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lfunc_lfunctions • Show schema
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{'Lhash': '449470766483403018684108666294', 'a10': [55.398330295585744, 31.98424090881223], 'a2': [0.0, -5.23840751109513], 'a3': [-2.334778965219018, 4.642069278195965], 'a4': [-19.440913252297875, 0.0], 'a5': [-6.105718358311851, 10.57541441330216], 'a6': [24.317050573925695, 12.23052366815022], 'a7': [18.423683431684506, 1.8888855997846696], 'a8': [0.0, 59.932165914625], 'a9': [-16.097614367141624, -21.67641141164274], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.7171203303616602, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.334778965219018, -4.642069278195965]]], [7, [[1.0, 0], [-18.423683431684506, -1.8888855997846696]]]], 'bad_primes': [3, 7], 'central_character': '63.38', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '3141375411720761915946602906167', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 5.23840751109513], [-8.0, 0]], [[1.0, 0], [2.334778965219018, 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'7.20724090932399392633932693423067', '8.045224787111196355683108525284872', '8.712150075777611935616458747906800', '10.97301547342553953777945018529307', '12.56330644262582138205235142119445', '13.38492830826442051668247563066712', '14.36778858939291916799241284371458'], 'prelabel': '2-63-63.38-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9279834880936249, 'root_angle': -0.16113129387822075, 'root_number': '0.5298117172416592 - 0.8481152894939721*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.161131293878', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35456991571847931837916822913', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.88282387571897591755444259788', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.52686012223809700216879040740', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.7171203303616602, 'bad_primes': [3, 7], 'central_character': '63.38', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/4/i/a/38/1'], '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': '2-63-63.38-c3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-63-63.38-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9279834880936249, 'root_angle': -0.16113129387822075, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35456991571847931837916822913', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '449470766483403018684108666294', 'Lhash_array': ['449470766483403018684108666294'], 'factors': ['2-63-63.38-c3-0-1'], 'label': '2-63-63.38-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/4/i/a/38/1'}