Basic properties
| Modulus: | \(76664\) | |
| Conductor: | \(1369\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1332\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1369}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 76664.od
\(\chi_{76664}(57,\cdot)\) \(\chi_{76664}(113,\cdot)\) \(\chi_{76664}(281,\cdot)\) \(\chi_{76664}(449,\cdot)\) \(\chi_{76664}(505,\cdot)\) \(\chi_{76664}(1345,\cdot)\) \(\chi_{76664}(1401,\cdot)\) \(\chi_{76664}(1569,\cdot)\) \(\chi_{76664}(1737,\cdot)\) \(\chi_{76664}(1905,\cdot)\) \(\chi_{76664}(2017,\cdot)\) \(\chi_{76664}(2129,\cdot)\) \(\chi_{76664}(2185,\cdot)\) \(\chi_{76664}(2353,\cdot)\) \(\chi_{76664}(2521,\cdot)\) \(\chi_{76664}(2577,\cdot)\) \(\chi_{76664}(3417,\cdot)\) \(\chi_{76664}(3473,\cdot)\) \(\chi_{76664}(3641,\cdot)\) \(\chi_{76664}(3809,\cdot)\) \(\chi_{76664}(3865,\cdot)\) \(\chi_{76664}(3977,\cdot)\) \(\chi_{76664}(4201,\cdot)\) \(\chi_{76664}(4257,\cdot)\) \(\chi_{76664}(4425,\cdot)\) \(\chi_{76664}(4593,\cdot)\) \(\chi_{76664}(4649,\cdot)\) \(\chi_{76664}(5489,\cdot)\) \(\chi_{76664}(5545,\cdot)\) \(\chi_{76664}(5713,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1332})$ |
| Fixed field: | Number field defined by a degree 1332 polynomial (not computed) |
Values on generators
\((19167,38333,43809,64345)\) → \((1,1,1,e\left(\frac{1}{1332}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 76664 }(64345, a) \) | \(-1\) | \(1\) | \(e\left(\frac{157}{666}\right)\) | \(e\left(\frac{1211}{1332}\right)\) | \(e\left(\frac{157}{333}\right)\) | \(e\left(\frac{113}{222}\right)\) | \(e\left(\frac{371}{1332}\right)\) | \(e\left(\frac{193}{1332}\right)\) | \(e\left(\frac{79}{1332}\right)\) | \(e\left(\frac{35}{1332}\right)\) | \(e\left(\frac{161}{444}\right)\) | \(e\left(\frac{545}{666}\right)\) |