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lfunc_lfunctions • Show schema
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{'A10': -3, 'A2': 1, 'A3': -1, 'A4': 1, 'A5': -3, 'A6': -1, 'A7': -1, 'A8': 1, 'A9': -1, 'Lhash': '1626099242564292047', 'a10': [-0.030927835051546393, 0.0], 'a2': [0.010309278350515464, 0.0], 'a3': [-0.010309278350515464, 0.0], 'a4': [0.010309278350515464, 0.0], 'a5': [-0.030927835051546393, 0.0], 'a6': [-0.010309278350515464, 0.0], 'a7': [-0.010309278350515464, 0.0], 'a8': [0.010309278350515464, 0.0], 'a9': [-0.010309278350515464, 0.0], 'algebraic': True, 'analytic_conductor': 0.10354764805607211, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, -1]], [7, [1, 1, 7, 7]], [29, [1, 3, 31, 29]]], 'bad_primes': [2, 7, 29], 'central_character': '1624.1', 'coefficient_field': '1.1.1.1', 'conductor': 1624, 'conductor_radical': 406, 'degree': 4, 'euler_factors': [[1, -1], [1, 1, 2, 3, 9], [1, 3, 4, 15, 25], [1, 1, 7, 7], [1, -1, -14, -11, 121], [1, 1, -8, 13, 169], [1, 4, 22, 68, 289], [1, -8, 54, -152, 361], [1, -2, 30, -46, 529], [1, 3, 31, 29], [1, 1, -2, 31, 961], [1, -2, -14, -74, 1369], [1, 2, -38, 82, 1681], [1, -5, 66, -215, 1849], [1, 1, 14, 47, 2209], [1, -1, -4, -53, 2809], [1, 2, 78, 118, 3481], [1, -4, -18, -244, 3721], [1, 0, 54, 0, 4489], [1, -6, 62, -426, 5041], [1, 6, 114, 438, 5329], [1, 3, 142, 237, 6241], [1, 2, 78, 166, 6889], [1, -6, 42, -534, 7921], [1, 2, 58, 194, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-1624-1.1-c1e2-0-0', 'leading_term': '0.627012253805', 'load_key': 'G2Q', '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, 'origin': 'Genus2Curve/Q/1624/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.627012253805227, 0.6518161077975388, 0.7268934537915205, 0.8538121410894352, 1.033760954933288, 1.265466226362144, 1.542472426849739, 1.85017059490276, 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1.59573362608531, 2.538538413485711, -0.006538696053868276], 'positive_zeros': [3.088097717286413, 4.036716675854185, 4.987343267959074, 5.81162420626203, 6.812832903433156, 7.373032587300458, 8.120366012006725, 9.086593174559095, 9.784358488686287, 10.82607810593109, 11.36902382814961, 11.65299059397589, 12.26003979720445, 12.88660353815201, 13.51784999235312, 14.21492735440211, 14.81884064457676, 15.41103722734066, 15.87109299797434, 16.31837981569343, 16.83044384193973, 17.54182562348141, 18.04369590153484, 18.83632377255781, 19.25339046884132, 19.87546339888487], 'prelabel': '4-1624-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.5672637867202864, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1626099242564292047, 'z1': {'__RealLiteral__': 0, 'data': '3.08809771729', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.03671667585', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.98734326796', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.10354764805607211, 'bad_primes': [2, 7, 29], 'central_character': '1.1', 'conductor': 1624, 'conductor_radical': 406, 'degree': 4, 'dirichlet_coefficients': [1, 1, -1, 1, -3, -1, -1, 1, -1, -3, 1, -1, -1, -1, 3, 1, -4, -1, 8, -3, 1, 1, 2, -1, 5, -1, 0, -1, -3, 3, -1, 1, -1, -4, 3, -1, 2, 8, 1, -3, -2, 1, 5, 1, 3, 2, -1, -1, -6, 5, 4, -1, 1, 0, -3, -1, -8, -3, -2, 3, 4, -1, 1, 1, 3, -1, 0, -4, -2, 3, 6, -1, -6, 2, -5, 8, -1, 1, -3, -3, -4, -2, -2, 1, 12, 5, 3, 1, 6, 3, 1, 2, 1, -1, -24, -1, -2, -6, -1, 5], 'euler11': [1, -1, -14, -11, 121], 'euler13': [1, 1, -8, 13, 169], 'euler17': [1, 4, 22, 68, 289], 'euler19': [1, -8, 54, -152, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, -2, 30, -46, 529], 'euler29': [1, 3, 31, 29, 0], 'euler3': [1, 1, 2, 3, 9], 'euler31': [1, 1, -2, 31, 961], 'euler37': [1, -2, -14, -74, 1369], 'euler41': [1, 2, -38, 82, 1681], 'euler43': [1, -5, 66, -215, 1849], 'euler47': [1, 1, 14, 47, 2209], 'euler5': [1, 3, 4, 15, 25], 'euler53': [1, -1, -4, -53, 2809], 'euler59': [1, 2, 78, 118, 3481], 'euler61': [1, -4, -18, -244, 3721], 'euler67': [1, 0, 54, 0, 4489], 'euler7': [1, 1, 7, 7, 0], 'euler71': [1, -6, 62, -426, 5041], 'euler73': [1, 6, 114, 438, 5329], 'euler79': [1, 3, 142, 237, 6241], 'euler83': [1, 2, 78, 166, 6889], 'euler89': [1, -6, 42, -534, 7921], 'euler97': [1, 2, 58, 194, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 1, 2, 3, 9], [1, 3, 4, 15, 25], [1, 1, 7, 7, 0], [1, -1, -14, -11, 121], [1, 1, -8, 13, 169], [1, 4, 22, 68, 289], [1, -8, 54, -152, 361], [1, -2, 30, -46, 529], [1, 3, 31, 29, 0], [1, 1, -2, 31, 961], [1, -2, -14, -74, 1369], [1, 2, -38, 82, 1681], [1, -5, 66, -215, 1849], [1, 1, 14, 47, 2209], [1, -1, -4, -53, 2809], [1, 2, 78, 118, 3481], [1, -4, -18, -244, 3721], [1, 0, 54, 0, 4489], [1, -6, 62, -426, 5041], [1, 6, 114, 438, 5329], [1, 3, 142, 237, 6241], [1, 2, 78, 166, 6889], [1, -6, 42, -534, 7921], [1, 2, 58, 194, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/1624/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': '4-1624-1.1-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': '4-1624-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.5672637867202864, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1626099242564292047, 'z1': {'__RealLiteral__': 0, 'data': '3.08809771729', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '1626099242564292047', 'Lhash_array': ['1626099242564292047'], 'label': '4-1624-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/1624/a'}