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lfunc_lfunctions • Show schema
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{'Lhash': '1485912080812933561541242953072', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [3.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.512708587065244, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '3696.1', 'coefficient_field': 'CDF', 'conductor': 3696, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.0, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [13.0, 0]], [[1.0, 0], [-7.58257569495584, 0], [17.0, 0]], [[1.0, 0], [-6.58257569495584, 0], [19.0, 0]], [[1.0, 0], [-5.58257569495584, 0], [23.0, 0]], [[1.0, 0], [8.16515138991168, 0], [29.0, 0]], 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'leading_term': '3.41039159817619556507547612985', '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': 'ModularForm/GL2/Q/holomorphic/3696/2/a/bl/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [3.4103915981761954, 3.404164308487822, 3.385392868037965, 3.353816586313313, 3.309027182035347, 3.2505062523814443, 3.1776742755753213, 3.0899481504145667, 2.9868039703856177, 2.8678416886670703, 2.732848501065869, 2.581858088233783, 2.415203248849293, 2.2335598673477177, 2.037980557402547, 1.8299166884636422, 1.6112278349239988, 1.3841779933219907, 1.1514182044203976, 0.9159555065957189, 0.6811084450238608, 0.45044967414764897, 0.22773652092485458, 0.016830721081944215, -0.17839110618192258, -0.3541343273670623, -0.5067882508068534, -0.6330306003341898, -0.7299316659812938, -0.79505507653027, 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'7.67137938126613580363559479595036', '8.721218405147397565040916811109445'], 'prelabel': '2-3696-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.432560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17217794914892801672586287374', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.90459815303010201662473188351', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22012070837500961362961836022', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.512708587065244, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 3696, 'conductor_radical': 462, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3696/2/a/bl/1/2'], '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': '2-3696-1.1-c1-0-36', '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': '2-3696-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.432560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17217794914892801672586287374', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1485912080812933561541242953072', 'Lhash_array': ['1485912080812933561541242953072'], 'label': '2-3696-1.1-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3696/2/a/bl/1/2'}