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 \(\chi_{4851}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9702.fu
\(\chi_{9702}(13,\cdot)\) \(\chi_{9702}(139,\cdot)\) \(\chi_{9702}(349,\cdot)\) \(\chi_{9702}(475,\cdot)\) \(\chi_{9702}(601,\cdot)\) \(\chi_{9702}(853,\cdot)\) \(\chi_{9702}(1399,\cdot)\) \(\chi_{9702}(1525,\cdot)\) \(\chi_{9702}(1735,\cdot)\) \(\chi_{9702}(1777,\cdot)\) \(\chi_{9702}(1987,\cdot)\) \(\chi_{9702}(2239,\cdot)\) \(\chi_{9702}(2659,\cdot)\) \(\chi_{9702}(2785,\cdot)\) \(\chi_{9702}(2911,\cdot)\) \(\chi_{9702}(3121,\cdot)\) \(\chi_{9702}(3163,\cdot)\) \(\chi_{9702}(3247,\cdot)\) \(\chi_{9702}(3373,\cdot)\) \(\chi_{9702}(4045,\cdot)\) \(\chi_{9702}(4171,\cdot)\) \(\chi_{9702}(4297,\cdot)\) \(\chi_{9702}(4549,\cdot)\) \(\chi_{9702}(4633,\cdot)\) \(\chi_{9702}(4759,\cdot)\) \(\chi_{9702}(5011,\cdot)\) \(\chi_{9702}(5431,\cdot)\) \(\chi_{9702}(5557,\cdot)\) \(\chi_{9702}(5893,\cdot)\) \(\chi_{9702}(5935,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,5293)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{11}{14}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9702 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{37}{210}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{79}{105}\right)\) |