Basic properties
| Modulus: | \(9702\) | |
| Conductor: | \(4851\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4851}(335,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9702.fn
\(\chi_{9702}(335,\cdot)\) \(\chi_{9702}(713,\cdot)\) \(\chi_{9702}(797,\cdot)\) \(\chi_{9702}(839,\cdot)\) \(\chi_{9702}(1049,\cdot)\) \(\chi_{9702}(1301,\cdot)\) \(\chi_{9702}(1721,\cdot)\) \(\chi_{9702}(1973,\cdot)\) \(\chi_{9702}(2099,\cdot)\) \(\chi_{9702}(2183,\cdot)\) \(\chi_{9702}(2225,\cdot)\) \(\chi_{9702}(2435,\cdot)\) \(\chi_{9702}(2561,\cdot)\) \(\chi_{9702}(2687,\cdot)\) \(\chi_{9702}(3107,\cdot)\) \(\chi_{9702}(3359,\cdot)\) \(\chi_{9702}(3485,\cdot)\) \(\chi_{9702}(3569,\cdot)\) \(\chi_{9702}(3611,\cdot)\) \(\chi_{9702}(3947,\cdot)\) \(\chi_{9702}(4073,\cdot)\) \(\chi_{9702}(4493,\cdot)\) \(\chi_{9702}(4745,\cdot)\) \(\chi_{9702}(4871,\cdot)\) \(\chi_{9702}(4955,\cdot)\) \(\chi_{9702}(5207,\cdot)\) \(\chi_{9702}(5333,\cdot)\) \(\chi_{9702}(5459,\cdot)\) \(\chi_{9702}(6131,\cdot)\) \(\chi_{9702}(6257,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,5293)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{5}{14}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9702 }(335, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{109}{210}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{83}{210}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{41}{105}\right)\) |