LMFDB - Group of Dirichlet characters of modulus 273600

Show commands: PariGP / SageMath

sage: H = DirichletGroup(273600)

pari: g = idealstar(,273600,2)

Character group

sage: G.order() pari: g.no
Order	=	69120
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{720}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{273600}(42751,\cdot)$, $\chi_{273600}(188101,\cdot)$, $\chi_{273600}(121601,\cdot)$, $\chi_{273600}(43777,\cdot)$, $\chi_{273600}(129601,\cdot)$

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	$-1$	$1$	$7$	$11$	$13$	$17$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{273600}(1,\cdot)$	273600.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{273600}(7,\cdot)$	273600.zz	24	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{273600}(11,\cdot)$	273600.dbb	240	yes	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{43}{48}\right)$
$\chi_{273600}(13,\cdot)$	273600.djb	720	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{121}{720}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{287}{360}\right)$	$e\left(\frac{193}{720}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{73}{360}\right)$	$e\left(\frac{31}{144}\right)$
$\chi_{273600}(17,\cdot)$	273600.cvs	180	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{273600}(23,\cdot)$	273600.dgt	360	no	$-1$	$1$	$1$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{287}{360}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{161}{360}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{17}{72}\right)$
$\chi_{273600}(29,\cdot)$	273600.dhe	720	yes	$1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{193}{720}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{161}{360}\right)$	$e\left(\frac{709}{720}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{49}{360}\right)$	$e\left(\frac{31}{144}\right)$
$\chi_{273600}(31,\cdot)$	273600.bhp	30	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{273600}(37,\cdot)$	273600.cfk	80	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{273600}(41,\cdot)$	273600.dft	360	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{73}{360}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{49}{360}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{19}{72}\right)$
$\chi_{273600}(43,\cdot)$	273600.cqs	144	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{29}{144}\right)$
$\chi_{273600}(47,\cdot)$	273600.cwh	180	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{273600}(49,\cdot)$	273600.lp	12	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$-i$
$\chi_{273600}(53,\cdot)$	273600.djy	720	no	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{283}{720}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{341}{360}\right)$	$e\left(\frac{19}{720}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{79}{360}\right)$	$e\left(\frac{13}{144}\right)$
$\chi_{273600}(59,\cdot)$	273600.dkk	720	yes	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{131}{720}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{127}{360}\right)$	$e\left(\frac{623}{720}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{203}{360}\right)$	$e\left(\frac{5}{144}\right)$
$\chi_{273600}(61,\cdot)$	273600.dkl	720	yes	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{649}{720}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{353}{360}\right)$	$e\left(\frac{157}{720}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{217}{360}\right)$	$e\left(\frac{127}{144}\right)$
$\chi_{273600}(67,\cdot)$	273600.din	720	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{397}{720}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{299}{360}\right)$	$e\left(\frac{541}{720}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{61}{360}\right)$	$e\left(\frac{19}{144}\right)$
$\chi_{273600}(71,\cdot)$	273600.dfo	360	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{259}{360}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{67}{360}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{61}{72}\right)$
$\chi_{273600}(73,\cdot)$	273600.dgk	360	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{67}{360}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{1}{360}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{49}{72}\right)$
$\chi_{273600}(77,\cdot)$	273600.cyk	240	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{13}{48}\right)$
$\chi_{273600}(79,\cdot)$	273600.csz	180	no	$1$	$1$	$-1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{273600}(83,\cdot)$	273600.czh	240	yes	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{273600}(89,\cdot)$	273600.dex	360	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{347}{360}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{71}{360}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{41}{72}\right)$
$\chi_{273600}(91,\cdot)$	273600.dij	720	no	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{211}{720}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{287}{360}\right)$	$e\left(\frac{703}{720}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{223}{360}\right)$	$e\left(\frac{85}{144}\right)$
$\chi_{273600}(97,\cdot)$	273600.cub	180	no	$1$	$1$	$i$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{273600}(101,\cdot)$	273600.cpm	144	no	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{83}{144}\right)$	$-1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{61}{144}\right)$
$\chi_{273600}(103,\cdot)$	273600.cot	120	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{273600}(107,\cdot)$	273600.btb	48	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{48}\right)$	$-1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{273600}(109,\cdot)$	273600.dje	720	no	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{581}{720}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{217}{360}\right)$	$e\left(\frac{593}{720}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{353}{360}\right)$	$e\left(\frac{59}{144}\right)$
$\chi_{273600}(113,\cdot)$	273600.bxi	60	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{273600}(119,\cdot)$	273600.dep	360	no	$1$	$1$	$-i$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{181}{360}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{73}{360}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{55}{72}\right)$
$\chi_{273600}(121,\cdot)$	273600.cml	120	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{24}\right)$

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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	$273600$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{720}\)
Order	$69120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{273600}(1,\cdot)\)	273600.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{273600}(7,\cdot)\)	273600.zz	24	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{273600}(11,\cdot)\)	273600.dbb	240	yes	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{43}{48}\right)\)
\(\chi_{273600}(13,\cdot)\)	273600.djb	720	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{121}{720}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{287}{360}\right)\)	\(e\left(\frac{193}{720}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{73}{360}\right)\)	\(e\left(\frac{31}{144}\right)\)
\(\chi_{273600}(17,\cdot)\)	273600.cvs	180	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{273600}(23,\cdot)\)	273600.dgt	360	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{287}{360}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{161}{360}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{17}{72}\right)\)
\(\chi_{273600}(29,\cdot)\)	273600.dhe	720	yes	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{193}{720}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{161}{360}\right)\)	\(e\left(\frac{709}{720}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{49}{360}\right)\)	\(e\left(\frac{31}{144}\right)\)
\(\chi_{273600}(31,\cdot)\)	273600.bhp	30	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{273600}(37,\cdot)\)	273600.cfk	80	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{273600}(41,\cdot)\)	273600.dft	360	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{73}{360}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{49}{360}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{19}{72}\right)\)
\(\chi_{273600}(43,\cdot)\)	273600.cqs	144	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{29}{144}\right)\)
\(\chi_{273600}(47,\cdot)\)	273600.cwh	180	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{273600}(49,\cdot)\)	273600.lp	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)
\(\chi_{273600}(53,\cdot)\)	273600.djy	720	no	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{283}{720}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{341}{360}\right)\)	\(e\left(\frac{19}{720}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{79}{360}\right)\)	\(e\left(\frac{13}{144}\right)\)
\(\chi_{273600}(59,\cdot)\)	273600.dkk	720	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{131}{720}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{127}{360}\right)\)	\(e\left(\frac{623}{720}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{203}{360}\right)\)	\(e\left(\frac{5}{144}\right)\)
\(\chi_{273600}(61,\cdot)\)	273600.dkl	720	yes	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{649}{720}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{353}{360}\right)\)	\(e\left(\frac{157}{720}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{217}{360}\right)\)	\(e\left(\frac{127}{144}\right)\)
\(\chi_{273600}(67,\cdot)\)	273600.din	720	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{397}{720}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{299}{360}\right)\)	\(e\left(\frac{541}{720}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{61}{360}\right)\)	\(e\left(\frac{19}{144}\right)\)
\(\chi_{273600}(71,\cdot)\)	273600.dfo	360	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{259}{360}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{67}{360}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{61}{72}\right)\)
\(\chi_{273600}(73,\cdot)\)	273600.dgk	360	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{67}{360}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{1}{360}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{49}{72}\right)\)
\(\chi_{273600}(77,\cdot)\)	273600.cyk	240	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{13}{48}\right)\)
\(\chi_{273600}(79,\cdot)\)	273600.csz	180	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{273600}(83,\cdot)\)	273600.czh	240	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{273600}(89,\cdot)\)	273600.dex	360	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{347}{360}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{71}{360}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{41}{72}\right)\)
\(\chi_{273600}(91,\cdot)\)	273600.dij	720	no	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{211}{720}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{287}{360}\right)\)	\(e\left(\frac{703}{720}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{223}{360}\right)\)	\(e\left(\frac{85}{144}\right)\)
\(\chi_{273600}(97,\cdot)\)	273600.cub	180	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{273600}(101,\cdot)\)	273600.cpm	144	no	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(-1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{61}{144}\right)\)
\(\chi_{273600}(103,\cdot)\)	273600.cot	120	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{273600}(107,\cdot)\)	273600.btb	48	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(-1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{273600}(109,\cdot)\)	273600.dje	720	no	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{581}{720}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{217}{360}\right)\)	\(e\left(\frac{593}{720}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{353}{360}\right)\)	\(e\left(\frac{59}{144}\right)\)
\(\chi_{273600}(113,\cdot)\)	273600.bxi	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{273600}(119,\cdot)\)	273600.dep	360	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{181}{360}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{73}{360}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{55}{72}\right)\)
\(\chi_{273600}(121,\cdot)\)	273600.cml	120	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{24}\right)\)

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