Basic properties
| Modulus: | \(987696\) | |
| Conductor: | \(61731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1083\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{61731}(41089,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 987696.pl
\(\chi_{987696}(49,\cdot)\) \(\chi_{987696}(2401,\cdot)\) \(\chi_{987696}(2785,\cdot)\) \(\chi_{987696}(5137,\cdot)\) \(\chi_{987696}(5521,\cdot)\) \(\chi_{987696}(8257,\cdot)\) \(\chi_{987696}(10609,\cdot)\) \(\chi_{987696}(10993,\cdot)\) \(\chi_{987696}(13345,\cdot)\) \(\chi_{987696}(13729,\cdot)\) \(\chi_{987696}(16081,\cdot)\) \(\chi_{987696}(16465,\cdot)\) \(\chi_{987696}(18817,\cdot)\) \(\chi_{987696}(21553,\cdot)\) \(\chi_{987696}(21937,\cdot)\) \(\chi_{987696}(24289,\cdot)\) \(\chi_{987696}(24673,\cdot)\) \(\chi_{987696}(27025,\cdot)\) \(\chi_{987696}(27409,\cdot)\) \(\chi_{987696}(29761,\cdot)\) \(\chi_{987696}(30145,\cdot)\) \(\chi_{987696}(32497,\cdot)\) \(\chi_{987696}(32881,\cdot)\) \(\chi_{987696}(35233,\cdot)\) \(\chi_{987696}(35617,\cdot)\) \(\chi_{987696}(37969,\cdot)\) \(\chi_{987696}(38353,\cdot)\) \(\chi_{987696}(40705,\cdot)\) \(\chi_{987696}(41089,\cdot)\) \(\chi_{987696}(43441,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1083})$ |
| Fixed field: | Number field defined by a degree 1083 polynomial (not computed) |
Values on generators
\((617311,740773,438977,857377)\) → \((1,1,e\left(\frac{1}{3}\right),e\left(\frac{122}{1083}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 987696 }(41089, a) \) | \(1\) | \(1\) | \(e\left(\frac{184}{1083}\right)\) | \(e\left(\frac{820}{1083}\right)\) | \(e\left(\frac{835}{1083}\right)\) | \(e\left(\frac{225}{361}\right)\) | \(e\left(\frac{1010}{1083}\right)\) | \(e\left(\frac{326}{361}\right)\) | \(e\left(\frac{368}{1083}\right)\) | \(e\left(\frac{953}{1083}\right)\) | \(e\left(\frac{125}{1083}\right)\) | \(e\left(\frac{1004}{1083}\right)\) |