Basic properties
| Modulus: | \(8042\) | |
| Conductor: | \(4021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(134\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4021}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8042.n
\(\chi_{8042}(13,\cdot)\) \(\chi_{8042}(409,\cdot)\) \(\chi_{8042}(421,\cdot)\) \(\chi_{8042}(643,\cdot)\) \(\chi_{8042}(871,\cdot)\) \(\chi_{8042}(873,\cdot)\) \(\chi_{8042}(981,\cdot)\) \(\chi_{8042}(1361,\cdot)\) \(\chi_{8042}(1391,\cdot)\) \(\chi_{8042}(1455,\cdot)\) \(\chi_{8042}(1507,\cdot)\) \(\chi_{8042}(1601,\cdot)\) \(\chi_{8042}(1635,\cdot)\) \(\chi_{8042}(1861,\cdot)\) \(\chi_{8042}(2063,\cdot)\) \(\chi_{8042}(2131,\cdot)\) \(\chi_{8042}(2197,\cdot)\) \(\chi_{8042}(2399,\cdot)\) \(\chi_{8042}(2425,\cdot)\) \(\chi_{8042}(2443,\cdot)\) \(\chi_{8042}(2569,\cdot)\) \(\chi_{8042}(2679,\cdot)\) \(\chi_{8042}(2721,\cdot)\) \(\chi_{8042}(2725,\cdot)\) \(\chi_{8042}(2781,\cdot)\) \(\chi_{8042}(2841,\cdot)\) \(\chi_{8042}(2871,\cdot)\) \(\chi_{8042}(2887,\cdot)\) \(\chi_{8042}(3241,\cdot)\) \(\chi_{8042}(3277,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{67})$ |
| Fixed field: | Number field defined by a degree 134 polynomial (not computed) |
Values on generators
\(4023\) → \(e\left(\frac{103}{134}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8042 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{67}\right)\) | \(e\left(\frac{52}{67}\right)\) | \(-1\) | \(e\left(\frac{23}{67}\right)\) | \(e\left(\frac{61}{134}\right)\) | \(e\left(\frac{10}{67}\right)\) | \(e\left(\frac{30}{67}\right)\) | \(e\left(\frac{43}{67}\right)\) | \(e\left(\frac{125}{134}\right)\) | \(e\left(\frac{23}{134}\right)\) |