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lfunc_lfunctions • Show schema
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{'A10': -1, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': 1, 'A6': 1, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '53056011135279371', 'a10': [-0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 104.68387704989864, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1, -1]], [19, [1, -1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 19, 23], 'central_character': '13110.1', 'coefficient_field': '1.1.1.1', 'conductor': 13110, 'conductor_radical': 13110, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, -1], [1, 0, 7], [1, 0, 11], [1, -2, 13], [1, 6, 17], [1, -1], [1, 1], [1, 2, 29], [1, 8, 31], [1, -2, 37], [1, -6, 41], [1, -4, 43], [1, -8, 47], [1, -6, 53], [1, -12, 59], [1, -2, 61], [1, 0, 67], [1, 12, 71], [1, 6, 73], [1, 16, 79], [1, -12, 83], [1, -6, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 20, 'label': '2-13110-1.1-c1-0-20', 'leading_term': '3.06905080605', '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/13110/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.7207128531389334, 1.152693723065616, 1.021274123860137, 0.2532139696879857, -0.8019531006049181, -1.430152758816639, -1.031412225845195, 0.2522109105879845, 1.351626685064477, 0.9454809838781227, -1.325547267193916, -4.157342586708182, -5.322834328562976, -3.569736564043097, -0.04518085708480924, 2.361039108954101, 1.540414487818157, -1.725940965931506, -4.352194887604058, -3.932157882669786, -1.142641581307048, 1.083726013018434, 0.8197929667411695, -0.8224158963509005, -1.271352270207526, 0.2164427781413061, 1.665332793715046, 1.082451448467341, -0.719157926070017, -1.017954351066381, 1.168794157522632, 3.52563058154673, 3.28215870127853, 0.823465570914996, -0.8535068497912615, -0.1940366734647006, 0.9470787538942818, 0.1929957398863219, -1.790638979534894, -2.295961418715779, -0.6749857532212495, 0.6633899613381463, -0.03103831559138219, -1.156426236059377, -0.4824552979800864, 0.8727577628659222, -0.1235836890871575, -3.247329922801264, -4.408456779379172, -1.510013362122276, 1.893155113724989, 1.517780356286765, -0.9501991759417664, -0.00902417774200977, 5.063066333432994, 8.23481180113395, 5.200211886305317, -0.03760217320501913, -0.6788295844407723, 3.262468940799126, 5.558801375794743, 3.196099999829758, 0.03259883488637232, -0.08575804768772204, 1.020024179773805, -0.003325297933262342, -2.091025174191791, -2.033041369224386, -0.2414879281101653, 0.2781820925281194, -0.6172511996058034, -0.4621151210491989, 0.6356866236158546, 0.0132190737797294, -1.991392299505831, -1.703857372668552, 1.269163864960643, 2.3781695810984, -0.4115423378102757, -2.739756932626618, -1.12462898302329, 0.9268157468145387, -0.835605810813455, -3.519235789430675, -1.956294282028806, 1.932544140926004, 2.259985736938538, -0.4292096462575524, -0.3440622155980766, 2.606991955868434, 2.19536508781061, -2.650379647539193, -5.014729220609001, -1.577455529158969, 1.821633416149678, 0.5119538199882254, -1.468850311478664, 0.2737326713976125, 2.325164857212014, 0.3913830368652236, -2.333894803622773, -1.183698803561104, 1.33380079899471, 0.6178856830421587, -1.34747731317866, -0.293914417857598, 1.887354464077759, 1.018073870245566, -1.133576363985101, -0.4585784578313332, 1.482494558778061, 0.8551211357676881, -0.8749250929435938, -0.3550190274049673, 0.784813681838359, -0.131442008395953, -0.7829807324826241, 0.8880386060933819, 1.110708686627069, -2.332183882717309], 'positive_zeros': ['1.060721511783229', '1.956029714089635', '2.624996094367984', '3.753252865330316', '4.378319747993671', '5.351728643453434', '5.875548388576909', '6.471869893543190', '7.146877428043509', '7.641200983528487', '8.587061171153447', '9.033775108484079', '9.526132080428732', '10.34104519043910', '10.74443462237254', '11.32511570482990', '11.73752115470970', '12.59298825195846', '13.14262568172970', '13.50062547512364', '14.49749473475921', '14.80704631962574', '15.75452352877368', '16.01726182253216', '16.49961064633771', '17.29274835123765', '17.58849885306898', '18.09778273870225', '18.50181903013018', '19.14982188802351', '19.72136047920393'], 'prelabel': '2-13110-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.231513917788444, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 53056011135279371, 'z1': {'__RealLiteral__': 0, 'data': '1.060721511783229', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.956029714089635', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.624996094367984', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 104.68387704989864, 'bad_primes': [2, 3, 5, 19, 23], 'central_character': '1.1', 'conductor': 13110, 'conductor_radical': 13110, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 1, 1, 0, -1, 1, -1, 0, -1, 2, 0, -1, 1, -6, -1, 1, 1, 0, 0, -1, 1, 1, -2, -1, 0, -2, 1, -8, -1, 0, 6, 0, 1, 2, -1, -2, -1, 6, 0, 4, 0, 1, 1, 8, -1, -7, -1, 6, 2, 6, 1, 0, 0, -1, 2, 12, -1, 2, 8, 0, 1, 2, 0, 0, -6, 1, 0, -12, -1, -6, -2, -1, 1, 0, 2, -16, 1, 1, -6, 12, 0, -6, -4, 2, 0, 6, -1, 0, -1, 8, -8, 1, 1, 10, 7, 0, 1], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, 6, 17], 'euler19': [1, -1, 0], 'euler2': [1, 1, 0], 'euler23': [1, 1, 0], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, -2, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -12, 59], 'euler61': [1, -2, 61], 'euler67': [1, 0, 67], 'euler7': [1, 0, 7], 'euler71': [1, 12, 71], 'euler73': [1, 6, 73], 'euler79': [1, 16, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, -1, 0], [1, 0, 7], [1, 0, 11], [1, -2, 13], [1, 6, 17], [1, -1, 0], [1, 1, 0], [1, 2, 29], [1, 8, 31], [1, -2, 37], [1, -6, 41], [1, -4, 43], [1, -8, 47], [1, -6, 53], [1, -12, 59], [1, -2, 61], [1, 0, 67], [1, 12, 71], [1, 6, 73], [1, 16, 79], [1, -12, 83], [1, -6, 89], [1, -10, 97]], 'index': 20, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/13110/h'], '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': '2-13110-1.1-c1-0-20', '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': '2-13110-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.231513917788444, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 53056011135279371, 'z1': {'__RealLiteral__': 0, 'data': '1.060721511783229', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '53056011135279371', 'Lhash_array': ['53056011135279371'], 'label': '2-13110-1.1-c1-0-20', 'type': 'ECQ', 'url': 'EllipticCurve/Q/13110/h'}