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lfunc_lfunctions • Show schema
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{'Lhash': '1394761057297398459061889014914', 'a10': [0.0, 0.0], 'a2': [-1.4129775074442381, -0.05911483279742884], 'a3': [-1.0, 0.0], 'a4': [1.993010873086664, 0.1670558581981878], 'a5': [0.0, 0.0], 'a6': [1.4129775074442381, 0.05911483279742884], 'a7': [0.0, -1.3341117163963756], 'a8': [-2.8062040566380424, -0.3538626746468093], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.791024121276825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.4129775074442381, 0.05911483279742884]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '600.349', 'coefficient_field': 'CDF', 'conductor': 600, 'conductor_radical': 30, 'conjugate': '1013514000447500123412919120795', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4129775074442381, 0.05911483279742884]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.3341117163963756], [-7.0, 0]], [[1.0, 0], [0, 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['1.10027247022664126195243664358946', '2.62346636959426063065352770315610', '4.05528042263026462920474087231539', '5.87123892464566269895121110986457', '6.01357109097480799142440482787967', '7.27685471614451363071515486155894', '8.358744065000573032624858142218269', '8.821539298158027074927332579530283', '9.973471925001616319216447697484273', '10.78417648825096905461549113789069'], 'prelabel': '2-600-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': 0.18751178740974794, 'root_number': '0.8314490382778845 + 0.5556010229893218*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0937558937049', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10027247022664126195243664359', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62346636959426063065352770316', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05528042263026462920474087232', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.791024121276825, 'bad_primes': [2, 3, 5], 'central_character': '40.29', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/600/2/d/g/349/1'], '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': '2-600-40.29-c1-0-15', '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': '2-600-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': 0.09375589370487397, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10027247022664126195243664359', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1394761057297398459061889014914', 'Lhash_array': ['1394761057297398459061889014914'], 'label': '2-600-40.29-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/2/d/g/349/1'}