Basic properties
| Modulus: | \(2005\) | |
| Conductor: | \(2005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(400\) | 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 2005.by
\(\chi_{2005}(12,\cdot)\) \(\chi_{2005}(13,\cdot)\) \(\chi_{2005}(23,\cdot)\) \(\chi_{2005}(37,\cdot)\) \(\chi_{2005}(42,\cdot)\) \(\chi_{2005}(62,\cdot)\) \(\chi_{2005}(67,\cdot)\) \(\chi_{2005}(87,\cdot)\) \(\chi_{2005}(117,\cdot)\) \(\chi_{2005}(122,\cdot)\) \(\chi_{2005}(137,\cdot)\) \(\chi_{2005}(152,\cdot)\) \(\chi_{2005}(163,\cdot)\) \(\chi_{2005}(187,\cdot)\) \(\chi_{2005}(192,\cdot)\) \(\chi_{2005}(193,\cdot)\) \(\chi_{2005}(207,\cdot)\) \(\chi_{2005}(208,\cdot)\) \(\chi_{2005}(217,\cdot)\) \(\chi_{2005}(238,\cdot)\) \(\chi_{2005}(297,\cdot)\) \(\chi_{2005}(347,\cdot)\) \(\chi_{2005}(367,\cdot)\) \(\chi_{2005}(378,\cdot)\) \(\chi_{2005}(388,\cdot)\) \(\chi_{2005}(418,\cdot)\) \(\chi_{2005}(428,\cdot)\) \(\chi_{2005}(447,\cdot)\) \(\chi_{2005}(453,\cdot)\) \(\chi_{2005}(467,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{400})$ |
| Fixed field: | Number field defined by a degree 400 polynomial (not computed) |
Values on generators
\((402,1206)\) → \((i,e\left(\frac{89}{400}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 2005 }(42, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{200}\right)\) | \(e\left(\frac{389}{400}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{3}{400}\right)\) | \(e\left(\frac{9}{200}\right)\) | \(e\left(\frac{21}{200}\right)\) | \(e\left(\frac{189}{200}\right)\) | \(e\left(\frac{33}{200}\right)\) | \(e\left(\frac{17}{400}\right)\) | \(e\left(\frac{291}{400}\right)\) |