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lfunc_lfunctions • Show schema
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{'Lhash': '4575318976688690565033061472688', 'a10': -12, 'a2': 2, 'a3': 0, 'a4': 4, 'a5': -6, 'a6': 0, 'a7': -16, 'a8': 8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0620343801033316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '18.1', 'coefficient_field': '1.1.1.1', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1, -2], [1], [1, 6, 125], [1, 16, 343], [1, 12, 1331], [1, -38, 2197], [1, -126, 4913], [1, -20, 6859], [1, 168, 12167], [1, 30, 24389], [1, 88, 29791], [1, -254, 50653], [1, 42, 68921], [1, 52, 79507], [1, -96, 103823], [1, 198, 148877], [1, -660, 205379], [1, 538, 226981], [1, -884, 300763], [1, 792, 357911], [1, -218, 389017], [1, 520, 493039], [1, -492, 571787], [1, 810, 704969], [1, -1154, 912673], [1, -618, 1030301], [1, -128, 1092727], [1, -1476, 1225043], [1, -1190, 1295029], [1, -462, 1442897]], 'euler_factors_factorization': [[[[1, -2], 1]], [1], [[[1, 6, 125], 1]], [[[1, 16, 343], 1]], [[[1, 12, 1331], 1]], [[[1, -38, 2197], 1]], [[[1, -126, 4913], 1]], [[[1, -20, 6859], 1]], [[[1, 168, 12167], 1]], [[[1, 30, 24389], 1]], [[[1, 88, 29791], 1]], [[[1, -254, 50653], 1]], [[[1, 42, 68921], 1]], [[[1, 52, 79507], 1]], [[[1, -96, 103823], 1]], [[[1, 198, 148877], 1]], [[[1, -660, 205379], 1]], [[[1, 538, 226981], 1]], [[[1, -884, 300763], 1]], [[[1, 792, 357911], 1]], [[[1, -218, 389017], 1]], [[[1, 520, 493039], 1]], [[[1, -492, 571787], 1]], [[[1, 810, 704969], 1]], [[[1, -1154, 912673], 1]], [[[1, -618, 1030301], 1]], [[[1, -128, 1092727], 1]], [[[1, -1476, 1225043], 1]], [[[1, -1190, 1295029], 1]], [[[1, -462, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-18-1.1-c3-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/18/4/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.3399377239915387, 1.3441346273755805, 1.3564343402225054, 1.3759697094035415, 1.4013136592676398, 1.430502944960996, 1.461067211853504, 1.4900638995318818, 1.514123122826214, 1.5295096880301287, 1.5322109718482955, 1.5180592496280865, 1.4828953437433647, 1.4227774233202717, 1.3342346461819745, 1.2145602765082681, 1.0621331348869476, 0.87675001805649, 0.6599454678362359, 0.4152695248505879, 0.14848956528181906, -0.13232021568926983, -0.4168378064019388, -0.6927330737046061, -0.9461121877068548, -1.1621780703648925, -1.3261009317769723, -1.424071860168775, -1.4444886985993604, -1.379198946696212, -1.2247016367226202, -0.9831919759477064, -0.6633221730332847, -0.2805523248062935, 0.14302092398780578, 0.579441429000371, 0.9963158081832002, 1.3588628466171857, 1.6325043702383186, 1.7858398942916387, 1.793778331670886, 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 646767367530437256, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.60929026962551384976945217111', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.91841366397310679443986977087', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.79784374777438716958608823195', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0620343801033316, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 4, -6, 0, -16, 8, 0, -12, -12, 0, 38, -32, 0, 16, 126, 0, 20, -24, 0, -24, -168, 0, -89, 76, 0, -64, -30, 0, -88, 32, 0, 252, 96, 0, 254, 40, 0, -48, -42, 0, -52, -48, 0, -336, 96, 0, -87, -178, 0, 152, -198, 0, 72, -128, 0, -60, 660, 0, -538, -176, 0, 64, -228, 0, 884, 504, 0, 192, -792, 0, 218, 508, 0, 80, 192, 0, -520, -96, 0, -84, 492, 0, -756, -104, 0, -96, -810, 0, -608, -672, 0, 192, -120, 0, 1154, -174, 0, -356], 'euler11': [1, 12, 1331], 'euler13': [1, -38, 2197], 'euler17': [1, -126, 4913], 'euler19': [1, -20, 6859], 'euler2': [1, -2, 0], 'euler23': [1, 168, 12167], 'euler29': [1, 30, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 88, 29791], 'euler37': [1, -254, 50653], 'euler41': [1, 42, 68921], 'euler43': [1, 52, 79507], 'euler47': [1, -96, 103823], 'euler5': [1, 6, 125], 'euler53': [1, 198, 148877], 'euler59': [1, -660, 205379], 'euler61': [1, 538, 226981], 'euler67': [1, -884, 300763], 'euler7': [1, 16, 343], 'euler71': [1, 792, 357911], 'euler73': [1, -218, 389017], 'euler79': [1, 520, 493039], 'euler83': [1, -492, 571787], 'euler89': [1, 810, 704969], 'euler97': [1, -1154, 912673], 'euler_factors': [[1, -2, 0], [1, 0, 0], [1, 6, 125], [1, 16, 343], [1, 12, 1331], [1, -38, 2197], [1, -126, 4913], [1, -20, 6859], [1, 168, 12167], [1, 30, 24389], [1, 88, 29791], [1, -254, 50653], [1, 42, 68921], [1, 52, 79507], [1, -96, 103823], [1, 198, 148877], [1, -660, 205379], [1, 538, 226981], [1, -884, 300763], [1, 792, 357911], [1, -218, 389017], [1, 520, 493039], [1, -492, 571787], [1, 810, 704969], [1, -1154, 912673]], 'index': 0, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/18/4/a/a'], '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': '2-18-1.1-c3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-18-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.0305505228291, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 646767367530437256, 'z1': {'__RealLiteral__': 0, 'data': '3.60929026962551384976945217111', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9958733
{'Lhash': '4575318976688690565033061472688', 'Lhash_array': ['4575318976688690565033061472688'], 'label': '2-18-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/4/a/a'}
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id: 24547105
{'Lhash': '4575318976688690565033061472688', 'Lhash_array': ['4575318976688690565033061472688'], 'label': '2-18-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/4/a/a/1/1'}