Basic properties
| Modulus: | \(6069\) | |
| Conductor: | \(6069\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | 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 6069.ci
\(\chi_{6069}(83,\cdot)\) \(\chi_{6069}(104,\cdot)\) \(\chi_{6069}(230,\cdot)\) \(\chi_{6069}(314,\cdot)\) \(\chi_{6069}(440,\cdot)\) \(\chi_{6069}(461,\cdot)\) \(\chi_{6069}(587,\cdot)\) \(\chi_{6069}(671,\cdot)\) \(\chi_{6069}(797,\cdot)\) \(\chi_{6069}(818,\cdot)\) \(\chi_{6069}(944,\cdot)\) \(\chi_{6069}(1028,\cdot)\) \(\chi_{6069}(1154,\cdot)\) \(\chi_{6069}(1175,\cdot)\) \(\chi_{6069}(1301,\cdot)\) \(\chi_{6069}(1385,\cdot)\) \(\chi_{6069}(1511,\cdot)\) \(\chi_{6069}(1532,\cdot)\) \(\chi_{6069}(1658,\cdot)\) \(\chi_{6069}(1742,\cdot)\) \(\chi_{6069}(2015,\cdot)\) \(\chi_{6069}(2099,\cdot)\) \(\chi_{6069}(2225,\cdot)\) \(\chi_{6069}(2246,\cdot)\) \(\chi_{6069}(2372,\cdot)\) \(\chi_{6069}(2456,\cdot)\) \(\chi_{6069}(2582,\cdot)\) \(\chi_{6069}(2603,\cdot)\) \(\chi_{6069}(2729,\cdot)\) \(\chi_{6069}(2813,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((2024,4336,3760)\) → \((-1,-1,e\left(\frac{59}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(19\) | \(20\) |
| \( \chi_{ 6069 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{47}{136}\right)\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{37}{136}\right)\) | \(e\left(\frac{65}{136}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{27}{136}\right)\) |