# Properties

 Modulus 349 Structure $$C_{348}$$ Order 348

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(349)

pari: g = idealstar(,349,2)

## Character group

 sage: G.order()  pari: g.no Order = 348 sage: H.invariants()  pari: g.cyc Structure = $$C_{348}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{349}(2,\cdot)$

## First 32 of 348 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.

orbit label order primitive -1 1 2 3 4 5 6 7 8 9 10 11
$$\chi_{349}(1,\cdot)$$ 349.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{349}(2,\cdot)$$ 349.l 348 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{348}\right)$$ $$e\left(\frac{13}{174}\right)$$ $$e\left(\frac{1}{174}\right)$$ $$e\left(\frac{157}{174}\right)$$ $$e\left(\frac{9}{116}\right)$$ $$e\left(\frac{67}{348}\right)$$ $$e\left(\frac{1}{116}\right)$$ $$e\left(\frac{13}{87}\right)$$ $$e\left(\frac{105}{116}\right)$$ $$e\left(\frac{7}{116}\right)$$
$$\chi_{349}(3,\cdot)$$ 349.k 174 Yes $$1$$ $$1$$ $$e\left(\frac{13}{174}\right)$$ $$e\left(\frac{82}{87}\right)$$ $$e\left(\frac{13}{87}\right)$$ $$e\left(\frac{40}{87}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{1}{174}\right)$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{77}{87}\right)$$ $$e\left(\frac{31}{58}\right)$$ $$e\left(\frac{33}{58}\right)$$
$$\chi_{349}(4,\cdot)$$ 349.k 174 Yes $$1$$ $$1$$ $$e\left(\frac{1}{174}\right)$$ $$e\left(\frac{13}{87}\right)$$ $$e\left(\frac{1}{87}\right)$$ $$e\left(\frac{70}{87}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{67}{174}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{26}{87}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{7}{58}\right)$$
$$\chi_{349}(5,\cdot)$$ 349.k 174 Yes $$1$$ $$1$$ $$e\left(\frac{157}{174}\right)$$ $$e\left(\frac{40}{87}\right)$$ $$e\left(\frac{70}{87}\right)$$ $$e\left(\frac{28}{87}\right)$$ $$e\left(\frac{21}{58}\right)$$ $$e\left(\frac{79}{174}\right)$$ $$e\left(\frac{41}{58}\right)$$ $$e\left(\frac{80}{87}\right)$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{55}{58}\right)$$
$$\chi_{349}(6,\cdot)$$ 349.j 116 Yes $$-1$$ $$1$$ $$e\left(\frac{9}{116}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{21}{58}\right)$$ $$e\left(\frac{11}{116}\right)$$ $$e\left(\frac{23}{116}\right)$$ $$e\left(\frac{27}{116}\right)$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{51}{116}\right)$$ $$e\left(\frac{73}{116}\right)$$
$$\chi_{349}(7,\cdot)$$ 349.l 348 Yes $$-1$$ $$1$$ $$e\left(\frac{67}{348}\right)$$ $$e\left(\frac{1}{174}\right)$$ $$e\left(\frac{67}{174}\right)$$ $$e\left(\frac{79}{174}\right)$$ $$e\left(\frac{23}{116}\right)$$ $$e\left(\frac{313}{348}\right)$$ $$e\left(\frac{67}{116}\right)$$ $$e\left(\frac{1}{87}\right)$$ $$e\left(\frac{75}{116}\right)$$ $$e\left(\frac{5}{116}\right)$$
$$\chi_{349}(8,\cdot)$$ 349.j 116 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{116}\right)$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{41}{58}\right)$$ $$e\left(\frac{27}{116}\right)$$ $$e\left(\frac{67}{116}\right)$$ $$e\left(\frac{3}{116}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{83}{116}\right)$$ $$e\left(\frac{21}{116}\right)$$
$$\chi_{349}(9,\cdot)$$ 349.i 87 Yes $$1$$ $$1$$ $$e\left(\frac{13}{87}\right)$$ $$e\left(\frac{77}{87}\right)$$ $$e\left(\frac{26}{87}\right)$$ $$e\left(\frac{80}{87}\right)$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{1}{87}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{67}{87}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{4}{29}\right)$$
$$\chi_{349}(10,\cdot)$$ 349.j 116 Yes $$-1$$ $$1$$ $$e\left(\frac{105}{116}\right)$$ $$e\left(\frac{31}{58}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{51}{116}\right)$$ $$e\left(\frac{75}{116}\right)$$ $$e\left(\frac{83}{116}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{15}{116}\right)$$ $$e\left(\frac{1}{116}\right)$$
$$\chi_{349}(11,\cdot)$$ 349.j 116 Yes $$-1$$ $$1$$ $$e\left(\frac{7}{116}\right)$$ $$e\left(\frac{33}{58}\right)$$ $$e\left(\frac{7}{58}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{73}{116}\right)$$ $$e\left(\frac{5}{116}\right)$$ $$e\left(\frac{21}{116}\right)$$ $$e\left(\frac{4}{29}\right)$$ $$e\left(\frac{1}{116}\right)$$ $$e\left(\frac{31}{116}\right)$$
$$\chi_{349}(12,\cdot)$$ 349.i 87 Yes $$1$$ $$1$$ $$e\left(\frac{7}{87}\right)$$ $$e\left(\frac{8}{87}\right)$$ $$e\left(\frac{14}{87}\right)$$ $$e\left(\frac{23}{87}\right)$$ $$e\left(\frac{5}{29}\right)$$ $$e\left(\frac{34}{87}\right)$$ $$e\left(\frac{7}{29}\right)$$ $$e\left(\frac{16}{87}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{20}{29}\right)$$
$$\chi_{349}(13,\cdot)$$ 349.l 348 Yes $$-1$$ $$1$$ $$e\left(\frac{271}{348}\right)$$ $$e\left(\frac{43}{174}\right)$$ $$e\left(\frac{97}{174}\right)$$ $$e\left(\frac{91}{174}\right)$$ $$e\left(\frac{3}{116}\right)$$ $$e\left(\frac{61}{348}\right)$$ $$e\left(\frac{39}{116}\right)$$ $$e\left(\frac{43}{87}\right)$$ $$e\left(\frac{35}{116}\right)$$ $$e\left(\frac{41}{116}\right)$$
$$\chi_{349}(14,\cdot)$$ 349.i 87 Yes $$1$$ $$1$$ $$e\left(\frac{17}{87}\right)$$ $$e\left(\frac{7}{87}\right)$$ $$e\left(\frac{34}{87}\right)$$ $$e\left(\frac{31}{87}\right)$$ $$e\left(\frac{8}{29}\right)$$ $$e\left(\frac{8}{87}\right)$$ $$e\left(\frac{17}{29}\right)$$ $$e\left(\frac{14}{87}\right)$$ $$e\left(\frac{16}{29}\right)$$ $$e\left(\frac{3}{29}\right)$$
$$\chi_{349}(15,\cdot)$$ 349.i 87 Yes $$1$$ $$1$$ $$e\left(\frac{85}{87}\right)$$ $$e\left(\frac{35}{87}\right)$$ $$e\left(\frac{83}{87}\right)$$ $$e\left(\frac{68}{87}\right)$$ $$e\left(\frac{11}{29}\right)$$ $$e\left(\frac{40}{87}\right)$$ $$e\left(\frac{27}{29}\right)$$ $$e\left(\frac{70}{87}\right)$$ $$e\left(\frac{22}{29}\right)$$ $$e\left(\frac{15}{29}\right)$$
$$\chi_{349}(16,\cdot)$$ 349.i 87 Yes $$1$$ $$1$$ $$e\left(\frac{1}{87}\right)$$ $$e\left(\frac{26}{87}\right)$$ $$e\left(\frac{2}{87}\right)$$ $$e\left(\frac{53}{87}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{67}{87}\right)$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{52}{87}\right)$$ $$e\left(\frac{18}{29}\right)$$ $$e\left(\frac{7}{29}\right)$$
$$\chi_{349}(17,\cdot)$$ 349.h 58 Yes $$1$$ $$1$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{8}{29}\right)$$ $$e\left(\frac{14}{29}\right)$$ $$e\left(\frac{23}{29}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{39}{58}\right)$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{16}{29}\right)$$ $$e\left(\frac{31}{58}\right)$$ $$e\left(\frac{33}{58}\right)$$
$$\chi_{349}(18,\cdot)$$ 349.l 348 Yes $$-1$$ $$1$$ $$e\left(\frac{53}{348}\right)$$ $$e\left(\frac{167}{174}\right)$$ $$e\left(\frac{53}{174}\right)$$ $$e\left(\frac{143}{174}\right)$$ $$e\left(\frac{13}{116}\right)$$ $$e\left(\frac{71}{348}\right)$$ $$e\left(\frac{53}{116}\right)$$ $$e\left(\frac{80}{87}\right)$$ $$e\left(\frac{113}{116}\right)$$ $$e\left(\frac{23}{116}\right)$$
$$\chi_{349}(19,\cdot)$$ 349.i 87 Yes $$1$$ $$1$$ $$e\left(\frac{47}{87}\right)$$ $$e\left(\frac{4}{87}\right)$$ $$e\left(\frac{7}{87}\right)$$ $$e\left(\frac{55}{87}\right)$$ $$e\left(\frac{17}{29}\right)$$ $$e\left(\frac{17}{87}\right)$$ $$e\left(\frac{18}{29}\right)$$ $$e\left(\frac{8}{87}\right)$$ $$e\left(\frac{5}{29}\right)$$ $$e\left(\frac{10}{29}\right)$$
$$\chi_{349}(20,\cdot)$$ 349.i 87 Yes $$1$$ $$1$$ $$e\left(\frac{79}{87}\right)$$ $$e\left(\frac{53}{87}\right)$$ $$e\left(\frac{71}{87}\right)$$ $$e\left(\frac{11}{87}\right)$$ $$e\left(\frac{15}{29}\right)$$ $$e\left(\frac{73}{87}\right)$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{19}{87}\right)$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{2}{29}\right)$$
$$\chi_{349}(21,\cdot)$$ 349.j 116 Yes $$-1$$ $$1$$ $$e\left(\frac{31}{116}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{31}{58}\right)$$ $$e\left(\frac{53}{58}\right)$$ $$e\left(\frac{25}{116}\right)$$ $$e\left(\frac{105}{116}\right)$$ $$e\left(\frac{93}{116}\right)$$ $$e\left(\frac{26}{29}\right)$$ $$e\left(\frac{21}{116}\right)$$ $$e\left(\frac{71}{116}\right)$$
$$\chi_{349}(22,\cdot)$$ 349.k 174 Yes $$1$$ $$1$$ $$e\left(\frac{11}{174}\right)$$ $$e\left(\frac{56}{87}\right)$$ $$e\left(\frac{11}{87}\right)$$ $$e\left(\frac{74}{87}\right)$$ $$e\left(\frac{41}{58}\right)$$ $$e\left(\frac{41}{174}\right)$$ $$e\left(\frac{11}{58}\right)$$ $$e\left(\frac{25}{87}\right)$$ $$e\left(\frac{53}{58}\right)$$ $$e\left(\frac{19}{58}\right)$$
$$\chi_{349}(23,\cdot)$$ 349.i 87 Yes $$1$$ $$1$$ $$e\left(\frac{46}{87}\right)$$ $$e\left(\frac{65}{87}\right)$$ $$e\left(\frac{5}{87}\right)$$ $$e\left(\frac{2}{87}\right)$$ $$e\left(\frac{8}{29}\right)$$ $$e\left(\frac{37}{87}\right)$$ $$e\left(\frac{17}{29}\right)$$ $$e\left(\frac{43}{87}\right)$$ $$e\left(\frac{16}{29}\right)$$ $$e\left(\frac{3}{29}\right)$$
$$\chi_{349}(24,\cdot)$$ 349.f 12 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$-i$$
$$\chi_{349}(25,\cdot)$$ 349.i 87 Yes $$1$$ $$1$$ $$e\left(\frac{70}{87}\right)$$ $$e\left(\frac{80}{87}\right)$$ $$e\left(\frac{53}{87}\right)$$ $$e\left(\frac{56}{87}\right)$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{79}{87}\right)$$ $$e\left(\frac{12}{29}\right)$$ $$e\left(\frac{73}{87}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{26}{29}\right)$$
$$\chi_{349}(26,\cdot)$$ 349.i 87 Yes $$1$$ $$1$$ $$e\left(\frac{68}{87}\right)$$ $$e\left(\frac{28}{87}\right)$$ $$e\left(\frac{49}{87}\right)$$ $$e\left(\frac{37}{87}\right)$$ $$e\left(\frac{3}{29}\right)$$ $$e\left(\frac{32}{87}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{56}{87}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{12}{29}\right)$$
$$\chi_{349}(27,\cdot)$$ 349.h 58 Yes $$1$$ $$1$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{11}{29}\right)$$ $$e\left(\frac{3}{58}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{39}{58}\right)$$ $$e\left(\frac{19}{29}\right)$$ $$e\left(\frac{35}{58}\right)$$ $$e\left(\frac{41}{58}\right)$$
$$\chi_{349}(28,\cdot)$$ 349.j 116 Yes $$-1$$ $$1$$ $$e\left(\frac{23}{116}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{23}{58}\right)$$ $$e\left(\frac{15}{58}\right)$$ $$e\left(\frac{41}{116}\right)$$ $$e\left(\frac{33}{116}\right)$$ $$e\left(\frac{69}{116}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{53}{116}\right)$$ $$e\left(\frac{19}{116}\right)$$
$$\chi_{349}(29,\cdot)$$ 349.k 174 Yes $$1$$ $$1$$ $$e\left(\frac{73}{174}\right)$$ $$e\left(\frac{79}{87}\right)$$ $$e\left(\frac{73}{87}\right)$$ $$e\left(\frac{64}{87}\right)$$ $$e\left(\frac{19}{58}\right)$$ $$e\left(\frac{19}{174}\right)$$ $$e\left(\frac{15}{58}\right)$$ $$e\left(\frac{71}{87}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{47}{58}\right)$$
$$\chi_{349}(30,\cdot)$$ 349.l 348 Yes $$-1$$ $$1$$ $$e\left(\frac{341}{348}\right)$$ $$e\left(\frac{83}{174}\right)$$ $$e\left(\frac{167}{174}\right)$$ $$e\left(\frac{119}{174}\right)$$ $$e\left(\frac{53}{116}\right)$$ $$e\left(\frac{227}{348}\right)$$ $$e\left(\frac{109}{116}\right)$$ $$e\left(\frac{83}{87}\right)$$ $$e\left(\frac{77}{116}\right)$$ $$e\left(\frac{67}{116}\right)$$
$$\chi_{349}(31,\cdot)$$ 349.g 29 Yes $$1$$ $$1$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{19}{29}\right)$$ $$e\left(\frac{26}{29}\right)$$ $$e\left(\frac{22}{29}\right)$$ $$e\left(\frac{3}{29}\right)$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{12}{29}\right)$$
$$\chi_{349}(32,\cdot)$$ 349.l 348 Yes $$-1$$ $$1$$ $$e\left(\frac{5}{348}\right)$$ $$e\left(\frac{65}{174}\right)$$ $$e\left(\frac{5}{174}\right)$$ $$e\left(\frac{89}{174}\right)$$ $$e\left(\frac{45}{116}\right)$$ $$e\left(\frac{335}{348}\right)$$ $$e\left(\frac{5}{116}\right)$$ $$e\left(\frac{65}{87}\right)$$ $$e\left(\frac{61}{116}\right)$$ $$e\left(\frac{35}{116}\right)$$