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Label	Degree	Type	Conductor	Field of Traces	$\Q$-character	Group	Image	Image Order	Kernel	Kernel Order	Center	Center Order	Center Index	Schur Index
672.809.1a	$1$	R	$1$	$\Q$	672.809.1a	$C_{24}.D_{14}$	$C_1$	$1$	1.a1.a1	$672$	1.a1.a1	$672$	$1$	$1$
672.809.1b	$1$	R	$1$	$\Q$	672.809.1b	$C_{24}.D_{14}$	$C_2$	$2$	2.g1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1c	$1$	R	$1$	$\Q$	672.809.1c	$C_{24}.D_{14}$	$C_2$	$2$	2.f1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1d	$1$	R	$1$	$\Q$	672.809.1d	$C_{24}.D_{14}$	$C_2$	$2$	2.e1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1e	$1$	R	$1$	$\Q$	672.809.1e	$C_{24}.D_{14}$	$C_2$	$2$	2.d1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1f	$1$	R	$1$	$\Q$	672.809.1f	$C_{24}.D_{14}$	$C_2$	$2$	2.c1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1g	$1$	R	$1$	$\Q$	672.809.1g	$C_{24}.D_{14}$	$C_2$	$2$	2.b1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1h	$1$	R	$1$	$\Q$	672.809.1h	$C_{24}.D_{14}$	$C_2$	$2$	2.a1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1i1	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1i	$C_{24}.D_{14}$	$C_3$	$3$	3.a1.a1	$224$	1.a1.a1	$672$	$1$	$1$
672.809.1i2	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1i	$C_{24}.D_{14}$	$C_3$	$3$	3.a1.a1	$224$	1.a1.a1	$672$	$1$	$1$
672.809.1j1	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1j	$C_{24}.D_{14}$	$C_6$	$6$	6.g1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1j2	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1j	$C_{24}.D_{14}$	$C_6$	$6$	6.g1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1k1	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1k	$C_{24}.D_{14}$	$C_6$	$6$	6.f1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1k2	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1k	$C_{24}.D_{14}$	$C_6$	$6$	6.f1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1l1	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1l	$C_{24}.D_{14}$	$C_6$	$6$	6.e1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1l2	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1l	$C_{24}.D_{14}$	$C_6$	$6$	6.e1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1m1	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1m	$C_{24}.D_{14}$	$C_6$	$6$	6.d1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1m2	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1m	$C_{24}.D_{14}$	$C_6$	$6$	6.d1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1n1	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1n	$C_{24}.D_{14}$	$C_6$	$6$	6.c1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1n2	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1n	$C_{24}.D_{14}$	$C_6$	$6$	6.c1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1o1	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1o	$C_{24}.D_{14}$	$C_6$	$6$	6.b1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1o2	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1o	$C_{24}.D_{14}$	$C_6$	$6$	6.b1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1p1	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1p	$C_{24}.D_{14}$	$C_6$	$6$	6.a1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1p2	$1$	C	$3$	$\Q(\sqrt{-3}) $	672.809.1p	$C_{24}.D_{14}$	$C_6$	$6$	6.a1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.2a	$2$	R	$1$	$\Q$	672.809.2a	$C_{24}.D_{14}$	$D_4$	$8$	8.c1.a1	$84$	4.b1.a1	$168$	$4$	$1$
672.809.2b	$2$	R	$1$	$\Q$	672.809.2b	$C_{24}.D_{14}$	$D_4$	$8$	8.a1.a1	$84$	4.b1.a1	$168$	$4$	$1$
672.809.2c1	$2$	C	$3$	$\Q(\sqrt{-3}) $	672.809.2c	$C_{24}.D_{14}$	$C_3\times D_4$	$24$	24.c1.a1	$28$	4.b1.a1	$168$	$4$	$1$
672.809.2c2	$2$	C	$3$	$\Q(\sqrt{-3}) $	672.809.2c	$C_{24}.D_{14}$	$C_3\times D_4$	$24$	24.c1.a1	$28$	4.b1.a1	$168$	$4$	$1$
672.809.2d1	$2$	C	$3$	$\Q(\sqrt{-3}) $	672.809.2d	$C_{24}.D_{14}$	$C_3\times D_4$	$24$	24.a1.a1	$28$	4.b1.a1	$168$	$4$	$1$
672.809.2d2	$2$	C	$3$	$\Q(\sqrt{-3}) $	672.809.2d	$C_{24}.D_{14}$	$C_3\times D_4$	$24$	24.a1.a1	$28$	4.b1.a1	$168$	$4$	$1$
672.809.2e1	$2$	R	$7$	$\Q(\zeta_{7})^+$	672.809.2e	$C_{24}.D_{14}$	$D_7$	$14$	14.a1.a1	$48$	14.a1.a1	$48$	$14$	$1$
672.809.2e2	$2$	R	$7$	$\Q(\zeta_{7})^+$	672.809.2e	$C_{24}.D_{14}$	$D_7$	$14$	14.a1.a1	$48$	14.a1.a1	$48$	$14$	$1$
672.809.2e3	$2$	R	$7$	$\Q(\zeta_{7})^+$	672.809.2e	$C_{24}.D_{14}$	$D_7$	$14$	14.a1.a1	$48$	14.a1.a1	$48$	$14$	$1$
672.809.2f1	$2$	R	$7$	$\Q(\zeta_{7})^+$	672.809.2f	$C_{24}.D_{14}$	$D_{14}$	$28$	28.c1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2f2	$2$	R	$7$	$\Q(\zeta_{7})^+$	672.809.2f	$C_{24}.D_{14}$	$D_{14}$	$28$	28.c1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2f3	$2$	R	$7$	$\Q(\zeta_{7})^+$	672.809.2f	$C_{24}.D_{14}$	$D_{14}$	$28$	28.c1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2g1	$2$	R	$7$	$\Q(\zeta_{7})^+$	672.809.2g	$C_{24}.D_{14}$	$D_{14}$	$28$	28.b1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2g2	$2$	R	$7$	$\Q(\zeta_{7})^+$	672.809.2g	$C_{24}.D_{14}$	$D_{14}$	$28$	28.b1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2g3	$2$	R	$7$	$\Q(\zeta_{7})^+$	672.809.2g	$C_{24}.D_{14}$	$D_{14}$	$28$	28.b1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2h1	$2$	R	$7$	$\Q(\zeta_{7})^+$	672.809.2h	$C_{24}.D_{14}$	$D_{14}$	$28$	28.a1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2h2	$2$	R	$7$	$\Q(\zeta_{7})^+$	672.809.2h	$C_{24}.D_{14}$	$D_{14}$	$28$	28.a1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2h3	$2$	R	$7$	$\Q(\zeta_{7})^+$	672.809.2h	$C_{24}.D_{14}$	$D_{14}$	$28$	28.a1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2i1	$2$	C	$8$	$\Q(\zeta_{8})$	672.809.2i	$C_{24}.D_{14}$	$D_8:C_2$	$32$	32.a1.a1	$21$	8.c1.a1	$84$	$8$	$1$
672.809.2i2	$2$	C	$8$	$\Q(\zeta_{8})$	672.809.2i	$C_{24}.D_{14}$	$D_8:C_2$	$32$	32.a1.a1	$21$	8.c1.a1	$84$	$8$	$1$
672.809.2i3	$2$	C	$8$	$\Q(\zeta_{8})$	672.809.2i	$C_{24}.D_{14}$	$D_8:C_2$	$32$	32.a1.a1	$21$	8.c1.a1	$84$	$8$	$1$
672.809.2i4	$2$	C	$8$	$\Q(\zeta_{8})$	672.809.2i	$C_{24}.D_{14}$	$D_8:C_2$	$32$	32.a1.a1	$21$	8.c1.a1	$84$	$8$	$1$
672.809.2j1	$2$	C	$21$	6.0.64827.1	672.809.2j	$C_{24}.D_{14}$	$C_3\times D_7$	$42$	42.a1.a1	$16$	14.a1.a1	$48$	$14$	$1$
672.809.2j2	$2$	C	$21$	6.0.64827.1	672.809.2j	$C_{24}.D_{14}$	$C_3\times D_7$	$42$	42.a1.a1	$16$	14.a1.a1	$48$	$14$	$1$
672.809.2j3	$2$	C	$21$	6.0.64827.1	672.809.2j	$C_{24}.D_{14}$	$C_3\times D_7$	$42$	42.a1.a1	$16$	14.a1.a1	$48$	$14$	$1$
672.809.2j4	$2$	C	$21$	6.0.64827.1	672.809.2j	$C_{24}.D_{14}$	$C_3\times D_7$	$42$	42.a1.a1	$16$	14.a1.a1	$48$	$14$	$1$

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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	Conductor	Field of Traces	$\Q$-character	Group	Image	Image Order	Kernel	Kernel Order	Center	Center Order	Center Index	Schur Index
672.809.1a	$1$	R	$1$	\(\Q\)	672.809.1a	$C_{24}.D_{14}$	$C_1$	$1$	1.a1.a1	$672$	1.a1.a1	$672$	$1$	$1$
672.809.1b	$1$	R	$1$	\(\Q\)	672.809.1b	$C_{24}.D_{14}$	$C_2$	$2$	2.g1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1c	$1$	R	$1$	\(\Q\)	672.809.1c	$C_{24}.D_{14}$	$C_2$	$2$	2.f1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1d	$1$	R	$1$	\(\Q\)	672.809.1d	$C_{24}.D_{14}$	$C_2$	$2$	2.e1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1e	$1$	R	$1$	\(\Q\)	672.809.1e	$C_{24}.D_{14}$	$C_2$	$2$	2.d1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1f	$1$	R	$1$	\(\Q\)	672.809.1f	$C_{24}.D_{14}$	$C_2$	$2$	2.c1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1g	$1$	R	$1$	\(\Q\)	672.809.1g	$C_{24}.D_{14}$	$C_2$	$2$	2.b1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1h	$1$	R	$1$	\(\Q\)	672.809.1h	$C_{24}.D_{14}$	$C_2$	$2$	2.a1.a1	$336$	1.a1.a1	$672$	$1$	$1$
672.809.1i1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1i	$C_{24}.D_{14}$	$C_3$	$3$	3.a1.a1	$224$	1.a1.a1	$672$	$1$	$1$
672.809.1i2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1i	$C_{24}.D_{14}$	$C_3$	$3$	3.a1.a1	$224$	1.a1.a1	$672$	$1$	$1$
672.809.1j1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1j	$C_{24}.D_{14}$	$C_6$	$6$	6.g1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1j2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1j	$C_{24}.D_{14}$	$C_6$	$6$	6.g1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1k1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1k	$C_{24}.D_{14}$	$C_6$	$6$	6.f1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1k2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1k	$C_{24}.D_{14}$	$C_6$	$6$	6.f1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1l1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1l	$C_{24}.D_{14}$	$C_6$	$6$	6.e1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1l2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1l	$C_{24}.D_{14}$	$C_6$	$6$	6.e1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1m1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1m	$C_{24}.D_{14}$	$C_6$	$6$	6.d1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1m2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1m	$C_{24}.D_{14}$	$C_6$	$6$	6.d1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1n1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1n	$C_{24}.D_{14}$	$C_6$	$6$	6.c1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1n2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1n	$C_{24}.D_{14}$	$C_6$	$6$	6.c1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1o1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1o	$C_{24}.D_{14}$	$C_6$	$6$	6.b1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1o2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1o	$C_{24}.D_{14}$	$C_6$	$6$	6.b1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1p1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1p	$C_{24}.D_{14}$	$C_6$	$6$	6.a1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.1p2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.1p	$C_{24}.D_{14}$	$C_6$	$6$	6.a1.a1	$112$	1.a1.a1	$672$	$1$	$1$
672.809.2a	$2$	R	$1$	\(\Q\)	672.809.2a	$C_{24}.D_{14}$	$D_4$	$8$	8.c1.a1	$84$	4.b1.a1	$168$	$4$	$1$
672.809.2b	$2$	R	$1$	\(\Q\)	672.809.2b	$C_{24}.D_{14}$	$D_4$	$8$	8.a1.a1	$84$	4.b1.a1	$168$	$4$	$1$
672.809.2c1	$2$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.2c	$C_{24}.D_{14}$	$C_3\times D_4$	$24$	24.c1.a1	$28$	4.b1.a1	$168$	$4$	$1$
672.809.2c2	$2$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.2c	$C_{24}.D_{14}$	$C_3\times D_4$	$24$	24.c1.a1	$28$	4.b1.a1	$168$	$4$	$1$
672.809.2d1	$2$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.2d	$C_{24}.D_{14}$	$C_3\times D_4$	$24$	24.a1.a1	$28$	4.b1.a1	$168$	$4$	$1$
672.809.2d2	$2$	C	$3$	\(\Q(\sqrt{-3}) \)	672.809.2d	$C_{24}.D_{14}$	$C_3\times D_4$	$24$	24.a1.a1	$28$	4.b1.a1	$168$	$4$	$1$
672.809.2e1	$2$	R	$7$	\(\Q(\zeta_{7})^+\)	672.809.2e	$C_{24}.D_{14}$	$D_7$	$14$	14.a1.a1	$48$	14.a1.a1	$48$	$14$	$1$
672.809.2e2	$2$	R	$7$	\(\Q(\zeta_{7})^+\)	672.809.2e	$C_{24}.D_{14}$	$D_7$	$14$	14.a1.a1	$48$	14.a1.a1	$48$	$14$	$1$
672.809.2e3	$2$	R	$7$	\(\Q(\zeta_{7})^+\)	672.809.2e	$C_{24}.D_{14}$	$D_7$	$14$	14.a1.a1	$48$	14.a1.a1	$48$	$14$	$1$
672.809.2f1	$2$	R	$7$	\(\Q(\zeta_{7})^+\)	672.809.2f	$C_{24}.D_{14}$	$D_{14}$	$28$	28.c1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2f2	$2$	R	$7$	\(\Q(\zeta_{7})^+\)	672.809.2f	$C_{24}.D_{14}$	$D_{14}$	$28$	28.c1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2f3	$2$	R	$7$	\(\Q(\zeta_{7})^+\)	672.809.2f	$C_{24}.D_{14}$	$D_{14}$	$28$	28.c1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2g1	$2$	R	$7$	\(\Q(\zeta_{7})^+\)	672.809.2g	$C_{24}.D_{14}$	$D_{14}$	$28$	28.b1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2g2	$2$	R	$7$	\(\Q(\zeta_{7})^+\)	672.809.2g	$C_{24}.D_{14}$	$D_{14}$	$28$	28.b1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2g3	$2$	R	$7$	\(\Q(\zeta_{7})^+\)	672.809.2g	$C_{24}.D_{14}$	$D_{14}$	$28$	28.b1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2h1	$2$	R	$7$	\(\Q(\zeta_{7})^+\)	672.809.2h	$C_{24}.D_{14}$	$D_{14}$	$28$	28.a1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2h2	$2$	R	$7$	\(\Q(\zeta_{7})^+\)	672.809.2h	$C_{24}.D_{14}$	$D_{14}$	$28$	28.a1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2h3	$2$	R	$7$	\(\Q(\zeta_{7})^+\)	672.809.2h	$C_{24}.D_{14}$	$D_{14}$	$28$	28.a1.a1	$24$	14.a1.a1	$48$	$14$	$1$
672.809.2i1	$2$	C	$8$	\(\Q(\zeta_{8})\)	672.809.2i	$C_{24}.D_{14}$	$D_8:C_2$	$32$	32.a1.a1	$21$	8.c1.a1	$84$	$8$	$1$
672.809.2i2	$2$	C	$8$	\(\Q(\zeta_{8})\)	672.809.2i	$C_{24}.D_{14}$	$D_8:C_2$	$32$	32.a1.a1	$21$	8.c1.a1	$84$	$8$	$1$
672.809.2i3	$2$	C	$8$	\(\Q(\zeta_{8})\)	672.809.2i	$C_{24}.D_{14}$	$D_8:C_2$	$32$	32.a1.a1	$21$	8.c1.a1	$84$	$8$	$1$
672.809.2i4	$2$	C	$8$	\(\Q(\zeta_{8})\)	672.809.2i	$C_{24}.D_{14}$	$D_8:C_2$	$32$	32.a1.a1	$21$	8.c1.a1	$84$	$8$	$1$
672.809.2j1	$2$	C	$21$	6.0.64827.1	672.809.2j	$C_{24}.D_{14}$	$C_3\times D_7$	$42$	42.a1.a1	$16$	14.a1.a1	$48$	$14$	$1$
672.809.2j2	$2$	C	$21$	6.0.64827.1	672.809.2j	$C_{24}.D_{14}$	$C_3\times D_7$	$42$	42.a1.a1	$16$	14.a1.a1	$48$	$14$	$1$
672.809.2j3	$2$	C	$21$	6.0.64827.1	672.809.2j	$C_{24}.D_{14}$	$C_3\times D_7$	$42$	42.a1.a1	$16$	14.a1.a1	$48$	$14$	$1$
672.809.2j4	$2$	C	$21$	6.0.64827.1	672.809.2j	$C_{24}.D_{14}$	$C_3\times D_7$	$42$	42.a1.a1	$16$	14.a1.a1	$48$	$14$	$1$