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{'Lhash': '382160271442866980395622443269,769812216815936179431919001340,1836091744753653437258335691506,2628129494744935812481085855059', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 3, 'a5': -6, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1829.127735481644, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1, 0, -7, 0, 49]], [13, [1, 4, 30, 52, 169]]], 'bad_primes': [3, 7, 13], 'central_character': '819.1', 'coefficient_field': '1.1.1.1', 'conductor': 449920319121, 'conductor_radical': 273, 'degree': 8, 'euler_factors': [[1, 0, -3, 0, 5, 0, -12, 0, 16], [1], [1, 6, 25, 78, 204, 390, 625, 750, 625], [1, 0, -7, 0, 49], [1, 12, 82, 408, 1563, 4488, 9922, 15972, 14641], [1, 4, 30, 52, 169], [1, 4, 74, 208, 1939, 3536, 21386, 19652, 83521], [1, 0, 10, 0, -261, 0, 3610, 0, 130321], [1, -16, 146, -1024, 5683, -23552, 77234, -194672, 279841], [1, 14, 89, 686, 4924, 19894, 74849, 341446, 707281], 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'10.68104763119975624106694997004192'], 'prelabel': '8-819e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 189029431058659667, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.30147129766992763349773226462', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.60727476220761322079540109663', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.44842099583519400398154705870', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 1829.127735481644, 'bad_primes': [3, 7, 13], 'central_character': '1.1', 'conductor': 449920319121, 'conductor_radical': 273, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 3, -6, 0, 0, 0, 0, 0, -12, 0, -4, 0, 0, 4, -4, 0, 0, -18, 0, 0, 16, 0, 11, 0, 0, 0, -14, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -36, 0, 0, 12, 0, 7, 0, 0, -12, 6, 0, 72, 0, 0, 0, 0, 0, -8, 0, 0, 9, 24, 0, -12, -12, 0, 0, -12, 0, -30, 0, 0, 0, 0, 0, 12, -24, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 18, 0, 0, 33], 'euler11': [1, 12, 82, 408, 1563, 4488, 9922, 15972, 14641], 'euler13': [1, 4, 30, 52, 169, 0, 0, 0, 0], 'euler17': [1, 4, 74, 208, 1939, 3536, 21386, 19652, 83521], 'euler19': [1, 0, 10, 0, -261, 0, 3610, 0, 130321], 'euler2': [1, 0, -3, 0, 5, 0, -12, 0, 16], 'euler23': [1, -16, 146, -1024, 5683, -23552, 77234, -194672, 279841], 'euler29': [1, 14, 89, 686, 4924, 19894, 74849, 341446, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -12, 115, -804, 5016, -24924, 110515, -357492, 923521], 'euler37': [1, 0, -86, 0, 4251, 0, -117734, 0, 1874161], 'euler41': [1, 6, 69, 342, 2060, 14022, 115989, 413526, 2825761], 'euler43': [1, 0, -65, 0, 2376, 0, -120185, 0, 3418801], 'euler47': [1, -12, 147, -1188, 9848, -55836, 324723, -1245876, 4879681], 'euler5': [1, 6, 25, 78, 204, 390, 625, 750, 625], 'euler53': [1, -6, 5, 450, -3756, 23850, 14045, -893262, 7890481], 'euler59': [1, 0, -126, 0, 9587, 0, -438606, 0, 12117361], 'euler61': [1, 8, 10, -544, -4709, -33184, 37210, 1815848, 13845841], 'euler67': [1, 12, 82, 408, -117, 27336, 368098, 3609156, 20151121], 'euler7': [1, 0, -7, 0, 49, 0, 0, 0, 0], 'euler71': [1, 12, 139, 1092, 6648, 77532, 700699, 4294932, 25411681], 'euler73': [1, 30, 521, 6630, 65412, 483990, 2776409, 11670510, 28398241], 'euler79': [1, -12, -29, -180, 12312, -14220, -180989, -5916468, 38950081], 'euler83': [1, 0, -308, 0, 37494, 0, -2121812, 0, 47458321], 'euler89': [1, 0, 130, 0, 20067, 0, 1029730, 0, 62742241], 'euler97': [1, -18, 301, -3474, 38316, -336978, 2832109, -16428114, 88529281], 'euler_factors': [[1, 0, -3, 0, 5, 0, -12, 0, 16], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 6, 25, 78, 204, 390, 625, 750, 625], [1, 0, -7, 0, 49, 0, 0, 0, 0], [1, 12, 82, 408, 1563, 4488, 9922, 15972, 14641], [1, 4, 30, 52, 169, 0, 0, 0, 0], [1, 4, 74, 208, 1939, 3536, 21386, 19652, 83521], [1, 0, 10, 0, -261, 0, 3610, 0, 130321], [1, -16, 146, -1024, 5683, -23552, 77234, -194672, 279841], [1, 14, 89, 686, 4924, 19894, 74849, 341446, 707281], [1, -12, 115, -804, 5016, -24924, 110515, -357492, 923521], [1, 0, -86, 0, 4251, 0, -117734, 0, 1874161], [1, 6, 69, 342, 2060, 14022, 115989, 413526, 2825761], [1, 0, -65, 0, 2376, 0, -120185, 0, 3418801], [1, -12, 147, -1188, 9848, -55836, 324723, -1245876, 4879681], [1, -6, 5, 450, -3756, 23850, 14045, -893262, 7890481], [1, 0, -126, 0, 9587, 0, -438606, 0, 12117361], [1, 8, 10, -544, -4709, -33184, 37210, 1815848, 13845841], [1, 12, 82, 408, -117, 27336, 368098, 3609156, 20151121], [1, 12, 139, 1092, 6648, 77532, 700699, 4294932, 25411681], [1, 30, 521, 6630, 65412, 483990, 2776409, 11670510, 28398241], [1, -12, -29, -180, 12312, -14220, -180989, -5916468, 38950081], [1, 0, -308, 0, 37494, 0, -2121812, 0, 47458321], [1, 0, 130, 0, 20067, 0, 1029730, 0, 62742241], [1, -18, 301, -3474, 38316, -336978, 2832109, -16428114, 88529281]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/bm/d'], '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': '8-819e4-1.1-c1e4-0-5', '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': '8-819e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 189029431058659667, 'z1': {'__RealLiteral__': 0, 'data': '0.30147129766992763349773226462', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '382160271442866980395622443269,769812216815936179431919001340,1836091744753653437258335691506,2628129494744935812481085855059', 'Lhash_array': ['382160271442866980395622443269', '769812216815936179431919001340', '1836091744753653437258335691506', '2628129494744935812481085855059'], 'label': '8-819e4-1.1-c1e4-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/bm/d'}