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lfunc_lfunctions • Show schema
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{'Lhash': '325271808987225237322342215014', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 7.379420310750413], 'a6': [0, 0], 'a7': [1.2661083604218115, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.542294840729653, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '864.161', 'coefficient_field': 'CDF', 'conductor': 864, 'conductor_radical': 6, 'conjugate': '2485178742880701897479942035072', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -7.379420310750413], [-25.0, 0]], [[1.0, 0], [-1.2661083604218115, 0], [49.0, 0]], [[1.0, 0], [0, -5.82842712474619], [-121.0, 0]], [[1.0, 0], [10.48528137423857, 0], [169.0, 0]], [[1.0, 0], [0, -18.339935850985803], [-289.0, 0]], [[1.0, 0], [20.872152571829425, 0], [361.0, 0]], [[1.0, 0], [0, 20.48528137423857], 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'4.40979757213520169153261040079220', '4.93688857640087056998332056554125', '5.88619593876182706671158144287522', '7.02040550135559155310762557725051', '8.107388488416502439851327509001087', '8.619708354032375203386299833847533', '9.504650142515587180090263880537565'], 'prelabel': '2-864-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8520402760828, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25659421368053854390674822334', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.51324066690022645921240430737', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92662509774570393933209609099', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.542294840729653, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 864, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/864/3/e/e/161/8'], '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': '2-864-3.2-c2-0-4', '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': '2-864-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8520402760828, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.25659421368053854390674822334', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '325271808987225237322342215014', 'Lhash_array': ['325271808987225237322342215014'], 'label': '2-864-3.2-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/864/3/e/e/161/8'}