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lfunc_lfunctions • Show schema
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{'Lhash': '1854711644682314978608553220087', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-0.5538274564583103, 0], 'a6': [0, 0], 'a7': [2.5063159470679937, 0.8475732260239615], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.1100711784264, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.5063159470679937, -0.8475732260239615]]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.1133', 'coefficient_field': 'CDF', 'conductor': 2268, 'conductor_radical': 42, 'conjugate': '472352066956620777271854354396', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5538274564583103, 0], [5.0, 0]], [[1.0, 0], [-2.5063159470679937, -0.8475732260239615]], [[1.0, 0], [0, 4.658959867031364], [-11.0, 0]], [[1.0, 0], [0, -4.136888518194967], [-13.0, 0]], [[1.0, 0], [7.245274403325002, 0], [17.0, 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'4.38932695646819249493350252080392', '5.23915703403832122783533394986797', '6.04997644313708528174598080728216', '7.27045092602670891035322651640471', '7.58509754556767378411877035165532', '8.376018565467650762171333380559892', '9.230774909413522463874875365550839'], 'prelabel': '2-2268-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': 0.6038013778875454, 'root_number': '-0.3203525677108772180656104622159978472952735755848398613 + 0.9472983861281765253741022351918257139592898053666385958*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3019006889437727', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46310950694804260062959378342', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.31518455600711260726211999395', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73141549516778962068165483910', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.1100711784264, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 2268, 'conductor_radical': 42, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/2/f/b/1133/6'], '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': '2-2268-21.20-c1-0-25', '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': '2-2268-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': 0.3019006889437727, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46310950694804260062959378342', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1854711644682314978608553220087', 'Lhash_array': ['1854711644682314978608553220087'], 'label': '2-2268-21.20-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2268/2/f/b/1133/6'}