Properties

Modulus $555579$
Structure \(C_{18}\times C_{19494}\)
Order $350892$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(555579)
 
pari: g = idealstar(,555579,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 350892
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{18}\times C_{19494}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{555579}(192053,\cdot)$, $\chi_{555579}(363529,\cdot)$

First 32 of 350892 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{555579}(1,\cdot)\) 555579.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{555579}(2,\cdot)\) 555579.lp 19494 yes \(1\) \(1\) \(e\left(\frac{182}{9747}\right)\) \(e\left(\frac{364}{9747}\right)\) \(e\left(\frac{3869}{19494}\right)\) \(e\left(\frac{3626}{9747}\right)\) \(e\left(\frac{182}{3249}\right)\) \(e\left(\frac{1411}{6498}\right)\) \(e\left(\frac{2947}{19494}\right)\) \(e\left(\frac{19265}{19494}\right)\) \(e\left(\frac{3808}{9747}\right)\) \(e\left(\frac{728}{9747}\right)\)
\(\chi_{555579}(4,\cdot)\) 555579.ks 9747 yes \(1\) \(1\) \(e\left(\frac{364}{9747}\right)\) \(e\left(\frac{728}{9747}\right)\) \(e\left(\frac{3869}{9747}\right)\) \(e\left(\frac{7252}{9747}\right)\) \(e\left(\frac{364}{3249}\right)\) \(e\left(\frac{1411}{3249}\right)\) \(e\left(\frac{2947}{9747}\right)\) \(e\left(\frac{9518}{9747}\right)\) \(e\left(\frac{7616}{9747}\right)\) \(e\left(\frac{1456}{9747}\right)\)
\(\chi_{555579}(5,\cdot)\) 555579.lg 19494 yes \(-1\) \(1\) \(e\left(\frac{3869}{19494}\right)\) \(e\left(\frac{3869}{9747}\right)\) \(e\left(\frac{18991}{19494}\right)\) \(e\left(\frac{8842}{9747}\right)\) \(e\left(\frac{3869}{6498}\right)\) \(e\left(\frac{187}{1083}\right)\) \(e\left(\frac{17849}{19494}\right)\) \(e\left(\frac{7142}{9747}\right)\) \(e\left(\frac{2059}{19494}\right)\) \(e\left(\frac{7738}{9747}\right)\)
\(\chi_{555579}(7,\cdot)\) 555579.kq 9747 yes \(1\) \(1\) \(e\left(\frac{3626}{9747}\right)\) \(e\left(\frac{7252}{9747}\right)\) \(e\left(\frac{8842}{9747}\right)\) \(e\left(\frac{9677}{9747}\right)\) \(e\left(\frac{377}{3249}\right)\) \(e\left(\frac{907}{3249}\right)\) \(e\left(\frac{7655}{9747}\right)\) \(e\left(\frac{6841}{9747}\right)\) \(e\left(\frac{3556}{9747}\right)\) \(e\left(\frac{4757}{9747}\right)\)
\(\chi_{555579}(8,\cdot)\) 555579.km 6498 no \(1\) \(1\) \(e\left(\frac{182}{3249}\right)\) \(e\left(\frac{364}{3249}\right)\) \(e\left(\frac{3869}{6498}\right)\) \(e\left(\frac{377}{3249}\right)\) \(e\left(\frac{182}{1083}\right)\) \(e\left(\frac{1411}{2166}\right)\) \(e\left(\frac{2947}{6498}\right)\) \(e\left(\frac{6269}{6498}\right)\) \(e\left(\frac{559}{3249}\right)\) \(e\left(\frac{728}{3249}\right)\)
\(\chi_{555579}(10,\cdot)\) 555579.jy 6498 no \(-1\) \(1\) \(e\left(\frac{1411}{6498}\right)\) \(e\left(\frac{1411}{3249}\right)\) \(e\left(\frac{187}{1083}\right)\) \(e\left(\frac{907}{3249}\right)\) \(e\left(\frac{1411}{2166}\right)\) \(e\left(\frac{2533}{6498}\right)\) \(e\left(\frac{217}{3249}\right)\) \(e\left(\frac{4685}{6498}\right)\) \(e\left(\frac{1075}{2166}\right)\) \(e\left(\frac{2822}{3249}\right)\)
\(\chi_{555579}(11,\cdot)\) 555579.lu 19494 yes \(-1\) \(1\) \(e\left(\frac{2947}{19494}\right)\) \(e\left(\frac{2947}{9747}\right)\) \(e\left(\frac{17849}{19494}\right)\) \(e\left(\frac{7655}{9747}\right)\) \(e\left(\frac{2947}{6498}\right)\) \(e\left(\frac{217}{3249}\right)\) \(e\left(\frac{5011}{19494}\right)\) \(e\left(\frac{9601}{9747}\right)\) \(e\left(\frac{18257}{19494}\right)\) \(e\left(\frac{5894}{9747}\right)\)
\(\chi_{555579}(13,\cdot)\) 555579.lk 19494 yes \(-1\) \(1\) \(e\left(\frac{19265}{19494}\right)\) \(e\left(\frac{9518}{9747}\right)\) \(e\left(\frac{7142}{9747}\right)\) \(e\left(\frac{6841}{9747}\right)\) \(e\left(\frac{6269}{6498}\right)\) \(e\left(\frac{4685}{6498}\right)\) \(e\left(\frac{9601}{9747}\right)\) \(e\left(\frac{6169}{19494}\right)\) \(e\left(\frac{13453}{19494}\right)\) \(e\left(\frac{9289}{9747}\right)\)
\(\chi_{555579}(14,\cdot)\) 555579.lf 19494 yes \(1\) \(1\) \(e\left(\frac{3808}{9747}\right)\) \(e\left(\frac{7616}{9747}\right)\) \(e\left(\frac{2059}{19494}\right)\) \(e\left(\frac{3556}{9747}\right)\) \(e\left(\frac{559}{3249}\right)\) \(e\left(\frac{1075}{2166}\right)\) \(e\left(\frac{18257}{19494}\right)\) \(e\left(\frac{13453}{19494}\right)\) \(e\left(\frac{7364}{9747}\right)\) \(e\left(\frac{5485}{9747}\right)\)
\(\chi_{555579}(16,\cdot)\) 555579.ks 9747 yes \(1\) \(1\) \(e\left(\frac{728}{9747}\right)\) \(e\left(\frac{1456}{9747}\right)\) \(e\left(\frac{7738}{9747}\right)\) \(e\left(\frac{4757}{9747}\right)\) \(e\left(\frac{728}{3249}\right)\) \(e\left(\frac{2822}{3249}\right)\) \(e\left(\frac{5894}{9747}\right)\) \(e\left(\frac{9289}{9747}\right)\) \(e\left(\frac{5485}{9747}\right)\) \(e\left(\frac{2912}{9747}\right)\)
\(\chi_{555579}(17,\cdot)\) 555579.js 6498 no \(-1\) \(1\) \(e\left(\frac{1285}{2166}\right)\) \(e\left(\frac{202}{1083}\right)\) \(e\left(\frac{2861}{6498}\right)\) \(e\left(\frac{3232}{3249}\right)\) \(e\left(\frac{563}{722}\right)\) \(e\left(\frac{109}{3249}\right)\) \(e\left(\frac{2171}{6498}\right)\) \(e\left(\frac{473}{1083}\right)\) \(e\left(\frac{3821}{6498}\right)\) \(e\left(\frac{404}{1083}\right)\)
\(\chi_{555579}(20,\cdot)\) 555579.lz 19494 yes \(-1\) \(1\) \(e\left(\frac{4597}{19494}\right)\) \(e\left(\frac{4597}{9747}\right)\) \(e\left(\frac{7235}{19494}\right)\) \(e\left(\frac{6347}{9747}\right)\) \(e\left(\frac{4597}{6498}\right)\) \(e\left(\frac{1972}{3249}\right)\) \(e\left(\frac{4249}{19494}\right)\) \(e\left(\frac{6913}{9747}\right)\) \(e\left(\frac{17291}{19494}\right)\) \(e\left(\frac{9194}{9747}\right)\)
\(\chi_{555579}(22,\cdot)\) 555579.lc 19494 yes \(-1\) \(1\) \(e\left(\frac{3311}{19494}\right)\) \(e\left(\frac{3311}{9747}\right)\) \(e\left(\frac{1112}{9747}\right)\) \(e\left(\frac{1534}{9747}\right)\) \(e\left(\frac{3311}{6498}\right)\) \(e\left(\frac{205}{722}\right)\) \(e\left(\frac{3979}{9747}\right)\) \(e\left(\frac{18973}{19494}\right)\) \(e\left(\frac{6379}{19494}\right)\) \(e\left(\frac{6622}{9747}\right)\)
\(\chi_{555579}(23,\cdot)\) 555579.lh 19494 yes \(-1\) \(1\) \(e\left(\frac{15695}{19494}\right)\) \(e\left(\frac{5948}{9747}\right)\) \(e\left(\frac{15451}{19494}\right)\) \(e\left(\frac{1519}{9747}\right)\) \(e\left(\frac{2699}{6498}\right)\) \(e\left(\frac{1942}{3249}\right)\) \(e\left(\frac{12167}{19494}\right)\) \(e\left(\frac{7394}{9747}\right)\) \(e\left(\frac{18733}{19494}\right)\) \(e\left(\frac{2149}{9747}\right)\)
\(\chi_{555579}(25,\cdot)\) 555579.kv 9747 yes \(1\) \(1\) \(e\left(\frac{3869}{9747}\right)\) \(e\left(\frac{7738}{9747}\right)\) \(e\left(\frac{9244}{9747}\right)\) \(e\left(\frac{7937}{9747}\right)\) \(e\left(\frac{620}{3249}\right)\) \(e\left(\frac{374}{1083}\right)\) \(e\left(\frac{8102}{9747}\right)\) \(e\left(\frac{4537}{9747}\right)\) \(e\left(\frac{2059}{9747}\right)\) \(e\left(\frac{5729}{9747}\right)\)
\(\chi_{555579}(26,\cdot)\) 555579.im 2166 no \(-1\) \(1\) \(e\left(\frac{5}{722}\right)\) \(e\left(\frac{5}{361}\right)\) \(e\left(\frac{2017}{2166}\right)\) \(e\left(\frac{80}{1083}\right)\) \(e\left(\frac{15}{722}\right)\) \(e\left(\frac{1016}{1083}\right)\) \(e\left(\frac{295}{2166}\right)\) \(e\left(\frac{110}{361}\right)\) \(e\left(\frac{175}{2166}\right)\) \(e\left(\frac{10}{361}\right)\)
\(\chi_{555579}(28,\cdot)\) 555579.ew 171 no \(1\) \(1\) \(e\left(\frac{70}{171}\right)\) \(e\left(\frac{140}{171}\right)\) \(e\left(\frac{52}{171}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{122}{171}\right)\) \(e\left(\frac{5}{57}\right)\) \(e\left(\frac{116}{171}\right)\) \(e\left(\frac{25}{171}\right)\) \(e\left(\frac{109}{171}\right)\)
\(\chi_{555579}(29,\cdot)\) 555579.lt 19494 yes \(1\) \(1\) \(e\left(\frac{9269}{9747}\right)\) \(e\left(\frac{8791}{9747}\right)\) \(e\left(\frac{18425}{19494}\right)\) \(e\left(\frac{7055}{9747}\right)\) \(e\left(\frac{2771}{3249}\right)\) \(e\left(\frac{647}{722}\right)\) \(e\left(\frac{4423}{19494}\right)\) \(e\left(\frac{6671}{19494}\right)\) \(e\left(\frac{6577}{9747}\right)\) \(e\left(\frac{7835}{9747}\right)\)
\(\chi_{555579}(31,\cdot)\) 555579.lw 19494 yes \(-1\) \(1\) \(e\left(\frac{947}{19494}\right)\) \(e\left(\frac{947}{9747}\right)\) \(e\left(\frac{1229}{9747}\right)\) \(e\left(\frac{5893}{9747}\right)\) \(e\left(\frac{947}{6498}\right)\) \(e\left(\frac{1135}{6498}\right)\) \(e\left(\frac{949}{9747}\right)\) \(e\left(\frac{5929}{19494}\right)\) \(e\left(\frac{12733}{19494}\right)\) \(e\left(\frac{1894}{9747}\right)\)
\(\chi_{555579}(32,\cdot)\) 555579.lp 19494 yes \(1\) \(1\) \(e\left(\frac{910}{9747}\right)\) \(e\left(\frac{1820}{9747}\right)\) \(e\left(\frac{19345}{19494}\right)\) \(e\left(\frac{8383}{9747}\right)\) \(e\left(\frac{910}{3249}\right)\) \(e\left(\frac{557}{6498}\right)\) \(e\left(\frac{14735}{19494}\right)\) \(e\left(\frac{18349}{19494}\right)\) \(e\left(\frac{9293}{9747}\right)\) \(e\left(\frac{3640}{9747}\right)\)
\(\chi_{555579}(34,\cdot)\) 555579.lc 19494 yes \(-1\) \(1\) \(e\left(\frac{11929}{19494}\right)\) \(e\left(\frac{2182}{9747}\right)\) \(e\left(\frac{6226}{9747}\right)\) \(e\left(\frac{3575}{9747}\right)\) \(e\left(\frac{5431}{6498}\right)\) \(e\left(\frac{181}{722}\right)\) \(e\left(\frac{4730}{9747}\right)\) \(e\left(\frac{8285}{19494}\right)\) \(e\left(\frac{19079}{19494}\right)\) \(e\left(\frac{4364}{9747}\right)\)
\(\chi_{555579}(35,\cdot)\) 555579.jv 6498 no \(-1\) \(1\) \(e\left(\frac{3707}{6498}\right)\) \(e\left(\frac{458}{3249}\right)\) \(e\left(\frac{1909}{2166}\right)\) \(e\left(\frac{2924}{3249}\right)\) \(e\left(\frac{1541}{2166}\right)\) \(e\left(\frac{1468}{3249}\right)\) \(e\left(\frac{4555}{6498}\right)\) \(e\left(\frac{1412}{3249}\right)\) \(e\left(\frac{1019}{2166}\right)\) \(e\left(\frac{916}{3249}\right)\)
\(\chi_{555579}(37,\cdot)\) 555579.ji 6498 no \(-1\) \(1\) \(e\left(\frac{4415}{6498}\right)\) \(e\left(\frac{1166}{3249}\right)\) \(e\left(\frac{755}{3249}\right)\) \(e\left(\frac{202}{3249}\right)\) \(e\left(\frac{83}{2166}\right)\) \(e\left(\frac{1975}{2166}\right)\) \(e\left(\frac{1117}{3249}\right)\) \(e\left(\frac{2569}{6498}\right)\) \(e\left(\frac{4819}{6498}\right)\) \(e\left(\frac{2332}{3249}\right)\)
\(\chi_{555579}(40,\cdot)\) 555579.lc 19494 yes \(-1\) \(1\) \(e\left(\frac{4961}{19494}\right)\) \(e\left(\frac{4961}{9747}\right)\) \(e\left(\frac{5552}{9747}\right)\) \(e\left(\frac{226}{9747}\right)\) \(e\left(\frac{4961}{6498}\right)\) \(e\left(\frac{595}{722}\right)\) \(e\left(\frac{3598}{9747}\right)\) \(e\left(\frac{13597}{19494}\right)\) \(e\left(\frac{5413}{19494}\right)\) \(e\left(\frac{175}{9747}\right)\)
\(\chi_{555579}(41,\cdot)\) 555579.ld 19494 yes \(1\) \(1\) \(e\left(\frac{1459}{9747}\right)\) \(e\left(\frac{2918}{9747}\right)\) \(e\left(\frac{18835}{19494}\right)\) \(e\left(\frac{4492}{9747}\right)\) \(e\left(\frac{1459}{3249}\right)\) \(e\left(\frac{251}{2166}\right)\) \(e\left(\frac{16835}{19494}\right)\) \(e\left(\frac{1681}{19494}\right)\) \(e\left(\frac{5951}{9747}\right)\) \(e\left(\frac{5836}{9747}\right)\)
\(\chi_{555579}(43,\cdot)\) 555579.kt 9747 yes \(1\) \(1\) \(e\left(\frac{7127}{9747}\right)\) \(e\left(\frac{4507}{9747}\right)\) \(e\left(\frac{7855}{9747}\right)\) \(e\left(\frac{8033}{9747}\right)\) \(e\left(\frac{629}{3249}\right)\) \(e\left(\frac{1745}{3249}\right)\) \(e\left(\frac{8279}{9747}\right)\) \(e\left(\frac{8182}{9747}\right)\) \(e\left(\frac{5413}{9747}\right)\) \(e\left(\frac{9014}{9747}\right)\)
\(\chi_{555579}(44,\cdot)\) 555579.jv 6498 no \(-1\) \(1\) \(e\left(\frac{1225}{6498}\right)\) \(e\left(\frac{1225}{3249}\right)\) \(e\left(\frac{677}{2166}\right)\) \(e\left(\frac{1720}{3249}\right)\) \(e\left(\frac{1225}{2166}\right)\) \(e\left(\frac{1628}{3249}\right)\) \(e\left(\frac{3635}{6498}\right)\) \(e\left(\frac{3124}{3249}\right)\) \(e\left(\frac{1555}{2166}\right)\) \(e\left(\frac{2450}{3249}\right)\)
\(\chi_{555579}(46,\cdot)\) 555579.kn 6498 no \(-1\) \(1\) \(e\left(\frac{5353}{6498}\right)\) \(e\left(\frac{2104}{3249}\right)\) \(e\left(\frac{3220}{3249}\right)\) \(e\left(\frac{1715}{3249}\right)\) \(e\left(\frac{1021}{2166}\right)\) \(e\left(\frac{1765}{2166}\right)\) \(e\left(\frac{2519}{3249}\right)\) \(e\left(\frac{4853}{6498}\right)\) \(e\left(\frac{2285}{6498}\right)\) \(e\left(\frac{959}{3249}\right)\)
\(\chi_{555579}(47,\cdot)\) 555579.lg 19494 yes \(-1\) \(1\) \(e\left(\frac{9787}{19494}\right)\) \(e\left(\frac{40}{9747}\right)\) \(e\left(\frac{10553}{19494}\right)\) \(e\left(\frac{2981}{9747}\right)\) \(e\left(\frac{3289}{6498}\right)\) \(e\left(\frac{47}{1083}\right)\) \(e\left(\frac{18235}{19494}\right)\) \(e\left(\frac{880}{9747}\right)\) \(e\left(\frac{15749}{19494}\right)\) \(e\left(\frac{80}{9747}\right)\)
\(\chi_{555579}(49,\cdot)\) 555579.kq 9747 yes \(1\) \(1\) \(e\left(\frac{7252}{9747}\right)\) \(e\left(\frac{4757}{9747}\right)\) \(e\left(\frac{7937}{9747}\right)\) \(e\left(\frac{9607}{9747}\right)\) \(e\left(\frac{754}{3249}\right)\) \(e\left(\frac{1814}{3249}\right)\) \(e\left(\frac{5563}{9747}\right)\) \(e\left(\frac{3935}{9747}\right)\) \(e\left(\frac{7112}{9747}\right)\) \(e\left(\frac{9514}{9747}\right)\)
\(\chi_{555579}(50,\cdot)\) 555579.lv 19494 yes \(1\) \(1\) \(e\left(\frac{4051}{9747}\right)\) \(e\left(\frac{8102}{9747}\right)\) \(e\left(\frac{2863}{19494}\right)\) \(e\left(\frac{1816}{9747}\right)\) \(e\left(\frac{802}{3249}\right)\) \(e\left(\frac{3655}{6498}\right)\) \(e\left(\frac{19151}{19494}\right)\) \(e\left(\frac{8845}{19494}\right)\) \(e\left(\frac{5867}{9747}\right)\) \(e\left(\frac{6457}{9747}\right)\)
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