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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': 4, 'A8': 0, 'A9': 0, 'Lhash': '563103483732653954', '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': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 747.3997629191848, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '93600.1', 'coefficient_field': '1.1.1.1', 'conductor': 93600, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, -4, 7], [1, 0, 11], [1, -1], [1, 0, 17], [1, -3, 19], [1, -4, 23], [1, -1, 29], [1, -8, 31], [1, -1, 37], [1, 1, 41], [1, -6, 43], [1, -11, 47], [1, 3, 53], [1, -10, 59], [1, -4, 61], [1, -13, 67], [1, -9, 71], [1, 0, 73], [1, -3, 79], [1, 2, 83], [1, 10, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 77, 'label': '2-93600-1.1-c1-0-77', 'leading_term': '4.55007077659', '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/93600/eu', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.550070776586053, 3.864163344255081, 2.13839773061834, 0.3833584865187225, -0.1518176530433847, 0.8793016579641193, 2.229297082363626, 2.111788124332592, 0.3314341003988519, -1.08697888206117, -0.1727314650047829, 2.186989328274721, 2.835212246586276, 0.330967932523751, -2.741851645836269, -2.848516677383486, -0.2758383749464616, 1.241697707373219, -0.09455627619324816, -1.667887514071599, -0.8528969908865327, 0.5863772315416366, -0.4648850995983039, -2.67550002714701, -1.807135458983762, 2.081777826897615, 3.85516778411623, 1.231100062388883, -1.413978944428399, -0.160568969939017, 2.221905464173198, 1.569255319738804, 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0.6157638438759857, 0.1965460918107416, 1.422498269788036, -0.2592740628865435, -1.430029242821997, 1.515915701008154, 2.101291528930338, -2.310178486431969, -3.275682862651568, 0.6984673329736946, 0.8313578390007121, -2.531665971176363, -1.461298372594155, 1.589861611656684, 0.5768643459356017, -0.2655958931188883, 2.063564841661945, 1.858045644401498, -0.441196352966805, 1.265602720646741, 2.569993776901663, -2.509736751247026, -6.051071023919354, -2.040450378065076, 1.039837729718584, -0.8567763662869827, -0.799107127400125, 0.9849055727721356, -0.698687991792937, -1.433398059586648, 1.845222831914433, 2.122506042098114, -0.7160701030039359, 0.7402231039940551, 2.438929347395384, -2.339471766296704, -5.621815408654934, -1.538931283494978, 1.122137358389205], 'positive_zeros': ['0.8399980321543461', '1.068604367936621', '2.041322828387786', '2.520194711914288', '3.273583833646157', '4.026226431385478', '4.488803738397935', '5.119542213444373', '5.445136086354128', '6.122909067078706', '6.836985672310381', '7.264469253583800', '7.930993468902883', '8.224063663917346', '8.772695003126832', '9.272864922501530', '9.931130160270584', '10.40389572478739', '11.02641608634684', '11.34630629094900', '11.72803874718559', '12.35064982894474', '12.77299266970862', '13.47662891893998', '13.94233558269590', '14.22844551532520', '14.71302985842728', '15.36006899709973', '15.58567318504563', '16.12642987380954', '16.83500541444167', '17.27360529537484', '17.49815507502428', '18.11122477936095', '18.41163837240667', '19.02490210057380', '19.33855089582524'], 'prelabel': '2-93600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.338613039420725, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 563103483732653954, 'z1': {'__RealLiteral__': 0, 'data': '0.8399980321543461', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.068604367936621', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.041322828387786', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 747.3997629191848, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 93600, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 8, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 6, 0, 0, 0, 11, 0, 9, 0, 0, 0, -3, 0, 0, 0, 0, 0, 10, 0, 4, 0, 0, 0, 0, 0, 13, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, -10, 0, 4, 0, 0, 0, 0, 0, 8, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -1, 0], 'euler17': [1, 0, 17], 'euler19': [1, -3, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -1, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, -1, 37], 'euler41': [1, 1, 41], 'euler43': [1, -6, 43], 'euler47': [1, -11, 47], 'euler5': [1, 0, 0], 'euler53': [1, 3, 53], 'euler59': [1, -10, 59], 'euler61': [1, -4, 61], 'euler67': [1, -13, 67], 'euler7': [1, -4, 7], 'euler71': [1, -9, 71], 'euler73': [1, 0, 73], 'euler79': [1, -3, 79], 'euler83': [1, 2, 83], 'euler89': [1, 10, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, -4, 7], [1, 0, 11], [1, -1, 0], [1, 0, 17], [1, -3, 19], [1, -4, 23], [1, -1, 29], [1, -8, 31], [1, -1, 37], [1, 1, 41], [1, -6, 43], [1, -11, 47], [1, 3, 53], [1, -10, 59], [1, -4, 61], [1, -13, 67], [1, -9, 71], [1, 0, 73], [1, -3, 79], [1, 2, 83], [1, 10, 89], [1, -8, 97]], 'index': 77, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/93600/eu'], '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': '2-93600-1.1-c1-0-77', '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': '2-93600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.338613039420725, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 563103483732653954, 'z1': {'__RealLiteral__': 0, 'data': '0.8399980321543461', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '563103483732653954', 'Lhash_array': ['563103483732653954'], 'label': '2-93600-1.1-c1-0-77', 'type': 'ECQ', 'url': 'EllipticCurve/Q/93600/eu'}