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lfunc_lfunctions • Show schema
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{'Lhash': '552823364299395643084893345618', 'a10': [0.2079883512862957, 0.36024639181034784], 'a2': [-0.7032515340964575, 1.218067387555821], 'a3': [0, 0], 'a4': [0.010874559581958296, 0.01883528970588674], 'a5': [0.14787621583614505, -0.25612911905922464], 'a6': [0, 0], 'a7': [-1.4340325896458084, -2.223409663519914], 'a8': [-2.8435963392203716, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.558093121947266, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.4340325896458084, 2.223409663519914]]], [19, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [3, 7, 19], 'central_character': '1197.856', 'coefficient_field': 'CDF', 'conductor': 1197, 'conductor_radical': 399, 'conjugate': '1761304008142576676530065872878', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7032515340964575, -1.218067387555821], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'6.13339913883133018894914330936064', '6.69412171885468812121411052678259', '8.102045113268348745009792462309384', '8.844237583519477008115139857408340', '9.463790651661858693587499112866758'], 'prelabel': '2-1197-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.091616587151011, 'root_angle': -0.8691774156125377, 'root_number': '-0.9167252428098102428466695072419960154580370163375355537 - 0.3995182463859372388963132266715411935602507142218544837*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.43458870780626885', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43610073958854642777460111858', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.00158559117847632147920170559', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.79192119173243052097677756663', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.558093121947266, 'bad_primes': [3, 7, 19], 'central_character': '7.2', 'conductor': 1197, 'conductor_radical': 399, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1197/2/j/l/856/2'], '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': '2-1197-7.2-c1-0-8', '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': '2-1197-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.091616587151011, 'root_angle': -0.43458870780626885, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.43610073958854642777460111858', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '552823364299395643084893345618', 'Lhash_array': ['552823364299395643084893345618'], 'label': '2-1197-7.2-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1197/2/j/l/856/2'}