Basic properties
| Modulus: | \(9600\) | |
| Conductor: | \(1600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1600}(821,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9600.fz
\(\chi_{9600}(121,\cdot)\) \(\chi_{9600}(361,\cdot)\) \(\chi_{9600}(841,\cdot)\) \(\chi_{9600}(1081,\cdot)\) \(\chi_{9600}(1321,\cdot)\) \(\chi_{9600}(1561,\cdot)\) \(\chi_{9600}(2041,\cdot)\) \(\chi_{9600}(2281,\cdot)\) \(\chi_{9600}(2521,\cdot)\) \(\chi_{9600}(2761,\cdot)\) \(\chi_{9600}(3241,\cdot)\) \(\chi_{9600}(3481,\cdot)\) \(\chi_{9600}(3721,\cdot)\) \(\chi_{9600}(3961,\cdot)\) \(\chi_{9600}(4441,\cdot)\) \(\chi_{9600}(4681,\cdot)\) \(\chi_{9600}(4921,\cdot)\) \(\chi_{9600}(5161,\cdot)\) \(\chi_{9600}(5641,\cdot)\) \(\chi_{9600}(5881,\cdot)\) \(\chi_{9600}(6121,\cdot)\) \(\chi_{9600}(6361,\cdot)\) \(\chi_{9600}(6841,\cdot)\) \(\chi_{9600}(7081,\cdot)\) \(\chi_{9600}(7321,\cdot)\) \(\chi_{9600}(7561,\cdot)\) \(\chi_{9600}(8041,\cdot)\) \(\chi_{9600}(8281,\cdot)\) \(\chi_{9600}(8521,\cdot)\) \(\chi_{9600}(8761,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4351,901,6401,5377)\) → \((1,e\left(\frac{5}{16}\right),1,e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9600 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{31}{40}\right)\) |