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lfunc_lfunctions • Show schema
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{'Lhash': '263645476987643333538263393510', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-1.0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.847069993022323, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [4.0, -1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.577', 'coefficient_field': 'CDF', 'conductor': 2736, 'conductor_radical': 114, 'conjugate': '1695935588929175814527415737608', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [1.0, 0], [7.0, 0]], [[1.0, 0], [2.0, 0], [11.0, 0]], [[1.0, 0], [-1.5, 2.598076211353316], [-6.5, -11.258330249197702]], [[1.0, 0], [-2.0, -3.4641016151377544], [-8.5, 14.722431864335457]], [[1.0, 0], [4.0, -1.7320508075688772]], [[1.0, 0], [2.0, 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-0.2267611876103548, 0.08363034537992459, 0.31512297480732004], 'positive_zeros': ['0.20797960963389775676988670255760', '1.74217892660147439893482688744659', '2.80731273971856373700670131271468', '3.66021506325547834898682859232485', '4.70758701232997568595353666593660', '5.33513026917926569138637212402706', '6.50234408314565223826133130662439', '6.80695692885730810265991100203375', '7.896486269005897439567859813887355', '8.518480271794223725325165149377627'], 'prelabel': '2-2736-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.67408493643647, 'root_angle': -0.7289868477508928, 'root_number': '-0.658920982234909900009603157735776939856542578169789281 - 0.752212163668324065976623431348872021420779767069214576*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3644934238754464', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.20797960963389775676988670256', 'prec': 103}, 'z2': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.847069993022323, 'bad_primes': [2, 3, 19], 'central_character': '19.7', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/s/k/577/1'], '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': '2-2736-19.7-c1-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2736-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.67408493643647, 'root_angle': -0.3644934238754464, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.20797960963389775676988670256', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '263645476987643333538263393510', 'Lhash_array': ['263645476987643333538263393510'], 'label': '2-2736-19.7-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/s/k/577/1'}