Basic properties
| Modulus: | \(5070\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{845}(307,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5070.by
\(\chi_{5070}(307,\cdot)\) \(\chi_{5070}(343,\cdot)\) \(\chi_{5070}(697,\cdot)\) \(\chi_{5070}(733,\cdot)\) \(\chi_{5070}(1087,\cdot)\) \(\chi_{5070}(1123,\cdot)\) \(\chi_{5070}(1477,\cdot)\) \(\chi_{5070}(1513,\cdot)\) \(\chi_{5070}(1867,\cdot)\) \(\chi_{5070}(1903,\cdot)\) \(\chi_{5070}(2257,\cdot)\) \(\chi_{5070}(2293,\cdot)\) \(\chi_{5070}(2647,\cdot)\) \(\chi_{5070}(2683,\cdot)\) \(\chi_{5070}(3037,\cdot)\) \(\chi_{5070}(3073,\cdot)\) \(\chi_{5070}(3427,\cdot)\) \(\chi_{5070}(3463,\cdot)\) \(\chi_{5070}(3853,\cdot)\) \(\chi_{5070}(4207,\cdot)\) \(\chi_{5070}(4243,\cdot)\) \(\chi_{5070}(4597,\cdot)\) \(\chi_{5070}(4987,\cdot)\) \(\chi_{5070}(5023,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1691,4057,1861)\) → \((1,i,e\left(\frac{33}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 5070 }(307, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(-i\) | \(i\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) |