Basic properties
| Modulus: | \(33327\) | |
| Conductor: | \(4761\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(138\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4761}(22,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 33327.eg
\(\chi_{33327}(22,\cdot)\) \(\chi_{33327}(988,\cdot)\) \(\chi_{33327}(1471,\cdot)\) \(\chi_{33327}(2437,\cdot)\) \(\chi_{33327}(2920,\cdot)\) \(\chi_{33327}(3886,\cdot)\) \(\chi_{33327}(4369,\cdot)\) \(\chi_{33327}(5335,\cdot)\) \(\chi_{33327}(6784,\cdot)\) \(\chi_{33327}(7267,\cdot)\) \(\chi_{33327}(8233,\cdot)\) \(\chi_{33327}(8716,\cdot)\) \(\chi_{33327}(9682,\cdot)\) \(\chi_{33327}(10165,\cdot)\) \(\chi_{33327}(11131,\cdot)\) \(\chi_{33327}(11614,\cdot)\) \(\chi_{33327}(12580,\cdot)\) \(\chi_{33327}(13063,\cdot)\) \(\chi_{33327}(14029,\cdot)\) \(\chi_{33327}(14512,\cdot)\) \(\chi_{33327}(15478,\cdot)\) \(\chi_{33327}(15961,\cdot)\) \(\chi_{33327}(17410,\cdot)\) \(\chi_{33327}(18376,\cdot)\) \(\chi_{33327}(18859,\cdot)\) \(\chi_{33327}(19825,\cdot)\) \(\chi_{33327}(20308,\cdot)\) \(\chi_{33327}(21274,\cdot)\) \(\chi_{33327}(21757,\cdot)\) \(\chi_{33327}(22723,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{69})$ |
| Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\((25922,9523,10585)\) → \((e\left(\frac{1}{3}\right),1,e\left(\frac{13}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 33327 }(22, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{69}\right)\) | \(e\left(\frac{49}{69}\right)\) | \(e\left(\frac{131}{138}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{31}{138}\right)\) | \(e\left(\frac{25}{69}\right)\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{1}{46}\right)\) |