Basic properties
| Modulus: | \(5070\) | |
| Conductor: | \(2535\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2535}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5070.cf
\(\chi_{5070}(53,\cdot)\) \(\chi_{5070}(287,\cdot)\) \(\chi_{5070}(443,\cdot)\) \(\chi_{5070}(833,\cdot)\) \(\chi_{5070}(1067,\cdot)\) \(\chi_{5070}(1223,\cdot)\) \(\chi_{5070}(1457,\cdot)\) \(\chi_{5070}(1613,\cdot)\) \(\chi_{5070}(1847,\cdot)\) \(\chi_{5070}(2003,\cdot)\) \(\chi_{5070}(2237,\cdot)\) \(\chi_{5070}(2393,\cdot)\) \(\chi_{5070}(2627,\cdot)\) \(\chi_{5070}(2783,\cdot)\) \(\chi_{5070}(3017,\cdot)\) \(\chi_{5070}(3173,\cdot)\) \(\chi_{5070}(3407,\cdot)\) \(\chi_{5070}(3563,\cdot)\) \(\chi_{5070}(3797,\cdot)\) \(\chi_{5070}(3953,\cdot)\) \(\chi_{5070}(4187,\cdot)\) \(\chi_{5070}(4343,\cdot)\) \(\chi_{5070}(4577,\cdot)\) \(\chi_{5070}(4967,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1691,4057,1861)\) → \((-1,-i,e\left(\frac{10}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 5070 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(-1\) | \(-i\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{5}{52}\right)\) |