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  • lfunc_lfunctions • Show schema
    {'Lhash': '829210899120496311693715975987', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.532088886237956, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.4402847137056, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '9072.1', 'coefficient_field': 'CDF', 'conductor': 9072, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.532088886237956, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.2266815969056775, 0], [11.0, 0]], [[1.0, 0], [-2.064177772475912, 0], [13.0, 0]], [[1.0, 0], [0.8152074690959046, 0], [17.0, 0]], [[1.0, 0], [-7.9435630140477285, 0], [19.0, 0]], [[1.0, 0], [-6.800659549145216, 0], [23.0, 0]], [[1.0, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 32, 'label': '2-9072-1.1-c1-0-32', 'leading_term': '1.76016144451614983125982796325', '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/9072/2/a/cc/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 17}, 'plot_values': [1.7601614445161498, 1.7504517657575036, 1.7213307818505863, 1.6728292651366394, 1.6050200755608428, 1.5180488908592593, 1.412174123331627, 1.2878132476149948, 1.145592383533577, 0.9863958206668602, 0.8114122161675398, 0.6221744083736056, 0.4205901235478688, 0.20896127114152224, -0.010010009149642113, -0.23322989186521453, -0.4572368416229006, -0.678241355047846, -0.8921813009529422, -1.094792193236277, -1.2816912406757932, -1.4484735391213697, -1.5908183111065448, -1.704602664822341, -1.7860199502797331, -1.8316994487359022, -1.8388238565792177, 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'6.42428192542730361503269565275724', '7.14714694552327799355863953810611', '7.61560058896578302344334582407084'], 'prelabel': '2-9072-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.51118585825181, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65413206049932382237357048379', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.65389287250209917126837319312', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.89644965119238528042385376950', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 72.4402847137056, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 9072, 'conductor_radical': 42, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9072/2/a/cc/1/1'], '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': '2-9072-1.1-c1-0-32', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-9072-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.51118585825181, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.65413206049932382237357048379', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '829210899120496311693715975987', 'Lhash_array': ['829210899120496311693715975987'], 'factors': ['2-9072-1.1-c1-0-32'], 'label': '2-9072-1.1-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9072/2/a/cc/1/1'}