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lfunc_lfunctions • Show schema
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{'Lhash': '1331076100125876513616471826775', 'a10': 12, 'a2': 2, 'a3': -3, 'a4': 4, 'a5': 6, 'a6': -6, 'a7': 16, 'a8': 8, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.83538666416771, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1, 3]], [11, [1]]], 'bad_primes': [2, 3, 11], 'central_character': '726.1', 'coefficient_field': '1.1.1.1', 'conductor': 726, 'conductor_radical': 66, 'degree': 2, 'euler_factors': [[1, -2], [1, 3], [1, -6, 125], [1, -16, 343], [1], [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, 3], 1]], [[[1, -6, 125], 1]], [[[1, -16, 343], 1]], [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': 20, 'label': '2-726-1.1-c3-0-20', 'leading_term': '3.43518375775342703008300124714000000000000000000000000000000000000000000000000000000000000', '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/726/4/a/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [3.435183757753427, 3.4194899615786496, 3.3725517408808066, 3.29480001872841, 3.186957580673105, 3.050045422057472, 2.8853906123574564, 2.694634711254336, 2.4797415729435666, 2.2430032299122478, 1.9870424615347924, 1.7148106303995976, 1.4295794119731988, 1.1349251505192837, 0.8347047436318, 0.5330221850922154, 0.23418517527720437, -0.057348467069269174, -0.3370344965474585, -0.6003155525206482, -0.8427032010984419, -1.0598674079902353, -1.2477317392750267, -1.4025722044183349, -1.521117307512761, -1.6006465728194037, -1.6390845732455972, -1.635087328878495, -1.5881178695299427, -1.498507781265022, -1.367501690737179, -1.1972818887342493, -0.9909706582451794, -0.7526083513871172, -0.48710584829600023, 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True, 'root_analytic_conductor': 6.544874839457796, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 2226279812235057438, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05003389726335309247895753665', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22918951058934538772009941198', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54850621145690462271714946194', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.83538666416771, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 726, 'conductor_radical': 66, 'degree': 2, 'dirichlet_coefficients': [1, 2, -3, 4, 6, -6, 16, 8, 9, 12, 0, -12, -38, 32, -18, 16, 126, 18, -20, 24, -48, 0, 168, -24, -89, -76, -27, 64, -30, -36, -88, 32, 0, 252, 96, 36, 254, -40, 114, 48, -42, -96, 52, 0, 54, 336, -96, -48, -87, -178, -378, -152, 198, -54, 0, 128, 60, -60, -660, -72, 538, -176, 144, 64, -228, 0, 884, 504, -504, 192, 792, 72, -218, 508, 267, -80, 0, 228, 520, 96, 81, -84, 492, -192, 756, 104, 90, 0, 810, 108, -608, 672, 264, -192, -120, -96, 1154, -174, 0, -356], 'euler11': [1, 0, 0], '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, 3, 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, 3, 0], [1, -6, 125], [1, -16, 343], [1, 0, 0], [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': 20, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/726/4/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/726/4/a/f'], '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': '2-726-1.1-c3-0-20', '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': '2-726-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.544874839457796, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 2226279812235057438, 'z1': {'__RealLiteral__': 0, 'data': '1.05003389726335309247895753665', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20146995
{'Lhash': '1331076100125876513616471826775', 'Lhash_array': ['1331076100125876513616471826775'], 'label': '2-726-1.1-c3-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/726/4/a/f'}
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id: 24570021
{'Lhash': '1331076100125876513616471826775', 'Lhash_array': ['1331076100125876513616471826775'], 'label': '2-726-1.1-c3-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/726/4/a/f/1/1'}