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lfunc_lfunctions • Show schema
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{'Lhash': '1442445362246687747395198163121', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [21.114118599027844, 0], 'a6': [0, 0], 'a7': [-13.579954407790522, 12.593047219888074], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 133.81633189301976, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [13.579954407790522, -12.593047219888074]]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.1133', 'coefficient_field': 'CDF', 'conductor': 2268, 'conductor_radical': 42, 'conjugate': '771828071590502773355607940794', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-21.114118599027844, 0], [125.0, 0]], [[1.0, 0], [13.579954407790522, -12.593047219888074]], [[1.0, 0], [0, -24.853235801704834], [-1331.0, 0]], [[1.0, 0], [0, 60.69692602997775], [-2197.0, 0]], [[1.0, 0], [-117.39738424140317, 0], 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'positive_zeros': ['1.13788875419377238338050268943380', '1.73803579932684796745733391409530', '2.99259953123604647313182182953986', '3.71619624734111661595601170155216', '5.02092343102495642039415188086037', '5.74059450750342124730497925514815', '6.38751611909588056292255946657293', '6.95595937041194334764155557918404', '8.058133003937673561525035304884190', '9.016483319464712214086785600355674'], 'prelabel': '2-2268-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.567900928561748, 'root_angle': 0.26199684931345274, 'root_number': '0.6799606365779014134791698365785435415274264719743559098 + 0.7332486158899824874301130038292409647133263596681338695*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1309984246567264', 'prec': 60}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13788875419377238338050268943', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.73803579932684796745733391410', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99259953123604647313182182954', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 133.81633189301976, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 2268, 'conductor_radical': 42, 'degree': 2, 'index': 80, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/4/f/a/1133/48'], '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': '2-2268-21.20-c3-0-80', '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': '2-2268-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.567900928561748, 'root_angle': 0.13099842465672637, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13788875419377238338050268943', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1442445362246687747395198163121', 'Lhash_array': ['1442445362246687747395198163121'], 'label': '2-2268-21.20-c3-0-80', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2268/4/f/a/1133/48'}