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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': -2, 'Lhash': '1412206192448790392', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 1614.255727262205, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1]], [7, [1, 1]], [19, [1]]], 'bad_primes': [2, 5, 7, 19], 'central_character': '202160.1', 'coefficient_field': '1.1.1.1', 'conductor': 202160, 'conductor_radical': 1330, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, -1], [1, 1], [1, 2, 11], [1, -6, 13], [1, 5, 17], [1], [1, -3, 23], [1, 4, 29], [1, 2, 31], [1, 1, 37], [1, 11, 41], [1, -1, 43], [1, 0, 47], [1, -3, 53], [1, 2, 59], [1, 10, 61], [1, 0, 67], [1, 1, 71], [1, -1, 73], [1, 4, 79], [1, 16, 83], [1, -6, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 30, 'label': '2-202160-1.1-c1-0-30', 'leading_term': '5.15829967543', '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/202160/z', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.066533556898054, 0.9597288885539684, -0.6009130351638806, -2.367205470272713, -2.41677752217165, -0.4326701631038428, 1.297653805977372, 0.3232725957289572, -2.516688850968753, -3.647785334806712, -1.57095148107637, 0.6558568823937992, -0.2874453979733546, -2.679544637422714, -2.056319457396941, 1.590730309215939, 3.214845017231473, 0.5112942145530719, -2.310739849115901, -1.349273231763157, 0.9176669155142787, 0.5891047949270539, -0.8781119040333563, -0.3154973388837902, 0.6635425818023729, -0.6243844248578051, -1.527167625432778, 0.9642597588528035, 2.701352627609516, -1.165967063941318, -6.108783104139573, -4.844798630472494, -0.05158809059773141, 0.8301166755503044, -1.015057918907688, -0.001116136156156575, 1.434727778930612, -1.890987166382302, -5.886255653276568, -4.115927676860222, -0.1690506602383612, -0.1816779201902375, -1.399517356892862, 0.09381454009082577, 0.9316376809851492, -0.3261475055565206, 1.331287133794307, 5.339867504820607, 4.46462353924164, -0.3309041270769669, -1.139835482052638, 1.146299468401665, 0.426827877048288, -0.8044296725399827, 1.044662705818889, 0.4637645433874131, -4.108264964621905, -3.643051449237594, 2.949675314506094, 4.88531818017223, 0.8260042341176133, -0.05311585563579275, 1.725707538119024, -0.5244787244107002, -3.116940863780457, -1.054982614748536, 0.3776994667974032, -1.180475507914037, -0.0429933847949898, 2.597352197620236, 1.037532444494259, -1.063114323060913, 0.1102538644417395, -0.5161201769141902, -2.321188443657376, 1.566975417484985, 5.742251746741953, 1.497688531686965, -3.279600814271667, -0.460845441208636, 1.854482329840138, -0.3406508952881315, 0.7945753527142745, 3.727900027679983, 1.069670259946397, -1.516195722621292, 1.400829601877237, 2.292687618023187, -0.6726829987092983, -0.3093794783921821, 1.340986054083845, -0.2219194605880612, -0.0568548079593479, 1.900897133967068, -0.140837718870857, -1.174656013891338, 2.950964327477262, 2.698638770959591, -3.038026203341029, -2.71045403220512, 1.63499903897828, 0.6473164030942986, -0.8656099801053728, 0.6561290798871762, -1.095614713443606, -2.316899429476524, 2.847139596311994, 4.186144353467623, -2.105735528215915, -3.252462281183192, 1.234138450782954, 0.7815046665598896, -1.454133013082945, -0.1135236685880995, 0.05894090285043937, -0.4354905535156275, 0.7107652724351485, -2.001971490837161, -5.409965024492215, -1.280752537851037], 'positive_zeros': ['0.6715113342204400', '1.546084311094715', '2.032034033411266', '2.895717480744703', '3.218680576695995', '3.896672473037425', '4.533942858773481', '5.130390599591385', '5.585811008890943', '6.054012496360145', '6.417175712747035', '6.927148288111761', '7.448988205447348', '8.253597088099679', '8.603781524099896', '9.000116556434243', '9.398829461988186', '10.26976748416134', '10.47188198563001', '10.98865836080529', '11.42418399141949', '11.63887000345330', '12.47918357139244', '12.86612339607294', '13.30018645402559', '13.63359246633509', '14.03022282778298', '14.64208634406318', '15.31842840702462', '15.50732321149322', '15.96566915774601', '16.60099899839826', '16.82615493122096', '17.25349137242520', '17.83461919710615', '18.22971682807782', '18.43916330247737', '18.93362264342778', '19.55439235060952'], 'prelabel': '2-202160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.17780142394809, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1412206192448790392, 'z1': {'__RealLiteral__': 0, 'data': '0.6715113342204400', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.546084311094715', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.032034033411266', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1614.255727262205, 'bad_primes': [2, 5, 7, 19], 'central_character': '1.1', 'conductor': 202160, 'conductor_radical': 1330, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, -1, 0, -2, 0, -2, 0, 6, 0, -1, 0, -5, 0, 0, 0, 1, 0, 3, 0, 1, 0, 5, 0, -4, 0, -2, 0, 2, 0, -1, 0, -1, 0, -6, 0, -11, 0, 1, 0, -2, 0, 0, 0, 1, 0, 5, 0, 3, 0, -2, 0, 0, 0, -2, 0, -10, 0, 2, 0, 6, 0, 0, 0, -3, 0, -1, 0, 1, 0, -1, 0, 2, 0, -4, 0, 1, 0, -16, 0, -5, 0, 4, 0, 6, 0, -6, 0, 2, 0, 0, 0, -10, 0, 4, 0], 'euler11': [1, 2, 11], 'euler13': [1, -6, 13], 'euler17': [1, 5, 17], 'euler19': [1, 0, 0], 'euler2': [1, 0, 0], 'euler23': [1, -3, 23], 'euler29': [1, 4, 29], 'euler3': [1, 1, 3], 'euler31': [1, 2, 31], 'euler37': [1, 1, 37], 'euler41': [1, 11, 41], 'euler43': [1, -1, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, -3, 53], 'euler59': [1, 2, 59], 'euler61': [1, 10, 61], 'euler67': [1, 0, 67], 'euler7': [1, 1, 0], 'euler71': [1, 1, 71], 'euler73': [1, -1, 73], 'euler79': [1, 4, 79], 'euler83': [1, 16, 83], 'euler89': [1, -6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, -1, 0], [1, 1, 0], [1, 2, 11], [1, -6, 13], [1, 5, 17], [1, 0, 0], [1, -3, 23], [1, 4, 29], [1, 2, 31], [1, 1, 37], [1, 11, 41], [1, -1, 43], [1, 0, 47], [1, -3, 53], [1, 2, 59], [1, 10, 61], [1, 0, 67], [1, 1, 71], [1, -1, 73], [1, 4, 79], [1, 16, 83], [1, -6, 89], [1, 10, 97]], 'index': 30, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/202160/z'], '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': '2-202160-1.1-c1-0-30', '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': '2-202160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.17780142394809, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1412206192448790392, 'z1': {'__RealLiteral__': 0, 'data': '0.6715113342204400', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1412206192448790392', 'Lhash_array': ['1412206192448790392'], 'label': '2-202160-1.1-c1-0-30', 'type': 'ECQ', 'url': 'EllipticCurve/Q/202160/z'}