Basic properties
| Modulus: | \(2025\) | |
| Conductor: | \(405\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{405}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2025.bm
\(\chi_{2025}(7,\cdot)\) \(\chi_{2025}(43,\cdot)\) \(\chi_{2025}(157,\cdot)\) \(\chi_{2025}(193,\cdot)\) \(\chi_{2025}(232,\cdot)\) \(\chi_{2025}(268,\cdot)\) \(\chi_{2025}(382,\cdot)\) \(\chi_{2025}(418,\cdot)\) \(\chi_{2025}(457,\cdot)\) \(\chi_{2025}(493,\cdot)\) \(\chi_{2025}(607,\cdot)\) \(\chi_{2025}(643,\cdot)\) \(\chi_{2025}(682,\cdot)\) \(\chi_{2025}(718,\cdot)\) \(\chi_{2025}(832,\cdot)\) \(\chi_{2025}(868,\cdot)\) \(\chi_{2025}(907,\cdot)\) \(\chi_{2025}(943,\cdot)\) \(\chi_{2025}(1057,\cdot)\) \(\chi_{2025}(1093,\cdot)\) \(\chi_{2025}(1132,\cdot)\) \(\chi_{2025}(1168,\cdot)\) \(\chi_{2025}(1282,\cdot)\) \(\chi_{2025}(1318,\cdot)\) \(\chi_{2025}(1357,\cdot)\) \(\chi_{2025}(1393,\cdot)\) \(\chi_{2025}(1507,\cdot)\) \(\chi_{2025}(1543,\cdot)\) \(\chi_{2025}(1582,\cdot)\) \(\chi_{2025}(1618,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((326,1702)\) → \((e\left(\frac{11}{27}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2025 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{108}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{55}{108}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) |