Basic properties
| Modulus: | \(1900\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{475}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1900.cs
\(\chi_{1900}(13,\cdot)\) \(\chi_{1900}(33,\cdot)\) \(\chi_{1900}(53,\cdot)\) \(\chi_{1900}(97,\cdot)\) \(\chi_{1900}(117,\cdot)\) \(\chi_{1900}(173,\cdot)\) \(\chi_{1900}(317,\cdot)\) \(\chi_{1900}(333,\cdot)\) \(\chi_{1900}(337,\cdot)\) \(\chi_{1900}(413,\cdot)\) \(\chi_{1900}(433,\cdot)\) \(\chi_{1900}(477,\cdot)\) \(\chi_{1900}(497,\cdot)\) \(\chi_{1900}(553,\cdot)\) \(\chi_{1900}(573,\cdot)\) \(\chi_{1900}(637,\cdot)\) \(\chi_{1900}(697,\cdot)\) \(\chi_{1900}(713,\cdot)\) \(\chi_{1900}(717,\cdot)\) \(\chi_{1900}(737,\cdot)\) \(\chi_{1900}(773,\cdot)\) \(\chi_{1900}(813,\cdot)\) \(\chi_{1900}(877,\cdot)\) \(\chi_{1900}(933,\cdot)\) \(\chi_{1900}(953,\cdot)\) \(\chi_{1900}(1017,\cdot)\) \(\chi_{1900}(1077,\cdot)\) \(\chi_{1900}(1097,\cdot)\) \(\chi_{1900}(1117,\cdot)\) \(\chi_{1900}(1153,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((951,77,401)\) → \((1,e\left(\frac{7}{20}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1900 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{180}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{127}{180}\right)\) | \(e\left(\frac{119}{180}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{13}{180}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{4}{45}\right)\) |