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lfunc_lfunctions • Show schema
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{'Lhash': '949831135558522773293429590211', 'a10': [-1.23880726922417, 1.290452391161238e-61], 'a2': [1.0728385655409598, -0.619403634612085], 'a3': [-1.4821885136542443, -0.8961680701695536], 'a4': [-0.23267827485867723, 0.4030105938727051], 'a5': [-0.8660254037844386, -0.5], 'a6': [-2.145238758736426, -0.04337071434659101], 'a7': [-0.16662906883422993, 0.09620333774625933], 'a8': [0.0, 3.054101615019278], 'a9': [1.3937655800171562, 2.656580039818006], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.4821885136542443, 0.8961680701695536]]], [5, [[1.0, 0], [0.8660254037844386, 0.5]]], [13, [[1.0, 0], [-2.6209471772688584, -2.4760120948748217]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.571', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '1874489238575124143765878891935', 'degree': 2, 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[-109.0, 0]], [[1.0, 0], [-1.2797497058092167, 2.216591511432887], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-585-117.103-c1-0-17', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/37', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3484769598571937, 1.2248978080539676, 1.0738734965932486, 0.8861591203399599, 0.6509192577484176, 0.35759830296945183, -0.002259844309861703, -0.4333981916037405, -0.9355035924911398, -1.5021788200929331, -2.1202968093988317, -2.7698311069609733, -3.4242647592773987, -4.051660430111909, -4.616427396365754, -5.081750844359445, -5.412563221809466, -5.578846477147907, -5.558970122469881, -5.3427067107976995, -4.933536850980015, -4.349871540633033, -3.62488743666912, 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'5.93463304224928079289635735488148', '6.66251894364049738688547883829227', '7.74494457414787650391893680354263', '9.010392275886328383485156873950119', '10.09580398337278648667076466901146', '10.50278254331575582778735590774840'], 'prelabel': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.13506886815092767, 'root_number': '0.9113142218371872 - 0.4117115362450776*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0675344340755', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74928464940379784950942610905', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.31694319611160235438545494446', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.20383054557145836568341362524', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '117.103', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/37'], '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': '2-585-117.103-c1-0-17', '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': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.06753443407546383, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74928464940379784950942610905', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '949831135558522773293429590211', 'Lhash_array': ['949831135558522773293429590211'], 'label': '2-585-117.103-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/37'}