Basic properties
| Modulus: | \(5070\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5070.bw
\(\chi_{5070}(61,\cdot)\) \(\chi_{5070}(211,\cdot)\) \(\chi_{5070}(451,\cdot)\) \(\chi_{5070}(601,\cdot)\) \(\chi_{5070}(841,\cdot)\) \(\chi_{5070}(1231,\cdot)\) \(\chi_{5070}(1381,\cdot)\) \(\chi_{5070}(1621,\cdot)\) \(\chi_{5070}(1771,\cdot)\) \(\chi_{5070}(2011,\cdot)\) \(\chi_{5070}(2161,\cdot)\) \(\chi_{5070}(2401,\cdot)\) \(\chi_{5070}(2551,\cdot)\) \(\chi_{5070}(2791,\cdot)\) \(\chi_{5070}(2941,\cdot)\) \(\chi_{5070}(3181,\cdot)\) \(\chi_{5070}(3331,\cdot)\) \(\chi_{5070}(3721,\cdot)\) \(\chi_{5070}(3961,\cdot)\) \(\chi_{5070}(4111,\cdot)\) \(\chi_{5070}(4351,\cdot)\) \(\chi_{5070}(4501,\cdot)\) \(\chi_{5070}(4741,\cdot)\) \(\chi_{5070}(4891,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((1691,4057,1861)\) → \((1,1,e\left(\frac{35}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 5070 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) |