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lfunc_lfunctions • Show schema
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{'Lhash': '1097333615184951845118810251184,2674781978326004824660628716631', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 4, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.87218325373419, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1]], [13, [1, 0, 13]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': '1.1.1.1', 'conductor': 405769, 'conductor_radical': 91, 'degree': 4, 'euler_factors': [[1, 0, -4, 0, 4], [1, 0, 6, 0, 9], [1, 0, 3, 0, 25], [1], [1, 0, -22, 0, 121], [1, 0, 13], [1, 0, 34, 0, 289], [1, 0, -25, 0, 361], [1, -2, 47, -46, 529], [1, 10, 83, 290, 841], [1, 0, 55, 0, 961], [1, 0, -74, 0, 1369], [1, 0, -30, 0, 1681], [1, -18, 167, -774, 1849], [1, 0, -81, 0, 2209], [1, -22, 227, -1166, 2809], [1, 0, 90, 0, 3481], [1, 0, 122, 0, 3721], [1, 0, -134, 0, 4489], [1, 0, -142, 0, 5041], [1, 0, -29, 0, 5329], [1, -30, 383, -2370, 6241], [1, 0, 159, 0, 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'2.36122142279252356623599827621748', '2.90183652915865826561172861349528', '3.60556027641073429976861898299899', '3.93798235111331440903582746562340', '5.18648095530453650072178156841979', '5.54240797548505922390033308920910', '5.85277215831893289814021448476878', '6.24538692255915754878503141909819', '6.80306429687961310874924384933615', '7.26779433921307144355118806725878', '7.82472286374025567874595526250238', '7.87888024039073588277570836718113', '8.599949348034413221895450657824314', '9.177948290762569783891091012030356', '9.310666724135831601117130001293130', '10.17301053760386419033308267863421', '10.53758706961148283263872825774734', '10.95501419740165719230398927606955'], 'prelabel': '4-637e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, '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': 1838903898155851377, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.865643589004246538352849698417', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.11003093269110094512873523839', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.36122142279252356623599827622', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.87218325373419, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 405769, 'conductor_radical': 91, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 4, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -12], 'euler11': [1, 0, -22, 0, 121], 'euler13': [1, 0, 13, 0, 0], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, 0, -25, 0, 361], 'euler2': [1, 0, -4, 0, 4], 'euler23': [1, -2, 47, -46, 529], 'euler29': [1, 10, 83, 290, 841], 'euler3': [1, 0, 6, 0, 9], 'euler31': [1, 0, 55, 0, 961], 'euler37': [1, 0, -74, 0, 1369], 'euler41': [1, 0, -30, 0, 1681], 'euler43': [1, -18, 167, -774, 1849], 'euler47': [1, 0, -81, 0, 2209], 'euler5': [1, 0, 3, 0, 25], 'euler53': [1, -22, 227, -1166, 2809], 'euler59': [1, 0, 90, 0, 3481], 'euler61': [1, 0, 122, 0, 3721], 'euler67': [1, 0, -134, 0, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, -142, 0, 5041], 'euler73': [1, 0, -29, 0, 5329], 'euler79': [1, -30, 383, -2370, 6241], 'euler83': [1, 0, 159, 0, 6889], 'euler89': [1, 0, -165, 0, 7921], 'euler97': [1, 0, 131, 0, 9409], 'euler_factors': [[1, 0, -4, 0, 4], [1, 0, 6, 0, 9], [1, 0, 3, 0, 25], [1, 0, 0, 0, 0], [1, 0, -22, 0, 121], [1, 0, 13, 0, 0], [1, 0, 34, 0, 289], [1, 0, -25, 0, 361], [1, -2, 47, -46, 529], [1, 10, 83, 290, 841], [1, 0, 55, 0, 961], [1, 0, -74, 0, 1369], [1, 0, -30, 0, 1681], [1, -18, 167, -774, 1849], [1, 0, -81, 0, 2209], [1, -22, 227, -1166, 2809], [1, 0, 90, 0, 3481], [1, 0, 122, 0, 3721], [1, 0, -134, 0, 4489], [1, 0, -142, 0, 5041], [1, 0, -29, 0, 5329], [1, -30, 383, -2370, 6241], [1, 0, 159, 0, 6889], [1, 0, -165, 0, 7921], [1, 0, 131, 0, 9409]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/c/b'], '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': '4-637e2-1.1-c1e2-0-6', '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': '4-637e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1838903898155851377, 'z1': {'__RealLiteral__': 0, 'data': '0.865643589004246538352849698417', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1097333615184951845118810251184,2674781978326004824660628716631', 'Lhash_array': ['1097333615184951845118810251184', '2674781978326004824660628716631'], 'label': '4-637e2-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/c/b'}