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lfunc_lfunctions • Show schema
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{'Lhash': '2935256121998053525010984069461', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.6660601710109255, -1.5988632989073508], 'a4': [0.0, 0.0], 'a5': [-0.46816914347639776, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.390068981540561, 1.1347115331561877], 'a8': [0.0, 0.0], 'a9': [-2.1127276971857936, -2.1298783245866453], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.024460261872533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.6660601710109255, 1.5988632989073508]]], [7, [[1.0, 0], [2.390068981540561, -1.1347115331561877]]]], 'bad_primes': [2, 3, 7], 'central_character': '504.457', 'coefficient_field': 'CDF', 'conductor': 504, 'conductor_radical': 42, 'conjugate': '608130381285153713768118904984', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.6660601710109255, 1.5988632989073508]], [[1.0, 0], [0.46816914347639776, 0], [5.0, 0]], [[1.0, 0], [2.390068981540561, 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'8.804327551878322633338225966541790', '9.651566037486263455706650239048769', '10.14206535067015832386450725821335', '11.19563634384176419637905735909715'], 'prelabel': '2-504-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': 0.8122441100234755, 'root_number': '-0.831022719617933 + 0.5562384735693985*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.406122055012', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.31550880145490116684722383587', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.66364804165151032914956567720', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.34574272046265913481620108220', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.024460261872533, 'bad_primes': [2, 3, 7], 'central_character': '63.16', 'conductor': 504, 'conductor_radical': 42, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/504/2/t/c/457/7'], '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': '2-504-63.16-c1-0-21', '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': '2-504-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': 0.40612205501173776, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.31550880145490116684722383587', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2935256121998053525010984069461', 'Lhash_array': ['2935256121998053525010984069461'], 'label': '2-504-63.16-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/504/2/t/c/457/7'}