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lfunc_lfunctions • Show schema
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{'Lhash': '1500131295982684654837649540805', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-14.90175425099138, 25.81059548462257], 'a4': [0, 0], 'a5': [10.5, 18.186533479473212], 'a6': [0, 0], 'a7': [10.410525505948279, -129.22314405202343], 'a8': [0, 0], 'a9': [-322.6245595138793, -558.8021288475679], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.962987819053836, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-10.410525505948279, 129.22314405202343]]]], 'bad_primes': [2, 7], 'central_character': '112.81', 'coefficient_field': 'CDF', 'conductor': 112, 'conductor_radical': 14, 'conjugate': '661399054206355640805119134079', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [14.90175425099138, -25.81059548462257], [-121.5, -210.4441731196186]], [[1.0, 0], [-10.5, -18.186533479473212], [-1562.5, 2706.329386826371]], [[1.0, 0], [-10.410525505948279, 129.22314405202343]], [[1.0, 0], 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'6.00371582937150277955967362630902', '7.01623086320030095955678947199017', '8.100480657984501323333018249978982', '9.360108954720015471134533054460906', '11.08492534294248369308532477309338', '11.88759183238627863435841879443473', '12.60629332957192195714944290484347'], 'prelabel': '2-112-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.2382765151714485, 'root_angle': 0.022880747538142527, 'root_number': '0.98968374596919570144127939816905083139549092283418657921 + 0.1432692673408380042311327049537429126667205352607994895*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.022880747538142527', 'prec': 67}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18339493209927020722461013537', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34166758984774436905838911203', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.05038953382927653831815912440', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.962987819053836, 'bad_primes': [2, 7], 'central_character': '7.4', 'conductor': 112, 'conductor_radical': 14, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/112/6/i/b/81/1'], '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': '2-112-7.4-c5-0-11', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-112-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.2382765151714485, 'root_angle': 0.022880747538142527, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18339493209927020722461013537', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1500131295982684654837649540805', 'Lhash_array': ['1500131295982684654837649540805'], 'factors': ['2-112-7.4-c5-0-11'], 'label': '2-112-7.4-c5-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/112/6/i/b/81/1'}