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.cb
\(\chi_{2005}(3,\cdot)\) \(\chi_{2005}(17,\cdot)\) \(\chi_{2005}(27,\cdot)\) \(\chi_{2005}(38,\cdot)\) \(\chi_{2005}(52,\cdot)\) \(\chi_{2005}(53,\cdot)\) \(\chi_{2005}(92,\cdot)\) \(\chi_{2005}(97,\cdot)\) \(\chi_{2005}(107,\cdot)\) \(\chi_{2005}(118,\cdot)\) \(\chi_{2005}(123,\cdot)\) \(\chi_{2005}(127,\cdot)\) \(\chi_{2005}(132,\cdot)\) \(\chi_{2005}(143,\cdot)\) \(\chi_{2005}(167,\cdot)\) \(\chi_{2005}(168,\cdot)\) \(\chi_{2005}(182,\cdot)\) \(\chi_{2005}(227,\cdot)\) \(\chi_{2005}(233,\cdot)\) \(\chi_{2005}(258,\cdot)\) \(\chi_{2005}(262,\cdot)\) \(\chi_{2005}(267,\cdot)\) \(\chi_{2005}(272,\cdot)\) \(\chi_{2005}(277,\cdot)\) \(\chi_{2005}(278,\cdot)\) \(\chi_{2005}(283,\cdot)\) \(\chi_{2005}(322,\cdot)\) \(\chi_{2005}(327,\cdot)\) \(\chi_{2005}(342,\cdot)\) \(\chi_{2005}(348,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{400})$ |
| Fixed field: | Number field defined by a degree 400 polynomial (not computed) |
Values on generators
\((402,1206)\) → \((-i,e\left(\frac{1}{400}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 2005 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{200}\right)\) | \(e\left(\frac{101}{400}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{27}{400}\right)\) | \(e\left(\frac{181}{200}\right)\) | \(e\left(\frac{89}{200}\right)\) | \(e\left(\frac{101}{200}\right)\) | \(e\left(\frac{97}{200}\right)\) | \(e\left(\frac{353}{400}\right)\) | \(e\left(\frac{19}{400}\right)\) |