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lfunc_lfunctions • Show schema
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{'Lhash': '1909817665464852159146869365103', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [7.671011028783098, 0.0], 'a6': [0.0, 0.0], 'a7': [7.211102550927978, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.847431613576552, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '288.17', 'coefficient_field': 'CDF', 'conductor': 288, 'conductor_radical': 6, 'conjugate': '1904652288100547766924613571261', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.671011028783098, 0], [25.0, 0]], [[1.0, 0], [-7.211102550927978, 0], [49.0, 0]], [[1.0, 0], [6.051641032410328, 0], [121.0, 0]], [[1.0, 0], [0, 2.29013501137044], [-169.0, 0]], [[1.0, 0], [0, -21.810291616744234], [-289.0, 0]], [[1.0, 0], [0, 34.835478513426374], [-361.0, 0]], [[1.0, 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'6.49799547089217442382159187023365', '7.82142618228697493399681939399562', '8.747494593214243341644964935521182', '9.920978892900802600508266816831300', '10.39249287843133203400256985201552', '11.60088514830199889628648892376846'], 'prelabel': '2-288-24.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8013267595153106, 'root_angle': 0.0012877779454881083, 'root_number': '0.9999918162731853 + 0.00404566269676484*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.000643888972744', 'prec': 57}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50658049238568277020740302238', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68114372964456075806356629471', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.64538288003719821493114741381', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.847431613576552, 'bad_primes': [2, 3], 'central_character': '24.5', 'conductor': 288, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/288/3/h/a/17/7'], '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': '2-288-24.5-c2-0-4', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-288-24.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8013267595153106, 'root_angle': 0.0006438889727440542, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50658049238568277020740302238', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1909817665464852159146869365103', 'Lhash_array': ['1909817665464852159146869365103'], 'label': '2-288-24.5-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/288/3/h/a/17/7'}