Basic properties
| Modulus: | \(1900\) | |
| Conductor: | \(1900\) | 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 1900.cq
\(\chi_{1900}(23,\cdot)\) \(\chi_{1900}(47,\cdot)\) \(\chi_{1900}(63,\cdot)\) \(\chi_{1900}(123,\cdot)\) \(\chi_{1900}(187,\cdot)\) \(\chi_{1900}(263,\cdot)\) \(\chi_{1900}(283,\cdot)\) \(\chi_{1900}(327,\cdot)\) \(\chi_{1900}(347,\cdot)\) \(\chi_{1900}(367,\cdot)\) \(\chi_{1900}(403,\cdot)\) \(\chi_{1900}(423,\cdot)\) \(\chi_{1900}(427,\cdot)\) \(\chi_{1900}(503,\cdot)\) \(\chi_{1900}(567,\cdot)\) \(\chi_{1900}(587,\cdot)\) \(\chi_{1900}(663,\cdot)\) \(\chi_{1900}(727,\cdot)\) \(\chi_{1900}(747,\cdot)\) \(\chi_{1900}(783,\cdot)\) \(\chi_{1900}(803,\cdot)\) \(\chi_{1900}(823,\cdot)\) \(\chi_{1900}(883,\cdot)\) \(\chi_{1900}(947,\cdot)\) \(\chi_{1900}(967,\cdot)\) \(\chi_{1900}(1023,\cdot)\) \(\chi_{1900}(1087,\cdot)\) \(\chi_{1900}(1127,\cdot)\) \(\chi_{1900}(1163,\cdot)\) \(\chi_{1900}(1183,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((951,77,401)\) → \((-1,e\left(\frac{13}{20}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1900 }(367, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{180}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{43}{180}\right)\) | \(e\left(\frac{41}{180}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{37}{180}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{47}{90}\right)\) |