Group of Dirichlet characters of modulus 132300

• Modulus: $132300$
• Structure: $C_{2}\times C_{2}\times C_{6}\times C_{1260}$
• Order: $30240$

Character group

Order	=	30240
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{1260}$
Generators	=	$\chi_{132300}(66151,\cdot)$, $\chi_{132300}(122501,\cdot)$, $\chi_{132300}(15877,\cdot)$, $\chi_{132300}(54001,\cdot)$

First 32 of 30240 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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{132300}(1,\cdot)$	132300.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{132300}(11,\cdot)$	132300.bbc	630	yes	$1$	$1$	$e\left(\frac{247}{315}\right)$	$e\left(\frac{128}{315}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{137}{315}\right)$	$e\left(\frac{293}{630}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{481}{630}\right)$	$e\left(\frac{13}{126}\right)$
$\chi_{132300}(13,\cdot)$	132300.bdd	1260	no	$1$	$1$	$e\left(\frac{128}{315}\right)$	$e\left(\frac{673}{1260}\right)$	$e\left(\frac{277}{420}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{247}{1260}\right)$	$e\left(\frac{307}{630}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{89}{630}\right)$	$e\left(\frac{187}{252}\right)$
$\chi_{132300}(17,\cdot)$	132300.zt	420	no	$-1$	$1$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{277}{420}\right)$	$e\left(\frac{349}{420}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{132300}(19,\cdot)$	132300.kx	30	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{132300}(23,\cdot)$	132300.bcq	1260	yes	$-1$	$1$	$e\left(\frac{137}{315}\right)$	$e\left(\frac{247}{1260}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{823}{1260}\right)$	$e\left(\frac{314}{315}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{239}{420}\right)$	$e\left(\frac{101}{630}\right)$	$e\left(\frac{157}{252}\right)$
$\chi_{132300}(29,\cdot)$	132300.bbr	630	no	$-1$	$1$	$e\left(\frac{293}{630}\right)$	$e\left(\frac{307}{630}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{314}{315}\right)$	$e\left(\frac{611}{630}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{487}{630}\right)$	$e\left(\frac{37}{126}\right)$
$\chi_{132300}(31,\cdot)$	132300.sc	90	no	$1$	$1$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{132300}(37,\cdot)$	132300.zz	420	no	$-1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{239}{420}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{132300}(41,\cdot)$	132300.bbh	630	no	$1$	$1$	$e\left(\frac{481}{630}\right)$	$e\left(\frac{89}{630}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{101}{630}\right)$	$e\left(\frac{487}{630}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{67}{315}\right)$	$e\left(\frac{58}{63}\right)$
$\chi_{132300}(43,\cdot)$	132300.yx	252	no	$1$	$1$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{187}{252}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{157}{252}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{125}{252}\right)$
$\chi_{132300}(47,\cdot)$	132300.bcx	1260	yes	$1$	$1$	$e\left(\frac{289}{315}\right)$	$e\left(\frac{239}{1260}\right)$	$e\left(\frac{361}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{821}{1260}\right)$	$e\left(\frac{73}{315}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{251}{315}\right)$	$e\left(\frac{131}{252}\right)$
$\chi_{132300}(53,\cdot)$	132300.bam	420	no	$1$	$1$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{1}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{132300}(59,\cdot)$	132300.bcb	630	yes	$-1$	$1$	$e\left(\frac{218}{315}\right)$	$e\left(\frac{232}{315}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{630}\right)$	$e\left(\frac{157}{630}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{52}{315}\right)$	$e\left(\frac{61}{63}\right)$
$\chi_{132300}(61,\cdot)$	132300.bbz	630	no	$-1$	$1$	$e\left(\frac{262}{315}\right)$	$e\left(\frac{601}{630}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{167}{315}\right)$	$e\left(\frac{64}{315}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{151}{630}\right)$	$e\left(\frac{8}{63}\right)$
$\chi_{132300}(67,\cdot)$	132300.vx	180	no	$1$	$1$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{132300}(71,\cdot)$	132300.wv	210	no	$1$	$1$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{132300}(73,\cdot)$	132300.bad	420	no	$1$	$1$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{359}{420}\right)$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{361}{420}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{132300}(79,\cdot)$	132300.rz	90	no	$-1$	$1$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{132300}(83,\cdot)$	132300.bcv	1260	yes	$1$	$1$	$e\left(\frac{61}{315}\right)$	$e\left(\frac{461}{1260}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1139}{1260}\right)$	$e\left(\frac{67}{315}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{227}{420}\right)$	$e\left(\frac{239}{315}\right)$	$e\left(\frac{65}{252}\right)$
$\chi_{132300}(89,\cdot)$	132300.wk	210	no	$1$	$1$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{19}{42}\right)$
$\chi_{132300}(97,\cdot)$	132300.wc	180	no	$1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{132300}(101,\cdot)$	132300.tl	126	no	$1$	$1$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{44}{63}\right)$
$\chi_{132300}(103,\cdot)$	132300.bdn	1260	yes	$-1$	$1$	$e\left(\frac{523}{630}\right)$	$e\left(\frac{829}{1260}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{181}{1260}\right)$	$e\left(\frac{571}{630}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{617}{630}\right)$	$e\left(\frac{1}{252}\right)$
$\chi_{132300}(107,\cdot)$	132300.qy	84	no	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{132300}(109,\cdot)$	132300.wt	210	no	$1$	$1$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{132300}(113,\cdot)$	132300.bcy	1260	no	$1$	$1$	$e\left(\frac{241}{630}\right)$	$e\left(\frac{1063}{1260}\right)$	$e\left(\frac{157}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{817}{1260}\right)$	$e\left(\frac{11}{315}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{149}{630}\right)$	$e\left(\frac{163}{252}\right)$
$\chi_{132300}(121,\cdot)$	132300.zq	315	no	$1$	$1$	$e\left(\frac{179}{315}\right)$	$e\left(\frac{256}{315}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{274}{315}\right)$	$e\left(\frac{293}{315}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{166}{315}\right)$	$e\left(\frac{13}{63}\right)$
$\chi_{132300}(127,\cdot)$	132300.bai	420	no	$1$	$1$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{179}{420}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{281}{420}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{132300}(131,\cdot)$	132300.bcj	630	yes	$-1$	$1$	$e\left(\frac{281}{315}\right)$	$e\left(\frac{443}{630}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{226}{315}\right)$	$e\left(\frac{619}{630}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{199}{315}\right)$	$e\left(\frac{101}{126}\right)$
$\chi_{132300}(137,\cdot)$	132300.bdm	1260	no	$1$	$1$	$e\left(\frac{191}{630}\right)$	$e\left(\frac{893}{1260}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{407}{1260}\right)$	$e\left(\frac{166}{315}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{121}{420}\right)$	$e\left(\frac{559}{630}\right)$	$e\left(\frac{209}{252}\right)$
$\chi_{132300}(139,\cdot)$	132300.bbq	630	yes	$1$	$1$	$e\left(\frac{19}{630}\right)$	$e\left(\frac{118}{315}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{187}{315}\right)$	$e\left(\frac{44}{315}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{281}{630}\right)$	$e\left(\frac{37}{63}\right)$

Click here to search among the remaining 30208 characters.