Properties

Label 2675.v
Modulus $2675$
Conductor $2675$
Order $530$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2675, base_ring=CyclotomicField(530))
 
M = H._module
 
chi = DirichletCharacter(H, M([53,525]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(54,2675))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2675\)
Conductor: \(2675\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(530\)
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: $\Q(\zeta_{265})$
Fixed field: Number field defined by a degree 530 polynomial (not computed)

First 31 of 208 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{2675}(54,\cdot)\) \(-1\) \(1\) \(e\left(\frac{24}{265}\right)\) \(e\left(\frac{21}{530}\right)\) \(e\left(\frac{48}{265}\right)\) \(e\left(\frac{69}{530}\right)\) \(e\left(\frac{5}{53}\right)\) \(e\left(\frac{72}{265}\right)\) \(e\left(\frac{21}{265}\right)\) \(e\left(\frac{104}{265}\right)\) \(e\left(\frac{117}{530}\right)\) \(e\left(\frac{407}{530}\right)\)
\(\chi_{2675}(59,\cdot)\) \(-1\) \(1\) \(e\left(\frac{238}{265}\right)\) \(e\left(\frac{407}{530}\right)\) \(e\left(\frac{211}{265}\right)\) \(e\left(\frac{353}{530}\right)\) \(e\left(\frac{1}{53}\right)\) \(e\left(\frac{184}{265}\right)\) \(e\left(\frac{142}{265}\right)\) \(e\left(\frac{148}{265}\right)\) \(e\left(\frac{299}{530}\right)\) \(e\left(\frac{39}{530}\right)\)
\(\chi_{2675}(84,\cdot)\) \(-1\) \(1\) \(e\left(\frac{208}{265}\right)\) \(e\left(\frac{447}{530}\right)\) \(e\left(\frac{151}{265}\right)\) \(e\left(\frac{333}{530}\right)\) \(e\left(\frac{8}{53}\right)\) \(e\left(\frac{94}{265}\right)\) \(e\left(\frac{182}{265}\right)\) \(e\left(\frac{18}{265}\right)\) \(e\left(\frac{219}{530}\right)\) \(e\left(\frac{259}{530}\right)\)
\(\chi_{2675}(94,\cdot)\) \(-1\) \(1\) \(e\left(\frac{141}{265}\right)\) \(e\left(\frac{289}{530}\right)\) \(e\left(\frac{17}{265}\right)\) \(e\left(\frac{41}{530}\right)\) \(e\left(\frac{36}{53}\right)\) \(e\left(\frac{158}{265}\right)\) \(e\left(\frac{24}{265}\right)\) \(e\left(\frac{81}{265}\right)\) \(e\left(\frac{323}{530}\right)\) \(e\left(\frac{503}{530}\right)\)
\(\chi_{2675}(104,\cdot)\) \(-1\) \(1\) \(e\left(\frac{69}{265}\right)\) \(e\left(\frac{491}{530}\right)\) \(e\left(\frac{138}{265}\right)\) \(e\left(\frac{99}{530}\right)\) \(e\left(\frac{21}{53}\right)\) \(e\left(\frac{207}{265}\right)\) \(e\left(\frac{226}{265}\right)\) \(e\left(\frac{34}{265}\right)\) \(e\left(\frac{237}{530}\right)\) \(e\left(\frac{77}{530}\right)\)
\(\chi_{2675}(109,\cdot)\) \(-1\) \(1\) \(e\left(\frac{188}{265}\right)\) \(e\left(\frac{297}{530}\right)\) \(e\left(\frac{111}{265}\right)\) \(e\left(\frac{143}{530}\right)\) \(e\left(\frac{48}{53}\right)\) \(e\left(\frac{34}{265}\right)\) \(e\left(\frac{32}{265}\right)\) \(e\left(\frac{108}{265}\right)\) \(e\left(\frac{519}{530}\right)\) \(e\left(\frac{229}{530}\right)\)
\(\chi_{2675}(114,\cdot)\) \(-1\) \(1\) \(e\left(\frac{187}{265}\right)\) \(e\left(\frac{263}{530}\right)\) \(e\left(\frac{109}{265}\right)\) \(e\left(\frac{107}{530}\right)\) \(e\left(\frac{50}{53}\right)\) \(e\left(\frac{31}{265}\right)\) \(e\left(\frac{263}{265}\right)\) \(e\left(\frac{192}{265}\right)\) \(e\left(\frac{481}{530}\right)\) \(e\left(\frac{201}{530}\right)\)
\(\chi_{2675}(129,\cdot)\) \(-1\) \(1\) \(e\left(\frac{84}{265}\right)\) \(e\left(\frac{471}{530}\right)\) \(e\left(\frac{168}{265}\right)\) \(e\left(\frac{109}{530}\right)\) \(e\left(\frac{44}{53}\right)\) \(e\left(\frac{252}{265}\right)\) \(e\left(\frac{206}{265}\right)\) \(e\left(\frac{99}{265}\right)\) \(e\left(\frac{277}{530}\right)\) \(e\left(\frac{497}{530}\right)\)
\(\chi_{2675}(139,\cdot)\) \(-1\) \(1\) \(e\left(\frac{92}{265}\right)\) \(e\left(\frac{213}{530}\right)\) \(e\left(\frac{184}{265}\right)\) \(e\left(\frac{397}{530}\right)\) \(e\left(\frac{28}{53}\right)\) \(e\left(\frac{11}{265}\right)\) \(e\left(\frac{213}{265}\right)\) \(e\left(\frac{222}{265}\right)\) \(e\left(\frac{51}{530}\right)\) \(e\left(\frac{191}{530}\right)\)
\(\chi_{2675}(179,\cdot)\) \(-1\) \(1\) \(e\left(\frac{119}{265}\right)\) \(e\left(\frac{71}{530}\right)\) \(e\left(\frac{238}{265}\right)\) \(e\left(\frac{309}{530}\right)\) \(e\left(\frac{27}{53}\right)\) \(e\left(\frac{92}{265}\right)\) \(e\left(\frac{71}{265}\right)\) \(e\left(\frac{74}{265}\right)\) \(e\left(\frac{17}{530}\right)\) \(e\left(\frac{417}{530}\right)\)
\(\chi_{2675}(184,\cdot)\) \(-1\) \(1\) \(e\left(\frac{83}{265}\right)\) \(e\left(\frac{437}{530}\right)\) \(e\left(\frac{166}{265}\right)\) \(e\left(\frac{73}{530}\right)\) \(e\left(\frac{46}{53}\right)\) \(e\left(\frac{249}{265}\right)\) \(e\left(\frac{172}{265}\right)\) \(e\left(\frac{183}{265}\right)\) \(e\left(\frac{239}{530}\right)\) \(e\left(\frac{469}{530}\right)\)
\(\chi_{2675}(189,\cdot)\) \(-1\) \(1\) \(e\left(\frac{182}{265}\right)\) \(e\left(\frac{93}{530}\right)\) \(e\left(\frac{99}{265}\right)\) \(e\left(\frac{457}{530}\right)\) \(e\left(\frac{7}{53}\right)\) \(e\left(\frac{16}{265}\right)\) \(e\left(\frac{93}{265}\right)\) \(e\left(\frac{82}{265}\right)\) \(e\left(\frac{291}{530}\right)\) \(e\left(\frac{61}{530}\right)\)
\(\chi_{2675}(204,\cdot)\) \(-1\) \(1\) \(e\left(\frac{14}{265}\right)\) \(e\left(\frac{211}{530}\right)\) \(e\left(\frac{28}{265}\right)\) \(e\left(\frac{239}{530}\right)\) \(e\left(\frac{25}{53}\right)\) \(e\left(\frac{42}{265}\right)\) \(e\left(\frac{211}{265}\right)\) \(e\left(\frac{149}{265}\right)\) \(e\left(\frac{267}{530}\right)\) \(e\left(\frac{127}{530}\right)\)
\(\chi_{2675}(219,\cdot)\) \(-1\) \(1\) \(e\left(\frac{91}{265}\right)\) \(e\left(\frac{179}{530}\right)\) \(e\left(\frac{182}{265}\right)\) \(e\left(\frac{361}{530}\right)\) \(e\left(\frac{30}{53}\right)\) \(e\left(\frac{8}{265}\right)\) \(e\left(\frac{179}{265}\right)\) \(e\left(\frac{41}{265}\right)\) \(e\left(\frac{13}{530}\right)\) \(e\left(\frac{163}{530}\right)\)
\(\chi_{2675}(229,\cdot)\) \(-1\) \(1\) \(e\left(\frac{54}{265}\right)\) \(e\left(\frac{511}{530}\right)\) \(e\left(\frac{108}{265}\right)\) \(e\left(\frac{89}{530}\right)\) \(e\left(\frac{51}{53}\right)\) \(e\left(\frac{162}{265}\right)\) \(e\left(\frac{246}{265}\right)\) \(e\left(\frac{234}{265}\right)\) \(e\left(\frac{197}{530}\right)\) \(e\left(\frac{187}{530}\right)\)
\(\chi_{2675}(234,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{265}\right)\) \(e\left(\frac{137}{530}\right)\) \(e\left(\frac{86}{265}\right)\) \(e\left(\frac{223}{530}\right)\) \(e\left(\frac{20}{53}\right)\) \(e\left(\frac{129}{265}\right)\) \(e\left(\frac{137}{265}\right)\) \(e\left(\frac{98}{265}\right)\) \(e\left(\frac{309}{530}\right)\) \(e\left(\frac{409}{530}\right)\)
\(\chi_{2675}(259,\cdot)\) \(-1\) \(1\) \(e\left(\frac{123}{265}\right)\) \(e\left(\frac{207}{530}\right)\) \(e\left(\frac{246}{265}\right)\) \(e\left(\frac{453}{530}\right)\) \(e\left(\frac{19}{53}\right)\) \(e\left(\frac{104}{265}\right)\) \(e\left(\frac{207}{265}\right)\) \(e\left(\frac{3}{265}\right)\) \(e\left(\frac{169}{530}\right)\) \(e\left(\frac{529}{530}\right)\)
\(\chi_{2675}(264,\cdot)\) \(-1\) \(1\) \(e\left(\frac{52}{265}\right)\) \(e\left(\frac{443}{530}\right)\) \(e\left(\frac{104}{265}\right)\) \(e\left(\frac{17}{530}\right)\) \(e\left(\frac{2}{53}\right)\) \(e\left(\frac{156}{265}\right)\) \(e\left(\frac{178}{265}\right)\) \(e\left(\frac{137}{265}\right)\) \(e\left(\frac{121}{530}\right)\) \(e\left(\frac{131}{530}\right)\)
\(\chi_{2675}(269,\cdot)\) \(-1\) \(1\) \(e\left(\frac{146}{265}\right)\) \(e\left(\frac{459}{530}\right)\) \(e\left(\frac{27}{265}\right)\) \(e\left(\frac{221}{530}\right)\) \(e\left(\frac{26}{53}\right)\) \(e\left(\frac{173}{265}\right)\) \(e\left(\frac{194}{265}\right)\) \(e\left(\frac{191}{265}\right)\) \(e\left(\frac{513}{530}\right)\) \(e\left(\frac{113}{530}\right)\)
\(\chi_{2675}(279,\cdot)\) \(-1\) \(1\) \(e\left(\frac{179}{265}\right)\) \(e\left(\frac{521}{530}\right)\) \(e\left(\frac{93}{265}\right)\) \(e\left(\frac{349}{530}\right)\) \(e\left(\frac{13}{53}\right)\) \(e\left(\frac{7}{265}\right)\) \(e\left(\frac{256}{265}\right)\) \(e\left(\frac{69}{265}\right)\) \(e\left(\frac{177}{530}\right)\) \(e\left(\frac{507}{530}\right)\)
\(\chi_{2675}(284,\cdot)\) \(-1\) \(1\) \(e\left(\frac{148}{265}\right)\) \(e\left(\frac{527}{530}\right)\) \(e\left(\frac{31}{265}\right)\) \(e\left(\frac{293}{530}\right)\) \(e\left(\frac{22}{53}\right)\) \(e\left(\frac{179}{265}\right)\) \(e\left(\frac{262}{265}\right)\) \(e\left(\frac{23}{265}\right)\) \(e\left(\frac{59}{530}\right)\) \(e\left(\frac{169}{530}\right)\)
\(\chi_{2675}(294,\cdot)\) \(-1\) \(1\) \(e\left(\frac{101}{265}\right)\) \(e\left(\frac{519}{530}\right)\) \(e\left(\frac{202}{265}\right)\) \(e\left(\frac{191}{530}\right)\) \(e\left(\frac{10}{53}\right)\) \(e\left(\frac{38}{265}\right)\) \(e\left(\frac{254}{265}\right)\) \(e\left(\frac{261}{265}\right)\) \(e\left(\frac{393}{530}\right)\) \(e\left(\frac{443}{530}\right)\)
\(\chi_{2675}(309,\cdot)\) \(-1\) \(1\) \(e\left(\frac{233}{265}\right)\) \(e\left(\frac{237}{530}\right)\) \(e\left(\frac{201}{265}\right)\) \(e\left(\frac{173}{530}\right)\) \(e\left(\frac{11}{53}\right)\) \(e\left(\frac{169}{265}\right)\) \(e\left(\frac{237}{265}\right)\) \(e\left(\frac{38}{265}\right)\) \(e\left(\frac{109}{530}\right)\) \(e\left(\frac{429}{530}\right)\)
\(\chi_{2675}(329,\cdot)\) \(-1\) \(1\) \(e\left(\frac{34}{265}\right)\) \(e\left(\frac{361}{530}\right)\) \(e\left(\frac{68}{265}\right)\) \(e\left(\frac{429}{530}\right)\) \(e\left(\frac{38}{53}\right)\) \(e\left(\frac{102}{265}\right)\) \(e\left(\frac{96}{265}\right)\) \(e\left(\frac{59}{265}\right)\) \(e\left(\frac{497}{530}\right)\) \(e\left(\frac{157}{530}\right)\)
\(\chi_{2675}(339,\cdot)\) \(-1\) \(1\) \(e\left(\frac{167}{265}\right)\) \(e\left(\frac{113}{530}\right)\) \(e\left(\frac{69}{265}\right)\) \(e\left(\frac{447}{530}\right)\) \(e\left(\frac{37}{53}\right)\) \(e\left(\frac{236}{265}\right)\) \(e\left(\frac{113}{265}\right)\) \(e\left(\frac{17}{265}\right)\) \(e\left(\frac{251}{530}\right)\) \(e\left(\frac{171}{530}\right)\)
\(\chi_{2675}(359,\cdot)\) \(-1\) \(1\) \(e\left(\frac{118}{265}\right)\) \(e\left(\frac{37}{530}\right)\) \(e\left(\frac{236}{265}\right)\) \(e\left(\frac{273}{530}\right)\) \(e\left(\frac{29}{53}\right)\) \(e\left(\frac{89}{265}\right)\) \(e\left(\frac{37}{265}\right)\) \(e\left(\frac{158}{265}\right)\) \(e\left(\frac{509}{530}\right)\) \(e\left(\frac{389}{530}\right)\)
\(\chi_{2675}(364,\cdot)\) \(-1\) \(1\) \(e\left(\frac{227}{265}\right)\) \(e\left(\frac{33}{530}\right)\) \(e\left(\frac{189}{265}\right)\) \(e\left(\frac{487}{530}\right)\) \(e\left(\frac{23}{53}\right)\) \(e\left(\frac{151}{265}\right)\) \(e\left(\frac{33}{265}\right)\) \(e\left(\frac{12}{265}\right)\) \(e\left(\frac{411}{530}\right)\) \(e\left(\frac{261}{530}\right)\)
\(\chi_{2675}(379,\cdot)\) \(-1\) \(1\) \(e\left(\frac{109}{265}\right)\) \(e\left(\frac{261}{530}\right)\) \(e\left(\frac{218}{265}\right)\) \(e\left(\frac{479}{530}\right)\) \(e\left(\frac{47}{53}\right)\) \(e\left(\frac{62}{265}\right)\) \(e\left(\frac{261}{265}\right)\) \(e\left(\frac{119}{265}\right)\) \(e\left(\frac{167}{530}\right)\) \(e\left(\frac{137}{530}\right)\)
\(\chi_{2675}(384,\cdot)\) \(-1\) \(1\) \(e\left(\frac{113}{265}\right)\) \(e\left(\frac{397}{530}\right)\) \(e\left(\frac{226}{265}\right)\) \(e\left(\frac{93}{530}\right)\) \(e\left(\frac{39}{53}\right)\) \(e\left(\frac{74}{265}\right)\) \(e\left(\frac{132}{265}\right)\) \(e\left(\frac{48}{265}\right)\) \(e\left(\frac{319}{530}\right)\) \(e\left(\frac{249}{530}\right)\)
\(\chi_{2675}(389,\cdot)\) \(-1\) \(1\) \(e\left(\frac{157}{265}\right)\) \(e\left(\frac{303}{530}\right)\) \(e\left(\frac{49}{265}\right)\) \(e\left(\frac{87}{530}\right)\) \(e\left(\frac{4}{53}\right)\) \(e\left(\frac{206}{265}\right)\) \(e\left(\frac{38}{265}\right)\) \(e\left(\frac{62}{265}\right)\) \(e\left(\frac{401}{530}\right)\) \(e\left(\frac{421}{530}\right)\)
\(\chi_{2675}(394,\cdot)\) \(-1\) \(1\) \(e\left(\frac{181}{265}\right)\) \(e\left(\frac{59}{530}\right)\) \(e\left(\frac{97}{265}\right)\) \(e\left(\frac{421}{530}\right)\) \(e\left(\frac{9}{53}\right)\) \(e\left(\frac{13}{265}\right)\) \(e\left(\frac{59}{265}\right)\) \(e\left(\frac{166}{265}\right)\) \(e\left(\frac{253}{530}\right)\) \(e\left(\frac{33}{530}\right)\)