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{'Lhash': '386907869019742116009019873246,918142070247797347508217569335,1167284607322652377017879191617,1196176002267858837527778741266,1297746999080626940189564162559,1978759109710469085426565068614', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 362460140.6903397, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [11, [1, -6, 15, -20, 15, -6, 1]], [19, [1, -6, 15, -20, 15, -6, 1]]], 'bad_primes': [2, 11, 19], 'central_character': '3344.1', 'coefficient_field': '1.1.1.1', 'conductor': 1398291161776239149056, 'conductor_radical': 418, 'degree': 12, 'euler_factors': [[1], [1, 1, 1, 2, 0, -6, 6, -18, 0, 54, 81, 243, 729], [1, -5, 21, -48, 96, -86, 178, -430, 2400, -6000, 13125, -15625, 15625], [1, -2, 17, -12, 116, 82, 548, 574, 5684, -4116, 40817, -33614, 117649], [1, -6, 15, -20, 15, -6, 1], [1, -8, 55, -274, 1148, -4180, 15612, -54340, 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5.167395324137313, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e6-0', 'trace_hash': 2188851959378158345, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.30521649179204643516154821287', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.72428638465717122638185981304', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.920825191983100859628425416162', 'prec': 107}}
-
lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 362460140.6903397, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 1398291161776239149056, 'conductor_radical': 418, 'degree': 12, 'dirichlet_coefficients': [1, 0, -1, 0, 5, 0, 2, 0, 0, 0, 6, 0, 8, 0, -5, 0, -2, 0, 6, 0, -2, 0, -5, 0, 4, 0, -1, 0, 10, 0, -3, 0, -6, 0, 10, 0, 7, 0, -8, 0, 6, 0, -16, 0, 0, 0, 0, 0, -13, 0, 2, 0, 20, 0, 30, 0, -6, 0, -15, 0, 24, 0, 0, 0, 40, 0, -25, 0, 5, 0, 9, 0, -26, 0, -4, 0, 12, 0, 16, 0, 3, 0, 2, 0, -10, 0, -10, 0, 7, 0, 16, 0, 3, 0, 30, 0, 37, 0, 0, 0], 'euler11': [1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0], 'euler13': [1, -8, 55, -274, 1148, -4180, 15612, -54340, 194012, -601978, 1570855, -2970344, 4826809], 'euler17': [1, 2, 30, 122, 607, 2084, 12868, 35428, 175423, 599386, 2505630, 2839714, 24137569], 'euler19': [1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 5, 50, 243, 1967, 8550, 54684, 196650, 1040543, 2956581, 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'euler59': [1, 15, 248, 3029, 31879, 292034, 2417840, 17230006, 110970799, 622092991, 3005105528, 10723864485, 42180533641], 'euler61': [1, -24, 426, -5624, 63015, -601104, 4996652, -36667344, 234478815, -1276541144, 5898328266, -20270311224, 51520374361], 'euler67': [1, 25, 479, 5946, 65282, 570676, 4992830, 38235292, 293050898, 1788336798, 9652386959, 33753127675, 90458382169], 'euler7': [1, -2, 17, -12, 116, 82, 548, 574, 5684, -4116, 40817, -33614, 117649], 'euler71': [1, -9, 269, -1862, 35908, -199430, 3020546, -14159530, 181012228, -666430282, 6835742189, -16238064159, 128100283921], 'euler73': [1, 26, 458, 6474, 75263, 760652, 6945740, 55527596, 401076527, 2518496058, 13006394378, 53899861418, 151334226289], 'euler79': [1, -16, 454, -5264, 82511, -740480, 8351892, -58497920, 514951151, -2595357296, 17683336774, -49232902384, 243087455521], 'euler83': [1, -2, 421, -744, 79316, -117434, 8501524, -9747022, 546407924, -425409528, 19979953141, -7878081286, 326940373369], 'euler89': [1, -7, 308, -1931, 43111, -259078, 4205512, -23057942, 341482231, -1361295139, 19324610228, -39088416143, 496981290961], 'euler97': [1, -37, 916, -16581, 246255, -3080646, 32767192, -298822662, 2317013295, -15133031013, 81092821396, -317731589509, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 0, -6, 6, -18, 0, 54, 81, 243, 729], [1, -5, 21, -48, 96, -86, 178, -430, 2400, -6000, 13125, -15625, 15625], [1, -2, 17, -12, 116, 82, 548, 574, 5684, -4116, 40817, -33614, 117649], [1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0], [1, -8, 55, -274, 1148, -4180, 15612, -54340, 194012, -601978, 1570855, -2970344, 4826809], [1, 2, 30, 122, 607, 2084, 12868, 35428, 175423, 599386, 2505630, 2839714, 24137569], [1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0], [1, 5, 50, 243, 1967, 8550, 54684, 196650, 1040543, 2956581, 13992050, 32181715, 148035889], [1, -10, 83, -422, 2572, -8554, 46924, -248066, 2163052, -10292158, 58704323, -205111490, 594823321], [1, 3, 107, 78, 4418, -6464, 127702, -200384, 4245698, 2323698, 98816747, 85887453, 887503681], [1, -7, 112, -967, 8191, -54478, 394928, -2015686, 11213479, -48981451, 209906032, -485407699, 2565726409], [1, -6, 203, -766, 16684, -41824, 822548, -1714784, 28045804, -52793486, 573629483, -695137206, 4750104241], [1, 16, 209, 1924, 18072, 134610, 980204, 5788230, 33415128, 152971468, 714529409, 2352135088, 6321363049], [1, 0, 158, -176, 13039, -13104, 746020, -615888, 28803151, -18272848, 770989598, 0, 10779215329], [1, -20, 370, -4436, 49815, -434728, 3532444, -23040584, 139930335, -660418372, 2919477970, -8363909860, 22164361129], [1, 15, 248, 3029, 31879, 292034, 2417840, 17230006, 110970799, 622092991, 3005105528, 10723864485, 42180533641], [1, -24, 426, -5624, 63015, -601104, 4996652, -36667344, 234478815, -1276541144, 5898328266, -20270311224, 51520374361], [1, 25, 479, 5946, 65282, 570676, 4992830, 38235292, 293050898, 1788336798, 9652386959, 33753127675, 90458382169], [1, -9, 269, -1862, 35908, -199430, 3020546, -14159530, 181012228, -666430282, 6835742189, -16238064159, 128100283921], [1, 26, 458, 6474, 75263, 760652, 6945740, 55527596, 401076527, 2518496058, 13006394378, 53899861418, 151334226289], [1, -16, 454, -5264, 82511, -740480, 8351892, -58497920, 514951151, -2595357296, 17683336774, -49232902384, 243087455521], [1, -2, 421, -744, 79316, -117434, 8501524, -9747022, 546407924, -425409528, 19979953141, -7878081286, 326940373369], [1, -7, 308, -1931, 43111, -259078, 4205512, -23057942, 341482231, -1361295139, 19324610228, -39088416143, 496981290961], [1, -37, 916, -16581, 246255, -3080646, 32767192, -298822662, 2317013295, -15133031013, 81092821396, -317731589509, 832972004929]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3344/2/a/w'], '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': '12-3344e6-1.1-c1e6-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-3344e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.167395324137313, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 2188851959378158345, 'z1': {'__RealLiteral__': 0, 'data': '0.30521649179204643516154821287', 'prec': 103}}
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{'Lhash': '386907869019742116009019873246,918142070247797347508217569335,1167284607322652377017879191617,1196176002267858837527778741266,1297746999080626940189564162559,1978759109710469085426565068614', 'Lhash_array': ['386907869019742116009019873246', '918142070247797347508217569335', '1167284607322652377017879191617', '1196176002267858837527778741266', '1297746999080626940189564162559', '1978759109710469085426565068614'], 'label': '12-3344e6-1.1-c1e6-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3344/2/a/w'}