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lfunc_lfunctions • Show schema
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{'Lhash': '2074269405411138267037760646737', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-3.676869675804632, 0], 'a6': [0, 0], 'a7': [-1.0754227607743663, -2.4173261851906624], '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], [1.0754227607743663, 2.4173261851906624]]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.109', 'coefficient_field': 'CDF', 'conductor': 2268, 'conductor_radical': 42, 'conjugate': '68560306242512629350978575188', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.676869675804632, 0], [5.0, 0]], [[1.0, 0], [1.0754227607743663, 2.4173261851906624]], [[1.0, 0], [0.6031433706632227, 0], [11.0, 0]], [[1.0, 0], [-2.628508040430208, 4.552709474128429], [-6.5, -11.258330249197702]], [[1.0, 0], 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'8.003179757066435866065492031724468', '8.768091190583434188372027355891340', '9.122224390180530205778954679245106'], 'prelabel': '2-2268-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': -0.8352902575326175, 'root_number': '-0.86908294759612913021764626440657045108655770352812650073 - 0.4946663827243810875707585140966287869058138198605102596*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.41764512876630877', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63631004082488045661576793476', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11418830399907727615433744276', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.63901173229040188770453930016', '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': '63.4', 'conductor': 2268, 'conductor_radical': 42, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/2/l/n/109/1'], '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': '2-2268-63.4-c1-0-30', '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': '2-2268-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': -0.41764512876630877, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63631004082488045661576793476', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2074269405411138267037760646737', 'Lhash_array': ['2074269405411138267037760646737'], 'label': '2-2268-63.4-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2268/2/l/n/109/1'}