Basic properties
| Modulus: | \(4000\) | |
| 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 4000.cq
\(\chi_{4000}(33,\cdot)\) \(\chi_{4000}(97,\cdot)\) \(\chi_{4000}(353,\cdot)\) \(\chi_{4000}(417,\cdot)\) \(\chi_{4000}(513,\cdot)\) \(\chi_{4000}(577,\cdot)\) \(\chi_{4000}(673,\cdot)\) \(\chi_{4000}(737,\cdot)\) \(\chi_{4000}(833,\cdot)\) \(\chi_{4000}(897,\cdot)\) \(\chi_{4000}(1153,\cdot)\) \(\chi_{4000}(1217,\cdot)\) \(\chi_{4000}(1313,\cdot)\) \(\chi_{4000}(1377,\cdot)\) \(\chi_{4000}(1473,\cdot)\) \(\chi_{4000}(1537,\cdot)\) \(\chi_{4000}(1633,\cdot)\) \(\chi_{4000}(1697,\cdot)\) \(\chi_{4000}(1953,\cdot)\) \(\chi_{4000}(2017,\cdot)\) \(\chi_{4000}(2113,\cdot)\) \(\chi_{4000}(2177,\cdot)\) \(\chi_{4000}(2273,\cdot)\) \(\chi_{4000}(2337,\cdot)\) \(\chi_{4000}(2433,\cdot)\) \(\chi_{4000}(2497,\cdot)\) \(\chi_{4000}(2753,\cdot)\) \(\chi_{4000}(2817,\cdot)\) \(\chi_{4000}(2913,\cdot)\) \(\chi_{4000}(2977,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((2751,2501,1377)\) → \((1,1,e\left(\frac{37}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 4000 }(97, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{77}{100}\right)\) |