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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1213054889499281981', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1126.8488733243094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '141120.1', 'coefficient_field': '1.1.1.1', 'conductor': 141120, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1], [1, 4, 11], [1, 2, 13], [1, 2, 17], [1, 0, 19], [1, 0, 23], [1, -6, 29], [1, -8, 31], [1, 2, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, -8, 59], [1, 2, 61], [1, -4, 67], [1, 4, 71], [1, -10, 73], [1, 12, 79], [1, -4, 83], [1, 6, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 209, 'label': '2-141120-1.1-c1-0-209', 'leading_term': '5.23889915837', '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/141120/x', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.105521880389228, 1.109330940747824, -0.3673881373361408, -2.298884058865679, -2.715311542887595, -0.6656244541229249, 2.269998895679967, 3.282881057181121, 1.610417745458693, -0.3194352723725282, -0.01375230913506949, 1.49825665685824, 0.9983602701939814, -1.961577007476068, -3.843946482872454, -2.194910259539266, 0.4378589427861475, 0.3119340948232777, -1.615791256125894, -1.522256388793738, 0.3900753173744596, -0.10928885668333, -3.64328197814476, -5.210348208435012, -2.302403239078554, 0.5604093735341902, -0.5887534485612579, -2.46620389469, -0.8007996905075755, 1.836609187187929, 1.122621253602522, -0.8395511894317766, -0.1083211236510304, 0.8648599197715612, -1.74287675198692, -4.33048736721223, -1.732913844366325, 2.520422386675182, 2.108222560546334, -0.6218084827710378, 0.06251280261374532, 1.949284573660478, 0.2910451953359843, -1.671331225115746, 0.6381909772273769, 3.117147064182815, 1.115772487119827, -1.024223500167027, 0.6757730101608558, 1.467084009012014, -1.413840077731422, -2.256193497056434, 0.734938515806449, 1.141895151071143, -1.696650470191728, -0.9217404060196316, 2.637110243781446, 1.484447859055953, -2.607501491408799, -2.161489424844026, 0.6730960845930415, -0.005696050047469319, -1.247421870710989, -0.01347238162610254, -1.336883636831557, -5.664072608419313, -5.32279958630057, -0.8626052725265196, -0.7010203488677347, -3.378985374499747, -1.838260083367953, 0.2729774259914562, -2.451013911369098, -4.125339485772806, -0.9117711754985006, 0.4700813252158847, -1.319220508517576, 0.1817058148874479, 2.843227334125077, 0.6532294757532793, -1.433525870951042, 1.229603689707258, 2.028043513077677, -0.9520594310137128, -0.3619221147263203, 2.209867406778344, -0.3639594782085235, -3.069793511347754, 0.08364843846577331, 1.888224040056231, -1.262408278795247, -1.606444812827638, 1.052121327023897, 0.04530744395155961, -1.14892982701642, 1.670117332411526, 2.232393139707944, -0.06982778714787724, 2.061256211441231, 4.649799945939947, 0.4636420473913616, -3.075655474000649, -0.4518892925664064, -0.0981501888545351, -3.48344811830589, -2.568753954629081, 0.2402133808383311, -0.1447690443548237, 1.696919001677689, 5.476381526092943, 2.895908751762294, -1.770790882174952, -0.3262640715446508, 1.218032544156188, -0.8908749091523974, 0.1814868689835519, 2.086189880718206, -1.328820170619626, -2.421840755629184, 2.519783630874418], 'positive_zeros': ['0.7025641917200781', '1.554658507437359', '2.438606688135235', '2.752424281361998', '3.347221142637360', '4.193681861904724', '4.543008750596482', '5.191364263612259', '5.488845221786936', '6.417581426779719', '6.687687160506753', '7.312837565399262', '7.870157154949755', '8.265103735814435', '8.622670910917134', '9.338279863639238', '9.925343286492636', '10.24331363905652', '10.77433692309108', '11.20574423732670', '11.83812173016176', '12.18186162215575', '12.64309167437797', '13.19103295056154', '13.60212633057630', '14.06152569622524', '14.58399700756779', '15.17031902303036', '15.49930919596094', '16.00346206344568', '16.11802607088500', '17.11062934394766', '17.14464931416851', '17.90916344590369', '18.06142693558705', '18.82301072888025', '19.07202912186333', '19.48666167922625'], 'prelabel': '2-141120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.56856972413792, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1213054889499281981, 'z1': {'__RealLiteral__': 0, 'data': '0.7025641917200781', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.554658507437359', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.438606688135235', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1126.8488733243094, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 141120, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, 8, 0, 0, 0, 0, 0, -2, 0, 0, 0, -6, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 4, 0, 0, 0, 8, 0, -2, 0, 0, 0, 2, 0, 4, 0, 0, 0, -4, 0, 10, 0, 0, 0, 0, 0, -12, 0, 0, 0, 4, 0, 2, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 4, 11], 'euler13': [1, 2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, -8, 59], 'euler61': [1, 2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 4, 71], 'euler73': [1, -10, 73], 'euler79': [1, 12, 79], 'euler83': [1, -4, 83], 'euler89': [1, 6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 4, 11], [1, 2, 13], [1, 2, 17], [1, 0, 19], [1, 0, 23], [1, -6, 29], [1, -8, 31], [1, 2, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, -8, 59], [1, 2, 61], [1, -4, 67], [1, 4, 71], [1, -10, 73], [1, 12, 79], [1, -4, 83], [1, 6, 89], [1, -2, 97]], 'index': 209, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/141120/x'], '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': '2-141120-1.1-c1-0-209', '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': '2-141120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.56856972413792, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1213054889499281981, 'z1': {'__RealLiteral__': 0, 'data': '0.7025641917200781', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1213054889499281981', 'Lhash_array': ['1213054889499281981'], 'label': '2-141120-1.1-c1-0-209', 'type': 'ECQ', 'url': 'EllipticCurve/Q/141120/x'}