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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 1, 'A4': -1, 'A5': 0, 'A6': 1, 'A7': -3, 'A8': -3, 'A9': 1, 'Lhash': '1501796785913276334', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [-1.1338934190276817, 0], 'a8': [-1.0606601717798212, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2249.984702954629, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [5, [1]], [13, [1, 1]], [17, [1]]], 'bad_primes': [3, 5, 13, 17], 'central_character': '281775.1', 'coefficient_field': '1.1.1.1', 'conductor': 281775, 'conductor_radical': 3315, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, -1], [1], [1, 3, 7], [1, 2, 11], [1, 1], [1], [1, -5, 19], [1, -3, 23], [1, -4, 29], [1, -4, 31], [1, -2, 37], [1, -2, 41], [1, -4, 43], [1, -4, 47], [1, 8, 53], [1, 14, 59], [1, -5, 61], [1, 5, 67], [1, 12, 71], [1, -14, 73], [1, -4, 79], [1, -10, 83], [1, 6, 89], [1, 0, 97]], 'gamma_factors': [[], [0]], 'index': 38, 'label': '2-281775-1.1-c1-0-38', 'leading_term': '9.27849289654', '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/281775/bt', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.969398235633866, 2.093963070717299, -0.0729645286500326, -2.552401748224183, -2.202937206297422, 1.774765317354428, 6.108586310665983, 6.691035761408096, 3.481045325224573, 0.4172373815240287, 0.064202829986024, 0.6926954029857612, 0.05155933454225456, -0.6830716757798498, 0.4232494405844867, 1.807555915921543, 0.9039071824417393, -0.814799170936088, -0.219879131478695, 1.384193862306077, 0.4652457924557445, -1.537127542300009, -0.3724350355367625, 2.485155223822018, 2.010388249177384, -0.2860745255756844, 1.411958463235986, 5.362854670866327, 4.478955194919191, 0.04518540359482967, -0.2063554309226695, 2.858924626761375, 1.56229740695179, -2.987903460162894, -3.077078226864519, 0.2801126950803747, 0.5520186864912116, -0.5580409784513904, 1.196192321861962, 1.450397729501228, -2.473769222814067, -2.627929363608227, 3.382600270819322, 4.197475238827468, -4.006276531966485, -8.636083192567561, -3.82949838281794, 0.4491251613618286, -0.8215521617037415, -1.376600938959983, 0.2163087874023822, -0.2387740859170356, -1.204985100778735, -0.1914044106075482, -0.1169669377584579, -1.007513958536408, 0.3031945969709809, 0.8627345329586051, -1.969509959793751, -2.710860378461089, 0.04144873282692874, 0.105109999702266, -1.034704308486062, 1.699283253219319, 2.014039144609536, -3.439397633235962, -3.141633565213775, 4.605334678866547, 4.740870980857131, -3.020427858406183, -3.916906156377501, -0.07261513956845302, -2.41469637157033, -4.882075982285405, -0.9605911554781913, 1.134798224020001, -0.01592356606410947, 2.896631047010004, 5.004355966701946, 0.6802606385171277, -1.263679951591071, 1.85879209181805, 1.078242004915953, -1.737810108986942, 0.2463573462008511, 1.479353504416517, -1.178683612414524, -1.183831452730299, 0.3564581543453259, -1.061616404838928, -1.133976959005086, 0.558815714777306, -0.7211320021226012, -0.738484008723807, 2.56848061753242, 1.635403378523167, -1.177833845345505, 1.54461369448724, 2.823094652345372, -1.042670267360522, -0.492905639661572, 2.379693091430329, -0.9558145939984587, -3.091010119350377, 0.2952036404849916, 0.4547709185319226, -0.6806131255111247, 1.420545466011108, -1.494512085444972, -5.741368878764306, 1.01286155724201, 7.391795778605023, 1.925755535506285, -0.8579121777243296, 3.396789904986526, 1.328932806738573, -2.45734106061272, 0.5147018261703444, 0.1947131712885416, -4.288332251159563], 'positive_zeros': ['0.7435772058695952', '1.406722244384717', '2.585934952536099', '2.723891817023044', '3.261250898848967', '3.688265611532973', '4.362247349285538', '4.780000434585277', '5.299671464345294', '5.780897862250137', '6.449120995372212', '6.636905620584262', '7.503439982852128', '7.768564047587290', '8.333220913766268', '8.973820712097830', '9.334644574294131', '9.619233736841630', '10.10565986148437', '10.61910391744576', '11.14244629226096', '11.93944059708002', '12.15358113777083', '12.70578604633754', '12.95792572167512', '13.54814411843648', '13.71804411201743', '14.21137148914567', '14.59591873282694', '15.24546576545364', '15.51437782457641', '15.87655144012953', '16.35286938208270', '16.85544079782645', '17.40006289859610', '18.01585659914788', '18.06600465314931', '18.80595789601159', '19.21339977984983', '19.25982245041529'], 'prelabel': '2-281775-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.43400365723548, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1501796785913276334, 'z1': {'__RealLiteral__': 0, 'data': '0.7435772058695952', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.406722244384717', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.585934952536099', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2249.984702954629, 'bad_primes': [3, 5, 13, 17], 'central_character': '1.1', 'conductor': 281775, 'conductor_radical': 3315, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, -1, 0, 1, -3, -3, 1, 0, -2, -1, -1, -3, 0, -1, 0, 1, 5, 0, -3, -2, 3, -3, 0, -1, 1, 3, 4, 0, 4, 5, -2, 0, 0, -1, 2, 5, -1, 0, 2, -3, 4, 2, 0, 3, 4, -1, 2, 0, 0, 1, -8, 1, 0, 9, 5, 4, -14, 0, 5, 4, -3, 7, 0, -2, -5, 0, 3, 0, -12, -3, 14, 2, 0, -5, 6, -1, 4, 0, 1, 2, 10, 3, 0, 4, 4, 6, -6, 0, 3, -3, 4, 4, 0, 5, 0, 2, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 1, 0], 'euler17': [1, 0, 0], 'euler19': [1, -5, 19], 'euler2': [1, -1, 2], 'euler23': [1, -3, 23], 'euler29': [1, -4, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, -4, 47], 'euler5': [1, 0, 0], 'euler53': [1, 8, 53], 'euler59': [1, 14, 59], 'euler61': [1, -5, 61], 'euler67': [1, 5, 67], 'euler7': [1, 3, 7], 'euler71': [1, 12, 71], 'euler73': [1, -14, 73], 'euler79': [1, -4, 79], 'euler83': [1, -10, 83], 'euler89': [1, 6, 89], 'euler97': [1, 0, 97], 'euler_factors': [[1, -1, 2], [1, -1, 0], [1, 0, 0], [1, 3, 7], [1, 2, 11], [1, 1, 0], [1, 0, 0], [1, -5, 19], [1, -3, 23], [1, -4, 29], [1, -4, 31], [1, -2, 37], [1, -2, 41], [1, -4, 43], [1, -4, 47], [1, 8, 53], [1, 14, 59], [1, -5, 61], [1, 5, 67], [1, 12, 71], [1, -14, 73], [1, -4, 79], [1, -10, 83], [1, 6, 89], [1, 0, 97]], 'index': 38, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/281775/bt'], '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': '2-281775-1.1-c1-0-38', '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': '2-281775-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.43400365723548, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1501796785913276334, 'z1': {'__RealLiteral__': 0, 'data': '0.7435772058695952', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1501796785913276334', 'Lhash_array': ['1501796785913276334'], 'factors': ['2-281775-1.1-c1-0-38'], 'label': '2-281775-1.1-c1-0-38', 'type': 'ECQ', 'url': 'EllipticCurve/Q/281775/bt'}