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.iu
\(\chi_{7600}(13,\cdot)\) \(\chi_{7600}(117,\cdot)\) \(\chi_{7600}(173,\cdot)\) \(\chi_{7600}(333,\cdot)\) \(\chi_{7600}(413,\cdot)\) \(\chi_{7600}(573,\cdot)\) \(\chi_{7600}(813,\cdot)\) \(\chi_{7600}(1077,\cdot)\) \(\chi_{7600}(1237,\cdot)\) \(\chi_{7600}(1397,\cdot)\) \(\chi_{7600}(1477,\cdot)\) \(\chi_{7600}(1533,\cdot)\) \(\chi_{7600}(1637,\cdot)\) \(\chi_{7600}(1853,\cdot)\) \(\chi_{7600}(1877,\cdot)\) \(\chi_{7600}(1933,\cdot)\) \(\chi_{7600}(2333,\cdot)\) \(\chi_{7600}(2597,\cdot)\) \(\chi_{7600}(2917,\cdot)\) \(\chi_{7600}(2997,\cdot)\) \(\chi_{7600}(3053,\cdot)\) \(\chi_{7600}(3213,\cdot)\) \(\chi_{7600}(3373,\cdot)\) \(\chi_{7600}(3397,\cdot)\) \(\chi_{7600}(3453,\cdot)\) \(\chi_{7600}(3613,\cdot)\) \(\chi_{7600}(3853,\cdot)\) \(\chi_{7600}(4117,\cdot)\) \(\chi_{7600}(4277,\cdot)\) \(\chi_{7600}(4437,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4751,5701,5777,401)\) → \((1,-i,e\left(\frac{19}{20}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 7600 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{23}{180}\right)\) | \(e\left(\frac{77}{180}\right)\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{157}{180}\right)\) |