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lfunc_lfunctions • Show schema
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{'Lhash': '770976649601717426211938833989', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-8.736254417016418, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 104.07936925012649, '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], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1764.881', 'coefficient_field': 'CDF', 'conductor': 1764, 'conductor_radical': 42, 'conjugate': '674911988598452434970598394317', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [8.736254417016418, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 8.786302069388233], [-1331.0, 0]], [[1.0, 0], [0, 11.832156388802742], [-2197.0, 0]], [[1.0, 0], [-44.5839229842193, 0], [4913.0, 0]], [[1.0, 0], [0, 11.645822612562442], [-6859.0, 0]], [[1.0, 0], [0, -142.63010112319952], [-12167.0, 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'3.98847821606779540826409143091567', '4.74511484897290071237287946585326', '5.74997409790113609339389686214779', '6.66497084898448669827523658461802', '7.47291537939674484589831381630618', '8.113110278471278230389800999832399', '8.896098842465585154172033115149746'], 'prelabel': '2-42e2-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.201929682669181, 'root_angle': 0.07690119815619134, 'root_number': '0.9709582642968335319013019325907459468208082179462916497 + 0.239248926839140413829861314821819620870458622136635360*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.03845059907809567', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60819333770907363965458199966', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91515047850102293590651896082', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09076443165906947149595189370', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 104.07936925012649, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 1764, 'conductor_radical': 42, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1764/4/f/a/881/3'], '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': '2-42e2-21.20-c3-0-18', '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': '2-42e2-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.201929682669181, 'root_angle': 0.03845059907809567, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60819333770907363965458199966', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '770976649601717426211938833989', 'Lhash_array': ['770976649601717426211938833989'], 'label': '2-42e2-21.20-c3-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1764/4/f/a/881/3'}