Basic properties
| Modulus: | \(2695\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2695.dn
\(\chi_{2695}(61,\cdot)\) \(\chi_{2695}(96,\cdot)\) \(\chi_{2695}(101,\cdot)\) \(\chi_{2695}(171,\cdot)\) \(\chi_{2695}(206,\cdot)\) \(\chi_{2695}(271,\cdot)\) \(\chi_{2695}(376,\cdot)\) \(\chi_{2695}(381,\cdot)\) \(\chi_{2695}(446,\cdot)\) \(\chi_{2695}(481,\cdot)\) \(\chi_{2695}(486,\cdot)\) \(\chi_{2695}(556,\cdot)\) \(\chi_{2695}(591,\cdot)\) \(\chi_{2695}(761,\cdot)\) \(\chi_{2695}(831,\cdot)\) \(\chi_{2695}(866,\cdot)\) \(\chi_{2695}(871,\cdot)\) \(\chi_{2695}(941,\cdot)\) \(\chi_{2695}(976,\cdot)\) \(\chi_{2695}(1041,\cdot)\) \(\chi_{2695}(1151,\cdot)\) \(\chi_{2695}(1216,\cdot)\) \(\chi_{2695}(1251,\cdot)\) \(\chi_{2695}(1326,\cdot)\) \(\chi_{2695}(1361,\cdot)\) \(\chi_{2695}(1426,\cdot)\) \(\chi_{2695}(1531,\cdot)\) \(\chi_{2695}(1536,\cdot)\) \(\chi_{2695}(1601,\cdot)\) \(\chi_{2695}(1641,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2157,1816,981)\) → \((1,e\left(\frac{11}{42}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 2695 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{149}{210}\right)\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{68}{105}\right)\) |