Formats: - HTML - YAML - JSON - 2026-10-07T04:23:56.818526
  • lfunc_lfunctions • Show schema
    {'Lhash': '4351824909135875668251164835941', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.6742346141747673, -3.6742346141747673], 'a4': [0.0, -8.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-22.045407685048602, 22.045407685048602], 'a8': [0.0, 0.0], 'a9': [0.0, 27.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.425143250430549, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [3.6742346141747673, 3.6742346141747673]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.68', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '256246155827049506955343735289', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0, 8.0]], [[1.0, 0], [3.6742346141747673, 3.6742346141747673]], [[1.0, 0], [0, 0]], [[1.0, 0], [22.045407685048602, -22.045407685048602], [0, -343.0]], [[1.0, 0], [0, 0], [-1331.0, 0]], [[1.0, 0], [44.090815370097204, 44.090815370097204], [0, 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'12.40352596783328870155377848015302', '13.32362418330353420168064206826736', '14.66782358913820903356832962147871'], 'prelabel': '2-75-15.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.103602445908102, 'root_angle': -0.4631040955873917, 'root_number': '-0.9732489894677301 - 0.22975292054736132*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.463104095587', 'prec': 40}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.43298453718427432762794515768', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.47692402468959738687048463562', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.45187164590044599683944045112', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.425143250430549, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/4/e/a/68/1'], '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': '2-75-15.8-c3-0-15', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-75-15.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.103602445908102, 'root_angle': -0.4631040955873917, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.43298453718427432762794515768', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '4351824909135875668251164835941', 'Lhash_array': ['4351824909135875668251164835941'], 'factors': ['2-75-15.8-c3-0-15'], 'label': '2-75-15.8-c3-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/4/e/a/68/1'}