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lfunc_lfunctions • Show schema
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{'A10': -1, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': 1, 'A6': 1, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '833888526704405312', 'a10': [-0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 931.1355379701511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1, -1]], [13, [1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 13, 23], 'central_character': '116610.1', 'coefficient_field': '1.1.1.1', 'conductor': 116610, 'conductor_radical': 8970, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, -1], [1, 0, 7], [1, -4, 11], [1], [1, -2, 17], [1, 8, 19], [1, 1], [1, 6, 29], [1, 8, 31], [1, -6, 37], [1, 10, 41], [1, 4, 43], [1, 0, 47], [1, 14, 53], [1, 12, 59], [1, -2, 61], [1, -4, 67], [1, -12, 71], [1, -6, 73], [1, -8, 79], [1, 0, 83], [1, -2, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 5, 'label': '2-116610-1.1-c1-0-5', 'leading_term': '0.694723513871', '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/116610/p', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.6947235138705126, 0.1957527302136637, -0.9601934019188816, -1.849509532872638, -1.569931241045432, -0.258285569134131, 0.7251730983221428, 0.2942997802328218, -0.6021881237442877, 0.392490334635249, 3.891674125313268, 6.960818233440922, 6.053315498223475, 1.878738288745863, -0.6308013870944664, 1.484338111080382, 4.842757054519233, 4.100043716069593, -0.3075836277816865, -2.486229069284497, 0.3240090473105693, 3.652372721641035, 2.668482385045806, -0.7039383428195519, -1.602568918981545, -0.1472097270324736, -0.08419941677607841, -1.299145381852808, -0.1951485541346482, 2.747138278233421, 2.823002442002239, -0.4087701792940767, -1.682727342261124, 0.8276043612583953, 2.275203563773618, -0.001538443111765069, -1.947542883720658, -0.8003875154164738, 0.1108038533950957, -1.247677443229422, -1.406863010978682, 1.0382235176117, 1.95653065638416, -0.06470040796318242, -0.9035762000080498, 0.1891507914271959, -1.053227185909273, -3.990310213233749, -3.084047785963947, 0.4603324547204699, 0.2383424321283972, -1.899507043982279, 0.8048566215689213, 4.484483557136551, 0.145507783529073, -7.682116406071548, -7.263528261137687, -1.008176598510555, -0.1118135621077852, -3.351637722430519, -2.143012536099201, 0.643850880306459, -2.428986021089268, -6.700147291440216, -4.416636017922011, 0.306078583424096, 0.8662863172253011, -0.1720159355384014, 0.260423310374041, -0.2731601047274817, -1.24411286506966, 0.5278100783046376, 2.156465152180189, 0.2586775726706938, -1.112499705498841, 0.1729653332028074, -0.6875732582244409, -3.194481719663836, -1.30439625055217, 2.217724732779673, 1.002531776659623, -0.1085335229751776, 4.128456450607722, 6.15772523342537, 1.665541772266915, -0.5319264270637168, 2.121554488288463, 1.377980394021441, -1.826254758383573, -0.5128559781112318, -0.01777135016337781, -5.914783476347558, -8.59193841385421, -2.907158856241557, 0.5910793339482577, -1.089415288586666, 1.085529798049782, 5.225607389593465, 2.816693108319524, -1.070952760235309, 0.4531875719111603, 1.555434897133675, -0.5389415643000324, -0.06710775665618915, 0.6989629754360047, -3.448243044480312, -5.85834223982955, -1.787161361063177, 0.9679407720289077, -0.5398960508855936, -0.5505518416205261, 0.1197108942063065, -1.383766402575257, -0.9021110526718217, 1.314052189477819, 0.03198587433780809, -1.245975084805473, 1.455352537984478, 2.265869445316278, 0.09233872568478393, 0.3501897120831951], 'positive_zeros': ['0.2986635609857109', '1.296702396672494', '1.818571365974972', '2.205173901357506', '3.384489850827215', '3.633715073093688', '4.482587200550167', '4.980582163209193', '5.691680242078442', '6.282449795157575', '6.479703541013055', '7.017686892038115', '7.719213395766926', '8.182740097847389', '8.749873967442303', '9.385592037942738', '9.540890198250934', '10.15390099527500', '10.74264155914922', '11.19401757274424', '11.38161927601580', '12.20824985292713', '12.52327281381063', '12.95778901793907', '13.50439859512022', '14.31452231918995', '14.48938456024328', '15.15130191573683', '15.36498137943442', '16.22642840661805', '16.67214035942396', '16.89198213795063', '17.19658119658266', '17.70029241618853', '18.27476323844073', '18.71437478966365', '18.92277712199028', '19.57586009147497'], 'prelabel': '2-116610-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 30.51451356273193, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 833888526704405312, 'z1': {'__RealLiteral__': 0, 'data': '0.2986635609857109', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.296702396672494', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.818571365974972', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 931.1355379701511, 'bad_primes': [2, 3, 5, 13, 23], 'central_character': '1.1', 'conductor': 116610, 'conductor_radical': 8970, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 1, 1, 0, -1, 1, -1, 4, -1, 0, 0, -1, 1, 2, -1, -8, 1, 0, -4, -1, 1, 1, 0, -1, 0, -6, 1, -8, -1, -4, -2, 0, 1, 6, 8, 0, -1, -10, 0, -4, 4, 1, 1, 0, -1, -7, -1, -2, 0, -14, 1, 4, 0, 8, 6, -12, -1, 2, 8, 0, 1, 0, 4, 4, 2, 1, 0, 12, -1, 6, -6, -1, -8, 0, 0, 8, 1, 1, 10, 0, 0, 2, 4, 6, -4, 2, -1, 0, -1, 8, 0, -8, 1, -6, 7, 4, 1], 'euler11': [1, -4, 11], 'euler13': [1, 0, 0], 'euler17': [1, -2, 17], 'euler19': [1, 8, 19], 'euler2': [1, 1, 0], 'euler23': [1, 1, 0], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 10, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, 14, 53], 'euler59': [1, 12, 59], 'euler61': [1, -2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, -12, 71], 'euler73': [1, -6, 73], 'euler79': [1, -8, 79], 'euler83': [1, 0, 83], 'euler89': [1, -2, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, -1, 0], [1, 0, 7], [1, -4, 11], [1, 0, 0], [1, -2, 17], [1, 8, 19], [1, 1, 0], [1, 6, 29], [1, 8, 31], [1, -6, 37], [1, 10, 41], [1, 4, 43], [1, 0, 47], [1, 14, 53], [1, 12, 59], [1, -2, 61], [1, -4, 67], [1, -12, 71], [1, -6, 73], [1, -8, 79], [1, 0, 83], [1, -2, 89], [1, 6, 97]], 'index': 5, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/116610/p'], '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': '2-116610-1.1-c1-0-5', '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': '2-116610-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 30.51451356273193, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 833888526704405312, 'z1': {'__RealLiteral__': 0, 'data': '0.2986635609857109', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '833888526704405312', 'Lhash_array': ['833888526704405312'], 'label': '2-116610-1.1-c1-0-5', 'type': 'ECQ', 'url': 'EllipticCurve/Q/116610/p'}