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lfunc_lfunctions • Show schema
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{'Lhash': '925190053997631038009373021583', 'a10': [2054.4479452907326, -3972.3096103011267], 'a2': [7.350216419047754, -14.211766906094429], 'a3': [0, 0], 'a4': [-147.9486371863216, -208.91912491370954], 'a5': [279.5084971874737, 0], 'a6': [0, 0], 'a7': [0, 3540.6980544788466], 'a8': [-4056.5644077215056, 567.0107635725002], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 73.32814981100293, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-7.350216419047754, 14.211766906094429]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-279.5084971874737, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '180.91', 'coefficient_field': 'CDF', 'conductor': 180, 'conductor_radical': 30, 'conjugate': '990619705021929349071107186618', 'degree': 2, 'euler_factors': [[[1.0, 0], [-7.350216419047754, 14.211766906094429]], [[1.0, 0], [0, 0]], [[1.0, 0], [-279.5084971874737, 0]], [[1.0, 0], [0, -3540.6980544788466], 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'0.5779243640090687868202414838589329953456238320155589198 + 0.8160903316941779321285424418783914640434511673883801749*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.15193142917720032', 'prec': 64}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72984626349804801268315447527', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.55984629109237760186142805124', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16569406134087982741645422761', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 73.32814981100293, 'bad_primes': [2, 3, 5], 'central_character': '4.3', 'conductor': 180, 'conductor_radical': 30, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/180/9/c/a/91/11'], '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': '2-180-4.3-c8-0-40', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-180-4.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.563185727928767, 'root_angle': 0.15193142917720032, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '0.72984626349804801268315447527', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '925190053997631038009373021583', 'Lhash_array': ['925190053997631038009373021583'], 'factors': ['2-180-4.3-c8-0-40'], 'label': '2-180-4.3-c8-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/180/9/c/a/91/11'}