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lfunc_lfunctions • Show schema
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{'Lhash': '850802910796178362261172148126', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [3.414213562373095, 0], 'a6': [0, 0], 'a7': [0, 4.82842712474619], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.397532625703008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '2304.1151', 'coefficient_field': 'CDF', 'conductor': 2304, 'conductor_radical': 6, 'conjugate': '2275396899791597536338649414349', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.414213562373095, 0], [5.0, 0]], [[1.0, 0], [0, -4.82842712474619], [-7.0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-11.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-13.0, 0]], [[1.0, 0], [0, -5.414213562373095], [-17.0, 0]], [[1.0, 0], [5.656854249492381, 0], [19.0, 0]], [[1.0, 0], [-1.17157287525381, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-48e2-24.11-c1-0-11', 'leading_term': '2.089545528407932304170373075997548549603110653231584831', '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/2304/2/f/h/1151/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.0895455284079323, 1.956148594556088, 1.8182718778350375, 1.6759051515603876, 1.5290070447596849, 1.377551503432029, 1.221574592593074, 1.0612191940906592, 0.8967754364513176, 0.7287150801253311, 0.5577185125528916, 0.384693429748202, 0.21078465851942715, 0.03737488841597415, -0.13392366668018482, -0.3012864614731977, -0.4627022949715063, -0.6160069656051947, -0.7589242809812063, -0.8891136763539224, -1.0042235690515517, -1.1019494417478153, -1.1800955071809573, -1.236638664915224, 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'5.75342954271676378654892243712744', '6.54326021304858408639042391063949', '7.04456878691551356019486277993533', '7.985181640840948455460246837400737', '8.989381313536108481470657863133130'], 'prelabel': '2-48e2-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.289234503463644, 'root_angle': -0.2770433619923482, 'root_number': '-0.1691019787257627481429347680509755569866105044940151880 - 0.98559855965348878087536279295293935430859299804623856409*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2770433619923482', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67116515437534502075938333588', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77452068044452813381761043006', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.85406355455886356601623612481', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.397532625703008, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 2304, 'conductor_radical': 6, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2304/2/f/h/1151/4'], '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': '2-48e2-24.11-c1-0-11', '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': '2-48e2-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.289234503463644, 'root_angle': -0.2770433619923482, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67116515437534502075938333588', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '850802910796178362261172148126', 'Lhash_array': ['850802910796178362261172148126'], 'factors': ['2-48e2-24.11-c1-0-11'], 'label': '2-48e2-24.11-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2304/2/f/h/1151/4'}