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lfunc_lfunctions • Show schema
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{'Lhash': '1372311078783168913834563771063', 'a10': [-45621782.811367296, 218903295.84798953], 'a2': [0.0, 256.0], 'a3': [0.0, 2973.9060097317533], 'a4': [-65536.0, 0.0], 'a5': [855090.9994062091, 178210.0891069035], 'a6': [-761319.9384913289, 0.0], 'a7': [0.0, -7583430.579308511], 'a8': [0.0, -16777216.0], 'a9': [120296046.04528137, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.32220873445598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '8.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -256.0]]], [5, [[1.0, 0], [-855090.9994062091, -178210.0891069035]]]], 'bad_primes': [2, 5], 'central_character': '10.9', 'coefficient_field': 'CDF', 'conductor': 10, 'conductor_radical': 10, 'conjugate': '1780419314159163246287176769644', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -256.0]], [[1.0, 0], [0, -2973.9060097317533], [-129140163.0, 0]], [[1.0, 0], [-855090.9994062091, -178210.0891069035]], [[1.0, 0], [0, 7583430.579308511], [-232630513987207.0, 0]], 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'16.48933444199485118850181444370347'], 'prelabel': '2-10-5.4-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.280444922488313, 'root_angle': -0.4345970240256317, 'root_number': '0.2040268152418974 - 0.9789653000297042*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.217298512013', 'prec': 50}, 'spectral_label': 'c17-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08256255985371387724378603358', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40904194911407649297790750128', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.62655140148401512393662745612', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.32220873445598, 'bad_primes': [2, 5], 'central_character': '5.4', 'conductor': 10, 'conductor_radical': 10, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/10/18/b/a/9/7'], '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': '2-10-5.4-c17-0-3', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [17], 'order_of_vanishing': 0, 'prelabel': '2-10-5.4-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.280444922488313, 'root_angle': -0.21729851201281586, 'self_dual': False, 'spectral_label': 'c17-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08256255985371387724378603358', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1372311078783168913834563771063', 'Lhash_array': ['1372311078783168913834563771063'], 'label': '2-10-5.4-c17-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/10/18/b/a/9/7'}