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lfunc_lfunctions • Show schema
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{'Lhash': '647600668974971535881247065756', 'a10': [0, 0], 'a2': [0, -1.0], 'a3': [0, 1.0], 'a4': [1.0, 0], 'a5': [0, 0], 'a6': [1.0, 0], 'a7': [0, 4.47213595499958], 'a8': [0, -3.0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1249', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'conjugate': '2200623032471352571918998329745', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0], [-2.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -4.47213595499958], [-7.0, 0]], [[1.0, 0], [1.2360679774997898, 0], [11.0, 0]], [[1.0, 0], [0, -5.618033988749895], [-13.0, 0]], [[1.0, 0], [0, 3.8541019662496847], [-17.0, 0]], [[1.0, 0], [1.2360679774997898, 0], [19.0, 0]], [[1.0, 0], [0, -4.47213595499958], [-23.0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-1875-5.4-c1-0-16', 'leading_term': '1.526029918187144374562978635130845207661862623322037274', '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/1875/2/b/b/1249/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.5260299181871444, 1.395222657585214, 1.2599371535540858, 1.120059320812925, 0.9754610749808612, 0.8260431437757019, 0.6717779945710213, 0.512750849439558, 0.3491970062580569, 0.18153401100435332, 0.010387579640542948, -0.1633894952657914, -0.3387059259614733, -0.5142282365395011, -0.6883848536040331, -0.8593779045832023, -1.0252025448593418, -1.183673548357697, -1.3324588132463584, -1.4691193455519067, -1.5911551831262278, -1.6960566083481148, -1.7813598709967902, -1.8447065059836953, 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'6.85336717989599064275562177001554', '7.37666483402319331323341725819306', '8.033322906077083722415177073716056', '8.538711363551930427398033324360477'], 'prelabel': '2-1875-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': -0.5, 'root_number': '0.e-55 - 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51086684994932886118052218610', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.85584500361446718580802985438', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06369048533634157723613553442', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/b/b/1249/2'], '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': '2-1875-5.4-c1-0-16', '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': '2-1875-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51086684994932886118052218610', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '647600668974971535881247065756', 'Lhash_array': ['647600668974971535881247065756'], 'label': '2-1875-5.4-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/b/b/1249/2'}