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lfunc_lfunctions • Show schema
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{'Lhash': '3835575353808191846496526501137', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.6800507540952777, -2.0929810103226525], 'a4': [0.0, 0.0], 'a5': [3.3807412224975897, -2.456252274325333], 'a6': [0.0, 0.0], 'a7': [-1.0540354735739035, 0.34247688589234027], 'a8': [0.0, 0.0], 'a9': [3.363052467948851, 2.443400641878226], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1989131631853065, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [10.104652159715089, -4.346953500000338]]]], 'bad_primes': [2, 11], 'central_character': '44.29', 'coefficient_field': 'CDF', 'conductor': 44, 'conductor_radical': 22, 'conjugate': '2650779157042920208030421699729', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.6800507540952777, 2.0929810103226525], [-7.281152949374527, -5.2900672706322585]], [[1.0, 0], [-3.3807412224975897, 2.456252274325333], [7.725424859373685, 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0.6962945671465004], 'positive_zeros': ['3.02573544564853285017874901628136', '5.05048056648896935105798953308539', '6.72938513523557232140948636733925', '8.480180020560308628827573910100096', '10.05812064764471585634015974275611', '10.48401421374017222106396617180116', '12.38426576723532720731866696086808', '13.58105318479496894879637000842662', '14.78804696078371171633596728878121', '15.61802693998778086390230173733019'], 'prelabel': '2-44-11.7-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.094948931770476, 'root_angle': 0.09640813367046969, 'root_number': '0.8220751985780136 + 0.5693789317167606*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0964081336705', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.02573544564853285017874901628', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.05048056648896935105798953309', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.72938513523557232140948636734', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1989131631853065, 'bad_primes': [2, 11], 'central_character': '11.7', 'conductor': 44, 'conductor_radical': 22, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/44/3/f/a/29/2'], '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': '2-44-11.7-c2-0-1', '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': '2-44-11.7-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.094948931770476, 'root_angle': 0.09640813367046969, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.02573544564853285017874901628', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3835575353808191846496526501137', 'Lhash_array': ['3835575353808191846496526501137'], 'factors': ['2-44-11.7-c2-0-1'], 'label': '2-44-11.7-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/44/3/f/a/29/2'}