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lfunc_lfunctions • Show schema
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{'Lhash': '1310486532194673115721147345824', 'a10': [-0.26396702621611057, -0.4572043009291693], 'a2': [0.7719126066729565, -1.3369918537604915], 'a3': [0.6765974292268752, 1.1719011236914354], 'a4': [-0.19169814468127674, -0.33203092630466086], 'a5': [0.17098245574317195, -0.2961503005500708], 'a6': [2.0890963410509538, 0], 'a7': [-2.127492086627233, 1.5728246632535055], 'a8': [2.49575356847065, 0], 'a9': [0.5844318375271673, -1.012265636157893], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.446302559117473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [2.127492086627233, -1.5728246632535055]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 13], 'central_character': '1183.170', 'coefficient_field': 'CDF', 'conductor': 1183, 'conductor_radical': 91, 'conjugate': '2024810445070386917859853669276', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7719126066729565, 1.3369918537604915], [-1.0, -1.7320508075688772]], 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'5.92664623954124693258424846890654', '6.48999046036599238356059852520162', '6.94253893753944969367753670037296', '7.992981082404571020247883673974348', '8.543545992208413454818180464186511', '9.653777688393346418728667641054857'], 'prelabel': '2-1183-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0734837821464867, 'root_angle': -0.05614512126881691, 'root_number': '0.98448443711087041900987601568004184116388074775263267339 - 0.17547191537819556983489947001687384787149130725094539759*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.028072560634408456', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03379159206703446469505407928', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47034136213785697286793608086', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77364988460970174985325342839', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.446302559117473, 'bad_primes': [7, 13], 'central_character': '7.2', 'conductor': 1183, 'conductor_radical': 91, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1183/2/e/k/170/18'], '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': '2-1183-7.2-c1-0-41', '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': '2-1183-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0734837821464867, 'root_angle': -0.028072560634408456, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03379159206703446469505407928', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1310486532194673115721147345824', 'Lhash_array': ['1310486532194673115721147345824'], 'label': '2-1183-7.2-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1183/2/e/k/170/18'}