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lfunc_lfunctions • Show schema
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{'Lhash': '2655861406671391549391326242841', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.5, -2.598076211353316], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-4.5, -7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.02183954438546, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.5, 2.598076211353316]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.557', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '377710517444552870979474492249', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, 2.598076211353316]], [[1.0, 0], [0, 0], [12.5, -21.650635094610966]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [60.5, 104.78907385791707]], [[1.0, 0], [22.0, 0], [169.0, 0]], [[1.0, 0], [0, 0], [144.5, 250.28134169370276]], [[1.0, 0], [13.0, 22.516660498395403], [-180.5, 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'3.20254896310358304500820519513333', '4.38849390343872713736224695248937', '5.12273017027325649984311164229590', '6.34266505967319717829527087005500', '7.58279288877201456951900338993332', '8.318516202391227996821782381265012', '9.251823007726348740135108796656395', '10.17092957099179829229765038956548', '10.46585338978960106948698527716254'], 'prelabel': '2-588-21.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.002729012109795, 'root_angle': 0.9596540938921078, 'root_number': '-0.99197791640852265169404803750682485961305798168199772605 + 0.1264112865127400184730959576238026966982488495928982352*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4798270469460539', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.09510523340834369967397111383', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20254896310358304500820519513', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38849390343872713736224695249', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.02183954438546, 'bad_primes': [2, 3, 7], 'central_character': '21.11', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/3/p/c/557/1'], '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': '2-588-21.11-c2-0-24', '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': '2-588-21.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.002729012109795, 'root_angle': 0.4798270469460539, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.09510523340834369967397111383', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2655861406671391549391326242841', 'Lhash_array': ['2655861406671391549391326242841'], 'label': '2-588-21.11-c2-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/3/p/c/557/1'}