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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 0, 7, -4, -2, 1], 'conductor': 0, 'degree': 5, 'dirichlet_group': [], 'disc_abs': 180769, 'disc_rad': 180769, 'disc_sign': 1, 'frobs': [[2, [[5, 1]]], [3, [[5, 1]]], [5, [[3, 1], [1, 2]]], [7, [[3, 1], [1, 2]]], [11, [[3, 1], [2, 1]]], [13, [[5, 1]]], [17, [[5, 1]]], [19, [[4, 1], [1, 1]]], [23, [[2, 2], [1, 1]]], [29, [[3, 1], [2, 1]]], [31, [[5, 1]]], [37, [[4, 1], [1, 1]]], [41, [0]], [43, [[3, 1], [1, 2]]], [47, [[2, 2], [1, 1]]], [53, [[3, 1], [2, 1]]], [59, [[3, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [60, 60], 'galois_label': '5T5', 'galt': 5, 'grd': 425.1693780130455, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '5.5.180769.1', 'local_algs': ['41.2.1.2', '41.3.0.1', 'm4409.2.1.1', 'm4409.1.3.0'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [41, 4409], 'rd': 11.2570550811, 'regulator': {'__RealLiteral__': 0, 'data': '9.64320519613', 'prec': 44}, 'res': {'sib': ['-10429,-55911,-35536,180019,154460,-165657,-102408,66060,25744,-12771,-2941,1234,154,-57,-3,1', '-1568547309323,-2142372113444,8419863920475,10980722294622,-17175191692028,-21879839288628,17889558670958,22361701750066,-11085297585775,-13319737475804,4508781950021,4973184345420,-1279243470450,-1216481869588,260485781980,200521873178,-38286304083,-22666406708,4043328459,1769204996,-303755539,-94833746,15959610,3413974,-569315,-78562,13063,1040,-173,-6,1', '-1609218,-138391,53739,954,-427,-1,1', '-18236684766180583,6518551644516227,85225913717276614,-24435985487686839,-131003194031514145,40961310883424666,92985354725497772,-30005099003715906,-36267075022460960,11053480983805967,8749997251141997,-2285892159900770,-1407163630429229,283028501567835,155623613424265,-21446948089173,-11866873724854,979409499170,618606880338,-24966923962,-21859744948,237227647,517426458,4201886,-8009946,-146468,77289,1575,-421,-6,1', '-206543886,4471795601,-24851190762,-20383094240,270763920313,316364503043,-270855595986,-366710899609,116682108395,170448431924,-29773531184,-39793760914,5162673666,4967110583,-597232037,-334569767,41851450,11971157,-1597412,-220424,31429,1900,-291,-6,1', '-287366467565261,2010372065837465,4851192258220434,2695120390920418,-115080187723931,-418742071941475,-58713808975178,21189487154482,4737284469795,-490317282973,-161973710876,5078334002,3046836862,-5660426,-33748017,-338990,217812,2655,-745,-6,1', '-37435811,2266108861,15243528512,34995356038,30367123582,-144186350,-12830044654,-3238660298,2135156012,687414310,-202017402,-64430877,12301241,3245403,-490510,-90944,12214,1335,-170,-8,1', '-5685822068185,-73886939623,86459836471,866724532,-508300367,-3652779,1436954,6477,-1942,-4,1', '-922209524690234375,25813587813473734375,297177345418106292500,131503847331516906025,-1170545029223243785540,-506602148530451933053,1876429847901413989912,644217716394019072016,-1647313060503906593348,-419969350590427551405,900496762127015689719,159368472649512518562,-329059068180017627229,-36436024219244224976,83980671234282693047,4661293567602634905,-15405045062714515348,-151092441030038528,2070099347015617813,-58249920614779779,-206226156303234446,12401713305389563,15319690927866624,-1347371949688889,-848254338443448,96199091464357,34725590209100,-4817080375157,-1030695562120,172446369265,21296046305,-4397970704,-278994090,78055806,1669455,-915918,8470,6384,-206,-20,1', '1,-11,-282,1524,1505,-15907,11794,34869,-42733,-25178,49019,1440,-24715,5460,5472,-2155,-372,266,-15,-8,1', '1,-25,39,89,-99,-86,67,25,-15,-2,1', '125,-3775,-5170,192572,374774,-2176284,-4032437,11560029,17420833,-34792239,-37170528,63108739,42546355,-69921419,-27553417,48493211,10107507,-21584405,-1836528,6255783,5984,-1178959,68501,141254,-14192,-10186,1335,393,-60,-6,1', '28561,0,-81059,0,73505,0,-23262,0,2190,0,-80,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{4} - 2 a^{3} - 4 a^{2} + 7 a \\)', '\\( a - 1 \\)', '\\( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 2 \\)', '\\( a^{3} - a^{2} - 4 a + 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4']}