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lfunc_lfunctions • Show schema
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{'Lhash': '1672883169175213878757653230885', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.3472963553338606, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.1847925309040954, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.25339398085481, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '9800.1', 'coefficient_field': 'CDF', 'conductor': 9800, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.3472963553338606, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.4114741278097729, 0], [11.0, 0]], [[1.0, 0], [6.475651900285685, 0], [13.0, 0]], [[1.0, 0], [-2.5962666587138683, 0], [17.0, 0]], [[1.0, 0], [1.1625038244297654, 0], [19.0, 0]], [[1.0, 0], [-1.573977952239538, 0], [23.0, 0]], [[1.0, 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 163, 'label': '2-9800-1.1-c1-0-163', '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/9800/2/a/ch/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.3442685346317232e-60, 0.24998296044869225, 0.4982822460410704, 0.743167155511621, 0.9828170395343573, 1.2152862803662121, 1.4384803913075463, 1.650145675282472, 1.847873986201245, 2.029123210126185, 2.1912531985667876, 2.3315760959588916, 2.4474193373924074, 2.536199060842961, 2.5955012760294807, 2.623167847017622, 2.6173841628446386, 2.576765276347291, 2.500437276365951, 2.3881107172518745, 2.240143060605748, 2.0575872885246356, 1.8422241275879463, 1.5965756803366435, 1.3238986965025141, 1.0281562275781375, 0.7139669900728902, 0.3865324058877255, 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'6.77493235510581690083978697855231', '7.54478576410657432729527496943517'], 'prelabel': '2-9800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.846094843537164, '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': '1.31967213116455425342763077113', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52790453581539812220270093040', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.74031035322100761770630360057', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.25339398085481, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 9800, 'conductor_radical': 70, 'degree': 2, 'index': 163, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9800/2/a/ch/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': '2-9800-1.1-c1-0-163', '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': '2-9800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.846094843537164, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31967213116455425342763077113', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1672883169175213878757653230885', 'Lhash_array': ['1672883169175213878757653230885'], 'label': '2-9800-1.1-c1-0-163', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9800/2/a/ch/1/2'}