Basic properties
Modulus: | \(2166\) | |
Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{361}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2166.u
\(\chi_{2166}(25,\cdot)\) \(\chi_{2166}(43,\cdot)\) \(\chi_{2166}(55,\cdot)\) \(\chi_{2166}(61,\cdot)\) \(\chi_{2166}(73,\cdot)\) \(\chi_{2166}(85,\cdot)\) \(\chi_{2166}(139,\cdot)\) \(\chi_{2166}(157,\cdot)\) \(\chi_{2166}(169,\cdot)\) \(\chi_{2166}(175,\cdot)\) \(\chi_{2166}(187,\cdot)\) \(\chi_{2166}(199,\cdot)\) \(\chi_{2166}(253,\cdot)\) \(\chi_{2166}(271,\cdot)\) \(\chi_{2166}(283,\cdot)\) \(\chi_{2166}(289,\cdot)\) \(\chi_{2166}(301,\cdot)\) \(\chi_{2166}(313,\cdot)\) \(\chi_{2166}(367,\cdot)\) \(\chi_{2166}(385,\cdot)\) \(\chi_{2166}(397,\cdot)\) \(\chi_{2166}(403,\cdot)\) \(\chi_{2166}(427,\cdot)\) \(\chi_{2166}(481,\cdot)\) \(\chi_{2166}(499,\cdot)\) \(\chi_{2166}(511,\cdot)\) \(\chi_{2166}(517,\cdot)\) \(\chi_{2166}(529,\cdot)\) \(\chi_{2166}(541,\cdot)\) \(\chi_{2166}(613,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((1,e\left(\frac{61}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 2166 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{62}{171}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{14}{171}\right)\) | \(e\left(\frac{89}{171}\right)\) | \(e\left(\frac{11}{171}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{46}{171}\right)\) |