Basic properties
| Modulus: | \(2075\) | |
| Conductor: | \(2075\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(820\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2075.w
\(\chi_{2075}(2,\cdot)\) \(\chi_{2075}(8,\cdot)\) \(\chi_{2075}(13,\cdot)\) \(\chi_{2075}(22,\cdot)\) \(\chi_{2075}(42,\cdot)\) \(\chi_{2075}(47,\cdot)\) \(\chi_{2075}(52,\cdot)\) \(\chi_{2075}(53,\cdot)\) \(\chi_{2075}(58,\cdot)\) \(\chi_{2075}(62,\cdot)\) \(\chi_{2075}(67,\cdot)\) \(\chi_{2075}(72,\cdot)\) \(\chi_{2075}(73,\cdot)\) \(\chi_{2075}(88,\cdot)\) \(\chi_{2075}(97,\cdot)\) \(\chi_{2075}(98,\cdot)\) \(\chi_{2075}(102,\cdot)\) \(\chi_{2075}(103,\cdot)\) \(\chi_{2075}(117,\cdot)\) \(\chi_{2075}(122,\cdot)\) \(\chi_{2075}(128,\cdot)\) \(\chi_{2075}(133,\cdot)\) \(\chi_{2075}(137,\cdot)\) \(\chi_{2075}(138,\cdot)\) \(\chi_{2075}(162,\cdot)\) \(\chi_{2075}(163,\cdot)\) \(\chi_{2075}(172,\cdot)\) \(\chi_{2075}(188,\cdot)\) \(\chi_{2075}(198,\cdot)\) \(\chi_{2075}(208,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{820})$ |
| Fixed field: | Number field defined by a degree 820 polynomial (not computed) |
Values on generators
\((1827,251)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{1}{82}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 2075 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{820}\right)\) | \(e\left(\frac{187}{820}\right)\) | \(e\left(\frac{51}{410}\right)\) | \(e\left(\frac{119}{410}\right)\) | \(e\left(\frac{57}{164}\right)\) | \(e\left(\frac{153}{820}\right)\) | \(e\left(\frac{187}{410}\right)\) | \(e\left(\frac{19}{205}\right)\) | \(e\left(\frac{289}{820}\right)\) | \(e\left(\frac{729}{820}\right)\) |