Basic properties
| Modulus: | \(9702\) | |
| 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 \(\chi_{539}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9702.fz
\(\chi_{9702}(73,\cdot)\) \(\chi_{9702}(145,\cdot)\) \(\chi_{9702}(271,\cdot)\) \(\chi_{9702}(523,\cdot)\) \(\chi_{9702}(1333,\cdot)\) \(\chi_{9702}(1405,\cdot)\) \(\chi_{9702}(1459,\cdot)\) \(\chi_{9702}(1531,\cdot)\) \(\chi_{9702}(1657,\cdot)\) \(\chi_{9702}(1711,\cdot)\) \(\chi_{9702}(1909,\cdot)\) \(\chi_{9702}(2593,\cdot)\) \(\chi_{9702}(2719,\cdot)\) \(\chi_{9702}(2791,\cdot)\) \(\chi_{9702}(2845,\cdot)\) \(\chi_{9702}(2917,\cdot)\) \(\chi_{9702}(3043,\cdot)\) \(\chi_{9702}(3097,\cdot)\) \(\chi_{9702}(3295,\cdot)\) \(\chi_{9702}(3979,\cdot)\) \(\chi_{9702}(4105,\cdot)\) \(\chi_{9702}(4177,\cdot)\) \(\chi_{9702}(4231,\cdot)\) \(\chi_{9702}(4303,\cdot)\) \(\chi_{9702}(4483,\cdot)\) \(\chi_{9702}(4681,\cdot)\) \(\chi_{9702}(5365,\cdot)\) \(\chi_{9702}(5491,\cdot)\) \(\chi_{9702}(5563,\cdot)\) \(\chi_{9702}(5689,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,5293)\) → \((1,e\left(\frac{37}{42}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9702 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{210}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{11}{35}\right)\) |