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lfunc_lfunctions • Show schema
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{'Lhash': '2740118437034441556837105335400', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [0.0, 0.0], 'a5': [-0.7071067811865476, -0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.0, -1.0], 'a8': [0.0, 0.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6768584424468882, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [7, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '3360.1553', 'coefficient_field': 'CDF', 'conductor': 3360, 'conductor_radical': 210, 'conjugate': '620846769096382283629228208029', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 1.0]], [[1.0, 0], 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'leading_term': '0.94898014529591033001314887906157', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3360/1/cv/a/1553/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.9489801452959103, 1.0740188725855249, 1.2144182652123499, 1.3727708530152396, 1.5504681863979184, 1.747673247437679, 1.9634103267637641, 2.1957076007188276, 2.4417455835723403, 2.6979895835581775, 2.960302817371916, 3.224046176095473, 3.484173283764762, 3.7353286405490045, 3.9719544683027115, 4.188409475561151, 4.379100561212403, 4.538626591712015, 4.661931809070292, 4.7444651238910245, 4.78234049559534, 4.7724927923240035, 4.712822960830495, 4.602326035118277, 4.441195487823055, 4.230897695038096, 3.9742108527218347, 3.675223551867049, 3.339289380257075, 2.9729353483193046, 2.5837235991493506, 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'8.288460466444111777525642644058411', '9.057773567035041290430131479256629'], 'prelabel': '2-3360-840.293-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2949356904676341, 'root_angle': 0.9262081911747834, 'root_number': '-0.97324898946773016378805774830813 + 0.22975292054736118352393736938184*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4631040955873917', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.16157231065177360550707366089', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84176195310126380926635618530', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46433824453624529971639297433', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6768584424468882, 'bad_primes': [2, 3, 5, 7], 'central_character': '840.293', 'conductor': 3360, 'conductor_radical': 210, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3360/1/cv/a/1553/2'], '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': '2-3360-840.293-c0-0-11', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3360-840.293-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2949356904676341, 'root_angle': 0.4631040955873917, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.16157231065177360550707366089', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2740118437034441556837105335400', 'Lhash_array': ['2740118437034441556837105335400'], 'label': '2-3360-840.293-c0-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3360/1/cv/a/1553/2'}