# Properties

 Modulus $36864$ Structure $$C_{2}\times C_{2}\times C_{3072}$$ Order $12288$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(36864)

pari: g = idealstar(,36864,2)

## Character group

 sage: G.order()  pari: g.no Order = 12288 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{3072}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{36864}(8191,\cdot)$, $\chi_{36864}(20485,\cdot)$, $\chi_{36864}(4097,\cdot)$

## First 32 of 12288 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$
$$\chi_{36864}(1,\cdot)$$ 36864.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{36864}(5,\cdot)$$ 36864.dj 3072 yes $$-1$$ $$1$$ $$e\left(\frac{515}{3072}\right)$$ $$e\left(\frac{47}{1536}\right)$$ $$e\left(\frac{127}{3072}\right)$$ $$e\left(\frac{1997}{3072}\right)$$ $$e\left(\frac{231}{256}\right)$$ $$e\left(\frac{919}{1024}\right)$$ $$e\left(\frac{469}{1536}\right)$$ $$e\left(\frac{515}{1536}\right)$$ $$e\left(\frac{2161}{3072}\right)$$ $$e\left(\frac{19}{384}\right)$$
$$\chi_{36864}(7,\cdot)$$ 36864.dd 1536 no $$-1$$ $$1$$ $$e\left(\frac{47}{1536}\right)$$ $$e\left(\frac{11}{768}\right)$$ $$e\left(\frac{1051}{1536}\right)$$ $$e\left(\frac{737}{1536}\right)$$ $$e\left(\frac{35}{128}\right)$$ $$e\left(\frac{147}{512}\right)$$ $$e\left(\frac{649}{768}\right)$$ $$e\left(\frac{47}{768}\right)$$ $$e\left(\frac{1429}{1536}\right)$$ $$e\left(\frac{31}{192}\right)$$
$$\chi_{36864}(11,\cdot)$$ 36864.dh 3072 yes $$1$$ $$1$$ $$e\left(\frac{127}{3072}\right)$$ $$e\left(\frac{1051}{1536}\right)$$ $$e\left(\frac{2987}{3072}\right)$$ $$e\left(\frac{2449}{3072}\right)$$ $$e\left(\frac{51}{256}\right)$$ $$e\left(\frac{675}{1024}\right)$$ $$e\left(\frac{1337}{1536}\right)$$ $$e\left(\frac{127}{1536}\right)$$ $$e\left(\frac{1541}{3072}\right)$$ $$e\left(\frac{143}{384}\right)$$
$$\chi_{36864}(13,\cdot)$$ 36864.di 3072 yes $$1$$ $$1$$ $$e\left(\frac{1997}{3072}\right)$$ $$e\left(\frac{737}{1536}\right)$$ $$e\left(\frac{2449}{3072}\right)$$ $$e\left(\frac{2915}{3072}\right)$$ $$e\left(\frac{41}{256}\right)$$ $$e\left(\frac{761}{1024}\right)$$ $$e\left(\frac{475}{1536}\right)$$ $$e\left(\frac{461}{1536}\right)$$ $$e\left(\frac{1663}{3072}\right)$$ $$e\left(\frac{61}{384}\right)$$
$$\chi_{36864}(17,\cdot)$$ 36864.ci 256 no $$-1$$ $$1$$ $$e\left(\frac{231}{256}\right)$$ $$e\left(\frac{35}{128}\right)$$ $$e\left(\frac{51}{256}\right)$$ $$e\left(\frac{41}{256}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{193}{256}\right)$$ $$e\left(\frac{81}{128}\right)$$ $$e\left(\frac{103}{128}\right)$$ $$e\left(\frac{253}{256}\right)$$ $$e\left(\frac{23}{32}\right)$$
$$\chi_{36864}(19,\cdot)$$ 36864.db 1024 no $$-1$$ $$1$$ $$e\left(\frac{919}{1024}\right)$$ $$e\left(\frac{147}{512}\right)$$ $$e\left(\frac{675}{1024}\right)$$ $$e\left(\frac{761}{1024}\right)$$ $$e\left(\frac{193}{256}\right)$$ $$e\left(\frac{273}{1024}\right)$$ $$e\left(\frac{481}{512}\right)$$ $$e\left(\frac{407}{512}\right)$$ $$e\left(\frac{653}{1024}\right)$$ $$e\left(\frac{39}{128}\right)$$
$$\chi_{36864}(23,\cdot)$$ 36864.df 1536 no $$1$$ $$1$$ $$e\left(\frac{469}{1536}\right)$$ $$e\left(\frac{649}{768}\right)$$ $$e\left(\frac{1337}{1536}\right)$$ $$e\left(\frac{475}{1536}\right)$$ $$e\left(\frac{81}{128}\right)$$ $$e\left(\frac{481}{512}\right)$$ $$e\left(\frac{275}{768}\right)$$ $$e\left(\frac{469}{768}\right)$$ $$e\left(\frac{599}{1536}\right)$$ $$e\left(\frac{101}{192}\right)$$
$$\chi_{36864}(25,\cdot)$$ 36864.dc 1536 no $$1$$ $$1$$ $$e\left(\frac{515}{1536}\right)$$ $$e\left(\frac{47}{768}\right)$$ $$e\left(\frac{127}{1536}\right)$$ $$e\left(\frac{461}{1536}\right)$$ $$e\left(\frac{103}{128}\right)$$ $$e\left(\frac{407}{512}\right)$$ $$e\left(\frac{469}{768}\right)$$ $$e\left(\frac{515}{768}\right)$$ $$e\left(\frac{625}{1536}\right)$$ $$e\left(\frac{19}{192}\right)$$
$$\chi_{36864}(29,\cdot)$$ 36864.dj 3072 yes $$-1$$ $$1$$ $$e\left(\frac{2161}{3072}\right)$$ $$e\left(\frac{1429}{1536}\right)$$ $$e\left(\frac{1541}{3072}\right)$$ $$e\left(\frac{1663}{3072}\right)$$ $$e\left(\frac{253}{256}\right)$$ $$e\left(\frac{653}{1024}\right)$$ $$e\left(\frac{599}{1536}\right)$$ $$e\left(\frac{625}{1536}\right)$$ $$e\left(\frac{1355}{3072}\right)$$ $$e\left(\frac{161}{384}\right)$$
$$\chi_{36864}(31,\cdot)$$ 36864.cp 384 no $$-1$$ $$1$$ $$e\left(\frac{19}{384}\right)$$ $$e\left(\frac{31}{192}\right)$$ $$e\left(\frac{143}{384}\right)$$ $$e\left(\frac{61}{384}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{39}{128}\right)$$ $$e\left(\frac{101}{192}\right)$$ $$e\left(\frac{19}{192}\right)$$ $$e\left(\frac{161}{384}\right)$$ $$e\left(\frac{11}{48}\right)$$
$$\chi_{36864}(35,\cdot)$$ 36864.da 1024 no $$1$$ $$1$$ $$e\left(\frac{203}{1024}\right)$$ $$e\left(\frac{23}{512}\right)$$ $$e\left(\frac{743}{1024}\right)$$ $$e\left(\frac{133}{1024}\right)$$ $$e\left(\frac{45}{256}\right)$$ $$e\left(\frac{189}{1024}\right)$$ $$e\left(\frac{77}{512}\right)$$ $$e\left(\frac{203}{512}\right)$$ $$e\left(\frac{649}{1024}\right)$$ $$e\left(\frac{27}{128}\right)$$
$$\chi_{36864}(37,\cdot)$$ 36864.cz 1024 no $$1$$ $$1$$ $$e\left(\frac{281}{1024}\right)$$ $$e\left(\frac{477}{512}\right)$$ $$e\left(\frac{461}{1024}\right)$$ $$e\left(\frac{343}{1024}\right)$$ $$e\left(\frac{15}{256}\right)$$ $$e\left(\frac{191}{1024}\right)$$ $$e\left(\frac{495}{512}\right)$$ $$e\left(\frac{281}{512}\right)$$ $$e\left(\frac{515}{1024}\right)$$ $$e\left(\frac{73}{128}\right)$$
$$\chi_{36864}(41,\cdot)$$ 36864.de 1536 no $$-1$$ $$1$$ $$e\left(\frac{1405}{1536}\right)$$ $$e\left(\frac{337}{768}\right)$$ $$e\left(\frac{257}{1536}\right)$$ $$e\left(\frac{1459}{1536}\right)$$ $$e\left(\frac{89}{128}\right)$$ $$e\left(\frac{233}{512}\right)$$ $$e\left(\frac{299}{768}\right)$$ $$e\left(\frac{637}{768}\right)$$ $$e\left(\frac{527}{1536}\right)$$ $$e\left(\frac{173}{192}\right)$$
$$\chi_{36864}(43,\cdot)$$ 36864.dg 3072 yes $$-1$$ $$1$$ $$e\left(\frac{1975}{3072}\right)$$ $$e\left(\frac{307}{1536}\right)$$ $$e\left(\frac{323}{3072}\right)$$ $$e\left(\frac{217}{3072}\right)$$ $$e\left(\frac{139}{256}\right)$$ $$e\left(\frac{1019}{1024}\right)$$ $$e\left(\frac{1217}{1536}\right)$$ $$e\left(\frac{439}{1536}\right)$$ $$e\left(\frac{1517}{3072}\right)$$ $$e\left(\frac{71}{384}\right)$$
$$\chi_{36864}(47,\cdot)$$ 36864.cu 768 no $$1$$ $$1$$ $$e\left(\frac{1}{768}\right)$$ $$e\left(\frac{37}{384}\right)$$ $$e\left(\frac{341}{768}\right)$$ $$e\left(\frac{367}{768}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{221}{256}\right)$$ $$e\left(\frac{71}{384}\right)$$ $$e\left(\frac{1}{384}\right)$$ $$e\left(\frac{635}{768}\right)$$ $$e\left(\frac{65}{96}\right)$$
$$\chi_{36864}(49,\cdot)$$ 36864.cx 768 no $$1$$ $$1$$ $$e\left(\frac{47}{768}\right)$$ $$e\left(\frac{11}{384}\right)$$ $$e\left(\frac{283}{768}\right)$$ $$e\left(\frac{737}{768}\right)$$ $$e\left(\frac{35}{64}\right)$$ $$e\left(\frac{147}{256}\right)$$ $$e\left(\frac{265}{384}\right)$$ $$e\left(\frac{47}{384}\right)$$ $$e\left(\frac{661}{768}\right)$$ $$e\left(\frac{31}{96}\right)$$
$$\chi_{36864}(53,\cdot)$$ 36864.cy 1024 no $$-1$$ $$1$$ $$e\left(\frac{261}{1024}\right)$$ $$e\left(\frac{505}{512}\right)$$ $$e\left(\frac{297}{1024}\right)$$ $$e\left(\frac{171}{1024}\right)$$ $$e\left(\frac{131}{256}\right)$$ $$e\left(\frac{755}{1024}\right)$$ $$e\left(\frac{355}{512}\right)$$ $$e\left(\frac{261}{512}\right)$$ $$e\left(\frac{103}{1024}\right)$$ $$e\left(\frac{117}{128}\right)$$
$$\chi_{36864}(55,\cdot)$$ 36864.cq 512 no $$-1$$ $$1$$ $$e\left(\frac{107}{512}\right)$$ $$e\left(\frac{183}{256}\right)$$ $$e\left(\frac{7}{512}\right)$$ $$e\left(\frac{229}{512}\right)$$ $$e\left(\frac{13}{128}\right)$$ $$e\left(\frac{285}{512}\right)$$ $$e\left(\frac{45}{256}\right)$$ $$e\left(\frac{107}{256}\right)$$ $$e\left(\frac{105}{512}\right)$$ $$e\left(\frac{27}{64}\right)$$
$$\chi_{36864}(59,\cdot)$$ 36864.dh 3072 yes $$1$$ $$1$$ $$e\left(\frac{1139}{3072}\right)$$ $$e\left(\frac{863}{1536}\right)$$ $$e\left(\frac{2479}{3072}\right)$$ $$e\left(\frac{605}{3072}\right)$$ $$e\left(\frac{151}{256}\right)$$ $$e\left(\frac{71}{1024}\right)$$ $$e\left(\frac{997}{1536}\right)$$ $$e\left(\frac{1139}{1536}\right)$$ $$e\left(\frac{2113}{3072}\right)$$ $$e\left(\frac{67}{384}\right)$$
$$\chi_{36864}(61,\cdot)$$ 36864.di 3072 yes $$1$$ $$1$$ $$e\left(\frac{2041}{3072}\right)$$ $$e\left(\frac{61}{1536}\right)$$ $$e\left(\frac{557}{3072}\right)$$ $$e\left(\frac{2167}{3072}\right)$$ $$e\left(\frac{101}{256}\right)$$ $$e\left(\frac{245}{1024}\right)$$ $$e\left(\frac{527}{1536}\right)$$ $$e\left(\frac{505}{1536}\right)$$ $$e\left(\frac{1955}{3072}\right)$$ $$e\left(\frac{41}{384}\right)$$
$$\chi_{36864}(65,\cdot)$$ 36864.cf 192 no $$-1$$ $$1$$ $$e\left(\frac{157}{192}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{161}{192}\right)$$ $$e\left(\frac{115}{192}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{41}{64}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{47}{192}\right)$$ $$e\left(\frac{5}{24}\right)$$
$$\chi_{36864}(67,\cdot)$$ 36864.dg 3072 yes $$-1$$ $$1$$ $$e\left(\frac{2009}{3072}\right)$$ $$e\left(\frac{1181}{1536}\right)$$ $$e\left(\frac{397}{3072}\right)$$ $$e\left(\frac{2711}{3072}\right)$$ $$e\left(\frac{197}{256}\right)$$ $$e\left(\frac{853}{1024}\right)$$ $$e\left(\frac{559}{1536}\right)$$ $$e\left(\frac{473}{1536}\right)$$ $$e\left(\frac{67}{3072}\right)$$ $$e\left(\frac{73}{384}\right)$$
$$\chi_{36864}(71,\cdot)$$ 36864.cs 512 no $$1$$ $$1$$ $$e\left(\frac{173}{512}\right)$$ $$e\left(\frac{193}{256}\right)$$ $$e\left(\frac{241}{512}\right)$$ $$e\left(\frac{387}{512}\right)$$ $$e\left(\frac{91}{128}\right)$$ $$e\left(\frac{267}{512}\right)$$ $$e\left(\frac{251}{256}\right)$$ $$e\left(\frac{173}{256}\right)$$ $$e\left(\frac{31}{512}\right)$$ $$e\left(\frac{61}{64}\right)$$
$$\chi_{36864}(73,\cdot)$$ 36864.cr 512 no $$1$$ $$1$$ $$e\left(\frac{219}{512}\right)$$ $$e\left(\frac{103}{256}\right)$$ $$e\left(\frac{55}{512}\right)$$ $$e\left(\frac{373}{512}\right)$$ $$e\left(\frac{29}{128}\right)$$ $$e\left(\frac{45}{512}\right)$$ $$e\left(\frac{189}{256}\right)$$ $$e\left(\frac{219}{256}\right)$$ $$e\left(\frac{57}{512}\right)$$ $$e\left(\frac{43}{64}\right)$$
$$\chi_{36864}(77,\cdot)$$ 36864.dj 3072 yes $$-1$$ $$1$$ $$e\left(\frac{221}{3072}\right)$$ $$e\left(\frac{1073}{1536}\right)$$ $$e\left(\frac{2017}{3072}\right)$$ $$e\left(\frac{851}{3072}\right)$$ $$e\left(\frac{121}{256}\right)$$ $$e\left(\frac{969}{1024}\right)$$ $$e\left(\frac{1099}{1536}\right)$$ $$e\left(\frac{221}{1536}\right)$$ $$e\left(\frac{1327}{3072}\right)$$ $$e\left(\frac{205}{384}\right)$$
$$\chi_{36864}(79,\cdot)$$ 36864.cv 768 no $$-1$$ $$1$$ $$e\left(\frac{199}{768}\right)$$ $$e\left(\frac{67}{384}\right)$$ $$e\left(\frac{275}{768}\right)$$ $$e\left(\frac{457}{768}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{75}{256}\right)$$ $$e\left(\frac{113}{384}\right)$$ $$e\left(\frac{199}{384}\right)$$ $$e\left(\frac{413}{768}\right)$$ $$e\left(\frac{71}{96}\right)$$
$$\chi_{36864}(83,\cdot)$$ 36864.dh 3072 yes $$1$$ $$1$$ $$e\left(\frac{949}{3072}\right)$$ $$e\left(\frac{1129}{1536}\right)$$ $$e\left(\frac{2969}{3072}\right)$$ $$e\left(\frac{763}{3072}\right)$$ $$e\left(\frac{113}{256}\right)$$ $$e\left(\frac{577}{1024}\right)$$ $$e\left(\frac{1331}{1536}\right)$$ $$e\left(\frac{949}{1536}\right)$$ $$e\left(\frac{2807}{3072}\right)$$ $$e\left(\frac{101}{384}\right)$$
$$\chi_{36864}(85,\cdot)$$ 36864.di 3072 yes $$1$$ $$1$$ $$e\left(\frac{215}{3072}\right)$$ $$e\left(\frac{467}{1536}\right)$$ $$e\left(\frac{739}{3072}\right)$$ $$e\left(\frac{2489}{3072}\right)$$ $$e\left(\frac{43}{256}\right)$$ $$e\left(\frac{667}{1024}\right)$$ $$e\left(\frac{1441}{1536}\right)$$ $$e\left(\frac{215}{1536}\right)$$ $$e\left(\frac{2125}{3072}\right)$$ $$e\left(\frac{295}{384}\right)$$
$$\chi_{36864}(89,\cdot)$$ 36864.ct 512 no $$-1$$ $$1$$ $$e\left(\frac{441}{512}\right)$$ $$e\left(\frac{253}{256}\right)$$ $$e\left(\frac{237}{512}\right)$$ $$e\left(\frac{439}{512}\right)$$ $$e\left(\frac{47}{128}\right)$$ $$e\left(\frac{31}{512}\right)$$ $$e\left(\frac{207}{256}\right)$$ $$e\left(\frac{185}{256}\right)$$ $$e\left(\frac{227}{512}\right)$$ $$e\left(\frac{41}{64}\right)$$
$$\chi_{36864}(91,\cdot)$$ 36864.db 1024 no $$-1$$ $$1$$ $$e\left(\frac{697}{1024}\right)$$ $$e\left(\frac{253}{512}\right)$$ $$e\left(\frac{493}{1024}\right)$$ $$e\left(\frac{439}{1024}\right)$$ $$e\left(\frac{111}{256}\right)$$ $$e\left(\frac{31}{1024}\right)$$ $$e\left(\frac{79}{512}\right)$$ $$e\left(\frac{185}{512}\right)$$ $$e\left(\frac{483}{1024}\right)$$ $$e\left(\frac{41}{128}\right)$$
$$\chi_{36864}(95,\cdot)$$ 36864.cn 384 no $$1$$ $$1$$ $$e\left(\frac{25}{384}\right)$$ $$e\left(\frac{61}{192}\right)$$ $$e\left(\frac{269}{384}\right)$$ $$e\left(\frac{151}{384}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{21}{128}\right)$$ $$e\left(\frac{47}{192}\right)$$ $$e\left(\frac{25}{192}\right)$$ $$e\left(\frac{131}{384}\right)$$ $$e\left(\frac{17}{48}\right)$$