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lfunc_lfunctions • Show schema
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{'Lhash': '2043716086172921262338695809097', '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': '273.269', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2089900562520032259586281598128', 'degree': 2, 'euler_factors': 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'6.91121612424261789547969299712254', '8.209902666792774095966310444500520', '9.016248859002807734368540961160357', '10.46543042964214371869578243225015', '10.91036570158931466447020793073238', '11.90838122156871311620290471047118'], 'prelabel': '2-273-273.269-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': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61220772175311403545631515480', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.95638260628068660056873827855', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.14385298629465659950365293036', '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': '273.269', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/r/b/269/13'], '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': '2-273-273.269-c1-0-12', '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': '2-273-273.269-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': '1.61220772175311403545631515480', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2043716086172921262338695809097', 'Lhash_array': ['2043716086172921262338695809097'], 'label': '2-273-273.269-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/r/b/269/13'}