LMFDB - Complex character search results

Refine search

Degree	Type	Faithful	Conductor

Group	Image	Image Order (Kernel Index)	Kernel Order

Center Order	Center Index

		Sort order	Select

Results (1-50 of 64 matches)

Next Download displayed columns for results to

Label	Degree	Type	Conductor	Field of Traces	$\Q$-character	Group	Image	Image Order	Kernel	Kernel Order	Center	Center Order	Center Index	Schur Index
540.76.1a	$1$	R	$1$	$\Q$	540.76.1a	$C_3^2:D_{30}$	$C_1$	$1$	1.a1.a1	$540$	1.a1.a1	$540$	$1$	$1$
540.76.1b	$1$	R	$1$	$\Q$	540.76.1b	$C_3^2:D_{30}$	$C_2$	$2$	2.b1.b1	$270$	1.a1.a1	$540$	$1$	$1$
540.76.1c	$1$	R	$1$	$\Q$	540.76.1c	$C_3^2:D_{30}$	$C_2$	$2$	2.b1.a1	$270$	1.a1.a1	$540$	$1$	$1$
540.76.1d	$1$	R	$1$	$\Q$	540.76.1d	$C_3^2:D_{30}$	$C_2$	$2$	2.a1.a1	$270$	1.a1.a1	$540$	$1$	$1$
540.76.2a	$2$	R	$1$	$\Q$	540.76.2a	$C_3^2:D_{30}$	$S_3$	$6$	6.a1.d1	$90$	6.a1.d1	$90$	$6$	$1$
540.76.2b	$2$	R	$1$	$\Q$	540.76.2b	$C_3^2:D_{30}$	$S_3$	$6$	6.a1.c1	$90$	6.a1.c1	$90$	$6$	$1$
540.76.2c	$2$	R	$1$	$\Q$	540.76.2c	$C_3^2:D_{30}$	$S_3$	$6$	6.a1.b1	$90$	6.a1.b1	$90$	$6$	$1$
540.76.2d	$2$	R	$1$	$\Q$	540.76.2d	$C_3^2:D_{30}$	$S_3$	$6$	6.a1.a1	$90$	6.a1.a1	$90$	$6$	$1$
540.76.2e	$2$	R	$1$	$\Q$	540.76.2e	$C_3^2:D_{30}$	$D_6$	$12$	12.a1.d1	$45$	6.a1.d1	$90$	$6$	$1$
540.76.2f	$2$	R	$1$	$\Q$	540.76.2f	$C_3^2:D_{30}$	$D_6$	$12$	12.a1.c1	$45$	6.a1.c1	$90$	$6$	$1$
540.76.2g	$2$	R	$1$	$\Q$	540.76.2g	$C_3^2:D_{30}$	$D_6$	$12$	12.a1.b1	$45$	6.a1.b1	$90$	$6$	$1$
540.76.2h	$2$	R	$1$	$\Q$	540.76.2h	$C_3^2:D_{30}$	$D_6$	$12$	12.a1.a1	$45$	6.a1.a1	$90$	$6$	$1$
540.76.2i1	$2$	R	$5$	$\Q(\sqrt{5}) $	540.76.2i	$C_3^2:D_{30}$	$D_5$	$10$	10.a1.a1	$54$	10.a1.a1	$54$	$10$	$1$
540.76.2i2	$2$	R	$5$	$\Q(\sqrt{5}) $	540.76.2i	$C_3^2:D_{30}$	$D_5$	$10$	10.a1.a1	$54$	10.a1.a1	$54$	$10$	$1$
540.76.2j1	$2$	R	$5$	$\Q(\sqrt{5}) $	540.76.2j	$C_3^2:D_{30}$	$D_{10}$	$20$	20.a1.a1	$27$	10.a1.a1	$54$	$10$	$1$
540.76.2j2	$2$	R	$5$	$\Q(\sqrt{5}) $	540.76.2j	$C_3^2:D_{30}$	$D_{10}$	$20$	20.a1.a1	$27$	10.a1.a1	$54$	$10$	$1$
540.76.2k1	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2k	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.d1	$18$	30.a1.d1	$18$	$30$	$1$
540.76.2k2	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2k	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.d1	$18$	30.a1.d1	$18$	$30$	$1$
540.76.2k3	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2k	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.d1	$18$	30.a1.d1	$18$	$30$	$1$
540.76.2k4	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2k	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.d1	$18$	30.a1.d1	$18$	$30$	$1$
540.76.2l1	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2l	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.c1	$18$	30.a1.c1	$18$	$30$	$1$
540.76.2l2	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2l	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.c1	$18$	30.a1.c1	$18$	$30$	$1$
540.76.2l3	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2l	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.c1	$18$	30.a1.c1	$18$	$30$	$1$
540.76.2l4	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2l	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.c1	$18$	30.a1.c1	$18$	$30$	$1$
540.76.2m1	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2m	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.b1	$18$	30.a1.b1	$18$	$30$	$1$
540.76.2m2	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2m	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.b1	$18$	30.a1.b1	$18$	$30$	$1$
540.76.2m3	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2m	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.b1	$18$	30.a1.b1	$18$	$30$	$1$
540.76.2m4	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2m	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.b1	$18$	30.a1.b1	$18$	$30$	$1$
540.76.2n1	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2n	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.a1	$18$	30.a1.a1	$18$	$30$	$1$
540.76.2n2	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2n	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.a1	$18$	30.a1.a1	$18$	$30$	$1$
540.76.2n3	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2n	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.a1	$18$	30.a1.a1	$18$	$30$	$1$
540.76.2n4	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2n	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.a1	$18$	30.a1.a1	$18$	$30$	$1$
540.76.2o1	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2o	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.d1	$9$	30.a1.d1	$18$	$30$	$1$
540.76.2o2	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2o	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.d1	$9$	30.a1.d1	$18$	$30$	$1$
540.76.2o3	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2o	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.d1	$9$	30.a1.d1	$18$	$30$	$1$
540.76.2o4	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2o	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.d1	$9$	30.a1.d1	$18$	$30$	$1$
540.76.2p1	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2p	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.c1	$9$	30.a1.c1	$18$	$30$	$1$
540.76.2p2	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2p	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.c1	$9$	30.a1.c1	$18$	$30$	$1$
540.76.2p3	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2p	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.c1	$9$	30.a1.c1	$18$	$30$	$1$
540.76.2p4	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2p	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.c1	$9$	30.a1.c1	$18$	$30$	$1$
540.76.2q1	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2q	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.b1	$9$	30.a1.b1	$18$	$30$	$1$
540.76.2q2	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2q	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.b1	$9$	30.a1.b1	$18$	$30$	$1$
540.76.2q3	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2q	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.b1	$9$	30.a1.b1	$18$	$30$	$1$
540.76.2q4	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2q	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.b1	$9$	30.a1.b1	$18$	$30$	$1$
540.76.2r1	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2r	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.a1	$9$	30.a1.a1	$18$	$30$	$1$
540.76.2r2	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2r	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.a1	$9$	30.a1.a1	$18$	$30$	$1$
540.76.2r3	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2r	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.a1	$9$	30.a1.a1	$18$	$30$	$1$
540.76.2r4	$2$	R	$15$	$\Q(\zeta_{15})^+$	540.76.2r	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.a1	$9$	30.a1.a1	$18$	$30$	$1$
540.76.3a1	$3$	C	$3$	$\Q(\sqrt{-3}) $	540.76.3a	$C_3^2:D_{30}$	$C_3^2:S_3$	$54$	54.a1.a1	$10$	18.a1.a1	$30$	$18$	$1$
540.76.3a2	$3$	C	$3$	$\Q(\sqrt{-3}) $	540.76.3a	$C_3^2:D_{30}$	$C_3^2:S_3$	$54$	54.a1.a1	$10$	18.a1.a1	$30$	$18$	$1$

Next Download displayed columns for results to

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 64 matches)

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
540.76.1a	$1$	R	$1$	\(\Q\)	540.76.1a	$C_3^2:D_{30}$	$C_1$	$1$	1.a1.a1	$540$	1.a1.a1	$540$	$1$	$1$
540.76.1b	$1$	R	$1$	\(\Q\)	540.76.1b	$C_3^2:D_{30}$	$C_2$	$2$	2.b1.b1	$270$	1.a1.a1	$540$	$1$	$1$
540.76.1c	$1$	R	$1$	\(\Q\)	540.76.1c	$C_3^2:D_{30}$	$C_2$	$2$	2.b1.a1	$270$	1.a1.a1	$540$	$1$	$1$
540.76.1d	$1$	R	$1$	\(\Q\)	540.76.1d	$C_3^2:D_{30}$	$C_2$	$2$	2.a1.a1	$270$	1.a1.a1	$540$	$1$	$1$
540.76.2a	$2$	R	$1$	\(\Q\)	540.76.2a	$C_3^2:D_{30}$	$S_3$	$6$	6.a1.d1	$90$	6.a1.d1	$90$	$6$	$1$
540.76.2b	$2$	R	$1$	\(\Q\)	540.76.2b	$C_3^2:D_{30}$	$S_3$	$6$	6.a1.c1	$90$	6.a1.c1	$90$	$6$	$1$
540.76.2c	$2$	R	$1$	\(\Q\)	540.76.2c	$C_3^2:D_{30}$	$S_3$	$6$	6.a1.b1	$90$	6.a1.b1	$90$	$6$	$1$
540.76.2d	$2$	R	$1$	\(\Q\)	540.76.2d	$C_3^2:D_{30}$	$S_3$	$6$	6.a1.a1	$90$	6.a1.a1	$90$	$6$	$1$
540.76.2e	$2$	R	$1$	\(\Q\)	540.76.2e	$C_3^2:D_{30}$	$D_6$	$12$	12.a1.d1	$45$	6.a1.d1	$90$	$6$	$1$
540.76.2f	$2$	R	$1$	\(\Q\)	540.76.2f	$C_3^2:D_{30}$	$D_6$	$12$	12.a1.c1	$45$	6.a1.c1	$90$	$6$	$1$
540.76.2g	$2$	R	$1$	\(\Q\)	540.76.2g	$C_3^2:D_{30}$	$D_6$	$12$	12.a1.b1	$45$	6.a1.b1	$90$	$6$	$1$
540.76.2h	$2$	R	$1$	\(\Q\)	540.76.2h	$C_3^2:D_{30}$	$D_6$	$12$	12.a1.a1	$45$	6.a1.a1	$90$	$6$	$1$
540.76.2i1	$2$	R	$5$	\(\Q(\sqrt{5}) \)	540.76.2i	$C_3^2:D_{30}$	$D_5$	$10$	10.a1.a1	$54$	10.a1.a1	$54$	$10$	$1$
540.76.2i2	$2$	R	$5$	\(\Q(\sqrt{5}) \)	540.76.2i	$C_3^2:D_{30}$	$D_5$	$10$	10.a1.a1	$54$	10.a1.a1	$54$	$10$	$1$
540.76.2j1	$2$	R	$5$	\(\Q(\sqrt{5}) \)	540.76.2j	$C_3^2:D_{30}$	$D_{10}$	$20$	20.a1.a1	$27$	10.a1.a1	$54$	$10$	$1$
540.76.2j2	$2$	R	$5$	\(\Q(\sqrt{5}) \)	540.76.2j	$C_3^2:D_{30}$	$D_{10}$	$20$	20.a1.a1	$27$	10.a1.a1	$54$	$10$	$1$
540.76.2k1	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2k	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.d1	$18$	30.a1.d1	$18$	$30$	$1$
540.76.2k2	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2k	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.d1	$18$	30.a1.d1	$18$	$30$	$1$
540.76.2k3	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2k	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.d1	$18$	30.a1.d1	$18$	$30$	$1$
540.76.2k4	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2k	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.d1	$18$	30.a1.d1	$18$	$30$	$1$
540.76.2l1	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2l	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.c1	$18$	30.a1.c1	$18$	$30$	$1$
540.76.2l2	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2l	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.c1	$18$	30.a1.c1	$18$	$30$	$1$
540.76.2l3	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2l	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.c1	$18$	30.a1.c1	$18$	$30$	$1$
540.76.2l4	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2l	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.c1	$18$	30.a1.c1	$18$	$30$	$1$
540.76.2m1	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2m	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.b1	$18$	30.a1.b1	$18$	$30$	$1$
540.76.2m2	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2m	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.b1	$18$	30.a1.b1	$18$	$30$	$1$
540.76.2m3	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2m	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.b1	$18$	30.a1.b1	$18$	$30$	$1$
540.76.2m4	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2m	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.b1	$18$	30.a1.b1	$18$	$30$	$1$
540.76.2n1	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2n	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.a1	$18$	30.a1.a1	$18$	$30$	$1$
540.76.2n2	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2n	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.a1	$18$	30.a1.a1	$18$	$30$	$1$
540.76.2n3	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2n	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.a1	$18$	30.a1.a1	$18$	$30$	$1$
540.76.2n4	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2n	$C_3^2:D_{30}$	$D_{15}$	$30$	30.a1.a1	$18$	30.a1.a1	$18$	$30$	$1$
540.76.2o1	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2o	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.d1	$9$	30.a1.d1	$18$	$30$	$1$
540.76.2o2	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2o	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.d1	$9$	30.a1.d1	$18$	$30$	$1$
540.76.2o3	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2o	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.d1	$9$	30.a1.d1	$18$	$30$	$1$
540.76.2o4	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2o	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.d1	$9$	30.a1.d1	$18$	$30$	$1$
540.76.2p1	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2p	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.c1	$9$	30.a1.c1	$18$	$30$	$1$
540.76.2p2	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2p	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.c1	$9$	30.a1.c1	$18$	$30$	$1$
540.76.2p3	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2p	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.c1	$9$	30.a1.c1	$18$	$30$	$1$
540.76.2p4	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2p	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.c1	$9$	30.a1.c1	$18$	$30$	$1$
540.76.2q1	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2q	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.b1	$9$	30.a1.b1	$18$	$30$	$1$
540.76.2q2	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2q	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.b1	$9$	30.a1.b1	$18$	$30$	$1$
540.76.2q3	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2q	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.b1	$9$	30.a1.b1	$18$	$30$	$1$
540.76.2q4	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2q	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.b1	$9$	30.a1.b1	$18$	$30$	$1$
540.76.2r1	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2r	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.a1	$9$	30.a1.a1	$18$	$30$	$1$
540.76.2r2	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2r	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.a1	$9$	30.a1.a1	$18$	$30$	$1$
540.76.2r3	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2r	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.a1	$9$	30.a1.a1	$18$	$30$	$1$
540.76.2r4	$2$	R	$15$	\(\Q(\zeta_{15})^+\)	540.76.2r	$C_3^2:D_{30}$	$D_{30}$	$60$	60.a1.a1	$9$	30.a1.a1	$18$	$30$	$1$
540.76.3a1	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	540.76.3a	$C_3^2:D_{30}$	$C_3^2:S_3$	$54$	54.a1.a1	$10$	18.a1.a1	$30$	$18$	$1$
540.76.3a2	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	540.76.3a	$C_3^2:D_{30}$	$C_3^2:S_3$	$54$	54.a1.a1	$10$	18.a1.a1	$30$	$18$	$1$