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lfunc_lfunctions • Show schema
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{'Lhash': '2301588948608528538242460883471', 'a10': [1.8478587629625742, -3.2005852626625533], 'a2': [0.5, 0.8660254037844386], 'a3': [0.6420395219202062, 1.1120450724330289], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.8478587629625742, -3.2005852626625533], 'a6': [-0.6420395219202062, 1.1120450724330289], 'a7': [-0.4424634841649486, 0.0], 'a8': [-1.0, 0.0], 'a9': [0.6755705045849463, -1.1701224380360702], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.765199025936447, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 19], 'central_character': '722.653', 'coefficient_field': 'CDF', 'conductor': 722, 'conductor_radical': 38, 'conjugate': '745588009237442360799845250813', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.6420395219202062, -1.1120450724330289], [-1.5, 2.598076211353316]], [[1.0, 0], 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'group': 'GL2', 'index': 21, 'label': '2-722-19.7-c1-0-21', '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/722/2/c/n/653/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3218522182770793, 1.505340531857896, 1.669457144398913, 1.8131730990754675, 1.9309684856203493, 2.0139481246342466, 2.0514585569454944, 2.0329096567765275, 1.9495968899116518, 1.796386499733426, 1.5731429350093096, 1.2857657850076385, 0.9466906728618959, 0.574715299150671, 0.19404824251182315, -0.16745385581985003, -0.48079992384934284, -0.7189556306762299, -0.8602235031833632, -0.8915231123796834, -0.8111165927553224, -0.6303115273049842, -0.37372649678359793, -0.07783061489829535, 0.21233696119592563, 0.44811438226071204, 0.5834066086198434, 0.5814344306517356, 0.42115965562479984, 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'8.754408038046278722482942410200150', '9.910856050801155623607402154644381', '10.82351393978392196391348989003736'], 'prelabel': '2-722-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.401082886102945, 'root_angle': 0.24637665869380845, 'root_number': '0.7151098371259742 + 0.6990121035044119*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.123188329347', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81563354144600064224392784827', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90745297262201743047609901476', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65630169495947149407858674479', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.765199025936447, 'bad_primes': [2, 19], 'central_character': '19.7', 'conductor': 722, 'conductor_radical': 38, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/722/2/c/n/653/3'], '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': '2-722-19.7-c1-0-21', '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': '2-722-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.401082886102945, 'root_angle': 0.12318832934690423, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81563354144600064224392784827', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2301588948608528538242460883471', 'Lhash_array': ['2301588948608528538242460883471'], 'label': '2-722-19.7-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/722/2/c/n/653/3'}