Basic properties
| Modulus: | \(750\) | |
| 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 \(\chi_{125}(103,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 750.q
\(\chi_{750}(13,\cdot)\) \(\chi_{750}(37,\cdot)\) \(\chi_{750}(67,\cdot)\) \(\chi_{750}(73,\cdot)\) \(\chi_{750}(97,\cdot)\) \(\chi_{750}(103,\cdot)\) \(\chi_{750}(127,\cdot)\) \(\chi_{750}(133,\cdot)\) \(\chi_{750}(163,\cdot)\) \(\chi_{750}(187,\cdot)\) \(\chi_{750}(217,\cdot)\) \(\chi_{750}(223,\cdot)\) \(\chi_{750}(247,\cdot)\) \(\chi_{750}(253,\cdot)\) \(\chi_{750}(277,\cdot)\) \(\chi_{750}(283,\cdot)\) \(\chi_{750}(313,\cdot)\) \(\chi_{750}(337,\cdot)\) \(\chi_{750}(367,\cdot)\) \(\chi_{750}(373,\cdot)\) \(\chi_{750}(397,\cdot)\) \(\chi_{750}(403,\cdot)\) \(\chi_{750}(427,\cdot)\) \(\chi_{750}(433,\cdot)\) \(\chi_{750}(463,\cdot)\) \(\chi_{750}(487,\cdot)\) \(\chi_{750}(517,\cdot)\) \(\chi_{750}(523,\cdot)\) \(\chi_{750}(547,\cdot)\) \(\chi_{750}(553,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((251,127)\) → \((1,e\left(\frac{27}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 750 }(103, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{83}{100}\right)\) | \(e\left(\frac{22}{25}\right)\) |