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 \(\chi_{1600}(269,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9600.fx
\(\chi_{9600}(169,\cdot)\) \(\chi_{9600}(409,\cdot)\) \(\chi_{9600}(889,\cdot)\) \(\chi_{9600}(1129,\cdot)\) \(\chi_{9600}(1369,\cdot)\) \(\chi_{9600}(1609,\cdot)\) \(\chi_{9600}(2089,\cdot)\) \(\chi_{9600}(2329,\cdot)\) \(\chi_{9600}(2569,\cdot)\) \(\chi_{9600}(2809,\cdot)\) \(\chi_{9600}(3289,\cdot)\) \(\chi_{9600}(3529,\cdot)\) \(\chi_{9600}(3769,\cdot)\) \(\chi_{9600}(4009,\cdot)\) \(\chi_{9600}(4489,\cdot)\) \(\chi_{9600}(4729,\cdot)\) \(\chi_{9600}(4969,\cdot)\) \(\chi_{9600}(5209,\cdot)\) \(\chi_{9600}(5689,\cdot)\) \(\chi_{9600}(5929,\cdot)\) \(\chi_{9600}(6169,\cdot)\) \(\chi_{9600}(6409,\cdot)\) \(\chi_{9600}(6889,\cdot)\) \(\chi_{9600}(7129,\cdot)\) \(\chi_{9600}(7369,\cdot)\) \(\chi_{9600}(7609,\cdot)\) \(\chi_{9600}(8089,\cdot)\) \(\chi_{9600}(8329,\cdot)\) \(\chi_{9600}(8569,\cdot)\) \(\chi_{9600}(8809,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4351,901,6401,5377)\) → \((1,e\left(\frac{15}{16}\right),1,e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9600 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{29}{40}\right)\) |