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lfunc_lfunctions • Show schema
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{'Lhash': '2190728342343217548159728504492', 'a10': [0.0, 0.0], 'a2': [1.2360679774997898, 3.804226065180614], 'a3': [-5.205003597931286, -3.7816564723179957], 'a4': [-12.94427190999916, 9.40456403667957], 'a5': [0.0, 0.0], 'a6': [7.952537851377038, -24.47539482394617], 'a7': [0.0, 0.0], 'a8': [-51.77708763999664, -37.61825614671828], 'a9': [-12.239239764517695, -37.668506730796835], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.096556751378303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.2360679774997898, -3.804226065180614]]], [11, [[1.0, 0], [-88.43271641723597, 82.58725487064407]]]], 'bad_primes': [2, 11], 'central_character': '88.27', 'coefficient_field': 'CDF', 'conductor': 88, 'conductor_radical': 22, 'conjugate': '636471255558409931075985750031', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2360679774997898, -3.804226065180614]], [[1.0, 0], [5.205003597931286, 3.7816564723179957], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 26, 'label': '2-88-88.27-c4-0-26', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/88/5/l/a/27/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0302204173300258, 1.2015540473904112, 1.3355094027312575, 1.4307721190130795, 1.4862249499041944, 1.5009987406335876, 1.4745674641995863, 1.4068809877423023, 1.2985258689922452, 1.1509015113017598, 0.9663965467674108, 0.7485484843118485, 0.5021685801939362, 0.23341370948368376, -0.050212098336042635, -0.3399416862759296, -0.6259261161743342, -0.8975201893087724, -1.1436726842154379, -1.3534142815326164, -1.5164276091686186, -1.6236747994390086, -1.6680490181173855, -1.6450083544486434, -1.5531440977193678, -1.3946316535402423, -1.1755120161622494, -0.9057555284468574, 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'11.42481984426347225413708970691859', '12.31597338709382909582349466066108', '13.37554395300911761552621842817074'], 'prelabel': '2-88-88.27-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0160498589012588, 'root_angle': 0.27544133587587344, 'root_number': '0.6483931234217681 + 0.7613056925436482*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.137720667938', 'prec': 47}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72817994323419724176108238975', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.72875331657343385969811507061', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.94880012874282611074601569698', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.096556751378303, 'bad_primes': [2, 11], 'central_character': '88.27', 'conductor': 88, 'conductor_radical': 22, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/88/5/l/a/27/1'], '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': '2-88-88.27-c4-0-26', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-88-88.27-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0160498589012588, 'root_angle': 0.13772066793793672, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72817994323419724176108238975', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2190728342343217548159728504492', 'Lhash_array': ['2190728342343217548159728504492'], 'label': '2-88-88.27-c4-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/88/5/l/a/27/1'}