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lfunc_lfunctions • Show schema
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{'Lhash': '483633166171421906167938732773', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-8.5, -14.722431864335457], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.116618841859967, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '324.109', 'coefficient_field': 'CDF', 'conductor': 324, 'conductor_radical': 6, 'conjugate': '1843522948294885689853109130892', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-62.5, -108.25317547305482]], [[1.0, 0], [8.5, 14.722431864335457], [-171.5, 297.04671349806245]], [[1.0, 0], [0, 0], [-665.5, 1152.6798124370878]], [[1.0, 0], [44.5, -77.07626093681505], [-1098.5, -1902.6578121144116]], [[1.0, 0], [0, 0], [4913.0, 0]], [[1.0, 0], [-107.0, 0], [6859.0, 0]], [[1.0, 0], [0, 0], [-6083.5, 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['0.38151929726089190924900171524951', '2.39704149985424468385239901056019', '3.44595979829924927111067781996920', '5.12903352169656611318515130536302', '5.80002858783243465787826093162027', '7.15276909921579537655604378267178', '8.036583517604086068262059213961817', '9.144392188729630185390396760906016', '9.955576646757504687975032636207378', '10.83481079229787325935131551385887'], 'prelabel': '2-18e2-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372255578286792, 'root_angle': -0.5555555555555556, 'root_number': '-0.1736481776669303488517166267693147960003756771840693872 - 0.9848077530122080593667430245895230136706432517198424188*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2777777777777778', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38151929726089190924900171525', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39704149985424468385239901056', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44595979829924927111067781997', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.116618841859967, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 324, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/324/4/e/d/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': '2-18e2-9.4-c3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-18e2-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372255578286792, 'root_angle': -0.2777777777777778, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.38151929726089190924900171525', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '483633166171421906167938732773', 'Lhash_array': ['483633166171421906167938732773'], 'label': '2-18e2-9.4-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/324/4/e/d/109/1'}