Basic properties
| Modulus: | \(5780\) | |
| Conductor: | \(1445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1445}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5780.cn
\(\chi_{5780}(37,\cdot)\) \(\chi_{5780}(97,\cdot)\) \(\chi_{5780}(113,\cdot)\) \(\chi_{5780}(193,\cdot)\) \(\chi_{5780}(277,\cdot)\) \(\chi_{5780}(313,\cdot)\) \(\chi_{5780}(333,\cdot)\) \(\chi_{5780}(337,\cdot)\) \(\chi_{5780}(377,\cdot)\) \(\chi_{5780}(437,\cdot)\) \(\chi_{5780}(453,\cdot)\) \(\chi_{5780}(533,\cdot)\) \(\chi_{5780}(617,\cdot)\) \(\chi_{5780}(673,\cdot)\) \(\chi_{5780}(677,\cdot)\) \(\chi_{5780}(717,\cdot)\) \(\chi_{5780}(777,\cdot)\) \(\chi_{5780}(793,\cdot)\) \(\chi_{5780}(873,\cdot)\) \(\chi_{5780}(957,\cdot)\) \(\chi_{5780}(993,\cdot)\) \(\chi_{5780}(1013,\cdot)\) \(\chi_{5780}(1017,\cdot)\) \(\chi_{5780}(1057,\cdot)\) \(\chi_{5780}(1117,\cdot)\) \(\chi_{5780}(1133,\cdot)\) \(\chi_{5780}(1213,\cdot)\) \(\chi_{5780}(1297,\cdot)\) \(\chi_{5780}(1333,\cdot)\) \(\chi_{5780}(1353,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((2891,1157,581)\) → \((1,i,e\left(\frac{129}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 5780 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{272}\right)\) | \(e\left(\frac{207}{272}\right)\) | \(e\left(\frac{61}{136}\right)\) | \(e\left(\frac{247}{272}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{139}{272}\right)\) | \(e\left(\frac{183}{272}\right)\) | \(e\left(\frac{213}{272}\right)\) |