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lfunc_lfunctions • Show schema
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{'Lhash': '841148686547650405067675454441', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-0.26810366252622975, 0.46436916519073], 'a6': [0, 0], 'a7': [2.350141784452185, 4.070564975661769], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.596298938554515, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '3456.2305', 'coefficient_field': 'CDF', 'conductor': 3456, 'conductor_radical': 6, 'conjugate': '2027763028280967188512935983595', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.26810366252622975, -0.46436916519073], [-2.5, -4.330127018922194]], [[1.0, 0], [-2.350141784452185, -4.070564975661769], [-3.5, 6.06217782649107]], [[1.0, 0], [-2.599221106970559, -4.501983017378428], [-5.5, 9.526279441628825]], [[1.0, 0], [0.7782952696544437, 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'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3456/2/i/l/2305/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.0319853562230348, 1.8844726627495614, 1.7329706309886015, 1.5779734306217323, 1.4199834768220871, 1.2595632092884506, 1.097384904979249, 0.9342754108571486, 0.7712531340117348, 0.6095551993474421, 0.4506533025310511, 0.2962573849572003, 0.14830679667378058, 0.008949073634879692, -0.11949316314009677, -0.234566365501486, -0.3337401899041094, -0.4144702918863157, -0.4742682659194606, -0.5107770204272198, -0.5218496959013832, -0.505630065396767, -0.46063220731271437, -0.3858171188753546, -0.2806638551510588, -0.14523274315302973, 0.019781756453870564, 0.21301087774368208, 0.4323862422625243, 0.6751313488264006, 0.937771471811141, 1.216163179642036, 1.5055442116155828, 1.8006039116412538, 2.0955738231584546, 2.384337414703174, 2.660557247612772, 2.9178172359299204, 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'root_angle': -0.6476672348620007, 'root_number': '-0.44744853823472904881000187567106189304389210286556179929 - 0.89430968105662605340250353704281310845519687841778222220*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32383361743100036', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66354931429544461399890342167', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.31466366077842552458454229784', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84692279000353876433265707077', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.596298938554515, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 3456, 'conductor_radical': 6, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3456/2/i/l/2305/3'], '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': '2-3456-9.4-c1-0-15', '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': '2-3456-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.253217960312947, 'root_angle': -0.32383361743100036, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66354931429544461399890342167', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '841148686547650405067675454441', 'Lhash_array': ['841148686547650405067675454441'], 'label': '2-3456-9.4-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3456/2/i/l/2305/3'}