Basic properties
| Modulus: | \(8037\) | |
| Conductor: | \(423\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(138\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{423}(20,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8037.dk
\(\chi_{8037}(20,\cdot)\) \(\chi_{8037}(77,\cdot)\) \(\chi_{8037}(248,\cdot)\) \(\chi_{8037}(362,\cdot)\) \(\chi_{8037}(419,\cdot)\) \(\chi_{8037}(590,\cdot)\) \(\chi_{8037}(875,\cdot)\) \(\chi_{8037}(932,\cdot)\) \(\chi_{8037}(1103,\cdot)\) \(\chi_{8037}(1274,\cdot)\) \(\chi_{8037}(1445,\cdot)\) \(\chi_{8037}(1730,\cdot)\) \(\chi_{8037}(1958,\cdot)\) \(\chi_{8037}(2300,\cdot)\) \(\chi_{8037}(2642,\cdot)\) \(\chi_{8037}(2756,\cdot)\) \(\chi_{8037}(2813,\cdot)\) \(\chi_{8037}(2927,\cdot)\) \(\chi_{8037}(2984,\cdot)\) \(\chi_{8037}(3098,\cdot)\) \(\chi_{8037}(3269,\cdot)\) \(\chi_{8037}(3497,\cdot)\) \(\chi_{8037}(3611,\cdot)\) \(\chi_{8037}(3782,\cdot)\) \(\chi_{8037}(3953,\cdot)\) \(\chi_{8037}(4010,\cdot)\) \(\chi_{8037}(4124,\cdot)\) \(\chi_{8037}(4181,\cdot)\) \(\chi_{8037}(4523,\cdot)\) \(\chi_{8037}(4637,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{69})$ |
| Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\((4466,1693,7525)\) → \((e\left(\frac{1}{6}\right),1,e\left(\frac{37}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8037 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{138}\right)\) | \(e\left(\frac{20}{69}\right)\) | \(e\left(\frac{44}{69}\right)\) | \(e\left(\frac{28}{69}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{55}{69}\right)\) | \(e\left(\frac{25}{138}\right)\) | \(e\left(\frac{7}{138}\right)\) | \(e\left(\frac{40}{69}\right)\) |