Properties

Label 16245.gc
Modulus 1624516245
Conductor 1624516245
Order 228228
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16245, base_ring=CyclotomicField(228))
 
M = H._module
 
chi = DirichletCharacter(H, M([152,171,70]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(88,16245))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 1624516245
Conductor: 1624516245
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 228228
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ228)\Q(\zeta_{228})
Fixed field: Number field defined by a degree 228 polynomial (not computed)

First 31 of 72 characters in Galois orbit

Character 1-1 11 22 44 77 88 1111 1313 1414 1616 1717 2222
χ16245(88,)\chi_{16245}(88,\cdot) 11 11 e(5576)e\left(\frac{55}{76}\right) e(1738)e\left(\frac{17}{38}\right) e(107228)e\left(\frac{107}{228}\right) e(1376)e\left(\frac{13}{76}\right) e(5657)e\left(\frac{56}{57}\right) e(4576)e\left(\frac{45}{76}\right) e(1157)e\left(\frac{11}{57}\right) e(1719)e\left(\frac{17}{19}\right) e(31228)e\left(\frac{31}{228}\right) e(161228)e\left(\frac{161}{228}\right)
χ16245(103,)\chi_{16245}(103,\cdot) 11 11 e(1176)e\left(\frac{11}{76}\right) e(1138)e\left(\frac{11}{38}\right) e(67228)e\left(\frac{67}{228}\right) e(3376)e\left(\frac{33}{76}\right) e(3457)e\left(\frac{34}{57}\right) e(976)e\left(\frac{9}{76}\right) e(2557)e\left(\frac{25}{57}\right) e(1119)e\left(\frac{11}{19}\right) e(143228)e\left(\frac{143}{228}\right) e(169228)e\left(\frac{169}{228}\right)
χ16245(772,)\chi_{16245}(772,\cdot) 11 11 e(2176)e\left(\frac{21}{76}\right) e(2138)e\left(\frac{21}{38}\right) e(197228)e\left(\frac{197}{228}\right) e(6376)e\left(\frac{63}{76}\right) e(2057)e\left(\frac{20}{57}\right) e(3176)e\left(\frac{31}{76}\right) e(857)e\left(\frac{8}{57}\right) e(219)e\left(\frac{2}{19}\right) e(121228)e\left(\frac{121}{228}\right) e(143228)e\left(\frac{143}{228}\right)
χ16245(787,)\chi_{16245}(787,\cdot) 11 11 e(1776)e\left(\frac{17}{76}\right) e(1738)e\left(\frac{17}{38}\right) e(145228)e\left(\frac{145}{228}\right) e(5176)e\left(\frac{51}{76}\right) e(3757)e\left(\frac{37}{57}\right) e(776)e\left(\frac{7}{76}\right) e(4957)e\left(\frac{49}{57}\right) e(1719)e\left(\frac{17}{19}\right) e(221228)e\left(\frac{221}{228}\right) e(199228)e\left(\frac{199}{228}\right)
χ16245(943,)\chi_{16245}(943,\cdot) 11 11 e(376)e\left(\frac{3}{76}\right) e(338)e\left(\frac{3}{38}\right) e(191228)e\left(\frac{191}{228}\right) e(976)e\left(\frac{9}{76}\right) e(1157)e\left(\frac{11}{57}\right) e(3776)e\left(\frac{37}{76}\right) e(5057)e\left(\frac{50}{57}\right) e(319)e\left(\frac{3}{19}\right) e(115228)e\left(\frac{115}{228}\right) e(53228)e\left(\frac{53}{228}\right)
χ16245(958,)\chi_{16245}(958,\cdot) 11 11 e(4776)e\left(\frac{47}{76}\right) e(938)e\left(\frac{9}{38}\right) e(79228)e\left(\frac{79}{228}\right) e(6576)e\left(\frac{65}{76}\right) e(5257)e\left(\frac{52}{57}\right) e(7376)e\left(\frac{73}{76}\right) e(5557)e\left(\frac{55}{57}\right) e(919)e\left(\frac{9}{19}\right) e(155228)e\left(\frac{155}{228}\right) e(121228)e\left(\frac{121}{228}\right)
χ16245(1627,)\chi_{16245}(1627,\cdot) 11 11 e(4576)e\left(\frac{45}{76}\right) e(738)e\left(\frac{7}{38}\right) e(53228)e\left(\frac{53}{228}\right) e(5976)e\left(\frac{59}{76}\right) e(3257)e\left(\frac{32}{57}\right) e(2376)e\left(\frac{23}{76}\right) e(4757)e\left(\frac{47}{57}\right) e(719)e\left(\frac{7}{19}\right) e(205228)e\left(\frac{205}{228}\right) e(35228)e\left(\frac{35}{228}\right)
χ16245(1642,)\chi_{16245}(1642,\cdot) 11 11 e(5376)e\left(\frac{53}{76}\right) e(1538)e\left(\frac{15}{38}\right) e(157228)e\left(\frac{157}{228}\right) e(776)e\left(\frac{7}{76}\right) e(5557)e\left(\frac{55}{57}\right) e(7176)e\left(\frac{71}{76}\right) e(2257)e\left(\frac{22}{57}\right) e(1519)e\left(\frac{15}{19}\right) e(5228)e\left(\frac{5}{228}\right) e(151228)e\left(\frac{151}{228}\right)
χ16245(1798,)\chi_{16245}(1798,\cdot) 11 11 e(2776)e\left(\frac{27}{76}\right) e(2738)e\left(\frac{27}{38}\right) e(47228)e\left(\frac{47}{228}\right) e(576)e\left(\frac{5}{76}\right) e(2357)e\left(\frac{23}{57}\right) e(2976)e\left(\frac{29}{76}\right) e(3257)e\left(\frac{32}{57}\right) e(819)e\left(\frac{8}{19}\right) e(199228)e\left(\frac{199}{228}\right) e(173228)e\left(\frac{173}{228}\right)
χ16245(1813,)\chi_{16245}(1813,\cdot) 11 11 e(776)e\left(\frac{7}{76}\right) e(738)e\left(\frac{7}{38}\right) e(91228)e\left(\frac{91}{228}\right) e(2176)e\left(\frac{21}{76}\right) e(1357)e\left(\frac{13}{57}\right) e(6176)e\left(\frac{61}{76}\right) e(2857)e\left(\frac{28}{57}\right) e(719)e\left(\frac{7}{19}\right) e(167228)e\left(\frac{167}{228}\right) e(73228)e\left(\frac{73}{228}\right)
χ16245(2482,)\chi_{16245}(2482,\cdot) 11 11 e(6976)e\left(\frac{69}{76}\right) e(3138)e\left(\frac{31}{38}\right) e(137228)e\left(\frac{137}{228}\right) e(5576)e\left(\frac{55}{76}\right) e(4457)e\left(\frac{44}{57}\right) e(1576)e\left(\frac{15}{76}\right) e(2957)e\left(\frac{29}{57}\right) e(1219)e\left(\frac{12}{19}\right) e(61228)e\left(\frac{61}{228}\right) e(155228)e\left(\frac{155}{228}\right)
χ16245(2497,)\chi_{16245}(2497,\cdot) 11 11 e(1376)e\left(\frac{13}{76}\right) e(1338)e\left(\frac{13}{38}\right) e(169228)e\left(\frac{169}{228}\right) e(3976)e\left(\frac{39}{76}\right) e(1657)e\left(\frac{16}{57}\right) e(5976)e\left(\frac{59}{76}\right) e(5257)e\left(\frac{52}{57}\right) e(1319)e\left(\frac{13}{19}\right) e(17228)e\left(\frac{17}{228}\right) e(103228)e\left(\frac{103}{228}\right)
χ16245(2653,)\chi_{16245}(2653,\cdot) 11 11 e(5176)e\left(\frac{51}{76}\right) e(1338)e\left(\frac{13}{38}\right) e(131228)e\left(\frac{131}{228}\right) e(176)e\left(\frac{1}{76}\right) e(3557)e\left(\frac{35}{57}\right) e(2176)e\left(\frac{21}{76}\right) e(1457)e\left(\frac{14}{57}\right) e(1319)e\left(\frac{13}{19}\right) e(55228)e\left(\frac{55}{228}\right) e(65228)e\left(\frac{65}{228}\right)
χ16245(2668,)\chi_{16245}(2668,\cdot) 11 11 e(4376)e\left(\frac{43}{76}\right) e(538)e\left(\frac{5}{38}\right) e(103228)e\left(\frac{103}{228}\right) e(5376)e\left(\frac{53}{76}\right) e(3157)e\left(\frac{31}{57}\right) e(4976)e\left(\frac{49}{76}\right) e(157)e\left(\frac{1}{57}\right) e(519)e\left(\frac{5}{19}\right) e(179228)e\left(\frac{179}{228}\right) e(25228)e\left(\frac{25}{228}\right)
χ16245(3337,)\chi_{16245}(3337,\cdot) 11 11 e(1776)e\left(\frac{17}{76}\right) e(1738)e\left(\frac{17}{38}\right) e(221228)e\left(\frac{221}{228}\right) e(5176)e\left(\frac{51}{76}\right) e(5657)e\left(\frac{56}{57}\right) e(776)e\left(\frac{7}{76}\right) e(1157)e\left(\frac{11}{57}\right) e(1719)e\left(\frac{17}{19}\right) e(145228)e\left(\frac{145}{228}\right) e(47228)e\left(\frac{47}{228}\right)
χ16245(3352,)\chi_{16245}(3352,\cdot) 11 11 e(4976)e\left(\frac{49}{76}\right) e(1138)e\left(\frac{11}{38}\right) e(181228)e\left(\frac{181}{228}\right) e(7176)e\left(\frac{71}{76}\right) e(3457)e\left(\frac{34}{57}\right) e(4776)e\left(\frac{47}{76}\right) e(2557)e\left(\frac{25}{57}\right) e(1119)e\left(\frac{11}{19}\right) e(29228)e\left(\frac{29}{228}\right) e(55228)e\left(\frac{55}{228}\right)
χ16245(3508,)\chi_{16245}(3508,\cdot) 11 11 e(7576)e\left(\frac{75}{76}\right) e(3738)e\left(\frac{37}{38}\right) e(215228)e\left(\frac{215}{228}\right) e(7376)e\left(\frac{73}{76}\right) e(4757)e\left(\frac{47}{57}\right) e(1376)e\left(\frac{13}{76}\right) e(5357)e\left(\frac{53}{57}\right) e(1819)e\left(\frac{18}{19}\right) e(139228)e\left(\frac{139}{228}\right) e(185228)e\left(\frac{185}{228}\right)
χ16245(3523,)\chi_{16245}(3523,\cdot) 11 11 e(376)e\left(\frac{3}{76}\right) e(338)e\left(\frac{3}{38}\right) e(115228)e\left(\frac{115}{228}\right) e(976)e\left(\frac{9}{76}\right) e(4957)e\left(\frac{49}{57}\right) e(3776)e\left(\frac{37}{76}\right) e(3157)e\left(\frac{31}{57}\right) e(319)e\left(\frac{3}{19}\right) e(191228)e\left(\frac{191}{228}\right) e(205228)e\left(\frac{205}{228}\right)
χ16245(4192,)\chi_{16245}(4192,\cdot) 11 11 e(4176)e\left(\frac{41}{76}\right) e(338)e\left(\frac{3}{38}\right) e(77228)e\left(\frac{77}{228}\right) e(4776)e\left(\frac{47}{76}\right) e(1157)e\left(\frac{11}{57}\right) e(7576)e\left(\frac{75}{76}\right) e(5057)e\left(\frac{50}{57}\right) e(319)e\left(\frac{3}{19}\right) e(1228)e\left(\frac{1}{228}\right) e(167228)e\left(\frac{167}{228}\right)
χ16245(4207,)\chi_{16245}(4207,\cdot) 11 11 e(976)e\left(\frac{9}{76}\right) e(938)e\left(\frac{9}{38}\right) e(193228)e\left(\frac{193}{228}\right) e(2776)e\left(\frac{27}{76}\right) e(5257)e\left(\frac{52}{57}\right) e(3576)e\left(\frac{35}{76}\right) e(5557)e\left(\frac{55}{57}\right) e(919)e\left(\frac{9}{19}\right) e(41228)e\left(\frac{41}{228}\right) e(7228)e\left(\frac{7}{228}\right)
χ16245(4363,)\chi_{16245}(4363,\cdot) 11 11 e(2376)e\left(\frac{23}{76}\right) e(2338)e\left(\frac{23}{38}\right) e(71228)e\left(\frac{71}{228}\right) e(6976)e\left(\frac{69}{76}\right) e(257)e\left(\frac{2}{57}\right) e(576)e\left(\frac{5}{76}\right) e(3557)e\left(\frac{35}{57}\right) e(419)e\left(\frac{4}{19}\right) e(223228)e\left(\frac{223}{228}\right) e(77228)e\left(\frac{77}{228}\right)
χ16245(4378,)\chi_{16245}(4378,\cdot) 11 11 e(3976)e\left(\frac{39}{76}\right) e(138)e\left(\frac{1}{38}\right) e(127228)e\left(\frac{127}{228}\right) e(4176)e\left(\frac{41}{76}\right) e(1057)e\left(\frac{10}{57}\right) e(2576)e\left(\frac{25}{76}\right) e(457)e\left(\frac{4}{57}\right) e(119)e\left(\frac{1}{19}\right) e(203228)e\left(\frac{203}{228}\right) e(157228)e\left(\frac{157}{228}\right)
χ16245(5047,)\chi_{16245}(5047,\cdot) 11 11 e(6576)e\left(\frac{65}{76}\right) e(2738)e\left(\frac{27}{38}\right) e(161228)e\left(\frac{161}{228}\right) e(4376)e\left(\frac{43}{76}\right) e(2357)e\left(\frac{23}{57}\right) e(6776)e\left(\frac{67}{76}\right) e(3257)e\left(\frac{32}{57}\right) e(819)e\left(\frac{8}{19}\right) e(85228)e\left(\frac{85}{228}\right) e(59228)e\left(\frac{59}{228}\right)
χ16245(5062,)\chi_{16245}(5062,\cdot) 11 11 e(4576)e\left(\frac{45}{76}\right) e(738)e\left(\frac{7}{38}\right) e(205228)e\left(\frac{205}{228}\right) e(5976)e\left(\frac{59}{76}\right) e(1357)e\left(\frac{13}{57}\right) e(2376)e\left(\frac{23}{76}\right) e(2857)e\left(\frac{28}{57}\right) e(719)e\left(\frac{7}{19}\right) e(53228)e\left(\frac{53}{228}\right) e(187228)e\left(\frac{187}{228}\right)
χ16245(5218,)\chi_{16245}(5218,\cdot) 11 11 e(4776)e\left(\frac{47}{76}\right) e(938)e\left(\frac{9}{38}\right) e(155228)e\left(\frac{155}{228}\right) e(6576)e\left(\frac{65}{76}\right) e(1457)e\left(\frac{14}{57}\right) e(7376)e\left(\frac{73}{76}\right) e(1757)e\left(\frac{17}{57}\right) e(919)e\left(\frac{9}{19}\right) e(79228)e\left(\frac{79}{228}\right) e(197228)e\left(\frac{197}{228}\right)
χ16245(5233,)\chi_{16245}(5233,\cdot) 11 11 e(7576)e\left(\frac{75}{76}\right) e(3738)e\left(\frac{37}{38}\right) e(139228)e\left(\frac{139}{228}\right) e(7376)e\left(\frac{73}{76}\right) e(2857)e\left(\frac{28}{57}\right) e(1376)e\left(\frac{13}{76}\right) e(3457)e\left(\frac{34}{57}\right) e(1819)e\left(\frac{18}{19}\right) e(215228)e\left(\frac{215}{228}\right) e(109228)e\left(\frac{109}{228}\right)
χ16245(5902,)\chi_{16245}(5902,\cdot) 11 11 e(1376)e\left(\frac{13}{76}\right) e(1338)e\left(\frac{13}{38}\right) e(17228)e\left(\frac{17}{228}\right) e(3976)e\left(\frac{39}{76}\right) e(3557)e\left(\frac{35}{57}\right) e(5976)e\left(\frac{59}{76}\right) e(1457)e\left(\frac{14}{57}\right) e(1319)e\left(\frac{13}{19}\right) e(169228)e\left(\frac{169}{228}\right) e(179228)e\left(\frac{179}{228}\right)
χ16245(5917,)\chi_{16245}(5917,\cdot) 11 11 e(576)e\left(\frac{5}{76}\right) e(538)e\left(\frac{5}{38}\right) e(217228)e\left(\frac{217}{228}\right) e(1576)e\left(\frac{15}{76}\right) e(3157)e\left(\frac{31}{57}\right) e(1176)e\left(\frac{11}{76}\right) e(157)e\left(\frac{1}{57}\right) e(519)e\left(\frac{5}{19}\right) e(65228)e\left(\frac{65}{228}\right) e(139228)e\left(\frac{139}{228}\right)
χ16245(6073,)\chi_{16245}(6073,\cdot) 11 11 e(7176)e\left(\frac{71}{76}\right) e(3338)e\left(\frac{33}{38}\right) e(11228)e\left(\frac{11}{228}\right) e(6176)e\left(\frac{61}{76}\right) e(2657)e\left(\frac{26}{57}\right) e(6576)e\left(\frac{65}{76}\right) e(5657)e\left(\frac{56}{57}\right) e(1419)e\left(\frac{14}{19}\right) e(163228)e\left(\frac{163}{228}\right) e(89228)e\left(\frac{89}{228}\right)
χ16245(6088,)\chi_{16245}(6088,\cdot) 11 11 e(3576)e\left(\frac{35}{76}\right) e(3538)e\left(\frac{35}{38}\right) e(151228)e\left(\frac{151}{228}\right) e(2976)e\left(\frac{29}{76}\right) e(4657)e\left(\frac{46}{57}\right) e(176)e\left(\frac{1}{76}\right) e(757)e\left(\frac{7}{57}\right) e(1619)e\left(\frac{16}{19}\right) e(227228)e\left(\frac{227}{228}\right) e(61228)e\left(\frac{61}{228}\right)
χ16245(6757,)\chi_{16245}(6757,\cdot) 11 11 e(3776)e\left(\frac{37}{76}\right) e(3738)e\left(\frac{37}{38}\right) e(101228)e\left(\frac{101}{228}\right) e(3576)e\left(\frac{35}{76}\right) e(4757)e\left(\frac{47}{57}\right) e(5176)e\left(\frac{51}{76}\right) e(5357)e\left(\frac{53}{57}\right) e(1819)e\left(\frac{18}{19}\right) e(25228)e\left(\frac{25}{228}\right) e(71228)e\left(\frac{71}{228}\right)