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 \(\chi_{1053}(86,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5265.ia
\(\chi_{5265}(86,\cdot)\) \(\chi_{5265}(281,\cdot)\) \(\chi_{5265}(356,\cdot)\) \(\chi_{5265}(551,\cdot)\) \(\chi_{5265}(671,\cdot)\) \(\chi_{5265}(866,\cdot)\) \(\chi_{5265}(941,\cdot)\) \(\chi_{5265}(1136,\cdot)\) \(\chi_{5265}(1256,\cdot)\) \(\chi_{5265}(1451,\cdot)\) \(\chi_{5265}(1526,\cdot)\) \(\chi_{5265}(1721,\cdot)\) \(\chi_{5265}(1841,\cdot)\) \(\chi_{5265}(2036,\cdot)\) \(\chi_{5265}(2111,\cdot)\) \(\chi_{5265}(2306,\cdot)\) \(\chi_{5265}(2426,\cdot)\) \(\chi_{5265}(2621,\cdot)\) \(\chi_{5265}(2696,\cdot)\) \(\chi_{5265}(2891,\cdot)\) \(\chi_{5265}(3011,\cdot)\) \(\chi_{5265}(3206,\cdot)\) \(\chi_{5265}(3281,\cdot)\) \(\chi_{5265}(3476,\cdot)\) \(\chi_{5265}(3596,\cdot)\) \(\chi_{5265}(3791,\cdot)\) \(\chi_{5265}(3866,\cdot)\) \(\chi_{5265}(4061,\cdot)\) \(\chi_{5265}(4181,\cdot)\) \(\chi_{5265}(4376,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((326,2107,2836)\) → \((e\left(\frac{23}{54}\right),1,i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 5265 }(86, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{108}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{61}{108}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{31}{108}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{26}{27}\right)\) |