Basic properties
| Modulus: | \(2007\) | |
| Conductor: | \(223\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(74\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{223}(209,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2007.v
\(\chi_{2007}(91,\cdot)\) \(\chi_{2007}(118,\cdot)\) \(\chi_{2007}(163,\cdot)\) \(\chi_{2007}(190,\cdot)\) \(\chi_{2007}(208,\cdot)\) \(\chi_{2007}(334,\cdot)\) \(\chi_{2007}(397,\cdot)\) \(\chi_{2007}(442,\cdot)\) \(\chi_{2007}(505,\cdot)\) \(\chi_{2007}(541,\cdot)\) \(\chi_{2007}(550,\cdot)\) \(\chi_{2007}(613,\cdot)\) \(\chi_{2007}(667,\cdot)\) \(\chi_{2007}(721,\cdot)\) \(\chi_{2007}(919,\cdot)\) \(\chi_{2007}(946,\cdot)\) \(\chi_{2007}(1000,\cdot)\) \(\chi_{2007}(1081,\cdot)\) \(\chi_{2007}(1099,\cdot)\) \(\chi_{2007}(1108,\cdot)\) \(\chi_{2007}(1270,\cdot)\) \(\chi_{2007}(1297,\cdot)\) \(\chi_{2007}(1306,\cdot)\) \(\chi_{2007}(1324,\cdot)\) \(\chi_{2007}(1351,\cdot)\) \(\chi_{2007}(1441,\cdot)\) \(\chi_{2007}(1495,\cdot)\) \(\chi_{2007}(1531,\cdot)\) \(\chi_{2007}(1648,\cdot)\) \(\chi_{2007}(1702,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{37})$ |
| Fixed field: | Number field defined by a degree 74 polynomial |
Values on generators
\((893,226)\) → \((1,e\left(\frac{19}{74}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2007 }(1324, a) \) | \(-1\) | \(1\) | \(e\left(\frac{8}{37}\right)\) | \(e\left(\frac{16}{37}\right)\) | \(e\left(\frac{63}{74}\right)\) | \(e\left(\frac{34}{37}\right)\) | \(e\left(\frac{24}{37}\right)\) | \(e\left(\frac{5}{74}\right)\) | \(e\left(\frac{35}{74}\right)\) | \(e\left(\frac{55}{74}\right)\) | \(e\left(\frac{5}{37}\right)\) | \(e\left(\frac{32}{37}\right)\) |