Basic properties
| Modulus: | \(6069\) | |
| Conductor: | \(2023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2023}(97,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6069.ct
\(\chi_{6069}(97,\cdot)\) \(\chi_{6069}(139,\cdot)\) \(\chi_{6069}(160,\cdot)\) \(\chi_{6069}(181,\cdot)\) \(\chi_{6069}(244,\cdot)\) \(\chi_{6069}(265,\cdot)\) \(\chi_{6069}(286,\cdot)\) \(\chi_{6069}(328,\cdot)\) \(\chi_{6069}(454,\cdot)\) \(\chi_{6069}(496,\cdot)\) \(\chi_{6069}(517,\cdot)\) \(\chi_{6069}(601,\cdot)\) \(\chi_{6069}(622,\cdot)\) \(\chi_{6069}(685,\cdot)\) \(\chi_{6069}(811,\cdot)\) \(\chi_{6069}(853,\cdot)\) \(\chi_{6069}(874,\cdot)\) \(\chi_{6069}(895,\cdot)\) \(\chi_{6069}(958,\cdot)\) \(\chi_{6069}(979,\cdot)\) \(\chi_{6069}(1000,\cdot)\) \(\chi_{6069}(1042,\cdot)\) \(\chi_{6069}(1168,\cdot)\) \(\chi_{6069}(1210,\cdot)\) \(\chi_{6069}(1252,\cdot)\) \(\chi_{6069}(1315,\cdot)\) \(\chi_{6069}(1336,\cdot)\) \(\chi_{6069}(1357,\cdot)\) \(\chi_{6069}(1399,\cdot)\) \(\chi_{6069}(1525,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((2024,4336,3760)\) → \((1,-1,e\left(\frac{189}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(19\) | \(20\) |
| \( \chi_{ 6069 }(97, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{136}\right)\) | \(e\left(\frac{3}{68}\right)\) | \(e\left(\frac{169}{272}\right)\) | \(e\left(\frac{9}{136}\right)\) | \(e\left(\frac{175}{272}\right)\) | \(e\left(\frac{267}{272}\right)\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{31}{136}\right)\) | \(e\left(\frac{181}{272}\right)\) |