Properties

 Modulus $2347$ Structure $$C_{2346}$$ Order $2346$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(2347)

pari: g = idealstar(,2347,2)

Character group

 sage: G.order()  pari: g.no Order = 2346 sage: H.invariants()  pari: g.cyc Structure = $$C_{2346}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2347}(3,\cdot)$

First 32 of 2346 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{2347}(1,\cdot)$$ 2347.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2347}(2,\cdot)$$ 2347.n 782 yes $$-1$$ $$1$$ $$e\left(\frac{351}{782}\right)$$ $$e\left(\frac{741}{782}\right)$$ $$e\left(\frac{351}{391}\right)$$ $$e\left(\frac{695}{782}\right)$$ $$e\left(\frac{155}{391}\right)$$ $$e\left(\frac{57}{782}\right)$$ $$e\left(\frac{271}{782}\right)$$ $$e\left(\frac{350}{391}\right)$$ $$e\left(\frac{132}{391}\right)$$ $$e\left(\frac{367}{782}\right)$$
$$\chi_{2347}(3,\cdot)$$ 2347.p 2346 yes $$-1$$ $$1$$ $$e\left(\frac{741}{782}\right)$$ $$e\left(\frac{1}{2346}\right)$$ $$e\left(\frac{350}{391}\right)$$ $$e\left(\frac{1795}{2346}\right)$$ $$e\left(\frac{1112}{1173}\right)$$ $$e\left(\frac{381}{782}\right)$$ $$e\left(\frac{659}{782}\right)$$ $$e\left(\frac{1}{1173}\right)$$ $$e\left(\frac{836}{1173}\right)$$ $$e\left(\frac{239}{2346}\right)$$
$$\chi_{2347}(4,\cdot)$$ 2347.m 391 yes $$1$$ $$1$$ $$e\left(\frac{351}{391}\right)$$ $$e\left(\frac{350}{391}\right)$$ $$e\left(\frac{311}{391}\right)$$ $$e\left(\frac{304}{391}\right)$$ $$e\left(\frac{310}{391}\right)$$ $$e\left(\frac{57}{391}\right)$$ $$e\left(\frac{271}{391}\right)$$ $$e\left(\frac{309}{391}\right)$$ $$e\left(\frac{264}{391}\right)$$ $$e\left(\frac{367}{391}\right)$$
$$\chi_{2347}(5,\cdot)$$ 2347.p 2346 yes $$-1$$ $$1$$ $$e\left(\frac{695}{782}\right)$$ $$e\left(\frac{1795}{2346}\right)$$ $$e\left(\frac{304}{391}\right)$$ $$e\left(\frac{967}{2346}\right)$$ $$e\left(\frac{767}{1173}\right)$$ $$e\left(\frac{427}{782}\right)$$ $$e\left(\frac{521}{782}\right)$$ $$e\left(\frac{622}{1173}\right)$$ $$e\left(\frac{353}{1173}\right)$$ $$e\left(\frac{2033}{2346}\right)$$
$$\chi_{2347}(6,\cdot)$$ 2347.o 1173 yes $$1$$ $$1$$ $$e\left(\frac{155}{391}\right)$$ $$e\left(\frac{1112}{1173}\right)$$ $$e\left(\frac{310}{391}\right)$$ $$e\left(\frac{767}{1173}\right)$$ $$e\left(\frac{404}{1173}\right)$$ $$e\left(\frac{219}{391}\right)$$ $$e\left(\frac{74}{391}\right)$$ $$e\left(\frac{1051}{1173}\right)$$ $$e\left(\frac{59}{1173}\right)$$ $$e\left(\frac{670}{1173}\right)$$
$$\chi_{2347}(7,\cdot)$$ 2347.n 782 yes $$-1$$ $$1$$ $$e\left(\frac{57}{782}\right)$$ $$e\left(\frac{381}{782}\right)$$ $$e\left(\frac{57}{391}\right)$$ $$e\left(\frac{427}{782}\right)$$ $$e\left(\frac{219}{391}\right)$$ $$e\left(\frac{691}{782}\right)$$ $$e\left(\frac{171}{782}\right)$$ $$e\left(\frac{381}{391}\right)$$ $$e\left(\frac{242}{391}\right)$$ $$e\left(\frac{347}{782}\right)$$
$$\chi_{2347}(8,\cdot)$$ 2347.n 782 yes $$-1$$ $$1$$ $$e\left(\frac{271}{782}\right)$$ $$e\left(\frac{659}{782}\right)$$ $$e\left(\frac{271}{391}\right)$$ $$e\left(\frac{521}{782}\right)$$ $$e\left(\frac{74}{391}\right)$$ $$e\left(\frac{171}{782}\right)$$ $$e\left(\frac{31}{782}\right)$$ $$e\left(\frac{268}{391}\right)$$ $$e\left(\frac{5}{391}\right)$$ $$e\left(\frac{319}{782}\right)$$
$$\chi_{2347}(9,\cdot)$$ 2347.o 1173 yes $$1$$ $$1$$ $$e\left(\frac{350}{391}\right)$$ $$e\left(\frac{1}{1173}\right)$$ $$e\left(\frac{309}{391}\right)$$ $$e\left(\frac{622}{1173}\right)$$ $$e\left(\frac{1051}{1173}\right)$$ $$e\left(\frac{381}{391}\right)$$ $$e\left(\frac{268}{391}\right)$$ $$e\left(\frac{2}{1173}\right)$$ $$e\left(\frac{499}{1173}\right)$$ $$e\left(\frac{239}{1173}\right)$$
$$\chi_{2347}(10,\cdot)$$ 2347.o 1173 yes $$1$$ $$1$$ $$e\left(\frac{132}{391}\right)$$ $$e\left(\frac{836}{1173}\right)$$ $$e\left(\frac{264}{391}\right)$$ $$e\left(\frac{353}{1173}\right)$$ $$e\left(\frac{59}{1173}\right)$$ $$e\left(\frac{242}{391}\right)$$ $$e\left(\frac{5}{391}\right)$$ $$e\left(\frac{499}{1173}\right)$$ $$e\left(\frac{749}{1173}\right)$$ $$e\left(\frac{394}{1173}\right)$$
$$\chi_{2347}(11,\cdot)$$ 2347.p 2346 yes $$-1$$ $$1$$ $$e\left(\frac{367}{782}\right)$$ $$e\left(\frac{239}{2346}\right)$$ $$e\left(\frac{367}{391}\right)$$ $$e\left(\frac{2033}{2346}\right)$$ $$e\left(\frac{670}{1173}\right)$$ $$e\left(\frac{347}{782}\right)$$ $$e\left(\frac{319}{782}\right)$$ $$e\left(\frac{239}{1173}\right)$$ $$e\left(\frac{394}{1173}\right)$$ $$e\left(\frac{817}{2346}\right)$$
$$\chi_{2347}(12,\cdot)$$ 2347.p 2346 yes $$-1$$ $$1$$ $$e\left(\frac{661}{782}\right)$$ $$e\left(\frac{2101}{2346}\right)$$ $$e\left(\frac{270}{391}\right)$$ $$e\left(\frac{1273}{2346}\right)$$ $$e\left(\frac{869}{1173}\right)$$ $$e\left(\frac{495}{782}\right)$$ $$e\left(\frac{419}{782}\right)$$ $$e\left(\frac{928}{1173}\right)$$ $$e\left(\frac{455}{1173}\right)$$ $$e\left(\frac{95}{2346}\right)$$
$$\chi_{2347}(13,\cdot)$$ 2347.h 46 yes $$-1$$ $$1$$ $$e\left(\frac{41}{46}\right)$$ $$e\left(\frac{15}{46}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{15}{46}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{31}{46}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{43}{46}\right)$$
$$\chi_{2347}(14,\cdot)$$ 2347.f 23 yes $$1$$ $$1$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$
$$\chi_{2347}(15,\cdot)$$ 2347.o 1173 yes $$1$$ $$1$$ $$e\left(\frac{327}{391}\right)$$ $$e\left(\frac{898}{1173}\right)$$ $$e\left(\frac{263}{391}\right)$$ $$e\left(\frac{208}{1173}\right)$$ $$e\left(\frac{706}{1173}\right)$$ $$e\left(\frac{13}{391}\right)$$ $$e\left(\frac{199}{391}\right)$$ $$e\left(\frac{623}{1173}\right)$$ $$e\left(\frac{16}{1173}\right)$$ $$e\left(\frac{1136}{1173}\right)$$
$$\chi_{2347}(16,\cdot)$$ 2347.m 391 yes $$1$$ $$1$$ $$e\left(\frac{311}{391}\right)$$ $$e\left(\frac{309}{391}\right)$$ $$e\left(\frac{231}{391}\right)$$ $$e\left(\frac{217}{391}\right)$$ $$e\left(\frac{229}{391}\right)$$ $$e\left(\frac{114}{391}\right)$$ $$e\left(\frac{151}{391}\right)$$ $$e\left(\frac{227}{391}\right)$$ $$e\left(\frac{137}{391}\right)$$ $$e\left(\frac{343}{391}\right)$$
$$\chi_{2347}(17,\cdot)$$ 2347.o 1173 yes $$1$$ $$1$$ $$e\left(\frac{218}{391}\right)$$ $$e\left(\frac{1120}{1173}\right)$$ $$e\left(\frac{45}{391}\right)$$ $$e\left(\frac{1051}{1173}\right)$$ $$e\left(\frac{601}{1173}\right)$$ $$e\left(\frac{139}{391}\right)$$ $$e\left(\frac{263}{391}\right)$$ $$e\left(\frac{1067}{1173}\right)$$ $$e\left(\frac{532}{1173}\right)$$ $$e\left(\frac{236}{1173}\right)$$
$$\chi_{2347}(18,\cdot)$$ 2347.p 2346 yes $$-1$$ $$1$$ $$e\left(\frac{269}{782}\right)$$ $$e\left(\frac{2225}{2346}\right)$$ $$e\left(\frac{269}{391}\right)$$ $$e\left(\frac{983}{2346}\right)$$ $$e\left(\frac{343}{1173}\right)$$ $$e\left(\frac{37}{782}\right)$$ $$e\left(\frac{25}{782}\right)$$ $$e\left(\frac{1052}{1173}\right)$$ $$e\left(\frac{895}{1173}\right)$$ $$e\left(\frac{1579}{2346}\right)$$
$$\chi_{2347}(19,\cdot)$$ 2347.f 23 yes $$1$$ $$1$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$
$$\chi_{2347}(20,\cdot)$$ 2347.p 2346 yes $$-1$$ $$1$$ $$e\left(\frac{615}{782}\right)$$ $$e\left(\frac{1549}{2346}\right)$$ $$e\left(\frac{224}{391}\right)$$ $$e\left(\frac{445}{2346}\right)$$ $$e\left(\frac{524}{1173}\right)$$ $$e\left(\frac{541}{782}\right)$$ $$e\left(\frac{281}{782}\right)$$ $$e\left(\frac{376}{1173}\right)$$ $$e\left(\frac{1145}{1173}\right)$$ $$e\left(\frac{1889}{2346}\right)$$
$$\chi_{2347}(21,\cdot)$$ 2347.o 1173 yes $$1$$ $$1$$ $$e\left(\frac{8}{391}\right)$$ $$e\left(\frac{572}{1173}\right)$$ $$e\left(\frac{16}{391}\right)$$ $$e\left(\frac{365}{1173}\right)$$ $$e\left(\frac{596}{1173}\right)$$ $$e\left(\frac{145}{391}\right)$$ $$e\left(\frac{24}{391}\right)$$ $$e\left(\frac{1144}{1173}\right)$$ $$e\left(\frac{389}{1173}\right)$$ $$e\left(\frac{640}{1173}\right)$$
$$\chi_{2347}(22,\cdot)$$ 2347.o 1173 yes $$1$$ $$1$$ $$e\left(\frac{359}{391}\right)$$ $$e\left(\frac{58}{1173}\right)$$ $$e\left(\frac{327}{391}\right)$$ $$e\left(\frac{886}{1173}\right)$$ $$e\left(\frac{1135}{1173}\right)$$ $$e\left(\frac{202}{391}\right)$$ $$e\left(\frac{295}{391}\right)$$ $$e\left(\frac{116}{1173}\right)$$ $$e\left(\frac{790}{1173}\right)$$ $$e\left(\frac{959}{1173}\right)$$
$$\chi_{2347}(23,\cdot)$$ 2347.n 782 yes $$-1$$ $$1$$ $$e\left(\frac{427}{782}\right)$$ $$e\left(\frac{467}{782}\right)$$ $$e\left(\frac{36}{391}\right)$$ $$e\left(\frac{743}{782}\right)$$ $$e\left(\frac{56}{391}\right)$$ $$e\left(\frac{457}{782}\right)$$ $$e\left(\frac{499}{782}\right)$$ $$e\left(\frac{76}{391}\right)$$ $$e\left(\frac{194}{391}\right)$$ $$e\left(\frac{569}{782}\right)$$
$$\chi_{2347}(24,\cdot)$$ 2347.i 51 yes $$1$$ $$1$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{43}{51}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{22}{51}\right)$$ $$e\left(\frac{7}{51}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{35}{51}\right)$$ $$e\left(\frac{37}{51}\right)$$ $$e\left(\frac{26}{51}\right)$$
$$\chi_{2347}(25,\cdot)$$ 2347.o 1173 yes $$1$$ $$1$$ $$e\left(\frac{304}{391}\right)$$ $$e\left(\frac{622}{1173}\right)$$ $$e\left(\frac{217}{391}\right)$$ $$e\left(\frac{967}{1173}\right)$$ $$e\left(\frac{361}{1173}\right)$$ $$e\left(\frac{36}{391}\right)$$ $$e\left(\frac{130}{391}\right)$$ $$e\left(\frac{71}{1173}\right)$$ $$e\left(\frac{706}{1173}\right)$$ $$e\left(\frac{860}{1173}\right)$$
$$\chi_{2347}(26,\cdot)$$ 2347.m 391 yes $$1$$ $$1$$ $$e\left(\frac{133}{391}\right)$$ $$e\left(\frac{107}{391}\right)$$ $$e\left(\frac{266}{391}\right)$$ $$e\left(\frac{84}{391}\right)$$ $$e\left(\frac{240}{391}\right)$$ $$e\left(\frac{309}{391}\right)$$ $$e\left(\frac{8}{391}\right)$$ $$e\left(\frac{214}{391}\right)$$ $$e\left(\frac{217}{391}\right)$$ $$e\left(\frac{158}{391}\right)$$
$$\chi_{2347}(27,\cdot)$$ 2347.n 782 yes $$-1$$ $$1$$ $$e\left(\frac{659}{782}\right)$$ $$e\left(\frac{1}{782}\right)$$ $$e\left(\frac{268}{391}\right)$$ $$e\left(\frac{231}{782}\right)$$ $$e\left(\frac{330}{391}\right)$$ $$e\left(\frac{361}{782}\right)$$ $$e\left(\frac{413}{782}\right)$$ $$e\left(\frac{1}{391}\right)$$ $$e\left(\frac{54}{391}\right)$$ $$e\left(\frac{239}{782}\right)$$
$$\chi_{2347}(28,\cdot)$$ 2347.g 34 yes $$-1$$ $$1$$ $$e\left(\frac{33}{34}\right)$$ $$e\left(\frac{13}{34}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{1}{34}\right)$$ $$e\left(\frac{31}{34}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{13}{34}\right)$$
$$\chi_{2347}(29,\cdot)$$ 2347.p 2346 yes $$-1$$ $$1$$ $$e\left(\frac{515}{782}\right)$$ $$e\left(\frac{2219}{2346}\right)$$ $$e\left(\frac{124}{391}\right)$$ $$e\left(\frac{1943}{2346}\right)$$ $$e\left(\frac{709}{1173}\right)$$ $$e\left(\frac{97}{782}\right)$$ $$e\left(\frac{763}{782}\right)$$ $$e\left(\frac{1046}{1173}\right)$$ $$e\left(\frac{571}{1173}\right)$$ $$e\left(\frac{145}{2346}\right)$$
$$\chi_{2347}(30,\cdot)$$ 2347.p 2346 yes $$-1$$ $$1$$ $$e\left(\frac{223}{782}\right)$$ $$e\left(\frac{1673}{2346}\right)$$ $$e\left(\frac{223}{391}\right)$$ $$e\left(\frac{155}{2346}\right)$$ $$e\left(\frac{1171}{1173}\right)$$ $$e\left(\frac{83}{782}\right)$$ $$e\left(\frac{669}{782}\right)$$ $$e\left(\frac{500}{1173}\right)$$ $$e\left(\frac{412}{1173}\right)$$ $$e\left(\frac{1027}{2346}\right)$$
$$\chi_{2347}(31,\cdot)$$ 2347.o 1173 yes $$1$$ $$1$$ $$e\left(\frac{271}{391}\right)$$ $$e\left(\frac{22}{1173}\right)$$ $$e\left(\frac{151}{391}\right)$$ $$e\left(\frac{781}{1173}\right)$$ $$e\left(\frac{835}{1173}\right)$$ $$e\left(\frac{171}{391}\right)$$ $$e\left(\frac{31}{391}\right)$$ $$e\left(\frac{44}{1173}\right)$$ $$e\left(\frac{421}{1173}\right)$$ $$e\left(\frac{566}{1173}\right)$$
$$\chi_{2347}(32,\cdot)$$ 2347.n 782 yes $$-1$$ $$1$$ $$e\left(\frac{191}{782}\right)$$ $$e\left(\frac{577}{782}\right)$$ $$e\left(\frac{191}{391}\right)$$ $$e\left(\frac{347}{782}\right)$$ $$e\left(\frac{384}{391}\right)$$ $$e\left(\frac{285}{782}\right)$$ $$e\left(\frac{573}{782}\right)$$ $$e\left(\frac{186}{391}\right)$$ $$e\left(\frac{269}{391}\right)$$ $$e\left(\frac{271}{782}\right)$$