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lfunc_lfunctions • Show schema
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{'Lhash': '1061716126033045390293261893628', 'a10': -148, 'a2': 2, 'a3': -6, 'a4': -28, 'a5': -74, 'a6': -12, 'a7': 49, 'a8': -120, 'a9': -207, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 135.84509538159463, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[7, [1, -49]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.1', 'coefficient_field': '1.1.1.1', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'euler_factors': [[1, -2, 32], [1, 6, 243], [1, 74, 3125], [1, -49], [1], [1, 364, 371293], [1, 148, 1419857], [1, -1320, 2476099], [1, 436, 6436343], [1, 2970, 20511149], [1, -8842, 28629151], [1, -138, 69343957], [1, 532, 115856201], [1, -20676, 147008443], [1, 11722, 229345007], [1, -5274, 418195493], [1, 27670, 714924299], [1, 19512, 844596301], [1, -64088, 1350125107], [1, 3708, 1804229351], [1, -24296, 2073071593], [1, -2200, 3077056399], [1, 74424, 3939040643], [1, -34170, 5584059449], [1, -151718, 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'7.53306406011053878437312529836660', '8.107637521203690122317587213219668', '8.909072494120294567757134387822267'], 'prelabel': '2-847-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.655260416721482, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 109336794815510857, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.837546344270174044342130501474', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.75642935993811908650665270863', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71450757184218891945352562638', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 135.84509538159463, 'bad_primes': [7, 11], 'central_character': '1.1', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'dirichlet_coefficients': [1, 2, -6, -28, -74, -12, 49, -120, -207, -148, 0, 168, -364, 98, 444, 656, -148, -414, 1320, 2072, -294, 0, -436, 720, 2351, -728, 2700, -1372, -2970, 888, 8842, 5152, 0, -296, -3626, 5796, 138, 2640, 2184, 8880, -532, -588, 20676, 0, 15318, -872, -11722, -3936, 2401, 4702, 888, 10192, 5274, 5400, 0, -5880, -7920, -5940, -27670, -12432, -19512, 17684, -10143, -10688, 26936, 0, 64088, 4144, 2616, -7252, -3708, 24840, 24296, 276, -14106, -36960, 0, 4368, 2200, -48544, 34101, -1064, -74424, 8232, 10952, 41352, 17820, 0, 34170, 30636, -17836, 12208, -53052, -23444, -97680, -30912, 151718, 4802, 0, -65828], 'euler11': [1, 0, 0], 'euler13': [1, 364, 371293], 'euler17': [1, 148, 1419857], 'euler19': [1, -1320, 2476099], 'euler2': [1, -2, 32], 'euler23': [1, 436, 6436343], 'euler29': [1, 2970, 20511149], 'euler3': [1, 6, 243], 'euler31': [1, -8842, 28629151], 'euler37': [1, -138, 69343957], 'euler41': [1, 532, 115856201], 'euler43': [1, -20676, 147008443], 'euler47': [1, 11722, 229345007], 'euler5': [1, 74, 3125], 'euler53': [1, -5274, 418195493], 'euler59': [1, 27670, 714924299], 'euler61': [1, 19512, 844596301], 'euler67': [1, -64088, 1350125107], 'euler7': [1, -49, 0], 'euler71': [1, 3708, 1804229351], 'euler73': [1, -24296, 2073071593], 'euler79': [1, -2200, 3077056399], 'euler83': [1, 74424, 3939040643], 'euler89': [1, -34170, 5584059449], 'euler97': [1, -151718, 8587340257], 'euler_factors': [[1, -2, 32], [1, 6, 243], [1, 74, 3125], [1, -49, 0], [1, 0, 0], [1, 364, 371293], [1, 148, 1419857], [1, -1320, 2476099], [1, 436, 6436343], [1, 2970, 20511149], [1, -8842, 28629151], [1, -138, 69343957], [1, 532, 115856201], [1, -20676, 147008443], [1, 11722, 229345007], [1, -5274, 418195493], [1, 27670, 714924299], [1, 19512, 844596301], [1, -64088, 1350125107], [1, 3708, 1804229351], [1, -24296, 2073071593], [1, -2200, 3077056399], [1, 74424, 3939040643], [1, -34170, 5584059449], [1, -151718, 8587340257]], 'index': 129, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/847/6/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/847/6/a/a'], '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': '2-847-1.1-c5-0-129', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-847-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.655260416721482, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 109336794815510857, 'z1': {'__RealLiteral__': 0, 'data': '0.837546344270174044342130501474', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20849121
{'Lhash': '1061716126033045390293261893628', 'Lhash_array': ['1061716126033045390293261893628'], 'label': '2-847-1.1-c5-0-129', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/6/a/a'}
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id: 24593290
{'Lhash': '1061716126033045390293261893628', 'Lhash_array': ['1061716126033045390293261893628'], 'label': '2-847-1.1-c5-0-129', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/6/a/a/1/1'}