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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 0, 'Lhash': '968207991677715141', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2698.1131441382568, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1, -1]], [19, [1]]], 'bad_primes': [2, 3, 13, 19], 'central_character': '337896.1', 'coefficient_field': '1.1.1.1', 'conductor': 337896, 'conductor_radical': 1482, 'degree': 2, 'euler_factors': [[1], [1], [1, 0, 5], [1, 2, 7], [1, -5, 11], [1, -1], [1, -6, 17], [1], [1, -4, 23], [1, 4, 29], [1, -6, 31], [1, 4, 37], [1, -11, 41], [1, -12, 43], [1, -10, 47], [1, -12, 53], [1, -11, 59], [1, 2, 61], [1, -3, 67], [1, -6, 71], [1, 3, 73], [1, 2, 79], [1, -9, 83], [1, 10, 89], [1, 7, 97]], 'gamma_factors': [[], [0]], 'index': 23, 'label': '2-337896-1.1-c1-0-23', 'leading_term': '4.12776138654', '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/337896/y', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.127761386543784, 3.202343497381079, 1.151482866888409, -0.2438684836295881, 0.2865975721570384, 1.687772189502228, 1.330434586364503, -1.467560628190825, -3.759860994255778, -2.58811591030824, 0.4697718757013509, 1.10657612876501, -1.307404439767785, -2.725737782343599, -1.051461235616935, 0.5735967048710147, -0.1067539878091793, 0.1588372070632956, 3.89092867057324, 6.682219534306444, 3.80225447332943, -1.127961713409581, -1.869259424396179, -0.005363255678948238, -0.7440651058888395, -2.524754473712427, -0.9884065428509025, 1.238068013569553, -0.2460500674671545, -2.010063477906227, 0.1401585996915191, 1.523373900023398, 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-3.039324278935349, -1.010858506501633, 0.9343046495595317, -1.192070523890967, 1.029523787462152, 4.769775574063786, 1.537520973746826, -1.733366464537564, 0.02507382012670571, -0.04919407797226326, -0.5016677620283538, 2.256404506981026, 0.610654187321118, -3.705589812965399, -0.2123406609916639, 4.284014526390045, 1.079027406432579, -0.9724957870123192, 0.629735918572122, -1.477774120054908, -2.688068626952137, 0.2319116706642591, -0.01696599795217785, 0.1973323150144358, 5.783615536296777, 5.974249376910237, -0.2864018638146066, -1.099772747827102, 0.4193586354204504, -1.361721653673386, 0.06220992196942496, 1.35752461779128, -3.57340375040052, -4.517081859678691, 0.4374386162395579, 0.3435358960179193, -1.035759188153912, 1.588066931679663, 0.9440266631564264], 'positive_zeros': ['0.6742575083924847', '0.9411569463751097', '1.635065012713359', '2.456167284375521', '2.882464916789614', '3.620483304876198', '3.975289358445905', '4.229829701874666', '5.180381286648458', '5.751280822734256', '5.889929935231920', '6.583921103816665', '6.977641051281692', '7.488767379822340', '7.884290056823513', '8.591348940596304', '9.007041863331929', '9.413461461125137', '9.790914295578426', '10.18884703746848', '10.86176450853579', '11.19420406410136', '11.78468787546329', '12.16848072637222', '12.46839091365008', '12.95534765589468', '13.57417796326236', '13.87086755084952', '14.38182819810401', '14.66141101917667', '15.22153778188692', '15.68066378152070', '16.10275972322115', '16.54459107571172', '16.89683728628678', '17.33867345234838', '17.64473083120886', '18.17866001259021', '18.87556359432870', '19.17267800716842', '19.31372930746699', '19.70914243076987'], 'prelabel': '2-337896-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.94336477489937, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 968207991677715141, 'z1': {'__RealLiteral__': 0, 'data': '0.6742575083924847', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9411569463751097', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.635065012713359', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2698.1131441382568, 'bad_primes': [2, 3, 13, 19], 'central_character': '1.1', 'conductor': 337896, 'conductor_radical': 1482, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 5, 0, 1, 0, 0, 0, 6, 0, 0, 0, 0, 0, 4, 0, -5, 0, 0, 0, -4, 0, 6, 0, 0, 0, 0, 0, -4, 0, 0, 0, 11, 0, 12, 0, 0, 0, 10, 0, -3, 0, 0, 0, 12, 0, 0, 0, 0, 0, 11, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 6, 0, -3, 0, 0, 0, -10, 0, -2, 0, 0, 0, 9, 0, 0, 0, 0, 0, -10, 0, -2, 0, 0, 0, 0, 0, -7, 0, 0, 0], 'euler11': [1, -5, 11], 'euler13': [1, -1, 0], 'euler17': [1, -6, 17], 'euler19': [1, 0, 0], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 4, 29], 'euler3': [1, 0, 0], 'euler31': [1, -6, 31], 'euler37': [1, 4, 37], 'euler41': [1, -11, 41], 'euler43': [1, -12, 43], 'euler47': [1, -10, 47], 'euler5': [1, 0, 5], 'euler53': [1, -12, 53], 'euler59': [1, -11, 59], 'euler61': [1, 2, 61], 'euler67': [1, -3, 67], 'euler7': [1, 2, 7], 'euler71': [1, -6, 71], 'euler73': [1, 3, 73], 'euler79': [1, 2, 79], 'euler83': [1, -9, 83], 'euler89': [1, 10, 89], 'euler97': [1, 7, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 5], [1, 2, 7], [1, -5, 11], [1, -1, 0], [1, -6, 17], [1, 0, 0], [1, -4, 23], [1, 4, 29], [1, -6, 31], [1, 4, 37], [1, -11, 41], [1, -12, 43], [1, -10, 47], [1, -12, 53], [1, -11, 59], [1, 2, 61], [1, -3, 67], [1, -6, 71], [1, 3, 73], [1, 2, 79], [1, -9, 83], [1, 10, 89], [1, 7, 97]], 'index': 23, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/337896/y'], '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': '2-337896-1.1-c1-0-23', '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': '2-337896-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.94336477489937, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 968207991677715141, 'z1': {'__RealLiteral__': 0, 'data': '0.6742575083924847', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '968207991677715141', 'Lhash_array': ['968207991677715141'], 'factors': ['2-337896-1.1-c1-0-23'], 'label': '2-337896-1.1-c1-0-23', 'type': 'ECQ', 'url': 'EllipticCurve/Q/337896/y'}