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lfunc_lfunctions • Show schema
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{'Lhash': '1946196814037187539675481379607', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.1374586088176875, -3.7021869095477244], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.171221833107733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', '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': '3528.3313', 'coefficient_field': 'CDF', 'conductor': 3528, 'conductor_radical': 42, 'conjugate': '758698781302810871763106356700', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.1374586088176875, 3.7021869095477244], [-2.5, -4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.1374586088176875, 3.7021869095477244], [-5.5, 9.526279441628825]], [[1.0, 0], [-1.274917217635375, 0], [13.0, 0]], [[1.0, 0], [-2.0, -3.4641016151377544], [-8.5, 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[-1.774917217635375, 3.0742468001732557], [-39.5, -68.41600689897065]], [[1.0, 0], [0.27491721763537486, 0], [83.0, 0]], [[1.0, 0], [2.274917217635375, -3.9402722039576945], [-44.5, -77.07626093681505]], [[1.0, 0], [16.274917217635373, 0], [97.0, 0]], [[1.0, 0], [-3.0, -5.196152422706632], [-50.5, 87.4685657822283]], [[1.0, 0], [5.912375826453062, -10.240535324858735], [-51.5, -89.20061658979718]], [[1.0, 0], [-3.4123758264530624, 5.910408305936541], [-53.5, -92.66471820493493]], [[1.0, 0], [-2.9123758264530624, -5.044382902152103], [-54.5, 94.39676901250381]], [[1.0, 0], [10.54983443527075, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 44, 'label': '2-3528-7.2-c1-0-44', 'leading_term': '2.0102934248210270474481783377331513121927597757256886276', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 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'-0.6054643436493673635071294605077551469423497523567868621 + 0.7958724323465669471984178169629224157856347934855379281*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3535062863872795', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53527858045962493776003662470', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54293324283844981834855025050', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04221927774372943704200864024', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.171221833107733, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 3528, 'conductor_radical': 42, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3528/2/s/bk/3313/2'], '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': '2-3528-7.2-c1-0-44', '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': '2-3528-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.307656906122299, 'root_angle': 0.3535062863872795, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53527858045962493776003662470', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1946196814037187539675481379607', 'Lhash_array': ['1946196814037187539675481379607'], 'label': '2-3528-7.2-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3528/2/s/bk/3313/2'}