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lfunc_lfunctions • Show schema
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{'Lhash': '562471686879238805604524662756', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-11.0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.63765008224431, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [13.0, -13.856406460551018]]]], 'bad_primes': [2, 3, 19], 'central_character': '684.217', 'coefficient_field': 'CDF', 'conductor': 684, 'conductor_radical': 114, 'conjugate': '1558550655780939911153601300191', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-12.5, -21.650635094610966]], [[1.0, 0], [11.0, 0], [49.0, 0]], [[1.0, 0], [0, 0], [121.0, 0]], [[1.0, 0], [-22.5, 12.99038105676658], [84.5, -146.35829323957014]], [[1.0, 0], [0, 0], [-144.5, -250.28134169370276]], [[1.0, 0], [13.0, -13.856406460551018]], [[1.0, 0], [0, 0], [-264.5, 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['0.44371192407274583291046544366020', '2.24360501495517763523392124813735', '3.53294852899361318296913311926859', '4.27690279885097168009028848205268', '5.90565837167600327482695798339079', '6.40952927209120542109622744321681', '7.25627531938221094505396265960020', '8.666043772186825028148405398702105', '9.094984965812344253487554075683964', '10.07134004508359129576049360505180'], 'prelabel': '2-684-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.317134475811972, 'root_angle': -0.45797369550178574, 'root_number': '0.131646278341163103906236589252720341733321310337180589 - 0.9912967554667578000017655039864946507638514853046182621*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.22898684775089287', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44371192407274583291046544366', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24360501495517763523392124814', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53294852899361318296913311927', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.63765008224431, 'bad_primes': [2, 3, 19], 'central_character': '19.8', 'conductor': 684, 'conductor_radical': 114, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/684/3/y/c/217/1'], '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': '2-684-19.8-c2-0-2', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-684-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.317134475811972, 'root_angle': -0.22898684775089287, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44371192407274583291046544366', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '562471686879238805604524662756', 'Lhash_array': ['562471686879238805604524662756'], 'label': '2-684-19.8-c2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/684/3/y/c/217/1'}