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lfunc_lfunctions • Show schema
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{'Lhash': '868828119229485258387249343398', 'a10': [-1.6901092616023063, 0.0], 'a2': [-1.893761068078563, 0.0], 'a3': [1.0, 0.0], 'a4': [1.5863309829700598, 0.0], 'a5': [0.8924617208004573, 0.0], 'a6': [-1.893761068078563, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.783390279521629, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.338907677352424, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7, 13], 'central_character': '3549.1', 'coefficient_field': 'CDF', 'conductor': 3549, 'conductor_radical': 273, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.893761068078563, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.8924617208004573, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [5.277067130929286, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.759658147764461, 0], [17.0, 0]], [[1.0, 0], [-0.6392337045666773, 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'3.62871755309855251058453702224259', '4.90173956059810341306842612917385', '5.57915532206786499403723215915122', '6.64971878422027501440298329550535', '7.53200225251327355645500155727181', '7.87993210277412583783148036180549', '8.540102466551755913998982488778109'], 'prelabel': '2-3549-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3234300669166705, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68538453661684091483890945868', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.89445839593021344095608396491', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.71139688755497541935429975934', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.338907677352424, 'bad_primes': [3, 7, 13], 'central_character': '1.1', 'conductor': 3549, 'conductor_radical': 273, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3549/2/a/bh/1/4'], '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': '2-3549-1.1-c1-0-31', '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': '2-3549-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3234300669166705, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68538453661684091483890945868', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '868828119229485258387249343398', 'Lhash_array': ['868828119229485258387249343398'], 'label': '2-3549-1.1-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3549/2/a/bh/1/4'}