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lfunc_lfunctions • Show schema
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{'Lhash': '1422120797944579338672946485838', 'a10': [0.367278261403901, 0.63614460926712], 'a2': [0.0, -0.4116913539670642], 'a3': [0.0, 0.0], 'a4': [1.8305102290687654, 0.0], 'a5': [-1.5451978846221104, 0.8921204146378157], 'a6': [0.0, 0.0], 'a7': [2.4483343439394996, 1.0028254784788526], 'a8': [0.0, -1.5769879425900093], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.4483343439394996, -1.0028254784788526]]], [13, [[1.0, 0], [0.09610093219022926, 3.6042703298770706]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.550', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '1751784752924961173548563916192', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.4116913539670642], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5451978846221104, -0.8921204146378157], [2.5, 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'9.256333081033849470516805098445395', '10.52601616368368289091881450207524'], 'prelabel': '2-819-91.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': -0.035317613374977755, 'root_number': '0.9938509664700071 - 0.11072604231450169*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0176588066875', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12185550000018848201714158924', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62482600703991429021831515807', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77402152070178816495513555079', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '91.4', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/bm/h/550/8'], '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': '2-819-91.4-c1-0-18', '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': '2-819-91.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': -0.017658806687488877, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12185550000018848201714158924', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1422120797944579338672946485838', 'Lhash_array': ['1422120797944579338672946485838'], 'label': '2-819-91.4-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/bm/h/550/8'}