Formats: - HTML - YAML - JSON - 2026-10-15T19:52:54.434013
  • lfunc_lfunctions • Show schema
    {'Lhash': '475242904398343235967502575290', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-8.0, -13.856406460551018], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-35.5, 61.48780366869514], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.372967009791394, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '81.26', 'coefficient_field': 'CDF', 'conductor': 81, 'conductor_radical': 3, 'conjugate': '2472030743168803970958176731826', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [8.0, 13.856406460551018]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [312.5, -541.2658773652742]], [[1.0, 0], [35.5, -61.48780366869514], [-1200.5, -2079.3269944864373]], [[1.0, 0], [0, 0], [7320.5, 12679.477936807967]], [[1.0, 0], [-168.5, -291.8505610753558], [-14280.5, 24734.551557487353]], [[1.0, 0], [0, 0], [-83521.0, 0]], [[1.0, 0], 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'3.22892814327337813813069071861858', '4.30829255519721293153534732726370', '6.25103316880298593900780465613450', '7.64669056413070979617927312833997', '8.563035203194021190923595709795904', '10.05100088573048370879608789769347', '10.93720707151669629777714345889475', '12.64983328405788794463869124049121', '13.09516018904253517801615138367255'], 'prelabel': '2-3e4-9.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8936079571689377, 'root_angle': -0.3055555555555556, 'root_number': '-0.3420201433256687 - 0.9396926207859084*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.305555555556', 'prec': 40}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37490054776353981793614398891', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '3.22892814327337813813069071862', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.30829255519721293153534732726', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 8.372967009791394, 'bad_primes': [3], 'central_character': '9.2', 'conductor': 81, 'conductor_radical': 3, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/81/5/d/a/26/1'], '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': '2-3e4-9.2-c4-0-1', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-3e4-9.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8936079571689377, 'root_angle': -0.3055555555555556, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37490054776353981793614398891', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '475242904398343235967502575290', 'Lhash_array': ['475242904398343235967502575290'], 'factors': ['2-3e4-9.2-c4-0-1'], 'label': '2-3e4-9.2-c4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/81/5/d/a/26/1'}