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lfunc_lfunctions • Show schema
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{'Lhash': '1721895615667461911701842235549', 'a10': [1.5881559212252219, -3.477576385886737], 'a2': [-0.9594929736144974, -0.28173255684142967], 'a3': [0.6548607339452851, -0.7557495743542583], 'a4': [0.8412535328311812, 0.5406408174555976], 'a5': [-0.5440779606126109, 3.78414533581566], 'a6': [-0.8412535328311812, 0.5406408174555976], 'a7': [1.2021670783930483, 2.6323787153624476], 'a8': [-0.6548607339452851, -0.7557495743542583], 'a9': [-0.14231483827328514, -0.9898214418809327], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9594929736144974, 0.28173255684142967]]], [3, [[1.0, 0], [-0.6548607339452851, 0.7557495743542583]]], [23, [[1.0, 0], [-2.8890895288146936, 3.827944839531167]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.133', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': '2915411302596132221844502741878', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9594929736144974, 0.28173255684142967]], [[1.0, 0], [-0.6548607339452851, 0.7557495743542583]], [[1.0, 0], [0.5440779606126109, -3.78414533581566], [-4.7974648680724865, -1.4086627842071484]], [[1.0, 0], [-1.2021670783930483, -2.6323787153624476], [-4.584025137616996, 5.290247020479808]], [[1.0, 0], [-1.5166187300393268, 0.4453194388260871], [9.253788861142993, -5.947048992011573]], [[1.0, 0], [-1.9565261342377311, 4.284194638487579], [-8.513189541288705, -9.824744466605358]], [[1.0, 0], [3.985690759949058, -2.5614479184796495], [7.062055221032069, -15.463743921026813]], [[1.0, 0], [-1.8072842800495532, -1.1614710814376095], [7.892885247035842, 17.28300791173585]], [[1.0, 0], [-2.8890895288146936, 3.827944839531167]], [[1.0, 0], [0.49500827178590556, -0.31812249965233685], [12.047035377054707, -26.379327865281034]], [[1.0, 0], [0.11181901971150207, 0.12904602791276665], [-4.411759986471839, 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-59.704216373986405]], [[1.0, 0], [-0.016116829899108277, -0.11209501414498453], [-79.63791681000329, 23.383802217838664]], [[1.0, 0], [-8.01459853590486, 9.249339772807993], [-12.666020606322377, -88.094108327403]], [[1.0, 0], [0.12431731146317429, -0.8646458934025228], [-93.07081844060625, -27.32805801361868]], [[1.0, 0], [-1.5526952138436096, -10.799232420283788], [-96.90879033506424, 28.4549882409844]], [[1.0, 0], [3.543208006937928, -1.0403797408283237], [86.64911388161165, -55.68600419792655]], [[1.0, 0], [7.050526133079956, 8.136740909699974], [-15.22768769524151, 105.9108942812598]], [[1.0, 0], [6.993821270861775, -4.494656012072688], [45.28023641720562, -99.1498874936425]], [[1.0, 0], [7.208463160063334, 2.1165957571648133], [95.06164920992347, 61.09241237248253]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-138-23.18-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': 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-0.16518453770450725, 'root_number': '0.8683441301338668 - 0.49596216757133627*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0825922688523', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35833613407152544146735100438', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.10396741561284494546443903544', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.00404828242109854314901002784', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'bad_primes': [2, 3, 23], 'central_character': '23.18', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/2/e/b/133/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-138-23.18-c1-0-0', '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': '2-138-23.18-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0497311788708907, 'root_angle': -0.08259226885225363, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35833613407152544146735100438', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1721895615667461911701842235549', 'Lhash_array': ['1721895615667461911701842235549'], 'label': '2-138-23.18-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/2/e/b/133/1'}