Basic properties
| Modulus: | \(5070\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(161,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5070.cc
\(\chi_{5070}(161,\cdot)\) \(\chi_{5070}(281,\cdot)\) \(\chi_{5070}(551,\cdot)\) \(\chi_{5070}(671,\cdot)\) \(\chi_{5070}(941,\cdot)\) \(\chi_{5070}(1061,\cdot)\) \(\chi_{5070}(1331,\cdot)\) \(\chi_{5070}(1721,\cdot)\) \(\chi_{5070}(1841,\cdot)\) \(\chi_{5070}(2111,\cdot)\) \(\chi_{5070}(2231,\cdot)\) \(\chi_{5070}(2501,\cdot)\) \(\chi_{5070}(2621,\cdot)\) \(\chi_{5070}(2891,\cdot)\) \(\chi_{5070}(3011,\cdot)\) \(\chi_{5070}(3401,\cdot)\) \(\chi_{5070}(3671,\cdot)\) \(\chi_{5070}(3791,\cdot)\) \(\chi_{5070}(4061,\cdot)\) \(\chi_{5070}(4181,\cdot)\) \(\chi_{5070}(4451,\cdot)\) \(\chi_{5070}(4571,\cdot)\) \(\chi_{5070}(4841,\cdot)\) \(\chi_{5070}(4961,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1691,4057,1861)\) → \((-1,1,e\left(\frac{27}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 5070 }(161, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(-i\) | \(1\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{9}{26}\right)\) |