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lfunc_lfunctions • Show schema
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{'Lhash': '1369432543590936191359156602051', 'a10': [1.3781074994199958, 0.10319775333257945], 'a2': [-0.19098300562505258, 0.5877852522924731], 'a3': [0.36327126400268045, 2.293604493334841], 'a4': [1.3090169943749475, 0.9510565162951535], 'a5': [-0.5302487364574218, -2.1722882583776277], 'a6': [-1.4175255336304136, -0.2245139882897927], 'a7': [0.0, 2.344576516755256], 'a8': [-1.8090169943749475, 1.314327780297834], 'a9': [-2.2754860117102074, 0.7393502237071081], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.595138065691614, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.5302487364574218, 2.1722882583776277]]], [13, [[1.0, 0], [2.235135560135566, -2.8291640157151496]]]], 'bad_primes': [5, 13], 'central_character': '325.203', 'coefficient_field': 'CDF', 'conductor': 325, 'conductor_radical': 65, 'conjugate': '3152696572076172550426801626613', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.19098300562505258, 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[-25.648410533120636, 78.93769085249775]], [[1.0, 0], [0.837435758717828, -0.42669483138340936], [52.31288745403011, -72.00251249937033]], [[1.0, 0], [11.46203423988236, 8.327655332728135], [29.974648454369902, 92.2524820806299]], [[1.0, 0], [0, -9.984565952679564], [-101.0, 0]], [[1.0, 0], [8.579135811268031, -1.3588016239358738], [97.95882117840081, -31.828750420619585]], [[1.0, 0], [-12.124542072270295, 12.124542072270295], [0, -107.0]], [[1.0, 0], [-4.971524826762882, -2.53311842202907], [64.06859249987957, 88.18285238686927]], [[1.0, 0], [-6.964119188492165, 13.667853480924729], [-66.41973350904946, -91.41892036436906]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-325-325.203-c1-0-7', '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/325/2/z/a/203/1', 'plot_delta': 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.362999951628', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08029179597625863256144594285', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45433185370204295706983343722', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52565775190321141898340095563', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.595138065691614, 'bad_primes': [5, 13], 'central_character': '325.203', 'conductor': 325, 'conductor_radical': 65, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/325/2/z/a/203/1'], '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': '2-325-325.203-c1-0-7', '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': '2-325-325.203-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.610943222367447, 'root_angle': -0.36299995162753307, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08029179597625863256144594285', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1369432543590936191359156602051', 'Lhash_array': ['1369432543590936191359156602051'], 'label': '2-325-325.203-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/325/2/z/a/203/1'}