Basic properties
| Modulus: | \(9600\) | |
| Conductor: | \(4800\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4800}(2237,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9600.fq
\(\chi_{9600}(137,\cdot)\) \(\chi_{9600}(473,\cdot)\) \(\chi_{9600}(617,\cdot)\) \(\chi_{9600}(953,\cdot)\) \(\chi_{9600}(1097,\cdot)\) \(\chi_{9600}(1433,\cdot)\) \(\chi_{9600}(1577,\cdot)\) \(\chi_{9600}(1913,\cdot)\) \(\chi_{9600}(2537,\cdot)\) \(\chi_{9600}(2873,\cdot)\) \(\chi_{9600}(3017,\cdot)\) \(\chi_{9600}(3353,\cdot)\) \(\chi_{9600}(3497,\cdot)\) \(\chi_{9600}(3833,\cdot)\) \(\chi_{9600}(3977,\cdot)\) \(\chi_{9600}(4313,\cdot)\) \(\chi_{9600}(4937,\cdot)\) \(\chi_{9600}(5273,\cdot)\) \(\chi_{9600}(5417,\cdot)\) \(\chi_{9600}(5753,\cdot)\) \(\chi_{9600}(5897,\cdot)\) \(\chi_{9600}(6233,\cdot)\) \(\chi_{9600}(6377,\cdot)\) \(\chi_{9600}(6713,\cdot)\) \(\chi_{9600}(7337,\cdot)\) \(\chi_{9600}(7673,\cdot)\) \(\chi_{9600}(7817,\cdot)\) \(\chi_{9600}(8153,\cdot)\) \(\chi_{9600}(8297,\cdot)\) \(\chi_{9600}(8633,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4351,901,6401,5377)\) → \((1,e\left(\frac{3}{16}\right),-1,e\left(\frac{9}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9600 }(137, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{37}{40}\right)\) |