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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': -2, 'A9': 0, 'Lhash': '2247157434470399263', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.020618556701030927, 0.0], 'a4': [-0.010309278350515464, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.020618556701030927, 0.0], 'a9': [0.0, 0.0], 'algebraic': True, 'analytic_conductor': 21.685963528905734, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 0, 1, 2]], [170057, [1, -181, 169875, 170057]]], 'bad_primes': [2, 170057], 'central_character': '340114.1', 'coefficient_field': '1.1.1.1', 'conductor': 340114, 'conductor_radical': 340114, 'degree': 4, 'euler_factors': [[1, 0, 1, 2], [1, -2, 4, -6, 9], [1, 0, 4, 0, 25], [1, 0, -2, 0, 49], [1, -4, 20, -44, 121], [1, -3, 12, -39, 169], [1, -2, -6, -34, 289], [1, -13, 78, -247, 361], [1, -5, 46, -115, 529], [1, 1, -4, 29, 841], [1, 2, 54, 62, 961], [1, -2, -36, -74, 1369], [1, 6, 78, 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[0.9819174113370575, 1.657168984572004, 2.910945151105202, 3.135622555711602, 3.547402448207458, 4.101194698241771, 4.925185378222914, 5.412661683432028, 5.890335572535651, 6.35357214025532, 7.049639578129502, 7.468084487718222, 7.944377861167049, 8.348604238953985, 8.935498314227843, 9.139652051909252, 9.380051354624596, 9.880063766692778, 10.2447929472233, 11.04017522676121, 11.50100651830022, 11.78982636506166, 11.94240744111525, 12.68388020258585, 13.09537433405781, 13.49364668262066, 13.90355937466791, 14.13380823959854, 14.49924598223918, 14.70490121928617, 15.26864127904269, 15.67996009607877, 15.99186252398975, 16.37747515742199, 16.92275017308177, 17.25394802586638, 17.65998587518602, 18.05863532597822, 18.37702068332758, 18.65654121688129, 19.1767112675101, 19.51991729701144, 19.68129583577845], 'prelabel': '4-340114-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.157966412029495, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 2247157434470399263, 'z1': {'__RealLiteral__': 0, 'data': '0.981917411337', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.65716898457', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.91094515111', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.685963528905734, 'bad_primes': [2, 170057], 'central_character': '1.1', 'conductor': 340114, 'conductor_radical': 340114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, -1, 0, 0, 0, -2, 0, 0, 4, -2, 3, 0, 0, 1, 2, 0, 13, 0, 0, 0, 5, -4, -4, 0, -2, 0, -1, 0, -2, 4, 8, 0, 0, 0, 2, 0, 6, 0, -6, 0, 2, -4, 0, 0, 0, 2, 2, 0, 4, -3, -16, 0, 0, 0, 26, 0, 3, 0, 10, 0, 0, 3, 0, 0, -12, -2, 10, 0, -16, 0, 4, 0, -8, -13, 0, 0, -3, 0, -1, 0, 6, 0, 0, 0, -2, -8, -11, 0, 0, -5, -4, 0, 0, 8, 9, 0, 0, 4], 'euler11': [1, -4, 20, -44, 121], 'euler13': [1, -3, 12, -39, 169], 'euler17': [1, -2, -6, -34, 289], 'euler19': [1, -13, 78, -247, 361], 'euler2': [1, 0, 1, 2, 0], 'euler23': [1, -5, 46, -115, 529], 'euler29': [1, 1, -4, 29, 841], 'euler3': [1, -2, 4, -6, 9], 'euler31': [1, 2, 54, 62, 961], 'euler37': [1, -2, -36, -74, 1369], 'euler41': [1, 6, 78, 246, 1681], 'euler43': [1, -2, 42, -86, 1849], 'euler47': [1, 0, 46, 0, 2209], 'euler5': [1, 0, 4, 0, 25], 'euler53': [1, 16, 142, 848, 2809], 'euler59': [1, -3, 42, -177, 3481], 'euler61': [1, -10, 48, -610, 3721], 'euler67': [1, 12, 102, 804, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 16, 198, 1136, 5041], 'euler73': [1, -4, 102, -292, 5329], 'euler79': [1, 3, 30, 237, 6241], 'euler83': [1, -6, 48, -498, 6889], 'euler89': [1, 11, 96, 979, 7921], 'euler97': [1, -9, 48, -873, 9409], 'euler_factors': [[1, 0, 1, 2, 0], [1, -2, 4, -6, 9], [1, 0, 4, 0, 25], [1, 0, -2, 0, 49], [1, -4, 20, -44, 121], [1, -3, 12, -39, 169], [1, -2, -6, -34, 289], [1, -13, 78, -247, 361], [1, -5, 46, -115, 529], [1, 1, -4, 29, 841], [1, 2, 54, 62, 961], [1, -2, -36, -74, 1369], [1, 6, 78, 246, 1681], [1, -2, 42, -86, 1849], [1, 0, 46, 0, 2209], [1, 16, 142, 848, 2809], [1, -3, 42, -177, 3481], [1, -10, 48, -610, 3721], [1, 12, 102, 804, 4489], [1, 16, 198, 1136, 5041], [1, -4, 102, -292, 5329], [1, 3, 30, 237, 6241], [1, -6, 48, -498, 6889], [1, 11, 96, 979, 7921], [1, -9, 48, -873, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/340114/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': '4-340114-1.1-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': '4-340114-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.157966412029495, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2247157434470399263, 'z1': {'__RealLiteral__': 0, 'data': '0.981917411337', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': '2247157434470399263', 'Lhash_array': ['2247157434470399263'], 'label': '4-340114-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/340114/a'}