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lfunc_lfunctions • Show schema
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{'Lhash': '184139572476256997238861434851', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-6.708203932499369, 0], 'a6': [0, 0], 'a7': [0, -11.61895003862225], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.084589681459306, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1728.703', 'coefficient_field': 'CDF', 'conductor': 1728, 'conductor_radical': 6, 'conjugate': '1088043926822661269409938752917', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [6.708203932499369, 0], [25.0, 0]], [[1.0, 0], [0, 11.61895003862225], [-49.0, 0]], [[1.0, 0], [0, -15.588457268119896], [-121.0, 0]], [[1.0, 0], [-8.0, 0], [169.0, 0]], [[1.0, 0], [26.832815729997478, 0], [289.0, 0]], [[1.0, 0], [0, 23.2379000772445], [-361.0, 0]], [[1.0, 0], [0, 31.176914536239792], [-529.0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-12e3-4.3-c2-0-6', 'leading_term': '0.417919107660904989048200004019869469938602890276626289', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1728/3/g/h/703/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.417919107660905, 0.28307113361065983, 0.1357493610051637, -0.0227218595553748, -0.1909268814113469, -0.36735227050725183, -0.5503803460350917, -0.7382836439413943, -0.9292211854387621, -1.1212373872216492, -1.3122643711900457, -1.5001283235120602, -1.682560420853077, -1.8572126908522142, -2.0216790096266632, -2.1735212661018397, -2.310300545744959, -2.429613008835135, -2.5291299643837974, -2.606641473618236, -2.6601026598127993, -2.687681757414426, -2.6878088061119527, -2.6592237880508187, 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'4.79338074044487663673143746572781', '5.92553645230919867364688267683009', '6.22168114863865587815448351149790', '7.68646800242655541279378763898462', '8.125056757034416243095272316366019', '8.924164624426313496578129764243476'], 'prelabel': '2-12e3-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': -0.25, 'root_number': '0.e-55 - 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14526050983063020521515213326', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.80996296196706377800845717985', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09699210620809449499052393467', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.084589681459306, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/3/g/h/703/1'], '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': '2-12e3-4.3-c2-0-6', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-12e3-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.14526050983063020521515213326', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '184139572476256997238861434851', 'Lhash_array': ['184139572476256997238861434851'], 'factors': ['2-12e3-4.3-c2-0-6'], 'label': '2-12e3-4.3-c2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/3/g/h/703/1'}