Basic properties
| Modulus: | \(2700\) | |
| Conductor: | \(2700\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2700.cs
\(\chi_{2700}(67,\cdot)\) \(\chi_{2700}(103,\cdot)\) \(\chi_{2700}(187,\cdot)\) \(\chi_{2700}(223,\cdot)\) \(\chi_{2700}(247,\cdot)\) \(\chi_{2700}(283,\cdot)\) \(\chi_{2700}(367,\cdot)\) \(\chi_{2700}(403,\cdot)\) \(\chi_{2700}(427,\cdot)\) \(\chi_{2700}(463,\cdot)\) \(\chi_{2700}(547,\cdot)\) \(\chi_{2700}(583,\cdot)\) \(\chi_{2700}(727,\cdot)\) \(\chi_{2700}(763,\cdot)\) \(\chi_{2700}(787,\cdot)\) \(\chi_{2700}(823,\cdot)\) \(\chi_{2700}(967,\cdot)\) \(\chi_{2700}(1003,\cdot)\) \(\chi_{2700}(1087,\cdot)\) \(\chi_{2700}(1123,\cdot)\) \(\chi_{2700}(1147,\cdot)\) \(\chi_{2700}(1183,\cdot)\) \(\chi_{2700}(1267,\cdot)\) \(\chi_{2700}(1303,\cdot)\) \(\chi_{2700}(1327,\cdot)\) \(\chi_{2700}(1363,\cdot)\) \(\chi_{2700}(1447,\cdot)\) \(\chi_{2700}(1483,\cdot)\) \(\chi_{2700}(1627,\cdot)\) \(\chi_{2700}(1663,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1351,1001,2377)\) → \((-1,e\left(\frac{5}{9}\right),e\left(\frac{17}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 2700 }(2347, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{107}{180}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{173}{180}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{38}{45}\right)\) |