Dirichlet character χ100315(451,⋅)\chi_{100315}(451,\cdot)

• Label: 100315.451
• Modulus: $100315$
• Conductor: $20063$
• Order: $20062$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$100315$
Conductor:	$20063$
Order:	$20062$
Real:	no
Primitive:	no, induced from $\chi_{20063}(451,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 100315.t

$\chi_{100315}(21,\cdot)$ $\chi_{100315}(41,\cdot)$ $\chi_{100315}(51,\cdot)$ $\chi_{100315}(56,\cdot)$ $\chi_{100315}(86,\cdot)$ $\chi_{100315}(91,\cdot)$ $\chi_{100315}(126,\cdot)$ $\chi_{100315}(131,\cdot)$ $\chi_{100315}(136,\cdot)$ $\chi_{100315}(161,\cdot)$ $\chi_{100315}(181,\cdot)$ $\chi_{100315}(191,\cdot)$ $\chi_{100315}(206,\cdot)$ $\chi_{100315}(221,\cdot)$ $\chi_{100315}(231,\cdot)$ $\chi_{100315}(236,\cdot)$ $\chi_{100315}(246,\cdot)$ $\chi_{100315}(266,\cdot)$ $\chi_{100315}(311,\cdot)$ $\chi_{100315}(316,\cdot)$ $\chi_{100315}(326,\cdot)$ $\chi_{100315}(336,\cdot)$ $\chi_{100315}(356,\cdot)$ $\chi_{100315}(366,\cdot)$ $\chi_{100315}(371,\cdot)$ $\chi_{100315}(381,\cdot)$ $\chi_{100315}(391,\cdot)$ $\chi_{100315}(401,\cdot)$ $\chi_{100315}(421,\cdot)$ $\chi_{100315}(451,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{10031})$
Fixed field:	Number field defined by a degree 20062 polynomial (not computed)

Values on generators

$(40127,40131)$ → $(1,e\left(\frac{13183}{20062}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 100315 }(451, a)$	$-1$	$1$	$e\left(\frac{237}{1433}\right)$	$e\left(\frac{4038}{10031}\right)$	$e\left(\frac{474}{1433}\right)$	$e\left(\frac{5697}{10031}\right)$	$e\left(\frac{3015}{20062}\right)$	$e\left(\frac{711}{1433}\right)$	$e\left(\frac{8076}{10031}\right)$	$e\left(\frac{6374}{10031}\right)$	$e\left(\frac{7356}{10031}\right)$	$e\left(\frac{4024}{10031}\right)$