Basic properties
| Modulus: | \(2025\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{675}(83,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2025.bp
\(\chi_{2025}(8,\cdot)\) \(\chi_{2025}(17,\cdot)\) \(\chi_{2025}(62,\cdot)\) \(\chi_{2025}(98,\cdot)\) \(\chi_{2025}(152,\cdot)\) \(\chi_{2025}(197,\cdot)\) \(\chi_{2025}(233,\cdot)\) \(\chi_{2025}(278,\cdot)\) \(\chi_{2025}(287,\cdot)\) \(\chi_{2025}(413,\cdot)\) \(\chi_{2025}(422,\cdot)\) \(\chi_{2025}(467,\cdot)\) \(\chi_{2025}(503,\cdot)\) \(\chi_{2025}(548,\cdot)\) \(\chi_{2025}(602,\cdot)\) \(\chi_{2025}(638,\cdot)\) \(\chi_{2025}(683,\cdot)\) \(\chi_{2025}(692,\cdot)\) \(\chi_{2025}(737,\cdot)\) \(\chi_{2025}(773,\cdot)\) \(\chi_{2025}(827,\cdot)\) \(\chi_{2025}(872,\cdot)\) \(\chi_{2025}(908,\cdot)\) \(\chi_{2025}(953,\cdot)\) \(\chi_{2025}(962,\cdot)\) \(\chi_{2025}(1088,\cdot)\) \(\chi_{2025}(1097,\cdot)\) \(\chi_{2025}(1142,\cdot)\) \(\chi_{2025}(1178,\cdot)\) \(\chi_{2025}(1223,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((326,1702)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{3}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2025 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{180}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{53}{180}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) |