Formats: - HTML - YAML - JSON - 2026-10-23T19:56:06.597399
  • lfunc_lfunctions • Show schema
    {'Lhash': '1151166544954120888794667269835', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [3.695518130045147, 0], 'a6': [0, 0], 'a7': [0, 3.414213562373095], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.795065251406015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '4608.2303', 'coefficient_field': 'CDF', 'conductor': 4608, 'conductor_radical': 6, 'conjugate': '1588584542674111237592541246272', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.695518130045147, 0], [5.0, 0]], [[1.0, 0], [0, -3.414213562373095], [-7.0, 0]], [[1.0, 0], [0, -2.164784400584788], [-11.0, 0]], [[1.0, 0], [0, -2.164784400584788], [-13.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-17.0, 0]], [[1.0, 0], [-7.391036260090294, 0], [19.0, 0]], [[1.0, 0], [-4.82842712474619, 0], 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-9.414213562373096], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 37, 'label': '2-4608-24.11-c1-0-37', 'leading_term': '2.976616938283830053941799256543850682699779595650938894', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4608/2/f/o/2303/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [2.97661693828383, 2.882743707591841, 2.7767987441462942, 2.6590845831760337, 2.5298468377337735, 2.389330038577574, 2.2378392523989294, 2.075803355385182, 1.9038359331533665, 1.7227901351665547, 1.5338043479145127, 1.3383361806792393, 1.1381829090857407, 0.9354871458696901, 0.7327270798880964, 0.5326911371714109, 0.3384373782749497, 0.1532383668086898, -0.019487362207119805, -0.17625572874667841, -0.3136075589519513, -0.428206839446616, -0.5169442203873172, -0.5770429090803744, -0.6061638344112774, 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'5.95500271343394620203013285077767', '6.72960402869696341035305753822716', '7.42150671772310507678500096702571', '8.145708985645595883114418101553754'], 'prelabel': '2-4608-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': -0.1520433619923482, 'root_number': '0.57735026918962576450914878050195745564760175127012687602 - 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1520433619923482', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.908110282712652384243857631432', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.54428046636117024254612366167', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.87697194798294363656192014435', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 36.795065251406015, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 4608, 'conductor_radical': 6, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4608/2/f/o/2303/8'], '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': '2-4608-24.11-c1-0-37', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4608-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': -0.1520433619923482, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.908110282712652384243857631432', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1151166544954120888794667269835', 'Lhash_array': ['1151166544954120888794667269835'], 'factors': ['2-4608-24.11-c1-0-37'], 'label': '2-4608-24.11-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4608/2/f/o/2303/8'}