', '9.544008573538908', '10.19036763210807', '10.48434702567816', '11.08992814269265', '11.37385969021759', '12.09284548672608', '12.20368416760180', '12.78800370799881', '13.74953358081900', '13.89350902941419', '14.42455673964842', '15.00507062521238', '15.52010775372789', '16.03339620024341', '16.37704828436834', '16.87463572960455', '17.33842200255910', '17.68398144786594', '18.09726179313446', '18.52819125824575', '19.12689737626598', '19.36959431990833'], 'prelabel': '2-102550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.615832553469954, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 229359424569045103, 'z1': {'__RealLiteral__': 0, 'data': '0.8385138943966334', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.375331924987141', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.249873414772963', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 818.8658727282308, 'bad_primes': [2, 5, 7, 293], 'central_character': '1.1', 'conductor': 102550, 'conductor_radical': 20510, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, 1, -1, -2, 0, 0, -1, 2, -1, 0, 1, 3, 2, 0, 0, -1, 0, -4, 1, 0, -2, 5, 1, 6, 0, -1, -1, 0, -3, 0, -2, -2, 0, -2, 0, -5, 1, 5, 0, 0, 4, 9, -1, 1, 0, -3, 2, -2, -5, 0, -1, 0, -6, -7, 0, 12, 1, -2, 1, 0, 0, 7, 3, 4, 0, -8, 2, 6, 2, 0, 0, 0, 2, 7, 0, 1, 5, 4, -1, 0, -5, -6, 0, -5, 0, 2, -4, 1, -9, 0, 1, -19, -1, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, -3, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 0], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 3], 'euler31': [1, 1, 31], 'euler37': [1, 2, 37], 'euler41': [1, 5, 41], 'euler43': [1, -5, 43], 'euler47': [1, -9, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, 7, 59], 'euler61': [1, -12, 61], 'euler67': [1, -7, 67], 'euler7': [1, -1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -6, 73], 'euler79': [1, -7, 79], 'euler83': [1, -4, 83], 'euler89': [1, 5, 89], 'euler97': [1, 19, 97], 'euler_factors': [[1, 1, 0], [1, 1, 3], [1, 0, 0], [1, -1, 0], [1, 0, 11], [1, -2, 13], [1, -3, 17], [1, 0, 19], [1, 4, 23], [1, -6, 29], [1, 1, 31], [1, 2, 37], [1, 5, 41], [1, -5, 43], [1, -9, 47], [1, 2, 53], [1, 7, 59], [1, -12, 61], [1, -7, 67], [1, 8, 71], [1, -6, 73], [1, -7, 79], [1, -4, 83], [1, 5, 89], [1, 19, 97]], 'index': 14, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/102550/i'], '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': '2-102550-1.1-c1-0-14', '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': '2-102550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.615832553469954, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 229359424569045103, 'z1': {'__RealLiteral__': 0, 'data': '0.8385138943966334', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '229359424569045103', 'Lhash_array': ['229359424569045103'], 'label': '2-102550-1.1-c1-0-14', 'type': 'ECQ', 'url': 'EllipticCurve/Q/102550/i'}