Basic properties
| Modulus: | \(2001\) | |
| Conductor: | \(2001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(308\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2001.bs
\(\chi_{2001}(11,\cdot)\) \(\chi_{2001}(14,\cdot)\) \(\chi_{2001}(44,\cdot)\) \(\chi_{2001}(56,\cdot)\) \(\chi_{2001}(89,\cdot)\) \(\chi_{2001}(113,\cdot)\) \(\chi_{2001}(134,\cdot)\) \(\chi_{2001}(143,\cdot)\) \(\chi_{2001}(155,\cdot)\) \(\chi_{2001}(176,\cdot)\) \(\chi_{2001}(182,\cdot)\) \(\chi_{2001}(218,\cdot)\) \(\chi_{2001}(221,\cdot)\) \(\chi_{2001}(224,\cdot)\) \(\chi_{2001}(251,\cdot)\) \(\chi_{2001}(263,\cdot)\) \(\chi_{2001}(272,\cdot)\) \(\chi_{2001}(287,\cdot)\) \(\chi_{2001}(293,\cdot)\) \(\chi_{2001}(329,\cdot)\) \(\chi_{2001}(350,\cdot)\) \(\chi_{2001}(356,\cdot)\) \(\chi_{2001}(359,\cdot)\) \(\chi_{2001}(362,\cdot)\) \(\chi_{2001}(398,\cdot)\) \(\chi_{2001}(425,\cdot)\) \(\chi_{2001}(467,\cdot)\) \(\chi_{2001}(479,\cdot)\) \(\chi_{2001}(503,\cdot)\) \(\chi_{2001}(536,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{308})$ |
| Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((668,1132,553)\) → \((-1,e\left(\frac{13}{22}\right),e\left(\frac{27}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2001 }(44, a) \) | \(-1\) | \(1\) | \(e\left(\frac{199}{308}\right)\) | \(e\left(\frac{45}{154}\right)\) | \(e\left(\frac{47}{154}\right)\) | \(e\left(\frac{123}{154}\right)\) | \(e\left(\frac{289}{308}\right)\) | \(e\left(\frac{293}{308}\right)\) | \(e\left(\frac{285}{308}\right)\) | \(e\left(\frac{97}{154}\right)\) | \(e\left(\frac{137}{308}\right)\) | \(e\left(\frac{45}{77}\right)\) |