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Label	Degree	Type	Faithful	Conductor	Field of Traces	$\Q$-character	Group	Image	Image Order	Kernel	Kernel Order	Center	Center Order	Center Index	Schur Index
432.362.1a	$1$	R		$1$	$\Q$	432.362.1a	$D_{36}:C_6$	$C_1$	$1$	1.a1.a1	$432$	1.a1.a1	$432$	$1$	$1$
432.362.1b	$1$	R		$1$	$\Q$	432.362.1b	$D_{36}:C_6$	$C_2$	$2$	2.e1.a1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1c	$1$	R		$1$	$\Q$	432.362.1c	$D_{36}:C_6$	$C_2$	$2$	2.d1.a1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1d	$1$	R		$1$	$\Q$	432.362.1d	$D_{36}:C_6$	$C_2$	$2$	2.b1.b1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1e	$1$	R		$1$	$\Q$	432.362.1e	$D_{36}:C_6$	$C_2$	$2$	2.a1.b1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1f	$1$	R		$1$	$\Q$	432.362.1f	$D_{36}:C_6$	$C_2$	$2$	2.b1.a1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1g	$1$	R		$1$	$\Q$	432.362.1g	$D_{36}:C_6$	$C_2$	$2$	2.a1.a1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1h	$1$	R		$1$	$\Q$	432.362.1h	$D_{36}:C_6$	$C_2$	$2$	2.c1.a1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1i1	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1i	$D_{36}:C_6$	$C_3$	$3$	3.a1.a1	$144$	1.a1.a1	$432$	$1$	$1$
432.362.1i2	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1i	$D_{36}:C_6$	$C_3$	$3$	3.a1.a1	$144$	1.a1.a1	$432$	$1$	$1$
432.362.1j1	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1j	$D_{36}:C_6$	$C_6$	$6$	6.f1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1j2	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1j	$D_{36}:C_6$	$C_6$	$6$	6.f1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1k1	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1k	$D_{36}:C_6$	$C_6$	$6$	6.e1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1k2	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1k	$D_{36}:C_6$	$C_6$	$6$	6.e1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1l1	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1l	$D_{36}:C_6$	$C_6$	$6$	6.b1.b1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1l2	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1l	$D_{36}:C_6$	$C_6$	$6$	6.b1.b1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1m1	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1m	$D_{36}:C_6$	$C_6$	$6$	6.a1.b1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1m2	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1m	$D_{36}:C_6$	$C_6$	$6$	6.a1.b1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1n1	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1n	$D_{36}:C_6$	$C_6$	$6$	6.b1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1n2	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1n	$D_{36}:C_6$	$C_6$	$6$	6.b1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1o1	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1o	$D_{36}:C_6$	$C_6$	$6$	6.a1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1o2	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1o	$D_{36}:C_6$	$C_6$	$6$	6.a1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1p1	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1p	$D_{36}:C_6$	$C_6$	$6$	6.d1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1p2	$1$	C		$3$	$\Q(\sqrt{-3}) $	432.362.1p	$D_{36}:C_6$	$C_6$	$6$	6.d1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.2a	$2$	R		$1$	$\Q$	432.362.2a	$D_{36}:C_6$	$S_3$	$6$	6.c1.a1	$72$	6.c1.a1	$72$	$6$	$1$
432.362.2b	$2$	R		$1$	$\Q$	432.362.2b	$D_{36}:C_6$	$D_4$	$8$	8.b1.b1	$54$	4.b1.a1	$108$	$4$	$1$
432.362.2c	$2$	R		$1$	$\Q$	432.362.2c	$D_{36}:C_6$	$D_4$	$8$	8.b1.a1	$54$	4.b1.a1	$108$	$4$	$1$
432.362.2d	$2$	R		$1$	$\Q$	432.362.2d	$D_{36}:C_6$	$D_6$	$12$	12.e1.a1	$36$	6.c1.a1	$72$	$6$	$1$
432.362.2e	$2$	R		$1$	$\Q$	432.362.2e	$D_{36}:C_6$	$D_6$	$12$	12.a1.b1	$36$	6.c1.a1	$72$	$6$	$1$
432.362.2f	$2$	R		$1$	$\Q$	432.362.2f	$D_{36}:C_6$	$D_6$	$12$	12.a1.a1	$36$	6.c1.a1	$72$	$6$	$1$
432.362.2g1	$2$	C		$3$	$\Q(\sqrt{-3}) $	432.362.2g	$D_{36}:C_6$	$C_3\times S_3$	$18$	18.a1.a1	$24$	6.c1.a1	$72$	$6$	$1$
432.362.2g2	$2$	C		$3$	$\Q(\sqrt{-3}) $	432.362.2g	$D_{36}:C_6$	$C_3\times S_3$	$18$	18.a1.a1	$24$	6.c1.a1	$72$	$6$	$1$
432.362.2h1	$2$	C		$3$	$\Q(\sqrt{-3}) $	432.362.2h	$D_{36}:C_6$	$C_3\times D_4$	$24$	24.c1.b1	$18$	4.b1.a1	$108$	$4$	$1$
432.362.2h2	$2$	C		$3$	$\Q(\sqrt{-3}) $	432.362.2h	$D_{36}:C_6$	$C_3\times D_4$	$24$	24.c1.b1	$18$	4.b1.a1	$108$	$4$	$1$
432.362.2i1	$2$	C		$3$	$\Q(\sqrt{-3}) $	432.362.2i	$D_{36}:C_6$	$C_3\times D_4$	$24$	24.c1.a1	$18$	4.b1.a1	$108$	$4$	$1$
432.362.2i2	$2$	C		$3$	$\Q(\sqrt{-3}) $	432.362.2i	$D_{36}:C_6$	$C_3\times D_4$	$24$	24.c1.a1	$18$	4.b1.a1	$108$	$4$	$1$
432.362.2j1	$2$	C		$3$	$\Q(\sqrt{-3}) $	432.362.2j	$D_{36}:C_6$	$C_6\times S_3$	$36$	36.b1.a1	$12$	6.c1.a1	$72$	$6$	$1$
432.362.2j2	$2$	C		$3$	$\Q(\sqrt{-3}) $	432.362.2j	$D_{36}:C_6$	$C_6\times S_3$	$36$	36.b1.a1	$12$	6.c1.a1	$72$	$6$	$1$
432.362.2k1	$2$	C		$3$	$\Q(\sqrt{-3}) $	432.362.2k	$D_{36}:C_6$	$C_6\times S_3$	$36$	36.a1.b1	$12$	6.c1.a1	$72$	$6$	$1$
432.362.2k2	$2$	C		$3$	$\Q(\sqrt{-3}) $	432.362.2k	$D_{36}:C_6$	$C_6\times S_3$	$36$	36.a1.b1	$12$	6.c1.a1	$72$	$6$	$1$
432.362.2l1	$2$	C		$3$	$\Q(\sqrt{-3}) $	432.362.2l	$D_{36}:C_6$	$C_6\times S_3$	$36$	36.a1.a1	$12$	6.c1.a1	$72$	$6$	$1$
432.362.2l2	$2$	C		$3$	$\Q(\sqrt{-3}) $	432.362.2l	$D_{36}:C_6$	$C_6\times S_3$	$36$	36.a1.a1	$12$	6.c1.a1	$72$	$6$	$1$
432.362.4a	$4$	R		$1$	$\Q$	432.362.4a	$D_{36}:C_6$	$S_3\times D_4$	$48$	48.a1.a1	$9$	24.a1.a1	$18$	$24$	$1$
432.362.4b1	$4$	C		$3$	$\Q(\sqrt{-3}) $	432.362.4b	$D_{36}:C_6$	$C_{12}:D_6$	$144$	144.a1.a1	$3$	24.a1.a1	$18$	$24$	$1$
432.362.4b2	$4$	C		$3$	$\Q(\sqrt{-3}) $	432.362.4b	$D_{36}:C_6$	$C_{12}:D_6$	$144$	144.a1.a1	$3$	24.a1.a1	$18$	$24$	$1$
432.362.6a	$6$	R		$1$	$\Q$	432.362.6a	$D_{36}:C_6$	$C_9:C_6$	$54$	54.a1.a1	$8$	54.a1.a1	$8$	$54$	$1$
432.362.6b	$6$	R		$1$	$\Q$	432.362.6b	$D_{36}:C_6$	$C_{18}:C_6$	$108$	108.b1.a1	$4$	54.a1.a1	$8$	$54$	$1$
432.362.6c	$6$	R		$1$	$\Q$	432.362.6c	$D_{36}:C_6$	$C_{18}:C_6$	$108$	108.a1.b1	$4$	54.a1.a1	$8$	$54$	$1$
432.362.6d	$6$	R		$1$	$\Q$	432.362.6d	$D_{36}:C_6$	$C_{18}:C_6$	$108$	108.a1.a1	$4$	54.a1.a1	$8$	$54$	$1$
432.362.12a	$12$	R	✓	$1$	$\Q$	432.362.12a	$D_{36}:C_6$	$D_{36}:C_6$	$432$	432.a1.a1	$1$	216.a1.a1	$2$	$216$	$1$

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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.

Label	Degree	Type	Faithful	Conductor	Field of Traces	$\Q$-character	Group	Image	Image Order	Kernel	Kernel Order	Center	Center Order	Center Index	Schur Index
432.362.1a	$1$	R		$1$	\(\Q\)	432.362.1a	$D_{36}:C_6$	$C_1$	$1$	1.a1.a1	$432$	1.a1.a1	$432$	$1$	$1$
432.362.1b	$1$	R		$1$	\(\Q\)	432.362.1b	$D_{36}:C_6$	$C_2$	$2$	2.e1.a1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1c	$1$	R		$1$	\(\Q\)	432.362.1c	$D_{36}:C_6$	$C_2$	$2$	2.d1.a1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1d	$1$	R		$1$	\(\Q\)	432.362.1d	$D_{36}:C_6$	$C_2$	$2$	2.b1.b1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1e	$1$	R		$1$	\(\Q\)	432.362.1e	$D_{36}:C_6$	$C_2$	$2$	2.a1.b1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1f	$1$	R		$1$	\(\Q\)	432.362.1f	$D_{36}:C_6$	$C_2$	$2$	2.b1.a1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1g	$1$	R		$1$	\(\Q\)	432.362.1g	$D_{36}:C_6$	$C_2$	$2$	2.a1.a1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1h	$1$	R		$1$	\(\Q\)	432.362.1h	$D_{36}:C_6$	$C_2$	$2$	2.c1.a1	$216$	1.a1.a1	$432$	$1$	$1$
432.362.1i1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1i	$D_{36}:C_6$	$C_3$	$3$	3.a1.a1	$144$	1.a1.a1	$432$	$1$	$1$
432.362.1i2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1i	$D_{36}:C_6$	$C_3$	$3$	3.a1.a1	$144$	1.a1.a1	$432$	$1$	$1$
432.362.1j1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1j	$D_{36}:C_6$	$C_6$	$6$	6.f1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1j2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1j	$D_{36}:C_6$	$C_6$	$6$	6.f1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1k1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1k	$D_{36}:C_6$	$C_6$	$6$	6.e1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1k2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1k	$D_{36}:C_6$	$C_6$	$6$	6.e1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1l1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1l	$D_{36}:C_6$	$C_6$	$6$	6.b1.b1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1l2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1l	$D_{36}:C_6$	$C_6$	$6$	6.b1.b1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1m1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1m	$D_{36}:C_6$	$C_6$	$6$	6.a1.b1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1m2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1m	$D_{36}:C_6$	$C_6$	$6$	6.a1.b1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1n1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1n	$D_{36}:C_6$	$C_6$	$6$	6.b1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1n2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1n	$D_{36}:C_6$	$C_6$	$6$	6.b1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1o1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1o	$D_{36}:C_6$	$C_6$	$6$	6.a1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1o2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1o	$D_{36}:C_6$	$C_6$	$6$	6.a1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1p1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1p	$D_{36}:C_6$	$C_6$	$6$	6.d1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.1p2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.1p	$D_{36}:C_6$	$C_6$	$6$	6.d1.a1	$72$	1.a1.a1	$432$	$1$	$1$
432.362.2a	$2$	R		$1$	\(\Q\)	432.362.2a	$D_{36}:C_6$	$S_3$	$6$	6.c1.a1	$72$	6.c1.a1	$72$	$6$	$1$
432.362.2b	$2$	R		$1$	\(\Q\)	432.362.2b	$D_{36}:C_6$	$D_4$	$8$	8.b1.b1	$54$	4.b1.a1	$108$	$4$	$1$
432.362.2c	$2$	R		$1$	\(\Q\)	432.362.2c	$D_{36}:C_6$	$D_4$	$8$	8.b1.a1	$54$	4.b1.a1	$108$	$4$	$1$
432.362.2d	$2$	R		$1$	\(\Q\)	432.362.2d	$D_{36}:C_6$	$D_6$	$12$	12.e1.a1	$36$	6.c1.a1	$72$	$6$	$1$
432.362.2e	$2$	R		$1$	\(\Q\)	432.362.2e	$D_{36}:C_6$	$D_6$	$12$	12.a1.b1	$36$	6.c1.a1	$72$	$6$	$1$
432.362.2f	$2$	R		$1$	\(\Q\)	432.362.2f	$D_{36}:C_6$	$D_6$	$12$	12.a1.a1	$36$	6.c1.a1	$72$	$6$	$1$
432.362.2g1	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.2g	$D_{36}:C_6$	$C_3\times S_3$	$18$	18.a1.a1	$24$	6.c1.a1	$72$	$6$	$1$
432.362.2g2	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.2g	$D_{36}:C_6$	$C_3\times S_3$	$18$	18.a1.a1	$24$	6.c1.a1	$72$	$6$	$1$
432.362.2h1	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.2h	$D_{36}:C_6$	$C_3\times D_4$	$24$	24.c1.b1	$18$	4.b1.a1	$108$	$4$	$1$
432.362.2h2	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.2h	$D_{36}:C_6$	$C_3\times D_4$	$24$	24.c1.b1	$18$	4.b1.a1	$108$	$4$	$1$
432.362.2i1	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.2i	$D_{36}:C_6$	$C_3\times D_4$	$24$	24.c1.a1	$18$	4.b1.a1	$108$	$4$	$1$
432.362.2i2	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.2i	$D_{36}:C_6$	$C_3\times D_4$	$24$	24.c1.a1	$18$	4.b1.a1	$108$	$4$	$1$
432.362.2j1	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.2j	$D_{36}:C_6$	$C_6\times S_3$	$36$	36.b1.a1	$12$	6.c1.a1	$72$	$6$	$1$
432.362.2j2	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.2j	$D_{36}:C_6$	$C_6\times S_3$	$36$	36.b1.a1	$12$	6.c1.a1	$72$	$6$	$1$
432.362.2k1	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.2k	$D_{36}:C_6$	$C_6\times S_3$	$36$	36.a1.b1	$12$	6.c1.a1	$72$	$6$	$1$
432.362.2k2	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.2k	$D_{36}:C_6$	$C_6\times S_3$	$36$	36.a1.b1	$12$	6.c1.a1	$72$	$6$	$1$
432.362.2l1	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.2l	$D_{36}:C_6$	$C_6\times S_3$	$36$	36.a1.a1	$12$	6.c1.a1	$72$	$6$	$1$
432.362.2l2	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.2l	$D_{36}:C_6$	$C_6\times S_3$	$36$	36.a1.a1	$12$	6.c1.a1	$72$	$6$	$1$
432.362.4a	$4$	R		$1$	\(\Q\)	432.362.4a	$D_{36}:C_6$	$S_3\times D_4$	$48$	48.a1.a1	$9$	24.a1.a1	$18$	$24$	$1$
432.362.4b1	$4$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.4b	$D_{36}:C_6$	$C_{12}:D_6$	$144$	144.a1.a1	$3$	24.a1.a1	$18$	$24$	$1$
432.362.4b2	$4$	C		$3$	\(\Q(\sqrt{-3}) \)	432.362.4b	$D_{36}:C_6$	$C_{12}:D_6$	$144$	144.a1.a1	$3$	24.a1.a1	$18$	$24$	$1$
432.362.6a	$6$	R		$1$	\(\Q\)	432.362.6a	$D_{36}:C_6$	$C_9:C_6$	$54$	54.a1.a1	$8$	54.a1.a1	$8$	$54$	$1$
432.362.6b	$6$	R		$1$	\(\Q\)	432.362.6b	$D_{36}:C_6$	$C_{18}:C_6$	$108$	108.b1.a1	$4$	54.a1.a1	$8$	$54$	$1$
432.362.6c	$6$	R		$1$	\(\Q\)	432.362.6c	$D_{36}:C_6$	$C_{18}:C_6$	$108$	108.a1.b1	$4$	54.a1.a1	$8$	$54$	$1$
432.362.6d	$6$	R		$1$	\(\Q\)	432.362.6d	$D_{36}:C_6$	$C_{18}:C_6$	$108$	108.a1.a1	$4$	54.a1.a1	$8$	$54$	$1$
432.362.12a	$12$	R	✓	$1$	\(\Q\)	432.362.12a	$D_{36}:C_6$	$D_{36}:C_6$	$432$	432.a1.a1	$1$	216.a1.a1	$2$	$216$	$1$