Basic properties
| Modulus: | \(1988\) | |
| Conductor: | \(497\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{497}(424,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1988.ch
\(\chi_{1988}(53,\cdot)\) \(\chi_{1988}(65,\cdot)\) \(\chi_{1988}(93,\cdot)\) \(\chi_{1988}(149,\cdot)\) \(\chi_{1988}(177,\cdot)\) \(\chi_{1988}(205,\cdot)\) \(\chi_{1988}(305,\cdot)\) \(\chi_{1988}(317,\cdot)\) \(\chi_{1988}(345,\cdot)\) \(\chi_{1988}(417,\cdot)\) \(\chi_{1988}(457,\cdot)\) \(\chi_{1988}(473,\cdot)\) \(\chi_{1988}(485,\cdot)\) \(\chi_{1988}(541,\cdot)\) \(\chi_{1988}(681,\cdot)\) \(\chi_{1988}(765,\cdot)\) \(\chi_{1988}(809,\cdot)\) \(\chi_{1988}(837,\cdot)\) \(\chi_{1988}(849,\cdot)\) \(\chi_{1988}(865,\cdot)\) \(\chi_{1988}(905,\cdot)\) \(\chi_{1988}(921,\cdot)\) \(\chi_{1988}(1005,\cdot)\) \(\chi_{1988}(1061,\cdot)\) \(\chi_{1988}(1117,\cdot)\) \(\chi_{1988}(1157,\cdot)\) \(\chi_{1988}(1201,\cdot)\) \(\chi_{1988}(1229,\cdot)\) \(\chi_{1988}(1269,\cdot)\) \(\chi_{1988}(1285,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((995,1137,1569)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{41}{70}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 1988 }(921, a) \) | \(-1\) | \(1\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{7}{15}\right)\) |