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lfunc_lfunctions • Show schema
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{'Lhash': '1688906320992151635658770612165', 'a10': [-1.2271344421706896, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.7728655578293103, 0.0], 'a4': [1.0, 0.0], 'a5': [1.2271344421706896, 0.0], 'a6': [-0.7728655578293103, 0.0], 'a7': [-3.402678829521189, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.402678829521189, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.715214849384736, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '4598.1', 'coefficient_field': 'CDF', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.7728655578293103, 0], [3.0, 0]], [[1.0, 0], [-1.2271344421706896, 0], [5.0, 0]], [[1.0, 0], [3.402678829521189, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.402678829521189, 0], [13.0, 0]], [[1.0, 0], [-4.805357659042378, 0], [17.0, 0]], 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[[1.0, 0], [19.961804092785755, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 107, 'label': '2-4598-1.1-c1-0-107', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4598/2/a/bm/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-5.226360487266193e-61, 0.1422220256144995, 0.2836794045697567, 0.42357764415553584, 0.5610646231945321, 0.6952067927452013, 0.8249710096816711, 0.94921329064474, 1.066675359614924, 1.17598943651534, 1.2756913105645127, 1.3642413838473402, 1.4400530696406788, 1.5015276883993172, 1.5470948169732646, 1.5752569049009364, 1.58463686603894, 1.5740272761808878, 1.5424397519747393, 1.4891530504786044, 1.4137584118154622, 1.3162006713770837, 1.1968136960369018, 1.0563487546790777, 0.8959945208855383, 0.7173875281879464, 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'6.52229166538242133939419240546711', '7.44487620750161314651211900116108', '7.903108339144659327807809891535896'], 'prelabel': '2-4598-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33231216921135747237676385657', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48093162165497453002001686116', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19047303599234683116520019577', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.715214849384736, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'index': 107, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4598/2/a/bm/1/2'], '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': '2-4598-1.1-c1-0-107', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4598-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33231216921135747237676385657', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1688906320992151635658770612165', 'Lhash_array': ['1688906320992151635658770612165'], 'label': '2-4598-1.1-c1-0-107', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4598/2/a/bm/1/2'}