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lfunc_lfunctions • Show schema
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{'Lhash': '3303354473429710593667669164420', 'a10': 4, 'a2': 2, 'a3': 3, 'a4': 4, 'a5': 2, 'a6': 6, 'a7': -7, 'a8': 8, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.478080220241107, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1, -3]], [7, [1, 7]]], 'bad_primes': [2, 3, 7], 'central_character': '42.1', 'coefficient_field': '1.1.1.1', 'conductor': 42, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1, -2], [1, -3], [1, -2, 125], [1, 7], [1, 8, 1331], [1, 42, 2197], [1, 2, 4913], [1, 124, 6859], [1, -76, 12167], [1, -254, 24389], [1, 72, 29791], [1, -398, 50653], [1, -462, 68921], [1, -212, 79507], [1, 264, 103823], [1, 162, 148877], [1, 772, 205379], [1, -30, 226981], [1, 764, 300763], [1, 236, 357911], [1, -418, 389017], [1, -552, 493039], [1, -1036, 571787], [1, -30, 704969], [1, 1190, 912673], [1, -1370, 1030301], [1, -464, 1092727], [1, 2136, 1225043], [1, 1226, 1295029], [1, -338, 1442897]], 'euler_factors_factorization': [[[[1, -2], 1]], [[[1, -3], 1]], [[[1, -2, 125], 1]], [[[1, 7], 1]], [[[1, 8, 1331], 1]], [[[1, 42, 2197], 1]], [[[1, 2, 4913], 1]], [[[1, 124, 6859], 1]], [[[1, -76, 12167], 1]], [[[1, -254, 24389], 1]], [[[1, 72, 29791], 1]], [[[1, -398, 50653], 1]], [[[1, -462, 68921], 1]], [[[1, -212, 79507], 1]], [[[1, 264, 103823], 1]], [[[1, 162, 148877], 1]], [[[1, 772, 205379], 1]], [[[1, -30, 226981], 1]], [[[1, 764, 300763], 1]], [[[1, 236, 357911], 1]], [[[1, -418, 389017], 1]], [[[1, -552, 493039], 1]], [[[1, -1036, 571787], 1]], [[[1, -30, 704969], 1]], [[[1, 1190, 912673], 1]], [[[1, -1370, 1030301], 1]], [[[1, -464, 1092727], 1]], [[[1, 2136, 1225043], 1]], [[[1, 1226, 1295029], 1]], [[[1, -338, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-42-1.1-c3-0-1', '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/42/4/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.1222134917823183, 2.121083871132517, 2.1174926034207373, 2.1108407956718724, 2.1001576878804085, 2.0841405996847575, 2.0612088463111884, 2.029570152879521, 1.9872981959909937, 1.9324200810756573, 1.8630126708733048, 1.777306592654571, 1.6737964047892382, 1.5513547935677803, 1.4093478448949737, 1.2477474716932146, 1.067236073890462, 0.8692975689880871, 0.6562881643994958, 0.4314797527910205, 0.19906869761239704, -0.03585687299177185, -0.26739725599490505, -0.4889733593851898, -0.6935133053524667, -0.8736931858394316, -1.0222284857359714, -1.1322090471607174, -1.1974665491096748, -1.2129595372677706, -1.17515732314491, -1.0824008811771115, -0.9352165301310077, -0.7365570157153764, -0.49194491619951325, -0.20949532232249796, 0.10020133372959494, 0.4243495484750606, 0.7483776103135212, 1.0565211499521487, 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-0.31846681363609164, 0.28627991770975647, 0.9737613113163518, 1.5964533707850952, 2.02719147117748, 2.181464758639185, 2.031252330539743, 1.6080386959269724, 0.9946598358325469, 0.3077051792217343, -0.32604935992454626, -0.794604646667613, -1.0222899420147835, -0.9837720434396043, -0.7078591905233086, -0.27042280550100023, 0.22211202213944278, 0.6553951196156794, 0.9313558289764529, 0.9890884646772337, 0.8181327295934826], 'positive_zeros': ['2.60588720017564028889637504318476', '4.46044875094035441087699494163485', '6.29037507773754274652042152737766', '7.78628074367903158375486086399103', '9.413712194209449682264304021628835', '10.73751196562222595962090365806111', '12.34649018301336546275646549966919', '13.21770227343104200983664078423290', '14.38807398338182833411677577999877', '15.24907888356959080078119457130704'], 'prelabel': '2-42-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.574191926113556, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 676961687276118947, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.60588720017564028889637504318', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.46044875094035441087699494163', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.29037507773754274652042152738', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.478080220241107, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 42, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, 2, 3, 4, 2, 6, -7, 8, 9, 4, -8, 12, -42, -14, 6, 16, -2, 18, -124, 8, -21, -16, 76, 24, -121, -84, 27, -28, 254, 12, -72, 32, -24, -4, -14, 36, 398, -248, -126, 16, 462, -42, 212, -32, 18, 152, -264, 48, 49, -242, -6, -168, -162, 54, -16, -56, -372, 508, -772, 24, 30, -144, -63, 64, -84, -48, -764, -8, 228, -28, -236, 72, 418, 796, -363, -496, 56, -252, 552, 32, 81, 924, 1036, -84, -4, 424, 762, -64, 30, 36, 294, 304, -216, -528, -248, 96, -1190, 98, -72, -484], 'euler11': [1, 8, 1331], 'euler13': [1, 42, 2197], 'euler17': [1, 2, 4913], 'euler19': [1, 124, 6859], 'euler2': [1, -2, 0], 'euler23': [1, -76, 12167], 'euler29': [1, -254, 24389], 'euler3': [1, -3, 0], 'euler31': [1, 72, 29791], 'euler37': [1, -398, 50653], 'euler41': [1, -462, 68921], 'euler43': [1, -212, 79507], 'euler47': [1, 264, 103823], 'euler5': [1, -2, 125], 'euler53': [1, 162, 148877], 'euler59': [1, 772, 205379], 'euler61': [1, -30, 226981], 'euler67': [1, 764, 300763], 'euler7': [1, 7, 0], 'euler71': [1, 236, 357911], 'euler73': [1, -418, 389017], 'euler79': [1, -552, 493039], 'euler83': [1, -1036, 571787], 'euler89': [1, -30, 704969], 'euler97': [1, 1190, 912673], 'euler_factors': [[1, -2, 0], [1, -3, 0], [1, -2, 125], [1, 7, 0], [1, 8, 1331], [1, 42, 2197], [1, 2, 4913], [1, 124, 6859], [1, -76, 12167], [1, -254, 24389], [1, 72, 29791], [1, -398, 50653], [1, -462, 68921], [1, -212, 79507], [1, 264, 103823], [1, 162, 148877], [1, 772, 205379], [1, -30, 226981], [1, 764, 300763], [1, 236, 357911], [1, -418, 389017], [1, -552, 493039], [1, -1036, 571787], [1, -30, 704969], [1, 1190, 912673]], 'index': 1, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/42/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/42/4/a/b'], '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': '2-42-1.1-c3-0-1', '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': '2-42-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.574191926113556, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 676961687276118947, 'z1': {'__RealLiteral__': 0, 'data': '2.60588720017564028889637504318', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9999682
{'Lhash': '3303354473429710593667669164420', 'Lhash_array': ['3303354473429710593667669164420'], 'label': '2-42-1.1-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/42/4/a/b'}
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id: 24548945
{'Lhash': '3303354473429710593667669164420', 'Lhash_array': ['3303354473429710593667669164420'], 'label': '2-42-1.1-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/42/4/a/b/1/1'}