Basic properties
Modulus: | \(7500\) | |
Conductor: | \(375\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{375}(92,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7500.bi
\(\chi_{7500}(257,\cdot)\) \(\chi_{7500}(293,\cdot)\) \(\chi_{7500}(593,\cdot)\) \(\chi_{7500}(857,\cdot)\) \(\chi_{7500}(893,\cdot)\) \(\chi_{7500}(1157,\cdot)\) \(\chi_{7500}(1457,\cdot)\) \(\chi_{7500}(1493,\cdot)\) \(\chi_{7500}(1757,\cdot)\) \(\chi_{7500}(1793,\cdot)\) \(\chi_{7500}(2093,\cdot)\) \(\chi_{7500}(2357,\cdot)\) \(\chi_{7500}(2393,\cdot)\) \(\chi_{7500}(2657,\cdot)\) \(\chi_{7500}(2957,\cdot)\) \(\chi_{7500}(2993,\cdot)\) \(\chi_{7500}(3257,\cdot)\) \(\chi_{7500}(3293,\cdot)\) \(\chi_{7500}(3593,\cdot)\) \(\chi_{7500}(3857,\cdot)\) \(\chi_{7500}(3893,\cdot)\) \(\chi_{7500}(4157,\cdot)\) \(\chi_{7500}(4457,\cdot)\) \(\chi_{7500}(4493,\cdot)\) \(\chi_{7500}(4757,\cdot)\) \(\chi_{7500}(4793,\cdot)\) \(\chi_{7500}(5093,\cdot)\) \(\chi_{7500}(5357,\cdot)\) \(\chi_{7500}(5393,\cdot)\) \(\chi_{7500}(5657,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((3751,2501,6877)\) → \((1,-1,e\left(\frac{33}{100}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7500 }(857, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{87}{100}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{1}{50}\right)\) |