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lfunc_lfunctions • Show schema
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{'Lhash': '1277393829293686508721318138190', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.6126611452773953, 0.0], 'a6': [0.0, 0.0], 'a7': [22.744145016099033, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.31346688440881, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [3.0, 0]]]], 'bad_primes': [2, 3], 'central_character': '768.1', 'coefficient_field': 'CDF', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [-0.6126611452773953, 0], [125.0, 0]], [[1.0, 0], [-22.744145016099033, 0], [343.0, 0]], [[1.0, 0], [-60.26296774164328, 0], [1331.0, 0]], [[1.0, 0], [-52.90616158026685, 0], [2197.0, 0]], [[1.0, 0], [-47.16425690386244, 0], [4913.0, 0]], [[1.0, 0], [-29.16425690386244, 0], [6859.0, 0]], [[1.0, 0], [109.48829003219807, 0], 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[[1.0, 0], [-597.0088026814608, 0], [1295029.0, 0]], [[1.0, 0], [-496.4221935501403, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-768-1.1-c3-0-17', 'leading_term': '2.41750546444459476944763887574', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/768/4/a/r/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.4175054644445946, 2.4063032684760115, 2.3728183843205874, 2.3174164785020808, 2.2407087587619245, 2.143554317340589, 2.0270628209941655, 1.892596987974143, 1.7417741747438358, 1.5764663070723945, 1.3987973352799823, 1.2111373745097065, 1.0160927094301337, 0.8164908989820158, 0.6153603098092274, 0.4159035349703353, 0.2214643146060162, 0.03548776380105673, -0.13852607446359508, -0.2970751017074248, 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'4.38332206022596767761046015753949', '5.66071443774082057621598224566271', '6.19358130390038909314243512682121', '7.38704325984343857196157800357725', '8.159578213859178123920310894052614', '9.122725069709323141008836622902636', '9.915433652230749060032508076353528'], 'prelabel': '2-768-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00768605250035216649018847832', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.81637270437719407369744240494', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71734739814407388335297811575', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.31346688440881, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/4/a/r/1/2'], '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': '2-768-1.1-c3-0-17', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-768-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00768605250035216649018847832', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1277393829293686508721318138190', 'Lhash_array': ['1277393829293686508721318138190'], 'label': '2-768-1.1-c3-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/4/a/r/1/2'}