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lfunc_lfunctions • Show schema
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{'Lhash': '1571956728852612855439576384295', 'a10': [0.0, 0.0], 'a2': [0.8664770015879799, 0.0], 'a3': [-1.0, 0.0], 'a4': [-1.2492176057191038, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.8664770015879799, 0.0], 'a7': [1.0, 0.0], 'a8': [-2.8153723285103642, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.113607167289445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '5775.1', 'coefficient_field': 'CDF', 'conductor': 5775, 'conductor_radical': 1155, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8664770015879799, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.7485173258344242, 0], [13.0, 0]], [[1.0, 0], [3.424756559580078, 0], [17.0, 0]], [[1.0, 0], [-3.7563924906335866, 0], [19.0, 0]], 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[109.0, 0]], [[1.0, 0], [-13.969604269990432, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 139, 'label': '2-5775-1.1-c1-0-139', '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/5775/2/a/ch/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.152230172541477e-60, 0.1813177175603796, 0.36144257059297646, 0.5391424910390193, 0.7131098767410019, 0.8819308058142489, 1.0440620915668903, 1.1978179674077907, 1.341367611249634, 1.4727441211543908, 1.5898649853581779, 1.6905635830538903, 1.772630824519738, 1.8338656938891953, 1.8721331889600363, 1.8854279486989503, 1.8719417080983534, 1.830132611026539, 1.7587943371614703, 1.6571229552194768, 1.5247794011232367, 1.3619454988157542, 1.1693714971567355, 0.9484131935231981, 0.7010568580387536, 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'5.68770690409701384332266189961380', '5.96246897833982684376940443567449', '6.95838314914667821949286152285567', '7.67756670129572675974435599365964'], 'prelabel': '2-5775-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.790700049868898, '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': '1.24005520809093278342952943414', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40679845891748102556810126978', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60596589898224222069121009607', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 46.113607167289445, 'bad_primes': [3, 5, 7, 11], 'central_character': '1.1', 'conductor': 5775, 'conductor_radical': 1155, 'degree': 2, 'index': 139, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5775/2/a/ch/1/4'], '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': '2-5775-1.1-c1-0-139', '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': '2-5775-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.790700049868898, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24005520809093278342952943414', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1571956728852612855439576384295', 'Lhash_array': ['1571956728852612855439576384295'], 'label': '2-5775-1.1-c1-0-139', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5775/2/a/ch/1/4'}