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lfunc_lfunctions • Show schema
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{'Lhash': '1493472610141200436337251823352,1641273775651942641952869757078', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -4, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1353.876826855227, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '4608.1', 'coefficient_field': '1.1.1.1', 'conductor': 21233664, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 4, 12, 20, 25], [1, 4, 16, 28, 49], [1, -4, 26, -44, 121], [1, 0, 18, 0, 169], [1, -4, 6, -68, 289], [1, 0, 6, 0, 361], [1, -8, 54, -184, 529], [1, 4, 60, 116, 841], [1, 12, 96, 372, 961], [1, 8, 58, 296, 1369], [1, -12, 86, -492, 1681], [1, -8, 70, -344, 1849], [1, -8, 38, -376, 2209], [1, 4, 12, 212, 2809], [1, 8, 134, 472, 3481], [1, 8, 106, 488, 3721], [1, -16, 198, -1072, 4489], [1, -24, 278, -1704, 5041], [1, -8, 130, -584, 5329], [1, 20, 240, 1580, 6241], [1, 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'1.29473671637629931787079199585559', '2.53779806018088467459933808296961', '2.60043140340997059868422639638284', '3.55151630954207785930339717133422', '3.55820281626850075455067063818167', '3.87363686950431121127608338069609', '3.98860244767094249152022917354843', '4.92519029247021365464585717932800', '5.02831703732541069481056573312245', '5.67642853441712098474378789025826', '5.95494801008077829095745797459917', '6.43581499984762172646290301149901', '6.76125500524777023911826131943007', '7.22745404745803242089590525531657', '7.29654440008988167172121262173208', '7.82558676650077260235677786110460', '7.88167858710803595727087085594537'], 'prelabel': '4-4608e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.065893606996913, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 67577992298361281, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17814215515877463189567270695', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.29473671637629931787079199586', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.53779806018088467459933808297', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1353.876826855227, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 21233664, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -4, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, -4, 0, -12, 0, 0, 0, 16, 0, -8, 0, 0, 0, 12, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, -4, 0, -16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, 16, 0, 0, 0, 24, 0, 8, 0, 0, 0, -16, 0, -20, 0, 0, 0, -4, 0, -16, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, -4, 26, -44, 121], 'euler13': [1, 0, 18, 0, 169], 'euler17': [1, -4, 6, -68, 289], 'euler19': [1, 0, 6, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -8, 54, -184, 529], 'euler29': [1, 4, 60, 116, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 12, 96, 372, 961], 'euler37': [1, 8, 58, 296, 1369], 'euler41': [1, -12, 86, -492, 1681], 'euler43': [1, -8, 70, -344, 1849], 'euler47': [1, -8, 38, -376, 2209], 'euler5': [1, 4, 12, 20, 25], 'euler53': [1, 4, 12, 212, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, 8, 106, 488, 3721], 'euler67': [1, -16, 198, -1072, 4489], 'euler7': [1, 4, 16, 28, 49], 'euler71': [1, -24, 278, -1704, 5041], 'euler73': [1, -8, 130, -584, 5329], 'euler79': [1, 20, 240, 1580, 6241], 'euler83': [1, 4, 42, 332, 6889], 'euler89': [1, 4, 182, 356, 7921], 'euler97': [1, -4, 70, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 4, 12, 20, 25], [1, 4, 16, 28, 49], [1, -4, 26, -44, 121], [1, 0, 18, 0, 169], [1, -4, 6, -68, 289], [1, 0, 6, 0, 361], [1, -8, 54, -184, 529], [1, 4, 60, 116, 841], [1, 12, 96, 372, 961], [1, 8, 58, 296, 1369], [1, -12, 86, -492, 1681], [1, -8, 70, -344, 1849], [1, -8, 38, -376, 2209], [1, 4, 12, 212, 2809], [1, 8, 134, 472, 3481], [1, 8, 106, 488, 3721], [1, -16, 198, -1072, 4489], [1, -24, 278, -1704, 5041], [1, -8, 130, -584, 5329], [1, 20, 240, 1580, 6241], [1, 4, 42, 332, 6889], [1, 4, 182, 356, 7921], [1, -4, 70, -388, 9409]], 'index': 50, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4608/2/a/a'], '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': '4-4608e2-1.1-c1e2-0-50', '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': 2, 'prelabel': '4-4608e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.065893606996913, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 67577992298361281, 'z1': {'__RealLiteral__': 0, 'data': '1.17814215515877463189567270695', 'prec': 103}}
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{'Lhash': '1493472610141200436337251823352,1641273775651942641952869757078', 'Lhash_array': ['1493472610141200436337251823352', '1641273775651942641952869757078'], 'label': '4-4608e2-1.1-c1e2-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4608/2/a/a'}