Formats: - HTML - YAML - JSON - 2026-07-17T15:45:12.738127
  • lfunc_lfunctions • Show schema
    {'Lhash': '1937180307551779547859725847591', 'a10': [0.0, 0.0], 'a2': [2.801937735804838, 0.0], 'a3': [0.0, 0.0], 'a4': [5.850855075327144, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [3.0489173395223053, 0.0], 'a8': [10.789856150674707, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.13604686409738, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 19], 'central_character': '4275.1', 'coefficient_field': 'CDF', 'conductor': 4275, 'conductor_radical': 285, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.801937735804838, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.0489173395223053, 0], [7.0, 0]], [[1.0, 0], [-2.939001075347563, 0], [11.0, 0]], [[1.0, 0], [3.246979603717467, 0], [13.0, 0]], [[1.0, 0], [2.158833603697048, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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[[1.0, 0], [-3.4353531888884374, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 123, 'label': '2-4275-1.1-c1-0-123', 'leading_term': '8.79258153233132416844416592614', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4275/2/a/bn/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [8.792581532331324, 8.784637547985719, 8.760573330470812, 8.719706530171175, 8.660947078678413, 8.582864702611655, 8.48377733419271, 8.361855169228074, 8.215234650623229, 8.042136668417392, 7.84098366023285, 7.610510933979233, 7.349868286003119, 7.058708747435929, 6.737261990994095, 6.386390538155665, 6.007627419861382, 5.603194379060795, 5.17600008612992, 4.729618195424238, 4.268245426214771, 3.796640220587236, 3.3200429235299582, 2.844078847901477, 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'5.21411183120775026603201071001908', '5.93872211806772234407242806608339', '6.85193740281325428701340985296990', '7.24455088512502562142293503430113', '8.071056668055668515910690334523216'], 'prelabel': '2-4275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.842606170545588, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52816581099161486566518054274', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14916219650401031413050451141', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16934635859923543380146947119', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 34.13604686409738, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 4275, 'conductor_radical': 285, 'degree': 2, 'index': 123, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4275/2/a/bn/1/3'], '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': '2-4275-1.1-c1-0-123', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.842606170545588, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52816581099161486566518054274', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '1937180307551779547859725847591', 'Lhash_array': ['1937180307551779547859725847591'], 'factors': ['2-4275-1.1-c1-0-123'], 'label': '2-4275-1.1-c1-0-123', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4275/2/a/bn/1/3'}