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 \(\chi_{4851}(149,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9702.fw
\(\chi_{9702}(149,\cdot)\) \(\chi_{9702}(767,\cdot)\) \(\chi_{9702}(893,\cdot)\) \(\chi_{9702}(1019,\cdot)\) \(\chi_{9702}(1031,\cdot)\) \(\chi_{9702}(1271,\cdot)\) \(\chi_{9702}(1283,\cdot)\) \(\chi_{9702}(1535,\cdot)\) \(\chi_{9702}(2153,\cdot)\) \(\chi_{9702}(2279,\cdot)\) \(\chi_{9702}(2405,\cdot)\) \(\chi_{9702}(2417,\cdot)\) \(\chi_{9702}(2543,\cdot)\) \(\chi_{9702}(2657,\cdot)\) \(\chi_{9702}(2669,\cdot)\) \(\chi_{9702}(3539,\cdot)\) \(\chi_{9702}(3665,\cdot)\) \(\chi_{9702}(3929,\cdot)\) \(\chi_{9702}(4043,\cdot)\) \(\chi_{9702}(4055,\cdot)\) \(\chi_{9702}(4307,\cdot)\) \(\chi_{9702}(4925,\cdot)\) \(\chi_{9702}(5051,\cdot)\) \(\chi_{9702}(5177,\cdot)\) \(\chi_{9702}(5189,\cdot)\) \(\chi_{9702}(5315,\cdot)\) \(\chi_{9702}(5429,\cdot)\) \(\chi_{9702}(5441,\cdot)\) \(\chi_{9702}(5693,\cdot)\) \(\chi_{9702}(6311,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,5293)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{13}{21}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9702 }(149, a) \) | \(1\) | \(1\) | \(e\left(\frac{151}{210}\right)\) | \(e\left(\frac{209}{210}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{16}{105}\right)\) |