LMFDB - Dirichlet character orbit 197.g

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(197, base_ring=CyclotomicField(98)) M = H._module chi = DirichletCharacter(H, M([2])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(16,197)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$197$
Conductor:	$197$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$49$	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:	$\Q(\zeta_{49})$
Fixed field:	Number field defined by a degree 49 polynomial

First 31 of 42 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{197}(16,\cdot)$	$1$	$1$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{29}{49}\right)$
$\chi_{197}(23,\cdot)$	$1$	$1$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{37}{49}\right)$
$\chi_{197}(24,\cdot)$	$1$	$1$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{11}{49}\right)$
$\chi_{197}(28,\cdot)$	$1$	$1$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{44}{49}\right)$
$\chi_{197}(29,\cdot)$	$1$	$1$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{16}{49}\right)$
$\chi_{197}(34,\cdot)$	$1$	$1$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{33}{49}\right)$
$\chi_{197}(37,\cdot)$	$1$	$1$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{20}{49}\right)$
$\chi_{197}(40,\cdot)$	$1$	$1$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{30}{49}\right)$
$\chi_{197}(42,\cdot)$	$1$	$1$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{26}{49}\right)$
$\chi_{197}(49,\cdot)$	$1$	$1$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{10}{49}\right)$
$\chi_{197}(51,\cdot)$	$1$	$1$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{15}{49}\right)$
$\chi_{197}(53,\cdot)$	$1$	$1$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{32}{49}\right)$
$\chi_{197}(54,\cdot)$	$1$	$1$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{24}{49}\right)$
$\chi_{197}(59,\cdot)$	$1$	$1$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{9}{49}\right)$
$\chi_{197}(60,\cdot)$	$1$	$1$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{12}{49}\right)$
$\chi_{197}(61,\cdot)$	$1$	$1$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{23}{49}\right)$
$\chi_{197}(63,\cdot)$	$1$	$1$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{8}{49}\right)$
$\chi_{197}(70,\cdot)$	$1$	$1$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{45}{49}\right)$
$\chi_{197}(76,\cdot)$	$1$	$1$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{4}{49}\right)$
$\chi_{197}(81,\cdot)$	$1$	$1$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{6}{49}\right)$
$\chi_{197}(85,\cdot)$	$1$	$1$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{34}{49}\right)$
$\chi_{197}(88,\cdot)$	$1$	$1$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{36}{49}\right)$
$\chi_{197}(90,\cdot)$	$1$	$1$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{43}{49}\right)$
$\chi_{197}(100,\cdot)$	$1$	$1$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{31}{49}\right)$
$\chi_{197}(101,\cdot)$	$1$	$1$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{1}{49}\right)$
$\chi_{197}(105,\cdot)$	$1$	$1$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{27}{49}\right)$
$\chi_{197}(132,\cdot)$	$1$	$1$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{18}{49}\right)$
$\chi_{197}(133,\cdot)$	$1$	$1$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{19}{49}\right)$
$\chi_{197}(135,\cdot)$	$1$	$1$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{25}{49}\right)$
$\chi_{197}(142,\cdot)$	$1$	$1$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{47}{49}\right)$
$\chi_{197}(150,\cdot)$	$1$	$1$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{13}{49}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{197}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)
\(\chi_{197}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)
\(\chi_{197}(24,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{11}{49}\right)\)
\(\chi_{197}(28,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)
\(\chi_{197}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{16}{49}\right)\)
\(\chi_{197}(34,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)
\(\chi_{197}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)
\(\chi_{197}(40,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)
\(\chi_{197}(42,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)
\(\chi_{197}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)
\(\chi_{197}(51,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)
\(\chi_{197}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)
\(\chi_{197}(54,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)
\(\chi_{197}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)
\(\chi_{197}(60,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)
\(\chi_{197}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)
\(\chi_{197}(63,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)
\(\chi_{197}(70,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)
\(\chi_{197}(76,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)
\(\chi_{197}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)
\(\chi_{197}(85,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)
\(\chi_{197}(88,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{36}{49}\right)\)
\(\chi_{197}(90,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)
\(\chi_{197}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)
\(\chi_{197}(101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)
\(\chi_{197}(105,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)
\(\chi_{197}(132,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)
\(\chi_{197}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)
\(\chi_{197}(135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)
\(\chi_{197}(142,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)
\(\chi_{197}(150,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)

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First 31 of 42 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	197.g
Modulus	$197$
Conductor	$197$
Order	$49$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(197\)
Conductor:	\(197\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(49\)	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)