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lfunc_lfunctions • Show schema
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{'Lhash': '1678862364117188493895845305432', 'a10': [0.7817787512760914, 1.3540805174879427], 'a2': [0.8660254037844386, -0.5], 'a3': [0, 0], 'a4': [0.5, -0.8660254037844386], 'a5': [0, 1.5635575025521828], 'a6': [0, 0], 'a7': [-0.8660254037844386, -0.5], 'a8': [0, -1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.079495851085733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.8660254037844386, 0.5]]], [13, [[1.0, 0], [-2.995978294861323, 2.006019455718174]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '1638.127', 'coefficient_field': 'CDF', 'conductor': 1638, 'conductor_radical': 546, 'conjugate': '1120758040352941212981006921712', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.5635575025521828], [-5.0, 0]], [[1.0, 0], [0.8660254037844386, 0.5]], 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[-30.5, -52.827549630850754]], [[1.0, 0], [1.4210303294713833, -0.8204322432469258], [33.5, -58.023702053557386]], [[1.0, 0], [-1.9872355575643827, -1.1473309841029924], [35.5, 61.48780366869514]], [[1.0, 0], [0, 11.227743390495919], [-73.0, 0]], [[1.0, 0], [-4.260976523288903, 0], [79.0, 0]], [[1.0, 0], [0, 4.948285551989211], [-83.0, 0]], [[1.0, 0], [2.0968209345122624, -1.2106001309830974], [44.5, -77.07626093681505]], [[1.0, 0], [4.233381056658611, 2.4441436926441114], [48.5, 84.00446416709055]], [[1.0, 0], [3.6837343654525982, 6.380415082551399], [-50.5, 87.4685657822283]], [[1.0, 0], [5.785250203056553, 0], [103.0, 0]], [[1.0, 0], [0.5144780074435602, 0.8911020482690453], [-53.5, 92.66471820493493]], [[1.0, 0], [0, -14.15347722559712], [-109.0, 0]], [[1.0, 0], [6.77051413910801, -11.72687448229853], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-1638-13.10-c1-0-21', 'leading_term': 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'8.607544936891610342749944323931810', '9.325682861885630036064654778026164'], 'prelabel': '2-1638-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6165585645867444, 'root_angle': 0.3162757487136758, 'root_number': '0.54566859952456289703363638403936654230959259011388929329 + 0.8380010617492690244577020010094640855945602166807228161*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1581378743568379', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32438888429897324348160615643', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57009290462463113762655907093', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05969386808096150298022597000', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.079495851085733, 'bad_primes': [2, 3, 7, 13], 'central_character': '13.10', 'conductor': 1638, 'conductor_radical': 546, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1638/2/bj/g/127/6'], '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': '2-1638-13.10-c1-0-21', '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': '2-1638-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6165585645867444, 'root_angle': 0.1581378743568379, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32438888429897324348160615643', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1678862364117188493895845305432', 'Lhash_array': ['1678862364117188493895845305432'], 'label': '2-1638-13.10-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1638/2/bj/g/127/6'}