Dirichlet character χ2700(1603,⋅)\chi_{2700}(1603,\cdot)

• Label: 2700.1603
• Modulus: $2700$
• Conductor: $900$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$2700$
Conductor:	$900$
Order:	$60$
Real:	no
Primitive:	no, induced from $\chi_{900}(103,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 2700.cf

$\chi_{2700}(127,\cdot)$ $\chi_{2700}(523,\cdot)$ $\chi_{2700}(667,\cdot)$ $\chi_{2700}(847,\cdot)$ $\chi_{2700}(883,\cdot)$ $\chi_{2700}(1063,\cdot)$ $\chi_{2700}(1387,\cdot)$ $\chi_{2700}(1423,\cdot)$ $\chi_{2700}(1603,\cdot)$ $\chi_{2700}(1747,\cdot)$ $\chi_{2700}(1927,\cdot)$ $\chi_{2700}(1963,\cdot)$ $\chi_{2700}(2287,\cdot)$ $\chi_{2700}(2467,\cdot)$ $\chi_{2700}(2503,\cdot)$ $\chi_{2700}(2683,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{60})$
Fixed field:	Number field defined by a degree 60 polynomial

Values on generators

$(1351,1001,2377)$ → $(-1,e\left(\frac{1}{3}\right),e\left(\frac{7}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 2700 }(1603, a)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{15}\right)$