LMFDB - Dirichlet character search results

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Orbit label	Conrey labels	Modulus	Conductor	Order	Kernel field	Value field	Parity	Real	Primitive	Minimal
1.a	$\chi_{1}(1, \cdot)$	$1$	$1$	$1$	$\Q$	$\Q$	even	✓	✓	✓
2.a	$\chi_{2}(1, \cdot)$	$2$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
3.a	$\chi_{3}(1, \cdot)$	$3$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
3.b	$\chi_{3}(2, \cdot)$	$3$	$3$	$2$	$\Q(\sqrt{-3}) $	$\Q$	odd	✓	✓	✓
4.a	$\chi_{4}(1, \cdot)$	$4$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
4.b	$\chi_{4}(3, \cdot)$	$4$	$4$	$2$	$\Q(\sqrt{-1}) $	$\Q$	odd	✓	✓	✓
5.a	$\chi_{5}(1, \cdot)$	$5$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
5.b	$\chi_{5}(4, \cdot)$	$5$	$5$	$2$	$\Q(\sqrt{5}) $	$\Q$	even	✓	✓	✓
5.c	$\chi_{5}(2, \cdot)$$,$ $\chi_{5}(3, \cdot)$	$5$	$5$	$4$	$\Q(\zeta_{5})$	$\mathbb{Q}(i)$	odd		✓	✓
6.a	$\chi_{6}(1, \cdot)$	$6$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
6.b	$\chi_{6}(5, \cdot)$	$6$	$3$	$2$	$\Q(\sqrt{-3}) $	$\Q$	odd	✓		✓
7.a	$\chi_{7}(1, \cdot)$	$7$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
7.b	$\chi_{7}(6, \cdot)$	$7$	$7$	$2$	$\Q(\sqrt{-7}) $	$\Q$	odd	✓	✓	✓
7.c	$\chi_{7}(2, \cdot)$$,$ $\chi_{7}(4, \cdot)$	$7$	$7$	$3$	$\Q(\zeta_{7})^+$	$\mathbb{Q}(\zeta_3)$	even		✓	✓
7.d	$\chi_{7}(3, \cdot)$$,$ $\chi_{7}(5, \cdot)$	$7$	$7$	$6$	$\Q(\zeta_{7})$	$\mathbb{Q}(\zeta_3)$	odd		✓	✓
8.a	$\chi_{8}(1, \cdot)$	$8$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
8.b	$\chi_{8}(5, \cdot)$	$8$	$8$	$2$	$\Q(\sqrt{2}) $	$\Q$	even	✓	✓	✓
8.c	$\chi_{8}(7, \cdot)$	$8$	$4$	$2$	$\Q(\sqrt{-1}) $	$\Q$	odd	✓
8.d	$\chi_{8}(3, \cdot)$	$8$	$8$	$2$	$\Q(\sqrt{-2}) $	$\Q$	odd	✓	✓	✓
9.a	$\chi_{9}(1, \cdot)$	$9$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
9.b	$\chi_{9}(8, \cdot)$	$9$	$3$	$2$	$\Q(\sqrt{-3}) $	$\Q$	odd	✓		✓
9.c	$\chi_{9}(4, \cdot)$$,$ $\chi_{9}(7, \cdot)$	$9$	$9$	$3$	$\Q(\zeta_{9})^+$	$\mathbb{Q}(\zeta_3)$	even		✓	✓
9.d	$\chi_{9}(2, \cdot)$$,$ $\chi_{9}(5, \cdot)$	$9$	$9$	$6$	$\Q(\zeta_{9})$	$\mathbb{Q}(\zeta_3)$	odd		✓	✓
10.a	$\chi_{10}(1, \cdot)$	$10$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
10.b	$\chi_{10}(9, \cdot)$	$10$	$5$	$2$	$\Q(\sqrt{5}) $	$\Q$	even	✓		✓
10.c	$\chi_{10}(3, \cdot)$$,$ $\chi_{10}(7, \cdot)$	$10$	$5$	$4$	$\Q(\zeta_{5})$	$\mathbb{Q}(i)$	odd			✓
11.a	$\chi_{11}(1, \cdot)$	$11$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
12.a	$\chi_{12}(1, \cdot)$	$12$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
12.c	$\chi_{12}(5, \cdot)$	$12$	$3$	$2$	$\Q(\sqrt{-3}) $	$\Q$	odd	✓		✓
12.d	$\chi_{12}(7, \cdot)$	$12$	$4$	$2$	$\Q(\sqrt{-1}) $	$\Q$	odd	✓		✓
13.a	$\chi_{13}(1, \cdot)$	$13$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
14.a	$\chi_{14}(1, \cdot)$	$14$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
14.b	$\chi_{14}(13, \cdot)$	$14$	$7$	$2$	$\Q(\sqrt{-7}) $	$\Q$	odd	✓		✓
14.c	$\chi_{14}(9, \cdot)$$,$ $\chi_{14}(11, \cdot)$	$14$	$7$	$3$	$\Q(\zeta_{7})^+$	$\mathbb{Q}(\zeta_3)$	even			✓
14.d	$\chi_{14}(3, \cdot)$$,$ $\chi_{14}(5, \cdot)$	$14$	$7$	$6$	$\Q(\zeta_{7})$	$\mathbb{Q}(\zeta_3)$	odd			✓
15.a	$\chi_{15}(1, \cdot)$	$15$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
15.b	$\chi_{15}(4, \cdot)$	$15$	$5$	$2$	$\Q(\sqrt{5}) $	$\Q$	even	✓		✓
15.c	$\chi_{15}(11, \cdot)$	$15$	$3$	$2$	$\Q(\sqrt{-3}) $	$\Q$	odd	✓		✓
15.f	$\chi_{15}(7, \cdot)$$,$ $\chi_{15}(13, \cdot)$	$15$	$5$	$4$	$\Q(\zeta_{5})$	$\mathbb{Q}(i)$	odd			✓
16.a	$\chi_{16}(1, \cdot)$	$16$	$1$	$1$	$\Q$	$\Q$	even	✓
16.b	$\chi_{16}(9, \cdot)$	$16$	$8$	$2$	$\Q(\sqrt{2}) $	$\Q$	even	✓
16.c	$\chi_{16}(15, \cdot)$	$16$	$4$	$2$	$\Q(\sqrt{-1}) $	$\Q$	odd	✓		✓
16.d	$\chi_{16}(7, \cdot)$	$16$	$8$	$2$	$\Q(\sqrt{-2}) $	$\Q$	odd	✓
17.a	$\chi_{17}(1, \cdot)$	$17$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
18.a	$\chi_{18}(1, \cdot)$	$18$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
18.b	$\chi_{18}(17, \cdot)$	$18$	$3$	$2$	$\Q(\sqrt{-3}) $	$\Q$	odd	✓		✓
18.c	$\chi_{18}(7, \cdot)$$,$ $\chi_{18}(13, \cdot)$	$18$	$9$	$3$	$\Q(\zeta_{9})^+$	$\mathbb{Q}(\zeta_3)$	even			✓
18.d	$\chi_{18}(5, \cdot)$$,$ $\chi_{18}(11, \cdot)$	$18$	$9$	$6$	$\Q(\zeta_{9})$	$\mathbb{Q}(\zeta_3)$	odd			✓
19.a	$\chi_{19}(1, \cdot)$	$19$	$1$	$1$	$\Q$	$\Q$	even	✓		✓
20.a	$\chi_{20}(1, \cdot)$	$20$	$1$	$1$	$\Q$	$\Q$	even	✓		✓

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Results (1-50 of 2884126 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.

Orbit label	Conrey labels	Modulus	Conductor	Order	Kernel field	Value field	Parity	Real	Primitive	Minimal
1.a	\(\chi_{1}(1, \cdot)\)	$1$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓	✓	✓
2.a	\(\chi_{2}(1, \cdot)\)	$2$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
3.a	\(\chi_{3}(1, \cdot)\)	$3$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
3.b	\(\chi_{3}(2, \cdot)\)	$3$	$3$	$2$	\(\Q(\sqrt{-3}) \)	\(\Q\)	odd	✓	✓	✓
4.a	\(\chi_{4}(1, \cdot)\)	$4$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
4.b	\(\chi_{4}(3, \cdot)\)	$4$	$4$	$2$	\(\Q(\sqrt{-1}) \)	\(\Q\)	odd	✓	✓	✓
5.a	\(\chi_{5}(1, \cdot)\)	$5$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
5.b	\(\chi_{5}(4, \cdot)\)	$5$	$5$	$2$	\(\Q(\sqrt{5}) \)	\(\Q\)	even	✓	✓	✓
5.c	\(\chi_{5}(2, \cdot)\)$,$ \(\chi_{5}(3, \cdot)\)	$5$	$5$	$4$	\(\Q(\zeta_{5})\)	\(\mathbb{Q}(i)\)	odd		✓	✓
6.a	\(\chi_{6}(1, \cdot)\)	$6$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
6.b	\(\chi_{6}(5, \cdot)\)	$6$	$3$	$2$	\(\Q(\sqrt{-3}) \)	\(\Q\)	odd	✓		✓
7.a	\(\chi_{7}(1, \cdot)\)	$7$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
7.b	\(\chi_{7}(6, \cdot)\)	$7$	$7$	$2$	\(\Q(\sqrt{-7}) \)	\(\Q\)	odd	✓	✓	✓
7.c	\(\chi_{7}(2, \cdot)\)$,$ \(\chi_{7}(4, \cdot)\)	$7$	$7$	$3$	\(\Q(\zeta_{7})^+\)	\(\mathbb{Q}(\zeta_3)\)	even		✓	✓
7.d	\(\chi_{7}(3, \cdot)\)$,$ \(\chi_{7}(5, \cdot)\)	$7$	$7$	$6$	\(\Q(\zeta_{7})\)	\(\mathbb{Q}(\zeta_3)\)	odd		✓	✓
8.a	\(\chi_{8}(1, \cdot)\)	$8$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
8.b	\(\chi_{8}(5, \cdot)\)	$8$	$8$	$2$	\(\Q(\sqrt{2}) \)	\(\Q\)	even	✓	✓	✓
8.c	\(\chi_{8}(7, \cdot)\)	$8$	$4$	$2$	\(\Q(\sqrt{-1}) \)	\(\Q\)	odd	✓
8.d	\(\chi_{8}(3, \cdot)\)	$8$	$8$	$2$	\(\Q(\sqrt{-2}) \)	\(\Q\)	odd	✓	✓	✓
9.a	\(\chi_{9}(1, \cdot)\)	$9$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
9.b	\(\chi_{9}(8, \cdot)\)	$9$	$3$	$2$	\(\Q(\sqrt{-3}) \)	\(\Q\)	odd	✓		✓
9.c	\(\chi_{9}(4, \cdot)\)$,$ \(\chi_{9}(7, \cdot)\)	$9$	$9$	$3$	\(\Q(\zeta_{9})^+\)	\(\mathbb{Q}(\zeta_3)\)	even		✓	✓
9.d	\(\chi_{9}(2, \cdot)\)$,$ \(\chi_{9}(5, \cdot)\)	$9$	$9$	$6$	\(\Q(\zeta_{9})\)	\(\mathbb{Q}(\zeta_3)\)	odd		✓	✓
10.a	\(\chi_{10}(1, \cdot)\)	$10$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
10.b	\(\chi_{10}(9, \cdot)\)	$10$	$5$	$2$	\(\Q(\sqrt{5}) \)	\(\Q\)	even	✓		✓
10.c	\(\chi_{10}(3, \cdot)\)$,$ \(\chi_{10}(7, \cdot)\)	$10$	$5$	$4$	\(\Q(\zeta_{5})\)	\(\mathbb{Q}(i)\)	odd			✓
11.a	\(\chi_{11}(1, \cdot)\)	$11$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
12.a	\(\chi_{12}(1, \cdot)\)	$12$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
12.c	\(\chi_{12}(5, \cdot)\)	$12$	$3$	$2$	\(\Q(\sqrt{-3}) \)	\(\Q\)	odd	✓		✓
12.d	\(\chi_{12}(7, \cdot)\)	$12$	$4$	$2$	\(\Q(\sqrt{-1}) \)	\(\Q\)	odd	✓		✓
13.a	\(\chi_{13}(1, \cdot)\)	$13$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
14.a	\(\chi_{14}(1, \cdot)\)	$14$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
14.b	\(\chi_{14}(13, \cdot)\)	$14$	$7$	$2$	\(\Q(\sqrt{-7}) \)	\(\Q\)	odd	✓		✓
14.c	\(\chi_{14}(9, \cdot)\)$,$ \(\chi_{14}(11, \cdot)\)	$14$	$7$	$3$	\(\Q(\zeta_{7})^+\)	\(\mathbb{Q}(\zeta_3)\)	even			✓
14.d	\(\chi_{14}(3, \cdot)\)$,$ \(\chi_{14}(5, \cdot)\)	$14$	$7$	$6$	\(\Q(\zeta_{7})\)	\(\mathbb{Q}(\zeta_3)\)	odd			✓
15.a	\(\chi_{15}(1, \cdot)\)	$15$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
15.b	\(\chi_{15}(4, \cdot)\)	$15$	$5$	$2$	\(\Q(\sqrt{5}) \)	\(\Q\)	even	✓		✓
15.c	\(\chi_{15}(11, \cdot)\)	$15$	$3$	$2$	\(\Q(\sqrt{-3}) \)	\(\Q\)	odd	✓		✓
15.f	\(\chi_{15}(7, \cdot)\)$,$ \(\chi_{15}(13, \cdot)\)	$15$	$5$	$4$	\(\Q(\zeta_{5})\)	\(\mathbb{Q}(i)\)	odd			✓
16.a	\(\chi_{16}(1, \cdot)\)	$16$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓
16.b	\(\chi_{16}(9, \cdot)\)	$16$	$8$	$2$	\(\Q(\sqrt{2}) \)	\(\Q\)	even	✓
16.c	\(\chi_{16}(15, \cdot)\)	$16$	$4$	$2$	\(\Q(\sqrt{-1}) \)	\(\Q\)	odd	✓		✓
16.d	\(\chi_{16}(7, \cdot)\)	$16$	$8$	$2$	\(\Q(\sqrt{-2}) \)	\(\Q\)	odd	✓
17.a	\(\chi_{17}(1, \cdot)\)	$17$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
18.a	\(\chi_{18}(1, \cdot)\)	$18$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
18.b	\(\chi_{18}(17, \cdot)\)	$18$	$3$	$2$	\(\Q(\sqrt{-3}) \)	\(\Q\)	odd	✓		✓
18.c	\(\chi_{18}(7, \cdot)\)$,$ \(\chi_{18}(13, \cdot)\)	$18$	$9$	$3$	\(\Q(\zeta_{9})^+\)	\(\mathbb{Q}(\zeta_3)\)	even			✓
18.d	\(\chi_{18}(5, \cdot)\)$,$ \(\chi_{18}(11, \cdot)\)	$18$	$9$	$6$	\(\Q(\zeta_{9})\)	\(\mathbb{Q}(\zeta_3)\)	odd			✓
19.a	\(\chi_{19}(1, \cdot)\)	$19$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓
20.a	\(\chi_{20}(1, \cdot)\)	$20$	$1$	$1$	\(\Q\)	\(\Q\)	even	✓		✓