Basic properties
| Modulus: | \(8670\) | |
| Conductor: | \(867\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{867}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8670.cq
\(\chi_{8670}(11,\cdot)\) \(\chi_{8670}(41,\cdot)\) \(\chi_{8670}(71,\cdot)\) \(\chi_{8670}(311,\cdot)\) \(\chi_{8670}(371,\cdot)\) \(\chi_{8670}(401,\cdot)\) \(\chi_{8670}(431,\cdot)\) \(\chi_{8670}(521,\cdot)\) \(\chi_{8670}(551,\cdot)\) \(\chi_{8670}(581,\cdot)\) \(\chi_{8670}(641,\cdot)\) \(\chi_{8670}(821,\cdot)\) \(\chi_{8670}(881,\cdot)\) \(\chi_{8670}(911,\cdot)\) \(\chi_{8670}(941,\cdot)\) \(\chi_{8670}(1031,\cdot)\) \(\chi_{8670}(1061,\cdot)\) \(\chi_{8670}(1151,\cdot)\) \(\chi_{8670}(1331,\cdot)\) \(\chi_{8670}(1391,\cdot)\) \(\chi_{8670}(1421,\cdot)\) \(\chi_{8670}(1451,\cdot)\) \(\chi_{8670}(1541,\cdot)\) \(\chi_{8670}(1571,\cdot)\) \(\chi_{8670}(1601,\cdot)\) \(\chi_{8670}(1661,\cdot)\) \(\chi_{8670}(1841,\cdot)\) \(\chi_{8670}(1901,\cdot)\) \(\chi_{8670}(1931,\cdot)\) \(\chi_{8670}(1961,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((2891,6937,6361)\) → \((-1,1,e\left(\frac{23}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8670 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{272}\right)\) | \(e\left(\frac{121}{272}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{25}{136}\right)\) | \(e\left(\frac{97}{272}\right)\) | \(e\left(\frac{19}{272}\right)\) | \(e\left(\frac{207}{272}\right)\) | \(e\left(\frac{247}{272}\right)\) | \(e\left(\frac{261}{272}\right)\) | \(e\left(\frac{15}{136}\right)\) |