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lfunc_lfunctions • Show schema
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{'Lhash': '1842300044094744087767086406783', 'a10': [-2.0, -1.2350118326279651e-60], 'a2': [-0.8090169943749475, 0.5877852522924731], 'a3': [-0.30901699437494745, -0.9510565162951535], 'a4': [-0.30901699437494745, 0.9510565162951535], 'a5': [1.618033988749895, 1.1755705045849463], 'a6': [0.8090169943749475, 0.5877852522924731], 'a7': [1.2360679774997898, -3.804226065180614], 'a8': [-0.9270509831248422, -2.853169548885461], 'a9': [-0.8090169943749475, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8985695933724793, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.30901699437494745, 0.9510565162951535]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '363.124', 'coefficient_field': 'CDF', 'conductor': 363, 'conductor_radical': 33, 'conjugate': '1378949915197278199769597748251', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8090169943749475, -0.5877852522924731], 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['1.45331848047328978567482974789406', '2.76978359856214426281299607855502', '4.84801067984529428985842469974033', '5.41176829238472466554664166834668', '6.31574932757034554537252582885229', '8.246268470036361314252354269463927', '9.012676679030885163482067928499018', '9.460846099457401586346010017682540', '10.38832560941731692992475797034289', '11.40856045521685175147980469805787'], 'prelabel': '2-363-11.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7025186029446138, 'root_angle': 0.014565739860786438, 'root_number': '0.9958150363582329 + 0.09139153879244684*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0145657398608', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45331848047328978567482974789', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76978359856214426281299607856', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.84801067984529428985842469974', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8985695933724793, 'bad_primes': [3, 11], 'central_character': '11.3', 'conductor': 363, 'conductor_radical': 33, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/363/2/e/e/124/1'], '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': '2-363-11.3-c1-0-8', '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': '2-363-11.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7025186029446138, 'root_angle': 0.014565739860786438, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45331848047328978567482974789', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1842300044094744087767086406783', 'Lhash_array': ['1842300044094744087767086406783'], 'factors': ['2-363-11.3-c1-0-8'], 'label': '2-363-11.3-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/363/2/e/e/124/1'}