Properties

Modulus $81225$
Structure \(C_{2}\times C_{6}\times C_{3420}\)
Order $41040$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(81225)
 
pari: g = idealstar(,81225,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 41040
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{6}\times C_{3420}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{81225}(36101,\cdot)$, $\chi_{81225}(77977,\cdot)$, $\chi_{81225}(48376,\cdot)$

First 32 of 41040 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 \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(22\)
\(\chi_{81225}(1,\cdot)\) 81225.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{81225}(2,\cdot)\) 81225.or 3420 yes \(-1\) \(1\) \(e\left(\frac{751}{3420}\right)\) \(e\left(\frac{751}{1710}\right)\) \(e\left(\frac{27}{76}\right)\) \(e\left(\frac{751}{1140}\right)\) \(e\left(\frac{151}{570}\right)\) \(e\left(\frac{839}{3420}\right)\) \(e\left(\frac{983}{1710}\right)\) \(e\left(\frac{751}{855}\right)\) \(e\left(\frac{2773}{3420}\right)\) \(e\left(\frac{1657}{3420}\right)\)
\(\chi_{81225}(4,\cdot)\) 81225.og 1710 yes \(1\) \(1\) \(e\left(\frac{751}{1710}\right)\) \(e\left(\frac{751}{855}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{181}{570}\right)\) \(e\left(\frac{151}{285}\right)\) \(e\left(\frac{839}{1710}\right)\) \(e\left(\frac{128}{855}\right)\) \(e\left(\frac{647}{855}\right)\) \(e\left(\frac{1063}{1710}\right)\) \(e\left(\frac{1657}{1710}\right)\)
\(\chi_{81225}(7,\cdot)\) 81225.kb 228 no \(-1\) \(1\) \(e\left(\frac{27}{76}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{161}{228}\right)\) \(e\left(\frac{5}{76}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{29}{76}\right)\) \(e\left(\frac{7}{114}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{85}{228}\right)\) \(e\left(\frac{173}{228}\right)\)
\(\chi_{81225}(8,\cdot)\) 81225.nc 1140 no \(-1\) \(1\) \(e\left(\frac{751}{1140}\right)\) \(e\left(\frac{181}{570}\right)\) \(e\left(\frac{5}{76}\right)\) \(e\left(\frac{371}{380}\right)\) \(e\left(\frac{151}{190}\right)\) \(e\left(\frac{839}{1140}\right)\) \(e\left(\frac{413}{570}\right)\) \(e\left(\frac{181}{285}\right)\) \(e\left(\frac{493}{1140}\right)\) \(e\left(\frac{517}{1140}\right)\)
\(\chi_{81225}(11,\cdot)\) 81225.mb 570 yes \(-1\) \(1\) \(e\left(\frac{151}{570}\right)\) \(e\left(\frac{151}{285}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{151}{190}\right)\) \(e\left(\frac{221}{570}\right)\) \(e\left(\frac{187}{285}\right)\) \(e\left(\frac{127}{190}\right)\) \(e\left(\frac{17}{285}\right)\) \(e\left(\frac{173}{570}\right)\) \(e\left(\frac{62}{95}\right)\)
\(\chi_{81225}(13,\cdot)\) 81225.on 3420 yes \(1\) \(1\) \(e\left(\frac{839}{3420}\right)\) \(e\left(\frac{839}{1710}\right)\) \(e\left(\frac{29}{76}\right)\) \(e\left(\frac{839}{1140}\right)\) \(e\left(\frac{187}{285}\right)\) \(e\left(\frac{721}{3420}\right)\) \(e\left(\frac{536}{855}\right)\) \(e\left(\frac{839}{855}\right)\) \(e\left(\frac{2597}{3420}\right)\) \(e\left(\frac{3083}{3420}\right)\)
\(\chi_{81225}(14,\cdot)\) 81225.nu 1710 yes \(1\) \(1\) \(e\left(\frac{983}{1710}\right)\) \(e\left(\frac{128}{855}\right)\) \(e\left(\frac{7}{114}\right)\) \(e\left(\frac{413}{570}\right)\) \(e\left(\frac{127}{190}\right)\) \(e\left(\frac{536}{855}\right)\) \(e\left(\frac{544}{855}\right)\) \(e\left(\frac{256}{855}\right)\) \(e\left(\frac{157}{855}\right)\) \(e\left(\frac{208}{855}\right)\)
\(\chi_{81225}(16,\cdot)\) 81225.mu 855 yes \(1\) \(1\) \(e\left(\frac{751}{855}\right)\) \(e\left(\frac{647}{855}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{181}{285}\right)\) \(e\left(\frac{17}{285}\right)\) \(e\left(\frac{839}{855}\right)\) \(e\left(\frac{256}{855}\right)\) \(e\left(\frac{439}{855}\right)\) \(e\left(\frac{208}{855}\right)\) \(e\left(\frac{802}{855}\right)\)
\(\chi_{81225}(17,\cdot)\) 81225.oo 3420 no \(1\) \(1\) \(e\left(\frac{2773}{3420}\right)\) \(e\left(\frac{1063}{1710}\right)\) \(e\left(\frac{85}{228}\right)\) \(e\left(\frac{493}{1140}\right)\) \(e\left(\frac{173}{570}\right)\) \(e\left(\frac{2597}{3420}\right)\) \(e\left(\frac{157}{855}\right)\) \(e\left(\frac{208}{855}\right)\) \(e\left(\frac{1009}{3420}\right)\) \(e\left(\frac{391}{3420}\right)\)
\(\chi_{81225}(22,\cdot)\) 81225.os 3420 yes \(1\) \(1\) \(e\left(\frac{1657}{3420}\right)\) \(e\left(\frac{1657}{1710}\right)\) \(e\left(\frac{173}{228}\right)\) \(e\left(\frac{517}{1140}\right)\) \(e\left(\frac{62}{95}\right)\) \(e\left(\frac{3083}{3420}\right)\) \(e\left(\frac{208}{855}\right)\) \(e\left(\frac{802}{855}\right)\) \(e\left(\frac{391}{3420}\right)\) \(e\left(\frac{469}{3420}\right)\)
\(\chi_{81225}(23,\cdot)\) 81225.op 3420 yes \(1\) \(1\) \(e\left(\frac{2771}{3420}\right)\) \(e\left(\frac{1061}{1710}\right)\) \(e\left(\frac{9}{76}\right)\) \(e\left(\frac{491}{1140}\right)\) \(e\left(\frac{101}{570}\right)\) \(e\left(\frac{1939}{3420}\right)\) \(e\left(\frac{794}{855}\right)\) \(e\left(\frac{206}{855}\right)\) \(e\left(\frac{443}{3420}\right)\) \(e\left(\frac{3377}{3420}\right)\)
\(\chi_{81225}(26,\cdot)\) 81225.ht 114 no \(-1\) \(1\) \(e\left(\frac{53}{114}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{26}{57}\right)\) \(e\left(\frac{23}{114}\right)\) \(e\left(\frac{49}{57}\right)\) \(e\left(\frac{65}{114}\right)\) \(e\left(\frac{22}{57}\right)\)
\(\chi_{81225}(28,\cdot)\) 81225.jd 180 no \(-1\) \(1\) \(e\left(\frac{143}{180}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{157}{180}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{179}{180}\right)\) \(e\left(\frac{131}{180}\right)\)
\(\chi_{81225}(29,\cdot)\) 81225.nu 1710 yes \(1\) \(1\) \(e\left(\frac{541}{1710}\right)\) \(e\left(\frac{541}{855}\right)\) \(e\left(\frac{71}{114}\right)\) \(e\left(\frac{541}{570}\right)\) \(e\left(\frac{159}{190}\right)\) \(e\left(\frac{502}{855}\right)\) \(e\left(\frac{803}{855}\right)\) \(e\left(\frac{227}{855}\right)\) \(e\left(\frac{29}{855}\right)\) \(e\left(\frac{131}{855}\right)\)
\(\chi_{81225}(31,\cdot)\) 81225.lz 570 yes \(-1\) \(1\) \(e\left(\frac{353}{570}\right)\) \(e\left(\frac{68}{285}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{163}{190}\right)\) \(e\left(\frac{29}{285}\right)\) \(e\left(\frac{427}{570}\right)\) \(e\left(\frac{161}{190}\right)\) \(e\left(\frac{136}{285}\right)\) \(e\left(\frac{122}{285}\right)\) \(e\left(\frac{137}{190}\right)\)
\(\chi_{81225}(32,\cdot)\) 81225.ml 684 no \(-1\) \(1\) \(e\left(\frac{67}{684}\right)\) \(e\left(\frac{67}{342}\right)\) \(e\left(\frac{59}{76}\right)\) \(e\left(\frac{67}{228}\right)\) \(e\left(\frac{37}{114}\right)\) \(e\left(\frac{155}{684}\right)\) \(e\left(\frac{299}{342}\right)\) \(e\left(\frac{67}{171}\right)\) \(e\left(\frac{37}{684}\right)\) \(e\left(\frac{289}{684}\right)\)
\(\chi_{81225}(34,\cdot)\) 81225.nt 1710 yes \(-1\) \(1\) \(e\left(\frac{26}{855}\right)\) \(e\left(\frac{52}{855}\right)\) \(e\left(\frac{83}{114}\right)\) \(e\left(\frac{26}{285}\right)\) \(e\left(\frac{54}{95}\right)\) \(e\left(\frac{4}{855}\right)\) \(e\left(\frac{1297}{1710}\right)\) \(e\left(\frac{104}{855}\right)\) \(e\left(\frac{181}{1710}\right)\) \(e\left(\frac{512}{855}\right)\)
\(\chi_{81225}(37,\cdot)\) 81225.lf 380 no \(1\) \(1\) \(e\left(\frac{221}{380}\right)\) \(e\left(\frac{31}{190}\right)\) \(e\left(\frac{75}{76}\right)\) \(e\left(\frac{283}{380}\right)\) \(e\left(\frac{59}{95}\right)\) \(e\left(\frac{319}{380}\right)\) \(e\left(\frac{54}{95}\right)\) \(e\left(\frac{31}{95}\right)\) \(e\left(\frac{223}{380}\right)\) \(e\left(\frac{77}{380}\right)\)
\(\chi_{81225}(41,\cdot)\) 81225.ny 1710 yes \(1\) \(1\) \(e\left(\frac{196}{855}\right)\) \(e\left(\frac{392}{855}\right)\) \(e\left(\frac{41}{57}\right)\) \(e\left(\frac{196}{285}\right)\) \(e\left(\frac{3}{190}\right)\) \(e\left(\frac{1573}{1710}\right)\) \(e\left(\frac{811}{855}\right)\) \(e\left(\frac{784}{855}\right)\) \(e\left(\frac{641}{1710}\right)\) \(e\left(\frac{419}{1710}\right)\)
\(\chi_{81225}(43,\cdot)\) 81225.mr 684 no \(-1\) \(1\) \(e\left(\frac{389}{684}\right)\) \(e\left(\frac{47}{342}\right)\) \(e\left(\frac{17}{76}\right)\) \(e\left(\frac{161}{228}\right)\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{415}{684}\right)\) \(e\left(\frac{271}{342}\right)\) \(e\left(\frac{47}{171}\right)\) \(e\left(\frac{77}{684}\right)\) \(e\left(\frac{509}{684}\right)\)
\(\chi_{81225}(44,\cdot)\) 81225.ns 1710 no \(-1\) \(1\) \(e\left(\frac{602}{855}\right)\) \(e\left(\frac{349}{855}\right)\) \(e\left(\frac{13}{114}\right)\) \(e\left(\frac{32}{285}\right)\) \(e\left(\frac{523}{570}\right)\) \(e\left(\frac{251}{1710}\right)\) \(e\left(\frac{1399}{1710}\right)\) \(e\left(\frac{698}{855}\right)\) \(e\left(\frac{791}{855}\right)\) \(e\left(\frac{1063}{1710}\right)\)
\(\chi_{81225}(46,\cdot)\) 81225.lu 570 no \(-1\) \(1\) \(e\left(\frac{17}{570}\right)\) \(e\left(\frac{17}{285}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{17}{190}\right)\) \(e\left(\frac{42}{95}\right)\) \(e\left(\frac{463}{570}\right)\) \(e\left(\frac{287}{570}\right)\) \(e\left(\frac{34}{285}\right)\) \(e\left(\frac{268}{285}\right)\) \(e\left(\frac{269}{570}\right)\)
\(\chi_{81225}(47,\cdot)\) 81225.oj 3420 yes \(1\) \(1\) \(e\left(\frac{317}{3420}\right)\) \(e\left(\frac{317}{1710}\right)\) \(e\left(\frac{73}{228}\right)\) \(e\left(\frac{317}{1140}\right)\) \(e\left(\frac{99}{190}\right)\) \(e\left(\frac{1693}{3420}\right)\) \(e\left(\frac{353}{855}\right)\) \(e\left(\frac{317}{855}\right)\) \(e\left(\frac{2501}{3420}\right)\) \(e\left(\frac{2099}{3420}\right)\)
\(\chi_{81225}(49,\cdot)\) 81225.io 114 no \(1\) \(1\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{47}{114}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{46}{57}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{85}{114}\right)\) \(e\left(\frac{59}{114}\right)\)
\(\chi_{81225}(52,\cdot)\) 81225.on 3420 yes \(1\) \(1\) \(e\left(\frac{2341}{3420}\right)\) \(e\left(\frac{631}{1710}\right)\) \(e\left(\frac{7}{76}\right)\) \(e\left(\frac{61}{1140}\right)\) \(e\left(\frac{53}{285}\right)\) \(e\left(\frac{2399}{3420}\right)\) \(e\left(\frac{664}{855}\right)\) \(e\left(\frac{631}{855}\right)\) \(e\left(\frac{1303}{3420}\right)\) \(e\left(\frac{2977}{3420}\right)\)
\(\chi_{81225}(53,\cdot)\) 81225.oq 3420 no \(-1\) \(1\) \(e\left(\frac{317}{3420}\right)\) \(e\left(\frac{317}{1710}\right)\) \(e\left(\frac{35}{228}\right)\) \(e\left(\frac{317}{1140}\right)\) \(e\left(\frac{487}{570}\right)\) \(e\left(\frac{1693}{3420}\right)\) \(e\left(\frac{421}{1710}\right)\) \(e\left(\frac{317}{855}\right)\) \(e\left(\frac{3071}{3420}\right)\) \(e\left(\frac{3239}{3420}\right)\)
\(\chi_{81225}(56,\cdot)\) 81225.lp 570 yes \(1\) \(1\) \(e\left(\frac{4}{285}\right)\) \(e\left(\frac{8}{285}\right)\) \(e\left(\frac{44}{57}\right)\) \(e\left(\frac{4}{95}\right)\) \(e\left(\frac{113}{570}\right)\) \(e\left(\frac{67}{570}\right)\) \(e\left(\frac{224}{285}\right)\) \(e\left(\frac{16}{285}\right)\) \(e\left(\frac{153}{190}\right)\) \(e\left(\frac{121}{570}\right)\)
\(\chi_{81225}(58,\cdot)\) 81225.nf 1140 yes \(-1\) \(1\) \(e\left(\frac{611}{1140}\right)\) \(e\left(\frac{41}{570}\right)\) \(e\left(\frac{223}{228}\right)\) \(e\left(\frac{231}{380}\right)\) \(e\left(\frac{29}{285}\right)\) \(e\left(\frac{949}{1140}\right)\) \(e\left(\frac{293}{570}\right)\) \(e\left(\frac{41}{285}\right)\) \(e\left(\frac{321}{380}\right)\) \(e\left(\frac{727}{1140}\right)\)
\(\chi_{81225}(59,\cdot)\) 81225.nu 1710 yes \(1\) \(1\) \(e\left(\frac{107}{1710}\right)\) \(e\left(\frac{107}{855}\right)\) \(e\left(\frac{25}{114}\right)\) \(e\left(\frac{107}{570}\right)\) \(e\left(\frac{3}{190}\right)\) \(e\left(\frac{74}{855}\right)\) \(e\left(\frac{241}{855}\right)\) \(e\left(\frac{214}{855}\right)\) \(e\left(\frac{178}{855}\right)\) \(e\left(\frac{67}{855}\right)\)
\(\chi_{81225}(61,\cdot)\) 81225.mw 855 yes \(1\) \(1\) \(e\left(\frac{629}{855}\right)\) \(e\left(\frac{403}{855}\right)\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{59}{285}\right)\) \(e\left(\frac{86}{95}\right)\) \(e\left(\frac{31}{855}\right)\) \(e\left(\frac{644}{855}\right)\) \(e\left(\frac{806}{855}\right)\) \(e\left(\frac{167}{855}\right)\) \(e\left(\frac{548}{855}\right)\)
\(\chi_{81225}(62,\cdot)\) 81225.iz 180 no \(1\) \(1\) \(e\left(\frac{151}{180}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{179}{180}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{43}{180}\right)\) \(e\left(\frac{37}{180}\right)\)
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