Basic properties
| Modulus: | \(987696\) | |
| Conductor: | \(987696\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4332\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 987696.si
\(\chi_{987696}(77,\cdot)\) \(\chi_{987696}(533,\cdot)\) \(\chi_{987696}(1901,\cdot)\) \(\chi_{987696}(2813,\cdot)\) \(\chi_{987696}(3269,\cdot)\) \(\chi_{987696}(4181,\cdot)\) \(\chi_{987696}(4637,\cdot)\) \(\chi_{987696}(5549,\cdot)\) \(\chi_{987696}(6005,\cdot)\) \(\chi_{987696}(6917,\cdot)\) \(\chi_{987696}(7373,\cdot)\) \(\chi_{987696}(8285,\cdot)\) \(\chi_{987696}(8741,\cdot)\) \(\chi_{987696}(9653,\cdot)\) \(\chi_{987696}(11021,\cdot)\) \(\chi_{987696}(11477,\cdot)\) \(\chi_{987696}(12389,\cdot)\) \(\chi_{987696}(12845,\cdot)\) \(\chi_{987696}(13757,\cdot)\) \(\chi_{987696}(14213,\cdot)\) \(\chi_{987696}(15125,\cdot)\) \(\chi_{987696}(15581,\cdot)\) \(\chi_{987696}(16493,\cdot)\) \(\chi_{987696}(16949,\cdot)\) \(\chi_{987696}(17861,\cdot)\) \(\chi_{987696}(18317,\cdot)\) \(\chi_{987696}(19229,\cdot)\) \(\chi_{987696}(19685,\cdot)\) \(\chi_{987696}(20597,\cdot)\) \(\chi_{987696}(21053,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{4332})$ |
| Fixed field: | Number field defined by a degree 4332 polynomial (not computed) |
Values on generators
\((617311,740773,438977,857377)\) → \((1,-i,e\left(\frac{5}{6}\right),e\left(\frac{356}{361}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 987696 }(77, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1679}{4332}\right)\) | \(e\left(\frac{41}{2166}\right)\) | \(e\left(\frac{2791}{4332}\right)\) | \(e\left(\frac{1331}{4332}\right)\) | \(e\left(\frac{77}{722}\right)\) | \(e\left(\frac{584}{1083}\right)\) | \(e\left(\frac{1679}{2166}\right)\) | \(e\left(\frac{709}{4332}\right)\) | \(e\left(\frac{680}{1083}\right)\) | \(e\left(\frac{587}{1444}\right)\) |