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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': -3, 'A8': 0, 'A9': -2, 'Lhash': '2125089271243333209', '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': [-1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 431.83097413108453, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '54080.1', 'coefficient_field': '1.1.1.1', 'conductor': 54080, 'conductor_radical': 130, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, 1], [1, 3, 7], [1, -3, 11], [1], [1, 3, 17], [1, -5, 19], [1, 3, 23], [1, -5, 29], [1, 0, 31], [1, 11, 37], [1, -5, 41], [1, 7, 43], [1, 8, 47], [1, -10, 53], [1, -1, 59], [1, -5, 61], [1, 11, 67], [1, -3, 71], [1, -6, 73], [1, 0, 79], [1, -16, 83], [1, -13, 89], [1, -7, 97]], 'gamma_factors': [[], [0]], 'index': 6, 'label': '2-54080-1.1-c1-0-6', 'leading_term': '0.747065894246', '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': 0, 'origin': 'EllipticCurve/Q/54080/x', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.7470658942459947, 0.3365735603294855, -0.6352886565602403, -1.38912241989322, -0.9516388296943916, 0.9639866167258772, 3.243303853990077, 3.911681156927893, 1.940360646969436, -1.358126745677842, -3.213333626751985, -2.164598600101478, 0.2445723811894349, 1.176294791101124, -0.04194807470298055, -1.032752581033436, 0.4292051006242424, 3.131308488640967, 3.758728256949081, 1.458787779686999, -0.7181247821138562, 0.05847081696661962, 2.39436660182233, 2.771990215240316, 0.7832230732999411, -0.5134127751029856, 0.293678182077874, 0.7132006317097773, -1.047233617294226, -2.229953357588106, 0.3695496985463499, 4.420003238001151, 4.664220793504815, 1.000620502919179, -1.073703706175784, 0.9478354019343078, 2.851914574036224, 1.145613914867568, -0.963056888541661, 0.6072585894052819, 3.402327074637184, 2.679988500660304, -0.1220221103082724, 0.0806748626853103, 2.974750995403675, 3.60457952822628, 1.245625395330418, -0.05969302644631403, 0.3591302638741229, -0.852717666483433, -3.127645863573089, -1.956737536895409, 1.963598820718771, 2.606178049964776, -0.5485335468137672, -1.173438412516107, 2.043345020320533, 2.673508150517231, -1.062940621476124, -2.304513148442059, 1.76208551178924, 4.47016363244538, 1.862330340217559, -0.8475640349974456, 0.02382045095175514, 0.6862886444615414, -0.7323575108419333, -0.2802037039746946, 2.358411794608853, 2.157069591345558, -0.7098465728027175, -0.78356960205671, 1.029452199915435, -1.122188044294459, -5.222049412658091, -4.081265527968456, 0.6964694923939264, 1.813386474345307, 0.004096970068009911, 0.3762439853236158, 0.7718164372660075, -1.960965593428678, -2.316791366572122, 3.182363260997748, 6.205592392122019, 0.8791059808556956, -4.718726356641853, -3.238772146375567, 0.03738000019884523, -0.2970031237708463, -0.8640434897607805, 0.1494091294851803, -0.358966906646393, -0.7729034503187509, 2.443518177304476, 4.717964737117183, 1.476330887853965, -1.382418689391967, 0.6412958516023644, 1.019466001538627, -3.180249289210961, -4.039768099341704, 0.3077462749880132, 1.446033751416889, -1.37958239345779, -0.6918192751196987, 1.900588139678315, -0.1823695046058779, -2.707317623217074, 0.4310146507477945, 3.47405568252677, 1.19872811551717, -0.5864429673566057, 1.082264806705788, 0.8700884353587398, -1.070963901277155, 0.07643706770504685, 1.476203624783855, -0.1312373063723272, 0.7103125364104778, 4.866333715106523], 'positive_zeros': ['0.3454972467640066', '1.142872400342107', '2.146116040891140', '2.971643466145011', '3.493617812957513', '3.956238704781993', '4.886484149675916', '5.243109549537141', '6.101021528433964', '6.439436346637704', '6.879086858866122', '7.477670769841537', '8.321446828159501', '8.667576500527143', '9.352443191810303', '9.698221845757324', '10.48497880336321', '10.74083164603710', '11.69437175920079', '11.81243930675123', '12.14172700595497', '12.87335788873217', '13.45689074261256', '13.85438502002727', '14.43509614718530', '14.91005655127748', '15.63310189704065', '15.99640858368149', '16.38141237402838', '16.77961675317046', '17.43172726269288', '17.84107264171156', '18.17822943987080', '18.95803612158463', '19.50090489893571', '19.67368705401629'], 'prelabel': '2-54080-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.78054316256157, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2125089271243333209, 'z1': {'__RealLiteral__': 0, 'data': '0.3454972467640066', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.142872400342107', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.146116040891140', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 431.83097413108453, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 54080, 'conductor_radical': 130, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -3, 0, -2, 0, 3, 0, 0, 0, 1, 0, -3, 0, 5, 0, 3, 0, -3, 0, 1, 0, 5, 0, 5, 0, 0, 0, -3, 0, 3, 0, -11, 0, 0, 0, 5, 0, -7, 0, 2, 0, -8, 0, 2, 0, 3, 0, 10, 0, -3, 0, -5, 0, 1, 0, 5, 0, 6, 0, 0, 0, -11, 0, 3, 0, 3, 0, 6, 0, -1, 0, -9, 0, 0, 0, 1, 0, 16, 0, 3, 0, -5, 0, 13, 0, 0, 0, 0, 0, -5, 0, 7, 0, -6, 0], 'euler11': [1, -3, 11], 'euler13': [1, 0, 0], 'euler17': [1, 3, 17], 'euler19': [1, -5, 19], 'euler2': [1, 0, 0], 'euler23': [1, 3, 23], 'euler29': [1, -5, 29], 'euler3': [1, 1, 3], 'euler31': [1, 0, 31], 'euler37': [1, 11, 37], 'euler41': [1, -5, 41], 'euler43': [1, 7, 43], 'euler47': [1, 8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -10, 53], 'euler59': [1, -1, 59], 'euler61': [1, -5, 61], 'euler67': [1, 11, 67], 'euler7': [1, 3, 7], 'euler71': [1, -3, 71], 'euler73': [1, -6, 73], 'euler79': [1, 0, 79], 'euler83': [1, -16, 83], 'euler89': [1, -13, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, 1, 0], [1, 3, 7], [1, -3, 11], [1, 0, 0], [1, 3, 17], [1, -5, 19], [1, 3, 23], [1, -5, 29], [1, 0, 31], [1, 11, 37], [1, -5, 41], [1, 7, 43], [1, 8, 47], [1, -10, 53], [1, -1, 59], [1, -5, 61], [1, 11, 67], [1, -3, 71], [1, -6, 73], [1, 0, 79], [1, -16, 83], [1, -13, 89], [1, -7, 97]], 'index': 6, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/54080/x'], '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': '2-54080-1.1-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-54080-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.78054316256157, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2125089271243333209, 'z1': {'__RealLiteral__': 0, 'data': '0.3454972467640066', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2125089271243333209', 'Lhash_array': ['2125089271243333209'], 'label': '2-54080-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/54080/x'}