Basic properties
Modulus: | \(2672\) | |
Conductor: | \(2672\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(332\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2672.w
\(\chi_{2672}(21,\cdot)\) \(\chi_{2672}(29,\cdot)\) \(\chi_{2672}(61,\cdot)\) \(\chi_{2672}(77,\cdot)\) \(\chi_{2672}(85,\cdot)\) \(\chi_{2672}(93,\cdot)\) \(\chi_{2672}(133,\cdot)\) \(\chi_{2672}(141,\cdot)\) \(\chi_{2672}(157,\cdot)\) \(\chi_{2672}(173,\cdot)\) \(\chi_{2672}(181,\cdot)\) \(\chi_{2672}(189,\cdot)\) \(\chi_{2672}(205,\cdot)\) \(\chi_{2672}(221,\cdot)\) \(\chi_{2672}(229,\cdot)\) \(\chi_{2672}(261,\cdot)\) \(\chi_{2672}(293,\cdot)\) \(\chi_{2672}(317,\cdot)\) \(\chi_{2672}(341,\cdot)\) \(\chi_{2672}(365,\cdot)\) \(\chi_{2672}(381,\cdot)\) \(\chi_{2672}(397,\cdot)\) \(\chi_{2672}(421,\cdot)\) \(\chi_{2672}(461,\cdot)\) \(\chi_{2672}(509,\cdot)\) \(\chi_{2672}(517,\cdot)\) \(\chi_{2672}(525,\cdot)\) \(\chi_{2672}(533,\cdot)\) \(\chi_{2672}(549,\cdot)\) \(\chi_{2672}(557,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{332})$ |
Fixed field: | Number field defined by a degree 332 polynomial (not computed) |
Values on generators
\((335,2005,673)\) → \((1,i,e\left(\frac{9}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 2672 }(1429, a) \) | \(1\) | \(1\) | \(e\left(\frac{313}{332}\right)\) | \(e\left(\frac{119}{332}\right)\) | \(e\left(\frac{49}{166}\right)\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{95}{332}\right)\) | \(e\left(\frac{305}{332}\right)\) | \(e\left(\frac{25}{83}\right)\) | \(e\left(\frac{62}{83}\right)\) | \(e\left(\frac{13}{332}\right)\) | \(e\left(\frac{79}{332}\right)\) |