Basic properties
| Modulus: | \(9036\) | |
| Conductor: | \(2259\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(750\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2259}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9036.cf
\(\chi_{9036}(29,\cdot)\) \(\chi_{9036}(77,\cdot)\) \(\chi_{9036}(137,\cdot)\) \(\chi_{9036}(185,\cdot)\) \(\chi_{9036}(257,\cdot)\) \(\chi_{9036}(281,\cdot)\) \(\chi_{9036}(293,\cdot)\) \(\chi_{9036}(329,\cdot)\) \(\chi_{9036}(401,\cdot)\) \(\chi_{9036}(437,\cdot)\) \(\chi_{9036}(461,\cdot)\) \(\chi_{9036}(545,\cdot)\) \(\chi_{9036}(641,\cdot)\) \(\chi_{9036}(725,\cdot)\) \(\chi_{9036}(797,\cdot)\) \(\chi_{9036}(857,\cdot)\) \(\chi_{9036}(869,\cdot)\) \(\chi_{9036}(929,\cdot)\) \(\chi_{9036}(965,\cdot)\) \(\chi_{9036}(977,\cdot)\) \(\chi_{9036}(1001,\cdot)\) \(\chi_{9036}(1037,\cdot)\) \(\chi_{9036}(1145,\cdot)\) \(\chi_{9036}(1181,\cdot)\) \(\chi_{9036}(1217,\cdot)\) \(\chi_{9036}(1289,\cdot)\) \(\chi_{9036}(1301,\cdot)\) \(\chi_{9036}(1325,\cdot)\) \(\chi_{9036}(1337,\cdot)\) \(\chi_{9036}(1433,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{375})$ |
| Fixed field: | Number field defined by a degree 750 polynomial (not computed) |
Values on generators
\((4519,2009,1261)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{83}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 9036 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{149}{150}\right)\) | \(e\left(\frac{1}{375}\right)\) | \(e\left(\frac{82}{375}\right)\) | \(e\left(\frac{284}{375}\right)\) | \(e\left(\frac{17}{250}\right)\) | \(e\left(\frac{29}{250}\right)\) | \(e\left(\frac{601}{750}\right)\) | \(e\left(\frac{74}{75}\right)\) | \(e\left(\frac{271}{375}\right)\) | \(e\left(\frac{32}{375}\right)\) |