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  • lfunc_lfunctions • Show schema
    {'Lhash': '1640815387606213519485404562817', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 1.0], 'a4': [0, 0], 'a5': [0, 0.585786437626905], 'a6': [0, 0], 'a7': [3.414213562373095, 0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.265021750468673, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3], 'central_character': '1536.769', 'coefficient_field': 'CDF', 'conductor': 1536, 'conductor_radical': 6, 'conjugate': '1179625341246983702663678005544', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -0.585786437626905], [-5.0, 0]], [[1.0, 0], [-3.414213562373095, 0], [7.0, 0]], [[1.0, 0], [0, 2.0], [-11.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-13.0, 0]], [[1.0, 0], [-3.65685424949238, 0], [17.0, 0]], [[1.0, 0], [0, 5.656854249492381], [-19.0, 0]], [[1.0, 0], [-1.17157287525381, 0], [23.0, 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'group': 'GL2', 'index': 21, 'label': '2-1536-8.5-c1-0-21', 'leading_term': '1.9987216559221413285708759098647322568667208134655194874', '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/1536/2/d/f/769/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [1.9987216559221412, 2.0183951900022326, 2.029070491725199, 2.03061071919345, 2.022653968093647, 2.004654176297507, 1.9759361112145994, 1.935760600557583, 1.8833959413255237, 1.8181915895503045, 1.7396506581577134, 1.647498287209899, 1.5417434831513688, 1.4227324802307098, 1.2911920318201238, 1.1482612998810071, 0.9955112053050149, 0.8349502657029434, 0.6690161143897971, 0.5005520923262551, 0.33276855258656707, 0.16918882475593106, 0.013580156777185484, -0.1301296203990143, -0.25794848467250214, -0.36592794243128446, -0.450279824898622, -0.5074993946277674, 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'7.961084945334124835116899710559021', '8.392706219590013956582903458296784', '9.428507348460495500270621796175967'], 'prelabel': '2-1536-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5021453068752977, 'root_angle': 0.0, 'root_number': '1', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29437511196760295176668582230', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.98320913006221134631679663812', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.42297991747308763712519065650', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 12.265021750468673, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 1536, 'conductor_radical': 6, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1536/2/d/f/769/3'], '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': '2-1536-8.5-c1-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1536-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5021453068752977, 'root_angle': 0.0, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29437511196760295176668582230', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1640815387606213519485404562817', 'Lhash_array': ['1640815387606213519485404562817'], 'factors': ['2-1536-8.5-c1-0-21'], 'label': '2-1536-8.5-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1536/2/d/f/769/3'}