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lfunc_lfunctions • Show schema
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{'A10': 6, 'A2': 2, 'A3': 0, 'A4': 1, 'A5': 3, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': -4, 'Lhash': '895570004834846167', 'a10': [0.061855670103092786, 0.0], 'a2': [0.020618556701030927, 0.0], 'a3': [0.0, 0.0], 'a4': [0.010309278350515464, 0.0], 'a5': [0.030927835051546393, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.020618556701030927, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.041237113402061855, 0.0], 'algebraic': True, 'analytic_conductor': 4.512420320551897, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[17, [1, -6, 22, -17]], [23, [1, -3, 19, 23]], [181, [1, -11, 191, -181]]], 'bad_primes': [17, 23, 181], 'central_character': '70771.1', 'coefficient_field': '1.1.1.1', 'conductor': 70771, 'conductor_radical': 70771, 'degree': 4, 'euler_factors': [[1, -2, 3, -4, 4], [1, 0, 4, 0, 9], [1, -3, 7, -15, 25], [1, 2, 14, 14, 49], [1, -5, 17, -55, 121], [1, 3, 21, 39, 169], [1, -6, 22, -17], [1, -5, 27, -95, 361], [1, -3, 19, 23], [1, -5, 58, -145, 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-0.8690627764583203, -0.01854683562753888, 0.9423570155191766, -1.710431561574323], 'positive_zeros': [1.347407886314983, 2.514906902417646, 3.278359362445029, 3.564666663546361, 4.508064523054728, 5.222592873101795, 5.431744543536506, 6.083050293263762, 6.317738343310361, 7.088600067387178, 7.657306371550404, 8.329408483337192, 9.154773348949211, 9.491966432646262, 9.577886198385873, 10.21858973612491, 10.99607577452046, 11.31577841872779, 11.99582198120073, 12.30783291291661, 12.70575882611186, 13.10507356732174, 13.69955417400676, 14.03600619638894, 14.34571735833486, 14.42747424997976, 14.80529513605139, 15.57701872222742, 16.18942599245976, 16.6007288080733, 16.8560803365784, 17.25160150655126, 17.66075343374998, 17.99662635553923, 18.5865589954861, 19.15176823744769, 19.56640796591249, 19.83220470863659], 'prelabel': '4-70771-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.4574792705030049, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 895570004834846167, 'z1': {'__RealLiteral__': 0, 'data': '1.34740788631', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.51490690242', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.27835936245', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.512420320551897, 'bad_primes': [17, 23, 181], 'central_character': '1.1', 'conductor': 70771, 'conductor_radical': 70771, 'degree': 4, 'dirichlet_coefficients': [1, 2, 0, 1, 3, 0, -2, 0, -4, 6, 5, 0, -3, -4, 0, 1, 6, -8, 5, 3, 0, 10, 3, 0, 2, -6, 0, -2, 5, 0, -7, -2, 0, 12, -6, -4, 1, 10, 0, 0, 9, 0, 2, 5, -12, 6, -2, 0, -10, 4, 0, -3, -5, 0, 15, 0, 0, 10, -4, 0, -4, -14, 8, -11, -9, 0, 6, 6, 0, -12, 5, 0, 10, 2, 0, 5, -10, 0, 6, 3, 7, 18, -15, 0, 18, 4, 0, 0, 3, -24, 6, 3, 0, -4, 15, 0, 11, -20, -20, 2], 'euler11': [1, -5, 17, -55, 121], 'euler13': [1, 3, 21, 39, 169], 'euler17': [1, -6, 22, -17, 0], 'euler19': [1, -5, 27, -95, 361], 'euler2': [1, -2, 3, -4, 4], 'euler23': [1, -3, 19, 23, 0], 'euler29': [1, -5, 58, -145, 841], 'euler3': [1, 0, 4, 0, 9], 'euler31': [1, 7, 31, 217, 961], 'euler37': [1, -1, 13, -37, 1369], 'euler41': [1, -9, 71, -369, 1681], 'euler43': [1, -2, -22, -86, 1849], 'euler47': [1, 2, 34, 94, 2209], 'euler5': [1, -3, 7, -15, 25], 'euler53': [1, 5, 88, 265, 2809], 'euler59': [1, 4, -26, 236, 3481], 'euler61': [1, 4, 40, 244, 3721], 'euler67': [1, -6, 112, -402, 4489], 'euler7': [1, 2, 14, 14, 49], 'euler71': [1, -5, -14, -355, 5041], 'euler73': [1, -10, 82, -730, 5329], 'euler79': [1, -6, 142, -474, 6241], 'euler83': [1, 15, 195, 1245, 6889], 'euler89': [1, -3, -43, -267, 7921], 'euler97': [1, -11, 58, -1067, 9409], 'euler_factors': [[1, -2, 3, -4, 4], [1, 0, 4, 0, 9], [1, -3, 7, -15, 25], [1, 2, 14, 14, 49], [1, -5, 17, -55, 121], [1, 3, 21, 39, 169], [1, -6, 22, -17, 0], [1, -5, 27, -95, 361], [1, -3, 19, 23, 0], [1, -5, 58, -145, 841], [1, 7, 31, 217, 961], [1, -1, 13, -37, 1369], [1, -9, 71, -369, 1681], [1, -2, -22, -86, 1849], [1, 2, 34, 94, 2209], [1, 5, 88, 265, 2809], [1, 4, -26, 236, 3481], [1, 4, 40, 244, 3721], [1, -6, 112, -402, 4489], [1, -5, -14, -355, 5041], [1, -10, 82, -730, 5329], [1, -6, 142, -474, 6241], [1, 15, 195, 1245, 6889], [1, -3, -43, -267, 7921], [1, -11, 58, -1067, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/70771/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-70771-1.1-c1e2-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-70771-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.4574792705030049, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 895570004834846167, 'z1': {'__RealLiteral__': 0, 'data': '1.34740788631', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '895570004834846167', 'Lhash_array': ['895570004834846167'], 'label': '4-70771-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/70771/a'}