Basic properties
| Modulus: | \(6815\) | |
| Conductor: | \(1363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(322\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1363}(6,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6815.cl
\(\chi_{6815}(6,\cdot)\) \(\chi_{6815}(51,\cdot)\) \(\chi_{6815}(71,\cdot)\) \(\chi_{6815}(96,\cdot)\) \(\chi_{6815}(121,\cdot)\) \(\chi_{6815}(196,\cdot)\) \(\chi_{6815}(216,\cdot)\) \(\chi_{6815}(241,\cdot)\) \(\chi_{6815}(296,\cdot)\) \(\chi_{6815}(341,\cdot)\) \(\chi_{6815}(361,\cdot)\) \(\chi_{6815}(441,\cdot)\) \(\chi_{6815}(486,\cdot)\) \(\chi_{6815}(506,\cdot)\) \(\chi_{6815}(526,\cdot)\) \(\chi_{6815}(531,\cdot)\) \(\chi_{6815}(676,\cdot)\) \(\chi_{6815}(776,\cdot)\) \(\chi_{6815}(816,\cdot)\) \(\chi_{6815}(921,\cdot)\) \(\chi_{6815}(961,\cdot)\) \(\chi_{6815}(991,\cdot)\) \(\chi_{6815}(1021,\cdot)\) \(\chi_{6815}(1066,\cdot)\) \(\chi_{6815}(1106,\cdot)\) \(\chi_{6815}(1136,\cdot)\) \(\chi_{6815}(1211,\cdot)\) \(\chi_{6815}(1231,\cdot)\) \(\chi_{6815}(1256,\cdot)\) \(\chi_{6815}(1281,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{161})$ |
| Fixed field: | Number field defined by a degree 322 polynomial (not computed) |
Values on generators
\((2727,2351,146)\) → \((1,e\left(\frac{3}{14}\right),e\left(\frac{19}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6815 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{322}\right)\) | \(e\left(\frac{191}{322}\right)\) | \(e\left(\frac{27}{161}\right)\) | \(e\left(\frac{109}{161}\right)\) | \(e\left(\frac{1}{161}\right)\) | \(e\left(\frac{81}{322}\right)\) | \(e\left(\frac{30}{161}\right)\) | \(e\left(\frac{45}{322}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{152}{161}\right)\) |