Basic properties
| Modulus: | \(987696\) | |
| Conductor: | \(61731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{61731}(40577,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 987696.ql
\(\chi_{987696}(65,\cdot)\) \(\chi_{987696}(2273,\cdot)\) \(\chi_{987696}(2801,\cdot)\) \(\chi_{987696}(5009,\cdot)\) \(\chi_{987696}(5537,\cdot)\) \(\chi_{987696}(7745,\cdot)\) \(\chi_{987696}(8273,\cdot)\) \(\chi_{987696}(10481,\cdot)\) \(\chi_{987696}(11009,\cdot)\) \(\chi_{987696}(13217,\cdot)\) \(\chi_{987696}(13745,\cdot)\) \(\chi_{987696}(16481,\cdot)\) \(\chi_{987696}(18689,\cdot)\) \(\chi_{987696}(19217,\cdot)\) \(\chi_{987696}(21425,\cdot)\) \(\chi_{987696}(24161,\cdot)\) \(\chi_{987696}(24689,\cdot)\) \(\chi_{987696}(26897,\cdot)\) \(\chi_{987696}(27425,\cdot)\) \(\chi_{987696}(29633,\cdot)\) \(\chi_{987696}(30161,\cdot)\) \(\chi_{987696}(32369,\cdot)\) \(\chi_{987696}(32897,\cdot)\) \(\chi_{987696}(35105,\cdot)\) \(\chi_{987696}(35633,\cdot)\) \(\chi_{987696}(37841,\cdot)\) \(\chi_{987696}(38369,\cdot)\) \(\chi_{987696}(40577,\cdot)\) \(\chi_{987696}(41105,\cdot)\) \(\chi_{987696}(43313,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1083})$ |
| Fixed field: | Number field defined by a degree 2166 polynomial (not computed) |
Values on generators
\((617311,740773,438977,857377)\) → \((1,1,e\left(\frac{5}{6}\right),e\left(\frac{197}{2166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 987696 }(40577, a) \) | \(1\) | \(1\) | \(e\left(\frac{535}{722}\right)\) | \(e\left(\frac{88}{1083}\right)\) | \(e\left(\frac{1949}{2166}\right)\) | \(e\left(\frac{365}{2166}\right)\) | \(e\left(\frac{2057}{2166}\right)\) | \(e\left(\frac{1307}{2166}\right)\) | \(e\left(\frac{174}{361}\right)\) | \(e\left(\frac{327}{361}\right)\) | \(e\left(\frac{1057}{2166}\right)\) | \(e\left(\frac{1781}{2166}\right)\) |