Basic properties
| Modulus: | \(5780\) | |
| Conductor: | \(1445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1445}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5780.ce
\(\chi_{5780}(9,\cdot)\) \(\chi_{5780}(49,\cdot)\) \(\chi_{5780}(189,\cdot)\) \(\chi_{5780}(229,\cdot)\) \(\chi_{5780}(349,\cdot)\) \(\chi_{5780}(389,\cdot)\) \(\chi_{5780}(529,\cdot)\) \(\chi_{5780}(569,\cdot)\) \(\chi_{5780}(689,\cdot)\) \(\chi_{5780}(729,\cdot)\) \(\chi_{5780}(869,\cdot)\) \(\chi_{5780}(909,\cdot)\) \(\chi_{5780}(1029,\cdot)\) \(\chi_{5780}(1069,\cdot)\) \(\chi_{5780}(1209,\cdot)\) \(\chi_{5780}(1249,\cdot)\) \(\chi_{5780}(1369,\cdot)\) \(\chi_{5780}(1409,\cdot)\) \(\chi_{5780}(1549,\cdot)\) \(\chi_{5780}(1589,\cdot)\) \(\chi_{5780}(1709,\cdot)\) \(\chi_{5780}(1749,\cdot)\) \(\chi_{5780}(1929,\cdot)\) \(\chi_{5780}(2049,\cdot)\) \(\chi_{5780}(2089,\cdot)\) \(\chi_{5780}(2229,\cdot)\) \(\chi_{5780}(2269,\cdot)\) \(\chi_{5780}(2389,\cdot)\) \(\chi_{5780}(2429,\cdot)\) \(\chi_{5780}(2569,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((2891,1157,581)\) → \((1,-1,e\left(\frac{1}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 5780 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{136}\right)\) | \(e\left(\frac{87}{136}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{23}{136}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{71}{136}\right)\) | \(e\left(\frac{125}{136}\right)\) |