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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 2, 'Lhash': '1811671585910545041', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.010309278350515464, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.010309278350515464, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.020618556701030927, 0.0], 'a8': [0.0, 0.0], 'a9': [0.020618556701030927, 0.0], 'algebraic': True, 'analytic_conductor': 1.9964802684308682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1]], [19, [1, -4, 14, 19]], [103, [1, -5, 97, 103]]], 'bad_primes': [2, 19, 103], 'central_character': '31312.1', 'coefficient_field': '1.1.1.1', 'conductor': 31312, 'conductor_radical': 3914, 'degree': 4, 'euler_factors': [[1], [1, 1, -1, 3, 9], [1, 1, 2, 5, 25], [1, 2, 2, 14, 49], [1, 0, -12, 0, 121], [1, 2, -2, 26, 169], [1, 9, 47, 153, 289], [1, -4, 14, 19], [1, 3, 7, 69, 529], [1, 0, -6, 0, 841], [1, 3, 55, 93, 961], [1, 2, -30, 74, 1369], [1, -10, 80, -410, 1681], [1, 9, 82, 387, 1849], [1, 5, 88, 235, 2209], [1, -5, 21, -265, 2809], [1, 2, 52, 118, 3481], [1, 3, -13, 183, 3721], [1, 3, 3, 201, 4489], [1, 8, 42, 568, 5041], [1, 0, 20, 0, 5329], [1, 6, 150, 474, 6241], [1, 3, 18, 249, 6889], [1, -17, 200, -1513, 7921], [1, 19, 198, 1843, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 2, 'label': '4-31312-1.1-c1e2-0-2', 'leading_term': '1.43868877617', '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': 1, 'origin': 'Genus2Curve/Q/31312/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.2761991757673038, 0.5882147215622233, 0.9574164287183693, 1.376048711513338, 1.794512724972734, 2.116494736109691, 2.210473970443335, 1.944701812999593, 1.244748520906478, 0.1584792679578169, -1.101968408398689, -2.177922019016811, 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2.928191037860218, 3.892042976796429, 4.380451534167664, 5.087038887380368, 5.838737667062065, 6.384331388577276, 7.009661238954717, 7.353435242707448, 8.00530312244316, 8.736356365905294, 9.293959541339946, 9.686782990801712, 10.22158559814831, 10.8068456908502, 11.25918131671552, 11.77096558450989, 12.05900422985796, 12.7919888998527, 13.0686033831667, 13.50881356477327, 13.96489504477845, 14.69409218708561, 15.16712471395699, 15.54139056842551, 15.92687914861226, 16.36098932540761, 16.61034749458755, 17.36199715509957, 17.75818060180918, 17.92935777633806, 18.51769589476371, 18.99543524718058, 19.39850905752796, 19.85774425285637], 'prelabel': '4-31312-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.1886835581266268, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1811671585910545041, 'z1': {'__RealLiteral__': 0, 'data': '1.89907963087', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.92819103786', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.8920429768', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9964802684308682, 'bad_primes': [2, 19, 103], 'central_character': '1.1', 'conductor': 31312, 'conductor_radical': 3914, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -2, 0, 2, 0, 0, 0, -2, 0, 1, 0, -9, 0, 4, 0, 2, 0, -3, 0, -1, 0, -6, 0, 0, 0, -3, 0, 0, 0, 2, 0, -2, 0, 2, 0, 10, 0, -9, 0, -2, 0, -5, 0, 2, 0, 9, 0, 5, 0, 0, 0, -4, 0, -2, 0, -3, 0, -4, 0, 2, 0, -3, 0, 3, 0, -8, 0, 0, 0, 1, 0, 0, 0, -6, 0, 2, 0, -3, 0, 9, 0, 0, 0, 17, 0, 4, 0, 3, 0, -4, 0, -19, 0, 0, 0], 'euler11': [1, 0, -12, 0, 121], 'euler13': [1, 2, -2, 26, 169], 'euler17': [1, 9, 47, 153, 289], 'euler19': [1, -4, 14, 19, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 3, 7, 69, 529], 'euler29': [1, 0, -6, 0, 841], 'euler3': [1, 1, -1, 3, 9], 'euler31': [1, 3, 55, 93, 961], 'euler37': [1, 2, -30, 74, 1369], 'euler41': [1, -10, 80, -410, 1681], 'euler43': [1, 9, 82, 387, 1849], 'euler47': [1, 5, 88, 235, 2209], 'euler5': [1, 1, 2, 5, 25], 'euler53': [1, -5, 21, -265, 2809], 'euler59': [1, 2, 52, 118, 3481], 'euler61': [1, 3, -13, 183, 3721], 'euler67': [1, 3, 3, 201, 4489], 'euler7': [1, 2, 2, 14, 49], 'euler71': [1, 8, 42, 568, 5041], 'euler73': [1, 0, 20, 0, 5329], 'euler79': [1, 6, 150, 474, 6241], 'euler83': [1, 3, 18, 249, 6889], 'euler89': [1, -17, 200, -1513, 7921], 'euler97': [1, 19, 198, 1843, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 1, -1, 3, 9], [1, 1, 2, 5, 25], [1, 2, 2, 14, 49], [1, 0, -12, 0, 121], [1, 2, -2, 26, 169], [1, 9, 47, 153, 289], [1, -4, 14, 19, 0], [1, 3, 7, 69, 529], [1, 0, -6, 0, 841], [1, 3, 55, 93, 961], [1, 2, -30, 74, 1369], [1, -10, 80, -410, 1681], [1, 9, 82, 387, 1849], [1, 5, 88, 235, 2209], [1, -5, 21, -265, 2809], [1, 2, 52, 118, 3481], [1, 3, -13, 183, 3721], [1, 3, 3, 201, 4489], [1, 8, 42, 568, 5041], [1, 0, 20, 0, 5329], [1, 6, 150, 474, 6241], [1, 3, 18, 249, 6889], [1, -17, 200, -1513, 7921], [1, 19, 198, 1843, 9409]], 'index': 2, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/31312/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': '4-31312-1.1-c1e2-0-2', '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': 1, 'prelabel': '4-31312-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.1886835581266268, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1811671585910545041, 'z1': {'__RealLiteral__': 0, 'data': '1.89907963087', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '1811671585910545041', 'Lhash_array': ['1811671585910545041'], 'label': '4-31312-1.1-c1e2-0-2', 'type': 'G2Q', 'url': 'Genus2Curve/Q/31312/a'}