LMFDB - Dirichlet character orbit 10700.bl

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10700, base_ring=CyclotomicField(530)) M = H._module chi = DirichletCharacter(H, M([265,212,135])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(31,10700)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$10700$
Conductor:	$10700$	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:	even	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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{10700}(31,\cdot)$	$1$	$1$	$e\left(\frac{69}{530}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{69}{265}\right)$	$e\left(\frac{267}{530}\right)$	$e\left(\frac{44}{265}\right)$	$e\left(\frac{311}{530}\right)$	$e\left(\frac{301}{530}\right)$	$e\left(\frac{309}{530}\right)$	$e\left(\frac{367}{530}\right)$	$e\left(\frac{207}{530}\right)$
$\chi_{10700}(71,\cdot)$	$1$	$1$	$e\left(\frac{251}{530}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{251}{265}\right)$	$e\left(\frac{303}{530}\right)$	$e\left(\frac{41}{265}\right)$	$e\left(\frac{79}{530}\right)$	$e\left(\frac{419}{530}\right)$	$e\left(\frac{41}{530}\right)$	$e\left(\frac{83}{530}\right)$	$e\left(\frac{223}{530}\right)$
$\chi_{10700}(91,\cdot)$	$1$	$1$	$e\left(\frac{287}{530}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{22}{265}\right)$	$e\left(\frac{281}{530}\right)$	$e\left(\frac{87}{265}\right)$	$e\left(\frac{103}{530}\right)$	$e\left(\frac{23}{530}\right)$	$e\left(\frac{87}{530}\right)$	$e\left(\frac{21}{530}\right)$	$e\left(\frac{331}{530}\right)$
$\chi_{10700}(131,\cdot)$	$1$	$1$	$e\left(\frac{269}{530}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{4}{265}\right)$	$e\left(\frac{27}{530}\right)$	$e\left(\frac{64}{265}\right)$	$e\left(\frac{91}{530}\right)$	$e\left(\frac{221}{530}\right)$	$e\left(\frac{329}{530}\right)$	$e\left(\frac{317}{530}\right)$	$e\left(\frac{277}{530}\right)$
$\chi_{10700}(191,\cdot)$	$1$	$1$	$e\left(\frac{447}{530}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{182}{265}\right)$	$e\left(\frac{301}{530}\right)$	$e\left(\frac{262}{265}\right)$	$e\left(\frac{33}{530}\right)$	$e\left(\frac{383}{530}\right)$	$e\left(\frac{527}{530}\right)$	$e\left(\frac{511}{530}\right)$	$e\left(\frac{281}{530}\right)$
$\chi_{10700}(211,\cdot)$	$1$	$1$	$e\left(\frac{173}{530}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{173}{265}\right)$	$e\left(\frac{439}{530}\right)$	$e\left(\frac{118}{265}\right)$	$e\left(\frac{27}{530}\right)$	$e\left(\frac{217}{530}\right)$	$e\left(\frac{383}{530}\right)$	$e\left(\frac{129}{530}\right)$	$e\left(\frac{519}{530}\right)$
$\chi_{10700}(231,\cdot)$	$1$	$1$	$e\left(\frac{239}{530}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{239}{265}\right)$	$e\left(\frac{487}{530}\right)$	$e\left(\frac{114}{265}\right)$	$e\left(\frac{71}{530}\right)$	$e\left(\frac{21}{530}\right)$	$e\left(\frac{379}{530}\right)$	$e\left(\frac{457}{530}\right)$	$e\left(\frac{187}{530}\right)$
$\chi_{10700}(291,\cdot)$	$1$	$1$	$e\left(\frac{437}{530}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{172}{265}\right)$	$e\left(\frac{101}{530}\right)$	$e\left(\frac{102}{265}\right)$	$e\left(\frac{203}{530}\right)$	$e\left(\frac{493}{530}\right)$	$e\left(\frac{367}{530}\right)$	$e\left(\frac{381}{530}\right)$	$e\left(\frac{251}{530}\right)$
$\chi_{10700}(311,\cdot)$	$1$	$1$	$e\left(\frac{423}{530}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{158}{265}\right)$	$e\left(\frac{139}{530}\right)$	$e\left(\frac{143}{265}\right)$	$e\left(\frac{17}{530}\right)$	$e\left(\frac{117}{530}\right)$	$e\left(\frac{143}{530}\right)$	$e\left(\frac{199}{530}\right)$	$e\left(\frac{209}{530}\right)$
$\chi_{10700}(371,\cdot)$	$1$	$1$	$e\left(\frac{231}{530}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{231}{265}\right)$	$e\left(\frac{433}{530}\right)$	$e\left(\frac{251}{265}\right)$	$e\left(\frac{419}{530}\right)$	$e\left(\frac{109}{530}\right)$	$e\left(\frac{251}{530}\right)$	$e\left(\frac{353}{530}\right)$	$e\left(\frac{163}{530}\right)$
$\chi_{10700}(391,\cdot)$	$1$	$1$	$e\left(\frac{527}{530}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{262}{265}\right)$	$e\left(\frac{311}{530}\right)$	$e\left(\frac{217}{265}\right)$	$e\left(\frac{263}{530}\right)$	$e\left(\frac{33}{530}\right)$	$e\left(\frac{217}{530}\right)$	$e\left(\frac{491}{530}\right)$	$e\left(\frac{521}{530}\right)$
$\chi_{10700}(471,\cdot)$	$1$	$1$	$e\left(\frac{351}{530}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{86}{265}\right)$	$e\left(\frac{183}{530}\right)$	$e\left(\frac{51}{265}\right)$	$e\left(\frac{499}{530}\right)$	$e\left(\frac{379}{530}\right)$	$e\left(\frac{51}{530}\right)$	$e\left(\frac{323}{530}\right)$	$e\left(\frac{523}{530}\right)$
$\chi_{10700}(491,\cdot)$	$1$	$1$	$e\left(\frac{397}{530}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{132}{265}\right)$	$e\left(\frac{361}{530}\right)$	$e\left(\frac{257}{265}\right)$	$e\left(\frac{353}{530}\right)$	$e\left(\frac{403}{530}\right)$	$e\left(\frac{257}{530}\right)$	$e\left(\frac{391}{530}\right)$	$e\left(\frac{131}{530}\right)$
$\chi_{10700}(531,\cdot)$	$1$	$1$	$e\left(\frac{329}{530}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{64}{265}\right)$	$e\left(\frac{167}{530}\right)$	$e\left(\frac{229}{265}\right)$	$e\left(\frac{131}{530}\right)$	$e\left(\frac{91}{530}\right)$	$e\left(\frac{229}{530}\right)$	$e\left(\frac{37}{530}\right)$	$e\left(\frac{457}{530}\right)$
$\chi_{10700}(631,\cdot)$	$1$	$1$	$e\left(\frac{439}{530}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{174}{265}\right)$	$e\left(\frac{247}{530}\right)$	$e\left(\frac{134}{265}\right)$	$e\left(\frac{381}{530}\right)$	$e\left(\frac{471}{530}\right)$	$e\left(\frac{399}{530}\right)$	$e\left(\frac{407}{530}\right)$	$e\left(\frac{257}{530}\right)$
$\chi_{10700}(771,\cdot)$	$1$	$1$	$e\left(\frac{471}{530}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{206}{265}\right)$	$e\left(\frac{463}{530}\right)$	$e\left(\frac{116}{265}\right)$	$e\left(\frac{49}{530}\right)$	$e\left(\frac{119}{530}\right)$	$e\left(\frac{381}{530}\right)$	$e\left(\frac{293}{530}\right)$	$e\left(\frac{353}{530}\right)$
$\chi_{10700}(831,\cdot)$	$1$	$1$	$e\left(\frac{199}{530}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{199}{265}\right)$	$e\left(\frac{217}{530}\right)$	$e\left(\frac{4}{265}\right)$	$e\left(\frac{221}{530}\right)$	$e\left(\frac{461}{530}\right)$	$e\left(\frac{269}{530}\right)$	$e\left(\frac{467}{530}\right)$	$e\left(\frac{67}{530}\right)$
$\chi_{10700}(871,\cdot)$	$1$	$1$	$e\left(\frac{511}{530}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{246}{265}\right)$	$e\left(\frac{203}{530}\right)$	$e\left(\frac{226}{265}\right)$	$e\left(\frac{429}{530}\right)$	$e\left(\frac{209}{530}\right)$	$e\left(\frac{491}{530}\right)$	$e\left(\frac{283}{530}\right)$	$e\left(\frac{473}{530}\right)$
$\chi_{10700}(911,\cdot)$	$1$	$1$	$e\left(\frac{353}{530}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{88}{265}\right)$	$e\left(\frac{329}{530}\right)$	$e\left(\frac{83}{265}\right)$	$e\left(\frac{147}{530}\right)$	$e\left(\frac{357}{530}\right)$	$e\left(\frac{83}{530}\right)$	$e\left(\frac{349}{530}\right)$	$e\left(\frac{529}{530}\right)$
$\chi_{10700}(971,\cdot)$	$1$	$1$	$e\left(\frac{361}{530}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{96}{265}\right)$	$e\left(\frac{383}{530}\right)$	$e\left(\frac{211}{265}\right)$	$e\left(\frac{329}{530}\right)$	$e\left(\frac{269}{530}\right)$	$e\left(\frac{211}{530}\right)$	$e\left(\frac{453}{530}\right)$	$e\left(\frac{23}{530}\right)$
$\chi_{10700}(991,\cdot)$	$1$	$1$	$e\left(\frac{327}{530}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{62}{265}\right)$	$e\left(\frac{21}{530}\right)$	$e\left(\frac{197}{265}\right)$	$e\left(\frac{483}{530}\right)$	$e\left(\frac{113}{530}\right)$	$e\left(\frac{197}{530}\right)$	$e\left(\frac{11}{530}\right)$	$e\left(\frac{451}{530}\right)$
$\chi_{10700}(1031,\cdot)$	$1$	$1$	$e\left(\frac{409}{530}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{144}{265}\right)$	$e\left(\frac{177}{530}\right)$	$e\left(\frac{184}{265}\right)$	$e\left(\frac{361}{530}\right)$	$e\left(\frac{271}{530}\right)$	$e\left(\frac{449}{530}\right)$	$e\left(\frac{17}{530}\right)$	$e\left(\frac{167}{530}\right)$
$\chi_{10700}(1091,\cdot)$	$1$	$1$	$e\left(\frac{277}{530}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{12}{265}\right)$	$e\left(\frac{81}{530}\right)$	$e\left(\frac{192}{265}\right)$	$e\left(\frac{273}{530}\right)$	$e\left(\frac{133}{530}\right)$	$e\left(\frac{457}{530}\right)$	$e\left(\frac{421}{530}\right)$	$e\left(\frac{301}{530}\right)$
$\chi_{10700}(1231,\cdot)$	$1$	$1$	$e\left(\frac{339}{530}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{74}{265}\right)$	$e\left(\frac{367}{530}\right)$	$e\left(\frac{124}{265}\right)$	$e\left(\frac{491}{530}\right)$	$e\left(\frac{511}{530}\right)$	$e\left(\frac{389}{530}\right)$	$e\left(\frac{167}{530}\right)$	$e\left(\frac{487}{530}\right)$
$\chi_{10700}(1271,\cdot)$	$1$	$1$	$e\left(\frac{501}{530}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{236}{265}\right)$	$e\left(\frac{3}{530}\right)$	$e\left(\frac{66}{265}\right)$	$e\left(\frac{69}{530}\right)$	$e\left(\frac{319}{530}\right)$	$e\left(\frac{331}{530}\right)$	$e\left(\frac{153}{530}\right)$	$e\left(\frac{443}{530}\right)$
$\chi_{10700}(1291,\cdot)$	$1$	$1$	$e\left(\frac{157}{530}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{157}{265}\right)$	$e\left(\frac{331}{530}\right)$	$e\left(\frac{127}{265}\right)$	$e\left(\frac{193}{530}\right)$	$e\left(\frac{393}{530}\right)$	$e\left(\frac{127}{530}\right)$	$e\left(\frac{451}{530}\right)$	$e\left(\frac{471}{530}\right)$
$\chi_{10700}(1411,\cdot)$	$1$	$1$	$e\left(\frac{243}{530}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{243}{265}\right)$	$e\left(\frac{249}{530}\right)$	$e\left(\frac{178}{265}\right)$	$e\left(\frac{427}{530}\right)$	$e\left(\frac{507}{530}\right)$	$e\left(\frac{443}{530}\right)$	$e\left(\frac{509}{530}\right)$	$e\left(\frac{199}{530}\right)$
$\chi_{10700}(1471,\cdot)$	$1$	$1$	$e\left(\frac{201}{530}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{201}{265}\right)$	$e\left(\frac{363}{530}\right)$	$e\left(\frac{36}{265}\right)$	$e\left(\frac{399}{530}\right)$	$e\left(\frac{439}{530}\right)$	$e\left(\frac{301}{530}\right)$	$e\left(\frac{493}{530}\right)$	$e\left(\frac{73}{530}\right)$
$\chi_{10700}(1571,\cdot)$	$1$	$1$	$e\left(\frac{271}{530}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{6}{265}\right)$	$e\left(\frac{173}{530}\right)$	$e\left(\frac{96}{265}\right)$	$e\left(\frac{269}{530}\right)$	$e\left(\frac{199}{530}\right)$	$e\left(\frac{361}{530}\right)$	$e\left(\frac{343}{530}\right)$	$e\left(\frac{283}{530}\right)$
$\chi_{10700}(1591,\cdot)$	$1$	$1$	$e\left(\frac{507}{530}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{242}{265}\right)$	$e\left(\frac{441}{530}\right)$	$e\left(\frac{162}{265}\right)$	$e\left(\frac{73}{530}\right)$	$e\left(\frac{253}{530}\right)$	$e\left(\frac{427}{530}\right)$	$e\left(\frac{231}{530}\right)$	$e\left(\frac{461}{530}\right)$
$\chi_{10700}(1611,\cdot)$	$1$	$1$	$e\left(\frac{523}{530}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{258}{265}\right)$	$e\left(\frac{19}{530}\right)$	$e\left(\frac{153}{265}\right)$	$e\left(\frac{437}{530}\right)$	$e\left(\frac{77}{530}\right)$	$e\left(\frac{153}{530}\right)$	$e\left(\frac{439}{530}\right)$	$e\left(\frac{509}{530}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{10700}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{530}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{69}{265}\right)\)	\(e\left(\frac{267}{530}\right)\)	\(e\left(\frac{44}{265}\right)\)	\(e\left(\frac{311}{530}\right)\)	\(e\left(\frac{301}{530}\right)\)	\(e\left(\frac{309}{530}\right)\)	\(e\left(\frac{367}{530}\right)\)	\(e\left(\frac{207}{530}\right)\)
\(\chi_{10700}(71,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{251}{530}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{251}{265}\right)\)	\(e\left(\frac{303}{530}\right)\)	\(e\left(\frac{41}{265}\right)\)	\(e\left(\frac{79}{530}\right)\)	\(e\left(\frac{419}{530}\right)\)	\(e\left(\frac{41}{530}\right)\)	\(e\left(\frac{83}{530}\right)\)	\(e\left(\frac{223}{530}\right)\)
\(\chi_{10700}(91,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{530}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{22}{265}\right)\)	\(e\left(\frac{281}{530}\right)\)	\(e\left(\frac{87}{265}\right)\)	\(e\left(\frac{103}{530}\right)\)	\(e\left(\frac{23}{530}\right)\)	\(e\left(\frac{87}{530}\right)\)	\(e\left(\frac{21}{530}\right)\)	\(e\left(\frac{331}{530}\right)\)
\(\chi_{10700}(131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{530}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{4}{265}\right)\)	\(e\left(\frac{27}{530}\right)\)	\(e\left(\frac{64}{265}\right)\)	\(e\left(\frac{91}{530}\right)\)	\(e\left(\frac{221}{530}\right)\)	\(e\left(\frac{329}{530}\right)\)	\(e\left(\frac{317}{530}\right)\)	\(e\left(\frac{277}{530}\right)\)
\(\chi_{10700}(191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{447}{530}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{182}{265}\right)\)	\(e\left(\frac{301}{530}\right)\)	\(e\left(\frac{262}{265}\right)\)	\(e\left(\frac{33}{530}\right)\)	\(e\left(\frac{383}{530}\right)\)	\(e\left(\frac{527}{530}\right)\)	\(e\left(\frac{511}{530}\right)\)	\(e\left(\frac{281}{530}\right)\)
\(\chi_{10700}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{530}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{173}{265}\right)\)	\(e\left(\frac{439}{530}\right)\)	\(e\left(\frac{118}{265}\right)\)	\(e\left(\frac{27}{530}\right)\)	\(e\left(\frac{217}{530}\right)\)	\(e\left(\frac{383}{530}\right)\)	\(e\left(\frac{129}{530}\right)\)	\(e\left(\frac{519}{530}\right)\)
\(\chi_{10700}(231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{530}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{239}{265}\right)\)	\(e\left(\frac{487}{530}\right)\)	\(e\left(\frac{114}{265}\right)\)	\(e\left(\frac{71}{530}\right)\)	\(e\left(\frac{21}{530}\right)\)	\(e\left(\frac{379}{530}\right)\)	\(e\left(\frac{457}{530}\right)\)	\(e\left(\frac{187}{530}\right)\)
\(\chi_{10700}(291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{437}{530}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{172}{265}\right)\)	\(e\left(\frac{101}{530}\right)\)	\(e\left(\frac{102}{265}\right)\)	\(e\left(\frac{203}{530}\right)\)	\(e\left(\frac{493}{530}\right)\)	\(e\left(\frac{367}{530}\right)\)	\(e\left(\frac{381}{530}\right)\)	\(e\left(\frac{251}{530}\right)\)
\(\chi_{10700}(311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{423}{530}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{158}{265}\right)\)	\(e\left(\frac{139}{530}\right)\)	\(e\left(\frac{143}{265}\right)\)	\(e\left(\frac{17}{530}\right)\)	\(e\left(\frac{117}{530}\right)\)	\(e\left(\frac{143}{530}\right)\)	\(e\left(\frac{199}{530}\right)\)	\(e\left(\frac{209}{530}\right)\)
\(\chi_{10700}(371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{231}{530}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{231}{265}\right)\)	\(e\left(\frac{433}{530}\right)\)	\(e\left(\frac{251}{265}\right)\)	\(e\left(\frac{419}{530}\right)\)	\(e\left(\frac{109}{530}\right)\)	\(e\left(\frac{251}{530}\right)\)	\(e\left(\frac{353}{530}\right)\)	\(e\left(\frac{163}{530}\right)\)
\(\chi_{10700}(391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{527}{530}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{262}{265}\right)\)	\(e\left(\frac{311}{530}\right)\)	\(e\left(\frac{217}{265}\right)\)	\(e\left(\frac{263}{530}\right)\)	\(e\left(\frac{33}{530}\right)\)	\(e\left(\frac{217}{530}\right)\)	\(e\left(\frac{491}{530}\right)\)	\(e\left(\frac{521}{530}\right)\)
\(\chi_{10700}(471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{351}{530}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{86}{265}\right)\)	\(e\left(\frac{183}{530}\right)\)	\(e\left(\frac{51}{265}\right)\)	\(e\left(\frac{499}{530}\right)\)	\(e\left(\frac{379}{530}\right)\)	\(e\left(\frac{51}{530}\right)\)	\(e\left(\frac{323}{530}\right)\)	\(e\left(\frac{523}{530}\right)\)
\(\chi_{10700}(491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{397}{530}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{132}{265}\right)\)	\(e\left(\frac{361}{530}\right)\)	\(e\left(\frac{257}{265}\right)\)	\(e\left(\frac{353}{530}\right)\)	\(e\left(\frac{403}{530}\right)\)	\(e\left(\frac{257}{530}\right)\)	\(e\left(\frac{391}{530}\right)\)	\(e\left(\frac{131}{530}\right)\)
\(\chi_{10700}(531,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{329}{530}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{64}{265}\right)\)	\(e\left(\frac{167}{530}\right)\)	\(e\left(\frac{229}{265}\right)\)	\(e\left(\frac{131}{530}\right)\)	\(e\left(\frac{91}{530}\right)\)	\(e\left(\frac{229}{530}\right)\)	\(e\left(\frac{37}{530}\right)\)	\(e\left(\frac{457}{530}\right)\)
\(\chi_{10700}(631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{439}{530}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{174}{265}\right)\)	\(e\left(\frac{247}{530}\right)\)	\(e\left(\frac{134}{265}\right)\)	\(e\left(\frac{381}{530}\right)\)	\(e\left(\frac{471}{530}\right)\)	\(e\left(\frac{399}{530}\right)\)	\(e\left(\frac{407}{530}\right)\)	\(e\left(\frac{257}{530}\right)\)
\(\chi_{10700}(771,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{471}{530}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{206}{265}\right)\)	\(e\left(\frac{463}{530}\right)\)	\(e\left(\frac{116}{265}\right)\)	\(e\left(\frac{49}{530}\right)\)	\(e\left(\frac{119}{530}\right)\)	\(e\left(\frac{381}{530}\right)\)	\(e\left(\frac{293}{530}\right)\)	\(e\left(\frac{353}{530}\right)\)
\(\chi_{10700}(831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{530}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{199}{265}\right)\)	\(e\left(\frac{217}{530}\right)\)	\(e\left(\frac{4}{265}\right)\)	\(e\left(\frac{221}{530}\right)\)	\(e\left(\frac{461}{530}\right)\)	\(e\left(\frac{269}{530}\right)\)	\(e\left(\frac{467}{530}\right)\)	\(e\left(\frac{67}{530}\right)\)
\(\chi_{10700}(871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{511}{530}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{246}{265}\right)\)	\(e\left(\frac{203}{530}\right)\)	\(e\left(\frac{226}{265}\right)\)	\(e\left(\frac{429}{530}\right)\)	\(e\left(\frac{209}{530}\right)\)	\(e\left(\frac{491}{530}\right)\)	\(e\left(\frac{283}{530}\right)\)	\(e\left(\frac{473}{530}\right)\)
\(\chi_{10700}(911,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{353}{530}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{88}{265}\right)\)	\(e\left(\frac{329}{530}\right)\)	\(e\left(\frac{83}{265}\right)\)	\(e\left(\frac{147}{530}\right)\)	\(e\left(\frac{357}{530}\right)\)	\(e\left(\frac{83}{530}\right)\)	\(e\left(\frac{349}{530}\right)\)	\(e\left(\frac{529}{530}\right)\)
\(\chi_{10700}(971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{361}{530}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{96}{265}\right)\)	\(e\left(\frac{383}{530}\right)\)	\(e\left(\frac{211}{265}\right)\)	\(e\left(\frac{329}{530}\right)\)	\(e\left(\frac{269}{530}\right)\)	\(e\left(\frac{211}{530}\right)\)	\(e\left(\frac{453}{530}\right)\)	\(e\left(\frac{23}{530}\right)\)
\(\chi_{10700}(991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{327}{530}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{62}{265}\right)\)	\(e\left(\frac{21}{530}\right)\)	\(e\left(\frac{197}{265}\right)\)	\(e\left(\frac{483}{530}\right)\)	\(e\left(\frac{113}{530}\right)\)	\(e\left(\frac{197}{530}\right)\)	\(e\left(\frac{11}{530}\right)\)	\(e\left(\frac{451}{530}\right)\)
\(\chi_{10700}(1031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{409}{530}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{144}{265}\right)\)	\(e\left(\frac{177}{530}\right)\)	\(e\left(\frac{184}{265}\right)\)	\(e\left(\frac{361}{530}\right)\)	\(e\left(\frac{271}{530}\right)\)	\(e\left(\frac{449}{530}\right)\)	\(e\left(\frac{17}{530}\right)\)	\(e\left(\frac{167}{530}\right)\)
\(\chi_{10700}(1091,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{277}{530}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{12}{265}\right)\)	\(e\left(\frac{81}{530}\right)\)	\(e\left(\frac{192}{265}\right)\)	\(e\left(\frac{273}{530}\right)\)	\(e\left(\frac{133}{530}\right)\)	\(e\left(\frac{457}{530}\right)\)	\(e\left(\frac{421}{530}\right)\)	\(e\left(\frac{301}{530}\right)\)
\(\chi_{10700}(1231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{339}{530}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{74}{265}\right)\)	\(e\left(\frac{367}{530}\right)\)	\(e\left(\frac{124}{265}\right)\)	\(e\left(\frac{491}{530}\right)\)	\(e\left(\frac{511}{530}\right)\)	\(e\left(\frac{389}{530}\right)\)	\(e\left(\frac{167}{530}\right)\)	\(e\left(\frac{487}{530}\right)\)
\(\chi_{10700}(1271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{501}{530}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{236}{265}\right)\)	\(e\left(\frac{3}{530}\right)\)	\(e\left(\frac{66}{265}\right)\)	\(e\left(\frac{69}{530}\right)\)	\(e\left(\frac{319}{530}\right)\)	\(e\left(\frac{331}{530}\right)\)	\(e\left(\frac{153}{530}\right)\)	\(e\left(\frac{443}{530}\right)\)
\(\chi_{10700}(1291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{530}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{157}{265}\right)\)	\(e\left(\frac{331}{530}\right)\)	\(e\left(\frac{127}{265}\right)\)	\(e\left(\frac{193}{530}\right)\)	\(e\left(\frac{393}{530}\right)\)	\(e\left(\frac{127}{530}\right)\)	\(e\left(\frac{451}{530}\right)\)	\(e\left(\frac{471}{530}\right)\)
\(\chi_{10700}(1411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{243}{530}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{243}{265}\right)\)	\(e\left(\frac{249}{530}\right)\)	\(e\left(\frac{178}{265}\right)\)	\(e\left(\frac{427}{530}\right)\)	\(e\left(\frac{507}{530}\right)\)	\(e\left(\frac{443}{530}\right)\)	\(e\left(\frac{509}{530}\right)\)	\(e\left(\frac{199}{530}\right)\)
\(\chi_{10700}(1471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{201}{530}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{201}{265}\right)\)	\(e\left(\frac{363}{530}\right)\)	\(e\left(\frac{36}{265}\right)\)	\(e\left(\frac{399}{530}\right)\)	\(e\left(\frac{439}{530}\right)\)	\(e\left(\frac{301}{530}\right)\)	\(e\left(\frac{493}{530}\right)\)	\(e\left(\frac{73}{530}\right)\)
\(\chi_{10700}(1571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{271}{530}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{6}{265}\right)\)	\(e\left(\frac{173}{530}\right)\)	\(e\left(\frac{96}{265}\right)\)	\(e\left(\frac{269}{530}\right)\)	\(e\left(\frac{199}{530}\right)\)	\(e\left(\frac{361}{530}\right)\)	\(e\left(\frac{343}{530}\right)\)	\(e\left(\frac{283}{530}\right)\)
\(\chi_{10700}(1591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{507}{530}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{242}{265}\right)\)	\(e\left(\frac{441}{530}\right)\)	\(e\left(\frac{162}{265}\right)\)	\(e\left(\frac{73}{530}\right)\)	\(e\left(\frac{253}{530}\right)\)	\(e\left(\frac{427}{530}\right)\)	\(e\left(\frac{231}{530}\right)\)	\(e\left(\frac{461}{530}\right)\)
\(\chi_{10700}(1611,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{523}{530}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{258}{265}\right)\)	\(e\left(\frac{19}{530}\right)\)	\(e\left(\frac{153}{265}\right)\)	\(e\left(\frac{437}{530}\right)\)	\(e\left(\frac{77}{530}\right)\)	\(e\left(\frac{153}{530}\right)\)	\(e\left(\frac{439}{530}\right)\)	\(e\left(\frac{509}{530}\right)\)

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First 31 of 208 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	10700.bl
Modulus	$10700$
Conductor	$10700$
Order	$530$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(10700\)
Conductor:	\(10700\)	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:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)