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lfunc_lfunctions • Show schema
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{'Lhash': '2879055306920790988286508371250', 'a10': [-0.47139673682599764, 0.881921264348355], 'a2': [0.881921264348355, -0.47139673682599764], 'a3': [0.0, 0.0], 'a4': [0.5555702330196022, -0.8314696123025452], 'a5': [-0.8314696123025452, 0.5555702330196022], 'a6': [0.0, 0.0], 'a7': [0.18111205957153528, 0.07501907138385383], 'a8': [0.0980171403295606, -0.9951847266721969], 'a9': [-0.9238795325112867, 0.3826834323650898], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7567088444681684, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.881921264348355, 0.47139673682599764]]], [5, [[1.0, 0], [0.8314696123025452, -0.5555702330196022]]], [11, [[1.0, 0], [0.9807852804032304, 0.19509032201612828]]]], 'bad_primes': [2, 5, 11], 'central_character': '3520.1429', 'coefficient_field': 'CDF', 'conductor': 3520, 'conductor_radical': 110, 'conjugate': '59200067993345769249204245898', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'5.12686713822187074590277464067425', '6.16678844136835223998087607448600', '7.00714467231458309658237548815523', '7.65331361426746790153822808927852', '8.122498559885652489585900344490433', '9.113032113042677103171640466872339'], 'prelabel': '2-3520-3520.1429-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3254089348077327, 'root_angle': -0.42187500000000006, 'root_number': '-0.88192126434835502971275686366042 - 0.47139673682599764855638762590521*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.421875', 'prec': 30}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27117417559889315359832171227', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.85591340416006339272439922765', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05349328202939786499044983193', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7567088444681684, 'bad_primes': [2, 5, 11], 'central_character': '3520.1429', 'conductor': 3520, 'conductor_radical': 110, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3520/1/db/a/1429/4'], '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': '2-3520-3520.1429-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3520-3520.1429-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3254089348077327, 'root_angle': -0.42187500000000006, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.27117417559889315359832171227', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2879055306920790988286508371250', 'Lhash_array': ['2879055306920790988286508371250'], 'factors': ['2-3520-3520.1429-c0-0-3'], 'label': '2-3520-3520.1429-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3520/1/db/a/1429/4'}