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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': '1692887697431558740', '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': 563.4244366621547, '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': '70560.1', 'coefficient_field': '1.1.1.1', 'conductor': 70560, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1], [1, 4, 11], [1, 6, 13], [1, 2, 17], [1, -4, 19], [1, 0, 23], [1, -6, 29], [1, 8, 31], [1, -6, 37], [1, -6, 41], [1, 8, 43], [1, -4, 47], [1, -2, 53], [1, 0, 59], [1, 10, 61], [1, -8, 67], [1, 0, 71], [1, -10, 73], [1, 4, 79], [1, 4, 83], [1, 10, 89], [1, -18, 97]], 'gamma_factors': [[], [0]], 'index': 50, 'label': '2-70560-1.1-c1-0-50', 'leading_term': '4.4162780243', '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/70560/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.9492875394566594, 1.026511172404427, -0.2369063428185883, -2.325472367202103, -3.70643186483478, -2.978677861545634, -0.4176001092349408, 1.895660040262062, 2.058109729120049, 0.5379212726907342, -0.2350879520262937, 1.096368748279987, 2.809321068047589, 2.140509329671864, -0.8423067642741782, -2.879007058851943, -1.725658624976713, 0.7108854412871731, 1.100375613217002, -0.3948169398148846, -0.5264765944520781, 1.546384724553393, 2.30357981454132, -0.763173638160353, -4.541110527242143, -4.337149727940674, -0.874144860360446, 0.9012706126561078, -0.5160404069028469, -1.551695173966874, -0.4034229343856475, -0.2027788143178674, -2.741112984818814, -4.198662013861217, -1.428967090789997, 1.909707699728758, 1.013496115659764, -1.919405503011651, -1.709701120888021, 0.5699803090292309, -0.04103010801259314, -2.810696693586371, -2.584246729077852, 0.3070932159517374, 0.4599159544279601, -2.311147429512974, -2.536720467650819, 0.4430753607024182, 1.397817005970059, -0.4119603775185537, -0.09906063279505822, 2.370169072575771, 1.533058933276488, -2.279125213824585, -2.569464772861303, 0.9019111750237895, 1.399227743638423, -1.824639965383355, -2.466600783307806, 0.1295222784720128, 0.3102748191209169, -1.799854899535609, -0.9568815279649084, 1.555632341694468, 0.5327837505078339, -1.606145381286891, 0.3822169666196427, 2.857497093955541, 0.1911521196354576, -3.286294784639671, -1.717867353684114, 0.6898133904062929, -0.8542307449320565, -1.736928224025263, 1.206050842096994, 2.033209021979528, -1.65035630952296, -3.213873474616305, -0.6879457337607102, 0.3186261807549419, 0.07403952146214111, 3.53721411405439, 7.034303691691397, 4.154658091012302, -0.4153902254293244, -0.01944870940623624, 0.9225872885583534, -1.904379776968277, -2.766248711363465, 0.631490951306459, 1.241771506431215, -1.795821760251359, -1.324155541175269, 1.772963280028703, 1.021236472197888, -0.9591613397974466, 0.5583276884345598, 0.9387577071121963, -2.150101754698722, -1.756964217225262, 2.363298876402166, 1.555883404656148, -2.910111657631383, -2.07582104784834, 1.776098704467888, 1.283454822493265, -0.3933833791577243, 0.578737139888235, -0.4454800948581829, -2.975216324428681, -0.09004890157943872, 4.675854515536753, 2.931137957271613, -0.9096225058387959, -0.004951134025178701, 0.8823625156598925, -0.8396018680761002, 0.7648813571805816, 3.538123056223448, -0.04136988092013906], 'positive_zeros': ['0.7171044052122643', '1.786857326917936', '2.600479783666773', '2.833885036672467', '3.684901579240581', '4.417045105401203', '4.934901231018025', '5.329461882922155', '5.954975129193989', '6.821973540201085', '7.184446223352429', '7.844505889088990', '7.951591808567473', '8.836923416657954', '9.330268716473735', '9.924607939168859', '10.24585579613563', '10.96918584807065', '11.29886917137870', '11.96278489994219', '12.44163783262949', '12.76118671948764', '13.35094757986194', '13.93406403753003', '14.36671466645762', '14.98583985839220', '15.28872717240044', '15.83279974306538', '16.29715986810023', '16.72289612682676', '17.26048732433153', '17.88652192542202', '18.16205344061826', '18.66184887591399', '19.15103299096264', '19.82874704192237'], 'prelabel': '2-70560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.73656328667136, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1692887697431558740, 'z1': {'__RealLiteral__': 0, 'data': '0.7171044052122643', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.786857326917936', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.600479783666773', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 563.4244366621547, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 70560, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -4, 0, -6, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, -8, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, -8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, -10, 0, 0, 0, 6, 0, 8, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 2, 0, 0, 0, -10, 0, 0, 0, 0, 0, -4, 0, 18, 0, 0, 0], 'euler11': [1, 4, 11], 'euler13': [1, 6, 13], 'euler17': [1, 2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, -6, 37], 'euler41': [1, -6, 41], 'euler43': [1, 8, 43], 'euler47': [1, -4, 47], 'euler5': [1, 1, 0], 'euler53': [1, -2, 53], 'euler59': [1, 0, 59], 'euler61': [1, 10, 61], 'euler67': [1, -8, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, -10, 73], 'euler79': [1, 4, 79], 'euler83': [1, 4, 83], 'euler89': [1, 10, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 4, 11], [1, 6, 13], [1, 2, 17], [1, -4, 19], [1, 0, 23], [1, -6, 29], [1, 8, 31], [1, -6, 37], [1, -6, 41], [1, 8, 43], [1, -4, 47], [1, -2, 53], [1, 0, 59], [1, 10, 61], [1, -8, 67], [1, 0, 71], [1, -10, 73], [1, 4, 79], [1, 4, 83], [1, 10, 89], [1, -18, 97]], 'index': 50, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/70560/c'], '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': '2-70560-1.1-c1-0-50', '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': '2-70560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.73656328667136, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1692887697431558740, 'z1': {'__RealLiteral__': 0, 'data': '0.7171044052122643', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1692887697431558740', 'Lhash_array': ['1692887697431558740'], 'label': '2-70560-1.1-c1-0-50', 'type': 'ECQ', 'url': 'EllipticCurve/Q/70560/c'}