# Properties

 Modulus $2153$ Structure $$C_{2152}$$ Order $2152$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(2153)

pari: g = idealstar(,2153,2)

## Character group

 sage: G.order()  pari: g.no Order = 2152 sage: H.invariants()  pari: g.cyc Structure = $$C_{2152}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2153}(3,\cdot)$

## First 32 of 2152 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{2153}(1,\cdot)$$ 2153.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2153}(2,\cdot)$$ 2153.g 1076 yes $$1$$ $$1$$ $$e\left(\frac{115}{538}\right)$$ $$e\left(\frac{955}{1076}\right)$$ $$e\left(\frac{115}{269}\right)$$ $$e\left(\frac{1047}{1076}\right)$$ $$e\left(\frac{109}{1076}\right)$$ $$e\left(\frac{132}{269}\right)$$ $$e\left(\frac{345}{538}\right)$$ $$e\left(\frac{417}{538}\right)$$ $$e\left(\frac{201}{1076}\right)$$ $$e\left(\frac{515}{1076}\right)$$
$$\chi_{2153}(3,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{955}{1076}\right)$$ $$e\left(\frac{1}{2152}\right)$$ $$e\left(\frac{417}{538}\right)$$ $$e\left(\frac{765}{2152}\right)$$ $$e\left(\frac{1911}{2152}\right)$$ $$e\left(\frac{244}{269}\right)$$ $$e\left(\frac{713}{1076}\right)$$ $$e\left(\frac{1}{1076}\right)$$ $$e\left(\frac{523}{2152}\right)$$ $$e\left(\frac{885}{2152}\right)$$
$$\chi_{2153}(4,\cdot)$$ 2153.f 538 yes $$1$$ $$1$$ $$e\left(\frac{115}{269}\right)$$ $$e\left(\frac{417}{538}\right)$$ $$e\left(\frac{230}{269}\right)$$ $$e\left(\frac{509}{538}\right)$$ $$e\left(\frac{109}{538}\right)$$ $$e\left(\frac{264}{269}\right)$$ $$e\left(\frac{76}{269}\right)$$ $$e\left(\frac{148}{269}\right)$$ $$e\left(\frac{201}{538}\right)$$ $$e\left(\frac{515}{538}\right)$$
$$\chi_{2153}(5,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{1047}{1076}\right)$$ $$e\left(\frac{765}{2152}\right)$$ $$e\left(\frac{509}{538}\right)$$ $$e\left(\frac{2033}{2152}\right)$$ $$e\left(\frac{707}{2152}\right)$$ $$e\left(\frac{243}{269}\right)$$ $$e\left(\frac{989}{1076}\right)$$ $$e\left(\frac{765}{1076}\right)$$ $$e\left(\frac{1975}{2152}\right)$$ $$e\left(\frac{1297}{2152}\right)$$
$$\chi_{2153}(6,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{109}{1076}\right)$$ $$e\left(\frac{1911}{2152}\right)$$ $$e\left(\frac{109}{538}\right)$$ $$e\left(\frac{707}{2152}\right)$$ $$e\left(\frac{2129}{2152}\right)$$ $$e\left(\frac{107}{269}\right)$$ $$e\left(\frac{327}{1076}\right)$$ $$e\left(\frac{835}{1076}\right)$$ $$e\left(\frac{925}{2152}\right)$$ $$e\left(\frac{1915}{2152}\right)$$
$$\chi_{2153}(7,\cdot)$$ 2153.e 269 yes $$1$$ $$1$$ $$e\left(\frac{132}{269}\right)$$ $$e\left(\frac{244}{269}\right)$$ $$e\left(\frac{264}{269}\right)$$ $$e\left(\frac{243}{269}\right)$$ $$e\left(\frac{107}{269}\right)$$ $$e\left(\frac{158}{269}\right)$$ $$e\left(\frac{127}{269}\right)$$ $$e\left(\frac{219}{269}\right)$$ $$e\left(\frac{106}{269}\right)$$ $$e\left(\frac{202}{269}\right)$$
$$\chi_{2153}(8,\cdot)$$ 2153.g 1076 yes $$1$$ $$1$$ $$e\left(\frac{345}{538}\right)$$ $$e\left(\frac{713}{1076}\right)$$ $$e\left(\frac{76}{269}\right)$$ $$e\left(\frac{989}{1076}\right)$$ $$e\left(\frac{327}{1076}\right)$$ $$e\left(\frac{127}{269}\right)$$ $$e\left(\frac{497}{538}\right)$$ $$e\left(\frac{175}{538}\right)$$ $$e\left(\frac{603}{1076}\right)$$ $$e\left(\frac{469}{1076}\right)$$
$$\chi_{2153}(9,\cdot)$$ 2153.g 1076 yes $$1$$ $$1$$ $$e\left(\frac{417}{538}\right)$$ $$e\left(\frac{1}{1076}\right)$$ $$e\left(\frac{148}{269}\right)$$ $$e\left(\frac{765}{1076}\right)$$ $$e\left(\frac{835}{1076}\right)$$ $$e\left(\frac{219}{269}\right)$$ $$e\left(\frac{175}{538}\right)$$ $$e\left(\frac{1}{538}\right)$$ $$e\left(\frac{523}{1076}\right)$$ $$e\left(\frac{885}{1076}\right)$$
$$\chi_{2153}(10,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{201}{1076}\right)$$ $$e\left(\frac{523}{2152}\right)$$ $$e\left(\frac{201}{538}\right)$$ $$e\left(\frac{1975}{2152}\right)$$ $$e\left(\frac{925}{2152}\right)$$ $$e\left(\frac{106}{269}\right)$$ $$e\left(\frac{603}{1076}\right)$$ $$e\left(\frac{523}{1076}\right)$$ $$e\left(\frac{225}{2152}\right)$$ $$e\left(\frac{175}{2152}\right)$$
$$\chi_{2153}(11,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{515}{1076}\right)$$ $$e\left(\frac{885}{2152}\right)$$ $$e\left(\frac{515}{538}\right)$$ $$e\left(\frac{1297}{2152}\right)$$ $$e\left(\frac{1915}{2152}\right)$$ $$e\left(\frac{202}{269}\right)$$ $$e\left(\frac{469}{1076}\right)$$ $$e\left(\frac{885}{1076}\right)$$ $$e\left(\frac{175}{2152}\right)$$ $$e\left(\frac{2049}{2152}\right)$$
$$\chi_{2153}(12,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{339}{1076}\right)$$ $$e\left(\frac{1669}{2152}\right)$$ $$e\left(\frac{339}{538}\right)$$ $$e\left(\frac{649}{2152}\right)$$ $$e\left(\frac{195}{2152}\right)$$ $$e\left(\frac{239}{269}\right)$$ $$e\left(\frac{1017}{1076}\right)$$ $$e\left(\frac{593}{1076}\right)$$ $$e\left(\frac{1327}{2152}\right)$$ $$e\left(\frac{793}{2152}\right)$$
$$\chi_{2153}(13,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{325}{1076}\right)$$ $$e\left(\frac{851}{2152}\right)$$ $$e\left(\frac{325}{538}\right)$$ $$e\left(\frac{1111}{2152}\right)$$ $$e\left(\frac{1501}{2152}\right)$$ $$e\left(\frac{245}{269}\right)$$ $$e\left(\frac{975}{1076}\right)$$ $$e\left(\frac{851}{1076}\right)$$ $$e\left(\frac{1761}{2152}\right)$$ $$e\left(\frac{2087}{2152}\right)$$
$$\chi_{2153}(14,\cdot)$$ 2153.g 1076 yes $$1$$ $$1$$ $$e\left(\frac{379}{538}\right)$$ $$e\left(\frac{855}{1076}\right)$$ $$e\left(\frac{110}{269}\right)$$ $$e\left(\frac{943}{1076}\right)$$ $$e\left(\frac{537}{1076}\right)$$ $$e\left(\frac{21}{269}\right)$$ $$e\left(\frac{61}{538}\right)$$ $$e\left(\frac{317}{538}\right)$$ $$e\left(\frac{625}{1076}\right)$$ $$e\left(\frac{247}{1076}\right)$$
$$\chi_{2153}(15,\cdot)$$ 2153.g 1076 yes $$1$$ $$1$$ $$e\left(\frac{463}{538}\right)$$ $$e\left(\frac{383}{1076}\right)$$ $$e\left(\frac{194}{269}\right)$$ $$e\left(\frac{323}{1076}\right)$$ $$e\left(\frac{233}{1076}\right)$$ $$e\left(\frac{218}{269}\right)$$ $$e\left(\frac{313}{538}\right)$$ $$e\left(\frac{383}{538}\right)$$ $$e\left(\frac{173}{1076}\right)$$ $$e\left(\frac{15}{1076}\right)$$
$$\chi_{2153}(16,\cdot)$$ 2153.e 269 yes $$1$$ $$1$$ $$e\left(\frac{230}{269}\right)$$ $$e\left(\frac{148}{269}\right)$$ $$e\left(\frac{191}{269}\right)$$ $$e\left(\frac{240}{269}\right)$$ $$e\left(\frac{109}{269}\right)$$ $$e\left(\frac{259}{269}\right)$$ $$e\left(\frac{152}{269}\right)$$ $$e\left(\frac{27}{269}\right)$$ $$e\left(\frac{201}{269}\right)$$ $$e\left(\frac{246}{269}\right)$$
$$\chi_{2153}(17,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{1075}{1076}\right)$$ $$e\left(\frac{249}{2152}\right)$$ $$e\left(\frac{537}{538}\right)$$ $$e\left(\frac{1109}{2152}\right)$$ $$e\left(\frac{247}{2152}\right)$$ $$e\left(\frac{231}{269}\right)$$ $$e\left(\frac{1073}{1076}\right)$$ $$e\left(\frac{249}{1076}\right)$$ $$e\left(\frac{1107}{2152}\right)$$ $$e\left(\frac{861}{2152}\right)$$
$$\chi_{2153}(18,\cdot)$$ 2153.e 269 yes $$1$$ $$1$$ $$e\left(\frac{266}{269}\right)$$ $$e\left(\frac{239}{269}\right)$$ $$e\left(\frac{263}{269}\right)$$ $$e\left(\frac{184}{269}\right)$$ $$e\left(\frac{236}{269}\right)$$ $$e\left(\frac{82}{269}\right)$$ $$e\left(\frac{260}{269}\right)$$ $$e\left(\frac{209}{269}\right)$$ $$e\left(\frac{181}{269}\right)$$ $$e\left(\frac{81}{269}\right)$$
$$\chi_{2153}(19,\cdot)$$ 2153.g 1076 yes $$1$$ $$1$$ $$e\left(\frac{323}{538}\right)$$ $$e\left(\frac{811}{1076}\right)$$ $$e\left(\frac{54}{269}\right)$$ $$e\left(\frac{639}{1076}\right)$$ $$e\left(\frac{381}{1076}\right)$$ $$e\left(\frac{69}{269}\right)$$ $$e\left(\frac{431}{538}\right)$$ $$e\left(\frac{273}{538}\right)$$ $$e\left(\frac{209}{1076}\right)$$ $$e\left(\frac{43}{1076}\right)$$
$$\chi_{2153}(20,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{431}{1076}\right)$$ $$e\left(\frac{281}{2152}\right)$$ $$e\left(\frac{431}{538}\right)$$ $$e\left(\frac{1917}{2152}\right)$$ $$e\left(\frac{1143}{2152}\right)$$ $$e\left(\frac{238}{269}\right)$$ $$e\left(\frac{217}{1076}\right)$$ $$e\left(\frac{281}{1076}\right)$$ $$e\left(\frac{627}{2152}\right)$$ $$e\left(\frac{1205}{2152}\right)$$
$$\chi_{2153}(21,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{407}{1076}\right)$$ $$e\left(\frac{1953}{2152}\right)$$ $$e\left(\frac{407}{538}\right)$$ $$e\left(\frac{557}{2152}\right)$$ $$e\left(\frac{615}{2152}\right)$$ $$e\left(\frac{133}{269}\right)$$ $$e\left(\frac{145}{1076}\right)$$ $$e\left(\frac{877}{1076}\right)$$ $$e\left(\frac{1371}{2152}\right)$$ $$e\left(\frac{349}{2152}\right)$$
$$\chi_{2153}(22,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{745}{1076}\right)$$ $$e\left(\frac{643}{2152}\right)$$ $$e\left(\frac{207}{538}\right)$$ $$e\left(\frac{1239}{2152}\right)$$ $$e\left(\frac{2133}{2152}\right)$$ $$e\left(\frac{65}{269}\right)$$ $$e\left(\frac{83}{1076}\right)$$ $$e\left(\frac{643}{1076}\right)$$ $$e\left(\frac{577}{2152}\right)$$ $$e\left(\frac{927}{2152}\right)$$
$$\chi_{2153}(23,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{533}{1076}\right)$$ $$e\left(\frac{707}{2152}\right)$$ $$e\left(\frac{533}{538}\right)$$ $$e\left(\frac{703}{2152}\right)$$ $$e\left(\frac{1773}{2152}\right)$$ $$e\left(\frac{79}{269}\right)$$ $$e\left(\frac{523}{1076}\right)$$ $$e\left(\frac{707}{1076}\right)$$ $$e\left(\frac{1769}{2152}\right)$$ $$e\left(\frac{1615}{2152}\right)$$
$$\chi_{2153}(24,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{569}{1076}\right)$$ $$e\left(\frac{1427}{2152}\right)$$ $$e\left(\frac{31}{538}\right)$$ $$e\left(\frac{591}{2152}\right)$$ $$e\left(\frac{413}{2152}\right)$$ $$e\left(\frac{102}{269}\right)$$ $$e\left(\frac{631}{1076}\right)$$ $$e\left(\frac{351}{1076}\right)$$ $$e\left(\frac{1729}{2152}\right)$$ $$e\left(\frac{1823}{2152}\right)$$
$$\chi_{2153}(25,\cdot)$$ 2153.g 1076 yes $$1$$ $$1$$ $$e\left(\frac{509}{538}\right)$$ $$e\left(\frac{765}{1076}\right)$$ $$e\left(\frac{240}{269}\right)$$ $$e\left(\frac{957}{1076}\right)$$ $$e\left(\frac{707}{1076}\right)$$ $$e\left(\frac{217}{269}\right)$$ $$e\left(\frac{451}{538}\right)$$ $$e\left(\frac{227}{538}\right)$$ $$e\left(\frac{899}{1076}\right)$$ $$e\left(\frac{221}{1076}\right)$$
$$\chi_{2153}(26,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{555}{1076}\right)$$ $$e\left(\frac{609}{2152}\right)$$ $$e\left(\frac{17}{538}\right)$$ $$e\left(\frac{1053}{2152}\right)$$ $$e\left(\frac{1719}{2152}\right)$$ $$e\left(\frac{108}{269}\right)$$ $$e\left(\frac{589}{1076}\right)$$ $$e\left(\frac{609}{1076}\right)$$ $$e\left(\frac{11}{2152}\right)$$ $$e\left(\frac{965}{2152}\right)$$
$$\chi_{2153}(27,\cdot)$$ 2153.h 2152 yes $$-1$$ $$1$$ $$e\left(\frac{713}{1076}\right)$$ $$e\left(\frac{3}{2152}\right)$$ $$e\left(\frac{175}{538}\right)$$ $$e\left(\frac{143}{2152}\right)$$ $$e\left(\frac{1429}{2152}\right)$$ $$e\left(\frac{194}{269}\right)$$ $$e\left(\frac{1063}{1076}\right)$$ $$e\left(\frac{3}{1076}\right)$$ $$e\left(\frac{1569}{2152}\right)$$ $$e\left(\frac{503}{2152}\right)$$
$$\chi_{2153}(28,\cdot)$$ 2153.f 538 yes $$1$$ $$1$$ $$e\left(\frac{247}{269}\right)$$ $$e\left(\frac{367}{538}\right)$$ $$e\left(\frac{225}{269}\right)$$ $$e\left(\frac{457}{538}\right)$$ $$e\left(\frac{323}{538}\right)$$ $$e\left(\frac{153}{269}\right)$$ $$e\left(\frac{203}{269}\right)$$ $$e\left(\frac{98}{269}\right)$$ $$e\left(\frac{413}{538}\right)$$ $$e\left(\frac{381}{538}\right)$$
$$\chi_{2153}(29,\cdot)$$ 2153.e 269 yes $$1$$ $$1$$ $$e\left(\frac{231}{269}\right)$$ $$e\left(\frac{158}{269}\right)$$ $$e\left(\frac{193}{269}\right)$$ $$e\left(\frac{89}{269}\right)$$ $$e\left(\frac{120}{269}\right)$$ $$e\left(\frac{142}{269}\right)$$ $$e\left(\frac{155}{269}\right)$$ $$e\left(\frac{47}{269}\right)$$ $$e\left(\frac{51}{269}\right)$$ $$e\left(\frac{219}{269}\right)$$
$$\chi_{2153}(30,\cdot)$$ 2153.f 538 yes $$1$$ $$1$$ $$e\left(\frac{20}{269}\right)$$ $$e\left(\frac{131}{538}\right)$$ $$e\left(\frac{40}{269}\right)$$ $$e\left(\frac{147}{538}\right)$$ $$e\left(\frac{171}{538}\right)$$ $$e\left(\frac{81}{269}\right)$$ $$e\left(\frac{60}{269}\right)$$ $$e\left(\frac{131}{269}\right)$$ $$e\left(\frac{187}{538}\right)$$ $$e\left(\frac{265}{538}\right)$$
$$\chi_{2153}(31,\cdot)$$ 2153.g 1076 yes $$1$$ $$1$$ $$e\left(\frac{173}{538}\right)$$ $$e\left(\frac{1039}{1076}\right)$$ $$e\left(\frac{173}{269}\right)$$ $$e\left(\frac{747}{1076}\right)$$ $$e\left(\frac{309}{1076}\right)$$ $$e\left(\frac{236}{269}\right)$$ $$e\left(\frac{519}{538}\right)$$ $$e\left(\frac{501}{538}\right)$$ $$e\left(\frac{17}{1076}\right)$$ $$e\left(\frac{611}{1076}\right)$$
$$\chi_{2153}(32,\cdot)$$ 2153.g 1076 yes $$1$$ $$1$$ $$e\left(\frac{37}{538}\right)$$ $$e\left(\frac{471}{1076}\right)$$ $$e\left(\frac{37}{269}\right)$$ $$e\left(\frac{931}{1076}\right)$$ $$e\left(\frac{545}{1076}\right)$$ $$e\left(\frac{122}{269}\right)$$ $$e\left(\frac{111}{538}\right)$$ $$e\left(\frac{471}{538}\right)$$ $$e\left(\frac{1005}{1076}\right)$$ $$e\left(\frac{423}{1076}\right)$$