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lfunc_lfunctions • Show schema
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{'Lhash': '2272473133969473644730031840180', 'a10': [2.594644523757836, -1.7628272924978807], 'a2': [-0.12774173524969917, 1.4084324794165306], 'a3': [0.881921264348355, -0.47139673682599764], 'a4': [-1.9673640981507916, -0.3598312178054076], 'a5': [-1.4071338040884374, -1.714597501255782], 'a6': [0.551272322175234, 1.302343590149514], 'a7': [0.0127962059507938, -0.008550151462736228], 'a8': [0.7581124780308814, -2.7249340305141105], 'a9': [0.5555702330196022, -0.8314696123025452], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.12774173524969917, -1.4084324794165306]]], [3, [[1.0, 0], [-0.881921264348355, 0.47139673682599764]]]], 'bad_primes': [2, 3], 'central_character': '384.229', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '1132913614481554524743175788463', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[[1.0, 0], [5.5184953753799855, -0.5435243539411957], [81.40517827346812, -16.192496727338646]], [[1.0, 0], [6.608957799474155, 1.3146034418056591], [82.22527839350452, 34.05882548049299]], [[1.0, 0], [-10.023638415531437, -10.023638415531437], [0, 97.0]], [[1.0, 0], [-0.627601060116727, 6.372140498809081], [-99.05931332072628, -19.704122523628953]], [[1.0, 0], [-2.141737784268602, 10.767242944631654], [-95.15959184866253, -39.41639353360425]], [[1.0, 0], [-7.004129214075693, 13.103804098705456], [-59.44601493309744, -88.96724851637234]], [[1.0, 0], [-0.6117386673477294, -6.211086922270274], [-106.90559556395212, 21.26484509975798]], [[1.0, 0], [-10.638017719524129, -4.406411216192198], [79.90306627407988, 79.90306627407988]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-384-128.101-c1-0-20', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 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0.09216363922309638, 'root_number': '0.9583751374415505 + 0.2855119891246061*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0460818196115', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79266521355358861184362368634', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.31662301241413692925169780592', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88932087137612894784119966176', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'bad_primes': [2, 3], 'central_character': '128.101', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/2/v/a/229/15'], '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': '2-384-128.101-c1-0-20', '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': '2-384-128.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': 0.04608181961154819, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79266521355358861184362368634', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2272473133969473644730031840180', 'Lhash_array': ['2272473133969473644730031840180'], 'label': '2-384-128.101-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/2/v/a/229/15'}