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lfunc_lfunctions • Show schema
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{'Lhash': '1471317431118985584450574421394', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.5, 0.8660254037844386], 'a4': [0, 0], 'a5': [6.36048219425407, 3.6722261070284086], 'a6': [0, 0], 'a7': [-6.341331329915654, 2.9643746329082896], 'a8': [0, 0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.310673765011956, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5, -0.8660254037844386]]], [7, [[1.0, 0], [6.341331329915654, -2.9643746329082896]]]], 'bad_primes': [2, 3, 7], 'central_character': '672.481', 'coefficient_field': 'CDF', 'conductor': 672, 'conductor_radical': 42, 'conjugate': '978580139488429315328480042948', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5, -0.8660254037844386]], [[1.0, 0], [-6.36048219425407, -3.6722261070284086], [12.5, 21.650635094610966]], [[1.0, 0], [6.341331329915654, -2.9643746329082896]], [[1.0, 0], 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'8.915220911397681927489890027612565', '9.624167568632621929563561874726897', '10.03467165414559450064800777016585'], 'prelabel': '2-672-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.279097307261423, 'root_angle': 0.03391011292522671, 'root_number': '0.97738770447144486131268836748763275005031770926186334158 + 0.2114551374359099430762669178772765459470749084056147508*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.03391011292522671', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16066480057997665261698765461', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20118838132061180812321864673', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85071204256351124325612751975', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.310673765011956, 'bad_primes': [2, 3, 7], 'central_character': '7.5', 'conductor': 672, 'conductor_radical': 42, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/672/3/bh/b/481/7'], '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': '2-672-7.5-c2-0-18', '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': '2-672-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.279097307261423, 'root_angle': 0.03391011292522671, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16066480057997665261698765461', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1471317431118985584450574421394', 'Lhash_array': ['1471317431118985584450574421394'], 'factors': ['2-672-7.5-c2-0-18'], 'label': '2-672-7.5-c2-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/672/3/bh/b/481/7'}