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.je
\(\chi_{7600}(59,\cdot)\) \(\chi_{7600}(219,\cdot)\) \(\chi_{7600}(459,\cdot)\) \(\chi_{7600}(659,\cdot)\) \(\chi_{7600}(819,\cdot)\) \(\chi_{7600}(979,\cdot)\) \(\chi_{7600}(1059,\cdot)\) \(\chi_{7600}(1219,\cdot)\) \(\chi_{7600}(1419,\cdot)\) \(\chi_{7600}(1459,\cdot)\) \(\chi_{7600}(1579,\cdot)\) \(\chi_{7600}(1739,\cdot)\) \(\chi_{7600}(1819,\cdot)\) \(\chi_{7600}(1979,\cdot)\) \(\chi_{7600}(2179,\cdot)\) \(\chi_{7600}(2219,\cdot)\) \(\chi_{7600}(2339,\cdot)\) \(\chi_{7600}(2579,\cdot)\) \(\chi_{7600}(2739,\cdot)\) \(\chi_{7600}(2939,\cdot)\) \(\chi_{7600}(2979,\cdot)\) \(\chi_{7600}(3259,\cdot)\) \(\chi_{7600}(3339,\cdot)\) \(\chi_{7600}(3739,\cdot)\) \(\chi_{7600}(3859,\cdot)\) \(\chi_{7600}(4019,\cdot)\) \(\chi_{7600}(4259,\cdot)\) \(\chi_{7600}(4459,\cdot)\) \(\chi_{7600}(4619,\cdot)\) \(\chi_{7600}(4779,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4751,5701,5777,401)\) → \((-1,i,e\left(\frac{7}{10}\right),e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 7600 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{157}{180}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{59}{180}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{127}{180}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{17}{180}\right)\) |