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lfunc_lfunctions • Show schema
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{'Lhash': '540664863086294181359391537780', 'a10': [0.3774171655769146, 1.6747116706545129], 'a2': [-0.7509604091550264, -0.1596215625203054], 'a3': [-1.6986460500974103, -0.33852857558626614], 'a4': [-1.288628422388341, -0.573734338351174], 'a5': [-0.9343844820308121, -2.0314836055799246], 'a6': [1.2215794725978675, 0.5253620943184243], 'a7': [-1.5411527103970484, 2.669354796630172], 'a8': [2.1183536200683375, 1.5390739943337577], 'a9': [2.7707968070230673, 1.1500804555294273], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.6986460500974103, 0.33852857558626614]]], [5, [[1.0, 0], [0.9343844820308121, 2.0314836055799246]]]], 'bad_primes': [3, 5], 'central_character': '225.106', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1818513085438536930016796066288', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[[1.0, 0], [5.534505114145827, -2.4641204358045163], [55.53784032778523, -61.68102051462372]], [[1.0, 0], [0.6710501076148581, 2.065279868825931], [-72.00251249937033, 52.31288745403011]], [[1.0, 0], [1.6497126711253542, 15.695967597835663], [-94.88031727117915, 20.167434009322655]], [[1.0, 0], [3.002309328445406, -5.200152296905439], [-50.5, -87.4685657822283]], [[1.0, 0], [-12.625860471994457, -5.621395258835106], [68.9204524549624, 76.5439170241716]], [[1.0, 0], [-8.627388177622375, 0], [107.0, 0]], [[1.0, 0], [5.906807409088239, -18.17928392021569], [-88.18285238686927, -64.06859249987957]], [[1.0, 0], [-3.0558928192118073, 0.6495500704837723], [103.2306367136139, -45.96124066756542]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-15e2-225.106-c1-0-1', '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': 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'root_number': '0.3671778873361526 - 0.9301507399617331*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.190162013282', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42650937331544843851679065490', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.56779014218296693277460121617', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.43947323940957521559289285989', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '225.106', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/q/a/106/11'], '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': '2-15e2-225.106-c1-0-1', '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': '2-15e2-225.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.19016201328155966, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.42650937331544843851679065490', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '540664863086294181359391537780', 'Lhash_array': ['540664863086294181359391537780'], 'label': '2-15e2-225.106-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/q/a/106/11'}