Properties

Label 1849.n
Modulus $1849$
Conductor $1849$
Order $602$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1849, base_ring=CyclotomicField(602))
 
M = H._module
 
chi = DirichletCharacter(H, M([513]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(2,1849))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1849\)
Conductor: \(1849\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(602\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: $\Q(\zeta_{301})$
Fixed field: Number field defined by a degree 602 polynomial (not computed)

First 31 of 252 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{1849}(2,\cdot)\) \(-1\) \(1\) \(e\left(\frac{285}{602}\right)\) \(e\left(\frac{513}{602}\right)\) \(e\left(\frac{285}{301}\right)\) \(e\left(\frac{281}{602}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{67}{86}\right)\) \(e\left(\frac{253}{602}\right)\) \(e\left(\frac{212}{301}\right)\) \(e\left(\frac{283}{301}\right)\) \(e\left(\frac{135}{301}\right)\)
\(\chi_{1849}(8,\cdot)\) \(-1\) \(1\) \(e\left(\frac{253}{602}\right)\) \(e\left(\frac{335}{602}\right)\) \(e\left(\frac{253}{301}\right)\) \(e\left(\frac{241}{602}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{29}{86}\right)\) \(e\left(\frac{157}{602}\right)\) \(e\left(\frac{34}{301}\right)\) \(e\left(\frac{247}{301}\right)\) \(e\left(\frac{104}{301}\right)\)
\(\chi_{1849}(22,\cdot)\) \(-1\) \(1\) \(e\left(\frac{555}{602}\right)\) \(e\left(\frac{397}{602}\right)\) \(e\left(\frac{254}{301}\right)\) \(e\left(\frac{167}{602}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{49}{86}\right)\) \(e\left(\frac{461}{602}\right)\) \(e\left(\frac{96}{301}\right)\) \(e\left(\frac{60}{301}\right)\) \(e\left(\frac{152}{301}\right)\)
\(\chi_{1849}(27,\cdot)\) \(-1\) \(1\) \(e\left(\frac{335}{602}\right)\) \(e\left(\frac{1}{602}\right)\) \(e\left(\frac{34}{301}\right)\) \(e\left(\frac{193}{602}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{35}{86}\right)\) \(e\left(\frac{403}{602}\right)\) \(e\left(\frac{1}{301}\right)\) \(e\left(\frac{264}{301}\right)\) \(e\left(\frac{127}{301}\right)\)
\(\chi_{1849}(32,\cdot)\) \(-1\) \(1\) \(e\left(\frac{221}{602}\right)\) \(e\left(\frac{157}{602}\right)\) \(e\left(\frac{221}{301}\right)\) \(e\left(\frac{201}{602}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{77}{86}\right)\) \(e\left(\frac{61}{602}\right)\) \(e\left(\frac{157}{301}\right)\) \(e\left(\frac{211}{301}\right)\) \(e\left(\frac{73}{301}\right)\)
\(\chi_{1849}(39,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{602}\right)\) \(e\left(\frac{347}{602}\right)\) \(e\left(\frac{59}{301}\right)\) \(e\left(\frac{149}{602}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{19}{86}\right)\) \(e\left(\frac{177}{602}\right)\) \(e\left(\frac{46}{301}\right)\) \(e\left(\frac{104}{301}\right)\) \(e\left(\frac{123}{301}\right)\)
\(\chi_{1849}(45,\cdot)\) \(-1\) \(1\) \(e\left(\frac{103}{602}\right)\) \(e\left(\frac{65}{602}\right)\) \(e\left(\frac{103}{301}\right)\) \(e\left(\frac{505}{602}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{39}{86}\right)\) \(e\left(\frac{309}{602}\right)\) \(e\left(\frac{65}{301}\right)\) \(e\left(\frac{3}{301}\right)\) \(e\left(\frac{128}{301}\right)\)
\(\chi_{1849}(51,\cdot)\) \(-1\) \(1\) \(e\left(\frac{57}{602}\right)\) \(e\left(\frac{223}{602}\right)\) \(e\left(\frac{57}{301}\right)\) \(e\left(\frac{297}{602}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{65}{86}\right)\) \(e\left(\frac{171}{602}\right)\) \(e\left(\frac{223}{301}\right)\) \(e\left(\frac{177}{301}\right)\) \(e\left(\frac{27}{301}\right)\)
\(\chi_{1849}(65,\cdot)\) \(-1\) \(1\) \(e\left(\frac{429}{602}\right)\) \(e\left(\frac{411}{602}\right)\) \(e\left(\frac{128}{301}\right)\) \(e\left(\frac{461}{602}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{23}{86}\right)\) \(e\left(\frac{83}{602}\right)\) \(e\left(\frac{110}{301}\right)\) \(e\left(\frac{144}{301}\right)\) \(e\left(\frac{124}{301}\right)\)
\(\chi_{1849}(70,\cdot)\) \(-1\) \(1\) \(e\left(\frac{433}{602}\right)\) \(e\left(\frac{57}{602}\right)\) \(e\left(\frac{132}{301}\right)\) \(e\left(\frac{165}{602}\right)\) \(e\left(\frac{35}{43}\right)\) \(e\left(\frac{17}{86}\right)\) \(e\left(\frac{95}{602}\right)\) \(e\left(\frac{57}{301}\right)\) \(e\left(\frac{299}{301}\right)\) \(e\left(\frac{15}{301}\right)\)
\(\chi_{1849}(82,\cdot)\) \(-1\) \(1\) \(e\left(\frac{451}{602}\right)\) \(e\left(\frac{571}{602}\right)\) \(e\left(\frac{150}{301}\right)\) \(e\left(\frac{37}{602}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{33}{86}\right)\) \(e\left(\frac{149}{602}\right)\) \(e\left(\frac{270}{301}\right)\) \(e\left(\frac{244}{301}\right)\) \(e\left(\frac{277}{301}\right)\)
\(\chi_{1849}(88,\cdot)\) \(-1\) \(1\) \(e\left(\frac{523}{602}\right)\) \(e\left(\frac{219}{602}\right)\) \(e\left(\frac{222}{301}\right)\) \(e\left(\frac{127}{602}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{11}{86}\right)\) \(e\left(\frac{365}{602}\right)\) \(e\left(\frac{219}{301}\right)\) \(e\left(\frac{24}{301}\right)\) \(e\left(\frac{121}{301}\right)\)
\(\chi_{1849}(94,\cdot)\) \(-1\) \(1\) \(e\left(\frac{463}{602}\right)\) \(e\left(\frac{111}{602}\right)\) \(e\left(\frac{162}{301}\right)\) \(e\left(\frac{353}{602}\right)\) \(e\left(\frac{41}{43}\right)\) \(e\left(\frac{15}{86}\right)\) \(e\left(\frac{185}{602}\right)\) \(e\left(\frac{111}{301}\right)\) \(e\left(\frac{107}{301}\right)\) \(e\left(\frac{251}{301}\right)\)
\(\chi_{1849}(108,\cdot)\) \(-1\) \(1\) \(e\left(\frac{303}{602}\right)\) \(e\left(\frac{425}{602}\right)\) \(e\left(\frac{2}{301}\right)\) \(e\left(\frac{153}{602}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{83}{86}\right)\) \(e\left(\frac{307}{602}\right)\) \(e\left(\frac{124}{301}\right)\) \(e\left(\frac{228}{301}\right)\) \(e\left(\frac{96}{301}\right)\)
\(\chi_{1849}(113,\cdot)\) \(-1\) \(1\) \(e\left(\frac{531}{602}\right)\) \(e\left(\frac{113}{602}\right)\) \(e\left(\frac{230}{301}\right)\) \(e\left(\frac{137}{602}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{85}{86}\right)\) \(e\left(\frac{389}{602}\right)\) \(e\left(\frac{113}{301}\right)\) \(e\left(\frac{33}{301}\right)\) \(e\left(\frac{204}{301}\right)\)
\(\chi_{1849}(118,\cdot)\) \(-1\) \(1\) \(e\left(\frac{123}{602}\right)\) \(e\left(\frac{101}{602}\right)\) \(e\left(\frac{123}{301}\right)\) \(e\left(\frac{229}{602}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{9}{86}\right)\) \(e\left(\frac{369}{602}\right)\) \(e\left(\frac{101}{301}\right)\) \(e\left(\frac{176}{301}\right)\) \(e\left(\frac{185}{301}\right)\)
\(\chi_{1849}(125,\cdot)\) \(-1\) \(1\) \(e\left(\frac{241}{602}\right)\) \(e\left(\frac{193}{602}\right)\) \(e\left(\frac{241}{301}\right)\) \(e\left(\frac{527}{602}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{47}{86}\right)\) \(e\left(\frac{121}{602}\right)\) \(e\left(\frac{193}{301}\right)\) \(e\left(\frac{83}{301}\right)\) \(e\left(\frac{130}{301}\right)\)
\(\chi_{1849}(131,\cdot)\) \(-1\) \(1\) \(e\left(\frac{341}{602}\right)\) \(e\left(\frac{373}{602}\right)\) \(e\left(\frac{40}{301}\right)\) \(e\left(\frac{351}{602}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{69}{86}\right)\) \(e\left(\frac{421}{602}\right)\) \(e\left(\frac{72}{301}\right)\) \(e\left(\frac{45}{301}\right)\) \(e\left(\frac{114}{301}\right)\)
\(\chi_{1849}(137,\cdot)\) \(-1\) \(1\) \(e\left(\frac{267}{602}\right)\) \(e\left(\frac{601}{602}\right)\) \(e\left(\frac{267}{301}\right)\) \(e\left(\frac{409}{602}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{51}{86}\right)\) \(e\left(\frac{199}{602}\right)\) \(e\left(\frac{300}{301}\right)\) \(e\left(\frac{37}{301}\right)\) \(e\left(\frac{174}{301}\right)\)
\(\chi_{1849}(151,\cdot)\) \(-1\) \(1\) \(e\left(\frac{177}{602}\right)\) \(e\left(\frac{439}{602}\right)\) \(e\left(\frac{177}{301}\right)\) \(e\left(\frac{447}{602}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{57}{86}\right)\) \(e\left(\frac{531}{602}\right)\) \(e\left(\frac{138}{301}\right)\) \(e\left(\frac{11}{301}\right)\) \(e\left(\frac{68}{301}\right)\)
\(\chi_{1849}(156,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{602}\right)\) \(e\left(\frac{169}{602}\right)\) \(e\left(\frac{27}{301}\right)\) \(e\left(\frac{109}{602}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{67}{86}\right)\) \(e\left(\frac{81}{602}\right)\) \(e\left(\frac{169}{301}\right)\) \(e\left(\frac{68}{301}\right)\) \(e\left(\frac{92}{301}\right)\)
\(\chi_{1849}(161,\cdot)\) \(-1\) \(1\) \(e\left(\frac{375}{602}\right)\) \(e\left(\frac{73}{602}\right)\) \(e\left(\frac{74}{301}\right)\) \(e\left(\frac{243}{602}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{61}{86}\right)\) \(e\left(\frac{523}{602}\right)\) \(e\left(\frac{73}{301}\right)\) \(e\left(\frac{8}{301}\right)\) \(e\left(\frac{241}{301}\right)\)
\(\chi_{1849}(168,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{602}\right)\) \(e\left(\frac{417}{602}\right)\) \(e\left(\frac{31}{301}\right)\) \(e\left(\frac{415}{602}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{61}{86}\right)\) \(e\left(\frac{93}{602}\right)\) \(e\left(\frac{116}{301}\right)\) \(e\left(\frac{223}{301}\right)\) \(e\left(\frac{284}{301}\right)\)
\(\chi_{1849}(174,\cdot)\) \(-1\) \(1\) \(e\left(\frac{159}{602}\right)\) \(e\left(\frac{527}{602}\right)\) \(e\left(\frac{159}{301}\right)\) \(e\left(\frac{575}{602}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{41}{86}\right)\) \(e\left(\frac{477}{602}\right)\) \(e\left(\frac{226}{301}\right)\) \(e\left(\frac{66}{301}\right)\) \(e\left(\frac{107}{301}\right)\)
\(\chi_{1849}(180,\cdot)\) \(-1\) \(1\) \(e\left(\frac{71}{602}\right)\) \(e\left(\frac{489}{602}\right)\) \(e\left(\frac{71}{301}\right)\) \(e\left(\frac{465}{602}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{1}{86}\right)\) \(e\left(\frac{213}{602}\right)\) \(e\left(\frac{188}{301}\right)\) \(e\left(\frac{268}{301}\right)\) \(e\left(\frac{97}{301}\right)\)
\(\chi_{1849}(194,\cdot)\) \(-1\) \(1\) \(e\left(\frac{51}{602}\right)\) \(e\left(\frac{453}{602}\right)\) \(e\left(\frac{51}{301}\right)\) \(e\left(\frac{139}{602}\right)\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{31}{86}\right)\) \(e\left(\frac{153}{602}\right)\) \(e\left(\frac{152}{301}\right)\) \(e\left(\frac{95}{301}\right)\) \(e\left(\frac{40}{301}\right)\)
\(\chi_{1849}(199,\cdot)\) \(-1\) \(1\) \(e\left(\frac{125}{602}\right)\) \(e\left(\frac{225}{602}\right)\) \(e\left(\frac{125}{301}\right)\) \(e\left(\frac{81}{602}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{49}{86}\right)\) \(e\left(\frac{375}{602}\right)\) \(e\left(\frac{225}{301}\right)\) \(e\left(\frac{103}{301}\right)\) \(e\left(\frac{281}{301}\right)\)
\(\chi_{1849}(204,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{602}\right)\) \(e\left(\frac{45}{602}\right)\) \(e\left(\frac{25}{301}\right)\) \(e\left(\frac{257}{602}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{27}{86}\right)\) \(e\left(\frac{75}{602}\right)\) \(e\left(\frac{45}{301}\right)\) \(e\left(\frac{141}{301}\right)\) \(e\left(\frac{297}{301}\right)\)
\(\chi_{1849}(211,\cdot)\) \(-1\) \(1\) \(e\left(\frac{423}{602}\right)\) \(e\left(\frac{39}{602}\right)\) \(e\left(\frac{122}{301}\right)\) \(e\left(\frac{303}{602}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{75}{86}\right)\) \(e\left(\frac{65}{602}\right)\) \(e\left(\frac{39}{301}\right)\) \(e\left(\frac{62}{301}\right)\) \(e\left(\frac{137}{301}\right)\)
\(\chi_{1849}(217,\cdot)\) \(-1\) \(1\) \(e\left(\frac{579}{602}\right)\) \(e\left(\frac{79}{602}\right)\) \(e\left(\frac{278}{301}\right)\) \(e\left(\frac{197}{602}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{13}{86}\right)\) \(e\left(\frac{533}{602}\right)\) \(e\left(\frac{79}{301}\right)\) \(e\left(\frac{87}{301}\right)\) \(e\left(\frac{100}{301}\right)\)
\(\chi_{1849}(223,\cdot)\) \(-1\) \(1\) \(e\left(\frac{477}{602}\right)\) \(e\left(\frac{377}{602}\right)\) \(e\left(\frac{176}{301}\right)\) \(e\left(\frac{521}{602}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{37}{86}\right)\) \(e\left(\frac{227}{602}\right)\) \(e\left(\frac{76}{301}\right)\) \(e\left(\frac{198}{301}\right)\) \(e\left(\frac{20}{301}\right)\)