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lfunc_lfunctions • Show schema
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{'Lhash': '2026226983818945795029293100656', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5, 0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8863394624362123, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [37, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 37], 'central_character': '1776.1025', 'coefficient_field': 'CDF', 'conductor': 1776, 'conductor_radical': 222, 'conjugate': '1260631853333910893763589683559', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, 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[-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-1776-111.26-c0-0-0', 'leading_term': '1.26748189003607095038117332316', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1776/1/bw/a/1025/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.267481890036071, 1.3174112076804427, 1.380220598939679, 1.4556574917607108, 1.5423773958342077, 1.6381625059485527, 1.7401705309244568, 1.845155778669057, 1.9496385575695765, 2.050024720791596, 2.1426890030303527, 2.224037452431923, 2.290561189868145, 2.338889565810786, 2.365847145681797, 2.368516246972936, 2.344304883226527, 2.291018723606296, 2.206934856818945, 2.090874617097392, 1.9422724030562653, 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'5.56949854893600664994369288042449', '6.36920046172565192977629468871961', '7.49246560253283693970212461781316', '8.010529295559822910899513070243025', '9.042186843722134281448232793419594', '9.677853962000689571077258512863502'], 'prelabel': '2-1776-111.26-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9414560331933788, 'root_angle': 0.38015740008528104, 'root_number': '0.36766474535682618144342076991055 + 0.92995840499546008504176937183236*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.19007870004264055', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59841125263865401988053918924', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.05718088586235969492704925960', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80568205553149369716010253161', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8863394624362123, 'bad_primes': [2, 3, 37], 'central_character': '111.26', 'conductor': 1776, 'conductor_radical': 222, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1776/1/bw/a/1025/1', 'ArtinRepresentation/2.1776.12t18.b.a'], 'is_instance_Artin': True, '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': '2-1776-111.26-c0-0-0', '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': '2-1776-111.26-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9414560331933788, 'root_angle': 0.19007870004264052, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59841125263865401988053918924', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24605226
{'Lhash': '2026226983818945795029293100656', 'Lhash_array': ['2026226983818945795029293100656'], 'label': '2-1776-111.26-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1776.12t18.b.a'}
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id: 19813417
{'Lhash': '2026226983818945795029293100656', 'Lhash_array': ['2026226983818945795029293100656'], 'label': '2-1776-111.26-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1776/1/bw/a/1025/1'}