Formats: - HTML - YAML - JSON - 2026-10-17T02:57:43.180902
  • lfunc_lfunctions • Show schema
    {'Lhash': '1461822927813976341297884128086', 'a10': -1060, 'a2': -10, 'a3': 0, 'a4': 68, 'a5': 106, 'a6': 0, 'a7': -49, 'a8': -360, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.104180648217781, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[3, [1]], [7, [1, 49]]], 'bad_primes': [3, 7], 'central_character': '63.1', 'coefficient_field': '1.1.1.1', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[1, 10, 32], [1], [1, -106, 3125], [1, 49], [1, 92, 161051], [1, -670, 371293], [1, -222, 1419857], [1, 908, 2476099], [1, -1176, 6436343], [1, 1118, 20511149], [1, -3696, 28629151], [1, -4182, 69343957], [1, -6662, 115856201], [1, 3700, 147008443], [1, -7056, 229345007], [1, -37578, 418195493], [1, 32700, 714924299], [1, 10802, 844596301], [1, -64996, 1350125107], [1, -61320, 1804229351], [1, -38922, 2073071593], [1, 88096, 3077056399], [1, 71892, 3939040643], [1, 111818, 5584059449], [1, 150846, 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17906, 18424351793], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-63-1.1-c5-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/63/6/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.0517725300905314, 1.0368694520895727, 0.992503002172443, 0.9197105871071808, 0.8202502262371263, 0.6966400099776127, 0.5522054279963335, 0.3911270999891777, 0.2184799353453366, 0.04025369458678585, -0.13665558906141598, -0.3044937661896419, -0.4547459524256827, -0.5782912445239485, -0.665620564584083, -0.707120323689112, -0.6934207469638959, -0.6158031969925647, -0.4666558267733799, -0.23996161180716954, 0.0682024506950083, 0.45918106789712343, 0.9313014807157105, 1.4795124205177452, 2.095135376898762, 2.765761421182387, 3.475323455348521, 4.204367727948579, 4.930539722438323, 5.629288225136829, 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'12.85788543879532501420650681768722', '13.92084141542177293929001006089522'], 'prelabel': '2-63-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'trace_hash': 381696492750188976, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15317495810816317271326362005', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.47502002723649242430446656244', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.84161629605689731879169257754', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 10.104180648217781, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'dirichlet_coefficients': [1, -10, 0, 68, 106, 0, -49, -360, 0, -1060, -92, 0, 670, 490, 0, 1424, 222, 0, -908, 7208, 0, 920, 1176, 0, 8111, -6700, 0, -3332, -1118, 0, 3696, -2720, 0, -2220, -5194, 0, 4182, 9080, 0, -38160, 6662, 0, -3700, -6256, 0, -11760, 7056, 0, 2401, -81110, 0, 45560, 37578, 0, -9752, 17640, 0, 11180, -32700, 0, -10802, -36960, 0, -18368, 71020, 0, 64996, 15096, 0, 51940, 61320, 0, 38922, -41820, 0, -61744, 4508, 0, -88096, 150944, 0, -66620, -71892, 0, 23532, 37000, 0, 33120, -111818, 0, -32830, 79968, 0, -70560, -96248, 0, -150846, -24010, 0, 551548], 'euler11': [1, 92, 161051], 'euler13': [1, -670, 371293], 'euler17': [1, -222, 1419857], 'euler19': [1, 908, 2476099], 'euler2': [1, 10, 32], 'euler23': [1, -1176, 6436343], 'euler29': [1, 1118, 20511149], 'euler3': [1, 0, 0], 'euler31': [1, -3696, 28629151], 'euler37': [1, -4182, 69343957], 'euler41': [1, -6662, 115856201], 'euler43': [1, 3700, 147008443], 'euler47': [1, -7056, 229345007], 'euler5': [1, -106, 3125], 'euler53': [1, -37578, 418195493], 'euler59': [1, 32700, 714924299], 'euler61': [1, 10802, 844596301], 'euler67': [1, -64996, 1350125107], 'euler7': [1, 49, 0], 'euler71': [1, -61320, 1804229351], 'euler73': [1, -38922, 2073071593], 'euler79': [1, 88096, 3077056399], 'euler83': [1, 71892, 3939040643], 'euler89': [1, 111818, 5584059449], 'euler97': [1, 150846, 8587340257], 'euler_factors': [[1, 10, 32], [1, 0, 0], [1, -106, 3125], [1, 49, 0], [1, 92, 161051], [1, -670, 371293], [1, -222, 1419857], [1, 908, 2476099], [1, -1176, 6436343], [1, 1118, 20511149], [1, -3696, 28629151], [1, -4182, 69343957], [1, -6662, 115856201], [1, 3700, 147008443], [1, -7056, 229345007], [1, -37578, 418195493], [1, 32700, 714924299], [1, 10802, 844596301], [1, -64996, 1350125107], [1, -61320, 1804229351], [1, -38922, 2073071593], [1, 88096, 3077056399], [1, 71892, 3939040643], [1, 111818, 5584059449], [1, 150846, 8587340257]], 'index': 4, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/6/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/63/6/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': '2-63-1.1-c5-0-4', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-63-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 381696492750188976, 'z1': {'__RealLiteral__': 0, 'data': '1.15317495810816317271326362005', 'prec': 100}}
  • lfunc_instances • Show schema
    • id: 11724204
      {'Lhash': '1461822927813976341297884128086', 'Lhash_array': ['1461822927813976341297884128086'], 'factors': ['2-63-1.1-c5-0-4'], 'label': '2-63-1.1-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/6/a/a'}
    • id: 24552432
      {'Lhash': '1461822927813976341297884128086', 'Lhash_array': ['1461822927813976341297884128086'], 'factors': ['2-63-1.1-c5-0-4'], 'label': '2-63-1.1-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/6/a/a/1/1'}