Basic properties
| Modulus: | \(1125\) | |
| 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 \(\chi_{125}(97,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1125.bd
\(\chi_{1125}(28,\cdot)\) \(\chi_{1125}(37,\cdot)\) \(\chi_{1125}(73,\cdot)\) \(\chi_{1125}(127,\cdot)\) \(\chi_{1125}(163,\cdot)\) \(\chi_{1125}(172,\cdot)\) \(\chi_{1125}(208,\cdot)\) \(\chi_{1125}(217,\cdot)\) \(\chi_{1125}(253,\cdot)\) \(\chi_{1125}(262,\cdot)\) \(\chi_{1125}(298,\cdot)\) \(\chi_{1125}(352,\cdot)\) \(\chi_{1125}(388,\cdot)\) \(\chi_{1125}(397,\cdot)\) \(\chi_{1125}(433,\cdot)\) \(\chi_{1125}(442,\cdot)\) \(\chi_{1125}(478,\cdot)\) \(\chi_{1125}(487,\cdot)\) \(\chi_{1125}(523,\cdot)\) \(\chi_{1125}(577,\cdot)\) \(\chi_{1125}(613,\cdot)\) \(\chi_{1125}(622,\cdot)\) \(\chi_{1125}(658,\cdot)\) \(\chi_{1125}(667,\cdot)\) \(\chi_{1125}(703,\cdot)\) \(\chi_{1125}(712,\cdot)\) \(\chi_{1125}(748,\cdot)\) \(\chi_{1125}(802,\cdot)\) \(\chi_{1125}(838,\cdot)\) \(\chi_{1125}(847,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1001,127)\) → \((1,e\left(\frac{37}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1125 }(847, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{33}{50}\right)\) |