Basic properties
| Modulus: | \(7600\) | |
| Conductor: | \(7600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7600.jf
\(\chi_{7600}(61,\cdot)\) \(\chi_{7600}(461,\cdot)\) \(\chi_{7600}(541,\cdot)\) \(\chi_{7600}(821,\cdot)\) \(\chi_{7600}(861,\cdot)\) \(\chi_{7600}(1061,\cdot)\) \(\chi_{7600}(1221,\cdot)\) \(\chi_{7600}(1461,\cdot)\) \(\chi_{7600}(1581,\cdot)\) \(\chi_{7600}(1621,\cdot)\) \(\chi_{7600}(1821,\cdot)\) \(\chi_{7600}(1981,\cdot)\) \(\chi_{7600}(2061,\cdot)\) \(\chi_{7600}(2221,\cdot)\) \(\chi_{7600}(2341,\cdot)\) \(\chi_{7600}(2381,\cdot)\) \(\chi_{7600}(2581,\cdot)\) \(\chi_{7600}(2741,\cdot)\) \(\chi_{7600}(2821,\cdot)\) \(\chi_{7600}(2981,\cdot)\) \(\chi_{7600}(3141,\cdot)\) \(\chi_{7600}(3341,\cdot)\) \(\chi_{7600}(3581,\cdot)\) \(\chi_{7600}(3741,\cdot)\) \(\chi_{7600}(3861,\cdot)\) \(\chi_{7600}(4261,\cdot)\) \(\chi_{7600}(4341,\cdot)\) \(\chi_{7600}(4621,\cdot)\) \(\chi_{7600}(4661,\cdot)\) \(\chi_{7600}(4861,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4751,5701,5777,401)\) → \((1,-i,e\left(\frac{4}{5}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 7600 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{180}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{83}{180}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{133}{180}\right)\) |