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'8-96e8-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.578469006927287, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 2038128857073119005, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.22855338159461432523021291804', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.71552529136574057574932915843', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.811667604645753709043682570700', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29327719.396729242, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 7213895789838336, 'conductor_radical': 6, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -4, 0, 246, 0, -484, 0, 14641], 'euler13': [1, 0, 48, 0, 914, 0, 8112, 0, 28561], 'euler17': [1, 0, 20, 0, 678, 0, 5780, 0, 83521], 'euler19': [1, -24, 292, -2232, 11670, -42408, 105412, -164616, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -4, 0, 1062, 0, -2116, 0, 279841], 'euler29': [1, 0, 92, 0, 3798, 0, 77372, 0, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, 120, 0, 5522, 0, 115320, 0, 923521], 'euler37': [1, 0, -48, 0, 3314, 0, -65712, 0, 1874161], 'euler41': [1, 0, 116, 0, 6726, 0, 194996, 0, 2825761], 'euler43': [1, -24, 388, -3960, 30966, -170280, 717412, -1908168, 3418801], 'euler47': [1, 0, 92, 0, 6534, 0, 203228, 0, 4879681], 'euler5': [1, 0, -4, 0, 54, 0, -100, 0, 625], 'euler53': [1, 0, 188, 0, 14454, 0, 528092, 0, 7890481], 'euler59': [1, 0, 44, 0, 7446, 0, 153164, 0, 12117361], 'euler61': [1, 0, 144, 0, 12626, 0, 535824, 0, 13845841], 'euler67': [1, 32, 652, 8480, 82486, 568160, 2926828, 9624416, 20151121], 'euler7': [1, 0, 24, 0, 242, 0, 1176, 0, 2401], 'euler71': [1, 0, -100, 0, 12582, 0, -504100, 0, 25411681], 'euler73': [1, 48, 1156, 17424, 178854, 1271952, 6160324, 18672816, 28398241], 'euler79': [1, 0, -168, 0, 19538, 0, -1048488, 0, 38950081], 'euler83': [1, 0, -100, 0, 16278, 0, -688900, 0, 47458321], 'euler89': [1, 0, 164, 0, 22566, 0, 1299044, 0, 62742241], 'euler97': [1, 0, 388, 0, 56454, 0, 3650692, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -4, 0, 54, 0, -100, 0, 625], [1, 0, 24, 0, 242, 0, 1176, 0, 2401], [1, 0, -4, 0, 246, 0, -484, 0, 14641], [1, 0, 48, 0, 914, 0, 8112, 0, 28561], [1, 0, 20, 0, 678, 0, 5780, 0, 83521], [1, -24, 292, -2232, 11670, -42408, 105412, -164616, 130321], [1, 0, -4, 0, 1062, 0, -2116, 0, 279841], [1, 0, 92, 0, 3798, 0, 77372, 0, 707281], [1, 0, 120, 0, 5522, 0, 115320, 0, 923521], [1, 0, -48, 0, 3314, 0, -65712, 0, 1874161], [1, 0, 116, 0, 6726, 0, 194996, 0, 2825761], [1, -24, 388, -3960, 30966, -170280, 717412, -1908168, 3418801], [1, 0, 92, 0, 6534, 0, 203228, 0, 4879681], [1, 0, 188, 0, 14454, 0, 528092, 0, 7890481], [1, 0, 44, 0, 7446, 0, 153164, 0, 12117361], [1, 0, 144, 0, 12626, 0, 535824, 0, 13845841], [1, 32, 652, 8480, 82486, 568160, 2926828, 9624416, 20151121], [1, 0, -100, 0, 12582, 0, -504100, 0, 25411681], [1, 48, 1156, 17424, 178854, 1271952, 6160324, 18672816, 28398241], [1, 0, -168, 0, 19538, 0, -1048488, 0, 38950081], [1, 0, -100, 0, 16278, 0, -688900, 0, 47458321], [1, 0, 164, 0, 22566, 0, 1299044, 0, 62742241], [1, 0, 388, 0, 56454, 0, 3650692, 0, 88529281]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9216/2/a/bh'], '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': '8-96e8-1.1-c1e4-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-96e8-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.578469006927287, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 2038128857073119005, 'z1': {'__RealLiteral__': 0, 'data': '0.22855338159461432523021291804', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '289725831362604407638060993188,907036065078259769297139706554,1028910926214998888344012724093,1390344648305635381472798231857', 'Lhash_array': ['289725831362604407638060993188', '907036065078259769297139706554', '1028910926214998888344012724093', '1390344648305635381472798231857'], 'label': '8-96e8-1.1-c1e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9216/2/a/bh'}