Formats: - HTML - YAML - JSON - 2026-09-07T14:44:08.618051
  • lfunc_lfunctions • Show schema
    {'Lhash': '1739842512930945106320975053213', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-2.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.0, 1.7320508075688772], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.0, -1.7320508075688772]]]], 'bad_primes': [3, 7], 'central_character': '567.352', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '778917492723496534704877664715', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [2.0, -1.7320508075688772]], [[1.0, 0], [0, 0], [-5.5, -9.526279441628825]], [[1.0, 0], [-3.5, 6.06217782649107], [-6.5, -11.258330249197702]], [[1.0, 0], [0, 0], [-8.5, 14.722431864335457]], [[1.0, 0], [-3.5, 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'5.31698835194822299066323289089436', '6.36666313955292461004663780361381', '7.32098244514331785876673549569018', '8.400476829571526562684828868595067', '9.299169858018905773334290988006947', '9.793425632807019798259112527875153', '10.82759041890091521834681882238794'], 'prelabel': '2-567-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.18187631611433, 'root_number': '0.41508272533181745 + 0.9097836727107774*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.181876316114', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37249373969270529399263248093', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.51969146954012380067435747340', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.05001089569354521390274323715', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '63.58', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/h/c/352/1'], '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': '2-567-63.58-c1-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-567-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.18187631611433, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37249373969270529399263248093', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1739842512930945106320975053213', 'Lhash_array': ['1739842512930945106320975053213'], 'factors': ['2-567-63.58-c1-0-14'], 'label': '2-567-63.58-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/h/c/352/1'}