Basic properties
| Modulus: | \(5070\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5070.cw
\(\chi_{5070}(11,\cdot)\) \(\chi_{5070}(41,\cdot)\) \(\chi_{5070}(71,\cdot)\) \(\chi_{5070}(371,\cdot)\) \(\chi_{5070}(401,\cdot)\) \(\chi_{5070}(431,\cdot)\) \(\chi_{5070}(461,\cdot)\) \(\chi_{5070}(761,\cdot)\) \(\chi_{5070}(791,\cdot)\) \(\chi_{5070}(821,\cdot)\) \(\chi_{5070}(851,\cdot)\) \(\chi_{5070}(1151,\cdot)\) \(\chi_{5070}(1181,\cdot)\) \(\chi_{5070}(1211,\cdot)\) \(\chi_{5070}(1241,\cdot)\) \(\chi_{5070}(1541,\cdot)\) \(\chi_{5070}(1571,\cdot)\) \(\chi_{5070}(1631,\cdot)\) \(\chi_{5070}(1931,\cdot)\) \(\chi_{5070}(1961,\cdot)\) \(\chi_{5070}(1991,\cdot)\) \(\chi_{5070}(2021,\cdot)\) \(\chi_{5070}(2321,\cdot)\) \(\chi_{5070}(2351,\cdot)\) \(\chi_{5070}(2381,\cdot)\) \(\chi_{5070}(2411,\cdot)\) \(\chi_{5070}(2711,\cdot)\) \(\chi_{5070}(2741,\cdot)\) \(\chi_{5070}(2771,\cdot)\) \(\chi_{5070}(2801,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1691,4057,1861)\) → \((-1,1,e\left(\frac{103}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 5070 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{43}{78}\right)\) |