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lfunc_lfunctions • Show schema
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{'Lhash': '3219685772027326315207150748798', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.8660254037844386, -1.5], 'a4': [0, 0], 'a5': [2.099261603699118, -3.636027755985394], 'a6': [0, 0], 'a7': [-4.289177825037856, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.7098088857877, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-0.6254134396820276, -4.313798561530788]]]], 'bad_primes': [2, 19], 'central_character': '1216.961', 'coefficient_field': 'CDF', 'conductor': 1216, 'conductor_radical': 38, 'conjugate': '482396950508618566733854997180', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.8660254037844386, 1.5], [-1.5, -2.598076211353316]], [[1.0, 0], [-2.099261603699118, 3.636027755985394], [-2.5, -4.330127018922194]], [[1.0, 0], [4.289177825037856, 0], [7.0, 0]], [[1.0, 0], [4.71492849450181, 0], [11.0, 0]], [[1.0, 0], [0.6152753541325513, 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'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/1216/2/i/r/961/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.0584529228485413, 1.2459963025021472, 1.4388102791843045, 1.6372831668027141, 1.8415593377583162, 2.051463349987217, 2.2664409749753127, 2.4855193358722873, 2.7072868182049117, 2.9298922507886167, 3.151062138588217, 3.368134405834117, 3.5781070510342436, 3.777700186039016, 3.963430012951706, 4.131693309251048, 4.2788609070059955, 4.401378462490959, 4.495872535284801, 4.559259660625716, 4.588855740272495, 4.582482731180545, 4.538569312073491, 4.456241986531136, 4.335402964662078, 4.176791176424548, 3.9820229258052575, 3.7536090083721465, 3.494945591018417, 3.210276791119149, 2.9046276847352788, 2.583707404315177, 2.2537830323427213, 1.921526127915652, 1.593834900739783, 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'2-1216-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.11605662429098, 'root_angle': -0.9469157931327803, 'root_number': '-0.98612625727866648371978672449351815417717280584338291764 - 0.1659970020981381393527349895435655282483329104987432485*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.47345789656639015', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.53988423264868888707884270399', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91838013073248156331484209828', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73976606857255447688193562096', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.7098088857877, 'bad_primes': [2, 19], 'central_character': '19.11', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1216/2/i/r/961/6'], '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': '2-1216-19.11-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': '2-1216-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.11605662429098, 'root_angle': -0.47345789656639015, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.53988423264868888707884270399', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3219685772027326315207150748798', 'Lhash_array': ['3219685772027326315207150748798'], 'label': '2-1216-19.11-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/2/i/r/961/6'}