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lfunc_lfunctions • Show schema
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{'Lhash': '208419095381488553139261334018', 'a10': [-8.738612787525831, 5.045240445221944], 'a2': [1.0686818135961957, 0.617003732757821], 'a3': [0.0, 0.0], 'a4': [-1.2386127875258306, -2.145340278899253], 'a5': [-4.08850074753295, 7.081491021510405], 'a6': [0.0, 0.0], 'a7': [-10.47722557505166, 0.0], 'a8': [0.0, -7.992944715442598], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6594125205610775, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [17.477225575051662, -7.452958217966885]]]], 'bad_primes': [3, 19], 'central_character': '171.46', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '3858602121250657523094570929341', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0686818135961957, -0.617003732757821], [2.0, 3.4641016151377544]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.08850074753295, -7.081491021510405], [-12.5, -21.650635094610966]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-171-19.8-c2-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/171/3/p/f/46/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.3324212466915369, 0.07968277457737084, -0.1733912712244498, -0.42819871001140664, -0.6853421514350603, -0.9442736205189206, -1.2030414304522838, -1.4581542744840652, -1.7045691063236126, -1.935804616032731, -2.1441796070073713, -2.32117322882573, -2.457900087641198, -2.5456868882858172, -2.5767284999837705, -2.544790905116569, -2.4459175659022687, -2.2790857725737164, -2.0467520850037557, -1.7552226002208173, -1.4147858645559506, -1.0395548739128075, -0.6469803481428146, -0.25702024659619793, 0.10902055996171886, 0.42993317126318986, 0.6862476057151915, 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'8.757004651285556158658704934928746', '9.957664231443265542245069878036309', '11.41607440739075013267021365006896', '12.46325046143278250997532541223858'], 'prelabel': '2-171-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': -0.9928004028117657, 'root_number': '-0.9997442193820889 - 0.022616273169946955*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.496400201406', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.16441367624798546082912033082', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96145746912870371067596575831', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17583081577912541164362512876', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.6594125205610775, 'bad_primes': [3, 19], 'central_character': '19.8', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/3/p/f/46/3'], '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': '2-171-19.8-c2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-171-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': -0.49640020140588287, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.16441367624798546082912033082', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '208419095381488553139261334018', 'Lhash_array': ['208419095381488553139261334018'], 'label': '2-171-19.8-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/3/p/f/46/3'}