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lfunc_lfunctions • Show schema
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{'Lhash': '2089900562520032259586281598128', 'a10': [1.552059686975147, 0.8960820780734675], 'a2': [0.0, 0.8431353130913546], 'a3': [-1.2962671522015528, 1.1487782510664435], 'a4': [1.2891228438183435, 0.0], 'a5': [1.0627974705364713, -1.8408192171248552], 'a6': [-0.9685755103854445, -1.0929286112214947], 'a7': [2.3446985367039086, -1.225719695517107], 'a8': [0.0, 2.7731756187187058], 'a9': [0.360617059753447, -2.978247024041958], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.2962671522015528, -1.1487782510664435]]], [7, [[1.0, 0], [-2.3446985367039086, 1.225719695517107]]], [13, [[1.0, 0], [-3.0829993095990034, 1.869522735088308]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.68', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2043716086172921262338695809097', 'degree': 2, 'euler_factors': 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'6.48424628868315668807842514079933', '7.69752997575354053977430059158925', '8.956778352051963023107613535232361', '10.44332739049861641988152903513479', '11.08941032151908809112279608561900', '11.44907336503623679415951471068552'], 'prelabel': '2-273-273.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.2693583383665677, 'root_number': '0.6628226241474617 - 0.7487764478923418*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.134679169183', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64864084957145442537996846562', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61531336372782118178279641888', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50531439529721313957569188175', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '273.68', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/r/b/68/20'], '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': '2-273-273.68-c1-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-273-273.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.13467916918328385, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64864084957145442537996846562', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2089900562520032259586281598128', 'Lhash_array': ['2089900562520032259586281598128'], 'label': '2-273-273.68-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/r/b/68/20'}