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lfunc_lfunctions • Show schema
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{'Lhash': '2072587337052158867679617258151', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.3176305290207164, 0.0], 'a4': [0.0, 0.0], 'a5': [6.101486712052302, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.573126585371459, 0.0], 'a8': [0.0, 0.0], 'a9': [-21.628588730951154, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.11384888555694, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 11], 'central_character': '968.1', 'coefficient_field': 'CDF', 'conductor': 968, 'conductor_radical': 22, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.3176305290207164, 0], [27.0, 0]], [[1.0, 0], [-6.101486712052302, 0], [125.0, 0]], [[1.0, 0], [4.573126585371459, 0], [343.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-47.50499679102513, 0], [2197.0, 0]], [[1.0, 0], [63.6174856024764, 0], [4913.0, 0]], [[1.0, 0], [18.450266685544005, 0], [6859.0, 0]], [[1.0, 0], 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'4.77886845999885543229021135350712', '6.02665647192699874197266937284427', '6.36753396874683770259723914641140', '7.70601778562587214935608358191922', '8.511727714492069974788728344829354', '9.117594225424453294753263717043129'], 'prelabel': '2-968-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.5573705007467336, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63498312285657234579690254152', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69199020785660166340275213416', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65365201529648490327149055823', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.11384888555694, 'bad_primes': [2, 11], 'central_character': '1.1', 'conductor': 968, 'conductor_radical': 22, 'degree': 2, 'index': 68, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/968/4/a/o/1/6'], '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': '2-968-1.1-c3-0-68', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-968-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.5573705007467336, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63498312285657234579690254152', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2072587337052158867679617258151', 'Lhash_array': ['2072587337052158867679617258151'], 'label': '2-968-1.1-c3-0-68', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/968/4/a/o/1/6'}