Basic properties
| Modulus: | \(7600\) | |
| Conductor: | \(3800\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3800}(1923,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7600.iy
\(\chi_{7600}(23,\cdot)\) \(\chi_{7600}(263,\cdot)\) \(\chi_{7600}(327,\cdot)\) \(\chi_{7600}(423,\cdot)\) \(\chi_{7600}(503,\cdot)\) \(\chi_{7600}(567,\cdot)\) \(\chi_{7600}(663,\cdot)\) \(\chi_{7600}(727,\cdot)\) \(\chi_{7600}(823,\cdot)\) \(\chi_{7600}(967,\cdot)\) \(\chi_{7600}(1127,\cdot)\) \(\chi_{7600}(1783,\cdot)\) \(\chi_{7600}(1847,\cdot)\) \(\chi_{7600}(2023,\cdot)\) \(\chi_{7600}(2087,\cdot)\) \(\chi_{7600}(2183,\cdot)\) \(\chi_{7600}(2247,\cdot)\) \(\chi_{7600}(2327,\cdot)\) \(\chi_{7600}(2487,\cdot)\) \(\chi_{7600}(2647,\cdot)\) \(\chi_{7600}(3063,\cdot)\) \(\chi_{7600}(3303,\cdot)\) \(\chi_{7600}(3367,\cdot)\) \(\chi_{7600}(3463,\cdot)\) \(\chi_{7600}(3703,\cdot)\) \(\chi_{7600}(3767,\cdot)\) \(\chi_{7600}(3847,\cdot)\) \(\chi_{7600}(3863,\cdot)\) \(\chi_{7600}(4167,\cdot)\) \(\chi_{7600}(4583,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4751,5701,5777,401)\) → \((-1,-1,e\left(\frac{11}{20}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 7600 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{180}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{47}{180}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{139}{180}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{22}{45}\right)\) |