Basic properties
| Modulus: | \(211\) | |
| Conductor: | \(211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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 211.p
\(\chi_{211}(2,\cdot)\) \(\chi_{211}(3,\cdot)\) \(\chi_{211}(7,\cdot)\) \(\chi_{211}(17,\cdot)\) \(\chi_{211}(22,\cdot)\) \(\chi_{211}(29,\cdot)\) \(\chi_{211}(35,\cdot)\) \(\chi_{211}(39,\cdot)\) \(\chi_{211}(41,\cdot)\) \(\chi_{211}(48,\cdot)\) \(\chi_{211}(57,\cdot)\) \(\chi_{211}(72,\cdot)\) \(\chi_{211}(75,\cdot)\) \(\chi_{211}(85,\cdot)\) \(\chi_{211}(91,\cdot)\) \(\chi_{211}(92,\cdot)\) \(\chi_{211}(106,\cdot)\) \(\chi_{211}(108,\cdot)\) \(\chi_{211}(112,\cdot)\) \(\chi_{211}(116,\cdot)\) \(\chi_{211}(118,\cdot)\) \(\chi_{211}(127,\cdot)\) \(\chi_{211}(130,\cdot)\) \(\chi_{211}(131,\cdot)\) \(\chi_{211}(133,\cdot)\) \(\chi_{211}(141,\cdot)\) \(\chi_{211}(142,\cdot)\) \(\chi_{211}(145,\cdot)\) \(\chi_{211}(149,\cdot)\) \(\chi_{211}(152,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{199}{210}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 211 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{199}{210}\right)\) | \(e\left(\frac{157}{210}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{151}{210}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{18}{35}\right)\) |