Basic properties
| Modulus: | \(9702\) | |
| Conductor: | \(4851\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4851}(445,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9702.fb
\(\chi_{9702}(445,\cdot)\) \(\chi_{9702}(697,\cdot)\) \(\chi_{9702}(709,\cdot)\) \(\chi_{9702}(823,\cdot)\) \(\chi_{9702}(1087,\cdot)\) \(\chi_{9702}(1213,\cdot)\) \(\chi_{9702}(2083,\cdot)\) \(\chi_{9702}(2095,\cdot)\) \(\chi_{9702}(2209,\cdot)\) \(\chi_{9702}(2335,\cdot)\) \(\chi_{9702}(2347,\cdot)\) \(\chi_{9702}(2473,\cdot)\) \(\chi_{9702}(2599,\cdot)\) \(\chi_{9702}(3217,\cdot)\) \(\chi_{9702}(3469,\cdot)\) \(\chi_{9702}(3481,\cdot)\) \(\chi_{9702}(3721,\cdot)\) \(\chi_{9702}(3733,\cdot)\) \(\chi_{9702}(3859,\cdot)\) \(\chi_{9702}(3985,\cdot)\) \(\chi_{9702}(4603,\cdot)\) \(\chi_{9702}(4855,\cdot)\) \(\chi_{9702}(4867,\cdot)\) \(\chi_{9702}(4981,\cdot)\) \(\chi_{9702}(5107,\cdot)\) \(\chi_{9702}(5119,\cdot)\) \(\chi_{9702}(5245,\cdot)\) \(\chi_{9702}(5989,\cdot)\) \(\chi_{9702}(6367,\cdot)\) \(\chi_{9702}(6493,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((4313,199,5293)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{21}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9702 }(445, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{46}{105}\right)\) |