Basic properties
| Modulus: | \(9036\) | |
| Conductor: | \(251\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(125\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{251}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9036.bp
\(\chi_{9036}(73,\cdot)\) \(\chi_{9036}(181,\cdot)\) \(\chi_{9036}(217,\cdot)\) \(\chi_{9036}(289,\cdot)\) \(\chi_{9036}(325,\cdot)\) \(\chi_{9036}(361,\cdot)\) \(\chi_{9036}(469,\cdot)\) \(\chi_{9036}(505,\cdot)\) \(\chi_{9036}(541,\cdot)\) \(\chi_{9036}(577,\cdot)\) \(\chi_{9036}(649,\cdot)\) \(\chi_{9036}(865,\cdot)\) \(\chi_{9036}(1045,\cdot)\) \(\chi_{9036}(1225,\cdot)\) \(\chi_{9036}(1369,\cdot)\) \(\chi_{9036}(1477,\cdot)\) \(\chi_{9036}(1513,\cdot)\) \(\chi_{9036}(1585,\cdot)\) \(\chi_{9036}(1621,\cdot)\) \(\chi_{9036}(1909,\cdot)\) \(\chi_{9036}(2017,\cdot)\) \(\chi_{9036}(2053,\cdot)\) \(\chi_{9036}(2089,\cdot)\) \(\chi_{9036}(2125,\cdot)\) \(\chi_{9036}(2161,\cdot)\) \(\chi_{9036}(2197,\cdot)\) \(\chi_{9036}(2233,\cdot)\) \(\chi_{9036}(2377,\cdot)\) \(\chi_{9036}(2413,\cdot)\) \(\chi_{9036}(2449,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 125 polynomial (not computed) |
Values on generators
\((4519,2009,1261)\) → \((1,1,e\left(\frac{17}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 9036 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{91}{125}\right)\) | \(e\left(\frac{87}{125}\right)\) | \(e\left(\frac{94}{125}\right)\) | \(e\left(\frac{8}{125}\right)\) | \(e\left(\frac{21}{125}\right)\) | \(e\left(\frac{33}{125}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{36}{125}\right)\) | \(e\left(\frac{37}{125}\right)\) |