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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '1837174831065899299', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, -1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, -1], [1, 1], [1, -4, 13], [1, 6, 17], [1, -6, 19], [1, 8, 23], [1, 0, 29], [1, 0, 31], [1, -2, 37], [1, 8, 41], [1, -8, 43], [1, 0, 47], [1, 10, 53], [1, -4, 59], [1, -2, 61], [1, -12, 67], [1, 8, 71], [1, -12, 73], [1, 10, 79], [1, -14, 83], [1, 10, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 128, 'label': '2-369600-1.1-c1-0-128', 'leading_term': '2.11336716576', '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/369600/iq', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.113367165761035, 1.321544592597017, -0.3125084523329894, -1.034230112103566, 0.2612516566808603, 2.324500860951391, 2.596895216134309, 0.7635744620166328, -0.1361955625270933, 2.079704080327371, 4.67857209173634, 3.274909244614988, -1.218503454825848, -3.138928129106614, -0.59606340753297, 1.540913608690081, -0.2054752873576667, -2.256045451107907, -0.8449474129189479, 1.034325348082024, -0.4109862033418988, -2.304036446460512, -0.7955764187733486, 1.270278212324083, 0.3074640891798129, -0.5511928295737905, 1.606043274385419, 2.462690497947249, -0.7284753550449294, -2.381929347094927, 0.471021390687371, 1.586901437119645, -1.718246853513924, -2.811311485937722, -0.05998510419901932, -0.6604293961025457, -4.695679451175325, -3.938155016658706, 0.7662722705906213, 1.016353167694671, -1.54623744492547, 0.3270292325819691, 3.480942010102164, 2.003897978063403, -0.08087279192085672, 0.7453215232540386, 0.1376062485979264, -1.708058896309205, 0.1530392644168926, 1.978474495612148, -1.270657573799548, -3.154393637404919, 0.3878700641342444, 1.572241878593715, -1.272278803444338, -0.6452483192225316, 1.1703532310696, -1.840606070223826, -2.325346031237814, 4.50725242458069, 7.509837637212445, 2.338030643380001, -0.7121050857917403, 0.2560101419230581, -0.7140288848465745, -0.3804663674146009, 2.924047910720679, 1.448181496310881, -3.333650709183773, -2.531021216991213, 0.2833010780501042, -0.8445998129082709, -1.068528755994343, 0.2729929793346763, -0.9349653196764883, 0.7591024385719688, 6.349987937330162, 4.58077063865168, -2.420369562196683, -1.495136849846086, 2.734315433313235, 0.8588359718578743, -0.2411401178703751, 1.569896666903024, -1.666455907393557, -4.69437638993156, -0.4665517000346219, 2.083621080909674, -0.3123131277714384, -0.1351647999795002, -0.1129136828928156, -3.132565010714435, -1.541437360048771, 2.488173240060939, 0.9778562285522459, -0.4778290043914527, 1.149691053945982, -0.2857988002388208, -0.6130294685925493, 3.005742986421879, 0.7937269729378389, -3.842072988452419, 0.169161428111202, 3.528069688056062, -0.8998484772915185, -1.645473223866297, 1.09038447404471, -1.06499677376289, -0.8185385313338955, 3.641610704373312, 2.2940893592952, -0.3908750354067399, 1.987339723412662, 1.789508102428029, -0.6532220870544094, 0.1126695647605794, -0.9168852226429222, -1.541715530632653, 3.85590634910346, 5.183884682182582, 0.007016217316324991], 'positive_zeros': ['0.4503425342386426', '0.9678275096676332', '1.867584813109622', '2.036645316597292', '2.931788597673474', '3.544892038479560', '3.982159163508841', '4.582030405833857', '4.959752535914518', '5.572691734976986', '6.042436375529774', '6.343233056685508', '6.952130408917957', '7.465680537074814', '7.886570038284424', '8.506862669694370', '8.693706219178329', '9.451645791287645', '9.835729758010289', '10.22893095536745', '10.96714821749249', '11.08289476181383', '11.51570950993206', '11.98830575687908', '12.42649808820567', '12.97594217312775', '13.38754560892016', '13.80650078645741', '14.13254364955860', '14.60251636095871', '15.37648845631163', '15.67529753314850', '15.88477615301006', '16.28218764991371', '16.81947820440924', '17.44763631386841', '17.63539716953983', '18.15941068281464', '18.35153143489894', '18.70802448239336', '19.39983107962998', '19.82012371538411'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1837174831065899299, 'z1': {'__RealLiteral__': 0, 'data': '0.4503425342386426', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9678275096676332', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.867584813109622', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 4, 0, 0, 0, -6, 0, 6, 0, -1, 0, -8, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, -4, 0, -8, 0, 8, 0, 0, 0, 0, 0, 1, 0, 6, 0, -10, 0, 0, 0, -6, 0, 4, 0, 2, 0, 1, 0, 0, 0, 12, 0, 8, 0, -8, 0, 12, 0, 0, 0, -1, 0, -10, 0, 1, 0, 14, 0, 0, 0, 0, 0, -10, 0, 4, 0, 0, 0, 0, 0, 14, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, -4, 13], 'euler17': [1, 6, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -2, 37], 'euler41': [1, 8, 41], 'euler43': [1, -8, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 10, 53], 'euler59': [1, -4, 59], 'euler61': [1, -2, 61], 'euler67': [1, -12, 67], 'euler7': [1, -1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -12, 73], 'euler79': [1, 10, 79], 'euler83': [1, -14, 83], 'euler89': [1, 10, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -4, 13], [1, 6, 17], [1, -6, 19], [1, 8, 23], [1, 0, 29], [1, 0, 31], [1, -2, 37], [1, 8, 41], [1, -8, 43], [1, 0, 47], [1, 10, 53], [1, -4, 59], [1, -2, 61], [1, -12, 67], [1, 8, 71], [1, -12, 73], [1, 10, 79], [1, -14, 83], [1, 10, 89], [1, -14, 97]], 'index': 128, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/iq'], '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': '2-369600-1.1-c1-0-128', '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': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1837174831065899299, 'z1': {'__RealLiteral__': 0, 'data': '0.4503425342386426', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1837174831065899299', 'Lhash_array': ['1837174831065899299'], 'label': '2-369600-1.1-c1-0-128', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/iq'}