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lfunc_lfunctions • Show schema
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{'Lhash': '1808724539046821279325756851108', 'a10': [2.349214846137425, -4.0689594714051225], 'a2': [1.1066609724613288, 1.9167930310566035], 'a3': [-1.2372141510346673, 2.1429177694352384], 'a4': [-1.4493970159381078, 2.5104292719435204], 'a5': [-1.0613977110408654, -1.8383947625600887], 'a6': [-5.476706462107769, 0], 'a7': [-2.631692258592556, -0.2723891628975218], 'a8': [-1.9893205547171422, 0], 'a9': [-1.5613977110408654, -2.7044201663445273], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.446302559117473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [2.631692258592556, 0.2723891628975218]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 13], 'central_character': '1183.508', 'coefficient_field': 'CDF', 'conductor': 1183, 'conductor_radical': 91, 'conjugate': '436236908300743874433208370306', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.1066609724613288, -1.9167930310566035], [-1.0, 1.7320508075688772]], 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'4.08494525304162319241022525521958', '5.58573959653048706305825860575747', '6.24791979831468884559565892798319', '7.19081076619295672696319919050247', '7.64684001595271913907805246397848', '9.316805510009513251602714750400975', '10.05833357760447310923690573267749'], 'prelabel': '2-1183-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0734837821464867, 'root_angle': -0.11366444991952951, 'root_number': '0.93691888614964178022598542861037545589459176576780877427 - 0.3495468506167872540410629201944634723952894436958081499*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.056832224959764754', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42683207716793274764940884928', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26397379009176753480227391705', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51974463214059652768854227097', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.446302559117473, 'bad_primes': [7, 13], 'central_character': '7.4', 'conductor': 1183, 'conductor_radical': 91, 'degree': 2, 'index': 61, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1183/2/e/f/508/4'], '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': '2-1183-7.4-c1-0-61', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1183-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0734837821464867, 'root_angle': -0.056832224959764754, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42683207716793274764940884928', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1808724539046821279325756851108', 'Lhash_array': ['1808724539046821279325756851108'], 'label': '2-1183-7.4-c1-0-61', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1183/2/e/f/508/4'}