Basic properties
| Modulus: | \(1600\) | |
| Conductor: | \(1600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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 1600.cn
\(\chi_{1600}(13,\cdot)\) \(\chi_{1600}(37,\cdot)\) \(\chi_{1600}(117,\cdot)\) \(\chi_{1600}(173,\cdot)\) \(\chi_{1600}(197,\cdot)\) \(\chi_{1600}(253,\cdot)\) \(\chi_{1600}(277,\cdot)\) \(\chi_{1600}(333,\cdot)\) \(\chi_{1600}(413,\cdot)\) \(\chi_{1600}(437,\cdot)\) \(\chi_{1600}(517,\cdot)\) \(\chi_{1600}(573,\cdot)\) \(\chi_{1600}(597,\cdot)\) \(\chi_{1600}(653,\cdot)\) \(\chi_{1600}(677,\cdot)\) \(\chi_{1600}(733,\cdot)\) \(\chi_{1600}(813,\cdot)\) \(\chi_{1600}(837,\cdot)\) \(\chi_{1600}(917,\cdot)\) \(\chi_{1600}(973,\cdot)\) \(\chi_{1600}(997,\cdot)\) \(\chi_{1600}(1053,\cdot)\) \(\chi_{1600}(1077,\cdot)\) \(\chi_{1600}(1133,\cdot)\) \(\chi_{1600}(1213,\cdot)\) \(\chi_{1600}(1237,\cdot)\) \(\chi_{1600}(1317,\cdot)\) \(\chi_{1600}(1373,\cdot)\) \(\chi_{1600}(1397,\cdot)\) \(\chi_{1600}(1453,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1151,901,577)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{9}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1600 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{41}{80}\right)\) |