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              lfunc_lfunctions •   Show schema
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{'Lhash': '1935979548813196592383620842985', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-1.7320508075688772, -1.0], 'a6': [0.0, 0.0], 'a7': [1.7320508075688772, -1.0], 'a8': [0.0, 0.0], 'a9': [1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.736998814595924, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.5, -0.8660254037844386]]], [13, [[1.0, 0], [3.232050807568877, -1.598076211353316]]]], 'bad_primes': [2, 3, 13], 'central_character': '468.337', 'coefficient_field': 'CDF', 'conductor': 468, 'conductor_radical': 78, 'conjugate': '1831524661408084525055692121118', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, -0.8660254037844386]], [[1.0, 0], [1.7320508075688772, 1.0], [2.5, 4.330127018922194]], [[1.0, 0], [-1.7320508075688772, 1.0], [3.5, -6.06217782649107]], [[1.0, 0], 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[3.4641016151377544, -2.0], [41.5, -71.88010851410841]], [[1.0, 0], [0, 6.0], [-89.0, 0]], [[1.0, 0], [10.392304845413264, -6.0], [48.5, -84.00446416709055]], [[1.0, 0], [3.5, 6.06217782649107], [-50.5, 87.4685657822283]], [[1.0, 0], [4.0, -6.928203230275509], [-51.5, -89.20061658979718]], [[1.0, 0], [11.0, 0], [107.0, 0]], [[1.0, 0], [0, -14.0], [-109.0, 0]], [[1.0, 0], [0.5, -0.8660254037844386], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-468-117.103-c1-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/468/2/bl/a/337/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.875495918101742, 1.8731141539579337, 1.8657816699450438, 1.8481278036730513, 1.812162953630145, 1.7486311373721422, 1.648423483998133, 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-1.364489193013935, -0.6961982989476505, 0.22698545061521339, 1.1037636947094913, 1.6225726554511017, 1.5753875584905264], 'positive_zeros': ['1.52721857936614427513404751412624', '2.95447991201873568136585590776262', '3.96893338787545051340815679694164', '5.20099525034466483901487050207867', '6.86037241358473885413147670240011', '7.32417629933033040134513029309701', '8.172263018858299848971878812172766', '9.236314687196555139135523584515064', '9.820132662788391203602865725291733', '11.33443772168481727898807806010474'], 'prelabel': '2-468-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9331318668409363, 'root_angle': -0.017527590205611704, 'root_number': '0.9939419175972846 - 0.10990661692106055*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0175275902056', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52721857936614427513404751413', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95447991201873568136585590776', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.96893338787545051340815679694', 'prec': 103}}
           
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              lfunc_search •   Show schema
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{'algebraic': True, 'analytic_conductor': 3.736998814595924, 'bad_primes': [2, 3, 13], 'central_character': '117.103', 'conductor': 468, 'conductor_radical': 78, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/468/2/bl/a/337/1'], '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': '2-468-117.103-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': '2-468-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9331318668409363, 'root_angle': -0.017527590205611704, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52721857936614427513404751413', 'prec': 103}}
           
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              lfunc_instances •   Show schema
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{'Lhash': '1935979548813196592383620842985', 'Lhash_array': ['1935979548813196592383620842985'], 'factors': ['2-468-117.103-c1-0-8'], 'label': '2-468-117.103-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/468/2/bl/a/337/1'}