Basic properties
| Modulus: | \(3380\) | |
| Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{676}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3380.ci
\(\chi_{3380}(31,\cdot)\) \(\chi_{3380}(151,\cdot)\) \(\chi_{3380}(291,\cdot)\) \(\chi_{3380}(411,\cdot)\) \(\chi_{3380}(551,\cdot)\) \(\chi_{3380}(671,\cdot)\) \(\chi_{3380}(811,\cdot)\) \(\chi_{3380}(931,\cdot)\) \(\chi_{3380}(1071,\cdot)\) \(\chi_{3380}(1191,\cdot)\) \(\chi_{3380}(1331,\cdot)\) \(\chi_{3380}(1711,\cdot)\) \(\chi_{3380}(1851,\cdot)\) \(\chi_{3380}(1971,\cdot)\) \(\chi_{3380}(2111,\cdot)\) \(\chi_{3380}(2231,\cdot)\) \(\chi_{3380}(2371,\cdot)\) \(\chi_{3380}(2491,\cdot)\) \(\chi_{3380}(2631,\cdot)\) \(\chi_{3380}(2751,\cdot)\) \(\chi_{3380}(2891,\cdot)\) \(\chi_{3380}(3011,\cdot)\) \(\chi_{3380}(3151,\cdot)\) \(\chi_{3380}(3271,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1691,677,1861)\) → \((-1,1,e\left(\frac{7}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3380 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(i\) | \(e\left(\frac{5}{52}\right)\) | \(1\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{5}{13}\right)\) |