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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [56448, 0, -232920, 0, -24480, 0, 4540, 0, 140, 0, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 272097792000000000000000000, 'disc_rad': 30, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[2, 3], [1, 4]]], [11, [[4, 2], [1, 2]]], [13, [[8, 1], [1, 2]]], [17, [[4, 1], [2, 1], [1, 4]]], [19, [[6, 1], [2, 1], [1, 2]]], [23, [[4, 1], [3, 2]]], [29, [[10, 1]]], [31, [[3, 2], [2, 1], [1, 2]]], [37, [[4, 1], [3, 2]]], [41, [[6, 1], [2, 1], [1, 2]]], [43, [[6, 1], [4, 1]]], [47, [[4, 1], [3, 2]]], [53, [[6, 1], [2, 2]]], [59, [[5, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [14760, 7040, 7488], 'galois_label': '10T39', 'galt': 39, 'grd': 2481.9775826377754, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 48, 'label': '10.4.272097792000000000000000000.48', 'local_algs': ['2.2.2.2', '2.8.25.47', '3.3.5.2', '3.3.5.2', '3.4.2.1', '5.10.18.5'], 'monogenic': 0, 'num_ram': 3, 'r2': 3, 'ramps': [2, 3, 5], 'rd': 440.020086187, 'regulator': {'__RealLiteral__': 0, 'data': '51233907436.9', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['11160.2850.-500.-150.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{397}{766106} a^{8} + \\frac{59821}{766106} a^{6} + \\frac{1215318}{383053} a^{4} + \\frac{7419935}{383053} a^{2} + \\frac{8503981}{383053} \\)', '\\( \\frac{172042931}{4596636} a^{8} + \\frac{23156899391}{4596636} a^{6} + \\frac{54667950531}{383053} a^{4} - \\frac{646218495661}{383053} a^{2} + \\frac{13624168213}{34823} \\)', '\\( \\frac{7416395}{4596636} a^{8} + \\frac{229982015}{2298318} a^{6} - \\frac{687841481}{2298318} a^{4} - \\frac{2120356746}{383053} a^{2} - \\frac{1506297491}{383053} \\)', '\\( \\frac{2346988117}{2298318} a^{8} + \\frac{658267833785}{4596636} a^{6} + \\frac{3577746260405}{766106} a^{4} - \\frac{9152248961784}{383053} a^{2} - \\frac{93276602013937}{383053} \\)', '\\( \\frac{1682917501708252779649}{257411616} a^{9} - \\frac{29243041302263956715}{9193272} a^{8} + \\frac{8428815391360238688919}{9193272} a^{7} - \\frac{683491367255219485053}{1532212} a^{6} + \\frac{641359421933758967654213}{21450968} a^{5} - \\frac{33433546289964220701979}{2298318} a^{4} - \\frac{820332228794052334624571}{5362742} a^{3} + \\frac{28508835666605237713950}{383053} a^{2} - \\frac{16721092920162163805734745}{10725484} a + \\frac{26413848698174259868376}{34823} \\)', '\\( \\frac{3404399783795406333204749468463495375227062322105316267217868203440986614260480076796989693264855379544053739514545794202552254160406044048215}{128705808} a^{9} - \\frac{358123636610636842996131767727138509810934959318950623329597509008609065681033493343066142632988488225415364405942952960101901676051054364559}{4596636} a^{8} + \\frac{3012805214947488536459600229544009904038129423011608724751177717569662760401777702578769191731528916094403421924012005765136862407204232405671}{766106} a^{7} - \\frac{17748085535160626831059892103738234626384674462926149385515140421350222850422086511743927757086827166168870946385216616050591872671119707977835}{1532212} a^{6} + \\frac{4961788811289907106160765622203040495322352613436496722647249485354595122800380719060378403714356192449680482545587090145444652227564707411062901}{32176452} a^{5} - \\frac{521952169557504162549211283033296158977840798923555659136406859388072300501412015041305017815709886658269475945600628866492858464274662018959159}{1149159} a^{4} + \\frac{3701951281758088250630128545801444037677351306467277248531398358379981953617533535563355124484326367906021666927253606830928006311058631068681931}{5362742} a^{3} - \\frac{778848748545384492959819520808694829230908505098410514884030685673868014783386900470473187133193378999408106524470467413445811612209786526334214}{383053} a^{2} - \\frac{922947389195846866560656121037694991383302653317249200063131415829137953125492506216265279775146016375416237098724006012983901212827213030976723}{5362742} a + \\frac{194177709088336166278011442427466758809039389152541493456161618030595532552978856239712070050900919915950805562520033999316558269037527039322183}{383053} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', '1/2*a^3', '1/2*a^4', '1/6*a^5 + 1/6*a^3', '1/132*a^6 - 5/33*a^4 - 3/11*a^2 + 4/11', '1/132*a^7 + 1/66*a^5 - 7/66*a^3 + 4/11*a', '1/9193272*a^8 - 2221/2298318*a^6 + 194329/2298318*a^4 - 106866/383053*a^2 + 169855/383053', '1/257411616*a^9 + 29531/9193272*a^7 - 13991/5850264*a^5 - 828844/8044113*a^3 - 4287489/10725484*a']}