Basic properties
| Modulus: | \(6534\) | |
| Conductor: | \(3267\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(99\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3267}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6534.bh
\(\chi_{6534}(67,\cdot)\) \(\chi_{6534}(133,\cdot)\) \(\chi_{6534}(265,\cdot)\) \(\chi_{6534}(331,\cdot)\) \(\chi_{6534}(463,\cdot)\) \(\chi_{6534}(529,\cdot)\) \(\chi_{6534}(661,\cdot)\) \(\chi_{6534}(859,\cdot)\) \(\chi_{6534}(925,\cdot)\) \(\chi_{6534}(1057,\cdot)\) \(\chi_{6534}(1123,\cdot)\) \(\chi_{6534}(1255,\cdot)\) \(\chi_{6534}(1321,\cdot)\) \(\chi_{6534}(1519,\cdot)\) \(\chi_{6534}(1651,\cdot)\) \(\chi_{6534}(1717,\cdot)\) \(\chi_{6534}(1849,\cdot)\) \(\chi_{6534}(1915,\cdot)\) \(\chi_{6534}(2047,\cdot)\) \(\chi_{6534}(2113,\cdot)\) \(\chi_{6534}(2245,\cdot)\) \(\chi_{6534}(2311,\cdot)\) \(\chi_{6534}(2443,\cdot)\) \(\chi_{6534}(2509,\cdot)\) \(\chi_{6534}(2641,\cdot)\) \(\chi_{6534}(2707,\cdot)\) \(\chi_{6534}(2839,\cdot)\) \(\chi_{6534}(3037,\cdot)\) \(\chi_{6534}(3103,\cdot)\) \(\chi_{6534}(3235,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{99})$ |
| Fixed field: | Number field defined by a degree 99 polynomial |
Values on generators
\((6293,3511)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{10}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6534 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{99}\right)\) | \(e\left(\frac{47}{99}\right)\) | \(e\left(\frac{37}{99}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{52}{99}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{89}{99}\right)\) | \(e\left(\frac{7}{99}\right)\) | \(e\left(\frac{32}{33}\right)\) |