Properties

Label 3525.bl
Modulus $3525$
Conductor $3525$
Order $230$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3525, base_ring=CyclotomicField(230))
 
M = H._module
 
chi = DirichletCharacter(H, M([115,92,200]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(56,3525))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3525\)
Conductor: \(3525\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(230\)
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: $\Q(\zeta_{115})$
Fixed field: Number field defined by a degree 230 polynomial (not computed)

First 31 of 88 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{3525}(56,\cdot)\) \(-1\) \(1\) \(e\left(\frac{127}{230}\right)\) \(e\left(\frac{12}{115}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{151}{230}\right)\) \(e\left(\frac{227}{230}\right)\) \(e\left(\frac{19}{115}\right)\) \(e\left(\frac{87}{230}\right)\) \(e\left(\frac{24}{115}\right)\) \(e\left(\frac{141}{230}\right)\) \(e\left(\frac{38}{115}\right)\)
\(\chi_{3525}(71,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{230}\right)\) \(e\left(\frac{13}{115}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{39}{230}\right)\) \(e\left(\frac{83}{230}\right)\) \(e\left(\frac{11}{115}\right)\) \(e\left(\frac{123}{230}\right)\) \(e\left(\frac{26}{115}\right)\) \(e\left(\frac{9}{230}\right)\) \(e\left(\frac{22}{115}\right)\)
\(\chi_{3525}(131,\cdot)\) \(-1\) \(1\) \(e\left(\frac{77}{230}\right)\) \(e\left(\frac{77}{115}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{1}{230}\right)\) \(e\left(\frac{67}{230}\right)\) \(e\left(\frac{74}{115}\right)\) \(e\left(\frac{127}{230}\right)\) \(e\left(\frac{39}{115}\right)\) \(e\left(\frac{71}{230}\right)\) \(e\left(\frac{33}{115}\right)\)
\(\chi_{3525}(191,\cdot)\) \(-1\) \(1\) \(e\left(\frac{121}{230}\right)\) \(e\left(\frac{6}{115}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{133}{230}\right)\) \(e\left(\frac{171}{230}\right)\) \(e\left(\frac{67}{115}\right)\) \(e\left(\frac{101}{230}\right)\) \(e\left(\frac{12}{115}\right)\) \(e\left(\frac{13}{230}\right)\) \(e\left(\frac{19}{115}\right)\)
\(\chi_{3525}(206,\cdot)\) \(-1\) \(1\) \(e\left(\frac{137}{230}\right)\) \(e\left(\frac{22}{115}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{181}{230}\right)\) \(e\left(\frac{167}{230}\right)\) \(e\left(\frac{54}{115}\right)\) \(e\left(\frac{217}{230}\right)\) \(e\left(\frac{44}{115}\right)\) \(e\left(\frac{201}{230}\right)\) \(e\left(\frac{108}{115}\right)\)
\(\chi_{3525}(296,\cdot)\) \(-1\) \(1\) \(e\left(\frac{153}{230}\right)\) \(e\left(\frac{38}{115}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{229}{230}\right)\) \(e\left(\frac{163}{230}\right)\) \(e\left(\frac{41}{115}\right)\) \(e\left(\frac{103}{230}\right)\) \(e\left(\frac{76}{115}\right)\) \(e\left(\frac{159}{230}\right)\) \(e\left(\frac{82}{115}\right)\)
\(\chi_{3525}(341,\cdot)\) \(-1\) \(1\) \(e\left(\frac{141}{230}\right)\) \(e\left(\frac{26}{115}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{193}{230}\right)\) \(e\left(\frac{51}{230}\right)\) \(e\left(\frac{22}{115}\right)\) \(e\left(\frac{131}{230}\right)\) \(e\left(\frac{52}{115}\right)\) \(e\left(\frac{133}{230}\right)\) \(e\left(\frac{44}{115}\right)\)
\(\chi_{3525}(356,\cdot)\) \(-1\) \(1\) \(e\left(\frac{87}{230}\right)\) \(e\left(\frac{87}{115}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{31}{230}\right)\) \(e\left(\frac{7}{230}\right)\) \(e\left(\frac{109}{115}\right)\) \(e\left(\frac{27}{230}\right)\) \(e\left(\frac{59}{115}\right)\) \(e\left(\frac{131}{230}\right)\) \(e\left(\frac{103}{115}\right)\)
\(\chi_{3525}(371,\cdot)\) \(-1\) \(1\) \(e\left(\frac{113}{230}\right)\) \(e\left(\frac{113}{115}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{109}{230}\right)\) \(e\left(\frac{173}{230}\right)\) \(e\left(\frac{16}{115}\right)\) \(e\left(\frac{43}{230}\right)\) \(e\left(\frac{111}{115}\right)\) \(e\left(\frac{149}{230}\right)\) \(e\left(\frac{32}{115}\right)\)
\(\chi_{3525}(431,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{230}\right)\) \(e\left(\frac{7}{115}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{21}{230}\right)\) \(e\left(\frac{27}{230}\right)\) \(e\left(\frac{59}{115}\right)\) \(e\left(\frac{137}{230}\right)\) \(e\left(\frac{14}{115}\right)\) \(e\left(\frac{111}{230}\right)\) \(e\left(\frac{3}{115}\right)\)
\(\chi_{3525}(491,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{230}\right)\) \(e\left(\frac{11}{115}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{33}{230}\right)\) \(e\left(\frac{141}{230}\right)\) \(e\left(\frac{27}{115}\right)\) \(e\left(\frac{51}{230}\right)\) \(e\left(\frac{22}{115}\right)\) \(e\left(\frac{43}{230}\right)\) \(e\left(\frac{54}{115}\right)\)
\(\chi_{3525}(506,\cdot)\) \(-1\) \(1\) \(e\left(\frac{147}{230}\right)\) \(e\left(\frac{32}{115}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{211}{230}\right)\) \(e\left(\frac{107}{230}\right)\) \(e\left(\frac{89}{115}\right)\) \(e\left(\frac{117}{230}\right)\) \(e\left(\frac{64}{115}\right)\) \(e\left(\frac{31}{230}\right)\) \(e\left(\frac{63}{115}\right)\)
\(\chi_{3525}(521,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{230}\right)\) \(e\left(\frac{43}{115}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{129}{230}\right)\) \(e\left(\frac{133}{230}\right)\) \(e\left(\frac{1}{115}\right)\) \(e\left(\frac{53}{230}\right)\) \(e\left(\frac{86}{115}\right)\) \(e\left(\frac{189}{230}\right)\) \(e\left(\frac{2}{115}\right)\)
\(\chi_{3525}(566,\cdot)\) \(-1\) \(1\) \(e\left(\frac{171}{230}\right)\) \(e\left(\frac{56}{115}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{53}{230}\right)\) \(e\left(\frac{101}{230}\right)\) \(e\left(\frac{12}{115}\right)\) \(e\left(\frac{61}{230}\right)\) \(e\left(\frac{112}{115}\right)\) \(e\left(\frac{83}{230}\right)\) \(e\left(\frac{24}{115}\right)\)
\(\chi_{3525}(581,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{230}\right)\) \(e\left(\frac{37}{115}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{111}{230}\right)\) \(e\left(\frac{77}{230}\right)\) \(e\left(\frac{49}{115}\right)\) \(e\left(\frac{67}{230}\right)\) \(e\left(\frac{74}{115}\right)\) \(e\left(\frac{61}{230}\right)\) \(e\left(\frac{98}{115}\right)\)
\(\chi_{3525}(596,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{230}\right)\) \(e\left(\frac{73}{115}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{219}{230}\right)\) \(e\left(\frac{183}{230}\right)\) \(e\left(\frac{106}{115}\right)\) \(e\left(\frac{213}{230}\right)\) \(e\left(\frac{31}{115}\right)\) \(e\left(\frac{139}{230}\right)\) \(e\left(\frac{97}{115}\right)\)
\(\chi_{3525}(686,\cdot)\) \(-1\) \(1\) \(e\left(\frac{209}{230}\right)\) \(e\left(\frac{94}{115}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{167}{230}\right)\) \(e\left(\frac{149}{230}\right)\) \(e\left(\frac{53}{115}\right)\) \(e\left(\frac{49}{230}\right)\) \(e\left(\frac{73}{115}\right)\) \(e\left(\frac{127}{230}\right)\) \(e\left(\frac{106}{115}\right)\)
\(\chi_{3525}(761,\cdot)\) \(-1\) \(1\) \(e\left(\frac{219}{230}\right)\) \(e\left(\frac{104}{115}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{197}{230}\right)\) \(e\left(\frac{89}{230}\right)\) \(e\left(\frac{88}{115}\right)\) \(e\left(\frac{179}{230}\right)\) \(e\left(\frac{93}{115}\right)\) \(e\left(\frac{187}{230}\right)\) \(e\left(\frac{61}{115}\right)\)
\(\chi_{3525}(806,\cdot)\) \(-1\) \(1\) \(e\left(\frac{97}{230}\right)\) \(e\left(\frac{97}{115}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{61}{230}\right)\) \(e\left(\frac{177}{230}\right)\) \(e\left(\frac{29}{115}\right)\) \(e\left(\frac{157}{230}\right)\) \(e\left(\frac{79}{115}\right)\) \(e\left(\frac{191}{230}\right)\) \(e\left(\frac{58}{115}\right)\)
\(\chi_{3525}(836,\cdot)\) \(-1\) \(1\) \(e\left(\frac{169}{230}\right)\) \(e\left(\frac{54}{115}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{47}{230}\right)\) \(e\left(\frac{159}{230}\right)\) \(e\left(\frac{28}{115}\right)\) \(e\left(\frac{219}{230}\right)\) \(e\left(\frac{108}{115}\right)\) \(e\left(\frac{117}{230}\right)\) \(e\left(\frac{56}{115}\right)\)
\(\chi_{3525}(896,\cdot)\) \(-1\) \(1\) \(e\left(\frac{213}{230}\right)\) \(e\left(\frac{98}{115}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{179}{230}\right)\) \(e\left(\frac{33}{230}\right)\) \(e\left(\frac{21}{115}\right)\) \(e\left(\frac{193}{230}\right)\) \(e\left(\frac{81}{115}\right)\) \(e\left(\frac{59}{230}\right)\) \(e\left(\frac{42}{115}\right)\)
\(\chi_{3525}(911,\cdot)\) \(-1\) \(1\) \(e\left(\frac{229}{230}\right)\) \(e\left(\frac{114}{115}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{227}{230}\right)\) \(e\left(\frac{29}{230}\right)\) \(e\left(\frac{8}{115}\right)\) \(e\left(\frac{79}{230}\right)\) \(e\left(\frac{113}{115}\right)\) \(e\left(\frac{17}{230}\right)\) \(e\left(\frac{16}{115}\right)\)
\(\chi_{3525}(956,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{230}\right)\) \(e\left(\frac{17}{115}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{51}{230}\right)\) \(e\left(\frac{197}{230}\right)\) \(e\left(\frac{94}{115}\right)\) \(e\left(\frac{37}{230}\right)\) \(e\left(\frac{34}{115}\right)\) \(e\left(\frac{171}{230}\right)\) \(e\left(\frac{73}{115}\right)\)
\(\chi_{3525}(1046,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{230}\right)\) \(e\left(\frac{3}{115}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{9}{230}\right)\) \(e\left(\frac{143}{230}\right)\) \(e\left(\frac{91}{115}\right)\) \(e\left(\frac{223}{230}\right)\) \(e\left(\frac{6}{115}\right)\) \(e\left(\frac{179}{230}\right)\) \(e\left(\frac{67}{115}\right)\)
\(\chi_{3525}(1061,\cdot)\) \(-1\) \(1\) \(e\left(\frac{179}{230}\right)\) \(e\left(\frac{64}{115}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{77}{230}\right)\) \(e\left(\frac{99}{230}\right)\) \(e\left(\frac{63}{115}\right)\) \(e\left(\frac{119}{230}\right)\) \(e\left(\frac{13}{115}\right)\) \(e\left(\frac{177}{230}\right)\) \(e\left(\frac{11}{115}\right)\)
\(\chi_{3525}(1106,\cdot)\) \(-1\) \(1\) \(e\left(\frac{157}{230}\right)\) \(e\left(\frac{42}{115}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{11}{230}\right)\) \(e\left(\frac{47}{230}\right)\) \(e\left(\frac{9}{115}\right)\) \(e\left(\frac{17}{230}\right)\) \(e\left(\frac{84}{115}\right)\) \(e\left(\frac{91}{230}\right)\) \(e\left(\frac{18}{115}\right)\)
\(\chi_{3525}(1136,\cdot)\) \(-1\) \(1\) \(e\left(\frac{99}{230}\right)\) \(e\left(\frac{99}{115}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{67}{230}\right)\) \(e\left(\frac{119}{230}\right)\) \(e\left(\frac{13}{115}\right)\) \(e\left(\frac{229}{230}\right)\) \(e\left(\frac{83}{115}\right)\) \(e\left(\frac{157}{230}\right)\) \(e\left(\frac{26}{115}\right)\)
\(\chi_{3525}(1181,\cdot)\) \(-1\) \(1\) \(e\left(\frac{177}{230}\right)\) \(e\left(\frac{62}{115}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{71}{230}\right)\) \(e\left(\frac{157}{230}\right)\) \(e\left(\frac{79}{115}\right)\) \(e\left(\frac{47}{230}\right)\) \(e\left(\frac{9}{115}\right)\) \(e\left(\frac{211}{230}\right)\) \(e\left(\frac{43}{115}\right)\)
\(\chi_{3525}(1196,\cdot)\) \(-1\) \(1\) \(e\left(\frac{103}{230}\right)\) \(e\left(\frac{103}{115}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{79}{230}\right)\) \(e\left(\frac{3}{230}\right)\) \(e\left(\frac{96}{115}\right)\) \(e\left(\frac{143}{230}\right)\) \(e\left(\frac{91}{115}\right)\) \(e\left(\frac{89}{230}\right)\) \(e\left(\frac{77}{115}\right)\)
\(\chi_{3525}(1211,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{230}\right)\) \(e\left(\frac{9}{115}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{27}{230}\right)\) \(e\left(\frac{199}{230}\right)\) \(e\left(\frac{43}{115}\right)\) \(e\left(\frac{209}{230}\right)\) \(e\left(\frac{18}{115}\right)\) \(e\left(\frac{77}{230}\right)\) \(e\left(\frac{86}{115}\right)\)
\(\chi_{3525}(1256,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{230}\right)\) \(e\left(\frac{47}{115}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{141}{230}\right)\) \(e\left(\frac{17}{230}\right)\) \(e\left(\frac{84}{115}\right)\) \(e\left(\frac{197}{230}\right)\) \(e\left(\frac{94}{115}\right)\) \(e\left(\frac{121}{230}\right)\) \(e\left(\frac{53}{115}\right)\)