Formats: - HTML - YAML - JSON - 2026-08-11T06:22:23.788973
  • lfunc_lfunctions • Show schema
    {'Lhash': '2034941984041121770345114575817', 'a10': 0, 'a2': 2, 'a3': -10, 'a4': 4, 'a5': 0, 'a6': -20, 'a7': -7, 'a8': 8, 'a9': 73, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.650668502009225, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[2, [1, -2]], [5, [1]], [7, [1, 7]]], 'bad_primes': [2, 5, 7], 'central_character': '350.1', 'coefficient_field': '1.1.1.1', 'conductor': 350, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1, -2], [1, 10, 27], [1], [1, 7], [1, -9, 1331], [1, -52, 2197], [1, 96, 4913], [1, 10, 6859], [1, 75, 12167], [1, -189, 24389], [1, 232, 29791], [1, 305, 50653], [1, 438, 68921], [1, 353, 79507], [1, -486, 103823], [1, -354, 148877], [1, 672, 205379], [1, -206, 226981], [1, 599, 300763], [1, 471, 357911], [1, 614, 389017], [1, -743, 493039], [1, 996, 571787], [1, -180, 704969], [1, -184, 912673], [1, 726, 1030301], [1, -1798, 1092727], [1, 876, 1225043], [1, 691, 1295029], [1, -1521, 1442897]], 'euler_factors_factorization': [[[[1, -2], 1]], [[[1, 10, 27], 1]], [1], [[[1, 7], 1]], [[[1, -9, 1331], 1]], [[[1, -52, 2197], 1]], [[[1, 96, 4913], 1]], [[[1, 10, 6859], 1]], [[[1, 75, 12167], 1]], [[[1, -189, 24389], 1]], [[[1, 232, 29791], 1]], [[[1, 305, 50653], 1]], [[[1, 438, 68921], 1]], [[[1, 353, 79507], 1]], [[[1, -486, 103823], 1]], [[[1, -354, 148877], 1]], [[[1, 672, 205379], 1]], [[[1, -206, 226981], 1]], [[[1, 599, 300763], 1]], [[[1, 471, 357911], 1]], [[[1, 614, 389017], 1]], [[[1, -743, 493039], 1]], [[[1, 996, 571787], 1]], [[[1, -180, 704969], 1]], [[[1, -184, 912673], 1]], [[[1, 726, 1030301], 1]], [[[1, -1798, 1092727], 1]], [[[1, 876, 1225043], 1]], [[[1, 691, 1295029], 1]], [[[1, -1521, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-350-1.1-c3-0-16', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/350/4/a/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 10}, 'plot_values': [-1.1206289230835884e-60, 0.1734108247591596, 0.34512905550405415, 0.5134577812238518, 0.6766921304315, 0.8331169515769528, 0.981006422319565, 1.1186261266178221, 1.2442380543198155, 1.3561088782117785, 1.4525217514099522, 1.5317917467758853, 1.5922849328672102, 1.6324409508289581, 1.6507988264103204, 1.6460256235816326, 1.616947423480143, 1.5625819969714179, 1.4821724332668755, 1.3752208930841232, 1.241521575116681, 1.0811919214894707, 0.8947010438480262, 0.6828943291805412, 0.4470131857286066, 0.18870891653811486, -0.0899502368408956, -0.38647975389353356, -0.6979879572429145, -1.0211942124987625, -1.3524566475074822, -1.6878096313545015, -2.0230110269787946, -2.3535989832090563, -2.674957767095239, -2.9823918612870775, -3.271207270563851, -3.5367987039653306, -3.7747410325417587, -3.9808831762821875, -4.151442356341721, -4.283096469347056, -4.373072208132843, 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0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c3-0', 'trace_hash': 2243622169122549498, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60528617560292107877070250682', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.77438064467328486695311126220', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.72247714877411296824162848541', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 20.650668502009225, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 350, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 2, -10, 4, 0, -20, -7, 8, 73, 0, 9, -40, 52, -14, 0, 16, -96, 146, -10, 0, 70, 18, -75, -80, 0, 104, -460, -28, 189, 0, -232, 32, -90, -192, 0, 292, -305, -20, -520, 0, -438, 140, -353, 36, 0, -150, 486, -160, 49, 0, 960, 208, 354, -920, 0, -56, 100, 378, -672, 0, 206, -464, -511, 64, 0, -180, -599, -384, 750, 0, -471, 584, -614, -610, 0, -40, -63, -1040, 743, 0, 2629, -876, -996, 280, 0, -706, -1890, 72, 180, 0, -364, -300, 2320, 972, 0, -320, 184, 98, 657, 0], 'euler11': [1, -9, 1331], 'euler13': [1, -52, 2197], 'euler17': [1, 96, 4913], 'euler19': [1, 10, 6859], 'euler2': [1, -2, 0], 'euler23': [1, 75, 12167], 'euler29': [1, -189, 24389], 'euler3': [1, 10, 27], 'euler31': [1, 232, 29791], 'euler37': [1, 305, 50653], 'euler41': [1, 438, 68921], 'euler43': [1, 353, 79507], 'euler47': [1, -486, 103823], 'euler5': [1, 0, 0], 'euler53': [1, -354, 148877], 'euler59': [1, 672, 205379], 'euler61': [1, -206, 226981], 'euler67': [1, 599, 300763], 'euler7': [1, 7, 0], 'euler71': [1, 471, 357911], 'euler73': [1, 614, 389017], 'euler79': [1, -743, 493039], 'euler83': [1, 996, 571787], 'euler89': [1, -180, 704969], 'euler97': [1, -184, 912673], 'euler_factors': [[1, -2, 0], [1, 10, 27], [1, 0, 0], [1, 7, 0], [1, -9, 1331], [1, -52, 2197], [1, 96, 4913], [1, 10, 6859], [1, 75, 12167], [1, -189, 24389], [1, 232, 29791], [1, 305, 50653], [1, 438, 68921], [1, 353, 79507], [1, -486, 103823], [1, -354, 148877], [1, 672, 205379], [1, -206, 226981], [1, 599, 300763], [1, 471, 357911], [1, 614, 389017], [1, -743, 493039], [1, 996, 571787], [1, -180, 704969], [1, -184, 912673]], 'index': 16, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/350/4/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/350/4/a/k'], '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': '2-350-1.1-c3-0-16', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-350-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.544300661488985, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 2243622169122549498, 'z1': {'__RealLiteral__': 0, 'data': '1.60528617560292107877070250682', 'prec': 100}}
  • lfunc_instances • Show schema
    • id: 20716740
      {'Lhash': '2034941984041121770345114575817', 'Lhash_array': ['2034941984041121770345114575817'], 'factors': ['2-350-1.1-c3-0-16'], 'label': '2-350-1.1-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/350/4/a/k'}
    • id: 24557887
      {'Lhash': '2034941984041121770345114575817', 'Lhash_array': ['2034941984041121770345114575817'], 'factors': ['2-350-1.1-c3-0-16'], 'label': '2-350-1.1-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/350/4/a/k/1/1'}