Basic properties
| Modulus: | \(6018\) | |
| Conductor: | \(3009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(464\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3009}(65,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.bm
\(\chi_{6018}(11,\cdot)\) \(\chi_{6018}(23,\cdot)\) \(\chi_{6018}(65,\cdot)\) \(\chi_{6018}(113,\cdot)\) \(\chi_{6018}(131,\cdot)\) \(\chi_{6018}(173,\cdot)\) \(\chi_{6018}(209,\cdot)\) \(\chi_{6018}(215,\cdot)\) \(\chi_{6018}(227,\cdot)\) \(\chi_{6018}(233,\cdot)\) \(\chi_{6018}(269,\cdot)\) \(\chi_{6018}(275,\cdot)\) \(\chi_{6018}(329,\cdot)\) \(\chi_{6018}(335,\cdot)\) \(\chi_{6018}(347,\cdot)\) \(\chi_{6018}(377,\cdot)\) \(\chi_{6018}(401,\cdot)\) \(\chi_{6018}(419,\cdot)\) \(\chi_{6018}(431,\cdot)\) \(\chi_{6018}(437,\cdot)\) \(\chi_{6018}(503,\cdot)\) \(\chi_{6018}(515,\cdot)\) \(\chi_{6018}(533,\cdot)\) \(\chi_{6018}(539,\cdot)\) \(\chi_{6018}(575,\cdot)\) \(\chi_{6018}(581,\cdot)\) \(\chi_{6018}(623,\cdot)\) \(\chi_{6018}(683,\cdot)\) \(\chi_{6018}(719,\cdot)\) \(\chi_{6018}(755,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{464})$ |
| Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((4013,1771,1123)\) → \((-1,e\left(\frac{9}{16}\right),e\left(\frac{51}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6018 }(65, a) \) | \(-1\) | \(1\) | \(e\left(\frac{273}{464}\right)\) | \(e\left(\frac{7}{464}\right)\) | \(e\left(\frac{195}{464}\right)\) | \(e\left(\frac{95}{116}\right)\) | \(e\left(\frac{67}{232}\right)\) | \(e\left(\frac{59}{464}\right)\) | \(e\left(\frac{41}{232}\right)\) | \(e\left(\frac{201}{464}\right)\) | \(e\left(\frac{69}{464}\right)\) | \(e\left(\frac{35}{58}\right)\) |