Basic properties
| Modulus: | \(8041\) | |
| Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | 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 8041.dv
\(\chi_{8041}(118,\cdot)\) \(\chi_{8041}(237,\cdot)\) \(\chi_{8041}(475,\cdot)\) \(\chi_{8041}(849,\cdot)\) \(\chi_{8041}(985,\cdot)\) \(\chi_{8041}(1206,\cdot)\) \(\chi_{8041}(1427,\cdot)\) \(\chi_{8041}(1580,\cdot)\) \(\chi_{8041}(2158,\cdot)\) \(\chi_{8041}(2668,\cdot)\) \(\chi_{8041}(2736,\cdot)\) \(\chi_{8041}(2889,\cdot)\) \(\chi_{8041}(3042,\cdot)\) \(\chi_{8041}(3467,\cdot)\) \(\chi_{8041}(4198,\cdot)\) \(\chi_{8041}(4351,\cdot)\) \(\chi_{8041}(5354,\cdot)\) \(\chi_{8041}(5660,\cdot)\) \(\chi_{8041}(6085,\cdot)\) \(\chi_{8041}(6102,\cdot)\) \(\chi_{8041}(6816,\cdot)\) \(\chi_{8041}(6833,\cdot)\) \(\chi_{8041}(7564,\cdot)\) \(\chi_{8041}(7785,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{3}{10}\right),-1,e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 8041 }(5354, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) |