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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': '1196106225008873679', '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': 3098.8344016418505, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]], [7, [1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '388080.1', 'coefficient_field': '1.1.1.1', 'conductor': 388080, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1], [1, 1], [1, 4, 13], [1, 6, 17], [1, 2, 19], [1, 9, 23], [1, 9, 29], [1, -4, 31], [1, -2, 37], [1, 3, 41], [1, 11, 43], [1, 12, 47], [1, 0, 53], [1, 0, 59], [1, 7, 61], [1, 5, 67], [1, 6, 71], [1, -2, 73], [1, -16, 79], [1, -9, 83], [1, 9, 89], [1, 4, 97]], 'gamma_factors': [[], [0]], 'index': 81, 'label': '2-388080-1.1-c1-0-81', 'leading_term': '3.08904940279', '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/388080/s', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.465694611278836, -0.6072137126659386, -3.278652758076188, -5.47726618373858, -4.788377057174057, -1.594742260246457, 0.7798810878999314, 0.301456937914492, -0.7363849774604851, 0.8383075789961654, 3.679585593019367, 3.613683250693726, 0.6426360197178866, -0.5036369501249987, 1.816775819854701, 3.254153516543252, 1.194404106162992, -0.664776056236863, 0.263471239826502, 0.121403725275322, -3.4973911578274, -5.501233328101294, -2.326514097283237, 0.686479386847967, -0.9927042762766777, -2.621314240624528, -0.04901047789298772, 1.902268246919321, -0.2547678909088092, -1.365056593006102, 1.191996449386772, 2.071387895914198, 0.163233020908979, 1.136718686983832, 3.960952213663483, 1.947922900206698, -2.386305202018795, -1.807560956795664, 0.4653023553384921, -1.494437536967768, -2.879102484372852, 0.4352407839835736, 1.747200466092897, -1.530361699861278, -1.986777997241603, 0.9918452049752182, 0.7666833633963739, -0.400753516216221, 2.478284028533561, 3.886056702528874, 0.5777969459829368, -0.06167099026993459, 2.626193288642559, 1.214440128616962, -1.039534863985368, 2.598681938058986, 5.248545728703417, 1.389849507959235, -0.8526350521644831, 1.219314825884879, 0.8693898813977218, 0.2310760760953037, 3.64438457132433, 4.250867706320852, 0.1487553922549775, -0.2982399172125261, 1.124903359153059, -2.200453084342614, -3.633360721013702, 0.7506893101430431, 1.73030350065784, -0.9891369997868884, 0.2606485694666162, 0.4951042617695419, -4.383606805464609, -4.916670451446417, -0.2970993780108977, 0.3030990860899836, -0.4491397249256637, 1.652453589908512, 0.7121628068674136, -0.9566153917879424, 2.939020632363305, 3.879235135605945, -2.017825603447806, -3.051014677843862, 0.7995062868539913, 0.02182692149687589, -1.124200613113347, 0.3864373633843858, -2.355127695325496, -4.54376905299335, 0.5466124989614837, 3.26327244190974, 0.3619345032281676, 0.5740248436329382, 1.197511941838442, -1.23052526790322, 0.1445723751368936, 1.228254877831733, -4.307370023914342, -5.104628306463247, 1.716675337801077, 2.924663700363827, 0.04252826230039887, 0.6158079334073479, -0.7269655764617766, -2.188356122189884, 2.241169139772331, 3.648069836826977, -0.2670318308931006, -0.06381894316023139, 0.02552579494471245, -3.680291594963145, -1.852361855083761, 1.62911104010139, -1.353832624956472, -1.58287492999898, 2.109621426725914, 0.5963395315539701], 'positive_zeros': ['0.4112895944739891', '1.633848507412971', '2.051231859521791', '2.417854399898395', '3.312778537158132', '3.581038876098312', '4.365944748578777', '4.703142772190904', '5.013307733551060', '5.900926916428299', '6.160799350155437', '6.753503688525031', '7.227754038533836', '7.650088427536115', '8.293601888246557', '8.352919741281555', '9.099016514375847', '9.658970068093406', '9.869483965508554', '10.47219376208791', '10.89421017352108', '11.40975567672175', '11.84462540667768', '12.06465804623854', '12.79943866266079', '13.00681684509066', '13.58643699952806', '13.86406266276781', '14.58325899057323', '14.86698517652854', '15.40445125801576', '15.44465329300643', '16.26128157099913', '16.53366201414448', '16.87031362185497', '17.45918796423438', '17.89202420772289', '18.22463151834239', '18.53464841919653', '19.27262321282600', '19.54553849718466', '19.81788746933983'], 'prelabel': '2-388080-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.66717526192478, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1196106225008873679, 'z1': {'__RealLiteral__': 0, 'data': '0.4112895944739891', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.633848507412971', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.051231859521791', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3098.8344016418505, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 388080, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -4, 0, 0, 0, -6, 0, -2, 0, 0, 0, -9, 0, 1, 0, 0, 0, -9, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, -3, 0, -11, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -7, 0, 0, 0, 4, 0, -5, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, 16, 0, 0, 0, 9, 0, 6, 0, 0, 0, -9, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0], 'euler11': [1, 1, 0], 'euler13': [1, 4, 13], 'euler17': [1, 6, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 9, 23], 'euler29': [1, 9, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 3, 41], 'euler43': [1, 11, 43], 'euler47': [1, 12, 47], 'euler5': [1, 1, 0], 'euler53': [1, 0, 53], 'euler59': [1, 0, 59], 'euler61': [1, 7, 61], 'euler67': [1, 5, 67], 'euler7': [1, 0, 0], 'euler71': [1, 6, 71], 'euler73': [1, -2, 73], 'euler79': [1, -16, 79], 'euler83': [1, -9, 83], 'euler89': [1, 9, 89], 'euler97': [1, 4, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 4, 13], [1, 6, 17], [1, 2, 19], [1, 9, 23], [1, 9, 29], [1, -4, 31], [1, -2, 37], [1, 3, 41], [1, 11, 43], [1, 12, 47], [1, 0, 53], [1, 0, 59], [1, 7, 61], [1, 5, 67], [1, 6, 71], [1, -2, 73], [1, -16, 79], [1, -9, 83], [1, 9, 89], [1, 4, 97]], 'index': 81, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/388080/s'], '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': '2-388080-1.1-c1-0-81', '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': '2-388080-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.66717526192478, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1196106225008873679, 'z1': {'__RealLiteral__': 0, 'data': '0.4112895944739891', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1196106225008873679', 'Lhash_array': ['1196106225008873679'], 'label': '2-388080-1.1-c1-0-81', 'type': 'ECQ', 'url': 'EllipticCurve/Q/388080/s'}