Basic properties
| Modulus: | \(8046\) | |
| Conductor: | \(4023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1332\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4023}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8046.bi
\(\chi_{8046}(11,\cdot)\) \(\chi_{8046}(23,\cdot)\) \(\chi_{8046}(41,\cdot)\) \(\chi_{8046}(59,\cdot)\) \(\chi_{8046}(65,\cdot)\) \(\chi_{8046}(77,\cdot)\) \(\chi_{8046}(83,\cdot)\) \(\chi_{8046}(101,\cdot)\) \(\chi_{8046}(131,\cdot)\) \(\chi_{8046}(137,\cdot)\) \(\chi_{8046}(167,\cdot)\) \(\chi_{8046}(209,\cdot)\) \(\chi_{8046}(221,\cdot)\) \(\chi_{8046}(227,\cdot)\) \(\chi_{8046}(239,\cdot)\) \(\chi_{8046}(257,\cdot)\) \(\chi_{8046}(275,\cdot)\) \(\chi_{8046}(311,\cdot)\) \(\chi_{8046}(353,\cdot)\) \(\chi_{8046}(389,\cdot)\) \(\chi_{8046}(407,\cdot)\) \(\chi_{8046}(437,\cdot)\) \(\chi_{8046}(455,\cdot)\) \(\chi_{8046}(461,\cdot)\) \(\chi_{8046}(479,\cdot)\) \(\chi_{8046}(497,\cdot)\) \(\chi_{8046}(509,\cdot)\) \(\chi_{8046}(545,\cdot)\) \(\chi_{8046}(569,\cdot)\) \(\chi_{8046}(581,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1332})$ |
| Fixed field: | Number field defined by a degree 1332 polynomial (not computed) |
Values on generators
\((299,3727)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{109}{148}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 8046 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{137}{666}\right)\) | \(e\left(\frac{91}{666}\right)\) | \(e\left(\frac{887}{1332}\right)\) | \(e\left(\frac{1081}{1332}\right)\) | \(e\left(\frac{35}{222}\right)\) | \(e\left(\frac{59}{111}\right)\) | \(e\left(\frac{1213}{1332}\right)\) | \(e\left(\frac{137}{333}\right)\) | \(e\left(\frac{67}{666}\right)\) | \(e\left(\frac{220}{333}\right)\) |