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lfunc_lfunctions • Show schema
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{'Lhash': '932138935509962501085247237626,965986415387047977421342127406', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2141.9580828194785, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 2, 1]], [23, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '5796.1', 'coefficient_field': '1.1.1.1', 'conductor': 33593616, 'conductor_radical': 966, 'degree': 4, 'euler_factors': [[1], [1], [1, -1, 9, -5, 25], [1, 2, 1], [1, -6, 31, -66, 121], [1, 1, 25, 13, 169], [1, 0, -11, 0, 289], [1, 4, 37, 76, 361], [1, -2, 1], [1, -8, 69, -232, 841], [1, 6, 71, 186, 961], [1, -10, 79, -370, 1369], [1, -6, 11, -246, 1681], [1, 7, 67, 301, 1849], [1, -14, 138, -658, 2209], [1, -3, 47, -159, 2809], [1, -17, 189, -1003, 3481], [1, -5, 117, -305, 3721], [1, 7, 45, 469, 4489], [1, -7, 153, -497, 5041], [1, -8, 157, -584, 5329], [1, 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['0.73532796445813936415379525243130', '0.76202891807342699441491496494158', '1.78443794178621808871467510211766', '2.03402978391882401862834238524346', '2.54808807299819027260777583289839', '2.97372072573913305483302064346870', '3.60467791695951807820240116993541', '3.88443672459926241105274017623304', '4.27125519440573059816496619224826', '4.38831192486960473502742275337027', '5.28604983352227562016277925962608', '5.33546866402550345257446633865974', '5.98811959682143940937268491732661', '6.16326257762804670589160905582779', '6.53321223720773139165057428001447', '6.72141782362359993198264871261114', '7.23504956966065202411745843266712', '7.43763539432361394242654250639191', '8.019869663907959982211528225933128', '8.251085227317418494539049818839598'], 'prelabel': '4-5796e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.803035573296243, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2141.9580828194785, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 33593616, 'conductor_radical': 966, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 6, 0, -1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, -8, 0, 0, 0, 8, 0, -6, 0, 0, 0, -2, 0, 10, 0, 0, 0, 6, 0, -7, 0, 0, 0, 14, 0, 3, 0, 0, 0, 3, 0, 6, 0, 0, 0, 17, 0, 5, 0, 0, 0, -1, 0, -7, 0, 0, 0, 7, 0, 8, 0, 0, 0, -12, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 9, 0, 2, 0, 0, 0, -4, 0, 2, 0, 0, 0], 'euler11': [1, -6, 31, -66, 121], 'euler13': [1, 1, 25, 13, 169], 'euler17': [1, 0, -11, 0, 289], 'euler19': [1, 4, 37, 76, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -2, 1, 0, 0], 'euler29': [1, -8, 69, -232, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 6, 71, 186, 961], 'euler37': [1, -10, 79, -370, 1369], 'euler41': [1, -6, 11, -246, 1681], 'euler43': [1, 7, 67, 301, 1849], 'euler47': [1, -14, 138, -658, 2209], 'euler5': [1, -1, 9, -5, 25], 'euler53': [1, -3, 47, -159, 2809], 'euler59': [1, -17, 189, -1003, 3481], 'euler61': [1, -5, 117, -305, 3721], 'euler67': [1, 7, 45, 469, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, -7, 153, -497, 5041], 'euler73': [1, -8, 157, -584, 5329], 'euler79': [1, 0, 113, 0, 6241], 'euler83': [1, -6, 155, -498, 6889], 'euler89': [1, -9, 47, -801, 7921], 'euler97': [1, -2, 15, -194, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -1, 9, -5, 25], [1, 2, 1, 0, 0], [1, -6, 31, -66, 121], [1, 1, 25, 13, 169], [1, 0, -11, 0, 289], [1, 4, 37, 76, 361], [1, -2, 1, 0, 0], [1, -8, 69, -232, 841], [1, 6, 71, 186, 961], [1, -10, 79, -370, 1369], [1, -6, 11, -246, 1681], [1, 7, 67, 301, 1849], [1, -14, 138, -658, 2209], [1, -3, 47, -159, 2809], [1, -17, 189, -1003, 3481], [1, -5, 117, -305, 3721], [1, 7, 45, 469, 4489], [1, -7, 153, -497, 5041], [1, -8, 157, -584, 5329], [1, 0, 113, 0, 6241], [1, -6, 155, -498, 6889], [1, -9, 47, -801, 7921], [1, -2, 15, -194, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5796/2/a/l'], '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': '4-5796e2-1.1-c1e2-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-5796e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.803035573296243, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 280474851339126953, 'z1': {'__RealLiteral__': 0, 'data': '0.73532796445813936415379525243', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '932138935509962501085247237626,965986415387047977421342127406', 'Lhash_array': ['932138935509962501085247237626', '965986415387047977421342127406'], 'label': '4-5796e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5796/2/a/l'}