Basic properties
| Modulus: | \(5265\) | |
| Conductor: | \(1053\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1053}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5265.ie
\(\chi_{5265}(41,\cdot)\) \(\chi_{5265}(371,\cdot)\) \(\chi_{5265}(401,\cdot)\) \(\chi_{5265}(461,\cdot)\) \(\chi_{5265}(626,\cdot)\) \(\chi_{5265}(956,\cdot)\) \(\chi_{5265}(986,\cdot)\) \(\chi_{5265}(1046,\cdot)\) \(\chi_{5265}(1211,\cdot)\) \(\chi_{5265}(1541,\cdot)\) \(\chi_{5265}(1571,\cdot)\) \(\chi_{5265}(1631,\cdot)\) \(\chi_{5265}(1796,\cdot)\) \(\chi_{5265}(2126,\cdot)\) \(\chi_{5265}(2156,\cdot)\) \(\chi_{5265}(2216,\cdot)\) \(\chi_{5265}(2381,\cdot)\) \(\chi_{5265}(2711,\cdot)\) \(\chi_{5265}(2741,\cdot)\) \(\chi_{5265}(2801,\cdot)\) \(\chi_{5265}(2966,\cdot)\) \(\chi_{5265}(3296,\cdot)\) \(\chi_{5265}(3326,\cdot)\) \(\chi_{5265}(3386,\cdot)\) \(\chi_{5265}(3551,\cdot)\) \(\chi_{5265}(3881,\cdot)\) \(\chi_{5265}(3911,\cdot)\) \(\chi_{5265}(3971,\cdot)\) \(\chi_{5265}(4136,\cdot)\) \(\chi_{5265}(4466,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((326,2107,2836)\) → \((e\left(\frac{53}{54}\right),1,e\left(\frac{1}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 5265 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{108}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{67}{108}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{37}{108}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{11}{27}\right)\) |