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lfunc_lfunctions • Show schema
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{'Lhash': '2975618741191687745605385258237', 'a10': [0.8550432727147452, 2.2535002180766665e-61], 'a2': [0.4800378660479807, 0.6607154399700037], 'a3': [0.0, 0.0], 'a4': [1.0299594377249333, -3.1698892054443077], 'a5': [0.6153893393702222, -0.8470107607598732], 'a6': [0.0, 0.0], 'a7': [2.1106701811151245, -6.495974868824728], 'a8': [5.695684604243164, -1.8506401114491302], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.6975546171669396, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-2.57143805950658, -10.69521885265192]]]], 'bad_primes': [3, 11], 'central_character': '99.80', 'coefficient_field': 'CDF', 'conductor': 99, 'conductor_radical': 33, 'conjugate': '1936195339701386173798635114965', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.4800378660479807, -0.6607154399700037], [-1.2360679774997898, 3.804226065180614]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.50426505052499709775746694275', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.6975546171669396, 'bad_primes': [3, 11], 'central_character': '33.14', 'conductor': 99, 'conductor_radical': 33, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/99/3/l/a/80/5'], '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': '2-99-33.14-c2-0-4', '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': '2-99-33.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6424233976557139, 'root_angle': 0.06827443668115969, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.34734929376908244368342398248', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2975618741191687745605385258237', 'Lhash_array': ['2975618741191687745605385258237'], 'label': '2-99-33.14-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/99/3/l/a/80/5'}