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lfunc_lfunctions • Show schema
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{'Lhash': '2214018704873165223538286540775', 'a10': 36, 'a2': 3, 'a3': 0, 'a4': 1, 'a5': 12, 'a6': 0, 'a7': -12, 'a8': -21, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.25307999625156, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '1089.1', 'coefficient_field': '1.1.1.1', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'euler_factors': [[1, -3, 8], [1], [1, -12, 125], [1, 12, 343], [1], [1, -66, 2197], [1, 114, 4913], [1, 42, 6859], [1, 18, 12167], [1, -186, 24389], [1, 308, 29791], [1, 146, 50653], [1, -42, 68921], [1, -366, 79507], [1, 618, 103823], [1, -408, 148877], [1, -132, 205379], [1, 630, 226981], [1, 452, 300763], [1, -282, 357911], [1, 684, 389017], [1, 1272, 493039], [1, 432, 571787], [1, 954, 704969], [1, -326, 912673], [1, -1326, 1030301], [1, 1564, 1092727], [1, 84, 1225043], [1, -1122, 1295029], [1, -906, 1442897]], 'euler_factors_factorization': [[[[1, -3, 8], 1]], [1], [[[1, -12, 125], 1]], [[[1, 12, 343], 1]], [1], [[[1, -66, 2197], 1]], [[[1, 114, 4913], 1]], [[[1, 42, 6859], 1]], [[[1, 18, 12167], 1]], [[[1, -186, 24389], 1]], [[[1, 308, 29791], 1]], [[[1, 146, 50653], 1]], [[[1, -42, 68921], 1]], [[[1, -366, 79507], 1]], [[[1, 618, 103823], 1]], [[[1, -408, 148877], 1]], [[[1, -132, 205379], 1]], [[[1, 630, 226981], 1]], [[[1, 452, 300763], 1]], [[[1, -282, 357911], 1]], [[[1, 684, 389017], 1]], [[[1, 1272, 493039], 1]], [[[1, 432, 571787], 1]], [[[1, 954, 704969], 1]], [[[1, -326, 912673], 1]], [[[1, -1326, 1030301], 1]], [[[1, 1564, 1092727], 1]], [[[1, 84, 1225043], 1]], [[[1, -1122, 1295029], 1]], [[[1, -906, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 115, 'label': '2-33e2-1.1-c3-0-115', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1089/4/a/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-2.58522529218958e-60, 0.3414621177450037, 0.6802332054041892, 1.0136340777480297, 1.3390096014694823, 1.653741609215373, 1.9552628310259597, 2.2410721036225834, 2.5087510539748497, 2.7559823776969816, 2.9805697475598887, 3.1804592955187205, 3.3537625160713835, 3.4987803424838755, 3.614028053436447, 3.6982605788704146, 3.7504976930136342, 3.770048512301803, 3.756534658525086, 3.7099114050781905, 3.630486098443738, 3.518933139440198, 3.376304820419973, 3.2040373462475644, 3.0039514188693857, 2.7782468375393803, 2.5294906587851544, 2.260598571027261, 1.9748092669649744, 1.6756517404965403, 1.3669055916462627, 1.0525545898446709, 0.7367339196176873, 0.4236717095355481, 0.11762562103673911, -0.1771845559360171, -0.4566471932974082, -0.716830748544078, -0.9540559433144807, -1.1649667165362882, -1.346598398732735, 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3.6921641380634567, 3.68190212944362, 3.583158038468994, 3.403678454151364, 3.154096608111287, 2.847386768767381, 2.4982277001908675, 2.12230519444944, 1.735586265838707, 1.3535986714619732, 0.9907489386356494, 0.6597100511015773, 0.37090646080535555, 0.13211930689529516, -0.05177114197753149, -0.17889547958068322, -0.2503544141264999, -0.2700314296332952, -0.24427013373407083, -0.18143415692086393, -0.09137319402848189], 'positive_zeros': ['1.74655279970249729963429530968919', '2.84850810699099482663415166215773', '3.83541396049379968015384410688195', '4.66854448928458628169696553925456', '5.80173663768574755323855184175771', '6.18316284092337417489211352823175', '6.94427527513079405464318448646390', '8.596356318810173680753919017784019', '8.994843914743951221101935483288185'], 'prelabel': '2-33e2-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.015801893525785, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 143669994854832616, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74655279970249729963429530969', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84850810699099482663415166216', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83541396049379968015384410688', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.25307999625156, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'dirichlet_coefficients': [1, 3, 0, 1, 12, 0, -12, -21, 0, 36, 0, 0, 66, -36, 0, -71, -114, 0, -42, 12, 0, 0, -18, 0, 19, 198, 0, -12, 186, 0, -308, -45, 0, -342, -144, 0, -146, -126, 0, -252, 42, 0, 366, 0, 0, -54, -618, 0, -199, 57, 0, 66, 408, 0, 0, 252, 0, 558, 132, 0, -630, -924, 0, 433, 792, 0, -452, -114, 0, -432, 282, 0, -684, -438, 0, -42, 0, 0, -1272, -852, 0, 126, -432, 0, -1368, 1098, 0, 0, -954, 0, -792, -18, 0, -1854, -504, 0, 326, -597, 0, 19], 'euler11': [1, 0, 0], 'euler13': [1, -66, 2197], 'euler17': [1, 114, 4913], 'euler19': [1, 42, 6859], 'euler2': [1, -3, 8], 'euler23': [1, 18, 12167], 'euler29': [1, -186, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 308, 29791], 'euler37': [1, 146, 50653], 'euler41': [1, -42, 68921], 'euler43': [1, -366, 79507], 'euler47': [1, 618, 103823], 'euler5': [1, -12, 125], 'euler53': [1, -408, 148877], 'euler59': [1, -132, 205379], 'euler61': [1, 630, 226981], 'euler67': [1, 452, 300763], 'euler7': [1, 12, 343], 'euler71': [1, -282, 357911], 'euler73': [1, 684, 389017], 'euler79': [1, 1272, 493039], 'euler83': [1, 432, 571787], 'euler89': [1, 954, 704969], 'euler97': [1, -326, 912673], 'euler_factors': [[1, -3, 8], [1, 0, 0], [1, -12, 125], [1, 12, 343], [1, 0, 0], [1, -66, 2197], [1, 114, 4913], [1, 42, 6859], [1, 18, 12167], [1, -186, 24389], [1, 308, 29791], [1, 146, 50653], [1, -42, 68921], [1, -366, 79507], [1, 618, 103823], [1, -408, 148877], [1, -132, 205379], [1, 630, 226981], [1, 452, 300763], [1, -282, 357911], [1, 684, 389017], [1, 1272, 493039], [1, 432, 571787], [1, 954, 704969], [1, -326, 912673]], 'index': 115, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/4/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/1089/4/a/i'], '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': '2-33e2-1.1-c3-0-115', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-33e2-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.015801893525785, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 143669994854832616, 'z1': {'__RealLiteral__': 0, 'data': '1.74655279970249729963429530969', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20021672
{'Lhash': '2214018704873165223538286540775', 'Lhash_array': ['2214018704873165223538286540775'], 'factors': ['2-33e2-1.1-c3-0-115'], 'label': '2-33e2-1.1-c3-0-115', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/4/a/i'}
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id: 24582319
{'Lhash': '2214018704873165223538286540775', 'Lhash_array': ['2214018704873165223538286540775'], 'factors': ['2-33e2-1.1-c3-0-115'], 'label': '2-33e2-1.1-c3-0-115', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/4/a/i/1/1'}