Basic properties
| Modulus: | \(2500\) | |
| Conductor: | \(125\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{125}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2500.q
\(\chi_{2500}(93,\cdot)\) \(\chi_{2500}(157,\cdot)\) \(\chi_{2500}(257,\cdot)\) \(\chi_{2500}(293,\cdot)\) \(\chi_{2500}(357,\cdot)\) \(\chi_{2500}(393,\cdot)\) \(\chi_{2500}(457,\cdot)\) \(\chi_{2500}(493,\cdot)\) \(\chi_{2500}(593,\cdot)\) \(\chi_{2500}(657,\cdot)\) \(\chi_{2500}(757,\cdot)\) \(\chi_{2500}(793,\cdot)\) \(\chi_{2500}(857,\cdot)\) \(\chi_{2500}(893,\cdot)\) \(\chi_{2500}(957,\cdot)\) \(\chi_{2500}(993,\cdot)\) \(\chi_{2500}(1093,\cdot)\) \(\chi_{2500}(1157,\cdot)\) \(\chi_{2500}(1257,\cdot)\) \(\chi_{2500}(1293,\cdot)\) \(\chi_{2500}(1357,\cdot)\) \(\chi_{2500}(1393,\cdot)\) \(\chi_{2500}(1457,\cdot)\) \(\chi_{2500}(1493,\cdot)\) \(\chi_{2500}(1593,\cdot)\) \(\chi_{2500}(1657,\cdot)\) \(\chi_{2500}(1757,\cdot)\) \(\chi_{2500}(1793,\cdot)\) \(\chi_{2500}(1857,\cdot)\) \(\chi_{2500}(1893,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1251,1877)\) → \((1,e\left(\frac{31}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2500 }(93, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{51}{100}\right)\) |