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lfunc_lfunctions • Show schema
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{'Lhash': '3409802643357545361420129890663', 'a10': [3.98562281364894e-61, 4.259964729037868], 'a2': [-0.8660254037844386, -0.5], 'a3': [1.1136450596404865, -1.32657253142764], 'a4': [0.5, 0.8660254037844386], 'a5': [-2.129982364518934, -3.6892376745724866], 'a6': [-1.6277311781615178, 0.5920229823587235], 'a7': [-1.071623002937796, -2.41901305072432], 'a8': [0.0, -1.0], 'a9': [-0.519589362276674, -2.954661891758331], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [3, [[1.0, 0], [-1.1136450596404865, 1.32657253142764]]], [7, [[1.0, 0], [1.071623002937796, 2.41901305072432]]], [13, [[1.0, 0], [-2.414013419507705, -2.678159668585261]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.185', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '768349642154214833802458298975', 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'6.00637139362098245162121620303081', '6.92586380789541119957806266413736', '7.87889210294400569073294145608616', '8.470073364945623273926519869323391', '9.694348738797026886530217018429248', '10.11387705973427292896535973027813', '11.24499252394535341263094045624727'], 'prelabel': '2-546-273.185-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.9363355518529672, 'root_number': '-0.9800650356224442 - 0.19867693864758731*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.468167775926', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.68985999986403211069457126171', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16564933986844178840029492914', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.59328160856407390336213977589', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.185', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/u/a/185/15'], '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': '2-546-273.185-c1-0-37', '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': '2-546-273.185-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.4681677759264836, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.68985999986403211069457126171', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3409802643357545361420129890663', 'Lhash_array': ['3409802643357545361420129890663'], 'label': '2-546-273.185-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/u/a/185/15'}