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Properties

Modulus 319319
Structure C2×C140C_{2}\times C_{140}
Order 280280

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(319)
 
pari: g = idealstar(,319,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 280
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C140C_{2}\times C_{140}
sage: H.gens()
 
pari: g.gen
 
Generators = χ319(233,⋅)\chi_{319}(233,\cdot), χ319(89,⋅)\chi_{319}(89,\cdot)

First 32 of 280 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 22 33 44 55 66 77 88 99 1010 1212
χ319(1,⋅)\chi_{319}(1,\cdot) 319.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ319(2,⋅)\chi_{319}(2,\cdot) 319.x 140 yes 11 11 e(19140)e\left(\frac{19}{140}\right) e(137140)e\left(\frac{137}{140}\right) e(1970)e\left(\frac{19}{70}\right) e(1370)e\left(\frac{13}{70}\right) e(435)e\left(\frac{4}{35}\right) e(970)e\left(\frac{9}{70}\right) e(57140)e\left(\frac{57}{140}\right) e(6770)e\left(\frac{67}{70}\right) e(928)e\left(\frac{9}{28}\right) ii
χ319(3,⋅)\chi_{319}(3,\cdot) 319.w 140 yes −1-1 11 e(137140)e\left(\frac{137}{140}\right) e(41140)e\left(\frac{41}{140}\right) e(6770)e\left(\frac{67}{70}\right) e(970)e\left(\frac{9}{70}\right) e(1970)e\left(\frac{19}{70}\right) e(2635)e\left(\frac{26}{35}\right) e(131140)e\left(\frac{131}{140}\right) e(4170)e\left(\frac{41}{70}\right) e(328)e\left(\frac{3}{28}\right) ii
χ319(4,⋅)\chi_{319}(4,\cdot) 319.t 70 yes 11 11 e(1970)e\left(\frac{19}{70}\right) e(6770)e\left(\frac{67}{70}\right) e(1935)e\left(\frac{19}{35}\right) e(1335)e\left(\frac{13}{35}\right) e(835)e\left(\frac{8}{35}\right) e(935)e\left(\frac{9}{35}\right) e(5770)e\left(\frac{57}{70}\right) e(3235)e\left(\frac{32}{35}\right) e(914)e\left(\frac{9}{14}\right) −1-1
χ319(5,⋅)\chi_{319}(5,\cdot) 319.t 70 yes 11 11 e(1370)e\left(\frac{13}{70}\right) e(970)e\left(\frac{9}{70}\right) e(1335)e\left(\frac{13}{35}\right) e(3135)e\left(\frac{31}{35}\right) e(1135)e\left(\frac{11}{35}\right) e(835)e\left(\frac{8}{35}\right) e(3970)e\left(\frac{39}{70}\right) e(935)e\left(\frac{9}{35}\right) e(114)e\left(\frac{1}{14}\right) −1-1
χ319(6,⋅)\chi_{319}(6,\cdot) 319.v 70 yes −1-1 11 e(435)e\left(\frac{4}{35}\right) e(1970)e\left(\frac{19}{70}\right) e(835)e\left(\frac{8}{35}\right) e(1135)e\left(\frac{11}{35}\right) e(2770)e\left(\frac{27}{70}\right) e(6170)e\left(\frac{61}{70}\right) e(1235)e\left(\frac{12}{35}\right) e(1935)e\left(\frac{19}{35}\right) e(37)e\left(\frac{3}{7}\right) −1-1
χ319(7,⋅)\chi_{319}(7,\cdot) 319.u 70 yes −1-1 11 e(970)e\left(\frac{9}{70}\right) e(2635)e\left(\frac{26}{35}\right) e(935)e\left(\frac{9}{35}\right) e(835)e\left(\frac{8}{35}\right) e(6170)e\left(\frac{61}{70}\right) e(370)e\left(\frac{3}{70}\right) e(2770)e\left(\frac{27}{70}\right) e(1735)e\left(\frac{17}{35}\right) e(514)e\left(\frac{5}{14}\right) 11
χ319(8,⋅)\chi_{319}(8,\cdot) 319.x 140 yes 11 11 e(57140)e\left(\frac{57}{140}\right) e(131140)e\left(\frac{131}{140}\right) e(5770)e\left(\frac{57}{70}\right) e(3970)e\left(\frac{39}{70}\right) e(1235)e\left(\frac{12}{35}\right) e(2770)e\left(\frac{27}{70}\right) e(31140)e\left(\frac{31}{140}\right) e(6170)e\left(\frac{61}{70}\right) e(2728)e\left(\frac{27}{28}\right) −i-i
χ319(9,⋅)\chi_{319}(9,\cdot) 319.t 70 yes 11 11 e(6770)e\left(\frac{67}{70}\right) e(4170)e\left(\frac{41}{70}\right) e(3235)e\left(\frac{32}{35}\right) e(935)e\left(\frac{9}{35}\right) e(1935)e\left(\frac{19}{35}\right) e(1735)e\left(\frac{17}{35}\right) e(6170)e\left(\frac{61}{70}\right) e(635)e\left(\frac{6}{35}\right) e(314)e\left(\frac{3}{14}\right) −1-1
χ319(10,⋅)\chi_{319}(10,\cdot) 319.q 28 yes 11 11 e(928)e\left(\frac{9}{28}\right) e(328)e\left(\frac{3}{28}\right) e(914)e\left(\frac{9}{14}\right) e(114)e\left(\frac{1}{14}\right) e(37)e\left(\frac{3}{7}\right) e(514)e\left(\frac{5}{14}\right) e(2728)e\left(\frac{27}{28}\right) e(314)e\left(\frac{3}{14}\right) e(1128)e\left(\frac{11}{28}\right) −i-i
χ319(12,⋅)\chi_{319}(12,\cdot) 319.e 4 no −1-1 11 ii ii −1-1 −1-1 −1-1 11 −i-i −1-1 −i-i −i-i
χ319(13,⋅)\chi_{319}(13,\cdot) 319.v 70 yes −1-1 11 e(2635)e\left(\frac{26}{35}\right) e(170)e\left(\frac{1}{70}\right) e(1735)e\left(\frac{17}{35}\right) e(1935)e\left(\frac{19}{35}\right) e(5370)e\left(\frac{53}{70}\right) e(2970)e\left(\frac{29}{70}\right) e(835)e\left(\frac{8}{35}\right) e(135)e\left(\frac{1}{35}\right) e(27)e\left(\frac{2}{7}\right) −1-1
χ319(14,⋅)\chi_{319}(14,\cdot) 319.w 140 yes −1-1 11 e(37140)e\left(\frac{37}{140}\right) e(101140)e\left(\frac{101}{140}\right) e(3770)e\left(\frac{37}{70}\right) e(2970)e\left(\frac{29}{70}\right) e(6970)e\left(\frac{69}{70}\right) e(635)e\left(\frac{6}{35}\right) e(111140)e\left(\frac{111}{140}\right) e(3170)e\left(\frac{31}{70}\right) e(1928)e\left(\frac{19}{28}\right) ii
χ319(15,⋅)\chi_{319}(15,\cdot) 319.w 140 yes −1-1 11 e(23140)e\left(\frac{23}{140}\right) e(59140)e\left(\frac{59}{140}\right) e(2370)e\left(\frac{23}{70}\right) e(170)e\left(\frac{1}{70}\right) e(4170)e\left(\frac{41}{70}\right) e(3435)e\left(\frac{34}{35}\right) e(69140)e\left(\frac{69}{140}\right) e(5970)e\left(\frac{59}{70}\right) e(528)e\left(\frac{5}{28}\right) −i-i
χ319(16,⋅)\chi_{319}(16,\cdot) 319.s 35 yes 11 11 e(1935)e\left(\frac{19}{35}\right) e(3235)e\left(\frac{32}{35}\right) e(335)e\left(\frac{3}{35}\right) e(2635)e\left(\frac{26}{35}\right) e(1635)e\left(\frac{16}{35}\right) e(1835)e\left(\frac{18}{35}\right) e(2235)e\left(\frac{22}{35}\right) e(2935)e\left(\frac{29}{35}\right) e(27)e\left(\frac{2}{7}\right) 11
χ319(17,⋅)\chi_{319}(17,\cdot) 319.o 20 yes 11 11 e(1320)e\left(\frac{13}{20}\right) e(1920)e\left(\frac{19}{20}\right) e(310)e\left(\frac{3}{10}\right) e(110)e\left(\frac{1}{10}\right) e(35)e\left(\frac{3}{5}\right) e(310)e\left(\frac{3}{10}\right) e(1920)e\left(\frac{19}{20}\right) e(910)e\left(\frac{9}{10}\right) −i-i ii
χ319(18,⋅)\chi_{319}(18,\cdot) 319.x 140 yes 11 11 e(13140)e\left(\frac{13}{140}\right) e(79140)e\left(\frac{79}{140}\right) e(1370)e\left(\frac{13}{70}\right) e(3170)e\left(\frac{31}{70}\right) e(2335)e\left(\frac{23}{35}\right) e(4370)e\left(\frac{43}{70}\right) e(39140)e\left(\frac{39}{140}\right) e(970)e\left(\frac{9}{70}\right) e(1528)e\left(\frac{15}{28}\right) −i-i
χ319(19,⋅)\chi_{319}(19,\cdot) 319.x 140 yes 11 11 e(87140)e\left(\frac{87}{140}\right) e(1140)e\left(\frac{1}{140}\right) e(1770)e\left(\frac{17}{70}\right) e(1970)e\left(\frac{19}{70}\right) e(2235)e\left(\frac{22}{35}\right) e(6770)e\left(\frac{67}{70}\right) e(121140)e\left(\frac{121}{140}\right) e(170)e\left(\frac{1}{70}\right) e(2528)e\left(\frac{25}{28}\right) ii
χ319(20,⋅)\chi_{319}(20,\cdot) 319.s 35 yes 11 11 e(1635)e\left(\frac{16}{35}\right) e(335)e\left(\frac{3}{35}\right) e(3235)e\left(\frac{32}{35}\right) e(935)e\left(\frac{9}{35}\right) e(1935)e\left(\frac{19}{35}\right) e(1735)e\left(\frac{17}{35}\right) e(1335)e\left(\frac{13}{35}\right) e(635)e\left(\frac{6}{35}\right) e(57)e\left(\frac{5}{7}\right) 11
χ319(21,⋅)\chi_{319}(21,\cdot) 319.q 28 yes 11 11 e(328)e\left(\frac{3}{28}\right) e(128)e\left(\frac{1}{28}\right) e(314)e\left(\frac{3}{14}\right) e(514)e\left(\frac{5}{14}\right) e(17)e\left(\frac{1}{7}\right) e(1114)e\left(\frac{11}{14}\right) e(928)e\left(\frac{9}{28}\right) e(114)e\left(\frac{1}{14}\right) e(1328)e\left(\frac{13}{28}\right) ii
χ319(23,⋅)\chi_{319}(23,\cdot) 319.h 7 no 11 11 e(57)e\left(\frac{5}{7}\right) e(47)e\left(\frac{4}{7}\right) e(37)e\left(\frac{3}{7}\right) e(57)e\left(\frac{5}{7}\right) e(27)e\left(\frac{2}{7}\right) e(47)e\left(\frac{4}{7}\right) e(17)e\left(\frac{1}{7}\right) e(17)e\left(\frac{1}{7}\right) e(37)e\left(\frac{3}{7}\right) 11
χ319(24,⋅)\chi_{319}(24,\cdot) 319.u 70 yes −1-1 11 e(2770)e\left(\frac{27}{70}\right) e(835)e\left(\frac{8}{35}\right) e(2735)e\left(\frac{27}{35}\right) e(2435)e\left(\frac{24}{35}\right) e(4370)e\left(\frac{43}{70}\right) e(970)e\left(\frac{9}{70}\right) e(1170)e\left(\frac{11}{70}\right) e(1635)e\left(\frac{16}{35}\right) e(114)e\left(\frac{1}{14}\right) 11
χ319(25,⋅)\chi_{319}(25,\cdot) 319.s 35 yes 11 11 e(1335)e\left(\frac{13}{35}\right) e(935)e\left(\frac{9}{35}\right) e(2635)e\left(\frac{26}{35}\right) e(2735)e\left(\frac{27}{35}\right) e(2235)e\left(\frac{22}{35}\right) e(1635)e\left(\frac{16}{35}\right) e(435)e\left(\frac{4}{35}\right) e(1835)e\left(\frac{18}{35}\right) e(17)e\left(\frac{1}{7}\right) 11
χ319(26,⋅)\chi_{319}(26,\cdot) 319.w 140 yes −1-1 11 e(123140)e\left(\frac{123}{140}\right) e(139140)e\left(\frac{139}{140}\right) e(5370)e\left(\frac{53}{70}\right) e(5170)e\left(\frac{51}{70}\right) e(6170)e\left(\frac{61}{70}\right) e(1935)e\left(\frac{19}{35}\right) e(89140)e\left(\frac{89}{140}\right) e(6970)e\left(\frac{69}{70}\right) e(1728)e\left(\frac{17}{28}\right) −i-i
χ319(27,⋅)\chi_{319}(27,\cdot) 319.w 140 yes −1-1 11 e(131140)e\left(\frac{131}{140}\right) e(123140)e\left(\frac{123}{140}\right) e(6170)e\left(\frac{61}{70}\right) e(2770)e\left(\frac{27}{70}\right) e(5770)e\left(\frac{57}{70}\right) e(835)e\left(\frac{8}{35}\right) e(113140)e\left(\frac{113}{140}\right) e(5370)e\left(\frac{53}{70}\right) e(928)e\left(\frac{9}{28}\right) −i-i
χ319(28,⋅)\chi_{319}(28,\cdot) 319.i 10 yes −1-1 11 e(25)e\left(\frac{2}{5}\right) e(710)e\left(\frac{7}{10}\right) e(45)e\left(\frac{4}{5}\right) e(35)e\left(\frac{3}{5}\right) e(110)e\left(\frac{1}{10}\right) e(310)e\left(\frac{3}{10}\right) e(15)e\left(\frac{1}{5}\right) e(25)e\left(\frac{2}{5}\right) 11 −1-1
χ319(30,⋅)\chi_{319}(30,\cdot) 319.j 10 no −1-1 11 e(310)e\left(\frac{3}{10}\right) e(25)e\left(\frac{2}{5}\right) e(35)e\left(\frac{3}{5}\right) e(15)e\left(\frac{1}{5}\right) e(710)e\left(\frac{7}{10}\right) e(110)e\left(\frac{1}{10}\right) e(910)e\left(\frac{9}{10}\right) e(45)e\left(\frac{4}{5}\right) −1-1 11
χ319(31,⋅)\chi_{319}(31,\cdot) 319.w 140 yes −1-1 11 e(89140)e\left(\frac{89}{140}\right) e(137140)e\left(\frac{137}{140}\right) e(1970)e\left(\frac{19}{70}\right) e(1370)e\left(\frac{13}{70}\right) e(4370)e\left(\frac{43}{70}\right) e(2235)e\left(\frac{22}{35}\right) e(127140)e\left(\frac{127}{140}\right) e(6770)e\left(\frac{67}{70}\right) e(2328)e\left(\frac{23}{28}\right) ii
χ319(32,⋅)\chi_{319}(32,\cdot) 319.q 28 yes 11 11 e(1928)e\left(\frac{19}{28}\right) e(2528)e\left(\frac{25}{28}\right) e(514)e\left(\frac{5}{14}\right) e(1314)e\left(\frac{13}{14}\right) e(47)e\left(\frac{4}{7}\right) e(914)e\left(\frac{9}{14}\right) e(128)e\left(\frac{1}{28}\right) e(1114)e\left(\frac{11}{14}\right) e(1728)e\left(\frac{17}{28}\right) ii
χ319(34,⋅)\chi_{319}(34,\cdot) 319.n 14 no 11 11 e(1114)e\left(\frac{11}{14}\right) e(1314)e\left(\frac{13}{14}\right) e(47)e\left(\frac{4}{7}\right) e(27)e\left(\frac{2}{7}\right) e(57)e\left(\frac{5}{7}\right) e(37)e\left(\frac{3}{7}\right) e(514)e\left(\frac{5}{14}\right) e(67)e\left(\frac{6}{7}\right) e(114)e\left(\frac{1}{14}\right) −1-1
χ319(35,⋅)\chi_{319}(35,\cdot) 319.v 70 yes −1-1 11 e(1135)e\left(\frac{11}{35}\right) e(6170)e\left(\frac{61}{70}\right) e(2235)e\left(\frac{22}{35}\right) e(435)e\left(\frac{4}{35}\right) e(1370)e\left(\frac{13}{70}\right) e(1970)e\left(\frac{19}{70}\right) e(3335)e\left(\frac{33}{35}\right) e(2635)e\left(\frac{26}{35}\right) e(37)e\left(\frac{3}{7}\right) −1-1
χ319(36,⋅)\chi_{319}(36,\cdot) 319.s 35 yes 11 11 e(835)e\left(\frac{8}{35}\right) e(1935)e\left(\frac{19}{35}\right) e(1635)e\left(\frac{16}{35}\right) e(2235)e\left(\frac{22}{35}\right) e(2735)e\left(\frac{27}{35}\right) e(2635)e\left(\frac{26}{35}\right) e(2435)e\left(\frac{24}{35}\right) e(335)e\left(\frac{3}{35}\right) e(67)e\left(\frac{6}{7}\right) 11
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