LMFDB - Group of Dirichlet characters of modulus 259200

Show commands: PariGP / SageMath

sage: H = DirichletGroup(259200)

pari: g = idealstar(,259200,2)

Character group

sage: G.order() pari: g.no
Order	=	69120
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{4320}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{259200}(157951,\cdot)$, $\chi_{259200}(202501,\cdot)$, $\chi_{259200}(6401,\cdot)$, $\chi_{259200}(72577,\cdot)$

First 32 of 69120 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{259200}(1,\cdot)$	259200.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{259200}(7,\cdot)$	259200.vg	432	no	$1$	$1$	$e\left(\frac{133}{216}\right)$	$e\left(\frac{395}{432}\right)$	$e\left(\frac{349}{432}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{191}{216}\right)$	$e\left(\frac{389}{432}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{17}{216}\right)$
$\chi_{259200}(11,\cdot)$	259200.baz	4320	yes	$1$	$1$	$e\left(\frac{395}{432}\right)$	$e\left(\frac{911}{4320}\right)$	$e\left(\frac{4189}{4320}\right)$	$e\left(\frac{259}{360}\right)$	$e\left(\frac{791}{1440}\right)$	$e\left(\frac{293}{2160}\right)$	$e\left(\frac{977}{4320}\right)$	$e\left(\frac{521}{540}\right)$	$e\left(\frac{1033}{1440}\right)$	$e\left(\frac{1397}{2160}\right)$
$\chi_{259200}(13,\cdot)$	259200.baq	4320	yes	$-1$	$1$	$e\left(\frac{349}{432}\right)$	$e\left(\frac{4189}{4320}\right)$	$e\left(\frac{1151}{4320}\right)$	$e\left(\frac{131}{360}\right)$	$e\left(\frac{1429}{1440}\right)$	$e\left(\frac{1387}{2160}\right)$	$e\left(\frac{163}{4320}\right)$	$e\left(\frac{169}{540}\right)$	$e\left(\frac{707}{1440}\right)$	$e\left(\frac{1543}{2160}\right)$
$\chi_{259200}(17,\cdot)$	259200.vb	360	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{259}{360}\right)$	$e\left(\frac{131}{360}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{193}{360}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{43}{180}\right)$
$\chi_{259200}(19,\cdot)$	259200.zv	1440	no	$-1$	$1$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{791}{1440}\right)$	$e\left(\frac{1429}{1440}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{431}{480}\right)$	$e\left(\frac{173}{720}\right)$	$e\left(\frac{137}{1440}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{193}{480}\right)$	$e\left(\frac{197}{720}\right)$
$\chi_{259200}(23,\cdot)$	259200.bad	2160	no	$-1$	$1$	$e\left(\frac{191}{216}\right)$	$e\left(\frac{293}{2160}\right)$	$e\left(\frac{1387}{2160}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{173}{720}\right)$	$e\left(\frac{989}{1080}\right)$	$e\left(\frac{971}{2160}\right)$	$e\left(\frac{64}{135}\right)$	$e\left(\frac{319}{720}\right)$	$e\left(\frac{131}{1080}\right)$
$\chi_{259200}(29,\cdot)$	259200.bay	4320	yes	$-1$	$1$	$e\left(\frac{389}{432}\right)$	$e\left(\frac{977}{4320}\right)$	$e\left(\frac{163}{4320}\right)$	$e\left(\frac{193}{360}\right)$	$e\left(\frac{137}{1440}\right)$	$e\left(\frac{971}{2160}\right)$	$e\left(\frac{1439}{4320}\right)$	$e\left(\frac{137}{540}\right)$	$e\left(\frac{1111}{1440}\right)$	$e\left(\frac{59}{2160}\right)$
$\chi_{259200}(31,\cdot)$	259200.wu	540	no	$-1$	$1$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{521}{540}\right)$	$e\left(\frac{169}{540}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{64}{135}\right)$	$e\left(\frac{137}{540}\right)$	$e\left(\frac{29}{270}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{197}{270}\right)$
$\chi_{259200}(37,\cdot)$	259200.zk	1440	no	$-1$	$1$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{1033}{1440}\right)$	$e\left(\frac{707}{1440}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{193}{480}\right)$	$e\left(\frac{319}{720}\right)$	$e\left(\frac{1111}{1440}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{119}{480}\right)$	$e\left(\frac{331}{720}\right)$
$\chi_{259200}(41,\cdot)$	259200.baa	2160	no	$-1$	$1$	$e\left(\frac{17}{216}\right)$	$e\left(\frac{1397}{2160}\right)$	$e\left(\frac{1543}{2160}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{197}{720}\right)$	$e\left(\frac{131}{1080}\right)$	$e\left(\frac{59}{2160}\right)$	$e\left(\frac{197}{270}\right)$	$e\left(\frac{331}{720}\right)$	$e\left(\frac{1019}{1080}\right)$
$\chi_{259200}(43,\cdot)$	259200.yk	864	no	$1$	$1$	$e\left(\frac{359}{432}\right)$	$e\left(\frac{715}{864}\right)$	$e\left(\frac{89}{864}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{115}{288}\right)$	$e\left(\frac{397}{432}\right)$	$e\left(\frac{37}{864}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{149}{288}\right)$	$e\left(\frac{337}{432}\right)$
$\chi_{259200}(47,\cdot)$	259200.zf	1080	no	$-1$	$1$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{713}{1080}\right)$	$e\left(\frac{877}{1080}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{233}{360}\right)$	$e\left(\frac{71}{135}\right)$	$e\left(\frac{671}{1080}\right)$	$e\left(\frac{241}{270}\right)$	$e\left(\frac{169}{360}\right)$	$e\left(\frac{281}{540}\right)$
$\chi_{259200}(49,\cdot)$	259200.sr	216	no	$1$	$1$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{179}{216}\right)$	$e\left(\frac{133}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{173}{216}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{17}{108}\right)$
$\chi_{259200}(53,\cdot)$	259200.wl	480	no	$1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{343}{480}\right)$	$e\left(\frac{317}{480}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{143}{160}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{361}{480}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{9}{160}\right)$	$e\left(\frac{61}{240}\right)$
$\chi_{259200}(59,\cdot)$	259200.bap	4320	yes	$1$	$1$	$e\left(\frac{199}{432}\right)$	$e\left(\frac{3139}{4320}\right)$	$e\left(\frac{1481}{4320}\right)$	$e\left(\frac{11}{360}\right)$	$e\left(\frac{1099}{1440}\right)$	$e\left(\frac{2137}{2160}\right)$	$e\left(\frac{3613}{4320}\right)$	$e\left(\frac{289}{540}\right)$	$e\left(\frac{677}{1440}\right)$	$e\left(\frac{2113}{2160}\right)$
$\chi_{259200}(61,\cdot)$	259200.bam	4320	yes	$1$	$1$	$e\left(\frac{149}{432}\right)$	$e\left(\frac{3401}{4320}\right)$	$e\left(\frac{3499}{4320}\right)$	$e\left(\frac{289}{360}\right)$	$e\left(\frac{401}{1440}\right)$	$e\left(\frac{1523}{2160}\right)$	$e\left(\frac{1127}{4320}\right)$	$e\left(\frac{221}{540}\right)$	$e\left(\frac{703}{1440}\right)$	$e\left(\frac{107}{2160}\right)$
$\chi_{259200}(67,\cdot)$	259200.bar	4320	yes	$1$	$1$	$e\left(\frac{313}{432}\right)$	$e\left(\frac{4153}{4320}\right)$	$e\left(\frac{3347}{4320}\right)$	$e\left(\frac{347}{360}\right)$	$e\left(\frac{1393}{1440}\right)$	$e\left(\frac{1999}{2160}\right)$	$e\left(\frac{2071}{4320}\right)$	$e\left(\frac{403}{540}\right)$	$e\left(\frac{1319}{1440}\right)$	$e\left(\frac{1291}{2160}\right)$
$\chi_{259200}(71,\cdot)$	259200.xp	720	no	$1$	$1$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{317}{720}\right)$	$e\left(\frac{103}{720}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{311}{360}\right)$	$e\left(\frac{59}{720}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{299}{360}\right)$
$\chi_{259200}(73,\cdot)$	259200.xx	720	no	$-1$	$1$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{331}{720}\right)$	$e\left(\frac{149}{720}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{283}{360}\right)$	$e\left(\frac{157}{720}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{97}{360}\right)$
$\chi_{259200}(77,\cdot)$	259200.bas	4320	yes	$1$	$1$	$e\left(\frac{229}{432}\right)$	$e\left(\frac{541}{4320}\right)$	$e\left(\frac{3359}{4320}\right)$	$e\left(\frac{179}{360}\right)$	$e\left(\frac{1381}{1440}\right)$	$e\left(\frac{43}{2160}\right)$	$e\left(\frac{547}{4320}\right)$	$e\left(\frac{481}{540}\right)$	$e\left(\frac{323}{1440}\right)$	$e\left(\frac{1567}{2160}\right)$
$\chi_{259200}(79,\cdot)$	259200.yv	1080	no	$-1$	$1$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{1043}{1080}\right)$	$e\left(\frac{457}{1080}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{203}{360}\right)$	$e\left(\frac{29}{540}\right)$	$e\left(\frac{281}{1080}\right)$	$e\left(\frac{181}{270}\right)$	$e\left(\frac{109}{360}\right)$	$e\left(\frac{341}{540}\right)$
$\chi_{259200}(83,\cdot)$	259200.bat	4320	yes	$-1$	$1$	$e\left(\frac{317}{432}\right)$	$e\left(\frac{3173}{4320}\right)$	$e\left(\frac{1207}{4320}\right)$	$e\left(\frac{247}{360}\right)$	$e\left(\frac{173}{1440}\right)$	$e\left(\frac{899}{2160}\right)$	$e\left(\frac{3851}{4320}\right)$	$e\left(\frac{443}{540}\right)$	$e\left(\frac{859}{1440}\right)$	$e\left(\frac{311}{2160}\right)$
$\chi_{259200}(89,\cdot)$	259200.xo	720	no	$-1$	$1$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{241}{720}\right)$	$e\left(\frac{419}{720}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{283}{360}\right)$	$e\left(\frac{607}{720}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{7}{360}\right)$
$\chi_{259200}(91,\cdot)$	259200.zi	1440	no	$-1$	$1$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{1273}{1440}\right)$	$e\left(\frac{107}{1440}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{193}{480}\right)$	$e\left(\frac{379}{720}\right)$	$e\left(\frac{1351}{1440}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{479}{480}\right)$	$e\left(\frac{571}{720}\right)$
$\chi_{259200}(97,\cdot)$	259200.xi	540	no	$-1$	$1$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{439}{540}\right)$	$e\left(\frac{133}{270}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{359}{540}\right)$	$e\left(\frac{103}{540}\right)$	$e\left(\frac{38}{135}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{223}{270}\right)$
$\chi_{259200}(101,\cdot)$	259200.yn	864	no	$-1$	$1$	$e\left(\frac{95}{432}\right)$	$e\left(\frac{799}{864}\right)$	$e\left(\frac{797}{864}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{199}{288}\right)$	$e\left(\frac{13}{432}\right)$	$e\left(\frac{625}{864}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{137}{288}\right)$	$e\left(\frac{421}{432}\right)$
$\chi_{259200}(103,\cdot)$	259200.baf	2160	no	$1$	$1$	$e\left(\frac{5}{216}\right)$	$e\left(\frac{1691}{2160}\right)$	$e\left(\frac{1429}{2160}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{491}{720}\right)$	$e\left(\frac{83}{1080}\right)$	$e\left(\frac{2117}{2160}\right)$	$e\left(\frac{133}{135}\right)$	$e\left(\frac{433}{720}\right)$	$e\left(\frac{17}{1080}\right)$
$\chi_{259200}(107,\cdot)$	259200.ok	96	no	$-1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{259200}(109,\cdot)$	259200.we	480	no	$1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{301}{480}\right)$	$e\left(\frac{359}{480}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{21}{160}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{67}{480}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{43}{160}\right)$	$e\left(\frac{7}{240}\right)$
$\chi_{259200}(113,\cdot)$	259200.ze	1080	no	$1$	$1$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{31}{1080}\right)$	$e\left(\frac{719}{1080}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{151}{360}\right)$	$e\left(\frac{59}{270}\right)$	$e\left(\frac{757}{1080}\right)$	$e\left(\frac{61}{135}\right)$	$e\left(\frac{203}{360}\right)$	$e\left(\frac{247}{540}\right)$
$\chi_{259200}(119,\cdot)$	259200.bab	2160	no	$1$	$1$	$e\left(\frac{85}{216}\right)$	$e\left(\frac{1369}{2160}\right)$	$e\left(\frac{371}{2160}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{409}{720}\right)$	$e\left(\frac{7}{1080}\right)$	$e\left(\frac{943}{2160}\right)$	$e\left(\frac{47}{135}\right)$	$e\left(\frac{647}{720}\right)$	$e\left(\frac{343}{1080}\right)$

Click here to search among the remaining 69088 characters.

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 $\F_{q}$

Modulus	$259200$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{4320}\)
Order	$69120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{259200}(1,\cdot)\)	259200.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{259200}(7,\cdot)\)	259200.vg	432	no	\(1\)	\(1\)	\(e\left(\frac{133}{216}\right)\)	\(e\left(\frac{395}{432}\right)\)	\(e\left(\frac{349}{432}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{191}{216}\right)\)	\(e\left(\frac{389}{432}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{17}{216}\right)\)
\(\chi_{259200}(11,\cdot)\)	259200.baz	4320	yes	\(1\)	\(1\)	\(e\left(\frac{395}{432}\right)\)	\(e\left(\frac{911}{4320}\right)\)	\(e\left(\frac{4189}{4320}\right)\)	\(e\left(\frac{259}{360}\right)\)	\(e\left(\frac{791}{1440}\right)\)	\(e\left(\frac{293}{2160}\right)\)	\(e\left(\frac{977}{4320}\right)\)	\(e\left(\frac{521}{540}\right)\)	\(e\left(\frac{1033}{1440}\right)\)	\(e\left(\frac{1397}{2160}\right)\)
\(\chi_{259200}(13,\cdot)\)	259200.baq	4320	yes	\(-1\)	\(1\)	\(e\left(\frac{349}{432}\right)\)	\(e\left(\frac{4189}{4320}\right)\)	\(e\left(\frac{1151}{4320}\right)\)	\(e\left(\frac{131}{360}\right)\)	\(e\left(\frac{1429}{1440}\right)\)	\(e\left(\frac{1387}{2160}\right)\)	\(e\left(\frac{163}{4320}\right)\)	\(e\left(\frac{169}{540}\right)\)	\(e\left(\frac{707}{1440}\right)\)	\(e\left(\frac{1543}{2160}\right)\)
\(\chi_{259200}(17,\cdot)\)	259200.vb	360	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{259}{360}\right)\)	\(e\left(\frac{131}{360}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{193}{360}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{43}{180}\right)\)
\(\chi_{259200}(19,\cdot)\)	259200.zv	1440	no	\(-1\)	\(1\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{791}{1440}\right)\)	\(e\left(\frac{1429}{1440}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{431}{480}\right)\)	\(e\left(\frac{173}{720}\right)\)	\(e\left(\frac{137}{1440}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{193}{480}\right)\)	\(e\left(\frac{197}{720}\right)\)
\(\chi_{259200}(23,\cdot)\)	259200.bad	2160	no	\(-1\)	\(1\)	\(e\left(\frac{191}{216}\right)\)	\(e\left(\frac{293}{2160}\right)\)	\(e\left(\frac{1387}{2160}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{173}{720}\right)\)	\(e\left(\frac{989}{1080}\right)\)	\(e\left(\frac{971}{2160}\right)\)	\(e\left(\frac{64}{135}\right)\)	\(e\left(\frac{319}{720}\right)\)	\(e\left(\frac{131}{1080}\right)\)
\(\chi_{259200}(29,\cdot)\)	259200.bay	4320	yes	\(-1\)	\(1\)	\(e\left(\frac{389}{432}\right)\)	\(e\left(\frac{977}{4320}\right)\)	\(e\left(\frac{163}{4320}\right)\)	\(e\left(\frac{193}{360}\right)\)	\(e\left(\frac{137}{1440}\right)\)	\(e\left(\frac{971}{2160}\right)\)	\(e\left(\frac{1439}{4320}\right)\)	\(e\left(\frac{137}{540}\right)\)	\(e\left(\frac{1111}{1440}\right)\)	\(e\left(\frac{59}{2160}\right)\)
\(\chi_{259200}(31,\cdot)\)	259200.wu	540	no	\(-1\)	\(1\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{521}{540}\right)\)	\(e\left(\frac{169}{540}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{64}{135}\right)\)	\(e\left(\frac{137}{540}\right)\)	\(e\left(\frac{29}{270}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{197}{270}\right)\)
\(\chi_{259200}(37,\cdot)\)	259200.zk	1440	no	\(-1\)	\(1\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{1033}{1440}\right)\)	\(e\left(\frac{707}{1440}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{193}{480}\right)\)	\(e\left(\frac{319}{720}\right)\)	\(e\left(\frac{1111}{1440}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{119}{480}\right)\)	\(e\left(\frac{331}{720}\right)\)
\(\chi_{259200}(41,\cdot)\)	259200.baa	2160	no	\(-1\)	\(1\)	\(e\left(\frac{17}{216}\right)\)	\(e\left(\frac{1397}{2160}\right)\)	\(e\left(\frac{1543}{2160}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{197}{720}\right)\)	\(e\left(\frac{131}{1080}\right)\)	\(e\left(\frac{59}{2160}\right)\)	\(e\left(\frac{197}{270}\right)\)	\(e\left(\frac{331}{720}\right)\)	\(e\left(\frac{1019}{1080}\right)\)
\(\chi_{259200}(43,\cdot)\)	259200.yk	864	no	\(1\)	\(1\)	\(e\left(\frac{359}{432}\right)\)	\(e\left(\frac{715}{864}\right)\)	\(e\left(\frac{89}{864}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{115}{288}\right)\)	\(e\left(\frac{397}{432}\right)\)	\(e\left(\frac{37}{864}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{149}{288}\right)\)	\(e\left(\frac{337}{432}\right)\)
\(\chi_{259200}(47,\cdot)\)	259200.zf	1080	no	\(-1\)	\(1\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{713}{1080}\right)\)	\(e\left(\frac{877}{1080}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{233}{360}\right)\)	\(e\left(\frac{71}{135}\right)\)	\(e\left(\frac{671}{1080}\right)\)	\(e\left(\frac{241}{270}\right)\)	\(e\left(\frac{169}{360}\right)\)	\(e\left(\frac{281}{540}\right)\)
\(\chi_{259200}(49,\cdot)\)	259200.sr	216	no	\(1\)	\(1\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{179}{216}\right)\)	\(e\left(\frac{133}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{173}{216}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{17}{108}\right)\)
\(\chi_{259200}(53,\cdot)\)	259200.wl	480	no	\(1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{343}{480}\right)\)	\(e\left(\frac{317}{480}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{143}{160}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{361}{480}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{9}{160}\right)\)	\(e\left(\frac{61}{240}\right)\)
\(\chi_{259200}(59,\cdot)\)	259200.bap	4320	yes	\(1\)	\(1\)	\(e\left(\frac{199}{432}\right)\)	\(e\left(\frac{3139}{4320}\right)\)	\(e\left(\frac{1481}{4320}\right)\)	\(e\left(\frac{11}{360}\right)\)	\(e\left(\frac{1099}{1440}\right)\)	\(e\left(\frac{2137}{2160}\right)\)	\(e\left(\frac{3613}{4320}\right)\)	\(e\left(\frac{289}{540}\right)\)	\(e\left(\frac{677}{1440}\right)\)	\(e\left(\frac{2113}{2160}\right)\)
\(\chi_{259200}(61,\cdot)\)	259200.bam	4320	yes	\(1\)	\(1\)	\(e\left(\frac{149}{432}\right)\)	\(e\left(\frac{3401}{4320}\right)\)	\(e\left(\frac{3499}{4320}\right)\)	\(e\left(\frac{289}{360}\right)\)	\(e\left(\frac{401}{1440}\right)\)	\(e\left(\frac{1523}{2160}\right)\)	\(e\left(\frac{1127}{4320}\right)\)	\(e\left(\frac{221}{540}\right)\)	\(e\left(\frac{703}{1440}\right)\)	\(e\left(\frac{107}{2160}\right)\)
\(\chi_{259200}(67,\cdot)\)	259200.bar	4320	yes	\(1\)	\(1\)	\(e\left(\frac{313}{432}\right)\)	\(e\left(\frac{4153}{4320}\right)\)	\(e\left(\frac{3347}{4320}\right)\)	\(e\left(\frac{347}{360}\right)\)	\(e\left(\frac{1393}{1440}\right)\)	\(e\left(\frac{1999}{2160}\right)\)	\(e\left(\frac{2071}{4320}\right)\)	\(e\left(\frac{403}{540}\right)\)	\(e\left(\frac{1319}{1440}\right)\)	\(e\left(\frac{1291}{2160}\right)\)
\(\chi_{259200}(71,\cdot)\)	259200.xp	720	no	\(1\)	\(1\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{317}{720}\right)\)	\(e\left(\frac{103}{720}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{311}{360}\right)\)	\(e\left(\frac{59}{720}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{299}{360}\right)\)
\(\chi_{259200}(73,\cdot)\)	259200.xx	720	no	\(-1\)	\(1\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{331}{720}\right)\)	\(e\left(\frac{149}{720}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{283}{360}\right)\)	\(e\left(\frac{157}{720}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{97}{360}\right)\)
\(\chi_{259200}(77,\cdot)\)	259200.bas	4320	yes	\(1\)	\(1\)	\(e\left(\frac{229}{432}\right)\)	\(e\left(\frac{541}{4320}\right)\)	\(e\left(\frac{3359}{4320}\right)\)	\(e\left(\frac{179}{360}\right)\)	\(e\left(\frac{1381}{1440}\right)\)	\(e\left(\frac{43}{2160}\right)\)	\(e\left(\frac{547}{4320}\right)\)	\(e\left(\frac{481}{540}\right)\)	\(e\left(\frac{323}{1440}\right)\)	\(e\left(\frac{1567}{2160}\right)\)
\(\chi_{259200}(79,\cdot)\)	259200.yv	1080	no	\(-1\)	\(1\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{1043}{1080}\right)\)	\(e\left(\frac{457}{1080}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{203}{360}\right)\)	\(e\left(\frac{29}{540}\right)\)	\(e\left(\frac{281}{1080}\right)\)	\(e\left(\frac{181}{270}\right)\)	\(e\left(\frac{109}{360}\right)\)	\(e\left(\frac{341}{540}\right)\)
\(\chi_{259200}(83,\cdot)\)	259200.bat	4320	yes	\(-1\)	\(1\)	\(e\left(\frac{317}{432}\right)\)	\(e\left(\frac{3173}{4320}\right)\)	\(e\left(\frac{1207}{4320}\right)\)	\(e\left(\frac{247}{360}\right)\)	\(e\left(\frac{173}{1440}\right)\)	\(e\left(\frac{899}{2160}\right)\)	\(e\left(\frac{3851}{4320}\right)\)	\(e\left(\frac{443}{540}\right)\)	\(e\left(\frac{859}{1440}\right)\)	\(e\left(\frac{311}{2160}\right)\)
\(\chi_{259200}(89,\cdot)\)	259200.xo	720	no	\(-1\)	\(1\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{241}{720}\right)\)	\(e\left(\frac{419}{720}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{283}{360}\right)\)	\(e\left(\frac{607}{720}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{7}{360}\right)\)
\(\chi_{259200}(91,\cdot)\)	259200.zi	1440	no	\(-1\)	\(1\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{1273}{1440}\right)\)	\(e\left(\frac{107}{1440}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{193}{480}\right)\)	\(e\left(\frac{379}{720}\right)\)	\(e\left(\frac{1351}{1440}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{479}{480}\right)\)	\(e\left(\frac{571}{720}\right)\)
\(\chi_{259200}(97,\cdot)\)	259200.xi	540	no	\(-1\)	\(1\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{439}{540}\right)\)	\(e\left(\frac{133}{270}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{359}{540}\right)\)	\(e\left(\frac{103}{540}\right)\)	\(e\left(\frac{38}{135}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{223}{270}\right)\)
\(\chi_{259200}(101,\cdot)\)	259200.yn	864	no	\(-1\)	\(1\)	\(e\left(\frac{95}{432}\right)\)	\(e\left(\frac{799}{864}\right)\)	\(e\left(\frac{797}{864}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{199}{288}\right)\)	\(e\left(\frac{13}{432}\right)\)	\(e\left(\frac{625}{864}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{137}{288}\right)\)	\(e\left(\frac{421}{432}\right)\)
\(\chi_{259200}(103,\cdot)\)	259200.baf	2160	no	\(1\)	\(1\)	\(e\left(\frac{5}{216}\right)\)	\(e\left(\frac{1691}{2160}\right)\)	\(e\left(\frac{1429}{2160}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{491}{720}\right)\)	\(e\left(\frac{83}{1080}\right)\)	\(e\left(\frac{2117}{2160}\right)\)	\(e\left(\frac{133}{135}\right)\)	\(e\left(\frac{433}{720}\right)\)	\(e\left(\frac{17}{1080}\right)\)
\(\chi_{259200}(107,\cdot)\)	259200.ok	96	no	\(-1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{259200}(109,\cdot)\)	259200.we	480	no	\(1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{301}{480}\right)\)	\(e\left(\frac{359}{480}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{21}{160}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{67}{480}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{43}{160}\right)\)	\(e\left(\frac{7}{240}\right)\)
\(\chi_{259200}(113,\cdot)\)	259200.ze	1080	no	\(1\)	\(1\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{31}{1080}\right)\)	\(e\left(\frac{719}{1080}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{151}{360}\right)\)	\(e\left(\frac{59}{270}\right)\)	\(e\left(\frac{757}{1080}\right)\)	\(e\left(\frac{61}{135}\right)\)	\(e\left(\frac{203}{360}\right)\)	\(e\left(\frac{247}{540}\right)\)
\(\chi_{259200}(119,\cdot)\)	259200.bab	2160	no	\(1\)	\(1\)	\(e\left(\frac{85}{216}\right)\)	\(e\left(\frac{1369}{2160}\right)\)	\(e\left(\frac{371}{2160}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{409}{720}\right)\)	\(e\left(\frac{7}{1080}\right)\)	\(e\left(\frac{943}{2160}\right)\)	\(e\left(\frac{47}{135}\right)\)	\(e\left(\frac{647}{720}\right)\)	\(e\left(\frac{343}{1080}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 69120 characters

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