sage: H = DirichletGroup(6044)
pari: g = idealstar(,6044,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 3020 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{1510}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{6044}(3023,\cdot)$, $\chi_{6044}(3033,\cdot)$ |
First 32 of 3020 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6044}(1,\cdot)\) | 6044.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{6044}(3,\cdot)\) | 6044.l | 302 | yes | \(-1\) | \(1\) | \(e\left(\frac{45}{302}\right)\) | \(e\left(\frac{126}{151}\right)\) | \(e\left(\frac{165}{302}\right)\) | \(e\left(\frac{45}{151}\right)\) | \(e\left(\frac{299}{302}\right)\) | \(e\left(\frac{91}{151}\right)\) | \(e\left(\frac{297}{302}\right)\) | \(e\left(\frac{149}{151}\right)\) | \(e\left(\frac{87}{302}\right)\) | \(e\left(\frac{105}{151}\right)\) |
| \(\chi_{6044}(5,\cdot)\) | 6044.m | 755 | no | \(1\) | \(1\) | \(e\left(\frac{126}{151}\right)\) | \(e\left(\frac{508}{755}\right)\) | \(e\left(\frac{498}{755}\right)\) | \(e\left(\frac{101}{151}\right)\) | \(e\left(\frac{562}{755}\right)\) | \(e\left(\frac{736}{755}\right)\) | \(e\left(\frac{383}{755}\right)\) | \(e\left(\frac{699}{755}\right)\) | \(e\left(\frac{161}{755}\right)\) | \(e\left(\frac{373}{755}\right)\) |
| \(\chi_{6044}(7,\cdot)\) | 6044.o | 1510 | yes | \(-1\) | \(1\) | \(e\left(\frac{165}{302}\right)\) | \(e\left(\frac{498}{755}\right)\) | \(e\left(\frac{911}{1510}\right)\) | \(e\left(\frac{14}{151}\right)\) | \(e\left(\frac{549}{1510}\right)\) | \(e\left(\frac{561}{755}\right)\) | \(e\left(\frac{311}{1510}\right)\) | \(e\left(\frac{64}{755}\right)\) | \(e\left(\frac{387}{1510}\right)\) | \(e\left(\frac{113}{755}\right)\) |
| \(\chi_{6044}(9,\cdot)\) | 6044.i | 151 | no | \(1\) | \(1\) | \(e\left(\frac{45}{151}\right)\) | \(e\left(\frac{101}{151}\right)\) | \(e\left(\frac{14}{151}\right)\) | \(e\left(\frac{90}{151}\right)\) | \(e\left(\frac{148}{151}\right)\) | \(e\left(\frac{31}{151}\right)\) | \(e\left(\frac{146}{151}\right)\) | \(e\left(\frac{147}{151}\right)\) | \(e\left(\frac{87}{151}\right)\) | \(e\left(\frac{59}{151}\right)\) |
| \(\chi_{6044}(11,\cdot)\) | 6044.p | 1510 | yes | \(1\) | \(1\) | \(e\left(\frac{299}{302}\right)\) | \(e\left(\frac{562}{755}\right)\) | \(e\left(\frac{549}{1510}\right)\) | \(e\left(\frac{148}{151}\right)\) | \(e\left(\frac{378}{755}\right)\) | \(e\left(\frac{624}{755}\right)\) | \(e\left(\frac{1109}{1510}\right)\) | \(e\left(\frac{51}{755}\right)\) | \(e\left(\frac{273}{1510}\right)\) | \(e\left(\frac{267}{755}\right)\) |
| \(\chi_{6044}(13,\cdot)\) | 6044.m | 755 | no | \(1\) | \(1\) | \(e\left(\frac{91}{151}\right)\) | \(e\left(\frac{736}{755}\right)\) | \(e\left(\frac{561}{755}\right)\) | \(e\left(\frac{31}{151}\right)\) | \(e\left(\frac{624}{755}\right)\) | \(e\left(\frac{347}{755}\right)\) | \(e\left(\frac{436}{755}\right)\) | \(e\left(\frac{228}{755}\right)\) | \(e\left(\frac{477}{755}\right)\) | \(e\left(\frac{261}{755}\right)\) |
| \(\chi_{6044}(15,\cdot)\) | 6044.o | 1510 | yes | \(-1\) | \(1\) | \(e\left(\frac{297}{302}\right)\) | \(e\left(\frac{383}{755}\right)\) | \(e\left(\frac{311}{1510}\right)\) | \(e\left(\frac{146}{151}\right)\) | \(e\left(\frac{1109}{1510}\right)\) | \(e\left(\frac{436}{755}\right)\) | \(e\left(\frac{741}{1510}\right)\) | \(e\left(\frac{689}{755}\right)\) | \(e\left(\frac{757}{1510}\right)\) | \(e\left(\frac{143}{755}\right)\) |
| \(\chi_{6044}(17,\cdot)\) | 6044.m | 755 | no | \(1\) | \(1\) | \(e\left(\frac{149}{151}\right)\) | \(e\left(\frac{699}{755}\right)\) | \(e\left(\frac{64}{755}\right)\) | \(e\left(\frac{147}{151}\right)\) | \(e\left(\frac{51}{755}\right)\) | \(e\left(\frac{228}{755}\right)\) | \(e\left(\frac{689}{755}\right)\) | \(e\left(\frac{672}{755}\right)\) | \(e\left(\frac{333}{755}\right)\) | \(e\left(\frac{54}{755}\right)\) |
| \(\chi_{6044}(19,\cdot)\) | 6044.o | 1510 | yes | \(-1\) | \(1\) | \(e\left(\frac{87}{302}\right)\) | \(e\left(\frac{161}{755}\right)\) | \(e\left(\frac{387}{1510}\right)\) | \(e\left(\frac{87}{151}\right)\) | \(e\left(\frac{273}{1510}\right)\) | \(e\left(\frac{477}{755}\right)\) | \(e\left(\frac{757}{1510}\right)\) | \(e\left(\frac{333}{755}\right)\) | \(e\left(\frac{539}{1510}\right)\) | \(e\left(\frac{411}{755}\right)\) |
| \(\chi_{6044}(21,\cdot)\) | 6044.m | 755 | no | \(1\) | \(1\) | \(e\left(\frac{105}{151}\right)\) | \(e\left(\frac{373}{755}\right)\) | \(e\left(\frac{113}{755}\right)\) | \(e\left(\frac{59}{151}\right)\) | \(e\left(\frac{267}{755}\right)\) | \(e\left(\frac{261}{755}\right)\) | \(e\left(\frac{143}{755}\right)\) | \(e\left(\frac{54}{755}\right)\) | \(e\left(\frac{411}{755}\right)\) | \(e\left(\frac{638}{755}\right)\) |
| \(\chi_{6044}(23,\cdot)\) | 6044.p | 1510 | yes | \(1\) | \(1\) | \(e\left(\frac{223}{302}\right)\) | \(e\left(\frac{102}{755}\right)\) | \(e\left(\frac{1169}{1510}\right)\) | \(e\left(\frac{72}{151}\right)\) | \(e\left(\frac{743}{755}\right)\) | \(e\left(\frac{124}{755}\right)\) | \(e\left(\frac{1319}{1510}\right)\) | \(e\left(\frac{286}{755}\right)\) | \(e\left(\frac{243}{1510}\right)\) | \(e\left(\frac{387}{755}\right)\) |
| \(\chi_{6044}(25,\cdot)\) | 6044.m | 755 | no | \(1\) | \(1\) | \(e\left(\frac{101}{151}\right)\) | \(e\left(\frac{261}{755}\right)\) | \(e\left(\frac{241}{755}\right)\) | \(e\left(\frac{51}{151}\right)\) | \(e\left(\frac{369}{755}\right)\) | \(e\left(\frac{717}{755}\right)\) | \(e\left(\frac{11}{755}\right)\) | \(e\left(\frac{643}{755}\right)\) | \(e\left(\frac{322}{755}\right)\) | \(e\left(\frac{746}{755}\right)\) |
| \(\chi_{6044}(27,\cdot)\) | 6044.l | 302 | yes | \(-1\) | \(1\) | \(e\left(\frac{135}{302}\right)\) | \(e\left(\frac{76}{151}\right)\) | \(e\left(\frac{193}{302}\right)\) | \(e\left(\frac{135}{151}\right)\) | \(e\left(\frac{293}{302}\right)\) | \(e\left(\frac{122}{151}\right)\) | \(e\left(\frac{287}{302}\right)\) | \(e\left(\frac{145}{151}\right)\) | \(e\left(\frac{261}{302}\right)\) | \(e\left(\frac{13}{151}\right)\) |
| \(\chi_{6044}(29,\cdot)\) | 6044.n | 1510 | no | \(-1\) | \(1\) | \(e\left(\frac{107}{151}\right)\) | \(e\left(\frac{731}{755}\right)\) | \(e\left(\frac{351}{755}\right)\) | \(e\left(\frac{63}{151}\right)\) | \(e\left(\frac{583}{1510}\right)\) | \(e\left(\frac{637}{755}\right)\) | \(e\left(\frac{511}{755}\right)\) | \(e\left(\frac{288}{755}\right)\) | \(e\left(\frac{682}{755}\right)\) | \(e\left(\frac{131}{755}\right)\) |
| \(\chi_{6044}(31,\cdot)\) | 6044.o | 1510 | yes | \(-1\) | \(1\) | \(e\left(\frac{125}{302}\right)\) | \(e\left(\frac{391}{755}\right)\) | \(e\left(\frac{77}{1510}\right)\) | \(e\left(\frac{125}{151}\right)\) | \(e\left(\frac{663}{1510}\right)\) | \(e\left(\frac{727}{755}\right)\) | \(e\left(\frac{1407}{1510}\right)\) | \(e\left(\frac{593}{755}\right)\) | \(e\left(\frac{1309}{1510}\right)\) | \(e\left(\frac{351}{755}\right)\) |
| \(\chi_{6044}(33,\cdot)\) | 6044.n | 1510 | no | \(-1\) | \(1\) | \(e\left(\frac{21}{151}\right)\) | \(e\left(\frac{437}{755}\right)\) | \(e\left(\frac{687}{755}\right)\) | \(e\left(\frac{42}{151}\right)\) | \(e\left(\frac{741}{1510}\right)\) | \(e\left(\frac{324}{755}\right)\) | \(e\left(\frac{542}{755}\right)\) | \(e\left(\frac{41}{755}\right)\) | \(e\left(\frac{354}{755}\right)\) | \(e\left(\frac{37}{755}\right)\) |
| \(\chi_{6044}(35,\cdot)\) | 6044.o | 1510 | yes | \(-1\) | \(1\) | \(e\left(\frac{115}{302}\right)\) | \(e\left(\frac{251}{755}\right)\) | \(e\left(\frac{397}{1510}\right)\) | \(e\left(\frac{115}{151}\right)\) | \(e\left(\frac{163}{1510}\right)\) | \(e\left(\frac{542}{755}\right)\) | \(e\left(\frac{1077}{1510}\right)\) | \(e\left(\frac{8}{755}\right)\) | \(e\left(\frac{709}{1510}\right)\) | \(e\left(\frac{486}{755}\right)\) |
| \(\chi_{6044}(37,\cdot)\) | 6044.n | 1510 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{151}\right)\) | \(e\left(\frac{6}{755}\right)\) | \(e\left(\frac{101}{755}\right)\) | \(e\left(\frac{22}{151}\right)\) | \(e\left(\frac{43}{1510}\right)\) | \(e\left(\frac{407}{755}\right)\) | \(e\left(\frac{61}{755}\right)\) | \(e\left(\frac{683}{755}\right)\) | \(e\left(\frac{207}{755}\right)\) | \(e\left(\frac{156}{755}\right)\) |
| \(\chi_{6044}(39,\cdot)\) | 6044.o | 1510 | yes | \(-1\) | \(1\) | \(e\left(\frac{227}{302}\right)\) | \(e\left(\frac{611}{755}\right)\) | \(e\left(\frac{437}{1510}\right)\) | \(e\left(\frac{76}{151}\right)\) | \(e\left(\frac{1233}{1510}\right)\) | \(e\left(\frac{47}{755}\right)\) | \(e\left(\frac{847}{1510}\right)\) | \(e\left(\frac{218}{755}\right)\) | \(e\left(\frac{1389}{1510}\right)\) | \(e\left(\frac{31}{755}\right)\) |
| \(\chi_{6044}(41,\cdot)\) | 6044.n | 1510 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{151}\right)\) | \(e\left(\frac{583}{755}\right)\) | \(e\left(\frac{628}{755}\right)\) | \(e\left(\frac{74}{151}\right)\) | \(e\left(\frac{529}{1510}\right)\) | \(e\left(\frac{161}{755}\right)\) | \(e\left(\frac{13}{755}\right)\) | \(e\left(\frac{554}{755}\right)\) | \(e\left(\frac{106}{755}\right)\) | \(e\left(\frac{58}{755}\right)\) |
| \(\chi_{6044}(43,\cdot)\) | 6044.p | 1510 | yes | \(1\) | \(1\) | \(e\left(\frac{283}{302}\right)\) | \(e\left(\frac{338}{755}\right)\) | \(e\left(\frac{1061}{1510}\right)\) | \(e\left(\frac{132}{151}\right)\) | \(e\left(\frac{582}{755}\right)\) | \(e\left(\frac{26}{755}\right)\) | \(e\left(\frac{581}{1510}\right)\) | \(e\left(\frac{474}{755}\right)\) | \(e\left(\frac{1427}{1510}\right)\) | \(e\left(\frac{483}{755}\right)\) |
| \(\chi_{6044}(45,\cdot)\) | 6044.m | 755 | no | \(1\) | \(1\) | \(e\left(\frac{20}{151}\right)\) | \(e\left(\frac{258}{755}\right)\) | \(e\left(\frac{568}{755}\right)\) | \(e\left(\frac{40}{151}\right)\) | \(e\left(\frac{547}{755}\right)\) | \(e\left(\frac{136}{755}\right)\) | \(e\left(\frac{358}{755}\right)\) | \(e\left(\frac{679}{755}\right)\) | \(e\left(\frac{596}{755}\right)\) | \(e\left(\frac{668}{755}\right)\) |
| \(\chi_{6044}(47,\cdot)\) | 6044.p | 1510 | yes | \(1\) | \(1\) | \(e\left(\frac{61}{302}\right)\) | \(e\left(\frac{703}{755}\right)\) | \(e\left(\frac{11}{1510}\right)\) | \(e\left(\frac{61}{151}\right)\) | \(e\left(\frac{317}{755}\right)\) | \(e\left(\frac{751}{755}\right)\) | \(e\left(\frac{201}{1510}\right)\) | \(e\left(\frac{624}{755}\right)\) | \(e\left(\frac{187}{1510}\right)\) | \(e\left(\frac{158}{755}\right)\) |
| \(\chi_{6044}(49,\cdot)\) | 6044.m | 755 | no | \(1\) | \(1\) | \(e\left(\frac{14}{151}\right)\) | \(e\left(\frac{241}{755}\right)\) | \(e\left(\frac{156}{755}\right)\) | \(e\left(\frac{28}{151}\right)\) | \(e\left(\frac{549}{755}\right)\) | \(e\left(\frac{367}{755}\right)\) | \(e\left(\frac{311}{755}\right)\) | \(e\left(\frac{128}{755}\right)\) | \(e\left(\frac{387}{755}\right)\) | \(e\left(\frac{226}{755}\right)\) |
| \(\chi_{6044}(51,\cdot)\) | 6044.o | 1510 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{302}\right)\) | \(e\left(\frac{574}{755}\right)\) | \(e\left(\frac{953}{1510}\right)\) | \(e\left(\frac{41}{151}\right)\) | \(e\left(\frac{87}{1510}\right)\) | \(e\left(\frac{683}{755}\right)\) | \(e\left(\frac{1353}{1510}\right)\) | \(e\left(\frac{662}{755}\right)\) | \(e\left(\frac{1101}{1510}\right)\) | \(e\left(\frac{579}{755}\right)\) |
| \(\chi_{6044}(53,\cdot)\) | 6044.n | 1510 | no | \(-1\) | \(1\) | \(e\left(\frac{85}{151}\right)\) | \(e\left(\frac{719}{755}\right)\) | \(e\left(\frac{149}{755}\right)\) | \(e\left(\frac{19}{151}\right)\) | \(e\left(\frac{497}{1510}\right)\) | \(e\left(\frac{578}{755}\right)\) | \(e\left(\frac{389}{755}\right)\) | \(e\left(\frac{432}{755}\right)\) | \(e\left(\frac{268}{755}\right)\) | \(e\left(\frac{574}{755}\right)\) |
| \(\chi_{6044}(55,\cdot)\) | 6044.k | 302 | yes | \(1\) | \(1\) | \(e\left(\frac{249}{302}\right)\) | \(e\left(\frac{63}{151}\right)\) | \(e\left(\frac{7}{302}\right)\) | \(e\left(\frac{98}{151}\right)\) | \(e\left(\frac{37}{151}\right)\) | \(e\left(\frac{121}{151}\right)\) | \(e\left(\frac{73}{302}\right)\) | \(e\left(\frac{150}{151}\right)\) | \(e\left(\frac{119}{302}\right)\) | \(e\left(\frac{128}{151}\right)\) |
| \(\chi_{6044}(57,\cdot)\) | 6044.m | 755 | no | \(1\) | \(1\) | \(e\left(\frac{66}{151}\right)\) | \(e\left(\frac{36}{755}\right)\) | \(e\left(\frac{606}{755}\right)\) | \(e\left(\frac{132}{151}\right)\) | \(e\left(\frac{129}{755}\right)\) | \(e\left(\frac{177}{755}\right)\) | \(e\left(\frac{366}{755}\right)\) | \(e\left(\frac{323}{755}\right)\) | \(e\left(\frac{487}{755}\right)\) | \(e\left(\frac{181}{755}\right)\) |
| \(\chi_{6044}(59,\cdot)\) | 6044.p | 1510 | yes | \(1\) | \(1\) | \(e\left(\frac{141}{302}\right)\) | \(e\left(\frac{162}{755}\right)\) | \(e\left(\frac{169}{1510}\right)\) | \(e\left(\frac{141}{151}\right)\) | \(e\left(\frac{203}{755}\right)\) | \(e\left(\frac{419}{755}\right)\) | \(e\left(\frac{1029}{1510}\right)\) | \(e\left(\frac{321}{755}\right)\) | \(e\left(\frac{1363}{1510}\right)\) | \(e\left(\frac{437}{755}\right)\) |
| \(\chi_{6044}(61,\cdot)\) | 6044.m | 755 | no | \(1\) | \(1\) | \(e\left(\frac{7}{151}\right)\) | \(e\left(\frac{196}{755}\right)\) | \(e\left(\frac{531}{755}\right)\) | \(e\left(\frac{14}{151}\right)\) | \(e\left(\frac{199}{755}\right)\) | \(e\left(\frac{712}{755}\right)\) | \(e\left(\frac{231}{755}\right)\) | \(e\left(\frac{668}{755}\right)\) | \(e\left(\frac{722}{755}\right)\) | \(e\left(\frac{566}{755}\right)\) |
| \(\chi_{6044}(63,\cdot)\) | 6044.o | 1510 | yes | \(-1\) | \(1\) | \(e\left(\frac{255}{302}\right)\) | \(e\left(\frac{248}{755}\right)\) | \(e\left(\frac{1051}{1510}\right)\) | \(e\left(\frac{104}{151}\right)\) | \(e\left(\frac{519}{1510}\right)\) | \(e\left(\frac{716}{755}\right)\) | \(e\left(\frac{261}{1510}\right)\) | \(e\left(\frac{44}{755}\right)\) | \(e\left(\frac{1257}{1510}\right)\) | \(e\left(\frac{408}{755}\right)\) |