Basic properties
| Modulus: | \(3750\) | |
| 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 3750.r
\(\chi_{3750}(107,\cdot)\) \(\chi_{3750}(143,\cdot)\) \(\chi_{3750}(257,\cdot)\) \(\chi_{3750}(293,\cdot)\) \(\chi_{3750}(407,\cdot)\) \(\chi_{3750}(593,\cdot)\) \(\chi_{3750}(707,\cdot)\) \(\chi_{3750}(743,\cdot)\) \(\chi_{3750}(857,\cdot)\) \(\chi_{3750}(893,\cdot)\) \(\chi_{3750}(1007,\cdot)\) \(\chi_{3750}(1043,\cdot)\) \(\chi_{3750}(1157,\cdot)\) \(\chi_{3750}(1343,\cdot)\) \(\chi_{3750}(1457,\cdot)\) \(\chi_{3750}(1493,\cdot)\) \(\chi_{3750}(1607,\cdot)\) \(\chi_{3750}(1643,\cdot)\) \(\chi_{3750}(1757,\cdot)\) \(\chi_{3750}(1793,\cdot)\) \(\chi_{3750}(1907,\cdot)\) \(\chi_{3750}(2093,\cdot)\) \(\chi_{3750}(2207,\cdot)\) \(\chi_{3750}(2243,\cdot)\) \(\chi_{3750}(2357,\cdot)\) \(\chi_{3750}(2393,\cdot)\) \(\chi_{3750}(2507,\cdot)\) \(\chi_{3750}(2543,\cdot)\) \(\chi_{3750}(2657,\cdot)\) \(\chi_{3750}(2843,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((2501,3127)\) → \((-1,e\left(\frac{33}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3750 }(857, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{87}{100}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{1}{50}\right)\) |